Properties

Label 108.5.g.a.89.1
Level 108
Weight 5
Character 108.89
Analytic conductor 11.164
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} + 6 x^{6} + 121 x^{5} + 1104 x^{4} - 1647 x^{3} + 6529 x^{2} + 85254 x + 440076\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{10} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.1
Root \(-3.05006 + 3.25531i\) of defining polynomial
Character \(\chi\) \(=\) 108.89
Dual form 108.5.g.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +O(q^{10})\) \(q+(-27.4152 + 15.8282i) q^{5} +(37.6830 - 65.2688i) q^{7} +(123.267 + 71.1682i) q^{11} +(96.3079 + 166.810i) q^{13} +325.855i q^{17} +314.164 q^{19} +(443.852 - 256.258i) q^{23} +(188.564 - 326.602i) q^{25} +(136.614 + 78.8739i) q^{29} +(183.725 + 318.221i) q^{31} +2385.82i q^{35} +1737.04 q^{37} +(342.317 - 197.637i) q^{41} +(-360.381 + 624.198i) q^{43} +(-2153.71 - 1243.45i) q^{47} +(-1639.52 - 2839.72i) q^{49} -3986.04i q^{53} -4505.86 q^{55} +(2136.75 - 1233.65i) q^{59} +(-1240.49 + 2148.59i) q^{61} +(-5280.61 - 3048.76i) q^{65} +(3298.19 + 5712.64i) q^{67} +5828.07i q^{71} -8790.44 q^{73} +(9290.13 - 5363.66i) q^{77} +(1934.52 - 3350.69i) q^{79} +(-10422.5 - 6017.43i) q^{83} +(-5157.70 - 8933.39i) q^{85} +7637.03i q^{89} +14516.7 q^{91} +(-8612.88 + 4972.65i) q^{95} +(1455.75 - 2521.44i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 9q^{5} + 13q^{7} + O(q^{10}) \) \( 8q + 9q^{5} + 13q^{7} + 18q^{11} - 5q^{13} + 562q^{19} + 1719q^{23} + 353q^{25} - 2115q^{29} + 187q^{31} + 16q^{37} + 7920q^{41} - 68q^{43} - 13689q^{47} - 327q^{49} - 1818q^{55} + 20052q^{59} - 1937q^{61} - 25965q^{65} + 154q^{67} - 7802q^{73} + 25641q^{77} - 2195q^{79} - 37017q^{83} - 3042q^{85} + 15830q^{91} + 37116q^{95} + 7282q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(5\) −27.4152 + 15.8282i −1.09661 + 0.633128i −0.935329 0.353780i \(-0.884896\pi\)
−0.161281 + 0.986908i \(0.551563\pi\)
\(6\) 0 0
\(7\) 37.6830 65.2688i 0.769041 1.33202i −0.169043 0.985609i \(-0.554068\pi\)
0.938084 0.346409i \(-0.112599\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 123.267 + 71.1682i 1.01873 + 0.588167i 0.913737 0.406306i \(-0.133183\pi\)
0.104997 + 0.994473i \(0.466517\pi\)
\(12\) 0 0
\(13\) 96.3079 + 166.810i 0.569870 + 0.987043i 0.996578 + 0.0826539i \(0.0263396\pi\)
−0.426709 + 0.904389i \(0.640327\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 325.855i 1.12753i 0.825937 + 0.563763i \(0.190647\pi\)
−0.825937 + 0.563763i \(0.809353\pi\)
\(18\) 0 0
\(19\) 314.164 0.870260 0.435130 0.900368i \(-0.356702\pi\)
0.435130 + 0.900368i \(0.356702\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 443.852 256.258i 0.839040 0.484420i −0.0178977 0.999840i \(-0.505697\pi\)
0.856938 + 0.515420i \(0.172364\pi\)
\(24\) 0 0
\(25\) 188.564 326.602i 0.301702 0.522564i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 136.614 + 78.8739i 0.162442 + 0.0937859i 0.579017 0.815315i \(-0.303436\pi\)
−0.416575 + 0.909101i \(0.636770\pi\)
\(30\) 0 0
\(31\) 183.725 + 318.221i 0.191181 + 0.331135i 0.945642 0.325210i \(-0.105435\pi\)
−0.754461 + 0.656345i \(0.772102\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2385.82i 1.94760i
\(36\) 0 0
\(37\) 1737.04 1.26884 0.634419 0.772989i \(-0.281239\pi\)
0.634419 + 0.772989i \(0.281239\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 342.317 197.637i 0.203639 0.117571i −0.394713 0.918805i \(-0.629156\pi\)
0.598352 + 0.801234i \(0.295823\pi\)
\(42\) 0 0
\(43\) −360.381 + 624.198i −0.194906 + 0.337587i −0.946870 0.321618i \(-0.895773\pi\)
0.751964 + 0.659204i \(0.229107\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2153.71 1243.45i −0.974971 0.562900i −0.0742227 0.997242i \(-0.523648\pi\)
−0.900748 + 0.434342i \(0.856981\pi\)
\(48\) 0 0
\(49\) −1639.52 2839.72i −0.682847 1.18273i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3986.04i 1.41902i −0.704694 0.709512i \(-0.748916\pi\)
0.704694 0.709512i \(-0.251084\pi\)
\(54\) 0 0
\(55\) −4505.86 −1.48954
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2136.75 1233.65i 0.613831 0.354396i −0.160632 0.987014i \(-0.551353\pi\)
0.774463 + 0.632619i \(0.218020\pi\)
\(60\) 0 0
\(61\) −1240.49 + 2148.59i −0.333375 + 0.577422i −0.983171 0.182686i \(-0.941521\pi\)
0.649796 + 0.760108i \(0.274854\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5280.61 3048.76i −1.24985 0.721601i
\(66\) 0 0
\(67\) 3298.19 + 5712.64i 0.734728 + 1.27259i 0.954843 + 0.297112i \(0.0960233\pi\)
−0.220115 + 0.975474i \(0.570643\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5828.07i 1.15613i 0.815990 + 0.578066i \(0.196193\pi\)
−0.815990 + 0.578066i \(0.803807\pi\)
\(72\) 0 0
\(73\) −8790.44 −1.64955 −0.824774 0.565463i \(-0.808697\pi\)
−0.824774 + 0.565463i \(0.808697\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9290.13 5363.66i 1.56690 0.904648i
\(78\) 0 0
\(79\) 1934.52 3350.69i 0.309970 0.536883i −0.668386 0.743815i \(-0.733014\pi\)
0.978355 + 0.206932i \(0.0663478\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −10422.5 6017.43i −1.51292 0.873483i −0.999886 0.0151136i \(-0.995189\pi\)
−0.513032 0.858370i \(-0.671478\pi\)
\(84\) 0 0
\(85\) −5157.70 8933.39i −0.713868 1.23646i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7637.03i 0.964150i 0.876130 + 0.482075i \(0.160117\pi\)
−0.876130 + 0.482075i \(0.839883\pi\)
\(90\) 0 0
\(91\) 14516.7 1.75301
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8612.88 + 4972.65i −0.954336 + 0.550986i
\(96\) 0 0
\(97\) 1455.75 2521.44i 0.154719 0.267981i −0.778238 0.627970i \(-0.783886\pi\)
0.932957 + 0.359989i \(0.117219\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9442.90 + 5451.86i 0.925683 + 0.534444i 0.885444 0.464746i \(-0.153855\pi\)
0.0402396 + 0.999190i \(0.487188\pi\)
\(102\) 0 0
\(103\) 3638.56 + 6302.16i 0.342969 + 0.594039i 0.984983 0.172654i \(-0.0552341\pi\)
−0.642014 + 0.766693i \(0.721901\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5525.48i 0.482617i 0.970449 + 0.241308i \(0.0775765\pi\)
−0.970449 + 0.241308i \(0.922424\pi\)
\(108\) 0 0
\(109\) 7186.35 0.604861 0.302431 0.953171i \(-0.402202\pi\)
0.302431 + 0.953171i \(0.402202\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10742.0 6201.93i 0.841260 0.485702i −0.0164323 0.999865i \(-0.505231\pi\)
0.857692 + 0.514163i \(0.171897\pi\)
\(114\) 0 0
\(115\) −8112.21 + 14050.8i −0.613400 + 1.06244i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 21268.2 + 12279.2i 1.50188 + 0.867113i
\(120\) 0 0
\(121\) 2809.31 + 4865.88i 0.191880 + 0.332346i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 7846.74i 0.502191i
\(126\) 0 0
\(127\) 9013.28 0.558824 0.279412 0.960171i \(-0.409860\pi\)
0.279412 + 0.960171i \(0.409860\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −309.401 + 178.633i −0.0180293 + 0.0104092i −0.508988 0.860774i \(-0.669980\pi\)
0.490958 + 0.871183i \(0.336647\pi\)
\(132\) 0 0
\(133\) 11838.6 20505.1i 0.669265 1.15920i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12811.2 7396.54i −0.682571 0.394083i 0.118252 0.992984i \(-0.462271\pi\)
−0.800823 + 0.598901i \(0.795604\pi\)
\(138\) 0 0
\(139\) −1079.62 1869.95i −0.0558779 0.0967834i 0.836733 0.547611i \(-0.184462\pi\)
−0.892611 + 0.450827i \(0.851129\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 27416.2i 1.34071i
\(144\) 0 0
\(145\) −4993.73 −0.237514
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −24982.1 + 14423.4i −1.12527 + 0.649675i −0.942741 0.333526i \(-0.891762\pi\)
−0.182529 + 0.983201i \(0.558428\pi\)
\(150\) 0 0
\(151\) 4752.65 8231.82i 0.208440 0.361029i −0.742783 0.669532i \(-0.766495\pi\)
0.951223 + 0.308503i \(0.0998280\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10073.7 5816.07i −0.419302 0.242084i
\(156\) 0 0
\(157\) 4937.68 + 8552.31i 0.200320 + 0.346964i 0.948631 0.316383i \(-0.102469\pi\)
−0.748312 + 0.663347i \(0.769135\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 38626.3i 1.49015i
\(162\) 0 0
\(163\) −22464.8 −0.845525 −0.422763 0.906240i \(-0.638940\pi\)
−0.422763 + 0.906240i \(0.638940\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14694.7 8484.01i 0.526901 0.304206i −0.212853 0.977084i \(-0.568275\pi\)
0.739753 + 0.672878i \(0.234942\pi\)
\(168\) 0 0
\(169\) −4269.94 + 7395.76i −0.149503 + 0.258946i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 32441.8 + 18730.3i 1.08396 + 0.625825i 0.931962 0.362556i \(-0.118096\pi\)
0.151998 + 0.988381i \(0.451429\pi\)
\(174\) 0 0
\(175\) −14211.3 24614.7i −0.464043 0.803745i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 44760.9i 1.39699i −0.715615 0.698495i \(-0.753853\pi\)
0.715615 0.698495i \(-0.246147\pi\)
\(180\) 0 0
\(181\) −29208.0 −0.891548 −0.445774 0.895146i \(-0.647071\pi\)
−0.445774 + 0.895146i \(0.647071\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −47621.4 + 27494.2i −1.39142 + 0.803337i
\(186\) 0 0
\(187\) −23190.5 + 40167.1i −0.663173 + 1.14865i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −25988.4 15004.4i −0.712383 0.411294i 0.0995598 0.995032i \(-0.468257\pi\)
−0.811943 + 0.583737i \(0.801590\pi\)
\(192\) 0 0
\(193\) 8615.87 + 14923.1i 0.231305 + 0.400632i 0.958192 0.286125i \(-0.0923672\pi\)
−0.726888 + 0.686756i \(0.759034\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 67892.1i 1.74939i −0.484673 0.874695i \(-0.661062\pi\)
0.484673 0.874695i \(-0.338938\pi\)
\(198\) 0 0
\(199\) −26996.5 −0.681713 −0.340857 0.940115i \(-0.610717\pi\)
−0.340857 + 0.940115i \(0.610717\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10296.0 5944.41i 0.249849 0.144250i
\(204\) 0 0
\(205\) −6256.47 + 10836.5i −0.148875 + 0.257859i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 38726.0 + 22358.5i 0.886564 + 0.511858i
\(210\) 0 0
\(211\) −11819.5 20472.1i −0.265482 0.459829i 0.702207 0.711972i \(-0.252198\pi\)
−0.967690 + 0.252143i \(0.918865\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 22816.7i 0.493601i
\(216\) 0 0
\(217\) 27693.2 0.588103
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −54355.9 + 31382.4i −1.11292 + 0.642543i
\(222\) 0 0
\(223\) 28978.0 50191.3i 0.582718 1.00930i −0.412438 0.910986i \(-0.635323\pi\)
0.995156 0.0983112i \(-0.0313441\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8712.47 5030.15i −0.169079 0.0976178i 0.413073 0.910698i \(-0.364456\pi\)
−0.582151 + 0.813080i \(0.697789\pi\)
\(228\) 0 0
\(229\) −28899.8 50056.0i −0.551093 0.954520i −0.998196 0.0600381i \(-0.980878\pi\)
0.447104 0.894482i \(-0.352456\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 68323.8i 1.25852i 0.777195 + 0.629260i \(0.216642\pi\)
−0.777195 + 0.629260i \(0.783358\pi\)
\(234\) 0 0
\(235\) 78726.0 1.42555
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 30122.2 17391.1i 0.527340 0.304460i −0.212592 0.977141i \(-0.568191\pi\)
0.739933 + 0.672681i \(0.234857\pi\)
\(240\) 0 0
\(241\) −45982.8 + 79644.5i −0.791701 + 1.37127i 0.133213 + 0.991087i \(0.457471\pi\)
−0.924913 + 0.380178i \(0.875863\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 89895.4 + 51901.2i 1.49763 + 0.864659i
\(246\) 0 0
\(247\) 30256.5 + 52405.7i 0.495935 + 0.858984i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 69806.6i 1.10802i 0.832509 + 0.554012i \(0.186904\pi\)
−0.832509 + 0.554012i \(0.813096\pi\)
\(252\) 0 0
\(253\) 72949.7 1.13968
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15210.4 + 8781.70i −0.230289 + 0.132957i −0.610705 0.791858i \(-0.709114\pi\)
0.380416 + 0.924815i \(0.375781\pi\)
\(258\) 0 0
\(259\) 65456.8 113375.i 0.975788 1.69011i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −26492.4 15295.4i −0.383009 0.221131i 0.296117 0.955152i \(-0.404308\pi\)
−0.679127 + 0.734021i \(0.737641\pi\)
\(264\) 0 0
\(265\) 63091.8 + 109278.i 0.898423 + 1.55611i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 59574.8i 0.823299i 0.911342 + 0.411650i \(0.135047\pi\)
−0.911342 + 0.411650i \(0.864953\pi\)
\(270\) 0 0
\(271\) −94290.1 −1.28389 −0.641945 0.766751i \(-0.721872\pi\)
−0.641945 + 0.766751i \(0.721872\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 46487.4 26839.5i 0.614709 0.354902i
\(276\) 0 0
\(277\) 49687.7 86061.7i 0.647574 1.12163i −0.336126 0.941817i \(-0.609117\pi\)
0.983700 0.179815i \(-0.0575499\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −68740.8 39687.5i −0.870567 0.502622i −0.00303013 0.999995i \(-0.500965\pi\)
−0.867536 + 0.497374i \(0.834298\pi\)
\(282\) 0 0
\(283\) −33460.0 57954.4i −0.417785 0.723625i 0.577931 0.816085i \(-0.303860\pi\)
−0.995716 + 0.0924607i \(0.970527\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 29790.2i 0.361667i
\(288\) 0 0
\(289\) −22660.4 −0.271314
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 48467.1 27982.5i 0.564562 0.325950i −0.190413 0.981704i \(-0.560983\pi\)
0.754974 + 0.655754i \(0.227649\pi\)
\(294\) 0 0
\(295\) −39053.0 + 67641.7i −0.448756 + 0.777268i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 85493.0 + 49359.4i 0.956287 + 0.552112i
\(300\) 0 0
\(301\) 27160.4 + 47043.3i 0.299781 + 0.519236i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 78538.8i 0.844276i
\(306\) 0 0
\(307\) 8707.80 0.0923914 0.0461957 0.998932i \(-0.485290\pi\)
0.0461957 + 0.998932i \(0.485290\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 48339.3 27908.7i 0.499781 0.288549i −0.228842 0.973464i \(-0.573494\pi\)
0.728623 + 0.684915i \(0.240161\pi\)
\(312\) 0 0
\(313\) −29519.7 + 51129.6i −0.301316 + 0.521895i −0.976434 0.215815i \(-0.930759\pi\)
0.675118 + 0.737710i \(0.264093\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26277.2 + 15171.2i 0.261494 + 0.150973i 0.625016 0.780612i \(-0.285093\pi\)
−0.363522 + 0.931586i \(0.618426\pi\)
\(318\) 0 0
\(319\) 11226.6 + 19445.1i 0.110323 + 0.191086i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 102372.i 0.981240i
\(324\) 0 0
\(325\) 72640.8 0.687724
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −162316. + 93713.5i −1.49958 + 0.865785i
\(330\) 0 0
\(331\) −63460.5 + 109917.i −0.579225 + 1.00325i 0.416343 + 0.909207i \(0.363311\pi\)
−0.995568 + 0.0940397i \(0.970022\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −180842. 104409.i −1.61142 0.930353i
\(336\) 0 0
\(337\) −89198.2 154496.i −0.785410 1.36037i −0.928754 0.370697i \(-0.879119\pi\)
0.143344 0.989673i \(-0.454214\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 52301.4i 0.449785i
\(342\) 0 0
\(343\) −66173.6 −0.562466
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 97741.3 56431.0i 0.811744 0.468661i −0.0358168 0.999358i \(-0.511403\pi\)
0.847561 + 0.530697i \(0.178070\pi\)
\(348\) 0 0
\(349\) 36754.1 63660.0i 0.301756 0.522656i −0.674778 0.738021i \(-0.735761\pi\)
0.976534 + 0.215365i \(0.0690940\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −183043. 105680.i −1.46894 0.848091i −0.469544 0.882909i \(-0.655582\pi\)
−0.999394 + 0.0348180i \(0.988915\pi\)
\(354\) 0 0
\(355\) −92247.8 159778.i −0.731980 1.26783i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 36755.1i 0.285186i −0.989781 0.142593i \(-0.954456\pi\)
0.989781 0.142593i \(-0.0455440\pi\)
\(360\) 0 0
\(361\) −31622.1 −0.242648
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 240992. 139137.i 1.80891 1.04437i
\(366\) 0 0
\(367\) 73577.0 127439.i 0.546273 0.946173i −0.452252 0.891890i \(-0.649379\pi\)
0.998526 0.0542832i \(-0.0172874\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −260164. 150206.i −1.89016 1.09129i
\(372\) 0 0
\(373\) 21799.0 + 37757.1i 0.156682 + 0.271382i 0.933670 0.358134i \(-0.116587\pi\)
−0.776988 + 0.629515i \(0.783253\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30384.7i 0.213783i
\(378\) 0 0
\(379\) −169833. −1.18234 −0.591170 0.806547i \(-0.701334\pi\)
−0.591170 + 0.806547i \(0.701334\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 106228. 61330.5i 0.724169 0.418099i −0.0921163 0.995748i \(-0.529363\pi\)
0.816285 + 0.577649i \(0.196030\pi\)
\(384\) 0 0
\(385\) −169794. + 294092.i −1.14552 + 1.98409i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 50495.3 + 29153.5i 0.333696 + 0.192660i 0.657481 0.753471i \(-0.271622\pi\)
−0.323785 + 0.946131i \(0.604955\pi\)
\(390\) 0 0
\(391\) 83503.0 + 144631.i 0.546196 + 0.946039i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 122480.i 0.785002i
\(396\) 0 0
\(397\) −134572. −0.853834 −0.426917 0.904291i \(-0.640400\pi\)
−0.426917 + 0.904291i \(0.640400\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −185654. + 107187.i −1.15456 + 0.666584i −0.949994 0.312269i \(-0.898911\pi\)
−0.204563 + 0.978853i \(0.565577\pi\)
\(402\) 0 0
\(403\) −35388.3 + 61294.4i −0.217896 + 0.377408i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 214119. + 123622.i 1.29261 + 0.746288i
\(408\) 0 0
\(409\) 24369.5 + 42209.2i 0.145680 + 0.252325i 0.929626 0.368503i \(-0.120130\pi\)
−0.783946 + 0.620828i \(0.786796\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 185951.i 1.09018i
\(414\) 0 0
\(415\) 380980. 2.21211
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 59650.3 34439.1i 0.339770 0.196166i −0.320400 0.947282i \(-0.603817\pi\)
0.660170 + 0.751116i \(0.270484\pi\)
\(420\) 0 0
\(421\) 157677. 273105.i 0.889620 1.54087i 0.0492953 0.998784i \(-0.484302\pi\)
0.840325 0.542083i \(-0.182364\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 106425. + 61444.5i 0.589204 + 0.340177i
\(426\) 0 0
\(427\) 93490.6 + 161930.i 0.512758 + 0.888122i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 151597.i 0.816088i 0.912962 + 0.408044i \(0.133789\pi\)
−0.912962 + 0.408044i \(0.866211\pi\)
\(432\) 0 0
\(433\) −237835. −1.26853 −0.634265 0.773116i \(-0.718697\pi\)
−0.634265 + 0.773116i \(0.718697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 139442. 80507.1i 0.730183 0.421571i
\(438\) 0 0
\(439\) −32350.4 + 56032.6i −0.167861 + 0.290745i −0.937668 0.347533i \(-0.887019\pi\)
0.769806 + 0.638278i \(0.220353\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4469.49 + 2580.46i 0.0227746 + 0.0131489i 0.511344 0.859376i \(-0.329148\pi\)
−0.488569 + 0.872525i \(0.662481\pi\)
\(444\) 0 0
\(445\) −120880. 209371.i −0.610430 1.05730i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 165679.i 0.821816i −0.911677 0.410908i \(-0.865212\pi\)
0.911677 0.410908i \(-0.134788\pi\)
\(450\) 0 0
\(451\) 56261.8 0.276605
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −397979. + 229773.i −1.92237 + 1.10988i
\(456\) 0 0
\(457\) 204489. 354185.i 0.979121 1.69589i 0.313519 0.949582i \(-0.398492\pi\)
0.665603 0.746306i \(-0.268174\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 75485.9 + 43581.8i 0.355193 + 0.205071i 0.666970 0.745085i \(-0.267591\pi\)
−0.311777 + 0.950155i \(0.600924\pi\)
\(462\) 0 0
\(463\) −8403.24 14554.8i −0.0391999 0.0678962i 0.845760 0.533564i \(-0.179148\pi\)
−0.884960 + 0.465668i \(0.845814\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 394500.i 1.80889i 0.426585 + 0.904447i \(0.359716\pi\)
−0.426585 + 0.904447i \(0.640284\pi\)
\(468\) 0 0
\(469\) 497143. 2.26014
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −88846.0 + 51295.3i −0.397114 + 0.229274i
\(474\) 0 0
\(475\) 59240.0 102607.i 0.262559 0.454766i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 90406.6 + 52196.3i 0.394030 + 0.227493i 0.683905 0.729571i \(-0.260280\pi\)
−0.289875 + 0.957065i \(0.593614\pi\)
\(480\) 0 0
\(481\) 167291. + 289756.i 0.723072 + 1.25240i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 92167.7i 0.391828i
\(486\) 0 0
\(487\) 106236. 0.447936 0.223968 0.974597i \(-0.428099\pi\)
0.223968 + 0.974597i \(0.428099\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −78832.6 + 45514.0i −0.326997 + 0.188792i −0.654507 0.756056i \(-0.727124\pi\)
0.327510 + 0.944848i \(0.393790\pi\)
\(492\) 0 0
\(493\) −25701.5 + 44516.2i −0.105746 + 0.183157i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 380391. + 219619.i 1.53999 + 0.889113i
\(498\) 0 0
\(499\) 69176.0 + 119816.i 0.277814 + 0.481188i 0.970841 0.239723i \(-0.0770567\pi\)
−0.693027 + 0.720912i \(0.743723\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 63792.4i 0.252135i −0.992022 0.126067i \(-0.959764\pi\)
0.992022 0.126067i \(-0.0402356\pi\)
\(504\) 0 0
\(505\) −345172. −1.35348
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 423634. 244585.i 1.63514 0.944049i 0.652668 0.757644i \(-0.273650\pi\)
0.982473 0.186405i \(-0.0596838\pi\)
\(510\) 0 0
\(511\) −331250. + 573742.i −1.26857 + 2.19723i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −199504. 115184.i −0.752206 0.434286i
\(516\) 0 0
\(517\) −176987. 306551.i −0.662158 1.14689i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 339386.i 1.25031i −0.780500 0.625156i \(-0.785035\pi\)
0.780500 0.625156i \(-0.214965\pi\)
\(522\) 0 0
\(523\) 379243. 1.38648 0.693242 0.720705i \(-0.256182\pi\)
0.693242 + 0.720705i \(0.256182\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −103694. + 59867.6i −0.373363 + 0.215561i
\(528\) 0 0
\(529\) −8583.94 + 14867.8i −0.0306744 + 0.0531295i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 65935.7 + 38068.0i 0.232095 + 0.134000i
\(534\) 0 0
\(535\) −87458.4 151482.i −0.305558 0.529242i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 466725.i 1.60651i
\(540\) 0 0
\(541\) −494913. −1.69096 −0.845481 0.534005i \(-0.820686\pi\)
−0.845481 + 0.534005i \(0.820686\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −197016. + 113747.i −0.663297 + 0.382955i
\(546\) 0 0
\(547\) 93045.4 161159.i 0.310971 0.538618i −0.667602 0.744519i \(-0.732679\pi\)
0.978573 + 0.205901i \(0.0660124\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 42919.1 + 24779.3i 0.141367 + 0.0816181i
\(552\) 0 0
\(553\) −145797. 252528.i −0.476759 0.825770i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 119662.i 0.385698i −0.981228 0.192849i \(-0.938227\pi\)
0.981228 0.192849i \(-0.0617728\pi\)
\(558\) 0 0
\(559\) −138830. −0.444283
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22885.5 + 13213.0i −0.0722012 + 0.0416854i −0.535666 0.844430i \(-0.679939\pi\)
0.463465 + 0.886115i \(0.346606\pi\)
\(564\) 0 0
\(565\) −196331. + 340055.i −0.615023 + 1.06525i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −453562. 261864.i −1.40092 0.808820i −0.406430 0.913682i \(-0.633226\pi\)
−0.994487 + 0.104862i \(0.966560\pi\)
\(570\) 0 0
\(571\) 161586. + 279875.i 0.495600 + 0.858405i 0.999987 0.00507280i \(-0.00161473\pi\)
−0.504387 + 0.863478i \(0.668281\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 193284.i 0.584603i
\(576\) 0 0
\(577\) 350692. 1.05335 0.526676 0.850066i \(-0.323438\pi\)
0.526676 + 0.850066i \(0.323438\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −785501. + 453509.i −2.32699 + 1.34349i
\(582\) 0 0
\(583\) 283679. 491346.i 0.834622 1.44561i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 415397. + 239829.i 1.20555 + 0.696027i 0.961785 0.273806i \(-0.0882827\pi\)
0.243769 + 0.969833i \(0.421616\pi\)
\(588\) 0 0
\(589\) 57719.7 + 99973.4i 0.166377 + 0.288173i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 177843.i 0.505740i −0.967500 0.252870i \(-0.918625\pi\)
0.967500 0.252870i \(-0.0813745\pi\)
\(594\) 0 0
\(595\) −777430. −2.19597
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16977.8 + 9802.11i −0.0473180 + 0.0273191i −0.523472 0.852043i \(-0.675364\pi\)
0.476154 + 0.879362i \(0.342030\pi\)
\(600\) 0 0
\(601\) −197404. + 341913.i −0.546520 + 0.946600i 0.451990 + 0.892023i \(0.350714\pi\)
−0.998510 + 0.0545772i \(0.982619\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −154036. 88932.8i −0.420835 0.242969i
\(606\) 0 0
\(607\) −351729. 609212.i −0.954620 1.65345i −0.735235 0.677813i \(-0.762928\pi\)
−0.219386 0.975638i \(-0.570405\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 479015.i 1.28312i
\(612\) 0 0
\(613\) 96392.2 0.256520 0.128260 0.991741i \(-0.459061\pi\)
0.128260 + 0.991741i \(0.459061\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 439772. 253903.i 1.15520 0.666956i 0.205052 0.978751i \(-0.434264\pi\)
0.950149 + 0.311796i \(0.100930\pi\)
\(618\) 0 0
\(619\) 43453.6 75263.9i 0.113408 0.196429i −0.803734 0.594989i \(-0.797157\pi\)
0.917142 + 0.398560i \(0.130490\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 498460. + 287786.i 1.28426 + 0.741470i
\(624\) 0 0
\(625\) 242052. + 419247.i 0.619654 + 1.07327i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 566023.i 1.43065i
\(630\) 0 0
\(631\) −571591. −1.43558 −0.717788 0.696261i \(-0.754846\pi\)
−0.717788 + 0.696261i \(0.754846\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −247101. + 142664.i −0.612812 + 0.353807i
\(636\) 0 0
\(637\) 315797. 546976.i 0.778267 1.34800i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −332304. 191856.i −0.808759 0.466937i 0.0377659 0.999287i \(-0.487976\pi\)
−0.846525 + 0.532350i \(0.821309\pi\)
\(642\) 0 0
\(643\) 405119. + 701687.i 0.979853 + 1.69716i 0.662888 + 0.748718i \(0.269330\pi\)
0.316965 + 0.948437i \(0.397336\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 687173.i 1.64156i −0.571243 0.820781i \(-0.693539\pi\)
0.571243 0.820781i \(-0.306461\pi\)
\(648\) 0 0
\(649\) 351187. 0.833775
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 189470. 109391.i 0.444339 0.256539i −0.261097 0.965312i \(-0.584084\pi\)
0.705437 + 0.708773i \(0.250751\pi\)
\(654\) 0 0
\(655\) 5654.87 9794.52i 0.0131807 0.0228297i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −71298.2 41164.1i −0.164175 0.0947867i 0.415661 0.909520i \(-0.363550\pi\)
−0.579836 + 0.814733i \(0.696884\pi\)
\(660\) 0 0
\(661\) −205017. 355100.i −0.469231 0.812732i 0.530150 0.847904i \(-0.322136\pi\)
−0.999381 + 0.0351716i \(0.988802\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 749537.i 1.69492i
\(666\) 0 0
\(667\) 80848.4 0.181727
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −305822. + 176566.i −0.679241 + 0.392160i
\(672\) 0 0
\(673\) −265864. + 460490.i −0.586989 + 1.01669i 0.407636 + 0.913145i \(0.366353\pi\)
−0.994624 + 0.103549i \(0.966980\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −149580. 86360.3i −0.326361 0.188424i 0.327864 0.944725i \(-0.393671\pi\)
−0.654224 + 0.756301i \(0.727005\pi\)
\(678\) 0 0
\(679\) −109714. 190030.i −0.237970 0.412177i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 452646.i 0.970324i 0.874424 + 0.485162i \(0.161239\pi\)
−0.874424 + 0.485162i \(0.838761\pi\)
\(684\) 0 0
\(685\) 468296. 0.998019
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 664912. 383887.i 1.40064 0.808658i
\(690\) 0 0
\(691\) −117795. + 204027.i −0.246701 + 0.427298i −0.962608 0.270897i \(-0.912680\pi\)
0.715908 + 0.698195i \(0.246013\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 59196.0 + 34176.8i 0.122553 + 0.0707558i
\(696\) 0 0
\(697\) 64400.9 + 111546.i 0.132564 + 0.229608i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 41298.8i 0.0840430i −0.999117 0.0420215i \(-0.986620\pi\)
0.999117 0.0420215i \(-0.0133798\pi\)
\(702\) 0 0
\(703\) 545715. 1.10422
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 711673. 410885.i 1.42378 0.822018i
\(708\) 0 0
\(709\) −32914.9 + 57010.2i −0.0654786 + 0.113412i −0.896906 0.442221i \(-0.854191\pi\)
0.831428 + 0.555633i \(0.187524\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 163093. + 94162.0i 0.320817 + 0.185224i
\(714\) 0 0
\(715\) −433950. 751623.i −0.848843 1.47024i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 551850.i 1.06749i 0.845646 + 0.533745i \(0.179216\pi\)
−0.845646 + 0.533745i \(0.820784\pi\)
\(720\) 0 0
\(721\) 548447. 1.05503
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 51520.8 29745.6i 0.0980182 0.0565908i
\(726\) 0 0
\(727\) −69946.0 + 121150.i −0.132341 + 0.229221i −0.924579 0.380992i \(-0.875583\pi\)
0.792238 + 0.610213i \(0.208916\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −203398. 117432.i −0.380638 0.219761i
\(732\) 0 0
\(733\) 348037. + 602817.i 0.647764 + 1.12196i 0.983656 + 0.180060i \(0.0576291\pi\)
−0.335891 + 0.941901i \(0.609038\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 938905.i 1.72857i
\(738\) 0 0
\(739\) 360220. 0.659598 0.329799 0.944051i \(-0.393019\pi\)
0.329799 + 0.944051i \(0.393019\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −55134.1 + 31831.7i −0.0998718 + 0.0576610i −0.549104 0.835754i \(-0.685031\pi\)
0.449232 + 0.893415i \(0.351698\pi\)
\(744\) 0 0
\(745\) 456594. 790844.i 0.822655 1.42488i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 360641. + 208216.i 0.642854 + 0.371152i
\(750\) 0 0
\(751\) 369552. + 640082.i 0.655232 + 1.13490i 0.981836 + 0.189734i \(0.0607626\pi\)
−0.326603 + 0.945162i \(0.605904\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 300903.i 0.527877i
\(756\) 0 0
\(757\) −315416. −0.550416 −0.275208 0.961385i \(-0.588747\pi\)
−0.275208 + 0.961385i \(0.588747\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −814012. + 469970.i −1.40560 + 0.811523i −0.994960 0.100274i \(-0.968028\pi\)
−0.410640 + 0.911798i \(0.634695\pi\)
\(762\) 0 0
\(763\) 270803. 469045.i 0.465163 0.805685i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 411571. + 237621.i 0.699607 + 0.403919i
\(768\) 0 0
\(769\) −173503. 300517.i −0.293397 0.508178i 0.681214 0.732085i \(-0.261452\pi\)
−0.974611 + 0.223906i \(0.928119\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4630.27i 0.00774903i 0.999992 + 0.00387451i \(0.00123330\pi\)
−0.999992 + 0.00387451i \(0.998767\pi\)
\(774\) 0 0
\(775\) 138576. 0.230719
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 107544. 62090.3i 0.177219 0.102317i
\(780\) 0 0
\(781\) −414773. + 718407.i −0.679999 + 1.17779i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −270735. 156309.i −0.439345 0.253656i
\(786\) 0 0
\(787\) −251477. 435571.i −0.406021 0.703250i 0.588418 0.808557i \(-0.299751\pi\)
−0.994440 + 0.105307i \(0.966417\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 934828.i 1.49410i
\(792\) 0 0
\(793\) −477875. −0.759921
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −210541. + 121556.i −0.331451 + 0.191363i −0.656485 0.754339i \(-0.727958\pi\)
0.325034 + 0.945702i \(0.394624\pi\)
\(798\) 0 0
\(799\) 405183. 701797.i 0.634684 1.09930i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.08357e6 625599.i −1.68045 0.970209i
\(804\) 0 0
\(805\) 611385. + 1.05895e6i