Properties

Label 441.2.h.h.214.12
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 214.12
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.12

$q$-expansion

\(f(q)\) \(=\) \(q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +O(q^{10})\) \(q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +(1.38010 - 2.39040i) q^{10} +(2.73867 + 4.74351i) q^{11} +(1.38857 - 4.53149i) q^{12} +(-2.37268 - 4.10960i) q^{13} +(-1.49715 - 1.60755i) q^{15} -1.98516 q^{16} +(-2.40822 + 4.17116i) q^{17} +(-5.40807 - 3.65783i) q^{18} +(2.69059 + 4.66025i) q^{19} +(1.73523 - 3.00550i) q^{20} +(5.96019 + 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(0.813193 - 2.65378i) q^{24} +(1.69572 + 2.93707i) q^{25} +(-5.16368 - 8.94376i) q^{26} +(-4.04442 + 3.26231i) q^{27} +(2.01656 - 3.49278i) q^{29} +(-3.25826 - 3.49853i) q^{30} +1.46419 q^{31} -7.52529 q^{32} +(9.24522 - 2.12822i) q^{33} +(-5.24103 + 9.07773i) q^{34} +(-6.79970 - 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} +(5.85557 + 10.1421i) q^{38} +(-8.00971 + 1.84381i) q^{39} +(1.01621 - 1.76012i) q^{40} +(1.94808 + 3.37418i) q^{41} +(-1.66016 + 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(-3.42192 + 1.66358i) q^{45} +(5.63263 - 9.75600i) q^{46} -3.15546 q^{47} +(-1.00739 + 3.28752i) q^{48} +(3.69042 + 6.39199i) q^{50} +(5.68555 + 6.10481i) q^{51} +(-6.49243 - 11.2452i) q^{52} +(3.57149 - 6.18601i) q^{53} +(-8.80191 + 7.09981i) q^{54} +6.94684 q^{55} +(9.08294 - 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} -0.308683 q^{59} +(-4.09669 - 4.39879i) q^{60} -10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} -6.01848 q^{65} +(20.1205 - 4.63167i) q^{66} +4.47310 q^{67} +(-6.58968 + 11.4137i) q^{68} +(-6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(-3.98212 - 2.69337i) q^{72} +(-5.27515 + 9.13683i) q^{73} +(-2.08745 - 3.61557i) q^{74} +(5.72444 - 1.31775i) q^{75} +(7.36235 + 12.7520i) q^{76} +(-17.4316 + 4.01270i) q^{78} -9.01643 q^{79} +(-1.25888 + 2.18044i) q^{80} +(3.35017 + 8.35323i) q^{81} +(4.23963 + 7.34326i) q^{82} +(5.08023 - 8.79921i) q^{83} +(3.05432 + 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(-4.76089 - 5.11196i) q^{87} +(4.38866 + 7.60138i) q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.44716 + 3.62047i) q^{90} +(7.08205 - 12.2665i) q^{92} +(0.743014 - 2.42476i) q^{93} -6.86726 q^{94} +6.82490 q^{95} +(-3.81877 + 12.4622i) q^{96} +(2.48521 - 4.30451i) q^{97} +(1.16714 - 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17631 1.53888 0.769442 0.638717i \(-0.220534\pi\)
0.769442 + 0.638717i \(0.220534\pi\)
\(3\) 0.507459 1.65605i 0.292981 0.956118i
\(4\) 2.73633 1.36816
\(5\) 0.634145 1.09837i 0.283598 0.491206i −0.688670 0.725075i \(-0.741805\pi\)
0.972268 + 0.233868i \(0.0751385\pi\)
\(6\) 1.10439 3.60407i 0.450864 1.47136i
\(7\) 0 0
\(8\) 1.60248 0.566563
\(9\) −2.48497 1.68075i −0.828324 0.560250i
\(10\) 1.38010 2.39040i 0.436425 0.755910i
\(11\) 2.73867 + 4.74351i 0.825739 + 1.43022i 0.901353 + 0.433084i \(0.142575\pi\)
−0.0756148 + 0.997137i \(0.524092\pi\)
\(12\) 1.38857 4.53149i 0.400847 1.30813i
\(13\) −2.37268 4.10960i −0.658062 1.13980i −0.981117 0.193417i \(-0.938043\pi\)
0.323054 0.946380i \(-0.395290\pi\)
\(14\) 0 0
\(15\) −1.49715 1.60755i −0.386562 0.415068i
\(16\) −1.98516 −0.496290
\(17\) −2.40822 + 4.17116i −0.584079 + 1.01165i 0.410911 + 0.911676i \(0.365211\pi\)
−0.994990 + 0.0999785i \(0.968123\pi\)
\(18\) −5.40807 3.65783i −1.27469 0.862159i
\(19\) 2.69059 + 4.66025i 0.617265 + 1.06913i 0.989983 + 0.141189i \(0.0450925\pi\)
−0.372718 + 0.927945i \(0.621574\pi\)
\(20\) 1.73523 3.00550i 0.388009 0.672051i
\(21\) 0 0
\(22\) 5.96019 + 10.3233i 1.27072 + 2.20095i
\(23\) 2.58816 4.48282i 0.539668 0.934732i −0.459254 0.888305i \(-0.651883\pi\)
0.998922 0.0464269i \(-0.0147835\pi\)
\(24\) 0.813193 2.65378i 0.165992 0.541701i
\(25\) 1.69572 + 2.93707i 0.339144 + 0.587415i
\(26\) −5.16368 8.94376i −1.01268 1.75402i
\(27\) −4.04442 + 3.26231i −0.778348 + 0.627833i
\(28\) 0 0
\(29\) 2.01656 3.49278i 0.374466 0.648594i −0.615781 0.787917i \(-0.711159\pi\)
0.990247 + 0.139324i \(0.0444928\pi\)
\(30\) −3.25826 3.49853i −0.594875 0.638741i
\(31\) 1.46419 0.262976 0.131488 0.991318i \(-0.458025\pi\)
0.131488 + 0.991318i \(0.458025\pi\)
\(32\) −7.52529 −1.33030
\(33\) 9.24522 2.12822i 1.60939 0.370476i
\(34\) −5.24103 + 9.07773i −0.898830 + 1.55682i
\(35\) 0 0
\(36\) −6.79970 4.59908i −1.13328 0.766514i
\(37\) −0.959170 1.66133i −0.157687 0.273121i 0.776347 0.630305i \(-0.217070\pi\)
−0.934034 + 0.357184i \(0.883737\pi\)
\(38\) 5.85557 + 10.1421i 0.949899 + 1.64527i
\(39\) −8.00971 + 1.84381i −1.28258 + 0.295246i
\(40\) 1.01621 1.76012i 0.160676 0.278299i
\(41\) 1.94808 + 3.37418i 0.304239 + 0.526958i 0.977092 0.212819i \(-0.0682644\pi\)
−0.672852 + 0.739777i \(0.734931\pi\)
\(42\) 0 0
\(43\) −1.66016 + 2.87549i −0.253173 + 0.438508i −0.964398 0.264457i \(-0.914807\pi\)
0.711225 + 0.702964i \(0.248141\pi\)
\(44\) 7.49389 + 12.9798i 1.12975 + 1.95678i
\(45\) −3.42192 + 1.66358i −0.510109 + 0.247992i
\(46\) 5.63263 9.75600i 0.830486 1.43844i
\(47\) −3.15546 −0.460271 −0.230135 0.973159i \(-0.573917\pi\)
−0.230135 + 0.973159i \(0.573917\pi\)
\(48\) −1.00739 + 3.28752i −0.145404 + 0.474512i
\(49\) 0 0
\(50\) 3.69042 + 6.39199i 0.521904 + 0.903964i
\(51\) 5.68555 + 6.10481i 0.796137 + 0.854844i
\(52\) −6.49243 11.2452i −0.900338 1.55943i
\(53\) 3.57149 6.18601i 0.490582 0.849714i −0.509359 0.860554i \(-0.670117\pi\)
0.999941 + 0.0108405i \(0.00345071\pi\)
\(54\) −8.80191 + 7.09981i −1.19779 + 0.966162i
\(55\) 6.94684 0.936712
\(56\) 0 0
\(57\) 9.08294 2.09086i 1.20307 0.276942i
\(58\) 4.38866 7.60138i 0.576259 0.998111i
\(59\) −0.308683 −0.0401871 −0.0200935 0.999798i \(-0.506396\pi\)
−0.0200935 + 0.999798i \(0.506396\pi\)
\(60\) −4.09669 4.39879i −0.528881 0.567881i
\(61\) −10.3429 −1.32427 −0.662134 0.749385i \(-0.730349\pi\)
−0.662134 + 0.749385i \(0.730349\pi\)
\(62\) 3.18652 0.404689
\(63\) 0 0
\(64\) −12.4070 −1.55088
\(65\) −6.01848 −0.746501
\(66\) 20.1205 4.63167i 2.47666 0.570119i
\(67\) 4.47310 0.546476 0.273238 0.961946i \(-0.411905\pi\)
0.273238 + 0.961946i \(0.411905\pi\)
\(68\) −6.58968 + 11.4137i −0.799116 + 1.38411i
\(69\) −6.11037 6.56095i −0.735602 0.789845i
\(70\) 0 0
\(71\) −1.96688 −0.233426 −0.116713 0.993166i \(-0.537236\pi\)
−0.116713 + 0.993166i \(0.537236\pi\)
\(72\) −3.98212 2.69337i −0.469297 0.317417i
\(73\) −5.27515 + 9.13683i −0.617409 + 1.06938i 0.372547 + 0.928013i \(0.378484\pi\)
−0.989957 + 0.141371i \(0.954849\pi\)
\(74\) −2.08745 3.61557i −0.242662 0.420302i
\(75\) 5.72444 1.31775i 0.661001 0.152160i
\(76\) 7.36235 + 12.7520i 0.844520 + 1.46275i
\(77\) 0 0
\(78\) −17.4316 + 4.01270i −1.97374 + 0.454349i
\(79\) −9.01643 −1.01443 −0.507214 0.861820i \(-0.669325\pi\)
−0.507214 + 0.861820i \(0.669325\pi\)
\(80\) −1.25888 + 2.18044i −0.140747 + 0.243781i
\(81\) 3.35017 + 8.35323i 0.372241 + 0.928136i
\(82\) 4.23963 + 7.34326i 0.468189 + 0.810927i
\(83\) 5.08023 8.79921i 0.557627 0.965839i −0.440066 0.897965i \(-0.645045\pi\)
0.997694 0.0678739i \(-0.0216216\pi\)
\(84\) 0 0
\(85\) 3.05432 + 5.29023i 0.331287 + 0.573806i
\(86\) −3.61303 + 6.25796i −0.389603 + 0.674813i
\(87\) −4.76089 5.11196i −0.510421 0.548059i
\(88\) 4.38866 + 7.60138i 0.467833 + 0.810310i
\(89\) 2.59776 + 4.49945i 0.275362 + 0.476941i 0.970226 0.242200i \(-0.0778690\pi\)
−0.694864 + 0.719141i \(0.744536\pi\)
\(90\) −7.44716 + 3.62047i −0.784999 + 0.381631i
\(91\) 0 0
\(92\) 7.08205 12.2665i 0.738354 1.27887i
\(93\) 0.743014 2.42476i 0.0770469 0.251436i
\(94\) −6.86726 −0.708303
\(95\) 6.82490 0.700220
\(96\) −3.81877 + 12.4622i −0.389752 + 1.27192i
\(97\) 2.48521 4.30451i 0.252335 0.437057i −0.711833 0.702348i \(-0.752135\pi\)
0.964168 + 0.265291i \(0.0854682\pi\)
\(98\) 0 0
\(99\) 1.16714 16.3905i 0.117302 1.64731i
\(100\) 4.64005 + 8.03680i 0.464005 + 0.803680i
\(101\) 0.00266904 + 0.00462292i 0.000265580 + 0.000459997i 0.866158 0.499770i \(-0.166582\pi\)
−0.865893 + 0.500230i \(0.833249\pi\)
\(102\) 12.3735 + 13.2860i 1.22516 + 1.31551i
\(103\) 6.51741 11.2885i 0.642180 1.11229i −0.342765 0.939421i \(-0.611364\pi\)
0.984945 0.172867i \(-0.0553030\pi\)
\(104\) −3.80217 6.58555i −0.372834 0.645767i
\(105\) 0 0
\(106\) 7.77268 13.4627i 0.754950 1.30761i
\(107\) −4.71081 8.15936i −0.455411 0.788795i 0.543301 0.839538i \(-0.317174\pi\)
−0.998712 + 0.0507430i \(0.983841\pi\)
\(108\) −11.0669 + 8.92677i −1.06491 + 0.858979i
\(109\) −8.44513 + 14.6274i −0.808896 + 1.40105i 0.104732 + 0.994500i \(0.466601\pi\)
−0.913629 + 0.406549i \(0.866732\pi\)
\(110\) 15.1185 1.44149
\(111\) −3.23798 + 0.745372i −0.307335 + 0.0707476i
\(112\) 0 0
\(113\) −3.07313 5.32281i −0.289095 0.500728i 0.684499 0.729014i \(-0.260021\pi\)
−0.973594 + 0.228286i \(0.926688\pi\)
\(114\) 19.7673 4.55037i 1.85138 0.426181i
\(115\) −3.28253 5.68551i −0.306098 0.530176i
\(116\) 5.51797 9.55741i 0.512331 0.887383i
\(117\) −1.01117 + 14.2001i −0.0934823 + 1.31280i
\(118\) −0.671790 −0.0618432
\(119\) 0 0
\(120\) −2.39915 2.57607i −0.219012 0.235162i
\(121\) −9.50058 + 16.4555i −0.863689 + 1.49595i
\(122\) −22.5093 −2.03790
\(123\) 6.57636 1.51386i 0.592970 0.136500i
\(124\) 4.00649 0.359794
\(125\) 10.6428 0.951919
\(126\) 0 0
\(127\) −13.9305 −1.23613 −0.618065 0.786127i \(-0.712083\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(128\) −11.9510 −1.05633
\(129\) 3.91947 + 4.20850i 0.345090 + 0.370538i
\(130\) −13.0981 −1.14878
\(131\) −0.0895778 + 0.155153i −0.00782645 + 0.0135558i −0.869912 0.493207i \(-0.835825\pi\)
0.862086 + 0.506763i \(0.169158\pi\)
\(132\) 25.2980 5.82351i 2.20191 0.506872i
\(133\) 0 0
\(134\) 9.73486 0.840964
\(135\) 1.01849 + 6.51105i 0.0876574 + 0.560382i
\(136\) −3.85913 + 6.68420i −0.330917 + 0.573166i
\(137\) −1.57603 2.72977i −0.134649 0.233220i 0.790814 0.612056i \(-0.209657\pi\)
−0.925463 + 0.378837i \(0.876324\pi\)
\(138\) −13.2981 14.2787i −1.13201 1.21548i
\(139\) −9.42857 16.3308i −0.799721 1.38516i −0.919798 0.392392i \(-0.871648\pi\)
0.120077 0.992765i \(-0.461686\pi\)
\(140\) 0 0
\(141\) −1.60126 + 5.22558i −0.134851 + 0.440073i
\(142\) −4.28054 −0.359215
\(143\) 12.9959 22.5096i 1.08677 1.88235i
\(144\) 4.93307 + 3.33656i 0.411089 + 0.278046i
\(145\) −2.55758 4.42986i −0.212396 0.367880i
\(146\) −11.4804 + 19.8846i −0.950122 + 1.64566i
\(147\) 0 0
\(148\) −2.62461 4.54595i −0.215741 0.373675i
\(149\) 10.6370 18.4238i 0.871418 1.50934i 0.0108879 0.999941i \(-0.496534\pi\)
0.860530 0.509400i \(-0.170132\pi\)
\(150\) 12.4582 2.86783i 1.01720 0.234157i
\(151\) −3.18281 5.51278i −0.259013 0.448624i 0.706965 0.707249i \(-0.250064\pi\)
−0.965978 + 0.258625i \(0.916731\pi\)
\(152\) 4.31163 + 7.46796i 0.349719 + 0.605731i
\(153\) 12.9950 6.31759i 1.05059 0.510747i
\(154\) 0 0
\(155\) 0.928506 1.60822i 0.0745794 0.129175i
\(156\) −21.9172 + 5.04527i −1.75478 + 0.403945i
\(157\) −1.39595 −0.111409 −0.0557045 0.998447i \(-0.517740\pi\)
−0.0557045 + 0.998447i \(0.517740\pi\)
\(158\) −19.6226 −1.56109
\(159\) −8.43193 9.05370i −0.668695 0.718005i
\(160\) −4.77212 + 8.26556i −0.377269 + 0.653450i
\(161\) 0 0
\(162\) 7.29101 + 18.1792i 0.572836 + 1.42829i
\(163\) 9.53086 + 16.5079i 0.746515 + 1.29300i 0.949484 + 0.313816i \(0.101608\pi\)
−0.202969 + 0.979185i \(0.565059\pi\)
\(164\) 5.33059 + 9.23286i 0.416249 + 0.720965i
\(165\) 3.52523 11.5043i 0.274439 0.895607i
\(166\) 11.0562 19.1498i 0.858124 1.48631i
\(167\) −0.872003 1.51035i −0.0674776 0.116875i 0.830313 0.557298i \(-0.188162\pi\)
−0.897790 + 0.440423i \(0.854828\pi\)
\(168\) 0 0
\(169\) −4.75919 + 8.24317i −0.366092 + 0.634090i
\(170\) 6.64715 + 11.5132i 0.509813 + 0.883022i
\(171\) 1.14665 16.1028i 0.0876867 1.23141i
\(172\) −4.54276 + 7.86828i −0.346382 + 0.599951i
\(173\) 10.0759 0.766056 0.383028 0.923737i \(-0.374881\pi\)
0.383028 + 0.923737i \(0.374881\pi\)
\(174\) −10.3612 11.1252i −0.785478 0.843400i
\(175\) 0 0
\(176\) −5.43669 9.41662i −0.409806 0.709805i
\(177\) −0.156644 + 0.511193i −0.0117741 + 0.0384236i
\(178\) 5.65353 + 9.79221i 0.423750 + 0.733957i
\(179\) 9.27118 16.0582i 0.692961 1.20024i −0.277902 0.960609i \(-0.589639\pi\)
0.970863 0.239634i \(-0.0770275\pi\)
\(180\) −9.36349 + 4.55211i −0.697914 + 0.339294i
\(181\) 8.80982 0.654829 0.327414 0.944881i \(-0.393823\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(182\) 0 0
\(183\) −5.24858 + 17.1283i −0.387986 + 1.26616i
\(184\) 4.14747 7.18363i 0.305756 0.529584i
\(185\) −2.43301 −0.178879
\(186\) 1.61703 5.27703i 0.118566 0.386930i
\(187\) −26.3812 −1.92919
\(188\) −8.63437 −0.629726
\(189\) 0 0
\(190\) 14.8531 1.07756
\(191\) 4.90939 0.355231 0.177615 0.984100i \(-0.443162\pi\)
0.177615 + 0.984100i \(0.443162\pi\)
\(192\) −6.29606 + 20.5466i −0.454379 + 1.48283i
\(193\) −9.76760 −0.703087 −0.351544 0.936171i \(-0.614343\pi\)
−0.351544 + 0.936171i \(0.614343\pi\)
\(194\) 5.40859 9.36796i 0.388314 0.672580i
\(195\) −3.05413 + 9.96688i −0.218711 + 0.713743i
\(196\) 0 0
\(197\) 3.31445 0.236145 0.118073 0.993005i \(-0.462328\pi\)
0.118073 + 0.993005i \(0.462328\pi\)
\(198\) 2.54006 35.6708i 0.180514 2.53501i
\(199\) 5.54432 9.60304i 0.393026 0.680742i −0.599821 0.800134i \(-0.704761\pi\)
0.992847 + 0.119393i \(0.0380948\pi\)
\(200\) 2.71736 + 4.70661i 0.192146 + 0.332807i
\(201\) 2.26991 7.40766i 0.160107 0.522496i
\(202\) 0.00580866 + 0.0100609i 0.000408696 + 0.000707883i
\(203\) 0 0
\(204\) 15.5575 + 16.7048i 1.08925 + 1.16957i
\(205\) 4.94146 0.345127
\(206\) 14.1839 24.5673i 0.988240 1.71168i
\(207\) −13.9660 + 6.78963i −0.970703 + 0.471912i
\(208\) 4.71014 + 8.15821i 0.326590 + 0.565670i
\(209\) −14.7373 + 25.5257i −1.01940 + 1.76565i
\(210\) 0 0
\(211\) −3.66118 6.34135i −0.252046 0.436557i 0.712043 0.702136i \(-0.247770\pi\)
−0.964089 + 0.265579i \(0.914437\pi\)
\(212\) 9.77278 16.9270i 0.671198 1.16255i
\(213\) −0.998111 + 3.25724i −0.0683894 + 0.223183i
\(214\) −10.2522 17.7573i −0.700825 1.21386i
\(215\) 2.10557 + 3.64695i 0.143599 + 0.248720i
\(216\) −6.48110 + 5.22780i −0.440983 + 0.355707i
\(217\) 0 0
\(218\) −18.3792 + 31.8337i −1.24480 + 2.15605i
\(219\) 12.4541 + 13.3724i 0.841569 + 0.903626i
\(220\) 19.0088 1.28158
\(221\) 22.8557 1.53744
\(222\) −7.04685 + 1.62216i −0.472954 + 0.108872i
\(223\) −2.02765 + 3.51199i −0.135782 + 0.235181i −0.925896 0.377779i \(-0.876688\pi\)
0.790114 + 0.612960i \(0.210021\pi\)
\(224\) 0 0
\(225\) 0.722667 10.1486i 0.0481778 0.676575i
\(226\) −6.68808 11.5841i −0.444884 0.770562i
\(227\) 0.667087 + 1.15543i 0.0442761 + 0.0766884i 0.887314 0.461165i \(-0.152569\pi\)
−0.843038 + 0.537854i \(0.819235\pi\)
\(228\) 24.8539 5.72129i 1.64599 0.378902i
\(229\) −7.99832 + 13.8535i −0.528544 + 0.915465i 0.470902 + 0.882185i \(0.343928\pi\)
−0.999446 + 0.0332795i \(0.989405\pi\)
\(230\) −7.14381 12.3734i −0.471049 0.815880i
\(231\) 0 0
\(232\) 3.23150 5.59712i 0.212158 0.367469i
\(233\) −4.06542 7.04151i −0.266334 0.461305i 0.701578 0.712593i \(-0.252479\pi\)
−0.967912 + 0.251288i \(0.919146\pi\)
\(234\) −2.20061 + 30.9038i −0.143858 + 2.02025i
\(235\) −2.00102 + 3.46586i −0.130532 + 0.226088i
\(236\) −0.844658 −0.0549825
\(237\) −4.57547 + 14.9316i −0.297208 + 0.969913i
\(238\) 0 0
\(239\) 11.0509 + 19.1407i 0.714823 + 1.23811i 0.963028 + 0.269403i \(0.0868262\pi\)
−0.248204 + 0.968708i \(0.579840\pi\)
\(240\) 2.97208 + 3.19124i 0.191847 + 0.205994i
\(241\) 13.7973 + 23.8977i 0.888765 + 1.53939i 0.841336 + 0.540512i \(0.181770\pi\)
0.0474292 + 0.998875i \(0.484897\pi\)
\(242\) −20.6762 + 35.8122i −1.32912 + 2.30210i
\(243\) 15.5334 1.30911i 0.996467 0.0839796i
\(244\) −28.3015 −1.81182
\(245\) 0 0
\(246\) 14.3122 3.29462i 0.912513 0.210057i
\(247\) 12.7678 22.1145i 0.812397 1.40711i
\(248\) 2.34633 0.148992
\(249\) −11.9939 12.8783i −0.760082 0.816131i
\(250\) 23.1620 1.46489
\(251\) 16.5610 1.04532 0.522661 0.852541i \(-0.324939\pi\)
0.522661 + 0.852541i \(0.324939\pi\)
\(252\) 0 0
\(253\) 28.3524 1.78250
\(254\) −30.3171 −1.90226
\(255\) 10.3108 2.37351i 0.645688 0.148635i
\(256\) −1.19503 −0.0746896
\(257\) 1.03287 1.78898i 0.0644285 0.111593i −0.832012 0.554758i \(-0.812811\pi\)
0.896440 + 0.443164i \(0.146144\pi\)
\(258\) 8.53000 + 9.15900i 0.531054 + 0.570214i
\(259\) 0 0
\(260\) −16.4686 −1.02134
\(261\) −10.8816 + 5.29014i −0.673553 + 0.327451i
\(262\) −0.194949 + 0.337662i −0.0120440 + 0.0208608i
\(263\) −5.06482 8.77252i −0.312310 0.540937i 0.666552 0.745458i \(-0.267769\pi\)
−0.978862 + 0.204522i \(0.934436\pi\)
\(264\) 14.8153 3.41043i 0.911819 0.209898i
\(265\) −4.52969 7.84565i −0.278257 0.481954i
\(266\) 0 0
\(267\) 8.76955 2.01872i 0.536688 0.123544i
\(268\) 12.2399 0.747670
\(269\) −7.54972 + 13.0765i −0.460315 + 0.797289i −0.998976 0.0452336i \(-0.985597\pi\)
0.538662 + 0.842522i \(0.318930\pi\)
\(270\) 2.21654 + 14.1701i 0.134895 + 0.862363i
\(271\) −14.4026 24.9459i −0.874893 1.51536i −0.856877 0.515521i \(-0.827598\pi\)
−0.0180156 0.999838i \(-0.505735\pi\)
\(272\) 4.78070 8.28041i 0.289872 0.502074i
\(273\) 0 0
\(274\) −3.42993 5.94082i −0.207210 0.358898i
\(275\) −9.28802 + 16.0873i −0.560089 + 0.970102i
\(276\) −16.7200 17.9529i −1.00642 1.08064i
\(277\) 1.34982 + 2.33795i 0.0811026 + 0.140474i 0.903724 0.428116i \(-0.140823\pi\)
−0.822621 + 0.568590i \(0.807489\pi\)
\(278\) −20.5195 35.5408i −1.23068 2.13160i
\(279\) −3.63846 2.46093i −0.217829 0.147332i
\(280\) 0 0
\(281\) −2.46312 + 4.26626i −0.146938 + 0.254503i −0.930094 0.367321i \(-0.880275\pi\)
0.783157 + 0.621825i \(0.213608\pi\)
\(282\) −3.48485 + 11.3725i −0.207520 + 0.677222i
\(283\) −3.58157 −0.212903 −0.106451 0.994318i \(-0.533949\pi\)
−0.106451 + 0.994318i \(0.533949\pi\)
\(284\) −5.38203 −0.319365
\(285\) 3.46336 11.3024i 0.205152 0.669493i
\(286\) 28.2832 48.9879i 1.67242 2.89672i
\(287\) 0 0
\(288\) 18.7001 + 12.6481i 1.10192 + 0.745298i
\(289\) −3.09903 5.36768i −0.182296 0.315746i
\(290\) −5.56609 9.64075i −0.326852 0.566125i
\(291\) −5.86732 6.29998i −0.343949 0.369312i
\(292\) −14.4345 + 25.0014i −0.844718 + 1.46309i
\(293\) −12.1955 21.1232i −0.712469 1.23403i −0.963928 0.266164i \(-0.914244\pi\)
0.251459 0.967868i \(-0.419090\pi\)
\(294\) 0 0
\(295\) −0.195750 + 0.339048i −0.0113970 + 0.0197401i
\(296\) −1.53705 2.66225i −0.0893394 0.154740i
\(297\) −26.5511 10.2503i −1.54065 0.594784i
\(298\) 23.1494 40.0960i 1.34101 2.32270i
\(299\) −24.5634 −1.42054
\(300\) 15.6639 3.60579i 0.904358 0.208180i
\(301\) 0 0
\(302\) −6.92678 11.9975i −0.398591 0.690380i
\(303\) 0.00901018 0.00207412i 0.000517622 0.000119155i
\(304\) −5.34126 9.25134i −0.306342 0.530600i
\(305\) −6.55887 + 11.3603i −0.375560 + 0.650489i
\(306\) 28.2812 13.7491i 1.61673 0.785981i
\(307\) 23.9025 1.36419 0.682094 0.731265i \(-0.261070\pi\)
0.682094 + 0.731265i \(0.261070\pi\)
\(308\) 0 0
\(309\) −15.3869 16.5216i −0.875332 0.939879i
\(310\) 2.02072 3.49998i 0.114769 0.198786i
\(311\) 12.9416 0.733853 0.366926 0.930250i \(-0.380410\pi\)
0.366926 + 0.930250i \(0.380410\pi\)
\(312\) −12.8354 + 2.95467i −0.726663 + 0.167275i
\(313\) 26.8681 1.51867 0.759336 0.650698i \(-0.225524\pi\)
0.759336 + 0.650698i \(0.225524\pi\)
\(314\) −3.03802 −0.171446
\(315\) 0 0
\(316\) −24.6719 −1.38790
\(317\) 8.31169 0.466831 0.233415 0.972377i \(-0.425010\pi\)
0.233415 + 0.972377i \(0.425010\pi\)
\(318\) −18.3505 19.7037i −1.02904 1.10493i
\(319\) 22.0907 1.23684
\(320\) −7.86786 + 13.6275i −0.439827 + 0.761803i
\(321\) −15.9028 + 3.66078i −0.887608 + 0.204325i
\(322\) 0 0
\(323\) −25.9182 −1.44212
\(324\) 9.16716 + 22.8572i 0.509287 + 1.26984i
\(325\) 8.04680 13.9375i 0.446356 0.773111i
\(326\) 20.7421 + 35.9264i 1.14880 + 1.98978i
\(327\) 19.9381 + 21.4083i 1.10258 + 1.18388i
\(328\) 3.12177 + 5.40706i 0.172371 + 0.298555i
\(329\) 0 0
\(330\) 7.67201 25.0369i 0.422330 1.37824i
\(331\) 12.3978 0.681443 0.340722 0.940164i \(-0.389329\pi\)
0.340722 + 0.940164i \(0.389329\pi\)
\(332\) 13.9012 24.0775i 0.762926 1.32143i
\(333\) −0.408770 + 5.74049i −0.0224005 + 0.314577i
\(334\) −1.89775 3.28700i −0.103840 0.179857i
\(335\) 2.83659 4.91312i 0.154980 0.268433i
\(336\) 0 0
\(337\) −12.9588 22.4454i −0.705913 1.22268i −0.966361 0.257189i \(-0.917204\pi\)
0.260448 0.965488i \(-0.416130\pi\)
\(338\) −10.3575 + 17.9397i −0.563373 + 0.975791i
\(339\) −10.3743 + 2.38813i −0.563455 + 0.129705i
\(340\) 8.35762 + 14.4758i 0.453256 + 0.785062i
\(341\) 4.00992 + 6.94538i 0.217149 + 0.376113i
\(342\) 2.49547 35.0447i 0.134940 1.89500i
\(343\) 0 0
\(344\) −2.66038 + 4.60792i −0.143438 + 0.248442i
\(345\) −11.0812 + 2.55086i −0.596592 + 0.137334i
\(346\) 21.9283 1.17887
\(347\) −16.8483 −0.904464 −0.452232 0.891900i \(-0.649372\pi\)
−0.452232 + 0.891900i \(0.649372\pi\)
\(348\) −13.0274 13.9880i −0.698340 0.749835i
\(349\) −15.5503 + 26.9340i −0.832390 + 1.44174i 0.0637477 + 0.997966i \(0.479695\pi\)
−0.896138 + 0.443776i \(0.853639\pi\)
\(350\) 0 0
\(351\) 23.0029 + 8.88050i 1.22780 + 0.474006i
\(352\) −20.6092 35.6963i −1.09848 1.90262i
\(353\) 1.32969 + 2.30309i 0.0707722 + 0.122581i 0.899240 0.437456i \(-0.144120\pi\)
−0.828468 + 0.560037i \(0.810787\pi\)
\(354\) −0.340905 + 1.11251i −0.0181189 + 0.0591294i
\(355\) −1.24729 + 2.16036i −0.0661991 + 0.114660i
\(356\) 7.10833 + 12.3120i 0.376741 + 0.652534i
\(357\) 0 0
\(358\) 20.1770 34.9476i 1.06639 1.84704i
\(359\) 16.2715 + 28.1830i 0.858775 + 1.48744i 0.873098 + 0.487545i \(0.162107\pi\)
−0.0143230 + 0.999897i \(0.504559\pi\)
\(360\) −5.48356 + 2.66586i −0.289009 + 0.140503i
\(361\) −4.97859 + 8.62318i −0.262031 + 0.453852i
\(362\) 19.1729 1.00771
\(363\) 22.4299 + 24.0839i 1.17726 + 1.26407i
\(364\) 0 0
\(365\) 6.69042 + 11.5881i 0.350192 + 0.606551i
\(366\) −11.4225 + 37.2764i −0.597065 + 1.94847i
\(367\) 7.07678 + 12.2573i 0.369405 + 0.639828i 0.989473 0.144720i \(-0.0462283\pi\)
−0.620068 + 0.784548i \(0.712895\pi\)
\(368\) −5.13790 + 8.89911i −0.267832 + 0.463898i
\(369\) 0.830215 11.6590i 0.0432193 0.606942i
\(370\) −5.29499 −0.275273
\(371\) 0 0
\(372\) 2.03313 6.63494i 0.105413 0.344005i
\(373\) −1.33814 + 2.31773i −0.0692863 + 0.120007i −0.898587 0.438795i \(-0.855406\pi\)
0.829301 + 0.558802i \(0.188739\pi\)
\(374\) −57.4137 −2.96879
\(375\) 5.40077 17.6249i 0.278894 0.910147i
\(376\) −5.05656 −0.260772
\(377\) −19.1386 −0.985687
\(378\) 0 0
\(379\) −0.312929 −0.0160741 −0.00803705 0.999968i \(-0.502558\pi\)
−0.00803705 + 0.999968i \(0.502558\pi\)
\(380\) 18.6752 0.958017
\(381\) −7.06914 + 23.0695i −0.362163 + 1.18189i
\(382\) 10.6844 0.546659
\(383\) −4.49440 + 7.78453i −0.229653 + 0.397771i −0.957705 0.287751i \(-0.907093\pi\)
0.728052 + 0.685522i \(0.240426\pi\)
\(384\) −6.06465 + 19.7914i −0.309485 + 1.00998i
\(385\) 0 0
\(386\) −21.2573 −1.08197
\(387\) 8.95843 4.35519i 0.455383 0.221387i
\(388\) 6.80036 11.7786i 0.345236 0.597966i
\(389\) 13.4934 + 23.3713i 0.684144 + 1.18497i 0.973705 + 0.227813i \(0.0731575\pi\)
−0.289560 + 0.957160i \(0.593509\pi\)
\(390\) −6.64674 + 21.6910i −0.336571 + 1.09837i
\(391\) 12.4657 + 21.5912i 0.630417 + 1.09191i
\(392\) 0 0
\(393\) 0.211484 + 0.227079i 0.0106680 + 0.0114546i
\(394\) 7.21328 0.363400
\(395\) −5.71772 + 9.90339i −0.287690 + 0.498293i
\(396\) 3.19368 44.8498i 0.160488 2.25379i
\(397\) 14.7503 + 25.5482i 0.740295 + 1.28223i 0.952361 + 0.304973i \(0.0986475\pi\)
−0.212066 + 0.977255i \(0.568019\pi\)
\(398\) 12.0662 20.8992i 0.604822 1.04758i
\(399\) 0 0
\(400\) −3.36628 5.83056i −0.168314 0.291528i
\(401\) 17.1392 29.6860i 0.855891 1.48245i −0.0199251 0.999801i \(-0.506343\pi\)
0.875816 0.482645i \(-0.160324\pi\)
\(402\) 4.94004 16.1214i 0.246387 0.804061i
\(403\) −3.47404 6.01721i −0.173054 0.299739i
\(404\) 0.00730338 + 0.0126498i 0.000363357 + 0.000629352i
\(405\) 11.2994 + 1.61743i 0.561473 + 0.0803706i
\(406\) 0 0
\(407\) 5.25369 9.09966i 0.260416 0.451054i
\(408\) 9.11099 + 9.78284i 0.451061 + 0.484323i
\(409\) −10.9845 −0.543149 −0.271574 0.962417i \(-0.587544\pi\)
−0.271574 + 0.962417i \(0.587544\pi\)
\(410\) 10.7542 0.531110
\(411\) −5.32038 + 1.22474i −0.262435 + 0.0604117i
\(412\) 17.8338 30.8890i 0.878608 1.52179i
\(413\) 0 0
\(414\) −30.3943 + 14.7764i −1.49380 + 0.726218i
\(415\) −6.44320 11.1599i −0.316284 0.547820i
\(416\) 17.8551 + 30.9259i 0.875417 + 1.51627i
\(417\) −31.8291 + 7.32695i −1.55868 + 0.358802i
\(418\) −32.0729 + 55.5519i −1.56874 + 2.71713i
\(419\) 3.33207 + 5.77132i 0.162782 + 0.281947i 0.935866 0.352357i \(-0.114620\pi\)
−0.773083 + 0.634305i \(0.781286\pi\)
\(420\) 0 0
\(421\) −17.0430 + 29.5193i −0.830625 + 1.43868i 0.0669186 + 0.997758i \(0.478683\pi\)
−0.897543 + 0.440926i \(0.854650\pi\)
\(422\) −7.96787 13.8008i −0.387870 0.671810i
\(423\) 7.84122 + 5.30353i 0.381253 + 0.257867i
\(424\) 5.72325 9.91297i 0.277946 0.481416i
\(425\) −16.3347 −0.792348
\(426\) −2.17220 + 7.08877i −0.105243 + 0.343452i
\(427\) 0 0
\(428\) −12.8903 22.3267i −0.623077 1.07920i
\(429\) −30.6821 32.9446i −1.48134 1.59058i
\(430\) 4.58237 + 7.93690i 0.220982 + 0.382751i
\(431\) −1.12969 + 1.95669i −0.0544155 + 0.0942504i −0.891950 0.452134i \(-0.850663\pi\)
0.837535 + 0.546384i \(0.183996\pi\)
\(432\) 8.02881 6.47622i 0.386287 0.311587i
\(433\) −34.3904 −1.65270 −0.826348 0.563160i \(-0.809585\pi\)
−0.826348 + 0.563160i \(0.809585\pi\)
\(434\) 0 0
\(435\) −8.63392 + 1.98750i −0.413965 + 0.0952933i
\(436\) −23.1086 + 40.0254i −1.10670 + 1.91687i
\(437\) 27.8547 1.33247
\(438\) 27.1039 + 29.1026i 1.29508 + 1.39058i
\(439\) −5.99139 −0.285953 −0.142977 0.989726i \(-0.545667\pi\)
−0.142977 + 0.989726i \(0.545667\pi\)
\(440\) 11.1322 0.530706
\(441\) 0 0
\(442\) 49.7411 2.36594
\(443\) −39.4380 −1.87376 −0.936879 0.349654i \(-0.886299\pi\)
−0.936879 + 0.349654i \(0.886299\pi\)
\(444\) −8.86018 + 2.03958i −0.420486 + 0.0967944i
\(445\) 6.58942 0.312369
\(446\) −4.41280 + 7.64319i −0.208952 + 0.361916i
\(447\) −25.1129 26.9647i −1.18780 1.27539i
\(448\) 0 0
\(449\) 2.45092 0.115666 0.0578330 0.998326i \(-0.481581\pi\)
0.0578330 + 0.998326i \(0.481581\pi\)
\(450\) 1.57275 22.0866i 0.0741400 1.04117i
\(451\) −10.6703 + 18.4815i −0.502444 + 0.870259i
\(452\) −8.40909 14.5650i −0.395530 0.685078i
\(453\) −10.7446 + 2.47336i −0.504824 + 0.116209i
\(454\) 1.45179 + 2.51457i 0.0681358 + 0.118015i
\(455\) 0 0
\(456\) 14.5552 3.35057i 0.681612 0.156905i
\(457\) 11.0212 0.515548 0.257774 0.966205i \(-0.417011\pi\)
0.257774 + 0.966205i \(0.417011\pi\)
\(458\) −17.4068 + 30.1495i −0.813368 + 1.40879i
\(459\) −3.86779 24.7263i −0.180533 1.15412i
\(460\) −8.98208 15.5574i −0.418792 0.725369i
\(461\) −14.6540 + 25.3814i −0.682503 + 1.18213i 0.291711 + 0.956506i \(0.405775\pi\)
−0.974215 + 0.225624i \(0.927558\pi\)
\(462\) 0 0
\(463\) 0.593566 + 1.02809i 0.0275853 + 0.0477792i 0.879489 0.475920i \(-0.157885\pi\)
−0.851903 + 0.523699i \(0.824552\pi\)
\(464\) −4.00319 + 6.93374i −0.185844 + 0.321891i
\(465\) −2.19211 2.35375i −0.101656 0.109153i
\(466\) −8.84761 15.3245i −0.409858 0.709894i
\(467\) 11.0573 + 19.1519i 0.511673 + 0.886243i 0.999908 + 0.0135313i \(0.00430729\pi\)
−0.488236 + 0.872712i \(0.662359\pi\)
\(468\) −2.76688 + 38.8562i −0.127899 + 1.79613i
\(469\) 0 0
\(470\) −4.35483 + 7.54280i −0.200874 + 0.347923i
\(471\) −0.708387 + 2.31176i −0.0326408 + 0.106520i
\(472\) −0.494658 −0.0227685
\(473\) −18.1865 −0.836218
\(474\) −9.95764 + 32.4958i −0.457369 + 1.49258i
\(475\) −9.12499 + 15.8050i −0.418683 + 0.725181i
\(476\) 0 0
\(477\) −19.2722 + 9.36927i −0.882413 + 0.428990i
\(478\) 24.0502 + 41.6562i 1.10003 + 1.90531i
\(479\) −12.5714 21.7743i −0.574402 0.994894i −0.996106 0.0881606i \(-0.971901\pi\)
0.421704 0.906734i \(-0.361432\pi\)
\(480\) 11.2665 + 12.0973i 0.514242 + 0.552163i
\(481\) −4.55160 + 7.88361i −0.207535 + 0.359462i
\(482\) 30.0273 + 52.0088i 1.36771 + 2.36894i
\(483\) 0 0
\(484\) −25.9967 + 45.0276i −1.18167 + 2.04671i
\(485\) −3.15197 5.45937i −0.143123 0.247897i
\(486\) 33.8055 2.84904i 1.53345 0.129235i
\(487\) −6.78904 + 11.7590i −0.307641 + 0.532849i −0.977846 0.209327i \(-0.932873\pi\)
0.670205 + 0.742176i \(0.266206\pi\)
\(488\) −16.5743 −0.750281
\(489\) 32.1744 7.40644i 1.45498 0.334931i
\(490\) 0 0
\(491\) 7.25177 + 12.5604i 0.327268 + 0.566844i 0.981969 0.189044i \(-0.0605387\pi\)
−0.654701 + 0.755888i \(0.727205\pi\)
\(492\) 17.9951 4.14241i 0.811281 0.186754i
\(493\) 9.71263 + 16.8228i 0.437435 + 0.757659i
\(494\) 27.7868 48.1281i 1.25019 2.16538i
\(495\) −17.2627 11.6759i −0.775901 0.524792i
\(496\) −2.90664 −0.130512
\(497\) 0 0
\(498\) −26.1024 28.0272i −1.16968 1.25593i
\(499\) −6.99574 + 12.1170i −0.313172 + 0.542431i −0.979047 0.203633i \(-0.934725\pi\)
0.665875 + 0.746063i \(0.268058\pi\)
\(500\) 29.1221 1.30238
\(501\) −2.94372 + 0.677635i −0.131516 + 0.0302745i
\(502\) 36.0419 1.60863
\(503\) −28.4011 −1.26634 −0.633171 0.774012i \(-0.718247\pi\)
−0.633171 + 0.774012i \(0.718247\pi\)
\(504\) 0 0
\(505\) 0.00677023 0.000301271
\(506\) 61.7036 2.74306
\(507\) 11.2360 + 12.0645i 0.499007 + 0.535803i
\(508\) −38.1184 −1.69123
\(509\) −1.72997 + 2.99639i −0.0766794 + 0.132813i −0.901815 0.432122i \(-0.857765\pi\)
0.825136 + 0.564934i \(0.191098\pi\)
\(510\) 22.4395 5.16550i 0.993639 0.228732i
\(511\) 0 0
\(512\) 21.3013 0.941392
\(513\) −26.0851 10.0704i −1.15168 0.444619i
\(514\) 2.24784 3.89337i 0.0991480 0.171729i
\(515\) −8.26597 14.3171i −0.364242 0.630886i
\(516\) 10.7250 + 11.5158i 0.472141 + 0.506956i
\(517\) −8.64174 14.9679i −0.380063 0.658289i
\(518\) 0 0
\(519\) 5.11310 16.6861i 0.224440 0.732440i
\(520\) −9.64451 −0.422940
\(521\) 3.56797 6.17991i 0.156316 0.270747i −0.777222 0.629227i \(-0.783372\pi\)
0.933537 + 0.358480i \(0.116705\pi\)
\(522\) −23.6817 + 11.5130i −1.03652 + 0.503910i
\(523\) −6.53235 11.3144i −0.285640 0.494743i 0.687124 0.726540i \(-0.258873\pi\)
−0.972764 + 0.231797i \(0.925539\pi\)
\(524\) −0.245114 + 0.424551i −0.0107079 + 0.0185466i
\(525\) 0 0
\(526\) −11.0226 19.0917i −0.480609 0.832439i
\(527\) −3.52608 + 6.10735i −0.153598 + 0.266040i
\(528\) −18.3532 + 4.22486i −0.798723 + 0.183863i
\(529\) −1.89710 3.28587i −0.0824825 0.142864i
\(530\) −9.85801 17.0746i −0.428205 0.741672i
\(531\) 0.767068 + 0.518818i 0.0332879 + 0.0225148i
\(532\) 0 0
\(533\) 9.24434 16.0117i 0.400417 0.693542i
\(534\) 19.0853 4.39337i 0.825900 0.190120i
\(535\) −11.9493 −0.516615
\(536\) 7.16806 0.309613
\(537\) −21.8883 23.5024i −0.944550 1.01420i
\(538\) −16.4305 + 28.4585i −0.708371 + 1.22693i
\(539\) 0 0
\(540\) 2.78691 + 17.8164i 0.119930 + 0.766695i
\(541\) −2.46788 4.27450i −0.106103 0.183775i 0.808086 0.589065i \(-0.200504\pi\)
−0.914188 + 0.405290i \(0.867171\pi\)
\(542\) −31.3444 54.2901i −1.34636 2.33196i
\(543\) 4.47062 14.5895i 0.191853 0.626094i
\(544\) 18.1225 31.3892i 0.776997 1.34580i
\(545\) 10.7109 + 18.5518i 0.458803 + 0.794670i
\(546\) 0 0
\(547\) 0.559964 0.969887i 0.0239423 0.0414694i −0.853806 0.520591i \(-0.825712\pi\)
0.877748 + 0.479122i \(0.159045\pi\)
\(548\) −4.31254 7.46954i −0.184223 0.319083i
\(549\) 25.7017 + 17.3838i 1.09692 + 0.741921i
\(550\) −20.2136 + 35.0110i −0.861912 + 1.49288i
\(551\) 21.7030 0.924578
\(552\) −9.79175 10.5138i −0.416764 0.447497i
\(553\) 0 0
\(554\) 2.93762 + 5.08811i 0.124808 + 0.216173i
\(555\) −1.23465 + 4.02918i −0.0524081 + 0.171029i
\(556\) −25.7997 44.6863i −1.09415 1.89512i
\(557\) 5.47832 9.48873i 0.232124 0.402050i −0.726309 0.687368i \(-0.758766\pi\)
0.958433 + 0.285318i \(0.0920992\pi\)
\(558\) −7.91842 5.35575i −0.335213 0.226727i
\(559\) 15.7561 0.666413
\(560\) 0 0
\(561\) −13.3874 + 43.6885i −0.565215 + 1.84453i
\(562\) −5.36052 + 9.28470i −0.226120 + 0.391651i
\(563\) 4.76096 0.200650 0.100325 0.994955i \(-0.468012\pi\)
0.100325 + 0.994955i \(0.468012\pi\)
\(564\) −4.38159 + 14.2989i −0.184498 + 0.602093i
\(565\) −7.79523 −0.327948
\(566\) −7.79462 −0.327632
\(567\) 0 0
\(568\) −3.15189 −0.132250
\(569\) 3.49976 0.146718 0.0733588 0.997306i \(-0.476628\pi\)
0.0733588 + 0.997306i \(0.476628\pi\)
\(570\) 7.53734 24.5974i 0.315704 1.03027i
\(571\) 7.06101 0.295494 0.147747 0.989025i \(-0.452798\pi\)
0.147747 + 0.989025i \(0.452798\pi\)
\(572\) 35.5612 61.5937i 1.48689 2.57536i
\(573\) 2.49131 8.13017i 0.104076 0.339643i
\(574\) 0 0
\(575\) 17.5552 0.732101
\(576\) 30.8312 + 20.8531i 1.28463 + 0.868881i
\(577\) 6.44149 11.1570i 0.268163 0.464472i −0.700225 0.713923i \(-0.746917\pi\)
0.968387 + 0.249451i \(0.0802502\pi\)
\(578\) −6.74445 11.6817i −0.280532 0.485896i
\(579\) −4.95665 + 16.1756i −0.205991 + 0.672235i
\(580\) −6.99838 12.1216i −0.290592 0.503320i
\(581\) 0 0
\(582\) −12.7691 13.7107i −0.529297 0.568328i
\(583\) 39.1245 1.62037
\(584\) −8.45333 + 14.6416i −0.349801 + 0.605874i
\(585\) 14.9558 + 10.1156i 0.618345 + 0.418227i
\(586\) −26.5412 45.9707i −1.09641 1.89903i
\(587\) 19.5044 33.7826i 0.805034 1.39436i −0.111235 0.993794i \(-0.535481\pi\)
0.916268 0.400565i \(-0.131186\pi\)
\(588\) 0 0
\(589\) 3.93953 + 6.82347i 0.162326 + 0.281156i
\(590\) −0.426012 + 0.737874i −0.0175386 + 0.0303778i
\(591\) 1.68195 5.48889i 0.0691861 0.225783i
\(592\) 1.90411 + 3.29801i 0.0782583 + 0.135547i
\(593\) 20.1513 + 34.9031i 0.827515 + 1.43330i 0.899982 + 0.435927i \(0.143579\pi\)
−0.0724676 + 0.997371i \(0.523087\pi\)
\(594\) −57.7835 22.3079i −2.37089 0.915304i
\(595\) 0 0
\(596\) 29.1064 50.4137i 1.19224 2.06503i
\(597\) −13.0896 14.0548i −0.535720 0.575224i
\(598\) −53.4577 −2.18605
\(599\) −12.7821 −0.522261 −0.261130 0.965304i \(-0.584095\pi\)
−0.261130 + 0.965304i \(0.584095\pi\)
\(600\) 9.17330 2.11166i 0.374499 0.0862084i
\(601\) 4.86311 8.42316i 0.198371 0.343588i −0.749630 0.661858i \(-0.769768\pi\)
0.948000 + 0.318270i \(0.103102\pi\)
\(602\) 0 0
\(603\) −11.1155 7.51816i −0.452659 0.306163i
\(604\) −8.70921 15.0848i −0.354373 0.613792i
\(605\) 12.0495 + 20.8703i 0.489881 + 0.848499i
\(606\) 0.0196090 0.00451392i 0.000796560 0.000183365i
\(607\) 20.7437 35.9291i 0.841959 1.45832i −0.0462763 0.998929i \(-0.514735\pi\)
0.888236 0.459388i \(-0.151931\pi\)
\(608\) −20.2475 35.0697i −0.821145 1.42226i
\(609\) 0 0
\(610\) −14.2742 + 24.7236i −0.577943 + 1.00103i
\(611\) 7.48688 + 12.9677i 0.302887 + 0.524615i
\(612\) 35.5587 17.2870i 1.43737 0.698786i
\(613\) −7.64783 + 13.2464i −0.308893 + 0.535018i −0.978120 0.208039i \(-0.933292\pi\)
0.669228 + 0.743057i \(0.266625\pi\)
\(614\) 52.0193 2.09933
\(615\) 2.50759 8.18329i 0.101116 0.329982i
\(616\) 0 0
\(617\) −2.66563 4.61700i −0.107314 0.185873i 0.807367 0.590049i \(-0.200892\pi\)
−0.914681 + 0.404176i \(0.867558\pi\)
\(618\) −33.4867 35.9561i −1.34703 1.44637i
\(619\) −6.34205 10.9847i −0.254908 0.441514i 0.709962 0.704240i \(-0.248712\pi\)
−0.964871 + 0.262726i \(0.915379\pi\)
\(620\) 2.54070 4.40062i 0.102037 0.176733i
\(621\) 4.15678 + 26.5738i 0.166806 + 1.06637i
\(622\) 28.1650 1.12931
\(623\) 0 0
\(624\) 15.9006 3.66026i 0.636532 0.146528i
\(625\) −1.72954 + 2.99566i −0.0691817 + 0.119826i
\(626\) 58.4733 2.33706
\(627\) 34.7932 + 37.3588i 1.38951 + 1.49197i
\(628\) −3.81978 −0.152426
\(629\) 9.23957 0.368406
\(630\) 0 0
\(631\) 0.123764 0.00492698 0.00246349 0.999997i \(-0.499216\pi\)
0.00246349 + 0.999997i \(0.499216\pi\)
\(632\) −14.4487 −0.574737
\(633\) −12.3595 + 2.84511i −0.491245 + 0.113083i
\(634\) 18.0888 0.718399
\(635\) −8.83394 + 15.3008i −0.350564 + 0.607195i
\(636\) −23.0725 24.7739i −0.914885 0.982349i
\(637\) 0 0
\(638\) 48.0763 1.90336
\(639\) 4.88764 + 3.30583i 0.193352 + 0.130777i
\(640\) −7.57868 + 13.1267i −0.299573 + 0.518876i
\(641\) −2.96588 5.13706i −0.117145 0.202902i 0.801490 0.598008i \(-0.204041\pi\)
−0.918635 + 0.395107i \(0.870708\pi\)
\(642\) −34.6095 + 7.96699i −1.36593 + 0.314432i
\(643\) 23.4140 + 40.5542i 0.923358 + 1.59930i 0.794180 + 0.607682i \(0.207900\pi\)
0.129178 + 0.991621i \(0.458766\pi\)
\(644\) 0 0
\(645\) 7.10801 1.63624i 0.279877 0.0644269i
\(646\) −56.4060 −2.21926
\(647\) −19.5701 + 33.8964i −0.769379 + 1.33260i 0.168521 + 0.985698i \(0.446101\pi\)
−0.937900 + 0.346905i \(0.887233\pi\)
\(648\) 5.36858 + 13.3859i 0.210898 + 0.525847i
\(649\) −0.845379 1.46424i −0.0331840 0.0574764i
\(650\) 17.5123 30.3322i 0.686890 1.18973i
\(651\) 0 0
\(652\) 26.0796 + 45.1711i 1.02135 + 1.76904i
\(653\) −21.6640 + 37.5232i −0.847779 + 1.46840i 0.0354068 + 0.999373i \(0.488727\pi\)
−0.883186 + 0.469023i \(0.844606\pi\)
\(654\) 43.3914 + 46.5911i 1.69674 + 1.82186i
\(655\) 0.113611 + 0.196779i 0.00443913 + 0.00768881i
\(656\) −3.86726 6.69828i −0.150991 0.261524i
\(657\) 28.4653 13.8386i 1.11054 0.539893i
\(658\) 0 0
\(659\) 3.43895 5.95643i 0.133962 0.232030i −0.791238 0.611508i \(-0.790563\pi\)
0.925201 + 0.379478i \(0.123897\pi\)
\(660\) 9.64620 31.4795i 0.375478 1.22534i
\(661\) −38.7671 −1.50786 −0.753932 0.656952i \(-0.771845\pi\)
−0.753932 + 0.656952i \(0.771845\pi\)
\(662\) 26.9814 1.04866
\(663\) 11.5983 37.8501i 0.450441 1.46997i
\(664\) 8.14097 14.1006i 0.315931 0.547209i
\(665\) 0 0
\(666\) −0.889611 + 12.4931i −0.0344717 + 0.484097i
\(667\) −10.4383 18.0797i −0.404174 0.700050i
\(668\) −2.38609 4.13282i −0.0923205 0.159904i
\(669\) 4.78707 + 5.14007i 0.185079 + 0.198727i
\(670\) 6.17331 10.6925i 0.238496 0.413087i
\(671\) −28.3257 49.0615i −1.09350 1.89400i
\(672\) 0 0
\(673\) 17.9897 31.1591i 0.693452 1.20109i −0.277248 0.960798i \(-0.589422\pi\)
0.970700 0.240295i \(-0.0772443\pi\)
\(674\) −28.2025 48.8481i −1.08632 1.88156i
\(675\) −16.4399 6.34678i −0.632771 0.244288i
\(676\) −13.0227 + 22.5560i −0.500874 + 0.867539i
\(677\) −4.46658 −0.171664 −0.0858322 0.996310i \(-0.527355\pi\)
−0.0858322 + 0.996310i \(0.527355\pi\)
\(678\) −22.5777 + 5.19731i −0.867092 + 0.199602i
\(679\) 0 0
\(680\) 4.89449 + 8.47750i 0.187695 + 0.325097i
\(681\) 2.25196 0.518394i 0.0862953 0.0198649i
\(682\) 8.72682 + 15.1153i 0.334167 + 0.578795i
\(683\) 13.3356 23.0980i 0.510274 0.883821i −0.489655 0.871916i \(-0.662877\pi\)
0.999929 0.0119046i \(-0.00378945\pi\)
\(684\) 3.13762 44.0625i 0.119970 1.68477i
\(685\) −3.99773 −0.152745
\(686\) 0 0
\(687\) 18.8832 + 20.2757i 0.720439 + 0.773565i
\(688\) 3.29569 5.70831i 0.125647 0.217627i
\(689\) −33.8960 −1.29134
\(690\) −24.1162 + 5.55146i −0.918086 + 0.211340i
\(691\) 41.0440 1.56139 0.780694 0.624913i \(-0.214866\pi\)
0.780694 + 0.624913i \(0.214866\pi\)
\(692\) 27.5709 1.04809
\(693\) 0 0
\(694\) −36.6671 −1.39187
\(695\) −23.9163 −0.907197
\(696\) −7.62923 8.19182i −0.289185 0.310510i
\(697\) −18.7656 −0.710799
\(698\) −33.8424 + 58.6167i −1.28095 + 2.21867i
\(699\) −13.7241 + 3.15924i −0.519093 + 0.119493i
\(700\) 0 0
\(701\) 9.63355 0.363854 0.181927 0.983312i \(-0.441767\pi\)
0.181927 + 0.983312i \(0.441767\pi\)
\(702\) 50.0615 + 19.3267i 1.88945 + 0.729441i
\(703\) 5.16148 8.93994i 0.194669 0.337176i
\(704\) −33.9788 58.8529i −1.28062 2.21810i
\(705\) 4.72419 + 5.07256i 0.177923 + 0.191044i
\(706\) 2.89382 + 5.01224i 0.108910 + 0.188638i
\(707\) 0 0
\(708\) −0.428629 + 1.39879i −0.0161089 + 0.0525698i
\(709\) −10.1426 −0.380914 −0.190457 0.981696i \(-0.560997\pi\)
−0.190457 + 0.981696i \(0.560997\pi\)
\(710\) −2.71448 + 4.70162i −0.101873 + 0.176449i
\(711\) 22.4056 + 15.1544i 0.840275 + 0.568333i
\(712\) 4.16286 + 7.21029i 0.156010 + 0.270217i
\(713\) 3.78954 6.56368i 0.141919 0.245812i
\(714\) 0 0
\(715\) −16.4826 28.5487i −0.616415 1.06766i
\(716\) 25.3690 43.9404i 0.948085 1.64213i
\(717\) 37.3058 8.58767i 1.39321 0.320712i
\(718\) 35.4118 + 61.3350i 1.32156 + 2.28900i
\(719\) −20.6844 35.8264i −0.771397 1.33610i −0.936797 0.349873i \(-0.886225\pi\)
0.165400 0.986227i \(-0.447109\pi\)
\(720\) 6.79305 3.30248i 0.253162 0.123076i
\(721\) 0 0
\(722\) −10.8350 + 18.7667i −0.403236 + 0.698425i
\(723\) 46.5773 10.7219i 1.73223 0.398753i
\(724\) 24.1066 0.895914
\(725\) 13.6781 0.507991
\(726\) 48.8144 + 52.4140i 1.81167 + 1.94526i
\(727\) 4.86372 8.42422i 0.180386 0.312437i −0.761626 0.648016i \(-0.775599\pi\)
0.942012 + 0.335580i \(0.108932\pi\)
\(728\) 0 0
\(729\) 5.71460 26.3883i 0.211652 0.977345i
\(730\) 14.5604 + 25.2194i 0.538906 + 0.933412i
\(731\) −7.99607 13.8496i −0.295745 0.512246i
\(732\) −14.3618 + 46.8685i −0.530829 + 1.73231i
\(733\) 14.4554 25.0375i 0.533922 0.924780i −0.465292 0.885157i \(-0.654051\pi\)
0.999215 0.0396234i \(-0.0126158\pi\)
\(734\) 15.4013 + 26.6758i 0.568471 + 0.984621i
\(735\) 0 0
\(736\) −19.4766 + 33.7345i −0.717918 + 1.24347i
\(737\) 12.2503 + 21.2182i 0.451247 + 0.781582i
\(738\) 1.80681 25.3735i 0.0665095 0.934013i
\(739\) 6.67467 11.5609i 0.245532 0.425273i −0.716749 0.697331i \(-0.754371\pi\)
0.962281 + 0.272058i \(0.0877041\pi\)
\(740\) −6.65752 −0.244735
\(741\) −30.1435 32.3663i −1.10735 1.18901i
\(742\) 0 0
\(743\) 19.9100 + 34.4851i 0.730425 + 1.26513i 0.956702 + 0.291071i \(0.0940115\pi\)
−0.226276 + 0.974063i \(0.572655\pi\)
\(744\) 1.19067 3.88563i 0.0436519 0.142454i
\(745\) −13.4908 23.3668i −0.494265 0.856092i
\(746\) −2.91221 + 5.04410i −0.106624 + 0.184678i
\(747\) −27.4135 + 13.3272i −1.00301 + 0.487617i
\(748\) −72.1877 −2.63944
\(749\) 0 0
\(750\) 11.7538 38.3573i 0.429186 1.40061i
\(751\) 19.2173 33.2853i 0.701248 1.21460i −0.266780 0.963757i \(-0.585960\pi\)
0.968029 0.250840i \(-0.0807069\pi\)
\(752\) 6.26409 0.228428
\(753\) 8.40402 27.4258i 0.306260 0.999451i
\(754\) −41.6515 −1.51686
\(755\) −8.07344 −0.293823
\(756\) 0 0
\(757\) −5.66698 −0.205970 −0.102985 0.994683i \(-0.532839\pi\)
−0.102985 + 0.994683i \(0.532839\pi\)
\(758\) −0.681032 −0.0247362
\(759\) 14.3877 46.9528i 0.522239 1.70428i
\(760\) 10.9368 0.396719
\(761\) 26.1661 45.3210i 0.948519 1.64288i 0.199973 0.979801i \(-0.435915\pi\)
0.748546 0.663082i \(-0.230752\pi\)
\(762\) −15.3846 + 50.2064i −0.557327 + 1.81879i
\(763\) 0 0
\(764\) 13.4337 0.486014
\(765\) 1.30166 18.2796i 0.0470616 0.660901i
\(766\) −9.78121 + 16.9416i −0.353410 + 0.612123i
\(767\) 0.732404 + 1.26856i 0.0264456 + 0.0458051i
\(768\) −0.606430 + 1.97903i −0.0218826 + 0.0714120i
\(769\) −1.17360 2.03274i −0.0423212 0.0733025i 0.844089 0.536203i \(-0.180142\pi\)
−0.886410 + 0.462901i \(0.846809\pi\)
\(770\) 0 0
\(771\) −2.43849 2.61831i −0.0878201 0.0942960i
\(772\) −26.7274 −0.961939
\(773\) 18.1814 31.4912i 0.653941 1.13266i −0.328217 0.944602i \(-0.606448\pi\)
0.982158 0.188057i \(-0.0602189\pi\)
\(774\) 19.4963 9.47824i 0.700781 0.340688i
\(775\) 2.48285 + 4.30042i 0.0891866 + 0.154476i
\(776\) 3.98251 6.89790i 0.142964 0.247620i
\(777\) 0 0
\(778\) 29.3659 + 50.8633i 1.05282 + 1.82354i
\(779\) −10.4830 + 18.1571i −0.375592 + 0.650545i
\(780\) −8.35711 + 27.2727i −0.299232 + 0.976518i
\(781\) −5.38663 9.32991i −0.192749 0.333851i
\(782\) 27.1292 + 46.9892i 0.970139 + 1.68033i