L(s) = 1 | + 8.19e3·2-s − 9.70e4·3-s + 5.03e7·4-s − 4.88e8·5-s − 7.95e8·6-s − 1.61e10·7-s + 2.74e11·8-s − 1.24e12·9-s − 4.00e12·10-s + 1.44e13·11-s − 4.88e12·12-s + 9.34e13·13-s − 1.32e14·14-s + 4.74e13·15-s + 1.40e15·16-s + 4.99e14·17-s − 1.01e16·18-s − 3.83e15·19-s − 2.45e16·20-s + 1.56e15·21-s + 1.18e17·22-s + 1.69e17·23-s − 2.66e16·24-s + 1.78e17·25-s + 7.65e17·26-s + 1.59e17·27-s − 8.12e17·28-s + ⋯ |
L(s) = 1 | + 1.41·2-s − 0.105·3-s + 3/2·4-s − 0.894·5-s − 0.149·6-s − 0.440·7-s + 1.41·8-s − 1.46·9-s − 1.26·10-s + 1.38·11-s − 0.158·12-s + 1.11·13-s − 0.623·14-s + 0.0943·15-s + 5/4·16-s + 0.207·17-s − 2.07·18-s − 0.397·19-s − 1.34·20-s + 0.0464·21-s + 1.95·22-s + 1.61·23-s − 0.149·24-s + 3/5·25-s + 1.57·26-s + 0.205·27-s − 0.660·28-s + ⋯ |
Λ(s)=(=(100s/2ΓC(s)2L(s)Λ(26−s)
Λ(s)=(=(100s/2ΓC(s+25/2)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
100
= 22⋅52
|
Sign: |
1
|
Analytic conductor: |
1568.13 |
Root analytic conductor: |
6.29282 |
Motivic weight: |
25 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(4, 100, ( :25/2,25/2), 1)
|
Particular Values
L(13) |
≈ |
6.958534474 |
L(21) |
≈ |
6.958534474 |
L(227) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1
L(s)=p∏ j=1∏4(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−14.87198458028148213054408099432, −14.56420477160205827152756985243, −13.79238779399364083481388158639, −13.17722026568140347982586287076, −12.10701551749495798808679016525, −12.00045798559841793275080789727, −10.92490040001171314166845916862, −10.90507687333009033194744043577, −9.150923791724951314718736346031, −8.674934187930878223447820595810, −7.59939937718354106091567344807, −6.77611697309666041293193480564, −6.03026217565657804221099389387, −5.61075416557292730241010202054, −4.20830786797002826222917943676, −4.13850937697760931376022353106, −2.94693380386204346244762430629, −2.79622925444236206197409075218, −1.23991409486712841662795472706, −0.67250797503421422148198550273,
0.67250797503421422148198550273, 1.23991409486712841662795472706, 2.79622925444236206197409075218, 2.94693380386204346244762430629, 4.13850937697760931376022353106, 4.20830786797002826222917943676, 5.61075416557292730241010202054, 6.03026217565657804221099389387, 6.77611697309666041293193480564, 7.59939937718354106091567344807, 8.674934187930878223447820595810, 9.150923791724951314718736346031, 10.90507687333009033194744043577, 10.92490040001171314166845916862, 12.00045798559841793275080789727, 12.10701551749495798808679016525, 13.17722026568140347982586287076, 13.79238779399364083481388158639, 14.56420477160205827152756985243, 14.87198458028148213054408099432