L(s) = 1 | + (1.50 − 1.18i)2-s + (0.632 − 2.60i)4-s + (−1.34 − 2.93i)8-s + (−0.327 + 0.945i)9-s + (−0.653 − 0.513i)11-s + (−3.12 − 1.60i)16-s + (0.627 + 1.81i)18-s − 1.59·22-s + (0.981 + 0.189i)23-s + (0.928 + 0.371i)25-s + (0.273 + 0.0801i)29-s + (−3.44 + 0.664i)32-s + (2.25 + 1.45i)36-s + (−0.550 + 1.58i)37-s + (−0.544 + 1.19i)43-s + (−1.75 + 1.37i)44-s + ⋯ |
L(s) = 1 | + (1.50 − 1.18i)2-s + (0.632 − 2.60i)4-s + (−1.34 − 2.93i)8-s + (−0.327 + 0.945i)9-s + (−0.653 − 0.513i)11-s + (−3.12 − 1.60i)16-s + (0.627 + 1.81i)18-s − 1.59·22-s + (0.981 + 0.189i)23-s + (0.928 + 0.371i)25-s + (0.273 + 0.0801i)29-s + (−3.44 + 0.664i)32-s + (2.25 + 1.45i)36-s + (−0.550 + 1.58i)37-s + (−0.544 + 1.19i)43-s + (−1.75 + 1.37i)44-s + ⋯ |
Λ(s)=(=(1127s/2ΓC(s)L(s)(−0.462+0.886i)Λ(1−s)
Λ(s)=(=(1127s/2ΓC(s)L(s)(−0.462+0.886i)Λ(1−s)
Degree: |
2 |
Conductor: |
1127
= 72⋅23
|
Sign: |
−0.462+0.886i
|
Analytic conductor: |
0.562446 |
Root analytic conductor: |
0.749964 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1127(325,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1127, ( :0), −0.462+0.886i)
|
Particular Values
L(21) |
≈ |
2.166734829 |
L(21) |
≈ |
2.166734829 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 7 | 1 |
| 23 | 1+(−0.981−0.189i)T |
good | 2 | 1+(−1.50+1.18i)T+(0.235−0.971i)T2 |
| 3 | 1+(0.327−0.945i)T2 |
| 5 | 1+(−0.928−0.371i)T2 |
| 11 | 1+(0.653+0.513i)T+(0.235+0.971i)T2 |
| 13 | 1+(−0.415−0.909i)T2 |
| 17 | 1+(−0.0475+0.998i)T2 |
| 19 | 1+(−0.0475−0.998i)T2 |
| 29 | 1+(−0.273−0.0801i)T+(0.841+0.540i)T2 |
| 31 | 1+(−0.981−0.189i)T2 |
| 37 | 1+(0.550−1.58i)T+(−0.786−0.618i)T2 |
| 41 | 1+(0.142+0.989i)T2 |
| 43 | 1+(0.544−1.19i)T+(−0.654−0.755i)T2 |
| 47 | 1+(0.5−0.866i)T2 |
| 53 | 1+(0.0135+0.284i)T+(−0.995+0.0950i)T2 |
| 59 | 1+(−0.580+0.814i)T2 |
| 61 | 1+(0.327+0.945i)T2 |
| 67 | 1+(1.78+0.713i)T+(0.723+0.690i)T2 |
| 71 | 1+(0.118+0.822i)T+(−0.959+0.281i)T2 |
| 73 | 1+(0.888+0.458i)T2 |
| 79 | 1+(0.0135−0.284i)T+(−0.995−0.0950i)T2 |
| 83 | 1+(0.142−0.989i)T2 |
| 89 | 1+(−0.981+0.189i)T2 |
| 97 | 1+(0.142+0.989i)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
−10.28594287660078257479863710406, −9.234160759326829274576350425656, −8.155628571223475129004486822576, −6.92885273848245166747990047922, −5.97734376810402675638248821633, −5.08120266492599458417377440190, −4.68260706031711349690108405013, −3.26880390614205131684428745042, −2.75254036681795501308162052269, −1.47669665814270921933352119751,
2.57437384039313020388566752442, 3.45570445423395629131178945840, 4.41703500435576621049991599536, 5.24008749437731047217468126920, 5.98366452303404522029924652680, 6.89773818281505889556336627348, 7.35674945918912766232064473122, 8.457660111961138907653648283800, 9.060629186595598492397508690873, 10.43448655596122400110413422963