Properties

Label 1008.4.bt.d.17.5
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 17.5
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.29543 - 12.6361i) q^{5} +(-18.4933 - 0.998739i) q^{7} +O(q^{10})\) \(q+(-7.29543 - 12.6361i) q^{5} +(-18.4933 - 0.998739i) q^{7} +(-38.7318 - 22.3618i) q^{11} -76.8588i q^{13} +(-58.3464 + 101.059i) q^{17} +(-83.5432 + 48.2337i) q^{19} +(6.88438 - 3.97470i) q^{23} +(-43.9467 + 76.1180i) q^{25} -86.8540i q^{29} +(-216.262 - 124.859i) q^{31} +(122.297 + 240.969i) q^{35} +(-160.031 - 277.182i) q^{37} +231.290 q^{41} +413.282 q^{43} +(235.508 + 407.911i) q^{47} +(341.005 + 36.9400i) q^{49} +(-600.339 - 346.606i) q^{53} +652.557i q^{55} +(143.802 - 249.072i) q^{59} +(740.898 - 427.758i) q^{61} +(-971.193 + 560.718i) q^{65} +(-240.341 + 416.283i) q^{67} +930.276i q^{71} +(-98.4174 - 56.8213i) q^{73} +(693.946 + 452.227i) q^{77} +(-111.374 - 192.905i) q^{79} -692.424 q^{83} +1702.65 q^{85} +(258.667 + 448.025i) q^{89} +(-76.7619 + 1421.37i) q^{91} +(1218.97 + 703.771i) q^{95} -807.511i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

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
\(5\) −7.29543 12.6361i −0.652523 1.13020i −0.982509 0.186218i \(-0.940377\pi\)
0.329985 0.943986i \(-0.392956\pi\)
\(6\) 0 0
\(7\) −18.4933 0.998739i −0.998545 0.0539268i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −38.7318 22.3618i −1.06164 0.612940i −0.135757 0.990742i \(-0.543347\pi\)
−0.925886 + 0.377802i \(0.876680\pi\)
\(12\) 0 0
\(13\) 76.8588i 1.63975i −0.572540 0.819877i \(-0.694042\pi\)
0.572540 0.819877i \(-0.305958\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −58.3464 + 101.059i −0.832416 + 1.44179i 0.0637008 + 0.997969i \(0.479710\pi\)
−0.896117 + 0.443818i \(0.853624\pi\)
\(18\) 0 0
\(19\) −83.5432 + 48.2337i −1.00874 + 0.582398i −0.910823 0.412796i \(-0.864552\pi\)
−0.0979195 + 0.995194i \(0.531219\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.88438 3.97470i 0.0624127 0.0360340i −0.468469 0.883480i \(-0.655194\pi\)
0.530882 + 0.847446i \(0.321861\pi\)
\(24\) 0 0
\(25\) −43.9467 + 76.1180i −0.351574 + 0.608944i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 86.8540i 0.556151i −0.960559 0.278076i \(-0.910303\pi\)
0.960559 0.278076i \(-0.0896966\pi\)
\(30\) 0 0
\(31\) −216.262 124.859i −1.25296 0.723397i −0.281265 0.959630i \(-0.590754\pi\)
−0.971696 + 0.236233i \(0.924087\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 122.297 + 240.969i 0.590626 + 1.16375i
\(36\) 0 0
\(37\) −160.031 277.182i −0.711053 1.23158i −0.964462 0.264221i \(-0.914885\pi\)
0.253409 0.967359i \(-0.418448\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 231.290 0.881010 0.440505 0.897750i \(-0.354799\pi\)
0.440505 + 0.897750i \(0.354799\pi\)
\(42\) 0 0
\(43\) 413.282 1.46569 0.732847 0.680393i \(-0.238191\pi\)
0.732847 + 0.680393i \(0.238191\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 235.508 + 407.911i 0.730901 + 1.26596i 0.956499 + 0.291737i \(0.0942331\pi\)
−0.225598 + 0.974220i \(0.572434\pi\)
\(48\) 0 0
\(49\) 341.005 + 36.9400i 0.994184 + 0.107697i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −600.339 346.606i −1.55590 0.898301i −0.997642 0.0686360i \(-0.978135\pi\)
−0.558261 0.829665i \(-0.688531\pi\)
\(54\) 0 0
\(55\) 652.557i 1.59983i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 143.802 249.072i 0.317312 0.549600i −0.662615 0.748961i \(-0.730553\pi\)
0.979926 + 0.199361i \(0.0638866\pi\)
\(60\) 0 0
\(61\) 740.898 427.758i 1.55512 0.897849i 0.557408 0.830238i \(-0.311796\pi\)
0.997712 0.0676105i \(-0.0215375\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −971.193 + 560.718i −1.85326 + 1.06998i
\(66\) 0 0
\(67\) −240.341 + 416.283i −0.438244 + 0.759061i −0.997554 0.0698977i \(-0.977733\pi\)
0.559310 + 0.828958i \(0.311066\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 930.276i 1.55498i 0.628897 + 0.777489i \(0.283507\pi\)
−0.628897 + 0.777489i \(0.716493\pi\)
\(72\) 0 0
\(73\) −98.4174 56.8213i −0.157793 0.0911018i 0.419024 0.907975i \(-0.362372\pi\)
−0.576817 + 0.816873i \(0.695706\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 693.946 + 452.227i 1.02704 + 0.669299i
\(78\) 0 0
\(79\) −111.374 192.905i −0.158614 0.274727i 0.775755 0.631034i \(-0.217369\pi\)
−0.934369 + 0.356307i \(0.884036\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −692.424 −0.915703 −0.457852 0.889029i \(-0.651381\pi\)
−0.457852 + 0.889029i \(0.651381\pi\)
\(84\) 0 0
\(85\) 1702.65 2.17268
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 258.667 + 448.025i 0.308075 + 0.533602i 0.977941 0.208880i \(-0.0669818\pi\)
−0.669866 + 0.742482i \(0.733648\pi\)
\(90\) 0 0
\(91\) −76.7619 + 1421.37i −0.0884267 + 1.63737i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1218.97 + 703.771i 1.31646 + 0.760057i
\(96\) 0 0
\(97\) 807.511i 0.845261i −0.906302 0.422630i \(-0.861107\pi\)
0.906302 0.422630i \(-0.138893\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 115.748 200.482i 0.114033 0.197511i −0.803360 0.595494i \(-0.796956\pi\)
0.917393 + 0.397983i \(0.130290\pi\)
\(102\) 0 0
\(103\) 1028.60 593.864i 0.983992 0.568108i 0.0805191 0.996753i \(-0.474342\pi\)
0.903473 + 0.428645i \(0.141009\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.77425 2.17906i 0.00341000 0.00196877i −0.498294 0.867008i \(-0.666040\pi\)
0.501704 + 0.865039i \(0.332707\pi\)
\(108\) 0 0
\(109\) −113.726 + 196.980i −0.0999360 + 0.173094i −0.911658 0.410950i \(-0.865197\pi\)
0.811722 + 0.584044i \(0.198530\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 517.680i 0.430967i −0.976507 0.215483i \(-0.930867\pi\)
0.976507 0.215483i \(-0.0691327\pi\)
\(114\) 0 0
\(115\) −100.449 57.9943i −0.0814515 0.0470261i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1179.95 1810.64i 0.908956 1.39480i
\(120\) 0 0
\(121\) 334.602 + 579.548i 0.251392 + 0.435423i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −541.417 −0.387406
\(126\) 0 0
\(127\) 1665.46 1.16367 0.581833 0.813308i \(-0.302336\pi\)
0.581833 + 0.813308i \(0.302336\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 342.534 + 593.286i 0.228453 + 0.395692i 0.957350 0.288931i \(-0.0932999\pi\)
−0.728897 + 0.684624i \(0.759967\pi\)
\(132\) 0 0
\(133\) 1593.16 808.562i 1.03868 0.527152i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 910.457 + 525.653i 0.567778 + 0.327807i 0.756261 0.654270i \(-0.227024\pi\)
−0.188483 + 0.982076i \(0.560357\pi\)
\(138\) 0 0
\(139\) 26.6372i 0.0162542i −0.999967 0.00812712i \(-0.997413\pi\)
0.999967 0.00812712i \(-0.00258697\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1718.70 + 2976.88i −1.00507 + 1.74083i
\(144\) 0 0
\(145\) −1097.49 + 633.638i −0.628564 + 0.362902i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1914.14 + 1105.13i −1.05243 + 0.607622i −0.923329 0.384010i \(-0.874543\pi\)
−0.129102 + 0.991631i \(0.541210\pi\)
\(150\) 0 0
\(151\) −958.101 + 1659.48i −0.516352 + 0.894348i 0.483468 + 0.875362i \(0.339377\pi\)
−0.999820 + 0.0189855i \(0.993956\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3643.60i 1.88814i
\(156\) 0 0
\(157\) 1859.51 + 1073.59i 0.945255 + 0.545743i 0.891604 0.452816i \(-0.149581\pi\)
0.0536515 + 0.998560i \(0.482914\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −131.285 + 66.6296i −0.0642651 + 0.0326159i
\(162\) 0 0
\(163\) −713.783 1236.31i −0.342993 0.594081i 0.641994 0.766710i \(-0.278107\pi\)
−0.984987 + 0.172628i \(0.944774\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −558.327 −0.258710 −0.129355 0.991598i \(-0.541291\pi\)
−0.129355 + 0.991598i \(0.541291\pi\)
\(168\) 0 0
\(169\) −3710.28 −1.68879
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 317.963 + 550.728i 0.139736 + 0.242029i 0.927397 0.374080i \(-0.122041\pi\)
−0.787661 + 0.616109i \(0.788708\pi\)
\(174\) 0 0
\(175\) 888.742 1363.78i 0.383901 0.589098i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1071.64 618.711i −0.447475 0.258350i 0.259288 0.965800i \(-0.416512\pi\)
−0.706763 + 0.707450i \(0.749845\pi\)
\(180\) 0 0
\(181\) 252.299i 0.103609i −0.998657 0.0518046i \(-0.983503\pi\)
0.998657 0.0518046i \(-0.0164973\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2334.99 + 4044.33i −0.927958 + 1.60727i
\(186\) 0 0
\(187\) 4519.72 2609.46i 1.76746 1.02044i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2004.84 + 1157.50i −0.759505 + 0.438500i −0.829118 0.559074i \(-0.811157\pi\)
0.0696131 + 0.997574i \(0.477824\pi\)
\(192\) 0 0
\(193\) −1128.33 + 1954.32i −0.420824 + 0.728888i −0.996020 0.0891273i \(-0.971592\pi\)
0.575197 + 0.818015i \(0.304926\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4940.41i 1.78675i 0.449312 + 0.893375i \(0.351669\pi\)
−0.449312 + 0.893375i \(0.648331\pi\)
\(198\) 0 0
\(199\) 505.394 + 291.789i 0.180032 + 0.103942i 0.587308 0.809364i \(-0.300188\pi\)
−0.407276 + 0.913305i \(0.633521\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −86.7445 + 1606.22i −0.0299915 + 0.555342i
\(204\) 0 0
\(205\) −1687.36 2922.59i −0.574879 0.995720i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4314.37 1.42790
\(210\) 0 0
\(211\) −3849.63 −1.25602 −0.628009 0.778206i \(-0.716130\pi\)
−0.628009 + 0.778206i \(0.716130\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3015.07 5222.25i −0.956400 1.65653i
\(216\) 0 0
\(217\) 3874.70 + 2525.04i 1.21213 + 0.789913i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7767.27 + 4484.43i 2.36418 + 1.36496i
\(222\) 0 0
\(223\) 6244.17i 1.87507i −0.347889 0.937536i \(-0.613102\pi\)
0.347889 0.937536i \(-0.386898\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −703.572 + 1218.62i −0.205717 + 0.356312i −0.950361 0.311150i \(-0.899286\pi\)
0.744644 + 0.667462i \(0.232619\pi\)
\(228\) 0 0
\(229\) 2122.90 1225.66i 0.612600 0.353685i −0.161382 0.986892i \(-0.551595\pi\)
0.773982 + 0.633207i \(0.218262\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2021.13 + 1166.90i −0.568278 + 0.328095i −0.756461 0.654039i \(-0.773073\pi\)
0.188184 + 0.982134i \(0.439740\pi\)
\(234\) 0 0
\(235\) 3436.26 5951.78i 0.953860 1.65213i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1158.54i 0.313555i −0.987634 0.156778i \(-0.949889\pi\)
0.987634 0.156778i \(-0.0501106\pi\)
\(240\) 0 0
\(241\) 2667.43 + 1540.04i 0.712964 + 0.411630i 0.812158 0.583438i \(-0.198293\pi\)
−0.0991935 + 0.995068i \(0.531626\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2021.00 4578.45i −0.527009 1.19390i
\(246\) 0 0
\(247\) 3707.18 + 6421.03i 0.954989 + 1.65409i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1292.55 0.325039 0.162520 0.986705i \(-0.448038\pi\)
0.162520 + 0.986705i \(0.448038\pi\)
\(252\) 0 0
\(253\) −355.526 −0.0883468
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −393.202 681.045i −0.0954368 0.165301i 0.814354 0.580368i \(-0.197091\pi\)
−0.909791 + 0.415067i \(0.863758\pi\)
\(258\) 0 0
\(259\) 2682.67 + 5285.85i 0.643603 + 1.26813i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3353.52 + 1936.16i 0.786262 + 0.453948i 0.838645 0.544679i \(-0.183348\pi\)
−0.0523831 + 0.998627i \(0.516682\pi\)
\(264\) 0 0
\(265\) 10114.6i 2.34465i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1629.53 2822.43i 0.369347 0.639727i −0.620117 0.784510i \(-0.712915\pi\)
0.989464 + 0.144782i \(0.0462481\pi\)
\(270\) 0 0
\(271\) 2607.80 1505.61i 0.584548 0.337489i −0.178391 0.983960i \(-0.557089\pi\)
0.762939 + 0.646471i \(0.223756\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3404.27 1965.46i 0.746492 0.430987i
\(276\) 0 0
\(277\) −2955.86 + 5119.70i −0.641157 + 1.11052i 0.344018 + 0.938963i \(0.388212\pi\)
−0.985175 + 0.171553i \(0.945122\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 594.162i 0.126138i −0.998009 0.0630690i \(-0.979911\pi\)
0.998009 0.0630690i \(-0.0200888\pi\)
\(282\) 0 0
\(283\) 1858.80 + 1073.18i 0.390440 + 0.225420i 0.682351 0.731025i \(-0.260958\pi\)
−0.291911 + 0.956446i \(0.594291\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4277.31 230.998i −0.879728 0.0475101i
\(288\) 0 0
\(289\) −4352.10 7538.06i −0.885833 1.53431i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3508.37 0.699527 0.349763 0.936838i \(-0.386262\pi\)
0.349763 + 0.936838i \(0.386262\pi\)
\(294\) 0 0
\(295\) −4196.38 −0.828213
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −305.491 529.125i −0.0590869 0.102341i
\(300\) 0 0
\(301\) −7642.95 412.760i −1.46356 0.0790403i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10810.4 6241.36i −2.02950 1.17174i
\(306\) 0 0
\(307\) 3932.23i 0.731024i 0.930807 + 0.365512i \(0.119106\pi\)
−0.930807 + 0.365512i \(0.880894\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2383.96 + 4129.14i −0.434669 + 0.752868i −0.997269 0.0738611i \(-0.976468\pi\)
0.562600 + 0.826729i \(0.309801\pi\)
\(312\) 0 0
\(313\) −1322.49 + 763.537i −0.238822 + 0.137884i −0.614635 0.788811i \(-0.710697\pi\)
0.375813 + 0.926695i \(0.377363\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5430.41 3135.25i 0.962152 0.555499i 0.0653175 0.997865i \(-0.479194\pi\)
0.896835 + 0.442366i \(0.145861\pi\)
\(318\) 0 0
\(319\) −1942.21 + 3364.01i −0.340888 + 0.590435i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11257.0i 1.93919i
\(324\) 0 0
\(325\) 5850.34 + 3377.69i 0.998518 + 0.576494i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3947.92 7778.84i −0.661568 1.30353i
\(330\) 0 0
\(331\) −4010.93 6947.14i −0.666045 1.15362i −0.979001 0.203856i \(-0.934653\pi\)
0.312956 0.949768i \(-0.398681\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7013.57 1.14386
\(336\) 0 0
\(337\) 7526.55 1.21661 0.608305 0.793704i \(-0.291850\pi\)
0.608305 + 0.793704i \(0.291850\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5584.14 + 9672.02i 0.886799 + 1.53598i
\(342\) 0 0
\(343\) −6269.42 1023.72i −0.986929 0.161153i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9728.57 5616.79i −1.50506 0.868948i −0.999983 0.00587585i \(-0.998130\pi\)
−0.505080 0.863073i \(-0.668537\pi\)
\(348\) 0 0
\(349\) 88.0987i 0.0135124i 0.999977 + 0.00675618i \(0.00215058\pi\)
−0.999977 + 0.00675618i \(0.997849\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2911.54 5042.93i 0.438996 0.760363i −0.558616 0.829426i \(-0.688668\pi\)
0.997612 + 0.0690628i \(0.0220009\pi\)
\(354\) 0 0
\(355\) 11755.0 6786.77i 1.75744 1.01466i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3226.19 1862.64i 0.474295 0.273834i −0.243741 0.969840i \(-0.578375\pi\)
0.718036 + 0.696006i \(0.245041\pi\)
\(360\) 0 0
\(361\) 1223.47 2119.12i 0.178375 0.308954i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1658.14i 0.237784i
\(366\) 0 0
\(367\) −8554.28 4938.81i −1.21670 0.702463i −0.252491 0.967599i \(-0.581250\pi\)
−0.964211 + 0.265136i \(0.914583\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10756.1 + 7009.47i 1.50520 + 0.980899i
\(372\) 0 0
\(373\) −6764.39 11716.3i −0.938999 1.62639i −0.767342 0.641238i \(-0.778421\pi\)
−0.171657 0.985157i \(-0.554912\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6675.50 −0.911951
\(378\) 0 0
\(379\) −5023.35 −0.680824 −0.340412 0.940276i \(-0.610567\pi\)
−0.340412 + 0.940276i \(0.610567\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6925.52 11995.4i −0.923962 1.60035i −0.793222 0.608933i \(-0.791598\pi\)
−0.130741 0.991417i \(-0.541736\pi\)
\(384\) 0 0
\(385\) 651.734 12067.9i 0.0862739 1.59750i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3180.84 + 1836.46i 0.414589 + 0.239363i 0.692760 0.721169i \(-0.256395\pi\)
−0.278171 + 0.960532i \(0.589728\pi\)
\(390\) 0 0
\(391\) 927.637i 0.119981i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1625.04 + 2814.65i −0.206999 + 0.358532i
\(396\) 0 0
\(397\) −1790.92 + 1033.99i −0.226407 + 0.130716i −0.608913 0.793237i \(-0.708394\pi\)
0.382506 + 0.923953i \(0.375061\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2813.54 + 1624.40i −0.350377 + 0.202290i −0.664851 0.746976i \(-0.731505\pi\)
0.314474 + 0.949266i \(0.398172\pi\)
\(402\) 0 0
\(403\) −9596.51 + 16621.6i −1.18619 + 2.05455i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14314.4i 1.74333i
\(408\) 0 0
\(409\) −4769.99 2753.96i −0.576677 0.332945i 0.183135 0.983088i \(-0.441376\pi\)
−0.759812 + 0.650143i \(0.774709\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2908.13 + 4462.54i −0.346488 + 0.531688i
\(414\) 0 0
\(415\) 5051.53 + 8749.51i 0.597518 + 1.03493i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7281.32 0.848964 0.424482 0.905436i \(-0.360456\pi\)
0.424482 + 0.905436i \(0.360456\pi\)
\(420\) 0 0
\(421\) 1524.24 0.176453 0.0882265 0.996100i \(-0.471880\pi\)
0.0882265 + 0.996100i \(0.471880\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5128.26 8882.41i −0.585311 1.01379i
\(426\) 0 0
\(427\) −14128.9 + 7170.70i −1.60128 + 0.812680i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4465.09 2577.92i −0.499016 0.288107i 0.229291 0.973358i \(-0.426359\pi\)
−0.728307 + 0.685251i \(0.759692\pi\)
\(432\) 0 0
\(433\) 1041.23i 0.115562i 0.998329 + 0.0577811i \(0.0184026\pi\)
−0.998329 + 0.0577811i \(0.981597\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −383.429 + 664.118i −0.0419723 + 0.0726981i
\(438\) 0 0
\(439\) −4138.98 + 2389.64i −0.449983 + 0.259798i −0.707823 0.706390i \(-0.750323\pi\)
0.257840 + 0.966188i \(0.416989\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2397.66 + 1384.29i −0.257148 + 0.148464i −0.623033 0.782196i \(-0.714100\pi\)
0.365885 + 0.930660i \(0.380766\pi\)
\(444\) 0 0
\(445\) 3774.18 6537.08i 0.402053 0.696376i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14237.8i 1.49649i −0.663422 0.748245i \(-0.730897\pi\)
0.663422 0.748245i \(-0.269103\pi\)
\(450\) 0 0
\(451\) −8958.27 5172.06i −0.935318 0.540006i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 18520.6 9399.57i 1.90826 0.968481i
\(456\) 0 0
\(457\) 1764.03 + 3055.39i 0.180564 + 0.312747i 0.942073 0.335408i \(-0.108874\pi\)
−0.761508 + 0.648155i \(0.775541\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5905.31 0.596611 0.298306 0.954470i \(-0.403579\pi\)
0.298306 + 0.954470i \(0.403579\pi\)
\(462\) 0 0
\(463\) −5242.57 −0.526227 −0.263113 0.964765i \(-0.584749\pi\)
−0.263113 + 0.964765i \(0.584749\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5974.83 + 10348.7i 0.592039 + 1.02544i 0.993957 + 0.109766i \(0.0350101\pi\)
−0.401919 + 0.915675i \(0.631657\pi\)
\(468\) 0 0
\(469\) 4860.46 7458.41i 0.478540 0.734323i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16007.1 9241.73i −1.55605 0.898383i
\(474\) 0 0
\(475\) 8478.85i 0.819023i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −886.818 + 1536.01i −0.0845923 + 0.146518i −0.905217 0.424949i \(-0.860292\pi\)
0.820625 + 0.571467i \(0.193625\pi\)
\(480\) 0 0
\(481\) −21303.9 + 12299.8i −2.01949 + 1.16595i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10203.8 + 5891.14i −0.955317 + 0.551553i
\(486\) 0 0
\(487\) 1340.79 2322.32i 0.124758 0.216087i −0.796880 0.604137i \(-0.793518\pi\)
0.921638 + 0.388050i \(0.126851\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5871.49i 0.539667i −0.962907 0.269834i \(-0.913031\pi\)
0.962907 0.269834i \(-0.0869687\pi\)
\(492\) 0 0
\(493\) 8777.37 + 5067.62i 0.801852 + 0.462949i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 929.103 17203.9i 0.0838550 1.55272i
\(498\) 0 0
\(499\) 6882.08 + 11920.1i 0.617403 + 1.06937i 0.989958 + 0.141363i \(0.0451486\pi\)
−0.372555 + 0.928010i \(0.621518\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −9430.25 −0.835933 −0.417966 0.908462i \(-0.637257\pi\)
−0.417966 + 0.908462i \(0.637257\pi\)
\(504\) 0 0
\(505\) −3377.73 −0.297638
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3495.09 + 6053.68i 0.304356 + 0.527160i 0.977118 0.212699i \(-0.0682254\pi\)
−0.672762 + 0.739859i \(0.734892\pi\)
\(510\) 0 0
\(511\) 1763.31 + 1149.11i 0.152650 + 0.0994785i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15008.2 8664.99i −1.28416 0.741408i
\(516\) 0 0
\(517\) 21065.5i 1.79199i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8093.72 14018.7i 0.680600 1.17883i −0.294199 0.955744i \(-0.595053\pi\)
0.974798 0.223089i \(-0.0716140\pi\)
\(522\) 0 0
\(523\) −12519.5 + 7228.11i −1.04673 + 0.604327i −0.921731 0.387830i \(-0.873225\pi\)
−0.124995 + 0.992157i \(0.539891\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 25236.2 14570.1i 2.08597 1.20434i
\(528\) 0 0
\(529\) −6051.90 + 10482.2i −0.497403 + 0.861527i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 17776.7i 1.44464i
\(534\) 0 0
\(535\) −55.0696 31.7944i −0.00445021 0.00256933i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −12381.7 9056.25i −0.989457 0.723711i
\(540\) 0 0
\(541\) −8083.69 14001.4i −0.642412 1.11269i −0.984893 0.173165i \(-0.944601\pi\)
0.342481 0.939525i \(-0.388733\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3318.74 0.260842
\(546\) 0 0
\(547\) 15779.2 1.23340 0.616700 0.787199i \(-0.288469\pi\)
0.616700 + 0.787199i \(0.288469\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4189.29 + 7256.06i 0.323901 + 0.561014i
\(552\) 0 0
\(553\) 1867.00 + 3678.68i 0.143568 + 0.282881i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3537.74 2042.51i −0.269118 0.155375i 0.359369 0.933196i \(-0.382992\pi\)
−0.628487 + 0.777820i \(0.716325\pi\)
\(558\) 0 0
\(559\) 31764.3i 2.40338i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1330.97 + 2305.30i −0.0996332 + 0.172570i −0.911533 0.411227i \(-0.865100\pi\)
0.811900 + 0.583797i \(0.198434\pi\)
\(564\) 0 0
\(565\) −6541.44 + 3776.70i −0.487080 + 0.281216i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11350.6 + 6553.27i −0.836278 + 0.482825i −0.855997 0.516980i \(-0.827056\pi\)
0.0197197 + 0.999806i \(0.493723\pi\)
\(570\) 0 0
\(571\) 3592.46 6222.32i 0.263292 0.456035i −0.703823 0.710376i \(-0.748525\pi\)
0.967115 + 0.254340i \(0.0818584\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 698.700i 0.0506744i
\(576\) 0 0
\(577\) 3870.62 + 2234.70i 0.279265 + 0.161234i 0.633091 0.774078i \(-0.281786\pi\)
−0.353826 + 0.935311i \(0.615119\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12805.2 + 691.550i 0.914371 + 0.0493810i
\(582\) 0 0
\(583\) 15501.5 + 26849.3i 1.10121 + 1.90735i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4137.01 −0.290891 −0.145445 0.989366i \(-0.546461\pi\)
−0.145445 + 0.989366i \(0.546461\pi\)
\(588\) 0 0
\(589\) 24089.6 1.68522
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12000.7 + 20785.8i 0.831044 + 1.43941i 0.897211 + 0.441602i \(0.145590\pi\)
−0.0661665 + 0.997809i \(0.521077\pi\)
\(594\) 0 0
\(595\) −31487.6 1700.50i −2.16952 0.117166i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1301.96 751.686i −0.0888089 0.0512739i 0.454938 0.890523i \(-0.349661\pi\)
−0.543747 + 0.839249i \(0.682995\pi\)
\(600\) 0 0
\(601\) 3475.50i 0.235888i −0.993020 0.117944i \(-0.962370\pi\)
0.993020 0.117944i \(-0.0376303\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4882.14 8456.11i 0.328078 0.568247i
\(606\) 0 0
\(607\) 1722.46 994.463i 0.115177 0.0664975i −0.441305 0.897357i \(-0.645484\pi\)
0.556482 + 0.830860i \(0.312151\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 31351.6 18100.8i 2.07586 1.19850i
\(612\) 0 0
\(613\) −11830.3 + 20490.7i −0.779479 + 1.35010i 0.152763 + 0.988263i \(0.451183\pi\)
−0.932242 + 0.361835i \(0.882150\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15390.3i 1.00420i 0.864811 + 0.502098i \(0.167438\pi\)
−0.864811 + 0.502098i \(0.832562\pi\)
\(618\) 0 0
\(619\) −6817.56 3936.12i −0.442683 0.255583i 0.262052 0.965054i \(-0.415601\pi\)
−0.704735 + 0.709470i \(0.748934\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4336.16 8543.81i −0.278852 0.549439i
\(624\) 0 0
\(625\) 9443.21 + 16356.1i 0.604366 + 1.04679i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 37349.0 2.36757
\(630\) 0 0
\(631\) −6083.98 −0.383834 −0.191917 0.981411i \(-0.561471\pi\)
−0.191917 + 0.981411i \(0.561471\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12150.3 21044.9i −0.759320 1.31518i
\(636\) 0 0
\(637\) 2839.16 26209.2i 0.176596 1.63022i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20571.8 11877.2i −1.26761 0.731855i −0.293075 0.956089i \(-0.594679\pi\)
−0.974535 + 0.224234i \(0.928012\pi\)
\(642\) 0 0
\(643\) 12895.8i 0.790918i 0.918484 + 0.395459i \(0.129415\pi\)
−0.918484 + 0.395459i \(0.870585\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −552.298 + 956.608i −0.0335596 + 0.0581270i −0.882317 0.470655i \(-0.844018\pi\)
0.848758 + 0.528782i \(0.177351\pi\)
\(648\) 0 0
\(649\) −11139.4 + 6431.33i −0.673744 + 0.388986i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15648.4 9034.58i 0.937775 0.541425i 0.0485131 0.998823i \(-0.484552\pi\)
0.889262 + 0.457398i \(0.151218\pi\)
\(654\) 0 0
\(655\) 4997.87 8656.56i 0.298142 0.516397i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 15980.9i 0.944656i 0.881423 + 0.472328i \(0.156586\pi\)
−0.881423 + 0.472328i \(0.843414\pi\)
\(660\) 0 0
\(661\) 26260.0 + 15161.2i 1.54523 + 0.892138i 0.998496 + 0.0548308i \(0.0174619\pi\)
0.546733 + 0.837307i \(0.315871\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21839.9 14232.5i −1.27355 0.829943i
\(666\) 0 0
\(667\) −345.219 597.936i −0.0200404 0.0347109i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −38261.8 −2.20131
\(672\) 0 0
\(673\) −17767.4 −1.01766 −0.508829 0.860868i \(-0.669921\pi\)
−0.508829 + 0.860868i \(0.669921\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8243.00 + 14277.3i 0.467953 + 0.810519i 0.999329 0.0366172i \(-0.0116582\pi\)
−0.531376 + 0.847136i \(0.678325\pi\)
\(678\) 0 0
\(679\) −806.493 + 14933.6i −0.0455822 + 0.844031i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1757.98 + 1014.97i 0.0984877 + 0.0568619i 0.548435 0.836193i \(-0.315224\pi\)
−0.449947 + 0.893055i \(0.648557\pi\)
\(684\) 0 0
\(685\) 15339.5i 0.855607i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −26639.7 + 46141.3i −1.47299 + 2.55130i
\(690\) 0 0
\(691\) 27185.8 15695.7i 1.49667 0.864101i 0.496674 0.867937i \(-0.334554\pi\)
0.999993 + 0.00383605i \(0.00122105\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −336.590 + 194.330i −0.0183706 + 0.0106063i
\(696\) 0 0
\(697\) −13494.9 + 23373.9i −0.733367 + 1.27023i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7749.11i 0.417517i 0.977967 + 0.208759i \(0.0669423\pi\)
−0.977967 + 0.208759i \(0.933058\pi\)
\(702\) 0 0
\(703\) 26739.0 + 15437.8i 1.43454 + 0.828232i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2340.79 + 3591.96i −0.124519 + 0.191075i
\(708\) 0 0
\(709\) 8907.48 + 15428.2i 0.471830 + 0.817233i 0.999481 0.0322280i \(-0.0102603\pi\)
−0.527651 + 0.849462i \(0.676927\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1985.11 −0.104268
\(714\) 0 0
\(715\) 50154.7 2.62333
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10695.4 + 18525.0i 0.554759 + 0.960871i 0.997922 + 0.0644299i \(0.0205229\pi\)
−0.443163 + 0.896441i \(0.646144\pi\)
\(720\) 0 0
\(721\) −19615.4 + 9955.20i −1.01320 + 0.514218i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6611.15 + 3816.95i 0.338665 + 0.195528i
\(726\) 0 0
\(727\) 27791.9i 1.41780i −0.705307 0.708902i \(-0.749191\pi\)
0.705307 0.708902i \(-0.250809\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24113.5 + 41765.8i −1.22007 + 2.11322i
\(732\) 0 0
\(733\) −17159.5 + 9907.02i −0.864665 + 0.499214i −0.865572 0.500785i \(-0.833045\pi\)
0.000906890 1.00000i \(0.499711\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18617.7 10748.9i 0.930518 0.537235i
\(738\) 0 0
\(739\) 15164.2 26265.2i 0.754838 1.30742i −0.190617 0.981664i \(-0.561049\pi\)
0.945455 0.325753i \(-0.105618\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9992.06i 0.493369i 0.969096 + 0.246685i \(0.0793411\pi\)
−0.969096 + 0.246685i \(0.920659\pi\)
\(744\) 0 0
\(745\) 27928.9 + 16124.8i 1.37347 + 0.792975i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −71.9746 + 36.5286i −0.00351121 + 0.00178201i
\(750\) 0 0
\(751\) −19991.9 34627.1i −0.971393 1.68250i −0.691358 0.722513i \(-0.742987\pi\)
−0.280035 0.959990i \(-0.590346\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 27959.0 1.34773
\(756\) 0 0
\(757\) −11981.7 −0.575273 −0.287637 0.957740i \(-0.592870\pi\)
−0.287637 + 0.957740i \(0.592870\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10395.4 + 18005.4i 0.495182 + 0.857680i 0.999985 0.00555440i \(-0.00176803\pi\)
−0.504803 + 0.863235i \(0.668435\pi\)
\(762\) 0 0
\(763\) 2299.91 3529.23i 0.109125 0.167453i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19143.4 11052.4i −0.901208 0.520313i
\(768\) 0 0
\(769\) 24512.2i 1.14946i 0.818344 + 0.574728i \(0.194892\pi\)
−0.818344 + 0.574728i \(0.805108\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18063.2 + 31286.4i −0.840477 + 1.45575i 0.0490158 + 0.998798i \(0.484392\pi\)
−0.889492 + 0.456950i \(0.848942\pi\)
\(774\) 0 0
\(775\) 19008.0 10974.3i 0.881017 0.508655i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −19322.7 + 11156.0i −0.888712 + 0.513098i
\(780\) 0 0
\(781\) 20802.7 36031.3i 0.953109 1.65083i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 31329.2i 1.42444i
\(786\) 0 0
\(787\) −22356.7 12907.6i −1.01262 0.584634i −0.100660 0.994921i \(-0.532095\pi\)
−0.911957 + 0.410287i \(0.865429\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −517.027 + 9573.62i −0.0232407 + 0.430340i
\(792\) 0 0
\(793\) −32877.0 56944.6i −1.47225 2.55001i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11502.7 0.511223 0.255612 0.966780i \(-0.417723\pi\)
0.255612 + 0.966780i \(0.417723\pi\)
\(798\) 0 0
\(799\) −54964.1 −2.43365
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2541.26 + 4401.58i