L(s) = 1 | + (0.698 − 0.715i)2-s + (−0.0249 − 0.999i)4-s + (0.797 − 0.603i)5-s + (−0.733 − 0.680i)8-s + (0.124 − 0.992i)10-s + (0.900 − 0.433i)11-s + (−0.995 + 0.0995i)13-s + (−0.998 + 0.0498i)16-s + (−0.878 + 0.478i)17-s + (−0.623 − 0.781i)20-s + (0.318 − 0.947i)22-s + (0.853 − 0.521i)23-s + (0.270 − 0.962i)25-s + (−0.623 + 0.781i)26-s + (0.980 + 0.198i)29-s + ⋯ |
L(s) = 1 | + (0.698 − 0.715i)2-s + (−0.0249 − 0.999i)4-s + (0.797 − 0.603i)5-s + (−0.733 − 0.680i)8-s + (0.124 − 0.992i)10-s + (0.900 − 0.433i)11-s + (−0.995 + 0.0995i)13-s + (−0.998 + 0.0498i)16-s + (−0.878 + 0.478i)17-s + (−0.623 − 0.781i)20-s + (0.318 − 0.947i)22-s + (0.853 − 0.521i)23-s + (0.270 − 0.962i)25-s + (−0.623 + 0.781i)26-s + (0.980 + 0.198i)29-s + ⋯ |
Λ(s)=(=(2793s/2ΓR(s)L(s)(−0.963−0.268i)Λ(1−s)
Λ(s)=(=(2793s/2ΓR(s)L(s)(−0.963−0.268i)Λ(1−s)
Degree: |
1 |
Conductor: |
2793
= 3⋅72⋅19
|
Sign: |
−0.963−0.268i
|
Analytic conductor: |
12.9706 |
Root analytic conductor: |
12.9706 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2793(452,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2793, (0: ), −0.963−0.268i)
|
Particular Values
L(21) |
≈ |
0.3423685596−2.507460673i |
L(21) |
≈ |
0.3423685596−2.507460673i |
L(1) |
≈ |
1.215173907−1.094650517i |
L(1) |
≈ |
1.215173907−1.094650517i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 7 | 1 |
| 19 | 1 |
good | 2 | 1+(0.698−0.715i)T |
| 5 | 1+(0.797−0.603i)T |
| 11 | 1+(0.900−0.433i)T |
| 13 | 1+(−0.995+0.0995i)T |
| 17 | 1+(−0.878+0.478i)T |
| 23 | 1+(0.853−0.521i)T |
| 29 | 1+(0.980+0.198i)T |
| 31 | 1+(0.5−0.866i)T |
| 37 | 1+(0.988−0.149i)T |
| 41 | 1+(−0.124−0.992i)T |
| 43 | 1+(−0.998+0.0498i)T |
| 47 | 1+(0.583+0.811i)T |
| 53 | 1+(−0.0249−0.999i)T |
| 59 | 1+(−0.998+0.0498i)T |
| 61 | 1+(−0.318−0.947i)T |
| 67 | 1+(0.939+0.342i)T |
| 71 | 1+(−0.661−0.749i)T |
| 73 | 1+(−0.411−0.911i)T |
| 79 | 1+(−0.173+0.984i)T |
| 83 | 1+(−0.0747−0.997i)T |
| 89 | 1+(−0.969+0.246i)T |
| 97 | 1+(−0.766−0.642i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.735827393654214572419565211, −18.61050984870820045641342701451, −17.87859100813179268408081896721, −17.27985926286564099733643985761, −16.89672100458898339143453975931, −15.88979064847963104946308990716, −15.02608472968311629440611797477, −14.74858317735971788472979820090, −13.853234377706893514101876561454, −13.45532584660062766459776150741, −12.55050261495307521038073822016, −11.84476352443279635747990437955, −11.153496422324754153904371987790, −10.099458827952214433270744122735, −9.39852877489081373881132498702, −8.71823244035882049415396885465, −7.65913798240669212084547990132, −6.80427477468414847672853528617, −6.6385708535091830802985881687, −5.60040935511478559692554394771, −4.842309309475478059759013234048, −4.20380157573138844712953659220, −2.98492317898736441975778003605, −2.58610282523337214339472314747, −1.42213607539465770380445362680,
0.58255376342132951719543504240, 1.527710755414235855612016201184, 2.30654459060206674734208098728, 3.057049789185571167016172445853, 4.24239255985213798262716513994, 4.666658976883466754778209950003, 5.52872305694695974910401648114, 6.3385156053187099230313291521, 6.83450584901840886699138668288, 8.25121053536570841778621810917, 9.09520654766890430277189426548, 9.549440982575412863967935540360, 10.371363268775478093265403459372, 11.09424178900588987477487147180, 11.920715921514961606786474602, 12.521953658202837870737824015136, 13.18513073511158327593990651529, 13.83820493489101401130417029773, 14.48348197505905280781282280705, 15.11278208360697537211069022586, 16.0326344355768360707546154465, 16.963770999427403660028049833, 17.37812225314010070491998602024, 18.30682662352397637414954056454, 19.15585540002637464131699708274