L(s) = 1 | + 1.41·2-s + (−2.94 − 0.581i)3-s + 2.00·4-s + (−4.16 − 0.821i)6-s − 11.4i·7-s + 2.82·8-s + (8.32 + 3.42i)9-s − 8.48i·11-s + (−5.88 − 1.16i)12-s − 10i·13-s − 16.2i·14-s + 4.00·16-s + 3.55·17-s + (11.7 + 4.83i)18-s + 10.9·19-s + ⋯ |
L(s) = 1 | + 0.707·2-s + (−0.981 − 0.193i)3-s + 0.500·4-s + (−0.693 − 0.136i)6-s − 1.64i·7-s + 0.353·8-s + (0.924 + 0.380i)9-s − 0.771i·11-s + (−0.490 − 0.0968i)12-s − 0.769i·13-s − 1.16i·14-s + 0.250·16-s + 0.209·17-s + (0.654 + 0.268i)18-s + 0.577·19-s + ⋯ |
Λ(s)=(=(150s/2ΓC(s)L(s)(0.265+0.964i)Λ(3−s)
Λ(s)=(=(150s/2ΓC(s+1)L(s)(0.265+0.964i)Λ(1−s)
Degree: |
2 |
Conductor: |
150
= 2⋅3⋅52
|
Sign: |
0.265+0.964i
|
Analytic conductor: |
4.08720 |
Root analytic conductor: |
2.02168 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ150(149,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 150, ( :1), 0.265+0.964i)
|
Particular Values
L(23) |
≈ |
1.23400−0.940133i |
L(21) |
≈ |
1.23400−0.940133i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1−1.41T |
| 3 | 1+(2.94+0.581i)T |
| 5 | 1 |
good | 7 | 1+11.4iT−49T2 |
| 11 | 1+8.48iT−121T2 |
| 13 | 1+10iT−169T2 |
| 17 | 1−3.55T+289T2 |
| 19 | 1−10.9T+361T2 |
| 23 | 1+17.6T+529T2 |
| 29 | 1−26.8iT−841T2 |
| 31 | 1−8T+961T2 |
| 37 | 1−59.9iT−1.36e3T2 |
| 41 | 1+20.5iT−1.68e3T2 |
| 43 | 1−42.4iT−1.84e3T2 |
| 47 | 1−88.2T+2.20e3T2 |
| 53 | 1+3.55T+2.80e3T2 |
| 59 | 1+77.7iT−3.48e3T2 |
| 61 | 1−21.9T+3.72e3T2 |
| 67 | 1−53.5iT−4.48e3T2 |
| 71 | 1+69.2iT−5.04e3T2 |
| 73 | 1−12.0iT−5.32e3T2 |
| 79 | 1−9.02T+6.24e3T2 |
| 83 | 1+0.688T+6.88e3T2 |
| 89 | 1−7.10iT−7.92e3T2 |
| 97 | 1+111.iT−9.40e3T2 |
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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
−12.65498674180014101887927847194, −11.57404322635515980743865465586, −10.71128495996772482866525087807, −10.04973508948896779284195224586, −7.937818850961356524949436099746, −7.02528036431670267185252558277, −5.94489441369533459328623327066, −4.76969077378106107655043014792, −3.52953055754004709474721755848, −0.964200928946424616129808671689,
2.18991163283358657407662226652, 4.17313098606916738180379088757, 5.38654630373253069874280721883, 6.11638611596209040401708569206, 7.37713661315932666495708297689, 9.053513165235013559243034970168, 10.05998108095342431461236868199, 11.39581031325839089791694398442, 12.07831079669037945649985798242, 12.57824048514611523524379936269