L(s) = 1 | − 2.52·3-s + (−1.33 − 2.31i)5-s + 3.38·9-s − 2.14·11-s + (−2.05 + 2.96i)13-s + (3.37 + 5.83i)15-s + (−1.96 − 3.40i)17-s + 5.07·19-s + (−3.48 + 6.03i)23-s + (−1.06 + 1.83i)25-s − 0.960·27-s + (0.0611 + 0.106i)29-s + (−1.96 + 3.40i)31-s + 5.41·33-s + (−0.724 + 1.25i)37-s + ⋯ |
L(s) = 1 | − 1.45·3-s + (−0.596 − 1.03i)5-s + 1.12·9-s − 0.646·11-s + (−0.570 + 0.821i)13-s + (0.870 + 1.50i)15-s + (−0.476 − 0.825i)17-s + 1.16·19-s + (−0.726 + 1.25i)23-s + (−0.212 + 0.367i)25-s − 0.184·27-s + (0.0113 + 0.0196i)29-s + (−0.353 + 0.612i)31-s + 0.942·33-s + (−0.119 + 0.206i)37-s + ⋯ |
Λ(s)=(=(2548s/2ΓC(s)L(s)(0.741+0.671i)Λ(2−s)
Λ(s)=(=(2548s/2ΓC(s+1/2)L(s)(0.741+0.671i)Λ(1−s)
Degree: |
2 |
Conductor: |
2548
= 22⋅72⋅13
|
Sign: |
0.741+0.671i
|
Analytic conductor: |
20.3458 |
Root analytic conductor: |
4.51064 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2548(1537,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2548, ( :1/2), 0.741+0.671i)
|
Particular Values
L(1) |
≈ |
0.5498748078 |
L(21) |
≈ |
0.5498748078 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 7 | 1 |
| 13 | 1+(2.05−2.96i)T |
good | 3 | 1+2.52T+3T2 |
| 5 | 1+(1.33+2.31i)T+(−2.5+4.33i)T2 |
| 11 | 1+2.14T+11T2 |
| 17 | 1+(1.96+3.40i)T+(−8.5+14.7i)T2 |
| 19 | 1−5.07T+19T2 |
| 23 | 1+(3.48−6.03i)T+(−11.5−19.9i)T2 |
| 29 | 1+(−0.0611−0.106i)T+(−14.5+25.1i)T2 |
| 31 | 1+(1.96−3.40i)T+(−15.5−26.8i)T2 |
| 37 | 1+(0.724−1.25i)T+(−18.5−32.0i)T2 |
| 41 | 1+(−2.29−3.97i)T+(−20.5+35.5i)T2 |
| 43 | 1+(0.997−1.72i)T+(−21.5−37.2i)T2 |
| 47 | 1+(−4.35−7.54i)T+(−23.5+40.7i)T2 |
| 53 | 1+(−0.0515+0.0892i)T+(−26.5−45.8i)T2 |
| 59 | 1+(4.60+7.97i)T+(−29.5+51.0i)T2 |
| 61 | 1+13.0T+61T2 |
| 67 | 1+7.27T+67T2 |
| 71 | 1+(−5.76+9.98i)T+(−35.5−61.4i)T2 |
| 73 | 1+(4.53−7.86i)T+(−36.5−63.2i)T2 |
| 79 | 1+(−0.409−0.708i)T+(−39.5+68.4i)T2 |
| 83 | 1−13.1T+83T2 |
| 89 | 1+(−7.50+13.0i)T+(−44.5−77.0i)T2 |
| 97 | 1+(−9.49+16.4i)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
−8.976912868632199975146607369684, −7.78289653676421805631535892769, −7.37520574778216750961105181761, −6.36053908617028907764290299234, −5.55852010057712242773407238392, −4.83107336339794050725524009083, −4.51025057632657633182941575218, −3.16487212013591831968178080582, −1.60780410794389725190108186443, −0.45151403228862271376371805003,
0.55198531179334388361879941084, 2.30742312885888431569756592018, 3.32760953608167629362486609509, 4.33469512082626019491489188556, 5.23328609753019067256147743596, 5.89853001974281706079860120164, 6.59406733696733477731276896007, 7.41989127685686027076645577333, 7.87687086969086339182354737945, 9.024772461607119401488919657703