L(s) = 1 | + (−0.533 + 0.845i)2-s + (0.147 − 0.989i)3-s + (−0.430 − 0.902i)4-s + (0.972 − 0.234i)5-s + (0.757 + 0.652i)6-s + (−0.794 − 0.606i)7-s + (0.992 + 0.118i)8-s + (−0.956 − 0.292i)9-s + (−0.320 + 0.947i)10-s + (−0.984 + 0.176i)11-s + (−0.956 + 0.292i)12-s + (0.0296 − 0.999i)13-s + (0.937 − 0.348i)14-s + (−0.0887 − 0.996i)15-s + (−0.630 + 0.776i)16-s + (0.582 − 0.812i)17-s + ⋯ |
L(s) = 1 | + (−0.533 + 0.845i)2-s + (0.147 − 0.989i)3-s + (−0.430 − 0.902i)4-s + (0.972 − 0.234i)5-s + (0.757 + 0.652i)6-s + (−0.794 − 0.606i)7-s + (0.992 + 0.118i)8-s + (−0.956 − 0.292i)9-s + (−0.320 + 0.947i)10-s + (−0.984 + 0.176i)11-s + (−0.956 + 0.292i)12-s + (0.0296 − 0.999i)13-s + (0.937 − 0.348i)14-s + (−0.0887 − 0.996i)15-s + (−0.630 + 0.776i)16-s + (0.582 − 0.812i)17-s + ⋯ |
Λ(s)=(=(107s/2ΓR(s)L(s)(0.431−0.902i)Λ(1−s)
Λ(s)=(=(107s/2ΓR(s)L(s)(0.431−0.902i)Λ(1−s)
Degree: |
1 |
Conductor: |
107
|
Sign: |
0.431−0.902i
|
Analytic conductor: |
0.496905 |
Root analytic conductor: |
0.496905 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ107(36,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 107, (0: ), 0.431−0.902i)
|
Particular Values
L(21) |
≈ |
0.6370485574−0.4016218425i |
L(21) |
≈ |
0.6370485574−0.4016218425i |
L(1) |
≈ |
0.7923731144−0.1688009906i |
L(1) |
≈ |
0.7923731144−0.1688009906i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 107 | 1 |
good | 2 | 1+(−0.533+0.845i)T |
| 3 | 1+(0.147−0.989i)T |
| 5 | 1+(0.972−0.234i)T |
| 7 | 1+(−0.794−0.606i)T |
| 11 | 1+(−0.984+0.176i)T |
| 13 | 1+(0.0296−0.999i)T |
| 17 | 1+(0.582−0.812i)T |
| 19 | 1+(−0.998+0.0592i)T |
| 23 | 1+(0.937+0.348i)T |
| 29 | 1+(0.674−0.737i)T |
| 31 | 1+(0.482+0.875i)T |
| 37 | 1+(0.829−0.558i)T |
| 41 | 1+(−0.861−0.508i)T |
| 43 | 1+(0.972+0.234i)T |
| 47 | 1+(−0.861+0.508i)T |
| 53 | 1+(−0.533−0.845i)T |
| 59 | 1+(0.674+0.737i)T |
| 61 | 1+(−0.794+0.606i)T |
| 67 | 1+(0.992−0.118i)T |
| 71 | 1+(0.147+0.989i)T |
| 73 | 1+(0.375+0.926i)T |
| 79 | 1+(−0.205+0.978i)T |
| 83 | 1+(0.263−0.964i)T |
| 89 | 1+(0.757−0.652i)T |
| 97 | 1+(−0.320+0.947i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−29.39054886719085367835269145594, −28.733120839042818889650315905976, −28.011818138015119380754118985241, −26.65487934031272626415819819798, −25.94315666756777768967566708478, −25.35569565023649197126292574378, −23.238570761311334504671592992, −21.97284065564228268533935518380, −21.471675499052586996336495816203, −20.73991903314572952316835823605, −19.28867086052800907306596963585, −18.540393634797313693180220714606, −17.120706670932665035459823609890, −16.38991982268225222589037164911, −14.97935050216084242400800442570, −13.615047446284294342556363923706, −12.58191993524787835816442035207, −11.03601365950921015084099412104, −10.17052250892682321295893082092, −9.35027456159406090531746432663, −8.39477750030691568109141430026, −6.31505936497330013638623538735, −4.82447759030551080439848112881, −3.23784362683429279955326013127, −2.257738372475846391561349487825,
0.890373353073936187505146783357, 2.66993278530947208305253927419, 5.19711909543686760463144462016, 6.23927454735988086076674388081, 7.260502961617611007629769461971, 8.35013227526222151688619570833, 9.65149579211176037237499961559, 10.61067004830156134072469558387, 12.81266184856926959240977450780, 13.37992746082396930747332747241, 14.43076065790184729892565139526, 15.852584330916337950372902266852, 17.07469259133757434778332715388, 17.75608983531083624189438272278, 18.74073404931388774012262774690, 19.74601387777895930371413569256, 20.90811436084836018363000355923, 22.83125823061708114996021539922, 23.32661529135448526582914221962, 24.59940250933545022478699026281, 25.46921054065563009098611250377, 25.85840572898474232670645612083, 27.21209846831663053316982001104, 28.70876222893575825084316470349, 29.16894482353334422871287871783