Properties

Label 648.4.i.r.217.1
Level $648$
Weight $4$
Character 648.217
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 217.1
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 648.217
Dual form 648.4.i.r.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.70820 - 9.88690i) q^{5} +(14.9164 - 25.8360i) q^{7} +O(q^{10})\) \(q+(-5.70820 - 9.88690i) q^{5} +(14.9164 - 25.8360i) q^{7} +(33.1246 - 57.3735i) q^{11} +(-19.9164 - 34.4962i) q^{13} -107.416 q^{17} +70.3313 q^{19} +(3.45898 + 5.99113i) q^{23} +(-2.66718 + 4.61970i) q^{25} +(18.3344 - 31.7561i) q^{29} +(115.666 + 200.339i) q^{31} -340.584 q^{35} +36.8359 q^{37} +(214.663 + 371.806i) q^{41} +(37.1672 - 64.3755i) q^{43} +(26.2918 - 45.5387i) q^{47} +(-273.498 - 473.713i) q^{49} -288.170 q^{53} -756.328 q^{55} +(-391.872 - 678.743i) q^{59} +(-219.579 + 380.322i) q^{61} +(-227.374 + 393.823i) q^{65} +(109.169 + 189.086i) q^{67} -790.492 q^{71} +1098.00 q^{73} +(-988.200 - 1711.61i) q^{77} +(-219.913 + 380.901i) q^{79} +(-25.4226 + 44.0333i) q^{83} +(613.155 + 1062.02i) q^{85} -719.745 q^{89} -1188.33 q^{91} +(-401.465 - 695.358i) q^{95} +(599.822 - 1038.92i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 4q^{5} + 6q^{7} + 52q^{11} - 26q^{13} - 376q^{17} - 148q^{19} + 148q^{23} - 118q^{25} + 288q^{29} + 248q^{31} - 1416q^{35} + 684q^{37} + 256q^{43} + 132q^{47} - 772q^{49} - 1904q^{53} - 1952q^{55} - 1004q^{59} + 34q^{61} - 668q^{65} + 866q^{67} - 1552q^{71} + 3748q^{73} - 2316q^{77} - 182q^{79} - 1336q^{83} - 16q^{85} - 1752q^{89} - 3036q^{91} - 3028q^{95} + 38q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(4\) 0 0
\(5\) −5.70820 9.88690i −0.510557 0.884311i −0.999925 0.0122337i \(-0.996106\pi\)
0.489368 0.872077i \(-0.337228\pi\)
\(6\) 0 0
\(7\) 14.9164 25.8360i 0.805410 1.39501i −0.110603 0.993865i \(-0.535278\pi\)
0.916014 0.401147i \(-0.131388\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 33.1246 57.3735i 0.907950 1.57261i 0.0910416 0.995847i \(-0.470980\pi\)
0.816908 0.576768i \(-0.195686\pi\)
\(12\) 0 0
\(13\) −19.9164 34.4962i −0.424909 0.735964i 0.571503 0.820600i \(-0.306361\pi\)
−0.996412 + 0.0846360i \(0.973027\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −107.416 −1.53249 −0.766244 0.642549i \(-0.777877\pi\)
−0.766244 + 0.642549i \(0.777877\pi\)
\(18\) 0 0
\(19\) 70.3313 0.849216 0.424608 0.905377i \(-0.360412\pi\)
0.424608 + 0.905377i \(0.360412\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.45898 + 5.99113i 0.0313586 + 0.0543146i 0.881279 0.472597i \(-0.156683\pi\)
−0.849920 + 0.526911i \(0.823350\pi\)
\(24\) 0 0
\(25\) −2.66718 + 4.61970i −0.0213375 + 0.0369576i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 18.3344 31.7561i 0.117400 0.203343i −0.801336 0.598214i \(-0.795877\pi\)
0.918737 + 0.394871i \(0.129211\pi\)
\(30\) 0 0
\(31\) 115.666 + 200.339i 0.670134 + 1.16071i 0.977866 + 0.209233i \(0.0670968\pi\)
−0.307732 + 0.951473i \(0.599570\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −340.584 −1.64483
\(36\) 0 0
\(37\) 36.8359 0.163670 0.0818350 0.996646i \(-0.473922\pi\)
0.0818350 + 0.996646i \(0.473922\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 214.663 + 371.806i 0.817674 + 1.41625i 0.907391 + 0.420286i \(0.138070\pi\)
−0.0897170 + 0.995967i \(0.528596\pi\)
\(42\) 0 0
\(43\) 37.1672 64.3755i 0.131813 0.228306i −0.792563 0.609790i \(-0.791254\pi\)
0.924375 + 0.381484i \(0.124587\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 26.2918 45.5387i 0.0815969 0.141330i −0.822339 0.568998i \(-0.807331\pi\)
0.903936 + 0.427668i \(0.140665\pi\)
\(48\) 0 0
\(49\) −273.498 473.713i −0.797372 1.38109i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −288.170 −0.746853 −0.373427 0.927660i \(-0.621817\pi\)
−0.373427 + 0.927660i \(0.621817\pi\)
\(54\) 0 0
\(55\) −756.328 −1.85424
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −391.872 678.743i −0.864702 1.49771i −0.867343 0.497712i \(-0.834174\pi\)
0.00264051 0.999997i \(-0.499159\pi\)
\(60\) 0 0
\(61\) −219.579 + 380.322i −0.460889 + 0.798282i −0.999005 0.0445878i \(-0.985803\pi\)
0.538117 + 0.842870i \(0.319136\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −227.374 + 393.823i −0.433881 + 0.751504i
\(66\) 0 0
\(67\) 109.169 + 189.086i 0.199061 + 0.344784i 0.948224 0.317602i \(-0.102877\pi\)
−0.749163 + 0.662385i \(0.769544\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −790.492 −1.32133 −0.660663 0.750682i \(-0.729725\pi\)
−0.660663 + 0.750682i \(0.729725\pi\)
\(72\) 0 0
\(73\) 1098.00 1.76042 0.880211 0.474582i \(-0.157401\pi\)
0.880211 + 0.474582i \(0.157401\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −988.200 1711.61i −1.46254 2.53320i
\(78\) 0 0
\(79\) −219.913 + 380.901i −0.313192 + 0.542465i −0.979052 0.203613i \(-0.934732\pi\)
0.665859 + 0.746077i \(0.268065\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −25.4226 + 44.0333i −0.0336204 + 0.0582323i −0.882346 0.470601i \(-0.844037\pi\)
0.848726 + 0.528833i \(0.177370\pi\)
\(84\) 0 0
\(85\) 613.155 + 1062.02i 0.782423 + 1.35520i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −719.745 −0.857222 −0.428611 0.903489i \(-0.640997\pi\)
−0.428611 + 0.903489i \(0.640997\pi\)
\(90\) 0 0
\(91\) −1188.33 −1.36890
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −401.465 695.358i −0.433573 0.750971i
\(96\) 0 0
\(97\) 599.822 1038.92i 0.627863 1.08749i −0.360117 0.932907i \(-0.617263\pi\)
0.987980 0.154583i \(-0.0494034\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 122.991 213.026i 0.121169 0.209870i −0.799060 0.601251i \(-0.794669\pi\)
0.920229 + 0.391381i \(0.128002\pi\)
\(102\) 0 0
\(103\) −287.910 498.675i −0.275424 0.477048i 0.694818 0.719185i \(-0.255485\pi\)
−0.970242 + 0.242138i \(0.922151\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1015.89 0.917849 0.458924 0.888475i \(-0.348235\pi\)
0.458924 + 0.888475i \(0.348235\pi\)
\(108\) 0 0
\(109\) 1471.64 1.29319 0.646595 0.762834i \(-0.276193\pi\)
0.646595 + 0.762834i \(0.276193\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −951.787 1648.54i −0.792359 1.37241i −0.924503 0.381176i \(-0.875519\pi\)
0.132143 0.991231i \(-0.457814\pi\)
\(114\) 0 0
\(115\) 39.4891 68.3972i 0.0320207 0.0554615i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1602.27 + 2775.21i −1.23428 + 2.13784i
\(120\) 0 0
\(121\) −1528.98 2648.27i −1.14875 1.98968i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1366.15 −0.977539
\(126\) 0 0
\(127\) 230.310 0.160919 0.0804593 0.996758i \(-0.474361\pi\)
0.0804593 + 0.996758i \(0.474361\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 397.155 + 687.892i 0.264882 + 0.458789i 0.967533 0.252746i \(-0.0813336\pi\)
−0.702651 + 0.711535i \(0.748000\pi\)
\(132\) 0 0
\(133\) 1049.09 1817.08i 0.683967 1.18467i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −341.538 + 591.561i −0.212989 + 0.368909i −0.952649 0.304073i \(-0.901653\pi\)
0.739659 + 0.672982i \(0.234987\pi\)
\(138\) 0 0
\(139\) 756.320 + 1309.99i 0.461513 + 0.799363i 0.999037 0.0438851i \(-0.0139736\pi\)
−0.537524 + 0.843248i \(0.680640\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2638.89 −1.54318
\(144\) 0 0
\(145\) −418.625 −0.239758
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1153.57 + 1998.04i 0.634255 + 1.09856i 0.986672 + 0.162719i \(0.0520263\pi\)
−0.352418 + 0.935843i \(0.614640\pi\)
\(150\) 0 0
\(151\) −1261.59 + 2185.13i −0.679910 + 1.17764i 0.295098 + 0.955467i \(0.404648\pi\)
−0.975008 + 0.222171i \(0.928686\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1320.49 2287.15i 0.684284 1.18521i
\(156\) 0 0
\(157\) 1459.49 + 2527.91i 0.741912 + 1.28503i 0.951624 + 0.307266i \(0.0994141\pi\)
−0.209712 + 0.977763i \(0.567253\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 206.382 0.101026
\(162\) 0 0
\(163\) 1096.99 0.527133 0.263567 0.964641i \(-0.415101\pi\)
0.263567 + 0.964641i \(0.415101\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −366.365 634.562i −0.169761 0.294035i 0.768575 0.639760i \(-0.220966\pi\)
−0.938336 + 0.345725i \(0.887633\pi\)
\(168\) 0 0
\(169\) 305.173 528.576i 0.138905 0.240590i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 361.337 625.855i 0.158798 0.275045i −0.775638 0.631178i \(-0.782572\pi\)
0.934435 + 0.356133i \(0.115905\pi\)
\(174\) 0 0
\(175\) 79.5696 + 137.819i 0.0343708 + 0.0595320i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1010.16 −0.421806 −0.210903 0.977507i \(-0.567640\pi\)
−0.210903 + 0.977507i \(0.567640\pi\)
\(180\) 0 0
\(181\) −4256.79 −1.74809 −0.874045 0.485844i \(-0.838512\pi\)
−0.874045 + 0.485844i \(0.838512\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −210.267 364.193i −0.0835629 0.144735i
\(186\) 0 0
\(187\) −3558.13 + 6162.86i −1.39142 + 2.41001i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1714.69 2969.93i 0.649585 1.12511i −0.333637 0.942702i \(-0.608276\pi\)
0.983222 0.182413i \(-0.0583908\pi\)
\(192\) 0 0
\(193\) −483.670 837.742i −0.180390 0.312445i 0.761623 0.648020i \(-0.224403\pi\)
−0.942014 + 0.335575i \(0.891069\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 468.413 0.169406 0.0847032 0.996406i \(-0.473006\pi\)
0.0847032 + 0.996406i \(0.473006\pi\)
\(198\) 0 0
\(199\) −2673.47 −0.952347 −0.476174 0.879351i \(-0.657977\pi\)
−0.476174 + 0.879351i \(0.657977\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −546.966 947.373i −0.189111 0.327549i
\(204\) 0 0
\(205\) 2450.67 4244.69i 0.834939 1.44616i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2329.70 4035.15i 0.771045 1.33549i
\(210\) 0 0
\(211\) −1435.31 2486.03i −0.468297 0.811114i 0.531046 0.847343i \(-0.321799\pi\)
−0.999344 + 0.0362284i \(0.988466\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −848.631 −0.269192
\(216\) 0 0
\(217\) 6901.26 2.15893
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2139.35 + 3705.46i 0.651168 + 1.12786i
\(222\) 0 0
\(223\) 623.300 1079.59i 0.187172 0.324191i −0.757135 0.653259i \(-0.773401\pi\)
0.944306 + 0.329068i \(0.106735\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 280.231 485.374i 0.0819364 0.141918i −0.822145 0.569278i \(-0.807223\pi\)
0.904082 + 0.427360i \(0.140556\pi\)
\(228\) 0 0
\(229\) 572.690 + 991.929i 0.165260 + 0.286238i 0.936747 0.350006i \(-0.113820\pi\)
−0.771488 + 0.636244i \(0.780487\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 623.709 0.175367 0.0876836 0.996148i \(-0.472054\pi\)
0.0876836 + 0.996148i \(0.472054\pi\)
\(234\) 0 0
\(235\) −600.316 −0.166639
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3132.90 + 5426.34i 0.847910 + 1.46862i 0.883070 + 0.469241i \(0.155472\pi\)
−0.0351605 + 0.999382i \(0.511194\pi\)
\(240\) 0 0
\(241\) 320.327 554.822i 0.0856185 0.148296i −0.820036 0.572312i \(-0.806047\pi\)
0.905655 + 0.424016i \(0.139380\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3122.37 + 5408.10i −0.814208 + 1.41025i
\(246\) 0 0
\(247\) −1400.75 2426.16i −0.360839 0.624992i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7748.91 1.94863 0.974316 0.225183i \(-0.0722980\pi\)
0.974316 + 0.225183i \(0.0722980\pi\)
\(252\) 0 0
\(253\) 458.310 0.113888
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1595.88 + 2764.14i 0.387347 + 0.670904i 0.992092 0.125515i \(-0.0400583\pi\)
−0.604745 + 0.796419i \(0.706725\pi\)
\(258\) 0 0
\(259\) 549.460 951.692i 0.131821 0.228321i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1888.21 + 3270.47i −0.442706 + 0.766790i −0.997889 0.0649384i \(-0.979315\pi\)
0.555183 + 0.831728i \(0.312648\pi\)
\(264\) 0 0
\(265\) 1644.93 + 2849.11i 0.381311 + 0.660451i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4065.91 0.921572 0.460786 0.887511i \(-0.347568\pi\)
0.460786 + 0.887511i \(0.347568\pi\)
\(270\) 0 0
\(271\) −5508.17 −1.23468 −0.617339 0.786697i \(-0.711789\pi\)
−0.617339 + 0.786697i \(0.711789\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 176.699 + 306.051i 0.0387467 + 0.0671113i
\(276\) 0 0
\(277\) 4153.45 7194.00i 0.900928 1.56045i 0.0746351 0.997211i \(-0.476221\pi\)
0.826292 0.563241i \(-0.190446\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1481.34 + 2565.75i −0.314481 + 0.544697i −0.979327 0.202283i \(-0.935164\pi\)
0.664846 + 0.746980i \(0.268497\pi\)
\(282\) 0 0
\(283\) 2254.83 + 3905.48i 0.473625 + 0.820343i 0.999544 0.0301919i \(-0.00961185\pi\)
−0.525919 + 0.850535i \(0.676279\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12808.0 2.63425
\(288\) 0 0
\(289\) 6625.28 1.34852
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 907.228 + 1571.37i 0.180890 + 0.313311i 0.942184 0.335096i \(-0.108769\pi\)
−0.761294 + 0.648407i \(0.775435\pi\)
\(294\) 0 0
\(295\) −4473.77 + 7748.80i −0.882960 + 1.52933i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 137.781 238.644i 0.0266491 0.0461576i
\(300\) 0 0
\(301\) −1108.80 1920.50i −0.212326 0.367760i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5013.61 0.941240
\(306\) 0 0
\(307\) 4395.62 0.817171 0.408585 0.912720i \(-0.366022\pi\)
0.408585 + 0.912720i \(0.366022\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −688.614 1192.71i −0.125555 0.217468i 0.796395 0.604777i \(-0.206738\pi\)
−0.921950 + 0.387309i \(0.873405\pi\)
\(312\) 0 0
\(313\) −3673.97 + 6363.51i −0.663467 + 1.14916i 0.316231 + 0.948682i \(0.397582\pi\)
−0.979698 + 0.200477i \(0.935751\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1303.89 2258.40i 0.231021 0.400141i −0.727088 0.686545i \(-0.759127\pi\)
0.958109 + 0.286404i \(0.0924600\pi\)
\(318\) 0 0
\(319\) −1214.64 2103.81i −0.213187 0.369251i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7554.73 −1.30141
\(324\) 0 0
\(325\) 212.483 0.0362659
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −784.358 1358.55i −0.131438 0.227657i
\(330\) 0 0
\(331\) 3270.67 5664.96i 0.543118 0.940708i −0.455605 0.890182i \(-0.650577\pi\)
0.998723 0.0505260i \(-0.0160898\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1246.31 2158.68i 0.203264 0.352064i
\(336\) 0 0
\(337\) −2157.83 3737.47i −0.348797 0.604134i 0.637239 0.770666i \(-0.280076\pi\)
−0.986036 + 0.166532i \(0.946743\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15325.5 2.43379
\(342\) 0 0
\(343\) −6085.80 −0.958025
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1947.88 + 3373.82i 0.301347 + 0.521949i 0.976441 0.215783i \(-0.0692303\pi\)
−0.675094 + 0.737732i \(0.735897\pi\)
\(348\) 0 0
\(349\) 2438.71 4223.97i 0.374044 0.647863i −0.616140 0.787637i \(-0.711304\pi\)
0.990183 + 0.139774i \(0.0446377\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 869.896 1506.70i 0.131161 0.227178i −0.792963 0.609269i \(-0.791463\pi\)
0.924124 + 0.382092i \(0.124796\pi\)
\(354\) 0 0
\(355\) 4512.29 + 7815.52i 0.674613 + 1.16846i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −188.828 −0.0277604 −0.0138802 0.999904i \(-0.504418\pi\)
−0.0138802 + 0.999904i \(0.504418\pi\)
\(360\) 0 0
\(361\) −1912.51 −0.278833
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6267.59 10855.8i −0.898796 1.55676i
\(366\) 0 0
\(367\) 3169.07 5489.00i 0.450747 0.780718i −0.547685 0.836685i \(-0.684491\pi\)
0.998433 + 0.0559670i \(0.0178242\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4298.47 + 7445.16i −0.601523 + 1.04187i
\(372\) 0 0
\(373\) −4320.70 7483.68i −0.599779 1.03885i −0.992853 0.119341i \(-0.961922\pi\)
0.393075 0.919507i \(-0.371411\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1460.62 −0.199538
\(378\) 0 0
\(379\) −4143.88 −0.561627 −0.280814 0.959762i \(-0.590604\pi\)
−0.280814 + 0.959762i \(0.590604\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2096.97 3632.06i −0.279766 0.484568i 0.691561 0.722318i \(-0.256923\pi\)
−0.971326 + 0.237750i \(0.923590\pi\)
\(384\) 0 0
\(385\) −11281.7 + 19540.5i −1.49343 + 2.58669i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5435.21 9414.07i 0.708422 1.22702i −0.257020 0.966406i \(-0.582741\pi\)
0.965442 0.260617i \(-0.0839261\pi\)
\(390\) 0 0
\(391\) −371.551 643.546i −0.0480567 0.0832366i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5021.24 0.639610
\(396\) 0 0
\(397\) −8890.87 −1.12398 −0.561990 0.827144i \(-0.689964\pi\)
−0.561990 + 0.827144i \(0.689964\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7547.71 + 13073.0i 0.939936 + 1.62802i 0.765586 + 0.643334i \(0.222449\pi\)
0.174351 + 0.984684i \(0.444217\pi\)
\(402\) 0 0
\(403\) 4607.29 7980.06i 0.569492 0.986389i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1220.18 2113.41i 0.148604 0.257390i
\(408\) 0 0
\(409\) −809.169 1401.52i −0.0978260 0.169440i 0.812959 0.582322i \(-0.197856\pi\)
−0.910785 + 0.412882i \(0.864522\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −23381.3 −2.78576
\(414\) 0 0
\(415\) 580.470 0.0686606
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5005.94 + 8670.54i 0.583666 + 1.01094i 0.995040 + 0.0994728i \(0.0317156\pi\)
−0.411374 + 0.911467i \(0.634951\pi\)
\(420\) 0 0
\(421\) −3617.22 + 6265.20i −0.418747 + 0.725291i −0.995814 0.0914063i \(-0.970864\pi\)
0.577067 + 0.816697i \(0.304197\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 286.499 496.231i 0.0326994 0.0566371i
\(426\) 0 0
\(427\) 6550.66 + 11346.1i 0.742409 + 1.28589i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5379.03 −0.601157 −0.300579 0.953757i \(-0.597180\pi\)
−0.300579 + 0.953757i \(0.597180\pi\)
\(432\) 0 0
\(433\) −1602.96 −0.177906 −0.0889530 0.996036i \(-0.528352\pi\)
−0.0889530 + 0.996036i \(0.528352\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 243.274 + 421.364i 0.0266302 + 0.0461249i
\(438\) 0 0
\(439\) −3362.93 + 5824.77i −0.365613 + 0.633260i −0.988874 0.148753i \(-0.952474\pi\)
0.623261 + 0.782014i \(0.285807\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 584.961 1013.18i 0.0627367 0.108663i −0.832951 0.553347i \(-0.813350\pi\)
0.895688 + 0.444683i \(0.146684\pi\)
\(444\) 0 0
\(445\) 4108.45 + 7116.04i 0.437661 + 0.758051i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2996.56 0.314958 0.157479 0.987522i \(-0.449663\pi\)
0.157479 + 0.987522i \(0.449663\pi\)
\(450\) 0 0
\(451\) 28442.5 2.96963
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6783.20 + 11748.9i 0.698904 + 1.21054i
\(456\) 0 0
\(457\) 5576.04 9657.98i 0.570757 0.988580i −0.425731 0.904850i \(-0.639983\pi\)
0.996488 0.0837307i \(-0.0266835\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1473.59 + 2552.33i −0.148876 + 0.257860i −0.930812 0.365498i \(-0.880899\pi\)
0.781936 + 0.623358i \(0.214232\pi\)
\(462\) 0 0
\(463\) −3281.69 5684.05i −0.329402 0.570541i 0.652991 0.757365i \(-0.273514\pi\)
−0.982393 + 0.186824i \(0.940180\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2727.33 0.270248 0.135124 0.990829i \(-0.456857\pi\)
0.135124 + 0.990829i \(0.456857\pi\)
\(468\) 0 0
\(469\) 6513.62 0.641303
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2462.30 4264.82i −0.239358 0.414581i
\(474\) 0 0
\(475\) −187.586 + 324.909i −0.0181201 + 0.0313850i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7256.06 12567.9i 0.692146 1.19883i −0.278988 0.960295i \(-0.589999\pi\)
0.971133 0.238537i \(-0.0766678\pi\)
\(480\) 0 0
\(481\) −733.639 1270.70i −0.0695448 0.120455i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −13695.6 −1.28224
\(486\) 0 0
\(487\) −14189.9 −1.32034 −0.660170 0.751116i \(-0.729516\pi\)
−0.660170 + 0.751116i \(0.729516\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3607.96 6249.17i −0.331619 0.574381i 0.651211 0.758897i \(-0.274261\pi\)
−0.982829 + 0.184516i \(0.940928\pi\)
\(492\) 0 0
\(493\) −1969.41 + 3411.12i −0.179915 + 0.311621i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11791.3 + 20423.1i −1.06421 + 1.84327i
\(498\) 0 0
\(499\) −6516.28 11286.5i −0.584587 1.01253i −0.994927 0.100601i \(-0.967923\pi\)
0.410340 0.911932i \(-0.365410\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −9502.84 −0.842367 −0.421184 0.906975i \(-0.638385\pi\)
−0.421184 + 0.906975i \(0.638385\pi\)
\(504\) 0 0
\(505\) −2808.22 −0.247454
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1897.15 + 3285.96i 0.165206 + 0.286145i 0.936728 0.350057i \(-0.113838\pi\)
−0.771523 + 0.636202i \(0.780505\pi\)
\(510\) 0 0
\(511\) 16378.2 28367.8i 1.41786 2.45581i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3286.90 + 5693.08i −0.281239 + 0.487120i
\(516\) 0 0
\(517\) −1741.81 3016.91i −0.148172 0.256641i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −14811.2 −1.24547 −0.622735 0.782432i \(-0.713979\pi\)
−0.622735 + 0.782432i \(0.713979\pi\)
\(522\) 0 0
\(523\) −345.532 −0.0288892 −0.0144446 0.999896i \(-0.504598\pi\)
−0.0144446 + 0.999896i \(0.504598\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12424.4 21519.7i −1.02697 1.77877i
\(528\) 0 0
\(529\) 6059.57 10495.5i 0.498033 0.862619i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8550.61 14810.1i 0.694875 1.20356i
\(534\) 0 0
\(535\) −5798.91 10044.0i −0.468614 0.811664i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −36238.1 −2.89589
\(540\) 0 0
\(541\) −5474.45 −0.435056 −0.217528 0.976054i \(-0.569799\pi\)
−0.217528 + 0.976054i \(0.569799\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8400.43 14550.0i −0.660247 1.14358i
\(546\) 0 0
\(547\) −488.639 + 846.348i −0.0381951 + 0.0661558i −0.884491 0.466557i \(-0.845494\pi\)
0.846296 + 0.532713i \(0.178827\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1289.48 2233.44i 0.0996981 0.172682i
\(552\) 0 0
\(553\) 6560.63 + 11363.3i 0.504496 + 0.873813i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18833.3 1.43266 0.716330 0.697762i \(-0.245821\pi\)
0.716330 + 0.697762i \(0.245821\pi\)
\(558\) 0 0
\(559\) −2960.95 −0.224033
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10483.5 18158.0i −0.784772 1.35927i −0.929135 0.369741i \(-0.879447\pi\)
0.144363 0.989525i \(-0.453887\pi\)
\(564\) 0 0
\(565\) −10866.0 + 18820.4i −0.809090 + 1.40138i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6744.33 11681.5i 0.496902 0.860659i −0.503092 0.864233i \(-0.667804\pi\)
0.999994 + 0.00357372i \(0.00113755\pi\)
\(570\) 0 0
\(571\) 1124.45 + 1947.60i 0.0824110 + 0.142740i 0.904285 0.426929i \(-0.140405\pi\)
−0.821874 + 0.569669i \(0.807071\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −36.9030 −0.00267645
\(576\) 0 0
\(577\) −1968.87 −0.142054 −0.0710270 0.997474i \(-0.522628\pi\)
−0.0710270 + 0.997474i \(0.522628\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 758.428 + 1313.64i 0.0541565 + 0.0938018i
\(582\) 0 0
\(583\) −9545.53 + 16533.3i −0.678105 + 1.17451i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2053.83 3557.34i 0.144413 0.250131i −0.784741 0.619824i \(-0.787204\pi\)
0.929154 + 0.369693i \(0.120537\pi\)
\(588\) 0 0
\(589\) 8134.91 + 14090.1i 0.569088 + 0.985690i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7497.21 0.519180 0.259590 0.965719i \(-0.416413\pi\)
0.259590 + 0.965719i \(0.416413\pi\)
\(594\) 0 0
\(595\) 36584.3 2.52069
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13553.6 23475.4i −0.924513 1.60130i −0.792343 0.610076i \(-0.791139\pi\)
−0.132170 0.991227i \(-0.542195\pi\)
\(600\) 0 0
\(601\) −3401.08 + 5890.85i −0.230837 + 0.399822i −0.958055 0.286585i \(-0.907480\pi\)
0.727218 + 0.686407i \(0.240813\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −17455.5 + 30233.7i −1.17300 + 2.03170i
\(606\) 0 0
\(607\) −8496.22 14715.9i −0.568123 0.984019i −0.996752 0.0805376i \(-0.974336\pi\)
0.428628 0.903481i \(-0.358997\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2094.55 −0.138685
\(612\) 0 0
\(613\) −13766.6 −0.907062 −0.453531 0.891241i \(-0.649836\pi\)
−0.453531 + 0.891241i \(0.649836\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8678.00 15030.7i −0.566229 0.980737i −0.996934 0.0782443i \(-0.975069\pi\)
0.430706 0.902493i \(-0.358265\pi\)
\(618\) 0 0
\(619\) −1462.45 + 2533.03i −0.0949608 + 0.164477i −0.909592 0.415502i \(-0.863606\pi\)
0.814631 + 0.579979i \(0.196939\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10736.0 + 18595.3i −0.690416 + 1.19583i
\(624\) 0 0
\(625\) 8131.67 + 14084.5i 0.520427 + 0.901406i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3956.78 −0.250822
\(630\) 0 0
\(631\) 6158.40 0.388530 0.194265 0.980949i \(-0.437768\pi\)
0.194265 + 0.980949i \(0.437768\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1314.65 2277.05i −0.0821582 0.142302i
\(636\) 0 0
\(637\) −10894.2 + 18869.3i −0.677621 + 1.17367i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5907.12 10231.4i 0.363990 0.630448i −0.624624 0.780926i \(-0.714748\pi\)
0.988613 + 0.150477i \(0.0480811\pi\)
\(642\) 0 0
\(643\) 8457.37 + 14648.6i 0.518703 + 0.898420i 0.999764 + 0.0217330i \(0.00691836\pi\)
−0.481061 + 0.876687i \(0.659748\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28652.4 1.74103 0.870513 0.492145i \(-0.163787\pi\)
0.870513 + 0.492145i \(0.163787\pi\)
\(648\) 0 0
\(649\) −51922.5 −3.14042
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2749.24 4761.82i −0.164757 0.285367i 0.771812 0.635851i \(-0.219351\pi\)
−0.936569 + 0.350484i \(0.886017\pi\)
\(654\) 0 0
\(655\) 4534.08 7853.26i 0.270475 0.468477i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9392.57 + 16268.4i −0.555209 + 0.961650i 0.442679 + 0.896680i \(0.354028\pi\)
−0.997887 + 0.0649692i \(0.979305\pi\)
\(660\) 0 0
\(661\) 8652.23 + 14986.1i 0.509127 + 0.881834i 0.999944 + 0.0105712i \(0.00336497\pi\)
−0.490817 + 0.871263i \(0.663302\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −23953.7 −1.39682
\(666\) 0 0
\(667\) 253.673 0.0147260
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 14546.9 + 25196.0i 0.836927 + 1.44960i
\(672\) 0 0
\(673\) 6855.73 11874.5i 0.392673 0.680129i −0.600128 0.799904i \(-0.704884\pi\)
0.992801 + 0.119774i \(0.0382172\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15283.4 + 26471.7i −0.867637 + 1.50279i −0.00323298 + 0.999995i \(0.501029\pi\)
−0.864404 + 0.502797i \(0.832304\pi\)
\(678\) 0 0
\(679\) −17894.4 30994.0i −1.01137 1.75175i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4445.72 −0.249064 −0.124532 0.992216i \(-0.539743\pi\)
−0.124532 + 0.992216i \(0.539743\pi\)
\(684\) 0 0
\(685\) 7798.27 0.434973
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5739.32 + 9940.79i 0.317345 + 0.549657i
\(690\) 0 0
\(691\) 6099.36 10564.4i 0.335790 0.581605i −0.647846 0.761771i \(-0.724330\pi\)
0.983636 + 0.180166i \(0.0576635\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8634.46 14955.3i 0.471257 0.816242i
\(696\) 0 0
\(697\) −23058.3 39938.1i −1.25308 2.17039i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −21613.4 −1.16452 −0.582258 0.813004i \(-0.697831\pi\)
−0.582258 + 0.813004i \(0.697831\pi\)
\(702\) 0 0
\(703\) 2590.72 0.138991
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3669.16 6355.17i −0.195181 0.338063i
\(708\) 0 0
\(709\) 2462.43 4265.05i 0.130435 0.225920i −0.793409 0.608688i \(-0.791696\pi\)
0.923844 + 0.382768i \(0.125029\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −800.170 + 1385.94i −0.0420289 + 0.0727962i
\(714\) 0 0
\(715\) 15063.3 + 26090.5i 0.787884 + 1.36465i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 205.354 0.0106515 0.00532573 0.999986i \(-0.498305\pi\)
0.00532573 + 0.999986i \(0.498305\pi\)
\(720\) 0 0
\(721\) −17178.3 −0.887316
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 97.8023 + 169.399i 0.00501005 + 0.00867766i
\(726\) 0 0
\(727\) −7898.02 + 13679.8i −0.402918 + 0.697875i −0.994077 0.108681i \(-0.965337\pi\)
0.591159 + 0.806555i \(0.298671\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3992.37 + 6914.98i −0.202001 + 0.349877i
\(732\) 0 0
\(733\) −16062.7 27821.4i −0.809398 1.40192i −0.913282 0.407328i \(-0.866460\pi\)
0.103884 0.994589i \(-0.466873\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14464.7 0.722949
\(738\) 0 0
\(739\) 28938.9 1.44051 0.720255 0.693710i \(-0.244025\pi\)
0.720255 + 0.693710i \(0.244025\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18054.2 + 31270.8i 0.891447 + 1.54403i 0.838141 + 0.545454i \(0.183643\pi\)
0.0533063 + 0.998578i \(0.483024\pi\)
\(744\) 0 0
\(745\) 13169.6 22810.4i 0.647647 1.12176i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15153.4 26246.5i 0.739245 1.28041i
\(750\) 0 0
\(751\) 11615.8 + 20119.2i 0.564405 + 0.977578i 0.997105 + 0.0760399i \(0.0242277\pi\)
−0.432700 + 0.901538i \(0.642439\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 28805.5 1.38853
\(756\) 0 0
\(757\) 22762.6 1.09289 0.546447 0.837494i \(-0.315980\pi\)
0.546447 + 0.837494i \(0.315980\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20259.3 35090.1i −0.965044 1.67150i −0.709497 0.704708i \(-0.751078\pi\)
−0.255547 0.966797i \(-0.582255\pi\)
\(762\) 0 0
\(763\) 21951.6 38021.3i 1.04155 1.80401i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15609.4 + 27036.2i −0.734840 + 1.27278i
\(768\) 0 0
\(769\) 13700.6 + 23730.1i 0.642464 + 1.11278i 0.984881 + 0.173232i \(0.0554212\pi\)
−0.342417 + 0.939548i \(0.611246\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 35698.4 1.66104 0.830520 0.556989i \(-0.188043\pi\)
0.830520 + 0.556989i \(0.188043\pi\)
\(774\) 0 0
\(775\) −1234.01 −0.0571959
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 15097.5 + 26149.6i 0.694382 + 1.20270i
\(780\) 0 0
\(781\) −26184.7 + 45353.3i −1.19970 + 2.07794i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 16662.2 28859.7i 0.757577 1.31216i
\(786\) 0 0
\(787\) 4783.18 + 8284.71i 0.216648 + 0.375245i 0.953781 0.300502i \(-0.0971543\pi\)
−0.737133 + 0.675748i \(0.763821\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −56789.0 −2.55270
\(792\) 0 0
\(793\) 17492.9 0.783343
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2653.01 4595.14i −0.117910 0.204226i 0.801029 0.598625i \(-0.204286\pi\)
−0.918939 + 0.394399i \(0.870953\pi\)
\(798\) 0 0
\(799\) −2824.17 + 4891.61i −0.125046 + 0.216586i
\(800\) 0 0
\(801\)