Properties

Label 192.2.c.b.191.3
Level $192$
Weight $2$
Character 192.191
Analytic conductor $1.533$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.53312771881\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 191.3
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 192.191
Dual form 192.2.c.b.191.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41421 - 1.00000i) q^{3} -2.82843i q^{5} +2.00000i q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.41421 - 1.00000i) q^{3} -2.82843i q^{5} +2.00000i q^{7} +(1.00000 - 2.82843i) q^{9} -2.82843 q^{11} +2.00000 q^{13} +(-2.82843 - 4.00000i) q^{15} +6.00000i q^{19} +(2.00000 + 2.82843i) q^{21} +5.65685 q^{23} -3.00000 q^{25} +(-1.41421 - 5.00000i) q^{27} +2.82843i q^{29} +2.00000i q^{31} +(-4.00000 + 2.82843i) q^{33} +5.65685 q^{35} -6.00000 q^{37} +(2.82843 - 2.00000i) q^{39} +5.65685i q^{41} -2.00000i q^{43} +(-8.00000 - 2.82843i) q^{45} -11.3137 q^{47} +3.00000 q^{49} +8.48528i q^{53} +8.00000i q^{55} +(6.00000 + 8.48528i) q^{57} -2.82843 q^{59} +2.00000 q^{61} +(5.65685 + 2.00000i) q^{63} -5.65685i q^{65} -2.00000i q^{67} +(8.00000 - 5.65685i) q^{69} -5.65685 q^{71} -6.00000 q^{73} +(-4.24264 + 3.00000i) q^{75} -5.65685i q^{77} -14.0000i q^{79} +(-7.00000 - 5.65685i) q^{81} +2.82843 q^{83} +(2.82843 + 4.00000i) q^{87} -16.9706i q^{89} +4.00000i q^{91} +(2.00000 + 2.82843i) q^{93} +16.9706 q^{95} +10.0000 q^{97} +(-2.82843 + 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} + 8q^{13} + 8q^{21} - 12q^{25} - 16q^{33} - 24q^{37} - 32q^{45} + 12q^{49} + 24q^{57} + 8q^{61} + 32q^{69} - 24q^{73} - 28q^{81} + 8q^{93} + 40q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) 1.41421 1.00000i 0.816497 0.577350i
\(4\) 0 0
\(5\) 2.82843i 1.26491i −0.774597 0.632456i \(-0.782047\pi\)
0.774597 0.632456i \(-0.217953\pi\)
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 0 0
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 0 0
\(11\) −2.82843 −0.852803 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −2.82843 4.00000i −0.730297 1.03280i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) 0 0
\(21\) 2.00000 + 2.82843i 0.436436 + 0.617213i
\(22\) 0 0
\(23\) 5.65685 1.17954 0.589768 0.807573i \(-0.299219\pi\)
0.589768 + 0.807573i \(0.299219\pi\)
\(24\) 0 0
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) −1.41421 5.00000i −0.272166 0.962250i
\(28\) 0 0
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 0 0
\(31\) 2.00000i 0.359211i 0.983739 + 0.179605i \(0.0574821\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(32\) 0 0
\(33\) −4.00000 + 2.82843i −0.696311 + 0.492366i
\(34\) 0 0
\(35\) 5.65685 0.956183
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 2.82843 2.00000i 0.452911 0.320256i
\(40\) 0 0
\(41\) 5.65685i 0.883452i 0.897150 + 0.441726i \(0.145634\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 0 0
\(45\) −8.00000 2.82843i −1.19257 0.421637i
\(46\) 0 0
\(47\) −11.3137 −1.65027 −0.825137 0.564933i \(-0.808902\pi\)
−0.825137 + 0.564933i \(0.808902\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.48528i 1.16554i 0.812636 + 0.582772i \(0.198032\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(54\) 0 0
\(55\) 8.00000i 1.07872i
\(56\) 0 0
\(57\) 6.00000 + 8.48528i 0.794719 + 1.12390i
\(58\) 0 0
\(59\) −2.82843 −0.368230 −0.184115 0.982905i \(-0.558942\pi\)
−0.184115 + 0.982905i \(0.558942\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 5.65685 + 2.00000i 0.712697 + 0.251976i
\(64\) 0 0
\(65\) 5.65685i 0.701646i
\(66\) 0 0
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 0 0
\(69\) 8.00000 5.65685i 0.963087 0.681005i
\(70\) 0 0
\(71\) −5.65685 −0.671345 −0.335673 0.941979i \(-0.608964\pi\)
−0.335673 + 0.941979i \(0.608964\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) −4.24264 + 3.00000i −0.489898 + 0.346410i
\(76\) 0 0
\(77\) 5.65685i 0.644658i
\(78\) 0 0
\(79\) 14.0000i 1.57512i −0.616236 0.787562i \(-0.711343\pi\)
0.616236 0.787562i \(-0.288657\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 2.82843 0.310460 0.155230 0.987878i \(-0.450388\pi\)
0.155230 + 0.987878i \(0.450388\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.82843 + 4.00000i 0.303239 + 0.428845i
\(88\) 0 0
\(89\) 16.9706i 1.79888i −0.437048 0.899438i \(-0.643976\pi\)
0.437048 0.899438i \(-0.356024\pi\)
\(90\) 0 0
\(91\) 4.00000i 0.419314i
\(92\) 0 0
\(93\) 2.00000 + 2.82843i 0.207390 + 0.293294i
\(94\) 0 0
\(95\) 16.9706 1.74114
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) −2.82843 + 8.00000i −0.284268 + 0.804030i
\(100\) 0 0
\(101\) 2.82843i 0.281439i −0.990050 0.140720i \(-0.955058\pi\)
0.990050 0.140720i \(-0.0449416\pi\)
\(102\) 0 0
\(103\) 14.0000i 1.37946i −0.724066 0.689730i \(-0.757729\pi\)
0.724066 0.689730i \(-0.242271\pi\)
\(104\) 0 0
\(105\) 8.00000 5.65685i 0.780720 0.552052i
\(106\) 0 0
\(107\) 8.48528 0.820303 0.410152 0.912017i \(-0.365476\pi\)
0.410152 + 0.912017i \(0.365476\pi\)
\(108\) 0 0
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 0 0
\(111\) −8.48528 + 6.00000i −0.805387 + 0.569495i
\(112\) 0 0
\(113\) 11.3137i 1.06430i 0.846649 + 0.532152i \(0.178617\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 16.0000i 1.49201i
\(116\) 0 0
\(117\) 2.00000 5.65685i 0.184900 0.522976i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) 0 0
\(123\) 5.65685 + 8.00000i 0.510061 + 0.721336i
\(124\) 0 0
\(125\) 5.65685i 0.505964i
\(126\) 0 0
\(127\) 18.0000i 1.59724i 0.601834 + 0.798621i \(0.294437\pi\)
−0.601834 + 0.798621i \(0.705563\pi\)
\(128\) 0 0
\(129\) −2.00000 2.82843i −0.176090 0.249029i
\(130\) 0 0
\(131\) −19.7990 −1.72985 −0.864923 0.501905i \(-0.832633\pi\)
−0.864923 + 0.501905i \(0.832633\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) 0 0
\(135\) −14.1421 + 4.00000i −1.21716 + 0.344265i
\(136\) 0 0
\(137\) 5.65685i 0.483298i 0.970364 + 0.241649i \(0.0776882\pi\)
−0.970364 + 0.241649i \(0.922312\pi\)
\(138\) 0 0
\(139\) 10.0000i 0.848189i −0.905618 0.424094i \(-0.860592\pi\)
0.905618 0.424094i \(-0.139408\pi\)
\(140\) 0 0
\(141\) −16.0000 + 11.3137i −1.34744 + 0.952786i
\(142\) 0 0
\(143\) −5.65685 −0.473050
\(144\) 0 0
\(145\) 8.00000 0.664364
\(146\) 0 0
\(147\) 4.24264 3.00000i 0.349927 0.247436i
\(148\) 0 0
\(149\) 14.1421i 1.15857i −0.815125 0.579284i \(-0.803332\pi\)
0.815125 0.579284i \(-0.196668\pi\)
\(150\) 0 0
\(151\) 14.0000i 1.13930i −0.821886 0.569652i \(-0.807078\pi\)
0.821886 0.569652i \(-0.192922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.65685 0.454369
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 8.48528 + 12.0000i 0.672927 + 0.951662i
\(160\) 0 0
\(161\) 11.3137i 0.891645i
\(162\) 0 0
\(163\) 6.00000i 0.469956i 0.972001 + 0.234978i \(0.0755019\pi\)
−0.972001 + 0.234978i \(0.924498\pi\)
\(164\) 0 0
\(165\) 8.00000 + 11.3137i 0.622799 + 0.880771i
\(166\) 0 0
\(167\) −5.65685 −0.437741 −0.218870 0.975754i \(-0.570237\pi\)
−0.218870 + 0.975754i \(0.570237\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 16.9706 + 6.00000i 1.29777 + 0.458831i
\(172\) 0 0
\(173\) 14.1421i 1.07521i 0.843198 + 0.537603i \(0.180670\pi\)
−0.843198 + 0.537603i \(0.819330\pi\)
\(174\) 0 0
\(175\) 6.00000i 0.453557i
\(176\) 0 0
\(177\) −4.00000 + 2.82843i −0.300658 + 0.212598i
\(178\) 0 0
\(179\) −8.48528 −0.634220 −0.317110 0.948389i \(-0.602712\pi\)
−0.317110 + 0.948389i \(0.602712\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 2.82843 2.00000i 0.209083 0.147844i
\(184\) 0 0
\(185\) 16.9706i 1.24770i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 10.0000 2.82843i 0.727393 0.205738i
\(190\) 0 0
\(191\) 22.6274 1.63726 0.818631 0.574320i \(-0.194733\pi\)
0.818631 + 0.574320i \(0.194733\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 0 0
\(195\) −5.65685 8.00000i −0.405096 0.572892i
\(196\) 0 0
\(197\) 19.7990i 1.41062i 0.708899 + 0.705310i \(0.249192\pi\)
−0.708899 + 0.705310i \(0.750808\pi\)
\(198\) 0 0
\(199\) 2.00000i 0.141776i 0.997484 + 0.0708881i \(0.0225833\pi\)
−0.997484 + 0.0708881i \(0.977417\pi\)
\(200\) 0 0
\(201\) −2.00000 2.82843i −0.141069 0.199502i
\(202\) 0 0
\(203\) −5.65685 −0.397033
\(204\) 0 0
\(205\) 16.0000 1.11749
\(206\) 0 0
\(207\) 5.65685 16.0000i 0.393179 1.11208i
\(208\) 0 0
\(209\) 16.9706i 1.17388i
\(210\) 0 0
\(211\) 2.00000i 0.137686i −0.997628 0.0688428i \(-0.978069\pi\)
0.997628 0.0688428i \(-0.0219307\pi\)
\(212\) 0 0
\(213\) −8.00000 + 5.65685i −0.548151 + 0.387601i
\(214\) 0 0
\(215\) −5.65685 −0.385794
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 0 0
\(219\) −8.48528 + 6.00000i −0.573382 + 0.405442i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.00000i 0.133930i 0.997755 + 0.0669650i \(0.0213316\pi\)
−0.997755 + 0.0669650i \(0.978668\pi\)
\(224\) 0 0
\(225\) −3.00000 + 8.48528i −0.200000 + 0.565685i
\(226\) 0 0
\(227\) 14.1421 0.938647 0.469323 0.883026i \(-0.344498\pi\)
0.469323 + 0.883026i \(0.344498\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −5.65685 8.00000i −0.372194 0.526361i
\(232\) 0 0
\(233\) 5.65685i 0.370593i −0.982683 0.185296i \(-0.940675\pi\)
0.982683 0.185296i \(-0.0593245\pi\)
\(234\) 0 0
\(235\) 32.0000i 2.08745i
\(236\) 0 0
\(237\) −14.0000 19.7990i −0.909398 1.28608i
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) −15.5563 1.00000i −0.997940 0.0641500i
\(244\) 0 0
\(245\) 8.48528i 0.542105i
\(246\) 0 0
\(247\) 12.0000i 0.763542i
\(248\) 0 0
\(249\) 4.00000 2.82843i 0.253490 0.179244i
\(250\) 0 0
\(251\) 8.48528 0.535586 0.267793 0.963476i \(-0.413706\pi\)
0.267793 + 0.963476i \(0.413706\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.6274i 1.41146i −0.708481 0.705730i \(-0.750619\pi\)
0.708481 0.705730i \(-0.249381\pi\)
\(258\) 0 0
\(259\) 12.0000i 0.745644i
\(260\) 0 0
\(261\) 8.00000 + 2.82843i 0.495188 + 0.175075i
\(262\) 0 0
\(263\) −5.65685 −0.348817 −0.174408 0.984673i \(-0.555801\pi\)
−0.174408 + 0.984673i \(0.555801\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) −16.9706 24.0000i −1.03858 1.46878i
\(268\) 0 0
\(269\) 8.48528i 0.517357i −0.965964 0.258678i \(-0.916713\pi\)
0.965964 0.258678i \(-0.0832870\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i 0.837321 + 0.546711i \(0.184120\pi\)
−0.837321 + 0.546711i \(0.815880\pi\)
\(272\) 0 0
\(273\) 4.00000 + 5.65685i 0.242091 + 0.342368i
\(274\) 0 0
\(275\) 8.48528 0.511682
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) 5.65685 + 2.00000i 0.338667 + 0.119737i
\(280\) 0 0
\(281\) 5.65685i 0.337460i 0.985662 + 0.168730i \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 0 0
\(283\) 10.0000i 0.594438i −0.954809 0.297219i \(-0.903941\pi\)
0.954809 0.297219i \(-0.0960592\pi\)
\(284\) 0 0
\(285\) 24.0000 16.9706i 1.42164 1.00525i
\(286\) 0 0
\(287\) −11.3137 −0.667827
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 14.1421 10.0000i 0.829027 0.586210i
\(292\) 0 0
\(293\) 2.82843i 0.165238i −0.996581 0.0826192i \(-0.973671\pi\)
0.996581 0.0826192i \(-0.0263285\pi\)
\(294\) 0 0
\(295\) 8.00000i 0.465778i
\(296\) 0 0
\(297\) 4.00000 + 14.1421i 0.232104 + 0.820610i
\(298\) 0 0
\(299\) 11.3137 0.654289
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 0 0
\(303\) −2.82843 4.00000i −0.162489 0.229794i
\(304\) 0 0
\(305\) 5.65685i 0.323911i
\(306\) 0 0
\(307\) 30.0000i 1.71219i 0.516818 + 0.856095i \(0.327116\pi\)
−0.516818 + 0.856095i \(0.672884\pi\)
\(308\) 0 0
\(309\) −14.0000 19.7990i −0.796432 1.12633i
\(310\) 0 0
\(311\) 5.65685 0.320771 0.160385 0.987054i \(-0.448726\pi\)
0.160385 + 0.987054i \(0.448726\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 5.65685 16.0000i 0.318728 0.901498i
\(316\) 0 0
\(317\) 2.82843i 0.158860i 0.996840 + 0.0794301i \(0.0253101\pi\)
−0.996840 + 0.0794301i \(0.974690\pi\)
\(318\) 0 0
\(319\) 8.00000i 0.447914i
\(320\) 0 0
\(321\) 12.0000 8.48528i 0.669775 0.473602i
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −6.00000 −0.332820
\(326\) 0 0
\(327\) 25.4558 18.0000i 1.40771 0.995402i
\(328\) 0 0
\(329\) 22.6274i 1.24749i
\(330\) 0 0
\(331\) 10.0000i 0.549650i −0.961494 0.274825i \(-0.911380\pi\)
0.961494 0.274825i \(-0.0886199\pi\)
\(332\) 0 0
\(333\) −6.00000 + 16.9706i −0.328798 + 0.929981i
\(334\) 0 0
\(335\) −5.65685 −0.309067
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 11.3137 + 16.0000i 0.614476 + 0.869001i
\(340\) 0 0
\(341\) 5.65685i 0.306336i
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) −16.0000 22.6274i −0.861411 1.21822i
\(346\) 0 0
\(347\) −14.1421 −0.759190 −0.379595 0.925153i \(-0.623937\pi\)
−0.379595 + 0.925153i \(0.623937\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −2.82843 10.0000i −0.150970 0.533761i
\(352\) 0 0
\(353\) 22.6274i 1.20434i 0.798369 + 0.602168i \(0.205696\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 16.0000i 0.849192i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.9706 0.895672 0.447836 0.894116i \(-0.352195\pi\)
0.447836 + 0.894116i \(0.352195\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) 0 0
\(363\) −4.24264 + 3.00000i −0.222681 + 0.157459i
\(364\) 0 0
\(365\) 16.9706i 0.888280i
\(366\) 0 0
\(367\) 14.0000i 0.730794i −0.930852 0.365397i \(-0.880933\pi\)
0.930852 0.365397i \(-0.119067\pi\)
\(368\) 0 0
\(369\) 16.0000 + 5.65685i 0.832927 + 0.294484i
\(370\) 0 0
\(371\) −16.9706 −0.881068
\(372\) 0 0
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) −5.65685 8.00000i −0.292119 0.413118i
\(376\) 0 0
\(377\) 5.65685i 0.291343i
\(378\) 0 0
\(379\) 2.00000i 0.102733i −0.998680 0.0513665i \(-0.983642\pi\)
0.998680 0.0513665i \(-0.0163577\pi\)
\(380\) 0 0
\(381\) 18.0000 + 25.4558i 0.922168 + 1.30414i
\(382\) 0 0
\(383\) −22.6274 −1.15621 −0.578103 0.815963i \(-0.696207\pi\)
−0.578103 + 0.815963i \(0.696207\pi\)
\(384\) 0 0
\(385\) −16.0000 −0.815436
\(386\) 0 0
\(387\) −5.65685 2.00000i −0.287554 0.101666i
\(388\) 0 0
\(389\) 2.82843i 0.143407i −0.997426 0.0717035i \(-0.977156\pi\)
0.997426 0.0717035i \(-0.0228435\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −28.0000 + 19.7990i −1.41241 + 0.998727i
\(394\) 0 0
\(395\) −39.5980 −1.99239
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) −16.9706 + 12.0000i −0.849591 + 0.600751i
\(400\) 0 0
\(401\) 22.6274i 1.12996i 0.825105 + 0.564980i \(0.191116\pi\)
−0.825105 + 0.564980i \(0.808884\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 0 0
\(405\) −16.0000 + 19.7990i −0.795046 + 0.983820i
\(406\) 0 0
\(407\) 16.9706 0.841200
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 0 0
\(411\) 5.65685 + 8.00000i 0.279032 + 0.394611i
\(412\) 0 0
\(413\) 5.65685i 0.278356i
\(414\) 0 0
\(415\) 8.00000i 0.392705i
\(416\) 0 0
\(417\) −10.0000 14.1421i −0.489702 0.692543i
\(418\) 0 0
\(419\) 36.7696 1.79631 0.898155 0.439679i \(-0.144908\pi\)
0.898155 + 0.439679i \(0.144908\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) −11.3137 + 32.0000i −0.550091 + 1.55589i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) 0 0
\(429\) −8.00000 + 5.65685i −0.386244 + 0.273115i
\(430\) 0 0
\(431\) 33.9411 1.63489 0.817443 0.576009i \(-0.195391\pi\)
0.817443 + 0.576009i \(0.195391\pi\)
\(432\) 0 0
\(433\) −6.00000 −0.288342 −0.144171 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 0 0
\(435\) 11.3137 8.00000i 0.542451 0.383571i
\(436\) 0 0
\(437\) 33.9411i 1.62362i
\(438\) 0 0
\(439\) 14.0000i 0.668184i −0.942541 0.334092i \(-0.891570\pi\)
0.942541 0.334092i \(-0.108430\pi\)
\(440\) 0 0
\(441\) 3.00000 8.48528i 0.142857 0.404061i
\(442\) 0 0
\(443\) −14.1421 −0.671913 −0.335957 0.941877i \(-0.609060\pi\)
−0.335957 + 0.941877i \(0.609060\pi\)
\(444\) 0 0
\(445\) −48.0000 −2.27542
\(446\) 0 0
\(447\) −14.1421 20.0000i −0.668900 0.945968i
\(448\) 0 0
\(449\) 33.9411i 1.60178i 0.598811 + 0.800890i \(0.295640\pi\)
−0.598811 + 0.800890i \(0.704360\pi\)
\(450\) 0 0
\(451\) 16.0000i 0.753411i
\(452\) 0 0
\(453\) −14.0000 19.7990i −0.657777 0.930238i
\(454\) 0 0
\(455\) 11.3137 0.530395
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.1127i 1.44906i −0.689242 0.724531i \(-0.742056\pi\)
0.689242 0.724531i \(-0.257944\pi\)
\(462\) 0 0
\(463\) 2.00000i 0.0929479i 0.998920 + 0.0464739i \(0.0147984\pi\)
−0.998920 + 0.0464739i \(0.985202\pi\)
\(464\) 0 0
\(465\) 8.00000 5.65685i 0.370991 0.262330i
\(466\) 0 0
\(467\) 25.4558 1.17796 0.588978 0.808149i \(-0.299530\pi\)
0.588978 + 0.808149i \(0.299530\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) −19.7990 + 14.0000i −0.912289 + 0.645086i
\(472\) 0 0
\(473\) 5.65685i 0.260102i
\(474\) 0 0
\(475\) 18.0000i 0.825897i
\(476\) 0 0
\(477\) 24.0000 + 8.48528i 1.09888 + 0.388514i
\(478\) 0 0
\(479\) −22.6274 −1.03387 −0.516937 0.856024i \(-0.672928\pi\)
−0.516937 + 0.856024i \(0.672928\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 0 0
\(483\) 11.3137 + 16.0000i 0.514792 + 0.728025i
\(484\) 0 0
\(485\) 28.2843i 1.28432i
\(486\) 0 0
\(487\) 18.0000i 0.815658i 0.913058 + 0.407829i \(0.133714\pi\)
−0.913058 + 0.407829i \(0.866286\pi\)
\(488\) 0 0
\(489\) 6.00000 + 8.48528i 0.271329 + 0.383718i
\(490\) 0 0
\(491\) 31.1127 1.40410 0.702048 0.712129i \(-0.252269\pi\)
0.702048 + 0.712129i \(0.252269\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 22.6274 + 8.00000i 1.01703 + 0.359573i
\(496\) 0 0
\(497\) 11.3137i 0.507489i
\(498\) 0 0
\(499\) 34.0000i 1.52205i −0.648723 0.761025i \(-0.724697\pi\)
0.648723 0.761025i \(-0.275303\pi\)
\(500\) 0 0
\(501\) −8.00000 + 5.65685i −0.357414 + 0.252730i
\(502\) 0 0
\(503\) 5.65685 0.252227 0.126113 0.992016i \(-0.459750\pi\)
0.126113 + 0.992016i \(0.459750\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) 0 0
\(507\) −12.7279 + 9.00000i −0.565267 + 0.399704i
\(508\) 0 0
\(509\) 2.82843i 0.125368i 0.998033 + 0.0626839i \(0.0199660\pi\)
−0.998033 + 0.0626839i \(0.980034\pi\)
\(510\) 0 0
\(511\) 12.0000i 0.530849i
\(512\) 0 0
\(513\) 30.0000 8.48528i 1.32453 0.374634i
\(514\) 0 0
\(515\) −39.5980 −1.74490
\(516\) 0 0
\(517\) 32.0000 1.40736
\(518\) 0 0
\(519\) 14.1421 + 20.0000i 0.620771 + 0.877903i
\(520\) 0 0
\(521\) 5.65685i 0.247831i 0.992293 + 0.123916i \(0.0395452\pi\)
−0.992293 + 0.123916i \(0.960455\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) 0 0
\(525\) −6.00000 8.48528i −0.261861 0.370328i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 9.00000 0.391304
\(530\) 0 0
\(531\) −2.82843 + 8.00000i −0.122743 + 0.347170i
\(532\) 0 0
\(533\) 11.3137i 0.490051i
\(534\) 0 0
\(535\) 24.0000i 1.03761i
\(536\) 0 0
\(537\) −12.0000 + 8.48528i −0.517838 + 0.366167i
\(538\) 0 0
\(539\) −8.48528 −0.365487
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 0 0
\(543\) −8.48528 + 6.00000i −0.364138 + 0.257485i
\(544\) 0 0
\(545\) 50.9117i 2.18082i
\(546\) 0 0
\(547\) 38.0000i 1.62476i 0.583127 + 0.812381i \(0.301829\pi\)
−0.583127 + 0.812381i \(0.698171\pi\)
\(548\) 0 0
\(549\) 2.00000 5.65685i 0.0853579 0.241429i
\(550\) 0 0
\(551\) −16.9706 −0.722970
\(552\) 0 0
\(553\) 28.0000 1.19068
\(554\) 0 0
\(555\) 16.9706 + 24.0000i 0.720360 + 1.01874i
\(556\) 0 0
\(557\) 8.48528i 0.359533i −0.983709 0.179766i \(-0.942466\pi\)
0.983709 0.179766i \(-0.0575342\pi\)
\(558\) 0 0
\(559\) 4.00000i 0.169182i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.82843 0.119204 0.0596020 0.998222i \(-0.481017\pi\)
0.0596020 + 0.998222i \(0.481017\pi\)
\(564\) 0 0
\(565\) 32.0000 1.34625
\(566\) 0 0
\(567\) 11.3137 14.0000i 0.475131 0.587945i
\(568\) 0 0
\(569\) 5.65685i 0.237148i −0.992945 0.118574i \(-0.962168\pi\)
0.992945 0.118574i \(-0.0378322\pi\)
\(570\) 0 0
\(571\) 22.0000i 0.920671i 0.887745 + 0.460336i \(0.152271\pi\)
−0.887745 + 0.460336i \(0.847729\pi\)
\(572\) 0 0
\(573\) 32.0000 22.6274i 1.33682 0.945274i
\(574\) 0 0
\(575\) −16.9706 −0.707721
\(576\) 0 0
\(577\) −6.00000 −0.249783 −0.124892 0.992170i \(-0.539858\pi\)
−0.124892 + 0.992170i \(0.539858\pi\)
\(578\) 0 0
\(579\) −19.7990 + 14.0000i −0.822818 + 0.581820i
\(580\) 0 0
\(581\) 5.65685i 0.234686i
\(582\) 0 0
\(583\) 24.0000i 0.993978i
\(584\) 0 0
\(585\) −16.0000 5.65685i −0.661519 0.233882i
\(586\) 0 0
\(587\) −14.1421 −0.583708 −0.291854 0.956463i \(-0.594272\pi\)
−0.291854 + 0.956463i \(0.594272\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 19.7990 + 28.0000i 0.814422 + 1.15177i
\(592\) 0 0
\(593\) 33.9411i 1.39379i −0.717171 0.696897i \(-0.754563\pi\)
0.717171 0.696897i \(-0.245437\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.00000 + 2.82843i 0.0818546 + 0.115760i
\(598\) 0 0
\(599\) −39.5980 −1.61793 −0.808965 0.587857i \(-0.799972\pi\)
−0.808965 + 0.587857i \(0.799972\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −5.65685 2.00000i −0.230365 0.0814463i
\(604\) 0 0
\(605\) 8.48528i 0.344976i
\(606\) 0 0
\(607\) 14.0000i 0.568242i −0.958788 0.284121i \(-0.908298\pi\)
0.958788 0.284121i \(-0.0917018\pi\)
\(608\) 0 0
\(609\) −8.00000 + 5.65685i −0.324176 + 0.229227i
\(610\) 0 0
\(611\) −22.6274 −0.915407
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 0 0
\(615\) 22.6274 16.0000i 0.912426 0.645182i
\(616\) 0 0
\(617\) 28.2843i 1.13868i −0.822102 0.569341i \(-0.807198\pi\)
0.822102 0.569341i \(-0.192802\pi\)
\(618\) 0 0
\(619\) 10.0000i 0.401934i −0.979598 0.200967i \(-0.935592\pi\)
0.979598 0.200967i \(-0.0644084\pi\)
\(620\) 0 0
\(621\) −8.00000 28.2843i −0.321029 1.13501i
\(622\) 0 0
\(623\) 33.9411 1.35982
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) −16.9706 24.0000i −0.677739 0.958468i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 0 0
\(633\) −2.00000 2.82843i −0.0794929 0.112420i
\(634\) 0 0
\(635\) 50.9117 2.02037
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) −5.65685 + 16.0000i −0.223782 + 0.632950i
\(640\) 0 0
\(641\) 11.3137i 0.446865i 0.974719 + 0.223432i \(0.0717262\pi\)
−0.974719 + 0.223432i \(0.928274\pi\)
\(642\) 0 0
\(643\) 26.0000i 1.02534i −0.858586 0.512670i \(-0.828656\pi\)
0.858586 0.512670i \(-0.171344\pi\)
\(644\) 0 0
\(645\) −8.00000 + 5.65685i −0.315000 + 0.222738i
\(646\) 0 0
\(647\) 16.9706 0.667182 0.333591 0.942718i \(-0.391740\pi\)
0.333591 + 0.942718i \(0.391740\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) −5.65685 + 4.00000i −0.221710 + 0.156772i
\(652\) 0 0
\(653\) 14.1421i 0.553425i 0.960953 + 0.276712i \(0.0892449\pi\)
−0.960953 + 0.276712i \(0.910755\pi\)
\(654\) 0 0
\(655\) 56.0000i 2.18810i
\(656\) 0 0
\(657\) −6.00000 + 16.9706i −0.234082 + 0.662085i
\(658\) 0 0
\(659\) 14.1421 0.550899 0.275450 0.961315i \(-0.411173\pi\)
0.275450 + 0.961315i \(0.411173\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 33.9411i 1.31618i
\(666\) 0 0
\(667\) 16.0000i 0.619522i
\(668\) 0 0
\(669\) 2.00000 + 2.82843i 0.0773245 + 0.109353i
\(670\) 0 0
\(671\) −5.65685 −0.218380
\(672\) 0 0
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 0 0
\(675\) 4.24264 + 15.0000i 0.163299 + 0.577350i
\(676\) 0 0
\(677\) 2.82843i 0.108705i −0.998522 0.0543526i \(-0.982690\pi\)
0.998522 0.0543526i \(-0.0173095\pi\)
\(678\) 0 0
\(679\) 20.0000i 0.767530i
\(680\) 0 0
\(681\) 20.0000 14.1421i 0.766402 0.541928i
\(682\) 0 0
\(683\) 42.4264 1.62340 0.811701 0.584074i \(-0.198542\pi\)
0.811701 + 0.584074i \(0.198542\pi\)
\(684\) 0 0
\(685\) 16.0000 0.611329
\(686\) 0 0
\(687\) 14.1421 10.0000i 0.539556 0.381524i
\(688\) 0 0
\(689\) 16.9706i 0.646527i
\(690\) 0 0
\(691\) 26.0000i 0.989087i −0.869153 0.494543i \(-0.835335\pi\)
0.869153 0.494543i \(-0.164665\pi\)
\(692\) 0 0
\(693\) −16.0000 5.65685i −0.607790 0.214886i
\(694\) 0 0
\(695\) −28.2843 −1.07288
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −5.65685 8.00000i −0.213962 0.302588i
\(700\) 0 0
\(701\) 25.4558i 0.961454i 0.876870 + 0.480727i \(0.159627\pi\)
−0.876870 + 0.480727i \(0.840373\pi\)
\(702\) 0 0
\(703\) 36.0000i 1.35777i
\(704\) 0 0
\(705\) 32.0000 + 45.2548i 1.20519 + 1.70440i
\(706\) 0 0
\(707\) 5.65685 0.212748
\(708\) 0 0
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) −39.5980 14.0000i −1.48504 0.525041i
\(712\) 0 0
\(713\) 11.3137i 0.423702i
\(714\) 0 0
\(715\) 16.0000i 0.598366i
\(716\) 0 0
\(717\) −16.0000 + 11.3137i −0.597531 + 0.422518i
\(718\) 0 0
\(719\) 33.9411 1.26579 0.632895 0.774237i \(-0.281866\pi\)
0.632895 + 0.774237i \(0.281866\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) 0 0
\(723\) 2.82843 2.00000i 0.105190 0.0743808i
\(724\) 0 0
\(725\) 8.48528i 0.315135i
\(726\) 0 0
\(727\) 34.0000i 1.26099i 0.776193 + 0.630495i \(0.217148\pi\)
−0.776193 + 0.630495i \(0.782852\pi\)
\(728\) 0 0
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −46.0000 −1.69905 −0.849524 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 0 0
\(735\) −8.48528 12.0000i −0.312984 0.442627i
\(736\) 0 0
\(737\) 5.65685i 0.208373i
\(738\) 0 0
\(739\) 34.0000i 1.25071i −0.780340 0.625355i \(-0.784954\pi\)
0.780340 0.625355i \(-0.215046\pi\)
\(740\) 0 0
\(741\) 12.0000 + 16.9706i 0.440831 + 0.623429i
\(742\) 0 0
\(743\) −5.65685 −0.207530 −0.103765 0.994602i \(-0.533089\pi\)
−0.103765 + 0.994602i \(0.533089\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) 0 0
\(747\) 2.82843 8.00000i 0.103487 0.292705i
\(748\) 0 0
\(749\) 16.9706i 0.620091i
\(750\) 0 0
\(751\) 34.0000i 1.24068i 0.784334 + 0.620339i \(0.213005\pi\)
−0.784334 + 0.620339i \(0.786995\pi\)
\(752\) 0 0
\(753\) 12.0000 8.48528i 0.437304 0.309221i
\(754\) 0 0
\(755\) −39.5980 −1.44112
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 0 0
\(759\) −22.6274 + 16.0000i −0.821323 + 0.580763i
\(760\) 0 0
\(761\) 28.2843i 1.02530i −0.858596 0.512652i \(-0.828663\pi\)
0.858596 0.512652i \(-0.171337\pi\)
\(762\) 0 0
\(763\) 36.0000i 1.30329i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.65685 −0.204257
\(768\) 0 0
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) 0 0
\(771\) −22.6274 32.0000i −0.814907 1.15245i
\(772\) 0 0
\(773\) 25.4558i 0.915583i −0.889060 0.457792i \(-0.848641\pi\)
0.889060 0.457792i \(-0.151359\pi\)
\(774\) 0 0
\(775\) 6.00000i 0.215526i
\(776\) 0 0
\(777\) −12.0000 16.9706i −0.430498 0.608816i
\(778\) 0 0
\(779\) −33.9411 −1.21607
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) 0 0
\(783\) 14.1421 4.00000i 0.505399 0.142948i
\(784\) 0 0
\(785\) 39.5980i 1.41331i
\(786\) 0 0
\(787\) 38.0000i 1.35455i 0.735728 + 0.677277i \(0.236840\pi\)
−0.735728 + 0.677277i \(0.763160\pi\)
\(788\) 0 0
\(789\) −8.00000 + 5.65685i −0.284808 + 0.201389i
\(790\) 0 0
\(791\) −22.6274 −0.804538
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) 0 0
\(795\) 33.9411 24.0000i 1.20377 0.851192i
\(796\) 0 0
\(797\) 2.82843i 0.100188i 0.998745 + 0.0500940i \(0.0159521\pi\)
−0.998745 + 0.0500940i \(0.984048\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −48.0000 16.9706i −1.69600 0.599625i
\(802\) 0