Properties

Label 475.2.e.g.201.3
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.3
Root \(1.05958 - 1.83525i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.235942 + 0.408663i) q^{2} +(0.520111 - 0.900858i) q^{3} +(0.888663 + 1.53921i) q^{4} +(0.245432 + 0.425100i) q^{6} -1.17540 q^{7} -1.78246 q^{8} +(0.958970 + 1.66098i) q^{9} +O(q^{10})\) \(q+(-0.235942 + 0.408663i) q^{2} +(0.520111 - 0.900858i) q^{3} +(0.888663 + 1.53921i) q^{4} +(0.245432 + 0.425100i) q^{6} -1.17540 q^{7} -1.78246 q^{8} +(0.958970 + 1.66098i) q^{9} +0.713538 q^{11} +1.84881 q^{12} +(2.05158 + 3.55344i) q^{13} +(0.277326 - 0.480342i) q^{14} +(-1.35677 + 2.34999i) q^{16} +(1.27616 - 2.21038i) q^{17} -0.905045 q^{18} +(1.57031 + 4.06622i) q^{19} +(-0.611337 + 1.05887i) q^{21} +(-0.168353 + 0.291597i) q^{22} +(-0.303530 - 0.525730i) q^{23} +(-0.927076 + 1.60574i) q^{24} -1.93621 q^{26} +5.11575 q^{27} +(-1.04453 - 1.80918i) q^{28} +(0.429693 + 0.744250i) q^{29} +2.50914 q^{31} +(-2.42270 - 4.19623i) q^{32} +(0.371119 - 0.642796i) q^{33} +(0.602201 + 1.04304i) q^{34} +(-1.70440 + 2.95211i) q^{36} -9.38171 q^{37} +(-2.03222 - 0.317665i) q^{38} +4.26819 q^{39} +(2.06117 - 3.57005i) q^{41} +(-0.288480 - 0.499662i) q^{42} +(5.06197 - 8.76759i) q^{43} +(0.634095 + 1.09828i) q^{44} +0.286462 q^{46} +(5.25919 + 9.10919i) q^{47} +(1.41134 + 2.44451i) q^{48} -5.61844 q^{49} +(-1.32749 - 2.29928i) q^{51} +(-3.64632 + 6.31561i) q^{52} +(2.49028 + 4.31330i) q^{53} +(-1.20702 + 2.09062i) q^{54} +2.09510 q^{56} +(4.47982 + 0.700260i) q^{57} -0.405530 q^{58} +(3.12496 - 5.41259i) q^{59} +(2.27733 + 3.94444i) q^{61} +(-0.592010 + 1.02539i) q^{62} +(-1.12717 - 1.95232i) q^{63} -3.14061 q^{64} +(0.175125 + 0.303325i) q^{66} +(-2.59105 - 4.48783i) q^{67} +4.53632 q^{68} -0.631477 q^{69} +(6.58393 - 11.4037i) q^{71} +(-1.70932 - 2.96064i) q^{72} +(-6.18914 + 10.7199i) q^{73} +(2.21354 - 3.83396i) q^{74} +(-4.86329 + 6.03053i) q^{76} -0.838691 q^{77} +(-1.00704 + 1.74425i) q^{78} +(2.98173 - 5.16450i) q^{79} +(-0.216155 + 0.374392i) q^{81} +(0.972633 + 1.68465i) q^{82} -13.8603 q^{83} -2.17309 q^{84} +(2.38866 + 4.13729i) q^{86} +0.893952 q^{87} -1.27185 q^{88} +(-7.98173 - 13.8248i) q^{89} +(-2.41142 - 4.17670i) q^{91} +(0.539472 - 0.934393i) q^{92} +(1.30503 - 2.26038i) q^{93} -4.96345 q^{94} -5.04028 q^{96} +(8.35099 - 14.4643i) q^{97} +(1.32563 - 2.29605i) q^{98} +(0.684261 + 1.18518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.235942 + 0.408663i −0.166836 + 0.288969i −0.937306 0.348508i \(-0.886688\pi\)
0.770470 + 0.637477i \(0.220022\pi\)
\(3\) 0.520111 0.900858i 0.300286 0.520111i −0.675915 0.736980i \(-0.736251\pi\)
0.976201 + 0.216869i \(0.0695845\pi\)
\(4\) 0.888663 + 1.53921i 0.444331 + 0.769605i
\(5\) 0 0
\(6\) 0.245432 + 0.425100i 0.100197 + 0.173546i
\(7\) −1.17540 −0.444259 −0.222129 0.975017i \(-0.571301\pi\)
−0.222129 + 0.975017i \(0.571301\pi\)
\(8\) −1.78246 −0.630194
\(9\) 0.958970 + 1.66098i 0.319657 + 0.553661i
\(10\) 0 0
\(11\) 0.713538 0.215140 0.107570 0.994198i \(-0.465693\pi\)
0.107570 + 0.994198i \(0.465693\pi\)
\(12\) 1.84881 0.533706
\(13\) 2.05158 + 3.55344i 0.569005 + 0.985546i 0.996665 + 0.0816060i \(0.0260049\pi\)
−0.427659 + 0.903940i \(0.640662\pi\)
\(14\) 0.277326 0.480342i 0.0741184 0.128377i
\(15\) 0 0
\(16\) −1.35677 + 2.34999i −0.339192 + 0.587498i
\(17\) 1.27616 2.21038i 0.309515 0.536096i −0.668741 0.743495i \(-0.733167\pi\)
0.978256 + 0.207399i \(0.0665000\pi\)
\(18\) −0.905045 −0.213321
\(19\) 1.57031 + 4.06622i 0.360253 + 0.932855i
\(20\) 0 0
\(21\) −0.611337 + 1.05887i −0.133405 + 0.231064i
\(22\) −0.168353 + 0.291597i −0.0358931 + 0.0621686i
\(23\) −0.303530 0.525730i −0.0632904 0.109622i 0.832644 0.553809i \(-0.186826\pi\)
−0.895934 + 0.444186i \(0.853493\pi\)
\(24\) −0.927076 + 1.60574i −0.189239 + 0.327771i
\(25\) 0 0
\(26\) −1.93621 −0.379722
\(27\) 5.11575 0.984526
\(28\) −1.04453 1.80918i −0.197398 0.341904i
\(29\) 0.429693 + 0.744250i 0.0797920 + 0.138204i 0.903160 0.429304i \(-0.141241\pi\)
−0.823368 + 0.567508i \(0.807908\pi\)
\(30\) 0 0
\(31\) 2.50914 0.450654 0.225327 0.974283i \(-0.427655\pi\)
0.225327 + 0.974283i \(0.427655\pi\)
\(32\) −2.42270 4.19623i −0.428276 0.741796i
\(33\) 0.371119 0.642796i 0.0646035 0.111897i
\(34\) 0.602201 + 1.04304i 0.103277 + 0.178880i
\(35\) 0 0
\(36\) −1.70440 + 2.95211i −0.284067 + 0.492018i
\(37\) −9.38171 −1.54234 −0.771172 0.636627i \(-0.780329\pi\)
−0.771172 + 0.636627i \(0.780329\pi\)
\(38\) −2.03222 0.317665i −0.329669 0.0515320i
\(39\) 4.26819 0.683457
\(40\) 0 0
\(41\) 2.06117 3.57005i 0.321901 0.557548i −0.658979 0.752161i \(-0.729012\pi\)
0.980880 + 0.194612i \(0.0623449\pi\)
\(42\) −0.288480 0.499662i −0.0445134 0.0770996i
\(43\) 5.06197 8.76759i 0.771944 1.33705i −0.164553 0.986368i \(-0.552618\pi\)
0.936496 0.350677i \(-0.114049\pi\)
\(44\) 0.634095 + 1.09828i 0.0955934 + 0.165573i
\(45\) 0 0
\(46\) 0.286462 0.0422365
\(47\) 5.25919 + 9.10919i 0.767132 + 1.32871i 0.939112 + 0.343611i \(0.111650\pi\)
−0.171980 + 0.985100i \(0.555016\pi\)
\(48\) 1.41134 + 2.44451i 0.203709 + 0.352835i
\(49\) −5.61844 −0.802634
\(50\) 0 0
\(51\) −1.32749 2.29928i −0.185886 0.321964i
\(52\) −3.64632 + 6.31561i −0.505654 + 0.875818i
\(53\) 2.49028 + 4.31330i 0.342067 + 0.592477i 0.984816 0.173599i \(-0.0555397\pi\)
−0.642750 + 0.766076i \(0.722206\pi\)
\(54\) −1.20702 + 2.09062i −0.164254 + 0.284497i
\(55\) 0 0
\(56\) 2.09510 0.279969
\(57\) 4.47982 + 0.700260i 0.593367 + 0.0927517i
\(58\) −0.405530 −0.0532488
\(59\) 3.12496 5.41259i 0.406835 0.704659i −0.587698 0.809080i \(-0.699966\pi\)
0.994533 + 0.104421i \(0.0332991\pi\)
\(60\) 0 0
\(61\) 2.27733 + 3.94444i 0.291582 + 0.505034i 0.974184 0.225756i \(-0.0724852\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(62\) −0.592010 + 1.02539i −0.0751854 + 0.130225i
\(63\) −1.12717 1.95232i −0.142010 0.245969i
\(64\) −3.14061 −0.392577
\(65\) 0 0
\(66\) 0.175125 + 0.303325i 0.0215564 + 0.0373368i
\(67\) −2.59105 4.48783i −0.316547 0.548276i 0.663218 0.748426i \(-0.269190\pi\)
−0.979765 + 0.200151i \(0.935857\pi\)
\(68\) 4.53632 0.550109
\(69\) −0.631477 −0.0760209
\(70\) 0 0
\(71\) 6.58393 11.4037i 0.781368 1.35337i −0.149776 0.988720i \(-0.547855\pi\)
0.931145 0.364650i \(-0.118811\pi\)
\(72\) −1.70932 2.96064i −0.201446 0.348914i
\(73\) −6.18914 + 10.7199i −0.724384 + 1.25467i 0.234842 + 0.972033i \(0.424543\pi\)
−0.959227 + 0.282637i \(0.908791\pi\)
\(74\) 2.21354 3.83396i 0.257319 0.445689i
\(75\) 0 0
\(76\) −4.86329 + 6.03053i −0.557857 + 0.691749i
\(77\) −0.838691 −0.0955777
\(78\) −1.00704 + 1.74425i −0.114025 + 0.197498i
\(79\) 2.98173 5.16450i 0.335471 0.581052i −0.648105 0.761551i \(-0.724438\pi\)
0.983575 + 0.180499i \(0.0577714\pi\)
\(80\) 0 0
\(81\) −0.216155 + 0.374392i −0.0240172 + 0.0415991i
\(82\) 0.972633 + 1.68465i 0.107409 + 0.186038i
\(83\) −13.8603 −1.52136 −0.760682 0.649124i \(-0.775136\pi\)
−0.760682 + 0.649124i \(0.775136\pi\)
\(84\) −2.17309 −0.237104
\(85\) 0 0
\(86\) 2.38866 + 4.13729i 0.257576 + 0.446135i
\(87\) 0.893952 0.0958417
\(88\) −1.27185 −0.135580
\(89\) −7.98173 13.8248i −0.846061 1.46542i −0.884696 0.466168i \(-0.845634\pi\)
0.0386349 0.999253i \(-0.487699\pi\)
\(90\) 0 0
\(91\) −2.41142 4.17670i −0.252786 0.437837i
\(92\) 0.539472 0.934393i 0.0562439 0.0974172i
\(93\) 1.30503 2.26038i 0.135325 0.234390i
\(94\) −4.96345 −0.511941
\(95\) 0 0
\(96\) −5.04028 −0.514421
\(97\) 8.35099 14.4643i 0.847915 1.46863i −0.0351512 0.999382i \(-0.511191\pi\)
0.883066 0.469249i \(-0.155475\pi\)
\(98\) 1.32563 2.29605i 0.133908 0.231936i
\(99\) 0.684261 + 1.18518i 0.0687708 + 0.119115i
\(100\) 0 0
\(101\) −7.01362 12.1479i −0.697881 1.20877i −0.969200 0.246276i \(-0.920793\pi\)
0.271318 0.962490i \(-0.412540\pi\)
\(102\) 1.25284 0.124050
\(103\) −3.55382 −0.350169 −0.175084 0.984553i \(-0.556020\pi\)
−0.175084 + 0.984553i \(0.556020\pi\)
\(104\) −3.65685 6.33385i −0.358584 0.621085i
\(105\) 0 0
\(106\) −2.35025 −0.228276
\(107\) −3.63127 −0.351048 −0.175524 0.984475i \(-0.556162\pi\)
−0.175524 + 0.984475i \(0.556162\pi\)
\(108\) 4.54617 + 7.87420i 0.437456 + 0.757696i
\(109\) 3.11134 5.38899i 0.298012 0.516172i −0.677669 0.735367i \(-0.737010\pi\)
0.975681 + 0.219195i \(0.0703431\pi\)
\(110\) 0 0
\(111\) −4.87953 + 8.45159i −0.463144 + 0.802189i
\(112\) 1.59474 2.76218i 0.150689 0.261001i
\(113\) 12.2707 1.15433 0.577167 0.816626i \(-0.304158\pi\)
0.577167 + 0.816626i \(0.304158\pi\)
\(114\) −1.34315 + 1.66552i −0.125797 + 0.155990i
\(115\) 0 0
\(116\) −0.763705 + 1.32278i −0.0709082 + 0.122817i
\(117\) −3.93480 + 6.81528i −0.363773 + 0.630072i
\(118\) 1.47462 + 2.55411i 0.135750 + 0.235125i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) −10.4909 −0.953715
\(122\) −2.14927 −0.194585
\(123\) −2.14407 3.71364i −0.193325 0.334848i
\(124\) 2.22978 + 3.86209i 0.200240 + 0.346826i
\(125\) 0 0
\(126\) 1.06379 0.0947697
\(127\) 1.07894 + 1.86879i 0.0957408 + 0.165828i 0.909918 0.414789i \(-0.136145\pi\)
−0.814177 + 0.580617i \(0.802811\pi\)
\(128\) 5.58639 9.67592i 0.493772 0.855239i
\(129\) −5.26557 9.12024i −0.463608 0.802992i
\(130\) 0 0
\(131\) 8.77471 15.1982i 0.766650 1.32788i −0.172720 0.984971i \(-0.555256\pi\)
0.939370 0.342906i \(-0.111411\pi\)
\(132\) 1.31920 0.114821
\(133\) −1.84574 4.77943i −0.160046 0.414429i
\(134\) 2.44535 0.211246
\(135\) 0 0
\(136\) −2.27471 + 3.93991i −0.195055 + 0.337845i
\(137\) 2.53728 + 4.39469i 0.216774 + 0.375464i 0.953820 0.300379i \(-0.0971131\pi\)
−0.737046 + 0.675843i \(0.763780\pi\)
\(138\) 0.148992 0.258062i 0.0126830 0.0219677i
\(139\) −2.99086 5.18033i −0.253682 0.439390i 0.710855 0.703339i \(-0.248308\pi\)
−0.964537 + 0.263949i \(0.914975\pi\)
\(140\) 0 0
\(141\) 10.9414 0.921436
\(142\) 3.10685 + 5.38122i 0.260721 + 0.451582i
\(143\) 1.46388 + 2.53551i 0.122416 + 0.212030i
\(144\) −5.20440 −0.433700
\(145\) 0 0
\(146\) −2.92056 5.05855i −0.241707 0.418649i
\(147\) −2.92221 + 5.06142i −0.241020 + 0.417459i
\(148\) −8.33718 14.4404i −0.685312 1.18699i
\(149\) −4.80008 + 8.31399i −0.393238 + 0.681108i −0.992875 0.119164i \(-0.961979\pi\)
0.599636 + 0.800273i \(0.295312\pi\)
\(150\) 0 0
\(151\) 7.53638 0.613302 0.306651 0.951822i \(-0.400792\pi\)
0.306651 + 0.951822i \(0.400792\pi\)
\(152\) −2.79901 7.24787i −0.227029 0.587880i
\(153\) 4.89521 0.395754
\(154\) 0.197882 0.342742i 0.0159458 0.0276190i
\(155\) 0 0
\(156\) 3.79298 + 6.56964i 0.303682 + 0.525992i
\(157\) −4.92803 + 8.53560i −0.393300 + 0.681215i −0.992883 0.119098i \(-0.962000\pi\)
0.599583 + 0.800313i \(0.295333\pi\)
\(158\) 1.40703 + 2.43705i 0.111937 + 0.193881i
\(159\) 5.18089 0.410872
\(160\) 0 0
\(161\) 0.356769 + 0.617942i 0.0281173 + 0.0487007i
\(162\) −0.102000 0.176669i −0.00801389 0.0138805i
\(163\) 0.0688234 0.00539067 0.00269533 0.999996i \(-0.499142\pi\)
0.00269533 + 0.999996i \(0.499142\pi\)
\(164\) 7.32674 0.572122
\(165\) 0 0
\(166\) 3.27022 5.66419i 0.253819 0.439627i
\(167\) −8.32212 14.4143i −0.643985 1.11542i −0.984535 0.175189i \(-0.943946\pi\)
0.340550 0.940227i \(-0.389387\pi\)
\(168\) 1.08968 1.88739i 0.0840709 0.145615i
\(169\) −1.91794 + 3.32197i −0.147534 + 0.255536i
\(170\) 0 0
\(171\) −5.24805 + 6.50764i −0.401328 + 0.497651i
\(172\) 17.9935 1.37200
\(173\) 6.06778 10.5097i 0.461325 0.799038i −0.537702 0.843135i \(-0.680708\pi\)
0.999027 + 0.0440965i \(0.0140409\pi\)
\(174\) −0.210921 + 0.365325i −0.0159899 + 0.0276952i
\(175\) 0 0
\(176\) −0.968106 + 1.67681i −0.0729737 + 0.126394i
\(177\) −3.25065 5.63029i −0.244334 0.423198i
\(178\) 7.53290 0.564614
\(179\) 11.7538 0.878522 0.439261 0.898360i \(-0.355240\pi\)
0.439261 + 0.898360i \(0.355240\pi\)
\(180\) 0 0
\(181\) 4.41794 + 7.65210i 0.328383 + 0.568776i 0.982191 0.187884i \(-0.0601631\pi\)
−0.653808 + 0.756660i \(0.726830\pi\)
\(182\) 2.27582 0.168695
\(183\) 4.73785 0.350232
\(184\) 0.541030 + 0.937092i 0.0398853 + 0.0690833i
\(185\) 0 0
\(186\) 0.615822 + 1.06663i 0.0451543 + 0.0782095i
\(187\) 0.910591 1.57719i 0.0665890 0.115336i
\(188\) −9.34730 + 16.1900i −0.681722 + 1.18078i
\(189\) −6.01304 −0.437384
\(190\) 0 0
\(191\) 14.2447 1.03071 0.515355 0.856977i \(-0.327660\pi\)
0.515355 + 0.856977i \(0.327660\pi\)
\(192\) −1.63347 + 2.82925i −0.117885 + 0.204183i
\(193\) −9.75283 + 16.8924i −0.702024 + 1.21594i 0.265731 + 0.964047i \(0.414387\pi\)
−0.967755 + 0.251894i \(0.918947\pi\)
\(194\) 3.94070 + 6.82549i 0.282926 + 0.490041i
\(195\) 0 0
\(196\) −4.99290 8.64795i −0.356636 0.617711i
\(197\) −4.33232 −0.308665 −0.154332 0.988019i \(-0.549323\pi\)
−0.154332 + 0.988019i \(0.549323\pi\)
\(198\) −0.645784 −0.0458938
\(199\) 6.31574 + 10.9392i 0.447711 + 0.775458i 0.998237 0.0593602i \(-0.0189061\pi\)
−0.550526 + 0.834818i \(0.685573\pi\)
\(200\) 0 0
\(201\) −5.39053 −0.380219
\(202\) 6.61923 0.465727
\(203\) −0.505060 0.874790i −0.0354483 0.0613983i
\(204\) 2.35939 4.08658i 0.165190 0.286118i
\(205\) 0 0
\(206\) 0.838496 1.45232i 0.0584208 0.101188i
\(207\) 0.582153 1.00832i 0.0404624 0.0700830i
\(208\) −11.1341 −0.772009
\(209\) 1.12047 + 2.90140i 0.0775048 + 0.200694i
\(210\) 0 0
\(211\) −11.1223 + 19.2645i −0.765694 + 1.32622i 0.174186 + 0.984713i \(0.444271\pi\)
−0.939879 + 0.341507i \(0.889063\pi\)
\(212\) −4.42605 + 7.66614i −0.303982 + 0.526512i
\(213\) −6.84874 11.8624i −0.469268 0.812796i
\(214\) 0.856769 1.48397i 0.0585675 0.101442i
\(215\) 0 0
\(216\) −9.11861 −0.620443
\(217\) −2.94923 −0.200207
\(218\) 1.46819 + 2.54298i 0.0994383 + 0.172232i
\(219\) 6.43808 + 11.1511i 0.435045 + 0.753520i
\(220\) 0 0
\(221\) 10.4726 0.704463
\(222\) −2.30257 3.98817i −0.154538 0.267668i
\(223\) −6.81125 + 11.7974i −0.456115 + 0.790015i −0.998752 0.0499529i \(-0.984093\pi\)
0.542636 + 0.839968i \(0.317426\pi\)
\(224\) 2.84763 + 4.93224i 0.190265 + 0.329549i
\(225\) 0 0
\(226\) −2.89518 + 5.01460i −0.192585 + 0.333566i
\(227\) 6.58913 0.437336 0.218668 0.975799i \(-0.429829\pi\)
0.218668 + 0.975799i \(0.429829\pi\)
\(228\) 2.90320 + 7.51768i 0.192269 + 0.497870i
\(229\) −0.585962 −0.0387215 −0.0193607 0.999813i \(-0.506163\pi\)
−0.0193607 + 0.999813i \(0.506163\pi\)
\(230\) 0 0
\(231\) −0.436212 + 0.755542i −0.0287007 + 0.0497110i
\(232\) −0.765910 1.32660i −0.0502845 0.0870953i
\(233\) −3.57873 + 6.19855i −0.234451 + 0.406080i −0.959113 0.283024i \(-0.908662\pi\)
0.724662 + 0.689104i \(0.241996\pi\)
\(234\) −1.85677 3.21602i −0.121381 0.210238i
\(235\) 0 0
\(236\) 11.1081 0.723078
\(237\) −3.10166 5.37223i −0.201474 0.348964i
\(238\) −0.707826 1.22599i −0.0458815 0.0794691i
\(239\) 3.65498 0.236421 0.118211 0.992989i \(-0.462284\pi\)
0.118211 + 0.992989i \(0.462284\pi\)
\(240\) 0 0
\(241\) −8.63148 14.9502i −0.556002 0.963024i −0.997825 0.0659218i \(-0.979001\pi\)
0.441822 0.897103i \(-0.354332\pi\)
\(242\) 2.47523 4.28723i 0.159114 0.275594i
\(243\) 7.89847 + 13.6805i 0.506687 + 0.877608i
\(244\) −4.04755 + 7.01056i −0.259118 + 0.448805i
\(245\) 0 0
\(246\) 2.02351 0.129014
\(247\) −11.2274 + 13.9221i −0.714385 + 0.885845i
\(248\) −4.47243 −0.284000
\(249\) −7.20889 + 12.4862i −0.456845 + 0.791278i
\(250\) 0 0
\(251\) 9.70702 + 16.8130i 0.612702 + 1.06123i 0.990783 + 0.135458i \(0.0432506\pi\)
−0.378082 + 0.925772i \(0.623416\pi\)
\(252\) 2.00335 3.46990i 0.126199 0.218583i
\(253\) −0.216580 0.375128i −0.0136163 0.0235841i
\(254\) −1.01827 −0.0638921
\(255\) 0 0
\(256\) −0.504485 0.873793i −0.0315303 0.0546121i
\(257\) 6.94643 + 12.0316i 0.433306 + 0.750509i 0.997156 0.0753689i \(-0.0240134\pi\)
−0.563849 + 0.825878i \(0.690680\pi\)
\(258\) 4.96948 0.309386
\(259\) 11.0272 0.685199
\(260\) 0 0
\(261\) −0.824125 + 1.42743i −0.0510121 + 0.0883555i
\(262\) 4.14064 + 7.17180i 0.255810 + 0.443076i
\(263\) 7.49417 12.9803i 0.462110 0.800399i −0.536955 0.843611i \(-0.680426\pi\)
0.999066 + 0.0432118i \(0.0137590\pi\)
\(264\) −0.661504 + 1.14576i −0.0407127 + 0.0705165i
\(265\) 0 0
\(266\) 2.38866 + 0.373382i 0.146458 + 0.0228935i
\(267\) −16.6055 −1.01624
\(268\) 4.60514 7.97633i 0.281304 0.487232i
\(269\) −9.68613 + 16.7769i −0.590574 + 1.02290i 0.403582 + 0.914944i \(0.367765\pi\)
−0.994155 + 0.107960i \(0.965568\pi\)
\(270\) 0 0
\(271\) −5.95897 + 10.3212i −0.361982 + 0.626971i −0.988287 0.152607i \(-0.951233\pi\)
0.626305 + 0.779578i \(0.284566\pi\)
\(272\) 3.46292 + 5.99795i 0.209970 + 0.363679i
\(273\) −5.01682 −0.303632
\(274\) −2.39460 −0.144663
\(275\) 0 0
\(276\) −0.561171 0.971976i −0.0337785 0.0585061i
\(277\) 10.9824 0.659866 0.329933 0.944004i \(-0.392974\pi\)
0.329933 + 0.944004i \(0.392974\pi\)
\(278\) 2.82268 0.169293
\(279\) 2.40619 + 4.16764i 0.144055 + 0.249510i
\(280\) 0 0
\(281\) −7.32488 12.6871i −0.436965 0.756846i 0.560488 0.828162i \(-0.310613\pi\)
−0.997454 + 0.0713160i \(0.977280\pi\)
\(282\) −2.58155 + 4.47137i −0.153729 + 0.266266i
\(283\) 9.46435 16.3927i 0.562597 0.974447i −0.434672 0.900589i \(-0.643136\pi\)
0.997269 0.0738576i \(-0.0235310\pi\)
\(284\) 23.4036 1.38875
\(285\) 0 0
\(286\) −1.38156 −0.0816934
\(287\) −2.42270 + 4.19623i −0.143007 + 0.247696i
\(288\) 4.64658 8.04812i 0.273803 0.474240i
\(289\) 5.24281 + 9.08082i 0.308401 + 0.534166i
\(290\) 0 0
\(291\) −8.68688 15.0461i −0.509234 0.882019i
\(292\) −22.0002 −1.28747
\(293\) 5.59625 0.326937 0.163468 0.986549i \(-0.447732\pi\)
0.163468 + 0.986549i \(0.447732\pi\)
\(294\) −1.37894 2.38840i −0.0804216 0.139294i
\(295\) 0 0
\(296\) 16.7225 0.971976
\(297\) 3.65028 0.211811
\(298\) −2.26508 3.92324i −0.131213 0.227267i
\(299\) 1.24543 2.15715i 0.0720252 0.124751i
\(300\) 0 0
\(301\) −5.94983 + 10.3054i −0.342943 + 0.593994i
\(302\) −1.77815 + 3.07984i −0.102321 + 0.177225i
\(303\) −14.5914 −0.838256
\(304\) −11.6861 1.82671i −0.670245 0.104769i
\(305\) 0 0
\(306\) −1.15498 + 2.00049i −0.0660261 + 0.114361i
\(307\) 10.3160 17.8678i 0.588764 1.01977i −0.405631 0.914037i \(-0.632948\pi\)
0.994395 0.105732i \(-0.0337184\pi\)
\(308\) −0.745314 1.29092i −0.0424682 0.0735571i
\(309\) −1.84838 + 3.20149i −0.105151 + 0.182127i
\(310\) 0 0
\(311\) −24.6587 −1.39827 −0.699134 0.714991i \(-0.746431\pi\)
−0.699134 + 0.714991i \(0.746431\pi\)
\(312\) −7.60787 −0.430711
\(313\) 1.74928 + 3.02985i 0.0988753 + 0.171257i 0.911219 0.411921i \(-0.135142\pi\)
−0.812344 + 0.583178i \(0.801809\pi\)
\(314\) −2.32546 4.02781i −0.131233 0.227303i
\(315\) 0 0
\(316\) 10.5990 0.596240
\(317\) 15.6854 + 27.1680i 0.880982 + 1.52590i 0.850251 + 0.526377i \(0.176450\pi\)
0.0307305 + 0.999528i \(0.490217\pi\)
\(318\) −1.22239 + 2.11724i −0.0685482 + 0.118729i
\(319\) 0.306602 + 0.531051i 0.0171664 + 0.0297331i
\(320\) 0 0
\(321\) −1.88866 + 3.27126i −0.105415 + 0.182584i
\(322\) −0.336707 −0.0187639
\(323\) 10.9919 + 1.71818i 0.611603 + 0.0956024i
\(324\) −0.768356 −0.0426865
\(325\) 0 0
\(326\) −0.0162383 + 0.0281256i −0.000899358 + 0.00155773i
\(327\) −3.23648 5.60575i −0.178978 0.309999i
\(328\) −3.67395 + 6.36347i −0.202860 + 0.351364i
\(329\) −6.18164 10.7069i −0.340805 0.590292i
\(330\) 0 0
\(331\) 35.7497 1.96498 0.982492 0.186305i \(-0.0596512\pi\)
0.982492 + 0.186305i \(0.0596512\pi\)
\(332\) −12.3171 21.3339i −0.675990 1.17085i
\(333\) −8.99677 15.5829i −0.493020 0.853936i
\(334\) 7.85415 0.429760
\(335\) 0 0
\(336\) −1.65889 2.87328i −0.0904997 0.156750i
\(337\) 13.2446 22.9403i 0.721480 1.24964i −0.238927 0.971038i \(-0.576796\pi\)
0.960407 0.278602i \(-0.0898711\pi\)
\(338\) −0.905045 1.56758i −0.0492279 0.0852653i
\(339\) 6.38214 11.0542i 0.346630 0.600382i
\(340\) 0 0
\(341\) 1.79036 0.0969536
\(342\) −1.42120 3.68011i −0.0768496 0.198998i
\(343\) 14.8317 0.800836
\(344\) −9.02276 + 15.6279i −0.486474 + 0.842599i
\(345\) 0 0
\(346\) 2.86329 + 4.95936i 0.153931 + 0.266617i
\(347\) 17.1699 29.7392i 0.921729 1.59648i 0.124990 0.992158i \(-0.460110\pi\)
0.796739 0.604323i \(-0.206556\pi\)
\(348\) 0.794422 + 1.37598i 0.0425855 + 0.0737602i
\(349\) −21.4308 −1.14717 −0.573583 0.819148i \(-0.694447\pi\)
−0.573583 + 0.819148i \(0.694447\pi\)
\(350\) 0 0
\(351\) 10.4953 + 18.1785i 0.560200 + 0.970295i
\(352\) −1.72869 2.99417i −0.0921393 0.159590i
\(353\) −19.5659 −1.04139 −0.520693 0.853744i \(-0.674326\pi\)
−0.520693 + 0.853744i \(0.674326\pi\)
\(354\) 3.06786 0.163055
\(355\) 0 0
\(356\) 14.1861 24.5711i 0.751863 1.30227i
\(357\) 1.56033 + 2.70257i 0.0825815 + 0.143035i
\(358\) −2.77322 + 4.80335i −0.146569 + 0.253865i
\(359\) 8.23630 14.2657i 0.434695 0.752914i −0.562576 0.826746i \(-0.690189\pi\)
0.997271 + 0.0738319i \(0.0235228\pi\)
\(360\) 0 0
\(361\) −14.0683 + 12.7704i −0.740435 + 0.672128i
\(362\) −4.16951 −0.219144
\(363\) −5.45641 + 9.45078i −0.286387 + 0.496037i
\(364\) 4.28588 7.42336i 0.224641 0.389090i
\(365\) 0 0
\(366\) −1.11786 + 1.93618i −0.0584313 + 0.101206i
\(367\) 6.36735 + 11.0286i 0.332373 + 0.575687i 0.982977 0.183730i \(-0.0588173\pi\)
−0.650603 + 0.759418i \(0.725484\pi\)
\(368\) 1.64728 0.0858705
\(369\) 7.90640 0.411591
\(370\) 0 0
\(371\) −2.92708 5.06984i −0.151966 0.263213i
\(372\) 4.63892 0.240517
\(373\) 19.3342 1.00109 0.500544 0.865711i \(-0.333133\pi\)
0.500544 + 0.865711i \(0.333133\pi\)
\(374\) 0.429693 + 0.744250i 0.0222189 + 0.0384843i
\(375\) 0 0
\(376\) −9.37429 16.2368i −0.483442 0.837346i
\(377\) −1.76310 + 3.05377i −0.0908041 + 0.157277i
\(378\) 1.41873 2.45731i 0.0729715 0.126390i
\(379\) 9.85789 0.506366 0.253183 0.967418i \(-0.418523\pi\)
0.253183 + 0.967418i \(0.418523\pi\)
\(380\) 0 0
\(381\) 2.24468 0.114999
\(382\) −3.36092 + 5.82128i −0.171959 + 0.297843i
\(383\) −10.1666 + 17.6091i −0.519490 + 0.899784i 0.480253 + 0.877130i \(0.340545\pi\)
−0.999743 + 0.0226536i \(0.992789\pi\)
\(384\) −5.81109 10.0651i −0.296546 0.513632i
\(385\) 0 0
\(386\) −4.60220 7.97125i −0.234246 0.405726i
\(387\) 19.4171 0.987027
\(388\) 29.6849 1.50702
\(389\) 0.502617 + 0.870559i 0.0254837 + 0.0441391i 0.878486 0.477768i \(-0.158554\pi\)
−0.853002 + 0.521907i \(0.825221\pi\)
\(390\) 0 0
\(391\) −1.54942 −0.0783574
\(392\) 10.0146 0.505816
\(393\) −9.12764 15.8095i −0.460428 0.797486i
\(394\) 1.02217 1.77046i 0.0514964 0.0891944i
\(395\) 0 0
\(396\) −1.21616 + 2.10644i −0.0611141 + 0.105853i
\(397\) −4.93111 + 8.54093i −0.247485 + 0.428657i −0.962827 0.270117i \(-0.912937\pi\)
0.715342 + 0.698774i \(0.246271\pi\)
\(398\) −5.96059 −0.298777
\(399\) −5.26557 0.823085i −0.263608 0.0412058i
\(400\) 0 0
\(401\) −14.9159 + 25.8351i −0.744865 + 1.29014i 0.205393 + 0.978680i \(0.434153\pi\)
−0.950258 + 0.311464i \(0.899181\pi\)
\(402\) 1.27185 2.20291i 0.0634342 0.109871i
\(403\) 5.14769 + 8.91606i 0.256425 + 0.444140i
\(404\) 12.4655 21.5909i 0.620181 1.07419i
\(405\) 0 0
\(406\) 0.476660 0.0236562
\(407\) −6.69420 −0.331819
\(408\) 2.36620 + 4.09838i 0.117144 + 0.202900i
\(409\) −13.8221 23.9406i −0.683458 1.18378i −0.973919 0.226898i \(-0.927142\pi\)
0.290460 0.956887i \(-0.406192\pi\)
\(410\) 0 0
\(411\) 5.27866 0.260377
\(412\) −3.15815 5.47008i −0.155591 0.269491i
\(413\) −3.67307 + 6.36194i −0.180740 + 0.313051i
\(414\) 0.274708 + 0.475809i 0.0135012 + 0.0233847i
\(415\) 0 0
\(416\) 9.94070 17.2178i 0.487383 0.844172i
\(417\) −6.22232 −0.304708
\(418\) −1.45006 0.226666i −0.0709249 0.0110866i
\(419\) −11.2902 −0.551562 −0.275781 0.961220i \(-0.588936\pi\)
−0.275781 + 0.961220i \(0.588936\pi\)
\(420\) 0 0
\(421\) −2.27471 + 3.93991i −0.110863 + 0.192019i −0.916118 0.400908i \(-0.868695\pi\)
0.805256 + 0.592928i \(0.202028\pi\)
\(422\) −5.24845 9.09059i −0.255491 0.442523i
\(423\) −10.0868 + 17.4709i −0.490438 + 0.849463i
\(424\) −4.43883 7.68828i −0.215569 0.373376i
\(425\) 0 0
\(426\) 6.46362 0.313163
\(427\) −2.67676 4.63629i −0.129538 0.224366i
\(428\) −3.22698 5.58929i −0.155982 0.270168i
\(429\) 3.04551 0.147039
\(430\) 0 0
\(431\) −16.4517 28.4952i −0.792451 1.37256i −0.924445 0.381314i \(-0.875472\pi\)
0.131995 0.991250i \(-0.457862\pi\)
\(432\) −6.94089 + 12.0220i −0.333943 + 0.578407i
\(433\) −11.1547 19.3204i −0.536059 0.928481i −0.999111 0.0421503i \(-0.986579\pi\)
0.463052 0.886331i \(-0.346754\pi\)
\(434\) 0.695848 1.20524i 0.0334018 0.0578536i
\(435\) 0 0
\(436\) 11.0597 0.529664
\(437\) 1.66110 2.05978i 0.0794611 0.0985325i
\(438\) −6.07605 −0.290325
\(439\) −2.85287 + 4.94131i −0.136160 + 0.235836i −0.926040 0.377425i \(-0.876809\pi\)
0.789880 + 0.613261i \(0.210143\pi\)
\(440\) 0 0
\(441\) −5.38791 9.33214i −0.256567 0.444388i
\(442\) −2.47092 + 4.27976i −0.117530 + 0.203568i
\(443\) −5.78881 10.0265i −0.275034 0.476374i 0.695109 0.718904i \(-0.255356\pi\)
−0.970144 + 0.242530i \(0.922023\pi\)
\(444\) −17.3450 −0.823158
\(445\) 0 0
\(446\) −3.21412 5.56702i −0.152193 0.263606i
\(447\) 4.99315 + 8.64839i 0.236168 + 0.409055i
\(448\) 3.69147 0.174406
\(449\) −25.4726 −1.20213 −0.601063 0.799202i \(-0.705256\pi\)
−0.601063 + 0.799202i \(0.705256\pi\)
\(450\) 0 0
\(451\) 1.47072 2.54737i 0.0692537 0.119951i
\(452\) 10.9046 + 18.8872i 0.512907 + 0.888381i
\(453\) 3.91975 6.78921i 0.184166 0.318985i
\(454\) −1.55465 + 2.69274i −0.0729634 + 0.126376i
\(455\) 0 0
\(456\) −7.98509 1.24818i −0.373936 0.0584516i
\(457\) −6.92830 −0.324092 −0.162046 0.986783i \(-0.551809\pi\)
−0.162046 + 0.986783i \(0.551809\pi\)
\(458\) 0.138253 0.239461i 0.00646014 0.0111893i
\(459\) 6.52853 11.3077i 0.304726 0.527800i
\(460\) 0 0
\(461\) −16.2473 + 28.1411i −0.756712 + 1.31066i 0.187806 + 0.982206i \(0.439862\pi\)
−0.944519 + 0.328458i \(0.893471\pi\)
\(462\) −0.205841 0.356528i −0.00957661 0.0165872i
\(463\) 21.5062 0.999477 0.499738 0.866176i \(-0.333429\pi\)
0.499738 + 0.866176i \(0.333429\pi\)
\(464\) −2.33198 −0.108259
\(465\) 0 0
\(466\) −1.68875 2.92499i −0.0782296 0.135498i
\(467\) −16.9509 −0.784392 −0.392196 0.919882i \(-0.628285\pi\)
−0.392196 + 0.919882i \(0.628285\pi\)
\(468\) −13.9868 −0.646542
\(469\) 3.04551 + 5.27499i 0.140629 + 0.243576i
\(470\) 0 0
\(471\) 5.12624 + 8.87891i 0.236205 + 0.409119i
\(472\) −5.57011 + 9.64771i −0.256385 + 0.444072i
\(473\) 3.61191 6.25601i 0.166076 0.287652i
\(474\) 2.92724 0.134453
\(475\) 0 0
\(476\) −5.33198 −0.244391
\(477\) −4.77621 + 8.27265i −0.218688 + 0.378778i
\(478\) −0.862364 + 1.49366i −0.0394436 + 0.0683183i
\(479\) −4.42894 7.67115i −0.202364 0.350504i 0.746926 0.664907i \(-0.231529\pi\)
−0.949290 + 0.314403i \(0.898196\pi\)
\(480\) 0 0
\(481\) −19.2473 33.3373i −0.877601 1.52005i
\(482\) 8.14611 0.371045
\(483\) 0.742237 0.0337730
\(484\) −9.32284 16.1476i −0.423765 0.733983i
\(485\) 0 0
\(486\) −7.45432 −0.338135
\(487\) −30.0628 −1.36227 −0.681137 0.732156i \(-0.738514\pi\)
−0.681137 + 0.732156i \(0.738514\pi\)
\(488\) −4.05924 7.03081i −0.183753 0.318270i
\(489\) 0.0357958 0.0620001i 0.00161874 0.00280374i
\(490\) 0 0
\(491\) −1.55017 + 2.68497i −0.0699580 + 0.121171i −0.898883 0.438190i \(-0.855620\pi\)
0.828925 + 0.559360i \(0.188953\pi\)
\(492\) 3.81072 6.60036i 0.171800 0.297567i
\(493\) 2.19343 0.0987873
\(494\) −3.04045 7.87306i −0.136796 0.354226i
\(495\) 0 0
\(496\) −3.40432 + 5.89645i −0.152858 + 0.264759i
\(497\) −7.73874 + 13.4039i −0.347130 + 0.601246i
\(498\) −3.40176 5.89202i −0.152436 0.264028i
\(499\) −16.0696 + 27.8333i −0.719372 + 1.24599i 0.241877 + 0.970307i \(0.422237\pi\)
−0.961249 + 0.275682i \(0.911096\pi\)
\(500\) 0 0
\(501\) −17.3137 −0.773519
\(502\) −9.16117 −0.408883
\(503\) 4.20911 + 7.29040i 0.187675 + 0.325063i 0.944475 0.328584i \(-0.106571\pi\)
−0.756800 + 0.653647i \(0.773238\pi\)
\(504\) 2.00914 + 3.47993i 0.0894940 + 0.155008i
\(505\) 0 0
\(506\) 0.204402 0.00908676
\(507\) 1.99508 + 3.45558i 0.0886047 + 0.153468i
\(508\) −1.91764 + 3.32144i −0.0850813 + 0.147365i
\(509\) −10.1725 17.6193i −0.450888 0.780962i 0.547553 0.836771i \(-0.315559\pi\)
−0.998441 + 0.0558093i \(0.982226\pi\)
\(510\) 0 0
\(511\) 7.27471 12.6002i 0.321814 0.557398i
\(512\) 22.8217 1.00859
\(513\) 8.03329 + 20.8017i 0.354678 + 0.918419i
\(514\) −6.55582 −0.289165
\(515\) 0 0
\(516\) 9.35864 16.2096i 0.411991 0.713589i
\(517\) 3.75263 + 6.49975i 0.165041 + 0.285859i
\(518\) −2.60179 + 4.50643i −0.114316 + 0.198001i
\(519\) −6.31184 10.9324i −0.277059 0.479880i
\(520\) 0 0
\(521\) 15.3502 0.672507 0.336253 0.941772i \(-0.390840\pi\)
0.336253 + 0.941772i \(0.390840\pi\)
\(522\) −0.388891 0.673580i −0.0170213 0.0294818i
\(523\) 6.61835 + 11.4633i 0.289400 + 0.501256i 0.973667 0.227976i \(-0.0732109\pi\)
−0.684267 + 0.729232i \(0.739878\pi\)
\(524\) 31.1910 1.36259
\(525\) 0 0
\(526\) 3.53638 + 6.12519i 0.154193 + 0.267071i
\(527\) 3.20207 5.54614i 0.139484 0.241594i
\(528\) 1.00704 + 1.74425i 0.0438260 + 0.0759088i
\(529\) 11.3157 19.5994i 0.491989 0.852149i
\(530\) 0 0
\(531\) 11.9870 0.520190
\(532\) 5.71630 7.08827i 0.247833 0.307316i
\(533\) 16.9146 0.732653
\(534\) 3.91794 6.78607i 0.169546 0.293662i
\(535\) 0 0
\(536\) 4.61844 + 7.99937i 0.199486 + 0.345520i
\(537\) 6.11329 10.5885i 0.263808 0.456928i
\(538\) −4.57073 7.91673i −0.197058 0.341315i
\(539\) −4.00897 −0.172679
\(540\) 0 0
\(541\) 13.8704 + 24.0242i 0.596335 + 1.03288i 0.993357 + 0.115073i \(0.0367102\pi\)
−0.397022 + 0.917809i \(0.629956\pi\)
\(542\) −2.81194 4.87043i −0.120783 0.209203i
\(543\) 9.19127 0.394435
\(544\) −12.3670 −0.530232
\(545\) 0 0
\(546\) 1.18368 2.05019i 0.0506568 0.0877401i
\(547\) 8.53008 + 14.7745i 0.364720 + 0.631714i 0.988731 0.149702i \(-0.0478314\pi\)
−0.624011 + 0.781415i \(0.714498\pi\)
\(548\) −4.50957 + 7.81080i −0.192639 + 0.333661i
\(549\) −4.36777 + 7.56520i −0.186412 + 0.322875i
\(550\) 0 0
\(551\) −2.35153 + 2.91593i −0.100179 + 0.124223i
\(552\) 1.12558 0.0479080
\(553\) −3.50472 + 6.07035i −0.149036 + 0.258137i
\(554\) −2.59120 + 4.48808i −0.110089 + 0.190680i
\(555\) 0 0
\(556\) 5.31574 9.20713i 0.225438 0.390469i
\(557\) −13.2708 22.9856i −0.562300 0.973932i −0.997295 0.0734992i \(-0.976583\pi\)
0.434995 0.900433i \(-0.356750\pi\)
\(558\) −2.27088 −0.0961340
\(559\) 41.5401 1.75696
\(560\) 0 0
\(561\) −0.947216 1.64063i −0.0399915 0.0692673i
\(562\) 6.91298 0.291606
\(563\) −35.5594 −1.49865 −0.749325 0.662203i \(-0.769622\pi\)
−0.749325 + 0.662203i \(0.769622\pi\)
\(564\) 9.72326 + 16.8412i 0.409423 + 0.709141i
\(565\) 0 0
\(566\) 4.46607 + 7.73546i 0.187723 + 0.325146i
\(567\) 0.254068 0.440059i 0.0106699 0.0184808i
\(568\) −11.7356 + 20.3266i −0.492414 + 0.852886i
\(569\) −14.9713 −0.627628 −0.313814 0.949485i \(-0.601607\pi\)
−0.313814 + 0.949485i \(0.601607\pi\)
\(570\) 0 0
\(571\) 5.92724 0.248047 0.124024 0.992279i \(-0.460420\pi\)
0.124024 + 0.992279i \(0.460420\pi\)
\(572\) −2.60179 + 4.50643i −0.108786 + 0.188423i
\(573\) 7.40881 12.8324i 0.309508 0.536083i
\(574\) −1.14323 1.98013i −0.0477175 0.0826492i
\(575\) 0 0
\(576\) −3.01175 5.21651i −0.125490 0.217355i
\(577\) −14.5559 −0.605970 −0.302985 0.952995i \(-0.597983\pi\)
−0.302985 + 0.952995i \(0.597983\pi\)
\(578\) −4.94800 −0.205810
\(579\) 10.1451 + 17.5718i 0.421616 + 0.730260i
\(580\) 0 0
\(581\) 16.2914 0.675880
\(582\) 8.19839 0.339834
\(583\) 1.77691 + 3.07770i 0.0735922 + 0.127465i
\(584\) 11.0319 19.1078i 0.456503 0.790686i
\(585\) 0 0
\(586\) −1.32039 + 2.28698i −0.0545448 + 0.0944744i
\(587\) −10.2919 + 17.8262i −0.424794 + 0.735765i −0.996401 0.0847626i \(-0.972987\pi\)
0.571607 + 0.820527i \(0.306320\pi\)
\(588\) −10.3874 −0.428371
\(589\) 3.94011 + 10.2027i 0.162350 + 0.420395i
\(590\) 0 0
\(591\) −2.25328 + 3.90280i −0.0926877 + 0.160540i
\(592\) 12.7288 22.0469i 0.523151 0.906124i
\(593\) −7.16609 12.4120i −0.294276 0.509701i 0.680540 0.732711i \(-0.261745\pi\)
−0.974816 + 0.223010i \(0.928412\pi\)
\(594\) −0.861254 + 1.49174i −0.0353377 + 0.0612066i
\(595\) 0 0
\(596\) −17.0626 −0.698912
\(597\) 13.1395 0.537765
\(598\) 0.587699 + 1.01792i 0.0240328 + 0.0416260i
\(599\) −1.25008 2.16521i −0.0510770 0.0884680i 0.839356 0.543581i \(-0.182932\pi\)
−0.890434 + 0.455113i \(0.849599\pi\)
\(600\) 0 0
\(601\) 14.5259 0.592524 0.296262 0.955107i \(-0.404260\pi\)
0.296262 + 0.955107i \(0.404260\pi\)
\(602\) −2.80763 4.86296i −0.114430 0.198199i
\(603\) 4.96948 8.60739i 0.202373 0.350520i
\(604\) 6.69730 + 11.6001i 0.272509 + 0.472000i
\(605\) 0 0
\(606\) 3.44273 5.96299i 0.139851 0.242230i
\(607\) 31.8704 1.29358 0.646789 0.762669i \(-0.276111\pi\)
0.646789 + 0.762669i \(0.276111\pi\)
\(608\) 13.2584 16.4406i 0.537700 0.666754i
\(609\) −1.05075 −0.0425785
\(610\) 0 0
\(611\) −21.5793 + 37.3764i −0.873004 + 1.51209i
\(612\) 4.35019 + 7.53475i 0.175846 + 0.304574i
\(613\) 10.0244 17.3628i 0.404882 0.701277i −0.589425 0.807823i \(-0.700646\pi\)
0.994308 + 0.106546i \(0.0339792\pi\)
\(614\) 4.86794 + 8.43152i 0.196454 + 0.340268i
\(615\) 0 0
\(616\) 1.49493 0.0602325
\(617\) −10.0410 17.3914i −0.404234 0.700153i 0.589998 0.807404i \(-0.299128\pi\)
−0.994232 + 0.107251i \(0.965795\pi\)
\(618\) −0.872222 1.51073i −0.0350859 0.0607706i
\(619\) 5.62217 0.225974 0.112987 0.993596i \(-0.463958\pi\)
0.112987 + 0.993596i \(0.463958\pi\)
\(620\) 0 0
\(621\) −1.55278 2.68950i −0.0623111 0.107926i
\(622\) 5.81803 10.0771i 0.233282 0.404056i
\(623\) 9.38171 + 16.2496i 0.375870 + 0.651026i
\(624\) −5.79095 + 10.0302i −0.231823 + 0.401530i
\(625\) 0 0
\(626\) −1.65092 −0.0659839
\(627\) 3.19652 + 0.499662i 0.127657 + 0.0199546i
\(628\) −17.5174 −0.699022
\(629\) −11.9726 + 20.7371i −0.477378 + 0.826844i
\(630\) 0 0
\(631\) 2.42184 + 4.19475i 0.0964120 + 0.166990i 0.910197 0.414176i \(-0.135930\pi\)
−0.813785 + 0.581166i \(0.802597\pi\)
\(632\) −5.31481 + 9.20551i −0.211412 + 0.366176i
\(633\) 11.5697 + 20.0393i 0.459854 + 0.796491i
\(634\) −14.8034 −0.587918
\(635\) 0 0
\(636\) 4.60407 + 7.97448i 0.182563 + 0.316209i
\(637\) −11.5267 19.9648i −0.456703 0.791033i
\(638\) −0.289361 −0.0114559
\(639\) 25.2552 0.999078
\(640\) 0 0
\(641\) 12.6503 21.9110i 0.499658 0.865433i −0.500342 0.865828i \(-0.666792\pi\)
1.00000 0.000394734i \(0.000125648\pi\)
\(642\) −0.891229 1.54365i −0.0351740 0.0609232i
\(643\) 6.97283 12.0773i 0.274981 0.476282i −0.695149 0.718866i \(-0.744662\pi\)
0.970130 + 0.242584i \(0.0779950\pi\)
\(644\) −0.634095 + 1.09828i −0.0249868 + 0.0432785i
\(645\) 0 0
\(646\) −3.29560 + 4.08658i −0.129664 + 0.160784i
\(647\) 2.51360 0.0988200 0.0494100 0.998779i \(-0.484266\pi\)
0.0494100 + 0.998779i \(0.484266\pi\)
\(648\) 0.385288 0.667338i 0.0151355 0.0262155i
\(649\) 2.22978 3.86209i 0.0875264 0.151600i
\(650\) 0 0
\(651\) −1.53393 + 2.65684i −0.0601194 + 0.104130i
\(652\) 0.0611608 + 0.105934i 0.00239524 + 0.00414868i
\(653\) −1.92873 −0.0754770 −0.0377385 0.999288i \(-0.512015\pi\)
−0.0377385 + 0.999288i \(0.512015\pi\)
\(654\) 3.05448 0.119440
\(655\) 0 0
\(656\) 5.59306 + 9.68747i 0.218372 + 0.378232i
\(657\) −23.7408 −0.926217
\(658\) 5.83404 0.227434
\(659\) −7.90042 13.6839i −0.307757 0.533050i 0.670115 0.742258i \(-0.266245\pi\)
−0.977871 + 0.209208i \(0.932912\pi\)
\(660\) 0 0
\(661\) −8.20178 14.2059i −0.319012 0.552546i 0.661270 0.750148i \(-0.270018\pi\)
−0.980282 + 0.197602i \(0.936685\pi\)
\(662\) −8.43486 + 14.6096i −0.327830 + 0.567819i
\(663\) 5.44691 9.43432i 0.211540 0.366399i
\(664\) 24.7054 0.958755
\(665\) 0 0
\(666\) 8.49086 0.329014
\(667\) 0.260850 0.451805i 0.0101001 0.0174940i
\(668\) 14.7911 25.6190i 0.572286 0.991228i
\(669\) 7.08521 + 12.2719i 0.273930 + 0.474461i
\(670\) 0 0
\(671\) 1.62496 + 2.81451i 0.0627308 + 0.108653i
\(672\) 5.92434 0.228536
\(673\) −17.0878 −0.658686 −0.329343 0.944210i \(-0.606827\pi\)
−0.329343 + 0.944210i \(0.606827\pi\)
\(674\) 6.24992 + 10.8252i 0.240738 + 0.416970i
\(675\) 0 0
\(676\) −6.81761 −0.262216
\(677\) 4.57680 0.175901 0.0879504 0.996125i \(-0.471968\pi\)
0.0879504 + 0.996125i \(0.471968\pi\)
\(678\) 3.01163 + 5.21630i 0.115661 + 0.200331i
\(679\) −9.81574 + 17.0014i −0.376693 + 0.652452i
\(680\) 0 0
\(681\) 3.42708 5.93587i 0.131326 0.227463i
\(682\) −0.422422 + 0.731656i −0.0161754 + 0.0280166i
\(683\) 29.0692 1.11230 0.556151 0.831082i \(-0.312278\pi\)
0.556151 + 0.831082i \(0.312278\pi\)
\(684\) −14.6804 2.29475i −0.561318 0.0877420i
\(685\) 0 0
\(686\) −3.49942 + 6.06117i −0.133608 + 0.231416i
\(687\) −0.304765 + 0.527869i −0.0116275 + 0.0201395i
\(688\) 13.7359 + 23.7912i 0.523675 + 0.907031i
\(689\) −10.2180 + 17.6981i −0.389276 + 0.674245i
\(690\) 0 0
\(691\) −6.07833 −0.231230 −0.115615 0.993294i \(-0.536884\pi\)
−0.115615 + 0.993294i \(0.536884\pi\)
\(692\) 21.5689 0.819925
\(693\) −0.804279 1.39305i −0.0305521 0.0529177i
\(694\) 8.10220 + 14.0334i 0.307555 + 0.532701i
\(695\) 0 0
\(696\) −1.59343 −0.0603989
\(697\) −5.26078 9.11194i −0.199266 0.345139i
\(698\) 5.05643 8.75799i 0.191389 0.331495i
\(699\) 3.72267 + 6.44786i 0.140804 + 0.243881i
\(700\) 0 0
\(701\) −5.20569 + 9.01651i −0.196616 + 0.340549i −0.947429 0.319966i \(-0.896329\pi\)
0.750813 + 0.660515i \(0.229662\pi\)
\(702\) −9.90517 −0.373847
\(703\) −14.7322 38.1481i −0.555634 1.43878i
\(704\) −2.24095 −0.0844589
\(705\) 0 0
\(706\) 4.61640 7.99585i 0.173741 0.300928i
\(707\) 8.24380 + 14.2787i 0.310040 + 0.537005i
\(708\) 5.77746 10.0069i 0.217130 0.376081i
\(709\) 0.265572 + 0.459984i 0.00997377 + 0.0172751i 0.870969 0.491338i \(-0.163492\pi\)
−0.860995 + 0.508613i \(0.830159\pi\)
\(710\) 0 0
\(711\) 11.4375 0.428941
\(712\) 14.2271 + 24.6421i 0.533183 + 0.923500i
\(713\) −0.761599 1.31913i −0.0285221 0.0494017i
\(714\) −1.47259 −0.0551103
\(715\) 0 0
\(716\) 10.4452 + 18.0916i 0.390355 + 0.676114i
\(717\) 1.90100 3.29262i 0.0709940 0.122965i
\(718\) 3.88657 + 6.73174i 0.145046 + 0.251226i
\(719\) −11.2135 + 19.4224i −0.418194 + 0.724334i −0.995758 0.0920118i \(-0.970670\pi\)
0.577564 + 0.816346i \(0.304004\pi\)
\(720\) 0 0
\(721\) 4.17716 0.155566
\(722\) −1.89951 8.76227i −0.0706924 0.326098i
\(723\) −17.9573 −0.667839
\(724\) −7.85212 + 13.6003i −0.291822 + 0.505450i
\(725\) 0 0
\(726\) −2.57479 4.45967i −0.0955595 0.165514i
\(727\) −22.9867 + 39.8141i −0.852529 + 1.47662i 0.0263888 + 0.999652i \(0.491599\pi\)
−0.878918 + 0.476972i \(0.841734\pi\)
\(728\) 4.29826 + 7.44480i 0.159304 + 0.275923i
\(729\) 15.1354 0.560570
\(730\) 0 0
\(731\) −12.9198 22.3778i −0.477856 0.827671i
\(732\) 4.21035 + 7.29254i 0.155619 + 0.269540i
\(733\) −42.5178 −1.57043 −0.785215 0.619223i \(-0.787448\pi\)
−0.785215 + 0.619223i \(0.787448\pi\)
\(734\) −6.00930 −0.221807
\(735\) 0 0
\(736\) −1.47072 + 2.54737i −0.0542116 + 0.0938972i
\(737\) −1.84881 3.20224i −0.0681019 0.117956i
\(738\) −1.86545 + 3.23106i −0.0686682 + 0.118937i
\(739\) 1.70889 2.95988i 0.0628624 0.108881i −0.832881 0.553452i \(-0.813310\pi\)
0.895744 + 0.444571i \(0.146644\pi\)
\(740\) 0 0
\(741\) 6.70237 + 17.3554i 0.246218 + 0.637566i
\(742\) 2.76248 0.101414
\(743\) −4.86044 + 8.41853i −0.178312 + 0.308846i −0.941303 0.337564i \(-0.890397\pi\)
0.762990 + 0.646410i \(0.223730\pi\)
\(744\) −2.32616 + 4.02903i −0.0852812 + 0.147711i
\(745\) 0 0
\(746\) −4.56175 + 7.90119i −0.167018 + 0.289283i
\(747\) −13.2916 23.0217i −0.486314 0.842321i
\(748\) 3.23683 0.118350
\(749\) 4.26819 0.155956
\(750\) 0 0
\(751\) 5.69265 + 9.85996i 0.207728 + 0.359795i 0.950998 0.309196i \(-0.100060\pi\)
−0.743271 + 0.668991i \(0.766727\pi\)
\(752\) −28.5420 −1.04082
\(753\) 20.1949 0.735943
\(754\) −0.831977 1.44103i −0.0302988 0.0524791i
\(755\) 0 0
\(756\) −5.34356 9.25532i −0.194344 0.336613i
\(757\) 11.3921 19.7317i 0.414053 0.717160i −0.581276 0.813707i \(-0.697446\pi\)
0.995328 + 0.0965464i \(0.0307796\pi\)
\(758\) −2.32589 + 4.02856i −0.0844801 + 0.146324i
\(759\) −0.450583 −0.0163551
\(760\) 0 0
\(761\) −36.7665 −1.33279 −0.666393 0.745601i \(-0.732163\pi\)
−0.666393 + 0.745601i \(0.732163\pi\)
\(762\) −0.529615 + 0.917319i −0.0191859 + 0.0332310i
\(763\) −3.65706 + 6.33421i −0.132394 + 0.229314i
\(764\) 12.6587 + 21.9255i 0.457976 + 0.793238i
\(765\) 0 0
\(766\) −4.79747 8.30945i −0.173339 0.300233i
\(767\) 25.6444 0.925965
\(768\) −1.04955 −0.0378724
\(769\) 10.4004 + 18.0140i 0.375049 + 0.649603i 0.990334 0.138701i \(-0.0442927\pi\)
−0.615286 + 0.788304i \(0.710959\pi\)
\(770\) 0 0
\(771\) 14.4517 0.520464
\(772\) −34.6679 −1.24772
\(773\) 10.5046 + 18.1944i 0.377823 + 0.654409i 0.990745 0.135735i \(-0.0433394\pi\)
−0.612922 + 0.790143i \(0.710006\pi\)
\(774\) −4.58131 + 7.93506i −0.164672 + 0.285220i
\(775\) 0 0
\(776\) −14.8853 + 25.7821i −0.534351 + 0.925523i
\(777\) 5.73539 9.93398i 0.205756 0.356380i
\(778\) −0.474354 −0.0170064
\(779\) 17.7533 + 2.77509i 0.636077 + 0.0994280i
\(780\) 0 0
\(781\) 4.69788 8.13697i 0.168103 0.291164i
\(782\) 0.365572 0.633190i 0.0130728 0.0226428i
\(783\) 2.19820 + 3.80740i 0.0785573 + 0.136065i