L(s) = 1 | + (0.0938 − 1.79i)2-s + (−2.61 + 2.11i)3-s + (−1.21 − 0.127i)4-s + (1.96 − 1.06i)5-s + (3.54 + 4.88i)6-s + (−1.70 − 2.02i)7-s + (0.219 − 1.38i)8-s + (1.72 − 8.13i)9-s + (−1.71 − 3.62i)10-s + (2.72 − 0.579i)11-s + (3.43 − 2.23i)12-s + (0.649 − 1.27i)13-s + (−3.78 + 2.85i)14-s + (−2.89 + 6.94i)15-s + (−4.84 − 1.02i)16-s + (1.22 − 0.470i)17-s + ⋯ |
L(s) = 1 | + (0.0663 − 1.26i)2-s + (−1.50 + 1.22i)3-s + (−0.605 − 0.0636i)4-s + (0.879 − 0.475i)5-s + (1.44 + 1.99i)6-s + (−0.643 − 0.765i)7-s + (0.0775 − 0.489i)8-s + (0.576 − 2.71i)9-s + (−0.543 − 1.14i)10-s + (0.821 − 0.174i)11-s + (0.992 − 0.644i)12-s + (0.180 − 0.353i)13-s + (−1.01 + 0.763i)14-s + (−0.747 + 1.79i)15-s + (−1.21 − 0.257i)16-s + (0.297 − 0.114i)17-s + ⋯ |
Λ(s)=(=(175s/2ΓC(s)L(s)(−0.277+0.960i)Λ(2−s)
Λ(s)=(=(175s/2ΓC(s+1/2)L(s)(−0.277+0.960i)Λ(1−s)
Degree: |
2 |
Conductor: |
175
= 52⋅7
|
Sign: |
−0.277+0.960i
|
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), −0.277+0.960i)
|
Particular Values
L(1) |
≈ |
0.503023−0.668803i |
L(21) |
≈ |
0.503023−0.668803i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(−1.96+1.06i)T |
| 7 | 1+(1.70+2.02i)T |
good | 2 | 1+(−0.0938+1.79i)T+(−1.98−0.209i)T2 |
| 3 | 1+(2.61−2.11i)T+(0.623−2.93i)T2 |
| 11 | 1+(−2.72+0.579i)T+(10.0−4.47i)T2 |
| 13 | 1+(−0.649+1.27i)T+(−7.64−10.5i)T2 |
| 17 | 1+(−1.22+0.470i)T+(12.6−11.3i)T2 |
| 19 | 1+(−0.229−2.18i)T+(−18.5+3.95i)T2 |
| 23 | 1+(1.79+0.0940i)T+(22.8+2.40i)T2 |
| 29 | 1+(1.22−1.68i)T+(−8.96−27.5i)T2 |
| 31 | 1+(−1.74+3.92i)T+(−20.7−23.0i)T2 |
| 37 | 1+(−0.0698−0.107i)T+(−15.0+33.8i)T2 |
| 41 | 1+(6.08−1.97i)T+(33.1−24.0i)T2 |
| 43 | 1+(−2.62+2.62i)T−43iT2 |
| 47 | 1+(2.63−6.85i)T+(−34.9−31.4i)T2 |
| 53 | 1+(−7.79−9.62i)T+(−11.0+51.8i)T2 |
| 59 | 1+(−0.660+0.733i)T+(−6.16−58.6i)T2 |
| 61 | 1+(−5.97+5.37i)T+(6.37−60.6i)T2 |
| 67 | 1+(1.09+2.86i)T+(−49.7+44.8i)T2 |
| 71 | 1+(−4.78−3.47i)T+(21.9+67.5i)T2 |
| 73 | 1+(1.03+0.670i)T+(29.6+66.6i)T2 |
| 79 | 1+(−3.47−7.80i)T+(−52.8+58.7i)T2 |
| 83 | 1+(6.21+0.983i)T+(78.9+25.6i)T2 |
| 89 | 1+(−2.11−2.35i)T+(−9.30+88.5i)T2 |
| 97 | 1+(−13.4+2.12i)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
−12.18140626930253938131332349760, −11.30794093394763684604124797580, −10.42885285488520522941763556090, −9.906274812435908826104823901651, −9.229297016086815082624806379728, −6.66903383128037092845891393129, −5.78348000641277455279608154756, −4.44931498164182704102770907502, −3.52947587407153190165107113627, −0.971893047643615735618022109360,
2.02826508278341169478955474470, 5.15984459977698012903905113082, 5.95445378534834451950638830313, 6.60277862735116365257526998580, 7.15648719095670677464113880848, 8.617066661793233178382058508898, 10.06665287979182304721285912978, 11.32900971061006243139439302120, 12.03604748398632492909989036968, 13.14452607599504347462728458761