Properties

Label 864.2.w.a.107.14
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 107.14
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.14

$q$-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 \(-0.973838\pi\)
−0.762771 0.646669i \(-0.776162\pi\)
\(6\) 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 0.301664 0.953414i \(-0.402458\pi\)
−0.460857 + 0.887474i \(0.652458\pi\)
\(12\) 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 \(-0.639736\pi\)
−0.425027 + 0.905180i \(0.639736\pi\)
\(18\) 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 −0.284541 0.958664i \(-0.591841\pi\)
0.958664 + 0.284541i \(0.0918413\pi\)
\(24\) 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 \(0.160758\pi\)
−0.276704 + 0.960955i \(0.589242\pi\)
\(30\) 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 0.493663 0.869653i \(-0.335658\pi\)
−0.869653 + 0.493663i \(0.835658\pi\)
\(42\) 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 \(0.236479\pi\)
−0.736496 + 0.676441i \(0.763521\pi\)
\(48\) 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 \(0.295007\pi\)
−0.990020 + 0.140924i \(0.954993\pi\)
\(54\) 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 −0.924310 0.381643i \(-0.875358\pi\)
0.923448 + 0.383723i \(0.125358\pi\)
\(60\) 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 0.987546 0.157333i \(-0.0502897\pi\)
−0.157333 + 0.987546i \(0.550290\pi\)
\(72\) 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 \(0.247463\pi\)
−0.00797127 + 0.999968i \(0.502537\pi\)
\(84\) 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 −0.591597 0.806234i \(-0.701502\pi\)
0.806234 + 0.591597i \(0.201502\pi\)
\(90\) 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 0.692920 0.721014i \(-0.256324\pi\)
−0.0198656 + 0.999803i \(0.506324\pi\)
\(102\) 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 0.304944 0.952370i \(-0.401362\pi\)
−0.457800 + 0.889055i \(0.651362\pi\)
\(108\) 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 \(-0.429504\pi\)
0.219664 + 0.975576i \(0.429504\pi\)
\(114\) 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 −0.727769 0.685823i \(-0.759443\pi\)
−0.0296603 + 0.999560i \(0.509443\pi\)
\(132\) 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 0.403251 0.915089i \(-0.367880\pi\)
−0.915089 + 0.403251i \(0.867880\pi\)
\(138\) 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 −0.943231 0.332137i \(-0.892230\pi\)
0.901821 + 0.432109i \(0.142230\pi\)
\(150\) 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 0.680202 0.733024i \(-0.261892\pi\)
−0.733024 + 0.680202i \(0.761892\pi\)
\(168\) 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 −0.300679 0.953725i \(-0.597213\pi\)
0.461773 + 0.886998i \(0.347213\pi\)
\(174\) 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 0.999957 0.00928754i \(-0.00295636\pi\)
−0.713644 + 0.700509i \(0.752956\pi\)
\(180\) 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 \(-0.606468\pi\)
−0.328276 + 0.944582i \(0.606468\pi\)
\(192\) 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 0.190920 0.981606i \(-0.438853\pi\)
−0.559099 + 0.829101i \(0.688853\pi\)
\(198\) 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 0.131480 0.991319i \(-0.458027\pi\)
0.793939 + 0.607997i \(0.208027\pi\)
\(228\) 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 0.114502 0.993423i \(-0.463473\pi\)
−0.993423 + 0.114502i \(0.963473\pi\)
\(234\) 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 \(-0.933594\pi\)
0.978317 0.207111i \(-0.0664061\pi\)
\(240\) 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 \(0.281020\pi\)
−0.995255 + 0.0972985i \(0.968980\pi\)
\(252\) 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 \(0.321909\pi\)
−0.530753 + 0.847526i \(0.678091\pi\)
\(258\) 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 0.390081 0.920780i \(-0.372447\pi\)
−0.920780 + 0.390081i \(0.872447\pi\)
\(264\) 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 0.690025 0.723786i \(-0.257600\pi\)
0.999715 + 0.0238727i \(0.00759963\pi\)
\(270\) 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 −0.662727 0.748861i \(-0.730601\pi\)
0.748861 + 0.662727i \(0.230601\pi\)
\(282\) 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 0.368213 0.929742i \(-0.379970\pi\)
−0.397061 + 0.917792i \(0.629970\pi\)
\(294\) 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 −0.774926 0.632052i \(-0.782213\pi\)
0.632052 + 0.774926i \(0.282213\pi\)
\(312\) 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 \(-0.944262\pi\)
0.573108 0.819480i \(-0.305738\pi\)
\(318\) 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 −0.724840 0.688917i \(-0.758086\pi\)
0.999677 + 0.0254011i \(0.00808630\pi\)
\(348\) 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 \(0.101457\pi\)
−0.949632 + 0.313366i \(0.898543\pi\)
\(354\) 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 0.118578 0.992945i \(-0.462166\pi\)
−0.992945 + 0.118578i \(0.962166\pi\)
\(360\) 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 \(-0.218533\pi\)
0.773442 + 0.633867i \(0.218533\pi\)
\(384\) 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 0.543247 0.839573i \(-0.317195\pi\)
−0.209534 + 0.977801i \(0.567195\pi\)
\(390\) 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 \(-0.602046\pi\)
−0.315125 + 0.949050i \(0.602046\pi\)
\(402\) 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 −0.464474 0.885587i \(-0.653756\pi\)
0.297772 + 0.954637i \(0.403756\pi\)
\(420\) 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 \(0.263792\pi\)
−0.675816 + 0.737071i \(0.736208\pi\)
\(432\) 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 −0.771679 0.636012i \(-0.780583\pi\)
0.995388 + 0.0959313i \(0.0305829\pi\)
\(444\) 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 \(-0.988933\pi\)
0.999396 0.0347614i \(-0.0110671\pi\)
\(450\) 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 −0.693884 0.720087i \(-0.744102\pi\)
0.0185280 + 0.999828i \(0.494102\pi\)
\(462\) 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 \(0.0125122\pi\)
−0.678773 + 0.734349i \(0.737488\pi\)
\(468\) 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 \(-0.429469\pi\)
0.219772 + 0.975551i \(0.429469\pi\)
\(480\) 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 −0.0232215 0.999730i \(-0.507392\pi\)
−0.723336 + 0.690496i \(0.757392\pi\)
\(492\) 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 \(0.576056\pi\)
−0.971590 + 0.236671i \(0.923944\pi\)
\(504\) 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 \(-0.854973\pi\)
0.323837 0.946113i \(-0.395027\pi\)
\(510\) 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 0.992328 0.123635i \(-0.0394552\pi\)
−0.123635 + 0.992328i \(0.539455\pi\)
\(522\) 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 −0.837475 0.546476i \(-0.815969\pi\)
−0.205768 + 0.978601i \(0.565969\pi\)
\(558\) 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 0.903744 0.428073i \(-0.140807\pi\)
−0.941737 + 0.336350i \(0.890807\pi\)
\(564\) 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 \(0.532281\pi\)
−0.994862 + 0.101241i \(0.967719\pi\)
\(570\) 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 −0.650490 0.759515i \(-0.725436\pi\)
−0.997024 + 0.0770926i \(0.975436\pi\)
\(588\) 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 \(-0.404692\pi\)
0.294965 + 0.955508i \(0.404692\pi\)
\(594\) 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 −0.830576 0.556905i \(-0.811989\pi\)
0.556905 + 0.830576i \(0.311989\pi\)
\(600\) 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 0.495788 0.868443i \(-0.334879\pi\)
−0.868443 + 0.495788i \(0.834879\pi\)
\(618\) 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 \(0.0506969\pi\)
−0.987344 + 0.158596i \(0.949303\pi\)
\(642\) 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 0.656352 0.754455i \(-0.272099\pi\)
−0.754455 + 0.656352i \(0.772099\pi\)
\(648\) 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 0.438034 0.898958i \(-0.355675\pi\)
0.945397 + 0.325922i \(0.105675\pi\)
\(654\) 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 0.890238 0.455496i \(-0.150538\pi\)
−0.951578 + 0.307409i \(0.900538\pi\)
\(660\) 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 0.163166 0.986599i \(-0.447829\pi\)
−0.582255 + 0.813006i \(0.697829\pi\)
\(678\) 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 \(0.00366397\pi\)
0.715199 + 0.698921i \(0.246336\pi\)
\(684\) 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 0.845836 0.533443i \(-0.179102\pi\)
−0.975298 + 0.220895i \(0.929102\pi\)
\(702\) 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 \(-0.874642\pi\)
0.923448 0.383722i \(-0.125358\pi\)
\(720\) 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 0.957448 0.288607i \(-0.0931919\pi\)
−0.288607 + 0.957448i \(0.593192\pi\)
\(744\) 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 −0.878786 0.477216i \(-0.841646\pi\)
0.477216 + 0.878786i \(0.341646\pi\)
\(762\) 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 \(0.0438990\pi\)
0.797603 + 0.603183i \(0.206101\pi\)
\(774\) 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