L(s) = 1 | + (−0.841 − 0.540i)2-s + (0.415 + 0.909i)4-s + (0.654 − 0.755i)5-s + (0.841 + 0.540i)7-s + (0.142 − 0.989i)8-s + (−0.959 + 0.281i)10-s + (0.654 − 0.755i)11-s + (−0.142 − 0.989i)13-s + (−0.415 − 0.909i)14-s + (−0.654 + 0.755i)16-s + (−0.415 + 0.909i)17-s + (0.841 − 0.540i)19-s + (0.959 + 0.281i)20-s + (−0.959 + 0.281i)22-s + (0.959 + 0.281i)23-s + ⋯ |
L(s) = 1 | + (−0.841 − 0.540i)2-s + (0.415 + 0.909i)4-s + (0.654 − 0.755i)5-s + (0.841 + 0.540i)7-s + (0.142 − 0.989i)8-s + (−0.959 + 0.281i)10-s + (0.654 − 0.755i)11-s + (−0.142 − 0.989i)13-s + (−0.415 − 0.909i)14-s + (−0.654 + 0.755i)16-s + (−0.415 + 0.909i)17-s + (0.841 − 0.540i)19-s + (0.959 + 0.281i)20-s + (−0.959 + 0.281i)22-s + (0.959 + 0.281i)23-s + ⋯ |
Λ(s)=(=(201s/2ΓR(s+1)L(s)(0.206−0.978i)Λ(1−s)
Λ(s)=(=(201s/2ΓR(s+1)L(s)(0.206−0.978i)Λ(1−s)
Degree: |
1 |
Conductor: |
201
= 3⋅67
|
Sign: |
0.206−0.978i
|
Analytic conductor: |
21.6004 |
Root analytic conductor: |
21.6004 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ201(131,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 201, (1: ), 0.206−0.978i)
|
Particular Values
L(21) |
≈ |
1.251252733−1.014526502i |
L(21) |
≈ |
1.251252733−1.014526502i |
L(1) |
≈ |
0.9163069849−0.3694589882i |
L(1) |
≈ |
0.9163069849−0.3694589882i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 67 | 1 |
good | 2 | 1+(−0.841−0.540i)T |
| 5 | 1+(0.654−0.755i)T |
| 7 | 1+(0.841+0.540i)T |
| 11 | 1+(0.654−0.755i)T |
| 13 | 1+(−0.142−0.989i)T |
| 17 | 1+(−0.415+0.909i)T |
| 19 | 1+(0.841−0.540i)T |
| 23 | 1+(0.959+0.281i)T |
| 29 | 1−T |
| 31 | 1+(−0.142+0.989i)T |
| 37 | 1+T |
| 41 | 1+(−0.415+0.909i)T |
| 43 | 1+(0.415−0.909i)T |
| 47 | 1+(0.959+0.281i)T |
| 53 | 1+(−0.415−0.909i)T |
| 59 | 1+(0.142−0.989i)T |
| 61 | 1+(−0.654−0.755i)T |
| 71 | 1+(−0.415−0.909i)T |
| 73 | 1+(−0.654−0.755i)T |
| 79 | 1+(−0.142−0.989i)T |
| 83 | 1+(0.654−0.755i)T |
| 89 | 1+(0.959−0.281i)T |
| 97 | 1+T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−26.79139584235165663814946334031, −26.04482907098026450452557196721, −25.01235865098829272583714065752, −24.356157296837546546198280237364, −23.17735917083518996554133548123, −22.29775336685322615460111075908, −20.89074477590760459563491694821, −20.17731031696701794455480714450, −18.85442558518442532882097996196, −18.17764174899544173524682336095, −17.26838725454406375133945367301, −16.592793857487905565244142275381, −15.10968542507951390540775599156, −14.42658303736794698508561311092, −13.656810064702328759045186461136, −11.67378352412692441490918195875, −10.94214478271723522429100413944, −9.76117228156964464115272125352, −9.09254057900303407124734274155, −7.45065991583612781731954451467, −6.99982673341680718519533328270, −5.70777348402986167638949231483, −4.40230892577804797222208872461, −2.35901732195398109399799306382, −1.271164906245596898452449183771,
0.84549039482581205524580869001, 1.87657896101624303304854787689, 3.27708056062769572391082211674, 4.90405359421030576417874598437, 6.098398938448225418810209537505, 7.69230210973896305599551076829, 8.70168729864453523755797554646, 9.29919347822865410557468886275, 10.63219618644768741824091805508, 11.51831787614300795460179538080, 12.58484947924865636095569486641, 13.47312784797919571133088828201, 14.916897643788863457618295469000, 16.09625598328348078563083180316, 17.21927743056350268739094725541, 17.6657762060668947629476689772, 18.742492284966106527975404689305, 19.88037681024035012472814532308, 20.59844618343276859297284300936, 21.6238590244748210848507265132, 22.09942157681608952598453594880, 23.99647411648541062958936139874, 24.82990119471810695101736487778, 25.36929103081811845694546253958, 26.728010867675172498610911977236