Properties

Label 441.2.g.h.67.1
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 67.1
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.1

$q$-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 \(-0.408472\pi\)
0.283598 + 0.958943i \(0.408472\pi\)
\(6\) −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 \(-0.604710\pi\)
0.981117 0.193417i \(-0.0619570\pi\)
\(14\) 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 \(-0.634789\pi\)
0.994990 0.0999785i \(-0.0318774\pi\)
\(18\) 5.87181 + 2.85461i 1.38400 + 0.672838i
\(19\) −2.69059 4.66025i −0.617265 1.06913i −0.989983 0.141189i \(-0.954907\pi\)
0.372718 0.927945i \(-0.378426\pi\)
\(20\) −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 0.924250 0.381787i \(-0.124691\pi\)
−0.792763 + 0.609531i \(0.791358\pi\)
\(32\) 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 −0.977092 0.212819i \(-0.931736\pi\)
0.672852 + 0.739777i \(0.265069\pi\)
\(42\) 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 −0.957848 0.287276i \(-0.907250\pi\)
0.727712 + 0.685882i \(0.240584\pi\)
\(48\) 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 0.855804 0.517301i \(-0.173063\pi\)
−0.875897 + 0.482498i \(0.839730\pi\)
\(60\) 5.85781 + 1.34845i 0.756240 + 0.174084i
\(61\) −5.17143 + 8.95719i −0.662134 + 1.14685i 0.317920 + 0.948118i \(0.397016\pi\)
−0.980054 + 0.198732i \(0.936318\pi\)
\(62\) −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 \(-0.621516\pi\)
0.989957 0.141371i \(-0.0451512\pi\)
\(74\) 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 \(-0.978378\pi\)
0.440066 0.897965i \(-0.354955\pi\)
\(84\) 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 0.694864 0.719141i \(-0.255464\pi\)
−0.970226 + 0.242200i \(0.922131\pi\)
\(90\) 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 0.711833 0.702348i \(-0.247865\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(98\) 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 \(-0.499915\pi\)
0.000265580 1.00000i \(0.499915\pi\)
\(102\) −17.6927 4.07281i −1.75184 0.403268i
\(103\) 13.0348 1.28436 0.642180 0.766554i \(-0.278030\pi\)
0.642180 + 0.766554i \(0.278030\pi\)
\(104\) 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 \(-0.502491\pi\)
−0.00782645 + 0.999969i \(0.502491\pi\)
\(132\) −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 \(-0.538314\pi\)
0.919798 0.392392i \(-0.128352\pi\)
\(140\) 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 0.836828 0.547465i \(-0.184407\pi\)
−0.892533 + 0.450982i \(0.851074\pi\)
\(158\) 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 −0.830313 0.557298i \(-0.811838\pi\)
0.897790 + 0.440423i \(0.145172\pi\)
\(168\) 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 −0.608466 0.793580i \(-0.708215\pi\)
0.991493 + 0.130157i \(0.0415480\pi\)
\(174\) 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 \(-0.606177\pi\)
−0.327414 + 0.944881i \(0.606177\pi\)
\(182\) 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 −0.992847 0.119393i \(-0.961905\pi\)
0.599821 + 0.800134i \(0.295239\pi\)
\(200\) −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 0.925896 0.377779i \(-0.123312\pi\)
−0.790114 + 0.612960i \(0.789979\pi\)
\(224\) 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 \(-0.485902\pi\)
0.0442761 + 0.999019i \(0.485902\pi\)
\(228\) −7.47218 24.3848i −0.494857 1.61492i
\(229\) −15.9966 −1.05709 −0.528544 0.848906i \(-0.677262\pi\)
−0.528544 + 0.848906i \(0.677262\pi\)
\(230\) 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 \(-0.151564\pi\)
0.888765 + 0.458362i \(0.151564\pi\)
\(242\) −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 \(-0.675061\pi\)
−0.522661 + 0.852541i \(0.675061\pi\)
\(252\) 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 \(-0.479478\pi\)
0.0644285 + 0.997922i \(0.479478\pi\)
\(258\) −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 −0.538662 0.842522i \(-0.681070\pi\)
0.998976 + 0.0452336i \(0.0144032\pi\)
\(270\) −13.3799 + 5.16545i −0.814275 + 0.314359i
\(271\) 14.4026 + 24.9459i 0.874893 + 1.51536i 0.856877 + 0.515521i \(0.172402\pi\)
0.0180156 + 0.999838i \(0.494265\pi\)
\(272\) −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 0.807879 0.589348i \(-0.200615\pi\)
−0.914330 + 0.404969i \(0.867282\pi\)
\(284\) 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 \(-0.580910\pi\)
0.963928 0.266164i \(-0.0857563\pi\)
\(294\) 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 \(-0.738930\pi\)
−0.682094 + 0.731265i \(0.738930\pi\)
\(308\) 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 0.989083 0.147357i \(-0.0470768\pi\)
−0.622157 + 0.782893i \(0.713743\pi\)
\(312\) 3.85889 + 12.5931i 0.218467 + 0.712946i
\(313\) 13.4340 23.2684i 0.759336 1.31521i −0.183853 0.982954i \(-0.558857\pi\)
0.943189 0.332255i \(-0.107810\pi\)
\(314\) 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 \(0.146361\pi\)
−0.0637477 + 0.997966i \(0.520305\pi\)
\(350\) 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 \(-0.477454\pi\)
0.0707722 + 0.997493i \(0.477454\pi\)
\(354\) −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 \(-0.379562\pi\)
0.369405 + 0.929269i \(0.379562\pi\)
\(368\) −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 \(-0.573759\pi\)
−0.229653 + 0.973273i \(0.573759\pi\)
\(384\) 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 \(-0.901352\pi\)
0.212066 0.977255i \(-0.431981\pi\)
\(398\) −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 0.697691 0.716399i \(-0.254211\pi\)
−0.969265 + 0.246018i \(0.920878\pi\)
\(410\) −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 −0.935866 0.352357i \(-0.885380\pi\)
0.773083 + 0.634305i \(0.218714\pi\)
\(420\) 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 \(-0.190415\pi\)
0.826348 + 0.563160i \(0.190415\pi\)
\(434\) 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 −0.928616 0.371042i \(-0.879001\pi\)
0.785640 + 0.618684i \(0.212334\pi\)
\(440\) −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 \(0.0724420\pi\)
−0.291711 + 0.956506i \(0.594225\pi\)
\(462\) 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 \(-0.995693\pi\)
0.488236 0.872712i \(-0.337641\pi\)
\(468\) 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 \(-0.694766\pi\)
−0.574402 + 0.818573i \(0.694766\pi\)
\(480\) −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 \(-0.281753\pi\)
0.633171 + 0.774012i \(0.281753\pi\)
\(504\) 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 \(-0.524432\pi\)
−0.0766794 + 0.997056i \(0.524432\pi\)
\(510\) −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 −0.933537 0.358480i \(-0.883295\pi\)
0.777222 + 0.629227i \(0.216628\pi\)
\(522\) 1.87032 + 26.2655i 0.0818616 + 1.14961i
\(523\) 6.53235 + 11.3144i 0.285640 + 0.494743i 0.972764 0.231797i \(-0.0744606\pi\)
−0.687124 + 0.726540i \(0.741127\pi\)
\(524\) 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 0.911819 0.410593i \(-0.134678\pi\)
−0.811493 + 0.584361i \(0.801345\pi\)
\(564\) −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 −0.968387 0.249451i \(-0.919750\pi\)
0.700225 + 0.713923i \(0.253083\pi\)
\(578\) 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 \(-0.868814\pi\)
0.111235 0.993794i \(-0.464519\pi\)
\(588\) 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 \(-0.856421\pi\)
0.0724676 0.997371i \(-0.476913\pi\)
\(594\) 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 0.749630 0.661858i \(-0.230232\pi\)
−0.948000 + 0.318270i \(0.896898\pi\)
\(602\) 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 \(-0.181402\pi\)
0.841959 + 0.539541i \(0.181402\pi\)
\(608\) 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 \(-0.582045\pi\)
−0.254908 + 0.966965i \(0.582045\pi\)
\(620\) 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 \(0.541234\pi\)
−0.794180 + 0.607682i \(0.792100\pi\)
\(644\) 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 \(-0.553899\pi\)
0.937900 0.346905i \(-0.112767\pi\)
\(648\) −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 \(-0.894821\pi\)
0.191971 0.981401i \(-0.438512\pi\)
\(662\) −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 −0.905746 0.423822i \(-0.860688\pi\)
0.819913 + 0.572488i \(0.194022\pi\)
\(678\) 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 \(-0.548199\pi\)
0.931538 0.363644i \(-0.118468\pi\)
\(692\) −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 \(0.113775\pi\)
−0.165400 + 0.986227i \(0.552891\pi\)
\(720\) −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 0.761626 0.648016i \(-0.224401\pi\)
−0.942012 + 0.335580i \(0.891068\pi\)
\(728\) 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 \(-0.320718\pi\)
0.533922 + 0.845534i \(0.320718\pi\)
\(734\) −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 \(-0.102581\pi\)
0.948519 + 0.316719i \(0.102581\pi\)
\(762\) 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 −0.844089 0.536203i \(-0.819858\pi\)
0.886410 + 0.462901i \(0.153191\pi\)
\(770\) 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 \(0.393552\pi\)
−0.982158 + 0.188057i \(0.939781\pi\)
\(774\) −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