L(s) = 1 | + (0.998 − 0.725i)2-s + (0.112 + 0.346i)3-s + (−0.147 + 0.453i)4-s + (0.363 + 0.264i)6-s + (−0.798 + 2.45i)7-s + (0.944 + 2.90i)8-s + (2.31 − 1.68i)9-s + (3.12 + 1.12i)11-s − 0.173·12-s + (2.23 − 1.62i)13-s + (0.985 + 3.03i)14-s + (2.27 + 1.65i)16-s + (−3.11 − 2.26i)17-s + (1.09 − 3.36i)18-s + (−0.0857 − 0.264i)19-s + ⋯ |
L(s) = 1 | + (0.705 − 0.512i)2-s + (0.0649 + 0.199i)3-s + (−0.0737 + 0.226i)4-s + (0.148 + 0.107i)6-s + (−0.301 + 0.929i)7-s + (0.333 + 1.02i)8-s + (0.773 − 0.561i)9-s + (0.940 + 0.339i)11-s − 0.0501·12-s + (0.619 − 0.449i)13-s + (0.263 + 0.810i)14-s + (0.569 + 0.414i)16-s + (−0.755 − 0.549i)17-s + (0.257 − 0.793i)18-s + (−0.0196 − 0.0605i)19-s + ⋯ |
Λ(s)=(=(275s/2ΓC(s)L(s)(0.966−0.255i)Λ(2−s)
Λ(s)=(=(275s/2ΓC(s+1/2)L(s)(0.966−0.255i)Λ(1−s)
Degree: |
2 |
Conductor: |
275
= 52⋅11
|
Sign: |
0.966−0.255i
|
Analytic conductor: |
2.19588 |
Root analytic conductor: |
1.48185 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ275(201,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 275, ( :1/2), 0.966−0.255i)
|
Particular Values
L(1) |
≈ |
1.83350+0.238458i |
L(21) |
≈ |
1.83350+0.238458i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 11 | 1+(−3.12−1.12i)T |
good | 2 | 1+(−0.998+0.725i)T+(0.618−1.90i)T2 |
| 3 | 1+(−0.112−0.346i)T+(−2.42+1.76i)T2 |
| 7 | 1+(0.798−2.45i)T+(−5.66−4.11i)T2 |
| 13 | 1+(−2.23+1.62i)T+(4.01−12.3i)T2 |
| 17 | 1+(3.11+2.26i)T+(5.25+16.1i)T2 |
| 19 | 1+(0.0857+0.264i)T+(−15.3+11.1i)T2 |
| 23 | 1+8.40T+23T2 |
| 29 | 1+(−1.02+3.16i)T+(−23.4−17.0i)T2 |
| 31 | 1+(0.456−0.331i)T+(9.57−29.4i)T2 |
| 37 | 1+(0.161−0.497i)T+(−29.9−21.7i)T2 |
| 41 | 1+(1.57+4.86i)T+(−33.1+24.0i)T2 |
| 43 | 1−2.54T+43T2 |
| 47 | 1+(1.52+4.68i)T+(−38.0+27.6i)T2 |
| 53 | 1+(−7.05+5.12i)T+(16.3−50.4i)T2 |
| 59 | 1+(−2.31+7.13i)T+(−47.7−34.6i)T2 |
| 61 | 1+(11.4+8.33i)T+(18.8+58.0i)T2 |
| 67 | 1−3.20T+67T2 |
| 71 | 1+(−6.79−4.93i)T+(21.9+67.5i)T2 |
| 73 | 1+(4.02−12.3i)T+(−59.0−42.9i)T2 |
| 79 | 1+(7.85−5.70i)T+(24.4−75.1i)T2 |
| 83 | 1+(2.66+1.93i)T+(25.6+78.9i)T2 |
| 89 | 1−2.48T+89T2 |
| 97 | 1+(−8.81+6.40i)T+(29.9−92.2i)T2 |
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
−12.08314533885069181050020716240, −11.35262886041007331558282788418, −10.05337690815622198534033182630, −9.128241804000805848108522423494, −8.245200541027073197856584745754, −6.83688012300393925175593408233, −5.72483662127444157633965721954, −4.37938681863028102427488082150, −3.57388536955125010835977295478, −2.14902997725055210749328661247,
1.45351825844076690202510518963, 3.88441716435767249506435041818, 4.42742872416721682266996871926, 6.02326916224367815198507408506, 6.68823582228389188294216155422, 7.64152279728711459882958843390, 8.987628839032050229268415398455, 10.11205564788360576706302770740, 10.76413705919457427357633848919, 12.07178860895747786266278524650