Properties

Label 672.2.h.b.575.4
Level $672$
Weight $2$
Character 672.575
Analytic conductor $5.366$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
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: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 575.4
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 672.575
Dual form 672.2.h.b.575.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41421 + 1.00000i) q^{3} +4.24264i q^{5} -1.00000i q^{7} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(1.41421 + 1.00000i) q^{3} +4.24264i q^{5} -1.00000i q^{7} +(1.00000 + 2.82843i) q^{9} +4.24264 q^{11} -2.00000 q^{13} +(-4.24264 + 6.00000i) q^{15} -7.07107i q^{17} +4.00000i q^{19} +(1.00000 - 1.41421i) q^{21} +1.41421 q^{23} -13.0000 q^{25} +(-1.41421 + 5.00000i) q^{27} +2.82843i q^{29} +2.00000i q^{31} +(6.00000 + 4.24264i) q^{33} +4.24264 q^{35} -4.00000 q^{37} +(-2.82843 - 2.00000i) q^{39} +1.41421i q^{41} -8.00000i q^{43} +(-12.0000 + 4.24264i) q^{45} -2.82843 q^{47} -1.00000 q^{49} +(7.07107 - 10.0000i) q^{51} -5.65685i q^{53} +18.0000i q^{55} +(-4.00000 + 5.65685i) q^{57} +11.3137 q^{59} -2.00000 q^{61} +(2.82843 - 1.00000i) q^{63} -8.48528i q^{65} -8.00000i q^{67} +(2.00000 + 1.41421i) q^{69} +12.7279 q^{71} +14.0000 q^{73} +(-18.3848 - 13.0000i) q^{75} -4.24264i q^{77} -4.00000i q^{79} +(-7.00000 + 5.65685i) q^{81} +2.82843 q^{83} +30.0000 q^{85} +(-2.82843 + 4.00000i) q^{87} +9.89949i q^{89} +2.00000i q^{91} +(-2.00000 + 2.82843i) q^{93} -16.9706 q^{95} -10.0000 q^{97} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} - 8q^{13} + 4q^{21} - 52q^{25} + 24q^{33} - 16q^{37} - 48q^{45} - 4q^{49} - 16q^{57} - 8q^{61} + 8q^{69} + 56q^{73} - 28q^{81} + 120q^{85} - 8q^{93} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(5\) 4.24264i 1.89737i 0.316228 + 0.948683i \(0.397584\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0 0
\(11\) 4.24264 1.27920 0.639602 0.768706i \(-0.279099\pi\)
0.639602 + 0.768706i \(0.279099\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −4.24264 + 6.00000i −1.09545 + 1.54919i
\(16\) 0 0
\(17\) 7.07107i 1.71499i −0.514496 0.857493i \(-0.672021\pi\)
0.514496 0.857493i \(-0.327979\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 0 0
\(21\) 1.00000 1.41421i 0.218218 0.308607i
\(22\) 0 0
\(23\) 1.41421 0.294884 0.147442 0.989071i \(-0.452896\pi\)
0.147442 + 0.989071i \(0.452896\pi\)
\(24\) 0 0
\(25\) −13.0000 −2.60000
\(26\) 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
\(33\) 6.00000 + 4.24264i 1.04447 + 0.738549i
\(34\) 0 0
\(35\) 4.24264 0.717137
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) −2.82843 2.00000i −0.452911 0.320256i
\(40\) 0 0
\(41\) 1.41421i 0.220863i 0.993884 + 0.110432i \(0.0352233\pi\)
−0.993884 + 0.110432i \(0.964777\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) 0 0
\(45\) −12.0000 + 4.24264i −1.78885 + 0.632456i
\(46\) 0 0
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 7.07107 10.0000i 0.990148 1.40028i
\(52\) 0 0
\(53\) 5.65685i 0.777029i −0.921443 0.388514i \(-0.872988\pi\)
0.921443 0.388514i \(-0.127012\pi\)
\(54\) 0 0
\(55\) 18.0000i 2.42712i
\(56\) 0 0
\(57\) −4.00000 + 5.65685i −0.529813 + 0.749269i
\(58\) 0 0
\(59\) 11.3137 1.47292 0.736460 0.676481i \(-0.236496\pi\)
0.736460 + 0.676481i \(0.236496\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 2.82843 1.00000i 0.356348 0.125988i
\(64\) 0 0
\(65\) 8.48528i 1.05247i
\(66\) 0 0
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 0 0
\(69\) 2.00000 + 1.41421i 0.240772 + 0.170251i
\(70\) 0 0
\(71\) 12.7279 1.51053 0.755263 0.655422i \(-0.227509\pi\)
0.755263 + 0.655422i \(0.227509\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 0 0
\(75\) −18.3848 13.0000i −2.12289 1.50111i
\(76\) 0 0
\(77\) 4.24264i 0.483494i
\(78\) 0 0
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 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
\(85\) 30.0000 3.25396
\(86\) 0 0
\(87\) −2.82843 + 4.00000i −0.303239 + 0.428845i
\(88\) 0 0
\(89\) 9.89949i 1.04934i 0.851304 + 0.524672i \(0.175812\pi\)
−0.851304 + 0.524672i \(0.824188\pi\)
\(90\) 0 0
\(91\) 2.00000i 0.209657i
\(92\) 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 \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 4.24264 + 12.0000i 0.426401 + 1.20605i
\(100\) 0 0
\(101\) 4.24264i 0.422159i 0.977469 + 0.211079i \(0.0676978\pi\)
−0.977469 + 0.211079i \(0.932302\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 0 0
\(105\) 6.00000 + 4.24264i 0.585540 + 0.414039i
\(106\) 0 0
\(107\) 1.41421 0.136717 0.0683586 0.997661i \(-0.478224\pi\)
0.0683586 + 0.997661i \(0.478224\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −5.65685 4.00000i −0.536925 0.379663i
\(112\) 0 0
\(113\) 11.3137i 1.06430i −0.846649 0.532152i \(-0.821383\pi\)
0.846649 0.532152i \(-0.178617\pi\)
\(114\) 0 0
\(115\) 6.00000i 0.559503i
\(116\) 0 0
\(117\) −2.00000 5.65685i −0.184900 0.522976i
\(118\) 0 0
\(119\) −7.07107 −0.648204
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) −1.41421 + 2.00000i −0.127515 + 0.180334i
\(124\) 0 0
\(125\) 33.9411i 3.03579i
\(126\) 0 0
\(127\) 12.0000i 1.06483i −0.846484 0.532414i \(-0.821285\pi\)
0.846484 0.532414i \(-0.178715\pi\)
\(128\) 0 0
\(129\) 8.00000 11.3137i 0.704361 0.996116i
\(130\) 0 0
\(131\) 8.48528 0.741362 0.370681 0.928760i \(-0.379124\pi\)
0.370681 + 0.928760i \(0.379124\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) −21.2132 6.00000i −1.82574 0.516398i
\(136\) 0 0
\(137\) 8.48528i 0.724947i 0.931994 + 0.362473i \(0.118068\pi\)
−0.931994 + 0.362473i \(0.881932\pi\)
\(138\) 0 0
\(139\) 10.0000i 0.848189i 0.905618 + 0.424094i \(0.139408\pi\)
−0.905618 + 0.424094i \(0.860592\pi\)
\(140\) 0 0
\(141\) −4.00000 2.82843i −0.336861 0.238197i
\(142\) 0 0
\(143\) −8.48528 −0.709575
\(144\) 0 0
\(145\) −12.0000 −0.996546
\(146\) 0 0
\(147\) −1.41421 1.00000i −0.116642 0.0824786i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 24.0000i 1.95309i −0.215308 0.976546i \(-0.569076\pi\)
0.215308 0.976546i \(-0.430924\pi\)
\(152\) 0 0
\(153\) 20.0000 7.07107i 1.61690 0.571662i
\(154\) 0 0
\(155\) −8.48528 −0.681554
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) 5.65685 8.00000i 0.448618 0.634441i
\(160\) 0 0
\(161\) 1.41421i 0.111456i
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 0 0
\(165\) −18.0000 + 25.4558i −1.40130 + 1.98173i
\(166\) 0 0
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −11.3137 + 4.00000i −0.865181 + 0.305888i
\(172\) 0 0
\(173\) 7.07107i 0.537603i −0.963196 0.268802i \(-0.913372\pi\)
0.963196 0.268802i \(-0.0866276\pi\)
\(174\) 0 0
\(175\) 13.0000i 0.982708i
\(176\) 0 0
\(177\) 16.0000 + 11.3137i 1.20263 + 0.850390i
\(178\) 0 0
\(179\) −15.5563 −1.16274 −0.581368 0.813641i \(-0.697482\pi\)
−0.581368 + 0.813641i \(0.697482\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) −2.82843 2.00000i −0.209083 0.147844i
\(184\) 0 0
\(185\) 16.9706i 1.24770i
\(186\) 0 0
\(187\) 30.0000i 2.19382i
\(188\) 0 0
\(189\) 5.00000 + 1.41421i 0.363696 + 0.102869i
\(190\) 0 0
\(191\) −1.41421 −0.102329 −0.0511645 0.998690i \(-0.516293\pi\)
−0.0511645 + 0.998690i \(0.516293\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 8.48528 12.0000i 0.607644 0.859338i
\(196\) 0 0
\(197\) 5.65685i 0.403034i 0.979485 + 0.201517i \(0.0645872\pi\)
−0.979485 + 0.201517i \(0.935413\pi\)
\(198\) 0 0
\(199\) 8.00000i 0.567105i −0.958957 0.283552i \(-0.908487\pi\)
0.958957 0.283552i \(-0.0915130\pi\)
\(200\) 0 0
\(201\) 8.00000 11.3137i 0.564276 0.798007i
\(202\) 0 0
\(203\) 2.82843 0.198517
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 0 0
\(207\) 1.41421 + 4.00000i 0.0982946 + 0.278019i
\(208\) 0 0
\(209\) 16.9706i 1.17388i
\(210\) 0 0
\(211\) 8.00000i 0.550743i −0.961338 0.275371i \(-0.911199\pi\)
0.961338 0.275371i \(-0.0888008\pi\)
\(212\) 0 0
\(213\) 18.0000 + 12.7279i 1.23334 + 0.872103i
\(214\) 0 0
\(215\) 33.9411 2.31477
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) 19.7990 + 14.0000i 1.33789 + 0.946032i
\(220\) 0 0
\(221\) 14.1421i 0.951303i
\(222\) 0 0
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) −13.0000 36.7696i −0.866667 2.45130i
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −30.0000 −1.98246 −0.991228 0.132164i \(-0.957808\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 4.24264 6.00000i 0.279145 0.394771i
\(232\) 0 0
\(233\) 19.7990i 1.29707i 0.761183 + 0.648537i \(0.224619\pi\)
−0.761183 + 0.648537i \(0.775381\pi\)
\(234\) 0 0
\(235\) 12.0000i 0.782794i
\(236\) 0 0
\(237\) 4.00000 5.65685i 0.259828 0.367452i
\(238\) 0 0
\(239\) 18.3848 1.18921 0.594606 0.804017i \(-0.297308\pi\)
0.594606 + 0.804017i \(0.297308\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) 0 0
\(245\) 4.24264i 0.271052i
\(246\) 0 0
\(247\) 8.00000i 0.509028i
\(248\) 0 0
\(249\) 4.00000 + 2.82843i 0.253490 + 0.179244i
\(250\) 0 0
\(251\) −5.65685 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 42.4264 + 30.0000i 2.65684 + 1.87867i
\(256\) 0 0
\(257\) 1.41421i 0.0882162i 0.999027 + 0.0441081i \(0.0140446\pi\)
−0.999027 + 0.0441081i \(0.985955\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) 0 0
\(261\) −8.00000 + 2.82843i −0.495188 + 0.175075i
\(262\) 0 0
\(263\) −29.6985 −1.83129 −0.915644 0.401991i \(-0.868318\pi\)
−0.915644 + 0.401991i \(0.868318\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) −9.89949 + 14.0000i −0.605839 + 0.856786i
\(268\) 0 0
\(269\) 15.5563i 0.948487i −0.880394 0.474244i \(-0.842722\pi\)
0.880394 0.474244i \(-0.157278\pi\)
\(270\) 0 0
\(271\) 22.0000i 1.33640i −0.743980 0.668202i \(-0.767064\pi\)
0.743980 0.668202i \(-0.232936\pi\)
\(272\) 0 0
\(273\) −2.00000 + 2.82843i −0.121046 + 0.171184i
\(274\) 0 0
\(275\) −55.1543 −3.32593
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −5.65685 + 2.00000i −0.338667 + 0.119737i
\(280\) 0 0
\(281\) 19.7990i 1.18111i −0.806998 0.590554i \(-0.798909\pi\)
0.806998 0.590554i \(-0.201091\pi\)
\(282\) 0 0
\(283\) 20.0000i 1.18888i 0.804141 + 0.594438i \(0.202626\pi\)
−0.804141 + 0.594438i \(0.797374\pi\)
\(284\) 0 0
\(285\) −24.0000 16.9706i −1.42164 1.00525i
\(286\) 0 0
\(287\) 1.41421 0.0834784
\(288\) 0 0
\(289\) −33.0000 −1.94118
\(290\) 0 0
\(291\) −14.1421 10.0000i −0.829027 0.586210i
\(292\) 0 0
\(293\) 32.5269i 1.90024i 0.311881 + 0.950121i \(0.399041\pi\)
−0.311881 + 0.950121i \(0.600959\pi\)
\(294\) 0 0
\(295\) 48.0000i 2.79467i
\(296\) 0 0
\(297\) −6.00000 + 21.2132i −0.348155 + 1.23091i
\(298\) 0 0
\(299\) −2.82843 −0.163572
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 0 0
\(303\) −4.24264 + 6.00000i −0.243733 + 0.344691i
\(304\) 0 0
\(305\) 8.48528i 0.485866i
\(306\) 0 0
\(307\) 20.0000i 1.14146i 0.821138 + 0.570730i \(0.193340\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(308\) 0 0
\(309\) −6.00000 + 8.48528i −0.341328 + 0.482711i
\(310\) 0 0
\(311\) −19.7990 −1.12270 −0.561349 0.827579i \(-0.689717\pi\)
−0.561349 + 0.827579i \(0.689717\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 4.24264 + 12.0000i 0.239046 + 0.676123i
\(316\) 0 0
\(317\) 11.3137i 0.635441i −0.948184 0.317721i \(-0.897083\pi\)
0.948184 0.317721i \(-0.102917\pi\)
\(318\) 0 0
\(319\) 12.0000i 0.671871i
\(320\) 0 0
\(321\) 2.00000 + 1.41421i 0.111629 + 0.0789337i
\(322\) 0 0
\(323\) 28.2843 1.57378
\(324\) 0 0
\(325\) 26.0000 1.44222
\(326\) 0 0
\(327\) 2.82843 + 2.00000i 0.156412 + 0.110600i
\(328\) 0 0
\(329\) 2.82843i 0.155936i
\(330\) 0 0
\(331\) 20.0000i 1.09930i 0.835395 + 0.549650i \(0.185239\pi\)
−0.835395 + 0.549650i \(0.814761\pi\)
\(332\) 0 0
\(333\) −4.00000 11.3137i −0.219199 0.619987i
\(334\) 0 0
\(335\) 33.9411 1.85440
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0 0
\(339\) 11.3137 16.0000i 0.614476 0.869001i
\(340\) 0 0
\(341\) 8.48528i 0.459504i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −6.00000 + 8.48528i −0.323029 + 0.456832i
\(346\) 0 0
\(347\) 7.07107 0.379595 0.189797 0.981823i \(-0.439217\pi\)
0.189797 + 0.981823i \(0.439217\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 2.82843 10.0000i 0.150970 0.533761i
\(352\) 0 0
\(353\) 12.7279i 0.677439i 0.940887 + 0.338719i \(0.109994\pi\)
−0.940887 + 0.338719i \(0.890006\pi\)
\(354\) 0 0
\(355\) 54.0000i 2.86602i
\(356\) 0 0
\(357\) −10.0000 7.07107i −0.529256 0.374241i
\(358\) 0 0
\(359\) 18.3848 0.970311 0.485156 0.874428i \(-0.338763\pi\)
0.485156 + 0.874428i \(0.338763\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 0 0
\(363\) 9.89949 + 7.00000i 0.519589 + 0.367405i
\(364\) 0 0
\(365\) 59.3970i 3.10898i
\(366\) 0 0
\(367\) 24.0000i 1.25279i −0.779506 0.626395i \(-0.784530\pi\)
0.779506 0.626395i \(-0.215470\pi\)
\(368\) 0 0
\(369\) −4.00000 + 1.41421i −0.208232 + 0.0736210i
\(370\) 0 0
\(371\) −5.65685 −0.293689
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 33.9411 48.0000i 1.75271 2.47871i
\(376\) 0 0
\(377\) 5.65685i 0.291343i
\(378\) 0 0
\(379\) 12.0000i 0.616399i 0.951322 + 0.308199i \(0.0997264\pi\)
−0.951322 + 0.308199i \(0.900274\pi\)
\(380\) 0 0
\(381\) 12.0000 16.9706i 0.614779 0.869428i
\(382\) 0 0
\(383\) −33.9411 −1.73431 −0.867155 0.498038i \(-0.834054\pi\)
−0.867155 + 0.498038i \(0.834054\pi\)
\(384\) 0 0
\(385\) 18.0000 0.917365
\(386\) 0 0
\(387\) 22.6274 8.00000i 1.15022 0.406663i
\(388\) 0 0
\(389\) 25.4558i 1.29066i 0.763903 + 0.645331i \(0.223281\pi\)
−0.763903 + 0.645331i \(0.776719\pi\)
\(390\) 0 0
\(391\) 10.0000i 0.505722i
\(392\) 0 0
\(393\) 12.0000 + 8.48528i 0.605320 + 0.428026i
\(394\) 0 0
\(395\) 16.9706 0.853882
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 5.65685 + 4.00000i 0.283197 + 0.200250i
\(400\) 0 0
\(401\) 8.48528i 0.423735i −0.977298 0.211867i \(-0.932046\pi\)
0.977298 0.211867i \(-0.0679545\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 0 0
\(405\) −24.0000 29.6985i −1.19257 1.47573i
\(406\) 0 0
\(407\) −16.9706 −0.841200
\(408\) 0 0
\(409\) −34.0000 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) 0 0
\(411\) −8.48528 + 12.0000i −0.418548 + 0.591916i
\(412\) 0 0
\(413\) 11.3137i 0.556711i
\(414\) 0 0
\(415\) 12.0000i 0.589057i
\(416\) 0 0
\(417\) −10.0000 + 14.1421i −0.489702 + 0.692543i
\(418\) 0 0
\(419\) −5.65685 −0.276355 −0.138178 0.990407i \(-0.544125\pi\)
−0.138178 + 0.990407i \(0.544125\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 0 0
\(423\) −2.82843 8.00000i −0.137523 0.388973i
\(424\) 0 0
\(425\) 91.9239i 4.45896i
\(426\) 0 0
\(427\) 2.00000i 0.0967868i
\(428\) 0 0
\(429\) −12.0000 8.48528i −0.579365 0.409673i
\(430\) 0 0
\(431\) 15.5563 0.749323 0.374661 0.927162i \(-0.377759\pi\)
0.374661 + 0.927162i \(0.377759\pi\)
\(432\) 0 0
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) −16.9706 12.0000i −0.813676 0.575356i
\(436\) 0 0
\(437\) 5.65685i 0.270604i
\(438\) 0 0
\(439\) 16.0000i 0.763638i 0.924237 + 0.381819i \(0.124702\pi\)
−0.924237 + 0.381819i \(0.875298\pi\)
\(440\) 0 0
\(441\) −1.00000 2.82843i −0.0476190 0.134687i
\(442\) 0 0
\(443\) −7.07107 −0.335957 −0.167978 0.985791i \(-0.553724\pi\)
−0.167978 + 0.985791i \(0.553724\pi\)
\(444\) 0 0
\(445\) −42.0000 −1.99099
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.65685i 0.266963i −0.991051 0.133482i \(-0.957384\pi\)
0.991051 0.133482i \(-0.0426157\pi\)
\(450\) 0 0
\(451\) 6.00000i 0.282529i
\(452\) 0 0
\(453\) 24.0000 33.9411i 1.12762 1.59469i
\(454\) 0 0
\(455\) −8.48528 −0.397796
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 35.3553 + 10.0000i 1.65025 + 0.466760i
\(460\) 0 0
\(461\) 9.89949i 0.461065i −0.973065 0.230533i \(-0.925953\pi\)
0.973065 0.230533i \(-0.0740469\pi\)
\(462\) 0 0
\(463\) 8.00000i 0.371792i −0.982569 0.185896i \(-0.940481\pi\)
0.982569 0.185896i \(-0.0595187\pi\)
\(464\) 0 0
\(465\) −12.0000 8.48528i −0.556487 0.393496i
\(466\) 0 0
\(467\) 11.3137 0.523536 0.261768 0.965131i \(-0.415694\pi\)
0.261768 + 0.965131i \(0.415694\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 19.7990 + 14.0000i 0.912289 + 0.645086i
\(472\) 0 0
\(473\) 33.9411i 1.56061i
\(474\) 0 0
\(475\) 52.0000i 2.38592i
\(476\) 0 0
\(477\) 16.0000 5.65685i 0.732590 0.259010i
\(478\) 0 0
\(479\) 8.48528 0.387702 0.193851 0.981031i \(-0.437902\pi\)
0.193851 + 0.981031i \(0.437902\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) 1.41421 2.00000i 0.0643489 0.0910032i
\(484\) 0 0
\(485\) 42.4264i 1.92648i
\(486\) 0 0
\(487\) 8.00000i 0.362515i 0.983436 + 0.181257i \(0.0580167\pi\)
−0.983436 + 0.181257i \(0.941983\pi\)
\(488\) 0 0
\(489\) −4.00000 + 5.65685i −0.180886 + 0.255812i
\(490\) 0 0
\(491\) −18.3848 −0.829693 −0.414847 0.909891i \(-0.636165\pi\)
−0.414847 + 0.909891i \(0.636165\pi\)
\(492\) 0 0
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) −50.9117 + 18.0000i −2.28831 + 0.809040i
\(496\) 0 0
\(497\) 12.7279i 0.570925i
\(498\) 0 0
\(499\) 36.0000i 1.61158i −0.592200 0.805791i \(-0.701741\pi\)
0.592200 0.805791i \(-0.298259\pi\)
\(500\) 0 0
\(501\) 28.0000 + 19.7990i 1.25095 + 0.884554i
\(502\) 0 0
\(503\) −33.9411 −1.51336 −0.756680 0.653785i \(-0.773180\pi\)
−0.756680 + 0.653785i \(0.773180\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −12.7279 9.00000i −0.565267 0.399704i
\(508\) 0 0
\(509\) 24.0416i 1.06563i 0.846233 + 0.532813i \(0.178865\pi\)
−0.846233 + 0.532813i \(0.821135\pi\)
\(510\) 0 0
\(511\) 14.0000i 0.619324i
\(512\) 0 0
\(513\) −20.0000 5.65685i −0.883022 0.249756i
\(514\) 0 0
\(515\) −25.4558 −1.12172
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 7.07107 10.0000i 0.310385 0.438951i
\(520\) 0 0
\(521\) 26.8701i 1.17720i −0.808425 0.588599i \(-0.799680\pi\)
0.808425 0.588599i \(-0.200320\pi\)
\(522\) 0 0
\(523\) 26.0000i 1.13690i −0.822718 0.568450i \(-0.807543\pi\)
0.822718 0.568450i \(-0.192457\pi\)
\(524\) 0 0
\(525\) −13.0000 + 18.3848i −0.567367 + 0.802377i
\(526\) 0 0
\(527\) 14.1421 0.616041
\(528\) 0 0
\(529\) −21.0000 −0.913043
\(530\) 0 0
\(531\) 11.3137 + 32.0000i 0.490973 + 1.38868i
\(532\) 0 0
\(533\) 2.82843i 0.122513i
\(534\) 0 0
\(535\) 6.00000i 0.259403i
\(536\) 0 0
\(537\) −22.0000 15.5563i −0.949370 0.671306i
\(538\) 0 0
\(539\) −4.24264 −0.182743
\(540\) 0 0
\(541\) −32.0000 −1.37579 −0.687894 0.725811i \(-0.741464\pi\)
−0.687894 + 0.725811i \(0.741464\pi\)
\(542\) 0 0
\(543\) 8.48528 + 6.00000i 0.364138 + 0.257485i
\(544\) 0 0
\(545\) 8.48528i 0.363470i
\(546\) 0 0
\(547\) 32.0000i 1.36822i 0.729378 + 0.684111i \(0.239809\pi\)
−0.729378 + 0.684111i \(0.760191\pi\)
\(548\) 0 0
\(549\) −2.00000 5.65685i −0.0853579 0.241429i
\(550\) 0 0
\(551\) −11.3137 −0.481980
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 0 0
\(555\) 16.9706 24.0000i 0.720360 1.01874i
\(556\) 0 0
\(557\) 22.6274i 0.958754i −0.877609 0.479377i \(-0.840863\pi\)
0.877609 0.479377i \(-0.159137\pi\)
\(558\) 0 0
\(559\) 16.0000i 0.676728i
\(560\) 0 0
\(561\) 30.0000 42.4264i 1.26660 1.79124i
\(562\) 0 0
\(563\) −11.3137 −0.476816 −0.238408 0.971165i \(-0.576626\pi\)
−0.238408 + 0.971165i \(0.576626\pi\)
\(564\) 0 0
\(565\) 48.0000 2.01938
\(566\) 0 0
\(567\) 5.65685 + 7.00000i 0.237566 + 0.293972i
\(568\) 0 0
\(569\) 19.7990i 0.830017i 0.909818 + 0.415008i \(0.136221\pi\)
−0.909818 + 0.415008i \(0.863779\pi\)
\(570\) 0 0
\(571\) 32.0000i 1.33916i −0.742741 0.669579i \(-0.766474\pi\)
0.742741 0.669579i \(-0.233526\pi\)
\(572\) 0 0
\(573\) −2.00000 1.41421i −0.0835512 0.0590796i
\(574\) 0 0
\(575\) −18.3848 −0.766698
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −5.65685 4.00000i −0.235091 0.166234i
\(580\) 0 0
\(581\) 2.82843i 0.117343i
\(582\) 0 0
\(583\) 24.0000i 0.993978i
\(584\) 0 0
\(585\) 24.0000 8.48528i 0.992278 0.350823i
\(586\) 0 0
\(587\) −28.2843 −1.16742 −0.583708 0.811963i \(-0.698399\pi\)
−0.583708 + 0.811963i \(0.698399\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −5.65685 + 8.00000i −0.232692 + 0.329076i
\(592\) 0 0
\(593\) 1.41421i 0.0580748i −0.999578 0.0290374i \(-0.990756\pi\)
0.999578 0.0290374i \(-0.00924419\pi\)
\(594\) 0 0
\(595\) 30.0000i 1.22988i
\(596\) 0 0
\(597\) 8.00000 11.3137i 0.327418 0.463039i
\(598\) 0 0
\(599\) −9.89949 −0.404482 −0.202241 0.979336i \(-0.564822\pi\)
−0.202241 + 0.979336i \(0.564822\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 22.6274 8.00000i 0.921460 0.325785i
\(604\) 0 0
\(605\) 29.6985i 1.20742i
\(606\) 0 0
\(607\) 24.0000i 0.974130i −0.873366 0.487065i \(-0.838067\pi\)
0.873366 0.487065i \(-0.161933\pi\)
\(608\) 0 0
\(609\) 4.00000 + 2.82843i 0.162088 + 0.114614i
\(610\) 0 0
\(611\) 5.65685 0.228852
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) −8.48528 6.00000i −0.342160 0.241943i
\(616\) 0 0
\(617\) 14.1421i 0.569341i −0.958625 0.284670i \(-0.908116\pi\)
0.958625 0.284670i \(-0.0918842\pi\)
\(618\) 0 0
\(619\) 30.0000i 1.20580i 0.797816 + 0.602901i \(0.205989\pi\)
−0.797816 + 0.602901i \(0.794011\pi\)
\(620\) 0 0
\(621\) −2.00000 + 7.07107i −0.0802572 + 0.283752i
\(622\) 0 0
\(623\) 9.89949 0.396615
\(624\) 0 0
\(625\) 79.0000 3.16000
\(626\) 0 0
\(627\) −16.9706 + 24.0000i −0.677739 + 0.958468i
\(628\) 0 0
\(629\) 28.2843i 1.12777i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 8.00000 11.3137i 0.317971 0.449680i
\(634\) 0 0
\(635\) 50.9117 2.02037
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 12.7279 + 36.0000i 0.503509 + 1.42414i
\(640\) 0 0
\(641\) 25.4558i 1.00545i −0.864448 0.502723i \(-0.832332\pi\)
0.864448 0.502723i \(-0.167668\pi\)
\(642\) 0 0
\(643\) 44.0000i 1.73519i −0.497271 0.867595i \(-0.665665\pi\)
0.497271 0.867595i \(-0.334335\pi\)
\(644\) 0 0
\(645\) 48.0000 + 33.9411i 1.89000 + 1.33643i
\(646\) 0 0
\(647\) −2.82843 −0.111197 −0.0555985 0.998453i \(-0.517707\pi\)
−0.0555985 + 0.998453i \(0.517707\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 0 0
\(651\) 2.82843 + 2.00000i 0.110855 + 0.0783862i
\(652\) 0 0
\(653\) 14.1421i 0.553425i −0.960953 0.276712i \(-0.910755\pi\)
0.960953 0.276712i \(-0.0892449\pi\)
\(654\) 0 0
\(655\) 36.0000i 1.40664i
\(656\) 0 0
\(657\) 14.0000 + 39.5980i 0.546192 + 1.54486i
\(658\) 0 0
\(659\) 7.07107 0.275450 0.137725 0.990471i \(-0.456021\pi\)
0.137725 + 0.990471i \(0.456021\pi\)
\(660\) 0 0
\(661\) −50.0000 −1.94477 −0.972387 0.233373i \(-0.925024\pi\)
−0.972387 + 0.233373i \(0.925024\pi\)
\(662\) 0 0
\(663\) −14.1421 + 20.0000i −0.549235 + 0.776736i
\(664\) 0 0
\(665\) 16.9706i 0.658090i
\(666\) 0 0
\(667\) 4.00000i 0.154881i
\(668\) 0 0
\(669\) 8.00000 11.3137i 0.309298 0.437413i
\(670\) 0 0
\(671\) −8.48528 −0.327571
\(672\) 0 0
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) 0 0
\(675\) 18.3848 65.0000i 0.707630 2.50185i
\(676\) 0 0
\(677\) 9.89949i 0.380468i −0.981739 0.190234i \(-0.939075\pi\)
0.981739 0.190234i \(-0.0609248\pi\)
\(678\) 0 0
\(679\) 10.0000i 0.383765i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.07107 −0.270567 −0.135283 0.990807i \(-0.543195\pi\)
−0.135283 + 0.990807i \(0.543195\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) 0 0
\(687\) −42.4264 30.0000i −1.61867 1.14457i
\(688\) 0 0
\(689\) 11.3137i 0.431018i
\(690\) 0 0
\(691\) 14.0000i 0.532585i −0.963892 0.266293i \(-0.914201\pi\)
0.963892 0.266293i \(-0.0857987\pi\)
\(692\) 0 0
\(693\) 12.0000 4.24264i 0.455842 0.161165i
\(694\) 0 0
\(695\) −42.4264 −1.60933
\(696\) 0 0
\(697\) 10.0000 0.378777
\(698\) 0 0
\(699\) −19.7990 + 28.0000i −0.748867 + 1.05906i
\(700\) 0 0
\(701\) 25.4558i 0.961454i 0.876870 + 0.480727i \(0.159627\pi\)
−0.876870 + 0.480727i \(0.840373\pi\)
\(702\) 0 0
\(703\) 16.0000i 0.603451i
\(704\) 0 0
\(705\) 12.0000 16.9706i 0.451946 0.639148i
\(706\) 0 0
\(707\) 4.24264 0.159561
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 0 0
\(711\) 11.3137 4.00000i 0.424297 0.150012i
\(712\) 0 0
\(713\) 2.82843i 0.105925i
\(714\) 0 0
\(715\) 36.0000i 1.34632i
\(716\) 0 0
\(717\) 26.0000 + 18.3848i 0.970988 + 0.686592i
\(718\) 0 0
\(719\) 22.6274 0.843860 0.421930 0.906628i \(-0.361353\pi\)
0.421930 + 0.906628i \(0.361353\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) −25.4558 18.0000i −0.946713 0.669427i
\(724\) 0 0
\(725\) 36.7696i 1.36559i
\(726\) 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
\(731\) −56.5685 −2.09226
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 4.24264 6.00000i 0.156492 0.221313i
\(736\) 0 0
\(737\) 33.9411i 1.25024i
\(738\) 0 0
\(739\) 4.00000i 0.147142i 0.997290 + 0.0735712i \(0.0234396\pi\)
−0.997290 + 0.0735712i \(0.976560\pi\)
\(740\) 0 0
\(741\) 8.00000 11.3137i 0.293887 0.415619i
\(742\) 0 0
\(743\) −1.41421 −0.0518825 −0.0259412 0.999663i \(-0.508258\pi\)
−0.0259412 + 0.999663i \(0.508258\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.82843 + 8.00000i 0.103487 + 0.292705i
\(748\) 0 0
\(749\) 1.41421i 0.0516742i
\(750\) 0 0
\(751\) 36.0000i 1.31366i −0.754039 0.656829i \(-0.771897\pi\)
0.754039 0.656829i \(-0.228103\pi\)
\(752\) 0 0
\(753\) −8.00000 5.65685i −0.291536 0.206147i
\(754\) 0 0
\(755\) 101.823 3.70573
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 0 0
\(759\) 8.48528 + 6.00000i 0.307996 + 0.217786i
\(760\) 0 0
\(761\) 21.2132i 0.768978i −0.923130 0.384489i \(-0.874378\pi\)
0.923130 0.384489i \(-0.125622\pi\)
\(762\) 0 0
\(763\) 2.00000i 0.0724049i
\(764\) 0 0
\(765\) 30.0000 + 84.8528i 1.08465 + 3.06786i
\(766\) 0 0
\(767\) −22.6274 −0.817029
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) −1.41421 + 2.00000i −0.0509317 + 0.0720282i
\(772\) 0 0
\(773\) 32.5269i 1.16991i −0.811065 0.584956i \(-0.801112\pi\)
0.811065 0.584956i \(-0.198888\pi\)
\(774\) 0 0
\(775\) 26.0000i 0.933948i
\(776\) 0 0
\(777\) −4.00000 + 5.65685i −0.143499 + 0.202939i
\(778\) 0 0
\(779\) −5.65685 −0.202678
\(780\) 0 0
\(781\) 54.0000 1.93227
\(782\) 0 0
\(783\) −14.1421 4.00000i −0.505399 0.142948i
\(784\) 0 0
\(785\) 59.3970i 2.11997i
\(786\) 0 0
\(787\) 22.0000i 0.784215i 0.919919 + 0.392108i \(0.128254\pi\)
−0.919919 + 0.392108i \(0.871746\pi\)
\(788\) 0 0
\(789\) −42.0000 29.6985i −1.49524 1.05729i
\(790\) 0 0
\(791\) −11.3137 −0.402269
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) 0 0
\(795\) 33.9411 + 24.0000i 1.20377 + 0.851192i
\(796\) 0 0
\(797\) 32.5269i 1.15216i −0.817392 0.576081i \(-0.804581\pi\)
0.817392 0.576081i \(-0.195419\pi\)
\(798\) 0 0
\(799\) 20.0000i 0.707549i
\(800\) 0 0
\(801\) −28.0000 + 9.89949i −0.989331 +