Properties

Label 20.6.a.a.1.1
Level 20
Weight 6
Character 20.1
Self dual Yes
Analytic conductor 3.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.20767639626\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 20.1

$q$-expansion

\(f(q)\) \(=\) \(q+22.0000 q^{3} -25.0000 q^{5} +218.000 q^{7} +241.000 q^{9} +O(q^{10})\) \(q+22.0000 q^{3} -25.0000 q^{5} +218.000 q^{7} +241.000 q^{9} -480.000 q^{11} -622.000 q^{13} -550.000 q^{15} +186.000 q^{17} -1204.00 q^{19} +4796.00 q^{21} -3186.00 q^{23} +625.000 q^{25} -44.0000 q^{27} +5526.00 q^{29} +9356.00 q^{31} -10560.0 q^{33} -5450.00 q^{35} +5618.00 q^{37} -13684.0 q^{39} -14394.0 q^{41} -370.000 q^{43} -6025.00 q^{45} +16146.0 q^{47} +30717.0 q^{49} +4092.00 q^{51} -4374.00 q^{53} +12000.0 q^{55} -26488.0 q^{57} -11748.0 q^{59} +13202.0 q^{61} +52538.0 q^{63} +15550.0 q^{65} -11542.0 q^{67} -70092.0 q^{69} -29532.0 q^{71} +33698.0 q^{73} +13750.0 q^{75} -104640. q^{77} +31208.0 q^{79} -59531.0 q^{81} -38466.0 q^{83} -4650.00 q^{85} +121572. q^{87} +119514. q^{89} -135596. q^{91} +205832. q^{93} +30100.0 q^{95} +94658.0 q^{97} -115680. q^{99} +O(q^{100})\)

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
\(3\) 22.0000 1.41130 0.705650 0.708560i \(-0.250655\pi\)
0.705650 + 0.708560i \(0.250655\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 218.000 1.68156 0.840778 0.541380i \(-0.182098\pi\)
0.840778 + 0.541380i \(0.182098\pi\)
\(8\) 0 0
\(9\) 241.000 0.991770
\(10\) 0 0
\(11\) −480.000 −1.19608 −0.598039 0.801467i \(-0.704053\pi\)
−0.598039 + 0.801467i \(0.704053\pi\)
\(12\) 0 0
\(13\) −622.000 −1.02078 −0.510390 0.859943i \(-0.670499\pi\)
−0.510390 + 0.859943i \(0.670499\pi\)
\(14\) 0 0
\(15\) −550.000 −0.631153
\(16\) 0 0
\(17\) 186.000 0.156096 0.0780478 0.996950i \(-0.475131\pi\)
0.0780478 + 0.996950i \(0.475131\pi\)
\(18\) 0 0
\(19\) −1204.00 −0.765143 −0.382571 0.923926i \(-0.624961\pi\)
−0.382571 + 0.923926i \(0.624961\pi\)
\(20\) 0 0
\(21\) 4796.00 2.37318
\(22\) 0 0
\(23\) −3186.00 −1.25582 −0.627908 0.778287i \(-0.716089\pi\)
−0.627908 + 0.778287i \(0.716089\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −44.0000 −0.0116156
\(28\) 0 0
\(29\) 5526.00 1.22016 0.610079 0.792341i \(-0.291138\pi\)
0.610079 + 0.792341i \(0.291138\pi\)
\(30\) 0 0
\(31\) 9356.00 1.74858 0.874291 0.485402i \(-0.161327\pi\)
0.874291 + 0.485402i \(0.161327\pi\)
\(32\) 0 0
\(33\) −10560.0 −1.68803
\(34\) 0 0
\(35\) −5450.00 −0.752015
\(36\) 0 0
\(37\) 5618.00 0.674648 0.337324 0.941389i \(-0.390478\pi\)
0.337324 + 0.941389i \(0.390478\pi\)
\(38\) 0 0
\(39\) −13684.0 −1.44063
\(40\) 0 0
\(41\) −14394.0 −1.33728 −0.668639 0.743587i \(-0.733123\pi\)
−0.668639 + 0.743587i \(0.733123\pi\)
\(42\) 0 0
\(43\) −370.000 −0.0305162 −0.0152581 0.999884i \(-0.504857\pi\)
−0.0152581 + 0.999884i \(0.504857\pi\)
\(44\) 0 0
\(45\) −6025.00 −0.443533
\(46\) 0 0
\(47\) 16146.0 1.06615 0.533077 0.846066i \(-0.321035\pi\)
0.533077 + 0.846066i \(0.321035\pi\)
\(48\) 0 0
\(49\) 30717.0 1.82763
\(50\) 0 0
\(51\) 4092.00 0.220298
\(52\) 0 0
\(53\) −4374.00 −0.213889 −0.106945 0.994265i \(-0.534107\pi\)
−0.106945 + 0.994265i \(0.534107\pi\)
\(54\) 0 0
\(55\) 12000.0 0.534902
\(56\) 0 0
\(57\) −26488.0 −1.07985
\(58\) 0 0
\(59\) −11748.0 −0.439374 −0.219687 0.975570i \(-0.570504\pi\)
−0.219687 + 0.975570i \(0.570504\pi\)
\(60\) 0 0
\(61\) 13202.0 0.454271 0.227136 0.973863i \(-0.427064\pi\)
0.227136 + 0.973863i \(0.427064\pi\)
\(62\) 0 0
\(63\) 52538.0 1.66772
\(64\) 0 0
\(65\) 15550.0 0.456507
\(66\) 0 0
\(67\) −11542.0 −0.314119 −0.157059 0.987589i \(-0.550201\pi\)
−0.157059 + 0.987589i \(0.550201\pi\)
\(68\) 0 0
\(69\) −70092.0 −1.77233
\(70\) 0 0
\(71\) −29532.0 −0.695260 −0.347630 0.937632i \(-0.613013\pi\)
−0.347630 + 0.937632i \(0.613013\pi\)
\(72\) 0 0
\(73\) 33698.0 0.740111 0.370056 0.929010i \(-0.379339\pi\)
0.370056 + 0.929010i \(0.379339\pi\)
\(74\) 0 0
\(75\) 13750.0 0.282260
\(76\) 0 0
\(77\) −104640. −2.01127
\(78\) 0 0
\(79\) 31208.0 0.562598 0.281299 0.959620i \(-0.409235\pi\)
0.281299 + 0.959620i \(0.409235\pi\)
\(80\) 0 0
\(81\) −59531.0 −1.00816
\(82\) 0 0
\(83\) −38466.0 −0.612889 −0.306444 0.951889i \(-0.599139\pi\)
−0.306444 + 0.951889i \(0.599139\pi\)
\(84\) 0 0
\(85\) −4650.00 −0.0698081
\(86\) 0 0
\(87\) 121572. 1.72201
\(88\) 0 0
\(89\) 119514. 1.59935 0.799675 0.600432i \(-0.205005\pi\)
0.799675 + 0.600432i \(0.205005\pi\)
\(90\) 0 0
\(91\) −135596. −1.71650
\(92\) 0 0
\(93\) 205832. 2.46777
\(94\) 0 0
\(95\) 30100.0 0.342182
\(96\) 0 0
\(97\) 94658.0 1.02148 0.510738 0.859737i \(-0.329372\pi\)
0.510738 + 0.859737i \(0.329372\pi\)
\(98\) 0 0
\(99\) −115680. −1.18623
\(100\) 0 0
\(101\) 101046. 0.985634 0.492817 0.870133i \(-0.335967\pi\)
0.492817 + 0.870133i \(0.335967\pi\)
\(102\) 0 0
\(103\) −143434. −1.33217 −0.666084 0.745877i \(-0.732031\pi\)
−0.666084 + 0.745877i \(0.732031\pi\)
\(104\) 0 0
\(105\) −119900. −1.06132
\(106\) 0 0
\(107\) −57054.0 −0.481755 −0.240878 0.970555i \(-0.577435\pi\)
−0.240878 + 0.970555i \(0.577435\pi\)
\(108\) 0 0
\(109\) −3118.00 −0.0251368 −0.0125684 0.999921i \(-0.504001\pi\)
−0.0125684 + 0.999921i \(0.504001\pi\)
\(110\) 0 0
\(111\) 123596. 0.952132
\(112\) 0 0
\(113\) −54534.0 −0.401764 −0.200882 0.979615i \(-0.564381\pi\)
−0.200882 + 0.979615i \(0.564381\pi\)
\(114\) 0 0
\(115\) 79650.0 0.561618
\(116\) 0 0
\(117\) −149902. −1.01238
\(118\) 0 0
\(119\) 40548.0 0.262484
\(120\) 0 0
\(121\) 69349.0 0.430603
\(122\) 0 0
\(123\) −316668. −1.88730
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 24698.0 0.135879 0.0679395 0.997689i \(-0.478358\pi\)
0.0679395 + 0.997689i \(0.478358\pi\)
\(128\) 0 0
\(129\) −8140.00 −0.0430675
\(130\) 0 0
\(131\) 236640. 1.20479 0.602393 0.798200i \(-0.294214\pi\)
0.602393 + 0.798200i \(0.294214\pi\)
\(132\) 0 0
\(133\) −262472. −1.28663
\(134\) 0 0
\(135\) 1100.00 0.00519467
\(136\) 0 0
\(137\) −22158.0 −0.100862 −0.0504312 0.998728i \(-0.516060\pi\)
−0.0504312 + 0.998728i \(0.516060\pi\)
\(138\) 0 0
\(139\) −193204. −0.848163 −0.424081 0.905624i \(-0.639403\pi\)
−0.424081 + 0.905624i \(0.639403\pi\)
\(140\) 0 0
\(141\) 355212. 1.50467
\(142\) 0 0
\(143\) 298560. 1.22093
\(144\) 0 0
\(145\) −138150. −0.545671
\(146\) 0 0
\(147\) 675774. 2.57934
\(148\) 0 0
\(149\) 448554. 1.65519 0.827597 0.561322i \(-0.189707\pi\)
0.827597 + 0.561322i \(0.189707\pi\)
\(150\) 0 0
\(151\) −140860. −0.502742 −0.251371 0.967891i \(-0.580881\pi\)
−0.251371 + 0.967891i \(0.580881\pi\)
\(152\) 0 0
\(153\) 44826.0 0.154811
\(154\) 0 0
\(155\) −233900. −0.781990
\(156\) 0 0
\(157\) −335878. −1.08751 −0.543754 0.839245i \(-0.682998\pi\)
−0.543754 + 0.839245i \(0.682998\pi\)
\(158\) 0 0
\(159\) −96228.0 −0.301862
\(160\) 0 0
\(161\) −694548. −2.11173
\(162\) 0 0
\(163\) −101650. −0.299667 −0.149833 0.988711i \(-0.547874\pi\)
−0.149833 + 0.988711i \(0.547874\pi\)
\(164\) 0 0
\(165\) 264000. 0.754908
\(166\) 0 0
\(167\) 139242. 0.386348 0.193174 0.981164i \(-0.438122\pi\)
0.193174 + 0.981164i \(0.438122\pi\)
\(168\) 0 0
\(169\) 15591.0 0.0419911
\(170\) 0 0
\(171\) −290164. −0.758845
\(172\) 0 0
\(173\) −265014. −0.673215 −0.336607 0.941645i \(-0.609279\pi\)
−0.336607 + 0.941645i \(0.609279\pi\)
\(174\) 0 0
\(175\) 136250. 0.336311
\(176\) 0 0
\(177\) −258456. −0.620088
\(178\) 0 0
\(179\) −142812. −0.333144 −0.166572 0.986029i \(-0.553270\pi\)
−0.166572 + 0.986029i \(0.553270\pi\)
\(180\) 0 0
\(181\) 109670. 0.248824 0.124412 0.992231i \(-0.460296\pi\)
0.124412 + 0.992231i \(0.460296\pi\)
\(182\) 0 0
\(183\) 290444. 0.641113
\(184\) 0 0
\(185\) −140450. −0.301712
\(186\) 0 0
\(187\) −89280.0 −0.186703
\(188\) 0 0
\(189\) −9592.00 −0.0195324
\(190\) 0 0
\(191\) 294948. 0.585008 0.292504 0.956264i \(-0.405511\pi\)
0.292504 + 0.956264i \(0.405511\pi\)
\(192\) 0 0
\(193\) 1.00303e6 1.93831 0.969153 0.246459i \(-0.0792672\pi\)
0.969153 + 0.246459i \(0.0792672\pi\)
\(194\) 0 0
\(195\) 342100. 0.644268
\(196\) 0 0
\(197\) −823998. −1.51273 −0.756364 0.654151i \(-0.773026\pi\)
−0.756364 + 0.654151i \(0.773026\pi\)
\(198\) 0 0
\(199\) −906712. −1.62307 −0.811534 0.584305i \(-0.801367\pi\)
−0.811534 + 0.584305i \(0.801367\pi\)
\(200\) 0 0
\(201\) −253924. −0.443316
\(202\) 0 0
\(203\) 1.20467e6 2.05176
\(204\) 0 0
\(205\) 359850. 0.598049
\(206\) 0 0
\(207\) −767826. −1.24548
\(208\) 0 0
\(209\) 577920. 0.915170
\(210\) 0 0
\(211\) 506384. 0.783022 0.391511 0.920173i \(-0.371953\pi\)
0.391511 + 0.920173i \(0.371953\pi\)
\(212\) 0 0
\(213\) −649704. −0.981220
\(214\) 0 0
\(215\) 9250.00 0.0136473
\(216\) 0 0
\(217\) 2.03961e6 2.94034
\(218\) 0 0
\(219\) 741356. 1.04452
\(220\) 0 0
\(221\) −115692. −0.159339
\(222\) 0 0
\(223\) −542050. −0.729923 −0.364962 0.931023i \(-0.618918\pi\)
−0.364962 + 0.931023i \(0.618918\pi\)
\(224\) 0 0
\(225\) 150625. 0.198354
\(226\) 0 0
\(227\) −1.44857e6 −1.86585 −0.932924 0.360075i \(-0.882751\pi\)
−0.932924 + 0.360075i \(0.882751\pi\)
\(228\) 0 0
\(229\) −478786. −0.603327 −0.301663 0.953414i \(-0.597542\pi\)
−0.301663 + 0.953414i \(0.597542\pi\)
\(230\) 0 0
\(231\) −2.30208e6 −2.83851
\(232\) 0 0
\(233\) 374106. 0.451445 0.225723 0.974192i \(-0.427526\pi\)
0.225723 + 0.974192i \(0.427526\pi\)
\(234\) 0 0
\(235\) −403650. −0.476799
\(236\) 0 0
\(237\) 686576. 0.793995
\(238\) 0 0
\(239\) 169416. 0.191849 0.0959245 0.995389i \(-0.469419\pi\)
0.0959245 + 0.995389i \(0.469419\pi\)
\(240\) 0 0
\(241\) −353746. −0.392328 −0.196164 0.980571i \(-0.562848\pi\)
−0.196164 + 0.980571i \(0.562848\pi\)
\(242\) 0 0
\(243\) −1.29899e6 −1.41121
\(244\) 0 0
\(245\) −767925. −0.817342
\(246\) 0 0
\(247\) 748888. 0.781042
\(248\) 0 0
\(249\) −846252. −0.864971
\(250\) 0 0
\(251\) 1.25520e6 1.25756 0.628780 0.777583i \(-0.283555\pi\)
0.628780 + 0.777583i \(0.283555\pi\)
\(252\) 0 0
\(253\) 1.52928e6 1.50205
\(254\) 0 0
\(255\) −102300. −0.0985202
\(256\) 0 0
\(257\) −1.12877e6 −1.06604 −0.533021 0.846102i \(-0.678943\pi\)
−0.533021 + 0.846102i \(0.678943\pi\)
\(258\) 0 0
\(259\) 1.22472e6 1.13446
\(260\) 0 0
\(261\) 1.33177e6 1.21012
\(262\) 0 0
\(263\) −263082. −0.234532 −0.117266 0.993101i \(-0.537413\pi\)
−0.117266 + 0.993101i \(0.537413\pi\)
\(264\) 0 0
\(265\) 109350. 0.0956542
\(266\) 0 0
\(267\) 2.62931e6 2.25717
\(268\) 0 0
\(269\) −1.18774e6 −1.00079 −0.500393 0.865798i \(-0.666811\pi\)
−0.500393 + 0.865798i \(0.666811\pi\)
\(270\) 0 0
\(271\) 431300. 0.356744 0.178372 0.983963i \(-0.442917\pi\)
0.178372 + 0.983963i \(0.442917\pi\)
\(272\) 0 0
\(273\) −2.98311e6 −2.42250
\(274\) 0 0
\(275\) −300000. −0.239216
\(276\) 0 0
\(277\) 743114. 0.581910 0.290955 0.956737i \(-0.406027\pi\)
0.290955 + 0.956737i \(0.406027\pi\)
\(278\) 0 0
\(279\) 2.25480e6 1.73419
\(280\) 0 0
\(281\) 1.92193e6 1.45201 0.726007 0.687687i \(-0.241374\pi\)
0.726007 + 0.687687i \(0.241374\pi\)
\(282\) 0 0
\(283\) −1.63071e6 −1.21035 −0.605176 0.796092i \(-0.706897\pi\)
−0.605176 + 0.796092i \(0.706897\pi\)
\(284\) 0 0
\(285\) 662200. 0.482922
\(286\) 0 0
\(287\) −3.13789e6 −2.24871
\(288\) 0 0
\(289\) −1.38526e6 −0.975634
\(290\) 0 0
\(291\) 2.08248e6 1.44161
\(292\) 0 0
\(293\) 71250.0 0.0484859 0.0242430 0.999706i \(-0.492282\pi\)
0.0242430 + 0.999706i \(0.492282\pi\)
\(294\) 0 0
\(295\) 293700. 0.196494
\(296\) 0 0
\(297\) 21120.0 0.0138932
\(298\) 0 0
\(299\) 1.98169e6 1.28191
\(300\) 0 0
\(301\) −80660.0 −0.0513147
\(302\) 0 0
\(303\) 2.22301e6 1.39103
\(304\) 0 0
\(305\) −330050. −0.203156
\(306\) 0 0
\(307\) −1.61762e6 −0.979560 −0.489780 0.871846i \(-0.662923\pi\)
−0.489780 + 0.871846i \(0.662923\pi\)
\(308\) 0 0
\(309\) −3.15555e6 −1.88009
\(310\) 0 0
\(311\) −682788. −0.400299 −0.200150 0.979765i \(-0.564143\pi\)
−0.200150 + 0.979765i \(0.564143\pi\)
\(312\) 0 0
\(313\) −2.70444e6 −1.56033 −0.780165 0.625574i \(-0.784865\pi\)
−0.780165 + 0.625574i \(0.784865\pi\)
\(314\) 0 0
\(315\) −1.31345e6 −0.745825
\(316\) 0 0
\(317\) 2.60347e6 1.45514 0.727568 0.686035i \(-0.240650\pi\)
0.727568 + 0.686035i \(0.240650\pi\)
\(318\) 0 0
\(319\) −2.65248e6 −1.45940
\(320\) 0 0
\(321\) −1.25519e6 −0.679902
\(322\) 0 0
\(323\) −223944. −0.119435
\(324\) 0 0
\(325\) −388750. −0.204156
\(326\) 0 0
\(327\) −68596.0 −0.0354756
\(328\) 0 0
\(329\) 3.51983e6 1.79280
\(330\) 0 0
\(331\) −661432. −0.331830 −0.165915 0.986140i \(-0.553058\pi\)
−0.165915 + 0.986140i \(0.553058\pi\)
\(332\) 0 0
\(333\) 1.35394e6 0.669096
\(334\) 0 0
\(335\) 288550. 0.140478
\(336\) 0 0
\(337\) 1.71706e6 0.823588 0.411794 0.911277i \(-0.364902\pi\)
0.411794 + 0.911277i \(0.364902\pi\)
\(338\) 0 0
\(339\) −1.19975e6 −0.567010
\(340\) 0 0
\(341\) −4.49088e6 −2.09144
\(342\) 0 0
\(343\) 3.03238e6 1.39171
\(344\) 0 0
\(345\) 1.75230e6 0.792612
\(346\) 0 0
\(347\) 131370. 0.0585696 0.0292848 0.999571i \(-0.490677\pi\)
0.0292848 + 0.999571i \(0.490677\pi\)
\(348\) 0 0
\(349\) 3.50951e6 1.54235 0.771175 0.636623i \(-0.219669\pi\)
0.771175 + 0.636623i \(0.219669\pi\)
\(350\) 0 0
\(351\) 27368.0 0.0118570
\(352\) 0 0
\(353\) 2.21992e6 0.948202 0.474101 0.880470i \(-0.342773\pi\)
0.474101 + 0.880470i \(0.342773\pi\)
\(354\) 0 0
\(355\) 738300. 0.310930
\(356\) 0 0
\(357\) 892056. 0.370443
\(358\) 0 0
\(359\) 4.39730e6 1.80074 0.900369 0.435128i \(-0.143297\pi\)
0.900369 + 0.435128i \(0.143297\pi\)
\(360\) 0 0
\(361\) −1.02648e6 −0.414557
\(362\) 0 0
\(363\) 1.52568e6 0.607710
\(364\) 0 0
\(365\) −842450. −0.330988
\(366\) 0 0
\(367\) −2.29824e6 −0.890697 −0.445348 0.895357i \(-0.646920\pi\)
−0.445348 + 0.895357i \(0.646920\pi\)
\(368\) 0 0
\(369\) −3.46895e6 −1.32627
\(370\) 0 0
\(371\) −953532. −0.359667
\(372\) 0 0
\(373\) −1.73561e6 −0.645920 −0.322960 0.946413i \(-0.604678\pi\)
−0.322960 + 0.946413i \(0.604678\pi\)
\(374\) 0 0
\(375\) −343750. −0.126231
\(376\) 0 0
\(377\) −3.43717e6 −1.24551
\(378\) 0 0
\(379\) −5.39115e6 −1.92789 −0.963947 0.266094i \(-0.914267\pi\)
−0.963947 + 0.266094i \(0.914267\pi\)
\(380\) 0 0
\(381\) 543356. 0.191766
\(382\) 0 0
\(383\) 3.27281e6 1.14005 0.570026 0.821627i \(-0.306933\pi\)
0.570026 + 0.821627i \(0.306933\pi\)
\(384\) 0 0
\(385\) 2.61600e6 0.899468
\(386\) 0 0
\(387\) −89170.0 −0.0302650
\(388\) 0 0
\(389\) 603114. 0.202081 0.101040 0.994882i \(-0.467783\pi\)
0.101040 + 0.994882i \(0.467783\pi\)
\(390\) 0 0
\(391\) −592596. −0.196027
\(392\) 0 0
\(393\) 5.20608e6 1.70032
\(394\) 0 0
\(395\) −780200. −0.251601
\(396\) 0 0
\(397\) −749422. −0.238644 −0.119322 0.992856i \(-0.538072\pi\)
−0.119322 + 0.992856i \(0.538072\pi\)
\(398\) 0 0
\(399\) −5.77438e6 −1.81582
\(400\) 0 0
\(401\) 5.31357e6 1.65016 0.825079 0.565018i \(-0.191131\pi\)
0.825079 + 0.565018i \(0.191131\pi\)
\(402\) 0 0
\(403\) −5.81943e6 −1.78492
\(404\) 0 0
\(405\) 1.48827e6 0.450864
\(406\) 0 0
\(407\) −2.69664e6 −0.806932
\(408\) 0 0
\(409\) 999326. 0.295392 0.147696 0.989033i \(-0.452814\pi\)
0.147696 + 0.989033i \(0.452814\pi\)
\(410\) 0 0
\(411\) −487476. −0.142347
\(412\) 0 0
\(413\) −2.56106e6 −0.738831
\(414\) 0 0
\(415\) 961650. 0.274092
\(416\) 0 0
\(417\) −4.25049e6 −1.19701
\(418\) 0 0
\(419\) 2.03740e6 0.566944 0.283472 0.958980i \(-0.408514\pi\)
0.283472 + 0.958980i \(0.408514\pi\)
\(420\) 0 0
\(421\) −5.11461e6 −1.40640 −0.703198 0.710994i \(-0.748245\pi\)
−0.703198 + 0.710994i \(0.748245\pi\)
\(422\) 0 0
\(423\) 3.89119e6 1.05738
\(424\) 0 0
\(425\) 116250. 0.0312191
\(426\) 0 0
\(427\) 2.87804e6 0.763882
\(428\) 0 0
\(429\) 6.56832e6 1.72310
\(430\) 0 0
\(431\) −3.30404e6 −0.856747 −0.428374 0.903602i \(-0.640913\pi\)
−0.428374 + 0.903602i \(0.640913\pi\)
\(432\) 0 0
\(433\) −2.01638e6 −0.516836 −0.258418 0.966033i \(-0.583201\pi\)
−0.258418 + 0.966033i \(0.583201\pi\)
\(434\) 0 0
\(435\) −3.03930e6 −0.770106
\(436\) 0 0
\(437\) 3.83594e6 0.960879
\(438\) 0 0
\(439\) 6.58321e6 1.63033 0.815166 0.579227i \(-0.196645\pi\)
0.815166 + 0.579227i \(0.196645\pi\)
\(440\) 0 0
\(441\) 7.40280e6 1.81259
\(442\) 0 0
\(443\) −4.81783e6 −1.16638 −0.583192 0.812334i \(-0.698197\pi\)
−0.583192 + 0.812334i \(0.698197\pi\)
\(444\) 0 0
\(445\) −2.98785e6 −0.715251
\(446\) 0 0
\(447\) 9.86819e6 2.33598
\(448\) 0 0
\(449\) −6.20399e6 −1.45230 −0.726149 0.687538i \(-0.758692\pi\)
−0.726149 + 0.687538i \(0.758692\pi\)
\(450\) 0 0
\(451\) 6.90912e6 1.59949
\(452\) 0 0
\(453\) −3.09892e6 −0.709520
\(454\) 0 0
\(455\) 3.38990e6 0.767641
\(456\) 0 0
\(457\) 2.84383e6 0.636962 0.318481 0.947929i \(-0.396827\pi\)
0.318481 + 0.947929i \(0.396827\pi\)
\(458\) 0 0
\(459\) −8184.00 −0.00181315
\(460\) 0 0
\(461\) −1.75605e6 −0.384844 −0.192422 0.981312i \(-0.561634\pi\)
−0.192422 + 0.981312i \(0.561634\pi\)
\(462\) 0 0
\(463\) 7.66857e6 1.66250 0.831250 0.555899i \(-0.187626\pi\)
0.831250 + 0.555899i \(0.187626\pi\)
\(464\) 0 0
\(465\) −5.14580e6 −1.10362
\(466\) 0 0
\(467\) −1.35903e6 −0.288361 −0.144181 0.989551i \(-0.546055\pi\)
−0.144181 + 0.989551i \(0.546055\pi\)
\(468\) 0 0
\(469\) −2.51616e6 −0.528209
\(470\) 0 0
\(471\) −7.38932e6 −1.53480
\(472\) 0 0
\(473\) 177600. 0.0364998
\(474\) 0 0
\(475\) −752500. −0.153029
\(476\) 0 0
\(477\) −1.05413e6 −0.212129
\(478\) 0 0
\(479\) −2.02706e6 −0.403672 −0.201836 0.979419i \(-0.564691\pi\)
−0.201836 + 0.979419i \(0.564691\pi\)
\(480\) 0 0
\(481\) −3.49440e6 −0.688667
\(482\) 0 0
\(483\) −1.52801e7 −2.98028
\(484\) 0 0
\(485\) −2.36645e6 −0.456818
\(486\) 0 0
\(487\) 2.46427e6 0.470833 0.235416 0.971895i \(-0.424355\pi\)
0.235416 + 0.971895i \(0.424355\pi\)
\(488\) 0 0
\(489\) −2.23630e6 −0.422920
\(490\) 0 0
\(491\) 1.03848e7 1.94399 0.971996 0.234998i \(-0.0755084\pi\)
0.971996 + 0.234998i \(0.0755084\pi\)
\(492\) 0 0
\(493\) 1.02784e6 0.190461
\(494\) 0 0
\(495\) 2.89200e6 0.530500
\(496\) 0 0
\(497\) −6.43798e6 −1.16912
\(498\) 0 0
\(499\) 6.49416e6 1.16754 0.583769 0.811919i \(-0.301577\pi\)
0.583769 + 0.811919i \(0.301577\pi\)
\(500\) 0 0
\(501\) 3.06332e6 0.545254
\(502\) 0 0
\(503\) −1.03565e7 −1.82513 −0.912565 0.408931i \(-0.865902\pi\)
−0.912565 + 0.408931i \(0.865902\pi\)
\(504\) 0 0
\(505\) −2.52615e6 −0.440789
\(506\) 0 0
\(507\) 343002. 0.0592621
\(508\) 0 0
\(509\) 5.87305e6 1.00478 0.502388 0.864643i \(-0.332455\pi\)
0.502388 + 0.864643i \(0.332455\pi\)
\(510\) 0 0
\(511\) 7.34616e6 1.24454
\(512\) 0 0
\(513\) 52976.0 0.00888763
\(514\) 0 0
\(515\) 3.58585e6 0.595764
\(516\) 0 0
\(517\) −7.75008e6 −1.27520
\(518\) 0 0
\(519\) −5.83031e6 −0.950108
\(520\) 0 0
\(521\) 2.17295e6 0.350717 0.175358 0.984505i \(-0.443892\pi\)
0.175358 + 0.984505i \(0.443892\pi\)
\(522\) 0 0
\(523\) 1.07361e6 0.171629 0.0858145 0.996311i \(-0.472651\pi\)
0.0858145 + 0.996311i \(0.472651\pi\)
\(524\) 0 0
\(525\) 2.99750e6 0.474636
\(526\) 0 0
\(527\) 1.74022e6 0.272946
\(528\) 0 0
\(529\) 3.71425e6 0.577075
\(530\) 0 0
\(531\) −2.83127e6 −0.435757
\(532\) 0 0
\(533\) 8.95307e6 1.36507
\(534\) 0 0
\(535\) 1.42635e6 0.215448
\(536\) 0 0
\(537\) −3.14186e6 −0.470166
\(538\) 0 0
\(539\) −1.47442e7 −2.18599
\(540\) 0 0
\(541\) 7.09033e6 1.04153 0.520767 0.853699i \(-0.325646\pi\)
0.520767 + 0.853699i \(0.325646\pi\)
\(542\) 0 0
\(543\) 2.41274e6 0.351165
\(544\) 0 0
\(545\) 77950.0 0.0112415
\(546\) 0 0
\(547\) 6.69763e6 0.957091 0.478545 0.878063i \(-0.341164\pi\)
0.478545 + 0.878063i \(0.341164\pi\)
\(548\) 0 0
\(549\) 3.18168e6 0.450532
\(550\) 0 0
\(551\) −6.65330e6 −0.933595
\(552\) 0 0
\(553\) 6.80334e6 0.946040
\(554\) 0 0
\(555\) −3.08990e6 −0.425806
\(556\) 0 0
\(557\) 1.19008e7 1.62532 0.812662 0.582735i \(-0.198018\pi\)
0.812662 + 0.582735i \(0.198018\pi\)
\(558\) 0 0
\(559\) 230140. 0.0311503
\(560\) 0 0
\(561\) −1.96416e6 −0.263493
\(562\) 0 0
\(563\) 8.75636e6 1.16427 0.582133 0.813093i \(-0.302218\pi\)
0.582133 + 0.813093i \(0.302218\pi\)
\(564\) 0 0
\(565\) 1.36335e6 0.179674
\(566\) 0 0
\(567\) −1.29778e7 −1.69528
\(568\) 0 0
\(569\) −1.15677e6 −0.149784 −0.0748922 0.997192i \(-0.523861\pi\)
−0.0748922 + 0.997192i \(0.523861\pi\)
\(570\) 0 0
\(571\) −7.07807e6 −0.908500 −0.454250 0.890874i \(-0.650093\pi\)
−0.454250 + 0.890874i \(0.650093\pi\)
\(572\) 0 0
\(573\) 6.48886e6 0.825623
\(574\) 0 0
\(575\) −1.99125e6 −0.251163
\(576\) 0 0
\(577\) −3.13404e6 −0.391890 −0.195945 0.980615i \(-0.562777\pi\)
−0.195945 + 0.980615i \(0.562777\pi\)
\(578\) 0 0
\(579\) 2.20667e7 2.73553
\(580\) 0 0
\(581\) −8.38559e6 −1.03061
\(582\) 0 0
\(583\) 2.09952e6 0.255828
\(584\) 0 0
\(585\) 3.74755e6 0.452749
\(586\) 0 0
\(587\) 1.13833e7 1.36355 0.681776 0.731561i \(-0.261208\pi\)
0.681776 + 0.731561i \(0.261208\pi\)
\(588\) 0 0
\(589\) −1.12646e7 −1.33791
\(590\) 0 0
\(591\) −1.81280e7 −2.13491
\(592\) 0 0
\(593\) −1.58655e7 −1.85275 −0.926376 0.376599i \(-0.877094\pi\)
−0.926376 + 0.376599i \(0.877094\pi\)
\(594\) 0 0
\(595\) −1.01370e6 −0.117386
\(596\) 0 0
\(597\) −1.99477e7 −2.29064
\(598\) 0 0
\(599\) −1.50998e7 −1.71951 −0.859756 0.510705i \(-0.829385\pi\)
−0.859756 + 0.510705i \(0.829385\pi\)
\(600\) 0 0
\(601\) −8.08705e6 −0.913280 −0.456640 0.889652i \(-0.650947\pi\)
−0.456640 + 0.889652i \(0.650947\pi\)
\(602\) 0 0
\(603\) −2.78162e6 −0.311534
\(604\) 0 0
\(605\) −1.73373e6 −0.192571
\(606\) 0 0
\(607\) −710398. −0.0782582 −0.0391291 0.999234i \(-0.512458\pi\)
−0.0391291 + 0.999234i \(0.512458\pi\)
\(608\) 0 0
\(609\) 2.65027e7 2.89566
\(610\) 0 0
\(611\) −1.00428e7 −1.08831
\(612\) 0 0
\(613\) 5.96434e6 0.641078 0.320539 0.947235i \(-0.396136\pi\)
0.320539 + 0.947235i \(0.396136\pi\)
\(614\) 0 0
\(615\) 7.91670e6 0.844027
\(616\) 0 0
\(617\) 1.48432e7 1.56970 0.784848 0.619689i \(-0.212741\pi\)
0.784848 + 0.619689i \(0.212741\pi\)
\(618\) 0 0
\(619\) −1.82042e7 −1.90961 −0.954807 0.297227i \(-0.903938\pi\)
−0.954807 + 0.297227i \(0.903938\pi\)
\(620\) 0 0
\(621\) 140184. 0.0145871
\(622\) 0 0
\(623\) 2.60541e7 2.68940
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 1.27142e7 1.29158
\(628\) 0 0
\(629\) 1.04495e6 0.105310
\(630\) 0 0
\(631\) 1.09461e6 0.109443 0.0547214 0.998502i \(-0.482573\pi\)
0.0547214 + 0.998502i \(0.482573\pi\)
\(632\) 0 0
\(633\) 1.11404e7 1.10508
\(634\) 0 0
\(635\) −617450. −0.0607670
\(636\) 0 0
\(637\) −1.91060e7 −1.86561
\(638\) 0 0
\(639\) −7.11721e6 −0.689537
\(640\) 0 0
\(641\) 7.44046e6 0.715245 0.357622 0.933866i \(-0.383587\pi\)
0.357622 + 0.933866i \(0.383587\pi\)
\(642\) 0 0
\(643\) −1.07915e7 −1.02933 −0.514665 0.857391i \(-0.672084\pi\)
−0.514665 + 0.857391i \(0.672084\pi\)
\(644\) 0 0
\(645\) 203500. 0.0192604
\(646\) 0 0
\(647\) −9.62998e6 −0.904409 −0.452204 0.891914i \(-0.649362\pi\)
−0.452204 + 0.891914i \(0.649362\pi\)
\(648\) 0 0
\(649\) 5.63904e6 0.525525
\(650\) 0 0
\(651\) 4.48714e7 4.14970
\(652\) 0 0
\(653\) −1.00019e7 −0.917905 −0.458953 0.888461i \(-0.651775\pi\)
−0.458953 + 0.888461i \(0.651775\pi\)
\(654\) 0 0
\(655\) −5.91600e6 −0.538797
\(656\) 0 0
\(657\) 8.12122e6 0.734020
\(658\) 0 0
\(659\) −4.01060e6 −0.359746 −0.179873 0.983690i \(-0.557569\pi\)
−0.179873 + 0.983690i \(0.557569\pi\)
\(660\) 0 0
\(661\) 1.20338e7 1.07127 0.535636 0.844449i \(-0.320072\pi\)
0.535636 + 0.844449i \(0.320072\pi\)
\(662\) 0 0
\(663\) −2.54522e6 −0.224876
\(664\) 0 0
\(665\) 6.56180e6 0.575399
\(666\) 0 0
\(667\) −1.76058e7 −1.53229
\(668\) 0 0
\(669\) −1.19251e7 −1.03014
\(670\) 0 0
\(671\) −6.33696e6 −0.543344
\(672\) 0 0
\(673\) 2.01231e6 0.171260 0.0856301 0.996327i \(-0.472710\pi\)
0.0856301 + 0.996327i \(0.472710\pi\)
\(674\) 0 0
\(675\) −27500.0 −0.00232313
\(676\) 0 0
\(677\) 1.62410e7 1.36188 0.680942 0.732337i \(-0.261571\pi\)
0.680942 + 0.732337i \(0.261571\pi\)
\(678\) 0 0
\(679\) 2.06354e7 1.71767
\(680\) 0 0
\(681\) −3.18686e7 −2.63327
\(682\) 0 0
\(683\) 4.62910e6 0.379704 0.189852 0.981813i \(-0.439199\pi\)
0.189852 + 0.981813i \(0.439199\pi\)
\(684\) 0 0
\(685\) 553950. 0.0451070
\(686\) 0 0
\(687\) −1.05333e7 −0.851476
\(688\) 0 0
\(689\) 2.72063e6 0.218334
\(690\) 0 0
\(691\) 1.16794e7 0.930517 0.465258 0.885175i \(-0.345961\pi\)
0.465258 + 0.885175i \(0.345961\pi\)
\(692\) 0 0
\(693\) −2.52182e7 −1.99472
\(694\) 0 0
\(695\) 4.83010e6 0.379310
\(696\) 0 0
\(697\) −2.67728e6 −0.208743
\(698\) 0 0
\(699\) 8.23033e6 0.637125
\(700\) 0 0
\(701\) 1.99543e7 1.53370 0.766851 0.641825i \(-0.221822\pi\)
0.766851 + 0.641825i \(0.221822\pi\)
\(702\) 0 0
\(703\) −6.76407e6 −0.516202
\(704\) 0 0
\(705\) −8.88030e6 −0.672907
\(706\) 0 0
\(707\) 2.20280e7 1.65740
\(708\) 0 0
\(709\) −4.88331e6 −0.364837 −0.182419 0.983221i \(-0.558393\pi\)
−0.182419 + 0.983221i \(0.558393\pi\)
\(710\) 0 0
\(711\) 7.52113e6 0.557968
\(712\) 0 0
\(713\) −2.98082e7 −2.19590
\(714\) 0 0
\(715\) −7.46400e6 −0.546017
\(716\) 0 0
\(717\) 3.72715e6 0.270757
\(718\) 0 0
\(719\) −1.35778e7 −0.979505 −0.489753 0.871861i \(-0.662913\pi\)
−0.489753 + 0.871861i \(0.662913\pi\)
\(720\) 0 0
\(721\) −3.12686e7 −2.24012
\(722\) 0 0
\(723\) −7.78241e6 −0.553692
\(724\) 0 0
\(725\) 3.45375e6 0.244031
\(726\) 0 0
\(727\) 6.42411e6 0.450792 0.225396 0.974267i \(-0.427632\pi\)
0.225396 + 0.974267i \(0.427632\pi\)
\(728\) 0 0
\(729\) −1.41117e7 −0.983472
\(730\) 0 0
\(731\) −68820.0 −0.00476345
\(732\) 0 0
\(733\) 9.08556e6 0.624585 0.312293 0.949986i \(-0.398903\pi\)
0.312293 + 0.949986i \(0.398903\pi\)
\(734\) 0 0
\(735\) −1.68944e7 −1.15351
\(736\) 0 0
\(737\) 5.54016e6 0.375711
\(738\) 0 0
\(739\) 2.02457e7 1.36371 0.681854 0.731488i \(-0.261174\pi\)
0.681854 + 0.731488i \(0.261174\pi\)
\(740\) 0 0
\(741\) 1.64755e7 1.10229
\(742\) 0 0
\(743\) −5.44831e6 −0.362067 −0.181034 0.983477i \(-0.557944\pi\)
−0.181034 + 0.983477i \(0.557944\pi\)
\(744\) 0 0
\(745\) −1.12138e7 −0.740226
\(746\) 0 0
\(747\) −9.27031e6 −0.607845
\(748\) 0 0
\(749\) −1.24378e7 −0.810099
\(750\) 0 0
\(751\) −1.14072e6 −0.0738041 −0.0369021 0.999319i \(-0.511749\pi\)
−0.0369021 + 0.999319i \(0.511749\pi\)
\(752\) 0 0
\(753\) 2.76144e7 1.77479
\(754\) 0 0
\(755\) 3.52150e6 0.224833
\(756\) 0 0
\(757\) 1.90153e7 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(758\) 0 0
\(759\) 3.36442e7 2.11985
\(760\) 0 0
\(761\) 2.23551e7 1.39931 0.699656 0.714480i \(-0.253337\pi\)
0.699656 + 0.714480i \(0.253337\pi\)
\(762\) 0 0
\(763\) −679724. −0.0422689
\(764\) 0 0
\(765\) −1.12065e6 −0.0692335
\(766\) 0 0
\(767\) 7.30726e6 0.448504
\(768\) 0 0
\(769\) −1.00704e7 −0.614088 −0.307044 0.951695i \(-0.599340\pi\)
−0.307044 + 0.951695i \(0.599340\pi\)
\(770\) 0 0
\(771\) −2.48330e7 −1.50451
\(772\) 0 0
\(773\) −4.05963e6 −0.244364 −0.122182 0.992508i \(-0.538989\pi\)
−0.122182 + 0.992508i \(0.538989\pi\)
\(774\) 0 0
\(775\) 5.84750e6 0.349716
\(776\) 0 0
\(777\) 2.69439e7 1.60106
\(778\) 0 0
\(779\) 1.73304e7 1.02321
\(780\) 0 0
\(781\) 1.41754e7 0.831585
\(782\) 0 0
\(783\) −243144. −0.0141729
\(784\) 0 0
\(785\) 8.39695e6 0.486348
\(786\) 0 0
\(787\) −1.72256e7 −0.991372 −0.495686 0.868502i \(-0.665083\pi\)
−0.495686 + 0.868502i \(0.665083\pi\)
\(788\) 0 0
\(789\) −5.78780e6 −0.330995
\(790\) 0 0
\(791\) −1.18884e7 −0.675589
\(792\) 0 0
\(793\) −8.21164e6 −0.463711
\(794\) 0 0
\(795\) 2.40570e6 0.134997
\(796\) 0 0
\(797\) −2.10793e7 −1.17547 −0.587733 0.809055i \(-0.699980\pi\)
−0.587733 + 0.809055i \(0.699980\pi\)
\(798\) 0 0
\(799\) 3.00316e6 0.166422
\(800\) 0 0
\(801\) 2.88029e7 1.58619
\(802\) 0 0
\(803\) −1.61750e7 −0.885231
\(804\) 0 0
\(805\) 1.73637e7 0.944393
\(806\) 0 0
\(807\) −2.61303e7 −1.41241
\(808\) 0 0
\(809\) −1.87877e7 −1.00926 −0.504629 0.863336i \(-0.668371\pi\)
−0.504629 + 0.863336i \(0.668371\pi\)
\(810\) 0 0
\(811\) −1.32456e7 −0.707164 −0.353582 0.935404i \(-0.615036\pi\)
−0.353582 + 0.935404i \(0.615036\pi\)
\(812\) 0 0
\(813\) 9.48860e6 0.503473
\(814\) 0 0
\(815\) 2.54125e6 0.134015
\(816\) 0 0
\(817\) 445480. 0.0233493
\(818\) 0 0
\(819\) −3.26786e7 −1.70237
\(820\) 0 0
\(821\) −7.66925e6 −0.397096 −0.198548 0.980091i \(-0.563623\pi\)
−0.198548 + 0.980091i \(0.563623\pi\)
\(822\) 0 0
\(823\) −8.82786e6 −0.454314 −0.227157 0.973858i \(-0.572943\pi\)
−0.227157 + 0.973858i \(0.572943\pi\)
\(824\) 0 0
\(825\) −6.60000e6 −0.337605
\(826\) 0 0
\(827\) −3.06923e7 −1.56051 −0.780254 0.625463i \(-0.784910\pi\)
−0.780254 + 0.625463i \(0.784910\pi\)
\(828\) 0 0
\(829\) 3.28414e7 1.65972 0.829860 0.557972i \(-0.188420\pi\)
0.829860 + 0.557972i \(0.188420\pi\)
\(830\) 0 0
\(831\) 1.63485e7 0.821250
\(832\) 0 0
\(833\) 5.71336e6 0.285285
\(834\) 0 0
\(835\) −3.48105e6 −0.172780
\(836\) 0 0
\(837\) −411664. −0.0203109
\(838\) 0 0
\(839\) −8.42117e6 −0.413017 −0.206508 0.978445i \(-0.566210\pi\)
−0.206508 + 0.978445i \(0.566210\pi\)
\(840\) 0 0
\(841\) 1.00255e7 0.488784
\(842\) 0 0
\(843\) 4.22824e7 2.04923
\(844\) 0 0
\(845\) −389775. −0.0187790
\(846\) 0 0
\(847\) 1.51181e7 0.724083
\(848\) 0 0
\(849\) −3.58757e7 −1.70817
\(850\) 0 0
\(851\) −1.78989e7 −0.847234
\(852\) 0 0
\(853\) 2.35126e7 1.10644 0.553221 0.833035i \(-0.313399\pi\)
0.553221 + 0.833035i \(0.313399\pi\)
\(854\) 0 0
\(855\) 7.25410e6 0.339366
\(856\) 0 0
\(857\) −1.13050e7 −0.525799 −0.262900 0.964823i \(-0.584679\pi\)
−0.262900 + 0.964823i \(0.584679\pi\)
\(858\) 0 0
\(859\) 1.00078e7 0.462758 0.231379 0.972864i \(-0.425676\pi\)
0.231379 + 0.972864i \(0.425676\pi\)
\(860\) 0 0
\(861\) −6.90336e7 −3.17360
\(862\) 0 0
\(863\) 2.61429e7 1.19489 0.597443 0.801911i \(-0.296183\pi\)
0.597443 + 0.801911i \(0.296183\pi\)
\(864\) 0 0
\(865\) 6.62535e6 0.301071
\(866\) 0 0
\(867\) −3.04757e7 −1.37691
\(868\) 0 0
\(869\) −1.49798e7 −0.672911
\(870\) 0 0
\(871\) 7.17912e6 0.320646
\(872\) 0 0
\(873\) 2.28126e7 1.01307
\(874\) 0 0
\(875\) −3.40625e6 −0.150403
\(876\) 0 0
\(877\) −1.92041e6 −0.0843129 −0.0421565 0.999111i \(-0.513423\pi\)
−0.0421565 + 0.999111i \(0.513423\pi\)
\(878\) 0 0
\(879\) 1.56750e6 0.0684282
\(880\) 0 0
\(881\) −2.56594e7 −1.11380 −0.556899 0.830580i \(-0.688009\pi\)
−0.556899 + 0.830580i \(0.688009\pi\)
\(882\) 0 0
\(883\) −2.05643e7 −0.887590 −0.443795 0.896128i \(-0.646368\pi\)
−0.443795 + 0.896128i \(0.646368\pi\)
\(884\) 0 0
\(885\) 6.46140e6 0.277312
\(886\) 0 0
\(887\) 3.16868e7 1.35229 0.676143 0.736770i \(-0.263650\pi\)
0.676143 + 0.736770i \(0.263650\pi\)
\(888\) 0 0
\(889\) 5.38416e6 0.228488
\(890\) 0 0
\(891\) 2.85749e7 1.20584
\(892\) 0 0
\(893\) −1.94398e7 −0.815761
\(894\) 0 0
\(895\) 3.57030e6 0.148987
\(896\) 0 0
\(897\) 4.35972e7 1.80916
\(898\) 0 0
\(899\) 5.17013e7 2.13355
\(900\) 0 0
\(901\) −813564. −0.0333872
\(902\) 0 0
\(903\) −1.77452e6 −0.0724205
\(904\) 0 0
\(905\) −2.74175e6 −0.111277
\(906\) 0 0
\(907\) 3.96963e6 0.160225 0.0801127 0.996786i \(-0.474472\pi\)
0.0801127 + 0.996786i \(0.474472\pi\)
\(908\) 0 0
\(909\) 2.43521e7 0.977522
\(910\) 0 0
\(911\) −1.37945e7 −0.550692 −0.275346 0.961345i \(-0.588792\pi\)
−0.275346 + 0.961345i \(0.588792\pi\)
\(912\) 0 0
\(913\) 1.84637e7 0.733063
\(914\) 0 0
\(915\) −7.26110e6 −0.286715
\(916\) 0 0
\(917\) 5.15875e7 2.02592
\(918\) 0 0
\(919\) 8.08126e6 0.315639 0.157819 0.987468i \(-0.449554\pi\)
0.157819 + 0.987468i \(0.449554\pi\)
\(920\) 0 0
\(921\) −3.55877e7 −1.38245
\(922\) 0 0
\(923\) 1.83689e7 0.709707
\(924\) 0 0
\(925\) 3.51125e6 0.134930
\(926\) 0 0
\(927\) −3.45676e7 −1.32120
\(928\) 0 0
\(929\) 2.99956e7 1.14030 0.570150 0.821541i \(-0.306885\pi\)
0.570150 + 0.821541i \(0.306885\pi\)
\(930\) 0 0
\(931\) −3.69833e7 −1.39840
\(932\) 0 0
\(933\) −1.50213e7 −0.564943
\(934\) 0 0
\(935\) 2.23200e6 0.0834959
\(936\) 0 0
\(937\) −2.07620e7 −0.772540 −0.386270 0.922386i \(-0.626237\pi\)
−0.386270 + 0.922386i \(0.626237\pi\)
\(938\) 0 0
\(939\) −5.94976e7 −2.20209
\(940\) 0 0
\(941\) −3.47642e6 −0.127985 −0.0639923 0.997950i \(-0.520383\pi\)
−0.0639923 + 0.997950i \(0.520383\pi\)
\(942\) 0 0
\(943\) 4.58593e7 1.67938
\(944\) 0 0
\(945\) 239800. 0.00873514
\(946\) 0 0
\(947\) 1.86700e6 0.0676503 0.0338252 0.999428i \(-0.489231\pi\)
0.0338252 + 0.999428i \(0.489231\pi\)
\(948\) 0 0
\(949\) −2.09602e7 −0.755490
\(950\) 0 0
\(951\) 5.72763e7 2.05364
\(952\) 0 0
\(953\) −3.85501e7 −1.37497 −0.687484 0.726199i \(-0.741285\pi\)
−0.687484 + 0.726199i \(0.741285\pi\)
\(954\) 0 0
\(955\) −7.37370e6 −0.261624
\(956\) 0 0
\(957\) −5.83546e7 −2.05966
\(958\) 0 0
\(959\) −4.83044e6 −0.169606
\(960\) 0 0
\(961\) 5.89056e7 2.05754
\(962\) 0 0
\(963\) −1.37500e7 −0.477790
\(964\) 0 0
\(965\) −2.50758e7 −0.866837
\(966\) 0 0
\(967\) 1.64875e7 0.567008 0.283504 0.958971i \(-0.408503\pi\)
0.283504 + 0.958971i \(0.408503\pi\)
\(968\) 0 0
\(969\) −4.92677e6 −0.168559
\(970\) 0 0
\(971\) −2.36976e7 −0.806597 −0.403299 0.915068i \(-0.632136\pi\)
−0.403299 + 0.915068i \(0.632136\pi\)
\(972\) 0 0
\(973\) −4.21185e7 −1.42623
\(974\) 0 0
\(975\) −8.55250e6 −0.288125
\(976\) 0 0
\(977\) −5.77590e7 −1.93590 −0.967950 0.251143i \(-0.919194\pi\)
−0.967950 + 0.251143i \(0.919194\pi\)
\(978\) 0 0
\(979\) −5.73667e7 −1.91295
\(980\) 0 0
\(981\) −751438. −0.0249299
\(982\) 0 0
\(983\) −1.10103e7 −0.363425 −0.181712 0.983352i \(-0.558164\pi\)
−0.181712 + 0.983352i \(0.558164\pi\)
\(984\) 0 0
\(985\) 2.05999e7 0.676512
\(986\) 0 0
\(987\) 7.74362e7 2.53018
\(988\) 0 0
\(989\) 1.17882e6 0.0383228
\(990\) 0 0
\(991\) 3.70807e7 1.19940 0.599700 0.800225i \(-0.295287\pi\)
0.599700 + 0.800225i \(0.295287\pi\)
\(992\) 0 0
\(993\) −1.45515e7 −0.468311
\(994\) 0 0
\(995\) 2.26678e7 0.725858
\(996\) 0 0
\(997\) 4.52935e6 0.144311 0.0721553 0.997393i \(-0.477012\pi\)
0.0721553 + 0.997393i \(0.477012\pi\)
\(998\) 0 0
\(999\) −247192. −0.00783647
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 \(a_p\))