Properties

Label 432.2.be.c.191.1
Level $432$
Weight $2$
Character 432.191
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 191.1
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.c.95.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70424 - 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(1.49276 + 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +O(q^{10})\) \(q+(-1.70424 - 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(1.49276 + 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +(-1.83629 - 1.54083i) q^{11} +(-0.219577 - 1.24528i) q^{13} +(1.94226 + 3.40247i) q^{15} +(4.23513 - 2.44515i) q^{17} +(5.93526 + 3.42672i) q^{19} +(-1.27623 - 7.45112i) q^{21} +(2.43275 + 0.885449i) q^{23} +(-0.0202120 + 0.114628i) q^{25} +(-4.46133 - 2.66392i) q^{27} +(9.76428 + 1.72171i) q^{29} +(2.15421 - 5.91865i) q^{31} +(2.65319 + 3.19359i) q^{33} +(4.93619 - 8.54973i) q^{35} +(2.49781 + 4.32633i) q^{37} +(-0.0107288 + 2.19014i) q^{39} +(0.206477 - 0.0364075i) q^{41} +(-0.863871 + 1.02952i) q^{43} +(-2.25831 - 6.39903i) q^{45} +(-5.30035 + 1.92917i) q^{47} +(-9.23031 + 7.74515i) q^{49} +(-7.97353 + 2.85797i) q^{51} +12.0068i q^{53} +5.42214i q^{55} +(-9.05585 - 7.67467i) q^{57} +(6.16576 - 5.17368i) q^{59} +(-3.59708 + 1.30923i) q^{61} +(-0.128280 + 13.0930i) q^{63} +(-1.83851 + 2.19105i) q^{65} +(-2.97797 + 0.525097i) q^{67} +(-3.87229 - 2.26103i) q^{69} +(-1.29426 - 2.24172i) q^{71} +(4.41358 - 7.64454i) q^{73} +(0.0698800 - 0.189106i) q^{75} +(3.57833 - 9.83137i) q^{77} +(1.39249 + 0.245534i) q^{79} +(6.77973 + 5.91906i) q^{81} +(1.55586 - 8.82370i) q^{83} +(-10.3945 - 3.78329i) q^{85} +(-16.1085 - 5.95254i) q^{87} +(-15.4462 - 8.91788i) q^{89} +(4.77955 - 2.75947i) q^{91} +(-5.50088 + 9.42091i) q^{93} +(-2.69191 - 15.2666i) q^{95} +(11.8986 + 9.98414i) q^{97} +(-3.53448 - 6.26281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.70424 0.309120i −0.983945 0.178470i
\(4\) 0 0
\(5\) −1.45395 1.73275i −0.650226 0.774910i 0.335722 0.941961i \(-0.391020\pi\)
−0.985948 + 0.167052i \(0.946575\pi\)
\(6\) 0 0
\(7\) 1.49276 + 4.10134i 0.564212 + 1.55016i 0.813400 + 0.581705i \(0.197614\pi\)
−0.249188 + 0.968455i \(0.580164\pi\)
\(8\) 0 0
\(9\) 2.80889 + 1.05363i 0.936297 + 0.351210i
\(10\) 0 0
\(11\) −1.83629 1.54083i −0.553664 0.464579i 0.322516 0.946564i \(-0.395471\pi\)
−0.876179 + 0.481985i \(0.839916\pi\)
\(12\) 0 0
\(13\) −0.219577 1.24528i −0.0608997 0.345379i −0.999999 0.00173201i \(-0.999449\pi\)
0.939099 0.343647i \(-0.111662\pi\)
\(14\) 0 0
\(15\) 1.94226 + 3.40247i 0.501489 + 0.878515i
\(16\) 0 0
\(17\) 4.23513 2.44515i 1.02717 0.593036i 0.110997 0.993821i \(-0.464596\pi\)
0.916172 + 0.400784i \(0.131262\pi\)
\(18\) 0 0
\(19\) 5.93526 + 3.42672i 1.36164 + 0.786144i 0.989842 0.142170i \(-0.0454078\pi\)
0.371799 + 0.928313i \(0.378741\pi\)
\(20\) 0 0
\(21\) −1.27623 7.45112i −0.278496 1.62597i
\(22\) 0 0
\(23\) 2.43275 + 0.885449i 0.507264 + 0.184629i 0.582958 0.812502i \(-0.301895\pi\)
−0.0756944 + 0.997131i \(0.524117\pi\)
\(24\) 0 0
\(25\) −0.0202120 + 0.114628i −0.00404241 + 0.0229256i
\(26\) 0 0
\(27\) −4.46133 2.66392i −0.858584 0.512673i
\(28\) 0 0
\(29\) 9.76428 + 1.72171i 1.81318 + 0.319713i 0.974411 0.224773i \(-0.0721640\pi\)
0.838770 + 0.544486i \(0.183275\pi\)
\(30\) 0 0
\(31\) 2.15421 5.91865i 0.386908 1.06302i −0.581477 0.813563i \(-0.697525\pi\)
0.968385 0.249459i \(-0.0802527\pi\)
\(32\) 0 0
\(33\) 2.65319 + 3.19359i 0.461861 + 0.555933i
\(34\) 0 0
\(35\) 4.93619 8.54973i 0.834368 1.44517i
\(36\) 0 0
\(37\) 2.49781 + 4.32633i 0.410637 + 0.711244i 0.994960 0.100278i \(-0.0319731\pi\)
−0.584323 + 0.811521i \(0.698640\pi\)
\(38\) 0 0
\(39\) −0.0107288 + 2.19014i −0.00171798 + 0.350703i
\(40\) 0 0
\(41\) 0.206477 0.0364075i 0.0322463 0.00568590i −0.157502 0.987519i \(-0.550344\pi\)
0.189748 + 0.981833i \(0.439233\pi\)
\(42\) 0 0
\(43\) −0.863871 + 1.02952i −0.131739 + 0.157001i −0.827881 0.560903i \(-0.810454\pi\)
0.696142 + 0.717904i \(0.254898\pi\)
\(44\) 0 0
\(45\) −2.25831 6.39903i −0.336649 0.953911i
\(46\) 0 0
\(47\) −5.30035 + 1.92917i −0.773135 + 0.281398i −0.698307 0.715798i \(-0.746063\pi\)
−0.0748282 + 0.997196i \(0.523841\pi\)
\(48\) 0 0
\(49\) −9.23031 + 7.74515i −1.31862 + 1.10645i
\(50\) 0 0
\(51\) −7.97353 + 2.85797i −1.11652 + 0.400196i
\(52\) 0 0
\(53\) 12.0068i 1.64926i 0.565670 + 0.824632i \(0.308618\pi\)
−0.565670 + 0.824632i \(0.691382\pi\)
\(54\) 0 0
\(55\) 5.42214i 0.731121i
\(56\) 0 0
\(57\) −9.05585 7.67467i −1.19948 1.01654i
\(58\) 0 0
\(59\) 6.16576 5.17368i 0.802713 0.673556i −0.146144 0.989263i \(-0.546686\pi\)
0.948857 + 0.315707i \(0.102242\pi\)
\(60\) 0 0
\(61\) −3.59708 + 1.30923i −0.460559 + 0.167630i −0.561871 0.827225i \(-0.689918\pi\)
0.101312 + 0.994855i \(0.467696\pi\)
\(62\) 0 0
\(63\) −0.128280 + 13.0930i −0.0161618 + 1.64957i
\(64\) 0 0
\(65\) −1.83851 + 2.19105i −0.228039 + 0.271766i
\(66\) 0 0
\(67\) −2.97797 + 0.525097i −0.363817 + 0.0641508i −0.352569 0.935786i \(-0.614692\pi\)
−0.0112486 + 0.999937i \(0.503581\pi\)
\(68\) 0 0
\(69\) −3.87229 2.26103i −0.466169 0.272196i
\(70\) 0 0
\(71\) −1.29426 2.24172i −0.153600 0.266043i 0.778948 0.627088i \(-0.215753\pi\)
−0.932548 + 0.361045i \(0.882420\pi\)
\(72\) 0 0
\(73\) 4.41358 7.64454i 0.516570 0.894726i −0.483244 0.875485i \(-0.660542\pi\)
0.999815 0.0192407i \(-0.00612489\pi\)
\(74\) 0 0
\(75\) 0.0698800 0.189106i 0.00806905 0.0218361i
\(76\) 0 0
\(77\) 3.57833 9.83137i 0.407788 1.12039i
\(78\) 0 0
\(79\) 1.39249 + 0.245534i 0.156668 + 0.0276247i 0.251432 0.967875i \(-0.419099\pi\)
−0.0947642 + 0.995500i \(0.530210\pi\)
\(80\) 0 0
\(81\) 6.77973 + 5.91906i 0.753303 + 0.657674i
\(82\) 0 0
\(83\) 1.55586 8.82370i 0.170777 0.968527i −0.772128 0.635467i \(-0.780808\pi\)
0.942906 0.333060i \(-0.108081\pi\)
\(84\) 0 0
\(85\) −10.3945 3.78329i −1.12744 0.410355i
\(86\) 0 0
\(87\) −16.1085 5.95254i −1.72701 0.638179i
\(88\) 0 0
\(89\) −15.4462 8.91788i −1.63730 0.945293i −0.981759 0.190130i \(-0.939109\pi\)
−0.655537 0.755163i \(-0.727558\pi\)
\(90\) 0 0
\(91\) 4.77955 2.75947i 0.501033 0.289271i
\(92\) 0 0
\(93\) −5.50088 + 9.42091i −0.570414 + 0.976903i
\(94\) 0 0
\(95\) −2.69191 15.2666i −0.276185 1.56632i
\(96\) 0 0
\(97\) 11.8986 + 9.98414i 1.20812 + 1.01374i 0.999360 + 0.0357690i \(0.0113881\pi\)
0.208763 + 0.977966i \(0.433056\pi\)
\(98\) 0 0
\(99\) −3.53448 6.26281i −0.355229 0.629436i
\(100\) 0 0
\(101\) 4.09820 + 11.2597i 0.407786 + 1.12038i 0.958351 + 0.285592i \(0.0921901\pi\)
−0.550565 + 0.834792i \(0.685588\pi\)
\(102\) 0 0
\(103\) 11.4815 + 13.6831i 1.13130 + 1.34823i 0.929506 + 0.368806i \(0.120233\pi\)
0.201796 + 0.979428i \(0.435322\pi\)
\(104\) 0 0
\(105\) −11.0554 + 13.0449i −1.07889 + 1.27306i
\(106\) 0 0
\(107\) −16.3881 −1.58430 −0.792150 0.610326i \(-0.791039\pi\)
−0.792150 + 0.610326i \(0.791039\pi\)
\(108\) 0 0
\(109\) −1.59295 −0.152577 −0.0762883 0.997086i \(-0.524307\pi\)
−0.0762883 + 0.997086i \(0.524307\pi\)
\(110\) 0 0
\(111\) −2.91952 8.14524i −0.277108 0.773112i
\(112\) 0 0
\(113\) −3.82521 4.55871i −0.359846 0.428847i 0.555500 0.831517i \(-0.312527\pi\)
−0.915346 + 0.402669i \(0.868083\pi\)
\(114\) 0 0
\(115\) −2.00284 5.50275i −0.186766 0.513134i
\(116\) 0 0
\(117\) 0.695300 3.72921i 0.0642805 0.344766i
\(118\) 0 0
\(119\) 16.3504 + 13.7196i 1.49884 + 1.25768i
\(120\) 0 0
\(121\) −0.912322 5.17403i −0.0829383 0.470367i
\(122\) 0 0
\(123\) −0.363142 0.00177892i −0.0327434 0.000160399i
\(124\) 0 0
\(125\) −9.56650 + 5.52322i −0.855654 + 0.494012i
\(126\) 0 0
\(127\) −0.498482 0.287799i −0.0442331 0.0255380i 0.477720 0.878512i \(-0.341463\pi\)
−0.521953 + 0.852974i \(0.674797\pi\)
\(128\) 0 0
\(129\) 1.79049 1.48752i 0.157644 0.130968i
\(130\) 0 0
\(131\) 0.393105 + 0.143079i 0.0343458 + 0.0125008i 0.359136 0.933285i \(-0.383071\pi\)
−0.324790 + 0.945786i \(0.605294\pi\)
\(132\) 0 0
\(133\) −5.19420 + 29.4578i −0.450394 + 2.55431i
\(134\) 0 0
\(135\) 1.87064 + 11.6036i 0.160999 + 0.998678i
\(136\) 0 0
\(137\) 7.23523 + 1.27577i 0.618147 + 0.108996i 0.473948 0.880553i \(-0.342828\pi\)
0.144199 + 0.989549i \(0.453939\pi\)
\(138\) 0 0
\(139\) 3.90843 10.7383i 0.331509 0.910814i −0.656211 0.754578i \(-0.727842\pi\)
0.987720 0.156236i \(-0.0499361\pi\)
\(140\) 0 0
\(141\) 9.62943 1.64933i 0.810944 0.138899i
\(142\) 0 0
\(143\) −1.51557 + 2.62504i −0.126738 + 0.219517i
\(144\) 0 0
\(145\) −11.2135 19.4223i −0.931230 1.61294i
\(146\) 0 0
\(147\) 18.1249 10.3464i 1.49491 0.853353i
\(148\) 0 0
\(149\) 11.5485 2.03631i 0.946089 0.166821i 0.320741 0.947167i \(-0.396068\pi\)
0.625348 + 0.780346i \(0.284957\pi\)
\(150\) 0 0
\(151\) −4.73929 + 5.64807i −0.385678 + 0.459634i −0.923598 0.383363i \(-0.874766\pi\)
0.537920 + 0.842996i \(0.319210\pi\)
\(152\) 0 0
\(153\) 14.4723 2.40591i 1.17002 0.194506i
\(154\) 0 0
\(155\) −13.3877 + 4.87271i −1.07532 + 0.391386i
\(156\) 0 0
\(157\) −8.59341 + 7.21073i −0.685829 + 0.575479i −0.917703 0.397267i \(-0.869959\pi\)
0.231874 + 0.972746i \(0.425514\pi\)
\(158\) 0 0
\(159\) 3.71154 20.4625i 0.294345 1.62279i
\(160\) 0 0
\(161\) 11.2993i 0.890510i
\(162\) 0 0
\(163\) 2.13355i 0.167113i 0.996503 + 0.0835565i \(0.0266279\pi\)
−0.996503 + 0.0835565i \(0.973372\pi\)
\(164\) 0 0
\(165\) 1.67609 9.24064i 0.130483 0.719383i
\(166\) 0 0
\(167\) 0.742162 0.622748i 0.0574302 0.0481897i −0.613621 0.789601i \(-0.710288\pi\)
0.671051 + 0.741411i \(0.265843\pi\)
\(168\) 0 0
\(169\) 10.7135 3.89939i 0.824115 0.299953i
\(170\) 0 0
\(171\) 13.0610 + 15.8788i 0.998798 + 1.21429i
\(172\) 0 0
\(173\) 5.38552 6.41821i 0.409453 0.487967i −0.521425 0.853297i \(-0.674599\pi\)
0.930878 + 0.365330i \(0.119044\pi\)
\(174\) 0 0
\(175\) −0.500301 + 0.0882165i −0.0378192 + 0.00666854i
\(176\) 0 0
\(177\) −12.1072 + 6.91126i −0.910036 + 0.519482i
\(178\) 0 0
\(179\) −4.91202 8.50787i −0.367142 0.635908i 0.621976 0.783036i \(-0.286330\pi\)
−0.989117 + 0.147129i \(0.952997\pi\)
\(180\) 0 0
\(181\) 6.82245 11.8168i 0.507109 0.878338i −0.492857 0.870110i \(-0.664048\pi\)
0.999966 0.00822799i \(-0.00261908\pi\)
\(182\) 0 0
\(183\) 6.53502 1.11932i 0.483082 0.0827425i
\(184\) 0 0
\(185\) 3.86476 10.6183i 0.284143 0.780676i
\(186\) 0 0
\(187\) −11.5445 2.03561i −0.844218 0.148858i
\(188\) 0 0
\(189\) 4.26593 22.2741i 0.310301 1.62020i
\(190\) 0 0
\(191\) −0.158946 + 0.901427i −0.0115009 + 0.0652250i −0.990018 0.140940i \(-0.954987\pi\)
0.978517 + 0.206165i \(0.0660985\pi\)
\(192\) 0 0
\(193\) 3.10590 + 1.13045i 0.223567 + 0.0813718i 0.451375 0.892334i \(-0.350934\pi\)
−0.227808 + 0.973706i \(0.573156\pi\)
\(194\) 0 0
\(195\) 3.81057 3.16576i 0.272880 0.226705i
\(196\) 0 0
\(197\) 1.95985 + 1.13152i 0.139634 + 0.0806176i 0.568189 0.822898i \(-0.307644\pi\)
−0.428556 + 0.903515i \(0.640977\pi\)
\(198\) 0 0
\(199\) −7.82807 + 4.51954i −0.554917 + 0.320381i −0.751103 0.660185i \(-0.770478\pi\)
0.196186 + 0.980567i \(0.437144\pi\)
\(200\) 0 0
\(201\) 5.23751 + 0.0256569i 0.369425 + 0.00180970i
\(202\) 0 0
\(203\) 7.51448 + 42.6167i 0.527413 + 2.99111i
\(204\) 0 0
\(205\) −0.363293 0.304839i −0.0253735 0.0212909i
\(206\) 0 0
\(207\) 5.90040 + 5.05035i 0.410106 + 0.351024i
\(208\) 0 0
\(209\) −5.61887 15.4377i −0.388665 1.06785i
\(210\) 0 0
\(211\) −14.7121 17.5332i −1.01282 1.20704i −0.978206 0.207634i \(-0.933424\pi\)
−0.0346162 0.999401i \(-0.511021\pi\)
\(212\) 0 0
\(213\) 1.51277 + 4.22052i 0.103653 + 0.289185i
\(214\) 0 0
\(215\) 3.03993 0.207321
\(216\) 0 0
\(217\) 27.4901 1.86615
\(218\) 0 0
\(219\) −9.88489 + 11.6638i −0.667959 + 0.788169i
\(220\) 0 0
\(221\) −3.97484 4.73703i −0.267377 0.318647i
\(222\) 0 0
\(223\) −2.89561 7.95563i −0.193905 0.532748i 0.804195 0.594365i \(-0.202597\pi\)
−0.998100 + 0.0616168i \(0.980374\pi\)
\(224\) 0 0
\(225\) −0.177549 + 0.300682i −0.0118366 + 0.0200455i
\(226\) 0 0
\(227\) 13.9998 + 11.7472i 0.929200 + 0.779691i 0.975674 0.219228i \(-0.0703540\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(228\) 0 0
\(229\) −2.27137 12.8816i −0.150096 0.851237i −0.963133 0.269025i \(-0.913299\pi\)
0.813037 0.582212i \(-0.197813\pi\)
\(230\) 0 0
\(231\) −9.13741 + 15.6489i −0.601197 + 1.02962i
\(232\) 0 0
\(233\) −23.8420 + 13.7652i −1.56194 + 0.901789i −0.564884 + 0.825170i \(0.691079\pi\)
−0.997060 + 0.0766185i \(0.975588\pi\)
\(234\) 0 0
\(235\) 11.0492 + 6.37927i 0.720771 + 0.416137i
\(236\) 0 0
\(237\) −2.29725 0.848896i −0.149222 0.0551417i
\(238\) 0 0
\(239\) 14.2322 + 5.18010i 0.920604 + 0.335073i 0.758479 0.651698i \(-0.225943\pi\)
0.162125 + 0.986770i \(0.448165\pi\)
\(240\) 0 0
\(241\) 2.45072 13.8987i 0.157864 0.895294i −0.798256 0.602319i \(-0.794244\pi\)
0.956120 0.292975i \(-0.0946453\pi\)
\(242\) 0 0
\(243\) −9.72461 12.1833i −0.623834 0.781557i
\(244\) 0 0
\(245\) 26.8408 + 4.73276i 1.71480 + 0.302365i
\(246\) 0 0
\(247\) 2.96399 8.14350i 0.188594 0.518158i
\(248\) 0 0
\(249\) −5.37914 + 14.5568i −0.340889 + 0.922499i
\(250\) 0 0
\(251\) 0.336061 0.582074i 0.0212120 0.0367402i −0.855225 0.518258i \(-0.826581\pi\)
0.876437 + 0.481517i \(0.159914\pi\)
\(252\) 0 0
\(253\) −3.10292 5.37441i −0.195079 0.337886i
\(254\) 0 0
\(255\) 16.5453 + 9.66079i 1.03610 + 0.604982i
\(256\) 0 0
\(257\) −11.9006 + 2.09839i −0.742337 + 0.130894i −0.532011 0.846737i \(-0.678564\pi\)
−0.210326 + 0.977631i \(0.567453\pi\)
\(258\) 0 0
\(259\) −14.0151 + 16.7025i −0.870856 + 1.03785i
\(260\) 0 0
\(261\) 25.6127 + 15.1240i 1.58539 + 0.936153i
\(262\) 0 0
\(263\) −22.9065 + 8.33729i −1.41248 + 0.514099i −0.931855 0.362830i \(-0.881811\pi\)
−0.480620 + 0.876929i \(0.659588\pi\)
\(264\) 0 0
\(265\) 20.8048 17.4573i 1.27803 1.07239i
\(266\) 0 0
\(267\) 23.5674 + 19.9730i 1.44230 + 1.22233i
\(268\) 0 0
\(269\) 14.6341i 0.892260i −0.894968 0.446130i \(-0.852802\pi\)
0.894968 0.446130i \(-0.147198\pi\)
\(270\) 0 0
\(271\) 11.5240i 0.700036i −0.936743 0.350018i \(-0.886175\pi\)
0.936743 0.350018i \(-0.113825\pi\)
\(272\) 0 0
\(273\) −8.99852 + 3.22536i −0.544615 + 0.195208i
\(274\) 0 0
\(275\) 0.213738 0.179348i 0.0128889 0.0108151i
\(276\) 0 0
\(277\) −1.53344 + 0.558126i −0.0921354 + 0.0335346i −0.387677 0.921795i \(-0.626722\pi\)
0.295541 + 0.955330i \(0.404500\pi\)
\(278\) 0 0
\(279\) 12.2870 14.3551i 0.735605 0.859417i
\(280\) 0 0
\(281\) −15.2140 + 18.1313i −0.907590 + 1.08162i 0.0887421 + 0.996055i \(0.471715\pi\)
−0.996332 + 0.0855691i \(0.972729\pi\)
\(282\) 0 0
\(283\) −11.5507 + 2.03669i −0.686615 + 0.121069i −0.506063 0.862497i \(-0.668900\pi\)
−0.180552 + 0.983565i \(0.557789\pi\)
\(284\) 0 0
\(285\) −0.131530 + 26.8501i −0.00779118 + 1.59046i
\(286\) 0 0
\(287\) 0.457541 + 0.792485i 0.0270078 + 0.0467789i
\(288\) 0 0
\(289\) 3.45753 5.98862i 0.203384 0.352272i
\(290\) 0 0
\(291\) −17.1919 20.6935i −1.00781 1.21307i
\(292\) 0 0
\(293\) 0.897942 2.46708i 0.0524583 0.144128i −0.910696 0.413077i \(-0.864454\pi\)
0.963154 + 0.268949i \(0.0866763\pi\)
\(294\) 0 0
\(295\) −17.9294 3.16144i −1.04389 0.184066i
\(296\) 0 0
\(297\) 4.08766 + 11.7659i 0.237190 + 0.682728i
\(298\) 0 0
\(299\) 0.568458 3.22389i 0.0328748 0.186442i
\(300\) 0 0
\(301\) −5.51197 2.00619i −0.317705 0.115635i
\(302\) 0 0
\(303\) −3.50373 20.4561i −0.201284 1.17517i
\(304\) 0 0
\(305\) 7.49855 + 4.32929i 0.429366 + 0.247895i
\(306\) 0 0
\(307\) 25.4578 14.6981i 1.45296 0.838865i 0.454308 0.890845i \(-0.349887\pi\)
0.998648 + 0.0519800i \(0.0165532\pi\)
\(308\) 0 0
\(309\) −15.3375 26.8684i −0.872520 1.52849i
\(310\) 0 0
\(311\) −3.47343 19.6988i −0.196960 1.11702i −0.909599 0.415486i \(-0.863611\pi\)
0.712639 0.701531i \(-0.247500\pi\)
\(312\) 0 0
\(313\) 15.4507 + 12.9647i 0.873324 + 0.732806i 0.964795 0.263002i \(-0.0847126\pi\)
−0.0914716 + 0.995808i \(0.529157\pi\)
\(314\) 0 0
\(315\) 22.8735 18.8143i 1.28877 1.06007i
\(316\) 0 0
\(317\) −5.18750 14.2525i −0.291359 0.800503i −0.995868 0.0908080i \(-0.971055\pi\)
0.704509 0.709695i \(-0.251167\pi\)
\(318\) 0 0
\(319\) −15.2772 18.2067i −0.855361 1.01938i
\(320\) 0 0
\(321\) 27.9294 + 5.06589i 1.55887 + 0.282751i
\(322\) 0 0
\(323\) 33.5154 1.86485
\(324\) 0 0
\(325\) 0.147182 0.00816422
\(326\) 0 0
\(327\) 2.71477 + 0.492411i 0.150127 + 0.0272304i
\(328\) 0 0
\(329\) −15.8244 18.8587i −0.872425 1.03972i
\(330\) 0 0
\(331\) 7.76246 + 21.3272i 0.426663 + 1.17225i 0.947825 + 0.318790i \(0.103277\pi\)
−0.521162 + 0.853458i \(0.674501\pi\)
\(332\) 0 0
\(333\) 2.45771 + 14.7839i 0.134682 + 0.810155i
\(334\) 0 0
\(335\) 5.23969 + 4.39662i 0.286275 + 0.240213i
\(336\) 0 0
\(337\) −0.768067 4.35592i −0.0418393 0.237282i 0.956716 0.291025i \(-0.0939961\pi\)
−0.998555 + 0.0537423i \(0.982885\pi\)
\(338\) 0 0
\(339\) 5.10991 + 8.95160i 0.277532 + 0.486184i
\(340\) 0 0
\(341\) −13.0754 + 7.54910i −0.708074 + 0.408807i
\(342\) 0 0
\(343\) −19.0855 11.0190i −1.03052 0.594970i
\(344\) 0 0
\(345\) 1.71231 + 9.99714i 0.0921879 + 0.538228i
\(346\) 0 0
\(347\) 6.10935 + 2.22362i 0.327967 + 0.119370i 0.500756 0.865589i \(-0.333055\pi\)
−0.172788 + 0.984959i \(0.555278\pi\)
\(348\) 0 0
\(349\) 2.48215 14.0770i 0.132866 0.753522i −0.843456 0.537199i \(-0.819482\pi\)
0.976322 0.216323i \(-0.0694065\pi\)
\(350\) 0 0
\(351\) −2.33773 + 6.14056i −0.124779 + 0.327759i
\(352\) 0 0
\(353\) 13.3084 + 2.34663i 0.708335 + 0.124898i 0.516197 0.856470i \(-0.327347\pi\)
0.192137 + 0.981368i \(0.438458\pi\)
\(354\) 0 0
\(355\) −2.00256 + 5.50197i −0.106285 + 0.292014i
\(356\) 0 0
\(357\) −23.6241 28.4359i −1.25032 1.50499i
\(358\) 0 0
\(359\) −12.2376 + 21.1961i −0.645875 + 1.11869i 0.338224 + 0.941066i \(0.390174\pi\)
−0.984099 + 0.177623i \(0.943159\pi\)
\(360\) 0 0
\(361\) 13.9848 + 24.2225i 0.736044 + 1.27487i
\(362\) 0 0
\(363\) −0.0445772 + 9.09983i −0.00233969 + 0.477617i
\(364\) 0 0
\(365\) −19.6632 + 3.46715i −1.02922 + 0.181479i
\(366\) 0 0
\(367\) 17.9171 21.3528i 0.935266 1.11461i −0.0579497 0.998320i \(-0.518456\pi\)
0.993216 0.116287i \(-0.0370993\pi\)
\(368\) 0 0
\(369\) 0.618332 + 0.115286i 0.0321891 + 0.00600154i
\(370\) 0 0
\(371\) −49.2440 + 17.9234i −2.55662 + 0.930535i
\(372\) 0 0
\(373\) −23.7579 + 19.9352i −1.23014 + 1.03221i −0.231905 + 0.972738i \(0.574496\pi\)
−0.998230 + 0.0594676i \(0.981060\pi\)
\(374\) 0 0
\(375\) 18.0110 6.45572i 0.930083 0.333372i
\(376\) 0 0
\(377\) 12.5373i 0.645706i
\(378\) 0 0
\(379\) 21.9119i 1.12554i 0.826614 + 0.562770i \(0.190264\pi\)
−0.826614 + 0.562770i \(0.809736\pi\)
\(380\) 0 0
\(381\) 0.760571 + 0.644570i 0.0389652 + 0.0330223i
\(382\) 0 0
\(383\) −15.8681 + 13.3149i −0.810823 + 0.680361i −0.950804 0.309793i \(-0.899740\pi\)
0.139981 + 0.990154i \(0.455296\pi\)
\(384\) 0 0
\(385\) −22.2380 + 8.09398i −1.13335 + 0.412507i
\(386\) 0 0
\(387\) −3.51125 + 1.98161i −0.178487 + 0.100731i
\(388\) 0 0
\(389\) −21.6840 + 25.8420i −1.09942 + 1.31024i −0.152673 + 0.988277i \(0.548788\pi\)
−0.946751 + 0.321966i \(0.895656\pi\)
\(390\) 0 0
\(391\) 12.4681 2.19846i 0.630537 0.111181i
\(392\) 0 0
\(393\) −0.625719 0.365357i −0.0315633 0.0184298i
\(394\) 0 0
\(395\) −1.59916 2.76983i −0.0804627 0.139366i
\(396\) 0 0
\(397\) −8.88109 + 15.3825i −0.445729 + 0.772025i −0.998103 0.0615713i \(-0.980389\pi\)
0.552374 + 0.833597i \(0.313722\pi\)
\(398\) 0 0
\(399\) 17.9582 48.5976i 0.899032 2.43292i
\(400\) 0 0
\(401\) 0.0232749 0.0639472i 0.00116229 0.00319337i −0.939110 0.343616i \(-0.888348\pi\)
0.940272 + 0.340423i \(0.110570\pi\)
\(402\) 0 0
\(403\) −7.84341 1.38300i −0.390708 0.0688924i
\(404\) 0 0
\(405\) 0.398871 20.3536i 0.0198201 1.01138i
\(406\) 0 0
\(407\) 2.07944 11.7931i 0.103074 0.584563i
\(408\) 0 0
\(409\) −31.4276 11.4387i −1.55399 0.565607i −0.584642 0.811291i \(-0.698765\pi\)
−0.969350 + 0.245684i \(0.920987\pi\)
\(410\) 0 0
\(411\) −11.9362 4.41077i −0.588771 0.217567i
\(412\) 0 0
\(413\) 30.4231 + 17.5648i 1.49702 + 0.864305i
\(414\) 0 0
\(415\) −17.5514 + 10.1333i −0.861565 + 0.497425i
\(416\) 0 0
\(417\) −9.98035 + 17.0926i −0.488740 + 0.837026i
\(418\) 0 0
\(419\) 0.504953 + 2.86373i 0.0246686 + 0.139903i 0.994655 0.103258i \(-0.0329268\pi\)
−0.969986 + 0.243161i \(0.921816\pi\)
\(420\) 0 0
\(421\) −16.9409 14.2151i −0.825650 0.692802i 0.128638 0.991692i \(-0.458939\pi\)
−0.954288 + 0.298889i \(0.903384\pi\)
\(422\) 0 0
\(423\) −16.9207 0.165783i −0.822714 0.00806062i
\(424\) 0 0
\(425\) 0.194683 + 0.534886i 0.00944349 + 0.0259458i
\(426\) 0 0
\(427\) −10.7392 12.7985i −0.519706 0.619362i
\(428\) 0 0
\(429\) 3.39434 4.00521i 0.163880 0.193373i
\(430\) 0 0
\(431\) −28.6882 −1.38186 −0.690930 0.722922i \(-0.742799\pi\)
−0.690930 + 0.722922i \(0.742799\pi\)
\(432\) 0 0
\(433\) −18.3114 −0.879989 −0.439994 0.898000i \(-0.645020\pi\)
−0.439994 + 0.898000i \(0.645020\pi\)
\(434\) 0 0
\(435\) 13.1067 + 36.5667i 0.628418 + 1.75324i
\(436\) 0 0
\(437\) 11.4048 + 13.5917i 0.545566 + 0.650181i
\(438\) 0 0
\(439\) −9.59114 26.3514i −0.457760 1.25769i −0.927149 0.374694i \(-0.877748\pi\)
0.469388 0.882992i \(-0.344474\pi\)
\(440\) 0 0
\(441\) −34.0875 + 12.0299i −1.62321 + 0.572855i
\(442\) 0 0
\(443\) 5.21984 + 4.37997i 0.248002 + 0.208099i 0.758312 0.651892i \(-0.226025\pi\)
−0.510309 + 0.859991i \(0.670469\pi\)
\(444\) 0 0
\(445\) 7.00558 + 39.7306i 0.332096 + 1.88341i
\(446\) 0 0
\(447\) −20.3109 0.0994966i −0.960672 0.00470603i
\(448\) 0 0
\(449\) 3.01463 1.74050i 0.142269 0.0821392i −0.427176 0.904169i \(-0.640491\pi\)
0.569445 + 0.822029i \(0.307158\pi\)
\(450\) 0 0
\(451\) −0.435251 0.251292i −0.0204952 0.0118329i
\(452\) 0 0
\(453\) 9.82284 8.16068i 0.461517 0.383422i
\(454\) 0 0
\(455\) −11.7307 4.26963i −0.549944 0.200163i
\(456\) 0 0
\(457\) −0.671127 + 3.80615i −0.0313940 + 0.178044i −0.996473 0.0839151i \(-0.973258\pi\)
0.965079 + 0.261959i \(0.0843686\pi\)
\(458\) 0 0
\(459\) −25.4080 0.373421i −1.18594 0.0174298i
\(460\) 0 0
\(461\) −4.36591 0.769827i −0.203341 0.0358544i 0.0710500 0.997473i \(-0.477365\pi\)
−0.274391 + 0.961618i \(0.588476\pi\)
\(462\) 0 0
\(463\) −6.18880 + 17.0036i −0.287618 + 0.790224i 0.708781 + 0.705429i \(0.249246\pi\)
−0.996398 + 0.0847946i \(0.972977\pi\)
\(464\) 0 0
\(465\) 24.3221 4.16590i 1.12791 0.193189i
\(466\) 0 0
\(467\) −1.87326 + 3.24458i −0.0866840 + 0.150141i −0.906108 0.423047i \(-0.860960\pi\)
0.819424 + 0.573189i \(0.194294\pi\)
\(468\) 0 0
\(469\) −6.59901 11.4298i −0.304714 0.527780i
\(470\) 0 0
\(471\) 16.8742 9.63244i 0.777524 0.443839i
\(472\) 0 0
\(473\) 3.17264 0.559423i 0.145878 0.0257223i
\(474\) 0 0
\(475\) −0.512762 + 0.611086i −0.0235271 + 0.0280386i
\(476\) 0 0
\(477\) −12.6507 + 33.7258i −0.579238 + 1.54420i
\(478\) 0 0
\(479\) 31.1399 11.3340i 1.42282 0.517864i 0.487955 0.872869i \(-0.337743\pi\)
0.934864 + 0.355005i \(0.115521\pi\)
\(480\) 0 0
\(481\) 4.83904 4.06044i 0.220641 0.185140i
\(482\) 0 0
\(483\) 3.49284 19.2568i 0.158930 0.876213i
\(484\) 0 0
\(485\) 35.1338i 1.59534i
\(486\) 0 0
\(487\) 1.38462i 0.0627433i −0.999508 0.0313716i \(-0.990012\pi\)
0.999508 0.0313716i \(-0.00998754\pi\)
\(488\) 0 0
\(489\) 0.659524 3.63610i 0.0298247 0.164430i
\(490\) 0 0
\(491\) 19.4337 16.3068i 0.877029 0.735915i −0.0885369 0.996073i \(-0.528219\pi\)
0.965566 + 0.260158i \(0.0837747\pi\)
\(492\) 0 0
\(493\) 45.5628 16.5835i 2.05204 0.746883i
\(494\) 0 0
\(495\) −5.71293 + 15.2302i −0.256777 + 0.684546i
\(496\) 0 0
\(497\) 7.26203 8.65455i 0.325746 0.388210i
\(498\) 0 0
\(499\) 30.2436 5.33276i 1.35389 0.238727i 0.550825 0.834621i \(-0.314313\pi\)
0.803063 + 0.595894i \(0.203202\pi\)
\(500\) 0 0
\(501\) −1.45733 + 0.831897i −0.0651086 + 0.0371664i
\(502\) 0 0
\(503\) −3.84990 6.66821i −0.171658 0.297321i 0.767341 0.641239i \(-0.221579\pi\)
−0.939000 + 0.343918i \(0.888246\pi\)
\(504\) 0 0
\(505\) 13.5517 23.4722i 0.603043 1.04450i
\(506\) 0 0
\(507\) −19.4638 + 3.33376i −0.864416 + 0.148058i
\(508\) 0 0
\(509\) −10.3886 + 28.5425i −0.460468 + 1.26513i 0.464666 + 0.885486i \(0.346174\pi\)
−0.925134 + 0.379640i \(0.876048\pi\)
\(510\) 0 0
\(511\) 37.9413 + 6.69007i 1.67842 + 0.295951i
\(512\) 0 0
\(513\) −17.3506 31.0988i −0.766049 1.37305i
\(514\) 0 0
\(515\) 7.01588 39.7890i 0.309157 1.75331i
\(516\) 0 0
\(517\) 12.7055 + 4.62444i 0.558789 + 0.203382i
\(518\) 0 0
\(519\) −11.1622 + 9.27342i −0.489967 + 0.407058i
\(520\) 0 0
\(521\) −27.8916 16.1032i −1.22196 0.705496i −0.256621 0.966512i \(-0.582609\pi\)
−0.965334 + 0.261016i \(0.915942\pi\)
\(522\) 0 0
\(523\) −30.4157 + 17.5605i −1.32999 + 0.767869i −0.985297 0.170848i \(-0.945349\pi\)
−0.344690 + 0.938717i \(0.612016\pi\)
\(524\) 0 0
\(525\) 0.879903 + 0.00431037i 0.0384021 + 0.000188120i
\(526\) 0 0
\(527\) −5.34864 30.3336i −0.232990 1.32135i
\(528\) 0 0
\(529\) −12.4848 10.4760i −0.542816 0.455476i
\(530\) 0 0
\(531\) 22.7701 8.03588i 0.988137 0.348728i
\(532\) 0 0
\(533\) −0.0906752 0.249128i −0.00392758 0.0107909i
\(534\) 0 0
\(535\) 23.8275 + 28.3966i 1.03015 + 1.22769i
\(536\) 0 0
\(537\) 5.74133 + 16.0179i 0.247757 + 0.691222i
\(538\) 0 0
\(539\) 28.8836 1.24410
\(540\) 0 0
\(541\) 2.60427 0.111966 0.0559831 0.998432i \(-0.482171\pi\)
0.0559831 + 0.998432i \(0.482171\pi\)
\(542\) 0 0
\(543\) −15.2799 + 18.0298i −0.655725 + 0.773733i
\(544\) 0 0
\(545\) 2.31606 + 2.76018i 0.0992093 + 0.118233i
\(546\) 0 0
\(547\) 6.87308 + 18.8836i 0.293871 + 0.807405i 0.995491 + 0.0948537i \(0.0302383\pi\)
−0.701620 + 0.712552i \(0.747539\pi\)
\(548\) 0 0
\(549\) −11.4833 0.112508i −0.490094 0.00480174i
\(550\) 0 0
\(551\) 52.0537 + 43.6782i 2.21756 + 1.86076i
\(552\) 0 0
\(553\) 1.07165 + 6.07760i 0.0455710 + 0.258446i
\(554\) 0 0
\(555\) −9.86883 + 16.9016i −0.418908 + 0.717431i
\(556\) 0 0
\(557\) 8.72320 5.03634i 0.369614 0.213397i −0.303676 0.952775i \(-0.598214\pi\)
0.673290 + 0.739379i \(0.264881\pi\)
\(558\) 0 0
\(559\) 1.47173 + 0.849704i 0.0622476 + 0.0359387i
\(560\) 0 0
\(561\) 19.0454 + 7.03781i 0.804098 + 0.297137i
\(562\) 0 0
\(563\) −24.5071 8.91984i −1.03285 0.375927i −0.230684 0.973029i \(-0.574096\pi\)
−0.802165 + 0.597102i \(0.796319\pi\)
\(564\) 0 0
\(565\) −2.33744 + 13.2563i −0.0983368 + 0.557696i
\(566\) 0 0
\(567\) −14.1555 + 36.6417i −0.594477 + 1.53881i
\(568\) 0 0
\(569\) −3.55298 0.626486i −0.148949 0.0262636i 0.0986767 0.995120i \(-0.468539\pi\)
−0.247625 + 0.968856i \(0.579650\pi\)
\(570\) 0 0
\(571\) −5.25538 + 14.4390i −0.219931 + 0.604255i −0.999764 0.0217327i \(-0.993082\pi\)
0.779833 + 0.625988i \(0.215304\pi\)
\(572\) 0 0
\(573\) 0.549531 1.48712i 0.0229570 0.0621252i
\(574\) 0 0
\(575\) −0.150668 + 0.260965i −0.00628330 + 0.0108830i
\(576\) 0 0
\(577\) 11.3889 + 19.7261i 0.474124 + 0.821208i 0.999561 0.0296252i \(-0.00943137\pi\)
−0.525437 + 0.850833i \(0.676098\pi\)
\(578\) 0 0
\(579\) −4.94376 2.88666i −0.205455 0.119966i
\(580\) 0 0
\(581\) 38.5115 6.79061i 1.59773 0.281722i
\(582\) 0 0
\(583\) 18.5005 22.0481i 0.766213 0.913138i
\(584\) 0 0
\(585\) −7.47273 + 4.21731i −0.308959 + 0.174364i
\(586\) 0 0
\(587\) −8.66309 + 3.15311i −0.357564 + 0.130143i −0.514555 0.857457i \(-0.672043\pi\)
0.156991 + 0.987600i \(0.449821\pi\)
\(588\) 0 0
\(589\) 33.0674 27.7468i 1.36252 1.14329i
\(590\) 0 0
\(591\) −2.99029 2.53422i −0.123004 0.104244i
\(592\) 0 0
\(593\) 24.1512i 0.991772i 0.868388 + 0.495886i \(0.165157\pi\)
−0.868388 + 0.495886i \(0.834843\pi\)
\(594\) 0 0
\(595\) 48.2789i 1.97924i
\(596\) 0 0
\(597\) 14.7380 5.28258i 0.603187 0.216202i
\(598\) 0 0
\(599\) 13.4644 11.2980i 0.550140 0.461622i −0.324848 0.945766i \(-0.605313\pi\)
0.874988 + 0.484144i \(0.160869\pi\)
\(600\) 0 0
\(601\) −22.9928 + 8.36871i −0.937898 + 0.341367i −0.765335 0.643632i \(-0.777427\pi\)
−0.172562 + 0.984999i \(0.555205\pi\)
\(602\) 0 0
\(603\) −8.91806 1.66274i −0.363171 0.0677121i
\(604\) 0 0
\(605\) −7.63884 + 9.10361i −0.310563 + 0.370115i
\(606\) 0 0
\(607\) 1.07547 0.189635i 0.0436521 0.00769705i −0.151779 0.988414i \(-0.548500\pi\)
0.195432 + 0.980717i \(0.437389\pi\)
\(608\) 0 0
\(609\) 0.367167 74.9521i 0.0148783 3.03721i
\(610\) 0 0
\(611\) 3.56619 + 6.17683i 0.144273 + 0.249888i
\(612\) 0 0
\(613\) −8.33767 + 14.4413i −0.336755 + 0.583277i −0.983820 0.179158i \(-0.942663\pi\)
0.647065 + 0.762435i \(0.275996\pi\)
\(614\) 0 0
\(615\) 0.524908 + 0.631820i 0.0211663 + 0.0254775i
\(616\) 0 0
\(617\) 4.05382 11.1378i 0.163201 0.448390i −0.830956 0.556338i \(-0.812206\pi\)
0.994157 + 0.107948i \(0.0344281\pi\)
\(618\) 0 0
\(619\) 26.4189 + 4.65836i 1.06186 + 0.187235i 0.677183 0.735815i \(-0.263201\pi\)
0.384680 + 0.923050i \(0.374312\pi\)
\(620\) 0 0
\(621\) −8.49455 10.4310i −0.340875 0.418580i
\(622\) 0 0
\(623\) 13.5177 76.6625i 0.541574 3.07142i
\(624\) 0 0
\(625\) 24.0265 + 8.74492i 0.961059 + 0.349797i
\(626\) 0 0
\(627\) 4.80382 + 28.0465i 0.191846 + 1.12007i
\(628\) 0 0
\(629\) 21.1571 + 12.2150i 0.843587 + 0.487045i
\(630\) 0 0
\(631\) −0.440800 + 0.254496i −0.0175480 + 0.0101313i −0.508748 0.860915i \(-0.669892\pi\)
0.491200 + 0.871047i \(0.336558\pi\)
\(632\) 0 0
\(633\) 19.6531 + 34.4286i 0.781142 + 1.36842i
\(634\) 0 0
\(635\) 0.226085 + 1.28219i 0.00897190 + 0.0508822i
\(636\) 0 0
\(637\) 11.6717 + 9.79369i 0.462448 + 0.388040i
\(638\) 0 0
\(639\) −1.27348 7.66041i −0.0503782 0.303041i
\(640\) 0 0
\(641\) −1.51995 4.17603i −0.0600345 0.164943i 0.906049 0.423172i \(-0.139083\pi\)
−0.966084 + 0.258229i \(0.916861\pi\)
\(642\) 0 0
\(643\) 3.68943 + 4.39689i 0.145497 + 0.173397i 0.833871 0.551959i \(-0.186120\pi\)
−0.688374 + 0.725356i \(0.741675\pi\)
\(644\) 0 0
\(645\) −5.18078 0.939702i −0.203993 0.0370007i
\(646\) 0 0
\(647\) −30.5457 −1.20088 −0.600439 0.799671i \(-0.705007\pi\)
−0.600439 + 0.799671i \(0.705007\pi\)
\(648\) 0 0
\(649\) −19.2939 −0.757353
\(650\) 0 0
\(651\) −46.8499 8.49774i −1.83619 0.333053i
\(652\) 0 0
\(653\) 18.0659 + 21.5301i 0.706972 + 0.842537i 0.993296 0.115596i \(-0.0368778\pi\)
−0.286324 + 0.958133i \(0.592433\pi\)
\(654\) 0 0
\(655\) −0.323636 0.889183i −0.0126455 0.0347432i
\(656\) 0 0
\(657\) 20.4518 16.8224i 0.797900 0.656304i
\(658\) 0 0
\(659\) −4.20561 3.52893i −0.163827 0.137467i 0.557188 0.830386i \(-0.311880\pi\)
−0.721016 + 0.692919i \(0.756325\pi\)
\(660\) 0 0
\(661\) −1.70979 9.69669i −0.0665031 0.377158i −0.999835 0.0181440i \(-0.994224\pi\)
0.933332 0.359014i \(-0.116887\pi\)
\(662\) 0 0
\(663\) 5.30979 + 9.30175i 0.206215 + 0.361250i
\(664\) 0 0
\(665\) 58.5951 33.8299i 2.27222 1.31187i
\(666\) 0 0
\(667\) 22.2296 + 12.8343i 0.860733 + 0.496944i
\(668\) 0 0
\(669\) 2.47559 + 14.4534i 0.0957117 + 0.558801i
\(670\) 0 0
\(671\) 8.62262 + 3.13838i 0.332872 + 0.121156i
\(672\) 0 0
\(673\) 4.78552 27.1400i 0.184468 1.04617i −0.742168 0.670213i \(-0.766203\pi\)
0.926637 0.375958i \(-0.122686\pi\)
\(674\) 0 0
\(675\) 0.395533 0.457551i 0.0152241 0.0176111i
\(676\) 0 0
\(677\) −12.6484 2.23025i −0.486117 0.0857155i −0.0747822 0.997200i \(-0.523826\pi\)
−0.411335 + 0.911484i \(0.634937\pi\)
\(678\) 0 0
\(679\) −23.1865 + 63.7043i −0.889814 + 2.44475i
\(680\) 0 0
\(681\) −20.2278 24.3478i −0.775130 0.933008i
\(682\) 0 0
\(683\) 10.8372 18.7705i 0.414673 0.718234i −0.580721 0.814102i \(-0.697229\pi\)
0.995394 + 0.0958684i \(0.0305628\pi\)
\(684\) 0 0
\(685\) −8.30908 14.3918i −0.317474 0.549881i
\(686\) 0 0
\(687\) −0.110982 + 22.6554i −0.00423422 + 0.864358i
\(688\) 0 0
\(689\) 14.9519 2.63642i 0.569621 0.100440i
\(690\) 0 0
\(691\) −16.6079 + 19.7925i −0.631794 + 0.752943i −0.983050 0.183337i \(-0.941310\pi\)
0.351256 + 0.936279i \(0.385755\pi\)
\(692\) 0 0
\(693\) 20.4097 23.8450i 0.775302 0.905797i
\(694\) 0 0
\(695\) −24.2895 + 8.84067i −0.921354 + 0.335346i
\(696\) 0 0
\(697\) 0.785435 0.659058i 0.0297505 0.0249636i
\(698\) 0 0
\(699\) 44.8877 16.0892i 1.69781 0.608550i
\(700\) 0 0
\(701\) 6.91690i 0.261248i −0.991432 0.130624i \(-0.958302\pi\)
0.991432 0.130624i \(-0.0416980\pi\)
\(702\) 0 0
\(703\) 34.2371i 1.29128i
\(704\) 0 0
\(705\) −16.8586 14.2874i −0.634931 0.538093i
\(706\) 0 0
\(707\) −40.0623 + 33.6162i −1.50670 + 1.26427i
\(708\) 0 0
\(709\) −19.5668 + 7.12175i −0.734848 + 0.267463i −0.682215 0.731151i \(-0.738983\pi\)
−0.0526325 + 0.998614i \(0.516761\pi\)
\(710\) 0 0
\(711\) 3.65265 + 2.15685i 0.136985 + 0.0808881i
\(712\) 0 0
\(713\) 10.4813 12.4912i 0.392529 0.467798i
\(714\) 0 0
\(715\) 6.75209 1.19058i 0.252514 0.0445250i
\(716\) 0 0
\(717\) −22.6539 13.2276i −0.846024 0.493994i
\(718\) 0 0
\(719\) 16.8797 + 29.2366i 0.629508 + 1.09034i 0.987650 + 0.156673i \(0.0500770\pi\)
−0.358142 + 0.933667i \(0.616590\pi\)
\(720\) 0 0
\(721\) −38.9798 + 67.5150i −1.45168 + 2.51439i
\(722\) 0 0
\(723\) −8.47298 + 22.9292i −0.315113 + 0.852746i
\(724\) 0 0
\(725\) −0.394712 + 1.08446i −0.0146592 + 0.0402759i
\(726\) 0 0
\(727\) 6.91332 + 1.21900i 0.256401 + 0.0452104i 0.300371 0.953822i \(-0.402890\pi\)
−0.0439701 + 0.999033i \(0.514001\pi\)
\(728\) 0 0
\(729\) 12.8070 + 23.7693i 0.474334 + 0.880345i
\(730\) 0 0
\(731\) −1.14127 + 6.47245i −0.0422113 + 0.239392i
\(732\) 0 0
\(733\) 9.47228 + 3.44763i 0.349867 + 0.127341i 0.510975 0.859596i \(-0.329285\pi\)
−0.161108 + 0.986937i \(0.551507\pi\)
\(734\) 0 0
\(735\) −44.2803 16.3628i −1.63330 0.603551i
\(736\) 0 0
\(737\) 6.27752 + 3.62433i 0.231236 + 0.133504i
\(738\) 0 0
\(739\) 39.2380 22.6541i 1.44339 0.833344i 0.445319 0.895372i \(-0.353090\pi\)
0.998074 + 0.0620283i \(0.0197569\pi\)
\(740\) 0 0
\(741\) −7.56868 + 12.9623i −0.278042 + 0.476181i
\(742\) 0 0
\(743\) 0.341948 + 1.93929i 0.0125449 + 0.0711455i 0.990438 0.137962i \(-0.0440552\pi\)
−0.977893 + 0.209108i \(0.932944\pi\)
\(744\) 0 0
\(745\) −20.3193 17.0500i −0.744443 0.624662i
\(746\) 0 0
\(747\) 13.6671 23.1455i 0.500055 0.846850i
\(748\) 0 0
\(749\) −24.4636 67.2133i −0.893882 2.45592i
\(750\) 0 0
\(751\) 14.6392 + 17.4463i 0.534191 + 0.636624i 0.963875 0.266355i \(-0.0858195\pi\)
−0.429684 + 0.902979i \(0.641375\pi\)
\(752\) 0 0
\(753\) −0.752659 + 0.888113i −0.0274284 + 0.0323646i
\(754\) 0 0
\(755\) 16.6774 0.606953
\(756\) 0 0
\(757\) −40.2708 −1.46367 −0.731834 0.681483i \(-0.761335\pi\)
−0.731834 + 0.681483i \(0.761335\pi\)
\(758\) 0 0
\(759\) 3.62679 + 10.1185i 0.131644 + 0.367278i
\(760\) 0 0
\(761\) 28.9631 + 34.5168i 1.04991 + 1.25123i 0.967027 + 0.254675i \(0.0819684\pi\)
0.0828832 + 0.996559i \(0.473587\pi\)
\(762\) 0 0
\(763\) −2.37789 6.53321i −0.0860855 0.236518i
\(764\) 0 0
\(765\) −25.2108 21.5788i −0.911499 0.780183i
\(766\) 0 0
\(767\) −7.79656 6.54209i −0.281517 0.236221i
\(768\) 0 0
\(769\) 2.24847 + 12.7517i 0.0810817 + 0.459837i 0.998134 + 0.0610693i \(0.0194511\pi\)
−0.917052 + 0.398768i \(0.869438\pi\)
\(770\) 0 0
\(771\) 20.9301 + 0.102530i 0.753780 + 0.00369253i
\(772\) 0 0
\(773\) 7.17077 4.14005i 0.257915 0.148907i −0.365468 0.930824i \(-0.619091\pi\)
0.623383 + 0.781917i \(0.285758\pi\)
\(774\) 0 0
\(775\) 0.634903 + 0.366561i 0.0228064 + 0.0131673i
\(776\) 0 0
\(777\) 29.0482 24.1328i 1.04210 0.865761i
\(778\) 0 0
\(779\) 1.35025 + 0.491452i 0.0483778 + 0.0176081i
\(780\) 0 0
\(781\) −1.07748 + 6.11069i −0.0385553 + 0.218658i
\(782\) 0 0
\(783\) −38.9752 33.6924i −1.39286 1.20407i
\(784\) 0 0
\(785\) 24.9888 + 4.40620i 0.891888 + 0.157264i
\(786\) 0 0
\(787\) 15.5001 42.5862i 0.552519 1.51803i −0.277741 0.960656i \(-0.589586\pi\)
0.830260 0.557377i \(-0.188192\pi\)
\(788\) 0 0
\(789\) 41.6155 7.12791i 1.48155 0.253760i
\(790\) 0 0
\(791\) 12.9867 22.4936i 0.461753 0.799779i
\(792\) 0 0
\(793\) 2.42020 + 4.19191i 0.0859438 + 0.148859i
\(794\) 0 0
\(795\) −40.8529 + 23.3203i −1.44890 + 0.827087i
\(796\) 0 0
\(797\) −22.2457 + 3.92252i −0.787984 + 0.138943i −0.553138 0.833090i \(-0.686570\pi\)
−0.234846 + 0.972033i \(0.575459\pi\)
\(798\) 0 0
\(799\) −17.7305 + 21.1304i −0.627261 + 0.747541i
\(800\) 0 0
\(801\) −33.9906 41.3239i −1.20100 1.46011i
\(802\) 0 0
\(803\) −19.8836 + 7.23704i −0.701677 + 0.255390i
\(804\) 0 0
\(805\) 19.5789 16.4286i 0.690065 0.579033i
\(806\) 0 0
\(807\) −4.52370 + 24.9402i −0.159242 + 0.877935i
\(808\) 0 0
\(809\) 52.8089i 1.85666i 0.371754 + 0.928331i \(0.378756\pi\)
−0.371754 + 0.928331i \(0.621244\pi\)
\(810\) 0 0
\(811\) 0.900633i 0.0316255i 0.999875 + 0.0158127i \(0.00503356\pi\)
−0.999875 + 0.0158127i \(0.994966\pi\)
\(812\) 0 0
\(813\) −3.56231 + 19.6398i −0.124936 + 0.688797i
\(814\) 0 0
\(815\) 3.69692 3.10208i 0.129497 0.108661i
\(816\) 0 0
\(817\) −8.65518 + 3.15023i −0.302806 + 0.110213i
\(818\) 0 0
\(819\) 16.3327 2.71518i 0.570710 0.0948761i
\(820\) 0 0
\(821\) −2.21658 + 2.64162i −0.0773592 + 0.0921931i −0.803336 0.595526i \(-0.796944\pi\)
0.725977 + 0.687719i \(0.241388\pi\)
\(822\) 0 0
\(823\) 29.9820 5.28664i 1.04511 0.184281i 0.375367 0.926876i \(-0.377517\pi\)
0.669740 + 0.742595i \(0.266405\pi\)
\(824\) 0 0
\(825\) −0.419702 + 0.239581i −0.0146121 + 0.00834115i
\(826\) 0 0
\(827\) −12.4911 21.6352i −0.434358 0.752331i 0.562885 0.826535i \(-0.309692\pi\)
−0.997243 + 0.0742047i \(0.976358\pi\)
\(828\) 0 0
\(829\) 2.77640 4.80887i 0.0964284 0.167019i −0.813775 0.581179i \(-0.802591\pi\)
0.910204 + 0.414161i \(0.135925\pi\)
\(830\) 0 0
\(831\) 2.78588 0.477167i 0.0966411 0.0165527i
\(832\) 0 0
\(833\) −20.1535 + 55.3712i −0.698276 + 1.91850i
\(834\) 0 0
\(835\) −2.15813 0.380537i −0.0746853 0.0131690i
\(836\) 0 0
\(837\) −25.3775 + 20.6664i −0.877175 + 0.714336i
\(838\) 0 0
\(839\) 1.77532 10.0683i 0.0612909 0.347598i −0.938705 0.344722i \(-0.887973\pi\)
0.999996 0.00287636i \(-0.000915576\pi\)
\(840\) 0 0
\(841\) 65.1258 + 23.7039i 2.24572 + 0.817374i
\(842\) 0 0
\(843\) 31.5331 26.1972i 1.08606 0.902281i
\(844\) 0 0
\(845\) −22.3336 12.8943i −0.768298 0.443577i
\(846\) 0 0
\(847\) 19.8586 11.4654i 0.682349 0.393954i
\(848\) 0 0
\(849\) 20.3147 + 0.0995153i 0.697199 + 0.00341536i
\(850\) 0 0
\(851\) 2.24580 + 12.7366i 0.0769850 + 0.436604i
\(852\) 0 0
\(853\) −26.8162 22.5015i −0.918169 0.770435i 0.0554864 0.998459i \(-0.482329\pi\)
−0.973655 + 0.228024i \(0.926773\pi\)
\(854\) 0 0
\(855\) 8.52406 45.7185i 0.291517 1.56354i
\(856\) 0 0
\(857\) −18.4198 50.6079i −0.629207 1.72873i −0.683241 0.730193i \(-0.739430\pi\)
0.0540344 0.998539i \(-0.482792\pi\)
\(858\) 0 0
\(859\) −3.85064 4.58902i −0.131382 0.156575i 0.696342 0.717710i \(-0.254809\pi\)
−0.827725 + 0.561134i \(0.810365\pi\)
\(860\) 0 0
\(861\) −0.534789 1.49202i −0.0182256 0.0508480i
\(862\) 0 0
\(863\) 7.82514 0.266371 0.133185 0.991091i \(-0.457479\pi\)
0.133185 + 0.991091i \(0.457479\pi\)
\(864\) 0 0
\(865\) −18.9514 −0.644368
\(866\) 0 0
\(867\) −7.74367 + 9.13727i −0.262989 + 0.310318i
\(868\) 0 0
\(869\) −2.17870 2.59647i −0.0739073 0.0880793i
\(870\) 0 0
\(871\) 1.30779 + 3.59312i 0.0443127 + 0.121748i
\(872\) 0 0
\(873\) 22.9024 + 40.5811i 0.775127 + 1.37346i
\(874\) 0 0
\(875\) −36.9331 30.9906i −1.24857 1.04767i
\(876\) 0 0
\(877\) −0.226004 1.28173i −0.00763162 0.0432810i 0.980754 0.195247i \(-0.0625508\pi\)
−0.988386 + 0.151966i \(0.951440\pi\)
\(878\) 0 0
\(879\) −2.29293 + 3.92692i −0.0773387 + 0.132452i
\(880\) 0 0
\(881\) 36.9169 21.3140i 1.24376 0.718086i 0.273904 0.961757i \(-0.411685\pi\)
0.969858 + 0.243671i \(0.0783517\pi\)
\(882\) 0 0
\(883\) −17.6250 10.1758i −0.593129 0.342443i 0.173205 0.984886i \(-0.444588\pi\)
−0.766334 + 0.642443i \(0.777921\pi\)
\(884\) 0 0
\(885\) 29.5788 + 10.9302i 0.994281 + 0.367414i
\(886\) 0 0
\(887\) −38.8177 14.1285i −1.30337 0.474388i −0.405278 0.914193i \(-0.632825\pi\)
−0.898093 + 0.439805i \(0.855048\pi\)
\(888\) 0 0
\(889\) 0.436243 2.47406i 0.0146311 0.0829773i
\(890\) 0 0
\(891\) −3.32928 21.3156i −0.111535 0.714099i
\(892\) 0 0
\(893\) −38.0697 6.71271i −1.27395 0.224632i
\(894\) 0 0
\(895\) −7.60018 + 20.8813i −0.254046 + 0.697985i
\(896\) 0 0
\(897\) −1.96536 + 5.31857i −0.0656214 + 0.177582i
\(898\) 0 0
\(899\) 31.2245 54.0825i 1.04140 1.80375i
\(900\) 0 0
\(901\) 29.3585 + 50.8504i 0.978073 + 1.69407i
\(902\) 0 0
\(903\) 8.77359 + 5.12290i 0.291967 + 0.170479i
\(904\) 0 0
\(905\) −30.3951 + 5.35948i −1.01037 + 0.178155i
\(906\) 0 0
\(907\) 9.24815 11.0215i 0.307080 0.365963i −0.590330 0.807162i \(-0.701002\pi\)
0.897409 + 0.441199i \(0.145447\pi\)
\(908\) 0 0
\(909\) −0.352178 + 35.9453i −0.0116810 + 1.19223i
\(910\) 0 0
\(911\) 38.9959 14.1934i 1.29199 0.470247i 0.397613 0.917553i \(-0.369839\pi\)
0.894381 + 0.447306i \(0.147617\pi\)
\(912\) 0 0
\(913\) −16.4529 + 13.8056i −0.544510 + 0.456898i
\(914\) 0 0
\(915\) −11.4411 9.69612i −0.378231 0.320544i
\(916\) 0 0
\(917\) 1.82584i 0.0602946i
\(918\) 0 0
\(919\) 6.14658i 0.202757i −0.994848 0.101379i \(-0.967675\pi\)
0.994848 0.101379i \(-0.0323253\pi\)
\(920\) 0 0
\(921\) −47.9298 + 17.1796i −1.57934 + 0.566087i
\(922\) 0 0
\(923\) −2.50739 + 2.10395i −0.0825316 + 0.0692522i
\(924\) 0 0
\(925\) −0.546405 + 0.198875i −0.0179657 + 0.00653897i
\(926\) 0 0
\(927\) 17.8333 + 50.5315i 0.585722 + 1.65967i
\(928\) 0 0
\(929\) −33.3476 + 39.7422i −1.09410 + 1.30390i −0.144824 + 0.989457i \(0.546262\pi\)
−0.949277 + 0.314441i \(0.898183\pi\)
\(930\) 0 0
\(931\) −81.3248 + 14.3397i −2.66531 + 0.469966i
\(932\) 0 0
\(933\) −0.169716 + 34.6453i −0.00555626 + 1.13424i
\(934\) 0 0
\(935\) 13.2579 + 22.9634i 0.433581 + 0.750985i
\(936\) 0 0
\(937\) −2.59393 + 4.49282i −0.0847400 + 0.146774i −0.905280 0.424815i \(-0.860339\pi\)
0.820540 + 0.571589i \(0.193673\pi\)
\(938\) 0 0
\(939\) −22.3241 26.8710i −0.728519 0.876903i
\(940\) 0 0
\(941\) 2.88354 7.92247i 0.0940008 0.258265i −0.883777 0.467908i \(-0.845008\pi\)
0.977778 + 0.209643i \(0.0672301\pi\)
\(942\) 0 0
\(943\) 0.534545 + 0.0942547i 0.0174072 + 0.00306935i
\(944\) 0 0
\(945\) −44.7978 + 24.9936i −1.45727 + 0.813041i
\(946\) 0 0
\(947\) 9.81475 55.6622i 0.318936 1.80878i −0.230310 0.973117i \(-0.573974\pi\)
0.549246 0.835661i \(-0.314915\pi\)
\(948\) 0 0
\(949\) −10.4887 3.81759i −0.340479 0.123924i
\(950\) 0 0
\(951\) 4.43503 + 25.8934i 0.143816 + 0.839650i
\(952\) 0 0
\(953\) −19.7588 11.4077i −0.640049 0.369532i 0.144584 0.989492i \(-0.453815\pi\)
−0.784633 + 0.619960i \(0.787149\pi\)
\(954\) 0 0
\(955\) 1.79305 1.03522i 0.0580217 0.0334988i
\(956\) 0 0
\(957\) 20.4081 + 35.7511i 0.659699 + 1.15567i
\(958\) 0 0
\(959\) 5.56815 + 31.5785i 0.179805 + 1.01972i
\(960\) 0 0
\(961\) −6.64243 5.57366i −0.214272 0.179796i
\(962\) 0 0
\(963\) −46.0325 17.2670i −1.48338 0.556422i
\(964\) 0 0
\(965\) −2.55702 7.02537i −0.0823135 0.226155i
\(966\) 0 0
\(967\) −5.38006 6.41170i −0.173011 0.206186i 0.672570 0.740033i \(-0.265190\pi\)
−0.845581 + 0.533847i \(0.820746\pi\)
\(968\) 0 0
\(969\) −57.1184 10.3603i −1.83491 0.332820i
\(970\) 0 0
\(971\) −12.7798 −0.410123 −0.205061 0.978749i \(-0.565739\pi\)
−0.205061 + 0.978749i \(0.565739\pi\)
\(972\) 0 0
\(973\) 49.8759 1.59895
\(974\) 0 0
\(975\) −0.250835 0.0454970i −0.00803314 0.00145707i
\(976\) 0 0
\(977\) 24.6162 + 29.3365i 0.787543 + 0.938557i 0.999248 0.0387762i \(-0.0123459\pi\)
−0.211705 + 0.977334i \(0.567902\pi\)
\(978\) 0 0
\(979\) 14.6228 + 40.1759i 0.467348 + 1.28403i
\(980\) 0 0
\(981\) −4.47441 1.67838i −0.142857 0.0535864i
\(982\) 0 0
\(983\) 24.2171 + 20.3206i 0.772407 + 0.648126i 0.941324 0.337504i \(-0.109583\pi\)
−0.168917 + 0.985630i \(0.554027\pi\)
\(984\) 0 0
\(985\) −0.888884 5.04111i −0.0283222 0.160623i
\(986\) 0 0
\(987\) 21.1389 + 37.0315i 0.672860 + 1.17872i
\(988\) 0 0
\(989\) −3.01317 + 1.73966i −0.0958133 + 0.0553178i
\(990\) 0 0
\(991\) −33.3761 19.2697i −1.06023 0.612122i −0.134731 0.990882i \(-0.543017\pi\)
−0.925495 + 0.378760i \(0.876350\pi\)
\(992\) 0 0
\(993\) −6.63647 38.7462i −0.210602 1.22957i
\(994\) 0 0
\(995\) 19.2129 + 6.99291i 0.609088 + 0.221690i
\(996\) 0 0
\(997\) 10.0294 56.8793i 0.317633 1.80139i −0.239428 0.970914i \(-0.576960\pi\)
0.557061 0.830471i \(-0.311929\pi\)
\(998\) 0 0
\(999\) 0.381463 25.9552i 0.0120689 0.821185i
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.191.1 yes 36
4.3 odd 2 432.2.be.b.191.6 yes 36
27.14 odd 18 432.2.be.b.95.6 36
108.95 even 18 inner 432.2.be.c.95.1 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.be.b.95.6 36 27.14 odd 18
432.2.be.b.191.6 yes 36 4.3 odd 2
432.2.be.c.95.1 yes 36 108.95 even 18 inner
432.2.be.c.191.1 yes 36 1.1 even 1 trivial