Properties

Label 441.2.f.h.148.1
Level $441$
Weight $2$
Character 441.148
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.f (of order \(3\), degree \(2\), 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 148.1
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08816 - 1.88474i) q^{2} +(-1.68791 - 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 + 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} +O(q^{10})\) \(q+(-1.08816 - 1.88474i) q^{2} +(-1.68791 - 0.388551i) q^{3} +(-1.36816 + 2.36973i) q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 + 3.60407i) q^{6} +1.60248 q^{8} +(2.69806 + 1.31167i) q^{9} -2.76019 q^{10} +(2.73867 + 4.74351i) q^{11} +(3.23009 - 3.46828i) q^{12} +(-2.37268 + 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 + 1.71920i) q^{16} +4.81644 q^{17} +(-0.463740 - 6.51244i) q^{18} -5.38119 q^{19} +(1.73523 + 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(-2.70484 - 0.622645i) q^{24} +(1.69572 + 2.93707i) q^{25} +10.3274 q^{26} +(-4.04442 - 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(4.65895 + 1.07247i) q^{30} +(-0.732093 + 1.26802i) q^{31} +(3.76264 - 6.51709i) q^{32} +(-2.77952 - 9.07071i) q^{33} +(-5.24103 - 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +1.91834 q^{37} +(5.85557 + 10.1421i) q^{38} +(5.60164 - 6.01471i) q^{39} +(1.01621 - 1.76012i) q^{40} +(1.94808 - 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} -14.9878 q^{44} +(3.15166 - 2.13168i) q^{45} -11.2653 q^{46} +(1.57773 + 2.73271i) q^{47} +(-1.00739 - 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(-8.12969 - 1.87143i) q^{51} +(-6.49243 - 11.2452i) q^{52} -7.14299 q^{53} +(-1.74766 + 11.1726i) q^{54} +6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} +(0.154341 - 0.267327i) q^{59} +(-1.76111 - 5.74723i) q^{60} +(5.17143 + 8.95719i) q^{61} +3.18652 q^{62} -12.4070 q^{64} +(3.00924 + 5.21216i) q^{65} +(-14.0714 + 15.1090i) q^{66} +(-2.23655 + 3.87382i) q^{67} +(-6.58968 + 11.4137i) q^{68} +(-6.11037 + 6.56095i) q^{69} -1.96688 q^{71} +(4.32359 + 2.10193i) q^{72} +10.5503 q^{73} +(-2.08745 - 3.61557i) q^{74} +(-1.72102 - 5.61638i) q^{75} +(7.36235 - 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 + 7.80846i) q^{79} +2.51776 q^{80} +(5.55902 + 7.07794i) q^{81} -8.47926 q^{82} +(5.08023 + 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(-2.04664 - 6.67903i) q^{87} +(4.38866 + 7.60138i) q^{88} -5.19552 q^{89} +(-7.44716 - 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(1.72840 - 1.85585i) q^{93} +(3.43363 - 5.94722i) q^{94} +(-3.41245 + 5.91054i) q^{95} +(-8.88321 + 9.53826i) q^{96} +(2.48521 + 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08816 1.88474i −0.769442 1.33271i −0.937866 0.346998i \(-0.887201\pi\)
0.168424 0.985715i \(-0.446132\pi\)
\(3\) −1.68791 0.388551i −0.974513 0.224330i
\(4\) −1.36816 + 2.36973i −0.684082 + 1.18487i
\(5\) 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
\(9\) 2.69806 + 1.31167i 0.899352 + 0.437225i
\(10\) −2.76019 −0.872849
\(11\) 2.73867 + 4.74351i 0.825739 + 1.43022i 0.901353 + 0.433084i \(0.142575\pi\)
−0.0756148 + 0.997137i \(0.524092\pi\)
\(12\) 3.23009 3.46828i 0.932448 1.00121i
\(13\) −2.37268 + 4.10960i −0.658062 + 1.13980i 0.323054 + 0.946380i \(0.395290\pi\)
−0.981117 + 0.193417i \(0.938043\pi\)
\(14\) 0 0
\(15\) −1.49715 + 1.60755i −0.386562 + 0.415068i
\(16\) 0.992580 + 1.71920i 0.248145 + 0.429800i
\(17\) 4.81644 1.16816 0.584079 0.811697i \(-0.301456\pi\)
0.584079 + 0.811697i \(0.301456\pi\)
\(18\) −0.463740 6.51244i −0.109305 1.53500i
\(19\) −5.38119 −1.23453 −0.617265 0.786756i \(-0.711759\pi\)
−0.617265 + 0.786756i \(0.711759\pi\)
\(20\) 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 \(-0.0147835\pi\)
\(24\) −2.70484 0.622645i −0.552123 0.127097i
\(25\) 1.69572 + 2.93707i 0.339144 + 0.587415i
\(26\) 10.3274 2.02536
\(27\) −4.04442 3.26231i −0.778348 0.627833i
\(28\) 0 0
\(29\) 2.01656 + 3.49278i 0.374466 + 0.648594i 0.990247 0.139324i \(-0.0444928\pi\)
−0.615781 + 0.787917i \(0.711159\pi\)
\(30\) 4.65895 + 1.07247i 0.850603 + 0.195806i
\(31\) −0.732093 + 1.26802i −0.131488 + 0.227744i −0.924250 0.381787i \(-0.875309\pi\)
0.792763 + 0.609531i \(0.208642\pi\)
\(32\) 3.76264 6.51709i 0.665148 1.15207i
\(33\) −2.77952 9.07071i −0.483852 1.57901i
\(34\) −5.24103 9.07773i −0.898830 1.55682i
\(35\) 0 0
\(36\) −6.79970 + 4.59908i −1.13328 + 0.766514i
\(37\) 1.91834 0.315373 0.157687 0.987489i \(-0.449596\pi\)
0.157687 + 0.987489i \(0.449596\pi\)
\(38\) 5.85557 + 10.1421i 0.949899 + 1.64527i
\(39\) 5.60164 6.01471i 0.896981 0.963125i
\(40\) 1.01621 1.76012i 0.160676 0.278299i
\(41\) 1.94808 3.37418i 0.304239 0.526958i −0.672852 0.739777i \(-0.734931\pi\)
0.977092 + 0.212819i \(0.0682644\pi\)
\(42\) 0 0
\(43\) −1.66016 2.87549i −0.253173 0.438508i 0.711225 0.702964i \(-0.248141\pi\)
−0.964398 + 0.264457i \(0.914807\pi\)
\(44\) −14.9878 −2.25949
\(45\) 3.15166 2.13168i 0.469822 0.317771i
\(46\) −11.2653 −1.66097
\(47\) 1.57773 + 2.73271i 0.230135 + 0.398606i 0.957848 0.287276i \(-0.0927498\pi\)
−0.727712 + 0.685882i \(0.759416\pi\)
\(48\) −1.00739 3.28752i −0.145404 0.474512i
\(49\) 0 0
\(50\) 3.69042 6.39199i 0.521904 0.903964i
\(51\) −8.12969 1.87143i −1.13838 0.262052i
\(52\) −6.49243 11.2452i −0.900338 1.55943i
\(53\) −7.14299 −0.981165 −0.490582 0.871395i \(-0.663216\pi\)
−0.490582 + 0.871395i \(0.663216\pi\)
\(54\) −1.74766 + 11.1726i −0.237827 + 1.52040i
\(55\) 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
\(59\) 0.154341 0.267327i 0.0200935 0.0348030i −0.855804 0.517301i \(-0.826937\pi\)
0.875897 + 0.482498i \(0.160270\pi\)
\(60\) −1.76111 5.74723i −0.227359 0.741965i
\(61\) 5.17143 + 8.95719i 0.662134 + 1.14685i 0.980054 + 0.198732i \(0.0636825\pi\)
−0.317920 + 0.948118i \(0.602984\pi\)
\(62\) 3.18652 0.404689
\(63\) 0 0
\(64\) −12.4070 −1.55088
\(65\) 3.00924 + 5.21216i 0.373250 + 0.646489i
\(66\) −14.0714 + 15.1090i −1.73207 + 1.85979i
\(67\) −2.23655 + 3.87382i −0.273238 + 0.473262i −0.969689 0.244342i \(-0.921428\pi\)
0.696451 + 0.717604i \(0.254761\pi\)
\(68\) −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 \(0.537236\pi\)
\(72\) 4.32359 + 2.10193i 0.509540 + 0.247715i
\(73\) 10.5503 1.23482 0.617409 0.786642i \(-0.288182\pi\)
0.617409 + 0.786642i \(0.288182\pi\)
\(74\) −2.08745 3.61557i −0.242662 0.420302i
\(75\) −1.72102 5.61638i −0.198726 0.648524i
\(76\) 7.36235 12.7520i 0.844520 1.46275i
\(77\) 0 0
\(78\) −17.4316 4.01270i −1.97374 0.454349i
\(79\) 4.50822 + 7.80846i 0.507214 + 0.878520i 0.999965 + 0.00835000i \(0.00265792\pi\)
−0.492751 + 0.870170i \(0.664009\pi\)
\(80\) 2.51776 0.281494
\(81\) 5.55902 + 7.07794i 0.617669 + 0.786438i
\(82\) −8.47926 −0.936378
\(83\) 5.08023 + 8.79921i 0.557627 + 0.965839i 0.997694 + 0.0678739i \(0.0216216\pi\)
−0.440066 + 0.897965i \(0.645045\pi\)
\(84\) 0 0
\(85\) 3.05432 5.29023i 0.331287 0.573806i
\(86\) −3.61303 + 6.25796i −0.389603 + 0.674813i
\(87\) −2.04664 6.67903i −0.219423 0.716067i
\(88\) 4.38866 + 7.60138i 0.467833 + 0.810310i
\(89\) −5.19552 −0.550724 −0.275362 0.961341i \(-0.588798\pi\)
−0.275362 + 0.961341i \(0.588798\pi\)
\(90\) −7.44716 3.62047i −0.784999 0.381631i
\(91\) 0 0
\(92\) 7.08205 + 12.2665i 0.738354 + 1.27887i
\(93\) 1.72840 1.85585i 0.179226 0.192442i
\(94\) 3.43363 5.94722i 0.354152 0.613409i
\(95\) −3.41245 + 5.91054i −0.350110 + 0.606409i
\(96\) −8.88321 + 9.53826i −0.906639 + 0.973495i
\(97\) 2.48521 + 4.30451i 0.252335 + 0.437057i 0.964168 0.265291i \(-0.0854682\pi\)
−0.711833 + 0.702348i \(0.752135\pi\)
\(98\) 0 0
\(99\) 1.16714 + 16.3905i 0.117302 + 1.64731i
\(100\) −9.28010 −0.928010
\(101\) 0.00266904 + 0.00462292i 0.000265580 + 0.000459997i 0.866158 0.499770i \(-0.166582\pi\)
−0.865893 + 0.500230i \(0.833249\pi\)
\(102\) 5.31921 + 17.3588i 0.526681 + 1.71877i
\(103\) 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
\(107\) 9.42162 0.910822 0.455411 0.890281i \(-0.349492\pi\)
0.455411 + 0.890281i \(0.349492\pi\)
\(108\) 13.2642 5.12079i 1.27635 0.492749i
\(109\) 16.8903 1.61779 0.808896 0.587951i \(-0.200065\pi\)
0.808896 + 0.587951i \(0.200065\pi\)
\(110\) −7.55924 13.0930i −0.720746 1.24837i
\(111\) −3.23798 0.745372i −0.307335 0.0707476i
\(112\) 0 0
\(113\) −3.07313 + 5.32281i −0.289095 + 0.500728i −0.973594 0.228286i \(-0.926688\pi\)
0.684499 + 0.729014i \(0.260021\pi\)
\(114\) −5.94292 19.3942i −0.556605 1.81643i
\(115\) −3.28253 5.68551i −0.306098 0.530176i
\(116\) −11.0359 −1.02466
\(117\) −11.7921 + 7.97575i −1.09018 + 0.737358i
\(118\) −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
\(122\) 11.2546 19.4936i 1.01895 1.76487i
\(123\) −4.59922 + 4.93837i −0.414698 + 0.445278i
\(124\) −2.00325 3.46973i −0.179897 0.311591i
\(125\) 10.6428 0.951919
\(126\) 0 0
\(127\) −13.9305 −1.23613 −0.618065 0.786127i \(-0.712083\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(128\) 5.97551 + 10.3499i 0.528165 + 0.914809i
\(129\) 1.68493 + 5.49861i 0.148350 + 0.484126i
\(130\) 6.54905 11.3433i 0.574389 0.994871i
\(131\) −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
\(135\) −6.14798 + 2.37349i −0.529134 + 0.204277i
\(136\) 7.71825 0.661835
\(137\) −1.57603 2.72977i −0.134649 0.233220i 0.790814 0.612056i \(-0.209657\pi\)
−0.925463 + 0.378837i \(0.876324\pi\)
\(138\) 19.0147 + 4.37712i 1.61864 + 0.372606i
\(139\) −9.42857 + 16.3308i −0.799721 + 1.38516i 0.120077 + 0.992765i \(0.461686\pi\)
−0.919798 + 0.392392i \(0.871648\pi\)
\(140\) 0 0
\(141\) −1.60126 5.22558i −0.134851 0.440073i
\(142\) 2.14027 + 3.70706i 0.179608 + 0.311090i
\(143\) −25.9919 −2.17355
\(144\) 0.423009 + 5.94044i 0.0352507 + 0.495037i
\(145\) 5.11516 0.424791
\(146\) −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 \(-0.170132\pi\)
\(150\) −8.71269 + 9.35516i −0.711388 + 0.763846i
\(151\) −3.18281 5.51278i −0.259013 0.448624i 0.706965 0.707249i \(-0.250064\pi\)
−0.965978 + 0.258625i \(0.916731\pi\)
\(152\) −8.62326 −0.699438
\(153\) 12.9950 + 6.31759i 1.05059 + 0.510747i
\(154\) 0 0
\(155\) 0.928506 + 1.60822i 0.0745794 + 0.129175i
\(156\) 6.58927 + 21.5035i 0.527564 + 1.72166i
\(157\) 0.697976 1.20893i 0.0557045 0.0964830i −0.836828 0.547465i \(-0.815593\pi\)
0.892533 + 0.450982i \(0.148926\pi\)
\(158\) 9.81128 16.9936i 0.780543 1.35194i
\(159\) 12.0567 + 2.77541i 0.956158 + 0.220105i
\(160\) −4.77212 8.26556i −0.377269 0.653450i
\(161\) 0 0
\(162\) 7.29101 18.1792i 0.572836 1.42829i
\(163\) −19.0617 −1.49303 −0.746515 0.665369i \(-0.768274\pi\)
−0.746515 + 0.665369i \(0.768274\pi\)
\(164\) 5.33059 + 9.23286i 0.416249 + 0.720965i
\(165\) −11.7256 2.69920i −0.912838 0.210132i
\(166\) 11.0562 19.1498i 0.858124 1.48631i
\(167\) −0.872003 + 1.51035i −0.0674776 + 0.116875i −0.897790 0.440423i \(-0.854828\pi\)
0.830313 + 0.557298i \(0.188162\pi\)
\(168\) 0 0
\(169\) −4.75919 8.24317i −0.366092 0.634090i
\(170\) −13.2943 −1.01963
\(171\) −14.5188 7.05837i −1.11028 0.539767i
\(172\) 9.08551 0.692764
\(173\) −5.03794 8.72598i −0.383028 0.663424i 0.608466 0.793580i \(-0.291785\pi\)
−0.991493 + 0.130157i \(0.958452\pi\)
\(174\) −10.3612 + 11.1252i −0.785478 + 0.843400i
\(175\) 0 0
\(176\) −5.43669 + 9.41662i −0.409806 + 0.709805i
\(177\) −0.364384 + 0.391254i −0.0273888 + 0.0294084i
\(178\) 5.65353 + 9.79221i 0.423750 + 0.733957i
\(179\) −18.5424 −1.38592 −0.692961 0.720975i \(-0.743694\pi\)
−0.692961 + 0.720975i \(0.743694\pi\)
\(180\) 0.739504 + 10.3851i 0.0551193 + 0.774058i
\(181\) 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
\(185\) 1.21651 2.10705i 0.0894393 0.154913i
\(186\) −5.37855 1.23813i −0.394375 0.0907838i
\(187\) 13.1906 + 22.8468i 0.964593 + 1.67072i
\(188\) −8.63437 −0.629726
\(189\) 0 0
\(190\) 14.8531 1.07756
\(191\) −2.45469 4.25165i −0.177615 0.307639i 0.763448 0.645869i \(-0.223505\pi\)
−0.941063 + 0.338231i \(0.890172\pi\)
\(192\) 20.9419 + 4.82077i 1.51135 + 0.347909i
\(193\) 4.88380 8.45899i 0.351544 0.608892i −0.634976 0.772531i \(-0.718990\pi\)
0.986520 + 0.163640i \(0.0523235\pi\)
\(194\) 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 \(0.462328\pi\)
\(198\) 29.6218 20.0352i 2.10513 1.42384i
\(199\) −11.0886 −0.786053 −0.393026 0.919527i \(-0.628572\pi\)
−0.393026 + 0.919527i \(0.628572\pi\)
\(200\) 2.71736 + 4.70661i 0.192146 + 0.332807i
\(201\) 5.28026 5.66963i 0.372441 0.399905i
\(202\) 0.00580866 0.0100609i 0.000408696 0.000707883i
\(203\) 0 0
\(204\) 15.5575 16.7048i 1.08925 1.16957i
\(205\) −2.47073 4.27943i −0.172563 0.298889i
\(206\) −28.3678 −1.97648
\(207\) 12.8630 8.70008i 0.894039 0.604697i
\(208\) −9.42029 −0.653180
\(209\) −14.7373 25.5257i −1.01940 1.76565i
\(210\) 0 0
\(211\) −3.66118 + 6.34135i −0.252046 + 0.436557i −0.964089 0.265579i \(-0.914437\pi\)
0.712043 + 0.702136i \(0.247770\pi\)
\(212\) 9.77278 16.9270i 0.671198 1.16255i
\(213\) 3.31991 + 0.764233i 0.227477 + 0.0523644i
\(214\) −10.2522 17.7573i −0.700825 1.21386i
\(215\) −4.21114 −0.287197
\(216\) −6.48110 5.22780i −0.440983 0.355707i
\(217\) 0 0
\(218\) −18.3792 31.8337i −1.24480 2.15605i
\(219\) −17.8079 4.09932i −1.20335 0.277007i
\(220\) −9.50442 + 16.4621i −0.640788 + 1.10988i
\(221\) −11.4278 + 19.7936i −0.768720 + 1.33146i
\(222\) 2.11859 + 6.91383i 0.142191 + 0.464026i
\(223\) −2.02765 3.51199i −0.135782 0.235181i 0.790114 0.612960i \(-0.210021\pi\)
−0.925896 + 0.377779i \(0.876688\pi\)
\(224\) 0 0
\(225\) 0.722667 + 10.1486i 0.0481778 + 0.676575i
\(226\) 13.3762 0.889769
\(227\) 0.667087 + 1.15543i 0.0442761 + 0.0766884i 0.887314 0.461165i \(-0.152569\pi\)
−0.843038 + 0.537854i \(0.819235\pi\)
\(228\) −17.3817 + 18.6635i −1.15113 + 1.23602i
\(229\) −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
\(233\) 8.13083 0.532669 0.266334 0.963881i \(-0.414187\pi\)
0.266334 + 0.963881i \(0.414187\pi\)
\(234\) 27.8638 + 13.5461i 1.82152 + 0.885539i
\(235\) 4.00203 0.261064
\(236\) 0.422329 + 0.731495i 0.0274913 + 0.0476163i
\(237\) −4.57547 14.9316i −0.297208 0.969913i
\(238\) 0 0
\(239\) 11.0509 19.1407i 0.714823 1.23811i −0.248204 0.968708i \(-0.579840\pi\)
0.963028 0.269403i \(-0.0868262\pi\)
\(240\) −4.24974 0.978276i −0.274320 0.0631475i
\(241\) 13.7973 + 23.8977i 0.888765 + 1.53939i 0.841336 + 0.540512i \(0.181770\pi\)
0.0474292 + 0.998875i \(0.484897\pi\)
\(242\) 41.3524 2.65823
\(243\) −6.63297 14.1069i −0.425505 0.904956i
\(244\) −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
\(248\) −1.17317 + 2.03198i −0.0744961 + 0.129031i
\(249\) −5.15601 16.8262i −0.326749 1.06632i
\(250\) −11.5810 20.0589i −0.732447 1.26863i
\(251\) 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
\(254\) 15.1585 + 26.2553i 0.951130 + 1.64741i
\(255\) −7.21093 + 7.74266i −0.451566 + 0.484864i
\(256\) 0.597516 1.03493i 0.0373448 0.0646831i
\(257\) 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
\(261\) 0.859399 + 12.0688i 0.0531954 + 0.747040i
\(262\) 0.389898 0.0240880
\(263\) −5.06482 8.77252i −0.312310 0.540937i 0.666552 0.745458i \(-0.267769\pi\)
−0.978862 + 0.204522i \(0.934436\pi\)
\(264\) −4.45413 14.5356i −0.274133 0.894607i
\(265\) −4.52969 + 7.84565i −0.278257 + 0.481954i
\(266\) 0 0
\(267\) 8.76955 + 2.01872i 0.536688 + 0.123544i
\(268\) −6.11994 10.6000i −0.373835 0.647501i
\(269\) 15.0994 0.920630 0.460315 0.887756i \(-0.347737\pi\)
0.460315 + 0.887756i \(0.347737\pi\)
\(270\) 11.1634 + 9.00462i 0.679381 + 0.548003i
\(271\) 28.8051 1.74979 0.874893 0.484317i \(-0.160932\pi\)
0.874893 + 0.484317i \(0.160932\pi\)
\(272\) 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
\(276\) −7.18769 23.4564i −0.432648 1.41191i
\(277\) 1.34982 + 2.33795i 0.0811026 + 0.140474i 0.903724 0.428116i \(-0.140823\pi\)
−0.822621 + 0.568590i \(0.807489\pi\)
\(278\) 41.0390 2.46135
\(279\) −3.63846 + 2.46093i −0.217829 + 0.147332i
\(280\) 0 0
\(281\) −2.46312 4.26626i −0.146938 0.254503i 0.783157 0.621825i \(-0.213608\pi\)
−0.930094 + 0.367321i \(0.880275\pi\)
\(282\) −8.10644 + 8.70421i −0.482731 + 0.518328i
\(283\) 1.79079 3.10173i 0.106451 0.184379i −0.807879 0.589348i \(-0.799385\pi\)
0.914330 + 0.404969i \(0.132718\pi\)
\(284\) 2.69102 4.66098i 0.159682 0.276578i
\(285\) 8.05644 8.65053i 0.477223 0.512413i
\(286\) 28.2832 + 48.9879i 1.67242 + 2.89672i
\(287\) 0 0
\(288\) 18.7001 12.6481i 1.10192 0.745298i
\(289\) 6.19806 0.364592
\(290\) −5.56609 9.64075i −0.326852 0.566125i
\(291\) −2.52228 8.23124i −0.147859 0.482524i
\(292\) −14.4345 + 25.0014i −0.844718 + 1.46309i
\(293\) −12.1955 + 21.1232i −0.712469 + 1.23403i 0.251459 + 0.967868i \(0.419090\pi\)
−0.963928 + 0.266164i \(0.914244\pi\)
\(294\) 0 0
\(295\) −0.195750 0.339048i −0.0113970 0.0197401i
\(296\) 3.07411 0.178679
\(297\) 4.39851 28.1191i 0.255228 1.63164i
\(298\) −46.2989 −2.68202
\(299\) 12.2817 + 21.2726i 0.710270 + 1.23022i
\(300\) 15.6639 + 3.60579i 0.904358 + 0.208180i
\(301\) 0 0
\(302\) −6.92678 + 11.9975i −0.398591 + 0.690380i
\(303\) −0.00270886 0.00884011i −0.000155620 0.000507851i
\(304\) −5.34126 9.25134i −0.306342 0.530600i
\(305\) 13.1177 0.751120
\(306\) −2.23357 31.3668i −0.127685 1.79312i
\(307\) 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
\(311\) −6.47082 + 11.2078i −0.366926 + 0.635535i −0.989083 0.147357i \(-0.952923\pi\)
0.622157 + 0.782893i \(0.286257\pi\)
\(312\) 8.97653 9.63846i 0.508196 0.545671i
\(313\) −13.4340 23.2684i −0.759336 1.31521i −0.943189 0.332255i \(-0.892190\pi\)
0.183853 0.982954i \(-0.441143\pi\)
\(314\) −3.03802 −0.171446
\(315\) 0 0
\(316\) −24.6719 −1.38790
\(317\) −4.15584 7.19813i −0.233415 0.404287i 0.725396 0.688332i \(-0.241657\pi\)
−0.958811 + 0.284045i \(0.908324\pi\)
\(318\) −7.88863 25.7438i −0.442372 1.44364i
\(319\) −11.0454 + 19.1311i −0.618422 + 1.07114i
\(320\) −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
\(324\) −24.3785 + 3.48959i −1.35436 + 0.193866i
\(325\) −16.0936 −0.892712
\(326\) 20.7421 + 35.9264i 1.14880 + 1.98978i
\(327\) −28.5092 6.56272i −1.57656 0.362919i
\(328\) 3.12177 5.40706i 0.172371 0.298555i
\(329\) 0 0
\(330\) 7.67201 + 25.0369i 0.422330 + 1.37824i
\(331\) −6.19889 10.7368i −0.340722 0.590147i 0.643845 0.765156i \(-0.277338\pi\)
−0.984567 + 0.175009i \(0.944005\pi\)
\(332\) −27.8024 −1.52585
\(333\) 5.17579 + 2.51624i 0.283632 + 0.137889i
\(334\) 3.79550 0.207680
\(335\) 2.83659 + 4.91312i 0.154980 + 0.268433i
\(336\) 0 0
\(337\) −12.9588 + 22.4454i −0.705913 + 1.22268i 0.260448 + 0.965488i \(0.416130\pi\)
−0.966361 + 0.257189i \(0.917204\pi\)
\(338\) −10.3575 + 17.9397i −0.563373 + 0.975791i
\(339\) 7.25533 7.79034i 0.394056 0.423113i
\(340\) 8.35762 + 14.4758i 0.453256 + 0.785062i
\(341\) −8.01983 −0.434298
\(342\) 2.49547 + 35.0447i 0.134940 + 1.89500i
\(343\) 0 0
\(344\) −2.66038 4.60792i −0.143438 0.248442i
\(345\) 3.33150 + 10.8720i 0.179362 + 0.585331i
\(346\) −10.9641 + 18.9904i −0.589435 + 1.02093i
\(347\) 8.42415 14.5911i 0.452232 0.783289i −0.546292 0.837595i \(-0.683961\pi\)
0.998524 + 0.0543058i \(0.0172946\pi\)
\(348\) 18.6276 + 4.28802i 0.998546 + 0.229862i
\(349\) −15.5503 26.9340i −0.832390 1.44174i −0.896138 0.443776i \(-0.853639\pi\)
0.0637477 0.997966i \(-0.479695\pi\)
\(350\) 0 0
\(351\) 23.0029 8.88050i 1.22780 0.474006i
\(352\) 41.2185 2.19695
\(353\) 1.32969 + 2.30309i 0.0707722 + 0.122581i 0.899240 0.437456i \(-0.144120\pi\)
−0.828468 + 0.560037i \(0.810787\pi\)
\(354\) 1.13392 + 0.261024i 0.0602671 + 0.0138733i
\(355\) −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
\(359\) −32.5429 −1.71755 −0.858775 0.512353i \(-0.828774\pi\)
−0.858775 + 0.512353i \(0.828774\pi\)
\(360\) 5.05048 3.41597i 0.266184 0.180038i
\(361\) 9.95719 0.524063
\(362\) −9.58646 16.6042i −0.503853 0.872699i
\(363\) 22.4299 24.0839i 1.17726 1.26407i
\(364\) 0 0
\(365\) 6.69042 11.5881i 0.350192 0.606551i
\(366\) −26.5711 + 28.5304i −1.38889 + 1.49131i
\(367\) 7.07678 + 12.2573i 0.369405 + 0.639828i 0.989473 0.144720i \(-0.0462283\pi\)
−0.620068 + 0.784548i \(0.712895\pi\)
\(368\) 10.2758 0.535663
\(369\) 9.68186 6.54847i 0.504017 0.340900i
\(370\) −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 \(0.188739\pi\)
\(374\) 28.7069 49.7217i 1.48440 2.57105i
\(375\) −17.9640 4.13526i −0.927658 0.213544i
\(376\) 2.52828 + 4.37911i 0.130386 + 0.225835i
\(377\) −19.1386 −0.985687
\(378\) 0 0
\(379\) −0.312929 −0.0160741 −0.00803705 0.999968i \(-0.502558\pi\)
−0.00803705 + 0.999968i \(0.502558\pi\)
\(380\) −9.33759 16.1732i −0.479008 0.829667i
\(381\) 23.5133 + 5.41270i 1.20463 + 0.277301i
\(382\) −5.34218 + 9.25292i −0.273330 + 0.473421i
\(383\) −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
\(387\) −0.707513 9.93583i −0.0359649 0.505066i
\(388\) −13.6007 −0.690472
\(389\) 13.4934 + 23.3713i 0.684144 + 1.18497i 0.973705 + 0.227813i \(0.0731575\pi\)
−0.289560 + 0.957160i \(0.593509\pi\)
\(390\) −15.4616 + 16.6018i −0.782929 + 0.840663i
\(391\) 12.4657 21.5912i 0.630417 1.09191i
\(392\) 0 0
\(393\) 0.211484 0.227079i 0.0106680 0.0114546i
\(394\) −3.60664 6.24689i −0.181700 0.314714i
\(395\) 11.4354 0.575380
\(396\) −40.4379 19.6591i −2.03208 0.987906i
\(397\) −29.5005 −1.48059 −0.740295 0.672282i \(-0.765314\pi\)
−0.740295 + 0.672282i \(0.765314\pi\)
\(398\) 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 \(-0.160324\pi\)
\(402\) −16.4315 3.78248i −0.819530 0.188653i
\(403\) −3.47404 6.01721i −0.173054 0.299739i
\(404\) −0.0146068 −0.000726713
\(405\) 11.2994 1.61743i 0.561473 0.0803706i
\(406\) 0 0
\(407\) 5.25369 + 9.09966i 0.260416 + 0.451054i
\(408\) −13.0277 2.99893i −0.644967 0.148469i
\(409\) 5.49225 9.51286i 0.271574 0.470381i −0.697691 0.716399i \(-0.745789\pi\)
0.969265 + 0.246018i \(0.0791224\pi\)
\(410\) −5.37708 + 9.31338i −0.265555 + 0.459955i
\(411\) 1.59954 + 5.21996i 0.0788995 + 0.257481i
\(412\) 17.8338 + 30.8890i 0.878608 + 1.52179i
\(413\) 0 0
\(414\) −30.3943 14.7764i −1.49380 0.726218i
\(415\) 12.8864 0.632568
\(416\) 17.8551 + 30.9259i 0.875417 + 1.51627i
\(417\) 22.2599 23.9013i 1.09007 1.17045i
\(418\) −32.0729 + 55.5519i −1.56874 + 2.71713i
\(419\) 3.33207 5.77132i 0.162782 0.281947i −0.773083 0.634305i \(-0.781286\pi\)
0.935866 + 0.352357i \(0.114620\pi\)
\(420\) 0 0
\(421\) −17.0430 29.5193i −0.830625 1.43868i −0.897543 0.440926i \(-0.854650\pi\)
0.0669186 0.997758i \(-0.478683\pi\)
\(422\) 15.9357 0.775740
\(423\) 0.672382 + 9.44246i 0.0326923 + 0.459108i
\(424\) −11.4465 −0.555892
\(425\) 8.16733 + 14.1462i 0.396174 + 0.686193i
\(426\) −2.17220 7.08877i −0.105243 0.343452i
\(427\) 0 0
\(428\) −12.8903 + 22.3267i −0.623077 + 1.07920i
\(429\) 43.8719 + 10.0992i 2.11815 + 0.487592i
\(430\) 4.58237 + 7.93690i 0.220982 + 0.382751i
\(431\) 2.25939 0.108831 0.0544155 0.998518i \(-0.482670\pi\)
0.0544155 + 0.998518i \(0.482670\pi\)
\(432\) 1.59416 10.1913i 0.0766992 0.490328i
\(433\) −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
\(437\) −13.9274 + 24.1229i −0.666236 + 1.15395i
\(438\) 11.6516 + 38.0240i 0.556736 + 1.81686i
\(439\) 2.99569 + 5.18869i 0.142977 + 0.247643i 0.928616 0.371042i \(-0.120999\pi\)
−0.785640 + 0.618684i \(0.787666\pi\)
\(440\) 11.1322 0.530706
\(441\) 0 0
\(442\) 49.7411 2.36594
\(443\) 19.7190 + 34.1543i 0.936879 + 1.62272i 0.771249 + 0.636534i \(0.219632\pi\)
0.165630 + 0.986188i \(0.447034\pi\)
\(444\) 6.19642 6.65335i 0.294069 0.315754i
\(445\) −3.29471 + 5.70661i −0.156184 + 0.270519i
\(446\) −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 \(0.481581\pi\)
\(450\) 18.3412 12.4053i 0.864610 0.584793i
\(451\) 21.3406 1.00489
\(452\) −8.40909 14.5650i −0.395530 0.685078i
\(453\) 3.23029 + 10.5417i 0.151772 + 0.495294i
\(454\) 1.45179 2.51457i 0.0681358 0.118015i
\(455\) 0 0
\(456\) 14.5552 + 3.35057i 0.681612 + 0.156905i
\(457\) −5.51058 9.54461i −0.257774 0.446478i 0.707871 0.706342i \(-0.249656\pi\)
−0.965645 + 0.259864i \(0.916322\pi\)
\(458\) 34.8137 1.62674
\(459\) −19.4797 15.7127i −0.909233 0.733408i
\(460\) 17.9642 0.837584
\(461\) −14.6540 25.3814i −0.682503 1.18213i −0.974215 0.225624i \(-0.927558\pi\)
0.291711 0.956506i \(-0.405775\pi\)
\(462\) 0 0
\(463\) 0.593566 1.02809i 0.0275853 0.0477792i −0.851903 0.523699i \(-0.824552\pi\)
0.879489 + 0.475920i \(0.157885\pi\)
\(464\) −4.00319 + 6.93374i −0.185844 + 0.321891i
\(465\) −0.942356 3.07530i −0.0437007 0.142613i
\(466\) −8.84761 15.3245i −0.409858 0.709894i
\(467\) −22.1147 −1.02335 −0.511673 0.859180i \(-0.670974\pi\)
−0.511673 + 0.859180i \(0.670974\pi\)
\(468\) −2.76688 38.8562i −0.127899 1.79613i
\(469\) 0 0
\(470\) −4.35483 7.54280i −0.200874 0.347923i
\(471\) −1.64785 + 1.76936i −0.0759288 + 0.0815278i
\(472\) 0.247329 0.428387i 0.0113842 0.0197181i
\(473\) 9.09327 15.7500i 0.418109 0.724186i
\(474\) −23.1634 + 24.8715i −1.06393 + 1.14239i
\(475\) −9.12499 15.8050i −0.418683 0.725181i
\(476\) 0 0
\(477\) −19.2722 9.36927i −0.882413 0.428990i
\(478\) −48.1004 −2.20006
\(479\) −12.5714 21.7743i −0.574402 0.994894i −0.996106 0.0881606i \(-0.971901\pi\)
0.421704 0.906734i \(-0.361432\pi\)
\(480\) 4.84331 + 15.8057i 0.221066 + 0.721428i
\(481\) −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
\(485\) 6.30393 0.286247
\(486\) −19.3701 + 27.8519i −0.878645 + 1.26339i
\(487\) 13.5781 0.615281 0.307641 0.951503i \(-0.400461\pi\)
0.307641 + 0.951503i \(0.400461\pi\)
\(488\) 8.28713 + 14.3537i 0.375141 + 0.649763i
\(489\) 32.1744 + 7.40644i 1.45498 + 0.334931i
\(490\) 0 0
\(491\) 7.25177 12.5604i 0.327268 0.566844i −0.654701 0.755888i \(-0.727205\pi\)
0.981969 + 0.189044i \(0.0605387\pi\)
\(492\) −5.41011 17.6554i −0.243907 0.795967i
\(493\) 9.71263 + 16.8228i 0.437435 + 0.757659i
\(494\) −55.5735 −2.50037
\(495\) 18.7430 + 9.11199i 0.842434 + 0.409554i
\(496\) −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 \(0.268058\pi\)
\(500\) −14.5611 + 25.2205i −0.651191 + 1.12790i
\(501\) 2.05871 2.21052i 0.0919763 0.0987587i
\(502\) −18.0209 31.2132i −0.804314 1.39311i
\(503\) −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
\(506\) −30.8518 53.4369i −1.37153 2.37556i
\(507\) 4.83019 + 15.7629i 0.214516 + 0.700054i
\(508\) 19.0592 33.0115i 0.845615 1.46465i
\(509\) −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
\(513\) 21.7638 + 17.5551i 0.960894 + 0.775078i
\(514\) −4.49568 −0.198296
\(515\) −8.26597 14.3171i −0.364242 0.630886i
\(516\) −15.3355 3.53018i −0.675107 0.155408i
\(517\) −8.64174 + 14.9679i −0.380063 + 0.658289i
\(518\) 0 0
\(519\) 5.11310 + 16.6861i 0.224440 + 0.732440i
\(520\) 4.82225 + 8.35239i 0.211470 + 0.366276i
\(521\) −7.13594 −0.312631 −0.156316 0.987707i \(-0.549962\pi\)
−0.156316 + 0.987707i \(0.549962\pi\)
\(522\) 21.8114 14.7525i 0.954659 0.645698i
\(523\) 13.0647 0.571280 0.285640 0.958337i \(-0.407794\pi\)
0.285640 + 0.958337i \(0.407794\pi\)
\(524\) −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
\(528\) 12.8355 13.7820i 0.558592 0.599782i
\(529\) −1.89710 3.28587i −0.0824825 0.142864i
\(530\) 19.7160 0.856409
\(531\) 0.767068 0.518818i 0.0332879 0.0225148i
\(532\) 0 0
\(533\) 9.24434 + 16.0117i 0.400417 + 0.693542i
\(534\) −5.73787 18.7250i −0.248302 0.810311i
\(535\) 5.97467 10.3484i 0.258308 0.447402i
\(536\) −3.58403 + 6.20772i −0.154807 + 0.268133i
\(537\) 31.2978 + 7.20465i 1.35060 + 0.310904i
\(538\) −16.4305 28.4585i −0.708371 1.22693i
\(539\) 0 0
\(540\) 2.78691 17.8164i 0.119930 0.766695i
\(541\) 4.93577 0.212205 0.106103 0.994355i \(-0.466163\pi\)
0.106103 + 0.994355i \(0.466163\pi\)
\(542\) −31.3444 54.2901i −1.34636 2.33196i
\(543\) −14.8702 3.42306i −0.638139 0.146898i
\(544\) 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 0.877748 0.479122i \(-0.159045\pi\)
−0.853806 + 0.520591i \(0.825712\pi\)
\(548\) 8.62508 0.368445
\(549\) 2.20391 + 30.9502i 0.0940607 + 1.32092i
\(550\) 40.4273 1.72382
\(551\) −10.8515 18.7953i −0.462289 0.800708i
\(552\) −9.79175 + 10.5138i −0.416764 + 0.447497i
\(553\) 0 0
\(554\) 2.93762 5.08811i 0.124808 0.216173i
\(555\) −2.87204 + 3.08383i −0.121911 + 0.130901i
\(556\) −25.7997 44.6863i −1.09415 1.89512i
\(557\) −10.9566 −0.464248 −0.232124 0.972686i \(-0.574567\pi\)
−0.232124 + 0.972686i \(0.574567\pi\)
\(558\) 8.59742 + 4.17968i 0.363958 + 0.176940i
\(559\) 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
\(563\) −2.38048 + 4.12311i −0.100325 + 0.173768i −0.911819 0.410593i \(-0.865322\pi\)
0.811493 + 0.584361i \(0.198655\pi\)
\(564\) 14.5740 + 3.35489i 0.613677 + 0.141266i
\(565\) 3.89761 + 6.75087i 0.163974 + 0.284011i
\(566\) −7.79462 −0.327632
\(567\) 0 0
\(568\) −3.15189 −0.132250
\(569\) −1.74988 3.03088i −0.0733588 0.127061i 0.827013 0.562183i \(-0.190038\pi\)
−0.900371 + 0.435122i \(0.856705\pi\)
\(570\) −25.0707 5.77119i −1.05009 0.241728i
\(571\) −3.53051 + 6.11501i −0.147747 + 0.255905i −0.930394 0.366560i \(-0.880535\pi\)
0.782647 + 0.622465i \(0.213869\pi\)
\(572\) 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
\(576\) −33.4749 16.2740i −1.39479 0.678084i
\(577\) −12.8830 −0.536326 −0.268163 0.963374i \(-0.586416\pi\)
−0.268163 + 0.963374i \(0.586416\pi\)
\(578\) −6.74445 11.6817i −0.280532 0.485896i
\(579\) −11.5301 + 12.3804i −0.479176 + 0.514511i
\(580\) −6.99838 + 12.1216i −0.290592 + 0.503320i
\(581\) 0 0
\(582\) −12.7691 + 13.7107i −0.529297 + 0.568328i
\(583\) −19.5623 33.8828i −0.810186 1.40328i
\(584\) 16.9067 0.699603
\(585\) 1.28245 + 18.0098i 0.0530228 + 0.744615i
\(586\) 53.0824 2.19281
\(587\) 19.5044 + 33.7826i 0.805034 + 1.39436i 0.916268 + 0.400565i \(0.131186\pi\)
−0.111235 + 0.993794i \(0.535481\pi\)
\(588\) 0 0
\(589\) 3.93953 6.82347i 0.162326 0.281156i
\(590\) −0.426012 + 0.737874i −0.0175386 + 0.0303778i
\(591\) −5.59449 1.28783i −0.230127 0.0529744i
\(592\) 1.90411 + 3.29801i 0.0782583 + 0.135547i
\(593\) −40.3026 −1.65503 −0.827515 0.561444i \(-0.810246\pi\)
−0.827515 + 0.561444i \(0.810246\pi\)
\(594\) −57.7835 + 22.3079i −2.37089 + 0.915304i
\(595\) 0 0
\(596\) 29.1064 + 50.4137i 1.19224 + 2.06503i
\(597\) 18.7166 + 4.30850i 0.766019 + 0.176335i
\(598\) 26.7288 46.2957i 1.09302 1.89317i
\(599\) 6.39103 11.0696i 0.261130 0.452291i −0.705412 0.708797i \(-0.749238\pi\)
0.966543 + 0.256506i \(0.0825715\pi\)
\(600\) −2.75790 9.00015i −0.112591 0.367429i
\(601\) 4.86311 + 8.42316i 0.198371 + 0.343588i 0.948000 0.318270i \(-0.103102\pi\)
−0.749630 + 0.661858i \(0.769768\pi\)
\(602\) 0 0
\(603\) −11.1155 + 7.51816i −0.452659 + 0.306163i
\(604\) 17.4184 0.708745
\(605\) 12.0495 + 20.8703i 0.489881 + 0.848499i
\(606\) −0.0137137 + 0.0147249i −0.000557079 + 0.000598158i
\(607\) 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
\(611\) −14.9738 −0.605774
\(612\) −32.7503 + 22.1512i −1.32385 + 0.895409i
\(613\) 15.2957 0.617785 0.308893 0.951097i \(-0.400042\pi\)
0.308893 + 0.951097i \(0.400042\pi\)
\(614\) −26.0096 45.0500i −1.04966 1.81807i
\(615\) 2.50759 + 8.18329i 0.101116 + 0.329982i
\(616\) 0 0
\(617\) −2.66563 + 4.61700i −0.107314 + 0.185873i −0.914681 0.404176i \(-0.867558\pi\)
0.807367 + 0.590049i \(0.200892\pi\)
\(618\) 47.8822 + 11.0223i 1.92611 + 0.443383i
\(619\) −6.34205 10.9847i −0.254908 0.441514i 0.709962 0.704240i \(-0.248712\pi\)
−0.964871 + 0.262726i \(0.915379\pi\)
\(620\) −5.08140 −0.204074
\(621\) −25.0919 + 9.68700i −1.00690 + 0.388726i
\(622\) 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
\(626\) −29.2366 + 50.6393i −1.16853 + 2.02395i
\(627\) 14.9571 + 48.8112i 0.597330 + 1.94933i
\(628\) 1.90989 + 3.30803i 0.0762129 + 0.132005i
\(629\) 9.23957 0.368406
\(630\) 0 0
\(631\) 0.123764 0.00492698 0.00246349 0.999997i \(-0.499216\pi\)
0.00246349 + 0.999997i \(0.499216\pi\)
\(632\) 7.22433 + 12.5129i 0.287369 + 0.497737i
\(633\) 8.64367 9.28105i 0.343555 0.368889i
\(634\) −9.04441 + 15.6654i −0.359199 + 0.622151i
\(635\) −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
\(639\) −5.30676 2.57991i −0.209932 0.102060i
\(640\) 15.1574 0.599147
\(641\) −2.96588 5.13706i −0.117145 0.202902i 0.801490 0.598008i \(-0.204041\pi\)
−0.918635 + 0.395107i \(0.870708\pi\)
\(642\) 10.4051 + 33.9562i 0.410657 + 1.34014i
\(643\) 23.4140 40.5542i 0.923358 1.59930i 0.129178 0.991621i \(-0.458766\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(644\) 0 0
\(645\) 7.10801 + 1.63624i 0.279877 + 0.0644269i
\(646\) 28.2030 + 48.8490i 1.10963 + 1.92194i
\(647\) 39.1401 1.53876 0.769379 0.638793i \(-0.220566\pi\)
0.769379 + 0.638793i \(0.220566\pi\)
\(648\) 8.90823 + 11.3423i 0.349948 + 0.445567i
\(649\) 1.69076 0.0663680
\(650\) 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 \(0.844606\pi\)
\(654\) 18.6534 + 60.8736i 0.729405 + 2.38035i
\(655\) 0.113611 + 0.196779i 0.00443913 + 0.00768881i
\(656\) 7.73451 0.301982
\(657\) 28.4653 + 13.8386i 1.11054 + 0.539893i
\(658\) 0 0
\(659\) 3.43895 + 5.95643i 0.133962 + 0.232030i 0.925201 0.379478i \(-0.123897\pi\)
−0.791238 + 0.611508i \(0.790563\pi\)
\(660\) 22.4390 24.0936i 0.873435 0.937842i
\(661\) 19.3835 33.5733i 0.753932 1.30585i −0.191971 0.981401i \(-0.561488\pi\)
0.945903 0.324449i \(-0.105179\pi\)
\(662\) −13.4907 + 23.3666i −0.524331 + 0.908168i
\(663\) 26.9800 28.9695i 1.04781 1.12508i
\(664\) 8.14097 + 14.1006i 0.315931 + 0.547209i
\(665\) 0 0
\(666\) −0.889611 12.4931i −0.0344717 0.484097i
\(667\) 20.8767 0.808348
\(668\) −2.38609 4.13282i −0.0923205 0.159904i
\(669\) 2.05790 + 6.71576i 0.0795629 + 0.259646i
\(670\) 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 0.970700 + 0.240295i \(0.0772443\pi\)
−0.277248 + 0.960798i \(0.589422\pi\)
\(674\) 56.4049 2.17264
\(675\) 2.72346 17.4107i 0.104826 0.670139i
\(676\) 26.0454 1.00175
\(677\) 2.23329 + 3.86817i 0.0858322 + 0.148666i 0.905746 0.423822i \(-0.139312\pi\)
−0.819913 + 0.572488i \(0.805978\pi\)
\(678\) −22.5777 5.19731i −0.867092 0.199602i
\(679\) 0 0
\(680\) 4.89449 8.47750i 0.187695 0.325097i
\(681\) −0.677038 2.20945i −0.0259441 0.0846664i
\(682\) 8.72682 + 15.1153i 0.334167 + 0.578795i
\(683\) −26.6713 −1.02055 −0.510274 0.860012i \(-0.670456\pi\)
−0.510274 + 0.860012i \(0.670456\pi\)
\(684\) 36.5905 24.7485i 1.39907 0.946284i
\(685\) −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
\(689\) 16.9480 29.3548i 0.645668 1.11833i
\(690\) 16.8658 18.1095i 0.642069 0.689416i
\(691\) −20.5220 35.5452i −0.780694 1.35220i −0.931538 0.363644i \(-0.881532\pi\)
0.150844 0.988558i \(-0.451801\pi\)
\(692\) 27.5709 1.04809
\(693\) 0 0
\(694\) −36.6671 −1.39187
\(695\) 11.9582 + 20.7121i 0.453599 + 0.785656i
\(696\) −3.27970 10.7030i −0.124317 0.405697i
\(697\) 9.38281 16.2515i 0.355399 0.615570i
\(698\) −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 \(0.441767\pi\)
\(702\) −41.7682 33.6911i −1.57644 1.27159i
\(703\) −10.3230 −0.389338
\(704\) −33.9788 58.8529i −1.28062 2.21810i
\(705\) −6.75506 1.55499i −0.254410 0.0585644i
\(706\) 2.89382 5.01224i 0.108910 0.188638i
\(707\) 0 0
\(708\) −0.428629 1.39879i −0.0161089 0.0525698i
\(709\) 5.07131 + 8.78376i 0.190457 + 0.329881i 0.945402 0.325907i \(-0.105670\pi\)
−0.754945 + 0.655788i \(0.772336\pi\)
\(710\) 5.42897 0.203746
\(711\) 1.92127 + 26.9810i 0.0720532 + 1.01187i
\(712\) −8.32572 −0.312020
\(713\) 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
\(717\) −26.0900 + 28.0139i −0.974350 + 1.04620i
\(718\) 35.4118 + 61.3350i 1.32156 + 2.28900i
\(719\) 41.3688 1.54279 0.771397 0.636354i \(-0.219558\pi\)
0.771397 + 0.636354i \(0.219558\pi\)
\(720\) 6.79305 + 3.30248i 0.253162 + 0.123076i
\(721\) 0 0
\(722\) −10.8350 18.7667i −0.403236 0.698425i
\(723\) −14.0032 45.6981i −0.520783 1.69953i
\(724\) −12.0533 + 20.8769i −0.447957 + 0.775884i
\(725\) −6.83904 + 11.8456i −0.253996 + 0.439934i
\(726\) −69.7990 16.0675i −2.59048 0.596321i
\(727\) 4.86372 + 8.42422i 0.180386 + 0.312437i 0.942012 0.335580i \(-0.108932\pi\)
−0.761626 + 0.648016i \(0.775599\pi\)
\(728\) 0 0
\(729\) 5.71460 + 26.3883i 0.211652 + 0.977345i
\(730\) −29.1209 −1.07781
\(731\) −7.99607 13.8496i −0.295745 0.512246i
\(732\) 47.7703 + 10.9966i 1.76564 + 0.406445i
\(733\) 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
\(737\) −24.5007 −0.902493
\(738\) −22.8775 11.1220i −0.842134 0.409408i
\(739\) −13.3493 −0.491063 −0.245532 0.969389i \(-0.578963\pi\)
−0.245532 + 0.969389i \(0.578963\pi\)
\(740\) 3.32876 + 5.76558i 0.122368 + 0.211947i
\(741\) −30.1435 + 32.3663i −1.10735 + 1.18901i
\(742\) 0 0
\(743\) 19.9100 34.4851i 0.730425 1.26513i −0.226276 0.974063i \(-0.572655\pi\)
0.956702 0.291071i \(-0.0940115\pi\)
\(744\) 2.76972 2.97396i 0.101543 0.109031i
\(745\) −13.4908 23.3668i −0.494265 0.856092i
\(746\) 5.82442 0.213247
\(747\) 2.16504 + 30.4044i 0.0792148 + 1.11244i
\(748\) −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 \(-0.0807069\pi\)
\(752\) −3.13204 + 5.42486i −0.114214 + 0.197824i
\(753\) −27.9534 6.43479i −1.01868 0.234497i
\(754\) 20.8258 + 36.0713i 0.758429 + 1.31364i
\(755\) −8.07344 −0.293823
\(756\) 0 0
\(757\) −5.66698 −0.205970 −0.102985 0.994683i \(-0.532839\pi\)
−0.102985 + 0.994683i \(0.532839\pi\)
\(758\) 0.340516 + 0.589791i 0.0123681 + 0.0214222i
\(759\) −47.8561 11.0163i −1.73707 0.399867i
\(760\) −5.46839 + 9.47153i −0.198359 + 0.343569i
\(761\) 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
\(765\) 15.1798 10.2671i 0.548826 0.371207i
\(766\) 19.5624 0.706819
\(767\) 0.732404 + 1.26856i 0.0264456 + 0.0458051i
\(768\) −1.41067 + 1.51470i −0.0509033 + 0.0546569i
\(769\) −1.17360 + 2.03274i −0.0423212 + 0.0733025i −0.886410 0.462901i \(-0.846809\pi\)
0.844089 + 0.536203i \(0.180142\pi\)
\(770\) 0 0
\(771\) −2.43849 + 2.61831i −0.0878201 + 0.0942960i
\(772\) 13.3637 + 23.1466i 0.480970 + 0.833064i
\(773\) −36.3629 −1.30788 −0.653941 0.756545i \(-0.726886\pi\)
−0.653941 + 0.756545i \(0.726886\pi\)
\(774\) −17.9566 + 12.1452i −0.645436 + 0.436550i
\(775\) −4.96570 −0.178373
\(776\) 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
\(780\) 27.7974 + 6.39887i 0.995306 + 0.229116i
\(781\) −5.38663 9.32991i −0.192749 0.333851i
\(782\) −54.2584 −1.94028
\(783\) 3.23875 20.7049i 0.115744 0.739934i
\(784\) 0