L(s) = 1 | + (−1.17 + 0.792i)2-s − 1.26i·3-s + (0.743 − 1.85i)4-s + 3.51i·5-s + (1 + 1.47i)6-s − 2.23i·7-s + (0.601 + 2.76i)8-s + 1.40·9-s + (−2.78 − 4.12i)10-s + 2.89·11-s + (−2.34 − 0.937i)12-s + 6.30·13-s + (1.77 + 2.61i)14-s + 4.43·15-s + (−2.89 − 2.76i)16-s − 4.79·17-s + ⋯ |
L(s) = 1 | + (−0.828 + 0.560i)2-s − 0.728i·3-s + (0.371 − 0.928i)4-s + 1.57i·5-s + (0.408 + 0.603i)6-s − 0.845i·7-s + (0.212 + 0.977i)8-s + 0.469·9-s + (−0.882 − 1.30i)10-s + 0.872·11-s + (−0.676 − 0.270i)12-s + 1.74·13-s + (0.473 + 0.699i)14-s + 1.14·15-s + (−0.723 − 0.690i)16-s − 1.16·17-s + ⋯ |
Λ(s)=(=(152s/2ΓC(s)L(s)(0.912−0.408i)Λ(2−s)
Λ(s)=(=(152s/2ΓC(s+1/2)L(s)(0.912−0.408i)Λ(1−s)
Degree: |
2 |
Conductor: |
152
= 23⋅19
|
Sign: |
0.912−0.408i
|
Analytic conductor: |
1.21372 |
Root analytic conductor: |
1.10169 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ152(75,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 152, ( :1/2), 0.912−0.408i)
|
Particular Values
L(1) |
≈ |
0.832185+0.177838i |
L(21) |
≈ |
0.832185+0.177838i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.17−0.792i)T |
| 19 | 1+(−0.895−4.26i)T |
good | 3 | 1+1.26iT−3T2 |
| 5 | 1−3.51iT−5T2 |
| 7 | 1+2.23iT−7T2 |
| 11 | 1−2.89T+11T2 |
| 13 | 1−6.30T+13T2 |
| 17 | 1+4.79T+17T2 |
| 23 | 1+0.524iT−23T2 |
| 29 | 1+0.415T+29T2 |
| 31 | 1+1.20T+31T2 |
| 37 | 1+5.88T+37T2 |
| 41 | 1+4.87iT−41T2 |
| 43 | 1+10.6T+43T2 |
| 47 | 1+4.27iT−47T2 |
| 53 | 1+6.05T+53T2 |
| 59 | 1−8.08iT−59T2 |
| 61 | 1−8.38iT−61T2 |
| 67 | 1+9.79iT−67T2 |
| 71 | 1+10.2T+71T2 |
| 73 | 1−7.76T+73T2 |
| 79 | 1−7.33T+79T2 |
| 83 | 1−2T+83T2 |
| 89 | 1+12.1iT−89T2 |
| 97 | 1−2.19iT−97T2 |
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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
−13.50538529979423743216202916454, −11.71077299296906940886551198616, −10.78280497035339202325248284827, −10.20193334225964975960730927305, −8.749947164833994760098899168652, −7.53699034863407855576274257615, −6.74270851361341054006055784802, −6.24460713044118081077069465629, −3.77905431970872009933633846973, −1.64962453199860879846504505147,
1.48996415324906174572912104417, 3.75099645536233009548356757254, 4.86058757100017245891316146689, 6.53773729613293747511879699525, 8.382998536360891458685669663192, 8.979111253069402394513259396324, 9.503679705357900724163168498389, 10.94725584319405234744814259206, 11.73203713809189707470464920181, 12.79391017318517494604320062928