L(s) = 1 | + (−0.861 + 0.508i)2-s + (0.937 + 0.348i)3-s + (0.482 − 0.875i)4-s + (−0.998 − 0.0592i)5-s + (−0.984 + 0.176i)6-s + (0.582 − 0.812i)7-s + (0.0296 + 0.999i)8-s + (0.757 + 0.652i)9-s + (0.889 − 0.456i)10-s + (0.674 + 0.737i)11-s + (0.757 − 0.652i)12-s + (0.375 − 0.926i)13-s + (−0.0887 + 0.996i)14-s + (−0.915 − 0.403i)15-s + (−0.533 − 0.845i)16-s + (0.972 + 0.234i)17-s + ⋯ |
L(s) = 1 | + (−0.861 + 0.508i)2-s + (0.937 + 0.348i)3-s + (0.482 − 0.875i)4-s + (−0.998 − 0.0592i)5-s + (−0.984 + 0.176i)6-s + (0.582 − 0.812i)7-s + (0.0296 + 0.999i)8-s + (0.757 + 0.652i)9-s + (0.889 − 0.456i)10-s + (0.674 + 0.737i)11-s + (0.757 − 0.652i)12-s + (0.375 − 0.926i)13-s + (−0.0887 + 0.996i)14-s + (−0.915 − 0.403i)15-s + (−0.533 − 0.845i)16-s + (0.972 + 0.234i)17-s + ⋯ |
Λ(s)=(=(107s/2ΓR(s)L(s)(0.835+0.549i)Λ(1−s)
Λ(s)=(=(107s/2ΓR(s)L(s)(0.835+0.549i)Λ(1−s)
Degree: |
1 |
Conductor: |
107
|
Sign: |
0.835+0.549i
|
Analytic conductor: |
0.496905 |
Root analytic conductor: |
0.496905 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ107(14,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 107, (0: ), 0.835+0.549i)
|
Particular Values
L(21) |
≈ |
0.8633419657+0.2582726637i |
L(21) |
≈ |
0.8633419657+0.2582726637i |
L(1) |
≈ |
0.8911449009+0.2091979000i |
L(1) |
≈ |
0.8911449009+0.2091979000i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 107 | 1 |
good | 2 | 1+(−0.861+0.508i)T |
| 3 | 1+(0.937+0.348i)T |
| 5 | 1+(−0.998−0.0592i)T |
| 7 | 1+(0.582−0.812i)T |
| 11 | 1+(0.674+0.737i)T |
| 13 | 1+(0.375−0.926i)T |
| 17 | 1+(0.972+0.234i)T |
| 19 | 1+(−0.717+0.696i)T |
| 23 | 1+(−0.0887−0.996i)T |
| 29 | 1+(−0.205+0.978i)T |
| 31 | 1+(0.263+0.964i)T |
| 37 | 1+(0.147−0.989i)T |
| 41 | 1+(−0.794−0.606i)T |
| 43 | 1+(−0.998+0.0592i)T |
| 47 | 1+(−0.794+0.606i)T |
| 53 | 1+(−0.861−0.508i)T |
| 59 | 1+(−0.205−0.978i)T |
| 61 | 1+(0.582+0.812i)T |
| 67 | 1+(0.0296−0.999i)T |
| 71 | 1+(0.937−0.348i)T |
| 73 | 1+(−0.956+0.292i)T |
| 79 | 1+(−0.430−0.902i)T |
| 83 | 1+(−0.320+0.947i)T |
| 89 | 1+(−0.984−0.176i)T |
| 97 | 1+(0.889−0.456i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−29.75244209099276382557553994925, −28.221221849259555183571614305282, −27.466850665701619367740085270861, −26.60109928437692560856488196762, −25.60284500056244765546265649312, −24.615989795583764448840881802557, −23.67944289901507339887578344164, −21.802368964181929492360292376368, −21.0167385943986320299297956125, −19.88887859429835470570855321044, −18.93809886042448155833758547748, −18.62720370164514090971603059617, −17.018574281971032708756631148728, −15.74428368089458659657579275610, −14.80296876675989326721555730615, −13.36326953390912457815757516955, −11.86220167313765460061371900481, −11.458823734911026795779843012434, −9.586219429521271832084240592066, −8.57820540305017769549138664530, −7.93402000249816549546707062104, −6.62713918422086665468229760163, −4.08904953439529524681511515370, −2.95794098381527022066430297614, −1.48653297622429575440924865355,
1.494010531897157102693682615336, 3.52860533953620700231919518441, 4.82590221923622177983864427221, 6.92720366766697960688047223848, 7.92739971598855134099998521986, 8.56148176002512797237844235766, 10.07105666353398455758654191723, 10.860795634419125071934150212387, 12.50698433983187814436781663763, 14.393446123516684078107154843207, 14.8129921389250142674006175290, 16.00273725971296493048142846336, 16.92679115578867154822424456959, 18.281307831600135194784857034053, 19.40782022585684661386113745104, 20.16197235333156040425761150773, 20.83150536709116489940720285969, 22.84187898176313826554047014760, 23.73714271211976824205913885901, 24.895279533131967804376264772310, 25.681844929638692692681489757901, 26.82170987698121377670556892785, 27.43418978125446807537487207345, 28.061284758539666789932906197702, 29.97881765003021532830120595527