L(s) = 1 | + (1.17 − 0.792i)2-s + 1.26i·3-s + (0.743 − 1.85i)4-s + 3.51i·5-s + (1 + 1.47i)6-s − 2.23i·7-s + (−0.601 − 2.76i)8-s + 1.40·9-s + (2.78 + 4.12i)10-s + 2.89·11-s + (2.34 + 0.937i)12-s − 6.30·13-s + (−1.77 − 2.61i)14-s − 4.43·15-s + (−2.89 − 2.76i)16-s − 4.79·17-s + ⋯ |
L(s) = 1 | + (0.828 − 0.560i)2-s + 0.728i·3-s + (0.371 − 0.928i)4-s + 1.57i·5-s + (0.408 + 0.603i)6-s − 0.845i·7-s + (−0.212 − 0.977i)8-s + 0.469·9-s + (0.882 + 1.30i)10-s + 0.872·11-s + (0.676 + 0.270i)12-s − 1.74·13-s + (−0.473 − 0.699i)14-s − 1.14·15-s + (−0.723 − 0.690i)16-s − 1.16·17-s + ⋯ |
Λ(s)=(=(152s/2ΓC(s)L(s)(0.999−0.00742i)Λ(2−s)
Λ(s)=(=(152s/2ΓC(s+1/2)L(s)(0.999−0.00742i)Λ(1−s)
Degree: |
2 |
Conductor: |
152
= 23⋅19
|
Sign: |
0.999−0.00742i
|
Analytic conductor: |
1.21372 |
Root analytic conductor: |
1.10169 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ152(75,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 152, ( :1/2), 0.999−0.00742i)
|
Particular Values
L(1) |
≈ |
1.69259+0.00628203i |
L(21) |
≈ |
1.69259+0.00628203i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−1.17+0.792i)T |
| 19 | 1+(−0.895+4.26i)T |
good | 3 | 1−1.26iT−3T2 |
| 5 | 1−3.51iT−5T2 |
| 7 | 1+2.23iT−7T2 |
| 11 | 1−2.89T+11T2 |
| 13 | 1+6.30T+13T2 |
| 17 | 1+4.79T+17T2 |
| 23 | 1+0.524iT−23T2 |
| 29 | 1−0.415T+29T2 |
| 31 | 1−1.20T+31T2 |
| 37 | 1−5.88T+37T2 |
| 41 | 1−4.87iT−41T2 |
| 43 | 1+10.6T+43T2 |
| 47 | 1+4.27iT−47T2 |
| 53 | 1−6.05T+53T2 |
| 59 | 1+8.08iT−59T2 |
| 61 | 1−8.38iT−61T2 |
| 67 | 1−9.79iT−67T2 |
| 71 | 1−10.2T+71T2 |
| 73 | 1−7.76T+73T2 |
| 79 | 1+7.33T+79T2 |
| 83 | 1−2T+83T2 |
| 89 | 1−12.1iT−89T2 |
| 97 | 1+2.19iT−97T2 |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−13.14462850675538789688551154582, −11.74203368274968186935728059604, −10.99083382043444719162600933526, −10.15549384259909853588677396030, −9.560610797848217401175824163095, −7.09840289472504744007593242374, −6.72230089693255330090973792315, −4.80788758680666564587646636720, −3.87456427252729340573779285553, −2.56031094997546536249620810375,
2.05344631968229969942982782198, 4.30693357454120374388475122856, 5.22026986713213091880322157099, 6.45764449576966844874723350908, 7.61587160948123993200056348692, 8.616764249550777714323104156174, 9.582095765145775153227139495626, 11.79783632444781162566417866936, 12.27453423792831390391718966579, 12.83776245530726145310363963597