Properties

Label 441.2.g.h.67.2
Level $441$
Weight $2$
Character 441.67
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.g (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 67.2
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08816 + 1.88474i) q^{2} +(1.18045 - 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} -1.26829 q^{5} +(1.10439 + 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +O(q^{10})\) \(q+(-1.08816 + 1.88474i) q^{2} +(1.18045 - 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} -1.26829 q^{5} +(1.10439 + 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +(1.38010 - 2.39040i) q^{10} -5.47733 q^{11} +(-4.61867 - 1.06320i) q^{12} +(-2.37268 + 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 - 1.71920i) q^{16} +(-2.40822 + 4.17116i) q^{17} +(5.87181 + 2.85461i) q^{18} +(2.69059 + 4.66025i) q^{19} +(1.73523 + 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} -5.17631 q^{23} +(1.89165 - 2.03114i) q^{24} -3.39144 q^{25} +(-5.16368 - 8.94376i) q^{26} +(-4.04442 - 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(-1.40068 - 4.57100i) q^{30} +(-0.732093 - 1.26802i) q^{31} +(3.76264 + 6.51709i) q^{32} +(-6.46570 + 6.94249i) q^{33} +(-5.24103 - 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} -11.7111 q^{38} +(2.40807 + 7.85852i) q^{39} -2.03241 q^{40} +(1.94808 - 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(0.270254 + 3.79526i) q^{45} +(5.63263 - 9.75600i) q^{46} +(1.57773 - 2.73271i) q^{47} +(-1.00739 - 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(2.44414 + 7.97624i) q^{51} +12.9849 q^{52} +(3.57149 - 6.18601i) q^{53} +(10.5496 - 4.07277i) q^{54} +6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} -8.77732 q^{58} +(0.154341 + 0.267327i) q^{59} +(5.85781 + 1.34845i) q^{60} +(5.17143 - 8.95719i) q^{61} +3.18652 q^{62} -12.4070 q^{64} +(3.00924 - 5.21216i) q^{65} +(-6.04910 - 19.7407i) q^{66} +(-2.23655 - 3.87382i) q^{67} +13.1794 q^{68} +(-6.11037 + 6.56095i) q^{69} -1.96688 q^{71} +(-0.341465 - 4.79530i) q^{72} +(-5.27515 + 9.13683i) q^{73} +4.17491 q^{74} +(-4.00342 + 4.29863i) q^{75} +(7.36235 - 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 - 7.80846i) q^{79} +(-1.25888 + 2.18044i) q^{80} +(-8.90919 + 1.27528i) q^{81} +(4.23963 + 7.34326i) q^{82} +(5.08023 + 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +7.22607 q^{86} +(6.80753 + 1.56707i) q^{87} -8.77732 q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.44716 - 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(-2.47141 - 0.568910i) q^{93} +(3.43363 + 5.94722i) q^{94} +(-3.41245 - 5.91054i) q^{95} +(12.7020 + 2.92396i) q^{96} +(2.48521 + 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 0.168424 + 0.985715i \(0.446132\pi\)
−0.937866 + 0.346998i \(0.887201\pi\)
\(3\) 1.18045 1.26749i 0.681532 0.731788i
\(4\) −1.36816 2.36973i −0.684082 1.18487i
\(5\) −1.26829 −0.567196 −0.283598 0.958943i \(-0.591528\pi\)
−0.283598 + 0.958943i \(0.591528\pi\)
\(6\) 1.10439 + 3.60407i 0.450864 + 1.47136i
\(7\) 0 0
\(8\) 1.60248 0.566563
\(9\) −0.213085 2.99242i −0.0710284 0.997474i
\(10\) 1.38010 2.39040i 0.436425 0.755910i
\(11\) −5.47733 −1.65148 −0.825739 0.564053i \(-0.809241\pi\)
−0.825739 + 0.564053i \(0.809241\pi\)
\(12\) −4.61867 1.06320i −1.33329 0.306920i
\(13\) −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
\(17\) −2.40822 + 4.17116i −0.584079 + 1.01165i 0.410911 + 0.911676i \(0.365211\pi\)
−0.994990 + 0.0999785i \(0.968123\pi\)
\(18\) 5.87181 + 2.85461i 1.38400 + 0.672838i
\(19\) 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
\(23\) −5.17631 −1.07934 −0.539668 0.841878i \(-0.681450\pi\)
−0.539668 + 0.841878i \(0.681450\pi\)
\(24\) 1.89165 2.03114i 0.386131 0.414604i
\(25\) −3.39144 −0.678288
\(26\) −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 0.990247 0.139324i \(-0.0444928\pi\)
−0.615781 + 0.787917i \(0.711159\pi\)
\(30\) −1.40068 4.57100i −0.255729 0.834547i
\(31\) −0.732093 1.26802i −0.131488 0.227744i 0.792763 0.609531i \(-0.208642\pi\)
−0.924250 + 0.381787i \(0.875309\pi\)
\(32\) 3.76264 + 6.51709i 0.665148 + 1.15207i
\(33\) −6.46570 + 6.94249i −1.12553 + 1.20853i
\(34\) −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 \(0.883737\pi\)
\(38\) −11.7111 −1.89980
\(39\) 2.40807 + 7.85852i 0.385600 + 1.25837i
\(40\) −2.03241 −0.321352
\(41\) 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 \(0.914807\pi\)
\(44\) 7.49389 + 12.9798i 1.12975 + 1.95678i
\(45\) 0.270254 + 3.79526i 0.0402871 + 0.565764i
\(46\) 5.63263 9.75600i 0.830486 1.43844i
\(47\) 1.57773 2.73271i 0.230135 0.398606i −0.727712 0.685882i \(-0.759416\pi\)
0.957848 + 0.287276i \(0.0927498\pi\)
\(48\) −1.00739 3.28752i −0.145404 0.474512i
\(49\) 0 0
\(50\) 3.69042 6.39199i 0.521904 0.903964i
\(51\) 2.44414 + 7.97624i 0.342248 + 1.11690i
\(52\) 12.9849 1.80068
\(53\) 3.57149 6.18601i 0.490582 0.849714i −0.509359 0.860554i \(-0.670117\pi\)
0.999941 + 0.0108405i \(0.00345071\pi\)
\(54\) 10.5496 4.07277i 1.43561 0.554234i
\(55\) 6.94684 0.936712
\(56\) 0 0
\(57\) 9.08294 + 2.09086i 1.20307 + 0.276942i
\(58\) −8.77732 −1.15252
\(59\) 0.154341 + 0.267327i 0.0200935 + 0.0348030i 0.875897 0.482498i \(-0.160270\pi\)
−0.855804 + 0.517301i \(0.826937\pi\)
\(60\) 5.85781 + 1.34845i 0.756240 + 0.174084i
\(61\) 5.17143 8.95719i 0.662134 1.14685i −0.317920 0.948118i \(-0.602984\pi\)
0.980054 0.198732i \(-0.0636825\pi\)
\(62\) 3.18652 0.404689
\(63\) 0 0
\(64\) −12.4070 −1.55088
\(65\) 3.00924 5.21216i 0.373250 0.646489i
\(66\) −6.04910 19.7407i −0.744592 2.42991i
\(67\) −2.23655 3.87382i −0.273238 0.473262i 0.696451 0.717604i \(-0.254761\pi\)
−0.969689 + 0.244342i \(0.921428\pi\)
\(68\) 13.1794 1.59823
\(69\) −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 \(0.537236\pi\)
\(72\) −0.341465 4.79530i −0.0402421 0.565132i
\(73\) −5.27515 + 9.13683i −0.617409 + 1.06938i 0.372547 + 0.928013i \(0.378484\pi\)
−0.989957 + 0.141371i \(0.954849\pi\)
\(74\) 4.17491 0.485323
\(75\) −4.00342 + 4.29863i −0.462275 + 0.496364i
\(76\) 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 −0.492751 0.870170i \(-0.664009\pi\)
0.999965 0.00835000i \(-0.00265792\pi\)
\(80\) −1.25888 + 2.18044i −0.140747 + 0.243781i
\(81\) −8.90919 + 1.27528i −0.989910 + 0.141698i
\(82\) 4.23963 + 7.34326i 0.468189 + 0.810927i
\(83\) 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
\(86\) 7.22607 0.779207
\(87\) 6.80753 + 1.56707i 0.729844 + 0.168008i
\(88\) −8.77732 −0.935666
\(89\) 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
\(93\) −2.47141 0.568910i −0.256273 0.0589932i
\(94\) 3.43363 + 5.94722i 0.354152 + 0.613409i
\(95\) −3.41245 5.91054i −0.350110 0.606409i
\(96\) 12.7020 + 2.92396i 1.29639 + 0.298425i
\(97\) 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
\(100\) 4.64005 + 8.03680i 0.464005 + 0.803680i
\(101\) −0.00533808 −0.000531159 −0.000265580 1.00000i \(-0.500085\pi\)
−0.000265580 1.00000i \(0.500085\pi\)
\(102\) −17.6927 4.07281i −1.75184 0.403268i
\(103\) −13.0348 −1.28436 −0.642180 0.766554i \(-0.721970\pi\)
−0.642180 + 0.766554i \(0.721970\pi\)
\(104\) −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 \(0.983841\pi\)
\(108\) −2.19738 + 14.0476i −0.211443 + 1.35173i
\(109\) −8.44513 + 14.6274i −0.808896 + 1.40105i 0.104732 + 0.994500i \(0.466601\pi\)
−0.913629 + 0.406549i \(0.866732\pi\)
\(110\) −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 \(0.260021\pi\)
\(114\) −13.8244 + 14.8438i −1.29477 + 1.39025i
\(115\) 6.56506 0.612195
\(116\) 5.51797 9.55741i 0.512331 0.887383i
\(117\) 12.8032 + 6.22436i 1.18366 + 0.575442i
\(118\) −0.671790 −0.0618432
\(119\) 0 0
\(120\) −2.39915 + 2.57607i −0.219012 + 0.235162i
\(121\) 19.0012 1.72738
\(122\) 11.2546 + 19.4936i 1.01895 + 1.76487i
\(123\) −1.97714 6.45222i −0.178273 0.581777i
\(124\) −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
\(129\) −5.60440 1.29012i −0.493440 0.113588i
\(130\) 6.54905 + 11.3433i 0.574389 + 0.994871i
\(131\) 0.179156 0.0156529 0.00782645 0.999969i \(-0.497509\pi\)
0.00782645 + 0.999969i \(0.497509\pi\)
\(132\) 25.2980 + 5.82351i 2.20191 + 0.506872i
\(133\) 0 0
\(134\) 9.73486 0.840964
\(135\) 5.12949 + 4.13756i 0.441476 + 0.356104i
\(136\) −3.85913 + 6.68420i −0.330917 + 0.573166i
\(137\) 3.15206 0.269299 0.134649 0.990893i \(-0.457009\pi\)
0.134649 + 0.990893i \(0.457009\pi\)
\(138\) −5.71665 18.6558i −0.486634 1.58809i
\(139\) −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
\(143\) 12.9959 22.5096i 1.08677 1.88235i
\(144\) −5.35608 2.60388i −0.446340 0.216990i
\(145\) −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
\(149\) −21.2740 −1.74284 −0.871418 0.490541i \(-0.836799\pi\)
−0.871418 + 0.490541i \(0.836799\pi\)
\(150\) −3.74547 12.2230i −0.305816 0.998003i
\(151\) 6.36561 0.518026 0.259013 0.965874i \(-0.416603\pi\)
0.259013 + 0.965874i \(0.416603\pi\)
\(152\) 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
\(156\) 15.3279 16.4582i 1.22722 1.31771i
\(157\) 0.697976 + 1.20893i 0.0557045 + 0.0964830i 0.892533 0.450982i \(-0.148926\pi\)
−0.836828 + 0.547465i \(0.815593\pi\)
\(158\) 9.81128 + 16.9936i 0.780543 + 1.35194i
\(159\) −3.62477 11.8291i −0.287463 0.938110i
\(160\) −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 \(0.565059\pi\)
\(164\) −10.6612 −0.832499
\(165\) 8.20038 8.80508i 0.638399 0.685475i
\(166\) −22.1123 −1.71625
\(167\) −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
\(170\) 6.64715 + 11.5132i 0.509813 + 0.883022i
\(171\) 13.3721 9.04443i 1.02259 0.691645i
\(172\) −4.54276 + 7.86828i −0.346382 + 0.599951i
\(173\) −5.03794 + 8.72598i −0.383028 + 0.663424i −0.991493 0.130157i \(-0.958452\pi\)
0.608466 + 0.793580i \(0.291785\pi\)
\(174\) −10.3612 + 11.1252i −0.785478 + 0.843400i
\(175\) 0 0
\(176\) −5.43669 + 9.41662i −0.409806 + 0.709805i
\(177\) 0.521028 + 0.119939i 0.0391628 + 0.00901516i
\(178\) −11.3071 −0.847500
\(179\) 9.27118 16.0582i 0.692961 1.20024i −0.277902 0.960609i \(-0.589639\pi\)
0.970863 0.239634i \(-0.0770275\pi\)
\(180\) 8.62399 5.83297i 0.642794 0.434764i
\(181\) 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
\(184\) −8.29494 −0.611511
\(185\) 1.21651 + 2.10705i 0.0894393 + 0.154913i
\(186\) 3.76153 4.03890i 0.275808 0.296147i
\(187\) 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 −0.941063 0.338231i \(-0.890172\pi\)
0.763448 + 0.645869i \(0.223505\pi\)
\(192\) −14.6459 + 15.7259i −1.05698 + 1.13492i
\(193\) 4.88380 + 8.45899i 0.351544 + 0.608892i 0.986520 0.163640i \(-0.0523235\pi\)
−0.634976 + 0.772531i \(0.718990\pi\)
\(194\) −10.8172 −0.776629
\(195\) −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 \(0.462328\pi\)
\(198\) −32.1618 15.6356i −2.28564 1.11118i
\(199\) 5.54432 9.60304i 0.393026 0.680742i −0.599821 0.800134i \(-0.704761\pi\)
0.992847 + 0.119393i \(0.0380948\pi\)
\(200\) −5.43472 −0.384293
\(201\) −7.55018 1.73803i −0.532548 0.122591i
\(202\) 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
\(206\) 14.1839 24.5673i 0.988240 1.71168i
\(207\) 1.10300 + 15.4897i 0.0766635 + 1.07661i
\(208\) 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 −0.964089 0.265579i \(-0.914437\pi\)
0.712043 + 0.702136i \(0.247770\pi\)
\(212\) −19.5456 −1.34240
\(213\) −2.32180 + 2.49301i −0.159087 + 0.170818i
\(214\) 20.5044 1.40165
\(215\) 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
\(219\) 5.35384 + 17.4718i 0.361779 + 1.18063i
\(220\) −9.50442 16.4621i −0.640788 1.10988i
\(221\) −11.4278 19.7936i −0.768720 1.33146i
\(222\) 4.92826 5.29167i 0.330763 0.355154i
\(223\) −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
\(226\) −6.68808 11.5841i −0.444884 0.770562i
\(227\) −1.33417 −0.0885522 −0.0442761 0.999019i \(-0.514098\pi\)
−0.0442761 + 0.999019i \(0.514098\pi\)
\(228\) −7.47218 24.3848i −0.494857 1.61492i
\(229\) 15.9966 1.05709 0.528544 0.848906i \(-0.322738\pi\)
0.528544 + 0.848906i \(0.322738\pi\)
\(230\) −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 \(0.919146\pi\)
\(234\) −25.6632 + 17.3577i −1.67766 + 1.13471i
\(235\) −2.00102 + 3.46586i −0.130532 + 0.226088i
\(236\) 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 \(-0.0868262\pi\)
\(240\) 1.27766 + 4.16952i 0.0824725 + 0.269141i
\(241\) −27.5947 −1.77753 −0.888765 0.458362i \(-0.848436\pi\)
−0.888765 + 0.458362i \(0.848436\pi\)
\(242\) −20.6762 + 35.8122i −1.32912 + 2.30210i
\(243\) −8.90042 + 12.7978i −0.570962 + 0.820976i
\(244\) −28.3015 −1.81182
\(245\) 0 0
\(246\) 14.3122 + 3.29462i 0.912513 + 0.210057i
\(247\) −25.5356 −1.62479
\(248\) −1.17317 2.03198i −0.0744961 0.129031i
\(249\) 17.1499 + 3.94785i 1.08683 + 0.250185i
\(250\) −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
\(255\) −3.09988 10.1162i −0.194122 0.633500i
\(256\) 0.597516 + 1.03493i 0.0373448 + 0.0646831i
\(257\) −2.06573 −0.128857 −0.0644285 0.997922i \(-0.520522\pi\)
−0.0644285 + 0.997922i \(0.520522\pi\)
\(258\) 8.53000 9.15900i 0.531054 0.570214i
\(259\) 0 0
\(260\) −16.4686 −1.02134
\(261\) 10.0222 6.77866i 0.620358 0.419589i
\(262\) −0.194949 + 0.337662i −0.0120440 + 0.0208608i
\(263\) 10.1296 0.624620 0.312310 0.949980i \(-0.398897\pi\)
0.312310 + 0.949980i \(0.398897\pi\)
\(264\) −10.3612 + 11.1252i −0.637686 + 0.684709i
\(265\) −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
\(269\) −7.54972 + 13.0765i −0.460315 + 0.797289i −0.998976 0.0452336i \(-0.985597\pi\)
0.538662 + 0.842522i \(0.318930\pi\)
\(270\) −13.3799 + 5.16545i −0.814275 + 0.314359i
\(271\) −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
\(275\) 18.5760 1.12018
\(276\) 23.9077 + 5.50347i 1.43907 + 0.331270i
\(277\) −2.69963 −0.162205 −0.0811026 0.996706i \(-0.525844\pi\)
−0.0811026 + 0.996706i \(0.525844\pi\)
\(278\) −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 0.783157 0.621825i \(-0.213608\pi\)
−0.930094 + 0.367321i \(0.880275\pi\)
\(282\) 11.5913 + 2.66828i 0.690251 + 0.158894i
\(283\) 1.79079 + 3.10173i 0.106451 + 0.184379i 0.914330 0.404969i \(-0.132718\pi\)
−0.807879 + 0.589348i \(0.799385\pi\)
\(284\) 2.69102 + 4.66098i 0.159682 + 0.276578i
\(285\) −11.5198 2.65182i −0.682374 0.157080i
\(286\) 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
\(290\) 11.1322 0.653704
\(291\) 8.38961 + 1.93126i 0.491808 + 0.113212i
\(292\) 28.8691 1.68944
\(293\) −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
\(296\) −1.53705 2.66225i −0.0893394 0.154740i
\(297\) 22.1526 + 17.8688i 1.28542 + 1.03685i
\(298\) 23.1494 40.0960i 1.34101 2.32270i
\(299\) 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
\(303\) −0.00630133 + 0.00676599i −0.000362002 + 0.000388696i
\(304\) 10.6825 0.612685
\(305\) −6.55887 + 11.3603i −0.375560 + 0.650489i
\(306\) −26.0476 + 17.6177i −1.48904 + 1.00714i
\(307\) 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
\(310\) −4.04143 −0.229538
\(311\) −6.47082 11.2078i −0.366926 0.635535i 0.622157 0.782893i \(-0.286257\pi\)
−0.989083 + 0.147357i \(0.952923\pi\)
\(312\) 3.85889 + 12.5931i 0.218467 + 0.712946i
\(313\) −13.4340 + 23.2684i −0.759336 + 1.31521i 0.183853 + 0.982954i \(0.441143\pi\)
−0.943189 + 0.332255i \(0.892190\pi\)
\(314\) −3.03802 −0.171446
\(315\) 0 0
\(316\) −24.6719 −1.38790
\(317\) −4.15584 + 7.19813i −0.233415 + 0.404287i −0.958811 0.284045i \(-0.908324\pi\)
0.725396 + 0.688332i \(0.241657\pi\)
\(318\) 26.2391 + 6.04016i 1.47142 + 0.338715i
\(319\) −11.0454 19.1311i −0.618422 1.07114i
\(320\) 15.7357 0.879654
\(321\) −15.9028 3.66078i −0.887608 0.204325i
\(322\) 0 0
\(323\) −25.9182 −1.44212
\(324\) 15.2113 + 19.3676i 0.845073 + 1.07598i
\(325\) 8.04680 13.9375i 0.446356 0.773111i
\(326\) −41.4842 −2.29760
\(327\) 8.57110 + 27.9710i 0.473983 + 1.54680i
\(328\) 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 −0.984567 0.175009i \(-0.944005\pi\)
0.643845 + 0.765156i \(0.277338\pi\)
\(332\) 13.9012 24.0775i 0.762926 1.32143i
\(333\) −4.76702 + 3.22425i −0.261231 + 0.176688i
\(334\) −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 0.260448 + 0.965488i \(0.416130\pi\)
−0.966361 + 0.257189i \(0.917204\pi\)
\(338\) 20.7150 1.12675
\(339\) 3.11897 + 10.1785i 0.169399 + 0.552819i
\(340\) −16.7152 −0.906511
\(341\) 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
\(345\) 7.74971 8.32118i 0.417230 0.447997i
\(346\) −10.9641 18.9904i −0.589435 1.02093i
\(347\) 8.42415 + 14.5911i 0.452232 + 0.783289i 0.998524 0.0543058i \(-0.0172946\pi\)
−0.546292 + 0.837595i \(0.683961\pi\)
\(348\) −5.60028 18.2760i −0.300207 0.979698i
\(349\) −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
\(352\) −20.6092 35.6963i −1.09848 1.90262i
\(353\) −2.65938 −0.141544 −0.0707722 0.997493i \(-0.522546\pi\)
−0.0707722 + 0.997493i \(0.522546\pi\)
\(354\) −0.793013 + 0.851490i −0.0421481 + 0.0452562i
\(355\) 2.49457 0.132398
\(356\) 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 \(0.504559\pi\)
\(360\) 0.433077 + 6.08183i 0.0228252 + 0.320541i
\(361\) −4.97859 + 8.62318i −0.262031 + 0.453852i
\(362\) −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
\(366\) 37.9936 + 8.74600i 1.98596 + 0.457161i
\(367\) −14.1536 −0.738809 −0.369405 0.929269i \(-0.620438\pi\)
−0.369405 + 0.929269i \(0.620438\pi\)
\(368\) −5.13790 + 8.89911i −0.267832 + 0.463898i
\(369\) −10.5121 5.11050i −0.547237 0.266042i
\(370\) −5.29499 −0.275273
\(371\) 0 0
\(372\) 2.03313 + 6.63494i 0.105413 + 0.344005i
\(373\) 2.67628 0.138573 0.0692863 0.997597i \(-0.477928\pi\)
0.0692863 + 0.997597i \(0.477928\pi\)
\(374\) 28.7069 + 49.7217i 1.48440 + 2.57105i
\(375\) 12.5632 13.4897i 0.648763 0.696603i
\(376\) 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
\(381\) −16.4442 + 17.6568i −0.842462 + 0.904586i
\(382\) −5.34218 9.25292i −0.273330 0.473421i
\(383\) 8.98880 0.459306 0.229653 0.973273i \(-0.426241\pi\)
0.229653 + 0.973273i \(0.426241\pi\)
\(384\) −6.06465 19.7914i −0.309485 1.00998i
\(385\) 0 0
\(386\) −21.2573 −1.08197
\(387\) −8.25092 + 5.58064i −0.419418 + 0.283680i
\(388\) 6.80036 11.7786i 0.345236 0.597966i
\(389\) −26.9869 −1.36829 −0.684144 0.729347i \(-0.739824\pi\)
−0.684144 + 0.729347i \(0.739824\pi\)
\(390\) 22.1084 + 5.08927i 1.11950 + 0.257705i
\(391\) 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
\(395\) −5.71772 + 9.90339i −0.287690 + 0.498293i
\(396\) 37.2442 25.1907i 1.87159 1.26588i
\(397\) 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
\(401\) −34.2784 −1.71178 −0.855891 0.517156i \(-0.826991\pi\)
−0.855891 + 0.517156i \(0.826991\pi\)
\(402\) 11.4915 12.3389i 0.573144 0.615407i
\(403\) 6.94808 0.346109
\(404\) 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
\(408\) 3.91669 + 12.7818i 0.193905 + 0.632792i
\(409\) 5.49225 + 9.51286i 0.271574 + 0.470381i 0.969265 0.246018i \(-0.0791224\pi\)
−0.697691 + 0.716399i \(0.745789\pi\)
\(410\) −5.37708 9.31338i −0.265555 0.459955i
\(411\) 3.72084 3.99522i 0.183536 0.197070i
\(412\) 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
\(416\) −35.7102 −1.75083
\(417\) 9.56921 + 31.2283i 0.468606 + 1.52925i
\(418\) 64.1458 3.13747
\(419\) 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 \(-0.478683\pi\)
\(422\) −7.96787 13.8008i −0.387870 0.671810i
\(423\) −8.51360 4.13893i −0.413946 0.201242i
\(424\) 5.72325 9.91297i 0.277946 0.481416i
\(425\) 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
\(429\) −13.1898 43.0437i −0.636810 2.07817i
\(430\) −9.16474 −0.441963
\(431\) −1.12969 + 1.95669i −0.0544155 + 0.0942504i −0.891950 0.452134i \(-0.850663\pi\)
0.837535 + 0.546384i \(0.183996\pi\)
\(432\) −9.62298 + 3.71505i −0.462986 + 0.178740i
\(433\) −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
\(436\) 46.2173 2.21341
\(437\) −13.9274 24.1229i −0.666236 1.15395i
\(438\) −38.7556 8.92140i −1.85181 0.426281i
\(439\) 2.99569 5.18869i 0.142977 0.247643i −0.785640 0.618684i \(-0.787666\pi\)
0.928616 + 0.371042i \(0.120999\pi\)
\(440\) 11.1322 0.530706
\(441\) 0 0
\(442\) 49.7411 2.36594
\(443\) 19.7190 34.1543i 0.936879 1.62272i 0.165630 0.986188i \(-0.447034\pi\)
0.771249 0.636534i \(-0.219632\pi\)
\(444\) 2.66376 + 8.69293i 0.126416 + 0.412548i
\(445\) −3.29471 5.70661i −0.156184 0.270519i
\(446\) 8.82560 0.417904
\(447\) −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 \(0.481581\pi\)
\(450\) −19.9139 9.68125i −0.938750 0.456378i
\(451\) −10.6703 + 18.4815i −0.502444 + 0.870259i
\(452\) 16.8182 0.791060
\(453\) 7.51428 8.06838i 0.353052 0.379086i
\(454\) 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 −0.965645 0.259864i \(-0.916322\pi\)
0.707871 + 0.706342i \(0.249656\pi\)
\(458\) −17.4068 + 30.1495i −0.813368 + 1.40879i
\(459\) 23.3475 9.01353i 1.08977 0.420715i
\(460\) −8.98208 15.5574i −0.418792 0.725369i
\(461\) −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 \(0.157885\pi\)
\(464\) 8.00639 0.371687
\(465\) 3.13446 + 0.721543i 0.145357 + 0.0334608i
\(466\) 17.6952 0.819715
\(467\) 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
\(471\) 2.35623 + 0.542398i 0.108570 + 0.0249924i
\(472\) 0.247329 + 0.428387i 0.0113842 + 0.0197181i
\(473\) 9.09327 + 15.7500i 0.418109 + 0.724186i
\(474\) 33.1210 + 7.62436i 1.52130 + 0.350198i
\(475\) −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
\(479\) 25.1428 1.14880 0.574402 0.818573i \(-0.305234\pi\)
0.574402 + 0.818573i \(0.305234\pi\)
\(480\) −16.1098 3.70842i −0.735308 0.169266i
\(481\) 9.10321 0.415071
\(482\) 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
\(486\) −14.4354 30.7009i −0.654803 1.39262i
\(487\) −6.78904 + 11.7590i −0.307641 + 0.532849i −0.977846 0.209327i \(-0.932873\pi\)
0.670205 + 0.742176i \(0.266206\pi\)
\(488\) 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 \(0.0605387\pi\)
\(492\) −12.5850 + 13.5130i −0.567375 + 0.609213i
\(493\) −19.4253 −0.874870
\(494\) 27.7868 48.1281i 1.25019 2.16538i
\(495\) −1.48027 20.7879i −0.0665332 0.934346i
\(496\) −2.90664 −0.130512
\(497\) 0 0
\(498\) −26.1024 + 28.0272i −1.16968 + 1.25593i
\(499\) 13.9915 0.626345 0.313172 0.949696i \(-0.398608\pi\)
0.313172 + 0.949696i \(0.398608\pi\)
\(500\) −14.5611 25.2205i −0.651191 1.12790i
\(501\) 0.885011 + 2.88815i 0.0395394 + 0.129033i
\(502\) −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
\(507\) −16.0661 3.69837i −0.713523 0.164251i
\(508\) 19.0592 + 33.0115i 0.845615 + 1.46465i
\(509\) 3.45993 0.153359 0.0766794 0.997056i \(-0.475568\pi\)
0.0766794 + 0.997056i \(0.475568\pi\)
\(510\) 22.4395 + 5.16550i 0.993639 + 0.228732i
\(511\) 0 0
\(512\) 21.3013 0.941392
\(513\) 4.32131 27.6255i 0.190790 1.21970i
\(514\) 2.24784 3.89337i 0.0991480 0.171729i
\(515\) 16.5319 0.728484
\(516\) 4.61052 + 15.0460i 0.202967 + 0.662364i
\(517\) −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
\(521\) 3.56797 6.17991i 0.156316 0.270747i −0.777222 0.629227i \(-0.783372\pi\)
0.933537 + 0.358480i \(0.116705\pi\)
\(522\) 1.87032 + 26.2655i 0.0818616 + 1.14961i
\(523\) −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
\(527\) 7.05216 0.307197
\(528\) 5.51779 + 18.0068i 0.240131 + 0.783646i
\(529\) 3.79420 0.164965
\(530\) −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
\(534\) −13.3474 + 14.3316i −0.577599 + 0.620191i
\(535\) 5.97467 + 10.3484i 0.258308 + 0.447402i
\(536\) −3.58403 6.20772i −0.154807 0.268133i
\(537\) −9.40948 30.7070i −0.406049 1.32510i
\(538\) −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 \(0.867171\pi\)
\(542\) 62.6889 2.69272
\(543\) 10.3995 11.1664i 0.446287 0.479196i
\(544\) −36.2451 −1.55399
\(545\) 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 \(0.825712\pi\)
\(548\) −4.31254 7.46954i −0.184223 0.319083i
\(549\) −27.9056 13.5665i −1.19098 0.579003i
\(550\) −20.2136 + 35.0110i −0.861912 + 1.49288i
\(551\) −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
\(555\) 4.10670 + 0.945348i 0.174320 + 0.0401278i
\(556\) 51.5993 2.18830
\(557\) 5.47832 9.48873i 0.232124 0.402050i −0.726309 0.687368i \(-0.758766\pi\)
0.958433 + 0.285318i \(0.0920992\pi\)
\(558\) −0.679001 9.53543i −0.0287444 0.403667i
\(559\) 15.7561 0.666413
\(560\) 0 0
\(561\) −13.3874 43.6885i −0.565215 1.84453i
\(562\) 10.7210 0.452240
\(563\) −2.38048 4.12311i −0.100325 0.173768i 0.811493 0.584361i \(-0.198655\pi\)
−0.911819 + 0.410593i \(0.865322\pi\)
\(564\) −10.1924 + 10.9440i −0.429179 + 0.460826i
\(565\) 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 −0.900371 0.435122i \(-0.856705\pi\)
0.827013 + 0.562183i \(0.190038\pi\)
\(570\) 17.5333 18.8262i 0.734390 0.788545i
\(571\) −3.53051 6.11501i −0.147747 0.255905i 0.782647 0.622465i \(-0.213869\pi\)
−0.930394 + 0.366560i \(0.880535\pi\)
\(572\) −71.1223 −2.97377
\(573\) 2.49131 + 8.13017i 0.104076 + 0.339643i
\(574\) 0 0
\(575\) 17.5552 0.732101
\(576\) 2.64376 + 37.1271i 0.110157 + 1.54696i
\(577\) 6.44149 11.1570i 0.268163 0.464472i −0.700225 0.713923i \(-0.746917\pi\)
0.968387 + 0.249451i \(0.0802502\pi\)
\(578\) 13.4889 0.561064
\(579\) 16.4868 + 3.79521i 0.685168 + 0.157723i
\(580\) −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
\(584\) −8.45333 + 14.6416i −0.349801 + 0.605874i
\(585\) −16.2382 7.89429i −0.671367 0.326389i
\(586\) −26.5412 45.9707i −1.09641 1.89903i
\(587\) 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
\(590\) 0.852024 0.0350773
\(591\) 3.91254 4.20105i 0.160940 0.172808i
\(592\) −3.80821 −0.156517
\(593\) 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
\(597\) −5.62703 18.3633i −0.230299 0.751559i
\(598\) 26.7288 + 46.2957i 1.09302 + 1.89317i
\(599\) 6.39103 + 11.0696i 0.261130 + 0.452291i 0.966543 0.256506i \(-0.0825715\pi\)
−0.705412 + 0.708797i \(0.749238\pi\)
\(600\) −6.41541 + 6.88848i −0.261908 + 0.281221i
\(601\) 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
\(604\) −8.70921 15.0848i −0.354373 0.613792i
\(605\) −24.0990 −0.979762
\(606\) −0.00589531 0.0192388i −0.000239481 0.000781524i
\(607\) −41.4873 −1.68392 −0.841959 0.539541i \(-0.818598\pi\)
−0.841959 + 0.539541i \(0.818598\pi\)
\(608\) −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
\(612\) −2.80833 39.4382i −0.113520 1.59420i
\(613\) −7.64783 + 13.2464i −0.308893 + 0.535018i −0.978120 0.208039i \(-0.933292\pi\)
0.669228 + 0.743057i \(0.266625\pi\)
\(614\) −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 \(0.200892\pi\)
\(618\) −14.3955 46.9784i −0.579072 1.88975i
\(619\) 12.6841 0.509817 0.254908 0.966965i \(-0.417955\pi\)
0.254908 + 0.966965i \(0.417955\pi\)
\(620\) 2.54070 4.40062i 0.102037 0.176733i
\(621\) 20.9352 + 16.8868i 0.840099 + 0.677642i
\(622\) 28.1650 1.12931
\(623\) 0 0
\(624\) 15.9006 + 3.66026i 0.636532 + 0.146528i
\(625\) 3.45909 0.138363
\(626\) −29.2366 50.6393i −1.16853 2.02395i
\(627\) −49.7503 11.4524i −1.98683 0.457363i
\(628\) 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
\(633\) 3.71580 + 12.1262i 0.147690 + 0.481972i
\(634\) −9.04441 15.6654i −0.359199 0.622151i
\(635\) 17.6679 0.701128
\(636\) −23.0725 + 24.7739i −0.914885 + 0.982349i
\(637\) 0 0
\(638\) 48.0763 1.90336
\(639\) 0.419113 + 5.88574i 0.0165799 + 0.232836i
\(640\) −7.57868 + 13.1267i −0.299573 + 0.518876i
\(641\) 5.93177 0.234291 0.117145 0.993115i \(-0.462626\pi\)
0.117145 + 0.993115i \(0.462626\pi\)
\(642\) 24.2043 25.9892i 0.955269 1.02571i
\(643\) 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
\(647\) −19.5701 + 33.8964i −0.769379 + 1.33260i 0.168521 + 0.985698i \(0.446101\pi\)
−0.937900 + 0.346905i \(0.887233\pi\)
\(648\) −14.2768 + 2.04362i −0.560846 + 0.0802809i
\(649\) −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
\(653\) 43.3281 1.69556 0.847779 0.530350i \(-0.177939\pi\)
0.847779 + 0.530350i \(0.177939\pi\)
\(654\) −62.0448 14.2825i −2.42614 0.558491i
\(655\) −0.227221 −0.00887827
\(656\) −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 0.925201 0.379478i \(-0.123897\pi\)
−0.791238 + 0.611508i \(0.790563\pi\)
\(660\) −32.0852 7.38590i −1.24891 0.287496i
\(661\) 19.3835 + 33.5733i 0.753932 + 1.30585i 0.945903 + 0.324449i \(0.105179\pi\)
−0.191971 + 0.981401i \(0.561488\pi\)
\(662\) −13.4907 23.3666i −0.524331 0.908168i
\(663\) −38.5783 8.88059i −1.49826 0.344894i
\(664\) 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
\(668\) 4.77217 0.184641
\(669\) −6.84497 1.57569i −0.264642 0.0609197i
\(670\) −12.3466 −0.476991
\(671\) −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 \(0.589422\pi\)
\(674\) −28.2025 48.8481i −1.08632 1.88156i
\(675\) 13.7164 + 11.0640i 0.527945 + 0.425852i
\(676\) −13.0227 + 22.5560i −0.500874 + 0.867539i
\(677\) 2.23329 3.86817i 0.0858322 0.148666i −0.819913 0.572488i \(-0.805978\pi\)
0.905746 + 0.423822i \(0.139312\pi\)
\(678\) −22.5777 5.19731i −0.867092 0.199602i
\(679\) 0 0
\(680\) 4.89449 8.47750i 0.187695 0.325097i
\(681\) −1.57492 + 1.69106i −0.0603511 + 0.0648015i
\(682\) −17.4536 −0.668335
\(683\) 13.3356 23.0980i 0.510274 0.883821i −0.489655 0.871916i \(-0.662877\pi\)
0.999929 0.0119046i \(-0.00378945\pi\)
\(684\) −39.7281 19.3140i −1.51904 0.738490i
\(685\) −3.99773 −0.152745
\(686\) 0 0
\(687\) 18.8832 20.2757i 0.720439 0.773565i
\(688\) −6.59138 −0.251294
\(689\) 16.9480 + 29.3548i 0.645668 + 1.11833i
\(690\) 7.25037 + 23.6609i 0.276017 + 0.900756i
\(691\) −20.5220 + 35.5452i −0.780694 + 1.35220i 0.150844 + 0.988558i \(0.451801\pi\)
−0.931538 + 0.363644i \(0.881532\pi\)
\(692\) 27.5709 1.04809
\(693\) 0 0
\(694\) −36.6671 −1.39187
\(695\) 11.9582 20.7121i 0.453599 0.785656i
\(696\) 10.9089 + 2.51120i 0.413502 + 0.0951869i
\(697\) 9.38281 + 16.2515i 0.355399 + 0.615570i
\(698\) 67.6847 2.56190
\(699\) −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 \(0.441767\pi\)
\(702\) −8.29328 + 53.0179i −0.313010 + 2.00103i
\(703\) 5.16148 8.93994i 0.194669 0.337176i
\(704\) 67.9575 2.56125
\(705\) 2.03087 + 6.62755i 0.0764869 + 0.249608i
\(706\) 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 −0.754945 0.655788i \(-0.772336\pi\)
0.945402 + 0.325907i \(0.105670\pi\)
\(710\) −2.71448 + 4.70162i −0.101873 + 0.176449i
\(711\) −24.3268 11.8266i −0.912328 0.443533i
\(712\) 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
\(716\) −50.7380 −1.89617
\(717\) −11.2157 36.6016i −0.418860 1.36691i
\(718\) −70.8235 −2.64311
\(719\) −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
\(723\) −32.5741 + 34.9761i −1.21144 + 1.30078i
\(724\) −12.0533 20.8769i −0.447957 0.775884i
\(725\) −6.83904 11.8456i −0.253996 0.439934i
\(726\) 20.9846 + 68.4815i 0.778813 + 2.54159i
\(727\) 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
\(730\) 14.5604 + 25.2194i 0.538906 + 0.933412i
\(731\) 15.9921 0.591491
\(732\) −33.4084 + 35.8720i −1.23481 + 1.32587i
\(733\) −28.9108 −1.06784 −0.533922 0.845534i \(-0.679282\pi\)
−0.533922 + 0.845534i \(0.679282\pi\)
\(734\) 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
\(738\) 21.0707 14.2515i 0.775624 0.524605i
\(739\) 6.67467 11.5609i 0.245532 0.425273i −0.716749 0.697331i \(-0.754371\pi\)
0.962281 + 0.272058i \(0.0877041\pi\)
\(740\) 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 \(-0.0940115\pi\)
\(744\) −3.96039 0.911668i −0.145195 0.0334234i
\(745\) 26.9816 0.988530
\(746\) −2.91221 + 5.04410i −0.106624 + 0.184678i
\(747\) 25.2484 17.0772i 0.923792 0.624821i
\(748\) −72.1877 −2.63944
\(749\) 0 0
\(750\) 11.7538 + 38.3573i 0.429186 + 1.40061i
\(751\) −38.4345 −1.40250 −0.701248 0.712917i \(-0.747374\pi\)
−0.701248 + 0.712917i \(0.747374\pi\)
\(752\) −3.13204 5.42486i −0.114214 0.197824i
\(753\) 19.5494 20.9910i 0.712420 0.764954i
\(754\) 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
\(759\) 33.4685 35.9365i 1.21483 1.30441i
\(760\) −5.46839 9.47153i −0.198359 0.343569i
\(761\) −52.3321 −1.89704 −0.948519 0.316719i \(-0.897419\pi\)
−0.948519 + 0.316719i \(0.897419\pi\)
\(762\) −15.3846 50.2064i −0.557327 1.81879i
\(763\) 0 0
\(764\) 13.4337 0.486014
\(765\) −16.4814 8.01254i −0.595888 0.289694i
\(766\) −9.78121 + 16.9416i −0.353410 + 0.612123i
\(767\) −1.46481 −0.0528912
\(768\) 2.01710 + 0.464331i 0.0727860 + 0.0167551i
\(769\) −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
\(773\) 18.1814 31.4912i 0.653941 1.13266i −0.328217 0.944602i \(-0.606448\pi\)
0.982158 0.188057i \(-0.0602189\pi\)
\(774\) −1.53977 21.6234i −0.0553458 0.777239i
\(775\) 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
\(779\) 20.9660 0.751185
\(780\) −19.4403 + 20.8738i −0.696073 + 0.747402i
\(781\) 10.7733 0.385497
\(782\) 27.1292 + 46.9892i 0.970139 + 1.68033i
\(783\) 3.23875 20.7049i 0.115744