L(s) = 1 | + (−0.423 + 0.651i)2-s + (0.402 − 1.04i)3-s + (0.567 + 1.27i)4-s + (0.567 − 2.16i)5-s + (0.513 + 0.706i)6-s + (1.24 − 2.33i)7-s + (−2.60 − 0.412i)8-s + (1.29 + 1.16i)9-s + (1.16 + 1.28i)10-s + (−0.888 − 0.986i)11-s + (1.56 − 0.0820i)12-s + (1.79 + 0.912i)13-s + (0.995 + 1.79i)14-s + (−2.03 − 1.46i)15-s + (−0.495 + 0.550i)16-s + (−0.585 + 0.722i)17-s + ⋯ |
L(s) = 1 | + (−0.299 + 0.460i)2-s + (0.232 − 0.605i)3-s + (0.283 + 0.637i)4-s + (0.253 − 0.967i)5-s + (0.209 + 0.288i)6-s + (0.470 − 0.882i)7-s + (−0.921 − 0.145i)8-s + (0.430 + 0.387i)9-s + (0.369 + 0.406i)10-s + (−0.267 − 0.297i)11-s + (0.451 − 0.0236i)12-s + (0.496 + 0.253i)13-s + (0.266 + 0.480i)14-s + (−0.526 − 0.378i)15-s + (−0.123 + 0.137i)16-s + (−0.141 + 0.175i)17-s + ⋯ |
Λ(s)=(=(175s/2ΓC(s)L(s)(0.994+0.100i)Λ(2−s)
Λ(s)=(=(175s/2ΓC(s+1/2)L(s)(0.994+0.100i)Λ(1−s)
Degree: |
2 |
Conductor: |
175
= 52⋅7
|
Sign: |
0.994+0.100i
|
Analytic conductor: |
1.39738 |
Root analytic conductor: |
1.18210 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ175(3,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 175, ( :1/2), 0.994+0.100i)
|
Particular Values
L(1) |
≈ |
1.21513−0.0614907i |
L(21) |
≈ |
1.21513−0.0614907i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(−0.567+2.16i)T |
| 7 | 1+(−1.24+2.33i)T |
good | 2 | 1+(0.423−0.651i)T+(−0.813−1.82i)T2 |
| 3 | 1+(−0.402+1.04i)T+(−2.22−2.00i)T2 |
| 11 | 1+(0.888+0.986i)T+(−1.14+10.9i)T2 |
| 13 | 1+(−1.79−0.912i)T+(7.64+10.5i)T2 |
| 17 | 1+(0.585−0.722i)T+(−3.53−16.6i)T2 |
| 19 | 1+(−4.81−2.14i)T+(12.7+14.1i)T2 |
| 23 | 1+(0.960+0.623i)T+(9.35+21.0i)T2 |
| 29 | 1+(4.04−5.56i)T+(−8.96−27.5i)T2 |
| 31 | 1+(9.74−1.02i)T+(30.3−6.44i)T2 |
| 37 | 1+(−0.401−7.65i)T+(−36.7+3.86i)T2 |
| 41 | 1+(−0.0622+0.0202i)T+(33.1−24.0i)T2 |
| 43 | 1+(3.34+3.34i)T+43iT2 |
| 47 | 1+(0.145−0.117i)T+(9.77−45.9i)T2 |
| 53 | 1+(10.4+4.00i)T+(39.3+35.4i)T2 |
| 59 | 1+(4.71+1.00i)T+(53.8+23.9i)T2 |
| 61 | 1+(−0.951−4.47i)T+(−55.7+24.8i)T2 |
| 67 | 1+(−6.60−5.34i)T+(13.9+65.5i)T2 |
| 71 | 1+(−8.72−6.33i)T+(21.9+67.5i)T2 |
| 73 | 1+(−1.64−0.0861i)T+(72.6+7.63i)T2 |
| 79 | 1+(−10.3−1.09i)T+(77.2+16.4i)T2 |
| 83 | 1+(−0.978+6.17i)T+(−78.9−25.6i)T2 |
| 89 | 1+(−15.3+3.26i)T+(81.3−36.1i)T2 |
| 97 | 1+(−2.72−17.1i)T+(−92.2+29.9i)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
−12.89590383793083870995095371167, −11.88870523275337039388612956246, −10.76301099840245335840155887502, −9.389998247981883586403015269253, −8.284126993511750145193647263077, −7.69921064273530942891769106816, −6.72142635009885580331616616423, −5.21161586589850371946068123844, −3.69774702702757647685315101983, −1.60632515910715394738086843577,
2.06983385587951446651387685000, 3.39226014384930405785506177108, 5.24438547934150726866184236817, 6.27318895305764801859243389984, 7.59198689923332142847934799762, 9.281203349324206897637248978578, 9.614669755955948902482235806391, 10.83143348408193384050798222160, 11.32386686793847216508293385055, 12.50661385254470068829606793893