Properties

Label 80.6.n.d.47.3
Level $80$
Weight $6$
Character 80.47
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.3
Root \(-10.8505 + 10.2794i\) of defining polynomial
Character \(\chi\) \(=\) 80.47
Dual form 80.6.n.d.63.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.68301 - 9.68301i) q^{3} +(-49.1893 - 26.5597i) q^{5} +(-48.6629 + 48.6629i) q^{7} -55.4787i q^{9} +O(q^{10})\) \(q+(-9.68301 - 9.68301i) q^{3} +(-49.1893 - 26.5597i) q^{5} +(-48.6629 + 48.6629i) q^{7} -55.4787i q^{9} +463.177i q^{11} +(320.800 - 320.800i) q^{13} +(219.122 + 733.478i) q^{15} +(1045.30 + 1045.30i) q^{17} -701.290 q^{19} +942.407 q^{21} +(2001.88 + 2001.88i) q^{23} +(1714.16 + 2612.90i) q^{25} +(-2890.17 + 2890.17i) q^{27} -3567.76i q^{29} +9044.72i q^{31} +(4484.95 - 4484.95i) q^{33} +(3686.17 - 1101.22i) q^{35} +(1642.14 + 1642.14i) q^{37} -6212.62 q^{39} -14338.6 q^{41} +(-3941.99 - 3941.99i) q^{43} +(-1473.50 + 2728.95i) q^{45} +(7944.15 - 7944.15i) q^{47} +12070.8i q^{49} -20243.2i q^{51} +(11621.9 - 11621.9i) q^{53} +(12301.9 - 22783.3i) q^{55} +(6790.60 + 6790.60i) q^{57} -1121.30 q^{59} -29320.4 q^{61} +(2699.75 + 2699.75i) q^{63} +(-24300.3 + 7259.56i) q^{65} +(-9199.75 + 9199.75i) q^{67} -38768.5i q^{69} -52643.9i q^{71} +(-27965.6 + 27965.6i) q^{73} +(8702.49 - 41899.0i) q^{75} +(-22539.6 - 22539.6i) q^{77} -82263.7 q^{79} +42489.8 q^{81} +(77236.8 + 77236.8i) q^{83} +(-23654.6 - 79180.1i) q^{85} +(-34546.7 + 34546.7i) q^{87} +145955. i q^{89} +31222.2i q^{91} +(87580.1 - 87580.1i) q^{93} +(34495.9 + 18626.1i) q^{95} +(97856.7 + 97856.7i) q^{97} +25696.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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
\(3\) −9.68301 9.68301i −0.621165 0.621165i 0.324664 0.945829i \(-0.394749\pi\)
−0.945829 + 0.324664i \(0.894749\pi\)
\(4\) 0 0
\(5\) −49.1893 26.5597i −0.879924 0.475114i
\(6\) 0 0
\(7\) −48.6629 + 48.6629i −0.375364 + 0.375364i −0.869427 0.494062i \(-0.835512\pi\)
0.494062 + 0.869427i \(0.335512\pi\)
\(8\) 0 0
\(9\) 55.4787i 0.228307i
\(10\) 0 0
\(11\) 463.177i 1.15416i 0.816688 + 0.577080i \(0.195808\pi\)
−0.816688 + 0.577080i \(0.804192\pi\)
\(12\) 0 0
\(13\) 320.800 320.800i 0.526473 0.526473i −0.393046 0.919519i \(-0.628579\pi\)
0.919519 + 0.393046i \(0.128579\pi\)
\(14\) 0 0
\(15\) 219.122 + 733.478i 0.251454 + 0.841703i
\(16\) 0 0
\(17\) 1045.30 + 1045.30i 0.877238 + 0.877238i 0.993248 0.116010i \(-0.0370106\pi\)
−0.116010 + 0.993248i \(0.537011\pi\)
\(18\) 0 0
\(19\) −701.290 −0.445670 −0.222835 0.974856i \(-0.571531\pi\)
−0.222835 + 0.974856i \(0.571531\pi\)
\(20\) 0 0
\(21\) 942.407 0.466327
\(22\) 0 0
\(23\) 2001.88 + 2001.88i 0.789076 + 0.789076i 0.981343 0.192266i \(-0.0615838\pi\)
−0.192266 + 0.981343i \(0.561584\pi\)
\(24\) 0 0
\(25\) 1714.16 + 2612.90i 0.548533 + 0.836129i
\(26\) 0 0
\(27\) −2890.17 + 2890.17i −0.762982 + 0.762982i
\(28\) 0 0
\(29\) 3567.76i 0.787773i −0.919159 0.393886i \(-0.871130\pi\)
0.919159 0.393886i \(-0.128870\pi\)
\(30\) 0 0
\(31\) 9044.72i 1.69041i 0.534446 + 0.845203i \(0.320520\pi\)
−0.534446 + 0.845203i \(0.679480\pi\)
\(32\) 0 0
\(33\) 4484.95 4484.95i 0.716924 0.716924i
\(34\) 0 0
\(35\) 3686.17 1101.22i 0.508633 0.151951i
\(36\) 0 0
\(37\) 1642.14 + 1642.14i 0.197199 + 0.197199i 0.798798 0.601599i \(-0.205470\pi\)
−0.601599 + 0.798798i \(0.705470\pi\)
\(38\) 0 0
\(39\) −6212.62 −0.654054
\(40\) 0 0
\(41\) −14338.6 −1.33213 −0.666067 0.745892i \(-0.732024\pi\)
−0.666067 + 0.745892i \(0.732024\pi\)
\(42\) 0 0
\(43\) −3941.99 3941.99i −0.325120 0.325120i 0.525607 0.850727i \(-0.323838\pi\)
−0.850727 + 0.525607i \(0.823838\pi\)
\(44\) 0 0
\(45\) −1473.50 + 2728.95i −0.108472 + 0.200893i
\(46\) 0 0
\(47\) 7944.15 7944.15i 0.524569 0.524569i −0.394379 0.918948i \(-0.629040\pi\)
0.918948 + 0.394379i \(0.129040\pi\)
\(48\) 0 0
\(49\) 12070.8i 0.718203i
\(50\) 0 0
\(51\) 20243.2i 1.08982i
\(52\) 0 0
\(53\) 11621.9 11621.9i 0.568313 0.568313i −0.363342 0.931656i \(-0.618364\pi\)
0.931656 + 0.363342i \(0.118364\pi\)
\(54\) 0 0
\(55\) 12301.9 22783.3i 0.548358 1.01557i
\(56\) 0 0
\(57\) 6790.60 + 6790.60i 0.276835 + 0.276835i
\(58\) 0 0
\(59\) −1121.30 −0.0419365 −0.0209683 0.999780i \(-0.506675\pi\)
−0.0209683 + 0.999780i \(0.506675\pi\)
\(60\) 0 0
\(61\) −29320.4 −1.00889 −0.504447 0.863442i \(-0.668304\pi\)
−0.504447 + 0.863442i \(0.668304\pi\)
\(62\) 0 0
\(63\) 2699.75 + 2699.75i 0.0856984 + 0.0856984i
\(64\) 0 0
\(65\) −24300.3 + 7259.56i −0.713391 + 0.213121i
\(66\) 0 0
\(67\) −9199.75 + 9199.75i −0.250374 + 0.250374i −0.821124 0.570750i \(-0.806653\pi\)
0.570750 + 0.821124i \(0.306653\pi\)
\(68\) 0 0
\(69\) 38768.5i 0.980294i
\(70\) 0 0
\(71\) 52643.9i 1.23937i −0.784849 0.619687i \(-0.787260\pi\)
0.784849 0.619687i \(-0.212740\pi\)
\(72\) 0 0
\(73\) −27965.6 + 27965.6i −0.614209 + 0.614209i −0.944040 0.329831i \(-0.893008\pi\)
0.329831 + 0.944040i \(0.393008\pi\)
\(74\) 0 0
\(75\) 8702.49 41899.0i 0.178645 0.860104i
\(76\) 0 0
\(77\) −22539.6 22539.6i −0.433230 0.433230i
\(78\) 0 0
\(79\) −82263.7 −1.48300 −0.741499 0.670954i \(-0.765885\pi\)
−0.741499 + 0.670954i \(0.765885\pi\)
\(80\) 0 0
\(81\) 42489.8 0.719569
\(82\) 0 0
\(83\) 77236.8 + 77236.8i 1.23063 + 1.23063i 0.963720 + 0.266914i \(0.0860039\pi\)
0.266914 + 0.963720i \(0.413996\pi\)
\(84\) 0 0
\(85\) −23654.6 79180.1i −0.355114 1.18869i
\(86\) 0 0
\(87\) −34546.7 + 34546.7i −0.489337 + 0.489337i
\(88\) 0 0
\(89\) 145955.i 1.95318i 0.215100 + 0.976592i \(0.430992\pi\)
−0.215100 + 0.976592i \(0.569008\pi\)
\(90\) 0 0
\(91\) 31222.2i 0.395239i
\(92\) 0 0
\(93\) 87580.1 87580.1i 1.05002 1.05002i
\(94\) 0 0
\(95\) 34495.9 + 18626.1i 0.392156 + 0.211744i
\(96\) 0 0
\(97\) 97856.7 + 97856.7i 1.05599 + 1.05599i 0.998336 + 0.0576570i \(0.0183630\pi\)
0.0576570 + 0.998336i \(0.481637\pi\)
\(98\) 0 0
\(99\) 25696.5 0.263503
\(100\) 0 0
\(101\) 86555.1 0.844286 0.422143 0.906529i \(-0.361278\pi\)
0.422143 + 0.906529i \(0.361278\pi\)
\(102\) 0 0
\(103\) 125928. + 125928.i 1.16958 + 1.16958i 0.982308 + 0.187273i \(0.0599650\pi\)
0.187273 + 0.982308i \(0.440035\pi\)
\(104\) 0 0
\(105\) −46356.3 25030.1i −0.410332 0.221559i
\(106\) 0 0
\(107\) −152309. + 152309.i −1.28607 + 1.28607i −0.348917 + 0.937154i \(0.613450\pi\)
−0.937154 + 0.348917i \(0.886550\pi\)
\(108\) 0 0
\(109\) 62440.1i 0.503382i 0.967808 + 0.251691i \(0.0809866\pi\)
−0.967808 + 0.251691i \(0.919013\pi\)
\(110\) 0 0
\(111\) 31801.6i 0.244986i
\(112\) 0 0
\(113\) 32875.2 32875.2i 0.242199 0.242199i −0.575560 0.817759i \(-0.695216\pi\)
0.817759 + 0.575560i \(0.195216\pi\)
\(114\) 0 0
\(115\) −45301.7 151641.i −0.319426 1.06923i
\(116\) 0 0
\(117\) −17797.6 17797.6i −0.120198 0.120198i
\(118\) 0 0
\(119\) −101734. −0.658568
\(120\) 0 0
\(121\) −53482.3 −0.332083
\(122\) 0 0
\(123\) 138841. + 138841.i 0.827476 + 0.827476i
\(124\) 0 0
\(125\) −14920.6 174054.i −0.0854102 0.996346i
\(126\) 0 0
\(127\) −120503. + 120503.i −0.662960 + 0.662960i −0.956077 0.293116i \(-0.905308\pi\)
0.293116 + 0.956077i \(0.405308\pi\)
\(128\) 0 0
\(129\) 76340.6i 0.403907i
\(130\) 0 0
\(131\) 88630.4i 0.451237i −0.974216 0.225618i \(-0.927560\pi\)
0.974216 0.225618i \(-0.0724402\pi\)
\(132\) 0 0
\(133\) 34126.8 34126.8i 0.167289 0.167289i
\(134\) 0 0
\(135\) 218927. 65403.3i 1.03387 0.308862i
\(136\) 0 0
\(137\) −46725.7 46725.7i −0.212694 0.212694i 0.592717 0.805411i \(-0.298055\pi\)
−0.805411 + 0.592717i \(0.798055\pi\)
\(138\) 0 0
\(139\) −280242. −1.23026 −0.615128 0.788427i \(-0.710896\pi\)
−0.615128 + 0.788427i \(0.710896\pi\)
\(140\) 0 0
\(141\) −153846. −0.651688
\(142\) 0 0
\(143\) 148587. + 148587.i 0.607634 + 0.607634i
\(144\) 0 0
\(145\) −94758.7 + 175496.i −0.374282 + 0.693180i
\(146\) 0 0
\(147\) 116882. 116882.i 0.446123 0.446123i
\(148\) 0 0
\(149\) 114782.i 0.423555i −0.977318 0.211777i \(-0.932075\pi\)
0.977318 0.211777i \(-0.0679251\pi\)
\(150\) 0 0
\(151\) 388996.i 1.38836i −0.719801 0.694181i \(-0.755767\pi\)
0.719801 0.694181i \(-0.244233\pi\)
\(152\) 0 0
\(153\) 57991.7 57991.7i 0.200280 0.200280i
\(154\) 0 0
\(155\) 240225. 444903.i 0.803136 1.48743i
\(156\) 0 0
\(157\) 230322. + 230322.i 0.745738 + 0.745738i 0.973676 0.227938i \(-0.0731984\pi\)
−0.227938 + 0.973676i \(0.573198\pi\)
\(158\) 0 0
\(159\) −225070. −0.706033
\(160\) 0 0
\(161\) −194835. −0.592382
\(162\) 0 0
\(163\) −334147. 334147.i −0.985073 0.985073i 0.0148175 0.999890i \(-0.495283\pi\)
−0.999890 + 0.0148175i \(0.995283\pi\)
\(164\) 0 0
\(165\) −339730. + 101492.i −0.971459 + 0.290218i
\(166\) 0 0
\(167\) 287959. 287959.i 0.798987 0.798987i −0.183949 0.982936i \(-0.558888\pi\)
0.982936 + 0.183949i \(0.0588880\pi\)
\(168\) 0 0
\(169\) 165467.i 0.445652i
\(170\) 0 0
\(171\) 38906.6i 0.101750i
\(172\) 0 0
\(173\) 176255. 176255.i 0.447741 0.447741i −0.446862 0.894603i \(-0.647458\pi\)
0.894603 + 0.446862i \(0.147458\pi\)
\(174\) 0 0
\(175\) −210568. 43735.3i −0.519753 0.107953i
\(176\) 0 0
\(177\) 10857.6 + 10857.6i 0.0260495 + 0.0260495i
\(178\) 0 0
\(179\) 409192. 0.954540 0.477270 0.878757i \(-0.341626\pi\)
0.477270 + 0.878757i \(0.341626\pi\)
\(180\) 0 0
\(181\) −607951. −1.37934 −0.689671 0.724123i \(-0.742245\pi\)
−0.689671 + 0.724123i \(0.742245\pi\)
\(182\) 0 0
\(183\) 283910. + 283910.i 0.626691 + 0.626691i
\(184\) 0 0
\(185\) −37160.8 124390.i −0.0798281 0.267212i
\(186\) 0 0
\(187\) −484158. + 484158.i −1.01247 + 1.01247i
\(188\) 0 0
\(189\) 281288.i 0.572793i
\(190\) 0 0
\(191\) 67781.7i 0.134440i 0.997738 + 0.0672201i \(0.0214130\pi\)
−0.997738 + 0.0672201i \(0.978587\pi\)
\(192\) 0 0
\(193\) 373274. 373274.i 0.721330 0.721330i −0.247546 0.968876i \(-0.579624\pi\)
0.968876 + 0.247546i \(0.0796241\pi\)
\(194\) 0 0
\(195\) 305594. + 165005.i 0.575518 + 0.310750i
\(196\) 0 0
\(197\) 76924.7 + 76924.7i 0.141221 + 0.141221i 0.774183 0.632962i \(-0.218161\pi\)
−0.632962 + 0.774183i \(0.718161\pi\)
\(198\) 0 0
\(199\) −908495. −1.62626 −0.813130 0.582083i \(-0.802238\pi\)
−0.813130 + 0.582083i \(0.802238\pi\)
\(200\) 0 0
\(201\) 178162. 0.311047
\(202\) 0 0
\(203\) 173618. + 173618.i 0.295702 + 0.295702i
\(204\) 0 0
\(205\) 705306. + 380830.i 1.17218 + 0.632916i
\(206\) 0 0
\(207\) 111062. 111062.i 0.180152 0.180152i
\(208\) 0 0
\(209\) 324822.i 0.514374i
\(210\) 0 0
\(211\) 732879.i 1.13325i 0.823975 + 0.566626i \(0.191751\pi\)
−0.823975 + 0.566626i \(0.808249\pi\)
\(212\) 0 0
\(213\) −509751. + 509751.i −0.769856 + 0.769856i
\(214\) 0 0
\(215\) 89205.4 + 298601.i 0.131612 + 0.440550i
\(216\) 0 0
\(217\) −440143. 440143.i −0.634518 0.634518i
\(218\) 0 0
\(219\) 541581. 0.763051
\(220\) 0 0
\(221\) 670663. 0.923684
\(222\) 0 0
\(223\) −346705. 346705.i −0.466872 0.466872i 0.434027 0.900900i \(-0.357092\pi\)
−0.900900 + 0.434027i \(0.857092\pi\)
\(224\) 0 0
\(225\) 144960. 95099.6i 0.190894 0.125234i
\(226\) 0 0
\(227\) −262744. + 262744.i −0.338429 + 0.338429i −0.855776 0.517347i \(-0.826920\pi\)
0.517347 + 0.855776i \(0.326920\pi\)
\(228\) 0 0
\(229\) 1.36759e6i 1.72332i 0.507487 + 0.861660i \(0.330575\pi\)
−0.507487 + 0.861660i \(0.669425\pi\)
\(230\) 0 0
\(231\) 436502.i 0.538215i
\(232\) 0 0
\(233\) 171228. 171228.i 0.206626 0.206626i −0.596206 0.802832i \(-0.703326\pi\)
0.802832 + 0.596206i \(0.203326\pi\)
\(234\) 0 0
\(235\) −601761. + 179772.i −0.710811 + 0.212351i
\(236\) 0 0
\(237\) 796560. + 796560.i 0.921187 + 0.921187i
\(238\) 0 0
\(239\) 1.31148e6 1.48514 0.742569 0.669769i \(-0.233607\pi\)
0.742569 + 0.669769i \(0.233607\pi\)
\(240\) 0 0
\(241\) 1.31737e6 1.46105 0.730526 0.682884i \(-0.239275\pi\)
0.730526 + 0.682884i \(0.239275\pi\)
\(242\) 0 0
\(243\) 290883. + 290883.i 0.316011 + 0.316011i
\(244\) 0 0
\(245\) 320598. 593755.i 0.341229 0.631964i
\(246\) 0 0
\(247\) −224974. + 224974.i −0.234633 + 0.234633i
\(248\) 0 0
\(249\) 1.49577e6i 1.52885i
\(250\) 0 0
\(251\) 188218.i 0.188572i 0.995545 + 0.0942859i \(0.0300568\pi\)
−0.995545 + 0.0942859i \(0.969943\pi\)
\(252\) 0 0
\(253\) −927227. + 927227.i −0.910720 + 0.910720i
\(254\) 0 0
\(255\) −537654. + 995750.i −0.517789 + 0.958958i
\(256\) 0 0
\(257\) −784122. 784122.i −0.740544 0.740544i 0.232139 0.972683i \(-0.425428\pi\)
−0.972683 + 0.232139i \(0.925428\pi\)
\(258\) 0 0
\(259\) −159822. −0.148043
\(260\) 0 0
\(261\) −197935. −0.179854
\(262\) 0 0
\(263\) −554379. 554379.i −0.494217 0.494217i 0.415415 0.909632i \(-0.363636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(264\) 0 0
\(265\) −880348. + 262999.i −0.770086 + 0.230059i
\(266\) 0 0
\(267\) 1.41328e6 1.41328e6i 1.21325 1.21325i
\(268\) 0 0
\(269\) 146638.i 0.123557i 0.998090 + 0.0617785i \(0.0196772\pi\)
−0.998090 + 0.0617785i \(0.980323\pi\)
\(270\) 0 0
\(271\) 620115.i 0.512919i −0.966555 0.256460i \(-0.917444\pi\)
0.966555 0.256460i \(-0.0825560\pi\)
\(272\) 0 0
\(273\) 302324. 302324.i 0.245509 0.245509i
\(274\) 0 0
\(275\) −1.21024e6 + 793962.i −0.965026 + 0.633094i
\(276\) 0 0
\(277\) −571067. 571067.i −0.447185 0.447185i 0.447233 0.894418i \(-0.352410\pi\)
−0.894418 + 0.447233i \(0.852410\pi\)
\(278\) 0 0
\(279\) 501789. 0.385932
\(280\) 0 0
\(281\) −623155. −0.470793 −0.235397 0.971899i \(-0.575639\pi\)
−0.235397 + 0.971899i \(0.575639\pi\)
\(282\) 0 0
\(283\) −1.66016e6 1.66016e6i −1.23221 1.23221i −0.963115 0.269091i \(-0.913277\pi\)
−0.269091 0.963115i \(1.41328\pi\)
\(284\) 0 0
\(285\) −153668. 514381.i −0.112065 0.375122i
\(286\) 0 0
\(287\) 697760. 697760.i 0.500036 0.500036i
\(288\) 0 0
\(289\) 765434.i 0.539092i
\(290\) 0 0
\(291\) 1.89509e6i 1.31189i
\(292\) 0 0
\(293\) −1.72577e6 + 1.72577e6i −1.17439 + 1.17439i −0.193242 + 0.981151i \(0.561900\pi\)
−0.981151 + 0.193242i \(0.938100\pi\)
\(294\) 0 0
\(295\) 55156.0 + 29781.4i 0.0369010 + 0.0199247i
\(296\) 0 0
\(297\) −1.33866e6 1.33866e6i −0.880602 0.880602i
\(298\) 0 0
\(299\) 1.28441e6 0.830855
\(300\) 0 0
\(301\) 383657. 0.244077
\(302\) 0 0
\(303\) −838114. 838114.i −0.524441 0.524441i
\(304\) 0 0
\(305\) 1.44225e6 + 778742.i 0.887751 + 0.479340i
\(306\) 0 0
\(307\) 693642. 693642.i 0.420039 0.420039i −0.465178 0.885217i \(-0.654010\pi\)
0.885217 + 0.465178i \(0.154010\pi\)
\(308\) 0 0
\(309\) 2.43873e6i 1.45301i
\(310\) 0 0
\(311\) 839243.i 0.492024i 0.969267 + 0.246012i \(0.0791203\pi\)
−0.969267 + 0.246012i \(0.920880\pi\)
\(312\) 0 0
\(313\) −1.45976e6 + 1.45976e6i −0.842208 + 0.842208i −0.989146 0.146938i \(-0.953058\pi\)
0.146938 + 0.989146i \(0.453058\pi\)
\(314\) 0 0
\(315\) −61094.2 204504.i −0.0346916 0.116125i
\(316\) 0 0
\(317\) 768911. + 768911.i 0.429762 + 0.429762i 0.888547 0.458785i \(-0.151715\pi\)
−0.458785 + 0.888547i \(0.651715\pi\)
\(318\) 0 0
\(319\) 1.65251e6 0.909215
\(320\) 0 0
\(321\) 2.94961e6 1.59772
\(322\) 0 0
\(323\) −733056. 733056.i −0.390959 0.390959i
\(324\) 0 0
\(325\) 1.38812e6 + 288316.i 0.728987 + 0.151412i
\(326\) 0 0
\(327\) 604608. 604608.i 0.312683 0.312683i
\(328\) 0 0
\(329\) 773171.i 0.393809i
\(330\) 0 0
\(331\) 1.53718e6i 0.771179i 0.922671 + 0.385589i \(0.126002\pi\)
−0.922671 + 0.385589i \(0.873998\pi\)
\(332\) 0 0
\(333\) 91103.5 91103.5i 0.0450220 0.0450220i
\(334\) 0 0
\(335\) 696871. 208186.i 0.339266 0.101354i
\(336\) 0 0
\(337\) −600219. 600219.i −0.287895 0.287895i 0.548352 0.836248i \(-0.315255\pi\)
−0.836248 + 0.548352i \(0.815255\pi\)
\(338\) 0 0
\(339\) −636661. −0.300891
\(340\) 0 0
\(341\) −4.18931e6 −1.95100
\(342\) 0 0
\(343\) −1.40528e6 1.40528e6i −0.644952 0.644952i
\(344\) 0 0
\(345\) −1.02968e6 + 1.90699e6i −0.465752 + 0.862584i
\(346\) 0 0
\(347\) −15540.8 + 15540.8i −0.00692868 + 0.00692868i −0.710563 0.703634i \(-0.751560\pi\)
0.703634 + 0.710563i \(0.251560\pi\)
\(348\) 0 0
\(349\) 1.37621e6i 0.604815i −0.953179 0.302407i \(-0.902210\pi\)
0.953179 0.302407i \(-0.0977903\pi\)
\(350\) 0 0
\(351\) 1.85434e6i 0.803379i
\(352\) 0 0
\(353\) 2.13095e6 2.13095e6i 0.910198 0.910198i −0.0860896 0.996287i \(-0.527437\pi\)
0.996287 + 0.0860896i \(0.0274371\pi\)
\(354\) 0 0
\(355\) −1.39821e6 + 2.58951e6i −0.588844 + 1.09055i
\(356\) 0 0
\(357\) 985095. + 985095.i 0.409079 + 0.409079i
\(358\) 0 0
\(359\) 346230. 0.141785 0.0708923 0.997484i \(-0.477415\pi\)
0.0708923 + 0.997484i \(0.477415\pi\)
\(360\) 0 0
\(361\) −1.98429e6 −0.801378
\(362\) 0 0
\(363\) 517870. + 517870.i 0.206278 + 0.206278i
\(364\) 0 0
\(365\) 2.11836e6 632848.i 0.832277 0.248638i
\(366\) 0 0
\(367\) −857952. + 857952.i −0.332505 + 0.332505i −0.853537 0.521032i \(-0.825547\pi\)
0.521032 + 0.853537i \(0.325547\pi\)
\(368\) 0 0
\(369\) 795488.i 0.304136i
\(370\) 0 0
\(371\) 1.13111e6i 0.426649i
\(372\) 0 0
\(373\) 1.92433e6 1.92433e6i 0.716157 0.716157i −0.251659 0.967816i \(-0.580976\pi\)
0.967816 + 0.251659i \(0.0809762\pi\)
\(374\) 0 0
\(375\) −1.54090e6 + 1.82985e6i −0.565842 + 0.671949i
\(376\) 0 0
\(377\) −1.14454e6 1.14454e6i −0.414741 0.414741i
\(378\) 0 0
\(379\) 5919.00 0.00211666 0.00105833 0.999999i \(-0.499663\pi\)
0.00105833 + 0.999999i \(0.499663\pi\)
\(380\) 0 0
\(381\) 2.33366e6 0.823616
\(382\) 0 0
\(383\) −121366. 121366.i −0.0422767 0.0422767i 0.685652 0.727929i \(-0.259517\pi\)
−0.727929 + 0.685652i \(0.759517\pi\)
\(384\) 0 0
\(385\) 510060. + 1.70735e6i 0.175376 + 0.587044i
\(386\) 0 0
\(387\) −218696. + 218696.i −0.0742273 + 0.0742273i
\(388\) 0 0
\(389\) 2.60692e6i 0.873482i −0.899587 0.436741i \(-0.856133\pi\)
0.899587 0.436741i \(-0.143867\pi\)
\(390\) 0 0
\(391\) 4.18512e6i 1.38442i
\(392\) 0 0
\(393\) −858209. + 858209.i −0.280293 + 0.280293i
\(394\) 0 0
\(395\) 4.04649e6 + 2.18490e6i 1.30493 + 0.704593i
\(396\) 0 0
\(397\) 2.66197e6 + 2.66197e6i 0.847669 + 0.847669i 0.989842 0.142173i \(-0.0454089\pi\)
−0.142173 + 0.989842i \(0.545409\pi\)
\(398\) 0 0
\(399\) −660901. −0.207828
\(400\) 0 0
\(401\) 3.31838e6 1.03054 0.515270 0.857028i \(-0.327692\pi\)
0.515270 + 0.857028i \(0.327692\pi\)
\(402\) 0 0
\(403\) 2.90155e6 + 2.90155e6i 0.889953 + 0.889953i
\(404\) 0 0
\(405\) −2.09004e6 1.12852e6i −0.633166 0.341877i
\(406\) 0 0
\(407\) −760600. + 760600.i −0.227599 + 0.227599i
\(408\) 0 0
\(409\) 1.71967e6i 0.508319i 0.967162 + 0.254159i \(0.0817988\pi\)
−0.967162 + 0.254159i \(0.918201\pi\)
\(410\) 0 0
\(411\) 904891.i 0.264236i
\(412\) 0 0
\(413\) 54565.8 54565.8i 0.0157415 0.0157415i
\(414\) 0 0
\(415\) −1.74783e6 5.85061e6i −0.498173 1.66756i
\(416\) 0 0
\(417\) 2.71358e6 + 2.71358e6i 0.764193 + 0.764193i
\(418\) 0 0
\(419\) −2.43886e6 −0.678660 −0.339330 0.940667i \(-0.610200\pi\)
−0.339330 + 0.940667i \(0.610200\pi\)
\(420\) 0 0
\(421\) −2.76737e6 −0.760961 −0.380480 0.924789i \(-0.624241\pi\)
−0.380480 + 0.924789i \(0.624241\pi\)
\(422\) 0 0
\(423\) −440731. 440731.i −0.119763 0.119763i
\(424\) 0 0
\(425\) −939449. + 4.52307e6i −0.252290 + 1.21468i
\(426\) 0 0
\(427\) 1.42682e6 1.42682e6i 0.378703 0.378703i
\(428\) 0 0
\(429\) 2.87755e6i 0.754882i
\(430\) 0 0
\(431\) 3.98814e6i 1.03413i −0.855945 0.517067i \(-0.827024\pi\)
0.855945 0.517067i \(-0.172976\pi\)
\(432\) 0 0
\(433\) 386926. 386926.i 0.0991765 0.0991765i −0.655778 0.754954i \(-0.727659\pi\)
0.754954 + 0.655778i \(0.227659\pi\)
\(434\) 0 0
\(435\) 2.61688e6 781776.i 0.663071 0.198088i
\(436\) 0 0
\(437\) −1.40390e6 1.40390e6i −0.351668 0.351668i
\(438\) 0 0
\(439\) 1.85711e6 0.459913 0.229956 0.973201i \(-0.426142\pi\)
0.229956 + 0.973201i \(0.426142\pi\)
\(440\) 0 0
\(441\) 669674. 0.163971
\(442\) 0 0
\(443\) −2.58101e6 2.58101e6i −0.624857 0.624857i 0.321913 0.946769i \(-0.395674\pi\)
−0.946769 + 0.321913i \(0.895674\pi\)
\(444\) 0 0
\(445\) 3.87651e6 7.17940e6i 0.927986 1.71865i
\(446\) 0 0
\(447\) −1.11144e6 + 1.11144e6i −0.263097 + 0.263097i
\(448\) 0 0
\(449\) 4.66935e6i 1.09305i 0.837443 + 0.546525i \(0.184050\pi\)
−0.837443 + 0.546525i \(0.815950\pi\)
\(450\) 0 0
\(451\) 6.64133e6i 1.53749i
\(452\) 0 0
\(453\) −3.76665e6 + 3.76665e6i −0.862402 + 0.862402i
\(454\) 0 0
\(455\) 829251. 1.53579e6i 0.187784 0.347780i
\(456\) 0 0
\(457\) −5.03755e6 5.03755e6i −1.12831 1.12831i −0.990452 0.137858i \(-0.955978\pi\)
−0.137858 0.990452i \(-0.544022\pi\)
\(458\) 0 0
\(459\) −6.04217e6 −1.33863
\(460\) 0 0
\(461\) −2.77546e6 −0.608250 −0.304125 0.952632i \(-0.598364\pi\)
−0.304125 + 0.952632i \(0.598364\pi\)
\(462\) 0 0
\(463\) 6.00377e6 + 6.00377e6i 1.30158 + 1.30158i 0.927325 + 0.374258i \(0.122103\pi\)
0.374258 + 0.927325i \(0.377897\pi\)
\(464\) 0 0
\(465\) −6.63410e6 + 1.98190e6i −1.42282 + 0.425059i
\(466\) 0 0
\(467\) −2.93586e6 + 2.93586e6i −0.622935 + 0.622935i −0.946281 0.323346i \(-0.895192\pi\)
0.323346 + 0.946281i \(0.395192\pi\)
\(468\) 0 0
\(469\) 895373.i 0.187963i
\(470\) 0 0
\(471\) 4.46042e6i 0.926453i
\(472\) 0 0
\(473\) 1.82584e6 1.82584e6i 0.375240 0.375240i
\(474\) 0 0
\(475\) −1.20213e6 1.83240e6i −0.244465 0.372638i
\(476\) 0 0
\(477\) −644768. 644768.i −0.129750 0.129750i
\(478\) 0 0
\(479\) 850769. 0.169423 0.0847116 0.996406i \(-0.473003\pi\)
0.0847116 + 0.996406i \(0.473003\pi\)
\(480\) 0 0
\(481\) 1.05360e6 0.207640
\(482\) 0 0
\(483\) 1.88659e6 + 1.88659e6i 0.367967 + 0.367967i
\(484\) 0 0
\(485\) −2.21445e6 7.41254e6i −0.427476 1.43091i
\(486\) 0 0
\(487\) 2.08676e6 2.08676e6i 0.398704 0.398704i −0.479072 0.877776i \(-0.659027\pi\)
0.877776 + 0.479072i \(0.159027\pi\)
\(488\) 0 0
\(489\) 6.47109e6i 1.22379i
\(490\) 0 0
\(491\) 3.55745e6i 0.665940i −0.942937 0.332970i \(-0.891949\pi\)
0.942937 0.332970i \(-0.108051\pi\)
\(492\) 0 0
\(493\) 3.72937e6 3.72937e6i 0.691064 0.691064i
\(494\) 0 0
\(495\) −1.26399e6 682490.i −0.231863 0.125194i
\(496\) 0 0
\(497\) 2.56181e6 + 2.56181e6i 0.465217 + 0.465217i
\(498\) 0 0
\(499\) 4.06234e6 0.730339 0.365170 0.930941i \(-0.381011\pi\)
0.365170 + 0.930941i \(0.381011\pi\)
\(500\) 0 0
\(501\) −5.57662e6 −0.992606
\(502\) 0 0
\(503\) −2.25876e6 2.25876e6i −0.398061 0.398061i 0.479488 0.877549i \(-0.340823\pi\)
−0.877549 + 0.479488i \(0.840823\pi\)
\(504\) 0 0
\(505\) −4.25758e6 2.29888e6i −0.742907 0.401132i
\(506\) 0 0
\(507\) 1.60222e6 1.60222e6i 0.276824 0.276824i
\(508\) 0 0
\(509\) 5.20653e6i 0.890746i 0.895345 + 0.445373i \(0.146929\pi\)
−0.895345 + 0.445373i \(0.853071\pi\)
\(510\) 0 0
\(511\) 2.72177e6i 0.461105i
\(512\) 0 0
\(513\) 2.02685e6 2.02685e6i 0.340038 0.340038i
\(514\) 0 0
\(515\) −2.84970e6 9.53894e6i −0.473458 1.58483i
\(516\) 0 0
\(517\) 3.67955e6 + 3.67955e6i 0.605436 + 0.605436i
\(518\) 0 0
\(519\) −3.41336e6 −0.556242
\(520\) 0 0
\(521\) 1.82071e6 0.293864 0.146932 0.989147i \(-0.453060\pi\)
0.146932 + 0.989147i \(0.453060\pi\)
\(522\) 0 0
\(523\) 3.25978e6 + 3.25978e6i 0.521116 + 0.521116i 0.917908 0.396793i \(-0.129877\pi\)
−0.396793 + 0.917908i \(0.629877\pi\)
\(524\) 0 0
\(525\) 1.61544e6 + 2.46242e6i 0.255796 + 0.389909i
\(526\) 0 0
\(527\) −9.45442e6 + 9.45442e6i −1.48289 + 1.48289i
\(528\) 0 0
\(529\) 1.57872e6i 0.245283i
\(530\) 0 0
\(531\) 62208.3i 0.00957442i
\(532\) 0 0
\(533\) −4.59983e6 + 4.59983e6i −0.701333 + 0.701333i
\(534\) 0 0
\(535\) 1.15372e7 3.44667e6i 1.74268 0.520614i
\(536\) 0 0
\(537\) −3.96221e6 3.96221e6i −0.592927 0.592927i
\(538\) 0 0
\(539\) −5.59094e6 −0.828920
\(540\) 0 0
\(541\) 6.09633e6 0.895520 0.447760 0.894154i \(-0.352222\pi\)
0.447760 + 0.894154i \(0.352222\pi\)
\(542\) 0 0
\(543\) 5.88679e6 + 5.88679e6i 0.856799 + 0.856799i
\(544\) 0 0
\(545\) 1.65839e6 3.07138e6i 0.239164 0.442938i
\(546\) 0 0
\(547\) 2.00865e6 2.00865e6i 0.287036 0.287036i −0.548871 0.835907i \(-0.684942\pi\)
0.835907 + 0.548871i \(0.184942\pi\)
\(548\) 0 0
\(549\) 1.62666e6i 0.230338i
\(550\) 0 0
\(551\) 2.50204e6i 0.351087i
\(552\) 0 0
\(553\) 4.00319e6 4.00319e6i 0.556665 0.556665i
\(554\) 0 0
\(555\) −844642. + 1.56430e6i −0.116397 + 0.215569i
\(556\) 0 0
\(557\) 1.00540e7 + 1.00540e7i 1.37309 + 1.37309i 0.855821 + 0.517272i \(0.173052\pi\)
0.517272 + 0.855821i \(0.326948\pi\)
\(558\) 0 0
\(559\) −2.52918e6 −0.342334
\(560\) 0 0
\(561\) 9.37621e6 1.25782
\(562\) 0 0
\(563\) 6.99182e6 + 6.99182e6i 0.929650 + 0.929650i 0.997683 0.0680335i \(-0.0216725\pi\)
−0.0680335 + 0.997683i \(0.521672\pi\)
\(564\) 0 0
\(565\) −2.49026e6 + 743951.i −0.328189 + 0.0980444i
\(566\) 0 0
\(567\) −2.06768e6 + 2.06768e6i −0.270100 + 0.270100i
\(568\) 0 0
\(569\) 3.15878e6i 0.409015i −0.978865 0.204507i \(-0.934441\pi\)
0.978865 0.204507i \(-0.0655592\pi\)
\(570\) 0 0
\(571\) 9.35381e6i 1.20060i 0.799775 + 0.600300i \(0.204952\pi\)
−0.799775 + 0.600300i \(0.795048\pi\)
\(572\) 0 0
\(573\) 656331. 656331.i 0.0835095 0.0835095i
\(574\) 0 0
\(575\) −1.79917e6 + 8.66228e6i −0.226935 + 1.09260i
\(576\) 0 0
\(577\) −1.00683e7 1.00683e7i −1.25897 1.25897i −0.951583 0.307391i \(-0.900544\pi\)
−0.307391 0.951583i \(-0.599456\pi\)
\(578\) 0 0
\(579\) −7.22883e6 −0.896131
\(580\) 0 0
\(581\) −7.51714e6 −0.923873
\(582\) 0 0
\(583\) 5.38301e6 + 5.38301e6i 0.655924 + 0.655924i
\(584\) 0 0
\(585\) 402751. + 1.34815e6i 0.0486572 + 0.162872i
\(586\) 0 0
\(587\) −9.87805e6 + 9.87805e6i −1.18325 + 1.18325i −0.204351 + 0.978898i \(0.565508\pi\)
−0.978898 + 0.204351i \(0.934492\pi\)
\(588\) 0 0
\(589\) 6.34297e6i 0.753364i
\(590\) 0 0
\(591\) 1.48972e6i 0.175444i
\(592\) 0 0
\(593\) 6.47163e6 6.47163e6i 0.755748 0.755748i −0.219797 0.975546i \(-0.570540\pi\)
0.975546 + 0.219797i \(0.0705396\pi\)
\(594\) 0 0
\(595\) 5.00424e6 + 2.70204e6i 0.579490 + 0.312895i
\(596\) 0 0
\(597\) 8.79696e6 + 8.79696e6i 1.01018 + 1.01018i
\(598\) 0 0
\(599\) −5.49595e6 −0.625858 −0.312929 0.949777i \(-0.601310\pi\)
−0.312929 + 0.949777i \(0.601310\pi\)
\(600\) 0 0
\(601\) −2.92293e6 −0.330090 −0.165045 0.986286i \(-0.552777\pi\)
−0.165045 + 0.986286i \(0.552777\pi\)
\(602\) 0 0
\(603\) 510390. + 510390.i 0.0571622 + 0.0571622i
\(604\) 0 0
\(605\) 2.63075e6 + 1.42047e6i 0.292208 + 0.157777i
\(606\) 0 0
\(607\) 3.15887e6 3.15887e6i 0.347984 0.347984i −0.511374 0.859358i \(-0.670863\pi\)
0.859358 + 0.511374i \(0.170863\pi\)
\(608\) 0 0
\(609\) 3.36229e6i 0.367360i
\(610\) 0 0
\(611\) 5.09697e6i 0.552343i
\(612\) 0 0
\(613\) 1.01465e6 1.01465e6i 0.109060 0.109060i −0.650471 0.759531i \(-0.725429\pi\)
0.759531 + 0.650471i \(0.225429\pi\)
\(614\) 0 0
\(615\) −3.14191e6 1.05171e7i −0.334970 1.12126i
\(616\) 0 0
\(617\) 2.48588e6 + 2.48588e6i 0.262886 + 0.262886i 0.826226 0.563340i \(-0.190484\pi\)
−0.563340 + 0.826226i \(0.690484\pi\)
\(618\) 0 0
\(619\) 4.49651e6 0.471682 0.235841 0.971792i \(-0.424216\pi\)
0.235841 + 0.971792i \(0.424216\pi\)
\(620\) 0 0
\(621\) −1.15716e7 −1.20410
\(622\) 0 0
\(623\) −7.10259e6 7.10259e6i −0.733156 0.733156i
\(624\) 0 0
\(625\) −3.88890e6 + 8.95789e6i −0.398224 + 0.917288i
\(626\) 0 0
\(627\) −3.14525e6 + 3.14525e6i −0.319512 + 0.319512i
\(628\) 0 0
\(629\) 3.43304e6i 0.345981i
\(630\) 0 0
\(631\) 8.34293e6i 0.834152i 0.908872 + 0.417076i \(0.136945\pi\)
−0.908872 + 0.417076i \(0.863055\pi\)
\(632\) 0 0
\(633\) 7.09648e6 7.09648e6i 0.703936 0.703936i
\(634\) 0 0
\(635\) 9.12795e6 2.72692e6i 0.898337 0.268373i
\(636\) 0 0
\(637\) 3.87233e6 + 3.87233e6i 0.378115 + 0.378115i
\(638\) 0 0
\(639\) −2.92061e6 −0.282958
\(640\) 0 0
\(641\) −4.67634e6 −0.449532 −0.224766 0.974413i \(-0.572162\pi\)
−0.224766 + 0.974413i \(0.572162\pi\)
\(642\) 0 0
\(643\) −1.95020e6 1.95020e6i −0.186017 0.186017i 0.607955 0.793972i \(-0.291990\pi\)
−0.793972 + 0.607955i \(0.791990\pi\)
\(644\) 0 0
\(645\) 2.02758e6 3.75514e6i 0.191902 0.355407i
\(646\) 0 0
\(647\) 7.09333e6 7.09333e6i 0.666177 0.666177i −0.290652 0.956829i \(-0.593872\pi\)
0.956829 + 0.290652i \(0.0938722\pi\)
\(648\) 0 0
\(649\) 519362.i 0.0484014i
\(650\) 0 0
\(651\) 8.52381e6i 0.788281i
\(652\) 0 0
\(653\) −1.02700e7 + 1.02700e7i −0.942516 + 0.942516i −0.998435 0.0559194i \(-0.982191\pi\)
0.0559194 + 0.998435i \(0.482191\pi\)
\(654\) 0 0
\(655\) −2.35400e6 + 4.35966e6i −0.214389 + 0.397054i
\(656\) 0 0
\(657\) 1.55149e6 + 1.55149e6i 0.140228 + 0.140228i
\(658\) 0 0
\(659\) 2.21615e7 1.98786 0.993930 0.110013i \(-0.0350891\pi\)
0.993930 + 0.110013i \(0.0350891\pi\)
\(660\) 0 0
\(661\) 3.85454e6 0.343138 0.171569 0.985172i \(-0.445116\pi\)
0.171569 + 0.985172i \(0.445116\pi\)
\(662\) 0 0
\(663\) −6.49403e6 6.49403e6i −0.573761 0.573761i
\(664\) 0 0
\(665\) −2.58507e6 + 772275.i −0.226683 + 0.0677201i
\(666\) 0 0
\(667\) 7.14224e6 7.14224e6i 0.621613 0.621613i
\(668\) 0 0
\(669\) 6.71430e6i 0.580010i
\(670\) 0 0
\(671\) 1.35806e7i 1.16443i
\(672\) 0 0
\(673\) 8.70626e6 8.70626e6i 0.740958 0.740958i −0.231804 0.972762i \(-0.574463\pi\)
0.972762 + 0.231804i \(0.0744629\pi\)
\(674\) 0 0
\(675\) −1.25060e7 2.59751e6i −1.05647 0.219431i
\(676\) 0 0
\(677\) −2.81144e6 2.81144e6i −0.235753 0.235753i 0.579336 0.815089i \(-0.303312\pi\)
−0.815089 + 0.579336i \(0.803312\pi\)
\(678\) 0 0
\(679\) −9.52399e6 −0.792765
\(680\) 0 0
\(681\) 5.08830e6 0.420441
\(682\) 0 0
\(683\) −8.19141e6 8.19141e6i −0.671903 0.671903i 0.286251 0.958155i \(-0.407591\pi\)
−0.958155 + 0.286251i \(0.907591\pi\)
\(684\) 0 0
\(685\) 1.05738e6 + 3.53942e6i 0.0861004 + 0.288208i
\(686\) 0 0
\(687\) 1.32423e7 1.32423e7i 1.07047 1.07047i
\(688\) 0 0
\(689\) 7.45662e6i 0.598403i
\(690\) 0 0
\(691\) 6.47639e6i 0.515986i −0.966147 0.257993i \(-0.916939\pi\)
0.966147 0.257993i \(-0.0830611\pi\)
\(692\) 0 0
\(693\) −1.25047e6 + 1.25047e6i −0.0989096 + 0.0989096i
\(694\) 0 0
\(695\) 1.37849e7 + 7.44313e6i 1.08253 + 0.584512i
\(696\) 0 0
\(697\) −1.49881e7 1.49881e7i −1.16860 1.16860i
\(698\) 0 0
\(699\) −3.31600e6 −0.256697
\(700\) 0 0
\(701\) −1.17245e7 −0.901155 −0.450578 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(702\) 0 0
\(703\) −1.15161e6 1.15161e6i −0.0878858 0.0878858i
\(704\) 0 0
\(705\) 7.56759e6 + 4.08612e6i 0.573436 + 0.309626i
\(706\) 0 0
\(707\) −4.21203e6 + 4.21203e6i −0.316915 + 0.316915i
\(708\) 0 0
\(709\) 5.40476e6i 0.403795i 0.979407 + 0.201897i \(0.0647107\pi\)
−0.979407 + 0.201897i \(0.935289\pi\)
\(710\) 0 0
\(711\) 4.56388e6i 0.338579i
\(712\) 0 0
\(713\) −1.81065e7 + 1.81065e7i −1.33386 + 1.33386i
\(714\) 0 0
\(715\) −3.36247e6 1.12553e7i −0.245976 0.823367i
\(716\) 0 0
\(717\) −1.26991e7 1.26991e7i −0.922516 0.922516i
\(718\) 0 0
\(719\) −4.95216e6 −0.357250 −0.178625 0.983917i \(-0.557165\pi\)
−0.178625 + 0.983917i \(0.557165\pi\)
\(720\) 0 0
\(721\) −1.22561e7 −0.878038
\(722\) 0 0
\(723\) −1.27561e7 1.27561e7i −0.907555 0.907555i
\(724\) 0 0
\(725\) 9.32222e6 6.11573e6i 0.658680 0.432119i
\(726\) 0 0
\(727\) 824940. 824940.i 0.0578877 0.0578877i −0.677570 0.735458i \(-0.736967\pi\)
0.735458 + 0.677570i \(0.236967\pi\)
\(728\) 0 0
\(729\) 1.59583e7i 1.11216i
\(730\) 0 0
\(731\) 8.24109e6i 0.570415i
\(732\) 0 0
\(733\) −1.29259e7 + 1.29259e7i −0.888590 + 0.888590i −0.994388 0.105798i \(-0.966260\pi\)
0.105798 + 0.994388i \(0.466260\pi\)
\(734\) 0 0
\(735\) −8.85369e6 + 2.64499e6i −0.604514 + 0.180595i
\(736\) 0 0
\(737\) −4.26111e6 4.26111e6i −0.288971 0.288971i
\(738\) 0 0
\(739\) 1.48270e7 0.998714 0.499357 0.866396i \(-0.333570\pi\)
0.499357 + 0.866396i \(0.333570\pi\)
\(740\) 0 0
\(741\) 4.35685e6 0.291492
\(742\) 0 0
\(743\) 2.13856e6 + 2.13856e6i 0.142118 + 0.142118i 0.774586 0.632468i \(-0.217958\pi\)
−0.632468 + 0.774586i \(0.717958\pi\)
\(744\) 0 0
\(745\) −3.04858e6 + 5.64606e6i −0.201237 + 0.372696i
\(746\) 0 0
\(747\) 4.28499e6 4.28499e6i 0.280963 0.280963i
\(748\) 0 0
\(749\) 1.48236e7i 0.965491i
\(750\) 0 0
\(751\) 499674.i 0.0323286i 0.999869 + 0.0161643i \(0.00514548\pi\)
−0.999869 + 0.0161643i \(0.994855\pi\)
\(752\) 0 0
\(753\) 1.82252e6 1.82252e6i 0.117134 0.117134i
\(754\) 0 0
\(755\) −1.03316e7 + 1.91344e7i −0.659630 + 1.22165i
\(756\) 0 0
\(757\) 1.51219e7 + 1.51219e7i 0.959105 + 0.959105i 0.999196 0.0400909i \(-0.0127647\pi\)
−0.0400909 + 0.999196i \(0.512765\pi\)
\(758\) 0 0
\(759\) 1.79567e7 1.13141
\(760\) 0 0
\(761\) 3.08023e7 1.92806 0.964032 0.265788i \(-0.0856321\pi\)
0.964032 + 0.265788i \(0.0856321\pi\)
\(762\) 0 0
\(763\) −3.03852e6 3.03852e6i −0.188952 0.188952i
\(764\) 0 0
\(765\) −4.39281e6 + 1.31233e6i −0.271387 + 0.0810752i
\(766\) 0 0
\(767\) −359714. + 359714.i −0.0220785 + 0.0220785i
\(768\) 0 0
\(769\) 6.19605e6i 0.377832i 0.981993 + 0.188916i \(0.0604975\pi\)
−0.981993 + 0.188916i \(0.939503\pi\)
\(770\) 0 0
\(771\) 1.51853e7i 0.920001i
\(772\) 0 0
\(773\) 6.65596e6 6.65596e6i 0.400647 0.400647i −0.477814 0.878461i \(-0.658571\pi\)
0.878461 + 0.477814i \(0.158571\pi\)
\(774\) 0 0
\(775\) −2.36330e7 + 1.55041e7i −1.41340 + 0.927243i
\(776\) 0 0
\(777\) 1.54756e6 + 1.54756e6i 0.0919592 + 0.0919592i
\(778\) 0 0
\(779\) 1.00555e7 0.593693
\(780\) 0 0
\(781\) 2.43835e7 1.43043
\(782\) 0 0
\(783\) 1.03114e7 + 1.03114e7i 0.601056 + 0.601056i
\(784\) 0 0
\(785\) −5.21208e6 1.74466e7i −0.301882 1.01050i
\(786\) 0 0
\(787\) −2.68934e6 + 2.68934e6i −0.154778 + 0.154778i −0.780248 0.625470i \(-0.784907\pi\)
0.625470 + 0.780248i \(0.284907\pi\)
\(788\) 0 0
\(789\) 1.07361e7i 0.613981i
\(790\) 0 0