L(s) = 1 | + (−0.309 + 0.951i)2-s + (−0.809 − 0.587i)4-s + (0.809 − 0.587i)8-s + (−0.809 − 0.587i)9-s + (−0.809 + 0.587i)11-s + (0.309 + 0.951i)16-s + (0.809 − 0.587i)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 + (0.309 + 0.951i)36-s + (−0.190 − 0.587i)37-s + 1.17i·43-s + 0.999·44-s + ⋯ |
L(s) = 1 | + (−0.309 + 0.951i)2-s + (−0.809 − 0.587i)4-s + (0.809 − 0.587i)8-s + (−0.809 − 0.587i)9-s + (−0.809 + 0.587i)11-s + (0.309 + 0.951i)16-s + (0.809 − 0.587i)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 + (0.309 + 0.951i)36-s + (−0.190 − 0.587i)37-s + 1.17i·43-s + 0.999·44-s + ⋯ |
Λ(s)=(=(2156s/2ΓC(s)L(s)(−0.822−0.568i)Λ(1−s)
Λ(s)=(=(2156s/2ΓC(s)L(s)(−0.822−0.568i)Λ(1−s)
Degree: |
2 |
Conductor: |
2156
= 22⋅72⋅11
|
Sign: |
−0.822−0.568i
|
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), −0.822−0.568i)
|
Particular Values
L(21) |
≈ |
0.5978304981 |
L(21) |
≈ |
0.5978304981 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.309−0.951i)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
−9.277803151725284698560150750564, −8.889559194824773682558100429175, −7.84202131972720242155577538013, −7.37984184573931236026362532338, −6.52730173290851273359128547822, −5.55000621923335633472208920160, −5.20392382048623533902776014333, −3.99432370900219462247714018816, −3.00846288659231015062940276482, −1.44882292241068811408419734826,
0.47548975821345062308886031626, 2.29961280087197328923065562649, 2.71655429696924485186212542077, 3.92023985262677330884460178430, 4.80219421442290289189964615938, 5.60628586288114440575739415966, 6.59790669053554305356205092444, 7.86346958204365734180921590450, 8.317397984434804676167563591192, 8.826687232056809798004631289991