Properties

Label 1840.2.e.f.369.5
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 369.5
Root \(3.08006i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.8

$q$-expansion

\(f(q)\) \(=\) \(q-0.873449i q^{3} +(-1.89824 - 1.18182i) q^{5} -0.992530i q^{7} +2.23709 q^{9} +O(q^{10})\) \(q-0.873449i q^{3} +(-1.89824 - 1.18182i) q^{5} -0.992530i q^{7} +2.23709 q^{9} -1.83236 q^{11} +3.28666i q^{13} +(-1.03226 + 1.65801i) q^{15} +6.63631i q^{17} -5.64378 q^{19} -0.866924 q^{21} +1.00000i q^{23} +(2.20661 + 4.48675i) q^{25} -4.57433i q^{27} -2.01596 q^{29} +0.315080 q^{31} +1.60047i q^{33} +(-1.17299 + 1.88406i) q^{35} +3.07470i q^{37} +2.87073 q^{39} -1.34964 q^{41} +5.97905i q^{43} +(-4.24652 - 2.64383i) q^{45} +0.306285i q^{47} +6.01489 q^{49} +5.79647 q^{51} -6.98500i q^{53} +(3.47826 + 2.16552i) q^{55} +4.92955i q^{57} +9.49533 q^{59} +5.56160 q^{61} -2.22038i q^{63} +(3.88424 - 6.23887i) q^{65} +0.853521i q^{67} +0.873449 q^{69} -0.797419 q^{71} +7.67189i q^{73} +(3.91894 - 1.92736i) q^{75} +1.81867i q^{77} -3.62884 q^{79} +2.71582 q^{81} +17.1966i q^{83} +(7.84291 - 12.5973i) q^{85} +1.76084i q^{87} +7.01565 q^{89} +3.26211 q^{91} -0.275207i q^{93} +(10.7132 + 6.66992i) q^{95} +18.5807i q^{97} -4.09915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 20 q^{9} + O(q^{10}) \) \( 12 q - 20 q^{9} - 4 q^{11} - 2 q^{15} + 8 q^{19} + 8 q^{25} - 10 q^{29} - 18 q^{31} + 10 q^{35} - 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} + 24 q^{51} - 16 q^{55} - 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} + 34 q^{71} - 16 q^{75} + 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} + 8 q^{91} - 12 q^{95} - 32 q^{99} + O(q^{100}) \)

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
\(3\) 0.873449i 0.504286i −0.967690 0.252143i \(-0.918865\pi\)
0.967690 0.252143i \(-0.0811353\pi\)
\(4\) 0 0
\(5\) −1.89824 1.18182i −0.848917 0.528526i
\(6\) 0 0
\(7\) 0.992530i 0.375141i −0.982251 0.187570i \(-0.939939\pi\)
0.982251 0.187570i \(-0.0600613\pi\)
\(8\) 0 0
\(9\) 2.23709 0.745696
\(10\) 0 0
\(11\) −1.83236 −0.552478 −0.276239 0.961089i \(-0.589088\pi\)
−0.276239 + 0.961089i \(0.589088\pi\)
\(12\) 0 0
\(13\) 3.28666i 0.911556i 0.890093 + 0.455778i \(0.150639\pi\)
−0.890093 + 0.455778i \(0.849361\pi\)
\(14\) 0 0
\(15\) −1.03226 + 1.65801i −0.266528 + 0.428097i
\(16\) 0 0
\(17\) 6.63631i 1.60954i 0.593586 + 0.804770i \(0.297712\pi\)
−0.593586 + 0.804770i \(0.702288\pi\)
\(18\) 0 0
\(19\) −5.64378 −1.29477 −0.647386 0.762163i \(-0.724138\pi\)
−0.647386 + 0.762163i \(0.724138\pi\)
\(20\) 0 0
\(21\) −0.866924 −0.189178
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 2.20661 + 4.48675i 0.441321 + 0.897349i
\(26\) 0 0
\(27\) 4.57433i 0.880330i
\(28\) 0 0
\(29\) −2.01596 −0.374354 −0.187177 0.982326i \(-0.559934\pi\)
−0.187177 + 0.982326i \(0.559934\pi\)
\(30\) 0 0
\(31\) 0.315080 0.0565901 0.0282951 0.999600i \(-0.490992\pi\)
0.0282951 + 0.999600i \(0.490992\pi\)
\(32\) 0 0
\(33\) 1.60047i 0.278607i
\(34\) 0 0
\(35\) −1.17299 + 1.88406i −0.198272 + 0.318464i
\(36\) 0 0
\(37\) 3.07470i 0.505478i 0.967534 + 0.252739i \(0.0813314\pi\)
−0.967534 + 0.252739i \(0.918669\pi\)
\(38\) 0 0
\(39\) 2.87073 0.459685
\(40\) 0 0
\(41\) −1.34964 −0.210779 −0.105389 0.994431i \(-0.533609\pi\)
−0.105389 + 0.994431i \(0.533609\pi\)
\(42\) 0 0
\(43\) 5.97905i 0.911797i 0.890032 + 0.455899i \(0.150682\pi\)
−0.890032 + 0.455899i \(0.849318\pi\)
\(44\) 0 0
\(45\) −4.24652 2.64383i −0.633034 0.394119i
\(46\) 0 0
\(47\) 0.306285i 0.0446762i 0.999750 + 0.0223381i \(0.00711103\pi\)
−0.999750 + 0.0223381i \(0.992889\pi\)
\(48\) 0 0
\(49\) 6.01489 0.859269
\(50\) 0 0
\(51\) 5.79647 0.811669
\(52\) 0 0
\(53\) 6.98500i 0.959464i −0.877415 0.479732i \(-0.840734\pi\)
0.877415 0.479732i \(-0.159266\pi\)
\(54\) 0 0
\(55\) 3.47826 + 2.16552i 0.469008 + 0.291999i
\(56\) 0 0
\(57\) 4.92955i 0.652935i
\(58\) 0 0
\(59\) 9.49533 1.23619 0.618094 0.786105i \(-0.287905\pi\)
0.618094 + 0.786105i \(0.287905\pi\)
\(60\) 0 0
\(61\) 5.56160 0.712090 0.356045 0.934469i \(-0.384125\pi\)
0.356045 + 0.934469i \(0.384125\pi\)
\(62\) 0 0
\(63\) 2.22038i 0.279741i
\(64\) 0 0
\(65\) 3.88424 6.23887i 0.481781 0.773836i
\(66\) 0 0
\(67\) 0.853521i 0.104274i 0.998640 + 0.0521371i \(0.0166033\pi\)
−0.998640 + 0.0521371i \(0.983397\pi\)
\(68\) 0 0
\(69\) 0.873449 0.105151
\(70\) 0 0
\(71\) −0.797419 −0.0946363 −0.0473181 0.998880i \(-0.515067\pi\)
−0.0473181 + 0.998880i \(0.515067\pi\)
\(72\) 0 0
\(73\) 7.67189i 0.897926i 0.893550 + 0.448963i \(0.148207\pi\)
−0.893550 + 0.448963i \(0.851793\pi\)
\(74\) 0 0
\(75\) 3.91894 1.92736i 0.452521 0.222552i
\(76\) 0 0
\(77\) 1.81867i 0.207257i
\(78\) 0 0
\(79\) −3.62884 −0.408276 −0.204138 0.978942i \(-0.565439\pi\)
−0.204138 + 0.978942i \(0.565439\pi\)
\(80\) 0 0
\(81\) 2.71582 0.301758
\(82\) 0 0
\(83\) 17.1966i 1.88757i 0.330560 + 0.943785i \(0.392762\pi\)
−0.330560 + 0.943785i \(0.607238\pi\)
\(84\) 0 0
\(85\) 7.84291 12.5973i 0.850683 1.36637i
\(86\) 0 0
\(87\) 1.76084i 0.188782i
\(88\) 0 0
\(89\) 7.01565 0.743658 0.371829 0.928301i \(-0.378731\pi\)
0.371829 + 0.928301i \(0.378731\pi\)
\(90\) 0 0
\(91\) 3.26211 0.341962
\(92\) 0 0
\(93\) 0.275207i 0.0285376i
\(94\) 0 0
\(95\) 10.7132 + 6.66992i 1.09915 + 0.684320i
\(96\) 0 0
\(97\) 18.5807i 1.88659i 0.331958 + 0.943294i \(0.392291\pi\)
−0.331958 + 0.943294i \(0.607709\pi\)
\(98\) 0 0
\(99\) −4.09915 −0.411980
\(100\) 0 0
\(101\) −7.96538 −0.792585 −0.396293 0.918124i \(-0.629703\pi\)
−0.396293 + 0.918124i \(0.629703\pi\)
\(102\) 0 0
\(103\) 16.8268i 1.65799i 0.559253 + 0.828997i \(0.311088\pi\)
−0.559253 + 0.828997i \(0.688912\pi\)
\(104\) 0 0
\(105\) 1.64563 + 1.02455i 0.160597 + 0.0999856i
\(106\) 0 0
\(107\) 10.7429i 1.03855i 0.854606 + 0.519276i \(0.173798\pi\)
−0.854606 + 0.519276i \(0.826202\pi\)
\(108\) 0 0
\(109\) −8.34117 −0.798939 −0.399470 0.916746i \(-0.630806\pi\)
−0.399470 + 0.916746i \(0.630806\pi\)
\(110\) 0 0
\(111\) 2.68560 0.254906
\(112\) 0 0
\(113\) 8.28008i 0.778925i −0.921042 0.389462i \(-0.872661\pi\)
0.921042 0.389462i \(-0.127339\pi\)
\(114\) 0 0
\(115\) 1.18182 1.89824i 0.110205 0.177012i
\(116\) 0 0
\(117\) 7.35255i 0.679744i
\(118\) 0 0
\(119\) 6.58673 0.603805
\(120\) 0 0
\(121\) −7.64245 −0.694768
\(122\) 0 0
\(123\) 1.17884i 0.106293i
\(124\) 0 0
\(125\) 1.11386 11.1247i 0.0996265 0.995025i
\(126\) 0 0
\(127\) 10.5531i 0.936437i −0.883613 0.468219i \(-0.844896\pi\)
0.883613 0.468219i \(-0.155104\pi\)
\(128\) 0 0
\(129\) 5.22240 0.459806
\(130\) 0 0
\(131\) −7.84966 −0.685828 −0.342914 0.939367i \(-0.611414\pi\)
−0.342914 + 0.939367i \(0.611414\pi\)
\(132\) 0 0
\(133\) 5.60161i 0.485722i
\(134\) 0 0
\(135\) −5.40603 + 8.68316i −0.465277 + 0.747327i
\(136\) 0 0
\(137\) 9.27261i 0.792213i −0.918205 0.396106i \(-0.870361\pi\)
0.918205 0.396106i \(-0.129639\pi\)
\(138\) 0 0
\(139\) 18.5293 1.57163 0.785816 0.618461i \(-0.212243\pi\)
0.785816 + 0.618461i \(0.212243\pi\)
\(140\) 0 0
\(141\) 0.267524 0.0225296
\(142\) 0 0
\(143\) 6.02236i 0.503615i
\(144\) 0 0
\(145\) 3.82677 + 2.38250i 0.317796 + 0.197856i
\(146\) 0 0
\(147\) 5.25369i 0.433317i
\(148\) 0 0
\(149\) −23.6227 −1.93525 −0.967624 0.252395i \(-0.918782\pi\)
−0.967624 + 0.252395i \(0.918782\pi\)
\(150\) 0 0
\(151\) 19.2472 1.56631 0.783157 0.621825i \(-0.213608\pi\)
0.783157 + 0.621825i \(0.213608\pi\)
\(152\) 0 0
\(153\) 14.8460i 1.20023i
\(154\) 0 0
\(155\) −0.598097 0.372368i −0.0480403 0.0299093i
\(156\) 0 0
\(157\) 6.61180i 0.527679i −0.964567 0.263840i \(-0.915011\pi\)
0.964567 0.263840i \(-0.0849890\pi\)
\(158\) 0 0
\(159\) −6.10104 −0.483844
\(160\) 0 0
\(161\) 0.992530 0.0782223
\(162\) 0 0
\(163\) 11.6157i 0.909809i 0.890540 + 0.454905i \(0.150327\pi\)
−0.890540 + 0.454905i \(0.849673\pi\)
\(164\) 0 0
\(165\) 1.89147 3.03808i 0.147251 0.236514i
\(166\) 0 0
\(167\) 18.4280i 1.42600i −0.701162 0.713002i \(-0.747335\pi\)
0.701162 0.713002i \(-0.252665\pi\)
\(168\) 0 0
\(169\) 2.19784 0.169065
\(170\) 0 0
\(171\) −12.6256 −0.965505
\(172\) 0 0
\(173\) 5.51955i 0.419644i 0.977740 + 0.209822i \(0.0672884\pi\)
−0.977740 + 0.209822i \(0.932712\pi\)
\(174\) 0 0
\(175\) 4.45323 2.19012i 0.336632 0.165558i
\(176\) 0 0
\(177\) 8.29369i 0.623392i
\(178\) 0 0
\(179\) −9.73640 −0.727733 −0.363866 0.931451i \(-0.618544\pi\)
−0.363866 + 0.931451i \(0.618544\pi\)
\(180\) 0 0
\(181\) 21.8277 1.62244 0.811220 0.584741i \(-0.198804\pi\)
0.811220 + 0.584741i \(0.198804\pi\)
\(182\) 0 0
\(183\) 4.85777i 0.359097i
\(184\) 0 0
\(185\) 3.63374 5.83652i 0.267158 0.429109i
\(186\) 0 0
\(187\) 12.1601i 0.889235i
\(188\) 0 0
\(189\) −4.54016 −0.330248
\(190\) 0 0
\(191\) −16.4807 −1.19250 −0.596251 0.802798i \(-0.703344\pi\)
−0.596251 + 0.802798i \(0.703344\pi\)
\(192\) 0 0
\(193\) 4.60541i 0.331504i 0.986167 + 0.165752i \(0.0530052\pi\)
−0.986167 + 0.165752i \(0.946995\pi\)
\(194\) 0 0
\(195\) −5.44933 3.39269i −0.390235 0.242955i
\(196\) 0 0
\(197\) 0.157186i 0.0111990i 0.999984 + 0.00559951i \(0.00178239\pi\)
−0.999984 + 0.00559951i \(0.998218\pi\)
\(198\) 0 0
\(199\) −1.94253 −0.137702 −0.0688511 0.997627i \(-0.521933\pi\)
−0.0688511 + 0.997627i \(0.521933\pi\)
\(200\) 0 0
\(201\) 0.745507 0.0525840
\(202\) 0 0
\(203\) 2.00090i 0.140436i
\(204\) 0 0
\(205\) 2.56194 + 1.59503i 0.178934 + 0.111402i
\(206\) 0 0
\(207\) 2.23709i 0.155488i
\(208\) 0 0
\(209\) 10.3414 0.715332
\(210\) 0 0
\(211\) −23.5602 −1.62195 −0.810976 0.585079i \(-0.801063\pi\)
−0.810976 + 0.585079i \(0.801063\pi\)
\(212\) 0 0
\(213\) 0.696505i 0.0477237i
\(214\) 0 0
\(215\) 7.06616 11.3497i 0.481908 0.774040i
\(216\) 0 0
\(217\) 0.312727i 0.0212293i
\(218\) 0 0
\(219\) 6.70100 0.452812
\(220\) 0 0
\(221\) −21.8113 −1.46719
\(222\) 0 0
\(223\) 9.59356i 0.642432i 0.947006 + 0.321216i \(0.104092\pi\)
−0.947006 + 0.321216i \(0.895908\pi\)
\(224\) 0 0
\(225\) 4.93637 + 10.0372i 0.329091 + 0.669149i
\(226\) 0 0
\(227\) 9.90765i 0.657594i −0.944401 0.328797i \(-0.893357\pi\)
0.944401 0.328797i \(-0.106643\pi\)
\(228\) 0 0
\(229\) 4.90156 0.323904 0.161952 0.986799i \(-0.448221\pi\)
0.161952 + 0.986799i \(0.448221\pi\)
\(230\) 0 0
\(231\) 1.58852 0.104517
\(232\) 0 0
\(233\) 15.3123i 1.00314i 0.865116 + 0.501571i \(0.167245\pi\)
−0.865116 + 0.501571i \(0.832755\pi\)
\(234\) 0 0
\(235\) 0.361973 0.581401i 0.0236125 0.0379264i
\(236\) 0 0
\(237\) 3.16960i 0.205888i
\(238\) 0 0
\(239\) −3.88065 −0.251018 −0.125509 0.992092i \(-0.540056\pi\)
−0.125509 + 0.992092i \(0.540056\pi\)
\(240\) 0 0
\(241\) 6.64578 0.428092 0.214046 0.976824i \(-0.431336\pi\)
0.214046 + 0.976824i \(0.431336\pi\)
\(242\) 0 0
\(243\) 16.0951i 1.03250i
\(244\) 0 0
\(245\) −11.4177 7.10851i −0.729449 0.454146i
\(246\) 0 0
\(247\) 18.5492i 1.18026i
\(248\) 0 0
\(249\) 15.0203 0.951875
\(250\) 0 0
\(251\) −5.82636 −0.367756 −0.183878 0.982949i \(-0.558865\pi\)
−0.183878 + 0.982949i \(0.558865\pi\)
\(252\) 0 0
\(253\) 1.83236i 0.115200i
\(254\) 0 0
\(255\) −11.0031 6.85038i −0.689040 0.428988i
\(256\) 0 0
\(257\) 17.1979i 1.07278i −0.843971 0.536388i \(-0.819788\pi\)
0.843971 0.536388i \(-0.180212\pi\)
\(258\) 0 0
\(259\) 3.05173 0.189626
\(260\) 0 0
\(261\) −4.50988 −0.279154
\(262\) 0 0
\(263\) 19.5353i 1.20460i 0.798269 + 0.602301i \(0.205749\pi\)
−0.798269 + 0.602301i \(0.794251\pi\)
\(264\) 0 0
\(265\) −8.25501 + 13.2592i −0.507101 + 0.814506i
\(266\) 0 0
\(267\) 6.12781i 0.375016i
\(268\) 0 0
\(269\) 21.2275 1.29426 0.647132 0.762378i \(-0.275968\pi\)
0.647132 + 0.762378i \(0.275968\pi\)
\(270\) 0 0
\(271\) −9.19621 −0.558630 −0.279315 0.960200i \(-0.590107\pi\)
−0.279315 + 0.960200i \(0.590107\pi\)
\(272\) 0 0
\(273\) 2.84929i 0.172447i
\(274\) 0 0
\(275\) −4.04330 8.22134i −0.243820 0.495765i
\(276\) 0 0
\(277\) 2.77325i 0.166628i 0.996523 + 0.0833141i \(0.0265505\pi\)
−0.996523 + 0.0833141i \(0.973450\pi\)
\(278\) 0 0
\(279\) 0.704862 0.0421990
\(280\) 0 0
\(281\) −32.7971 −1.95651 −0.978255 0.207407i \(-0.933497\pi\)
−0.978255 + 0.207407i \(0.933497\pi\)
\(282\) 0 0
\(283\) 23.6017i 1.40298i 0.712680 + 0.701489i \(0.247481\pi\)
−0.712680 + 0.701489i \(0.752519\pi\)
\(284\) 0 0
\(285\) 5.82584 9.35745i 0.345093 0.554288i
\(286\) 0 0
\(287\) 1.33956i 0.0790717i
\(288\) 0 0
\(289\) −27.0406 −1.59062
\(290\) 0 0
\(291\) 16.2293 0.951380
\(292\) 0 0
\(293\) 1.83939i 0.107458i 0.998556 + 0.0537291i \(0.0171107\pi\)
−0.998556 + 0.0537291i \(0.982889\pi\)
\(294\) 0 0
\(295\) −18.0244 11.2218i −1.04942 0.653356i
\(296\) 0 0
\(297\) 8.38182i 0.486363i
\(298\) 0 0
\(299\) −3.28666 −0.190073
\(300\) 0 0
\(301\) 5.93439 0.342052
\(302\) 0 0
\(303\) 6.95735i 0.399690i
\(304\) 0 0
\(305\) −10.5572 6.57281i −0.604506 0.376358i
\(306\) 0 0
\(307\) 10.3956i 0.593310i −0.954985 0.296655i \(-0.904129\pi\)
0.954985 0.296655i \(-0.0958711\pi\)
\(308\) 0 0
\(309\) 14.6973 0.836103
\(310\) 0 0
\(311\) 12.2967 0.697281 0.348640 0.937257i \(-0.386643\pi\)
0.348640 + 0.937257i \(0.386643\pi\)
\(312\) 0 0
\(313\) 17.2954i 0.977592i 0.872398 + 0.488796i \(0.162564\pi\)
−0.872398 + 0.488796i \(0.837436\pi\)
\(314\) 0 0
\(315\) −2.62408 + 4.21480i −0.147850 + 0.237477i
\(316\) 0 0
\(317\) 33.6362i 1.88920i −0.328227 0.944599i \(-0.606451\pi\)
0.328227 0.944599i \(-0.393549\pi\)
\(318\) 0 0
\(319\) 3.69397 0.206822
\(320\) 0 0
\(321\) 9.38335 0.523728
\(322\) 0 0
\(323\) 37.4538i 2.08399i
\(324\) 0 0
\(325\) −14.7464 + 7.25237i −0.817984 + 0.402289i
\(326\) 0 0
\(327\) 7.28559i 0.402894i
\(328\) 0 0
\(329\) 0.303997 0.0167599
\(330\) 0 0
\(331\) 9.81704 0.539593 0.269797 0.962917i \(-0.413044\pi\)
0.269797 + 0.962917i \(0.413044\pi\)
\(332\) 0 0
\(333\) 6.87838i 0.376933i
\(334\) 0 0
\(335\) 1.00871 1.62018i 0.0551115 0.0885201i
\(336\) 0 0
\(337\) 9.15644i 0.498783i 0.968403 + 0.249392i \(0.0802306\pi\)
−0.968403 + 0.249392i \(0.919769\pi\)
\(338\) 0 0
\(339\) −7.23223 −0.392801
\(340\) 0 0
\(341\) −0.577341 −0.0312648
\(342\) 0 0
\(343\) 12.9177i 0.697488i
\(344\) 0 0
\(345\) −1.65801 1.03226i −0.0892644 0.0555749i
\(346\) 0 0
\(347\) 32.5921i 1.74963i 0.484453 + 0.874817i \(0.339019\pi\)
−0.484453 + 0.874817i \(0.660981\pi\)
\(348\) 0 0
\(349\) 15.5701 0.833448 0.416724 0.909033i \(-0.363178\pi\)
0.416724 + 0.909033i \(0.363178\pi\)
\(350\) 0 0
\(351\) 15.0343 0.802470
\(352\) 0 0
\(353\) 10.9313i 0.581816i 0.956751 + 0.290908i \(0.0939573\pi\)
−0.956751 + 0.290908i \(0.906043\pi\)
\(354\) 0 0
\(355\) 1.51369 + 0.942405i 0.0803384 + 0.0500177i
\(356\) 0 0
\(357\) 5.75317i 0.304490i
\(358\) 0 0
\(359\) 0.405120 0.0213814 0.0106907 0.999943i \(-0.496597\pi\)
0.0106907 + 0.999943i \(0.496597\pi\)
\(360\) 0 0
\(361\) 12.8522 0.676432
\(362\) 0 0
\(363\) 6.67529i 0.350362i
\(364\) 0 0
\(365\) 9.06678 14.5631i 0.474577 0.762265i
\(366\) 0 0
\(367\) 7.26443i 0.379200i 0.981861 + 0.189600i \(0.0607191\pi\)
−0.981861 + 0.189600i \(0.939281\pi\)
\(368\) 0 0
\(369\) −3.01927 −0.157177
\(370\) 0 0
\(371\) −6.93282 −0.359934
\(372\) 0 0
\(373\) 3.36770i 0.174373i −0.996192 0.0871866i \(-0.972212\pi\)
0.996192 0.0871866i \(-0.0277876\pi\)
\(374\) 0 0
\(375\) −9.71687 0.972898i −0.501777 0.0502402i
\(376\) 0 0
\(377\) 6.62578i 0.341245i
\(378\) 0 0
\(379\) −4.54534 −0.233478 −0.116739 0.993163i \(-0.537244\pi\)
−0.116739 + 0.993163i \(0.537244\pi\)
\(380\) 0 0
\(381\) −9.21760 −0.472232
\(382\) 0 0
\(383\) 12.0978i 0.618167i 0.951035 + 0.309084i \(0.100022\pi\)
−0.951035 + 0.309084i \(0.899978\pi\)
\(384\) 0 0
\(385\) 2.14934 3.45227i 0.109541 0.175944i
\(386\) 0 0
\(387\) 13.3757i 0.679923i
\(388\) 0 0
\(389\) −22.8934 −1.16074 −0.580371 0.814352i \(-0.697092\pi\)
−0.580371 + 0.814352i \(0.697092\pi\)
\(390\) 0 0
\(391\) −6.63631 −0.335612
\(392\) 0 0
\(393\) 6.85627i 0.345853i
\(394\) 0 0
\(395\) 6.88839 + 4.28863i 0.346593 + 0.215784i
\(396\) 0 0
\(397\) 23.9748i 1.20326i −0.798774 0.601631i \(-0.794518\pi\)
0.798774 0.601631i \(-0.205482\pi\)
\(398\) 0 0
\(399\) 4.89272 0.244943
\(400\) 0 0
\(401\) 26.8722 1.34193 0.670967 0.741487i \(-0.265879\pi\)
0.670967 + 0.741487i \(0.265879\pi\)
\(402\) 0 0
\(403\) 1.03556i 0.0515851i
\(404\) 0 0
\(405\) −5.15527 3.20961i −0.256167 0.159487i
\(406\) 0 0
\(407\) 5.63397i 0.279266i
\(408\) 0 0
\(409\) −15.7840 −0.780467 −0.390233 0.920716i \(-0.627606\pi\)
−0.390233 + 0.920716i \(0.627606\pi\)
\(410\) 0 0
\(411\) −8.09915 −0.399502
\(412\) 0 0
\(413\) 9.42440i 0.463744i
\(414\) 0 0
\(415\) 20.3232 32.6432i 0.997629 1.60239i
\(416\) 0 0
\(417\) 16.1844i 0.792552i
\(418\) 0 0
\(419\) 19.6999 0.962402 0.481201 0.876610i \(-0.340201\pi\)
0.481201 + 0.876610i \(0.340201\pi\)
\(420\) 0 0
\(421\) −15.6913 −0.764748 −0.382374 0.924008i \(-0.624893\pi\)
−0.382374 + 0.924008i \(0.624893\pi\)
\(422\) 0 0
\(423\) 0.685185i 0.0333149i
\(424\) 0 0
\(425\) −29.7754 + 14.6437i −1.44432 + 0.710325i
\(426\) 0 0
\(427\) 5.52005i 0.267134i
\(428\) 0 0
\(429\) −5.26022 −0.253966
\(430\) 0 0
\(431\) 1.33660 0.0643819 0.0321909 0.999482i \(-0.489752\pi\)
0.0321909 + 0.999482i \(0.489752\pi\)
\(432\) 0 0
\(433\) 4.26379i 0.204905i −0.994738 0.102452i \(-0.967331\pi\)
0.994738 0.102452i \(-0.0326689\pi\)
\(434\) 0 0
\(435\) 2.08099 3.34249i 0.0997759 0.160260i
\(436\) 0 0
\(437\) 5.64378i 0.269978i
\(438\) 0 0
\(439\) −32.6899 −1.56020 −0.780101 0.625653i \(-0.784833\pi\)
−0.780101 + 0.625653i \(0.784833\pi\)
\(440\) 0 0
\(441\) 13.4558 0.640753
\(442\) 0 0
\(443\) 16.8373i 0.799964i −0.916523 0.399982i \(-0.869016\pi\)
0.916523 0.399982i \(-0.130984\pi\)
\(444\) 0 0
\(445\) −13.3174 8.29123i −0.631304 0.393042i
\(446\) 0 0
\(447\) 20.6332i 0.975919i
\(448\) 0 0
\(449\) −12.8502 −0.606440 −0.303220 0.952921i \(-0.598062\pi\)
−0.303220 + 0.952921i \(0.598062\pi\)
\(450\) 0 0
\(451\) 2.47303 0.116451
\(452\) 0 0
\(453\) 16.8114i 0.789870i
\(454\) 0 0
\(455\) −6.19226 3.85522i −0.290298 0.180736i
\(456\) 0 0
\(457\) 40.1900i 1.88001i −0.341161 0.940005i \(-0.610820\pi\)
0.341161 0.940005i \(-0.389180\pi\)
\(458\) 0 0
\(459\) 30.3566 1.41693
\(460\) 0 0
\(461\) −34.7208 −1.61711 −0.808554 0.588422i \(-0.799750\pi\)
−0.808554 + 0.588422i \(0.799750\pi\)
\(462\) 0 0
\(463\) 26.7292i 1.24221i 0.783727 + 0.621106i \(0.213316\pi\)
−0.783727 + 0.621106i \(0.786684\pi\)
\(464\) 0 0
\(465\) −0.325245 + 0.522408i −0.0150829 + 0.0242261i
\(466\) 0 0
\(467\) 17.6579i 0.817112i 0.912733 + 0.408556i \(0.133968\pi\)
−0.912733 + 0.408556i \(0.866032\pi\)
\(468\) 0 0
\(469\) 0.847144 0.0391175
\(470\) 0 0
\(471\) −5.77507 −0.266101
\(472\) 0 0
\(473\) 10.9558i 0.503748i
\(474\) 0 0
\(475\) −12.4536 25.3222i −0.571410 1.16186i
\(476\) 0 0
\(477\) 15.6261i 0.715468i
\(478\) 0 0
\(479\) −37.8085 −1.72752 −0.863758 0.503907i \(-0.831896\pi\)
−0.863758 + 0.503907i \(0.831896\pi\)
\(480\) 0 0
\(481\) −10.1055 −0.460772
\(482\) 0 0
\(483\) 0.866924i 0.0394464i
\(484\) 0 0
\(485\) 21.9591 35.2706i 0.997110 1.60156i
\(486\) 0 0
\(487\) 27.9951i 1.26858i 0.773096 + 0.634289i \(0.218707\pi\)
−0.773096 + 0.634289i \(0.781293\pi\)
\(488\) 0 0
\(489\) 10.1457 0.458804
\(490\) 0 0
\(491\) −10.1212 −0.456762 −0.228381 0.973572i \(-0.573343\pi\)
−0.228381 + 0.973572i \(0.573343\pi\)
\(492\) 0 0
\(493\) 13.3785i 0.602538i
\(494\) 0 0
\(495\) 7.78116 + 4.84446i 0.349737 + 0.217742i
\(496\) 0 0
\(497\) 0.791462i 0.0355019i
\(498\) 0 0
\(499\) −37.0240 −1.65742 −0.828712 0.559676i \(-0.810926\pi\)
−0.828712 + 0.559676i \(0.810926\pi\)
\(500\) 0 0
\(501\) −16.0960 −0.719114
\(502\) 0 0
\(503\) 22.5700i 1.00635i −0.864185 0.503174i \(-0.832166\pi\)
0.864185 0.503174i \(-0.167834\pi\)
\(504\) 0 0
\(505\) 15.1202 + 9.41364i 0.672839 + 0.418902i
\(506\) 0 0
\(507\) 1.91970i 0.0852571i
\(508\) 0 0
\(509\) −29.3212 −1.29964 −0.649819 0.760089i \(-0.725155\pi\)
−0.649819 + 0.760089i \(0.725155\pi\)
\(510\) 0 0
\(511\) 7.61457 0.336849
\(512\) 0 0
\(513\) 25.8165i 1.13983i
\(514\) 0 0
\(515\) 19.8862 31.9413i 0.876292 1.40750i
\(516\) 0 0
\(517\) 0.561224i 0.0246826i
\(518\) 0 0
\(519\) 4.82105 0.211620
\(520\) 0 0
\(521\) 13.9057 0.609220 0.304610 0.952477i \(-0.401474\pi\)
0.304610 + 0.952477i \(0.401474\pi\)
\(522\) 0 0
\(523\) 36.6591i 1.60299i 0.598001 + 0.801496i \(0.295962\pi\)
−0.598001 + 0.801496i \(0.704038\pi\)
\(524\) 0 0
\(525\) −1.91296 3.88967i −0.0834884 0.169759i
\(526\) 0 0
\(527\) 2.09097i 0.0910841i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 21.2419 0.921819
\(532\) 0 0
\(533\) 4.43582i 0.192137i
\(534\) 0 0
\(535\) 12.6961 20.3925i 0.548902 0.881645i
\(536\) 0 0
\(537\) 8.50425i 0.366986i
\(538\) 0 0
\(539\) −11.0214 −0.474727
\(540\) 0 0
\(541\) 15.8082 0.679647 0.339823 0.940489i \(-0.389633\pi\)
0.339823 + 0.940489i \(0.389633\pi\)
\(542\) 0 0
\(543\) 19.0654i 0.818174i
\(544\) 0 0
\(545\) 15.8335 + 9.85776i 0.678233 + 0.422260i
\(546\) 0 0
\(547\) 25.6129i 1.09513i −0.836764 0.547563i \(-0.815556\pi\)
0.836764 0.547563i \(-0.184444\pi\)
\(548\) 0 0
\(549\) 12.4418 0.531003
\(550\) 0 0
\(551\) 11.3776 0.484703
\(552\) 0 0
\(553\) 3.60173i 0.153161i
\(554\) 0 0
\(555\) −5.09790 3.17389i −0.216394 0.134724i
\(556\) 0 0
\(557\) 21.9292i 0.929172i 0.885528 + 0.464586i \(0.153797\pi\)
−0.885528 + 0.464586i \(0.846203\pi\)
\(558\) 0 0
\(559\) −19.6511 −0.831154
\(560\) 0 0
\(561\) −10.6212 −0.448429
\(562\) 0 0
\(563\) 34.2718i 1.44439i −0.691692 0.722193i \(-0.743134\pi\)
0.691692 0.722193i \(-0.256866\pi\)
\(564\) 0 0
\(565\) −9.78556 + 15.7176i −0.411682 + 0.661243i
\(566\) 0 0
\(567\) 2.69553i 0.113202i
\(568\) 0 0
\(569\) −4.05998 −0.170203 −0.0851015 0.996372i \(-0.527121\pi\)
−0.0851015 + 0.996372i \(0.527121\pi\)
\(570\) 0 0
\(571\) 21.7533 0.910347 0.455174 0.890403i \(-0.349577\pi\)
0.455174 + 0.890403i \(0.349577\pi\)
\(572\) 0 0
\(573\) 14.3951i 0.601362i
\(574\) 0 0
\(575\) −4.48675 + 2.20661i −0.187110 + 0.0920219i
\(576\) 0 0
\(577\) 23.6094i 0.982872i −0.870914 0.491436i \(-0.836472\pi\)
0.870914 0.491436i \(-0.163528\pi\)
\(578\) 0 0
\(579\) 4.02259 0.167173
\(580\) 0 0
\(581\) 17.0681 0.708105
\(582\) 0 0
\(583\) 12.7991i 0.530083i
\(584\) 0 0
\(585\) 8.68939 13.9569i 0.359262 0.577046i
\(586\) 0 0
\(587\) 13.2321i 0.546146i −0.961993 0.273073i \(-0.911960\pi\)
0.961993 0.273073i \(-0.0880400\pi\)
\(588\) 0 0
\(589\) −1.77824 −0.0732713
\(590\) 0 0
\(591\) 0.137294 0.00564750
\(592\) 0 0
\(593\) 8.85971i 0.363825i 0.983315 + 0.181912i \(0.0582287\pi\)
−0.983315 + 0.181912i \(0.941771\pi\)
\(594\) 0 0
\(595\) −12.5032 7.78432i −0.512580 0.319126i
\(596\) 0 0
\(597\) 1.69670i 0.0694412i
\(598\) 0 0
\(599\) 8.01552 0.327505 0.163753 0.986501i \(-0.447640\pi\)
0.163753 + 0.986501i \(0.447640\pi\)
\(600\) 0 0
\(601\) 24.3621 0.993752 0.496876 0.867821i \(-0.334480\pi\)
0.496876 + 0.867821i \(0.334480\pi\)
\(602\) 0 0
\(603\) 1.90940i 0.0777568i
\(604\) 0 0
\(605\) 14.5072 + 9.03199i 0.589801 + 0.367203i
\(606\) 0 0
\(607\) 36.5642i 1.48409i 0.670348 + 0.742047i \(0.266145\pi\)
−0.670348 + 0.742047i \(0.733855\pi\)
\(608\) 0 0
\(609\) 1.74768 0.0708197
\(610\) 0 0
\(611\) −1.00665 −0.0407249
\(612\) 0 0
\(613\) 9.21498i 0.372190i −0.982532 0.186095i \(-0.940417\pi\)
0.982532 0.186095i \(-0.0595832\pi\)
\(614\) 0 0
\(615\) 1.39318 2.23773i 0.0561784 0.0902338i
\(616\) 0 0
\(617\) 36.4154i 1.46603i −0.680213 0.733015i \(-0.738113\pi\)
0.680213 0.733015i \(-0.261887\pi\)
\(618\) 0 0
\(619\) 34.3781 1.38177 0.690886 0.722963i \(-0.257220\pi\)
0.690886 + 0.722963i \(0.257220\pi\)
\(620\) 0 0
\(621\) 4.57433 0.183561
\(622\) 0 0
\(623\) 6.96324i 0.278976i
\(624\) 0 0
\(625\) −15.2618 + 19.8010i −0.610471 + 0.792039i
\(626\) 0 0
\(627\) 9.03272i 0.360732i
\(628\) 0 0
\(629\) −20.4047 −0.813588
\(630\) 0 0
\(631\) −42.3309 −1.68517 −0.842584 0.538565i \(-0.818967\pi\)
−0.842584 + 0.538565i \(0.818967\pi\)
\(632\) 0 0
\(633\) 20.5786i 0.817928i
\(634\) 0 0
\(635\) −12.4719 + 20.0323i −0.494931 + 0.794958i
\(636\) 0 0
\(637\) 19.7689i 0.783272i
\(638\) 0 0
\(639\) −1.78390 −0.0705699
\(640\) 0 0
\(641\) 43.2608 1.70870 0.854349 0.519699i \(-0.173956\pi\)
0.854349 + 0.519699i \(0.173956\pi\)
\(642\) 0 0
\(643\) 2.36283i 0.0931809i −0.998914 0.0465905i \(-0.985164\pi\)
0.998914 0.0465905i \(-0.0148356\pi\)
\(644\) 0 0
\(645\) −9.91335 6.17193i −0.390338 0.243019i
\(646\) 0 0
\(647\) 21.9473i 0.862837i −0.902152 0.431418i \(-0.858013\pi\)
0.902152 0.431418i \(-0.141987\pi\)
\(648\) 0 0
\(649\) −17.3989 −0.682966
\(650\) 0 0
\(651\) −0.273151 −0.0107056
\(652\) 0 0
\(653\) 34.7170i 1.35858i 0.733869 + 0.679291i \(0.237713\pi\)
−0.733869 + 0.679291i \(0.762287\pi\)
\(654\) 0 0
\(655\) 14.9005 + 9.27687i 0.582211 + 0.362477i
\(656\) 0 0
\(657\) 17.1627i 0.669580i
\(658\) 0 0
\(659\) −23.1858 −0.903192 −0.451596 0.892223i \(-0.649145\pi\)
−0.451596 + 0.892223i \(0.649145\pi\)
\(660\) 0 0
\(661\) −39.6148 −1.54084 −0.770418 0.637539i \(-0.779953\pi\)
−0.770418 + 0.637539i \(0.779953\pi\)
\(662\) 0 0
\(663\) 19.0511i 0.739882i
\(664\) 0 0
\(665\) 6.62010 10.6332i 0.256716 0.412338i
\(666\) 0 0
\(667\) 2.01596i 0.0780583i
\(668\) 0 0
\(669\) 8.37949 0.323970
\(670\) 0 0
\(671\) −10.1909 −0.393414
\(672\) 0 0
\(673\) 30.3084i 1.16830i 0.811645 + 0.584152i \(0.198573\pi\)
−0.811645 + 0.584152i \(0.801427\pi\)
\(674\) 0 0
\(675\) 20.5238 10.0937i 0.789963 0.388508i
\(676\) 0 0
\(677\) 9.26419i 0.356052i 0.984026 + 0.178026i \(0.0569711\pi\)
−0.984026 + 0.178026i \(0.943029\pi\)
\(678\) 0 0
\(679\) 18.4419 0.707736
\(680\) 0 0
\(681\) −8.65382 −0.331615
\(682\) 0 0
\(683\) 22.9835i 0.879439i 0.898135 + 0.439720i \(0.144922\pi\)
−0.898135 + 0.439720i \(0.855078\pi\)
\(684\) 0 0
\(685\) −10.9585 + 17.6016i −0.418705 + 0.672523i
\(686\) 0 0
\(687\) 4.28126i 0.163340i
\(688\) 0 0
\(689\) 22.9574 0.874606
\(690\) 0 0
\(691\) 27.2916 1.03822 0.519111 0.854707i \(-0.326263\pi\)
0.519111 + 0.854707i \(0.326263\pi\)
\(692\) 0 0
\(693\) 4.06853i 0.154551i
\(694\) 0 0
\(695\) −35.1729 21.8982i −1.33419 0.830648i
\(696\) 0 0
\(697\) 8.95664i 0.339257i
\(698\) 0 0
\(699\) 13.3745 0.505871
\(700\) 0 0
\(701\) 24.1308 0.911407 0.455704 0.890132i \(-0.349388\pi\)
0.455704 + 0.890132i \(0.349388\pi\)
\(702\) 0 0
\(703\) 17.3529i 0.654479i
\(704\) 0 0
\(705\) −0.507824 0.316165i −0.0191258 0.0119075i
\(706\) 0 0
\(707\) 7.90588i 0.297331i
\(708\) 0 0
\(709\) 15.0156 0.563922 0.281961 0.959426i \(-0.409015\pi\)
0.281961 + 0.959426i \(0.409015\pi\)
\(710\) 0 0
\(711\) −8.11802 −0.304450
\(712\) 0 0
\(713\) 0.315080i 0.0117999i
\(714\) 0 0
\(715\) −7.11733 + 11.4319i −0.266173 + 0.427527i
\(716\) 0 0
\(717\) 3.38955i 0.126585i
\(718\) 0 0
\(719\) 29.4211 1.09722 0.548611 0.836078i \(-0.315157\pi\)
0.548611 + 0.836078i \(0.315157\pi\)
\(720\) 0 0
\(721\) 16.7011 0.621981
\(722\) 0 0
\(723\) 5.80475i 0.215881i
\(724\) 0 0
\(725\) −4.44843 9.04510i −0.165211 0.335926i
\(726\) 0 0
\(727\) 47.8025i 1.77290i −0.462829 0.886448i \(-0.653166\pi\)
0.462829 0.886448i \(-0.346834\pi\)
\(728\) 0 0
\(729\) −5.91080 −0.218918
\(730\) 0 0
\(731\) −39.6788 −1.46757
\(732\) 0 0
\(733\) 44.0763i 1.62800i −0.580867 0.813998i \(-0.697286\pi\)
0.580867 0.813998i \(-0.302714\pi\)
\(734\) 0 0
\(735\) −6.20892 + 9.97276i −0.229019 + 0.367851i
\(736\) 0 0
\(737\) 1.56396i 0.0576091i
\(738\) 0 0
\(739\) 3.75235 0.138032 0.0690162 0.997616i \(-0.478014\pi\)
0.0690162 + 0.997616i \(0.478014\pi\)
\(740\) 0 0
\(741\) −16.2018 −0.595187
\(742\) 0 0
\(743\) 19.6859i 0.722205i −0.932526 0.361103i \(-0.882400\pi\)
0.932526 0.361103i \(-0.117600\pi\)
\(744\) 0 0
\(745\) 44.8415 + 27.9178i 1.64287 + 1.02283i
\(746\) 0 0
\(747\) 38.4703i 1.40755i
\(748\) 0 0
\(749\) 10.6626 0.389604
\(750\) 0 0
\(751\) 26.3594 0.961868 0.480934 0.876757i \(-0.340298\pi\)
0.480934 + 0.876757i \(0.340298\pi\)
\(752\) 0 0
\(753\) 5.08902i 0.185454i
\(754\) 0 0
\(755\) −36.5357 22.7467i −1.32967 0.827837i
\(756\) 0 0
\(757\) 11.9270i 0.433493i 0.976228 + 0.216747i \(0.0695446\pi\)
−0.976228 + 0.216747i \(0.930455\pi\)
\(758\) 0 0
\(759\) −1.60047 −0.0580935
\(760\) 0 0
\(761\) 1.03123 0.0373821 0.0186911 0.999825i \(-0.494050\pi\)
0.0186911 + 0.999825i \(0.494050\pi\)
\(762\) 0 0
\(763\) 8.27886i 0.299715i
\(764\) 0 0
\(765\) 17.5453 28.1812i 0.634351 1.01889i
\(766\) 0 0
\(767\) 31.2080i 1.12685i
\(768\) 0 0
\(769\) 3.37170 0.121587 0.0607933 0.998150i \(-0.480637\pi\)
0.0607933 + 0.998150i \(0.480637\pi\)
\(770\) 0 0
\(771\) −15.0215 −0.540986
\(772\) 0 0
\(773\) 33.0031i 1.18704i 0.804819 + 0.593520i \(0.202262\pi\)
−0.804819 + 0.593520i \(0.797738\pi\)
\(774\) 0 0
\(775\) 0.695259 + 1.41369i 0.0249744 + 0.0507811i
\(776\) 0 0
\(777\) 2.66553i 0.0956255i
\(778\) 0 0
\(779\) 7.61708 0.272910
\(780\) 0 0
\(781\) 1.46116 0.0522844
\(782\) 0 0
\(783\) 9.22166i 0.329555i
\(784\) 0 0
\(785\) −7.81395 + 12.5508i −0.278892 + 0.447956i
\(786\) 0 0
\(787\) 7.29525i 0.260048i 0.991511 + 0.130024i \(0.0415054\pi\)
−0.991511 + 0.130024i \(0.958495\pi\)
\(788\) 0 0
\(789\) 17.0631 0.607463
\(790\) 0 0
\(791\) −8.21823 −0.292206
\(792\) 0 0
\(793\) 18.2791i 0.649110i
\(794\) 0 0
\(795\) 11.5812 + 7.21033i 0.410744 + 0.255724i
\(796\) 0 0
\(797\) 32.1730i 1.13963i 0.821775 + 0.569813i \(0.192984\pi\)
−0.821775 + 0.569813i \(0.807016\pi\)
\(798\) 0 0
\(799\) −2.03260 −0.0719082
\(800\) 0 0
\(801\) 15.6946 0.554542
\(802\) 0 0