Properties

Label 668.2.e.a.9.2
Level $668$
Weight $2$
Character 668.9
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 9.2
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +O(q^{10})\) \(q+(-0.360076 - 2.70211i) q^{3} +(2.66599 + 1.17892i) q^{5} +(0.359959 - 0.774059i) q^{7} +(-4.27644 + 1.16034i) q^{9} +(1.41822 - 1.81840i) q^{11} +(0.212957 - 0.416003i) q^{13} +(2.22562 - 7.62829i) q^{15} +(0.00376620 + 0.000285651i) q^{17} +(2.82122 - 4.24396i) q^{19} +(-2.22121 - 0.693930i) q^{21} +(4.68688 + 1.86388i) q^{23} +(2.35326 + 2.58718i) q^{25} +(1.50992 + 3.59703i) q^{27} +(1.55654 - 0.619007i) q^{29} +(-4.46558 + 1.03195i) q^{31} +(-5.42418 - 3.17744i) q^{33} +(1.87220 - 1.63927i) q^{35} +(-7.73988 - 2.10008i) q^{37} +(-1.20077 - 0.425641i) q^{39} +(-4.78039 + 2.33404i) q^{41} +(-0.447049 + 4.71025i) q^{43} +(-12.7689 - 1.94814i) q^{45} +(-0.117670 - 6.21686i) q^{47} +(4.04118 + 4.79558i) q^{49} +(-0.000584257 - 0.0102795i) q^{51} +(-0.235266 - 1.36787i) q^{53} +(5.92471 - 3.17584i) q^{55} +(-12.4835 - 6.09511i) q^{57} +(4.70272 - 0.356683i) q^{59} +(6.63150 - 6.75821i) q^{61} +(-0.641175 + 3.72789i) q^{63} +(1.05818 - 0.858000i) q^{65} +(1.55333 - 0.686896i) q^{67} +(3.34878 - 13.3356i) q^{69} +(-10.4919 + 1.19652i) q^{71} +(-12.8510 + 9.63743i) q^{73} +(6.14351 - 7.29036i) q^{75} +(-0.897042 - 1.75234i) q^{77} +(3.48394 - 9.26768i) q^{79} +(-2.29420 + 1.34393i) q^{81} +(-1.64790 + 2.28629i) q^{83} +(0.00970387 + 0.00520159i) q^{85} +(-2.23310 - 3.98307i) q^{87} +(4.34168 + 14.8811i) q^{89} +(-0.245355 - 0.314586i) q^{91} +(4.39639 + 11.6949i) q^{93} +(12.5246 - 7.98833i) q^{95} +(8.95939 + 2.07042i) q^{97} +(-3.95500 + 9.42188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{11}{83}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.360076 2.70211i −0.207890 1.56007i −0.715583 0.698527i \(-0.753839\pi\)
0.507693 0.861538i \(-0.330498\pi\)
\(4\) 0 0
\(5\) 2.66599 + 1.17892i 1.19227 + 0.527230i 0.902842 0.429972i \(-0.141476\pi\)
0.289423 + 0.957201i \(0.406537\pi\)
\(6\) 0 0
\(7\) 0.359959 0.774059i 0.136052 0.292567i −0.826848 0.562425i \(-0.809868\pi\)
0.962900 + 0.269858i \(0.0869769\pi\)
\(8\) 0 0
\(9\) −4.27644 + 1.16034i −1.42548 + 0.386780i
\(10\) 0 0
\(11\) 1.41822 1.81840i 0.427611 0.548267i −0.525537 0.850770i \(-0.676136\pi\)
0.953148 + 0.302504i \(0.0978225\pi\)
\(12\) 0 0
\(13\) 0.212957 0.416003i 0.0590636 0.115379i −0.858743 0.512407i \(-0.828754\pi\)
0.917806 + 0.397029i \(0.129959\pi\)
\(14\) 0 0
\(15\) 2.22562 7.62829i 0.574653 1.96962i
\(16\) 0 0
\(17\) 0.00376620 0.000285651i 0.000913437 6.92805e-5i 0.0760855 0.997101i \(-0.475758\pi\)
−0.0751720 + 0.997171i \(0.523951\pi\)
\(18\) 0 0
\(19\) 2.82122 4.24396i 0.647233 0.973630i −0.352058 0.935978i \(-0.614518\pi\)
0.999291 0.0376523i \(-0.0119879\pi\)
\(20\) 0 0
\(21\) −2.22121 0.693930i −0.484707 0.151428i
\(22\) 0 0
\(23\) 4.68688 + 1.86388i 0.977281 + 0.388646i 0.802953 0.596042i \(-0.203261\pi\)
0.174328 + 0.984688i \(0.444225\pi\)
\(24\) 0 0
\(25\) 2.35326 + 2.58718i 0.470652 + 0.517437i
\(26\) 0 0
\(27\) 1.50992 + 3.59703i 0.290583 + 0.692248i
\(28\) 0 0
\(29\) 1.55654 0.619007i 0.289043 0.114947i −0.220513 0.975384i \(-0.570773\pi\)
0.509557 + 0.860437i \(0.329809\pi\)
\(30\) 0 0
\(31\) −4.46558 + 1.03195i −0.802041 + 0.185344i −0.606221 0.795296i \(-0.707315\pi\)
−0.195820 + 0.980640i \(0.562737\pi\)
\(32\) 0 0
\(33\) −5.42418 3.17744i −0.944228 0.553121i
\(34\) 0 0
\(35\) 1.87220 1.63927i 0.316460 0.277087i
\(36\) 0 0
\(37\) −7.73988 2.10008i −1.27243 0.345251i −0.439305 0.898338i \(-0.644775\pi\)
−0.833124 + 0.553087i \(0.813450\pi\)
\(38\) 0 0
\(39\) −1.20077 0.425641i −0.192277 0.0681571i
\(40\) 0 0
\(41\) −4.78039 + 2.33404i −0.746571 + 0.364516i −0.772388 0.635151i \(-0.780938\pi\)
0.0258170 + 0.999667i \(0.491781\pi\)
\(42\) 0 0
\(43\) −0.447049 + 4.71025i −0.0681743 + 0.718307i 0.894396 + 0.447276i \(0.147606\pi\)
−0.962571 + 0.271031i \(0.912635\pi\)
\(44\) 0 0
\(45\) −12.7689 1.94814i −1.90347 0.290412i
\(46\) 0 0
\(47\) −0.117670 6.21686i −0.0171639 0.906823i −0.899682 0.436545i \(-0.856202\pi\)
0.882518 0.470278i \(-0.155846\pi\)
\(48\) 0 0
\(49\) 4.04118 + 4.79558i 0.577312 + 0.685083i
\(50\) 0 0
\(51\) −0.000584257 0.0102795i −8.18124e−5 0.00143942i
\(52\) 0 0
\(53\) −0.235266 1.36787i −0.0323163 0.187892i 0.964883 0.262679i \(-0.0846060\pi\)
−0.997200 + 0.0747871i \(0.976172\pi\)
\(54\) 0 0
\(55\) 5.92471 3.17584i 0.798888 0.428230i
\(56\) 0 0
\(57\) −12.4835 6.09511i −1.65348 0.807317i
\(58\) 0 0
\(59\) 4.70272 0.356683i 0.612243 0.0464361i 0.234145 0.972202i \(-0.424771\pi\)
0.378098 + 0.925766i \(0.376578\pi\)
\(60\) 0 0
\(61\) 6.63150 6.75821i 0.849077 0.865300i −0.143155 0.989700i \(-0.545725\pi\)
0.992232 + 0.124400i \(0.0397006\pi\)
\(62\) 0 0
\(63\) −0.641175 + 3.72789i −0.0807804 + 0.469670i
\(64\) 0 0
\(65\) 1.05818 0.858000i 0.131251 0.106422i
\(66\) 0 0
\(67\) 1.55333 0.686896i 0.189769 0.0839176i −0.307363 0.951592i \(-0.599447\pi\)
0.497132 + 0.867675i \(0.334386\pi\)
\(68\) 0 0
\(69\) 3.34878 13.3356i 0.403145 1.60542i
\(70\) 0 0
\(71\) −10.4919 + 1.19652i −1.24516 + 0.142000i −0.710883 0.703310i \(-0.751704\pi\)
−0.534275 + 0.845311i \(0.679415\pi\)
\(72\) 0 0
\(73\) −12.8510 + 9.63743i −1.50410 + 1.12798i −0.547411 + 0.836864i \(0.684386\pi\)
−0.956689 + 0.291111i \(0.905975\pi\)
\(74\) 0 0
\(75\) 6.14351 7.29036i 0.709391 0.841818i
\(76\) 0 0
\(77\) −0.897042 1.75234i −0.102227 0.199697i
\(78\) 0 0
\(79\) 3.48394 9.26768i 0.391973 1.04270i −0.581430 0.813597i \(-0.697506\pi\)
0.973403 0.229099i \(-0.0735779\pi\)
\(80\) 0 0
\(81\) −2.29420 + 1.34393i −0.254911 + 0.149325i
\(82\) 0 0
\(83\) −1.64790 + 2.28629i −0.180881 + 0.250953i −0.891914 0.452206i \(-0.850637\pi\)
0.711033 + 0.703159i \(0.248228\pi\)
\(84\) 0 0
\(85\) 0.00970387 + 0.00520159i 0.00105253 + 0.000564192i
\(86\) 0 0
\(87\) −2.23310 3.98307i −0.239414 0.427030i
\(88\) 0 0
\(89\) 4.34168 + 14.8811i 0.460218 + 1.57739i 0.777387 + 0.629023i \(0.216545\pi\)
−0.317169 + 0.948369i \(0.602732\pi\)
\(90\) 0 0
\(91\) −0.245355 0.314586i −0.0257202 0.0329775i
\(92\) 0 0
\(93\) 4.39639 + 11.6949i 0.455884 + 1.21271i
\(94\) 0 0
\(95\) 12.5246 7.98833i 1.28500 0.819585i
\(96\) 0 0
\(97\) 8.95939 + 2.07042i 0.909688 + 0.210220i 0.653960 0.756529i \(-0.273106\pi\)
0.255728 + 0.966749i \(0.417685\pi\)
\(98\) 0 0
\(99\) −3.95500 + 9.42188i −0.397493 + 0.946935i
\(100\) 0 0
\(101\) 0.700273 + 7.37831i 0.0696798 + 0.734169i 0.960216 + 0.279257i \(0.0900883\pi\)
−0.890536 + 0.454912i \(0.849671\pi\)
\(102\) 0 0
\(103\) −4.27542 + 2.96031i −0.421270 + 0.291688i −0.760897 0.648872i \(-0.775241\pi\)
0.339628 + 0.940560i \(0.389699\pi\)
\(104\) 0 0
\(105\) −5.10362 4.46864i −0.498062 0.436094i
\(106\) 0 0
\(107\) 10.2193 + 7.07586i 0.987937 + 0.684049i 0.949028 0.315193i \(-0.102069\pi\)
0.0389098 + 0.999243i \(0.487612\pi\)
\(108\) 0 0
\(109\) 9.35869 + 5.96906i 0.896400 + 0.571732i 0.903664 0.428241i \(-0.140867\pi\)
−0.00726466 + 0.999974i \(0.502312\pi\)
\(110\) 0 0
\(111\) −2.88771 + 21.6702i −0.274090 + 2.05685i
\(112\) 0 0
\(113\) 6.08987 9.95891i 0.572887 0.936856i −0.426587 0.904446i \(-0.640284\pi\)
0.999475 0.0324094i \(-0.0103180\pi\)
\(114\) 0 0
\(115\) 10.2978 + 10.4945i 0.960273 + 0.978620i
\(116\) 0 0
\(117\) −0.427993 + 2.02612i −0.0395680 + 0.187315i
\(118\) 0 0
\(119\) 0.00157679 0.00281244i 0.000144544 0.000257816i
\(120\) 0 0
\(121\) 1.38389 + 5.51098i 0.125808 + 0.500998i
\(122\) 0 0
\(123\) 8.02814 + 12.0767i 0.723873 + 1.08892i
\(124\) 0 0
\(125\) −1.38508 4.15554i −0.123886 0.371683i
\(126\) 0 0
\(127\) −8.68374 0.990312i −0.770557 0.0878760i −0.280837 0.959756i \(-0.590612\pi\)
−0.489720 + 0.871880i \(0.662901\pi\)
\(128\) 0 0
\(129\) 12.8886 0.488073i 1.13478 0.0429725i
\(130\) 0 0
\(131\) −0.0196468 + 0.345670i −0.00171655 + 0.0302013i −0.999133 0.0416381i \(-0.986742\pi\)
0.997416 + 0.0718394i \(0.0228869\pi\)
\(132\) 0 0
\(133\) −2.26955 3.71144i −0.196795 0.321823i
\(134\) 0 0
\(135\) −0.215200 + 11.3697i −0.0185215 + 0.978548i
\(136\) 0 0
\(137\) 13.0445 4.62394i 1.11447 0.395050i 0.287773 0.957699i \(-0.407085\pi\)
0.826696 + 0.562649i \(0.190218\pi\)
\(138\) 0 0
\(139\) 6.50848 + 6.14906i 0.552042 + 0.521556i 0.911333 0.411669i \(-0.135054\pi\)
−0.359292 + 0.933225i \(0.616982\pi\)
\(140\) 0 0
\(141\) −16.7563 + 2.55650i −1.41113 + 0.215296i
\(142\) 0 0
\(143\) −0.454438 0.977226i −0.0380020 0.0817197i
\(144\) 0 0
\(145\) 4.87949 + 0.184779i 0.405219 + 0.0153451i
\(146\) 0 0
\(147\) 11.5031 12.6465i 0.948756 1.04307i
\(148\) 0 0
\(149\) 3.77569 + 3.06144i 0.309316 + 0.250803i 0.771858 0.635795i \(-0.219328\pi\)
−0.462542 + 0.886597i \(0.653063\pi\)
\(150\) 0 0
\(151\) 12.8517 + 9.63794i 1.04586 + 0.784325i 0.976987 0.213301i \(-0.0684214\pi\)
0.0688721 + 0.997625i \(0.478060\pi\)
\(152\) 0 0
\(153\) −0.0164374 + 0.00314850i −0.00132888 + 0.000254541i
\(154\) 0 0
\(155\) −13.1218 2.51340i −1.05396 0.201882i
\(156\) 0 0
\(157\) 1.95548 + 9.25724i 0.156065 + 0.738808i 0.984026 + 0.178024i \(0.0569703\pi\)
−0.827962 + 0.560785i \(0.810500\pi\)
\(158\) 0 0
\(159\) −3.61144 + 1.12825i −0.286406 + 0.0894763i
\(160\) 0 0
\(161\) 3.12984 2.95700i 0.246666 0.233044i
\(162\) 0 0
\(163\) −3.38123 + 10.1444i −0.264838 + 0.794571i 0.729078 + 0.684431i \(0.239949\pi\)
−0.993916 + 0.110140i \(0.964870\pi\)
\(164\) 0 0
\(165\) −10.7148 14.8657i −0.834148 1.15729i
\(166\) 0 0
\(167\) −9.73848 8.49482i −0.753586 0.657349i
\(168\) 0 0
\(169\) 7.47364 + 10.3689i 0.574895 + 0.797607i
\(170\) 0 0
\(171\) −7.14037 + 21.4226i −0.546037 + 1.63823i
\(172\) 0 0
\(173\) 2.02587 1.91399i 0.154024 0.145518i −0.605874 0.795560i \(-0.707177\pi\)
0.759898 + 0.650042i \(0.225249\pi\)
\(174\) 0 0
\(175\) 2.84971 0.890282i 0.215418 0.0672990i
\(176\) 0 0
\(177\) −2.65714 12.5789i −0.199723 0.945485i
\(178\) 0 0
\(179\) −0.653800 0.125232i −0.0488673 0.00936029i 0.163633 0.986521i \(-0.447679\pi\)
−0.212500 + 0.977161i \(0.568161\pi\)
\(180\) 0 0
\(181\) −3.94947 + 0.756500i −0.293561 + 0.0562302i −0.332793 0.943000i \(-0.607991\pi\)
0.0392314 + 0.999230i \(0.487509\pi\)
\(182\) 0 0
\(183\) −20.6493 15.4856i −1.52644 1.14473i
\(184\) 0 0
\(185\) −18.1586 14.7235i −1.33505 1.08249i
\(186\) 0 0
\(187\) 0.00586074 0.00644332i 0.000428580 0.000471182i
\(188\) 0 0
\(189\) 3.32782 + 0.126020i 0.242063 + 0.00916660i
\(190\) 0 0
\(191\) −0.476049 1.02370i −0.0344457 0.0740722i 0.888772 0.458349i \(-0.151559\pi\)
−0.923218 + 0.384277i \(0.874451\pi\)
\(192\) 0 0
\(193\) 1.66894 0.254629i 0.120133 0.0183286i −0.0904793 0.995898i \(-0.528840\pi\)
0.210612 + 0.977570i \(0.432454\pi\)
\(194\) 0 0
\(195\) −2.69943 2.55036i −0.193311 0.182635i
\(196\) 0 0
\(197\) 1.99891 0.708562i 0.142417 0.0504829i −0.261941 0.965084i \(-0.584363\pi\)
0.404358 + 0.914601i \(0.367495\pi\)
\(198\) 0 0
\(199\) −0.258661 + 13.6659i −0.0183360 + 0.968749i 0.865488 + 0.500930i \(0.167008\pi\)
−0.883824 + 0.467820i \(0.845040\pi\)
\(200\) 0 0
\(201\) −2.41539 3.94994i −0.170368 0.278607i
\(202\) 0 0
\(203\) 0.0811446 1.42768i 0.00569523 0.100203i
\(204\) 0 0
\(205\) −15.4961 + 0.586815i −1.08229 + 0.0409850i
\(206\) 0 0
\(207\) −22.2059 2.53241i −1.54342 0.176014i
\(208\) 0 0
\(209\) −3.71606 11.1490i −0.257046 0.771191i
\(210\) 0 0
\(211\) 3.22627 + 4.85326i 0.222105 + 0.334112i 0.926906 0.375293i \(-0.122458\pi\)
−0.704801 + 0.709405i \(0.748964\pi\)
\(212\) 0 0
\(213\) 7.01100 + 27.9194i 0.480386 + 1.91301i
\(214\) 0 0
\(215\) −6.74484 + 12.0304i −0.459995 + 0.820469i
\(216\) 0 0
\(217\) −0.808637 + 3.82808i −0.0548939 + 0.259867i
\(218\) 0 0
\(219\) 30.6688 + 31.2547i 2.07240 + 2.11200i
\(220\) 0 0
\(221\) 0.000920870 0.00150592i 6.19444e−5 0.000101299i
\(222\) 0 0
\(223\) 2.35123 17.6443i 0.157450 1.18155i −0.717226 0.696841i \(-0.754588\pi\)
0.874676 0.484709i \(-0.161074\pi\)
\(224\) 0 0
\(225\) −13.0656 8.33336i −0.871040 0.555557i
\(226\) 0 0
\(227\) −21.9251 15.1810i −1.45522 1.00760i −0.992651 0.121012i \(-0.961386\pi\)
−0.462567 0.886584i \(-0.653072\pi\)
\(228\) 0 0
\(229\) −7.36394 6.44774i −0.486623 0.426079i 0.380042 0.924969i \(-0.375910\pi\)
−0.866665 + 0.498891i \(0.833741\pi\)
\(230\) 0 0
\(231\) −4.41201 + 3.05488i −0.290289 + 0.200997i
\(232\) 0 0
\(233\) −1.74697 18.4067i −0.114448 1.20586i −0.849403 0.527745i \(-0.823038\pi\)
0.734955 0.678116i \(-0.237203\pi\)
\(234\) 0 0
\(235\) 7.01549 16.7128i 0.457640 1.09022i
\(236\) 0 0
\(237\) −26.2968 6.07692i −1.70816 0.394738i
\(238\) 0 0
\(239\) 4.84805 3.09213i 0.313595 0.200014i −0.371564 0.928407i \(-0.621179\pi\)
0.685159 + 0.728394i \(0.259733\pi\)
\(240\) 0 0
\(241\) 8.64612 + 22.9997i 0.556946 + 1.48154i 0.850696 + 0.525658i \(0.176181\pi\)
−0.293750 + 0.955882i \(0.594903\pi\)
\(242\) 0 0
\(243\) 11.6550 + 14.9436i 0.747669 + 0.958634i
\(244\) 0 0
\(245\) 5.12012 + 17.5492i 0.327113 + 1.12118i
\(246\) 0 0
\(247\) −1.16470 2.07742i −0.0741082 0.132183i
\(248\) 0 0
\(249\) 6.77119 + 3.62958i 0.429106 + 0.230015i
\(250\) 0 0
\(251\) −2.53316 + 3.51449i −0.159892 + 0.221833i −0.883563 0.468311i \(-0.844863\pi\)
0.723672 + 0.690144i \(0.242453\pi\)
\(252\) 0 0
\(253\) 10.0363 5.87919i 0.630977 0.369622i
\(254\) 0 0
\(255\) 0.0105612 0.0280939i 0.000661365 0.00175931i
\(256\) 0 0
\(257\) −8.20254 16.0233i −0.511660 0.999509i −0.992447 0.122672i \(-0.960854\pi\)
0.480787 0.876837i \(-0.340351\pi\)
\(258\) 0 0
\(259\) −4.41163 + 5.23518i −0.274125 + 0.325298i
\(260\) 0 0
\(261\) −5.93822 + 4.45327i −0.367566 + 0.275650i
\(262\) 0 0
\(263\) −9.87494 + 1.12616i −0.608915 + 0.0694419i −0.412314 0.911042i \(-0.635279\pi\)
−0.196601 + 0.980484i \(0.562990\pi\)
\(264\) 0 0
\(265\) 0.985401 3.92409i 0.0605327 0.241055i
\(266\) 0 0
\(267\) 38.6470 17.0900i 2.36516 1.04589i
\(268\) 0 0
\(269\) −8.78453 + 7.12275i −0.535602 + 0.434282i −0.858996 0.511983i \(-0.828911\pi\)
0.323394 + 0.946265i \(0.395176\pi\)
\(270\) 0 0
\(271\) 1.48628 8.64148i 0.0902852 0.524933i −0.904794 0.425850i \(-0.859975\pi\)
0.995079 0.0990832i \(-0.0315910\pi\)
\(272\) 0 0
\(273\) −0.761699 + 0.776253i −0.0461001 + 0.0469809i
\(274\) 0 0
\(275\) 8.04197 0.609951i 0.484949 0.0367814i
\(276\) 0 0
\(277\) 13.0611 + 6.37711i 0.784764 + 0.383164i 0.787093 0.616834i \(-0.211585\pi\)
−0.00232964 + 0.999997i \(0.500742\pi\)
\(278\) 0 0
\(279\) 17.8994 9.59465i 1.07161 0.574417i
\(280\) 0 0
\(281\) −3.35769 19.5222i −0.200303 1.16459i −0.895260 0.445543i \(-0.853011\pi\)
0.694957 0.719051i \(-0.255423\pi\)
\(282\) 0 0
\(283\) 1.19226 + 20.9769i 0.0708725 + 1.24695i 0.815219 + 0.579153i \(0.196616\pi\)
−0.744347 + 0.667793i \(0.767239\pi\)
\(284\) 0 0
\(285\) −26.0952 30.9666i −1.54575 1.83430i
\(286\) 0 0
\(287\) 0.0859397 + 4.54046i 0.00507286 + 0.268015i
\(288\) 0 0
\(289\) −16.8055 2.56401i −0.988560 0.150824i
\(290\) 0 0
\(291\) 2.36845 24.9548i 0.138841 1.46288i
\(292\) 0 0
\(293\) −27.8816 + 13.6133i −1.62886 + 0.795296i −0.629020 + 0.777389i \(0.716543\pi\)
−0.999840 + 0.0179065i \(0.994300\pi\)
\(294\) 0 0
\(295\) 12.9579 + 4.59323i 0.754438 + 0.267428i
\(296\) 0 0
\(297\) 8.68222 + 2.35577i 0.503793 + 0.136696i
\(298\) 0 0
\(299\) 1.77348 1.55283i 0.102563 0.0898025i
\(300\) 0 0
\(301\) 3.48510 + 2.04154i 0.200878 + 0.117673i
\(302\) 0 0
\(303\) 19.6849 4.54897i 1.13087 0.261332i
\(304\) 0 0
\(305\) 25.6469 10.1993i 1.46854 0.584008i
\(306\) 0 0
\(307\) −7.85568 18.7144i −0.448347 1.06808i −0.975832 0.218520i \(-0.929877\pi\)
0.527485 0.849564i \(-0.323135\pi\)
\(308\) 0 0
\(309\) 9.53856 + 10.4867i 0.542630 + 0.596569i
\(310\) 0 0
\(311\) 20.1904 + 8.02933i 1.14489 + 0.455302i 0.863529 0.504299i \(-0.168249\pi\)
0.281364 + 0.959601i \(0.409213\pi\)
\(312\) 0 0
\(313\) 17.1322 + 5.35230i 0.968370 + 0.302530i 0.741169 0.671318i \(-0.234272\pi\)
0.227201 + 0.973848i \(0.427043\pi\)
\(314\) 0 0
\(315\) −6.10426 + 9.18262i −0.343936 + 0.517382i
\(316\) 0 0
\(317\) −4.81593 0.365269i −0.270489 0.0205155i −0.0603149 0.998179i \(-0.519210\pi\)
−0.210175 + 0.977664i \(0.567403\pi\)
\(318\) 0 0
\(319\) 1.08193 3.70830i 0.0605764 0.207625i
\(320\) 0 0
\(321\) 15.4400 30.1616i 0.861780 1.68345i
\(322\) 0 0
\(323\) 0.0118376 0.0151777i 0.000658660 0.000844510i
\(324\) 0 0
\(325\) 1.57742 0.428006i 0.0874995 0.0237415i
\(326\) 0 0
\(327\) 12.7592 27.4375i 0.705587 1.51730i
\(328\) 0 0
\(329\) −4.85458 2.14674i −0.267641 0.118353i
\(330\) 0 0
\(331\) 4.42474 + 33.2045i 0.243206 + 1.82508i 0.508668 + 0.860963i \(0.330138\pi\)
−0.265462 + 0.964121i \(0.585525\pi\)
\(332\) 0 0
\(333\) 35.5360 1.94736
\(334\) 0 0
\(335\) 4.95095 0.270499
\(336\) 0 0
\(337\) 0.678789 + 5.09382i 0.0369760 + 0.277478i 0.999968 + 0.00794965i \(0.00253048\pi\)
−0.962992 + 0.269528i \(0.913132\pi\)
\(338\) 0 0
\(339\) −29.1029 12.8696i −1.58065 0.698978i
\(340\) 0 0
\(341\) −4.45670 + 9.58372i −0.241344 + 0.518987i
\(342\) 0 0
\(343\) 10.9338 2.96671i 0.590371 0.160187i
\(344\) 0 0
\(345\) 24.6494 31.6046i 1.32708 1.70153i
\(346\) 0 0
\(347\) −6.56407 + 12.8227i −0.352378 + 0.688357i −0.997103 0.0760574i \(-0.975767\pi\)
0.644726 + 0.764414i \(0.276972\pi\)
\(348\) 0 0
\(349\) −8.56481 + 29.3558i −0.458464 + 1.57138i 0.322353 + 0.946619i \(0.395526\pi\)
−0.780817 + 0.624760i \(0.785197\pi\)
\(350\) 0 0
\(351\) 1.81792 + 0.137882i 0.0970335 + 0.00735960i
\(352\) 0 0
\(353\) 7.79623 11.7278i 0.414951 0.624210i −0.564610 0.825358i \(-0.690973\pi\)
0.979561 + 0.201148i \(0.0644672\pi\)
\(354\) 0 0
\(355\) −29.3818 9.17921i −1.55943 0.487182i
\(356\) 0 0
\(357\) −0.00816729 0.00324797i −0.000432259 0.000171901i
\(358\) 0 0
\(359\) −8.85868 9.73926i −0.467543 0.514018i 0.459906 0.887967i \(-0.347883\pi\)
−0.927449 + 0.373949i \(0.878003\pi\)
\(360\) 0 0
\(361\) −2.69792 6.42718i −0.141996 0.338272i
\(362\) 0 0
\(363\) 14.3930 5.72380i 0.755435 0.300422i
\(364\) 0 0
\(365\) −45.6224 + 10.5429i −2.38799 + 0.551839i
\(366\) 0 0
\(367\) −6.58858 3.85954i −0.343921 0.201466i 0.323353 0.946278i \(-0.395190\pi\)
−0.667274 + 0.744812i \(0.732539\pi\)
\(368\) 0 0
\(369\) 17.7348 15.5283i 0.923236 0.808369i
\(370\) 0 0
\(371\) −1.14350 0.310269i −0.0593676 0.0161084i
\(372\) 0 0
\(373\) 29.3753 + 10.4128i 1.52100 + 0.539153i 0.957866 0.287215i \(-0.0927294\pi\)
0.563130 + 0.826368i \(0.309597\pi\)
\(374\) 0 0
\(375\) −10.7300 + 5.23896i −0.554095 + 0.270539i
\(376\) 0 0
\(377\) 0.0739679 0.779350i 0.00380954 0.0401386i
\(378\) 0 0
\(379\) −1.74850 0.266767i −0.0898142 0.0137029i 0.105761 0.994392i \(-0.466272\pi\)
−0.195576 + 0.980689i \(0.562658\pi\)
\(380\) 0 0
\(381\) 0.450873 + 23.8210i 0.0230989 + 1.22039i
\(382\) 0 0
\(383\) −20.3609 24.1618i −1.04039 1.23461i −0.971513 0.236986i \(-0.923840\pi\)
−0.0688808 0.997625i \(-0.521943\pi\)
\(384\) 0 0
\(385\) −0.325633 5.72925i −0.0165958 0.291990i
\(386\) 0 0
\(387\) −3.55371 20.6619i −0.180645 1.05030i
\(388\) 0 0
\(389\) 6.81756 3.65444i 0.345664 0.185287i −0.290435 0.956895i \(-0.593800\pi\)
0.636099 + 0.771607i \(0.280547\pi\)
\(390\) 0 0
\(391\) 0.0171193 + 0.00835855i 0.000865759 + 0.000422710i
\(392\) 0 0
\(393\) 0.941114 0.0713797i 0.0474729 0.00360063i
\(394\) 0 0
\(395\) 20.2140 20.6002i 1.01708 1.03651i
\(396\) 0 0
\(397\) −3.96560 + 23.0567i −0.199028 + 1.15718i 0.698296 + 0.715809i \(0.253942\pi\)
−0.897324 + 0.441372i \(0.854492\pi\)
\(398\) 0 0
\(399\) −9.21153 + 7.46898i −0.461153 + 0.373917i
\(400\) 0 0
\(401\) −30.8579 + 13.6456i −1.54097 + 0.681431i −0.988378 0.152019i \(-0.951422\pi\)
−0.552595 + 0.833450i \(0.686362\pi\)
\(402\) 0 0
\(403\) −0.521682 + 2.07746i −0.0259868 + 0.103485i
\(404\) 0 0
\(405\) −7.70069 + 0.878203i −0.382650 + 0.0436383i
\(406\) 0 0
\(407\) −14.7957 + 11.0958i −0.733394 + 0.549997i
\(408\) 0 0
\(409\) −2.51598 + 2.98565i −0.124407 + 0.147631i −0.823324 0.567572i \(-0.807883\pi\)
0.698917 + 0.715203i \(0.253666\pi\)
\(410\) 0 0
\(411\) −17.1914 33.5828i −0.847990 1.65652i
\(412\) 0 0
\(413\) 1.41670 3.76858i 0.0697111 0.185440i
\(414\) 0 0
\(415\) −7.08864 + 4.15247i −0.347968 + 0.203837i
\(416\) 0 0
\(417\) 14.2719 19.8008i 0.698898 0.969648i
\(418\) 0 0
\(419\) −26.4994 14.2046i −1.29458 0.693939i −0.326649 0.945146i \(-0.605920\pi\)
−0.967933 + 0.251207i \(0.919173\pi\)
\(420\) 0 0
\(421\) −11.5432 20.5890i −0.562580 1.00345i −0.994817 0.101685i \(-0.967577\pi\)
0.432237 0.901760i \(-0.357725\pi\)
\(422\) 0 0
\(423\) 7.71688 + 26.4495i 0.375207 + 1.28602i
\(424\) 0 0
\(425\) 0.00812382 + 0.0104161i 0.000394063 + 0.000505253i
\(426\) 0 0
\(427\) −2.84418 7.56586i −0.137640 0.366138i
\(428\) 0 0
\(429\) −2.47694 + 1.57982i −0.119588 + 0.0762743i
\(430\) 0 0
\(431\) 13.4428 + 3.10648i 0.647515 + 0.149634i 0.536120 0.844142i \(-0.319890\pi\)
0.111396 + 0.993776i \(0.464468\pi\)
\(432\) 0 0
\(433\) 6.22588 14.8317i 0.299197 0.712768i −0.700803 0.713355i \(-0.747175\pi\)
1.00000 0.000586982i \(0.000186842\pi\)
\(434\) 0 0
\(435\) −1.25769 13.2515i −0.0603017 0.635359i
\(436\) 0 0
\(437\) 21.1329 14.6325i 1.01093 0.699967i
\(438\) 0 0
\(439\) −13.3010 11.6461i −0.634821 0.555838i 0.279846 0.960045i \(-0.409716\pi\)
−0.914668 + 0.404206i \(0.867548\pi\)
\(440\) 0 0
\(441\) −22.8464 15.8189i −1.08792 0.753280i
\(442\) 0 0
\(443\) 7.50010 + 4.78363i 0.356340 + 0.227277i 0.703769 0.710429i \(-0.251499\pi\)
−0.347428 + 0.937707i \(0.612945\pi\)
\(444\) 0 0
\(445\) −5.96876 + 44.7913i −0.282946 + 2.12331i
\(446\) 0 0
\(447\) 6.91281 11.3047i 0.326965 0.534693i
\(448\) 0 0
\(449\) 8.34740 + 8.50689i 0.393938 + 0.401465i 0.881928 0.471385i \(-0.156246\pi\)
−0.487990 + 0.872849i \(0.662270\pi\)
\(450\) 0 0
\(451\) −2.53546 + 12.0028i −0.119390 + 0.565191i
\(452\) 0 0
\(453\) 21.4152 38.1972i 1.00617 1.79466i
\(454\) 0 0
\(455\) −0.283242 1.12794i −0.0132786 0.0528784i
\(456\) 0 0
\(457\) −5.92303 8.91000i −0.277068 0.416792i 0.667752 0.744384i \(-0.267257\pi\)
−0.944819 + 0.327592i \(0.893763\pi\)
\(458\) 0 0
\(459\) 0.00465915 + 0.0139784i 0.000217470 + 0.000652457i
\(460\) 0 0
\(461\) 16.8222 + 1.91844i 0.783489 + 0.0893507i 0.495873 0.868395i \(-0.334848\pi\)
0.287616 + 0.957746i \(0.407137\pi\)
\(462\) 0 0
\(463\) −30.1352 + 1.14118i −1.40050 + 0.0530351i −0.727248 0.686375i \(-0.759201\pi\)
−0.673256 + 0.739410i \(0.735105\pi\)
\(464\) 0 0
\(465\) −2.06667 + 36.3615i −0.0958396 + 1.68622i
\(466\) 0 0
\(467\) −18.4871 30.2323i −0.855479 1.39898i −0.916154 0.400827i \(-0.868723\pi\)
0.0606748 0.998158i \(-0.480675\pi\)
\(468\) 0 0
\(469\) 0.0274378 1.44962i 0.00126696 0.0669374i
\(470\) 0 0
\(471\) 24.3100 8.61725i 1.12014 0.397062i
\(472\) 0 0
\(473\) 7.93109 + 7.49311i 0.364672 + 0.344533i
\(474\) 0 0
\(475\) 17.6190 2.68812i 0.808414 0.123339i
\(476\) 0 0
\(477\) 2.59330 + 5.57665i 0.118739 + 0.255337i
\(478\) 0 0
\(479\) 13.0908 + 0.495729i 0.598133 + 0.0226504i 0.335173 0.942156i \(-0.391205\pi\)
0.262959 + 0.964807i \(0.415302\pi\)
\(480\) 0 0
\(481\) −2.52190 + 2.77259i −0.114989 + 0.126419i
\(482\) 0 0
\(483\) −9.11712 7.39243i −0.414843 0.336367i
\(484\) 0 0
\(485\) 21.4447 + 16.0821i 0.973756 + 0.730252i
\(486\) 0 0
\(487\) −37.7632 + 7.23334i −1.71121 + 0.327774i −0.947975 0.318344i \(-0.896873\pi\)
−0.763237 + 0.646118i \(0.776391\pi\)
\(488\) 0 0
\(489\) 28.6288 + 5.48370i 1.29464 + 0.247982i
\(490\) 0 0
\(491\) 4.66933 + 22.1046i 0.210724 + 0.997566i 0.947086 + 0.320979i \(0.104012\pi\)
−0.736362 + 0.676587i \(0.763458\pi\)
\(492\) 0 0
\(493\) 0.00603908 0.00188668i 0.000271986 8.49716e-5i
\(494\) 0 0
\(495\) −21.6516 + 20.4560i −0.973169 + 0.919427i
\(496\) 0 0
\(497\) −2.85048 + 8.55204i −0.127861 + 0.383611i
\(498\) 0 0
\(499\) −10.6315 14.7501i −0.475931 0.660304i 0.503050 0.864257i \(-0.332211\pi\)
−0.978981 + 0.203954i \(0.934621\pi\)
\(500\) 0 0
\(501\) −19.4474 + 29.3732i −0.868845 + 1.31230i
\(502\) 0 0
\(503\) −25.1806 34.9355i −1.12275 1.55770i −0.788311 0.615277i \(-0.789044\pi\)
−0.334438 0.942418i \(-0.608546\pi\)
\(504\) 0 0
\(505\) −6.83153 + 20.4960i −0.303999 + 0.912062i
\(506\) 0 0
\(507\) 25.3268 23.9282i 1.12480 1.06269i
\(508\) 0 0
\(509\) 20.8270 6.50660i 0.923142 0.288400i 0.200557 0.979682i \(-0.435725\pi\)
0.722585 + 0.691282i \(0.242954\pi\)
\(510\) 0 0
\(511\) 2.83409 + 13.4165i 0.125373 + 0.593513i
\(512\) 0 0
\(513\) 19.5254 + 3.74000i 0.862069 + 0.165125i
\(514\) 0 0
\(515\) −14.8882 + 2.85175i −0.656051 + 0.125663i
\(516\) 0 0
\(517\) −11.4716 8.60294i −0.504520 0.378357i
\(518\) 0 0
\(519\) −5.90129 4.78494i −0.259038 0.210035i
\(520\) 0 0
\(521\) −23.9180 + 26.2955i −1.04787 + 1.15203i −0.0597675 + 0.998212i \(0.519036\pi\)
−0.988099 + 0.153816i \(0.950844\pi\)
\(522\) 0 0
\(523\) −30.2973 1.14732i −1.32481 0.0501686i −0.634071 0.773275i \(-0.718617\pi\)
−0.690737 + 0.723106i \(0.742714\pi\)
\(524\) 0 0
\(525\) −3.43176 7.37967i −0.149774 0.322075i
\(526\) 0 0
\(527\) −0.0171130 + 0.00261093i −0.000745455 + 0.000113734i
\(528\) 0 0
\(529\) 1.77423 + 1.67625i 0.0771405 + 0.0728806i
\(530\) 0 0
\(531\) −19.6971 + 6.98209i −0.854779 + 0.302997i
\(532\) 0 0
\(533\) −0.0470483 + 2.48571i −0.00203789 + 0.107668i
\(534\) 0 0
\(535\) 18.9026 + 30.9119i 0.817232 + 1.33644i
\(536\) 0 0
\(537\) −0.102973 + 1.81174i −0.00444363 + 0.0781821i
\(538\) 0 0
\(539\) 14.4516 0.547260i 0.622473 0.0235722i
\(540\) 0 0
\(541\) −30.3669 3.46310i −1.30557 0.148890i −0.567367 0.823465i \(-0.692038\pi\)
−0.738206 + 0.674575i \(0.764327\pi\)
\(542\) 0 0
\(543\) 3.46626 + 10.3995i 0.148751 + 0.446285i
\(544\) 0 0
\(545\) 17.9131 + 26.9466i 0.767312 + 1.15427i
\(546\) 0 0
\(547\) 8.41781 + 33.5217i 0.359920 + 1.43328i 0.833494 + 0.552529i \(0.186337\pi\)
−0.473574 + 0.880754i \(0.657036\pi\)
\(548\) 0 0
\(549\) −20.5174 + 36.5959i −0.875663 + 1.56187i
\(550\) 0 0
\(551\) 1.76432 8.35227i 0.0751625 0.355819i
\(552\) 0 0
\(553\) −5.91966 6.03276i −0.251729 0.256539i
\(554\) 0 0
\(555\) −33.2461 + 54.3681i −1.41122 + 2.30780i
\(556\) 0 0
\(557\) −3.91899 + 29.4092i −0.166053 + 1.24611i 0.687919 + 0.725787i \(0.258524\pi\)
−0.853972 + 0.520319i \(0.825813\pi\)
\(558\) 0 0
\(559\) 1.86428 + 1.18906i 0.0788506 + 0.0502917i
\(560\) 0 0
\(561\) −0.0195209 0.0135163i −0.000824172 0.000570658i
\(562\) 0 0
\(563\) −2.53019 2.21539i −0.106635 0.0933674i 0.603779 0.797152i \(-0.293661\pi\)
−0.710414 + 0.703784i \(0.751492\pi\)
\(564\) 0 0
\(565\) 27.9763 19.3708i 1.17697 0.814937i
\(566\) 0 0
\(567\) 0.214459 + 2.25961i 0.00900642 + 0.0948945i
\(568\) 0 0
\(569\) −0.599848 + 1.42900i −0.0251469 + 0.0599068i −0.934145 0.356893i \(-0.883836\pi\)
0.908998 + 0.416799i \(0.136848\pi\)
\(570\) 0 0
\(571\) 14.4824 + 3.34674i 0.606071 + 0.140057i 0.517024 0.855971i \(-0.327040\pi\)
0.0890466 + 0.996027i \(0.471618\pi\)
\(572\) 0 0
\(573\) −2.59473 + 1.65495i −0.108397 + 0.0691364i
\(574\) 0 0
\(575\) 6.20725 + 16.5120i 0.258860 + 0.688598i
\(576\) 0 0
\(577\) 16.5578 + 21.2298i 0.689310 + 0.883808i 0.997723 0.0674446i \(-0.0214846\pi\)
−0.308413 + 0.951253i \(0.599798\pi\)
\(578\) 0 0
\(579\) −1.28898 4.41796i −0.0535681 0.183604i
\(580\) 0 0
\(581\) 1.17655 + 2.09855i 0.0488114 + 0.0870623i
\(582\) 0 0
\(583\) −2.82100 1.51215i −0.116834 0.0626267i
\(584\) 0 0
\(585\) −3.52966 + 4.89703i −0.145933 + 0.202467i
\(586\) 0 0
\(587\) 24.0997 14.1174i 0.994700 0.582688i 0.0843104 0.996440i \(-0.473131\pi\)
0.910390 + 0.413752i \(0.135782\pi\)
\(588\) 0 0
\(589\) −8.21884 + 21.8631i −0.338651 + 0.900852i
\(590\) 0 0
\(591\) −2.63437 5.14615i −0.108364 0.211684i
\(592\) 0 0
\(593\) −3.21278 + 3.81253i −0.131933 + 0.156562i −0.826640 0.562731i \(-0.809751\pi\)
0.694707 + 0.719293i \(0.255534\pi\)
\(594\) 0 0
\(595\) 0.00751934 0.00563901i 0.000308263 0.000231177i
\(596\) 0 0
\(597\) 37.0199 4.22183i 1.51512 0.172788i
\(598\) 0 0
\(599\) −0.0298905 + 0.119031i −0.00122129 + 0.00486347i −0.970495 0.241121i \(-0.922485\pi\)
0.969274 + 0.245985i \(0.0791113\pi\)
\(600\) 0 0
\(601\) 23.9324 10.5831i 0.976224 0.431695i 0.146098 0.989270i \(-0.453329\pi\)
0.830126 + 0.557576i \(0.188268\pi\)
\(602\) 0 0
\(603\) −5.84569 + 4.73986i −0.238055 + 0.193022i
\(604\) 0 0
\(605\) −2.80757 + 16.3237i −0.114144 + 0.663652i
\(606\) 0 0
\(607\) 23.5263 23.9758i 0.954901 0.973146i −0.0447646 0.998998i \(-0.514254\pi\)
0.999666 + 0.0258514i \(0.00822967\pi\)
\(608\) 0 0
\(609\) −3.88696 + 0.294810i −0.157507 + 0.0119463i
\(610\) 0 0
\(611\) −2.61130 1.27497i −0.105642 0.0515799i
\(612\) 0 0
\(613\) 40.6368 21.7827i 1.64130 0.879793i 0.648344 0.761347i \(-0.275462\pi\)
0.992960 0.118446i \(-0.0377913\pi\)
\(614\) 0 0
\(615\) 7.16542 + 41.6609i 0.288937 + 1.67993i
\(616\) 0 0
\(617\) −2.52189 44.3708i −0.101528 1.78630i −0.496929 0.867791i \(-0.665539\pi\)
0.395401 0.918508i \(-0.370606\pi\)
\(618\) 0 0
\(619\) −29.3939 34.8811i −1.18144 1.40199i −0.896268 0.443513i \(-0.853732\pi\)
−0.285173 0.958476i \(-0.592051\pi\)
\(620\) 0 0
\(621\) 0.372363 + 19.6731i 0.0149424 + 0.789455i
\(622\) 0 0
\(623\) 13.0817 + 1.99586i 0.524106 + 0.0799626i
\(624\) 0 0
\(625\) 2.85868 30.1200i 0.114347 1.20480i
\(626\) 0 0
\(627\) −28.7877 + 14.0557i −1.14967 + 0.561331i
\(628\) 0 0
\(629\) −0.0285500 0.0101202i −0.00113836 0.000403520i
\(630\) 0 0
\(631\) −22.9586 6.22943i −0.913969 0.247990i −0.226337 0.974049i \(-0.572675\pi\)
−0.687632 + 0.726060i \(0.741350\pi\)
\(632\) 0 0
\(633\) 11.9524 10.4653i 0.475064 0.415957i
\(634\) 0 0
\(635\) −21.9832 12.8776i −0.872377 0.511032i
\(636\) 0 0
\(637\) 2.85557 0.659894i 0.113142 0.0261459i
\(638\) 0 0
\(639\) 43.4796 17.2910i 1.72003 0.684021i
\(640\) 0 0
\(641\) −3.22495 7.68270i −0.127378 0.303448i 0.845801 0.533498i \(-0.179123\pi\)
−0.973179 + 0.230050i \(0.926111\pi\)
\(642\) 0 0
\(643\) −6.94902 7.63978i −0.274043 0.301284i 0.587237 0.809415i \(-0.300216\pi\)
−0.861279 + 0.508132i \(0.830336\pi\)
\(644\) 0 0
\(645\) 34.9362 + 13.8935i 1.37561 + 0.547054i
\(646\) 0 0
\(647\) 41.6009 + 12.9966i 1.63550 + 0.510948i 0.971551 0.236831i \(-0.0761088\pi\)
0.663947 + 0.747779i \(0.268880\pi\)
\(648\) 0 0
\(649\) 6.02093 9.05727i 0.236342 0.355529i
\(650\) 0 0
\(651\) 10.6351 + 0.806628i 0.416821 + 0.0316142i
\(652\) 0 0
\(653\) −5.44088 + 18.6486i −0.212918 + 0.729775i 0.781466 + 0.623948i \(0.214472\pi\)
−0.994384 + 0.105828i \(0.966251\pi\)
\(654\) 0 0
\(655\) −0.459896 + 0.898389i −0.0179696 + 0.0351030i
\(656\) 0 0
\(657\) 43.7740 56.1255i 1.70779 2.18966i
\(658\) 0 0
\(659\) 42.0411 11.4071i 1.63769 0.444358i 0.680246 0.732984i \(-0.261873\pi\)
0.957442 + 0.288625i \(0.0931981\pi\)
\(660\) 0 0
\(661\) 16.9460 36.4408i 0.659122 1.41738i −0.236086 0.971732i \(-0.575865\pi\)
0.895208 0.445649i \(-0.147027\pi\)
\(662\) 0 0
\(663\) −0.00440075 0.00194605i −0.000170911 7.55783e-5i
\(664\) 0 0
\(665\) −1.67508 12.5703i −0.0649569 0.487454i
\(666\) 0 0
\(667\) 8.44909 0.327150
\(668\) 0 0
\(669\) −48.5235 −1.87603
\(670\) 0 0
\(671\) −2.88413 21.6434i −0.111341 0.835532i
\(672\) 0 0
\(673\) 5.70712 + 2.52374i 0.219993 + 0.0972829i 0.511491 0.859289i \(-0.329093\pi\)
−0.291498 + 0.956572i \(0.594154\pi\)
\(674\) 0 0
\(675\) −5.75294 + 12.3712i −0.221431 + 0.476167i
\(676\) 0 0
\(677\) −40.8690 + 11.0891i −1.57072 + 0.426188i −0.937558 0.347830i \(-0.886919\pi\)
−0.633164 + 0.774018i \(0.718244\pi\)
\(678\) 0 0
\(679\) 4.82765 6.18983i 0.185268 0.237544i
\(680\) 0 0
\(681\) −33.1260 + 64.7103i −1.26939 + 2.47970i
\(682\) 0 0
\(683\) −9.64220 + 33.0485i −0.368948 + 1.26457i 0.537864 + 0.843032i \(0.319232\pi\)
−0.906812 + 0.421535i \(0.861491\pi\)
\(684\) 0 0
\(685\) 40.2278 + 3.05111i 1.53702 + 0.116577i
\(686\) 0 0
\(687\) −14.7709 + 22.2199i −0.563546 + 0.847741i
\(688\) 0 0
\(689\) −0.619142 0.193427i −0.0235874 0.00736898i
\(690\) 0 0
\(691\) 16.2203 + 6.45050i 0.617050 + 0.245389i 0.657093 0.753809i \(-0.271786\pi\)
−0.0400435 + 0.999198i \(0.512750\pi\)
\(692\) 0 0
\(693\) 5.86945 + 6.45290i 0.222962 + 0.245125i
\(694\) 0 0
\(695\) 10.1022 + 24.0663i 0.383200 + 0.912886i
\(696\) 0 0
\(697\) −0.0186706 + 0.00742494i −0.000707200 + 0.000281240i
\(698\) 0 0
\(699\) −49.1078 + 11.3483i −1.85743 + 0.429232i
\(700\) 0 0
\(701\) 7.90465 + 4.63048i 0.298555 + 0.174891i 0.647109 0.762398i \(-0.275978\pi\)
−0.348554 + 0.937289i \(0.613327\pi\)
\(702\) 0 0
\(703\) −30.7486 + 26.9229i −1.15970 + 1.01542i
\(704\) 0 0
\(705\) −47.6860 12.9388i −1.79596 0.487302i
\(706\) 0 0
\(707\) 5.96332 + 2.11384i 0.224274 + 0.0794991i
\(708\) 0 0
\(709\) 6.78755 3.31404i 0.254912 0.124462i −0.306857 0.951755i \(-0.599277\pi\)
0.561769 + 0.827294i \(0.310121\pi\)
\(710\) 0 0
\(711\) −4.14521 + 43.6752i −0.155457 + 1.63795i
\(712\) 0 0
\(713\) −22.8530 3.48668i −0.855853 0.130577i
\(714\) 0 0
\(715\) −0.0594517 3.14102i −0.00222337 0.117467i
\(716\) 0 0
\(717\) −10.1010 11.9866i −0.377227 0.447647i
\(718\) 0 0
\(719\) 0.645672 + 11.3601i 0.0240795 + 0.423660i 0.987697 + 0.156377i \(0.0499814\pi\)
−0.963618 + 0.267283i \(0.913874\pi\)
\(720\) 0 0
\(721\) 0.752476 + 4.37502i 0.0280237 + 0.162934i
\(722\) 0 0
\(723\) 59.0345 31.6444i 2.19552 1.17687i
\(724\) 0 0
\(725\) 5.26444 + 2.57038i 0.195516 + 0.0954616i
\(726\) 0 0
\(727\) −20.5371 + 1.55766i −0.761678 + 0.0577702i −0.450735 0.892658i \(-0.648838\pi\)
−0.310944 + 0.950428i \(0.600645\pi\)
\(728\) 0 0
\(729\) 30.5960 31.1806i 1.13318 1.15484i
\(730\) 0 0
\(731\) −0.00302916 + 0.0176120i −0.000112038 + 0.000651405i
\(732\) 0 0
\(733\) −28.7655 + 23.3239i −1.06248 + 0.861487i −0.990718 0.135935i \(-0.956596\pi\)
−0.0717592 + 0.997422i \(0.522861\pi\)
\(734\) 0 0
\(735\) 45.5762 20.1542i 1.68110 0.743399i
\(736\) 0 0
\(737\) 0.953922 3.79874i 0.0351382 0.139928i
\(738\) 0 0
\(739\) −2.44802 + 0.279178i −0.0900520 + 0.0102697i −0.158217 0.987404i \(-0.550575\pi\)
0.0681653 + 0.997674i \(0.478285\pi\)
\(740\) 0 0
\(741\) −5.19404 + 3.89518i −0.190808 + 0.143093i
\(742\) 0 0
\(743\) 25.1879 29.8899i 0.924053 1.09655i −0.0710261 0.997474i \(-0.522627\pi\)
0.995080 0.0990785i \(-0.0315895\pi\)
\(744\) 0 0
\(745\) 6.45673 + 12.6130i 0.236556 + 0.462104i
\(746\) 0 0
\(747\) 4.39429 11.6893i 0.160779 0.427690i
\(748\) 0 0
\(749\) 9.15567 5.36332i 0.334541 0.195972i
\(750\) 0 0
\(751\) −24.2979 + 33.7108i −0.886643 + 1.23012i 0.0856418 + 0.996326i \(0.472706\pi\)
−0.972285 + 0.233798i \(0.924884\pi\)
\(752\) 0 0
\(753\) 10.4087 + 5.57939i 0.379313 + 0.203324i
\(754\) 0 0
\(755\) 22.9001 + 40.8458i 0.833421 + 1.48653i
\(756\) 0 0
\(757\) −5.71345 19.5828i −0.207659 0.711749i −0.995405 0.0957493i \(-0.969475\pi\)
0.787747 0.615999i \(-0.211248\pi\)
\(758\) 0 0
\(759\) −19.5001 25.0023i −0.707808 0.907525i
\(760\) 0 0
\(761\) 6.56857 + 17.4732i 0.238110 + 0.633401i 0.999896 0.0144278i \(-0.00459267\pi\)
−0.761786 + 0.647829i \(0.775677\pi\)
\(762\) 0 0
\(763\) 7.98915 5.09556i 0.289227 0.184472i
\(764\) 0 0
\(765\) −0.0475337 0.0109845i −0.00171858 0.000397147i
\(766\) 0 0
\(767\) 0.853097 2.03231i 0.0308035 0.0733824i
\(768\) 0 0
\(769\) 0.177905 + 1.87447i 0.00641543 + 0.0675951i 0.998160 0.0606331i \(-0.0193120\pi\)
−0.991745 + 0.128228i \(0.959071\pi\)
\(770\) 0 0
\(771\) −40.3434 + 27.9338i −1.45293 + 1.00601i
\(772\) 0 0
\(773\) 0.0574883 + 0.0503358i 0.00206771 + 0.00181045i 0.659786 0.751454i \(-0.270647\pi\)
−0.657718 + 0.753264i \(0.728478\pi\)
\(774\) 0 0
\(775\) −13.1785 9.12482i −0.473386 0.327773i
\(776\) 0 0
\(777\) 15.7346 + 10.0357i 0.564474 + 0.360027i
\(778\) 0 0
\(779\) −3.58097 + 26.8726i −0.128302 + 0.962811i
\(780\) 0 0
\(781\) −12.7041 + 20.7753i −0.454589 + 0.743400i
\(782\) 0 0
\(783\) 4.57684 + 4.66429i 0.163563 + 0.166688i
\(784\) 0 0
\(785\) −5.70027 + 26.9850i −0.203451 + 0.963137i
\(786\) 0 0
\(787\) 26.1774 46.6913i 0.933124 1.66437i 0.205185 0.978723i \(-0.434220\pi\)
0.727939 0.685642i \(-0.240478\pi\)
\(788\) 0 0
\(789\) 6.59874 + 26.2777i 0.234921 + 0.935511i
\(790\) 0 0
\(791\) −5.51668 8.29873i −0.196151 0.295069i
\(792\) 0 0
\(793\) −1.39921 4.19794i −0.0496875 0.149073i
\(794\) 0 0
\(795\) −10.9582 1.24969i −0.388646 0.0443220i
\(796\) 0 0