Properties

Label 1260.2.s.e.541.1
Level $1260$
Weight $2$
Character 1260.541
Analytic conductor $10.061$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1260.541
Dual form 1260.2.s.e.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(2.12132 + 3.67423i) q^{11} -5.24264 q^{13} +(-2.12132 - 3.67423i) q^{17} +(3.50000 - 6.06218i) q^{19} +(2.12132 - 3.67423i) q^{23} +(-0.500000 - 0.866025i) q^{25} +10.2426 q^{29} +(-3.74264 - 6.48244i) q^{31} +(1.62132 - 2.09077i) q^{35} +(2.62132 - 4.54026i) q^{37} -4.24264 q^{41} -5.24264 q^{43} +(-3.00000 + 5.19615i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-4.24264 - 7.34847i) q^{53} -4.24264 q^{55} +(-0.878680 - 1.52192i) q^{59} +(6.24264 - 10.8126i) q^{61} +(2.62132 - 4.54026i) q^{65} +(-1.62132 - 2.80821i) q^{67} -12.7279 q^{71} +(-0.378680 - 0.655892i) q^{73} +(-4.24264 - 10.3923i) q^{77} +(-5.50000 + 9.52628i) q^{79} +1.75736 q^{83} +4.24264 q^{85} +(-0.878680 + 1.52192i) q^{89} +(13.7426 + 1.88064i) q^{91} +(3.50000 + 6.06218i) q^{95} +16.4853 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{5} - 2 q^{7} - 4 q^{13} + 14 q^{19} - 2 q^{25} + 24 q^{29} + 2 q^{31} - 2 q^{35} + 2 q^{37} - 4 q^{43} - 12 q^{47} + 10 q^{49} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 2 q^{67} - 10 q^{73} - 22 q^{79} + 24 q^{83} - 12 q^{89} + 38 q^{91} + 14 q^{95} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.62132 0.358719i −0.990766 0.135583i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.12132 + 3.67423i 0.639602 + 1.10782i 0.985520 + 0.169559i \(0.0542342\pi\)
−0.345918 + 0.938265i \(0.612432\pi\)
\(12\) 0 0
\(13\) −5.24264 −1.45405 −0.727023 0.686613i \(-0.759097\pi\)
−0.727023 + 0.686613i \(0.759097\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.12132 3.67423i −0.514496 0.891133i −0.999859 0.0168199i \(-0.994646\pi\)
0.485363 0.874313i \(-0.338688\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.12132 3.67423i 0.442326 0.766131i −0.555536 0.831493i \(-0.687487\pi\)
0.997862 + 0.0653618i \(0.0208201\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.2426 1.90201 0.951005 0.309175i \(-0.100053\pi\)
0.951005 + 0.309175i \(0.100053\pi\)
\(30\) 0 0
\(31\) −3.74264 6.48244i −0.672198 1.16428i −0.977279 0.211955i \(-0.932017\pi\)
0.305081 0.952326i \(-0.401316\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.62132 2.09077i 0.274053 0.353405i
\(36\) 0 0
\(37\) 2.62132 4.54026i 0.430942 0.746414i −0.566012 0.824397i \(-0.691515\pi\)
0.996955 + 0.0779826i \(0.0248479\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.24264 −0.662589 −0.331295 0.943527i \(-0.607485\pi\)
−0.331295 + 0.943527i \(0.607485\pi\)
\(42\) 0 0
\(43\) −5.24264 −0.799495 −0.399748 0.916625i \(-0.630902\pi\)
−0.399748 + 0.916625i \(0.630902\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.24264 7.34847i −0.582772 1.00939i −0.995149 0.0983769i \(-0.968635\pi\)
0.412378 0.911013i \(-0.364698\pi\)
\(54\) 0 0
\(55\) −4.24264 −0.572078
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.878680 1.52192i −0.114394 0.198137i 0.803143 0.595786i \(-0.203159\pi\)
−0.917537 + 0.397649i \(0.869826\pi\)
\(60\) 0 0
\(61\) 6.24264 10.8126i 0.799288 1.38441i −0.120792 0.992678i \(-0.538543\pi\)
0.920080 0.391730i \(-0.128123\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.62132 4.54026i 0.325135 0.563150i
\(66\) 0 0
\(67\) −1.62132 2.80821i −0.198076 0.343077i 0.749829 0.661632i \(-0.230136\pi\)
−0.947904 + 0.318555i \(0.896803\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.7279 −1.51053 −0.755263 0.655422i \(-0.772491\pi\)
−0.755263 + 0.655422i \(0.772491\pi\)
\(72\) 0 0
\(73\) −0.378680 0.655892i −0.0443211 0.0767664i 0.843014 0.537892i \(-0.180779\pi\)
−0.887335 + 0.461125i \(0.847446\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.24264 10.3923i −0.483494 1.18431i
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.75736 0.192895 0.0964476 0.995338i \(-0.469252\pi\)
0.0964476 + 0.995338i \(0.469252\pi\)
\(84\) 0 0
\(85\) 4.24264 0.460179
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.878680 + 1.52192i −0.0931399 + 0.161323i −0.908831 0.417165i \(-0.863024\pi\)
0.815691 + 0.578488i \(0.196357\pi\)
\(90\) 0 0
\(91\) 13.7426 + 1.88064i 1.44062 + 0.197144i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.50000 + 6.06218i 0.359092 + 0.621966i
\(96\) 0 0
\(97\) 16.4853 1.67383 0.836913 0.547335i \(-0.184358\pi\)
0.836913 + 0.547335i \(0.184358\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.12132 14.0665i −0.808102 1.39967i −0.914177 0.405315i \(-0.867162\pi\)
0.106076 0.994358i \(-0.466171\pi\)
\(102\) 0 0
\(103\) 4.37868 7.58410i 0.431444 0.747283i −0.565554 0.824711i \(-0.691338\pi\)
0.996998 + 0.0774283i \(0.0246709\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.36396 + 11.0227i −0.615227 + 1.06561i 0.375117 + 0.926977i \(0.377602\pi\)
−0.990345 + 0.138628i \(0.955731\pi\)
\(108\) 0 0
\(109\) −3.74264 6.48244i −0.358480 0.620906i 0.629227 0.777221i \(-0.283372\pi\)
−0.987707 + 0.156316i \(0.950038\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 2.12132 + 3.67423i 0.197814 + 0.342624i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.24264 + 10.3923i 0.388922 + 0.952661i
\(120\) 0 0
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −11.2426 −0.997623 −0.498812 0.866710i \(-0.666230\pi\)
−0.498812 + 0.866710i \(0.666230\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.24264 + 2.15232i −0.108570 + 0.188049i −0.915191 0.403020i \(-0.867961\pi\)
0.806621 + 0.591069i \(0.201294\pi\)
\(132\) 0 0
\(133\) −11.3492 + 14.6354i −0.984104 + 1.26905i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.12132 3.67423i −0.181237 0.313911i 0.761065 0.648675i \(-0.224677\pi\)
−0.942302 + 0.334764i \(0.891343\pi\)
\(138\) 0 0
\(139\) 1.48528 0.125980 0.0629900 0.998014i \(-0.479936\pi\)
0.0629900 + 0.998014i \(0.479936\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.1213 19.2627i −0.930012 1.61083i
\(144\) 0 0
\(145\) −5.12132 + 8.87039i −0.425303 + 0.736646i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) 0 0
\(151\) −2.75736 4.77589i −0.224391 0.388656i 0.731746 0.681578i \(-0.238706\pi\)
−0.956136 + 0.292922i \(0.905373\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.48528 0.601232
\(156\) 0 0
\(157\) −5.24264 9.08052i −0.418408 0.724704i 0.577371 0.816482i \(-0.304079\pi\)
−0.995780 + 0.0917773i \(0.970745\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.87868 + 8.87039i −0.542116 + 0.699084i
\(162\) 0 0
\(163\) −4.00000 + 6.92820i −0.313304 + 0.542659i −0.979076 0.203497i \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.72792 0.520622 0.260311 0.965525i \(-0.416175\pi\)
0.260311 + 0.965525i \(0.416175\pi\)
\(168\) 0 0
\(169\) 14.4853 1.11425
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.75736 + 3.04384i −0.133610 + 0.231419i −0.925065 0.379808i \(-0.875990\pi\)
0.791456 + 0.611226i \(0.209323\pi\)
\(174\) 0 0
\(175\) 1.00000 + 2.44949i 0.0755929 + 0.185164i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.62132 + 4.54026i 0.192723 + 0.333807i
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) −7.62132 13.2005i −0.548595 0.950194i −0.998371 0.0570527i \(-0.981830\pi\)
0.449777 0.893141i \(-0.351504\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.75736 0.552689 0.276344 0.961059i \(-0.410877\pi\)
0.276344 + 0.961059i \(0.410877\pi\)
\(198\) 0 0
\(199\) 3.24264 + 5.61642i 0.229865 + 0.398137i 0.957768 0.287543i \(-0.0928383\pi\)
−0.727903 + 0.685680i \(0.759505\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −26.8492 3.67423i −1.88445 0.257881i
\(204\) 0 0
\(205\) 2.12132 3.67423i 0.148159 0.256620i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 29.6985 2.05429
\(210\) 0 0
\(211\) 5.51472 0.379649 0.189824 0.981818i \(-0.439208\pi\)
0.189824 + 0.981818i \(0.439208\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.62132 4.54026i 0.178773 0.309643i
\(216\) 0 0
\(217\) 7.48528 + 18.3351i 0.508134 + 1.24467i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 11.1213 + 19.2627i 0.748101 + 1.29575i
\(222\) 0 0
\(223\) −24.4853 −1.63966 −0.819828 0.572610i \(-0.805931\pi\)
−0.819828 + 0.572610i \(0.805931\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.6066 + 23.5673i 0.903102 + 1.56422i 0.823445 + 0.567396i \(0.192049\pi\)
0.0796568 + 0.996822i \(0.474618\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.24264 + 2.15232i −0.0814081 + 0.141003i −0.903855 0.427839i \(-0.859275\pi\)
0.822447 + 0.568842i \(0.192608\pi\)
\(234\) 0 0
\(235\) −3.00000 5.19615i −0.195698 0.338960i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.9706 1.48584 0.742921 0.669379i \(-0.233440\pi\)
0.742921 + 0.669379i \(0.233440\pi\)
\(240\) 0 0
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.00000 + 4.89898i −0.319438 + 0.312984i
\(246\) 0 0
\(247\) −18.3492 + 31.7818i −1.16753 + 2.02223i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.72792 −0.424663 −0.212331 0.977198i \(-0.568106\pi\)
−0.212331 + 0.977198i \(0.568106\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.878680 1.52192i 0.0548105 0.0949346i −0.837318 0.546716i \(-0.815878\pi\)
0.892129 + 0.451781i \(0.149211\pi\)
\(258\) 0 0
\(259\) −8.50000 + 10.9612i −0.528164 + 0.681093i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.24264 + 7.34847i 0.261612 + 0.453126i 0.966671 0.256023i \(-0.0824124\pi\)
−0.705058 + 0.709150i \(0.749079\pi\)
\(264\) 0 0
\(265\) 8.48528 0.521247
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.24264 + 12.5446i 0.441592 + 0.764859i 0.997808 0.0661785i \(-0.0210807\pi\)
−0.556216 + 0.831038i \(0.687747\pi\)
\(270\) 0 0
\(271\) −13.7279 + 23.7775i −0.833912 + 1.44438i 0.0610014 + 0.998138i \(0.480571\pi\)
−0.894913 + 0.446240i \(0.852763\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.12132 3.67423i 0.127920 0.221565i
\(276\) 0 0
\(277\) 3.86396 + 6.69258i 0.232163 + 0.402118i 0.958444 0.285279i \(-0.0920864\pi\)
−0.726281 + 0.687397i \(0.758753\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.97056 0.296519 0.148259 0.988948i \(-0.452633\pi\)
0.148259 + 0.988948i \(0.452633\pi\)
\(282\) 0 0
\(283\) 0.863961 + 1.49642i 0.0513572 + 0.0889532i 0.890561 0.454864i \(-0.150312\pi\)
−0.839204 + 0.543817i \(0.816979\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.1213 + 1.52192i 0.656471 + 0.0898360i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −28.9706 −1.69248 −0.846239 0.532803i \(-0.821139\pi\)
−0.846239 + 0.532803i \(0.821139\pi\)
\(294\) 0 0
\(295\) 1.75736 0.102317
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −11.1213 + 19.2627i −0.643163 + 1.11399i
\(300\) 0 0
\(301\) 13.7426 + 1.88064i 0.792113 + 0.108398i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.24264 + 10.8126i 0.357453 + 0.619126i
\(306\) 0 0
\(307\) −5.24264 −0.299213 −0.149607 0.988746i \(-0.547801\pi\)
−0.149607 + 0.988746i \(0.547801\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −10.6066 18.3712i −0.601445 1.04173i −0.992602 0.121410i \(-0.961258\pi\)
0.391157 0.920324i \(-0.372075\pi\)
\(312\) 0 0
\(313\) 0.863961 1.49642i 0.0488340 0.0845829i −0.840575 0.541695i \(-0.817783\pi\)
0.889409 + 0.457112i \(0.151116\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.363961 0.630399i 0.0204421 0.0354067i −0.855623 0.517599i \(-0.826826\pi\)
0.876065 + 0.482192i \(0.160159\pi\)
\(318\) 0 0
\(319\) 21.7279 + 37.6339i 1.21653 + 2.10709i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −29.6985 −1.65247
\(324\) 0 0
\(325\) 2.62132 + 4.54026i 0.145405 + 0.251848i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.72792 12.5446i 0.536318 0.691607i
\(330\) 0 0
\(331\) −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.24264 0.177164
\(336\) 0 0
\(337\) 11.7279 0.638861 0.319430 0.947610i \(-0.396508\pi\)
0.319430 + 0.947610i \(0.396508\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.8787 27.5027i 0.859879 1.48935i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.878680 1.52192i −0.0467674 0.0810035i 0.841694 0.539955i \(-0.181559\pi\)
−0.888462 + 0.458951i \(0.848225\pi\)
\(354\) 0 0
\(355\) 6.36396 11.0227i 0.337764 0.585024i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.12132 8.87039i 0.270293 0.468161i −0.698644 0.715470i \(-0.746213\pi\)
0.968937 + 0.247309i \(0.0795461\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.757359 0.0396420
\(366\) 0 0
\(367\) −5.13604 8.89588i −0.268099 0.464361i 0.700272 0.713876i \(-0.253062\pi\)
−0.968371 + 0.249515i \(0.919729\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.48528 + 20.7846i 0.440534 + 1.07908i
\(372\) 0 0
\(373\) 3.86396 6.69258i 0.200068 0.346528i −0.748482 0.663155i \(-0.769217\pi\)
0.948550 + 0.316627i \(0.102550\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −53.6985 −2.76561
\(378\) 0 0
\(379\) 30.4558 1.56441 0.782206 0.623020i \(-0.214095\pi\)
0.782206 + 0.623020i \(0.214095\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.7279 + 22.0454i −0.650366 + 1.12647i 0.332668 + 0.943044i \(0.392051\pi\)
−0.983034 + 0.183424i \(0.941282\pi\)
\(384\) 0 0
\(385\) 11.1213 + 1.52192i 0.566795 + 0.0775641i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.6066 + 18.3712i 0.537776 + 0.931455i 0.999023 + 0.0441839i \(0.0140687\pi\)
−0.461247 + 0.887272i \(0.652598\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.50000 9.52628i −0.276735 0.479319i
\(396\) 0 0
\(397\) 8.62132 14.9326i 0.432692 0.749444i −0.564412 0.825493i \(-0.690897\pi\)
0.997104 + 0.0760490i \(0.0242305\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.2426 + 17.7408i −0.511493 + 0.885932i 0.488418 + 0.872610i \(0.337574\pi\)
−0.999911 + 0.0133223i \(0.995759\pi\)
\(402\) 0 0
\(403\) 19.6213 + 33.9851i 0.977408 + 1.69292i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.2426 1.10253
\(408\) 0 0
\(409\) −8.50000 14.7224i −0.420298 0.727977i 0.575670 0.817682i \(-0.304741\pi\)
−0.995968 + 0.0897044i \(0.971408\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.75736 + 4.30463i 0.0864740 + 0.211817i
\(414\) 0 0
\(415\) −0.878680 + 1.52192i −0.0431327 + 0.0747080i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.48528 −0.121414 −0.0607070 0.998156i \(-0.519336\pi\)
−0.0607070 + 0.998156i \(0.519336\pi\)
\(420\) 0 0
\(421\) 14.5147 0.707404 0.353702 0.935358i \(-0.384923\pi\)
0.353702 + 0.935358i \(0.384923\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.12132 + 3.67423i −0.102899 + 0.178227i
\(426\) 0 0
\(427\) −20.2426 + 26.1039i −0.979610 + 1.26325i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.7279 27.2416i −0.757587 1.31218i −0.944078 0.329723i \(-0.893045\pi\)
0.186490 0.982457i \(-0.440289\pi\)
\(432\) 0 0
\(433\) 24.7574 1.18976 0.594881 0.803814i \(-0.297199\pi\)
0.594881 + 0.803814i \(0.297199\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14.8492 25.7196i −0.710336 1.23034i
\(438\) 0 0
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.75736 3.04384i 0.0834947 0.144617i −0.821254 0.570563i \(-0.806725\pi\)
0.904749 + 0.425946i \(0.140059\pi\)
\(444\) 0 0
\(445\) −0.878680 1.52192i −0.0416534 0.0721458i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −9.00000 15.5885i −0.423793 0.734032i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.50000 + 10.9612i −0.398486 + 0.513867i
\(456\) 0 0
\(457\) 5.10660 8.84489i 0.238877 0.413747i −0.721516 0.692398i \(-0.756554\pi\)
0.960392 + 0.278652i \(0.0898875\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.72792 0.313351 0.156675 0.987650i \(-0.449922\pi\)
0.156675 + 0.987650i \(0.449922\pi\)
\(462\) 0 0
\(463\) 35.7279 1.66042 0.830209 0.557453i \(-0.188221\pi\)
0.830209 + 0.557453i \(0.188221\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.4853 19.8931i 0.531475 0.920542i −0.467850 0.883808i \(-0.654971\pi\)
0.999325 0.0367344i \(-0.0116955\pi\)
\(468\) 0 0
\(469\) 3.24264 + 7.94282i 0.149731 + 0.366765i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −11.1213 19.2627i −0.511359 0.885700i
\(474\) 0 0
\(475\) −7.00000 −0.321182
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.00000 + 10.3923i 0.274147 + 0.474837i 0.969920 0.243426i \(-0.0782712\pi\)
−0.695773 + 0.718262i \(0.744938\pi\)
\(480\) 0 0
\(481\) −13.7426 + 23.8030i −0.626610 + 1.08532i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.24264 + 14.2767i −0.374279 + 0.648270i
\(486\) 0 0
\(487\) 6.13604 + 10.6279i 0.278050 + 0.481598i 0.970900 0.239484i \(-0.0769784\pi\)
−0.692850 + 0.721082i \(0.743645\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −32.4853 −1.46604 −0.733020 0.680207i \(-0.761890\pi\)
−0.733020 + 0.680207i \(0.761890\pi\)
\(492\) 0 0
\(493\) −21.7279 37.6339i −0.978576 1.69494i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 33.3640 + 4.56575i 1.49658 + 0.204802i
\(498\) 0 0
\(499\) −1.25736 + 2.17781i −0.0562871 + 0.0974922i −0.892796 0.450461i \(-0.851260\pi\)
0.836509 + 0.547953i \(0.184593\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.51472 0.424240 0.212120 0.977244i \(-0.431963\pi\)
0.212120 + 0.977244i \(0.431963\pi\)
\(504\) 0 0
\(505\) 16.2426 0.722788
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.7279 27.2416i 0.697128 1.20746i −0.272330 0.962204i \(-0.587794\pi\)
0.969458 0.245257i \(-0.0788724\pi\)
\(510\) 0 0
\(511\) 0.757359 + 1.85514i 0.0335036 + 0.0820667i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.37868 + 7.58410i 0.192948 + 0.334195i
\(516\) 0 0
\(517\) −25.4558 −1.11955
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.7279 + 32.4377i 0.820485 + 1.42112i 0.905321 + 0.424727i \(0.139630\pi\)
−0.0848363 + 0.996395i \(0.527037\pi\)
\(522\) 0 0
\(523\) −1.62132 + 2.80821i −0.0708954 + 0.122794i −0.899294 0.437345i \(-0.855919\pi\)
0.828399 + 0.560139i \(0.189252\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.8787 + 27.5027i −0.691686 + 1.19804i
\(528\) 0 0
\(529\) 2.50000 + 4.33013i 0.108696 + 0.188266i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 22.2426 0.963436
\(534\) 0 0
\(535\) −6.36396 11.0227i −0.275138 0.476553i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.39340 + 28.7635i 0.318456 + 1.23893i
\(540\) 0 0
\(541\) −13.4706 + 23.3317i −0.579145 + 1.00311i 0.416433 + 0.909166i \(0.363280\pi\)
−0.995578 + 0.0939417i \(0.970053\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.48528 0.320634
\(546\) 0 0
\(547\) −17.4558 −0.746358 −0.373179 0.927759i \(-0.621732\pi\)
−0.373179 + 0.927759i \(0.621732\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 35.8492 62.0927i 1.52723 2.64524i
\(552\) 0 0
\(553\) 17.8345 22.9985i 0.758401 0.977995i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 0 0
\(559\) 27.4853 1.16250
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.00000 5.19615i −0.126435 0.218992i 0.795858 0.605483i \(-0.207020\pi\)
−0.922293 + 0.386492i \(0.873687\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.84924 15.3273i 0.370980 0.642555i −0.618737 0.785598i \(-0.712355\pi\)
0.989717 + 0.143043i \(0.0456887\pi\)
\(570\) 0 0
\(571\) −19.4706 33.7240i −0.814818 1.41131i −0.909459 0.415794i \(-0.863504\pi\)
0.0946410 0.995511i \(-0.469830\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.24264 −0.176930
\(576\) 0 0
\(577\) −10.6213 18.3967i −0.442171 0.765863i 0.555679 0.831397i \(-0.312458\pi\)
−0.997850 + 0.0655337i \(0.979125\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.60660 0.630399i −0.191114 0.0261534i
\(582\) 0 0
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.78680 −0.115023 −0.0575117 0.998345i \(-0.518317\pi\)
−0.0575117 + 0.998345i \(0.518317\pi\)
\(588\) 0 0
\(589\) −52.3970 −2.15898
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.6066 + 33.9596i −0.805147 + 1.39455i 0.111045 + 0.993815i \(0.464580\pi\)
−0.916192 + 0.400740i \(0.868753\pi\)
\(594\) 0 0
\(595\) −11.1213 1.52192i −0.455930 0.0623925i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.75736 13.4361i −0.316957 0.548986i 0.662894 0.748713i \(-0.269328\pi\)
−0.979852 + 0.199727i \(0.935994\pi\)
\(600\) 0 0
\(601\) 13.4853 0.550076 0.275038 0.961433i \(-0.411310\pi\)
0.275038 + 0.961433i \(0.411310\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) 0 0
\(607\) 10.3787 17.9764i 0.421258 0.729640i −0.574805 0.818290i \(-0.694922\pi\)
0.996063 + 0.0886507i \(0.0282555\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.7279 27.2416i 0.636284 1.10208i
\(612\) 0 0
\(613\) −22.7279 39.3659i −0.917972 1.58997i −0.802491 0.596665i \(-0.796492\pi\)
−0.115482 0.993310i \(-0.536841\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.51472 0.383048 0.191524 0.981488i \(-0.438657\pi\)
0.191524 + 0.981488i \(0.438657\pi\)
\(618\) 0 0
\(619\) −10.9853 19.0271i −0.441536 0.764762i 0.556268 0.831003i \(-0.312233\pi\)
−0.997804 + 0.0662407i \(0.978899\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.84924 3.67423i 0.114152 0.147205i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22.2426 −0.886872
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.62132 9.73641i 0.223075 0.386378i
\(636\) 0 0
\(637\) −35.3492 9.85951i −1.40059 0.390648i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.8787 + 22.3065i 0.508677 + 0.881055i 0.999950 + 0.0100488i \(0.00319868\pi\)
−0.491272 + 0.871006i \(0.663468\pi\)
\(642\) 0 0
\(643\) 5.72792 0.225887 0.112944 0.993601i \(-0.463972\pi\)
0.112944 + 0.993601i \(0.463972\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.878680 + 1.52192i 0.0345445 + 0.0598328i 0.882781 0.469785i \(-0.155669\pi\)
−0.848236 + 0.529618i \(0.822335\pi\)
\(648\) 0 0
\(649\) 3.72792 6.45695i 0.146334 0.253457i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.878680 1.52192i 0.0343854 0.0595572i −0.848321 0.529483i \(-0.822386\pi\)
0.882706 + 0.469926i \(0.155719\pi\)
\(654\) 0 0
\(655\) −1.24264 2.15232i −0.0485540 0.0840980i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.02944 −0.273828 −0.136914 0.990583i \(-0.543718\pi\)
−0.136914 + 0.990583i \(0.543718\pi\)
\(660\) 0 0
\(661\) 17.9853 + 31.1514i 0.699546 + 1.21165i 0.968624 + 0.248531i \(0.0799479\pi\)
−0.269077 + 0.963119i \(0.586719\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.00000 17.1464i −0.271448 0.664910i
\(666\) 0 0
\(667\) 21.7279 37.6339i 0.841309 1.45719i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 52.9706 2.04491
\(672\) 0 0
\(673\) 4.27208 0.164677 0.0823383 0.996604i \(-0.473761\pi\)
0.0823383 + 0.996604i \(0.473761\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.36396 + 11.0227i −0.244587 + 0.423637i −0.962015 0.272995i \(-0.911986\pi\)
0.717428 + 0.696632i \(0.245319\pi\)
\(678\) 0 0
\(679\) −43.2132 5.91359i −1.65837 0.226943i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.60660 7.97887i −0.176267 0.305303i 0.764332 0.644823i \(-0.223069\pi\)
−0.940599 + 0.339520i \(0.889735\pi\)
\(684\) 0 0
\(685\) 4.24264 0.162103
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 22.2426 + 38.5254i 0.847377 + 1.46770i
\(690\) 0 0
\(691\) 20.4706 35.4561i 0.778737 1.34881i −0.153933 0.988081i \(-0.549194\pi\)
0.932670 0.360731i \(-0.117473\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.742641 + 1.28629i −0.0281700 + 0.0487918i
\(696\) 0 0
\(697\) 9.00000 + 15.5885i 0.340899 + 0.590455i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −51.2132 −1.93430 −0.967148 0.254214i \(-0.918183\pi\)
−0.967148 + 0.254214i \(0.918183\pi\)
\(702\) 0 0
\(703\) −18.3492 31.7818i −0.692055 1.19867i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.2426 + 39.7862i 0.610867 + 1.49631i
\(708\) 0 0
\(709\) 9.75736 16.9002i 0.366445 0.634702i −0.622562 0.782571i \(-0.713908\pi\)
0.989007 + 0.147869i \(0.0472413\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31.7574 −1.18932
\(714\) 0 0
\(715\) 22.2426 0.831828
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.75736 8.23999i 0.177420 0.307300i −0.763576 0.645718i \(-0.776558\pi\)
0.940996 + 0.338418i \(0.109892\pi\)
\(720\) 0 0
\(721\) −14.1985 + 18.3096i −0.528779 + 0.681886i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.12132 8.87039i −0.190201 0.329438i
\(726\) 0 0
\(727\) 9.24264 0.342791 0.171395 0.985202i \(-0.445172\pi\)
0.171395 + 0.985202i \(0.445172\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.1213 + 19.2627i 0.411337 + 0.712456i
\(732\) 0 0
\(733\) −22.1066 + 38.2898i −0.816526 + 1.41426i 0.0917010 + 0.995787i \(0.470770\pi\)
−0.908227 + 0.418478i \(0.862564\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.87868 11.9142i 0.253379 0.438866i
\(738\) 0 0
\(739\) −0.742641 1.28629i −0.0273185 0.0473170i 0.852043 0.523472i \(-0.175363\pi\)
−0.879361 + 0.476155i \(0.842030\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27.2132 0.998356 0.499178 0.866500i \(-0.333635\pi\)
0.499178 + 0.866500i \(0.333635\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20.6360 26.6112i 0.754024 0.972351i
\(750\) 0 0
\(751\) 11.4706 19.8676i 0.418567 0.724979i −0.577229 0.816582i \(-0.695866\pi\)
0.995796 + 0.0916035i \(0.0291992\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.51472 0.200701
\(756\) 0 0
\(757\) 42.9706 1.56179 0.780896 0.624661i \(-0.214763\pi\)
0.780896 + 0.624661i \(0.214763\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.8787 32.6988i 0.684352 1.18533i −0.289288 0.957242i \(-0.593419\pi\)
0.973640 0.228090i \(-0.0732480\pi\)
\(762\) 0 0
\(763\) 7.48528 + 18.3351i 0.270985 + 0.663776i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.60660 + 7.97887i 0.166335 + 0.288100i
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.8492 41.3081i −0.857798 1.48575i −0.874025 0.485881i \(-0.838499\pi\)
0.0162275 0.999868i \(-0.494834\pi\)
\(774\) 0 0
\(775\) −3.74264 + 6.48244i −0.134440 + 0.232856i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −14.8492 + 25.7196i −0.532029 + 0.921502i
\(780\) 0 0
\(781\) −27.0000 46.7654i −0.966136 1.67340i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.4853 0.374236
\(786\) 0 0
\(787\) −5.75736 9.97204i −0.205228 0.355465i 0.744978 0.667090i \(-0.232460\pi\)
−0.950205 + 0.311625i \(0.899127\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −47.1838 6.45695i −1.67766 0.229583i
\(792\) 0 0
\(793\) −32.7279 + 56.6864i −1.16220 + 2.01299i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 40.2426 1.42547 0.712734 0.701435i \(-0.247457\pi\)
0.712734 + 0.701435i \(0.247457\pi\)
\(798\) 0 0
\(799\) 25.4558 0.900563
\(800\) 0 0
\(801\) 0 0
\(802\)