Properties

Label 405.2.p.a.289.8
Level $405$
Weight $2$
Character 405.289
Analytic conductor $3.234$
Analytic rank $0$
Dimension $96$
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] = [405,2,Mod(19,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.p (of order \(18\), degree \(6\), 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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 289.8
Character \(\chi\) \(=\) 405.289
Dual form 405.2.p.a.199.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.133405 + 0.158986i) q^{2} +(0.339817 + 1.92720i) q^{4} +(-1.06091 + 1.96837i) q^{5} +(-2.83580 - 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +O(q^{10})\) \(q+(-0.133405 + 0.158986i) q^{2} +(0.339817 + 1.92720i) q^{4} +(-1.06091 + 1.96837i) q^{5} +(-2.83580 - 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.171413 - 0.431259i) q^{10} +(-1.38169 + 0.502894i) q^{11} +(-1.55650 - 1.85496i) q^{13} +(0.457807 - 0.384146i) q^{14} +(-3.51766 + 1.28032i) q^{16} +(-1.21975 + 0.704220i) q^{17} +(2.34516 - 4.06194i) q^{19} +(-4.15395 - 1.37569i) q^{20} +(0.104371 - 0.286757i) q^{22} +(-2.36796 + 0.417535i) q^{23} +(-2.74896 - 4.17651i) q^{25} +0.502557 q^{26} -5.63507i q^{28} +(6.73596 + 5.65214i) q^{29} +(1.00865 + 5.72033i) q^{31} +(0.827470 - 2.27346i) q^{32} +(0.0507589 - 0.287868i) q^{34} +(3.99276 - 5.05143i) q^{35} +(-7.57034 + 4.37074i) q^{37} +(0.332934 + 0.914728i) q^{38} +(1.56275 - 0.964286i) q^{40} +(-8.32538 + 6.98582i) q^{41} +(2.63439 + 7.23793i) q^{43} +(-1.43870 - 2.49190i) q^{44} +(0.249515 - 0.432172i) q^{46} +(6.68918 + 1.17948i) q^{47} +(1.21391 + 0.441827i) q^{49} +(1.03073 + 0.120122i) q^{50} +(3.04596 - 3.63003i) q^{52} +5.43934i q^{53} +(0.475961 - 3.25320i) q^{55} +(1.81151 + 1.52004i) q^{56} +(-1.79722 + 0.316898i) q^{58} +(-6.83272 - 2.48691i) q^{59} +(-1.03952 + 5.89541i) q^{61} +(-1.04401 - 0.602759i) q^{62} +(-3.49236 - 6.04894i) q^{64} +(5.30255 - 1.09582i) q^{65} +(4.95280 + 5.90251i) q^{67} +(-1.77166 - 2.11138i) q^{68} +(0.270451 + 1.30868i) q^{70} +(-4.51802 - 7.82544i) q^{71} +(10.8910 + 6.28791i) q^{73} +(0.315035 - 1.78665i) q^{74} +(8.62507 + 3.13927i) q^{76} +(4.16966 - 0.735224i) q^{77} +(-1.14861 - 0.963795i) q^{79} +(1.21176 - 8.28236i) q^{80} -2.25556i q^{82} +(7.46590 - 8.89751i) q^{83} +(-0.0921308 - 3.14802i) q^{85} +(-1.50217 - 0.546744i) q^{86} +(1.18915 + 0.209680i) q^{88} +(5.96766 - 10.3363i) q^{89} +(3.48639 + 6.03861i) q^{91} +(-1.60934 - 4.42164i) q^{92} +(-1.07989 + 0.906134i) q^{94} +(5.50740 + 8.92547i) q^{95} +(-1.92260 - 5.28231i) q^{97} +(-0.232185 + 0.134052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 12 q^{4} + 9 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46} - 30 q^{49} - 84 q^{50} - 12 q^{55} + 96 q^{56} - 66 q^{59} + 6 q^{61} - 45 q^{65} - 33 q^{70} + 90 q^{71} - 66 q^{74} + 12 q^{76} + 24 q^{79} - 30 q^{80} - 21 q^{85} - 18 q^{86} - 96 q^{89} - 6 q^{91} + 24 q^{94} - 87 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.133405 + 0.158986i −0.0943314 + 0.112420i −0.811145 0.584845i \(-0.801155\pi\)
0.716814 + 0.697265i \(0.245600\pi\)
\(3\) 0 0
\(4\) 0.339817 + 1.92720i 0.169908 + 0.963598i
\(5\) −1.06091 + 1.96837i −0.474452 + 0.880282i
\(6\) 0 0
\(7\) −2.83580 0.500029i −1.07183 0.188993i −0.390232 0.920717i \(-0.627605\pi\)
−0.681602 + 0.731724i \(0.738716\pi\)
\(8\) −0.711201 0.410612i −0.251448 0.145173i
\(9\) 0 0
\(10\) −0.171413 0.431259i −0.0542054 0.136376i
\(11\) −1.38169 + 0.502894i −0.416595 + 0.151628i −0.541809 0.840502i \(-0.682260\pi\)
0.125214 + 0.992130i \(0.460038\pi\)
\(12\) 0 0
\(13\) −1.55650 1.85496i −0.431695 0.514474i 0.505715 0.862700i \(-0.331229\pi\)
−0.937411 + 0.348226i \(0.886784\pi\)
\(14\) 0.457807 0.384146i 0.122354 0.102667i
\(15\) 0 0
\(16\) −3.51766 + 1.28032i −0.879415 + 0.320081i
\(17\) −1.21975 + 0.704220i −0.295832 + 0.170799i −0.640569 0.767901i \(-0.721301\pi\)
0.344737 + 0.938699i \(0.387968\pi\)
\(18\) 0 0
\(19\) 2.34516 4.06194i 0.538017 0.931872i −0.460994 0.887403i \(-0.652507\pi\)
0.999011 0.0444689i \(-0.0141595\pi\)
\(20\) −4.15395 1.37569i −0.928851 0.307613i
\(21\) 0 0
\(22\) 0.104371 0.286757i 0.0222520 0.0611368i
\(23\) −2.36796 + 0.417535i −0.493753 + 0.0870620i −0.414980 0.909831i \(-0.636211\pi\)
−0.0787733 + 0.996893i \(0.525100\pi\)
\(24\) 0 0
\(25\) −2.74896 4.17651i −0.549791 0.835302i
\(26\) 0.502557 0.0985595
\(27\) 0 0
\(28\) 5.63507i 1.06493i
\(29\) 6.73596 + 5.65214i 1.25084 + 1.04958i 0.996596 + 0.0824353i \(0.0262698\pi\)
0.254240 + 0.967141i \(0.418175\pi\)
\(30\) 0 0
\(31\) 1.00865 + 5.72033i 0.181159 + 1.02740i 0.930792 + 0.365549i \(0.119119\pi\)
−0.749634 + 0.661853i \(0.769770\pi\)
\(32\) 0.827470 2.27346i 0.146277 0.401894i
\(33\) 0 0
\(34\) 0.0507589 0.287868i 0.00870509 0.0493690i
\(35\) 3.99276 5.05143i 0.674900 0.853847i
\(36\) 0 0
\(37\) −7.57034 + 4.37074i −1.24456 + 0.718545i −0.970019 0.243031i \(-0.921858\pi\)
−0.274538 + 0.961576i \(0.588525\pi\)
\(38\) 0.332934 + 0.914728i 0.0540090 + 0.148388i
\(39\) 0 0
\(40\) 1.56275 0.964286i 0.247093 0.152467i
\(41\) −8.32538 + 6.98582i −1.30021 + 1.09100i −0.310096 + 0.950705i \(0.600361\pi\)
−0.990110 + 0.140297i \(0.955194\pi\)
\(42\) 0 0
\(43\) 2.63439 + 7.23793i 0.401741 + 1.10377i 0.961425 + 0.275068i \(0.0887003\pi\)
−0.559684 + 0.828706i \(0.689077\pi\)
\(44\) −1.43870 2.49190i −0.216892 0.375667i
\(45\) 0 0
\(46\) 0.249515 0.432172i 0.0367889 0.0637203i
\(47\) 6.68918 + 1.17948i 0.975717 + 0.172045i 0.638702 0.769454i \(-0.279472\pi\)
0.337015 + 0.941499i \(0.390583\pi\)
\(48\) 0 0
\(49\) 1.21391 + 0.441827i 0.173416 + 0.0631181i
\(50\) 1.03073 + 0.120122i 0.145767 + 0.0169878i
\(51\) 0 0
\(52\) 3.04596 3.63003i 0.422398 0.503394i
\(53\) 5.43934i 0.747151i 0.927600 + 0.373575i \(0.121868\pi\)
−0.927600 + 0.373575i \(0.878132\pi\)
\(54\) 0 0
\(55\) 0.475961 3.25320i 0.0641786 0.438661i
\(56\) 1.81151 + 1.52004i 0.242073 + 0.203123i
\(57\) 0 0
\(58\) −1.79722 + 0.316898i −0.235986 + 0.0416108i
\(59\) −6.83272 2.48691i −0.889545 0.323768i −0.143489 0.989652i \(-0.545832\pi\)
−0.746055 + 0.665884i \(0.768055\pi\)
\(60\) 0 0
\(61\) −1.03952 + 5.89541i −0.133097 + 0.754830i 0.843069 + 0.537805i \(0.180746\pi\)
−0.976166 + 0.217025i \(0.930365\pi\)
\(62\) −1.04401 0.602759i −0.132589 0.0765504i
\(63\) 0 0
\(64\) −3.49236 6.04894i −0.436545 0.756118i
\(65\) 5.30255 1.09582i 0.657701 0.135920i
\(66\) 0 0
\(67\) 4.95280 + 5.90251i 0.605081 + 0.721107i 0.978429 0.206584i \(-0.0662348\pi\)
−0.373348 + 0.927691i \(0.621790\pi\)
\(68\) −1.77166 2.11138i −0.214845 0.256043i
\(69\) 0 0
\(70\) 0.270451 + 1.30868i 0.0323250 + 0.156417i
\(71\) −4.51802 7.82544i −0.536190 0.928708i −0.999105 0.0423056i \(-0.986530\pi\)
0.462915 0.886403i \(-0.346804\pi\)
\(72\) 0 0
\(73\) 10.8910 + 6.28791i 1.27469 + 0.735944i 0.975867 0.218364i \(-0.0700721\pi\)
0.298825 + 0.954308i \(0.403405\pi\)
\(74\) 0.315035 1.78665i 0.0366221 0.207694i
\(75\) 0 0
\(76\) 8.62507 + 3.13927i 0.989364 + 0.360099i
\(77\) 4.16966 0.735224i 0.475177 0.0837865i
\(78\) 0 0
\(79\) −1.14861 0.963795i −0.129228 0.108435i 0.575883 0.817532i \(-0.304658\pi\)
−0.705111 + 0.709097i \(0.749103\pi\)
\(80\) 1.21176 8.28236i 0.135478 0.925996i
\(81\) 0 0
\(82\) 2.25556i 0.249085i
\(83\) 7.46590 8.89751i 0.819489 0.976629i −0.180487 0.983577i \(-0.557767\pi\)
0.999976 + 0.00694857i \(0.00221182\pi\)
\(84\) 0 0
\(85\) −0.0921308 3.14802i −0.00999299 0.341451i
\(86\) −1.50217 0.546744i −0.161983 0.0589569i
\(87\) 0 0
\(88\) 1.18915 + 0.209680i 0.126764 + 0.0223519i
\(89\) 5.96766 10.3363i 0.632571 1.09564i −0.354454 0.935074i \(-0.615333\pi\)
0.987024 0.160571i \(-0.0513336\pi\)
\(90\) 0 0
\(91\) 3.48639 + 6.03861i 0.365473 + 0.633018i
\(92\) −1.60934 4.42164i −0.167786 0.460987i
\(93\) 0 0
\(94\) −1.07989 + 0.906134i −0.111382 + 0.0934606i
\(95\) 5.50740 + 8.92547i 0.565047 + 0.915734i
\(96\) 0 0
\(97\) −1.92260 5.28231i −0.195211 0.536337i 0.803010 0.595966i \(-0.203231\pi\)
−0.998221 + 0.0596285i \(0.981008\pi\)
\(98\) −0.232185 + 0.134052i −0.0234543 + 0.0135413i
\(99\) 0 0
\(100\) 7.11481 6.71703i 0.711481 0.671703i
\(101\) −1.86284 + 10.5647i −0.185360 + 1.05123i 0.740133 + 0.672461i \(0.234763\pi\)
−0.925492 + 0.378766i \(0.876348\pi\)
\(102\) 0 0
\(103\) −0.183395 + 0.503873i −0.0180704 + 0.0496480i −0.948400 0.317077i \(-0.897299\pi\)
0.930329 + 0.366725i \(0.119521\pi\)
\(104\) 0.345313 + 1.95837i 0.0338608 + 0.192034i
\(105\) 0 0
\(106\) −0.864777 0.725634i −0.0839945 0.0704798i
\(107\) 2.82482i 0.273086i −0.990634 0.136543i \(-0.956401\pi\)
0.990634 0.136543i \(-0.0435992\pi\)
\(108\) 0 0
\(109\) −0.479801 −0.0459566 −0.0229783 0.999736i \(-0.507315\pi\)
−0.0229783 + 0.999736i \(0.507315\pi\)
\(110\) 0.453716 + 0.509663i 0.0432601 + 0.0485945i
\(111\) 0 0
\(112\) 10.6156 1.87182i 1.00308 0.176870i
\(113\) 1.45557 3.99915i 0.136928 0.376208i −0.852209 0.523202i \(-0.824737\pi\)
0.989137 + 0.146994i \(0.0469597\pi\)
\(114\) 0 0
\(115\) 1.69032 5.10398i 0.157623 0.475949i
\(116\) −8.60380 + 14.9022i −0.798843 + 1.38364i
\(117\) 0 0
\(118\) 1.30690 0.754539i 0.120310 0.0694609i
\(119\) 3.81109 1.38712i 0.349362 0.127157i
\(120\) 0 0
\(121\) −6.77033 + 5.68098i −0.615484 + 0.516453i
\(122\) −0.798608 0.951744i −0.0723026 0.0861669i
\(123\) 0 0
\(124\) −10.6814 + 3.88773i −0.959222 + 0.349128i
\(125\) 11.1373 0.980081i 0.996150 0.0876611i
\(126\) 0 0
\(127\) 10.4667 + 6.04293i 0.928765 + 0.536223i 0.886421 0.462880i \(-0.153184\pi\)
0.0423444 + 0.999103i \(0.486517\pi\)
\(128\) 6.19280 + 1.09196i 0.547371 + 0.0965164i
\(129\) 0 0
\(130\) −0.533166 + 0.989218i −0.0467617 + 0.0867601i
\(131\) −0.0451328 0.255961i −0.00394327 0.0223634i 0.982773 0.184819i \(-0.0591698\pi\)
−0.986716 + 0.162455i \(0.948059\pi\)
\(132\) 0 0
\(133\) −8.68150 + 10.3462i −0.752781 + 0.897130i
\(134\) −1.59914 −0.138145
\(135\) 0 0
\(136\) 1.15665 0.0991816
\(137\) −12.0038 + 14.3056i −1.02555 + 1.22221i −0.0508517 + 0.998706i \(0.516194\pi\)
−0.974703 + 0.223503i \(0.928251\pi\)
\(138\) 0 0
\(139\) −1.20743 6.84769i −0.102413 0.580813i −0.992222 0.124480i \(-0.960274\pi\)
0.889809 0.456333i \(-0.150837\pi\)
\(140\) 11.0919 + 5.97828i 0.937437 + 0.505257i
\(141\) 0 0
\(142\) 1.84686 + 0.325651i 0.154985 + 0.0273280i
\(143\) 3.08345 + 1.78023i 0.257851 + 0.148870i
\(144\) 0 0
\(145\) −18.2717 + 7.26247i −1.51738 + 0.603115i
\(146\) −2.45259 + 0.892671i −0.202978 + 0.0738780i
\(147\) 0 0
\(148\) −10.9958 13.1043i −0.903850 1.07717i
\(149\) 6.29367 5.28102i 0.515598 0.432638i −0.347496 0.937681i \(-0.612968\pi\)
0.863094 + 0.505044i \(0.168524\pi\)
\(150\) 0 0
\(151\) 8.32039 3.02837i 0.677103 0.246445i 0.0195001 0.999810i \(-0.493793\pi\)
0.657603 + 0.753364i \(0.271570\pi\)
\(152\) −3.33576 + 1.92590i −0.270566 + 0.156211i
\(153\) 0 0
\(154\) −0.439363 + 0.760998i −0.0354049 + 0.0613230i
\(155\) −12.3298 4.08334i −0.990354 0.327982i
\(156\) 0 0
\(157\) 2.12942 5.85053i 0.169946 0.466923i −0.825256 0.564758i \(-0.808969\pi\)
0.995203 + 0.0978347i \(0.0311917\pi\)
\(158\) 0.306459 0.0540370i 0.0243806 0.00429895i
\(159\) 0 0
\(160\) 3.59713 + 4.04069i 0.284378 + 0.319445i
\(161\) 6.92384 0.545675
\(162\) 0 0
\(163\) 20.6617i 1.61835i −0.587569 0.809174i \(-0.699915\pi\)
0.587569 0.809174i \(-0.300085\pi\)
\(164\) −16.2922 13.6707i −1.27220 1.06751i
\(165\) 0 0
\(166\) 0.418590 + 2.37394i 0.0324889 + 0.184254i
\(167\) −2.14444 + 5.89179i −0.165942 + 0.455921i −0.994594 0.103843i \(-0.966886\pi\)
0.828652 + 0.559764i \(0.189108\pi\)
\(168\) 0 0
\(169\) 1.23923 7.02800i 0.0953251 0.540615i
\(170\) 0.512781 + 0.405314i 0.0393285 + 0.0310861i
\(171\) 0 0
\(172\) −13.0537 + 7.53656i −0.995336 + 0.574657i
\(173\) 1.35761 + 3.72999i 0.103217 + 0.283586i 0.980542 0.196311i \(-0.0628963\pi\)
−0.877325 + 0.479897i \(0.840674\pi\)
\(174\) 0 0
\(175\) 5.70713 + 13.2183i 0.431419 + 0.999211i
\(176\) 4.21645 3.53802i 0.317827 0.266688i
\(177\) 0 0
\(178\) 0.847207 + 2.32768i 0.0635008 + 0.174467i
\(179\) 7.02005 + 12.1591i 0.524703 + 0.908813i 0.999586 + 0.0287637i \(0.00915704\pi\)
−0.474883 + 0.880049i \(0.657510\pi\)
\(180\) 0 0
\(181\) −3.31514 + 5.74198i −0.246412 + 0.426798i −0.962528 0.271183i \(-0.912585\pi\)
0.716116 + 0.697982i \(0.245918\pi\)
\(182\) −1.42515 0.251293i −0.105639 0.0186271i
\(183\) 0 0
\(184\) 1.85554 + 0.675361i 0.136792 + 0.0497883i
\(185\) −0.571809 19.5382i −0.0420403 1.43648i
\(186\) 0 0
\(187\) 1.33116 1.58642i 0.0973441 0.116010i
\(188\) 13.2922i 0.969431i
\(189\) 0 0
\(190\) −2.15373 0.315104i −0.156248 0.0228600i
\(191\) −7.50310 6.29585i −0.542905 0.455552i 0.329625 0.944112i \(-0.393078\pi\)
−0.872530 + 0.488560i \(0.837522\pi\)
\(192\) 0 0
\(193\) −19.1316 + 3.37342i −1.37712 + 0.242824i −0.812710 0.582668i \(-0.802009\pi\)
−0.564414 + 0.825492i \(0.690898\pi\)
\(194\) 1.09630 + 0.399019i 0.0787094 + 0.0286479i
\(195\) 0 0
\(196\) −0.438980 + 2.48958i −0.0313557 + 0.177827i
\(197\) −5.60720 3.23732i −0.399497 0.230649i 0.286770 0.957999i \(-0.407418\pi\)
−0.686267 + 0.727350i \(0.740752\pi\)
\(198\) 0 0
\(199\) 8.61414 + 14.9201i 0.610640 + 1.05766i 0.991133 + 0.132875i \(0.0424210\pi\)
−0.380493 + 0.924784i \(0.624246\pi\)
\(200\) 0.240136 + 4.09909i 0.0169802 + 0.289850i
\(201\) 0 0
\(202\) −1.43112 1.70555i −0.100693 0.120002i
\(203\) −16.2756 19.3965i −1.14233 1.36137i
\(204\) 0 0
\(205\) −4.91824 23.7987i −0.343504 1.66217i
\(206\) −0.0556428 0.0963761i −0.00387681 0.00671484i
\(207\) 0 0
\(208\) 7.85019 + 4.53231i 0.544313 + 0.314259i
\(209\) −1.19756 + 6.79170i −0.0828369 + 0.469792i
\(210\) 0 0
\(211\) −18.9632 6.90203i −1.30548 0.475156i −0.406702 0.913561i \(-0.633321\pi\)
−0.898777 + 0.438405i \(0.855543\pi\)
\(212\) −10.4827 + 1.84838i −0.719953 + 0.126947i
\(213\) 0 0
\(214\) 0.449106 + 0.376845i 0.0307003 + 0.0257606i
\(215\) −17.0418 2.49331i −1.16224 0.170042i
\(216\) 0 0
\(217\) 16.7261i 1.13544i
\(218\) 0.0640078 0.0762815i 0.00433515 0.00516644i
\(219\) 0 0
\(220\) 6.43129 0.188220i 0.433598 0.0126898i
\(221\) 3.20484 + 1.16647i 0.215581 + 0.0784649i
\(222\) 0 0
\(223\) 9.20020 + 1.62224i 0.616091 + 0.108633i 0.472980 0.881073i \(-0.343178\pi\)
0.143111 + 0.989707i \(0.454289\pi\)
\(224\) −3.48334 + 6.03332i −0.232740 + 0.403118i
\(225\) 0 0
\(226\) 0.441627 + 0.764920i 0.0293766 + 0.0508817i
\(227\) −2.68962 7.38967i −0.178516 0.490470i 0.817870 0.575403i \(-0.195155\pi\)
−0.996387 + 0.0849329i \(0.972932\pi\)
\(228\) 0 0
\(229\) 12.7733 10.7181i 0.844086 0.708272i −0.114393 0.993436i \(-0.536492\pi\)
0.958479 + 0.285163i \(0.0920478\pi\)
\(230\) 0.585963 + 0.949631i 0.0386373 + 0.0626168i
\(231\) 0 0
\(232\) −2.46978 6.78568i −0.162149 0.445502i
\(233\) −25.8565 + 14.9283i −1.69391 + 0.977982i −0.742613 + 0.669720i \(0.766414\pi\)
−0.951302 + 0.308262i \(0.900253\pi\)
\(234\) 0 0
\(235\) −9.41825 + 11.9155i −0.614379 + 0.777279i
\(236\) 2.47089 14.0131i 0.160841 0.912174i
\(237\) 0 0
\(238\) −0.287885 + 0.790957i −0.0186608 + 0.0512701i
\(239\) 4.19886 + 23.8129i 0.271602 + 1.54033i 0.749554 + 0.661943i \(0.230268\pi\)
−0.477952 + 0.878386i \(0.658621\pi\)
\(240\) 0 0
\(241\) 11.3477 + 9.52183i 0.730968 + 0.613355i 0.930395 0.366558i \(-0.119464\pi\)
−0.199427 + 0.979913i \(0.563908\pi\)
\(242\) 1.83425i 0.117910i
\(243\) 0 0
\(244\) −11.7149 −0.749967
\(245\) −2.15752 + 1.92069i −0.137839 + 0.122708i
\(246\) 0 0
\(247\) −11.1850 + 1.97221i −0.711683 + 0.125489i
\(248\) 1.63149 4.48247i 0.103599 0.284637i
\(249\) 0 0
\(250\) −1.32995 + 1.90142i −0.0841134 + 0.120256i
\(251\) −3.98405 + 6.90057i −0.251471 + 0.435560i −0.963931 0.266152i \(-0.914248\pi\)
0.712460 + 0.701712i \(0.247581\pi\)
\(252\) 0 0
\(253\) 3.06181 1.76773i 0.192494 0.111137i
\(254\) −2.35704 + 0.857892i −0.147894 + 0.0538289i
\(255\) 0 0
\(256\) 9.70145 8.14048i 0.606341 0.508780i
\(257\) 13.0075 + 15.5017i 0.811386 + 0.966972i 0.999886 0.0151015i \(-0.00480713\pi\)
−0.188500 + 0.982073i \(0.560363\pi\)
\(258\) 0 0
\(259\) 23.6535 8.60917i 1.46976 0.534948i
\(260\) 3.91377 + 9.84668i 0.242721 + 0.610665i
\(261\) 0 0
\(262\) 0.0467150 + 0.0269709i 0.00288606 + 0.00166627i
\(263\) 21.4662 + 3.78508i 1.32367 + 0.233398i 0.790421 0.612563i \(-0.209862\pi\)
0.533244 + 0.845961i \(0.320973\pi\)
\(264\) 0 0
\(265\) −10.7066 5.77063i −0.657703 0.354487i
\(266\) −0.486745 2.76047i −0.0298442 0.169255i
\(267\) 0 0
\(268\) −9.69226 + 11.5508i −0.592049 + 0.705577i
\(269\) 4.34109 0.264681 0.132341 0.991204i \(-0.457751\pi\)
0.132341 + 0.991204i \(0.457751\pi\)
\(270\) 0 0
\(271\) −13.1672 −0.799852 −0.399926 0.916547i \(-0.630964\pi\)
−0.399926 + 0.916547i \(0.630964\pi\)
\(272\) 3.38902 4.03888i 0.205490 0.244893i
\(273\) 0 0
\(274\) −0.673017 3.81687i −0.0406584 0.230585i
\(275\) 5.89855 + 4.38820i 0.355696 + 0.264619i
\(276\) 0 0
\(277\) 0.500044 + 0.0881712i 0.0300447 + 0.00529770i 0.188650 0.982044i \(-0.439589\pi\)
−0.158606 + 0.987342i \(0.550700\pi\)
\(278\) 1.24976 + 0.721550i 0.0749557 + 0.0432757i
\(279\) 0 0
\(280\) −4.91383 + 1.95310i −0.293658 + 0.116720i
\(281\) 0.459552 0.167263i 0.0274146 0.00997809i −0.328276 0.944582i \(-0.606468\pi\)
0.355691 + 0.934604i \(0.384246\pi\)
\(282\) 0 0
\(283\) −2.70977 3.22938i −0.161079 0.191967i 0.679468 0.733705i \(-0.262211\pi\)
−0.840547 + 0.541739i \(0.817766\pi\)
\(284\) 13.5459 11.3663i 0.803799 0.674467i
\(285\) 0 0
\(286\) −0.694377 + 0.252733i −0.0410594 + 0.0149444i
\(287\) 27.1023 15.6475i 1.59980 0.923642i
\(288\) 0 0
\(289\) −7.50815 + 13.0045i −0.441656 + 0.764970i
\(290\) 1.28291 3.87379i 0.0753349 0.227477i
\(291\) 0 0
\(292\) −8.41710 + 23.1258i −0.492573 + 1.35333i
\(293\) −22.7756 + 4.01595i −1.33056 + 0.234614i −0.793315 0.608811i \(-0.791647\pi\)
−0.537247 + 0.843425i \(0.680536\pi\)
\(294\) 0 0
\(295\) 12.1440 10.8109i 0.707053 0.629438i
\(296\) 7.17872 0.417254
\(297\) 0 0
\(298\) 1.70512i 0.0987747i
\(299\) 4.46024 + 3.74258i 0.257942 + 0.216439i
\(300\) 0 0
\(301\) −3.85144 21.8426i −0.221994 1.25899i
\(302\) −0.628511 + 1.72682i −0.0361668 + 0.0993674i
\(303\) 0 0
\(304\) −3.04888 + 17.2911i −0.174865 + 0.991711i
\(305\) −10.5015 8.30063i −0.601315 0.475293i
\(306\) 0 0
\(307\) 2.88589 1.66617i 0.164706 0.0950932i −0.415381 0.909648i \(-0.636352\pi\)
0.580087 + 0.814554i \(0.303018\pi\)
\(308\) 2.83384 + 7.78592i 0.161473 + 0.443644i
\(309\) 0 0
\(310\) 2.29405 1.41552i 0.130293 0.0803964i
\(311\) 8.46844 7.10587i 0.480201 0.402937i −0.370298 0.928913i \(-0.620744\pi\)
0.850499 + 0.525976i \(0.176300\pi\)
\(312\) 0 0
\(313\) 3.19684 + 8.78326i 0.180696 + 0.496459i 0.996662 0.0816417i \(-0.0260163\pi\)
−0.815965 + 0.578101i \(0.803794\pi\)
\(314\) 0.646076 + 1.11904i 0.0364602 + 0.0631509i
\(315\) 0 0
\(316\) 1.46711 2.54110i 0.0825312 0.142948i
\(317\) −26.8303 4.73090i −1.50694 0.265714i −0.641654 0.766994i \(-0.721752\pi\)
−0.865285 + 0.501280i \(0.832863\pi\)
\(318\) 0 0
\(319\) −12.1494 4.42203i −0.680238 0.247586i
\(320\) 15.6116 0.456894i 0.872716 0.0255411i
\(321\) 0 0
\(322\) −0.923674 + 1.10079i −0.0514743 + 0.0613447i
\(323\) 6.60604i 0.367570i
\(324\) 0 0
\(325\) −3.46852 + 11.6000i −0.192399 + 0.643450i
\(326\) 3.28491 + 2.75637i 0.181934 + 0.152661i
\(327\) 0 0
\(328\) 8.78948 1.54982i 0.485318 0.0855746i
\(329\) −18.3794 6.68956i −1.01329 0.368808i
\(330\) 0 0
\(331\) 4.40921 25.0059i 0.242352 1.37445i −0.584210 0.811602i \(-0.698596\pi\)
0.826562 0.562845i \(-0.190293\pi\)
\(332\) 19.6843 + 11.3647i 1.08032 + 0.623721i
\(333\) 0 0
\(334\) −0.650632 1.12693i −0.0356010 0.0616628i
\(335\) −16.8728 + 3.48692i −0.921859 + 0.190511i
\(336\) 0 0
\(337\) −3.09214 3.68507i −0.168440 0.200739i 0.675221 0.737616i \(-0.264048\pi\)
−0.843661 + 0.536877i \(0.819604\pi\)
\(338\) 0.952032 + 1.13459i 0.0517837 + 0.0617134i
\(339\) 0 0
\(340\) 6.03555 1.24730i 0.327324 0.0676446i
\(341\) −4.27036 7.39648i −0.231253 0.400542i
\(342\) 0 0
\(343\) 14.2349 + 8.21851i 0.768611 + 0.443758i
\(344\) 1.09840 6.22934i 0.0592218 0.335863i
\(345\) 0 0
\(346\) −0.774126 0.281759i −0.0416173 0.0151474i
\(347\) 23.4852 4.14108i 1.26075 0.222305i 0.496964 0.867771i \(-0.334448\pi\)
0.763789 + 0.645466i \(0.223337\pi\)
\(348\) 0 0
\(349\) 10.1403 + 8.50874i 0.542799 + 0.455462i 0.872494 0.488625i \(-0.162501\pi\)
−0.329695 + 0.944087i \(0.606946\pi\)
\(350\) −2.86288 0.856035i −0.153027 0.0457570i
\(351\) 0 0
\(352\) 3.55734i 0.189607i
\(353\) 12.6452 15.0700i 0.673036 0.802093i −0.316158 0.948707i \(-0.602393\pi\)
0.989194 + 0.146614i \(0.0468375\pi\)
\(354\) 0 0
\(355\) 20.1965 0.591077i 1.07192 0.0313711i
\(356\) 21.9480 + 7.98841i 1.16324 + 0.423385i
\(357\) 0 0
\(358\) −2.86963 0.505993i −0.151665 0.0267425i
\(359\) −5.85683 + 10.1443i −0.309112 + 0.535397i −0.978168 0.207814i \(-0.933365\pi\)
0.669057 + 0.743211i \(0.266698\pi\)
\(360\) 0 0
\(361\) −1.49955 2.59729i −0.0789236 0.136700i
\(362\) −0.470638 1.29307i −0.0247362 0.0679621i
\(363\) 0 0
\(364\) −10.4529 + 8.77098i −0.547878 + 0.459724i
\(365\) −23.9312 + 14.7666i −1.25262 + 0.772918i
\(366\) 0 0
\(367\) 8.09527 + 22.2416i 0.422569 + 1.16100i 0.950231 + 0.311546i \(0.100847\pi\)
−0.527662 + 0.849455i \(0.676931\pi\)
\(368\) 7.79509 4.50050i 0.406347 0.234605i
\(369\) 0 0
\(370\) 3.18257 + 2.51558i 0.165454 + 0.130779i
\(371\) 2.71983 15.4249i 0.141206 0.800821i
\(372\) 0 0
\(373\) 7.08072 19.4541i 0.366626 1.00730i −0.610010 0.792394i \(-0.708834\pi\)
0.976636 0.214902i \(-0.0689434\pi\)
\(374\) 0.0746341 + 0.423271i 0.00385924 + 0.0218868i
\(375\) 0 0
\(376\) −4.27304 3.58551i −0.220365 0.184908i
\(377\) 21.2925i 1.09662i
\(378\) 0 0
\(379\) 14.1618 0.727442 0.363721 0.931508i \(-0.381506\pi\)
0.363721 + 0.931508i \(0.381506\pi\)
\(380\) −15.3296 + 13.6469i −0.786394 + 0.700069i
\(381\) 0 0
\(382\) 2.00190 0.352989i 0.102426 0.0180605i
\(383\) 6.96733 19.1426i 0.356014 0.978140i −0.624385 0.781117i \(-0.714650\pi\)
0.980399 0.197023i \(-0.0631274\pi\)
\(384\) 0 0
\(385\) −2.97643 + 8.98744i −0.151693 + 0.458042i
\(386\) 2.01592 3.49168i 0.102608 0.177722i
\(387\) 0 0
\(388\) 9.52672 5.50025i 0.483646 0.279233i
\(389\) −10.7321 + 3.90618i −0.544141 + 0.198051i −0.599441 0.800419i \(-0.704611\pi\)
0.0553005 + 0.998470i \(0.482388\pi\)
\(390\) 0 0
\(391\) 2.59427 2.17685i 0.131198 0.110088i
\(392\) −0.681914 0.812674i −0.0344419 0.0410462i
\(393\) 0 0
\(394\) 1.26271 0.459590i 0.0636146 0.0231538i
\(395\) 3.11567 1.23839i 0.156766 0.0623099i
\(396\) 0 0
\(397\) 2.93301 + 1.69337i 0.147204 + 0.0849880i 0.571793 0.820398i \(-0.306248\pi\)
−0.424589 + 0.905386i \(0.639581\pi\)
\(398\) −3.52125 0.620891i −0.176504 0.0311225i
\(399\) 0 0
\(400\) 15.0172 + 11.1720i 0.750859 + 0.558599i
\(401\) −3.73348 21.1736i −0.186441 1.05736i −0.924090 0.382175i \(-0.875175\pi\)
0.737649 0.675184i \(-0.235936\pi\)
\(402\) 0 0
\(403\) 9.04105 10.7747i 0.450367 0.536726i
\(404\) −20.9933 −1.04445
\(405\) 0 0
\(406\) 5.25502 0.260802
\(407\) 8.26184 9.84608i 0.409524 0.488052i
\(408\) 0 0
\(409\) 2.13010 + 12.0804i 0.105327 + 0.597338i 0.991089 + 0.133199i \(0.0425250\pi\)
−0.885762 + 0.464139i \(0.846364\pi\)
\(410\) 4.43977 + 2.39293i 0.219265 + 0.118179i
\(411\) 0 0
\(412\) −1.03338 0.182213i −0.0509111 0.00897700i
\(413\) 18.1327 + 10.4689i 0.892254 + 0.515143i
\(414\) 0 0
\(415\) 9.59298 + 24.1351i 0.470901 + 1.18474i
\(416\) −5.50513 + 2.00370i −0.269911 + 0.0982397i
\(417\) 0 0
\(418\) −0.920022 1.09644i −0.0449998 0.0536286i
\(419\) 23.2229 19.4864i 1.13451 0.951971i 0.135269 0.990809i \(-0.456810\pi\)
0.999246 + 0.0388381i \(0.0123657\pi\)
\(420\) 0 0
\(421\) −8.53967 + 3.10819i −0.416198 + 0.151484i −0.541627 0.840619i \(-0.682191\pi\)
0.125429 + 0.992103i \(0.459969\pi\)
\(422\) 3.62710 2.09411i 0.176565 0.101940i
\(423\) 0 0
\(424\) 2.23346 3.86847i 0.108466 0.187869i
\(425\) 6.29421 + 3.15841i 0.305314 + 0.153205i
\(426\) 0 0
\(427\) 5.89575 16.1984i 0.285315 0.783897i
\(428\) 5.44399 0.959922i 0.263145 0.0463996i
\(429\) 0 0
\(430\) 2.66985 2.37678i 0.128752 0.114618i
\(431\) 17.7056 0.852847 0.426424 0.904524i \(-0.359773\pi\)
0.426424 + 0.904524i \(0.359773\pi\)
\(432\) 0 0
\(433\) 6.74677i 0.324229i −0.986772 0.162114i \(-0.948169\pi\)
0.986772 0.162114i \(-0.0518314\pi\)
\(434\) 2.65921 + 2.23134i 0.127646 + 0.107108i
\(435\) 0 0
\(436\) −0.163045 0.924672i −0.00780842 0.0442837i
\(437\) −3.85724 + 10.5977i −0.184517 + 0.506956i
\(438\) 0 0
\(439\) 0.774036 4.38977i 0.0369427 0.209512i −0.960749 0.277419i \(-0.910521\pi\)
0.997692 + 0.0679067i \(0.0216320\pi\)
\(440\) −1.67431 + 2.11824i −0.0798195 + 0.100983i
\(441\) 0 0
\(442\) −0.612991 + 0.353911i −0.0291570 + 0.0168338i
\(443\) −2.74386 7.53869i −0.130365 0.358174i 0.857287 0.514838i \(-0.172148\pi\)
−0.987652 + 0.156665i \(0.949926\pi\)
\(444\) 0 0
\(445\) 14.0145 + 22.7124i 0.664352 + 1.07667i
\(446\) −1.48526 + 1.24628i −0.0703293 + 0.0590133i
\(447\) 0 0
\(448\) 6.87900 + 18.8999i 0.325002 + 0.892936i
\(449\) −2.62606 4.54847i −0.123931 0.214655i 0.797383 0.603473i \(-0.206217\pi\)
−0.921315 + 0.388818i \(0.872884\pi\)
\(450\) 0 0
\(451\) 7.98996 13.8390i 0.376232 0.651654i
\(452\) 8.20177 + 1.44619i 0.385779 + 0.0680232i
\(453\) 0 0
\(454\) 1.53366 + 0.558206i 0.0719782 + 0.0261979i
\(455\) −15.5849 + 0.456113i −0.730634 + 0.0213829i
\(456\) 0 0
\(457\) 1.94777 2.32127i 0.0911130 0.108584i −0.718562 0.695463i \(-0.755199\pi\)
0.809675 + 0.586879i \(0.199644\pi\)
\(458\) 3.46062i 0.161704i
\(459\) 0 0
\(460\) 10.4108 + 1.52316i 0.485405 + 0.0710175i
\(461\) 2.25112 + 1.88892i 0.104845 + 0.0879757i 0.693703 0.720261i \(-0.255978\pi\)
−0.588858 + 0.808236i \(0.700422\pi\)
\(462\) 0 0
\(463\) −18.1798 + 3.20559i −0.844886 + 0.148976i −0.579304 0.815112i \(-0.696675\pi\)
−0.265583 + 0.964088i \(0.585564\pi\)
\(464\) −30.9314 11.2581i −1.43595 0.522644i
\(465\) 0 0
\(466\) 1.07600 6.10231i 0.0498448 0.282684i
\(467\) −18.7117 10.8032i −0.865875 0.499913i 9.99457e−5 1.00000i \(-0.499968\pi\)
−0.865975 + 0.500087i \(0.833302\pi\)
\(468\) 0 0
\(469\) −11.0937 19.2149i −0.512261 0.887263i
\(470\) −0.637947 3.08694i −0.0294263 0.142390i
\(471\) 0 0
\(472\) 3.83828 + 4.57429i 0.176671 + 0.210549i
\(473\) −7.27982 8.67575i −0.334726 0.398911i
\(474\) 0 0
\(475\) −23.4115 + 1.37151i −1.07419 + 0.0629290i
\(476\) 3.96833 + 6.87335i 0.181888 + 0.315040i
\(477\) 0 0
\(478\) −4.34606 2.50920i −0.198784 0.114768i
\(479\) −0.173381 + 0.983295i −0.00792200 + 0.0449279i −0.988513 0.151139i \(-0.951706\pi\)
0.980591 + 0.196067i \(0.0628170\pi\)
\(480\) 0 0
\(481\) 19.8908 + 7.23966i 0.906942 + 0.330100i
\(482\) −3.02767 + 0.533859i −0.137906 + 0.0243166i
\(483\) 0 0
\(484\) −13.2490 11.1173i −0.602229 0.505330i
\(485\) 12.4372 + 1.81964i 0.564746 + 0.0826255i
\(486\) 0 0
\(487\) 18.3516i 0.831589i 0.909459 + 0.415794i \(0.136496\pi\)
−0.909459 + 0.415794i \(0.863504\pi\)
\(488\) 3.16003 3.76598i 0.143048 0.170478i
\(489\) 0 0
\(490\) −0.0175376 0.599243i −0.000792269 0.0270711i
\(491\) 10.2329 + 3.72447i 0.461805 + 0.168083i 0.562436 0.826841i \(-0.309864\pi\)
−0.100632 + 0.994924i \(0.532086\pi\)
\(492\) 0 0
\(493\) −12.1965 2.15057i −0.549303 0.0968570i
\(494\) 1.17858 2.04135i 0.0530266 0.0918449i
\(495\) 0 0
\(496\) −10.8720 18.8308i −0.488165 0.845527i
\(497\) 8.89927 + 24.4505i 0.399187 + 1.09676i
\(498\) 0 0
\(499\) −22.2753 + 18.6912i −0.997180 + 0.836733i −0.986591 0.163211i \(-0.947815\pi\)
−0.0105884 + 0.999944i \(0.503370\pi\)
\(500\) 5.67345 + 21.1307i 0.253724 + 0.944994i
\(501\) 0 0
\(502\) −0.565600 1.55397i −0.0252440 0.0693573i
\(503\) −16.5027 + 9.52781i −0.735817 + 0.424824i −0.820546 0.571580i \(-0.806331\pi\)
0.0847294 + 0.996404i \(0.472997\pi\)
\(504\) 0 0
\(505\) −18.8189 14.8749i −0.837432 0.661925i
\(506\) −0.127415 + 0.722607i −0.00566429 + 0.0321238i
\(507\) 0 0
\(508\) −8.08916 + 22.2248i −0.358898 + 0.986065i
\(509\) 6.00851 + 34.0759i 0.266322 + 1.51039i 0.765243 + 0.643741i \(0.222619\pi\)
−0.498921 + 0.866648i \(0.666270\pi\)
\(510\) 0 0
\(511\) −27.7405 23.2771i −1.22717 1.02972i
\(512\) 15.2050i 0.671974i
\(513\) 0 0
\(514\) −4.19981 −0.185246
\(515\) −0.797243 0.895550i −0.0351307 0.0394626i
\(516\) 0 0
\(517\) −9.83552 + 1.73427i −0.432566 + 0.0762730i
\(518\) −1.78676 + 4.90907i −0.0785055 + 0.215692i
\(519\) 0 0
\(520\) −4.22114 1.39794i −0.185109 0.0613038i
\(521\) 10.0641 17.4315i 0.440915 0.763686i −0.556843 0.830618i \(-0.687988\pi\)
0.997758 + 0.0669313i \(0.0213208\pi\)
\(522\) 0 0
\(523\) 15.9232 9.19327i 0.696274 0.401994i −0.109684 0.993966i \(-0.534984\pi\)
0.805958 + 0.591973i \(0.201651\pi\)
\(524\) 0.477950 0.173960i 0.0208793 0.00759946i
\(525\) 0 0
\(526\) −3.46547 + 2.90788i −0.151102 + 0.126789i
\(527\) −5.25867 6.26704i −0.229071 0.272996i
\(528\) 0 0
\(529\) −16.1800 + 5.88905i −0.703480 + 0.256046i
\(530\) 2.34576 0.932371i 0.101893 0.0404996i
\(531\) 0 0
\(532\) −22.8893 13.2151i −0.992377 0.572949i
\(533\) 25.9169 + 4.56985i 1.12259 + 0.197942i
\(534\) 0 0
\(535\) 5.56030 + 2.99687i 0.240393 + 0.129566i
\(536\) −1.09879 6.23155i −0.0474605 0.269162i
\(537\) 0 0
\(538\) −0.579122 + 0.690171i −0.0249677 + 0.0297554i
\(539\) −1.89944 −0.0818146
\(540\) 0 0
\(541\) 4.17044 0.179301 0.0896506 0.995973i \(-0.471425\pi\)
0.0896506 + 0.995973i \(0.471425\pi\)
\(542\) 1.75657 2.09340i 0.0754512 0.0899192i
\(543\) 0 0
\(544\) 0.591711 + 3.35576i 0.0253694 + 0.143877i
\(545\) 0.509024 0.944427i 0.0218042 0.0404548i
\(546\) 0 0
\(547\) −23.2507 4.09973i −0.994128 0.175292i −0.347158 0.937807i \(-0.612853\pi\)
−0.646970 + 0.762515i \(0.723964\pi\)
\(548\) −31.6488 18.2724i −1.35197 0.780560i
\(549\) 0 0
\(550\) −1.48456 + 0.352376i −0.0633016 + 0.0150254i
\(551\) 38.7555 14.1059i 1.65104 0.600930i
\(552\) 0 0
\(553\) 2.77530 + 3.30747i 0.118018 + 0.140648i
\(554\) −0.0807262 + 0.0677373i −0.00342973 + 0.00287788i
\(555\) 0 0
\(556\) 12.7865 4.65392i 0.542270 0.197370i
\(557\) −23.3763 + 13.4963i −0.990484 + 0.571856i −0.905419 0.424519i \(-0.860443\pi\)
−0.0850648 + 0.996375i \(0.527110\pi\)
\(558\) 0 0
\(559\) 9.32567 16.1525i 0.394434 0.683179i
\(560\) −7.57772 + 22.8812i −0.320217 + 0.966909i
\(561\) 0 0
\(562\) −0.0347140 + 0.0953759i −0.00146432 + 0.00402319i
\(563\) 13.8182 2.43652i 0.582366 0.102687i 0.125299 0.992119i \(-0.460011\pi\)
0.457067 + 0.889432i \(0.348900\pi\)
\(564\) 0 0
\(565\) 6.32757 + 7.10782i 0.266203 + 0.299028i
\(566\) 0.874921 0.0367757
\(567\) 0 0
\(568\) 7.42061i 0.311362i
\(569\) 17.5672 + 14.7406i 0.736454 + 0.617958i 0.931883 0.362760i \(-0.118165\pi\)
−0.195429 + 0.980718i \(0.562610\pi\)
\(570\) 0 0
\(571\) 0.200726 + 1.13838i 0.00840013 + 0.0476395i 0.988720 0.149778i \(-0.0478558\pi\)
−0.980320 + 0.197417i \(0.936745\pi\)
\(572\) −2.38305 + 6.54736i −0.0996401 + 0.273759i
\(573\) 0 0
\(574\) −1.12784 + 6.39632i −0.0470753 + 0.266977i
\(575\) 8.25325 + 8.74201i 0.344184 + 0.364567i
\(576\) 0 0
\(577\) 22.9770 13.2658i 0.956544 0.552261i 0.0614366 0.998111i \(-0.480432\pi\)
0.895108 + 0.445850i \(0.147098\pi\)
\(578\) −1.06590 2.92855i −0.0443358 0.121812i
\(579\) 0 0
\(580\) −20.2052 32.7453i −0.838977 1.35967i
\(581\) −25.6208 + 21.4984i −1.06293 + 0.891906i
\(582\) 0 0
\(583\) −2.73541 7.51548i −0.113289 0.311259i
\(584\) −5.16378 8.94393i −0.213679 0.370102i
\(585\) 0 0
\(586\) 2.39989 4.15673i 0.0991385 0.171713i
\(587\) −31.2941 5.51799i −1.29165 0.227752i −0.514728 0.857354i \(-0.672107\pi\)
−0.776918 + 0.629602i \(0.783218\pi\)
\(588\) 0 0
\(589\) 25.6011 + 9.31802i 1.05487 + 0.383942i
\(590\) 0.0987138 + 3.37296i 0.00406398 + 0.138862i
\(591\) 0 0
\(592\) 21.0339 25.0673i 0.864489 1.03026i
\(593\) 10.3324i 0.424303i 0.977237 + 0.212151i \(0.0680470\pi\)
−0.977237 + 0.212151i \(0.931953\pi\)
\(594\) 0 0
\(595\) −1.31284 + 8.97324i −0.0538210 + 0.367867i
\(596\) 12.3163 + 10.3346i 0.504494 + 0.423320i
\(597\) 0 0
\(598\) −1.19003 + 0.209835i −0.0486641 + 0.00858079i
\(599\) −30.6411 11.1524i −1.25196 0.455677i −0.370897 0.928674i \(-0.620950\pi\)
−0.881064 + 0.472997i \(0.843172\pi\)
\(600\) 0 0
\(601\) −4.69496 + 26.6264i −0.191511 + 1.08611i 0.725789 + 0.687918i \(0.241475\pi\)
−0.917300 + 0.398197i \(0.869636\pi\)
\(602\) 3.98646 + 2.30159i 0.162476 + 0.0938056i
\(603\) 0 0
\(604\) 8.66368 + 15.0059i 0.352520 + 0.610583i
\(605\) −3.99959 19.3535i −0.162606 0.786831i
\(606\) 0 0
\(607\) 4.08135 + 4.86396i 0.165657 + 0.197422i 0.842486 0.538718i \(-0.181091\pi\)
−0.676830 + 0.736140i \(0.736647\pi\)
\(608\) −7.29408 8.69275i −0.295814 0.352537i
\(609\) 0 0
\(610\) 2.72063 0.562245i 0.110155 0.0227646i
\(611\) −8.22381 14.2440i −0.332700 0.576253i
\(612\) 0 0
\(613\) −33.0811 19.0994i −1.33613 0.771416i −0.349900 0.936787i \(-0.613784\pi\)
−0.986231 + 0.165371i \(0.947118\pi\)
\(614\) −0.120094 + 0.681089i −0.00484661 + 0.0274865i
\(615\) 0 0
\(616\) −3.26736 1.18922i −0.131646 0.0479151i
\(617\) −16.9692 + 2.99213i −0.683155 + 0.120459i −0.504446 0.863443i \(-0.668303\pi\)
−0.178709 + 0.983902i \(0.557192\pi\)
\(618\) 0 0
\(619\) 3.05553 + 2.56390i 0.122812 + 0.103052i 0.702125 0.712053i \(-0.252235\pi\)
−0.579313 + 0.815105i \(0.696679\pi\)
\(620\) 3.67952 25.1495i 0.147773 1.01003i
\(621\) 0 0
\(622\) 2.29432i 0.0919937i
\(623\) −22.0916 + 26.3277i −0.885080 + 1.05480i
\(624\) 0 0
\(625\) −9.88647 + 22.9621i −0.395459 + 0.918484i
\(626\) −1.82289 0.663476i −0.0728571 0.0265178i
\(627\) 0 0
\(628\) 11.9987 + 2.11570i 0.478802 + 0.0844257i
\(629\) 6.15593 10.6624i 0.245453 0.425137i
\(630\) 0 0
\(631\) −3.17235 5.49468i −0.126289 0.218740i 0.795947 0.605367i \(-0.206973\pi\)
−0.922236 + 0.386627i \(0.873640\pi\)
\(632\) 0.421144 + 1.15708i 0.0167522 + 0.0460263i
\(633\) 0 0
\(634\) 4.33143 3.63450i 0.172023 0.144345i
\(635\) −22.9988 + 14.1913i −0.912681 + 0.563163i
\(636\) 0 0
\(637\) −1.06988 2.93946i −0.0423900 0.116466i
\(638\) 2.32383 1.34166i 0.0920014 0.0531170i
\(639\) 0 0
\(640\) −8.71936 + 11.0313i −0.344663 + 0.436049i
\(641\) −5.63430 + 31.9537i −0.222542 + 1.26210i 0.644788 + 0.764362i \(0.276946\pi\)
−0.867329 + 0.497734i \(0.834165\pi\)
\(642\) 0 0
\(643\) 5.98189 16.4351i 0.235903 0.648137i −0.764093 0.645106i \(-0.776813\pi\)
0.999995 0.00303079i \(-0.000964731\pi\)
\(644\) 2.35284 + 13.3436i 0.0927148 + 0.525812i
\(645\) 0 0
\(646\) −1.05026 0.881277i −0.0413221 0.0346734i
\(647\) 3.69757i 0.145367i 0.997355 + 0.0726833i \(0.0231562\pi\)
−0.997355 + 0.0726833i \(0.976844\pi\)
\(648\) 0 0
\(649\) 10.6913 0.419672
\(650\) −1.38151 2.09893i −0.0541872 0.0823270i
\(651\) 0 0
\(652\) 39.8191 7.02118i 1.55944 0.274971i
\(653\) −9.02248 + 24.7891i −0.353077 + 0.970071i 0.628299 + 0.777972i \(0.283752\pi\)
−0.981376 + 0.192099i \(0.938471\pi\)
\(654\) 0 0
\(655\) 0.551707 + 0.182712i 0.0215570 + 0.00713916i
\(656\) 20.3417 35.2329i 0.794211 1.37561i
\(657\) 0 0
\(658\) 3.51545 2.02964i 0.137046 0.0791238i
\(659\) 14.2209 5.17599i 0.553968 0.201628i −0.0498407 0.998757i \(-0.515871\pi\)
0.603809 + 0.797129i \(0.293649\pi\)
\(660\) 0 0
\(661\) 14.8757 12.4822i 0.578598 0.485501i −0.305889 0.952067i \(-0.598953\pi\)
0.884486 + 0.466566i \(0.154509\pi\)
\(662\) 3.38736 + 4.03690i 0.131654 + 0.156899i
\(663\) 0 0
\(664\) −8.96318 + 3.26233i −0.347839 + 0.126603i
\(665\) −11.1549 28.0648i −0.432569 1.08830i
\(666\) 0 0
\(667\) −18.3104 10.5715i −0.708983 0.409332i
\(668\) −12.0834 2.13062i −0.467519 0.0824363i
\(669\) 0 0
\(670\) 1.69654 3.14770i 0.0655430 0.121606i
\(671\) −1.52847 8.66839i −0.0590060 0.334640i
\(672\) 0 0
\(673\) −15.8772 + 18.9217i −0.612021 + 0.729378i −0.979677 0.200584i \(-0.935716\pi\)
0.367656 + 0.929962i \(0.380161\pi\)
\(674\) 0.998381 0.0384562
\(675\) 0 0
\(676\) 13.9654 0.537133
\(677\) −6.58819 + 7.85150i −0.253205 + 0.301758i −0.877641 0.479318i \(-0.840884\pi\)
0.624437 + 0.781075i \(0.285329\pi\)
\(678\) 0 0
\(679\) 2.81082 + 15.9410i 0.107869 + 0.611758i
\(680\) −1.22709 + 2.27671i −0.0470568 + 0.0873077i
\(681\) 0 0
\(682\) 1.74562 + 0.307800i 0.0668432 + 0.0117863i
\(683\) 12.1386 + 7.00820i 0.464469 + 0.268161i 0.713921 0.700226i \(-0.246917\pi\)
−0.249453 + 0.968387i \(0.580251\pi\)
\(684\) 0 0
\(685\) −15.4238 38.8048i −0.589312 1.48266i
\(686\) −3.20562 + 1.16675i −0.122391 + 0.0445468i
\(687\) 0 0
\(688\) −18.5338 22.0877i −0.706594 0.842086i
\(689\) 10.0898 8.46633i 0.384390 0.322542i
\(690\) 0 0
\(691\) −15.6160 + 5.68375i −0.594060 + 0.216220i −0.621514 0.783403i \(-0.713482\pi\)
0.0274543 + 0.999623i \(0.491260\pi\)
\(692\) −6.72709 + 3.88389i −0.255725 + 0.147643i
\(693\) 0 0
\(694\) −2.47467 + 4.28625i −0.0939372 + 0.162704i
\(695\) 14.7597 + 4.88808i 0.559869 + 0.185415i
\(696\) 0 0
\(697\) 5.23528 14.3838i 0.198301 0.544826i
\(698\) −2.70553 + 0.477058i −0.102406 + 0.0180569i
\(699\) 0 0
\(700\) −23.5349 + 15.4906i −0.889537 + 0.585489i
\(701\) −23.2471 −0.878029 −0.439015 0.898480i \(-0.644672\pi\)
−0.439015 + 0.898480i \(0.644672\pi\)
\(702\) 0 0
\(703\) 41.0003i 1.54636i
\(704\) 7.86733 + 6.60147i 0.296511 + 0.248802i
\(705\) 0 0
\(706\) 0.708977 + 4.02081i 0.0266827 + 0.151325i
\(707\) 10.5653 29.0280i 0.397349 1.09171i
\(708\) 0 0
\(709\) 0.376750 2.13666i 0.0141492 0.0802438i −0.976916 0.213626i \(-0.931473\pi\)
0.991065 + 0.133382i \(0.0425837\pi\)
\(710\) −2.60034 + 3.28981i −0.0975891 + 0.123464i
\(711\) 0 0
\(712\) −8.48841 + 4.90079i −0.318117 + 0.183665i
\(713\) −4.77688 13.1244i −0.178895 0.491511i
\(714\) 0 0
\(715\) −6.77540 + 4.18071i −0.253386 + 0.156350i
\(716\) −21.0474 + 17.6609i −0.786579 + 0.660018i
\(717\) 0 0
\(718\) −0.831472 2.28445i −0.0310303 0.0852550i
\(719\) −2.14999 3.72389i −0.0801810 0.138878i 0.823147 0.567829i \(-0.192217\pi\)
−0.903328 + 0.428951i \(0.858883\pi\)
\(720\) 0 0
\(721\) 0.772022 1.33718i 0.0287516 0.0497992i
\(722\) 0.612979 + 0.108085i 0.0228127 + 0.00402250i
\(723\) 0 0
\(724\) −12.1925 4.43770i −0.453130 0.164926i
\(725\) 5.08936 43.6703i 0.189014 1.62187i
\(726\) 0 0
\(727\) −14.7760 + 17.6094i −0.548011 + 0.653095i −0.966964 0.254914i \(-0.917953\pi\)
0.418952 + 0.908008i \(0.362397\pi\)
\(728\) 5.72622i 0.212228i
\(729\) 0 0
\(730\) 0.844864 5.77465i 0.0312698 0.213729i
\(731\) −8.31038 6.97324i −0.307371 0.257915i
\(732\) 0 0
\(733\) −1.93062 + 0.340421i −0.0713092 + 0.0125737i −0.209189 0.977875i \(-0.567082\pi\)
0.137880 + 0.990449i \(0.455971\pi\)
\(734\) −4.61603 1.68010i −0.170381 0.0620136i
\(735\) 0 0
\(736\) −1.01017 + 5.72894i −0.0372353 + 0.211172i
\(737\) −9.81157 5.66471i −0.361414 0.208662i
\(738\) 0 0
\(739\) 2.11839 + 3.66916i 0.0779263 + 0.134972i 0.902355 0.430993i \(-0.141837\pi\)
−0.824429 + 0.565966i \(0.808503\pi\)
\(740\) 37.4596 7.74139i 1.37704 0.284579i
\(741\) 0 0
\(742\) 2.08950 + 2.49017i 0.0767080 + 0.0914170i
\(743\) 26.6003 + 31.7011i 0.975872 + 1.16300i 0.986617 + 0.163057i \(0.0521353\pi\)
−0.0107448 + 0.999942i \(0.503420\pi\)
\(744\) 0 0
\(745\) 3.71800 + 17.9909i 0.136217 + 0.659137i
\(746\) 2.14832 + 3.72101i 0.0786557 + 0.136236i
\(747\) 0 0
\(748\) 3.50969 + 2.02632i 0.128327 + 0.0740895i
\(749\) −1.41249 + 8.01065i −0.0516114 + 0.292703i
\(750\) 0 0
\(751\) −16.4803 5.99834i −0.601375 0.218883i 0.0233500 0.999727i \(-0.492567\pi\)
−0.624725 + 0.780845i \(0.714789\pi\)
\(752\) −25.0404 + 4.41529i −0.913129 + 0.161009i
\(753\) 0 0
\(754\) 3.38520 + 2.84052i 0.123282 + 0.103446i
\(755\) −2.86619 + 19.5904i −0.104311 + 0.712968i
\(756\) 0 0
\(757\) 31.2786i 1.13684i 0.822739 + 0.568420i \(0.192445\pi\)
−0.822739 + 0.568420i \(0.807555\pi\)
\(758\) −1.88925 + 2.25152i −0.0686206 + 0.0817789i
\(759\) 0 0
\(760\) −0.251959 8.60921i −0.00913953 0.312289i
\(761\) −12.3465 4.49377i −0.447561 0.162899i 0.108400 0.994107i \(-0.465427\pi\)
−0.555961 + 0.831208i \(0.687650\pi\)
\(762\) 0 0
\(763\) 1.36062 + 0.239915i 0.0492579 + 0.00868549i
\(764\) 9.58366 16.5994i 0.346725 0.600545i
\(765\) 0 0
\(766\) 2.11392 + 3.66141i 0.0763790 + 0.132292i
\(767\) 6.02200 + 16.5453i 0.217442 + 0.597417i
\(768\) 0 0
\(769\) 36.6235 30.7307i 1.32068 1.10818i 0.334514 0.942391i \(-0.391428\pi\)
0.986161 0.165788i \(-0.0530166\pi\)
\(770\) −1.03180 1.67218i −0.0371836 0.0602610i
\(771\) 0 0
\(772\) −13.0025 35.7240i −0.467970 1.28574i
\(773\) 45.6728 26.3692i 1.64274 0.948434i 0.662881 0.748725i \(-0.269333\pi\)
0.979855 0.199710i \(-0.0639999\pi\)
\(774\) 0 0
\(775\) 21.1183 19.9376i 0.758591 0.716179i
\(776\) −0.801623 + 4.54623i −0.0287766 + 0.163200i
\(777\) 0 0
\(778\) 0.810692 2.22736i 0.0290647 0.0798546i
\(779\) 8.85162 + 50.2000i 0.317142 + 1.79860i
\(780\) 0 0
\(781\) 10.1779 + 8.54024i 0.364192 + 0.305594i
\(782\) 0.702854i 0.0251340i
\(783\) 0 0
\(784\) −4.83580 −0.172707
\(785\) 9.25690 + 10.3984i 0.330393 + 0.371133i
\(786\) 0 0
\(787\) −8.67001 + 1.52876i −0.309053 + 0.0544943i −0.326023 0.945362i \(-0.605709\pi\)
0.0169709 + 0.999856i \(0.494598\pi\)
\(788\) 4.33353 11.9063i 0.154376 0.424144i
\(789\) 0 0
\(790\) −0.218759 + 0.660553i −0.00778311 + 0.0235014i
\(791\) −6.12740 + 10.6130i −0.217865 + 0.377354i
\(792\) 0 0
\(793\) 12.5538 7.24793i 0.445798 0.257382i
\(794\) −0.660500 + 0.240402i −0.0234403 + 0.00853156i
\(795\) 0 0
\(796\) −25.8268 + 21.6712i −0.915406 + 0.768117i
\(797\) 5.59255 + 6.66494i 0.198098 + 0.236084i 0.855944 0.517068i \(-0.172977\pi\)
−0.657846 + 0.753153i \(0.728532\pi\)
\(798\) 0 0
\(799\) −8.98971 + 3.27199i −0.318033 + 0.115755i
\(800\) −11.7698 + 2.79370i −0.416125 + 0.0987720i
\(801\) 0 0
\(802\) 3.86436 + 2.23109i 0.136455 + 0.0787825i
\(803\) −18.2101 3.21093i −0.642620 0.113311i
\(804\) 0 0
\(805\) −7.34555 + 13.6287i −0.258897 + 0.480348i
\(806\) 0.506903 + 2.87479i 0.0178549 + 0.101260i
\(807\) 0 0
\(808\) 5.66285 6.74872i 0.199218 0.237419i
\(809\) 37.8226 1.32977 0.664886 0.746945i \(-0.268480\pi\)
0.664886 + 0.746945i \(0.268480\pi\)
\(810\) 0 0
\(811\) −0.322691 −0.0113312 −0.00566561 0.999984i \(-0.501803\pi\)
−0.00566561 + 0.999984i \(0.501803\pi\)
\(812\) 31.8502 37.9576i 1.11772 1.33205i
\(813\) 0 0
\(814\) 0.463216 + 2.62703i 0.0162357 + 0.0920773i
\(815\) 40.6698 + 21.9201i 1.42460 + 0.767827i
\(816\) 0 0
\(817\) 35.5781 + 6.27337i 1.24472 + 0.219478i
\(818\) −2.20478 1.27293i −0.0770883 0.0445069i
\(819\) 0 0
\(820\) 44.1935 17.5656i 1.54330 0.613418i
\(821\) 0.715925 0.260575i 0.0249859 0.00909414i −0.329497 0.944157i \(-0.606879\pi\)
0.354483 + 0.935063i \(0.384657\pi\)
\(822\) 0 0
\(823\) 34.5795 + 41.2102i 1.20537 + 1.43650i 0.869033 + 0.494755i \(0.164742\pi\)
0.336332 + 0.941743i \(0.390813\pi\)
\(824\) 0.337327 0.283051i 0.0117513 0.00986054i
\(825\) 0 0
\(826\) −4.08340 + 1.48624i −0.142080 + 0.0517128i
\(827\) −15.4598 + 8.92572i −0.537590 + 0.310378i −0.744102 0.668066i \(-0.767122\pi\)
0.206512 + 0.978444i \(0.433789\pi\)
\(828\) 0 0
\(829\) 3.49405 6.05188i 0.121354 0.210190i −0.798948 0.601400i \(-0.794610\pi\)
0.920302 + 0.391209i \(0.127943\pi\)
\(830\) −5.11688 1.69459i −0.177609 0.0588200i
\(831\) 0 0
\(832\) −5.78471 + 15.8934i −0.200549 + 0.551003i
\(833\) −1.79180 + 0.315943i −0.0620823 + 0.0109468i
\(834\) 0 0
\(835\) −9.32218 10.4717i −0.322607 0.362388i
\(836\) −13.4959 −0.466765
\(837\) 0 0
\(838\) 6.29168i 0.217343i
\(839\) −34.2020 28.6989i −1.18078 0.990795i −0.999974 0.00727705i \(-0.997684\pi\)
−0.180810 0.983518i \(-0.557872\pi\)
\(840\) 0 0
\(841\) 8.39066 + 47.5858i 0.289333 + 1.64089i
\(842\) 0.645076 1.77233i 0.0222308 0.0610786i
\(843\) 0 0
\(844\) 6.85757 38.8912i 0.236047 1.33869i
\(845\) 12.5190 + 9.89530i 0.430667 + 0.340409i
\(846\) 0 0
\(847\) 22.0400 12.7248i 0.757302 0.437229i
\(848\) −6.96412 19.1338i −0.239149 0.657056i
\(849\) 0 0
\(850\) −1.34182 + 0.579342i −0.0460240 + 0.0198713i
\(851\) 16.1013 13.5106i 0.551946 0.463138i
\(852\) 0 0
\(853\) −6.47405 17.7873i −0.221667 0.609026i 0.778151 0.628077i \(-0.216158\pi\)
−0.999819 + 0.0190511i \(0.993935\pi\)
\(854\) 1.78880 + 3.09829i 0.0612114 + 0.106021i
\(855\) 0 0
\(856\) −1.15991 + 2.00902i −0.0396448 + 0.0686668i
\(857\) 55.0204 + 9.70158i 1.87946 + 0.331400i 0.991665 0.128840i \(-0.0411252\pi\)
0.887795 + 0.460239i \(0.152236\pi\)
\(858\) 0 0
\(859\) 5.69311 + 2.07212i 0.194246 + 0.0706999i 0.437312 0.899310i \(-0.355931\pi\)
−0.243065 + 0.970010i \(0.578153\pi\)
\(860\) −0.985983 33.6901i −0.0336217 1.14882i
\(861\) 0 0
\(862\) −2.36201 + 2.81493i −0.0804503 + 0.0958769i
\(863\) 31.2067i 1.06229i −0.847281 0.531145i \(-0.821762\pi\)
0.847281 0.531145i \(-0.178238\pi\)
\(864\) 0 0
\(865\) −8.78229 1.28490i −0.298607 0.0436879i
\(866\) 1.07264 + 0.900051i 0.0364497 + 0.0305850i
\(867\) 0 0
\(868\) 32.2345 5.68381i 1.09411 0.192921i
\(869\) 2.07170 + 0.754038i 0.0702777 + 0.0255790i
\(870\) 0 0
\(871\) 3.23992 18.3745i 0.109781 0.622597i
\(872\) 0.341235 + 0.197012i 0.0115557 + 0.00667168i
\(873\) 0 0
\(874\) −1.17030 2.02703i −0.0395861 0.0685652i
\(875\) −32.0733 2.78965i −1.08427 0.0943075i
\(876\) 0 0
\(877\) 0.574169 + 0.684268i 0.0193883 + 0.0231061i 0.775651 0.631161i \(-0.217421\pi\)
−0.756263 + 0.654268i \(0.772977\pi\)
\(878\) 0.594651 + 0.708677i 0.0200685 + 0.0239167i
\(879\) 0 0
\(880\) 2.49088 + 12.0530i 0.0839674 + 0.406308i
\(881\) 28.2154 + 48.8706i 0.950602 + 1.64649i 0.744126 + 0.668039i \(0.232866\pi\)
0.206476 + 0.978452i \(0.433801\pi\)
\(882\) 0 0
\(883\) −45.6611 26.3625i −1.53662 0.887168i −0.999033 0.0439585i \(-0.986003\pi\)
−0.537586 0.843209i \(-0.680664\pi\)
\(884\) −1.15895 + 6.57273i −0.0389797 + 0.221065i
\(885\) 0 0
\(886\) 1.56459 + 0.569463i 0.0525633 + 0.0191315i
\(887\) 51.5601 9.09144i 1.73122 0.305261i 0.782799 0.622275i \(-0.213792\pi\)
0.948421 + 0.317015i \(0.102680\pi\)
\(888\) 0 0
\(889\) −26.6597 22.3702i −0.894139 0.750272i
\(890\) −5.48055 0.801835i −0.183708 0.0268776i
\(891\) 0 0
\(892\) 18.2819i 0.612122i
\(893\) 20.4782 24.4049i 0.685276 0.816680i
\(894\) 0 0
\(895\) −31.3812 + 0.918410i −1.04896 + 0.0306991i
\(896\) −17.0156 6.19316i −0.568450 0.206899i
\(897\) 0 0
\(898\) 1.07347 + 0.189282i 0.0358221 + 0.00631641i
\(899\) −25.5379 + 44.2330i −0.851737 + 1.47525i
\(900\) 0 0
\(901\) −3.83049 6.63461i −0.127612 0.221031i
\(902\) 1.13431 + 3.11648i 0.0377682 + 0.103767i
\(903\) 0 0
\(904\) −2.67730 + 2.24652i −0.0890457 + 0.0747182i
\(905\) −7.78530 12.6171i −0.258792 0.419407i
\(906\) 0 0
\(907\) 6.80568 + 18.6984i 0.225979 + 0.620872i 0.999923 0.0123817i \(-0.00394131\pi\)
−0.773945 + 0.633253i \(0.781719\pi\)
\(908\) 13.3274 7.69456i 0.442284 0.255353i
\(909\) 0 0
\(910\) 2.00659 2.53863i 0.0665178 0.0841548i
\(911\) 2.63013 14.9162i 0.0871400 0.494195i −0.909734 0.415191i \(-0.863715\pi\)
0.996874 0.0790044i \(-0.0251741\pi\)
\(912\) 0 0
\(913\) −5.84105 + 16.0482i −0.193311 + 0.531116i
\(914\) 0.109206 + 0.619336i 0.00361220 + 0.0204858i
\(915\) 0 0
\(916\) 24.9965 + 20.9746i 0.825907 + 0.693019i
\(917\) 0.748423i 0.0247151i
\(918\) 0 0
\(919\) 31.1704 1.02822 0.514109 0.857725i \(-0.328123\pi\)
0.514109 + 0.857725i \(0.328123\pi\)
\(920\) −3.29791 + 2.93589i −0.108729 + 0.0967935i
\(921\) 0 0
\(922\) −0.600621 + 0.105906i −0.0197804 + 0.00348782i
\(923\) −7.48361 + 20.5610i −0.246326 + 0.676775i
\(924\) 0 0
\(925\) 39.0650 + 19.6026i 1.28445 + 0.644531i
\(926\) 1.91563 3.31796i 0.0629514 0.109035i
\(927\) 0 0
\(928\) 18.4237 10.6369i 0.604788 0.349174i
\(929\) −9.60870 + 3.49728i −0.315251 + 0.114742i −0.494800 0.869007i \(-0.664759\pi\)
0.179548 + 0.983749i \(0.442536\pi\)
\(930\) 0 0
\(931\) 4.64148 3.89467i 0.152118 0.127643i
\(932\) −37.5561 44.7577i −1.23019 1.46609i
\(933\) 0 0
\(934\) 4.21379 1.53369i 0.137879 0.0501840i
\(935\) 1.71042 + 4.30326i 0.0559366 + 0.140731i
\(936\) 0 0
\(937\) 0.758718 + 0.438046i 0.0247862 + 0.0143103i 0.512342 0.858782i \(-0.328778\pi\)
−0.487556 + 0.873092i \(0.662111\pi\)
\(938\) 4.53485 + 0.799617i 0.148068 + 0.0261084i
\(939\) 0 0
\(940\) −26.1639 14.1017i −0.853373 0.459948i
\(941\) −0.921099 5.22381i −0.0300270 0.170291i 0.966107 0.258144i \(-0.0831108\pi\)
−0.996134 + 0.0878522i \(0.972000\pi\)
\(942\) 0 0
\(943\) 16.7973 20.0183i 0.546996 0.651884i
\(944\) 27.2192 0.885911
\(945\) 0 0
\(946\) 2.35048 0.0764208
\(947\) −14.4581 + 17.2305i −0.469825 + 0.559916i −0.947968 0.318366i \(-0.896866\pi\)
0.478143 + 0.878282i \(0.341310\pi\)
\(948\) 0 0
\(949\) −5.28795 29.9895i −0.171654 0.973500i
\(950\) 2.90515 3.90505i 0.0942555 0.126697i
\(951\) 0 0
\(952\) −3.28002 0.578356i −0.106306 0.0187446i
\(953\) −3.69060 2.13077i −0.119550 0.0690223i 0.439032 0.898471i \(-0.355321\pi\)
−0.558583 + 0.829449i \(0.688655\pi\)
\(954\) 0 0
\(955\) 20.3526 8.08957i 0.658596 0.261772i
\(956\) −44.4653 + 16.1840i −1.43811 + 0.523430i
\(957\) 0 0
\(958\) −0.133200 0.158741i −0.00430349 0.00512870i
\(959\) 41.1937 34.5656i 1.33021 1.11618i
\(960\) 0 0
\(961\) −2.57434 + 0.936985i −0.0830434 + 0.0302253i
\(962\) −3.80453 + 2.19655i −0.122663 + 0.0708195i
\(963\) 0 0
\(964\) −14.4943 + 25.1049i −0.466830 + 0.808573i
\(965\) 13.6567 41.2370i 0.439625 1.32747i
\(966\) 0 0
\(967\) −1.30770 + 3.59289i −0.0420529 + 0.115539i −0.958942 0.283604i \(-0.908470\pi\)
0.916889 + 0.399143i \(0.130692\pi\)
\(968\) 7.14774 1.26034i 0.229737 0.0405089i
\(969\) 0 0
\(970\) −1.94848 + 1.73459i −0.0625620 + 0.0556944i
\(971\) −57.0974 −1.83234 −0.916171 0.400787i \(-0.868737\pi\)
−0.916171 + 0.400787i \(0.868737\pi\)
\(972\) 0 0
\(973\) 20.0225i 0.641890i
\(974\) −2.91763 2.44819i −0.0934870 0.0784449i
\(975\) 0 0
\(976\) −3.89136 22.0690i −0.124559 0.706411i
\(977\) 9.83942 27.0336i 0.314791 0.864881i −0.676881 0.736092i \(-0.736669\pi\)
0.991672 0.128789i \(-0.0411089\pi\)
\(978\) 0 0
\(979\) −3.04740 + 17.2826i −0.0973952 + 0.552356i
\(980\) −4.43470 3.50529i −0.141661 0.111972i
\(981\) 0 0
\(982\) −1.95726 + 1.13002i −0.0624586 + 0.0360605i
\(983\) 14.8222 + 40.7237i 0.472756 + 1.29889i 0.915529 + 0.402252i \(0.131772\pi\)
−0.442773 + 0.896634i \(0.646005\pi\)
\(984\) 0 0
\(985\) 12.3210 7.60255i 0.392578 0.242238i
\(986\) 1.96898 1.65217i 0.0627052 0.0526159i
\(987\) 0 0
\(988\) −7.60169 20.8855i −0.241842 0.664455i
\(989\) −9.26022 16.0392i −0.294458 0.510016i
\(990\) 0 0
\(991\) −23.9951 + 41.5607i −0.762230 + 1.32022i 0.179469 + 0.983764i \(0.442562\pi\)
−0.941699 + 0.336457i \(0.890771\pi\)
\(992\) 13.8395 + 2.44028i 0.439406 + 0.0774791i
\(993\) 0 0
\(994\) −5.07449 1.84696i −0.160953 0.0585821i
\(995\) −38.5071 + 1.12696i −1.22076 + 0.0357270i
\(996\) 0 0
\(997\) −21.4919 + 25.6130i −0.680655 + 0.811173i −0.990192 0.139715i \(-0.955382\pi\)
0.309537 + 0.950887i \(0.399826\pi\)
\(998\) 6.03495i 0.191033i
\(999\) 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 405.2.p.a.289.8 96
3.2 odd 2 135.2.p.a.124.9 yes 96
5.4 even 2 inner 405.2.p.a.289.9 96
15.2 even 4 675.2.l.h.151.9 96
15.8 even 4 675.2.l.h.151.8 96
15.14 odd 2 135.2.p.a.124.8 yes 96
27.5 odd 18 135.2.p.a.49.8 96
27.22 even 9 inner 405.2.p.a.199.9 96
135.32 even 36 675.2.l.h.76.9 96
135.49 even 18 inner 405.2.p.a.199.8 96
135.59 odd 18 135.2.p.a.49.9 yes 96
135.113 even 36 675.2.l.h.76.8 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.p.a.49.8 96 27.5 odd 18
135.2.p.a.49.9 yes 96 135.59 odd 18
135.2.p.a.124.8 yes 96 15.14 odd 2
135.2.p.a.124.9 yes 96 3.2 odd 2
405.2.p.a.199.8 96 135.49 even 18 inner
405.2.p.a.199.9 96 27.22 even 9 inner
405.2.p.a.289.8 96 1.1 even 1 trivial
405.2.p.a.289.9 96 5.4 even 2 inner
675.2.l.h.76.8 96 135.113 even 36
675.2.l.h.76.9 96 135.32 even 36
675.2.l.h.151.8 96 15.8 even 4
675.2.l.h.151.9 96 15.2 even 4