Properties

Label 729.2.e.u.325.1
Level $729$
Weight $2$
Character 729.325
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(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.1
Root \(-0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.u.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +O(q^{10})\) \(q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +(0.323168 - 0.559743i) q^{10} +(-2.34143 - 0.852210i) q^{11} +(-0.586130 - 0.491822i) q^{13} +(-0.401695 - 0.337062i) q^{14} +(-3.59091 - 1.30699i) q^{16} +(2.31139 - 4.00345i) q^{17} +(0.305922 + 0.529872i) q^{19} +(-1.27828 - 7.24949i) q^{20} +(0.405011 - 0.147412i) q^{22} +(-1.13295 + 6.42526i) q^{23} +(6.86521 - 5.76060i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(5.01827 - 4.21083i) q^{29} +(1.13747 - 6.45091i) q^{31} +(1.91177 - 0.695827i) q^{32} +(0.138854 + 0.787482i) q^{34} +(-5.66369 - 9.80980i) q^{35} +(-2.47984 + 4.29522i) q^{37} +(-0.0994517 - 0.0361975i) q^{38} +(1.96567 + 1.64939i) q^{40} +(-4.02958 - 3.38122i) q^{41} +(-5.23463 - 1.90525i) q^{43} +(2.45442 - 4.25118i) q^{44} +(-0.564280 - 0.977362i) q^{46} +(-0.192335 - 1.09079i) q^{47} +(-2.05791 + 0.749017i) q^{49} +(-0.269188 + 1.52664i) q^{50} +(1.15472 - 0.968928i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(1.59476 - 1.33816i) q^{56} +(-0.196769 + 1.11593i) q^{58} +(-11.1370 + 4.05354i) q^{59} +(1.42166 + 8.06263i) q^{61} +(0.566533 + 0.981264i) q^{62} +(3.64541 - 6.31404i) q^{64} +(2.68657 + 0.977832i) q^{65} +(-0.928705 - 0.779276i) q^{67} +(6.97656 + 5.85403i) q^{68} +(1.84120 + 0.670142i) q^{70} +(-2.45973 + 4.26038i) q^{71} +(-2.14972 - 3.72343i) q^{73} +(-0.148974 - 0.844873i) q^{74} +(-1.13269 + 0.412265i) q^{76} +(1.31166 - 7.43882i) q^{77} +(-9.03519 + 7.58143i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(-6.90671 + 5.79542i) q^{83} +(-2.99948 + 17.0109i) q^{85} +(0.905464 - 0.329562i) q^{86} +(0.297133 + 1.68512i) q^{88} +(3.76943 + 6.52884i) q^{89} +(1.15976 - 2.00876i) q^{91} +(-12.0784 - 4.39617i) q^{92} +(0.146767 + 0.123152i) q^{94} +(-1.75133 - 1.46954i) q^{95} +(0.891161 + 0.324356i) q^{97} +(0.189407 - 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.132507 + 0.111187i −0.0936968 + 0.0786209i −0.688433 0.725300i \(-0.741701\pi\)
0.594736 + 0.803921i \(0.297257\pi\)
\(3\) 0 0
\(4\) −0.342101 + 1.94015i −0.171050 + 0.970075i
\(5\) −3.51122 + 1.27798i −1.57027 + 0.571530i −0.973059 0.230557i \(-0.925945\pi\)
−0.597207 + 0.802087i \(0.703723\pi\)
\(6\) 0 0
\(7\) 0.526414 + 2.98544i 0.198966 + 1.12839i 0.906657 + 0.421869i \(0.138626\pi\)
−0.707691 + 0.706522i \(0.750263\pi\)
\(8\) −0.343364 0.594724i −0.121398 0.210267i
\(9\) 0 0
\(10\) 0.323168 0.559743i 0.102195 0.177006i
\(11\) −2.34143 0.852210i −0.705967 0.256951i −0.0360107 0.999351i \(-0.511465\pi\)
−0.669957 + 0.742400i \(0.733687\pi\)
\(12\) 0 0
\(13\) −0.586130 0.491822i −0.162563 0.136407i 0.557877 0.829923i \(-0.311616\pi\)
−0.720441 + 0.693517i \(0.756060\pi\)
\(14\) −0.401695 0.337062i −0.107358 0.0900837i
\(15\) 0 0
\(16\) −3.59091 1.30699i −0.897729 0.326746i
\(17\) 2.31139 4.00345i 0.560595 0.970979i −0.436850 0.899534i \(-0.643906\pi\)
0.997445 0.0714442i \(-0.0227608\pi\)
\(18\) 0 0
\(19\) 0.305922 + 0.529872i 0.0701833 + 0.121561i 0.898982 0.437987i \(-0.144308\pi\)
−0.828798 + 0.559548i \(0.810975\pi\)
\(20\) −1.27828 7.24949i −0.285832 1.62104i
\(21\) 0 0
\(22\) 0.405011 0.147412i 0.0863486 0.0314283i
\(23\) −1.13295 + 6.42526i −0.236236 + 1.33976i 0.603760 + 0.797166i \(0.293668\pi\)
−0.839996 + 0.542593i \(0.817443\pi\)
\(24\) 0 0
\(25\) 6.86521 5.76060i 1.37304 1.15212i
\(26\) 0.132351 0.0259561
\(27\) 0 0
\(28\) −5.97229 −1.12866
\(29\) 5.01827 4.21083i 0.931870 0.781932i −0.0442820 0.999019i \(-0.514100\pi\)
0.976152 + 0.217087i \(0.0696556\pi\)
\(30\) 0 0
\(31\) 1.13747 6.45091i 0.204296 1.15862i −0.694249 0.719735i \(-0.744263\pi\)
0.898544 0.438883i \(-0.144626\pi\)
\(32\) 1.91177 0.695827i 0.337956 0.123006i
\(33\) 0 0
\(34\) 0.138854 + 0.787482i 0.0238133 + 0.135052i
\(35\) −5.66369 9.80980i −0.957338 1.65816i
\(36\) 0 0
\(37\) −2.47984 + 4.29522i −0.407684 + 0.706129i −0.994630 0.103497i \(-0.966997\pi\)
0.586946 + 0.809626i \(0.300330\pi\)
\(38\) −0.0994517 0.0361975i −0.0161332 0.00587200i
\(39\) 0 0
\(40\) 1.96567 + 1.64939i 0.310800 + 0.260792i
\(41\) −4.02958 3.38122i −0.629314 0.528057i 0.271402 0.962466i \(-0.412513\pi\)
−0.900716 + 0.434409i \(0.856957\pi\)
\(42\) 0 0
\(43\) −5.23463 1.90525i −0.798273 0.290548i −0.0895024 0.995987i \(-0.528528\pi\)
−0.708771 + 0.705439i \(0.750750\pi\)
\(44\) 2.45442 4.25118i 0.370018 0.640889i
\(45\) 0 0
\(46\) −0.564280 0.977362i −0.0831986 0.144104i
\(47\) −0.192335 1.09079i −0.0280550 0.159108i 0.967562 0.252635i \(-0.0812971\pi\)
−0.995617 + 0.0935267i \(0.970186\pi\)
\(48\) 0 0
\(49\) −2.05791 + 0.749017i −0.293987 + 0.107002i
\(50\) −0.269188 + 1.52664i −0.0380690 + 0.215900i
\(51\) 0 0
\(52\) 1.15472 0.968928i 0.160131 0.134366i
\(53\) −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
\(56\) 1.59476 1.33816i 0.213109 0.178820i
\(57\) 0 0
\(58\) −0.196769 + 1.11593i −0.0258370 + 0.146529i
\(59\) −11.1370 + 4.05354i −1.44992 + 0.527726i −0.942568 0.334016i \(-0.891596\pi\)
−0.507347 + 0.861742i \(0.669374\pi\)
\(60\) 0 0
\(61\) 1.42166 + 8.06263i 0.182025 + 1.03231i 0.929719 + 0.368270i \(0.120050\pi\)
−0.747694 + 0.664043i \(0.768839\pi\)
\(62\) 0.566533 + 0.981264i 0.0719498 + 0.124621i
\(63\) 0 0
\(64\) 3.64541 6.31404i 0.455677 0.789255i
\(65\) 2.68657 + 0.977832i 0.333228 + 0.121285i
\(66\) 0 0
\(67\) −0.928705 0.779276i −0.113459 0.0952037i 0.584293 0.811543i \(-0.301372\pi\)
−0.697752 + 0.716339i \(0.745816\pi\)
\(68\) 6.97656 + 5.85403i 0.846032 + 0.709905i
\(69\) 0 0
\(70\) 1.84120 + 0.670142i 0.220066 + 0.0800973i
\(71\) −2.45973 + 4.26038i −0.291916 + 0.505614i −0.974263 0.225415i \(-0.927626\pi\)
0.682346 + 0.731029i \(0.260960\pi\)
\(72\) 0 0
\(73\) −2.14972 3.72343i −0.251606 0.435795i 0.712362 0.701812i \(-0.247625\pi\)
−0.963968 + 0.266017i \(0.914292\pi\)
\(74\) −0.148974 0.844873i −0.0173179 0.0982145i
\(75\) 0 0
\(76\) −1.13269 + 0.412265i −0.129928 + 0.0472900i
\(77\) 1.31166 7.43882i 0.149478 0.847732i
\(78\) 0 0
\(79\) −9.03519 + 7.58143i −1.01654 + 0.852977i −0.989189 0.146649i \(-0.953151\pi\)
−0.0273498 + 0.999626i \(0.508707\pi\)
\(80\) 14.2788 1.59642
\(81\) 0 0
\(82\) 0.909895 0.100481
\(83\) −6.90671 + 5.79542i −0.758110 + 0.636130i −0.937634 0.347624i \(-0.886989\pi\)
0.179524 + 0.983754i \(0.442544\pi\)
\(84\) 0 0
\(85\) −2.99948 + 17.0109i −0.325339 + 1.84509i
\(86\) 0.905464 0.329562i 0.0976387 0.0355376i
\(87\) 0 0
\(88\) 0.297133 + 1.68512i 0.0316744 + 0.179635i
\(89\) 3.76943 + 6.52884i 0.399558 + 0.692055i 0.993671 0.112326i \(-0.0358302\pi\)
−0.594113 + 0.804382i \(0.702497\pi\)
\(90\) 0 0
\(91\) 1.15976 2.00876i 0.121576 0.210575i
\(92\) −12.0784 4.39617i −1.25926 0.458332i
\(93\) 0 0
\(94\) 0.146767 + 0.123152i 0.0151379 + 0.0127022i
\(95\) −1.75133 1.46954i −0.179682 0.150771i
\(96\) 0 0
\(97\) 0.891161 + 0.324356i 0.0904837 + 0.0329334i 0.386865 0.922136i \(-0.373558\pi\)
−0.296382 + 0.955070i \(0.595780\pi\)
\(98\) 0.189407 0.328062i 0.0191330 0.0331393i
\(99\) 0 0
\(100\) 8.82783 + 15.2902i 0.882783 + 1.52902i
\(101\) 0.973846 + 5.52295i 0.0969013 + 0.549554i 0.994148 + 0.108025i \(0.0344527\pi\)
−0.897247 + 0.441529i \(0.854436\pi\)
\(102\) 0 0
\(103\) 8.85662 3.22355i 0.872669 0.317625i 0.133421 0.991059i \(-0.457404\pi\)
0.739247 + 0.673434i \(0.235181\pi\)
\(104\) −0.0912421 + 0.517460i −0.00894702 + 0.0507411i
\(105\) 0 0
\(106\) 1.17177 0.983235i 0.113813 0.0955003i
\(107\) 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 \(0.615426\pi\)
\(110\) −1.23369 + 1.03519i −0.117628 + 0.0987016i
\(111\) 0 0
\(112\) 2.01162 11.4085i 0.190081 1.07800i
\(113\) 8.78797 3.19856i 0.826703 0.300895i 0.106198 0.994345i \(-0.466132\pi\)
0.720505 + 0.693450i \(0.243910\pi\)
\(114\) 0 0
\(115\) −4.23332 24.0084i −0.394759 2.23879i
\(116\) 6.45289 + 11.1767i 0.599136 + 1.03773i
\(117\) 0 0
\(118\) 1.02503 1.77541i 0.0943621 0.163440i
\(119\) 13.1688 + 4.79306i 1.20718 + 0.439379i
\(120\) 0 0
\(121\) −3.67046 3.07989i −0.333679 0.279990i
\(122\) −1.08484 0.910287i −0.0982166 0.0824135i
\(123\) 0 0
\(124\) 12.1266 + 4.41372i 1.08900 + 0.396364i
\(125\) −7.40194 + 12.8205i −0.662050 + 1.14670i
\(126\) 0 0
\(127\) −10.3984 18.0106i −0.922710 1.59818i −0.795204 0.606342i \(-0.792636\pi\)
−0.127505 0.991838i \(-0.540697\pi\)
\(128\) 0.925555 + 5.24909i 0.0818083 + 0.463958i
\(129\) 0 0
\(130\) −0.464712 + 0.169141i −0.0407579 + 0.0148347i
\(131\) 0.113884 0.645866i 0.00995006 0.0564296i −0.979428 0.201792i \(-0.935324\pi\)
0.989379 + 0.145362i \(0.0464347\pi\)
\(132\) 0 0
\(133\) −1.42086 + 1.19224i −0.123204 + 0.103381i
\(134\) 0.209705 0.0181158
\(135\) 0 0
\(136\) −3.17460 −0.272219
\(137\) −6.57849 + 5.52001i −0.562038 + 0.471606i −0.878993 0.476835i \(-0.841784\pi\)
0.316955 + 0.948441i \(0.397340\pi\)
\(138\) 0 0
\(139\) 2.33490 13.2419i 0.198043 1.12316i −0.709974 0.704228i \(-0.751293\pi\)
0.908017 0.418932i \(-0.137596\pi\)
\(140\) 20.9700 7.63247i 1.77229 0.645061i
\(141\) 0 0
\(142\) −0.147766 0.838021i −0.0124002 0.0703251i
\(143\) 0.953247 + 1.65107i 0.0797145 + 0.138070i
\(144\) 0 0
\(145\) −12.2389 + 21.1984i −1.01639 + 1.76043i
\(146\) 0.698851 + 0.254361i 0.0578373 + 0.0210511i
\(147\) 0 0
\(148\) −7.48500 6.28066i −0.615264 0.516267i
\(149\) −7.37093 6.18495i −0.603850 0.506691i 0.288830 0.957380i \(-0.406734\pi\)
−0.892681 + 0.450690i \(0.851178\pi\)
\(150\) 0 0
\(151\) 6.69832 + 2.43799i 0.545101 + 0.198401i 0.599869 0.800098i \(-0.295219\pi\)
−0.0547672 + 0.998499i \(0.517442\pi\)
\(152\) 0.210085 0.363878i 0.0170402 0.0295144i
\(153\) 0 0
\(154\) 0.653293 + 1.13154i 0.0526439 + 0.0911818i
\(155\) 4.25023 + 24.1042i 0.341386 + 1.93610i
\(156\) 0 0
\(157\) −7.22226 + 2.62869i −0.576399 + 0.209792i −0.613737 0.789511i \(-0.710334\pi\)
0.0373379 + 0.999303i \(0.488112\pi\)
\(158\) 0.354274 2.00919i 0.0281845 0.159842i
\(159\) 0 0
\(160\) −5.82339 + 4.88640i −0.460379 + 0.386304i
\(161\) −19.7786 −1.55877
\(162\) 0 0
\(163\) 1.04750 0.0820465 0.0410232 0.999158i \(-0.486938\pi\)
0.0410232 + 0.999158i \(0.486938\pi\)
\(164\) 7.93859 6.66126i 0.619899 0.520157i
\(165\) 0 0
\(166\) 0.270815 1.53587i 0.0210193 0.119207i
\(167\) 7.85026 2.85726i 0.607472 0.221102i −0.0199249 0.999801i \(-0.506343\pi\)
0.627397 + 0.778700i \(0.284120\pi\)
\(168\) 0 0
\(169\) −2.15577 12.2260i −0.165828 0.940458i
\(170\) −1.49393 2.58757i −0.114580 0.198458i
\(171\) 0 0
\(172\) 5.48724 9.50417i 0.418398 0.724686i
\(173\) 20.5283 + 7.47170i 1.56074 + 0.568063i 0.970906 0.239462i \(-0.0769710\pi\)
0.589834 + 0.807525i \(0.299193\pi\)
\(174\) 0 0
\(175\) 20.8119 + 17.4632i 1.57323 + 1.32010i
\(176\) 7.29404 + 6.12043i 0.549809 + 0.461345i
\(177\) 0 0
\(178\) −1.22540 0.446008i −0.0918474 0.0334297i
\(179\) −4.54433 + 7.87101i −0.339659 + 0.588307i −0.984369 0.176121i \(-0.943645\pi\)
0.644709 + 0.764428i \(0.276978\pi\)
\(180\) 0 0
\(181\) 3.56539 + 6.17543i 0.265013 + 0.459016i 0.967567 0.252614i \(-0.0812904\pi\)
−0.702554 + 0.711630i \(0.747957\pi\)
\(182\) 0.0696712 + 0.395125i 0.00516437 + 0.0292886i
\(183\) 0 0
\(184\) 4.21027 1.53241i 0.310385 0.112971i
\(185\) 3.21808 18.2506i 0.236598 1.34181i
\(186\) 0 0
\(187\) −8.82374 + 7.40399i −0.645256 + 0.541434i
\(188\) 2.18209 0.159145
\(189\) 0 0
\(190\) 0.395456 0.0286894
\(191\) −9.15854 + 7.68493i −0.662689 + 0.556062i −0.910891 0.412646i \(-0.864605\pi\)
0.248203 + 0.968708i \(0.420160\pi\)
\(192\) 0 0
\(193\) −1.54089 + 8.73883i −0.110916 + 0.629034i 0.877776 + 0.479071i \(0.159027\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(194\) −0.154149 + 0.0561058i −0.0110673 + 0.00402816i
\(195\) 0 0
\(196\) −0.749193 4.24889i −0.0535138 0.303492i
\(197\) 3.69895 + 6.40677i 0.263539 + 0.456464i 0.967180 0.254093i \(-0.0817768\pi\)
−0.703641 + 0.710556i \(0.748443\pi\)
\(198\) 0 0
\(199\) 5.19187 8.99259i 0.368042 0.637468i −0.621217 0.783638i \(-0.713362\pi\)
0.989259 + 0.146171i \(0.0466948\pi\)
\(200\) −5.78323 2.10493i −0.408936 0.148841i
\(201\) 0 0
\(202\) −0.743121 0.623553i −0.0522858 0.0438730i
\(203\) 15.2129 + 12.7651i 1.06774 + 0.895936i
\(204\) 0 0
\(205\) 18.4699 + 6.72248i 1.28999 + 0.469518i
\(206\) −0.815151 + 1.41188i −0.0567942 + 0.0983705i
\(207\) 0 0
\(208\) 1.46194 + 2.53215i 0.101367 + 0.175573i
\(209\) −0.264732 1.50137i −0.0183119 0.103852i
\(210\) 0 0
\(211\) −19.6031 + 7.13493i −1.34953 + 0.491189i −0.912801 0.408404i \(-0.866085\pi\)
−0.436729 + 0.899593i \(0.643863\pi\)
\(212\) 3.02523 17.1569i 0.207774 1.17834i
\(213\) 0 0
\(214\) −0.169377 + 0.142124i −0.0115784 + 0.00971540i
\(215\) 20.8148 1.41956
\(216\) 0 0
\(217\) 19.8576 1.34802
\(218\) 0.981466 0.823548i 0.0664733 0.0557777i
\(219\) 0 0
\(220\) −3.18509 + 18.0635i −0.214739 + 1.21784i
\(221\) −3.32376 + 1.20975i −0.223580 + 0.0813765i
\(222\) 0 0
\(223\) 4.09436 + 23.2203i 0.274179 + 1.55494i 0.741558 + 0.670888i \(0.234087\pi\)
−0.467380 + 0.884057i \(0.654802\pi\)
\(224\) 3.08373 + 5.34118i 0.206041 + 0.356873i
\(225\) 0 0
\(226\) −0.808832 + 1.40094i −0.0538027 + 0.0931890i
\(227\) −9.85186 3.58578i −0.653891 0.237997i −0.00629435 0.999980i \(-0.502004\pi\)
−0.647597 + 0.761983i \(0.724226\pi\)
\(228\) 0 0
\(229\) −10.6345 8.92345i −0.702751 0.589678i 0.219804 0.975544i \(-0.429458\pi\)
−0.922555 + 0.385866i \(0.873903\pi\)
\(230\) 3.23036 + 2.71059i 0.213004 + 0.178731i
\(231\) 0 0
\(232\) −4.22738 1.53864i −0.277541 0.101017i
\(233\) 3.79982 6.58149i 0.248935 0.431167i −0.714296 0.699844i \(-0.753253\pi\)
0.963230 + 0.268676i \(0.0865862\pi\)
\(234\) 0 0
\(235\) 2.06934 + 3.58420i 0.134989 + 0.233807i
\(236\) −4.05449 22.9942i −0.263925 1.49679i
\(237\) 0 0
\(238\) −2.27789 + 0.829083i −0.147654 + 0.0537415i
\(239\) −2.87539 + 16.3071i −0.185993 + 1.05482i 0.738679 + 0.674057i \(0.235450\pi\)
−0.924673 + 0.380763i \(0.875661\pi\)
\(240\) 0 0
\(241\) −11.1218 + 9.33230i −0.716419 + 0.601147i −0.926392 0.376560i \(-0.877107\pi\)
0.209973 + 0.977707i \(0.432662\pi\)
\(242\) 0.828806 0.0532776
\(243\) 0 0
\(244\) −16.1290 −1.03256
\(245\) 6.26854 5.25993i 0.400482 0.336044i
\(246\) 0 0
\(247\) 0.0812926 0.461033i 0.00517252 0.0293348i
\(248\) −4.22708 + 1.53853i −0.268420 + 0.0976968i
\(249\) 0 0
\(250\) −0.444664 2.52181i −0.0281230 0.159493i
\(251\) 4.52591 + 7.83910i 0.285673 + 0.494800i 0.972772 0.231764i \(-0.0744497\pi\)
−0.687099 + 0.726563i \(0.741116\pi\)
\(252\) 0 0
\(253\) 8.12838 14.0788i 0.511027 0.885125i
\(254\) 3.38040 + 1.23037i 0.212105 + 0.0772000i
\(255\) 0 0
\(256\) 10.4639 + 8.78028i 0.653995 + 0.548767i
\(257\) −7.43054 6.23496i −0.463504 0.388926i 0.380914 0.924610i \(-0.375609\pi\)
−0.844418 + 0.535684i \(0.820054\pi\)
\(258\) 0 0
\(259\) −14.1285 5.14237i −0.877905 0.319531i
\(260\) −2.81622 + 4.87783i −0.174654 + 0.302510i
\(261\) 0 0
\(262\) 0.0567214 + 0.0982443i 0.00350426 + 0.00606955i
\(263\) 4.66336 + 26.4473i 0.287555 + 1.63081i 0.696012 + 0.718030i \(0.254956\pi\)
−0.408457 + 0.912778i \(0.633933\pi\)
\(264\) 0 0
\(265\) 31.0501 11.3013i 1.90739 0.694233i
\(266\) 0.0557126 0.315962i 0.00341596 0.0193729i
\(267\) 0 0
\(268\) 1.82962 1.53524i 0.111762 0.0937794i
\(269\) −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 \(0.498602\pi\)
\(272\) −13.5325 + 11.3551i −0.820526 + 0.688503i
\(273\) 0 0
\(274\) 0.257945 1.46288i 0.0155831 0.0883759i
\(275\) −20.9836 + 7.63742i −1.26536 + 0.460554i
\(276\) 0 0
\(277\) −0.176153 0.999013i −0.0105840 0.0600249i 0.979058 0.203580i \(-0.0652577\pi\)
−0.989642 + 0.143555i \(0.954147\pi\)
\(278\) 1.16293 + 2.01425i 0.0697479 + 0.120807i
\(279\) 0 0
\(280\) −3.88942 + 6.73667i −0.232437 + 0.402593i
\(281\) −25.8692 9.41563i −1.54323 0.561689i −0.576412 0.817159i \(-0.695548\pi\)
−0.966817 + 0.255470i \(0.917770\pi\)
\(282\) 0 0
\(283\) −20.5322 17.2286i −1.22051 1.02413i −0.998798 0.0490201i \(-0.984390\pi\)
−0.221715 0.975112i \(-0.571165\pi\)
\(284\) −7.42430 6.22973i −0.440551 0.369666i
\(285\) 0 0
\(286\) −0.309889 0.112791i −0.0183241 0.00666944i
\(287\) 7.97320 13.8100i 0.470643 0.815178i
\(288\) 0 0
\(289\) −2.18506 3.78464i −0.128533 0.222626i
\(290\) −0.735239 4.16975i −0.0431747 0.244856i
\(291\) 0 0
\(292\) 7.95944 2.89700i 0.465791 0.169534i
\(293\) −3.23980 + 18.3738i −0.189271 + 1.07341i 0.731073 + 0.682299i \(0.239020\pi\)
−0.920344 + 0.391110i \(0.872091\pi\)
\(294\) 0 0
\(295\) 33.9241 28.4657i 1.97514 1.65734i
\(296\) 3.40596 0.197967
\(297\) 0 0
\(298\) 1.66439 0.0964153
\(299\) 3.82413 3.20883i 0.221155 0.185571i
\(300\) 0 0
\(301\) 2.93243 16.6306i 0.169022 0.958573i
\(302\) −1.15865 + 0.421713i −0.0666727 + 0.0242669i
\(303\) 0 0
\(304\) −0.406004 2.30256i −0.0232859 0.132061i
\(305\) −15.2956 26.4928i −0.875825 1.51697i
\(306\) 0 0
\(307\) −16.8946 + 29.2624i −0.964227 + 1.67009i −0.252551 + 0.967584i \(0.581269\pi\)
−0.711677 + 0.702507i \(0.752064\pi\)
\(308\) 13.9837 + 5.08965i 0.796795 + 0.290010i
\(309\) 0 0
\(310\) −3.24326 2.72142i −0.184205 0.154566i
\(311\) −26.5715 22.2961i −1.50673 1.26430i −0.869833 0.493346i \(-0.835774\pi\)
−0.636896 0.770950i \(-0.719782\pi\)
\(312\) 0 0
\(313\) −3.13893 1.14248i −0.177423 0.0645766i 0.251781 0.967784i \(-0.418984\pi\)
−0.429204 + 0.903208i \(0.641206\pi\)
\(314\) 0.664726 1.15134i 0.0375127 0.0649739i
\(315\) 0 0
\(316\) −11.6182 20.1232i −0.653572 1.13202i
\(317\) −5.38879 30.5613i −0.302665 1.71650i −0.634299 0.773088i \(-0.718711\pi\)
0.331634 0.943408i \(-0.392400\pi\)
\(318\) 0 0
\(319\) −15.3384 + 5.58274i −0.858788 + 0.312573i
\(320\) −4.73063 + 26.8288i −0.264451 + 1.49977i
\(321\) 0 0
\(322\) 2.62081 2.19912i 0.146052 0.122552i
\(323\) 2.82842 0.157378
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) −0.138801 + 0.116468i −0.00768749 + 0.00645057i
\(327\) 0 0
\(328\) −0.627279 + 3.55747i −0.0346357 + 0.196429i
\(329\) 3.15524 1.14841i 0.173954 0.0633141i
\(330\) 0 0
\(331\) 0.568121 + 3.22197i 0.0312267 + 0.177096i 0.996432 0.0843970i \(-0.0268964\pi\)
−0.965205 + 0.261493i \(0.915785\pi\)
\(332\) −8.88119 15.3827i −0.487419 0.844234i
\(333\) 0 0
\(334\) −0.722527 + 1.25145i −0.0395349 + 0.0684765i
\(335\) 4.25679 + 1.54934i 0.232573 + 0.0846497i
\(336\) 0 0
\(337\) 4.87649 + 4.09186i 0.265639 + 0.222898i 0.765872 0.642993i \(-0.222308\pi\)
−0.500232 + 0.865891i \(0.666752\pi\)
\(338\) 1.64502 + 1.38034i 0.0894773 + 0.0750803i
\(339\) 0 0
\(340\) −31.9776 11.6389i −1.73423 0.631207i
\(341\) −8.16083 + 14.1350i −0.441934 + 0.765452i
\(342\) 0 0
\(343\) 7.29078 + 12.6280i 0.393665 + 0.681848i
\(344\) 0.664286 + 3.76735i 0.0358159 + 0.203122i
\(345\) 0 0
\(346\) −3.55091 + 1.29242i −0.190898 + 0.0694812i
\(347\) −1.52679 + 8.65883i −0.0819622 + 0.464831i 0.916009 + 0.401158i \(0.131392\pi\)
−0.997971 + 0.0636721i \(0.979719\pi\)
\(348\) 0 0
\(349\) 11.0312 9.25628i 0.590487 0.495478i −0.297885 0.954602i \(-0.596281\pi\)
0.888372 + 0.459124i \(0.151837\pi\)
\(350\) −4.69941 −0.251194
\(351\) 0 0
\(352\) −5.06926 −0.270192
\(353\) 25.4330 21.3409i 1.35366 1.13586i 0.375781 0.926709i \(-0.377375\pi\)
0.977883 0.209150i \(-0.0670699\pi\)
\(354\) 0 0
\(355\) 3.19198 18.1026i 0.169413 0.960787i
\(356\) −13.9564 + 5.07973i −0.739690 + 0.269225i
\(357\) 0 0
\(358\) −0.272996 1.54824i −0.0144283 0.0818268i
\(359\) −2.47257 4.28262i −0.130497 0.226028i 0.793371 0.608738i \(-0.208324\pi\)
−0.923868 + 0.382710i \(0.874991\pi\)
\(360\) 0 0
\(361\) 9.31282 16.1303i 0.490149 0.848962i
\(362\) −1.15907 0.421865i −0.0609191 0.0221728i
\(363\) 0 0
\(364\) 3.50054 + 2.93730i 0.183478 + 0.153956i
\(365\) 12.3066 + 10.3265i 0.644158 + 0.540513i
\(366\) 0 0
\(367\) 2.34214 + 0.852469i 0.122259 + 0.0444985i 0.402425 0.915453i \(-0.368167\pi\)
−0.280166 + 0.959951i \(0.590390\pi\)
\(368\) 12.4660 21.5918i 0.649837 1.12555i
\(369\) 0 0
\(370\) 1.60281 + 2.77615i 0.0833262 + 0.144325i
\(371\) −4.65513 26.4006i −0.241682 1.37065i
\(372\) 0 0
\(373\) 26.3561 9.59284i 1.36467 0.496698i 0.447173 0.894447i \(-0.352431\pi\)
0.917494 + 0.397749i \(0.130209\pi\)
\(374\) 0.345983 1.96217i 0.0178903 0.101461i
\(375\) 0 0
\(376\) −0.582677 + 0.488924i −0.0300493 + 0.0252143i
\(377\) −5.01234 −0.258149
\(378\) 0 0
\(379\) 5.13991 0.264019 0.132010 0.991248i \(-0.457857\pi\)
0.132010 + 0.991248i \(0.457857\pi\)
\(380\) 3.45025 2.89510i 0.176994 0.148516i
\(381\) 0 0
\(382\) 0.359111 2.03662i 0.0183737 0.104202i
\(383\) 0.0419788 0.0152790i 0.00214502 0.000780722i −0.340947 0.940082i \(-0.610748\pi\)
0.343092 + 0.939302i \(0.388526\pi\)
\(384\) 0 0
\(385\) 4.90111 + 27.7956i 0.249784 + 1.41659i
\(386\) −0.767463 1.32928i −0.0390628 0.0676588i
\(387\) 0 0
\(388\) −0.934167 + 1.61802i −0.0474251 + 0.0821427i
\(389\) −19.7169 7.17636i −0.999685 0.363856i −0.210222 0.977654i \(-0.567419\pi\)
−0.789463 + 0.613798i \(0.789641\pi\)
\(390\) 0 0
\(391\) 23.1045 + 19.3870i 1.16844 + 0.980441i
\(392\) 1.15207 + 0.966701i 0.0581883 + 0.0488258i
\(393\) 0 0
\(394\) −1.20249 0.437669i −0.0605804 0.0220495i
\(395\) 22.0356 38.1668i 1.10873 1.92038i
\(396\) 0 0
\(397\) 0.00122821 + 0.00212731i 6.16419e−5 + 0.000106767i 0.866056 0.499947i \(-0.166647\pi\)
−0.865995 + 0.500053i \(0.833314\pi\)
\(398\) 0.311896 + 1.76885i 0.0156339 + 0.0886645i
\(399\) 0 0
\(400\) −32.1814 + 11.7131i −1.60907 + 0.585654i
\(401\) 4.38571 24.8726i 0.219012 1.24208i −0.654795 0.755807i \(-0.727245\pi\)
0.873807 0.486273i \(-0.161644\pi\)
\(402\) 0 0
\(403\) −3.83940 + 3.22164i −0.191254 + 0.160481i
\(404\) −11.0485 −0.549684
\(405\) 0 0
\(406\) −3.43513 −0.170483
\(407\) 9.46680 7.94359i 0.469252 0.393749i
\(408\) 0 0
\(409\) −4.04401 + 22.9347i −0.199964 + 1.13405i 0.705207 + 0.709001i \(0.250854\pi\)
−0.905171 + 0.425048i \(0.860257\pi\)
\(410\) −3.19484 + 1.16283i −0.157782 + 0.0574279i
\(411\) 0 0
\(412\) 3.22431 + 18.2859i 0.158850 + 0.900884i
\(413\) −17.9643 31.1151i −0.883965 1.53107i
\(414\) 0 0
\(415\) 16.8446 29.1756i 0.826867 1.43218i
\(416\) −1.46277 0.532404i −0.0717181 0.0261033i
\(417\) 0 0
\(418\) 0.202011 + 0.169507i 0.00988069 + 0.00829088i
\(419\) 23.9683 + 20.1118i 1.17093 + 0.982524i 0.999996 0.00275857i \(-0.000878081\pi\)
0.170931 + 0.985283i \(0.445323\pi\)
\(420\) 0 0
\(421\) −28.6884 10.4417i −1.39819 0.508899i −0.470548 0.882374i \(-0.655944\pi\)
−0.927640 + 0.373476i \(0.878166\pi\)
\(422\) 1.80424 3.12503i 0.0878289 0.152124i
\(423\) 0 0
\(424\) 3.03640 + 5.25920i 0.147461 + 0.255409i
\(425\) −7.19406 40.7995i −0.348963 1.97907i
\(426\) 0 0
\(427\) −23.3221 + 8.48856i −1.12864 + 0.410790i
\(428\) −0.437289 + 2.47999i −0.0211372 + 0.119875i
\(429\) 0 0
\(430\) −2.75811 + 2.31433i −0.133008 + 0.111607i
\(431\) 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 \(0.505818\pi\)
\(434\) −2.63128 + 2.20790i −0.126305 + 0.105983i
\(435\) 0 0
\(436\) 2.53390 14.3705i 0.121352 0.688221i
\(437\) −3.75116 + 1.36531i −0.179442 + 0.0653116i
\(438\) 0 0
\(439\) 5.22844 + 29.6519i 0.249540 + 1.41521i 0.809709 + 0.586831i \(0.199625\pi\)
−0.560170 + 0.828378i \(0.689264\pi\)
\(440\) −3.19685 5.53711i −0.152404 0.263971i
\(441\) 0 0
\(442\) 0.305914 0.529859i 0.0145508 0.0252028i
\(443\) 12.8377 + 4.67254i 0.609937 + 0.221999i 0.628476 0.777829i \(-0.283679\pi\)
−0.0185388 + 0.999828i \(0.505901\pi\)
\(444\) 0 0
\(445\) −21.5790 18.1069i −1.02294 0.858351i
\(446\) −3.12432 2.62162i −0.147941 0.124137i
\(447\) 0 0
\(448\) 20.7692 + 7.55937i 0.981253 + 0.357147i
\(449\) −10.9995 + 19.0516i −0.519097 + 0.899102i 0.480657 + 0.876909i \(0.340398\pi\)
−0.999754 + 0.0221934i \(0.992935\pi\)
\(450\) 0 0
\(451\) 6.55346 + 11.3509i 0.308590 + 0.534494i
\(452\) 3.19931 + 18.1442i 0.150483 + 0.853432i
\(453\) 0 0
\(454\) 1.70413 0.620254i 0.0799790 0.0291100i
\(455\) −1.50501 + 8.53535i −0.0705560 + 0.400143i
\(456\) 0 0
\(457\) −1.14051 + 0.957000i −0.0533507 + 0.0447666i −0.669073 0.743197i \(-0.733309\pi\)
0.615722 + 0.787963i \(0.288864\pi\)
\(458\) 2.40132 0.112206
\(459\) 0 0
\(460\) 48.0281 2.23932
\(461\) 5.44913 4.57236i 0.253791 0.212956i −0.507011 0.861939i \(-0.669250\pi\)
0.760803 + 0.648983i \(0.224805\pi\)
\(462\) 0 0
\(463\) −4.60875 + 26.1375i −0.214187 + 1.21471i 0.668125 + 0.744049i \(0.267097\pi\)
−0.882312 + 0.470665i \(0.844014\pi\)
\(464\) −23.5237 + 8.56192i −1.09206 + 0.397477i
\(465\) 0 0
\(466\) 0.228270 + 1.29458i 0.0105744 + 0.0599705i
\(467\) 13.0760 + 22.6482i 0.605084 + 1.04804i 0.992038 + 0.125937i \(0.0401937\pi\)
−0.386955 + 0.922099i \(0.626473\pi\)
\(468\) 0 0
\(469\) 1.83760 3.18282i 0.0848525 0.146969i
\(470\) −0.672718 0.244849i −0.0310302 0.0112941i
\(471\) 0 0
\(472\) 6.23479 + 5.23161i 0.286979 + 0.240804i
\(473\) 10.6328 + 8.92201i 0.488898 + 0.410234i
\(474\) 0 0
\(475\) 5.15260 + 1.87539i 0.236418 + 0.0860490i
\(476\) −13.8043 + 23.9098i −0.632719 + 1.09590i
\(477\) 0 0
\(478\) −1.43213 2.48052i −0.0655040 0.113456i
\(479\) 1.80708 + 10.2485i 0.0825675 + 0.468264i 0.997855 + 0.0654625i \(0.0208523\pi\)
−0.915288 + 0.402801i \(0.868037\pi\)
\(480\) 0 0
\(481\) 3.56599 1.29791i 0.162595 0.0591798i
\(482\) 0.436091 2.47320i 0.0198634 0.112651i
\(483\) 0 0
\(484\) 7.23111 6.06762i 0.328687 0.275801i
\(485\) −3.54358 −0.160906
\(486\) 0 0
\(487\) −18.4664 −0.836791 −0.418396 0.908265i \(-0.637407\pi\)
−0.418396 + 0.908265i \(0.637407\pi\)
\(488\) 4.30689 3.61391i 0.194964 0.163594i
\(489\) 0 0
\(490\) −0.245792 + 1.39396i −0.0111038 + 0.0629725i
\(491\) −15.9502 + 5.80541i −0.719824 + 0.261995i −0.675851 0.737038i \(-0.736224\pi\)
−0.0439731 + 0.999033i \(0.514002\pi\)
\(492\) 0 0
\(493\) −5.25865 29.8233i −0.236838 1.34317i
\(494\) 0.0404890 + 0.0701289i 0.00182168 + 0.00315525i
\(495\) 0 0
\(496\) −12.5158 + 21.6780i −0.561976 + 0.973371i
\(497\) −14.0140 5.10066i −0.628612 0.228796i
\(498\) 0 0
\(499\) 18.8801 + 15.8423i 0.845188 + 0.709197i 0.958724 0.284337i \(-0.0917735\pi\)
−0.113537 + 0.993534i \(0.536218\pi\)
\(500\) −22.3416 18.7468i −0.999145 0.838382i
\(501\) 0 0
\(502\) −1.47132 0.535517i −0.0656682 0.0239013i
\(503\) 20.0569 34.7395i 0.894291 1.54896i 0.0596120 0.998222i \(-0.481014\pi\)
0.834679 0.550736i \(-0.185653\pi\)
\(504\) 0 0
\(505\) −10.4776 18.1478i −0.466248 0.807564i
\(506\) 0.488304 + 2.76931i 0.0217077 + 0.123111i
\(507\) 0 0
\(508\) 38.5005 14.0130i 1.70818 0.621728i
\(509\) −0.859301 + 4.87334i −0.0380879 + 0.216007i −0.997911 0.0645972i \(-0.979424\pi\)
0.959824 + 0.280604i \(0.0905348\pi\)
\(510\) 0 0
\(511\) 9.98445 8.37795i 0.441686 0.370619i
\(512\) −13.0229 −0.575537
\(513\) 0 0
\(514\) 1.67785 0.0740066
\(515\) −26.9779 + 22.6372i −1.18879 + 0.997513i
\(516\) 0 0
\(517\) −0.479242 + 2.71791i −0.0210770 + 0.119534i
\(518\) 2.44390 0.889506i 0.107379 0.0390827i
\(519\) 0 0
\(520\) −0.340932 1.93352i −0.0149508 0.0847905i
\(521\) 3.86979 + 6.70267i 0.169539 + 0.293649i 0.938258 0.345937i \(-0.112439\pi\)
−0.768719 + 0.639586i \(0.779106\pi\)
\(522\) 0 0
\(523\) −18.0070 + 31.1891i −0.787391 + 1.36380i 0.140169 + 0.990128i \(0.455236\pi\)
−0.927560 + 0.373674i \(0.878098\pi\)
\(524\) 1.21412 + 0.441903i 0.0530390 + 0.0193046i
\(525\) 0 0
\(526\) −3.55851 2.98595i −0.155159 0.130194i
\(527\) −23.1967 19.4644i −1.01047 0.847882i
\(528\) 0 0
\(529\) −18.3874 6.69247i −0.799453 0.290977i
\(530\) −2.85780 + 4.94986i −0.124135 + 0.215008i
\(531\) 0 0
\(532\) −1.82705 3.16455i −0.0792129 0.137201i
\(533\) 0.698901 + 3.96367i 0.0302728 + 0.171685i
\(534\) 0 0
\(535\) −4.48820 + 1.63357i −0.194042 + 0.0706255i
\(536\) −0.144570 + 0.819899i −0.00624448 + 0.0354142i
\(537\) 0 0
\(538\) 1.55548 1.30520i 0.0670615 0.0562713i
\(539\) 5.45676 0.235039
\(540\) 0 0
\(541\) −24.4147 −1.04967 −0.524834 0.851204i \(-0.675873\pi\)
−0.524834 + 0.851204i \(0.675873\pi\)
\(542\) −0.0191574 + 0.0160750i −0.000822881 + 0.000690479i
\(543\) 0 0
\(544\) 1.63314 9.26199i 0.0700203 0.397105i
\(545\) 26.0072 9.46585i 1.11403 0.405473i
\(546\) 0 0
\(547\) −4.92497 27.9309i −0.210577 1.19424i −0.888420 0.459032i \(-0.848196\pi\)
0.677843 0.735207i \(-0.262915\pi\)
\(548\) −8.45913 14.6516i −0.361356 0.625887i
\(549\) 0 0
\(550\) 1.93130 3.34512i 0.0823511 0.142636i
\(551\) 3.76640 + 1.37086i 0.160454 + 0.0584006i
\(552\) 0 0
\(553\) −27.3902 22.9831i −1.16475 0.977340i
\(554\) 0.134419 + 0.112791i 0.00571090 + 0.00479201i
\(555\) 0 0
\(556\) 24.8924 + 9.06010i 1.05567 + 0.384234i
\(557\) −18.4687 + 31.9887i −0.782542 + 1.35540i 0.147914 + 0.989000i \(0.452744\pi\)
−0.930456 + 0.366403i \(0.880589\pi\)
\(558\) 0 0
\(559\) 2.13113 + 3.69123i 0.0901372 + 0.156122i
\(560\) 7.51656 + 42.6285i 0.317633 + 1.80138i
\(561\) 0 0
\(562\) 4.47475 1.62868i 0.188756 0.0687016i
\(563\) −3.95491 + 22.4294i −0.166680 + 0.945287i 0.780636 + 0.624986i \(0.214895\pi\)
−0.947316 + 0.320301i \(0.896216\pi\)
\(564\) 0 0
\(565\) −26.7688 + 22.4617i −1.12617 + 0.944971i
\(566\) 4.63625 0.194876
\(567\) 0 0
\(568\) 3.37833 0.141752
\(569\) −23.6468 + 19.8421i −0.991327 + 0.831822i −0.985759 0.168162i \(-0.946217\pi\)
−0.00556781 + 0.999984i \(0.501772\pi\)
\(570\) 0 0
\(571\) 2.22626 12.6257i 0.0931659 0.528370i −0.902128 0.431468i \(-0.857996\pi\)
0.995294 0.0969016i \(-0.0308932\pi\)
\(572\) −3.52943 + 1.28461i −0.147573 + 0.0537122i
\(573\) 0 0
\(574\) 0.478981 + 2.71644i 0.0199923 + 0.113382i
\(575\) 29.2354 + 50.6372i 1.21920 + 2.11172i
\(576\) 0 0
\(577\) 11.7632 20.3745i 0.489708 0.848200i −0.510222 0.860043i \(-0.670437\pi\)
0.999930 + 0.0118433i \(0.00376992\pi\)
\(578\) 0.710338 + 0.258542i 0.0295462 + 0.0107539i
\(579\) 0 0
\(580\) −36.9411 30.9973i −1.53390 1.28709i
\(581\) −20.9377 17.5688i −0.868641 0.728877i
\(582\) 0 0
\(583\) 20.7055 + 7.53618i 0.857533 + 0.312117i
\(584\) −1.47628 + 2.55699i −0.0610888 + 0.105809i
\(585\) 0 0
\(586\) −1.61363 2.79489i −0.0666584 0.115456i
\(587\) −1.97741 11.2144i −0.0816164 0.462870i −0.998036 0.0626498i \(-0.980045\pi\)
0.916419 0.400220i \(-0.131066\pi\)
\(588\) 0 0
\(589\) 3.76614 1.37076i 0.155181 0.0564812i
\(590\) −1.33018 + 7.54383i −0.0547627 + 0.310575i
\(591\) 0 0
\(592\) 14.5187 12.1826i 0.596715 0.500703i
\(593\) 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
\(596\) 14.5213 12.1848i 0.594816 0.499110i
\(597\) 0 0
\(598\) −0.149946 + 0.850386i −0.00613175 + 0.0347749i
\(599\) 44.5021 16.1975i 1.81831 0.661810i 0.822669 0.568520i \(-0.192484\pi\)
0.995639 0.0932901i \(-0.0297384\pi\)
\(600\) 0 0
\(601\) −5.40175 30.6348i −0.220342 1.24962i −0.871392 0.490587i \(-0.836782\pi\)
0.651050 0.759035i \(-0.274329\pi\)
\(602\) 1.46054 + 2.52973i 0.0595271 + 0.103104i
\(603\) 0 0
\(604\) −7.02156 + 12.1617i −0.285703 + 0.494853i
\(605\) 16.8238 + 6.12338i 0.683986 + 0.248951i
\(606\) 0 0
\(607\) 22.5879 + 18.9535i 0.916815 + 0.769300i 0.973403 0.229098i \(-0.0735777\pi\)
−0.0565879 + 0.998398i \(0.518022\pi\)
\(608\) 0.953551 + 0.800125i 0.0386716 + 0.0324493i
\(609\) 0 0
\(610\) 4.97243 + 1.80982i 0.201328 + 0.0732773i
\(611\) −0.423740 + 0.733939i −0.0171427 + 0.0296920i
\(612\) 0 0
\(613\) 3.05214 + 5.28646i 0.123275 + 0.213518i 0.921057 0.389427i \(-0.127327\pi\)
−0.797782 + 0.602945i \(0.793994\pi\)
\(614\) −1.01493 5.75593i −0.0409591 0.232291i
\(615\) 0 0
\(616\) −4.87442 + 1.77414i −0.196396 + 0.0714823i
\(617\) 3.32017 18.8296i 0.133665 0.758052i −0.842115 0.539298i \(-0.818690\pi\)
0.975780 0.218754i \(-0.0701993\pi\)
\(618\) 0 0
\(619\) −5.17375 + 4.34129i −0.207951 + 0.174491i −0.740814 0.671710i \(-0.765560\pi\)
0.532864 + 0.846201i \(0.321116\pi\)
\(620\) −48.2198 −1.93655
\(621\) 0 0
\(622\) 5.99994 0.240576
\(623\) −17.5072 + 14.6903i −0.701411 + 0.588553i
\(624\) 0 0
\(625\) 1.82437 10.3465i 0.0729749 0.413861i
\(626\) 0.542959 0.197621i 0.0217010 0.00789853i
\(627\) 0 0
\(628\) −2.62931 14.9115i −0.104921 0.595035i
\(629\) 11.4638 + 19.8559i 0.457091 + 0.791705i
\(630\) 0 0
\(631\) 0.228453 0.395693i 0.00909458 0.0157523i −0.861442 0.507855i \(-0.830438\pi\)
0.870537 + 0.492103i \(0.163772\pi\)
\(632\) 7.61122 + 2.77026i 0.302758 + 0.110195i
\(633\) 0 0
\(634\) 4.11207 + 3.45044i 0.163311 + 0.137034i
\(635\) 59.5282 + 49.9501i 2.36231 + 1.98221i
\(636\) 0 0
\(637\) 1.57458 + 0.573102i 0.0623873 + 0.0227071i
\(638\) 1.41173 2.44519i 0.0558909 0.0968058i
\(639\) 0 0
\(640\) −9.95805 17.2479i −0.393627 0.681781i
\(641\) −0.498549 2.82741i −0.0196915 0.111676i 0.973378 0.229207i \(-0.0736132\pi\)
−0.993069 + 0.117531i \(0.962502\pi\)
\(642\) 0 0
\(643\) 1.60015 0.582407i 0.0631037 0.0229679i −0.310275 0.950647i \(-0.600421\pi\)
0.373379 + 0.927679i \(0.378199\pi\)
\(644\) 6.76628 38.3735i 0.266629 1.51213i
\(645\) 0 0
\(646\) −0.374786 + 0.314483i −0.0147458 + 0.0123732i
\(647\) 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
\(650\) 0.908615 0.762419i 0.0356388 0.0299045i
\(651\) 0 0
\(652\) −0.358350 + 2.03231i −0.0140341 + 0.0795912i
\(653\) 40.9405 14.9011i 1.60213 0.583126i 0.622265 0.782807i \(-0.286213\pi\)
0.979861 + 0.199681i \(0.0639905\pi\)
\(654\) 0 0
\(655\) 0.425533 + 2.41332i 0.0166270 + 0.0942962i
\(656\) 10.0507 + 17.4083i 0.392412 + 0.679678i
\(657\) 0 0
\(658\) −0.290404 + 0.502994i −0.0113211 + 0.0196087i
\(659\) −23.9443 8.71501i −0.932737 0.339489i −0.169443 0.985540i \(-0.554197\pi\)
−0.763294 + 0.646051i \(0.776419\pi\)
\(660\) 0 0
\(661\) 26.1736 + 21.9623i 1.01803 + 0.854233i 0.989379 0.145357i \(-0.0464330\pi\)
0.0286555 + 0.999589i \(0.490877\pi\)
\(662\) −0.433521 0.363767i −0.0168493 0.0141382i
\(663\) 0 0
\(664\) 5.81819 + 2.11765i 0.225790 + 0.0821807i
\(665\) 3.46529 6.00207i 0.134378 0.232750i
\(666\) 0 0
\(667\) 21.3702 + 37.0143i 0.827459 + 1.43320i
\(668\) 2.85794 + 16.2082i 0.110577 + 0.627112i
\(669\) 0 0
\(670\) −0.736322 + 0.267999i −0.0284466 + 0.0103537i
\(671\) 3.54234 20.0896i 0.136751 0.775551i
\(672\) 0 0
\(673\) −22.6318 + 18.9903i −0.872392 + 0.732024i −0.964600 0.263716i \(-0.915052\pi\)
0.0922084 + 0.995740i \(0.470607\pi\)
\(674\) −1.10113 −0.0424140
\(675\) 0 0
\(676\) 24.4577 0.940680
\(677\) 31.2395 26.2130i 1.20063 1.00745i 0.201019 0.979587i \(-0.435575\pi\)
0.999612 0.0278613i \(-0.00886968\pi\)
\(678\) 0 0
\(679\) −0.499227 + 2.83126i −0.0191586 + 0.108654i
\(680\) 11.1467 4.05707i 0.427457 0.155581i
\(681\) 0 0
\(682\) −0.490253 2.78036i −0.0187728 0.106466i
\(683\) −15.8213 27.4033i −0.605384 1.04856i −0.991991 0.126312i \(-0.959686\pi\)
0.386606 0.922245i \(-0.373647\pi\)
\(684\) 0 0
\(685\) 16.0441 27.7891i 0.613012 1.06177i
\(686\) −2.37015 0.862664i −0.0904927 0.0329367i
\(687\) 0 0
\(688\) 16.3070 + 13.6832i 0.621697 + 0.521666i
\(689\) 5.18321 + 4.34923i 0.197464 + 0.165692i
\(690\) 0 0
\(691\) 26.8609 + 9.77656i 1.02184 + 0.371918i 0.797967 0.602701i \(-0.205909\pi\)
0.223869 + 0.974619i \(0.428131\pi\)
\(692\) −21.5190 + 37.2719i −0.818028 + 1.41687i
\(693\) 0 0
\(694\) −0.760438 1.31712i −0.0288658 0.0499971i
\(695\) 8.72449 + 49.4791i 0.330939 + 1.87685i
\(696\) 0 0
\(697\) −22.8505 + 8.31688i −0.865523 + 0.315024i
\(698\) −0.432539 + 2.45305i −0.0163718 + 0.0928493i
\(699\) 0 0
\(700\) −41.0011 + 34.4040i −1.54969 + 1.30035i
\(701\) −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
\(704\) −13.9164 + 11.6772i −0.524493 + 0.440102i
\(705\) 0 0
\(706\) −0.997241 + 5.65564i −0.0375317 + 0.212853i
\(707\) −15.9758 + 5.81472i −0.600832 + 0.218685i
\(708\) 0 0
\(709\) 1.39161 + 7.89224i 0.0522632 + 0.296399i 0.999725 0.0234711i \(-0.00747176\pi\)
−0.947461 + 0.319870i \(0.896361\pi\)
\(710\) 1.58981 + 2.75363i 0.0596646 + 0.103342i
\(711\) 0 0
\(712\) 2.58857 4.48354i 0.0970108 0.168028i
\(713\) 40.1601 + 14.6171i 1.50401 + 0.547413i
\(714\) 0 0
\(715\) −5.45709 4.57905i −0.204084 0.171247i
\(716\) −13.7163 11.5094i −0.512603 0.430125i
\(717\) 0 0
\(718\) 0.803805 + 0.292561i 0.0299977 + 0.0109183i
\(719\) −13.4913 + 23.3676i −0.503140 + 0.871464i 0.496854 + 0.867834i \(0.334489\pi\)
−0.999993 + 0.00362928i \(0.998845\pi\)
\(720\) 0 0
\(721\) 14.2860 + 24.7440i 0.532037 + 0.921515i
\(722\) 0.559458 + 3.17284i 0.0208209 + 0.118081i
\(723\) 0 0
\(724\) −13.2010 + 4.80476i −0.490610 + 0.178568i
\(725\) 10.1946 57.8165i 0.378618 2.14725i
\(726\) 0 0
\(727\) −11.2565 + 9.44534i −0.417481 + 0.350308i −0.827204 0.561902i \(-0.810070\pi\)
0.409723 + 0.912210i \(0.365625\pi\)
\(728\) −1.59288 −0.0590360
\(729\) 0 0
\(730\) −2.77889 −0.102851
\(731\) −19.7268 + 16.5528i −0.729623 + 0.612227i
\(732\) 0 0
\(733\) −5.44279 + 30.8676i −0.201034 + 1.14012i 0.702526 + 0.711658i \(0.252056\pi\)
−0.903560 + 0.428462i \(0.859056\pi\)
\(734\) −0.405134 + 0.147457i −0.0149538 + 0.00544272i
\(735\) 0 0
\(736\) 2.30494 + 13.0719i 0.0849610 + 0.481838i
\(737\) 1.51039 + 2.61607i 0.0556359 + 0.0963642i
\(738\) 0 0
\(739\) −0.241454 + 0.418211i −0.00888205 + 0.0153842i −0.870432 0.492288i \(-0.836161\pi\)
0.861550 + 0.507672i \(0.169494\pi\)
\(740\) 34.3081 + 12.4871i 1.26119 + 0.459035i
\(741\) 0 0
\(742\) 3.55223 + 2.98068i 0.130407 + 0.109424i
\(743\) 32.9788 + 27.6725i 1.20987 + 1.01520i 0.999292 + 0.0376288i \(0.0119804\pi\)
0.210582 + 0.977576i \(0.432464\pi\)
\(744\) 0 0
\(745\) 33.7852 + 12.2968i 1.23779 + 0.450520i
\(746\) −2.42578 + 4.20157i −0.0888140 + 0.153830i
\(747\) 0 0
\(748\) −11.3462 19.6523i −0.414860 0.718558i
\(749\) 0.672887 + 3.81613i 0.0245867 + 0.139438i
\(750\) 0 0
\(751\) −41.2728 + 15.0221i −1.50607 + 0.548163i −0.957623 0.288024i \(-0.907002\pi\)
−0.548443 + 0.836188i \(0.684779\pi\)
\(752\) −0.734985 + 4.16831i −0.0268022 + 0.152003i
\(753\) 0 0
\(754\) 0.664172 0.557306i 0.0241877 0.0202959i
\(755\) −26.6350 −0.969346
\(756\) 0 0
\(757\) 22.4143 0.814661 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(758\) −0.681075 + 0.571490i −0.0247378 + 0.0207575i
\(759\) 0 0
\(760\) −0.272626 + 1.54614i −0.00988920 + 0.0560844i
\(761\) 9.39386 3.41909i 0.340527 0.123942i −0.166095 0.986110i \(-0.553116\pi\)
0.506623 + 0.862168i \(0.330894\pi\)
\(762\) 0 0
\(763\) −3.89909 22.1128i −0.141157 0.800538i
\(764\) −11.7768 20.3980i −0.426069 0.737972i
\(765\) 0 0
\(766\) −0.00386367 + 0.00669207i −0.000139600 + 0.000241794i
\(767\) 8.52136 + 3.10152i 0.307688 + 0.111989i
\(768\) 0 0
\(769\) −5.74242 4.81846i −0.207077 0.173758i 0.533351 0.845894i \(-0.320933\pi\)
−0.740428 + 0.672136i \(0.765377\pi\)
\(770\) −3.73994 3.13818i −0.134778 0.113092i
\(771\) 0 0
\(772\) −16.4275 5.97912i −0.591238 0.215193i
\(773\) 9.91954 17.1812i 0.356781 0.617963i −0.630640 0.776076i \(-0.717207\pi\)
0.987421 + 0.158112i \(0.0505408\pi\)
\(774\) 0 0
\(775\) −29.3521 50.8394i −1.05436 1.82620i
\(776\) −0.113090 0.641367i −0.00405971 0.0230237i
\(777\) 0 0
\(778\) 3.41055 1.24134i 0.122274 0.0445041i
\(779\) 0.558877 3.16955i 0.0200239 0.113561i