Properties

Label 80.6.n.d.63.3
Level $80$
Weight $6$
Character 80.63
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 63.3
Root \(-10.8505 - 10.2794i\) of defining polynomial
Character \(\chi\) \(=\) 80.63
Dual form 80.6.n.d.47.3

$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 −0.945829 0.324664i \(-0.894749\pi\)
0.324664 + 0.945829i \(0.394749\pi\)
\(4\) 0 0
\(5\) −49.1893 + 26.5597i −0.879924 + 0.475114i
\(6\) 0 0
\(7\) −48.6629 48.6629i −0.375364 0.375364i 0.494062 0.869427i \(-0.335512\pi\)
−0.869427 + 0.494062i \(0.835512\pi\)
\(8\) 0 0
\(9\) 55.4787i 0.228307i
\(10\) 0 0
\(11\) 463.177i 1.15416i −0.816688 0.577080i \(-0.804192\pi\)
0.816688 0.577080i \(-0.195808\pi\)
\(12\) 0 0
\(13\) 320.800 + 320.800i 0.526473 + 0.526473i 0.919519 0.393046i \(-0.128579\pi\)
−0.393046 + 0.919519i \(0.628579\pi\)
\(14\) 0 0
\(15\) 219.122 733.478i 0.251454 0.841703i
\(16\) 0 0
\(17\) 1045.30 1045.30i 0.877238 0.877238i −0.116010 0.993248i \(-0.537011\pi\)
0.993248 + 0.116010i \(0.0370106\pi\)
\(18\) 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 −0.192266 0.981343i \(-0.561584\pi\)
0.981343 + 0.192266i \(0.0615838\pi\)
\(24\) 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 \(0.128870\pi\)
−0.919159 + 0.393886i \(0.871130\pi\)
\(30\) 0 0
\(31\) 9044.72i 1.69041i −0.534446 0.845203i \(-0.679480\pi\)
0.534446 0.845203i \(-0.320520\pi\)
\(32\) 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 −0.601599 0.798798i \(-0.705470\pi\)
0.798798 + 0.601599i \(0.205470\pi\)
\(38\) 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 −0.850727 0.525607i \(-0.823838\pi\)
0.525607 + 0.850727i \(0.323838\pi\)
\(44\) 0 0
\(45\) −1473.50 2728.95i −0.108472 0.200893i
\(46\) 0 0
\(47\) 7944.15 + 7944.15i 0.524569 + 0.524569i 0.918948 0.394379i \(-0.129040\pi\)
−0.394379 + 0.918948i \(0.629040\pi\)
\(48\) 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 0.931656 0.363342i \(-0.118364\pi\)
−0.363342 + 0.931656i \(0.618364\pi\)
\(54\) 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 0.570750 0.821124i \(-0.306653\pi\)
−0.821124 + 0.570750i \(0.806653\pi\)
\(68\) 0 0
\(69\) 38768.5i 0.980294i
\(70\) 0 0
\(71\) 52643.9i 1.23937i 0.784849 + 0.619687i \(0.212740\pi\)
−0.784849 + 0.619687i \(0.787260\pi\)
\(72\) 0 0
\(73\) −27965.6 27965.6i −0.614209 0.614209i 0.329831 0.944040i \(-0.393008\pi\)
−0.944040 + 0.329831i \(0.893008\pi\)
\(74\) 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 0.266914 0.963720i \(-0.413996\pi\)
0.963720 0.266914i \(-0.0860039\pi\)
\(84\) 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 \(-0.569008\pi\)
0.215100 0.976592i \(-0.430992\pi\)
\(90\) 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 0.0576570 0.998336i \(-0.481637\pi\)
0.998336 0.0576570i \(-0.0183630\pi\)
\(98\) 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 0.187273 0.982308i \(-0.440035\pi\)
0.982308 0.187273i \(-0.0599650\pi\)
\(104\) 0 0
\(105\) −46356.3 + 25030.1i −0.410332 + 0.221559i
\(106\) 0 0
\(107\) −152309. 152309.i −1.28607 1.28607i −0.937154 0.348917i \(-0.886550\pi\)
−0.348917 0.937154i \(1.38655\pi\)
\(108\) 0 0
\(109\) 62440.1i 0.503382i −0.967808 0.251691i \(-0.919013\pi\)
0.967808 0.251691i \(-0.0809866\pi\)
\(110\) 0 0
\(111\) 31801.6i 0.244986i
\(112\) 0 0
\(113\) 32875.2 + 32875.2i 0.242199 + 0.242199i 0.817759 0.575560i \(-0.195216\pi\)
−0.575560 + 0.817759i \(0.695216\pi\)
\(114\) 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 0.293116 0.956077i \(-0.405308\pi\)
−0.956077 + 0.293116i \(0.905308\pi\)
\(128\) 0 0
\(129\) 76340.6i 0.403907i
\(130\) 0 0
\(131\) 88630.4i 0.451237i 0.974216 + 0.225618i \(0.0724402\pi\)
−0.974216 + 0.225618i \(0.927560\pi\)
\(132\) 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 −0.805411 0.592717i \(-0.798055\pi\)
0.592717 + 0.805411i \(0.298055\pi\)
\(138\) 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 \(0.0679251\pi\)
−0.977318 + 0.211777i \(0.932075\pi\)
\(150\) 0 0
\(151\) 388996.i 1.38836i 0.719801 + 0.694181i \(0.244233\pi\)
−0.719801 + 0.694181i \(0.755767\pi\)
\(152\) 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 −0.227938 0.973676i \(-0.573198\pi\)
0.973676 + 0.227938i \(0.0731984\pi\)
\(158\) 0 0
\(159\) −225070. −0.706033
\(160\) 0 0
\(161\) −194835. −0.592382
\(162\) 0 0
\(163\) −334147. + 334147.i −0.985073 + 0.985073i −0.999890 0.0148175i \(-0.995283\pi\)
0.0148175 + 0.999890i \(0.495283\pi\)
\(164\) 0 0
\(165\) −339730. 101492.i −0.971459 0.290218i
\(166\) 0 0
\(167\) 287959. + 287959.i 0.798987 + 0.798987i 0.982936 0.183949i \(-0.0588880\pi\)
−0.183949 + 0.982936i \(0.558888\pi\)
\(168\) 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 0.894603 0.446862i \(-0.147458\pi\)
−0.446862 + 0.894603i \(0.647458\pi\)
\(174\) 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 \(-0.978587\pi\)
0.997738 0.0672201i \(-0.0214130\pi\)
\(192\) 0 0
\(193\) 373274. + 373274.i 0.721330 + 0.721330i 0.968876 0.247546i \(-0.0796241\pi\)
−0.247546 + 0.968876i \(0.579624\pi\)
\(194\) 0 0
\(195\) 305594. 165005.i 0.575518 0.310750i
\(196\) 0 0
\(197\) 76924.7 76924.7i 0.141221 0.141221i −0.632962 0.774183i \(-0.718161\pi\)
0.774183 + 0.632962i \(0.218161\pi\)
\(198\) 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 \(-0.808249\pi\)
0.823975 0.566626i \(-0.191751\pi\)
\(212\) 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 −0.900900 0.434027i \(-0.857092\pi\)
0.434027 + 0.900900i \(0.357092\pi\)
\(224\) 0 0
\(225\) 144960. + 95099.6i 0.190894 + 0.125234i
\(226\) 0 0
\(227\) −262744. 262744.i −0.338429 0.338429i 0.517347 0.855776i \(-0.326920\pi\)
−0.855776 + 0.517347i \(0.826920\pi\)
\(228\) 0 0
\(229\) 1.36759e6i 1.72332i −0.507487 0.861660i \(-0.669425\pi\)
0.507487 0.861660i \(-0.330575\pi\)
\(230\) 0 0
\(231\) 436502.i 0.538215i
\(232\) 0 0
\(233\) 171228. + 171228.i 0.206626 + 0.206626i 0.802832 0.596206i \(-0.203326\pi\)
−0.596206 + 0.802832i \(0.703326\pi\)
\(234\) 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 \(-0.969943\pi\)
0.995545 0.0942859i \(-0.0300568\pi\)
\(252\) 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 −0.972683 0.232139i \(-0.925428\pi\)
0.232139 + 0.972683i \(0.425428\pi\)
\(258\) 0 0
\(259\) −159822. −0.148043
\(260\) 0 0
\(261\) −197935. −0.179854
\(262\) 0 0
\(263\) −554379. + 554379.i −0.494217 + 0.494217i −0.909632 0.415415i \(-0.863636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(264\) 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 \(-0.980323\pi\)
0.998090 0.0617785i \(-0.0196772\pi\)
\(270\) 0 0
\(271\) 620115.i 0.512919i 0.966555 + 0.256460i \(0.0825560\pi\)
−0.966555 + 0.256460i \(0.917444\pi\)
\(272\) 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 −0.894418 0.447233i \(-0.852410\pi\)
0.447233 + 0.894418i \(0.352410\pi\)
\(278\) 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 −0.269091 + 0.963115i \(0.586723\pi\)
−0.963115 + 0.269091i \(0.913277\pi\)
\(284\) 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 −0.981151 0.193242i \(-0.938100\pi\)
−0.193242 0.981151i \(-0.561900\pi\)
\(294\) 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 0.885217 0.465178i \(-0.154010\pi\)
−0.465178 + 0.885217i \(0.654010\pi\)
\(308\) 0 0
\(309\) 2.43873e6i 1.45301i
\(310\) 0 0
\(311\) 839243.i 0.492024i −0.969267 0.246012i \(-0.920880\pi\)
0.969267 0.246012i \(-0.0791203\pi\)
\(312\) 0 0
\(313\) −1.45976e6 1.45976e6i −0.842208 0.842208i 0.146938 0.989146i \(-0.453058\pi\)
−0.989146 + 0.146938i \(0.953058\pi\)
\(314\) 0 0
\(315\) −61094.2 + 204504.i −0.0346916 + 0.116125i
\(316\) 0 0
\(317\) 768911. 768911.i 0.429762 0.429762i −0.458785 0.888547i \(-0.651715\pi\)
0.888547 + 0.458785i \(0.151715\pi\)
\(318\) 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 \(-0.873998\pi\)
0.922671 0.385589i \(-0.126002\pi\)
\(332\) 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 −0.836248 0.548352i \(-0.815255\pi\)
0.548352 + 0.836248i \(0.315255\pi\)
\(338\) 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 0.703634 0.710563i \(-0.251560\pi\)
−0.710563 + 0.703634i \(0.751560\pi\)
\(348\) 0 0
\(349\) 1.37621e6i 0.604815i 0.953179 + 0.302407i \(0.0977903\pi\)
−0.953179 + 0.302407i \(0.902210\pi\)
\(350\) 0 0
\(351\) 1.85434e6i 0.803379i
\(352\) 0 0
\(353\) 2.13095e6 + 2.13095e6i 0.910198 + 0.910198i 0.996287 0.0860896i \(-0.0274371\pi\)
−0.0860896 + 0.996287i \(0.527437\pi\)
\(354\) 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 0.521032 0.853537i \(-0.325547\pi\)
−0.853537 + 0.521032i \(0.825547\pi\)
\(368\) 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 0.967816 0.251659i \(-0.0809762\pi\)
−0.251659 + 0.967816i \(0.580976\pi\)
\(374\) 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 −0.727929 0.685652i \(-0.759517\pi\)
0.685652 + 0.727929i \(0.259517\pi\)
\(384\) 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 \(0.143867\pi\)
−0.899587 + 0.436741i \(0.856133\pi\)
\(390\) 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 −0.142173 0.989842i \(-0.545409\pi\)
0.989842 + 0.142173i \(0.0454089\pi\)
\(398\) 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 \(-0.918201\pi\)
0.967162 0.254159i \(-0.0817988\pi\)
\(410\) 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 \(0.172976\pi\)
−0.855945 + 0.517067i \(0.827024\pi\)
\(432\) 0 0
\(433\) 386926. + 386926.i 0.0991765 + 0.0991765i 0.754954 0.655778i \(-0.227659\pi\)
−0.655778 + 0.754954i \(0.727659\pi\)
\(434\) 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 −0.946769 0.321913i \(-0.895674\pi\)
0.321913 + 0.946769i \(0.395674\pi\)
\(444\) 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 \(-0.815950\pi\)
0.837443 0.546525i \(-0.184050\pi\)
\(450\) 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 −0.137858 + 0.990452i \(0.544022\pi\)
−0.990452 + 0.137858i \(0.955978\pi\)
\(458\) 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 0.374258 0.927325i \(-0.377897\pi\)
0.927325 0.374258i \(-0.122103\pi\)
\(464\) 0 0
\(465\) −6.63410e6 1.98190e6i −1.42282 0.425059i
\(466\) 0 0
\(467\) −2.93586e6 2.93586e6i −0.622935 0.622935i 0.323346 0.946281i \(-0.395192\pi\)
−0.946281 + 0.323346i \(0.895192\pi\)
\(468\) 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 0.877776 0.479072i \(-0.159027\pi\)
−0.479072 + 0.877776i \(0.659027\pi\)
\(488\) 0 0
\(489\) 6.47109e6i 1.22379i
\(490\) 0 0
\(491\) 3.55745e6i 0.665940i 0.942937 + 0.332970i \(0.108051\pi\)
−0.942937 + 0.332970i \(0.891949\pi\)
\(492\) 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 −0.877549 0.479488i \(-0.840823\pi\)
0.479488 + 0.877549i \(0.340823\pi\)
\(504\) 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 \(-0.853071\pi\)
0.895345 0.445373i \(-0.146929\pi\)
\(510\) 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 −0.396793 0.917908i \(-0.629877\pi\)
0.917908 + 0.396793i \(0.129877\pi\)
\(524\) 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 0.835907 0.548871i \(-0.184942\pi\)
−0.548871 + 0.835907i \(0.684942\pi\)
\(548\) 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 0.517272 0.855821i \(-0.326948\pi\)
0.855821 0.517272i \(-0.173052\pi\)
\(558\) 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 −0.0680335 0.997683i \(-0.521672\pi\)
0.997683 + 0.0680335i \(0.0216725\pi\)
\(564\) 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 \(0.0655592\pi\)
−0.978865 + 0.204507i \(0.934441\pi\)
\(570\) 0 0
\(571\) 9.35381e6i 1.20060i −0.799775 0.600300i \(-0.795048\pi\)
0.799775 0.600300i \(-0.204952\pi\)
\(572\) 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 −0.307391 + 0.951583i \(0.599456\pi\)
−0.951583 + 0.307391i \(0.900544\pi\)
\(578\) 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 −0.978898 0.204351i \(-0.934492\pi\)
−0.204351 0.978898i \(1.43449\pi\)
\(588\) 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 0.975546 0.219797i \(-0.0705396\pi\)
−0.219797 + 0.975546i \(0.570540\pi\)
\(594\) 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 0.859358 0.511374i \(-0.170863\pi\)
−0.511374 + 0.859358i \(0.670863\pi\)
\(608\) 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 0.759531 0.650471i \(-0.225429\pi\)
−0.650471 + 0.759531i \(0.725429\pi\)
\(614\) 0 0
\(615\) −3.14191e6 + 1.05171e7i −0.334970 + 1.12126i
\(616\) 0 0
\(617\) 2.48588e6 2.48588e6i 0.262886 0.262886i −0.563340 0.826226i \(-0.690484\pi\)
0.826226 + 0.563340i \(0.190484\pi\)
\(618\) 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 \(-0.863055\pi\)
0.908872 0.417076i \(-0.136945\pi\)
\(632\) 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 −0.793972 0.607955i \(-0.791990\pi\)
0.607955 + 0.793972i \(0.291990\pi\)
\(644\) 0 0
\(645\) 2.02758e6 + 3.75514e6i 0.191902 + 0.355407i
\(646\) 0 0
\(647\) 7.09333e6 + 7.09333e6i 0.666177 + 0.666177i 0.956829 0.290652i \(-0.0938722\pi\)
−0.290652 + 0.956829i \(0.593872\pi\)
\(648\) 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 0.0559194 0.998435i \(-0.482191\pi\)
−0.998435 + 0.0559194i \(0.982191\pi\)
\(654\) 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 0.972762 0.231804i \(-0.0744629\pi\)
−0.231804 + 0.972762i \(0.574463\pi\)
\(674\) 0 0
\(675\) −1.25060e7 + 2.59751e6i −1.05647 + 0.219431i
\(676\) 0 0
\(677\) −2.81144e6 + 2.81144e6i −0.235753 + 0.235753i −0.815089 0.579336i \(-0.803312\pi\)
0.579336 + 0.815089i \(0.303312\pi\)
\(678\) 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 −0.958155 0.286251i \(-0.907591\pi\)
0.286251 + 0.958155i \(0.407591\pi\)
\(684\) 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 \(0.0830611\pi\)
−0.966147 + 0.257993i \(0.916939\pi\)
\(692\) 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 \(-0.935289\pi\)
0.979407 0.201897i \(-0.0647107\pi\)
\(710\) 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 0.735458 0.677570i \(-0.236967\pi\)
−0.677570 + 0.735458i \(0.736967\pi\)
\(728\) 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 0.105798 0.994388i \(-0.466260\pi\)
−0.994388 + 0.105798i \(0.966260\pi\)
\(734\) 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 −0.632468 0.774586i \(-0.717958\pi\)
0.774586 + 0.632468i \(0.217958\pi\)
\(744\) 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 \(-0.994855\pi\)
0.999869 0.0161643i \(-0.00514548\pi\)
\(752\) 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 −0.0400909 0.999196i \(-0.512765\pi\)
0.999196 + 0.0400909i \(0.0127647\pi\)
\(758\) 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 \(-0.939503\pi\)
0.981993 0.188916i \(-0.0604975\pi\)
\(770\) 0 0
\(771\) 1.51853e7i 0.920001i
\(772\) 0 0
\(773\) 6.65596e6 + 6.65596e6i 0.400647 + 0.400647i 0.878461 0.477814i \(-0.158571\pi\)
−0.477814 + 0.878461i \(0.658571\pi\)
\(774\) 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 0.625470 0.780248i \(-0.284907\pi\)
−0.780248 + 0.625470i \(0.784907\pi\)
\(788\) 0 0
\(789\) 1.07361e7i 0.613981i
\(790\) 0