L(s) = 1 | + (2.32 − 2.32i)3-s + (0.707 + 0.707i)5-s + 0.982i·7-s − 7.82i·9-s + (1.62 + 1.62i)11-s + (−0.690 + 0.690i)13-s + 3.28·15-s − 2.19·17-s + (−1.92 + 1.92i)19-s + (2.28 + 2.28i)21-s − 2.01i·23-s + 1.00i·25-s + (−11.2 − 11.2i)27-s + (−5.27 + 5.27i)29-s − 0.435·31-s + ⋯ |
L(s) = 1 | + (1.34 − 1.34i)3-s + (0.316 + 0.316i)5-s + 0.371i·7-s − 2.60i·9-s + (0.490 + 0.490i)11-s + (−0.191 + 0.191i)13-s + 0.849·15-s − 0.532·17-s + (−0.441 + 0.441i)19-s + (0.498 + 0.498i)21-s − 0.420i·23-s + 0.200i·25-s + (−2.15 − 2.15i)27-s + (−0.978 + 0.978i)29-s − 0.0781·31-s + ⋯ |
Λ(s)=(=(320s/2ΓC(s)L(s)(0.557+0.830i)Λ(2−s)
Λ(s)=(=(320s/2ΓC(s+1/2)L(s)(0.557+0.830i)Λ(1−s)
Degree: |
2 |
Conductor: |
320
= 26⋅5
|
Sign: |
0.557+0.830i
|
Analytic conductor: |
2.55521 |
Root analytic conductor: |
1.59850 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ320(241,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 320, ( :1/2), 0.557+0.830i)
|
Particular Values
L(1) |
≈ |
1.78166−0.950157i |
L(21) |
≈ |
1.78166−0.950157i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.707−0.707i)T |
good | 3 | 1+(−2.32+2.32i)T−3iT2 |
| 7 | 1−0.982iT−7T2 |
| 11 | 1+(−1.62−1.62i)T+11iT2 |
| 13 | 1+(0.690−0.690i)T−13iT2 |
| 17 | 1+2.19T+17T2 |
| 19 | 1+(1.92−1.92i)T−19iT2 |
| 23 | 1+2.01iT−23T2 |
| 29 | 1+(5.27−5.27i)T−29iT2 |
| 31 | 1+0.435T+31T2 |
| 37 | 1+(5.79+5.79i)T+37iT2 |
| 41 | 1−3.93iT−41T2 |
| 43 | 1+(−0.507−0.507i)T+43iT2 |
| 47 | 1−9.21T+47T2 |
| 53 | 1+(−6.29−6.29i)T+53iT2 |
| 59 | 1+(−5.67−5.67i)T+59iT2 |
| 61 | 1+(3.60−3.60i)T−61iT2 |
| 67 | 1+(4.53−4.53i)T−67iT2 |
| 71 | 1+10.3iT−71T2 |
| 73 | 1+9.24iT−73T2 |
| 79 | 1+15.4T+79T2 |
| 83 | 1+(−0.683+0.683i)T−83iT2 |
| 89 | 1−5.44iT−89T2 |
| 97 | 1−5.54T+97T2 |
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
−11.88337152405043553905585572262, −10.45821353937183284835655903518, −9.127912757250589837672882681093, −8.814604844581719509380062168749, −7.52368578910402500039656226620, −6.93817077339998694128270177824, −5.91600465655867296964484728964, −3.95974038263984441374759071592, −2.64006209011260313467411738457, −1.70961435925483631530039717175,
2.26847662515630972629507063813, 3.58901982868440714644626810033, 4.40912153767375379151585791299, 5.55574143730971205646307758081, 7.21607424936166234516508225610, 8.401746163462147500016589119775, 8.974876629632275636956181151706, 9.812231921978649597133476114656, 10.55229597552234797182944133633, 11.50469487829456717190338453447