L(s) = 1 | + (0.809 − 0.587i)2-s + (0.309 − 0.951i)4-s + (−0.309 − 0.951i)8-s + (−0.809 − 0.587i)9-s + (0.809 − 0.587i)11-s + (−0.809 − 0.587i)16-s − 18-s + (0.309 − 0.951i)22-s − 1.90i·23-s + (−0.309 + 0.951i)25-s + (0.5 + 1.53i)29-s − 32-s + (−0.809 + 0.587i)36-s + (−0.190 − 0.587i)37-s − 1.17i·43-s + (−0.309 − 0.951i)44-s + ⋯ |
L(s) = 1 | + (0.809 − 0.587i)2-s + (0.309 − 0.951i)4-s + (−0.309 − 0.951i)8-s + (−0.809 − 0.587i)9-s + (0.809 − 0.587i)11-s + (−0.809 − 0.587i)16-s − 18-s + (0.309 − 0.951i)22-s − 1.90i·23-s + (−0.309 + 0.951i)25-s + (0.5 + 1.53i)29-s − 32-s + (−0.809 + 0.587i)36-s + (−0.190 − 0.587i)37-s − 1.17i·43-s + (−0.309 − 0.951i)44-s + ⋯ |
Λ(s)=(=(2156s/2ΓC(s)L(s)(−0.286+0.958i)Λ(1−s)
Λ(s)=(=(2156s/2ΓC(s)L(s)(−0.286+0.958i)Λ(1−s)
Degree: |
2 |
Conductor: |
2156
= 22⋅72⋅11
|
Sign: |
−0.286+0.958i
|
Analytic conductor: |
1.07598 |
Root analytic conductor: |
1.03729 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2156(1863,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2156, ( :0), −0.286+0.958i)
|
Particular Values
L(21) |
≈ |
1.731714765 |
L(21) |
≈ |
1.731714765 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.809+0.587i)T |
| 7 | 1 |
| 11 | 1+(−0.809+0.587i)T |
good | 3 | 1+(0.809+0.587i)T2 |
| 5 | 1+(0.309−0.951i)T2 |
| 13 | 1+(0.309+0.951i)T2 |
| 17 | 1+(0.309−0.951i)T2 |
| 19 | 1+(0.809+0.587i)T2 |
| 23 | 1+1.90iT−T2 |
| 29 | 1+(−0.5−1.53i)T+(−0.809+0.587i)T2 |
| 31 | 1+(−0.309−0.951i)T2 |
| 37 | 1+(0.190+0.587i)T+(−0.809+0.587i)T2 |
| 41 | 1+(−0.809−0.587i)T2 |
| 43 | 1+1.17iT−T2 |
| 47 | 1+(0.809+0.587i)T2 |
| 53 | 1+(−1.30−0.951i)T+(0.309+0.951i)T2 |
| 59 | 1+(0.809−0.587i)T2 |
| 61 | 1+(0.309−0.951i)T2 |
| 67 | 1+1.17iT−T2 |
| 71 | 1+(−0.690−0.951i)T+(−0.309+0.951i)T2 |
| 73 | 1+(−0.809+0.587i)T2 |
| 79 | 1+(0.690−0.951i)T+(−0.309−0.951i)T2 |
| 83 | 1+(−0.309+0.951i)T2 |
| 89 | 1+T2 |
| 97 | 1+(0.309+0.951i)T2 |
show more | |
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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
−8.912864791482909603938348477830, −8.675237519144662839495920612250, −7.18127077204117080544613769631, −6.49033458759685869512369331743, −5.80168470568820513954718102093, −5.00792384787480750087675018877, −3.95570889537423960554649426246, −3.30080513058424071049616693781, −2.34378197902843575970533307881, −0.963113067085820361643528446419,
1.93613290028870277772552978196, 2.94963164383529625575826051288, 3.94747622880843381280010349217, 4.70402838962780319898764472890, 5.60841165878992448041848328950, 6.22730742995106082540599559250, 7.09280914247039021216855352188, 7.87671405816392816643041156320, 8.443798418431548599369426063837, 9.395294917626435868040980214970