Properties

Label 864.2.w.a.107.19
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.19
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.167507 - 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(3.93413 + 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(-0.986240 + 2.65091i) q^{8} +O(q^{10})\) \(q+(0.167507 - 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(3.93413 + 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(-0.986240 + 2.65091i) q^{8} +(2.94733 - 5.25157i) q^{10} +(0.527986 + 0.218699i) q^{11} +(1.75560 + 4.23839i) q^{13} +(-2.22752 - 2.83092i) q^{14} +(3.55736 + 1.82898i) q^{16} +3.50487 q^{17} +(-4.81224 + 1.99330i) q^{19} +(-6.88086 - 5.01848i) q^{20} +(0.395551 - 0.704796i) q^{22} +(-3.23298 + 3.23298i) q^{23} +(9.28633 + 9.28633i) q^{25} +(6.24586 - 1.75535i) q^{26} +(-4.34847 + 2.65382i) q^{28} +(-3.22277 - 7.78045i) q^{29} +5.47393i q^{31} +(3.16424 - 4.68909i) q^{32} +(0.587088 - 4.92174i) q^{34} +(10.0208 - 4.15076i) q^{35} +(1.93653 - 4.67520i) q^{37} +(1.99302 + 7.09152i) q^{38} +(-8.19984 + 8.82188i) q^{40} +(2.40752 + 2.40752i) q^{41} +(0.505016 - 1.21922i) q^{43} +(-0.923458 - 0.673514i) q^{44} +(3.99839 + 5.08148i) q^{46} -9.27490i q^{47} +0.512021i q^{49} +(14.5959 - 11.4849i) q^{50} +(-1.41875 - 9.06484i) q^{52} +(2.83647 - 6.84783i) q^{53} +(1.72078 + 1.72078i) q^{55} +(2.99825 + 6.55090i) q^{56} +(-11.4656 + 3.22232i) q^{58} +(0.00661636 - 0.0159733i) q^{59} +(-9.30765 + 3.85536i) q^{61} +(7.68682 + 0.916920i) q^{62} +(-6.05466 - 5.22887i) q^{64} +19.5352i q^{65} +(-3.08636 - 7.45113i) q^{67} +(-6.81305 - 1.64885i) q^{68} +(-4.15018 - 14.7671i) q^{70} +(-6.99549 - 6.99549i) q^{71} +(5.27477 - 5.27477i) q^{73} +(-6.24081 - 3.50252i) q^{74} +(10.2922 - 1.61084i) q^{76} +(1.34486 - 0.557060i) q^{77} +4.36861 q^{79} +(11.0147 + 12.9924i) q^{80} +(3.78405 - 2.97750i) q^{82} +(-6.42057 - 15.5006i) q^{83} +(13.7886 + 5.71142i) q^{85} +(-1.62750 - 0.913400i) q^{86} +(-1.10047 + 1.18396i) q^{88} +(-2.02487 + 2.02487i) q^{89} +(10.7958 + 4.47177i) q^{91} +(7.80547 - 4.76359i) q^{92} +(-13.0244 - 1.55361i) q^{94} -22.1802 q^{95} -8.35869 q^{97} +(0.719010 + 0.0857670i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.167507 1.40426i 0.118445 0.992961i
\(3\) 0 0
\(4\) −1.94388 0.470445i −0.971942 0.235223i
\(5\) 3.93413 + 1.62957i 1.75940 + 0.728765i 0.996624 + 0.0820966i \(0.0261616\pi\)
0.762771 + 0.646669i \(0.223838\pi\)
\(6\) 0 0
\(7\) 1.80111 1.80111i 0.680755 0.680755i −0.279416 0.960170i \(-0.590141\pi\)
0.960170 + 0.279416i \(0.0901407\pi\)
\(8\) −0.986240 + 2.65091i −0.348688 + 0.937239i
\(9\) 0 0
\(10\) 2.94733 5.25157i 0.932027 1.66069i
\(11\) 0.527986 + 0.218699i 0.159194 + 0.0659402i 0.460857 0.887474i \(-0.347542\pi\)
−0.301664 + 0.953414i \(0.597542\pi\)
\(12\) 0 0
\(13\) 1.75560 + 4.23839i 0.486915 + 1.17552i 0.956264 + 0.292504i \(0.0944886\pi\)
−0.469349 + 0.883013i \(0.655511\pi\)
\(14\) −2.22752 2.83092i −0.595331 0.756595i
\(15\) 0 0
\(16\) 3.55736 + 1.82898i 0.889341 + 0.457245i
\(17\) 3.50487 0.850055 0.425027 0.905180i \(-0.360264\pi\)
0.425027 + 0.905180i \(0.360264\pi\)
\(18\) 0 0
\(19\) −4.81224 + 1.99330i −1.10400 + 0.457293i −0.858869 0.512196i \(-0.828832\pi\)
−0.245135 + 0.969489i \(0.578832\pi\)
\(20\) −6.88086 5.01848i −1.53861 1.12217i
\(21\) 0 0
\(22\) 0.395551 0.704796i 0.0843318 0.150263i
\(23\) −3.23298 + 3.23298i −0.674123 + 0.674123i −0.958664 0.284541i \(-0.908159\pi\)
0.284541 + 0.958664i \(0.408159\pi\)
\(24\) 0 0
\(25\) 9.28633 + 9.28633i 1.85727 + 1.85727i
\(26\) 6.24586 1.75535i 1.22491 0.344253i
\(27\) 0 0
\(28\) −4.34847 + 2.65382i −0.821783 + 0.501525i
\(29\) −3.22277 7.78045i −0.598453 1.44479i −0.875157 0.483839i \(-0.839242\pi\)
0.276704 0.960955i \(-0.410758\pi\)
\(30\) 0 0
\(31\) 5.47393i 0.983148i 0.870836 + 0.491574i \(0.163578\pi\)
−0.870836 + 0.491574i \(0.836422\pi\)
\(32\) 3.16424 4.68909i 0.559364 0.828922i
\(33\) 0 0
\(34\) 0.587088 4.92174i 0.100685 0.844071i
\(35\) 10.0208 4.15076i 1.69383 0.701606i
\(36\) 0 0
\(37\) 1.93653 4.67520i 0.318364 0.768599i −0.680977 0.732305i \(-0.738445\pi\)
0.999341 0.0362941i \(-0.0115553\pi\)
\(38\) 1.99302 + 7.09152i 0.323310 + 1.15040i
\(39\) 0 0
\(40\) −8.19984 + 8.82188i −1.29651 + 1.39486i
\(41\) 2.40752 + 2.40752i 0.375991 + 0.375991i 0.869653 0.493663i \(-0.164342\pi\)
−0.493663 + 0.869653i \(0.664342\pi\)
\(42\) 0 0
\(43\) 0.505016 1.21922i 0.0770143 0.185929i −0.880683 0.473706i \(-0.842916\pi\)
0.957698 + 0.287777i \(0.0929161\pi\)
\(44\) −0.923458 0.673514i −0.139216 0.101536i
\(45\) 0 0
\(46\) 3.99839 + 5.08148i 0.589531 + 0.749224i
\(47\) 9.27490i 1.35288i −0.736496 0.676441i \(-0.763521\pi\)
0.736496 0.676441i \(-0.236479\pi\)
\(48\) 0 0
\(49\) 0.512021i 0.0731459i
\(50\) 14.5959 11.4849i 2.06418 1.62421i
\(51\) 0 0
\(52\) −1.41875 9.06484i −0.196745 1.25707i
\(53\) 2.83647 6.84783i 0.389619 0.940622i −0.600402 0.799698i \(-0.704993\pi\)
0.990020 0.140924i \(-0.0450073\pi\)
\(54\) 0 0
\(55\) 1.72078 + 1.72078i 0.232030 + 0.232030i
\(56\) 2.99825 + 6.55090i 0.400658 + 0.875401i
\(57\) 0 0
\(58\) −11.4656 + 3.22232i −1.50551 + 0.423112i
\(59\) 0.00661636 0.0159733i 0.000861377 0.00207955i −0.923448 0.383723i \(-0.874642\pi\)
0.924310 + 0.381643i \(0.124642\pi\)
\(60\) 0 0
\(61\) −9.30765 + 3.85536i −1.19172 + 0.493628i −0.888316 0.459233i \(-0.848124\pi\)
−0.303407 + 0.952861i \(0.598124\pi\)
\(62\) 7.68682 + 0.916920i 0.976227 + 0.116449i
\(63\) 0 0
\(64\) −6.05466 5.22887i −0.756833 0.653608i
\(65\) 19.5352i 2.42305i
\(66\) 0 0
\(67\) −3.08636 7.45113i −0.377059 0.910300i −0.992514 0.122129i \(-0.961028\pi\)
0.615456 0.788171i \(-0.288972\pi\)
\(68\) −6.81305 1.64885i −0.826204 0.199952i
\(69\) 0 0
\(70\) −4.15018 14.7671i −0.496042 1.76501i
\(71\) −6.99549 6.99549i −0.830212 0.830212i 0.157333 0.987546i \(-0.449710\pi\)
−0.987546 + 0.157333i \(0.949710\pi\)
\(72\) 0 0
\(73\) 5.27477 5.27477i 0.617366 0.617366i −0.327489 0.944855i \(-0.606203\pi\)
0.944855 + 0.327489i \(0.106203\pi\)
\(74\) −6.24081 3.50252i −0.725480 0.407160i
\(75\) 0 0
\(76\) 10.2922 1.61084i 1.18059 0.184776i
\(77\) 1.34486 0.557060i 0.153261 0.0634828i
\(78\) 0 0
\(79\) 4.36861 0.491507 0.245753 0.969332i \(-0.420965\pi\)
0.245753 + 0.969332i \(0.420965\pi\)
\(80\) 11.0147 + 12.9924i 1.23148 + 1.45260i
\(81\) 0 0
\(82\) 3.78405 2.97750i 0.417878 0.328810i
\(83\) −6.42057 15.5006i −0.704750 1.70142i −0.712721 0.701448i \(-0.752537\pi\)
0.00797127 0.999968i \(-0.497463\pi\)
\(84\) 0 0
\(85\) 13.7886 + 5.71142i 1.49558 + 0.619490i
\(86\) −1.62750 0.913400i −0.175498 0.0984945i
\(87\) 0 0
\(88\) −1.10047 + 1.18396i −0.117311 + 0.126210i
\(89\) −2.02487 + 2.02487i −0.214636 + 0.214636i −0.806234 0.591597i \(-0.798498\pi\)
0.591597 + 0.806234i \(0.298498\pi\)
\(90\) 0 0
\(91\) 10.7958 + 4.47177i 1.13171 + 0.468769i
\(92\) 7.80547 4.76359i 0.813777 0.496639i
\(93\) 0 0
\(94\) −13.0244 1.55361i −1.34336 0.160242i
\(95\) −22.1802 −2.27564
\(96\) 0 0
\(97\) −8.35869 −0.848697 −0.424348 0.905499i \(-0.639497\pi\)
−0.424348 + 0.905499i \(0.639497\pi\)
\(98\) 0.719010 + 0.0857670i 0.0726310 + 0.00866377i
\(99\) 0 0
\(100\) −13.6828 22.4202i −1.36828 2.24202i
\(101\) −6.76411 2.80179i −0.673055 0.278788i 0.0198656 0.999803i \(-0.493676\pi\)
−0.692920 + 0.721014i \(0.743676\pi\)
\(102\) 0 0
\(103\) 11.2645 11.2645i 1.10993 1.10993i 0.116768 0.993159i \(-0.462747\pi\)
0.993159 0.116768i \(-0.0372533\pi\)
\(104\) −12.9670 + 0.473868i −1.27152 + 0.0464666i
\(105\) 0 0
\(106\) −9.14100 5.13019i −0.887853 0.498288i
\(107\) 1.58115 + 0.654935i 0.152856 + 0.0633150i 0.457800 0.889055i \(-0.348638\pi\)
−0.304944 + 0.952370i \(0.598638\pi\)
\(108\) 0 0
\(109\) 2.77346 + 6.69572i 0.265649 + 0.641333i 0.999269 0.0382265i \(-0.0121708\pi\)
−0.733620 + 0.679560i \(0.762171\pi\)
\(110\) 2.70466 2.12818i 0.257879 0.202914i
\(111\) 0 0
\(112\) 9.70138 3.11300i 0.916695 0.294151i
\(113\) −4.67012 −0.439328 −0.219664 0.975576i \(-0.570496\pi\)
−0.219664 + 0.975576i \(0.570496\pi\)
\(114\) 0 0
\(115\) −17.9873 + 7.45059i −1.67733 + 0.694771i
\(116\) 2.60441 + 16.6404i 0.241813 + 1.54502i
\(117\) 0 0
\(118\) −0.0213224 0.0119667i −0.00196288 0.00110163i
\(119\) 6.31264 6.31264i 0.578679 0.578679i
\(120\) 0 0
\(121\) −7.54723 7.54723i −0.686112 0.686112i
\(122\) 3.85482 + 13.7161i 0.348999 + 1.24180i
\(123\) 0 0
\(124\) 2.57519 10.6407i 0.231258 0.955562i
\(125\) 13.2530 + 31.9957i 1.18539 + 2.86178i
\(126\) 0 0
\(127\) 19.9447i 1.76981i 0.465775 + 0.884903i \(0.345776\pi\)
−0.465775 + 0.884903i \(0.654224\pi\)
\(128\) −8.35688 + 7.62644i −0.738651 + 0.674088i
\(129\) 0 0
\(130\) 27.4325 + 3.27228i 2.40599 + 0.286998i
\(131\) 8.66917 3.59089i 0.757429 0.313737i 0.0296603 0.999560i \(-0.490557\pi\)
0.727769 + 0.685823i \(0.240557\pi\)
\(132\) 0 0
\(133\) −5.07722 + 12.2575i −0.440251 + 1.06286i
\(134\) −10.9803 + 3.08593i −0.948553 + 0.266584i
\(135\) 0 0
\(136\) −3.45664 + 9.29109i −0.296404 + 0.796704i
\(137\) 5.99092 + 5.99092i 0.511838 + 0.511838i 0.915089 0.403251i \(-0.132120\pi\)
−0.403251 + 0.915089i \(0.632120\pi\)
\(138\) 0 0
\(139\) −4.61103 + 11.1320i −0.391103 + 0.944205i 0.598598 + 0.801050i \(0.295725\pi\)
−0.989700 + 0.143155i \(0.954275\pi\)
\(140\) −21.4320 + 3.35434i −1.81133 + 0.283494i
\(141\) 0 0
\(142\) −10.9953 + 8.65169i −0.922703 + 0.726034i
\(143\) 2.62176i 0.219242i
\(144\) 0 0
\(145\) 35.8610i 2.97810i
\(146\) −6.52359 8.29070i −0.539896 0.686144i
\(147\) 0 0
\(148\) −5.96382 + 8.17702i −0.490223 + 0.672147i
\(149\) 0.505473 1.22032i 0.0414100 0.0999725i −0.901821 0.432109i \(-0.857770\pi\)
0.943231 + 0.332137i \(0.107770\pi\)
\(150\) 0 0
\(151\) 7.49947 + 7.49947i 0.610298 + 0.610298i 0.943024 0.332725i \(-0.107968\pi\)
−0.332725 + 0.943024i \(0.607968\pi\)
\(152\) −0.538027 14.7227i −0.0436397 1.19417i
\(153\) 0 0
\(154\) −0.556983 1.98184i −0.0448829 0.159701i
\(155\) −8.92015 + 21.5352i −0.716484 + 1.72975i
\(156\) 0 0
\(157\) −22.8339 + 9.45810i −1.82234 + 0.754839i −0.847916 + 0.530131i \(0.822143\pi\)
−0.974426 + 0.224708i \(0.927857\pi\)
\(158\) 0.731771 6.13465i 0.0582165 0.488047i
\(159\) 0 0
\(160\) 20.0897 13.2911i 1.58823 1.05076i
\(161\) 11.6459i 0.917824i
\(162\) 0 0
\(163\) 1.38360 + 3.34030i 0.108372 + 0.261632i 0.968757 0.248012i \(-0.0797772\pi\)
−0.860385 + 0.509644i \(0.829777\pi\)
\(164\) −3.54733 5.81253i −0.277000 0.453883i
\(165\) 0 0
\(166\) −22.8424 + 6.41969i −1.77291 + 0.498264i
\(167\) 0.682611 + 0.682611i 0.0528220 + 0.0528220i 0.733024 0.680202i \(-0.238108\pi\)
−0.680202 + 0.733024i \(0.738108\pi\)
\(168\) 0 0
\(169\) −5.68942 + 5.68942i −0.437647 + 0.437647i
\(170\) 10.3300 18.4060i 0.792274 1.41168i
\(171\) 0 0
\(172\) −1.55527 + 2.13243i −0.118588 + 0.162597i
\(173\) −2.11886 + 0.877660i −0.161094 + 0.0667272i −0.461773 0.886998i \(-0.652787\pi\)
0.300679 + 0.953725i \(0.402787\pi\)
\(174\) 0 0
\(175\) 33.4514 2.52869
\(176\) 1.47824 + 1.74367i 0.111427 + 0.131434i
\(177\) 0 0
\(178\) 2.50427 + 3.18262i 0.187703 + 0.238548i
\(179\) −3.83061 9.24791i −0.286313 0.691221i 0.713644 0.700509i \(-0.247044\pi\)
−0.999957 + 0.00928754i \(0.997044\pi\)
\(180\) 0 0
\(181\) −2.97359 1.23170i −0.221026 0.0915518i 0.269423 0.963022i \(-0.413167\pi\)
−0.490449 + 0.871470i \(0.663167\pi\)
\(182\) 8.08789 14.4111i 0.599515 1.06822i
\(183\) 0 0
\(184\) −5.38185 11.7588i −0.396755 0.866872i
\(185\) 15.2371 15.2371i 1.12026 1.12026i
\(186\) 0 0
\(187\) 1.85052 + 0.766511i 0.135323 + 0.0560528i
\(188\) −4.36333 + 18.0293i −0.318229 + 1.31492i
\(189\) 0 0
\(190\) −3.71533 + 31.1467i −0.269538 + 2.25962i
\(191\) 9.07372 0.656551 0.328276 0.944582i \(-0.393532\pi\)
0.328276 + 0.944582i \(0.393532\pi\)
\(192\) 0 0
\(193\) 5.12981 0.369252 0.184626 0.982809i \(-0.440893\pi\)
0.184626 + 0.982809i \(0.440893\pi\)
\(194\) −1.40014 + 11.7378i −0.100524 + 0.842722i
\(195\) 0 0
\(196\) 0.240878 0.995310i 0.0172056 0.0710936i
\(197\) 5.16765 + 2.14051i 0.368180 + 0.152505i 0.559099 0.829101i \(-0.311147\pi\)
−0.190920 + 0.981606i \(0.561147\pi\)
\(198\) 0 0
\(199\) 1.57923 1.57923i 0.111949 0.111949i −0.648914 0.760862i \(-0.724776\pi\)
0.760862 + 0.648914i \(0.224776\pi\)
\(200\) −33.7758 + 15.4587i −2.38831 + 1.09309i
\(201\) 0 0
\(202\) −5.06747 + 9.02925i −0.356546 + 0.635296i
\(203\) −19.8180 8.20888i −1.39095 0.576150i
\(204\) 0 0
\(205\) 5.54826 + 13.3947i 0.387507 + 0.935526i
\(206\) −13.9314 17.7052i −0.970648 1.23358i
\(207\) 0 0
\(208\) −1.50663 + 18.2884i −0.104466 + 1.26807i
\(209\) −2.97673 −0.205905
\(210\) 0 0
\(211\) 1.13475 0.470028i 0.0781193 0.0323581i −0.343282 0.939233i \(-0.611539\pi\)
0.421401 + 0.906874i \(0.361539\pi\)
\(212\) −8.73529 + 11.9770i −0.599942 + 0.822583i
\(213\) 0 0
\(214\) 1.18455 2.11064i 0.0809743 0.144281i
\(215\) 3.97360 3.97360i 0.270997 0.270997i
\(216\) 0 0
\(217\) 9.85915 + 9.85915i 0.669282 + 0.669282i
\(218\) 9.86709 2.77307i 0.668284 0.187816i
\(219\) 0 0
\(220\) −2.53546 4.15453i −0.170941 0.280098i
\(221\) 6.15313 + 14.8550i 0.413905 + 0.999254i
\(222\) 0 0
\(223\) 19.0240i 1.27394i 0.770889 + 0.636969i \(0.219812\pi\)
−0.770889 + 0.636969i \(0.780188\pi\)
\(224\) −2.74641 14.1447i −0.183503 0.945082i
\(225\) 0 0
\(226\) −0.782275 + 6.55805i −0.0520362 + 0.436235i
\(227\) −13.9428 + 5.77532i −0.925419 + 0.383321i −0.793939 0.607997i \(-0.791973\pi\)
−0.131480 + 0.991319i \(0.541973\pi\)
\(228\) 0 0
\(229\) 9.94047 23.9984i 0.656885 1.58586i −0.145705 0.989328i \(-0.546545\pi\)
0.802589 0.596532i \(-0.203455\pi\)
\(230\) 7.44956 + 26.5069i 0.491209 + 1.74781i
\(231\) 0 0
\(232\) 23.8037 0.869884i 1.56279 0.0571107i
\(233\) 13.4161 + 13.4161i 0.878921 + 0.878921i 0.993423 0.114502i \(-0.0365273\pi\)
−0.114502 + 0.993423i \(0.536527\pi\)
\(234\) 0 0
\(235\) 15.1141 36.4886i 0.985934 2.38026i
\(236\) −0.0203760 + 0.0279376i −0.00132636 + 0.00181858i
\(237\) 0 0
\(238\) −7.80717 9.92199i −0.506064 0.643147i
\(239\) 6.40372i 0.414222i 0.978317 + 0.207111i \(0.0664061\pi\)
−0.978317 + 0.207111i \(0.933594\pi\)
\(240\) 0 0
\(241\) 4.41728i 0.284542i −0.989828 0.142271i \(-0.954560\pi\)
0.989828 0.142271i \(-0.0454405\pi\)
\(242\) −11.8625 + 9.33406i −0.762549 + 0.600016i
\(243\) 0 0
\(244\) 19.9067 3.11562i 1.27440 0.199457i
\(245\) −0.834374 + 2.01436i −0.0533062 + 0.128693i
\(246\) 0 0
\(247\) −16.8967 16.8967i −1.07511 1.07511i
\(248\) −14.5109 5.39861i −0.921444 0.342812i
\(249\) 0 0
\(250\) 47.1502 13.2512i 2.98204 0.838080i
\(251\) 5.70829 13.7810i 0.360304 0.869851i −0.634951 0.772552i \(-0.718980\pi\)
0.995255 0.0972985i \(-0.0310202\pi\)
\(252\) 0 0
\(253\) −2.41402 + 0.999919i −0.151768 + 0.0628644i
\(254\) 28.0075 + 3.34087i 1.75735 + 0.209625i
\(255\) 0 0
\(256\) 9.30966 + 13.0127i 0.581854 + 0.813293i
\(257\) 27.1738i 1.69505i −0.530753 0.847526i \(-0.678091\pi\)
0.530753 0.847526i \(-0.321909\pi\)
\(258\) 0 0
\(259\) −4.93264 11.9085i −0.306499 0.739955i
\(260\) 9.19025 37.9742i 0.569955 2.35506i
\(261\) 0 0
\(262\) −3.59039 12.7753i −0.221815 0.789258i
\(263\) 8.60649 + 8.60649i 0.530699 + 0.530699i 0.920780 0.390081i \(-0.127553\pi\)
−0.390081 + 0.920780i \(0.627553\pi\)
\(264\) 0 0
\(265\) 22.3180 22.3180i 1.37099 1.37099i
\(266\) 16.3622 + 9.18295i 1.00323 + 0.563043i
\(267\) 0 0
\(268\) 2.49417 + 15.9361i 0.152356 + 0.973451i
\(269\) −27.7138 + 11.4794i −1.68974 + 0.699913i −0.999715 0.0238727i \(-0.992400\pi\)
−0.690025 + 0.723786i \(0.742400\pi\)
\(270\) 0 0
\(271\) −30.3410 −1.84308 −0.921542 0.388279i \(-0.873070\pi\)
−0.921542 + 0.388279i \(0.873070\pi\)
\(272\) 12.4681 + 6.41033i 0.755988 + 0.388683i
\(273\) 0 0
\(274\) 9.41631 7.40928i 0.568860 0.447611i
\(275\) 2.87214 + 6.93397i 0.173197 + 0.418134i
\(276\) 0 0
\(277\) −9.64561 3.99534i −0.579549 0.240057i 0.0735984 0.997288i \(-0.476552\pi\)
−0.653147 + 0.757231i \(0.726552\pi\)
\(278\) 14.8598 + 8.33976i 0.891234 + 0.500186i
\(279\) 0 0
\(280\) 1.12037 + 30.6579i 0.0669546 + 1.83216i
\(281\) −1.44386 + 1.44386i −0.0861335 + 0.0861335i −0.748861 0.662727i \(-0.769399\pi\)
0.662727 + 0.748861i \(0.269399\pi\)
\(282\) 0 0
\(283\) −19.8747 8.23236i −1.18143 0.489363i −0.296473 0.955041i \(-0.595810\pi\)
−0.884954 + 0.465678i \(0.845810\pi\)
\(284\) 10.3074 + 16.8894i 0.611633 + 1.00220i
\(285\) 0 0
\(286\) 3.68163 + 0.439162i 0.217699 + 0.0259682i
\(287\) 8.67239 0.511915
\(288\) 0 0
\(289\) −4.71592 −0.277407
\(290\) −50.3581 6.00696i −2.95713 0.352741i
\(291\) 0 0
\(292\) −12.7350 + 7.77205i −0.745261 + 0.454825i
\(293\) 0.493799 + 0.204538i 0.0288481 + 0.0119493i 0.397061 0.917792i \(-0.370030\pi\)
−0.368213 + 0.929742i \(0.620030\pi\)
\(294\) 0 0
\(295\) 0.0520592 0.0520592i 0.00303100 0.00303100i
\(296\) 10.4837 + 9.74445i 0.609351 + 0.566385i
\(297\) 0 0
\(298\) −1.62897 0.914226i −0.0943639 0.0529597i
\(299\) −19.3784 8.02681i −1.12068 0.464202i
\(300\) 0 0
\(301\) −1.28635 3.10553i −0.0741442 0.179000i
\(302\) 11.7874 9.27499i 0.678289 0.533715i
\(303\) 0 0
\(304\) −20.7646 1.71062i −1.19093 0.0981107i
\(305\) −42.9000 −2.45645
\(306\) 0 0
\(307\) −4.88633 + 2.02398i −0.278878 + 0.115515i −0.517738 0.855539i \(-0.673226\pi\)
0.238861 + 0.971054i \(0.423226\pi\)
\(308\) −2.87632 + 0.450176i −0.163893 + 0.0256511i
\(309\) 0 0
\(310\) 28.7467 + 16.1335i 1.63271 + 0.916320i
\(311\) 2.51961 2.51961i 0.142874 0.142874i −0.632052 0.774926i \(-0.717787\pi\)
0.774926 + 0.632052i \(0.217787\pi\)
\(312\) 0 0
\(313\) −3.77971 3.77971i −0.213642 0.213642i 0.592171 0.805812i \(-0.298271\pi\)
−0.805812 + 0.592171i \(0.798271\pi\)
\(314\) 9.45679 + 33.6490i 0.533678 + 1.89892i
\(315\) 0 0
\(316\) −8.49206 2.05519i −0.477716 0.115613i
\(317\) 7.32833 + 17.6922i 0.411600 + 0.993691i 0.984708 + 0.174211i \(0.0557375\pi\)
−0.573108 + 0.819480i \(0.694262\pi\)
\(318\) 0 0
\(319\) 4.81279i 0.269464i
\(320\) −15.2990 30.4375i −0.855241 1.70151i
\(321\) 0 0
\(322\) 16.3538 + 1.95076i 0.911363 + 0.108712i
\(323\) −16.8663 + 6.98623i −0.938464 + 0.388724i
\(324\) 0 0
\(325\) −23.0560 + 55.6621i −1.27892 + 3.08758i
\(326\) 4.92240 1.38340i 0.272627 0.0766197i
\(327\) 0 0
\(328\) −8.75650 + 4.00772i −0.483497 + 0.221290i
\(329\) −16.7051 16.7051i −0.920981 0.920981i
\(330\) 0 0
\(331\) −4.19347 + 10.1239i −0.230494 + 0.556462i −0.996236 0.0866867i \(-0.972372\pi\)
0.765742 + 0.643148i \(0.222372\pi\)
\(332\) 5.18865 + 33.1520i 0.284764 + 1.81945i
\(333\) 0 0
\(334\) 1.07290 0.844220i 0.0587067 0.0461937i
\(335\) 34.3431i 1.87636i
\(336\) 0 0
\(337\) 1.77494i 0.0966873i −0.998831 0.0483436i \(-0.984606\pi\)
0.998831 0.0483436i \(-0.0153943\pi\)
\(338\) 7.03640 + 8.94242i 0.382729 + 0.486404i
\(339\) 0 0
\(340\) −24.1165 17.5891i −1.30790 0.953903i
\(341\) −1.19714 + 2.89016i −0.0648290 + 0.156511i
\(342\) 0 0
\(343\) 13.5300 + 13.5300i 0.730549 + 0.730549i
\(344\) 2.73397 + 2.54119i 0.147406 + 0.137012i
\(345\) 0 0
\(346\) 0.877538 + 3.12244i 0.0471768 + 0.167863i
\(347\) −5.11965 + 12.3599i −0.274837 + 0.663516i −0.999677 0.0254011i \(-0.991914\pi\)
0.724840 + 0.688917i \(0.241914\pi\)
\(348\) 0 0
\(349\) 16.1690 6.69741i 0.865506 0.358504i 0.0946474 0.995511i \(-0.469828\pi\)
0.770858 + 0.637007i \(0.219828\pi\)
\(350\) 5.60332 46.9744i 0.299510 2.51088i
\(351\) 0 0
\(352\) 2.69618 1.78376i 0.143707 0.0950746i
\(353\) 11.7752i 0.626733i −0.949632 0.313366i \(-0.898543\pi\)
0.949632 0.313366i \(-0.101457\pi\)
\(354\) 0 0
\(355\) −16.1215 38.9208i −0.855642 2.06570i
\(356\) 4.88871 2.98353i 0.259101 0.158127i
\(357\) 0 0
\(358\) −13.6281 + 3.83008i −0.720268 + 0.202426i
\(359\) 16.5669 + 16.5669i 0.874367 + 0.874367i 0.992945 0.118578i \(-0.0378336\pi\)
−0.118578 + 0.992945i \(0.537834\pi\)
\(360\) 0 0
\(361\) 5.74940 5.74940i 0.302600 0.302600i
\(362\) −2.22773 + 3.96938i −0.117087 + 0.208626i
\(363\) 0 0
\(364\) −18.8821 13.7714i −0.989690 0.721820i
\(365\) 29.3472 12.1560i 1.53610 0.636275i
\(366\) 0 0
\(367\) −6.58947 −0.343967 −0.171984 0.985100i \(-0.555018\pi\)
−0.171984 + 0.985100i \(0.555018\pi\)
\(368\) −17.4139 + 5.58782i −0.907764 + 0.291285i
\(369\) 0 0
\(370\) −18.8446 23.9492i −0.979682 1.24506i
\(371\) −7.22491 17.4425i −0.375098 0.905568i
\(372\) 0 0
\(373\) 9.15352 + 3.79151i 0.473951 + 0.196317i 0.606856 0.794812i \(-0.292430\pi\)
−0.132905 + 0.991129i \(0.542430\pi\)
\(374\) 1.38635 2.47021i 0.0716866 0.127732i
\(375\) 0 0
\(376\) 24.5869 + 9.14727i 1.26797 + 0.471734i
\(377\) 27.3187 27.3187i 1.40698 1.40698i
\(378\) 0 0
\(379\) −24.3094 10.0693i −1.24869 0.517224i −0.342269 0.939602i \(-0.611196\pi\)
−0.906420 + 0.422378i \(0.861196\pi\)
\(380\) 43.1157 + 10.4346i 2.21179 + 0.535281i
\(381\) 0 0
\(382\) 1.51991 12.7418i 0.0777653 0.651930i
\(383\) −30.2731 −1.54688 −0.773442 0.633867i \(-0.781467\pi\)
−0.773442 + 0.633867i \(0.781467\pi\)
\(384\) 0 0
\(385\) 6.19862 0.315911
\(386\) 0.859277 7.20358i 0.0437360 0.366652i
\(387\) 0 0
\(388\) 16.2483 + 3.93231i 0.824883 + 0.199633i
\(389\) −6.58185 2.72629i −0.333713 0.138229i 0.209534 0.977801i \(-0.432805\pi\)
−0.543247 + 0.839573i \(0.682805\pi\)
\(390\) 0 0
\(391\) −11.3312 + 11.3312i −0.573041 + 0.573041i
\(392\) −1.35732 0.504976i −0.0685552 0.0255051i
\(393\) 0 0
\(394\) 3.87145 6.89817i 0.195041 0.347525i
\(395\) 17.1867 + 7.11895i 0.864755 + 0.358193i
\(396\) 0 0
\(397\) 6.79902 + 16.4143i 0.341233 + 0.823810i 0.997592 + 0.0693605i \(0.0220959\pi\)
−0.656359 + 0.754449i \(0.727904\pi\)
\(398\) −1.95311 2.48218i −0.0979008 0.124420i
\(399\) 0 0
\(400\) 16.0503 + 50.0194i 0.802516 + 2.50097i
\(401\) 12.6207 0.630250 0.315125 0.949050i \(-0.397954\pi\)
0.315125 + 0.949050i \(0.397954\pi\)
\(402\) 0 0
\(403\) −23.2007 + 9.61003i −1.15571 + 0.478709i
\(404\) 11.8306 + 8.62849i 0.588592 + 0.429284i
\(405\) 0 0
\(406\) −14.8470 + 26.4545i −0.736846 + 1.31292i
\(407\) 2.04493 2.04493i 0.101363 0.101363i
\(408\) 0 0
\(409\) −23.6256 23.6256i −1.16821 1.16821i −0.982628 0.185585i \(-0.940582\pi\)
−0.185585 0.982628i \(-0.559418\pi\)
\(410\) 19.7390 5.54749i 0.974838 0.273971i
\(411\) 0 0
\(412\) −27.1963 + 16.5976i −1.33986 + 0.817704i
\(413\) −0.0168529 0.0406864i −0.000829276 0.00200205i
\(414\) 0 0
\(415\) 71.4443i 3.50706i
\(416\) 25.4293 + 5.17913i 1.24677 + 0.253928i
\(417\) 0 0
\(418\) −0.498622 + 4.18010i −0.0243884 + 0.204455i
\(419\) 3.41229 1.41342i 0.166701 0.0690500i −0.297772 0.954637i \(-0.596244\pi\)
0.464474 + 0.885587i \(0.346244\pi\)
\(420\) 0 0
\(421\) 1.11626 2.69489i 0.0544031 0.131341i −0.894341 0.447386i \(-0.852355\pi\)
0.948744 + 0.316045i \(0.102355\pi\)
\(422\) −0.469963 1.67221i −0.0228775 0.0814021i
\(423\) 0 0
\(424\) 15.3556 + 14.2728i 0.745732 + 0.693150i
\(425\) 32.5473 + 32.5473i 1.57878 + 1.57878i
\(426\) 0 0
\(427\) −9.82017 + 23.7080i −0.475231 + 1.14731i
\(428\) −2.76547 2.01696i −0.133674 0.0974936i
\(429\) 0 0
\(430\) −4.91435 6.24556i −0.236991 0.301188i
\(431\) 30.6040i 1.47414i −0.675816 0.737071i \(-0.736208\pi\)
0.675816 0.737071i \(-0.263792\pi\)
\(432\) 0 0
\(433\) 8.52659i 0.409762i −0.978787 0.204881i \(-0.934319\pi\)
0.978787 0.204881i \(-0.0656807\pi\)
\(434\) 15.4963 12.1933i 0.743844 0.585298i
\(435\) 0 0
\(436\) −2.24131 14.3204i −0.107339 0.685825i
\(437\) 9.11359 22.0021i 0.435962 1.05251i
\(438\) 0 0
\(439\) 25.4910 + 25.4910i 1.21662 + 1.21662i 0.968808 + 0.247811i \(0.0797112\pi\)
0.247811 + 0.968808i \(0.420289\pi\)
\(440\) −6.25874 + 2.86453i −0.298374 + 0.136561i
\(441\) 0 0
\(442\) 21.8909 6.15228i 1.04124 0.292634i
\(443\) −4.70852 + 11.3674i −0.223709 + 0.540081i −0.995388 0.0959313i \(-0.969417\pi\)
0.771679 + 0.636012i \(0.219417\pi\)
\(444\) 0 0
\(445\) −11.2658 + 4.66644i −0.534049 + 0.221210i
\(446\) 26.7146 + 3.18664i 1.26497 + 0.150892i
\(447\) 0 0
\(448\) −20.3229 + 1.48735i −0.960165 + 0.0702705i
\(449\) 1.47316i 0.0695229i 0.999396 + 0.0347614i \(0.0110671\pi\)
−0.999396 + 0.0347614i \(0.988933\pi\)
\(450\) 0 0
\(451\) 0.744614 + 1.79766i 0.0350625 + 0.0846484i
\(452\) 9.07816 + 2.19703i 0.427001 + 0.103340i
\(453\) 0 0
\(454\) 5.77452 + 20.5468i 0.271012 + 0.964308i
\(455\) 35.1850 + 35.1850i 1.64950 + 1.64950i
\(456\) 0 0
\(457\) −4.10233 + 4.10233i −0.191899 + 0.191899i −0.796516 0.604617i \(-0.793326\pi\)
0.604617 + 0.796516i \(0.293326\pi\)
\(458\) −32.0349 17.9789i −1.49689 0.840098i
\(459\) 0 0
\(460\) 38.4703 6.02103i 1.79369 0.280732i
\(461\) 14.5005 6.00631i 0.675356 0.279742i −0.0185280 0.999828i \(-0.505898\pi\)
0.693884 + 0.720087i \(0.255898\pi\)
\(462\) 0 0
\(463\) 33.2789 1.54660 0.773302 0.634038i \(-0.218604\pi\)
0.773302 + 0.634038i \(0.218604\pi\)
\(464\) 2.76574 33.5723i 0.128396 1.55855i
\(465\) 0 0
\(466\) 21.0870 16.5924i 0.976837 0.768630i
\(467\) −6.92509 16.7186i −0.320455 0.773647i −0.999228 0.0392982i \(-0.987488\pi\)
0.678773 0.734349i \(-0.262512\pi\)
\(468\) 0 0
\(469\) −18.9791 7.86142i −0.876376 0.363007i
\(470\) −48.7077 27.3362i −2.24672 1.26092i
\(471\) 0 0
\(472\) 0.0358185 + 0.0332929i 0.00164868 + 0.00153243i
\(473\) 0.533283 0.533283i 0.0245204 0.0245204i
\(474\) 0 0
\(475\) −63.1984 26.1777i −2.89974 1.20111i
\(476\) −15.2408 + 9.30128i −0.698560 + 0.426324i
\(477\) 0 0
\(478\) 8.99247 + 1.07266i 0.411306 + 0.0490625i
\(479\) −9.61988 −0.439543 −0.219772 0.975551i \(-0.570531\pi\)
−0.219772 + 0.975551i \(0.570531\pi\)
\(480\) 0 0
\(481\) 23.2151 1.05852
\(482\) −6.20300 0.739924i −0.282539 0.0337026i
\(483\) 0 0
\(484\) 11.1204 + 18.2215i 0.505472 + 0.828250i
\(485\) −32.8842 13.6211i −1.49319 0.618501i
\(486\) 0 0
\(487\) 12.8304 12.8304i 0.581403 0.581403i −0.353886 0.935289i \(-0.615140\pi\)
0.935289 + 0.353886i \(0.115140\pi\)
\(488\) −1.04063 28.4761i −0.0471071 1.28905i
\(489\) 0 0
\(490\) 2.68892 + 1.50910i 0.121473 + 0.0681740i
\(491\) 16.5426 + 6.85218i 0.746558 + 0.309234i 0.723336 0.690496i \(-0.242608\pi\)
0.0232215 + 0.999730i \(0.492608\pi\)
\(492\) 0 0
\(493\) −11.2954 27.2694i −0.508718 1.22815i
\(494\) −26.5577 + 20.8970i −1.19489 + 0.940202i
\(495\) 0 0
\(496\) −10.0117 + 19.4728i −0.449539 + 0.874353i
\(497\) −25.1993 −1.13034
\(498\) 0 0
\(499\) 21.6276 8.95845i 0.968185 0.401035i 0.158149 0.987415i \(-0.449448\pi\)
0.810036 + 0.586380i \(0.199448\pi\)
\(500\) −10.7102 68.4307i −0.478973 3.06031i
\(501\) 0 0
\(502\) −18.3959 10.3243i −0.821051 0.460797i
\(503\) 27.0985 27.0985i 1.20826 1.20826i 0.236671 0.971590i \(-0.423944\pi\)
0.971590 0.236671i \(-0.0760563\pi\)
\(504\) 0 0
\(505\) −22.0452 22.0452i −0.980998 0.980998i
\(506\) 0.999780 + 3.55740i 0.0444457 + 0.158146i
\(507\) 0 0
\(508\) 9.38289 38.7702i 0.416298 1.72015i
\(509\) 12.9535 + 31.2725i 0.574153 + 1.38613i 0.897990 + 0.440016i \(0.145027\pi\)
−0.323837 + 0.946113i \(0.604973\pi\)
\(510\) 0 0
\(511\) 19.0009i 0.840549i
\(512\) 19.8326 10.8935i 0.876486 0.481427i
\(513\) 0 0
\(514\) −38.1590 4.55178i −1.68312 0.200771i
\(515\) 62.6724 25.9598i 2.76168 1.14392i
\(516\) 0 0
\(517\) 2.02841 4.89702i 0.0892094 0.215371i
\(518\) −17.5488 + 4.93196i −0.771050 + 0.216698i
\(519\) 0 0
\(520\) −51.7861 19.2664i −2.27097 0.844888i
\(521\) −19.8283 19.8283i −0.868693 0.868693i 0.123635 0.992328i \(-0.460545\pi\)
−0.992328 + 0.123635i \(0.960545\pi\)
\(522\) 0 0
\(523\) −7.19963 + 17.3815i −0.314818 + 0.760038i 0.684695 + 0.728830i \(0.259935\pi\)
−0.999513 + 0.0312081i \(0.990065\pi\)
\(524\) −18.5412 + 2.90190i −0.809975 + 0.126770i
\(525\) 0 0
\(526\) 13.5274 10.6441i 0.589822 0.464105i
\(527\) 19.1854i 0.835729i
\(528\) 0 0
\(529\) 2.09570i 0.0911175i
\(530\) −27.6019 35.0787i −1.19895 1.52372i
\(531\) 0 0
\(532\) 15.6360 21.4386i 0.677907 0.929481i
\(533\) −5.97736 + 14.4306i −0.258908 + 0.625059i
\(534\) 0 0
\(535\) 5.15320 + 5.15320i 0.222792 + 0.222792i
\(536\) 22.7962 0.833064i 0.984644 0.0359829i
\(537\) 0 0
\(538\) 11.4778 + 40.8402i 0.494845 + 1.76075i
\(539\) −0.111979 + 0.270340i −0.00482326 + 0.0116444i
\(540\) 0 0
\(541\) 29.2905 12.1325i 1.25930 0.521619i 0.349605 0.936897i \(-0.386316\pi\)
0.909694 + 0.415279i \(0.136316\pi\)
\(542\) −5.08232 + 42.6066i −0.218304 + 1.83011i
\(543\) 0 0
\(544\) 11.0902 16.4346i 0.475490 0.704629i
\(545\) 30.8613i 1.32195i
\(546\) 0 0
\(547\) 12.7177 + 30.7032i 0.543769 + 1.31278i 0.922045 + 0.387082i \(0.126517\pi\)
−0.378276 + 0.925693i \(0.623483\pi\)
\(548\) −8.82724 14.4640i −0.377081 0.617873i
\(549\) 0 0
\(550\) 10.2182 2.87175i 0.435705 0.122452i
\(551\) 31.0175 + 31.0175i 1.32139 + 1.32139i
\(552\) 0 0
\(553\) 7.86833 7.86833i 0.334596 0.334596i
\(554\) −7.22620 + 12.8757i −0.307012 + 0.547036i
\(555\) 0 0
\(556\) 14.2003 19.4701i 0.602227 0.825716i
\(557\) 24.6214 10.1985i 1.04324 0.432125i 0.205768 0.978601i \(-0.434031\pi\)
0.837475 + 0.546476i \(0.184031\pi\)
\(558\) 0 0
\(559\) 6.05412 0.256062
\(560\) 43.2393 + 3.56212i 1.82720 + 0.150527i
\(561\) 0 0
\(562\) 1.78570 + 2.26941i 0.0753251 + 0.0957292i
\(563\) 0.901476 + 2.17636i 0.0379927 + 0.0917225i 0.941737 0.336350i \(-0.109193\pi\)
−0.903744 + 0.428073i \(0.859193\pi\)
\(564\) 0 0
\(565\) −18.3728 7.61028i −0.772951 0.320167i
\(566\) −14.8895 + 26.5302i −0.625853 + 1.11515i
\(567\) 0 0
\(568\) 25.4437 11.6452i 1.06759 0.488622i
\(569\) 26.1461 26.1461i 1.09610 1.09610i 0.101241 0.994862i \(-0.467719\pi\)
0.994862 0.101241i \(-0.0322812\pi\)
\(570\) 0 0
\(571\) −3.62983 1.50352i −0.151903 0.0629205i 0.305436 0.952212i \(-0.401198\pi\)
−0.457340 + 0.889292i \(0.651198\pi\)
\(572\) 1.23339 5.09639i 0.0515708 0.213091i
\(573\) 0 0
\(574\) 1.45268 12.1783i 0.0606338 0.508312i
\(575\) −60.0450 −2.50405
\(576\) 0 0
\(577\) 5.12912 0.213528 0.106764 0.994284i \(-0.465951\pi\)
0.106764 + 0.994284i \(0.465951\pi\)
\(578\) −0.789947 + 6.62237i −0.0328575 + 0.275454i
\(579\) 0 0
\(580\) −16.8706 + 69.7096i −0.700515 + 2.89453i
\(581\) −39.4825 16.3542i −1.63801 0.678485i
\(582\) 0 0
\(583\) 2.99523 2.99523i 0.124050 0.124050i
\(584\) 8.78077 + 19.1851i 0.363351 + 0.793887i
\(585\) 0 0
\(586\) 0.369939 0.659160i 0.0152821 0.0272297i
\(587\) 39.9161 + 16.5338i 1.64751 + 0.682422i 0.997024 0.0770926i \(-0.0245637\pi\)
0.650490 + 0.759515i \(0.274564\pi\)
\(588\) 0 0
\(589\) −10.9112 26.3419i −0.449587 1.08540i
\(590\) −0.0643843 0.0818248i −0.00265066 0.00336868i
\(591\) 0 0
\(592\) 15.4398 13.0895i 0.634572 0.537976i
\(593\) −14.3658 −0.589931 −0.294965 0.955508i \(-0.595308\pi\)
−0.294965 + 0.955508i \(0.595308\pi\)
\(594\) 0 0
\(595\) 35.1216 14.5478i 1.43985 0.596404i
\(596\) −1.55667 + 2.13436i −0.0637638 + 0.0874268i
\(597\) 0 0
\(598\) −14.5177 + 25.8678i −0.593674 + 1.05781i
\(599\) 6.69798 6.69798i 0.273672 0.273672i −0.556905 0.830576i \(-0.688011\pi\)
0.830576 + 0.556905i \(0.188011\pi\)
\(600\) 0 0
\(601\) −9.70012 9.70012i −0.395676 0.395676i 0.481029 0.876705i \(-0.340263\pi\)
−0.876705 + 0.481029i \(0.840263\pi\)
\(602\) −4.57644 + 1.28618i −0.186522 + 0.0524206i
\(603\) 0 0
\(604\) −11.0500 18.1062i −0.449618 0.736730i
\(605\) −17.3930 41.9905i −0.707128 1.70716i
\(606\) 0 0
\(607\) 38.7414i 1.57247i 0.617931 + 0.786233i \(0.287971\pi\)
−0.617931 + 0.786233i \(0.712029\pi\)
\(608\) −5.88036 + 28.8723i −0.238480 + 1.17093i
\(609\) 0 0
\(610\) −7.18604 + 60.2428i −0.290954 + 2.43916i
\(611\) 39.3106 16.2830i 1.59034 0.658739i
\(612\) 0 0
\(613\) −14.1998 + 34.2813i −0.573524 + 1.38461i 0.325013 + 0.945710i \(0.394631\pi\)
−0.898536 + 0.438899i \(0.855369\pi\)
\(614\) 2.02370 + 7.20070i 0.0816700 + 0.290597i
\(615\) 0 0
\(616\) 0.150361 + 4.11450i 0.00605820 + 0.165778i
\(617\) 9.25656 + 9.25656i 0.372655 + 0.372655i 0.868443 0.495788i \(-0.165121\pi\)
−0.495788 + 0.868443i \(0.665121\pi\)
\(618\) 0 0
\(619\) 0.139195 0.336046i 0.00559470 0.0135068i −0.921057 0.389427i \(-0.872673\pi\)
0.926652 + 0.375920i \(0.122673\pi\)
\(620\) 27.4708 37.6654i 1.10326 1.51268i
\(621\) 0 0
\(622\) −3.11613 3.96023i −0.124945 0.158791i
\(623\) 7.29403i 0.292229i
\(624\) 0 0
\(625\) 81.8076i 3.27230i
\(626\) −5.94081 + 4.67456i −0.237443 + 0.186833i
\(627\) 0 0
\(628\) 48.8359 7.64336i 1.94876 0.305003i
\(629\) 6.78729 16.3860i 0.270627 0.653351i
\(630\) 0 0
\(631\) −8.98002 8.98002i −0.357489 0.357489i 0.505397 0.862887i \(-0.331346\pi\)
−0.862887 + 0.505397i \(0.831346\pi\)
\(632\) −4.30849 + 11.5808i −0.171383 + 0.460659i
\(633\) 0 0
\(634\) 26.0719 7.32732i 1.03545 0.291005i
\(635\) −32.5013 + 78.4650i −1.28977 + 3.11379i
\(636\) 0 0
\(637\) −2.17015 + 0.898904i −0.0859843 + 0.0356159i
\(638\) −6.75840 0.806174i −0.267568 0.0319167i
\(639\) 0 0
\(640\) −45.3048 + 16.3853i −1.79083 + 0.647685i
\(641\) 8.03068i 0.317193i −0.987344 0.158596i \(-0.949303\pi\)
0.987344 0.158596i \(-0.0506969\pi\)
\(642\) 0 0
\(643\) 8.46145 + 20.4278i 0.333687 + 0.805592i 0.998293 + 0.0583982i \(0.0185993\pi\)
−0.664606 + 0.747194i \(0.731401\pi\)
\(644\) 5.47875 22.6382i 0.215893 0.892072i
\(645\) 0 0
\(646\) 6.98526 + 24.8548i 0.274832 + 0.977900i
\(647\) 2.49537 + 2.49537i 0.0981030 + 0.0981030i 0.754455 0.656352i \(-0.227901\pi\)
−0.656352 + 0.754455i \(0.727901\pi\)
\(648\) 0 0
\(649\) 0.00698670 0.00698670i 0.000274252 0.000274252i
\(650\) 74.3020 + 41.7004i 2.91436 + 1.63562i
\(651\) 0 0
\(652\) −1.11812 7.14405i −0.0437891 0.279783i
\(653\) −35.3520 + 14.6433i −1.38343 + 0.573036i −0.945397 0.325922i \(-0.894325\pi\)
−0.438034 + 0.898958i \(0.644325\pi\)
\(654\) 0 0
\(655\) 39.9572 1.56126
\(656\) 4.16111 + 12.9677i 0.162464 + 0.506304i
\(657\) 0 0
\(658\) −26.2565 + 20.6600i −1.02358 + 0.805413i
\(659\) 1.57465 + 3.80154i 0.0613397 + 0.148087i 0.951578 0.307409i \(-0.0994619\pi\)
−0.890238 + 0.455496i \(0.849462\pi\)
\(660\) 0 0
\(661\) −31.7340 13.1446i −1.23431 0.511267i −0.332377 0.943147i \(-0.607851\pi\)
−0.901932 + 0.431879i \(0.857851\pi\)
\(662\) 13.5142 + 7.58454i 0.525244 + 0.294782i
\(663\) 0 0
\(664\) 47.4230 1.73303i 1.84037 0.0672546i
\(665\) −39.9489 + 39.9489i −1.54915 + 1.54915i
\(666\) 0 0
\(667\) 35.5732 + 14.7349i 1.37740 + 0.570537i
\(668\) −1.00578 1.64805i −0.0389150 0.0637648i
\(669\) 0 0
\(670\) −48.2266 5.75270i −1.86316 0.222246i
\(671\) −5.75747 −0.222265
\(672\) 0 0
\(673\) 21.6309 0.833810 0.416905 0.908950i \(-0.363115\pi\)
0.416905 + 0.908950i \(0.363115\pi\)
\(674\) −2.49248 0.297315i −0.0960067 0.0114521i
\(675\) 0 0
\(676\) 13.7361 8.38300i 0.528312 0.322423i
\(677\) 10.9044 + 4.51674i 0.419089 + 0.173592i 0.582255 0.813006i \(-0.302171\pi\)
−0.163166 + 0.986599i \(0.552171\pi\)
\(678\) 0 0
\(679\) −15.0549 + 15.0549i −0.577754 + 0.577754i
\(680\) −28.7393 + 30.9195i −1.10210 + 1.18571i
\(681\) 0 0
\(682\) 3.85800 + 2.16522i 0.147731 + 0.0829106i
\(683\) −44.8237 18.5666i −1.71513 0.710431i −0.999934 0.0115104i \(-0.996336\pi\)
−0.715199 0.698921i \(-0.753664\pi\)
\(684\) 0 0
\(685\) 13.8064 + 33.3316i 0.527516 + 1.27354i
\(686\) 21.2659 16.7332i 0.811937 0.638877i
\(687\) 0 0
\(688\) 4.02645 3.41353i 0.153507 0.130140i
\(689\) 34.0035 1.29543
\(690\) 0 0
\(691\) 12.6306 5.23178i 0.480492 0.199026i −0.129272 0.991609i \(-0.541264\pi\)
0.609764 + 0.792583i \(0.291264\pi\)
\(692\) 4.53170 0.709262i 0.172270 0.0269621i
\(693\) 0 0
\(694\) 16.4990 + 9.25969i 0.626292 + 0.351493i
\(695\) −36.2808 + 36.2808i −1.37621 + 1.37621i
\(696\) 0 0
\(697\) 8.43802 + 8.43802i 0.319613 + 0.319613i
\(698\) −6.69648 23.8273i −0.253466 0.901876i
\(699\) 0 0
\(700\) −65.0255 15.7370i −2.45773 0.594804i
\(701\) 3.42768 + 8.27515i 0.129462 + 0.312548i 0.975298 0.220895i \(-0.0708978\pi\)
−0.845836 + 0.533443i \(0.820898\pi\)
\(702\) 0 0
\(703\) 26.3583i 0.994122i
\(704\) −2.05323 4.08492i −0.0773840 0.153956i
\(705\) 0 0
\(706\) −16.5355 1.97243i −0.622321 0.0742334i
\(707\) −17.2292 + 7.13658i −0.647972 + 0.268399i
\(708\) 0 0
\(709\) 5.69918 13.7590i 0.214037 0.516731i −0.779999 0.625780i \(-0.784781\pi\)
0.994036 + 0.109049i \(0.0347806\pi\)
\(710\) −57.3553 + 16.1193i −2.15251 + 0.604946i
\(711\) 0 0
\(712\) −3.37075 7.36477i −0.126324 0.276006i
\(713\) −17.6971 17.6971i −0.662762 0.662762i
\(714\) 0 0
\(715\) −4.27233 + 10.3143i −0.159776 + 0.385734i
\(716\) 3.09562 + 19.7790i 0.115689 + 0.739174i
\(717\) 0 0
\(718\) 26.0392 20.4891i 0.971776 0.764647i
\(719\) 20.5784i 0.767445i 0.923448 + 0.383722i \(0.125358\pi\)
−0.923448 + 0.383722i \(0.874642\pi\)
\(720\) 0 0
\(721\) 40.5773i 1.51118i
\(722\) −7.11058 9.03671i −0.264628 0.336311i
\(723\) 0 0
\(724\) 5.20087 + 3.79320i 0.193289 + 0.140973i
\(725\) 42.3242 102.180i 1.57188 3.79485i
\(726\) 0 0
\(727\) 27.0543 + 27.0543i 1.00339 + 1.00339i 0.999994 + 0.00339404i \(0.00108036\pi\)
0.00339404 + 0.999994i \(0.498920\pi\)
\(728\) −22.5015 + 24.2085i −0.833962 + 0.897227i
\(729\) 0 0
\(730\) −12.1543 43.2473i −0.449852 1.60066i
\(731\) 1.77001 4.27319i 0.0654664 0.158050i
\(732\) 0 0
\(733\) 8.68221 3.59629i 0.320685 0.132832i −0.216534 0.976275i \(-0.569475\pi\)
0.537218 + 0.843443i \(0.319475\pi\)
\(734\) −1.10378 + 9.25332i −0.0407412 + 0.341546i
\(735\) 0 0
\(736\) 4.92980 + 25.3897i 0.181715 + 0.935875i
\(737\) 4.60908i 0.169777i
\(738\) 0 0
\(739\) 7.29030 + 17.6003i 0.268178 + 0.647439i 0.999398 0.0347030i \(-0.0110485\pi\)
−0.731220 + 0.682142i \(0.761049\pi\)
\(740\) −36.7874 + 22.4510i −1.35233 + 0.825314i
\(741\) 0 0
\(742\) −25.7040 + 7.22391i −0.943622 + 0.265198i
\(743\) −18.2313 18.2313i −0.668841 0.668841i 0.288607 0.957448i \(-0.406808\pi\)
−0.957448 + 0.288607i \(0.906808\pi\)
\(744\) 0 0
\(745\) 3.97719 3.97719i 0.145713 0.145713i
\(746\) 6.85754 12.2188i 0.251072 0.447362i
\(747\) 0 0
\(748\) −3.23659 2.36058i −0.118342 0.0863112i
\(749\) 4.02744 1.66822i 0.147159 0.0609554i
\(750\) 0 0
\(751\) −10.8193 −0.394802 −0.197401 0.980323i \(-0.563250\pi\)
−0.197401 + 0.980323i \(0.563250\pi\)
\(752\) 16.9636 32.9942i 0.618599 1.20317i
\(753\) 0 0
\(754\) −33.7864 42.9386i −1.23043 1.56373i
\(755\) 17.2830 + 41.7248i 0.628992 + 1.51852i
\(756\) 0 0
\(757\) 47.3522 + 19.6139i 1.72105 + 0.712881i 0.999796 + 0.0202058i \(0.00643214\pi\)
0.721250 + 0.692675i \(0.243568\pi\)
\(758\) −18.2118 + 32.4500i −0.661484 + 1.17864i
\(759\) 0 0
\(760\) 21.8750 58.7977i 0.793489 2.13282i
\(761\) 11.0778 11.0778i 0.401570 0.401570i −0.477216 0.878786i \(-0.658354\pi\)
0.878786 + 0.477216i \(0.158354\pi\)
\(762\) 0 0
\(763\) 17.0550 + 7.06441i 0.617432 + 0.255749i
\(764\) −17.6383 4.26869i −0.638130 0.154436i
\(765\) 0 0
\(766\) −5.07095 + 42.5113i −0.183221 + 1.53599i
\(767\) 0.0793167 0.00286396
\(768\) 0 0
\(769\) −5.28351 −0.190528 −0.0952641 0.995452i \(-0.530370\pi\)
−0.0952641 + 0.995452i \(0.530370\pi\)
\(770\) 1.03831 8.70446i 0.0374181 0.313687i
\(771\) 0 0
\(772\) −9.97175 2.41329i −0.358891 0.0868563i
\(773\) −49.7146 20.5924i −1.78811 0.740659i −0.990505 0.137476i \(-0.956101\pi\)
−0.797603 0.603183i \(-0.793899\pi\)
\(774\) 0 0
\(775\) −50.8328 + 50.8328i −1.82597 + 1.82597i
\(776\) 8.24367 22.1582i 0.295931 0.795431i
\(777\) 0 0
\(778\) −4.93092 + 8.78595i −0.176782 + 0.314992i
\(779\) −16.3844 6.78666i −0.587033 0.243157i
\(780\) 0 0
\(781\) −2.16362 5.22343i −0.0774203 0.186909i
\(782\) 14.0138 + 17.8099i 0.501133 + 0.636881i
\(783\) 0 0
\(784\) −0.936477 + 1.82145i −0.0334456 + 0.0650516i
\(785\) −105.244 −3.75632
\(786\) 0 0
\(787\) −7.70131 + 3.18999i −0.274522 + 0.113711i −0.515697 0.856771i \(-0.672467\pi\)
0.241175 + 0.970482i \(0.422467\pi\)
\(788\) −9.03831 6.59200i −0.321977 0.234830i