L(s) = 1 | + (−0.0825 + 1.57i)2-s + (−0.0997 + 0.0808i)3-s + (−0.483 − 0.0508i)4-s + (−1.93 + 1.11i)5-s + (−0.118 − 0.163i)6-s + (2.63 − 0.202i)7-s + (−0.373 + 2.35i)8-s + (−0.620 + 2.91i)9-s + (−1.59 − 3.14i)10-s + (−3.49 + 0.743i)11-s + (0.0523 − 0.0339i)12-s + (0.403 − 0.791i)13-s + (0.101 + 4.17i)14-s + (0.103 − 0.267i)15-s + (−4.63 − 0.984i)16-s + (6.15 − 2.36i)17-s + ⋯ |
L(s) = 1 | + (−0.0583 + 1.11i)2-s + (−0.0576 + 0.0466i)3-s + (−0.241 − 0.0254i)4-s + (−0.866 + 0.499i)5-s + (−0.0485 − 0.0668i)6-s + (0.997 − 0.0765i)7-s + (−0.132 + 0.833i)8-s + (−0.206 + 0.972i)9-s + (−0.505 − 0.993i)10-s + (−1.05 + 0.224i)11-s + (0.0151 − 0.00981i)12-s + (0.111 − 0.219i)13-s + (0.0270 + 1.11i)14-s + (0.0266 − 0.0691i)15-s + (−1.15 − 0.246i)16-s + (1.49 − 0.572i)17-s + ⋯ |
Λ(s)=(=(175s/2ΓC(s)L(s)(−0.661−0.749i)Λ(2−s)
Λ(s)=(=(175s/2ΓC(s+1/2)L(s)(−0.661−0.749i)Λ(1−s)
Degree: |
2 |
Conductor: |
175
= 52⋅7
|
Sign: |
−0.661−0.749i
|
Analytic conductor: |
1.39738 |
Root analytic conductor: |
1.18210 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ175(47,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 175, ( :1/2), −0.661−0.749i)
|
Particular Values
L(1) |
≈ |
0.438507+0.971756i |
L(21) |
≈ |
0.438507+0.971756i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(1.93−1.11i)T |
| 7 | 1+(−2.63+0.202i)T |
good | 2 | 1+(0.0825−1.57i)T+(−1.98−0.209i)T2 |
| 3 | 1+(0.0997−0.0808i)T+(0.623−2.93i)T2 |
| 11 | 1+(3.49−0.743i)T+(10.0−4.47i)T2 |
| 13 | 1+(−0.403+0.791i)T+(−7.64−10.5i)T2 |
| 17 | 1+(−6.15+2.36i)T+(12.6−11.3i)T2 |
| 19 | 1+(0.107+1.02i)T+(−18.5+3.95i)T2 |
| 23 | 1+(−2.68−0.140i)T+(22.8+2.40i)T2 |
| 29 | 1+(0.242−0.334i)T+(−8.96−27.5i)T2 |
| 31 | 1+(−1.79+4.02i)T+(−20.7−23.0i)T2 |
| 37 | 1+(−5.67−8.74i)T+(−15.0+33.8i)T2 |
| 41 | 1+(0.884−0.287i)T+(33.1−24.0i)T2 |
| 43 | 1+(−3.39+3.39i)T−43iT2 |
| 47 | 1+(−2.43+6.33i)T+(−34.9−31.4i)T2 |
| 53 | 1+(5.17+6.38i)T+(−11.0+51.8i)T2 |
| 59 | 1+(−3.83+4.25i)T+(−6.16−58.6i)T2 |
| 61 | 1+(3.99−3.59i)T+(6.37−60.6i)T2 |
| 67 | 1+(−3.90−10.1i)T+(−49.7+44.8i)T2 |
| 71 | 1+(−5.23−3.80i)T+(21.9+67.5i)T2 |
| 73 | 1+(9.62+6.25i)T+(29.6+66.6i)T2 |
| 79 | 1+(5.43+12.2i)T+(−52.8+58.7i)T2 |
| 83 | 1+(10.5+1.67i)T+(78.9+25.6i)T2 |
| 89 | 1+(−3.49−3.88i)T+(−9.30+88.5i)T2 |
| 97 | 1+(14.9−2.36i)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
−13.37279906005886106468150311906, −11.83707346695819399686556554786, −11.17102621183245438560379269150, −10.24147895161352968322093684481, −8.338532942096355084417170902184, −7.83477511630986241166786312720, −7.17128778178475511638814986527, −5.56501810626016505867541505376, −4.75826800579302726028119731342, −2.70784218509486283743422208273,
1.13434108344645080041028676974, 3.05991778022188021729141635215, 4.25080564090156924566601077570, 5.70782975799851445230582793175, 7.40901232207654782296715275805, 8.362224804597699335190724055186, 9.492482754637843378385169209461, 10.74362333400670285490031529673, 11.34942630966504280122967945212, 12.34224031183747493377354737373