L(s) = 1 | − 0.250i·2-s + 0.442i·3-s + 1.93·4-s + (−0.235 − 2.22i)5-s + 0.110·6-s − 1.63i·7-s − 0.985i·8-s + 2.80·9-s + (−0.556 + 0.0588i)10-s − 5.60·11-s + 0.858i·12-s − 1.36i·13-s − 0.410·14-s + (0.984 − 0.104i)15-s + 3.62·16-s − 6.74i·17-s + ⋯ |
L(s) = 1 | − 0.176i·2-s + 0.255i·3-s + 0.968·4-s + (−0.105 − 0.994i)5-s + 0.0452·6-s − 0.619i·7-s − 0.348i·8-s + 0.934·9-s + (−0.175 + 0.0186i)10-s − 1.69·11-s + 0.247i·12-s − 0.377i·13-s − 0.109·14-s + (0.254 − 0.0269i)15-s + 0.907·16-s − 1.63i·17-s + ⋯ |
Λ(s)=(=(755s/2ΓC(s)L(s)(0.105+0.994i)Λ(2−s)
Λ(s)=(=(755s/2ΓC(s+1/2)L(s)(0.105+0.994i)Λ(1−s)
Degree: |
2 |
Conductor: |
755
= 5⋅151
|
Sign: |
0.105+0.994i
|
Analytic conductor: |
6.02870 |
Root analytic conductor: |
2.45534 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ755(454,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 755, ( :1/2), 0.105+0.994i)
|
Particular Values
L(1) |
≈ |
1.30373−1.17307i |
L(21) |
≈ |
1.30373−1.17307i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1+(0.235+2.22i)T |
| 151 | 1+T |
good | 2 | 1+0.250iT−2T2 |
| 3 | 1−0.442iT−3T2 |
| 7 | 1+1.63iT−7T2 |
| 11 | 1+5.60T+11T2 |
| 13 | 1+1.36iT−13T2 |
| 17 | 1+6.74iT−17T2 |
| 19 | 1+0.591T+19T2 |
| 23 | 1−2.58iT−23T2 |
| 29 | 1−6.70T+29T2 |
| 31 | 1+7.88T+31T2 |
| 37 | 1−3.52iT−37T2 |
| 41 | 1−3.19T+41T2 |
| 43 | 1−11.8iT−43T2 |
| 47 | 1+7.93iT−47T2 |
| 53 | 1+11.3iT−53T2 |
| 59 | 1−4.11T+59T2 |
| 61 | 1−8.31T+61T2 |
| 67 | 1+9.36iT−67T2 |
| 71 | 1−11.6T+71T2 |
| 73 | 1−11.1iT−73T2 |
| 79 | 1−5.19T+79T2 |
| 83 | 1−3.94iT−83T2 |
| 89 | 1+17.8T+89T2 |
| 97 | 1+5.09iT−97T2 |
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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
−10.08981509283661374327200975661, −9.641738322849345904766837406760, −8.238522800705814154473124737035, −7.55478654190111491512224844364, −6.87230556949962694614744806653, −5.41747964002810975107737488506, −4.82505010637232825577023002590, −3.55754449868791099597288543473, −2.34643231180975377318999023376, −0.877519970642938233558487678818,
1.98121494225564122066304245614, 2.67607339406946285849369037504, 3.98093292909405736546090966146, 5.50452271503474316034319434819, 6.25019920753567665547816924157, 7.12197151674008213981217392125, 7.72019300868299310392055525197, 8.582676636538905531110823419234, 10.07939603682858956974717668972, 10.59354254344767668451852103257