L(s) = 1 | + (4.94 + 2.74i)2-s + 23.5·3-s + (16.8 + 27.1i)4-s + (116. + 64.7i)6-s + 39.5i·7-s + (8.81 + 180. i)8-s + 311.·9-s − 236. i·11-s + (397. + 639. i)12-s + 942.·13-s + (−108. + 195. i)14-s + (−453. + 918. i)16-s − 1.10e3i·17-s + (1.53e3 + 856. i)18-s + 2.31e3i·19-s + ⋯ |
L(s) = 1 | + (0.874 + 0.485i)2-s + 1.51·3-s + (0.527 + 0.849i)4-s + (1.32 + 0.733i)6-s + 0.305i·7-s + (0.0486 + 0.998i)8-s + 1.28·9-s − 0.589i·11-s + (0.797 + 1.28i)12-s + 1.54·13-s + (−0.148 + 0.266i)14-s + (−0.442 + 0.896i)16-s − 0.925i·17-s + (1.12 + 0.622i)18-s + 1.47i·19-s + ⋯ |
Λ(s)=(=(200s/2ΓC(s)L(s)(0.403−0.915i)Λ(6−s)
Λ(s)=(=(200s/2ΓC(s+5/2)L(s)(0.403−0.915i)Λ(1−s)
Degree: |
2 |
Conductor: |
200
= 23⋅52
|
Sign: |
0.403−0.915i
|
Analytic conductor: |
32.0767 |
Root analytic conductor: |
5.66363 |
Motivic weight: |
5 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ200(149,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 200, ( :5/2), 0.403−0.915i)
|
Particular Values
L(3) |
≈ |
5.974087753 |
L(21) |
≈ |
5.974087753 |
L(27) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−4.94−2.74i)T |
| 5 | 1 |
good | 3 | 1−23.5T+243T2 |
| 7 | 1−39.5iT−1.68e4T2 |
| 11 | 1+236.iT−1.61e5T2 |
| 13 | 1−942.T+3.71e5T2 |
| 17 | 1+1.10e3iT−1.41e6T2 |
| 19 | 1−2.31e3iT−2.47e6T2 |
| 23 | 1−861.iT−6.43e6T2 |
| 29 | 1−1.66e3iT−2.05e7T2 |
| 31 | 1+4.18e3T+2.86e7T2 |
| 37 | 1−1.45e4T+6.93e7T2 |
| 41 | 1+2.00e4T+1.15e8T2 |
| 43 | 1+5.24e3T+1.47e8T2 |
| 47 | 1+2.16e4iT−2.29e8T2 |
| 53 | 1+1.49e4T+4.18e8T2 |
| 59 | 1+4.24e4iT−7.14e8T2 |
| 61 | 1+3.11e4iT−8.44e8T2 |
| 67 | 1+2.78e4T+1.35e9T2 |
| 71 | 1−4.23e4T+1.80e9T2 |
| 73 | 1+1.17e4iT−2.07e9T2 |
| 79 | 1−6.98e4T+3.07e9T2 |
| 83 | 1+6.45e3T+3.93e9T2 |
| 89 | 1+2.56e4T+5.58e9T2 |
| 97 | 1−1.51e5iT−8.58e9T2 |
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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
−12.01111849326713233366252608296, −10.95287543930087956953689542476, −9.433711677132999338213710325691, −8.426986814726835929080934231098, −7.919343978201733881988276299687, −6.58756314737593498305679988668, −5.43196443524764680544740084551, −3.79536470089855203791602441131, −3.21636302404407496970634896658, −1.82940664296443008607828149098,
1.32122389604748337673496048353, 2.52550865256725532870674391186, 3.60433716391253172123757477085, 4.47041793696328614695262569853, 6.14239880411160770018495813406, 7.29936796933131473106335123276, 8.510549476037181597073523464986, 9.412765549620005320602485278627, 10.49654078174791012693643698352, 11.39991002522366641352963003020