L(s) = 1 | + (−0.707 + 0.707i)2-s − 1.00i·4-s + (−1.44 − 1.44i)7-s + (0.707 + 0.707i)8-s + 1.09i·11-s + (−4.22 + 4.22i)13-s + 2.04·14-s − 1.00·16-s + (4.17 − 4.17i)17-s − 4.44i·19-s + (−0.775 − 0.775i)22-s + (4.48 + 4.48i)23-s − 5.97i·26-s + (−1.44 + 1.44i)28-s + 3.14·29-s + ⋯ |
L(s) = 1 | + (−0.499 + 0.499i)2-s − 0.500i·4-s + (−0.547 − 0.547i)7-s + (0.250 + 0.250i)8-s + 0.330i·11-s + (−1.17 + 1.17i)13-s + 0.547·14-s − 0.250·16-s + (1.01 − 1.01i)17-s − 1.02i·19-s + (−0.165 − 0.165i)22-s + (0.936 + 0.936i)23-s − 1.17i·26-s + (−0.273 + 0.273i)28-s + 0.584·29-s + ⋯ |
Λ(s)=(=(1350s/2ΓC(s)L(s)(0.850+0.525i)Λ(2−s)
Λ(s)=(=(1350s/2ΓC(s+1/2)L(s)(0.850+0.525i)Λ(1−s)
Degree: |
2 |
Conductor: |
1350
= 2⋅33⋅52
|
Sign: |
0.850+0.525i
|
Analytic conductor: |
10.7798 |
Root analytic conductor: |
3.28326 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1350(107,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1350, ( :1/2), 0.850+0.525i)
|
Particular Values
L(1) |
≈ |
0.9816381952 |
L(21) |
≈ |
0.9816381952 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.707−0.707i)T |
| 3 | 1 |
| 5 | 1 |
good | 7 | 1+(1.44+1.44i)T+7iT2 |
| 11 | 1−1.09iT−11T2 |
| 13 | 1+(4.22−4.22i)T−13iT2 |
| 17 | 1+(−4.17+4.17i)T−17iT2 |
| 19 | 1+4.44iT−19T2 |
| 23 | 1+(−4.48−4.48i)T+23iT2 |
| 29 | 1−3.14T+29T2 |
| 31 | 1+1.44T+31T2 |
| 37 | 1+37iT2 |
| 41 | 1+4.87iT−41T2 |
| 43 | 1+(−7.22+7.22i)T−43iT2 |
| 47 | 1+(−7.31+7.31i)T−47iT2 |
| 53 | 1+(5.65+5.65i)T+53iT2 |
| 59 | 1+2.82T+59T2 |
| 61 | 1+8.44T+61T2 |
| 67 | 1+(2+2i)T+67iT2 |
| 71 | 1+13.9iT−71T2 |
| 73 | 1+(−4.44+4.44i)T−73iT2 |
| 79 | 1+5.44iT−79T2 |
| 83 | 1+(−10.2−10.2i)T+83iT2 |
| 89 | 1−17.4T+89T2 |
| 97 | 1+(8.44+8.44i)T+97iT2 |
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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
−9.333887327933462977308143403775, −9.051815829365069031504201014932, −7.55740647140918706378847322305, −7.24259506660472686014800444190, −6.56255281204160970744002967954, −5.30473274194676816442431372672, −4.66221612915879196103838012391, −3.39123738519958149344029146984, −2.15384539760650816871920239587, −0.56959322387944410185735935517,
1.08264834605008568852995560002, 2.63466959303357571749364922695, 3.21417846065559138306633367289, 4.47721054556024230477444769867, 5.62801603461650053274762145209, 6.30023162150392864711127522162, 7.59773164270785052987779680286, 8.039876861911468151640327741824, 8.998444112748535737630952265102, 9.743584453556233508353433652679