L(s) = 1 | + (−1.22 − 0.707i)3-s + (0.5 − 0.866i)4-s + (−0.258 + 0.965i)5-s + (0.499 + 0.866i)9-s + (−0.5 + 0.866i)11-s + (−1.22 + 0.707i)12-s + (1 − 0.999i)15-s + (−0.499 − 0.866i)16-s + (0.707 + 0.707i)20-s + (1.73 − i)23-s + (−0.866 − 0.499i)25-s + (0.707 − 1.22i)31-s + (1.22 − 0.707i)33-s + 0.999·36-s + (0.499 + 0.866i)44-s + (−0.965 + 0.258i)45-s + ⋯ |
L(s) = 1 | + (−1.22 − 0.707i)3-s + (0.5 − 0.866i)4-s + (−0.258 + 0.965i)5-s + (0.499 + 0.866i)9-s + (−0.5 + 0.866i)11-s + (−1.22 + 0.707i)12-s + (1 − 0.999i)15-s + (−0.499 − 0.866i)16-s + (0.707 + 0.707i)20-s + (1.73 − i)23-s + (−0.866 − 0.499i)25-s + (0.707 − 1.22i)31-s + (1.22 − 0.707i)33-s + 0.999·36-s + (0.499 + 0.866i)44-s + (−0.965 + 0.258i)45-s + ⋯ |
Λ(s)=(=(2695s/2ΓC(s)L(s)(0.328+0.944i)Λ(1−s)
Λ(s)=(=(2695s/2ΓC(s)L(s)(0.328+0.944i)Λ(1−s)
Degree: |
2 |
Conductor: |
2695
= 5⋅72⋅11
|
Sign: |
0.328+0.944i
|
Analytic conductor: |
1.34498 |
Root analytic conductor: |
1.15973 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2695(2419,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2695, ( :0), 0.328+0.944i)
|
Particular Values
L(21) |
≈ |
0.7829996784 |
L(21) |
≈ |
0.7829996784 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(0.258−0.965i)T |
| 7 | 1 |
| 11 | 1+(0.5−0.866i)T |
good | 2 | 1+(−0.5+0.866i)T2 |
| 3 | 1+(1.22+0.707i)T+(0.5+0.866i)T2 |
| 13 | 1+T2 |
| 17 | 1+(−0.5−0.866i)T2 |
| 19 | 1+(0.5−0.866i)T2 |
| 23 | 1+(−1.73+i)T+(0.5−0.866i)T2 |
| 29 | 1−T2 |
| 31 | 1+(−0.707+1.22i)T+(−0.5−0.866i)T2 |
| 37 | 1+(0.5−0.866i)T2 |
| 41 | 1−T2 |
| 43 | 1+T2 |
| 47 | 1+(−1.22+0.707i)T+(0.5−0.866i)T2 |
| 53 | 1+(−1.73−i)T+(0.5+0.866i)T2 |
| 59 | 1+(−0.707+1.22i)T+(−0.5−0.866i)T2 |
| 61 | 1+(0.5−0.866i)T2 |
| 67 | 1+(1.73+i)T+(0.5+0.866i)T2 |
| 71 | 1+T2 |
| 73 | 1+(−0.5−0.866i)T2 |
| 79 | 1+(0.5−0.866i)T2 |
| 83 | 1+T2 |
| 89 | 1+(0.707+1.22i)T+(−0.5+0.866i)T2 |
| 97 | 1−1.41iT−T2 |
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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
−8.952565841678309393584710467693, −7.64076060784873612259706004692, −7.12782232833497550880412687891, −6.61084890592465899042443091408, −5.95070040028989505877822276498, −5.22411615682836248400278104398, −4.38262605739193287721777198036, −2.84830007165578642747408836879, −2.05244296524252265900292960449, −0.71885221688529286051645531665,
1.07305421619055593239645515158, 2.77749679417656683171763146478, 3.72067288005102341631711277355, 4.54788257366943927555891010175, 5.31577927695807387920028645600, 5.85081032061875640082497510171, 6.90661779813281065210807759010, 7.60848900579968908989184195382, 8.592510303444214183176486170027, 8.947484832249715924605580129400