L(s) = 1 | + (−0.994 − 0.104i)2-s + (−0.965 − 0.258i)3-s + (0.978 + 0.207i)4-s + (0.933 + 0.358i)6-s + (0.156 − 0.987i)7-s + (−0.951 − 0.309i)8-s + (0.866 + 0.5i)9-s + (0.453 + 0.891i)11-s + (−0.891 − 0.453i)12-s + (0.358 − 0.933i)13-s + (−0.258 + 0.965i)14-s + (0.913 + 0.406i)16-s + (0.838 + 0.544i)17-s + (−0.809 − 0.587i)18-s + (−0.406 + 0.913i)21-s + (−0.358 − 0.933i)22-s + ⋯ |
L(s) = 1 | + (−0.994 − 0.104i)2-s + (−0.965 − 0.258i)3-s + (0.978 + 0.207i)4-s + (0.933 + 0.358i)6-s + (0.156 − 0.987i)7-s + (−0.951 − 0.309i)8-s + (0.866 + 0.5i)9-s + (0.453 + 0.891i)11-s + (−0.891 − 0.453i)12-s + (0.358 − 0.933i)13-s + (−0.258 + 0.965i)14-s + (0.913 + 0.406i)16-s + (0.838 + 0.544i)17-s + (−0.809 − 0.587i)18-s + (−0.406 + 0.913i)21-s + (−0.358 − 0.933i)22-s + ⋯ |
Λ(s)=(=(3895s/2ΓR(s)L(s)(0.231−0.972i)Λ(1−s)
Λ(s)=(=(3895s/2ΓR(s)L(s)(0.231−0.972i)Λ(1−s)
Degree: |
1 |
Conductor: |
3895
= 5⋅19⋅41
|
Sign: |
0.231−0.972i
|
Analytic conductor: |
18.0883 |
Root analytic conductor: |
18.0883 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3895(1129,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 3895, (0: ), 0.231−0.972i)
|
Particular Values
L(21) |
≈ |
0.7376302701−0.5825382466i |
L(21) |
≈ |
0.7376302701−0.5825382466i |
L(1) |
≈ |
0.6154276176−0.1766258810i |
L(1) |
≈ |
0.6154276176−0.1766258810i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 19 | 1 |
| 41 | 1 |
good | 2 | 1+(−0.994−0.104i)T |
| 3 | 1+(−0.965−0.258i)T |
| 7 | 1+(0.156−0.987i)T |
| 11 | 1+(0.453+0.891i)T |
| 13 | 1+(0.358−0.933i)T |
| 17 | 1+(0.838+0.544i)T |
| 23 | 1+(0.913−0.406i)T |
| 29 | 1+(0.838−0.544i)T |
| 31 | 1+(0.309−0.951i)T |
| 37 | 1+(0.309+0.951i)T |
| 43 | 1+(0.994+0.104i)T |
| 47 | 1+(−0.933−0.358i)T |
| 53 | 1+(0.838−0.544i)T |
| 59 | 1+(0.104−0.994i)T |
| 61 | 1+(0.994−0.104i)T |
| 67 | 1+(−0.544−0.838i)T |
| 71 | 1+(0.544−0.838i)T |
| 73 | 1+(−0.866+0.5i)T |
| 79 | 1+(−0.965−0.258i)T |
| 83 | 1−T |
| 89 | 1+(0.777+0.629i)T |
| 97 | 1+(−0.998+0.0523i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−18.64606165043932508424582524705, −17.95962053063652876651475706858, −17.38843644614429448993898734359, −16.58496100558791071547046865435, −16.103672061962525252741531316681, −15.72946499617319133958335204148, −14.70505949050479226181608703480, −14.18660760539134495290807814276, −12.92722989028684690362170831974, −12.072134492984250407523336716827, −11.66132028995449572430978079546, −11.13074371456695336635435174792, −10.403506500478585873476355105281, −9.56329405461297652034284705997, −8.9604089942121608564913297498, −8.48432664275618470342666580790, −7.30629308917810733111937846682, −6.77811431346272987415263090288, −5.88702858261765264062705422308, −5.56768782063447049436689717870, −4.57868754952092562120935038036, −3.43478654352096332208968825951, −2.651544689352273280238415947324, −1.45246068904458023113658232428, −0.92120586964272113340790750725,
0.62174960491229469688316981042, 1.148132664608076206952438866846, 2.00457945040929160508300842611, 3.138263201644072887272098310089, 4.07990479734661433890333026148, 4.90267376119409977056418046952, 5.89995225097616232470074327869, 6.54909617520459017334817994557, 7.19630216304417083382519111726, 7.83891743631617124964606385424, 8.430437598314911183893740157602, 9.76199099015583469994609846129, 10.03086708268017448951282457923, 10.716380331966357530816727540940, 11.34898044149104556317564482413, 12.02197388383507400718431441551, 12.76586264892085160288558644665, 13.27955233497808032091471344978, 14.48402455051558672392552497509, 15.1929404474201990125307157921, 15.88524593631898673385758736332, 16.7996605619405645251032778627, 17.026544786073101566419990136219, 17.68024712045264944274660650580, 18.15923436784966673964704582614