Properties

Label 1840.2.e.f.369.10
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 24 x^{10} + 188 x^{8} + 530 x^{6} + 508 x^{4} + 80 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 460)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.10
Root \(1.26443i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.40050i q^{3} +(-0.817027 - 2.08146i) q^{5} +4.41307i q^{7} -2.76241 q^{9} +O(q^{10})\) \(q+2.40050i q^{3} +(-0.817027 - 2.08146i) q^{5} +4.41307i q^{7} -2.76241 q^{9} -2.29289 q^{11} +6.92936i q^{13} +(4.99655 - 1.96128i) q^{15} -1.51387i q^{17} +2.89920 q^{19} -10.5936 q^{21} -1.00000i q^{23} +(-3.66493 + 3.40122i) q^{25} +0.570328i q^{27} +7.68764 q^{29} -3.85746 q^{31} -5.50408i q^{33} +(9.18562 - 3.60560i) q^{35} -8.62830i q^{37} -16.6340 q^{39} -6.44324 q^{41} +3.48497i q^{43} +(2.25697 + 5.74985i) q^{45} -6.19747i q^{47} -12.4752 q^{49} +3.63405 q^{51} +2.17710i q^{53} +(1.87335 + 4.77255i) q^{55} +6.95953i q^{57} -11.7637 q^{59} -5.11443 q^{61} -12.1907i q^{63} +(14.4232 - 5.66148i) q^{65} +9.94597i q^{67} +2.40050 q^{69} -3.41407 q^{71} -8.95307i q^{73} +(-8.16463 - 8.79768i) q^{75} -10.1187i q^{77} -1.92694 q^{79} -9.65631 q^{81} -8.04131i q^{83} +(-3.15106 + 1.23687i) q^{85} +18.4542i q^{87} +1.09273 q^{89} -30.5798 q^{91} -9.25985i q^{93} +(-2.36872 - 6.03456i) q^{95} +16.9208i q^{97} +6.33390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 20 q^{9} + O(q^{10}) \) \( 12 q - 20 q^{9} - 4 q^{11} - 2 q^{15} + 8 q^{19} + 8 q^{25} - 10 q^{29} - 18 q^{31} + 10 q^{35} - 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} + 24 q^{51} - 16 q^{55} - 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} + 34 q^{71} - 16 q^{75} + 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} + 8 q^{91} - 12 q^{95} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 2.40050i 1.38593i 0.720971 + 0.692965i \(0.243696\pi\)
−0.720971 + 0.692965i \(0.756304\pi\)
\(4\) 0 0
\(5\) −0.817027 2.08146i −0.365386 0.930856i
\(6\) 0 0
\(7\) 4.41307i 1.66798i 0.551777 + 0.833992i \(0.313950\pi\)
−0.551777 + 0.833992i \(0.686050\pi\)
\(8\) 0 0
\(9\) −2.76241 −0.920804
\(10\) 0 0
\(11\) −2.29289 −0.691332 −0.345666 0.938358i \(-0.612347\pi\)
−0.345666 + 0.938358i \(0.612347\pi\)
\(12\) 0 0
\(13\) 6.92936i 1.92186i 0.276792 + 0.960930i \(0.410729\pi\)
−0.276792 + 0.960930i \(0.589271\pi\)
\(14\) 0 0
\(15\) 4.99655 1.96128i 1.29010 0.506399i
\(16\) 0 0
\(17\) 1.51387i 0.367168i −0.983004 0.183584i \(-0.941230\pi\)
0.983004 0.183584i \(-0.0587699\pi\)
\(18\) 0 0
\(19\) 2.89920 0.665121 0.332561 0.943082i \(-0.392087\pi\)
0.332561 + 0.943082i \(0.392087\pi\)
\(20\) 0 0
\(21\) −10.5936 −2.31171
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −3.66493 + 3.40122i −0.732987 + 0.680243i
\(26\) 0 0
\(27\) 0.570328i 0.109760i
\(28\) 0 0
\(29\) 7.68764 1.42756 0.713779 0.700371i \(-0.246982\pi\)
0.713779 + 0.700371i \(0.246982\pi\)
\(30\) 0 0
\(31\) −3.85746 −0.692821 −0.346410 0.938083i \(-0.612599\pi\)
−0.346410 + 0.938083i \(0.612599\pi\)
\(32\) 0 0
\(33\) 5.50408i 0.958138i
\(34\) 0 0
\(35\) 9.18562 3.60560i 1.55265 0.609457i
\(36\) 0 0
\(37\) 8.62830i 1.41848i −0.704965 0.709242i \(-0.749037\pi\)
0.704965 0.709242i \(-0.250963\pi\)
\(38\) 0 0
\(39\) −16.6340 −2.66356
\(40\) 0 0
\(41\) −6.44324 −1.00626 −0.503132 0.864209i \(-0.667819\pi\)
−0.503132 + 0.864209i \(0.667819\pi\)
\(42\) 0 0
\(43\) 3.48497i 0.531453i 0.964048 + 0.265727i \(0.0856119\pi\)
−0.964048 + 0.265727i \(0.914388\pi\)
\(44\) 0 0
\(45\) 2.25697 + 5.74985i 0.336449 + 0.857136i
\(46\) 0 0
\(47\) 6.19747i 0.903994i −0.892019 0.451997i \(-0.850712\pi\)
0.892019 0.451997i \(-0.149288\pi\)
\(48\) 0 0
\(49\) −12.4752 −1.78217
\(50\) 0 0
\(51\) 3.63405 0.508869
\(52\) 0 0
\(53\) 2.17710i 0.299047i 0.988758 + 0.149524i \(0.0477740\pi\)
−0.988758 + 0.149524i \(0.952226\pi\)
\(54\) 0 0
\(55\) 1.87335 + 4.77255i 0.252603 + 0.643530i
\(56\) 0 0
\(57\) 6.95953i 0.921812i
\(58\) 0 0
\(59\) −11.7637 −1.53150 −0.765750 0.643138i \(-0.777632\pi\)
−0.765750 + 0.643138i \(0.777632\pi\)
\(60\) 0 0
\(61\) −5.11443 −0.654835 −0.327418 0.944880i \(-0.606178\pi\)
−0.327418 + 0.944880i \(0.606178\pi\)
\(62\) 0 0
\(63\) 12.1907i 1.53589i
\(64\) 0 0
\(65\) 14.4232 5.66148i 1.78898 0.702220i
\(66\) 0 0
\(67\) 9.94597i 1.21509i 0.794284 + 0.607547i \(0.207846\pi\)
−0.794284 + 0.607547i \(0.792154\pi\)
\(68\) 0 0
\(69\) 2.40050 0.288987
\(70\) 0 0
\(71\) −3.41407 −0.405175 −0.202588 0.979264i \(-0.564935\pi\)
−0.202588 + 0.979264i \(0.564935\pi\)
\(72\) 0 0
\(73\) 8.95307i 1.04788i −0.851756 0.523939i \(-0.824462\pi\)
0.851756 0.523939i \(-0.175538\pi\)
\(74\) 0 0
\(75\) −8.16463 8.79768i −0.942770 1.01587i
\(76\) 0 0
\(77\) 10.1187i 1.15313i
\(78\) 0 0
\(79\) −1.92694 −0.216798 −0.108399 0.994107i \(-0.534572\pi\)
−0.108399 + 0.994107i \(0.534572\pi\)
\(80\) 0 0
\(81\) −9.65631 −1.07292
\(82\) 0 0
\(83\) 8.04131i 0.882648i −0.897348 0.441324i \(-0.854509\pi\)
0.897348 0.441324i \(-0.145491\pi\)
\(84\) 0 0
\(85\) −3.15106 + 1.23687i −0.341781 + 0.134158i
\(86\) 0 0
\(87\) 18.4542i 1.97850i
\(88\) 0 0
\(89\) 1.09273 0.115829 0.0579147 0.998322i \(-0.481555\pi\)
0.0579147 + 0.998322i \(0.481555\pi\)
\(90\) 0 0
\(91\) −30.5798 −3.20563
\(92\) 0 0
\(93\) 9.25985i 0.960201i
\(94\) 0 0
\(95\) −2.36872 6.03456i −0.243026 0.619132i
\(96\) 0 0
\(97\) 16.9208i 1.71805i 0.511933 + 0.859026i \(0.328930\pi\)
−0.511933 + 0.859026i \(0.671070\pi\)
\(98\) 0 0
\(99\) 6.33390 0.636581
\(100\) 0 0
\(101\) 12.9497 1.28855 0.644274 0.764795i \(-0.277160\pi\)
0.644274 + 0.764795i \(0.277160\pi\)
\(102\) 0 0
\(103\) 10.9754i 1.08144i −0.841202 0.540721i \(-0.818152\pi\)
0.841202 0.540721i \(-0.181848\pi\)
\(104\) 0 0
\(105\) 8.65525 + 22.0501i 0.844666 + 2.15187i
\(106\) 0 0
\(107\) 19.8821i 1.92208i 0.276411 + 0.961040i \(0.410855\pi\)
−0.276411 + 0.961040i \(0.589145\pi\)
\(108\) 0 0
\(109\) −0.427249 −0.0409231 −0.0204615 0.999791i \(-0.506514\pi\)
−0.0204615 + 0.999791i \(0.506514\pi\)
\(110\) 0 0
\(111\) 20.7123 1.96592
\(112\) 0 0
\(113\) 5.38533i 0.506609i −0.967387 0.253304i \(-0.918483\pi\)
0.967387 0.253304i \(-0.0815174\pi\)
\(114\) 0 0
\(115\) −2.08146 + 0.817027i −0.194097 + 0.0761882i
\(116\) 0 0
\(117\) 19.1418i 1.76966i
\(118\) 0 0
\(119\) 6.68082 0.612430
\(120\) 0 0
\(121\) −5.74267 −0.522061
\(122\) 0 0
\(123\) 15.4670i 1.39461i
\(124\) 0 0
\(125\) 10.0738 + 4.84952i 0.901031 + 0.433754i
\(126\) 0 0
\(127\) 6.16014i 0.546624i 0.961925 + 0.273312i \(0.0881191\pi\)
−0.961925 + 0.273312i \(0.911881\pi\)
\(128\) 0 0
\(129\) −8.36569 −0.736558
\(130\) 0 0
\(131\) −14.6325 −1.27845 −0.639225 0.769020i \(-0.720745\pi\)
−0.639225 + 0.769020i \(0.720745\pi\)
\(132\) 0 0
\(133\) 12.7944i 1.10941i
\(134\) 0 0
\(135\) 1.18711 0.465974i 0.102171 0.0401046i
\(136\) 0 0
\(137\) 0.972256i 0.0830654i −0.999137 0.0415327i \(-0.986776\pi\)
0.999137 0.0415327i \(-0.0132241\pi\)
\(138\) 0 0
\(139\) 7.74312 0.656763 0.328382 0.944545i \(-0.393497\pi\)
0.328382 + 0.944545i \(0.393497\pi\)
\(140\) 0 0
\(141\) 14.8770 1.25287
\(142\) 0 0
\(143\) 15.8883i 1.32864i
\(144\) 0 0
\(145\) −6.28101 16.0015i −0.521609 1.32885i
\(146\) 0 0
\(147\) 29.9467i 2.46996i
\(148\) 0 0
\(149\) 17.6823 1.44859 0.724293 0.689492i \(-0.242166\pi\)
0.724293 + 0.689492i \(0.242166\pi\)
\(150\) 0 0
\(151\) 2.01286 0.163804 0.0819022 0.996640i \(-0.473900\pi\)
0.0819022 + 0.996640i \(0.473900\pi\)
\(152\) 0 0
\(153\) 4.18194i 0.338090i
\(154\) 0 0
\(155\) 3.15165 + 8.02914i 0.253147 + 0.644916i
\(156\) 0 0
\(157\) 5.82703i 0.465048i 0.972591 + 0.232524i \(0.0746984\pi\)
−0.972591 + 0.232524i \(0.925302\pi\)
\(158\) 0 0
\(159\) −5.22612 −0.414459
\(160\) 0 0
\(161\) 4.41307 0.347799
\(162\) 0 0
\(163\) 6.75147i 0.528816i 0.964411 + 0.264408i \(0.0851765\pi\)
−0.964411 + 0.264408i \(0.914823\pi\)
\(164\) 0 0
\(165\) −11.4565 + 4.49698i −0.891889 + 0.350090i
\(166\) 0 0
\(167\) 23.4541i 1.81493i −0.420125 0.907466i \(-0.638014\pi\)
0.420125 0.907466i \(-0.361986\pi\)
\(168\) 0 0
\(169\) −35.0161 −2.69355
\(170\) 0 0
\(171\) −8.00878 −0.612447
\(172\) 0 0
\(173\) 8.28850i 0.630163i −0.949065 0.315081i \(-0.897968\pi\)
0.949065 0.315081i \(-0.102032\pi\)
\(174\) 0 0
\(175\) −15.0098 16.1736i −1.13463 1.22261i
\(176\) 0 0
\(177\) 28.2387i 2.12255i
\(178\) 0 0
\(179\) 1.04002 0.0777345 0.0388673 0.999244i \(-0.487625\pi\)
0.0388673 + 0.999244i \(0.487625\pi\)
\(180\) 0 0
\(181\) 2.71850 0.202065 0.101032 0.994883i \(-0.467785\pi\)
0.101032 + 0.994883i \(0.467785\pi\)
\(182\) 0 0
\(183\) 12.2772i 0.907557i
\(184\) 0 0
\(185\) −17.9594 + 7.04956i −1.32040 + 0.518294i
\(186\) 0 0
\(187\) 3.47114i 0.253835i
\(188\) 0 0
\(189\) −2.51690 −0.183077
\(190\) 0 0
\(191\) −8.04858 −0.582375 −0.291187 0.956666i \(-0.594050\pi\)
−0.291187 + 0.956666i \(0.594050\pi\)
\(192\) 0 0
\(193\) 16.0276i 1.15370i −0.816852 0.576848i \(-0.804283\pi\)
0.816852 0.576848i \(-0.195717\pi\)
\(194\) 0 0
\(195\) 13.5904 + 34.6229i 0.973228 + 2.47940i
\(196\) 0 0
\(197\) 4.06316i 0.289488i −0.989469 0.144744i \(-0.953764\pi\)
0.989469 0.144744i \(-0.0462359\pi\)
\(198\) 0 0
\(199\) 18.7042 1.32590 0.662952 0.748662i \(-0.269303\pi\)
0.662952 + 0.748662i \(0.269303\pi\)
\(200\) 0 0
\(201\) −23.8753 −1.68404
\(202\) 0 0
\(203\) 33.9261i 2.38114i
\(204\) 0 0
\(205\) 5.26430 + 13.4113i 0.367675 + 0.936688i
\(206\) 0 0
\(207\) 2.76241i 0.192001i
\(208\) 0 0
\(209\) −6.64753 −0.459819
\(210\) 0 0
\(211\) −7.87839 −0.542371 −0.271185 0.962527i \(-0.587416\pi\)
−0.271185 + 0.962527i \(0.587416\pi\)
\(212\) 0 0
\(213\) 8.19548i 0.561545i
\(214\) 0 0
\(215\) 7.25382 2.84732i 0.494707 0.194185i
\(216\) 0 0
\(217\) 17.0232i 1.15561i
\(218\) 0 0
\(219\) 21.4919 1.45229
\(220\) 0 0
\(221\) 10.4902 0.705645
\(222\) 0 0
\(223\) 2.29263i 0.153526i 0.997049 + 0.0767628i \(0.0244584\pi\)
−0.997049 + 0.0767628i \(0.975542\pi\)
\(224\) 0 0
\(225\) 10.1241 9.39556i 0.674937 0.626371i
\(226\) 0 0
\(227\) 12.8325i 0.851725i 0.904788 + 0.425862i \(0.140029\pi\)
−0.904788 + 0.425862i \(0.859971\pi\)
\(228\) 0 0
\(229\) 16.2528 1.07401 0.537007 0.843578i \(-0.319555\pi\)
0.537007 + 0.843578i \(0.319555\pi\)
\(230\) 0 0
\(231\) 24.2899 1.59816
\(232\) 0 0
\(233\) 21.5410i 1.41120i 0.708613 + 0.705598i \(0.249321\pi\)
−0.708613 + 0.705598i \(0.750679\pi\)
\(234\) 0 0
\(235\) −12.8998 + 5.06350i −0.841489 + 0.330307i
\(236\) 0 0
\(237\) 4.62563i 0.300467i
\(238\) 0 0
\(239\) −11.0622 −0.715555 −0.357778 0.933807i \(-0.616465\pi\)
−0.357778 + 0.933807i \(0.616465\pi\)
\(240\) 0 0
\(241\) 18.2164 1.17342 0.586710 0.809797i \(-0.300423\pi\)
0.586710 + 0.809797i \(0.300423\pi\)
\(242\) 0 0
\(243\) 21.4690i 1.37724i
\(244\) 0 0
\(245\) 10.1926 + 25.9666i 0.651179 + 1.65894i
\(246\) 0 0
\(247\) 20.0896i 1.27827i
\(248\) 0 0
\(249\) 19.3032 1.22329
\(250\) 0 0
\(251\) 10.0182 0.632345 0.316172 0.948702i \(-0.397602\pi\)
0.316172 + 0.948702i \(0.397602\pi\)
\(252\) 0 0
\(253\) 2.29289i 0.144153i
\(254\) 0 0
\(255\) −2.96912 7.56413i −0.185934 0.473684i
\(256\) 0 0
\(257\) 14.3021i 0.892141i 0.894998 + 0.446070i \(0.147177\pi\)
−0.894998 + 0.446070i \(0.852823\pi\)
\(258\) 0 0
\(259\) 38.0773 2.36601
\(260\) 0 0
\(261\) −21.2364 −1.31450
\(262\) 0 0
\(263\) 9.44361i 0.582318i 0.956675 + 0.291159i \(0.0940409\pi\)
−0.956675 + 0.291159i \(0.905959\pi\)
\(264\) 0 0
\(265\) 4.53153 1.77875i 0.278370 0.109268i
\(266\) 0 0
\(267\) 2.62311i 0.160531i
\(268\) 0 0
\(269\) −23.7630 −1.44886 −0.724428 0.689350i \(-0.757896\pi\)
−0.724428 + 0.689350i \(0.757896\pi\)
\(270\) 0 0
\(271\) 17.5939 1.06875 0.534375 0.845247i \(-0.320547\pi\)
0.534375 + 0.845247i \(0.320547\pi\)
\(272\) 0 0
\(273\) 73.4068i 4.44278i
\(274\) 0 0
\(275\) 8.40328 7.79860i 0.506737 0.470273i
\(276\) 0 0
\(277\) 29.6582i 1.78199i 0.454014 + 0.890995i \(0.349992\pi\)
−0.454014 + 0.890995i \(0.650008\pi\)
\(278\) 0 0
\(279\) 10.6559 0.637952
\(280\) 0 0
\(281\) −8.25484 −0.492442 −0.246221 0.969214i \(-0.579189\pi\)
−0.246221 + 0.969214i \(0.579189\pi\)
\(282\) 0 0
\(283\) 9.21317i 0.547666i −0.961777 0.273833i \(-0.911708\pi\)
0.961777 0.273833i \(-0.0882916\pi\)
\(284\) 0 0
\(285\) 14.4860 5.68613i 0.858075 0.336817i
\(286\) 0 0
\(287\) 28.4344i 1.67843i
\(288\) 0 0
\(289\) 14.7082 0.865188
\(290\) 0 0
\(291\) −40.6185 −2.38110
\(292\) 0 0
\(293\) 11.1138i 0.649277i 0.945838 + 0.324639i \(0.105243\pi\)
−0.945838 + 0.324639i \(0.894757\pi\)
\(294\) 0 0
\(295\) 9.61125 + 24.4856i 0.559588 + 1.42561i
\(296\) 0 0
\(297\) 1.30770i 0.0758804i
\(298\) 0 0
\(299\) 6.92936 0.400735
\(300\) 0 0
\(301\) −15.3794 −0.886455
\(302\) 0 0
\(303\) 31.0859i 1.78584i
\(304\) 0 0
\(305\) 4.17863 + 10.6455i 0.239267 + 0.609558i
\(306\) 0 0
\(307\) 18.7800i 1.07183i 0.844272 + 0.535916i \(0.180033\pi\)
−0.844272 + 0.535916i \(0.819967\pi\)
\(308\) 0 0
\(309\) 26.3465 1.49880
\(310\) 0 0
\(311\) −2.51258 −0.142475 −0.0712377 0.997459i \(-0.522695\pi\)
−0.0712377 + 0.997459i \(0.522695\pi\)
\(312\) 0 0
\(313\) 19.9278i 1.12638i 0.826326 + 0.563192i \(0.190427\pi\)
−0.826326 + 0.563192i \(0.809573\pi\)
\(314\) 0 0
\(315\) −25.3745 + 9.96015i −1.42969 + 0.561191i
\(316\) 0 0
\(317\) 27.8849i 1.56617i 0.621912 + 0.783087i \(0.286356\pi\)
−0.621912 + 0.783087i \(0.713644\pi\)
\(318\) 0 0
\(319\) −17.6269 −0.986916
\(320\) 0 0
\(321\) −47.7271 −2.66387
\(322\) 0 0
\(323\) 4.38901i 0.244211i
\(324\) 0 0
\(325\) −23.5683 25.3957i −1.30733 1.40870i
\(326\) 0 0
\(327\) 1.02561i 0.0567165i
\(328\) 0 0
\(329\) 27.3499 1.50785
\(330\) 0 0
\(331\) 28.5409 1.56875 0.784375 0.620287i \(-0.212984\pi\)
0.784375 + 0.620287i \(0.212984\pi\)
\(332\) 0 0
\(333\) 23.8349i 1.30615i
\(334\) 0 0
\(335\) 20.7021 8.12612i 1.13108 0.443978i
\(336\) 0 0
\(337\) 3.71371i 0.202298i −0.994871 0.101149i \(-0.967748\pi\)
0.994871 0.101149i \(-0.0322520\pi\)
\(338\) 0 0
\(339\) 12.9275 0.702125
\(340\) 0 0
\(341\) 8.84472 0.478969
\(342\) 0 0
\(343\) 24.1624i 1.30464i
\(344\) 0 0
\(345\) −1.96128 4.99655i −0.105592 0.269005i
\(346\) 0 0
\(347\) 14.1459i 0.759393i 0.925111 + 0.379696i \(0.123972\pi\)
−0.925111 + 0.379696i \(0.876028\pi\)
\(348\) 0 0
\(349\) 21.2802 1.13910 0.569550 0.821957i \(-0.307117\pi\)
0.569550 + 0.821957i \(0.307117\pi\)
\(350\) 0 0
\(351\) −3.95201 −0.210943
\(352\) 0 0
\(353\) 24.4641i 1.30209i 0.759038 + 0.651046i \(0.225669\pi\)
−0.759038 + 0.651046i \(0.774331\pi\)
\(354\) 0 0
\(355\) 2.78939 + 7.10624i 0.148045 + 0.377160i
\(356\) 0 0
\(357\) 16.0373i 0.848786i
\(358\) 0 0
\(359\) −23.0252 −1.21522 −0.607612 0.794234i \(-0.707872\pi\)
−0.607612 + 0.794234i \(0.707872\pi\)
\(360\) 0 0
\(361\) −10.5947 −0.557613
\(362\) 0 0
\(363\) 13.7853i 0.723540i
\(364\) 0 0
\(365\) −18.6354 + 7.31490i −0.975424 + 0.382880i
\(366\) 0 0
\(367\) 0.478057i 0.0249544i 0.999922 + 0.0124772i \(0.00397171\pi\)
−0.999922 + 0.0124772i \(0.996028\pi\)
\(368\) 0 0
\(369\) 17.7989 0.926573
\(370\) 0 0
\(371\) −9.60767 −0.498806
\(372\) 0 0
\(373\) 27.3508i 1.41617i 0.706127 + 0.708085i \(0.250441\pi\)
−0.706127 + 0.708085i \(0.749559\pi\)
\(374\) 0 0
\(375\) −11.6413 + 24.1823i −0.601153 + 1.24877i
\(376\) 0 0
\(377\) 53.2704i 2.74357i
\(378\) 0 0
\(379\) −7.35358 −0.377728 −0.188864 0.982003i \(-0.560481\pi\)
−0.188864 + 0.982003i \(0.560481\pi\)
\(380\) 0 0
\(381\) −14.7874 −0.757583
\(382\) 0 0
\(383\) 3.34108i 0.170721i 0.996350 + 0.0853606i \(0.0272042\pi\)
−0.996350 + 0.0853606i \(0.972796\pi\)
\(384\) 0 0
\(385\) −21.0616 + 8.26723i −1.07340 + 0.421337i
\(386\) 0 0
\(387\) 9.62693i 0.489364i
\(388\) 0 0
\(389\) −0.366568 −0.0185858 −0.00929288 0.999957i \(-0.502958\pi\)
−0.00929288 + 0.999957i \(0.502958\pi\)
\(390\) 0 0
\(391\) −1.51387 −0.0765598
\(392\) 0 0
\(393\) 35.1254i 1.77184i
\(394\) 0 0
\(395\) 1.57436 + 4.01085i 0.0792148 + 0.201808i
\(396\) 0 0
\(397\) 11.3222i 0.568245i 0.958788 + 0.284122i \(0.0917022\pi\)
−0.958788 + 0.284122i \(0.908298\pi\)
\(398\) 0 0
\(399\) −30.7129 −1.53757
\(400\) 0 0
\(401\) 37.1673 1.85605 0.928024 0.372520i \(-0.121506\pi\)
0.928024 + 0.372520i \(0.121506\pi\)
\(402\) 0 0
\(403\) 26.7298i 1.33150i
\(404\) 0 0
\(405\) 7.88947 + 20.0992i 0.392031 + 0.998738i
\(406\) 0 0
\(407\) 19.7837i 0.980643i
\(408\) 0 0
\(409\) 13.7745 0.681107 0.340553 0.940225i \(-0.389386\pi\)
0.340553 + 0.940225i \(0.389386\pi\)
\(410\) 0 0
\(411\) 2.33390 0.115123
\(412\) 0 0
\(413\) 51.9139i 2.55452i
\(414\) 0 0
\(415\) −16.7376 + 6.56997i −0.821619 + 0.322507i
\(416\) 0 0
\(417\) 18.5874i 0.910228i
\(418\) 0 0
\(419\) 7.50726 0.366753 0.183377 0.983043i \(-0.441297\pi\)
0.183377 + 0.983043i \(0.441297\pi\)
\(420\) 0 0
\(421\) −7.65685 −0.373172 −0.186586 0.982439i \(-0.559742\pi\)
−0.186586 + 0.982439i \(0.559742\pi\)
\(422\) 0 0
\(423\) 17.1200i 0.832402i
\(424\) 0 0
\(425\) 5.14900 + 5.54824i 0.249763 + 0.269129i
\(426\) 0 0
\(427\) 22.5703i 1.09225i
\(428\) 0 0
\(429\) 38.1398 1.84141
\(430\) 0 0
\(431\) −6.22764 −0.299975 −0.149987 0.988688i \(-0.547923\pi\)
−0.149987 + 0.988688i \(0.547923\pi\)
\(432\) 0 0
\(433\) 0.704087i 0.0338362i 0.999857 + 0.0169181i \(0.00538546\pi\)
−0.999857 + 0.0169181i \(0.994615\pi\)
\(434\) 0 0
\(435\) 38.4116 15.0776i 1.84170 0.722914i
\(436\) 0 0
\(437\) 2.89920i 0.138687i
\(438\) 0 0
\(439\) −34.8570 −1.66363 −0.831816 0.555052i \(-0.812699\pi\)
−0.831816 + 0.555052i \(0.812699\pi\)
\(440\) 0 0
\(441\) 34.4616 1.64103
\(442\) 0 0
\(443\) 24.8165i 1.17907i 0.807745 + 0.589533i \(0.200688\pi\)
−0.807745 + 0.589533i \(0.799312\pi\)
\(444\) 0 0
\(445\) −0.892792 2.27448i −0.0423224 0.107820i
\(446\) 0 0
\(447\) 42.4463i 2.00764i
\(448\) 0 0
\(449\) −6.77738 −0.319844 −0.159922 0.987130i \(-0.551124\pi\)
−0.159922 + 0.987130i \(0.551124\pi\)
\(450\) 0 0
\(451\) 14.7736 0.695662
\(452\) 0 0
\(453\) 4.83188i 0.227021i
\(454\) 0 0
\(455\) 24.9845 + 63.6505i 1.17129 + 2.98398i
\(456\) 0 0
\(457\) 1.47169i 0.0688429i −0.999407 0.0344214i \(-0.989041\pi\)
0.999407 0.0344214i \(-0.0109588\pi\)
\(458\) 0 0
\(459\) 0.863404 0.0403003
\(460\) 0 0
\(461\) 25.8037 1.20180 0.600899 0.799325i \(-0.294809\pi\)
0.600899 + 0.799325i \(0.294809\pi\)
\(462\) 0 0
\(463\) 15.3469i 0.713231i 0.934251 + 0.356616i \(0.116069\pi\)
−0.934251 + 0.356616i \(0.883931\pi\)
\(464\) 0 0
\(465\) −19.2740 + 7.56555i −0.893809 + 0.350844i
\(466\) 0 0
\(467\) 10.2933i 0.476315i 0.971227 + 0.238157i \(0.0765434\pi\)
−0.971227 + 0.238157i \(0.923457\pi\)
\(468\) 0 0
\(469\) −43.8922 −2.02676
\(470\) 0 0
\(471\) −13.9878 −0.644524
\(472\) 0 0
\(473\) 7.99065i 0.367410i
\(474\) 0 0
\(475\) −10.6254 + 9.86079i −0.487525 + 0.452444i
\(476\) 0 0
\(477\) 6.01404i 0.275364i
\(478\) 0 0
\(479\) 4.50453 0.205817 0.102909 0.994691i \(-0.467185\pi\)
0.102909 + 0.994691i \(0.467185\pi\)
\(480\) 0 0
\(481\) 59.7886 2.72613
\(482\) 0 0
\(483\) 10.5936i 0.482025i
\(484\) 0 0
\(485\) 35.2200 13.8248i 1.59926 0.627751i
\(486\) 0 0
\(487\) 27.2669i 1.23558i −0.786343 0.617790i \(-0.788028\pi\)
0.786343 0.617790i \(-0.211972\pi\)
\(488\) 0 0
\(489\) −16.2069 −0.732902
\(490\) 0 0
\(491\) −24.4866 −1.10507 −0.552533 0.833491i \(-0.686339\pi\)
−0.552533 + 0.833491i \(0.686339\pi\)
\(492\) 0 0
\(493\) 11.6381i 0.524154i
\(494\) 0 0
\(495\) −5.17497 13.1838i −0.232598 0.592566i
\(496\) 0 0
\(497\) 15.0665i 0.675826i
\(498\) 0 0
\(499\) −24.1892 −1.08286 −0.541429 0.840746i \(-0.682117\pi\)
−0.541429 + 0.840746i \(0.682117\pi\)
\(500\) 0 0
\(501\) 56.3016 2.51537
\(502\) 0 0
\(503\) 30.6230i 1.36541i −0.730693 0.682706i \(-0.760803\pi\)
0.730693 0.682706i \(-0.239197\pi\)
\(504\) 0 0
\(505\) −10.5803 26.9543i −0.470817 1.19945i
\(506\) 0 0
\(507\) 84.0562i 3.73307i
\(508\) 0 0
\(509\) 2.56826 0.113836 0.0569181 0.998379i \(-0.481873\pi\)
0.0569181 + 0.998379i \(0.481873\pi\)
\(510\) 0 0
\(511\) 39.5105 1.74784
\(512\) 0 0
\(513\) 1.65349i 0.0730035i
\(514\) 0 0
\(515\) −22.8449 + 8.96722i −1.00667 + 0.395143i
\(516\) 0 0
\(517\) 14.2101i 0.624960i
\(518\) 0 0
\(519\) 19.8966 0.873362
\(520\) 0 0
\(521\) −44.1355 −1.93361 −0.966807 0.255509i \(-0.917757\pi\)
−0.966807 + 0.255509i \(0.917757\pi\)
\(522\) 0 0
\(523\) 42.2884i 1.84914i −0.381008 0.924572i \(-0.624423\pi\)
0.381008 0.924572i \(-0.375577\pi\)
\(524\) 0 0
\(525\) 38.8248 36.0311i 1.69445 1.57252i
\(526\) 0 0
\(527\) 5.83970i 0.254381i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 32.4961 1.41021
\(532\) 0 0
\(533\) 44.6475i 1.93390i
\(534\) 0 0
\(535\) 41.3838 16.2443i 1.78918 0.702300i
\(536\) 0 0
\(537\) 2.49656i 0.107735i
\(538\) 0 0
\(539\) 28.6042 1.23207
\(540\) 0 0
\(541\) 10.2776 0.441871 0.220935 0.975288i \(-0.429089\pi\)
0.220935 + 0.975288i \(0.429089\pi\)
\(542\) 0 0
\(543\) 6.52577i 0.280048i
\(544\) 0 0
\(545\) 0.349074 + 0.889302i 0.0149527 + 0.0380935i
\(546\) 0 0
\(547\) 3.87305i 0.165600i −0.996566 0.0827998i \(-0.973614\pi\)
0.996566 0.0827998i \(-0.0263862\pi\)
\(548\) 0 0
\(549\) 14.1282 0.602975
\(550\) 0 0
\(551\) 22.2880 0.949500
\(552\) 0 0
\(553\) 8.50373i 0.361615i
\(554\) 0 0
\(555\) −16.9225 43.1117i −0.718319 1.82999i
\(556\) 0 0
\(557\) 9.62364i 0.407767i 0.978995 + 0.203883i \(0.0653563\pi\)
−0.978995 + 0.203883i \(0.934644\pi\)
\(558\) 0 0
\(559\) −24.1486 −1.02138
\(560\) 0 0
\(561\) −8.33248 −0.351797
\(562\) 0 0
\(563\) 3.35865i 0.141550i −0.997492 0.0707751i \(-0.977453\pi\)
0.997492 0.0707751i \(-0.0225473\pi\)
\(564\) 0 0
\(565\) −11.2093 + 4.39996i −0.471580 + 0.185108i
\(566\) 0 0
\(567\) 42.6140i 1.78962i
\(568\) 0 0
\(569\) 4.26939 0.178982 0.0894910 0.995988i \(-0.471476\pi\)
0.0894910 + 0.995988i \(0.471476\pi\)
\(570\) 0 0
\(571\) −16.4567 −0.688689 −0.344345 0.938843i \(-0.611899\pi\)
−0.344345 + 0.938843i \(0.611899\pi\)
\(572\) 0 0
\(573\) 19.3206i 0.807131i
\(574\) 0 0
\(575\) 3.40122 + 3.66493i 0.141840 + 0.152838i
\(576\) 0 0
\(577\) 1.98780i 0.0827530i −0.999144 0.0413765i \(-0.986826\pi\)
0.999144 0.0413765i \(-0.0131743\pi\)
\(578\) 0 0
\(579\) 38.4744 1.59894
\(580\) 0 0
\(581\) 35.4869 1.47224
\(582\) 0 0
\(583\) 4.99184i 0.206741i
\(584\) 0 0
\(585\) −39.8428 + 15.6393i −1.64730 + 0.646607i
\(586\) 0 0
\(587\) 28.9720i 1.19580i −0.801570 0.597900i \(-0.796002\pi\)
0.801570 0.597900i \(-0.203998\pi\)
\(588\) 0 0
\(589\) −11.1835 −0.460810
\(590\) 0 0
\(591\) 9.75363 0.401211
\(592\) 0 0
\(593\) 19.4799i 0.799944i −0.916527 0.399972i \(-0.869020\pi\)
0.916527 0.399972i \(-0.130980\pi\)
\(594\) 0 0
\(595\) −5.45841 13.9059i −0.223773 0.570084i
\(596\) 0 0
\(597\) 44.8994i 1.83761i
\(598\) 0 0
\(599\) 37.8442 1.54627 0.773136 0.634240i \(-0.218687\pi\)
0.773136 + 0.634240i \(0.218687\pi\)
\(600\) 0 0
\(601\) −20.2347 −0.825389 −0.412695 0.910869i \(-0.635412\pi\)
−0.412695 + 0.910869i \(0.635412\pi\)
\(602\) 0 0
\(603\) 27.4749i 1.11886i
\(604\) 0 0
\(605\) 4.69191 + 11.9531i 0.190753 + 0.485963i
\(606\) 0 0
\(607\) 24.4075i 0.990670i 0.868702 + 0.495335i \(0.164955\pi\)
−0.868702 + 0.495335i \(0.835045\pi\)
\(608\) 0 0
\(609\) −81.4396 −3.30010
\(610\) 0 0
\(611\) 42.9445 1.73735
\(612\) 0 0
\(613\) 10.6964i 0.432025i 0.976391 + 0.216012i \(0.0693051\pi\)
−0.976391 + 0.216012i \(0.930695\pi\)
\(614\) 0 0
\(615\) −32.1939 + 12.6370i −1.29818 + 0.509572i
\(616\) 0 0
\(617\) 27.4738i 1.10605i 0.833164 + 0.553026i \(0.186527\pi\)
−0.833164 + 0.553026i \(0.813473\pi\)
\(618\) 0 0
\(619\) −0.389330 −0.0156485 −0.00782425 0.999969i \(-0.502491\pi\)
−0.00782425 + 0.999969i \(0.502491\pi\)
\(620\) 0 0
\(621\) 0.570328 0.0228865
\(622\) 0 0
\(623\) 4.82230i 0.193201i
\(624\) 0 0
\(625\) 1.86347 24.9305i 0.0745389 0.997218i
\(626\) 0 0
\(627\) 15.9574i 0.637278i
\(628\) 0 0
\(629\) −13.0621 −0.520822
\(630\) 0 0
\(631\) 11.9330 0.475047 0.237523 0.971382i \(-0.423664\pi\)
0.237523 + 0.971382i \(0.423664\pi\)
\(632\) 0 0
\(633\) 18.9121i 0.751689i
\(634\) 0 0
\(635\) 12.8221 5.03300i 0.508828 0.199729i
\(636\) 0 0
\(637\) 86.4451i 3.42508i
\(638\) 0 0
\(639\) 9.43106 0.373087
\(640\) 0 0
\(641\) 22.8525 0.902621 0.451311 0.892367i \(-0.350957\pi\)
0.451311 + 0.892367i \(0.350957\pi\)
\(642\) 0 0
\(643\) 34.9279i 1.37742i −0.725036 0.688711i \(-0.758177\pi\)
0.725036 0.688711i \(-0.241823\pi\)
\(644\) 0 0
\(645\) 6.83499 + 17.4128i 0.269128 + 0.685629i
\(646\) 0 0
\(647\) 26.3738i 1.03686i 0.855120 + 0.518430i \(0.173483\pi\)
−0.855120 + 0.518430i \(0.826517\pi\)
\(648\) 0 0
\(649\) 26.9728 1.05877
\(650\) 0 0
\(651\) 40.8643 1.60160
\(652\) 0 0
\(653\) 2.17022i 0.0849274i −0.999098 0.0424637i \(-0.986479\pi\)
0.999098 0.0424637i \(-0.0135207\pi\)
\(654\) 0 0
\(655\) 11.9552 + 30.4570i 0.467127 + 1.19005i
\(656\) 0 0
\(657\) 24.7321i 0.964891i
\(658\) 0 0
\(659\) 19.7820 0.770596 0.385298 0.922792i \(-0.374099\pi\)
0.385298 + 0.922792i \(0.374099\pi\)
\(660\) 0 0
\(661\) 45.7505 1.77949 0.889743 0.456461i \(-0.150883\pi\)
0.889743 + 0.456461i \(0.150883\pi\)
\(662\) 0 0
\(663\) 25.1817i 0.977976i
\(664\) 0 0
\(665\) 26.6309 10.4533i 1.03270 0.405363i
\(666\) 0 0
\(667\) 7.68764i 0.297666i
\(668\) 0 0
\(669\) −5.50346 −0.212776
\(670\) 0 0
\(671\) 11.7268 0.452708
\(672\) 0 0
\(673\) 6.99940i 0.269807i 0.990859 + 0.134904i \(0.0430725\pi\)
−0.990859 + 0.134904i \(0.956928\pi\)
\(674\) 0 0
\(675\) −1.93981 2.09021i −0.0746633 0.0804524i
\(676\) 0 0
\(677\) 26.7178i 1.02685i −0.858134 0.513425i \(-0.828376\pi\)
0.858134 0.513425i \(-0.171624\pi\)
\(678\) 0 0
\(679\) −74.6728 −2.86568
\(680\) 0 0
\(681\) −30.8045 −1.18043
\(682\) 0 0
\(683\) 19.8947i 0.761248i 0.924730 + 0.380624i \(0.124291\pi\)
−0.924730 + 0.380624i \(0.875709\pi\)
\(684\) 0 0
\(685\) −2.02371 + 0.794359i −0.0773219 + 0.0303509i
\(686\) 0 0
\(687\) 39.0148i 1.48851i
\(688\) 0 0
\(689\) −15.0859 −0.574727
\(690\) 0 0
\(691\) −1.24438 −0.0473385 −0.0236693 0.999720i \(-0.507535\pi\)
−0.0236693 + 0.999720i \(0.507535\pi\)
\(692\) 0 0
\(693\) 27.9520i 1.06181i
\(694\) 0 0
\(695\) −6.32634 16.1170i −0.239972 0.611352i
\(696\) 0 0
\(697\) 9.75424i 0.369468i
\(698\) 0 0
\(699\) −51.7091 −1.95582
\(700\) 0 0
\(701\) −29.8454 −1.12724 −0.563622 0.826033i \(-0.690592\pi\)
−0.563622 + 0.826033i \(0.690592\pi\)
\(702\) 0 0
\(703\) 25.0151i 0.943464i
\(704\) 0 0
\(705\) −12.1550 30.9660i −0.457782 1.16625i
\(706\) 0 0
\(707\) 57.1481i 2.14928i
\(708\) 0 0
\(709\) −25.2255 −0.947362 −0.473681 0.880697i \(-0.657075\pi\)
−0.473681 + 0.880697i \(0.657075\pi\)
\(710\) 0 0
\(711\) 5.32301 0.199628
\(712\) 0 0
\(713\) 3.85746i 0.144463i
\(714\) 0 0
\(715\) −33.0707 + 12.9811i −1.23678 + 0.485467i
\(716\) 0 0
\(717\) 26.5549i 0.991710i
\(718\) 0 0
\(719\) −23.7787 −0.886797 −0.443398 0.896325i \(-0.646227\pi\)
−0.443398 + 0.896325i \(0.646227\pi\)
\(720\) 0 0
\(721\) 48.4353 1.80383
\(722\) 0 0
\(723\) 43.7285i 1.62628i
\(724\) 0 0
\(725\) −28.1747 + 26.1473i −1.04638 + 0.971086i
\(726\) 0 0
\(727\) 36.5849i 1.35686i 0.734666 + 0.678429i \(0.237339\pi\)
−0.734666 + 0.678429i \(0.762661\pi\)
\(728\) 0 0
\(729\) 22.5675 0.835833
\(730\) 0 0
\(731\) 5.27580 0.195133
\(732\) 0 0
\(733\) 21.7593i 0.803698i −0.915706 0.401849i \(-0.868368\pi\)
0.915706 0.401849i \(-0.131632\pi\)
\(734\) 0 0
\(735\) −62.3328 + 24.4673i −2.29918 + 0.902489i
\(736\) 0 0
\(737\) 22.8050i 0.840032i
\(738\) 0 0
\(739\) 2.72303 0.100168 0.0500842 0.998745i \(-0.484051\pi\)
0.0500842 + 0.998745i \(0.484051\pi\)
\(740\) 0 0
\(741\) −48.2251 −1.77159
\(742\) 0 0
\(743\) 32.0161i 1.17456i 0.809385 + 0.587278i \(0.199800\pi\)
−0.809385 + 0.587278i \(0.800200\pi\)
\(744\) 0 0
\(745\) −14.4469 36.8049i −0.529293 1.34843i
\(746\) 0 0
\(747\) 22.2134i 0.812746i
\(748\) 0 0
\(749\) −87.7413 −3.20600
\(750\) 0 0
\(751\) 36.0949 1.31712 0.658561 0.752527i \(-0.271165\pi\)
0.658561 + 0.752527i \(0.271165\pi\)
\(752\) 0 0
\(753\) 24.0488i 0.876386i
\(754\) 0 0
\(755\) −1.64456 4.18969i −0.0598517 0.152478i
\(756\) 0 0
\(757\) 46.8188i 1.70166i 0.525442 + 0.850830i \(0.323900\pi\)
−0.525442 + 0.850830i \(0.676100\pi\)
\(758\) 0 0
\(759\) −5.50408 −0.199786
\(760\) 0 0
\(761\) −28.8182 −1.04466 −0.522330 0.852744i \(-0.674937\pi\)
−0.522330 + 0.852744i \(0.674937\pi\)
\(762\) 0 0
\(763\) 1.88548i 0.0682590i
\(764\) 0 0
\(765\) 8.70453 3.41676i 0.314713 0.123533i
\(766\) 0 0
\(767\) 81.5148i 2.94333i
\(768\) 0 0
\(769\) −51.6243 −1.86162 −0.930811 0.365501i \(-0.880898\pi\)
−0.930811 + 0.365501i \(0.880898\pi\)
\(770\) 0 0
\(771\) −34.3322 −1.23645
\(772\) 0 0
\(773\) 25.9610i 0.933753i 0.884322 + 0.466877i \(0.154621\pi\)
−0.884322 + 0.466877i \(0.845379\pi\)
\(774\) 0 0
\(775\) 14.1373 13.1201i 0.507828 0.471286i
\(776\) 0 0
\(777\) 91.4046i 3.27912i
\(778\) 0 0
\(779\) −18.6802 −0.669288
\(780\) 0 0
\(781\) 7.82807 0.280110
\(782\) 0 0
\(783\) 4.38448i 0.156688i
\(784\) 0 0
\(785\) 12.1287 4.76084i 0.432893 0.169922i
\(786\) 0 0
\(787\) 53.2258i 1.89730i 0.316333 + 0.948648i \(0.397548\pi\)
−0.316333 + 0.948648i \(0.602452\pi\)
\(788\) 0 0
\(789\) −22.6694 −0.807053
\(790\) 0 0
\(791\) 23.7658 0.845015
\(792\) 0 0
\(793\) 35.4397i 1.25850i
\(794\) 0 0
\(795\) 4.26988 + 10.8780i 0.151437 + 0.385801i
\(796\) 0 0
\(797\) 31.1874i 1.10471i −0.833608 0.552357i \(-0.813729\pi\)
0.833608 0.552357i \(-0.186271\pi\)
\(798\) 0 0
\(799\) −9.38218 −0.331918
\(800\) 0 0
\(801\) −3.01858 −0.106656
\(802\) 0 0