Properties

Label 729.2.e.j.325.2
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 325.2
Root \(0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.j.406.2

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

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

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 −0.594736 0.803921i \(-0.702743\pi\)
0.688433 + 0.725300i \(0.258299\pi\)
\(3\) 0 0
\(4\) −0.342101 + 1.94015i −0.171050 + 0.970075i
\(5\) 3.51122 1.27798i 1.57027 0.571530i 0.597207 0.802087i \(-0.296277\pi\)
0.973059 + 0.230557i \(0.0740550\pi\)
\(6\) 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 0.669957 0.742400i \(-0.266313\pi\)
0.0360107 + 0.999351i \(0.488535\pi\)
\(12\) 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 \(0.356094\pi\)
−0.997445 + 0.0714442i \(0.977239\pi\)
\(18\) 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 \(-0.706332\pi\)
0.839996 0.542593i \(-0.182557\pi\)
\(24\) 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 −0.976152 0.217087i \(-0.930344\pi\)
0.0442820 + 0.999019i \(0.485900\pi\)
\(30\) 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 0.900716 0.434409i \(-0.143043\pi\)
−0.271402 + 0.962466i \(0.587487\pi\)
\(42\) 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 0.995617 0.0935267i \(-0.0298141\pi\)
−0.967562 + 0.252635i \(0.918703\pi\)
\(48\) 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 0.507347 0.861742i \(-0.330626\pi\)
0.942568 + 0.334016i \(0.108404\pi\)
\(60\) 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 −0.682346 0.731029i \(-0.739040\pi\)
0.974263 + 0.225415i \(0.0723738\pi\)
\(72\) 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 −0.179524 0.983754i \(-0.557456\pi\)
0.937634 + 0.347624i \(0.113011\pi\)
\(84\) 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 0.594113 0.804382i \(-0.297503\pi\)
−0.993671 + 0.112326i \(0.964170\pi\)
\(90\) 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 \(-0.965547\pi\)
0.897247 0.441529i \(-0.145564\pi\)
\(102\) 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 \(-0.519680\pi\)
−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 −0.720505 0.693450i \(-0.756090\pi\)
−0.106198 + 0.994345i \(0.533868\pi\)
\(114\) 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 −0.989379 0.145362i \(-0.953565\pi\)
0.979428 + 0.201792i \(0.0646764\pi\)
\(132\) 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 −0.316955 0.948441i \(-0.602660\pi\)
0.878993 + 0.476835i \(0.158216\pi\)
\(138\) 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 0.892681 0.450690i \(-0.148822\pi\)
−0.288830 + 0.957380i \(0.593266\pi\)
\(150\) 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 −0.627397 0.778700i \(-0.715880\pi\)
0.0199249 + 0.999801i \(0.493657\pi\)
\(168\) 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 −0.589834 0.807525i \(-0.700807\pi\)
−0.970906 + 0.239462i \(0.923029\pi\)
\(174\) 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 −0.644709 0.764428i \(-0.723022\pi\)
0.984369 + 0.176121i \(0.0563549\pi\)
\(180\) 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 −0.248203 0.968708i \(-0.579840\pi\)
0.910891 + 0.412646i \(0.135395\pi\)
\(192\) 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 0.703641 0.710556i \(-0.251557\pi\)
−0.967180 + 0.254093i \(0.918223\pi\)
\(198\) 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 0.647597 0.761983i \(-0.275774\pi\)
0.00629435 + 0.999980i \(0.497996\pi\)
\(228\) 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 −0.963230 0.268676i \(-0.913414\pi\)
0.714296 + 0.699844i \(0.246747\pi\)
\(234\) 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 \(-0.764550\pi\)
0.924673 0.380763i \(-0.124339\pi\)
\(240\) 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 0.687099 0.726563i \(-0.258884\pi\)
−0.972772 + 0.231764i \(0.925550\pi\)
\(252\) 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 0.844418 0.535684i \(-0.179946\pi\)
−0.380914 + 0.924610i \(0.624391\pi\)
\(258\) 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 \(-0.745044\pi\)
0.408457 0.912778i \(-0.366067\pi\)
\(264\) 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 0.979058 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 0.966817 0.255470i \(-0.0822302\pi\)
0.576412 + 0.817159i \(0.304452\pi\)
\(282\) 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 \(-0.760980\pi\)
0.920344 0.391110i \(-0.127909\pi\)
\(294\) 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 \(0.164226\pi\)
0.636896 + 0.770950i \(0.280218\pi\)
\(312\) 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 \(0.281289\pi\)
−0.331634 + 0.943408i \(0.607600\pi\)
\(318\) 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 \(-0.868608\pi\)
0.997971 0.0636721i \(-0.0202812\pi\)
\(348\) 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 \(0.622625\pi\)
−0.977883 + 0.209150i \(0.932930\pi\)
\(354\) 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 0.923868 0.382710i \(-0.125009\pi\)
−0.793371 + 0.608738i \(0.791676\pi\)
\(360\) 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 −0.343092 0.939302i \(-0.611474\pi\)
0.340947 + 0.940082i \(0.389252\pi\)
\(384\) 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 0.789463 0.613798i \(-0.210359\pi\)
0.210222 + 0.977654i \(0.432581\pi\)
\(390\) 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 \(0.272755\pi\)
−0.873807 + 0.486273i \(0.838356\pi\)
\(402\) 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 −0.170931 0.985283i \(-0.554677\pi\)
−0.999996 + 0.00275857i \(0.999122\pi\)
\(420\) 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 \(-0.596732\pi\)
−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 0.809709 + 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 0.0185388 0.999828i \(-0.494099\pi\)
−0.628476 + 0.777829i \(0.716321\pi\)
\(444\) 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 \(-0.659602\pi\)
0.999754 0.0221934i \(-0.00706496\pi\)
\(450\) 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 −0.760803 0.648983i \(-0.775195\pi\)
0.507011 + 0.861939i \(0.330750\pi\)
\(462\) 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 \(-0.959806\pi\)
0.386955 0.922099i \(-0.373527\pi\)
\(468\) 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 \(-0.979148\pi\)
0.915288 0.402801i \(-0.131963\pi\)
\(480\) 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 0.0439731 0.999033i \(-0.485998\pi\)
0.675851 + 0.737038i \(0.263776\pi\)
\(492\) 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 \(0.518986\pi\)
−0.834679 + 0.550736i \(0.814347\pi\)
\(504\) 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 −0.959824 0.280604i \(-0.909465\pi\)
0.997911 + 0.0645972i \(0.0205763\pi\)
\(510\) 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 0.768719 0.639586i \(-0.220894\pi\)
−0.938258 + 0.345937i \(0.887561\pi\)
\(522\) 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 \(-0.547256\pi\)
0.930456 0.366403i \(-0.119411\pi\)
\(558\) 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 \(-0.785105\pi\)
0.947316 0.320301i \(-0.103784\pi\)
\(564\) 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 0.00556781 0.999984i \(-0.498228\pi\)
0.985759 + 0.168162i \(0.0537833\pi\)
\(570\) 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 \(0.0199551\pi\)
−0.916419 + 0.400220i \(0.868934\pi\)
\(588\) 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 −0.822669 + 0.568520i \(0.807516\pi\)
−0.995639 + 0.0932901i \(0.970262\pi\)
\(600\) 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 \(0.181310\pi\)
−0.975780 + 0.218754i \(0.929801\pi\)
\(618\) 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 0.993069 0.117531i \(-0.0374979\pi\)
−0.973378 + 0.229207i \(0.926387\pi\)
\(642\) 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 \(-0.751136\pi\)
−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 −0.979861 0.199681i \(-0.936010\pi\)
−0.622265 + 0.782807i \(0.713787\pi\)
\(654\) 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 0.763294 0.646051i \(-0.223581\pi\)
0.169443 + 0.985540i \(0.445803\pi\)
\(660\) 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 \(0.564425\pi\)
−0.999612 + 0.0278613i \(0.991130\pi\)
\(678\) 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 \(0.0403139\pi\)
−0.386606 + 0.922245i \(0.626353\pi\)
\(684\) 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 \(-0.454583\pi\)
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 0.999725 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 \(-0.665511\pi\)
0.999993 0.00362928i \(-0.00115524\pi\)
\(720\) 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 \(-0.988020\pi\)
−0.210582 0.977576i \(-0.567536\pi\)
\(744\) 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 −0.506623 0.862168i \(-0.669106\pi\)
0.166095 + 0.986110i \(0.446884\pi\)
\(762\) 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 −0.987421 0.158112i \(-0.949459\pi\)
0.630640 + 0.776076i \(0.282793\pi\)
\(774\) 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 −0.572448 0.819941i \(-0.694006\pi\)
0.818362 0.574704i \(-0.194883\pi\)
\(788\) 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 0.757917 0.652351i \(-0.226217\pi\)
−0.510830 + 0.859682i \(0.670662\pi\)
\(798\) 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 0.928890 0.370357i \(-0.120765\pi\)
0.473510 + 0.880788i \(0.342987\pi\)
\(822\) 0 0
\(823\) −26.9869 22.6447i −0.940703 0.789344i 0.0370044 0.999315i \(-0.488218\pi\)
−0.977708 + 0.209971i \(0.932663\pi\)
\(824\) 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 −0.545839 0.837890i \(-0.683789\pi\)
0.998554 + 0.0537655i \(0.0171223\pi\)
\(828\) 0 0
\(829\) 3.95134 + 6.84392i 0.137236 + 0.237699i 0.926449 0.376420i \(-0.122845\pi\)
−0.789214 + 0.614119i \(0.789512\pi\)
\(830\) −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 −0.708323 0.705888i \(-0.750548\pi\)
0.572165 + 0.820139i \(0.306104\pi\)
\(840\) 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 −0.111816 0.993729i \(-0.535667\pi\)
−0.724413 + 0.689366i \(0.757889\pi\)
\(854\) −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 0.994584 0.103933i \(-0.0331428\pi\)
−0.970151 + 0.242503i \(0.922032\pi\)
\(858\) 0 0
\(859\) 6.04168 2.19899i 0.206140 0.0750287i −0.236887 0.971537i \(-0.576127\pi\)
0.443026 + 0.896509i \(0.353905\pi\)
\(860\) 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 0.129647 0.991560i \(-0.458616\pi\)
−0.953983 + 0.299860i \(0.903060\pi\)
\(878\) 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 −0.408760 0.912642i \(-0.634039\pi\)
0.994751 0.102325i \(-0.0326280\pi\)
\(882\) 0 0
\(883\) 15.1882 + 26.3067i 0.511124 + 0.885292i 0.999917 + 0.0128924i \(0.00410388\pi\)
−0.488793 + 0.872400i \(0.662563\pi\)
\(884\) 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 −0.388679 0.921373i \(-0.627069\pi\)
0.680367 0.732871i \(-0.261820\pi\)
\(888\) 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 0.920626 0.390445i \(-0.127679\pi\)
0.454268 + 0.890865i \(0.349901\pi\)
\(908\) −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 0.882814 + 0.469723i \(0.155646\pi\)
−0.668919 + 0.743335i \(0.733243\pi\)
\(912\) 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 0.800841 0.598878i \(-0.204386\pi\)
0.228528 + 0.973537i \(0.426609\pi\)
\(930\) 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 0.994415 0.105537i \(-0.0336561\pi\)
−0.588605 + 0.808421i \(0.700323\pi\)
\(938\) −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 0.824249 + 0.566227i \(0.191597\pi\)
−0.968202 + 0.250169i \(0.919514\pi\)
\(942\) 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 −0.825866 0.563866i \(-0.809313\pi\)
0.411890 + 0.911234i \(0.364869\pi\)
\(948\) 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 0.958126 0.286347i \(-0.0924411\pi\)
−0.727047 + 0.686588i \(0.759108\pi\)
\(954\) 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 0.324498 0.945886i \(-0.394805\pi\)
0.856584 + 0.516008i \(0.172582\pi\)
\(968\) 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 0.380534 0.924767i \(-0.375740\pi\)
0.885935 + 0.463810i \(0.153518\pi\)
\(978\) 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 0.0172640 0.999851i \(-0.494504\pi\)
−0.629467 + 0.777027i \(0.716727\pi\)
\(984\) 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 0.865484 0.500936i \(-0.167011\pi\)
−0.866565 + 0.499063i \(0.833677\pi\)
\(992\) 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 −0.504446 0.863443i \(-0.668303\pi\)
0.762730 + 0.646718i \(0.223859\pi\)
\(998\) 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.325.2 12
3.2 odd 2 729.2.e.u.325.1 12
9.2 odd 6 729.2.e.k.568.2 12
9.4 even 3 729.2.e.s.82.2 12
9.5 odd 6 729.2.e.l.82.1 12
9.7 even 3 729.2.e.t.568.1 12
27.2 odd 18 729.2.e.k.163.2 12
27.4 even 9 729.2.a.b.1.4 6
27.5 odd 18 729.2.c.a.244.4 12
27.7 even 9 729.2.e.s.649.2 12
27.11 odd 18 729.2.e.u.406.1 12
27.13 even 9 729.2.c.d.487.3 12
27.14 odd 18 729.2.c.a.487.4 12
27.16 even 9 inner 729.2.e.j.406.2 12
27.20 odd 18 729.2.e.l.649.1 12
27.22 even 9 729.2.c.d.244.3 12
27.23 odd 18 729.2.a.e.1.3 yes 6
27.25 even 9 729.2.e.t.163.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.4 6 27.4 even 9
729.2.a.e.1.3 yes 6 27.23 odd 18
729.2.c.a.244.4 12 27.5 odd 18
729.2.c.a.487.4 12 27.14 odd 18
729.2.c.d.244.3 12 27.22 even 9
729.2.c.d.487.3 12 27.13 even 9
729.2.e.j.325.2 12 1.1 even 1 trivial
729.2.e.j.406.2 12 27.16 even 9 inner
729.2.e.k.163.2 12 27.2 odd 18
729.2.e.k.568.2 12 9.2 odd 6
729.2.e.l.82.1 12 9.5 odd 6
729.2.e.l.649.1 12 27.20 odd 18
729.2.e.s.82.2 12 9.4 even 3
729.2.e.s.649.2 12 27.7 even 9
729.2.e.t.163.1 12 27.25 even 9
729.2.e.t.568.1 12 9.7 even 3
729.2.e.u.325.1 12 3.2 odd 2
729.2.e.u.406.1 12 27.11 odd 18