Properties

Label 252.2.be.a.107.2
Level $252$
Weight $2$
Character 252.107
Analytic conductor $2.012$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.be (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Character \(\chi\) \(=\) 252.107
Dual form 252.2.be.a.179.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40272 - 0.179921i) q^{2} +(1.93526 + 0.504757i) q^{4} +(-0.604694 - 0.349120i) q^{5} +(-1.16254 - 2.37666i) q^{7} +(-2.62381 - 1.05623i) q^{8} +O(q^{10})\) \(q+(-1.40272 - 0.179921i) q^{2} +(1.93526 + 0.504757i) q^{4} +(-0.604694 - 0.349120i) q^{5} +(-1.16254 - 2.37666i) q^{7} +(-2.62381 - 1.05623i) q^{8} +(0.785403 + 0.598515i) q^{10} +(-1.27599 - 2.21008i) q^{11} +1.88088 q^{13} +(1.20312 + 3.54295i) q^{14} +(3.49044 + 1.95367i) q^{16} +(3.44095 - 1.98663i) q^{17} +(-6.11257 - 3.52909i) q^{19} +(-0.994017 - 0.980861i) q^{20} +(1.39222 + 3.32971i) q^{22} +(2.01328 - 3.48710i) q^{23} +(-2.25623 - 3.90791i) q^{25} +(-2.63835 - 0.338409i) q^{26} +(-1.05019 - 5.18624i) q^{28} -1.86081i q^{29} +(-0.815018 + 0.470551i) q^{31} +(-4.54461 - 3.36846i) q^{32} +(-5.18413 + 2.16759i) q^{34} +(-0.126755 + 1.84302i) q^{35} +(3.74996 - 6.49512i) q^{37} +(7.93928 + 6.05012i) q^{38} +(1.21785 + 1.55472i) q^{40} +10.6065i q^{41} +3.97212i q^{43} +(-1.35382 - 4.92114i) q^{44} +(-3.45147 + 4.52920i) q^{46} +(4.45219 - 7.71142i) q^{47} +(-4.29698 + 5.52593i) q^{49} +(2.46175 + 5.88765i) q^{50} +(3.63998 + 0.949386i) q^{52} +(0.458798 - 0.264887i) q^{53} +1.78190i q^{55} +(0.540009 + 7.46381i) q^{56} +(-0.334798 + 2.61020i) q^{58} +(6.65037 + 11.5188i) q^{59} +(-5.18413 + 8.97918i) q^{61} +(1.22791 - 0.513413i) q^{62} +(5.76877 + 5.54268i) q^{64} +(-1.13735 - 0.656652i) q^{65} +(2.35819 - 1.36150i) q^{67} +(7.66189 - 2.10780i) q^{68} +(0.509399 - 2.56243i) q^{70} +3.51310 q^{71} +(1.37535 + 2.38218i) q^{73} +(-6.42876 + 8.43615i) q^{74} +(-10.0481 - 9.91507i) q^{76} +(-3.76921 + 5.60191i) q^{77} +(11.7206 + 6.76690i) q^{79} +(-1.42858 - 2.39995i) q^{80} +(1.90833 - 14.8780i) q^{82} -17.1516 q^{83} -2.77429 q^{85} +(0.714666 - 5.57178i) q^{86} +(1.01361 + 7.14657i) q^{88} +(-10.2797 - 5.93499i) q^{89} +(-2.18660 - 4.47020i) q^{91} +(5.65635 - 5.73222i) q^{92} +(-7.63263 + 10.0159i) q^{94} +(2.46415 + 4.26804i) q^{95} +10.8682 q^{97} +(7.02170 - 6.97823i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{13} + 4q^{16} - 32q^{22} + 24q^{25} - 44q^{28} - 16q^{34} + 8q^{37} - 52q^{40} - 24q^{46} - 16q^{49} - 52q^{52} - 12q^{58} - 16q^{61} + 120q^{64} + 60q^{70} - 8q^{73} + 72q^{76} + 68q^{82} - 32q^{85} + 44q^{88} + 60q^{94} - 176q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40272 0.179921i −0.991874 0.127223i
\(3\) 0 0
\(4\) 1.93526 + 0.504757i 0.967629 + 0.252379i
\(5\) −0.604694 0.349120i −0.270427 0.156131i 0.358655 0.933470i \(-0.383236\pi\)
−0.629082 + 0.777339i \(0.716569\pi\)
\(6\) 0 0
\(7\) −1.16254 2.37666i −0.439400 0.898291i
\(8\) −2.62381 1.05623i −0.927657 0.373433i
\(9\) 0 0
\(10\) 0.785403 + 0.598515i 0.248366 + 0.189267i
\(11\) −1.27599 2.21008i −0.384726 0.666365i 0.607005 0.794698i \(-0.292371\pi\)
−0.991731 + 0.128333i \(0.959037\pi\)
\(12\) 0 0
\(13\) 1.88088 0.521661 0.260831 0.965385i \(-0.416004\pi\)
0.260831 + 0.965385i \(0.416004\pi\)
\(14\) 1.20312 + 3.54295i 0.321546 + 0.946894i
\(15\) 0 0
\(16\) 3.49044 + 1.95367i 0.872610 + 0.488418i
\(17\) 3.44095 1.98663i 0.834553 0.481829i −0.0208563 0.999782i \(-0.506639\pi\)
0.855409 + 0.517953i \(0.173306\pi\)
\(18\) 0 0
\(19\) −6.11257 3.52909i −1.40232 0.809630i −0.407689 0.913121i \(-0.633665\pi\)
−0.994630 + 0.103491i \(0.966999\pi\)
\(20\) −0.994017 0.980861i −0.222269 0.219327i
\(21\) 0 0
\(22\) 1.39222 + 3.32971i 0.296823 + 0.709896i
\(23\) 2.01328 3.48710i 0.419798 0.727111i −0.576121 0.817364i \(-0.695434\pi\)
0.995919 + 0.0902534i \(0.0287677\pi\)
\(24\) 0 0
\(25\) −2.25623 3.90791i −0.451246 0.781581i
\(26\) −2.63835 0.338409i −0.517422 0.0663674i
\(27\) 0 0
\(28\) −1.05019 5.18624i −0.198467 0.980108i
\(29\) 1.86081i 0.345544i −0.984962 0.172772i \(-0.944728\pi\)
0.984962 0.172772i \(-0.0552724\pi\)
\(30\) 0 0
\(31\) −0.815018 + 0.470551i −0.146382 + 0.0845134i −0.571402 0.820670i \(-0.693600\pi\)
0.425020 + 0.905184i \(0.360267\pi\)
\(32\) −4.54461 3.36846i −0.803381 0.595465i
\(33\) 0 0
\(34\) −5.18413 + 2.16759i −0.889071 + 0.371739i
\(35\) −0.126755 + 1.84302i −0.0214255 + 0.311527i
\(36\) 0 0
\(37\) 3.74996 6.49512i 0.616490 1.06779i −0.373631 0.927577i \(-0.621888\pi\)
0.990121 0.140214i \(-0.0447792\pi\)
\(38\) 7.93928 + 6.05012i 1.28792 + 0.981458i
\(39\) 0 0
\(40\) 1.21785 + 1.55472i 0.192559 + 0.245823i
\(41\) 10.6065i 1.65646i 0.560392 + 0.828228i \(0.310651\pi\)
−0.560392 + 0.828228i \(0.689349\pi\)
\(42\) 0 0
\(43\) 3.97212i 0.605743i 0.953031 + 0.302871i \(0.0979452\pi\)
−0.953031 + 0.302871i \(0.902055\pi\)
\(44\) −1.35382 4.92114i −0.204096 0.741890i
\(45\) 0 0
\(46\) −3.45147 + 4.52920i −0.508892 + 0.667795i
\(47\) 4.45219 7.71142i 0.649418 1.12483i −0.333844 0.942628i \(-0.608346\pi\)
0.983262 0.182197i \(-0.0583209\pi\)
\(48\) 0 0
\(49\) −4.29698 + 5.52593i −0.613855 + 0.789419i
\(50\) 2.46175 + 5.88765i 0.348144 + 0.832639i
\(51\) 0 0
\(52\) 3.63998 + 0.949386i 0.504774 + 0.131656i
\(53\) 0.458798 0.264887i 0.0630207 0.0363850i −0.468159 0.883644i \(-0.655082\pi\)
0.531179 + 0.847259i \(0.321749\pi\)
\(54\) 0 0
\(55\) 1.78190i 0.240271i
\(56\) 0.540009 + 7.46381i 0.0721617 + 0.997393i
\(57\) 0 0
\(58\) −0.334798 + 2.61020i −0.0439612 + 0.342736i
\(59\) 6.65037 + 11.5188i 0.865804 + 1.49962i 0.866246 + 0.499617i \(0.166526\pi\)
−0.000442051 1.00000i \(0.500141\pi\)
\(60\) 0 0
\(61\) −5.18413 + 8.97918i −0.663760 + 1.14967i 0.315860 + 0.948806i \(0.397707\pi\)
−0.979620 + 0.200860i \(0.935626\pi\)
\(62\) 1.22791 0.513413i 0.155944 0.0652036i
\(63\) 0 0
\(64\) 5.76877 + 5.54268i 0.721096 + 0.692835i
\(65\) −1.13735 0.656652i −0.141071 0.0814476i
\(66\) 0 0
\(67\) 2.35819 1.36150i 0.288098 0.166334i −0.348986 0.937128i \(-0.613474\pi\)
0.637084 + 0.770794i \(0.280140\pi\)
\(68\) 7.66189 2.10780i 0.929140 0.255608i
\(69\) 0 0
\(70\) 0.509399 2.56243i 0.0608848 0.306269i
\(71\) 3.51310 0.416928 0.208464 0.978030i \(-0.433154\pi\)
0.208464 + 0.978030i \(0.433154\pi\)
\(72\) 0 0
\(73\) 1.37535 + 2.38218i 0.160973 + 0.278813i 0.935218 0.354073i \(-0.115203\pi\)
−0.774245 + 0.632886i \(0.781870\pi\)
\(74\) −6.42876 + 8.43615i −0.747328 + 0.980683i
\(75\) 0 0
\(76\) −10.0481 9.91507i −1.15259 1.13734i
\(77\) −3.76921 + 5.60191i −0.429541 + 0.638397i
\(78\) 0 0
\(79\) 11.7206 + 6.76690i 1.31867 + 0.761335i 0.983515 0.180827i \(-0.0578775\pi\)
0.335157 + 0.942162i \(0.391211\pi\)
\(80\) −1.42858 2.39995i −0.159720 0.268323i
\(81\) 0 0
\(82\) 1.90833 14.8780i 0.210739 1.64300i
\(83\) −17.1516 −1.88264 −0.941319 0.337520i \(-0.890412\pi\)
−0.941319 + 0.337520i \(0.890412\pi\)
\(84\) 0 0
\(85\) −2.77429 −0.300914
\(86\) 0.714666 5.57178i 0.0770645 0.600820i
\(87\) 0 0
\(88\) 1.01361 + 7.14657i 0.108051 + 0.761827i
\(89\) −10.2797 5.93499i −1.08965 0.629107i −0.156164 0.987731i \(-0.549913\pi\)
−0.933482 + 0.358624i \(0.883246\pi\)
\(90\) 0 0
\(91\) −2.18660 4.47020i −0.229218 0.468604i
\(92\) 5.65635 5.73222i 0.589715 0.597625i
\(93\) 0 0
\(94\) −7.63263 + 10.0159i −0.787245 + 1.03306i
\(95\) 2.46415 + 4.26804i 0.252817 + 0.437892i
\(96\) 0 0
\(97\) 10.8682 1.10350 0.551748 0.834011i \(-0.313961\pi\)
0.551748 + 0.834011i \(0.313961\pi\)
\(98\) 7.02170 6.97823i 0.709299 0.704908i
\(99\) 0 0
\(100\) −2.39384 8.70165i −0.239384 0.870165i
\(101\) 9.18549 5.30325i 0.913990 0.527693i 0.0322775 0.999479i \(-0.489724\pi\)
0.881713 + 0.471786i \(0.156391\pi\)
\(102\) 0 0
\(103\) 11.4970 + 6.63779i 1.13283 + 0.654041i 0.944646 0.328092i \(-0.106406\pi\)
0.188187 + 0.982133i \(0.439739\pi\)
\(104\) −4.93507 1.98663i −0.483923 0.194805i
\(105\) 0 0
\(106\) −0.691224 + 0.289016i −0.0671377 + 0.0280717i
\(107\) −4.80599 + 8.32422i −0.464613 + 0.804733i −0.999184 0.0403906i \(-0.987140\pi\)
0.534571 + 0.845123i \(0.320473\pi\)
\(108\) 0 0
\(109\) −7.11203 12.3184i −0.681209 1.17989i −0.974612 0.223899i \(-0.928121\pi\)
0.293403 0.955989i \(-0.405212\pi\)
\(110\) 0.320600 2.49951i 0.0305680 0.238319i
\(111\) 0 0
\(112\) 0.585411 10.5668i 0.0553161 0.998469i
\(113\) 12.1039i 1.13864i −0.822117 0.569319i \(-0.807207\pi\)
0.822117 0.569319i \(-0.192793\pi\)
\(114\) 0 0
\(115\) −2.43483 + 1.40575i −0.227049 + 0.131087i
\(116\) 0.939258 3.60115i 0.0872079 0.334358i
\(117\) 0 0
\(118\) −7.25615 17.3542i −0.667983 1.59758i
\(119\) −8.72179 5.86840i −0.799526 0.537955i
\(120\) 0 0
\(121\) 2.24369 3.88619i 0.203972 0.353290i
\(122\) 8.88743 11.6626i 0.804630 1.05588i
\(123\) 0 0
\(124\) −1.81478 + 0.499251i −0.162972 + 0.0448340i
\(125\) 6.64198i 0.594077i
\(126\) 0 0
\(127\) 0.582584i 0.0516960i −0.999666 0.0258480i \(-0.991771\pi\)
0.999666 0.0258480i \(-0.00822859\pi\)
\(128\) −7.09474 8.81276i −0.627092 0.778945i
\(129\) 0 0
\(130\) 1.47725 + 1.12573i 0.129563 + 0.0987333i
\(131\) −5.44621 + 9.43310i −0.475837 + 0.824174i −0.999617 0.0276796i \(-0.991188\pi\)
0.523780 + 0.851854i \(0.324522\pi\)
\(132\) 0 0
\(133\) −1.28131 + 18.6302i −0.111104 + 1.61544i
\(134\) −3.55284 + 1.48552i −0.306919 + 0.128329i
\(135\) 0 0
\(136\) −11.1267 + 1.57813i −0.954109 + 0.135323i
\(137\) 11.5198 6.65096i 0.984203 0.568230i 0.0806665 0.996741i \(-0.474295\pi\)
0.903536 + 0.428511i \(0.140962\pi\)
\(138\) 0 0
\(139\) 0.840795i 0.0713153i 0.999364 + 0.0356577i \(0.0113526\pi\)
−0.999364 + 0.0356577i \(0.988647\pi\)
\(140\) −1.17558 + 3.50273i −0.0993546 + 0.296035i
\(141\) 0 0
\(142\) −4.92790 0.632079i −0.413540 0.0530429i
\(143\) −2.39998 4.15689i −0.200697 0.347617i
\(144\) 0 0
\(145\) −0.649646 + 1.12522i −0.0539502 + 0.0934445i
\(146\) −1.50063 3.58899i −0.124193 0.297027i
\(147\) 0 0
\(148\) 10.5356 10.6769i 0.866021 0.877637i
\(149\) −4.89898 2.82843i −0.401340 0.231714i 0.285722 0.958313i \(-0.407767\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(150\) 0 0
\(151\) 14.7077 8.49147i 1.19689 0.691026i 0.237031 0.971502i \(-0.423826\pi\)
0.959861 + 0.280476i \(0.0904925\pi\)
\(152\) 12.3107 + 15.7159i 0.998530 + 1.27473i
\(153\) 0 0
\(154\) 6.29505 7.17976i 0.507270 0.578562i
\(155\) 0.657115 0.0527807
\(156\) 0 0
\(157\) 0.987461 + 1.71033i 0.0788079 + 0.136499i 0.902736 0.430195i \(-0.141555\pi\)
−0.823928 + 0.566695i \(0.808222\pi\)
\(158\) −15.2232 11.6009i −1.21110 0.922914i
\(159\) 0 0
\(160\) 1.57210 + 3.62350i 0.124286 + 0.286463i
\(161\) −10.6282 0.730962i −0.837617 0.0576079i
\(162\) 0 0
\(163\) −2.43483 1.40575i −0.190711 0.110107i 0.401604 0.915813i \(-0.368453\pi\)
−0.592315 + 0.805706i \(0.701786\pi\)
\(164\) −5.35370 + 20.5263i −0.418054 + 1.60283i
\(165\) 0 0
\(166\) 24.0590 + 3.08593i 1.86734 + 0.239515i
\(167\) 2.40833 0.186362 0.0931810 0.995649i \(-0.470296\pi\)
0.0931810 + 0.995649i \(0.470296\pi\)
\(168\) 0 0
\(169\) −9.46230 −0.727869
\(170\) 3.89156 + 0.499153i 0.298469 + 0.0382833i
\(171\) 0 0
\(172\) −2.00496 + 7.68707i −0.152876 + 0.586134i
\(173\) −4.05322 2.34013i −0.308161 0.177917i 0.337942 0.941167i \(-0.390269\pi\)
−0.646103 + 0.763250i \(0.723602\pi\)
\(174\) 0 0
\(175\) −6.66478 + 9.90539i −0.503810 + 0.748777i
\(176\) −0.136000 10.2070i −0.0102514 0.769384i
\(177\) 0 0
\(178\) 13.3517 + 10.1747i 1.00075 + 0.762623i
\(179\) 6.59544 + 11.4236i 0.492966 + 0.853843i 0.999967 0.00810267i \(-0.00257919\pi\)
−0.507001 + 0.861946i \(0.669246\pi\)
\(180\) 0 0
\(181\) 17.6801 1.31415 0.657075 0.753825i \(-0.271793\pi\)
0.657075 + 0.753825i \(0.271793\pi\)
\(182\) 2.26291 + 6.66386i 0.167738 + 0.493958i
\(183\) 0 0
\(184\) −8.96563 + 7.02302i −0.660955 + 0.517744i
\(185\) −4.53515 + 2.61837i −0.333431 + 0.192507i
\(186\) 0 0
\(187\) −8.78124 5.06985i −0.642148 0.370744i
\(188\) 12.5085 12.6763i 0.912278 0.924514i
\(189\) 0 0
\(190\) −2.68862 6.43023i −0.195053 0.466498i
\(191\) 10.6220 18.3978i 0.768581 1.33122i −0.169752 0.985487i \(-0.554297\pi\)
0.938332 0.345734i \(-0.112370\pi\)
\(192\) 0 0
\(193\) −2.08382 3.60927i −0.149996 0.259801i 0.781230 0.624244i \(-0.214593\pi\)
−0.931226 + 0.364443i \(0.881260\pi\)
\(194\) −15.2450 1.95541i −1.09453 0.140390i
\(195\) 0 0
\(196\) −11.1050 + 8.52517i −0.793216 + 0.608941i
\(197\) 8.04744i 0.573356i 0.958027 + 0.286678i \(0.0925510\pi\)
−0.958027 + 0.286678i \(0.907449\pi\)
\(198\) 0 0
\(199\) −1.31955 + 0.761843i −0.0935405 + 0.0540056i −0.546041 0.837759i \(-0.683866\pi\)
0.452500 + 0.891764i \(0.350532\pi\)
\(200\) 1.79229 + 12.6367i 0.126734 + 0.893549i
\(201\) 0 0
\(202\) −13.8389 + 5.78632i −0.973698 + 0.407124i
\(203\) −4.42251 + 2.16327i −0.310399 + 0.151832i
\(204\) 0 0
\(205\) 3.70294 6.41368i 0.258624 0.447951i
\(206\) −14.9328 11.3795i −1.04042 0.792849i
\(207\) 0 0
\(208\) 6.56509 + 3.67461i 0.455207 + 0.254789i
\(209\) 18.0124i 1.24594i
\(210\) 0 0
\(211\) 19.2878i 1.32783i −0.747809 0.663914i \(-0.768894\pi\)
0.747809 0.663914i \(-0.231106\pi\)
\(212\) 1.02160 0.281043i 0.0701635 0.0193021i
\(213\) 0 0
\(214\) 8.23917 10.8119i 0.563218 0.739084i
\(215\) 1.38675 2.40192i 0.0945753 0.163809i
\(216\) 0 0
\(217\) 2.06583 + 1.38998i 0.140238 + 0.0943580i
\(218\) 7.75986 + 18.5589i 0.525564 + 1.25697i
\(219\) 0 0
\(220\) −0.899425 + 3.44843i −0.0606393 + 0.232493i
\(221\) 6.47200 3.73661i 0.435354 0.251352i
\(222\) 0 0
\(223\) 18.1390i 1.21468i 0.794443 + 0.607338i \(0.207763\pi\)
−0.794443 + 0.607338i \(0.792237\pi\)
\(224\) −2.72235 + 14.7170i −0.181895 + 0.983318i
\(225\) 0 0
\(226\) −2.17774 + 16.9784i −0.144861 + 1.12938i
\(227\) −4.78909 8.29495i −0.317863 0.550555i 0.662179 0.749346i \(-0.269632\pi\)
−0.980042 + 0.198791i \(0.936299\pi\)
\(228\) 0 0
\(229\) −2.42163 + 4.19438i −0.160026 + 0.277173i −0.934878 0.354970i \(-0.884491\pi\)
0.774852 + 0.632143i \(0.217824\pi\)
\(230\) 3.66832 1.53380i 0.241882 0.101136i
\(231\) 0 0
\(232\) −1.96544 + 4.88242i −0.129037 + 0.320546i
\(233\) 18.7348 + 10.8165i 1.22736 + 0.708615i 0.966476 0.256755i \(-0.0826535\pi\)
0.260881 + 0.965371i \(0.415987\pi\)
\(234\) 0 0
\(235\) −5.38442 + 3.10870i −0.351241 + 0.202789i
\(236\) 7.05599 + 25.6486i 0.459306 + 1.66958i
\(237\) 0 0
\(238\) 11.1784 + 9.80097i 0.724588 + 0.635302i
\(239\) 20.5549 1.32958 0.664792 0.747028i \(-0.268520\pi\)
0.664792 + 0.747028i \(0.268520\pi\)
\(240\) 0 0
\(241\) −5.37528 9.31025i −0.346252 0.599726i 0.639328 0.768934i \(-0.279212\pi\)
−0.985580 + 0.169208i \(0.945879\pi\)
\(242\) −3.84648 + 5.04755i −0.247261 + 0.324469i
\(243\) 0 0
\(244\) −14.5649 + 14.7603i −0.932424 + 0.944930i
\(245\) 4.52757 1.84133i 0.289256 0.117639i
\(246\) 0 0
\(247\) −11.4970 6.63779i −0.731536 0.422353i
\(248\) 2.63546 0.373793i 0.167352 0.0237359i
\(249\) 0 0
\(250\) 1.19503 9.31685i 0.0755803 0.589249i
\(251\) 19.4316 1.22651 0.613257 0.789884i \(-0.289859\pi\)
0.613257 + 0.789884i \(0.289859\pi\)
\(252\) 0 0
\(253\) −10.2757 −0.646028
\(254\) −0.104819 + 0.817203i −0.00657692 + 0.0512759i
\(255\) 0 0
\(256\) 8.36634 + 13.6383i 0.522897 + 0.852396i
\(257\) 7.56621 + 4.36835i 0.471967 + 0.272490i 0.717063 0.697009i \(-0.245486\pi\)
−0.245096 + 0.969499i \(0.578819\pi\)
\(258\) 0 0
\(259\) −19.7962 1.36150i −1.23007 0.0845994i
\(260\) −1.86962 1.84488i −0.115949 0.114414i
\(261\) 0 0
\(262\) 9.33672 12.2521i 0.576825 0.756940i
\(263\) −10.9040 18.8862i −0.672368 1.16458i −0.977231 0.212179i \(-0.931944\pi\)
0.304863 0.952396i \(1.59861\pi\)
\(264\) 0 0
\(265\) −0.369910 −0.0227234
\(266\) 5.14928 25.9025i 0.315723 1.58818i
\(267\) 0 0
\(268\) 5.25092 1.44454i 0.320751 0.0882393i
\(269\) −12.7340 + 7.35200i −0.776408 + 0.448259i −0.835156 0.550014i \(-0.814623\pi\)
0.0587478 + 0.998273i \(0.481289\pi\)
\(270\) 0 0
\(271\) −4.49275 2.59389i −0.272915 0.157568i 0.357296 0.933991i \(-0.383699\pi\)
−0.630212 + 0.776423i \(0.717032\pi\)
\(272\) 15.8916 0.211743i 0.963573 0.0128388i
\(273\) 0 0
\(274\) −17.3557 + 7.25680i −1.04850 + 0.438399i
\(275\) −5.75786 + 9.97291i −0.347212 + 0.601389i
\(276\) 0 0
\(277\) −11.8627 20.5469i −0.712763 1.23454i −0.963816 0.266568i \(-0.914110\pi\)
0.251053 0.967973i \(-0.419223\pi\)
\(278\) 0.151276 1.17940i 0.00907296 0.0707358i
\(279\) 0 0
\(280\) 2.27922 4.70184i 0.136210 0.280989i
\(281\) 4.12400i 0.246017i −0.992406 0.123009i \(-0.960746\pi\)
0.992406 0.123009i \(-0.0392542\pi\)
\(282\) 0 0
\(283\) −6.11257 + 3.52909i −0.363355 + 0.209783i −0.670551 0.741863i \(-0.733942\pi\)
0.307197 + 0.951646i \(0.400609\pi\)
\(284\) 6.79875 + 1.77326i 0.403432 + 0.105224i
\(285\) 0 0
\(286\) 2.61860 + 6.26277i 0.154841 + 0.370325i
\(287\) 25.2080 12.3305i 1.48798 0.727847i
\(288\) 0 0
\(289\) −0.606584 + 1.05063i −0.0356814 + 0.0618020i
\(290\) 1.11372 1.46149i 0.0654001 0.0858215i
\(291\) 0 0
\(292\) 1.45924 + 5.30436i 0.0853955 + 0.310414i
\(293\) 15.9675i 0.932830i −0.884566 0.466415i \(-0.845545\pi\)
0.884566 0.466415i \(-0.154455\pi\)
\(294\) 0 0
\(295\) 9.28711i 0.540716i
\(296\) −16.6995 + 13.0812i −0.970639 + 0.760327i
\(297\) 0 0
\(298\) 6.36301 + 4.84892i 0.368599 + 0.280891i
\(299\) 3.78673 6.55881i 0.218992 0.379306i
\(300\) 0 0
\(301\) 9.44036 4.61776i 0.544133 0.266163i
\(302\) −22.1585 + 9.26495i −1.27508 + 0.533138i
\(303\) 0 0
\(304\) −14.4409 24.2600i −0.828241 1.39141i
\(305\) 6.26962 3.61977i 0.358997 0.207267i
\(306\) 0 0
\(307\) 5.53450i 0.315871i −0.987449 0.157935i \(-0.949516\pi\)
0.987449 0.157935i \(-0.0504838\pi\)
\(308\) −10.1220 + 8.93860i −0.576754 + 0.509324i
\(309\) 0 0
\(310\) −0.921749 0.118229i −0.0523518 0.00671493i
\(311\) −5.24440 9.08357i −0.297383 0.515082i 0.678154 0.734920i \(-0.262780\pi\)
−0.975536 + 0.219838i \(0.929447\pi\)
\(312\) 0 0
\(313\) −1.13158 + 1.95996i −0.0639609 + 0.110784i −0.896233 0.443584i \(-0.853707\pi\)
0.832272 + 0.554368i \(0.187040\pi\)
\(314\) −1.07741 2.57678i −0.0608017 0.145416i
\(315\) 0 0
\(316\) 19.2668 + 19.0117i 1.08384 + 1.06949i
\(317\) 8.23233 + 4.75294i 0.462374 + 0.266952i 0.713042 0.701122i \(-0.247317\pi\)
−0.250668 + 0.968073i \(0.580650\pi\)
\(318\) 0 0
\(319\) −4.11255 + 2.37438i −0.230258 + 0.132940i
\(320\) −1.55328 5.36562i −0.0868309 0.299947i
\(321\) 0 0
\(322\) 14.7768 + 2.93756i 0.823481 + 0.163704i
\(323\) −28.0441 −1.56041
\(324\) 0 0
\(325\) −4.24369 7.35029i −0.235398 0.407721i
\(326\) 3.16247 + 2.40996i 0.175153 + 0.133475i
\(327\) 0 0
\(328\) 11.2029 27.8294i 0.618574 1.53662i
\(329\) −23.5032 1.61646i −1.29578 0.0891182i
\(330\) 0 0
\(331\) −8.60924 4.97055i −0.473207 0.273206i 0.244374 0.969681i \(-0.421417\pi\)
−0.717581 + 0.696475i \(0.754751\pi\)
\(332\) −33.1928 8.65742i −1.82169 0.475137i
\(333\) 0 0
\(334\) −3.37821 0.433308i −0.184848 0.0237095i
\(335\) −1.90131 −0.103879
\(336\) 0 0
\(337\) 10.6441 0.579822 0.289911 0.957054i \(-0.406374\pi\)
0.289911 + 0.957054i \(0.406374\pi\)
\(338\) 13.2730 + 1.70246i 0.721955 + 0.0926018i
\(339\) 0 0
\(340\) −5.36897 1.40034i −0.291173 0.0759443i
\(341\) 2.07991 + 1.20084i 0.112634 + 0.0650290i
\(342\) 0 0
\(343\) 18.1287 + 3.78831i 0.978856 + 0.204549i
\(344\) 4.19546 10.4221i 0.226204 0.561922i
\(345\) 0 0
\(346\) 5.26451 + 4.01181i 0.283022 + 0.215676i
\(347\) 8.77440 + 15.1977i 0.471035 + 0.815856i 0.999451 0.0331294i \(-0.0105473\pi\)
−0.528416 + 0.848985i \(0.677214\pi\)
\(348\) 0 0
\(349\) 29.0703 1.55610 0.778049 0.628204i \(-0.216210\pi\)
0.778049 + 0.628204i \(0.216210\pi\)
\(350\) 11.1310 12.6954i 0.594978 0.678597i
\(351\) 0 0
\(352\) −1.64568 + 14.3421i −0.0877153 + 0.764436i
\(353\) 9.73945 5.62308i 0.518379 0.299286i −0.217892 0.975973i \(-0.569918\pi\)
0.736271 + 0.676687i \(0.236585\pi\)
\(354\) 0 0
\(355\) −2.12435 1.22649i −0.112749 0.0650955i
\(356\) −16.8981 16.6745i −0.895599 0.883745i
\(357\) 0 0
\(358\) −7.19622 17.2108i −0.380332 0.909621i
\(359\) −14.5218 + 25.1525i −0.766431 + 1.32750i 0.173055 + 0.984912i \(0.444636\pi\)
−0.939486 + 0.342586i \(0.888697\pi\)
\(360\) 0 0
\(361\) 15.4090 + 26.6892i 0.811001 + 1.40469i
\(362\) −24.8002 3.18101i −1.30347 0.167190i
\(363\) 0 0
\(364\) −1.97527 9.75468i −0.103532 0.511284i
\(365\) 1.92065i 0.100532i
\(366\) 0 0
\(367\) 20.8594 12.0432i 1.08885 0.628649i 0.155582 0.987823i \(-0.450275\pi\)
0.933271 + 0.359174i \(0.116941\pi\)
\(368\) 13.8399 8.23824i 0.721453 0.429448i
\(369\) 0 0
\(370\) 6.83266 2.85688i 0.355213 0.148522i
\(371\) −1.16292 0.782462i −0.0603757 0.0406234i
\(372\) 0 0
\(373\) −6.69734 + 11.6001i −0.346775 + 0.600632i −0.985675 0.168658i \(-0.946057\pi\)
0.638900 + 0.769290i \(0.279390\pi\)
\(374\) 11.4055 + 8.69152i 0.589763 + 0.449428i
\(375\) 0 0
\(376\) −19.8267 + 15.5308i −1.02248 + 0.800939i
\(377\) 3.49996i 0.180257i
\(378\) 0 0
\(379\) 12.9558i 0.665493i 0.943016 + 0.332746i \(0.107975\pi\)
−0.943016 + 0.332746i \(0.892025\pi\)
\(380\) 2.61445 + 9.50356i 0.134118 + 0.487522i
\(381\) 0 0
\(382\) −18.2099 + 23.8959i −0.931698 + 1.22262i
\(383\) 1.26675 2.19407i 0.0647277 0.112112i −0.831845 0.555007i \(-0.812715\pi\)
0.896573 + 0.442896i \(0.146049\pi\)
\(384\) 0 0
\(385\) 4.23496 2.07153i 0.215833 0.105575i
\(386\) 2.27363 + 5.43773i 0.115725 + 0.276773i
\(387\) 0 0
\(388\) 21.0327 + 5.48579i 1.06777 + 0.278499i
\(389\) −13.2543 + 7.65235i −0.672018 + 0.387990i −0.796841 0.604189i \(-0.793497\pi\)
0.124823 + 0.992179i \(0.460164\pi\)
\(390\) 0 0
\(391\) 15.9986i 0.809083i
\(392\) 17.1111 9.96042i 0.864242 0.503077i
\(393\) 0 0
\(394\) 1.44790 11.2883i 0.0729442 0.568697i
\(395\) −4.72492 8.18380i −0.237736 0.411772i
\(396\) 0 0
\(397\) −6.55329 + 11.3506i −0.328900 + 0.569672i −0.982294 0.187346i \(-0.940011\pi\)
0.653394 + 0.757018i \(0.273345\pi\)
\(398\) 1.98803 0.831239i 0.0996511 0.0416663i
\(399\) 0 0
\(400\) −0.240478 18.0482i −0.0120239 0.902412i
\(401\) −1.00499 0.580229i −0.0501866 0.0289753i 0.474697 0.880149i \(-0.342558\pi\)
−0.524883 + 0.851174i \(0.675891\pi\)
\(402\) 0 0
\(403\) −1.53295 + 0.885048i −0.0763616 + 0.0440874i
\(404\) 20.4531 5.62670i 1.01758 0.279939i
\(405\) 0 0
\(406\) 6.59276 2.23877i 0.327193 0.111108i
\(407\) −19.1397 −0.948718
\(408\) 0 0
\(409\) −3.59404 6.22507i −0.177714 0.307810i 0.763383 0.645946i \(-0.223537\pi\)
−0.941097 + 0.338136i \(0.890204\pi\)
\(410\) −6.34815 + 8.33037i −0.313513 + 0.411408i
\(411\) 0 0
\(412\) 18.8992 + 18.6490i 0.931095 + 0.918771i
\(413\) 19.6448 29.1967i 0.966658 1.43668i
\(414\) 0 0
\(415\) 10.3715 + 5.98798i 0.509116 + 0.293938i
\(416\) −8.54785 6.33565i −0.419093 0.310631i
\(417\) 0 0
\(418\) 3.24080 25.2664i 0.158513 1.23582i
\(419\) −16.1127 −0.787155 −0.393578 0.919291i \(-0.628763\pi\)
−0.393578 + 0.919291i \(0.628763\pi\)
\(420\) 0 0
\(421\) 5.49992 0.268050 0.134025 0.990978i \(-0.457210\pi\)
0.134025 + 0.990978i \(0.457210\pi\)
\(422\) −3.47028 + 27.0554i −0.168930 + 1.31704i
\(423\) 0 0
\(424\) −1.48358 + 0.210419i −0.0720490 + 0.0102189i
\(425\) −15.5271 8.96460i −0.753177 0.434847i
\(426\) 0 0
\(427\) 27.3672 + 1.88220i 1.32439 + 0.0910862i
\(428\) −13.5025 + 13.6836i −0.652670 + 0.661424i
\(429\) 0 0
\(430\) −2.37737 + 3.11971i −0.114647 + 0.150446i
\(431\) 6.70530 + 11.6139i 0.322983 + 0.559423i 0.981102 0.193491i \(-0.0619811\pi\)
−0.658119 + 0.752914i \(0.728648\pi\)
\(432\) 0 0
\(433\) −31.6801 −1.52245 −0.761224 0.648489i \(-0.775401\pi\)
−0.761224 + 0.648489i \(0.775401\pi\)
\(434\) −2.64770 2.32144i −0.127094 0.111433i
\(435\) 0 0
\(436\) −7.54580 27.4291i −0.361378 1.31362i
\(437\) −24.6126 + 14.2101i −1.17738 + 0.679761i
\(438\) 0 0
\(439\) −16.8712 9.74059i −0.805218 0.464893i 0.0400745 0.999197i \(-0.487240\pi\)
−0.845292 + 0.534304i \(0.820574\pi\)
\(440\) 1.88209 4.67536i 0.0897250 0.222889i
\(441\) 0 0
\(442\) −9.75071 + 4.07698i −0.463794 + 0.193922i
\(443\) −3.44127 + 5.96046i −0.163500 + 0.283190i −0.936121 0.351677i \(-0.885612\pi\)
0.772622 + 0.634867i \(0.218945\pi\)
\(444\) 0 0
\(445\) 4.14404 + 7.17770i 0.196447 + 0.340255i
\(446\) 3.26358 25.4440i 0.154535 1.20481i
\(447\) 0 0
\(448\) 6.46659 20.1540i 0.305518 0.952186i
\(449\) 19.3255i 0.912025i 0.889973 + 0.456012i \(0.150723\pi\)
−0.889973 + 0.456012i \(0.849277\pi\)
\(450\) 0 0
\(451\) 23.4412 13.5338i 1.10380 0.637281i
\(452\) 6.10952 23.4241i 0.287368 1.10178i
\(453\) 0 0
\(454\) 5.22533 + 12.4972i 0.245237 + 0.586521i
\(455\) −0.238411 + 3.46649i −0.0111769 + 0.162511i
\(456\) 0 0
\(457\) −2.41849 + 4.18896i −0.113132 + 0.195951i −0.917032 0.398814i \(-0.869422\pi\)
0.803899 + 0.594766i \(0.202755\pi\)
\(458\) 4.15153 5.44785i 0.193988 0.254562i
\(459\) 0 0
\(460\) −5.42159 + 1.49149i −0.252783 + 0.0695411i
\(461\) 26.3490i 1.22720i −0.789618 0.613599i \(-0.789721\pi\)
0.789618 0.613599i \(-0.210279\pi\)
\(462\) 0 0
\(463\) 38.1024i 1.77077i 0.464858 + 0.885385i \(0.346105\pi\)
−0.464858 + 0.885385i \(0.653895\pi\)
\(464\) 3.63541 6.49505i 0.168770 0.301525i
\(465\) 0 0
\(466\) −24.3336 18.5434i −1.12723 0.859006i
\(467\) −3.19220 + 5.52905i −0.147717 + 0.255854i −0.930383 0.366588i \(-0.880526\pi\)
0.782666 + 0.622442i \(0.213859\pi\)
\(468\) 0 0
\(469\) −5.97731 4.02179i −0.276007 0.185709i
\(470\) 8.11216 3.39187i 0.374186 0.156455i
\(471\) 0 0
\(472\) −5.28287 37.2474i −0.243164 1.71445i
\(473\) 8.77871 5.06839i 0.403646 0.233045i
\(474\) 0 0
\(475\) 31.8498i 1.46137i
\(476\) −13.9168 15.7593i −0.637875 0.722324i
\(477\) 0 0
\(478\) −28.8328 3.69825i −1.31878 0.169154i
\(479\) 10.5205 + 18.2220i 0.480693 + 0.832585i 0.999755 0.0221516i \(-0.00705165\pi\)
−0.519061 + 0.854737i \(0.673718\pi\)
\(480\) 0 0
\(481\) 7.05321 12.2165i 0.321599 0.557026i
\(482\) 5.86491 + 14.0268i 0.267139 + 0.638904i
\(483\) 0 0
\(484\) 6.30370 6.38825i 0.286532 0.290375i
\(485\) −6.57192 3.79430i −0.298415 0.172290i
\(486\) 0 0
\(487\) −13.6690 + 7.89181i −0.619402 + 0.357612i −0.776636 0.629949i \(-0.783076\pi\)
0.157234 + 0.987561i \(0.449742\pi\)
\(488\) 23.0862 18.0840i 1.04506 0.818626i
\(489\) 0 0
\(490\) −6.68222 + 1.76828i −0.301872 + 0.0798825i
\(491\) 18.8204 0.849351 0.424675 0.905346i \(-0.360388\pi\)
0.424675 + 0.905346i \(0.360388\pi\)
\(492\) 0 0
\(493\) −3.69675 6.40295i −0.166493 0.288375i
\(494\) 14.9328 + 11.3795i 0.671859 + 0.511989i
\(495\) 0 0
\(496\) −3.76407 + 0.0501532i −0.169012 + 0.00225194i
\(497\) −4.08413 8.34943i −0.183198 0.374523i
\(498\) 0 0
\(499\) 6.97921 + 4.02945i 0.312432 + 0.180383i 0.648014 0.761628i \(-0.275600\pi\)
−0.335582 + 0.942011i \(0.608933\pi\)
\(500\) −3.35259 + 12.8539i −0.149932 + 0.574846i
\(501\) 0 0
\(502\) −27.2572 3.49615i −1.21655 0.156041i
\(503\) 0.823898 0.0367358 0.0183679 0.999831i \(-0.494153\pi\)
0.0183679 + 0.999831i \(0.494153\pi\)
\(504\) 0 0
\(505\) −7.40588 −0.329557
\(506\) 14.4140 + 1.84881i 0.640779 + 0.0821897i
\(507\) 0 0
\(508\) 0.294064 1.12745i 0.0130470 0.0500225i
\(509\) 33.8626 + 19.5506i 1.50093 + 0.866563i 0.999999 + 0.00107666i \(0.000342710\pi\)
0.500932 + 0.865487i \(0.332991\pi\)
\(510\) 0 0
\(511\) 4.06272 6.03813i 0.179724 0.267111i
\(512\) −9.28184 20.6361i −0.410203 0.911994i
\(513\) 0 0
\(514\) −9.82733 7.48890i −0.433465 0.330321i
\(515\) −4.63477 8.02766i −0.204232 0.353741i
\(516\) 0 0
\(517\) −22.7238 −0.999392
\(518\) 27.5235 + 5.47154i 1.20932 + 0.240406i
\(519\) 0 0
\(520\) 2.29063 + 2.92423i 0.100451 + 0.128236i
\(521\) −0.453045 + 0.261566i −0.0198483 + 0.0114594i −0.509891 0.860239i \(-0.670314\pi\)
0.490043 + 0.871698i \(0.336981\pi\)
\(522\) 0 0
\(523\) 32.5034 + 18.7658i 1.42127 + 0.820573i 0.996408 0.0846840i \(-0.0269881\pi\)
0.424865 + 0.905257i \(0.360321\pi\)
\(524\) −15.3012 + 15.5065i −0.668438 + 0.677403i
\(525\) 0 0
\(526\) 11.8972 + 28.4540i 0.518743 + 1.24065i
\(527\) −1.86962 + 3.23828i −0.0814421 + 0.141062i
\(528\) 0 0
\(529\) 3.39342 + 5.87757i 0.147540 + 0.255546i
\(530\) 0.518880 + 0.0665544i 0.0225387 + 0.00289094i
\(531\) 0 0
\(532\) −11.8834 + 35.4075i −0.515210 + 1.53511i
\(533\) 19.9495i 0.864109i
\(534\) 0 0
\(535\) 5.81230 3.35574i 0.251288 0.145081i
\(536\) −7.62549 + 1.08154i −0.329371 + 0.0467153i
\(537\) 0 0
\(538\) 19.1851 8.02169i 0.827128 0.345840i
\(539\) 17.6957 + 2.44564i 0.762207 + 0.105341i
\(540\) 0 0
\(541\) −11.1770 + 19.3592i −0.480538 + 0.832317i −0.999751 0.0223286i \(-0.992892\pi\)
0.519212 + 0.854645i \(0.326225\pi\)
\(542\) 5.83539 + 4.44685i 0.250651 + 0.191009i
\(543\) 0 0
\(544\) −22.3297 2.56222i −0.957376 0.109854i
\(545\) 9.93181i 0.425432i
\(546\) 0 0
\(547\) 8.09960i 0.346314i −0.984894 0.173157i \(-0.944603\pi\)
0.984894 0.173157i \(-0.0553968\pi\)
\(548\) 25.6509 7.05661i 1.09575 0.301444i
\(549\) 0 0
\(550\) 9.87101 12.9533i 0.420901 0.552329i
\(551\) −6.56698 + 11.3743i −0.279763 + 0.484563i
\(552\) 0 0
\(553\) 2.45686 35.7227i 0.104476 1.51908i
\(554\) 12.9433 + 30.9559i 0.549909 + 1.31519i
\(555\) 0 0
\(556\) −0.424398 + 1.62716i −0.0179985 + 0.0690067i
\(557\) −27.3598 + 15.7962i −1.15927 + 0.669307i −0.951130 0.308791i \(-0.900076\pi\)
−0.208144 + 0.978098i \(0.566742\pi\)
\(558\) 0 0
\(559\) 7.47107i 0.315992i
\(560\) −4.04308 + 6.18530i −0.170851 + 0.261377i
\(561\) 0 0
\(562\) −0.741992 + 5.78482i −0.0312991 + 0.244018i
\(563\) −4.17946 7.23904i −0.176143 0.305089i 0.764413 0.644727i \(-0.223029\pi\)
−0.940556 + 0.339638i \(0.889696\pi\)
\(564\) 0 0
\(565\) −4.22571 + 7.31914i −0.177777 + 0.307919i
\(566\) 9.20919 3.85056i 0.387091 0.161851i
\(567\) 0 0
\(568\) −9.21771 3.71063i −0.386766 0.155695i
\(569\) 11.2838 + 6.51469i 0.473041 + 0.273110i 0.717512 0.696546i \(-0.245281\pi\)
−0.244471 + 0.969657i \(0.578614\pi\)
\(570\) 0 0
\(571\) −12.4590 + 7.19319i −0.521392 + 0.301026i −0.737504 0.675343i \(-0.763996\pi\)
0.216112 + 0.976369i \(0.430662\pi\)
\(572\) −2.54636 9.25606i −0.106469 0.387015i
\(573\) 0 0
\(574\) −37.5783 + 12.7608i −1.56849 + 0.532627i
\(575\) −18.1697 −0.757728
\(576\) 0 0
\(577\) 12.8808 + 22.3102i 0.536235 + 0.928786i 0.999102 + 0.0423583i \(0.0134871\pi\)
−0.462868 + 0.886427i \(0.653180\pi\)
\(578\) 1.03990 1.36461i 0.0432541 0.0567603i
\(579\) 0 0
\(580\) −1.82520 + 1.84968i −0.0757871 + 0.0768037i
\(581\) 19.9395 + 40.7635i 0.827231 + 1.69116i
\(582\) 0 0
\(583\) −1.17084 0.675987i −0.0484914 0.0279965i
\(584\) −1.09254 7.70308i −0.0452098 0.318756i
\(585\) 0 0
\(586\) −2.87288 + 22.3979i −0.118678 + 0.925250i
\(587\) 33.3927 1.37826 0.689131 0.724637i \(-0.257992\pi\)
0.689131 + 0.724637i \(0.257992\pi\)
\(588\) 0 0
\(589\) 6.64247 0.273698
\(590\) −1.67094 + 13.0272i −0.0687916 + 0.536323i
\(591\) 0 0
\(592\) 25.7783 15.3446i 1.05948 0.630661i
\(593\) −25.5907 14.7748i −1.05089 0.606729i −0.127989 0.991776i \(-0.540852\pi\)
−0.922897 + 0.385046i \(0.874185\pi\)
\(594\) 0 0
\(595\) 3.22524 + 6.59354i 0.132222 + 0.270309i
\(596\) −8.05312 7.94653i −0.329868 0.325503i
\(597\) 0 0
\(598\) −6.49179 + 8.51887i −0.265469 + 0.348363i
\(599\) −2.99964 5.19553i −0.122562 0.212284i 0.798215 0.602372i \(-0.205778\pi\)
−0.920777 + 0.390089i \(0.872444\pi\)
\(600\) 0 0
\(601\) −5.44843 −0.222246 −0.111123 0.993807i \(-0.535445\pi\)
−0.111123 + 0.993807i \(0.535445\pi\)
\(602\) −14.0730 + 4.77892i −0.573574 + 0.194774i
\(603\) 0 0
\(604\) 32.7492 9.00938i 1.33255 0.366586i
\(605\) −2.71349 + 1.56663i −0.110319 + 0.0636928i
\(606\) 0 0
\(607\) −3.76460 2.17350i −0.152801 0.0882195i 0.421650 0.906759i \(-0.361451\pi\)
−0.574451 + 0.818539i \(0.694784\pi\)
\(608\) 15.8916 + 36.6283i 0.644491 + 1.48547i
\(609\) 0 0
\(610\) −9.44580 + 3.94949i −0.382449 + 0.159910i
\(611\) 8.37402 14.5042i 0.338776 0.586778i
\(612\) 0 0
\(613\) 7.48103 + 12.9575i 0.302156 + 0.523350i 0.976624 0.214954i \(-0.0689603\pi\)
−0.674468 + 0.738304i \(0.735627\pi\)
\(614\) −0.995771 + 7.76337i −0.0401861 + 0.313304i
\(615\) 0 0
\(616\) 15.8066 10.7172i 0.636865 0.431809i
\(617\) 21.4967i 0.865425i −0.901532 0.432713i \(-0.857557\pi\)
0.901532 0.432713i \(-0.142443\pi\)
\(618\) 0 0
\(619\) −12.4590 + 7.19319i −0.500769 + 0.289119i −0.729031 0.684481i \(-0.760029\pi\)
0.228262 + 0.973600i \(0.426696\pi\)
\(620\) 1.27169 + 0.331684i 0.0510721 + 0.0133207i
\(621\) 0 0
\(622\) 5.72212 + 13.6853i 0.229436 + 0.548731i
\(623\) −2.15482 + 31.3310i −0.0863309 + 1.25525i
\(624\) 0 0
\(625\) −8.96230 + 15.5232i −0.358492 + 0.620927i
\(626\) 1.93994 2.54569i 0.0775354 0.101746i
\(627\) 0 0
\(628\) 1.04769 + 3.80836i 0.0418073 + 0.151970i
\(629\) 29.7992i 1.18817i
\(630\) 0 0
\(631\) 15.8983i 0.632900i −0.948609 0.316450i \(-0.897509\pi\)
0.948609 0.316450i \(-0.102491\pi\)
\(632\) −23.6053 30.1347i −0.938968 1.19869i
\(633\) 0 0
\(634\) −10.6925 8.14822i −0.424654 0.323607i
\(635\) −0.203392 + 0.352285i −0.00807136 + 0.0139800i
\(636\) 0 0
\(637\) −8.08209 + 10.3936i −0.320224 + 0.411809i
\(638\) 6.19596 2.59066i 0.245300 0.102565i
\(639\) 0 0
\(640\) 1.21343 + 7.80593i 0.0479651 + 0.308557i
\(641\) −1.35619 + 0.782995i −0.0535661 + 0.0309264i −0.526544 0.850148i \(-0.676512\pi\)
0.472978 + 0.881074i \(0.343179\pi\)
\(642\) 0 0
\(643\) 33.5314i 1.32235i −0.750232 0.661174i \(-0.770058\pi\)
0.750232 0.661174i \(-0.229942\pi\)
\(644\) −20.1993 6.77924i −0.795963 0.267140i
\(645\) 0 0
\(646\) 39.3380 + 5.04570i 1.54773 + 0.198521i
\(647\) −8.65921 14.9982i −0.340429 0.589640i 0.644084 0.764955i \(-0.277239\pi\)
−0.984512 + 0.175315i \(0.943906\pi\)
\(648\) 0 0
\(649\) 16.9716 29.3957i 0.666195 1.15388i
\(650\) 4.63025 + 11.0739i 0.181613 + 0.434356i
\(651\) 0 0
\(652\) −4.00247 3.94949i −0.156749 0.154674i
\(653\) −23.4648 13.5474i −0.918247 0.530150i −0.0351715 0.999381i \(-0.511198\pi\)
−0.883075 + 0.469231i \(0.844531\pi\)
\(654\) 0 0
\(655\) 6.58657 3.80276i 0.257359 0.148586i
\(656\) −20.7216 + 37.0213i −0.809042 + 1.44544i
\(657\) 0 0
\(658\) 32.6777 + 6.49616i 1.27391 + 0.253247i
\(659\) 10.9749 0.427521 0.213761 0.976886i \(-0.431429\pi\)
0.213761 + 0.976886i \(0.431429\pi\)
\(660\) 0 0
\(661\) −1.44036 2.49478i −0.0560235 0.0970355i 0.836654 0.547732i \(-0.184509\pi\)
−0.892677 + 0.450697i \(0.851176\pi\)
\(662\) 11.1821 + 8.52128i 0.434603 + 0.331189i
\(663\) 0 0
\(664\) 45.0027 + 18.1160i 1.74644 + 0.703038i
\(665\) 7.27898 10.8182i 0.282267 0.419513i
\(666\) 0 0
\(667\) −6.48884 3.74633i −0.251249 0.145059i
\(668\) 4.66073 + 1.21562i 0.180329 + 0.0470338i
\(669\) 0 0
\(670\) 2.66700 + 0.342084i 0.103035 + 0.0132159i
\(671\) 26.4596 1.02146
\(672\) 0 0
\(673\) 9.09255 0.350492 0.175246 0.984525i \(-0.443928\pi\)
0.175246 + 0.984525i \(0.443928\pi\)
\(674\) −14.9307 1.91510i −0.575111 0.0737668i
\(675\) 0 0
\(676\) −18.3120 4.77617i −0.704307 0.183699i
\(677\) 13.8282 + 7.98374i 0.531463 + 0.306840i 0.741612 0.670829i \(-0.234062\pi\)
−0.210149 + 0.977669i \(0.567395\pi\)
\(678\) 0 0
\(679\) −12.6347 25.8299i −0.484877 0.991261i
\(680\) 7.27922 + 2.93028i 0.279145 + 0.112371i
\(681\) 0 0
\(682\) −2.70148 2.05866i −0.103445 0.0788302i
\(683\) −22.2769 38.5848i −0.852404 1.47641i −0.879033 0.476761i \(-0.841811\pi\)
0.0266295 0.999645i \(1.50848\pi\)
\(684\) 0 0
\(685\) −9.28793 −0.354874
\(686\) −24.7479 8.57566i −0.944879 0.327420i
\(687\) 0 0
\(688\) −7.76021 + 13.8644i −0.295855 + 0.528577i
\(689\) 0.862942 0.498220i 0.0328755 0.0189807i
\(690\) 0 0
\(691\) −12.1180 6.99631i −0.460989 0.266152i 0.251471 0.967865i \(-0.419086\pi\)
−0.712460 + 0.701713i \(0.752419\pi\)
\(692\) −6.66283 6.57465i −0.253283 0.249931i
\(693\) 0 0
\(694\) −9.57366 22.8969i −0.363411 0.869153i
\(695\) 0.293538 0.508424i 0.0111345 0.0192856i
\(696\) 0 0
\(697\) 21.0712 + 36.4964i 0.798128 + 1.38240i
\(698\) −40.7775 5.23035i −1.54345 0.197972i
\(699\) 0 0
\(700\) −17.8979 + 15.8054i −0.676476 + 0.597388i
\(701\) 14.4059i 0.544104i 0.962283 + 0.272052i \(0.0877022\pi\)
−0.962283 + 0.272052i \(0.912298\pi\)
\(702\) 0 0
\(703\) −45.8438 + 26.4679i −1.72903 + 0.998257i
\(704\) 4.88888 19.8219i 0.184256 0.747065i
\(705\) 0 0
\(706\) −14.6735 + 6.13528i −0.552243 + 0.230904i
\(707\) −23.2825 15.6655i −0.875629 0.589161i
\(708\) 0 0
\(709\) 22.0939 38.2677i 0.829753 1.43717i −0.0684783 0.997653i \(-0.521814\pi\)
0.898232 0.439522i \(-0.144852\pi\)
\(710\) 2.75920 + 2.10264i 0.103551 + 0.0789108i
\(711\) 0 0
\(712\) 20.7033 + 26.4300i 0.775889 + 0.990505i
\(713\) 3.78940i 0.141914i
\(714\) 0 0
\(715\) 3.35153i 0.125340i
\(716\) 6.99771 + 25.4368i 0.261517 + 0.950617i
\(717\) 0 0
\(718\) 24.8955 32.6692i 0.929092 1.21920i
\(719\) 6.06830 10.5106i 0.226309 0.391979i −0.730402 0.683017i \(-0.760667\pi\)
0.956711 + 0.291038i \(0.0940006\pi\)
\(720\) 0 0
\(721\) 2.40998 35.0411i 0.0897525 1.30500i
\(722\) −16.8126 40.2099i −0.625701 1.49646i
\(723\) 0 0
\(724\) 34.2155 + 8.92415i 1.27161 + 0.331664i
\(725\) −7.27187 + 4.19842i −0.270071 + 0.155925i
\(726\) 0 0
\(727\) 27.8081i 1.03134i −0.856786 0.515672i \(-0.827542\pi\)
0.856786 0.515672i \(-0.172458\pi\)
\(728\) 1.01569 + 14.0385i 0.0376440 + 0.520301i
\(729\) 0 0
\(730\) −0.345565 + 2.69414i −0.0127899 + 0.0997147i
\(731\) 7.89114 + 13.6679i 0.291864 + 0.505524i
\(732\) 0 0
\(733\) 19.8313 34.3488i 0.732486 1.26870i −0.223331 0.974743i \(-0.571693\pi\)
0.955818 0.293961i \(-0.0949734\pi\)
\(734\) −31.4268 + 13.1402i −1.15998 + 0.485014i
\(735\) 0 0
\(736\) −20.8957 + 9.06587i −0.770227 + 0.334173i
\(737\) −6.01805 3.47452i −0.221678 0.127986i
\(738\) 0 0
\(739\) 28.2813 16.3282i 1.04034 0.600643i 0.120414 0.992724i \(-0.461578\pi\)
0.919931 + 0.392080i \(0.128244\pi\)
\(740\) −10.0983 + 2.77807i −0.371222 + 0.102124i
\(741\) 0 0
\(742\) 1.49047 + 1.30681i 0.0547169 + 0.0479745i
\(743\) −33.8538 −1.24198 −0.620988 0.783820i \(-0.713268\pi\)
−0.620988 + 0.783820i \(0.713268\pi\)
\(744\) 0 0
\(745\) 1.97492 + 3.42066i 0.0723555 + 0.125323i
\(746\) 11.4816 15.0668i 0.420371 0.551633i
\(747\) 0 0
\(748\) −14.4349 14.2439i −0.527793 0.520807i
\(749\) 25.3710 + 1.74491i 0.927036 + 0.0637577i
\(750\) 0 0
\(751\) −25.7744 14.8808i −0.940520 0.543010i −0.0503969 0.998729i \(-0.516049\pi\)
−0.890123 + 0.455720i \(0.849382\pi\)
\(752\) 30.6057 18.2181i 1.11607 0.664347i
\(753\) 0 0
\(754\) −0.629714 + 4.90946i −0.0229328 + 0.178792i
\(755\) −11.8582 −0.431563
\(756\) 0 0
\(757\) 21.4183 0.778460 0.389230 0.921141i \(-0.372741\pi\)
0.389230 + 0.921141i \(0.372741\pi\)
\(758\) 2.33101 18.1733i 0.0846661 0.660085i
\(759\) 0 0
\(760\) −1.95746 13.8012i −0.0710044 0.500624i
\(761\) 37.9234 + 21.8951i 1.37472 + 0.793696i 0.991518 0.129969i \(-0.0414877\pi\)
0.383203 + 0.923664i \(0.374821\pi\)
\(762\) 0 0
\(763\) −21.0085 + 31.2235i −0.760560 + 1.13037i
\(764\) 29.8427 30.2430i 1.07967 1.09415i
\(765\) 0 0
\(766\) −2.17165 + 2.84975i −0.0784649 + 0.102966i
\(767\) 12.5085 + 21.6654i 0.451657 + 0.782292i
\(768\) 0 0
\(769\) −53.6687 −1.93534 −0.967672 0.252212i \(-0.918842\pi\)
−0.967672 + 0.252212i \(0.918842\pi\)
\(770\) −6.31318 + 2.14383i −0.227511 + 0.0772582i
\(771\) 0 0
\(772\) −2.21091 8.03669i −0.0795724 0.289247i
\(773\) 37.6921 21.7615i 1.35569 0.782708i 0.366651 0.930359i \(-0.380504\pi\)
0.989040 + 0.147650i \(0.0471710\pi\)
\(774\) 0 0
\(775\) 3.67774 + 2.12334i 0.132108 + 0.0762727i
\(776\) −28.5161 11.4793i −1.02367 0.412082i
\(777\) 0 0
\(778\) 19.9689 8.34941i 0.715918 0.299341i
\(779\) 37.4313 64.8329i 1.34112 2.32288i
\(780\) 0 0
\(781\) −4.48268 7.76424i −0.160403 0.277826i
\(782\) −2.87848 + 22.4416i −0.102934 + 0.802508i
\(783\) 0 0
\(784\) −25.7942 + 10.8931i −0.921222 + 0.389038i
\(785\) 1.37897i 0.0492175i
\(786\) 0 0
\(787\) −9.79031 + 5.65244i −0.348987 + 0.201488i −0.664239 0.747520i \(-0.731244\pi\)
0.315252 + 0.949008i \(0.397911\pi\)
\(788\) −4.06200 + 15.5739i −0.144703 + 0.554796i
\(789\) 0 0
\(790\) 5.15531