Properties

Label 729.2.i.a.685.21
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.21
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.21

$q$-expansion

\(f(q)\) \(=\) \(q+(1.83047 + 0.509546i) q^{2} +(1.37865 + 0.832017i) q^{4} +(-3.83386 + 0.148771i) q^{5} +(0.365157 + 0.0571095i) q^{7} +(-0.508193 - 0.538653i) q^{8} +O(q^{10})\) \(q+(1.83047 + 0.509546i) q^{2} +(1.37865 + 0.832017i) q^{4} +(-3.83386 + 0.148771i) q^{5} +(0.365157 + 0.0571095i) q^{7} +(-0.508193 - 0.538653i) q^{8} +(-7.09357 - 1.68121i) q^{10} +(0.814808 + 5.96545i) q^{11} +(-3.43162 + 5.00342i) q^{13} +(0.639308 + 0.290601i) q^{14} +(-2.15666 - 4.09432i) q^{16} +(-3.18666 + 1.60040i) q^{17} +(0.159287 + 2.73485i) q^{19} +(-5.40932 - 2.98473i) q^{20} +(-1.54819 + 11.3348i) q^{22} +(0.230565 - 0.597178i) q^{23} +(9.69140 - 0.753275i) q^{25} +(-8.83094 + 7.41004i) q^{26} +(0.455905 + 0.382550i) q^{28} +(-0.792323 - 0.566318i) q^{29} +(3.51822 - 4.03144i) q^{31} +(-1.54790 - 7.14591i) q^{32} +(-6.64856 + 1.30573i) q^{34} +(-1.40846 - 0.164625i) q^{35} +(-3.14819 - 4.22875i) q^{37} +(-1.10196 + 5.08722i) q^{38} +(2.02848 + 1.98952i) q^{40} +(0.857298 - 3.32824i) q^{41} +(3.41495 + 3.09891i) q^{43} +(-3.84002 + 8.90218i) q^{44} +(0.726332 - 0.975633i) q^{46} +(2.84239 + 3.25702i) q^{47} +(-6.53566 - 2.09557i) q^{49} +(18.1236 + 3.55936i) q^{50} +(-8.89391 + 4.04278i) q^{52} +(0.566709 - 3.21397i) q^{53} +(-4.01135 - 22.7495i) q^{55} +(-0.154808 - 0.225715i) q^{56} +(-1.16176 - 1.44035i) q^{58} +(1.88217 - 0.768951i) q^{59} +(-12.5244 + 7.55850i) q^{61} +(8.49420 - 5.58672i) q^{62} +(0.269642 - 4.62958i) q^{64} +(12.4120 - 19.6929i) q^{65} +(6.29045 - 4.49615i) q^{67} +(-5.72483 - 0.444969i) q^{68} +(-2.49425 - 1.01901i) q^{70} +(2.46771 + 8.24271i) q^{71} +(-6.59819 + 1.56380i) q^{73} +(-3.60792 - 9.34473i) q^{74} +(-2.05584 + 3.90291i) q^{76} +(-0.0431511 + 2.22486i) q^{77} +(2.56450 - 2.51525i) q^{79} +(8.87745 + 15.3762i) q^{80} +(3.26515 - 5.65540i) q^{82} +(3.79446 + 14.7310i) q^{83} +(11.9791 - 6.60979i) q^{85} +(4.67193 + 7.41253i) q^{86} +(2.79923 - 3.47050i) q^{88} +(-1.54379 + 5.15662i) q^{89} +(-1.53882 + 1.63105i) q^{91} +(0.814730 - 0.631463i) q^{92} +(3.54331 + 7.41019i) q^{94} +(-1.01755 - 10.4613i) q^{95} +(12.6536 + 0.491018i) q^{97} +(-10.8955 - 7.16610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.83047 + 0.509546i 1.29434 + 0.360303i 0.845819 0.533470i \(-0.179112\pi\)
0.448518 + 0.893774i \(0.351952\pi\)
\(3\) 0 0
\(4\) 1.37865 + 0.832017i 0.689323 + 0.416008i
\(5\) −3.83386 + 0.148771i −1.71456 + 0.0665325i −0.877199 0.480126i \(-0.840591\pi\)
−0.837356 + 0.546659i \(0.815900\pi\)
\(6\) 0 0
\(7\) 0.365157 + 0.0571095i 0.138016 + 0.0215853i 0.223150 0.974784i \(-0.428366\pi\)
−0.0851333 + 0.996370i \(0.527132\pi\)
\(8\) −0.508193 0.538653i −0.179673 0.190443i
\(9\) 0 0
\(10\) −7.09357 1.68121i −2.24318 0.531644i
\(11\) 0.814808 + 5.96545i 0.245674 + 1.79865i 0.538648 + 0.842531i \(0.318935\pi\)
−0.292974 + 0.956120i \(0.594645\pi\)
\(12\) 0 0
\(13\) −3.43162 + 5.00342i −0.951759 + 1.38770i −0.0301651 + 0.999545i \(0.509603\pi\)
−0.921594 + 0.388154i \(0.873113\pi\)
\(14\) 0.639308 + 0.290601i 0.170862 + 0.0776664i
\(15\) 0 0
\(16\) −2.15666 4.09432i −0.539165 1.02358i
\(17\) −3.18666 + 1.60040i −0.772878 + 0.388154i −0.791105 0.611680i \(-0.790494\pi\)
0.0182273 + 0.999834i \(0.494198\pi\)
\(18\) 0 0
\(19\) 0.159287 + 2.73485i 0.0365429 + 0.627417i 0.966009 + 0.258509i \(0.0832312\pi\)
−0.929466 + 0.368908i \(0.879732\pi\)
\(20\) −5.40932 2.98473i −1.20956 0.667407i
\(21\) 0 0
\(22\) −1.54819 + 11.3348i −0.330075 + 2.41658i
\(23\) 0.230565 0.597178i 0.0480761 0.124520i −0.906766 0.421635i \(-0.861456\pi\)
0.954842 + 0.297115i \(0.0960243\pi\)
\(24\) 0 0
\(25\) 9.69140 0.753275i 1.93828 0.150655i
\(26\) −8.83094 + 7.41004i −1.73189 + 1.45323i
\(27\) 0 0
\(28\) 0.455905 + 0.382550i 0.0861580 + 0.0722952i
\(29\) −0.792323 0.566318i −0.147131 0.105163i 0.505545 0.862801i \(-0.331292\pi\)
−0.652675 + 0.757638i \(0.726353\pi\)
\(30\) 0 0
\(31\) 3.51822 4.03144i 0.631891 0.724067i −0.344809 0.938673i \(-0.612056\pi\)
0.976701 + 0.214605i \(0.0688466\pi\)
\(32\) −1.54790 7.14591i −0.273633 1.26323i
\(33\) 0 0
\(34\) −6.64856 + 1.30573i −1.14022 + 0.223931i
\(35\) −1.40846 0.164625i −0.238073 0.0278267i
\(36\) 0 0
\(37\) −3.14819 4.22875i −0.517559 0.695202i 0.464114 0.885775i \(-0.346373\pi\)
−0.981673 + 0.190574i \(0.938965\pi\)
\(38\) −1.10196 + 5.08722i −0.178762 + 0.825256i
\(39\) 0 0
\(40\) 2.02848 + 1.98952i 0.320731 + 0.314570i
\(41\) 0.857298 3.32824i 0.133887 0.519783i −0.865920 0.500182i \(-0.833267\pi\)
0.999808 0.0196012i \(-0.00623966\pi\)
\(42\) 0 0
\(43\) 3.41495 + 3.09891i 0.520776 + 0.472579i 0.889484 0.456966i \(-0.151064\pi\)
−0.368708 + 0.929545i \(0.620200\pi\)
\(44\) −3.84002 + 8.90218i −0.578905 + 1.34205i
\(45\) 0 0
\(46\) 0.726332 0.975633i 0.107092 0.143849i
\(47\) 2.84239 + 3.25702i 0.414605 + 0.475085i 0.922313 0.386445i \(-0.126297\pi\)
−0.507707 + 0.861530i \(0.669507\pi\)
\(48\) 0 0
\(49\) −6.53566 2.09557i −0.933665 0.299368i
\(50\) 18.1236 + 3.55936i 2.56307 + 0.503370i
\(51\) 0 0
\(52\) −8.89391 + 4.04278i −1.23336 + 0.560633i
\(53\) 0.566709 3.21397i 0.0778435 0.441472i −0.920829 0.389966i \(-0.872487\pi\)
0.998673 0.0515062i \(-0.0164022\pi\)
\(54\) 0 0
\(55\) −4.01135 22.7495i −0.540890 3.06754i
\(56\) −0.154808 0.225715i −0.0206871 0.0301625i
\(57\) 0 0
\(58\) −1.16176 1.44035i −0.152546 0.189128i
\(59\) 1.88217 0.768951i 0.245038 0.100109i −0.252354 0.967635i \(-0.581205\pi\)
0.497392 + 0.867526i \(0.334291\pi\)
\(60\) 0 0
\(61\) −12.5244 + 7.55850i −1.60358 + 0.967767i −0.620586 + 0.784138i \(0.713105\pi\)
−0.982996 + 0.183629i \(0.941216\pi\)
\(62\) 8.49420 5.58672i 1.07876 0.709514i
\(63\) 0 0
\(64\) 0.269642 4.62958i 0.0337053 0.578697i
\(65\) 12.4120 19.6929i 1.53952 2.44261i
\(66\) 0 0
\(67\) 6.29045 4.49615i 0.768501 0.549292i −0.128295 0.991736i \(-0.540950\pi\)
0.896796 + 0.442444i \(0.145889\pi\)
\(68\) −5.72483 0.444969i −0.694238 0.0539604i
\(69\) 0 0
\(70\) −2.49425 1.01901i −0.298120 0.121795i
\(71\) 2.46771 + 8.24271i 0.292863 + 0.978230i 0.970149 + 0.242510i \(0.0779707\pi\)
−0.677286 + 0.735720i \(0.736844\pi\)
\(72\) 0 0
\(73\) −6.59819 + 1.56380i −0.772260 + 0.183029i −0.597811 0.801637i \(-0.703963\pi\)
−0.174449 + 0.984666i \(0.555814\pi\)
\(74\) −3.60792 9.34473i −0.419412 1.08630i
\(75\) 0 0
\(76\) −2.05584 + 3.90291i −0.235821 + 0.447695i
\(77\) −0.0431511 + 2.22486i −0.00491752 + 0.253546i
\(78\) 0 0
\(79\) 2.56450 2.51525i 0.288529 0.282988i −0.541508 0.840696i \(-0.682146\pi\)
0.830037 + 0.557708i \(0.188319\pi\)
\(80\) 8.87745 + 15.3762i 0.992529 + 1.71911i
\(81\) 0 0
\(82\) 3.26515 5.65540i 0.360575 0.624534i
\(83\) 3.79446 + 14.7310i 0.416496 + 1.61694i 0.741312 + 0.671160i \(0.234204\pi\)
−0.324816 + 0.945777i \(0.605302\pi\)
\(84\) 0 0
\(85\) 11.9791 6.60979i 1.29932 0.716933i
\(86\) 4.67193 + 7.41253i 0.503787 + 0.799313i
\(87\) 0 0
\(88\) 2.79923 3.47050i 0.298399 0.369957i
\(89\) −1.54379 + 5.15662i −0.163642 + 0.546601i −0.999999 0.00158400i \(-0.999496\pi\)
0.836357 + 0.548185i \(0.184681\pi\)
\(90\) 0 0
\(91\) −1.53882 + 1.63105i −0.161312 + 0.170981i
\(92\) 0.814730 0.631463i 0.0849414 0.0658346i
\(93\) 0 0
\(94\) 3.54331 + 7.41019i 0.365464 + 0.764303i
\(95\) −1.01755 10.4613i −0.104398 1.07331i
\(96\) 0 0
\(97\) 12.6536 + 0.491018i 1.28478 + 0.0498553i 0.672091 0.740469i \(-0.265396\pi\)
0.612689 + 0.790324i \(0.290088\pi\)
\(98\) −10.8955 7.16610i −1.10061 0.723885i
\(99\) 0 0
\(100\) 13.9877 + 7.02490i 1.39877 + 0.702490i
\(101\) 0.0632735 + 3.26237i 0.00629595 + 0.324618i 0.989697 + 0.143175i \(0.0457311\pi\)
−0.983401 + 0.181443i \(0.941923\pi\)
\(102\) 0 0
\(103\) 5.54166 + 4.29511i 0.546036 + 0.423210i 0.847912 0.530137i \(-0.177860\pi\)
−0.301876 + 0.953347i \(0.597613\pi\)
\(104\) 4.43903 0.694252i 0.435283 0.0680770i
\(105\) 0 0
\(106\) 2.67501 5.59430i 0.259820 0.543367i
\(107\) 11.6038 + 4.22343i 1.12178 + 0.408294i 0.835301 0.549792i \(-0.185293\pi\)
0.286478 + 0.958087i \(0.407515\pi\)
\(108\) 0 0
\(109\) −3.33087 + 1.21234i −0.319039 + 0.116121i −0.496576 0.867993i \(-0.665409\pi\)
0.177536 + 0.984114i \(0.443187\pi\)
\(110\) 4.24926 43.6862i 0.405151 4.16532i
\(111\) 0 0
\(112\) −0.553694 1.61823i −0.0523192 0.152909i
\(113\) −1.67618 + 1.52105i −0.157681 + 0.143088i −0.747029 0.664791i \(-0.768521\pi\)
0.589348 + 0.807879i \(0.299385\pi\)
\(114\) 0 0
\(115\) −0.795111 + 2.32380i −0.0741445 + 0.216696i
\(116\) −0.621146 1.43998i −0.0576719 0.133699i
\(117\) 0 0
\(118\) 3.83707 0.448489i 0.353231 0.0412868i
\(119\) −1.25503 + 0.402408i −0.115048 + 0.0368887i
\(120\) 0 0
\(121\) −24.3256 + 6.77150i −2.21142 + 0.615591i
\(122\) −26.7769 + 7.45385i −2.42427 + 0.674840i
\(123\) 0 0
\(124\) 8.20460 2.63070i 0.736795 0.236244i
\(125\) −17.9894 + 2.10266i −1.60902 + 0.188067i
\(126\) 0 0
\(127\) 0.784834 + 1.81945i 0.0696427 + 0.161450i 0.949482 0.313821i \(-0.101609\pi\)
−0.879839 + 0.475271i \(0.842350\pi\)
\(128\) −1.88150 + 5.49889i −0.166303 + 0.486038i
\(129\) 0 0
\(130\) 32.7542 29.7229i 2.87273 2.60687i
\(131\) 2.28947 + 6.69123i 0.200032 + 0.584615i 0.999878 0.0155891i \(-0.00496238\pi\)
−0.799847 + 0.600205i \(0.795086\pi\)
\(132\) 0 0
\(133\) −0.0980211 + 1.00774i −0.00849951 + 0.0873826i
\(134\) 13.8055 5.02478i 1.19261 0.434075i
\(135\) 0 0
\(136\) 2.48150 + 0.903192i 0.212787 + 0.0774480i
\(137\) 3.43526 7.18423i 0.293494 0.613790i −0.701617 0.712554i \(-0.747538\pi\)
0.995111 + 0.0987639i \(0.0314889\pi\)
\(138\) 0 0
\(139\) −6.80283 + 1.06394i −0.577009 + 0.0902425i −0.436288 0.899807i \(-0.643707\pi\)
−0.140720 + 0.990049i \(0.544942\pi\)
\(140\) −1.80479 1.39882i −0.152533 0.118222i
\(141\) 0 0
\(142\) 0.317019 + 16.3454i 0.0266037 + 1.37168i
\(143\) −32.6438 16.3943i −2.72981 1.37096i
\(144\) 0 0
\(145\) 3.12191 + 2.05331i 0.259260 + 0.170518i
\(146\) −12.8746 0.499593i −1.06551 0.0413467i
\(147\) 0 0
\(148\) −0.821843 8.44929i −0.0675551 0.694527i
\(149\) 3.41391 + 7.13959i 0.279678 + 0.584898i 0.993291 0.115643i \(-0.0368928\pi\)
−0.713612 + 0.700541i \(0.752942\pi\)
\(150\) 0 0
\(151\) −10.5396 + 8.16882i −0.857702 + 0.664769i −0.943438 0.331549i \(-0.892429\pi\)
0.0857362 + 0.996318i \(0.472676\pi\)
\(152\) 1.39219 1.47563i 0.112921 0.119690i
\(153\) 0 0
\(154\) −1.21265 + 4.05055i −0.0977184 + 0.326402i
\(155\) −12.8886 + 15.9794i −1.03524 + 1.28349i
\(156\) 0 0
\(157\) 0.589524 + 0.935343i 0.0470491 + 0.0746485i 0.868687 0.495361i \(-0.164964\pi\)
−0.821638 + 0.570009i \(0.806940\pi\)
\(158\) 5.97588 3.29735i 0.475415 0.262323i
\(159\) 0 0
\(160\) 6.99755 + 27.1662i 0.553205 + 2.14767i
\(161\) 0.118297 0.204896i 0.00932310 0.0161481i
\(162\) 0 0
\(163\) 1.68677 + 2.92157i 0.132118 + 0.228835i 0.924493 0.381200i \(-0.124489\pi\)
−0.792375 + 0.610034i \(0.791156\pi\)
\(164\) 3.95106 3.87517i 0.308526 0.302600i
\(165\) 0 0
\(166\) −0.560478 + 28.8981i −0.0435015 + 2.24293i
\(167\) 6.13741 11.6516i 0.474927 0.901627i −0.523832 0.851822i \(-0.675498\pi\)
0.998759 0.0498053i \(-0.0158601\pi\)
\(168\) 0 0
\(169\) −8.57591 22.2122i −0.659685 1.70863i
\(170\) 25.2954 5.99512i 1.94007 0.459804i
\(171\) 0 0
\(172\) 2.12967 + 7.11359i 0.162386 + 0.542406i
\(173\) −11.8943 4.85935i −0.904306 0.369450i −0.122135 0.992513i \(-0.538974\pi\)
−0.782171 + 0.623064i \(0.785888\pi\)
\(174\) 0 0
\(175\) 3.58190 + 0.278407i 0.270766 + 0.0210456i
\(176\) 22.6672 16.2015i 1.70860 1.22124i
\(177\) 0 0
\(178\) −5.45340 + 8.65240i −0.408749 + 0.648525i
\(179\) −0.135815 + 2.33186i −0.0101513 + 0.174291i 0.989422 + 0.145068i \(0.0463402\pi\)
−0.999573 + 0.0292227i \(0.990697\pi\)
\(180\) 0 0
\(181\) −13.5145 + 8.88860i −1.00452 + 0.660685i −0.941390 0.337320i \(-0.890479\pi\)
−0.0631324 + 0.998005i \(0.520109\pi\)
\(182\) −3.64786 + 2.20149i −0.270397 + 0.163186i
\(183\) 0 0
\(184\) −0.438844 + 0.179287i −0.0323520 + 0.0132172i
\(185\) 12.6988 + 15.7441i 0.933636 + 1.15753i
\(186\) 0 0
\(187\) −12.1436 17.7058i −0.888030 1.29478i
\(188\) 1.20875 + 6.85518i 0.0881574 + 0.499966i
\(189\) 0 0
\(190\) 3.46793 19.6676i 0.251590 1.42684i
\(191\) −4.21141 + 1.91432i −0.304727 + 0.138515i −0.560337 0.828264i \(-0.689328\pi\)
0.255610 + 0.966780i \(0.417724\pi\)
\(192\) 0 0
\(193\) 16.2928 + 3.19981i 1.17278 + 0.230327i 0.740908 0.671606i \(-0.234395\pi\)
0.431875 + 0.901933i \(0.357852\pi\)
\(194\) 22.9118 + 7.34639i 1.64497 + 0.527440i
\(195\) 0 0
\(196\) −7.26680 8.32683i −0.519057 0.594774i
\(197\) 0.444791 0.597458i 0.0316901 0.0425671i −0.785996 0.618232i \(-0.787849\pi\)
0.817686 + 0.575665i \(0.195257\pi\)
\(198\) 0 0
\(199\) 3.62013 8.39241i 0.256624 0.594922i −0.740387 0.672181i \(-0.765358\pi\)
0.997011 + 0.0772590i \(0.0246168\pi\)
\(200\) −5.33086 4.83749i −0.376948 0.342062i
\(201\) 0 0
\(202\) −1.54651 + 6.00390i −0.108812 + 0.422433i
\(203\) −0.256980 0.252044i −0.0180364 0.0176900i
\(204\) 0 0
\(205\) −2.79162 + 12.8875i −0.194975 + 0.900104i
\(206\) 7.95528 + 10.6858i 0.554271 + 0.744515i
\(207\) 0 0
\(208\) 27.8864 + 3.25945i 1.93357 + 0.226003i
\(209\) −16.1848 + 3.17859i −1.11953 + 0.219868i
\(210\) 0 0
\(211\) −1.19271 5.50618i −0.0821097 0.379061i 0.917725 0.397215i \(-0.130023\pi\)
−0.999835 + 0.0181545i \(0.994221\pi\)
\(212\) 3.45537 3.95941i 0.237315 0.271933i
\(213\) 0 0
\(214\) 19.0883 + 13.6435i 1.30485 + 0.932651i
\(215\) −13.5535 11.3727i −0.924340 0.775614i
\(216\) 0 0
\(217\) 1.51494 1.27118i 0.102841 0.0862934i
\(218\) −6.71479 + 0.521915i −0.454783 + 0.0353485i
\(219\) 0 0
\(220\) 13.3977 34.7010i 0.903275 2.33954i
\(221\) 2.92792 21.4362i 0.196953 1.44195i
\(222\) 0 0
\(223\) −9.66379 5.33225i −0.647135 0.357074i 0.125345 0.992113i \(-0.459996\pi\)
−0.772480 + 0.635039i \(0.780984\pi\)
\(224\) −0.157128 2.69778i −0.0104985 0.180253i
\(225\) 0 0
\(226\) −3.84323 + 1.93014i −0.255648 + 0.128391i
\(227\) 2.26337 + 4.29690i 0.150225 + 0.285195i 0.948307 0.317353i \(-0.102794\pi\)
−0.798082 + 0.602548i \(0.794152\pi\)
\(228\) 0 0
\(229\) 16.9342 + 7.69754i 1.11904 + 0.508668i 0.885948 0.463785i \(-0.153509\pi\)
0.233097 + 0.972454i \(0.425114\pi\)
\(230\) −2.63951 + 3.84850i −0.174044 + 0.253763i
\(231\) 0 0
\(232\) 0.0976038 + 0.714586i 0.00640800 + 0.0469149i
\(233\) 26.1030 + 6.18653i 1.71007 + 0.405293i 0.965115 0.261826i \(-0.0843245\pi\)
0.744951 + 0.667119i \(0.232473\pi\)
\(234\) 0 0
\(235\) −11.3819 12.0641i −0.742472 0.786974i
\(236\) 3.23462 + 0.505886i 0.210556 + 0.0329304i
\(237\) 0 0
\(238\) −2.50233 + 0.0971020i −0.162202 + 0.00629419i
\(239\) −0.213596 0.128906i −0.0138164 0.00833823i 0.509774 0.860308i \(-0.329729\pi\)
−0.523591 + 0.851970i \(0.675408\pi\)
\(240\) 0 0
\(241\) 21.7431 + 6.05259i 1.40059 + 0.389882i 0.884456 0.466624i \(-0.154530\pi\)
0.516137 + 0.856506i \(0.327369\pi\)
\(242\) −47.9777 −3.08412
\(243\) 0 0
\(244\) −23.5555 −1.50798
\(245\) 25.3686 + 7.06182i 1.62074 + 0.451163i
\(246\) 0 0
\(247\) −14.2302 8.58797i −0.905446 0.546440i
\(248\) −3.95948 + 0.153646i −0.251427 + 0.00975653i
\(249\) 0 0
\(250\) −34.0004 5.31757i −2.15037 0.336312i
\(251\) −15.0656 15.9686i −0.950930 1.00793i −0.999958 0.00912994i \(-0.997094\pi\)
0.0490279 0.998797i \(-0.484388\pi\)
\(252\) 0 0
\(253\) 3.75031 + 0.888839i 0.235780 + 0.0558808i
\(254\) 0.509521 + 3.73035i 0.0319702 + 0.234063i
\(255\) 0 0
\(256\) −11.4919 + 16.7556i −0.718243 + 1.04722i
\(257\) −17.5843 7.99306i −1.09688 0.498593i −0.218152 0.975915i \(-0.570003\pi\)
−0.878729 + 0.477322i \(0.841608\pi\)
\(258\) 0 0
\(259\) −0.908080 1.72395i −0.0564253 0.107121i
\(260\) 33.4966 16.8226i 2.07737 1.04329i
\(261\) 0 0
\(262\) 0.781316 + 13.4147i 0.0482699 + 0.828761i
\(263\) 3.27645 + 1.80787i 0.202034 + 0.111478i 0.580904 0.813972i \(-0.302699\pi\)
−0.378869 + 0.925450i \(0.623687\pi\)
\(264\) 0 0
\(265\) −1.69454 + 12.4062i −0.104095 + 0.762108i
\(266\) −0.692917 + 1.79470i −0.0424855 + 0.110040i
\(267\) 0 0
\(268\) 12.4132 0.964828i 0.758255 0.0589363i
\(269\) 5.26789 4.42029i 0.321189 0.269510i −0.467909 0.883776i \(-0.654993\pi\)
0.789098 + 0.614267i \(0.210548\pi\)
\(270\) 0 0
\(271\) 6.11967 + 5.13501i 0.371744 + 0.311930i 0.809451 0.587188i \(-0.199765\pi\)
−0.437707 + 0.899118i \(0.644209\pi\)
\(272\) 13.4251 + 9.59567i 0.814015 + 0.581823i
\(273\) 0 0
\(274\) 9.94883 11.4001i 0.601031 0.688705i
\(275\) 12.3903 + 57.1998i 0.747160 + 3.44928i
\(276\) 0 0
\(277\) 15.4258 3.02953i 0.926848 0.182027i 0.293558 0.955941i \(-0.405161\pi\)
0.633290 + 0.773914i \(0.281704\pi\)
\(278\) −12.9945 1.51884i −0.779358 0.0910939i
\(279\) 0 0
\(280\) 0.627092 + 0.842331i 0.0374759 + 0.0503389i
\(281\) −3.87954 + 17.9099i −0.231434 + 1.06842i 0.702698 + 0.711489i \(0.251979\pi\)
−0.934132 + 0.356929i \(0.883824\pi\)
\(282\) 0 0
\(283\) 13.3626 + 13.1060i 0.794327 + 0.779070i 0.979028 0.203724i \(-0.0653046\pi\)
−0.184701 + 0.982795i \(0.559132\pi\)
\(284\) −3.45598 + 13.4169i −0.205075 + 0.796149i
\(285\) 0 0
\(286\) −51.3998 46.6428i −3.03933 2.75805i
\(287\) 0.503122 1.16637i 0.0296983 0.0688485i
\(288\) 0 0
\(289\) −2.55819 + 3.43624i −0.150482 + 0.202132i
\(290\) 4.66830 + 5.34928i 0.274132 + 0.314120i
\(291\) 0 0
\(292\) −10.3977 3.33388i −0.608478 0.195101i
\(293\) −30.5279 5.99548i −1.78346 0.350259i −0.811307 0.584621i \(-0.801243\pi\)
−0.972150 + 0.234361i \(0.924700\pi\)
\(294\) 0 0
\(295\) −7.10158 + 3.22806i −0.413470 + 0.187945i
\(296\) −0.677942 + 3.84480i −0.0394046 + 0.223475i
\(297\) 0 0
\(298\) 2.61111 + 14.8083i 0.151258 + 0.857824i
\(299\) 2.19672 + 3.20290i 0.127040 + 0.185229i
\(300\) 0 0
\(301\) 1.07002 + 1.32661i 0.0616747 + 0.0764647i
\(302\) −23.4548 + 9.58235i −1.34967 + 0.551402i
\(303\) 0 0
\(304\) 10.8538 6.55031i 0.622509 0.375686i
\(305\) 46.8922 30.8415i 2.68504 1.76598i
\(306\) 0 0
\(307\) −0.356622 + 6.12296i −0.0203535 + 0.349456i 0.972722 + 0.231975i \(0.0745188\pi\)
−0.993075 + 0.117481i \(0.962518\pi\)
\(308\) −1.91061 + 3.03139i −0.108867 + 0.172729i
\(309\) 0 0
\(310\) −31.7344 + 22.6824i −1.80239 + 1.28827i
\(311\) −3.49696 0.271805i −0.198294 0.0154127i −0.0220390 0.999757i \(-0.507016\pi\)
−0.176256 + 0.984344i \(0.556399\pi\)
\(312\) 0 0
\(313\) −8.88875 3.63145i −0.502422 0.205262i 0.112797 0.993618i \(-0.464019\pi\)
−0.615219 + 0.788356i \(0.710932\pi\)
\(314\) 0.602505 + 2.01251i 0.0340013 + 0.113572i
\(315\) 0 0
\(316\) 5.62827 1.33392i 0.316615 0.0750391i
\(317\) −11.5915 30.0227i −0.651042 1.68624i −0.724796 0.688964i \(-0.758066\pi\)
0.0737538 0.997276i \(-0.476502\pi\)
\(318\) 0 0
\(319\) 2.73275 5.18800i 0.153005 0.290472i
\(320\) −0.345022 + 17.7893i −0.0192873 + 0.994450i
\(321\) 0 0
\(322\) 0.320943 0.314778i 0.0178854 0.0175419i
\(323\) −4.88444 8.46010i −0.271778 0.470733i
\(324\) 0 0
\(325\) −29.4882 + 51.0751i −1.63571 + 2.83314i
\(326\) 1.59890 + 6.20732i 0.0885550 + 0.343792i
\(327\) 0 0
\(328\) −2.22844 + 1.22960i −0.123045 + 0.0678933i
\(329\) 0.851911 + 1.35165i 0.0469674 + 0.0745188i
\(330\) 0 0
\(331\) −6.84266 + 8.48356i −0.376106 + 0.466299i −0.930679 0.365836i \(-0.880783\pi\)
0.554573 + 0.832135i \(0.312882\pi\)
\(332\) −7.02522 + 23.4659i −0.385559 + 1.28786i
\(333\) 0 0
\(334\) 17.1714 18.2006i 0.939575 0.995891i
\(335\) −23.4478 + 18.1734i −1.28109 + 0.992921i
\(336\) 0 0
\(337\) −5.54930 11.6054i −0.302290 0.632186i 0.693835 0.720134i \(-0.255920\pi\)
−0.996125 + 0.0879482i \(0.971969\pi\)
\(338\) −4.37982 45.0285i −0.238231 2.44923i
\(339\) 0 0
\(340\) 22.0144 + 0.854259i 1.19390 + 0.0463287i
\(341\) 26.9160 + 17.7029i 1.45758 + 0.958668i
\(342\) 0 0
\(343\) −4.57884 2.29958i −0.247234 0.124166i
\(344\) −0.0662206 3.41432i −0.00357038 0.184088i
\(345\) 0 0
\(346\) −19.2961 14.9556i −1.03736 0.804017i
\(347\) 1.13303 0.177203i 0.0608245 0.00951277i −0.124033 0.992278i \(-0.539583\pi\)
0.184858 + 0.982765i \(0.440818\pi\)
\(348\) 0 0
\(349\) 10.1008 21.1241i 0.540685 1.13075i −0.432693 0.901541i \(-0.642437\pi\)
0.973378 0.229206i \(-0.0736128\pi\)
\(350\) 6.41469 + 2.33476i 0.342880 + 0.124798i
\(351\) 0 0
\(352\) 41.3674 15.0565i 2.20489 0.802513i
\(353\) −1.54022 + 15.8349i −0.0819777 + 0.842805i 0.860703 + 0.509108i \(0.170025\pi\)
−0.942680 + 0.333697i \(0.891704\pi\)
\(354\) 0 0
\(355\) −10.6871 31.2343i −0.567213 1.65774i
\(356\) −6.41874 + 5.82469i −0.340192 + 0.308708i
\(357\) 0 0
\(358\) −1.43679 + 4.19919i −0.0759369 + 0.221934i
\(359\) −9.23621 21.4119i −0.487468 1.13008i −0.967510 0.252833i \(-0.918638\pi\)
0.480042 0.877246i \(-0.340622\pi\)
\(360\) 0 0
\(361\) 11.4175 1.33451i 0.600921 0.0702376i
\(362\) −29.2670 + 9.38407i −1.53824 + 0.493216i
\(363\) 0 0
\(364\) −3.47855 + 0.968321i −0.182326 + 0.0507538i
\(365\) 25.0639 6.97701i 1.31190 0.365194i
\(366\) 0 0
\(367\) 30.9294 9.91710i 1.61450 0.517668i 0.645297 0.763932i \(-0.276734\pi\)
0.969203 + 0.246264i \(0.0792029\pi\)
\(368\) −2.94229 + 0.343904i −0.153377 + 0.0179272i
\(369\) 0 0
\(370\) 15.2225 + 35.2897i 0.791379 + 1.83462i
\(371\) 0.390486 1.14124i 0.0202730 0.0592501i
\(372\) 0 0
\(373\) 13.2643 12.0367i 0.686798 0.623236i −0.251991 0.967730i \(-0.581085\pi\)
0.938789 + 0.344494i \(0.111949\pi\)
\(374\) −13.2066 38.5977i −0.682896 1.99584i
\(375\) 0 0
\(376\) 0.309920 3.18626i 0.0159829 0.164319i
\(377\) 5.55248 2.02094i 0.285967 0.104084i
\(378\) 0 0
\(379\) −30.2298 11.0028i −1.55280 0.565173i −0.583728 0.811949i \(-0.698407\pi\)
−0.969073 + 0.246776i \(0.920629\pi\)
\(380\) 7.30116 15.2691i 0.374542 0.783288i
\(381\) 0 0
\(382\) −8.68429 + 1.35820i −0.444327 + 0.0694914i
\(383\) −11.3891 8.82722i −0.581956 0.451050i 0.278599 0.960408i \(-0.410130\pi\)
−0.860555 + 0.509357i \(0.829883\pi\)
\(384\) 0 0
\(385\) −0.165560 8.53622i −0.00843770 0.435046i
\(386\) 28.1931 + 14.1591i 1.43499 + 0.720679i
\(387\) 0 0
\(388\) 17.0363 + 11.2050i 0.864887 + 0.568845i
\(389\) 18.1288 + 0.703479i 0.919166 + 0.0356678i 0.494014 0.869454i \(-0.335529\pi\)
0.425152 + 0.905122i \(0.360221\pi\)
\(390\) 0 0
\(391\) 0.220992 + 2.27200i 0.0111761 + 0.114900i
\(392\) 2.19259 + 4.58541i 0.110742 + 0.231598i
\(393\) 0 0
\(394\) 1.11861 0.866987i 0.0563547 0.0436782i
\(395\) −9.45776 + 10.0246i −0.475871 + 0.504394i
\(396\) 0 0
\(397\) −2.42279 + 8.09268i −0.121596 + 0.406160i −0.997015 0.0772050i \(-0.975400\pi\)
0.875419 + 0.483365i \(0.160586\pi\)
\(398\) 10.9029 13.5174i 0.546511 0.677567i
\(399\) 0 0
\(400\) −23.9852 38.0551i −1.19926 1.90275i
\(401\) −8.98803 + 4.95939i −0.448841 + 0.247660i −0.691394 0.722478i \(-0.743003\pi\)
0.242553 + 0.970138i \(0.422015\pi\)
\(402\) 0 0
\(403\) 8.09778 + 31.4375i 0.403379 + 1.56601i
\(404\) −2.62711 + 4.55029i −0.130704 + 0.226385i
\(405\) 0 0
\(406\) −0.341966 0.592302i −0.0169715 0.0293954i
\(407\) 22.6612 22.2260i 1.12327 1.10170i
\(408\) 0 0
\(409\) −0.0370489 + 1.91023i −0.00183195 + 0.0944548i 0.997780 + 0.0665971i \(0.0212142\pi\)
−0.999612 + 0.0278577i \(0.991131\pi\)
\(410\) −11.6768 + 22.1678i −0.576674 + 1.09479i
\(411\) 0 0
\(412\) 4.06638 + 10.5322i 0.200336 + 0.518884i
\(413\) 0.731201 0.173298i 0.0359801 0.00852743i
\(414\) 0 0
\(415\) −16.7390 55.9121i −0.821685 2.74462i
\(416\) 41.0658 + 16.7772i 2.01342 + 0.822572i
\(417\) 0 0
\(418\) −31.2454 2.42859i −1.52826 0.118786i
\(419\) −14.3029 + 10.2231i −0.698743 + 0.499431i −0.874514 0.485000i \(-0.838820\pi\)
0.175772 + 0.984431i \(0.443758\pi\)
\(420\) 0 0
\(421\) −17.4518 + 27.6892i −0.850549 + 1.34949i 0.0850324 + 0.996378i \(0.472901\pi\)
−0.935582 + 0.353110i \(0.885124\pi\)
\(422\) 0.622425 10.6866i 0.0302992 0.520217i
\(423\) 0 0
\(424\) −2.01921 + 1.32806i −0.0980616 + 0.0644961i
\(425\) −29.6776 + 17.9105i −1.43958 + 0.868789i
\(426\) 0 0
\(427\) −5.00502 + 2.04478i −0.242210 + 0.0989537i
\(428\) 12.4835 + 15.4771i 0.603414 + 0.748116i
\(429\) 0 0
\(430\) −19.0143 27.7235i −0.916952 1.33695i
\(431\) −4.66966 26.4829i −0.224929 1.27564i −0.862820 0.505511i \(-0.831304\pi\)
0.637890 0.770127i \(-0.279807\pi\)
\(432\) 0 0
\(433\) −3.62220 + 20.5425i −0.174072 + 0.987210i 0.765138 + 0.643866i \(0.222671\pi\)
−0.939210 + 0.343344i \(0.888440\pi\)
\(434\) 3.42077 1.55493i 0.164202 0.0746390i
\(435\) 0 0
\(436\) −5.60077 1.09996i −0.268228 0.0526783i
\(437\) 1.66992 + 0.535438i 0.0798830 + 0.0256135i
\(438\) 0 0
\(439\) 3.52039 + 4.03392i 0.168019 + 0.192529i 0.831270 0.555868i \(-0.187614\pi\)
−0.663251 + 0.748397i \(0.730824\pi\)
\(440\) −10.2155 + 13.7219i −0.487007 + 0.654164i
\(441\) 0 0
\(442\) 16.2822 37.7463i 0.774464 1.79541i
\(443\) 17.5904 + 15.9625i 0.835747 + 0.758400i 0.972672 0.232182i \(-0.0745864\pi\)
−0.136926 + 0.990581i \(0.543722\pi\)
\(444\) 0 0
\(445\) 5.15153 19.9994i 0.244206 0.948065i
\(446\) −14.9722 14.6847i −0.708956 0.695339i
\(447\) 0 0
\(448\) 0.362854 1.67512i 0.0171432 0.0791420i
\(449\) −1.53418 2.06077i −0.0724027 0.0972536i 0.764447 0.644687i \(-0.223012\pi\)
−0.836849 + 0.547433i \(0.815605\pi\)
\(450\) 0 0
\(451\) 20.5530 + 2.40230i 0.967801 + 0.113120i
\(452\) −3.57639 + 0.702380i −0.168219 + 0.0330372i
\(453\) 0 0
\(454\) 1.95356 + 9.01864i 0.0916851 + 0.423266i
\(455\) 5.65697 6.48217i 0.265203 0.303889i
\(456\) 0 0
\(457\) 19.4136 + 13.8760i 0.908131 + 0.649093i 0.936562 0.350503i \(-0.113989\pi\)
−0.0284307 + 0.999596i \(0.509051\pi\)
\(458\) 27.0753 + 22.7189i 1.26515 + 1.06158i
\(459\) 0 0
\(460\) −3.02962 + 2.54215i −0.141257 + 0.118528i
\(461\) −21.5717 + 1.67669i −1.00469 + 0.0780911i −0.569284 0.822141i \(-0.692780\pi\)
−0.435411 + 0.900232i \(0.643397\pi\)
\(462\) 0 0
\(463\) −11.6715 + 30.2300i −0.542422 + 1.40491i 0.342654 + 0.939462i \(0.388674\pi\)
−0.885076 + 0.465446i \(0.845894\pi\)
\(464\) −0.609916 + 4.46538i −0.0283146 + 0.207300i
\(465\) 0 0
\(466\) 44.6285 + 24.6249i 2.06737 + 1.14073i
\(467\) 1.76572 + 30.3163i 0.0817079 + 1.40287i 0.751211 + 0.660062i \(0.229470\pi\)
−0.669503 + 0.742809i \(0.733493\pi\)
\(468\) 0 0
\(469\) 2.55377 1.28255i 0.117922 0.0592228i
\(470\) −14.6870 27.8825i −0.677459 1.28612i
\(471\) 0 0
\(472\) −1.37070 0.623061i −0.0630917 0.0286787i
\(473\) −15.7038 + 22.8968i −0.722063 + 1.05279i
\(474\) 0 0
\(475\) 3.60380 + 26.3845i 0.165354 + 1.21060i
\(476\) −2.06505 0.489425i −0.0946513 0.0224328i
\(477\) 0 0
\(478\) −0.325297 0.344795i −0.0148788 0.0157706i
\(479\) 21.1768 + 3.31199i 0.967594 + 0.151329i 0.618522 0.785767i \(-0.287732\pi\)
0.349071 + 0.937096i \(0.386497\pi\)
\(480\) 0 0
\(481\) 31.9616 1.24025i 1.45732 0.0565507i
\(482\) 36.7159 + 22.1582i 1.67236 + 1.00928i
\(483\) 0 0
\(484\) −39.1704 10.9038i −1.78047 0.495628i
\(485\) −48.5852 −2.20614
\(486\) 0 0
\(487\) −36.3883 −1.64891 −0.824456 0.565926i \(-0.808519\pi\)
−0.824456 + 0.565926i \(0.808519\pi\)
\(488\) 10.4362 + 2.90512i 0.472425 + 0.131509i
\(489\) 0 0
\(490\) 42.8380 + 25.8529i 1.93523 + 1.16791i
\(491\) −17.5231 + 0.679976i −0.790806 + 0.0306869i −0.431014 0.902345i \(-0.641844\pi\)
−0.359793 + 0.933032i \(0.617153\pi\)
\(492\) 0 0
\(493\) 3.43120 + 0.536629i 0.154533 + 0.0241686i
\(494\) −21.6720 22.9710i −0.975069 1.03351i
\(495\) 0 0
\(496\) −24.0936 5.71028i −1.08183 0.256399i
\(497\) 0.430362 + 3.15081i 0.0193044 + 0.141333i
\(498\) 0 0
\(499\) 11.8935 17.3412i 0.532428 0.776300i −0.461404 0.887190i \(-0.652654\pi\)
0.993833 + 0.110890i \(0.0353703\pi\)
\(500\) −26.5504 12.0687i −1.18737 0.539726i
\(501\) 0 0
\(502\) −19.4403 36.9066i −0.867665 1.64722i
\(503\) 16.7170 8.39558i 0.745373 0.374340i −0.0352203 0.999380i \(-0.511213\pi\)
0.780593 + 0.625039i \(0.214917\pi\)
\(504\) 0 0
\(505\) −0.727929 12.4980i −0.0323924 0.556156i
\(506\) 6.41191 + 3.53794i 0.285044 + 0.157281i
\(507\) 0 0
\(508\) −0.431805 + 3.16137i −0.0191582 + 0.140263i
\(509\) 2.47878 6.42019i 0.109870 0.284570i −0.867034 0.498249i \(-0.833977\pi\)
0.976904 + 0.213679i \(0.0685446\pi\)
\(510\) 0 0
\(511\) −2.49868 + 0.194213i −0.110535 + 0.00859147i
\(512\) −20.6690 + 17.3433i −0.913447 + 0.766473i
\(513\) 0 0
\(514\) −28.1147 23.5911i −1.24009 1.04056i
\(515\) −21.8849 15.6424i −0.964366 0.689287i
\(516\) 0 0
\(517\) −17.1136 + 19.6100i −0.752654 + 0.862446i
\(518\) −0.783782 3.61834i −0.0344374 0.158981i
\(519\) 0 0
\(520\) −16.9154 + 3.32207i −0.741787 + 0.145682i
\(521\) −20.5766 2.40506i −0.901478 0.105368i −0.347289 0.937758i \(-0.612898\pi\)
−0.554189 + 0.832391i \(0.686972\pi\)
\(522\) 0 0
\(523\) 14.0428 + 18.8627i 0.614047 + 0.824808i 0.995009 0.0997827i \(-0.0318148\pi\)
−0.380963 + 0.924590i \(0.624407\pi\)
\(524\) −2.41085 + 11.1297i −0.105318 + 0.486204i
\(525\) 0 0
\(526\) 5.07624 + 4.97874i 0.221335 + 0.217084i
\(527\) −4.75946 + 18.4774i −0.207325 + 0.804887i
\(528\) 0 0
\(529\) 16.7291 + 15.1808i 0.727350 + 0.660035i
\(530\) −9.42333 + 21.8457i −0.409323 + 0.948919i
\(531\) 0 0
\(532\) −0.973597 + 1.30777i −0.0422108 + 0.0566989i
\(533\) 13.7106 + 15.7107i 0.593874 + 0.680504i
\(534\) 0 0
\(535\) −45.1156 14.4657i −1.95052 0.625408i
\(536\) −5.61863 1.10346i −0.242688 0.0476623i
\(537\) 0 0
\(538\) 11.8950 5.40696i 0.512832 0.233111i
\(539\) 7.17574 40.6956i 0.309081 1.75289i
\(540\) 0 0
\(541\) 2.43507 + 13.8100i 0.104692 + 0.593737i 0.991343 + 0.131298i \(0.0419145\pi\)
−0.886651 + 0.462439i \(0.846974\pi\)
\(542\) 8.58534 + 12.5177i 0.368772 + 0.537683i
\(543\) 0 0
\(544\) 16.3690 + 20.2943i 0.701813 + 0.870112i
\(545\) 12.5897 5.14347i 0.539285 0.220322i
\(546\) 0 0
\(547\) 17.0527 10.2913i 0.729120 0.440026i −0.102957 0.994686i \(-0.532831\pi\)
0.832077 + 0.554660i \(0.187152\pi\)
\(548\) 10.7134 7.04631i 0.457654 0.301004i
\(549\) 0 0
\(550\) −6.46594 + 111.016i −0.275708 + 4.73373i
\(551\) 1.42259 2.25709i 0.0606043 0.0961553i
\(552\) 0 0
\(553\) 1.08009 0.772002i 0.0459301 0.0328289i
\(554\) 29.7802 + 2.31470i 1.26524 + 0.0983421i
\(555\) 0 0
\(556\) −10.2639 4.19327i −0.435287 0.177834i
\(557\) −2.59529 8.66887i −0.109966 0.367312i 0.885237 0.465139i \(-0.153996\pi\)
−0.995203 + 0.0978276i \(0.968811\pi\)
\(558\) 0 0
\(559\) −27.2239 + 6.45219i −1.15145 + 0.272899i
\(560\) 2.36353 + 6.12171i 0.0998775 + 0.258689i
\(561\) 0 0
\(562\) −16.2273 + 30.8068i −0.684508 + 1.29951i
\(563\) 0.395559 20.3949i 0.0166708 0.859544i −0.894394 0.447280i \(-0.852393\pi\)
0.911065 0.412263i \(-0.135262\pi\)
\(564\) 0 0
\(565\) 6.19994 6.08086i 0.260833 0.255824i
\(566\) 17.7818 + 30.7990i 0.747425 + 1.29458i
\(567\) 0 0
\(568\) 3.18589 5.51813i 0.133677 0.231535i
\(569\) −0.319945 1.24210i −0.0134128 0.0520717i 0.961334 0.275387i \(-0.0888059\pi\)
−0.974746 + 0.223315i \(0.928312\pi\)
\(570\) 0 0
\(571\) −27.2113 + 15.0146i −1.13876 + 0.628340i −0.936387 0.350969i \(-0.885852\pi\)
−0.202371 + 0.979309i \(0.564865\pi\)
\(572\) −31.3638 49.7621i −1.31139 2.08066i
\(573\) 0 0
\(574\) 1.51527 1.87864i 0.0632460 0.0784127i
\(575\) 1.78466 5.96117i 0.0744254 0.248598i
\(576\) 0 0
\(577\) 10.5171 11.1474i 0.437831 0.464074i −0.470455 0.882424i \(-0.655910\pi\)
0.908286 + 0.418350i \(0.137392\pi\)
\(578\) −6.43360 + 4.98642i −0.267603 + 0.207408i
\(579\) 0 0
\(580\) 2.59561 + 5.42827i 0.107777 + 0.225397i
\(581\) 0.544293 + 5.59582i 0.0225811 + 0.232154i
\(582\) 0 0
\(583\) 19.6345 + 0.761909i 0.813179 + 0.0315550i
\(584\) 4.19550 + 2.75942i 0.173611 + 0.114186i
\(585\) 0 0
\(586\) −52.8253 26.5299i −2.18219 1.09594i
\(587\) −0.674639 34.7842i −0.0278453 1.43570i −0.709852 0.704351i \(-0.751238\pi\)
0.682007 0.731346i \(-0.261108\pi\)
\(588\) 0 0
\(589\) 11.5858 + 8.97965i 0.477383 + 0.370000i
\(590\) −14.6441 + 2.29029i −0.602887 + 0.0942898i
\(591\) 0 0
\(592\) −10.5243 + 22.0096i −0.432545 + 0.904590i
\(593\) 17.5078 + 6.37231i 0.718958 + 0.261679i 0.675483 0.737375i \(-0.263935\pi\)
0.0434745 + 0.999055i \(0.486157\pi\)
\(594\) 0 0
\(595\) 4.75173 1.72949i 0.194802 0.0709022i
\(596\) −1.23369 + 12.6834i −0.0505337 + 0.519532i
\(597\) 0 0
\(598\) 2.38901 + 6.98214i 0.0976939 + 0.285521i
\(599\) −8.29494 + 7.52726i −0.338922 + 0.307555i −0.823638 0.567116i \(-0.808059\pi\)
0.484716 + 0.874672i \(0.338923\pi\)
\(600\) 0 0
\(601\) 2.16061 6.31463i 0.0881332 0.257579i −0.893275 0.449510i \(-0.851599\pi\)
0.981408 + 0.191931i \(0.0614751\pi\)
\(602\) 1.28266 + 2.97354i 0.0522774 + 0.121193i
\(603\) 0 0
\(604\) −21.3270 + 2.49277i −0.867783 + 0.101429i
\(605\) 92.2536 29.5799i 3.75064 1.20260i
\(606\) 0 0
\(607\) −42.6705 + 11.8781i −1.73194 + 0.482119i −0.983473 0.181052i \(-0.942050\pi\)
−0.748468 + 0.663171i \(0.769210\pi\)
\(608\) 19.2964 5.37153i 0.782574 0.217844i
\(609\) 0 0
\(610\) 101.550 32.5607i 4.11164 1.31834i
\(611\) −26.0502 + 3.04483i −1.05388 + 0.123181i
\(612\) 0 0
\(613\) 8.39707 + 19.4666i 0.339154 + 0.786248i 0.999381 + 0.0351816i \(0.0112010\pi\)
−0.660227 + 0.751066i \(0.729540\pi\)
\(614\) −3.77272 + 11.0262i −0.152254 + 0.444980i
\(615\) 0 0
\(616\) 1.22036 1.10741i 0.0491695 0.0446190i
\(617\) −3.75263 10.9675i −0.151075 0.441534i 0.844494 0.535565i \(-0.179901\pi\)
−0.995569 + 0.0940307i \(0.970025\pi\)
\(618\) 0 0
\(619\) −1.10297 + 11.3395i −0.0443321 + 0.455773i 0.946697 + 0.322126i \(0.104397\pi\)
−0.991029 + 0.133648i \(0.957331\pi\)
\(620\) −31.0639 + 11.3063i −1.24756 + 0.454074i
\(621\) 0 0
\(622\) −6.26258 2.27939i −0.251107 0.0913953i
\(623\) −0.858218 + 1.79481i −0.0343838 + 0.0719075i
\(624\) 0 0
\(625\) 20.6366 3.22751i 0.825464 0.129100i
\(626\) −14.4202 11.1765i −0.576346 0.446702i
\(627\) 0 0
\(628\) 0.0345231 + 1.78000i 0.00137762 + 0.0710297i
\(629\) 16.7999 + 8.43722i 0.669855 + 0.336414i
\(630\) 0 0
\(631\) 14.2115 + 9.34704i 0.565750 + 0.372100i 0.799930 0.600094i \(-0.204870\pi\)
−0.234180 + 0.972193i \(0.575240\pi\)
\(632\) −2.65811 0.103147i −0.105734 0.00410296i
\(633\) 0 0
\(634\) −5.91990 60.8619i −0.235109 2.41714i
\(635\) −3.27963 6.85876i −0.130148 0.272181i
\(636\) 0 0
\(637\) 32.9129 25.5094i 1.30406 1.01072i
\(638\) 7.64574 8.10402i 0.302698 0.320841i
\(639\) 0 0
\(640\) 6.39533 21.3619i 0.252798 0.844403i
\(641\) −17.0709 + 21.1646i −0.674259 + 0.835950i −0.993749 0.111640i \(-0.964390\pi\)
0.319490 + 0.947590i \(0.396489\pi\)
\(642\) 0 0
\(643\) −2.49816 3.96360i −0.0985177 0.156309i 0.793110 0.609079i \(-0.208461\pi\)
−0.891627 + 0.452770i \(0.850436\pi\)
\(644\) 0.333567 0.184054i 0.0131444 0.00725275i
\(645\) 0 0
\(646\) −4.63001 17.9748i −0.182165 0.707209i
\(647\) −6.72265 + 11.6440i −0.264295 + 0.457772i −0.967379 0.253335i \(-0.918472\pi\)
0.703084 + 0.711107i \(0.251806\pi\)
\(648\) 0 0
\(649\) 6.12075 + 10.6014i 0.240260 + 0.416143i
\(650\) −80.0024 + 78.4658i −3.13795 + 3.07768i
\(651\) 0 0
\(652\) −0.105338 + 5.43122i −0.00412537 + 0.212703i
\(653\) 9.82656 18.6553i 0.384543 0.730037i −0.613684 0.789551i \(-0.710313\pi\)
0.998227 + 0.0595146i \(0.0189553\pi\)
\(654\) 0 0
\(655\) −9.77297 25.3126i −0.381862 0.989047i
\(656\) −15.4757 + 3.66782i −0.604226 + 0.143204i
\(657\) 0 0
\(658\) 0.870669 + 2.90824i 0.0339422 + 0.113375i
\(659\) 39.0595 + 15.9576i 1.52154 + 0.621619i 0.976254 0.216629i \(-0.0695063\pi\)
0.545289 + 0.838248i \(0.316420\pi\)
\(660\) 0 0
\(661\) 19.1195 + 1.48609i 0.743663 + 0.0578021i 0.443733 0.896159i \(-0.353654\pi\)
0.299930 + 0.953961i \(0.403037\pi\)
\(662\) −16.8480 + 12.0422i −0.654817 + 0.468035i
\(663\) 0 0
\(664\) 6.00658 9.53009i 0.233101 0.369839i
\(665\) 0.225876 3.87814i 0.00875909 0.150388i
\(666\) 0 0
\(667\) −0.520875 + 0.342585i −0.0201684 + 0.0132649i
\(668\) 18.1556 10.9570i 0.702462 0.423938i
\(669\) 0 0
\(670\) −52.1807 + 21.3182i −2.01592 + 0.823593i
\(671\) −55.2948 68.5548i −2.13463 2.64653i
\(672\) 0 0
\(673\) −9.05960 13.2092i −0.349222 0.509178i 0.609783 0.792569i \(-0.291257\pi\)
−0.959005 + 0.283391i \(0.908541\pi\)
\(674\) −4.24435 24.0709i −0.163486 0.927177i
\(675\) 0 0
\(676\) 6.65775 37.7580i 0.256067 1.45223i
\(677\) 34.1612 15.5282i 1.31292 0.596796i 0.369759 0.929128i \(-0.379440\pi\)
0.943163 + 0.332332i \(0.107835\pi\)
\(678\) 0 0
\(679\) 4.59251 + 0.901939i 0.176244 + 0.0346133i
\(680\) −9.64809 3.09354i −0.369987 0.118632i
\(681\) 0 0
\(682\) 40.2485 + 46.1196i 1.54119 + 1.76601i
\(683\) 1.91713 2.57516i 0.0733571 0.0985357i −0.763930 0.645299i \(-0.776733\pi\)
0.837287 + 0.546763i \(0.184140\pi\)
\(684\) 0 0
\(685\) −12.1015 + 28.0544i −0.462374 + 1.07190i
\(686\) −7.20968 6.54244i −0.275267 0.249791i
\(687\) 0 0
\(688\) 5.32301 20.6652i 0.202938 0.787853i
\(689\) 14.1361 + 13.8646i 0.538543 + 0.528199i
\(690\) 0 0
\(691\) 8.13012 37.5328i 0.309284 1.42782i −0.512828 0.858491i \(-0.671402\pi\)
0.822113 0.569325i \(-0.192795\pi\)
\(692\) −12.3549 16.5956i −0.469664 0.630869i
\(693\) 0 0
\(694\) 2.16428 + 0.252968i 0.0821548 + 0.00960252i
\(695\) 25.9228 5.09108i 0.983309 0.193116i
\(696\) 0 0
\(697\) 2.59459 + 11.9780i 0.0982772 + 0.453698i
\(698\) 29.2529 33.5202i 1.10724 1.26876i
\(699\) 0 0
\(700\) 4.70653 + 3.36402i 0.177890 + 0.127148i
\(701\) 14.6668 + 12.3069i 0.553959 + 0.464826i 0.876279 0.481804i \(-0.160018\pi\)
−0.322320 + 0.946631i \(0.604463\pi\)
\(702\) 0 0
\(703\) 11.0635 9.28339i 0.417268 0.350130i
\(704\) 27.8372 2.16368i 1.04915 0.0815467i
\(705\) 0 0
\(706\) −10.8879 + 28.2004i −0.409772 + 1.06134i
\(707\) −0.163207 + 1.19489i −0.00613804 + 0.0449384i
\(708\) 0 0
\(709\) 10.3188 + 5.69366i 0.387530 + 0.213830i 0.664899 0.746933i \(-0.268475\pi\)
−0.277369 + 0.960764i \(0.589462\pi\)
\(710\) −3.64714 62.6190i −0.136875 2.35005i
\(711\) 0 0
\(712\) 3.56218 1.78899i 0.133498 0.0670453i
\(713\) −1.59631 3.03051i −0.0597822 0.113494i
\(714\) 0 0
\(715\) 127.591 + 57.9971i 4.77162 + 2.16897i
\(716\) −2.12738 + 3.10180i −0.0795041 + 0.115920i
\(717\) 0 0
\(718\) −5.99623 43.9001i −0.223777 1.63834i
\(719\) −28.3270 6.71361i −1.05642 0.250375i −0.334529 0.942385i \(-0.608577\pi\)
−0.721888 + 0.692010i \(0.756725\pi\)
\(720\) 0 0
\(721\) 1.77828 + 1.88487i 0.0662267 + 0.0701962i
\(722\) 21.5794 + 3.37495i 0.803101 + 0.125603i
\(723\) 0 0
\(724\) −26.0271 + 1.00997i −0.967290 + 0.0375353i
\(725\) −8.10531 4.89158i −0.301024 0.181669i
\(726\) 0 0
\(727\) 10.0026 + 2.78442i 0.370976 + 0.103268i 0.448643 0.893711i \(-0.351908\pi\)
−0.0776667 + 0.996979i \(0.524747\pi\)
\(728\) 1.66059 0.0615456
\(729\) 0 0
\(730\) 49.4338 1.82963
\(731\) −15.8418 4.40986i −0.585929 0.163105i
\(732\) 0 0
\(733\) 21.5112 + 12.9821i 0.794535 + 0.479504i 0.854976 0.518668i \(-0.173572\pi\)
−0.0604413 + 0.998172i \(0.519251\pi\)
\(734\) 61.6684 2.39302i 2.27622 0.0883279i
\(735\) 0 0
\(736\) −4.62428 0.723224i −0.170453 0.0266584i
\(737\) 31.9471 + 33.8619i 1.17679 + 1.24732i
\(738\) 0 0
\(739\) 48.0758 + 11.3942i 1.76850 + 0.419141i 0.980497 0.196534i \(-0.0629687\pi\)
0.788000 + 0.615676i \(0.211117\pi\)
\(740\) 4.40784 + 32.2711i 0.162036 + 1.18631i
\(741\) 0 0
\(742\) 1.29628 1.89003i 0.0475881 0.0693851i
\(743\) 18.2957 + 8.31643i 0.671205 + 0.305100i 0.720268 0.693696i \(-0.244019\pi\)
−0.0490633 + 0.998796i \(0.515624\pi\)
\(744\) 0 0
\(745\) −14.1506 26.8643i −0.518439 0.984232i
\(746\) 30.4131 15.2740i 1.11350 0.559222i
\(747\) 0 0
\(748\) −2.01020 34.5138i −0.0735001 1.26195i
\(749\) 3.99600 + 2.20490i 0.146011 + 0.0805653i
\(750\) 0 0
\(751\) 6.60673 48.3698i 0.241083 1.76504i −0.329841 0.944036i \(-0.606995\pi\)
0.570924 0.821003i \(-0.306585\pi\)
\(752\) 7.20519 18.6619i 0.262746 0.680530i
\(753\) 0 0
\(754\) 11.1934 0.870020i 0.407639 0.0316842i
\(755\) 39.1921 32.8861i 1.42635 1.19685i
\(756\) 0 0
\(757\) 13.1017 + 10.9936i 0.476189 + 0.399570i 0.849046 0.528319i \(-0.177177\pi\)
−0.372857 + 0.927889i \(0.621622\pi\)
\(758\) −49.7283 35.5437i −1.80621 1.29100i
\(759\) 0 0
\(760\) −5.11792 + 5.86448i −0.185646 + 0.212727i
\(761\) 7.60910 + 35.1275i 0.275830 + 1.27337i 0.879408 + 0.476068i \(0.157938\pi\)
−0.603579 + 0.797303i \(0.706259\pi\)
\(762\) 0 0
\(763\) −1.28552 + 0.252469i −0.0465391 + 0.00913998i
\(764\) −7.39879 0.864794i −0.267679 0.0312872i
\(765\) 0 0
\(766\) −16.3495 21.9612i −0.590733 0.793491i
\(767\) −2.61150 + 12.0560i −0.0942958 + 0.435318i
\(768\) 0 0
\(769\) −17.6078 17.2696i −0.634953 0.622758i 0.309698 0.950835i \(-0.399772\pi\)
−0.944651 + 0.328078i \(0.893599\pi\)
\(770\) 4.04654 15.7096i 0.145827 0.566136i
\(771\) 0 0
\(772\) 19.7997 + 17.9673i 0.712608 + 0.646657i
\(773\) 18.6705 43.2831i 0.671531 1.55678i −0.151294 0.988489i \(-0.548344\pi\)
0.822825 0.568295i \(-0.192397\pi\)
\(774\) 0 0
\(775\) 31.0597 41.7204i 1.11570 1.49864i
\(776\) −6.16599 7.06544i −0.221346 0.253635i
\(777\) 0 0
\(778\) 32.8257 + 10.5251i 1.17686 + 0.377345i
\(779\) 9.23878 + 1.81444i 0.331013 + 0.0650089i
\(780\) 0 0
\(781\) −47.1608 + 21.4372i −1.68755 + 0.767083i
\(782\) −0.753168 + 4.27143i −0.0269332 + 0.152746i
\(783\) 0 0
\(784\) 5.51524 + 31.2785i 0.196973 + 1.11709i
\(785\) −2.39931 3.49827i −0.0856349 0.124859i
\(786\) 0 0
\(787\) −17.5571