Properties

Label 432.2.be.a.191.6
Level $432$
Weight $2$
Character 432.191
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 191.6
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.a.95.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.64304 + 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(0.279932 + 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +O(q^{10})\) \(q+(1.64304 + 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(0.279932 + 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +(1.96594 + 1.64962i) q^{11} +(-0.388912 - 2.20563i) q^{13} +(-0.0120279 - 0.0304543i) q^{15} +(-2.75406 + 1.59006i) q^{17} +(4.32292 + 2.49584i) q^{19} +(0.0383846 + 1.41711i) q^{21} +(3.28364 + 1.19515i) q^{23} +(0.868179 - 4.92369i) q^{25} +(2.95469 + 4.27432i) q^{27} +(-5.83580 - 1.02901i) q^{29} +(1.49520 - 4.10802i) q^{31} +(2.32594 + 3.78794i) q^{33} +(0.00773633 - 0.0133997i) q^{35} +(-1.45299 - 2.51666i) q^{37} +(0.569928 - 3.83710i) q^{39} +(-7.87828 + 1.38915i) q^{41} +(-3.41556 + 4.07051i) q^{43} +(-0.00307009 - 0.0566302i) q^{45} +(-5.87609 + 2.13872i) q^{47} +(4.84915 - 4.06892i) q^{49} +(-5.39655 + 1.10300i) q^{51} +0.726185i q^{53} -0.0485155i q^{55} +(5.73473 + 6.47019i) q^{57} +(6.30988 - 5.29462i) q^{59} +(2.02402 - 0.736682i) q^{61} +(-0.713662 + 2.34940i) q^{63} +(-0.0272152 + 0.0324338i) q^{65} +(1.07701 - 0.189906i) q^{67} +(4.74007 + 3.76346i) q^{69} +(-7.43829 - 12.8835i) q^{71} +(4.99594 - 8.65322i) q^{73} +(4.12517 - 7.61395i) q^{75} +(-0.718404 + 1.97380i) q^{77} +(-10.3732 - 1.82907i) q^{79} +(2.51187 + 8.64237i) q^{81} +(-2.22015 + 12.5911i) q^{83} +(0.0564927 + 0.0205617i) q^{85} +(-9.02444 - 4.88936i) q^{87} +(-8.53036 - 4.92500i) q^{89} +(1.58749 - 0.916540i) q^{91} +(4.70831 - 5.93010i) q^{93} +(-0.0163863 - 0.0929313i) q^{95} +(-2.01900 - 1.69414i) q^{97} +(1.74541 + 7.49860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 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
\(3\) 1.64304 + 0.548109i 0.948609 + 0.316451i
\(4\) 0 0
\(5\) −0.0121515 0.0144816i −0.00543433 0.00647639i 0.763320 0.646020i \(-0.223568\pi\)
−0.768755 + 0.639544i \(0.779123\pi\)
\(6\) 0 0
\(7\) 0.279932 + 0.769107i 0.105804 + 0.290695i 0.981286 0.192556i \(-0.0616779\pi\)
−0.875482 + 0.483252i \(0.839456\pi\)
\(8\) 0 0
\(9\) 2.39915 + 1.80113i 0.799718 + 0.600376i
\(10\) 0 0
\(11\) 1.96594 + 1.64962i 0.592753 + 0.497379i 0.889107 0.457699i \(-0.151326\pi\)
−0.296354 + 0.955078i \(0.595771\pi\)
\(12\) 0 0
\(13\) −0.388912 2.20563i −0.107865 0.611731i −0.990037 0.140805i \(-0.955031\pi\)
0.882173 0.470926i \(-0.156080\pi\)
\(14\) 0 0
\(15\) −0.0120279 0.0304543i −0.00310560 0.00786326i
\(16\) 0 0
\(17\) −2.75406 + 1.59006i −0.667957 + 0.385645i −0.795302 0.606213i \(-0.792688\pi\)
0.127345 + 0.991858i \(0.459354\pi\)
\(18\) 0 0
\(19\) 4.32292 + 2.49584i 0.991746 + 0.572585i 0.905796 0.423715i \(-0.139274\pi\)
0.0859503 + 0.996299i \(0.472607\pi\)
\(20\) 0 0
\(21\) 0.0383846 + 1.41711i 0.00837620 + 0.309238i
\(22\) 0 0
\(23\) 3.28364 + 1.19515i 0.684685 + 0.249205i 0.660858 0.750511i \(-0.270193\pi\)
0.0238273 + 0.999716i \(0.492415\pi\)
\(24\) 0 0
\(25\) 0.868179 4.92369i 0.173636 0.984737i
\(26\) 0 0
\(27\) 2.95469 + 4.27432i 0.568629 + 0.822594i
\(28\) 0 0
\(29\) −5.83580 1.02901i −1.08368 0.191082i −0.396839 0.917888i \(-0.629893\pi\)
−0.686843 + 0.726806i \(0.741004\pi\)
\(30\) 0 0
\(31\) 1.49520 4.10802i 0.268545 0.737822i −0.729977 0.683472i \(-0.760469\pi\)
0.998522 0.0543499i \(-0.0173086\pi\)
\(32\) 0 0
\(33\) 2.32594 + 3.78794i 0.404895 + 0.659396i
\(34\) 0 0
\(35\) 0.00773633 0.0133997i 0.00130768 0.00226496i
\(36\) 0 0
\(37\) −1.45299 2.51666i −0.238871 0.413736i 0.721520 0.692394i \(-0.243444\pi\)
−0.960391 + 0.278658i \(0.910111\pi\)
\(38\) 0 0
\(39\) 0.569928 3.83710i 0.0912615 0.614427i
\(40\) 0 0
\(41\) −7.87828 + 1.38915i −1.23038 + 0.216949i −0.750789 0.660543i \(-0.770326\pi\)
−0.479592 + 0.877492i \(0.659215\pi\)
\(42\) 0 0
\(43\) −3.41556 + 4.07051i −0.520868 + 0.620746i −0.960786 0.277292i \(-0.910563\pi\)
0.439918 + 0.898038i \(0.355008\pi\)
\(44\) 0 0
\(45\) −0.00307009 0.0566302i −0.000457662 0.00844193i
\(46\) 0 0
\(47\) −5.87609 + 2.13872i −0.857116 + 0.311965i −0.732938 0.680295i \(-0.761852\pi\)
−0.124178 + 0.992260i \(0.539629\pi\)
\(48\) 0 0
\(49\) 4.84915 4.06892i 0.692735 0.581274i
\(50\) 0 0
\(51\) −5.39655 + 1.10300i −0.755668 + 0.154451i
\(52\) 0 0
\(53\) 0.726185i 0.0997492i 0.998755 + 0.0498746i \(0.0158822\pi\)
−0.998755 + 0.0498746i \(0.984118\pi\)
\(54\) 0 0
\(55\) 0.0485155i 0.00654182i
\(56\) 0 0
\(57\) 5.73473 + 6.47019i 0.759584 + 0.856998i
\(58\) 0 0
\(59\) 6.30988 5.29462i 0.821476 0.689301i −0.131841 0.991271i \(-0.542089\pi\)
0.953317 + 0.301970i \(0.0976443\pi\)
\(60\) 0 0
\(61\) 2.02402 0.736682i 0.259149 0.0943224i −0.209179 0.977877i \(-0.567079\pi\)
0.468327 + 0.883555i \(0.344857\pi\)
\(62\) 0 0
\(63\) −0.713662 + 2.34940i −0.0899129 + 0.295996i
\(64\) 0 0
\(65\) −0.0272152 + 0.0324338i −0.00337563 + 0.00402292i
\(66\) 0 0
\(67\) 1.07701 0.189906i 0.131577 0.0232007i −0.107472 0.994208i \(-0.534275\pi\)
0.239049 + 0.971008i \(0.423164\pi\)
\(68\) 0 0
\(69\) 4.74007 + 3.76346i 0.570637 + 0.453067i
\(70\) 0 0
\(71\) −7.43829 12.8835i −0.882762 1.52899i −0.848257 0.529585i \(-0.822348\pi\)
−0.0345051 0.999405i \(-0.510985\pi\)
\(72\) 0 0
\(73\) 4.99594 8.65322i 0.584730 1.01278i −0.410179 0.912005i \(-0.634534\pi\)
0.994909 0.100777i \(-0.0321329\pi\)
\(74\) 0 0
\(75\) 4.12517 7.61395i 0.476334 0.879183i
\(76\) 0 0
\(77\) −0.718404 + 1.97380i −0.0818698 + 0.224935i
\(78\) 0 0
\(79\) −10.3732 1.82907i −1.16708 0.205787i −0.443657 0.896197i \(-0.646319\pi\)
−0.723418 + 0.690410i \(0.757430\pi\)
\(80\) 0 0
\(81\) 2.51187 + 8.64237i 0.279096 + 0.960263i
\(82\) 0 0
\(83\) −2.22015 + 12.5911i −0.243693 + 1.38205i 0.579816 + 0.814747i \(0.303124\pi\)
−0.823509 + 0.567303i \(0.807987\pi\)
\(84\) 0 0
\(85\) 0.0564927 + 0.0205617i 0.00612749 + 0.00223022i
\(86\) 0 0
\(87\) −9.02444 4.88936i −0.967522 0.524195i
\(88\) 0 0
\(89\) −8.53036 4.92500i −0.904216 0.522049i −0.0256503 0.999671i \(-0.508166\pi\)
−0.878566 + 0.477622i \(0.841499\pi\)
\(90\) 0 0
\(91\) 1.58749 0.916540i 0.166415 0.0960795i
\(92\) 0 0
\(93\) 4.70831 5.93010i 0.488229 0.614923i
\(94\) 0 0
\(95\) −0.0163863 0.0929313i −0.00168120 0.00953455i
\(96\) 0 0
\(97\) −2.01900 1.69414i −0.204998 0.172014i 0.534509 0.845163i \(-0.320497\pi\)
−0.739507 + 0.673149i \(0.764941\pi\)
\(98\) 0 0
\(99\) 1.74541 + 7.49860i 0.175421 + 0.753638i
\(100\) 0 0
\(101\) 4.16372 + 11.4397i 0.414306 + 1.13830i 0.954878 + 0.296998i \(0.0959856\pi\)
−0.540572 + 0.841298i \(0.681792\pi\)
\(102\) 0 0
\(103\) −12.1410 14.4691i −1.19629 1.42568i −0.878645 0.477475i \(-0.841552\pi\)
−0.317646 0.948209i \(-0.602892\pi\)
\(104\) 0 0
\(105\) 0.0200556 0.0177759i 0.00195723 0.00173475i
\(106\) 0 0
\(107\) −11.7933 −1.14010 −0.570051 0.821609i \(-0.693077\pi\)
−0.570051 + 0.821609i \(0.693077\pi\)
\(108\) 0 0
\(109\) −1.02614 −0.0982868 −0.0491434 0.998792i \(-0.515649\pi\)
−0.0491434 + 0.998792i \(0.515649\pi\)
\(110\) 0 0
\(111\) −1.00792 4.93137i −0.0956677 0.468065i
\(112\) 0 0
\(113\) −2.72293 3.24507i −0.256152 0.305270i 0.622608 0.782534i \(-0.286073\pi\)
−0.878760 + 0.477264i \(0.841629\pi\)
\(114\) 0 0
\(115\) −0.0225936 0.0620753i −0.00210686 0.00578855i
\(116\) 0 0
\(117\) 3.03956 5.99212i 0.281008 0.553971i
\(118\) 0 0
\(119\) −1.99387 1.67306i −0.182778 0.153369i
\(120\) 0 0
\(121\) −0.766454 4.34678i −0.0696777 0.395162i
\(122\) 0 0
\(123\) −13.7057 2.03572i −1.23580 0.183555i
\(124\) 0 0
\(125\) −0.163711 + 0.0945188i −0.0146428 + 0.00845402i
\(126\) 0 0
\(127\) 14.2152 + 8.20714i 1.26139 + 0.728266i 0.973344 0.229349i \(-0.0736598\pi\)
0.288050 + 0.957615i \(0.406993\pi\)
\(128\) 0 0
\(129\) −7.84298 + 4.81590i −0.690536 + 0.424016i
\(130\) 0 0
\(131\) 9.07325 + 3.30239i 0.792733 + 0.288531i 0.706472 0.707741i \(-0.250286\pi\)
0.0862615 + 0.996273i \(0.472508\pi\)
\(132\) 0 0
\(133\) −0.709444 + 4.02345i −0.0615166 + 0.348878i
\(134\) 0 0
\(135\) 0.0259952 0.0947283i 0.00223731 0.00815291i
\(136\) 0 0
\(137\) −16.8404 2.96942i −1.43877 0.253695i −0.600797 0.799402i \(-0.705150\pi\)
−0.837976 + 0.545707i \(0.816261\pi\)
\(138\) 0 0
\(139\) 4.99251 13.7168i 0.423459 1.16344i −0.526255 0.850327i \(-0.676404\pi\)
0.949714 0.313118i \(-0.101373\pi\)
\(140\) 0 0
\(141\) −10.8269 + 0.293264i −0.911789 + 0.0246973i
\(142\) 0 0
\(143\) 2.87387 4.97769i 0.240325 0.416255i
\(144\) 0 0
\(145\) 0.0560123 + 0.0970161i 0.00465157 + 0.00805675i
\(146\) 0 0
\(147\) 10.1975 4.02753i 0.841080 0.332185i
\(148\) 0 0
\(149\) 10.9692 1.93417i 0.898633 0.158453i 0.294795 0.955560i \(-0.404749\pi\)
0.603838 + 0.797107i \(0.293637\pi\)
\(150\) 0 0
\(151\) −12.6944 + 15.1286i −1.03305 + 1.23114i −0.0605712 + 0.998164i \(0.519292\pi\)
−0.972481 + 0.232980i \(0.925152\pi\)
\(152\) 0 0
\(153\) −9.47130 1.14563i −0.765709 0.0926185i
\(154\) 0 0
\(155\) −0.0776598 + 0.0282659i −0.00623778 + 0.00227037i
\(156\) 0 0
\(157\) −7.68024 + 6.44449i −0.612950 + 0.514326i −0.895579 0.444903i \(-0.853238\pi\)
0.282629 + 0.959229i \(0.408794\pi\)
\(158\) 0 0
\(159\) −0.398029 + 1.19315i −0.0315657 + 0.0946230i
\(160\) 0 0
\(161\) 2.86003i 0.225402i
\(162\) 0 0
\(163\) 14.1932i 1.11169i 0.831285 + 0.555847i \(0.187606\pi\)
−0.831285 + 0.555847i \(0.812394\pi\)
\(164\) 0 0
\(165\) 0.0265918 0.0797128i 0.00207017 0.00620563i
\(166\) 0 0
\(167\) 8.67488 7.27909i 0.671283 0.563273i −0.242162 0.970236i \(-0.577857\pi\)
0.913445 + 0.406963i \(0.133412\pi\)
\(168\) 0 0
\(169\) 7.50247 2.73067i 0.577113 0.210052i
\(170\) 0 0
\(171\) 5.87602 + 13.7740i 0.449350 + 1.05333i
\(172\) 0 0
\(173\) 16.0703 19.1519i 1.22181 1.45609i 0.372630 0.927980i \(-0.378456\pi\)
0.849175 0.528111i \(-0.177100\pi\)
\(174\) 0 0
\(175\) 4.02987 0.710575i 0.304630 0.0537145i
\(176\) 0 0
\(177\) 13.2694 5.24076i 0.997390 0.393920i
\(178\) 0 0
\(179\) −4.12505 7.14480i −0.308321 0.534027i 0.669674 0.742655i \(-0.266434\pi\)
−0.977995 + 0.208628i \(0.933100\pi\)
\(180\) 0 0
\(181\) −8.58970 + 14.8778i −0.638467 + 1.10586i 0.347302 + 0.937753i \(0.387098\pi\)
−0.985769 + 0.168105i \(0.946235\pi\)
\(182\) 0 0
\(183\) 3.72932 0.101015i 0.275679 0.00746721i
\(184\) 0 0
\(185\) −0.0187892 + 0.0516230i −0.00138141 + 0.00379540i
\(186\) 0 0
\(187\) −8.03730 1.41719i −0.587746 0.103635i
\(188\) 0 0
\(189\) −2.46030 + 3.46899i −0.178961 + 0.252332i
\(190\) 0 0
\(191\) −3.50531 + 19.8796i −0.253635 + 1.43844i 0.545916 + 0.837840i \(0.316182\pi\)
−0.799551 + 0.600598i \(0.794929\pi\)
\(192\) 0 0
\(193\) −0.293430 0.106800i −0.0211216 0.00768763i 0.331438 0.943477i \(-0.392466\pi\)
−0.352559 + 0.935789i \(0.614689\pi\)
\(194\) 0 0
\(195\) −0.0624930 + 0.0383731i −0.00447521 + 0.00274796i
\(196\) 0 0
\(197\) 16.8720 + 9.74108i 1.20208 + 0.694023i 0.961018 0.276486i \(-0.0891699\pi\)
0.241065 + 0.970509i \(0.422503\pi\)
\(198\) 0 0
\(199\) 21.7766 12.5727i 1.54370 0.891257i 0.545101 0.838370i \(-0.316491\pi\)
0.998601 0.0528866i \(-0.0168422\pi\)
\(200\) 0 0
\(201\) 1.87365 + 0.278296i 0.132157 + 0.0196295i
\(202\) 0 0
\(203\) −0.842210 4.77641i −0.0591116 0.335238i
\(204\) 0 0
\(205\) 0.115850 + 0.0972101i 0.00809135 + 0.00678945i
\(206\) 0 0
\(207\) 5.72533 + 8.78159i 0.397938 + 0.610363i
\(208\) 0 0
\(209\) 4.38142 + 12.0378i 0.303069 + 0.832675i
\(210\) 0 0
\(211\) 4.53910 + 5.40949i 0.312485 + 0.372405i 0.899312 0.437307i \(-0.144068\pi\)
−0.586827 + 0.809712i \(0.699623\pi\)
\(212\) 0 0
\(213\) −5.15983 25.2451i −0.353546 1.72976i
\(214\) 0 0
\(215\) 0.100452 0.00685076
\(216\) 0 0
\(217\) 3.57806 0.242894
\(218\) 0 0
\(219\) 12.9514 11.4792i 0.875176 0.775696i
\(220\) 0 0
\(221\) 4.57816 + 5.45603i 0.307960 + 0.367013i
\(222\) 0 0
\(223\) 4.65066 + 12.7776i 0.311431 + 0.855650i 0.992368 + 0.123308i \(0.0393504\pi\)
−0.680937 + 0.732342i \(0.738427\pi\)
\(224\) 0 0
\(225\) 10.9511 10.2490i 0.730073 0.683265i
\(226\) 0 0
\(227\) 13.2797 + 11.1430i 0.881405 + 0.739587i 0.966467 0.256789i \(-0.0826645\pi\)
−0.0850625 + 0.996376i \(0.527109\pi\)
\(228\) 0 0
\(229\) 3.14221 + 17.8204i 0.207643 + 1.17760i 0.893226 + 0.449608i \(0.148436\pi\)
−0.685583 + 0.727995i \(0.740453\pi\)
\(230\) 0 0
\(231\) −2.26222 + 2.84927i −0.148843 + 0.187468i
\(232\) 0 0
\(233\) 5.82383 3.36239i 0.381532 0.220277i −0.296953 0.954892i \(-0.595970\pi\)
0.678484 + 0.734615i \(0.262637\pi\)
\(234\) 0 0
\(235\) 0.102376 + 0.0591067i 0.00667826 + 0.00385569i
\(236\) 0 0
\(237\) −16.0410 8.69088i −1.04198 0.564533i
\(238\) 0 0
\(239\) 24.5175 + 8.92365i 1.58591 + 0.577223i 0.976478 0.215618i \(-0.0691767\pi\)
0.609428 + 0.792841i \(0.291399\pi\)
\(240\) 0 0
\(241\) −1.48013 + 8.39426i −0.0953439 + 0.540722i 0.899298 + 0.437337i \(0.144078\pi\)
−0.994641 + 0.103385i \(0.967033\pi\)
\(242\) 0 0
\(243\) −0.609868 + 15.5765i −0.0391231 + 0.999234i
\(244\) 0 0
\(245\) −0.117849 0.0207800i −0.00752911 0.00132759i
\(246\) 0 0
\(247\) 3.82366 10.5054i 0.243293 0.668443i
\(248\) 0 0
\(249\) −10.5491 + 19.4707i −0.668520 + 1.23391i
\(250\) 0 0
\(251\) −0.283561 + 0.491141i −0.0178982 + 0.0310006i −0.874836 0.484420i \(-0.839031\pi\)
0.856938 + 0.515420i \(0.172364\pi\)
\(252\) 0 0
\(253\) 4.48389 + 7.76633i 0.281900 + 0.488265i
\(254\) 0 0
\(255\) 0.0815496 + 0.0647477i 0.00510684 + 0.00405466i
\(256\) 0 0
\(257\) 10.0178 1.76640i 0.624891 0.110185i 0.147769 0.989022i \(-0.452791\pi\)
0.477123 + 0.878837i \(0.341680\pi\)
\(258\) 0 0
\(259\) 1.52884 1.82200i 0.0949976 0.113214i
\(260\) 0 0
\(261\) −12.1476 12.9798i −0.751918 0.803429i
\(262\) 0 0
\(263\) −17.8324 + 6.49047i −1.09959 + 0.400220i −0.827167 0.561957i \(-0.810049\pi\)
−0.272428 + 0.962176i \(0.587826\pi\)
\(264\) 0 0
\(265\) 0.0105164 0.00882427i 0.000646014 0.000542071i
\(266\) 0 0
\(267\) −11.3163 12.7675i −0.692544 0.781361i
\(268\) 0 0
\(269\) 14.4803i 0.882879i −0.897291 0.441440i \(-0.854468\pi\)
0.897291 0.441440i \(-0.145532\pi\)
\(270\) 0 0
\(271\) 12.8310i 0.779426i 0.920936 + 0.389713i \(0.127426\pi\)
−0.920936 + 0.389713i \(0.872574\pi\)
\(272\) 0 0
\(273\) 3.11068 0.635791i 0.188267 0.0384798i
\(274\) 0 0
\(275\) 9.82900 8.24751i 0.592711 0.497343i
\(276\) 0 0
\(277\) −26.2620 + 9.55859i −1.57793 + 0.574320i −0.974753 0.223286i \(-0.928322\pi\)
−0.603179 + 0.797606i \(0.706099\pi\)
\(278\) 0 0
\(279\) 10.9863 7.16272i 0.657731 0.428821i
\(280\) 0 0
\(281\) 16.2168 19.3264i 0.967414 1.15292i −0.0207912 0.999784i \(-0.506619\pi\)
0.988205 0.153135i \(-0.0489370\pi\)
\(282\) 0 0
\(283\) 0.388602 0.0685210i 0.0231000 0.00407315i −0.162086 0.986777i \(-0.551822\pi\)
0.185186 + 0.982703i \(0.440711\pi\)
\(284\) 0 0
\(285\) 0.0240132 0.161671i 0.00142242 0.00957658i
\(286\) 0 0
\(287\) −3.27379 5.67037i −0.193246 0.334711i
\(288\) 0 0
\(289\) −3.44344 + 5.96422i −0.202555 + 0.350836i
\(290\) 0 0
\(291\) −2.38872 3.89017i −0.140029 0.228046i
\(292\) 0 0
\(293\) 1.92575 5.29095i 0.112503 0.309101i −0.870644 0.491913i \(-0.836298\pi\)
0.983148 + 0.182812i \(0.0585201\pi\)
\(294\) 0 0
\(295\) −0.153350 0.0270397i −0.00892836 0.00157431i
\(296\) 0 0
\(297\) −1.24227 + 13.2772i −0.0720840 + 0.770419i
\(298\) 0 0
\(299\) 1.35900 7.70728i 0.0785931 0.445724i
\(300\) 0 0
\(301\) −4.08678 1.48747i −0.235558 0.0857361i
\(302\) 0 0
\(303\) 0.570934 + 21.0781i 0.0327993 + 1.21091i
\(304\) 0 0
\(305\) −0.0352633 0.0203593i −0.00201917 0.00116577i
\(306\) 0 0
\(307\) −7.95778 + 4.59443i −0.454174 + 0.262218i −0.709592 0.704613i \(-0.751121\pi\)
0.255417 + 0.966831i \(0.417787\pi\)
\(308\) 0 0
\(309\) −12.0175 30.4279i −0.683653 1.73098i
\(310\) 0 0
\(311\) 2.84829 + 16.1535i 0.161512 + 0.915979i 0.952588 + 0.304262i \(0.0984098\pi\)
−0.791077 + 0.611717i \(0.790479\pi\)
\(312\) 0 0
\(313\) 7.80759 + 6.55135i 0.441311 + 0.370304i 0.836200 0.548425i \(-0.184772\pi\)
−0.394889 + 0.918729i \(0.629217\pi\)
\(314\) 0 0
\(315\) 0.0426952 0.0182138i 0.00240560 0.00102623i
\(316\) 0 0
\(317\) 10.8312 + 29.7584i 0.608339 + 1.67140i 0.733856 + 0.679305i \(0.237719\pi\)
−0.125517 + 0.992091i \(0.540059\pi\)
\(318\) 0 0
\(319\) −9.77537 11.6498i −0.547315 0.652265i
\(320\) 0 0
\(321\) −19.3769 6.46402i −1.08151 0.360786i
\(322\) 0 0
\(323\) −15.8741 −0.883259
\(324\) 0 0
\(325\) −11.1975 −0.621123
\(326\) 0 0
\(327\) −1.68600 0.562439i −0.0932357 0.0311030i
\(328\) 0 0
\(329\) −3.28981 3.92065i −0.181373 0.216152i
\(330\) 0 0
\(331\) −5.91684 16.2564i −0.325219 0.893531i −0.989303 0.145874i \(-0.953401\pi\)
0.664085 0.747658i \(-0.268821\pi\)
\(332\) 0 0
\(333\) 1.04688 8.65488i 0.0573684 0.474285i
\(334\) 0 0
\(335\) −0.0158375 0.0132892i −0.000865292 0.000726067i
\(336\) 0 0
\(337\) −0.352302 1.99800i −0.0191911 0.108838i 0.973707 0.227802i \(-0.0731539\pi\)
−0.992899 + 0.118964i \(0.962043\pi\)
\(338\) 0 0
\(339\) −2.69524 6.82424i −0.146385 0.370642i
\(340\) 0 0
\(341\) 9.71613 5.60961i 0.526158 0.303778i
\(342\) 0 0
\(343\) 9.44856 + 5.45513i 0.510174 + 0.294549i
\(344\) 0 0
\(345\) −0.00309805 0.114376i −0.000166794 0.00615779i
\(346\) 0 0
\(347\) −23.1850 8.43866i −1.24464 0.453011i −0.366051 0.930595i \(-0.619290\pi\)
−0.878586 + 0.477584i \(0.841513\pi\)
\(348\) 0 0
\(349\) −2.10358 + 11.9300i −0.112602 + 0.638599i 0.875307 + 0.483567i \(0.160659\pi\)
−0.987910 + 0.155032i \(0.950452\pi\)
\(350\) 0 0
\(351\) 8.27845 8.17927i 0.441871 0.436577i
\(352\) 0 0
\(353\) −17.6612 3.11415i −0.940013 0.165750i −0.317411 0.948288i \(-0.602813\pi\)
−0.622602 + 0.782539i \(0.713924\pi\)
\(354\) 0 0
\(355\) −0.0961875 + 0.264273i −0.00510510 + 0.0140261i
\(356\) 0 0
\(357\) −2.35899 3.84176i −0.124851 0.203327i
\(358\) 0 0
\(359\) 10.8071 18.7185i 0.570378 0.987924i −0.426149 0.904653i \(-0.640130\pi\)
0.996527 0.0832712i \(-0.0265368\pi\)
\(360\) 0 0
\(361\) 2.95843 + 5.12415i 0.155707 + 0.269692i
\(362\) 0 0
\(363\) 1.12320 7.56203i 0.0589525 0.396903i
\(364\) 0 0
\(365\) −0.186021 + 0.0328005i −0.00973679 + 0.00171686i
\(366\) 0 0
\(367\) −9.66580 + 11.5193i −0.504551 + 0.601300i −0.956856 0.290563i \(-0.906157\pi\)
0.452305 + 0.891863i \(0.350602\pi\)
\(368\) 0 0
\(369\) −21.4032 10.8570i −1.11421 0.565193i
\(370\) 0 0
\(371\) −0.558514 + 0.203283i −0.0289966 + 0.0105539i
\(372\) 0 0
\(373\) −5.17790 + 4.34478i −0.268102 + 0.224964i −0.766920 0.641742i \(-0.778212\pi\)
0.498819 + 0.866706i \(0.333767\pi\)
\(374\) 0 0
\(375\) −0.320791 + 0.0655664i −0.0165656 + 0.00338583i
\(376\) 0 0
\(377\) 13.2718i 0.683533i
\(378\) 0 0
\(379\) 12.2938i 0.631488i −0.948844 0.315744i \(-0.897746\pi\)
0.948844 0.315744i \(-0.102254\pi\)
\(380\) 0 0
\(381\) 18.8577 + 21.2761i 0.966109 + 1.09001i
\(382\) 0 0
\(383\) −7.65912 + 6.42677i −0.391363 + 0.328392i −0.817144 0.576434i \(-0.804444\pi\)
0.425781 + 0.904826i \(0.359999\pi\)
\(384\) 0 0
\(385\) 0.0373136 0.0135810i 0.00190168 0.000692154i
\(386\) 0 0
\(387\) −15.5260 + 3.61390i −0.789229 + 0.183705i
\(388\) 0 0
\(389\) 18.8109 22.4180i 0.953752 1.13664i −0.0367756 0.999324i \(-0.511709\pi\)
0.990528 0.137314i \(-0.0438469\pi\)
\(390\) 0 0
\(391\) −10.9437 + 1.92966i −0.553445 + 0.0975873i
\(392\) 0 0
\(393\) 13.0976 + 10.3991i 0.660688 + 0.524565i
\(394\) 0 0
\(395\) 0.0995623 + 0.172447i 0.00500952 + 0.00867675i
\(396\) 0 0
\(397\) 4.05724 7.02735i 0.203627 0.352692i −0.746067 0.665871i \(-0.768060\pi\)
0.949694 + 0.313178i \(0.101394\pi\)
\(398\) 0 0
\(399\) −3.37094 + 6.22184i −0.168758 + 0.311482i
\(400\) 0 0
\(401\) 0.0227239 0.0624334i 0.00113478 0.00311777i −0.939124 0.343579i \(-0.888361\pi\)
0.940259 + 0.340461i \(0.110583\pi\)
\(402\) 0 0
\(403\) −9.64226 1.70019i −0.480315 0.0846925i
\(404\) 0 0
\(405\) 0.0946326 0.141394i 0.00470233 0.00702593i
\(406\) 0 0
\(407\) 1.29503 7.34449i 0.0641923 0.364053i
\(408\) 0 0
\(409\) 17.1419 + 6.23912i 0.847610 + 0.308505i 0.729066 0.684444i \(-0.239955\pi\)
0.118545 + 0.992949i \(0.462177\pi\)
\(410\) 0 0
\(411\) −26.0419 14.1093i −1.28455 0.695958i
\(412\) 0 0
\(413\) 5.83847 + 3.37084i 0.287292 + 0.165868i
\(414\) 0 0
\(415\) 0.209318 0.120850i 0.0102750 0.00593227i
\(416\) 0 0
\(417\) 15.7212 19.8008i 0.769870 0.969649i
\(418\) 0 0
\(419\) −4.45673 25.2754i −0.217726 1.23478i −0.876114 0.482105i \(-0.839872\pi\)
0.658388 0.752679i \(-0.271239\pi\)
\(420\) 0 0
\(421\) 3.64903 + 3.06190i 0.177843 + 0.149228i 0.727364 0.686252i \(-0.240745\pi\)
−0.549521 + 0.835480i \(0.685190\pi\)
\(422\) 0 0
\(423\) −17.9498 5.45248i −0.872747 0.265109i
\(424\) 0 0
\(425\) 5.43792 + 14.9406i 0.263778 + 0.724724i
\(426\) 0 0
\(427\) 1.13317 + 1.35046i 0.0548382 + 0.0653536i
\(428\) 0 0
\(429\) 7.45019 6.60334i 0.359699 0.318812i
\(430\) 0 0
\(431\) −3.71646 −0.179015 −0.0895077 0.995986i \(-0.528529\pi\)
−0.0895077 + 0.995986i \(0.528529\pi\)
\(432\) 0 0
\(433\) −6.80238 −0.326902 −0.163451 0.986551i \(-0.552263\pi\)
−0.163451 + 0.986551i \(0.552263\pi\)
\(434\) 0 0
\(435\) 0.0388549 + 0.190102i 0.00186295 + 0.00911469i
\(436\) 0 0
\(437\) 11.2120 + 13.3619i 0.536343 + 0.639189i
\(438\) 0 0
\(439\) 3.94761 + 10.8460i 0.188409 + 0.517650i 0.997549 0.0699655i \(-0.0222889\pi\)
−0.809140 + 0.587616i \(0.800067\pi\)
\(440\) 0 0
\(441\) 18.9625 1.02801i 0.902976 0.0489530i
\(442\) 0 0
\(443\) −4.43577 3.72205i −0.210750 0.176840i 0.531302 0.847182i \(-0.321703\pi\)
−0.742052 + 0.670342i \(0.766147\pi\)
\(444\) 0 0
\(445\) 0.0323348 + 0.183380i 0.00153282 + 0.00869304i
\(446\) 0 0
\(447\) 19.0830 + 2.83441i 0.902594 + 0.134063i
\(448\) 0 0
\(449\) 9.85789 5.69146i 0.465223 0.268597i −0.249015 0.968500i \(-0.580107\pi\)
0.714238 + 0.699903i \(0.246774\pi\)
\(450\) 0 0
\(451\) −17.7798 10.2652i −0.837218 0.483368i
\(452\) 0 0
\(453\) −29.1494 + 17.8989i −1.36956 + 0.840964i
\(454\) 0 0
\(455\) −0.0325635 0.0118522i −0.00152660 0.000555637i
\(456\) 0 0
\(457\) 4.55553 25.8357i 0.213099 1.20854i −0.671076 0.741388i \(-0.734168\pi\)
0.884175 0.467155i \(-0.154721\pi\)
\(458\) 0 0
\(459\) −14.9338 7.07362i −0.697049 0.330168i
\(460\) 0 0
\(461\) −28.7574 5.07071i −1.33937 0.236167i −0.542365 0.840143i \(-0.682471\pi\)
−0.797002 + 0.603976i \(0.793582\pi\)
\(462\) 0 0
\(463\) −1.28134 + 3.52046i −0.0595491 + 0.163610i −0.965900 0.258917i \(-0.916634\pi\)
0.906351 + 0.422527i \(0.138857\pi\)
\(464\) 0 0
\(465\) −0.143091 + 0.00387584i −0.00663568 + 0.000179738i
\(466\) 0 0
\(467\) −14.4646 + 25.0535i −0.669344 + 1.15934i 0.308744 + 0.951145i \(0.400091\pi\)
−0.978088 + 0.208192i \(0.933242\pi\)
\(468\) 0 0
\(469\) 0.447547 + 0.775174i 0.0206658 + 0.0357942i
\(470\) 0 0
\(471\) −16.1512 + 6.37893i −0.744209 + 0.293926i
\(472\) 0 0
\(473\) −13.4296 + 2.36800i −0.617492 + 0.108881i
\(474\) 0 0
\(475\) 16.0418 19.1179i 0.736048 0.877188i
\(476\) 0 0
\(477\) −1.30795 + 1.74223i −0.0598871 + 0.0797712i
\(478\) 0 0
\(479\) 5.06227 1.84252i 0.231301 0.0841867i −0.223769 0.974642i \(-0.571836\pi\)
0.455071 + 0.890455i \(0.349614\pi\)
\(480\) 0 0
\(481\) −4.98573 + 4.18352i −0.227330 + 0.190752i
\(482\) 0 0
\(483\) −1.56761 + 4.69913i −0.0713286 + 0.213818i
\(484\) 0 0
\(485\) 0.0498248i 0.00226243i
\(486\) 0 0
\(487\) 18.4641i 0.836687i −0.908289 0.418344i \(-0.862611\pi\)
0.908289 0.418344i \(-0.137389\pi\)
\(488\) 0 0
\(489\) −7.77940 + 23.3199i −0.351797 + 1.05456i
\(490\) 0 0
\(491\) 0.307856 0.258322i 0.0138933 0.0116579i −0.635815 0.771842i \(-0.719336\pi\)
0.649708 + 0.760184i \(0.274891\pi\)
\(492\) 0 0
\(493\) 17.7083 6.44530i 0.797543 0.290282i
\(494\) 0 0
\(495\) 0.0873826 0.116396i 0.00392756 0.00523161i
\(496\) 0 0
\(497\) 7.82657 9.32734i 0.351070 0.418388i
\(498\) 0 0
\(499\) 14.1301 2.49152i 0.632551 0.111536i 0.151826 0.988407i \(-0.451485\pi\)
0.480725 + 0.876872i \(0.340374\pi\)
\(500\) 0 0
\(501\) 18.2429 7.20505i 0.815033 0.321898i
\(502\) 0 0
\(503\) 11.8663 + 20.5530i 0.529092 + 0.916414i 0.999424 + 0.0339249i \(0.0108007\pi\)
−0.470332 + 0.882489i \(0.655866\pi\)
\(504\) 0 0
\(505\) 0.115071 0.199308i 0.00512057 0.00886909i
\(506\) 0 0
\(507\) 13.8235 0.374433i 0.613925 0.0166291i
\(508\) 0 0
\(509\) 4.56674 12.5470i 0.202417 0.556137i −0.796399 0.604771i \(-0.793265\pi\)
0.998817 + 0.0486340i \(0.0154868\pi\)
\(510\) 0 0
\(511\) 8.05377 + 1.42010i 0.356278 + 0.0628214i
\(512\) 0 0
\(513\) 2.10485 + 25.8520i 0.0929312 + 1.14139i
\(514\) 0 0
\(515\) −0.0620043 + 0.351644i −0.00273224 + 0.0154953i
\(516\) 0 0
\(517\) −15.0801 5.48872i −0.663223 0.241393i
\(518\) 0 0
\(519\) 36.9015 22.6590i 1.61980 0.994619i
\(520\) 0 0
\(521\) −29.8146 17.2135i −1.30620 0.754136i −0.324742 0.945803i \(-0.605278\pi\)
−0.981460 + 0.191666i \(0.938611\pi\)
\(522\) 0 0
\(523\) −20.7818 + 11.9984i −0.908726 + 0.524653i −0.880021 0.474935i \(-0.842472\pi\)
−0.0287047 + 0.999588i \(0.509138\pi\)
\(524\) 0 0
\(525\) 7.01071 + 1.04131i 0.305973 + 0.0454464i
\(526\) 0 0
\(527\) 2.41412 + 13.6912i 0.105161 + 0.596397i
\(528\) 0 0
\(529\) −8.26514 6.93527i −0.359354 0.301534i
\(530\) 0 0
\(531\) 24.6747 1.33769i 1.07079 0.0580506i
\(532\) 0 0
\(533\) 6.12791 + 16.8363i 0.265429 + 0.729261i
\(534\) 0 0
\(535\) 0.143307 + 0.170786i 0.00619569 + 0.00738374i
\(536\) 0 0
\(537\) −2.86149 14.0002i −0.123482 0.604151i
\(538\) 0 0
\(539\) 16.2453 0.699735
\(540\) 0 0
\(541\) 19.8702 0.854285 0.427142 0.904184i \(-0.359520\pi\)
0.427142 + 0.904184i \(0.359520\pi\)
\(542\) 0 0
\(543\) −22.2679 + 19.7367i −0.955606 + 0.846983i
\(544\) 0 0
\(545\) 0.0124692 + 0.0148603i 0.000534123 + 0.000636543i
\(546\) 0 0
\(547\) −3.06916 8.43244i −0.131228 0.360545i 0.856625 0.515940i \(-0.172557\pi\)
−0.987852 + 0.155395i \(0.950335\pi\)
\(548\) 0 0
\(549\) 6.18278 + 1.87810i 0.263875 + 0.0801555i
\(550\) 0 0
\(551\) −22.6595 19.0136i −0.965326 0.810005i
\(552\) 0 0
\(553\) −1.49704 8.49011i −0.0636604 0.361036i
\(554\) 0 0
\(555\) −0.0591665 + 0.0745201i −0.00251148 + 0.00316320i
\(556\) 0 0
\(557\) −37.9234 + 21.8951i −1.60687 + 0.927724i −0.616799 + 0.787121i \(0.711571\pi\)
−0.990066 + 0.140603i \(0.955096\pi\)
\(558\) 0 0
\(559\) 10.3064 + 5.95038i 0.435913 + 0.251674i
\(560\) 0 0
\(561\) −12.4288 6.73382i −0.524745 0.284302i
\(562\) 0 0
\(563\) −8.31364 3.02592i −0.350378 0.127527i 0.160835 0.986981i \(-0.448581\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(564\) 0 0
\(565\) −0.0139060 + 0.0788651i −0.000585032 + 0.00331788i
\(566\) 0 0
\(567\) −5.94375 + 4.35117i −0.249614 + 0.182732i
\(568\) 0 0
\(569\) −43.9003 7.74081i −1.84040 0.324512i −0.858337 0.513086i \(-0.828502\pi\)
−0.982059 + 0.188574i \(0.939613\pi\)
\(570\) 0 0
\(571\) −13.0832 + 35.9457i −0.547514 + 1.50428i 0.289542 + 0.957165i \(0.406497\pi\)
−0.837056 + 0.547117i \(0.815725\pi\)
\(572\) 0 0
\(573\) −16.6556 + 30.7417i −0.695796 + 1.28425i
\(574\) 0 0
\(575\) 8.73530 15.1300i 0.364287 0.630964i
\(576\) 0 0
\(577\) −14.5146 25.1400i −0.604249 1.04659i −0.992170 0.124897i \(-0.960140\pi\)
0.387921 0.921693i \(-0.373193\pi\)
\(578\) 0 0
\(579\) −0.423580 0.336308i −0.0176034 0.0139765i
\(580\) 0 0
\(581\) −10.3054 + 1.81712i −0.427539 + 0.0753867i
\(582\) 0 0
\(583\) −1.19793 + 1.42764i −0.0496132 + 0.0591267i
\(584\) 0 0
\(585\) −0.123711 + 0.0287956i −0.00511482 + 0.00119055i
\(586\) 0 0
\(587\) 37.6420 13.7006i 1.55365 0.565483i 0.584382 0.811479i \(-0.301337\pi\)
0.969271 + 0.245995i \(0.0791148\pi\)
\(588\) 0 0
\(589\) 16.7166 14.0269i 0.688794 0.577967i
\(590\) 0 0
\(591\) 22.3822 + 25.2527i 0.920683 + 1.03876i
\(592\) 0 0
\(593\) 9.22302i 0.378744i 0.981905 + 0.189372i \(0.0606452\pi\)
−0.981905 + 0.189372i \(0.939355\pi\)
\(594\) 0 0
\(595\) 0.0492048i 0.00201720i
\(596\) 0 0
\(597\) 42.6710 8.72152i 1.74641 0.356948i
\(598\) 0 0
\(599\) −26.2587 + 22.0337i −1.07290 + 0.900272i −0.995312 0.0967135i \(-0.969167\pi\)
−0.0775900 + 0.996985i \(0.524723\pi\)
\(600\) 0 0
\(601\) 7.57807 2.75819i 0.309116 0.112509i −0.182804 0.983149i \(-0.558517\pi\)
0.491920 + 0.870640i \(0.336295\pi\)
\(602\) 0 0
\(603\) 2.92595 + 1.48422i 0.119154 + 0.0604420i
\(604\) 0 0
\(605\) −0.0536349 + 0.0639196i −0.00218057 + 0.00259870i
\(606\) 0 0
\(607\) −1.42100 + 0.250561i −0.0576767 + 0.0101700i −0.202412 0.979300i \(-0.564878\pi\)
0.144735 + 0.989470i \(0.453767\pi\)
\(608\) 0 0
\(609\) 1.23421 8.30945i 0.0500128 0.336716i
\(610\) 0 0
\(611\) 7.00250 + 12.1287i 0.283291 + 0.490674i
\(612\) 0 0
\(613\) 5.58677 9.67657i 0.225648 0.390833i −0.730866 0.682521i \(-0.760884\pi\)
0.956514 + 0.291688i \(0.0942169\pi\)
\(614\) 0 0
\(615\) 0.137065 + 0.223219i 0.00552700 + 0.00900104i
\(616\) 0 0
\(617\) −2.31899 + 6.37137i −0.0933590 + 0.256502i −0.977579 0.210569i \(-0.932468\pi\)
0.884220 + 0.467071i \(0.154691\pi\)
\(618\) 0 0
\(619\) 32.9943 + 5.81778i 1.32615 + 0.233836i 0.791466 0.611214i \(-0.209318\pi\)
0.534687 + 0.845050i \(0.320430\pi\)
\(620\) 0 0
\(621\) 4.59367 + 17.5666i 0.184338 + 0.704923i
\(622\) 0 0
\(623\) 1.39993 7.93942i 0.0560872 0.318086i
\(624\) 0 0
\(625\) −23.4873 8.54867i −0.939491 0.341947i
\(626\) 0 0
\(627\) 0.600785 + 22.1801i 0.0239930 + 0.885790i
\(628\) 0 0
\(629\) 8.00326 + 4.62068i 0.319111 + 0.184239i
\(630\) 0 0
\(631\) −1.26037 + 0.727676i −0.0501746 + 0.0289683i −0.524877 0.851178i \(-0.675889\pi\)
0.474703 + 0.880146i \(0.342556\pi\)
\(632\) 0 0
\(633\) 4.49293 + 11.3759i 0.178578 + 0.452153i
\(634\) 0 0
\(635\) −0.0538835 0.305589i −0.00213830 0.0121269i
\(636\) 0 0
\(637\) −10.8604 9.11296i −0.430305 0.361069i
\(638\) 0 0
\(639\) 5.35925 44.3068i 0.212009 1.75275i
\(640\) 0 0
\(641\) 10.6661 + 29.3049i 0.421286 + 1.15747i 0.950971 + 0.309279i \(0.100088\pi\)
−0.529686 + 0.848194i \(0.677690\pi\)
\(642\) 0 0
\(643\) 28.8010 + 34.3237i 1.13580 + 1.35360i 0.926745 + 0.375692i \(0.122595\pi\)
0.209057 + 0.977904i \(0.432961\pi\)
\(644\) 0 0
\(645\) 0.165046 + 0.0550586i 0.00649870 + 0.00216793i
\(646\) 0 0
\(647\) 38.8651 1.52794 0.763972 0.645250i \(-0.223247\pi\)
0.763972 + 0.645250i \(0.223247\pi\)
\(648\) 0 0
\(649\) 21.1390 0.829777
\(650\) 0 0
\(651\) 5.87889 + 1.96117i 0.230412 + 0.0768642i
\(652\) 0 0
\(653\) −16.7376 19.9471i −0.654993 0.780591i 0.331665 0.943397i \(-0.392390\pi\)
−0.986658 + 0.162807i \(0.947945\pi\)
\(654\) 0 0
\(655\) −0.0624299 0.171525i −0.00243934 0.00670202i
\(656\) 0 0
\(657\) 27.5716 11.7621i 1.07567 0.458882i
\(658\) 0 0
\(659\) 16.9364 + 14.2113i 0.659747 + 0.553593i 0.910011 0.414584i \(-0.136073\pi\)
−0.250264 + 0.968178i \(0.580517\pi\)
\(660\) 0 0
\(661\) −4.73444 26.8503i −0.184148 1.04436i −0.927045 0.374951i \(-0.877660\pi\)
0.742896 0.669406i \(-0.233452\pi\)
\(662\) 0 0
\(663\) 4.53158 + 11.4738i 0.175992 + 0.445606i
\(664\) 0 0
\(665\) 0.0668871 0.0386173i 0.00259377 0.00149751i
\(666\) 0 0
\(667\) −17.9328 10.3535i −0.694362 0.400890i
\(668\) 0 0
\(669\) 0.637703 + 23.5431i 0.0246550 + 0.910230i
\(670\) 0 0
\(671\) 5.19434 + 1.89059i 0.200525 + 0.0729852i
\(672\) 0 0
\(673\) −2.18086 + 12.3683i −0.0840660 + 0.476762i 0.913488 + 0.406865i \(0.133378\pi\)
−0.997554 + 0.0698969i \(0.977733\pi\)
\(674\) 0 0
\(675\) 23.6106 10.8371i 0.908773 0.417119i
\(676\) 0 0
\(677\) −23.5891 4.15940i −0.906604 0.159859i −0.299143 0.954208i \(-0.596701\pi\)
−0.607461 + 0.794350i \(0.707812\pi\)
\(678\) 0 0
\(679\) 0.737793 2.02707i 0.0283139 0.0777918i
\(680\) 0 0
\(681\) 15.7115 + 25.5871i 0.602066 + 0.980500i
\(682\) 0 0
\(683\) −13.0186 + 22.5489i −0.498143 + 0.862809i −0.999998 0.00214274i \(-0.999318\pi\)
0.501855 + 0.864952i \(0.332651\pi\)
\(684\) 0 0
\(685\) 0.161635 + 0.279960i 0.00617575 + 0.0106967i
\(686\) 0 0
\(687\) −4.60473 + 31.0018i −0.175681 + 1.18279i
\(688\) 0 0
\(689\) 1.60169 0.282422i 0.0610197 0.0107594i
\(690\) 0 0
\(691\) 29.2057 34.8060i 1.11104 1.32408i 0.170128 0.985422i \(-0.445582\pi\)
0.940909 0.338660i \(-0.109974\pi\)
\(692\) 0 0
\(693\) −5.27863 + 3.44151i −0.200519 + 0.130732i
\(694\) 0 0
\(695\) −0.259309 + 0.0943806i −0.00983613 + 0.00358006i
\(696\) 0 0
\(697\) 19.4884 16.3527i 0.738176 0.619403i
\(698\) 0 0
\(699\) 11.4117 2.33244i 0.431631 0.0882210i
\(700\) 0 0
\(701\) 24.3025i 0.917892i −0.888464 0.458946i \(-0.848227\pi\)
0.888464 0.458946i \(-0.151773\pi\)
\(702\) 0 0
\(703\) 14.5058i 0.547095i
\(704\) 0 0
\(705\) 0.135810 + 0.153228i 0.00511492 + 0.00577089i
\(706\) 0 0
\(707\) −7.63282 + 6.40470i −0.287062 + 0.240873i
\(708\) 0 0
\(709\) 26.4183 9.61548i 0.992160 0.361117i 0.205604 0.978635i \(-0.434084\pi\)
0.786556 + 0.617518i \(0.211862\pi\)
\(710\) 0 0
\(711\) −21.5925 23.0717i −0.809781 0.865256i
\(712\) 0 0
\(713\) 9.81936 11.7023i 0.367738 0.438253i
\(714\) 0 0
\(715\) −0.107007 + 0.0188682i −0.00400184 + 0.000705632i
\(716\) 0 0
\(717\) 35.3921 + 28.1002i 1.32174 + 1.04942i
\(718\) 0 0
\(719\) 3.70047 + 6.40940i 0.138004 + 0.239030i 0.926741 0.375701i \(-0.122598\pi\)
−0.788737 + 0.614731i \(0.789265\pi\)
\(720\) 0 0
\(721\) 7.72964 13.3881i 0.287867 0.498600i
\(722\) 0 0
\(723\) −7.03289 + 12.9808i −0.261556 + 0.482762i
\(724\) 0 0
\(725\) −10.1330 + 27.8403i −0.376332 + 1.03396i
\(726\) 0 0
\(727\) 24.3136 + 4.28714i 0.901740 + 0.159001i 0.605251 0.796035i \(-0.293073\pi\)
0.296489 + 0.955036i \(0.404184\pi\)
\(728\) 0 0
\(729\) −9.53967 + 25.2586i −0.353321 + 0.935502i
\(730\) 0 0
\(731\) 2.93432 16.6413i 0.108530 0.615502i
\(732\) 0 0
\(733\) 40.8883 + 14.8821i 1.51024 + 0.549684i 0.958689 0.284455i \(-0.0918126\pi\)
0.551555 + 0.834139i \(0.314035\pi\)
\(734\) 0 0
\(735\) −0.182241 0.0987366i −0.00672207 0.00364195i
\(736\) 0 0
\(737\) 2.43061 + 1.40331i 0.0895325 + 0.0516916i
\(738\) 0 0
\(739\) −21.6332 + 12.4899i −0.795790 + 0.459450i −0.841997 0.539482i \(-0.818620\pi\)
0.0462069 + 0.998932i \(0.485287\pi\)
\(740\) 0 0
\(741\) 12.0405 15.1650i 0.442320 0.557101i
\(742\) 0 0
\(743\) 2.72865 + 15.4750i 0.100105 + 0.567721i 0.993063 + 0.117582i \(0.0375144\pi\)
−0.892959 + 0.450139i \(0.851374\pi\)
\(744\) 0 0
\(745\) −0.161303 0.135349i −0.00590968 0.00495881i
\(746\) 0 0
\(747\) −28.0046 + 26.2091i −1.02464 + 0.958942i
\(748\) 0 0
\(749\) −3.30132 9.07031i −0.120628 0.331422i
\(750\) 0 0
\(751\) 15.6810 + 18.6879i 0.572207 + 0.681930i 0.972082 0.234639i \(-0.0753909\pi\)
−0.399875 + 0.916570i \(0.630947\pi\)
\(752\) 0 0
\(753\) −0.735100 + 0.651542i −0.0267885 + 0.0237435i
\(754\) 0 0
\(755\) 0.373342 0.0135873
\(756\) 0 0
\(757\) −30.3936 −1.10467 −0.552337 0.833621i \(-0.686264\pi\)
−0.552337 + 0.833621i \(0.686264\pi\)
\(758\) 0 0
\(759\) 3.11041 + 15.2180i 0.112901 + 0.552380i
\(760\) 0 0
\(761\) −1.89198 2.25477i −0.0685841 0.0817354i 0.730661 0.682740i \(-0.239212\pi\)
−0.799246 + 0.601005i \(0.794767\pi\)
\(762\) 0 0
\(763\) −0.287251 0.789215i −0.0103992 0.0285715i
\(764\) 0 0
\(765\) 0.0985003 + 0.151081i 0.00356129 + 0.00546235i
\(766\) 0 0
\(767\) −14.1319 11.8581i −0.510275 0.428171i
\(768\) 0 0
\(769\) 4.08145 + 23.1471i 0.147181 + 0.834705i 0.965590 + 0.260069i \(0.0837453\pi\)
−0.818409 + 0.574636i \(0.805144\pi\)
\(770\) 0 0
\(771\) 17.4278 + 2.58856i 0.627646 + 0.0932248i
\(772\) 0 0
\(773\) −19.3318 + 11.1612i −0.695317 + 0.401441i −0.805601 0.592459i \(-0.798157\pi\)
0.110284 + 0.993900i \(0.464824\pi\)
\(774\) 0 0
\(775\) −18.9285 10.9284i −0.679932 0.392559i
\(776\) 0 0
\(777\) 3.51060 2.15565i 0.125942 0.0773334i
\(778\) 0 0
\(779\) −37.5243 13.6577i −1.34445 0.489339i
\(780\) 0 0
\(781\) 6.62963 37.5985i 0.237227 1.34538i
\(782\) 0 0
\(783\) −12.8446 27.9845i −0.459030 1.00008i
\(784\) 0 0
\(785\) 0.186654 + 0.0329121i 0.00666195 + 0.00117468i
\(786\) 0 0
\(787\) −9.01696 + 24.7739i −0.321420 + 0.883094i 0.668783 + 0.743458i \(0.266816\pi\)
−0.990203 + 0.139636i \(0.955407\pi\)
\(788\) 0 0
\(789\) −32.8568 + 0.889980i −1.16973 + 0.0316841i
\(790\) 0 0
\(791\) 1.73357 3.00263i 0.0616385 0.106761i
\(792\) 0 0
\(793\) −2.41201 4.17772i −0.0856529 0.148355i
\(794\) 0 0
\(795\) 0.0221154 0.00873450i 0.000784354 0.000309781i
\(796\) 0 0
\(797\) −26.6755 + 4.70360i −0.944893 + 0.166610i −0.624808 0.780779i \(-0.714823\pi\)
−0.320085 + 0.947389i \(0.603712\pi\)
\(798\) 0 0
\(799\) 12.7824 15.2335i 0.452209 0.538922i
\(800\) 0 0
\(801\) −11.5951 27.1801i −0.409691 0.960362i
\(802\) 0 0
\(803\) 24.0962 8.77031i 0.850337 0.309497i
\(804\) 0 0
\(805\) 0.0414179 0.0347537i 0.00145979 0.00122491i
\(806\) 0 0
\(807\) 7.93678 23.7917i 0.279388 0.837507i
\(808\) 0 0
\(809\) 4.56330i 0.160437i 0.996777 + 0.0802186i \(0.0255618\pi\)
−0.996777 + 0.0802186i \(0.974438\pi\)
\(810\) 0 0
\(811\) 8.56935i 0.300910i −0.988617 0.150455i \(-0.951926\pi\)
0.988617 0.150455i \(-0.0480739\pi\)
\(812\) 0 0
\(813\) −7.03278 + 21.0818i −0.246650 + 0.739371i
\(814\) 0 0
\(815\) 0.205540 0.172469i 0.00719976 0.00604132i
\(816\) 0 0
\(817\) −24.9245 + 9.07179i −0.871999 + 0.317382i
\(818\) 0 0
\(819\) 5.45945 + 0.660363i 0.190769 + 0.0230749i
\(820\) 0 0
\(821\) −0.839182 + 1.00010i −0.0292876 + 0.0349036i −0.780489 0.625169i \(-0.785030\pi\)
0.751202 + 0.660073i \(0.229475\pi\)
\(822\) 0 0
\(823\) −43.8415 + 7.73043i −1.52822 + 0.269466i −0.873656 0.486543i \(-0.838258\pi\)
−0.654561 + 0.756009i \(0.727146\pi\)
\(824\) 0 0
\(825\) 20.6700 8.16361i 0.719636 0.284220i
\(826\) 0 0
\(827\) 19.6573 + 34.0474i 0.683551 + 1.18395i 0.973890 + 0.227022i \(0.0728988\pi\)
−0.290338 + 0.956924i \(0.593768\pi\)
\(828\) 0 0
\(829\) 7.32657 12.6900i 0.254462 0.440741i −0.710287 0.703912i \(-0.751435\pi\)
0.964749 + 0.263171i \(0.0847682\pi\)
\(830\) 0 0
\(831\) −48.3887 + 1.31068i −1.67858 + 0.0454671i
\(832\) 0 0
\(833\) −6.88503 + 18.9165i −0.238552 + 0.655416i
\(834\) 0 0
\(835\) −0.210826 0.0371744i −0.00729595 0.00128647i
\(836\) 0 0
\(837\) 21.9768 5.74695i 0.759630 0.198644i
\(838\) 0 0
\(839\) 9.70590 55.0449i 0.335085 1.90036i −0.0913093 0.995823i \(-0.529105\pi\)
0.426394 0.904537i \(-0.359784\pi\)
\(840\) 0 0
\(841\) 5.74666 + 2.09161i 0.198161 + 0.0721247i
\(842\) 0 0
\(843\) 37.2379 22.8655i 1.28254 0.787530i
\(844\) 0 0
\(845\) −0.130711 0.0754661i −0.00449660 0.00259611i
\(846\) 0 0
\(847\) 3.12858 1.80629i 0.107499 0.0620648i
\(848\) 0 0
\(849\) 0.676045 + 0.100414i 0.0232018 + 0.00344619i
\(850\) 0 0
\(851\) −1.76333 10.0003i −0.0604461 0.342807i
\(852\) 0 0
\(853\) −9.56047 8.02219i −0.327344 0.274674i 0.464272 0.885692i \(-0.346316\pi\)
−0.791617 + 0.611018i \(0.790760\pi\)
\(854\) 0 0
\(855\) 0.128068 0.252470i 0.00437984 0.00863430i
\(856\) 0 0
\(857\) 9.13210 + 25.0902i 0.311946 + 0.857066i 0.992264 + 0.124148i \(0.0396198\pi\)
−0.680317 + 0.732918i \(0.738158\pi\)
\(858\) 0 0
\(859\) 5.19720 + 6.19378i 0.177326 + 0.211329i 0.847385 0.530979i \(-0.178176\pi\)
−0.670059 + 0.742308i \(0.733731\pi\)
\(860\) 0 0
\(861\) −2.27098 11.1110i −0.0773948 0.378663i
\(862\) 0 0
\(863\) 6.46547 0.220087 0.110044 0.993927i \(-0.464901\pi\)
0.110044 + 0.993927i \(0.464901\pi\)
\(864\) 0 0
\(865\) −0.472630 −0.0160699
\(866\) 0 0
\(867\) −8.92675 + 7.91206i −0.303168 + 0.268708i
\(868\) 0 0
\(869\) −17.3758 20.7077i −0.589434 0.702460i
\(870\) 0 0
\(871\) −0.837722 2.30162i −0.0283851 0.0779875i
\(872\) 0 0
\(873\) −1.79252 7.70098i −0.0606676 0.260639i
\(874\) 0 0
\(875\) −0.118523 0.0994528i −0.00400681 0.00336212i
\(876\) 0 0
\(877\) −5.28234 29.9577i −0.178372 1.01160i −0.934179 0.356804i \(-0.883866\pi\)
0.755807 0.654794i \(-0.227245\pi\)
\(878\) 0 0
\(879\) 6.06410 7.63772i 0.204537 0.257614i
\(880\) 0 0
\(881\) 33.5819 19.3885i 1.13140 0.653215i 0.187115 0.982338i \(-0.440086\pi\)
0.944287 + 0.329123i \(0.106753\pi\)
\(882\) 0 0
\(883\) −31.7600 18.3366i −1.06881 0.617077i −0.140953 0.990016i \(-0.545017\pi\)
−0.927856 + 0.372939i \(0.878350\pi\)
\(884\) 0 0
\(885\) −0.237139 0.128480i −0.00797133 0.00431879i
\(886\) 0 0
\(887\) −43.9814 16.0079i −1.47675 0.537493i −0.526826 0.849973i \(-0.676618\pi\)
−0.949924 + 0.312480i \(0.898840\pi\)
\(888\) 0 0
\(889\) −2.33288 + 13.2304i −0.0782424 + 0.443735i
\(890\) 0 0
\(891\) −9.31844 + 21.1340i −0.312180 + 0.708016i
\(892\) 0 0
\(893\) −30.7398 5.42025i −1.02867 0.181382i
\(894\) 0 0
\(895\) −0.0533427 + 0.146558i −0.00178305 + 0.00489889i
\(896\) 0 0
\(897\) 6.45732 11.9185i 0.215604 0.397946i
\(898\) 0 0
\(899\) −12.9529 + 22.4350i −0.432002 + 0.748250i
\(900\) 0 0
\(901\) −1.15468 1.99996i −0.0384678 0.0666282i
\(902\) 0 0
\(903\) −5.89944 4.68397i −0.196321 0.155873i
\(904\) 0 0
\(905\) 0.319833 0.0563952i 0.0106316 0.00187464i
\(906\) 0 0
\(907\) −4.25828 + 5.07482i −0.141394 + 0.168507i −0.832094 0.554635i \(-0.812858\pi\)
0.690700 + 0.723141i \(0.257302\pi\)
\(908\) 0 0
\(909\) −10.6150 + 34.9451i −0.352078 + 1.15905i
\(910\) 0 0
\(911\) −39.1498 + 14.2494i −1.29709 + 0.472102i −0.896048 0.443957i \(-0.853574\pi\)
−0.401042 + 0.916060i \(0.631352\pi\)
\(912\) 0 0
\(913\) −25.1352 + 21.0909i −0.831852 + 0.698007i
\(914\) 0 0
\(915\) −0.0467798 0.0527792i −0.00154649 0.00174483i
\(916\) 0 0
\(917\) 7.90274i 0.260972i
\(918\) 0 0
\(919\) 9.73291i 0.321059i −0.987031 0.160530i \(-0.948680\pi\)
0.987031 0.160530i \(-0.0513202\pi\)
\(920\) 0 0
\(921\) −15.5932 + 3.18709i −0.513813 + 0.105018i
\(922\) 0 0
\(923\) −25.5233 + 21.4166i −0.840111 + 0.704937i
\(924\) 0 0
\(925\) −13.6527 + 4.96918i −0.448898 + 0.163386i
\(926\) 0 0
\(927\) −3.06743 56.5812i −0.100748 1.85837i
\(928\) 0 0
\(929\) 29.1284 34.7139i 0.955673 1.13893i −0.0345463 0.999403i \(-0.510999\pi\)
0.990219 0.139523i \(-0.0445569\pi\)
\(930\) 0 0
\(931\) 31.1178 5.48692i 1.01985 0.179826i
\(932\) 0 0
\(933\) −4.17401 + 28.1019i −0.136651 + 0.920016i
\(934\) 0 0
\(935\) 0.0771423 + 0.133614i 0.00252282 + 0.00436966i
\(936\) 0 0
\(937\) −7.91764 + 13.7138i −0.258658 + 0.448009i −0.965883 0.258980i \(-0.916614\pi\)
0.707225 + 0.706989i \(0.249947\pi\)
\(938\) 0 0
\(939\) 9.23732 + 15.0435i 0.301449 + 0.490927i
\(940\) 0 0
\(941\) 4.47054 12.2827i 0.145736 0.400405i −0.845250 0.534370i \(-0.820549\pi\)
0.990986 + 0.133965i \(0.0427710\pi\)
\(942\) 0 0
\(943\) −27.5296 4.85422i −0.896488 0.158075i
\(944\) 0 0
\(945\) 0.0801331 0.00652437i 0.00260673 0.000212238i
\(946\) 0 0
\(947\) 4.92733 27.9443i 0.160117 0.908066i −0.793841 0.608125i \(-0.791922\pi\)
0.953958 0.299941i \(-0.0969670\pi\)
\(948\) 0 0
\(949\) −21.0287 7.65384i −0.682622 0.248454i
\(950\) 0 0
\(951\) 1.48518 + 54.8308i 0.0481603 + 1.77801i
\(952\) 0 0
\(953\) −15.7197 9.07579i −0.509212 0.293994i 0.223298 0.974750i \(-0.428318\pi\)
−0.732510 + 0.680757i \(0.761651\pi\)
\(954\) 0 0
\(955\) 0.330484 0.190805i 0.0106942 0.00617431i
\(956\) 0 0
\(957\) −9.67593 24.4991i −0.312778 0.791943i
\(958\) 0 0
\(959\) −2.43037 13.7833i −0.0784807 0.445086i
\(960\) 0 0
\(961\) 9.10718 + 7.64183i 0.293780 + 0.246511i
\(962\) 0 0
\(963\) −28.2939 21.2413i −0.911759 0.684490i
\(964\) 0 0
\(965\) 0.00201899 + 0.00554714i 6.49937e−5 + 0.000178569i
\(966\) 0 0
\(967\) −18.4550 21.9938i −0.593472 0.707273i 0.382797 0.923832i \(-0.374961\pi\)
−0.976269 + 0.216560i \(0.930516\pi\)
\(968\) 0 0
\(969\) −26.0818 8.70074i −0.837867 0.279508i
\(970\) 0 0
\(971\) 16.9148 0.542821 0.271410 0.962464i \(-0.412510\pi\)
0.271410 + 0.962464i \(0.412510\pi\)
\(972\) 0 0
\(973\) 11.9473 0.383011
\(974\) 0 0
\(975\) −18.3979 6.13743i −0.589203 0.196555i
\(976\) 0 0
\(977\) 25.0203 + 29.8180i 0.800469 + 0.953962i 0.999662 0.0259984i \(-0.00827649\pi\)
−0.199193 + 0.979960i \(0.563832\pi\)
\(978\) 0 0
\(979\) −8.64579 23.7541i −0.276321 0.759184i
\(980\) 0 0
\(981\) −2.46188 1.84822i −0.0786017 0.0590091i
\(982\) 0 0
\(983\) −10.9915 9.22298i −0.350575 0.294168i 0.450446 0.892804i \(-0.351265\pi\)
−0.801021 + 0.598636i \(0.795710\pi\)
\(984\) 0 0
\(985\) −0.0639545 0.362704i −0.00203776 0.0115567i
\(986\) 0 0
\(987\) −3.25635 8.24495i −0.103651 0.262440i
\(988\) 0 0
\(989\) −16.0803 + 9.28397i −0.511324 + 0.295213i
\(990\) 0 0
\(991\) −49.1415 28.3719i −1.56103 0.901262i −0.997153 0.0754050i \(-0.975975\pi\)
−0.563879 0.825857i \(-0.690692\pi\)
\(992\) 0 0
\(993\) −0.811323 29.9529i −0.0257465 0.950527i
\(994\) 0 0
\(995\) −0.446693 0.162583i −0.0141611 0.00515422i
\(996\) 0 0
\(997\) −1.69129 + 9.59179i −0.0535637 + 0.303775i −0.999806 0.0196829i \(-0.993734\pi\)
0.946243 + 0.323458i \(0.104845\pi\)
\(998\) 0 0
\(999\) 6.46388 13.6465i 0.204508 0.431756i
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.a.191.6 yes 36
4.3 odd 2 inner 432.2.be.a.191.1 yes 36
27.14 odd 18 inner 432.2.be.a.95.1 36
108.95 even 18 inner 432.2.be.a.95.6 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.be.a.95.1 36 27.14 odd 18 inner
432.2.be.a.95.6 yes 36 108.95 even 18 inner
432.2.be.a.191.1 yes 36 4.3 odd 2 inner
432.2.be.a.191.6 yes 36 1.1 even 1 trivial