Properties

Label 729.2.c.a.244.4
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.4
Root \(-1.37340i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.a.487.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0864880 + 0.149802i) q^{2} +(0.985040 - 1.70614i) q^{4} +(-1.86828 + 3.23596i) q^{5} +(-1.51575 - 2.62535i) q^{7} +0.686728 q^{8} +O(q^{10})\) \(q+(0.0864880 + 0.149802i) q^{2} +(0.985040 - 1.70614i) q^{4} +(-1.86828 + 3.23596i) q^{5} +(-1.51575 - 2.62535i) q^{7} +0.686728 q^{8} -0.646335 q^{10} +(-1.24585 - 2.15787i) q^{11} +(0.382569 - 0.662630i) q^{13} +(0.262188 - 0.454123i) q^{14} +(-1.91069 - 3.30940i) q^{16} -4.62278 q^{17} -0.611844 q^{19} +(3.68066 + 6.37509i) q^{20} +(0.215502 - 0.373260i) q^{22} +(3.26219 - 5.65028i) q^{23} +(-4.48095 - 7.76123i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(-3.27545 - 5.67324i) q^{29} +(-3.27521 + 5.67283i) q^{31} +(1.01723 - 1.76190i) q^{32} +(-0.399815 - 0.692500i) q^{34} +11.3274 q^{35} +4.95969 q^{37} +(-0.0529171 - 0.0916552i) q^{38} +(-1.28300 + 2.22222i) q^{40} +(2.63012 - 4.55550i) q^{41} +(-2.78529 - 4.82426i) q^{43} -4.90884 q^{44} +1.12856 q^{46} +(0.553808 + 0.959223i) q^{47} +(-1.09499 + 1.89658i) q^{49} +(0.775096 - 1.34251i) q^{50} +(-0.753692 - 1.30543i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(-1.04091 - 1.80290i) q^{56} +(0.566573 - 0.981334i) q^{58} +(-5.92588 + 10.2639i) q^{59} +(-4.09350 - 7.09015i) q^{61} -1.13307 q^{62} -7.29083 q^{64} +(1.42949 + 2.47596i) q^{65} +(0.606169 - 1.04992i) q^{67} +(-4.55362 + 7.88711i) q^{68} +(0.979682 + 1.69686i) q^{70} +4.91946 q^{71} +4.29945 q^{73} +(0.428953 + 0.742969i) q^{74} +(-0.602691 + 1.04389i) q^{76} +(-3.77679 + 6.54158i) q^{77} +(5.89730 + 10.2144i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(4.50804 + 7.80815i) q^{83} +(8.63666 - 14.9591i) q^{85} +(0.481788 - 0.834481i) q^{86} +(-0.855559 - 1.48187i) q^{88} -7.53885 q^{89} -2.31952 q^{91} +(-6.42677 - 11.1315i) q^{92} +(-0.0957954 + 0.165923i) q^{94} +(1.14310 - 1.97990i) q^{95} +(0.474177 + 0.821299i) q^{97} -0.378814 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0864880 + 0.149802i 0.0611562 + 0.105926i 0.894982 0.446101i \(-0.147188\pi\)
−0.833826 + 0.552027i \(0.813855\pi\)
\(3\) 0 0
\(4\) 0.985040 1.70614i 0.492520 0.853069i
\(5\) −1.86828 + 3.23596i −0.835521 + 1.44716i 0.0580849 + 0.998312i \(0.481501\pi\)
−0.893606 + 0.448853i \(0.851833\pi\)
\(6\) 0 0
\(7\) −1.51575 2.62535i −0.572899 0.992291i −0.996266 0.0863324i \(-0.972485\pi\)
0.423367 0.905958i \(-0.360848\pi\)
\(8\) 0.686728 0.242795
\(9\) 0 0
\(10\) −0.646335 −0.204389
\(11\) −1.24585 2.15787i −0.375637 0.650623i 0.614785 0.788695i \(-0.289243\pi\)
−0.990422 + 0.138072i \(0.955909\pi\)
\(12\) 0 0
\(13\) 0.382569 0.662630i 0.106106 0.183780i −0.808084 0.589068i \(-0.799495\pi\)
0.914189 + 0.405287i \(0.132828\pi\)
\(14\) 0.262188 0.454123i 0.0700727 0.121369i
\(15\) 0 0
\(16\) −1.91069 3.30940i −0.477671 0.827351i
\(17\) −4.62278 −1.12119 −0.560595 0.828090i \(-0.689427\pi\)
−0.560595 + 0.828090i \(0.689427\pi\)
\(18\) 0 0
\(19\) −0.611844 −0.140367 −0.0701833 0.997534i \(-0.522358\pi\)
−0.0701833 + 0.997534i \(0.522358\pi\)
\(20\) 3.68066 + 6.37509i 0.823021 + 1.42551i
\(21\) 0 0
\(22\) 0.215502 0.373260i 0.0459451 0.0795793i
\(23\) 3.26219 5.65028i 0.680213 1.17816i −0.294702 0.955589i \(-0.595221\pi\)
0.974916 0.222575i \(-0.0714462\pi\)
\(24\) 0 0
\(25\) −4.48095 7.76123i −0.896190 1.55225i
\(26\) 0.132351 0.0259561
\(27\) 0 0
\(28\) −5.97229 −1.12866
\(29\) −3.27545 5.67324i −0.608235 1.05349i −0.991531 0.129869i \(-0.958544\pi\)
0.383296 0.923626i \(-0.374789\pi\)
\(30\) 0 0
\(31\) −3.27521 + 5.67283i −0.588246 + 1.01887i 0.406217 + 0.913777i \(0.366848\pi\)
−0.994462 + 0.105094i \(0.966486\pi\)
\(32\) 1.01723 1.76190i 0.179823 0.311462i
\(33\) 0 0
\(34\) −0.399815 0.692500i −0.0685677 0.118763i
\(35\) 11.3274 1.91468
\(36\) 0 0
\(37\) 4.95969 0.815368 0.407684 0.913123i \(-0.366337\pi\)
0.407684 + 0.913123i \(0.366337\pi\)
\(38\) −0.0529171 0.0916552i −0.00858429 0.0148684i
\(39\) 0 0
\(40\) −1.28300 + 2.22222i −0.202860 + 0.351364i
\(41\) 2.63012 4.55550i 0.410756 0.711450i −0.584217 0.811598i \(-0.698598\pi\)
0.994973 + 0.100148i \(0.0319316\pi\)
\(42\) 0 0
\(43\) −2.78529 4.82426i −0.424752 0.735692i 0.571645 0.820501i \(-0.306305\pi\)
−0.996397 + 0.0848086i \(0.972972\pi\)
\(44\) −4.90884 −0.740035
\(45\) 0 0
\(46\) 1.12856 0.166397
\(47\) 0.553808 + 0.959223i 0.0807812 + 0.139917i 0.903586 0.428407i \(-0.140925\pi\)
−0.822805 + 0.568324i \(0.807592\pi\)
\(48\) 0 0
\(49\) −1.09499 + 1.89658i −0.156427 + 0.270940i
\(50\) 0.775096 1.34251i 0.109615 0.189859i
\(51\) 0 0
\(52\) −0.753692 1.30543i −0.104518 0.181031i
\(53\) −8.84310 −1.21469 −0.607346 0.794437i \(-0.707766\pi\)
−0.607346 + 0.794437i \(0.707766\pi\)
\(54\) 0 0
\(55\) 9.31038 1.25541
\(56\) −1.04091 1.80290i −0.139097 0.240923i
\(57\) 0 0
\(58\) 0.566573 0.981334i 0.0743947 0.128855i
\(59\) −5.92588 + 10.2639i −0.771484 + 1.33625i 0.165266 + 0.986249i \(0.447152\pi\)
−0.936750 + 0.350000i \(0.886182\pi\)
\(60\) 0 0
\(61\) −4.09350 7.09015i −0.524119 0.907801i −0.999606 0.0280781i \(-0.991061\pi\)
0.475486 0.879723i \(-0.342272\pi\)
\(62\) −1.13307 −0.143900
\(63\) 0 0
\(64\) −7.29083 −0.911354
\(65\) 1.42949 + 2.47596i 0.177307 + 0.307105i
\(66\) 0 0
\(67\) 0.606169 1.04992i 0.0740553 0.128268i −0.826620 0.562761i \(-0.809739\pi\)
0.900675 + 0.434493i \(0.143073\pi\)
\(68\) −4.55362 + 7.88711i −0.552208 + 0.956452i
\(69\) 0 0
\(70\) 0.979682 + 1.69686i 0.117094 + 0.202813i
\(71\) 4.91946 0.583833 0.291916 0.956444i \(-0.405707\pi\)
0.291916 + 0.956444i \(0.405707\pi\)
\(72\) 0 0
\(73\) 4.29945 0.503213 0.251606 0.967830i \(-0.419041\pi\)
0.251606 + 0.967830i \(0.419041\pi\)
\(74\) 0.428953 + 0.742969i 0.0498648 + 0.0863684i
\(75\) 0 0
\(76\) −0.602691 + 1.04389i −0.0691333 + 0.119742i
\(77\) −3.77679 + 6.54158i −0.430405 + 0.745483i
\(78\) 0 0
\(79\) 5.89730 + 10.2144i 0.663498 + 1.14921i 0.979690 + 0.200518i \(0.0642624\pi\)
−0.316192 + 0.948695i \(0.602404\pi\)
\(80\) 14.2788 1.59642
\(81\) 0 0
\(82\) 0.909895 0.100481
\(83\) 4.50804 + 7.80815i 0.494821 + 0.857056i 0.999982 0.00596962i \(-0.00190020\pi\)
−0.505161 + 0.863025i \(0.668567\pi\)
\(84\) 0 0
\(85\) 8.63666 14.9591i 0.936777 1.62255i
\(86\) 0.481788 0.834481i 0.0519525 0.0899844i
\(87\) 0 0
\(88\) −0.855559 1.48187i −0.0912029 0.157968i
\(89\) −7.53885 −0.799117 −0.399558 0.916708i \(-0.630837\pi\)
−0.399558 + 0.916708i \(0.630837\pi\)
\(90\) 0 0
\(91\) −2.31952 −0.243151
\(92\) −6.42677 11.1315i −0.670037 1.16054i
\(93\) 0 0
\(94\) −0.0957954 + 0.165923i −0.00988055 + 0.0171136i
\(95\) 1.14310 1.97990i 0.117279 0.203134i
\(96\) 0 0
\(97\) 0.474177 + 0.821299i 0.0481454 + 0.0833903i 0.889094 0.457725i \(-0.151336\pi\)
−0.840948 + 0.541115i \(0.818002\pi\)
\(98\) −0.378814 −0.0382659
\(99\) 0 0
\(100\) −17.6557 −1.76557
\(101\) −2.80408 4.85680i −0.279016 0.483270i 0.692124 0.721778i \(-0.256675\pi\)
−0.971140 + 0.238508i \(0.923342\pi\)
\(102\) 0 0
\(103\) 4.71251 8.16231i 0.464337 0.804256i −0.534834 0.844957i \(-0.679626\pi\)
0.999171 + 0.0407012i \(0.0129592\pi\)
\(104\) 0.262721 0.455046i 0.0257619 0.0446210i
\(105\) 0 0
\(106\) −0.764821 1.32471i −0.0742860 0.128667i
\(107\) 1.27825 0.123573 0.0617864 0.998089i \(-0.480320\pi\)
0.0617864 + 0.998089i \(0.480320\pi\)
\(108\) 0 0
\(109\) −7.40689 −0.709451 −0.354726 0.934970i \(-0.615426\pi\)
−0.354726 + 0.934970i \(0.615426\pi\)
\(110\) 0.805236 + 1.39471i 0.0767762 + 0.132980i
\(111\) 0 0
\(112\) −5.79224 + 10.0325i −0.547315 + 0.947978i
\(113\) 4.67598 8.09904i 0.439879 0.761893i −0.557800 0.829975i \(-0.688355\pi\)
0.997680 + 0.0680818i \(0.0216879\pi\)
\(114\) 0 0
\(115\) 12.1894 + 21.1126i 1.13666 + 1.96876i
\(116\) −12.9058 −1.19827
\(117\) 0 0
\(118\) −2.05007 −0.188724
\(119\) 7.00698 + 12.1364i 0.642329 + 1.11255i
\(120\) 0 0
\(121\) 2.39573 4.14952i 0.217793 0.377229i
\(122\) 0.708077 1.22643i 0.0641063 0.111035i
\(123\) 0 0
\(124\) 6.45243 + 11.1759i 0.579445 + 1.00363i
\(125\) 14.8039 1.32410
\(126\) 0 0
\(127\) 20.7968 1.84542 0.922710 0.385496i \(-0.125970\pi\)
0.922710 + 0.385496i \(0.125970\pi\)
\(128\) −2.66503 4.61597i −0.235558 0.407998i
\(129\) 0 0
\(130\) −0.247268 + 0.428281i −0.0216868 + 0.0375627i
\(131\) −0.327915 + 0.567965i −0.0286501 + 0.0496233i −0.879995 0.474983i \(-0.842454\pi\)
0.851345 + 0.524606i \(0.175788\pi\)
\(132\) 0 0
\(133\) 0.927402 + 1.60631i 0.0804159 + 0.139284i
\(134\) 0.209705 0.0181158
\(135\) 0 0
\(136\) −3.17460 −0.272219
\(137\) 4.29380 + 7.43708i 0.366844 + 0.635393i 0.989070 0.147445i \(-0.0471049\pi\)
−0.622226 + 0.782838i \(0.713772\pi\)
\(138\) 0 0
\(139\) −6.72307 + 11.6447i −0.570243 + 0.987691i 0.426297 + 0.904583i \(0.359818\pi\)
−0.996541 + 0.0831074i \(0.973516\pi\)
\(140\) 11.1579 19.3261i 0.943016 1.63335i
\(141\) 0 0
\(142\) 0.425474 + 0.736943i 0.0357050 + 0.0618429i
\(143\) −1.90649 −0.159429
\(144\) 0 0
\(145\) 24.4778 2.03277
\(146\) 0.371851 + 0.644064i 0.0307746 + 0.0533031i
\(147\) 0 0
\(148\) 4.88549 8.46192i 0.401585 0.695565i
\(149\) 4.81103 8.33295i 0.394135 0.682662i −0.598855 0.800857i \(-0.704377\pi\)
0.992990 + 0.118195i \(0.0377108\pi\)
\(150\) 0 0
\(151\) 3.56410 + 6.17320i 0.290042 + 0.502368i 0.973819 0.227323i \(-0.0729972\pi\)
−0.683777 + 0.729691i \(0.739664\pi\)
\(152\) −0.420170 −0.0340803
\(153\) 0 0
\(154\) −1.30659 −0.105288
\(155\) −12.2380 21.1969i −0.982983 1.70258i
\(156\) 0 0
\(157\) −3.84288 + 6.65607i −0.306696 + 0.531212i −0.977637 0.210298i \(-0.932557\pi\)
0.670942 + 0.741510i \(0.265890\pi\)
\(158\) −1.02009 + 1.76685i −0.0811541 + 0.140563i
\(159\) 0 0
\(160\) 3.80095 + 6.58343i 0.300491 + 0.520466i
\(161\) −19.7786 −1.55877
\(162\) 0 0
\(163\) 1.04750 0.0820465 0.0410232 0.999158i \(-0.486938\pi\)
0.0410232 + 0.999158i \(0.486938\pi\)
\(164\) −5.18154 8.97470i −0.404611 0.700806i
\(165\) 0 0
\(166\) −0.779782 + 1.35062i −0.0605228 + 0.104829i
\(167\) 4.17704 7.23484i 0.323229 0.559849i −0.657923 0.753085i \(-0.728565\pi\)
0.981152 + 0.193236i \(0.0618983\pi\)
\(168\) 0 0
\(169\) 6.20728 + 10.7513i 0.477483 + 0.827025i
\(170\) 2.98787 0.229159
\(171\) 0 0
\(172\) −10.9745 −0.836796
\(173\) 10.9229 + 18.9190i 0.830452 + 1.43839i 0.897680 + 0.440648i \(0.145251\pi\)
−0.0672277 + 0.997738i \(0.521415\pi\)
\(174\) 0 0
\(175\) −13.5840 + 23.5282i −1.02685 + 1.77856i
\(176\) −4.76085 + 8.24603i −0.358862 + 0.621568i
\(177\) 0 0
\(178\) −0.652020 1.12933i −0.0488710 0.0846470i
\(179\) 9.08866 0.679319 0.339659 0.940549i \(-0.389688\pi\)
0.339659 + 0.940549i \(0.389688\pi\)
\(180\) 0 0
\(181\) −7.13077 −0.530026 −0.265013 0.964245i \(-0.585376\pi\)
−0.265013 + 0.964245i \(0.585376\pi\)
\(182\) −0.200610 0.347467i −0.0148702 0.0257560i
\(183\) 0 0
\(184\) 2.24024 3.88020i 0.165152 0.286052i
\(185\) −9.26609 + 16.0493i −0.681257 + 1.17997i
\(186\) 0 0
\(187\) 5.75929 + 9.97537i 0.421161 + 0.729472i
\(188\) 2.18209 0.159145
\(189\) 0 0
\(190\) 0.395456 0.0286894
\(191\) 5.97781 + 10.3539i 0.432539 + 0.749180i 0.997091 0.0762174i \(-0.0242843\pi\)
−0.564552 + 0.825398i \(0.690951\pi\)
\(192\) 0 0
\(193\) 4.43682 7.68479i 0.319369 0.553164i −0.660987 0.750397i \(-0.729862\pi\)
0.980357 + 0.197233i \(0.0631957\pi\)
\(194\) −0.0820212 + 0.142065i −0.00588878 + 0.0101997i
\(195\) 0 0
\(196\) 2.15722 + 3.73641i 0.154087 + 0.266886i
\(197\) −7.39790 −0.527079 −0.263539 0.964649i \(-0.584890\pi\)
−0.263539 + 0.964649i \(0.584890\pi\)
\(198\) 0 0
\(199\) −10.3837 −0.736084 −0.368042 0.929809i \(-0.619972\pi\)
−0.368042 + 0.929809i \(0.619972\pi\)
\(200\) −3.07719 5.32986i −0.217591 0.376878i
\(201\) 0 0
\(202\) 0.485038 0.840110i 0.0341271 0.0591099i
\(203\) −9.92951 + 17.1984i −0.696915 + 1.20709i
\(204\) 0 0
\(205\) 9.82761 + 17.0219i 0.686390 + 1.18886i
\(206\) 1.63030 0.113588
\(207\) 0 0
\(208\) −2.92388 −0.202735
\(209\) 0.762265 + 1.32028i 0.0527269 + 0.0913257i
\(210\) 0 0
\(211\) −10.4306 + 18.0663i −0.718070 + 1.24373i 0.243693 + 0.969852i \(0.421641\pi\)
−0.961763 + 0.273882i \(0.911692\pi\)
\(212\) −8.71080 + 15.0875i −0.598260 + 1.03622i
\(213\) 0 0
\(214\) 0.110553 + 0.191483i 0.00755724 + 0.0130895i
\(215\) 20.8148 1.41956
\(216\) 0 0
\(217\) 19.8576 1.34802
\(218\) −0.640607 1.10956i −0.0433874 0.0751491i
\(219\) 0 0
\(220\) 9.17109 15.8848i 0.618315 1.07095i
\(221\) −1.76854 + 3.06319i −0.118965 + 0.206053i
\(222\) 0 0
\(223\) −11.7892 20.4196i −0.789466 1.36740i −0.926294 0.376801i \(-0.877024\pi\)
0.136828 0.990595i \(-0.456309\pi\)
\(224\) −6.16747 −0.412081
\(225\) 0 0
\(226\) 1.61766 0.107605
\(227\) −5.24207 9.07952i −0.347928 0.602629i 0.637953 0.770075i \(-0.279781\pi\)
−0.985881 + 0.167446i \(0.946448\pi\)
\(228\) 0 0
\(229\) 6.94121 12.0225i 0.458688 0.794471i −0.540204 0.841534i \(-0.681653\pi\)
0.998892 + 0.0470633i \(0.0149862\pi\)
\(230\) −2.10847 + 3.65197i −0.139028 + 0.240804i
\(231\) 0 0
\(232\) −2.24934 3.89597i −0.147676 0.255783i
\(233\) −7.59964 −0.497869 −0.248935 0.968520i \(-0.580080\pi\)
−0.248935 + 0.968520i \(0.580080\pi\)
\(234\) 0 0
\(235\) −4.13868 −0.269977
\(236\) 11.6745 + 20.2207i 0.759942 + 1.31626i
\(237\) 0 0
\(238\) −1.21204 + 2.09931i −0.0785648 + 0.136078i
\(239\) 8.27934 14.3402i 0.535546 0.927593i −0.463591 0.886050i \(-0.653439\pi\)
0.999137 0.0415436i \(-0.0132275\pi\)
\(240\) 0 0
\(241\) 7.25924 + 12.5734i 0.467609 + 0.809923i 0.999315 0.0370064i \(-0.0117822\pi\)
−0.531706 + 0.846929i \(0.678449\pi\)
\(242\) 0.828806 0.0532776
\(243\) 0 0
\(244\) −16.1290 −1.03256
\(245\) −4.09150 7.08668i −0.261396 0.452751i
\(246\) 0 0
\(247\) −0.234073 + 0.405426i −0.0148937 + 0.0257966i
\(248\) −2.24918 + 3.89570i −0.142823 + 0.247377i
\(249\) 0 0
\(250\) 1.28036 + 2.21765i 0.0809769 + 0.140256i
\(251\) −9.05181 −0.571345 −0.285673 0.958327i \(-0.592217\pi\)
−0.285673 + 0.958327i \(0.592217\pi\)
\(252\) 0 0
\(253\) −16.2568 −1.02205
\(254\) 1.79867 + 3.11540i 0.112859 + 0.195477i
\(255\) 0 0
\(256\) −6.82984 + 11.8296i −0.426865 + 0.739352i
\(257\) 4.84994 8.40034i 0.302531 0.523999i −0.674178 0.738569i \(-0.735502\pi\)
0.976709 + 0.214570i \(0.0688351\pi\)
\(258\) 0 0
\(259\) −7.51764 13.0209i −0.467124 0.809082i
\(260\) 5.63243 0.349309
\(261\) 0 0
\(262\) −0.113443 −0.00700852
\(263\) −13.4276 23.2573i −0.827983 1.43411i −0.899618 0.436677i \(-0.856155\pi\)
0.0716358 0.997431i \(-0.477178\pi\)
\(264\) 0 0
\(265\) 16.5214 28.6159i 1.01490 1.75786i
\(266\) −0.160418 + 0.277852i −0.00983587 + 0.0170362i
\(267\) 0 0
\(268\) −1.19420 2.06842i −0.0729474 0.126349i
\(269\) −11.7388 −0.715729 −0.357865 0.933774i \(-0.616495\pi\)
−0.357865 + 0.933774i \(0.616495\pi\)
\(270\) 0 0
\(271\) 0.144576 0.00878238 0.00439119 0.999990i \(-0.498602\pi\)
0.00439119 + 0.999990i \(0.498602\pi\)
\(272\) 8.83268 + 15.2987i 0.535560 + 0.927617i
\(273\) 0 0
\(274\) −0.742724 + 1.28644i −0.0448696 + 0.0777165i
\(275\) −11.1652 + 19.3386i −0.673285 + 1.16616i
\(276\) 0 0
\(277\) 0.507212 + 0.878518i 0.0304754 + 0.0527850i 0.880861 0.473375i \(-0.156965\pi\)
−0.850385 + 0.526160i \(0.823631\pi\)
\(278\) −2.32586 −0.139496
\(279\) 0 0
\(280\) 7.77883 0.464874
\(281\) −13.7647 23.8412i −0.821135 1.42225i −0.904838 0.425756i \(-0.860008\pi\)
0.0837029 0.996491i \(-0.473325\pi\)
\(282\) 0 0
\(283\) 13.4014 23.2120i 0.796633 1.37981i −0.125164 0.992136i \(-0.539946\pi\)
0.921797 0.387673i \(-0.126721\pi\)
\(284\) 4.84587 8.39329i 0.287549 0.498050i
\(285\) 0 0
\(286\) −0.164889 0.285596i −0.00975007 0.0168876i
\(287\) −15.9464 −0.941286
\(288\) 0 0
\(289\) 4.37012 0.257066
\(290\) 2.11704 + 3.66682i 0.124317 + 0.215323i
\(291\) 0 0
\(292\) 4.23513 7.33546i 0.247842 0.429275i
\(293\) 9.32863 16.1577i 0.544984 0.943941i −0.453624 0.891193i \(-0.649869\pi\)
0.998608 0.0527472i \(-0.0167977\pi\)
\(294\) 0 0
\(295\) −22.1424 38.3518i −1.28918 2.23293i
\(296\) 3.40596 0.197967
\(297\) 0 0
\(298\) 1.66439 0.0964153
\(299\) −2.49603 4.32324i −0.144349 0.250020i
\(300\) 0 0
\(301\) −8.44359 + 14.6247i −0.486680 + 0.842955i
\(302\) −0.616504 + 1.06782i −0.0354758 + 0.0614459i
\(303\) 0 0
\(304\) 1.16904 + 2.02484i 0.0670491 + 0.116132i
\(305\) 30.5913 1.75165
\(306\) 0 0
\(307\) 33.7893 1.92845 0.964227 0.265077i \(-0.0853973\pi\)
0.964227 + 0.265077i \(0.0853973\pi\)
\(308\) 7.44057 + 12.8874i 0.423966 + 0.734330i
\(309\) 0 0
\(310\) 2.11689 3.66655i 0.120231 0.208246i
\(311\) 17.3433 30.0395i 0.983448 1.70338i 0.334806 0.942287i \(-0.391329\pi\)
0.648642 0.761094i \(-0.275337\pi\)
\(312\) 0 0
\(313\) −1.67019 2.89285i −0.0944047 0.163514i 0.814955 0.579524i \(-0.196761\pi\)
−0.909360 + 0.416010i \(0.863428\pi\)
\(314\) −1.32945 −0.0750254
\(315\) 0 0
\(316\) 23.2363 1.30714
\(317\) 15.5164 + 26.8752i 0.871488 + 1.50946i 0.860458 + 0.509522i \(0.170178\pi\)
0.0110301 + 0.999939i \(0.496489\pi\)
\(318\) 0 0
\(319\) −8.16142 + 14.1360i −0.456952 + 0.791463i
\(320\) 13.6213 23.5928i 0.761455 1.31888i
\(321\) 0 0
\(322\) −1.71061 2.96287i −0.0953288 0.165114i
\(323\) 2.82842 0.157378
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) 0.0905961 + 0.156917i 0.00501765 + 0.00869083i
\(327\) 0 0
\(328\) 1.80618 3.12839i 0.0997295 0.172736i
\(329\) 1.67887 2.90788i 0.0925590 0.160317i
\(330\) 0 0
\(331\) −1.63584 2.83336i −0.0899138 0.155735i 0.817561 0.575842i \(-0.195326\pi\)
−0.907475 + 0.420107i \(0.861992\pi\)
\(332\) 17.7624 0.974837
\(333\) 0 0
\(334\) 1.44505 0.0790699
\(335\) 2.26499 + 3.92308i 0.123750 + 0.214341i
\(336\) 0 0
\(337\) −3.18290 + 5.51295i −0.173384 + 0.300310i −0.939601 0.342272i \(-0.888803\pi\)
0.766217 + 0.642582i \(0.222137\pi\)
\(338\) −1.07371 + 1.85972i −0.0584021 + 0.101155i
\(339\) 0 0
\(340\) −17.0149 29.4707i −0.922763 1.59827i
\(341\) 16.3217 0.883868
\(342\) 0 0
\(343\) −14.5816 −0.787331
\(344\) −1.91273 3.31295i −0.103128 0.178623i
\(345\) 0 0
\(346\) −1.88940 + 3.27253i −0.101575 + 0.175932i
\(347\) 4.39620 7.61445i 0.236001 0.408765i −0.723562 0.690259i \(-0.757497\pi\)
0.959563 + 0.281494i \(0.0908299\pi\)
\(348\) 0 0
\(349\) −7.20011 12.4710i −0.385413 0.667555i 0.606413 0.795150i \(-0.292608\pi\)
−0.991826 + 0.127595i \(0.959274\pi\)
\(350\) −4.69941 −0.251194
\(351\) 0 0
\(352\) −5.06926 −0.270192
\(353\) −16.6002 28.7525i −0.883542 1.53034i −0.847376 0.530993i \(-0.821819\pi\)
−0.0361653 0.999346i \(-0.511514\pi\)
\(354\) 0 0
\(355\) −9.19094 + 15.9192i −0.487804 + 0.844902i
\(356\) −7.42607 + 12.8623i −0.393581 + 0.681702i
\(357\) 0 0
\(358\) 0.786060 + 1.36150i 0.0415446 + 0.0719573i
\(359\) 4.94514 0.260995 0.130497 0.991449i \(-0.458343\pi\)
0.130497 + 0.991449i \(0.458343\pi\)
\(360\) 0 0
\(361\) −18.6256 −0.980297
\(362\) −0.616726 1.06820i −0.0324144 0.0561434i
\(363\) 0 0
\(364\) −2.28482 + 3.95742i −0.119757 + 0.207425i
\(365\) −8.03258 + 13.9128i −0.420445 + 0.728231i
\(366\) 0 0
\(367\) 1.24623 + 2.15853i 0.0650525 + 0.112674i 0.896717 0.442604i \(-0.145945\pi\)
−0.831665 + 0.555278i \(0.812612\pi\)
\(368\) −24.9321 −1.29967
\(369\) 0 0
\(370\) −3.20562 −0.166652
\(371\) 13.4039 + 23.2163i 0.695896 + 1.20533i
\(372\) 0 0
\(373\) 14.0238 24.2899i 0.726124 1.25768i −0.232385 0.972624i \(-0.574653\pi\)
0.958510 0.285060i \(-0.0920136\pi\)
\(374\) −0.996218 + 1.72550i −0.0515132 + 0.0892235i
\(375\) 0 0
\(376\) 0.380316 + 0.658726i 0.0196133 + 0.0339712i
\(377\) −5.01234 −0.258149
\(378\) 0 0
\(379\) 5.13991 0.264019 0.132010 0.991248i \(-0.457857\pi\)
0.132010 + 0.991248i \(0.457857\pi\)
\(380\) −2.25199 3.90056i −0.115525 0.200095i
\(381\) 0 0
\(382\) −1.03402 + 1.79097i −0.0529050 + 0.0916341i
\(383\) 0.0223364 0.0386879i 0.00114134 0.00197686i −0.865454 0.500988i \(-0.832970\pi\)
0.866596 + 0.499011i \(0.166303\pi\)
\(384\) 0 0
\(385\) −14.1122 24.4430i −0.719224 1.24573i
\(386\) 1.53493 0.0781256
\(387\) 0 0
\(388\) 1.86833 0.0948502
\(389\) −10.4911 18.1712i −0.531921 0.921315i −0.999306 0.0372607i \(-0.988137\pi\)
0.467384 0.884054i \(-0.345197\pi\)
\(390\) 0 0
\(391\) −15.0804 + 26.1200i −0.762648 + 1.32095i
\(392\) −0.751960 + 1.30243i −0.0379797 + 0.0657828i
\(393\) 0 0
\(394\) −0.639830 1.10822i −0.0322341 0.0558312i
\(395\) −44.0713 −2.21747
\(396\) 0 0
\(397\) −0.00245641 −0.000123284 −6.16419e−5 1.00000i \(-0.500020\pi\)
−6.16419e−5 1.00000i \(0.500020\pi\)
\(398\) −0.898069 1.55550i −0.0450161 0.0779703i
\(399\) 0 0
\(400\) −17.1234 + 29.6586i −0.856169 + 1.48293i
\(401\) −12.6282 + 21.8726i −0.630620 + 1.09227i 0.356805 + 0.934179i \(0.383866\pi\)
−0.987425 + 0.158088i \(0.949467\pi\)
\(402\) 0 0
\(403\) 2.50599 + 4.34051i 0.124832 + 0.216216i
\(404\) −11.0485 −0.549684
\(405\) 0 0
\(406\) −3.43513 −0.170483
\(407\) −6.17902 10.7024i −0.306283 0.530497i
\(408\) 0 0
\(409\) 11.6443 20.1685i 0.575772 0.997267i −0.420185 0.907438i \(-0.638035\pi\)
0.995957 0.0898282i \(-0.0286318\pi\)
\(410\) −1.69994 + 2.94438i −0.0839540 + 0.145413i
\(411\) 0 0
\(412\) −9.28402 16.0804i −0.457391 0.792224i
\(413\) 35.9286 1.76793
\(414\) 0 0
\(415\) −33.6891 −1.65373
\(416\) −0.778323 1.34809i −0.0381604 0.0660958i
\(417\) 0 0
\(418\) −0.131853 + 0.228377i −0.00644916 + 0.0111703i
\(419\) −15.6442 + 27.0965i −0.764268 + 1.32375i 0.176364 + 0.984325i \(0.443566\pi\)
−0.940633 + 0.339427i \(0.889767\pi\)
\(420\) 0 0
\(421\) −15.2648 26.4394i −0.743960 1.28858i −0.950679 0.310177i \(-0.899612\pi\)
0.206719 0.978400i \(-0.433722\pi\)
\(422\) −3.60848 −0.175658
\(423\) 0 0
\(424\) −6.07280 −0.294921
\(425\) 20.7145 + 35.8785i 1.00480 + 1.74036i
\(426\) 0 0
\(427\) −12.4094 + 21.4938i −0.600535 + 1.04016i
\(428\) 1.25912 2.18087i 0.0608620 0.105416i
\(429\) 0 0
\(430\) 1.80023 + 3.11809i 0.0868148 + 0.150368i
\(431\) 12.4246 0.598474 0.299237 0.954179i \(-0.403268\pi\)
0.299237 + 0.954179i \(0.403268\pi\)
\(432\) 0 0
\(433\) −0.760649 −0.0365545 −0.0182772 0.999833i \(-0.505818\pi\)
−0.0182772 + 0.999833i \(0.505818\pi\)
\(434\) 1.71744 + 2.97470i 0.0824399 + 0.142790i
\(435\) 0 0
\(436\) −7.29608 + 12.6372i −0.349419 + 0.605211i
\(437\) −1.99595 + 3.45709i −0.0954792 + 0.165375i
\(438\) 0 0
\(439\) −15.0547 26.0755i −0.718521 1.24451i −0.961586 0.274504i \(-0.911486\pi\)
0.243065 0.970010i \(-0.421847\pi\)
\(440\) 6.39370 0.304808
\(441\) 0 0
\(442\) −0.611828 −0.0291017
\(443\) 6.83079 + 11.8313i 0.324541 + 0.562121i 0.981419 0.191875i \(-0.0614570\pi\)
−0.656879 + 0.753996i \(0.728124\pi\)
\(444\) 0 0
\(445\) 14.0847 24.3954i 0.667679 1.15645i
\(446\) 2.03926 3.53209i 0.0965616 0.167250i
\(447\) 0 0
\(448\) 11.0511 + 19.1410i 0.522114 + 0.904328i
\(449\) 21.9989 1.03819 0.519097 0.854715i \(-0.326268\pi\)
0.519097 + 0.854715i \(0.326268\pi\)
\(450\) 0 0
\(451\) −13.1069 −0.617181
\(452\) −9.21205 15.9557i −0.433299 0.750495i
\(453\) 0 0
\(454\) 0.906751 1.57054i 0.0425559 0.0737091i
\(455\) 4.33351 7.50586i 0.203158 0.351880i
\(456\) 0 0
\(457\) 0.744414 + 1.28936i 0.0348222 + 0.0603138i 0.882911 0.469540i \(-0.155580\pi\)
−0.848089 + 0.529854i \(0.822247\pi\)
\(458\) 2.40132 0.112206
\(459\) 0 0
\(460\) 48.0281 2.23932
\(461\) −3.55667 6.16033i −0.165651 0.286915i 0.771236 0.636550i \(-0.219639\pi\)
−0.936886 + 0.349635i \(0.886306\pi\)
\(462\) 0 0
\(463\) 13.2704 22.9849i 0.616726 1.06820i −0.373353 0.927689i \(-0.621792\pi\)
0.990079 0.140512i \(-0.0448748\pi\)
\(464\) −12.5167 + 21.6796i −0.581073 + 1.00645i
\(465\) 0 0
\(466\) −0.657278 1.13844i −0.0304478 0.0527371i
\(467\) −26.1519 −1.21017 −0.605084 0.796162i \(-0.706860\pi\)
−0.605084 + 0.796162i \(0.706860\pi\)
\(468\) 0 0
\(469\) −3.67520 −0.169705
\(470\) −0.357946 0.619980i −0.0165108 0.0285975i
\(471\) 0 0
\(472\) −4.06947 + 7.04852i −0.187312 + 0.324435i
\(473\) −6.94009 + 12.0206i −0.319106 + 0.552707i
\(474\) 0 0
\(475\) 2.74164 + 4.74866i 0.125795 + 0.217884i
\(476\) 27.6086 1.26544
\(477\) 0 0
\(478\) 2.86425 0.131008
\(479\) −5.20327 9.01234i −0.237744 0.411784i 0.722323 0.691556i \(-0.243074\pi\)
−0.960067 + 0.279772i \(0.909741\pi\)
\(480\) 0 0
\(481\) 1.89742 3.28644i 0.0865151 0.149849i
\(482\) −1.25567 + 2.17489i −0.0571944 + 0.0990636i
\(483\) 0 0
\(484\) −4.71977 8.17488i −0.214535 0.371585i
\(485\) −3.54358 −0.160906
\(486\) 0 0
\(487\) −18.4664 −0.836791 −0.418396 0.908265i \(-0.637407\pi\)
−0.418396 + 0.908265i \(0.637407\pi\)
\(488\) −2.81112 4.86901i −0.127254 0.220410i
\(489\) 0 0
\(490\) 0.707730 1.22582i 0.0319720 0.0553771i
\(491\) −8.48695 + 14.6998i −0.383011 + 0.663394i −0.991491 0.130175i \(-0.958446\pi\)
0.608480 + 0.793569i \(0.291779\pi\)
\(492\) 0 0
\(493\) 15.1417 + 26.2262i 0.681947 + 1.18117i
\(494\) −0.0809779 −0.00364337
\(495\) 0 0
\(496\) 25.0316 1.12395
\(497\) −7.45667 12.9153i −0.334477 0.579332i
\(498\) 0 0
\(499\) −12.3231 + 21.3442i −0.551657 + 0.955498i 0.446498 + 0.894785i \(0.352671\pi\)
−0.998155 + 0.0607136i \(0.980662\pi\)
\(500\) 14.5824 25.2575i 0.652145 1.12955i
\(501\) 0 0
\(502\) −0.782873 1.35598i −0.0349413 0.0605201i
\(503\) −40.1137 −1.78858 −0.894291 0.447485i \(-0.852320\pi\)
−0.894291 + 0.447485i \(0.852320\pi\)
\(504\) 0 0
\(505\) 20.9552 0.932495
\(506\) −1.40601 2.43529i −0.0625050 0.108262i
\(507\) 0 0
\(508\) 20.4857 35.4823i 0.908905 1.57427i
\(509\) 2.47426 4.28554i 0.109670 0.189953i −0.805967 0.591961i \(-0.798354\pi\)
0.915636 + 0.402007i \(0.131687\pi\)
\(510\) 0 0
\(511\) −6.51689 11.2876i −0.288290 0.499333i
\(512\) −13.0229 −0.575537
\(513\) 0 0
\(514\) 1.67785 0.0740066
\(515\) 17.6086 + 30.4990i 0.775927 + 1.34395i
\(516\) 0 0
\(517\) 1.37992 2.39009i 0.0606889 0.105116i
\(518\) 1.30037 2.25231i 0.0571350 0.0989608i
\(519\) 0 0
\(520\) 0.981674 + 1.70031i 0.0430493 + 0.0745635i
\(521\) −7.73958 −0.339077 −0.169539 0.985524i \(-0.554228\pi\)
−0.169539 + 0.985524i \(0.554228\pi\)
\(522\) 0 0
\(523\) 36.0140 1.57478 0.787391 0.616453i \(-0.211431\pi\)
0.787391 + 0.616453i \(0.211431\pi\)
\(524\) 0.646018 + 1.11894i 0.0282214 + 0.0488810i
\(525\) 0 0
\(526\) 2.32266 4.02296i 0.101273 0.175409i
\(527\) 15.1406 26.2243i 0.659535 1.14235i
\(528\) 0 0
\(529\) −9.78374 16.9459i −0.425380 0.736780i
\(530\) 5.71561 0.248270
\(531\) 0 0
\(532\) 3.65411 0.158426
\(533\) −2.01241 3.48559i −0.0871670 0.150978i
\(534\) 0 0
\(535\) −2.38812 + 4.13635i −0.103248 + 0.178830i
\(536\) 0.416273 0.721007i 0.0179803 0.0311427i
\(537\) 0 0
\(538\) −1.01527 1.75849i −0.0437713 0.0758141i
\(539\) 5.45676 0.235039
\(540\) 0 0
\(541\) −24.4147 −1.04967 −0.524834 0.851204i \(-0.675873\pi\)
−0.524834 + 0.851204i \(0.675873\pi\)
\(542\) 0.0125041 + 0.0216577i 0.000537097 + 0.000930280i
\(543\) 0 0
\(544\) −4.70244 + 8.14486i −0.201615 + 0.349208i
\(545\) 13.8381 23.9684i 0.592761 1.02669i
\(546\) 0 0
\(547\) 14.1809 + 24.5620i 0.606331 + 1.05020i 0.991840 + 0.127492i \(0.0406927\pi\)
−0.385509 + 0.922704i \(0.625974\pi\)
\(548\) 16.9183 0.722712
\(549\) 0 0
\(550\) −3.86261 −0.164702
\(551\) 2.00406 + 3.47114i 0.0853759 + 0.147875i
\(552\) 0 0
\(553\) 17.8777 30.9650i 0.760235 1.31677i
\(554\) −0.0877355 + 0.151962i −0.00372753 + 0.00645626i
\(555\) 0 0
\(556\) 13.2450 + 22.9410i 0.561712 + 0.972914i
\(557\) 36.9373 1.56508 0.782542 0.622598i \(-0.213923\pi\)
0.782542 + 0.622598i \(0.213923\pi\)
\(558\) 0 0
\(559\) −4.26226 −0.180274
\(560\) −21.6431 37.4869i −0.914586 1.58411i
\(561\) 0 0
\(562\) 2.38097 4.12396i 0.100435 0.173959i
\(563\) 11.3877 19.7241i 0.479935 0.831271i −0.519800 0.854288i \(-0.673994\pi\)
0.999735 + 0.0230164i \(0.00732700\pi\)
\(564\) 0 0
\(565\) 17.4721 + 30.2626i 0.735057 + 1.27316i
\(566\) 4.63625 0.194876
\(567\) 0 0
\(568\) 3.37833 0.141752
\(569\) 15.4344 + 26.7331i 0.647043 + 1.12071i 0.983826 + 0.179129i \(0.0573279\pi\)
−0.336783 + 0.941582i \(0.609339\pi\)
\(570\) 0 0
\(571\) −6.41025 + 11.1029i −0.268260 + 0.464641i −0.968413 0.249353i \(-0.919782\pi\)
0.700152 + 0.713994i \(0.253115\pi\)
\(572\) −1.87797 + 3.25274i −0.0785219 + 0.136004i
\(573\) 0 0
\(574\) −1.37917 2.38880i −0.0575655 0.0997064i
\(575\) −58.4708 −2.43840
\(576\) 0 0
\(577\) −23.5264 −0.979417 −0.489708 0.871886i \(-0.662897\pi\)
−0.489708 + 0.871886i \(0.662897\pi\)
\(578\) 0.377963 + 0.654651i 0.0157212 + 0.0272299i
\(579\) 0 0
\(580\) 24.1116 41.7626i 1.00118 1.73410i
\(581\) 13.6661 23.6704i 0.566965 0.982013i
\(582\) 0 0
\(583\) 11.0172 + 19.0823i 0.456284 + 0.790307i
\(584\) 2.95255 0.122178
\(585\) 0 0
\(586\) 3.22726 0.133317
\(587\) 5.69372 + 9.86181i 0.235005 + 0.407041i 0.959274 0.282477i \(-0.0911560\pi\)
−0.724269 + 0.689517i \(0.757823\pi\)
\(588\) 0 0
\(589\) 2.00392 3.47089i 0.0825700 0.143016i
\(590\) 3.83011 6.63394i 0.157683 0.273115i
\(591\) 0 0
\(592\) −9.47640 16.4136i −0.389478 0.674595i
\(593\) 37.7324 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(594\) 0 0
\(595\) −52.3640 −2.14672
\(596\) −9.47812 16.4166i −0.388239 0.672449i
\(597\) 0 0
\(598\) 0.431753 0.747817i 0.0176557 0.0305805i
\(599\) 23.6791 41.0134i 0.967502 1.67576i 0.264764 0.964313i \(-0.414706\pi\)
0.702738 0.711449i \(-0.251961\pi\)
\(600\) 0 0
\(601\) 15.5537 + 26.9398i 0.634449 + 1.09890i 0.986631 + 0.162967i \(0.0521065\pi\)
−0.352182 + 0.935932i \(0.614560\pi\)
\(602\) −2.92108 −0.119054
\(603\) 0 0
\(604\) 14.0431 0.571407
\(605\) 8.95178 + 15.5049i 0.363942 + 0.630365i
\(606\) 0 0
\(607\) −14.7432 + 25.5360i −0.598409 + 1.03647i 0.394647 + 0.918833i \(0.370867\pi\)
−0.993056 + 0.117642i \(0.962467\pi\)
\(608\) −0.622386 + 1.07801i −0.0252411 + 0.0437189i
\(609\) 0 0
\(610\) 2.64578 + 4.58262i 0.107124 + 0.185545i
\(611\) 0.847480 0.0342854
\(612\) 0 0
\(613\) −6.10428 −0.246550 −0.123275 0.992373i \(-0.539340\pi\)
−0.123275 + 0.992373i \(0.539340\pi\)
\(614\) 2.92236 + 5.06168i 0.117937 + 0.204273i
\(615\) 0 0
\(616\) −2.59363 + 4.49229i −0.104500 + 0.181000i
\(617\) −9.56005 + 16.5585i −0.384873 + 0.666620i −0.991752 0.128175i \(-0.959088\pi\)
0.606878 + 0.794795i \(0.292422\pi\)
\(618\) 0 0
\(619\) 3.37693 + 5.84901i 0.135730 + 0.235092i 0.925876 0.377827i \(-0.123329\pi\)
−0.790146 + 0.612919i \(0.789995\pi\)
\(620\) −48.2198 −1.93655
\(621\) 0 0
\(622\) 5.99994 0.240576
\(623\) 11.4270 + 19.7922i 0.457813 + 0.792956i
\(624\) 0 0
\(625\) −5.25307 + 9.09859i −0.210123 + 0.363944i
\(626\) 0.288903 0.500394i 0.0115469 0.0199998i
\(627\) 0 0
\(628\) 7.57079 + 13.1130i 0.302107 + 0.523265i
\(629\) −22.9276 −0.914182
\(630\) 0 0
\(631\) −0.456907 −0.0181892 −0.00909458 0.999959i \(-0.502895\pi\)
−0.00909458 + 0.999959i \(0.502895\pi\)
\(632\) 4.04984 + 7.01454i 0.161094 + 0.279023i
\(633\) 0 0
\(634\) −2.68396 + 4.64876i −0.106594 + 0.184626i
\(635\) −38.8543 + 67.2976i −1.54189 + 2.67062i
\(636\) 0 0
\(637\) 0.837819 + 1.45114i 0.0331956 + 0.0574964i
\(638\) −2.82346 −0.111782
\(639\) 0 0
\(640\) 19.9161 0.787253
\(641\) 1.43552 + 2.48639i 0.0566994 + 0.0982063i 0.892982 0.450092i \(-0.148609\pi\)
−0.836282 + 0.548299i \(0.815276\pi\)
\(642\) 0 0
\(643\) 0.851422 1.47471i 0.0335768 0.0581567i −0.848749 0.528796i \(-0.822643\pi\)
0.882325 + 0.470640i \(0.155977\pi\)
\(644\) −19.4827 + 33.7451i −0.767727 + 1.32974i
\(645\) 0 0
\(646\) 0.244624 + 0.423702i 0.00962462 + 0.0166703i
\(647\) 36.1004 1.41925 0.709626 0.704579i \(-0.248864\pi\)
0.709626 + 0.704579i \(0.248864\pi\)
\(648\) 0 0
\(649\) 29.5310 1.15919
\(650\) −0.593056 1.02720i −0.0232616 0.0402902i
\(651\) 0 0
\(652\) 1.03183 1.78718i 0.0404095 0.0699914i
\(653\) 21.7840 37.7310i 0.852473 1.47653i −0.0264960 0.999649i \(-0.508435\pi\)
0.878969 0.476878i \(-0.158232\pi\)
\(654\) 0 0
\(655\) −1.22527 2.12224i −0.0478754 0.0829227i
\(656\) −20.1013 −0.784825
\(657\) 0 0
\(658\) 0.580807 0.0226422
\(659\) −12.7405 22.0672i −0.496299 0.859615i 0.503692 0.863883i \(-0.331975\pi\)
−0.999991 + 0.00426823i \(0.998641\pi\)
\(660\) 0 0
\(661\) −17.0836 + 29.5897i −0.664475 + 1.15090i 0.314952 + 0.949107i \(0.398011\pi\)
−0.979427 + 0.201797i \(0.935322\pi\)
\(662\) 0.282961 0.490102i 0.0109976 0.0190484i
\(663\) 0 0
\(664\) 3.09580 + 5.36207i 0.120140 + 0.208089i
\(665\) −6.93059 −0.268757
\(666\) 0 0
\(667\) −42.7405 −1.65492
\(668\) −8.22910 14.2532i −0.318393 0.551473i
\(669\) 0 0
\(670\) −0.391789 + 0.678598i −0.0151361 + 0.0262165i
\(671\) −10.1998 + 17.6665i −0.393757 + 0.682008i
\(672\) 0 0
\(673\) 14.7719 + 25.5856i 0.569413 + 0.986253i 0.996624 + 0.0821009i \(0.0261630\pi\)
−0.427211 + 0.904152i \(0.640504\pi\)
\(674\) −1.10113 −0.0424140
\(675\) 0 0
\(676\) 24.4577 0.940680
\(677\) −20.3901 35.3167i −0.783656 1.35733i −0.929799 0.368068i \(-0.880019\pi\)
0.146143 0.989264i \(-0.453314\pi\)
\(678\) 0 0
\(679\) 1.43747 2.48977i 0.0551649 0.0955484i
\(680\) 5.93104 10.2729i 0.227445 0.393946i
\(681\) 0 0
\(682\) 1.41163 + 2.44501i 0.0540540 + 0.0936243i
\(683\) 31.6426 1.21077 0.605384 0.795933i \(-0.293019\pi\)
0.605384 + 0.795933i \(0.293019\pi\)
\(684\) 0 0
\(685\) −32.0881 −1.22602
\(686\) −1.26113 2.18434i −0.0481502 0.0833986i
\(687\) 0 0
\(688\) −10.6436 + 18.4353i −0.405784 + 0.702839i
\(689\) −3.38310 + 5.85970i −0.128886 + 0.223237i
\(690\) 0 0
\(691\) 14.2924 + 24.7551i 0.543708 + 0.941729i 0.998687 + 0.0512273i \(0.0163133\pi\)
−0.454979 + 0.890502i \(0.650353\pi\)
\(692\) 43.0379 1.63606
\(693\) 0 0
\(694\) 1.52088 0.0577316
\(695\) −25.1212 43.5112i −0.952900 1.65047i
\(696\) 0 0
\(697\) −12.1585 + 21.0591i −0.460535 + 0.797670i
\(698\) 1.24545 2.15718i 0.0471408 0.0816503i
\(699\) 0 0
\(700\) 26.7615 + 46.3523i 1.01149 + 1.75195i
\(701\) −7.52982 −0.284397 −0.142199 0.989838i \(-0.545417\pi\)
−0.142199 + 0.989838i \(0.545417\pi\)
\(702\) 0 0
\(703\) −3.03455 −0.114450
\(704\) 9.08327 + 15.7327i 0.342338 + 0.592948i
\(705\) 0 0
\(706\) 2.87144 4.97348i 0.108068 0.187180i
\(707\) −8.50055 + 14.7234i −0.319696 + 0.553730i
\(708\) 0 0
\(709\) −4.00699 6.94032i −0.150486 0.260649i 0.780920 0.624631i \(-0.214750\pi\)
−0.931406 + 0.363982i \(0.881417\pi\)
\(710\) −3.17962 −0.119329
\(711\) 0 0
\(712\) −5.17714 −0.194022
\(713\) 21.3687 + 37.0117i 0.800265 + 1.38610i
\(714\) 0 0
\(715\) 3.56187 6.16933i 0.133206 0.230720i
\(716\) 8.95269 15.5065i 0.334578 0.579506i
\(717\) 0 0
\(718\) 0.427695 + 0.740790i 0.0159615 + 0.0276460i
\(719\) 26.9826 1.00628 0.503140 0.864205i \(-0.332178\pi\)
0.503140 + 0.864205i \(0.332178\pi\)
\(720\) 0 0
\(721\) −28.5719 −1.06407
\(722\) −1.61089 2.79015i −0.0599513 0.103839i
\(723\) 0 0
\(724\) −7.02409 + 12.1661i −0.261048 + 0.452149i
\(725\) −29.3542 + 50.8430i −1.09019 + 1.88826i
\(726\) 0 0
\(727\) 7.34717 + 12.7257i 0.272491 + 0.471969i 0.969499 0.245095i \(-0.0788190\pi\)
−0.697008 + 0.717064i \(0.745486\pi\)
\(728\) −1.59288 −0.0590360
\(729\) 0 0
\(730\) −2.77889 −0.102851
\(731\) 12.8758 + 22.3015i 0.476228 + 0.824851i
\(732\) 0 0
\(733\) 15.6719 27.1445i 0.578854 1.00261i −0.416757 0.909018i \(-0.636833\pi\)
0.995611 0.0935872i \(-0.0298334\pi\)
\(734\) −0.215567 + 0.373373i −0.00795673 + 0.0137815i
\(735\) 0 0
\(736\) −6.63680 11.4953i −0.244636 0.423721i
\(737\) −3.02078 −0.111272
\(738\) 0 0
\(739\) 0.482909 0.0177641 0.00888205 0.999961i \(-0.497173\pi\)
0.00888205 + 0.999961i \(0.497173\pi\)
\(740\) 18.2549 + 31.6185i 0.671065 + 1.16232i
\(741\) 0 0
\(742\) −2.31855 + 4.01585i −0.0851168 + 0.147427i
\(743\) −21.5254 + 37.2830i −0.789689 + 1.36778i 0.136468 + 0.990644i \(0.456425\pi\)
−0.926157 + 0.377137i \(0.876908\pi\)
\(744\) 0 0
\(745\) 17.9767 + 31.1366i 0.658616 + 1.14076i
\(746\) 4.85156 0.177628
\(747\) 0 0
\(748\) 22.6925 0.829720
\(749\) −1.93750 3.35585i −0.0707947 0.122620i
\(750\) 0 0
\(751\) −21.9608 + 38.0372i −0.801361 + 1.38800i 0.117359 + 0.993090i \(0.462557\pi\)
−0.918720 + 0.394909i \(0.870776\pi\)
\(752\) 2.11631 3.66555i 0.0771737 0.133669i
\(753\) 0 0
\(754\) −0.433507 0.750857i −0.0157874 0.0273446i
\(755\) −26.6350 −0.969346
\(756\) 0 0
\(757\) 22.4143 0.814661 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(758\) 0.444540 + 0.769966i 0.0161464 + 0.0279664i
\(759\) 0 0
\(760\) 0.784997 1.35965i 0.0284748 0.0493198i
\(761\) 4.99837 8.65743i 0.181191 0.313832i −0.761096 0.648640i \(-0.775338\pi\)
0.942286 + 0.334808i \(0.108672\pi\)
\(762\) 0 0
\(763\) 11.2270 + 19.4457i 0.406444 + 0.703982i
\(764\) 23.5535 0.852137
\(765\) 0 0
\(766\) 0.00772733 0.000279200
\(767\) 4.53412 + 7.85332i 0.163718 + 0.283567i
\(768\) 0 0
\(769\) 3.74810 6.49189i 0.135160 0.234104i −0.790499 0.612464i \(-0.790179\pi\)
0.925658 + 0.378360i \(0.123512\pi\)
\(770\) 2.44107 4.22806i 0.0879701 0.152369i
\(771\) 0 0
\(772\) −8.74088 15.1397i −0.314591 0.544888i
\(773\) −19.8391 −0.713562 −0.356781 0.934188i \(-0.616126\pi\)
−0.356781 + 0.934188i \(0.616126\pi\)
\(774\) 0 0
\(775\) 58.7043 2.10872
\(776\) 0.325631 + 0.564009i 0.0116895 + 0.0202467i
\(777\) 0 0
\(778\) 1.81471 3.14318i 0.0650606 0.112688i
\(779\) −1.60922 + 2.78726i −0.0576564 + 0.0998638i
\(780\) 0 0
\(781\) −6.12890 10.6156i −0.219309 0.379855i
\(782\) −5.21709 −0.186563
\(783\) 0 0
\(784\) 8.36872 0.298883
\(785\) −14.3592 24.8708i −0.512501 0.887678i
\(786\) 0 0
\(787\) −19.8641 + 34.4057i −0.708080 + 1.22643i 0.257489 + 0.966281i \(0.417105\pi\)
−0.965569 + 0.260149i \(0.916228\pi\)
\(788\) −7.28723 + 12.6218i −0.259597 + 0.449635i
\(789\) 0 0
\(790\) −3.81164 6.60195i −0.135612 0.234887i
\(791\) −28.3505 −1.00803
\(792\) 0 0
\(793\) −6.26419 −0.222448
\(794\) −0.000212450 0 0.000367974i −7.53957e−6 0 1.30589e-5i
\(795\) 0 0
\(796\) −10.2284 + 17.7161i −0.362536 + 0.627931i
\(797\) 4.55298 7.88599i 0.161275 0.279336i −0.774051 0.633123i \(-0.781773\pi\)
0.935326 + 0.353787i \(0.115106\pi\)
\(798\) 0 0
\(799\) −2.56013 4.43428i −0.0905710 0.156874i
\(800\) −18.2326 −0.644621
\(801\) 0 0
\(802\) −4.36874 −0.154265
\(803\) −5.35646 9.27766i −0.189025 0.327402i
\(804\) 0 0
\(805\) 36.9520 64.0028i 1.30239 2.25580i
\(806\) −0.433476 + 0.750803i −0.0152686 + 0.0264459i
\(807\) 0 0
\(808\) −1.92564 3.33530i −0.0677437 0.117336i
\(809\) 3.01910 0.106146 0.0530730 0.998591i \(-0.483098\pi\)
0.0530730 + 0.998591i \(0.483098\pi\)
\(810\) 0 0
\(811\) 33.1722 1.16483 0.582416 0.812891i \(-0.302107\pi\)
0.582416 + 0.812891i \(0.302107\pi\)
\(812\) 19.5619 + 33.8822i 0.686489 + 1.18903i
\(813\) 0 0
\(814\) 1.06882 1.85125i 0.0374622 0.0648864i
\(815\) −1.95702 + 3.38966i −0.0685516 + 0.118735i
\(816\) 0 0
\(817\) 1.70416 + 2.95169i 0.0596210 + 0.103267i
\(818\) 4.02836 0.140848
\(819\) 0 0
\(820\) 38.7223 1.35224
\(821\) −21.3810 37.0329i −0.746201 1.29246i −0.949631 0.313369i \(-0.898542\pi\)
0.203430 0.979089i \(-0.434791\pi\)
\(822\) 0 0
\(823\) 17.6144 30.5091i 0.614000 1.06348i −0.376559 0.926393i \(-0.622893\pi\)
0.990559 0.137087i \(-0.0437740\pi\)
\(824\) 3.23621 5.60529i 0.112739 0.195269i
\(825\) 0 0
\(826\) 3.10739 + 5.38216i 0.108120 + 0.187269i
\(827\) 26.0380 0.905429 0.452714 0.891656i \(-0.350456\pi\)
0.452714 + 0.891656i \(0.350456\pi\)
\(828\) 0 0
\(829\) −7.90268 −0.274471 −0.137236 0.990538i \(-0.543822\pi\)
−0.137236 + 0.990538i \(0.543822\pi\)
\(830\) −2.91370 5.04668i −0.101136 0.175173i
\(831\) 0 0
\(832\) −2.78925 + 4.83112i −0.0966998 + 0.167489i
\(833\) 5.06190 8.76746i 0.175384 0.303775i
\(834\) 0 0
\(835\) 15.6078 + 27.0334i 0.540129 + 0.935531i
\(836\) 3.00344 0.103876
\(837\) 0 0
\(838\) −5.41213 −0.186959
\(839\) −2.57420 4.45864i −0.0888711 0.153929i 0.818163 0.574986i \(-0.194993\pi\)
−0.907034 + 0.421057i \(0.861659\pi\)
\(840\) 0 0
\(841\) −6.95710 + 12.0500i −0.239900 + 0.415519i
\(842\) 2.64044 4.57338i 0.0909956 0.157609i
\(843\) 0 0
\(844\) 20.5491 + 35.5920i 0.707328 + 1.22513i
\(845\) −46.3878 −1.59579
\(846\) 0 0
\(847\) −14.5253 −0.499094
\(848\) 16.8964 + 29.2654i 0.580224 + 1.00498i
\(849\) 0 0
\(850\) −3.58310 + 6.20612i −0.122899 + 0.212868i
\(851\) 16.1794 28.0236i 0.554624 0.960637i
\(852\) 0 0
\(853\) −12.9952 22.5084i −0.444948 0.770673i 0.553100 0.833115i \(-0.313445\pi\)
−0.998049 + 0.0624418i \(0.980111\pi\)
\(854\) −4.29307 −0.146906
\(855\) 0 0
\(856\) 0.877808 0.0300028
\(857\) 2.05957 + 3.56727i 0.0703535 + 0.121856i 0.899056 0.437833i \(-0.144254\pi\)
−0.828703 + 0.559689i \(0.810921\pi\)
\(858\) 0 0
\(859\) 3.21471 5.56805i 0.109685 0.189979i −0.805958 0.591973i \(-0.798349\pi\)
0.915642 + 0.401994i \(0.131683\pi\)
\(860\) 20.5034 35.5129i 0.699160 1.21098i
\(861\) 0 0
\(862\) 1.07458 + 1.86123i 0.0366004 + 0.0633938i
\(863\) 29.6195 1.00826 0.504129 0.863628i \(-0.331813\pi\)
0.504129 + 0.863628i \(0.331813\pi\)
\(864\) 0 0
\(865\) −81.6282 −2.77544
\(866\) −0.0657870 0.113946i −0.00223553 0.00387206i
\(867\) 0 0
\(868\) 19.5605 33.8798i 0.663927 1.14996i
\(869\) 14.6943 25.4512i 0.498469 0.863374i
\(870\) 0 0
\(871\) −0.463803 0.803331i −0.0157154 0.0272198i
\(872\) −5.08652 −0.172251
\(873\) 0 0
\(874\) −0.690503 −0.0233566
\(875\) −22.4390 38.8654i −0.758576 1.31389i
\(876\) 0 0
\(877\) 15.9338 27.5982i 0.538048 0.931926i −0.460962 0.887420i \(-0.652495\pi\)
0.999009 0.0445057i \(-0.0141713\pi\)
\(878\) 2.60410 4.51043i 0.0878840 0.152220i
\(879\) 0 0
\(880\) −17.7892 30.8118i −0.599674 1.03867i
\(881\) 34.7864 1.17198 0.585991 0.810317i \(-0.300705\pi\)
0.585991 + 0.810317i \(0.300705\pi\)
\(882\) 0 0
\(883\) −30.3764 −1.02225 −0.511124 0.859507i \(-0.670771\pi\)
−0.511124 + 0.859507i \(0.670771\pi\)
\(884\) 3.48415 + 6.03473i 0.117185 + 0.202970i
\(885\) 0 0
\(886\) −1.18156 + 2.04653i −0.0396954 + 0.0687544i
\(887\) 25.0138 43.3252i 0.839882 1.45472i −0.0501110 0.998744i \(-0.515958\pi\)
0.889993 0.455974i \(-0.150709\pi\)
\(888\) 0 0
\(889\) −31.5228 54.5990i −1.05724 1.83119i
\(890\) 4.87263 0.163331
\(891\) 0 0
\(892\) −46.4515 −1.55531
\(893\) −0.338844 0.586895i −0.0113390 0.0196397i
\(894\) 0 0
\(895\) −16.9802 + 29.4105i −0.567585 + 0.983086i
\(896\) −8.07903 + 13.9933i −0.269902 + 0.467483i
\(897\) 0 0
\(898\) 1.90264 + 3.29547i 0.0634920 + 0.109971i
\(899\) 42.9111 1.43117
\(900\) 0 0
\(901\) 40.8797 1.36190
\(902\) −1.13359 1.96344i −0.0377444 0.0653753i
\(903\) 0 0
\(904\) 3.21113 5.56184i 0.106801 0.184984i
\(905\) 13.3223 23.0749i 0.442848 0.767035i
\(906\) 0 0
\(907\) 22.0322 + 38.1608i 0.731566 + 1.26711i 0.956214 + 0.292669i \(0.0945434\pi\)
−0.224648 + 0.974440i \(0.572123\pi\)
\(908\) −20.6546 −0.685446
\(909\) 0 0
\(910\) 1.49919 0.0496975
\(911\) 18.5891 + 32.1973i 0.615885 + 1.06674i 0.990228 + 0.139455i \(0.0445349\pi\)
−0.374343 + 0.927290i \(0.622132\pi\)
\(912\) 0 0
\(913\) 11.2327 19.4555i 0.371747 0.643884i
\(914\) −0.128766 + 0.223029i −0.00425919 + 0.00737713i
\(915\) 0 0
\(916\) −13.6747 23.6853i −0.451826 0.782585i
\(917\) 1.98815 0.0656544
\(918\) 0 0
\(919\) 12.3976 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(920\) 8.37078 + 14.4986i 0.275977 + 0.478005i
\(921\) 0 0
\(922\) 0.615218 1.06559i 0.0202611 0.0350933i
\(923\) 1.88204 3.25978i 0.0619480 0.107297i
\(924\) 0 0
\(925\) −22.2241 38.4933i −0.730724 1.26565i
\(926\) 4.59091 0.150867
\(927\) 0 0
\(928\) −13.3275 −0.437498
\(929\) −16.6941 28.9150i −0.547716 0.948672i −0.998431 0.0560035i \(-0.982164\pi\)
0.450715 0.892668i \(-0.351169\pi\)
\(930\) 0 0
\(931\) 0.669963 1.16041i 0.0219571 0.0380309i
\(932\) −7.48595 + 12.9660i −0.245210 + 0.424717i
\(933\) 0 0
\(934\) −2.26183 3.91760i −0.0740093 0.128188i
\(935\) −43.0399 −1.40755
\(936\) 0 0
\(937\) −24.8441 −0.811620 −0.405810 0.913957i \(-0.633011\pi\)
−0.405810 + 0.913957i \(0.633011\pi\)
\(938\) −0.317861 0.550551i −0.0103785 0.0179761i
\(939\) 0 0
\(940\) −4.07676 + 7.06116i −0.132969 + 0.230309i
\(941\) −12.7149 + 22.0229i −0.414495 + 0.717927i −0.995375 0.0960624i \(-0.969375\pi\)
0.580880 + 0.813989i \(0.302709\pi\)
\(942\) 0 0
\(943\) −17.1599 29.7218i −0.558803 0.967875i
\(944\) 45.2900 1.47406
\(945\) 0 0
\(946\) −2.40094 −0.0780612
\(947\) −8.31507 14.4021i −0.270204 0.468006i 0.698710 0.715405i \(-0.253758\pi\)
−0.968914 + 0.247398i \(0.920424\pi\)
\(948\) 0 0
\(949\) 1.64484 2.84894i 0.0533937 0.0924806i
\(950\) −0.474238 + 0.821404i −0.0153863 + 0.0266499i
\(951\) 0 0
\(952\) 4.81189 + 8.33444i 0.155954 + 0.270121i
\(953\) 14.2671 0.462158 0.231079 0.972935i \(-0.425774\pi\)
0.231079 + 0.972935i \(0.425774\pi\)
\(954\) 0 0
\(955\) −44.6730 −1.44558
\(956\) −16.3110 28.2514i −0.527534 0.913716i
\(957\) 0 0
\(958\) 0.900041 1.55892i 0.0290790 0.0503663i
\(959\) 13.0167 22.5455i 0.420330 0.728032i
\(960\) 0 0
\(961\) −5.95404 10.3127i −0.192066 0.332668i
\(962\) 0.656418 0.0211638
\(963\) 0 0
\(964\) 28.6026 0.921227
\(965\) 16.5784 + 28.7147i 0.533679 + 0.924359i
\(966\) 0 0
\(967\) 19.5424 33.8484i 0.628440 1.08849i −0.359424 0.933174i \(-0.617027\pi\)
0.987865 0.155317i \(-0.0496398\pi\)
\(968\) 1.64521 2.84959i 0.0528791 0.0915893i
\(969\) 0 0
\(970\) −0.306477 0.530835i −0.00984040 0.0170441i
\(971\) −4.40370 −0.141321 −0.0706607 0.997500i \(-0.522511\pi\)
−0.0706607 + 0.997500i \(0.522511\pi\)
\(972\) 0 0
\(973\) 40.7619 1.30677
\(974\) −1.59712 2.76629i −0.0511750 0.0886377i
\(975\) 0 0
\(976\) −15.6428 + 27.0941i −0.500714 + 0.867261i
\(977\) −21.0633 + 36.4827i −0.673874 + 1.16718i 0.302923 + 0.953015i \(0.402038\pi\)
−0.976797 + 0.214169i \(0.931296\pi\)
\(978\) 0 0
\(979\) 9.39226 + 16.2679i 0.300178 + 0.519924i
\(980\) −16.1211 −0.514971
\(981\) 0 0
\(982\) −2.93608 −0.0936939
\(983\) 10.2131 + 17.6896i 0.325746 + 0.564209i 0.981663 0.190624i \(-0.0610511\pi\)
−0.655917 + 0.754833i \(0.727718\pi\)
\(984\) 0 0
\(985\) 13.8214 23.9393i 0.440385 0.762770i
\(986\) −2.61915 + 4.53649i −0.0834106 + 0.144471i
\(987\) 0 0
\(988\) 0.461142 + 0.798721i 0.0146709 + 0.0254107i
\(989\) −36.3445 −1.15569
\(990\) 0 0
\(991\) 0.0680712 0.00216235 0.00108118 0.999999i \(-0.499656\pi\)
0.00108118 + 0.999999i \(0.499656\pi\)
\(992\) 6.66329 + 11.5412i 0.211560 + 0.366432i
\(993\) 0 0
\(994\) 1.28982 2.23404i 0.0409107 0.0708595i
\(995\) 19.3998 33.6014i 0.615014 1.06524i
\(996\) 0 0
\(997\) −5.32305 9.21980i −0.168583 0.291994i 0.769339 0.638841i \(-0.220586\pi\)
−0.937922 + 0.346847i \(0.887252\pi\)
\(998\) −4.26319 −0.134949
\(999\) 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 729.2.c.a.244.4 12
3.2 odd 2 729.2.c.d.244.3 12
9.2 odd 6 729.2.c.d.487.3 12
9.4 even 3 729.2.a.e.1.3 yes 6
9.5 odd 6 729.2.a.b.1.4 6
9.7 even 3 inner 729.2.c.a.487.4 12
27.2 odd 18 729.2.e.s.82.2 12
27.4 even 9 729.2.e.l.649.1 12
27.5 odd 18 729.2.e.t.163.1 12
27.7 even 9 729.2.e.k.568.2 12
27.11 odd 18 729.2.e.j.325.2 12
27.13 even 9 729.2.e.u.406.1 12
27.14 odd 18 729.2.e.j.406.2 12
27.16 even 9 729.2.e.u.325.1 12
27.20 odd 18 729.2.e.t.568.1 12
27.22 even 9 729.2.e.k.163.2 12
27.23 odd 18 729.2.e.s.649.2 12
27.25 even 9 729.2.e.l.82.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.4 6 9.5 odd 6
729.2.a.e.1.3 yes 6 9.4 even 3
729.2.c.a.244.4 12 1.1 even 1 trivial
729.2.c.a.487.4 12 9.7 even 3 inner
729.2.c.d.244.3 12 3.2 odd 2
729.2.c.d.487.3 12 9.2 odd 6
729.2.e.j.325.2 12 27.11 odd 18
729.2.e.j.406.2 12 27.14 odd 18
729.2.e.k.163.2 12 27.22 even 9
729.2.e.k.568.2 12 27.7 even 9
729.2.e.l.82.1 12 27.25 even 9
729.2.e.l.649.1 12 27.4 even 9
729.2.e.s.82.2 12 27.2 odd 18
729.2.e.s.649.2 12 27.23 odd 18
729.2.e.t.163.1 12 27.5 odd 18
729.2.e.t.568.1 12 27.20 odd 18
729.2.e.u.325.1 12 27.16 even 9
729.2.e.u.406.1 12 27.13 even 9