L(s) = 1 | + (0.707 + 0.707i)2-s + 1.00i·4-s − 1.41i·5-s + 2i·7-s + (−0.707 + 0.707i)8-s + (1.00 − 1.00i)10-s + (−1.41 + 1.41i)14-s − 1.00·16-s + 1.41i·17-s + 1.41·20-s + 1.41·23-s − 1.00·25-s − 2.00·28-s − 1.41i·29-s + (−0.707 − 0.707i)32-s + ⋯ |
L(s) = 1 | + (0.707 + 0.707i)2-s + 1.00i·4-s − 1.41i·5-s + 2i·7-s + (−0.707 + 0.707i)8-s + (1.00 − 1.00i)10-s + (−1.41 + 1.41i)14-s − 1.00·16-s + 1.41i·17-s + 1.41·20-s + 1.41·23-s − 1.00·25-s − 2.00·28-s − 1.41i·29-s + (−0.707 − 0.707i)32-s + ⋯ |
Λ(s)=(=(1332s/2ΓC(s)L(s)−iΛ(1−s)
Λ(s)=(=(1332s/2ΓC(s)L(s)−iΛ(1−s)
Degree: |
2 |
Conductor: |
1332
= 22⋅32⋅37
|
Sign: |
−i
|
Analytic conductor: |
0.664754 |
Root analytic conductor: |
0.815324 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1332(739,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1332, ( :0), −i)
|
Particular Values
L(21) |
≈ |
1.497182289 |
L(21) |
≈ |
1.497182289 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.707−0.707i)T |
| 3 | 1 |
| 37 | 1−T |
good | 5 | 1+1.41iT−T2 |
| 7 | 1−2iT−T2 |
| 11 | 1−T2 |
| 13 | 1−T2 |
| 17 | 1−1.41iT−T2 |
| 19 | 1+T2 |
| 23 | 1−1.41T+T2 |
| 29 | 1+1.41iT−T2 |
| 31 | 1+T2 |
| 41 | 1+T2 |
| 43 | 1+T2 |
| 47 | 1−T2 |
| 53 | 1+T2 |
| 59 | 1+1.41T+T2 |
| 61 | 1−T2 |
| 67 | 1+2iT−T2 |
| 71 | 1−T2 |
| 73 | 1+T2 |
| 79 | 1+T2 |
| 83 | 1−T2 |
| 89 | 1+1.41iT−T2 |
| 97 | 1−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
−9.536514021284968627549872751522, −8.960838945991013022801378775495, −8.414778554632027298497333622971, −7.80162547623979677858169270845, −6.31494445234611737460733423633, −5.83519610973586499523029156412, −5.06465265240301241344898402296, −4.39234271263682380976384369493, −3.07719660515469963840583617553, −1.93885816684015931478909345699,
1.11343943498100243464676815912, 2.77612591838872342442985791975, 3.36725699574225717923528342956, 4.30956838860535088509575402938, 5.16834423345759994140862797861, 6.54000686327996443523670903605, 7.00585498757766112714450620749, 7.56839259189705911656198883057, 9.188191971362504663544386408686, 9.989054943683312493424151725686