Properties

Label 1815.2.c.j.364.13
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1815,2,Mod(364,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1815.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.13
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.j.364.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.288813i q^{2} -1.00000i q^{3} +1.91659 q^{4} +(-0.407156 - 2.19869i) q^{5} +0.288813 q^{6} +3.66740i q^{7} +1.13116i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+0.288813i q^{2} -1.00000i q^{3} +1.91659 q^{4} +(-0.407156 - 2.19869i) q^{5} +0.288813 q^{6} +3.66740i q^{7} +1.13116i q^{8} -1.00000 q^{9} +(0.635009 - 0.117592i) q^{10} -1.91659i q^{12} +4.82569i q^{13} -1.05919 q^{14} +(-2.19869 + 0.407156i) q^{15} +3.50648 q^{16} -3.84013i q^{17} -0.288813i q^{18} +6.96183 q^{19} +(-0.780351 - 4.21397i) q^{20} +3.66740 q^{21} -1.20633i q^{23} +1.13116 q^{24} +(-4.66845 + 1.79042i) q^{25} -1.39372 q^{26} +1.00000i q^{27} +7.02890i q^{28} -4.94672 q^{29} +(-0.117592 - 0.635009i) q^{30} +7.36932 q^{31} +3.27504i q^{32} +1.10908 q^{34} +(8.06347 - 1.49321i) q^{35} -1.91659 q^{36} +2.38692i q^{37} +2.01066i q^{38} +4.82569 q^{39} +(2.48707 - 0.460559i) q^{40} +4.30563 q^{41} +1.05919i q^{42} +0.772454i q^{43} +(0.407156 + 2.19869i) q^{45} +0.348403 q^{46} +6.47068i q^{47} -3.50648i q^{48} -6.44984 q^{49} +(-0.517096 - 1.34831i) q^{50} -3.84013 q^{51} +9.24885i q^{52} +10.7562i q^{53} -0.288813 q^{54} -4.14842 q^{56} -6.96183i q^{57} -1.42868i q^{58} +14.4979 q^{59} +(-4.21397 + 0.780351i) q^{60} -1.83091 q^{61} +2.12835i q^{62} -3.66740i q^{63} +6.06709 q^{64} +(10.6102 - 1.96481i) q^{65} -6.10784i q^{67} -7.35995i q^{68} -1.20633 q^{69} +(0.431257 + 2.32883i) q^{70} -3.29108 q^{71} -1.13116i q^{72} +0.191521i q^{73} -0.689373 q^{74} +(1.79042 + 4.66845i) q^{75} +13.3429 q^{76} +1.39372i q^{78} +3.15994 q^{79} +(-1.42769 - 7.70965i) q^{80} +1.00000 q^{81} +1.24352i q^{82} +1.53041i q^{83} +7.02890 q^{84} +(-8.44325 + 1.56354i) q^{85} -0.223095 q^{86} +4.94672i q^{87} +3.04594 q^{89} +(-0.635009 + 0.117592i) q^{90} -17.6977 q^{91} -2.31204i q^{92} -7.36932i q^{93} -1.86882 q^{94} +(-2.83455 - 15.3069i) q^{95} +3.27504 q^{96} -13.7770i q^{97} -1.86280i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.288813i 0.204221i 0.994773 + 0.102111i \(0.0325596\pi\)
−0.994773 + 0.102111i \(0.967440\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.91659 0.958294
\(5\) −0.407156 2.19869i −0.182086 0.983283i
\(6\) 0.288813 0.117907
\(7\) 3.66740i 1.38615i 0.720867 + 0.693074i \(0.243744\pi\)
−0.720867 + 0.693074i \(0.756256\pi\)
\(8\) 1.13116i 0.399926i
\(9\) −1.00000 −0.333333
\(10\) 0.635009 0.117592i 0.200807 0.0371859i
\(11\) 0 0
\(12\) 1.91659i 0.553271i
\(13\) 4.82569i 1.33840i 0.743080 + 0.669202i \(0.233364\pi\)
−0.743080 + 0.669202i \(0.766636\pi\)
\(14\) −1.05919 −0.283081
\(15\) −2.19869 + 0.407156i −0.567698 + 0.105127i
\(16\) 3.50648 0.876620
\(17\) 3.84013i 0.931369i −0.884951 0.465685i \(-0.845808\pi\)
0.884951 0.465685i \(-0.154192\pi\)
\(18\) 0.288813i 0.0680738i
\(19\) 6.96183 1.59715 0.798576 0.601894i \(-0.205587\pi\)
0.798576 + 0.601894i \(0.205587\pi\)
\(20\) −0.780351 4.21397i −0.174492 0.942273i
\(21\) 3.66740 0.800293
\(22\) 0 0
\(23\) 1.20633i 0.251537i −0.992060 0.125769i \(-0.959860\pi\)
0.992060 0.125769i \(-0.0401397\pi\)
\(24\) 1.13116 0.230897
\(25\) −4.66845 + 1.79042i −0.933689 + 0.358084i
\(26\) −1.39372 −0.273331
\(27\) 1.00000i 0.192450i
\(28\) 7.02890i 1.32834i
\(29\) −4.94672 −0.918583 −0.459292 0.888286i \(-0.651897\pi\)
−0.459292 + 0.888286i \(0.651897\pi\)
\(30\) −0.117592 0.635009i −0.0214693 0.115936i
\(31\) 7.36932 1.32357 0.661784 0.749694i \(-0.269800\pi\)
0.661784 + 0.749694i \(0.269800\pi\)
\(32\) 3.27504i 0.578950i
\(33\) 0 0
\(34\) 1.10908 0.190206
\(35\) 8.06347 1.49321i 1.36297 0.252398i
\(36\) −1.91659 −0.319431
\(37\) 2.38692i 0.392407i 0.980563 + 0.196204i \(0.0628614\pi\)
−0.980563 + 0.196204i \(0.937139\pi\)
\(38\) 2.01066i 0.326173i
\(39\) 4.82569 0.772728
\(40\) 2.48707 0.460559i 0.393240 0.0728208i
\(41\) 4.30563 0.672427 0.336213 0.941786i \(-0.390854\pi\)
0.336213 + 0.941786i \(0.390854\pi\)
\(42\) 1.05919i 0.163437i
\(43\) 0.772454i 0.117798i 0.998264 + 0.0588990i \(0.0187590\pi\)
−0.998264 + 0.0588990i \(0.981241\pi\)
\(44\) 0 0
\(45\) 0.407156 + 2.19869i 0.0606953 + 0.327761i
\(46\) 0.348403 0.0513693
\(47\) 6.47068i 0.943846i 0.881640 + 0.471923i \(0.156440\pi\)
−0.881640 + 0.471923i \(0.843560\pi\)
\(48\) 3.50648i 0.506117i
\(49\) −6.44984 −0.921405
\(50\) −0.517096 1.34831i −0.0731284 0.190679i
\(51\) −3.84013 −0.537726
\(52\) 9.24885i 1.28258i
\(53\) 10.7562i 1.47748i 0.673989 + 0.738741i \(0.264580\pi\)
−0.673989 + 0.738741i \(0.735420\pi\)
\(54\) −0.288813 −0.0393024
\(55\) 0 0
\(56\) −4.14842 −0.554356
\(57\) 6.96183i 0.922116i
\(58\) 1.42868i 0.187594i
\(59\) 14.4979 1.88746 0.943730 0.330717i \(-0.107291\pi\)
0.943730 + 0.330717i \(0.107291\pi\)
\(60\) −4.21397 + 0.780351i −0.544022 + 0.100743i
\(61\) −1.83091 −0.234424 −0.117212 0.993107i \(-0.537396\pi\)
−0.117212 + 0.993107i \(0.537396\pi\)
\(62\) 2.12835i 0.270301i
\(63\) 3.66740i 0.462049i
\(64\) 6.06709 0.758386
\(65\) 10.6102 1.96481i 1.31603 0.243705i
\(66\) 0 0
\(67\) 6.10784i 0.746191i −0.927793 0.373096i \(-0.878296\pi\)
0.927793 0.373096i \(-0.121704\pi\)
\(68\) 7.35995i 0.892525i
\(69\) −1.20633 −0.145225
\(70\) 0.431257 + 2.32883i 0.0515451 + 0.278349i
\(71\) −3.29108 −0.390579 −0.195289 0.980746i \(-0.562565\pi\)
−0.195289 + 0.980746i \(0.562565\pi\)
\(72\) 1.13116i 0.133309i
\(73\) 0.191521i 0.0224158i 0.999937 + 0.0112079i \(0.00356767\pi\)
−0.999937 + 0.0112079i \(0.996432\pi\)
\(74\) −0.689373 −0.0801380
\(75\) 1.79042 + 4.66845i 0.206740 + 0.539066i
\(76\) 13.3429 1.53054
\(77\) 0 0
\(78\) 1.39372i 0.157808i
\(79\) 3.15994 0.355522 0.177761 0.984074i \(-0.443115\pi\)
0.177761 + 0.984074i \(0.443115\pi\)
\(80\) −1.42769 7.70965i −0.159620 0.861965i
\(81\) 1.00000 0.111111
\(82\) 1.24352i 0.137324i
\(83\) 1.53041i 0.167985i 0.996466 + 0.0839923i \(0.0267671\pi\)
−0.996466 + 0.0839923i \(0.973233\pi\)
\(84\) 7.02890 0.766915
\(85\) −8.44325 + 1.56354i −0.915799 + 0.169589i
\(86\) −0.223095 −0.0240569
\(87\) 4.94672i 0.530344i
\(88\) 0 0
\(89\) 3.04594 0.322869 0.161434 0.986883i \(-0.448388\pi\)
0.161434 + 0.986883i \(0.448388\pi\)
\(90\) −0.635009 + 0.117592i −0.0669358 + 0.0123953i
\(91\) −17.6977 −1.85523
\(92\) 2.31204i 0.241046i
\(93\) 7.36932i 0.764163i
\(94\) −1.86882 −0.192754
\(95\) −2.83455 15.3069i −0.290819 1.57045i
\(96\) 3.27504 0.334257
\(97\) 13.7770i 1.39885i −0.714708 0.699423i \(-0.753440\pi\)
0.714708 0.699423i \(-0.246560\pi\)
\(98\) 1.86280i 0.188171i
\(99\) 0 0
\(100\) −8.94749 + 3.43149i −0.894749 + 0.343149i
\(101\) −4.65928 −0.463616 −0.231808 0.972762i \(-0.574464\pi\)
−0.231808 + 0.972762i \(0.574464\pi\)
\(102\) 1.10908i 0.109815i
\(103\) 9.81701i 0.967299i −0.875262 0.483649i \(-0.839311\pi\)
0.875262 0.483649i \(-0.160689\pi\)
\(104\) −5.45863 −0.535262
\(105\) −1.49321 8.06347i −0.145722 0.786914i
\(106\) −3.10654 −0.301734
\(107\) 11.8016i 1.14090i −0.821331 0.570452i \(-0.806768\pi\)
0.821331 0.570452i \(-0.193232\pi\)
\(108\) 1.91659i 0.184424i
\(109\) 10.4450 1.00045 0.500226 0.865895i \(-0.333250\pi\)
0.500226 + 0.865895i \(0.333250\pi\)
\(110\) 0 0
\(111\) 2.38692 0.226556
\(112\) 12.8597i 1.21513i
\(113\) 12.8654i 1.21028i −0.796120 0.605139i \(-0.793118\pi\)
0.796120 0.605139i \(-0.206882\pi\)
\(114\) 2.01066 0.188316
\(115\) −2.65234 + 0.491165i −0.247332 + 0.0458014i
\(116\) −9.48082 −0.880272
\(117\) 4.82569i 0.446135i
\(118\) 4.18717i 0.385460i
\(119\) 14.0833 1.29102
\(120\) −0.460559 2.48707i −0.0420431 0.227037i
\(121\) 0 0
\(122\) 0.528791i 0.0478745i
\(123\) 4.30563i 0.388226i
\(124\) 14.1239 1.26837
\(125\) 5.83736 + 9.53547i 0.522109 + 0.852879i
\(126\) 1.05919 0.0943604
\(127\) 0.185919i 0.0164977i −0.999966 0.00824884i \(-0.997374\pi\)
0.999966 0.00824884i \(-0.00262572\pi\)
\(128\) 8.30233i 0.733829i
\(129\) 0.772454 0.0680108
\(130\) 0.567462 + 3.06435i 0.0497697 + 0.268762i
\(131\) −9.27143 −0.810048 −0.405024 0.914306i \(-0.632737\pi\)
−0.405024 + 0.914306i \(0.632737\pi\)
\(132\) 0 0
\(133\) 25.5318i 2.21389i
\(134\) 1.76402 0.152388
\(135\) 2.19869 0.407156i 0.189233 0.0350425i
\(136\) 4.34381 0.372479
\(137\) 0.438101i 0.0374295i −0.999825 0.0187147i \(-0.994043\pi\)
0.999825 0.0187147i \(-0.00595744\pi\)
\(138\) 0.348403i 0.0296581i
\(139\) −8.60433 −0.729810 −0.364905 0.931045i \(-0.618898\pi\)
−0.364905 + 0.931045i \(0.618898\pi\)
\(140\) 15.4543 2.86186i 1.30613 0.241871i
\(141\) 6.47068 0.544930
\(142\) 0.950505i 0.0797646i
\(143\) 0 0
\(144\) −3.50648 −0.292207
\(145\) 2.01409 + 10.8763i 0.167261 + 0.903227i
\(146\) −0.0553137 −0.00457780
\(147\) 6.44984i 0.531974i
\(148\) 4.57474i 0.376041i
\(149\) 15.3241 1.25540 0.627700 0.778455i \(-0.283996\pi\)
0.627700 + 0.778455i \(0.283996\pi\)
\(150\) −1.34831 + 0.517096i −0.110089 + 0.0422207i
\(151\) −1.05059 −0.0854958 −0.0427479 0.999086i \(-0.513611\pi\)
−0.0427479 + 0.999086i \(0.513611\pi\)
\(152\) 7.87494i 0.638742i
\(153\) 3.84013i 0.310456i
\(154\) 0 0
\(155\) −3.00047 16.2028i −0.241003 1.30144i
\(156\) 9.24885 0.740501
\(157\) 4.93869i 0.394150i −0.980388 0.197075i \(-0.936856\pi\)
0.980388 0.197075i \(-0.0631443\pi\)
\(158\) 0.912632i 0.0726051i
\(159\) 10.7562 0.853025
\(160\) 7.20078 1.33345i 0.569272 0.105419i
\(161\) 4.42410 0.348668
\(162\) 0.288813i 0.0226913i
\(163\) 9.62856i 0.754167i −0.926179 0.377083i \(-0.876927\pi\)
0.926179 0.377083i \(-0.123073\pi\)
\(164\) 8.25212 0.644382
\(165\) 0 0
\(166\) −0.442003 −0.0343061
\(167\) 9.34416i 0.723073i 0.932358 + 0.361536i \(0.117748\pi\)
−0.932358 + 0.361536i \(0.882252\pi\)
\(168\) 4.14842i 0.320058i
\(169\) −10.2873 −0.791327
\(170\) −0.451569 2.43852i −0.0346338 0.187026i
\(171\) −6.96183 −0.532384
\(172\) 1.48047i 0.112885i
\(173\) 0.344694i 0.0262066i 0.999914 + 0.0131033i \(0.00417103\pi\)
−0.999914 + 0.0131033i \(0.995829\pi\)
\(174\) −1.42868 −0.108308
\(175\) −6.56619 17.1211i −0.496357 1.29423i
\(176\) 0 0
\(177\) 14.4979i 1.08973i
\(178\) 0.879706i 0.0659368i
\(179\) −16.0740 −1.20143 −0.600713 0.799465i \(-0.705117\pi\)
−0.600713 + 0.799465i \(0.705117\pi\)
\(180\) 0.780351 + 4.21397i 0.0581639 + 0.314091i
\(181\) −10.7349 −0.797922 −0.398961 0.916968i \(-0.630629\pi\)
−0.398961 + 0.916968i \(0.630629\pi\)
\(182\) 5.11133i 0.378877i
\(183\) 1.83091i 0.135345i
\(184\) 1.36455 0.100596
\(185\) 5.24809 0.971850i 0.385847 0.0714518i
\(186\) 2.12835 0.156058
\(187\) 0 0
\(188\) 12.4016i 0.904481i
\(189\) −3.66740 −0.266764
\(190\) 4.42082 0.818655i 0.320720 0.0593915i
\(191\) −13.5985 −0.983954 −0.491977 0.870608i \(-0.663726\pi\)
−0.491977 + 0.870608i \(0.663726\pi\)
\(192\) 6.06709i 0.437854i
\(193\) 25.9081i 1.86490i 0.361296 + 0.932451i \(0.382334\pi\)
−0.361296 + 0.932451i \(0.617666\pi\)
\(194\) 3.97899 0.285674
\(195\) −1.96481 10.6102i −0.140703 0.759810i
\(196\) −12.3617 −0.882977
\(197\) 1.18346i 0.0843177i −0.999111 0.0421588i \(-0.986576\pi\)
0.999111 0.0421588i \(-0.0134236\pi\)
\(198\) 0 0
\(199\) −3.13466 −0.222210 −0.111105 0.993809i \(-0.535439\pi\)
−0.111105 + 0.993809i \(0.535439\pi\)
\(200\) −2.02525 5.28076i −0.143207 0.373406i
\(201\) −6.10784 −0.430814
\(202\) 1.34566i 0.0946804i
\(203\) 18.1416i 1.27329i
\(204\) −7.35995 −0.515300
\(205\) −1.75307 9.46674i −0.122439 0.661186i
\(206\) 2.83528 0.197543
\(207\) 1.20633i 0.0838457i
\(208\) 16.9212i 1.17327i
\(209\) 0 0
\(210\) 2.32883 0.431257i 0.160705 0.0297596i
\(211\) −3.02303 −0.208114 −0.104057 0.994571i \(-0.533182\pi\)
−0.104057 + 0.994571i \(0.533182\pi\)
\(212\) 20.6153i 1.41586i
\(213\) 3.29108i 0.225501i
\(214\) 3.40846 0.232997
\(215\) 1.69838 0.314510i 0.115829 0.0214494i
\(216\) −1.13116 −0.0769657
\(217\) 27.0262i 1.83466i
\(218\) 3.01666i 0.204314i
\(219\) 0.191521 0.0129418
\(220\) 0 0
\(221\) 18.5313 1.24655
\(222\) 0.689373i 0.0462677i
\(223\) 0.0459708i 0.00307843i 0.999999 + 0.00153922i \(0.000489948\pi\)
−0.999999 + 0.00153922i \(0.999510\pi\)
\(224\) −12.0109 −0.802511
\(225\) 4.66845 1.79042i 0.311230 0.119361i
\(226\) 3.71570 0.247165
\(227\) 6.14586i 0.407915i 0.978980 + 0.203958i \(0.0653805\pi\)
−0.978980 + 0.203958i \(0.934620\pi\)
\(228\) 13.3429i 0.883658i
\(229\) −11.7365 −0.775570 −0.387785 0.921750i \(-0.626760\pi\)
−0.387785 + 0.921750i \(0.626760\pi\)
\(230\) −0.141855 0.766030i −0.00935362 0.0505105i
\(231\) 0 0
\(232\) 5.59554i 0.367365i
\(233\) 10.6588i 0.698280i −0.937071 0.349140i \(-0.886474\pi\)
0.937071 0.349140i \(-0.113526\pi\)
\(234\) 1.39372 0.0911103
\(235\) 14.2270 2.63458i 0.928067 0.171861i
\(236\) 27.7864 1.80874
\(237\) 3.15994i 0.205260i
\(238\) 4.06744i 0.263653i
\(239\) −4.59328 −0.297115 −0.148557 0.988904i \(-0.547463\pi\)
−0.148557 + 0.988904i \(0.547463\pi\)
\(240\) −7.70965 + 1.42769i −0.497656 + 0.0921568i
\(241\) −18.8716 −1.21563 −0.607814 0.794079i \(-0.707953\pi\)
−0.607814 + 0.794079i \(0.707953\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) −3.50911 −0.224647
\(245\) 2.62609 + 14.1812i 0.167775 + 0.906002i
\(246\) 1.24352 0.0792841
\(247\) 33.5956i 2.13764i
\(248\) 8.33588i 0.529329i
\(249\) 1.53041 0.0969860
\(250\) −2.75397 + 1.68590i −0.174176 + 0.106626i
\(251\) −19.4907 −1.23024 −0.615120 0.788434i \(-0.710892\pi\)
−0.615120 + 0.788434i \(0.710892\pi\)
\(252\) 7.02890i 0.442779i
\(253\) 0 0
\(254\) 0.0536959 0.00336918
\(255\) 1.56354 + 8.44325i 0.0979124 + 0.528737i
\(256\) 9.73636 0.608522
\(257\) 13.1814i 0.822234i 0.911582 + 0.411117i \(0.134861\pi\)
−0.911582 + 0.411117i \(0.865139\pi\)
\(258\) 0.223095i 0.0138893i
\(259\) −8.75380 −0.543934
\(260\) 20.3353 3.76573i 1.26114 0.233541i
\(261\) 4.94672 0.306194
\(262\) 2.67771i 0.165429i
\(263\) 29.8396i 1.83999i 0.391935 + 0.919993i \(0.371806\pi\)
−0.391935 + 0.919993i \(0.628194\pi\)
\(264\) 0 0
\(265\) 23.6496 4.37947i 1.45278 0.269029i
\(266\) −7.37391 −0.452124
\(267\) 3.04594i 0.186408i
\(268\) 11.7062i 0.715070i
\(269\) −0.251857 −0.0153560 −0.00767800 0.999971i \(-0.502444\pi\)
−0.00767800 + 0.999971i \(0.502444\pi\)
\(270\) 0.117592 + 0.635009i 0.00715642 + 0.0386454i
\(271\) −12.0897 −0.734400 −0.367200 0.930142i \(-0.619684\pi\)
−0.367200 + 0.930142i \(0.619684\pi\)
\(272\) 13.4654i 0.816457i
\(273\) 17.6977i 1.07112i
\(274\) 0.126529 0.00764391
\(275\) 0 0
\(276\) −2.31204 −0.139168
\(277\) 16.4655i 0.989318i −0.869087 0.494659i \(-0.835293\pi\)
0.869087 0.494659i \(-0.164707\pi\)
\(278\) 2.48504i 0.149043i
\(279\) −7.36932 −0.441189
\(280\) 1.68906 + 9.12108i 0.100940 + 0.545089i
\(281\) 12.6017 0.751756 0.375878 0.926669i \(-0.377341\pi\)
0.375878 + 0.926669i \(0.377341\pi\)
\(282\) 1.86882i 0.111286i
\(283\) 17.8478i 1.06094i 0.847703 + 0.530472i \(0.177985\pi\)
−0.847703 + 0.530472i \(0.822015\pi\)
\(284\) −6.30763 −0.374289
\(285\) −15.3069 + 2.83455i −0.906701 + 0.167904i
\(286\) 0 0
\(287\) 15.7905i 0.932083i
\(288\) 3.27504i 0.192983i
\(289\) 2.25337 0.132551
\(290\) −3.14121 + 0.581695i −0.184458 + 0.0341583i
\(291\) −13.7770 −0.807624
\(292\) 0.367067i 0.0214810i
\(293\) 9.90674i 0.578758i 0.957215 + 0.289379i \(0.0934488\pi\)
−0.957215 + 0.289379i \(0.906551\pi\)
\(294\) −1.86280 −0.108640
\(295\) −5.90289 31.8762i −0.343680 1.85591i
\(296\) −2.69999 −0.156934
\(297\) 0 0
\(298\) 4.42580i 0.256380i
\(299\) 5.82137 0.336658
\(300\) 3.43149 + 8.94749i 0.198117 + 0.516583i
\(301\) −2.83290 −0.163286
\(302\) 0.303424i 0.0174601i
\(303\) 4.65928i 0.267669i
\(304\) 24.4115 1.40010
\(305\) 0.745468 + 4.02561i 0.0426854 + 0.230505i
\(306\) −1.10908 −0.0634019
\(307\) 23.2505i 1.32698i −0.748186 0.663489i \(-0.769075\pi\)
0.748186 0.663489i \(-0.230925\pi\)
\(308\) 0 0
\(309\) −9.81701 −0.558470
\(310\) 4.67958 0.866573i 0.265782 0.0492180i
\(311\) 29.8628 1.69336 0.846681 0.532100i \(-0.178597\pi\)
0.846681 + 0.532100i \(0.178597\pi\)
\(312\) 5.45863i 0.309034i
\(313\) 25.6366i 1.44907i 0.689240 + 0.724533i \(0.257945\pi\)
−0.689240 + 0.724533i \(0.742055\pi\)
\(314\) 1.42636 0.0804940
\(315\) −8.06347 + 1.49321i −0.454325 + 0.0841327i
\(316\) 6.05631 0.340694
\(317\) 1.12070i 0.0629448i −0.999505 0.0314724i \(-0.989980\pi\)
0.999505 0.0314724i \(-0.0100196\pi\)
\(318\) 3.10654i 0.174206i
\(319\) 0 0
\(320\) −2.47025 13.3396i −0.138091 0.745708i
\(321\) −11.8016 −0.658702
\(322\) 1.27774i 0.0712054i
\(323\) 26.7343i 1.48754i
\(324\) 1.91659 0.106477
\(325\) −8.64000 22.5285i −0.479261 1.24965i
\(326\) 2.78085 0.154017
\(327\) 10.4450i 0.577612i
\(328\) 4.87036i 0.268921i
\(329\) −23.7306 −1.30831
\(330\) 0 0
\(331\) −10.9379 −0.601200 −0.300600 0.953750i \(-0.597187\pi\)
−0.300600 + 0.953750i \(0.597187\pi\)
\(332\) 2.93317i 0.160979i
\(333\) 2.38692i 0.130802i
\(334\) −2.69871 −0.147667
\(335\) −13.4292 + 2.48685i −0.733717 + 0.135871i
\(336\) 12.8597 0.701553
\(337\) 21.8160i 1.18839i −0.804320 0.594196i \(-0.797470\pi\)
0.804320 0.594196i \(-0.202530\pi\)
\(338\) 2.97109i 0.161606i
\(339\) −12.8654 −0.698754
\(340\) −16.1822 + 2.99665i −0.877605 + 0.162516i
\(341\) 0 0
\(342\) 2.01066i 0.108724i
\(343\) 2.01767i 0.108944i
\(344\) −0.873769 −0.0471105
\(345\) 0.491165 + 2.65234i 0.0264434 + 0.142797i
\(346\) −0.0995521 −0.00535195
\(347\) 25.3859i 1.36279i −0.731917 0.681394i \(-0.761374\pi\)
0.731917 0.681394i \(-0.238626\pi\)
\(348\) 9.48082i 0.508225i
\(349\) −32.1887 −1.72302 −0.861511 0.507739i \(-0.830482\pi\)
−0.861511 + 0.507739i \(0.830482\pi\)
\(350\) 4.94479 1.89640i 0.264310 0.101367i
\(351\) −4.82569 −0.257576
\(352\) 0 0
\(353\) 10.2135i 0.543611i −0.962352 0.271806i \(-0.912379\pi\)
0.962352 0.271806i \(-0.0876208\pi\)
\(354\) 4.18717 0.222545
\(355\) 1.33998 + 7.23604i 0.0711189 + 0.384049i
\(356\) 5.83781 0.309403
\(357\) 14.0833i 0.745368i
\(358\) 4.64237i 0.245357i
\(359\) −32.2585 −1.70254 −0.851270 0.524727i \(-0.824167\pi\)
−0.851270 + 0.524727i \(0.824167\pi\)
\(360\) −2.48707 + 0.460559i −0.131080 + 0.0242736i
\(361\) 29.4670 1.55090
\(362\) 3.10039i 0.162953i
\(363\) 0 0
\(364\) −33.9193 −1.77785
\(365\) 0.421095 0.0779790i 0.0220411 0.00408161i
\(366\) −0.528791 −0.0276404
\(367\) 15.2516i 0.796125i −0.917358 0.398063i \(-0.869683\pi\)
0.917358 0.398063i \(-0.130317\pi\)
\(368\) 4.22997i 0.220503i
\(369\) −4.30563 −0.224142
\(370\) 0.280683 + 1.51572i 0.0145920 + 0.0787983i
\(371\) −39.4474 −2.04801
\(372\) 14.1239i 0.732292i
\(373\) 14.4355i 0.747440i −0.927542 0.373720i \(-0.878082\pi\)
0.927542 0.373720i \(-0.121918\pi\)
\(374\) 0 0
\(375\) 9.53547 5.83736i 0.492410 0.301440i
\(376\) −7.31938 −0.377468
\(377\) 23.8713i 1.22944i
\(378\) 1.05919i 0.0544790i
\(379\) 20.1384 1.03444 0.517220 0.855852i \(-0.326967\pi\)
0.517220 + 0.855852i \(0.326967\pi\)
\(380\) −5.43267 29.3370i −0.278690 1.50495i
\(381\) −0.185919 −0.00952494
\(382\) 3.92743i 0.200945i
\(383\) 9.23909i 0.472096i 0.971741 + 0.236048i \(0.0758522\pi\)
−0.971741 + 0.236048i \(0.924148\pi\)
\(384\) 8.30233 0.423676
\(385\) 0 0
\(386\) −7.48258 −0.380853
\(387\) 0.772454i 0.0392660i
\(388\) 26.4049i 1.34051i
\(389\) −20.5859 −1.04375 −0.521874 0.853023i \(-0.674767\pi\)
−0.521874 + 0.853023i \(0.674767\pi\)
\(390\) 3.06435 0.567462i 0.155170 0.0287346i
\(391\) −4.63247 −0.234274
\(392\) 7.29580i 0.368494i
\(393\) 9.27143i 0.467682i
\(394\) 0.341797 0.0172195
\(395\) −1.28659 6.94773i −0.0647355 0.349578i
\(396\) 0 0
\(397\) 20.1311i 1.01035i 0.863017 + 0.505176i \(0.168572\pi\)
−0.863017 + 0.505176i \(0.831428\pi\)
\(398\) 0.905331i 0.0453801i
\(399\) 25.5318 1.27819
\(400\) −16.3698 + 6.27807i −0.818491 + 0.313904i
\(401\) 0.648927 0.0324059 0.0162029 0.999869i \(-0.494842\pi\)
0.0162029 + 0.999869i \(0.494842\pi\)
\(402\) 1.76402i 0.0879814i
\(403\) 35.5620i 1.77147i
\(404\) −8.92992 −0.444280
\(405\) −0.407156 2.19869i −0.0202318 0.109254i
\(406\) 5.23953 0.260034
\(407\) 0 0
\(408\) 4.34381i 0.215051i
\(409\) −13.1101 −0.648255 −0.324128 0.946013i \(-0.605071\pi\)
−0.324128 + 0.946013i \(0.605071\pi\)
\(410\) 2.73412 0.506308i 0.135028 0.0250048i
\(411\) −0.438101 −0.0216099
\(412\) 18.8152i 0.926956i
\(413\) 53.1695i 2.61630i
\(414\) −0.348403 −0.0171231
\(415\) 3.36490 0.623118i 0.165176 0.0305876i
\(416\) −15.8043 −0.774870
\(417\) 8.60433i 0.421356i
\(418\) 0 0
\(419\) 33.0462 1.61441 0.807206 0.590270i \(-0.200979\pi\)
0.807206 + 0.590270i \(0.200979\pi\)
\(420\) −2.86186 15.4543i −0.139644 0.754095i
\(421\) 8.71780 0.424879 0.212440 0.977174i \(-0.431859\pi\)
0.212440 + 0.977174i \(0.431859\pi\)
\(422\) 0.873091i 0.0425014i
\(423\) 6.47068i 0.314615i
\(424\) −12.1670 −0.590883
\(425\) 6.87545 + 17.9275i 0.333508 + 0.869610i
\(426\) −0.950505 −0.0460521
\(427\) 6.71470i 0.324947i
\(428\) 22.6188i 1.09332i
\(429\) 0 0
\(430\) 0.0908344 + 0.490515i 0.00438042 + 0.0236547i
\(431\) −16.3875 −0.789358 −0.394679 0.918819i \(-0.629144\pi\)
−0.394679 + 0.918819i \(0.629144\pi\)
\(432\) 3.50648i 0.168706i
\(433\) 34.9874i 1.68139i −0.541510 0.840695i \(-0.682147\pi\)
0.541510 0.840695i \(-0.317853\pi\)
\(434\) −7.80553 −0.374677
\(435\) 10.8763 2.01409i 0.521478 0.0965682i
\(436\) 20.0188 0.958728
\(437\) 8.39826i 0.401743i
\(438\) 0.0553137i 0.00264299i
\(439\) −18.5657 −0.886091 −0.443046 0.896499i \(-0.646102\pi\)
−0.443046 + 0.896499i \(0.646102\pi\)
\(440\) 0 0
\(441\) 6.44984 0.307135
\(442\) 5.35207i 0.254572i
\(443\) 8.85169i 0.420556i 0.977642 + 0.210278i \(0.0674370\pi\)
−0.977642 + 0.210278i \(0.932563\pi\)
\(444\) 4.57474 0.217108
\(445\) −1.24017 6.69706i −0.0587899 0.317471i
\(446\) −0.0132770 −0.000628682
\(447\) 15.3241i 0.724806i
\(448\) 22.2505i 1.05124i
\(449\) −3.18109 −0.150125 −0.0750624 0.997179i \(-0.523916\pi\)
−0.0750624 + 0.997179i \(0.523916\pi\)
\(450\) 0.517096 + 1.34831i 0.0243761 + 0.0635598i
\(451\) 0 0
\(452\) 24.6577i 1.15980i
\(453\) 1.05059i 0.0493610i
\(454\) −1.77500 −0.0833051
\(455\) 7.20575 + 38.9118i 0.337811 + 1.82421i
\(456\) 7.87494 0.368778
\(457\) 3.52754i 0.165011i −0.996591 0.0825056i \(-0.973708\pi\)
0.996591 0.0825056i \(-0.0262922\pi\)
\(458\) 3.38965i 0.158388i
\(459\) 3.84013 0.179242
\(460\) −5.08344 + 0.941360i −0.237017 + 0.0438912i
\(461\) −18.1321 −0.844496 −0.422248 0.906480i \(-0.638759\pi\)
−0.422248 + 0.906480i \(0.638759\pi\)
\(462\) 0 0
\(463\) 18.0104i 0.837013i 0.908214 + 0.418506i \(0.137446\pi\)
−0.908214 + 0.418506i \(0.862554\pi\)
\(464\) −17.3456 −0.805248
\(465\) −16.2028 + 3.00047i −0.751388 + 0.139143i
\(466\) 3.07839 0.142604
\(467\) 26.7217i 1.23653i −0.785969 0.618266i \(-0.787835\pi\)
0.785969 0.618266i \(-0.212165\pi\)
\(468\) 9.24885i 0.427528i
\(469\) 22.3999 1.03433
\(470\) 0.760900 + 4.10894i 0.0350977 + 0.189531i
\(471\) −4.93869 −0.227563
\(472\) 16.3994i 0.754844i
\(473\) 0 0
\(474\) 0.912632 0.0419186
\(475\) −32.5009 + 12.4646i −1.49124 + 0.571914i
\(476\) 26.9919 1.23717
\(477\) 10.7562i 0.492494i
\(478\) 1.32660i 0.0606772i
\(479\) −22.7687 −1.04033 −0.520163 0.854067i \(-0.674129\pi\)
−0.520163 + 0.854067i \(0.674129\pi\)
\(480\) −1.33345 7.20078i −0.0608635 0.328669i
\(481\) −11.5185 −0.525200
\(482\) 5.45037i 0.248257i
\(483\) 4.42410i 0.201303i
\(484\) 0 0
\(485\) −30.2914 + 5.60941i −1.37546 + 0.254710i
\(486\) 0.288813 0.0131008
\(487\) 13.5507i 0.614039i 0.951703 + 0.307020i \(0.0993318\pi\)
−0.951703 + 0.307020i \(0.900668\pi\)
\(488\) 2.07106i 0.0937523i
\(489\) −9.62856 −0.435418
\(490\) −4.09570 + 0.758449i −0.185025 + 0.0342633i
\(491\) 19.0361 0.859088 0.429544 0.903046i \(-0.358674\pi\)
0.429544 + 0.903046i \(0.358674\pi\)
\(492\) 8.25212i 0.372034i
\(493\) 18.9961i 0.855540i
\(494\) −9.70284 −0.436551
\(495\) 0 0
\(496\) 25.8404 1.16027
\(497\) 12.0697i 0.541400i
\(498\) 0.442003i 0.0198066i
\(499\) 23.1094 1.03452 0.517258 0.855829i \(-0.326953\pi\)
0.517258 + 0.855829i \(0.326953\pi\)
\(500\) 11.1878 + 18.2756i 0.500334 + 0.817308i
\(501\) 9.34416 0.417466
\(502\) 5.62915i 0.251241i
\(503\) 26.6808i 1.18964i −0.803859 0.594820i \(-0.797224\pi\)
0.803859 0.594820i \(-0.202776\pi\)
\(504\) 4.14842 0.184785
\(505\) 1.89706 + 10.2443i 0.0844180 + 0.455866i
\(506\) 0 0
\(507\) 10.2873i 0.456873i
\(508\) 0.356331i 0.0158096i
\(509\) −8.67668 −0.384587 −0.192294 0.981337i \(-0.561593\pi\)
−0.192294 + 0.981337i \(0.561593\pi\)
\(510\) −2.43852 + 0.451569i −0.107979 + 0.0199958i
\(511\) −0.702385 −0.0310717
\(512\) 19.4166i 0.858102i
\(513\) 6.96183i 0.307372i
\(514\) −3.80696 −0.167918
\(515\) −21.5845 + 3.99706i −0.951128 + 0.176132i
\(516\) 1.48047 0.0651743
\(517\) 0 0
\(518\) 2.52821i 0.111083i
\(519\) 0.344694 0.0151304
\(520\) 2.22252 + 12.0018i 0.0974637 + 0.526314i
\(521\) −6.51721 −0.285524 −0.142762 0.989757i \(-0.545598\pi\)
−0.142762 + 0.989757i \(0.545598\pi\)
\(522\) 1.42868i 0.0625315i
\(523\) 36.8608i 1.61181i 0.592045 + 0.805905i \(0.298321\pi\)
−0.592045 + 0.805905i \(0.701679\pi\)
\(524\) −17.7695 −0.776264
\(525\) −17.1211 + 6.56619i −0.747225 + 0.286572i
\(526\) −8.61805 −0.375765
\(527\) 28.2992i 1.23273i
\(528\) 0 0
\(529\) 21.5448 0.936729
\(530\) 1.26485 + 6.83031i 0.0549415 + 0.296690i
\(531\) −14.4979 −0.629153
\(532\) 48.9339i 2.12156i
\(533\) 20.7776i 0.899979i
\(534\) 0.879706 0.0380686
\(535\) −25.9480 + 4.80510i −1.12183 + 0.207743i
\(536\) 6.90895 0.298421
\(537\) 16.0740i 0.693644i
\(538\) 0.0727396i 0.00313603i
\(539\) 0 0
\(540\) 4.21397 0.780351i 0.181341 0.0335810i
\(541\) 20.3681 0.875691 0.437846 0.899050i \(-0.355742\pi\)
0.437846 + 0.899050i \(0.355742\pi\)
\(542\) 3.49167i 0.149980i
\(543\) 10.7349i 0.460680i
\(544\) 12.5766 0.539217
\(545\) −4.25276 22.9654i −0.182168 0.983728i
\(546\) −5.11133 −0.218745
\(547\) 24.0697i 1.02915i −0.857447 0.514573i \(-0.827950\pi\)
0.857447 0.514573i \(-0.172050\pi\)
\(548\) 0.839659i 0.0358684i
\(549\) 1.83091 0.0781415
\(550\) 0 0
\(551\) −34.4382 −1.46712
\(552\) 1.36455i 0.0580792i
\(553\) 11.5888i 0.492805i
\(554\) 4.75546 0.202040
\(555\) −0.971850 5.24809i −0.0412527 0.222769i
\(556\) −16.4909 −0.699372
\(557\) 38.0312i 1.61144i −0.592300 0.805718i \(-0.701780\pi\)
0.592300 0.805718i \(-0.298220\pi\)
\(558\) 2.12835i 0.0901004i
\(559\) −3.72762 −0.157662
\(560\) 28.2744 5.23590i 1.19481 0.221257i
\(561\) 0 0
\(562\) 3.63954i 0.153525i
\(563\) 1.45960i 0.0615147i 0.999527 + 0.0307574i \(0.00979192\pi\)
−0.999527 + 0.0307574i \(0.990208\pi\)
\(564\) 12.4016 0.522203
\(565\) −28.2870 + 5.23824i −1.19004 + 0.220374i
\(566\) −5.15468 −0.216668
\(567\) 3.66740i 0.154016i
\(568\) 3.72273i 0.156202i
\(569\) 1.06880 0.0448064 0.0224032 0.999749i \(-0.492868\pi\)
0.0224032 + 0.999749i \(0.492868\pi\)
\(570\) −0.818655 4.42082i −0.0342897 0.185168i
\(571\) −4.25241 −0.177958 −0.0889789 0.996034i \(-0.528360\pi\)
−0.0889789 + 0.996034i \(0.528360\pi\)
\(572\) 0 0
\(573\) 13.5985i 0.568086i
\(574\) −4.56050 −0.190351
\(575\) 2.15984 + 5.63169i 0.0900714 + 0.234858i
\(576\) −6.06709 −0.252795
\(577\) 3.03655i 0.126413i −0.998000 0.0632065i \(-0.979867\pi\)
0.998000 0.0632065i \(-0.0201327\pi\)
\(578\) 0.650801i 0.0270698i
\(579\) 25.9081 1.07670
\(580\) 3.86018 + 20.8454i 0.160285 + 0.865556i
\(581\) −5.61264 −0.232852
\(582\) 3.97899i 0.164934i
\(583\) 0 0
\(584\) −0.216641 −0.00896467
\(585\) −10.6102 + 1.96481i −0.438677 + 0.0812349i
\(586\) −2.86119 −0.118195
\(587\) 2.54270i 0.104949i 0.998622 + 0.0524743i \(0.0167108\pi\)
−0.998622 + 0.0524743i \(0.983289\pi\)
\(588\) 12.3617i 0.509787i
\(589\) 51.3039 2.11394
\(590\) 9.20627 1.70483i 0.379016 0.0701868i
\(591\) −1.18346 −0.0486808
\(592\) 8.36969i 0.343992i
\(593\) 40.7468i 1.67327i 0.547760 + 0.836636i \(0.315481\pi\)
−0.547760 + 0.836636i \(0.684519\pi\)
\(594\) 0 0
\(595\) −5.73411 30.9648i −0.235076 1.26943i
\(596\) 29.3700 1.20304
\(597\) 3.13466i 0.128293i
\(598\) 1.68129i 0.0687529i
\(599\) −6.76111 −0.276251 −0.138126 0.990415i \(-0.544108\pi\)
−0.138126 + 0.990415i \(0.544108\pi\)
\(600\) −5.28076 + 2.02525i −0.215586 + 0.0826805i
\(601\) −15.0937 −0.615685 −0.307843 0.951437i \(-0.599607\pi\)
−0.307843 + 0.951437i \(0.599607\pi\)
\(602\) 0.818177i 0.0333464i
\(603\) 6.10784i 0.248730i
\(604\) −2.01355 −0.0819301
\(605\) 0 0
\(606\) −1.34566 −0.0546637
\(607\) 7.86639i 0.319287i 0.987175 + 0.159643i \(0.0510344\pi\)
−0.987175 + 0.159643i \(0.948966\pi\)
\(608\) 22.8002i 0.924672i
\(609\) −18.1416 −0.735135
\(610\) −1.16265 + 0.215301i −0.0470742 + 0.00871727i
\(611\) −31.2255 −1.26325
\(612\) 7.35995i 0.297508i
\(613\) 27.1001i 1.09456i −0.836948 0.547282i \(-0.815662\pi\)
0.836948 0.547282i \(-0.184338\pi\)
\(614\) 6.71505 0.270997
\(615\) −9.46674 + 1.75307i −0.381736 + 0.0706905i
\(616\) 0 0
\(617\) 3.61737i 0.145630i −0.997345 0.0728149i \(-0.976802\pi\)
0.997345 0.0728149i \(-0.0231982\pi\)
\(618\) 2.83528i 0.114052i
\(619\) 16.5624 0.665698 0.332849 0.942980i \(-0.391990\pi\)
0.332849 + 0.942980i \(0.391990\pi\)
\(620\) −5.75065 31.0541i −0.230952 1.24716i
\(621\) 1.20633 0.0484083
\(622\) 8.62475i 0.345821i
\(623\) 11.1707i 0.447544i
\(624\) 16.9212 0.677389
\(625\) 18.5888 16.7170i 0.743552 0.668678i
\(626\) −7.40418 −0.295931
\(627\) 0 0
\(628\) 9.46543i 0.377712i
\(629\) 9.16609 0.365476
\(630\) −0.431257 2.32883i −0.0171817 0.0927829i
\(631\) 3.98943 0.158817 0.0794083 0.996842i \(-0.474697\pi\)
0.0794083 + 0.996842i \(0.474697\pi\)
\(632\) 3.57440i 0.142182i
\(633\) 3.02303i 0.120155i
\(634\) 0.323672 0.0128547
\(635\) −0.408779 + 0.0756983i −0.0162219 + 0.00300400i
\(636\) 20.6153 0.817448
\(637\) 31.1249i 1.23321i
\(638\) 0 0
\(639\) 3.29108 0.130193
\(640\) 18.2542 3.38035i 0.721561 0.133620i
\(641\) −34.2580 −1.35311 −0.676554 0.736393i \(-0.736527\pi\)
−0.676554 + 0.736393i \(0.736527\pi\)
\(642\) 3.40846i 0.134521i
\(643\) 41.5718i 1.63943i −0.572771 0.819716i \(-0.694131\pi\)
0.572771 0.819716i \(-0.305869\pi\)
\(644\) 8.47917 0.334126
\(645\) −0.314510 1.69838i −0.0123838 0.0668738i
\(646\) 7.72122 0.303787
\(647\) 9.86886i 0.387985i 0.981003 + 0.193993i \(0.0621438\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(648\) 1.13116i 0.0444362i
\(649\) 0 0
\(650\) 6.50651 2.49534i 0.255206 0.0978754i
\(651\) 27.0262 1.05924
\(652\) 18.4540i 0.722713i
\(653\) 20.7327i 0.811335i −0.914021 0.405667i \(-0.867039\pi\)
0.914021 0.405667i \(-0.132961\pi\)
\(654\) 3.01666 0.117961
\(655\) 3.77492 + 20.3850i 0.147498 + 0.796507i
\(656\) 15.0976 0.589463
\(657\) 0.191521i 0.00747195i
\(658\) 6.85370i 0.267185i
\(659\) −26.4580 −1.03066 −0.515329 0.856992i \(-0.672330\pi\)
−0.515329 + 0.856992i \(0.672330\pi\)
\(660\) 0 0
\(661\) 5.75931 0.224011 0.112006 0.993708i \(-0.464273\pi\)
0.112006 + 0.993708i \(0.464273\pi\)
\(662\) 3.15900i 0.122778i
\(663\) 18.5313i 0.719696i
\(664\) −1.73114 −0.0671814
\(665\) 56.1365 10.3954i 2.17688 0.403118i
\(666\) 0.689373 0.0267127
\(667\) 5.96738i 0.231058i
\(668\) 17.9089i 0.692916i
\(669\) 0.0459708 0.00177733
\(670\) −0.718233 3.87853i −0.0277478 0.149841i
\(671\) 0 0
\(672\) 12.0109i 0.463330i
\(673\) 15.8591i 0.611323i −0.952140 0.305662i \(-0.901122\pi\)
0.952140 0.305662i \(-0.0988776\pi\)
\(674\) 6.30074 0.242695
\(675\) −1.79042 4.66845i −0.0689133 0.179689i
\(676\) −19.7164 −0.758324
\(677\) 14.5303i 0.558446i −0.960226 0.279223i \(-0.909923\pi\)
0.960226 0.279223i \(-0.0900768\pi\)
\(678\) 3.71570i 0.142701i
\(679\) 50.5259 1.93901
\(680\) −1.76861 9.55067i −0.0678231 0.366252i
\(681\) 6.14586 0.235510
\(682\) 0 0
\(683\) 48.0516i 1.83864i 0.393509 + 0.919321i \(0.371261\pi\)
−0.393509 + 0.919321i \(0.628739\pi\)
\(684\) −13.3429 −0.510180
\(685\) −0.963247 + 0.178376i −0.0368038 + 0.00681538i
\(686\) −0.582728 −0.0222486
\(687\) 11.7365i 0.447776i
\(688\) 2.70859i 0.103264i
\(689\) −51.9062 −1.97747
\(690\) −0.766030 + 0.141855i −0.0291623 + 0.00540032i
\(691\) −28.1864 −1.07226 −0.536131 0.844135i \(-0.680115\pi\)
−0.536131 + 0.844135i \(0.680115\pi\)
\(692\) 0.660636i 0.0251136i
\(693\) 0 0
\(694\) 7.33178 0.278310
\(695\) 3.50331 + 18.9182i 0.132888 + 0.717609i
\(696\) −5.59554 −0.212098
\(697\) 16.5342i 0.626278i
\(698\) 9.29651i 0.351878i
\(699\) −10.6588 −0.403152
\(700\) −12.5847 32.8140i −0.475656 1.24025i
\(701\) 29.7610 1.12406 0.562029 0.827117i \(-0.310021\pi\)
0.562029 + 0.827117i \(0.310021\pi\)
\(702\) 1.39372i 0.0526026i
\(703\) 16.6173i 0.626734i
\(704\) 0 0
\(705\) −2.63458 14.2270i −0.0992240 0.535820i
\(706\) 2.94980 0.111017
\(707\) 17.0875i 0.642640i
\(708\) 27.7864i 1.04428i
\(709\) 2.53577 0.0952328 0.0476164 0.998866i \(-0.484838\pi\)
0.0476164 + 0.998866i \(0.484838\pi\)
\(710\) −2.08986 + 0.387004i −0.0784311 + 0.0145240i
\(711\) −3.15994 −0.118507
\(712\) 3.44545i 0.129124i
\(713\) 8.88983i 0.332927i
\(714\) 4.06744 0.152220
\(715\) 0 0
\(716\) −30.8072 −1.15132
\(717\) 4.59328i 0.171539i
\(718\) 9.31668i 0.347695i
\(719\) 37.9483 1.41523 0.707617 0.706597i \(-0.249770\pi\)
0.707617 + 0.706597i \(0.249770\pi\)
\(720\) 1.42769 + 7.70965i 0.0532067 + 0.287322i
\(721\) 36.0029 1.34082
\(722\) 8.51045i 0.316726i
\(723\) 18.8716i 0.701843i
\(724\) −20.5744 −0.764643
\(725\) 23.0935 8.85670i 0.857671 0.328930i
\(726\) 0 0
\(727\) 10.1521i 0.376520i −0.982119 0.188260i \(-0.939715\pi\)
0.982119 0.188260i \(-0.0602848\pi\)
\(728\) 20.0190i 0.741953i
\(729\) −1.00000 −0.0370370
\(730\) 0.0225213 + 0.121618i 0.000833552 + 0.00450127i
\(731\) 2.96633 0.109714
\(732\) 3.50911i 0.129700i
\(733\) 13.8705i 0.512320i 0.966634 + 0.256160i \(0.0824574\pi\)
−0.966634 + 0.256160i \(0.917543\pi\)
\(734\) 4.40485 0.162586
\(735\) 14.1812 2.62609i 0.523080 0.0968649i
\(736\) 3.95077 0.145627
\(737\) 0 0
\(738\) 1.24352i 0.0457747i
\(739\) −3.89107 −0.143135 −0.0715677 0.997436i \(-0.522800\pi\)
−0.0715677 + 0.997436i \(0.522800\pi\)
\(740\) 10.0584 1.86264i 0.369755 0.0684718i
\(741\) 33.5956 1.23416
\(742\) 11.3929i 0.418248i
\(743\) 42.0524i 1.54275i −0.636379 0.771376i \(-0.719569\pi\)
0.636379 0.771376i \(-0.280431\pi\)
\(744\) 8.33588 0.305608
\(745\) −6.23932 33.6929i −0.228591 1.23441i
\(746\) 4.16915 0.152643
\(747\) 1.53041i 0.0559949i
\(748\) 0 0
\(749\) 43.2812 1.58146
\(750\) 1.68590 + 2.75397i 0.0615605 + 0.100561i
\(751\) −5.01553 −0.183019 −0.0915096 0.995804i \(-0.529169\pi\)
−0.0915096 + 0.995804i \(0.529169\pi\)
\(752\) 22.6893i 0.827394i
\(753\) 19.4907i 0.710279i
\(754\) 6.89435 0.251077
\(755\) 0.427755 + 2.30992i 0.0155676 + 0.0840665i
\(756\) −7.02890 −0.255638
\(757\) 35.4560i 1.28867i 0.764743 + 0.644335i \(0.222866\pi\)
−0.764743 + 0.644335i \(0.777134\pi\)
\(758\) 5.81623i 0.211255i
\(759\) 0 0
\(760\) 17.3145 3.20633i 0.628064 0.116306i
\(761\) 14.3160 0.518954 0.259477 0.965749i \(-0.416450\pi\)
0.259477 + 0.965749i \(0.416450\pi\)
\(762\) 0.0536959i 0.00194520i
\(763\) 38.3061i 1.38678i
\(764\) −26.0627 −0.942917
\(765\) 8.44325 1.56354i 0.305266 0.0565298i
\(766\) −2.66837 −0.0964121
\(767\) 69.9621i 2.52619i
\(768\) 9.73636i 0.351331i
\(769\) 29.6869 1.07054 0.535269 0.844682i \(-0.320210\pi\)
0.535269 + 0.844682i \(0.320210\pi\)
\(770\) 0 0
\(771\) 13.1814 0.474717
\(772\) 49.6550i 1.78712i
\(773\) 48.2367i 1.73495i −0.497477 0.867477i \(-0.665740\pi\)
0.497477 0.867477i \(-0.334260\pi\)
\(774\) 0.223095 0.00801897
\(775\) −34.4033 + 13.1942i −1.23580 + 0.473948i
\(776\) 15.5840 0.559434
\(777\) 8.75380i 0.314041i
\(778\) 5.94548i 0.213156i
\(779\) 29.9751 1.07397
\(780\) −3.76573 20.3353i −0.134835 0.728121i
\(781\) 0 0
\(782\) 1.33792i 0.0478438i
\(783\) 4.94672i 0.176781i
\(784\) −22.6162 −0.807723
\(785\) −10.8586 + 2.01082i −0.387561 + 0.0717692i
\(786\) −2.67771 −0.0955106
\(787\) 51.4339i 1.83342i −0.399551 0.916711i \(-0.630834\pi\)
0.399551 0.916711i \(-0.369166\pi\)
\(788\) 2.26819i 0.0808011i
\(789\) 29.8396 1.06232
\(790\) 2.00659 0.371584i 0.0713914 0.0132204i
\(791\) 47.1827 1.67762
\(792\) 0 0
\(793\) 8.83542i 0.313755i
\(794\) −5.81412 −0.206335
\(795\) −4.37947 23.6496i −0.155324 0.838765i
\(796\) −6.00785 −0.212943
\(797\) 37.8789i 1.34174i 0.741575 + 0.670869i \(0.234079\pi\)
−0.741575 + 0.670869i \(0.765921\pi\)
\(798\) 7.37391i 0.261034i
\(799\) 24.8483 0.879069
\(800\) −5.86369 15.2893i −0.207313 0.540560i
\(801\) −3.04594 −0.107623
\(802\) 0.187419i 0.00661798i
\(803\) 0 0
\(804\) −11.7062 −0.412846
\(805\) −1.80130 9.72720i −0.0634875 0.342839i
\(806\) −10.2708 −0.361772
\(807\) 0.251857i 0.00886580i
\(808\) 5.27040i 0.185412i
\(809\) 33.8214 1.18910 0.594549 0.804060i \(-0.297331\pi\)
0.594549 + 0.804060i \(0.297331\pi\)
\(810\) 0.635009 0.117592i 0.0223119 0.00413176i
\(811\) −8.81396 −0.309500 −0.154750 0.987954i \(-0.549457\pi\)
−0.154750 + 0.987954i \(0.549457\pi\)
\(812\) 34.7700i 1.22019i
\(813\) 12.0897i 0.424006i
\(814\) 0 0
\(815\) −21.1702 + 3.92033i −0.741559 + 0.137323i
\(816\) −13.4654 −0.471382
\(817\) 5.37769i 0.188141i
\(818\) 3.78638i 0.132388i
\(819\) 17.6977 0.618409
\(820\) −3.35990 18.1438i −0.117333 0.633610i
\(821\) 38.7028 1.35074 0.675369 0.737480i \(-0.263984\pi\)
0.675369 + 0.737480i \(0.263984\pi\)
\(822\) 0.126529i 0.00441321i
\(823\) 6.85406i 0.238918i −0.992839 0.119459i \(-0.961884\pi\)
0.992839 0.119459i \(-0.0381159\pi\)
\(824\) 11.1046 0.386848
\(825\) 0 0
\(826\) −15.3560 −0.534304
\(827\) 38.0969i 1.32476i −0.749169 0.662379i \(-0.769547\pi\)
0.749169 0.662379i \(-0.230453\pi\)
\(828\) 2.31204i 0.0803488i
\(829\) −7.42028 −0.257717 −0.128859 0.991663i \(-0.541131\pi\)
−0.128859 + 0.991663i \(0.541131\pi\)
\(830\) 0.179964 + 0.971826i 0.00624665 + 0.0337326i
\(831\) −16.4655 −0.571183
\(832\) 29.2779i 1.01503i
\(833\) 24.7682i 0.858169i
\(834\) −2.48504 −0.0860499
\(835\) 20.5449 3.80453i 0.710985 0.131661i
\(836\) 0 0
\(837\) 7.36932i 0.254721i
\(838\) 9.54416i 0.329698i
\(839\) −55.1922 −1.90545 −0.952723 0.303840i \(-0.901731\pi\)
−0.952723 + 0.303840i \(0.901731\pi\)
\(840\) 9.12108 1.68906i 0.314707 0.0582780i
\(841\) −4.52995 −0.156205
\(842\) 2.51781i 0.0867695i
\(843\) 12.6017i 0.434026i
\(844\) −5.79391 −0.199435
\(845\) 4.18852 + 22.6185i 0.144090 + 0.778098i
\(846\) 1.86882 0.0642512
\(847\) 0 0
\(848\) 37.7165i 1.29519i
\(849\) 17.8478 0.612536
\(850\) −5.17768 + 1.98572i −0.177593 + 0.0681096i
\(851\) 2.87941 0.0987050
\(852\) 6.30763i 0.216096i
\(853\) 3.32152i 0.113727i −0.998382 0.0568634i \(-0.981890\pi\)
0.998382 0.0568634i \(-0.0181099\pi\)
\(854\) 1.93929 0.0663611
\(855\) 2.83455 + 15.3069i 0.0969396 + 0.523484i
\(856\) 13.3495 0.456277
\(857\) 34.6080i 1.18219i 0.806603 + 0.591094i \(0.201304\pi\)
−0.806603 + 0.591094i \(0.798696\pi\)
\(858\) 0 0
\(859\) −39.0606 −1.33273 −0.666366 0.745625i \(-0.732151\pi\)
−0.666366 + 0.745625i \(0.732151\pi\)
\(860\) 3.25510 0.602785i 0.110998 0.0205548i
\(861\) 15.7905 0.538138
\(862\) 4.73292i 0.161204i
\(863\) 0.520603i 0.0177215i −0.999961 0.00886077i \(-0.997179\pi\)
0.999961 0.00886077i \(-0.00282051\pi\)
\(864\) −3.27504 −0.111419
\(865\) 0.757874 0.140344i 0.0257685 0.00477185i
\(866\) 10.1048 0.343376
\(867\) 2.25337i 0.0765283i
\(868\) 51.7982i 1.75814i
\(869\) 0 0
\(870\) 0.581695 + 3.14121i 0.0197213 + 0.106497i
\(871\) 29.4745 0.998706
\(872\) 11.8150i 0.400107i
\(873\) 13.7770i 0.466282i
\(874\) 2.42552 0.0820446
\(875\) −34.9704 + 21.4079i −1.18222 + 0.723721i
\(876\) 0.367067 0.0124020
\(877\) 42.7795i 1.44456i −0.691601 0.722280i \(-0.743094\pi\)
0.691601 0.722280i \(-0.256906\pi\)
\(878\) 5.36200i 0.180959i
\(879\) 9.90674 0.334146
\(880\) 0 0
\(881\) 33.2644 1.12071 0.560353 0.828254i \(-0.310665\pi\)
0.560353 + 0.828254i \(0.310665\pi\)
\(882\) 1.86280i 0.0627236i
\(883\) 37.2817i 1.25463i 0.778766 + 0.627314i \(0.215846\pi\)
−0.778766 + 0.627314i \(0.784154\pi\)
\(884\) 35.5168 1.19456
\(885\) −31.8762 + 5.90289i −1.07151 + 0.198424i
\(886\) −2.55648 −0.0858867
\(887\) 47.7445i 1.60310i −0.597926 0.801551i \(-0.704008\pi\)
0.597926 0.801551i \(-0.295992\pi\)
\(888\) 2.69999i 0.0906057i
\(889\) 0.681841 0.0228682
\(890\) 1.93420 0.358178i 0.0648345 0.0120062i
\(891\) 0 0
\(892\) 0.0881070i 0.00295004i
\(893\) 45.0477i 1.50747i
\(894\) 4.42580 0.148021
\(895\) 6.54463 + 35.3417i 0.218763 + 1.18134i
\(896\) −30.4480 −1.01720
\(897\) 5.82137i 0.194370i
\(898\) 0.918739i 0.0306587i
\(899\) −36.4540 −1.21581
\(900\) 8.94749 3.43149i 0.298250 0.114383i
\(901\) 41.3054 1.37608
\(902\) 0 0
\(903\) 2.83290i 0.0942730i
\(904\) 14.5529 0.484021
\(905\) 4.37080 + 23.6028i 0.145290 + 0.784583i
\(906\) −0.303424 −0.0100806
\(907\) 12.2824i 0.407830i 0.978989 + 0.203915i \(0.0653665\pi\)
−0.978989 + 0.203915i \(0.934633\pi\)
\(908\) 11.7791i 0.390903i
\(909\) 4.65928 0.154539
\(910\) −11.2382 + 2.08111i −0.372543 + 0.0689882i
\(911\) 43.2323 1.43235 0.716174 0.697921i \(-0.245892\pi\)
0.716174 + 0.697921i \(0.245892\pi\)
\(912\) 24.4115i 0.808346i
\(913\) 0 0
\(914\) 1.01880 0.0336988
\(915\) 4.02561 0.745468i 0.133082 0.0246444i
\(916\) −22.4940 −0.743224
\(917\) 34.0021i 1.12285i
\(918\) 1.10908i 0.0366051i
\(919\) −55.4515 −1.82917 −0.914587 0.404388i \(-0.867484\pi\)
−0.914587 + 0.404388i \(0.867484\pi\)
\(920\) −0.555586 3.00022i −0.0183171 0.0989144i
\(921\) −23.2505 −0.766131
\(922\) 5.23678i 0.172464i
\(923\) 15.8817i 0.522753i
\(924\) 0 0
\(925\) −4.27359 11.1432i −0.140515 0.366387i
\(926\) −5.20162 −0.170936
\(927\) 9.81701i 0.322433i
\(928\) 16.2007i 0.531814i
\(929\) −47.3061 −1.55206 −0.776032 0.630694i \(-0.782770\pi\)
−0.776032 + 0.630694i \(0.782770\pi\)
\(930\) −0.866573 4.67958i −0.0284160 0.153450i
\(931\) −44.9026 −1.47162
\(932\) 20.4285i 0.669157i
\(933\) 29.8628i 0.977663i
\(934\) 7.71757 0.252527
\(935\) 0 0
\(936\) 5.45863 0.178421
\(937\) 34.6722i 1.13269i −0.824168 0.566346i \(-0.808357\pi\)
0.824168 0.566346i \(-0.191643\pi\)
\(938\) 6.46938i 0.211233i
\(939\) 25.6366 0.836619
\(940\) 27.2673 5.04940i 0.889361 0.164693i
\(941\) 22.0532 0.718913 0.359456 0.933162i \(-0.382962\pi\)
0.359456 + 0.933162i \(0.382962\pi\)
\(942\) 1.42636i 0.0464732i
\(943\) 5.19401i 0.169140i
\(944\) 50.8364 1.65459
\(945\) 1.49321 + 8.06347i 0.0485740 + 0.262305i
\(946\) 0 0
\(947\) 58.6395i 1.90553i −0.303711 0.952764i \(-0.598226\pi\)
0.303711 0.952764i \(-0.401774\pi\)
\(948\) 6.05631i 0.196700i
\(949\) −0.924221 −0.0300015
\(950\) −3.59993 9.38668i −0.116797 0.304544i
\(951\) −1.12070 −0.0363412
\(952\) 15.9305i 0.516310i
\(953\) 43.3834i 1.40533i 0.711523 + 0.702663i \(0.248006\pi\)
−0.711523 + 0.702663i \(0.751994\pi\)
\(954\) 3.10654 0.100578
\(955\) 5.53673 + 29.8989i 0.179164 + 0.967505i
\(956\) −8.80342 −0.284723
\(957\) 0 0
\(958\) 6.57588i 0.212457i
\(959\) 1.60669 0.0518828
\(960\) −13.3396 + 2.47025i −0.430535 + 0.0797271i
\(961\) 23.3068 0.751833
\(962\) 3.32670i 0.107257i
\(963\) 11.8016i 0.380302i
\(964\) −36.1691 −1.16493
\(965\) 56.9637 10.5486i 1.83373 0.339572i
\(966\) 1.27774 0.0411105
\(967\) 39.9415i 1.28443i 0.766523 + 0.642217i \(0.221985\pi\)
−0.766523 + 0.642217i \(0.778015\pi\)
\(968\) 0 0
\(969\) −26.7343 −0.858831
\(970\) −1.62007 8.74854i −0.0520173 0.280899i
\(971\) 41.7596 1.34013 0.670065 0.742302i \(-0.266266\pi\)
0.670065 + 0.742302i \(0.266266\pi\)
\(972\) 1.91659i 0.0614746i
\(973\) 31.5555i 1.01162i
\(974\) −3.91361 −0.125400
\(975\) −22.5285 + 8.64000i −0.721488 + 0.276702i
\(976\) −6.42006 −0.205501
\(977\) 31.7877i 1.01698i −0.861068 0.508489i \(-0.830204\pi\)
0.861068 0.508489i \(-0.169796\pi\)
\(978\) 2.78085i 0.0889218i
\(979\) 0 0
\(980\) 5.03314 + 27.1795i 0.160778 + 0.868216i
\(981\) −10.4450 −0.333484
\(982\) 5.49787i 0.175444i
\(983\) 23.9900i 0.765161i 0.923922 + 0.382580i \(0.124965\pi\)
−0.923922 + 0.382580i \(0.875035\pi\)
\(984\) 4.87036 0.155261
\(985\) −2.60205 + 0.481851i −0.0829081 + 0.0153531i
\(986\) −5.48631 −0.174720
\(987\) 23.7306i 0.755353i
\(988\) 64.3889i 2.04848i
\(989\) 0.931834 0.0296306
\(990\) 0 0
\(991\) −14.1684 −0.450074 −0.225037 0.974350i \(-0.572250\pi\)
−0.225037 + 0.974350i \(0.572250\pi\)
\(992\) 24.1348i 0.766280i
\(993\) 10.9379i 0.347103i
\(994\) 3.48588 0.110565
\(995\) 1.27630 + 6.89214i 0.0404614 + 0.218496i
\(996\) 2.93317 0.0929411
\(997\) 7.30718i 0.231421i 0.993283 + 0.115710i \(0.0369144\pi\)
−0.993283 + 0.115710i \(0.963086\pi\)
\(998\) 6.67428i 0.211271i
\(999\) −2.38692 −0.0755188
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1815.2.c.j.364.13 24
5.2 odd 4 9075.2.a.dz.1.5 12
5.3 odd 4 9075.2.a.dy.1.8 12
5.4 even 2 inner 1815.2.c.j.364.12 24
11.5 even 5 165.2.s.a.124.6 yes 48
11.9 even 5 165.2.s.a.4.7 yes 48
11.10 odd 2 1815.2.c.k.364.12 24
33.5 odd 10 495.2.ba.c.289.7 48
33.20 odd 10 495.2.ba.c.334.6 48
55.9 even 10 165.2.s.a.4.6 48
55.27 odd 20 825.2.n.o.751.4 24
55.32 even 4 9075.2.a.dx.1.8 12
55.38 odd 20 825.2.n.p.751.3 24
55.42 odd 20 825.2.n.o.301.4 24
55.43 even 4 9075.2.a.ea.1.5 12
55.49 even 10 165.2.s.a.124.7 yes 48
55.53 odd 20 825.2.n.p.301.3 24
55.54 odd 2 1815.2.c.k.364.13 24
165.104 odd 10 495.2.ba.c.289.6 48
165.119 odd 10 495.2.ba.c.334.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.s.a.4.6 48 55.9 even 10
165.2.s.a.4.7 yes 48 11.9 even 5
165.2.s.a.124.6 yes 48 11.5 even 5
165.2.s.a.124.7 yes 48 55.49 even 10
495.2.ba.c.289.6 48 165.104 odd 10
495.2.ba.c.289.7 48 33.5 odd 10
495.2.ba.c.334.6 48 33.20 odd 10
495.2.ba.c.334.7 48 165.119 odd 10
825.2.n.o.301.4 24 55.42 odd 20
825.2.n.o.751.4 24 55.27 odd 20
825.2.n.p.301.3 24 55.53 odd 20
825.2.n.p.751.3 24 55.38 odd 20
1815.2.c.j.364.12 24 5.4 even 2 inner
1815.2.c.j.364.13 24 1.1 even 1 trivial
1815.2.c.k.364.12 24 11.10 odd 2
1815.2.c.k.364.13 24 55.54 odd 2
9075.2.a.dx.1.8 12 55.32 even 4
9075.2.a.dy.1.8 12 5.3 odd 4
9075.2.a.dz.1.5 12 5.2 odd 4
9075.2.a.ea.1.5 12 55.43 even 4