Properties

Label 864.2.y.c.193.5
Level $864$
Weight $2$
Character 864.193
Analytic conductor $6.899$
Analytic rank $0$
Dimension $54$
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] = [864,2,Mod(97,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.y (of order \(9\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 193.5
Character \(\chi\) \(=\) 864.193
Dual form 864.2.y.c.385.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0599758 - 1.73101i) q^{3} +(0.392840 - 2.22791i) q^{5} +(3.55853 - 2.98596i) q^{7} +(-2.99281 - 0.207638i) q^{9} +O(q^{10})\) \(q+(0.0599758 - 1.73101i) q^{3} +(0.392840 - 2.22791i) q^{5} +(3.55853 - 2.98596i) q^{7} +(-2.99281 - 0.207638i) q^{9} +(-0.0857584 - 0.486360i) q^{11} +(-1.29725 + 0.472162i) q^{13} +(-3.83297 - 0.813631i) q^{15} +(2.34912 - 4.06879i) q^{17} +(0.368407 + 0.638099i) q^{19} +(-4.95531 - 6.33894i) q^{21} +(3.71710 + 3.11901i) q^{23} +(-0.110777 - 0.0403195i) q^{25} +(-0.538919 + 5.16813i) q^{27} +(-6.04895 - 2.20164i) q^{29} +(7.95399 + 6.67419i) q^{31} +(-0.847039 + 0.119279i) q^{33} +(-5.25451 - 9.10107i) q^{35} +(-3.34064 + 5.78616i) q^{37} +(0.739514 + 2.27388i) q^{39} +(-6.29948 + 2.29282i) q^{41} +(0.00111724 + 0.00633619i) q^{43} +(-1.63829 + 6.58612i) q^{45} +(-7.24088 + 6.07582i) q^{47} +(2.53163 - 14.3576i) q^{49} +(-6.90224 - 4.31038i) q^{51} +4.89390 q^{53} -1.11725 q^{55} +(1.12665 - 0.599446i) q^{57} +(1.96490 - 11.1435i) q^{59} +(-5.09432 + 4.27464i) q^{61} +(-11.2700 + 8.19752i) q^{63} +(0.542319 + 3.07564i) q^{65} +(6.31410 - 2.29815i) q^{67} +(5.62199 - 6.24727i) q^{69} +(4.36994 - 7.56897i) q^{71} +(-8.06930 - 13.9764i) q^{73} +(-0.0764375 + 0.189338i) q^{75} +(-1.75743 - 1.47466i) q^{77} +(3.82331 + 1.39157i) q^{79} +(8.91377 + 1.24284i) q^{81} +(-1.25679 - 0.457434i) q^{83} +(-8.14206 - 6.83200i) q^{85} +(-4.17385 + 10.3388i) q^{87} +(-1.21254 - 2.10019i) q^{89} +(-3.20646 + 5.55375i) q^{91} +(12.0302 - 13.3682i) q^{93} +(1.56635 - 0.570105i) q^{95} +(1.94180 + 11.0125i) q^{97} +(0.155672 + 1.47339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q+O(q^{10}) \) Copy content Toggle raw display \( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0599758 1.73101i 0.0346270 0.999400i
\(4\) 0 0
\(5\) 0.392840 2.22791i 0.175683 0.996350i −0.761669 0.647966i \(-0.775620\pi\)
0.937352 0.348383i \(-0.113269\pi\)
\(6\) 0 0
\(7\) 3.55853 2.98596i 1.34500 1.12859i 0.364686 0.931130i \(-0.381176\pi\)
0.980312 0.197457i \(-0.0632682\pi\)
\(8\) 0 0
\(9\) −2.99281 0.207638i −0.997602 0.0692125i
\(10\) 0 0
\(11\) −0.0857584 0.486360i −0.0258571 0.146643i 0.969146 0.246488i \(-0.0792765\pi\)
−0.995003 + 0.0998447i \(0.968165\pi\)
\(12\) 0 0
\(13\) −1.29725 + 0.472162i −0.359794 + 0.130954i −0.515591 0.856835i \(-0.672428\pi\)
0.155797 + 0.987789i \(0.450205\pi\)
\(14\) 0 0
\(15\) −3.83297 0.813631i −0.989669 0.210079i
\(16\) 0 0
\(17\) 2.34912 4.06879i 0.569745 0.986827i −0.426846 0.904324i \(-0.640375\pi\)
0.996591 0.0825025i \(-0.0262913\pi\)
\(18\) 0 0
\(19\) 0.368407 + 0.638099i 0.0845183 + 0.146390i 0.905186 0.425016i \(-0.139732\pi\)
−0.820668 + 0.571406i \(0.806398\pi\)
\(20\) 0 0
\(21\) −4.95531 6.33894i −1.08134 1.38327i
\(22\) 0 0
\(23\) 3.71710 + 3.11901i 0.775068 + 0.650359i 0.942001 0.335609i \(-0.108942\pi\)
−0.166933 + 0.985968i \(0.553386\pi\)
\(24\) 0 0
\(25\) −0.110777 0.0403195i −0.0221554 0.00806391i
\(26\) 0 0
\(27\) −0.538919 + 5.16813i −0.103715 + 0.994607i
\(28\) 0 0
\(29\) −6.04895 2.20164i −1.12326 0.408834i −0.287420 0.957805i \(-0.592798\pi\)
−0.835842 + 0.548971i \(0.815020\pi\)
\(30\) 0 0
\(31\) 7.95399 + 6.67419i 1.42858 + 1.19872i 0.946547 + 0.322567i \(0.104546\pi\)
0.482033 + 0.876153i \(0.339899\pi\)
\(32\) 0 0
\(33\) −0.847039 + 0.119279i −0.147451 + 0.0207638i
\(34\) 0 0
\(35\) −5.25451 9.10107i −0.888174 1.53836i
\(36\) 0 0
\(37\) −3.34064 + 5.78616i −0.549198 + 0.951238i 0.449132 + 0.893465i \(0.351733\pi\)
−0.998330 + 0.0577728i \(0.981600\pi\)
\(38\) 0 0
\(39\) 0.739514 + 2.27388i 0.118417 + 0.364112i
\(40\) 0 0
\(41\) −6.29948 + 2.29282i −0.983814 + 0.358079i −0.783322 0.621617i \(-0.786476\pi\)
−0.200492 + 0.979695i \(0.564254\pi\)
\(42\) 0 0
\(43\) 0.00111724 + 0.00633619i 0.000170378 + 0.000966260i 0.984893 0.173165i \(-0.0553994\pi\)
−0.984722 + 0.174131i \(0.944288\pi\)
\(44\) 0 0
\(45\) −1.63829 + 6.58612i −0.244222 + 0.981801i
\(46\) 0 0
\(47\) −7.24088 + 6.07582i −1.05619 + 0.886249i −0.993731 0.111798i \(-0.964339\pi\)
−0.0624597 + 0.998047i \(0.519894\pi\)
\(48\) 0 0
\(49\) 2.53163 14.3576i 0.361662 2.05109i
\(50\) 0 0
\(51\) −6.90224 4.31038i −0.966506 0.603574i
\(52\) 0 0
\(53\) 4.89390 0.672229 0.336115 0.941821i \(-0.390887\pi\)
0.336115 + 0.941821i \(0.390887\pi\)
\(54\) 0 0
\(55\) −1.11725 −0.150651
\(56\) 0 0
\(57\) 1.12665 0.599446i 0.149229 0.0793986i
\(58\) 0 0
\(59\) 1.96490 11.1435i 0.255809 1.45076i −0.538180 0.842830i \(-0.680888\pi\)
0.793989 0.607932i \(-0.208001\pi\)
\(60\) 0 0
\(61\) −5.09432 + 4.27464i −0.652261 + 0.547312i −0.907756 0.419498i \(-0.862206\pi\)
0.255495 + 0.966810i \(0.417762\pi\)
\(62\) 0 0
\(63\) −11.2700 + 8.19752i −1.41988 + 1.03279i
\(64\) 0 0
\(65\) 0.542319 + 3.07564i 0.0672664 + 0.381487i
\(66\) 0 0
\(67\) 6.31410 2.29815i 0.771390 0.280763i 0.0738125 0.997272i \(-0.476483\pi\)
0.697578 + 0.716509i \(0.254261\pi\)
\(68\) 0 0
\(69\) 5.62199 6.24727i 0.676808 0.752083i
\(70\) 0 0
\(71\) 4.36994 7.56897i 0.518617 0.898271i −0.481149 0.876639i \(-0.659780\pi\)
0.999766 0.0216322i \(-0.00688627\pi\)
\(72\) 0 0
\(73\) −8.06930 13.9764i −0.944440 1.63582i −0.756868 0.653568i \(-0.773271\pi\)
−0.187573 0.982251i \(-0.560062\pi\)
\(74\) 0 0
\(75\) −0.0764375 + 0.189338i −0.00882625 + 0.0218629i
\(76\) 0 0
\(77\) −1.75743 1.47466i −0.200277 0.168053i
\(78\) 0 0
\(79\) 3.82331 + 1.39157i 0.430156 + 0.156564i 0.548019 0.836466i \(-0.315382\pi\)
−0.117863 + 0.993030i \(0.537604\pi\)
\(80\) 0 0
\(81\) 8.91377 + 1.24284i 0.990419 + 0.138093i
\(82\) 0 0
\(83\) −1.25679 0.457434i −0.137951 0.0502100i 0.272122 0.962263i \(-0.412275\pi\)
−0.410073 + 0.912053i \(0.634497\pi\)
\(84\) 0 0
\(85\) −8.14206 6.83200i −0.883130 0.741034i
\(86\) 0 0
\(87\) −4.17385 + 10.3388i −0.447484 + 1.10843i
\(88\) 0 0
\(89\) −1.21254 2.10019i −0.128529 0.222619i 0.794578 0.607163i \(-0.207692\pi\)
−0.923107 + 0.384543i \(0.874359\pi\)
\(90\) 0 0
\(91\) −3.20646 + 5.55375i −0.336129 + 0.582192i
\(92\) 0 0
\(93\) 12.0302 13.3682i 1.24747 1.38621i
\(94\) 0 0
\(95\) 1.56635 0.570105i 0.160704 0.0584915i
\(96\) 0 0
\(97\) 1.94180 + 11.0125i 0.197160 + 1.11815i 0.909309 + 0.416122i \(0.136611\pi\)
−0.712149 + 0.702029i \(0.752278\pi\)
\(98\) 0 0
\(99\) 0.155672 + 1.47339i 0.0156456 + 0.148081i
\(100\) 0 0
\(101\) −7.72429 + 6.48145i −0.768596 + 0.644928i −0.940349 0.340212i \(-0.889501\pi\)
0.171753 + 0.985140i \(0.445057\pi\)
\(102\) 0 0
\(103\) −1.63208 + 9.25601i −0.160814 + 0.912022i 0.792462 + 0.609921i \(0.208799\pi\)
−0.953276 + 0.302100i \(0.902312\pi\)
\(104\) 0 0
\(105\) −16.0692 + 8.54977i −1.56819 + 0.834372i
\(106\) 0 0
\(107\) −3.86301 −0.373451 −0.186726 0.982412i \(-0.559788\pi\)
−0.186726 + 0.982412i \(0.559788\pi\)
\(108\) 0 0
\(109\) 17.7973 1.70467 0.852334 0.522998i \(-0.175186\pi\)
0.852334 + 0.522998i \(0.175186\pi\)
\(110\) 0 0
\(111\) 9.81555 + 6.12971i 0.931651 + 0.581807i
\(112\) 0 0
\(113\) −2.75210 + 15.6080i −0.258896 + 1.46827i 0.526974 + 0.849881i \(0.323326\pi\)
−0.785870 + 0.618391i \(0.787785\pi\)
\(114\) 0 0
\(115\) 8.40909 7.05607i 0.784152 0.657982i
\(116\) 0 0
\(117\) 3.98047 1.14373i 0.367995 0.105738i
\(118\) 0 0
\(119\) −3.78985 21.4933i −0.347415 1.97029i
\(120\) 0 0
\(121\) 10.1074 3.67880i 0.918857 0.334437i
\(122\) 0 0
\(123\) 3.59109 + 11.0420i 0.323798 + 0.995623i
\(124\) 0 0
\(125\) 5.52234 9.56497i 0.493933 0.855517i
\(126\) 0 0
\(127\) 2.08119 + 3.60472i 0.184675 + 0.319867i 0.943467 0.331466i \(-0.107543\pi\)
−0.758792 + 0.651333i \(0.774210\pi\)
\(128\) 0 0
\(129\) 0.0110350 0.00155394i 0.000971580 0.000136817i
\(130\) 0 0
\(131\) −4.03252 3.38368i −0.352323 0.295634i 0.449399 0.893331i \(-0.351638\pi\)
−0.801722 + 0.597697i \(0.796083\pi\)
\(132\) 0 0
\(133\) 3.21633 + 1.17065i 0.278891 + 0.101508i
\(134\) 0 0
\(135\) 11.3024 + 3.23091i 0.972755 + 0.278072i
\(136\) 0 0
\(137\) 7.75659 + 2.82317i 0.662690 + 0.241200i 0.651398 0.758737i \(-0.274183\pi\)
0.0112930 + 0.999936i \(0.496405\pi\)
\(138\) 0 0
\(139\) −1.67895 1.40881i −0.142407 0.119493i 0.568802 0.822475i \(-0.307407\pi\)
−0.711208 + 0.702981i \(0.751852\pi\)
\(140\) 0 0
\(141\) 10.0830 + 12.8984i 0.849145 + 1.08625i
\(142\) 0 0
\(143\) 0.340891 + 0.590441i 0.0285068 + 0.0493752i
\(144\) 0 0
\(145\) −7.28131 + 12.6116i −0.604680 + 1.04734i
\(146\) 0 0
\(147\) −24.7014 5.24340i −2.03733 0.432468i
\(148\) 0 0
\(149\) −4.43117 + 1.61281i −0.363016 + 0.132127i −0.517087 0.855933i \(-0.672984\pi\)
0.154071 + 0.988060i \(0.450761\pi\)
\(150\) 0 0
\(151\) 2.46982 + 14.0070i 0.200991 + 1.13988i 0.903625 + 0.428325i \(0.140896\pi\)
−0.702634 + 0.711552i \(0.747993\pi\)
\(152\) 0 0
\(153\) −7.87529 + 11.6893i −0.636679 + 0.945027i
\(154\) 0 0
\(155\) 17.9941 15.0989i 1.44532 1.21277i
\(156\) 0 0
\(157\) −1.73600 + 9.84533i −0.138548 + 0.785743i 0.833776 + 0.552103i \(0.186175\pi\)
−0.972323 + 0.233639i \(0.924936\pi\)
\(158\) 0 0
\(159\) 0.293516 8.47140i 0.0232773 0.671826i
\(160\) 0 0
\(161\) 22.5407 1.77645
\(162\) 0 0
\(163\) 14.6667 1.14878 0.574392 0.818580i \(-0.305238\pi\)
0.574392 + 0.818580i \(0.305238\pi\)
\(164\) 0 0
\(165\) −0.0670082 + 1.93398i −0.00521658 + 0.150560i
\(166\) 0 0
\(167\) 3.01907 17.1220i 0.233623 1.32494i −0.611873 0.790956i \(-0.709583\pi\)
0.845495 0.533983i \(-0.179305\pi\)
\(168\) 0 0
\(169\) −8.49865 + 7.13121i −0.653742 + 0.548555i
\(170\) 0 0
\(171\) −0.970077 1.98620i −0.0741836 0.151889i
\(172\) 0 0
\(173\) −3.57227 20.2594i −0.271595 1.54029i −0.749574 0.661920i \(-0.769742\pi\)
0.477979 0.878371i \(-0.341369\pi\)
\(174\) 0 0
\(175\) −0.514596 + 0.187298i −0.0388998 + 0.0141584i
\(176\) 0 0
\(177\) −19.1717 4.06961i −1.44103 0.305891i
\(178\) 0 0
\(179\) 3.72621 6.45399i 0.278510 0.482394i −0.692505 0.721413i \(-0.743493\pi\)
0.971015 + 0.239020i \(0.0768261\pi\)
\(180\) 0 0
\(181\) 9.06049 + 15.6932i 0.673461 + 1.16647i 0.976916 + 0.213623i \(0.0685264\pi\)
−0.303455 + 0.952846i \(0.598140\pi\)
\(182\) 0 0
\(183\) 7.09392 + 9.07471i 0.524398 + 0.670822i
\(184\) 0 0
\(185\) 11.5787 + 9.71566i 0.851281 + 0.714309i
\(186\) 0 0
\(187\) −2.18036 0.793584i −0.159443 0.0580326i
\(188\) 0 0
\(189\) 13.5141 + 20.0001i 0.983004 + 1.45480i
\(190\) 0 0
\(191\) −2.86526 1.04287i −0.207323 0.0754593i 0.236271 0.971687i \(-0.424075\pi\)
−0.443594 + 0.896228i \(0.646297\pi\)
\(192\) 0 0
\(193\) −8.37182 7.02479i −0.602617 0.505656i 0.289669 0.957127i \(-0.406455\pi\)
−0.892286 + 0.451471i \(0.850899\pi\)
\(194\) 0 0
\(195\) 5.35650 0.754297i 0.383587 0.0540163i
\(196\) 0 0
\(197\) 4.77836 + 8.27636i 0.340444 + 0.589666i 0.984515 0.175299i \(-0.0560893\pi\)
−0.644071 + 0.764966i \(0.722756\pi\)
\(198\) 0 0
\(199\) 11.0292 19.1032i 0.781841 1.35419i −0.149028 0.988833i \(-0.547614\pi\)
0.930868 0.365355i \(-0.119052\pi\)
\(200\) 0 0
\(201\) −3.59942 11.0676i −0.253884 0.780650i
\(202\) 0 0
\(203\) −28.0994 + 10.2273i −1.97219 + 0.717818i
\(204\) 0 0
\(205\) 2.63351 + 14.9354i 0.183932 + 1.04313i
\(206\) 0 0
\(207\) −10.4769 10.1064i −0.728196 0.702444i
\(208\) 0 0
\(209\) 0.278752 0.233901i 0.0192817 0.0161793i
\(210\) 0 0
\(211\) 4.44996 25.2370i 0.306348 1.73739i −0.310743 0.950494i \(-0.600578\pi\)
0.617091 0.786892i \(-0.288311\pi\)
\(212\) 0 0
\(213\) −12.8399 8.01838i −0.879774 0.549410i
\(214\) 0 0
\(215\) 0.0145553 0.000992665
\(216\) 0 0
\(217\) 48.2334 3.27430
\(218\) 0 0
\(219\) −24.6774 + 13.1298i −1.66754 + 0.887231i
\(220\) 0 0
\(221\) −1.12627 + 6.38742i −0.0757614 + 0.429664i
\(222\) 0 0
\(223\) −4.58235 + 3.84504i −0.306857 + 0.257483i −0.783191 0.621781i \(-0.786409\pi\)
0.476335 + 0.879264i \(0.341965\pi\)
\(224\) 0 0
\(225\) 0.323162 + 0.143670i 0.0215441 + 0.00957800i
\(226\) 0 0
\(227\) 3.97026 + 22.5165i 0.263516 + 1.49447i 0.773229 + 0.634127i \(0.218640\pi\)
−0.509713 + 0.860344i \(0.670249\pi\)
\(228\) 0 0
\(229\) −0.753045 + 0.274086i −0.0497626 + 0.0181121i −0.366782 0.930307i \(-0.619540\pi\)
0.317019 + 0.948419i \(0.397318\pi\)
\(230\) 0 0
\(231\) −2.65805 + 2.95368i −0.174887 + 0.194338i
\(232\) 0 0
\(233\) 3.74421 6.48516i 0.245291 0.424857i −0.716922 0.697153i \(-0.754450\pi\)
0.962213 + 0.272296i \(0.0877830\pi\)
\(234\) 0 0
\(235\) 10.6918 + 18.5188i 0.697459 + 1.20803i
\(236\) 0 0
\(237\) 2.63813 6.53474i 0.171365 0.424477i
\(238\) 0 0
\(239\) 5.58510 + 4.68646i 0.361270 + 0.303142i 0.805297 0.592872i \(-0.202006\pi\)
−0.444027 + 0.896014i \(0.646450\pi\)
\(240\) 0 0
\(241\) −7.45569 2.71365i −0.480263 0.174802i 0.0905327 0.995893i \(-0.471143\pi\)
−0.570796 + 0.821092i \(0.693365\pi\)
\(242\) 0 0
\(243\) 2.68598 15.3553i 0.172306 0.985044i
\(244\) 0 0
\(245\) −30.9929 11.2805i −1.98006 0.720684i
\(246\) 0 0
\(247\) −0.779204 0.653829i −0.0495795 0.0416022i
\(248\) 0 0
\(249\) −0.867202 + 2.14808i −0.0549567 + 0.136129i
\(250\) 0 0
\(251\) 8.83632 + 15.3050i 0.557744 + 0.966041i 0.997684 + 0.0680138i \(0.0216662\pi\)
−0.439941 + 0.898027i \(0.645000\pi\)
\(252\) 0 0
\(253\) 1.19819 2.07533i 0.0753297 0.130475i
\(254\) 0 0
\(255\) −12.3146 + 13.6842i −0.771170 + 0.856940i
\(256\) 0 0
\(257\) 25.4726 9.27126i 1.58894 0.578326i 0.611814 0.791002i \(-0.290440\pi\)
0.977123 + 0.212676i \(0.0682179\pi\)
\(258\) 0 0
\(259\) 5.38947 + 30.5652i 0.334886 + 1.89923i
\(260\) 0 0
\(261\) 17.6462 + 7.84506i 1.09227 + 0.485597i
\(262\) 0 0
\(263\) −0.925393 + 0.776497i −0.0570622 + 0.0478808i −0.670873 0.741573i \(-0.734080\pi\)
0.613811 + 0.789453i \(0.289636\pi\)
\(264\) 0 0
\(265\) 1.92252 10.9032i 0.118099 0.669775i
\(266\) 0 0
\(267\) −3.70817 + 1.97297i −0.226936 + 0.120744i
\(268\) 0 0
\(269\) −10.8066 −0.658891 −0.329446 0.944175i \(-0.606862\pi\)
−0.329446 + 0.944175i \(0.606862\pi\)
\(270\) 0 0
\(271\) 17.5515 1.06618 0.533088 0.846060i \(-0.321031\pi\)
0.533088 + 0.846060i \(0.321031\pi\)
\(272\) 0 0
\(273\) 9.42131 + 5.88351i 0.570203 + 0.356087i
\(274\) 0 0
\(275\) −0.0101098 + 0.0573353i −0.000609641 + 0.00345745i
\(276\) 0 0
\(277\) −11.8531 + 9.94592i −0.712183 + 0.597592i −0.925211 0.379454i \(-0.876112\pi\)
0.213028 + 0.977046i \(0.431668\pi\)
\(278\) 0 0
\(279\) −22.4189 21.6261i −1.34219 1.29472i
\(280\) 0 0
\(281\) −1.02603 5.81889i −0.0612076 0.347126i −0.999997 0.00263273i \(-0.999162\pi\)
0.938789 0.344493i \(-0.111949\pi\)
\(282\) 0 0
\(283\) −11.6778 + 4.25037i −0.694173 + 0.252658i −0.664921 0.746914i \(-0.731535\pi\)
−0.0292522 + 0.999572i \(0.509313\pi\)
\(284\) 0 0
\(285\) −0.892915 2.74556i −0.0528917 0.162633i
\(286\) 0 0
\(287\) −15.5706 + 26.9691i −0.919104 + 1.59193i
\(288\) 0 0
\(289\) −2.53671 4.39371i −0.149218 0.258453i
\(290\) 0 0
\(291\) 19.1792 2.70080i 1.12431 0.158324i
\(292\) 0 0
\(293\) 16.4638 + 13.8148i 0.961826 + 0.807068i 0.981249 0.192744i \(-0.0617386\pi\)
−0.0194235 + 0.999811i \(0.506183\pi\)
\(294\) 0 0
\(295\) −24.0548 8.75524i −1.40053 0.509749i
\(296\) 0 0
\(297\) 2.55979 0.181102i 0.148534 0.0105086i
\(298\) 0 0
\(299\) −6.29470 2.29108i −0.364032 0.132497i
\(300\) 0 0
\(301\) 0.0228954 + 0.0192115i 0.00131967 + 0.00110733i
\(302\) 0 0
\(303\) 10.7562 + 13.7596i 0.617927 + 0.790467i
\(304\) 0 0
\(305\) 7.52225 + 13.0289i 0.430723 + 0.746034i
\(306\) 0 0
\(307\) −4.37441 + 7.57669i −0.249661 + 0.432425i −0.963432 0.267954i \(-0.913652\pi\)
0.713771 + 0.700379i \(0.246986\pi\)
\(308\) 0 0
\(309\) 15.9244 + 3.38029i 0.905906 + 0.192298i
\(310\) 0 0
\(311\) −10.6679 + 3.88280i −0.604921 + 0.220173i −0.626279 0.779599i \(-0.715423\pi\)
0.0213585 + 0.999772i \(0.493201\pi\)
\(312\) 0 0
\(313\) −3.87957 22.0021i −0.219286 1.24363i −0.873312 0.487162i \(-0.838032\pi\)
0.654026 0.756472i \(-0.273079\pi\)
\(314\) 0 0
\(315\) 13.8360 + 28.3288i 0.779570 + 1.59615i
\(316\) 0 0
\(317\) 5.18327 4.34928i 0.291122 0.244280i −0.485516 0.874228i \(-0.661368\pi\)
0.776637 + 0.629948i \(0.216924\pi\)
\(318\) 0 0
\(319\) −0.552041 + 3.13078i −0.0309083 + 0.175290i
\(320\) 0 0
\(321\) −0.231687 + 6.68692i −0.0129315 + 0.373227i
\(322\) 0 0
\(323\) 3.46172 0.192615
\(324\) 0 0
\(325\) 0.162743 0.00902738
\(326\) 0 0
\(327\) 1.06740 30.8073i 0.0590276 1.70365i
\(328\) 0 0
\(329\) −7.62472 + 43.2420i −0.420365 + 2.38401i
\(330\) 0 0
\(331\) 16.5564 13.8925i 0.910021 0.763598i −0.0621018 0.998070i \(-0.519780\pi\)
0.972123 + 0.234471i \(0.0753359\pi\)
\(332\) 0 0
\(333\) 11.1993 16.6232i 0.613718 0.910946i
\(334\) 0 0
\(335\) −2.63962 14.9700i −0.144218 0.817900i
\(336\) 0 0
\(337\) −24.1627 + 8.79450i −1.31623 + 0.479067i −0.902247 0.431219i \(-0.858084\pi\)
−0.413979 + 0.910286i \(0.635861\pi\)
\(338\) 0 0
\(339\) 26.8525 + 5.70002i 1.45843 + 0.309583i
\(340\) 0 0
\(341\) 2.56394 4.44087i 0.138845 0.240487i
\(342\) 0 0
\(343\) −17.6037 30.4905i −0.950511 1.64633i
\(344\) 0 0
\(345\) −11.7098 14.9794i −0.630434 0.806466i
\(346\) 0 0
\(347\) 6.02970 + 5.05952i 0.323691 + 0.271609i 0.790123 0.612948i \(-0.210016\pi\)
−0.466432 + 0.884557i \(0.654461\pi\)
\(348\) 0 0
\(349\) −32.0098 11.6506i −1.71345 0.623643i −0.716206 0.697889i \(-0.754123\pi\)
−0.997240 + 0.0742458i \(0.976345\pi\)
\(350\) 0 0
\(351\) −1.74108 6.95884i −0.0929319 0.371435i
\(352\) 0 0
\(353\) −33.7248 12.2748i −1.79499 0.653322i −0.998836 0.0482262i \(-0.984643\pi\)
−0.796152 0.605096i \(-0.793135\pi\)
\(354\) 0 0
\(355\) −15.1463 12.7092i −0.803880 0.674535i
\(356\) 0 0
\(357\) −37.4324 + 5.27119i −1.98114 + 0.278981i
\(358\) 0 0
\(359\) 7.11161 + 12.3177i 0.375337 + 0.650102i 0.990377 0.138393i \(-0.0441938\pi\)
−0.615041 + 0.788495i \(0.710860\pi\)
\(360\) 0 0
\(361\) 9.22855 15.9843i 0.485713 0.841280i
\(362\) 0 0
\(363\) −5.76185 17.7167i −0.302419 0.929887i
\(364\) 0 0
\(365\) −34.3081 + 12.4871i −1.79577 + 0.653607i
\(366\) 0 0
\(367\) 0.983240 + 5.57623i 0.0513247 + 0.291077i 0.999657 0.0262031i \(-0.00834166\pi\)
−0.948332 + 0.317280i \(0.897231\pi\)
\(368\) 0 0
\(369\) 19.3292 5.55397i 1.00624 0.289128i
\(370\) 0 0
\(371\) 17.4151 14.6130i 0.904147 0.758669i
\(372\) 0 0
\(373\) 5.71024 32.3844i 0.295665 1.67680i −0.368822 0.929500i \(-0.620239\pi\)
0.664487 0.747300i \(-0.268650\pi\)
\(374\) 0 0
\(375\) −16.2259 10.1329i −0.837901 0.523261i
\(376\) 0 0
\(377\) 8.88656 0.457681
\(378\) 0 0
\(379\) −25.2534 −1.29718 −0.648591 0.761137i \(-0.724641\pi\)
−0.648591 + 0.761137i \(0.724641\pi\)
\(380\) 0 0
\(381\) 6.36463 3.38636i 0.326070 0.173489i
\(382\) 0 0
\(383\) 1.31166 7.43879i 0.0670226 0.380104i −0.932784 0.360436i \(-0.882628\pi\)
0.999807 0.0196682i \(-0.00626099\pi\)
\(384\) 0 0
\(385\) −3.97578 + 3.33608i −0.202625 + 0.170022i
\(386\) 0 0
\(387\) −0.00202805 0.0191950i −0.000103092 0.000975735i
\(388\) 0 0
\(389\) 0.0534572 + 0.303171i 0.00271039 + 0.0153714i 0.986133 0.165957i \(-0.0530714\pi\)
−0.983423 + 0.181329i \(0.941960\pi\)
\(390\) 0 0
\(391\) 21.4225 7.79716i 1.08338 0.394319i
\(392\) 0 0
\(393\) −6.09905 + 6.77740i −0.307656 + 0.341875i
\(394\) 0 0
\(395\) 4.60224 7.97131i 0.231564 0.401080i
\(396\) 0 0
\(397\) 7.90379 + 13.6898i 0.396680 + 0.687070i 0.993314 0.115444i \(-0.0368290\pi\)
−0.596634 + 0.802513i \(0.703496\pi\)
\(398\) 0 0
\(399\) 2.21931 5.49729i 0.111104 0.275209i
\(400\) 0 0
\(401\) −4.01983 3.37304i −0.200741 0.168442i 0.536876 0.843661i \(-0.319604\pi\)
−0.737617 + 0.675220i \(0.764049\pi\)
\(402\) 0 0
\(403\) −13.4697 4.90255i −0.670971 0.244214i
\(404\) 0 0
\(405\) 6.27061 19.3708i 0.311589 0.962543i
\(406\) 0 0
\(407\) 3.10064 + 1.12854i 0.153693 + 0.0559398i
\(408\) 0 0
\(409\) −14.6135 12.2622i −0.722589 0.606324i 0.205511 0.978655i \(-0.434114\pi\)
−0.928100 + 0.372330i \(0.878559\pi\)
\(410\) 0 0
\(411\) 5.35215 13.2574i 0.264002 0.653941i
\(412\) 0 0
\(413\) −26.2819 45.5217i −1.29325 2.23997i
\(414\) 0 0
\(415\) −1.51284 + 2.62031i −0.0742623 + 0.128626i
\(416\) 0 0
\(417\) −2.53936 + 2.82179i −0.124353 + 0.138184i
\(418\) 0 0
\(419\) −2.36859 + 0.862098i −0.115713 + 0.0421162i −0.399228 0.916852i \(-0.630722\pi\)
0.283515 + 0.958968i \(0.408500\pi\)
\(420\) 0 0
\(421\) 3.18072 + 18.0388i 0.155019 + 0.879155i 0.958769 + 0.284188i \(0.0917240\pi\)
−0.803750 + 0.594968i \(0.797165\pi\)
\(422\) 0 0
\(423\) 22.9321 16.6803i 1.11500 0.811022i
\(424\) 0 0
\(425\) −0.424280 + 0.356013i −0.0205806 + 0.0172692i
\(426\) 0 0
\(427\) −5.36438 + 30.4229i −0.259600 + 1.47227i
\(428\) 0 0
\(429\) 1.04251 0.554675i 0.0503327 0.0267800i
\(430\) 0 0
\(431\) 18.4805 0.890174 0.445087 0.895487i \(-0.353173\pi\)
0.445087 + 0.895487i \(0.353173\pi\)
\(432\) 0 0
\(433\) 10.1685 0.488665 0.244333 0.969691i \(-0.421431\pi\)
0.244333 + 0.969691i \(0.421431\pi\)
\(434\) 0 0
\(435\) 21.3941 + 13.3604i 1.02577 + 0.640583i
\(436\) 0 0
\(437\) −0.620837 + 3.52094i −0.0296987 + 0.168430i
\(438\) 0 0
\(439\) 16.0560 13.4726i 0.766311 0.643011i −0.173451 0.984843i \(-0.555492\pi\)
0.939761 + 0.341832i \(0.111047\pi\)
\(440\) 0 0
\(441\) −10.5579 + 42.4439i −0.502756 + 2.02114i
\(442\) 0 0
\(443\) 6.71710 + 38.0946i 0.319139 + 1.80993i 0.548011 + 0.836471i \(0.315385\pi\)
−0.228872 + 0.973457i \(0.573504\pi\)
\(444\) 0 0
\(445\) −5.15535 + 1.87639i −0.244387 + 0.0889496i
\(446\) 0 0
\(447\) 2.52604 + 7.76714i 0.119478 + 0.367373i
\(448\) 0 0
\(449\) −1.82208 + 3.15593i −0.0859893 + 0.148938i −0.905812 0.423679i \(-0.860738\pi\)
0.819823 + 0.572617i \(0.194072\pi\)
\(450\) 0 0
\(451\) 1.65537 + 2.86719i 0.0779484 + 0.135011i
\(452\) 0 0
\(453\) 24.3945 3.43520i 1.14615 0.161400i
\(454\) 0 0
\(455\) 11.1136 + 9.32543i 0.521014 + 0.437183i
\(456\) 0 0
\(457\) −9.50969 3.46124i −0.444845 0.161910i 0.109879 0.993945i \(-0.464954\pi\)
−0.554723 + 0.832035i \(0.687176\pi\)
\(458\) 0 0
\(459\) 19.7621 + 14.3333i 0.922414 + 0.669021i
\(460\) 0 0
\(461\) 13.1036 + 4.76931i 0.610295 + 0.222129i 0.628632 0.777703i \(-0.283615\pi\)
−0.0183375 + 0.999832i \(0.505837\pi\)
\(462\) 0 0
\(463\) −3.36922 2.82711i −0.156581 0.131387i 0.561131 0.827727i \(-0.310366\pi\)
−0.717712 + 0.696340i \(0.754811\pi\)
\(464\) 0 0
\(465\) −25.0571 32.0536i −1.16199 1.48645i
\(466\) 0 0
\(467\) −21.1566 36.6443i −0.979010 1.69569i −0.666012 0.745941i \(-0.732000\pi\)
−0.312997 0.949754i \(-0.601333\pi\)
\(468\) 0 0
\(469\) 15.6067 27.0317i 0.720653 1.24821i
\(470\) 0 0
\(471\) 16.9383 + 3.59551i 0.780474 + 0.165673i
\(472\) 0 0
\(473\) 0.00298586 0.00108676i 0.000137290 4.99694e-5i
\(474\) 0 0
\(475\) −0.0150831 0.0855407i −0.000692062 0.00392488i
\(476\) 0 0
\(477\) −14.6465 1.01616i −0.670617 0.0465267i
\(478\) 0 0
\(479\) −28.3497 + 23.7882i −1.29533 + 1.08691i −0.304397 + 0.952545i \(0.598455\pi\)
−0.990932 + 0.134365i \(0.957101\pi\)
\(480\) 0 0
\(481\) 1.60166 9.08344i 0.0730292 0.414169i
\(482\) 0 0
\(483\) 1.35189 39.0181i 0.0615133 1.77539i
\(484\) 0 0
\(485\) 25.2976 1.14871
\(486\) 0 0
\(487\) −16.6561 −0.754762 −0.377381 0.926058i \(-0.623175\pi\)
−0.377381 + 0.926058i \(0.623175\pi\)
\(488\) 0 0
\(489\) 0.879647 25.3882i 0.0397790 1.14810i
\(490\) 0 0
\(491\) −5.32604 + 30.2055i −0.240361 + 1.36315i 0.590663 + 0.806918i \(0.298866\pi\)
−0.831024 + 0.556236i \(0.812245\pi\)
\(492\) 0 0
\(493\) −23.1677 + 19.4400i −1.04342 + 0.875534i
\(494\) 0 0
\(495\) 3.34372 + 0.231984i 0.150289 + 0.0104269i
\(496\) 0 0
\(497\) −7.05006 39.9829i −0.316238 1.79348i
\(498\) 0 0
\(499\) −13.7046 + 4.98805i −0.613501 + 0.223296i −0.630034 0.776567i \(-0.716959\pi\)
0.0165336 + 0.999863i \(0.494737\pi\)
\(500\) 0 0
\(501\) −29.4573 6.25295i −1.31606 0.279361i
\(502\) 0 0
\(503\) −1.88683 + 3.26809i −0.0841296 + 0.145717i −0.905020 0.425369i \(-0.860144\pi\)
0.820890 + 0.571086i \(0.193478\pi\)
\(504\) 0 0
\(505\) 11.4056 + 19.7552i 0.507545 + 0.879093i
\(506\) 0 0
\(507\) 11.8345 + 15.1390i 0.525589 + 0.672345i
\(508\) 0 0
\(509\) 13.7117 + 11.5055i 0.607760 + 0.509971i 0.893929 0.448208i \(-0.147938\pi\)
−0.286169 + 0.958179i \(0.592382\pi\)
\(510\) 0 0
\(511\) −70.4480 25.6410i −3.11643 1.13429i
\(512\) 0 0
\(513\) −3.49632 + 1.56009i −0.154366 + 0.0688797i
\(514\) 0 0
\(515\) 19.9804 + 7.27226i 0.880440 + 0.320454i
\(516\) 0 0
\(517\) 3.57600 + 3.00062i 0.157272 + 0.131967i
\(518\) 0 0
\(519\) −35.2835 + 4.96858i −1.54877 + 0.218096i
\(520\) 0 0
\(521\) 4.35976 + 7.55132i 0.191004 + 0.330829i 0.945583 0.325380i \(-0.105492\pi\)
−0.754579 + 0.656209i \(0.772159\pi\)
\(522\) 0 0
\(523\) −7.62696 + 13.2103i −0.333504 + 0.577645i −0.983196 0.182552i \(-0.941564\pi\)
0.649693 + 0.760197i \(0.274898\pi\)
\(524\) 0 0
\(525\) 0.293351 + 0.902005i 0.0128029 + 0.0393667i
\(526\) 0 0
\(527\) 45.8408 16.6847i 1.99685 0.726796i
\(528\) 0 0
\(529\) 0.0946468 + 0.536769i 0.00411508 + 0.0233378i
\(530\) 0 0
\(531\) −8.19439 + 32.9424i −0.355606 + 1.42958i
\(532\) 0 0
\(533\) 7.08944 5.94875i 0.307078 0.257669i
\(534\) 0 0
\(535\) −1.51754 + 8.60642i −0.0656092 + 0.372088i
\(536\) 0 0
\(537\) −10.9484 6.83720i −0.472460 0.295047i
\(538\) 0 0
\(539\) −7.20008 −0.310129
\(540\) 0 0
\(541\) −31.3381 −1.34733 −0.673666 0.739036i \(-0.735281\pi\)
−0.673666 + 0.739036i \(0.735281\pi\)
\(542\) 0 0
\(543\) 27.7086 14.7426i 1.18909 0.632666i
\(544\) 0 0
\(545\) 6.99147 39.6506i 0.299482 1.69845i
\(546\) 0 0
\(547\) 17.2228 14.4517i 0.736396 0.617909i −0.195471 0.980709i \(-0.562624\pi\)
0.931867 + 0.362800i \(0.118179\pi\)
\(548\) 0 0
\(549\) 16.1339 11.7354i 0.688578 0.500855i
\(550\) 0 0
\(551\) −0.823611 4.67093i −0.0350870 0.198988i
\(552\) 0 0
\(553\) 17.7605 6.46431i 0.755255 0.274890i
\(554\) 0 0
\(555\) 17.5124 19.4601i 0.743358 0.826036i
\(556\) 0 0
\(557\) 13.5637 23.4930i 0.574711 0.995429i −0.421362 0.906893i \(-0.638448\pi\)
0.996073 0.0885364i \(-0.0282190\pi\)
\(558\) 0 0
\(559\) −0.00444105 0.00769213i −0.000187837 0.000325343i
\(560\) 0 0
\(561\) −1.50447 + 3.72663i −0.0635189 + 0.157338i
\(562\) 0 0
\(563\) 12.3708 + 10.3803i 0.521367 + 0.437478i 0.865108 0.501586i \(-0.167250\pi\)
−0.343741 + 0.939064i \(0.611694\pi\)
\(564\) 0 0
\(565\) 33.6919 + 12.2628i 1.41743 + 0.515902i
\(566\) 0 0
\(567\) 35.4310 22.1935i 1.48796 0.932040i
\(568\) 0 0
\(569\) −15.2951 5.56697i −0.641205 0.233379i 0.000896107 1.00000i \(-0.499715\pi\)
−0.642101 + 0.766620i \(0.721937\pi\)
\(570\) 0 0
\(571\) −13.1097 11.0003i −0.548622 0.460349i 0.325852 0.945421i \(-0.394349\pi\)
−0.874474 + 0.485072i \(0.838793\pi\)
\(572\) 0 0
\(573\) −1.97706 + 4.89725i −0.0825930 + 0.204586i
\(574\) 0 0
\(575\) −0.286012 0.495387i −0.0119275 0.0206590i
\(576\) 0 0
\(577\) 1.98126 3.43163i 0.0824807 0.142861i −0.821834 0.569727i \(-0.807049\pi\)
0.904315 + 0.426866i \(0.140382\pi\)
\(578\) 0 0
\(579\) −12.6621 + 14.0704i −0.526219 + 0.584746i
\(580\) 0 0
\(581\) −5.83821 + 2.12493i −0.242210 + 0.0881571i
\(582\) 0 0
\(583\) −0.419693 2.38020i −0.0173819 0.0985778i
\(584\) 0 0
\(585\) −0.984436 9.31741i −0.0407014 0.385228i
\(586\) 0 0
\(587\) −31.7228 + 26.6186i −1.30934 + 1.09867i −0.320891 + 0.947116i \(0.603982\pi\)
−0.988449 + 0.151551i \(0.951573\pi\)
\(588\) 0 0
\(589\) −1.32849 + 7.53425i −0.0547396 + 0.310444i
\(590\) 0 0
\(591\) 14.6131 7.77502i 0.601101 0.319821i
\(592\) 0 0
\(593\) −11.2304 −0.461175 −0.230588 0.973052i \(-0.574065\pi\)
−0.230588 + 0.973052i \(0.574065\pi\)
\(594\) 0 0
\(595\) −49.3738 −2.02413
\(596\) 0 0
\(597\) −32.4063 20.2374i −1.32630 0.828263i
\(598\) 0 0
\(599\) −1.77286 + 10.0544i −0.0724369 + 0.410810i 0.926930 + 0.375234i \(0.122438\pi\)
−0.999367 + 0.0355760i \(0.988673\pi\)
\(600\) 0 0
\(601\) 0.509071 0.427161i 0.0207654 0.0174243i −0.632346 0.774686i \(-0.717908\pi\)
0.653111 + 0.757262i \(0.273463\pi\)
\(602\) 0 0
\(603\) −19.3741 + 5.56686i −0.788973 + 0.226700i
\(604\) 0 0
\(605\) −4.22542 23.9636i −0.171788 0.974258i
\(606\) 0 0
\(607\) −24.3607 + 8.86658i −0.988771 + 0.359883i −0.785244 0.619186i \(-0.787463\pi\)
−0.203527 + 0.979069i \(0.565240\pi\)
\(608\) 0 0
\(609\) 16.0184 + 49.2538i 0.649097 + 1.99586i
\(610\) 0 0
\(611\) 6.52449 11.3007i 0.263953 0.457179i
\(612\) 0 0
\(613\) 8.97419 + 15.5438i 0.362464 + 0.627806i 0.988366 0.152096i \(-0.0486022\pi\)
−0.625902 + 0.779902i \(0.715269\pi\)
\(614\) 0 0
\(615\) 26.0112 3.66287i 1.04887 0.147701i
\(616\) 0 0
\(617\) 6.76451 + 5.67609i 0.272329 + 0.228511i 0.768716 0.639590i \(-0.220896\pi\)
−0.496387 + 0.868101i \(0.665340\pi\)
\(618\) 0 0
\(619\) 18.3976 + 6.69619i 0.739463 + 0.269143i 0.684165 0.729327i \(-0.260167\pi\)
0.0552981 + 0.998470i \(0.482389\pi\)
\(620\) 0 0
\(621\) −18.1227 + 17.5295i −0.727238 + 0.703436i
\(622\) 0 0
\(623\) −10.5859 3.85297i −0.424117 0.154366i
\(624\) 0 0
\(625\) −19.5920 16.4396i −0.783680 0.657585i
\(626\) 0 0
\(627\) −0.388167 0.496552i −0.0155019 0.0198304i
\(628\) 0 0
\(629\) 15.6951 + 27.1847i 0.625805 + 1.08393i
\(630\) 0 0
\(631\) −5.99069 + 10.3762i −0.238485 + 0.413069i −0.960280 0.279039i \(-0.909984\pi\)
0.721794 + 0.692107i \(0.243318\pi\)
\(632\) 0 0
\(633\) −43.4186 9.21654i −1.72574 0.366325i
\(634\) 0 0
\(635\) 8.84854 3.22061i 0.351144 0.127806i
\(636\) 0 0
\(637\) 3.49495 + 19.8208i 0.138475 + 0.785329i
\(638\) 0 0
\(639\) −14.6500 + 21.7451i −0.579545 + 0.860222i
\(640\) 0 0
\(641\) −34.0436 + 28.5660i −1.34464 + 1.12829i −0.364233 + 0.931308i \(0.618669\pi\)
−0.980408 + 0.196980i \(0.936887\pi\)
\(642\) 0 0
\(643\) 4.43276 25.1394i 0.174811 0.991403i −0.763551 0.645748i \(-0.776546\pi\)
0.938362 0.345655i \(-0.112343\pi\)
\(644\) 0 0
\(645\) 0.000872968 0.0251955i 3.43731e−5 0.000992070i
\(646\) 0 0
\(647\) −38.0816 −1.49714 −0.748571 0.663055i \(-0.769259\pi\)
−0.748571 + 0.663055i \(0.769259\pi\)
\(648\) 0 0
\(649\) −5.58827 −0.219359
\(650\) 0 0
\(651\) 2.89284 83.4926i 0.113379 3.27233i
\(652\) 0 0
\(653\) −0.360584 + 2.04497i −0.0141107 + 0.0800260i −0.991050 0.133492i \(-0.957381\pi\)
0.976939 + 0.213518i \(0.0684921\pi\)
\(654\) 0 0
\(655\) −9.12266 + 7.65482i −0.356452 + 0.299099i
\(656\) 0 0
\(657\) 21.2478 + 43.5043i 0.828956 + 1.69726i
\(658\) 0 0
\(659\) 2.70315 + 15.3303i 0.105300 + 0.597185i 0.991100 + 0.133118i \(0.0424990\pi\)
−0.885800 + 0.464066i \(0.846390\pi\)
\(660\) 0 0
\(661\) 9.18307 3.34237i 0.357180 0.130003i −0.157196 0.987567i \(-0.550246\pi\)
0.514377 + 0.857564i \(0.328023\pi\)
\(662\) 0 0
\(663\) 10.9892 + 2.33269i 0.426783 + 0.0905940i
\(664\) 0 0
\(665\) 3.87159 6.70579i 0.150134 0.260040i
\(666\) 0 0
\(667\) −15.6176 27.0505i −0.604716 1.04740i
\(668\) 0 0
\(669\) 6.38099 + 8.16270i 0.246703 + 0.315588i
\(670\) 0 0
\(671\) 2.51590 + 2.11109i 0.0971252 + 0.0814977i
\(672\) 0 0
\(673\) −1.28819 0.468862i −0.0496560 0.0180733i 0.317073 0.948401i \(-0.397300\pi\)
−0.366729 + 0.930328i \(0.619522\pi\)
\(674\) 0 0
\(675\) 0.268076 0.550781i 0.0103183 0.0211996i
\(676\) 0 0
\(677\) 11.7891 + 4.29089i 0.453093 + 0.164912i 0.558478 0.829519i \(-0.311385\pi\)
−0.105385 + 0.994431i \(0.533608\pi\)
\(678\) 0 0
\(679\) 39.7929 + 33.3902i 1.52711 + 1.28140i
\(680\) 0 0
\(681\) 39.2144 5.52213i 1.50270 0.211608i
\(682\) 0 0
\(683\) 13.8263 + 23.9478i 0.529047 + 0.916337i 0.999426 + 0.0338721i \(0.0107839\pi\)
−0.470379 + 0.882465i \(0.655883\pi\)
\(684\) 0 0
\(685\) 9.33685 16.1719i 0.356743 0.617897i
\(686\) 0 0
\(687\) 0.429282 + 1.31997i 0.0163781 + 0.0503599i
\(688\) 0 0
\(689\) −6.34864 + 2.31071i −0.241864 + 0.0880312i
\(690\) 0 0
\(691\) −0.333393 1.89077i −0.0126829 0.0719282i 0.977809 0.209496i \(-0.0671825\pi\)
−0.990492 + 0.137568i \(0.956071\pi\)
\(692\) 0 0
\(693\) 4.95344 + 4.77827i 0.188166 + 0.181511i
\(694\) 0 0
\(695\) −3.79825 + 3.18711i −0.144076 + 0.120894i
\(696\) 0 0
\(697\) −5.46920 + 31.0174i −0.207161 + 1.17487i
\(698\) 0 0
\(699\) −11.0013 6.87023i −0.416109 0.259856i
\(700\) 0 0
\(701\) 24.9902 0.943867 0.471933 0.881634i \(-0.343556\pi\)
0.471933 + 0.881634i \(0.343556\pi\)
\(702\) 0 0
\(703\) −4.92286 −0.185669
\(704\) 0 0
\(705\) 32.6975 17.3970i 1.23146 0.655210i
\(706\) 0 0
\(707\) −8.13376 + 46.1289i −0.305902 + 1.73485i
\(708\) 0 0
\(709\) 11.0046 9.23396i 0.413287 0.346789i −0.412316 0.911041i \(-0.635280\pi\)
0.825602 + 0.564252i \(0.190835\pi\)
\(710\) 0 0
\(711\) −11.1535 4.95857i −0.418288 0.185961i
\(712\) 0 0
\(713\) 8.74886 + 49.6172i 0.327647 + 1.85818i
\(714\) 0 0
\(715\) 1.44936 0.527525i 0.0542031 0.0197283i
\(716\) 0 0
\(717\) 8.44728 9.38680i 0.315470 0.350557i
\(718\) 0 0
\(719\) −13.0300 + 22.5686i −0.485937 + 0.841668i −0.999869 0.0161626i \(-0.994855\pi\)
0.513932 + 0.857831i \(0.328188\pi\)
\(720\) 0 0
\(721\) 21.8303 + 37.8111i 0.813002 + 1.40816i
\(722\) 0 0
\(723\) −5.14452 + 12.7431i −0.191327 + 0.473922i
\(724\) 0 0
\(725\) 0.581316 + 0.487782i 0.0215895 + 0.0181158i
\(726\) 0 0
\(727\) −16.5039 6.00694i −0.612097 0.222785i 0.0173234 0.999850i \(-0.494486\pi\)
−0.629421 + 0.777065i \(0.716708\pi\)
\(728\) 0 0
\(729\) −26.4191 5.57041i −0.978486 0.206311i
\(730\) 0 0
\(731\) 0.0284052 + 0.0103386i 0.00105060 + 0.000382388i
\(732\) 0 0
\(733\) −16.0100 13.4340i −0.591342 0.496195i 0.297307 0.954782i \(-0.403911\pi\)
−0.888650 + 0.458587i \(0.848356\pi\)
\(734\) 0 0
\(735\) −21.3855 + 52.9725i −0.788815 + 1.95392i
\(736\) 0 0
\(737\) −1.65921 2.87384i −0.0611179 0.105859i
\(738\) 0 0
\(739\) −6.25842 + 10.8399i −0.230220 + 0.398752i −0.957873 0.287193i \(-0.907278\pi\)
0.727653 + 0.685945i \(0.240611\pi\)
\(740\) 0 0
\(741\) −1.17852 + 1.30960i −0.0432940 + 0.0481092i
\(742\) 0 0
\(743\) 1.69954 0.618581i 0.0623499 0.0226935i −0.310657 0.950522i \(-0.600549\pi\)
0.373007 + 0.927829i \(0.378327\pi\)
\(744\) 0 0
\(745\) 1.85246 + 10.5058i 0.0678688 + 0.384903i
\(746\) 0 0
\(747\) 3.66635 + 1.62997i 0.134145 + 0.0596375i
\(748\) 0 0
\(749\) −13.7466 + 11.5348i −0.502291 + 0.421472i
\(750\) 0 0
\(751\) 0.577783 3.27677i 0.0210836 0.119571i −0.972450 0.233113i \(-0.925109\pi\)
0.993533 + 0.113542i \(0.0362198\pi\)
\(752\) 0 0
\(753\) 27.0230 14.3779i 0.984774 0.523958i
\(754\) 0 0
\(755\) 32.1766 1.17103
\(756\) 0 0
\(757\) −24.1091 −0.876259 −0.438130 0.898912i \(-0.644359\pi\)
−0.438130 + 0.898912i \(0.644359\pi\)
\(758\) 0 0
\(759\) −3.52056 2.19855i −0.127788 0.0798025i
\(760\) 0 0
\(761\) −6.40688 + 36.3352i −0.232249 + 1.31715i 0.616081 + 0.787683i \(0.288719\pi\)
−0.848330 + 0.529468i \(0.822392\pi\)
\(762\) 0 0
\(763\) 63.3321 53.1419i 2.29277 1.92387i
\(764\) 0 0
\(765\) 22.9490 + 22.1374i 0.829723 + 0.800381i
\(766\) 0 0
\(767\) 2.71257 + 15.3837i 0.0979451 + 0.555474i
\(768\) 0 0
\(769\) 9.02941 3.28644i 0.325609 0.118512i −0.174044 0.984738i \(-0.555683\pi\)
0.499652 + 0.866226i \(0.333461\pi\)
\(770\) 0 0
\(771\) −14.5209 44.6494i −0.522959 1.60801i
\(772\) 0 0
\(773\) −10.4760 + 18.1449i −0.376794 + 0.652626i −0.990594 0.136835i \(-0.956307\pi\)
0.613800 + 0.789462i \(0.289640\pi\)
\(774\) 0 0
\(775\) −0.612019 1.06005i −0.0219844 0.0380781i
\(776\) 0 0
\(777\) 53.2320 7.49607i 1.90969 0.268920i
\(778\) 0 0
\(779\) −3.78382 3.17500i −0.135569 0.113756i
\(780\) 0 0
\(781\) −4.05600 1.47626i −0.145135 0.0528249i
\(782\) 0 0
\(783\) 14.6382 30.0753i 0.523128 1.07480i
\(784\) 0 0
\(785\) 21.2525 + 7.73528i 0.758534 + 0.276084i
\(786\) 0 0
\(787\) −2.75781 2.31408i −0.0983055 0.0824881i 0.592310 0.805710i \(-0.298216\pi\)
−0.690616 + 0.723222i \(0.742660\pi\)
\(788\) 0 0
\(789\) 1.28862 + 1.64844i 0.0458762 + 0.0586859i
\(790\) 0 0
\(791\) 36.8113 + 63.7590i 1.30886 + 2.26701i
\(792\) 0 0
\(793\) 4.59031 7.95064i 0.163007 0.282336i
\(794\) 0 0
\(795\) −18.7582 3.98183i −0.665284 0.141221i
\(796\) 0 0
\(797\) −10.7418 + 3.90969i −0.380493 + 0.138488i −0.525184 0.850989i \(-0.676004\pi\)
0.144691 + 0.989477i \(0.453781\pi\)
\(798\) 0 0
\(799\) 7.71156 + 43.7344i 0.272815 + 1.54721i
\(800\) 0 0
\(801\) 3.19283 + 6.53722i 0.112813 + 0.230981i
\(802\) 0 0
\(803\) −6.10558 + 5.12319i −0.215461 + 0.180793i
\(804\) 0 0
\(805\) 8.85487 50.2184i 0.312093 1.76997i
\(806\) 0 0
\(807\) −0.648136 + 18.7064i −0.0228155 + 0.658496i
\(808\) 0 0
\(809\) 17.2384 0.606071 0.303036 0.952979i \(-0.402000\pi\)
0.303036 + 0.952979i \(0.402000\pi\)
\(810\) 0 0
\(811\) 39.4818 1.38639 0.693197 0.720749i \(-0.256202\pi\)
0.693197 + 0.720749i \(0.256202\pi\)
\(812\) 0 0
\(813\) 1.05266 30.3818i 0.0369186 1.06554i
\(814\) 0 0
\(815\) 5.76167 32.6760i 0.201822 1.14459i
\(816\) 0 0
\(817\) −0.00363152 + 0.00304721i −0.000127051 + 0.000106608i
\(818\) 0 0
\(819\) 10.7495 15.9555i 0.375617 0.557531i
\(820\) 0 0
\(821\) 8.83146 + 50.0857i 0.308220 + 1.74800i 0.607947 + 0.793977i \(0.291993\pi\)
−0.299727 + 0.954025i \(0.596896\pi\)
\(822\) 0 0
\(823\) 3.78997 1.37944i 0.132110 0.0480841i −0.275119 0.961410i \(-0.588717\pi\)
0.407229 + 0.913326i \(0.366495\pi\)
\(824\) 0 0
\(825\) 0.0986417 + 0.0209388i 0.00343426 + 0.000728997i
\(826\) 0 0
\(827\) 13.8069 23.9142i 0.480112 0.831578i −0.519628 0.854393i \(-0.673929\pi\)
0.999740 + 0.0228147i \(0.00726277\pi\)
\(828\) 0 0
\(829\) 6.43951 + 11.1536i 0.223654 + 0.387379i 0.955915 0.293645i \(-0.0948683\pi\)
−0.732261 + 0.681024i \(0.761535\pi\)
\(830\) 0 0
\(831\) 16.5056 + 21.1144i 0.572573 + 0.732449i
\(832\) 0 0
\(833\) −52.4710 44.0284i −1.81801 1.52549i
\(834\) 0 0
\(835\) −36.9602 13.4524i −1.27906 0.465540i
\(836\) 0 0
\(837\) −38.7797 + 37.5104i −1.34042 + 1.29655i
\(838\) 0 0
\(839\) 29.8306 + 10.8574i 1.02987 + 0.374841i 0.801030 0.598624i \(-0.204286\pi\)
0.228836 + 0.973465i \(0.426508\pi\)
\(840\) 0 0
\(841\) 9.52730 + 7.99436i 0.328528 + 0.275667i
\(842\) 0 0
\(843\) −10.1341 + 1.42707i −0.349037 + 0.0491510i
\(844\) 0 0
\(845\) 12.5491 + 21.7356i 0.431701 + 0.747727i
\(846\) 0 0
\(847\) 24.9828 43.2715i 0.858420 1.48683i
\(848\) 0 0
\(849\) 6.65706 + 20.4693i 0.228470 + 0.702506i
\(850\) 0 0
\(851\) −30.4646 + 11.0882i −1.04431 + 0.380099i
\(852\) 0 0
\(853\) −7.12442 40.4046i −0.243936 1.38343i −0.822952 0.568111i \(-0.807674\pi\)
0.579016 0.815316i \(-0.303437\pi\)
\(854\) 0 0
\(855\) −4.80616 + 1.38098i −0.164367 + 0.0472285i
\(856\) 0 0
\(857\) 27.3508 22.9501i 0.934287 0.783960i −0.0422952 0.999105i \(-0.513467\pi\)
0.976582 + 0.215145i \(0.0690226\pi\)
\(858\) 0 0
\(859\) 0.781011 4.42933i 0.0266477 0.151127i −0.968581 0.248700i \(-0.919997\pi\)
0.995228 + 0.0975728i \(0.0311079\pi\)
\(860\) 0 0
\(861\) 45.7500 + 28.5704i 1.55915 + 0.973677i
\(862\) 0 0
\(863\) −6.22982 −0.212065 −0.106033 0.994363i \(-0.533815\pi\)
−0.106033 + 0.994363i \(0.533815\pi\)
\(864\) 0 0
\(865\) −46.5393 −1.58238
\(866\) 0 0
\(867\) −7.75770 + 4.12756i −0.263465 + 0.140179i
\(868\) 0 0
\(869\) 0.348924 1.97885i 0.0118364 0.0671277i
\(870\) 0 0
\(871\) −7.10590 + 5.96256i −0.240774 + 0.202034i
\(872\) 0 0
\(873\) −3.52483 33.3615i −0.119297 1.12912i
\(874\) 0 0
\(875\) −8.90923 50.5267i −0.301187 1.70812i
\(876\) 0 0
\(877\) 12.2573 4.46130i 0.413901 0.150648i −0.126672 0.991945i \(-0.540430\pi\)
0.540573 + 0.841297i \(0.318207\pi\)
\(878\) 0 0
\(879\) 24.9010 27.6705i 0.839889 0.933303i
\(880\) 0 0
\(881\) 19.7593 34.2241i 0.665707 1.15304i −0.313386 0.949626i \(-0.601463\pi\)
0.979093 0.203413i \(-0.0652033\pi\)
\(882\) 0 0
\(883\) −1.28534 2.22628i −0.0432552 0.0749202i 0.843587 0.536992i \(-0.180440\pi\)
−0.886842 + 0.462072i \(0.847106\pi\)
\(884\) 0 0
\(885\) −16.5981 + 41.1141i −0.557940 + 1.38203i
\(886\) 0 0
\(887\) −31.4116 26.3574i −1.05470 0.884996i −0.0611178 0.998131i \(-0.519467\pi\)
−0.993580 + 0.113134i \(0.963911\pi\)
\(888\) 0 0
\(889\) 18.1695 + 6.61316i 0.609386 + 0.221798i
\(890\) 0 0
\(891\) −0.159964 4.44189i −0.00535900 0.148809i
\(892\) 0 0
\(893\) −6.54456 2.38203i −0.219005 0.0797115i
\(894\) 0 0
\(895\) −12.9151 10.8370i −0.431703 0.362242i
\(896\) 0 0
\(897\) −4.34342 + 10.7588i −0.145023 + 0.359226i
\(898\) 0 0
\(899\) −33.4192 57.8837i −1.11459 1.93053i
\(900\) 0 0
\(901\) 11.4964 19.9123i 0.382999 0.663374i
\(902\) 0 0
\(903\) 0.0346285 0.0384799i 0.00115236 0.00128053i
\(904\) 0 0
\(905\) 38.5224 14.0210i 1.28053 0.466074i
\(906\) 0 0
\(907\) 7.17389 + 40.6851i 0.238205 + 1.35093i 0.835758 + 0.549098i \(0.185029\pi\)
−0.597553 + 0.801830i \(0.703860\pi\)
\(908\) 0 0
\(909\) 24.4631 17.7939i 0.811390 0.590185i
\(910\) 0 0
\(911\) 10.7599 9.02864i 0.356492 0.299132i −0.446899 0.894585i \(-0.647472\pi\)
0.803391 + 0.595452i \(0.203027\pi\)
\(912\) 0 0
\(913\) −0.114698 + 0.650482i −0.00379593 + 0.0215278i
\(914\) 0 0
\(915\) 23.0044 12.2397i 0.760501 0.404631i
\(916\) 0 0
\(917\) −24.4534 −0.807522
\(918\) 0 0
\(919\) 27.1102 0.894284 0.447142 0.894463i \(-0.352442\pi\)
0.447142 + 0.894463i \(0.352442\pi\)
\(920\) 0 0
\(921\) 12.8530 + 8.02657i 0.423520 + 0.264484i
\(922\) 0 0
\(923\) −2.09515 + 11.8822i −0.0689628 + 0.391107i
\(924\) 0 0
\(925\) 0.603361 0.506280i 0.0198384 0.0166464i
\(926\) 0 0
\(927\) 6.80641 27.3626i 0.223552 0.898704i
\(928\) 0 0
\(929\) −3.48369 19.7570i −0.114296 0.648206i −0.987096 0.160128i \(-0.948809\pi\)
0.872800 0.488078i \(-0.162302\pi\)
\(930\) 0 0
\(931\) 10.0943 3.67401i 0.330826 0.120411i
\(932\) 0 0
\(933\) 6.08135 + 18.6991i 0.199095 + 0.612182i
\(934\) 0 0
\(935\) −2.62456 + 4.54587i −0.0858323 + 0.148666i
\(936\) 0 0
\(937\) −8.77086 15.1916i −0.286532 0.496287i 0.686448 0.727179i \(-0.259169\pi\)
−0.972979 + 0.230892i \(0.925836\pi\)
\(938\) 0 0
\(939\) −38.3186 + 5.39599i −1.25048 + 0.176091i
\(940\) 0 0
\(941\) 36.8470 + 30.9183i 1.20118 + 1.00791i 0.999596 + 0.0284363i \(0.00905279\pi\)
0.201582 + 0.979472i \(0.435392\pi\)
\(942\) 0 0
\(943\) −30.5671 11.1255i −0.995402 0.362297i
\(944\) 0 0
\(945\) 49.8673 22.2512i 1.62218 0.723833i
\(946\) 0 0
\(947\) 31.4351 + 11.4414i 1.02150 + 0.371796i 0.797839 0.602870i \(-0.205976\pi\)
0.223663 + 0.974667i \(0.428199\pi\)
\(948\) 0 0
\(949\) 17.0671 + 14.3210i 0.554021 + 0.464879i
\(950\) 0 0
\(951\) −7.21779 9.23316i −0.234053 0.299406i
\(952\) 0 0
\(953\) −4.37147 7.57160i −0.141606 0.245268i 0.786496 0.617596i \(-0.211893\pi\)
−0.928101 + 0.372327i \(0.878560\pi\)
\(954\) 0 0
\(955\) −3.44900 + 5.97384i −0.111607 + 0.193309i
\(956\) 0 0
\(957\) 5.38631 + 1.14336i 0.174115 + 0.0369596i
\(958\) 0 0
\(959\) 36.0319 13.1146i 1.16353 0.423491i
\(960\) 0 0
\(961\) 13.3381 + 75.6439i 0.430260 + 2.44013i
\(962\) 0 0
\(963\) 11.5612 + 0.802106i 0.372556 + 0.0258475i
\(964\) 0 0
\(965\) −18.9394 + 15.8920i −0.609679 + 0.511582i
\(966\) 0 0
\(967\) 3.78186 21.4480i 0.121616 0.689720i −0.861644 0.507513i \(-0.830565\pi\)
0.983260 0.182207i \(-0.0583241\pi\)
\(968\) 0 0
\(969\) 0.207620 5.99229i 0.00666970 0.192500i
\(970\) 0 0
\(971\) −4.16181 −0.133559 −0.0667795 0.997768i \(-0.521272\pi\)
−0.0667795 + 0.997768i \(0.521272\pi\)
\(972\) 0 0
\(973\) −10.1812 −0.326395
\(974\) 0 0
\(975\) 0.00976066 0.281711i 0.000312591 0.00902196i
\(976\) 0 0
\(977\) −9.25341 + 52.4787i −0.296043 + 1.67894i 0.366891 + 0.930264i \(0.380422\pi\)
−0.662933 + 0.748678i \(0.730689\pi\)
\(978\) 0 0
\(979\) −0.917461 + 0.769842i −0.0293222 + 0.0246042i
\(980\) 0 0
\(981\) −53.2637 3.69538i −1.70058 0.117984i
\(982\) 0 0
\(983\) −0.0564764 0.320293i −0.00180132 0.0102158i 0.983894 0.178754i \(-0.0572065\pi\)
−0.985695 + 0.168538i \(0.946095\pi\)
\(984\) 0 0
\(985\) 20.3161 7.39445i 0.647324 0.235607i
\(986\) 0 0
\(987\) 74.3951 + 15.7920i 2.36802 + 0.502664i
\(988\) 0 0
\(989\) −0.0156098 + 0.0270369i −0.000496362 + 0.000859724i
\(990\) 0 0
\(991\) 23.4316 + 40.5847i 0.744329 + 1.28922i 0.950508 + 0.310702i \(0.100564\pi\)
−0.206178 + 0.978514i \(0.566103\pi\)
\(992\) 0 0
\(993\) −23.0550 29.4925i −0.731629 0.935917i
\(994\) 0 0
\(995\) −38.2273 32.0765i −1.21189 1.01689i
\(996\) 0 0
\(997\) 18.1928 + 6.62164i 0.576172 + 0.209710i 0.613637 0.789588i \(-0.289706\pi\)
−0.0374646 + 0.999298i \(0.511928\pi\)
\(998\) 0 0
\(999\) −28.1033 20.3831i −0.889148 0.644893i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 864.2.y.c.193.5 yes 54
4.3 odd 2 864.2.y.b.193.5 54
27.7 even 9 inner 864.2.y.c.385.5 yes 54
108.7 odd 18 864.2.y.b.385.5 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.y.b.193.5 54 4.3 odd 2
864.2.y.b.385.5 yes 54 108.7 odd 18
864.2.y.c.193.5 yes 54 1.1 even 1 trivial
864.2.y.c.385.5 yes 54 27.7 even 9 inner