Properties

Label 1008.4.bt.d.17.11
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.11
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.56246 - 2.70625i) q^{5} +(-17.1949 + 6.88015i) q^{7} +O(q^{10})\) \(q+(-1.56246 - 2.70625i) q^{5} +(-17.1949 + 6.88015i) q^{7} +(-33.2914 - 19.2208i) q^{11} +13.8046i q^{13} +(-47.5817 + 82.4140i) q^{17} +(-9.86718 + 5.69682i) q^{19} +(-23.9992 + 13.8559i) q^{23} +(57.6175 - 99.7964i) q^{25} -44.2317i q^{29} +(119.149 + 68.7907i) q^{31} +(45.4857 + 35.7837i) q^{35} +(70.6631 + 122.392i) q^{37} +337.946 q^{41} -417.510 q^{43} +(-145.043 - 251.222i) q^{47} +(248.327 - 236.607i) q^{49} +(-14.7904 - 8.53925i) q^{53} +120.127i q^{55} +(299.818 - 519.300i) q^{59} +(459.882 - 265.513i) q^{61} +(37.3586 - 21.5690i) q^{65} +(-325.105 + 563.098i) q^{67} -934.128i q^{71} +(787.145 + 454.458i) q^{73} +(704.683 + 101.449i) q^{77} +(397.516 + 688.517i) q^{79} -314.865 q^{83} +297.378 q^{85} +(179.521 + 310.940i) q^{89} +(-94.9775 - 237.368i) q^{91} +(30.8341 + 17.8021i) q^{95} +80.5572i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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 0
\(4\) 0 0
\(5\) −1.56246 2.70625i −0.139750 0.242055i 0.787652 0.616121i \(-0.211297\pi\)
−0.927402 + 0.374066i \(0.877963\pi\)
\(6\) 0 0
\(7\) −17.1949 + 6.88015i −0.928436 + 0.371493i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −33.2914 19.2208i −0.912521 0.526844i −0.0312793 0.999511i \(-0.509958\pi\)
−0.881241 + 0.472667i \(0.843291\pi\)
\(12\) 0 0
\(13\) 13.8046i 0.294515i 0.989098 + 0.147258i \(0.0470446\pi\)
−0.989098 + 0.147258i \(0.952955\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −47.5817 + 82.4140i −0.678839 + 1.17578i 0.296491 + 0.955036i \(0.404183\pi\)
−0.975331 + 0.220749i \(0.929150\pi\)
\(18\) 0 0
\(19\) −9.86718 + 5.69682i −0.119141 + 0.0687863i −0.558386 0.829581i \(-0.688579\pi\)
0.439245 + 0.898367i \(0.355246\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −23.9992 + 13.8559i −0.217573 + 0.125616i −0.604826 0.796358i \(-0.706757\pi\)
0.387253 + 0.921973i \(0.373424\pi\)
\(24\) 0 0
\(25\) 57.6175 99.7964i 0.460940 0.798371i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 44.2317i 0.283228i −0.989922 0.141614i \(-0.954771\pi\)
0.989922 0.141614i \(-0.0452293\pi\)
\(30\) 0 0
\(31\) 119.149 + 68.7907i 0.690316 + 0.398554i 0.803730 0.594994i \(-0.202845\pi\)
−0.113414 + 0.993548i \(0.536179\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 45.4857 + 35.7837i 0.219671 + 0.172816i
\(36\) 0 0
\(37\) 70.6631 + 122.392i 0.313972 + 0.543815i 0.979218 0.202809i \(-0.0650070\pi\)
−0.665247 + 0.746624i \(0.731674\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 337.946 1.28728 0.643639 0.765330i \(-0.277424\pi\)
0.643639 + 0.765330i \(0.277424\pi\)
\(42\) 0 0
\(43\) −417.510 −1.48069 −0.740346 0.672226i \(-0.765338\pi\)
−0.740346 + 0.672226i \(0.765338\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −145.043 251.222i −0.450142 0.779670i 0.548252 0.836313i \(-0.315293\pi\)
−0.998394 + 0.0566436i \(0.981960\pi\)
\(48\) 0 0
\(49\) 248.327 236.607i 0.723985 0.689815i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −14.7904 8.53925i −0.0383324 0.0221312i 0.480711 0.876879i \(-0.340379\pi\)
−0.519044 + 0.854748i \(0.673712\pi\)
\(54\) 0 0
\(55\) 120.127i 0.294507i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 299.818 519.300i 0.661576 1.14588i −0.318625 0.947881i \(-0.603221\pi\)
0.980201 0.198003i \(-0.0634455\pi\)
\(60\) 0 0
\(61\) 459.882 265.513i 0.965276 0.557302i 0.0674831 0.997720i \(-0.478503\pi\)
0.897793 + 0.440418i \(0.145170\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 37.3586 21.5690i 0.0712888 0.0411586i
\(66\) 0 0
\(67\) −325.105 + 563.098i −0.592804 + 1.02677i 0.401048 + 0.916057i \(0.368646\pi\)
−0.993853 + 0.110710i \(0.964687\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 934.128i 1.56142i −0.624896 0.780708i \(-0.714858\pi\)
0.624896 0.780708i \(-0.285142\pi\)
\(72\) 0 0
\(73\) 787.145 + 454.458i 1.26203 + 0.728634i 0.973467 0.228826i \(-0.0734887\pi\)
0.288564 + 0.957460i \(0.406822\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 704.683 + 101.449i 1.04294 + 0.150145i
\(78\) 0 0
\(79\) 397.516 + 688.517i 0.566127 + 0.980560i 0.996944 + 0.0781211i \(0.0248921\pi\)
−0.430817 + 0.902439i \(0.641775\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −314.865 −0.416397 −0.208199 0.978087i \(-0.566760\pi\)
−0.208199 + 0.978087i \(0.566760\pi\)
\(84\) 0 0
\(85\) 297.378 0.379472
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 179.521 + 310.940i 0.213811 + 0.370332i 0.952904 0.303271i \(-0.0980789\pi\)
−0.739093 + 0.673604i \(0.764746\pi\)
\(90\) 0 0
\(91\) −94.9775 237.368i −0.109410 0.273438i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 30.8341 + 17.8021i 0.0333001 + 0.0192258i
\(96\) 0 0
\(97\) 80.5572i 0.0843231i 0.999111 + 0.0421616i \(0.0134244\pi\)
−0.999111 + 0.0421616i \(0.986576\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 434.184 752.028i 0.427752 0.740887i −0.568921 0.822392i \(-0.692639\pi\)
0.996673 + 0.0815045i \(0.0259725\pi\)
\(102\) 0 0
\(103\) −104.861 + 60.5413i −0.100313 + 0.0579157i −0.549317 0.835614i \(-0.685112\pi\)
0.449004 + 0.893530i \(0.351779\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 387.751 223.868i 0.350330 0.202263i −0.314501 0.949257i \(-0.601837\pi\)
0.664830 + 0.746994i \(0.268504\pi\)
\(108\) 0 0
\(109\) 507.544 879.092i 0.445999 0.772493i −0.552122 0.833763i \(-0.686182\pi\)
0.998121 + 0.0612702i \(0.0195151\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 889.812i 0.740765i −0.928879 0.370382i \(-0.879227\pi\)
0.928879 0.370382i \(-0.120773\pi\)
\(114\) 0 0
\(115\) 74.9954 + 43.2986i 0.0608118 + 0.0351097i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 251.141 1744.47i 0.193463 1.34382i
\(120\) 0 0
\(121\) 73.3769 + 127.093i 0.0551292 + 0.0954865i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −750.713 −0.537167
\(126\) 0 0
\(127\) −279.668 −0.195406 −0.0977029 0.995216i \(-0.531149\pi\)
−0.0977029 + 0.995216i \(0.531149\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 81.4798 + 141.127i 0.0543429 + 0.0941247i 0.891917 0.452199i \(-0.149360\pi\)
−0.837574 + 0.546324i \(0.816027\pi\)
\(132\) 0 0
\(133\) 130.470 165.844i 0.0850615 0.108124i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1004.98 + 580.224i 0.626723 + 0.361839i 0.779482 0.626425i \(-0.215482\pi\)
−0.152759 + 0.988263i \(0.548816\pi\)
\(138\) 0 0
\(139\) 674.863i 0.411807i 0.978572 + 0.205903i \(0.0660133\pi\)
−0.978572 + 0.205903i \(0.933987\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 265.334 459.573i 0.155163 0.268751i
\(144\) 0 0
\(145\) −119.702 + 69.1101i −0.0685568 + 0.0395813i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1230.83 710.619i 0.676734 0.390713i −0.121889 0.992544i \(-0.538895\pi\)
0.798623 + 0.601831i \(0.205562\pi\)
\(150\) 0 0
\(151\) 1280.08 2217.16i 0.689875 1.19490i −0.282003 0.959413i \(-0.590999\pi\)
0.971878 0.235485i \(-0.0756678\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 429.930i 0.222792i
\(156\) 0 0
\(157\) 1292.26 + 746.085i 0.656901 + 0.379262i 0.791095 0.611693i \(-0.209511\pi\)
−0.134194 + 0.990955i \(0.542845\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 317.332 403.369i 0.155337 0.197453i
\(162\) 0 0
\(163\) 1068.87 + 1851.34i 0.513623 + 0.889622i 0.999875 + 0.0158029i \(0.00503043\pi\)
−0.486252 + 0.873819i \(0.661636\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1154.81 0.535103 0.267552 0.963544i \(-0.413785\pi\)
0.267552 + 0.963544i \(0.413785\pi\)
\(168\) 0 0
\(169\) 2006.43 0.913261
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1881.14 3258.23i −0.826707 1.43190i −0.900608 0.434633i \(-0.856878\pi\)
0.0739006 0.997266i \(-0.476455\pi\)
\(174\) 0 0
\(175\) −304.110 + 2112.40i −0.131363 + 0.912472i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 331.662 + 191.485i 0.138489 + 0.0799568i 0.567644 0.823274i \(-0.307855\pi\)
−0.429155 + 0.903231i \(0.641188\pi\)
\(180\) 0 0
\(181\) 2689.85i 1.10461i 0.833641 + 0.552307i \(0.186252\pi\)
−0.833641 + 0.552307i \(0.813748\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 220.816 382.465i 0.0877553 0.151997i
\(186\) 0 0
\(187\) 3168.12 1829.12i 1.23891 0.715285i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 634.579 366.374i 0.240401 0.138795i −0.374960 0.927041i \(-0.622344\pi\)
0.615361 + 0.788246i \(0.289010\pi\)
\(192\) 0 0
\(193\) −2102.20 + 3641.11i −0.784039 + 1.35800i 0.145532 + 0.989354i \(0.453511\pi\)
−0.929571 + 0.368642i \(0.879823\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2837.28i 1.02613i −0.858349 0.513066i \(-0.828510\pi\)
0.858349 0.513066i \(-0.171490\pi\)
\(198\) 0 0
\(199\) 1256.70 + 725.558i 0.447665 + 0.258459i 0.706843 0.707370i \(-0.250119\pi\)
−0.259179 + 0.965829i \(0.583452\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 304.321 + 760.559i 0.105217 + 0.262959i
\(204\) 0 0
\(205\) −528.027 914.569i −0.179897 0.311591i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 437.989 0.144959
\(210\) 0 0
\(211\) 5902.14 1.92569 0.962844 0.270058i \(-0.0870430\pi\)
0.962844 + 0.270058i \(0.0870430\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 652.342 + 1129.89i 0.206927 + 0.358408i
\(216\) 0 0
\(217\) −2522.04 363.084i −0.788974 0.113584i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1137.69 656.845i −0.346286 0.199928i
\(222\) 0 0
\(223\) 1445.01i 0.433925i −0.976180 0.216962i \(-0.930385\pi\)
0.976180 0.216962i \(-0.0696149\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2754.73 4771.33i 0.805453 1.39509i −0.110532 0.993873i \(-0.535255\pi\)
0.915985 0.401213i \(-0.131411\pi\)
\(228\) 0 0
\(229\) −4147.74 + 2394.70i −1.19690 + 0.691032i −0.959863 0.280468i \(-0.909510\pi\)
−0.237039 + 0.971500i \(0.576177\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3268.04 1886.80i 0.918868 0.530509i 0.0355944 0.999366i \(-0.488668\pi\)
0.883274 + 0.468857i \(0.155334\pi\)
\(234\) 0 0
\(235\) −453.247 + 785.046i −0.125815 + 0.217918i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1246.09i 0.337250i 0.985680 + 0.168625i \(0.0539326\pi\)
−0.985680 + 0.168625i \(0.946067\pi\)
\(240\) 0 0
\(241\) 821.731 + 474.426i 0.219636 + 0.126807i 0.605782 0.795631i \(-0.292860\pi\)
−0.386146 + 0.922438i \(0.626194\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1028.32 302.348i −0.268150 0.0788421i
\(246\) 0 0
\(247\) −78.6421 136.212i −0.0202586 0.0350889i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1494.83 0.375908 0.187954 0.982178i \(-0.439814\pi\)
0.187954 + 0.982178i \(0.439814\pi\)
\(252\) 0 0
\(253\) 1065.29 0.264720
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1762.12 3052.09i −0.427697 0.740794i 0.568971 0.822358i \(-0.307342\pi\)
−0.996668 + 0.0815642i \(0.974008\pi\)
\(258\) 0 0
\(259\) −2057.12 1618.34i −0.493526 0.388259i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5514.20 + 3183.62i 1.29285 + 0.746428i 0.979159 0.203096i \(-0.0651004\pi\)
0.313693 + 0.949524i \(0.398434\pi\)
\(264\) 0 0
\(265\) 53.3688i 0.0123714i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1738.97 3011.98i 0.394152 0.682690i −0.598841 0.800868i \(-0.704372\pi\)
0.992992 + 0.118178i \(0.0377052\pi\)
\(270\) 0 0
\(271\) 4121.15 2379.35i 0.923772 0.533340i 0.0389354 0.999242i \(-0.487603\pi\)
0.884836 + 0.465902i \(0.154270\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3836.33 + 2214.91i −0.841234 + 0.485687i
\(276\) 0 0
\(277\) 1117.86 1936.19i 0.242476 0.419980i −0.718943 0.695069i \(-0.755374\pi\)
0.961419 + 0.275089i \(0.0887073\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8109.09i 1.72152i 0.509008 + 0.860762i \(0.330012\pi\)
−0.509008 + 0.860762i \(0.669988\pi\)
\(282\) 0 0
\(283\) −2858.65 1650.44i −0.600456 0.346673i 0.168765 0.985656i \(-0.446022\pi\)
−0.769221 + 0.638983i \(0.779355\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5810.94 + 2325.12i −1.19515 + 0.478215i
\(288\) 0 0
\(289\) −2071.55 3588.02i −0.421646 0.730312i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3129.58 −0.624001 −0.312001 0.950082i \(-0.600999\pi\)
−0.312001 + 0.950082i \(0.600999\pi\)
\(294\) 0 0
\(295\) −1873.81 −0.369822
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −191.275 331.298i −0.0369958 0.0640785i
\(300\) 0 0
\(301\) 7179.04 2872.54i 1.37473 0.550067i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1437.09 829.705i −0.269795 0.155766i
\(306\) 0 0
\(307\) 9190.88i 1.70864i −0.519751 0.854318i \(-0.673975\pi\)
0.519751 0.854318i \(-0.326025\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −953.133 + 1650.88i −0.173785 + 0.301005i −0.939740 0.341889i \(-0.888933\pi\)
0.765955 + 0.642894i \(0.222267\pi\)
\(312\) 0 0
\(313\) −8295.18 + 4789.22i −1.49799 + 0.864866i −0.999997 0.00231512i \(-0.999263\pi\)
−0.497994 + 0.867181i \(0.665930\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2310.11 + 1333.74i −0.409301 + 0.236310i −0.690489 0.723342i \(-0.742605\pi\)
0.281188 + 0.959653i \(0.409271\pi\)
\(318\) 0 0
\(319\) −850.168 + 1472.53i −0.149217 + 0.258452i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1084.26i 0.186779i
\(324\) 0 0
\(325\) 1377.64 + 795.384i 0.235132 + 0.135754i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4222.44 + 3321.81i 0.707570 + 0.556648i
\(330\) 0 0
\(331\) 3959.19 + 6857.53i 0.657453 + 1.13874i 0.981273 + 0.192624i \(0.0616996\pi\)
−0.323819 + 0.946119i \(0.604967\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2031.85 0.331379
\(336\) 0 0
\(337\) −5173.45 −0.836248 −0.418124 0.908390i \(-0.637312\pi\)
−0.418124 + 0.908390i \(0.637312\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2644.42 4580.28i −0.419952 0.727378i
\(342\) 0 0
\(343\) −2642.06 + 5776.95i −0.415912 + 0.909405i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −346.881 200.272i −0.0536644 0.0309831i 0.472928 0.881101i \(-0.343197\pi\)
−0.526592 + 0.850118i \(0.676530\pi\)
\(348\) 0 0
\(349\) 6360.10i 0.975496i −0.872984 0.487748i \(-0.837818\pi\)
0.872984 0.487748i \(-0.162182\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6154.02 + 10659.1i −0.927891 + 1.60715i −0.141047 + 0.990003i \(0.545047\pi\)
−0.786844 + 0.617152i \(0.788286\pi\)
\(354\) 0 0
\(355\) −2527.99 + 1459.53i −0.377948 + 0.218209i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7649.34 + 4416.35i −1.12456 + 0.649264i −0.942561 0.334035i \(-0.891590\pi\)
−0.181998 + 0.983299i \(0.558256\pi\)
\(360\) 0 0
\(361\) −3364.59 + 5827.65i −0.490537 + 0.849635i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2840.28i 0.407308i
\(366\) 0 0
\(367\) −3655.01 2110.22i −0.519864 0.300144i 0.217015 0.976168i \(-0.430368\pi\)
−0.736879 + 0.676025i \(0.763701\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 313.070 + 45.0709i 0.0438108 + 0.00630718i
\(372\) 0 0
\(373\) −2165.80 3751.28i −0.300646 0.520734i 0.675637 0.737235i \(-0.263869\pi\)
−0.976282 + 0.216501i \(0.930536\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 610.599 0.0834150
\(378\) 0 0
\(379\) −9160.86 −1.24159 −0.620794 0.783974i \(-0.713190\pi\)
−0.620794 + 0.783974i \(0.713190\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 382.423 + 662.376i 0.0510206 + 0.0883703i 0.890408 0.455164i \(-0.150419\pi\)
−0.839387 + 0.543534i \(0.817086\pi\)
\(384\) 0 0
\(385\) −826.489 2065.56i −0.109407 0.273430i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5806.30 + 3352.27i 0.756789 + 0.436932i 0.828142 0.560519i \(-0.189398\pi\)
−0.0713526 + 0.997451i \(0.522732\pi\)
\(390\) 0 0
\(391\) 2637.16i 0.341092i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1242.20 2151.56i 0.158233 0.274067i
\(396\) 0 0
\(397\) 4026.96 2324.97i 0.509087 0.293921i −0.223371 0.974733i \(-0.571706\pi\)
0.732458 + 0.680812i \(0.238373\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3072.03 1773.64i 0.382568 0.220876i −0.296367 0.955074i \(-0.595775\pi\)
0.678935 + 0.734198i \(0.262442\pi\)
\(402\) 0 0
\(403\) −949.626 + 1644.80i −0.117380 + 0.203309i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5432.80i 0.661656i
\(408\) 0 0
\(409\) 11353.0 + 6554.64i 1.37254 + 0.792436i 0.991247 0.132019i \(-0.0421460\pi\)
0.381292 + 0.924455i \(0.375479\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1582.47 + 10992.1i −0.188543 + 1.30965i
\(414\) 0 0
\(415\) 491.963 + 852.106i 0.0581916 + 0.100791i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5937.56 −0.692288 −0.346144 0.938181i \(-0.612509\pi\)
−0.346144 + 0.938181i \(0.612509\pi\)
\(420\) 0 0
\(421\) 12210.2 1.41351 0.706757 0.707456i \(-0.250157\pi\)
0.706757 + 0.707456i \(0.250157\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5483.08 + 9496.97i 0.625808 + 1.08393i
\(426\) 0 0
\(427\) −6080.84 + 7729.52i −0.689162 + 0.876013i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2782.80 1606.65i −0.311004 0.179558i 0.336372 0.941729i \(-0.390800\pi\)
−0.647376 + 0.762171i \(0.724134\pi\)
\(432\) 0 0
\(433\) 6616.31i 0.734318i −0.930158 0.367159i \(-0.880331\pi\)
0.930158 0.367159i \(-0.119669\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 157.870 273.438i 0.0172813 0.0299321i
\(438\) 0 0
\(439\) 2084.48 1203.48i 0.226622 0.130840i −0.382391 0.924001i \(-0.624899\pi\)
0.609013 + 0.793161i \(0.291566\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9059.31 + 5230.40i −0.971605 + 0.560956i −0.899725 0.436457i \(-0.856233\pi\)
−0.0718798 + 0.997413i \(0.522900\pi\)
\(444\) 0 0
\(445\) 560.988 971.660i 0.0597604 0.103508i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7633.63i 0.802346i 0.916002 + 0.401173i \(0.131397\pi\)
−0.916002 + 0.401173i \(0.868603\pi\)
\(450\) 0 0
\(451\) −11250.7 6495.59i −1.17467 0.678194i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −493.979 + 627.910i −0.0508969 + 0.0646964i
\(456\) 0 0
\(457\) −7723.99 13378.3i −0.790620 1.36939i −0.925584 0.378543i \(-0.876425\pi\)
0.134964 0.990850i \(-0.456908\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19428.0 −1.96280 −0.981401 0.191970i \(-0.938512\pi\)
−0.981401 + 0.191970i \(0.938512\pi\)
\(462\) 0 0
\(463\) −8196.41 −0.822720 −0.411360 0.911473i \(-0.634946\pi\)
−0.411360 + 0.911473i \(0.634946\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7344.66 + 12721.3i 0.727774 + 1.26054i 0.957822 + 0.287362i \(0.0927784\pi\)
−0.230048 + 0.973179i \(0.573888\pi\)
\(468\) 0 0
\(469\) 1715.93 11919.2i 0.168943 1.17351i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 13899.5 + 8024.88i 1.35116 + 0.780093i
\(474\) 0 0
\(475\) 1312.95i 0.126825i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8549.24 14807.7i 0.815500 1.41249i −0.0934678 0.995622i \(-0.529795\pi\)
0.908968 0.416866i \(-0.136871\pi\)
\(480\) 0 0
\(481\) −1689.57 + 975.473i −0.160162 + 0.0924693i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 218.008 125.867i 0.0204108 0.0117842i
\(486\) 0 0
\(487\) −2428.25 + 4205.85i −0.225944 + 0.391346i −0.956602 0.291397i \(-0.905880\pi\)
0.730659 + 0.682743i \(0.239213\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3844.24i 0.353336i 0.984270 + 0.176668i \(0.0565320\pi\)
−0.984270 + 0.176668i \(0.943468\pi\)
\(492\) 0 0
\(493\) 3645.31 + 2104.62i 0.333016 + 0.192267i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6426.94 + 16062.2i 0.580056 + 1.44967i
\(498\) 0 0
\(499\) 2307.84 + 3997.30i 0.207041 + 0.358605i 0.950781 0.309864i \(-0.100283\pi\)
−0.743740 + 0.668469i \(0.766950\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11692.2 −1.03644 −0.518219 0.855248i \(-0.673405\pi\)
−0.518219 + 0.855248i \(0.673405\pi\)
\(504\) 0 0
\(505\) −2713.57 −0.239114
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10752.4 18623.7i −0.936327 1.62177i −0.772250 0.635319i \(-0.780869\pi\)
−0.164077 0.986447i \(-0.552465\pi\)
\(510\) 0 0
\(511\) −16661.6 2398.67i −1.44240 0.207654i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 327.680 + 189.186i 0.0280375 + 0.0161875i
\(516\) 0 0
\(517\) 11151.4i 0.948619i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −184.719 + 319.942i −0.0155330 + 0.0269039i −0.873687 0.486488i \(-0.838278\pi\)
0.858154 + 0.513392i \(0.171611\pi\)
\(522\) 0 0
\(523\) 13219.0 7631.98i 1.10521 0.638094i 0.167626 0.985851i \(-0.446390\pi\)
0.937585 + 0.347757i \(0.113057\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11338.6 + 6546.37i −0.937228 + 0.541109i
\(528\) 0 0
\(529\) −5699.53 + 9871.87i −0.468441 + 0.811364i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4665.20i 0.379122i
\(534\) 0 0
\(535\) −1211.69 699.568i −0.0979173 0.0565326i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −12814.9 + 3103.92i −1.02408 + 0.248043i
\(540\) 0 0
\(541\) −8163.08 14138.9i −0.648721 1.12362i −0.983429 0.181296i \(-0.941971\pi\)
0.334707 0.942322i \(-0.391363\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3172.06 −0.249314
\(546\) 0 0
\(547\) −13065.7 −1.02130 −0.510649 0.859789i \(-0.670595\pi\)
−0.510649 + 0.859789i \(0.670595\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 251.980 + 436.442i 0.0194822 + 0.0337442i
\(552\) 0 0
\(553\) −11572.3 9104.00i −0.889884 0.700075i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9145.80 5280.33i −0.695727 0.401678i 0.110027 0.993929i \(-0.464906\pi\)
−0.805754 + 0.592250i \(0.798240\pi\)
\(558\) 0 0
\(559\) 5763.55i 0.436086i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6474.13 + 11213.5i −0.484640 + 0.839420i −0.999844 0.0176468i \(-0.994383\pi\)
0.515205 + 0.857067i \(0.327716\pi\)
\(564\) 0 0
\(565\) −2408.06 + 1390.29i −0.179306 + 0.103522i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12555.1 + 7248.69i −0.925021 + 0.534061i −0.885233 0.465147i \(-0.846001\pi\)
−0.0397876 + 0.999208i \(0.512668\pi\)
\(570\) 0 0
\(571\) −1966.46 + 3406.00i −0.144122 + 0.249626i −0.929045 0.369967i \(-0.879369\pi\)
0.784923 + 0.619593i \(0.212702\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3193.38i 0.231605i
\(576\) 0 0
\(577\) 7970.48 + 4601.76i 0.575070 + 0.332017i 0.759172 0.650890i \(-0.225604\pi\)
−0.184101 + 0.982907i \(0.558938\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5414.07 2166.32i 0.386598 0.154689i
\(582\) 0 0
\(583\) 328.262 + 568.566i 0.0233194 + 0.0403904i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4778.34 0.335985 0.167992 0.985788i \(-0.446272\pi\)
0.167992 + 0.985788i \(0.446272\pi\)
\(588\) 0 0
\(589\) −1567.55 −0.109660
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7388.21 + 12796.8i 0.511631 + 0.886172i 0.999909 + 0.0134834i \(0.00429202\pi\)
−0.488278 + 0.872688i \(0.662375\pi\)
\(594\) 0 0
\(595\) −5113.37 + 2046.00i −0.352315 + 0.140971i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20384.4 + 11769.0i 1.39046 + 0.802783i 0.993366 0.114995i \(-0.0366852\pi\)
0.397094 + 0.917778i \(0.370019\pi\)
\(600\) 0 0
\(601\) 13020.6i 0.883727i 0.897082 + 0.441864i \(0.145682\pi\)
−0.897082 + 0.441864i \(0.854318\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 229.296 397.153i 0.0154086 0.0266885i
\(606\) 0 0
\(607\) 15450.9 8920.59i 1.03317 0.596500i 0.115278 0.993333i \(-0.463224\pi\)
0.917891 + 0.396833i \(0.129891\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3468.01 2002.25i 0.229624 0.132574i
\(612\) 0 0
\(613\) 8589.91 14878.2i 0.565976 0.980299i −0.430982 0.902361i \(-0.641833\pi\)
0.996958 0.0779389i \(-0.0248339\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7147.22i 0.466347i 0.972435 + 0.233174i \(0.0749111\pi\)
−0.972435 + 0.233174i \(0.925089\pi\)
\(618\) 0 0
\(619\) 5170.09 + 2984.95i 0.335708 + 0.193821i 0.658373 0.752692i \(-0.271245\pi\)
−0.322664 + 0.946514i \(0.604578\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5226.16 4111.44i −0.336086 0.264400i
\(624\) 0 0
\(625\) −6029.23 10442.9i −0.385870 0.668347i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13449.1 −0.852545
\(630\) 0 0
\(631\) 15148.2 0.955693 0.477846 0.878443i \(-0.341418\pi\)
0.477846 + 0.878443i \(0.341418\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 436.969 + 756.853i 0.0273080 + 0.0472989i
\(636\) 0 0
\(637\) 3266.25 + 3428.04i 0.203161 + 0.213225i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4316.39 + 2492.07i 0.265971 + 0.153558i 0.627055 0.778975i \(-0.284260\pi\)
−0.361085 + 0.932533i \(0.617593\pi\)
\(642\) 0 0
\(643\) 6255.66i 0.383669i −0.981427 0.191834i \(-0.938556\pi\)
0.981427 0.191834i \(-0.0614436\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12254.3 21225.1i 0.744618 1.28972i −0.205755 0.978603i \(-0.565965\pi\)
0.950373 0.311112i \(-0.100702\pi\)
\(648\) 0 0
\(649\) −19962.7 + 11525.5i −1.20740 + 0.697095i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26910.6 15536.8i 1.61270 0.931093i 0.623959 0.781457i \(-0.285523\pi\)
0.988741 0.149636i \(-0.0478101\pi\)
\(654\) 0 0
\(655\) 254.617 441.010i 0.0151889 0.0263079i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13489.0i 0.797357i −0.917091 0.398678i \(-0.869469\pi\)
0.917091 0.398678i \(-0.130531\pi\)
\(660\) 0 0
\(661\) 16896.0 + 9754.92i 0.994219 + 0.574013i 0.906533 0.422135i \(-0.138719\pi\)
0.0876864 + 0.996148i \(0.472053\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −652.669 93.9609i −0.0380593 0.00547917i
\(666\) 0 0
\(667\) 612.872 + 1061.53i 0.0355780 + 0.0616229i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −20413.5 −1.17445
\(672\) 0 0
\(673\) −7967.95 −0.456377 −0.228189 0.973617i \(-0.573280\pi\)
−0.228189 + 0.973617i \(0.573280\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13315.2 23062.5i −0.755898 1.30925i −0.944926 0.327283i \(-0.893867\pi\)
0.189028 0.981972i \(-0.439466\pi\)
\(678\) 0 0
\(679\) −554.246 1385.17i −0.0313255 0.0782886i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26596.3 + 15355.4i 1.49001 + 0.860259i 0.999935 0.0114194i \(-0.00363498\pi\)
0.490078 + 0.871679i \(0.336968\pi\)
\(684\) 0 0
\(685\) 3626.30i 0.202268i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 117.881 204.175i 0.00651798 0.0112895i
\(690\) 0 0
\(691\) 25217.6 14559.4i 1.38831 0.801541i 0.395185 0.918602i \(-0.370680\pi\)
0.993125 + 0.117061i \(0.0373471\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1826.35 1054.44i 0.0996798 0.0575502i
\(696\) 0 0
\(697\) −16080.1 + 27851.5i −0.873854 + 1.51356i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30038.9i 1.61848i −0.587480 0.809239i \(-0.699880\pi\)
0.587480 0.809239i \(-0.300120\pi\)
\(702\) 0 0
\(703\) −1394.49 805.110i −0.0748140 0.0431939i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2291.66 + 15918.3i −0.121905 + 0.846773i
\(708\) 0 0
\(709\) −4914.07 8511.42i −0.260299 0.450851i 0.706023 0.708189i \(-0.250488\pi\)
−0.966321 + 0.257339i \(0.917154\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3812.64 −0.200259
\(714\) 0 0
\(715\) −1658.29 −0.0867366
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12838.1 + 22236.2i 0.665897 + 1.15337i 0.979041 + 0.203662i \(0.0652843\pi\)
−0.313144 + 0.949706i \(0.601382\pi\)
\(720\) 0 0
\(721\) 1386.53 1762.46i 0.0716188 0.0910366i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4414.17 2548.52i −0.226121 0.130551i
\(726\) 0 0
\(727\) 9770.68i 0.498452i −0.968445 0.249226i \(-0.919824\pi\)
0.968445 0.249226i \(-0.0801761\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19865.9 34408.7i 1.00515 1.74097i
\(732\) 0 0
\(733\) 1265.95 730.896i 0.0637912 0.0368298i −0.467765 0.883853i \(-0.654941\pi\)
0.531556 + 0.847023i \(0.321607\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21646.4 12497.5i 1.08189 0.624631i
\(738\) 0 0
\(739\) 6722.13 11643.1i 0.334611 0.579563i −0.648799 0.760960i \(-0.724728\pi\)
0.983410 + 0.181397i \(0.0580618\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13757.2i 0.679278i 0.940556 + 0.339639i \(0.110305\pi\)
−0.940556 + 0.339639i \(0.889695\pi\)
\(744\) 0 0
\(745\) −3846.23 2220.62i −0.189148 0.109204i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5127.07 + 6517.16i −0.250119 + 0.317933i
\(750\) 0 0
\(751\) 14594.6 + 25278.6i 0.709142 + 1.22827i 0.965176 + 0.261602i \(0.0842508\pi\)
−0.256034 + 0.966668i \(0.582416\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8000.25 −0.385641
\(756\) 0 0
\(757\) 8236.25 0.395445 0.197722 0.980258i \(-0.436646\pi\)
0.197722 + 0.980258i \(0.436646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16521.8 28616.6i −0.787011 1.36314i −0.927790 0.373102i \(-0.878294\pi\)
0.140779 0.990041i \(-0.455039\pi\)
\(762\) 0 0
\(763\) −2678.86 + 18607.9i −0.127105 + 0.882896i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7168.71 + 4138.86i 0.337480 + 0.194844i
\(768\) 0 0
\(769\) 23591.7i 1.10629i 0.833084 + 0.553146i \(0.186573\pi\)
−0.833084 + 0.553146i \(0.813427\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15883.6 27511.2i 0.739060 1.28009i −0.213858 0.976865i \(-0.568603\pi\)
0.952919 0.303225i \(-0.0980635\pi\)
\(774\) 0 0
\(775\) 13730.1 7927.10i 0.636388 0.367419i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3334.58 + 1925.22i −0.153368 + 0.0885471i
\(780\) 0 0
\(781\) −17954.7 + 31098.4i −0.822623 + 1.42482i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4662.90i 0.212008i
\(786\) 0 0
\(787\) 34978.6 + 20194.9i 1.58431 + 0.914702i 0.994220 + 0.107366i \(0.0342417\pi\)
0.590092 + 0.807336i \(0.299092\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6122.04 + 15300.2i 0.275189 + 0.687752i
\(792\) 0 0
\(793\) 3665.29 + 6348.46i 0.164134 + 0.284288i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14289.7 −0.635092 −0.317546 0.948243i \(-0.602859\pi\)
−0.317546 + 0.948243i \(0.602859\pi\)
\(798\) 0 0
\(799\) 27605.6 1.22230
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −17470.1 30259.1i −0.767753