Properties

Label 729.2.e.j.406.2
Level $729$
Weight $2$
Character 729.406
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 406.2
Root \(-0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.406
Dual form 729.2.e.j.325.2

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.132507 + 0.111187i 0.0936968 + 0.0786209i 0.688433 0.725300i \(-0.258299\pi\)
−0.594736 + 0.803921i \(0.702743\pi\)
\(3\) 0 0
\(4\) −0.342101 1.94015i −0.171050 0.970075i
\(5\) 3.51122 + 1.27798i 1.57027 + 0.571530i 0.973059 0.230557i \(-0.0740550\pi\)
0.597207 + 0.802087i \(0.296277\pi\)
\(6\) 0 0
\(7\) 0.526414 2.98544i 0.198966 1.12839i −0.707691 0.706522i \(-0.750263\pi\)
0.906657 0.421869i \(-0.138626\pi\)
\(8\) 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 \(-0.488535\pi\)
0.669957 + 0.742400i \(0.266313\pi\)
\(12\) 0 0
\(13\) −0.586130 + 0.491822i −0.162563 + 0.136407i −0.720441 0.693517i \(-0.756060\pi\)
0.557877 + 0.829923i \(0.311616\pi\)
\(14\) 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 −0.997445 0.0714442i \(-0.977239\pi\)
0.436850 0.899534i \(-0.356094\pi\)
\(18\) 0 0
\(19\) 0.305922 0.529872i 0.0701833 0.121561i −0.828798 0.559548i \(-0.810975\pi\)
0.898982 + 0.437987i \(0.144308\pi\)
\(20\) 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 0.839996 + 0.542593i \(0.182557\pi\)
−0.603760 + 0.797166i \(0.706332\pi\)
\(24\) 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 \(-0.485900\pi\)
−0.976152 + 0.217087i \(0.930344\pi\)
\(30\) 0 0
\(31\) 1.13747 + 6.45091i 0.204296 + 1.15862i 0.898544 + 0.438883i \(0.144626\pi\)
−0.694249 + 0.719735i \(0.744263\pi\)
\(32\) −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 0.586946 0.809626i \(-0.300330\pi\)
−0.994630 + 0.103497i \(0.966997\pi\)
\(38\) 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 \(-0.587487\pi\)
0.900716 + 0.434409i \(0.143043\pi\)
\(42\) 0 0
\(43\) −5.23463 + 1.90525i −0.798273 + 0.290548i −0.708771 0.705439i \(-0.750750\pi\)
−0.0895024 + 0.995987i \(0.528528\pi\)
\(44\) −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 \(-0.918703\pi\)
0.995617 + 0.0935267i \(0.0298141\pi\)
\(48\) 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 \(-0.292234\pi\)
0.607346 + 0.794437i \(0.292234\pi\)
\(54\) 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 \(-0.108404\pi\)
0.507347 + 0.861742i \(0.330626\pi\)
\(60\) 0 0
\(61\) 1.42166 8.06263i 0.182025 1.03231i −0.747694 0.664043i \(-0.768839\pi\)
0.929719 0.368270i \(-0.120050\pi\)
\(62\) −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 −0.697752 0.716339i \(-0.745816\pi\)
0.584293 + 0.811543i \(0.301372\pi\)
\(68\) −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 \(-0.0723738\pi\)
−0.682346 + 0.731029i \(0.739040\pi\)
\(72\) 0 0
\(73\) −2.14972 + 3.72343i −0.251606 + 0.435795i −0.963968 0.266017i \(-0.914292\pi\)
0.712362 + 0.701812i \(0.247625\pi\)
\(74\) 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 −0.0273498 0.999626i \(-0.508707\pi\)
−0.989189 + 0.146649i \(0.953151\pi\)
\(80\) −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 \(-0.113011\pi\)
−0.179524 + 0.983754i \(0.557456\pi\)
\(84\) 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 \(-0.964170\pi\)
0.594113 + 0.804382i \(0.297503\pi\)
\(90\) 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 −0.296382 0.955070i \(-0.595780\pi\)
0.386865 + 0.922136i \(0.373558\pi\)
\(98\) −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 0.897247 + 0.441529i \(0.145564\pi\)
−0.994148 + 0.108025i \(0.965547\pi\)
\(102\) 0 0
\(103\) 8.85662 + 3.22355i 0.872669 + 0.317625i 0.739247 0.673434i \(-0.235181\pi\)
0.133421 + 0.991059i \(0.457404\pi\)
\(104\) 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 \(-0.519680\pi\)
−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 \(0.615426\pi\)
\(110\) 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 \(-0.533868\pi\)
−0.720505 + 0.693450i \(0.756090\pi\)
\(114\) 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 −0.127505 + 0.991838i \(0.540697\pi\)
−0.795204 + 0.606342i \(0.792636\pi\)
\(128\) −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 \(-0.0646764\pi\)
−0.989379 + 0.145362i \(0.953565\pi\)
\(132\) 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 \(-0.158216\pi\)
−0.316955 + 0.948441i \(0.602660\pi\)
\(138\) 0 0
\(139\) 2.33490 + 13.2419i 0.198043 + 1.12316i 0.908017 + 0.418932i \(0.137596\pi\)
−0.709974 + 0.704228i \(0.751293\pi\)
\(140\) −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 \(-0.593266\pi\)
0.892681 + 0.450690i \(0.148822\pi\)
\(150\) 0 0
\(151\) 6.69832 2.43799i 0.545101 0.198401i −0.0547672 0.998499i \(-0.517442\pi\)
0.599869 + 0.800098i \(0.295219\pi\)
\(152\) −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 0.0373379 0.999303i \(-0.488112\pi\)
−0.613737 + 0.789511i \(0.710334\pi\)
\(158\) −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 \(-0.493657\pi\)
−0.627397 + 0.778700i \(0.715880\pi\)
\(168\) 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 \(-0.923029\pi\)
−0.589834 + 0.807525i \(0.700807\pi\)
\(174\) 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 \(-0.0563549\pi\)
−0.644709 + 0.764428i \(0.723022\pi\)
\(180\) 0 0
\(181\) 3.56539 6.17543i 0.265013 0.459016i −0.702554 0.711630i \(-0.747957\pi\)
0.967567 + 0.252614i \(0.0812904\pi\)
\(182\) −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 \(-0.135395\pi\)
−0.248203 + 0.968708i \(0.579840\pi\)
\(192\) 0 0
\(193\) −1.54089 8.73883i −0.110916 0.629034i −0.988692 0.149963i \(-0.952085\pi\)
0.877776 0.479071i \(-0.159027\pi\)
\(194\) 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 \(-0.918223\pi\)
0.703641 + 0.710556i \(0.251557\pi\)
\(198\) 0 0
\(199\) 5.19187 + 8.99259i 0.368042 + 0.637468i 0.989259 0.146171i \(-0.0466948\pi\)
−0.621217 + 0.783638i \(0.713362\pi\)
\(200\) 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 −0.436729 0.899593i \(-0.643863\pi\)
−0.912801 + 0.408404i \(0.866085\pi\)
\(212\) −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 −0.467380 0.884057i \(-0.654802\pi\)
0.741558 0.670888i \(-0.234087\pi\)
\(224\) −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 \(-0.497996\pi\)
0.647597 + 0.761983i \(0.275774\pi\)
\(228\) 0 0
\(229\) −10.6345 + 8.92345i −0.702751 + 0.589678i −0.922555 0.385866i \(-0.873903\pi\)
0.219804 + 0.975544i \(0.429458\pi\)
\(230\) −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 \(-0.246747\pi\)
−0.963230 + 0.268676i \(0.913414\pi\)
\(234\) 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 0.924673 + 0.380763i \(0.124339\pi\)
−0.738679 + 0.674057i \(0.764550\pi\)
\(240\) 0 0
\(241\) −11.1218 9.33230i −0.716419 0.601147i 0.209973 0.977707i \(-0.432662\pi\)
−0.926392 + 0.376560i \(0.877107\pi\)
\(242\) −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 \(-0.925550\pi\)
0.687099 + 0.726563i \(0.258884\pi\)
\(252\) 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 \(-0.624391\pi\)
0.844418 + 0.535684i \(0.179946\pi\)
\(258\) 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 0.408457 + 0.912778i \(0.366067\pi\)
−0.696012 + 0.718030i \(0.745044\pi\)
\(264\) 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 \(-0.383505\pi\)
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 \(0.498602\pi\)
\(272\) 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 −0.989642 0.143555i \(-0.954147\pi\)
0.979058 + 0.203580i \(0.0652577\pi\)
\(278\) −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 \(-0.304452\pi\)
0.966817 + 0.255470i \(0.0822302\pi\)
\(282\) 0 0
\(283\) −20.5322 + 17.2286i −1.22051 + 1.02413i −0.221715 + 0.975112i \(0.571165\pi\)
−0.998798 + 0.0490201i \(0.984390\pi\)
\(284\) 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 0.920344 + 0.391110i \(0.127909\pi\)
−0.731073 + 0.682299i \(0.760980\pi\)
\(294\) 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 −0.711677 0.702507i \(-0.752064\pi\)
−0.252551 0.967584i \(-0.581269\pi\)
\(308\) −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 0.636896 0.770950i \(-0.280218\pi\)
0.869833 0.493346i \(-0.164226\pi\)
\(312\) 0 0
\(313\) −3.13893 + 1.14248i −0.177423 + 0.0645766i −0.429204 0.903208i \(-0.641206\pi\)
0.251781 + 0.967784i \(0.418984\pi\)
\(314\) −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 −0.331634 0.943408i \(-0.607600\pi\)
0.634299 0.773088i \(-0.281289\pi\)
\(318\) 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 −0.965205 0.261493i \(-0.915785\pi\)
0.996432 + 0.0843970i \(0.0268964\pi\)
\(332\) 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 −0.500232 0.865891i \(-0.666752\pi\)
0.765872 + 0.642993i \(0.222308\pi\)
\(338\) −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 0.997971 + 0.0636721i \(0.0202812\pi\)
−0.916009 + 0.401158i \(0.868608\pi\)
\(348\) 0 0
\(349\) 11.0312 + 9.25628i 0.590487 + 0.495478i 0.888372 0.459124i \(-0.151837\pi\)
−0.297885 + 0.954602i \(0.596281\pi\)
\(350\) 4.69941 0.251194
\(351\) 0 0
\(352\) −5.06926 −0.270192
\(353\) −25.4330 21.3409i −1.35366 1.13586i −0.977883 0.209150i \(-0.932930\pi\)
−0.375781 0.926709i \(-0.622625\pi\)
\(354\) 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 \(-0.791676\pi\)
0.923868 + 0.382710i \(0.125009\pi\)
\(360\) 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 −0.280166 0.959951i \(-0.590390\pi\)
0.402425 + 0.915453i \(0.368167\pi\)
\(368\) −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 0.917494 0.397749i \(-0.130209\pi\)
0.447173 + 0.894447i \(0.352431\pi\)
\(374\) −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 \(-0.389252\pi\)
−0.343092 + 0.939302i \(0.611474\pi\)
\(384\) 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 \(-0.432581\pi\)
0.789463 + 0.613798i \(0.210359\pi\)
\(390\) 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 −0.865995 0.500053i \(-0.833314\pi\)
0.866056 + 0.499947i \(0.166647\pi\)
\(398\) −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 −0.873807 0.486273i \(-0.838356\pi\)
0.654795 0.755807i \(-0.272755\pi\)
\(402\) 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 −0.905171 0.425048i \(-0.860257\pi\)
0.705207 0.709001i \(-0.250854\pi\)
\(410\) 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 \(-0.999122\pi\)
−0.170931 + 0.985283i \(0.554677\pi\)
\(420\) 0 0
\(421\) −28.6884 + 10.4417i −1.39819 + 0.508899i −0.927640 0.373476i \(-0.878166\pi\)
−0.470548 + 0.882374i \(0.655944\pi\)
\(422\) −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 \(-0.596732\pi\)
−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 \(0.505818\pi\)
\(434\) 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 −0.560170 0.828378i \(-0.689264\pi\)
0.809709 0.586831i \(-0.199625\pi\)
\(440\) 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 \(-0.716321\pi\)
0.0185388 + 0.999828i \(0.494099\pi\)
\(444\) 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 0.999754 + 0.0221934i \(0.00706496\pi\)
−0.480657 + 0.876909i \(0.659602\pi\)
\(450\) 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 0.615722 0.787963i \(-0.288864\pi\)
−0.669073 + 0.743197i \(0.733309\pi\)
\(458\) −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 \(-0.330750\pi\)
−0.760803 + 0.648983i \(0.775195\pi\)
\(462\) 0 0
\(463\) −4.60875 26.1375i −0.214187 1.21471i −0.882312 0.470665i \(-0.844014\pi\)
0.668125 0.744049i \(-0.267097\pi\)
\(464\) 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 0.386955 + 0.922099i \(0.373527\pi\)
−0.992038 + 0.125937i \(0.959806\pi\)
\(468\) 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 0.915288 + 0.402801i \(0.131963\pi\)
−0.997855 + 0.0654625i \(0.979148\pi\)
\(480\) 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 \(-0.263776\pi\)
0.0439731 + 0.999033i \(0.485998\pi\)
\(492\) 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 −0.113537 0.993534i \(-0.536218\pi\)
0.958724 + 0.284337i \(0.0917735\pi\)
\(500\) 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 −0.834679 0.550736i \(-0.814347\pi\)
−0.0596120 0.998222i \(-0.518986\pi\)
\(504\) 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 \(-0.0205763\pi\)
−0.959824 + 0.280604i \(0.909465\pi\)
\(510\) 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 \(-0.887561\pi\)
0.768719 + 0.639586i \(0.220894\pi\)
\(522\) 0 0
\(523\) −18.0070 31.1891i −0.787391 1.36380i −0.927560 0.373674i \(-0.878098\pi\)
0.140169 0.990128i \(-0.455236\pi\)
\(524\) −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 0.677843 + 0.735207i \(0.262915\pi\)
−0.888420 + 0.459032i \(0.848196\pi\)
\(548\) 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 0.930456 + 0.366403i \(0.119411\pi\)
−0.147914 + 0.989000i \(0.547256\pi\)
\(558\) 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 0.947316 + 0.320301i \(0.103784\pi\)
−0.780636 + 0.624986i \(0.785105\pi\)
\(564\) 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 \(-0.0537833\pi\)
0.00556781 + 0.999984i \(0.498228\pi\)
\(570\) 0 0
\(571\) 2.22626 + 12.6257i 0.0931659 + 0.528370i 0.995294 + 0.0969016i \(0.0308932\pi\)
−0.902128 + 0.431468i \(0.857996\pi\)
\(572\) 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 0.999930 0.0118433i \(-0.00376992\pi\)
−0.510222 + 0.860043i \(0.670437\pi\)
\(578\) −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 −0.916419 0.400220i \(-0.868934\pi\)
0.998036 0.0626498i \(-0.0199551\pi\)
\(588\) 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 \(-0.782120\pi\)
−0.774742 + 0.632277i \(0.782120\pi\)
\(594\) 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 −0.995639 0.0932901i \(-0.970262\pi\)
−0.822669 0.568520i \(-0.807516\pi\)
\(600\) 0 0
\(601\) −5.40175 + 30.6348i −0.220342 + 1.24962i 0.651050 + 0.759035i \(0.274329\pi\)
−0.871392 + 0.490587i \(0.836782\pi\)
\(602\) −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 −0.0565879 0.998398i \(-0.518022\pi\)
0.973403 + 0.229098i \(0.0735777\pi\)
\(608\) −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 −0.797782 0.602945i \(-0.793994\pi\)
0.921057 + 0.389427i \(0.127327\pi\)
\(614\) 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 −0.975780 0.218754i \(-0.929801\pi\)
0.842115 0.539298i \(-0.181310\pi\)
\(618\) 0 0
\(619\) −5.17375 4.34129i −0.207951 0.174491i 0.532864 0.846201i \(-0.321116\pi\)
−0.740814 + 0.671710i \(0.765560\pi\)
\(620\) 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 0.870537 0.492103i \(-0.163772\pi\)
−0.861442 + 0.507855i \(0.830438\pi\)
\(632\) −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 \(-0.926387\pi\)
0.993069 + 0.117531i \(0.0374979\pi\)
\(642\) 0 0
\(643\) 1.60015 + 0.582407i 0.0631037 + 0.0229679i 0.373379 0.927679i \(-0.378199\pi\)
−0.310275 + 0.950647i \(0.600421\pi\)
\(644\) −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 \(-0.751136\pi\)
−0.709626 + 0.704579i \(0.751136\pi\)
\(648\) 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 \(-0.713787\pi\)
−0.979861 + 0.199681i \(0.936010\pi\)
\(654\) 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 \(-0.445803\pi\)
0.763294 + 0.646051i \(0.223581\pi\)
\(660\) 0 0
\(661\) 26.1736 21.9623i 1.01803 0.854233i 0.0286555 0.999589i \(-0.490877\pi\)
0.989379 + 0.145357i \(0.0464330\pi\)
\(662\) 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 0.0922084 0.995740i \(-0.470607\pi\)
−0.964600 + 0.263716i \(0.915052\pi\)
\(674\) 1.10113 0.0424140
\(675\) 0 0
\(676\) 24.4577 0.940680
\(677\) −31.2395 26.2130i −1.20063 1.00745i −0.999612 0.0278613i \(-0.991130\pi\)
−0.201019 0.979587i \(-0.564425\pi\)
\(678\) 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 −0.386606 0.922245i \(-0.626353\pi\)
0.991991 0.126312i \(-0.0403139\pi\)
\(684\) 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 0.223869 0.974619i \(-0.428131\pi\)
0.797967 + 0.602701i \(0.205909\pi\)
\(692\) 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 \(-0.454583\pi\)
0.142199 + 0.989838i \(0.454583\pi\)
\(702\) 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 −0.947461 0.319870i \(-0.896361\pi\)
0.999725 + 0.0234711i \(0.00747176\pi\)
\(710\) −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 0.999993 + 0.00362928i \(0.00115524\pi\)
−0.496854 + 0.867834i \(0.665511\pi\)
\(720\) 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 0.409723 0.912210i \(-0.365625\pi\)
−0.827204 + 0.561902i \(0.810070\pi\)
\(728\) 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 −0.903560 0.428462i \(-0.859056\pi\)
0.702526 0.711658i \(-0.252056\pi\)
\(734\) 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 0.861550 0.507672i \(-0.169494\pi\)
−0.870432 + 0.492288i \(0.836161\pi\)
\(740\) −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 −0.210582 + 0.977576i \(0.567536\pi\)
−0.999292 + 0.0376288i \(0.988020\pi\)
\(744\) 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 −0.548443 0.836188i \(-0.684779\pi\)
−0.957623 + 0.288024i \(0.907002\pi\)
\(752\) 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 \(-0.446884\pi\)
−0.506623 + 0.862168i \(0.669106\pi\)
\(762\) 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 −0.740428 0.672136i \(-0.765377\pi\)
0.533351 + 0.845894i \(0.320933\pi\)
\(770\) 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 \(-0.282793\pi\)
−0.987421 + 0.158112i \(0.949459\pi\)
\(774\) 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
\(780\) 0 0
\(781\) 9.39002 + 7.87917i 0.336001 + 0.281939i
\(782\) 5.21709 0.186563
\(783\) 0 0
\(784\) 8.36872 0.298883
\(785\) −21.9995 18.4598i −0.785197 0.658859i
\(786\) 0 0
\(787\) 6.89874 + 39.1247i 0.245913 + 1.39464i 0.818362 + 0.574704i \(0.194883\pi\)
−0.572448 + 0.819941i \(0.694006\pi\)
\(788\) 13.6955 + 4.98476i 0.487882 + 0.177575i
\(789\) 0 0
\(790\) 1.32377 7.50746i 0.0470975 0.267103i
\(791\) −14.1752 + 24.5522i −0.504013 + 0.872976i
\(792\) 0 0
\(793\) 3.13210 + 5.42495i 0.111224 + 0.192646i
\(794\) 0.000399275 0 0.000145324i 1.41698e−5 0 5.15737e-6i
\(795\) 0 0
\(796\) 15.6708 13.1494i 0.555438 0.466068i
\(797\) 6.97556 5.85319i 0.247087 0.207331i −0.510830 0.859682i \(-0.670662\pi\)
0.757917 + 0.652351i \(0.226217\pi\)
\(798\) 0 0
\(799\) −4.81148 + 1.75123i −0.170218 + 0.0619542i
\(800\) −9.11632 15.7899i −0.322311 0.558258i
\(801\) 0 0
\(802\) 2.18437 3.78344i 0.0771327 0.133598i
\(803\) −1.86028 + 10.5502i −0.0656478 + 0.372307i
\(804\) 0 0
\(805\) 69.4471 + 25.2767i 2.44769 + 0.890886i
\(806\) −0.150545 0.853782i −0.00530271 0.0300732i
\(807\) 0 0
\(808\) 2.95025 + 2.47555i 0.103789 + 0.0870897i
\(809\) −3.01910 −0.106146 −0.0530730 0.998591i \(-0.516902\pi\)
−0.0530730 + 0.998591i \(0.516902\pi\)
\(810\) 0 0
\(811\) 33.1722 1.16483 0.582416 0.812891i \(-0.302107\pi\)
0.582416 + 0.812891i \(0.302107\pi\)
\(812\) 29.9706 + 25.1483i 1.05176 + 0.882533i
\(813\) 0 0
\(814\) −0.371198 2.10517i −0.0130105 0.0737861i
\(815\) 3.67800 + 1.33868i 0.128835 + 0.0468920i
\(816\) 0 0
\(817\) −0.591849 + 3.35654i −0.0207062 + 0.117431i
\(818\) 2.01418 3.48866i 0.0704241 0.121978i
\(819\) 0 0
\(820\) −19.3612 33.5345i −0.676121 1.17108i
\(821\) 40.1831 14.6255i 1.40240 0.510432i 0.473510 0.880788i \(-0.342987\pi\)
0.928890 + 0.370357i \(0.120765\pi\)
\(822\) 0 0
\(823\) −26.9869 + 22.6447i −0.940703 + 0.789344i −0.977708 0.209971i \(-0.932663\pi\)
0.0370044 + 0.999315i \(0.488218\pi\)
\(824\) 4.95817 4.16040i 0.172726 0.144934i
\(825\) 0 0
\(826\) 5.83998 2.12558i 0.203199 0.0739584i
\(827\) 13.0190 + 22.5495i 0.452714 + 0.784125i 0.998554 0.0537655i \(-0.0171223\pi\)
−0.545839 + 0.837890i \(0.683789\pi\)
\(828\) 0 0
\(829\) 3.95134 6.84392i 0.137236 0.237699i −0.789214 0.614119i \(-0.789512\pi\)
0.926449 + 0.376420i \(0.122845\pi\)
\(830\) −1.01192 + 5.73888i −0.0351242 + 0.199199i
\(831\) 0 0
\(832\) −5.24207 1.90796i −0.181736 0.0661465i
\(833\) 1.75798 + 9.96999i 0.0609103 + 0.345440i
\(834\) 0 0
\(835\) −23.9125 20.0650i −0.827526 0.694376i
\(836\) −3.00344 −0.103876
\(837\) 0 0
\(838\) −5.41213 −0.186959
\(839\) −3.94390 3.30932i −0.136158 0.114250i 0.572165 0.820139i \(-0.306104\pi\)
−0.708323 + 0.705888i \(0.750548\pi\)
\(840\) 0 0
\(841\) 2.41617 + 13.7028i 0.0833163 + 0.472510i
\(842\) −4.96241 1.80617i −0.171016 0.0622447i
\(843\) 0 0
\(844\) −7.13661 + 40.4737i −0.245652 + 1.39316i
\(845\) −23.1939 + 40.1730i −0.797894 + 1.38199i
\(846\) 0 0
\(847\) 7.26264 + 12.5793i 0.249547 + 0.432228i
\(848\) −31.7548 + 11.5578i −1.09046 + 0.396897i
\(849\) 0 0
\(850\) 5.48963 4.60635i 0.188293 0.157996i
\(851\) 24.7883 20.7999i 0.849733 0.713011i
\(852\) 0 0
\(853\) −24.4230 + 8.88926i −0.836229 + 0.304362i −0.724413 0.689366i \(-0.757889\pi\)
−0.111816 + 0.993729i \(0.535667\pi\)
\(854\) −2.14653 3.71791i −0.0734529 0.127224i
\(855\) 0 0
\(856\) −0.438904 + 0.760204i −0.0150014 + 0.0259832i
\(857\) 0.715280 4.05656i 0.0244335 0.138569i −0.970151 0.242503i \(-0.922032\pi\)
0.994584 + 0.103933i \(0.0331428\pi\)
\(858\) 0 0
\(859\) 6.04168 + 2.19899i 0.206140 + 0.0750287i 0.443026 0.896509i \(-0.353905\pi\)
−0.236887 + 0.971537i \(0.576127\pi\)
\(860\) 7.12076 + 40.3838i 0.242816 + 1.37708i
\(861\) 0 0
\(862\) −1.64636 1.38146i −0.0560751 0.0470526i
\(863\) −29.6195 −1.00826 −0.504129 0.863628i \(-0.668187\pi\)
−0.504129 + 0.863628i \(0.668187\pi\)
\(864\) 0 0
\(865\) −81.6282 −2.77544
\(866\) −0.100792 0.0845742i −0.00342504 0.00287395i
\(867\) 0 0
\(868\) −6.79330 38.5267i −0.230580 1.30768i
\(869\) −27.6162 10.0515i −0.936816 0.340973i
\(870\) 0 0
\(871\) 0.161077 0.913514i 0.00545789 0.0309533i
\(872\) −2.54326 + 4.40505i −0.0861256 + 0.149174i
\(873\) 0 0
\(874\) 0.345251 + 0.597993i 0.0116783 + 0.0202274i
\(875\) 42.1715 15.3492i 1.42566 0.518896i
\(876\) 0 0
\(877\) −24.4121 + 20.4842i −0.824337 + 0.691701i −0.953983 0.299860i \(-0.903060\pi\)
0.129647 + 0.991560i \(0.458616\pi\)
\(878\) 3.98971 3.34776i 0.134646 0.112982i
\(879\) 0 0
\(880\) −33.4328 + 12.1685i −1.12702 + 0.410201i
\(881\) 17.3932 + 30.1259i 0.585991 + 1.01497i 0.994751 + 0.102325i \(0.0326280\pi\)
−0.408760 + 0.912642i \(0.634039\pi\)
\(882\) 0 0
\(883\) 15.1882 26.3067i 0.511124 0.885292i −0.488793 0.872400i \(-0.662563\pi\)
0.999917 0.0128924i \(-0.00410388\pi\)
\(884\) 1.21003 6.86244i 0.0406979 0.230809i
\(885\) 0 0
\(886\) −2.22061 0.808236i −0.0746029 0.0271532i
\(887\) 8.68721 + 49.2676i 0.291688 + 1.65424i 0.680367 + 0.732871i \(0.261820\pi\)
−0.388679 + 0.921373i \(0.627069\pi\)
\(888\) 0 0
\(889\) 48.2957 + 40.5249i 1.61978 + 1.35916i
\(890\) −4.87263 −0.163331
\(891\) 0 0
\(892\) −46.4515 −1.55531
\(893\) −0.519139 0.435609i −0.0173723 0.0145771i
\(894\) 0 0
\(895\) 5.89715 + 33.4444i 0.197120 + 1.11792i
\(896\) 15.1836 + 5.52638i 0.507249 + 0.184624i
\(897\) 0 0
\(898\) −0.660781 + 3.74747i −0.0220505 + 0.125055i
\(899\) 21.4556 37.1621i 0.715583 1.23943i
\(900\) 0 0
\(901\) −20.4399 35.4029i −0.680950 1.17944i
\(902\) 2.13045 0.775422i 0.0709363 0.0258187i
\(903\) 0 0
\(904\) −4.91973 + 4.12815i −0.163628 + 0.137300i
\(905\) 20.4109 17.1268i 0.678482 0.569314i
\(906\) 0 0
\(907\) 41.4069 15.0709i 1.37489 0.500420i 0.454268 0.890865i \(-0.349901\pi\)
0.920626 + 0.390445i \(0.127679\pi\)
\(908\) −10.3273 17.8874i −0.342723 0.593614i
\(909\) 0 0
\(910\) −0.749593 + 1.29833i −0.0248488 + 0.0430393i
\(911\) 6.45594 36.6134i 0.213895 1.21306i −0.668919 0.743335i \(-0.733243\pi\)
0.882814 0.469723i \(-0.155646\pi\)
\(912\) 0 0
\(913\) 21.1105 + 7.68359i 0.698655 + 0.254290i
\(914\) −0.0447198 0.253619i −0.00147920 0.00838896i
\(915\) 0 0
\(916\) 20.9509 + 17.5799i 0.692237 + 0.580856i
\(917\) −1.98815 −0.0656544
\(918\) 0 0
\(919\) 12.3976 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(920\) 12.8248 + 10.7613i 0.422821 + 0.354789i
\(921\) 0 0
\(922\) −0.213663 1.21174i −0.00703662 0.0399066i
\(923\) −3.53707 1.28739i −0.116424 0.0423749i
\(924\) 0 0
\(925\) 7.71835 43.7730i 0.253778 1.43925i
\(926\) 2.29545 3.97584i 0.0754333 0.130654i
\(927\) 0 0
\(928\) 6.66377 + 11.5420i 0.218749 + 0.378884i
\(929\) 31.3747 11.4194i 1.02937 0.374660i 0.228528 0.973537i \(-0.426609\pi\)
0.800841 + 0.598878i \(0.204386\pi\)
\(930\) 0 0
\(931\) −1.02644 + 0.861287i −0.0336403 + 0.0282275i
\(932\) −11.4691 + 9.62375i −0.375684 + 0.315237i
\(933\) 0 0
\(934\) −4.25085 + 1.54718i −0.139092 + 0.0506253i
\(935\) −21.5199 37.2736i −0.703777 1.21898i
\(936\) 0 0
\(937\) 12.4220 21.5156i 0.405810 0.702884i −0.588605 0.808421i \(-0.700323\pi\)
0.994415 + 0.105537i \(0.0336561\pi\)
\(938\) −0.110392 + 0.626063i −0.00360442 + 0.0204417i
\(939\) 0 0
\(940\) −7.66180 2.78867i −0.249900 0.0909563i
\(941\) −4.41585 25.0435i −0.143953 0.816396i −0.968202 0.250169i \(-0.919514\pi\)
0.824249 0.566227i \(-0.191597\pi\)
\(942\) 0 0
\(943\) 26.2905 + 22.0603i 0.856136 + 0.718383i
\(944\) −45.2900 −1.47406
\(945\) 0 0
\(946\) −2.40094 −0.0780612
\(947\) −12.7394 10.6897i −0.413976 0.347367i 0.411890 0.911234i \(-0.364869\pi\)
−0.825866 + 0.563866i \(0.809313\pi\)
\(948\) 0 0
\(949\) −0.571246 3.23970i −0.0185434 0.105165i
\(950\) 0.891276 + 0.324398i 0.0289168 + 0.0105249i
\(951\) 0 0
\(952\) −1.67115 + 9.47757i −0.0541623 + 0.307170i
\(953\) 7.13357 12.3557i 0.231079 0.400240i −0.727047 0.686588i \(-0.759108\pi\)
0.958126 + 0.286347i \(0.0924411\pi\)
\(954\) 0 0
\(955\) 22.3365 + 38.6879i 0.722791 + 1.25191i
\(956\) 30.6546 11.1574i 0.991440 0.360855i
\(957\) 0 0
\(958\) −1.37894 + 1.15707i −0.0445516 + 0.0373833i
\(959\) 19.9427 16.7339i 0.643982 0.540365i
\(960\) 0 0
\(961\) −11.1899 + 4.07280i −0.360965 + 0.131381i
\(962\) 0.328209 + 0.568474i 0.0105819 + 0.0183283i
\(963\) 0 0
\(964\) −14.3013 + 24.7706i −0.460613 + 0.797806i
\(965\) 5.75763 32.6532i 0.185345 1.05114i
\(966\) 0 0
\(967\) 36.7277 + 13.3678i 1.18108 + 0.429879i 0.856584 0.516008i \(-0.172582\pi\)
0.324498 + 0.945886i \(0.394805\pi\)
\(968\) 0.571376 + 3.24044i 0.0183647 + 0.104152i
\(969\) 0 0
\(970\) 0.469551 + 0.394000i 0.0150764 + 0.0126506i
\(971\) 4.40370 0.141321 0.0706607 0.997500i \(-0.477489\pi\)
0.0706607 + 0.997500i \(0.477489\pi\)
\(972\) 0 0
\(973\) 40.7619 1.30677
\(974\) −2.44693 2.05322i −0.0784046 0.0657893i
\(975\) 0 0
\(976\) 5.43268 + 30.8103i 0.173896 + 0.986213i
\(977\) 39.5860 + 14.4081i 1.26647 + 0.460957i 0.885935 0.463810i \(-0.153518\pi\)
0.380534 + 0.924767i \(0.375740\pi\)
\(978\) 0 0
\(979\) −3.26190 + 18.4991i −0.104251 + 0.591235i
\(980\) −8.06057 + 13.9613i −0.257486 + 0.445978i
\(981\) 0 0
\(982\) 1.46804 + 2.54272i 0.0468470 + 0.0811413i
\(983\) −19.1943 + 6.98615i −0.612203 + 0.222824i −0.629467 0.777027i \(-0.716727\pi\)
0.0172640 + 0.999851i \(0.494504\pi\)
\(984\) 0 0
\(985\) −21.1756 + 17.7684i −0.674709 + 0.566148i
\(986\) −4.01276 + 3.36711i −0.127792 + 0.107231i
\(987\) 0 0
\(988\) 0.866663 0.315440i 0.0275722 0.0100355i
\(989\) −18.1723 31.4753i −0.577844 1.00086i
\(990\) 0 0
\(991\) −0.0340356 + 0.0589514i −0.00108118 + 0.00187265i −0.866565 0.499063i \(-0.833677\pi\)
0.865484 + 0.500936i \(0.167011\pi\)
\(992\) 2.31414 13.1241i 0.0734740 0.416691i
\(993\) 0 0
\(994\) 2.42408 + 0.882292i 0.0768871 + 0.0279846i
\(995\) 6.73747 + 38.2101i 0.213592 + 1.21134i
\(996\) 0 0
\(997\) 8.15539 + 6.84318i 0.258284 + 0.216726i 0.762730 0.646718i \(-0.223859\pi\)
−0.504446 + 0.863443i \(0.668303\pi\)
\(998\) 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.e.j.406.2 12
3.2 odd 2 729.2.e.u.406.1 12
9.2 odd 6 729.2.e.l.649.1 12
9.4 even 3 729.2.e.t.163.1 12
9.5 odd 6 729.2.e.k.163.2 12
9.7 even 3 729.2.e.s.649.2 12
27.2 odd 18 729.2.c.a.244.4 12
27.4 even 9 729.2.e.s.82.2 12
27.5 odd 18 729.2.e.u.325.1 12
27.7 even 9 729.2.a.b.1.4 6
27.11 odd 18 729.2.c.a.487.4 12
27.13 even 9 729.2.e.t.568.1 12
27.14 odd 18 729.2.e.k.568.2 12
27.16 even 9 729.2.c.d.487.3 12
27.20 odd 18 729.2.a.e.1.3 yes 6
27.22 even 9 inner 729.2.e.j.325.2 12
27.23 odd 18 729.2.e.l.82.1 12
27.25 even 9 729.2.c.d.244.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.4 6 27.7 even 9
729.2.a.e.1.3 yes 6 27.20 odd 18
729.2.c.a.244.4 12 27.2 odd 18
729.2.c.a.487.4 12 27.11 odd 18
729.2.c.d.244.3 12 27.25 even 9
729.2.c.d.487.3 12 27.16 even 9
729.2.e.j.325.2 12 27.22 even 9 inner
729.2.e.j.406.2 12 1.1 even 1 trivial
729.2.e.k.163.2 12 9.5 odd 6
729.2.e.k.568.2 12 27.14 odd 18
729.2.e.l.82.1 12 27.23 odd 18
729.2.e.l.649.1 12 9.2 odd 6
729.2.e.s.82.2 12 27.4 even 9
729.2.e.s.649.2 12 9.7 even 3
729.2.e.t.163.1 12 9.4 even 3
729.2.e.t.568.1 12 27.13 even 9
729.2.e.u.325.1 12 27.5 odd 18
729.2.e.u.406.1 12 3.2 odd 2