L(s) = 1 | + (−2.96 − 2.96i)5-s − 7-s + (−0.569 + 0.569i)11-s + (2.53 + 2.53i)13-s + 1.03i·17-s + (5.23 − 5.23i)19-s − 8.71i·23-s + 12.6i·25-s + (6.05 − 6.05i)29-s − 3.00i·31-s + (2.96 + 2.96i)35-s + (−0.149 + 0.149i)37-s − 8.63·41-s + (−1.73 − 1.73i)43-s + 4.10·47-s + ⋯ |
L(s) = 1 | + (−1.32 − 1.32i)5-s − 0.377·7-s + (−0.171 + 0.171i)11-s + (0.703 + 0.703i)13-s + 0.251i·17-s + (1.20 − 1.20i)19-s − 1.81i·23-s + 2.52i·25-s + (1.12 − 1.12i)29-s − 0.539i·31-s + (0.501 + 0.501i)35-s + (−0.0246 + 0.0246i)37-s − 1.34·41-s + (−0.264 − 0.264i)43-s + 0.599·47-s + ⋯ |
Λ(s)=(=(4032s/2ΓC(s)L(s)(−0.960+0.276i)Λ(2−s)
Λ(s)=(=(4032s/2ΓC(s+1/2)L(s)(−0.960+0.276i)Λ(1−s)
Degree: |
2 |
Conductor: |
4032
= 26⋅32⋅7
|
Sign: |
−0.960+0.276i
|
Analytic conductor: |
32.1956 |
Root analytic conductor: |
5.67412 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ4032(1583,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 4032, ( :1/2), −0.960+0.276i)
|
Particular Values
L(1) |
≈ |
0.8135024106 |
L(21) |
≈ |
0.8135024106 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 7 | 1+T |
good | 5 | 1+(2.96+2.96i)T+5iT2 |
| 11 | 1+(0.569−0.569i)T−11iT2 |
| 13 | 1+(−2.53−2.53i)T+13iT2 |
| 17 | 1−1.03iT−17T2 |
| 19 | 1+(−5.23+5.23i)T−19iT2 |
| 23 | 1+8.71iT−23T2 |
| 29 | 1+(−6.05+6.05i)T−29iT2 |
| 31 | 1+3.00iT−31T2 |
| 37 | 1+(0.149−0.149i)T−37iT2 |
| 41 | 1+8.63T+41T2 |
| 43 | 1+(1.73+1.73i)T+43iT2 |
| 47 | 1−4.10T+47T2 |
| 53 | 1+(−6.04−6.04i)T+53iT2 |
| 59 | 1+(6.05−6.05i)T−59iT2 |
| 61 | 1+(−5.81−5.81i)T+61iT2 |
| 67 | 1+(0.0256−0.0256i)T−67iT2 |
| 71 | 1+14.5iT−71T2 |
| 73 | 1+5.38iT−73T2 |
| 79 | 1+3.89iT−79T2 |
| 83 | 1+(1.40+1.40i)T+83iT2 |
| 89 | 1+17.0T+89T2 |
| 97 | 1−3.75T+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
−8.269837395721747882645131179221, −7.44888312569580585645503218335, −6.76741977923826333402850150062, −5.84998619846809768336748075359, −4.78932784648779857421847950654, −4.44041665814572809233215099539, −3.63604090032493666242230341802, −2.60456284713814329114846353344, −1.14979752466374324111892401893, −0.28940014217040018026093584116,
1.23610662840399962058062311943, 2.84042493970552985669678212154, 3.44802445301509332759414925009, 3.76871640819167478986065485329, 5.13855820668511439902613752299, 5.84335764241466487549793464199, 6.88172042469598093019765492389, 7.17638654372050024683528039604, 8.093793857346096537966372420579, 8.399454697957408693050388929171