L(s) = 1 | + 1.84i·2-s + 2.98i·3-s − 1.39·4-s + (−2.09 − 0.784i)5-s − 5.49·6-s − 5.05i·7-s + 1.11i·8-s − 5.90·9-s + (1.44 − 3.85i)10-s − 3.23·11-s − 4.15i·12-s − 2.63i·13-s + 9.31·14-s + (2.34 − 6.25i)15-s − 4.84·16-s − 0.962i·17-s + ⋯ |
L(s) = 1 | + 1.30i·2-s + 1.72i·3-s − 0.696·4-s + (−0.936 − 0.350i)5-s − 2.24·6-s − 1.91i·7-s + 0.395i·8-s − 1.96·9-s + (0.456 − 1.21i)10-s − 0.974·11-s − 1.19i·12-s − 0.731i·13-s + 2.48·14-s + (0.604 − 1.61i)15-s − 1.21·16-s − 0.233i·17-s + ⋯ |
Λ(s)=(=(755s/2ΓC(s)L(s)(0.936+0.350i)Λ(2−s)
Λ(s)=(=(755s/2ΓC(s+1/2)L(s)(0.936+0.350i)Λ(1−s)
Degree: |
2 |
Conductor: |
755
= 5⋅151
|
Sign: |
0.936+0.350i
|
Analytic conductor: |
6.02870 |
Root analytic conductor: |
2.45534 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ755(454,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 755, ( :1/2), 0.936+0.350i)
|
Particular Values
L(1) |
≈ |
0.162792−0.0294775i |
L(21) |
≈ |
0.162792−0.0294775i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(2.09+0.784i)T |
| 151 | 1+T |
good | 2 | 1−1.84iT−2T2 |
| 3 | 1−2.98iT−3T2 |
| 7 | 1+5.05iT−7T2 |
| 11 | 1+3.23T+11T2 |
| 13 | 1+2.63iT−13T2 |
| 17 | 1+0.962iT−17T2 |
| 19 | 1−2.66T+19T2 |
| 23 | 1−5.80iT−23T2 |
| 29 | 1+2.13T+29T2 |
| 31 | 1+6.68T+31T2 |
| 37 | 1+7.66iT−37T2 |
| 41 | 1+9.30T+41T2 |
| 43 | 1+5.98iT−43T2 |
| 47 | 1+7.77iT−47T2 |
| 53 | 1−4.36iT−53T2 |
| 59 | 1+11.8T+59T2 |
| 61 | 1−6.78T+61T2 |
| 67 | 1−2.79iT−67T2 |
| 71 | 1−14.5T+71T2 |
| 73 | 1−11.7iT−73T2 |
| 79 | 1+4.34T+79T2 |
| 83 | 1+8.54iT−83T2 |
| 89 | 1+12.4T+89T2 |
| 97 | 1−6.10iT−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
−10.30333875360952798781709472817, −9.387615557818995146439873288163, −8.389562760699132963562659164642, −7.58670052591356537836982618873, −7.15820736795649262249584893208, −5.43910795319931736123141901347, −5.07220722375609586393717253738, −4.00345946960510397694997152680, −3.40940501466438605523173346494, −0.080161995680484824332040155426,
1.69944019164978905890006308332, 2.54280845588989417291192684690, 3.19229303221721661790313441936, 4.93967457959929073612613138867, 6.18306263988617094061904019054, 6.91057718280963438513554612564, 7.976709364191828230065297476507, 8.568841900875826006637661958777, 9.537959346595162183099081700923, 10.88502648720345787207292537336