Properties

Label 864.2.bf.a.49.4
Level $864$
Weight $2$
Character 864.49
Analytic conductor $6.899$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(49,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bf (of order \(18\), degree \(6\), not 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 49.4
Character \(\chi\) \(=\) 864.49
Dual form 864.2.bf.a.529.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.59613 + 0.672593i) q^{3} +(-0.882298 - 2.42409i) q^{5} +(-0.818935 - 4.64441i) q^{7} +(2.09524 - 2.14709i) q^{9} +O(q^{10})\) \(q+(-1.59613 + 0.672593i) q^{3} +(-0.882298 - 2.42409i) q^{5} +(-0.818935 - 4.64441i) q^{7} +(2.09524 - 2.14709i) q^{9} +(0.647163 - 1.77807i) q^{11} +(-2.09972 + 2.50235i) q^{13} +(3.03869 + 3.27573i) q^{15} +(-0.567141 + 0.982316i) q^{17} +(-4.48572 + 2.58983i) q^{19} +(4.43092 + 6.86226i) q^{21} +(-0.560942 + 3.18126i) q^{23} +(-1.26756 + 1.06361i) q^{25} +(-1.90015 + 4.83626i) q^{27} +(3.21760 + 3.83458i) q^{29} +(0.775862 - 4.40013i) q^{31} +(0.162961 + 3.27330i) q^{33} +(-10.5359 + 6.08293i) q^{35} +(-6.20995 - 3.58532i) q^{37} +(1.66836 - 5.40633i) q^{39} +(-2.91303 - 2.44432i) q^{41} +(1.90770 - 5.24136i) q^{43} +(-7.05337 - 3.18468i) q^{45} +(2.09323 + 11.8713i) q^{47} +(-14.3221 + 5.21280i) q^{49} +(0.244529 - 1.94936i) q^{51} +3.54525i q^{53} -4.88119 q^{55} +(5.41787 - 7.15077i) q^{57} +(-4.29386 - 11.7973i) q^{59} +(-3.67306 + 0.647659i) q^{61} +(-11.6878 - 7.97282i) q^{63} +(7.91852 + 2.88211i) q^{65} +(-0.836157 + 0.996493i) q^{67} +(-1.24436 - 5.45497i) q^{69} +(2.92491 - 5.06609i) q^{71} +(2.92352 + 5.06368i) q^{73} +(1.30781 - 2.55021i) q^{75} +(-8.78806 - 1.54957i) q^{77} +(-1.80639 + 1.51574i) q^{79} +(-0.219965 - 8.99731i) q^{81} +(8.86580 + 10.5658i) q^{83} +(2.88162 + 0.508107i) q^{85} +(-7.71481 - 3.95635i) q^{87} +(0.302925 + 0.524682i) q^{89} +(13.3415 + 7.70271i) q^{91} +(1.72113 + 7.54500i) q^{93} +(10.2357 + 8.58881i) q^{95} +(-15.8957 - 5.78557i) q^{97} +(-2.46170 - 5.11499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\) \(1\)

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 0
\(3\) −1.59613 + 0.672593i −0.921524 + 0.388322i
\(4\) 0 0
\(5\) −0.882298 2.42409i −0.394576 1.08409i −0.964888 0.262660i \(-0.915400\pi\)
0.570312 0.821428i \(-0.306822\pi\)
\(6\) 0 0
\(7\) −0.818935 4.64441i −0.309528 1.75542i −0.601384 0.798960i \(-0.705384\pi\)
0.291856 0.956462i \(-0.405727\pi\)
\(8\) 0 0
\(9\) 2.09524 2.14709i 0.698412 0.715696i
\(10\) 0 0
\(11\) 0.647163 1.77807i 0.195127 0.536107i −0.803086 0.595863i \(-0.796810\pi\)
0.998213 + 0.0597559i \(0.0190322\pi\)
\(12\) 0 0
\(13\) −2.09972 + 2.50235i −0.582358 + 0.694028i −0.974118 0.226040i \(-0.927422\pi\)
0.391760 + 0.920068i \(0.371866\pi\)
\(14\) 0 0
\(15\) 3.03869 + 3.27573i 0.784586 + 0.845791i
\(16\) 0 0
\(17\) −0.567141 + 0.982316i −0.137552 + 0.238247i −0.926569 0.376124i \(-0.877257\pi\)
0.789018 + 0.614371i \(0.210590\pi\)
\(18\) 0 0
\(19\) −4.48572 + 2.58983i −1.02910 + 0.594148i −0.916725 0.399518i \(-0.869177\pi\)
−0.112370 + 0.993666i \(0.535844\pi\)
\(20\) 0 0
\(21\) 4.43092 + 6.86226i 0.966907 + 1.49747i
\(22\) 0 0
\(23\) −0.560942 + 3.18126i −0.116964 + 0.663338i 0.868794 + 0.495173i \(0.164895\pi\)
−0.985759 + 0.168165i \(0.946216\pi\)
\(24\) 0 0
\(25\) −1.26756 + 1.06361i −0.253513 + 0.212722i
\(26\) 0 0
\(27\) −1.90015 + 4.83626i −0.365683 + 0.930739i
\(28\) 0 0
\(29\) 3.21760 + 3.83458i 0.597493 + 0.712064i 0.977028 0.213113i \(-0.0683603\pi\)
−0.379535 + 0.925178i \(0.623916\pi\)
\(30\) 0 0
\(31\) 0.775862 4.40013i 0.139349 0.790287i −0.832383 0.554201i \(-0.813024\pi\)
0.971732 0.236086i \(-0.0758648\pi\)
\(32\) 0 0
\(33\) 0.162961 + 3.27330i 0.0283679 + 0.569808i
\(34\) 0 0
\(35\) −10.5359 + 6.08293i −1.78090 + 1.02820i
\(36\) 0 0
\(37\) −6.20995 3.58532i −1.02091 0.589422i −0.106542 0.994308i \(-0.533978\pi\)
−0.914367 + 0.404886i \(0.867311\pi\)
\(38\) 0 0
\(39\) 1.66836 5.40633i 0.267151 0.865706i
\(40\) 0 0
\(41\) −2.91303 2.44432i −0.454938 0.381738i 0.386326 0.922362i \(-0.373744\pi\)
−0.841265 + 0.540624i \(0.818188\pi\)
\(42\) 0 0
\(43\) 1.90770 5.24136i 0.290921 0.799300i −0.705011 0.709196i \(-0.749058\pi\)
0.995932 0.0901037i \(-0.0287199\pi\)
\(44\) 0 0
\(45\) −7.05337 3.18468i −1.05145 0.474744i
\(46\) 0 0
\(47\) 2.09323 + 11.8713i 0.305329 + 1.73161i 0.621950 + 0.783057i \(0.286341\pi\)
−0.316621 + 0.948552i \(0.602548\pi\)
\(48\) 0 0
\(49\) −14.3221 + 5.21280i −2.04601 + 0.744686i
\(50\) 0 0
\(51\) 0.244529 1.94936i 0.0342409 0.272964i
\(52\) 0 0
\(53\) 3.54525i 0.486978i 0.969904 + 0.243489i \(0.0782920\pi\)
−0.969904 + 0.243489i \(0.921708\pi\)
\(54\) 0 0
\(55\) −4.88119 −0.658180
\(56\) 0 0
\(57\) 5.41787 7.15077i 0.717615 0.947142i
\(58\) 0 0
\(59\) −4.29386 11.7973i −0.559013 1.53588i −0.821072 0.570824i \(-0.806624\pi\)
0.262059 0.965052i \(-0.415599\pi\)
\(60\) 0 0
\(61\) −3.67306 + 0.647659i −0.470287 + 0.0829243i −0.403769 0.914861i \(-0.632300\pi\)
−0.0665178 + 0.997785i \(0.521189\pi\)
\(62\) 0 0
\(63\) −11.6878 7.97282i −1.47253 1.00448i
\(64\) 0 0
\(65\) 7.91852 + 2.88211i 0.982172 + 0.357481i
\(66\) 0 0
\(67\) −0.836157 + 0.996493i −0.102153 + 0.121741i −0.814699 0.579885i \(-0.803098\pi\)
0.712546 + 0.701626i \(0.247542\pi\)
\(68\) 0 0
\(69\) −1.24436 5.45497i −0.149803 0.656702i
\(70\) 0 0
\(71\) 2.92491 5.06609i 0.347123 0.601234i −0.638614 0.769527i \(-0.720492\pi\)
0.985737 + 0.168293i \(0.0538254\pi\)
\(72\) 0 0
\(73\) 2.92352 + 5.06368i 0.342172 + 0.592659i 0.984836 0.173489i \(-0.0555042\pi\)
−0.642664 + 0.766148i \(0.722171\pi\)
\(74\) 0 0
\(75\) 1.30781 2.55021i 0.151013 0.294473i
\(76\) 0 0
\(77\) −8.78806 1.54957i −1.00149 0.176590i
\(78\) 0 0
\(79\) −1.80639 + 1.51574i −0.203234 + 0.170534i −0.738724 0.674008i \(-0.764571\pi\)
0.535490 + 0.844542i \(0.320127\pi\)
\(80\) 0 0
\(81\) −0.219965 8.99731i −0.0244406 0.999701i
\(82\) 0 0
\(83\) 8.86580 + 10.5658i 0.973148 + 1.15975i 0.987141 + 0.159850i \(0.0511012\pi\)
−0.0139934 + 0.999902i \(0.504454\pi\)
\(84\) 0 0
\(85\) 2.88162 + 0.508107i 0.312555 + 0.0551119i
\(86\) 0 0
\(87\) −7.71481 3.95635i −0.827114 0.424165i
\(88\) 0 0
\(89\) 0.302925 + 0.524682i 0.0321100 + 0.0556162i 0.881634 0.471934i \(-0.156444\pi\)
−0.849524 + 0.527550i \(0.823111\pi\)
\(90\) 0 0
\(91\) 13.3415 + 7.70271i 1.39857 + 0.807464i
\(92\) 0 0
\(93\) 1.72113 + 7.54500i 0.178472 + 0.782380i
\(94\) 0 0
\(95\) 10.2357 + 8.58881i 1.05017 + 0.881193i
\(96\) 0 0
\(97\) −15.8957 5.78557i −1.61397 0.587436i −0.631747 0.775174i \(-0.717662\pi\)
−0.982219 + 0.187739i \(0.939884\pi\)
\(98\) 0 0
\(99\) −2.46170 5.11499i −0.247411 0.514076i
\(100\) 0 0
\(101\) 2.63438 0.464512i 0.262130 0.0462207i −0.0410382 0.999158i \(-0.513067\pi\)
0.303169 + 0.952937i \(0.401955\pi\)
\(102\) 0 0
\(103\) −14.5813 + 5.30716i −1.43674 + 0.522930i −0.938854 0.344314i \(-0.888111\pi\)
−0.497883 + 0.867244i \(0.665889\pi\)
\(104\) 0 0
\(105\) 12.7254 16.7955i 1.24187 1.63908i
\(106\) 0 0
\(107\) 11.5155i 1.11325i 0.830764 + 0.556625i \(0.187904\pi\)
−0.830764 + 0.556625i \(0.812096\pi\)
\(108\) 0 0
\(109\) 15.9553i 1.52824i −0.645075 0.764119i \(-0.723174\pi\)
0.645075 0.764119i \(-0.276826\pi\)
\(110\) 0 0
\(111\) 12.3233 + 1.54585i 1.16968 + 0.146725i
\(112\) 0 0
\(113\) −0.805672 + 0.293240i −0.0757912 + 0.0275857i −0.379638 0.925135i \(-0.623951\pi\)
0.303846 + 0.952721i \(0.401729\pi\)
\(114\) 0 0
\(115\) 8.20659 1.44704i 0.765268 0.134937i
\(116\) 0 0
\(117\) 0.973351 + 9.75131i 0.0899864 + 0.901509i
\(118\) 0 0
\(119\) 5.02673 + 1.82958i 0.460800 + 0.167717i
\(120\) 0 0
\(121\) 5.68379 + 4.76926i 0.516708 + 0.433569i
\(122\) 0 0
\(123\) 6.29359 + 1.94216i 0.567474 + 0.175119i
\(124\) 0 0
\(125\) −7.47362 4.31490i −0.668461 0.385936i
\(126\) 0 0
\(127\) −1.07290 1.85831i −0.0952042 0.164898i 0.814490 0.580178i \(-0.197017\pi\)
−0.909694 + 0.415280i \(0.863684\pi\)
\(128\) 0 0
\(129\) 0.480375 + 9.64898i 0.0422947 + 0.849545i
\(130\) 0 0
\(131\) 10.6350 + 1.87524i 0.929187 + 0.163841i 0.617704 0.786411i \(-0.288063\pi\)
0.311483 + 0.950252i \(0.399174\pi\)
\(132\) 0 0
\(133\) 15.7018 + 18.7126i 1.36152 + 1.62259i
\(134\) 0 0
\(135\) 13.4001 + 0.339107i 1.15329 + 0.0291857i
\(136\) 0 0
\(137\) −12.7808 + 10.7244i −1.09194 + 0.916245i −0.996857 0.0792243i \(-0.974756\pi\)
−0.0950817 + 0.995469i \(0.530311\pi\)
\(138\) 0 0
\(139\) −15.7604 2.77899i −1.33678 0.235710i −0.540861 0.841112i \(-0.681901\pi\)
−0.795920 + 0.605402i \(0.793012\pi\)
\(140\) 0 0
\(141\) −11.3256 17.5402i −0.953790 1.47715i
\(142\) 0 0
\(143\) 3.09049 + 5.35288i 0.258439 + 0.447630i
\(144\) 0 0
\(145\) 6.45651 11.1830i 0.536184 0.928698i
\(146\) 0 0
\(147\) 19.3537 17.9532i 1.59627 1.48076i
\(148\) 0 0
\(149\) −1.12442 + 1.34003i −0.0921157 + 0.109779i −0.810133 0.586246i \(-0.800605\pi\)
0.718018 + 0.696025i \(0.245050\pi\)
\(150\) 0 0
\(151\) 1.88609 + 0.686481i 0.153488 + 0.0558650i 0.417622 0.908621i \(-0.362864\pi\)
−0.264134 + 0.964486i \(0.585086\pi\)
\(152\) 0 0
\(153\) 0.920825 + 3.27589i 0.0744443 + 0.264840i
\(154\) 0 0
\(155\) −11.3509 + 2.00147i −0.911725 + 0.160762i
\(156\) 0 0
\(157\) −2.34039 6.43016i −0.186783 0.513182i 0.810590 0.585614i \(-0.199146\pi\)
−0.997373 + 0.0724314i \(0.976924\pi\)
\(158\) 0 0
\(159\) −2.38451 5.65867i −0.189104 0.448762i
\(160\) 0 0
\(161\) 15.2344 1.20064
\(162\) 0 0
\(163\) 6.85942i 0.537271i −0.963242 0.268636i \(-0.913427\pi\)
0.963242 0.268636i \(-0.0865728\pi\)
\(164\) 0 0
\(165\) 7.79100 3.28306i 0.606529 0.255586i
\(166\) 0 0
\(167\) −6.78917 + 2.47106i −0.525362 + 0.191216i −0.591066 0.806623i \(-0.701293\pi\)
0.0657043 + 0.997839i \(0.479071\pi\)
\(168\) 0 0
\(169\) 0.404495 + 2.29401i 0.0311150 + 0.176462i
\(170\) 0 0
\(171\) −3.83805 + 15.0575i −0.293503 + 1.15148i
\(172\) 0 0
\(173\) 2.35038 6.45762i 0.178696 0.490964i −0.817714 0.575625i \(-0.804759\pi\)
0.996410 + 0.0846617i \(0.0269810\pi\)
\(174\) 0 0
\(175\) 5.97791 + 5.01606i 0.451887 + 0.379178i
\(176\) 0 0
\(177\) 14.7883 + 15.9419i 1.11156 + 1.19827i
\(178\) 0 0
\(179\) −2.11037 1.21842i −0.157737 0.0910693i 0.419054 0.907961i \(-0.362362\pi\)
−0.576791 + 0.816892i \(0.695695\pi\)
\(180\) 0 0
\(181\) 21.1559 12.2143i 1.57250 0.907885i 0.576642 0.816997i \(-0.304363\pi\)
0.995861 0.0908887i \(-0.0289708\pi\)
\(182\) 0 0
\(183\) 5.42705 3.50422i 0.401179 0.259039i
\(184\) 0 0
\(185\) −3.21212 + 18.2168i −0.236160 + 1.33933i
\(186\) 0 0
\(187\) 1.37959 + 1.64413i 0.100886 + 0.120231i
\(188\) 0 0
\(189\) 24.0177 + 4.86447i 1.74703 + 0.353838i
\(190\) 0 0
\(191\) −0.483744 + 0.405909i −0.0350025 + 0.0293706i −0.660121 0.751159i \(-0.729495\pi\)
0.625119 + 0.780530i \(0.285051\pi\)
\(192\) 0 0
\(193\) 3.60135 20.4243i 0.259231 1.47017i −0.525744 0.850643i \(-0.676213\pi\)
0.784975 0.619527i \(-0.212676\pi\)
\(194\) 0 0
\(195\) −14.5774 + 0.725739i −1.04391 + 0.0519712i
\(196\) 0 0
\(197\) 8.16675 4.71508i 0.581857 0.335935i −0.180014 0.983664i \(-0.557614\pi\)
0.761871 + 0.647729i \(0.224281\pi\)
\(198\) 0 0
\(199\) −1.56260 + 2.70650i −0.110770 + 0.191859i −0.916081 0.400994i \(-0.868665\pi\)
0.805311 + 0.592852i \(0.201998\pi\)
\(200\) 0 0
\(201\) 0.664378 2.15292i 0.0468616 0.151855i
\(202\) 0 0
\(203\) 15.1744 18.0841i 1.06503 1.26926i
\(204\) 0 0
\(205\) −3.35510 + 9.21807i −0.234331 + 0.643818i
\(206\) 0 0
\(207\) 5.65513 + 7.86988i 0.393059 + 0.546994i
\(208\) 0 0
\(209\) 1.70190 + 9.65196i 0.117723 + 0.667640i
\(210\) 0 0
\(211\) −9.07630 24.9369i −0.624838 1.71673i −0.694823 0.719181i \(-0.744517\pi\)
0.0699851 0.997548i \(-0.477705\pi\)
\(212\) 0 0
\(213\) −1.26110 + 10.0534i −0.0864095 + 0.688847i
\(214\) 0 0
\(215\) −14.3887 −0.981303
\(216\) 0 0
\(217\) −21.0714 −1.43042
\(218\) 0 0
\(219\) −8.07209 6.11593i −0.545462 0.413276i
\(220\) 0 0
\(221\) −1.26726 3.48178i −0.0852454 0.234210i
\(222\) 0 0
\(223\) −0.840933 4.76917i −0.0563130 0.319367i 0.943619 0.331034i \(-0.107397\pi\)
−0.999932 + 0.0116667i \(0.996286\pi\)
\(224\) 0 0
\(225\) −0.372178 + 4.95009i −0.0248119 + 0.330006i
\(226\) 0 0
\(227\) 6.82487 18.7512i 0.452982 1.24456i −0.477633 0.878560i \(-0.658505\pi\)
0.930615 0.365999i \(-0.119273\pi\)
\(228\) 0 0
\(229\) −0.391830 + 0.466964i −0.0258928 + 0.0308579i −0.778835 0.627228i \(-0.784189\pi\)
0.752943 + 0.658086i \(0.228634\pi\)
\(230\) 0 0
\(231\) 15.0691 3.43748i 0.991473 0.226169i
\(232\) 0 0
\(233\) −3.02731 + 5.24345i −0.198326 + 0.343510i −0.947986 0.318313i \(-0.896884\pi\)
0.749660 + 0.661823i \(0.230217\pi\)
\(234\) 0 0
\(235\) 26.9303 15.5482i 1.75674 1.01426i
\(236\) 0 0
\(237\) 1.86375 3.63427i 0.121063 0.236071i
\(238\) 0 0
\(239\) 1.84795 10.4802i 0.119534 0.677910i −0.864871 0.501994i \(-0.832600\pi\)
0.984405 0.175916i \(-0.0562889\pi\)
\(240\) 0 0
\(241\) 1.94324 1.63057i 0.125175 0.105034i −0.578051 0.816000i \(-0.696187\pi\)
0.703226 + 0.710966i \(0.251742\pi\)
\(242\) 0 0
\(243\) 6.40262 + 14.2129i 0.410728 + 0.911758i
\(244\) 0 0
\(245\) 25.2727 + 30.1188i 1.61461 + 1.92422i
\(246\) 0 0
\(247\) 2.93810 16.6628i 0.186947 1.06023i
\(248\) 0 0
\(249\) −21.2575 10.9013i −1.34714 0.690845i
\(250\) 0 0
\(251\) −9.74106 + 5.62400i −0.614850 + 0.354984i −0.774861 0.632131i \(-0.782180\pi\)
0.160011 + 0.987115i \(0.448847\pi\)
\(252\) 0 0
\(253\) 5.29347 + 3.05619i 0.332798 + 0.192141i
\(254\) 0 0
\(255\) −4.94117 + 1.12715i −0.309428 + 0.0705850i
\(256\) 0 0
\(257\) −5.40395 4.53446i −0.337089 0.282852i 0.458492 0.888699i \(-0.348390\pi\)
−0.795581 + 0.605847i \(0.792834\pi\)
\(258\) 0 0
\(259\) −11.5661 + 31.7777i −0.718685 + 1.97457i
\(260\) 0 0
\(261\) 14.9748 + 1.12590i 0.926918 + 0.0696914i
\(262\) 0 0
\(263\) −5.03677 28.5649i −0.310580 1.76139i −0.595999 0.802985i \(-0.703244\pi\)
0.285418 0.958403i \(-0.407867\pi\)
\(264\) 0 0
\(265\) 8.59403 3.12797i 0.527927 0.192150i
\(266\) 0 0
\(267\) −0.836405 0.633713i −0.0511871 0.0387826i
\(268\) 0 0
\(269\) 14.3553i 0.875257i −0.899156 0.437628i \(-0.855819\pi\)
0.899156 0.437628i \(-0.144181\pi\)
\(270\) 0 0
\(271\) −15.9782 −0.970609 −0.485305 0.874345i \(-0.661291\pi\)
−0.485305 + 0.874345i \(0.661291\pi\)
\(272\) 0 0
\(273\) −26.4755 3.32111i −1.60237 0.201002i
\(274\) 0 0
\(275\) 1.07085 + 2.94214i 0.0645749 + 0.177418i
\(276\) 0 0
\(277\) −7.40970 + 1.30653i −0.445206 + 0.0785017i −0.391757 0.920069i \(-0.628133\pi\)
−0.0534488 + 0.998571i \(0.517021\pi\)
\(278\) 0 0
\(279\) −7.82185 10.8852i −0.468282 0.651678i
\(280\) 0 0
\(281\) −8.85360 3.22245i −0.528162 0.192235i 0.0641557 0.997940i \(-0.479565\pi\)
−0.592317 + 0.805705i \(0.701787\pi\)
\(282\) 0 0
\(283\) −15.8895 + 18.9364i −0.944533 + 1.12565i 0.0473989 + 0.998876i \(0.484907\pi\)
−0.991932 + 0.126774i \(0.959538\pi\)
\(284\) 0 0
\(285\) −22.1143 6.82433i −1.30994 0.404239i
\(286\) 0 0
\(287\) −8.96684 + 15.5310i −0.529296 + 0.916768i
\(288\) 0 0
\(289\) 7.85670 + 13.6082i 0.462159 + 0.800483i
\(290\) 0 0
\(291\) 29.2629 1.45686i 1.71542 0.0854024i
\(292\) 0 0
\(293\) −7.64101 1.34732i −0.446392 0.0787110i −0.0540666 0.998537i \(-0.517218\pi\)
−0.392326 + 0.919826i \(0.628329\pi\)
\(294\) 0 0
\(295\) −24.8093 + 20.8175i −1.44445 + 1.21204i
\(296\) 0 0
\(297\) 7.36950 + 6.50844i 0.427622 + 0.377658i
\(298\) 0 0
\(299\) −6.78281 8.08343i −0.392260 0.467477i
\(300\) 0 0
\(301\) −25.9053 4.56781i −1.49316 0.263284i
\(302\) 0 0
\(303\) −3.89237 + 2.51328i −0.223611 + 0.144384i
\(304\) 0 0
\(305\) 4.81072 + 8.33241i 0.275461 + 0.477112i
\(306\) 0 0
\(307\) −11.1421 6.43289i −0.635913 0.367145i 0.147125 0.989118i \(-0.452998\pi\)
−0.783038 + 0.621973i \(0.786331\pi\)
\(308\) 0 0
\(309\) 19.7040 18.2782i 1.12092 1.03981i
\(310\) 0 0
\(311\) 12.4067 + 10.4105i 0.703521 + 0.590324i 0.922773 0.385344i \(-0.125917\pi\)
−0.219252 + 0.975668i \(0.570362\pi\)
\(312\) 0 0
\(313\) −1.04686 0.381024i −0.0591718 0.0215368i 0.312265 0.949995i \(-0.398912\pi\)
−0.371436 + 0.928458i \(0.621135\pi\)
\(314\) 0 0
\(315\) −9.01472 + 35.3668i −0.507922 + 1.99269i
\(316\) 0 0
\(317\) −1.55544 + 0.274266i −0.0873623 + 0.0154043i −0.217158 0.976136i \(-0.569679\pi\)
0.129796 + 0.991541i \(0.458568\pi\)
\(318\) 0 0
\(319\) 8.90046 3.23950i 0.498330 0.181377i
\(320\) 0 0
\(321\) −7.74527 18.3803i −0.432299 1.02589i
\(322\) 0 0
\(323\) 5.87520i 0.326905i
\(324\) 0 0
\(325\) 5.40518i 0.299826i
\(326\) 0 0
\(327\) 10.7314 + 25.4666i 0.593448 + 1.40831i
\(328\) 0 0
\(329\) 53.4211 19.4437i 2.94520 1.07196i
\(330\) 0 0
\(331\) 12.2698 2.16350i 0.674411 0.118917i 0.174054 0.984736i \(-0.444313\pi\)
0.500357 + 0.865819i \(0.333202\pi\)
\(332\) 0 0
\(333\) −20.7093 + 5.82122i −1.13486 + 0.319001i
\(334\) 0 0
\(335\) 3.15333 + 1.14772i 0.172285 + 0.0627066i
\(336\) 0 0
\(337\) −3.46382 2.90649i −0.188686 0.158327i 0.543551 0.839376i \(-0.317079\pi\)
−0.732237 + 0.681049i \(0.761524\pi\)
\(338\) 0 0
\(339\) 1.08872 1.00994i 0.0591313 0.0548523i
\(340\) 0 0
\(341\) −7.32162 4.22714i −0.396488 0.228912i
\(342\) 0 0
\(343\) 19.4330 + 33.6590i 1.04928 + 1.81741i
\(344\) 0 0
\(345\) −12.1255 + 7.82936i −0.652814 + 0.421519i
\(346\) 0 0
\(347\) 3.23530 + 0.570470i 0.173680 + 0.0306244i 0.259812 0.965659i \(-0.416340\pi\)
−0.0861319 + 0.996284i \(0.527451\pi\)
\(348\) 0 0
\(349\) 0.513251 + 0.611669i 0.0274737 + 0.0327419i 0.779606 0.626270i \(-0.215419\pi\)
−0.752133 + 0.659012i \(0.770975\pi\)
\(350\) 0 0
\(351\) −8.11226 14.9096i −0.433000 0.795818i
\(352\) 0 0
\(353\) 18.2518 15.3150i 0.971443 0.815138i −0.0113333 0.999936i \(-0.503608\pi\)
0.982776 + 0.184798i \(0.0591631\pi\)
\(354\) 0 0
\(355\) −14.8613 2.62045i −0.788757 0.139079i
\(356\) 0 0
\(357\) −9.25386 + 0.460704i −0.489766 + 0.0243830i
\(358\) 0 0
\(359\) −8.66171 15.0025i −0.457148 0.791803i 0.541661 0.840597i \(-0.317796\pi\)
−0.998809 + 0.0487939i \(0.984462\pi\)
\(360\) 0 0
\(361\) 3.91447 6.78006i 0.206025 0.356845i
\(362\) 0 0
\(363\) −12.2798 3.78947i −0.644523 0.198896i
\(364\) 0 0
\(365\) 9.69542 11.5546i 0.507482 0.604793i
\(366\) 0 0
\(367\) 15.6943 + 5.71227i 0.819237 + 0.298178i 0.717434 0.696627i \(-0.245317\pi\)
0.101803 + 0.994805i \(0.467539\pi\)
\(368\) 0 0
\(369\) −11.3516 + 1.13309i −0.590943 + 0.0589865i
\(370\) 0 0
\(371\) 16.4656 2.90333i 0.854852 0.150733i
\(372\) 0 0
\(373\) −1.32927 3.65215i −0.0688272 0.189101i 0.900510 0.434835i \(-0.143193\pi\)
−0.969337 + 0.245734i \(0.920971\pi\)
\(374\) 0 0
\(375\) 14.8310 + 1.86041i 0.765870 + 0.0960714i
\(376\) 0 0
\(377\) −16.3515 −0.842147
\(378\) 0 0
\(379\) 10.9558i 0.562760i −0.959596 0.281380i \(-0.909208\pi\)
0.959596 0.281380i \(-0.0907922\pi\)
\(380\) 0 0
\(381\) 2.96237 + 2.24448i 0.151767 + 0.114988i
\(382\) 0 0
\(383\) −13.6840 + 4.98057i −0.699220 + 0.254495i −0.667078 0.744988i \(-0.732455\pi\)
−0.0321425 + 0.999483i \(0.510233\pi\)
\(384\) 0 0
\(385\) 3.99738 + 22.6703i 0.203725 + 1.15538i
\(386\) 0 0
\(387\) −7.25658 15.0779i −0.368873 0.766452i
\(388\) 0 0
\(389\) −1.59337 + 4.37774i −0.0807869 + 0.221960i −0.973510 0.228646i \(-0.926570\pi\)
0.892723 + 0.450607i \(0.148792\pi\)
\(390\) 0 0
\(391\) −2.80687 2.35524i −0.141949 0.119110i
\(392\) 0 0
\(393\) −18.2361 + 4.15993i −0.919891 + 0.209840i
\(394\) 0 0
\(395\) 5.26807 + 3.04152i 0.265065 + 0.153035i
\(396\) 0 0
\(397\) −2.23476 + 1.29024i −0.112160 + 0.0647554i −0.555030 0.831830i \(-0.687293\pi\)
0.442871 + 0.896585i \(0.353960\pi\)
\(398\) 0 0
\(399\) −37.6480 19.3068i −1.88476 0.966550i
\(400\) 0 0
\(401\) 2.06316 11.7008i 0.103029 0.584309i −0.888960 0.457986i \(-0.848571\pi\)
0.991989 0.126324i \(-0.0403178\pi\)
\(402\) 0 0
\(403\) 9.38158 + 11.1805i 0.467330 + 0.556942i
\(404\) 0 0
\(405\) −21.6163 + 8.47153i −1.07412 + 0.420954i
\(406\) 0 0
\(407\) −10.3938 + 8.72142i −0.515201 + 0.432305i
\(408\) 0 0
\(409\) −2.49747 + 14.1638i −0.123492 + 0.700357i 0.858700 + 0.512478i \(0.171272\pi\)
−0.982192 + 0.187879i \(0.939839\pi\)
\(410\) 0 0
\(411\) 13.1866 25.7137i 0.650449 1.26837i
\(412\) 0 0
\(413\) −51.2751 + 29.6037i −2.52308 + 1.45670i
\(414\) 0 0
\(415\) 17.7903 30.8138i 0.873293 1.51259i
\(416\) 0 0
\(417\) 27.0247 6.16473i 1.32341 0.301888i
\(418\) 0 0
\(419\) −15.8793 + 18.9242i −0.775755 + 0.924509i −0.998733 0.0503146i \(-0.983978\pi\)
0.222978 + 0.974823i \(0.428422\pi\)
\(420\) 0 0
\(421\) −10.8138 + 29.7106i −0.527032 + 1.44801i 0.335517 + 0.942034i \(0.391089\pi\)
−0.862549 + 0.505974i \(0.831133\pi\)
\(422\) 0 0
\(423\) 29.8746 + 20.3789i 1.45255 + 0.990854i
\(424\) 0 0
\(425\) −0.325917 1.84837i −0.0158093 0.0896589i
\(426\) 0 0
\(427\) 6.01599 + 16.5288i 0.291134 + 0.799885i
\(428\) 0 0
\(429\) −8.53312 6.46523i −0.411983 0.312144i
\(430\) 0 0
\(431\) 7.78707 0.375090 0.187545 0.982256i \(-0.439947\pi\)
0.187545 + 0.982256i \(0.439947\pi\)
\(432\) 0 0
\(433\) 8.41002 0.404160 0.202080 0.979369i \(-0.435230\pi\)
0.202080 + 0.979369i \(0.435230\pi\)
\(434\) 0 0
\(435\) −2.78379 + 22.1921i −0.133473 + 1.06403i
\(436\) 0 0
\(437\) −5.72270 15.7230i −0.273754 0.752132i
\(438\) 0 0
\(439\) 3.95770 + 22.4452i 0.188891 + 1.07125i 0.920854 + 0.389908i \(0.127493\pi\)
−0.731963 + 0.681344i \(0.761396\pi\)
\(440\) 0 0
\(441\) −18.8158 + 41.6728i −0.895989 + 1.98442i
\(442\) 0 0
\(443\) −7.54668 + 20.7343i −0.358554 + 0.985118i 0.620978 + 0.783828i \(0.286736\pi\)
−0.979532 + 0.201290i \(0.935487\pi\)
\(444\) 0 0
\(445\) 1.00461 1.19725i 0.0476230 0.0567549i
\(446\) 0 0
\(447\) 0.893416 2.89512i 0.0422571 0.136935i
\(448\) 0 0
\(449\) −0.937600 + 1.62397i −0.0442481 + 0.0766400i −0.887301 0.461190i \(-0.847423\pi\)
0.843053 + 0.537830i \(0.180756\pi\)
\(450\) 0 0
\(451\) −6.23137 + 3.59768i −0.293424 + 0.169408i
\(452\) 0 0
\(453\) −3.47216 + 0.172862i −0.163136 + 0.00812175i
\(454\) 0 0
\(455\) 6.90093 39.1371i 0.323521 1.83478i
\(456\) 0 0
\(457\) 20.8493 17.4947i 0.975290 0.818365i −0.00808235 0.999967i \(-0.502573\pi\)
0.983372 + 0.181602i \(0.0581283\pi\)
\(458\) 0 0
\(459\) −3.67309 4.60939i −0.171445 0.215148i
\(460\) 0 0
\(461\) 9.21149 + 10.9778i 0.429022 + 0.511289i 0.936640 0.350294i \(-0.113918\pi\)
−0.507618 + 0.861582i \(0.669474\pi\)
\(462\) 0 0
\(463\) 2.62893 14.9094i 0.122177 0.692899i −0.860768 0.508998i \(-0.830016\pi\)
0.982945 0.183901i \(-0.0588727\pi\)
\(464\) 0 0
\(465\) 16.7713 10.8291i 0.777749 0.502188i
\(466\) 0 0
\(467\) −8.60621 + 4.96880i −0.398248 + 0.229929i −0.685728 0.727858i \(-0.740516\pi\)
0.287480 + 0.957787i \(0.407183\pi\)
\(468\) 0 0
\(469\) 5.31288 + 3.06739i 0.245326 + 0.141639i
\(470\) 0 0
\(471\) 8.06043 + 8.68921i 0.371405 + 0.400378i
\(472\) 0 0
\(473\) −8.08490 6.78404i −0.371744 0.311930i
\(474\) 0 0
\(475\) 2.93136 8.05385i 0.134500 0.369536i
\(476\) 0 0
\(477\) 7.61197 + 7.42814i 0.348528 + 0.340111i
\(478\) 0 0
\(479\) −1.57169 8.91349i −0.0718123 0.407268i −0.999431 0.0337386i \(-0.989259\pi\)
0.927618 0.373529i \(-0.121852\pi\)
\(480\) 0 0
\(481\) 22.0109 8.01131i 1.00361 0.365284i
\(482\) 0 0
\(483\) −24.3161 + 10.2466i −1.10642 + 0.466236i
\(484\) 0 0
\(485\) 43.6373i 1.98147i
\(486\) 0 0
\(487\) −23.7830 −1.07771 −0.538856 0.842398i \(-0.681143\pi\)
−0.538856 + 0.842398i \(0.681143\pi\)
\(488\) 0 0
\(489\) 4.61360 + 10.9485i 0.208634 + 0.495108i
\(490\) 0 0
\(491\) −11.9837 32.9250i −0.540818 1.48589i −0.845786 0.533523i \(-0.820868\pi\)
0.304968 0.952363i \(-0.401354\pi\)
\(492\) 0 0
\(493\) −5.59160 + 0.985951i −0.251833 + 0.0444050i
\(494\) 0 0
\(495\) −10.2273 + 10.4803i −0.459681 + 0.471057i
\(496\) 0 0
\(497\) −25.9243 9.43568i −1.16286 0.423248i
\(498\) 0 0
\(499\) −4.72891 + 5.63569i −0.211695 + 0.252288i −0.861435 0.507869i \(-0.830434\pi\)
0.649739 + 0.760157i \(0.274878\pi\)
\(500\) 0 0
\(501\) 9.17436 8.51047i 0.409880 0.380220i
\(502\) 0 0
\(503\) 9.31955 16.1419i 0.415538 0.719733i −0.579947 0.814655i \(-0.696927\pi\)
0.995485 + 0.0949212i \(0.0302599\pi\)
\(504\) 0 0
\(505\) −3.45033 5.97615i −0.153538 0.265935i
\(506\) 0 0
\(507\) −2.18856 3.38946i −0.0971973 0.150531i
\(508\) 0 0
\(509\) −13.2305 2.33290i −0.586432 0.103404i −0.127443 0.991846i \(-0.540677\pi\)
−0.458989 + 0.888442i \(0.651788\pi\)
\(510\) 0 0
\(511\) 21.1236 17.7248i 0.934454 0.784100i
\(512\) 0 0
\(513\) −4.00159 26.6152i −0.176674 1.17509i
\(514\) 0 0
\(515\) 25.7301 + 30.6639i 1.13380 + 1.35121i
\(516\) 0 0
\(517\) 22.4627 + 3.96077i 0.987907 + 0.174195i
\(518\) 0 0
\(519\) 0.591846 + 11.8880i 0.0259791 + 0.521826i
\(520\) 0 0
\(521\) −18.3404 31.7664i −0.803505 1.39171i −0.917295 0.398207i \(-0.869632\pi\)
0.113790 0.993505i \(-0.463701\pi\)
\(522\) 0 0
\(523\) 4.88996 + 2.82322i 0.213823 + 0.123451i 0.603087 0.797676i \(-0.293937\pi\)
−0.389264 + 0.921126i \(0.627271\pi\)
\(524\) 0 0
\(525\) −12.9153 3.98556i −0.563668 0.173944i
\(526\) 0 0
\(527\) 3.88230 + 3.25764i 0.169116 + 0.141905i
\(528\) 0 0
\(529\) 11.8072 + 4.29746i 0.513356 + 0.186846i
\(530\) 0 0
\(531\) −34.3265 15.4988i −1.48964 0.672592i
\(532\) 0 0
\(533\) 12.2331 2.15702i 0.529874 0.0934311i
\(534\) 0 0
\(535\) 27.9148 10.1601i 1.20686 0.439261i
\(536\) 0 0
\(537\) 4.18793 + 0.525337i 0.180722 + 0.0226699i
\(538\) 0 0
\(539\) 28.8391i 1.24219i
\(540\) 0 0
\(541\) 17.4866i 0.751808i −0.926659 0.375904i \(-0.877332\pi\)
0.926659 0.375904i \(-0.122668\pi\)
\(542\) 0 0
\(543\) −25.5522 + 33.7249i −1.09655 + 1.44728i
\(544\) 0 0
\(545\) −38.6771 + 14.0773i −1.65674 + 0.603006i
\(546\) 0 0
\(547\) 30.3035 5.34332i 1.29568 0.228464i 0.517056 0.855952i \(-0.327028\pi\)
0.778626 + 0.627488i \(0.215917\pi\)
\(548\) 0 0
\(549\) −6.30534 + 9.24337i −0.269106 + 0.394498i
\(550\) 0 0
\(551\) −24.3642 8.86784i −1.03795 0.377783i
\(552\) 0 0
\(553\) 8.51903 + 7.14831i 0.362266 + 0.303977i
\(554\) 0 0
\(555\) −7.12557 31.2368i −0.302464 1.32593i
\(556\) 0 0
\(557\) −5.65968 3.26762i −0.239808 0.138453i 0.375280 0.926911i \(-0.377546\pi\)
−0.615089 + 0.788458i \(0.710880\pi\)
\(558\) 0 0
\(559\) 9.11009 + 15.7791i 0.385316 + 0.667387i
\(560\) 0 0
\(561\) −3.30783 1.69634i −0.139657 0.0716195i
\(562\) 0 0
\(563\) −25.8351 4.55543i −1.08882 0.191989i −0.399708 0.916642i \(-0.630889\pi\)
−0.689113 + 0.724654i \(0.742000\pi\)
\(564\) 0 0
\(565\) 1.42169 + 1.69430i 0.0598108 + 0.0712797i
\(566\) 0 0
\(567\) −41.6071 + 8.38982i −1.74733 + 0.352339i
\(568\) 0 0
\(569\) −7.81553 + 6.55801i −0.327644 + 0.274926i −0.791739 0.610859i \(-0.790824\pi\)
0.464095 + 0.885785i \(0.346380\pi\)
\(570\) 0 0
\(571\) −14.9514 2.63633i −0.625696 0.110327i −0.148195 0.988958i \(-0.547346\pi\)
−0.477501 + 0.878631i \(0.658457\pi\)
\(572\) 0 0
\(573\) 0.499105 0.973246i 0.0208504 0.0406579i
\(574\) 0 0
\(575\) −2.67260 4.62907i −0.111455 0.193046i
\(576\) 0 0
\(577\) 9.96264 17.2558i 0.414750 0.718369i −0.580652 0.814152i \(-0.697202\pi\)
0.995402 + 0.0957834i \(0.0305356\pi\)
\(578\) 0 0
\(579\) 7.98901 + 35.0219i 0.332012 + 1.45546i
\(580\) 0 0
\(581\) 41.8116 49.8292i 1.73464 2.06726i
\(582\) 0 0
\(583\) 6.30370 + 2.29436i 0.261072 + 0.0950226i
\(584\) 0 0
\(585\) 22.7793 10.9631i 0.941809 0.453267i
\(586\) 0 0
\(587\) 23.9630 4.22532i 0.989057 0.174397i 0.344362 0.938837i \(-0.388095\pi\)
0.644695 + 0.764440i \(0.276984\pi\)
\(588\) 0 0
\(589\) 7.91530 + 21.7471i 0.326144 + 0.896074i
\(590\) 0 0
\(591\) −9.86384 + 13.0188i −0.405744 + 0.535520i
\(592\) 0 0
\(593\) −38.6846 −1.58859 −0.794294 0.607534i \(-0.792159\pi\)
−0.794294 + 0.607534i \(0.792159\pi\)
\(594\) 0 0
\(595\) 13.7995i 0.565725i
\(596\) 0 0
\(597\) 0.673730 5.37090i 0.0275739 0.219816i
\(598\) 0 0
\(599\) −2.64435 + 0.962466i −0.108045 + 0.0393253i −0.395477 0.918476i \(-0.629421\pi\)
0.287432 + 0.957801i \(0.407199\pi\)
\(600\) 0 0
\(601\) −4.20959 23.8738i −0.171713 0.973831i −0.941870 0.335977i \(-0.890933\pi\)
0.770157 0.637854i \(-0.220178\pi\)
\(602\) 0 0
\(603\) 0.387610 + 3.88319i 0.0157847 + 0.158136i
\(604\) 0 0
\(605\) 6.54635 17.9860i 0.266147 0.731233i
\(606\) 0 0
\(607\) −14.5888 12.2415i −0.592143 0.496867i 0.296766 0.954950i \(-0.404092\pi\)
−0.888909 + 0.458083i \(0.848536\pi\)
\(608\) 0 0
\(609\) −12.0570 + 39.0707i −0.488573 + 1.58323i
\(610\) 0 0
\(611\) −34.1014 19.6885i −1.37960 0.796510i
\(612\) 0 0
\(613\) −42.4123 + 24.4868i −1.71302 + 0.989011i −0.782586 + 0.622542i \(0.786100\pi\)
−0.930430 + 0.366469i \(0.880567\pi\)
\(614\) 0 0
\(615\) −0.844843 16.9698i −0.0340674 0.684289i
\(616\) 0 0
\(617\) −5.23248 + 29.6749i −0.210652 + 1.19467i 0.677643 + 0.735391i \(0.263002\pi\)
−0.888295 + 0.459274i \(0.848110\pi\)
\(618\) 0 0
\(619\) 0.100470 + 0.119735i 0.00403821 + 0.00481256i 0.768060 0.640378i \(-0.221222\pi\)
−0.764022 + 0.645191i \(0.776778\pi\)
\(620\) 0 0
\(621\) −14.3195 8.75772i −0.574623 0.351435i
\(622\) 0 0
\(623\) 2.18876 1.83659i 0.0876909 0.0735814i
\(624\) 0 0
\(625\) −5.30242 + 30.0715i −0.212097 + 1.20286i
\(626\) 0 0
\(627\) −9.20829 14.2611i −0.367744 0.569532i
\(628\) 0 0
\(629\) 7.04383 4.06676i 0.280856 0.162152i
\(630\) 0 0
\(631\) 15.3663 26.6153i 0.611724 1.05954i −0.379226 0.925304i \(-0.623810\pi\)
0.990950 0.134233i \(-0.0428570\pi\)
\(632\) 0 0
\(633\) 31.2593 + 33.6978i 1.24245 + 1.33937i
\(634\) 0 0
\(635\) −3.55811 + 4.24039i −0.141199 + 0.168275i
\(636\) 0 0
\(637\) 17.0281 46.7843i 0.674677 1.85366i
\(638\) 0 0
\(639\) −4.74896 16.8947i −0.187866 0.668343i
\(640\) 0 0
\(641\) −4.59544 26.0620i −0.181509 1.02939i −0.930359 0.366649i \(-0.880505\pi\)
0.748850 0.662739i \(-0.230606\pi\)
\(642\) 0 0
\(643\) 5.39955 + 14.8351i 0.212937 + 0.585040i 0.999472 0.0325063i \(-0.0103489\pi\)
−0.786534 + 0.617547i \(0.788127\pi\)
\(644\) 0 0
\(645\) 22.9662 9.67775i 0.904294 0.381061i
\(646\) 0 0
\(647\) 20.7744 0.816724 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(648\) 0 0
\(649\) −23.7552 −0.932473
\(650\) 0 0
\(651\) 33.6326 14.1725i 1.31817 0.555463i
\(652\) 0 0
\(653\) 3.19032 + 8.76533i 0.124847 + 0.343014i 0.986332 0.164768i \(-0.0526877\pi\)
−0.861485 + 0.507782i \(0.830465\pi\)
\(654\) 0 0
\(655\) −4.83750 27.4349i −0.189017 1.07197i
\(656\) 0 0
\(657\) 16.9976 + 4.33256i 0.663140 + 0.169029i
\(658\) 0 0
\(659\) 5.15867 14.1733i 0.200953 0.552114i −0.797752 0.602986i \(-0.793978\pi\)
0.998705 + 0.0508713i \(0.0161998\pi\)
\(660\) 0 0
\(661\) −7.27008 + 8.66414i −0.282773 + 0.336996i −0.888670 0.458547i \(-0.848370\pi\)
0.605897 + 0.795543i \(0.292814\pi\)
\(662\) 0 0
\(663\) 4.36453 + 4.70500i 0.169504 + 0.182727i
\(664\) 0 0
\(665\) 31.5076 54.5727i 1.22181 2.11624i
\(666\) 0 0
\(667\) −14.0037 + 8.08503i −0.542225 + 0.313054i
\(668\) 0 0
\(669\) 4.54994 + 7.04659i 0.175911 + 0.272437i
\(670\) 0 0
\(671\) −1.22549 + 6.95008i −0.0473094 + 0.268305i
\(672\) 0 0
\(673\) −15.6114 + 13.0996i −0.601777 + 0.504951i −0.892016 0.452003i \(-0.850710\pi\)
0.290239 + 0.956954i \(0.406265\pi\)
\(674\) 0 0
\(675\) −2.73535 8.15129i −0.105284 0.313743i
\(676\) 0 0
\(677\) −18.6992 22.2848i −0.718668 0.856475i 0.275833 0.961206i \(-0.411046\pi\)
−0.994501 + 0.104731i \(0.966602\pi\)
\(678\) 0 0
\(679\) −13.8530 + 78.5643i −0.531630 + 3.01502i
\(680\) 0 0
\(681\) 1.71856 + 34.5196i 0.0658554 + 1.32279i
\(682\) 0 0
\(683\) 19.5414 11.2822i 0.747730 0.431702i −0.0771431 0.997020i \(-0.524580\pi\)
0.824873 + 0.565318i \(0.191247\pi\)
\(684\) 0 0
\(685\) 37.2734 + 21.5198i 1.42414 + 0.822229i
\(686\) 0 0
\(687\) 0.311332 1.00888i 0.0118781 0.0384910i
\(688\) 0 0
\(689\) −8.87147 7.44405i −0.337976 0.283596i
\(690\) 0 0
\(691\) −7.19879 + 19.7785i −0.273855 + 0.752410i 0.724172 + 0.689620i \(0.242222\pi\)
−0.998027 + 0.0627907i \(0.980000\pi\)
\(692\) 0 0
\(693\) −21.7401 + 15.6220i −0.825839 + 0.593431i
\(694\) 0 0
\(695\) 7.16886 + 40.6566i 0.271930 + 1.54219i
\(696\) 0 0
\(697\) 4.05319 1.47524i 0.153525 0.0558787i
\(698\) 0 0
\(699\) 1.30526 10.4054i 0.0493693 0.393567i
\(700\) 0 0
\(701\) 2.33170i 0.0880670i −0.999030 0.0440335i \(-0.985979\pi\)
0.999030 0.0440335i \(-0.0140208\pi\)
\(702\) 0 0
\(703\) 37.1415 1.40082
\(704\) 0 0
\(705\) −32.5266 + 42.9301i −1.22502 + 1.61684i
\(706\) 0 0
\(707\) −4.31477 11.8547i −0.162274 0.445843i
\(708\) 0 0
\(709\) 38.0666 6.71217i 1.42962 0.252081i 0.595364 0.803456i \(-0.297008\pi\)
0.834257 + 0.551375i \(0.185897\pi\)
\(710\) 0 0
\(711\) −0.530386 + 7.05430i −0.0198910 + 0.264557i
\(712\) 0 0
\(713\) 13.5627 + 4.93643i 0.507929 + 0.184871i
\(714\) 0 0
\(715\) 10.2492 12.2145i 0.383297 0.456795i
\(716\) 0 0
\(717\) 4.09938 + 17.9707i 0.153094 + 0.671128i
\(718\) 0 0
\(719\) −0.0699843 + 0.121216i −0.00260997 + 0.00452061i −0.867327 0.497738i \(-0.834164\pi\)
0.864717 + 0.502259i \(0.167497\pi\)
\(720\) 0 0
\(721\) 36.5898 + 63.3753i 1.36267 + 2.36022i
\(722\) 0 0
\(723\) −2.00494 + 3.90960i −0.0745646 + 0.145400i
\(724\) 0 0
\(725\) −8.15702 1.43830i −0.302944 0.0534172i
\(726\) 0 0
\(727\) 3.66655 3.07660i 0.135985 0.114105i −0.572258 0.820073i \(-0.693933\pi\)
0.708243 + 0.705969i \(0.249488\pi\)
\(728\) 0 0
\(729\) −19.7789 18.3792i −0.732551 0.680712i
\(730\) 0 0
\(731\) 4.06674 + 4.84655i 0.150414 + 0.179256i
\(732\) 0 0
\(733\) −46.3266 8.16862i −1.71111 0.301715i −0.769557 0.638578i \(-0.779523\pi\)
−0.941553 + 0.336864i \(0.890634\pi\)
\(734\) 0 0
\(735\) −60.5960 31.0751i −2.23512 1.14622i
\(736\) 0 0
\(737\) 1.23070 + 2.13164i 0.0453335 + 0.0785199i
\(738\) 0 0
\(739\) −12.2180 7.05405i −0.449446 0.259487i 0.258150 0.966105i \(-0.416887\pi\)
−0.707596 + 0.706617i \(0.750220\pi\)
\(740\) 0 0
\(741\) 6.51770 + 28.5721i 0.239434 + 1.04962i
\(742\) 0 0
\(743\) −30.5037 25.5956i −1.11907 0.939013i −0.120514 0.992712i \(-0.538454\pi\)
−0.998557 + 0.0536990i \(0.982899\pi\)
\(744\) 0 0
\(745\) 4.24042 + 1.54339i 0.155357 + 0.0565453i
\(746\) 0 0
\(747\) 41.2617 + 3.10231i 1.50969 + 0.113508i
\(748\) 0 0
\(749\) 53.4829 9.43048i 1.95422 0.344582i
\(750\) 0 0
\(751\) 21.2150 7.72164i 0.774147 0.281766i 0.0754172 0.997152i \(-0.475971\pi\)
0.698730 + 0.715386i \(0.253749\pi\)
\(752\) 0 0
\(753\) 11.7653 15.5284i 0.428751 0.565886i
\(754\) 0 0
\(755\) 5.17774i 0.188437i
\(756\) 0 0
\(757\) 18.5219i 0.673188i −0.941650 0.336594i \(-0.890725\pi\)
0.941650 0.336594i \(-0.109275\pi\)
\(758\) 0 0
\(759\) −10.5046 1.31771i −0.381293 0.0478297i
\(760\) 0 0
\(761\) 44.9798 16.3713i 1.63052 0.593460i 0.645173 0.764037i \(-0.276785\pi\)
0.985344 + 0.170577i \(0.0545632\pi\)
\(762\) 0 0
\(763\) −74.1029 + 13.0663i −2.68270 + 0.473033i
\(764\) 0 0
\(765\) 7.12862 5.12248i 0.257736 0.185203i
\(766\) 0 0
\(767\) 38.5369 + 14.0263i 1.39149 + 0.506460i
\(768\) 0 0
\(769\) −26.8445 22.5252i −0.968039 0.812281i 0.0142034 0.999899i \(-0.495479\pi\)
−0.982242 + 0.187618i \(0.939923\pi\)
\(770\) 0 0
\(771\) 11.6752 + 3.60290i 0.420473 + 0.129755i
\(772\) 0 0
\(773\) 33.2570 + 19.2010i 1.19617 + 0.690610i 0.959700 0.281028i \(-0.0906754\pi\)
0.236472 + 0.971638i \(0.424009\pi\)
\(774\) 0 0
\(775\) 3.69658 + 6.40266i 0.132785 + 0.229990i
\(776\) 0 0
\(777\) −2.91245 58.5005i −0.104484 2.09869i
\(778\) 0 0
\(779\) 19.3974 + 3.42029i 0.694984 + 0.122544i
\(780\) 0 0
\(781\) −7.11495 8.47927i −0.254593 0.303412i
\(782\) 0 0
\(783\) −24.6590 + 8.27488i −0.881240 + 0.295720i
\(784\) 0 0
\(785\) −13.5224 + 11.3466i −0.482635 + 0.404979i
\(786\) 0 0
\(787\) 41.3365 + 7.28874i 1.47349 + 0.259816i 0.851972 0.523587i \(-0.175406\pi\)
0.621515 + 0.783402i \(0.286518\pi\)
\(788\) 0 0
\(789\) 27.2519 + 42.2055i 0.970193 + 1.50256i
\(790\) 0 0
\(791\) 2.02172 + 3.50173i 0.0718842 + 0.124507i
\(792\) 0 0
\(793\) 6.09173 10.5512i 0.216324 0.374684i
\(794\) 0 0
\(795\) −11.6133 + 10.7729i −0.411881 + 0.382076i
\(796\) 0 0
\(797\) −0.294996 + 0.351563i −0.0104493 + 0.0124530i −0.771244 0.636540i \(-0.780365\pi\)
0.760794 + 0.648993i \(0.224810\pi\)
\(798\) 0 0
\(799\) −12.8485 4.67649i −0.454549 0.165442i
\(800\) 0 0
\(801\) 1.76124 + 0.448926i 0.0622303 + 0.0158620i
\(802\) 0 0
\(803\) 10.8956 1.92118i 0.384496 0.0677970i
\(804\) 0 0
\(805\) −13.4413 36.9297i −0.473745 1.30160i
\(806\) 0 0
\(807\) 9.65526 + 22.9128i 0.339881 + 0.806570i
\(808\) 0 0
\(809\) 29.3388 1.03150 0.515749 0.856740i \(-0.327514\pi\)
0.515749 + 0.856740i \(0.327514\pi\)
\(810\) 0 0
\(811\) 9.18827i 0.322644i −0.986902 0.161322i \(-0.948424\pi\)
0.986902 0.161322i \(-0.0515757\pi\)
\(812\) 0 0
\(813\) 25.5033 10.7469i 0.894440 0.376909i
\(814\) 0 0
\(815\) −16.6279 + 6.05206i −0.582450 + 0.211994i
\(816\) 0 0
\(817\) 5.01684 + 28.4519i 0.175517 + 0.995407i
\(818\) 0 0
\(819\) 44.4920 12.5063i 1.55468 0.437007i
\(820\) 0 0
\(821\) −14.5843 + 40.0700i −0.508995 + 1.39845i 0.373280 + 0.927719i \(0.378233\pi\)
−0.882275 + 0.470734i \(0.843989\pi\)
\(822\) 0 0
\(823\) −5.98871 5.02513i −0.208753 0.175165i 0.532416 0.846483i \(-0.321284\pi\)
−0.741170 + 0.671318i \(0.765729\pi\)
\(824\) 0 0
\(825\) −3.68808 3.97579i −0.128403 0.138419i
\(826\) 0 0
\(827\) 12.5094 + 7.22230i 0.434994 + 0.251144i 0.701472 0.712697i \(-0.252527\pi\)
−0.266478 + 0.963841i \(0.585860\pi\)
\(828\) 0 0
\(829\) 14.0046 8.08556i 0.486400 0.280823i −0.236680 0.971588i \(-0.576059\pi\)
0.723080 + 0.690765i \(0.242726\pi\)
\(830\) 0 0
\(831\) 10.9480 7.06910i 0.379784 0.245224i
\(832\) 0 0
\(833\) 3.00200 17.0252i 0.104013 0.589888i
\(834\) 0 0
\(835\) 11.9802 + 14.2774i 0.414590 + 0.494089i
\(836\) 0 0
\(837\) 19.8059 + 12.1132i 0.684594 + 0.418692i
\(838\) 0 0
\(839\) 41.0275 34.4262i 1.41643 1.18852i 0.463205 0.886251i \(-0.346700\pi\)
0.953222 0.302271i \(-0.0977449\pi\)
\(840\) 0 0
\(841\) 0.684700 3.88313i 0.0236103 0.133901i
\(842\) 0 0
\(843\) 16.2989 0.811439i 0.561362 0.0279475i
\(844\) 0 0
\(845\) 5.20400 3.00453i 0.179023 0.103359i
\(846\) 0 0
\(847\) 17.4958 30.3036i 0.601162 1.04124i
\(848\) 0 0
\(849\) 12.6252 40.9120i 0.433295 1.40410i
\(850\) 0 0
\(851\) 14.8892 17.7443i 0.510396 0.608267i
\(852\) 0 0
\(853\) 1.62827 4.47364i 0.0557509 0.153174i −0.908691 0.417469i \(-0.862917\pi\)
0.964442 + 0.264295i \(0.0851393\pi\)
\(854\) 0 0
\(855\) 39.8872 3.98144i 1.36411 0.136163i
\(856\) 0 0
\(857\) 3.69992 + 20.9833i 0.126387 + 0.716775i 0.980475 + 0.196646i \(0.0630050\pi\)
−0.854088 + 0.520129i \(0.825884\pi\)
\(858\) 0 0
\(859\) 0.568591 + 1.56219i 0.0194001 + 0.0533013i 0.949015 0.315232i \(-0.102082\pi\)
−0.929615 + 0.368533i \(0.879860\pi\)
\(860\) 0 0
\(861\) 3.86615 30.8205i 0.131758 1.05036i
\(862\) 0 0
\(863\) 4.65067 0.158311 0.0791554 0.996862i \(-0.474778\pi\)
0.0791554 + 0.996862i \(0.474778\pi\)
\(864\) 0 0
\(865\) −17.7276 −0.602757
\(866\) 0 0
\(867\) −21.6931 16.4361i −0.736736 0.558198i
\(868\) 0 0
\(869\) 1.52606 + 4.19281i 0.0517680 + 0.142231i
\(870\) 0 0
\(871\) −0.737879 4.18472i −0.0250021 0.141794i
\(872\) 0 0
\(873\) −45.7274 + 22.0074i −1.54764 + 0.744836i
\(874\) 0 0
\(875\) −13.9198 + 38.2442i −0.470574 + 1.29289i
\(876\) 0 0
\(877\) −28.6728 + 34.1709i −0.968211 + 1.15387i 0.0198497 + 0.999803i \(0.493681\pi\)
−0.988061 + 0.154066i \(0.950763\pi\)
\(878\) 0 0
\(879\) 13.1022 2.98880i 0.441926 0.100810i
\(880\) 0 0
\(881\) −11.4635 + 19.8554i −0.386215 + 0.668944i −0.991937 0.126732i \(-0.959551\pi\)
0.605722 + 0.795676i \(0.292884\pi\)
\(882\) 0 0
\(883\) 30.6898 17.7188i 1.03279 0.596284i 0.115010 0.993364i \(-0.463310\pi\)
0.917784 + 0.397081i \(0.129977\pi\)
\(884\) 0 0
\(885\) 25.5971 49.9138i 0.860436 1.67784i
\(886\) 0 0
\(887\) 5.26510 29.8598i 0.176785 1.00260i −0.759279 0.650765i \(-0.774448\pi\)
0.936064 0.351830i \(-0.114441\pi\)
\(888\) 0 0
\(889\) −7.75213 + 6.50481i −0.259998 + 0.218164i
\(890\) 0 0
\(891\) −16.1402 5.43162i −0.540716 0.181966i
\(892\) 0 0
\(893\) −40.1344 47.8303i −1.34305 1.60058i
\(894\) 0 0
\(895\) −1.09160 + 6.19076i −0.0364881 + 0.206934i
\(896\) 0 0
\(897\) 16.2631 + 8.34011i 0.543008 + 0.278468i
\(898\) 0 0
\(899\) 19.3691 11.1827i 0.645995 0.372965i
\(900\) 0 0
\(901\) −3.48256 2.01066i −0.116021 0.0669847i
\(902\) 0 0
\(903\) 44.4204 10.1329i 1.47822 0.337203i
\(904\) 0 0
\(905\) −48.2745 40.5071i −1.60470 1.34650i
\(906\) 0 0
\(907\) 6.25848 17.1950i 0.207809 0.570951i −0.791375 0.611331i \(-0.790634\pi\)
0.999184 + 0.0403795i \(0.0128567\pi\)
\(908\) 0 0
\(909\) 4.52230 6.62950i 0.149995 0.219887i
\(910\) 0 0
\(911\) 6.84735 + 38.8333i 0.226863 + 1.28660i 0.859092 + 0.511822i \(0.171029\pi\)
−0.632229 + 0.774782i \(0.717860\pi\)
\(912\) 0 0
\(913\) 24.5244 8.92615i 0.811639 0.295413i
\(914\) 0 0
\(915\) −13.2828 10.0639i −0.439117 0.332703i
\(916\) 0 0
\(917\) 50.9292i 1.68183i
\(918\) 0 0
\(919\) −28.0411 −0.924991 −0.462496 0.886622i \(-0.653046\pi\)
−0.462496 + 0.886622i \(0.653046\pi\)
\(920\) 0 0
\(921\) 22.1109 + 2.77361i 0.728579 + 0.0913935i
\(922\) 0 0
\(923\) 6.53564 + 17.9565i 0.215123 + 0.591046i
\(924\) 0 0
\(925\) 11.6849 2.06036i 0.384197 0.0677443i
\(926\) 0 0
\(927\) −19.1563 + 42.4271i −0.629177 + 1.39349i
\(928\) 0 0
\(929\) 48.6959 + 17.7239i 1.59766 + 0.581501i 0.978947 0.204115i \(-0.0654317\pi\)
0.618714 + 0.785616i \(0.287654\pi\)
\(930\) 0 0
\(931\) 50.7445 60.4749i 1.66308 1.98199i
\(932\) 0 0
\(933\) −26.8047 8.27176i −0.877547 0.270805i
\(934\) 0 0
\(935\) 2.76832 4.79488i 0.0905339 0.156809i
\(936\) 0 0
\(937\) 24.4737 + 42.3897i 0.799522 + 1.38481i 0.919928 + 0.392088i \(0.128247\pi\)
−0.120406 + 0.992725i \(0.538420\pi\)
\(938\) 0 0
\(939\) 1.92719 0.0959452i 0.0628914 0.00313105i
\(940\) 0 0
\(941\) 57.1903 + 10.0842i 1.86435 + 0.328735i 0.988184 0.153271i \(-0.0489808\pi\)
0.876167 + 0.482007i \(0.160092\pi\)
\(942\) 0 0
\(943\) 9.41005 7.89597i 0.306433 0.257128i
\(944\) 0 0
\(945\) −9.39882 62.5131i −0.305744 2.03355i
\(946\) 0 0
\(947\) −22.0563 26.2856i −0.716732 0.854168i 0.277577 0.960703i \(-0.410469\pi\)
−0.994309 + 0.106535i \(0.966024\pi\)
\(948\) 0 0
\(949\) −18.8097 3.31665i −0.610588 0.107663i
\(950\) 0 0
\(951\) 2.29821 1.48394i 0.0745246 0.0481202i
\(952\) 0 0
\(953\) 5.11095 + 8.85243i 0.165560 + 0.286758i 0.936854 0.349721i \(-0.113724\pi\)
−0.771294 + 0.636479i \(0.780390\pi\)
\(954\) 0 0
\(955\) 1.41077 + 0.814508i 0.0456514 + 0.0263569i
\(956\) 0 0
\(957\) −12.0274 + 11.1570i −0.388790 + 0.360656i
\(958\) 0 0
\(959\) 60.2751 + 50.5768i 1.94638 + 1.63321i
\(960\) 0 0
\(961\) 10.3713 + 3.77484i 0.334557 + 0.121769i
\(962\) 0 0
\(963\) 24.7249 + 24.1278i 0.796748 + 0.777507i
\(964\) 0 0
\(965\) −52.6878 + 9.29028i −1.69608 + 0.299065i
\(966\) 0 0
\(967\) −28.7380 + 10.4598i −0.924151 + 0.336364i −0.759889 0.650053i \(-0.774747\pi\)
−0.164262 + 0.986417i \(0.552524\pi\)
\(968\) 0 0
\(969\) 3.95162 + 9.37756i 0.126944 + 0.301250i
\(970\) 0 0
\(971\) 47.4592i 1.52304i −0.648142 0.761519i \(-0.724454\pi\)
0.648142 0.761519i \(-0.275546\pi\)
\(972\) 0 0
\(973\) 75.4736i 2.41957i
\(974\) 0 0
\(975\) 3.63549 + 8.62735i 0.116429 + 0.276296i
\(976\) 0 0
\(977\) −28.5748 + 10.4004i −0.914189 + 0.332737i −0.755924 0.654659i \(-0.772812\pi\)
−0.158264 + 0.987397i \(0.550590\pi\)
\(978\) 0 0
\(979\) 1.12896 0.199066i 0.0360818 0.00636219i
\(980\) 0 0
\(981\) −34.2574 33.4301i −1.09375 1.06734i
\(982\) 0 0
\(983\) −50.6147 18.4222i −1.61436 0.587578i −0.632063 0.774917i \(-0.717792\pi\)
−0.982295 + 0.187338i \(0.940014\pi\)
\(984\) 0 0
\(985\) −18.6353 15.6369i −0.593770 0.498232i
\(986\) 0 0
\(987\) −72.1890 + 66.9652i −2.29780 + 2.13153i
\(988\) 0 0
\(989\) 15.6040 + 9.00898i 0.496179 + 0.286469i
\(990\) 0 0
\(991\) 24.8280 + 43.0034i 0.788688 + 1.36605i 0.926771 + 0.375627i \(0.122573\pi\)
−0.138083 + 0.990421i \(0.544094\pi\)
\(992\) 0 0
\(993\) −18.1290 + 11.7058i −0.575307 + 0.371473i
\(994\) 0 0
\(995\) 7.93949 + 1.39995i 0.251699 + 0.0443813i
\(996\) 0 0
\(997\) 11.6323 + 13.8628i 0.368398 + 0.439040i 0.918117 0.396310i \(-0.129709\pi\)
−0.549719 + 0.835350i \(0.685265\pi\)
\(998\) 0 0
\(999\) 29.1393 23.2203i 0.921928 0.734659i
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 864.2.bf.a.49.4 204
4.3 odd 2 216.2.t.a.157.25 204
8.3 odd 2 216.2.t.a.157.30 yes 204
8.5 even 2 inner 864.2.bf.a.49.31 204
12.11 even 2 648.2.t.a.37.10 204
24.11 even 2 648.2.t.a.37.5 204
27.16 even 9 inner 864.2.bf.a.529.31 204
108.11 even 18 648.2.t.a.613.5 204
108.43 odd 18 216.2.t.a.205.30 yes 204
216.11 even 18 648.2.t.a.613.10 204
216.43 odd 18 216.2.t.a.205.25 yes 204
216.205 even 18 inner 864.2.bf.a.529.4 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.t.a.157.25 204 4.3 odd 2
216.2.t.a.157.30 yes 204 8.3 odd 2
216.2.t.a.205.25 yes 204 216.43 odd 18
216.2.t.a.205.30 yes 204 108.43 odd 18
648.2.t.a.37.5 204 24.11 even 2
648.2.t.a.37.10 204 12.11 even 2
648.2.t.a.613.5 204 108.11 even 18
648.2.t.a.613.10 204 216.11 even 18
864.2.bf.a.49.4 204 1.1 even 1 trivial
864.2.bf.a.49.31 204 8.5 even 2 inner
864.2.bf.a.529.4 204 216.205 even 18 inner
864.2.bf.a.529.31 204 27.16 even 9 inner