Properties

Label 108.3.d.d.55.7
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 55.7
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.55.8

$q$-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 \(-0.465544\pi\)
0.108036 + 0.994147i \(0.465544\pi\)
\(6\) 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 \(0.298193\pi\)
−0.592369 + 0.805667i \(0.701807\pi\)
\(12\) 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 \(-0.782674\pi\)
−0.775841 + 0.630929i \(0.782674\pi\)
\(18\) 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 \(0.224645\pi\)
−0.761129 + 0.648600i \(0.775355\pi\)
\(24\) 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 \(-0.476261\pi\)
0.0745078 + 0.997220i \(0.476261\pi\)
\(30\) 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 \(-0.243025\pi\)
0.722431 + 0.691443i \(0.243025\pi\)
\(42\) 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 \(-0.856097\pi\)
0.899539 0.436841i \(-0.143903\pi\)
\(48\) 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 \(-0.729776\pi\)
−0.660783 + 0.750577i \(0.729776\pi\)
\(54\) 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 \(-0.921095\pi\)
0.969433 0.245357i \(-0.0789052\pi\)
\(60\) 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 \(-0.798814\pi\)
0.806821 0.590797i \(-0.201186\pi\)
\(72\) 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 \(-0.931497\pi\)
0.976932 0.213550i \(-0.0685027\pi\)
\(84\) 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 \(-0.547346\pi\)
−0.148194 + 0.988958i \(0.547346\pi\)
\(90\) 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 \(-0.383648\pi\)
0.357444 + 0.933935i \(0.383648\pi\)
\(102\) 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 \(-0.902699\pi\)
0.953643 0.300942i \(-0.0973009\pi\)
\(108\) 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 \(-0.617127\pi\)
−0.359719 + 0.933061i \(0.617127\pi\)
\(114\) 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 \(0.182034\pi\)
−0.840887 + 0.541211i \(0.817966\pi\)
\(132\) 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 \(-0.603804\pi\)
−0.320360 + 0.947296i \(0.603804\pi\)
\(138\) 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 \(-0.672807\pi\)
−0.516611 + 0.856220i \(0.672807\pi\)
\(150\) 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 \(-0.864472\pi\)
0.910719 0.413026i \(-0.135528\pi\)
\(168\) 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 \(-0.653470\pi\)
−0.463677 + 0.886004i \(0.653470\pi\)
\(174\) 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 \(0.190261\pi\)
−0.826619 + 0.562762i \(0.809739\pi\)
\(180\) 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 \(-0.873893\pi\)
0.922544 0.385893i \(-0.126107\pi\)
\(192\) 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 \(-0.0662165\pi\)
0.978441 + 0.206528i \(0.0662165\pi\)
\(198\) 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 \(-0.771752\pi\)
0.753740 0.657172i \(-0.228248\pi\)
\(228\) 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 \(-0.494957\pi\)
0.0158410 + 0.999875i \(0.494957\pi\)
\(234\) 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 \(-0.945038\pi\)
0.985130 0.171812i \(-0.0549622\pi\)
\(240\) 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 \(-0.910015\pi\)
0.960307 0.278945i \(-0.0899847\pi\)
\(252\) 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 \(-0.541599\pi\)
−0.130316 + 0.991472i \(0.541599\pi\)
\(258\) 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 \(0.0225404\pi\)
−0.997494 + 0.0707534i \(0.977460\pi\)
\(264\) 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 \(-0.326395\pi\)
0.518758 + 0.854921i \(0.326395\pi\)
\(270\) 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 \(-0.497552\pi\)
0.00768942 + 0.999970i \(0.497552\pi\)
\(282\) 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 \(-0.268986\pi\)
0.663699 + 0.748000i \(0.268986\pi\)
\(294\) 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 \(0.0702615\pi\)
−0.975737 + 0.218945i \(0.929739\pi\)
\(312\) 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 \(-0.356916\pi\)
0.434526 + 0.900659i \(0.356916\pi\)
\(318\) 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 \(0.0627236\pi\)
−0.980648 + 0.195779i \(0.937276\pi\)
\(348\) 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 \(-0.590938\pi\)
−0.281819 + 0.959468i \(0.590938\pi\)
\(354\) 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 \(0.149350\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(360\) 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 \(0.374489\pi\)
−0.384167 + 0.923264i \(0.625511\pi\)
\(384\) 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 \(-0.766008\pi\)
−0.741758 + 0.670668i \(0.766008\pi\)
\(390\) 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 \(-0.283155\pi\)
0.629756 + 0.776793i \(0.283155\pi\)
\(402\) 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 \(0.119237\pi\)
−0.930656 + 0.365895i \(0.880763\pi\)
\(420\) 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 \(0.116357\pi\)
−0.933929 + 0.357459i \(0.883643\pi\)
\(432\) 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 \(-0.784080\pi\)
0.778619 0.627497i \(-0.215920\pi\)
\(444\) 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 \(-0.851244\pi\)
−0.892774 + 0.450504i \(0.851244\pi\)
\(450\) 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 \(-0.434517\pi\)
0.204274 + 0.978914i \(0.434517\pi\)
\(462\) 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 \(-0.769577\pi\)
0.749231 0.662309i \(-0.230423\pi\)
\(468\) 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 \(0.297407\pi\)
−0.594357 + 0.804202i \(0.702593\pi\)
\(480\) 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 \(-0.992536\pi\)
0.999725 0.0234476i \(-0.00746429\pi\)
\(492\) 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 \(-0.740206\pi\)
0.685019 0.728525i \(-0.259794\pi\)
\(504\) 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 \(-0.358644\pi\)
0.429630 + 0.903005i \(0.358644\pi\)
\(510\) 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 \(-0.620542\pi\)
−0.369709 + 0.929148i \(0.620542\pi\)
\(522\) 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 \(-0.500669\pi\)
−0.00210175 + 0.999998i \(0.500669\pi\)
\(558\) 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 \(0.103526\pi\)
−0.947575 + 0.319533i \(0.896474\pi\)
\(564\) 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 \(-0.494787\pi\)
0.0163756 + 0.999866i \(0.494787\pi\)
\(570\) 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 \(-0.777836\pi\)
0.766162 0.642647i \(-0.222164\pi\)
\(588\) 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 \(-0.346263\pi\)
0.464419 + 0.885615i \(0.346263\pi\)
\(594\) 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 \(-0.993094\pi\)
0.999765 0.0216935i \(-0.00690581\pi\)
\(600\) 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 \(-0.407216\pi\)
0.287378 + 0.957817i \(0.407216\pi\)
\(618\) 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 \(-0.297838\pi\)
0.593267 + 0.805005i \(0.297838\pi\)
\(642\) 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 \(0.273111\pi\)
−0.653948 + 0.756539i \(0.726889\pi\)
\(648\) 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 \(-0.755587\pi\)
−0.719409 + 0.694587i \(0.755587\pi\)
\(654\) 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 \(0.0361814\pi\)
−0.993547 + 0.113423i \(0.963819\pi\)
\(660\) 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 \(-0.684568\pi\)
−0.547889 + 0.836551i \(0.684568\pi\)
\(678\) 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 \(0.373188\pi\)
−0.387938 + 0.921686i \(0.626812\pi\)
\(684\) 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 \(-0.500532\pi\)
−0.00167000 + 0.999999i \(0.500532\pi\)
\(702\) 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 \(0.233400\pi\)
−0.743005 + 0.669286i \(0.766600\pi\)
\(720\) 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 \(0.108061\pi\)
−0.942927 + 0.332999i \(0.891939\pi\)
\(744\) 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 \(-0.715408\pi\)
−0.626241 + 0.779629i \(0.715408\pi\)
\(762\) 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 \(-0.512385\pi\)
−0.0388998 + 0.999243i \(0.512385\pi\)
\(774\) 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