Properties

Label 1512.2.c.f.757.19
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.19
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.09864 - 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} -1.58470i q^{5} +1.00000 q^{7} +(-1.28759 - 2.51836i) q^{8} +O(q^{10})\) \(q+(1.09864 - 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} -1.58470i q^{5} +1.00000 q^{7} +(-1.28759 - 2.51836i) q^{8} +(-1.41118 - 1.74101i) q^{10} +0.790533i q^{11} -0.494366i q^{13} +(1.09864 - 0.890504i) q^{14} +(-3.65720 - 1.62016i) q^{16} -4.46962 q^{17} -7.55705i q^{19} +(-3.10076 - 0.656077i) q^{20} +(0.703973 + 0.868509i) q^{22} -0.839644 q^{23} +2.48872 q^{25} +(-0.440235 - 0.543129i) q^{26} +(0.414007 - 1.95668i) q^{28} -2.76437i q^{29} -0.568664 q^{31} +(-5.46069 + 1.47678i) q^{32} +(-4.91049 + 3.98021i) q^{34} -1.58470i q^{35} -0.343650i q^{37} +(-6.72958 - 8.30245i) q^{38} +(-3.99084 + 2.04044i) q^{40} +5.93014 q^{41} -3.16166i q^{43} +(1.54682 + 0.327286i) q^{44} +(-0.922464 + 0.747706i) q^{46} -4.80964 q^{47} +1.00000 q^{49} +(2.73420 - 2.21621i) q^{50} +(-0.967316 - 0.204671i) q^{52} +4.36792i q^{53} +1.25276 q^{55} +(-1.28759 - 2.51836i) q^{56} +(-2.46168 - 3.03704i) q^{58} +4.50798i q^{59} -5.40103i q^{61} +(-0.624755 + 0.506397i) q^{62} +(-4.68423 + 6.48521i) q^{64} -0.783423 q^{65} +7.57396i q^{67} +(-1.85045 + 8.74561i) q^{68} +(-1.41118 - 1.74101i) q^{70} -9.52886 q^{71} +14.1344 q^{73} +(-0.306022 - 0.377547i) q^{74} +(-14.7867 - 3.12867i) q^{76} +0.790533i q^{77} -3.71341 q^{79} +(-2.56747 + 5.79557i) q^{80} +(6.51507 - 5.28081i) q^{82} -7.30905i q^{83} +7.08301i q^{85} +(-2.81547 - 3.47352i) q^{86} +(1.99084 - 1.01788i) q^{88} -11.5305 q^{89} -0.494366i q^{91} +(-0.347618 + 1.64292i) q^{92} +(-5.28405 + 4.28300i) q^{94} -11.9757 q^{95} +1.75839 q^{97} +(1.09864 - 0.890504i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09864 0.890504i 0.776854 0.629681i
\(3\) 0 0
\(4\) 0.414007 1.95668i 0.207003 0.978340i
\(5\) 1.58470i 0.708700i −0.935113 0.354350i \(-0.884702\pi\)
0.935113 0.354350i \(-0.115298\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.28759 2.51836i −0.455231 0.890373i
\(9\) 0 0
\(10\) −1.41118 1.74101i −0.446255 0.550557i
\(11\) 0.790533i 0.238355i 0.992873 + 0.119177i \(0.0380257\pi\)
−0.992873 + 0.119177i \(0.961974\pi\)
\(12\) 0 0
\(13\) 0.494366i 0.137112i −0.997647 0.0685562i \(-0.978161\pi\)
0.997647 0.0685562i \(-0.0218392\pi\)
\(14\) 1.09864 0.890504i 0.293623 0.237997i
\(15\) 0 0
\(16\) −3.65720 1.62016i −0.914299 0.405039i
\(17\) −4.46962 −1.08404 −0.542021 0.840365i \(-0.682340\pi\)
−0.542021 + 0.840365i \(0.682340\pi\)
\(18\) 0 0
\(19\) 7.55705i 1.73371i −0.498564 0.866853i \(-0.666139\pi\)
0.498564 0.866853i \(-0.333861\pi\)
\(20\) −3.10076 0.656077i −0.693350 0.146703i
\(21\) 0 0
\(22\) 0.703973 + 0.868509i 0.150088 + 0.185167i
\(23\) −0.839644 −0.175078 −0.0875390 0.996161i \(-0.527900\pi\)
−0.0875390 + 0.996161i \(0.527900\pi\)
\(24\) 0 0
\(25\) 2.48872 0.497744
\(26\) −0.440235 0.543129i −0.0863371 0.106516i
\(27\) 0 0
\(28\) 0.414007 1.95668i 0.0782399 0.369778i
\(29\) 2.76437i 0.513331i −0.966500 0.256665i \(-0.917376\pi\)
0.966500 0.256665i \(-0.0826238\pi\)
\(30\) 0 0
\(31\) −0.568664 −0.102135 −0.0510675 0.998695i \(-0.516262\pi\)
−0.0510675 + 0.998695i \(0.516262\pi\)
\(32\) −5.46069 + 1.47678i −0.965322 + 0.261061i
\(33\) 0 0
\(34\) −4.91049 + 3.98021i −0.842141 + 0.682600i
\(35\) 1.58470i 0.267864i
\(36\) 0 0
\(37\) 0.343650i 0.0564957i −0.999601 0.0282479i \(-0.991007\pi\)
0.999601 0.0282479i \(-0.00899277\pi\)
\(38\) −6.72958 8.30245i −1.09168 1.34684i
\(39\) 0 0
\(40\) −3.99084 + 2.04044i −0.631008 + 0.322622i
\(41\) 5.93014 0.926132 0.463066 0.886324i \(-0.346749\pi\)
0.463066 + 0.886324i \(0.346749\pi\)
\(42\) 0 0
\(43\) 3.16166i 0.482149i −0.970507 0.241074i \(-0.922500\pi\)
0.970507 0.241074i \(-0.0774998\pi\)
\(44\) 1.54682 + 0.327286i 0.233192 + 0.0493402i
\(45\) 0 0
\(46\) −0.922464 + 0.747706i −0.136010 + 0.110243i
\(47\) −4.80964 −0.701558 −0.350779 0.936458i \(-0.614083\pi\)
−0.350779 + 0.936458i \(0.614083\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.73420 2.21621i 0.386674 0.313420i
\(51\) 0 0
\(52\) −0.967316 0.204671i −0.134143 0.0283827i
\(53\) 4.36792i 0.599980i 0.953942 + 0.299990i \(0.0969833\pi\)
−0.953942 + 0.299990i \(0.903017\pi\)
\(54\) 0 0
\(55\) 1.25276 0.168922
\(56\) −1.28759 2.51836i −0.172061 0.336529i
\(57\) 0 0
\(58\) −2.46168 3.03704i −0.323235 0.398783i
\(59\) 4.50798i 0.586889i 0.955976 + 0.293445i \(0.0948016\pi\)
−0.955976 + 0.293445i \(0.905198\pi\)
\(60\) 0 0
\(61\) 5.40103i 0.691531i −0.938321 0.345766i \(-0.887619\pi\)
0.938321 0.345766i \(-0.112381\pi\)
\(62\) −0.624755 + 0.506397i −0.0793440 + 0.0643125i
\(63\) 0 0
\(64\) −4.68423 + 6.48521i −0.585529 + 0.810651i
\(65\) −0.783423 −0.0971716
\(66\) 0 0
\(67\) 7.57396i 0.925307i 0.886539 + 0.462653i \(0.153103\pi\)
−0.886539 + 0.462653i \(0.846897\pi\)
\(68\) −1.85045 + 8.74561i −0.224400 + 1.06056i
\(69\) 0 0
\(70\) −1.41118 1.74101i −0.168669 0.208091i
\(71\) −9.52886 −1.13087 −0.565434 0.824794i \(-0.691291\pi\)
−0.565434 + 0.824794i \(0.691291\pi\)
\(72\) 0 0
\(73\) 14.1344 1.65431 0.827155 0.561975i \(-0.189958\pi\)
0.827155 + 0.561975i \(0.189958\pi\)
\(74\) −0.306022 0.377547i −0.0355743 0.0438889i
\(75\) 0 0
\(76\) −14.7867 3.12867i −1.69615 0.358883i
\(77\) 0.790533i 0.0900896i
\(78\) 0 0
\(79\) −3.71341 −0.417791 −0.208896 0.977938i \(-0.566987\pi\)
−0.208896 + 0.977938i \(0.566987\pi\)
\(80\) −2.56747 + 5.79557i −0.287052 + 0.647964i
\(81\) 0 0
\(82\) 6.51507 5.28081i 0.719469 0.583168i
\(83\) 7.30905i 0.802273i −0.916018 0.401136i \(-0.868615\pi\)
0.916018 0.401136i \(-0.131385\pi\)
\(84\) 0 0
\(85\) 7.08301i 0.768260i
\(86\) −2.81547 3.47352i −0.303600 0.374559i
\(87\) 0 0
\(88\) 1.99084 1.01788i 0.212225 0.108507i
\(89\) −11.5305 −1.22223 −0.611114 0.791543i \(-0.709278\pi\)
−0.611114 + 0.791543i \(0.709278\pi\)
\(90\) 0 0
\(91\) 0.494366i 0.0518236i
\(92\) −0.347618 + 1.64292i −0.0362417 + 0.171286i
\(93\) 0 0
\(94\) −5.28405 + 4.28300i −0.545008 + 0.441758i
\(95\) −11.9757 −1.22868
\(96\) 0 0
\(97\) 1.75839 0.178538 0.0892689 0.996008i \(-0.471547\pi\)
0.0892689 + 0.996008i \(0.471547\pi\)
\(98\) 1.09864 0.890504i 0.110979 0.0899544i
\(99\) 0 0
\(100\) 1.03035 4.86963i 0.103035 0.486963i
\(101\) 17.5623i 1.74752i −0.486362 0.873758i \(-0.661676\pi\)
0.486362 0.873758i \(-0.338324\pi\)
\(102\) 0 0
\(103\) 8.30641 0.818454 0.409227 0.912432i \(-0.365798\pi\)
0.409227 + 0.912432i \(0.365798\pi\)
\(104\) −1.24499 + 0.636540i −0.122081 + 0.0624178i
\(105\) 0 0
\(106\) 3.88965 + 4.79876i 0.377796 + 0.466096i
\(107\) 18.7750i 1.81505i 0.419996 + 0.907526i \(0.362032\pi\)
−0.419996 + 0.907526i \(0.637968\pi\)
\(108\) 0 0
\(109\) 0.165074i 0.0158113i 0.999969 + 0.00790563i \(0.00251646\pi\)
−0.999969 + 0.00790563i \(0.997484\pi\)
\(110\) 1.37633 1.11559i 0.131228 0.106367i
\(111\) 0 0
\(112\) −3.65720 1.62016i −0.345573 0.153090i
\(113\) 10.8486 1.02055 0.510275 0.860012i \(-0.329544\pi\)
0.510275 + 0.860012i \(0.329544\pi\)
\(114\) 0 0
\(115\) 1.33059i 0.124078i
\(116\) −5.40899 1.14447i −0.502212 0.106261i
\(117\) 0 0
\(118\) 4.01437 + 4.95263i 0.369553 + 0.455927i
\(119\) −4.46962 −0.409729
\(120\) 0 0
\(121\) 10.3751 0.943187
\(122\) −4.80964 5.93377i −0.435444 0.537219i
\(123\) 0 0
\(124\) −0.235431 + 1.11269i −0.0211423 + 0.0999229i
\(125\) 11.8674i 1.06145i
\(126\) 0 0
\(127\) 21.0320 1.86629 0.933145 0.359499i \(-0.117052\pi\)
0.933145 + 0.359499i \(0.117052\pi\)
\(128\) 0.628830 + 11.2962i 0.0555813 + 0.998454i
\(129\) 0 0
\(130\) −0.860697 + 0.697641i −0.0754881 + 0.0611871i
\(131\) 5.17978i 0.452560i −0.974062 0.226280i \(-0.927344\pi\)
0.974062 0.226280i \(-0.0726564\pi\)
\(132\) 0 0
\(133\) 7.55705i 0.655279i
\(134\) 6.74464 + 8.32104i 0.582648 + 0.718828i
\(135\) 0 0
\(136\) 5.75502 + 11.2561i 0.493489 + 0.965201i
\(137\) 8.19905 0.700492 0.350246 0.936658i \(-0.386098\pi\)
0.350246 + 0.936658i \(0.386098\pi\)
\(138\) 0 0
\(139\) 3.89763i 0.330593i −0.986244 0.165296i \(-0.947142\pi\)
0.986244 0.165296i \(-0.0528581\pi\)
\(140\) −3.10076 0.656077i −0.262062 0.0554486i
\(141\) 0 0
\(142\) −10.4688 + 8.48548i −0.878518 + 0.712086i
\(143\) 0.390813 0.0326814
\(144\) 0 0
\(145\) −4.38070 −0.363798
\(146\) 15.5286 12.5868i 1.28516 1.04169i
\(147\) 0 0
\(148\) −0.672414 0.142273i −0.0552721 0.0116948i
\(149\) 3.71034i 0.303963i −0.988383 0.151981i \(-0.951435\pi\)
0.988383 0.151981i \(-0.0485654\pi\)
\(150\) 0 0
\(151\) −4.08172 −0.332165 −0.166083 0.986112i \(-0.553112\pi\)
−0.166083 + 0.986112i \(0.553112\pi\)
\(152\) −19.0313 + 9.73036i −1.54365 + 0.789237i
\(153\) 0 0
\(154\) 0.703973 + 0.868509i 0.0567277 + 0.0699865i
\(155\) 0.901163i 0.0723832i
\(156\) 0 0
\(157\) 9.64250i 0.769555i 0.923009 + 0.384778i \(0.125722\pi\)
−0.923009 + 0.384778i \(0.874278\pi\)
\(158\) −4.07969 + 3.30680i −0.324563 + 0.263075i
\(159\) 0 0
\(160\) 2.34026 + 8.65356i 0.185014 + 0.684124i
\(161\) −0.839644 −0.0661732
\(162\) 0 0
\(163\) 6.79301i 0.532069i −0.963963 0.266035i \(-0.914286\pi\)
0.963963 0.266035i \(-0.0857136\pi\)
\(164\) 2.45512 11.6034i 0.191712 0.906072i
\(165\) 0 0
\(166\) −6.50874 8.03000i −0.505176 0.623249i
\(167\) −5.35614 −0.414471 −0.207235 0.978291i \(-0.566447\pi\)
−0.207235 + 0.978291i \(0.566447\pi\)
\(168\) 0 0
\(169\) 12.7556 0.981200
\(170\) 6.30745 + 7.78166i 0.483759 + 0.596826i
\(171\) 0 0
\(172\) −6.18636 1.30895i −0.471705 0.0998064i
\(173\) 15.3862i 1.16979i −0.811110 0.584894i \(-0.801136\pi\)
0.811110 0.584894i \(-0.198864\pi\)
\(174\) 0 0
\(175\) 2.48872 0.188129
\(176\) 1.28079 2.89114i 0.0965431 0.217928i
\(177\) 0 0
\(178\) −12.6678 + 10.2679i −0.949492 + 0.769614i
\(179\) 19.5360i 1.46019i 0.683347 + 0.730094i \(0.260524\pi\)
−0.683347 + 0.730094i \(0.739476\pi\)
\(180\) 0 0
\(181\) 1.07045i 0.0795657i −0.999208 0.0397828i \(-0.987333\pi\)
0.999208 0.0397828i \(-0.0126666\pi\)
\(182\) −0.440235 0.543129i −0.0326324 0.0402594i
\(183\) 0 0
\(184\) 1.08112 + 2.11452i 0.0797009 + 0.155885i
\(185\) −0.544583 −0.0400386
\(186\) 0 0
\(187\) 3.53338i 0.258386i
\(188\) −1.99122 + 9.41093i −0.145225 + 0.686362i
\(189\) 0 0
\(190\) −13.1569 + 10.6644i −0.954503 + 0.773675i
\(191\) 17.7019 1.28086 0.640431 0.768016i \(-0.278756\pi\)
0.640431 + 0.768016i \(0.278756\pi\)
\(192\) 0 0
\(193\) −10.5405 −0.758719 −0.379359 0.925249i \(-0.623856\pi\)
−0.379359 + 0.925249i \(0.623856\pi\)
\(194\) 1.93184 1.56586i 0.138698 0.112422i
\(195\) 0 0
\(196\) 0.414007 1.95668i 0.0295719 0.139763i
\(197\) 15.1573i 1.07991i −0.841692 0.539957i \(-0.818440\pi\)
0.841692 0.539957i \(-0.181560\pi\)
\(198\) 0 0
\(199\) 19.8834 1.40950 0.704750 0.709456i \(-0.251059\pi\)
0.704750 + 0.709456i \(0.251059\pi\)
\(200\) −3.20444 6.26748i −0.226588 0.443178i
\(201\) 0 0
\(202\) −15.6393 19.2946i −1.10038 1.35756i
\(203\) 2.76437i 0.194021i
\(204\) 0 0
\(205\) 9.39751i 0.656350i
\(206\) 9.12572 7.39688i 0.635819 0.515365i
\(207\) 0 0
\(208\) −0.800950 + 1.80799i −0.0555359 + 0.125362i
\(209\) 5.97410 0.413237
\(210\) 0 0
\(211\) 26.0319i 1.79211i 0.443942 + 0.896055i \(0.353580\pi\)
−0.443942 + 0.896055i \(0.646420\pi\)
\(212\) 8.54662 + 1.80835i 0.586984 + 0.124198i
\(213\) 0 0
\(214\) 16.7192 + 20.6270i 1.14290 + 1.41003i
\(215\) −5.01029 −0.341699
\(216\) 0 0
\(217\) −0.568664 −0.0386034
\(218\) 0.146999 + 0.181357i 0.00995605 + 0.0122830i
\(219\) 0 0
\(220\) 0.518651 2.45125i 0.0349674 0.165263i
\(221\) 2.20963i 0.148635i
\(222\) 0 0
\(223\) 21.1231 1.41451 0.707255 0.706959i \(-0.249933\pi\)
0.707255 + 0.706959i \(0.249933\pi\)
\(224\) −5.46069 + 1.47678i −0.364858 + 0.0986717i
\(225\) 0 0
\(226\) 11.9187 9.66071i 0.792817 0.642621i
\(227\) 9.07343i 0.602224i 0.953589 + 0.301112i \(0.0973579\pi\)
−0.953589 + 0.301112i \(0.902642\pi\)
\(228\) 0 0
\(229\) 15.8950i 1.05037i 0.850987 + 0.525187i \(0.176005\pi\)
−0.850987 + 0.525187i \(0.823995\pi\)
\(230\) 1.18489 + 1.46183i 0.0781295 + 0.0963903i
\(231\) 0 0
\(232\) −6.96167 + 3.55937i −0.457056 + 0.233684i
\(233\) 25.2633 1.65505 0.827527 0.561426i \(-0.189747\pi\)
0.827527 + 0.561426i \(0.189747\pi\)
\(234\) 0 0
\(235\) 7.62185i 0.497194i
\(236\) 8.82068 + 1.86633i 0.574177 + 0.121488i
\(237\) 0 0
\(238\) −4.91049 + 3.98021i −0.318299 + 0.257999i
\(239\) −3.13797 −0.202979 −0.101489 0.994837i \(-0.532361\pi\)
−0.101489 + 0.994837i \(0.532361\pi\)
\(240\) 0 0
\(241\) 7.05736 0.454604 0.227302 0.973824i \(-0.427009\pi\)
0.227302 + 0.973824i \(0.427009\pi\)
\(242\) 11.3984 9.23903i 0.732718 0.593907i
\(243\) 0 0
\(244\) −10.5681 2.23606i −0.676553 0.143149i
\(245\) 1.58470i 0.101243i
\(246\) 0 0
\(247\) −3.73595 −0.237713
\(248\) 0.732205 + 1.43210i 0.0464951 + 0.0909384i
\(249\) 0 0
\(250\) −10.5680 13.0380i −0.668376 0.824593i
\(251\) 12.8195i 0.809158i 0.914503 + 0.404579i \(0.132582\pi\)
−0.914503 + 0.404579i \(0.867418\pi\)
\(252\) 0 0
\(253\) 0.663767i 0.0417307i
\(254\) 23.1066 18.7291i 1.44983 1.17517i
\(255\) 0 0
\(256\) 10.7502 + 11.8505i 0.671886 + 0.740654i
\(257\) 11.1680 0.696639 0.348319 0.937376i \(-0.386752\pi\)
0.348319 + 0.937376i \(0.386752\pi\)
\(258\) 0 0
\(259\) 0.343650i 0.0213534i
\(260\) −0.324342 + 1.53291i −0.0201148 + 0.0950669i
\(261\) 0 0
\(262\) −4.61262 5.69070i −0.284968 0.351573i
\(263\) −15.1277 −0.932817 −0.466408 0.884570i \(-0.654452\pi\)
−0.466408 + 0.884570i \(0.654452\pi\)
\(264\) 0 0
\(265\) 6.92185 0.425206
\(266\) −6.72958 8.30245i −0.412617 0.509056i
\(267\) 0 0
\(268\) 14.8198 + 3.13567i 0.905265 + 0.191542i
\(269\) 4.70567i 0.286910i −0.989657 0.143455i \(-0.954179\pi\)
0.989657 0.143455i \(-0.0458212\pi\)
\(270\) 0 0
\(271\) −19.6194 −1.19179 −0.595897 0.803061i \(-0.703203\pi\)
−0.595897 + 0.803061i \(0.703203\pi\)
\(272\) 16.3463 + 7.24148i 0.991138 + 0.439079i
\(273\) 0 0
\(274\) 9.00778 7.30129i 0.544180 0.441087i
\(275\) 1.96742i 0.118640i
\(276\) 0 0
\(277\) 10.0661i 0.604811i −0.953179 0.302406i \(-0.902210\pi\)
0.953179 0.302406i \(-0.0977897\pi\)
\(278\) −3.47086 4.28208i −0.208168 0.256822i
\(279\) 0 0
\(280\) −3.99084 + 2.04044i −0.238499 + 0.121940i
\(281\) 28.6669 1.71013 0.855063 0.518525i \(-0.173519\pi\)
0.855063 + 0.518525i \(0.173519\pi\)
\(282\) 0 0
\(283\) 8.69308i 0.516750i −0.966045 0.258375i \(-0.916813\pi\)
0.966045 0.258375i \(-0.0831870\pi\)
\(284\) −3.94501 + 18.6449i −0.234093 + 1.10637i
\(285\) 0 0
\(286\) 0.429361 0.348020i 0.0253887 0.0205789i
\(287\) 5.93014 0.350045
\(288\) 0 0
\(289\) 2.97746 0.175145
\(290\) −4.81280 + 3.90103i −0.282618 + 0.229077i
\(291\) 0 0
\(292\) 5.85174 27.6565i 0.342447 1.61848i
\(293\) 23.9254i 1.39774i 0.715250 + 0.698868i \(0.246313\pi\)
−0.715250 + 0.698868i \(0.753687\pi\)
\(294\) 0 0
\(295\) 7.14381 0.415928
\(296\) −0.865434 + 0.442480i −0.0503023 + 0.0257186i
\(297\) 0 0
\(298\) −3.30407 4.07631i −0.191400 0.236134i
\(299\) 0.415091i 0.0240054i
\(300\) 0 0
\(301\) 3.16166i 0.182235i
\(302\) −4.48432 + 3.63478i −0.258044 + 0.209158i
\(303\) 0 0
\(304\) −12.2436 + 27.6376i −0.702219 + 1.58513i
\(305\) −8.55903 −0.490089
\(306\) 0 0
\(307\) 7.88720i 0.450146i −0.974342 0.225073i \(-0.927738\pi\)
0.974342 0.225073i \(-0.0722621\pi\)
\(308\) 1.54682 + 0.327286i 0.0881383 + 0.0186489i
\(309\) 0 0
\(310\) 0.802489 + 0.990051i 0.0455783 + 0.0562311i
\(311\) −34.7041 −1.96789 −0.983944 0.178480i \(-0.942882\pi\)
−0.983944 + 0.178480i \(0.942882\pi\)
\(312\) 0 0
\(313\) −11.2387 −0.635249 −0.317624 0.948217i \(-0.602885\pi\)
−0.317624 + 0.948217i \(0.602885\pi\)
\(314\) 8.58668 + 10.5936i 0.484574 + 0.597832i
\(315\) 0 0
\(316\) −1.53738 + 7.26596i −0.0864842 + 0.408742i
\(317\) 30.2902i 1.70127i 0.525761 + 0.850633i \(0.323781\pi\)
−0.525761 + 0.850633i \(0.676219\pi\)
\(318\) 0 0
\(319\) 2.18533 0.122355
\(320\) 10.2771 + 7.42312i 0.574509 + 0.414965i
\(321\) 0 0
\(322\) −0.922464 + 0.747706i −0.0514069 + 0.0416680i
\(323\) 33.7771i 1.87941i
\(324\) 0 0
\(325\) 1.23034i 0.0682469i
\(326\) −6.04920 7.46305i −0.335034 0.413340i
\(327\) 0 0
\(328\) −7.63558 14.9342i −0.421604 0.824603i
\(329\) −4.80964 −0.265164
\(330\) 0 0
\(331\) 20.2855i 1.11499i −0.830180 0.557495i \(-0.811763\pi\)
0.830180 0.557495i \(-0.188237\pi\)
\(332\) −14.3015 3.02600i −0.784896 0.166073i
\(333\) 0 0
\(334\) −5.88445 + 4.76966i −0.321983 + 0.260984i
\(335\) 12.0025 0.655765
\(336\) 0 0
\(337\) 2.73774 0.149134 0.0745671 0.997216i \(-0.476242\pi\)
0.0745671 + 0.997216i \(0.476242\pi\)
\(338\) 14.0138 11.3589i 0.762249 0.617843i
\(339\) 0 0
\(340\) 13.8592 + 2.93241i 0.751620 + 0.159032i
\(341\) 0.449548i 0.0243444i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −7.96219 + 4.07092i −0.429292 + 0.219489i
\(345\) 0 0
\(346\) −13.7014 16.9038i −0.736593 0.908754i
\(347\) 5.91592i 0.317583i 0.987312 + 0.158792i \(0.0507598\pi\)
−0.987312 + 0.158792i \(0.949240\pi\)
\(348\) 0 0
\(349\) 26.5968i 1.42370i −0.702333 0.711848i \(-0.747858\pi\)
0.702333 0.711848i \(-0.252142\pi\)
\(350\) 2.73420 2.21621i 0.146149 0.118462i
\(351\) 0 0
\(352\) −1.16745 4.31686i −0.0622251 0.230089i
\(353\) 21.8800 1.16455 0.582277 0.812990i \(-0.302162\pi\)
0.582277 + 0.812990i \(0.302162\pi\)
\(354\) 0 0
\(355\) 15.1004i 0.801446i
\(356\) −4.77369 + 22.5615i −0.253005 + 1.19575i
\(357\) 0 0
\(358\) 17.3969 + 21.4630i 0.919453 + 1.13435i
\(359\) 18.4834 0.975519 0.487759 0.872978i \(-0.337814\pi\)
0.487759 + 0.872978i \(0.337814\pi\)
\(360\) 0 0
\(361\) −38.1090 −2.00573
\(362\) −0.953237 1.17603i −0.0501010 0.0618109i
\(363\) 0 0
\(364\) −0.967316 0.204671i −0.0507011 0.0107277i
\(365\) 22.3989i 1.17241i
\(366\) 0 0
\(367\) −32.8686 −1.71573 −0.857863 0.513878i \(-0.828208\pi\)
−0.857863 + 0.513878i \(0.828208\pi\)
\(368\) 3.07074 + 1.36036i 0.160074 + 0.0709134i
\(369\) 0 0
\(370\) −0.598299 + 0.484953i −0.0311041 + 0.0252115i
\(371\) 4.36792i 0.226771i
\(372\) 0 0
\(373\) 4.11202i 0.212912i 0.994317 + 0.106456i \(0.0339504\pi\)
−0.994317 + 0.106456i \(0.966050\pi\)
\(374\) −3.14649 3.88190i −0.162701 0.200728i
\(375\) 0 0
\(376\) 6.19283 + 12.1124i 0.319371 + 0.624649i
\(377\) −1.36661 −0.0703840
\(378\) 0 0
\(379\) 10.6063i 0.544811i 0.962183 + 0.272406i \(0.0878192\pi\)
−0.962183 + 0.272406i \(0.912181\pi\)
\(380\) −4.95801 + 23.4326i −0.254340 + 1.20206i
\(381\) 0 0
\(382\) 19.4479 15.7636i 0.995042 0.806534i
\(383\) 0.193380 0.00988125 0.00494063 0.999988i \(-0.498427\pi\)
0.00494063 + 0.999988i \(0.498427\pi\)
\(384\) 0 0
\(385\) 1.25276 0.0638466
\(386\) −11.5801 + 9.38631i −0.589413 + 0.477751i
\(387\) 0 0
\(388\) 0.727987 3.44062i 0.0369579 0.174671i
\(389\) 30.2102i 1.53172i −0.643008 0.765859i \(-0.722314\pi\)
0.643008 0.765859i \(-0.277686\pi\)
\(390\) 0 0
\(391\) 3.75289 0.189792
\(392\) −1.28759 2.51836i −0.0650330 0.127196i
\(393\) 0 0
\(394\) −13.4976 16.6524i −0.680002 0.838935i
\(395\) 5.88465i 0.296089i
\(396\) 0 0
\(397\) 19.1773i 0.962480i −0.876589 0.481240i \(-0.840186\pi\)
0.876589 0.481240i \(-0.159814\pi\)
\(398\) 21.8447 17.7063i 1.09497 0.887535i
\(399\) 0 0
\(400\) −9.10174 4.03212i −0.455087 0.201606i
\(401\) 33.6813 1.68196 0.840981 0.541065i \(-0.181979\pi\)
0.840981 + 0.541065i \(0.181979\pi\)
\(402\) 0 0
\(403\) 0.281128i 0.0140040i
\(404\) −34.3638 7.27091i −1.70966 0.361741i
\(405\) 0 0
\(406\) −2.46168 3.03704i −0.122171 0.150726i
\(407\) 0.271667 0.0134660
\(408\) 0 0
\(409\) 15.0414 0.743751 0.371876 0.928283i \(-0.378715\pi\)
0.371876 + 0.928283i \(0.378715\pi\)
\(410\) −8.36851 10.3244i −0.413291 0.509888i
\(411\) 0 0
\(412\) 3.43891 16.2530i 0.169423 0.800727i
\(413\) 4.50798i 0.221823i
\(414\) 0 0
\(415\) −11.5827 −0.568571
\(416\) 0.730071 + 2.69958i 0.0357947 + 0.132358i
\(417\) 0 0
\(418\) 6.56336 5.31996i 0.321025 0.260208i
\(419\) 15.8239i 0.773048i 0.922279 + 0.386524i \(0.126324\pi\)
−0.922279 + 0.386524i \(0.873676\pi\)
\(420\) 0 0
\(421\) 2.62118i 0.127748i −0.997958 0.0638742i \(-0.979654\pi\)
0.997958 0.0638742i \(-0.0203457\pi\)
\(422\) 23.1815 + 28.5996i 1.12846 + 1.39221i
\(423\) 0 0
\(424\) 11.0000 5.62408i 0.534206 0.273129i
\(425\) −11.1236 −0.539575
\(426\) 0 0
\(427\) 5.40103i 0.261374i
\(428\) 36.7368 + 7.77299i 1.77574 + 0.375722i
\(429\) 0 0
\(430\) −5.50449 + 4.46168i −0.265450 + 0.215161i
\(431\) 21.5464 1.03785 0.518927 0.854819i \(-0.326332\pi\)
0.518927 + 0.854819i \(0.326332\pi\)
\(432\) 0 0
\(433\) 12.4258 0.597145 0.298572 0.954387i \(-0.403490\pi\)
0.298572 + 0.954387i \(0.403490\pi\)
\(434\) −0.624755 + 0.506397i −0.0299892 + 0.0243079i
\(435\) 0 0
\(436\) 0.322998 + 0.0683419i 0.0154688 + 0.00327298i
\(437\) 6.34523i 0.303534i
\(438\) 0 0
\(439\) −24.2735 −1.15851 −0.579256 0.815146i \(-0.696657\pi\)
−0.579256 + 0.815146i \(0.696657\pi\)
\(440\) −1.61304 3.15490i −0.0768986 0.150404i
\(441\) 0 0
\(442\) 1.96768 + 2.42758i 0.0935930 + 0.115468i
\(443\) 0.931584i 0.0442609i −0.999755 0.0221304i \(-0.992955\pi\)
0.999755 0.0221304i \(-0.00704492\pi\)
\(444\) 0 0
\(445\) 18.2724i 0.866193i
\(446\) 23.2067 18.8102i 1.09887 0.890690i
\(447\) 0 0
\(448\) −4.68423 + 6.48521i −0.221309 + 0.306397i
\(449\) −20.8693 −0.984883 −0.492441 0.870346i \(-0.663895\pi\)
−0.492441 + 0.870346i \(0.663895\pi\)
\(450\) 0 0
\(451\) 4.68797i 0.220748i
\(452\) 4.49139 21.2272i 0.211257 0.998444i
\(453\) 0 0
\(454\) 8.07992 + 9.96840i 0.379209 + 0.467840i
\(455\) −0.783423 −0.0367274
\(456\) 0 0
\(457\) −31.3346 −1.46577 −0.732885 0.680353i \(-0.761827\pi\)
−0.732885 + 0.680353i \(0.761827\pi\)
\(458\) 14.1546 + 17.4629i 0.661401 + 0.815987i
\(459\) 0 0
\(460\) 2.60353 + 0.550871i 0.121390 + 0.0256845i
\(461\) 1.90910i 0.0889156i −0.999011 0.0444578i \(-0.985844\pi\)
0.999011 0.0444578i \(-0.0141560\pi\)
\(462\) 0 0
\(463\) 18.6081 0.864793 0.432397 0.901683i \(-0.357668\pi\)
0.432397 + 0.901683i \(0.357668\pi\)
\(464\) −4.47872 + 10.1098i −0.207919 + 0.469338i
\(465\) 0 0
\(466\) 27.7552 22.4971i 1.28573 1.04216i
\(467\) 17.7972i 0.823554i −0.911285 0.411777i \(-0.864908\pi\)
0.911285 0.411777i \(-0.135092\pi\)
\(468\) 0 0
\(469\) 7.57396i 0.349733i
\(470\) 6.78728 + 8.37364i 0.313074 + 0.386247i
\(471\) 0 0
\(472\) 11.3527 5.80442i 0.522550 0.267170i
\(473\) 2.49940 0.114922
\(474\) 0 0
\(475\) 18.8074i 0.862941i
\(476\) −1.85045 + 8.74561i −0.0848153 + 0.400854i
\(477\) 0 0
\(478\) −3.44749 + 2.79438i −0.157685 + 0.127812i
\(479\) −21.6737 −0.990294 −0.495147 0.868809i \(-0.664886\pi\)
−0.495147 + 0.868809i \(0.664886\pi\)
\(480\) 0 0
\(481\) −0.169889 −0.00774627
\(482\) 7.75347 6.28460i 0.353161 0.286256i
\(483\) 0 0
\(484\) 4.29534 20.3007i 0.195243 0.922758i
\(485\) 2.78653i 0.126530i
\(486\) 0 0
\(487\) −38.6259 −1.75030 −0.875152 0.483848i \(-0.839239\pi\)
−0.875152 + 0.483848i \(0.839239\pi\)
\(488\) −13.6017 + 6.95431i −0.615721 + 0.314807i
\(489\) 0 0
\(490\) −1.41118 1.74101i −0.0637508 0.0786509i
\(491\) 17.9010i 0.807863i 0.914789 + 0.403931i \(0.132357\pi\)
−0.914789 + 0.403931i \(0.867643\pi\)
\(492\) 0 0
\(493\) 12.3557i 0.556472i
\(494\) −4.10445 + 3.32687i −0.184668 + 0.149683i
\(495\) 0 0
\(496\) 2.07972 + 0.921325i 0.0933820 + 0.0413687i
\(497\) −9.52886 −0.427428
\(498\) 0 0
\(499\) 24.3201i 1.08872i 0.838853 + 0.544359i \(0.183227\pi\)
−0.838853 + 0.544359i \(0.816773\pi\)
\(500\) −23.2207 4.91318i −1.03846 0.219724i
\(501\) 0 0
\(502\) 11.4158 + 14.0840i 0.509512 + 0.628598i
\(503\) 36.3076 1.61888 0.809438 0.587205i \(-0.199772\pi\)
0.809438 + 0.587205i \(0.199772\pi\)
\(504\) 0 0
\(505\) −27.8310 −1.23846
\(506\) −0.591087 0.729239i −0.0262770 0.0324186i
\(507\) 0 0
\(508\) 8.70740 41.1530i 0.386328 1.82587i
\(509\) 3.12375i 0.138458i 0.997601 + 0.0692290i \(0.0220539\pi\)
−0.997601 + 0.0692290i \(0.977946\pi\)
\(510\) 0 0
\(511\) 14.1344 0.625270
\(512\) 22.3634 + 3.44629i 0.988333 + 0.152306i
\(513\) 0 0
\(514\) 12.2695 9.94512i 0.541186 0.438660i
\(515\) 13.1632i 0.580039i
\(516\) 0 0
\(517\) 3.80218i 0.167220i
\(518\) −0.306022 0.377547i −0.0134458 0.0165885i
\(519\) 0 0
\(520\) 1.00873 + 1.97294i 0.0442355 + 0.0865190i
\(521\) −1.68044 −0.0736213 −0.0368107 0.999322i \(-0.511720\pi\)
−0.0368107 + 0.999322i \(0.511720\pi\)
\(522\) 0 0
\(523\) 26.5738i 1.16199i −0.813906 0.580996i \(-0.802663\pi\)
0.813906 0.580996i \(-0.197337\pi\)
\(524\) −10.1352 2.14446i −0.442757 0.0936814i
\(525\) 0 0
\(526\) −16.6199 + 13.4713i −0.724662 + 0.587377i
\(527\) 2.54171 0.110719
\(528\) 0 0
\(529\) −22.2950 −0.969348
\(530\) 7.60460 6.16393i 0.330323 0.267744i
\(531\) 0 0
\(532\) −14.7867 3.12867i −0.641086 0.135645i
\(533\) 2.93166i 0.126984i
\(534\) 0 0
\(535\) 29.7529 1.28633
\(536\) 19.0739 9.75214i 0.823868 0.421228i
\(537\) 0 0
\(538\) −4.19041 5.16982i −0.180662 0.222887i
\(539\) 0.790533i 0.0340507i
\(540\) 0 0
\(541\) 26.0022i 1.11792i 0.829194 + 0.558962i \(0.188800\pi\)
−0.829194 + 0.558962i \(0.811200\pi\)
\(542\) −21.5546 + 17.4712i −0.925850 + 0.750450i
\(543\) 0 0
\(544\) 24.4072 6.60065i 1.04645 0.283001i
\(545\) 0.261594 0.0112054
\(546\) 0 0
\(547\) 13.4108i 0.573406i −0.958019 0.286703i \(-0.907441\pi\)
0.958019 0.286703i \(-0.0925594\pi\)
\(548\) 3.39446 16.0429i 0.145004 0.685320i
\(549\) 0 0
\(550\) 1.75199 + 2.16148i 0.0747051 + 0.0921656i
\(551\) −20.8905 −0.889964
\(552\) 0 0
\(553\) −3.71341 −0.157910
\(554\) −8.96387 11.0590i −0.380838 0.469850i
\(555\) 0 0
\(556\) −7.62642 1.61365i −0.323432 0.0684338i
\(557\) 38.9728i 1.65133i −0.564161 0.825665i \(-0.690800\pi\)
0.564161 0.825665i \(-0.309200\pi\)
\(558\) 0 0
\(559\) −1.56302 −0.0661086
\(560\) −2.56747 + 5.79557i −0.108495 + 0.244907i
\(561\) 0 0
\(562\) 31.4945 25.5280i 1.32852 1.07683i
\(563\) 15.8415i 0.667642i −0.942637 0.333821i \(-0.891662\pi\)
0.942637 0.333821i \(-0.108338\pi\)
\(564\) 0 0
\(565\) 17.1918i 0.723264i
\(566\) −7.74122 9.55054i −0.325388 0.401439i
\(567\) 0 0
\(568\) 12.2692 + 23.9971i 0.514806 + 1.00689i
\(569\) −17.4790 −0.732758 −0.366379 0.930466i \(-0.619403\pi\)
−0.366379 + 0.930466i \(0.619403\pi\)
\(570\) 0 0
\(571\) 11.4195i 0.477893i −0.971033 0.238946i \(-0.923198\pi\)
0.971033 0.238946i \(-0.0768020\pi\)
\(572\) 0.161799 0.764696i 0.00676516 0.0319735i
\(573\) 0 0
\(574\) 6.51507 5.28081i 0.271934 0.220417i
\(575\) −2.08964 −0.0871439
\(576\) 0 0
\(577\) 27.4108 1.14113 0.570564 0.821253i \(-0.306725\pi\)
0.570564 + 0.821253i \(0.306725\pi\)
\(578\) 3.27115 2.65144i 0.136062 0.110285i
\(579\) 0 0
\(580\) −1.81364 + 8.57164i −0.0753073 + 0.355918i
\(581\) 7.30905i 0.303231i
\(582\) 0 0
\(583\) −3.45299 −0.143008
\(584\) −18.1993 35.5955i −0.753093 1.47295i
\(585\) 0 0
\(586\) 21.3057 + 26.2853i 0.880128 + 1.08584i
\(587\) 23.8334i 0.983709i −0.870677 0.491855i \(-0.836319\pi\)
0.870677 0.491855i \(-0.163681\pi\)
\(588\) 0 0
\(589\) 4.29742i 0.177072i
\(590\) 7.84845 6.36159i 0.323116 0.261902i
\(591\) 0 0
\(592\) −0.556767 + 1.25680i −0.0228830 + 0.0516540i
\(593\) −28.0780 −1.15302 −0.576512 0.817088i \(-0.695587\pi\)
−0.576512 + 0.817088i \(0.695587\pi\)
\(594\) 0 0
\(595\) 7.08301i 0.290375i
\(596\) −7.25994 1.53610i −0.297379 0.0629213i
\(597\) 0 0
\(598\) 0.369640 + 0.456035i 0.0151157 + 0.0186487i
\(599\) −21.6780 −0.885738 −0.442869 0.896586i \(-0.646039\pi\)
−0.442869 + 0.896586i \(0.646039\pi\)
\(600\) 0 0
\(601\) 5.83369 0.237961 0.118981 0.992897i \(-0.462037\pi\)
0.118981 + 0.992897i \(0.462037\pi\)
\(602\) −2.81547 3.47352i −0.114750 0.141570i
\(603\) 0 0
\(604\) −1.68986 + 7.98661i −0.0687593 + 0.324971i
\(605\) 16.4414i 0.668437i
\(606\) 0 0
\(607\) −29.5358 −1.19882 −0.599410 0.800442i \(-0.704598\pi\)
−0.599410 + 0.800442i \(0.704598\pi\)
\(608\) 11.1601 + 41.2667i 0.452602 + 1.67358i
\(609\) 0 0
\(610\) −9.40327 + 7.62185i −0.380727 + 0.308600i
\(611\) 2.37772i 0.0961923i
\(612\) 0 0
\(613\) 19.5561i 0.789861i 0.918711 + 0.394931i \(0.129231\pi\)
−0.918711 + 0.394931i \(0.870769\pi\)
\(614\) −7.02358 8.66516i −0.283448 0.349698i
\(615\) 0 0
\(616\) 1.99084 1.01788i 0.0802134 0.0410116i
\(617\) 33.8435 1.36249 0.681244 0.732056i \(-0.261439\pi\)
0.681244 + 0.732056i \(0.261439\pi\)
\(618\) 0 0
\(619\) 20.6581i 0.830320i −0.909748 0.415160i \(-0.863726\pi\)
0.909748 0.415160i \(-0.136274\pi\)
\(620\) 1.76329 + 0.373088i 0.0708154 + 0.0149836i
\(621\) 0 0
\(622\) −38.1272 + 30.9041i −1.52876 + 1.23914i
\(623\) −11.5305 −0.461959
\(624\) 0 0
\(625\) −6.36268 −0.254507
\(626\) −12.3473 + 10.0081i −0.493495 + 0.400004i
\(627\) 0 0
\(628\) 18.8673 + 3.99206i 0.752887 + 0.159300i
\(629\) 1.53598i 0.0612437i
\(630\) 0 0
\(631\) −42.3648 −1.68651 −0.843257 0.537510i \(-0.819365\pi\)
−0.843257 + 0.537510i \(0.819365\pi\)
\(632\) 4.78134 + 9.35169i 0.190192 + 0.371990i
\(633\) 0 0
\(634\) 26.9735 + 33.2779i 1.07125 + 1.32163i
\(635\) 33.3295i 1.32264i
\(636\) 0 0
\(637\) 0.494366i 0.0195875i
\(638\) 2.40088 1.94604i 0.0950518 0.0770445i
\(639\) 0 0
\(640\) 17.9011 0.996509i 0.707605 0.0393905i
\(641\) 11.6219 0.459039 0.229519 0.973304i \(-0.426285\pi\)
0.229519 + 0.973304i \(0.426285\pi\)
\(642\) 0 0
\(643\) 40.4455i 1.59502i 0.603309 + 0.797508i \(0.293849\pi\)
−0.603309 + 0.797508i \(0.706151\pi\)
\(644\) −0.347618 + 1.64292i −0.0136981 + 0.0647399i
\(645\) 0 0
\(646\) 30.0786 + 37.1088i 1.18343 + 1.46002i
\(647\) −29.9913 −1.17908 −0.589540 0.807739i \(-0.700691\pi\)
−0.589540 + 0.807739i \(0.700691\pi\)
\(648\) 0 0
\(649\) −3.56371 −0.139888
\(650\) −1.09562 1.35169i −0.0429738 0.0530178i
\(651\) 0 0
\(652\) −13.2917 2.81235i −0.520545 0.110140i
\(653\) 14.9263i 0.584110i 0.956402 + 0.292055i \(0.0943390\pi\)
−0.956402 + 0.292055i \(0.905661\pi\)
\(654\) 0 0
\(655\) −8.20842 −0.320729
\(656\) −21.6877 9.60776i −0.846762 0.375120i
\(657\) 0 0
\(658\) −5.28405 + 4.28300i −0.205994 + 0.166969i
\(659\) 27.3581i 1.06572i 0.846204 + 0.532859i \(0.178883\pi\)
−0.846204 + 0.532859i \(0.821117\pi\)
\(660\) 0 0
\(661\) 14.3560i 0.558385i 0.960235 + 0.279192i \(0.0900667\pi\)
−0.960235 + 0.279192i \(0.909933\pi\)
\(662\) −18.0643 22.2864i −0.702088 0.866184i
\(663\) 0 0
\(664\) −18.4068 + 9.41105i −0.714322 + 0.365220i
\(665\) −11.9757 −0.464397
\(666\) 0 0
\(667\) 2.32109i 0.0898729i
\(668\) −2.21748 + 10.4803i −0.0857968 + 0.405493i
\(669\) 0 0
\(670\) 13.1864 10.6882i 0.509434 0.412923i
\(671\) 4.26970 0.164830
\(672\) 0 0
\(673\) 20.5132 0.790727 0.395364 0.918525i \(-0.370619\pi\)
0.395364 + 0.918525i \(0.370619\pi\)
\(674\) 3.00778 2.43797i 0.115856 0.0939071i
\(675\) 0 0
\(676\) 5.28090 24.9586i 0.203112 0.959948i
\(677\) 43.5656i 1.67436i 0.546926 + 0.837181i \(0.315798\pi\)
−0.546926 + 0.837181i \(0.684202\pi\)
\(678\) 0 0
\(679\) 1.75839 0.0674810
\(680\) 17.8375 9.12000i 0.684038 0.349736i
\(681\) 0 0
\(682\) −0.400324 0.493890i −0.0153292 0.0189120i
\(683\) 16.9585i 0.648898i −0.945903 0.324449i \(-0.894821\pi\)
0.945903 0.324449i \(-0.105179\pi\)
\(684\) 0 0
\(685\) 12.9931i 0.496439i
\(686\) 1.09864 0.890504i 0.0419462 0.0339996i
\(687\) 0 0
\(688\) −5.12239 + 11.5628i −0.195289 + 0.440828i
\(689\) 2.15935 0.0822647
\(690\) 0 0
\(691\) 27.7324i 1.05499i 0.849558 + 0.527495i \(0.176869\pi\)
−0.849558 + 0.527495i \(0.823131\pi\)
\(692\) −30.1058 6.36997i −1.14445 0.242150i
\(693\) 0 0
\(694\) 5.26815 + 6.49945i 0.199976 + 0.246716i
\(695\) −6.17659 −0.234291
\(696\) 0 0
\(697\) −26.5054 −1.00397
\(698\) −23.6846 29.2203i −0.896475 1.10600i
\(699\) 0 0
\(700\) 1.03035 4.86963i 0.0389434 0.184055i
\(701\) 29.5427i 1.11581i −0.829905 0.557905i \(-0.811605\pi\)
0.829905 0.557905i \(-0.188395\pi\)
\(702\) 0 0
\(703\) −2.59698 −0.0979470
\(704\) −5.12677 3.70304i −0.193223 0.139564i
\(705\) 0 0
\(706\) 24.0382 19.4842i 0.904688 0.733298i
\(707\) 17.5623i 0.660499i
\(708\) 0 0
\(709\) 45.9348i 1.72512i 0.505955 + 0.862560i \(0.331140\pi\)
−0.505955 + 0.862560i \(0.668860\pi\)
\(710\) 13.4470 + 16.5899i 0.504655 + 0.622606i
\(711\) 0 0
\(712\) 14.8465 + 29.0378i 0.556396 + 1.08824i
\(713\) 0.477476 0.0178816
\(714\) 0 0
\(715\) 0.619322i 0.0231613i
\(716\) 38.2257 + 8.08803i 1.42856 + 0.302264i
\(717\) 0 0
\(718\) 20.3066 16.4596i 0.757835 0.614266i
\(719\) 16.3756 0.610708 0.305354 0.952239i \(-0.401225\pi\)
0.305354 + 0.952239i \(0.401225\pi\)
\(720\) 0 0
\(721\) 8.30641 0.309347
\(722\) −41.8679 + 33.9362i −1.55816 + 1.26297i
\(723\) 0 0
\(724\) −2.09452 0.443172i −0.0778423 0.0164704i
\(725\) 6.87974i 0.255507i
\(726\) 0 0
\(727\) 3.43696 0.127470 0.0637348 0.997967i \(-0.479699\pi\)
0.0637348 + 0.997967i \(0.479699\pi\)
\(728\) −1.24499 + 0.636540i −0.0461424 + 0.0235917i
\(729\) 0 0
\(730\) −19.9463 24.6082i −0.738244 0.910791i
\(731\) 14.1314i 0.522669i
\(732\) 0 0
\(733\) 35.3171i 1.30447i 0.758019 + 0.652233i \(0.226167\pi\)
−0.758019 + 0.652233i \(0.773833\pi\)
\(734\) −36.1107 + 29.2696i −1.33287 + 1.08036i
\(735\) 0 0
\(736\) 4.58504 1.23997i 0.169007 0.0457060i
\(737\) −5.98747 −0.220551
\(738\) 0 0
\(739\) 41.3212i 1.52003i 0.649908 + 0.760013i \(0.274807\pi\)
−0.649908 + 0.760013i \(0.725193\pi\)
\(740\) −0.225461 + 1.06558i −0.00828811 + 0.0391713i
\(741\) 0 0
\(742\) 3.88965 + 4.79876i 0.142793 + 0.176168i
\(743\) −22.9110 −0.840524 −0.420262 0.907403i \(-0.638062\pi\)
−0.420262 + 0.907403i \(0.638062\pi\)
\(744\) 0 0
\(745\) −5.87978 −0.215418
\(746\) 3.66177 + 4.51762i 0.134067 + 0.165402i
\(747\) 0 0
\(748\) −6.91370 1.46284i −0.252790 0.0534868i
\(749\) 18.7750i 0.686025i
\(750\) 0 0
\(751\) −48.2764 −1.76163 −0.880815 0.473461i \(-0.843005\pi\)
−0.880815 + 0.473461i \(0.843005\pi\)
\(752\) 17.5898 + 7.79237i 0.641434 + 0.284159i
\(753\) 0 0
\(754\) −1.50141 + 1.21697i −0.0546781 + 0.0443195i
\(755\) 6.46830i 0.235406i
\(756\) 0 0
\(757\) 26.9389i 0.979112i −0.871972 0.489556i \(-0.837159\pi\)
0.871972 0.489556i \(-0.162841\pi\)
\(758\) 9.44498 + 11.6525i 0.343057 + 0.423239i
\(759\) 0 0
\(760\) 15.4197 + 30.1590i 0.559332 + 1.09398i
\(761\) −2.98366 −0.108158 −0.0540789 0.998537i \(-0.517222\pi\)
−0.0540789 + 0.998537i \(0.517222\pi\)
\(762\) 0 0
\(763\) 0.165074i 0.00597609i
\(764\) 7.32869 34.6369i 0.265143 1.25312i
\(765\) 0 0
\(766\) 0.212454 0.172206i 0.00767629 0.00622204i
\(767\) 2.22859 0.0804698
\(768\) 0 0
\(769\) 1.13907 0.0410760 0.0205380 0.999789i \(-0.493462\pi\)
0.0205380 + 0.999789i \(0.493462\pi\)
\(770\) 1.37633 1.11559i 0.0495994 0.0402030i
\(771\) 0 0
\(772\) −4.36382 + 20.6243i −0.157057 + 0.742285i
\(773\) 8.40051i 0.302145i −0.988523 0.151073i \(-0.951727\pi\)
0.988523 0.151073i \(-0.0482728\pi\)
\(774\) 0 0
\(775\) −1.41525 −0.0508371
\(776\) −2.26409 4.42826i −0.0812760 0.158965i
\(777\) 0 0
\(778\) −26.9023 33.1901i −0.964494 1.18992i
\(779\) 44.8143i 1.60564i
\(780\) 0 0
\(781\) 7.53288i 0.269548i
\(782\) 4.12306 3.34196i 0.147440 0.119508i
\(783\) 0 0
\(784\) −3.65720 1.62016i −0.130614 0.0578628i
\(785\) 15.2805 0.545384