Properties

Label 384.3.l.b.31.4
Level $384$
Weight $3$
Character 384.31
Analytic conductor $10.463$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
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 31.4
Root \(1.84258 - 0.777752i\) of defining polynomial
Character \(\chi\) \(=\) 384.31
Dual form 384.3.l.b.223.4

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) 4.78830 + 4.78830i 0.957661 + 0.957661i 0.999139 0.0414785i \(-0.0132068\pi\)
−0.0414785 + 0.999139i \(0.513207\pi\)
\(6\) 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 −0.730619 0.682785i \(-0.760768\pi\)
0.682785 + 0.730619i \(0.260768\pi\)
\(12\) 0 0
\(13\) −17.2840 + 17.2840i −1.32953 + 1.32953i −0.423761 + 0.905774i \(0.639290\pi\)
−0.905774 + 0.423761i \(0.860710\pi\)
\(14\) 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 0.637213 0.770688i \(-0.280087\pi\)
−0.770688 + 0.637213i \(0.780087\pi\)
\(20\) 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 −0.668215 0.743968i \(-0.732942\pi\)
0.743968 + 0.668215i \(0.232942\pi\)
\(30\) 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 0.992241 0.124327i \(-0.0396773\pi\)
−0.124327 + 0.992241i \(0.539677\pi\)
\(38\) 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 −0.649157 0.760655i \(-0.724878\pi\)
0.760655 + 0.649157i \(0.224878\pi\)
\(44\) 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 0.919935 0.392071i \(-0.128241\pi\)
−0.392071 + 0.919935i \(0.628241\pi\)
\(54\) 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 \(-0.343644\pi\)
0.881764 0.471691i \(-0.156356\pi\)
\(60\) 0 0
\(61\) 36.7762 36.7762i 0.602888 0.602888i −0.338190 0.941078i \(-0.609815\pi\)
0.941078 + 0.338190i \(0.109815\pi\)
\(62\) 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 0.620345 0.784329i \(-0.286992\pi\)
−0.784329 + 0.620345i \(0.786992\pi\)
\(68\) 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 0.261857 0.965107i \(-0.415665\pi\)
−0.965107 + 0.261857i \(0.915665\pi\)
\(84\) 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 \(-0.970248\pi\)
−0.0933326 0.995635i \(-0.529752\pi\)
\(102\) 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 −0.816055 0.577974i \(-0.803844\pi\)
0.577974 + 0.816055i \(0.303844\pi\)
\(108\) 0 0
\(109\) −33.0605 + 33.0605i −0.303307 + 0.303307i −0.842306 0.538999i \(-0.818803\pi\)
0.538999 + 0.842306i \(0.318803\pi\)
\(110\) 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 0.360220 0.932867i \(-0.382702\pi\)
−0.932867 + 0.360220i \(0.882702\pi\)
\(132\) 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 −0.619999 0.784602i \(-0.712867\pi\)
0.784602 + 0.619999i \(0.212867\pi\)
\(140\) 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 0.737694 0.675135i \(-0.235915\pi\)
−0.675135 + 0.737694i \(0.735915\pi\)
\(150\) 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 −0.332407 0.943136i \(-0.607861\pi\)
0.943136 + 0.332407i \(0.107861\pi\)
\(158\) 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 0.127513 0.991837i \(-0.459301\pi\)
−0.991837 + 0.127513i \(0.959301\pi\)
\(164\) 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 −0.534008 0.845479i \(-0.679315\pi\)
0.845479 + 0.534008i \(0.179315\pi\)
\(174\) 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 0.935453 0.353451i \(-0.114992\pi\)
−0.353451 + 0.935453i \(0.614992\pi\)
\(180\) 0 0
\(181\) 205.498 + 205.498i 1.13535 + 1.13535i 0.989274 + 0.146073i \(0.0466635\pi\)
0.146073 + 0.989274i \(0.453336\pi\)
\(182\) 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 \(-0.926188\pi\)
−0.229816 0.973234i \(-0.573812\pi\)
\(198\) 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 0.674606 0.738178i \(-0.264314\pi\)
−0.738178 + 0.674606i \(0.764314\pi\)
\(212\) 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 0.460184 0.887824i \(-0.347783\pi\)
−0.887824 + 0.460184i \(0.847783\pi\)
\(228\) 0 0
\(229\) −34.2565 34.2565i −0.149592 0.149592i 0.628344 0.777936i \(-0.283733\pi\)
−0.777936 + 0.628344i \(0.783733\pi\)
\(230\) 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 \(-0.380851\pi\)
0.930757 0.365638i \(-0.119149\pi\)
\(252\) 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 −0.981254 0.192719i \(-0.938269\pi\)
0.192719 + 0.981254i \(0.438269\pi\)
\(270\) 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 0.773023 0.634377i \(-0.218743\pi\)
−0.634377 + 0.773023i \(0.718743\pi\)
\(278\) 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 −0.117602 0.993061i \(-0.537521\pi\)
0.993061 + 0.117602i \(0.0375206\pi\)
\(284\) 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 0.859743 0.510727i \(-0.170624\pi\)
−0.510727 + 0.859743i \(0.670624\pi\)
\(294\) 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 0.895508 0.445045i \(-0.146812\pi\)
−0.445045 + 0.895508i \(0.646812\pi\)
\(308\) 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 −0.371635 0.928379i \(-0.621203\pi\)
0.928379 + 0.371635i \(0.121203\pi\)
\(318\) 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 −0.928082 0.372376i \(-0.878543\pi\)
0.372376 + 0.928082i \(0.378543\pi\)
\(332\) 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 −0.851529 0.524308i \(-0.824324\pi\)
0.524308 + 0.851529i \(0.324324\pi\)
\(348\) 0 0
\(349\) −90.9653 + 90.9653i −0.260645 + 0.260645i −0.825316 0.564671i \(-0.809003\pi\)
0.564671 + 0.825316i \(0.309003\pi\)
\(350\) 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 0.0964690 0.995336i \(-0.469245\pi\)
−0.995336 + 0.0964690i \(0.969245\pi\)
\(374\) 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 −0.825279 0.564725i \(-0.808982\pi\)
0.564725 + 0.825279i \(0.308982\pi\)
\(380\) 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 \(0.00167905\pi\)
0.00527486 + 0.999986i \(0.498321\pi\)
\(390\) 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 −0.944054 0.329791i \(-0.893022\pi\)
0.329791 + 0.944054i \(0.393022\pi\)
\(398\) 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 0.724778 0.688982i \(-0.241942\pi\)
−0.688982 + 0.724778i \(0.741942\pi\)
\(420\) 0 0
\(421\) −312.907 312.907i −0.743247 0.743247i 0.229954 0.973201i \(-0.426142\pi\)
−0.973201 + 0.229954i \(0.926142\pi\)
\(422\) 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 −0.254208 0.967149i \(-0.581815\pi\)
0.967149 + 0.254208i \(0.0818149\pi\)
\(444\) 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 −0.823465 0.567368i \(-0.807962\pi\)
0.567368 + 0.823465i \(0.307962\pi\)
\(462\) 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 \(0.0195356\pi\)
0.0613343 + 0.998117i \(0.480464\pi\)
\(468\) 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 −0.999992 0.00411514i \(-0.998690\pi\)
0.00411514 + 0.999992i \(0.498690\pi\)
\(492\) 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 0.596448 0.802652i \(-0.296578\pi\)
−0.802652 + 0.596448i \(0.796578\pi\)
\(500\) 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 −0.847830 0.530268i \(-0.822091\pi\)
0.530268 + 0.847830i \(0.322091\pi\)
\(510\) 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 −0.365616 0.930766i \(-0.619142\pi\)
0.930766 + 0.365616i \(0.119142\pi\)
\(524\) 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 −0.895100 0.445865i \(-0.852896\pi\)
0.445865 + 0.895100i \(0.352896\pi\)
\(542\) 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 0.979180 0.202993i \(-0.0650669\pi\)
−0.202993 + 0.979180i \(0.565067\pi\)
\(548\) 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 −0.182833 0.983144i \(-0.558527\pi\)
0.983144 + 0.182833i \(0.0585268\pi\)
\(558\) 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 0.0581732 0.998307i \(-0.481472\pi\)
−0.998307 + 0.0581732i \(0.981472\pi\)
\(564\) 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 −0.830186 0.557487i \(-0.811766\pi\)
0.557487 + 0.830186i \(0.311766\pi\)
\(572\) 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 −0.0422810 0.999106i \(-0.513462\pi\)
0.999106 + 0.0422810i \(0.0134625\pi\)
\(588\) 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 0.924442 0.381322i \(-0.124531\pi\)
−0.381322 + 0.924442i \(0.624531\pi\)
\(614\) 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 \(0.543021\pi\)
−0.990881 + 0.134744i \(0.956979\pi\)
\(620\) 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 0.870888 0.491482i \(-0.163545\pi\)
−0.491482 + 0.870888i \(0.663545\pi\)
\(644\) 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 −0.910102 0.414384i \(-0.863997\pi\)
0.414384 + 0.910102i \(0.363997\pi\)
\(654\) 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 0.978208 0.207629i \(-0.0665748\pi\)
−0.207629 + 0.978208i \(0.566575\pi\)
\(660\) 0 0
\(661\) −57.1593 57.1593i −0.0864741 0.0864741i 0.662547 0.749021i \(-0.269476\pi\)
−0.749021 + 0.662547i \(0.769476\pi\)
\(662\) 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 0.349747 0.936844i \(-0.386268\pi\)
−0.936844 + 0.349747i \(0.886268\pi\)
\(678\) 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 −0.859545 0.511060i \(-0.829253\pi\)
0.511060 + 0.859545i \(0.329253\pi\)
\(684\) 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 0.00839951 0.999965i \(-0.497326\pi\)
−0.999965 + 0.00839951i \(0.997326\pi\)
\(692\) 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 −0.978926 0.204214i \(-0.934536\pi\)
0.204214 + 0.978926i \(0.434536\pi\)
\(702\) 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 0.961860 0.273541i \(-0.0881948\pi\)
−0.273541 + 0.961860i \(0.588195\pi\)
\(710\) 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 −0.427917 0.903818i \(-0.640752\pi\)
0.903818 + 0.427917i \(0.140752\pi\)
\(734\) 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 \(0.0398482\pi\)
0.124860 + 0.992174i \(0.460152\pi\)
\(740\) 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 0.536019 0.844206i \(-0.319928\pi\)
−0.844206 + 0.536019i \(0.819928\pi\)
\(758\) 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 0.959498 0.281716i \(-0.0909037\pi\)
−0.281716 + 0.959498i \(0.590904\pi\)
\(774\) 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 0.676817 0.736152i \(-0.263359\pi\)
−0.736152 + 0.676817i \(0.763359\pi\)
\(788\) 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