L(s) = 1 | + (−0.5 + 0.866i)2-s + (1.5 − 0.866i)3-s + (−0.499 − 0.866i)4-s + (0.5 + 0.866i)5-s + 1.73i·6-s + (0.5 − 0.866i)7-s + 0.999·8-s + (1.5 − 2.59i)9-s − 0.999·10-s + (−3 + 5.19i)11-s + (−1.49 − 0.866i)12-s + (−1 − 1.73i)13-s + (0.499 + 0.866i)14-s + (1.5 + 0.866i)15-s + (−0.5 + 0.866i)16-s + ⋯ |
L(s) = 1 | + (−0.353 + 0.612i)2-s + (0.866 − 0.499i)3-s + (−0.249 − 0.433i)4-s + (0.223 + 0.387i)5-s + 0.707i·6-s + (0.188 − 0.327i)7-s + 0.353·8-s + (0.5 − 0.866i)9-s − 0.316·10-s + (−0.904 + 1.56i)11-s + (−0.433 − 0.250i)12-s + (−0.277 − 0.480i)13-s + (0.133 + 0.231i)14-s + (0.387 + 0.223i)15-s + (−0.125 + 0.216i)16-s + ⋯ |
Λ(s)=(=(90s/2ΓC(s)L(s)(0.939−0.342i)Λ(2−s)
Λ(s)=(=(90s/2ΓC(s+1/2)L(s)(0.939−0.342i)Λ(1−s)
Degree: |
2 |
Conductor: |
90
= 2⋅32⋅5
|
Sign: |
0.939−0.342i
|
Analytic conductor: |
0.718653 |
Root analytic conductor: |
0.847734 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ90(61,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 90, ( :1/2), 0.939−0.342i)
|
Particular Values
L(1) |
≈ |
1.02091+0.180015i |
L(21) |
≈ |
1.02091+0.180015i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.5−0.866i)T |
| 3 | 1+(−1.5+0.866i)T |
| 5 | 1+(−0.5−0.866i)T |
good | 7 | 1+(−0.5+0.866i)T+(−3.5−6.06i)T2 |
| 11 | 1+(3−5.19i)T+(−5.5−9.52i)T2 |
| 13 | 1+(1+1.73i)T+(−6.5+11.2i)T2 |
| 17 | 1+17T2 |
| 19 | 1+4T+19T2 |
| 23 | 1+(4.5+7.79i)T+(−11.5+19.9i)T2 |
| 29 | 1+(1.5−2.59i)T+(−14.5−25.1i)T2 |
| 31 | 1+(−2−3.46i)T+(−15.5+26.8i)T2 |
| 37 | 1−8T+37T2 |
| 41 | 1+(−1.5−2.59i)T+(−20.5+35.5i)T2 |
| 43 | 1+(4−6.92i)T+(−21.5−37.2i)T2 |
| 47 | 1+(−1.5+2.59i)T+(−23.5−40.7i)T2 |
| 53 | 1−6T+53T2 |
| 59 | 1+(3+5.19i)T+(−29.5+51.0i)T2 |
| 61 | 1+(−6.5+11.2i)T+(−30.5−52.8i)T2 |
| 67 | 1+(−6.5−11.2i)T+(−33.5+58.0i)T2 |
| 71 | 1+6T+71T2 |
| 73 | 1+4T+73T2 |
| 79 | 1+(−5+8.66i)T+(−39.5−68.4i)T2 |
| 83 | 1+(−4.5+7.79i)T+(−41.5−71.8i)T2 |
| 89 | 1−9T+89T2 |
| 97 | 1+(1−1.73i)T+(−48.5−84.0i)T2 |
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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
−14.56079602071985426039705926516, −13.20930217081189068297682058650, −12.45137356857302849413930973901, −10.50162404784282696573836333329, −9.747830227416623325614311522859, −8.321306931986745331309819886925, −7.48422726612557706065549337647, −6.45954662637191414006009843123, −4.55038068692036260792144174367, −2.33919010819884478167126981392,
2.37537030969457984752294204023, 3.93544610495337274078412802121, 5.57075319935115414868322336336, 7.83575954475383675984806026531, 8.641736633502856368430856265107, 9.612859932227793954121340908248, 10.68583135433577144212687711208, 11.76290228817964208844447116448, 13.27077342351155635351936184337, 13.74390613949249611289264562549