Properties

Label 729.2.e.n.568.2
Level $729$
Weight $2$
Character 729.568
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $12$

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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: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.2
Root \(-0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.n.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62760 + 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.601535 + 3.41147i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(-0.866025 - 1.50000i) q^{8} +O(q^{10})\) \(q+(1.62760 + 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.601535 + 3.41147i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(-0.866025 - 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(0.601535 + 3.41147i) q^{11} +(-4.69846 + 1.71010i) q^{13} +(-1.62760 + 0.592396i) q^{14} +(-0.868241 - 4.92404i) q^{16} +(0.500000 + 0.866025i) q^{19} +(-2.65366 + 2.22668i) q^{20} +(-1.04189 + 5.90885i) q^{22} +(5.30731 + 4.45336i) q^{23} +(-6.57785 - 2.39414i) q^{25} -8.66025 q^{26} -1.00000 q^{28} +(-3.25519 - 1.18479i) q^{29} +(3.83022 + 3.21394i) q^{31} +(0.902302 - 5.11721i) q^{32} +(-1.73205 - 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(0.300767 + 1.70574i) q^{38} +(5.63816 - 2.05212i) q^{40} +(3.25519 - 1.18479i) q^{41} +(-0.173648 - 0.984808i) q^{43} +(-1.73205 + 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(2.65366 - 2.22668i) q^{47} +(-1.04189 + 5.90885i) q^{49} +(-9.28780 - 7.79339i) q^{50} +(-4.69846 - 1.71010i) q^{52} +10.3923 q^{53} -12.0000 q^{55} +(1.62760 + 0.592396i) q^{56} +(-4.59627 - 3.85673i) q^{58} +(-0.601535 + 3.41147i) q^{59} +(1.53209 - 1.28558i) q^{61} +(4.33013 + 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-3.00767 - 17.0574i) q^{65} +(-7.51754 + 2.73616i) q^{67} +(-1.04189 - 5.90885i) q^{70} +(5.19615 - 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(1.32683 - 1.11334i) q^{74} +(-0.173648 + 0.984808i) q^{76} +(-2.65366 - 2.22668i) q^{77} +(0.939693 + 0.342020i) q^{79} +17.3205 q^{80} +6.00000 q^{82} +(6.51038 + 2.36959i) q^{83} +(0.300767 - 1.70574i) q^{86} +(4.59627 - 3.85673i) q^{88} +(5.19615 + 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(1.20307 + 6.82295i) q^{92} +(5.63816 - 2.05212i) q^{94} +(-3.25519 + 1.18479i) q^{95} +(2.95202 + 16.7417i) q^{97} +(-5.19615 + 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62760 + 0.592396i 1.15088 + 0.418887i 0.845833 0.533449i \(-0.179104\pi\)
0.305051 + 0.952336i \(0.401326\pi\)
\(3\) 0 0
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) −0.601535 + 3.41147i −0.269015 + 1.52566i 0.488340 + 0.872654i \(0.337603\pi\)
−0.757354 + 0.653004i \(0.773508\pi\)
\(6\) 0 0
\(7\) −0.766044 + 0.642788i −0.289538 + 0.242951i −0.775974 0.630765i \(-0.782741\pi\)
0.486436 + 0.873716i \(0.338297\pi\)
\(8\) −0.866025 1.50000i −0.306186 0.530330i
\(9\) 0 0
\(10\) −3.00000 + 5.19615i −0.948683 + 1.64317i
\(11\) 0.601535 + 3.41147i 0.181370 + 1.02860i 0.930532 + 0.366211i \(0.119345\pi\)
−0.749162 + 0.662387i \(0.769544\pi\)
\(12\) 0 0
\(13\) −4.69846 + 1.71010i −1.30312 + 0.474297i −0.898011 0.439972i \(-0.854988\pi\)
−0.405108 + 0.914269i \(0.632766\pi\)
\(14\) −1.62760 + 0.592396i −0.434993 + 0.158325i
\(15\) 0 0
\(16\) −0.868241 4.92404i −0.217060 1.23101i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −2.65366 + 2.22668i −0.593375 + 0.497901i
\(21\) 0 0
\(22\) −1.04189 + 5.90885i −0.222131 + 1.25977i
\(23\) 5.30731 + 4.45336i 1.10665 + 0.928590i 0.997854 0.0654736i \(-0.0208558\pi\)
0.108797 + 0.994064i \(0.465300\pi\)
\(24\) 0 0
\(25\) −6.57785 2.39414i −1.31557 0.478828i
\(26\) −8.66025 −1.69842
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −3.25519 1.18479i −0.604474 0.220010i 0.0216097 0.999766i \(-0.493121\pi\)
−0.626083 + 0.779756i \(0.715343\pi\)
\(30\) 0 0
\(31\) 3.83022 + 3.21394i 0.687928 + 0.577240i 0.918311 0.395860i \(-0.129553\pi\)
−0.230383 + 0.973100i \(0.573998\pi\)
\(32\) 0.902302 5.11721i 0.159506 0.904604i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.73205 3.00000i −0.292770 0.507093i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0.300767 + 1.70574i 0.0487909 + 0.276707i
\(39\) 0 0
\(40\) 5.63816 2.05212i 0.891471 0.324469i
\(41\) 3.25519 1.18479i 0.508375 0.185034i −0.0750818 0.997177i \(-0.523922\pi\)
0.583457 + 0.812144i \(0.301700\pi\)
\(42\) 0 0
\(43\) −0.173648 0.984808i −0.0264811 0.150182i 0.968700 0.248234i \(-0.0798500\pi\)
−0.995181 + 0.0980518i \(0.968739\pi\)
\(44\) −1.73205 + 3.00000i −0.261116 + 0.452267i
\(45\) 0 0
\(46\) 6.00000 + 10.3923i 0.884652 + 1.53226i
\(47\) 2.65366 2.22668i 0.387075 0.324795i −0.428397 0.903591i \(-0.640922\pi\)
0.815473 + 0.578796i \(0.196477\pi\)
\(48\) 0 0
\(49\) −1.04189 + 5.90885i −0.148841 + 0.844121i
\(50\) −9.28780 7.79339i −1.31349 1.10215i
\(51\) 0 0
\(52\) −4.69846 1.71010i −0.651560 0.237148i
\(53\) 10.3923 1.42749 0.713746 0.700404i \(-0.246997\pi\)
0.713746 + 0.700404i \(0.246997\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 1.62760 + 0.592396i 0.217497 + 0.0791623i
\(57\) 0 0
\(58\) −4.59627 3.85673i −0.603519 0.506413i
\(59\) −0.601535 + 3.41147i −0.0783132 + 0.444136i 0.920287 + 0.391244i \(0.127955\pi\)
−0.998600 + 0.0528923i \(0.983156\pi\)
\(60\) 0 0
\(61\) 1.53209 1.28558i 0.196164 0.164601i −0.539415 0.842040i \(-0.681355\pi\)
0.735579 + 0.677439i \(0.236910\pi\)
\(62\) 4.33013 + 7.50000i 0.549927 + 0.952501i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −3.00767 17.0574i −0.373056 2.11571i
\(66\) 0 0
\(67\) −7.51754 + 2.73616i −0.918414 + 0.334275i −0.757607 0.652711i \(-0.773632\pi\)
−0.160807 + 0.986986i \(0.551410\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.04189 5.90885i −0.124530 0.706242i
\(71\) 5.19615 9.00000i 0.616670 1.06810i −0.373419 0.927663i \(-0.621815\pi\)
0.990089 0.140441i \(-0.0448520\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 1.32683 1.11334i 0.154241 0.129423i
\(75\) 0 0
\(76\) −0.173648 + 0.984808i −0.0199188 + 0.112965i
\(77\) −2.65366 2.22668i −0.302412 0.253754i
\(78\) 0 0
\(79\) 0.939693 + 0.342020i 0.105724 + 0.0384803i 0.394340 0.918964i \(-0.370973\pi\)
−0.288617 + 0.957445i \(0.593195\pi\)
\(80\) 17.3205 1.93649
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) 6.51038 + 2.36959i 0.714607 + 0.260096i 0.673635 0.739065i \(-0.264732\pi\)
0.0409726 + 0.999160i \(0.486954\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.300767 1.70574i 0.0324326 0.183934i
\(87\) 0 0
\(88\) 4.59627 3.85673i 0.489964 0.411128i
\(89\) 5.19615 + 9.00000i 0.550791 + 0.953998i 0.998218 + 0.0596775i \(0.0190072\pi\)
−0.447427 + 0.894321i \(0.647659\pi\)
\(90\) 0 0
\(91\) 2.50000 4.33013i 0.262071 0.453921i
\(92\) 1.20307 + 6.82295i 0.125429 + 0.711342i
\(93\) 0 0
\(94\) 5.63816 2.05212i 0.581531 0.211660i
\(95\) −3.25519 + 1.18479i −0.333976 + 0.121557i
\(96\) 0 0
\(97\) 2.95202 + 16.7417i 0.299732 + 1.69987i 0.647320 + 0.762218i \(0.275890\pi\)
−0.347588 + 0.937647i \(0.612999\pi\)
\(98\) −5.19615 + 9.00000i −0.524891 + 0.909137i
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 10.6146 8.90673i 1.05619 0.886252i 0.0624632 0.998047i \(-0.480104\pi\)
0.993731 + 0.111795i \(0.0356600\pi\)
\(102\) 0 0
\(103\) 1.38919 7.87846i 0.136881 0.776288i −0.836651 0.547736i \(-0.815490\pi\)
0.973532 0.228552i \(-0.0733991\pi\)
\(104\) 6.63414 + 5.56670i 0.650531 + 0.545860i
\(105\) 0 0
\(106\) 16.9145 + 6.15636i 1.64288 + 0.597959i
\(107\) −10.3923 −1.00466 −0.502331 0.864675i \(-0.667524\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) 0 0
\(109\) 17.0000 1.62830 0.814152 0.580651i \(-0.197202\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) −19.5311 7.10876i −1.86222 0.677793i
\(111\) 0 0
\(112\) 3.83022 + 3.21394i 0.361922 + 0.303689i
\(113\) 3.00767 17.0574i 0.282938 1.60462i −0.429620 0.903010i \(-0.641353\pi\)
0.712558 0.701613i \(-0.247536\pi\)
\(114\) 0 0
\(115\) −18.3851 + 15.4269i −1.71442 + 1.43857i
\(116\) −1.73205 3.00000i −0.160817 0.278543i
\(117\) 0 0
\(118\) −3.00000 + 5.19615i −0.276172 + 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.939693 + 0.342020i −0.0854266 + 0.0310927i
\(122\) 3.25519 1.18479i 0.294711 0.107266i
\(123\) 0 0
\(124\) 0.868241 + 4.92404i 0.0779703 + 0.442192i
\(125\) 3.46410 6.00000i 0.309839 0.536656i
\(126\) 0 0
\(127\) −8.50000 14.7224i −0.754253 1.30640i −0.945745 0.324910i \(-0.894666\pi\)
0.191492 0.981494i \(-0.438667\pi\)
\(128\) −9.28780 + 7.79339i −0.820933 + 0.688844i
\(129\) 0 0
\(130\) 5.20945 29.5442i 0.456899 2.59120i
\(131\) −2.65366 2.22668i −0.231851 0.194546i 0.519459 0.854495i \(-0.326133\pi\)
−0.751310 + 0.659949i \(0.770578\pi\)
\(132\) 0 0
\(133\) −0.939693 0.342020i −0.0814817 0.0296569i
\(134\) −13.8564 −1.19701
\(135\) 0 0
\(136\) 0 0
\(137\) 6.51038 + 2.36959i 0.556219 + 0.202447i 0.604808 0.796372i \(-0.293250\pi\)
−0.0485882 + 0.998819i \(0.515472\pi\)
\(138\) 0 0
\(139\) −9.95858 8.35624i −0.844676 0.708767i 0.113935 0.993488i \(-0.463655\pi\)
−0.958610 + 0.284721i \(0.908099\pi\)
\(140\) 0.601535 3.41147i 0.0508390 0.288322i
\(141\) 0 0
\(142\) 13.7888 11.5702i 1.15713 0.970948i
\(143\) −8.66025 15.0000i −0.724207 1.25436i
\(144\) 0 0
\(145\) 6.00000 10.3923i 0.498273 0.863034i
\(146\) −0.601535 3.41147i −0.0497834 0.282336i
\(147\) 0 0
\(148\) 0.939693 0.342020i 0.0772423 0.0281139i
\(149\) −6.51038 + 2.36959i −0.533351 + 0.194124i −0.594634 0.803996i \(-0.702703\pi\)
0.0612828 + 0.998120i \(0.480481\pi\)
\(150\) 0 0
\(151\) −2.77837 15.7569i −0.226101 1.28228i −0.860570 0.509332i \(-0.829892\pi\)
0.634469 0.772948i \(-0.281219\pi\)
\(152\) 0.866025 1.50000i 0.0702439 0.121666i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) −13.2683 + 11.1334i −1.06573 + 0.894257i
\(156\) 0 0
\(157\) −2.25743 + 12.8025i −0.180162 + 1.02175i 0.751853 + 0.659331i \(0.229160\pi\)
−0.932015 + 0.362420i \(0.881951\pi\)
\(158\) 1.32683 + 1.11334i 0.105557 + 0.0885726i
\(159\) 0 0
\(160\) 16.9145 + 6.15636i 1.33721 + 0.486703i
\(161\) −6.92820 −0.546019
\(162\) 0 0
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 3.25519 + 1.18479i 0.254188 + 0.0925168i
\(165\) 0 0
\(166\) 9.19253 + 7.71345i 0.713479 + 0.598680i
\(167\) −4.21074 + 23.8803i −0.325837 + 1.84791i 0.177888 + 0.984051i \(0.443073\pi\)
−0.503725 + 0.863864i \(0.668038\pi\)
\(168\) 0 0
\(169\) 9.19253 7.71345i 0.707118 0.593342i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 2.40614 + 13.6459i 0.182935 + 1.03748i 0.928579 + 0.371134i \(0.121031\pi\)
−0.745644 + 0.666345i \(0.767858\pi\)
\(174\) 0 0
\(175\) 6.57785 2.39414i 0.497239 0.180980i
\(176\) 16.2760 5.92396i 1.22685 0.446535i
\(177\) 0 0
\(178\) 3.12567 + 17.7265i 0.234279 + 1.32866i
\(179\) −10.3923 + 18.0000i −0.776757 + 1.34538i 0.157044 + 0.987592i \(0.449804\pi\)
−0.933801 + 0.357792i \(0.883530\pi\)
\(180\) 0 0
\(181\) −8.50000 14.7224i −0.631800 1.09431i −0.987184 0.159589i \(-0.948983\pi\)
0.355383 0.934721i \(-0.384350\pi\)
\(182\) 6.63414 5.56670i 0.491755 0.412632i
\(183\) 0 0
\(184\) 2.08378 11.8177i 0.153618 0.871212i
\(185\) 2.65366 + 2.22668i 0.195101 + 0.163709i
\(186\) 0 0
\(187\) 0 0
\(188\) 3.46410 0.252646
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 6.51038 + 2.36959i 0.471075 + 0.171457i 0.566639 0.823966i \(-0.308243\pi\)
−0.0955644 + 0.995423i \(0.530466\pi\)
\(192\) 0 0
\(193\) −7.66044 6.42788i −0.551411 0.462689i 0.324008 0.946054i \(-0.394970\pi\)
−0.875418 + 0.483366i \(0.839414\pi\)
\(194\) −5.11305 + 28.9975i −0.367095 + 2.08190i
\(195\) 0 0
\(196\) −4.59627 + 3.85673i −0.328305 + 0.275480i
\(197\) −5.19615 9.00000i −0.370211 0.641223i 0.619387 0.785086i \(-0.287381\pi\)
−0.989598 + 0.143862i \(0.954048\pi\)
\(198\) 0 0
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 2.10537 + 11.9402i 0.148872 + 0.844297i
\(201\) 0 0
\(202\) 22.5526 8.20848i 1.58680 0.577547i
\(203\) 3.25519 1.18479i 0.228470 0.0831561i
\(204\) 0 0
\(205\) 2.08378 + 11.8177i 0.145537 + 0.825383i
\(206\) 6.92820 12.0000i 0.482711 0.836080i
\(207\) 0 0
\(208\) 12.5000 + 21.6506i 0.866719 + 1.50120i
\(209\) −2.65366 + 2.22668i −0.183557 + 0.154023i
\(210\) 0 0
\(211\) 0.868241 4.92404i 0.0597722 0.338985i −0.940227 0.340549i \(-0.889387\pi\)
0.999999 + 0.00156464i \(0.000498040\pi\)
\(212\) 7.96097 + 6.68004i 0.546761 + 0.458787i
\(213\) 0 0
\(214\) −16.9145 6.15636i −1.15625 0.420840i
\(215\) 3.46410 0.236250
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) 27.6691 + 10.0707i 1.87399 + 0.682076i
\(219\) 0 0
\(220\) −9.19253 7.71345i −0.619760 0.520041i
\(221\) 0 0
\(222\) 0 0
\(223\) −14.5548 + 12.2130i −0.974664 + 0.817841i −0.983276 0.182122i \(-0.941703\pi\)
0.00861141 + 0.999963i \(0.497259\pi\)
\(224\) 2.59808 + 4.50000i 0.173591 + 0.300669i
\(225\) 0 0
\(226\) 15.0000 25.9808i 0.997785 1.72821i
\(227\) 2.40614 + 13.6459i 0.159701 + 0.905710i 0.954361 + 0.298655i \(0.0965380\pi\)
−0.794660 + 0.607055i \(0.792351\pi\)
\(228\) 0 0
\(229\) −4.69846 + 1.71010i −0.310483 + 0.113007i −0.492562 0.870277i \(-0.663940\pi\)
0.182079 + 0.983284i \(0.441717\pi\)
\(230\) −39.0623 + 14.2175i −2.57569 + 0.937475i
\(231\) 0 0
\(232\) 1.04189 + 5.90885i 0.0684034 + 0.387935i
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) −2.65366 + 2.22668i −0.172738 + 0.144945i
\(237\) 0 0
\(238\) 0 0
\(239\) 5.30731 + 4.45336i 0.343301 + 0.288064i 0.798094 0.602533i \(-0.205842\pi\)
−0.454792 + 0.890598i \(0.650286\pi\)
\(240\) 0 0
\(241\) 17.8542 + 6.49838i 1.15009 + 0.418598i 0.845547 0.533902i \(-0.179275\pi\)
0.304541 + 0.952499i \(0.401497\pi\)
\(242\) −1.73205 −0.111340
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −19.5311 7.10876i −1.24780 0.454162i
\(246\) 0 0
\(247\) −3.83022 3.21394i −0.243711 0.204498i
\(248\) 1.50384 8.52869i 0.0954938 0.541572i
\(249\) 0 0
\(250\) 9.19253 7.71345i 0.581387 0.487841i
\(251\) 10.3923 + 18.0000i 0.655956 + 1.13615i 0.981653 + 0.190676i \(0.0610679\pi\)
−0.325697 + 0.945474i \(0.605599\pi\)
\(252\) 0 0
\(253\) −12.0000 + 20.7846i −0.754434 + 1.30672i
\(254\) −5.11305 28.9975i −0.320821 1.81947i
\(255\) 0 0
\(256\) −17.8542 + 6.49838i −1.11588 + 0.406149i
\(257\) 3.25519 1.18479i 0.203053 0.0739053i −0.238491 0.971145i \(-0.576653\pi\)
0.441545 + 0.897239i \(0.354431\pi\)
\(258\) 0 0
\(259\) 0.173648 + 0.984808i 0.0107900 + 0.0611930i
\(260\) 8.66025 15.0000i 0.537086 0.930261i
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) 10.6146 8.90673i 0.654526 0.549212i −0.253915 0.967227i \(-0.581718\pi\)
0.908440 + 0.418014i \(0.137274\pi\)
\(264\) 0 0
\(265\) −6.25133 + 35.4531i −0.384016 + 2.17787i
\(266\) −1.32683 1.11334i −0.0813530 0.0682633i
\(267\) 0 0
\(268\) −7.51754 2.73616i −0.459207 0.167138i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 9.19253 + 7.71345i 0.555341 + 0.465987i
\(275\) 4.21074 23.8803i 0.253917 1.44004i
\(276\) 0 0
\(277\) 13.0228 10.9274i 0.782462 0.656563i −0.161406 0.986888i \(-0.551603\pi\)
0.943867 + 0.330325i \(0.107158\pi\)
\(278\) −11.2583 19.5000i −0.675230 1.16953i
\(279\) 0 0
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 2.40614 + 13.6459i 0.143538 + 0.814046i 0.968529 + 0.248900i \(0.0800690\pi\)
−0.824991 + 0.565146i \(0.808820\pi\)
\(282\) 0 0
\(283\) 12.2160 4.44626i 0.726166 0.264303i 0.0476250 0.998865i \(-0.484835\pi\)
0.678541 + 0.734562i \(0.262613\pi\)
\(284\) 9.76557 3.55438i 0.579480 0.210914i
\(285\) 0 0
\(286\) −5.20945 29.5442i −0.308041 1.74699i
\(287\) −1.73205 + 3.00000i −0.102240 + 0.177084i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 15.9219 13.3601i 0.934968 0.784531i
\(291\) 0 0
\(292\) 0.347296 1.96962i 0.0203240 0.115263i
\(293\) −10.6146 8.90673i −0.620113 0.520337i 0.277726 0.960660i \(-0.410419\pi\)
−0.897839 + 0.440324i \(0.854864\pi\)
\(294\) 0 0
\(295\) −11.2763 4.10424i −0.656532 0.238958i
\(296\) −1.73205 −0.100673
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) −32.5519 11.8479i −1.88253 0.685183i
\(300\) 0 0
\(301\) 0.766044 + 0.642788i 0.0441541 + 0.0370497i
\(302\) 4.81228 27.2918i 0.276916 1.57047i
\(303\) 0 0
\(304\) 3.83022 3.21394i 0.219678 0.184332i
\(305\) 3.46410 + 6.00000i 0.198354 + 0.343559i
\(306\) 0 0
\(307\) −10.0000 + 17.3205i −0.570730 + 0.988534i 0.425761 + 0.904836i \(0.360006\pi\)
−0.996491 + 0.0836980i \(0.973327\pi\)
\(308\) −0.601535 3.41147i −0.0342756 0.194387i
\(309\) 0 0
\(310\) −28.1908 + 10.2606i −1.60113 + 0.582763i
\(311\) 13.0208 4.73917i 0.738340 0.268734i 0.0546491 0.998506i \(-0.482596\pi\)
0.683691 + 0.729772i \(0.260374\pi\)
\(312\) 0 0
\(313\) −0.173648 0.984808i −0.00981518 0.0556646i 0.979507 0.201411i \(-0.0645527\pi\)
−0.989322 + 0.145747i \(0.953442\pi\)
\(314\) −11.2583 + 19.5000i −0.635344 + 1.10045i
\(315\) 0 0
\(316\) 0.500000 + 0.866025i 0.0281272 + 0.0487177i
\(317\) −21.2292 + 17.8135i −1.19235 + 1.00050i −0.192538 + 0.981290i \(0.561672\pi\)
−0.999815 + 0.0192136i \(0.993884\pi\)
\(318\) 0 0
\(319\) 2.08378 11.8177i 0.116669 0.661664i
\(320\) −2.65366 2.22668i −0.148344 0.124475i
\(321\) 0 0
\(322\) −11.2763 4.10424i −0.628404 0.228720i
\(323\) 0 0
\(324\) 0 0
\(325\) 35.0000 1.94145
\(326\) −1.62760 0.592396i −0.0901442 0.0328098i
\(327\) 0 0
\(328\) −4.59627 3.85673i −0.253786 0.212952i
\(329\) −0.601535 + 3.41147i −0.0331637 + 0.188081i
\(330\) 0 0
\(331\) −14.5548 + 12.2130i −0.800007 + 0.671285i −0.948200 0.317673i \(-0.897099\pi\)
0.148194 + 0.988958i \(0.452654\pi\)
\(332\) 3.46410 + 6.00000i 0.190117 + 0.329293i
\(333\) 0 0
\(334\) −21.0000 + 36.3731i −1.14907 + 1.99025i
\(335\) −4.81228 27.2918i −0.262923 1.49111i
\(336\) 0 0
\(337\) −4.69846 + 1.71010i −0.255942 + 0.0931551i −0.466805 0.884361i \(-0.654595\pi\)
0.210863 + 0.977516i \(0.432373\pi\)
\(338\) 19.5311 7.10876i 1.06235 0.386665i
\(339\) 0 0
\(340\) 0 0
\(341\) −8.66025 + 15.0000i −0.468979 + 0.812296i
\(342\) 0 0
\(343\) −6.50000 11.2583i −0.350967 0.607893i
\(344\) −1.32683 + 1.11334i −0.0715378 + 0.0600273i
\(345\) 0 0
\(346\) −4.16756 + 23.6354i −0.224049 + 1.27065i
\(347\) −18.5756 15.5868i −0.997190 0.836742i −0.0105973 0.999944i \(-0.503373\pi\)
−0.986593 + 0.163202i \(0.947818\pi\)
\(348\) 0 0
\(349\) 0.939693 + 0.342020i 0.0503006 + 0.0183079i 0.367048 0.930202i \(-0.380369\pi\)
−0.316747 + 0.948510i \(0.602591\pi\)
\(350\) 12.1244 0.648074
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) 16.2760 + 5.92396i 0.866282 + 0.315301i 0.736660 0.676263i \(-0.236402\pi\)
0.129621 + 0.991564i \(0.458624\pi\)
\(354\) 0 0
\(355\) 27.5776 + 23.1404i 1.46367 + 1.22816i
\(356\) −1.80460 + 10.2344i −0.0956439 + 0.542423i
\(357\) 0 0
\(358\) −27.5776 + 23.1404i −1.45752 + 1.22301i
\(359\) 15.5885 + 27.0000i 0.822727 + 1.42501i 0.903644 + 0.428285i \(0.140882\pi\)
−0.0809166 + 0.996721i \(0.525785\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −5.11305 28.9975i −0.268736 1.52408i
\(363\) 0 0
\(364\) 4.69846 1.71010i 0.246266 0.0896336i
\(365\) 6.51038 2.36959i 0.340769 0.124030i
\(366\) 0 0
\(367\) −2.77837 15.7569i −0.145030 0.822505i −0.967343 0.253470i \(-0.918428\pi\)
0.822313 0.569035i \(-0.192683\pi\)
\(368\) 17.3205 30.0000i 0.902894 1.56386i
\(369\) 0 0
\(370\) 3.00000 + 5.19615i 0.155963 + 0.270135i
\(371\) −7.96097 + 6.68004i −0.413313 + 0.346811i
\(372\) 0 0
\(373\) 3.99391 22.6506i 0.206797 1.17280i −0.687791 0.725909i \(-0.741419\pi\)
0.894587 0.446893i \(-0.147470\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −5.63816 2.05212i −0.290766 0.105830i
\(377\) 17.3205 0.892052
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) −3.25519 1.18479i −0.166988 0.0607786i
\(381\) 0 0
\(382\) 9.19253 + 7.71345i 0.470331 + 0.394655i
\(383\) 3.00767 17.0574i 0.153685 0.871591i −0.806293 0.591516i \(-0.798530\pi\)
0.959978 0.280075i \(-0.0903593\pi\)
\(384\) 0 0
\(385\) 9.19253 7.71345i 0.468495 0.393114i
\(386\) −8.66025 15.0000i −0.440795 0.763480i
\(387\) 0 0
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) −1.20307 6.82295i −0.0609981 0.345937i −0.999998 0.00201979i \(-0.999357\pi\)
0.939000 0.343917i \(-0.111754\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 9.76557 3.55438i 0.493236 0.179523i
\(393\) 0 0
\(394\) −3.12567 17.7265i −0.157469 0.893050i
\(395\) −1.73205 + 3.00000i −0.0871489 + 0.150946i
\(396\) 0 0
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 25.2097 21.1535i 1.26365 1.06033i
\(399\) 0 0
\(400\) −6.07769 + 34.4683i −0.303884 + 1.72341i
\(401\) −2.65366 2.22668i −0.132517 0.111195i 0.574120 0.818771i \(-0.305344\pi\)
−0.706637 + 0.707576i \(0.749789\pi\)
\(402\) 0 0
\(403\) −23.4923 8.55050i −1.17024 0.425931i
\(404\) 13.8564 0.689382
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 3.25519 + 1.18479i 0.161354 + 0.0587280i
\(408\) 0 0
\(409\) 3.83022 + 3.21394i 0.189392 + 0.158919i 0.732554 0.680709i \(-0.238328\pi\)
−0.543161 + 0.839628i \(0.682773\pi\)
\(410\) −3.60921 + 20.4688i −0.178246 + 1.01088i
\(411\) 0 0
\(412\) 6.12836 5.14230i 0.301922 0.253343i
\(413\) −1.73205 3.00000i −0.0852286 0.147620i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 4.51151 + 25.5861i 0.221195 + 1.25446i
\(417\) 0 0
\(418\) −5.63816 + 2.05212i −0.275771 + 0.100373i
\(419\) −35.8071 + 13.0327i −1.74929 + 0.636690i −0.999683 0.0251915i \(-0.991980\pi\)
−0.749609 + 0.661881i \(0.769758\pi\)
\(420\) 0 0
\(421\) −3.29932 18.7113i −0.160799 0.911935i −0.953291 0.302053i \(-0.902328\pi\)
0.792492 0.609882i \(-0.208783\pi\)
\(422\) 4.33013 7.50000i 0.210787 0.365094i
\(423\) 0 0
\(424\) −9.00000 15.5885i −0.437079 0.757042i
\(425\) 0 0
\(426\) 0 0
\(427\) −0.347296 + 1.96962i −0.0168068 + 0.0953164i
\(428\) −7.96097 6.68004i −0.384808 0.322892i
\(429\) 0 0
\(430\) 5.63816 + 2.05212i 0.271896 + 0.0989621i
\(431\) 20.7846 1.00116 0.500580 0.865690i \(-0.333120\pi\)
0.500580 + 0.865690i \(0.333120\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) −8.13798 2.96198i −0.390635 0.142180i
\(435\) 0 0
\(436\) 13.0228 + 10.9274i 0.623677 + 0.523327i
\(437\) −1.20307 + 6.82295i −0.0575506 + 0.326386i
\(438\) 0 0
\(439\) 15.3209 12.8558i 0.731226 0.613572i −0.199239 0.979951i \(-0.563847\pi\)
0.930466 + 0.366379i \(0.119403\pi\)
\(440\) 10.3923 + 18.0000i 0.495434 + 0.858116i
\(441\) 0 0
\(442\) 0 0
\(443\) 2.40614 + 13.6459i 0.114319 + 0.648336i 0.987085 + 0.160197i \(0.0512130\pi\)
−0.872766 + 0.488139i \(0.837676\pi\)
\(444\) 0 0
\(445\) −33.8289 + 12.3127i −1.60365 + 0.583679i
\(446\) −30.9243 + 11.2555i −1.46431 + 0.532965i
\(447\) 0 0
\(448\) −0.173648 0.984808i −0.00820411 0.0465278i
\(449\) −5.19615 + 9.00000i −0.245222 + 0.424736i −0.962194 0.272365i \(-0.912194\pi\)
0.716972 + 0.697102i \(0.245527\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) 13.2683 11.1334i 0.624087 0.523671i
\(453\) 0 0
\(454\) −4.16756 + 23.6354i −0.195593 + 1.10926i
\(455\) 13.2683 + 11.1334i 0.622027 + 0.521942i
\(456\) 0 0
\(457\) −15.9748 5.81434i −0.747268 0.271983i −0.0598126 0.998210i \(-0.519050\pi\)
−0.687456 + 0.726226i \(0.741273\pi\)
\(458\) −8.66025 −0.404667
\(459\) 0 0
\(460\) −24.0000 −1.11901
\(461\) 26.0415 + 9.47834i 1.21287 + 0.441450i 0.867700 0.497088i \(-0.165597\pi\)
0.345175 + 0.938538i \(0.387820\pi\)
\(462\) 0 0
\(463\) −23.7474 19.9264i −1.10363 0.926059i −0.105970 0.994369i \(-0.533795\pi\)
−0.997664 + 0.0683102i \(0.978239\pi\)
\(464\) −3.00767 + 17.0574i −0.139628 + 0.791869i
\(465\) 0 0
\(466\) 0 0
\(467\) −5.19615 9.00000i −0.240449 0.416470i 0.720393 0.693566i \(-0.243961\pi\)
−0.960842 + 0.277096i \(0.910628\pi\)
\(468\) 0 0
\(469\) 4.00000 6.92820i 0.184703 0.319915i
\(470\) 3.60921 + 20.4688i 0.166480 + 0.944157i
\(471\) 0 0
\(472\) 5.63816 2.05212i 0.259517 0.0944565i
\(473\) 3.25519 1.18479i 0.149674 0.0544768i
\(474\) 0 0
\(475\) −1.21554 6.89365i −0.0557727 0.316303i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) 10.6146 8.90673i 0.484995 0.406959i −0.367234 0.930129i \(-0.619695\pi\)
0.852228 + 0.523170i \(0.175251\pi\)
\(480\) 0 0
\(481\) −0.868241 + 4.92404i −0.0395884 + 0.224517i
\(482\) 25.2097 + 21.1535i 1.14827 + 0.963514i
\(483\) 0 0
\(484\) −0.939693 0.342020i −0.0427133 0.0155464i
\(485\) −58.8897 −2.67404
\(486\) 0 0
\(487\) −19.0000 −0.860972 −0.430486 0.902597i \(-0.641658\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) −3.25519 1.18479i −0.147356 0.0536330i
\(489\) 0 0
\(490\) −27.5776 23.1404i −1.24583 1.04537i
\(491\) 6.61688 37.5262i 0.298616 1.69353i −0.353516 0.935429i \(-0.615014\pi\)
0.652132 0.758106i \(-0.273875\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −4.33013 7.50000i −0.194822 0.337441i
\(495\) 0 0
\(496\) 12.5000 21.6506i 0.561267 0.972142i
\(497\) 1.80460 + 10.2344i 0.0809476 + 0.459077i
\(498\) 0 0
\(499\) 26.3114 9.57656i 1.17786 0.428706i 0.322414 0.946599i \(-0.395506\pi\)
0.855446 + 0.517893i \(0.173283\pi\)
\(500\) 6.51038 2.36959i 0.291153 0.105971i
\(501\) 0 0
\(502\) 6.25133 + 35.4531i 0.279011 + 1.58235i
\(503\) 20.7846 36.0000i 0.926740 1.60516i 0.138001 0.990432i \(-0.455932\pi\)
0.788739 0.614729i \(-0.210734\pi\)
\(504\) 0 0
\(505\) 24.0000 + 41.5692i 1.06799 + 1.84981i
\(506\) −31.8439 + 26.7202i −1.41563 + 1.18786i
\(507\) 0 0
\(508\) 2.95202 16.7417i 0.130975 0.742794i
\(509\) 21.2292 + 17.8135i 0.940970 + 0.789567i 0.977754 0.209756i \(-0.0672669\pi\)
−0.0367840 + 0.999323i \(0.511711\pi\)
\(510\) 0 0
\(511\) 1.87939 + 0.684040i 0.0831391 + 0.0302602i
\(512\) −8.66025 −0.382733
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 26.0415 + 9.47834i 1.14753 + 0.417666i
\(516\) 0 0
\(517\) 9.19253 + 7.71345i 0.404287 + 0.339237i
\(518\) −0.300767 + 1.70574i −0.0132150 + 0.0749458i
\(519\) 0 0
\(520\) −22.9813 + 19.2836i −1.00780 + 0.845643i
\(521\) −10.3923 18.0000i −0.455295 0.788594i 0.543410 0.839467i \(-0.317133\pi\)
−0.998705 + 0.0508731i \(0.983800\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) −0.601535 3.41147i −0.0262782 0.149031i
\(525\) 0 0
\(526\) 22.5526 8.20848i 0.983341 0.357907i
\(527\) 0 0
\(528\) 0 0
\(529\) 4.34120 + 24.6202i 0.188748 + 1.07044i
\(530\) −31.1769 + 54.0000i −1.35424 + 2.34561i
\(531\) 0 0
\(532\) −0.500000 0.866025i −0.0216777 0.0375470i
\(533\) −13.2683 + 11.1334i −0.574713 + 0.482241i
\(534\) 0 0
\(535\) 6.25133 35.4531i 0.270269 1.53277i
\(536\) 10.6146 + 8.90673i 0.458482 + 0.384712i
\(537\) 0 0
\(538\) 0 0
\(539\) −20.7846 −0.895257
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) −26.0415 9.47834i −1.11858 0.407130i
\(543\) 0 0
\(544\) 0 0
\(545\) −10.2261 + 57.9951i −0.438038 + 2.48424i
\(546\) 0 0
\(547\) 15.3209 12.8558i 0.655074 0.549672i −0.253532 0.967327i \(-0.581592\pi\)
0.908606 + 0.417655i \(0.137148\pi\)
\(548\) 3.46410 + 6.00000i 0.147979 + 0.256307i
\(549\) 0 0
\(550\) 21.0000 36.3731i 0.895443 1.55095i
\(551\) −0.601535 3.41147i −0.0256262 0.145334i
\(552\) 0 0
\(553\) −0.939693 + 0.342020i −0.0399598 + 0.0145442i
\(554\) 27.6691 10.0707i 1.17555 0.427865i
\(555\) 0 0
\(556\) −2.25743 12.8025i −0.0957362 0.542947i
\(557\) 5.19615 9.00000i 0.220168 0.381342i −0.734691 0.678402i \(-0.762673\pi\)
0.954859 + 0.297060i \(0.0960061\pi\)
\(558\) 0 0
\(559\) 2.50000 + 4.33013i 0.105739 + 0.183145i
\(560\) −13.2683 + 11.1334i −0.560687 + 0.470472i
\(561\) 0 0
\(562\) −4.16756 + 23.6354i −0.175798 + 0.996999i
\(563\) −26.5366 22.2668i −1.11838 0.938434i −0.119861 0.992791i \(-0.538245\pi\)
−0.998522 + 0.0543563i \(0.982689\pi\)
\(564\) 0 0
\(565\) 56.3816 + 20.5212i 2.37199 + 0.863334i
\(566\) 22.5167 0.946446
\(567\) 0 0
\(568\) −18.0000 −0.755263
\(569\) −22.7863 8.29355i −0.955253 0.347684i −0.183081 0.983098i \(-0.558607\pi\)
−0.772172 + 0.635414i \(0.780829\pi\)
\(570\) 0 0
\(571\) 31.4078 + 26.3543i 1.31438 + 1.10289i 0.987465 + 0.157838i \(0.0504523\pi\)
0.326911 + 0.945055i \(0.393992\pi\)
\(572\) 3.00767 17.0574i 0.125757 0.713204i
\(573\) 0 0
\(574\) −4.59627 + 3.85673i −0.191844 + 0.160977i
\(575\) −24.2487 42.0000i −1.01124 1.75152i
\(576\) 0 0
\(577\) 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) 5.11305 + 28.9975i 0.212675 + 1.20614i
\(579\) 0 0
\(580\) 11.2763 4.10424i 0.468223 0.170419i
\(581\) −6.51038 + 2.36959i −0.270096 + 0.0983070i
\(582\) 0 0
\(583\) 6.25133 + 35.4531i 0.258904 + 1.46832i
\(584\) −1.73205 + 3.00000i −0.0716728 + 0.124141i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) −5.30731 + 4.45336i −0.219056 + 0.183810i −0.745712 0.666269i \(-0.767890\pi\)
0.526655 + 0.850079i \(0.323446\pi\)
\(588\) 0 0
\(589\) −0.868241 + 4.92404i −0.0357752 + 0.202891i
\(590\) −15.9219 13.3601i −0.655496 0.550026i
\(591\) 0 0
\(592\) −4.69846 1.71010i −0.193106 0.0702847i
\(593\) −20.7846 −0.853522 −0.426761 0.904365i \(-0.640345\pi\)
−0.426761 + 0.904365i \(0.640345\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.51038 2.36959i −0.266676 0.0970620i
\(597\) 0 0
\(598\) −45.9627 38.5673i −1.87955 1.57713i
\(599\) −4.21074 + 23.8803i −0.172046 + 0.975723i 0.769452 + 0.638705i \(0.220530\pi\)
−0.941498 + 0.337018i \(0.890582\pi\)
\(600\) 0 0
\(601\) 26.8116 22.4976i 1.09367 0.917695i 0.0966832 0.995315i \(-0.469177\pi\)
0.996983 + 0.0776203i \(0.0247322\pi\)
\(602\) 0.866025 + 1.50000i 0.0352966 + 0.0611354i
\(603\) 0 0
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) −0.601535 3.41147i −0.0244559 0.138696i
\(606\) 0 0
\(607\) 12.2160 4.44626i 0.495832 0.180468i −0.0819862 0.996633i \(-0.526126\pi\)
0.577819 + 0.816165i \(0.303904\pi\)
\(608\) 4.88279 1.77719i 0.198023 0.0720745i
\(609\) 0 0
\(610\) 2.08378 + 11.8177i 0.0843697 + 0.478484i
\(611\) −8.66025 + 15.0000i −0.350356 + 0.606835i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −26.5366 + 22.2668i −1.07093 + 0.898616i
\(615\) 0 0
\(616\) −1.04189 + 5.90885i −0.0419789 + 0.238074i
\(617\) 5.30731 + 4.45336i 0.213664 + 0.179286i 0.743338 0.668916i \(-0.233241\pi\)
−0.529674 + 0.848201i \(0.677686\pi\)
\(618\) 0 0
\(619\) −18.7939 6.84040i −0.755389 0.274939i −0.0645172 0.997917i \(-0.520551\pi\)
−0.690871 + 0.722978i \(0.742773\pi\)
\(620\) −17.3205 −0.695608
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −9.76557 3.55438i −0.391249 0.142403i
\(624\) 0 0
\(625\) −8.42649 7.07066i −0.337060 0.282827i
\(626\) 0.300767 1.70574i 0.0120211 0.0681750i
\(627\) 0 0
\(628\) −9.95858 + 8.35624i −0.397391 + 0.333450i
\(629\) 0 0
\(630\) 0 0
\(631\) −8.50000 + 14.7224i −0.338380 + 0.586091i −0.984128 0.177459i \(-0.943212\pi\)
0.645748 + 0.763550i \(0.276545\pi\)
\(632\) −0.300767 1.70574i −0.0119639 0.0678506i
\(633\) 0 0
\(634\) −45.1052 + 16.4170i −1.79136 + 0.652001i
\(635\) 55.3382 20.1415i 2.19603 0.799290i
\(636\) 0 0
\(637\) −5.20945 29.5442i −0.206406 1.17059i
\(638\) 10.3923 18.0000i 0.411435 0.712627i
\(639\) 0 0
\(640\) −21.0000 36.3731i −0.830098 1.43777i
\(641\) 34.4975 28.9469i 1.36257 1.14333i 0.387391 0.921915i \(-0.373376\pi\)
0.975179 0.221417i \(-0.0710681\pi\)
\(642\) 0 0
\(643\) 7.64052 43.3315i 0.301313 1.70883i −0.339060 0.940765i \(-0.610109\pi\)
0.640373 0.768064i \(-0.278780\pi\)
\(644\) −5.30731 4.45336i −0.209137 0.175487i
\(645\) 0 0
\(646\) 0 0
\(647\) 20.7846 0.817127 0.408564 0.912730i \(-0.366030\pi\)
0.408564 + 0.912730i \(0.366030\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 56.9658 + 20.7339i 2.23438 + 0.813249i
\(651\) 0 0
\(652\) −0.766044 0.642788i −0.0300006 0.0251735i
\(653\) 3.00767 17.0574i 0.117699 0.667506i −0.867679 0.497125i \(-0.834389\pi\)
0.985378 0.170381i \(-0.0544999\pi\)
\(654\) 0 0
\(655\) 9.19253 7.71345i 0.359182 0.301389i
\(656\) −8.66025 15.0000i −0.338126 0.585652i
\(657\) 0 0
\(658\) −3.00000 + 5.19615i −0.116952 + 0.202567i
\(659\) −4.81228 27.2918i −0.187460 1.06314i −0.922754 0.385389i \(-0.874067\pi\)
0.735294 0.677748i \(-0.237044\pi\)
\(660\) 0 0
\(661\) 9.39693 3.42020i 0.365498 0.133030i −0.152741 0.988266i \(-0.548810\pi\)
0.518239 + 0.855236i \(0.326588\pi\)
\(662\) −30.9243 + 11.2555i −1.20191 + 0.437459i
\(663\) 0 0
\(664\) −2.08378 11.8177i −0.0808663 0.458615i
\(665\) 1.73205 3.00000i 0.0671660 0.116335i
\(666\) 0 0
\(667\) −12.0000 20.7846i −0.464642 0.804783i
\(668\) −18.5756 + 15.5868i −0.718711 + 0.603070i
\(669\) 0 0
\(670\) 8.33511 47.2708i 0.322013 1.82623i
\(671\) 5.30731 + 4.45336i 0.204886 + 0.171920i
\(672\) 0 0
\(673\) 34.7686 + 12.6547i 1.34023 + 0.487805i 0.909886 0.414859i \(-0.136169\pi\)
0.430346 + 0.902664i \(0.358391\pi\)
\(674\) −8.66025 −0.333581
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 16.2760 + 5.92396i 0.625536 + 0.227676i 0.635287 0.772276i \(-0.280882\pi\)
−0.00975136 + 0.999952i \(0.503104\pi\)
\(678\) 0 0
\(679\) −13.0228 10.9274i −0.499767 0.419355i
\(680\) 0 0
\(681\) 0 0
\(682\) −22.9813 + 19.2836i −0.880001 + 0.738408i
\(683\) 20.7846 + 36.0000i 0.795301 + 1.37750i 0.922648 + 0.385643i \(0.126021\pi\)
−0.127347 + 0.991858i \(0.540646\pi\)
\(684\) 0 0
\(685\) −12.0000 + 20.7846i −0.458496 + 0.794139i
\(686\) −3.90998 22.1746i −0.149284 0.846629i
\(687\) 0 0
\(688\) −4.69846 + 1.71010i −0.179127 + 0.0651970i
\(689\) −48.8279 + 17.7719i −1.86019 + 0.677055i
\(690\) 0 0
\(691\) 2.95202 + 16.7417i 0.112300 + 0.636885i 0.988052 + 0.154123i \(0.0492553\pi\)
−0.875752 + 0.482762i \(0.839634\pi\)
\(692\) −6.92820 + 12.0000i −0.263371 + 0.456172i
\(693\) 0 0
\(694\) −21.0000 36.3731i −0.797149 1.38070i
\(695\) 34.4975 28.9469i 1.30857 1.09802i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.32683 + 1.11334i 0.0502212 + 0.0421406i
\(699\) 0 0
\(700\) 6.57785 + 2.39414i 0.248619 + 0.0904900i
\(701\) 41.5692 1.57005 0.785024 0.619466i \(-0.212651\pi\)
0.785024 + 0.619466i \(0.212651\pi\)
\(702\) 0 0
\(703\) 1.00000 0.0377157
\(704\) −3.25519 1.18479i −0.122685 0.0446535i
\(705\) 0 0
\(706\) 22.9813 + 19.2836i 0.864914 + 0.725749i
\(707\) −2.40614 + 13.6459i −0.0904922 + 0.513207i
\(708\) 0 0
\(709\) −14.5548 + 12.2130i −0.546619 + 0.458668i −0.873794 0.486296i \(-0.838348\pi\)
0.327175 + 0.944964i \(0.393903\pi\)
\(710\) 31.1769 + 54.0000i 1.17005 + 2.02658i
\(711\) 0 0
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 6.01535 + 34.1147i 0.225277 + 1.27761i
\(714\) 0 0
\(715\) 56.3816 20.5212i 2.10855 0.767450i
\(716\) −19.5311 + 7.10876i −0.729913 + 0.265667i
\(717\) 0 0
\(718\) 9.37700 + 53.1796i 0.349947 + 1.98465i
\(719\) 5.19615 9.00000i 0.193784 0.335643i −0.752717 0.658344i \(-0.771257\pi\)
0.946501 + 0.322700i \(0.104591\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) 23.8829 20.0401i 0.888830 0.745817i
\(723\) 0 0
\(724\) 2.95202 16.7417i 0.109711 0.622202i
\(725\) 18.5756 + 15.5868i 0.689880 + 0.578878i
\(726\) 0 0
\(727\) 15.0351 + 5.47232i 0.557620 + 0.202957i 0.605429 0.795899i \(-0.293002\pi\)
−0.0478087 + 0.998857i \(0.515224\pi\)
\(728\) −8.66025 −0.320970
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) 0 0
\(732\) 0 0
\(733\) 31.4078 + 26.3543i 1.16007 + 0.973418i 0.999907 0.0136718i \(-0.00435201\pi\)
0.160168 + 0.987090i \(0.448796\pi\)
\(734\) 4.81228 27.2918i 0.177624 1.00736i
\(735\) 0 0
\(736\) 27.5776 23.1404i 1.01652 0.852965i
\(737\) −13.8564 24.0000i −0.510407 0.884051i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 0.601535 + 3.41147i 0.0221129 + 0.125408i
\(741\) 0 0
\(742\) −16.9145 + 6.15636i −0.620950 + 0.226007i
\(743\) −6.51038 + 2.36959i −0.238843 + 0.0869316i −0.458668 0.888608i \(-0.651673\pi\)
0.219826 + 0.975539i \(0.429451\pi\)
\(744\) 0 0
\(745\) −4.16756 23.6354i −0.152687 0.865934i
\(746\) 19.9186 34.5000i 0.729271 1.26313i
\(747\) 0 0
\(748\) 0 0
\(749\) 7.96097 6.68004i 0.290887 0.244084i
\(750\) 0 0
\(751\) 0.868241 4.92404i 0.0316826 0.179681i −0.964860 0.262764i \(-0.915366\pi\)
0.996543 + 0.0830837i \(0.0264769\pi\)
\(752\) −13.2683 11.1334i −0.483844 0.405994i
\(753\) 0 0
\(754\) 28.1908 + 10.2606i 1.02665 + 0.373669i
\(755\) 55.4256 2.01715
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −30.9243 11.2555i −1.12322 0.408819i
\(759\) 0 0
\(760\) 4.59627 + 3.85673i 0.166724 + 0.139898i
\(761\) 4.81228 27.2918i 0.174445 0.989327i −0.764338 0.644816i \(-0.776934\pi\)
0.938783 0.344510i \(-0.111955\pi\)
\(762\) 0 0
\(763\) −13.0228 + 10.9274i −0.471455 + 0.395598i
\(764\) 3.46410 + 6.00000i 0.125327 + 0.217072i
\(765\) 0 0
\(766\) 15.0000 25.9808i 0.541972 0.938723i
\(767\) −3.00767 17.0574i −0.108601 0.615906i
\(768\) 0 0
\(769\) 12.2160 4.44626i 0.440520 0.160336i −0.112232 0.993682i \(-0.535800\pi\)
0.552752 + 0.833346i \(0.313578\pi\)
\(770\) 19.5311 7.10876i 0.703854 0.256182i
\(771\) 0 0
\(772\) −1.73648 9.84808i −0.0624973 0.354440i
\(773\) 10.3923 18.0000i 0.373785 0.647415i −0.616359 0.787465i \(-0.711393\pi\)
0.990144 + 0.140050i \(0.0447264\pi\)
\(774\) 0 0
\(775\) −17.5000 30.3109i −0.628619 1.08880i
\(776\) 22.5561 18.9268i 0.809716 0.679432i
\(777\) 0 0
\(778\) 2.08378 11.8177i 0.0747071 0.423685i
\(779\) 2.65366 + 2.22668i 0.0950771 + 0.0797791i
\(780\) 0 0
\(781\) 33.8289 + 12.3127i 1.21049 + 0.440584i
\(782\) 0 0
\(783\) 0 0
\(784\) 30.0000 1.07143
\(785\) −42.3175 15.4023i −1.51038 0.549732i
\(786\) 0 0
\(787\) −21.4492 17.9981i −0.764583 0.641561i 0.174732 0.984616i \(-0.444094\pi\)
−0.939315 + 0.343055i \(0.888538\pi\)
\(788\) 1.80460 10.2344i 0.0642864 0.364586i
\(789\) 0 0
\(790\) −4.59627 + 3.85673i −0.163528 + 0.137216i
\(791\) 8.66025 + 15.0000i 0.307923 + 0.533339i
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 0.300767 + 1.70574i 0.0106738 + 0.0605343i
\(795\) 0 0
\(796\) 17.8542 6.49838i 0.632824 0.230329i
\(797\) 13.0208 4.73917i 0.461219 0.167870i −0.100951 0.994891i \(-0.532189\pi\)
0.562171 + 0.827021i \(0.309966\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −18.1865 + 31.5000i −0.642991 + 1.11369i
\(801\) 0 0
\(802\) −3.00000 5.19615i −0.105934 0.183483i
\(803\) 5.30731 4.45336i 0.187291 0.157156i
\(804\) 0 0
\(805\) 4.16756 23.6354i 0.146887 0.833038i
\(806\) −33.1707 27.8335i −1.16839 0.980394i
\(807\) 0 0
\(808\) −22.5526 8.20848i −0.793399 0.288773i
\(809\) 31.1769 1.09612 0.548061 0.836438i \(-0.315366\pi\)
0.548061 + 0.836438i \(0.315366\pi\)
\(810\) 0 0
\(811\) 35.0000 1.22902 0.614508 0.788911i \(-0.289355\pi\)
0.614508 + 0.788911i \(0.289355\pi\)
\(812\) 3.25519 + 1.18479i 0.114235 + 0.0415781i
\(813\) 0 0
\(814\) 4.59627 + 3.85673i 0.161099 + 0.135178i
\(815\) 0.601535 3.41147i 0.0210708 0.119499i
\(816\) 0 0
\(817\) 0.766044 0.642788i 0.0268005 0.0224883i
\(818\) 4.33013 + 7.50000i 0.151399 + 0.262231i
\(819\) 0 0
\(820\) −6.00000 + 10.3923i −0.209529 + 0.362915i
\(821\) −6.61688 37.5262i −0.230931 1.30967i −0.851016 0.525140i \(-0.824013\pi\)
0.620085 0.784534i \(-0.287098\pi\)
\(822\) 0 0
\(823\) −21.6129 + 7.86646i −0.753379 + 0.274208i −0.690027 0.723784i \(-0.742401\pi\)
−0.0633523 + 0.997991i \(0.520179\pi\)
\(824\) −13.0208 + 4.73917i −0.453600 + 0.165097i
\(825\) 0 0
\(826\) −1.04189 5.90885i −0.0362520 0.205595i
\(827\) −5.19615 + 9.00000i −0.180688 + 0.312961i −0.942115 0.335290i \(-0.891166\pi\)
0.761427 + 0.648251i \(0.224499\pi\)
\(828\) 0 0
\(829\) 9.50000 + 16.4545i 0.329949 + 0.571488i 0.982501 0.186256i \(-0.0596352\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(830\) −31.8439 + 26.7202i −1.10532 + 0.927471i
\(831\) 0 0
\(832\) 0.868241 4.92404i 0.0301008 0.170710i
\(833\) 0 0
\(834\) 0 0
\(835\) −78.9342 28.7297i −2.73163 0.994232i
\(836\) −3.46410 −0.119808
\(837\) 0 0
\(838\) −66.0000 −2.27993
\(839\) −3.25519 1.18479i −0.112382 0.0409036i 0.285217 0.958463i \(-0.407934\pi\)
−0.397599 + 0.917559i \(0.630156\pi\)
\(840\) 0 0
\(841\) −13.0228 10.9274i −0.449061 0.376807i
\(842\) 5.71458 32.4090i 0.196937 1.11689i
\(843\) 0 0
\(844\) 3.83022 3.21394i 0.131842 0.110628i
\(845\) 20.7846 + 36.0000i 0.715012 + 1.23844i
\(846\) 0 0
\(847\) 0.500000 0.866025i 0.0171802 0.0297570i
\(848\) −9.02302 51.1721i −0.309852 1.75726i
\(849\) 0 0
\(850\) 0 0
\(851\) 6.51038 2.36959i 0.223173 0.0812283i
\(852\) 0 0
\(853\) 0.347296 + 1.96962i 0.0118912 + 0.0674384i 0.990176 0.139827i \(-0.0446547\pi\)
−0.978285 + 0.207266i \(0.933544\pi\)
\(854\) −1.73205 + 3.00000i −0.0592696 + 0.102658i
\(855\) 0 0
\(856\) 9.00000 + 15.5885i 0.307614 + 0.532803i
\(857\) −29.1902 + 24.4935i −0.997119 + 0.836682i −0.986583 0.163263i \(-0.947798\pi\)
−0.0105360 + 0.999944i \(0.503354\pi\)
\(858\) 0 0
\(859\) −8.50876 + 48.2556i −0.290315 + 1.64646i 0.395342 + 0.918534i \(0.370626\pi\)
−0.685657 + 0.727925i \(0.740485\pi\)
\(860\) 2.65366 + 2.22668i 0.0904889 + 0.0759292i
\(861\) 0 0
\(862\) 33.8289 + 12.3127i 1.15222 + 0.419373i
\(863\) −10.3923 −0.353758 −0.176879 0.984233i \(-0.556600\pi\)
−0.176879 + 0.984233i \(0.556600\pi\)
\(864\) 0 0
\(865\) −48.0000 −1.63205
\(866\) −1.62760 0.592396i −0.0553079 0.0201304i
\(867\) 0 0
\(868\) −3.83022 3.21394i −0.130006 0.109088i
\(869\) −0.601535 + 3.41147i −0.0204057 + 0.115726i
\(870\) 0 0
\(871\) 30.6418 25.7115i 1.03826 0.871201i
\(872\) −14.7224 25.5000i −0.498564 0.863539i
\(873\) 0 0
\(874\) −6.00000 + 10.3923i −0.202953 + 0.351525i
\(875\) 1.20307 + 6.82295i 0.0406712 + 0.230658i
\(876\) 0 0
\(877\) −21.6129 + 7.86646i −0.729817 + 0.265632i −0.680087 0.733131i \(-0.738058\pi\)
−0.0497295 + 0.998763i \(0.515836\pi\)
\(878\) 32.5519 11.8479i 1.09857 0.399848i
\(879\) 0 0
\(880\) 10.4189 + 59.0885i 0.351221 + 1.99187i
\(881\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(882\) 0 0
\(883\) 9.50000 + 16.4545i 0.319700 + 0.553737i 0.980425 0.196891i \(-0.0630844\pi\)
−0.660725 + 0.750628i \(0.729751\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −4.16756 + 23.6354i −0.140012 + 0.794046i
\(887\) −10.6146 8.90673i −0.356404 0.299059i 0.446951 0.894558i \(-0.352510\pi\)
−0.803356 + 0.595500i \(0.796954\pi\)
\(888\) 0 0
\(889\) 15.9748 + 5.81434i 0.535777 + 0.195007i
\(890\) −62.3538 −2.09011
\(891\) 0 0
\(892\) −19.0000 −0.636167
\(893\) 3.25519 + 1.18479i 0.108931 + 0.0396476i
\(894\) 0 0
\(895\) −55.1552 46.2807i −1.84364 1.54699i
\(896\) 2.10537 11.9402i 0.0703356 0.398893i
\(897\) 0 0
\(898\) −13.7888 + 11.5702i −0.460138 + 0.386102i
\(899\) −8.66025 15.0000i −0.288836 0.500278i
\(900\) 0 0
\(901\) 0 0
\(902\) 3.60921 + 20.4688i 0.120174 + 0.681538i
\(903\) 0 0
\(904\) −28.1908 + 10.2606i −0.937611 + 0.341263i
\(905\) 55.3382 20.1415i 1.83951 0.669525i
\(906\) 0 0
\(907\) −6.42498 36.4379i −0.213338 1.20990i −0.883767 0.467927i \(-0.845001\pi\)
0.670429 0.741973i \(-0.266110\pi\)
\(908\) −6.92820 + 12.0000i −0.229920 + 0.398234i
\(909\) 0 0
\(910\) 15.0000 + 25.9808i 0.497245 + 0.861254i
\(911\) −21.2292 + 17.8135i −0.703356 + 0.590186i −0.922726 0.385456i \(-0.874044\pi\)
0.219370 + 0.975642i \(0.429600\pi\)
\(912\) 0 0
\(913\) −4.16756 + 23.6354i −0.137926 + 0.782217i
\(914\) −22.5561 18.9268i −0.746089 0.626043i
\(915\) 0 0
\(916\) −4.69846 1.71010i −0.155242 0.0565033i
\(917\) 3.46410 0.114395
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 39.0623 + 14.2175i 1.28785 + 0.468737i
\(921\) 0 0
\(922\) 36.7701 + 30.8538i 1.21096 + 1.01612i
\(923\) −9.02302 + 51.1721i −0.296996 + 1.68435i
\(924\) 0 0
\(925\) −5.36231 + 4.49951i −0.176312 + 0.147943i
\(926\) −26.8468 46.5000i −0.882240 1.52808i
\(927\) 0 0
\(928\) −9.00000 + 15.5885i −0.295439 + 0.511716i
\(929\) −1.20307 6.82295i −0.0394714 0.223854i 0.958691 0.284450i \(-0.0918109\pi\)
−0.998162 + 0.0605962i \(0.980700\pi\)
\(930\) 0 0
\(931\) −5.63816 + 2.05212i −0.184783 + 0.0672555i
\(932\) 0 0
\(933\) 0 0
\(934\) −3.12567 17.7265i −0.102275 0.580030i
\(935\) 0 0
\(936\) 0 0
\(937\) 18.5000 + 32.0429i 0.604369 + 1.04680i 0.992151 + 0.125046i \(0.0399079\pi\)
−0.387782 + 0.921751i \(0.626759\pi\)
\(938\) 10.6146 8.90673i 0.346580 0.290815i
\(939\) 0 0
\(940\) −2.08378 + 11.8177i −0.0679653 + 0.385451i
\(941\) −2.65366 2.22668i −0.0865067 0.0725877i 0.598509 0.801116i \(-0.295760\pi\)
−0.685016 + 0.728528i \(0.740205\pi\)
\(942\) 0 0
\(943\) 22.5526 + 8.20848i 0.734414 + 0.267305i
\(944\) 17.3205 0.563735
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) −13.0208 4.73917i −0.423118 0.154002i 0.121681 0.992569i \(-0.461172\pi\)
−0.544799 + 0.838567i \(0.683394\pi\)
\(948\) 0 0
\(949\) 7.66044 + 6.42788i 0.248669 + 0.208658i
\(950\) 2.10537 11.9402i 0.0683073 0.387390i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(954\) 0 0
\(955\) −12.0000 + 20.7846i −0.388311 + 0.672574i
\(956\) 1.20307 + 6.82295i 0.0389101 + 0.220670i
\(957\) 0 0
\(958\) 22.5526 8.20848i 0.728642 0.265204i
\(959\) −6.51038 + 2.36959i −0.210231 + 0.0765179i
\(960\) 0 0
\(961\) −1.04189 5.90885i −0.0336093 0.190608i
\(962\) −4.33013 + 7.50000i −0.139609 + 0.241810i
\(963\) 0 0
\(964\) 9.50000 + 16.4545i 0.305974 + 0.529963i
\(965\) 26.5366 22.2668i 0.854242 0.716794i
\(966\) 0 0
\(967\) 1.38919 7.87846i 0.0446732 0.253354i −0.954290 0.298883i \(-0.903386\pi\)
0.998963 + 0.0455285i \(0.0144972\pi\)
\(968\) 1.32683 + 1.11334i 0.0426459 + 0.0357841i
\(969\) 0 0
\(970\) −95.8486 34.8861i −3.07751 1.12012i
\(971\) −51.9615 −1.66752 −0.833762 0.552124i \(-0.813818\pi\)
−0.833762 + 0.552124i \(0.813818\pi\)
\(972\) 0 0
\(973\) 13.0000 0.416761
\(974\) −30.9243 11.2555i −0.990879 0.360650i
\(975\) 0 0
\(976\) −7.66044 6.42788i −0.245205 0.205751i
\(977\) −0.601535 + 3.41147i −0.0192448 + 0.109143i −0.992917 0.118810i \(-0.962092\pi\)
0.973672 + 0.227953i \(0.0732032\pi\)
\(978\) 0 0
\(979\) −27.5776 + 23.1404i −0.881384 + 0.739569i
\(980\) −10.3923 18.0000i −0.331970 0.574989i
\(981\) 0 0
\(982\) 33.0000 57.1577i 1.05307 1.82397i
\(983\) −1.20307 6.82295i −0.0383720 0.217618i 0.959592 0.281394i \(-0.0907968\pi\)
−0.997964 + 0.0637759i \(0.979686\pi\)
\(984\) 0 0
\(985\) 33.8289 12.3127i 1.07788 0.392316i
\(986\) 0 0
\(987\) 0 0
\(988\) −0.868241 4.92404i −0.0276224 0.156655i
\(989\) 3.46410 6.00000i 0.110152 0.190789i
\(990\) 0 0
\(991\) −10.0000 17.3205i −0.317660 0.550204i 0.662339 0.749204i \(-0.269564\pi\)
−0.979999 + 0.199000i \(0.936231\pi\)
\(992\) 19.9024 16.7001i 0.631902 0.530229i
\(993\) 0 0
\(994\) −3.12567 + 17.7265i −0.0991401 + 0.562252i
\(995\) 50.4195 + 42.3070i 1.59840 + 1.34122i
\(996\) 0 0
\(997\) −1.87939 0.684040i −0.0595207 0.0216638i 0.312088 0.950053i \(-0.398972\pi\)
−0.371609 + 0.928389i \(0.621194\pi\)
\(998\) 48.4974 1.53516
\(999\) 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.n.568.2 12
3.2 odd 2 inner 729.2.e.n.568.1 12
9.2 odd 6 inner 729.2.e.n.82.2 12
9.4 even 3 inner 729.2.e.n.325.1 12
9.5 odd 6 inner 729.2.e.n.325.2 12
9.7 even 3 inner 729.2.e.n.82.1 12
27.2 odd 18 inner 729.2.e.n.406.2 12
27.4 even 9 243.2.c.d.82.2 4
27.5 odd 18 243.2.c.d.163.1 4
27.7 even 9 inner 729.2.e.n.163.2 12
27.11 odd 18 inner 729.2.e.n.649.2 12
27.13 even 9 243.2.a.c.1.1 2
27.14 odd 18 243.2.a.c.1.2 yes 2
27.16 even 9 inner 729.2.e.n.649.1 12
27.20 odd 18 inner 729.2.e.n.163.1 12
27.22 even 9 243.2.c.d.163.2 4
27.23 odd 18 243.2.c.d.82.1 4
27.25 even 9 inner 729.2.e.n.406.1 12
108.67 odd 18 3888.2.a.ba.1.1 2
108.95 even 18 3888.2.a.ba.1.2 2
135.14 odd 18 6075.2.a.bm.1.1 2
135.94 even 18 6075.2.a.bm.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.c.1.1 2 27.13 even 9
243.2.a.c.1.2 yes 2 27.14 odd 18
243.2.c.d.82.1 4 27.23 odd 18
243.2.c.d.82.2 4 27.4 even 9
243.2.c.d.163.1 4 27.5 odd 18
243.2.c.d.163.2 4 27.22 even 9
729.2.e.n.82.1 12 9.7 even 3 inner
729.2.e.n.82.2 12 9.2 odd 6 inner
729.2.e.n.163.1 12 27.20 odd 18 inner
729.2.e.n.163.2 12 27.7 even 9 inner
729.2.e.n.325.1 12 9.4 even 3 inner
729.2.e.n.325.2 12 9.5 odd 6 inner
729.2.e.n.406.1 12 27.25 even 9 inner
729.2.e.n.406.2 12 27.2 odd 18 inner
729.2.e.n.568.1 12 3.2 odd 2 inner
729.2.e.n.568.2 12 1.1 even 1 trivial
729.2.e.n.649.1 12 27.16 even 9 inner
729.2.e.n.649.2 12 27.11 odd 18 inner
3888.2.a.ba.1.1 2 108.67 odd 18
3888.2.a.ba.1.2 2 108.95 even 18
6075.2.a.bm.1.1 2 135.14 odd 18
6075.2.a.bm.1.2 2 135.94 even 18