L(s) = 1 | + (−1.15 − 0.819i)2-s + (2.04 + 2.04i)3-s + (0.655 + 1.88i)4-s + (0.814 − 0.814i)5-s + (−0.680 − 4.03i)6-s − 2.42i·7-s + (0.794 − 2.71i)8-s + 5.38i·9-s + (−1.60 + 0.270i)10-s + (−0.707 + 0.707i)11-s + (−2.52 + 5.21i)12-s + (4.19 + 4.19i)13-s + (−1.98 + 2.79i)14-s + 3.33·15-s + (−3.14 + 2.47i)16-s − 3.70·17-s + ⋯ |
L(s) = 1 | + (−0.814 − 0.579i)2-s + (1.18 + 1.18i)3-s + (0.327 + 0.944i)4-s + (0.364 − 0.364i)5-s + (−0.277 − 1.64i)6-s − 0.916i·7-s + (0.280 − 0.959i)8-s + 1.79i·9-s + (−0.508 + 0.0856i)10-s + (−0.213 + 0.213i)11-s + (−0.729 + 1.50i)12-s + (1.16 + 1.16i)13-s + (−0.531 + 0.746i)14-s + 0.861·15-s + (−0.785 + 0.619i)16-s − 0.897·17-s + ⋯ |
Λ(s)=(=(176s/2ΓC(s)L(s)(0.962−0.271i)Λ(2−s)
Λ(s)=(=(176s/2ΓC(s+1/2)L(s)(0.962−0.271i)Λ(1−s)
Degree: |
2 |
Conductor: |
176
= 24⋅11
|
Sign: |
0.962−0.271i
|
Analytic conductor: |
1.40536 |
Root analytic conductor: |
1.18548 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ176(45,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 176, ( :1/2), 0.962−0.271i)
|
Particular Values
L(1) |
≈ |
1.17683+0.162845i |
L(21) |
≈ |
1.17683+0.162845i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.15+0.819i)T |
| 11 | 1+(0.707−0.707i)T |
good | 3 | 1+(−2.04−2.04i)T+3iT2 |
| 5 | 1+(−0.814+0.814i)T−5iT2 |
| 7 | 1+2.42iT−7T2 |
| 13 | 1+(−4.19−4.19i)T+13iT2 |
| 17 | 1+3.70T+17T2 |
| 19 | 1+(1.91+1.91i)T+19iT2 |
| 23 | 1+5.56iT−23T2 |
| 29 | 1+(2.07+2.07i)T+29iT2 |
| 31 | 1+5.32T+31T2 |
| 37 | 1+(−5.40+5.40i)T−37iT2 |
| 41 | 1+7.68iT−41T2 |
| 43 | 1+(4.92−4.92i)T−43iT2 |
| 47 | 1+7.29T+47T2 |
| 53 | 1+(1.72−1.72i)T−53iT2 |
| 59 | 1+(−8.02+8.02i)T−59iT2 |
| 61 | 1+(5.82+5.82i)T+61iT2 |
| 67 | 1+(5.59+5.59i)T+67iT2 |
| 71 | 1−1.42iT−71T2 |
| 73 | 1−16.1iT−73T2 |
| 79 | 1−5.56T+79T2 |
| 83 | 1+(1.72+1.72i)T+83iT2 |
| 89 | 1−13.5iT−89T2 |
| 97 | 1−14.4T+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
−12.97676075593630706017791200359, −11.16758543284843849600116880914, −10.65908911281381507404730393493, −9.514474377678400264101407590301, −9.021154439873771601780343785782, −8.148621503513454181717597114788, −6.80877787047934647394704447707, −4.45757414720440223529544503803, −3.70808041666335096041899082437, −2.10101360936661096144344541944,
1.72697433902593104414351060292, 2.97702609820403254570224821552, 5.74475702848951376418747157395, 6.54903079200240760987344201677, 7.76733561480333427416789921137, 8.456894456264853182987840103426, 9.170230490297137136463662494439, 10.43809476510334605405314854329, 11.64415358972326828448762195537, 13.08191051128765430948272357601