L(s) = 1 | + (−0.0935 − 1.78i)2-s + (0.279 + 0.226i)3-s + (−1.19 + 0.125i)4-s + (1.07 + 1.95i)5-s + (0.378 − 0.520i)6-s + (−0.314 − 2.62i)7-s + (−0.224 − 1.41i)8-s + (−0.596 − 2.80i)9-s + (3.39 − 2.11i)10-s + (4.12 + 0.877i)11-s + (−0.361 − 0.234i)12-s + (0.268 + 0.527i)13-s + (−4.66 + 0.808i)14-s + (−0.141 + 0.792i)15-s + (−4.85 + 1.03i)16-s + (−0.811 − 0.311i)17-s + ⋯ |
L(s) = 1 | + (−0.0661 − 1.26i)2-s + (0.161 + 0.130i)3-s + (−0.595 + 0.0626i)4-s + (0.482 + 0.875i)5-s + (0.154 − 0.212i)6-s + (−0.119 − 0.992i)7-s + (−0.0793 − 0.500i)8-s + (−0.198 − 0.935i)9-s + (1.07 − 0.667i)10-s + (1.24 + 0.264i)11-s + (−0.104 − 0.0677i)12-s + (0.0745 + 0.146i)13-s + (−1.24 + 0.215i)14-s + (−0.0365 + 0.204i)15-s + (−1.21 + 0.257i)16-s + (−0.196 − 0.0755i)17-s + ⋯ |
Λ(s)=(=(175s/2ΓC(s)L(s)(−0.0443+0.999i)Λ(2−s)
Λ(s)=(=(175s/2ΓC(s+1/2)L(s)(−0.0443+0.999i)Λ(1−s)
Degree: |
2 |
Conductor: |
175
= 52⋅7
|
Sign: |
−0.0443+0.999i
|
Analytic conductor: |
1.39738 |
Root analytic conductor: |
1.18210 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ175(108,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 175, ( :1/2), −0.0443+0.999i)
|
Particular Values
L(1) |
≈ |
0.893362−0.933935i |
L(21) |
≈ |
0.893362−0.933935i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(−1.07−1.95i)T |
| 7 | 1+(0.314+2.62i)T |
good | 2 | 1+(0.0935+1.78i)T+(−1.98+0.209i)T2 |
| 3 | 1+(−0.279−0.226i)T+(0.623+2.93i)T2 |
| 11 | 1+(−4.12−0.877i)T+(10.0+4.47i)T2 |
| 13 | 1+(−0.268−0.527i)T+(−7.64+10.5i)T2 |
| 17 | 1+(0.811+0.311i)T+(12.6+11.3i)T2 |
| 19 | 1+(0.667−6.34i)T+(−18.5−3.95i)T2 |
| 23 | 1+(1.61−0.0848i)T+(22.8−2.40i)T2 |
| 29 | 1+(0.996+1.37i)T+(−8.96+27.5i)T2 |
| 31 | 1+(−3.65−8.22i)T+(−20.7+23.0i)T2 |
| 37 | 1+(2.37−3.65i)T+(−15.0−33.8i)T2 |
| 41 | 1+(5.70+1.85i)T+(33.1+24.0i)T2 |
| 43 | 1+(−3.73−3.73i)T+43iT2 |
| 47 | 1+(3.45+8.99i)T+(−34.9+31.4i)T2 |
| 53 | 1+(−5.33+6.59i)T+(−11.0−51.8i)T2 |
| 59 | 1+(−4.53−5.03i)T+(−6.16+58.6i)T2 |
| 61 | 1+(0.917+0.826i)T+(6.37+60.6i)T2 |
| 67 | 1+(4.10−10.7i)T+(−49.7−44.8i)T2 |
| 71 | 1+(11.3−8.23i)T+(21.9−67.5i)T2 |
| 73 | 1+(−2.92+1.89i)T+(29.6−66.6i)T2 |
| 79 | 1+(−5.74+12.9i)T+(−52.8−58.7i)T2 |
| 83 | 1+(−3.01+0.477i)T+(78.9−25.6i)T2 |
| 89 | 1+(−11.4+12.6i)T+(−9.30−88.5i)T2 |
| 97 | 1+(11.5+1.83i)T+(92.2+29.9i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−12.09945458666828680046465920657, −11.54728698347327874271219772410, −10.23545654822372905978165588560, −10.02972202865390136779398068709, −8.833758903773464827714388731479, −7.00618883127546318871016436728, −6.32663613869579827448238088694, −4.01261488633731249284579447765, −3.30206069371812071122280297726, −1.55934790217064757477056199825,
2.27780110539744026835555132910, 4.69987701092468526192099556245, 5.69368916027785546912160876926, 6.54220747236141164143369944178, 7.903879914395112911169796553397, 8.790865271191678078506469563370, 9.339507226615763152392983851746, 11.12832837418520788470546843633, 12.08343926801369146813089013471, 13.30324502963263853410533236531