L(s) = 1 | + (0.582 − 0.189i)3-s + (−0.858 + 1.18i)5-s + (−1.36 + 4.21i)7-s + (−2.12 + 1.54i)9-s + (−2.69 + 1.93i)11-s + (−3.27 − 4.50i)13-s + (−0.276 + 0.850i)15-s + (2.06 + 1.50i)17-s + (2.87 − 0.933i)19-s + 2.71i·21-s + 3.70·23-s + (0.886 + 2.72i)25-s + (−2.02 + 2.78i)27-s + (3.48 + 1.13i)29-s + (1.20 − 0.876i)31-s + ⋯ |
L(s) = 1 | + (0.336 − 0.109i)3-s + (−0.383 + 0.528i)5-s + (−0.517 + 1.59i)7-s + (−0.707 + 0.514i)9-s + (−0.811 + 0.584i)11-s + (−0.908 − 1.25i)13-s + (−0.0713 + 0.219i)15-s + (0.501 + 0.364i)17-s + (0.658 − 0.214i)19-s + 0.591i·21-s + 0.773·23-s + (0.177 + 0.545i)25-s + (−0.389 + 0.536i)27-s + (0.646 + 0.209i)29-s + (0.216 − 0.157i)31-s + ⋯ |
Λ(s)=(=(352s/2ΓC(s)L(s)(−0.362−0.932i)Λ(2−s)
Λ(s)=(=(352s/2ΓC(s+1/2)L(s)(−0.362−0.932i)Λ(1−s)
Degree: |
2 |
Conductor: |
352
= 25⋅11
|
Sign: |
−0.362−0.932i
|
Analytic conductor: |
2.81073 |
Root analytic conductor: |
1.67652 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ352(113,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 352, ( :1/2), −0.362−0.932i)
|
Particular Values
L(1) |
≈ |
0.538109+0.786521i |
L(21) |
≈ |
0.538109+0.786521i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 11 | 1+(2.69−1.93i)T |
good | 3 | 1+(−0.582+0.189i)T+(2.42−1.76i)T2 |
| 5 | 1+(0.858−1.18i)T+(−1.54−4.75i)T2 |
| 7 | 1+(1.36−4.21i)T+(−5.66−4.11i)T2 |
| 13 | 1+(3.27+4.50i)T+(−4.01+12.3i)T2 |
| 17 | 1+(−2.06−1.50i)T+(5.25+16.1i)T2 |
| 19 | 1+(−2.87+0.933i)T+(15.3−11.1i)T2 |
| 23 | 1−3.70T+23T2 |
| 29 | 1+(−3.48−1.13i)T+(23.4+17.0i)T2 |
| 31 | 1+(−1.20+0.876i)T+(9.57−29.4i)T2 |
| 37 | 1+(−1.41−0.460i)T+(29.9+21.7i)T2 |
| 41 | 1+(−0.970−2.98i)T+(−33.1+24.0i)T2 |
| 43 | 1+6.25iT−43T2 |
| 47 | 1+(−0.821−2.52i)T+(−38.0+27.6i)T2 |
| 53 | 1+(−5.75−7.92i)T+(−16.3+50.4i)T2 |
| 59 | 1+(−2.45−0.796i)T+(47.7+34.6i)T2 |
| 61 | 1+(3.28−4.51i)T+(−18.8−58.0i)T2 |
| 67 | 1−11.5iT−67T2 |
| 71 | 1+(−0.909−0.660i)T+(21.9+67.5i)T2 |
| 73 | 1+(−4.36+13.4i)T+(−59.0−42.9i)T2 |
| 79 | 1+(−0.619+0.450i)T+(24.4−75.1i)T2 |
| 83 | 1+(5.03−6.92i)T+(−25.6−78.9i)T2 |
| 89 | 1+8.84T+89T2 |
| 97 | 1+(−0.241+0.175i)T+(29.9−92.2i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−11.90182850425433833496953353769, −10.81498168967777664590787163123, −9.916550581096086060846570344136, −8.913548855960224507622993697164, −7.993495003839717367719290363504, −7.22299053829820748943282944406, −5.72467065889602698625336004896, −5.13292582710670235986446925545, −3.00911810451099059063107542960, −2.61721445623282846499850796311,
0.61388405386499024225865285607, 2.93732452195337259853817671863, 4.00870037131012106789797311325, 5.06142786117801898677767509941, 6.54598665635207576652885652312, 7.45185210938260658276553600247, 8.352333335279250178355384992024, 9.424428668279162609352686214967, 10.14199365434962644369535468032, 11.23303357930251296268241409641