Properties

Label 729.2.c.d.244.3
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 244.3
Root \(1.37340i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.d.487.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0864880 - 0.149802i) q^{2} +(0.985040 - 1.70614i) q^{4} +(1.86828 - 3.23596i) q^{5} +(-1.51575 - 2.62535i) q^{7} -0.686728 q^{8} +O(q^{10})\) \(q+(-0.0864880 - 0.149802i) q^{2} +(0.985040 - 1.70614i) q^{4} +(1.86828 - 3.23596i) q^{5} +(-1.51575 - 2.62535i) q^{7} -0.686728 q^{8} -0.646335 q^{10} +(1.24585 + 2.15787i) q^{11} +(0.382569 - 0.662630i) q^{13} +(-0.262188 + 0.454123i) q^{14} +(-1.91069 - 3.30940i) q^{16} +4.62278 q^{17} -0.611844 q^{19} +(-3.68066 - 6.37509i) q^{20} +(0.215502 - 0.373260i) q^{22} +(-3.26219 + 5.65028i) q^{23} +(-4.48095 - 7.76123i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(3.27545 + 5.67324i) q^{29} +(-3.27521 + 5.67283i) q^{31} +(-1.01723 + 1.76190i) q^{32} +(-0.399815 - 0.692500i) q^{34} -11.3274 q^{35} +4.95969 q^{37} +(0.0529171 + 0.0916552i) q^{38} +(-1.28300 + 2.22222i) q^{40} +(-2.63012 + 4.55550i) q^{41} +(-2.78529 - 4.82426i) q^{43} +4.90884 q^{44} +1.12856 q^{46} +(-0.553808 - 0.959223i) q^{47} +(-1.09499 + 1.89658i) q^{49} +(-0.775096 + 1.34251i) q^{50} +(-0.753692 - 1.30543i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(1.04091 + 1.80290i) q^{56} +(0.566573 - 0.981334i) q^{58} +(5.92588 - 10.2639i) q^{59} +(-4.09350 - 7.09015i) q^{61} +1.13307 q^{62} -7.29083 q^{64} +(-1.42949 - 2.47596i) q^{65} +(0.606169 - 1.04992i) q^{67} +(4.55362 - 7.88711i) q^{68} +(0.979682 + 1.69686i) q^{70} -4.91946 q^{71} +4.29945 q^{73} +(-0.428953 - 0.742969i) q^{74} +(-0.602691 + 1.04389i) q^{76} +(3.77679 - 6.54158i) q^{77} +(5.89730 + 10.2144i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(-4.50804 - 7.80815i) q^{83} +(8.63666 - 14.9591i) q^{85} +(-0.481788 + 0.834481i) q^{86} +(-0.855559 - 1.48187i) q^{88} +7.53885 q^{89} -2.31952 q^{91} +(6.42677 + 11.1315i) q^{92} +(-0.0957954 + 0.165923i) q^{94} +(-1.14310 + 1.97990i) q^{95} +(0.474177 + 0.821299i) q^{97} +0.378814 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 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 0.833826 0.552027i \(-0.186145\pi\)
−0.894982 + 0.446101i \(0.852812\pi\)
\(3\) 0 0
\(4\) 0.985040 1.70614i 0.492520 0.853069i
\(5\) 1.86828 3.23596i 0.835521 1.44716i −0.0580849 0.998312i \(-0.518499\pi\)
0.893606 0.448853i \(-0.148167\pi\)
\(6\) 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 0.990422 0.138072i \(-0.0440905\pi\)
−0.614785 + 0.788695i \(0.710757\pi\)
\(12\) 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 \(-0.310573\pi\)
0.560595 + 0.828090i \(0.310573\pi\)
\(18\) 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 \(0.404779\pi\)
−0.974916 + 0.222575i \(0.928554\pi\)
\(24\) 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 \(0.0414555\pi\)
−0.383296 + 0.923626i \(0.625211\pi\)
\(30\) 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 −0.994973 0.100148i \(-0.968068\pi\)
0.584217 + 0.811598i \(0.301402\pi\)
\(42\) 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 0.822805 0.568324i \(-0.192408\pi\)
−0.903586 + 0.428407i \(0.859075\pi\)
\(48\) 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 \(-0.292234\pi\)
0.607346 + 0.794437i \(0.292234\pi\)
\(54\) 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 \(-0.552848\pi\)
0.936750 0.350000i \(-0.113818\pi\)
\(60\) 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 \(-0.594293\pi\)
−0.291916 + 0.956444i \(0.594293\pi\)
\(72\) 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 0.505161 0.863025i \(-0.331433\pi\)
−0.999982 + 0.00596962i \(0.998100\pi\)
\(84\) 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 \(-0.369163\pi\)
0.399558 + 0.916708i \(0.369163\pi\)
\(90\) 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 0.971140 0.238508i \(-0.0766584\pi\)
−0.692124 + 0.721778i \(0.743325\pi\)
\(102\) 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 \(-0.519680\pi\)
−0.0617864 + 0.998089i \(0.519680\pi\)
\(108\) 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 −0.997680 0.0680818i \(-0.978312\pi\)
0.557800 + 0.829975i \(0.311645\pi\)
\(114\) 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 −0.851345 0.524606i \(-0.824212\pi\)
0.879995 + 0.474983i \(0.157546\pi\)
\(132\) 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 0.622226 0.782838i \(-0.286228\pi\)
−0.989070 + 0.147445i \(0.952895\pi\)
\(138\) 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 −0.992990 0.118195i \(-0.962289\pi\)
0.598855 + 0.800857i \(0.295623\pi\)
\(150\) 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 −0.981152 0.193236i \(-0.938102\pi\)
0.657923 + 0.753085i \(0.271435\pi\)
\(168\) 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 \(-0.854749\pi\)
0.0672277 0.997738i \(-0.478585\pi\)
\(174\) 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 \(-0.610312\pi\)
−0.339659 + 0.940549i \(0.610312\pi\)
\(180\) 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 0.564552 0.825398i \(-0.309049\pi\)
−0.997091 + 0.0762174i \(0.975716\pi\)
\(192\) 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 \(-0.415110\pi\)
0.263539 + 0.964649i \(0.415110\pi\)
\(198\) 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 0.985881 0.167446i \(-0.0535520\pi\)
−0.637953 + 0.770075i \(0.720219\pi\)
\(228\) 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 \(-0.419920\pi\)
0.248935 + 0.968520i \(0.419920\pi\)
\(234\) 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 \(0.346561\pi\)
−0.999137 + 0.0415436i \(0.986772\pi\)
\(240\) 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 \(-0.407783\pi\)
0.285673 + 0.958327i \(0.407783\pi\)
\(252\) 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 −0.976709 0.214570i \(-0.931165\pi\)
0.674178 + 0.738569i \(0.264498\pi\)
\(258\) 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 \(0.143845\pi\)
−0.0716358 + 0.997431i \(0.522822\pi\)
\(264\) 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 \(-0.383505\pi\)
0.357865 + 0.933774i \(0.383505\pi\)
\(270\) 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 \(0.139992\pi\)
−0.0837029 + 0.996491i \(0.526675\pi\)
\(282\) 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 \(0.350131\pi\)
−0.998608 + 0.0527472i \(0.983202\pi\)
\(294\) 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 \(0.608671\pi\)
−0.648642 + 0.761094i \(0.724663\pi\)
\(312\) 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 \(-0.829822\pi\)
−0.0110301 0.999939i \(-0.503511\pi\)
\(318\) 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 −0.959563 0.281494i \(-0.909170\pi\)
0.723562 + 0.690259i \(0.242503\pi\)
\(348\) 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 \(0.178181\pi\)
0.0361653 + 0.999346i \(0.488486\pi\)
\(354\) 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 \(-0.541657\pi\)
−0.130497 + 0.991449i \(0.541657\pi\)
\(360\) 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 −0.866596 0.499011i \(-0.833697\pi\)
0.865454 + 0.500988i \(0.167030\pi\)
\(384\) 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 \(0.0118632\pi\)
−0.467384 + 0.884054i \(0.654803\pi\)
\(390\) 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 \(-0.616134\pi\)
0.987425 0.158088i \(-0.0505328\pi\)
\(402\) 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 \(-0.556434\pi\)
0.940633 0.339427i \(-0.110233\pi\)
\(420\) 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 \(-0.596732\pi\)
−0.299237 + 0.954179i \(0.596732\pi\)
\(432\) 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 0.656879 0.753996i \(-0.271876\pi\)
−0.981419 + 0.191875i \(0.938543\pi\)
\(444\) 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 \(-0.673732\pi\)
−0.519097 + 0.854715i \(0.673732\pi\)
\(450\) 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 0.936886 0.349635i \(-0.113694\pi\)
−0.771236 + 0.636550i \(0.780361\pi\)
\(462\) 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 \(-0.293140\pi\)
0.605084 + 0.796162i \(0.293140\pi\)
\(468\) 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 0.960067 0.279772i \(-0.0902588\pi\)
−0.722323 + 0.691556i \(0.756926\pi\)
\(480\) 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 −0.608480 0.793569i \(-0.708221\pi\)
0.991491 + 0.130175i \(0.0415540\pi\)
\(492\) 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 \(-0.147680\pi\)
0.894291 + 0.447485i \(0.147680\pi\)
\(504\) 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 −0.915636 0.402007i \(-0.868313\pi\)
0.805967 + 0.591961i \(0.201646\pi\)
\(510\) 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 \(-0.445772\pi\)
0.169539 + 0.985524i \(0.445772\pi\)
\(522\) 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 \(-0.786077\pi\)
−0.782542 + 0.622598i \(0.786077\pi\)
\(558\) 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 −0.999735 0.0230164i \(-0.992673\pi\)
0.519800 + 0.854288i \(0.326006\pi\)
\(564\) 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 \(-0.942672\pi\)
0.336783 0.941582i \(-0.390661\pi\)
\(570\) 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 0.724269 0.689517i \(-0.242177\pi\)
−0.959274 + 0.282477i \(0.908844\pi\)
\(588\) 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 \(-0.782120\pi\)
−0.774742 + 0.632277i \(0.782120\pi\)
\(594\) 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 \(0.585294\pi\)
−0.702738 + 0.711449i \(0.748039\pi\)
\(600\) 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 −0.606878 0.794795i \(-0.707578\pi\)
0.991752 + 0.128175i \(0.0409118\pi\)
\(618\) 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 0.836282 0.548299i \(-0.184724\pi\)
−0.892982 + 0.450092i \(0.851391\pi\)
\(642\) 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 \(-0.751136\pi\)
−0.709626 + 0.704579i \(0.751136\pi\)
\(648\) 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 \(0.491565\pi\)
−0.878969 + 0.476878i \(0.841768\pi\)
\(654\) 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 0.999991 0.00426823i \(-0.00135862\pi\)
−0.503692 + 0.863883i \(0.668025\pi\)
\(660\) 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 \(0.119981\pi\)
−0.146143 + 0.989264i \(0.546686\pi\)
\(678\) 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 \(-0.706981\pi\)
−0.605384 + 0.795933i \(0.706981\pi\)
\(684\) 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 \(-0.454583\pi\)
0.142199 + 0.989838i \(0.454583\pi\)
\(702\) 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 \(-0.667822\pi\)
−0.503140 + 0.864205i \(0.667822\pi\)
\(720\) 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 \(-0.543575\pi\)
0.926157 0.377137i \(-0.123092\pi\)
\(744\) 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 −0.942286 0.334808i \(-0.891328\pi\)
0.761096 + 0.648640i \(0.224662\pi\)
\(762\) 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 \(-0.383874\pi\)
0.356781 + 0.934188i \(0.383874\pi\)
\(774\) 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