Properties

Label 432.2.v.a.35.3
Level $432$
Weight $2$
Character 432.35
Analytic conductor $3.450$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(35,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 35.3
Character \(\chi\) \(=\) 432.35
Dual form 432.2.v.a.395.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20346 + 0.742754i) q^{2} +(0.896632 - 1.78775i) q^{4} +(0.206232 - 0.769670i) q^{5} +(-2.17574 + 3.76849i) q^{7} +(0.248799 + 2.81746i) q^{8} +O(q^{10})\) \(q+(-1.20346 + 0.742754i) q^{2} +(0.896632 - 1.78775i) q^{4} +(0.206232 - 0.769670i) q^{5} +(-2.17574 + 3.76849i) q^{7} +(0.248799 + 2.81746i) q^{8} +(0.323483 + 1.07945i) q^{10} +(-1.05570 - 3.93991i) q^{11} +(-0.454903 + 1.69772i) q^{13} +(-0.180648 - 6.15127i) q^{14} +(-2.39210 - 3.20591i) q^{16} +6.68683i q^{17} +(-0.708282 + 0.708282i) q^{19} +(-1.19106 - 1.05880i) q^{20} +(4.19687 + 3.95740i) q^{22} +(-3.88191 + 2.24122i) q^{23} +(3.78027 + 2.18254i) q^{25} +(-0.713532 - 2.38102i) q^{26} +(4.78628 + 7.26863i) q^{28} +(1.06907 + 3.98981i) q^{29} +(-4.94177 + 2.85313i) q^{31} +(5.26000 + 2.08144i) q^{32} +(-4.96668 - 8.04734i) q^{34} +(2.45179 + 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(0.326309 - 1.37847i) q^{38} +(2.21983 + 0.389559i) q^{40} +(-1.36389 - 2.36233i) q^{41} +(-8.60436 + 2.30553i) q^{43} +(-7.99014 - 1.64533i) q^{44} +(3.00704 - 5.58052i) q^{46} +(-1.23164 + 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(-6.17049 + 0.181213i) q^{50} +(2.62722 + 2.33548i) q^{52} +(-1.68291 - 1.68291i) q^{53} -3.25015 q^{55} +(-11.1589 - 5.19247i) q^{56} +(-4.25002 - 4.00752i) q^{58} +(1.00516 + 0.269331i) q^{59} +(1.97401 - 0.528935i) q^{61} +(3.82804 - 7.10415i) q^{62} +(-7.87620 + 1.40197i) q^{64} +(1.21287 + 0.700250i) q^{65} +(8.01120 + 2.14659i) q^{67} +(11.9544 + 5.99563i) q^{68} +(-4.77170 - 1.12955i) q^{70} +8.05218i q^{71} -9.73126i q^{73} +(0.698727 - 2.95172i) q^{74} +(0.631163 + 1.90130i) q^{76} +(17.1444 + 4.59383i) q^{77} +(11.9835 + 6.91865i) q^{79} +(-2.96082 + 1.17997i) q^{80} +(3.39603 + 1.82994i) q^{82} +(-3.05012 + 0.817277i) q^{83} +(5.14666 + 1.37904i) q^{85} +(8.64256 - 9.16554i) q^{86} +(10.8379 - 3.95463i) q^{88} -1.71120 q^{89} +(-5.40809 - 5.40809i) q^{91} +(0.526101 + 8.94943i) q^{92} +(-0.102261 - 3.48211i) q^{94} +(0.399073 + 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +(14.8592 + 8.00683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20346 + 0.742754i −0.850975 + 0.525207i
\(3\) 0 0
\(4\) 0.896632 1.78775i 0.448316 0.893875i
\(5\) 0.206232 0.769670i 0.0922300 0.344207i −0.904355 0.426781i \(-0.859647\pi\)
0.996585 + 0.0825742i \(0.0263142\pi\)
\(6\) 0 0
\(7\) −2.17574 + 3.76849i −0.822352 + 1.42436i 0.0815745 + 0.996667i \(0.474005\pi\)
−0.903926 + 0.427688i \(0.859328\pi\)
\(8\) 0.248799 + 2.81746i 0.0879638 + 0.996124i
\(9\) 0 0
\(10\) 0.323483 + 1.07945i 0.102294 + 0.341351i
\(11\) −1.05570 3.93991i −0.318304 1.18793i −0.920874 0.389861i \(-0.872523\pi\)
0.602570 0.798066i \(-0.294144\pi\)
\(12\) 0 0
\(13\) −0.454903 + 1.69772i −0.126167 + 0.470863i −0.999879 0.0155820i \(-0.995040\pi\)
0.873711 + 0.486445i \(0.161707\pi\)
\(14\) −0.180648 6.15127i −0.0482803 1.64400i
\(15\) 0 0
\(16\) −2.39210 3.20591i −0.598026 0.801477i
\(17\) 6.68683i 1.62180i 0.585188 + 0.810898i \(0.301021\pi\)
−0.585188 + 0.810898i \(0.698979\pi\)
\(18\) 0 0
\(19\) −0.708282 + 0.708282i −0.162491 + 0.162491i −0.783669 0.621178i \(-0.786654\pi\)
0.621178 + 0.783669i \(0.286654\pi\)
\(20\) −1.19106 1.05880i −0.266330 0.236755i
\(21\) 0 0
\(22\) 4.19687 + 3.95740i 0.894776 + 0.843720i
\(23\) −3.88191 + 2.24122i −0.809433 + 0.467327i −0.846759 0.531977i \(-0.821449\pi\)
0.0373258 + 0.999303i \(0.488116\pi\)
\(24\) 0 0
\(25\) 3.78027 + 2.18254i 0.756053 + 0.436508i
\(26\) −0.713532 2.38102i −0.139935 0.466956i
\(27\) 0 0
\(28\) 4.78628 + 7.26863i 0.904523 + 1.37364i
\(29\) 1.06907 + 3.98981i 0.198520 + 0.740888i 0.991327 + 0.131415i \(0.0419522\pi\)
−0.792807 + 0.609473i \(0.791381\pi\)
\(30\) 0 0
\(31\) −4.94177 + 2.85313i −0.887568 + 0.512437i −0.873146 0.487459i \(-0.837924\pi\)
−0.0144215 + 0.999896i \(0.504591\pi\)
\(32\) 5.26000 + 2.08144i 0.929846 + 0.367949i
\(33\) 0 0
\(34\) −4.96668 8.04734i −0.851778 1.38011i
\(35\) 2.45179 + 2.45179i 0.414427 + 0.414427i
\(36\) 0 0
\(37\) −1.51665 + 1.51665i −0.249335 + 0.249335i −0.820698 0.571363i \(-0.806415\pi\)
0.571363 + 0.820698i \(0.306415\pi\)
\(38\) 0.326309 1.37847i 0.0529344 0.223617i
\(39\) 0 0
\(40\) 2.21983 + 0.389559i 0.350986 + 0.0615947i
\(41\) −1.36389 2.36233i −0.213005 0.368935i 0.739649 0.672993i \(-0.234992\pi\)
−0.952653 + 0.304058i \(0.901658\pi\)
\(42\) 0 0
\(43\) −8.60436 + 2.30553i −1.31215 + 0.351590i −0.846033 0.533131i \(-0.821015\pi\)
−0.466120 + 0.884722i \(0.654348\pi\)
\(44\) −7.99014 1.64533i −1.20456 0.248042i
\(45\) 0 0
\(46\) 3.00704 5.58052i 0.443364 0.822803i
\(47\) −1.23164 + 2.13327i −0.179654 + 0.311169i −0.941762 0.336280i \(-0.890831\pi\)
0.762108 + 0.647449i \(0.224164\pi\)
\(48\) 0 0
\(49\) −5.96768 10.3363i −0.852525 1.47662i
\(50\) −6.17049 + 0.181213i −0.872639 + 0.0256274i
\(51\) 0 0
\(52\) 2.62722 + 2.33548i 0.364330 + 0.323873i
\(53\) −1.68291 1.68291i −0.231165 0.231165i 0.582014 0.813179i \(-0.302265\pi\)
−0.813179 + 0.582014i \(0.802265\pi\)
\(54\) 0 0
\(55\) −3.25015 −0.438250
\(56\) −11.1589 5.19247i −1.49117 0.693872i
\(57\) 0 0
\(58\) −4.25002 4.00752i −0.558055 0.526213i
\(59\) 1.00516 + 0.269331i 0.130860 + 0.0350640i 0.323655 0.946175i \(-0.395088\pi\)
−0.192794 + 0.981239i \(0.561755\pi\)
\(60\) 0 0
\(61\) 1.97401 0.528935i 0.252747 0.0677232i −0.130221 0.991485i \(-0.541569\pi\)
0.382968 + 0.923762i \(0.374902\pi\)
\(62\) 3.82804 7.10415i 0.486162 0.902228i
\(63\) 0 0
\(64\) −7.87620 + 1.40197i −0.984525 + 0.175246i
\(65\) 1.21287 + 0.700250i 0.150438 + 0.0868553i
\(66\) 0 0
\(67\) 8.01120 + 2.14659i 0.978723 + 0.262248i 0.712507 0.701665i \(-0.247560\pi\)
0.266217 + 0.963913i \(0.414226\pi\)
\(68\) 11.9544 + 5.99563i 1.44968 + 0.727077i
\(69\) 0 0
\(70\) −4.77170 1.12955i −0.570327 0.135007i
\(71\) 8.05218i 0.955618i 0.878464 + 0.477809i \(0.158569\pi\)
−0.878464 + 0.477809i \(0.841431\pi\)
\(72\) 0 0
\(73\) 9.73126i 1.13896i −0.822006 0.569479i \(-0.807145\pi\)
0.822006 0.569479i \(-0.192855\pi\)
\(74\) 0.698727 2.95172i 0.0812254 0.343130i
\(75\) 0 0
\(76\) 0.631163 + 1.90130i 0.0723994 + 0.218094i
\(77\) 17.1444 + 4.59383i 1.95379 + 0.523516i
\(78\) 0 0
\(79\) 11.9835 + 6.91865i 1.34824 + 0.778409i 0.988001 0.154449i \(-0.0493604\pi\)
0.360243 + 0.932858i \(0.382694\pi\)
\(80\) −2.96082 + 1.17997i −0.331030 + 0.131924i
\(81\) 0 0
\(82\) 3.39603 + 1.82994i 0.375028 + 0.202083i
\(83\) −3.05012 + 0.817277i −0.334794 + 0.0897078i −0.422300 0.906456i \(-0.638777\pi\)
0.0875058 + 0.996164i \(0.472110\pi\)
\(84\) 0 0
\(85\) 5.14666 + 1.37904i 0.558233 + 0.149578i
\(86\) 8.64256 9.16554i 0.931951 0.988346i
\(87\) 0 0
\(88\) 10.8379 3.95463i 1.15532 0.421565i
\(89\) −1.71120 −0.181386 −0.0906932 0.995879i \(-0.528908\pi\)
−0.0906932 + 0.995879i \(0.528908\pi\)
\(90\) 0 0
\(91\) −5.40809 5.40809i −0.566922 0.566922i
\(92\) 0.526101 + 8.94943i 0.0548498 + 0.933042i
\(93\) 0 0
\(94\) −0.102261 3.48211i −0.0105475 0.359152i
\(95\) 0.399073 + 0.691214i 0.0409440 + 0.0709171i
\(96\) 0 0
\(97\) 3.66561 6.34903i 0.372187 0.644646i −0.617715 0.786402i \(-0.711941\pi\)
0.989902 + 0.141756i \(0.0452748\pi\)
\(98\) 14.8592 + 8.00683i 1.50101 + 0.808812i
\(99\) 0 0
\(100\) 7.29134 4.80124i 0.729134 0.480124i
\(101\) 14.0255 3.75813i 1.39559 0.373948i 0.518833 0.854876i \(-0.326367\pi\)
0.876760 + 0.480928i \(0.159700\pi\)
\(102\) 0 0
\(103\) −7.43866 12.8841i −0.732953 1.26951i −0.955616 0.294616i \(-0.904808\pi\)
0.222663 0.974895i \(-0.428525\pi\)
\(104\) −4.89644 0.859280i −0.480136 0.0842594i
\(105\) 0 0
\(106\) 3.27530 + 0.775325i 0.318125 + 0.0753062i
\(107\) 0.0974799 0.0974799i 0.00942374 0.00942374i −0.702379 0.711803i \(-0.747879\pi\)
0.711803 + 0.702379i \(0.247879\pi\)
\(108\) 0 0
\(109\) 8.80665 + 8.80665i 0.843524 + 0.843524i 0.989315 0.145791i \(-0.0465728\pi\)
−0.145791 + 0.989315i \(0.546573\pi\)
\(110\) 3.91142 2.41406i 0.372939 0.230172i
\(111\) 0 0
\(112\) 17.2860 2.03940i 1.63338 0.192705i
\(113\) −7.22037 + 4.16868i −0.679235 + 0.392157i −0.799567 0.600577i \(-0.794938\pi\)
0.120331 + 0.992734i \(0.461604\pi\)
\(114\) 0 0
\(115\) 0.924424 + 3.45000i 0.0862030 + 0.321714i
\(116\) 8.09133 + 1.66616i 0.751262 + 0.154699i
\(117\) 0 0
\(118\) −1.40971 + 0.422456i −0.129775 + 0.0388903i
\(119\) −25.1993 14.5488i −2.31001 1.33369i
\(120\) 0 0
\(121\) −4.88210 + 2.81868i −0.443827 + 0.256244i
\(122\) −1.98278 + 2.10276i −0.179512 + 0.190375i
\(123\) 0 0
\(124\) 0.669740 + 11.3929i 0.0601445 + 1.02311i
\(125\) 5.27664 5.27664i 0.471957 0.471957i
\(126\) 0 0
\(127\) 4.84829i 0.430216i −0.976590 0.215108i \(-0.930990\pi\)
0.976590 0.215108i \(-0.0690103\pi\)
\(128\) 8.43737 7.53729i 0.745765 0.666209i
\(129\) 0 0
\(130\) −1.97975 + 0.0581407i −0.173636 + 0.00509928i
\(131\) 5.49193 20.4961i 0.479832 1.79076i −0.122452 0.992474i \(-0.539076\pi\)
0.602284 0.798282i \(-0.294258\pi\)
\(132\) 0 0
\(133\) −1.12812 4.21019i −0.0978201 0.365070i
\(134\) −11.2355 + 3.36701i −0.970603 + 0.290866i
\(135\) 0 0
\(136\) −18.8399 + 1.66368i −1.61551 + 0.142659i
\(137\) 2.93860 5.08981i 0.251062 0.434852i −0.712757 0.701411i \(-0.752554\pi\)
0.963818 + 0.266560i \(0.0858869\pi\)
\(138\) 0 0
\(139\) −1.86863 + 6.97384i −0.158496 + 0.591513i 0.840285 + 0.542145i \(0.182388\pi\)
−0.998781 + 0.0493686i \(0.984279\pi\)
\(140\) 6.58153 2.18483i 0.556241 0.184652i
\(141\) 0 0
\(142\) −5.98079 9.69047i −0.501897 0.813206i
\(143\) 7.16910 0.599510
\(144\) 0 0
\(145\) 3.29131 0.273328
\(146\) 7.22794 + 11.7112i 0.598188 + 0.969224i
\(147\) 0 0
\(148\) 1.35151 + 4.07126i 0.111094 + 0.334655i
\(149\) −1.16425 + 4.34504i −0.0953792 + 0.355960i −0.997077 0.0764076i \(-0.975655\pi\)
0.901698 + 0.432367i \(0.142322\pi\)
\(150\) 0 0
\(151\) −4.23499 + 7.33521i −0.344638 + 0.596931i −0.985288 0.170902i \(-0.945332\pi\)
0.640650 + 0.767833i \(0.278665\pi\)
\(152\) −2.17178 1.81934i −0.176154 0.147568i
\(153\) 0 0
\(154\) −24.0447 + 7.20560i −1.93758 + 0.580644i
\(155\) 1.17682 + 4.39194i 0.0945241 + 0.352769i
\(156\) 0 0
\(157\) −4.38117 + 16.3507i −0.349655 + 1.30493i 0.537423 + 0.843313i \(0.319398\pi\)
−0.887079 + 0.461618i \(0.847269\pi\)
\(158\) −19.5605 + 0.574445i −1.55615 + 0.0457004i
\(159\) 0 0
\(160\) 2.68680 3.61921i 0.212410 0.286123i
\(161\) 19.5052i 1.53723i
\(162\) 0 0
\(163\) 13.6982 13.6982i 1.07293 1.07293i 0.0758059 0.997123i \(-0.475847\pi\)
0.997123 0.0758059i \(-0.0241529\pi\)
\(164\) −5.44618 + 0.320159i −0.425275 + 0.0250002i
\(165\) 0 0
\(166\) 3.06366 3.24905i 0.237786 0.252175i
\(167\) 7.11859 4.10992i 0.550853 0.318035i −0.198613 0.980078i \(-0.563644\pi\)
0.749466 + 0.662043i \(0.230310\pi\)
\(168\) 0 0
\(169\) 8.58301 + 4.95540i 0.660232 + 0.381185i
\(170\) −7.21808 + 2.16308i −0.553602 + 0.165901i
\(171\) 0 0
\(172\) −3.59323 + 17.4497i −0.273981 + 1.33052i
\(173\) 2.52258 + 9.41440i 0.191788 + 0.715764i 0.993075 + 0.117483i \(0.0374826\pi\)
−0.801287 + 0.598281i \(0.795851\pi\)
\(174\) 0 0
\(175\) −16.4497 + 9.49727i −1.24348 + 0.717926i
\(176\) −10.1056 + 12.8091i −0.761742 + 0.965524i
\(177\) 0 0
\(178\) 2.05936 1.27100i 0.154355 0.0952654i
\(179\) −2.59887 2.59887i −0.194248 0.194248i 0.603281 0.797529i \(-0.293860\pi\)
−0.797529 + 0.603281i \(0.793860\pi\)
\(180\) 0 0
\(181\) 6.92926 6.92926i 0.515048 0.515048i −0.401021 0.916069i \(-0.631345\pi\)
0.916069 + 0.401021i \(0.131345\pi\)
\(182\) 10.5253 + 2.49154i 0.780188 + 0.184685i
\(183\) 0 0
\(184\) −7.28037 10.3795i −0.536716 0.765188i
\(185\) 0.854536 + 1.48010i 0.0628267 + 0.108819i
\(186\) 0 0
\(187\) 26.3455 7.05926i 1.92657 0.516224i
\(188\) 2.70942 + 4.11462i 0.197605 + 0.300090i
\(189\) 0 0
\(190\) −0.993670 0.535435i −0.0720884 0.0388446i
\(191\) −6.96728 + 12.0677i −0.504135 + 0.873187i 0.495854 + 0.868406i \(0.334855\pi\)
−0.999989 + 0.00478132i \(0.998478\pi\)
\(192\) 0 0
\(193\) −1.34094 2.32257i −0.0965226 0.167182i 0.813720 0.581256i \(-0.197439\pi\)
−0.910243 + 0.414074i \(0.864105\pi\)
\(194\) 0.304350 + 10.3635i 0.0218511 + 0.744053i
\(195\) 0 0
\(196\) −23.8296 + 1.40085i −1.70211 + 0.100060i
\(197\) −14.2363 14.2363i −1.01430 1.01430i −0.999896 0.0144009i \(-0.995416\pi\)
−0.0144009 0.999896i \(-0.504584\pi\)
\(198\) 0 0
\(199\) 7.90078 0.560072 0.280036 0.959990i \(-0.409654\pi\)
0.280036 + 0.959990i \(0.409654\pi\)
\(200\) −5.20869 + 11.1938i −0.368310 + 0.791520i
\(201\) 0 0
\(202\) −14.0878 + 14.9403i −0.991214 + 1.05119i
\(203\) −17.3615 4.65201i −1.21854 0.326507i
\(204\) 0 0
\(205\) −2.09950 + 0.562559i −0.146635 + 0.0392908i
\(206\) 18.5219 + 9.98044i 1.29048 + 0.695370i
\(207\) 0 0
\(208\) 6.53091 2.60275i 0.452837 0.180468i
\(209\) 3.53830 + 2.04284i 0.244749 + 0.141306i
\(210\) 0 0
\(211\) 13.2108 + 3.53982i 0.909469 + 0.243691i 0.683078 0.730345i \(-0.260641\pi\)
0.226391 + 0.974037i \(0.427307\pi\)
\(212\) −4.51757 + 1.49967i −0.310268 + 0.102998i
\(213\) 0 0
\(214\) −0.0449095 + 0.189717i −0.00306995 + 0.0129688i
\(215\) 7.09799i 0.484079i
\(216\) 0 0
\(217\) 24.8307i 1.68562i
\(218\) −17.1396 4.05727i −1.16084 0.274793i
\(219\) 0 0
\(220\) −2.91418 + 5.81045i −0.196474 + 0.391741i
\(221\) −11.3524 3.04186i −0.763643 0.204618i
\(222\) 0 0
\(223\) −24.3372 14.0511i −1.62974 0.940931i −0.984169 0.177230i \(-0.943286\pi\)
−0.645570 0.763701i \(-0.723380\pi\)
\(224\) −19.2883 + 15.2936i −1.28875 + 1.02185i
\(225\) 0 0
\(226\) 5.59312 10.3798i 0.372049 0.690454i
\(227\) −0.489998 + 0.131295i −0.0325223 + 0.00871433i −0.275044 0.961432i \(-0.588692\pi\)
0.242521 + 0.970146i \(0.422026\pi\)
\(228\) 0 0
\(229\) −14.6181 3.91690i −0.965988 0.258836i −0.258855 0.965916i \(-0.583345\pi\)
−0.707133 + 0.707080i \(0.750012\pi\)
\(230\) −3.67501 3.46531i −0.242323 0.228496i
\(231\) 0 0
\(232\) −10.9751 + 4.00471i −0.720554 + 0.262922i
\(233\) −15.4968 −1.01523 −0.507614 0.861584i \(-0.669473\pi\)
−0.507614 + 0.861584i \(0.669473\pi\)
\(234\) 0 0
\(235\) 1.38791 + 1.38791i 0.0905371 + 0.0905371i
\(236\) 1.38275 1.55548i 0.0900096 0.101253i
\(237\) 0 0
\(238\) 41.1325 1.20797i 2.66622 0.0783007i
\(239\) 7.61709 + 13.1932i 0.492709 + 0.853397i 0.999965 0.00839869i \(-0.00267342\pi\)
−0.507256 + 0.861796i \(0.669340\pi\)
\(240\) 0 0
\(241\) −9.10697 + 15.7737i −0.586632 + 1.01608i 0.408038 + 0.912965i \(0.366213\pi\)
−0.994670 + 0.103111i \(0.967120\pi\)
\(242\) 3.78182 7.01837i 0.243105 0.451158i
\(243\) 0 0
\(244\) 0.824359 4.00330i 0.0527742 0.256285i
\(245\) −9.18628 + 2.46146i −0.586890 + 0.157257i
\(246\) 0 0
\(247\) −0.880265 1.52466i −0.0560099 0.0970121i
\(248\) −9.26810 13.2134i −0.588525 0.839051i
\(249\) 0 0
\(250\) −2.43097 + 10.2695i −0.153748 + 0.649498i
\(251\) −2.18418 + 2.18418i −0.137864 + 0.137864i −0.772671 0.634807i \(-0.781080\pi\)
0.634807 + 0.772671i \(0.281080\pi\)
\(252\) 0 0
\(253\) 12.9283 + 12.9283i 0.812796 + 0.812796i
\(254\) 3.60109 + 5.83472i 0.225952 + 0.366103i
\(255\) 0 0
\(256\) −4.55568 + 15.3377i −0.284730 + 0.958608i
\(257\) −16.6777 + 9.62887i −1.04033 + 0.600633i −0.919926 0.392093i \(-0.871751\pi\)
−0.120400 + 0.992725i \(0.538418\pi\)
\(258\) 0 0
\(259\) −2.41564 9.01529i −0.150101 0.560183i
\(260\) 2.33937 1.54044i 0.145081 0.0955340i
\(261\) 0 0
\(262\) 8.61429 + 28.7454i 0.532193 + 1.77590i
\(263\) 22.8254 + 13.1782i 1.40747 + 0.812605i 0.995144 0.0984300i \(-0.0313821\pi\)
0.412329 + 0.911035i \(0.364715\pi\)
\(264\) 0 0
\(265\) −1.64235 + 0.948214i −0.100889 + 0.0582483i
\(266\) 4.48478 + 4.22888i 0.274980 + 0.259289i
\(267\) 0 0
\(268\) 11.0207 12.3973i 0.673194 0.757287i
\(269\) 0.605506 0.605506i 0.0369184 0.0369184i −0.688407 0.725325i \(-0.741690\pi\)
0.725325 + 0.688407i \(0.241690\pi\)
\(270\) 0 0
\(271\) 19.1084i 1.16075i 0.814349 + 0.580376i \(0.197094\pi\)
−0.814349 + 0.580376i \(0.802906\pi\)
\(272\) 21.4374 15.9956i 1.29983 0.969876i
\(273\) 0 0
\(274\) 0.243988 + 8.30804i 0.0147398 + 0.501907i
\(275\) 4.60819 17.1980i 0.277884 1.03708i
\(276\) 0 0
\(277\) −1.82792 6.82191i −0.109829 0.409889i 0.889019 0.457871i \(-0.151388\pi\)
−0.998848 + 0.0479819i \(0.984721\pi\)
\(278\) −2.93102 9.78067i −0.175791 0.586606i
\(279\) 0 0
\(280\) −6.29781 + 7.51782i −0.376366 + 0.449276i
\(281\) 11.8490 20.5230i 0.706849 1.22430i −0.259171 0.965831i \(-0.583449\pi\)
0.966020 0.258467i \(-0.0832174\pi\)
\(282\) 0 0
\(283\) −0.194826 + 0.727099i −0.0115812 + 0.0432215i −0.971475 0.237143i \(-0.923789\pi\)
0.959893 + 0.280365i \(0.0904555\pi\)
\(284\) 14.3953 + 7.21984i 0.854203 + 0.428419i
\(285\) 0 0
\(286\) −8.62772 + 5.32488i −0.510168 + 0.314867i
\(287\) 11.8699 0.700659
\(288\) 0 0
\(289\) −27.7137 −1.63022
\(290\) −3.96096 + 2.44463i −0.232596 + 0.143554i
\(291\) 0 0
\(292\) −17.3971 8.72536i −1.01809 0.510613i
\(293\) −5.31070 + 19.8198i −0.310255 + 1.15789i 0.618072 + 0.786121i \(0.287914\pi\)
−0.928327 + 0.371765i \(0.878753\pi\)
\(294\) 0 0
\(295\) 0.414592 0.718095i 0.0241385 0.0418091i
\(296\) −4.65044 3.89576i −0.270301 0.226436i
\(297\) 0 0
\(298\) −1.82617 6.09384i −0.105787 0.353007i
\(299\) −2.03907 7.60993i −0.117923 0.440093i
\(300\) 0 0
\(301\) 10.0325 37.4417i 0.578262 2.15810i
\(302\) −0.351624 11.9732i −0.0202337 0.688979i
\(303\) 0 0
\(304\) 3.96497 + 0.576403i 0.227407 + 0.0330590i
\(305\) 1.62842i 0.0932432i
\(306\) 0 0
\(307\) −15.3450 + 15.3450i −0.875783 + 0.875783i −0.993095 0.117312i \(-0.962572\pi\)
0.117312 + 0.993095i \(0.462572\pi\)
\(308\) 23.5849 26.5310i 1.34387 1.51174i
\(309\) 0 0
\(310\) −4.67838 4.41144i −0.265714 0.250553i
\(311\) −0.576605 + 0.332903i −0.0326963 + 0.0188772i −0.516259 0.856432i \(-0.672676\pi\)
0.483563 + 0.875310i \(0.339342\pi\)
\(312\) 0 0
\(313\) 14.3283 + 8.27244i 0.809882 + 0.467586i 0.846915 0.531728i \(-0.178457\pi\)
−0.0370327 + 0.999314i \(0.511791\pi\)
\(314\) −6.87202 22.9316i −0.387811 1.29410i
\(315\) 0 0
\(316\) 23.1136 15.2199i 1.30024 0.856189i
\(317\) 1.75927 + 6.56570i 0.0988107 + 0.368767i 0.997570 0.0696766i \(-0.0221967\pi\)
−0.898759 + 0.438443i \(0.855530\pi\)
\(318\) 0 0
\(319\) 14.5909 8.42404i 0.816931 0.471656i
\(320\) −0.545277 + 6.35120i −0.0304819 + 0.355043i
\(321\) 0 0
\(322\) 14.4876 + 23.4738i 0.807362 + 1.30814i
\(323\) −4.73616 4.73616i −0.263527 0.263527i
\(324\) 0 0
\(325\) −5.42499 + 5.42499i −0.300924 + 0.300924i
\(326\) −6.31085 + 26.6597i −0.349526 + 1.47654i
\(327\) 0 0
\(328\) 6.31645 4.43047i 0.348768 0.244632i
\(329\) −5.35946 9.28286i −0.295477 0.511781i
\(330\) 0 0
\(331\) 9.39568 2.51757i 0.516434 0.138378i 0.00881711 0.999961i \(-0.497193\pi\)
0.507616 + 0.861583i \(0.330527\pi\)
\(332\) −1.27375 + 6.18565i −0.0699059 + 0.339481i
\(333\) 0 0
\(334\) −5.51427 + 10.2335i −0.301728 + 0.559951i
\(335\) 3.30434 5.72328i 0.180535 0.312696i
\(336\) 0 0
\(337\) 13.5580 + 23.4832i 0.738553 + 1.27921i 0.953147 + 0.302509i \(0.0978241\pi\)
−0.214593 + 0.976704i \(0.568843\pi\)
\(338\) −14.0100 + 0.411440i −0.762041 + 0.0223794i
\(339\) 0 0
\(340\) 7.08004 7.96444i 0.383969 0.431933i
\(341\) 16.4581 + 16.4581i 0.891254 + 0.891254i
\(342\) 0 0
\(343\) 21.4761 1.15960
\(344\) −8.63651 23.6689i −0.465649 1.27614i
\(345\) 0 0
\(346\) −10.0284 9.45620i −0.539131 0.508368i
\(347\) 30.1679 + 8.08347i 1.61950 + 0.433944i 0.950854 0.309638i \(-0.100208\pi\)
0.668645 + 0.743582i \(0.266875\pi\)
\(348\) 0 0
\(349\) −31.6714 + 8.48634i −1.69533 + 0.454263i −0.971757 0.235982i \(-0.924169\pi\)
−0.723576 + 0.690245i \(0.757503\pi\)
\(350\) 12.7425 23.6477i 0.681114 1.26402i
\(351\) 0 0
\(352\) 2.64771 22.9213i 0.141123 1.22171i
\(353\) 3.48989 + 2.01489i 0.185748 + 0.107242i 0.589990 0.807410i \(-0.299131\pi\)
−0.404243 + 0.914652i \(0.632465\pi\)
\(354\) 0 0
\(355\) 6.19752 + 1.66062i 0.328930 + 0.0881366i
\(356\) −1.53431 + 3.05919i −0.0813184 + 0.162137i
\(357\) 0 0
\(358\) 5.05795 + 1.19731i 0.267321 + 0.0632799i
\(359\) 14.8043i 0.781342i −0.920530 0.390671i \(-0.872243\pi\)
0.920530 0.390671i \(-0.127757\pi\)
\(360\) 0 0
\(361\) 17.9967i 0.947193i
\(362\) −3.19235 + 13.4858i −0.167786 + 0.708800i
\(363\) 0 0
\(364\) −14.5174 + 4.81925i −0.760918 + 0.252597i
\(365\) −7.48986 2.00690i −0.392037 0.105046i
\(366\) 0 0
\(367\) −2.66934 1.54114i −0.139338 0.0804470i 0.428710 0.903442i \(-0.358968\pi\)
−0.568049 + 0.822995i \(0.692301\pi\)
\(368\) 16.4711 + 7.08380i 0.858613 + 0.369269i
\(369\) 0 0
\(370\) −2.12775 1.14653i −0.110616 0.0596052i
\(371\) 10.0036 2.68045i 0.519361 0.139162i
\(372\) 0 0
\(373\) 28.2816 + 7.57804i 1.46437 + 0.392376i 0.900996 0.433828i \(-0.142837\pi\)
0.563372 + 0.826204i \(0.309504\pi\)
\(374\) −26.4625 + 28.0638i −1.36834 + 1.45114i
\(375\) 0 0
\(376\) −6.31683 2.93935i −0.325766 0.151585i
\(377\) −7.25990 −0.373904
\(378\) 0 0
\(379\) −13.0654 13.0654i −0.671124 0.671124i 0.286851 0.957975i \(-0.407392\pi\)
−0.957975 + 0.286851i \(0.907392\pi\)
\(380\) 1.59354 0.0936778i 0.0817468 0.00480557i
\(381\) 0 0
\(382\) −0.578483 19.6980i −0.0295978 1.00784i
\(383\) −1.66394 2.88203i −0.0850235 0.147265i 0.820378 0.571822i \(-0.193763\pi\)
−0.905401 + 0.424557i \(0.860430\pi\)
\(384\) 0 0
\(385\) 7.07147 12.2481i 0.360396 0.624223i
\(386\) 3.33886 + 1.79913i 0.169943 + 0.0915734i
\(387\) 0 0
\(388\) −8.06378 12.2459i −0.409376 0.621694i
\(389\) 6.62255 1.77451i 0.335777 0.0899711i −0.0869912 0.996209i \(-0.527725\pi\)
0.422768 + 0.906238i \(0.361059\pi\)
\(390\) 0 0
\(391\) −14.9867 25.9577i −0.757908 1.31274i
\(392\) 27.6374 19.3854i 1.39590 0.979110i
\(393\) 0 0
\(394\) 27.7070 + 6.55876i 1.39586 + 0.330426i
\(395\) 7.79645 7.79645i 0.392282 0.392282i
\(396\) 0 0
\(397\) 2.33820 + 2.33820i 0.117351 + 0.117351i 0.763344 0.645993i \(-0.223556\pi\)
−0.645993 + 0.763344i \(0.723556\pi\)
\(398\) −9.50828 + 5.86834i −0.476607 + 0.294153i
\(399\) 0 0
\(400\) −2.04577 17.3400i −0.102289 0.867002i
\(401\) −3.32787 + 1.92135i −0.166186 + 0.0959474i −0.580786 0.814056i \(-0.697255\pi\)
0.414600 + 0.910004i \(0.363921\pi\)
\(402\) 0 0
\(403\) −2.59579 9.68764i −0.129306 0.482575i
\(404\) 5.85714 28.4438i 0.291404 1.41513i
\(405\) 0 0
\(406\) 24.3492 7.29686i 1.20843 0.362137i
\(407\) 7.57656 + 4.37433i 0.375556 + 0.216828i
\(408\) 0 0
\(409\) 4.36888 2.52237i 0.216027 0.124723i −0.388082 0.921625i \(-0.626862\pi\)
0.604109 + 0.796901i \(0.293529\pi\)
\(410\) 2.10882 2.23643i 0.104147 0.110449i
\(411\) 0 0
\(412\) −29.7034 + 1.74614i −1.46338 + 0.0860262i
\(413\) −3.20193 + 3.20193i −0.157557 + 0.157557i
\(414\) 0 0
\(415\) 2.51613i 0.123512i
\(416\) −5.92649 + 7.98316i −0.290570 + 0.391407i
\(417\) 0 0
\(418\) −5.77552 + 0.169614i −0.282490 + 0.00829607i
\(419\) −5.72083 + 21.3504i −0.279481 + 1.04304i 0.673298 + 0.739371i \(0.264877\pi\)
−0.952779 + 0.303665i \(0.901790\pi\)
\(420\) 0 0
\(421\) 2.13099 + 7.95298i 0.103858 + 0.387604i 0.998213 0.0597538i \(-0.0190316\pi\)
−0.894355 + 0.447358i \(0.852365\pi\)
\(422\) −18.5279 + 5.55234i −0.901923 + 0.270284i
\(423\) 0 0
\(424\) 4.32283 5.16024i 0.209935 0.250603i
\(425\) −14.5943 + 25.2780i −0.707926 + 1.22616i
\(426\) 0 0
\(427\) −2.30165 + 8.58988i −0.111385 + 0.415693i
\(428\) −0.0868662 0.261673i −0.00419884 0.0126485i
\(429\) 0 0
\(430\) −5.27207 8.54215i −0.254242 0.411939i
\(431\) 1.08094 0.0520671 0.0260336 0.999661i \(-0.491712\pi\)
0.0260336 + 0.999661i \(0.491712\pi\)
\(432\) 0 0
\(433\) −15.5307 −0.746359 −0.373179 0.927759i \(-0.621732\pi\)
−0.373179 + 0.927759i \(0.621732\pi\)
\(434\) 18.4431 + 29.8827i 0.885297 + 1.43442i
\(435\) 0 0
\(436\) 23.6404 7.84777i 1.13217 0.375840i
\(437\) 1.16207 4.33690i 0.0555893 0.207462i
\(438\) 0 0
\(439\) −2.26321 + 3.91999i −0.108017 + 0.187091i −0.914967 0.403529i \(-0.867783\pi\)
0.806950 + 0.590620i \(0.201117\pi\)
\(440\) −0.808634 9.15717i −0.0385501 0.436551i
\(441\) 0 0
\(442\) 15.9215 4.77127i 0.757308 0.226946i
\(443\) 6.82958 + 25.4883i 0.324483 + 1.21099i 0.914830 + 0.403838i \(0.132324\pi\)
−0.590347 + 0.807149i \(0.701009\pi\)
\(444\) 0 0
\(445\) −0.352904 + 1.31706i −0.0167293 + 0.0624345i
\(446\) 39.7254 1.16664i 1.88105 0.0552420i
\(447\) 0 0
\(448\) 11.8533 32.7317i 0.560014 1.54643i
\(449\) 5.94688i 0.280650i −0.990105 0.140325i \(-0.955185\pi\)
0.990105 0.140325i \(-0.0448148\pi\)
\(450\) 0 0
\(451\) −7.86752 + 7.86752i −0.370467 + 0.370467i
\(452\) 0.978552 + 16.6460i 0.0460272 + 0.782962i
\(453\) 0 0
\(454\) 0.492173 0.521956i 0.0230988 0.0244966i
\(455\) −5.27777 + 3.04712i −0.247426 + 0.142851i
\(456\) 0 0
\(457\) −18.2318 10.5261i −0.852846 0.492391i 0.00876413 0.999962i \(-0.497210\pi\)
−0.861610 + 0.507571i \(0.830544\pi\)
\(458\) 20.5015 6.14380i 0.957974 0.287081i
\(459\) 0 0
\(460\) 6.99660 + 1.44074i 0.326218 + 0.0671747i
\(461\) −10.2518 38.2603i −0.477475 1.78196i −0.611788 0.791021i \(-0.709550\pi\)
0.134314 0.990939i \(-0.457117\pi\)
\(462\) 0 0
\(463\) 9.98020 5.76207i 0.463819 0.267786i −0.249829 0.968290i \(-0.580375\pi\)
0.713649 + 0.700504i \(0.247041\pi\)
\(464\) 10.2336 12.9714i 0.475085 0.602180i
\(465\) 0 0
\(466\) 18.6498 11.5103i 0.863934 0.533205i
\(467\) 25.1476 + 25.1476i 1.16369 + 1.16369i 0.983661 + 0.180032i \(0.0576202\pi\)
0.180032 + 0.983661i \(0.442380\pi\)
\(468\) 0 0
\(469\) −25.5197 + 25.5197i −1.17839 + 1.17839i
\(470\) −2.70116 0.639416i −0.124595 0.0294941i
\(471\) 0 0
\(472\) −0.508748 + 2.89901i −0.0234170 + 0.133438i
\(473\) 18.1672 + 31.4664i 0.835327 + 1.44683i
\(474\) 0 0
\(475\) −4.22335 + 1.13164i −0.193780 + 0.0519233i
\(476\) −48.6041 + 32.0051i −2.22776 + 1.46695i
\(477\) 0 0
\(478\) −18.9662 10.2199i −0.867493 0.467445i
\(479\) −2.64784 + 4.58619i −0.120983 + 0.209548i −0.920155 0.391553i \(-0.871938\pi\)
0.799173 + 0.601101i \(0.205271\pi\)
\(480\) 0 0
\(481\) −1.88491 3.26477i −0.0859447 0.148861i
\(482\) −0.756138 25.7473i −0.0344412 1.17276i
\(483\) 0 0
\(484\) 0.661654 + 11.2553i 0.0300752 + 0.511604i
\(485\) −4.13069 4.13069i −0.187565 0.187565i
\(486\) 0 0
\(487\) 1.85543 0.0840775 0.0420387 0.999116i \(-0.486615\pi\)
0.0420387 + 0.999116i \(0.486615\pi\)
\(488\) 1.98139 + 5.43011i 0.0896933 + 0.245810i
\(489\) 0 0
\(490\) 9.22707 9.78542i 0.416836 0.442060i
\(491\) 3.49505 + 0.936497i 0.157730 + 0.0422635i 0.336820 0.941569i \(-0.390649\pi\)
−0.179090 + 0.983833i \(0.557315\pi\)
\(492\) 0 0
\(493\) −26.6792 + 7.14866i −1.20157 + 0.321960i
\(494\) 2.19182 + 1.18105i 0.0986144 + 0.0531380i
\(495\) 0 0
\(496\) 20.9681 + 9.01786i 0.941495 + 0.404914i
\(497\) −30.3446 17.5194i −1.36114 0.785854i
\(498\) 0 0
\(499\) −12.0253 3.22216i −0.538325 0.144244i −0.0205953 0.999788i \(-0.506556\pi\)
−0.517730 + 0.855544i \(0.673223\pi\)
\(500\) −4.70211 14.1645i −0.210285 0.633456i
\(501\) 0 0
\(502\) 1.00626 4.25088i 0.0449118 0.189726i
\(503\) 16.6233i 0.741198i 0.928793 + 0.370599i \(0.120848\pi\)
−0.928793 + 0.370599i \(0.879152\pi\)
\(504\) 0 0
\(505\) 11.5701i 0.514862i
\(506\) −25.1613 5.95614i −1.11855 0.264783i
\(507\) 0 0
\(508\) −8.66753 4.34713i −0.384559 0.192873i
\(509\) −15.1091 4.04848i −0.669700 0.179446i −0.0920802 0.995752i \(-0.529352\pi\)
−0.577620 + 0.816306i \(0.696018\pi\)
\(510\) 0 0
\(511\) 36.6722 + 21.1727i 1.62228 + 0.936624i
\(512\) −5.90958 21.8421i −0.261169 0.965293i
\(513\) 0 0
\(514\) 12.9191 23.9754i 0.569835 1.05751i
\(515\) −11.4506 + 3.06819i −0.504575 + 0.135200i
\(516\) 0 0
\(517\) 9.70511 + 2.60048i 0.426830 + 0.114369i
\(518\) 9.60328 + 9.05532i 0.421944 + 0.397868i
\(519\) 0 0
\(520\) −1.67117 + 3.59143i −0.0732856 + 0.157495i
\(521\) 40.4461 1.77198 0.885988 0.463709i \(-0.153482\pi\)
0.885988 + 0.463709i \(0.153482\pi\)
\(522\) 0 0
\(523\) 7.69126 + 7.69126i 0.336315 + 0.336315i 0.854979 0.518663i \(-0.173570\pi\)
−0.518663 + 0.854979i \(0.673570\pi\)
\(524\) −31.7178 28.1957i −1.38560 1.23173i
\(525\) 0 0
\(526\) −37.2576 + 1.09417i −1.62451 + 0.0477080i
\(527\) −19.0784 33.0448i −0.831069 1.43945i
\(528\) 0 0
\(529\) −1.45387 + 2.51818i −0.0632119 + 0.109486i
\(530\) 1.27222 2.36100i 0.0552616 0.102555i
\(531\) 0 0
\(532\) −8.53827 1.75820i −0.370181 0.0762275i
\(533\) 4.63102 1.24088i 0.200592 0.0537484i
\(534\) 0 0
\(535\) −0.0549239 0.0951309i −0.00237457 0.00411287i
\(536\) −4.05477 + 23.1053i −0.175139 + 0.997998i
\(537\) 0 0
\(538\) −0.278960 + 1.17844i −0.0120268 + 0.0508063i
\(539\) −34.4241 + 34.4241i −1.48275 + 1.48275i
\(540\) 0 0
\(541\) −17.0176 17.0176i −0.731643 0.731643i 0.239302 0.970945i \(-0.423081\pi\)
−0.970945 + 0.239302i \(0.923081\pi\)
\(542\) −14.1928 22.9962i −0.609635 0.987771i
\(543\) 0 0
\(544\) −13.9182 + 35.1728i −0.596739 + 1.50802i
\(545\) 8.59443 4.96200i 0.368145 0.212549i
\(546\) 0 0
\(547\) −5.77510 21.5530i −0.246926 0.921539i −0.972406 0.233296i \(-0.925049\pi\)
0.725480 0.688243i \(-0.241618\pi\)
\(548\) −6.46447 9.81718i −0.276148 0.419369i
\(549\) 0 0
\(550\) 7.22812 + 24.1199i 0.308208 + 1.02847i
\(551\) −3.58311 2.06871i −0.152645 0.0881299i
\(552\) 0 0
\(553\) −52.1457 + 30.1064i −2.21746 + 1.28025i
\(554\) 7.26683 + 6.85219i 0.308738 + 0.291122i
\(555\) 0 0
\(556\) 10.7920 + 9.59362i 0.457683 + 0.406860i
\(557\) 11.6516 11.6516i 0.493695 0.493695i −0.415773 0.909468i \(-0.636489\pi\)
0.909468 + 0.415773i \(0.136489\pi\)
\(558\) 0 0
\(559\) 15.6566i 0.662203i
\(560\) 1.99527 13.7251i 0.0843157 0.579992i
\(561\) 0 0
\(562\) 0.983800 + 33.4994i 0.0414991 + 1.41309i
\(563\) 1.30826 4.88249i 0.0551365 0.205772i −0.932862 0.360233i \(-0.882697\pi\)
0.987999 + 0.154460i \(0.0493639\pi\)
\(564\) 0 0
\(565\) 1.71944 + 6.41702i 0.0723372 + 0.269966i
\(566\) −0.305591 1.01974i −0.0128450 0.0428629i
\(567\) 0 0
\(568\) −22.6867 + 2.00338i −0.951913 + 0.0840598i
\(569\) −2.79764 + 4.84565i −0.117283 + 0.203140i −0.918690 0.394979i \(-0.870752\pi\)
0.801407 + 0.598119i \(0.204085\pi\)
\(570\) 0 0
\(571\) −2.31993 + 8.65808i −0.0970859 + 0.362329i −0.997327 0.0730613i \(-0.976723\pi\)
0.900242 + 0.435391i \(0.143390\pi\)
\(572\) 6.42804 12.8166i 0.268770 0.535887i
\(573\) 0 0
\(574\) −14.2850 + 8.81643i −0.596243 + 0.367991i
\(575\) −19.5662 −0.815966
\(576\) 0 0
\(577\) 16.6893 0.694785 0.347393 0.937720i \(-0.387067\pi\)
0.347393 + 0.937720i \(0.387067\pi\)
\(578\) 33.3524 20.5845i 1.38728 0.856203i
\(579\) 0 0
\(580\) 2.95109 5.88404i 0.122537 0.244321i
\(581\) 3.55636 13.2725i 0.147543 0.550637i
\(582\) 0 0
\(583\) −4.85387 + 8.40714i −0.201027 + 0.348188i
\(584\) 27.4175 2.42113i 1.13454 0.100187i
\(585\) 0 0
\(586\) −8.33004 27.7969i −0.344111 1.14828i
\(587\) −1.34545 5.02128i −0.0555325 0.207250i 0.932585 0.360950i \(-0.117548\pi\)
−0.988118 + 0.153700i \(0.950881\pi\)
\(588\) 0 0
\(589\) 1.47934 5.52099i 0.0609553 0.227488i
\(590\) 0.0344230 + 1.17214i 0.00141717 + 0.0482562i
\(591\) 0 0
\(592\) 8.49020 + 1.23425i 0.348945 + 0.0507275i
\(593\) 44.7927i 1.83942i 0.392602 + 0.919708i \(0.371575\pi\)
−0.392602 + 0.919708i \(0.628425\pi\)
\(594\) 0 0
\(595\) −16.3947 + 16.3947i −0.672116 + 0.672116i
\(596\) 6.72395 + 5.97729i 0.275424 + 0.244840i
\(597\) 0 0
\(598\) 8.10625 + 7.64371i 0.331489 + 0.312575i
\(599\) 27.1165 15.6557i 1.10795 0.639674i 0.169651 0.985504i \(-0.445736\pi\)
0.938297 + 0.345830i \(0.112403\pi\)
\(600\) 0 0
\(601\) 15.4248 + 8.90549i 0.629189 + 0.363262i 0.780438 0.625233i \(-0.214996\pi\)
−0.151249 + 0.988496i \(0.548330\pi\)
\(602\) 15.7363 + 52.5112i 0.641364 + 2.14020i
\(603\) 0 0
\(604\) 9.31630 + 14.1481i 0.379075 + 0.575677i
\(605\) 1.16261 + 4.33891i 0.0472667 + 0.176402i
\(606\) 0 0
\(607\) 29.3159 16.9255i 1.18989 0.686986i 0.231612 0.972808i \(-0.425600\pi\)
0.958283 + 0.285823i \(0.0922668\pi\)
\(608\) −5.19981 + 2.25132i −0.210880 + 0.0913031i
\(609\) 0 0
\(610\) 1.20952 + 1.95974i 0.0489720 + 0.0793476i
\(611\) −3.06141 3.06141i −0.123852 0.123852i
\(612\) 0 0
\(613\) −11.3734 + 11.3734i −0.459367 + 0.459367i −0.898448 0.439081i \(-0.855304\pi\)
0.439081 + 0.898448i \(0.355304\pi\)
\(614\) 7.06951 29.8646i 0.285302 1.20524i
\(615\) 0 0
\(616\) −8.67744 + 49.4467i −0.349624 + 1.99226i
\(617\) −18.0269 31.2236i −0.725738 1.25701i −0.958670 0.284521i \(-0.908165\pi\)
0.232932 0.972493i \(-0.425168\pi\)
\(618\) 0 0
\(619\) 16.0209 4.29280i 0.643936 0.172542i 0.0779503 0.996957i \(-0.475162\pi\)
0.565986 + 0.824415i \(0.308496\pi\)
\(620\) 8.90686 + 1.83410i 0.357708 + 0.0736591i
\(621\) 0 0
\(622\) 0.446656 0.828912i 0.0179093 0.0332363i
\(623\) 3.72312 6.44863i 0.149163 0.258359i
\(624\) 0 0
\(625\) 7.93964 + 13.7519i 0.317585 + 0.550074i
\(626\) −23.3879 + 0.686848i −0.934769 + 0.0274520i
\(627\) 0 0
\(628\) 25.3027 + 22.4930i 1.00969 + 0.897569i
\(629\) −10.1416 10.1416i −0.404371 0.404371i
\(630\) 0 0
\(631\) 24.4330 0.972664 0.486332 0.873774i \(-0.338335\pi\)
0.486332 + 0.873774i \(0.338335\pi\)
\(632\) −16.5116 + 35.4843i −0.656795 + 1.41149i
\(633\) 0 0
\(634\) −6.99392 6.59485i −0.277764 0.261915i
\(635\) −3.73158 0.999874i −0.148083 0.0396788i
\(636\) 0 0
\(637\) 20.2629 5.42943i 0.802845 0.215122i
\(638\) −11.3025 + 20.9754i −0.447471 + 0.830425i
\(639\) 0 0
\(640\) −4.06117 8.04843i −0.160532 0.318142i
\(641\) 40.0952 + 23.1490i 1.58366 + 0.914329i 0.994318 + 0.106448i \(0.0339479\pi\)
0.589346 + 0.807881i \(0.299385\pi\)
\(642\) 0 0
\(643\) 10.5870 + 2.83678i 0.417511 + 0.111872i 0.461458 0.887162i \(-0.347326\pi\)
−0.0439466 + 0.999034i \(0.513993\pi\)
\(644\) −34.8705 17.4890i −1.37409 0.689163i
\(645\) 0 0
\(646\) 9.21759 + 2.18198i 0.362661 + 0.0858487i
\(647\) 10.0479i 0.395025i 0.980300 + 0.197512i \(0.0632863\pi\)
−0.980300 + 0.197512i \(0.936714\pi\)
\(648\) 0 0
\(649\) 4.24456i 0.166614i
\(650\) 2.49932 10.5582i 0.0980316 0.414127i
\(651\) 0 0
\(652\) −12.2068 36.7713i −0.478053 1.44008i
\(653\) 25.5935 + 6.85777i 1.00155 + 0.268365i 0.722096 0.691793i \(-0.243179\pi\)
0.279457 + 0.960158i \(0.409846\pi\)
\(654\) 0 0
\(655\) −14.6427 8.45394i −0.572136 0.330323i
\(656\) −4.31085 + 10.0235i −0.168310 + 0.391351i
\(657\) 0 0
\(658\) 13.3448 + 7.19079i 0.520234 + 0.280326i
\(659\) −6.76233 + 1.81196i −0.263423 + 0.0705840i −0.388113 0.921612i \(-0.626873\pi\)
0.124690 + 0.992196i \(0.460206\pi\)
\(660\) 0 0
\(661\) 20.1902 + 5.40993i 0.785306 + 0.210422i 0.629123 0.777306i \(-0.283414\pi\)
0.156183 + 0.987728i \(0.450081\pi\)
\(662\) −9.43740 + 10.0085i −0.366795 + 0.388990i
\(663\) 0 0
\(664\) −3.06151 8.39026i −0.118810 0.325605i
\(665\) −3.47311 −0.134681
\(666\) 0 0
\(667\) −13.0920 13.0920i −0.506926 0.506926i
\(668\) −0.964757 16.4113i −0.0373276 0.634974i
\(669\) 0 0
\(670\) 0.274354 + 9.34205i 0.0105992 + 0.360915i
\(671\) −4.16791 7.21904i −0.160901 0.278688i
\(672\) 0 0
\(673\) 3.86200 6.68918i 0.148869 0.257849i −0.781941 0.623353i \(-0.785770\pi\)
0.930810 + 0.365504i \(0.119103\pi\)
\(674\) −33.7588 18.1908i −1.30034 0.700684i
\(675\) 0 0
\(676\) 16.5548 10.9011i 0.636724 0.419274i
\(677\) −7.62160 + 2.04220i −0.292922 + 0.0784882i −0.402287 0.915513i \(-0.631785\pi\)
0.109366 + 0.994002i \(0.465118\pi\)
\(678\) 0 0
\(679\) 15.9508 + 27.6277i 0.612137 + 1.06025i
\(680\) −2.60492 + 14.8436i −0.0998940 + 0.569227i
\(681\) 0 0
\(682\) −32.0309 7.58232i −1.22653 0.290342i
\(683\) 23.0318 23.0318i 0.881288 0.881288i −0.112378 0.993666i \(-0.535847\pi\)
0.993666 + 0.112378i \(0.0358467\pi\)
\(684\) 0 0
\(685\) −3.31144 3.31144i −0.126524 0.126524i
\(686\) −25.8456 + 15.9515i −0.986790 + 0.609029i
\(687\) 0 0
\(688\) 27.9738 + 22.0697i 1.06649 + 0.841400i
\(689\) 3.62267 2.09155i 0.138013 0.0796816i
\(690\) 0 0
\(691\) −6.66520 24.8749i −0.253556 0.946285i −0.968888 0.247500i \(-0.920391\pi\)
0.715332 0.698785i \(-0.246276\pi\)
\(692\) 19.0924 + 3.93151i 0.725785 + 0.149453i
\(693\) 0 0
\(694\) −42.3099 + 12.6792i −1.60606 + 0.481297i
\(695\) 4.98218 + 2.87646i 0.188985 + 0.109111i
\(696\) 0 0
\(697\) 15.7965 9.12014i 0.598337 0.345450i
\(698\) 31.8120 33.7371i 1.20410 1.27697i
\(699\) 0 0
\(700\) 2.22938 + 37.9236i 0.0842625 + 1.43338i
\(701\) −35.0396 + 35.0396i −1.32343 + 1.32343i −0.412443 + 0.910983i \(0.635325\pi\)
−0.910983 + 0.412443i \(0.864675\pi\)
\(702\) 0 0
\(703\) 2.14843i 0.0810295i
\(704\) 13.8385 + 29.5514i 0.521557 + 1.11376i
\(705\) 0 0
\(706\) −5.69650 + 0.167293i −0.214391 + 0.00629616i
\(707\) −16.3534 + 61.0318i −0.615034 + 2.29534i
\(708\) 0 0
\(709\) −12.2110 45.5722i −0.458595 1.71150i −0.677297 0.735710i \(-0.736849\pi\)
0.218702 0.975792i \(-0.429818\pi\)
\(710\) −8.69190 + 2.60474i −0.326201 + 0.0977543i
\(711\) 0 0
\(712\) −0.425744 4.82123i −0.0159554 0.180683i
\(713\) 12.7890 22.1512i 0.478951 0.829568i
\(714\) 0 0
\(715\) 1.47850 5.51784i 0.0552928 0.206356i
\(716\) −6.97635 + 2.31590i −0.260719 + 0.0865492i
\(717\) 0 0
\(718\) 10.9960 + 17.8164i 0.410366 + 0.664902i
\(719\) −26.0582 −0.971806 −0.485903 0.874013i \(-0.661509\pi\)
−0.485903 + 0.874013i \(0.661509\pi\)
\(720\) 0 0
\(721\) 64.7383 2.41098
\(722\) −13.3671 21.6583i −0.497472 0.806038i
\(723\) 0 0
\(724\) −6.17480 18.6008i −0.229484 0.691293i
\(725\) −4.66655 + 17.4158i −0.173311 + 0.646807i
\(726\) 0 0
\(727\) −4.96698 + 8.60307i −0.184215 + 0.319070i −0.943312 0.331908i \(-0.892308\pi\)
0.759097 + 0.650978i \(0.225641\pi\)
\(728\) 13.8916 16.5826i 0.514856 0.614593i
\(729\) 0 0
\(730\) 10.5044 3.14790i 0.388785 0.116509i
\(731\) −15.4167 57.5359i −0.570207 2.12804i
\(732\) 0 0
\(733\) 3.40512 12.7081i 0.125771 0.469384i −0.874095 0.485755i \(-0.838545\pi\)
0.999866 + 0.0163712i \(0.00521135\pi\)
\(734\) 4.35713 0.127959i 0.160825 0.00472305i
\(735\) 0 0
\(736\) −25.0838 + 3.70888i −0.924601 + 0.136711i
\(737\) 33.8295i 1.24613i
\(738\) 0 0
\(739\) −32.6637 + 32.6637i −1.20155 + 1.20155i −0.227861 + 0.973694i \(0.573173\pi\)
−0.973694 + 0.227861i \(0.926827\pi\)
\(740\) 3.41225 0.200593i 0.125437 0.00737393i
\(741\) 0 0
\(742\) −10.0480 + 10.6560i −0.368874 + 0.391195i
\(743\) 8.76936 5.06299i 0.321717 0.185743i −0.330441 0.943827i \(-0.607197\pi\)
0.652157 + 0.758084i \(0.273864\pi\)
\(744\) 0 0
\(745\) 3.10414 + 1.79218i 0.113727 + 0.0656603i
\(746\) −39.6644 + 11.8864i −1.45222 + 0.435193i
\(747\) 0 0
\(748\) 11.0020 53.4287i 0.402274 1.95355i
\(749\) 0.155261 + 0.579443i 0.00567312 + 0.0211724i
\(750\) 0 0
\(751\) −22.6187 + 13.0589i −0.825368 + 0.476526i −0.852264 0.523112i \(-0.824771\pi\)
0.0268964 + 0.999638i \(0.491438\pi\)
\(752\) 9.78527 1.15446i 0.356832 0.0420990i
\(753\) 0 0
\(754\) 8.73699 5.39232i 0.318183 0.196377i
\(755\) 4.77230 + 4.77230i 0.173682 + 0.173682i
\(756\) 0 0
\(757\) 2.39808 2.39808i 0.0871596 0.0871596i −0.662183 0.749342i \(-0.730370\pi\)
0.749342 + 0.662183i \(0.230370\pi\)
\(758\) 25.4281 + 6.01930i 0.923589 + 0.218631i
\(759\) 0 0
\(760\) −1.84818 + 1.29635i −0.0670406 + 0.0470234i
\(761\) 23.1857 + 40.1589i 0.840482 + 1.45576i 0.889488 + 0.456959i \(0.151061\pi\)
−0.0490055 + 0.998799i \(0.515605\pi\)
\(762\) 0 0
\(763\) −52.3487 + 14.0268i −1.89515 + 0.507804i
\(764\) 15.3269 + 23.2760i 0.554509 + 0.842098i
\(765\) 0 0
\(766\) 4.14313 + 2.23251i 0.149697 + 0.0806639i
\(767\) −0.914499 + 1.58396i −0.0330206 + 0.0571934i
\(768\) 0 0
\(769\) −7.38255 12.7870i −0.266222 0.461109i 0.701661 0.712511i \(-0.252442\pi\)
−0.967883 + 0.251401i \(0.919109\pi\)
\(770\) 0.587134 + 19.9925i 0.0211588 + 0.720480i
\(771\) 0 0
\(772\) −5.35450 + 0.314770i −0.192713 + 0.0113288i
\(773\) −22.1409 22.1409i −0.796353 0.796353i 0.186165 0.982518i \(-0.440394\pi\)
−0.982518 + 0.186165i \(0.940394\pi\)
\(774\) 0 0
\(775\) −24.9083 −0.894731
\(776\) 18.8002 + 8.74810i 0.674887 + 0.314038i
\(777\) 0 0
\(778\) −6.65195 + 7.05448i −0.238484 + 0.252915i
\(779\) 2.63922 + 0.707177i 0.0945599 + 0.0253372i
\(780\) 0 0
\(781\) 31.7248 8.50064i 1.13520 0.304177i
\(782\) 37.3160 + 20.1076i 1.33442 + 0.719046i
\(783\) 0 0
\(784\) −18.8620 + 43.8574i −0.673642 + 1.56633i
\(785\) 11.6811 + 6.74410i 0.416917 + 0.240707i
\(786\) 0 0
\(787\) −4.18136 1.12039i −0.149050 0.0399377i 0.183523 0.983015i \(-0.441250\pi\)
−0.332572 + 0.943078i \(0.607917\pi\)
\(788\) −38.2158 + 12.6863i −1.36138 + 0.451930i
\(789\) 0 0
\(790\) −3.59187 + 15.1736i −0.127793 + 0.539851i
\(791\) 36.2799i 1.28996i
\(792\) 0 0
\(793\) 3.59194i 0.127553i
\(794\) −4.55064 1.07722i −0.161496 0.0382292i
\(795\) 0 0
\(796\) 7.08409 14.1246i 0.251089 0.500634i
\(797\) −51.5141 13.8032i −1.82472 0.488933i −0.827370 0.561657i \(-0.810164\pi\)
−0.997352 + 0.0727237i \(0.976831\pi\)
\(798\) 0 0
\(799\) −14.2648 8.23579i −0.504652 0.291361i
\(800\) 15.3414 + 19.3485i 0.542400 + 0.684074i
\(801\) 0 0
\(802\) 2.57787 4.78405i 0.0910277 0.168931i
\(803\) −38.3403 + 10.2732i −1.35300 + 0.362535i
\(804\) 0 0
\(805\) −15.0126 4.02261i −0.529124 0.141778i
\(806\) 10.3195 + 9.73064i 0.363488 + 0.342747i
\(807\) 0 0
\(808\) 14.0779 + 38.5814i 0.495260 + 1.35729i
\(809\) −30.1140 −1.05875 −0.529375 0.848388i \(-0.677574\pi\)
−0.529375 + 0.848388i \(0.677574\pi\)
\(810\) 0 0
\(811\) 20.5672 + 20.5672i 0.722214 + 0.722214i 0.969056 0.246842i \(-0.0793929\pi\)
−0.246842 + 0.969056i \(0.579393\pi\)
\(812\) −23.8836 + 26.8670i −0.838148 + 0.942846i
\(813\) 0 0
\(814\) −12.3671 + 0.363194i −0.433468 + 0.0127299i
\(815\) −7.71810 13.3681i −0.270353 0.468265i
\(816\) 0 0
\(817\) 4.46135 7.72728i 0.156083 0.270343i
\(818\) −3.38426 + 6.28057i −0.118328 + 0.219595i
\(819\) 0 0
\(820\) −0.876761 + 4.25779i −0.0306178 + 0.148688i
\(821\) −31.8546 + 8.53541i −1.11173 + 0.297888i −0.767533 0.641009i \(-0.778516\pi\)
−0.344199 + 0.938897i \(0.611849\pi\)
\(822\) 0 0
\(823\) 4.71220 + 8.16178i 0.164257 + 0.284502i 0.936391 0.350958i \(-0.114144\pi\)
−0.772134 + 0.635460i \(0.780811\pi\)
\(824\) 34.4498 24.1637i 1.20012 0.841783i
\(825\) 0 0
\(826\) 1.47515 6.23165i 0.0513270 0.216827i
\(827\) 38.7468 38.7468i 1.34736 1.34736i 0.458841 0.888518i \(-0.348265\pi\)
0.888518 0.458841i \(-0.151735\pi\)
\(828\) 0 0
\(829\) 11.0569 + 11.0569i 0.384021 + 0.384021i 0.872548 0.488528i \(-0.162466\pi\)
−0.488528 + 0.872548i \(0.662466\pi\)
\(830\) −1.86887 3.02807i −0.0648694 0.105106i
\(831\) 0 0
\(832\) 1.20276 14.0093i 0.0416982 0.485686i
\(833\) 69.1173 39.9049i 2.39477 1.38262i
\(834\) 0 0
\(835\) −1.69520 6.32656i −0.0586647 0.218940i
\(836\) 6.82463 4.49392i 0.236035 0.155425i
\(837\) 0 0
\(838\) −8.97333 29.9435i −0.309978 1.03438i
\(839\) −25.3695 14.6471i −0.875853 0.505674i −0.00656388 0.999978i \(-0.502089\pi\)
−0.869289 + 0.494305i \(0.835423\pi\)
\(840\) 0 0
\(841\) 10.3391 5.96927i 0.356520 0.205837i
\(842\) −8.47167 7.98828i −0.291953 0.275294i
\(843\) 0 0
\(844\) 18.1735 20.4437i 0.625559 0.703701i
\(845\) 5.58412 5.58412i 0.192100 0.192100i
\(846\) 0 0
\(847\) 24.5309i 0.842891i
\(848\) −1.36956 + 9.42094i −0.0470308 + 0.323516i
\(849\) 0 0
\(850\) −1.21174 41.2610i −0.0415623 1.41524i
\(851\) 2.48834 9.28662i 0.0852992 0.318341i
\(852\) 0 0
\(853\) −10.9035 40.6922i −0.373327 1.39328i −0.855774 0.517350i \(-0.826918\pi\)
0.482447 0.875925i \(-0.339748\pi\)
\(854\) −3.61022 12.0471i −0.123539 0.412244i
\(855\) 0 0
\(856\) 0.298899 + 0.250393i 0.0102162 + 0.00855826i
\(857\) −14.2207 + 24.6310i −0.485769 + 0.841377i −0.999866 0.0163548i \(-0.994794\pi\)
0.514097 + 0.857732i \(0.328127\pi\)
\(858\) 0 0
\(859\) −0.896437 + 3.34555i −0.0305860 + 0.114149i −0.979531 0.201293i \(-0.935486\pi\)
0.948945 + 0.315441i \(0.102152\pi\)
\(860\) 12.6894 + 6.36428i 0.432706 + 0.217020i
\(861\) 0 0
\(862\) −1.30087 + 0.802875i −0.0443078 + 0.0273460i
\(863\) 11.1356 0.379062 0.189531 0.981875i \(-0.439303\pi\)
0.189531 + 0.981875i \(0.439303\pi\)
\(864\) 0 0
\(865\) 7.76622 0.264059
\(866\) 18.6906 11.5355i 0.635133 0.391993i
\(867\) 0 0
\(868\) −44.3910 22.2640i −1.50673 0.755688i
\(869\) 14.6080 54.5177i 0.495541 1.84939i
\(870\) 0 0
\(871\) −7.28863 + 12.6243i −0.246966 + 0.427757i
\(872\) −22.6213 + 27.0035i −0.766055 + 0.914454i
\(873\) 0 0
\(874\) 1.82275 + 6.08242i 0.0616554 + 0.205741i
\(875\) 8.40437 + 31.3655i 0.284119 + 1.06035i
\(876\) 0 0
\(877\) 7.32539 27.3387i 0.247361 0.923163i −0.724821 0.688937i \(-0.758078\pi\)
0.972182 0.234226i \(-0.0752557\pi\)
\(878\) −0.187911 6.39856i −0.00634168 0.215941i
\(879\) 0 0
\(880\) 7.77469 + 10.4197i 0.262085 + 0.351247i
\(881\) 4.86363i 0.163860i −0.996638 0.0819299i \(-0.973892\pi\)
0.996638 0.0819299i \(-0.0261084\pi\)
\(882\) 0 0
\(883\) 8.56478 8.56478i 0.288228 0.288228i −0.548151 0.836379i \(-0.684668\pi\)
0.836379 + 0.548151i \(0.184668\pi\)
\(884\) −15.6170 + 17.5678i −0.525256 + 0.590869i
\(885\) 0 0
\(886\) −27.1507 25.6015i −0.912146 0.860099i
\(887\) −3.99885 + 2.30874i −0.134268 + 0.0775199i −0.565630 0.824659i \(-0.691367\pi\)
0.431361 + 0.902179i \(0.358033\pi\)
\(888\) 0 0
\(889\) 18.2707 + 10.5486i 0.612780 + 0.353789i
\(890\) −0.553543 1.84715i −0.0185548 0.0619165i
\(891\) 0 0
\(892\) −46.9414 + 30.9102i −1.57171 + 1.03495i
\(893\) −0.638605 2.38330i −0.0213701 0.0797543i
\(894\) 0 0
\(895\) −2.53624 + 1.46430i −0.0847772 + 0.0489461i
\(896\) 10.0467 + 48.1953i 0.335636 + 1.61009i
\(897\) 0 0
\(898\) 4.41707 + 7.15683i 0.147399 + 0.238826i
\(899\) −16.6665 16.6665i −0.555859 0.555859i
\(900\) 0 0
\(901\) 11.2533 11.2533i 0.374903 0.374903i
\(902\) 3.62461 15.3119i 0.120686 0.509830i
\(903\) 0 0
\(904\) −13.5415 19.3060i −0.450385 0.642107i
\(905\) −3.90421 6.76228i −0.129780 0.224786i
\(906\) 0 0
\(907\) 8.35931 2.23987i 0.277566 0.0743737i −0.117350 0.993091i \(-0.537440\pi\)
0.394917 + 0.918717i \(0.370773\pi\)
\(908\) −0.204626 + 0.993717i −0.00679075 + 0.0329777i
\(909\) 0 0
\(910\) 4.08832 7.58718i 0.135527 0.251512i
\(911\) 23.9969 41.5638i 0.795052 1.37707i −0.127755 0.991806i \(-0.540777\pi\)
0.922806 0.385264i \(-0.125890\pi\)
\(912\) 0 0
\(913\) 6.43999 + 11.1544i 0.213133 + 0.369156i
\(914\) 29.7595 0.873967i 0.984357 0.0289083i
\(915\) 0 0
\(916\) −20.1094 + 22.6214i −0.664435 + 0.747433i
\(917\) 65.2905 + 65.2905i 2.15608 + 2.15608i
\(918\) 0 0
\(919\) 51.8939 1.71182 0.855910 0.517124i \(-0.172997\pi\)
0.855910 + 0.517124i \(0.172997\pi\)
\(920\) −9.49025 + 3.46289i −0.312884 + 0.114168i
\(921\) 0 0
\(922\) 40.7557 + 38.4302i 1.34222 + 1.26563i
\(923\) −13.6703 3.66296i −0.449965 0.120568i
\(924\) 0 0
\(925\) −9.04347 + 2.42319i −0.297347 + 0.0796740i
\(926\) −7.73097 + 14.3473i −0.254055 + 0.471480i
\(927\) 0 0
\(928\) −2.68124 + 23.2116i −0.0880160 + 0.761957i
\(929\) −8.80130 5.08143i −0.288761 0.166716i 0.348622 0.937263i \(-0.386650\pi\)
−0.637383 + 0.770547i \(0.719983\pi\)
\(930\) 0 0
\(931\) 11.5478 + 3.09423i 0.378465 + 0.101409i
\(932\) −13.8949 + 27.7044i −0.455143 + 0.907488i
\(933\) 0 0
\(934\) −48.9427 11.5856i −1.60145 0.379094i
\(935\) 21.7332i 0.710751i
\(936\) 0 0
\(937\) 37.8157i 1.23539i 0.786420 + 0.617693i \(0.211932\pi\)
−0.786420 + 0.617693i \(0.788068\pi\)
\(938\) 11.7571 49.6668i 0.383882 1.62168i
\(939\) 0 0
\(940\) 3.72567 1.23679i 0.121518 0.0403396i
\(941\) 34.3731 + 9.21025i 1.12053 + 0.300246i 0.771099 0.636716i \(-0.219707\pi\)
0.349433 + 0.936961i \(0.386374\pi\)
\(942\) 0 0
\(943\) 10.5890 + 6.11357i 0.344826 + 0.199085i
\(944\) −1.54099 3.86671i −0.0501550 0.125851i
\(945\) 0 0
\(946\) −45.2353 24.3749i −1.47073 0.792495i
\(947\) 10.0399 2.69018i 0.326253 0.0874191i −0.0919752 0.995761i \(-0.529318\pi\)
0.418228 + 0.908342i \(0.362651\pi\)
\(948\) 0 0
\(949\) 16.5210 + 4.42678i 0.536293 + 0.143699i
\(950\) 4.24210 4.49880i 0.137632 0.145960i
\(951\) 0 0
\(952\) 34.7212 74.6177i 1.12532 2.41837i
\(953\) 24.6743 0.799280 0.399640 0.916672i \(-0.369135\pi\)
0.399640 + 0.916672i \(0.369135\pi\)
\(954\) 0 0
\(955\) 7.85126 + 7.85126i 0.254061 + 0.254061i
\(956\) 30.4159 1.78803i 0.983719 0.0578289i
\(957\) 0 0
\(958\) −0.219846 7.48599i −0.00710290 0.241861i
\(959\) 12.7873 + 22.1482i 0.412922 + 0.715203i
\(960\) 0 0
\(961\) 0.780708 1.35223i 0.0251841 0.0436202i
\(962\) 4.69334 + 2.52899i 0.151319 + 0.0815379i
\(963\) 0 0
\(964\) 20.0339 + 30.4242i 0.645249 + 0.979898i
\(965\) −2.06416 + 0.553089i −0.0664475 + 0.0178046i
\(966\) 0 0
\(967\) 12.5371 + 21.7150i 0.403167 + 0.698306i 0.994106 0.108410i \(-0.0345759\pi\)
−0.590939 + 0.806716i \(0.701243\pi\)
\(968\) −9.15620 13.0539i −0.294291 0.419567i
\(969\) 0 0
\(970\) 8.03921 + 1.90303i 0.258123 + 0.0611027i
\(971\) −18.9203 + 18.9203i −0.607180 + 0.607180i −0.942208 0.335028i \(-0.891254\pi\)
0.335028 + 0.942208i \(0.391254\pi\)
\(972\) 0 0
\(973\) −22.2152 22.2152i −0.712186 0.712186i
\(974\) −2.23293 + 1.37813i −0.0715478 + 0.0441581i
\(975\) 0 0
\(976\) −6.41776 5.06324i −0.205428 0.162070i
\(977\) 12.1897 7.03771i 0.389982 0.225156i −0.292170 0.956366i \(-0.594377\pi\)
0.682152 + 0.731210i \(0.261044\pi\)
\(978\) 0 0
\(979\) 1.80650 + 6.74196i 0.0577360 + 0.215474i
\(980\) −3.83624 + 18.6298i −0.122544 + 0.595107i
\(981\) 0 0
\(982\) −4.90175 + 1.46893i −0.156421 + 0.0468755i
\(983\) 0.562149 + 0.324557i 0.0179298 + 0.0103518i 0.508938 0.860803i \(-0.330038\pi\)
−0.491008 + 0.871155i \(0.663372\pi\)
\(984\) 0 0
\(985\) −13.8933 + 8.02129i −0.442677 + 0.255579i
\(986\) 26.7976 28.4192i 0.853410 0.905052i
\(987\) 0 0
\(988\) −3.51499 + 0.206632i −0.111827 + 0.00657385i
\(989\) 28.2341 28.2341i 0.897792 0.897792i
\(990\) 0 0
\(991\) 36.5529i 1.16114i −0.814210 0.580571i \(-0.802829\pi\)
0.814210 0.580571i \(-0.197171\pi\)
\(992\) −31.9323 + 4.72150i −1.01385 + 0.149908i
\(993\) 0 0
\(994\) 49.5311 1.45461i 1.57103 0.0461375i
\(995\) 1.62940 6.08100i 0.0516554 0.192781i
\(996\) 0 0
\(997\) −2.07498 7.74395i −0.0657154 0.245253i 0.925253 0.379352i \(-0.123853\pi\)
−0.990968 + 0.134098i \(0.957186\pi\)
\(998\) 16.8652 5.05408i 0.533859 0.159984i
\(999\) 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 432.2.v.a.35.3 88
3.2 odd 2 144.2.u.a.83.20 yes 88
4.3 odd 2 1728.2.z.a.1007.13 88
9.4 even 3 144.2.u.a.131.12 yes 88
9.5 odd 6 inner 432.2.v.a.179.11 88
12.11 even 2 576.2.y.a.47.8 88
16.5 even 4 1728.2.z.a.143.13 88
16.11 odd 4 inner 432.2.v.a.251.11 88
36.23 even 6 1728.2.z.a.1583.13 88
36.31 odd 6 576.2.y.a.239.4 88
48.5 odd 4 576.2.y.a.335.4 88
48.11 even 4 144.2.u.a.11.12 88
144.5 odd 12 1728.2.z.a.719.13 88
144.59 even 12 inner 432.2.v.a.395.3 88
144.85 even 12 576.2.y.a.527.8 88
144.139 odd 12 144.2.u.a.59.20 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.12 88 48.11 even 4
144.2.u.a.59.20 yes 88 144.139 odd 12
144.2.u.a.83.20 yes 88 3.2 odd 2
144.2.u.a.131.12 yes 88 9.4 even 3
432.2.v.a.35.3 88 1.1 even 1 trivial
432.2.v.a.179.11 88 9.5 odd 6 inner
432.2.v.a.251.11 88 16.11 odd 4 inner
432.2.v.a.395.3 88 144.59 even 12 inner
576.2.y.a.47.8 88 12.11 even 2
576.2.y.a.239.4 88 36.31 odd 6
576.2.y.a.335.4 88 48.5 odd 4
576.2.y.a.527.8 88 144.85 even 12
1728.2.z.a.143.13 88 16.5 even 4
1728.2.z.a.719.13 88 144.5 odd 12
1728.2.z.a.1007.13 88 4.3 odd 2
1728.2.z.a.1583.13 88 36.23 even 6