Properties

Label 108.6.b.c.107.1
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{40} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.1
Root \(3.14287 - 1.81454i\) of \(x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} - 32033996800 x^{2} + 41943040000\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.c.107.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.64474 - 0.370087i) q^{2} +(31.7261 + 4.17809i) q^{4} -38.9183i q^{5} +132.403i q^{7} +(-177.539 - 35.3256i) q^{8} +O(q^{10})\) \(q+(-5.64474 - 0.370087i) q^{2} +(31.7261 + 4.17809i) q^{4} -38.9183i q^{5} +132.403i q^{7} +(-177.539 - 35.3256i) q^{8} +(-14.4032 + 219.683i) q^{10} +190.441 q^{11} -416.631 q^{13} +(49.0008 - 747.382i) q^{14} +(989.087 + 265.109i) q^{16} -1145.55i q^{17} +768.976i q^{19} +(162.604 - 1234.72i) q^{20} +(-1074.99 - 70.4798i) q^{22} -2231.96 q^{23} +1610.37 q^{25} +(2351.77 + 154.190i) q^{26} +(-553.193 + 4200.64i) q^{28} +5919.93i q^{29} +10009.3i q^{31} +(-5485.02 - 1862.52i) q^{32} +(-423.953 + 6466.32i) q^{34} +5152.91 q^{35} +4317.45 q^{37} +(284.588 - 4340.67i) q^{38} +(-1374.81 + 6909.51i) q^{40} +18511.5i q^{41} +5568.60i q^{43} +(6041.95 + 795.680i) q^{44} +(12598.8 + 826.019i) q^{46} +12618.3 q^{47} -723.662 q^{49} +(-9090.10 - 595.977i) q^{50} +(-13218.1 - 1740.72i) q^{52} +30907.9i q^{53} -7411.64i q^{55} +(4677.23 - 23506.8i) q^{56} +(2190.89 - 33416.4i) q^{58} -39249.3 q^{59} -45204.0 q^{61} +(3704.31 - 56499.8i) q^{62} +(30272.2 + 12543.4i) q^{64} +16214.6i q^{65} -24713.4i q^{67} +(4786.20 - 36343.8i) q^{68} +(-29086.8 - 1907.03i) q^{70} +18755.2 q^{71} +81273.7 q^{73} +(-24370.9 - 1597.83i) q^{74} +(-3212.85 + 24396.6i) q^{76} +25215.0i q^{77} -33373.3i q^{79} +(10317.6 - 38493.6i) q^{80} +(6850.85 - 104492. i) q^{82} +47528.7 q^{83} -44582.8 q^{85} +(2060.87 - 31433.3i) q^{86} +(-33810.7 - 6727.45i) q^{88} +65440.5i q^{89} -55163.4i q^{91} +(-70811.3 - 9325.32i) q^{92} +(-71226.9 - 4669.86i) q^{94} +29927.2 q^{95} -29170.2 q^{97} +(4084.88 + 267.818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 20q^{4} + O(q^{10}) \) \( 20q + 20q^{4} + 184q^{10} - 116q^{13} - 4168q^{16} + 696q^{22} - 15228q^{25} - 4764q^{28} - 16520q^{34} - 6452q^{37} + 1504q^{40} - 9336q^{46} - 44464q^{49} + 8236q^{52} - 58736q^{58} + 84604q^{61} - 6496q^{64} + 138696q^{70} + 85420q^{73} + 89172q^{76} + 221200q^{82} + 180320q^{85} - 85824q^{88} - 60936q^{94} - 219908q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.64474 0.370087i −0.997858 0.0654228i
\(3\) 0 0
\(4\) 31.7261 + 4.17809i 0.991440 + 0.130565i
\(5\) 38.9183i 0.696191i −0.937459 0.348096i \(-0.886828\pi\)
0.937459 0.348096i \(-0.113172\pi\)
\(6\) 0 0
\(7\) 132.403i 1.02130i 0.859788 + 0.510651i \(0.170596\pi\)
−0.859788 + 0.510651i \(0.829404\pi\)
\(8\) −177.539 35.3256i −0.980774 0.195148i
\(9\) 0 0
\(10\) −14.4032 + 219.683i −0.0455468 + 0.694700i
\(11\) 190.441 0.474547 0.237273 0.971443i \(-0.423746\pi\)
0.237273 + 0.971443i \(0.423746\pi\)
\(12\) 0 0
\(13\) −416.631 −0.683744 −0.341872 0.939746i \(-0.611061\pi\)
−0.341872 + 0.939746i \(0.611061\pi\)
\(14\) 49.0008 747.382i 0.0668164 1.01911i
\(15\) 0 0
\(16\) 989.087 + 265.109i 0.965905 + 0.258895i
\(17\) 1145.55i 0.961371i −0.876893 0.480686i \(-0.840388\pi\)
0.876893 0.480686i \(-0.159612\pi\)
\(18\) 0 0
\(19\) 768.976i 0.488685i 0.969689 + 0.244342i \(0.0785721\pi\)
−0.969689 + 0.244342i \(0.921428\pi\)
\(20\) 162.604 1234.72i 0.0908984 0.690232i
\(21\) 0 0
\(22\) −1074.99 70.4798i −0.473530 0.0310462i
\(23\) −2231.96 −0.879765 −0.439882 0.898055i \(-0.644980\pi\)
−0.439882 + 0.898055i \(0.644980\pi\)
\(24\) 0 0
\(25\) 1610.37 0.515318
\(26\) 2351.77 + 154.190i 0.682279 + 0.0447325i
\(27\) 0 0
\(28\) −553.193 + 4200.64i −0.133347 + 1.01256i
\(29\) 5919.93i 1.30714i 0.756867 + 0.653569i \(0.226729\pi\)
−0.756867 + 0.653569i \(0.773271\pi\)
\(30\) 0 0
\(31\) 10009.3i 1.87068i 0.353751 + 0.935340i \(0.384906\pi\)
−0.353751 + 0.935340i \(0.615094\pi\)
\(32\) −5485.02 1862.52i −0.946898 0.321533i
\(33\) 0 0
\(34\) −423.953 + 6466.32i −0.0628956 + 0.959312i
\(35\) 5152.91 0.711021
\(36\) 0 0
\(37\) 4317.45 0.518470 0.259235 0.965814i \(-0.416530\pi\)
0.259235 + 0.965814i \(0.416530\pi\)
\(38\) 284.588 4340.67i 0.0319711 0.487638i
\(39\) 0 0
\(40\) −1374.81 + 6909.51i −0.135861 + 0.682806i
\(41\) 18511.5i 1.71981i 0.510453 + 0.859906i \(0.329478\pi\)
−0.510453 + 0.859906i \(0.670522\pi\)
\(42\) 0 0
\(43\) 5568.60i 0.459277i 0.973276 + 0.229638i \(0.0737544\pi\)
−0.973276 + 0.229638i \(0.926246\pi\)
\(44\) 6041.95 + 795.680i 0.470484 + 0.0619593i
\(45\) 0 0
\(46\) 12598.8 + 826.019i 0.877880 + 0.0575567i
\(47\) 12618.3 0.833212 0.416606 0.909087i \(-0.363219\pi\)
0.416606 + 0.909087i \(0.363219\pi\)
\(48\) 0 0
\(49\) −723.662 −0.0430572
\(50\) −9090.10 595.977i −0.514214 0.0337135i
\(51\) 0 0
\(52\) −13218.1 1740.72i −0.677891 0.0892732i
\(53\) 30907.9i 1.51140i 0.654918 + 0.755700i \(0.272703\pi\)
−0.654918 + 0.755700i \(0.727297\pi\)
\(54\) 0 0
\(55\) 7411.64i 0.330375i
\(56\) 4677.23 23506.8i 0.199305 1.00167i
\(57\) 0 0
\(58\) 2190.89 33416.4i 0.0855167 1.30434i
\(59\) −39249.3 −1.46792 −0.733959 0.679194i \(-0.762329\pi\)
−0.733959 + 0.679194i \(0.762329\pi\)
\(60\) 0 0
\(61\) −45204.0 −1.55544 −0.777719 0.628612i \(-0.783623\pi\)
−0.777719 + 0.628612i \(0.783623\pi\)
\(62\) 3704.31 56499.8i 0.122385 1.86667i
\(63\) 0 0
\(64\) 30272.2 + 12543.4i 0.923834 + 0.382793i
\(65\) 16214.6i 0.476017i
\(66\) 0 0
\(67\) 24713.4i 0.672582i −0.941758 0.336291i \(-0.890827\pi\)
0.941758 0.336291i \(-0.109173\pi\)
\(68\) 4786.20 36343.8i 0.125522 0.953142i
\(69\) 0 0
\(70\) −29086.8 1907.03i −0.709498 0.0465170i
\(71\) 18755.2 0.441546 0.220773 0.975325i \(-0.429142\pi\)
0.220773 + 0.975325i \(0.429142\pi\)
\(72\) 0 0
\(73\) 81273.7 1.78502 0.892510 0.451029i \(-0.148943\pi\)
0.892510 + 0.451029i \(0.148943\pi\)
\(74\) −24370.9 1597.83i −0.517359 0.0339197i
\(75\) 0 0
\(76\) −3212.85 + 24396.6i −0.0638053 + 0.484502i
\(77\) 25215.0i 0.484655i
\(78\) 0 0
\(79\) 33373.3i 0.601633i −0.953682 0.300817i \(-0.902741\pi\)
0.953682 0.300817i \(-0.0972592\pi\)
\(80\) 10317.6 38493.6i 0.180241 0.672455i
\(81\) 0 0
\(82\) 6850.85 104492.i 0.112515 1.71613i
\(83\) 47528.7 0.757288 0.378644 0.925542i \(-0.376391\pi\)
0.378644 + 0.925542i \(0.376391\pi\)
\(84\) 0 0
\(85\) −44582.8 −0.669298
\(86\) 2060.87 31433.3i 0.0300472 0.458293i
\(87\) 0 0
\(88\) −33810.7 6727.45i −0.465423 0.0926070i
\(89\) 65440.5i 0.875733i 0.899040 + 0.437866i \(0.144266\pi\)
−0.899040 + 0.437866i \(0.855734\pi\)
\(90\) 0 0
\(91\) 55163.4i 0.698309i
\(92\) −70811.3 9325.32i −0.872234 0.114867i
\(93\) 0 0
\(94\) −71226.9 4669.86i −0.831427 0.0545111i
\(95\) 29927.2 0.340218
\(96\) 0 0
\(97\) −29170.2 −0.314782 −0.157391 0.987536i \(-0.550308\pi\)
−0.157391 + 0.987536i \(0.550308\pi\)
\(98\) 4084.88 + 267.818i 0.0429649 + 0.00281692i
\(99\) 0 0
\(100\) 51090.6 + 6728.26i 0.510906 + 0.0672826i
\(101\) 94523.4i 0.922011i 0.887397 + 0.461005i \(0.152511\pi\)
−0.887397 + 0.461005i \(0.847489\pi\)
\(102\) 0 0
\(103\) 69615.0i 0.646561i −0.946303 0.323281i \(-0.895214\pi\)
0.946303 0.323281i \(-0.104786\pi\)
\(104\) 73968.3 + 14717.8i 0.670598 + 0.133432i
\(105\) 0 0
\(106\) 11438.6 174467.i 0.0988800 1.50816i
\(107\) −174764. −1.47568 −0.737840 0.674976i \(-0.764154\pi\)
−0.737840 + 0.674976i \(0.764154\pi\)
\(108\) 0 0
\(109\) 90100.9 0.726378 0.363189 0.931715i \(-0.381688\pi\)
0.363189 + 0.931715i \(0.381688\pi\)
\(110\) −2742.95 + 41836.7i −0.0216141 + 0.329667i
\(111\) 0 0
\(112\) −35101.3 + 130959.i −0.264410 + 0.986481i
\(113\) 53319.6i 0.392817i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(114\) 0 0
\(115\) 86864.0i 0.612485i
\(116\) −24734.0 + 187816.i −0.170667 + 1.29595i
\(117\) 0 0
\(118\) 221552. + 14525.7i 1.46477 + 0.0960353i
\(119\) 151675. 0.981850
\(120\) 0 0
\(121\) −124783. −0.774806
\(122\) 255165. + 16729.4i 1.55211 + 0.101761i
\(123\) 0 0
\(124\) −41819.7 + 317556.i −0.244246 + 1.85467i
\(125\) 184292.i 1.05495i
\(126\) 0 0
\(127\) 226128.i 1.24407i 0.782988 + 0.622036i \(0.213694\pi\)
−0.782988 + 0.622036i \(0.786306\pi\)
\(128\) −166236. 82007.3i −0.896812 0.442412i
\(129\) 0 0
\(130\) 6000.81 91527.0i 0.0311423 0.474997i
\(131\) −52645.4 −0.268029 −0.134015 0.990979i \(-0.542787\pi\)
−0.134015 + 0.990979i \(0.542787\pi\)
\(132\) 0 0
\(133\) −101815. −0.499095
\(134\) −9146.11 + 139501.i −0.0440022 + 0.671141i
\(135\) 0 0
\(136\) −40467.2 + 203380.i −0.187610 + 0.942888i
\(137\) 288620.i 1.31379i −0.753984 0.656893i \(-0.771870\pi\)
0.753984 0.656893i \(-0.228130\pi\)
\(138\) 0 0
\(139\) 241199.i 1.05886i 0.848354 + 0.529430i \(0.177594\pi\)
−0.848354 + 0.529430i \(0.822406\pi\)
\(140\) 163482. + 21529.3i 0.704935 + 0.0928347i
\(141\) 0 0
\(142\) −105868. 6941.07i −0.440600 0.0288872i
\(143\) −79343.7 −0.324468
\(144\) 0 0
\(145\) 230393. 0.910018
\(146\) −458768. 30078.4i −1.78119 0.116781i
\(147\) 0 0
\(148\) 136976. + 18038.7i 0.514031 + 0.0676941i
\(149\) 404813.i 1.49379i −0.664943 0.746894i \(-0.731544\pi\)
0.664943 0.746894i \(-0.268456\pi\)
\(150\) 0 0
\(151\) 107181.i 0.382540i 0.981537 + 0.191270i \(0.0612605\pi\)
−0.981537 + 0.191270i \(0.938739\pi\)
\(152\) 27164.6 136523.i 0.0953660 0.479289i
\(153\) 0 0
\(154\) 9331.77 142332.i 0.0317075 0.483617i
\(155\) 389545. 1.30235
\(156\) 0 0
\(157\) 289913. 0.938682 0.469341 0.883017i \(-0.344492\pi\)
0.469341 + 0.883017i \(0.344492\pi\)
\(158\) −12351.0 + 188384.i −0.0393605 + 0.600344i
\(159\) 0 0
\(160\) −72485.9 + 213468.i −0.223848 + 0.659222i
\(161\) 295519.i 0.898505i
\(162\) 0 0
\(163\) 383691.i 1.13113i −0.824703 0.565566i \(-0.808658\pi\)
0.824703 0.565566i \(-0.191342\pi\)
\(164\) −77342.5 + 587296.i −0.224548 + 1.70509i
\(165\) 0 0
\(166\) −268287. 17589.8i −0.755665 0.0495439i
\(167\) −552670. −1.53347 −0.766735 0.641964i \(-0.778120\pi\)
−0.766735 + 0.641964i \(0.778120\pi\)
\(168\) 0 0
\(169\) −197711. −0.532494
\(170\) 251658. + 16499.5i 0.667864 + 0.0437874i
\(171\) 0 0
\(172\) −23266.1 + 176670.i −0.0599656 + 0.455345i
\(173\) 388771.i 0.987594i −0.869577 0.493797i \(-0.835609\pi\)
0.869577 0.493797i \(-0.164391\pi\)
\(174\) 0 0
\(175\) 213218.i 0.526295i
\(176\) 188363. + 50487.6i 0.458367 + 0.122858i
\(177\) 0 0
\(178\) 24218.7 369394.i 0.0572929 0.873857i
\(179\) −300195. −0.700278 −0.350139 0.936698i \(-0.613866\pi\)
−0.350139 + 0.936698i \(0.613866\pi\)
\(180\) 0 0
\(181\) −197901. −0.449005 −0.224503 0.974474i \(-0.572076\pi\)
−0.224503 + 0.974474i \(0.572076\pi\)
\(182\) −20415.3 + 311383.i −0.0456853 + 0.696813i
\(183\) 0 0
\(184\) 396260. + 78845.3i 0.862850 + 0.171685i
\(185\) 168028.i 0.360954i
\(186\) 0 0
\(187\) 218159.i 0.456215i
\(188\) 400328. + 52720.3i 0.826080 + 0.108789i
\(189\) 0 0
\(190\) −168931. 11075.7i −0.339489 0.0222580i
\(191\) 911538. 1.80797 0.903986 0.427563i \(-0.140628\pi\)
0.903986 + 0.427563i \(0.140628\pi\)
\(192\) 0 0
\(193\) −148579. −0.287120 −0.143560 0.989642i \(-0.545855\pi\)
−0.143560 + 0.989642i \(0.545855\pi\)
\(194\) 164658. + 10795.5i 0.314108 + 0.0205939i
\(195\) 0 0
\(196\) −22959.0 3023.52i −0.0426886 0.00562177i
\(197\) 537867.i 0.987437i 0.869622 + 0.493718i \(0.164363\pi\)
−0.869622 + 0.493718i \(0.835637\pi\)
\(198\) 0 0
\(199\) 199552.i 0.357211i 0.983921 + 0.178605i \(0.0571585\pi\)
−0.983921 + 0.178605i \(0.942841\pi\)
\(200\) −285903. 56887.2i −0.505410 0.100563i
\(201\) 0 0
\(202\) 34981.9 533560.i 0.0603205 0.920035i
\(203\) −783819. −1.33498
\(204\) 0 0
\(205\) 720434. 1.19732
\(206\) −25763.6 + 392958.i −0.0422998 + 0.645176i
\(207\) 0 0
\(208\) −412085. 110453.i −0.660432 0.177018i
\(209\) 146445.i 0.231904i
\(210\) 0 0
\(211\) 778163.i 1.20327i −0.798770 0.601637i \(-0.794515\pi\)
0.798770 0.601637i \(-0.205485\pi\)
\(212\) −129136. + 980585.i −0.197336 + 1.49846i
\(213\) 0 0
\(214\) 986496. + 64677.9i 1.47252 + 0.0965431i
\(215\) 216720. 0.319745
\(216\) 0 0
\(217\) −1.32526e6 −1.91053
\(218\) −508596. 33345.2i −0.724822 0.0475217i
\(219\) 0 0
\(220\) 30966.5 235142.i 0.0431355 0.327547i
\(221\) 477271.i 0.657332i
\(222\) 0 0
\(223\) 681625.i 0.917875i −0.888469 0.458937i \(-0.848230\pi\)
0.888469 0.458937i \(-0.151770\pi\)
\(224\) 246604. 726236.i 0.328382 0.967069i
\(225\) 0 0
\(226\) 19732.9 300975.i 0.0256992 0.391976i
\(227\) 1.28670e6 1.65734 0.828671 0.559736i \(-0.189098\pi\)
0.828671 + 0.559736i \(0.189098\pi\)
\(228\) 0 0
\(229\) −74657.5 −0.0940773 −0.0470386 0.998893i \(-0.514978\pi\)
−0.0470386 + 0.998893i \(0.514978\pi\)
\(230\) 32147.3 490324.i 0.0400705 0.611172i
\(231\) 0 0
\(232\) 209125. 1.05102e6i 0.255086 1.28201i
\(233\) 638465.i 0.770455i −0.922822 0.385227i \(-0.874123\pi\)
0.922822 0.385227i \(-0.125877\pi\)
\(234\) 0 0
\(235\) 491082.i 0.580075i
\(236\) −1.24523e6 163987.i −1.45535 0.191659i
\(237\) 0 0
\(238\) −856162. 56132.8i −0.979747 0.0642354i
\(239\) −1.43424e6 −1.62415 −0.812077 0.583550i \(-0.801663\pi\)
−0.812077 + 0.583550i \(0.801663\pi\)
\(240\) 0 0
\(241\) 989623. 1.09756 0.548778 0.835968i \(-0.315093\pi\)
0.548778 + 0.835968i \(0.315093\pi\)
\(242\) 704368. + 46180.7i 0.773146 + 0.0506899i
\(243\) 0 0
\(244\) −1.43415e6 188866.i −1.54212 0.203086i
\(245\) 28163.7i 0.0299760i
\(246\) 0 0
\(247\) 320380.i 0.334135i
\(248\) 353585. 1.77704e6i 0.365060 1.83471i
\(249\) 0 0
\(250\) −68204.2 + 1.04028e6i −0.0690178 + 1.05269i
\(251\) 272737. 0.273250 0.136625 0.990623i \(-0.456375\pi\)
0.136625 + 0.990623i \(0.456375\pi\)
\(252\) 0 0
\(253\) −425057. −0.417489
\(254\) 83687.2 1.27643e6i 0.0813907 1.24141i
\(255\) 0 0
\(256\) 908011. + 524431.i 0.865947 + 0.500137i
\(257\) 1.22534e6i 1.15725i 0.815595 + 0.578623i \(0.196410\pi\)
−0.815595 + 0.578623i \(0.803590\pi\)
\(258\) 0 0
\(259\) 571645.i 0.529514i
\(260\) −67745.9 + 514425.i −0.0621513 + 0.471942i
\(261\) 0 0
\(262\) 297169. + 19483.4i 0.267455 + 0.0175352i
\(263\) 202375. 0.180413 0.0902065 0.995923i \(-0.471247\pi\)
0.0902065 + 0.995923i \(0.471247\pi\)
\(264\) 0 0
\(265\) 1.20288e6 1.05222
\(266\) 574719. + 37680.5i 0.498025 + 0.0326522i
\(267\) 0 0
\(268\) 103255. 784059.i 0.0878159 0.666824i
\(269\) 546051.i 0.460100i 0.973179 + 0.230050i \(0.0738890\pi\)
−0.973179 + 0.230050i \(0.926111\pi\)
\(270\) 0 0
\(271\) 1.95161e6i 1.61425i 0.590383 + 0.807123i \(0.298977\pi\)
−0.590383 + 0.807123i \(0.701023\pi\)
\(272\) 303695. 1.13305e6i 0.248894 0.928594i
\(273\) 0 0
\(274\) −106814. + 1.62918e6i −0.0859515 + 1.31097i
\(275\) 306680. 0.244542
\(276\) 0 0
\(277\) −128661. −0.100751 −0.0503754 0.998730i \(-0.516042\pi\)
−0.0503754 + 0.998730i \(0.516042\pi\)
\(278\) 89264.7 1.36150e6i 0.0692736 1.05659i
\(279\) 0 0
\(280\) −914843. 182030.i −0.697351 0.138755i
\(281\) 1.55530e6i 1.17503i 0.809213 + 0.587515i \(0.199894\pi\)
−0.809213 + 0.587515i \(0.800106\pi\)
\(282\) 0 0
\(283\) 520162.i 0.386076i 0.981191 + 0.193038i \(0.0618341\pi\)
−0.981191 + 0.193038i \(0.938166\pi\)
\(284\) 595030. + 78361.0i 0.437767 + 0.0576506i
\(285\) 0 0
\(286\) 447874. + 29364.1i 0.323773 + 0.0212276i
\(287\) −2.45098e6 −1.75645
\(288\) 0 0
\(289\) 107576. 0.0757652
\(290\) −1.30051e6 85265.7i −0.908069 0.0595360i
\(291\) 0 0
\(292\) 2.57850e6 + 339569.i 1.76974 + 0.233062i
\(293\) 398515.i 0.271191i −0.990764 0.135596i \(-0.956705\pi\)
0.990764 0.135596i \(-0.0432948\pi\)
\(294\) 0 0
\(295\) 1.52751e6i 1.02195i
\(296\) −766516. 152517.i −0.508501 0.101178i
\(297\) 0 0
\(298\) −149816. + 2.28506e6i −0.0977278 + 1.49059i
\(299\) 929904. 0.601534
\(300\) 0 0
\(301\) −737301. −0.469060
\(302\) 39666.4 605010.i 0.0250268 0.381720i
\(303\) 0 0
\(304\) −203862. + 760585.i −0.126518 + 0.472023i
\(305\) 1.75926e6i 1.08288i
\(306\) 0 0
\(307\) 1.24181e6i 0.751987i −0.926622 0.375994i \(-0.877301\pi\)
0.926622 0.375994i \(-0.122699\pi\)
\(308\) −105351. + 799974.i −0.0632791 + 0.480506i
\(309\) 0 0
\(310\) −2.19888e6 144165.i −1.29956 0.0852034i
\(311\) 2.77430e6 1.62649 0.813246 0.581921i \(-0.197699\pi\)
0.813246 + 0.581921i \(0.197699\pi\)
\(312\) 0 0
\(313\) −1.10249e6 −0.636080 −0.318040 0.948077i \(-0.603025\pi\)
−0.318040 + 0.948077i \(0.603025\pi\)
\(314\) −1.63648e6 107293.i −0.936671 0.0614112i
\(315\) 0 0
\(316\) 139437. 1.05880e6i 0.0785524 0.596483i
\(317\) 2.09886e6i 1.17310i 0.809914 + 0.586549i \(0.199514\pi\)
−0.809914 + 0.586549i \(0.800486\pi\)
\(318\) 0 0
\(319\) 1.12740e6i 0.620298i
\(320\) 488166. 1.17814e6i 0.266497 0.643165i
\(321\) 0 0
\(322\) −109368. + 1.66813e6i −0.0587827 + 0.896580i
\(323\) 880900. 0.469808
\(324\) 0 0
\(325\) −670930. −0.352345
\(326\) −141999. + 2.16584e6i −0.0740018 + 1.12871i
\(327\) 0 0
\(328\) 653929. 3.28651e6i 0.335618 1.68675i
\(329\) 1.67070e6i 0.850961i
\(330\) 0 0
\(331\) 1.27129e6i 0.637786i −0.947791 0.318893i \(-0.896689\pi\)
0.947791 0.318893i \(-0.103311\pi\)
\(332\) 1.50790e6 + 198579.i 0.750805 + 0.0988755i
\(333\) 0 0
\(334\) 3.11968e6 + 204536.i 1.53018 + 0.100324i
\(335\) −961802. −0.468246
\(336\) 0 0
\(337\) 1.39426e6 0.668760 0.334380 0.942438i \(-0.391473\pi\)
0.334380 + 0.942438i \(0.391473\pi\)
\(338\) 1.11603e6 + 73170.4i 0.531353 + 0.0348372i
\(339\) 0 0
\(340\) −1.41444e6 186271.i −0.663569 0.0873871i
\(341\) 1.90618e6i 0.887724i
\(342\) 0 0
\(343\) 2.12949e6i 0.977327i
\(344\) 196714. 988643.i 0.0896271 0.450447i
\(345\) 0 0
\(346\) −143879. + 2.19451e6i −0.0646111 + 0.985478i
\(347\) −762430. −0.339920 −0.169960 0.985451i \(-0.554364\pi\)
−0.169960 + 0.985451i \(0.554364\pi\)
\(348\) 0 0
\(349\) 356038. 0.156471 0.0782353 0.996935i \(-0.475071\pi\)
0.0782353 + 0.996935i \(0.475071\pi\)
\(350\) 78909.3 1.20356e6i 0.0344317 0.525167i
\(351\) 0 0
\(352\) −1.04457e6 354700.i −0.449347 0.152582i
\(353\) 3.82852e6i 1.63529i −0.575725 0.817643i \(-0.695280\pi\)
0.575725 0.817643i \(-0.304720\pi\)
\(354\) 0 0
\(355\) 729921.i 0.307401i
\(356\) −273416. + 2.07617e6i −0.114340 + 0.868236i
\(357\) 0 0
\(358\) 1.69452e6 + 111098.i 0.698778 + 0.0458141i
\(359\) 976058. 0.399705 0.199852 0.979826i \(-0.435954\pi\)
0.199852 + 0.979826i \(0.435954\pi\)
\(360\) 0 0
\(361\) 1.88477e6 0.761187
\(362\) 1.11710e6 + 73240.6i 0.448043 + 0.0293752i
\(363\) 0 0
\(364\) 230478. 1.75012e6i 0.0911749 0.692331i
\(365\) 3.16303e6i 1.24271i
\(366\) 0 0
\(367\) 378329.i 0.146624i 0.997309 + 0.0733119i \(0.0233569\pi\)
−0.997309 + 0.0733119i \(0.976643\pi\)
\(368\) −2.20760e6 591712.i −0.849770 0.227767i
\(369\) 0 0
\(370\) −62184.9 + 948472.i −0.0236146 + 0.360181i
\(371\) −4.09230e6 −1.54359
\(372\) 0 0
\(373\) −2.27236e6 −0.845678 −0.422839 0.906205i \(-0.638966\pi\)
−0.422839 + 0.906205i \(0.638966\pi\)
\(374\) −80738.0 + 1.23145e6i −0.0298469 + 0.455238i
\(375\) 0 0
\(376\) −2.24024e6 445749.i −0.817193 0.162600i
\(377\) 2.46643e6i 0.893748i
\(378\) 0 0
\(379\) 5.13906e6i 1.83775i −0.394551 0.918874i \(-0.629100\pi\)
0.394551 0.918874i \(-0.370900\pi\)
\(380\) 949473. + 125039.i 0.337306 + 0.0444207i
\(381\) 0 0
\(382\) −5.14539e6 337349.i −1.80410 0.118283i
\(383\) 70733.0 0.0246391 0.0123196 0.999924i \(-0.496078\pi\)
0.0123196 + 0.999924i \(0.496078\pi\)
\(384\) 0 0
\(385\) 981326. 0.337413
\(386\) 838686. + 54987.0i 0.286504 + 0.0187842i
\(387\) 0 0
\(388\) −925456. 121876.i −0.312088 0.0410996i
\(389\) 1.49179e6i 0.499843i −0.968266 0.249922i \(-0.919595\pi\)
0.968266 0.249922i \(-0.0804049\pi\)
\(390\) 0 0
\(391\) 2.55682e6i 0.845781i
\(392\) 128478. + 25563.8i 0.0422294 + 0.00840254i
\(393\) 0 0
\(394\) 199058. 3.03612e6i 0.0646009 0.985321i
\(395\) −1.29883e6 −0.418852
\(396\) 0 0
\(397\) 2.91290e6 0.927575 0.463787 0.885947i \(-0.346490\pi\)
0.463787 + 0.885947i \(0.346490\pi\)
\(398\) 73851.8 1.12642e6i 0.0233697 0.356445i
\(399\) 0 0
\(400\) 1.59279e6 + 426923.i 0.497748 + 0.133413i
\(401\) 1.18881e6i 0.369191i −0.982815 0.184595i \(-0.940903\pi\)
0.982815 0.184595i \(-0.0590975\pi\)
\(402\) 0 0
\(403\) 4.17019e6i 1.27907i
\(404\) −394927. + 2.99886e6i −0.120383 + 0.914118i
\(405\) 0 0
\(406\) 4.42445e6 + 290081.i 1.33212 + 0.0873383i
\(407\) 822220. 0.246038
\(408\) 0 0
\(409\) −3.31777e6 −0.980705 −0.490352 0.871524i \(-0.663132\pi\)
−0.490352 + 0.871524i \(0.663132\pi\)
\(410\) −4.06666e6 266623.i −1.19475 0.0783319i
\(411\) 0 0
\(412\) 290858. 2.20861e6i 0.0844184 0.641026i
\(413\) 5.19674e6i 1.49919i
\(414\) 0 0
\(415\) 1.84974e6i 0.527217i
\(416\) 2.28523e6 + 775983.i 0.647436 + 0.219846i
\(417\) 0 0
\(418\) 54197.3 826641.i 0.0151718 0.231407i
\(419\) 4.24309e6 1.18072 0.590361 0.807140i \(-0.298985\pi\)
0.590361 + 0.807140i \(0.298985\pi\)
\(420\) 0 0
\(421\) −3.70532e6 −1.01887 −0.509437 0.860508i \(-0.670146\pi\)
−0.509437 + 0.860508i \(0.670146\pi\)
\(422\) −287988. + 4.39252e6i −0.0787215 + 1.20070i
\(423\) 0 0
\(424\) 1.09184e6 5.48735e6i 0.294947 1.48234i
\(425\) 1.84475e6i 0.495412i
\(426\) 0 0
\(427\) 5.98517e6i 1.58857i
\(428\) −5.54457e6 730179.i −1.46305 0.192673i
\(429\) 0 0
\(430\) −1.22333e6 80205.4i −0.319060 0.0209186i
\(431\) 4.36762e6 1.13253 0.566267 0.824222i \(-0.308387\pi\)
0.566267 + 0.824222i \(0.308387\pi\)
\(432\) 0 0
\(433\) 2.08282e6 0.533865 0.266932 0.963715i \(-0.413990\pi\)
0.266932 + 0.963715i \(0.413990\pi\)
\(434\) 7.48077e6 + 490464.i 1.90643 + 0.124992i
\(435\) 0 0
\(436\) 2.85855e6 + 376450.i 0.720160 + 0.0948398i
\(437\) 1.71632e6i 0.429928i
\(438\) 0 0
\(439\) 2.60275e6i 0.644571i 0.946642 + 0.322286i \(0.104451\pi\)
−0.946642 + 0.322286i \(0.895549\pi\)
\(440\) −261821. + 1.31585e6i −0.0644722 + 0.324023i
\(441\) 0 0
\(442\) 176632. 2.69407e6i 0.0430045 0.655924i
\(443\) −4.93001e6 −1.19354 −0.596772 0.802411i \(-0.703551\pi\)
−0.596772 + 0.802411i \(0.703551\pi\)
\(444\) 0 0
\(445\) 2.54683e6 0.609678
\(446\) −252261. + 3.84759e6i −0.0600499 + 0.915908i
\(447\) 0 0
\(448\) −1.66078e6 + 4.00814e6i −0.390947 + 0.943514i
\(449\) 3.42135e6i 0.800906i −0.916317 0.400453i \(-0.868853\pi\)
0.916317 0.400453i \(-0.131147\pi\)
\(450\) 0 0
\(451\) 3.52534e6i 0.816131i
\(452\) −222774. + 1.69162e6i −0.0512883 + 0.389455i
\(453\) 0 0
\(454\) −7.26307e6 476190.i −1.65379 0.108428i
\(455\) −2.14687e6 −0.486157
\(456\) 0 0
\(457\) −7.87833e6 −1.76459 −0.882295 0.470697i \(-0.844002\pi\)
−0.882295 + 0.470697i \(0.844002\pi\)
\(458\) 421422. + 27629.8i 0.0938757 + 0.00615480i
\(459\) 0 0
\(460\) −362925. + 2.75585e6i −0.0799692 + 0.607241i
\(461\) 3.24234e6i 0.710569i 0.934758 + 0.355284i \(0.115616\pi\)
−0.934758 + 0.355284i \(0.884384\pi\)
\(462\) 0 0
\(463\) 3.95642e6i 0.857728i 0.903369 + 0.428864i \(0.141086\pi\)
−0.903369 + 0.428864i \(0.858914\pi\)
\(464\) −1.56942e6 + 5.85533e6i −0.338412 + 1.26257i
\(465\) 0 0
\(466\) −236288. + 3.60396e6i −0.0504053 + 0.768804i
\(467\) 3.80560e6 0.807478 0.403739 0.914874i \(-0.367710\pi\)
0.403739 + 0.914874i \(0.367710\pi\)
\(468\) 0 0
\(469\) 3.27214e6 0.686909
\(470\) −181743. + 2.77203e6i −0.0379501 + 0.578832i
\(471\) 0 0
\(472\) 6.96828e6 + 1.38650e6i 1.43969 + 0.286462i
\(473\) 1.06049e6i 0.217948i
\(474\) 0 0
\(475\) 1.23833e6i 0.251828i
\(476\) 4.81204e6 + 633710.i 0.973445 + 0.128196i
\(477\) 0 0
\(478\) 8.09591e6 + 530794.i 1.62067 + 0.106257i
\(479\) −6.76059e6 −1.34631 −0.673156 0.739500i \(-0.735062\pi\)
−0.673156 + 0.739500i \(0.735062\pi\)
\(480\) 0 0
\(481\) −1.79879e6 −0.354501
\(482\) −5.58616e6 366247.i −1.09521 0.0718052i
\(483\) 0 0
\(484\) −3.95888e6 521355.i −0.768173 0.101163i
\(485\) 1.13525e6i 0.219149i
\(486\) 0 0
\(487\) 3.94101e6i 0.752982i 0.926420 + 0.376491i \(0.122869\pi\)
−0.926420 + 0.376491i \(0.877131\pi\)
\(488\) 8.02548e6 + 1.59686e6i 1.52553 + 0.303541i
\(489\) 0 0
\(490\) 10423.0 158977.i 0.00196112 0.0299118i
\(491\) −2.38312e6 −0.446111 −0.223055 0.974806i \(-0.571603\pi\)
−0.223055 + 0.974806i \(0.571603\pi\)
\(492\) 0 0
\(493\) 6.78157e6 1.25665
\(494\) −118568. + 1.80846e6i −0.0218601 + 0.333420i
\(495\) 0 0
\(496\) −2.65355e6 + 9.90007e6i −0.484310 + 1.80690i
\(497\) 2.48326e6i 0.450952i
\(498\) 0 0
\(499\) 5.97843e6i 1.07482i −0.843321 0.537410i \(-0.819403\pi\)
0.843321 0.537410i \(-0.180597\pi\)
\(500\) 769990. 5.84687e6i 0.137740 1.04592i
\(501\) 0 0
\(502\) −1.53953e6 100936.i −0.272664 0.0178767i
\(503\) 2.75877e6 0.486179 0.243090 0.970004i \(-0.421839\pi\)
0.243090 + 0.970004i \(0.421839\pi\)
\(504\) 0 0
\(505\) 3.67869e6 0.641896
\(506\) 2.39933e6 + 157308.i 0.416595 + 0.0273133i
\(507\) 0 0
\(508\) −944785. + 7.17417e6i −0.162433 + 1.23342i
\(509\) 198012.i 0.0338764i 0.999857 + 0.0169382i \(0.00539186\pi\)
−0.999857 + 0.0169382i \(0.994608\pi\)
\(510\) 0 0
\(511\) 1.07609e7i 1.82304i
\(512\) −4.93140e6 3.29632e6i −0.831371 0.555718i
\(513\) 0 0
\(514\) 453484. 6.91675e6i 0.0757102 1.15477i
\(515\) −2.70929e6 −0.450130
\(516\) 0 0
\(517\) 2.40304e6 0.395398
\(518\) 211559. 3.22679e6i 0.0346423 0.528379i
\(519\) 0 0
\(520\) 572790. 2.87872e6i 0.0928939 0.466865i
\(521\) 499429.i 0.0806082i 0.999187 + 0.0403041i \(0.0128327\pi\)
−0.999187 + 0.0403041i \(0.987167\pi\)
\(522\) 0 0
\(523\) 2.10979e6i 0.337276i 0.985678 + 0.168638i \(0.0539369\pi\)
−0.985678 + 0.168638i \(0.946063\pi\)
\(524\) −1.67023e6 219957.i −0.265735 0.0349953i
\(525\) 0 0
\(526\) −1.14235e6 74896.5i −0.180027 0.0118031i
\(527\) 1.14661e7 1.79842
\(528\) 0 0
\(529\) −1.45470e6 −0.226014
\(530\) −6.78994e6 445171.i −1.04997 0.0688394i
\(531\) 0 0
\(532\) −3.23019e6 425392.i −0.494822 0.0651644i
\(533\) 7.71245e6i 1.17591i
\(534\) 0 0
\(535\) 6.80151e6i 1.02736i
\(536\) −873016. + 4.38759e6i −0.131253 + 0.659651i
\(537\) 0 0
\(538\) 202086. 3.08231e6i 0.0301010 0.459114i
\(539\) −137815. −0.0204326
\(540\) 0 0
\(541\) −7.08611e6 −1.04091 −0.520457 0.853888i \(-0.674238\pi\)
−0.520457 + 0.853888i \(0.674238\pi\)
\(542\) 722266. 1.10163e7i 0.105609 1.61079i
\(543\) 0 0
\(544\) −2.13360e6 + 6.28336e6i −0.309112 + 0.910321i
\(545\) 3.50657e6i 0.505698i
\(546\) 0 0
\(547\) 1.14218e7i 1.63218i −0.577925 0.816090i \(-0.696137\pi\)
0.577925 0.816090i \(-0.303863\pi\)
\(548\) 1.20588e6 9.15677e6i 0.171535 1.30254i
\(549\) 0 0
\(550\) −1.73113e6 113498.i −0.244018 0.0159986i
\(551\) −4.55229e6 −0.638779
\(552\) 0 0
\(553\) 4.41874e6 0.614449
\(554\) 726259. + 47615.9i 0.100535 + 0.00659140i
\(555\) 0 0
\(556\) −1.00775e6 + 7.65230e6i −0.138250 + 1.04980i
\(557\) 1.11633e7i 1.52459i 0.647227 + 0.762297i \(0.275929\pi\)
−0.647227 + 0.762297i \(0.724071\pi\)
\(558\) 0 0
\(559\) 2.32005e6i 0.314028i
\(560\) 5.09668e6 + 1.36608e6i 0.686779 + 0.184080i
\(561\) 0 0
\(562\) 575598. 8.77927e6i 0.0768738 1.17251i
\(563\) 6.63847e6 0.882668 0.441334 0.897343i \(-0.354505\pi\)
0.441334 + 0.897343i \(0.354505\pi\)
\(564\) 0 0
\(565\) 2.07511e6 0.273476
\(566\) 192506. 2.93618e6i 0.0252582 0.385249i
\(567\) 0 0
\(568\) −3.32978e6 662540.i −0.433057 0.0861670i
\(569\) 3.66619e6i 0.474716i 0.971422 + 0.237358i \(0.0762815\pi\)
−0.971422 + 0.237358i \(0.923719\pi\)
\(570\) 0 0
\(571\) 4.47869e6i 0.574858i 0.957802 + 0.287429i \(0.0928006\pi\)
−0.957802 + 0.287429i \(0.907199\pi\)
\(572\) −2.51726e6 331505.i −0.321691 0.0423643i
\(573\) 0 0
\(574\) 1.38351e7 + 907076.i 1.75268 + 0.114912i
\(575\) −3.59427e6 −0.453358
\(576\) 0 0
\(577\) −8.10380e6 −1.01333 −0.506663 0.862144i \(-0.669121\pi\)
−0.506663 + 0.862144i \(0.669121\pi\)
\(578\) −607236. 39812.4i −0.0756029 0.00495677i
\(579\) 0 0
\(580\) 7.30948e6 + 962604.i 0.902228 + 0.118817i
\(581\) 6.29296e6i 0.773419i
\(582\) 0 0
\(583\) 5.88612e6i 0.717229i
\(584\) −1.44293e7 2.87104e6i −1.75070 0.348343i
\(585\) 0 0
\(586\) −147485. + 2.24951e6i −0.0177421 + 0.270610i
\(587\) −6.56387e6 −0.786258 −0.393129 0.919483i \(-0.628607\pi\)
−0.393129 + 0.919483i \(0.628607\pi\)
\(588\) 0 0
\(589\) −7.69691e6 −0.914173
\(590\) 565313. 8.62241e6i 0.0668589 1.01976i
\(591\) 0 0
\(592\) 4.27034e6 + 1.14459e6i 0.500793 + 0.134229i
\(593\) 8.37601e6i 0.978139i 0.872245 + 0.489069i \(0.162664\pi\)
−0.872245 + 0.489069i \(0.837336\pi\)
\(594\) 0 0
\(595\) 5.90291e6i 0.683556i
\(596\) 1.69135e6 1.28431e7i 0.195037 1.48100i
\(597\) 0 0
\(598\) −5.24906e6 344146.i −0.600245 0.0393540i
\(599\) 3.96714e6 0.451763 0.225882 0.974155i \(-0.427474\pi\)
0.225882 + 0.974155i \(0.427474\pi\)
\(600\) 0 0
\(601\) 1.31467e7 1.48467 0.742335 0.670028i \(-0.233718\pi\)
0.742335 + 0.670028i \(0.233718\pi\)
\(602\) 4.16187e6 + 272866.i 0.468055 + 0.0306872i
\(603\) 0 0
\(604\) −447813. + 3.40044e6i −0.0499464 + 0.379265i
\(605\) 4.85635e6i 0.539413i
\(606\) 0 0
\(607\) 2.24278e6i 0.247067i 0.992340 + 0.123533i \(0.0394226\pi\)
−0.992340 + 0.123533i \(0.960577\pi\)
\(608\) 1.43223e6 4.21785e6i 0.157128 0.462735i
\(609\) 0 0
\(610\) 651081. 9.93058e6i 0.0708452 1.08056i
\(611\) −5.25717e6 −0.569704
\(612\) 0 0
\(613\) −3.46298e6 −0.372220 −0.186110 0.982529i \(-0.559588\pi\)
−0.186110 + 0.982529i \(0.559588\pi\)
\(614\) −459579. + 7.00971e6i −0.0491971 + 0.750376i
\(615\) 0 0
\(616\) 890737. 4.47665e6i 0.0945797 0.475337i
\(617\) 9.38415e6i 0.992389i 0.868211 + 0.496195i \(0.165270\pi\)
−0.868211 + 0.496195i \(0.834730\pi\)
\(618\) 0 0
\(619\) 1.62470e7i 1.70430i −0.523294 0.852152i \(-0.675297\pi\)
0.523294 0.852152i \(-0.324703\pi\)
\(620\) 1.23587e7 + 1.62755e6i 1.29120 + 0.170042i
\(621\) 0 0
\(622\) −1.56602e7 1.02673e6i −1.62301 0.106410i
\(623\) −8.66455e6 −0.894387
\(624\) 0 0
\(625\) −2.13994e6 −0.219130
\(626\) 6.22324e6 + 408016.i 0.634718 + 0.0416142i
\(627\) 0 0
\(628\) 9.19780e6 + 1.21128e6i 0.930646 + 0.122559i
\(629\) 4.94585e6i 0.498442i
\(630\) 0 0
\(631\) 5.28301e6i 0.528212i 0.964494 + 0.264106i \(0.0850768\pi\)
−0.964494 + 0.264106i \(0.914923\pi\)
\(632\) −1.17893e6 + 5.92507e6i −0.117408 + 0.590066i
\(633\) 0 0
\(634\) 776760. 1.18475e7i 0.0767474 1.17059i
\(635\) 8.80053e6 0.866113
\(636\) 0 0
\(637\) 301500. 0.0294401
\(638\) 417235. 6.36386e6i 0.0405816 0.618969i
\(639\) 0 0
\(640\) −3.19158e6 + 6.46963e6i −0.308004 + 0.624352i
\(641\) 1.82753e7i 1.75679i 0.477940 + 0.878393i \(0.341384\pi\)
−0.477940 + 0.878393i \(0.658616\pi\)
\(642\) 0 0
\(643\) 1.43208e7i 1.36596i −0.730435 0.682982i \(-0.760683\pi\)
0.730435 0.682982i \(-0.239317\pi\)
\(644\) 1.23470e6 9.37565e6i 0.117314 0.890814i
\(645\) 0 0
\(646\) −4.97244e6 326010.i −0.468801 0.0307361i
\(647\) 4.52939e6 0.425382 0.212691 0.977120i \(-0.431777\pi\)
0.212691 + 0.977120i \(0.431777\pi\)
\(648\) 0 0
\(649\) −7.47467e6 −0.696595
\(650\) 3.78722e6 + 248303.i 0.351591 + 0.0230514i
\(651\) 0 0
\(652\) 1.60310e6 1.21730e7i 0.147686 1.12145i
\(653\) 5.33309e6i 0.489436i 0.969594 + 0.244718i \(0.0786954\pi\)
−0.969594 + 0.244718i \(0.921305\pi\)
\(654\) 0 0
\(655\) 2.04887e6i 0.186600i
\(656\) −4.90755e6 + 1.83094e7i −0.445251 + 1.66118i
\(657\) 0 0
\(658\) 618306. 9.43068e6i 0.0556722 0.849138i
\(659\) 1.52786e7 1.37048 0.685238 0.728319i \(-0.259698\pi\)
0.685238 + 0.728319i \(0.259698\pi\)
\(660\) 0 0
\(661\) 1.14110e7 1.01582 0.507912 0.861409i \(-0.330418\pi\)
0.507912 + 0.861409i \(0.330418\pi\)
\(662\) −470488. + 7.17610e6i −0.0417257 + 0.636419i
\(663\) 0 0
\(664\) −8.43820e6 1.67898e6i −0.742728 0.147783i
\(665\) 3.96247e6i 0.347465i
\(666\) 0 0
\(667\) 1.32130e7i 1.14997i
\(668\) −1.75341e7 2.30911e6i −1.52034 0.200218i
\(669\) 0 0
\(670\) 5.42912e6 + 355951.i 0.467243 + 0.0306339i
\(671\) −8.60870e6 −0.738128
\(672\) 0 0
\(673\) −6.26029e6 −0.532791 −0.266395 0.963864i \(-0.585833\pi\)
−0.266395 + 0.963864i \(0.585833\pi\)
\(674\) −7.87025e6 515999.i −0.667327 0.0437521i
\(675\) 0 0
\(676\) −6.27260e6 826055.i −0.527936 0.0695252i
\(677\) 1.15594e7i 0.969311i 0.874705 + 0.484655i \(0.161055\pi\)
−0.874705 + 0.484655i \(0.838945\pi\)
\(678\) 0 0
\(679\) 3.86224e6i 0.321488i
\(680\) 7.91518e6 + 1.57491e6i 0.656430 + 0.130612i
\(681\) 0 0
\(682\) 705453. 1.07599e7i 0.0580774 0.885823i
\(683\) 3.36657e6 0.276145 0.138072 0.990422i \(-0.455909\pi\)
0.138072 + 0.990422i \(0.455909\pi\)
\(684\) 0 0
\(685\) −1.12326e7 −0.914646
\(686\) 788097. 1.20204e7i 0.0639395 0.975234i
\(687\) 0 0
\(688\) −1.47628e6 + 5.50783e6i −0.118905 + 0.443618i
\(689\) 1.28772e7i 1.03341i
\(690\) 0 0
\(691\) 297628.i 0.0237126i −0.999930 0.0118563i \(-0.996226\pi\)
0.999930 0.0118563i \(-0.00377406\pi\)
\(692\) 1.62432e6 1.23342e7i 0.128945 0.979139i
\(693\) 0 0
\(694\) 4.30372e6 + 282166.i 0.339192 + 0.0222385i
\(695\) 9.38705e6 0.737169
\(696\) 0 0
\(697\) 2.12058e7 1.65338
\(698\) −2.00974e6 131765.i −0.156135 0.0102367i
\(699\) 0 0
\(700\) −890845. + 6.76458e6i −0.0687158 + 0.521790i
\(701\) 1.45408e7i 1.11762i −0.829297 0.558808i \(-0.811259\pi\)
0.829297 0.558808i \(-0.188741\pi\)
\(702\) 0 0
\(703\) 3.32002e6i 0.253368i
\(704\) 5.76507e6 + 2.38877e6i 0.438402 + 0.181653i
\(705\) 0 0
\(706\) −1.41689e6 + 2.16110e7i −0.106985 + 1.63178i
\(707\) −1.25152e7 −0.941651
\(708\) 0 0
\(709\) 1.52103e7 1.13638 0.568188 0.822899i \(-0.307645\pi\)
0.568188 + 0.822899i \(0.307645\pi\)
\(710\) −270134. + 4.12021e6i −0.0201110 + 0.306742i
\(711\) 0 0
\(712\) 2.31173e6 1.16182e7i 0.170898 0.858896i
\(713\) 2.23403e7i 1.64576i
\(714\) 0 0
\(715\) 3.08792e6i 0.225892i
\(716\) −9.52400e6 1.25424e6i −0.694283 0.0914320i
\(717\) 0 0
\(718\) −5.50959e6 361227.i −0.398849 0.0261498i
\(719\) −1.04620e7 −0.754729 −0.377364 0.926065i \(-0.623170\pi\)
−0.377364 + 0.926065i \(0.623170\pi\)
\(720\) 0 0
\(721\) 9.21726e6 0.660334
\(722\) −1.06391e7 697531.i −0.759556 0.0497990i
\(723\) 0 0
\(724\) −6.27862e6 826847.i −0.445161 0.0586245i
\(725\) 9.53327e6i 0.673592i
\(726\) 0 0
\(727\) 8.49478e6i 0.596096i 0.954551 + 0.298048i \(0.0963355\pi\)
−0.954551 + 0.298048i \(0.903664\pi\)
\(728\) −1.94868e6 + 9.79366e6i −0.136274 + 0.684883i
\(729\) 0 0
\(730\) −1.17060e6 + 1.78545e7i −0.0813019 + 1.24005i
\(731\) 6.37910e6 0.441536
\(732\) 0 0
\(733\) −2.47868e7 −1.70397 −0.851984 0.523568i \(-0.824600\pi\)
−0.851984 + 0.523568i \(0.824600\pi\)
\(734\) 140015. 2.13557e6i 0.00959254 0.146310i
\(735\) 0 0
\(736\) 1.22423e7 + 4.15706e6i 0.833048 + 0.282873i
\(737\) 4.70644e6i 0.319171i
\(738\) 0 0
\(739\) 7.22886e6i 0.486921i 0.969911 + 0.243460i \(0.0782826\pi\)
−0.969911 + 0.243460i \(0.921717\pi\)
\(740\) 702035. 5.33086e6i 0.0471281 0.357864i
\(741\) 0 0
\(742\) 2.31000e7 + 1.51451e6i 1.54029 + 0.100986i
\(743\) −1.87060e7 −1.24311 −0.621555 0.783370i \(-0.713499\pi\)
−0.621555 + 0.783370i \(0.713499\pi\)
\(744\) 0 0
\(745\) −1.57546e7 −1.03996
\(746\) 1.28269e7 + 840972.i 0.843866 + 0.0553266i
\(747\) 0 0
\(748\) 911490. 6.92134e6i 0.0595659 0.452310i
\(749\) 2.31393e7i 1.50711i
\(750\) 0 0
\(751\) 2.63625e7i 1.70564i 0.522206 + 0.852819i \(0.325109\pi\)
−0.522206 + 0.852819i \(0.674891\pi\)
\(752\) 1.24806e7 + 3.34522e6i 0.804804 + 0.215715i
\(753\) 0 0
\(754\) −912794. + 1.39223e7i −0.0584715 + 0.891834i
\(755\) 4.17131e6 0.266321
\(756\) 0 0
\(757\) −1.33984e7 −0.849793 −0.424897 0.905242i \(-0.639690\pi\)
−0.424897 + 0.905242i \(0.639690\pi\)
\(758\) −1.90190e6 + 2.90087e7i −0.120231 + 1.83381i
\(759\) 0 0
\(760\) −5.31325e6 1.05720e6i −0.333677 0.0663930i
\(761\) 2.01529e7i 1.26147i −0.775998 0.630735i \(-0.782753\pi\)
0.775998 0.630735i \(-0.217247\pi\)
\(762\) 0 0
\(763\) 1.19297e7i 0.741851i
\(764\) 2.89195e7 + 3.80849e6i 1.79249 + 0.236058i
\(765\) 0 0
\(766\) −399269. 26177.4i −0.0245863 0.00161196i
\(767\) 1.63525e7 1.00368
\(768\) 0 0
\(769\) 9.59359e6 0.585013 0.292506 0.956264i \(-0.405511\pi\)
0.292506 + 0.956264i \(0.405511\pi\)
\(770\) −5.53933e6 363176.i −0.336690 0.0220745i
\(771\) 0 0
\(772\) −4.71381e6 620774.i −0.284662 0.0374878i
\(773\) 6.90703e6i 0.415760i −0.978154 0.207880i \(-0.933344\pi\)
0.978154 0.207880i \(-0.0666564\pi\)
\(774\) 0 0
\(775\) 1.61186e7i 0.963994i
\(776\) 5.17885e6 + 1.03046e6i 0.308730 + 0.0614292i
\(777\) 0 0
\(778\) −552093. + 8.42076e6i −0.0327011 + 0.498772i
\(779\) −1.42349e7 −0.840446
\(780\) 0 0
\(781\) 3.57176e6 0.209534
\(782\) 946245. 1.44326e7i 0.0553333 0.843969i
\(783\) 0 0
\(784\) −715765. 191849.i −0.0415892 0.0111473i
\(785\) 1.12829e7i 0.653502i
\(786\) 0 0