L(s) = 1 | + (−0.375 + 5.64i)2-s − 6.67·3-s + (−31.7 − 4.24i)4-s + (2.50 − 37.6i)6-s + 38.2i·7-s + (35.8 − 177. i)8-s − 198.·9-s + 491. i·11-s + (211. + 28.3i)12-s − 956.·13-s + (−216. − 14.3i)14-s + (988. + 269. i)16-s − 339. i·17-s + (74.5 − 1.12e3i)18-s − 1.86e3i·19-s + ⋯ |
L(s) = 1 | + (−0.0664 + 0.997i)2-s − 0.428·3-s + (−0.991 − 0.132i)4-s + (0.0284 − 0.427i)6-s + 0.295i·7-s + (0.198 − 0.980i)8-s − 0.816·9-s + 1.22i·11-s + (0.424 + 0.0567i)12-s − 1.56·13-s + (−0.294 − 0.0196i)14-s + (0.964 + 0.262i)16-s − 0.285i·17-s + (0.0542 − 0.814i)18-s − 1.18i·19-s + ⋯ |
Λ(s)=(=(200s/2ΓC(s)L(s)(0.965−0.261i)Λ(6−s)
Λ(s)=(=(200s/2ΓC(s+5/2)L(s)(0.965−0.261i)Λ(1−s)
Degree: |
2 |
Conductor: |
200
= 23⋅52
|
Sign: |
0.965−0.261i
|
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), 0.965−0.261i)
|
Particular Values
L(3) |
≈ |
0.7591383730 |
L(21) |
≈ |
0.7591383730 |
L(27) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.375−5.64i)T |
| 5 | 1 |
good | 3 | 1+6.67T+243T2 |
| 7 | 1−38.2iT−1.68e4T2 |
| 11 | 1−491.iT−1.61e5T2 |
| 13 | 1+956.T+3.71e5T2 |
| 17 | 1+339.iT−1.41e6T2 |
| 19 | 1+1.86e3iT−2.47e6T2 |
| 23 | 1+1.99e3iT−6.43e6T2 |
| 29 | 1−3.57e3iT−2.05e7T2 |
| 31 | 1−7.71e3T+2.86e7T2 |
| 37 | 1+2.83e3T+6.93e7T2 |
| 41 | 1−1.06e4T+1.15e8T2 |
| 43 | 1+2.05e4T+1.47e8T2 |
| 47 | 1−756.iT−2.29e8T2 |
| 53 | 1−3.16e4T+4.18e8T2 |
| 59 | 1−4.91e3iT−7.14e8T2 |
| 61 | 1+2.14e4iT−8.44e8T2 |
| 67 | 1−6.81e3T+1.35e9T2 |
| 71 | 1+1.11e4T+1.80e9T2 |
| 73 | 1−7.30e3iT−2.07e9T2 |
| 79 | 1−2.35e4T+3.07e9T2 |
| 83 | 1−2.37e4T+3.93e9T2 |
| 89 | 1−1.25e5T+5.58e9T2 |
| 97 | 1+1.26e5iT−8.58e9T2 |
show more | |
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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
−11.87415535647846747253727649367, −10.39865433192023626712907947567, −9.496023013761084664166526700972, −8.544193261175441980609889723112, −7.32156328774341323869785147008, −6.58429690226209908800585505431, −5.21650345702515544607824763872, −4.63442241584018000054133859795, −2.59779569765968550260995714071, −0.37183059294762901705913955112,
0.78445078425356259116948085501, 2.48224354329757778392844375436, 3.67012567046756779811012318896, 5.05992529777862055400929135655, 6.02766796261097661736438691968, 7.76408294899487113054827498475, 8.665127014216867801376370476799, 9.875601006756145272903865277943, 10.59580864176228426389987983193, 11.72241866606345609770693659914