Properties

Label 192.3.l.a.79.5
Level $192$
Weight $3$
Character 192.79
Analytic conductor $5.232$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.23162107572\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 79.5
Root \(1.84258 - 0.777752i\) of defining polynomial
Character \(\chi\) \(=\) 192.79
Dual form 192.3.l.a.175.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 1.22474i) q^{3} +(-4.78830 - 4.78830i) q^{5} +10.3302 q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 + 1.22474i) q^{3} +(-4.78830 - 4.78830i) q^{5} +10.3302 q^{7} +3.00000i q^{9} +(0.526169 - 0.526169i) q^{11} +(17.2840 - 17.2840i) q^{13} -11.7289i q^{15} +4.71650 q^{17} +(2.53604 + 2.53604i) q^{19} +(12.6519 + 12.6519i) q^{21} +12.5864 q^{23} +20.8557i q^{25} +(-3.67423 + 3.67423i) q^{27} +(-2.19683 + 2.19683i) q^{29} +28.0521i q^{31} +1.28884 q^{33} +(-49.4644 - 49.4644i) q^{35} +(-32.1128 - 32.1128i) q^{37} +42.3369 q^{39} +23.1145i q^{41} +(-4.79441 + 4.79441i) q^{43} +(14.3649 - 14.3649i) q^{45} -39.0095i q^{47} +57.7141 q^{49} +(5.77651 + 5.77651i) q^{51} +(-27.9768 - 27.9768i) q^{53} -5.03891 q^{55} +6.21200i q^{57} +(-79.8538 + 79.8538i) q^{59} +(-36.7762 + 36.7762i) q^{61} +30.9907i q^{63} -165.522 q^{65} +(10.9869 + 10.9869i) q^{67} +(15.4152 + 15.4152i) q^{69} -52.6605 q^{71} +67.8061i q^{73} +(-25.5429 + 25.5429i) q^{75} +(5.43545 - 5.43545i) q^{77} +56.4602i q^{79} -9.00000 q^{81} +(58.3697 + 58.3697i) q^{83} +(-22.5840 - 22.5840i) q^{85} -5.38110 q^{87} -131.566i q^{89} +(178.548 - 178.548i) q^{91} +(-34.3567 + 34.3567i) q^{93} -24.2866i q^{95} +60.9413 q^{97} +(1.57851 + 1.57851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} + 128q^{23} + 32q^{29} - 96q^{35} - 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} - 160q^{53} + 256q^{55} + 128q^{59} - 32q^{61} - 32q^{65} - 320q^{67} + 96q^{69} - 512q^{71} - 192q^{75} + 224q^{77} - 144q^{81} + 160q^{83} + 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 0 0
\(5\) −4.78830 4.78830i −0.957661 0.957661i 0.0414785 0.999139i \(-0.486793\pi\)
−0.999139 + 0.0414785i \(0.986793\pi\)
\(6\) 0 0
\(7\) 10.3302 1.47575 0.737875 0.674937i \(-0.235829\pi\)
0.737875 + 0.674937i \(0.235829\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 0.526169 0.526169i 0.0478335 0.0478335i −0.682785 0.730619i \(-0.739232\pi\)
0.730619 + 0.682785i \(0.239232\pi\)
\(12\) 0 0
\(13\) 17.2840 17.2840i 1.32953 1.32953i 0.423761 0.905774i \(-0.360710\pi\)
0.905774 0.423761i \(-0.139290\pi\)
\(14\) 0 0
\(15\) 11.7289i 0.781927i
\(16\) 0 0
\(17\) 4.71650 0.277441 0.138721 0.990332i \(-0.455701\pi\)
0.138721 + 0.990332i \(0.455701\pi\)
\(18\) 0 0
\(19\) 2.53604 + 2.53604i 0.133476 + 0.133476i 0.770688 0.637213i \(-0.219913\pi\)
−0.637213 + 0.770688i \(0.719913\pi\)
\(20\) 0 0
\(21\) 12.6519 + 12.6519i 0.602472 + 0.602472i
\(22\) 0 0
\(23\) 12.5864 0.547236 0.273618 0.961838i \(-0.411780\pi\)
0.273618 + 0.961838i \(0.411780\pi\)
\(24\) 0 0
\(25\) 20.8557i 0.834229i
\(26\) 0 0
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) −2.19683 + 2.19683i −0.0757526 + 0.0757526i −0.743968 0.668215i \(-0.767058\pi\)
0.668215 + 0.743968i \(0.267058\pi\)
\(30\) 0 0
\(31\) 28.0521i 0.904908i 0.891788 + 0.452454i \(0.149451\pi\)
−0.891788 + 0.452454i \(0.850549\pi\)
\(32\) 0 0
\(33\) 1.28884 0.0390559
\(34\) 0 0
\(35\) −49.4644 49.4644i −1.41327 1.41327i
\(36\) 0 0
\(37\) −32.1128 32.1128i −0.867914 0.867914i 0.124327 0.992241i \(-0.460323\pi\)
−0.992241 + 0.124327i \(0.960323\pi\)
\(38\) 0 0
\(39\) 42.3369 1.08556
\(40\) 0 0
\(41\) 23.1145i 0.563768i 0.959449 + 0.281884i \(0.0909593\pi\)
−0.959449 + 0.281884i \(0.909041\pi\)
\(42\) 0 0
\(43\) −4.79441 + 4.79441i −0.111498 + 0.111498i −0.760655 0.649157i \(-0.775122\pi\)
0.649157 + 0.760655i \(0.275122\pi\)
\(44\) 0 0
\(45\) 14.3649 14.3649i 0.319220 0.319220i
\(46\) 0 0
\(47\) 39.0095i 0.829989i −0.909824 0.414994i \(-0.863784\pi\)
0.909824 0.414994i \(-0.136216\pi\)
\(48\) 0 0
\(49\) 57.7141 1.17784
\(50\) 0 0
\(51\) 5.77651 + 5.77651i 0.113265 + 0.113265i
\(52\) 0 0
\(53\) −27.9768 27.9768i −0.527864 0.527864i 0.392071 0.919935i \(-0.371759\pi\)
−0.919935 + 0.392071i \(0.871759\pi\)
\(54\) 0 0
\(55\) −5.03891 −0.0916166
\(56\) 0 0
\(57\) 6.21200i 0.108982i
\(58\) 0 0
\(59\) −79.8538 + 79.8538i −1.35345 + 1.35345i −0.471691 + 0.881764i \(0.656356\pi\)
−0.881764 + 0.471691i \(0.843644\pi\)
\(60\) 0 0
\(61\) −36.7762 + 36.7762i −0.602888 + 0.602888i −0.941078 0.338190i \(-0.890185\pi\)
0.338190 + 0.941078i \(0.390185\pi\)
\(62\) 0 0
\(63\) 30.9907i 0.491917i
\(64\) 0 0
\(65\) −165.522 −2.54649
\(66\) 0 0
\(67\) 10.9869 + 10.9869i 0.163984 + 0.163984i 0.784329 0.620345i \(-0.213008\pi\)
−0.620345 + 0.784329i \(0.713008\pi\)
\(68\) 0 0
\(69\) 15.4152 + 15.4152i 0.223408 + 0.223408i
\(70\) 0 0
\(71\) −52.6605 −0.741697 −0.370849 0.928693i \(-0.620933\pi\)
−0.370849 + 0.928693i \(0.620933\pi\)
\(72\) 0 0
\(73\) 67.8061i 0.928850i 0.885612 + 0.464425i \(0.153739\pi\)
−0.885612 + 0.464425i \(0.846261\pi\)
\(74\) 0 0
\(75\) −25.5429 + 25.5429i −0.340573 + 0.340573i
\(76\) 0 0
\(77\) 5.43545 5.43545i 0.0705903 0.0705903i
\(78\) 0 0
\(79\) 56.4602i 0.714686i 0.933973 + 0.357343i \(0.116317\pi\)
−0.933973 + 0.357343i \(0.883683\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 58.3697 + 58.3697i 0.703249 + 0.703249i 0.965107 0.261857i \(-0.0843349\pi\)
−0.261857 + 0.965107i \(0.584335\pi\)
\(84\) 0 0
\(85\) −22.5840 22.5840i −0.265694 0.265694i
\(86\) 0 0
\(87\) −5.38110 −0.0618518
\(88\) 0 0
\(89\) 131.566i 1.47827i −0.673558 0.739135i \(-0.735235\pi\)
0.673558 0.739135i \(-0.264765\pi\)
\(90\) 0 0
\(91\) 178.548 178.548i 1.96206 1.96206i
\(92\) 0 0
\(93\) −34.3567 + 34.3567i −0.369427 + 0.369427i
\(94\) 0 0
\(95\) 24.2866i 0.255649i
\(96\) 0 0
\(97\) 60.9413 0.628261 0.314131 0.949380i \(-0.398287\pi\)
0.314131 + 0.949380i \(0.398287\pi\)
\(98\) 0 0
\(99\) 1.57851 + 1.57851i 0.0159445 + 0.0159445i
\(100\) 0 0
\(101\) 109.986 + 109.986i 1.08897 + 1.08897i 0.995635 + 0.0933326i \(0.0297520\pi\)
0.0933326 + 0.995635i \(0.470248\pi\)
\(102\) 0 0
\(103\) −173.295 −1.68248 −0.841239 0.540663i \(-0.818174\pi\)
−0.841239 + 0.540663i \(0.818174\pi\)
\(104\) 0 0
\(105\) 121.162i 1.15393i
\(106\) 0 0
\(107\) 25.4747 25.4747i 0.238081 0.238081i −0.577974 0.816055i \(-0.696156\pi\)
0.816055 + 0.577974i \(0.196156\pi\)
\(108\) 0 0
\(109\) 33.0605 33.0605i 0.303307 0.303307i −0.538999 0.842306i \(-0.681197\pi\)
0.842306 + 0.538999i \(0.181197\pi\)
\(110\) 0 0
\(111\) 78.6600i 0.708649i
\(112\) 0 0
\(113\) 140.159 1.24034 0.620171 0.784466i \(-0.287063\pi\)
0.620171 + 0.784466i \(0.287063\pi\)
\(114\) 0 0
\(115\) −60.2677 60.2677i −0.524067 0.524067i
\(116\) 0 0
\(117\) 51.8519 + 51.8519i 0.443178 + 0.443178i
\(118\) 0 0
\(119\) 48.7226 0.409434
\(120\) 0 0
\(121\) 120.446i 0.995424i
\(122\) 0 0
\(123\) −28.3093 + 28.3093i −0.230157 + 0.230157i
\(124\) 0 0
\(125\) −19.8441 + 19.8441i −0.158752 + 0.158752i
\(126\) 0 0
\(127\) 40.8458i 0.321620i −0.986985 0.160810i \(-0.948589\pi\)
0.986985 0.160810i \(-0.0514107\pi\)
\(128\) 0 0
\(129\) −11.7439 −0.0910377
\(130\) 0 0
\(131\) 75.0168 + 75.0168i 0.572647 + 0.572647i 0.932867 0.360220i \(-0.117298\pi\)
−0.360220 + 0.932867i \(0.617298\pi\)
\(132\) 0 0
\(133\) 26.1979 + 26.1979i 0.196977 + 0.196977i
\(134\) 0 0
\(135\) 35.1867 0.260642
\(136\) 0 0
\(137\) 134.028i 0.978308i −0.872197 0.489154i \(-0.837306\pi\)
0.872197 0.489154i \(-0.162694\pi\)
\(138\) 0 0
\(139\) −22.8798 + 22.8798i −0.164603 + 0.164603i −0.784602 0.619999i \(-0.787133\pi\)
0.619999 + 0.784602i \(0.287133\pi\)
\(140\) 0 0
\(141\) 47.7767 47.7767i 0.338842 0.338842i
\(142\) 0 0
\(143\) 18.1885i 0.127193i
\(144\) 0 0
\(145\) 21.0381 0.145091
\(146\) 0 0
\(147\) 70.6850 + 70.6850i 0.480850 + 0.480850i
\(148\) 0 0
\(149\) −9.32124 9.32124i −0.0625587 0.0625587i 0.675135 0.737694i \(-0.264085\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(150\) 0 0
\(151\) 50.5403 0.334704 0.167352 0.985897i \(-0.446478\pi\)
0.167352 + 0.985897i \(0.446478\pi\)
\(152\) 0 0
\(153\) 14.1495i 0.0924803i
\(154\) 0 0
\(155\) 134.322 134.322i 0.866595 0.866595i
\(156\) 0 0
\(157\) −95.8844 + 95.8844i −0.610729 + 0.610729i −0.943136 0.332407i \(-0.892139\pi\)
0.332407 + 0.943136i \(0.392139\pi\)
\(158\) 0 0
\(159\) 68.5288i 0.430999i
\(160\) 0 0
\(161\) 130.021 0.807584
\(162\) 0 0
\(163\) 140.885 + 140.885i 0.864324 + 0.864324i 0.991837 0.127513i \(-0.0406994\pi\)
−0.127513 + 0.991837i \(0.540699\pi\)
\(164\) 0 0
\(165\) −6.17138 6.17138i −0.0374023 0.0374023i
\(166\) 0 0
\(167\) 107.849 0.645800 0.322900 0.946433i \(-0.395342\pi\)
0.322900 + 0.946433i \(0.395342\pi\)
\(168\) 0 0
\(169\) 428.470i 2.53533i
\(170\) 0 0
\(171\) −7.60811 + 7.60811i −0.0444919 + 0.0444919i
\(172\) 0 0
\(173\) −53.8845 + 53.8845i −0.311471 + 0.311471i −0.845479 0.534008i \(-0.820685\pi\)
0.534008 + 0.845479i \(0.320685\pi\)
\(174\) 0 0
\(175\) 215.445i 1.23111i
\(176\) 0 0
\(177\) −195.601 −1.10509
\(178\) 0 0
\(179\) −104.178 104.178i −0.582002 0.582002i 0.353451 0.935453i \(-0.385008\pi\)
−0.935453 + 0.353451i \(0.885008\pi\)
\(180\) 0 0
\(181\) −205.498 205.498i −1.13535 1.13535i −0.989274 0.146073i \(-0.953336\pi\)
−0.146073 0.989274i \(-0.546664\pi\)
\(182\) 0 0
\(183\) −90.0828 −0.492256
\(184\) 0 0
\(185\) 307.532i 1.66233i
\(186\) 0 0
\(187\) 2.48167 2.48167i 0.0132710 0.0132710i
\(188\) 0 0
\(189\) −37.9558 + 37.9558i −0.200824 + 0.200824i
\(190\) 0 0
\(191\) 248.255i 1.29977i 0.760034 + 0.649883i \(0.225182\pi\)
−0.760034 + 0.649883i \(0.774818\pi\)
\(192\) 0 0
\(193\) −129.921 −0.673166 −0.336583 0.941654i \(-0.609271\pi\)
−0.336583 + 0.941654i \(0.609271\pi\)
\(194\) 0 0
\(195\) −202.722 202.722i −1.03960 1.03960i
\(196\) 0 0
\(197\) 237.001 + 237.001i 1.20305 + 1.20305i 0.973234 + 0.229816i \(0.0738123\pi\)
0.229816 + 0.973234i \(0.426188\pi\)
\(198\) 0 0
\(199\) −246.508 −1.23873 −0.619366 0.785102i \(-0.712610\pi\)
−0.619366 + 0.785102i \(0.712610\pi\)
\(200\) 0 0
\(201\) 26.9123i 0.133892i
\(202\) 0 0
\(203\) −22.6938 + 22.6938i −0.111792 + 0.111792i
\(204\) 0 0
\(205\) 110.679 110.679i 0.539898 0.539898i
\(206\) 0 0
\(207\) 37.7593i 0.182412i
\(208\) 0 0
\(209\) 2.66877 0.0127692
\(210\) 0 0
\(211\) 13.4139 + 13.4139i 0.0635728 + 0.0635728i 0.738178 0.674606i \(-0.235686\pi\)
−0.674606 + 0.738178i \(0.735686\pi\)
\(212\) 0 0
\(213\) −64.4957 64.4957i −0.302797 0.302797i
\(214\) 0 0
\(215\) 45.9142 0.213554
\(216\) 0 0
\(217\) 289.786i 1.33542i
\(218\) 0 0
\(219\) −83.0451 + 83.0451i −0.379201 + 0.379201i
\(220\) 0 0
\(221\) 81.5197 81.5197i 0.368867 0.368867i
\(222\) 0 0
\(223\) 295.580i 1.32547i −0.748854 0.662735i \(-0.769396\pi\)
0.748854 0.662735i \(-0.230604\pi\)
\(224\) 0 0
\(225\) −62.5672 −0.278076
\(226\) 0 0
\(227\) 97.0742 + 97.0742i 0.427640 + 0.427640i 0.887824 0.460184i \(-0.152217\pi\)
−0.460184 + 0.887824i \(0.652217\pi\)
\(228\) 0 0
\(229\) 34.2565 + 34.2565i 0.149592 + 0.149592i 0.777936 0.628344i \(-0.216267\pi\)
−0.628344 + 0.777936i \(0.716267\pi\)
\(230\) 0 0
\(231\) 13.3141 0.0576367
\(232\) 0 0
\(233\) 62.8176i 0.269604i 0.990873 + 0.134802i \(0.0430398\pi\)
−0.990873 + 0.134802i \(0.956960\pi\)
\(234\) 0 0
\(235\) −186.789 + 186.789i −0.794848 + 0.794848i
\(236\) 0 0
\(237\) −69.1493 + 69.1493i −0.291769 + 0.291769i
\(238\) 0 0
\(239\) 355.910i 1.48916i −0.667532 0.744581i \(-0.732649\pi\)
0.667532 0.744581i \(-0.267351\pi\)
\(240\) 0 0
\(241\) 66.2545 0.274915 0.137458 0.990508i \(-0.456107\pi\)
0.137458 + 0.990508i \(0.456107\pi\)
\(242\) 0 0
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) −276.352 276.352i −1.12797 1.12797i
\(246\) 0 0
\(247\) 87.6655 0.354921
\(248\) 0 0
\(249\) 142.976i 0.574201i
\(250\) 0 0
\(251\) −325.395 + 325.395i −1.29640 + 1.29640i −0.365638 + 0.930757i \(0.619149\pi\)
−0.930757 + 0.365638i \(0.880851\pi\)
\(252\) 0 0
\(253\) 6.62259 6.62259i 0.0261762 0.0261762i
\(254\) 0 0
\(255\) 55.3193i 0.216939i
\(256\) 0 0
\(257\) −312.011 −1.21405 −0.607026 0.794682i \(-0.707638\pi\)
−0.607026 + 0.794682i \(0.707638\pi\)
\(258\) 0 0
\(259\) −331.733 331.733i −1.28082 1.28082i
\(260\) 0 0
\(261\) −6.59048 6.59048i −0.0252509 0.0252509i
\(262\) 0 0
\(263\) 168.163 0.639403 0.319702 0.947518i \(-0.396417\pi\)
0.319702 + 0.947518i \(0.396417\pi\)
\(264\) 0 0
\(265\) 267.923i 1.01103i
\(266\) 0 0
\(267\) 161.135 161.135i 0.603501 0.603501i
\(268\) 0 0
\(269\) 212.116 212.116i 0.788535 0.788535i −0.192719 0.981254i \(-0.561731\pi\)
0.981254 + 0.192719i \(0.0617306\pi\)
\(270\) 0 0
\(271\) 173.450i 0.640037i 0.947411 + 0.320019i \(0.103689\pi\)
−0.947411 + 0.320019i \(0.896311\pi\)
\(272\) 0 0
\(273\) 437.350 1.60202
\(274\) 0 0
\(275\) 10.9736 + 10.9736i 0.0399041 + 0.0399041i
\(276\) 0 0
\(277\) −38.4049 38.4049i −0.138646 0.138646i 0.634377 0.773023i \(-0.281257\pi\)
−0.773023 + 0.634377i \(0.781257\pi\)
\(278\) 0 0
\(279\) −84.1564 −0.301636
\(280\) 0 0
\(281\) 223.573i 0.795632i 0.917465 + 0.397816i \(0.130232\pi\)
−0.917465 + 0.397816i \(0.869768\pi\)
\(282\) 0 0
\(283\) −247.755 + 247.755i −0.875459 + 0.875459i −0.993061 0.117602i \(-0.962479\pi\)
0.117602 + 0.993061i \(0.462479\pi\)
\(284\) 0 0
\(285\) 29.7449 29.7449i 0.104368 0.104368i
\(286\) 0 0
\(287\) 238.778i 0.831980i
\(288\) 0 0
\(289\) −266.755 −0.923026
\(290\) 0 0
\(291\) 74.6376 + 74.6376i 0.256487 + 0.256487i
\(292\) 0 0
\(293\) −102.262 102.262i −0.349016 0.349016i 0.510727 0.859743i \(-0.329376\pi\)
−0.859743 + 0.510727i \(0.829376\pi\)
\(294\) 0 0
\(295\) 764.729 2.59230
\(296\) 0 0
\(297\) 3.86653i 0.0130186i
\(298\) 0 0
\(299\) 217.543 217.543i 0.727570 0.727570i
\(300\) 0 0
\(301\) −49.5275 + 49.5275i −0.164543 + 0.164543i
\(302\) 0 0
\(303\) 269.409i 0.889138i
\(304\) 0 0
\(305\) 352.191 1.15472
\(306\) 0 0
\(307\) −138.292 138.292i −0.450463 0.450463i 0.445045 0.895508i \(-0.353188\pi\)
−0.895508 + 0.445045i \(0.853188\pi\)
\(308\) 0 0
\(309\) −212.243 212.243i −0.686869 0.686869i
\(310\) 0 0
\(311\) −205.789 −0.661702 −0.330851 0.943683i \(-0.607336\pi\)
−0.330851 + 0.943683i \(0.607336\pi\)
\(312\) 0 0
\(313\) 223.861i 0.715209i −0.933873 0.357605i \(-0.883594\pi\)
0.933873 0.357605i \(-0.116406\pi\)
\(314\) 0 0
\(315\) 148.393 148.393i 0.471089 0.471089i
\(316\) 0 0
\(317\) −176.488 + 176.488i −0.556744 + 0.556744i −0.928379 0.371635i \(-0.878797\pi\)
0.371635 + 0.928379i \(0.378797\pi\)
\(318\) 0 0
\(319\) 2.31180i 0.00724703i
\(320\) 0 0
\(321\) 62.4000 0.194393
\(322\) 0 0
\(323\) 11.9612 + 11.9612i 0.0370316 + 0.0370316i
\(324\) 0 0
\(325\) 360.469 + 360.469i 1.10914 + 1.10914i
\(326\) 0 0
\(327\) 80.9813 0.247649
\(328\) 0 0
\(329\) 402.978i 1.22486i
\(330\) 0 0
\(331\) 183.939 183.939i 0.555706 0.555706i −0.372376 0.928082i \(-0.621457\pi\)
0.928082 + 0.372376i \(0.121457\pi\)
\(332\) 0 0
\(333\) 96.3384 96.3384i 0.289305 0.289305i
\(334\) 0 0
\(335\) 105.217i 0.314081i
\(336\) 0 0
\(337\) 12.7162 0.0377336 0.0188668 0.999822i \(-0.493994\pi\)
0.0188668 + 0.999822i \(0.493994\pi\)
\(338\) 0 0
\(339\) 171.659 + 171.659i 0.506368 + 0.506368i
\(340\) 0 0
\(341\) 14.7602 + 14.7602i 0.0432849 + 0.0432849i
\(342\) 0 0
\(343\) 90.0184 0.262444
\(344\) 0 0
\(345\) 147.625i 0.427899i
\(346\) 0 0
\(347\) 113.546 113.546i 0.327221 0.327221i −0.524308 0.851529i \(-0.675676\pi\)
0.851529 + 0.524308i \(0.175676\pi\)
\(348\) 0 0
\(349\) 90.9653 90.9653i 0.260645 0.260645i −0.564671 0.825316i \(-0.690997\pi\)
0.825316 + 0.564671i \(0.190997\pi\)
\(350\) 0 0
\(351\) 127.011i 0.361854i
\(352\) 0 0
\(353\) 36.2208 0.102609 0.0513043 0.998683i \(-0.483662\pi\)
0.0513043 + 0.998683i \(0.483662\pi\)
\(354\) 0 0
\(355\) 252.155 + 252.155i 0.710294 + 0.710294i
\(356\) 0 0
\(357\) 59.6727 + 59.6727i 0.167151 + 0.167151i
\(358\) 0 0
\(359\) −142.121 −0.395880 −0.197940 0.980214i \(-0.563425\pi\)
−0.197940 + 0.980214i \(0.563425\pi\)
\(360\) 0 0
\(361\) 348.137i 0.964369i
\(362\) 0 0
\(363\) −147.516 + 147.516i −0.406380 + 0.406380i
\(364\) 0 0
\(365\) 324.676 324.676i 0.889523 0.889523i
\(366\) 0 0
\(367\) 654.218i 1.78261i −0.453404 0.891305i \(-0.649791\pi\)
0.453404 0.891305i \(-0.350209\pi\)
\(368\) 0 0
\(369\) −69.3434 −0.187923
\(370\) 0 0
\(371\) −289.007 289.007i −0.778995 0.778995i
\(372\) 0 0
\(373\) 335.277 + 335.277i 0.898867 + 0.898867i 0.995336 0.0964690i \(-0.0307549\pi\)
−0.0964690 + 0.995336i \(0.530755\pi\)
\(374\) 0 0
\(375\) −48.6078 −0.129621
\(376\) 0 0
\(377\) 75.9397i 0.201432i
\(378\) 0 0
\(379\) 98.7497 98.7497i 0.260553 0.260553i −0.564725 0.825279i \(-0.691018\pi\)
0.825279 + 0.564725i \(0.191018\pi\)
\(380\) 0 0
\(381\) 50.0257 50.0257i 0.131301 0.131301i
\(382\) 0 0
\(383\) 156.144i 0.407687i 0.979003 + 0.203844i \(0.0653434\pi\)
−0.979003 + 0.203844i \(0.934657\pi\)
\(384\) 0 0
\(385\) −52.0532 −0.135203
\(386\) 0 0
\(387\) −14.3832 14.3832i −0.0371660 0.0371660i
\(388\) 0 0
\(389\) −391.047 391.047i −1.00526 1.00526i −0.999986 0.00527486i \(-0.998321\pi\)
−0.00527486 0.999986i \(-0.501679\pi\)
\(390\) 0 0
\(391\) 59.3639 0.151826
\(392\) 0 0
\(393\) 183.753i 0.467565i
\(394\) 0 0
\(395\) 270.349 270.349i 0.684427 0.684427i
\(396\) 0 0
\(397\) 243.862 243.862i 0.614262 0.614262i −0.329791 0.944054i \(-0.606978\pi\)
0.944054 + 0.329791i \(0.106978\pi\)
\(398\) 0 0
\(399\) 64.1715i 0.160831i
\(400\) 0 0
\(401\) −175.261 −0.437059 −0.218529 0.975830i \(-0.570126\pi\)
−0.218529 + 0.975830i \(0.570126\pi\)
\(402\) 0 0
\(403\) 484.852 + 484.852i 1.20311 + 1.20311i
\(404\) 0 0
\(405\) 43.0947 + 43.0947i 0.106407 + 0.106407i
\(406\) 0 0
\(407\) −33.7935 −0.0830307
\(408\) 0 0
\(409\) 44.4504i 0.108681i 0.998522 + 0.0543404i \(0.0173056\pi\)
−0.998522 + 0.0543404i \(0.982694\pi\)
\(410\) 0 0
\(411\) 164.150 164.150i 0.399393 0.399393i
\(412\) 0 0
\(413\) −824.910 + 824.910i −1.99736 + 1.99736i
\(414\) 0 0
\(415\) 558.984i 1.34695i
\(416\) 0 0
\(417\) −56.0438 −0.134398
\(418\) 0 0
\(419\) −14.9985 14.9985i −0.0357959 0.0357959i 0.688982 0.724778i \(-0.258058\pi\)
−0.724778 + 0.688982i \(0.758058\pi\)
\(420\) 0 0
\(421\) 312.907 + 312.907i 0.743247 + 0.743247i 0.973201 0.229954i \(-0.0738576\pi\)
−0.229954 + 0.973201i \(0.573858\pi\)
\(422\) 0 0
\(423\) 117.028 0.276663
\(424\) 0 0
\(425\) 98.3660i 0.231449i
\(426\) 0 0
\(427\) −379.907 + 379.907i −0.889712 + 0.889712i
\(428\) 0 0
\(429\) 22.2763 22.2763i 0.0519262 0.0519262i
\(430\) 0 0
\(431\) 532.400i 1.23527i 0.786466 + 0.617633i \(0.211908\pi\)
−0.786466 + 0.617633i \(0.788092\pi\)
\(432\) 0 0
\(433\) 553.451 1.27818 0.639089 0.769133i \(-0.279312\pi\)
0.639089 + 0.769133i \(0.279312\pi\)
\(434\) 0 0
\(435\) 25.7664 + 25.7664i 0.0592330 + 0.0592330i
\(436\) 0 0
\(437\) 31.9197 + 31.9197i 0.0730427 + 0.0730427i
\(438\) 0 0
\(439\) −645.291 −1.46991 −0.734956 0.678115i \(-0.762797\pi\)
−0.734956 + 0.678115i \(0.762797\pi\)
\(440\) 0 0
\(441\) 173.142i 0.392613i
\(442\) 0 0
\(443\) −315.833 + 315.833i −0.712941 + 0.712941i −0.967149 0.254208i \(-0.918185\pi\)
0.254208 + 0.967149i \(0.418185\pi\)
\(444\) 0 0
\(445\) −629.978 + 629.978i −1.41568 + 1.41568i
\(446\) 0 0
\(447\) 22.8323i 0.0510789i
\(448\) 0 0
\(449\) 218.589 0.486835 0.243417 0.969922i \(-0.421732\pi\)
0.243417 + 0.969922i \(0.421732\pi\)
\(450\) 0 0
\(451\) 12.1621 + 12.1621i 0.0269670 + 0.0269670i
\(452\) 0 0
\(453\) 61.8990 + 61.8990i 0.136642 + 0.136642i
\(454\) 0 0
\(455\) −1709.88 −3.75798
\(456\) 0 0
\(457\) 296.561i 0.648930i −0.945898 0.324465i \(-0.894816\pi\)
0.945898 0.324465i \(-0.105184\pi\)
\(458\) 0 0
\(459\) −17.3295 + 17.3295i −0.0377549 + 0.0377549i
\(460\) 0 0
\(461\) 118.061 118.061i 0.256097 0.256097i −0.567368 0.823465i \(-0.692038\pi\)
0.823465 + 0.567368i \(0.192038\pi\)
\(462\) 0 0
\(463\) 409.453i 0.884348i 0.896929 + 0.442174i \(0.145793\pi\)
−0.896929 + 0.442174i \(0.854207\pi\)
\(464\) 0 0
\(465\) 329.021 0.707572
\(466\) 0 0
\(467\) −494.764 494.764i −1.05945 1.05945i −0.998117 0.0613343i \(-0.980464\pi\)
−0.0613343 0.998117i \(-0.519536\pi\)
\(468\) 0 0
\(469\) 113.497 + 113.497i 0.241999 + 0.241999i
\(470\) 0 0
\(471\) −234.868 −0.498658
\(472\) 0 0
\(473\) 5.04534i 0.0106667i
\(474\) 0 0
\(475\) −52.8909 + 52.8909i −0.111349 + 0.111349i
\(476\) 0 0
\(477\) 83.9303 83.9303i 0.175955 0.175955i
\(478\) 0 0
\(479\) 558.806i 1.16661i −0.812254 0.583305i \(-0.801759\pi\)
0.812254 0.583305i \(-0.198241\pi\)
\(480\) 0 0
\(481\) −1110.07 −2.30784
\(482\) 0 0
\(483\) 159.243 + 159.243i 0.329695 + 0.329695i
\(484\) 0 0
\(485\) −291.806 291.806i −0.601661 0.601661i
\(486\) 0 0
\(487\) 361.328 0.741946 0.370973 0.928644i \(-0.379024\pi\)
0.370973 + 0.928644i \(0.379024\pi\)
\(488\) 0 0
\(489\) 345.096i 0.705718i
\(490\) 0 0
\(491\) 488.975 488.975i 0.995876 0.995876i −0.00411514 0.999992i \(-0.501310\pi\)
0.999992 + 0.00411514i \(0.00130989\pi\)
\(492\) 0 0
\(493\) −10.3613 + 10.3613i −0.0210169 + 0.0210169i
\(494\) 0 0
\(495\) 15.1167i 0.0305389i
\(496\) 0 0
\(497\) −543.996 −1.09456
\(498\) 0 0
\(499\) 102.895 + 102.895i 0.206203 + 0.206203i 0.802652 0.596448i \(-0.203422\pi\)
−0.596448 + 0.802652i \(0.703422\pi\)
\(500\) 0 0
\(501\) 132.087 + 132.087i 0.263647 + 0.263647i
\(502\) 0 0
\(503\) 881.975 1.75343 0.876715 0.481011i \(-0.159730\pi\)
0.876715 + 0.481011i \(0.159730\pi\)
\(504\) 0 0
\(505\) 1053.29i 2.08572i
\(506\) 0 0
\(507\) 524.767 524.767i 1.03504 1.03504i
\(508\) 0 0
\(509\) 161.639 161.639i 0.317563 0.317563i −0.530268 0.847830i \(-0.677909\pi\)
0.847830 + 0.530268i \(0.177909\pi\)
\(510\) 0 0
\(511\) 700.454i 1.37075i
\(512\) 0 0
\(513\) −18.6360 −0.0363275
\(514\) 0 0
\(515\) 829.791 + 829.791i 1.61124 + 1.61124i
\(516\) 0 0
\(517\) −20.5256 20.5256i −0.0397013 0.0397013i
\(518\) 0 0
\(519\) −131.989 −0.254315
\(520\) 0 0
\(521\) 763.931i 1.46628i −0.680078 0.733140i \(-0.738054\pi\)
0.680078 0.733140i \(-0.261946\pi\)
\(522\) 0 0
\(523\) −295.573 + 295.573i −0.565150 + 0.565150i −0.930766 0.365616i \(-0.880858\pi\)
0.365616 + 0.930766i \(0.380858\pi\)
\(524\) 0 0
\(525\) −263.865 + 263.865i −0.502600 + 0.502600i
\(526\) 0 0
\(527\) 132.308i 0.251059i
\(528\) 0 0
\(529\) −370.582 −0.700532
\(530\) 0 0
\(531\) −239.561 239.561i −0.451152 0.451152i
\(532\) 0 0
\(533\) 399.509 + 399.509i 0.749549 + 0.749549i
\(534\) 0 0
\(535\) −243.961 −0.456002
\(536\) 0 0
\(537\) 255.184i 0.475203i
\(538\) 0 0
\(539\) 30.3673 30.3673i 0.0563401 0.0563401i
\(540\) 0 0
\(541\) 243.037 243.037i 0.449236 0.449236i −0.445865 0.895100i \(-0.647104\pi\)
0.895100 + 0.445865i \(0.147104\pi\)
\(542\) 0 0
\(543\) 503.365i 0.927007i
\(544\) 0 0
\(545\) −316.607 −0.580931
\(546\) 0 0
\(547\) −424.574 424.574i −0.776187 0.776187i 0.202993 0.979180i \(-0.434933\pi\)
−0.979180 + 0.202993i \(0.934933\pi\)
\(548\) 0 0
\(549\) −110.328 110.328i −0.200963 0.200963i
\(550\) 0 0
\(551\) −11.1425 −0.0202223
\(552\) 0 0
\(553\) 583.248i 1.05470i
\(554\) 0 0
\(555\) −376.648 + 376.648i −0.678645 + 0.678645i
\(556\) 0 0
\(557\) −445.773 + 445.773i −0.800311 + 0.800311i −0.983144 0.182833i \(-0.941473\pi\)
0.182833 + 0.983144i \(0.441473\pi\)
\(558\) 0 0
\(559\) 165.733i 0.296481i
\(560\) 0 0
\(561\) 6.07883 0.0108357
\(562\) 0 0
\(563\) 529.295 + 529.295i 0.940133 + 0.940133i 0.998307 0.0581732i \(-0.0185276\pi\)
−0.0581732 + 0.998307i \(0.518528\pi\)
\(564\) 0 0
\(565\) −671.123 671.123i −1.18783 1.18783i
\(566\) 0 0
\(567\) −92.9722 −0.163972
\(568\) 0 0
\(569\) 346.814i 0.609516i 0.952430 + 0.304758i \(0.0985755\pi\)
−0.952430 + 0.304758i \(0.901424\pi\)
\(570\) 0 0
\(571\) 155.711 155.711i 0.272699 0.272699i −0.557487 0.830186i \(-0.688234\pi\)
0.830186 + 0.557487i \(0.188234\pi\)
\(572\) 0 0
\(573\) −304.049 + 304.049i −0.530627 + 0.530627i
\(574\) 0 0
\(575\) 262.499i 0.456520i
\(576\) 0 0
\(577\) 620.510 1.07541 0.537704 0.843134i \(-0.319292\pi\)
0.537704 + 0.843134i \(0.319292\pi\)
\(578\) 0 0
\(579\) −159.120 159.120i −0.274819 0.274819i
\(580\) 0 0
\(581\) 602.974 + 602.974i 1.03782 + 1.03782i
\(582\) 0 0
\(583\) −29.4410 −0.0504992
\(584\) 0 0
\(585\) 496.565i 0.848829i
\(586\) 0 0
\(587\) −561.656 + 561.656i −0.956825 + 0.956825i −0.999106 0.0422810i \(-0.986538\pi\)
0.0422810 + 0.999106i \(0.486538\pi\)
\(588\) 0 0
\(589\) −71.1413 + 71.1413i −0.120783 + 0.120783i
\(590\) 0 0
\(591\) 580.531i 0.982286i
\(592\) 0 0
\(593\) 851.739 1.43632 0.718161 0.695877i \(-0.244984\pi\)
0.718161 + 0.695877i \(0.244984\pi\)
\(594\) 0 0
\(595\) −233.299 233.299i −0.392099 0.392099i
\(596\) 0 0
\(597\) −301.909 301.909i −0.505710 0.505710i
\(598\) 0 0
\(599\) 1001.69 1.67228 0.836138 0.548519i \(-0.184808\pi\)
0.836138 + 0.548519i \(0.184808\pi\)
\(600\) 0 0
\(601\) 955.182i 1.58932i 0.607054 + 0.794661i \(0.292351\pi\)
−0.607054 + 0.794661i \(0.707649\pi\)
\(602\) 0 0
\(603\) −32.9607 + 32.9607i −0.0546612 + 0.0546612i
\(604\) 0 0
\(605\) 576.734 576.734i 0.953279 0.953279i
\(606\) 0 0
\(607\) 291.885i 0.480865i 0.970666 + 0.240432i \(0.0772892\pi\)
−0.970666 + 0.240432i \(0.922711\pi\)
\(608\) 0 0
\(609\) −55.5881 −0.0912777
\(610\) 0 0
\(611\) −674.238 674.238i −1.10350 1.10350i
\(612\) 0 0
\(613\) −332.933 332.933i −0.543121 0.543121i 0.381322 0.924442i \(-0.375469\pi\)
−0.924442 + 0.381322i \(0.875469\pi\)
\(614\) 0 0
\(615\) 271.107 0.440825
\(616\) 0 0
\(617\) 970.864i 1.57352i 0.617257 + 0.786762i \(0.288244\pi\)
−0.617257 + 0.786762i \(0.711756\pi\)
\(618\) 0 0
\(619\) 696.761 696.761i 1.12562 1.12562i 0.134744 0.990881i \(-0.456979\pi\)
0.990881 0.134744i \(-0.0430210\pi\)
\(620\) 0 0
\(621\) −46.2455 + 46.2455i −0.0744694 + 0.0744694i
\(622\) 0 0
\(623\) 1359.11i 2.18156i
\(624\) 0 0
\(625\) 711.432 1.13829
\(626\) 0 0
\(627\) 3.26856 + 3.26856i 0.00521301 + 0.00521301i
\(628\) 0 0
\(629\) −151.460 151.460i −0.240795 0.240795i
\(630\) 0 0
\(631\) 377.591 0.598401 0.299200 0.954190i \(-0.403280\pi\)
0.299200 + 0.954190i \(0.403280\pi\)
\(632\) 0 0
\(633\) 32.8571i 0.0519069i
\(634\) 0 0
\(635\) −195.582 + 195.582i −0.308003 + 0.308003i
\(636\) 0 0
\(637\) 997.527 997.527i 1.56598 1.56598i
\(638\) 0 0
\(639\) 157.981i 0.247232i
\(640\) 0 0
\(641\) 729.200 1.13760 0.568799 0.822477i \(-0.307408\pi\)
0.568799 + 0.822477i \(0.307408\pi\)
\(642\) 0 0
\(643\) −243.958 243.958i −0.379406 0.379406i 0.491482 0.870888i \(-0.336455\pi\)
−0.870888 + 0.491482i \(0.836455\pi\)
\(644\) 0 0
\(645\) 56.2332 + 56.2332i 0.0871832 + 0.0871832i
\(646\) 0 0
\(647\) 281.594 0.435230 0.217615 0.976035i \(-0.430172\pi\)
0.217615 + 0.976035i \(0.430172\pi\)
\(648\) 0 0
\(649\) 84.0331i 0.129481i
\(650\) 0 0
\(651\) −354.913 + 354.913i −0.545182 + 0.545182i
\(652\) 0 0
\(653\) 323.704 323.704i 0.495718 0.495718i −0.414384 0.910102i \(-0.636003\pi\)
0.910102 + 0.414384i \(0.136003\pi\)
\(654\) 0 0
\(655\) 718.407i 1.09680i
\(656\) 0 0
\(657\) −203.418 −0.309617
\(658\) 0 0
\(659\) −507.811 507.811i −0.770578 0.770578i 0.207629 0.978208i \(-0.433425\pi\)
−0.978208 + 0.207629i \(0.933425\pi\)
\(660\) 0 0
\(661\) 57.1593 + 57.1593i 0.0864741 + 0.0864741i 0.749021 0.662547i \(-0.230524\pi\)
−0.662547 + 0.749021i \(0.730524\pi\)
\(662\) 0 0
\(663\) 199.682 0.301179
\(664\) 0 0
\(665\) 250.887i 0.377274i
\(666\) 0 0
\(667\) −27.6502 + 27.6502i −0.0414546 + 0.0414546i
\(668\) 0 0
\(669\) 362.010 362.010i 0.541121 0.541121i
\(670\) 0 0
\(671\) 38.7009i 0.0576765i
\(672\) 0 0
\(673\) 1110.84 1.65059 0.825293 0.564705i \(-0.191010\pi\)
0.825293 + 0.564705i \(0.191010\pi\)
\(674\) 0 0
\(675\) −76.6288 76.6288i −0.113524 0.113524i
\(676\) 0 0
\(677\) 397.465 + 397.465i 0.587097 + 0.587097i 0.936844 0.349747i \(-0.113732\pi\)
−0.349747 + 0.936844i \(0.613732\pi\)
\(678\) 0 0
\(679\) 629.539 0.927156
\(680\) 0 0
\(681\) 237.782i 0.349166i
\(682\) 0 0
\(683\) 238.015 238.015i 0.348485 0.348485i −0.511060 0.859545i \(-0.670747\pi\)
0.859545 + 0.511060i \(0.170747\pi\)
\(684\) 0 0
\(685\) −641.768 + 641.768i −0.936887 + 0.936887i
\(686\) 0 0
\(687\) 83.9109i 0.122141i
\(688\) 0 0
\(689\) −967.099 −1.40363
\(690\) 0 0
\(691\) 685.172 + 685.172i 0.991565 + 0.991565i 0.999965 0.00839951i \(-0.00267368\pi\)
−0.00839951 + 0.999965i \(0.502674\pi\)
\(692\) 0 0
\(693\) 16.3064 + 16.3064i 0.0235301 + 0.0235301i
\(694\) 0 0
\(695\) 219.111 0.315267
\(696\) 0 0
\(697\) 109.019i 0.156412i
\(698\) 0 0
\(699\) −76.9356 + 76.9356i −0.110065 + 0.110065i
\(700\) 0 0
\(701\) 543.074 543.074i 0.774713 0.774713i −0.204214 0.978926i \(-0.565464\pi\)
0.978926 + 0.204214i \(0.0654637\pi\)
\(702\) 0 0
\(703\) 162.879i 0.231691i
\(704\) 0 0
\(705\) −457.538 −0.648991
\(706\) 0 0
\(707\) 1136.18 + 1136.18i 1.60704 + 1.60704i
\(708\) 0 0
\(709\) −488.019 488.019i −0.688320 0.688320i 0.273541 0.961860i \(-0.411805\pi\)
−0.961860 + 0.273541i \(0.911805\pi\)
\(710\) 0 0
\(711\) −169.381 −0.238229
\(712\) 0 0
\(713\) 353.076i 0.495198i
\(714\) 0 0
\(715\) −87.0923 + 87.0923i −0.121807 + 0.121807i
\(716\) 0 0
\(717\) 435.899 435.899i 0.607948 0.607948i
\(718\) 0 0
\(719\) 297.369i 0.413587i 0.978385 + 0.206793i \(0.0663028\pi\)
−0.978385 + 0.206793i \(0.933697\pi\)
\(720\) 0 0
\(721\) −1790.18 −2.48292
\(722\) 0 0
\(723\) 81.1449 + 81.1449i 0.112234 + 0.112234i
\(724\) 0 0
\(725\) −45.8164 45.8164i −0.0631950 0.0631950i
\(726\) 0 0
\(727\) −1158.85 −1.59402 −0.797009 0.603967i \(-0.793586\pi\)
−0.797009 + 0.603967i \(0.793586\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −22.6128 + 22.6128i −0.0309341 + 0.0309341i
\(732\) 0 0
\(733\) −348.835 + 348.835i −0.475901 + 0.475901i −0.903818 0.427917i \(-0.859248\pi\)
0.427917 + 0.903818i \(0.359248\pi\)
\(734\) 0 0
\(735\) 676.923i 0.920983i
\(736\) 0 0
\(737\) 11.5619 0.0156878
\(738\) 0 0
\(739\) −825.489 825.489i −1.11703 1.11703i −0.992174 0.124860i \(-0.960152\pi\)
−0.124860 0.992174i \(-0.539848\pi\)
\(740\) 0 0
\(741\) 107.368 + 107.368i 0.144896 + 0.144896i
\(742\) 0 0
\(743\) 899.725 1.21094 0.605468 0.795870i \(-0.292986\pi\)
0.605468 + 0.795870i \(0.292986\pi\)
\(744\) 0 0
\(745\) 89.2659i 0.119820i
\(746\) 0 0
\(747\) −175.109 + 175.109i −0.234416 + 0.234416i
\(748\) 0 0
\(749\) 263.160 263.160i 0.351348 0.351348i
\(750\) 0 0
\(751\) 80.4386i 0.107109i −0.998565 0.0535543i \(-0.982945\pi\)
0.998565 0.0535543i \(-0.0170550\pi\)
\(752\) 0 0
\(753\) −797.052 −1.05850
\(754\) 0 0
\(755\) −242.003 242.003i −0.320533 0.320533i
\(756\) 0 0
\(757\) 233.298 + 233.298i 0.308187 + 0.308187i 0.844206 0.536019i \(-0.180072\pi\)
−0.536019 + 0.844206i \(0.680072\pi\)
\(758\) 0 0
\(759\) 16.2220 0.0213728
\(760\) 0 0
\(761\) 56.1906i 0.0738378i 0.999318 + 0.0369189i \(0.0117543\pi\)
−0.999318 + 0.0369189i \(0.988246\pi\)
\(762\) 0 0
\(763\) 341.523 341.523i 0.447606 0.447606i
\(764\) 0 0
\(765\) 67.7521 67.7521i 0.0885648 0.0885648i
\(766\) 0 0
\(767\) 2760.38i 3.59893i
\(768\) 0 0
\(769\) 517.343 0.672748 0.336374 0.941728i \(-0.390799\pi\)
0.336374 + 0.941728i \(0.390799\pi\)
\(770\) 0 0
\(771\) −382.134 382.134i −0.495635 0.495635i
\(772\) 0 0
\(773\) −523.925 523.925i −0.677781 0.677781i 0.281716 0.959498i \(-0.409096\pi\)
−0.959498 + 0.281716i \(0.909096\pi\)
\(774\) 0 0
\(775\) −585.048 −0.754900
\(776\) 0 0
\(777\) 812.578i 1.04579i
\(778\) 0 0
\(779\) −58.6192 + 58.6192i −0.0752492 + 0.0752492i
\(780\) 0 0
\(781\) −27.7083 + 27.7083i −0.0354780 + 0.0354780i
\(782\) 0 0
\(783\) 16.1433i 0.0206173i
\(784\) 0 0
\(785\) 918.248 1.16974
\(786\) 0 0
\(787\) 46.6965 + 46.6965i 0.0593348 + 0.0593348i 0.736152 0.676817i \(-0.236641\pi\)
−0.676817 + 0.736152i \(0.736641\pi\)
\(788\) 0 0
\(789\) 205.957 + 205.957i 0.261035 + 0.261035i
\(790\) 0 0
\(791\) 1447.87 1.83044
\(792\) 0 0
\(793\) 1271.27i 1.60312i
\(794\) 0 0
\(795\) −328.137 + 328.137i