Properties

Label 108.3.d.d.55.2
Level 108
Weight 3
Character 108.55
Analytic conductor 2.943
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.207360000.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.2
Root \(0.437016 + 0.756934i\) of \(x^{8} + 6 x^{6} + 32 x^{4} + 24 x^{2} + 16\)
Character \(\chi\) \(=\) 108.55
Dual form 108.3.d.d.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} -1.08036 q^{5} -6.01392i q^{7} +(-3.16228 + 7.34847i) q^{8} +O(q^{10})\) \(q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} -1.08036 q^{5} -6.01392i q^{7} +(-3.16228 + 7.34847i) q^{8} +(2.00000 - 0.817763i) q^{10} -17.7247i q^{11} +12.4164 q^{13} +(4.55214 + 11.1331i) q^{14} +(0.291796 - 15.9973i) q^{16} +26.3786 q^{17} -5.19615i q^{19} +(-3.08347 + 3.02774i) q^{20} +(13.4164 + 32.8124i) q^{22} -29.8356i q^{23} -23.8328 q^{25} +(-22.9856 + 9.39840i) q^{26} +(-16.8541 - 17.1643i) q^{28} -4.32145 q^{29} +44.8403i q^{31} +(11.5687 + 29.8356i) q^{32} +(-48.8328 + 19.9668i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(3.93314 + 9.61927i) q^{38} +(3.41641 - 7.93901i) q^{40} -59.2393 q^{41} -19.1491i q^{43} +(-49.6737 - 50.5880i) q^{44} +(22.5836 + 55.2326i) q^{46} +41.0631i q^{47} +12.8328 q^{49} +(44.1200 - 18.0399i) q^{50} +(35.4377 - 34.7972i) q^{52} +70.0430 q^{53} +19.1491i q^{55} +(44.1931 + 19.0177i) q^{56} +(8.00000 - 3.27105i) q^{58} +28.9521i q^{59} +18.4164 q^{61} +(-33.9411 - 83.0096i) q^{62} +(-44.0000 - 46.4758i) q^{64} -13.4142 q^{65} -94.8767i q^{67} +(75.2872 - 73.9264i) q^{68} +(-4.91796 - 12.0278i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(37.7955 - 15.4539i) q^{74} +(-14.5623 - 14.8303i) q^{76} -106.595 q^{77} +41.0410i q^{79} +(-0.315246 + 17.2829i) q^{80} +(109.666 - 44.8403i) q^{82} +35.4493i q^{83} -28.4984 q^{85} +(14.4946 + 35.4493i) q^{86} +(130.249 + 56.0503i) q^{88} +26.3786 q^{89} -74.6712i q^{91} +(-83.6148 - 85.1539i) q^{92} +(-31.0820 - 76.0172i) q^{94} +5.61373i q^{95} +76.3313 q^{97} +(-23.7565 + 9.71359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + O(q^{10}) \) \( 8q - 4q^{4} + 16q^{10} - 8q^{13} + 56q^{16} + 24q^{25} - 108q^{28} - 176q^{34} - 56q^{37} - 80q^{40} + 288q^{46} - 112q^{49} + 364q^{52} + 64q^{58} + 40q^{61} - 352q^{64} - 576q^{70} + 232q^{73} - 36q^{76} + 448q^{82} + 416q^{85} + 720q^{88} + 288q^{94} - 248q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85123 + 0.756934i −0.925615 + 0.378467i
\(3\) 0 0
\(4\) 2.85410 2.80252i 0.713525 0.700629i
\(5\) −1.08036 −0.216073 −0.108036 0.994147i \(-0.534456\pi\)
−0.108036 + 0.994147i \(0.534456\pi\)
\(6\) 0 0
\(7\) 6.01392i 0.859131i −0.903036 0.429565i \(-0.858667\pi\)
0.903036 0.429565i \(-0.141333\pi\)
\(8\) −3.16228 + 7.34847i −0.395285 + 0.918559i
\(9\) 0 0
\(10\) 2.00000 0.817763i 0.200000 0.0817763i
\(11\) 17.7247i 1.61133i −0.592369 0.805667i \(-0.701807\pi\)
0.592369 0.805667i \(-0.298193\pi\)
\(12\) 0 0
\(13\) 12.4164 0.955108 0.477554 0.878602i \(-0.341523\pi\)
0.477554 + 0.878602i \(0.341523\pi\)
\(14\) 4.55214 + 11.1331i 0.325153 + 0.795224i
\(15\) 0 0
\(16\) 0.291796 15.9973i 0.0182373 0.999834i
\(17\) 26.3786 1.55168 0.775841 0.630929i \(-0.217326\pi\)
0.775841 + 0.630929i \(0.217326\pi\)
\(18\) 0 0
\(19\) 5.19615i 0.273482i −0.990607 0.136741i \(-0.956337\pi\)
0.990607 0.136741i \(-0.0436628\pi\)
\(20\) −3.08347 + 3.02774i −0.154173 + 0.151387i
\(21\) 0 0
\(22\) 13.4164 + 32.8124i 0.609837 + 1.49147i
\(23\) 29.8356i 1.29720i −0.761129 0.648600i \(-0.775355\pi\)
0.761129 0.648600i \(-0.224645\pi\)
\(24\) 0 0
\(25\) −23.8328 −0.953313
\(26\) −22.9856 + 9.39840i −0.884062 + 0.361477i
\(27\) 0 0
\(28\) −16.8541 17.1643i −0.601932 0.613012i
\(29\) −4.32145 −0.149016 −0.0745078 0.997220i \(-0.523739\pi\)
−0.0745078 + 0.997220i \(0.523739\pi\)
\(30\) 0 0
\(31\) 44.8403i 1.44646i 0.690607 + 0.723230i \(0.257343\pi\)
−0.690607 + 0.723230i \(0.742657\pi\)
\(32\) 11.5687 + 29.8356i 0.361523 + 0.932363i
\(33\) 0 0
\(34\) −48.8328 + 19.9668i −1.43626 + 0.587260i
\(35\) 6.49721i 0.185635i
\(36\) 0 0
\(37\) −20.4164 −0.551795 −0.275897 0.961187i \(-0.588975\pi\)
−0.275897 + 0.961187i \(0.588975\pi\)
\(38\) 3.93314 + 9.61927i 0.103504 + 0.253139i
\(39\) 0 0
\(40\) 3.41641 7.93901i 0.0854102 0.198475i
\(41\) −59.2393 −1.44486 −0.722431 0.691443i \(-0.756975\pi\)
−0.722431 + 0.691443i \(0.756975\pi\)
\(42\) 0 0
\(43\) 19.1491i 0.445328i −0.974895 0.222664i \(-0.928525\pi\)
0.974895 0.222664i \(-0.0714752\pi\)
\(44\) −49.6737 50.5880i −1.12895 1.14973i
\(45\) 0 0
\(46\) 22.5836 + 55.2326i 0.490948 + 1.20071i
\(47\) 41.0631i 0.873683i 0.899539 + 0.436841i \(0.143903\pi\)
−0.899539 + 0.436841i \(0.856097\pi\)
\(48\) 0 0
\(49\) 12.8328 0.261894
\(50\) 44.1200 18.0399i 0.882400 0.360797i
\(51\) 0 0
\(52\) 35.4377 34.7972i 0.681494 0.669177i
\(53\) 70.0430 1.32157 0.660783 0.750577i \(-0.270224\pi\)
0.660783 + 0.750577i \(0.270224\pi\)
\(54\) 0 0
\(55\) 19.1491i 0.348165i
\(56\) 44.1931 + 19.0177i 0.789162 + 0.339601i
\(57\) 0 0
\(58\) 8.00000 3.27105i 0.137931 0.0563975i
\(59\) 28.9521i 0.490714i 0.969433 + 0.245357i \(0.0789052\pi\)
−0.969433 + 0.245357i \(0.921095\pi\)
\(60\) 0 0
\(61\) 18.4164 0.301908 0.150954 0.988541i \(-0.451765\pi\)
0.150954 + 0.988541i \(0.451765\pi\)
\(62\) −33.9411 83.0096i −0.547438 1.33887i
\(63\) 0 0
\(64\) −44.0000 46.4758i −0.687500 0.726184i
\(65\) −13.4142 −0.206373
\(66\) 0 0
\(67\) 94.8767i 1.41607i −0.706177 0.708035i \(-0.749582\pi\)
0.706177 0.708035i \(-0.250418\pi\)
\(68\) 75.2872 73.9264i 1.10716 1.08715i
\(69\) 0 0
\(70\) −4.91796 12.0278i −0.0702566 0.171826i
\(71\) 83.8931i 1.18159i 0.806821 + 0.590797i \(0.201186\pi\)
−0.806821 + 0.590797i \(0.798814\pi\)
\(72\) 0 0
\(73\) 55.8328 0.764833 0.382417 0.923990i \(-0.375092\pi\)
0.382417 + 0.923990i \(0.375092\pi\)
\(74\) 37.7955 15.4539i 0.510749 0.208836i
\(75\) 0 0
\(76\) −14.5623 14.8303i −0.191609 0.195136i
\(77\) −106.595 −1.38435
\(78\) 0 0
\(79\) 41.0410i 0.519507i 0.965675 + 0.259753i \(0.0836413\pi\)
−0.965675 + 0.259753i \(0.916359\pi\)
\(80\) −0.315246 + 17.2829i −0.00394057 + 0.216037i
\(81\) 0 0
\(82\) 109.666 44.8403i 1.33739 0.546833i
\(83\) 35.4493i 0.427101i 0.976932 + 0.213550i \(0.0685027\pi\)
−0.976932 + 0.213550i \(0.931497\pi\)
\(84\) 0 0
\(85\) −28.4984 −0.335276
\(86\) 14.4946 + 35.4493i 0.168542 + 0.412202i
\(87\) 0 0
\(88\) 130.249 + 56.0503i 1.48010 + 0.636936i
\(89\) 26.3786 0.296389 0.148194 0.988958i \(-0.452654\pi\)
0.148194 + 0.988958i \(0.452654\pi\)
\(90\) 0 0
\(91\) 74.6712i 0.820563i
\(92\) −83.6148 85.1539i −0.908857 0.925586i
\(93\) 0 0
\(94\) −31.0820 76.0172i −0.330660 0.808693i
\(95\) 5.61373i 0.0590919i
\(96\) 0 0
\(97\) 76.3313 0.786920 0.393460 0.919342i \(-0.371278\pi\)
0.393460 + 0.919342i \(0.371278\pi\)
\(98\) −23.7565 + 9.71359i −0.242413 + 0.0991183i
\(99\) 0 0
\(100\) −68.0213 + 66.7919i −0.680213 + 0.667919i
\(101\) −72.2037 −0.714888 −0.357444 0.933935i \(-0.616352\pi\)
−0.357444 + 0.933935i \(0.616352\pi\)
\(102\) 0 0
\(103\) 57.9754i 0.562868i 0.959581 + 0.281434i \(0.0908101\pi\)
−0.959581 + 0.281434i \(0.909190\pi\)
\(104\) −39.2641 + 91.2416i −0.377540 + 0.877323i
\(105\) 0 0
\(106\) −129.666 + 53.0179i −1.22326 + 0.500169i
\(107\) 64.4015i 0.601883i 0.953643 + 0.300942i \(0.0973009\pi\)
−0.953643 + 0.300942i \(0.902699\pi\)
\(108\) 0 0
\(109\) −43.1672 −0.396029 −0.198015 0.980199i \(-0.563449\pi\)
−0.198015 + 0.980199i \(0.563449\pi\)
\(110\) −14.4946 35.4493i −0.131769 0.322267i
\(111\) 0 0
\(112\) −96.2067 1.75484i −0.858988 0.0156682i
\(113\) 81.2965 0.719438 0.359719 0.933061i \(-0.382873\pi\)
0.359719 + 0.933061i \(0.382873\pi\)
\(114\) 0 0
\(115\) 32.2333i 0.280290i
\(116\) −12.3339 + 12.1109i −0.106326 + 0.104405i
\(117\) 0 0
\(118\) −21.9149 53.5971i −0.185719 0.454212i
\(119\) 158.639i 1.33310i
\(120\) 0 0
\(121\) −193.164 −1.59640
\(122\) −34.0930 + 13.9400i −0.279451 + 0.114262i
\(123\) 0 0
\(124\) 125.666 + 127.979i 1.01343 + 1.03209i
\(125\) 52.7572 0.422057
\(126\) 0 0
\(127\) 191.968i 1.51156i 0.654826 + 0.755780i \(0.272742\pi\)
−0.654826 + 0.755780i \(0.727258\pi\)
\(128\) 116.633 + 52.7323i 0.911197 + 0.411971i
\(129\) 0 0
\(130\) 24.8328 10.1537i 0.191022 0.0781053i
\(131\) 141.797i 1.08242i −0.840887 0.541211i \(-0.817966\pi\)
0.840887 0.541211i \(-0.182034\pi\)
\(132\) 0 0
\(133\) −31.2492 −0.234957
\(134\) 71.8154 + 175.639i 0.535936 + 1.31074i
\(135\) 0 0
\(136\) −83.4164 + 193.842i −0.613356 + 1.42531i
\(137\) 87.7787 0.640720 0.320360 0.947296i \(-0.396196\pi\)
0.320360 + 0.947296i \(0.396196\pi\)
\(138\) 0 0
\(139\) 183.501i 1.32015i −0.751200 0.660075i \(-0.770524\pi\)
0.751200 0.660075i \(-0.229476\pi\)
\(140\) 18.2085 + 18.5437i 0.130061 + 0.132455i
\(141\) 0 0
\(142\) −63.5016 155.305i −0.447194 1.09370i
\(143\) 220.077i 1.53900i
\(144\) 0 0
\(145\) 4.66874 0.0321982
\(146\) −103.359 + 42.2618i −0.707941 + 0.289464i
\(147\) 0 0
\(148\) −58.2705 + 57.2173i −0.393720 + 0.386604i
\(149\) 153.950 1.03322 0.516611 0.856220i \(-0.327193\pi\)
0.516611 + 0.856220i \(0.327193\pi\)
\(150\) 0 0
\(151\) 185.375i 1.22765i 0.789442 + 0.613825i \(0.210370\pi\)
−0.789442 + 0.613825i \(0.789630\pi\)
\(152\) 38.1838 + 16.4317i 0.251209 + 0.108103i
\(153\) 0 0
\(154\) 197.331 80.6851i 1.28137 0.523930i
\(155\) 48.4438i 0.312540i
\(156\) 0 0
\(157\) 196.164 1.24945 0.624726 0.780844i \(-0.285211\pi\)
0.624726 + 0.780844i \(0.285211\pi\)
\(158\) −31.0653 75.9764i −0.196616 0.480863i
\(159\) 0 0
\(160\) −12.4984 32.2333i −0.0781153 0.201458i
\(161\) −179.429 −1.11447
\(162\) 0 0
\(163\) 129.325i 0.793403i −0.917948 0.396701i \(-0.870155\pi\)
0.917948 0.396701i \(-0.129845\pi\)
\(164\) −169.075 + 166.019i −1.03095 + 1.01231i
\(165\) 0 0
\(166\) −26.8328 65.6249i −0.161643 0.395331i
\(167\) 137.951i 0.826052i 0.910719 + 0.413026i \(0.135528\pi\)
−0.910719 + 0.413026i \(0.864472\pi\)
\(168\) 0 0
\(169\) −14.8328 −0.0877681
\(170\) 52.7572 21.5714i 0.310336 0.126891i
\(171\) 0 0
\(172\) −53.6656 54.6534i −0.312009 0.317753i
\(173\) 160.432 0.927354 0.463677 0.886004i \(-0.346530\pi\)
0.463677 + 0.886004i \(0.346530\pi\)
\(174\) 0 0
\(175\) 143.329i 0.819020i
\(176\) −283.548 5.17199i −1.61107 0.0293863i
\(177\) 0 0
\(178\) −48.8328 + 19.9668i −0.274342 + 0.112173i
\(179\) 201.469i 1.12552i −0.826619 0.562762i \(-0.809739\pi\)
0.826619 0.562762i \(-0.190261\pi\)
\(180\) 0 0
\(181\) −48.2523 −0.266587 −0.133294 0.991077i \(-0.542555\pi\)
−0.133294 + 0.991077i \(0.542555\pi\)
\(182\) 56.5212 + 138.234i 0.310556 + 0.759525i
\(183\) 0 0
\(184\) 219.246 + 94.3485i 1.19155 + 0.512764i
\(185\) 22.0571 0.119228
\(186\) 0 0
\(187\) 467.552i 2.50028i
\(188\) 115.080 + 117.198i 0.612128 + 0.623395i
\(189\) 0 0
\(190\) −4.24922 10.3923i −0.0223643 0.0546963i
\(191\) 147.411i 0.771786i 0.922544 + 0.385893i \(0.126107\pi\)
−0.922544 + 0.385893i \(0.873893\pi\)
\(192\) 0 0
\(193\) 25.1641 0.130384 0.0651919 0.997873i \(-0.479234\pi\)
0.0651919 + 0.997873i \(0.479234\pi\)
\(194\) −141.307 + 57.7777i −0.728385 + 0.297823i
\(195\) 0 0
\(196\) 36.6262 35.9642i 0.186868 0.183491i
\(197\) −385.506 −1.95688 −0.978441 0.206528i \(-0.933784\pi\)
−0.978441 + 0.206528i \(0.933784\pi\)
\(198\) 0 0
\(199\) 121.386i 0.609978i −0.952356 0.304989i \(-0.901347\pi\)
0.952356 0.304989i \(-0.0986528\pi\)
\(200\) 75.3660 175.135i 0.376830 0.875674i
\(201\) 0 0
\(202\) 133.666 54.6534i 0.661711 0.270562i
\(203\) 25.9888i 0.128024i
\(204\) 0 0
\(205\) 64.0000 0.312195
\(206\) −43.8836 107.326i −0.213027 0.520999i
\(207\) 0 0
\(208\) 3.62306 198.629i 0.0174186 0.954949i
\(209\) −92.1001 −0.440670
\(210\) 0 0
\(211\) 261.631i 1.23996i 0.784619 + 0.619978i \(0.212859\pi\)
−0.784619 + 0.619978i \(0.787141\pi\)
\(212\) 199.910 196.297i 0.942971 0.925928i
\(213\) 0 0
\(214\) −48.7477 119.222i −0.227793 0.557112i
\(215\) 20.6880i 0.0962231i
\(216\) 0 0
\(217\) 269.666 1.24270
\(218\) 79.9124 32.6747i 0.366570 0.149884i
\(219\) 0 0
\(220\) 53.6656 + 54.6534i 0.243935 + 0.248425i
\(221\) 327.527 1.48202
\(222\) 0 0
\(223\) 70.0542i 0.314144i 0.987587 + 0.157072i \(0.0502056\pi\)
−0.987587 + 0.157072i \(0.949794\pi\)
\(224\) 179.429 69.5735i 0.801022 0.310596i
\(225\) 0 0
\(226\) −150.498 + 61.5361i −0.665922 + 0.272283i
\(227\) 298.356i 1.31434i 0.753740 + 0.657172i \(0.228248\pi\)
−0.753740 + 0.657172i \(0.771752\pi\)
\(228\) 0 0
\(229\) 259.666 1.13391 0.566956 0.823748i \(-0.308121\pi\)
0.566956 + 0.823748i \(0.308121\pi\)
\(230\) −24.3985 59.6712i −0.106080 0.259440i
\(231\) 0 0
\(232\) 13.6656 31.7561i 0.0589036 0.136880i
\(233\) −7.38192 −0.0316821 −0.0158410 0.999875i \(-0.505043\pi\)
−0.0158410 + 0.999875i \(0.505043\pi\)
\(234\) 0 0
\(235\) 44.3630i 0.188779i
\(236\) 81.1389 + 82.6323i 0.343809 + 0.350137i
\(237\) 0 0
\(238\) 120.079 + 293.676i 0.504533 + 1.23393i
\(239\) 82.1262i 0.343624i 0.985130 + 0.171812i \(0.0549622\pi\)
−0.985130 + 0.171812i \(0.945038\pi\)
\(240\) 0 0
\(241\) −415.827 −1.72542 −0.862711 0.505698i \(-0.831235\pi\)
−0.862711 + 0.505698i \(0.831235\pi\)
\(242\) 357.591 146.212i 1.47765 0.604184i
\(243\) 0 0
\(244\) 52.5623 51.6123i 0.215419 0.211526i
\(245\) −13.8641 −0.0565882
\(246\) 0 0
\(247\) 64.5175i 0.261205i
\(248\) −329.507 141.797i −1.32866 0.571764i
\(249\) 0 0
\(250\) −97.6656 + 39.9337i −0.390663 + 0.159735i
\(251\) 140.030i 0.557890i 0.960307 + 0.278945i \(0.0899847\pi\)
−0.960307 + 0.278945i \(0.910015\pi\)
\(252\) 0 0
\(253\) −528.827 −2.09022
\(254\) −145.307 355.377i −0.572075 1.39912i
\(255\) 0 0
\(256\) −255.830 9.33592i −0.999335 0.0364684i
\(257\) 66.9825 0.260632 0.130316 0.991472i \(-0.458401\pi\)
0.130316 + 0.991472i \(0.458401\pi\)
\(258\) 0 0
\(259\) 122.783i 0.474064i
\(260\) −38.2856 + 37.5936i −0.147252 + 0.144591i
\(261\) 0 0
\(262\) 107.331 + 262.500i 0.409661 + 1.00191i
\(263\) 37.2163i 0.141507i −0.997494 0.0707534i \(-0.977460\pi\)
0.997494 0.0707534i \(-0.0225404\pi\)
\(264\) 0 0
\(265\) −75.6718 −0.285554
\(266\) 57.8495 23.6536i 0.217479 0.0889233i
\(267\) 0 0
\(268\) −265.894 270.788i −0.992140 1.01040i
\(269\) −279.092 −1.03752 −0.518758 0.854921i \(-0.673605\pi\)
−0.518758 + 0.854921i \(0.673605\pi\)
\(270\) 0 0
\(271\) 406.305i 1.49928i 0.661845 + 0.749641i \(0.269774\pi\)
−0.661845 + 0.749641i \(0.730226\pi\)
\(272\) 7.69717 421.987i 0.0282984 1.55142i
\(273\) 0 0
\(274\) −162.498 + 66.4426i −0.593060 + 0.242491i
\(275\) 422.429i 1.53611i
\(276\) 0 0
\(277\) 4.83282 0.0174470 0.00872349 0.999962i \(-0.497223\pi\)
0.00872349 + 0.999962i \(0.497223\pi\)
\(278\) 138.898 + 339.702i 0.499633 + 1.22195i
\(279\) 0 0
\(280\) −47.7446 20.5460i −0.170516 0.0733785i
\(281\) −4.32145 −0.0153788 −0.00768942 0.999970i \(-0.502448\pi\)
−0.00768942 + 0.999970i \(0.502448\pi\)
\(282\) 0 0
\(283\) 44.3630i 0.156760i −0.996924 0.0783799i \(-0.975025\pi\)
0.996924 0.0783799i \(-0.0249747\pi\)
\(284\) 235.112 + 239.440i 0.827859 + 0.843097i
\(285\) 0 0
\(286\) 166.584 + 407.413i 0.582460 + 1.42452i
\(287\) 356.260i 1.24133i
\(288\) 0 0
\(289\) 406.830 1.40772
\(290\) −8.64290 + 3.53393i −0.0298031 + 0.0121860i
\(291\) 0 0
\(292\) 159.353 156.472i 0.545728 0.535864i
\(293\) −388.927 −1.32740 −0.663699 0.748000i \(-0.731014\pi\)
−0.663699 + 0.748000i \(0.731014\pi\)
\(294\) 0 0
\(295\) 31.2788i 0.106030i
\(296\) 64.5624 150.029i 0.218116 0.506856i
\(297\) 0 0
\(298\) −284.997 + 116.530i −0.956365 + 0.391040i
\(299\) 370.451i 1.23897i
\(300\) 0 0
\(301\) −115.161 −0.382595
\(302\) −140.317 343.172i −0.464625 1.13633i
\(303\) 0 0
\(304\) −83.1246 1.51622i −0.273436 0.00498756i
\(305\) −19.8964 −0.0652341
\(306\) 0 0
\(307\) 96.6999i 0.314983i −0.987520 0.157492i \(-0.949659\pi\)
0.987520 0.157492i \(-0.0503407\pi\)
\(308\) −304.232 + 298.733i −0.987767 + 0.969914i
\(309\) 0 0
\(310\) 36.6687 + 89.6805i 0.118286 + 0.289292i
\(311\) 136.184i 0.437890i −0.975737 0.218945i \(-0.929739\pi\)
0.975737 0.218945i \(-0.0702615\pi\)
\(312\) 0 0
\(313\) 282.161 0.901473 0.450736 0.892657i \(-0.351161\pi\)
0.450736 + 0.892657i \(0.351161\pi\)
\(314\) −363.145 + 148.483i −1.15651 + 0.472877i
\(315\) 0 0
\(316\) 115.018 + 117.135i 0.363982 + 0.370681i
\(317\) −275.489 −0.869051 −0.434526 0.900659i \(-0.643084\pi\)
−0.434526 + 0.900659i \(0.643084\pi\)
\(318\) 0 0
\(319\) 76.5963i 0.240114i
\(320\) 47.5360 + 50.2107i 0.148550 + 0.156909i
\(321\) 0 0
\(322\) 332.164 135.816i 1.03157 0.421788i
\(323\) 137.067i 0.424356i
\(324\) 0 0
\(325\) −295.918 −0.910517
\(326\) 97.8902 + 239.410i 0.300277 + 0.734385i
\(327\) 0 0
\(328\) 187.331 435.319i 0.571132 1.32719i
\(329\) 246.950 0.750608
\(330\) 0 0
\(331\) 55.5221i 0.167741i −0.996477 0.0838703i \(-0.973272\pi\)
0.996477 0.0838703i \(-0.0267281\pi\)
\(332\) 99.3474 + 101.176i 0.299239 + 0.304747i
\(333\) 0 0
\(334\) −104.420 255.378i −0.312633 0.764606i
\(335\) 102.501i 0.305974i
\(336\) 0 0
\(337\) −430.659 −1.27792 −0.638961 0.769239i \(-0.720635\pi\)
−0.638961 + 0.769239i \(0.720635\pi\)
\(338\) 27.4589 11.2275i 0.0812395 0.0332173i
\(339\) 0 0
\(340\) −81.3375 + 79.8674i −0.239228 + 0.234904i
\(341\) 794.779 2.33073
\(342\) 0 0
\(343\) 371.857i 1.08413i
\(344\) 140.716 + 60.5547i 0.409059 + 0.176031i
\(345\) 0 0
\(346\) −296.997 + 121.437i −0.858373 + 0.350973i
\(347\) 135.871i 0.391559i −0.980648 0.195779i \(-0.937276\pi\)
0.980648 0.195779i \(-0.0627236\pi\)
\(348\) 0 0
\(349\) 288.082 0.825450 0.412725 0.910856i \(-0.364577\pi\)
0.412725 + 0.910856i \(0.364577\pi\)
\(350\) −108.490 265.334i −0.309972 0.758097i
\(351\) 0 0
\(352\) 528.827 205.052i 1.50235 0.582535i
\(353\) 198.964 0.563638 0.281819 0.959468i \(-0.409062\pi\)
0.281819 + 0.959468i \(0.409062\pi\)
\(354\) 0 0
\(355\) 90.6350i 0.255310i
\(356\) 75.2872 73.9264i 0.211481 0.207659i
\(357\) 0 0
\(358\) 152.498 + 372.965i 0.425973 + 1.04180i
\(359\) 324.658i 0.904339i −0.891932 0.452170i \(-0.850650\pi\)
0.891932 0.452170i \(-0.149350\pi\)
\(360\) 0 0
\(361\) 334.000 0.925208
\(362\) 89.3261 36.5238i 0.246757 0.100895i
\(363\) 0 0
\(364\) −209.267 213.119i −0.574910 0.585493i
\(365\) −60.3197 −0.165259
\(366\) 0 0
\(367\) 176.141i 0.479948i 0.970779 + 0.239974i \(0.0771390\pi\)
−0.970779 + 0.239974i \(0.922861\pi\)
\(368\) −477.290 8.70592i −1.29699 0.0236574i
\(369\) 0 0
\(370\) −40.8328 + 16.6958i −0.110359 + 0.0451238i
\(371\) 421.233i 1.13540i
\(372\) 0 0
\(373\) 596.580 1.59941 0.799706 0.600392i \(-0.204989\pi\)
0.799706 + 0.600392i \(0.204989\pi\)
\(374\) 353.906 + 865.546i 0.946272 + 2.31429i
\(375\) 0 0
\(376\) −301.751 129.853i −0.802529 0.345353i
\(377\) −53.6569 −0.142326
\(378\) 0 0
\(379\) 30.3082i 0.0799689i 0.999200 + 0.0399844i \(0.0127308\pi\)
−0.999200 + 0.0399844i \(0.987269\pi\)
\(380\) 15.7326 + 16.0222i 0.0414015 + 0.0421636i
\(381\) 0 0
\(382\) −111.580 272.892i −0.292096 0.714377i
\(383\) 707.220i 1.84653i −0.384167 0.923264i \(-0.625511\pi\)
0.384167 0.923264i \(-0.374489\pi\)
\(384\) 0 0
\(385\) 115.161 0.299119
\(386\) −46.5845 + 19.0475i −0.120685 + 0.0493460i
\(387\) 0 0
\(388\) 217.857 213.920i 0.561488 0.551339i
\(389\) 577.088 1.48352 0.741758 0.670668i \(-0.233992\pi\)
0.741758 + 0.670668i \(0.233992\pi\)
\(390\) 0 0
\(391\) 787.021i 2.01284i
\(392\) −40.5809 + 94.3016i −0.103523 + 0.240565i
\(393\) 0 0
\(394\) 713.659 291.802i 1.81132 0.740615i
\(395\) 44.3392i 0.112251i
\(396\) 0 0
\(397\) 26.8266 0.0675733 0.0337867 0.999429i \(-0.489243\pi\)
0.0337867 + 0.999429i \(0.489243\pi\)
\(398\) 91.8809 + 224.713i 0.230857 + 0.564605i
\(399\) 0 0
\(400\) −6.95432 + 381.262i −0.0173858 + 0.953154i
\(401\) −505.065 −1.25951 −0.629756 0.776793i \(-0.716845\pi\)
−0.629756 + 0.776793i \(0.716845\pi\)
\(402\) 0 0
\(403\) 556.755i 1.38153i
\(404\) −206.077 + 202.352i −0.510091 + 0.500872i
\(405\) 0 0
\(406\) −19.6718 48.1113i −0.0484528 0.118501i
\(407\) 361.874i 0.889126i
\(408\) 0 0
\(409\) −683.328 −1.67073 −0.835364 0.549696i \(-0.814743\pi\)
−0.835364 + 0.549696i \(0.814743\pi\)
\(410\) −118.479 + 48.4438i −0.288972 + 0.118156i
\(411\) 0 0
\(412\) 162.477 + 165.468i 0.394362 + 0.401621i
\(413\) 174.116 0.421588
\(414\) 0 0
\(415\) 38.2982i 0.0922847i
\(416\) 143.642 + 370.451i 0.345294 + 0.890508i
\(417\) 0 0
\(418\) 170.498 69.7137i 0.407891 0.166779i
\(419\) 306.620i 0.731791i −0.930656 0.365895i \(-0.880763\pi\)
0.930656 0.365895i \(-0.119237\pi\)
\(420\) 0 0
\(421\) −18.5867 −0.0441489 −0.0220745 0.999756i \(-0.507027\pi\)
−0.0220745 + 0.999756i \(0.507027\pi\)
\(422\) −198.037 484.339i −0.469283 1.14772i
\(423\) 0 0
\(424\) −221.495 + 514.709i −0.522395 + 1.21394i
\(425\) −628.676 −1.47924
\(426\) 0 0
\(427\) 110.755i 0.259379i
\(428\) 180.486 + 183.808i 0.421697 + 0.429459i
\(429\) 0 0
\(430\) −15.6594 38.2982i −0.0364173 0.0890655i
\(431\) 308.130i 0.714918i −0.933929 0.357459i \(-0.883643\pi\)
0.933929 0.357459i \(-0.116357\pi\)
\(432\) 0 0
\(433\) 174.839 0.403785 0.201893 0.979408i \(-0.435291\pi\)
0.201893 + 0.979408i \(0.435291\pi\)
\(434\) −499.213 + 204.119i −1.15026 + 0.470320i
\(435\) 0 0
\(436\) −123.204 + 120.977i −0.282577 + 0.277470i
\(437\) −155.030 −0.354761
\(438\) 0 0
\(439\) 480.159i 1.09376i −0.837212 0.546878i \(-0.815816\pi\)
0.837212 0.546878i \(-0.184184\pi\)
\(440\) −140.716 60.5547i −0.319810 0.137624i
\(441\) 0 0
\(442\) −606.328 + 247.917i −1.37178 + 0.560897i
\(443\) 555.962i 1.25499i 0.778619 + 0.627497i \(0.215920\pi\)
−0.778619 + 0.627497i \(0.784080\pi\)
\(444\) 0 0
\(445\) −28.4984 −0.0640415
\(446\) −53.0264 129.686i −0.118893 0.290777i
\(447\) 0 0
\(448\) −279.502 + 264.612i −0.623887 + 0.590652i
\(449\) 801.711 1.78555 0.892774 0.450504i \(-0.148756\pi\)
0.892774 + 0.450504i \(0.148756\pi\)
\(450\) 0 0
\(451\) 1050.00i 2.32816i
\(452\) 232.028 227.835i 0.513337 0.504059i
\(453\) 0 0
\(454\) −225.836 552.326i −0.497436 1.21658i
\(455\) 80.6720i 0.177301i
\(456\) 0 0
\(457\) −137.830 −0.301597 −0.150798 0.988565i \(-0.548184\pi\)
−0.150798 + 0.988565i \(0.548184\pi\)
\(458\) −480.701 + 196.550i −1.04956 + 0.429148i
\(459\) 0 0
\(460\) 90.3344 + 91.9971i 0.196379 + 0.199994i
\(461\) −188.341 −0.408549 −0.204274 0.978914i \(-0.565483\pi\)
−0.204274 + 0.978914i \(0.565483\pi\)
\(462\) 0 0
\(463\) 548.425i 1.18450i 0.805753 + 0.592251i \(0.201761\pi\)
−0.805753 + 0.592251i \(0.798239\pi\)
\(464\) −1.26098 + 69.1317i −0.00271764 + 0.148991i
\(465\) 0 0
\(466\) 13.6656 5.58763i 0.0293254 0.0119906i
\(467\) 618.597i 1.32462i 0.749231 + 0.662309i \(0.230423\pi\)
−0.749231 + 0.662309i \(0.769577\pi\)
\(468\) 0 0
\(469\) −570.580 −1.21659
\(470\) 33.5799 + 82.1262i 0.0714466 + 0.174737i
\(471\) 0 0
\(472\) −212.754 91.5547i −0.450750 0.193972i
\(473\) −339.411 −0.717571
\(474\) 0 0
\(475\) 123.839i 0.260714i
\(476\) −444.587 452.771i −0.934007 0.951199i
\(477\) 0 0
\(478\) −62.1641 152.034i −0.130050 0.318064i
\(479\) 770.425i 1.60840i −0.594357 0.804202i \(-0.702593\pi\)
0.594357 0.804202i \(-0.297407\pi\)
\(480\) 0 0
\(481\) −253.498 −0.527024
\(482\) 769.791 314.753i 1.59708 0.653015i
\(483\) 0 0
\(484\) −551.310 + 541.346i −1.13907 + 1.11848i
\(485\) −82.4655 −0.170032
\(486\) 0 0
\(487\) 549.208i 1.12774i −0.825865 0.563868i \(-0.809313\pi\)
0.825865 0.563868i \(-0.190687\pi\)
\(488\) −58.2378 + 135.332i −0.119340 + 0.277321i
\(489\) 0 0
\(490\) 25.6656 10.4942i 0.0523788 0.0214168i
\(491\) 23.0256i 0.0468952i 0.999725 + 0.0234476i \(0.00746429\pi\)
−0.999725 + 0.0234476i \(0.992536\pi\)
\(492\) 0 0
\(493\) −113.994 −0.231225
\(494\) 48.8355 + 119.437i 0.0988573 + 0.241775i
\(495\) 0 0
\(496\) 717.325 + 13.0842i 1.44622 + 0.0263795i
\(497\) 504.526 1.01514
\(498\) 0 0
\(499\) 626.809i 1.25613i 0.778160 + 0.628065i \(0.216153\pi\)
−0.778160 + 0.628065i \(0.783847\pi\)
\(500\) 150.574 147.853i 0.301149 0.295706i
\(501\) 0 0
\(502\) −105.994 259.228i −0.211143 0.516391i
\(503\) 732.896i 1.45705i 0.685019 + 0.728525i \(0.259794\pi\)
−0.685019 + 0.728525i \(0.740206\pi\)
\(504\) 0 0
\(505\) 78.0062 0.154468
\(506\) 978.979 400.287i 1.93474 0.791081i
\(507\) 0 0
\(508\) 537.994 + 547.896i 1.05904 + 1.07854i
\(509\) −437.363 −0.859259 −0.429630 0.903005i \(-0.641356\pi\)
−0.429630 + 0.903005i \(0.641356\pi\)
\(510\) 0 0
\(511\) 335.774i 0.657092i
\(512\) 480.666 176.363i 0.938801 0.344459i
\(513\) 0 0
\(514\) −124.000 + 50.7013i −0.241245 + 0.0986407i
\(515\) 62.6345i 0.121620i
\(516\) 0 0
\(517\) 727.830 1.40779
\(518\) −92.9383 227.299i −0.179418 0.438801i
\(519\) 0 0
\(520\) 42.4195 98.5740i 0.0815760 0.189565i
\(521\) 385.236 0.739417 0.369709 0.929148i \(-0.379458\pi\)
0.369709 + 0.929148i \(0.379458\pi\)
\(522\) 0 0
\(523\) 418.572i 0.800328i −0.916443 0.400164i \(-0.868953\pi\)
0.916443 0.400164i \(-0.131047\pi\)
\(524\) −397.390 404.704i −0.758377 0.772336i
\(525\) 0 0
\(526\) 28.1703 + 68.8959i 0.0535557 + 0.130981i
\(527\) 1182.82i 2.24445i
\(528\) 0 0
\(529\) −361.164 −0.682730
\(530\) 140.086 57.2786i 0.264313 0.108073i
\(531\) 0 0
\(532\) −89.1885 + 87.5765i −0.167648 + 0.164617i
\(533\) −735.540 −1.38000
\(534\) 0 0
\(535\) 69.5770i 0.130050i
\(536\) 697.199 + 300.026i 1.30074 + 0.559751i
\(537\) 0 0
\(538\) 516.663 211.254i 0.960339 0.392665i
\(539\) 227.457i 0.421999i
\(540\) 0 0
\(541\) −23.4257 −0.0433008 −0.0216504 0.999766i \(-0.506892\pi\)
−0.0216504 + 0.999766i \(0.506892\pi\)
\(542\) −307.546 752.164i −0.567429 1.38776i
\(543\) 0 0
\(544\) 305.167 + 787.021i 0.560969 + 1.44673i
\(545\) 46.6362 0.0855711
\(546\) 0 0
\(547\) 722.163i 1.32023i 0.751167 + 0.660113i \(0.229491\pi\)
−0.751167 + 0.660113i \(0.770509\pi\)
\(548\) 250.529 246.001i 0.457170 0.448907i
\(549\) 0 0
\(550\) −319.751 782.013i −0.581365 1.42184i
\(551\) 22.4549i 0.0407530i
\(552\) 0 0
\(553\) 246.817 0.446324
\(554\) −8.94665 + 3.65812i −0.0161492 + 0.00660311i
\(555\) 0 0
\(556\) −514.264 523.730i −0.924936 0.941961i
\(557\) 2.34135 0.00420349 0.00210175 0.999998i \(-0.499331\pi\)
0.00210175 + 0.999998i \(0.499331\pi\)
\(558\) 0 0
\(559\) 237.763i 0.425336i
\(560\) 103.938 + 1.89586i 0.185604 + 0.00338547i
\(561\) 0 0
\(562\) 8.00000 3.27105i 0.0142349 0.00582038i
\(563\) 359.794i 0.639066i −0.947575 0.319533i \(-0.896474\pi\)
0.947575 0.319533i \(-0.103526\pi\)
\(564\) 0 0
\(565\) −87.8297 −0.155451
\(566\) 33.5799 + 82.1262i 0.0593284 + 0.145099i
\(567\) 0 0
\(568\) −616.486 265.293i −1.08536 0.467066i
\(569\) −18.6354 −0.0327512 −0.0163756 0.999866i \(-0.505213\pi\)
−0.0163756 + 0.999866i \(0.505213\pi\)
\(570\) 0 0
\(571\) 284.528i 0.498298i −0.968465 0.249149i \(-0.919849\pi\)
0.968465 0.249149i \(-0.0801509\pi\)
\(572\) −616.769 628.122i −1.07827 1.09811i
\(573\) 0 0
\(574\) −269.666 659.520i −0.469801 1.14899i
\(575\) 711.067i 1.23664i
\(576\) 0 0
\(577\) 664.823 1.15221 0.576104 0.817377i \(-0.304572\pi\)
0.576104 + 0.817377i \(0.304572\pi\)
\(578\) −753.135 + 307.943i −1.30300 + 0.532774i
\(579\) 0 0
\(580\) 13.3251 13.0842i 0.0229742 0.0225590i
\(581\) 213.189 0.366935
\(582\) 0 0
\(583\) 1241.49i 2.12948i
\(584\) −176.559 + 410.286i −0.302327 + 0.702544i
\(585\) 0 0
\(586\) 719.994 294.392i 1.22866 0.502376i
\(587\) 754.467i 1.28529i 0.766162 + 0.642647i \(0.222164\pi\)
−0.766162 + 0.642647i \(0.777836\pi\)
\(588\) 0 0
\(589\) 232.997 0.395580
\(590\) 23.6760 + 57.9043i 0.0401288 + 0.0981428i
\(591\) 0 0
\(592\) −5.95743 + 326.608i −0.0100632 + 0.551703i
\(593\) −550.801 −0.928838 −0.464419 0.885615i \(-0.653737\pi\)
−0.464419 + 0.885615i \(0.653737\pi\)
\(594\) 0 0
\(595\) 171.387i 0.288046i
\(596\) 439.389 431.448i 0.737230 0.723905i
\(597\) 0 0
\(598\) 280.407 + 685.790i 0.468908 + 1.14681i
\(599\) 25.9888i 0.0433871i 0.999765 + 0.0216935i \(0.00690581\pi\)
−0.999765 + 0.0216935i \(0.993094\pi\)
\(600\) 0 0
\(601\) 186.170 0.309768 0.154884 0.987933i \(-0.450500\pi\)
0.154884 + 0.987933i \(0.450500\pi\)
\(602\) 213.189 87.1693i 0.354135 0.144799i
\(603\) 0 0
\(604\) 519.517 + 529.079i 0.860127 + 0.875959i
\(605\) 208.687 0.344938
\(606\) 0 0
\(607\) 99.5447i 0.163994i 0.996633 + 0.0819972i \(0.0261299\pi\)
−0.996633 + 0.0819972i \(0.973870\pi\)
\(608\) 155.030 60.1130i 0.254984 0.0988700i
\(609\) 0 0
\(610\) 36.8328 15.0603i 0.0603817 0.0246890i
\(611\) 509.856i 0.834461i
\(612\) 0 0
\(613\) −960.234 −1.56645 −0.783225 0.621739i \(-0.786427\pi\)
−0.783225 + 0.621739i \(0.786427\pi\)
\(614\) 73.1954 + 179.014i 0.119211 + 0.291553i
\(615\) 0 0
\(616\) 337.082 783.308i 0.547211 1.27160i
\(617\) −354.625 −0.574757 −0.287378 0.957817i \(-0.592784\pi\)
−0.287378 + 0.957817i \(0.592784\pi\)
\(618\) 0 0
\(619\) 360.647i 0.582629i −0.956627 0.291314i \(-0.905907\pi\)
0.956627 0.291314i \(-0.0940926\pi\)
\(620\) −135.765 138.263i −0.218975 0.223006i
\(621\) 0 0
\(622\) 103.082 + 252.107i 0.165727 + 0.405317i
\(623\) 158.639i 0.254637i
\(624\) 0 0
\(625\) 538.823 0.862118
\(626\) −522.345 + 213.577i −0.834417 + 0.341178i
\(627\) 0 0
\(628\) 559.872 549.753i 0.891516 0.875403i
\(629\) −538.556 −0.856210
\(630\) 0 0
\(631\) 82.7121i 0.131081i −0.997850 0.0655405i \(-0.979123\pi\)
0.997850 0.0655405i \(-0.0208772\pi\)
\(632\) −301.589 129.783i −0.477197 0.205353i
\(633\) 0 0
\(634\) 509.994 208.527i 0.804407 0.328907i
\(635\) 207.395i 0.326607i
\(636\) 0 0
\(637\) 159.337 0.250137
\(638\) −57.9784 141.797i −0.0908752 0.222253i
\(639\) 0 0
\(640\) −126.006 56.9700i −0.196885 0.0890156i
\(641\) −760.569 −1.18653 −0.593267 0.805005i \(-0.702162\pi\)
−0.593267 + 0.805005i \(0.702162\pi\)
\(642\) 0 0
\(643\) 787.021i 1.22398i 0.790864 + 0.611992i \(0.209631\pi\)
−0.790864 + 0.611992i \(0.790369\pi\)
\(644\) −512.108 + 502.853i −0.795199 + 0.780827i
\(645\) 0 0
\(646\) 103.751 + 253.743i 0.160605 + 0.392791i
\(647\) 978.962i 1.51308i −0.653948 0.756539i \(-0.726889\pi\)
0.653948 0.756539i \(-0.273111\pi\)
\(648\) 0 0
\(649\) 513.167 0.790704
\(650\) 547.812 223.990i 0.842788 0.344601i
\(651\) 0 0
\(652\) −362.435 369.106i −0.555881 0.566113i
\(653\) 939.548 1.43882 0.719409 0.694587i \(-0.244413\pi\)
0.719409 + 0.694587i \(0.244413\pi\)
\(654\) 0 0
\(655\) 153.193i 0.233882i
\(656\) −17.2858 + 947.672i −0.0263503 + 1.44462i
\(657\) 0 0
\(658\) −457.161 + 186.925i −0.694774 + 0.284080i
\(659\) 149.491i 0.226845i −0.993547 0.113423i \(-0.963819\pi\)
0.993547 0.113423i \(-0.0361814\pi\)
\(660\) 0 0
\(661\) 337.420 0.510468 0.255234 0.966879i \(-0.417847\pi\)
0.255234 + 0.966879i \(0.417847\pi\)
\(662\) 42.0266 + 102.784i 0.0634843 + 0.155263i
\(663\) 0 0
\(664\) −260.498 112.101i −0.392317 0.168826i
\(665\) 33.7605 0.0507677
\(666\) 0 0
\(667\) 128.933i 0.193303i
\(668\) 386.609 + 393.725i 0.578756 + 0.589409i
\(669\) 0 0
\(670\) −77.5867 189.753i −0.115801 0.283214i
\(671\) 326.425i 0.486475i
\(672\) 0 0
\(673\) −321.341 −0.477475 −0.238737 0.971084i \(-0.576734\pi\)
−0.238737 + 0.971084i \(0.576734\pi\)
\(674\) 797.249 325.981i 1.18286 0.483651i
\(675\) 0 0
\(676\) −42.3344 + 41.5692i −0.0626248 + 0.0614929i
\(677\) 741.841 1.09578 0.547889 0.836551i \(-0.315432\pi\)
0.547889 + 0.836551i \(0.315432\pi\)
\(678\) 0 0
\(679\) 459.050i 0.676067i
\(680\) 90.1200 209.420i 0.132529 0.307971i
\(681\) 0 0
\(682\) −1471.32 + 601.595i −2.15736 + 0.882105i
\(683\) 1259.02i 1.84337i −0.387938 0.921686i \(-0.626812\pi\)
0.387938 0.921686i \(-0.373188\pi\)
\(684\) 0 0
\(685\) −94.8328 −0.138442
\(686\) 281.471 + 688.393i 0.410308 + 1.00349i
\(687\) 0 0
\(688\) −306.334 5.58763i −0.445253 0.00812155i
\(689\) 869.682 1.26224
\(690\) 0 0
\(691\) 222.770i 0.322387i 0.986923 + 0.161194i \(0.0515344\pi\)
−0.986923 + 0.161194i \(0.948466\pi\)
\(692\) 457.890 449.614i 0.661691 0.649731i
\(693\) 0 0
\(694\) 102.845 + 251.528i 0.148192 + 0.362432i
\(695\) 198.248i 0.285248i
\(696\) 0 0
\(697\) −1562.65 −2.24197
\(698\) −533.306 + 218.059i −0.764049 + 0.312406i
\(699\) 0 0
\(700\) 401.681 + 409.074i 0.573830 + 0.584392i
\(701\) 2.34135 0.00334001 0.00167000 0.999999i \(-0.499468\pi\)
0.00167000 + 0.999999i \(0.499468\pi\)
\(702\) 0 0
\(703\) 106.087i 0.150906i
\(704\) −823.768 + 779.886i −1.17013 + 1.10779i
\(705\) 0 0
\(706\) −368.328 + 150.603i −0.521711 + 0.213318i
\(707\) 434.227i 0.614182i
\(708\) 0 0
\(709\) −495.085 −0.698287 −0.349143 0.937069i \(-0.613527\pi\)
−0.349143 + 0.937069i \(0.613527\pi\)
\(710\) 68.6047 + 167.786i 0.0966264 + 0.236319i
\(711\) 0 0
\(712\) −83.4164 + 193.842i −0.117158 + 0.272250i
\(713\) 1337.84 1.87635
\(714\) 0 0
\(715\) 237.763i 0.332535i
\(716\) −564.619 575.012i −0.788574 0.803089i
\(717\) 0 0
\(718\) 245.745 + 601.016i 0.342263 + 0.837070i
\(719\) 962.433i 1.33857i −0.743005 0.669286i \(-0.766600\pi\)
0.743005 0.669286i \(-0.233400\pi\)
\(720\) 0 0
\(721\) 348.659 0.483578
\(722\) −618.311 + 252.816i −0.856386 + 0.350161i
\(723\) 0 0
\(724\) −137.717 + 135.228i −0.190217 + 0.186779i
\(725\) 102.992 0.142058
\(726\) 0 0
\(727\) 544.625i 0.749141i 0.927198 + 0.374570i \(0.122210\pi\)
−0.927198 + 0.374570i \(0.877790\pi\)
\(728\) 548.719 + 236.131i 0.753735 + 0.324356i
\(729\) 0 0
\(730\) 111.666 45.6580i 0.152967 0.0625453i
\(731\) 505.126i 0.691006i
\(732\) 0 0
\(733\) −146.170 −0.199414 −0.0997069 0.995017i \(-0.531791\pi\)
−0.0997069 + 0.995017i \(0.531791\pi\)
\(734\) −133.327 326.077i −0.181645 0.444247i
\(735\) 0 0
\(736\) 890.164 345.161i 1.20946 0.468968i
\(737\) −1681.66 −2.28176
\(738\) 0 0
\(739\) 1172.87i 1.58710i 0.608505 + 0.793550i \(0.291769\pi\)
−0.608505 + 0.793550i \(0.708231\pi\)
\(740\) 62.9533 61.8155i 0.0850720 0.0835344i
\(741\) 0 0
\(742\) 318.845 + 779.798i 0.429711 + 1.05094i
\(743\) 494.837i 0.665998i −0.942927 0.332999i \(-0.891939\pi\)
0.942927 0.332999i \(-0.108061\pi\)
\(744\) 0 0
\(745\) −166.322 −0.223251
\(746\) −1104.41 + 451.572i −1.48044 + 0.605324i
\(747\) 0 0
\(748\) −1310.32 1334.44i −1.75177 1.78401i
\(749\) 387.305 0.517096
\(750\) 0 0
\(751\) 927.250i 1.23469i −0.786693 0.617344i \(-0.788209\pi\)
0.786693 0.617344i \(-0.211791\pi\)
\(752\) 656.900 + 11.9820i 0.873537 + 0.0159336i
\(753\) 0 0
\(754\) 99.3313 40.6147i 0.131739 0.0538657i
\(755\) 200.272i 0.265261i
\(756\) 0 0
\(757\) −757.748 −1.00099 −0.500494 0.865740i \(-0.666848\pi\)
−0.500494 + 0.865740i \(0.666848\pi\)
\(758\) −22.9413 56.1074i −0.0302656 0.0740204i
\(759\) 0 0
\(760\) −41.2523 17.7522i −0.0542794 0.0233581i
\(761\) 953.139 1.25248 0.626241 0.779629i \(-0.284592\pi\)
0.626241 + 0.779629i \(0.284592\pi\)
\(762\) 0 0
\(763\) 259.604i 0.340241i
\(764\) 413.122 + 420.726i 0.540736 + 0.550689i
\(765\) 0 0
\(766\) 535.319 + 1309.23i 0.698850 + 1.70917i
\(767\) 359.482i 0.468685i
\(768\) 0 0
\(769\) 145.675 0.189434 0.0947171 0.995504i \(-0.469805\pi\)
0.0947171 + 0.995504i \(0.469805\pi\)
\(770\) −213.189 + 87.1693i −0.276869 + 0.113207i
\(771\) 0 0
\(772\) 71.8208 70.5228i 0.0930322 0.0913507i
\(773\) 60.1391 0.0777996 0.0388998 0.999243i \(-0.487615\pi\)
0.0388998 + 0.999243i \(0.487615\pi\)
\(774\) 0 0
\(775\) 1068.67i 1.37893i
\(776\) −241.381 + 560.918i −0.311058 + 0.722832i
\(777\) 0 0
\(778\) −1068.32 + 436.817i −1.37316 + 0.561462i
\(779\) 307.817i 0.395143i
\(780\) 0 0
\(781\) 1486.98 1.90394
\(782\) 595.723 + 1456.96i 0.761794 + 1.86312i
\(783\) 0 0
\(784\) 3.74457 205.291i 0.00477623 0.261851i
\(785\) −211.928 −0.269973
\(786\) 0 0
\(787\) 328.312i 0.417169i 0.978004 + 0.208585i \(0.0668856\pi\)
−0.978004 + 0.208585i \(0.933114\pi\)
\(788\) −1100.27 + 1080.39i −1.39628 + 1.37105i
\(789\) 0 0
\(790\) 33.5619 + 82.0821i 0.0424834 + 0.103901i
\(791\) 488.910i 0.618091i
\(792\) 0 0
\(793\) 228.666 0.288355
\(794\) −49.6622 + 20.3060i −0.0625469 +