The archetypes in the book are riddled with errors (though possibly fixed in the PDF if you have the latest version). It is discussed in this thread (
http://forums.shadowruntabletop.com/index.php?topic=11847.msg238750#msg238750) where they also offer legal versions of them.
As for the Paranormal Detective specifically (from that thread courtesy ZeConster):
Archetype: Occult Investigator
Metatype: E (Human (1))
Attributes: A (24+8 = 32 total attribute points)
Magic/Resonance: B (Magician with 4 Magic, 2x R4 Magical skills, 7 spells (alchemical preparations, in this case))
Skills: C (28/2)
Resources: D (50k)
Karma expenditure: 21-21 = 0 on Qualities, 15-15 = 0 on Contacts, 10 on Gear, 20 on Foci binding, 5 on +1 alchemical preparation
Nuyen expenditure: 73,000¥
[spoiler] 10,000 Chrysler-Nissan Jackrabbit [Handling 4/3, Speed 3, Accel 2, Body 8, Armor 4, Pilot 1, Sensor 2, Passengers 2]
20,000 Alchemy focus (Force 4) (also costs 12 Karma)
16,000 Counterspelling focus (Force 4, combat spells) (also costs 8 Karma)
800 fake license (Rating 4, private detective)
10,000 fake SIN (Rating 4)
900 lined coat [9]
2,500 magical lodge materials (Force 5)
10,000 Middle Lifestyle (2 months)
700 Sony Emperor commlink [Device Rating 2]
100 Staff [Club, Reach 2, Acc 6, DV 6P, AP —]
750 Stun baton [Club, Reach 1, Acc 4, DV 9S(e), AP –5, 10 charges]
Starting ¥ 1,250 + (4D6 x 100)¥[/spoiler]
Transgressions:1,750¥ nuyen over the limit (3k including starting nuyen)
10 Karma over the limit
'Simple' fixes:Drop 2 of the following: Bilingual, Mentor Spirit (Snake), Chrysler-Nissan Jackrabbit, 1 Alchemical Preparation
Drop 1 month of Middle Lifestyle, adjust starting nuyen to 3,250 + (4D6 x 100)¥
