Properties

Label 804.2.y.b.73.3
Level 804
Weight 2
Character 804.73
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 73.3
Character \(\chi\) = 804.73
Dual form 804.2.y.b.793.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(0.443767 + 0.130302i) q^{5} +(4.44269 - 0.856259i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(0.443767 + 0.130302i) q^{5} +(4.44269 - 0.856259i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.933622 - 0.890207i) q^{11} +(-0.196786 + 4.13104i) q^{13} +(-0.302874 + 0.349535i) q^{15} +(4.79811 - 3.77327i) q^{17} +(-7.26908 - 1.40100i) q^{19} +(-1.06668 + 4.39692i) q^{21} +(6.65607 - 0.635578i) q^{23} +(-4.02632 - 2.58756i) q^{25} +(0.959493 - 0.281733i) q^{27} +(3.87782 - 6.71658i) q^{29} +(0.116266 + 2.44073i) q^{31} +(0.421920 + 1.21906i) q^{33} +(2.08309 + 0.198911i) q^{35} +(4.26157 + 7.38126i) q^{37} +(-3.67598 - 1.89510i) q^{39} +(-1.94660 - 0.779302i) q^{41} +(0.606865 + 4.22084i) q^{43} +(-0.192130 - 0.420706i) q^{45} +(6.09589 + 8.56048i) q^{47} +(12.5058 - 5.00656i) q^{49} +(1.43908 + 5.93198i) q^{51} +(-1.36818 + 9.51587i) q^{53} +(0.530306 - 0.273392i) q^{55} +(4.29408 - 6.03019i) q^{57} +(-3.19620 + 2.05407i) q^{59} +(-5.68475 - 5.42040i) q^{61} +(-3.55646 - 2.79683i) q^{63} +(-0.625610 + 1.80758i) q^{65} +(4.28813 + 6.97223i) q^{67} +(-2.18689 + 6.31861i) q^{69} +(8.96929 + 7.05353i) q^{71} +(1.07868 + 1.02851i) q^{73} +(4.02632 - 2.58756i) q^{75} +(3.38555 - 4.75434i) q^{77} +(0.150757 - 0.0777207i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-1.28651 - 5.30307i) q^{83} +(2.62091 - 1.04925i) q^{85} +(4.49871 + 6.31756i) q^{87} +(-7.14393 - 15.6430i) q^{89} +(2.66298 + 18.5215i) q^{91} +(-2.26847 - 0.908158i) q^{93} +(-3.04322 - 1.56889i) q^{95} +(-8.15980 - 14.1332i) q^{97} +(-1.28417 - 0.122623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{20}{33}\right)\) \(1\)

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
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) 0.443767 + 0.130302i 0.198459 + 0.0582727i 0.379451 0.925212i \(-0.376113\pi\)
−0.180993 + 0.983484i \(0.557931\pi\)
\(6\) 0 0
\(7\) 4.44269 0.856259i 1.67918 0.323635i 0.741452 0.671006i \(-0.234137\pi\)
0.937728 + 0.347370i \(0.112925\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) 0.933622 0.890207i 0.281498 0.268407i −0.536155 0.844120i \(-0.680124\pi\)
0.817652 + 0.575712i \(0.195275\pi\)
\(12\) 0 0
\(13\) −0.196786 + 4.13104i −0.0545786 + 1.14575i 0.790973 + 0.611851i \(0.209575\pi\)
−0.845551 + 0.533894i \(0.820728\pi\)
\(14\) 0 0
\(15\) −0.302874 + 0.349535i −0.0782018 + 0.0902497i
\(16\) 0 0
\(17\) 4.79811 3.77327i 1.16371 0.915153i 0.166231 0.986087i \(-0.446840\pi\)
0.997481 + 0.0709340i \(0.0225980\pi\)
\(18\) 0 0
\(19\) −7.26908 1.40100i −1.66764 0.321411i −0.733872 0.679288i \(-0.762289\pi\)
−0.933769 + 0.357877i \(0.883501\pi\)
\(20\) 0 0
\(21\) −1.06668 + 4.39692i −0.232769 + 0.959486i
\(22\) 0 0
\(23\) 6.65607 0.635578i 1.38789 0.132527i 0.625791 0.779991i \(-0.284776\pi\)
0.762096 + 0.647464i \(0.224170\pi\)
\(24\) 0 0
\(25\) −4.02632 2.58756i −0.805263 0.517511i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) 3.87782 6.71658i 0.720093 1.24724i −0.240868 0.970558i \(-0.577432\pi\)
0.960962 0.276681i \(-0.0892344\pi\)
\(30\) 0 0
\(31\) 0.116266 + 2.44073i 0.0208821 + 0.438369i 0.984964 + 0.172762i \(0.0552692\pi\)
−0.964082 + 0.265607i \(0.914428\pi\)
\(32\) 0 0
\(33\) 0.421920 + 1.21906i 0.0734468 + 0.212211i
\(34\) 0 0
\(35\) 2.08309 + 0.198911i 0.352107 + 0.0336221i
\(36\) 0 0
\(37\) 4.26157 + 7.38126i 0.700598 + 1.21347i 0.968257 + 0.249958i \(0.0804167\pi\)
−0.267659 + 0.963514i \(0.586250\pi\)
\(38\) 0 0
\(39\) −3.67598 1.89510i −0.588628 0.303459i
\(40\) 0 0
\(41\) −1.94660 0.779302i −0.304008 0.121707i 0.214643 0.976693i \(-0.431141\pi\)
−0.518651 + 0.854986i \(0.673566\pi\)
\(42\) 0 0
\(43\) 0.606865 + 4.22084i 0.0925461 + 0.643672i 0.982312 + 0.187254i \(0.0599588\pi\)
−0.889765 + 0.456418i \(0.849132\pi\)
\(44\) 0 0
\(45\) −0.192130 0.420706i −0.0286411 0.0627152i
\(46\) 0 0
\(47\) 6.09589 + 8.56048i 0.889177 + 1.24867i 0.967787 + 0.251769i \(0.0810122\pi\)
−0.0786106 + 0.996905i \(0.525048\pi\)
\(48\) 0 0
\(49\) 12.5058 5.00656i 1.78654 0.715222i
\(50\) 0 0
\(51\) 1.43908 + 5.93198i 0.201512 + 0.830644i
\(52\) 0 0
\(53\) −1.36818 + 9.51587i −0.187933 + 1.30711i 0.649414 + 0.760435i \(0.275014\pi\)
−0.837348 + 0.546671i \(0.815895\pi\)
\(54\) 0 0
\(55\) 0.530306 0.273392i 0.0715065 0.0368642i
\(56\) 0 0
\(57\) 4.29408 6.03019i 0.568765 0.798718i
\(58\) 0 0
\(59\) −3.19620 + 2.05407i −0.416110 + 0.267417i −0.731901 0.681411i \(-0.761366\pi\)
0.315791 + 0.948829i \(0.397730\pi\)
\(60\) 0 0
\(61\) −5.68475 5.42040i −0.727858 0.694011i 0.232558 0.972583i \(-0.425291\pi\)
−0.960415 + 0.278572i \(0.910139\pi\)
\(62\) 0 0
\(63\) −3.55646 2.79683i −0.448072 0.352368i
\(64\) 0 0
\(65\) −0.625610 + 1.80758i −0.0775973 + 0.224203i
\(66\) 0 0
\(67\) 4.28813 + 6.97223i 0.523879 + 0.851793i
\(68\) 0 0
\(69\) −2.18689 + 6.31861i −0.263271 + 0.760671i
\(70\) 0 0
\(71\) 8.96929 + 7.05353i 1.06446 + 0.837100i 0.987132 0.159906i \(-0.0511190\pi\)
0.0773270 + 0.997006i \(0.475361\pi\)
\(72\) 0 0
\(73\) 1.07868 + 1.02851i 0.126249 + 0.120379i 0.750574 0.660787i \(-0.229777\pi\)
−0.624324 + 0.781165i \(0.714626\pi\)
\(74\) 0 0
\(75\) 4.02632 2.58756i 0.464919 0.298785i
\(76\) 0 0
\(77\) 3.38555 4.75434i 0.385819 0.541807i
\(78\) 0 0
\(79\) 0.150757 0.0777207i 0.0169615 0.00874426i −0.449725 0.893167i \(-0.648478\pi\)
0.466686 + 0.884423i \(0.345448\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) −1.28651 5.30307i −0.141213 0.582088i −0.997813 0.0661061i \(-0.978942\pi\)
0.856600 0.515982i \(-0.172573\pi\)
\(84\) 0 0
\(85\) 2.62091 1.04925i 0.284277 0.113807i
\(86\) 0 0
\(87\) 4.49871 + 6.31756i 0.482313 + 0.677314i
\(88\) 0 0
\(89\) −7.14393 15.6430i −0.757256 1.65816i −0.752871 0.658168i \(-0.771332\pi\)
−0.00438449 0.999990i \(-0.501396\pi\)
\(90\) 0 0
\(91\) 2.66298 + 18.5215i 0.279157 + 1.94158i
\(92\) 0 0
\(93\) −2.26847 0.908158i −0.235229 0.0941716i
\(94\) 0 0
\(95\) −3.04322 1.56889i −0.312228 0.160965i
\(96\) 0 0
\(97\) −8.15980 14.1332i −0.828502 1.43501i −0.899213 0.437511i \(-0.855860\pi\)
0.0707110 0.997497i \(-0.477473\pi\)
\(98\) 0 0
\(99\) −1.28417 0.122623i −0.129064 0.0123241i
\(100\) 0 0
\(101\) −5.39764 15.5955i −0.537085 1.55181i −0.807988 0.589199i \(-0.799443\pi\)
0.270903 0.962607i \(-0.412678\pi\)
\(102\) 0 0
\(103\) 0.0750624 + 1.57575i 0.00739612 + 0.155264i 0.999544 + 0.0301939i \(0.00961247\pi\)
−0.992148 + 0.125070i \(0.960085\pi\)
\(104\) 0 0
\(105\) −1.04628 + 1.81222i −0.102107 + 0.176854i
\(106\) 0 0
\(107\) −8.44633 + 2.48007i −0.816538 + 0.239757i −0.663225 0.748420i \(-0.730813\pi\)
−0.153313 + 0.988178i \(0.548994\pi\)
\(108\) 0 0
\(109\) −10.1876 6.54718i −0.975797 0.627107i −0.0474704 0.998873i \(-0.515116\pi\)
−0.928326 + 0.371766i \(0.878752\pi\)
\(110\) 0 0
\(111\) −8.48455 + 0.810176i −0.805318 + 0.0768985i
\(112\) 0 0
\(113\) 1.27623 5.26069i 0.120058 0.494884i −0.879753 0.475431i \(-0.842292\pi\)
0.999811 0.0194535i \(-0.00619263\pi\)
\(114\) 0 0
\(115\) 3.03656 + 0.585250i 0.283161 + 0.0545748i
\(116\) 0 0
\(117\) 3.25090 2.55654i 0.300546 0.236352i
\(118\) 0 0
\(119\) 18.0856 20.8719i 1.65791 1.91333i
\(120\) 0 0
\(121\) −0.444219 + 9.32531i −0.0403836 + 0.847755i
\(122\) 0 0
\(123\) 1.51753 1.44696i 0.136831 0.130468i
\(124\) 0 0
\(125\) −2.96395 3.42059i −0.265104 0.305946i
\(126\) 0 0
\(127\) −9.46140 + 1.82353i −0.839563 + 0.161813i −0.590867 0.806769i \(-0.701214\pi\)
−0.248696 + 0.968582i \(0.580002\pi\)
\(128\) 0 0
\(129\) −4.09151 1.20138i −0.360238 0.105775i
\(130\) 0 0
\(131\) −2.89683 + 6.34317i −0.253097 + 0.554205i −0.992946 0.118568i \(-0.962170\pi\)
0.739849 + 0.672773i \(0.234897\pi\)
\(132\) 0 0
\(133\) −33.4939 −2.90429
\(134\) 0 0
\(135\) 0.462502 0.0398058
\(136\) 0 0
\(137\) −6.31222 + 13.8218i −0.539289 + 1.18088i 0.422318 + 0.906448i \(0.361217\pi\)
−0.961607 + 0.274431i \(0.911511\pi\)
\(138\) 0 0
\(139\) 1.70024 + 0.499236i 0.144213 + 0.0423446i 0.353042 0.935607i \(-0.385147\pi\)
−0.208830 + 0.977952i \(0.566965\pi\)
\(140\) 0 0
\(141\) −10.3192 + 1.98886i −0.869034 + 0.167493i
\(142\) 0 0
\(143\) 3.49376 + 4.03201i 0.292163 + 0.337174i
\(144\) 0 0
\(145\) 2.59603 2.47531i 0.215589 0.205563i
\(146\) 0 0
\(147\) −0.640962 + 13.4554i −0.0528657 + 1.10979i
\(148\) 0 0
\(149\) 3.84367 4.43583i 0.314886 0.363397i −0.576139 0.817351i \(-0.695441\pi\)
0.891025 + 0.453954i \(0.149987\pi\)
\(150\) 0 0
\(151\) −5.78676 + 4.55076i −0.470920 + 0.370335i −0.825234 0.564791i \(-0.808957\pi\)
0.354314 + 0.935126i \(0.384714\pi\)
\(152\) 0 0
\(153\) −5.99374 1.15520i −0.484565 0.0933923i
\(154\) 0 0
\(155\) −0.266437 + 1.09827i −0.0214007 + 0.0882149i
\(156\) 0 0
\(157\) 8.87704 0.847654i 0.708465 0.0676502i 0.265398 0.964139i \(-0.414497\pi\)
0.443066 + 0.896489i \(0.353891\pi\)
\(158\) 0 0
\(159\) −8.08758 5.19757i −0.641387 0.412194i
\(160\) 0 0
\(161\) 29.0267 8.52300i 2.28762 0.671707i
\(162\) 0 0
\(163\) 10.1322 17.5495i 0.793617 1.37459i −0.130096 0.991501i \(-0.541529\pi\)
0.923713 0.383084i \(-0.125138\pi\)
\(164\) 0 0
\(165\) 0.0283888 + 0.595955i 0.00221007 + 0.0463950i
\(166\) 0 0
\(167\) −5.49789 15.8851i −0.425440 1.22923i −0.930548 0.366171i \(-0.880669\pi\)
0.505108 0.863056i \(-0.331453\pi\)
\(168\) 0 0
\(169\) −4.08567 0.390134i −0.314282 0.0300103i
\(170\) 0 0
\(171\) 3.70143 + 6.41106i 0.283055 + 0.490266i
\(172\) 0 0
\(173\) 14.5688 + 7.51073i 1.10764 + 0.571030i 0.912225 0.409690i \(-0.134363\pi\)
0.195419 + 0.980720i \(0.437393\pi\)
\(174\) 0 0
\(175\) −20.1033 8.04815i −1.51967 0.608383i
\(176\) 0 0
\(177\) −0.540701 3.76066i −0.0406416 0.282668i
\(178\) 0 0
\(179\) −0.785313 1.71959i −0.0586970 0.128529i 0.878011 0.478641i \(-0.158871\pi\)
−0.936708 + 0.350113i \(0.886143\pi\)
\(180\) 0 0
\(181\) 5.55531 + 7.80134i 0.412923 + 0.579869i 0.967692 0.252135i \(-0.0811327\pi\)
−0.554769 + 0.832004i \(0.687193\pi\)
\(182\) 0 0
\(183\) 7.29210 2.91932i 0.539048 0.215802i
\(184\) 0 0
\(185\) 0.929354 + 3.83085i 0.0683275 + 0.281650i
\(186\) 0 0
\(187\) 1.12062 7.79412i 0.0819482 0.569962i
\(188\) 0 0
\(189\) 4.02150 2.07323i 0.292521 0.150805i
\(190\) 0 0
\(191\) −10.4437 + 14.6661i −0.755681 + 1.06121i 0.240217 + 0.970719i \(0.422781\pi\)
−0.995898 + 0.0904860i \(0.971158\pi\)
\(192\) 0 0
\(193\) −3.64693 + 2.34374i −0.262512 + 0.168706i −0.665276 0.746598i \(-0.731686\pi\)
0.402764 + 0.915304i \(0.368050\pi\)
\(194\) 0 0
\(195\) −1.38435 1.31997i −0.0991350 0.0945250i
\(196\) 0 0
\(197\) −21.2982 16.7491i −1.51743 1.19332i −0.920319 0.391169i \(-0.872071\pi\)
−0.597116 0.802155i \(-0.703687\pi\)
\(198\) 0 0
\(199\) −1.42737 + 4.12412i −0.101184 + 0.292351i −0.984219 0.176956i \(-0.943375\pi\)
0.883035 + 0.469307i \(0.155496\pi\)
\(200\) 0 0
\(201\) −8.12351 + 1.00425i −0.572988 + 0.0708346i
\(202\) 0 0
\(203\) 11.4768 33.1601i 0.805516 2.32739i
\(204\) 0 0
\(205\) −0.762294 0.599475i −0.0532409 0.0418691i
\(206\) 0 0
\(207\) −4.83914 4.61411i −0.336343 0.320703i
\(208\) 0 0
\(209\) −8.03375 + 5.16298i −0.555706 + 0.357131i
\(210\) 0 0
\(211\) −4.96489 + 6.97221i −0.341797 + 0.479987i −0.949318 0.314317i \(-0.898225\pi\)
0.607521 + 0.794303i \(0.292164\pi\)
\(212\) 0 0
\(213\) −10.1421 + 5.22861i −0.694925 + 0.358259i
\(214\) 0 0
\(215\) −0.280676 + 1.95215i −0.0191420 + 0.133135i
\(216\) 0 0
\(217\) 2.60644 + 10.7439i 0.176936 + 0.729342i
\(218\) 0 0
\(219\) −1.38367 + 0.553937i −0.0934996 + 0.0374316i
\(220\) 0 0
\(221\) 14.6434 + 20.5637i 0.985019 + 1.38327i
\(222\) 0 0
\(223\) 4.74986 + 10.4007i 0.318074 + 0.696485i 0.999369 0.0355244i \(-0.0113101\pi\)
−0.681295 + 0.732009i \(0.738583\pi\)
\(224\) 0 0
\(225\) 0.681132 + 4.73738i 0.0454088 + 0.315825i
\(226\) 0 0
\(227\) −23.1283 9.25918i −1.53508 0.614553i −0.558461 0.829531i \(-0.688608\pi\)
−0.976619 + 0.214978i \(0.931032\pi\)
\(228\) 0 0
\(229\) −15.8541 8.17334i −1.04767 0.540110i −0.153642 0.988127i \(-0.549100\pi\)
−0.894025 + 0.448017i \(0.852130\pi\)
\(230\) 0 0
\(231\) 2.91829 + 5.05463i 0.192009 + 0.332570i
\(232\) 0 0
\(233\) 18.4565 + 1.76238i 1.20913 + 0.115457i 0.680081 0.733137i \(-0.261945\pi\)
0.529044 + 0.848594i \(0.322551\pi\)
\(234\) 0 0
\(235\) 1.58971 + 4.59316i 0.103701 + 0.299625i
\(236\) 0 0
\(237\) 0.00807046 + 0.169420i 0.000524233 + 0.0110050i
\(238\) 0 0
\(239\) −14.5255 + 25.1589i −0.939576 + 1.62739i −0.173311 + 0.984867i \(0.555447\pi\)
−0.766264 + 0.642525i \(0.777887\pi\)
\(240\) 0 0
\(241\) −26.5766 + 7.80361i −1.71195 + 0.502674i −0.983266 0.182174i \(-0.941687\pi\)
−0.728686 + 0.684848i \(0.759868\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) 6.20201 0.592220i 0.396232 0.0378356i
\(246\) 0 0
\(247\) 7.21804 29.7532i 0.459273 1.89315i
\(248\) 0 0
\(249\) 5.35828 + 1.03272i 0.339567 + 0.0654462i
\(250\) 0 0
\(251\) 6.36959 5.00910i 0.402045 0.316172i −0.396581 0.918000i \(-0.629803\pi\)
0.798626 + 0.601828i \(0.205561\pi\)
\(252\) 0 0
\(253\) 5.64846 6.51867i 0.355116 0.409825i
\(254\) 0 0
\(255\) −0.134330 + 2.81993i −0.00841207 + 0.176591i
\(256\) 0 0
\(257\) 3.01175 2.87170i 0.187868 0.179131i −0.590308 0.807178i \(-0.700994\pi\)
0.778176 + 0.628047i \(0.216145\pi\)
\(258\) 0 0
\(259\) 25.2531 + 29.1437i 1.56915 + 1.81090i
\(260\) 0 0
\(261\) −7.61549 + 1.46777i −0.471387 + 0.0908524i
\(262\) 0 0
\(263\) −10.7030 3.14268i −0.659975 0.193786i −0.0654409 0.997856i \(-0.520845\pi\)
−0.594534 + 0.804070i \(0.702664\pi\)
\(264\) 0 0
\(265\) −1.84709 + 4.04456i −0.113466 + 0.248455i
\(266\) 0 0
\(267\) 17.1971 1.05245
\(268\) 0 0
\(269\) −25.5472 −1.55764 −0.778820 0.627247i \(-0.784182\pi\)
−0.778820 + 0.627247i \(0.784182\pi\)
\(270\) 0 0
\(271\) 8.35202 18.2884i 0.507349 1.11094i −0.466661 0.884436i \(-0.654543\pi\)
0.974010 0.226504i \(-0.0727295\pi\)
\(272\) 0 0
\(273\) −17.9540 5.27176i −1.08662 0.319061i
\(274\) 0 0
\(275\) −6.06252 + 1.16845i −0.365584 + 0.0704605i
\(276\) 0 0
\(277\) 0.698768 + 0.806422i 0.0419849 + 0.0484532i 0.776354 0.630298i \(-0.217067\pi\)
−0.734369 + 0.678751i \(0.762522\pi\)
\(278\) 0 0
\(279\) 1.76844 1.68621i 0.105874 0.100951i
\(280\) 0 0
\(281\) 1.32659 27.8486i 0.0791379 1.66131i −0.515182 0.857081i \(-0.672276\pi\)
0.594320 0.804229i \(-0.297421\pi\)
\(282\) 0 0
\(283\) −10.3806 + 11.9799i −0.617064 + 0.712129i −0.975147 0.221560i \(-0.928885\pi\)
0.358083 + 0.933690i \(0.383430\pi\)
\(284\) 0 0
\(285\) 2.69131 2.11647i 0.159420 0.125369i
\(286\) 0 0
\(287\) −9.31545 1.79541i −0.549873 0.105979i
\(288\) 0 0
\(289\) 4.77634 19.6883i 0.280961 1.15814i
\(290\) 0 0
\(291\) 16.2457 1.55128i 0.952340 0.0909374i
\(292\) 0 0
\(293\) 5.48403 + 3.52437i 0.320381 + 0.205896i 0.690939 0.722913i \(-0.257197\pi\)
−0.370558 + 0.928809i \(0.620834\pi\)
\(294\) 0 0
\(295\) −1.68602 + 0.495059i −0.0981637 + 0.0288235i
\(296\) 0 0
\(297\) 0.645004 1.11718i 0.0374269 0.0648253i
\(298\) 0 0
\(299\) 1.31578 + 27.6216i 0.0760935 + 1.59740i
\(300\) 0 0
\(301\) 6.31025 + 18.2323i 0.363717 + 1.05089i
\(302\) 0 0
\(303\) 16.4284 + 1.56872i 0.943786 + 0.0901207i
\(304\) 0 0
\(305\) −1.81642 3.14613i −0.104008 0.180147i
\(306\) 0 0
\(307\) 17.5881 + 9.06728i 1.00380 + 0.517497i 0.880083 0.474820i \(-0.157487\pi\)
0.123721 + 0.992317i \(0.460517\pi\)
\(308\) 0 0
\(309\) −1.46454 0.586313i −0.0833147 0.0333542i
\(310\) 0 0
\(311\) −1.03561 7.20282i −0.0587240 0.408435i −0.997888 0.0649644i \(-0.979307\pi\)
0.939164 0.343470i \(-0.111602\pi\)
\(312\) 0 0
\(313\) −11.7079 25.6367i −0.661768 1.44907i −0.880865 0.473367i \(-0.843038\pi\)
0.219097 0.975703i \(-0.429689\pi\)
\(314\) 0 0
\(315\) −1.21381 1.70456i −0.0683904 0.0960408i
\(316\) 0 0
\(317\) 3.58622 1.43571i 0.201422 0.0806372i −0.268758 0.963208i \(-0.586613\pi\)
0.470180 + 0.882570i \(0.344189\pi\)
\(318\) 0 0
\(319\) −2.35873 9.72281i −0.132063 0.544373i
\(320\) 0 0
\(321\) 1.25279 8.71331i 0.0699237 0.486330i
\(322\) 0 0
\(323\) −40.1642 + 20.7061i −2.23479 + 1.15212i
\(324\) 0 0
\(325\) 11.4816 16.1237i 0.636887 0.894382i
\(326\) 0 0
\(327\) 10.1876 6.54718i 0.563377 0.362060i
\(328\) 0 0
\(329\) 34.4122 + 32.8119i 1.89720 + 1.80898i
\(330\) 0 0
\(331\) −1.43272 1.12670i −0.0787495 0.0619293i 0.578008 0.816031i \(-0.303830\pi\)
−0.656758 + 0.754102i \(0.728073\pi\)
\(332\) 0 0
\(333\) 2.78765 8.05438i 0.152762 0.441377i
\(334\) 0 0
\(335\) 0.994438 + 3.65280i 0.0543319 + 0.199574i
\(336\) 0 0
\(337\) −7.66688 + 22.1520i −0.417642 + 1.20670i 0.518501 + 0.855077i \(0.326490\pi\)
−0.936143 + 0.351619i \(0.885631\pi\)
\(338\) 0 0
\(339\) 4.25513 + 3.34627i 0.231107 + 0.181744i
\(340\) 0 0
\(341\) 2.28131 + 2.17522i 0.123540 + 0.117795i
\(342\) 0 0
\(343\) 24.6289 15.8280i 1.32984 0.854633i
\(344\) 0 0
\(345\) −1.79380 + 2.51903i −0.0965747 + 0.135620i
\(346\) 0 0
\(347\) −11.4672 + 5.91176i −0.615592 + 0.317360i −0.737671 0.675161i \(-0.764074\pi\)
0.122079 + 0.992520i \(0.461044\pi\)
\(348\) 0 0
\(349\) −1.28213 + 8.91743i −0.0686310 + 0.477339i 0.926301 + 0.376785i \(0.122971\pi\)
−0.994932 + 0.100554i \(0.967939\pi\)
\(350\) 0 0
\(351\) 0.975035 + 4.01915i 0.0520435 + 0.214526i
\(352\) 0 0
\(353\) 18.7774 7.51735i 0.999422 0.400108i 0.186483 0.982458i \(-0.440291\pi\)
0.812938 + 0.582350i \(0.197867\pi\)
\(354\) 0 0
\(355\) 3.06119 + 4.29884i 0.162471 + 0.228159i
\(356\) 0 0
\(357\) 11.4727 + 25.1218i 0.607201 + 1.32958i
\(358\) 0 0
\(359\) −0.210547 1.46438i −0.0111122 0.0772873i 0.983511 0.180850i \(-0.0578848\pi\)
−0.994623 + 0.103563i \(0.966976\pi\)
\(360\) 0 0
\(361\) 33.2377 + 13.3064i 1.74935 + 0.700335i
\(362\) 0 0
\(363\) −8.29806 4.27795i −0.435535 0.224534i
\(364\) 0 0
\(365\) 0.344663 + 0.596974i 0.0180405 + 0.0312471i
\(366\) 0 0
\(367\) 16.4340 + 1.56926i 0.857848 + 0.0819145i 0.514704 0.857368i \(-0.327902\pi\)
0.343144 + 0.939283i \(0.388508\pi\)
\(368\) 0 0
\(369\) 0.685797 + 1.98148i 0.0357011 + 0.103152i
\(370\) 0 0
\(371\) 2.06967 + 43.4476i 0.107452 + 2.25569i
\(372\) 0 0
\(373\) −2.18468 + 3.78397i −0.113118 + 0.195927i −0.917026 0.398827i \(-0.869417\pi\)
0.803908 + 0.594754i \(0.202751\pi\)
\(374\) 0 0
\(375\) 4.34275 1.27515i 0.224258 0.0658482i
\(376\) 0 0
\(377\) 26.9834 + 17.3412i 1.38972 + 0.893116i
\(378\) 0 0
\(379\) 8.80222 0.840510i 0.452140 0.0431741i 0.133498 0.991049i \(-0.457379\pi\)
0.318642 + 0.947875i \(0.396773\pi\)
\(380\) 0 0
\(381\) 2.27166 9.36391i 0.116381 0.479728i
\(382\) 0 0
\(383\) −8.40094 1.61915i −0.429268 0.0827347i −0.0299593 0.999551i \(-0.509538\pi\)
−0.399309 + 0.916816i \(0.630750\pi\)
\(384\) 0 0
\(385\) 2.12189 1.66868i 0.108142 0.0850436i
\(386\) 0 0
\(387\) 2.79249 3.22270i 0.141950 0.163819i
\(388\) 0 0
\(389\) 0.850653 17.8574i 0.0431298 0.905407i −0.868826 0.495118i \(-0.835125\pi\)
0.911956 0.410289i \(-0.134572\pi\)
\(390\) 0 0
\(391\) 29.5383 28.1647i 1.49382 1.42435i
\(392\) 0 0
\(393\) −4.56656 5.27009i −0.230353 0.265841i
\(394\) 0 0
\(395\) 0.0770282 0.0148460i 0.00387571 0.000746981i
\(396\) 0 0
\(397\) 12.0951 + 3.55144i 0.607036 + 0.178242i 0.570783 0.821101i \(-0.306640\pi\)
0.0362526 + 0.999343i \(0.488458\pi\)
\(398\) 0 0
\(399\) 13.9139 30.4671i 0.696565 1.52526i
\(400\) 0 0
\(401\) −14.4486 −0.721526 −0.360763 0.932657i \(-0.617484\pi\)
−0.360763 + 0.932657i \(0.617484\pi\)
\(402\) 0 0
\(403\) −10.1057 −0.503399
\(404\) 0 0
\(405\) −0.192130 + 0.420706i −0.00954702 + 0.0209051i
\(406\) 0 0
\(407\) 10.5495 + 3.09763i 0.522921 + 0.153544i
\(408\) 0 0
\(409\) −38.0463 + 7.33283i −1.88127 + 0.362585i −0.994940 0.100469i \(-0.967966\pi\)
−0.886330 + 0.463054i \(0.846754\pi\)
\(410\) 0 0
\(411\) −9.95059 11.4836i −0.490826 0.566444i
\(412\) 0 0
\(413\) −12.4409 + 11.8624i −0.612177 + 0.583710i
\(414\) 0 0
\(415\) 0.120088 2.52096i 0.00589490 0.123749i
\(416\) 0 0
\(417\) −1.16043 + 1.33920i −0.0568263 + 0.0655811i
\(418\) 0 0
\(419\) 3.46307 2.72339i 0.169182 0.133046i −0.529978 0.848011i \(-0.677800\pi\)
0.699160 + 0.714965i \(0.253557\pi\)
\(420\) 0 0
\(421\) 20.5853 + 3.96749i 1.00327 + 0.193364i 0.664325 0.747444i \(-0.268719\pi\)
0.338941 + 0.940808i \(0.389931\pi\)
\(422\) 0 0
\(423\) 2.47762 10.2129i 0.120466 0.496568i
\(424\) 0 0
\(425\) −29.0823 + 2.77702i −1.41070 + 0.134705i
\(426\) 0 0
\(427\) −29.8969 19.2136i −1.44681 0.929809i
\(428\) 0 0
\(429\) −5.11901 + 1.50308i −0.247148 + 0.0725692i
\(430\) 0 0
\(431\) 14.3739 24.8963i 0.692366 1.19921i −0.278695 0.960380i \(-0.589902\pi\)
0.971061 0.238833i \(-0.0767648\pi\)
\(432\) 0 0
\(433\) −0.947341 19.8871i −0.0455263 0.955715i −0.899911 0.436074i \(-0.856369\pi\)
0.854385 0.519641i \(-0.173934\pi\)
\(434\) 0 0
\(435\) 1.17319 + 3.38972i 0.0562503 + 0.162524i
\(436\) 0 0
\(437\) −49.2740 4.70509i −2.35709 0.225075i
\(438\) 0 0
\(439\) 5.58970 + 9.68164i 0.266782 + 0.462079i 0.968029 0.250839i \(-0.0807064\pi\)
−0.701247 + 0.712918i \(0.747373\pi\)
\(440\) 0 0
\(441\) −11.9732 6.17263i −0.570154 0.293935i
\(442\) 0 0
\(443\) −7.66023 3.06670i −0.363949 0.145703i 0.182478 0.983210i \(-0.441588\pi\)
−0.546427 + 0.837507i \(0.684012\pi\)
\(444\) 0 0
\(445\) −1.13193 7.87273i −0.0536585 0.373203i
\(446\) 0 0
\(447\) 2.43826 + 5.33904i 0.115326 + 0.252528i
\(448\) 0 0
\(449\) 10.7143 + 15.0462i 0.505640 + 0.710072i 0.985953 0.167025i \(-0.0534161\pi\)
−0.480312 + 0.877097i \(0.659477\pi\)
\(450\) 0 0
\(451\) −2.51113 + 1.00531i −0.118245 + 0.0473380i
\(452\) 0 0
\(453\) −1.73561 7.15427i −0.0815459 0.336137i
\(454\) 0 0
\(455\) −1.23163 + 8.56621i −0.0577399 + 0.401590i
\(456\) 0 0
\(457\) 9.27409 4.78113i 0.433824 0.223652i −0.227460 0.973787i \(-0.573042\pi\)
0.661284 + 0.750136i \(0.270012\pi\)
\(458\) 0 0
\(459\) 3.54070 4.97221i 0.165265 0.232083i
\(460\) 0 0
\(461\) 29.5554 18.9941i 1.37653 0.884643i 0.377388 0.926055i \(-0.376822\pi\)
0.999142 + 0.0414125i \(0.0131858\pi\)
\(462\) 0 0
\(463\) −8.04027 7.66639i −0.373663 0.356287i 0.479857 0.877347i \(-0.340688\pi\)
−0.853520 + 0.521059i \(0.825537\pi\)
\(464\) 0 0
\(465\) −0.888337 0.698596i −0.0411956 0.0323966i
\(466\) 0 0
\(467\) −0.917338 + 2.65047i −0.0424493 + 0.122649i −0.964234 0.265054i \(-0.914610\pi\)
0.921784 + 0.387703i \(0.126731\pi\)
\(468\) 0 0
\(469\) 25.0209 + 27.3037i 1.15536 + 1.26077i
\(470\) 0 0
\(471\) −2.91660 + 8.42696i −0.134390 + 0.388294i
\(472\) 0 0
\(473\) 4.32400 + 3.40043i 0.198818 + 0.156352i
\(474\) 0 0
\(475\) 25.6424 + 24.4500i 1.17656 + 1.12184i
\(476\) 0 0
\(477\) 8.08758 5.19757i 0.370305 0.237981i
\(478\) 0 0
\(479\) 16.5546 23.2476i 0.756397 1.06221i −0.239427 0.970914i \(-0.576959\pi\)
0.995824 0.0912967i \(-0.0291012\pi\)
\(480\) 0 0
\(481\) −31.3309 + 16.1522i −1.42857 + 0.736478i
\(482\) 0 0
\(483\) −4.30532 + 29.9442i −0.195899 + 1.36251i
\(484\) 0 0
\(485\) −1.77947 7.33508i −0.0808016 0.333069i
\(486\) 0 0
\(487\) −11.4527 + 4.58496i −0.518971 + 0.207765i −0.616335 0.787484i \(-0.711383\pi\)
0.0973640 + 0.995249i \(0.468959\pi\)
\(488\) 0 0
\(489\) 11.7545 + 16.5069i 0.531559 + 0.746470i
\(490\) 0 0
\(491\) 5.39578 + 11.8151i 0.243508 + 0.533208i 0.991439 0.130568i \(-0.0416800\pi\)
−0.747931 + 0.663776i \(0.768953\pi\)
\(492\) 0 0
\(493\) −6.73730 46.8590i −0.303433 2.11042i
\(494\) 0 0
\(495\) −0.553893 0.221745i −0.0248956 0.00996670i
\(496\) 0 0
\(497\) 45.8875 + 23.6566i 2.05833 + 1.06115i
\(498\) 0 0
\(499\) −0.288377 0.499483i −0.0129095 0.0223599i 0.859498 0.511138i \(-0.170776\pi\)
−0.872408 + 0.488778i \(0.837443\pi\)
\(500\) 0 0
\(501\) 16.7335 + 1.59786i 0.747598 + 0.0713870i
\(502\) 0 0
\(503\) 0.338711 + 0.978642i 0.0151024 + 0.0436355i 0.952300 0.305163i \(-0.0987110\pi\)
−0.937198 + 0.348799i \(0.886590\pi\)
\(504\) 0 0
\(505\) −0.363179 7.62407i −0.0161613 0.339267i
\(506\) 0 0
\(507\) 2.05213 3.55439i 0.0911382 0.157856i
\(508\) 0 0
\(509\) 22.7176 6.67050i 1.00694 0.295665i 0.263640 0.964621i \(-0.415077\pi\)
0.743302 + 0.668956i \(0.233259\pi\)
\(510\) 0 0
\(511\) 5.67290 + 3.64575i 0.250954 + 0.161279i
\(512\) 0 0
\(513\) −7.36934 + 0.703686i −0.325364 + 0.0310685i
\(514\) 0 0
\(515\) −0.172013 + 0.709049i −0.00757981 + 0.0312444i
\(516\) 0 0
\(517\) 13.3119 + 2.56565i 0.585455 + 0.112837i
\(518\) 0 0
\(519\) −12.8841 + 10.1322i −0.565549 + 0.444753i
\(520\) 0 0
\(521\) −9.05968 + 10.4554i −0.396912 + 0.458061i −0.918666 0.395035i \(-0.870732\pi\)
0.521754 + 0.853096i \(0.325278\pi\)
\(522\) 0 0
\(523\) −2.11523 + 44.4042i −0.0924926 + 1.94166i 0.188757 + 0.982024i \(0.439554\pi\)
−0.281249 + 0.959635i \(0.590749\pi\)
\(524\) 0 0
\(525\) 15.6721 14.9433i 0.683985 0.652179i
\(526\) 0 0
\(527\) 9.76741 + 11.2722i 0.425475 + 0.491024i
\(528\) 0 0
\(529\) 21.3150 4.10813i 0.926739 0.178614i
\(530\) 0 0
\(531\) 3.64543 + 1.07039i 0.158198 + 0.0464512i
\(532\) 0 0
\(533\) 3.60240 7.88815i 0.156037 0.341674i
\(534\) 0 0
\(535\) −4.07136 −0.176020
\(536\) 0 0
\(537\) 1.89043 0.0815780
\(538\) 0 0
\(539\) 7.21879 15.8070i 0.310935 0.680854i
\(540\) 0 0
\(541\) 1.06666 + 0.313201i 0.0458595 + 0.0134656i 0.304582 0.952486i \(-0.401483\pi\)
−0.258722 + 0.965952i \(0.583301\pi\)
\(542\) 0 0
\(543\) −9.40411 + 1.81249i −0.403569 + 0.0777816i
\(544\) 0 0
\(545\) −3.66782 4.23289i −0.157112 0.181317i
\(546\) 0 0
\(547\) 3.18943 3.04112i 0.136370 0.130029i −0.618824 0.785529i \(-0.712391\pi\)
0.755195 + 0.655501i \(0.227542\pi\)
\(548\) 0 0
\(549\) −0.373744 + 7.84586i −0.0159510 + 0.334853i
\(550\) 0 0
\(551\) −37.5981 + 43.3905i −1.60173 + 1.84850i
\(552\) 0 0
\(553\) 0.603218 0.474376i 0.0256515 0.0201725i
\(554\) 0 0
\(555\) −3.87073 0.746022i −0.164303 0.0316669i
\(556\) 0 0
\(557\) −1.04329 + 4.30049i −0.0442056 + 0.182218i −0.989634 0.143612i \(-0.954128\pi\)
0.945429 + 0.325829i \(0.105644\pi\)
\(558\) 0 0
\(559\) −17.5559 + 1.67639i −0.742536 + 0.0709036i
\(560\) 0 0
\(561\) 6.62425 + 4.25715i 0.279676 + 0.179737i
\(562\) 0 0
\(563\) 2.47575 0.726946i 0.104340 0.0306371i −0.229146 0.973392i \(-0.573593\pi\)
0.333486 + 0.942755i \(0.391775\pi\)
\(564\) 0 0
\(565\) 1.25183 2.16823i 0.0526647 0.0912180i
\(566\) 0 0
\(567\) 0.215282 + 4.51933i 0.00904101 + 0.189794i
\(568\) 0 0
\(569\) 3.93655 + 11.3739i 0.165029 + 0.476819i 0.996947 0.0780787i \(-0.0248785\pi\)
−0.831918 + 0.554898i \(0.812757\pi\)
\(570\) 0 0
\(571\) −13.7686 1.31474i −0.576196 0.0550201i −0.197110 0.980381i \(-0.563156\pi\)
−0.379086 + 0.925361i \(0.623762\pi\)
\(572\) 0 0
\(573\) −9.00232 15.5925i −0.376077 0.651385i
\(574\) 0 0
\(575\) −28.4441 14.6639i −1.18620 0.611528i
\(576\) 0 0
\(577\) −6.05192 2.42282i −0.251945 0.100863i 0.242253 0.970213i \(-0.422114\pi\)
−0.494197 + 0.869350i \(0.664538\pi\)
\(578\) 0 0
\(579\) −0.616951 4.29099i −0.0256396 0.178327i
\(580\) 0 0
\(581\) −10.2564 22.4583i −0.425506 0.931729i
\(582\) 0 0
\(583\) 7.19374 + 10.1022i 0.297934 + 0.418390i
\(584\) 0 0
\(585\) 1.77576 0.710909i 0.0734188 0.0293925i
\(586\) 0 0
\(587\) 2.70415 + 11.1467i 0.111612 + 0.460072i 1.00000 0.000976996i \(0.000310988\pi\)
−0.888387 + 0.459095i \(0.848174\pi\)
\(588\) 0 0
\(589\) 2.57432 17.9048i 0.106073 0.737753i
\(590\) 0 0
\(591\) 24.0831 12.4157i 0.990647 0.510714i
\(592\) 0 0
\(593\) −5.04467 + 7.08425i −0.207160 + 0.290915i −0.905064 0.425276i \(-0.860177\pi\)
0.697904 + 0.716191i \(0.254116\pi\)
\(594\) 0 0
\(595\) 10.7454 6.90568i 0.440520 0.283105i
\(596\) 0 0
\(597\) −3.15848 3.01161i −0.129268 0.123257i
\(598\) 0 0
\(599\) −6.90627 5.43115i −0.282183 0.221911i 0.467028 0.884242i \(-0.345325\pi\)
−0.749211 + 0.662332i \(0.769567\pi\)
\(600\) 0 0
\(601\) 0.531721 1.53631i 0.0216894 0.0626673i −0.933637 0.358222i \(-0.883383\pi\)
0.955326 + 0.295554i \(0.0955044\pi\)
\(602\) 0 0
\(603\) 2.46113 7.80659i 0.100225 0.317909i
\(604\) 0 0
\(605\) −1.41223 + 4.08038i −0.0574155 + 0.165891i
\(606\) 0 0
\(607\) −5.07851 3.99379i −0.206131 0.162103i 0.509757 0.860318i \(-0.329735\pi\)
−0.715888 + 0.698216i \(0.753978\pi\)
\(608\) 0 0
\(609\) 25.3959 + 24.2149i 1.02909 + 0.981238i
\(610\) 0 0
\(611\) −36.5633 + 23.4978i −1.47919 + 0.950620i
\(612\) 0 0
\(613\) −11.6611 + 16.3757i −0.470986 + 0.661407i −0.979918 0.199400i \(-0.936101\pi\)
0.508933 + 0.860806i \(0.330040\pi\)
\(614\) 0 0
\(615\) 0.861970 0.444376i 0.0347580 0.0179190i
\(616\) 0 0
\(617\) −5.06202 + 35.2071i −0.203789 + 1.41738i 0.589121 + 0.808045i \(0.299474\pi\)
−0.792910 + 0.609339i \(0.791435\pi\)
\(618\) 0 0
\(619\) −3.33400 13.7429i −0.134005 0.552375i −0.998742 0.0501502i \(-0.984030\pi\)
0.864737 0.502225i \(-0.167485\pi\)
\(620\) 0 0
\(621\) 6.20739 2.48507i 0.249094 0.0997222i
\(622\) 0 0
\(623\) −45.1328 63.3802i −1.80821 2.53927i
\(624\) 0 0
\(625\) 9.07148 + 19.8638i 0.362859 + 0.794550i
\(626\) 0 0
\(627\) −1.35907 9.45254i −0.0542760 0.377498i
\(628\) 0 0
\(629\) 48.2990 + 19.3360i 1.92581 + 0.770976i
\(630\) 0 0
\(631\) 30.5792 + 15.7647i 1.21734 + 0.627583i 0.942596 0.333935i \(-0.108377\pi\)
0.274744 + 0.961517i \(0.411407\pi\)
\(632\) 0 0
\(633\) −4.27966 7.41258i −0.170101 0.294624i
\(634\) 0 0
\(635\) −4.43627 0.423612i −0.176048 0.0168105i
\(636\) 0 0
\(637\) 18.2213 + 52.6471i 0.721956 + 2.08595i
\(638\) 0 0
\(639\) −0.542936 11.3976i −0.0214782 0.450883i
\(640\) 0 0
\(641\) −17.8869 + 30.9810i −0.706490 + 1.22368i 0.259661 + 0.965700i \(0.416389\pi\)
−0.966151 + 0.257977i \(0.916944\pi\)
\(642\) 0 0
\(643\) 5.33839 1.56749i 0.210526 0.0618159i −0.174769 0.984609i \(-0.555918\pi\)
0.385295 + 0.922794i \(0.374100\pi\)
\(644\) 0 0
\(645\) −1.65914 1.06626i −0.0653285 0.0419841i
\(646\) 0 0
\(647\) 25.3901 2.42446i 0.998186 0.0953152i 0.416847 0.908977i \(-0.363135\pi\)
0.581339 + 0.813661i \(0.302529\pi\)
\(648\) 0 0
\(649\) −1.15549 + 4.76300i −0.0453570 + 0.186964i
\(650\) 0 0
\(651\) −10.8557 2.09227i −0.425469 0.0820025i
\(652\) 0 0
\(653\) 13.7580 10.8194i 0.538392 0.423396i −0.311583 0.950219i \(-0.600859\pi\)
0.849975 + 0.526823i \(0.176617\pi\)
\(654\) 0 0
\(655\) −2.11204 + 2.43743i −0.0825243 + 0.0952382i
\(656\) 0 0
\(657\) 0.0709175 1.48874i 0.00276676 0.0580814i
\(658\) 0 0
\(659\) −9.23905 + 8.80942i −0.359902 + 0.343166i −0.848358 0.529422i \(-0.822409\pi\)
0.488456 + 0.872588i \(0.337560\pi\)
\(660\) 0 0
\(661\) −24.4483 28.2148i −0.950928 1.09743i −0.995146 0.0984078i \(-0.968625\pi\)
0.0442180 0.999022i \(-0.485920\pi\)
\(662\) 0 0
\(663\) −24.7885 + 4.77759i −0.962705 + 0.185546i
\(664\) 0 0
\(665\) −14.8635 4.36431i −0.576381 0.169241i
\(666\) 0 0
\(667\) 21.5422 47.1707i 0.834116 1.82646i
\(668\) 0 0
\(669\) −11.4340 −0.442064
\(670\) 0 0
\(671\) −10.1327 −0.391168
\(672\) 0 0
\(673\) 6.50508 14.2441i 0.250752 0.549071i −0.741838 0.670579i \(-0.766046\pi\)
0.992590 + 0.121508i \(0.0387729\pi\)
\(674\) 0 0
\(675\) −4.59222 1.34840i −0.176755 0.0518999i
\(676\) 0 0
\(677\) −13.7574 + 2.65152i −0.528739 + 0.101906i −0.446632 0.894718i \(-0.647377\pi\)
−0.0821063 + 0.996624i \(0.526165\pi\)
\(678\) 0 0
\(679\) −48.3532 55.8025i −1.85562 2.14150i
\(680\) 0 0
\(681\) 18.0303 17.1918i 0.690922 0.658793i
\(682\) 0 0
\(683\) −0.0405241 + 0.850706i −0.00155061 + 0.0325514i −0.999510 0.0312999i \(-0.990035\pi\)
0.997959 + 0.0638513i \(0.0203383\pi\)
\(684\) 0 0
\(685\) −4.60216 + 5.31118i −0.175840 + 0.202930i
\(686\) 0 0
\(687\) 14.0208 11.0260i 0.534925 0.420670i
\(688\) 0 0
\(689\) −39.0413 7.52459i −1.48735 0.286664i
\(690\) 0 0
\(691\) 1.20962 4.98613i 0.0460162 0.189681i −0.944165 0.329474i \(-0.893129\pi\)
0.990181 + 0.139793i \(0.0446437\pi\)
\(692\) 0 0
\(693\) −5.81015 + 0.554802i −0.220709 + 0.0210752i
\(694\) 0 0
\(695\) 0.689459 + 0.443089i 0.0261527 + 0.0168073i
\(696\) 0 0
\(697\) −12.2805 + 3.60589i −0.465158 + 0.136583i
\(698\) 0 0
\(699\) −9.27022 + 16.0565i −0.350632 + 0.607313i
\(700\) 0 0
\(701\) 1.87467 + 39.3542i 0.0708054 + 1.48639i 0.702785 + 0.711402i \(0.251940\pi\)
−0.631980 + 0.774985i \(0.717757\pi\)
\(702\) 0 0
\(703\) −20.6366 59.6254i −0.778322 2.24881i
\(704\) 0 0
\(705\) −4.83848 0.462019i −0.182228 0.0174006i
\(706\) 0 0
\(707\) −37.3338 64.6641i −1.40408 2.43194i
\(708\) 0 0
\(709\) 9.71524 + 5.00855i 0.364863 + 0.188100i 0.630903 0.775862i \(-0.282685\pi\)
−0.266039 + 0.963962i \(0.585715\pi\)
\(710\) 0 0
\(711\) −0.157462 0.0630384i −0.00590530 0.00236412i
\(712\) 0 0
\(713\) 2.32515 + 16.1718i 0.0870777 + 0.605639i
\(714\) 0 0
\(715\) 1.02504 + 2.24452i 0.0383342 + 0.0839402i
\(716\) 0 0
\(717\) −16.8512 23.6642i −0.629320 0.883757i
\(718\) 0 0
\(719\) −38.6915 + 15.4897i −1.44295 + 0.577670i −0.955371 0.295409i \(-0.904544\pi\)
−0.487579 + 0.873079i \(0.662120\pi\)
\(720\) 0 0
\(721\) 1.68273 + 6.93632i 0.0626683 + 0.258322i
\(722\) 0 0
\(723\) 3.94193 27.4167i 0.146602 1.01964i
\(724\) 0 0
\(725\) −32.9929 + 17.0090i −1.22532 + 0.631699i
\(726\) 0 0
\(727\) 6.01515 8.44710i 0.223090 0.313286i −0.687828 0.725874i \(-0.741436\pi\)
0.910918 + 0.412588i \(0.135375\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) 18.8382 + 17.9622i 0.696756 + 0.664355i
\(732\) 0 0
\(733\) −18.1257 14.2542i −0.669488 0.526491i 0.224561 0.974460i \(-0.427905\pi\)
−0.894049 + 0.447969i \(0.852147\pi\)
\(734\) 0 0
\(735\) −2.03771 + 5.88757i −0.0751619 + 0.217166i
\(736\) 0 0
\(737\) 10.2102 + 2.69210i 0.376098 + 0.0991648i
\(738\) 0 0
\(739\) 4.86287 14.0503i 0.178884 0.516850i −0.819537 0.573026i \(-0.805769\pi\)
0.998421 + 0.0561756i \(0.0178907\pi\)
\(740\) 0 0
\(741\) 24.0660 + 18.9257i 0.884085 + 0.695252i
\(742\) 0 0
\(743\) 2.44962 + 2.33571i 0.0898678 + 0.0856888i 0.733682 0.679493i \(-0.237800\pi\)
−0.643814 + 0.765182i \(0.722649\pi\)
\(744\) 0 0
\(745\) 2.28369 1.46764i 0.0836680 0.0537701i
\(746\) 0 0
\(747\) −3.16531 + 4.44505i −0.115813 + 0.162636i
\(748\) 0 0
\(749\) −35.4009 + 18.2504i −1.29352 + 0.666856i
\(750\) 0 0
\(751\) −2.54757 + 17.7187i −0.0929622 + 0.646566i 0.889059 + 0.457793i \(0.151360\pi\)
−0.982021 + 0.188773i \(0.939549\pi\)
\(752\) 0 0
\(753\) 1.91042 + 7.87484i 0.0696194 + 0.286975i
\(754\) 0 0
\(755\) −3.16094 + 1.26545i −0.115039 + 0.0460545i
\(756\) 0 0
\(757\) 22.0340 + 30.9424i 0.800839 + 1.12462i 0.989776 + 0.142632i \(0.0455566\pi\)
−0.188936 + 0.981989i \(0.560504\pi\)
\(758\) 0 0
\(759\) 3.58314 + 7.84597i 0.130060 + 0.284791i
\(760\) 0 0
\(761\) −3.62480 25.2111i −0.131399 0.913900i −0.943733 0.330708i \(-0.892713\pi\)
0.812334 0.583192i \(-0.198197\pi\)
\(762\) 0 0
\(763\) −50.8665 20.3639i −1.84149 0.737222i
\(764\) 0 0
\(765\) −2.50930 1.29363i −0.0907239 0.0467714i
\(766\) 0 0
\(767\) −7.85650 13.6078i −0.283682 0.491351i
\(768\) 0 0
\(769\) −27.7762 2.65231i −1.00164 0.0956446i −0.418667 0.908140i \(-0.637503\pi\)
−0.582968 + 0.812495i \(0.698109\pi\)
\(770\) 0 0
\(771\) 1.36106 + 3.93253i 0.0490174 + 0.141627i
\(772\) 0 0
\(773\) 0.596720 + 12.5267i 0.0214625 + 0.450554i 0.983863 + 0.178921i \(0.0572606\pi\)
−0.962401 + 0.271633i \(0.912436\pi\)
\(774\) 0 0
\(775\) 5.84741 10.1280i 0.210045 0.363809i
\(776\) 0 0
\(777\) −37.0005 + 10.8643i −1.32739 + 0.389756i
\(778\)