Properties

Label 1520.2.g.f.1519.13
Level $1520$
Weight $2$
Character 1520.1519
Analytic conductor $12.137$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 32 x^{14} + 380 x^{12} - 1752 x^{10} + 1904 x^{8} + 7824 x^{6} + 7352 x^{4} + 2992 x^{2} + 484\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1519.13
Root \(3.52761 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1520.1519
Dual form 1520.2.g.f.1519.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.59462i q^{3} +(-1.73205 - 1.41421i) q^{5} -3.38587 q^{7} -3.73205 q^{9} +O(q^{10})\) \(q+2.59462i q^{3} +(-1.73205 - 1.41421i) q^{5} -3.38587 q^{7} -3.73205 q^{9} -1.75265i q^{11} +6.21196 q^{13} +(3.66935 - 4.49401i) q^{15} -6.69213i q^{17} +(-1.34307 + 4.14682i) q^{19} -8.78504i q^{21} +5.86450 q^{23} +(1.00000 + 4.89898i) q^{25} -1.89939i q^{27} -6.43110i q^{29} -6.35549 q^{31} +4.54747 q^{33} +(5.86450 + 4.78834i) q^{35} +1.66449 q^{37} +16.1177i q^{39} +8.78504i q^{41} -0.907241 q^{43} +(6.46410 + 5.27792i) q^{45} +10.1576 q^{47} +4.46410 q^{49} +17.3635 q^{51} +10.7594 q^{53} +(-2.47863 + 3.03569i) q^{55} +(-10.7594 - 3.48477i) q^{57} +6.35549 q^{59} -2.19615 q^{61} +12.6362 q^{63} +(-10.7594 - 8.78504i) q^{65} -4.49401i q^{67} +15.2161i q^{69} -1.70295 q^{71} +3.58630i q^{73} +(-12.7110 + 2.59462i) q^{75} +5.93426i q^{77} +16.3803 q^{79} -6.26795 q^{81} -1.57139 q^{83} +(-9.46410 + 11.5911i) q^{85} +16.6862 q^{87} +6.43110i q^{89} -21.0329 q^{91} -16.4901i q^{93} +(8.19077 - 5.28312i) q^{95} -1.66449 q^{97} +6.54099i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 32q^{9} + O(q^{10}) \) \( 16q - 32q^{9} + 16q^{25} + 48q^{45} + 16q^{49} + 48q^{61} - 128q^{81} - 96q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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
\(3\) 2.59462i 1.49800i 0.662568 + 0.749002i \(0.269467\pi\)
−0.662568 + 0.749002i \(0.730533\pi\)
\(4\) 0 0
\(5\) −1.73205 1.41421i −0.774597 0.632456i
\(6\) 0 0
\(7\) −3.38587 −1.27974 −0.639869 0.768484i \(-0.721011\pi\)
−0.639869 + 0.768484i \(0.721011\pi\)
\(8\) 0 0
\(9\) −3.73205 −1.24402
\(10\) 0 0
\(11\) 1.75265i 0.528445i −0.964462 0.264223i \(-0.914885\pi\)
0.964462 0.264223i \(-0.0851153\pi\)
\(12\) 0 0
\(13\) 6.21196 1.72289 0.861444 0.507853i \(-0.169561\pi\)
0.861444 + 0.507853i \(0.169561\pi\)
\(14\) 0 0
\(15\) 3.66935 4.49401i 0.947421 1.16035i
\(16\) 0 0
\(17\) 6.69213i 1.62308i −0.584297 0.811540i \(-0.698630\pi\)
0.584297 0.811540i \(-0.301370\pi\)
\(18\) 0 0
\(19\) −1.34307 + 4.14682i −0.308122 + 0.951347i
\(20\) 0 0
\(21\) 8.78504i 1.91705i
\(22\) 0 0
\(23\) 5.86450 1.22283 0.611416 0.791309i \(-0.290600\pi\)
0.611416 + 0.791309i \(0.290600\pi\)
\(24\) 0 0
\(25\) 1.00000 + 4.89898i 0.200000 + 0.979796i
\(26\) 0 0
\(27\) 1.89939i 0.365538i
\(28\) 0 0
\(29\) 6.43110i 1.19422i −0.802158 0.597112i \(-0.796315\pi\)
0.802158 0.597112i \(-0.203685\pi\)
\(30\) 0 0
\(31\) −6.35549 −1.14148 −0.570740 0.821131i \(-0.693344\pi\)
−0.570740 + 0.821131i \(0.693344\pi\)
\(32\) 0 0
\(33\) 4.54747 0.791613
\(34\) 0 0
\(35\) 5.86450 + 4.78834i 0.991281 + 0.809377i
\(36\) 0 0
\(37\) 1.66449 0.273640 0.136820 0.990596i \(-0.456312\pi\)
0.136820 + 0.990596i \(0.456312\pi\)
\(38\) 0 0
\(39\) 16.1177i 2.58089i
\(40\) 0 0
\(41\) 8.78504i 1.37199i 0.727605 + 0.685996i \(0.240633\pi\)
−0.727605 + 0.685996i \(0.759367\pi\)
\(42\) 0 0
\(43\) −0.907241 −0.138353 −0.0691764 0.997604i \(-0.522037\pi\)
−0.0691764 + 0.997604i \(0.522037\pi\)
\(44\) 0 0
\(45\) 6.46410 + 5.27792i 0.963611 + 0.786785i
\(46\) 0 0
\(47\) 10.1576 1.48164 0.740819 0.671704i \(-0.234437\pi\)
0.740819 + 0.671704i \(0.234437\pi\)
\(48\) 0 0
\(49\) 4.46410 0.637729
\(50\) 0 0
\(51\) 17.3635 2.43138
\(52\) 0 0
\(53\) 10.7594 1.47792 0.738961 0.673748i \(-0.235317\pi\)
0.738961 + 0.673748i \(0.235317\pi\)
\(54\) 0 0
\(55\) −2.47863 + 3.03569i −0.334218 + 0.409332i
\(56\) 0 0
\(57\) −10.7594 3.48477i −1.42512 0.461569i
\(58\) 0 0
\(59\) 6.35549 0.827415 0.413707 0.910410i \(-0.364234\pi\)
0.413707 + 0.910410i \(0.364234\pi\)
\(60\) 0 0
\(61\) −2.19615 −0.281189 −0.140594 0.990067i \(-0.544901\pi\)
−0.140594 + 0.990067i \(0.544901\pi\)
\(62\) 0 0
\(63\) 12.6362 1.59202
\(64\) 0 0
\(65\) −10.7594 8.78504i −1.33454 1.08965i
\(66\) 0 0
\(67\) 4.49401i 0.549031i −0.961583 0.274516i \(-0.911483\pi\)
0.961583 0.274516i \(-0.0885175\pi\)
\(68\) 0 0
\(69\) 15.2161i 1.83181i
\(70\) 0 0
\(71\) −1.70295 −0.202103 −0.101051 0.994881i \(-0.532221\pi\)
−0.101051 + 0.994881i \(0.532221\pi\)
\(72\) 0 0
\(73\) 3.58630i 0.419745i 0.977729 + 0.209872i \(0.0673049\pi\)
−0.977729 + 0.209872i \(0.932695\pi\)
\(74\) 0 0
\(75\) −12.7110 + 2.59462i −1.46774 + 0.299601i
\(76\) 0 0
\(77\) 5.93426i 0.676271i
\(78\) 0 0
\(79\) 16.3803 1.84293 0.921466 0.388459i \(-0.126993\pi\)
0.921466 + 0.388459i \(0.126993\pi\)
\(80\) 0 0
\(81\) −6.26795 −0.696439
\(82\) 0 0
\(83\) −1.57139 −0.172482 −0.0862411 0.996274i \(-0.527486\pi\)
−0.0862411 + 0.996274i \(0.527486\pi\)
\(84\) 0 0
\(85\) −9.46410 + 11.5911i −1.02653 + 1.25723i
\(86\) 0 0
\(87\) 16.6862 1.78895
\(88\) 0 0
\(89\) 6.43110i 0.681695i 0.940119 + 0.340847i \(0.110714\pi\)
−0.940119 + 0.340847i \(0.889286\pi\)
\(90\) 0 0
\(91\) −21.0329 −2.20484
\(92\) 0 0
\(93\) 16.4901i 1.70994i
\(94\) 0 0
\(95\) 8.19077 5.28312i 0.840355 0.542036i
\(96\) 0 0
\(97\) −1.66449 −0.169003 −0.0845017 0.996423i \(-0.526930\pi\)
−0.0845017 + 0.996423i \(0.526930\pi\)
\(98\) 0 0
\(99\) 6.54099i 0.657395i
\(100\) 0 0
\(101\) 8.19615 0.815548 0.407774 0.913083i \(-0.366305\pi\)
0.407774 + 0.913083i \(0.366305\pi\)
\(102\) 0 0
\(103\) 13.4820i 1.32842i −0.747544 0.664212i \(-0.768767\pi\)
0.747544 0.664212i \(-0.231233\pi\)
\(104\) 0 0
\(105\) −12.4239 + 15.2161i −1.21245 + 1.48494i
\(106\) 0 0
\(107\) 9.68325i 0.936115i −0.883698 0.468058i \(-0.844954\pi\)
0.883698 0.468058i \(-0.155046\pi\)
\(108\) 0 0
\(109\) 15.2161i 1.45744i −0.684811 0.728721i \(-0.740115\pi\)
0.684811 0.728721i \(-0.259885\pi\)
\(110\) 0 0
\(111\) 4.31872i 0.409915i
\(112\) 0 0
\(113\) 2.88298 0.271208 0.135604 0.990763i \(-0.456703\pi\)
0.135604 + 0.990763i \(0.456703\pi\)
\(114\) 0 0
\(115\) −10.1576 8.29365i −0.947201 0.773387i
\(116\) 0 0
\(117\) −23.1834 −2.14330
\(118\) 0 0
\(119\) 22.6587i 2.07712i
\(120\) 0 0
\(121\) 7.92820 0.720746
\(122\) 0 0
\(123\) −22.7938 −2.05525
\(124\) 0 0
\(125\) 5.19615 9.89949i 0.464758 0.885438i
\(126\) 0 0
\(127\) 16.7719i 1.48826i 0.668033 + 0.744132i \(0.267137\pi\)
−0.668033 + 0.744132i \(0.732863\pi\)
\(128\) 0 0
\(129\) 2.35394i 0.207253i
\(130\) 0 0
\(131\) 13.0820i 1.14298i 0.820609 + 0.571489i \(0.193634\pi\)
−0.820609 + 0.571489i \(0.806366\pi\)
\(132\) 0 0
\(133\) 4.54747 14.0406i 0.394316 1.21747i
\(134\) 0 0
\(135\) −2.68615 + 3.28985i −0.231187 + 0.283145i
\(136\) 0 0
\(137\) 0.277401i 0.0237000i −0.999930 0.0118500i \(-0.996228\pi\)
0.999930 0.0118500i \(-0.00377206\pi\)
\(138\) 0 0
\(139\) 17.4007i 1.47591i −0.674851 0.737954i \(-0.735792\pi\)
0.674851 0.737954i \(-0.264208\pi\)
\(140\) 0 0
\(141\) 26.3551i 2.21950i
\(142\) 0 0
\(143\) 10.8874i 0.910452i
\(144\) 0 0
\(145\) −9.09494 + 11.1390i −0.755294 + 0.925042i
\(146\) 0 0
\(147\) 11.5826i 0.955320i
\(148\) 0 0
\(149\) −11.6603 −0.955245 −0.477623 0.878565i \(-0.658501\pi\)
−0.477623 + 0.878565i \(0.658501\pi\)
\(150\) 0 0
\(151\) 17.3635 1.41302 0.706512 0.707701i \(-0.250268\pi\)
0.706512 + 0.707701i \(0.250268\pi\)
\(152\) 0 0
\(153\) 24.9754i 2.01914i
\(154\) 0 0
\(155\) 11.0080 + 8.98803i 0.884187 + 0.721936i
\(156\) 0 0
\(157\) 1.79315i 0.143109i −0.997437 0.0715545i \(-0.977204\pi\)
0.997437 0.0715545i \(-0.0227960\pi\)
\(158\) 0 0
\(159\) 27.9166i 2.21393i
\(160\) 0 0
\(161\) −19.8564 −1.56490
\(162\) 0 0
\(163\) 12.6362 0.989746 0.494873 0.868965i \(-0.335215\pi\)
0.494873 + 0.868965i \(0.335215\pi\)
\(164\) 0 0
\(165\) −7.87645 6.43110i −0.613181 0.500660i
\(166\) 0 0
\(167\) 10.1922i 0.788696i −0.918961 0.394348i \(-0.870971\pi\)
0.918961 0.394348i \(-0.129029\pi\)
\(168\) 0 0
\(169\) 25.5885 1.96834
\(170\) 0 0
\(171\) 5.01242 15.4762i 0.383309 1.18349i
\(172\) 0 0
\(173\) 18.6359 1.41686 0.708430 0.705781i \(-0.249404\pi\)
0.708430 + 0.705781i \(0.249404\pi\)
\(174\) 0 0
\(175\) −3.38587 16.5873i −0.255948 1.25388i
\(176\) 0 0
\(177\) 16.4901i 1.23947i
\(178\) 0 0
\(179\) −15.6606 −1.17053 −0.585263 0.810843i \(-0.699009\pi\)
−0.585263 + 0.810843i \(0.699009\pi\)
\(180\) 0 0
\(181\) 11.1390i 0.827954i −0.910287 0.413977i \(-0.864139\pi\)
0.910287 0.413977i \(-0.135861\pi\)
\(182\) 0 0
\(183\) 5.69818i 0.421222i
\(184\) 0 0
\(185\) −2.88298 2.35394i −0.211961 0.173065i
\(186\) 0 0
\(187\) −11.7290 −0.857709
\(188\) 0 0
\(189\) 6.43110i 0.467793i
\(190\) 0 0
\(191\) 1.28303i 0.0928369i 0.998922 + 0.0464185i \(0.0147808\pi\)
−0.998922 + 0.0464185i \(0.985219\pi\)
\(192\) 0 0
\(193\) 14.0884 1.01411 0.507053 0.861915i \(-0.330735\pi\)
0.507053 + 0.861915i \(0.330735\pi\)
\(194\) 0 0
\(195\) 22.7938 27.9166i 1.63230 1.99915i
\(196\) 0 0
\(197\) 1.79315i 0.127757i −0.997958 0.0638784i \(-0.979653\pi\)
0.997958 0.0638784i \(-0.0203470\pi\)
\(198\) 0 0
\(199\) 2.22228i 0.157533i 0.996893 + 0.0787665i \(0.0250982\pi\)
−0.996893 + 0.0787665i \(0.974902\pi\)
\(200\) 0 0
\(201\) 11.6603 0.822451
\(202\) 0 0
\(203\) 21.7748i 1.52829i
\(204\) 0 0
\(205\) 12.4239 15.2161i 0.867724 1.06274i
\(206\) 0 0
\(207\) −21.8866 −1.52122
\(208\) 0 0
\(209\) 7.26795 + 2.35394i 0.502735 + 0.162826i
\(210\) 0 0
\(211\) 2.68615 0.184922 0.0924610 0.995716i \(-0.470527\pi\)
0.0924610 + 0.995716i \(0.470527\pi\)
\(212\) 0 0
\(213\) 4.41851i 0.302751i
\(214\) 0 0
\(215\) 1.57139 + 1.28303i 0.107168 + 0.0875021i
\(216\) 0 0
\(217\) 21.5189 1.46080
\(218\) 0 0
\(219\) −9.30509 −0.628780
\(220\) 0 0
\(221\) 41.5713i 2.79639i
\(222\) 0 0
\(223\) 19.1802i 1.28440i 0.766536 + 0.642201i \(0.221979\pi\)
−0.766536 + 0.642201i \(0.778021\pi\)
\(224\) 0 0
\(225\) −3.73205 18.2832i −0.248803 1.21888i
\(226\) 0 0
\(227\) 11.0737i 0.734988i −0.930026 0.367494i \(-0.880216\pi\)
0.930026 0.367494i \(-0.119784\pi\)
\(228\) 0 0
\(229\) −15.1244 −0.999446 −0.499723 0.866185i \(-0.666565\pi\)
−0.499723 + 0.866185i \(0.666565\pi\)
\(230\) 0 0
\(231\) −15.3971 −1.01306
\(232\) 0 0
\(233\) 8.76268i 0.574062i 0.957921 + 0.287031i \(0.0926683\pi\)
−0.957921 + 0.287031i \(0.907332\pi\)
\(234\) 0 0
\(235\) −17.5935 14.3650i −1.14767 0.937071i
\(236\) 0 0
\(237\) 42.5007i 2.76072i
\(238\) 0 0
\(239\) 7.01062i 0.453479i 0.973955 + 0.226740i \(0.0728066\pi\)
−0.973955 + 0.226740i \(0.927193\pi\)
\(240\) 0 0
\(241\) 15.2161i 0.980157i −0.871678 0.490079i \(-0.836968\pi\)
0.871678 0.490079i \(-0.163032\pi\)
\(242\) 0 0
\(243\) 21.9611i 1.40881i
\(244\) 0 0
\(245\) −7.73205 6.31319i −0.493983 0.403335i
\(246\) 0 0
\(247\) −8.34312 + 25.7599i −0.530860 + 1.63906i
\(248\) 0 0
\(249\) 4.07715i 0.258379i
\(250\) 0 0
\(251\) 7.35440i 0.464206i −0.972691 0.232103i \(-0.925439\pi\)
0.972691 0.232103i \(-0.0745606\pi\)
\(252\) 0 0
\(253\) 10.2784i 0.646200i
\(254\) 0 0
\(255\) −30.0745 24.5557i −1.88334 1.53774i
\(256\) 0 0
\(257\) 26.5123 1.65379 0.826897 0.562353i \(-0.190104\pi\)
0.826897 + 0.562353i \(0.190104\pi\)
\(258\) 0 0
\(259\) −5.63574 −0.350188
\(260\) 0 0
\(261\) 24.0012i 1.48564i
\(262\) 0 0
\(263\) −14.4507 −0.891069 −0.445535 0.895265i \(-0.646986\pi\)
−0.445535 + 0.895265i \(0.646986\pi\)
\(264\) 0 0
\(265\) −18.6359 15.2161i −1.14479 0.934720i
\(266\) 0 0
\(267\) −16.6862 −1.02118
\(268\) 0 0
\(269\) 8.78504i 0.535633i −0.963470 0.267817i \(-0.913698\pi\)
0.963470 0.267817i \(-0.0863021\pi\)
\(270\) 0 0
\(271\) 17.4007i 1.05702i −0.848928 0.528509i \(-0.822751\pi\)
0.848928 0.528509i \(-0.177249\pi\)
\(272\) 0 0
\(273\) 54.5723i 3.30287i
\(274\) 0 0
\(275\) 8.58622 1.75265i 0.517768 0.105689i
\(276\) 0 0
\(277\) 18.7637i 1.12740i −0.825979 0.563701i \(-0.809377\pi\)
0.825979 0.563701i \(-0.190623\pi\)
\(278\) 0 0
\(279\) 23.7190 1.42002
\(280\) 0 0
\(281\) 2.35394i 0.140425i 0.997532 + 0.0702123i \(0.0223677\pi\)
−0.997532 + 0.0702123i \(0.977632\pi\)
\(282\) 0 0
\(283\) −6.52864 −0.388087 −0.194044 0.980993i \(-0.562160\pi\)
−0.194044 + 0.980993i \(0.562160\pi\)
\(284\) 0 0
\(285\) 13.7077 + 21.2519i 0.811973 + 1.25886i
\(286\) 0 0
\(287\) 29.7450i 1.75579i
\(288\) 0 0
\(289\) −27.7846 −1.63439
\(290\) 0 0
\(291\) 4.31872i 0.253168i
\(292\) 0 0
\(293\) −10.7594 −0.628573 −0.314286 0.949328i \(-0.601765\pi\)
−0.314286 + 0.949328i \(0.601765\pi\)
\(294\) 0 0
\(295\) −11.0080 8.98803i −0.640913 0.523303i
\(296\) 0 0
\(297\) −3.32898 −0.193167
\(298\) 0 0
\(299\) 36.4300 2.10680
\(300\) 0 0
\(301\) 3.07180 0.177055
\(302\) 0 0
\(303\) 21.2659i 1.22169i
\(304\) 0 0
\(305\) 3.80385 + 3.10583i 0.217808 + 0.177839i
\(306\) 0 0
\(307\) 15.8904i 0.906911i 0.891279 + 0.453456i \(0.149809\pi\)
−0.891279 + 0.453456i \(0.850191\pi\)
\(308\) 0 0
\(309\) 34.9808 1.98999
\(310\) 0 0
\(311\) 25.3506i 1.43750i −0.695269 0.718749i \(-0.744715\pi\)
0.695269 0.718749i \(-0.255285\pi\)
\(312\) 0 0
\(313\) 8.00481i 0.452459i 0.974074 + 0.226229i \(0.0726399\pi\)
−0.974074 + 0.226229i \(0.927360\pi\)
\(314\) 0 0
\(315\) −21.8866 17.8703i −1.23317 1.00688i
\(316\) 0 0
\(317\) 18.6359 1.04670 0.523348 0.852119i \(-0.324683\pi\)
0.523348 + 0.852119i \(0.324683\pi\)
\(318\) 0 0
\(319\) −11.2715 −0.631082
\(320\) 0 0
\(321\) 25.1244 1.40230
\(322\) 0 0
\(323\) 27.7511 + 8.98803i 1.54411 + 0.500107i
\(324\) 0 0
\(325\) 6.21196 + 30.4323i 0.344578 + 1.68808i
\(326\) 0 0
\(327\) 39.4801 2.18325
\(328\) 0 0
\(329\) −34.3923 −1.89611
\(330\) 0 0
\(331\) −9.30509 −0.511454 −0.255727 0.966749i \(-0.582315\pi\)
−0.255727 + 0.966749i \(0.582315\pi\)
\(332\) 0 0
\(333\) −6.21196 −0.340413
\(334\) 0 0
\(335\) −6.35549 + 7.78386i −0.347238 + 0.425278i
\(336\) 0 0
\(337\) 15.3069 0.833820 0.416910 0.908948i \(-0.363113\pi\)
0.416910 + 0.908948i \(0.363113\pi\)
\(338\) 0 0
\(339\) 7.48024i 0.406271i
\(340\) 0 0
\(341\) 11.1390i 0.603210i
\(342\) 0 0
\(343\) 8.58622 0.463612
\(344\) 0 0
\(345\) 21.5189 26.3551i 1.15854 1.41891i
\(346\) 0 0
\(347\) −5.86450 −0.314823 −0.157411 0.987533i \(-0.550315\pi\)
−0.157411 + 0.987533i \(0.550315\pi\)
\(348\) 0 0
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 0 0
\(351\) 11.7990i 0.629782i
\(352\) 0 0
\(353\) 31.9449i 1.70026i 0.526576 + 0.850128i \(0.323475\pi\)
−0.526576 + 0.850128i \(0.676525\pi\)
\(354\) 0 0
\(355\) 2.94960 + 2.40833i 0.156548 + 0.127821i
\(356\) 0 0
\(357\) −58.7906 −3.11153
\(358\) 0 0
\(359\) 14.8346i 0.782943i 0.920190 + 0.391471i \(0.128034\pi\)
−0.920190 + 0.391471i \(0.871966\pi\)
\(360\) 0 0
\(361\) −15.3923 11.1390i −0.810121 0.586262i
\(362\) 0 0
\(363\) 20.5707i 1.07968i
\(364\) 0 0
\(365\) 5.07180 6.21166i 0.265470 0.325133i
\(366\) 0 0
\(367\) −24.3652 −1.27185 −0.635927 0.771749i \(-0.719382\pi\)
−0.635927 + 0.771749i \(0.719382\pi\)
\(368\) 0 0
\(369\) 32.7862i 1.70678i
\(370\) 0 0
\(371\) −36.4300 −1.89135
\(372\) 0 0
\(373\) −1.66449 −0.0861840 −0.0430920 0.999071i \(-0.513721\pi\)
−0.0430920 + 0.999071i \(0.513721\pi\)
\(374\) 0 0
\(375\) 25.6854 + 13.4820i 1.32639 + 0.696209i
\(376\) 0 0
\(377\) 39.9497i 2.05751i
\(378\) 0 0
\(379\) 8.05844 0.413934 0.206967 0.978348i \(-0.433641\pi\)
0.206967 + 0.978348i \(0.433641\pi\)
\(380\) 0 0
\(381\) −43.5167 −2.22943
\(382\) 0 0
\(383\) 9.68325i 0.494791i 0.968915 + 0.247396i \(0.0795747\pi\)
−0.968915 + 0.247396i \(0.920425\pi\)
\(384\) 0 0
\(385\) 8.39230 10.2784i 0.427711 0.523837i
\(386\) 0 0
\(387\) 3.38587 0.172113
\(388\) 0 0
\(389\) 21.4641 1.08827 0.544137 0.838997i \(-0.316857\pi\)
0.544137 + 0.838997i \(0.316857\pi\)
\(390\) 0 0
\(391\) 39.2460i 1.98475i
\(392\) 0 0
\(393\) −33.9428 −1.71219
\(394\) 0 0
\(395\) −28.3716 23.1653i −1.42753 1.16557i
\(396\) 0 0
\(397\) 1.31268i 0.0658814i −0.999457 0.0329407i \(-0.989513\pi\)
0.999457 0.0329407i \(-0.0104872\pi\)
\(398\) 0 0
\(399\) 36.4300 + 11.7990i 1.82378 + 0.590687i
\(400\) 0 0
\(401\) 12.8622i 0.642307i 0.947027 + 0.321154i \(0.104071\pi\)
−0.947027 + 0.321154i \(0.895929\pi\)
\(402\) 0 0
\(403\) −39.4801 −1.96664
\(404\) 0 0
\(405\) 10.8564 + 8.86422i 0.539459 + 0.440467i
\(406\) 0 0
\(407\) 2.91728i 0.144604i
\(408\) 0 0
\(409\) 26.3551i 1.30318i 0.758573 + 0.651588i \(0.225897\pi\)
−0.758573 + 0.651588i \(0.774103\pi\)
\(410\) 0 0
\(411\) 0.719751 0.0355027
\(412\) 0 0
\(413\) −21.5189 −1.05887
\(414\) 0 0
\(415\) 2.72172 + 2.22228i 0.133604 + 0.109087i
\(416\) 0 0
\(417\) 45.1482 2.21092
\(418\) 0 0
\(419\) 20.0926i 0.981588i 0.871276 + 0.490794i \(0.163293\pi\)
−0.871276 + 0.490794i \(0.836707\pi\)
\(420\) 0 0
\(421\) 26.3551i 1.28447i 0.766508 + 0.642235i \(0.221993\pi\)
−0.766508 + 0.642235i \(0.778007\pi\)
\(422\) 0 0
\(423\) −37.9087 −1.84318
\(424\) 0 0
\(425\) 32.7846 6.69213i 1.59029 0.324616i
\(426\) 0 0
\(427\) 7.43588 0.359848
\(428\) 0 0
\(429\) 28.2487 1.36386
\(430\) 0 0
\(431\) −20.7694 −1.00043 −0.500214 0.865902i \(-0.666745\pi\)
−0.500214 + 0.865902i \(0.666745\pi\)
\(432\) 0 0
\(433\) −15.3069 −0.735603 −0.367801 0.929904i \(-0.619889\pi\)
−0.367801 + 0.929904i \(0.619889\pi\)
\(434\) 0 0
\(435\) −28.9014 23.5979i −1.38572 1.13143i
\(436\) 0 0
\(437\) −7.87645 + 24.3190i −0.376782 + 1.16334i
\(438\) 0 0
\(439\) −38.3964 −1.83256 −0.916280 0.400537i \(-0.868823\pi\)
−0.916280 + 0.400537i \(0.868823\pi\)
\(440\) 0 0
\(441\) −16.6603 −0.793345
\(442\) 0 0
\(443\) 5.86450 0.278631 0.139315 0.990248i \(-0.455510\pi\)
0.139315 + 0.990248i \(0.455510\pi\)
\(444\) 0 0
\(445\) 9.09494 11.1390i 0.431142 0.528038i
\(446\) 0 0
\(447\) 30.2539i 1.43096i
\(448\) 0 0
\(449\) 2.35394i 0.111089i −0.998456 0.0555447i \(-0.982310\pi\)
0.998456 0.0555447i \(-0.0176895\pi\)
\(450\) 0 0
\(451\) 15.3971 0.725023
\(452\) 0 0
\(453\) 45.0518i 2.11672i
\(454\) 0 0
\(455\) 36.4300 + 29.7450i 1.70787 + 1.39447i
\(456\) 0 0
\(457\) 25.4558i 1.19077i 0.803439 + 0.595387i \(0.203001\pi\)
−0.803439 + 0.595387i \(0.796999\pi\)
\(458\) 0 0
\(459\) −12.7110 −0.593298
\(460\) 0 0
\(461\) 24.2487 1.12938 0.564688 0.825305i \(-0.308997\pi\)
0.564688 + 0.825305i \(0.308997\pi\)
\(462\) 0 0
\(463\) −9.49346 −0.441198 −0.220599 0.975365i \(-0.570801\pi\)
−0.220599 + 0.975365i \(0.570801\pi\)
\(464\) 0 0
\(465\) −23.3205 + 28.5617i −1.08146 + 1.32452i
\(466\) 0 0
\(467\) −17.5935 −0.814129 −0.407065 0.913399i \(-0.633448\pi\)
−0.407065 + 0.913399i \(0.633448\pi\)
\(468\) 0 0
\(469\) 15.2161i 0.702616i
\(470\) 0 0
\(471\) 4.65254 0.214378
\(472\) 0 0
\(473\) 1.59008i 0.0731119i
\(474\) 0 0
\(475\) −21.6583 2.43287i −0.993750 0.111628i
\(476\) 0 0
\(477\) −40.1547 −1.83856
\(478\) 0 0
\(479\) 1.75265i 0.0800808i 0.999198 + 0.0400404i \(0.0127487\pi\)
−0.999198 + 0.0400404i \(0.987251\pi\)
\(480\) 0 0
\(481\) 10.3397 0.471452
\(482\) 0 0
\(483\) 51.5198i 2.34423i
\(484\) 0 0
\(485\) 2.88298 + 2.35394i 0.130909 + 0.106887i
\(486\) 0 0
\(487\) 26.6414i 1.20724i −0.797273 0.603619i \(-0.793725\pi\)
0.797273 0.603619i \(-0.206275\pi\)
\(488\) 0 0
\(489\) 32.7862i 1.48264i
\(490\) 0 0
\(491\) 37.9629i 1.71324i −0.515945 0.856622i \(-0.672559\pi\)
0.515945 0.856622i \(-0.327441\pi\)
\(492\) 0 0
\(493\) −43.0377 −1.93832
\(494\) 0 0
\(495\) 9.25036 11.3293i 0.415773 0.509216i
\(496\) 0 0
\(497\) 5.76596 0.258639
\(498\) 0 0
\(499\) 17.4007i 0.778963i −0.921034 0.389481i \(-0.872654\pi\)
0.921034 0.389481i \(-0.127346\pi\)
\(500\) 0 0
\(501\) 26.4449 1.18147
\(502\) 0 0
\(503\) −14.4507 −0.644325 −0.322163 0.946684i \(-0.604410\pi\)
−0.322163 + 0.946684i \(0.604410\pi\)
\(504\) 0 0
\(505\) −14.1962 11.5911i −0.631720 0.515798i
\(506\) 0 0
\(507\) 66.3923i 2.94859i
\(508\) 0 0
\(509\) 35.1402i 1.55756i 0.627297 + 0.778780i \(0.284161\pi\)
−0.627297 + 0.778780i \(0.715839\pi\)
\(510\) 0 0
\(511\) 12.1427i 0.537163i
\(512\) 0 0
\(513\) 7.87645 + 2.55103i 0.347754 + 0.112631i
\(514\) 0 0
\(515\) −19.0665 + 23.3516i −0.840170 + 1.02899i
\(516\) 0 0
\(517\) 17.8028i 0.782965i
\(518\) 0 0
\(519\) 48.3530i 2.12246i
\(520\) 0 0
\(521\) 6.43110i 0.281751i 0.990027 + 0.140876i \(0.0449918\pi\)
−0.990027 + 0.140876i \(0.955008\pi\)
\(522\) 0 0
\(523\) 16.7719i 0.733383i −0.930343 0.366692i \(-0.880490\pi\)
0.930343 0.366692i \(-0.119510\pi\)
\(524\) 0 0
\(525\) 43.0377 8.78504i 1.87832 0.383411i
\(526\) 0 0
\(527\) 42.5318i 1.85271i
\(528\) 0 0
\(529\) 11.3923 0.495318
\(530\) 0 0
\(531\) −23.7190 −1.02932
\(532\) 0 0
\(533\) 54.5723i 2.36379i
\(534\) 0 0
\(535\) −13.6942 + 16.7719i −0.592051 + 0.725112i
\(536\) 0 0
\(537\) 40.6333i 1.75345i
\(538\) 0 0
\(539\) 7.82403i 0.337005i
\(540\) 0 0
\(541\) 12.1962 0.524354 0.262177 0.965020i \(-0.415560\pi\)
0.262177 + 0.965020i \(0.415560\pi\)
\(542\) 0 0
\(543\) 28.9014 1.24028
\(544\) 0 0
\(545\) −21.5189 + 26.3551i −0.921767 + 1.12893i
\(546\) 0 0
\(547\) 3.61250i 0.154459i −0.997013 0.0772297i \(-0.975393\pi\)
0.997013 0.0772297i \(-0.0246075\pi\)
\(548\) 0 0
\(549\) 8.19615 0.349803
\(550\) 0 0
\(551\) 26.6686 + 8.63744i 1.13612 + 0.367967i
\(552\) 0 0
\(553\) −55.4616 −2.35847
\(554\) 0 0
\(555\) 6.10759 7.48024i 0.259253 0.317518i
\(556\) 0 0
\(557\) 25.7332i 1.09035i −0.838321 0.545176i \(-0.816463\pi\)
0.838321 0.545176i \(-0.183537\pi\)
\(558\) 0 0
\(559\) −5.63574 −0.238367
\(560\) 0 0
\(561\) 30.4323i 1.28485i
\(562\) 0 0
\(563\) 10.1922i 0.429550i −0.976664 0.214775i \(-0.931098\pi\)
0.976664 0.214775i \(-0.0689018\pi\)
\(564\) 0 0
\(565\) −4.99347 4.07715i −0.210077 0.171527i
\(566\) 0 0
\(567\) 21.2224 0.891259
\(568\) 0 0
\(569\) 32.7862i 1.37447i −0.726435 0.687235i \(-0.758824\pi\)
0.726435 0.687235i \(-0.241176\pi\)
\(570\) 0 0
\(571\) 23.4721i 0.982276i −0.871082 0.491138i \(-0.836581\pi\)
0.871082 0.491138i \(-0.163419\pi\)
\(572\) 0 0
\(573\) −3.32898 −0.139070
\(574\) 0 0
\(575\) 5.86450 + 28.7300i 0.244566 + 1.19813i
\(576\) 0 0
\(577\) 16.4901i 0.686491i −0.939246 0.343246i \(-0.888474\pi\)
0.939246 0.343246i \(-0.111526\pi\)
\(578\) 0 0
\(579\) 36.5541i 1.51914i
\(580\) 0 0
\(581\) 5.32051 0.220732
\(582\) 0 0
\(583\) 18.8576i 0.781000i
\(584\) 0 0
\(585\) 40.1547 + 32.7862i 1.66019 + 1.35554i
\(586\) 0 0
\(587\) 33.6156 1.38746 0.693732 0.720233i \(-0.255965\pi\)
0.693732 + 0.720233i \(0.255965\pi\)
\(588\) 0 0
\(589\) 8.53590 26.3551i 0.351716 1.08594i
\(590\) 0 0
\(591\) 4.65254 0.191380
\(592\) 0 0
\(593\) 17.5254i 0.719681i 0.933014 + 0.359840i \(0.117169\pi\)
−0.933014 + 0.359840i \(0.882831\pi\)
\(594\) 0 0
\(595\) 32.0442 39.2460i 1.31368 1.60893i
\(596\) 0 0
\(597\) −5.76596 −0.235985
\(598\) 0 0
\(599\) 1.70295 0.0695806 0.0347903 0.999395i \(-0.488924\pi\)
0.0347903 + 0.999395i \(0.488924\pi\)
\(600\) 0 0
\(601\) 15.2161i 0.620679i 0.950626 + 0.310340i \(0.100443\pi\)
−0.950626 + 0.310340i \(0.899557\pi\)
\(602\) 0 0
\(603\) 16.7719i 0.683004i
\(604\) 0 0
\(605\) −13.7321 11.2122i −0.558287 0.455840i
\(606\) 0 0
\(607\) 17.6534i 0.716529i −0.933620 0.358265i \(-0.883369\pi\)
0.933620 0.358265i \(-0.116631\pi\)
\(608\) 0 0
\(609\) −56.4974 −2.28939
\(610\) 0 0
\(611\) 63.0986 2.55270
\(612\) 0 0
\(613\) 38.8401i 1.56874i −0.620295 0.784369i \(-0.712987\pi\)
0.620295 0.784369i \(-0.287013\pi\)
\(614\) 0 0
\(615\) 39.4801 + 32.2354i 1.59199 + 1.29985i
\(616\) 0 0
\(617\) 20.9086i 0.841748i −0.907119 0.420874i \(-0.861723\pi\)
0.907119 0.420874i \(-0.138277\pi\)
\(618\) 0 0
\(619\) 21.8453i 0.878035i 0.898478 + 0.439018i \(0.144673\pi\)
−0.898478 + 0.439018i \(0.855327\pi\)
\(620\) 0 0
\(621\) 11.1390i 0.446992i
\(622\) 0 0
\(623\) 21.7748i 0.872390i
\(624\) 0 0
\(625\) −23.0000 + 9.79796i −0.920000 + 0.391918i
\(626\) 0 0
\(627\) −6.10759 + 18.8576i −0.243914 + 0.753099i
\(628\) 0 0
\(629\) 11.1390i 0.444140i
\(630\) 0 0
\(631\) 27.9166i 1.11134i 0.831402 + 0.555672i \(0.187539\pi\)
−0.831402 + 0.555672i \(0.812461\pi\)
\(632\) 0 0
\(633\) 6.96953i 0.277014i
\(634\) 0 0
\(635\) 23.7190 29.0498i 0.941261 1.15280i
\(636\) 0 0
\(637\) 27.7308 1.09874
\(638\) 0 0
\(639\) 6.35549 0.251419
\(640\) 0 0
\(641\) 28.0783i 1.10903i −0.832175 0.554514i \(-0.812904\pi\)
0.832175 0.554514i \(-0.187096\pi\)
\(642\) 0 0
\(643\) −24.3652 −0.960871 −0.480435 0.877030i \(-0.659521\pi\)
−0.480435 + 0.877030i \(0.659521\pi\)
\(644\) 0 0
\(645\) −3.32898 + 4.07715i −0.131078 + 0.160538i
\(646\) 0 0
\(647\) −27.3300 −1.07445 −0.537227 0.843437i \(-0.680528\pi\)
−0.537227 + 0.843437i \(0.680528\pi\)
\(648\) 0 0
\(649\) 11.1390i 0.437243i
\(650\) 0 0
\(651\) 55.8333i 2.18828i
\(652\) 0 0
\(653\) 5.85993i 0.229317i −0.993405 0.114658i \(-0.963423\pi\)
0.993405 0.114658i \(-0.0365773\pi\)
\(654\) 0 0
\(655\) 18.5007 22.6587i 0.722883 0.885347i
\(656\) 0 0
\(657\) 13.3843i 0.522170i
\(658\) 0 0
\(659\) 33.0241 1.28644 0.643218 0.765683i \(-0.277599\pi\)
0.643218 + 0.765683i \(0.277599\pi\)
\(660\) 0 0
\(661\) 4.07715i 0.158583i 0.996851 + 0.0792914i \(0.0252658\pi\)
−0.996851 + 0.0792914i \(0.974734\pi\)
\(662\) 0 0
\(663\) 107.862 4.18900
\(664\) 0 0
\(665\) −27.7329 + 17.8879i −1.07543 + 0.693664i
\(666\) 0 0
\(667\) 37.7151i 1.46034i
\(668\) 0 0
\(669\) −49.7654 −1.92404
\(670\) 0 0
\(671\) 3.84910i 0.148593i
\(672\) 0 0
\(673\) 15.3069 0.590038 0.295019 0.955491i \(-0.404674\pi\)
0.295019 + 0.955491i \(0.404674\pi\)
\(674\) 0 0
\(675\) 9.30509 1.89939i 0.358153 0.0731077i
\(676\) 0 0
\(677\) 4.99347 0.191915 0.0959573 0.995385i \(-0.469409\pi\)
0.0959573 + 0.995385i \(0.469409\pi\)
\(678\) 0 0
\(679\) 5.63574 0.216280
\(680\) 0 0
\(681\) 28.7321 1.10101
\(682\) 0 0
\(683\) 0.186285i 0.00712801i 0.999994 + 0.00356400i \(0.00113446\pi\)
−0.999994 + 0.00356400i \(0.998866\pi\)
\(684\) 0 0
\(685\) −0.392305 + 0.480473i −0.0149892 + 0.0183579i
\(686\) 0 0
\(687\) 39.2419i 1.49717i
\(688\) 0 0
\(689\) 66.8372 2.54629
\(690\) 0 0
\(691\) 40.0594i 1.52393i 0.647618 + 0.761965i \(0.275765\pi\)
−0.647618 + 0.761965i \(0.724235\pi\)
\(692\) 0 0
\(693\) 22.1469i 0.841293i
\(694\) 0 0
\(695\) −24.6083 + 30.1389i −0.933447 + 1.14323i
\(696\) 0 0
\(697\) 58.7906 2.22685
\(698\) 0 0
\(699\) −22.7358 −0.859948
\(700\) 0 0
\(701\) −37.5167 −1.41698 −0.708492 0.705718i \(-0.750624\pi\)
−0.708492 + 0.705718i \(0.750624\pi\)
\(702\) 0 0
\(703\) −2.23553 + 6.90235i −0.0843147 + 0.260327i
\(704\) 0 0
\(705\) 37.2718 45.6484i 1.40374 1.71922i
\(706\) 0 0
\(707\) −27.7511 −1.04369
\(708\) 0 0
\(709\) −28.3923 −1.06630 −0.533148 0.846022i \(-0.678991\pi\)
−0.533148 + 0.846022i \(0.678991\pi\)
\(710\) 0 0
\(711\) −61.1322 −2.29264
\(712\) 0 0
\(713\) −37.2718 −1.39584
\(714\) 0 0
\(715\) −15.3971 + 18.8576i −0.575820 + 0.705233i
\(716\) 0 0
\(717\) −18.1899 −0.679314
\(718\) 0 0
\(719\) 47.0700i 1.75541i 0.479197 + 0.877707i \(0.340928\pi\)
−0.479197 + 0.877707i \(0.659072\pi\)
\(720\) 0 0
\(721\) 45.6484i 1.70004i
\(722\) 0 0
\(723\) 39.4801 1.46828
\(724\) 0 0
\(725\) 31.5058 6.43110i 1.17010 0.238845i
\(726\) 0 0
\(727\) 18.0797 0.670538 0.335269 0.942122i \(-0.391173\pi\)
0.335269 + 0.942122i \(0.391173\pi\)
\(728\) 0 0
\(729\) 38.1769 1.41396
\(730\) 0 0
\(731\) 6.07137i 0.224558i
\(732\) 0 0
\(733\) 5.37945i 0.198695i −0.995053 0.0993473i \(-0.968325\pi\)
0.995053 0.0993473i \(-0.0316755\pi\)
\(734\) 0 0
\(735\) 16.3803 20.0617i 0.604198 0.739988i
\(736\) 0 0
\(737\) −7.87645 −0.290133
\(738\) 0 0
\(739\) 3.84910i 0.141591i 0.997491 + 0.0707956i \(0.0225538\pi\)
−0.997491 + 0.0707956i \(0.977446\pi\)
\(740\) 0 0
\(741\) −66.8372 21.6472i −2.45532 0.795231i
\(742\) 0 0
\(743\) 7.41129i 0.271894i −0.990716 0.135947i \(-0.956592\pi\)
0.990716 0.135947i \(-0.0434077\pi\)
\(744\) 0 0
\(745\) 20.1962 + 16.4901i 0.739930 + 0.604150i
\(746\) 0 0
\(747\) 5.86450 0.214571
\(748\) 0 0
\(749\) 32.7862i 1.19798i
\(750\) 0 0
\(751\) −26.6686 −0.973152 −0.486576 0.873638i \(-0.661754\pi\)
−0.486576 + 0.873638i \(0.661754\pi\)
\(752\) 0 0
\(753\) 19.0819 0.695382
\(754\) 0 0
\(755\) −30.0745 24.5557i −1.09452 0.893675i
\(756\) 0 0
\(757\) 49.4703i 1.79803i 0.437920 + 0.899014i \(0.355715\pi\)
−0.437920 + 0.899014i \(0.644285\pi\)
\(758\) 0 0
\(759\) 26.6686 0.968010
\(760\) 0 0
\(761\) −26.4449 −0.958626 −0.479313 0.877644i \(-0.659114\pi\)
−0.479313 + 0.877644i \(0.659114\pi\)
\(762\) 0 0
\(763\) 51.5198i 1.86514i
\(764\) 0 0
\(765\) 35.3205 43.2586i 1.27702 1.56402i
\(766\) 0 0
\(767\) 39.4801 1.42554
\(768\) 0 0
\(769\) 24.1962 0.872536 0.436268 0.899817i \(-0.356300\pi\)
0.436268 + 0.899817i \(0.356300\pi\)
\(770\) 0 0
\(771\) 68.7894i 2.47739i
\(772\) 0 0
\(773\) 2.88298 0.103694 0.0518468 0.998655i \(-0.483489\pi\)
0.0518468 + 0.998655i \(0.483489\pi\)
\(774\) 0 0
\(775\) −6.35549 31.1354i −0.228296 1.11842i
\(776\) 0 0
\(777\) 14.6226i 0.524583i
\(778\) 0 0
\(779\) −36.4300 11.7990i −1.30524 0.422742i
\(780\) 0 0
\(781\) 2.98468i 0.106800i
\(782\) 0 0
\(783\) −12.2152 −0.436535
\(784\) 0 0
\(785\) −2.53590 + 3.10583i −0.0905101 + 0.110852i
\(786\) 0 0
\(787\) 45.4990i 1.62186i 0.585141 + 0.810932i \(0.301039\pi\)
−0.585141 + 0.810932i \(0.698961\pi\)
\(788\) 0 0
\(789\) 37.4941i 1.33483i
\(790\) 0 0
\(791\) −9.76139 −0.347075
\(792\) 0 0
\(793\) −13.6424 −0.484456
\(794\) 0 0
\(795\) 39.4801 48.3530i 1.40021 1.71491i
\(796\) 0 0
\(797\) 38.0443 1.34760 0.673798 0.738915i \(-0.264662\pi\)
0.673798 + 0.738915i \(0.264662\pi\)
\(798\) 0 0
\(799\) 67.9760i 2.40482i
\(800\) 0 0
\(801\) 24.0012i 0.848040i