Properties

Label 864.2.bf.a.49.20
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 49.20
Character \(\chi\) \(=\) 864.49
Dual form 864.2.bf.a.529.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.368292 - 1.69244i) q^{3} +(0.355965 + 0.978005i) q^{5} +(0.272085 + 1.54307i) q^{7} +(-2.72872 - 1.24663i) q^{9} +O(q^{10})\) \(q+(0.368292 - 1.69244i) q^{3} +(0.355965 + 0.978005i) q^{5} +(0.272085 + 1.54307i) q^{7} +(-2.72872 - 1.24663i) q^{9} +(-1.44773 + 3.97760i) q^{11} +(-4.33941 + 5.17151i) q^{13} +(1.78632 - 0.242259i) q^{15} +(-0.494959 + 0.857294i) q^{17} +(-2.70129 + 1.55959i) q^{19} +(2.71177 + 0.107812i) q^{21} +(-1.17888 + 6.68573i) q^{23} +(3.00044 - 2.51767i) q^{25} +(-3.11481 + 4.15908i) q^{27} +(-2.84964 - 3.39607i) q^{29} +(0.409166 - 2.32049i) q^{31} +(6.19868 + 3.91512i) q^{33} +(-1.41228 + 0.815381i) q^{35} +(-3.19157 - 1.84266i) q^{37} +(7.15431 + 9.24883i) q^{39} +(-2.44191 - 2.04900i) q^{41} +(3.71087 - 10.1955i) q^{43} +(0.247877 - 3.11246i) q^{45} +(0.155220 + 0.880296i) q^{47} +(4.27080 - 1.55445i) q^{49} +(1.26863 + 1.15342i) q^{51} +5.00251i q^{53} -4.40546 q^{55} +(1.64465 + 5.14616i) q^{57} +(3.85475 + 10.5908i) q^{59} +(-5.41575 + 0.954943i) q^{61} +(1.18119 - 4.54981i) q^{63} +(-6.60244 - 2.40309i) q^{65} +(0.467287 - 0.556891i) q^{67} +(10.8810 + 4.45748i) q^{69} +(2.52073 - 4.36603i) q^{71} +(7.01816 + 12.1558i) q^{73} +(-3.15597 - 6.00531i) q^{75} +(-6.53164 - 1.15170i) q^{77} +(6.78017 - 5.68924i) q^{79} +(5.89185 + 6.80339i) q^{81} +(4.03223 + 4.80543i) q^{83} +(-1.01463 - 0.178906i) q^{85} +(-6.79716 + 3.57211i) q^{87} +(4.02279 + 6.96768i) q^{89} +(-9.16071 - 5.28894i) q^{91} +(-3.77661 - 1.54711i) q^{93} +(-2.48685 - 2.08672i) q^{95} +(-10.1365 - 3.68937i) q^{97} +(8.90903 - 9.04900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 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
\(3\) 0.368292 1.69244i 0.212633 0.977132i
\(4\) 0 0
\(5\) 0.355965 + 0.978005i 0.159192 + 0.437377i 0.993488 0.113941i \(-0.0363474\pi\)
−0.834295 + 0.551318i \(0.814125\pi\)
\(6\) 0 0
\(7\) 0.272085 + 1.54307i 0.102839 + 0.583227i 0.992062 + 0.125753i \(0.0401346\pi\)
−0.889223 + 0.457474i \(0.848754\pi\)
\(8\) 0 0
\(9\) −2.72872 1.24663i −0.909574 0.415542i
\(10\) 0 0
\(11\) −1.44773 + 3.97760i −0.436507 + 1.19929i 0.505243 + 0.862977i \(0.331403\pi\)
−0.941750 + 0.336315i \(0.890819\pi\)
\(12\) 0 0
\(13\) −4.33941 + 5.17151i −1.20354 + 1.43432i −0.332497 + 0.943104i \(0.607891\pi\)
−0.871039 + 0.491214i \(0.836553\pi\)
\(14\) 0 0
\(15\) 1.78632 0.242259i 0.461225 0.0625509i
\(16\) 0 0
\(17\) −0.494959 + 0.857294i −0.120045 + 0.207924i −0.919785 0.392422i \(-0.871637\pi\)
0.799740 + 0.600346i \(0.204971\pi\)
\(18\) 0 0
\(19\) −2.70129 + 1.55959i −0.619719 + 0.357795i −0.776759 0.629797i \(-0.783138\pi\)
0.157041 + 0.987592i \(0.449805\pi\)
\(20\) 0 0
\(21\) 2.71177 + 0.107812i 0.591757 + 0.0235266i
\(22\) 0 0
\(23\) −1.17888 + 6.68573i −0.245812 + 1.39407i 0.572786 + 0.819705i \(0.305863\pi\)
−0.818598 + 0.574367i \(0.805248\pi\)
\(24\) 0 0
\(25\) 3.00044 2.51767i 0.600088 0.503533i
\(26\) 0 0
\(27\) −3.11481 + 4.15908i −0.599445 + 0.800416i
\(28\) 0 0
\(29\) −2.84964 3.39607i −0.529166 0.630635i 0.433557 0.901126i \(-0.357258\pi\)
−0.962722 + 0.270491i \(0.912814\pi\)
\(30\) 0 0
\(31\) 0.409166 2.32049i 0.0734883 0.416773i −0.925764 0.378103i \(-0.876577\pi\)
0.999252 0.0386704i \(-0.0123123\pi\)
\(32\) 0 0
\(33\) 6.19868 + 3.91512i 1.07905 + 0.681534i
\(34\) 0 0
\(35\) −1.41228 + 0.815381i −0.238719 + 0.137825i
\(36\) 0 0
\(37\) −3.19157 1.84266i −0.524691 0.302931i 0.214161 0.976798i \(-0.431298\pi\)
−0.738852 + 0.673868i \(0.764632\pi\)
\(38\) 0 0
\(39\) 7.15431 + 9.24883i 1.14561 + 1.48100i
\(40\) 0 0
\(41\) −2.44191 2.04900i −0.381362 0.320000i 0.431875 0.901933i \(-0.357852\pi\)
−0.813237 + 0.581933i \(0.802297\pi\)
\(42\) 0 0
\(43\) 3.71087 10.1955i 0.565903 1.55481i −0.244938 0.969539i \(-0.578767\pi\)
0.810841 0.585267i \(-0.199010\pi\)
\(44\) 0 0
\(45\) 0.247877 3.11246i 0.0369513 0.463978i
\(46\) 0 0
\(47\) 0.155220 + 0.880296i 0.0226411 + 0.128404i 0.994033 0.109077i \(-0.0347894\pi\)
−0.971392 + 0.237481i \(0.923678\pi\)
\(48\) 0 0
\(49\) 4.27080 1.55445i 0.610115 0.222064i
\(50\) 0 0
\(51\) 1.26863 + 1.15342i 0.177644 + 0.161512i
\(52\) 0 0
\(53\) 5.00251i 0.687148i 0.939126 + 0.343574i \(0.111638\pi\)
−0.939126 + 0.343574i \(0.888362\pi\)
\(54\) 0 0
\(55\) −4.40546 −0.594032
\(56\) 0 0
\(57\) 1.64465 + 5.14616i 0.217840 + 0.681626i
\(58\) 0 0
\(59\) 3.85475 + 10.5908i 0.501846 + 1.37881i 0.889470 + 0.456993i \(0.151073\pi\)
−0.387625 + 0.921817i \(0.626704\pi\)
\(60\) 0 0
\(61\) −5.41575 + 0.954943i −0.693416 + 0.122268i −0.509239 0.860625i \(-0.670073\pi\)
−0.184177 + 0.982893i \(0.558962\pi\)
\(62\) 0 0
\(63\) 1.18119 4.54981i 0.148816 0.573222i
\(64\) 0 0
\(65\) −6.60244 2.40309i −0.818932 0.298067i
\(66\) 0 0
\(67\) 0.467287 0.556891i 0.0570882 0.0680351i −0.736745 0.676171i \(-0.763638\pi\)
0.793833 + 0.608136i \(0.208082\pi\)
\(68\) 0 0
\(69\) 10.8810 + 4.45748i 1.30992 + 0.536617i
\(70\) 0 0
\(71\) 2.52073 4.36603i 0.299155 0.518152i −0.676788 0.736178i \(-0.736628\pi\)
0.975943 + 0.218026i \(0.0699618\pi\)
\(72\) 0 0
\(73\) 7.01816 + 12.1558i 0.821413 + 1.42273i 0.904630 + 0.426198i \(0.140147\pi\)
−0.0832165 + 0.996531i \(0.526519\pi\)
\(74\) 0 0
\(75\) −3.15597 6.00531i −0.364420 0.693433i
\(76\) 0 0
\(77\) −6.53164 1.15170i −0.744349 0.131249i
\(78\) 0 0
\(79\) 6.78017 5.68924i 0.762829 0.640090i −0.176032 0.984384i \(-0.556326\pi\)
0.938862 + 0.344295i \(0.111882\pi\)
\(80\) 0 0
\(81\) 5.89185 + 6.80339i 0.654650 + 0.755932i
\(82\) 0 0
\(83\) 4.03223 + 4.80543i 0.442595 + 0.527464i 0.940512 0.339760i \(-0.110346\pi\)
−0.497917 + 0.867225i \(0.665902\pi\)
\(84\) 0 0
\(85\) −1.01463 0.178906i −0.110052 0.0194051i
\(86\) 0 0
\(87\) −6.79716 + 3.57211i −0.728732 + 0.382971i
\(88\) 0 0
\(89\) 4.02279 + 6.96768i 0.426415 + 0.738573i 0.996551 0.0829775i \(-0.0264430\pi\)
−0.570136 + 0.821550i \(0.693110\pi\)
\(90\) 0 0
\(91\) −9.16071 5.28894i −0.960303 0.554431i
\(92\) 0 0
\(93\) −3.77661 1.54711i −0.391616 0.160428i
\(94\) 0 0
\(95\) −2.48685 2.08672i −0.255146 0.214093i
\(96\) 0 0
\(97\) −10.1365 3.68937i −1.02920 0.374599i −0.228425 0.973561i \(-0.573358\pi\)
−0.800777 + 0.598963i \(0.795580\pi\)
\(98\) 0 0
\(99\) 8.90903 9.04900i 0.895391 0.909458i
\(100\) 0 0
\(101\) 6.50659 1.14729i 0.647430 0.114159i 0.159716 0.987163i \(-0.448942\pi\)
0.487714 + 0.873004i \(0.337831\pi\)
\(102\) 0 0
\(103\) 14.9315 5.43464i 1.47125 0.535491i 0.522809 0.852450i \(-0.324884\pi\)
0.948439 + 0.316959i \(0.102662\pi\)
\(104\) 0 0
\(105\) 0.859854 + 2.69050i 0.0839131 + 0.262566i
\(106\) 0 0
\(107\) 3.85513i 0.372689i 0.982484 + 0.186345i \(0.0596641\pi\)
−0.982484 + 0.186345i \(0.940336\pi\)
\(108\) 0 0
\(109\) 3.32803i 0.318767i −0.987217 0.159384i \(-0.949049\pi\)
0.987217 0.159384i \(-0.0509507\pi\)
\(110\) 0 0
\(111\) −4.29402 + 4.72292i −0.407570 + 0.448279i
\(112\) 0 0
\(113\) 7.85208 2.85792i 0.738662 0.268851i 0.0548351 0.998495i \(-0.482537\pi\)
0.683827 + 0.729645i \(0.260314\pi\)
\(114\) 0 0
\(115\) −6.95832 + 1.22694i −0.648867 + 0.114413i
\(116\) 0 0
\(117\) 18.2880 8.70199i 1.69072 0.804499i
\(118\) 0 0
\(119\) −1.45754 0.530501i −0.133612 0.0486309i
\(120\) 0 0
\(121\) −5.29891 4.44632i −0.481719 0.404211i
\(122\) 0 0
\(123\) −4.36715 + 3.37815i −0.393773 + 0.304598i
\(124\) 0 0
\(125\) 8.03702 + 4.64017i 0.718853 + 0.415030i
\(126\) 0 0
\(127\) −1.83012 3.16986i −0.162397 0.281280i 0.773331 0.634003i \(-0.218589\pi\)
−0.935728 + 0.352723i \(0.885256\pi\)
\(128\) 0 0
\(129\) −15.8887 10.0354i −1.39892 0.883566i
\(130\) 0 0
\(131\) −9.66082 1.70346i −0.844070 0.148832i −0.265140 0.964210i \(-0.585418\pi\)
−0.578930 + 0.815378i \(0.696529\pi\)
\(132\) 0 0
\(133\) −3.14155 3.74395i −0.272407 0.324641i
\(134\) 0 0
\(135\) −5.17637 1.56581i −0.445511 0.134764i
\(136\) 0 0
\(137\) −16.9231 + 14.2001i −1.44583 + 1.21320i −0.510284 + 0.860006i \(0.670460\pi\)
−0.935550 + 0.353193i \(0.885096\pi\)
\(138\) 0 0
\(139\) 4.68849 + 0.826707i 0.397672 + 0.0701203i 0.368908 0.929466i \(-0.379732\pi\)
0.0287641 + 0.999586i \(0.490843\pi\)
\(140\) 0 0
\(141\) 1.54702 + 0.0615050i 0.130282 + 0.00517966i
\(142\) 0 0
\(143\) −14.2879 24.7474i −1.19482 2.06948i
\(144\) 0 0
\(145\) 2.30701 3.99585i 0.191586 0.331837i
\(146\) 0 0
\(147\) −1.05791 7.80058i −0.0872547 0.643381i
\(148\) 0 0
\(149\) −14.7916 + 17.6280i −1.21178 + 1.44414i −0.350076 + 0.936721i \(0.613844\pi\)
−0.861700 + 0.507418i \(0.830600\pi\)
\(150\) 0 0
\(151\) −18.6779 6.79819i −1.51998 0.553229i −0.558840 0.829276i \(-0.688753\pi\)
−0.961144 + 0.276047i \(0.910975\pi\)
\(152\) 0 0
\(153\) 2.41933 1.72229i 0.195591 0.139239i
\(154\) 0 0
\(155\) 2.41510 0.425848i 0.193986 0.0342049i
\(156\) 0 0
\(157\) −1.67263 4.59552i −0.133491 0.366762i 0.854880 0.518825i \(-0.173631\pi\)
−0.988371 + 0.152063i \(0.951408\pi\)
\(158\) 0 0
\(159\) 8.46647 + 1.84239i 0.671435 + 0.146111i
\(160\) 0 0
\(161\) −10.6373 −0.838339
\(162\) 0 0
\(163\) 4.18081i 0.327466i 0.986505 + 0.163733i \(0.0523536\pi\)
−0.986505 + 0.163733i \(0.947646\pi\)
\(164\) 0 0
\(165\) −1.62249 + 7.45598i −0.126311 + 0.580447i
\(166\) 0 0
\(167\) −5.72775 + 2.08473i −0.443227 + 0.161321i −0.553986 0.832526i \(-0.686894\pi\)
0.110759 + 0.993847i \(0.464672\pi\)
\(168\) 0 0
\(169\) −5.65659 32.0801i −0.435122 2.46770i
\(170\) 0 0
\(171\) 9.31530 0.888193i 0.712359 0.0679218i
\(172\) 0 0
\(173\) −0.453627 + 1.24633i −0.0344886 + 0.0947567i −0.955742 0.294207i \(-0.904945\pi\)
0.921253 + 0.388964i \(0.127167\pi\)
\(174\) 0 0
\(175\) 4.70132 + 3.94488i 0.355386 + 0.298205i
\(176\) 0 0
\(177\) 19.3441 2.62342i 1.45399 0.197189i
\(178\) 0 0
\(179\) 9.68622 + 5.59234i 0.723982 + 0.417991i 0.816217 0.577746i \(-0.196068\pi\)
−0.0922343 + 0.995737i \(0.529401\pi\)
\(180\) 0 0
\(181\) 3.21058 1.85363i 0.238641 0.137779i −0.375911 0.926656i \(-0.622670\pi\)
0.614552 + 0.788876i \(0.289337\pi\)
\(182\) 0 0
\(183\) −0.378391 + 9.51754i −0.0279714 + 0.703557i
\(184\) 0 0
\(185\) 0.666039 3.77730i 0.0489682 0.277712i
\(186\) 0 0
\(187\) −2.69341 3.20988i −0.196961 0.234730i
\(188\) 0 0
\(189\) −7.26526 3.67475i −0.528470 0.267299i
\(190\) 0 0
\(191\) −13.8306 + 11.6053i −1.00075 + 0.839729i −0.987088 0.160178i \(-0.948793\pi\)
−0.0136618 + 0.999907i \(0.504349\pi\)
\(192\) 0 0
\(193\) 0.770660 4.37063i 0.0554733 0.314605i −0.944427 0.328721i \(-0.893382\pi\)
0.999900 + 0.0141163i \(0.00449352\pi\)
\(194\) 0 0
\(195\) −6.49872 + 10.2892i −0.465383 + 0.736826i
\(196\) 0 0
\(197\) 14.1519 8.17063i 1.00828 0.582133i 0.0975957 0.995226i \(-0.468885\pi\)
0.910689 + 0.413093i \(0.135551\pi\)
\(198\) 0 0
\(199\) 0.458824 0.794707i 0.0325252 0.0563353i −0.849305 0.527903i \(-0.822978\pi\)
0.881830 + 0.471568i \(0.156312\pi\)
\(200\) 0 0
\(201\) −0.770408 0.995955i −0.0543404 0.0702493i
\(202\) 0 0
\(203\) 4.46504 5.32123i 0.313385 0.373477i
\(204\) 0 0
\(205\) 1.13470 3.11757i 0.0792511 0.217741i
\(206\) 0 0
\(207\) 11.5514 16.7739i 0.802880 1.16587i
\(208\) 0 0
\(209\) −2.29270 13.0025i −0.158589 0.899403i
\(210\) 0 0
\(211\) 2.09734 + 5.76240i 0.144387 + 0.396700i 0.990714 0.135964i \(-0.0434131\pi\)
−0.846327 + 0.532664i \(0.821191\pi\)
\(212\) 0 0
\(213\) −6.46089 5.87416i −0.442693 0.402491i
\(214\) 0 0
\(215\) 11.2922 0.770124
\(216\) 0 0
\(217\) 3.69202 0.250631
\(218\) 0 0
\(219\) 23.1577 7.40094i 1.56485 0.500109i
\(220\) 0 0
\(221\) −2.28567 6.27983i −0.153751 0.422427i
\(222\) 0 0
\(223\) 3.72326 + 21.1156i 0.249328 + 1.41401i 0.810223 + 0.586121i \(0.199346\pi\)
−0.560896 + 0.827887i \(0.689543\pi\)
\(224\) 0 0
\(225\) −11.3260 + 3.12959i −0.755063 + 0.208639i
\(226\) 0 0
\(227\) 6.36438 17.4860i 0.422419 1.16059i −0.527900 0.849307i \(-0.677020\pi\)
0.950319 0.311279i \(-0.100757\pi\)
\(228\) 0 0
\(229\) 5.70813 6.80268i 0.377204 0.449534i −0.543726 0.839263i \(-0.682987\pi\)
0.920930 + 0.389729i \(0.127431\pi\)
\(230\) 0 0
\(231\) −4.35474 + 10.6303i −0.286521 + 0.699420i
\(232\) 0 0
\(233\) 9.39731 16.2766i 0.615638 1.06632i −0.374634 0.927173i \(-0.622232\pi\)
0.990272 0.139144i \(-0.0444350\pi\)
\(234\) 0 0
\(235\) −0.805681 + 0.465160i −0.0525568 + 0.0303437i
\(236\) 0 0
\(237\) −7.13163 13.5704i −0.463249 0.881489i
\(238\) 0 0
\(239\) −3.56653 + 20.2268i −0.230700 + 1.30836i 0.620784 + 0.783982i \(0.286815\pi\)
−0.851483 + 0.524382i \(0.824297\pi\)
\(240\) 0 0
\(241\) −10.5529 + 8.85497i −0.679775 + 0.570399i −0.915941 0.401314i \(-0.868554\pi\)
0.236166 + 0.971713i \(0.424109\pi\)
\(242\) 0 0
\(243\) 13.6843 7.46598i 0.877846 0.478943i
\(244\) 0 0
\(245\) 3.04051 + 3.62354i 0.194251 + 0.231499i
\(246\) 0 0
\(247\) 3.65657 20.7374i 0.232662 1.31949i
\(248\) 0 0
\(249\) 9.61795 5.05452i 0.609513 0.320317i
\(250\) 0 0
\(251\) 0.419101 0.241968i 0.0264534 0.0152729i −0.486715 0.873561i \(-0.661805\pi\)
0.513168 + 0.858288i \(0.328472\pi\)
\(252\) 0 0
\(253\) −24.8865 14.3682i −1.56460 0.903323i
\(254\) 0 0
\(255\) −0.676466 + 1.65131i −0.0423620 + 0.103409i
\(256\) 0 0
\(257\) 13.5896 + 11.4030i 0.847695 + 0.711300i 0.959281 0.282454i \(-0.0911486\pi\)
−0.111586 + 0.993755i \(0.535593\pi\)
\(258\) 0 0
\(259\) 1.97497 5.42619i 0.122719 0.337167i
\(260\) 0 0
\(261\) 3.54226 + 12.8194i 0.219260 + 0.793500i
\(262\) 0 0
\(263\) −1.39832 7.93029i −0.0862243 0.489002i −0.997086 0.0762899i \(-0.975693\pi\)
0.910861 0.412712i \(-0.135419\pi\)
\(264\) 0 0
\(265\) −4.89249 + 1.78072i −0.300543 + 0.109389i
\(266\) 0 0
\(267\) 13.2740 4.24220i 0.812353 0.259619i
\(268\) 0 0
\(269\) 6.56538i 0.400298i 0.979765 + 0.200149i \(0.0641426\pi\)
−0.979765 + 0.200149i \(0.935857\pi\)
\(270\) 0 0
\(271\) −10.8623 −0.659839 −0.329919 0.944009i \(-0.607022\pi\)
−0.329919 + 0.944009i \(0.607022\pi\)
\(272\) 0 0
\(273\) −12.3250 + 13.5561i −0.745945 + 0.820452i
\(274\) 0 0
\(275\) 5.67046 + 15.5795i 0.341941 + 0.939476i
\(276\) 0 0
\(277\) 31.2235 5.50555i 1.87604 0.330796i 0.885131 0.465342i \(-0.154069\pi\)
0.990907 + 0.134546i \(0.0429575\pi\)
\(278\) 0 0
\(279\) −4.00929 + 5.82191i −0.240030 + 0.348549i
\(280\) 0 0
\(281\) −18.4488 6.71481i −1.10056 0.400572i −0.273039 0.962003i \(-0.588029\pi\)
−0.827523 + 0.561431i \(0.810251\pi\)
\(282\) 0 0
\(283\) −12.6768 + 15.1076i −0.753556 + 0.898053i −0.997422 0.0717558i \(-0.977140\pi\)
0.243866 + 0.969809i \(0.421584\pi\)
\(284\) 0 0
\(285\) −4.44754 + 3.44033i −0.263449 + 0.203788i
\(286\) 0 0
\(287\) 2.49735 4.32554i 0.147414 0.255329i
\(288\) 0 0
\(289\) 8.01003 + 13.8738i 0.471178 + 0.816105i
\(290\) 0 0
\(291\) −9.97723 + 15.7966i −0.584875 + 0.926014i
\(292\) 0 0
\(293\) 26.1866 + 4.61741i 1.52984 + 0.269752i 0.874292 0.485401i \(-0.161326\pi\)
0.655549 + 0.755153i \(0.272437\pi\)
\(294\) 0 0
\(295\) −8.98574 + 7.53993i −0.523170 + 0.438992i
\(296\) 0 0
\(297\) −12.0338 18.4107i −0.698271 1.06830i
\(298\) 0 0
\(299\) −29.4597 35.1087i −1.70370 2.03039i
\(300\) 0 0
\(301\) 16.7421 + 2.95209i 0.965001 + 0.170156i
\(302\) 0 0
\(303\) 0.454606 11.4346i 0.0261164 0.656898i
\(304\) 0 0
\(305\) −2.86175 4.95671i −0.163864 0.283820i
\(306\) 0 0
\(307\) −20.0407 11.5705i −1.14379 0.660365i −0.196420 0.980520i \(-0.562932\pi\)
−0.947365 + 0.320155i \(0.896265\pi\)
\(308\) 0 0
\(309\) −3.69864 27.2723i −0.210409 1.55147i
\(310\) 0 0
\(311\) 18.6806 + 15.6749i 1.05928 + 0.888842i 0.994039 0.109027i \(-0.0347735\pi\)
0.0652424 + 0.997869i \(0.479218\pi\)
\(312\) 0 0
\(313\) 24.2156 + 8.81377i 1.36875 + 0.498184i 0.918748 0.394845i \(-0.129202\pi\)
0.450000 + 0.893028i \(0.351424\pi\)
\(314\) 0 0
\(315\) 4.87020 0.464362i 0.274405 0.0261639i
\(316\) 0 0
\(317\) −18.1371 + 3.19806i −1.01868 + 0.179621i −0.657960 0.753053i \(-0.728580\pi\)
−0.360721 + 0.932674i \(0.617469\pi\)
\(318\) 0 0
\(319\) 17.6337 6.41816i 0.987300 0.359348i
\(320\) 0 0
\(321\) 6.52458 + 1.41981i 0.364167 + 0.0792462i
\(322\) 0 0
\(323\) 3.08773i 0.171806i
\(324\) 0 0
\(325\) 26.4420i 1.46674i
\(326\) 0 0
\(327\) −5.63249 1.22568i −0.311478 0.0677805i
\(328\) 0 0
\(329\) −1.31613 + 0.479031i −0.0725605 + 0.0264099i
\(330\) 0 0
\(331\) 15.2370 2.68670i 0.837502 0.147674i 0.261583 0.965181i \(-0.415755\pi\)
0.575919 + 0.817507i \(0.304644\pi\)
\(332\) 0 0
\(333\) 6.41181 + 9.00679i 0.351365 + 0.493569i
\(334\) 0 0
\(335\) 0.710980 + 0.258776i 0.0388450 + 0.0141384i
\(336\) 0 0
\(337\) 9.32566 + 7.82516i 0.508001 + 0.426264i 0.860425 0.509577i \(-0.170198\pi\)
−0.352424 + 0.935840i \(0.614643\pi\)
\(338\) 0 0
\(339\) −1.94501 14.3417i −0.105639 0.778937i
\(340\) 0 0
\(341\) 8.63764 + 4.98695i 0.467755 + 0.270058i
\(342\) 0 0
\(343\) 9.04472 + 15.6659i 0.488369 + 0.845880i
\(344\) 0 0
\(345\) −0.486168 + 12.2284i −0.0261744 + 0.658356i
\(346\) 0 0
\(347\) −23.2143 4.09332i −1.24621 0.219741i −0.488636 0.872488i \(-0.662505\pi\)
−0.757576 + 0.652747i \(0.773616\pi\)
\(348\) 0 0
\(349\) −14.7087 17.5291i −0.787338 0.938312i 0.211902 0.977291i \(-0.432034\pi\)
−0.999240 + 0.0389784i \(0.987590\pi\)
\(350\) 0 0
\(351\) −7.99230 34.1562i −0.426598 1.82312i
\(352\) 0 0
\(353\) 0.541929 0.454733i 0.0288440 0.0242030i −0.628252 0.778010i \(-0.716229\pi\)
0.657096 + 0.753807i \(0.271785\pi\)
\(354\) 0 0
\(355\) 5.16729 + 0.911132i 0.274251 + 0.0483579i
\(356\) 0 0
\(357\) −1.43464 + 2.27142i −0.0759293 + 0.120216i
\(358\) 0 0
\(359\) 5.07907 + 8.79721i 0.268063 + 0.464299i 0.968362 0.249551i \(-0.0802831\pi\)
−0.700298 + 0.713850i \(0.746950\pi\)
\(360\) 0 0
\(361\) −4.63535 + 8.02867i −0.243966 + 0.422561i
\(362\) 0 0
\(363\) −9.47668 + 7.33056i −0.497397 + 0.384755i
\(364\) 0 0
\(365\) −9.39023 + 11.1908i −0.491507 + 0.585755i
\(366\) 0 0
\(367\) 1.79478 + 0.653245i 0.0936866 + 0.0340991i 0.388438 0.921475i \(-0.373015\pi\)
−0.294752 + 0.955574i \(0.595237\pi\)
\(368\) 0 0
\(369\) 4.10894 + 8.63530i 0.213903 + 0.449536i
\(370\) 0 0
\(371\) −7.71925 + 1.36111i −0.400763 + 0.0706654i
\(372\) 0 0
\(373\) 11.8307 + 32.5046i 0.612571 + 1.68303i 0.724470 + 0.689306i \(0.242084\pi\)
−0.111899 + 0.993720i \(0.535693\pi\)
\(374\) 0 0
\(375\) 10.8132 11.8932i 0.558391 0.614165i
\(376\) 0 0
\(377\) 29.9286 1.54140
\(378\) 0 0
\(379\) 27.1937i 1.39685i 0.715685 + 0.698423i \(0.246114\pi\)
−0.715685 + 0.698423i \(0.753886\pi\)
\(380\) 0 0
\(381\) −6.03883 + 1.92994i −0.309378 + 0.0988738i
\(382\) 0 0
\(383\) 5.67775 2.06653i 0.290120 0.105595i −0.192861 0.981226i \(-0.561777\pi\)
0.482980 + 0.875631i \(0.339554\pi\)
\(384\) 0 0
\(385\) −1.19866 6.79794i −0.0610894 0.346455i
\(386\) 0 0
\(387\) −22.8360 + 23.1947i −1.16082 + 1.17905i
\(388\) 0 0
\(389\) 3.99747 10.9830i 0.202680 0.556858i −0.796156 0.605091i \(-0.793137\pi\)
0.998836 + 0.0482330i \(0.0153590\pi\)
\(390\) 0 0
\(391\) −5.14814 4.31980i −0.260353 0.218462i
\(392\) 0 0
\(393\) −6.44102 + 15.7230i −0.324906 + 0.793121i
\(394\) 0 0
\(395\) 7.97761 + 4.60588i 0.401397 + 0.231747i
\(396\) 0 0
\(397\) −2.31327 + 1.33556i −0.116099 + 0.0670301i −0.556925 0.830563i \(-0.688019\pi\)
0.440826 + 0.897593i \(0.354686\pi\)
\(398\) 0 0
\(399\) −7.49342 + 3.93802i −0.375140 + 0.197148i
\(400\) 0 0
\(401\) −2.15776 + 12.2372i −0.107753 + 0.611099i 0.882332 + 0.470628i \(0.155973\pi\)
−0.990085 + 0.140470i \(0.955138\pi\)
\(402\) 0 0
\(403\) 10.2249 + 12.1856i 0.509339 + 0.607007i
\(404\) 0 0
\(405\) −4.55646 + 8.18403i −0.226412 + 0.406668i
\(406\) 0 0
\(407\) 11.9499 10.0271i 0.592334 0.497027i
\(408\) 0 0
\(409\) −0.895032 + 5.07598i −0.0442565 + 0.250991i −0.998907 0.0467370i \(-0.985118\pi\)
0.954651 + 0.297728i \(0.0962288\pi\)
\(410\) 0 0
\(411\) 17.8003 + 33.8711i 0.878023 + 1.67074i
\(412\) 0 0
\(413\) −15.2936 + 8.82978i −0.752550 + 0.434485i
\(414\) 0 0
\(415\) −3.26440 + 5.65411i −0.160243 + 0.277549i
\(416\) 0 0
\(417\) 3.12588 7.63052i 0.153075 0.373668i
\(418\) 0 0
\(419\) −1.84481 + 2.19856i −0.0901248 + 0.107407i −0.809222 0.587503i \(-0.800111\pi\)
0.719097 + 0.694909i \(0.244556\pi\)
\(420\) 0 0
\(421\) 4.61049 12.6672i 0.224701 0.617362i −0.775195 0.631721i \(-0.782349\pi\)
0.999897 + 0.0143594i \(0.00457089\pi\)
\(422\) 0 0
\(423\) 0.673847 2.59558i 0.0327636 0.126202i
\(424\) 0 0
\(425\) 0.673287 + 3.81840i 0.0326592 + 0.185220i
\(426\) 0 0
\(427\) −2.94709 8.09707i −0.142620 0.391845i
\(428\) 0 0
\(429\) −47.1457 + 15.0672i −2.27621 + 0.727452i
\(430\) 0 0
\(431\) −25.2153 −1.21458 −0.607290 0.794480i \(-0.707743\pi\)
−0.607290 + 0.794480i \(0.707743\pi\)
\(432\) 0 0
\(433\) −15.5658 −0.748046 −0.374023 0.927419i \(-0.622022\pi\)
−0.374023 + 0.927419i \(0.622022\pi\)
\(434\) 0 0
\(435\) −5.91309 5.37611i −0.283511 0.257765i
\(436\) 0 0
\(437\) −7.24252 19.8987i −0.346457 0.951882i
\(438\) 0 0
\(439\) −5.53290 31.3787i −0.264071 1.49762i −0.771667 0.636026i \(-0.780577\pi\)
0.507596 0.861595i \(-0.330534\pi\)
\(440\) 0 0
\(441\) −13.5916 1.08244i −0.647221 0.0515449i
\(442\) 0 0
\(443\) −2.16330 + 5.94362i −0.102782 + 0.282390i −0.980415 0.196942i \(-0.936899\pi\)
0.877634 + 0.479332i \(0.159121\pi\)
\(444\) 0 0
\(445\) −5.38246 + 6.41456i −0.255153 + 0.304079i
\(446\) 0 0
\(447\) 24.3867 + 31.5262i 1.15345 + 1.49114i
\(448\) 0 0
\(449\) −4.18149 + 7.24256i −0.197337 + 0.341797i −0.947664 0.319269i \(-0.896563\pi\)
0.750327 + 0.661067i \(0.229896\pi\)
\(450\) 0 0
\(451\) 11.6853 6.74653i 0.550241 0.317682i
\(452\) 0 0
\(453\) −18.3845 + 29.1075i −0.863777 + 1.36759i
\(454\) 0 0
\(455\) 1.91172 10.8419i 0.0896228 0.508276i
\(456\) 0 0
\(457\) −21.5741 + 18.1028i −1.00919 + 0.846812i −0.988231 0.152968i \(-0.951117\pi\)
−0.0209605 + 0.999780i \(0.506672\pi\)
\(458\) 0 0
\(459\) −2.02385 4.72888i −0.0944655 0.220725i
\(460\) 0 0
\(461\) −16.8013 20.0230i −0.782513 0.932563i 0.216531 0.976276i \(-0.430526\pi\)
−0.999044 + 0.0437126i \(0.986081\pi\)
\(462\) 0 0
\(463\) −3.84612 + 21.8124i −0.178744 + 1.01371i 0.754988 + 0.655738i \(0.227642\pi\)
−0.933733 + 0.357971i \(0.883469\pi\)
\(464\) 0 0
\(465\) 0.168740 4.24426i 0.00782513 0.196823i
\(466\) 0 0
\(467\) 19.1663 11.0657i 0.886910 0.512058i 0.0139792 0.999902i \(-0.495550\pi\)
0.872930 + 0.487845i \(0.162217\pi\)
\(468\) 0 0
\(469\) 0.986466 + 0.569536i 0.0455508 + 0.0262987i
\(470\) 0 0
\(471\) −8.39367 + 1.13834i −0.386760 + 0.0524520i
\(472\) 0 0
\(473\) 35.1815 + 29.5208i 1.61765 + 1.35737i
\(474\) 0 0
\(475\) −4.17853 + 11.4804i −0.191724 + 0.526757i
\(476\) 0 0
\(477\) 6.23626 13.6505i 0.285539 0.625012i
\(478\) 0 0
\(479\) 2.06488 + 11.7105i 0.0943470 + 0.535068i 0.994946 + 0.100416i \(0.0320175\pi\)
−0.900599 + 0.434652i \(0.856871\pi\)
\(480\) 0 0
\(481\) 23.3788 8.50920i 1.06598 0.387986i
\(482\) 0 0
\(483\) −3.91764 + 18.0031i −0.178259 + 0.819168i
\(484\) 0 0
\(485\) 11.2268i 0.509783i
\(486\) 0 0
\(487\) −22.1183 −1.00228 −0.501138 0.865367i \(-0.667085\pi\)
−0.501138 + 0.865367i \(0.667085\pi\)
\(488\) 0 0
\(489\) 7.07578 + 1.53976i 0.319978 + 0.0696303i
\(490\) 0 0
\(491\) −2.55319 7.01484i −0.115224 0.316575i 0.868653 0.495421i \(-0.164986\pi\)
−0.983877 + 0.178845i \(0.942764\pi\)
\(492\) 0 0
\(493\) 4.32189 0.762066i 0.194648 0.0343217i
\(494\) 0 0
\(495\) 12.0213 + 5.49195i 0.540316 + 0.246845i
\(496\) 0 0
\(497\) 7.42295 + 2.70173i 0.332965 + 0.121189i
\(498\) 0 0
\(499\) 6.65452 7.93054i 0.297897 0.355020i −0.596246 0.802802i \(-0.703342\pi\)
0.894143 + 0.447782i \(0.147786\pi\)
\(500\) 0 0
\(501\) 1.41880 + 10.4617i 0.0633874 + 0.467393i
\(502\) 0 0
\(503\) 16.9435 29.3471i 0.755475 1.30852i −0.189663 0.981849i \(-0.560739\pi\)
0.945138 0.326672i \(-0.105927\pi\)
\(504\) 0 0
\(505\) 3.43817 + 5.95508i 0.152997 + 0.264998i
\(506\) 0 0
\(507\) −56.3770 2.24139i −2.50379 0.0995436i
\(508\) 0 0
\(509\) 16.7517 + 2.95378i 0.742508 + 0.130924i 0.532090 0.846688i \(-0.321407\pi\)
0.210417 + 0.977612i \(0.432518\pi\)
\(510\) 0 0
\(511\) −16.8478 + 14.1370i −0.745301 + 0.625382i
\(512\) 0 0
\(513\) 1.92753 16.0927i 0.0851026 0.710511i
\(514\) 0 0
\(515\) 10.6302 + 12.6686i 0.468423 + 0.558245i
\(516\) 0 0
\(517\) −3.72618 0.657026i −0.163877 0.0288960i
\(518\) 0 0
\(519\) 1.94227 + 1.22675i 0.0852564 + 0.0538484i
\(520\) 0 0
\(521\) −14.6553 25.3837i −0.642060 1.11208i −0.984972 0.172714i \(-0.944746\pi\)
0.342912 0.939368i \(-0.388587\pi\)
\(522\) 0 0
\(523\) 3.33680 + 1.92651i 0.145908 + 0.0842402i 0.571177 0.820827i \(-0.306487\pi\)
−0.425269 + 0.905067i \(0.639820\pi\)
\(524\) 0 0
\(525\) 8.40793 6.50385i 0.366952 0.283851i
\(526\) 0 0
\(527\) 1.78683 + 1.49932i 0.0778353 + 0.0653116i
\(528\) 0 0
\(529\) −21.6963 7.89682i −0.943319 0.343340i
\(530\) 0 0
\(531\) 2.68427 33.7049i 0.116487 1.46267i
\(532\) 0 0
\(533\) 21.1929 3.73687i 0.917965 0.161862i
\(534\) 0 0
\(535\) −3.77033 + 1.37229i −0.163006 + 0.0593292i
\(536\) 0 0
\(537\) 13.0321 14.3338i 0.562376 0.618547i
\(538\) 0 0
\(539\) 19.2380i 0.828638i
\(540\) 0 0
\(541\) 4.51542i 0.194133i 0.995278 + 0.0970665i \(0.0309460\pi\)
−0.995278 + 0.0970665i \(0.969054\pi\)
\(542\) 0 0
\(543\) −1.95473 6.11640i −0.0838856 0.262480i
\(544\) 0 0
\(545\) 3.25483 1.18466i 0.139421 0.0507453i
\(546\) 0 0
\(547\) 12.3037 2.16948i 0.526069 0.0927602i 0.0956949 0.995411i \(-0.469493\pi\)
0.430374 + 0.902651i \(0.358382\pi\)
\(548\) 0 0
\(549\) 15.9685 + 4.14564i 0.681520 + 0.176931i
\(550\) 0 0
\(551\) 12.9942 + 4.72950i 0.553572 + 0.201484i
\(552\) 0 0
\(553\) 10.6237 + 8.91435i 0.451766 + 0.379077i
\(554\) 0 0
\(555\) −6.14756 2.51838i −0.260949 0.106899i
\(556\) 0 0
\(557\) −3.03004 1.74940i −0.128387 0.0741243i 0.434431 0.900705i \(-0.356949\pi\)
−0.562818 + 0.826581i \(0.690283\pi\)
\(558\) 0 0
\(559\) 36.6233 + 63.4335i 1.54900 + 2.68295i
\(560\) 0 0
\(561\) −6.42449 + 3.37627i −0.271242 + 0.142546i
\(562\) 0 0
\(563\) −26.9436 4.75088i −1.13554 0.200226i −0.425885 0.904777i \(-0.640037\pi\)
−0.709653 + 0.704552i \(0.751148\pi\)
\(564\) 0 0
\(565\) 5.59013 + 6.66206i 0.235179 + 0.280275i
\(566\) 0 0
\(567\) −8.89504 + 10.9427i −0.373557 + 0.459549i
\(568\) 0 0
\(569\) 3.15771 2.64963i 0.132378 0.111078i −0.574195 0.818719i \(-0.694685\pi\)
0.706573 + 0.707640i \(0.250240\pi\)
\(570\) 0 0
\(571\) −2.91629 0.514220i −0.122043 0.0215194i 0.112293 0.993675i \(-0.464180\pi\)
−0.234336 + 0.972156i \(0.575292\pi\)
\(572\) 0 0
\(573\) 14.5476 + 27.6817i 0.607733 + 1.15642i
\(574\) 0 0
\(575\) 13.2953 + 23.0281i 0.554453 + 0.960340i
\(576\) 0 0
\(577\) −4.23106 + 7.32841i −0.176141 + 0.305086i −0.940556 0.339640i \(-0.889695\pi\)
0.764414 + 0.644725i \(0.223028\pi\)
\(578\) 0 0
\(579\) −7.11321 2.91396i −0.295615 0.121100i
\(580\) 0 0
\(581\) −6.31802 + 7.52952i −0.262115 + 0.312377i
\(582\) 0 0
\(583\) −19.8980 7.24228i −0.824092 0.299945i
\(584\) 0 0
\(585\) 15.0205 + 14.7881i 0.621020 + 0.611414i
\(586\) 0 0
\(587\) 45.4714 8.01784i 1.87681 0.330932i 0.885727 0.464206i \(-0.153660\pi\)
0.991079 + 0.133275i \(0.0425493\pi\)
\(588\) 0 0
\(589\) 2.51375 + 6.90646i 0.103577 + 0.284576i
\(590\) 0 0
\(591\) −8.61628 26.9605i −0.354426 1.10901i
\(592\) 0 0
\(593\) 22.0816 0.906784 0.453392 0.891311i \(-0.350214\pi\)
0.453392 + 0.891311i \(0.350214\pi\)
\(594\) 0 0
\(595\) 1.61432i 0.0661807i
\(596\) 0 0
\(597\) −1.17601 1.06922i −0.0481311 0.0437602i
\(598\) 0 0
\(599\) 23.2555 8.46431i 0.950194 0.345842i 0.180010 0.983665i \(-0.442387\pi\)
0.770184 + 0.637822i \(0.220165\pi\)
\(600\) 0 0
\(601\) 2.55983 + 14.5175i 0.104418 + 0.592182i 0.991451 + 0.130477i \(0.0416509\pi\)
−0.887034 + 0.461705i \(0.847238\pi\)
\(602\) 0 0
\(603\) −1.96933 + 0.937069i −0.0801974 + 0.0381604i
\(604\) 0 0
\(605\) 2.46229 6.76510i 0.100107 0.275040i
\(606\) 0 0
\(607\) 23.2768 + 19.5315i 0.944775 + 0.792761i 0.978410 0.206674i \(-0.0662638\pi\)
−0.0336346 + 0.999434i \(0.510708\pi\)
\(608\) 0 0
\(609\) −7.36144 9.51660i −0.298301 0.385632i
\(610\) 0 0
\(611\) −5.22602 3.01724i −0.211422 0.122065i
\(612\) 0 0
\(613\) 8.97166 5.17979i 0.362362 0.209210i −0.307754 0.951466i \(-0.599578\pi\)
0.670116 + 0.742256i \(0.266244\pi\)
\(614\) 0 0
\(615\) −4.85841 3.06859i −0.195910 0.123738i
\(616\) 0 0
\(617\) 2.09885 11.9032i 0.0844965 0.479204i −0.912968 0.408032i \(-0.866215\pi\)
0.997464 0.0711715i \(-0.0226738\pi\)
\(618\) 0 0
\(619\) 1.25371 + 1.49411i 0.0503908 + 0.0600535i 0.790651 0.612267i \(-0.209742\pi\)
−0.740260 + 0.672320i \(0.765298\pi\)
\(620\) 0 0
\(621\) −24.1345 25.7278i −0.968486 1.03242i
\(622\) 0 0
\(623\) −9.65710 + 8.10327i −0.386904 + 0.324651i
\(624\) 0 0
\(625\) 1.72350 9.77447i 0.0689401 0.390979i
\(626\) 0 0
\(627\) −22.8504 0.908468i −0.912557 0.0362807i
\(628\) 0 0
\(629\) 3.15939 1.82408i 0.125973 0.0727307i
\(630\) 0 0
\(631\) 6.64702 11.5130i 0.264614 0.458325i −0.702849 0.711340i \(-0.748089\pi\)
0.967462 + 0.253015i \(0.0814222\pi\)
\(632\) 0 0
\(633\) 10.5250 1.42739i 0.418330 0.0567335i
\(634\) 0 0
\(635\) 2.44868 2.91823i 0.0971730 0.115806i
\(636\) 0 0
\(637\) −10.4939 + 28.8319i −0.415785 + 1.14236i
\(638\) 0 0
\(639\) −12.3212 + 8.77127i −0.487418 + 0.346986i
\(640\) 0 0
\(641\) 4.99251 + 28.3139i 0.197192 + 1.11833i 0.909262 + 0.416225i \(0.136647\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(642\) 0 0
\(643\) 12.8078 + 35.1891i 0.505090 + 1.38772i 0.886247 + 0.463213i \(0.153303\pi\)
−0.381157 + 0.924510i \(0.624474\pi\)
\(644\) 0 0
\(645\) 4.15884 19.1115i 0.163754 0.752513i
\(646\) 0 0
\(647\) 23.8383 0.937182 0.468591 0.883415i \(-0.344762\pi\)
0.468591 + 0.883415i \(0.344762\pi\)
\(648\) 0 0
\(649\) −47.7068 −1.87266
\(650\) 0 0
\(651\) 1.35974 6.24853i 0.0532925 0.244899i
\(652\) 0 0
\(653\) −16.8138 46.1955i −0.657974 1.80777i −0.585921 0.810368i \(-0.699267\pi\)
−0.0720526 0.997401i \(-0.522955\pi\)
\(654\) 0 0
\(655\) −1.77292 10.0547i −0.0692736 0.392870i
\(656\) 0 0
\(657\) −3.99687 41.9188i −0.155933 1.63541i
\(658\) 0 0
\(659\) 9.01137 24.7585i 0.351033 0.964456i −0.631006 0.775778i \(-0.717358\pi\)
0.982039 0.188678i \(-0.0604202\pi\)
\(660\) 0 0
\(661\) 0.937603 1.11739i 0.0364685 0.0434615i −0.747502 0.664260i \(-0.768747\pi\)
0.783970 + 0.620798i \(0.213191\pi\)
\(662\) 0 0
\(663\) −11.4701 + 1.55556i −0.445460 + 0.0604128i
\(664\) 0 0
\(665\) 2.54332 4.40516i 0.0986258 0.170825i
\(666\) 0 0
\(667\) 26.0646 15.0484i 1.00923 0.582677i
\(668\) 0 0
\(669\) 37.1082 + 1.47532i 1.43469 + 0.0570392i
\(670\) 0 0
\(671\) 4.04215 22.9242i 0.156046 0.884979i
\(672\) 0 0
\(673\) 14.2562 11.9623i 0.549534 0.461114i −0.325249 0.945628i \(-0.605448\pi\)
0.874783 + 0.484514i \(0.161004\pi\)
\(674\) 0 0
\(675\) 1.12540 + 20.3211i 0.0433165 + 0.782160i
\(676\) 0 0
\(677\) −2.04257 2.43424i −0.0785022 0.0935553i 0.725364 0.688366i \(-0.241672\pi\)
−0.803866 + 0.594810i \(0.797227\pi\)
\(678\) 0 0
\(679\) 2.93499 16.6451i 0.112634 0.638782i
\(680\) 0 0
\(681\) −27.2501 17.2113i −1.04423 0.659538i
\(682\) 0 0
\(683\) 7.95770 4.59438i 0.304493 0.175799i −0.339967 0.940437i \(-0.610416\pi\)
0.644459 + 0.764639i \(0.277082\pi\)
\(684\) 0 0
\(685\) −19.9118 11.4961i −0.760792 0.439243i
\(686\) 0 0
\(687\) −9.41089 12.1660i −0.359048 0.464164i
\(688\) 0 0
\(689\) −25.8705 21.7080i −0.985589 0.827008i
\(690\) 0 0
\(691\) 6.14708 16.8890i 0.233846 0.642487i −0.766154 0.642657i \(-0.777832\pi\)
1.00000 0.000170287i \(5.42042e-5\pi\)
\(692\) 0 0
\(693\) 16.3873 + 11.2852i 0.622501 + 0.428689i
\(694\) 0 0
\(695\) 0.860413 + 4.87964i 0.0326373 + 0.185095i
\(696\) 0 0
\(697\) 2.96524 1.07926i 0.112316 0.0408799i
\(698\) 0 0
\(699\) −24.0863 21.8989i −0.911027 0.828294i
\(700\) 0 0
\(701\) 19.1567i 0.723538i −0.932268 0.361769i \(-0.882173\pi\)
0.932268 0.361769i \(-0.117827\pi\)
\(702\) 0 0
\(703\) 11.4952 0.433548
\(704\) 0 0
\(705\) 0.490531 + 1.53488i 0.0184745 + 0.0578070i
\(706\) 0 0
\(707\) 3.54070 + 9.72798i 0.133162 + 0.365858i
\(708\) 0 0
\(709\) −9.23990 + 1.62924i −0.347012 + 0.0611875i −0.344438 0.938809i \(-0.611930\pi\)
−0.00257396 + 0.999997i \(0.500819\pi\)
\(710\) 0 0
\(711\) −25.5936 + 7.07202i −0.959834 + 0.265222i
\(712\) 0 0
\(713\) 15.0318 + 5.47115i 0.562947 + 0.204896i
\(714\) 0 0
\(715\) 19.1171 22.7829i 0.714938 0.852031i
\(716\) 0 0
\(717\) 32.9192 + 13.4855i 1.22939 + 0.503626i
\(718\) 0 0
\(719\) −10.7417 + 18.6051i −0.400596 + 0.693853i −0.993798 0.111201i \(-0.964530\pi\)
0.593202 + 0.805054i \(0.297864\pi\)
\(720\) 0 0
\(721\) 12.4487 + 21.5618i 0.463614 + 0.803003i
\(722\) 0 0
\(723\) 11.1000 + 21.1215i 0.412812 + 0.785516i
\(724\) 0 0
\(725\) −17.1004 3.01526i −0.635092 0.111984i
\(726\) 0 0
\(727\) 22.5451 18.9176i 0.836151 0.701614i −0.120543 0.992708i \(-0.538464\pi\)
0.956694 + 0.291094i \(0.0940193\pi\)
\(728\) 0 0
\(729\) −7.59595 25.9095i −0.281331 0.959611i
\(730\) 0 0
\(731\) 6.90385 + 8.22768i 0.255348 + 0.304312i
\(732\) 0 0
\(733\) 43.1488 + 7.60829i 1.59374 + 0.281019i 0.898901 0.438151i \(-0.144366\pi\)
0.694835 + 0.719170i \(0.255478\pi\)
\(734\) 0 0
\(735\) 7.25243 3.81137i 0.267510 0.140584i
\(736\) 0 0
\(737\) 1.53859 + 2.66491i 0.0566746 + 0.0981632i
\(738\) 0 0
\(739\) −21.9574 12.6771i −0.807716 0.466335i 0.0384462 0.999261i \(-0.487759\pi\)
−0.846162 + 0.532926i \(0.821093\pi\)
\(740\) 0 0
\(741\) −33.7503 13.8260i −1.23985 0.507910i
\(742\) 0 0
\(743\) 3.44991 + 2.89482i 0.126565 + 0.106201i 0.703873 0.710326i \(-0.251452\pi\)
−0.577308 + 0.816526i \(0.695897\pi\)
\(744\) 0 0
\(745\) −22.5055 8.19135i −0.824539 0.300108i
\(746\) 0 0
\(747\) −5.01228 18.1394i −0.183390 0.663685i
\(748\) 0 0
\(749\) −5.94874 + 1.04892i −0.217362 + 0.0383268i
\(750\) 0 0
\(751\) −36.9941 + 13.4647i −1.34993 + 0.491335i −0.912927 0.408124i \(-0.866183\pi\)
−0.437006 + 0.899459i \(0.643961\pi\)
\(752\) 0 0
\(753\) −0.255166 0.798419i −0.00929875 0.0290960i
\(754\) 0 0
\(755\) 20.6870i 0.752876i
\(756\) 0 0
\(757\) 33.7213i 1.22562i 0.790229 + 0.612811i \(0.209961\pi\)
−0.790229 + 0.612811i \(0.790039\pi\)
\(758\) 0 0
\(759\) −33.4829 + 36.8273i −1.21535 + 1.33674i
\(760\) 0 0
\(761\) −34.7776 + 12.6580i −1.26069 + 0.458852i −0.883999 0.467489i \(-0.845159\pi\)
−0.376687 + 0.926341i \(0.622937\pi\)
\(762\) 0 0
\(763\) 5.13539 0.905508i 0.185914 0.0327816i
\(764\) 0 0
\(765\) 2.54560 + 1.75304i 0.0920365 + 0.0633814i
\(766\) 0 0
\(767\) −71.4980 26.0231i −2.58164 0.939641i
\(768\) 0 0
\(769\) −4.44297 3.72810i −0.160218 0.134439i 0.559154 0.829064i \(-0.311126\pi\)
−0.719372 + 0.694625i \(0.755570\pi\)
\(770\) 0 0
\(771\) 24.3039 18.7999i 0.875283 0.677064i
\(772\) 0 0
\(773\) −36.8149 21.2551i −1.32414 0.764492i −0.339753 0.940515i \(-0.610344\pi\)
−0.984386 + 0.176022i \(0.943677\pi\)
\(774\) 0 0
\(775\) −4.61456 7.99264i −0.165760 0.287104i
\(776\) 0 0
\(777\) −8.45615 5.34095i −0.303363 0.191605i
\(778\) 0 0
\(779\) 9.79190 + 1.72658i 0.350831 + 0.0618610i
\(780\) 0 0
\(781\) 13.7170 + 16.3473i 0.490833 + 0.584951i
\(782\) 0 0
\(783\) 23.0006 1.27379i 0.821976 0.0455216i
\(784\) 0 0
\(785\) 3.89904 3.27169i 0.139163 0.116771i
\(786\) 0 0
\(787\) 16.8983 + 2.97963i 0.602359 + 0.106212i 0.466508 0.884517i \(-0.345512\pi\)
0.135851 + 0.990729i \(0.456623\pi\)
\(788\) 0 0
\(789\) −13.9365 0.554078i −0.496154 0.0197257i
\(790\) 0 0
\(791\) 6.54642 + 11.3387i 0.232764 + 0.403159i
\(792\) 0 0
\(793\) 18.5627 32.1515i 0.659179 1.14173i
\(794\) 0 0
\(795\) 1.21190 + 8.93607i 0.0429817 + 0.316930i
\(796\) 0 0
\(797\) −4.53298 + 5.40220i −0.160567 + 0.191356i −0.840329 0.542076i \(-0.817638\pi\)
0.679763 + 0.733432i \(0.262083\pi\)
\(798\) 0 0
\(799\) −0.831499 0.302641i −0.0294163 0.0107067i
\(800\) 0 0
\(801\) −2.29100 24.0278i −0.0809483 0.848980i
\(802\) 0 0
\(803\) −58.5114 + 10.3171i −2.06482 + 0.364084i
\(804\) 0 0
\(805\) −3.78652 10.4034i −0.133457 0.366670i
\(806\) 0 0
\(807\) 11.1115 + 2.41797i 0.391144 + 0.0851167i
\(808\) 0 0
\(809\) −34.2649 −1.20469 −0.602345 0.798236i \(-0.705767\pi\)
−0.602345 + 0.798236i \(0.705767\pi\)
\(810\) 0 0
\(811\) 5.06146i 0.177732i −0.996044 0.0888659i \(-0.971676\pi\)
0.996044 0.0888659i \(-0.0283243\pi\)
\(812\) 0 0
\(813\) −4.00050 + 18.3839i −0.140304 + 0.644750i
\(814\) 0 0
\(815\) −4.08885 + 1.48822i −0.143226 + 0.0521301i
\(816\) 0 0
\(817\) 5.87673 + 33.3286i 0.205601 + 1.16602i
\(818\) 0 0
\(819\) 18.4037 + 25.8520i 0.643077 + 0.903342i
\(820\) 0 0
\(821\) 5.19050 14.2608i 0.181150 0.497705i −0.815568 0.578661i \(-0.803575\pi\)
0.996718 + 0.0809566i \(0.0257975\pi\)
\(822\) 0 0
\(823\) −22.8496 19.1731i −0.796487 0.668332i 0.150855 0.988556i \(-0.451797\pi\)
−0.947342 + 0.320224i \(0.896242\pi\)
\(824\) 0 0
\(825\) 28.4557 3.85914i 0.990701 0.134358i
\(826\) 0 0
\(827\) 7.24554 + 4.18322i 0.251952 + 0.145465i 0.620658 0.784082i \(-0.286866\pi\)
−0.368706 + 0.929546i \(0.620199\pi\)
\(828\) 0 0
\(829\) 26.4946 15.2967i 0.920196 0.531276i 0.0364987 0.999334i \(-0.488380\pi\)
0.883698 + 0.468058i \(0.155046\pi\)
\(830\) 0 0
\(831\) 2.18154 54.8716i 0.0756768 1.90348i
\(832\) 0 0
\(833\) −0.781255 + 4.43072i −0.0270689 + 0.153515i
\(834\) 0 0
\(835\) −4.07776 4.85968i −0.141117 0.168176i
\(836\) 0 0
\(837\) 8.37666 + 8.92965i 0.289540 + 0.308654i
\(838\) 0 0
\(839\) −5.60536 + 4.70346i −0.193519 + 0.162381i −0.734399 0.678718i \(-0.762536\pi\)
0.540880 + 0.841100i \(0.318091\pi\)
\(840\) 0 0
\(841\) 1.62295 9.20422i 0.0559639 0.317387i
\(842\) 0 0
\(843\) −18.1590 + 28.7505i −0.625428 + 0.990219i
\(844\) 0 0
\(845\) 29.3610 16.9516i 1.01005 0.583151i
\(846\) 0 0
\(847\) 5.41924 9.38639i 0.186207 0.322520i
\(848\) 0 0
\(849\) 20.9000 + 27.0187i 0.717285 + 0.927280i
\(850\) 0 0
\(851\) 16.0820 19.1657i 0.551283 0.656993i
\(852\) 0 0
\(853\) 15.5473 42.7160i 0.532331 1.46257i −0.323959 0.946071i \(-0.605014\pi\)
0.856290 0.516496i \(-0.172764\pi\)
\(854\) 0 0
\(855\) 4.18458 + 8.79424i 0.143109 + 0.300757i
\(856\) 0 0
\(857\) −3.84017 21.7787i −0.131178 0.743946i −0.977445 0.211188i \(-0.932267\pi\)
0.846268 0.532758i \(-0.178844\pi\)
\(858\) 0 0
\(859\) 10.5655 + 29.0285i 0.360491 + 0.990441i 0.978856 + 0.204550i \(0.0655730\pi\)
−0.618365 + 0.785891i \(0.712205\pi\)
\(860\) 0 0
\(861\) −6.40098 5.81969i −0.218145 0.198335i
\(862\) 0 0
\(863\) 27.4661 0.934956 0.467478 0.884005i \(-0.345163\pi\)
0.467478 + 0.884005i \(0.345163\pi\)
\(864\) 0 0
\(865\) −1.38039 −0.0469348
\(866\) 0 0
\(867\) 26.4306 8.44692i 0.897630 0.286872i
\(868\) 0 0
\(869\) 12.8137 + 35.2053i 0.434675 + 1.19426i
\(870\) 0 0
\(871\) 0.852216 + 4.83316i 0.0288762 + 0.163765i
\(872\) 0 0
\(873\) 23.0603 + 22.7036i 0.780474 + 0.768402i
\(874\) 0 0
\(875\) −4.97337 + 13.6642i −0.168131 + 0.461935i
\(876\) 0 0
\(877\) −7.68788 + 9.16206i −0.259601 + 0.309381i −0.880064 0.474855i \(-0.842500\pi\)
0.620463 + 0.784236i \(0.286945\pi\)
\(878\) 0 0
\(879\) 17.4590 42.6188i 0.588879 1.43750i
\(880\) 0 0
\(881\) 18.8243 32.6046i 0.634205 1.09848i −0.352478 0.935820i \(-0.614661\pi\)
0.986683 0.162655i \(-0.0520059\pi\)
\(882\) 0 0
\(883\) 19.8345 11.4515i 0.667485 0.385373i −0.127638 0.991821i \(-0.540739\pi\)
0.795123 + 0.606448i \(0.207406\pi\)
\(884\) 0 0
\(885\) 9.45153 + 17.9847i 0.317710 + 0.604551i
\(886\) 0 0
\(887\) −0.995710 + 5.64695i −0.0334327 + 0.189606i −0.996950 0.0780387i \(-0.975134\pi\)
0.963518 + 0.267645i \(0.0862454\pi\)
\(888\) 0 0
\(889\) 4.39338 3.68648i 0.147349 0.123641i
\(890\) 0 0
\(891\) −35.5910 + 13.5860i −1.19234 + 0.455147i
\(892\) 0 0
\(893\) −1.79219 2.13585i −0.0599735 0.0714737i
\(894\) 0 0
\(895\) −2.02139 + 11.4639i −0.0675675 + 0.383194i
\(896\) 0 0
\(897\) −70.2692 + 36.9286i −2.34622 + 1.23301i
\(898\) 0 0
\(899\) −9.04655 + 5.22303i −0.301719 + 0.174198i
\(900\) 0 0
\(901\) −4.28862 2.47604i −0.142875 0.0824888i
\(902\) 0 0
\(903\) 11.1622 27.2479i 0.371456 0.906753i
\(904\) 0 0
\(905\) 2.95572 + 2.48014i 0.0982513 + 0.0824426i
\(906\) 0 0
\(907\) 8.42248 23.1406i 0.279664 0.768370i −0.717737 0.696315i \(-0.754822\pi\)
0.997401 0.0720557i \(-0.0229559\pi\)
\(908\) 0 0
\(909\) −19.1849 4.98065i −0.636323 0.165198i
\(910\) 0 0
\(911\) −6.32793 35.8875i −0.209654 1.18901i −0.889947 0.456065i \(-0.849259\pi\)
0.680293 0.732940i \(-0.261853\pi\)
\(912\) 0 0
\(913\) −24.9517 + 9.08166i −0.825780 + 0.300559i
\(914\) 0 0
\(915\) −9.44290 + 3.01784i −0.312173 + 0.0997668i
\(916\) 0 0
\(917\) 15.3708i 0.507590i
\(918\) 0 0
\(919\) −27.8245 −0.917845 −0.458923 0.888476i \(-0.651764\pi\)
−0.458923 + 0.888476i \(0.651764\pi\)
\(920\) 0 0
\(921\) −26.9633 + 29.6565i −0.888470 + 0.977213i
\(922\) 0 0
\(923\) 11.6405 + 31.9819i 0.383151 + 1.05270i
\(924\) 0 0
\(925\) −14.2153 + 2.50654i −0.467397 + 0.0824146i
\(926\) 0 0
\(927\) −47.5190 3.78443i −1.56073 0.124297i
\(928\) 0 0
\(929\) 14.0864 + 5.12703i 0.462160 + 0.168212i 0.562598 0.826731i \(-0.309802\pi\)
−0.100438 + 0.994943i \(0.532024\pi\)
\(930\) 0 0
\(931\) −9.11238 + 10.8597i −0.298646 + 0.355913i
\(932\) 0 0
\(933\) 33.4088 25.8429i 1.09375 0.846060i
\(934\) 0 0
\(935\) 2.18052 3.77677i 0.0713106 0.123514i
\(936\) 0 0
\(937\) −9.57278 16.5805i −0.312729 0.541663i 0.666223 0.745753i \(-0.267910\pi\)
−0.978952 + 0.204090i \(0.934577\pi\)
\(938\) 0 0
\(939\) 23.8352 37.7375i 0.777833 1.23152i
\(940\) 0 0
\(941\) 36.4053 + 6.41923i 1.18678 + 0.209261i 0.731975 0.681331i \(-0.238599\pi\)
0.454803 + 0.890592i \(0.349710\pi\)
\(942\) 0 0
\(943\) 16.5778 13.9104i 0.539847 0.452985i
\(944\) 0 0
\(945\) 1.00775 8.41355i 0.0327820 0.273693i
\(946\) 0 0
\(947\) 16.0406 + 19.1164i 0.521248 + 0.621199i 0.960875 0.276981i \(-0.0893340\pi\)
−0.439627 + 0.898180i \(0.644890\pi\)
\(948\) 0 0
\(949\) −93.3185 16.4546i −3.02925 0.534138i
\(950\) 0 0
\(951\) −1.26721 + 31.8738i −0.0410922 + 1.03358i
\(952\) 0 0
\(953\) −7.31014 12.6615i −0.236799 0.410147i 0.722995 0.690853i \(-0.242765\pi\)
−0.959794 + 0.280706i \(0.909432\pi\)
\(954\) 0 0
\(955\) −16.2733 9.39537i −0.526590 0.304027i
\(956\) 0 0
\(957\) −4.36800 32.2079i −0.141197 1.04113i
\(958\) 0 0
\(959\) −26.5164 22.2499i −0.856258 0.718486i
\(960\) 0 0
\(961\) 23.9132 + 8.70369i 0.771393 + 0.280764i
\(962\) 0 0
\(963\) 4.80590 10.5196i 0.154868 0.338988i
\(964\) 0 0
\(965\) 4.54883 0.802081i 0.146432 0.0258199i
\(966\) 0 0
\(967\) −48.8192 + 17.7687i −1.56992 + 0.571404i −0.972981 0.230884i \(-0.925838\pi\)
−0.596937 + 0.802288i \(0.703616\pi\)
\(968\) 0 0
\(969\) −5.22581 1.13719i −0.167877 0.0365317i
\(970\) 0 0
\(971\) 20.4952i 0.657724i −0.944378 0.328862i \(-0.893335\pi\)
0.944378 0.328862i \(-0.106665\pi\)
\(972\) 0 0
\(973\) 7.45961i 0.239144i
\(974\) 0 0
\(975\) 44.7515 + 9.73837i 1.43320 + 0.311877i
\(976\) 0 0
\(977\) −7.72505 + 2.81169i −0.247146 + 0.0899539i −0.462623 0.886555i \(-0.653092\pi\)
0.215477 + 0.976509i \(0.430869\pi\)
\(978\) 0 0
\(979\) −33.5386 + 5.91376i −1.07190 + 0.189004i
\(980\) 0 0
\(981\) −4.14880 + 9.08126i −0.132461 + 0.289942i
\(982\) 0 0
\(983\) 22.5289 + 8.19984i 0.718559 + 0.261534i 0.675314 0.737530i \(-0.264008\pi\)
0.0432453 + 0.999064i \(0.486230\pi\)
\(984\) 0 0
\(985\) 13.0285 + 10.9322i 0.415123 + 0.348330i
\(986\) 0 0
\(987\) 0.326014 + 2.40389i 0.0103771 + 0.0765168i
\(988\) 0 0
\(989\) 63.7900 + 36.8292i 2.02840 + 1.17110i
\(990\) 0 0
\(991\) −8.43544 14.6106i −0.267960 0.464121i 0.700375 0.713776i \(-0.253016\pi\)
−0.968335 + 0.249654i \(0.919683\pi\)
\(992\) 0 0
\(993\) 1.06459 26.7773i 0.0337837 0.849751i
\(994\) 0 0
\(995\) 0.940553 + 0.165845i 0.0298175 + 0.00525763i
\(996\) 0 0
\(997\) 21.3234 + 25.4122i 0.675317 + 0.804812i 0.989497 0.144552i \(-0.0461740\pi\)
−0.314180 + 0.949363i \(0.601730\pi\)
\(998\) 0 0
\(999\) 17.6049 7.53450i 0.556994 0.238381i
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.49.20 204
4.3 odd 2 216.2.t.a.157.32 yes 204
8.3 odd 2 216.2.t.a.157.18 204
8.5 even 2 inner 864.2.bf.a.49.15 204
12.11 even 2 648.2.t.a.37.3 204
24.11 even 2 648.2.t.a.37.17 204
27.16 even 9 inner 864.2.bf.a.529.15 204
108.11 even 18 648.2.t.a.613.17 204
108.43 odd 18 216.2.t.a.205.18 yes 204
216.11 even 18 648.2.t.a.613.3 204
216.43 odd 18 216.2.t.a.205.32 yes 204
216.205 even 18 inner 864.2.bf.a.529.20 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.t.a.157.18 204 8.3 odd 2
216.2.t.a.157.32 yes 204 4.3 odd 2
216.2.t.a.205.18 yes 204 108.43 odd 18
216.2.t.a.205.32 yes 204 216.43 odd 18
648.2.t.a.37.3 204 12.11 even 2
648.2.t.a.37.17 204 24.11 even 2
648.2.t.a.613.3 204 216.11 even 18
648.2.t.a.613.17 204 108.11 even 18
864.2.bf.a.49.15 204 8.5 even 2 inner
864.2.bf.a.49.20 204 1.1 even 1 trivial
864.2.bf.a.529.15 204 27.16 even 9 inner
864.2.bf.a.529.20 204 216.205 even 18 inner