L(s) = 1 | + (1.35 + 0.392i)2-s + (0.727 − 0.420i)3-s + (1.69 + 1.06i)4-s + (0.249 + 0.432i)5-s + (1.15 − 0.285i)6-s + (0.235 + 0.407i)7-s + (1.88 + 2.11i)8-s + (−1.14 + 1.98i)9-s + (0.169 + 0.685i)10-s − 1.14i·11-s + (1.67 + 0.0646i)12-s + (−3.10 − 5.37i)13-s + (0.159 + 0.646i)14-s + (0.363 + 0.209i)15-s + (1.72 + 3.60i)16-s + (−0.363 − 0.209i)17-s + ⋯ |
L(s) = 1 | + (0.960 + 0.277i)2-s + (0.420 − 0.242i)3-s + (0.846 + 0.532i)4-s + (0.111 + 0.193i)5-s + (0.470 − 0.116i)6-s + (0.0889 + 0.154i)7-s + (0.665 + 0.746i)8-s + (−0.382 + 0.662i)9-s + (0.0536 + 0.216i)10-s − 0.346i·11-s + (0.484 + 0.0186i)12-s + (−0.861 − 1.49i)13-s + (0.0427 + 0.172i)14-s + (0.0937 + 0.0541i)15-s + (0.431 + 0.901i)16-s + (−0.0881 − 0.0508i)17-s + ⋯ |
Λ(s)=(=(296s/2ΓC(s)L(s)(0.896−0.443i)Λ(2−s)
Λ(s)=(=(296s/2ΓC(s+1/2)L(s)(0.896−0.443i)Λ(1−s)
Degree: |
2 |
Conductor: |
296
= 23⋅37
|
Sign: |
0.896−0.443i
|
Analytic conductor: |
2.36357 |
Root analytic conductor: |
1.53739 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ296(101,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 296, ( :1/2), 0.896−0.443i)
|
Particular Values
L(1) |
≈ |
2.41658+0.565431i |
L(21) |
≈ |
2.41658+0.565431i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−1.35−0.392i)T |
| 37 | 1+(5.34+2.90i)T |
good | 3 | 1+(−0.727+0.420i)T+(1.5−2.59i)T2 |
| 5 | 1+(−0.249−0.432i)T+(−2.5+4.33i)T2 |
| 7 | 1+(−0.235−0.407i)T+(−3.5+6.06i)T2 |
| 11 | 1+1.14iT−11T2 |
| 13 | 1+(3.10+5.37i)T+(−6.5+11.2i)T2 |
| 17 | 1+(0.363+0.209i)T+(8.5+14.7i)T2 |
| 19 | 1+(−1.39−2.41i)T+(−9.5+16.4i)T2 |
| 23 | 1+7.74iT−23T2 |
| 29 | 1+5.48T+29T2 |
| 31 | 1−7.40iT−31T2 |
| 41 | 1+(−1.51−2.61i)T+(−20.5+35.5i)T2 |
| 43 | 1+1.44T+43T2 |
| 47 | 1+0.412T+47T2 |
| 53 | 1+(6.89+3.98i)T+(26.5+45.8i)T2 |
| 59 | 1+(5.73−9.92i)T+(−29.5−51.0i)T2 |
| 61 | 1+(−2.66−4.62i)T+(−30.5+52.8i)T2 |
| 67 | 1+(−8.66+5.00i)T+(33.5−58.0i)T2 |
| 71 | 1+(−2.85−4.94i)T+(−35.5+61.4i)T2 |
| 73 | 1+5.09T+73T2 |
| 79 | 1+(−5.88+3.39i)T+(39.5−68.4i)T2 |
| 83 | 1+(−11.4−6.63i)T+(41.5+71.8i)T2 |
| 89 | 1+(10.0+5.80i)T+(44.5+77.0i)T2 |
| 97 | 1−8.36iT−97T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−12.21160550329829020031426634136, −10.91376901980250347641784266266, −10.30378912350638515725274951409, −8.577560006971596775091384494378, −7.904473999726819165837067143891, −6.91723355100902994522574777407, −5.68423050371746997785378485793, −4.88296392686743763682305005574, −3.26306550065223765541691652716, −2.35262631940459937586014086656,
1.91771258799043687497159019276, 3.35598851081208381578713843260, 4.39163985640075956692283161225, 5.46101142415887051611928176693, 6.70543104862531724108505236390, 7.57819909843212481738035429198, 9.338990995007024812066100002098, 9.571343892316556800516952036506, 11.13536081922160915747505451917, 11.71210116822765485703427522306