Properties

Label 432.2.be.c.239.1
Level $432$
Weight $2$
Character 432.239
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(47,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 239.1
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.c.47.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50778 + 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(2.50142 + 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +O(q^{10})\) \(q+(-1.50778 + 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(2.50142 + 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +(0.0357619 + 0.202816i) q^{11} +(-2.01394 + 0.733014i) q^{13} +(3.52786 - 1.24796i) q^{15} +(-5.87137 - 3.38984i) q^{17} +(-6.56062 + 3.78777i) q^{19} +(-6.31267 - 2.36260i) q^{21} +(-3.99143 - 3.34921i) q^{23} +(-0.312223 - 0.113640i) q^{25} +(-0.141195 + 5.19423i) q^{27} +(-0.709501 + 1.94934i) q^{29} +(-1.02516 + 1.22174i) q^{31} +(-0.226802 - 0.275319i) q^{33} +(-4.20380 - 7.28120i) q^{35} +(3.90071 - 6.75622i) q^{37} +(2.41176 - 2.82191i) q^{39} +(4.12650 + 11.3375i) q^{41} +(-6.15496 + 1.08528i) q^{43} +(-4.25549 + 4.88881i) q^{45} +(3.44521 - 2.89087i) q^{47} +(-1.41417 + 8.02017i) q^{49} +(11.7423 + 0.106374i) q^{51} -6.89537i q^{53} -0.444942i q^{55} +(6.66329 - 11.3034i) q^{57} +(0.0937549 - 0.531710i) q^{59} +(0.695271 - 0.583402i) q^{61} +(11.5320 - 1.81864i) q^{63} +(4.56001 - 0.804052i) q^{65} +(1.77754 + 4.88376i) q^{67} +(8.87308 + 1.64758i) q^{69} +(-5.04889 + 8.74494i) q^{71} +(1.46358 + 2.53500i) q^{73} +(0.567631 - 0.0947951i) q^{75} +(-0.515154 + 0.613936i) q^{77} +(-1.25749 + 3.45493i) q^{79} +(-4.21468 - 7.95213i) q^{81} +(-10.0574 - 3.66058i) q^{83} +(11.2206 + 9.41520i) q^{85} +(-0.591846 - 3.54396i) q^{87} +(-9.79768 + 5.65669i) q^{89} +(-7.22287 - 4.17013i) q^{91} +(0.504309 - 2.71597i) q^{93} +(15.3799 - 5.59782i) q^{95} +(1.67663 + 9.50863i) q^{97} +(0.576651 + 0.221795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

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
\(3\) −1.50778 + 0.852402i −0.870519 + 0.492134i
\(4\) 0 0
\(5\) −2.12767 0.375166i −0.951524 0.167779i −0.323722 0.946152i \(-0.604934\pi\)
−0.627802 + 0.778373i \(0.716045\pi\)
\(6\) 0 0
\(7\) 2.50142 + 2.98107i 0.945447 + 1.12674i 0.991798 + 0.127815i \(0.0407964\pi\)
−0.0463507 + 0.998925i \(0.514759\pi\)
\(8\) 0 0
\(9\) 1.54682 2.57047i 0.515607 0.856825i
\(10\) 0 0
\(11\) 0.0357619 + 0.202816i 0.0107826 + 0.0611513i 0.989724 0.142989i \(-0.0456713\pi\)
−0.978942 + 0.204140i \(0.934560\pi\)
\(12\) 0 0
\(13\) −2.01394 + 0.733014i −0.558566 + 0.203302i −0.605848 0.795580i \(-0.707166\pi\)
0.0472822 + 0.998882i \(0.484944\pi\)
\(14\) 0 0
\(15\) 3.52786 1.24796i 0.910890 0.322223i
\(16\) 0 0
\(17\) −5.87137 3.38984i −1.42402 0.822156i −0.427377 0.904074i \(-0.640562\pi\)
−0.996639 + 0.0819176i \(0.973896\pi\)
\(18\) 0 0
\(19\) −6.56062 + 3.78777i −1.50511 + 0.868975i −0.505127 + 0.863045i \(0.668554\pi\)
−0.999982 + 0.00592975i \(0.998112\pi\)
\(20\) 0 0
\(21\) −6.31267 2.36260i −1.37754 0.515562i
\(22\) 0 0
\(23\) −3.99143 3.34921i −0.832271 0.698358i 0.123540 0.992340i \(-0.460575\pi\)
−0.955811 + 0.293982i \(0.905020\pi\)
\(24\) 0 0
\(25\) −0.312223 0.113640i −0.0624446 0.0227280i
\(26\) 0 0
\(27\) −0.141195 + 5.19423i −0.0271730 + 0.999631i
\(28\) 0 0
\(29\) −0.709501 + 1.94934i −0.131751 + 0.361983i −0.987973 0.154625i \(-0.950583\pi\)
0.856222 + 0.516608i \(0.172805\pi\)
\(30\) 0 0
\(31\) −1.02516 + 1.22174i −0.184125 + 0.219431i −0.850209 0.526445i \(-0.823525\pi\)
0.666084 + 0.745876i \(0.267969\pi\)
\(32\) 0 0
\(33\) −0.226802 0.275319i −0.0394811 0.0479269i
\(34\) 0 0
\(35\) −4.20380 7.28120i −0.710572 1.23075i
\(36\) 0 0
\(37\) 3.90071 6.75622i 0.641272 1.11072i −0.343877 0.939015i \(-0.611740\pi\)
0.985149 0.171701i \(-0.0549264\pi\)
\(38\) 0 0
\(39\) 2.41176 2.82191i 0.386191 0.451868i
\(40\) 0 0
\(41\) 4.12650 + 11.3375i 0.644452 + 1.77062i 0.637269 + 0.770642i \(0.280064\pi\)
0.00718287 + 0.999974i \(0.497714\pi\)
\(42\) 0 0
\(43\) −6.15496 + 1.08528i −0.938622 + 0.165504i −0.621973 0.783038i \(-0.713669\pi\)
−0.316649 + 0.948543i \(0.602558\pi\)
\(44\) 0 0
\(45\) −4.25549 + 4.88881i −0.634370 + 0.728781i
\(46\) 0 0
\(47\) 3.44521 2.89087i 0.502535 0.421677i −0.355958 0.934502i \(-0.615845\pi\)
0.858493 + 0.512825i \(0.171401\pi\)
\(48\) 0 0
\(49\) −1.41417 + 8.02017i −0.202025 + 1.14574i
\(50\) 0 0
\(51\) 11.7423 + 0.106374i 1.64424 + 0.0148953i
\(52\) 0 0
\(53\) 6.89537i 0.947152i −0.880753 0.473576i \(-0.842963\pi\)
0.880753 0.473576i \(-0.157037\pi\)
\(54\) 0 0
\(55\) 0.444942i 0.0599960i
\(56\) 0 0
\(57\) 6.66329 11.3034i 0.882574 1.49718i
\(58\) 0 0
\(59\) 0.0937549 0.531710i 0.0122058 0.0692228i −0.978096 0.208152i \(-0.933255\pi\)
0.990302 + 0.138930i \(0.0443661\pi\)
\(60\) 0 0
\(61\) 0.695271 0.583402i 0.0890203 0.0746969i −0.597191 0.802099i \(-0.703717\pi\)
0.686212 + 0.727402i \(0.259272\pi\)
\(62\) 0 0
\(63\) 11.5320 1.81864i 1.45290 0.229127i
\(64\) 0 0
\(65\) 4.56001 0.804052i 0.565599 0.0997304i
\(66\) 0 0
\(67\) 1.77754 + 4.88376i 0.217161 + 0.596646i 0.999662 0.0260040i \(-0.00827827\pi\)
−0.782500 + 0.622650i \(0.786056\pi\)
\(68\) 0 0
\(69\) 8.87308 + 1.64758i 1.06819 + 0.198345i
\(70\) 0 0
\(71\) −5.04889 + 8.74494i −0.599193 + 1.03783i 0.393747 + 0.919219i \(0.371179\pi\)
−0.992940 + 0.118614i \(0.962155\pi\)
\(72\) 0 0
\(73\) 1.46358 + 2.53500i 0.171299 + 0.296699i 0.938874 0.344260i \(-0.111870\pi\)
−0.767575 + 0.640959i \(0.778537\pi\)
\(74\) 0 0
\(75\) 0.567631 0.0947951i 0.0655444 0.0109460i
\(76\) 0 0
\(77\) −0.515154 + 0.613936i −0.0587072 + 0.0699645i
\(78\) 0 0
\(79\) −1.25749 + 3.45493i −0.141479 + 0.388710i −0.990113 0.140270i \(-0.955203\pi\)
0.848634 + 0.528980i \(0.177425\pi\)
\(80\) 0 0
\(81\) −4.21468 7.95213i −0.468298 0.883571i
\(82\) 0 0
\(83\) −10.0574 3.66058i −1.10394 0.401800i −0.275171 0.961395i \(-0.588735\pi\)
−0.828766 + 0.559595i \(0.810957\pi\)
\(84\) 0 0
\(85\) 11.2206 + 9.41520i 1.21704 + 1.02122i
\(86\) 0 0
\(87\) −0.591846 3.54396i −0.0634525 0.379953i
\(88\) 0 0
\(89\) −9.79768 + 5.65669i −1.03855 + 0.599608i −0.919423 0.393270i \(-0.871344\pi\)
−0.119129 + 0.992879i \(0.538010\pi\)
\(90\) 0 0
\(91\) −7.22287 4.17013i −0.757163 0.437148i
\(92\) 0 0
\(93\) 0.504309 2.71597i 0.0522944 0.281633i
\(94\) 0 0
\(95\) 15.3799 5.59782i 1.57794 0.574324i
\(96\) 0 0
\(97\) 1.67663 + 9.50863i 0.170236 + 0.965455i 0.943500 + 0.331372i \(0.107511\pi\)
−0.773265 + 0.634084i \(0.781378\pi\)
\(98\) 0 0
\(99\) 0.576651 + 0.221795i 0.0579556 + 0.0222912i
\(100\) 0 0
\(101\) 5.78270 + 6.89155i 0.575400 + 0.685735i 0.972730 0.231941i \(-0.0745076\pi\)
−0.397330 + 0.917676i \(0.630063\pi\)
\(102\) 0 0
\(103\) 5.36511 + 0.946015i 0.528640 + 0.0932136i 0.431597 0.902067i \(-0.357950\pi\)
0.0970435 + 0.995280i \(0.469061\pi\)
\(104\) 0 0
\(105\) 12.5449 + 7.39514i 1.22426 + 0.721692i
\(106\) 0 0
\(107\) −1.67182 −0.161621 −0.0808106 0.996729i \(-0.525751\pi\)
−0.0808106 + 0.996729i \(0.525751\pi\)
\(108\) 0 0
\(109\) 15.6614 1.50009 0.750043 0.661389i \(-0.230033\pi\)
0.750043 + 0.661389i \(0.230033\pi\)
\(110\) 0 0
\(111\) −0.122405 + 13.5119i −0.0116181 + 1.28249i
\(112\) 0 0
\(113\) −18.6094 3.28135i −1.75063 0.308683i −0.795738 0.605641i \(-0.792917\pi\)
−0.954890 + 0.296958i \(0.904028\pi\)
\(114\) 0 0
\(115\) 7.23595 + 8.62347i 0.674755 + 0.804142i
\(116\) 0 0
\(117\) −1.23101 + 6.31062i −0.113807 + 0.583417i
\(118\) 0 0
\(119\) −4.58140 25.9824i −0.419976 2.38180i
\(120\) 0 0
\(121\) 10.2968 3.74772i 0.936069 0.340701i
\(122\) 0 0
\(123\) −15.8860 13.5770i −1.43239 1.22420i
\(124\) 0 0
\(125\) 9.97689 + 5.76016i 0.892360 + 0.515205i
\(126\) 0 0
\(127\) 13.2182 7.63155i 1.17293 0.677191i 0.218561 0.975823i \(-0.429864\pi\)
0.954368 + 0.298633i \(0.0965305\pi\)
\(128\) 0 0
\(129\) 8.35524 6.88287i 0.735638 0.606003i
\(130\) 0 0
\(131\) 6.54614 + 5.49286i 0.571939 + 0.479914i 0.882289 0.470709i \(-0.156002\pi\)
−0.310350 + 0.950622i \(0.600446\pi\)
\(132\) 0 0
\(133\) −27.7025 10.0829i −2.40211 0.874297i
\(134\) 0 0
\(135\) 2.24912 10.9987i 0.193573 0.946614i
\(136\) 0 0
\(137\) 3.62113 9.94898i 0.309374 0.849999i −0.683405 0.730040i \(-0.739501\pi\)
0.992779 0.119959i \(-0.0382763\pi\)
\(138\) 0 0
\(139\) 3.73633 4.45278i 0.316911 0.377680i −0.583948 0.811791i \(-0.698493\pi\)
0.900859 + 0.434111i \(0.142937\pi\)
\(140\) 0 0
\(141\) −2.73044 + 7.29551i −0.229945 + 0.614393i
\(142\) 0 0
\(143\) −0.220689 0.382245i −0.0184550 0.0319649i
\(144\) 0 0
\(145\) 2.24091 3.88137i 0.186098 0.322331i
\(146\) 0 0
\(147\) −4.70414 13.2981i −0.387991 1.09681i
\(148\) 0 0
\(149\) 2.99214 + 8.22085i 0.245126 + 0.673478i 0.999848 + 0.0174333i \(0.00554947\pi\)
−0.754722 + 0.656045i \(0.772228\pi\)
\(150\) 0 0
\(151\) −21.7992 + 3.84379i −1.77400 + 0.312803i −0.962445 0.271478i \(-0.912487\pi\)
−0.811551 + 0.584282i \(0.801376\pi\)
\(152\) 0 0
\(153\) −17.7955 + 9.84873i −1.43868 + 0.796223i
\(154\) 0 0
\(155\) 2.63957 2.21486i 0.212015 0.177902i
\(156\) 0 0
\(157\) −0.835627 + 4.73908i −0.0666903 + 0.378220i 0.933135 + 0.359526i \(0.117062\pi\)
−0.999825 + 0.0186933i \(0.994049\pi\)
\(158\) 0 0
\(159\) 5.87763 + 10.3967i 0.466126 + 0.824514i
\(160\) 0 0
\(161\) 20.2765i 1.59801i
\(162\) 0 0
\(163\) 0.859928i 0.0673547i −0.999433 0.0336774i \(-0.989278\pi\)
0.999433 0.0336774i \(-0.0107219\pi\)
\(164\) 0 0
\(165\) 0.379270 + 0.670877i 0.0295261 + 0.0522277i
\(166\) 0 0
\(167\) −2.13490 + 12.1076i −0.165203 + 0.936915i 0.783651 + 0.621201i \(0.213355\pi\)
−0.948854 + 0.315714i \(0.897756\pi\)
\(168\) 0 0
\(169\) −6.43994 + 5.40375i −0.495380 + 0.415673i
\(170\) 0 0
\(171\) −0.411729 + 22.7229i −0.0314857 + 1.73766i
\(172\) 0 0
\(173\) 18.9738 3.34560i 1.44255 0.254361i 0.603045 0.797707i \(-0.293954\pi\)
0.839509 + 0.543346i \(0.182843\pi\)
\(174\) 0 0
\(175\) −0.442231 1.21502i −0.0334295 0.0918469i
\(176\) 0 0
\(177\) 0.311869 + 0.881621i 0.0234415 + 0.0662667i
\(178\) 0 0
\(179\) −6.93879 + 12.0183i −0.518629 + 0.898292i 0.481136 + 0.876646i \(0.340224\pi\)
−0.999766 + 0.0216464i \(0.993109\pi\)
\(180\) 0 0
\(181\) −12.0771 20.9182i −0.897687 1.55484i −0.830443 0.557103i \(-0.811913\pi\)
−0.0672441 0.997737i \(-0.521421\pi\)
\(182\) 0 0
\(183\) −0.551026 + 1.47229i −0.0407330 + 0.108835i
\(184\) 0 0
\(185\) −10.8341 + 12.9116i −0.796541 + 0.949281i
\(186\) 0 0
\(187\) 0.477541 1.31203i 0.0349213 0.0959454i
\(188\) 0 0
\(189\) −15.8376 + 12.5720i −1.15201 + 0.914481i
\(190\) 0 0
\(191\) 6.84293 + 2.49062i 0.495137 + 0.180215i 0.577505 0.816387i \(-0.304026\pi\)
−0.0823686 + 0.996602i \(0.526248\pi\)
\(192\) 0 0
\(193\) 7.46660 + 6.26522i 0.537458 + 0.450981i 0.870667 0.491872i \(-0.163687\pi\)
−0.333210 + 0.942853i \(0.608132\pi\)
\(194\) 0 0
\(195\) −6.19013 + 5.09929i −0.443284 + 0.365168i
\(196\) 0 0
\(197\) −5.00953 + 2.89226i −0.356914 + 0.206065i −0.667726 0.744407i \(-0.732732\pi\)
0.310812 + 0.950471i \(0.399399\pi\)
\(198\) 0 0
\(199\) −3.57936 2.06654i −0.253734 0.146493i 0.367739 0.929929i \(-0.380132\pi\)
−0.621473 + 0.783436i \(0.713465\pi\)
\(200\) 0 0
\(201\) −6.84307 5.84847i −0.482673 0.412519i
\(202\) 0 0
\(203\) −7.58588 + 2.76104i −0.532425 + 0.193787i
\(204\) 0 0
\(205\) −4.52641 25.6706i −0.316138 1.79291i
\(206\) 0 0
\(207\) −14.7831 + 5.07924i −1.02750 + 0.353032i
\(208\) 0 0
\(209\) −1.00284 1.19514i −0.0693680 0.0826695i
\(210\) 0 0
\(211\) 9.16208 + 1.61552i 0.630744 + 0.111217i 0.479875 0.877337i \(-0.340682\pi\)
0.150868 + 0.988554i \(0.451793\pi\)
\(212\) 0 0
\(213\) 0.158435 17.4892i 0.0108558 1.19834i
\(214\) 0 0
\(215\) 13.5029 0.920890
\(216\) 0 0
\(217\) −6.20646 −0.421322
\(218\) 0 0
\(219\) −4.36760 2.57467i −0.295135 0.173980i
\(220\) 0 0
\(221\) 14.3094 + 2.52313i 0.962553 + 0.169724i
\(222\) 0 0
\(223\) −0.613674 0.731349i −0.0410947 0.0489747i 0.745106 0.666946i \(-0.232399\pi\)
−0.786200 + 0.617972i \(0.787955\pi\)
\(224\) 0 0
\(225\) −0.775062 + 0.626781i −0.0516708 + 0.0417854i
\(226\) 0 0
\(227\) 4.84335 + 27.4680i 0.321465 + 1.82312i 0.533436 + 0.845840i \(0.320900\pi\)
−0.211972 + 0.977276i \(0.567989\pi\)
\(228\) 0 0
\(229\) −11.0424 + 4.01909i −0.729700 + 0.265589i −0.680038 0.733177i \(-0.738037\pi\)
−0.0496624 + 0.998766i \(0.515815\pi\)
\(230\) 0 0
\(231\) 0.253420 1.36480i 0.0166738 0.0897973i
\(232\) 0 0
\(233\) −12.8253 7.40471i −0.840216 0.485099i 0.0171219 0.999853i \(-0.494550\pi\)
−0.857337 + 0.514755i \(0.827883\pi\)
\(234\) 0 0
\(235\) −8.41483 + 4.85831i −0.548923 + 0.316921i
\(236\) 0 0
\(237\) −1.04896 6.28118i −0.0681375 0.408006i
\(238\) 0 0
\(239\) 18.1559 + 15.2346i 1.17441 + 0.985446i 1.00000 0.000772466i \(0.000245884\pi\)
0.174409 + 0.984673i \(0.444199\pi\)
\(240\) 0 0
\(241\) −7.90441 2.87697i −0.509168 0.185322i 0.0746451 0.997210i \(-0.476218\pi\)
−0.583813 + 0.811888i \(0.698440\pi\)
\(242\) 0 0
\(243\) 13.1332 + 8.39749i 0.842498 + 0.538700i
\(244\) 0 0
\(245\) 6.01779 16.5338i 0.384463 1.05630i
\(246\) 0 0
\(247\) 10.4362 12.4374i 0.664039 0.791371i
\(248\) 0 0
\(249\) 18.2846 3.05355i 1.15874 0.193511i
\(250\) 0 0
\(251\) −7.92565 13.7276i −0.500263 0.866481i −1.00000 0.000303448i \(-0.999903\pi\)
0.499737 0.866177i \(-0.333430\pi\)
\(252\) 0 0
\(253\) 0.536531 0.929300i 0.0337314 0.0584246i
\(254\) 0 0
\(255\) −24.9438 4.63162i −1.56204 0.290044i
\(256\) 0 0
\(257\) −3.10717 8.53688i −0.193820 0.532516i 0.804272 0.594261i \(-0.202555\pi\)
−0.998092 + 0.0617455i \(0.980333\pi\)
\(258\) 0 0
\(259\) 29.8981 5.27184i 1.85778 0.327576i
\(260\) 0 0
\(261\) 3.91325 + 4.83904i 0.242224 + 0.299529i
\(262\) 0 0
\(263\) −14.0506 + 11.7898i −0.866396 + 0.726993i −0.963336 0.268297i \(-0.913539\pi\)
0.0969397 + 0.995290i \(0.469095\pi\)
\(264\) 0 0
\(265\) −2.58691 + 14.6711i −0.158913 + 0.901238i
\(266\) 0 0
\(267\) 9.95101 16.8806i 0.608992 1.03308i
\(268\) 0 0
\(269\) 15.0367i 0.916806i −0.888745 0.458403i \(-0.848422\pi\)
0.888745 0.458403i \(-0.151578\pi\)
\(270\) 0 0
\(271\) 17.2892i 1.05025i −0.851027 0.525123i \(-0.824019\pi\)
0.851027 0.525123i \(-0.175981\pi\)
\(272\) 0 0
\(273\) 14.4452 + 0.130859i 0.874261 + 0.00791996i
\(274\) 0 0
\(275\) 0.0118823 0.0673878i 0.000716528 0.00406363i
\(276\) 0 0
\(277\) −9.22261 + 7.73869i −0.554133 + 0.464973i −0.876338 0.481697i \(-0.840020\pi\)
0.322205 + 0.946670i \(0.395576\pi\)
\(278\) 0 0
\(279\) 1.55471 + 4.52497i 0.0930781 + 0.270903i
\(280\) 0 0
\(281\) 7.09306 1.25070i 0.423137 0.0746104i 0.0419746 0.999119i \(-0.486635\pi\)
0.381162 + 0.924508i \(0.375524\pi\)
\(282\) 0 0
\(283\) −10.6550 29.2743i −0.633373 1.74018i −0.671604 0.740910i \(-0.734395\pi\)
0.0382310 0.999269i \(-0.487828\pi\)
\(284\) 0 0
\(285\) −18.4179 + 21.5502i −1.09099 + 1.27652i
\(286\) 0 0
\(287\) −23.4757 + 40.6612i −1.38573 + 2.40015i
\(288\) 0 0
\(289\) 14.4820 + 25.0835i 0.851881 + 1.47550i
\(290\) 0 0
\(291\) −10.6332 12.9078i −0.623327 0.756668i
\(292\) 0 0
\(293\) −14.3668 + 17.1217i −0.839316 + 1.00026i 0.160596 + 0.987020i \(0.448658\pi\)
−0.999912 + 0.0132378i \(0.995786\pi\)
\(294\) 0 0
\(295\) −0.398959 + 1.09613i −0.0232283 + 0.0638193i
\(296\) 0 0
\(297\) −1.05852 + 0.157119i −0.0614217 + 0.00911698i
\(298\) 0 0
\(299\) 10.4935 + 3.81933i 0.606856 + 0.220877i
\(300\) 0 0
\(301\) −18.6314 15.6336i −1.07390 0.901107i
\(302\) 0 0
\(303\) −14.5934 5.46179i −0.838371 0.313771i
\(304\) 0 0
\(305\) −1.69818 + 0.980446i −0.0972376 + 0.0561402i
\(306\) 0 0
\(307\) −8.17802 4.72158i −0.466744 0.269475i 0.248132 0.968726i \(-0.420183\pi\)
−0.714876 + 0.699252i \(0.753517\pi\)
\(308\) 0 0
\(309\) −8.89582 + 3.14685i −0.506065 + 0.179018i
\(310\) 0 0
\(311\) −11.0789 + 4.03239i −0.628227 + 0.228656i −0.636460 0.771310i \(-0.719602\pi\)
0.00823228 + 0.999966i \(0.497380\pi\)
\(312\) 0 0
\(313\) −1.74976 9.92336i −0.0989020 0.560901i −0.993482 0.113993i \(-0.963636\pi\)
0.894580 0.446909i \(-0.147475\pi\)
\(314\) 0 0
\(315\) −25.2187 0.456951i −1.42091 0.0257463i
\(316\) 0 0
\(317\) 9.34365 + 11.1353i 0.524792 + 0.625422i 0.961707 0.274080i \(-0.0883734\pi\)
−0.436915 + 0.899503i \(0.643929\pi\)
\(318\) 0 0
\(319\) −0.420730 0.0741861i −0.0235564 0.00415362i
\(320\) 0 0
\(321\) 2.52075 1.42506i 0.140694 0.0795394i
\(322\) 0 0
\(323\) 51.3597 2.85773
\(324\) 0 0
\(325\) 0.712098 0.0395001
\(326\) 0 0
\(327\) −23.6140 + 13.3498i −1.30585 + 0.738244i
\(328\) 0 0
\(329\) 17.2358 + 3.03914i 0.950241 + 0.167553i
\(330\) 0 0
\(331\) 6.36795 + 7.58902i 0.350014 + 0.417130i 0.912113 0.409940i \(-0.134450\pi\)
−0.562099 + 0.827070i \(0.690006\pi\)
\(332\) 0 0
\(333\) −11.3330 20.4773i −0.621045 1.12215i
\(334\) 0 0
\(335\) −1.94981 11.0579i −0.106529 0.604158i
\(336\) 0 0
\(337\) −15.9688 + 5.81216i −0.869874 + 0.316608i −0.738116 0.674674i \(-0.764284\pi\)
−0.131758 + 0.991282i \(0.542062\pi\)
\(338\) 0 0
\(339\) 30.8560 10.9152i 1.67587 0.592830i
\(340\) 0 0
\(341\) −0.284450 0.164227i −0.0154039 0.00889342i
\(342\) 0 0
\(343\) −3.85511 + 2.22575i −0.208156 + 0.120179i
\(344\) 0 0
\(345\) −18.2609 6.83438i −0.983134 0.367951i
\(346\) 0 0
\(347\) −4.11669 3.45432i −0.220996 0.185437i 0.525568 0.850752i \(-0.323853\pi\)
−0.746563 + 0.665314i \(0.768297\pi\)
\(348\) 0 0
\(349\) 16.9030 + 6.15220i 0.904799 + 0.329320i 0.752174 0.658964i \(-0.229005\pi\)
0.152625 + 0.988284i \(0.451227\pi\)
\(350\) 0 0
\(351\) −3.52309 10.5644i −0.188049 0.563884i
\(352\) 0 0
\(353\) −2.47242 + 6.79292i −0.131594 + 0.361551i −0.987937 0.154856i \(-0.950509\pi\)
0.856343 + 0.516407i \(0.172731\pi\)
\(354\) 0 0
\(355\) 14.0232 16.7122i 0.744274 0.886991i
\(356\) 0 0
\(357\) 29.0552 + 35.2706i 1.53776 + 1.86672i
\(358\) 0 0
\(359\) −10.4680 18.1311i −0.552481 0.956925i −0.998095 0.0616998i \(-0.980348\pi\)
0.445614 0.895225i \(-0.352985\pi\)
\(360\) 0 0
\(361\) 19.1945 33.2458i 1.01024 1.74978i
\(362\) 0 0
\(363\) −12.3307 + 14.4277i −0.647195 + 0.757259i
\(364\) 0 0
\(365\) −2.16298 5.94273i −0.113215 0.311057i
\(366\) 0 0
\(367\) 10.0472 1.77160i 0.524461 0.0924766i 0.0948516 0.995491i \(-0.469762\pi\)
0.429609 + 0.903015i \(0.358651\pi\)
\(368\) 0 0
\(369\) 35.5257 + 6.92998i 1.84939 + 0.360760i
\(370\) 0 0
\(371\) 20.5556 17.2482i 1.06719 0.895482i
\(372\) 0 0
\(373\) 2.55154 14.4705i 0.132114 0.749254i −0.844712 0.535220i \(-0.820229\pi\)
0.976826 0.214034i \(-0.0686603\pi\)
\(374\) 0 0
\(375\) −19.9530 0.180755i −1.03037 0.00933413i
\(376\) 0 0
\(377\) 4.44593i 0.228977i
\(378\) 0 0
\(379\) 1.47535i 0.0757834i −0.999282 0.0378917i \(-0.987936\pi\)
0.999282 0.0378917i \(-0.0120642\pi\)
\(380\) 0 0
\(381\) −13.4251 + 22.7740i −0.687788 + 1.16675i
\(382\) 0 0
\(383\) 3.50484 19.8770i 0.179089 1.01567i −0.754228 0.656613i \(-0.771989\pi\)
0.933317 0.359053i \(-0.116900\pi\)
\(384\) 0 0
\(385\) 1.32641 1.11299i 0.0675999 0.0567231i
\(386\) 0 0
\(387\) −6.73092 + 17.4999i −0.342152 + 0.889570i
\(388\) 0 0
\(389\) 12.1450 2.14149i 0.615777 0.108578i 0.142945 0.989731i \(-0.454343\pi\)
0.472832 + 0.881153i \(0.343232\pi\)
\(390\) 0 0
\(391\) 12.0819 + 33.1947i 0.611008 + 1.67873i
\(392\) 0 0
\(393\) −14.5523 2.70211i −0.734066 0.136303i
\(394\) 0 0
\(395\) 3.97170 6.87919i 0.199838 0.346130i
\(396\) 0 0
\(397\) −8.83157 15.2967i −0.443244 0.767720i 0.554684 0.832061i \(-0.312839\pi\)
−0.997928 + 0.0643404i \(0.979506\pi\)
\(398\) 0 0
\(399\) 50.3640 8.41085i 2.52135 0.421069i
\(400\) 0 0
\(401\) 9.13835 10.8907i 0.456347 0.543853i −0.487983 0.872853i \(-0.662267\pi\)
0.944330 + 0.329000i \(0.106712\pi\)
\(402\) 0 0
\(403\) 1.16906 3.21197i 0.0582351 0.160000i
\(404\) 0 0
\(405\) 5.98409 + 18.5007i 0.297352 + 0.919309i
\(406\) 0 0
\(407\) 1.50977 + 0.549510i 0.0748363 + 0.0272382i
\(408\) 0 0
\(409\) 14.7136 + 12.3461i 0.727539 + 0.610477i 0.929459 0.368925i \(-0.120274\pi\)
−0.201921 + 0.979402i \(0.564718\pi\)
\(410\) 0 0
\(411\) 3.02065 + 18.0876i 0.148997 + 0.892194i
\(412\) 0 0
\(413\) 1.81959 1.05054i 0.0895361 0.0516937i
\(414\) 0 0
\(415\) 20.0254 + 11.5617i 0.983009 + 0.567541i
\(416\) 0 0
\(417\) −1.83801 + 9.89868i −0.0900079 + 0.484741i
\(418\) 0 0
\(419\) 5.36997 1.95451i 0.262340 0.0954840i −0.207502 0.978235i \(-0.566533\pi\)
0.469842 + 0.882751i \(0.344311\pi\)
\(420\) 0 0
\(421\) 4.99357 + 28.3200i 0.243372 + 1.38023i 0.824244 + 0.566235i \(0.191601\pi\)
−0.580872 + 0.813995i \(0.697288\pi\)
\(422\) 0 0
\(423\) −2.10179 13.3275i −0.102193 0.648005i
\(424\) 0 0
\(425\) 1.44796 + 1.72561i 0.0702361 + 0.0837042i
\(426\) 0 0
\(427\) 3.47833 + 0.613323i 0.168328 + 0.0296808i
\(428\) 0 0
\(429\) 0.658578 + 0.388227i 0.0317964 + 0.0187438i
\(430\) 0 0
\(431\) −14.3077 −0.689176 −0.344588 0.938754i \(-0.611981\pi\)
−0.344588 + 0.938754i \(0.611981\pi\)
\(432\) 0 0
\(433\) 2.66463 0.128054 0.0640269 0.997948i \(-0.479606\pi\)
0.0640269 + 0.997948i \(0.479606\pi\)
\(434\) 0 0
\(435\) −0.0703202 + 7.76243i −0.00337159 + 0.372180i
\(436\) 0 0
\(437\) 38.8723 + 6.85423i 1.85951 + 0.327882i
\(438\) 0 0
\(439\) −24.2181 28.8620i −1.15587 1.37751i −0.913257 0.407383i \(-0.866441\pi\)
−0.242609 0.970124i \(-0.578003\pi\)
\(440\) 0 0
\(441\) 18.4282 + 16.0409i 0.877533 + 0.763851i
\(442\) 0 0
\(443\) 3.46327 + 19.6412i 0.164545 + 0.933179i 0.949533 + 0.313668i \(0.101558\pi\)
−0.784988 + 0.619511i \(0.787331\pi\)
\(444\) 0 0
\(445\) 22.9685 8.35983i 1.08881 0.396294i
\(446\) 0 0
\(447\) −11.5190 9.84475i −0.544828 0.465641i
\(448\) 0 0
\(449\) 24.0203 + 13.8682i 1.13359 + 0.654479i 0.944835 0.327546i \(-0.106222\pi\)
0.188755 + 0.982024i \(0.439555\pi\)
\(450\) 0 0
\(451\) −2.15185 + 1.24237i −0.101327 + 0.0585009i
\(452\) 0 0
\(453\) 29.5921 24.3773i 1.39036 1.14535i
\(454\) 0 0
\(455\) 13.8034 + 11.5824i 0.647114 + 0.542993i
\(456\) 0 0
\(457\) −0.0182308 0.00663549i −0.000852803 0.000310395i 0.341594 0.939848i \(-0.389033\pi\)
−0.342447 + 0.939537i \(0.611256\pi\)
\(458\) 0 0
\(459\) 18.4366 30.0186i 0.860547 1.40115i
\(460\) 0 0
\(461\) −7.58160 + 20.8303i −0.353110 + 0.970163i 0.628254 + 0.778008i \(0.283770\pi\)
−0.981365 + 0.192155i \(0.938452\pi\)
\(462\) 0 0
\(463\) −26.6835 + 31.8001i −1.24009 + 1.47788i −0.418068 + 0.908416i \(0.637293\pi\)
−0.822018 + 0.569461i \(0.807152\pi\)
\(464\) 0 0
\(465\) −2.09194 + 5.58950i −0.0970116 + 0.259207i
\(466\) 0 0
\(467\) −11.4135 19.7688i −0.528154 0.914789i −0.999461 0.0328204i \(-0.989551\pi\)
0.471307 0.881969i \(-0.343782\pi\)
\(468\) 0 0
\(469\) −10.1125 + 17.5153i −0.466950 + 0.808782i
\(470\) 0 0
\(471\) −2.77965 7.85779i −0.128080 0.362068i
\(472\) 0 0
\(473\) −0.440226 1.20951i −0.0202416 0.0556134i
\(474\) 0 0
\(475\) 2.47882 0.437082i 0.113736 0.0200547i
\(476\) 0 0
\(477\) −17.7244 10.6659i −0.811543 0.488358i
\(478\) 0 0
\(479\) 2.42704 2.03652i 0.110894 0.0930512i −0.585655 0.810561i \(-0.699162\pi\)
0.696549 + 0.717510i \(0.254718\pi\)
\(480\) 0 0
\(481\) −2.90338 + 16.4659i −0.132383 + 0.750780i
\(482\) 0 0
\(483\) 17.2837 + 30.5726i 0.786438 + 1.39110i
\(484\) 0 0
\(485\) 20.8603i 0.947216i
\(486\) 0 0
\(487\) 26.6585i 1.20801i −0.796980 0.604005i \(-0.793571\pi\)
0.796980 0.604005i \(-0.206429\pi\)
\(488\) 0 0
\(489\) 0.733004 + 1.29658i 0.0331476 + 0.0586336i
\(490\) 0 0
\(491\) −0.111406 + 0.631817i −0.00502770 + 0.0285135i −0.987218 0.159373i \(-0.949053\pi\)
0.982191 + 0.187887i \(0.0601638\pi\)
\(492\) 0 0
\(493\) 10.7737 9.04019i 0.485222 0.407150i
\(494\) 0 0
\(495\) −1.14371 0.688247i −0.0514061 0.0309344i
\(496\) 0 0
\(497\) −38.6987 + 6.82363i −1.73587 + 0.306081i
\(498\) 0 0
\(499\) −0.174102 0.478340i −0.00779386 0.0214134i 0.935735 0.352705i \(-0.114738\pi\)
−0.943529 + 0.331291i \(0.892516\pi\)
\(500\) 0 0
\(501\) −7.10159 20.0755i −0.317276 0.896905i
\(502\) 0 0
\(503\) −17.3187 + 29.9969i −0.772203 + 1.33750i 0.164150 + 0.986435i \(0.447512\pi\)
−0.936353 + 0.351060i \(0.885821\pi\)
\(504\) 0 0
\(505\) −9.71821 16.8324i −0.432455 0.749034i
\(506\) 0 0
\(507\) 5.10386 13.6371i 0.226671 0.605645i
\(508\) 0 0
\(509\) −6.71875 + 8.00710i −0.297804 + 0.354908i −0.894109 0.447849i \(-0.852190\pi\)
0.596306 + 0.802757i \(0.296635\pi\)
\(510\) 0 0
\(511\) −3.89599 + 10.7041i −0.172348 + 0.473523i
\(512\) 0 0
\(513\) −18.7483 34.6122i −0.827756 1.52817i
\(514\) 0 0
\(515\) −11.0603 4.02562i −0.487375 0.177390i
\(516\) 0 0
\(517\) 0.709522 + 0.595360i 0.0312048 + 0.0261839i
\(518\) 0 0
\(519\) −25.7566 + 21.2178i −1.13059 + 0.931357i
\(520\) 0 0
\(521\) −18.6891 + 10.7902i −0.818785 + 0.472726i −0.849997 0.526787i \(-0.823397\pi\)
0.0312124 + 0.999513i \(0.490063\pi\)
\(522\) 0 0
\(523\) 2.21284 + 1.27758i 0.0967607 + 0.0558648i 0.547600 0.836741i \(-0.315542\pi\)
−0.450839 + 0.892605i \(0.648875\pi\)
\(524\) 0 0
\(525\) 1.70247 + 1.45503i 0.0743021 + 0.0635027i
\(526\) 0 0
\(527\) 10.1606 3.69816i 0.442603 0.161094i
\(528\) 0 0
\(529\) 0.720415 + 4.08568i 0.0313224 + 0.177638i
\(530\) 0 0
\(531\) −1.22173 1.06346i −0.0530184 0.0461501i
\(532\) 0 0
\(533\) −16.6211 19.8082i −0.719938 0.857988i
\(534\) 0 0
\(535\) 3.55709 + 0.627211i 0.153786 + 0.0271167i
\(536\) 0 0
\(537\) 0.217740 24.0357i 0.00939618 1.03722i
\(538\) 0 0
\(539\) −1.67719 −0.0722418
\(540\) 0 0
\(541\) −11.9264 −0.512754 −0.256377 0.966577i \(-0.582529\pi\)
−0.256377 + 0.966577i \(0.582529\pi\)
\(542\) 0 0
\(543\) 36.0405 + 21.2456i 1.54664 + 0.911735i
\(544\) 0 0
\(545\) −33.3223 5.87561i −1.42737 0.251684i
\(546\) 0 0
\(547\) −13.7484 16.3847i −0.587838 0.700558i 0.387351 0.921932i \(-0.373390\pi\)
−0.975189 + 0.221374i \(0.928946\pi\)
\(548\) 0 0
\(549\) −0.424159 2.68960i −0.0181027 0.114789i
\(550\) 0 0
\(551\) −2.72889 15.4763i −0.116255 0.659313i
\(552\) 0 0
\(553\) −13.4449 + 4.89355i −0.571736 + 0.208095i
\(554\) 0 0
\(555\) 5.32964 28.7030i 0.226231 1.21837i
\(556\) 0 0
\(557\) 23.2042 + 13.3970i 0.983196 + 0.567648i 0.903233 0.429150i \(-0.141187\pi\)
0.0799622 + 0.996798i \(0.474520\pi\)
\(558\) 0 0
\(559\) 11.6002 6.69737i 0.490635 0.283268i
\(560\) 0 0
\(561\) 0.398351 + 2.38532i 0.0168184 + 0.100708i
\(562\) 0 0
\(563\) −22.0741 18.5223i −0.930311 0.780624i 0.0455620 0.998962i \(-0.485492\pi\)
−0.975873 + 0.218338i \(0.929937\pi\)
\(564\) 0 0
\(565\) 38.3637 + 13.9633i 1.61397 + 0.587439i
\(566\) 0 0
\(567\) 13.1632 32.4559i 0.552803 1.36302i
\(568\) 0 0
\(569\) −9.21939 + 25.3301i −0.386497 + 1.06189i 0.582070 + 0.813138i \(0.302243\pi\)
−0.968567 + 0.248753i \(0.919979\pi\)
\(570\) 0 0
\(571\) −2.01830 + 2.40531i −0.0844631 + 0.100659i −0.806621 0.591069i \(-0.798706\pi\)
0.722158 + 0.691728i \(0.243150\pi\)
\(572\) 0 0
\(573\) −12.4407 + 2.07761i −0.519716 + 0.0867932i
\(574\) 0 0
\(575\) 0.865612 + 1.49928i 0.0360985 + 0.0625245i
\(576\) 0 0
\(577\) −19.8980 + 34.4644i −0.828366 + 1.43477i 0.0709533 + 0.997480i \(0.477396\pi\)
−0.899319 + 0.437292i \(0.855937\pi\)
\(578\) 0 0
\(579\) −16.5985 3.08205i −0.689811 0.128086i
\(580\) 0 0
\(581\) −14.2452 39.1383i −0.590990 1.62373i
\(582\) 0 0
\(583\) 1.39849 0.246592i 0.0579196 0.0102128i
\(584\) 0 0
\(585\) 4.98672 12.9651i 0.206176 0.536041i
\(586\) 0 0
\(587\) −12.9410 + 10.8588i −0.534132 + 0.448190i −0.869525 0.493888i \(-0.835575\pi\)
0.335394 + 0.942078i \(0.391131\pi\)
\(588\) 0 0
\(589\) 2.09802 11.8985i 0.0864474 0.490268i
\(590\) 0 0
\(591\) 5.08793 8.63103i 0.209289 0.355033i
\(592\) 0 0
\(593\) 0.0610029i 0.00250509i 0.999999 + 0.00125254i \(0.000398697\pi\)
−0.999999 + 0.00125254i \(0.999601\pi\)
\(594\) 0 0
\(595\) 57.0008i 2.33680i
\(596\) 0 0
\(597\) 7.15842 + 0.0648484i 0.292975 + 0.00265407i
\(598\) 0 0
\(599\) 4.17873 23.6987i 0.170738 0.968304i −0.772211 0.635366i \(-0.780849\pi\)
0.942949 0.332938i \(-0.108040\pi\)
\(600\) 0 0
\(601\) −18.4133 + 15.4506i −0.751095 + 0.630244i −0.935792 0.352552i \(-0.885314\pi\)
0.184697 + 0.982795i \(0.440870\pi\)
\(602\) 0 0
\(603\) 15.3031 + 2.98518i 0.623191 + 0.121566i
\(604\) 0 0
\(605\) −23.3142 + 4.11091i −0.947855 + 0.167132i
\(606\) 0 0
\(607\) 0.920929 + 2.53023i 0.0373794 + 0.102699i 0.956978 0.290160i \(-0.0937084\pi\)
−0.919599 + 0.392859i \(0.871486\pi\)
\(608\) 0 0
\(609\) 9.08436 10.6293i 0.368117 0.430720i
\(610\) 0 0
\(611\) −4.81939 + 8.34743i −0.194972 + 0.337701i
\(612\) 0 0
\(613\) 13.5649 + 23.4951i 0.547880 + 0.948957i 0.998420 + 0.0562001i \(0.0178985\pi\)
−0.450539 + 0.892757i \(0.648768\pi\)
\(614\) 0 0
\(615\) 28.7065 + 34.8473i 1.15756 + 1.40518i
\(616\) 0 0
\(617\) 21.5765 25.7138i 0.868635 1.03520i −0.130408 0.991460i \(-0.541629\pi\)
0.999043 0.0437387i \(-0.0139269\pi\)
\(618\) 0 0
\(619\) −15.2455 + 41.8867i −0.612769 + 1.68357i 0.111254 + 0.993792i \(0.464513\pi\)
−0.724022 + 0.689776i \(0.757709\pi\)
\(620\) 0 0
\(621\) 17.9601 20.2595i 0.720715 0.812987i
\(622\) 0 0
\(623\) −41.3711 15.0579i −1.65750 0.603280i
\(624\) 0 0
\(625\) −17.7939 14.9309i −0.711756 0.597235i
\(626\) 0 0
\(627\) 2.53081 + 0.947188i 0.101071 + 0.0378270i
\(628\) 0 0
\(629\) −45.8050 + 26.4455i −1.82636 + 1.05445i
\(630\) 0 0
\(631\) −22.8750 13.2069i −0.910640 0.525758i −0.0300027 0.999550i \(-0.509552\pi\)
−0.880637 + 0.473792i \(0.842885\pi\)
\(632\) 0 0
\(633\) −15.1915 + 5.37392i −0.603808 + 0.213594i
\(634\) 0 0
\(635\) −30.9872 + 11.2784i −1.22969 + 0.447570i
\(636\) 0 0
\(637\) −3.03084 17.1888i −0.120086 0.681043i
\(638\) 0 0
\(639\) 14.6689 + 26.5049i 0.580293 + 1.04852i
\(640\) 0 0
\(641\) −11.6135 13.8404i −0.458704 0.546663i 0.486269 0.873809i \(-0.338357\pi\)
−0.944974 + 0.327146i \(0.893913\pi\)
\(642\) 0 0
\(643\) −42.9848 7.57937i −1.69515 0.298901i −0.759156 0.650908i \(-0.774388\pi\)
−0.935997 + 0.352007i \(0.885499\pi\)
\(644\) 0 0
\(645\) −20.3594 + 11.5099i −0.801652 + 0.453201i
\(646\) 0 0
\(647\) 44.0779 1.73288 0.866441 0.499279i \(-0.166402\pi\)
0.866441 + 0.499279i \(0.166402\pi\)
\(648\) 0 0
\(649\) 0.111192 0.00436468
\(650\) 0 0
\(651\) 9.35800 5.29040i 0.366769 0.207347i
\(652\) 0 0
\(653\) −14.7422 2.59945i −0.576906 0.101724i −0.122421 0.992478i \(-0.539066\pi\)
−0.454486 + 0.890754i \(0.650177\pi\)
\(654\) 0 0
\(655\) −11.8673 14.1429i −0.463694 0.552609i
\(656\) 0 0
\(657\) 8.78005 + 0.159091i 0.342542 + 0.00620672i
\(658\) 0 0
\(659\) −2.62215 14.8709i −0.102144 0.579290i −0.992323 0.123677i \(-0.960531\pi\)
0.890178 0.455613i \(-0.150580\pi\)
\(660\) 0 0
\(661\) 18.1294 6.59856i 0.705152 0.256654i 0.0355431 0.999368i \(-0.488684\pi\)
0.669609 + 0.742714i \(0.266462\pi\)
\(662\) 0 0
\(663\) −23.7262 + 8.39301i −0.921448 + 0.325957i
\(664\) 0 0
\(665\) 55.1591 + 31.8461i 2.13898 + 1.23494i
\(666\) 0 0
\(667\) 9.36067 5.40438i 0.362446 0.209259i
\(668\) 0 0
\(669\) 1.54869 + 0.579618i 0.0598759 + 0.0224093i
\(670\) 0 0
\(671\) 0.143187 + 0.120148i 0.00552769 + 0.00463828i
\(672\) 0 0
\(673\) 10.3140 + 3.75400i 0.397576 + 0.144706i 0.533068 0.846073i \(-0.321039\pi\)
−0.135491 + 0.990779i \(0.543261\pi\)
\(674\) 0 0
\(675\) 0.634356 1.60571i 0.0244164 0.0618039i
\(676\) 0 0
\(677\) 10.9926 30.2020i 0.422481 1.16076i −0.527802 0.849367i \(-0.676984\pi\)
0.950283 0.311388i \(-0.100794\pi\)
\(678\) 0 0
\(679\) −24.1520 + 28.7832i −0.926868 + 1.10460i
\(680\) 0 0
\(681\) −30.7165 37.2873i −1.17706 1.42885i
\(682\) 0 0
\(683\) −16.0306 27.7658i −0.613394 1.06243i −0.990664 0.136327i \(-0.956470\pi\)
0.377270 0.926103i \(-0.376863\pi\)
\(684\) 0 0
\(685\) −11.4371 + 19.8097i −0.436989 + 0.756888i
\(686\) 0 0
\(687\) 13.2236 15.4725i 0.504513 0.590311i
\(688\) 0 0
\(689\) 5.05440 + 13.8869i 0.192557 + 0.529047i
\(690\) 0 0
\(691\) 4.37408 0.771269i 0.166398 0.0293405i −0.0898284 0.995957i \(-0.528632\pi\)
0.256226 + 0.966617i \(0.417521\pi\)
\(692\) 0 0
\(693\) 0.781257 + 2.27384i 0.0296775 + 0.0863761i
\(694\) 0 0
\(695\) −9.62021 + 8.07232i −0.364915 + 0.306200i
\(696\) 0 0
\(697\) 14.2040 80.5547i 0.538013 3.05123i
\(698\) 0 0
\(699\) 25.6496 + 0.232361i 0.970158 + 0.00878870i
\(700\) 0 0
\(701\) 27.5938i 1.04220i 0.853495 + 0.521101i \(0.174478\pi\)
−0.853495 + 0.521101i \(0.825522\pi\)
\(702\) 0 0
\(703\) 59.1000i 2.22900i
\(704\) 0 0
\(705\) 8.54652 14.4981i 0.321880 0.546030i
\(706\) 0 0
\(707\) −6.07928 + 34.4773i −0.228635 + 1.29665i
\(708\) 0 0
\(709\) 7.46960 6.26774i 0.280527 0.235390i −0.491657 0.870789i \(-0.663609\pi\)
0.772184 + 0.635399i \(0.219164\pi\)
\(710\) 0 0
\(711\) 6.93570 + 8.57652i 0.260109 + 0.321644i
\(712\) 0 0
\(713\) 8.18373 1.44301i 0.306483 0.0540412i
\(714\) 0 0
\(715\) 0.326149 + 0.896087i 0.0121973 + 0.0335118i
\(716\) 0 0
\(717\) −40.3612 7.49438i −1.50732 0.279883i
\(718\) 0 0
\(719\) 16.5609 28.6843i 0.617616 1.06974i −0.372304 0.928111i \(-0.621432\pi\)
0.989920 0.141631i \(-0.0452347\pi\)
\(720\) 0 0
\(721\) 10.6003 + 18.3602i 0.394774 + 0.683769i
\(722\) 0 0
\(723\) 14.3705 2.39989i 0.534444 0.0892527i
\(724\) 0 0
\(725\) 0.443045 0.528001i 0.0164543 0.0196095i
\(726\) 0 0
\(727\) 3.52972 9.69783i 0.130910 0.359673i −0.856869 0.515535i \(-0.827593\pi\)
0.987779 + 0.155862i \(0.0498156\pi\)
\(728\) 0 0
\(729\) −26.9601 1.46680i −0.998523 0.0543260i
\(730\) 0 0
\(731\) 39.8170 + 14.4922i 1.47268 + 0.536013i
\(732\) 0 0
\(733\) −18.0067 15.1094i −0.665091 0.558078i 0.246517 0.969138i \(-0.420714\pi\)
−0.911608 + 0.411061i \(0.865158\pi\)
\(734\) 0 0
\(735\) 5.01987 + 30.0589i 0.185161 + 1.10874i
\(736\) 0 0
\(737\) −0.926936 + 0.535166i −0.0341441 + 0.0197131i
\(738\) 0 0
\(739\) 18.0525 + 10.4226i 0.664073 + 0.383403i 0.793827 0.608143i \(-0.208085\pi\)
−0.129754 + 0.991546i \(0.541419\pi\)
\(740\) 0 0
\(741\) −5.13388 + 27.6487i −0.188598 + 1.01570i
\(742\) 0 0
\(743\) 17.7561 6.46269i 0.651408 0.237093i 0.00488550 0.999988i \(-0.498445\pi\)
0.646522 + 0.762895i \(0.276223\pi\)
\(744\) 0 0
\(745\) −3.28212 18.6138i −0.120247 0.681957i
\(746\) 0 0
\(747\) −24.9664 + 20.1899i −0.913471 + 0.738710i
\(748\) 0 0
\(749\) −4.18193 4.98383i −0.152804 0.182105i
\(750\) 0 0
\(751\) 0.970086 + 0.171052i 0.0353989 + 0.00624179i 0.191320 0.981528i \(-0.438723\pi\)
−0.155921 + 0.987770i \(0.549834\pi\)
\(752\) 0 0
\(753\) 23.6516 + 13.9425i 0.861913 + 0.508091i
\(754\) 0 0
\(755\) 47.8237 1.74048
\(756\) 0 0
\(757\) 1.04898 0.0381259 0.0190630 0.999818i \(-0.493932\pi\)
0.0190630 + 0.999818i \(0.493932\pi\)
\(758\) 0 0
\(759\) −0.0168364 + 1.85852i −0.000611124 + 0.0674601i
\(760\) 0 0
\(761\) −45.5984 8.04023i −1.65294 0.291458i −0.732043 0.681259i \(-0.761433\pi\)
−0.920899 + 0.389801i \(0.872544\pi\)
\(762\) 0 0
\(763\) 39.1756 + 46.6877i 1.41825 + 1.69021i
\(764\) 0 0
\(765\) 41.5578 14.2786i 1.50253 0.516245i
\(766\) 0 0
\(767\) 0.200935 + 1.13956i 0.00725532 + 0.0411470i
\(768\) 0 0
\(769\) 7.85772 2.85997i 0.283356 0.103133i −0.196432 0.980517i \(-0.562936\pi\)
0.479789 + 0.877384i \(0.340713\pi\)
\(770\) 0 0
\(771\) 11.9618 + 10.2232i 0.430793 + 0.368180i
\(772\) 0 0
\(773\) −18.6959 10.7941i −0.672445 0.388236i 0.124557 0.992212i \(-0.460249\pi\)
−0.797003 + 0.603976i \(0.793582\pi\)
\(774\) 0 0
\(775\) 0.458918 0.264956i 0.0164848 0.00951751i
\(776\) 0 0
\(777\) −40.5861 + 33.4340i −1.45602 + 1.19944i
\(778\) 0 0
\(779\) −70.0162 58.7506i −2.50859 2.10496i
\(780\) 0 0
\(781\) −1.95417 0.711260i −0.0699257 0.0254509i
\(782\) 0 0
\(783\) −10.0251 3.96055i −0.358269 0.141539i
\(784\) 0 0
\(785\) 3.55588 9.76971i 0.126915 0.348696i
\(786\) 0 0
\(787\) −0.551585 + 0.657353i −0.0196619 + 0.0234321i −0.775786 0.630996i \(-0.782646\pi\)
0.756124 + 0.654428i \(0.227091\pi\)
\(788\) 0 0
\(789\) 11.1356 29.7533i 0.396436 1.05924i
\(790\) 0 0
\(791\) −36.7680 63.6841i −1.30732 2.26435i
\(792\) 0 0
\(793\) −0.972592 + 1.68458i −0.0345378 + 0.0598212i
\(794\) 0 0
\(795\) −8.60516 24.3259i −0.305194 0.862751i
\(796\) 0 0
\(797\) 3.33003 + 9.14917i 0.117956 + 0.324080i 0.984594 0.174857i \(-0.0559462\pi\)
−0.866638 + 0.498937i \(0.833724\pi\)
\(798\) 0 0
\(799\) −30.0277 + 5.29469i −1.06230 + 0.187313i
\(800\) 0 0
\(801\) −0.614880 + 33.9346i −0.0217257 + 1.19902i
\(802\) 0 0
\(803\) −0.461798 + 0.387494i −0.0162965 + 0.0136744i
\(804\) 0 0
\(805\) −7.60706 + 43.1418i −0.268114 + 1.52055i
\(806\) 0 0
\(807\) 12.8173 + 22.6721i 0.451192 + 0.798097i
\(808\) 0 0
\(809\) 10.0689i 0.354005i 0.984210 + 0.177003i \(0.0566401\pi\)
−0.984210 + 0.177003i \(0.943360\pi\)
\(810\) 0 0
\(811\) 18.3336i 0.643779i −0.946777 0.321889i \(-0.895682\pi\)
0.946777 0.321889i \(-0.104318\pi\)
\(812\) 0 0
\(813\) 14.7374 + 26.0684i 0.516862 + 0.914259i
\(814\) 0 0
\(815\) −0.322616 + 1.82964i −0.0113007 + 0.0640896i
\(816\) 0 0
\(817\) 36.2695 30.4337i 1.26891 1.06474i
\(818\) 0 0
\(819\) −21.8917 + 12.1158i −0.764958 + 0.423359i
\(820\) 0 0
\(821\) −40.0948 + 7.06979i −1.39932 + 0.246737i −0.821862 0.569686i \(-0.807065\pi\)
−0.577454 + 0.816423i \(0.695954\pi\)
\(822\) 0 0
\(823\) 2.35467 + 6.46940i 0.0820786 + 0.225509i 0.973943 0.226795i \(-0.0728246\pi\)
−0.891864 + 0.452304i \(0.850602\pi\)
\(824\) 0 0
\(825\) 0.0395255 + 0.111735i 0.00137610 + 0.00389010i
\(826\) 0 0
\(827\) 9.10736 15.7744i 0.316694 0.548530i −0.663102 0.748529i \(-0.730761\pi\)
0.979796 + 0.199999i \(0.0640939\pi\)
\(828\) 0 0
\(829\) 6.97068 + 12.0736i 0.242102 + 0.419333i 0.961313 0.275459i \(-0.0888299\pi\)
−0.719211 + 0.694792i \(0.755497\pi\)
\(830\) 0 0
\(831\) 7.30923 19.5296i 0.253554 0.677475i
\(832\) 0 0
\(833\) 35.4902 42.2956i 1.22966 1.46546i
\(834\) 0 0
\(835\) 9.08473 24.9601i 0.314390 0.863780i
\(836\) 0 0
\(837\) −6.20126 5.49744i −0.214347 0.190019i
\(838\) 0 0
\(839\) 21.4902 + 7.82180i 0.741925 + 0.270039i 0.685204 0.728352i \(-0.259713\pi\)
0.0567211 + 0.998390i \(0.481935\pi\)
\(840\) 0 0
\(841\) 18.9188 + 15.8747i 0.652371 + 0.547404i
\(842\) 0 0
\(843\) −9.62870 + 7.93192i −0.331630 + 0.273190i
\(844\) 0 0
\(845\) 15.7294 9.08136i 0.541107 0.312408i
\(846\) 0 0
\(847\) 36.9287 + 21.3208i 1.26889 + 0.732592i
\(848\) 0 0
\(849\) 41.0189 + 35.0570i 1.40777 + 1.20315i
\(850\) 0 0
\(851\) −38.1974 + 13.9027i −1.30939 + 0.476579i
\(852\) 0 0
\(853\) 4.14225 + 23.4919i 0.141828 + 0.804346i 0.969860 + 0.243664i \(0.0783496\pi\)
−0.828032 + 0.560681i \(0.810539\pi\)
\(854\) 0 0
\(855\) 9.40089 48.1925i 0.321504 1.64815i
\(856\) 0 0
\(857\) 9.33534 + 11.1254i 0.318889 + 0.380037i 0.901548 0.432680i \(-0.142432\pi\)
−0.582659 + 0.812717i \(0.697987\pi\)
\(858\) 0 0
\(859\) −30.2973 5.34222i −1.03373 0.182274i −0.369055 0.929408i \(-0.620319\pi\)
−0.664674 + 0.747133i \(0.731430\pi\)
\(860\) 0 0
\(861\) 0.736672 81.3190i 0.0251057 2.77134i
\(862\) 0 0
\(863\) 0.740209 0.0251970 0.0125985 0.999921i \(-0.495990\pi\)
0.0125985 + 0.999921i \(0.495990\pi\)
\(864\) 0 0
\(865\) −41.6253 −1.41530
\(866\) 0 0
\(867\) −43.2169 25.4761i −1.46772 0.865212i
\(868\) 0 0
\(869\) −0.745685 0.131484i −0.0252956 0.00446030i
\(870\) 0 0
\(871\) −7.15973 8.53263i −0.242598 0.289117i
\(872\) 0 0
\(873\) 27.0351 + 10.3984i 0.915001 + 0.351934i
\(874\) 0 0
\(875\) 7.78491 + 44.1504i 0.263178 + 1.49256i
\(876\) 0 0
\(877\) −0.300658 + 0.109431i −0.0101525 + 0.00369521i −0.347091 0.937831i \(-0.612831\pi\)
0.336939 + 0.941527i \(0.390608\pi\)
\(878\) 0 0
\(879\) 7.06746 38.0620i 0.238379 1.28380i
\(880\) 0 0
\(881\) −2.53702 1.46475i −0.0854744 0.0493487i 0.456654 0.889645i \(-0.349048\pi\)
−0.542128 + 0.840296i \(0.682381\pi\)
\(882\) 0 0
\(883\) −47.0872 + 27.1858i −1.58461 + 0.914876i −0.590438 + 0.807083i \(0.701045\pi\)
−0.994173 + 0.107793i \(0.965622\pi\)
\(884\) 0 0
\(885\) −0.332800 1.99280i −0.0111870 0.0669873i
\(886\) 0 0
\(887\) 8.16957 + 6.85508i 0.274307 + 0.230171i 0.769555 0.638581i \(-0.220478\pi\)
−0.495248 + 0.868752i \(0.664923\pi\)
\(888\) 0 0
\(889\) 55.8146 + 20.3148i 1.87196 + 0.681338i
\(890\) 0 0
\(891\) 1.46209 1.13919i 0.0489820 0.0381642i
\(892\) 0 0
\(893\) −11.6527 + 32.0156i −0.389943 + 1.07136i
\(894\) 0 0
\(895\) 19.2723 22.9679i 0.644203 0.767731i
\(896\) 0 0
\(897\) −19.0775 + 3.18597i −0.636981 + 0.106377i
\(898\) 0 0
\(899\) −1.65423 2.86522i −0.0551718 0.0955603i
\(900\) 0 0
\(901\) −23.3742 + 40.4852i −0.778706 + 1.34876i
\(902\) 0 0
\(903\) 41.4183 + 7.69066i 1.37831 + 0.255929i
\(904\) 0 0
\(905\) 17.8484 + 49.0381i 0.593301 + 1.63008i
\(906\) 0 0
\(907\) 24.1993 4.26700i 0.803526 0.141683i 0.243222 0.969971i \(-0.421796\pi\)
0.560304 + 0.828287i \(0.310684\pi\)
\(908\) 0 0
\(909\) 26.6594 4.20428i 0.884235 0.139447i
\(910\) 0 0
\(911\) −4.38166 + 3.67665i −0.145171 + 0.121813i −0.712481 0.701691i \(-0.752429\pi\)
0.567310 + 0.823504i \(0.307984\pi\)
\(912\) 0 0
\(913\) 0.382753 2.17070i 0.0126673 0.0718397i
\(914\) 0 0
\(915\) 1.72476 2.92583i 0.0570187 0.0967250i
\(916\) 0 0
\(917\) 33.2545i 1.09816i
\(918\) 0 0
\(919\) 18.1413i 0.598426i −0.954186 0.299213i \(-0.903276\pi\)
0.954186 0.299213i \(-0.0967242\pi\)
\(920\) 0 0
\(921\) 16.3554 + 0.148164i 0.538927 + 0.00488216i
\(922\) 0 0
\(923\) 3.75800 21.3127i 0.123696 0.701516i
\(924\) 0 0
\(925\) −1.98567 + 1.66617i −0.0652883 + 0.0547834i
\(926\) 0 0
\(927\) 10.7306 12.3276i 0.352439 0.404891i
\(928\) 0 0
\(929\) −5.76282 + 1.01614i −0.189072 + 0.0333385i −0.267382 0.963591i \(-0.586159\pi\)
0.0783102 + 0.996929i \(0.475048\pi\)
\(930\) 0 0
\(931\) −21.1008 57.9739i −0.691550 1.90002i
\(932\) 0 0
\(933\) 13.2674 15.5237i 0.434354 0.508222i
\(934\) 0 0
\(935\) −1.50828 + 2.61242i −0.0493261 + 0.0854353i
\(936\) 0 0
\(937\) 6.55013 + 11.3452i 0.213983 + 0.370630i 0.952958 0.303104i \(-0.0980228\pi\)
−0.738974 + 0.673734i \(0.764690\pi\)
\(938\) 0 0
\(939\) 11.0969 + 13.4708i 0.362135 + 0.439602i
\(940\) 0 0
\(941\) 2.91952 3.47934i 0.0951735 0.113423i −0.716356 0.697735i \(-0.754191\pi\)
0.811529 + 0.584312i \(0.198636\pi\)
\(942\) 0 0
\(943\) 21.5009 59.0732i 0.700166 1.92369i
\(944\) 0 0
\(945\) 38.4138 20.8075i 1.24960 0.676867i
\(946\) 0 0
\(947\) 1.58228 + 0.575904i 0.0514173 + 0.0187144i 0.367601 0.929984i \(-0.380179\pi\)
−0.316183 + 0.948698i \(0.602402\pi\)
\(948\) 0 0
\(949\) −4.80576 4.03251i −0.156001 0.130901i
\(950\) 0 0
\(951\) −23.5800 8.82512i −0.764633 0.286174i
\(952\) 0 0
\(953\) 20.8678 12.0481i 0.675975 0.390275i −0.122362 0.992486i \(-0.539047\pi\)
0.798337 + 0.602211i \(0.205713\pi\)
\(954\) 0 0
\(955\) −13.6251 7.86646i −0.440898 0.254553i
\(956\) 0 0
\(957\) 0.697606 0.246775i 0.0225504 0.00797709i
\(958\) 0 0
\(959\) 38.7166 14.0917i 1.25023 0.455045i
\(960\) 0 0
\(961\) 4.94140 + 28.0241i 0.159400 + 0.904002i
\(962\) 0 0
\(963\) −2.58601 + 4.29738i −0.0833331 + 0.138481i
\(964\) 0 0
\(965\) −13.5360 16.1316i −0.435739 0.519293i
\(966\) 0 0
\(967\) 26.2346 + 4.62588i 0.843649 + 0.148758i 0.578737 0.815514i \(-0.303546\pi\)
0.264912 + 0.964272i \(0.414657\pi\)
\(968\) 0 0
\(969\) −77.4394 + 43.7791i −2.48771 + 1.40639i
\(970\) 0 0
\(971\) 15.7928 0.506815 0.253408 0.967360i \(-0.418449\pi\)
0.253408 + 0.967360i \(0.418449\pi\)
\(972\) 0 0
\(973\) 22.6202 0.725170
\(974\) 0 0
\(975\) −1.07369 + 0.606993i −0.0343856 + 0.0194393i
\(976\) 0 0
\(977\) 17.9884 + 3.17184i 0.575501 + 0.101476i 0.453821 0.891093i \(-0.350061\pi\)
0.121680 + 0.992569i \(0.461172\pi\)
\(978\) 0 0
\(979\) −1.49765 1.78483i −0.0478651 0.0570435i
\(980\) 0 0
\(981\) 24.2253 40.2572i 0.773456 1.28531i
\(982\) 0 0
\(983\) 2.63000 + 14.9154i 0.0838838 + 0.475729i 0.997592 + 0.0693576i \(0.0220949\pi\)
−0.913708 + 0.406371i \(0.866794\pi\)
\(984\) 0 0
\(985\) 11.7437 4.27436i 0.374186 0.136193i
\(986\) 0 0
\(987\) −28.5784 + 10.1095i −0.909662 + 0.321788i
\(988\) 0 0
\(989\) 28.2019 + 16.2824i 0.896769 + 0.517750i
\(990\) 0 0
\(991\) 21.4600 12.3899i 0.681698 0.393578i −0.118797 0.992919i \(-0.537904\pi\)
0.800494 + 0.599340i \(0.204570\pi\)
\(992\) 0 0
\(993\) −16.0704 6.01455i −0.509978 0.190866i
\(994\) 0 0
\(995\) 6.84040 + 5.73978i 0.216855 + 0.181963i
\(996\) 0 0
\(997\) −14.8546 5.40662i −0.470448 0.171229i 0.0959070 0.995390i \(-0.469425\pi\)
−0.566356 + 0.824161i \(0.691647\pi\)
\(998\) 0 0
\(999\) 34.5426 + 21.2151i 1.09288 + 0.671217i
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 432.2.be.c.239.1 yes 36
4.3 odd 2 432.2.be.b.239.6 yes 36
27.20 odd 18 432.2.be.b.47.6 36
108.47 even 18 inner 432.2.be.c.47.1 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.be.b.47.6 36 27.20 odd 18
432.2.be.b.239.6 yes 36 4.3 odd 2
432.2.be.c.47.1 yes 36 108.47 even 18 inner
432.2.be.c.239.1 yes 36 1.1 even 1 trivial