Properties

Label 855.2.be.d.334.3
Level $855$
Weight $2$
Character 855.334
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
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] = [855,2,Mod(64,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.be (of order \(6\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 334.3
Root \(-1.83525 - 1.05958i\) of defining polynomial
Character \(\chi\) \(=\) 855.334
Dual form 855.2.be.d.64.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.408663 - 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(-1.47848 - 1.67752i) q^{5} +1.17540i q^{7} +1.78246i q^{8} +O(q^{10})\) \(q+(-0.408663 - 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(-1.47848 - 1.67752i) q^{5} +1.17540i q^{7} +1.78246i q^{8} +(0.208403 + 1.03438i) q^{10} -0.713538 q^{11} +(-3.55344 + 2.05158i) q^{13} +(0.277326 - 0.480342i) q^{14} +(-1.35677 + 2.34999i) q^{16} +(2.21038 + 1.27616i) q^{17} +(-1.57031 - 4.06622i) q^{19} +(-1.26819 + 3.76645i) q^{20} +(0.291597 + 0.168353i) q^{22} +(-0.525730 + 0.303530i) q^{23} +(-0.628179 + 4.96038i) q^{25} +1.93621 q^{26} +(1.80918 - 1.04453i) q^{28} +(0.429693 + 0.744250i) q^{29} +2.50914 q^{31} +(4.19623 - 2.42270i) q^{32} +(-0.602201 - 1.04304i) q^{34} +(1.97176 - 1.73781i) q^{35} +9.38171i q^{37} +(-0.317665 + 2.03222i) q^{38} +(2.99012 - 2.63533i) q^{40} +(-2.06117 + 3.57005i) q^{41} +(8.76759 + 5.06197i) q^{43} +(0.634095 + 1.09828i) q^{44} +0.286462 q^{46} +(-9.10919 + 5.25919i) q^{47} +5.61844 q^{49} +(1.42708 - 1.87891i) q^{50} +(6.31561 + 3.64632i) q^{52} +(4.31330 - 2.49028i) q^{53} +(1.05495 + 1.19698i) q^{55} -2.09510 q^{56} -0.405530i q^{58} +(3.12496 - 5.41259i) q^{59} +(2.27733 + 3.94444i) q^{61} +(-1.02539 - 0.592010i) q^{62} +3.14061 q^{64} +(8.69527 + 2.92776i) q^{65} +(-4.48783 + 2.59105i) q^{67} -4.53632i q^{68} +(-1.21581 + 0.244957i) q^{70} +(-6.58393 + 11.4037i) q^{71} +(-10.7199 - 6.18914i) q^{73} +(2.21354 - 3.83396i) q^{74} +(-4.86329 + 6.03053i) q^{76} -0.838691i q^{77} +(-2.98173 + 5.16450i) q^{79} +(5.94813 - 1.19841i) q^{80} +(1.68465 - 0.972633i) q^{82} +13.8603i q^{83} +(-1.12721 - 5.59475i) q^{85} +(-2.38866 - 4.13729i) q^{86} -1.27185i q^{88} +(-7.98173 - 13.8248i) q^{89} +(-2.41142 - 4.17670i) q^{91} +(0.934393 + 0.539472i) q^{92} +4.96345 q^{94} +(-4.49951 + 8.64606i) q^{95} +(-14.4643 - 8.35099i) q^{97} +(-2.29605 - 1.32563i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.408663 0.235942i −0.288969 0.166836i 0.348508 0.937306i \(-0.386688\pi\)
−0.637477 + 0.770470i \(0.720022\pi\)
\(3\) 0 0
\(4\) −0.888663 1.53921i −0.444331 0.769605i
\(5\) −1.47848 1.67752i −0.661197 0.750212i
\(6\) 0 0
\(7\) 1.17540i 0.444259i 0.975017 + 0.222129i \(0.0713007\pi\)
−0.975017 + 0.222129i \(0.928699\pi\)
\(8\) 1.78246i 0.630194i
\(9\) 0 0
\(10\) 0.208403 + 1.03438i 0.0659029 + 0.327099i
\(11\) −0.713538 −0.215140 −0.107570 0.994198i \(-0.534307\pi\)
−0.107570 + 0.994198i \(0.534307\pi\)
\(12\) 0 0
\(13\) −3.55344 + 2.05158i −0.985546 + 0.569005i −0.903940 0.427659i \(-0.859338\pi\)
−0.0816060 + 0.996665i \(0.526005\pi\)
\(14\) 0.277326 0.480342i 0.0741184 0.128377i
\(15\) 0 0
\(16\) −1.35677 + 2.34999i −0.339192 + 0.587498i
\(17\) 2.21038 + 1.27616i 0.536096 + 0.309515i 0.743495 0.668741i \(-0.233167\pi\)
−0.207399 + 0.978256i \(0.566500\pi\)
\(18\) 0 0
\(19\) −1.57031 4.06622i −0.360253 0.932855i
\(20\) −1.26819 + 3.76645i −0.283576 + 0.842203i
\(21\) 0 0
\(22\) 0.291597 + 0.168353i 0.0621686 + 0.0358931i
\(23\) −0.525730 + 0.303530i −0.109622 + 0.0632904i −0.553809 0.832644i \(-0.686826\pi\)
0.444186 + 0.895934i \(0.353493\pi\)
\(24\) 0 0
\(25\) −0.628179 + 4.96038i −0.125636 + 0.992076i
\(26\) 1.93621 0.379722
\(27\) 0 0
\(28\) 1.80918 1.04453i 0.341904 0.197398i
\(29\) 0.429693 + 0.744250i 0.0797920 + 0.138204i 0.903160 0.429304i \(-0.141241\pi\)
−0.823368 + 0.567508i \(0.807908\pi\)
\(30\) 0 0
\(31\) 2.50914 0.450654 0.225327 0.974283i \(-0.427655\pi\)
0.225327 + 0.974283i \(0.427655\pi\)
\(32\) 4.19623 2.42270i 0.741796 0.428276i
\(33\) 0 0
\(34\) −0.602201 1.04304i −0.103277 0.178880i
\(35\) 1.97176 1.73781i 0.333288 0.293743i
\(36\) 0 0
\(37\) 9.38171i 1.54234i 0.636627 + 0.771172i \(0.280329\pi\)
−0.636627 + 0.771172i \(0.719671\pi\)
\(38\) −0.317665 + 2.03222i −0.0515320 + 0.329669i
\(39\) 0 0
\(40\) 2.99012 2.63533i 0.472779 0.416683i
\(41\) −2.06117 + 3.57005i −0.321901 + 0.557548i −0.980880 0.194612i \(-0.937655\pi\)
0.658979 + 0.752161i \(0.270988\pi\)
\(42\) 0 0
\(43\) 8.76759 + 5.06197i 1.33705 + 0.771944i 0.986368 0.164553i \(-0.0526181\pi\)
0.350677 + 0.936496i \(0.385951\pi\)
\(44\) 0.634095 + 1.09828i 0.0955934 + 0.165573i
\(45\) 0 0
\(46\) 0.286462 0.0422365
\(47\) −9.10919 + 5.25919i −1.32871 + 0.767132i −0.985100 0.171980i \(-0.944984\pi\)
−0.343611 + 0.939112i \(0.611650\pi\)
\(48\) 0 0
\(49\) 5.61844 0.802634
\(50\) 1.42708 1.87891i 0.201819 0.265718i
\(51\) 0 0
\(52\) 6.31561 + 3.64632i 0.875818 + 0.505654i
\(53\) 4.31330 2.49028i 0.592477 0.342067i −0.173599 0.984816i \(-0.555540\pi\)
0.766076 + 0.642750i \(0.222206\pi\)
\(54\) 0 0
\(55\) 1.05495 + 1.19698i 0.142250 + 0.161400i
\(56\) −2.09510 −0.279969
\(57\) 0 0
\(58\) 0.405530i 0.0532488i
\(59\) 3.12496 5.41259i 0.406835 0.704659i −0.587698 0.809080i \(-0.699966\pi\)
0.994533 + 0.104421i \(0.0332991\pi\)
\(60\) 0 0
\(61\) 2.27733 + 3.94444i 0.291582 + 0.505034i 0.974184 0.225756i \(-0.0724852\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(62\) −1.02539 0.592010i −0.130225 0.0751854i
\(63\) 0 0
\(64\) 3.14061 0.392577
\(65\) 8.69527 + 2.92776i 1.07851 + 0.363144i
\(66\) 0 0
\(67\) −4.48783 + 2.59105i −0.548276 + 0.316547i −0.748426 0.663218i \(-0.769190\pi\)
0.200151 + 0.979765i \(0.435857\pi\)
\(68\) 4.53632i 0.550109i
\(69\) 0 0
\(70\) −1.21581 + 0.244957i −0.145317 + 0.0292779i
\(71\) −6.58393 + 11.4037i −0.781368 + 1.35337i 0.149776 + 0.988720i \(0.452145\pi\)
−0.931145 + 0.364650i \(0.881189\pi\)
\(72\) 0 0
\(73\) −10.7199 6.18914i −1.25467 0.724384i −0.282637 0.959227i \(-0.591209\pi\)
−0.972033 + 0.234842i \(0.924543\pi\)
\(74\) 2.21354 3.83396i 0.257319 0.445689i
\(75\) 0 0
\(76\) −4.86329 + 6.03053i −0.557857 + 0.691749i
\(77\) 0.838691i 0.0955777i
\(78\) 0 0
\(79\) −2.98173 + 5.16450i −0.335471 + 0.581052i −0.983575 0.180499i \(-0.942229\pi\)
0.648105 + 0.761551i \(0.275562\pi\)
\(80\) 5.94813 1.19841i 0.665021 0.133986i
\(81\) 0 0
\(82\) 1.68465 0.972633i 0.186038 0.107409i
\(83\) 13.8603i 1.52136i 0.649124 + 0.760682i \(0.275136\pi\)
−0.649124 + 0.760682i \(0.724864\pi\)
\(84\) 0 0
\(85\) −1.12721 5.59475i −0.122263 0.606836i
\(86\) −2.38866 4.13729i −0.257576 0.446135i
\(87\) 0 0
\(88\) 1.27185i 0.135580i
\(89\) −7.98173 13.8248i −0.846061 1.46542i −0.884696 0.466168i \(-0.845634\pi\)
0.0386349 0.999253i \(-0.487699\pi\)
\(90\) 0 0
\(91\) −2.41142 4.17670i −0.252786 0.437837i
\(92\) 0.934393 + 0.539472i 0.0974172 + 0.0562439i
\(93\) 0 0
\(94\) 4.96345 0.511941
\(95\) −4.49951 + 8.64606i −0.461640 + 0.887067i
\(96\) 0 0
\(97\) −14.4643 8.35099i −1.46863 0.847915i −0.469249 0.883066i \(-0.655475\pi\)
−0.999382 + 0.0351512i \(0.988809\pi\)
\(98\) −2.29605 1.32563i −0.231936 0.133908i
\(99\) 0 0
\(100\) 8.19331 3.44121i 0.819331 0.344121i
\(101\) 7.01362 + 12.1479i 0.697881 + 1.20877i 0.969200 + 0.246276i \(0.0792071\pi\)
−0.271318 + 0.962490i \(0.587460\pi\)
\(102\) 0 0
\(103\) 3.55382i 0.350169i −0.984553 0.175084i \(-0.943980\pi\)
0.984553 0.175084i \(-0.0560198\pi\)
\(104\) −3.65685 6.33385i −0.358584 0.621085i
\(105\) 0 0
\(106\) −2.35025 −0.228276
\(107\) 3.63127i 0.351048i −0.984475 0.175524i \(-0.943838\pi\)
0.984475 0.175524i \(-0.0561620\pi\)
\(108\) 0 0
\(109\) −3.11134 + 5.38899i −0.298012 + 0.516172i −0.975681 0.219195i \(-0.929657\pi\)
0.677669 + 0.735367i \(0.262990\pi\)
\(110\) −0.148704 0.738069i −0.0141783 0.0703721i
\(111\) 0 0
\(112\) −2.76218 1.59474i −0.261001 0.150689i
\(113\) 12.2707i 1.15433i −0.816626 0.577167i \(-0.804158\pi\)
0.816626 0.577167i \(-0.195842\pi\)
\(114\) 0 0
\(115\) 1.28646 + 0.433161i 0.119963 + 0.0403925i
\(116\) 0.763705 1.32278i 0.0709082 0.122817i
\(117\) 0 0
\(118\) −2.55411 + 1.47462i −0.235125 + 0.135750i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) −10.4909 −0.953715
\(122\) 2.14927i 0.194585i
\(123\) 0 0
\(124\) −2.22978 3.86209i −0.200240 0.346826i
\(125\) 9.24992 6.28005i 0.827338 0.561705i
\(126\) 0 0
\(127\) 1.86879 1.07894i 0.165828 0.0957408i −0.414789 0.909918i \(-0.636145\pi\)
0.580617 + 0.814177i \(0.302811\pi\)
\(128\) −9.67592 5.58639i −0.855239 0.493772i
\(129\) 0 0
\(130\) −2.86266 3.24804i −0.251072 0.284872i
\(131\) −8.77471 + 15.1982i −0.766650 + 1.32788i 0.172720 + 0.984971i \(0.444744\pi\)
−0.939370 + 0.342906i \(0.888589\pi\)
\(132\) 0 0
\(133\) 4.77943 1.84574i 0.414429 0.160046i
\(134\) 2.44535 0.211246
\(135\) 0 0
\(136\) −2.27471 + 3.93991i −0.195055 + 0.337845i
\(137\) −4.39469 + 2.53728i −0.375464 + 0.216774i −0.675843 0.737046i \(-0.736220\pi\)
0.300379 + 0.953820i \(0.402887\pi\)
\(138\) 0 0
\(139\) 2.99086 + 5.18033i 0.253682 + 0.439390i 0.964537 0.263949i \(-0.0850251\pi\)
−0.710855 + 0.703339i \(0.751692\pi\)
\(140\) −4.42708 1.49063i −0.374156 0.125981i
\(141\) 0 0
\(142\) 5.38122 3.10685i 0.451582 0.260721i
\(143\) 2.53551 1.46388i 0.212030 0.122416i
\(144\) 0 0
\(145\) 0.613205 1.82118i 0.0509239 0.151241i
\(146\) 2.92056 + 5.05855i 0.241707 + 0.418649i
\(147\) 0 0
\(148\) 14.4404 8.33718i 1.18699 0.685312i
\(149\) −4.80008 + 8.31399i −0.393238 + 0.681108i −0.992875 0.119164i \(-0.961979\pi\)
0.599636 + 0.800273i \(0.295312\pi\)
\(150\) 0 0
\(151\) 7.53638 0.613302 0.306651 0.951822i \(-0.400792\pi\)
0.306651 + 0.951822i \(0.400792\pi\)
\(152\) 7.24787 2.79901i 0.587880 0.227029i
\(153\) 0 0
\(154\) −0.197882 + 0.342742i −0.0159458 + 0.0276190i
\(155\) −3.70971 4.20914i −0.297971 0.338086i
\(156\) 0 0
\(157\) 8.53560 + 4.92803i 0.681215 + 0.393300i 0.800313 0.599583i \(-0.204667\pi\)
−0.119098 + 0.992883i \(0.538000\pi\)
\(158\) 2.43705 1.40703i 0.193881 0.111937i
\(159\) 0 0
\(160\) −10.2682 3.45737i −0.811772 0.273329i
\(161\) −0.356769 0.617942i −0.0281173 0.0487007i
\(162\) 0 0
\(163\) 0.0688234i 0.00539067i 0.999996 + 0.00269533i \(0.000857952\pi\)
−0.999996 + 0.00269533i \(0.999142\pi\)
\(164\) 7.32674 0.572122
\(165\) 0 0
\(166\) 3.27022 5.66419i 0.253819 0.439627i
\(167\) 14.4143 8.32212i 1.11542 0.643985i 0.175189 0.984535i \(-0.443946\pi\)
0.940227 + 0.340550i \(0.110613\pi\)
\(168\) 0 0
\(169\) 1.91794 3.32197i 0.147534 0.255536i
\(170\) −0.859386 + 2.55233i −0.0659119 + 0.195755i
\(171\) 0 0
\(172\) 17.9935i 1.37200i
\(173\) −10.5097 6.06778i −0.799038 0.461325i 0.0440965 0.999027i \(-0.485959\pi\)
−0.843135 + 0.537702i \(0.819292\pi\)
\(174\) 0 0
\(175\) −5.83042 0.738361i −0.440739 0.0558148i
\(176\) 0.968106 1.67681i 0.0729737 0.126394i
\(177\) 0 0
\(178\) 7.53290i 0.564614i
\(179\) 11.7538 0.878522 0.439261 0.898360i \(-0.355240\pi\)
0.439261 + 0.898360i \(0.355240\pi\)
\(180\) 0 0
\(181\) 4.41794 + 7.65210i 0.328383 + 0.568776i 0.982191 0.187884i \(-0.0601631\pi\)
−0.653808 + 0.756660i \(0.726830\pi\)
\(182\) 2.27582i 0.168695i
\(183\) 0 0
\(184\) −0.541030 0.937092i −0.0398853 0.0690833i
\(185\) 15.7380 13.8707i 1.15708 1.01979i
\(186\) 0 0
\(187\) −1.57719 0.910591i −0.115336 0.0665890i
\(188\) 16.1900 + 9.34730i 1.18078 + 0.681722i
\(189\) 0 0
\(190\) 3.87875 2.47171i 0.281394 0.179316i
\(191\) −14.2447 −1.03071 −0.515355 0.856977i \(-0.672340\pi\)
−0.515355 + 0.856977i \(0.672340\pi\)
\(192\) 0 0
\(193\) −16.8924 9.75283i −1.21594 0.702024i −0.251894 0.967755i \(-0.581053\pi\)
−0.964047 + 0.265731i \(0.914387\pi\)
\(194\) 3.94070 + 6.82549i 0.282926 + 0.490041i
\(195\) 0 0
\(196\) −4.99290 8.64795i −0.356636 0.617711i
\(197\) 4.33232i 0.308665i −0.988019 0.154332i \(-0.950677\pi\)
0.988019 0.154332i \(-0.0493226\pi\)
\(198\) 0 0
\(199\) −6.31574 10.9392i −0.447711 0.775458i 0.550526 0.834818i \(-0.314427\pi\)
−0.998237 + 0.0593602i \(0.981094\pi\)
\(200\) −8.84168 1.11970i −0.625201 0.0791750i
\(201\) 0 0
\(202\) 6.61923i 0.465727i
\(203\) −0.874790 + 0.505060i −0.0613983 + 0.0354483i
\(204\) 0 0
\(205\) 9.03626 1.82059i 0.631119 0.127156i
\(206\) −0.838496 + 1.45232i −0.0584208 + 0.101188i
\(207\) 0 0
\(208\) 11.1341i 0.772009i
\(209\) 1.12047 + 2.90140i 0.0775048 + 0.200694i
\(210\) 0 0
\(211\) −11.1223 + 19.2645i −0.765694 + 1.32622i 0.174186 + 0.984713i \(0.444271\pi\)
−0.939879 + 0.341507i \(0.889063\pi\)
\(212\) −7.66614 4.42605i −0.526512 0.303982i
\(213\) 0 0
\(214\) −0.856769 + 1.48397i −0.0585675 + 0.101442i
\(215\) −4.47115 22.1919i −0.304930 1.51347i
\(216\) 0 0
\(217\) 2.94923i 0.200207i
\(218\) 2.54298 1.46819i 0.172232 0.0994383i
\(219\) 0 0
\(220\) 0.904901 2.68750i 0.0610084 0.181191i
\(221\) −10.4726 −0.704463
\(222\) 0 0
\(223\) −11.7974 6.81125i −0.790015 0.456115i 0.0499529 0.998752i \(-0.484093\pi\)
−0.839968 + 0.542636i \(0.817426\pi\)
\(224\) 2.84763 + 4.93224i 0.190265 + 0.329549i
\(225\) 0 0
\(226\) −2.89518 + 5.01460i −0.192585 + 0.333566i
\(227\) 6.58913i 0.437336i 0.975799 + 0.218668i \(0.0701711\pi\)
−0.975799 + 0.218668i \(0.929829\pi\)
\(228\) 0 0
\(229\) 0.585962 0.0387215 0.0193607 0.999813i \(-0.493837\pi\)
0.0193607 + 0.999813i \(0.493837\pi\)
\(230\) −0.423529 0.480547i −0.0279267 0.0316863i
\(231\) 0 0
\(232\) −1.32660 + 0.765910i −0.0870953 + 0.0502845i
\(233\) 6.19855 + 3.57873i 0.406080 + 0.234451i 0.689104 0.724662i \(-0.258004\pi\)
−0.283024 + 0.959113i \(0.591338\pi\)
\(234\) 0 0
\(235\) 22.2902 + 7.50527i 1.45405 + 0.489590i
\(236\) −11.1081 −0.723078
\(237\) 0 0
\(238\) 1.22599 0.707826i 0.0794691 0.0458815i
\(239\) 3.65498 0.236421 0.118211 0.992989i \(-0.462284\pi\)
0.118211 + 0.992989i \(0.462284\pi\)
\(240\) 0 0
\(241\) −8.63148 14.9502i −0.556002 0.963024i −0.997825 0.0659218i \(-0.979001\pi\)
0.441822 0.897103i \(-0.354332\pi\)
\(242\) 4.28723 + 2.47523i 0.275594 + 0.159114i
\(243\) 0 0
\(244\) 4.04755 7.01056i 0.259118 0.448805i
\(245\) −8.30676 9.42507i −0.530700 0.602146i
\(246\) 0 0
\(247\) 13.9221 + 11.2274i 0.885845 + 0.714385i
\(248\) 4.47243i 0.284000i
\(249\) 0 0
\(250\) −5.26183 + 0.383984i −0.332787 + 0.0242853i
\(251\) −9.70702 16.8130i −0.612702 1.06123i −0.990783 0.135458i \(-0.956749\pi\)
0.378082 0.925772i \(-0.376584\pi\)
\(252\) 0 0
\(253\) 0.375128 0.216580i 0.0235841 0.0136163i
\(254\) −1.01827 −0.0638921
\(255\) 0 0
\(256\) −0.504485 0.873793i −0.0315303 0.0546121i
\(257\) −12.0316 + 6.94643i −0.750509 + 0.433306i −0.825878 0.563849i \(-0.809320\pi\)
0.0753689 + 0.997156i \(0.475987\pi\)
\(258\) 0 0
\(259\) −11.0272 −0.685199
\(260\) −3.22073 15.9856i −0.199741 0.991386i
\(261\) 0 0
\(262\) 7.17180 4.14064i 0.443076 0.255810i
\(263\) −12.9803 7.49417i −0.800399 0.462110i 0.0432118 0.999066i \(-0.486241\pi\)
−0.843611 + 0.536955i \(0.819574\pi\)
\(264\) 0 0
\(265\) −10.5547 3.55382i −0.648367 0.218310i
\(266\) −2.38866 0.373382i −0.146458 0.0228935i
\(267\) 0 0
\(268\) 7.97633 + 4.60514i 0.487232 + 0.281304i
\(269\) −9.68613 + 16.7769i −0.590574 + 1.02290i 0.403582 + 0.914944i \(0.367765\pi\)
−0.994155 + 0.107960i \(0.965568\pi\)
\(270\) 0 0
\(271\) −5.95897 + 10.3212i −0.361982 + 0.626971i −0.988287 0.152607i \(-0.951233\pi\)
0.626305 + 0.779578i \(0.284566\pi\)
\(272\) −5.99795 + 3.46292i −0.363679 + 0.209970i
\(273\) 0 0
\(274\) 2.39460 0.144663
\(275\) 0.448230 3.53942i 0.0270293 0.213435i
\(276\) 0 0
\(277\) 10.9824i 0.659866i −0.944004 0.329933i \(-0.892974\pi\)
0.944004 0.329933i \(-0.107026\pi\)
\(278\) 2.82268i 0.169293i
\(279\) 0 0
\(280\) 3.09757 + 3.51458i 0.185115 + 0.210036i
\(281\) 7.32488 + 12.6871i 0.436965 + 0.756846i 0.997454 0.0713160i \(-0.0227199\pi\)
−0.560488 + 0.828162i \(0.689387\pi\)
\(282\) 0 0
\(283\) 16.3927 + 9.46435i 0.974447 + 0.562597i 0.900589 0.434672i \(-0.143136\pi\)
0.0738576 + 0.997269i \(0.476469\pi\)
\(284\) 23.4036 1.38875
\(285\) 0 0
\(286\) −1.38156 −0.0816934
\(287\) −4.19623 2.42270i −0.247696 0.143007i
\(288\) 0 0
\(289\) −5.24281 9.08082i −0.308401 0.534166i
\(290\) −0.680287 + 0.599570i −0.0399478 + 0.0352079i
\(291\) 0 0
\(292\) 22.0002i 1.28747i
\(293\) 5.59625i 0.326937i −0.986549 0.163468i \(-0.947732\pi\)
0.986549 0.163468i \(-0.0522681\pi\)
\(294\) 0 0
\(295\) −13.6999 + 2.76022i −0.797642 + 0.160706i
\(296\) −16.7225 −0.971976
\(297\) 0 0
\(298\) 3.92324 2.26508i 0.227267 0.131213i
\(299\) 1.24543 2.15715i 0.0720252 0.124751i
\(300\) 0 0
\(301\) −5.94983 + 10.3054i −0.342943 + 0.593994i
\(302\) −3.07984 1.77815i −0.177225 0.102321i
\(303\) 0 0
\(304\) 11.6861 + 1.82671i 0.670245 + 0.104769i
\(305\) 3.24992 9.65206i 0.186090 0.552675i
\(306\) 0 0
\(307\) −17.8678 10.3160i −1.01977 0.588764i −0.105732 0.994395i \(-0.533718\pi\)
−0.914037 + 0.405631i \(0.867052\pi\)
\(308\) −1.29092 + 0.745314i −0.0735571 + 0.0424682i
\(309\) 0 0
\(310\) 0.522912 + 2.59540i 0.0296994 + 0.147409i
\(311\) 24.6587 1.39827 0.699134 0.714991i \(-0.253569\pi\)
0.699134 + 0.714991i \(0.253569\pi\)
\(312\) 0 0
\(313\) −3.02985 + 1.74928i −0.171257 + 0.0988753i −0.583178 0.812344i \(-0.698191\pi\)
0.411921 + 0.911219i \(0.364858\pi\)
\(314\) −2.32546 4.02781i −0.131233 0.227303i
\(315\) 0 0
\(316\) 10.5990 0.596240
\(317\) −27.1680 + 15.6854i −1.52590 + 0.880982i −0.526377 + 0.850251i \(0.676450\pi\)
−0.999528 + 0.0307305i \(0.990217\pi\)
\(318\) 0 0
\(319\) −0.306602 0.531051i −0.0171664 0.0297331i
\(320\) −4.64334 5.26846i −0.259571 0.294516i
\(321\) 0 0
\(322\) 0.336707i 0.0187639i
\(323\) 1.71818 10.9919i 0.0956024 0.611603i
\(324\) 0 0
\(325\) −7.94441 18.9152i −0.440677 1.04922i
\(326\) 0.0162383 0.0281256i 0.000899358 0.00155773i
\(327\) 0 0
\(328\) −6.36347 3.67395i −0.351364 0.202860i
\(329\) −6.18164 10.7069i −0.340805 0.590292i
\(330\) 0 0
\(331\) 35.7497 1.96498 0.982492 0.186305i \(-0.0596512\pi\)
0.982492 + 0.186305i \(0.0596512\pi\)
\(332\) 21.3339 12.3171i 1.17085 0.675990i
\(333\) 0 0
\(334\) −7.85415 −0.429760
\(335\) 10.9817 + 3.69762i 0.599996 + 0.202023i
\(336\) 0 0
\(337\) −22.9403 13.2446i −1.24964 0.721480i −0.278602 0.960407i \(-0.589871\pi\)
−0.971038 + 0.238927i \(0.923204\pi\)
\(338\) −1.56758 + 0.905045i −0.0852653 + 0.0492279i
\(339\) 0 0
\(340\) −7.60978 + 6.70686i −0.412698 + 0.363731i
\(341\) −1.79036 −0.0969536
\(342\) 0 0
\(343\) 14.8317i 0.800836i
\(344\) −9.02276 + 15.6279i −0.486474 + 0.842599i
\(345\) 0 0
\(346\) 2.86329 + 4.95936i 0.153931 + 0.266617i
\(347\) 29.7392 + 17.1699i 1.59648 + 0.921729i 0.992158 + 0.124990i \(0.0398898\pi\)
0.604323 + 0.796739i \(0.293444\pi\)
\(348\) 0 0
\(349\) 21.4308 1.14717 0.573583 0.819148i \(-0.305553\pi\)
0.573583 + 0.819148i \(0.305553\pi\)
\(350\) 2.20847 + 1.67738i 0.118048 + 0.0896599i
\(351\) 0 0
\(352\) −2.99417 + 1.72869i −0.159590 + 0.0921393i
\(353\) 19.5659i 1.04139i 0.853744 + 0.520693i \(0.174326\pi\)
−0.853744 + 0.520693i \(0.825674\pi\)
\(354\) 0 0
\(355\) 28.8642 5.81546i 1.53195 0.308653i
\(356\) −14.1861 + 24.5711i −0.751863 + 1.30227i
\(357\) 0 0
\(358\) −4.80335 2.77322i −0.253865 0.146569i
\(359\) 8.23630 14.2657i 0.434695 0.752914i −0.562576 0.826746i \(-0.690189\pi\)
0.997271 + 0.0738319i \(0.0235228\pi\)
\(360\) 0 0
\(361\) −14.0683 + 12.7704i −0.740435 + 0.672128i
\(362\) 4.16951i 0.219144i
\(363\) 0 0
\(364\) −4.28588 + 7.42336i −0.224641 + 0.389090i
\(365\) 5.46676 + 27.1335i 0.286143 + 1.42023i
\(366\) 0 0
\(367\) 11.0286 6.36735i 0.575687 0.332373i −0.183730 0.982977i \(-0.558817\pi\)
0.759418 + 0.650603i \(0.225484\pi\)
\(368\) 1.64728i 0.0858705i
\(369\) 0 0
\(370\) −9.70424 + 1.95518i −0.504499 + 0.101645i
\(371\) 2.92708 + 5.06984i 0.151966 + 0.263213i
\(372\) 0 0
\(373\) 19.3342i 1.00109i 0.865711 + 0.500544i \(0.166867\pi\)
−0.865711 + 0.500544i \(0.833133\pi\)
\(374\) 0.429693 + 0.744250i 0.0222189 + 0.0384843i
\(375\) 0 0
\(376\) −9.37429 16.2368i −0.483442 0.837346i
\(377\) −3.05377 1.76310i −0.157277 0.0908041i
\(378\) 0 0
\(379\) −9.85789 −0.506366 −0.253183 0.967418i \(-0.581477\pi\)
−0.253183 + 0.967418i \(0.581477\pi\)
\(380\) 17.3066 0.757744i 0.887812 0.0388714i
\(381\) 0 0
\(382\) 5.82128 + 3.36092i 0.297843 + 0.171959i
\(383\) 17.6091 + 10.1666i 0.899784 + 0.519490i 0.877130 0.480253i \(-0.159455\pi\)
0.0226536 + 0.999743i \(0.492789\pi\)
\(384\) 0 0
\(385\) −1.40693 + 1.23999i −0.0717036 + 0.0631958i
\(386\) 4.60220 + 7.97125i 0.234246 + 0.405726i
\(387\) 0 0
\(388\) 29.6849i 1.50702i
\(389\) 0.502617 + 0.870559i 0.0254837 + 0.0441391i 0.878486 0.477768i \(-0.158554\pi\)
−0.853002 + 0.521907i \(0.825221\pi\)
\(390\) 0 0
\(391\) −1.54942 −0.0783574
\(392\) 10.0146i 0.505816i
\(393\) 0 0
\(394\) −1.02217 + 1.77046i −0.0514964 + 0.0891944i
\(395\) 13.0720 2.63371i 0.657724 0.132516i
\(396\) 0 0
\(397\) 8.54093 + 4.93111i 0.428657 + 0.247485i 0.698774 0.715342i \(-0.253729\pi\)
−0.270117 + 0.962827i \(0.587063\pi\)
\(398\) 5.96059i 0.298777i
\(399\) 0 0
\(400\) −10.8046 8.20631i −0.540228 0.410315i
\(401\) 14.9159 25.8351i 0.744865 1.29014i −0.205393 0.978680i \(-0.565847\pi\)
0.950258 0.311464i \(-0.100819\pi\)
\(402\) 0 0
\(403\) −8.91606 + 5.14769i −0.444140 + 0.256425i
\(404\) 12.4655 21.5909i 0.620181 1.07419i
\(405\) 0 0
\(406\) 0.476660 0.0236562
\(407\) 6.69420i 0.331819i
\(408\) 0 0
\(409\) 13.8221 + 23.9406i 0.683458 + 1.18378i 0.973919 + 0.226898i \(0.0728583\pi\)
−0.290460 + 0.956887i \(0.593808\pi\)
\(410\) −4.12234 1.38802i −0.203588 0.0685495i
\(411\) 0 0
\(412\) −5.47008 + 3.15815i −0.269491 + 0.155591i
\(413\) 6.36194 + 3.67307i 0.313051 + 0.180740i
\(414\) 0 0
\(415\) 23.2510 20.4922i 1.14135 1.00592i
\(416\) −9.94070 + 17.2178i −0.487383 + 0.844172i
\(417\) 0 0
\(418\) 0.226666 1.45006i 0.0110866 0.0709249i
\(419\) −11.2902 −0.551562 −0.275781 0.961220i \(-0.588936\pi\)
−0.275781 + 0.961220i \(0.588936\pi\)
\(420\) 0 0
\(421\) −2.27471 + 3.93991i −0.110863 + 0.192019i −0.916118 0.400908i \(-0.868695\pi\)
0.805256 + 0.592928i \(0.202028\pi\)
\(422\) 9.09059 5.24845i 0.442523 0.255491i
\(423\) 0 0
\(424\) 4.43883 + 7.68828i 0.215569 + 0.373376i
\(425\) −7.71877 + 10.1627i −0.374415 + 0.492962i
\(426\) 0 0
\(427\) −4.63629 + 2.67676i −0.224366 + 0.129538i
\(428\) −5.58929 + 3.22698i −0.270168 + 0.155982i
\(429\) 0 0
\(430\) −3.40880 + 10.1239i −0.164387 + 0.488220i
\(431\) 16.4517 + 28.4952i 0.792451 + 1.37256i 0.924445 + 0.381314i \(0.124528\pi\)
−0.131995 + 0.991250i \(0.542138\pi\)
\(432\) 0 0
\(433\) 19.3204 11.1547i 0.928481 0.536059i 0.0421503 0.999111i \(-0.486579\pi\)
0.886331 + 0.463052i \(0.153246\pi\)
\(434\) 0.695848 1.20524i 0.0334018 0.0578536i
\(435\) 0 0
\(436\) 11.0597 0.529664
\(437\) 2.05978 + 1.66110i 0.0985325 + 0.0794611i
\(438\) 0 0
\(439\) 2.85287 4.94131i 0.136160 0.235836i −0.789880 0.613261i \(-0.789857\pi\)
0.926040 + 0.377425i \(0.123191\pi\)
\(440\) −2.13356 + 1.88041i −0.101714 + 0.0896451i
\(441\) 0 0
\(442\) 4.27976 + 2.47092i 0.203568 + 0.117530i
\(443\) −10.0265 + 5.78881i −0.476374 + 0.275034i −0.718904 0.695109i \(-0.755356\pi\)
0.242530 + 0.970144i \(0.422023\pi\)
\(444\) 0 0
\(445\) −11.3905 + 33.8292i −0.539963 + 1.60366i
\(446\) 3.21412 + 5.56702i 0.152193 + 0.263606i
\(447\) 0 0
\(448\) 3.69147i 0.174406i
\(449\) −25.4726 −1.20213 −0.601063 0.799202i \(-0.705256\pi\)
−0.601063 + 0.799202i \(0.705256\pi\)
\(450\) 0 0
\(451\) 1.47072 2.54737i 0.0692537 0.119951i
\(452\) −18.8872 + 10.9046i −0.888381 + 0.512907i
\(453\) 0 0
\(454\) 1.55465 2.69274i 0.0729634 0.126376i
\(455\) −3.44128 + 10.2204i −0.161330 + 0.479140i
\(456\) 0 0
\(457\) 6.92830i 0.324092i 0.986783 + 0.162046i \(0.0518094\pi\)
−0.986783 + 0.162046i \(0.948191\pi\)
\(458\) −0.239461 0.138253i −0.0111893 0.00646014i
\(459\) 0 0
\(460\) −0.476506 2.36507i −0.0222172 0.110272i
\(461\) 16.2473 28.1411i 0.756712 1.31066i −0.187806 0.982206i \(-0.560138\pi\)
0.944519 0.328458i \(-0.106529\pi\)
\(462\) 0 0
\(463\) 21.5062i 0.999477i 0.866176 + 0.499738i \(0.166571\pi\)
−0.866176 + 0.499738i \(0.833429\pi\)
\(464\) −2.33198 −0.108259
\(465\) 0 0
\(466\) −1.68875 2.92499i −0.0782296 0.135498i
\(467\) 16.9509i 0.784392i −0.919882 0.392196i \(-0.871715\pi\)
0.919882 0.392196i \(-0.128285\pi\)
\(468\) 0 0
\(469\) −3.04551 5.27499i −0.140629 0.243576i
\(470\) −7.33838 8.32632i −0.338494 0.384064i
\(471\) 0 0
\(472\) 9.64771 + 5.57011i 0.444072 + 0.256385i
\(473\) −6.25601 3.61191i −0.287652 0.166076i
\(474\) 0 0
\(475\) 21.1564 5.23501i 0.970724 0.240199i
\(476\) 5.33198 0.244391
\(477\) 0 0
\(478\) −1.49366 0.862364i −0.0683183 0.0394436i
\(479\) −4.42894 7.67115i −0.202364 0.350504i 0.746926 0.664907i \(-0.231529\pi\)
−0.949290 + 0.314403i \(0.898196\pi\)
\(480\) 0 0
\(481\) −19.2473 33.3373i −0.877601 1.52005i
\(482\) 8.14611i 0.371045i
\(483\) 0 0
\(484\) 9.32284 + 16.1476i 0.423765 + 0.733983i
\(485\) 7.37628 + 36.6111i 0.334940 + 1.66242i
\(486\) 0 0
\(487\) 30.0628i 1.36227i 0.732156 + 0.681137i \(0.238514\pi\)
−0.732156 + 0.681137i \(0.761486\pi\)
\(488\) −7.03081 + 4.05924i −0.318270 + 0.183753i
\(489\) 0 0
\(490\) 1.17090 + 5.81159i 0.0528959 + 0.262541i
\(491\) 1.55017 2.68497i 0.0699580 0.121171i −0.828925 0.559360i \(-0.811047\pi\)
0.898883 + 0.438190i \(0.144380\pi\)
\(492\) 0 0
\(493\) 2.19343i 0.0987873i
\(494\) −3.04045 7.87306i −0.136796 0.354226i
\(495\) 0 0
\(496\) −3.40432 + 5.89645i −0.152858 + 0.264759i
\(497\) −13.4039 7.73874i −0.601246 0.347130i
\(498\) 0 0
\(499\) 16.0696 27.8333i 0.719372 1.24599i −0.241877 0.970307i \(-0.577763\pi\)
0.961249 0.275682i \(-0.0889037\pi\)
\(500\) −17.8864 8.65671i −0.799903 0.387140i
\(501\) 0 0
\(502\) 9.16117i 0.408883i
\(503\) 7.29040 4.20911i 0.325063 0.187675i −0.328584 0.944475i \(-0.606571\pi\)
0.653647 + 0.756800i \(0.273238\pi\)
\(504\) 0 0
\(505\) 10.0090 29.7261i 0.445393 1.32279i
\(506\) −0.204402 −0.00908676
\(507\) 0 0
\(508\) −3.32144 1.91764i −0.147365 0.0850813i
\(509\) −10.1725 17.6193i −0.450888 0.780962i 0.547553 0.836771i \(-0.315559\pi\)
−0.998441 + 0.0558093i \(0.982226\pi\)
\(510\) 0 0
\(511\) 7.27471 12.6002i 0.321814 0.557398i
\(512\) 22.8217i 1.00859i
\(513\) 0 0
\(514\) 6.55582 0.289165
\(515\) −5.96163 + 5.25427i −0.262701 + 0.231531i
\(516\) 0 0
\(517\) 6.49975 3.75263i 0.285859 0.165041i
\(518\) 4.50643 + 2.60179i 0.198001 + 0.114316i
\(519\) 0 0
\(520\) −5.21861 + 15.4990i −0.228851 + 0.679674i
\(521\) −15.3502 −0.672507 −0.336253 0.941772i \(-0.609160\pi\)
−0.336253 + 0.941772i \(0.609160\pi\)
\(522\) 0 0
\(523\) −11.4633 + 6.61835i −0.501256 + 0.289400i −0.729232 0.684267i \(-0.760122\pi\)
0.227976 + 0.973667i \(0.426789\pi\)
\(524\) 31.1910 1.36259
\(525\) 0 0
\(526\) 3.53638 + 6.12519i 0.154193 + 0.267071i
\(527\) 5.54614 + 3.20207i 0.241594 + 0.139484i
\(528\) 0 0
\(529\) −11.3157 + 19.5994i −0.491989 + 0.852149i
\(530\) 3.47480 + 3.94260i 0.150936 + 0.171256i
\(531\) 0 0
\(532\) −7.08827 5.71630i −0.307316 0.247833i
\(533\) 16.9146i 0.732653i
\(534\) 0 0
\(535\) −6.09155 + 5.36877i −0.263361 + 0.232112i
\(536\) −4.61844 7.99937i −0.199486 0.345520i
\(537\) 0 0
\(538\) 7.91673 4.57073i 0.341315 0.197058i
\(539\) −4.00897 −0.172679
\(540\) 0 0
\(541\) 13.8704 + 24.0242i 0.596335 + 1.03288i 0.993357 + 0.115073i \(0.0367102\pi\)
−0.397022 + 0.917809i \(0.629956\pi\)
\(542\) 4.87043 2.81194i 0.209203 0.120783i
\(543\) 0 0
\(544\) 12.3670 0.530232
\(545\) 13.6402 2.74819i 0.584283 0.117719i
\(546\) 0 0
\(547\) 14.7745 8.53008i 0.631714 0.364720i −0.149702 0.988731i \(-0.547831\pi\)
0.781415 + 0.624011i \(0.214498\pi\)
\(548\) 7.81080 + 4.50957i 0.333661 + 0.192639i
\(549\) 0 0
\(550\) −1.01827 + 1.34068i −0.0434193 + 0.0571666i
\(551\) 2.35153 2.91593i 0.100179 0.124223i
\(552\) 0 0
\(553\) −6.07035 3.50472i −0.258137 0.149036i
\(554\) −2.59120 + 4.48808i −0.110089 + 0.190680i
\(555\) 0 0
\(556\) 5.31574 9.20713i 0.225438 0.390469i
\(557\) 22.9856 13.2708i 0.973932 0.562300i 0.0734992 0.997295i \(-0.476583\pi\)
0.900433 + 0.434995i \(0.143250\pi\)
\(558\) 0 0
\(559\) −41.5401 −1.75696
\(560\) 1.40861 + 6.99142i 0.0595246 + 0.295441i
\(561\) 0 0
\(562\) 6.91298i 0.291606i
\(563\) 35.5594i 1.49865i 0.662203 + 0.749325i \(0.269622\pi\)
−0.662203 + 0.749325i \(0.730378\pi\)
\(564\) 0 0
\(565\) −20.5845 + 18.1421i −0.865995 + 0.763243i
\(566\) −4.46607 7.73546i −0.187723 0.325146i
\(567\) 0 0
\(568\) −20.3266 11.7356i −0.852886 0.492414i
\(569\) −14.9713 −0.627628 −0.313814 0.949485i \(-0.601607\pi\)
−0.313814 + 0.949485i \(0.601607\pi\)
\(570\) 0 0
\(571\) 5.92724 0.248047 0.124024 0.992279i \(-0.460420\pi\)
0.124024 + 0.992279i \(0.460420\pi\)
\(572\) −4.50643 2.60179i −0.188423 0.108786i
\(573\) 0 0
\(574\) 1.14323 + 1.98013i 0.0477175 + 0.0826492i
\(575\) −1.17537 2.79849i −0.0490165 0.116705i
\(576\) 0 0
\(577\) 14.5559i 0.605970i 0.952995 + 0.302985i \(0.0979832\pi\)
−0.952995 + 0.302985i \(0.902017\pi\)
\(578\) 4.94800i 0.205810i
\(579\) 0 0
\(580\) −3.34811 + 0.674566i −0.139023 + 0.0280098i
\(581\) −16.2914 −0.675880
\(582\) 0 0
\(583\) −3.07770 + 1.77691i −0.127465 + 0.0735922i
\(584\) 11.0319 19.1078i 0.456503 0.790686i
\(585\) 0 0
\(586\) −1.32039 + 2.28698i −0.0545448 + 0.0944744i
\(587\) −17.8262 10.2919i −0.735765 0.424794i 0.0847626 0.996401i \(-0.472987\pi\)
−0.820527 + 0.571607i \(0.806320\pi\)
\(588\) 0 0
\(589\) −3.94011 10.2027i −0.162350 0.420395i
\(590\) 6.24992 + 2.10439i 0.257305 + 0.0866364i
\(591\) 0 0
\(592\) −22.0469 12.7288i −0.906124 0.523151i
\(593\) −12.4120 + 7.16609i −0.509701 + 0.294276i −0.732711 0.680540i \(-0.761745\pi\)
0.223010 + 0.974816i \(0.428412\pi\)
\(594\) 0 0
\(595\) 6.57606 1.32492i 0.269592 0.0543165i
\(596\) 17.0626 0.698912
\(597\) 0 0
\(598\) −1.01792 + 0.587699i −0.0416260 + 0.0240328i
\(599\) −1.25008 2.16521i −0.0510770 0.0884680i 0.839356 0.543581i \(-0.182932\pi\)
−0.890434 + 0.455113i \(0.849599\pi\)
\(600\) 0 0
\(601\) 14.5259 0.592524 0.296262 0.955107i \(-0.404260\pi\)
0.296262 + 0.955107i \(0.404260\pi\)
\(602\) 4.86296 2.80763i 0.198199 0.114430i
\(603\) 0 0
\(604\) −6.69730 11.6001i −0.272509 0.472000i
\(605\) 15.5106 + 17.5987i 0.630594 + 0.715488i
\(606\) 0 0
\(607\) 31.8704i 1.29358i −0.762669 0.646789i \(-0.776111\pi\)
0.762669 0.646789i \(-0.223889\pi\)
\(608\) −16.4406 13.2584i −0.666754 0.537700i
\(609\) 0 0
\(610\) −3.60545 + 3.17765i −0.145980 + 0.128659i
\(611\) 21.5793 37.3764i 0.873004 1.51209i
\(612\) 0 0
\(613\) 17.3628 + 10.0244i 0.701277 + 0.404882i 0.807823 0.589425i \(-0.200646\pi\)
−0.106546 + 0.994308i \(0.533979\pi\)
\(614\) 4.86794 + 8.43152i 0.196454 + 0.340268i
\(615\) 0 0
\(616\) 1.49493 0.0602325
\(617\) 17.3914 10.0410i 0.700153 0.404234i −0.107251 0.994232i \(-0.534205\pi\)
0.807404 + 0.589998i \(0.200872\pi\)
\(618\) 0 0
\(619\) −5.62217 −0.225974 −0.112987 0.993596i \(-0.536042\pi\)
−0.112987 + 0.993596i \(0.536042\pi\)
\(620\) −3.18206 + 9.45053i −0.127795 + 0.379542i
\(621\) 0 0
\(622\) −10.0771 5.81803i −0.404056 0.233282i
\(623\) 16.2496 9.38171i 0.651026 0.375870i
\(624\) 0 0
\(625\) −24.2108 6.23202i −0.968431 0.249281i
\(626\) 1.65092 0.0659839
\(627\) 0 0
\(628\) 17.5174i 0.699022i
\(629\) −11.9726 + 20.7371i −0.477378 + 0.826844i
\(630\) 0 0
\(631\) 2.42184 + 4.19475i 0.0964120 + 0.166990i 0.910197 0.414176i \(-0.135930\pi\)
−0.813785 + 0.581166i \(0.802597\pi\)
\(632\) −9.20551 5.31481i −0.366176 0.211412i
\(633\) 0 0
\(634\) 14.8034 0.587918
\(635\) −4.57292 1.53974i −0.181471 0.0611025i
\(636\) 0 0
\(637\) −19.9648 + 11.5267i −0.791033 + 0.456703i
\(638\) 0.289361i 0.0114559i
\(639\) 0 0
\(640\) 4.93436 + 24.4910i 0.195048 + 0.968091i
\(641\) −12.6503 + 21.9110i −0.499658 + 0.865433i −1.00000 0.000394734i \(-0.999874\pi\)
0.500342 + 0.865828i \(0.333208\pi\)
\(642\) 0 0
\(643\) 12.0773 + 6.97283i 0.476282 + 0.274981i 0.718866 0.695149i \(-0.244662\pi\)
−0.242584 + 0.970130i \(0.577995\pi\)
\(644\) −0.634095 + 1.09828i −0.0249868 + 0.0432785i
\(645\) 0 0
\(646\) −3.29560 + 4.08658i −0.129664 + 0.160784i
\(647\) 2.51360i 0.0988200i 0.998779 + 0.0494100i \(0.0157341\pi\)
−0.998779 + 0.0494100i \(0.984266\pi\)
\(648\) 0 0
\(649\) −2.22978 + 3.86209i −0.0875264 + 0.151600i
\(650\) −1.21629 + 9.60435i −0.0477068 + 0.376714i
\(651\) 0 0
\(652\) 0.105934 0.0611608i 0.00414868 0.00239524i
\(653\) 1.92873i 0.0754770i 0.999288 + 0.0377385i \(0.0120154\pi\)
−0.999288 + 0.0377385i \(0.987985\pi\)
\(654\) 0 0
\(655\) 38.4687 7.75054i 1.50310 0.302839i
\(656\) −5.59306 9.68747i −0.218372 0.378232i
\(657\) 0 0
\(658\) 5.83404i 0.227434i
\(659\) −7.90042 13.6839i −0.307757 0.533050i 0.670115 0.742258i \(-0.266245\pi\)
−0.977871 + 0.209208i \(0.932912\pi\)
\(660\) 0 0
\(661\) −8.20178 14.2059i −0.319012 0.552546i 0.661270 0.750148i \(-0.270018\pi\)
−0.980282 + 0.197602i \(0.936685\pi\)
\(662\) −14.6096 8.43486i −0.567819 0.327830i
\(663\) 0 0
\(664\) −24.7054 −0.958755
\(665\) −10.1626 5.28872i −0.394087 0.205088i
\(666\) 0 0
\(667\) −0.451805 0.260850i −0.0174940 0.0101001i
\(668\) −25.6190 14.7911i −0.991228 0.572286i
\(669\) 0 0
\(670\) −3.61541 4.10213i −0.139675 0.158479i
\(671\) −1.62496 2.81451i −0.0627308 0.108653i
\(672\) 0 0
\(673\) 17.0878i 0.658686i −0.944210 0.329343i \(-0.893173\pi\)
0.944210 0.329343i \(-0.106827\pi\)
\(674\) 6.24992 + 10.8252i 0.240738 + 0.416970i
\(675\) 0 0
\(676\) −6.81761 −0.262216
\(677\) 4.57680i 0.175901i 0.996125 + 0.0879504i \(0.0280317\pi\)
−0.996125 + 0.0879504i \(0.971968\pi\)
\(678\) 0 0
\(679\) 9.81574 17.0014i 0.376693 0.652452i
\(680\) 9.97241 2.00921i 0.382425 0.0770496i
\(681\) 0 0
\(682\) 0.731656 + 0.422422i 0.0280166 + 0.0161754i
\(683\) 29.0692i 1.11230i −0.831082 0.556151i \(-0.812278\pi\)
0.831082 0.556151i \(-0.187722\pi\)
\(684\) 0 0
\(685\) 10.7538 + 3.62089i 0.410882 + 0.138347i
\(686\) 3.49942 6.06117i 0.133608 0.231416i
\(687\) 0 0
\(688\) −23.7912 + 13.7359i −0.907031 + 0.523675i
\(689\) −10.2180 + 17.6981i −0.389276 + 0.674245i
\(690\) 0 0
\(691\) −6.07833 −0.231230 −0.115615 0.993294i \(-0.536884\pi\)
−0.115615 + 0.993294i \(0.536884\pi\)
\(692\) 21.5689i 0.819925i
\(693\) 0 0
\(694\) −8.10220 14.0334i −0.307555 0.532701i
\(695\) 4.26819 12.6763i 0.161902 0.480838i
\(696\) 0 0
\(697\) −9.11194 + 5.26078i −0.345139 + 0.199266i
\(698\) −8.75799 5.05643i −0.331495 0.191389i
\(699\) 0 0
\(700\) 4.04479 + 9.63040i 0.152879 + 0.363995i
\(701\) 5.20569 9.01651i 0.196616 0.340549i −0.750813 0.660515i \(-0.770338\pi\)
0.947429 + 0.319966i \(0.103671\pi\)
\(702\) 0 0
\(703\) 38.1481 14.7322i 1.43878 0.555634i
\(704\) −2.24095 −0.0844589
\(705\) 0 0
\(706\) 4.61640 7.99585i 0.173741 0.300928i
\(707\) −14.2787 + 8.24380i −0.537005 + 0.310040i
\(708\) 0 0
\(709\) −0.265572 0.459984i −0.00997377 0.0172751i 0.860995 0.508613i \(-0.169841\pi\)
−0.870969 + 0.491338i \(0.836508\pi\)
\(710\) −13.1679 4.43371i −0.494181 0.166394i
\(711\) 0 0
\(712\) 24.6421 14.2271i 0.923500 0.533183i
\(713\) −1.31913 + 0.761599i −0.0494017 + 0.0285221i
\(714\) 0 0
\(715\) −6.20440 2.08907i −0.232031 0.0781266i
\(716\) −10.4452 18.0916i −0.390355 0.676114i
\(717\) 0 0
\(718\) −6.73174 + 3.88657i −0.251226 + 0.145046i
\(719\) −11.2135 + 19.4224i −0.418194 + 0.724334i −0.995758 0.0920118i \(-0.970670\pi\)
0.577564 + 0.816346i \(0.304004\pi\)
\(720\) 0 0
\(721\) 4.17716 0.155566
\(722\) 8.76227 1.89951i 0.326098 0.0706924i
\(723\) 0 0
\(724\) 7.85212 13.6003i 0.291822 0.505450i
\(725\) −3.96169 + 1.66392i −0.147133 + 0.0617964i
\(726\) 0 0
\(727\) 39.8141 + 22.9867i 1.47662 + 0.852529i 0.999652 0.0263888i \(-0.00840080\pi\)
0.476972 + 0.878918i \(0.341734\pi\)
\(728\) 7.44480 4.29826i 0.275923 0.159304i
\(729\) 0 0
\(730\) 4.16786 12.3783i 0.154259 0.458141i
\(731\) 12.9198 + 22.3778i 0.477856 + 0.827671i
\(732\) 0 0
\(733\) 42.5178i 1.57043i −0.619223 0.785215i \(-0.712552\pi\)
0.619223 0.785215i \(-0.287448\pi\)
\(734\) −6.00930 −0.221807
\(735\) 0 0
\(736\) −1.47072 + 2.54737i −0.0542116 + 0.0938972i
\(737\) 3.20224 1.84881i 0.117956 0.0681019i
\(738\) 0 0
\(739\) −1.70889 + 2.95988i −0.0628624 + 0.108881i −0.895744 0.444571i \(-0.853356\pi\)
0.832881 + 0.553452i \(0.186690\pi\)
\(740\) −35.3357 11.8978i −1.29897 0.437371i
\(741\) 0 0
\(742\) 2.76248i 0.101414i
\(743\) 8.41853 + 4.86044i 0.308846 + 0.178312i 0.646410 0.762990i \(-0.276270\pi\)
−0.337564 + 0.941303i \(0.609603\pi\)
\(744\) 0 0
\(745\) 21.0438 4.23983i 0.770984 0.155335i
\(746\) 4.56175 7.90119i 0.167018 0.289283i
\(747\) 0 0
\(748\) 3.23683i 0.118350i
\(749\) 4.26819 0.155956
\(750\) 0 0
\(751\) 5.69265 + 9.85996i 0.207728 + 0.359795i 0.950998 0.309196i \(-0.100060\pi\)
−0.743271 + 0.668991i \(0.766727\pi\)
\(752\) 28.5420i 1.04082i
\(753\) 0 0
\(754\) 0.831977 + 1.44103i 0.0302988 + 0.0524791i
\(755\) −11.1424 12.6425i −0.405514 0.460106i
\(756\) 0 0
\(757\) −19.7317 11.3921i −0.717160 0.414053i 0.0965464 0.995328i \(-0.469220\pi\)
−0.813707 + 0.581276i \(0.802554\pi\)
\(758\) 4.02856 + 2.32589i 0.146324 + 0.0844801i
\(759\) 0 0
\(760\) −15.4112 8.02020i −0.559025 0.290923i
\(761\) 36.7665 1.33279 0.666393 0.745601i \(-0.267837\pi\)
0.666393 + 0.745601i \(0.267837\pi\)
\(762\) 0 0
\(763\) −6.33421 3.65706i −0.229314 0.132394i
\(764\) 12.6587 + 21.9255i 0.457976 + 0.793238i
\(765\) 0 0
\(766\) −4.79747 8.30945i −0.173339 0.300233i
\(767\) 25.6444i 0.925965i
\(768\) 0 0
\(769\) −10.4004 18.0140i −0.375049 0.649603i 0.615286 0.788304i \(-0.289041\pi\)
−0.990334 + 0.138701i \(0.955707\pi\)
\(770\) 0.867524 0.174786i 0.0312634 0.00629885i
\(771\) 0 0
\(772\) 34.6679i 1.24772i
\(773\) 18.1944 10.5046i 0.654409 0.377823i −0.135735 0.990745i \(-0.543339\pi\)
0.790143 + 0.612922i \(0.210006\pi\)
\(774\) 0 0
\(775\) −1.57619 + 12.4463i −0.0566183 + 0.447083i
\(776\) 14.8853 25.7821i 0.534351 0.925523i
\(777\) 0 0
\(778\) 0.474354i 0.0170064i
\(779\) 17.7533 + 2.77509i 0.636077 + 0.0994280i
\(780\) 0 0
\(781\) 4.69788 8.13697i 0.168103 0.291164i
\(782\) 0.633190 + 0.365572i 0.0226428 + 0.0130728i
\(783\) 0 0
\(784\) −7.62292 + 13.2033i −0.272247 + 0.471546i
\(785\) −4.35284 21.6047i −0.155360 0.771104i
\(786\) 0 0
\(787\) 18.0606i 0.643791i −0.946775 0.321896i \(-0.895680\pi\)
0.946775 0.321896i \(-0.104320\pi\)
\(788\) −6.66834 + 3.84997i −0.237550 + 0.137149i
\(789\) 0 0
\(790\) −5.96345 2.00794i −0.212170 0.0714392i
\(791\) 14.4230 0.512823
\(792\) 0 0
\(793\) −16.1847 9.34422i −0.574734 0.331823i
\(794\) −2.32691 4.03033i −0.0825789 0.143031i
\(795\) 0 0
\(796\) −11.2251 + 19.4425i −0.397864 + 0.689121i
\(797\) 24.2571i 0.859229i −0.903012 0.429615i \(-0.858649\pi\)
0.903012 0.429615i \(-0.141351\pi\)
\(798\) 0 0
\(799\) −26.8463 −0.949756
\(800\) 9.38151 + 22.3368i 0.331687 + 0.789725i
\(801\) 0 0
\(802\) −12.1912 + 7.03857i −0.430485 + 0.248541i
\(803\) 7.64906 + 4.41619i 0.269930 + 0.155844i
\(804\) 0 0
\(805\) −0.509136 + 1.51211i −0.0179447 + 0.0532947i
\(806\) 4.85822 0.171124
\(807\) 0 0
\(808\) −21.6532 + 12.5015i −0.761758 + 0.439801i
\(809\) −4.27192 −0.150193 −0.0750964 0.997176i \(-0.523926\pi\)
−0.0750964 + 0.997176i \(0.523926\pi\)
\(810\) 0 0
\(811\) −5.09120 8.81821i −0.178776 0.309649i 0.762685 0.646770i \(-0.223880\pi\)
−0.941462 + 0.337120i \(0.890547\pi\)
\(812\) 1.55479 + 0.897657i 0.0545623 + 0.0315016i
\(813\) 0 0
\(814\) −1.57944 + 2.73568i −0.0553595 + 0.0958854i
\(815\) 0.115453 0.101754i 0.00404414 0.00356430i
\(816\) 0 0
\(817\) 6.81528 43.5998i 0.238436 1.52536i
\(818\) 13.0448i 0.456102i
\(819\) 0 0
\(820\) −10.8325 12.2908i −0.378286 0.429213i
\(821\) −28.0108 48.5162i −0.977585 1.69323i −0.671127 0.741343i \(-0.734189\pi\)
−0.306458 0.951884i \(-0.599144\pi\)
\(822\) 0 0
\(823\) 29.0479 16.7708i 1.01255 0.584593i 0.100610 0.994926i \(-0.467921\pi\)
0.911936 + 0.410333i \(0.134587\pi\)
\(824\) 6.33455 0.220674
\(825\) 0 0
\(826\) −1.73326 3.00210i −0.0603079 0.104456i
\(827\) −0.0313960 + 0.0181265i −0.00109175 + 0.000630320i −0.500546 0.865710i \(-0.666867\pi\)
0.499454 + 0.866340i \(0.333534\pi\)
\(828\) 0 0
\(829\) −39.5662 −1.37419 −0.687095 0.726567i \(-0.741115\pi\)
−0.687095 + 0.726567i \(0.741115\pi\)
\(830\) −14.3368 + 2.88853i −0.497637 + 0.100262i
\(831\) 0 0
\(832\) −11.1600 + 6.44321i −0.386902 + 0.223378i
\(833\) 12.4189 + 7.17005i 0.430289 + 0.248427i
\(834\) 0 0
\(835\) −35.2719 11.8763i −1.22064 0.410996i
\(836\) 3.47014 4.30301i 0.120017 0.148823i
\(837\) 0 0
\(838\) 4.61389 + 2.66383i 0.159384 + 0.0920205i
\(839\) −20.0811 + 34.7816i −0.693278 + 1.20079i 0.277480 + 0.960732i \(0.410501\pi\)
−0.970758 + 0.240061i \(0.922832\pi\)
\(840\) 0 0
\(841\) 14.1307 24.4751i 0.487266 0.843970i
\(842\) 1.85918 1.07340i 0.0640716 0.0369917i
\(843\) 0 0
\(844\) 39.5360 1.36089
\(845\) −8.40832 + 1.69408i −0.289255 + 0.0582782i
\(846\) 0 0
\(847\) 12.3309i 0.423696i
\(848\) 13.5150i 0.464106i
\(849\) 0 0
\(850\) 5.55218 2.33193i 0.190438 0.0799845i
\(851\) −2.84763 4.93224i −0.0976156 0.169075i
\(852\) 0 0
\(853\) −14.2563 8.23086i −0.488126 0.281819i 0.235671 0.971833i \(-0.424271\pi\)
−0.723796 + 0.690014i \(0.757605\pi\)
\(854\) 2.52624 0.0864463
\(855\) 0 0
\(856\) 6.47259 0.221229
\(857\) −4.85549 2.80332i −0.165860 0.0957595i 0.414772 0.909925i \(-0.363861\pi\)
−0.580632 + 0.814166i \(0.697195\pi\)
\(858\) 0 0
\(859\) 12.5149 + 21.6765i 0.427003 + 0.739591i 0.996605 0.0823296i \(-0.0262360\pi\)
−0.569602 + 0.821921i \(0.692903\pi\)
\(860\) −30.1846 + 26.6031i −1.02929 + 0.907160i
\(861\) 0 0
\(862\) 15.5266i 0.528837i
\(863\) 42.4307i 1.44436i 0.691707 + 0.722178i \(0.256859\pi\)
−0.691707 + 0.722178i \(0.743141\pi\)
\(864\) 0 0
\(865\) 5.35956 + 26.6014i 0.182231 + 0.904475i
\(866\) −10.5274 −0.357736
\(867\) 0 0
\(868\) 4.53949 2.62087i 0.154080 0.0889583i
\(869\) 2.12758 3.68507i 0.0721731 0.125007i
\(870\) 0 0
\(871\) 10.6315 18.4143i 0.360234 0.623943i
\(872\) −9.60566 5.54583i −0.325289 0.187806i
\(873\) 0 0
\(874\) −0.449833 1.16482i −0.0152158 0.0394005i
\(875\) 7.38156 + 10.8723i 0.249542 + 0.367552i
\(876\) 0 0
\(877\) 0.482588 + 0.278622i 0.0162958 + 0.00940841i 0.508126 0.861283i \(-0.330338\pi\)
−0.491830 + 0.870691i \(0.663672\pi\)
\(878\) −2.33172 + 1.34622i −0.0786919 + 0.0454328i
\(879\) 0 0
\(880\) −4.24422 + 0.855111i −0.143073 + 0.0288258i
\(881\) −8.35432 −0.281464 −0.140732 0.990048i \(-0.544946\pi\)
−0.140732 + 0.990048i \(0.544946\pi\)
\(882\) 0 0
\(883\) 16.8738 9.74209i 0.567848 0.327847i −0.188441 0.982084i \(-0.560343\pi\)
0.756289 + 0.654237i \(0.227010\pi\)
\(884\) 9.30660 + 16.1195i 0.313015 + 0.542158i
\(885\) 0 0
\(886\) 5.46329 0.183543
\(887\) 31.1226 17.9686i 1.04499 0.603328i 0.123751 0.992313i \(-0.460508\pi\)
0.921244 + 0.388985i \(0.127174\pi\)
\(888\) 0 0
\(889\) 1.26819 + 2.19657i 0.0425337 + 0.0736705i
\(890\) 12.6366 11.1373i 0.423580 0.373322i
\(891\) 0 0
\(892\) 24.2116i 0.810666i
\(893\) 35.6892 + 28.7814i 1.19429 + 0.963133i
\(894\) 0 0
\(895\) −17.3778 19.7173i −0.580876 0.659077i
\(896\) 6.56624 11.3731i 0.219363 0.379947i
\(897\) 0 0
\(898\) 10.4097 + 6.01005i 0.347377 + 0.200558i
\(899\) 1.07816 + 1.86743i 0.0359586 + 0.0622821i
\(900\) 0 0
\(901\) 12.7120 0.423499
\(902\) −1.20206 + 0.694011i −0.0400243 + 0.0231080i
\(903\) 0 0
\(904\) 21.8721 0.727455
\(905\) 6.30473 18.7247i 0.209576 0.622430i
\(906\) 0 0
\(907\) 42.3922 + 24.4751i 1.40761 + 0.812683i 0.995157 0.0982962i \(-0.0313393\pi\)
0.412452 + 0.910980i \(0.364673\pi\)
\(908\) 10.1420 5.85551i 0.336576 0.194322i
\(909\) 0 0
\(910\) 3.81775 3.36476i 0.126557 0.111541i
\(911\) 19.7811 0.655376 0.327688 0.944786i \(-0.393731\pi\)
0.327688 + 0.944786i \(0.393731\pi\)
\(912\) 0 0
\(913\) 9.88984i 0.327306i
\(914\) 1.63468 2.83134i 0.0540703 0.0936525i
\(915\) 0 0
\(916\) −0.520723 0.901919i −0.0172052 0.0298002i
\(917\) −17.8640 10.3138i −0.589921 0.340591i
\(918\) 0 0
\(919\) −26.0582 −0.859581 −0.429791 0.902929i \(-0.641413\pi\)
−0.429791 + 0.902929i \(0.641413\pi\)
\(920\) −0.772091 + 2.29307i −0.0254551 + 0.0756001i
\(921\) 0 0
\(922\) −13.2794 + 7.66684i −0.437332 + 0.252494i
\(923\) 54.0298i 1.77841i
\(924\) 0 0
\(925\) −46.5369 5.89340i −1.53012 0.193774i
\(926\) 5.07421 8.78879i 0.166749 0.288817i
\(927\) 0 0
\(928\) 3.60618 + 2.08203i 0.118379 + 0.0683460i
\(929\) 3.98900 6.90914i 0.130875 0.226682i −0.793139 0.609040i \(-0.791555\pi\)
0.924014 + 0.382359i \(0.124888\pi\)
\(930\) 0 0
\(931\) −8.82267 22.8458i −0.289151 0.748741i
\(932\) 12.7211i 0.416695i
\(933\) 0 0
\(934\) −3.99942 + 6.92719i −0.130865 + 0.226665i
\(935\) 0.804308 + 3.99207i 0.0263037 + 0.130555i
\(936\) 0 0
\(937\) 40.4037 23.3271i 1.31993 0.762063i 0.336215 0.941785i \(-0.390853\pi\)
0.983717 + 0.179722i \(0.0575198\pi\)
\(938\) 2.87426i 0.0938479i
\(939\) 0 0
\(940\) −8.25630 40.9789i −0.269291 1.33659i
\(941\) −0.700500 1.21330i −0.0228356 0.0395525i 0.854382 0.519646i \(-0.173936\pi\)
−0.877217 + 0.480093i \(0.840603\pi\)
\(942\) 0 0
\(943\) 2.50251i 0.0814930i
\(944\) 8.47969 + 14.6873i 0.275990 + 0.478030i
\(945\) 0 0
\(946\) 1.70440 + 2.95211i 0.0554149 + 0.0959814i
\(947\) 33.1255 + 19.1250i 1.07643 + 0.621480i 0.929932 0.367730i \(-0.119865\pi\)
0.146502 + 0.989210i \(0.453198\pi\)
\(948\) 0 0
\(949\) 50.7900 1.64871
\(950\) −9.88102 2.85233i −0.320583 0.0925419i
\(951\) 0 0
\(952\) −4.63096 2.67369i −0.150090 0.0866547i
\(953\) −47.1455 27.2195i −1.52719 0.881726i −0.999478 0.0323042i \(-0.989715\pi\)
−0.527715 0.849421i \(-0.676951\pi\)
\(954\) 0 0
\(955\) 21.0605 + 23.8958i 0.681502 + 0.773250i
\(956\) −3.24805 5.62579i −0.105049 0.181951i
\(957\) 0 0
\(958\) 4.17989i 0.135046i
\(959\) −2.98231 5.16551i −0.0963038 0.166803i
\(960\) 0 0
\(961\) −24.7042 −0.796911
\(962\) 18.1650i 0.585662i
\(963\) 0 0
\(964\) −15.3409 + 26.5713i −0.494099 + 0.855804i
\(965\) 8.61449 + 42.7568i 0.277310 + 1.37639i
\(966\) 0 0
\(967\) −4.32077 2.49460i −0.138946 0.0802208i 0.428915 0.903345i \(-0.358896\pi\)
−0.567862 + 0.823124i \(0.692229\pi\)
\(968\) 18.6995i 0.601026i
\(969\) 0 0
\(970\) 5.62367 16.7020i 0.180565 0.536268i
\(971\) −7.27006 + 12.5921i −0.233307 + 0.404100i −0.958779 0.284152i \(-0.908288\pi\)
0.725472 + 0.688252i \(0.241621\pi\)
\(972\) 0 0
\(973\) −6.08895 + 3.51546i −0.195203 + 0.112700i
\(974\) 7.09306 12.2855i 0.227276 0.393654i
\(975\) 0 0
\(976\) −12.3592 −0.395609
\(977\) 26.1353i 0.836141i −0.908415 0.418071i \(-0.862706\pi\)
0.908415 0.418071i \(-0.137294\pi\)
\(978\) 0 0
\(979\) 5.69527 + 9.86449i 0.182021 + 0.315270i
\(980\) −7.12524 + 21.1616i −0.227608 + 0.675981i
\(981\) 0 0
\(982\) −1.26699 + 0.731499i −0.0404314 + 0.0233431i
\(983\) −39.9376 23.0580i −1.27381 0.735436i −0.298109 0.954532i \(-0.596356\pi\)
−0.975703 + 0.219096i \(0.929689\pi\)
\(984\) 0 0
\(985\) −7.26757 + 6.40525i −0.231564 + 0.204088i
\(986\) 0.517523 0.896376i 0.0164813 0.0285464i
\(987\) 0 0
\(988\) 4.90929 31.4065i 0.156185 0.999174i
\(989\) −6.14585 −0.195427
\(990\) 0 0
\(991\) 15.6640 27.1308i 0.497582 0.861837i −0.502414 0.864627i \(-0.667555\pi\)
0.999996 + 0.00278993i \(0.000888065\pi\)
\(992\) 10.5289 6.07887i 0.334294 0.193004i
\(993\) 0 0
\(994\) 3.65178 + 6.32508i 0.115828 + 0.200619i
\(995\) −9.01304 + 26.7682i −0.285733 + 0.848609i
\(996\) 0 0
\(997\) −18.7186 + 10.8072i −0.592826 + 0.342268i −0.766214 0.642586i \(-0.777862\pi\)
0.173388 + 0.984854i \(0.444528\pi\)
\(998\) −13.1341 + 7.58296i −0.415752 + 0.240035i
\(999\) 0 0
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 855.2.be.d.334.3 12
3.2 odd 2 95.2.i.b.49.4 yes 12
5.4 even 2 inner 855.2.be.d.334.4 12
15.2 even 4 475.2.e.g.201.3 12
15.8 even 4 475.2.e.g.201.4 12
15.14 odd 2 95.2.i.b.49.3 12
19.7 even 3 inner 855.2.be.d.64.4 12
57.8 even 6 1805.2.b.g.1084.4 6
57.11 odd 6 1805.2.b.f.1084.3 6
57.26 odd 6 95.2.i.b.64.3 yes 12
95.64 even 6 inner 855.2.be.d.64.3 12
285.8 odd 12 9025.2.a.bt.1.4 6
285.68 even 12 9025.2.a.bu.1.3 6
285.83 even 12 475.2.e.g.26.4 12
285.122 odd 12 9025.2.a.bt.1.3 6
285.179 even 6 1805.2.b.g.1084.3 6
285.182 even 12 9025.2.a.bu.1.4 6
285.197 even 12 475.2.e.g.26.3 12
285.239 odd 6 1805.2.b.f.1084.4 6
285.254 odd 6 95.2.i.b.64.4 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.3 12 15.14 odd 2
95.2.i.b.49.4 yes 12 3.2 odd 2
95.2.i.b.64.3 yes 12 57.26 odd 6
95.2.i.b.64.4 yes 12 285.254 odd 6
475.2.e.g.26.3 12 285.197 even 12
475.2.e.g.26.4 12 285.83 even 12
475.2.e.g.201.3 12 15.2 even 4
475.2.e.g.201.4 12 15.8 even 4
855.2.be.d.64.3 12 95.64 even 6 inner
855.2.be.d.64.4 12 19.7 even 3 inner
855.2.be.d.334.3 12 1.1 even 1 trivial
855.2.be.d.334.4 12 5.4 even 2 inner
1805.2.b.f.1084.3 6 57.11 odd 6
1805.2.b.f.1084.4 6 285.239 odd 6
1805.2.b.g.1084.3 6 285.179 even 6
1805.2.b.g.1084.4 6 57.8 even 6
9025.2.a.bt.1.3 6 285.122 odd 12
9025.2.a.bt.1.4 6 285.8 odd 12
9025.2.a.bu.1.3 6 285.68 even 12
9025.2.a.bu.1.4 6 285.182 even 12