L(s) = 1 | + (−1.33 + 0.470i)2-s + (0.879 − 3.28i)3-s + (1.55 − 1.25i)4-s + (−1.53 − 1.62i)5-s + (0.372 + 4.79i)6-s + (−1.21 + 1.21i)7-s + (−1.48 + 2.40i)8-s + (−7.40 − 4.27i)9-s + (2.81 + 1.44i)10-s − 2.37i·11-s + (−2.75 − 6.21i)12-s + (0.816 + 3.04i)13-s + (1.05 − 2.19i)14-s + (−6.68 + 3.61i)15-s + (0.847 − 3.90i)16-s + (0.0115 − 0.0430i)17-s + ⋯ |
L(s) = 1 | + (−0.942 + 0.332i)2-s + (0.507 − 1.89i)3-s + (0.778 − 0.627i)4-s + (−0.686 − 0.726i)5-s + (0.151 + 1.95i)6-s + (−0.460 + 0.460i)7-s + (−0.525 + 0.851i)8-s + (−2.46 − 1.42i)9-s + (0.889 + 0.456i)10-s − 0.716i·11-s + (−0.794 − 1.79i)12-s + (0.226 + 0.845i)13-s + (0.280 − 0.587i)14-s + (−1.72 + 0.932i)15-s + (0.211 − 0.977i)16-s + (0.00279 − 0.0104i)17-s + ⋯ |
Λ(s)=(=(380s/2ΓC(s)L(s)(−0.996−0.0862i)Λ(2−s)
Λ(s)=(=(380s/2ΓC(s+1/2)L(s)(−0.996−0.0862i)Λ(1−s)
Degree: |
2 |
Conductor: |
380
= 22⋅5⋅19
|
Sign: |
−0.996−0.0862i
|
Analytic conductor: |
3.03431 |
Root analytic conductor: |
1.74192 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ380(7,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 380, ( :1/2), −0.996−0.0862i)
|
Particular Values
L(1) |
≈ |
0.0260188+0.602005i |
L(21) |
≈ |
0.0260188+0.602005i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.33−0.470i)T |
| 5 | 1+(1.53+1.62i)T |
| 19 | 1+(−3.17+2.98i)T |
good | 3 | 1+(−0.879+3.28i)T+(−2.59−1.5i)T2 |
| 7 | 1+(1.21−1.21i)T−7iT2 |
| 11 | 1+2.37iT−11T2 |
| 13 | 1+(−0.816−3.04i)T+(−11.2+6.5i)T2 |
| 17 | 1+(−0.0115+0.0430i)T+(−14.7−8.5i)T2 |
| 23 | 1+(3.19−0.857i)T+(19.9−11.5i)T2 |
| 29 | 1+(−4.14−2.39i)T+(14.5+25.1i)T2 |
| 31 | 1+4.08iT−31T2 |
| 37 | 1+(−1.11−1.11i)T+37iT2 |
| 41 | 1+(4.95+8.58i)T+(−20.5+35.5i)T2 |
| 43 | 1+(−1.25+4.66i)T+(−37.2−21.5i)T2 |
| 47 | 1+(1.09+4.09i)T+(−40.7+23.5i)T2 |
| 53 | 1+(2.09+7.81i)T+(−45.8+26.5i)T2 |
| 59 | 1+(7.40+12.8i)T+(−29.5+51.0i)T2 |
| 61 | 1+(3.96−6.87i)T+(−30.5−52.8i)T2 |
| 67 | 1+(0.0397+0.148i)T+(−58.0+33.5i)T2 |
| 71 | 1+(−0.923+0.533i)T+(35.5−61.4i)T2 |
| 73 | 1+(−0.0287−0.00770i)T+(63.2+36.5i)T2 |
| 79 | 1+(−1.12−1.94i)T+(−39.5+68.4i)T2 |
| 83 | 1+(−2.41−2.41i)T+83iT2 |
| 89 | 1+(0.155+0.0894i)T+(44.5+77.0i)T2 |
| 97 | 1+(−2.93+10.9i)T+(−84.0−48.5i)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
−11.22860520737384328151196950121, −9.399596928173644675528431467707, −8.742801898660484091952078414269, −8.148343037487158344204611078609, −7.26327028550210309538823182323, −6.50162404492681779012602709143, −5.55016499914139517290648536686, −3.19014789879144986663607785687, −1.83770393051102254542198286697, −0.49857177944703565805652804982,
2.84822498522227346372614603919, 3.51120153861646813885310626175, 4.51384623225561592297486247531, 6.17169073460534192065214028669, 7.64451426352718351021111632058, 8.247752898137590718873585911163, 9.385420234874435917788900330701, 10.16790740454723707674075970105, 10.43942835298322908961546517975, 11.35559209850301583238452859219