L(s) = 1 | + (−0.258 + 0.965i)2-s + (−0.866 − 0.499i)4-s + (−0.448 − 1.67i)5-s + (0.633 − 1.09i)7-s + (0.707 − 0.707i)8-s + 1.73·10-s − 2.44·11-s + (0.366 − 0.0980i)13-s + (0.896 + 0.896i)14-s + (0.500 + 0.866i)16-s + (−6.24 − 1.67i)17-s + (−5.09 + 1.36i)19-s + (−0.448 + 1.67i)20-s + (0.633 − 2.36i)22-s + (−2.44 + 2.44i)23-s + ⋯ |
L(s) = 1 | + (−0.183 + 0.683i)2-s + (−0.433 − 0.249i)4-s + (−0.200 − 0.748i)5-s + (0.239 − 0.415i)7-s + (0.249 − 0.249i)8-s + 0.547·10-s − 0.738·11-s + (0.101 − 0.0272i)13-s + (0.239 + 0.239i)14-s + (0.125 + 0.216i)16-s + (−1.51 − 0.405i)17-s + (−1.16 + 0.313i)19-s + (−0.100 + 0.374i)20-s + (0.135 − 0.504i)22-s + (−0.510 + 0.510i)23-s + ⋯ |
Λ(s)=(=(666s/2ΓC(s)L(s)(−0.316+0.948i)Λ(2−s)
Λ(s)=(=(666s/2ΓC(s+1/2)L(s)(−0.316+0.948i)Λ(1−s)
Degree: |
2 |
Conductor: |
666
= 2⋅32⋅37
|
Sign: |
−0.316+0.948i
|
Analytic conductor: |
5.31803 |
Root analytic conductor: |
2.30608 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ666(341,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 666, ( :1/2), −0.316+0.948i)
|
Particular Values
L(1) |
≈ |
0.318253−0.441462i |
L(21) |
≈ |
0.318253−0.441462i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.258−0.965i)T |
| 3 | 1 |
| 37 | 1+(4.69+3.86i)T |
good | 5 | 1+(0.448+1.67i)T+(−4.33+2.5i)T2 |
| 7 | 1+(−0.633+1.09i)T+(−3.5−6.06i)T2 |
| 11 | 1+2.44T+11T2 |
| 13 | 1+(−0.366+0.0980i)T+(11.2−6.5i)T2 |
| 17 | 1+(6.24+1.67i)T+(14.7+8.5i)T2 |
| 19 | 1+(5.09−1.36i)T+(16.4−9.5i)T2 |
| 23 | 1+(2.44−2.44i)T−23iT2 |
| 29 | 1+(6.12+6.12i)T+29iT2 |
| 31 | 1+(−5.73+5.73i)T−31iT2 |
| 41 | 1+(2.89−5.01i)T+(−20.5−35.5i)T2 |
| 43 | 1+(−0.267−0.267i)T+43iT2 |
| 47 | 1+4.24iT−47T2 |
| 53 | 1+(−5.22+3.01i)T+(26.5−45.8i)T2 |
| 59 | 1+(−5.79−1.55i)T+(51.0+29.5i)T2 |
| 61 | 1+(2.86+10.6i)T+(−52.8+30.5i)T2 |
| 67 | 1+(3.63+2.09i)T+(33.5+58.0i)T2 |
| 71 | 1+(2.12+1.22i)T+(35.5+61.4i)T2 |
| 73 | 1−6.39iT−73T2 |
| 79 | 1+(3.36−0.901i)T+(68.4−39.5i)T2 |
| 83 | 1+(−3.10+1.79i)T+(41.5−71.8i)T2 |
| 89 | 1+(−1.10+4.12i)T+(−77.0−44.5i)T2 |
| 97 | 1+(−0.366−0.366i)T+97iT2 |
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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
−10.15811084900956790462747297145, −9.198049493956212662487223625003, −8.384689489570842420830098925828, −7.78095735257748501369530617884, −6.74674857767966815821958254550, −5.78690164049919864103163838394, −4.71618941877889700905297065031, −4.05111291404073753373981057168, −2.15202898439888007987714522803, −0.29157420529835669830939098201,
1.99381195249715373085267894109, 2.91476556795921281214558140393, 4.13494628923853959211672468714, 5.15693866801822024287442296485, 6.44902257247318876356956554427, 7.26537866432331529632725949643, 8.564630022989225841198221621650, 8.832852237725522020241453721344, 10.35354839015437447487699223493, 10.64400117104226275108570621856