Properties

Label 1600.2.l.f.401.5
Level $1600$
Weight $2$
Character 1600.401
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.5
Root \(1.22306 - 0.710021i\) of defining polynomial
Character \(\chi\) \(=\) 1600.401
Dual form 1600.2.l.f.1201.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.09156 + 1.09156i) q^{3} -0.973926i q^{7} -0.616985i q^{9} +O(q^{10})\) \(q+(1.09156 + 1.09156i) q^{3} -0.973926i q^{7} -0.616985i q^{9} +(-1.40810 + 1.40810i) q^{11} +(-4.60317 - 4.60317i) q^{13} +0.490104 q^{17} +(-4.54863 - 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} -1.94308i q^{23} +(3.94816 - 3.94816i) q^{27} +(-3.74613 - 3.74613i) q^{29} -4.29021 q^{31} -3.07405 q^{33} +(4.55320 - 4.55320i) q^{37} -10.0493i q^{39} +10.1542i q^{41} +(1.79055 - 1.79055i) q^{43} -10.0162 q^{47} +6.05147 q^{49} +(0.534979 + 0.534979i) q^{51} +(5.61412 - 5.61412i) q^{53} -9.93022i q^{57} +(-8.44185 + 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} -0.600897 q^{63} +(-7.07504 - 7.07504i) q^{67} +(2.12099 - 2.12099i) q^{69} +0.897891i q^{71} +9.71555i q^{73} +(1.37138 + 1.37138i) q^{77} +14.7857 q^{79} +6.76838 q^{81} +(-0.815000 - 0.815000i) q^{83} -8.17827i q^{87} -1.12404i q^{89} +(-4.48314 + 4.48314i) q^{91} +(-4.68303 - 4.68303i) q^{93} -7.54442 q^{97} +(0.868775 + 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{3} + O(q^{10}) \) \( 12q - 2q^{3} + 2q^{11} - 4q^{13} - 8q^{17} + 14q^{19} - 20q^{21} + 10q^{27} + 4q^{31} + 28q^{33} + 8q^{37} - 8q^{47} + 4q^{49} - 10q^{51} - 16q^{53} - 20q^{59} + 4q^{61} + 8q^{63} - 50q^{67} - 8q^{77} - 12q^{79} - 8q^{81} + 2q^{83} - 44q^{93} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 1.09156 + 1.09156i 0.630214 + 0.630214i 0.948122 0.317908i \(-0.102980\pi\)
−0.317908 + 0.948122i \(0.602980\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.973926i 0.368109i −0.982916 0.184055i \(-0.941078\pi\)
0.982916 0.184055i \(-0.0589224\pi\)
\(8\) 0 0
\(9\) 0.616985i 0.205662i
\(10\) 0 0
\(11\) −1.40810 + 1.40810i −0.424558 + 0.424558i −0.886769 0.462212i \(-0.847056\pi\)
0.462212 + 0.886769i \(0.347056\pi\)
\(12\) 0 0
\(13\) −4.60317 4.60317i −1.27669 1.27669i −0.942510 0.334179i \(-0.891541\pi\)
−0.334179 0.942510i \(-0.608459\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.490104 0.118868 0.0594338 0.998232i \(-0.481070\pi\)
0.0594338 + 0.998232i \(0.481070\pi\)
\(18\) 0 0
\(19\) −4.54863 4.54863i −1.04353 1.04353i −0.999009 0.0445187i \(-0.985825\pi\)
−0.0445187 0.999009i \(-0.514175\pi\)
\(20\) 0 0
\(21\) 1.06310 1.06310i 0.231988 0.231988i
\(22\) 0 0
\(23\) 1.94308i 0.405160i −0.979266 0.202580i \(-0.935067\pi\)
0.979266 0.202580i \(-0.0649325\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.94816 3.94816i 0.759824 0.759824i
\(28\) 0 0
\(29\) −3.74613 3.74613i −0.695640 0.695640i 0.267827 0.963467i \(-0.413694\pi\)
−0.963467 + 0.267827i \(0.913694\pi\)
\(30\) 0 0
\(31\) −4.29021 −0.770545 −0.385272 0.922803i \(-0.625893\pi\)
−0.385272 + 0.922803i \(0.625893\pi\)
\(32\) 0 0
\(33\) −3.07405 −0.535124
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.55320 4.55320i 0.748542 0.748542i −0.225663 0.974205i \(-0.572455\pi\)
0.974205 + 0.225663i \(0.0724549\pi\)
\(38\) 0 0
\(39\) 10.0493i 1.60917i
\(40\) 0 0
\(41\) 10.1542i 1.58582i 0.609341 + 0.792908i \(0.291434\pi\)
−0.609341 + 0.792908i \(0.708566\pi\)
\(42\) 0 0
\(43\) 1.79055 1.79055i 0.273057 0.273057i −0.557273 0.830329i \(-0.688152\pi\)
0.830329 + 0.557273i \(0.188152\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.0162 −1.46102 −0.730510 0.682902i \(-0.760717\pi\)
−0.730510 + 0.682902i \(0.760717\pi\)
\(48\) 0 0
\(49\) 6.05147 0.864495
\(50\) 0 0
\(51\) 0.534979 + 0.534979i 0.0749120 + 0.0749120i
\(52\) 0 0
\(53\) 5.61412 5.61412i 0.771158 0.771158i −0.207151 0.978309i \(-0.566419\pi\)
0.978309 + 0.207151i \(0.0664190\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 9.93022i 1.31529i
\(58\) 0 0
\(59\) −8.44185 + 8.44185i −1.09904 + 1.09904i −0.104512 + 0.994524i \(0.533328\pi\)
−0.994524 + 0.104512i \(0.966672\pi\)
\(60\) 0 0
\(61\) 3.01095 + 3.01095i 0.385513 + 0.385513i 0.873084 0.487571i \(-0.162117\pi\)
−0.487571 + 0.873084i \(0.662117\pi\)
\(62\) 0 0
\(63\) −0.600897 −0.0757060
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.07504 7.07504i −0.864354 0.864354i 0.127486 0.991840i \(-0.459309\pi\)
−0.991840 + 0.127486i \(0.959309\pi\)
\(68\) 0 0
\(69\) 2.12099 2.12099i 0.255337 0.255337i
\(70\) 0 0
\(71\) 0.897891i 0.106560i 0.998580 + 0.0532800i \(0.0169676\pi\)
−0.998580 + 0.0532800i \(0.983032\pi\)
\(72\) 0 0
\(73\) 9.71555i 1.13712i 0.822642 + 0.568559i \(0.192499\pi\)
−0.822642 + 0.568559i \(0.807501\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.37138 + 1.37138i 0.156284 + 0.156284i
\(78\) 0 0
\(79\) 14.7857 1.66352 0.831760 0.555135i \(-0.187334\pi\)
0.831760 + 0.555135i \(0.187334\pi\)
\(80\) 0 0
\(81\) 6.76838 0.752042
\(82\) 0 0
\(83\) −0.815000 0.815000i −0.0894579 0.0894579i 0.660962 0.750420i \(-0.270149\pi\)
−0.750420 + 0.660962i \(0.770149\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.17827i 0.876803i
\(88\) 0 0
\(89\) 1.12404i 0.119148i −0.998224 0.0595739i \(-0.981026\pi\)
0.998224 0.0595739i \(-0.0189742\pi\)
\(90\) 0 0
\(91\) −4.48314 + 4.48314i −0.469961 + 0.469961i
\(92\) 0 0
\(93\) −4.68303 4.68303i −0.485608 0.485608i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −7.54442 −0.766019 −0.383010 0.923744i \(-0.625112\pi\)
−0.383010 + 0.923744i \(0.625112\pi\)
\(98\) 0 0
\(99\) 0.868775 + 0.868775i 0.0873152 + 0.0873152i
\(100\) 0 0
\(101\) −2.60535 + 2.60535i −0.259242 + 0.259242i −0.824746 0.565504i \(-0.808682\pi\)
0.565504 + 0.824746i \(0.308682\pi\)
\(102\) 0 0
\(103\) 13.8146i 1.36120i −0.732657 0.680598i \(-0.761720\pi\)
0.732657 0.680598i \(-0.238280\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.89124 9.89124i 0.956222 0.956222i −0.0428589 0.999081i \(-0.513647\pi\)
0.999081 + 0.0428589i \(0.0136466\pi\)
\(108\) 0 0
\(109\) −11.5454 11.5454i −1.10584 1.10584i −0.993691 0.112154i \(-0.964225\pi\)
−0.112154 0.993691i \(-0.535775\pi\)
\(110\) 0 0
\(111\) 9.94021 0.943483
\(112\) 0 0
\(113\) 17.2057 1.61857 0.809286 0.587415i \(-0.199854\pi\)
0.809286 + 0.587415i \(0.199854\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.84008 + 2.84008i −0.262566 + 0.262566i
\(118\) 0 0
\(119\) 0.477325i 0.0437563i
\(120\) 0 0
\(121\) 7.03452i 0.639502i
\(122\) 0 0
\(123\) −11.0839 + 11.0839i −0.999403 + 0.999403i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.37608 0.122107 0.0610535 0.998134i \(-0.480554\pi\)
0.0610535 + 0.998134i \(0.480554\pi\)
\(128\) 0 0
\(129\) 3.90900 0.344168
\(130\) 0 0
\(131\) 9.03973 + 9.03973i 0.789804 + 0.789804i 0.981462 0.191657i \(-0.0613863\pi\)
−0.191657 + 0.981462i \(0.561386\pi\)
\(132\) 0 0
\(133\) −4.43003 + 4.43003i −0.384132 + 0.384132i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.3056i 1.30764i −0.756649 0.653822i \(-0.773165\pi\)
0.756649 0.653822i \(-0.226835\pi\)
\(138\) 0 0
\(139\) 0.346824 0.346824i 0.0294173 0.0294173i −0.692245 0.721662i \(-0.743378\pi\)
0.721662 + 0.692245i \(0.243378\pi\)
\(140\) 0 0
\(141\) −10.9334 10.9334i −0.920754 0.920754i
\(142\) 0 0
\(143\) 12.9634 1.08406
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.60555 + 6.60555i 0.544817 + 0.544817i
\(148\) 0 0
\(149\) 4.30028 4.30028i 0.352293 0.352293i −0.508669 0.860962i \(-0.669862\pi\)
0.860962 + 0.508669i \(0.169862\pi\)
\(150\) 0 0
\(151\) 2.02102i 0.164468i 0.996613 + 0.0822341i \(0.0262055\pi\)
−0.996613 + 0.0822341i \(0.973794\pi\)
\(152\) 0 0
\(153\) 0.302387i 0.0244465i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2.93327 2.93327i −0.234101 0.234101i 0.580301 0.814402i \(-0.302935\pi\)
−0.814402 + 0.580301i \(0.802935\pi\)
\(158\) 0 0
\(159\) 12.2563 0.971989
\(160\) 0 0
\(161\) −1.89241 −0.149143
\(162\) 0 0
\(163\) −5.74697 5.74697i −0.450137 0.450137i 0.445263 0.895400i \(-0.353110\pi\)
−0.895400 + 0.445263i \(0.853110\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.41553i 0.496449i 0.968703 + 0.248224i \(0.0798470\pi\)
−0.968703 + 0.248224i \(0.920153\pi\)
\(168\) 0 0
\(169\) 29.3783i 2.25987i
\(170\) 0 0
\(171\) −2.80644 + 2.80644i −0.214613 + 0.214613i
\(172\) 0 0
\(173\) 0.545724 + 0.545724i 0.0414907 + 0.0414907i 0.727548 0.686057i \(-0.240660\pi\)
−0.686057 + 0.727548i \(0.740660\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.4296 −1.38525
\(178\) 0 0
\(179\) 3.57757 + 3.57757i 0.267400 + 0.267400i 0.828052 0.560652i \(-0.189449\pi\)
−0.560652 + 0.828052i \(0.689449\pi\)
\(180\) 0 0
\(181\) −1.64176 + 1.64176i −0.122031 + 0.122031i −0.765485 0.643454i \(-0.777501\pi\)
0.643454 + 0.765485i \(0.277501\pi\)
\(182\) 0 0
\(183\) 6.57328i 0.485911i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.690114 + 0.690114i −0.0504662 + 0.0504662i
\(188\) 0 0
\(189\) −3.84522 3.84522i −0.279698 0.279698i
\(190\) 0 0
\(191\) 15.3359 1.10967 0.554835 0.831960i \(-0.312781\pi\)
0.554835 + 0.831960i \(0.312781\pi\)
\(192\) 0 0
\(193\) 0.0812703 0.00584996 0.00292498 0.999996i \(-0.499069\pi\)
0.00292498 + 0.999996i \(0.499069\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.40711 + 1.40711i −0.100252 + 0.100252i −0.755454 0.655202i \(-0.772584\pi\)
0.655202 + 0.755454i \(0.272584\pi\)
\(198\) 0 0
\(199\) 14.3046i 1.01402i −0.861939 0.507011i \(-0.830750\pi\)
0.861939 0.507011i \(-0.169250\pi\)
\(200\) 0 0
\(201\) 15.4457i 1.08946i
\(202\) 0 0
\(203\) −3.64846 + 3.64846i −0.256071 + 0.256071i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.19885 −0.0833258
\(208\) 0 0
\(209\) 12.8098 0.886075
\(210\) 0 0
\(211\) −8.70115 8.70115i −0.599012 0.599012i 0.341038 0.940050i \(-0.389222\pi\)
−0.940050 + 0.341038i \(0.889222\pi\)
\(212\) 0 0
\(213\) −0.980103 + 0.980103i −0.0671556 + 0.0671556i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.17835i 0.283645i
\(218\) 0 0
\(219\) −10.6051 + 10.6051i −0.716628 + 0.716628i
\(220\) 0 0
\(221\) −2.25603 2.25603i −0.151757 0.151757i
\(222\) 0 0
\(223\) 7.78095 0.521051 0.260525 0.965467i \(-0.416104\pi\)
0.260525 + 0.965467i \(0.416104\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.15443 + 2.15443i 0.142995 + 0.142995i 0.774980 0.631986i \(-0.217760\pi\)
−0.631986 + 0.774980i \(0.717760\pi\)
\(228\) 0 0
\(229\) −7.63865 + 7.63865i −0.504776 + 0.504776i −0.912918 0.408142i \(-0.866177\pi\)
0.408142 + 0.912918i \(0.366177\pi\)
\(230\) 0 0
\(231\) 2.99390i 0.196984i
\(232\) 0 0
\(233\) 7.51503i 0.492326i −0.969228 0.246163i \(-0.920830\pi\)
0.969228 0.246163i \(-0.0791699\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 16.1395 + 16.1395i 1.04837 + 1.04837i
\(238\) 0 0
\(239\) −20.5776 −1.33105 −0.665526 0.746375i \(-0.731793\pi\)
−0.665526 + 0.746375i \(0.731793\pi\)
\(240\) 0 0
\(241\) −23.2914 −1.50033 −0.750166 0.661250i \(-0.770026\pi\)
−0.750166 + 0.661250i \(0.770026\pi\)
\(242\) 0 0
\(243\) −4.45639 4.45639i −0.285877 0.285877i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 41.8762i 2.66452i
\(248\) 0 0
\(249\) 1.77925i 0.112755i
\(250\) 0 0
\(251\) 3.34230 3.34230i 0.210964 0.210964i −0.593713 0.804677i \(-0.702339\pi\)
0.804677 + 0.593713i \(0.202339\pi\)
\(252\) 0 0
\(253\) 2.73604 + 2.73604i 0.172014 + 0.172014i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.4537 1.40062 0.700311 0.713838i \(-0.253045\pi\)
0.700311 + 0.713838i \(0.253045\pi\)
\(258\) 0 0
\(259\) −4.43448 4.43448i −0.275545 0.275545i
\(260\) 0 0
\(261\) −2.31131 + 2.31131i −0.143066 + 0.143066i
\(262\) 0 0
\(263\) 8.23670i 0.507897i 0.967218 + 0.253948i \(0.0817294\pi\)
−0.967218 + 0.253948i \(0.918271\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.22696 1.22696i 0.0750885 0.0750885i
\(268\) 0 0
\(269\) −17.2960 17.2960i −1.05455 1.05455i −0.998423 0.0561306i \(-0.982124\pi\)
−0.0561306 0.998423i \(-0.517876\pi\)
\(270\) 0 0
\(271\) 12.4753 0.757822 0.378911 0.925433i \(-0.376299\pi\)
0.378911 + 0.925433i \(0.376299\pi\)
\(272\) 0 0
\(273\) −9.78726 −0.592352
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.2583 + 10.2583i −0.616363 + 0.616363i −0.944597 0.328234i \(-0.893547\pi\)
0.328234 + 0.944597i \(0.393547\pi\)
\(278\) 0 0
\(279\) 2.64700i 0.158472i
\(280\) 0 0
\(281\) 21.4066i 1.27701i −0.769618 0.638505i \(-0.779553\pi\)
0.769618 0.638505i \(-0.220447\pi\)
\(282\) 0 0
\(283\) −7.39635 + 7.39635i −0.439668 + 0.439668i −0.891900 0.452232i \(-0.850628\pi\)
0.452232 + 0.891900i \(0.350628\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.88942 0.583754
\(288\) 0 0
\(289\) −16.7598 −0.985870
\(290\) 0 0
\(291\) −8.23520 8.23520i −0.482756 0.482756i
\(292\) 0 0
\(293\) 0.556728 0.556728i 0.0325244 0.0325244i −0.690658 0.723182i \(-0.742679\pi\)
0.723182 + 0.690658i \(0.242679\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 11.1188i 0.645178i
\(298\) 0 0
\(299\) −8.94430 + 8.94430i −0.517263 + 0.517263i
\(300\) 0 0
\(301\) −1.74387 1.74387i −0.100515 0.100515i
\(302\) 0 0
\(303\) −5.68781 −0.326756
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.76852 + 9.76852i 0.557519 + 0.557519i 0.928600 0.371082i \(-0.121013\pi\)
−0.371082 + 0.928600i \(0.621013\pi\)
\(308\) 0 0
\(309\) 15.0795 15.0795i 0.857844 0.857844i
\(310\) 0 0
\(311\) 30.6874i 1.74013i −0.492941 0.870063i \(-0.664078\pi\)
0.492941 0.870063i \(-0.335922\pi\)
\(312\) 0 0
\(313\) 1.71127i 0.0967268i −0.998830 0.0483634i \(-0.984599\pi\)
0.998830 0.0483634i \(-0.0154006\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.0380 + 10.0380i 0.563790 + 0.563790i 0.930382 0.366592i \(-0.119476\pi\)
−0.366592 + 0.930382i \(0.619476\pi\)
\(318\) 0 0
\(319\) 10.5498 0.590678
\(320\) 0 0
\(321\) 21.5938 1.20525
\(322\) 0 0
\(323\) −2.22930 2.22930i −0.124042 0.124042i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 25.2049i 1.39384i
\(328\) 0 0
\(329\) 9.75508i 0.537815i
\(330\) 0 0
\(331\) −7.89713 + 7.89713i −0.434066 + 0.434066i −0.890009 0.455943i \(-0.849302\pi\)
0.455943 + 0.890009i \(0.349302\pi\)
\(332\) 0 0
\(333\) −2.80926 2.80926i −0.153946 0.153946i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.46077 0.188520 0.0942601 0.995548i \(-0.469951\pi\)
0.0942601 + 0.995548i \(0.469951\pi\)
\(338\) 0 0
\(339\) 18.7810 + 18.7810i 1.02005 + 1.02005i
\(340\) 0 0
\(341\) 6.04104 6.04104i 0.327141 0.327141i
\(342\) 0 0
\(343\) 12.7112i 0.686338i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.4637 + 17.4637i −0.937498 + 0.937498i −0.998158 0.0606600i \(-0.980679\pi\)
0.0606600 + 0.998158i \(0.480679\pi\)
\(348\) 0 0
\(349\) 24.2159 + 24.2159i 1.29625 + 1.29625i 0.930852 + 0.365397i \(0.119067\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(350\) 0 0
\(351\) −36.3481 −1.94012
\(352\) 0 0
\(353\) 10.7028 0.569650 0.284825 0.958580i \(-0.408065\pi\)
0.284825 + 0.958580i \(0.408065\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.521030 0.521030i 0.0275758 0.0275758i
\(358\) 0 0
\(359\) 23.6390i 1.24762i 0.781577 + 0.623809i \(0.214416\pi\)
−0.781577 + 0.623809i \(0.785584\pi\)
\(360\) 0 0
\(361\) 22.3801i 1.17790i
\(362\) 0 0
\(363\) −7.67861 + 7.67861i −0.403023 + 0.403023i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −13.7431 −0.717386 −0.358693 0.933456i \(-0.616777\pi\)
−0.358693 + 0.933456i \(0.616777\pi\)
\(368\) 0 0
\(369\) 6.26498 0.326142
\(370\) 0 0
\(371\) −5.46773 5.46773i −0.283871 0.283871i
\(372\) 0 0
\(373\) −18.4703 + 18.4703i −0.956355 + 0.956355i −0.999087 0.0427313i \(-0.986394\pi\)
0.0427313 + 0.999087i \(0.486394\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 34.4881i 1.77623i
\(378\) 0 0
\(379\) 16.1028 16.1028i 0.827143 0.827143i −0.159978 0.987121i \(-0.551142\pi\)
0.987121 + 0.159978i \(0.0511423\pi\)
\(380\) 0 0
\(381\) 1.50207 + 1.50207i 0.0769535 + 0.0769535i
\(382\) 0 0
\(383\) 23.1255 1.18166 0.590830 0.806796i \(-0.298800\pi\)
0.590830 + 0.806796i \(0.298800\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.10474 1.10474i −0.0561573 0.0561573i
\(388\) 0 0
\(389\) −19.4044 + 19.4044i −0.983842 + 0.983842i −0.999872 0.0160295i \(-0.994897\pi\)
0.0160295 + 0.999872i \(0.494897\pi\)
\(390\) 0 0
\(391\) 0.952310i 0.0481604i
\(392\) 0 0
\(393\) 19.7348i 0.995491i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.00102 + 4.00102i 0.200806 + 0.200806i 0.800345 0.599540i \(-0.204650\pi\)
−0.599540 + 0.800345i \(0.704650\pi\)
\(398\) 0 0
\(399\) −9.67130 −0.484171
\(400\) 0 0
\(401\) 38.9287 1.94401 0.972003 0.234967i \(-0.0754980\pi\)
0.972003 + 0.234967i \(0.0754980\pi\)
\(402\) 0 0
\(403\) 19.7486 + 19.7486i 0.983746 + 0.983746i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.8227i 0.635598i
\(408\) 0 0
\(409\) 4.59845i 0.227379i −0.993516 0.113689i \(-0.963733\pi\)
0.993516 0.113689i \(-0.0362669\pi\)
\(410\) 0 0
\(411\) 16.7070 16.7070i 0.824095 0.824095i
\(412\) 0 0
\(413\) 8.22174 + 8.22174i 0.404565 + 0.404565i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.757161 0.0370783
\(418\) 0 0
\(419\) −16.6774 16.6774i −0.814746 0.814746i 0.170595 0.985341i \(-0.445431\pi\)
−0.985341 + 0.170595i \(0.945431\pi\)
\(420\) 0 0
\(421\) 15.4169 15.4169i 0.751372 0.751372i −0.223364 0.974735i \(-0.571704\pi\)
0.974735 + 0.223364i \(0.0717037\pi\)
\(422\) 0 0
\(423\) 6.17987i 0.300476i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.93244 2.93244i 0.141911 0.141911i
\(428\) 0 0
\(429\) 14.1504 + 14.1504i 0.683186 + 0.683186i
\(430\) 0 0
\(431\) −20.2234 −0.974126 −0.487063 0.873367i \(-0.661932\pi\)
−0.487063 + 0.873367i \(0.661932\pi\)
\(432\) 0 0
\(433\) −0.676118 −0.0324922 −0.0162461 0.999868i \(-0.505172\pi\)
−0.0162461 + 0.999868i \(0.505172\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8.83834 + 8.83834i −0.422795 + 0.422795i
\(438\) 0 0
\(439\) 13.3550i 0.637400i 0.947856 + 0.318700i \(0.103246\pi\)
−0.947856 + 0.318700i \(0.896754\pi\)
\(440\) 0 0
\(441\) 3.73366i 0.177794i
\(442\) 0 0
\(443\) 28.1262 28.1262i 1.33631 1.33631i 0.436714 0.899600i \(-0.356142\pi\)
0.899600 0.436714i \(-0.143858\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.38805 0.444039
\(448\) 0 0
\(449\) −8.37972 −0.395464 −0.197732 0.980256i \(-0.563358\pi\)
−0.197732 + 0.980256i \(0.563358\pi\)
\(450\) 0 0
\(451\) −14.2981 14.2981i −0.673271 0.673271i
\(452\) 0 0
\(453\) −2.20607 + 2.20607i −0.103650 + 0.103650i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.66561i 0.265026i −0.991181 0.132513i \(-0.957695\pi\)
0.991181 0.132513i \(-0.0423046\pi\)
\(458\) 0 0
\(459\) 1.93501 1.93501i 0.0903186 0.0903186i
\(460\) 0 0
\(461\) 16.6375 + 16.6375i 0.774887 + 0.774887i 0.978956 0.204069i \(-0.0654168\pi\)
−0.204069 + 0.978956i \(0.565417\pi\)
\(462\) 0 0
\(463\) −41.6835 −1.93720 −0.968598 0.248631i \(-0.920019\pi\)
−0.968598 + 0.248631i \(0.920019\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.11020 + 3.11020i 0.143923 + 0.143923i 0.775397 0.631474i \(-0.217550\pi\)
−0.631474 + 0.775397i \(0.717550\pi\)
\(468\) 0 0
\(469\) −6.89057 + 6.89057i −0.318177 + 0.318177i
\(470\) 0 0
\(471\) 6.40370i 0.295067i
\(472\) 0 0
\(473\) 5.04255i 0.231857i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.46383 3.46383i −0.158598 0.158598i
\(478\) 0 0
\(479\) 8.32325 0.380299 0.190149 0.981755i \(-0.439103\pi\)
0.190149 + 0.981755i \(0.439103\pi\)
\(480\) 0 0
\(481\) −41.9183 −1.91131
\(482\) 0 0
\(483\) −2.06569 2.06569i −0.0939920 0.0939920i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.29577i 0.330603i −0.986243 0.165301i \(-0.947140\pi\)
0.986243 0.165301i \(-0.0528597\pi\)
\(488\) 0 0
\(489\) 12.5463i 0.567365i
\(490\) 0 0
\(491\) −3.57528 + 3.57528i −0.161350 + 0.161350i −0.783165 0.621815i \(-0.786396\pi\)
0.621815 + 0.783165i \(0.286396\pi\)
\(492\) 0 0
\(493\) −1.83600 1.83600i −0.0826891 0.0826891i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.874479 0.0392257
\(498\) 0 0
\(499\) 10.8833 + 10.8833i 0.487203 + 0.487203i 0.907422 0.420220i \(-0.138047\pi\)
−0.420220 + 0.907422i \(0.638047\pi\)
\(500\) 0 0
\(501\) −7.00295 + 7.00295i −0.312869 + 0.312869i
\(502\) 0 0
\(503\) 29.3781i 1.30991i 0.755670 + 0.654953i \(0.227312\pi\)
−0.755670 + 0.654953i \(0.772688\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −32.0682 + 32.0682i −1.42420 + 1.42420i
\(508\) 0 0
\(509\) 17.4592 + 17.4592i 0.773863 + 0.773863i 0.978780 0.204916i \(-0.0656922\pi\)
−0.204916 + 0.978780i \(0.565692\pi\)
\(510\) 0 0
\(511\) 9.46222 0.418584
\(512\) 0 0
\(513\) −35.9175 −1.58579
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 14.1039 14.1039i 0.620287 0.620287i
\(518\) 0 0
\(519\) 1.19138i 0.0522959i
\(520\) 0 0
\(521\) 9.48578i 0.415580i −0.978174 0.207790i \(-0.933373\pi\)
0.978174 0.207790i \(-0.0666270\pi\)
\(522\) 0 0
\(523\) 16.2705 16.2705i 0.711460 0.711460i −0.255380 0.966841i \(-0.582201\pi\)
0.966841 + 0.255380i \(0.0822006\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.10265 −0.0915929
\(528\) 0 0
\(529\) 19.2245 0.835846
\(530\) 0 0
\(531\) 5.20849 + 5.20849i 0.226029 + 0.226029i
\(532\) 0 0
\(533\) 46.7414 46.7414i 2.02459 2.02459i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 7.81028i 0.337039i
\(538\) 0 0
\(539\) −8.52106 + 8.52106i −0.367028 + 0.367028i
\(540\) 0 0
\(541\) −2.55686 2.55686i −0.109928 0.109928i 0.650003 0.759931i \(-0.274767\pi\)
−0.759931 + 0.650003i \(0.774767\pi\)
\(542\) 0 0
\(543\) −3.58416 −0.153811
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −21.9660 21.9660i −0.939197 0.939197i 0.0590579 0.998255i \(-0.481190\pi\)
−0.998255 + 0.0590579i \(0.981190\pi\)
\(548\) 0 0
\(549\) 1.85771 1.85771i 0.0792852 0.0792852i
\(550\) 0 0
\(551\) 34.0796i 1.45184i
\(552\) 0 0
\(553\) 14.4002i 0.612357i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.5409 17.5409i −0.743234 0.743234i 0.229965 0.973199i \(-0.426139\pi\)
−0.973199 + 0.229965i \(0.926139\pi\)
\(558\) 0 0
\(559\) −16.4844 −0.697217
\(560\) 0 0
\(561\) −1.50661 −0.0636089
\(562\) 0 0
\(563\) 27.5975 + 27.5975i 1.16309 + 1.16309i 0.983794 + 0.179300i \(0.0573833\pi\)
0.179300 + 0.983794i \(0.442617\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.59190i 0.276834i
\(568\) 0 0
\(569\) 23.6390i 0.990998i −0.868608 0.495499i \(-0.834985\pi\)
0.868608 0.495499i \(-0.165015\pi\)
\(570\) 0 0
\(571\) 21.7518 21.7518i 0.910284 0.910284i −0.0860105 0.996294i \(-0.527412\pi\)
0.996294 + 0.0860105i \(0.0274118\pi\)
\(572\) 0 0
\(573\) 16.7401 + 16.7401i 0.699329 + 0.699329i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.69585 0.153860 0.0769302 0.997036i \(-0.475488\pi\)
0.0769302 + 0.997036i \(0.475488\pi\)
\(578\) 0 0
\(579\) 0.0887116 + 0.0887116i 0.00368673 + 0.00368673i
\(580\) 0 0
\(581\) −0.793750 + 0.793750i −0.0329303 + 0.0329303i
\(582\) 0 0
\(583\) 15.8105i 0.654802i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 27.0313 27.0313i 1.11570 1.11570i 0.123335 0.992365i \(-0.460641\pi\)
0.992365 0.123335i \(-0.0393590\pi\)
\(588\) 0 0
\(589\) 19.5146 + 19.5146i 0.804085 + 0.804085i
\(590\) 0 0
\(591\) −3.07189 −0.126361
\(592\) 0 0
\(593\) 4.55524 0.187061 0.0935306 0.995616i \(-0.470185\pi\)
0.0935306 + 0.995616i \(0.470185\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 15.6143 15.6143i 0.639051 0.639051i
\(598\) 0 0
\(599\) 7.46846i 0.305153i 0.988292 + 0.152576i \(0.0487570\pi\)
−0.988292 + 0.152576i \(0.951243\pi\)
\(600\) 0 0
\(601\) 12.2638i 0.500250i 0.968214 + 0.250125i \(0.0804717\pi\)
−0.968214 + 0.250125i \(0.919528\pi\)
\(602\) 0 0
\(603\) −4.36519 + 4.36519i −0.177764 + 0.177764i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 5.23884 0.212638 0.106319 0.994332i \(-0.466094\pi\)
0.106319 + 0.994332i \(0.466094\pi\)
\(608\) 0 0
\(609\) −7.96503 −0.322759
\(610\) 0 0
\(611\) 46.1064 + 46.1064i 1.86527 + 1.86527i
\(612\) 0 0
\(613\) −20.7209 + 20.7209i −0.836910 + 0.836910i −0.988451 0.151541i \(-0.951576\pi\)
0.151541 + 0.988451i \(0.451576\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.20286i 0.0886838i 0.999016 + 0.0443419i \(0.0141191\pi\)
−0.999016 + 0.0443419i \(0.985881\pi\)
\(618\) 0 0
\(619\) 31.4569 31.4569i 1.26436 1.26436i 0.315404 0.948958i \(-0.397860\pi\)
0.948958 0.315404i \(-0.102140\pi\)
\(620\) 0 0
\(621\) −7.67158 7.67158i −0.307850 0.307850i
\(622\) 0 0
\(623\) −1.09473 −0.0438594
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 13.9827 + 13.9827i 0.558416 + 0.558416i
\(628\) 0 0
\(629\) 2.23154 2.23154i 0.0889775 0.0889775i
\(630\) 0 0
\(631\) 16.8215i 0.669655i 0.942279 + 0.334828i \(0.108678\pi\)
−0.942279 + 0.334828i \(0.891322\pi\)
\(632\) 0 0
\(633\) 18.9957i 0.755011i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −27.8559 27.8559i −1.10369 1.10369i
\(638\) 0 0
\(639\) 0.553985 0.0219153
\(640\) 0 0
\(641\) −14.9208 −0.589336 −0.294668 0.955600i \(-0.595209\pi\)
−0.294668 + 0.955600i \(0.595209\pi\)
\(642\) 0 0
\(643\) −0.541845 0.541845i −0.0213683 0.0213683i 0.696342 0.717710i \(-0.254810\pi\)
−0.717710 + 0.696342i \(0.754810\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.6391i 1.28318i −0.767049 0.641588i \(-0.778276\pi\)
0.767049 0.641588i \(-0.221724\pi\)
\(648\) 0 0
\(649\) 23.7739i 0.933208i
\(650\) 0 0
\(651\) −4.56093 + 4.56093i −0.178757 + 0.178757i
\(652\) 0 0
\(653\) −9.73805 9.73805i −0.381079 0.381079i 0.490412 0.871491i \(-0.336846\pi\)
−0.871491 + 0.490412i \(0.836846\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.99434 0.233862
\(658\) 0 0
\(659\) −1.26445 1.26445i −0.0492560 0.0492560i 0.682050 0.731306i \(-0.261089\pi\)
−0.731306 + 0.682050i \(0.761089\pi\)
\(660\) 0 0
\(661\) 22.6701 22.6701i 0.881763 0.881763i −0.111951 0.993714i \(-0.535710\pi\)
0.993714 + 0.111951i \(0.0357099\pi\)
\(662\) 0 0
\(663\) 4.92519i 0.191279i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.27903 + 7.27903i −0.281845 + 0.281845i
\(668\) 0 0
\(669\) 8.49339 + 8.49339i 0.328373 + 0.328373i
\(670\) 0 0
\(671\) −8.47943 −0.327345
\(672\) 0 0
\(673\) −3.58765 −0.138294 −0.0691469 0.997606i \(-0.522028\pi\)
−0.0691469 + 0.997606i \(0.522028\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.1507 + 10.1507i −0.390124 + 0.390124i −0.874731 0.484608i \(-0.838962\pi\)
0.484608 + 0.874731i \(0.338962\pi\)
\(678\) 0 0
\(679\) 7.34770i 0.281979i
\(680\) 0 0
\(681\) 4.70339i 0.180234i
\(682\) 0 0
\(683\) 16.6805 16.6805i 0.638260 0.638260i −0.311866 0.950126i \(-0.600954\pi\)
0.950126 + 0.311866i \(0.100954\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −16.6761 −0.636234
\(688\) 0 0
\(689\) −51.6854 −1.96906
\(690\) 0 0
\(691\) −12.4781 12.4781i −0.474689 0.474689i 0.428739 0.903428i \(-0.358958\pi\)
−0.903428 + 0.428739i \(0.858958\pi\)
\(692\) 0 0
\(693\) 0.846123 0.846123i 0.0321415 0.0321415i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4.97661i 0.188502i
\(698\) 0 0
\(699\) 8.20312 8.20312i 0.310271 0.310271i
\(700\) 0 0
\(701\) 6.40945 + 6.40945i 0.242082 + 0.242082i 0.817711 0.575629i \(-0.195243\pi\)
−0.575629 + 0.817711i \(0.695243\pi\)
\(702\) 0 0
\(703\) −41.4217 −1.56225
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.53742 + 2.53742i 0.0954295 + 0.0954295i
\(708\) 0 0
\(709\) 8.78514 8.78514i 0.329933 0.329933i −0.522628 0.852561i \(-0.675048\pi\)
0.852561 + 0.522628i \(0.175048\pi\)
\(710\) 0 0
\(711\) 9.12255i 0.342122i
\(712\) 0 0
\(713\) 8.33621i 0.312194i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −22.4617 22.4617i −0.838847 0.838847i
\(718\) 0 0
\(719\) −46.2329 −1.72420 −0.862099 0.506740i \(-0.830850\pi\)
−0.862099 + 0.506740i \(0.830850\pi\)
\(720\) 0 0
\(721\) −13.4544 −0.501069
\(722\) 0 0
\(723\) −25.4240 25.4240i −0.945530 0.945530i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 17.4640i 0.647703i 0.946108 + 0.323852i \(0.104978\pi\)
−0.946108 + 0.323852i \(0.895022\pi\)
\(728\) 0 0
\(729\) 30.0340i 1.11237i
\(730\) 0 0
\(731\) 0.877557 0.877557i 0.0324576 0.0324576i
\(732\) 0 0
\(733\) −7.89695 7.89695i −0.291680 0.291680i 0.546063 0.837744i \(-0.316126\pi\)
−0.837744 + 0.546063i \(0.816126\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.9247 0.733936
\(738\) 0 0
\(739\) −26.1724 26.1724i −0.962769 0.962769i 0.0365624 0.999331i \(-0.488359\pi\)
−0.999331 + 0.0365624i \(0.988359\pi\)
\(740\) 0 0
\(741\) −45.7105 + 45.7105i −1.67922 + 1.67922i
\(742\) 0 0
\(743\) 49.7660i 1.82574i −0.408254 0.912868i \(-0.633862\pi\)
0.408254 0.912868i \(-0.366138\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.502843 + 0.502843i −0.0183981 + 0.0183981i
\(748\) 0 0
\(749\) −9.63333 9.63333i −0.351994 0.351994i
\(750\) 0 0
\(751\) 24.2379 0.884454 0.442227 0.896903i \(-0.354189\pi\)
0.442227 + 0.896903i \(0.354189\pi\)
\(752\) 0 0
\(753\) 7.29665 0.265905
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 15.4872 15.4872i 0.562890 0.562890i −0.367237 0.930127i \(-0.619696\pi\)
0.930127 + 0.367237i \(0.119696\pi\)
\(758\) 0 0
\(759\) 5.97312i 0.216811i
\(760\) 0 0
\(761\) 25.9821i 0.941849i −0.882174 0.470924i \(-0.843920\pi\)
0.882174 0.470924i \(-0.156080\pi\)
\(762\) 0 0
\(763\) −11.2443 + 11.2443i −0.407072 + 0.407072i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 77.7185 2.80625
\(768\) 0 0
\(769\) −24.9737 −0.900573 −0.450287 0.892884i \(-0.648678\pi\)
−0.450287 + 0.892884i \(0.648678\pi\)
\(770\) 0 0
\(771\) 24.5096 + 24.5096i 0.882691 + 0.882691i
\(772\) 0 0
\(773\) 1.32495 1.32495i 0.0476550 0.0476550i −0.682878 0.730533i \(-0.739272\pi\)
0.730533 + 0.682878i \(0.239272\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 9.68103i 0.347305i
\(778\) 0 0
\(779\) 46.1876 46.1876i 1.65484 1.65484i
\(780\) 0 0
\(781\) −1.26432 1.26432i −0.0452409 0.0452409i
\(782\) 0 0
\(783\) −29.5807 −1.05713
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.647036 + 0.647036i 0.0230644 + 0.0230644i 0.718545 0.695481i \(-0.244808\pi\)
−0.695481 + 0.718545i \(0.744808\pi\)
\(788\) 0 0
\(789\) −8.99087 + 8.99087i −0.320084 + 0.320084i
\(790\) 0 0
\(791\) 16.7570i 0.595811i
\(792\) 0 0
\(793\) 27.7198i 0.984360i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.3024 18.3024i −0.648303 0.648303i 0.304280 0.952583i \(-0.401584\pi\)
−0.952583 + 0.304280i \(0.901584\pi\)
\(798\) 0 0
\(799\) −4.90900 −0.173668
\(800\) 0 0
\(801\) −0.693514 −0.0245041
\(802\) 0 0
\(803\) −13.6804