Properties

Label 320.6.a.t.1.1
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 1
Dimension 2
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-13.4164 q^{3} +25.0000 q^{5} +138.636 q^{7} -63.0000 q^{9} +O(q^{10})\) \(q-13.4164 q^{3} +25.0000 q^{5} +138.636 q^{7} -63.0000 q^{9} -259.384 q^{11} -154.000 q^{13} -335.410 q^{15} +178.000 q^{17} -965.981 q^{19} -1860.00 q^{21} +2634.09 q^{23} +625.000 q^{25} +4105.42 q^{27} -4110.00 q^{29} +3157.33 q^{31} +3480.00 q^{33} +3465.91 q^{35} -7442.00 q^{37} +2066.13 q^{39} +7270.00 q^{41} +17910.9 q^{43} -1575.00 q^{45} -7410.33 q^{47} +2413.00 q^{49} -2388.12 q^{51} -32226.0 q^{53} -6484.60 q^{55} +12960.0 q^{57} -34041.9 q^{59} -26770.0 q^{61} -8734.08 q^{63} -3850.00 q^{65} -49806.2 q^{67} -35340.0 q^{69} +54103.9 q^{71} -18534.0 q^{73} -8385.25 q^{75} -35960.0 q^{77} -86741.5 q^{79} -39771.0 q^{81} +78642.5 q^{83} +4450.00 q^{85} +55141.4 q^{87} -107590. q^{89} -21350.0 q^{91} -42360.0 q^{93} -24149.5 q^{95} -108838. q^{97} +16341.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 50q^{5} - 126q^{9} + O(q^{10}) \) \( 2q + 50q^{5} - 126q^{9} - 308q^{13} + 356q^{17} - 3720q^{21} + 1250q^{25} - 8220q^{29} + 6960q^{33} - 14884q^{37} + 14540q^{41} - 3150q^{45} + 4826q^{49} - 64452q^{53} + 25920q^{57} - 53540q^{61} - 7700q^{65} - 70680q^{69} - 37068q^{73} - 71920q^{77} - 79542q^{81} + 8900q^{85} - 215180q^{89} - 84720q^{93} - 217676q^{97} + O(q^{100}) \)

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
\(3\) −13.4164 −0.860663 −0.430331 0.902671i \(-0.641603\pi\)
−0.430331 + 0.902671i \(0.641603\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 138.636 1.06938 0.534689 0.845049i \(-0.320429\pi\)
0.534689 + 0.845049i \(0.320429\pi\)
\(8\) 0 0
\(9\) −63.0000 −0.259259
\(10\) 0 0
\(11\) −259.384 −0.646340 −0.323170 0.946341i \(-0.604749\pi\)
−0.323170 + 0.946341i \(0.604749\pi\)
\(12\) 0 0
\(13\) −154.000 −0.252733 −0.126367 0.991984i \(-0.540332\pi\)
−0.126367 + 0.991984i \(0.540332\pi\)
\(14\) 0 0
\(15\) −335.410 −0.384900
\(16\) 0 0
\(17\) 178.000 0.149382 0.0746909 0.997207i \(-0.476203\pi\)
0.0746909 + 0.997207i \(0.476203\pi\)
\(18\) 0 0
\(19\) −965.981 −0.613882 −0.306941 0.951729i \(-0.599305\pi\)
−0.306941 + 0.951729i \(0.599305\pi\)
\(20\) 0 0
\(21\) −1860.00 −0.920375
\(22\) 0 0
\(23\) 2634.09 1.03827 0.519135 0.854692i \(-0.326254\pi\)
0.519135 + 0.854692i \(0.326254\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 4105.42 1.08380
\(28\) 0 0
\(29\) −4110.00 −0.907500 −0.453750 0.891129i \(-0.649914\pi\)
−0.453750 + 0.891129i \(0.649914\pi\)
\(30\) 0 0
\(31\) 3157.33 0.590086 0.295043 0.955484i \(-0.404666\pi\)
0.295043 + 0.955484i \(0.404666\pi\)
\(32\) 0 0
\(33\) 3480.00 0.556281
\(34\) 0 0
\(35\) 3465.91 0.478241
\(36\) 0 0
\(37\) −7442.00 −0.893687 −0.446843 0.894612i \(-0.647452\pi\)
−0.446843 + 0.894612i \(0.647452\pi\)
\(38\) 0 0
\(39\) 2066.13 0.217518
\(40\) 0 0
\(41\) 7270.00 0.675421 0.337711 0.941250i \(-0.390347\pi\)
0.337711 + 0.941250i \(0.390347\pi\)
\(42\) 0 0
\(43\) 17910.9 1.47722 0.738612 0.674131i \(-0.235482\pi\)
0.738612 + 0.674131i \(0.235482\pi\)
\(44\) 0 0
\(45\) −1575.00 −0.115944
\(46\) 0 0
\(47\) −7410.33 −0.489320 −0.244660 0.969609i \(-0.578676\pi\)
−0.244660 + 0.969609i \(0.578676\pi\)
\(48\) 0 0
\(49\) 2413.00 0.143571
\(50\) 0 0
\(51\) −2388.12 −0.128567
\(52\) 0 0
\(53\) −32226.0 −1.57586 −0.787928 0.615767i \(-0.788846\pi\)
−0.787928 + 0.615767i \(0.788846\pi\)
\(54\) 0 0
\(55\) −6484.60 −0.289052
\(56\) 0 0
\(57\) 12960.0 0.528345
\(58\) 0 0
\(59\) −34041.9 −1.27316 −0.636581 0.771210i \(-0.719652\pi\)
−0.636581 + 0.771210i \(0.719652\pi\)
\(60\) 0 0
\(61\) −26770.0 −0.921136 −0.460568 0.887624i \(-0.652354\pi\)
−0.460568 + 0.887624i \(0.652354\pi\)
\(62\) 0 0
\(63\) −8734.08 −0.277246
\(64\) 0 0
\(65\) −3850.00 −0.113026
\(66\) 0 0
\(67\) −49806.2 −1.35549 −0.677745 0.735297i \(-0.737043\pi\)
−0.677745 + 0.735297i \(0.737043\pi\)
\(68\) 0 0
\(69\) −35340.0 −0.893601
\(70\) 0 0
\(71\) 54103.9 1.27375 0.636873 0.770969i \(-0.280228\pi\)
0.636873 + 0.770969i \(0.280228\pi\)
\(72\) 0 0
\(73\) −18534.0 −0.407063 −0.203532 0.979068i \(-0.565242\pi\)
−0.203532 + 0.979068i \(0.565242\pi\)
\(74\) 0 0
\(75\) −8385.25 −0.172133
\(76\) 0 0
\(77\) −35960.0 −0.691183
\(78\) 0 0
\(79\) −86741.5 −1.56372 −0.781861 0.623453i \(-0.785729\pi\)
−0.781861 + 0.623453i \(0.785729\pi\)
\(80\) 0 0
\(81\) −39771.0 −0.673525
\(82\) 0 0
\(83\) 78642.5 1.25303 0.626516 0.779409i \(-0.284480\pi\)
0.626516 + 0.779409i \(0.284480\pi\)
\(84\) 0 0
\(85\) 4450.00 0.0668056
\(86\) 0 0
\(87\) 55141.4 0.781052
\(88\) 0 0
\(89\) −107590. −1.43978 −0.719891 0.694087i \(-0.755808\pi\)
−0.719891 + 0.694087i \(0.755808\pi\)
\(90\) 0 0
\(91\) −21350.0 −0.270268
\(92\) 0 0
\(93\) −42360.0 −0.507865
\(94\) 0 0
\(95\) −24149.5 −0.274536
\(96\) 0 0
\(97\) −108838. −1.17450 −0.587248 0.809407i \(-0.699788\pi\)
−0.587248 + 0.809407i \(0.699788\pi\)
\(98\) 0 0
\(99\) 16341.2 0.167570
\(100\) 0 0
\(101\) −59198.0 −0.577436 −0.288718 0.957414i \(-0.593229\pi\)
−0.288718 + 0.957414i \(0.593229\pi\)
\(102\) 0 0
\(103\) −112908. −1.04865 −0.524326 0.851517i \(-0.675683\pi\)
−0.524326 + 0.851517i \(0.675683\pi\)
\(104\) 0 0
\(105\) −46500.0 −0.411604
\(106\) 0 0
\(107\) −40039.0 −0.338084 −0.169042 0.985609i \(-0.554067\pi\)
−0.169042 + 0.985609i \(0.554067\pi\)
\(108\) 0 0
\(109\) 139614. 1.12554 0.562772 0.826612i \(-0.309735\pi\)
0.562772 + 0.826612i \(0.309735\pi\)
\(110\) 0 0
\(111\) 99844.9 0.769163
\(112\) 0 0
\(113\) −43046.0 −0.317130 −0.158565 0.987349i \(-0.550687\pi\)
−0.158565 + 0.987349i \(0.550687\pi\)
\(114\) 0 0
\(115\) 65852.2 0.464329
\(116\) 0 0
\(117\) 9702.00 0.0655234
\(118\) 0 0
\(119\) 24677.2 0.159746
\(120\) 0 0
\(121\) −93771.0 −0.582244
\(122\) 0 0
\(123\) −97537.3 −0.581310
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −157370. −0.865790 −0.432895 0.901444i \(-0.642508\pi\)
−0.432895 + 0.901444i \(0.642508\pi\)
\(128\) 0 0
\(129\) −240300. −1.27139
\(130\) 0 0
\(131\) 267729. 1.36307 0.681533 0.731787i \(-0.261314\pi\)
0.681533 + 0.731787i \(0.261314\pi\)
\(132\) 0 0
\(133\) −133920. −0.656472
\(134\) 0 0
\(135\) 102636. 0.484689
\(136\) 0 0
\(137\) −112158. −0.510539 −0.255269 0.966870i \(-0.582164\pi\)
−0.255269 + 0.966870i \(0.582164\pi\)
\(138\) 0 0
\(139\) −147348. −0.646855 −0.323428 0.946253i \(-0.604835\pi\)
−0.323428 + 0.946253i \(0.604835\pi\)
\(140\) 0 0
\(141\) 99420.0 0.421139
\(142\) 0 0
\(143\) 39945.1 0.163352
\(144\) 0 0
\(145\) −102750. −0.405847
\(146\) 0 0
\(147\) −32373.8 −0.123566
\(148\) 0 0
\(149\) 174566. 0.644160 0.322080 0.946712i \(-0.395618\pi\)
0.322080 + 0.946712i \(0.395618\pi\)
\(150\) 0 0
\(151\) 345258. 1.23226 0.616128 0.787646i \(-0.288700\pi\)
0.616128 + 0.787646i \(0.288700\pi\)
\(152\) 0 0
\(153\) −11214.0 −0.0387286
\(154\) 0 0
\(155\) 78933.2 0.263895
\(156\) 0 0
\(157\) 26502.0 0.0858083 0.0429042 0.999079i \(-0.486339\pi\)
0.0429042 + 0.999079i \(0.486339\pi\)
\(158\) 0 0
\(159\) 432357. 1.35628
\(160\) 0 0
\(161\) 365180. 1.11030
\(162\) 0 0
\(163\) −141709. −0.417760 −0.208880 0.977941i \(-0.566982\pi\)
−0.208880 + 0.977941i \(0.566982\pi\)
\(164\) 0 0
\(165\) 87000.0 0.248777
\(166\) 0 0
\(167\) −411047. −1.14051 −0.570257 0.821466i \(-0.693156\pi\)
−0.570257 + 0.821466i \(0.693156\pi\)
\(168\) 0 0
\(169\) −347577. −0.936126
\(170\) 0 0
\(171\) 60856.8 0.159155
\(172\) 0 0
\(173\) −595946. −1.51388 −0.756940 0.653484i \(-0.773307\pi\)
−0.756940 + 0.653484i \(0.773307\pi\)
\(174\) 0 0
\(175\) 86647.6 0.213876
\(176\) 0 0
\(177\) 456720. 1.09576
\(178\) 0 0
\(179\) 300939. 0.702014 0.351007 0.936373i \(-0.385839\pi\)
0.351007 + 0.936373i \(0.385839\pi\)
\(180\) 0 0
\(181\) −217022. −0.492388 −0.246194 0.969221i \(-0.579180\pi\)
−0.246194 + 0.969221i \(0.579180\pi\)
\(182\) 0 0
\(183\) 359157. 0.792788
\(184\) 0 0
\(185\) −186050. −0.399669
\(186\) 0 0
\(187\) −46170.3 −0.0965515
\(188\) 0 0
\(189\) 569160. 1.15899
\(190\) 0 0
\(191\) −916260. −1.81734 −0.908668 0.417519i \(-0.862900\pi\)
−0.908668 + 0.417519i \(0.862900\pi\)
\(192\) 0 0
\(193\) 864114. 1.66985 0.834926 0.550363i \(-0.185511\pi\)
0.834926 + 0.550363i \(0.185511\pi\)
\(194\) 0 0
\(195\) 51653.2 0.0972771
\(196\) 0 0
\(197\) −432522. −0.794040 −0.397020 0.917810i \(-0.629956\pi\)
−0.397020 + 0.917810i \(0.629956\pi\)
\(198\) 0 0
\(199\) −795182. −1.42342 −0.711711 0.702473i \(-0.752079\pi\)
−0.711711 + 0.702473i \(0.752079\pi\)
\(200\) 0 0
\(201\) 668220. 1.16662
\(202\) 0 0
\(203\) −569795. −0.970462
\(204\) 0 0
\(205\) 181750. 0.302058
\(206\) 0 0
\(207\) −165948. −0.269181
\(208\) 0 0
\(209\) 250560. 0.396777
\(210\) 0 0
\(211\) 453126. 0.700669 0.350334 0.936625i \(-0.386068\pi\)
0.350334 + 0.936625i \(0.386068\pi\)
\(212\) 0 0
\(213\) −725880. −1.09627
\(214\) 0 0
\(215\) 447773. 0.660635
\(216\) 0 0
\(217\) 437720. 0.631026
\(218\) 0 0
\(219\) 248660. 0.350344
\(220\) 0 0
\(221\) −27412.0 −0.0377537
\(222\) 0 0
\(223\) −430358. −0.579519 −0.289760 0.957099i \(-0.593575\pi\)
−0.289760 + 0.957099i \(0.593575\pi\)
\(224\) 0 0
\(225\) −39375.0 −0.0518519
\(226\) 0 0
\(227\) −1.12403e6 −1.44782 −0.723909 0.689896i \(-0.757656\pi\)
−0.723909 + 0.689896i \(0.757656\pi\)
\(228\) 0 0
\(229\) 812410. 1.02373 0.511866 0.859065i \(-0.328954\pi\)
0.511866 + 0.859065i \(0.328954\pi\)
\(230\) 0 0
\(231\) 482454. 0.594875
\(232\) 0 0
\(233\) 846194. 1.02113 0.510564 0.859840i \(-0.329437\pi\)
0.510564 + 0.859840i \(0.329437\pi\)
\(234\) 0 0
\(235\) −185258. −0.218831
\(236\) 0 0
\(237\) 1.16376e6 1.34584
\(238\) 0 0
\(239\) −56688.8 −0.0641952 −0.0320976 0.999485i \(-0.510219\pi\)
−0.0320976 + 0.999485i \(0.510219\pi\)
\(240\) 0 0
\(241\) 1.27571e6 1.41485 0.707423 0.706790i \(-0.249857\pi\)
0.707423 + 0.706790i \(0.249857\pi\)
\(242\) 0 0
\(243\) −464033. −0.504119
\(244\) 0 0
\(245\) 60325.0 0.0642070
\(246\) 0 0
\(247\) 148761. 0.155148
\(248\) 0 0
\(249\) −1.05510e6 −1.07844
\(250\) 0 0
\(251\) 50937.6 0.0510334 0.0255167 0.999674i \(-0.491877\pi\)
0.0255167 + 0.999674i \(0.491877\pi\)
\(252\) 0 0
\(253\) −683240. −0.671076
\(254\) 0 0
\(255\) −59703.0 −0.0574971
\(256\) 0 0
\(257\) 1.64806e6 1.55647 0.778233 0.627976i \(-0.216116\pi\)
0.778233 + 0.627976i \(0.216116\pi\)
\(258\) 0 0
\(259\) −1.03173e6 −0.955690
\(260\) 0 0
\(261\) 258930. 0.235278
\(262\) 0 0
\(263\) 522994. 0.466238 0.233119 0.972448i \(-0.425107\pi\)
0.233119 + 0.972448i \(0.425107\pi\)
\(264\) 0 0
\(265\) −805650. −0.704745
\(266\) 0 0
\(267\) 1.44347e6 1.23917
\(268\) 0 0
\(269\) 1.93789e6 1.63285 0.816427 0.577448i \(-0.195951\pi\)
0.816427 + 0.577448i \(0.195951\pi\)
\(270\) 0 0
\(271\) 1.00132e6 0.828228 0.414114 0.910225i \(-0.364092\pi\)
0.414114 + 0.910225i \(0.364092\pi\)
\(272\) 0 0
\(273\) 286440. 0.232609
\(274\) 0 0
\(275\) −162115. −0.129268
\(276\) 0 0
\(277\) 445702. 0.349016 0.174508 0.984656i \(-0.444167\pi\)
0.174508 + 0.984656i \(0.444167\pi\)
\(278\) 0 0
\(279\) −198912. −0.152985
\(280\) 0 0
\(281\) 1.24647e6 0.941708 0.470854 0.882211i \(-0.343946\pi\)
0.470854 + 0.882211i \(0.343946\pi\)
\(282\) 0 0
\(283\) 2.27900e6 1.69153 0.845764 0.533557i \(-0.179145\pi\)
0.845764 + 0.533557i \(0.179145\pi\)
\(284\) 0 0
\(285\) 324000. 0.236283
\(286\) 0 0
\(287\) 1.00789e6 0.722281
\(288\) 0 0
\(289\) −1.38817e6 −0.977685
\(290\) 0 0
\(291\) 1.46021e6 1.01084
\(292\) 0 0
\(293\) −2.45427e6 −1.67014 −0.835072 0.550140i \(-0.814574\pi\)
−0.835072 + 0.550140i \(0.814574\pi\)
\(294\) 0 0
\(295\) −851047. −0.569375
\(296\) 0 0
\(297\) −1.06488e6 −0.700502
\(298\) 0 0
\(299\) −405650. −0.262406
\(300\) 0 0
\(301\) 2.48310e6 1.57971
\(302\) 0 0
\(303\) 794225. 0.496977
\(304\) 0 0
\(305\) −669250. −0.411945
\(306\) 0 0
\(307\) 20710.5 0.0125413 0.00627067 0.999980i \(-0.498004\pi\)
0.00627067 + 0.999980i \(0.498004\pi\)
\(308\) 0 0
\(309\) 1.51482e6 0.902537
\(310\) 0 0
\(311\) −47270.5 −0.0277133 −0.0138567 0.999904i \(-0.504411\pi\)
−0.0138567 + 0.999904i \(0.504411\pi\)
\(312\) 0 0
\(313\) −2.79169e6 −1.61067 −0.805333 0.592822i \(-0.798014\pi\)
−0.805333 + 0.592822i \(0.798014\pi\)
\(314\) 0 0
\(315\) −218352. −0.123988
\(316\) 0 0
\(317\) 471582. 0.263578 0.131789 0.991278i \(-0.457928\pi\)
0.131789 + 0.991278i \(0.457928\pi\)
\(318\) 0 0
\(319\) 1.06607e6 0.586554
\(320\) 0 0
\(321\) 537180. 0.290976
\(322\) 0 0
\(323\) −171945. −0.0917028
\(324\) 0 0
\(325\) −96250.0 −0.0505466
\(326\) 0 0
\(327\) −1.87312e6 −0.968715
\(328\) 0 0
\(329\) −1.02734e6 −0.523268
\(330\) 0 0
\(331\) −3.09092e6 −1.55066 −0.775331 0.631555i \(-0.782417\pi\)
−0.775331 + 0.631555i \(0.782417\pi\)
\(332\) 0 0
\(333\) 468846. 0.231697
\(334\) 0 0
\(335\) −1.24515e6 −0.606193
\(336\) 0 0
\(337\) −665838. −0.319370 −0.159685 0.987168i \(-0.551048\pi\)
−0.159685 + 0.987168i \(0.551048\pi\)
\(338\) 0 0
\(339\) 577523. 0.272942
\(340\) 0 0
\(341\) −818960. −0.381397
\(342\) 0 0
\(343\) −1.99553e6 −0.915847
\(344\) 0 0
\(345\) −883500. −0.399631
\(346\) 0 0
\(347\) 1.80908e6 0.806556 0.403278 0.915078i \(-0.367871\pi\)
0.403278 + 0.915078i \(0.367871\pi\)
\(348\) 0 0
\(349\) 2.36181e6 1.03796 0.518981 0.854786i \(-0.326312\pi\)
0.518981 + 0.854786i \(0.326312\pi\)
\(350\) 0 0
\(351\) −632235. −0.273912
\(352\) 0 0
\(353\) 1.14535e6 0.489215 0.244608 0.969622i \(-0.421341\pi\)
0.244608 + 0.969622i \(0.421341\pi\)
\(354\) 0 0
\(355\) 1.35260e6 0.569636
\(356\) 0 0
\(357\) −331080. −0.137487
\(358\) 0 0
\(359\) −767275. −0.314206 −0.157103 0.987582i \(-0.550216\pi\)
−0.157103 + 0.987582i \(0.550216\pi\)
\(360\) 0 0
\(361\) −1.54298e6 −0.623149
\(362\) 0 0
\(363\) 1.25807e6 0.501116
\(364\) 0 0
\(365\) −463350. −0.182044
\(366\) 0 0
\(367\) 3.99537e6 1.54843 0.774215 0.632923i \(-0.218145\pi\)
0.774215 + 0.632923i \(0.218145\pi\)
\(368\) 0 0
\(369\) −458010. −0.175109
\(370\) 0 0
\(371\) −4.46769e6 −1.68519
\(372\) 0 0
\(373\) −4.68131e6 −1.74219 −0.871094 0.491117i \(-0.836589\pi\)
−0.871094 + 0.491117i \(0.836589\pi\)
\(374\) 0 0
\(375\) −209631. −0.0769800
\(376\) 0 0
\(377\) 632940. 0.229356
\(378\) 0 0
\(379\) −337271. −0.120609 −0.0603046 0.998180i \(-0.519207\pi\)
−0.0603046 + 0.998180i \(0.519207\pi\)
\(380\) 0 0
\(381\) 2.11134e6 0.745153
\(382\) 0 0
\(383\) −598689. −0.208547 −0.104274 0.994549i \(-0.533252\pi\)
−0.104274 + 0.994549i \(0.533252\pi\)
\(384\) 0 0
\(385\) −899000. −0.309106
\(386\) 0 0
\(387\) −1.12839e6 −0.382984
\(388\) 0 0
\(389\) −3.97243e6 −1.33101 −0.665506 0.746393i \(-0.731784\pi\)
−0.665506 + 0.746393i \(0.731784\pi\)
\(390\) 0 0
\(391\) 468868. 0.155099
\(392\) 0 0
\(393\) −3.59196e6 −1.17314
\(394\) 0 0
\(395\) −2.16854e6 −0.699318
\(396\) 0 0
\(397\) 179398. 0.0571270 0.0285635 0.999592i \(-0.490907\pi\)
0.0285635 + 0.999592i \(0.490907\pi\)
\(398\) 0 0
\(399\) 1.79673e6 0.565001
\(400\) 0 0
\(401\) 6.14504e6 1.90838 0.954188 0.299208i \(-0.0967224\pi\)
0.954188 + 0.299208i \(0.0967224\pi\)
\(402\) 0 0
\(403\) −486229. −0.149134
\(404\) 0 0
\(405\) −994275. −0.301210
\(406\) 0 0
\(407\) 1.93033e6 0.577626
\(408\) 0 0
\(409\) −2.64503e6 −0.781847 −0.390923 0.920423i \(-0.627844\pi\)
−0.390923 + 0.920423i \(0.627844\pi\)
\(410\) 0 0
\(411\) 1.50476e6 0.439402
\(412\) 0 0
\(413\) −4.71944e6 −1.36149
\(414\) 0 0
\(415\) 1.96606e6 0.560373
\(416\) 0 0
\(417\) 1.97688e6 0.556724
\(418\) 0 0
\(419\) 2.15984e6 0.601018 0.300509 0.953779i \(-0.402843\pi\)
0.300509 + 0.953779i \(0.402843\pi\)
\(420\) 0 0
\(421\) −1.47209e6 −0.404789 −0.202395 0.979304i \(-0.564872\pi\)
−0.202395 + 0.979304i \(0.564872\pi\)
\(422\) 0 0
\(423\) 466851. 0.126861
\(424\) 0 0
\(425\) 111250. 0.0298764
\(426\) 0 0
\(427\) −3.71129e6 −0.985043
\(428\) 0 0
\(429\) −535920. −0.140591
\(430\) 0 0
\(431\) −6.63748e6 −1.72112 −0.860558 0.509352i \(-0.829885\pi\)
−0.860558 + 0.509352i \(0.829885\pi\)
\(432\) 0 0
\(433\) −6.27853e6 −1.60931 −0.804653 0.593746i \(-0.797649\pi\)
−0.804653 + 0.593746i \(0.797649\pi\)
\(434\) 0 0
\(435\) 1.37854e6 0.349297
\(436\) 0 0
\(437\) −2.54448e6 −0.637376
\(438\) 0 0
\(439\) −2.44021e6 −0.604319 −0.302160 0.953257i \(-0.597708\pi\)
−0.302160 + 0.953257i \(0.597708\pi\)
\(440\) 0 0
\(441\) −152019. −0.0372221
\(442\) 0 0
\(443\) 2.30646e6 0.558390 0.279195 0.960234i \(-0.409932\pi\)
0.279195 + 0.960234i \(0.409932\pi\)
\(444\) 0 0
\(445\) −2.68975e6 −0.643890
\(446\) 0 0
\(447\) −2.34205e6 −0.554405
\(448\) 0 0
\(449\) 7.60241e6 1.77965 0.889826 0.456300i \(-0.150825\pi\)
0.889826 + 0.456300i \(0.150825\pi\)
\(450\) 0 0
\(451\) −1.88572e6 −0.436552
\(452\) 0 0
\(453\) −4.63212e6 −1.06056
\(454\) 0 0
\(455\) −533749. −0.120867
\(456\) 0 0
\(457\) −1.56938e6 −0.351510 −0.175755 0.984434i \(-0.556237\pi\)
−0.175755 + 0.984434i \(0.556237\pi\)
\(458\) 0 0
\(459\) 730765. 0.161900
\(460\) 0 0
\(461\) 562602. 0.123296 0.0616480 0.998098i \(-0.480364\pi\)
0.0616480 + 0.998098i \(0.480364\pi\)
\(462\) 0 0
\(463\) −4.87382e6 −1.05662 −0.528308 0.849053i \(-0.677173\pi\)
−0.528308 + 0.849053i \(0.677173\pi\)
\(464\) 0 0
\(465\) −1.05900e6 −0.227124
\(466\) 0 0
\(467\) 5.11862e6 1.08608 0.543039 0.839708i \(-0.317274\pi\)
0.543039 + 0.839708i \(0.317274\pi\)
\(468\) 0 0
\(469\) −6.90494e6 −1.44953
\(470\) 0 0
\(471\) −355562. −0.0738521
\(472\) 0 0
\(473\) −4.64580e6 −0.954790
\(474\) 0 0
\(475\) −603738. −0.122776
\(476\) 0 0
\(477\) 2.03024e6 0.408555
\(478\) 0 0
\(479\) 4.00179e6 0.796922 0.398461 0.917185i \(-0.369544\pi\)
0.398461 + 0.917185i \(0.369544\pi\)
\(480\) 0 0
\(481\) 1.14607e6 0.225864
\(482\) 0 0
\(483\) −4.89940e6 −0.955598
\(484\) 0 0
\(485\) −2.72095e6 −0.525250
\(486\) 0 0
\(487\) 1.68175e6 0.321321 0.160661 0.987010i \(-0.448638\pi\)
0.160661 + 0.987010i \(0.448638\pi\)
\(488\) 0 0
\(489\) 1.90122e6 0.359551
\(490\) 0 0
\(491\) −115927. −0.0217010 −0.0108505 0.999941i \(-0.503454\pi\)
−0.0108505 + 0.999941i \(0.503454\pi\)
\(492\) 0 0
\(493\) −731580. −0.135564
\(494\) 0 0
\(495\) 408530. 0.0749395
\(496\) 0 0
\(497\) 7.50076e6 1.36212
\(498\) 0 0
\(499\) 7.98867e6 1.43623 0.718113 0.695926i \(-0.245006\pi\)
0.718113 + 0.695926i \(0.245006\pi\)
\(500\) 0 0
\(501\) 5.51478e6 0.981598
\(502\) 0 0
\(503\) 8.07650e6 1.42332 0.711661 0.702523i \(-0.247943\pi\)
0.711661 + 0.702523i \(0.247943\pi\)
\(504\) 0 0
\(505\) −1.47995e6 −0.258237
\(506\) 0 0
\(507\) 4.66323e6 0.805689
\(508\) 0 0
\(509\) −2.83427e6 −0.484894 −0.242447 0.970165i \(-0.577950\pi\)
−0.242447 + 0.970165i \(0.577950\pi\)
\(510\) 0 0
\(511\) −2.56948e6 −0.435305
\(512\) 0 0
\(513\) −3.96576e6 −0.665324
\(514\) 0 0
\(515\) −2.82270e6 −0.468972
\(516\) 0 0
\(517\) 1.92212e6 0.316267
\(518\) 0 0
\(519\) 7.99545e6 1.30294
\(520\) 0 0
\(521\) 2.97526e6 0.480209 0.240105 0.970747i \(-0.422818\pi\)
0.240105 + 0.970747i \(0.422818\pi\)
\(522\) 0 0
\(523\) −7.72888e6 −1.23556 −0.617778 0.786352i \(-0.711967\pi\)
−0.617778 + 0.786352i \(0.711967\pi\)
\(524\) 0 0
\(525\) −1.16250e6 −0.184075
\(526\) 0 0
\(527\) 562004. 0.0881481
\(528\) 0 0
\(529\) 502077. 0.0780066
\(530\) 0 0
\(531\) 2.14464e6 0.330079
\(532\) 0 0
\(533\) −1.11958e6 −0.170701
\(534\) 0 0
\(535\) −1.00098e6 −0.151196
\(536\) 0 0
\(537\) −4.03752e6 −0.604198
\(538\) 0 0
\(539\) −625893. −0.0927958
\(540\) 0 0
\(541\) 9.83660e6 1.44495 0.722474 0.691399i \(-0.243005\pi\)
0.722474 + 0.691399i \(0.243005\pi\)
\(542\) 0 0
\(543\) 2.91166e6 0.423780
\(544\) 0 0
\(545\) 3.49035e6 0.503359
\(546\) 0 0
\(547\) 3.45608e6 0.493873 0.246937 0.969032i \(-0.420576\pi\)
0.246937 + 0.969032i \(0.420576\pi\)
\(548\) 0 0
\(549\) 1.68651e6 0.238813
\(550\) 0 0
\(551\) 3.97018e6 0.557098
\(552\) 0 0
\(553\) −1.20255e7 −1.67221
\(554\) 0 0
\(555\) 2.49612e6 0.343980
\(556\) 0 0
\(557\) 7.05760e6 0.963871 0.481936 0.876207i \(-0.339934\pi\)
0.481936 + 0.876207i \(0.339934\pi\)
\(558\) 0 0
\(559\) −2.75828e6 −0.373344
\(560\) 0 0
\(561\) 619440. 0.0830983
\(562\) 0 0
\(563\) −2.32495e6 −0.309131 −0.154566 0.987983i \(-0.549398\pi\)
−0.154566 + 0.987983i \(0.549398\pi\)
\(564\) 0 0
\(565\) −1.07615e6 −0.141825
\(566\) 0 0
\(567\) −5.51370e6 −0.720254
\(568\) 0 0
\(569\) 1.01947e7 1.32006 0.660029 0.751240i \(-0.270544\pi\)
0.660029 + 0.751240i \(0.270544\pi\)
\(570\) 0 0
\(571\) 1.21297e7 1.55689 0.778446 0.627712i \(-0.216008\pi\)
0.778446 + 0.627712i \(0.216008\pi\)
\(572\) 0 0
\(573\) 1.22929e7 1.56411
\(574\) 0 0
\(575\) 1.64631e6 0.207654
\(576\) 0 0
\(577\) 1.46358e6 0.183011 0.0915053 0.995805i \(-0.470832\pi\)
0.0915053 + 0.995805i \(0.470832\pi\)
\(578\) 0 0
\(579\) −1.15933e7 −1.43718
\(580\) 0 0
\(581\) 1.09027e7 1.33997
\(582\) 0 0
\(583\) 8.35891e6 1.01854
\(584\) 0 0
\(585\) 242550. 0.0293030
\(586\) 0 0
\(587\) −5.18425e6 −0.620998 −0.310499 0.950574i \(-0.600496\pi\)
−0.310499 + 0.950574i \(0.600496\pi\)
\(588\) 0 0
\(589\) −3.04992e6 −0.362243
\(590\) 0 0
\(591\) 5.80289e6 0.683401
\(592\) 0 0
\(593\) −1.02722e7 −1.19957 −0.599785 0.800161i \(-0.704747\pi\)
−0.599785 + 0.800161i \(0.704747\pi\)
\(594\) 0 0
\(595\) 616931. 0.0714405
\(596\) 0 0
\(597\) 1.06685e7 1.22509
\(598\) 0 0
\(599\) −1.39289e7 −1.58617 −0.793085 0.609111i \(-0.791526\pi\)
−0.793085 + 0.609111i \(0.791526\pi\)
\(600\) 0 0
\(601\) −4.81441e6 −0.543697 −0.271848 0.962340i \(-0.587635\pi\)
−0.271848 + 0.962340i \(0.587635\pi\)
\(602\) 0 0
\(603\) 3.13779e6 0.351423
\(604\) 0 0
\(605\) −2.34427e6 −0.260387
\(606\) 0 0
\(607\) −1.04800e7 −1.15449 −0.577245 0.816571i \(-0.695872\pi\)
−0.577245 + 0.816571i \(0.695872\pi\)
\(608\) 0 0
\(609\) 7.64460e6 0.835240
\(610\) 0 0
\(611\) 1.14119e6 0.123667
\(612\) 0 0
\(613\) 3.07977e6 0.331029 0.165515 0.986207i \(-0.447071\pi\)
0.165515 + 0.986207i \(0.447071\pi\)
\(614\) 0 0
\(615\) −2.43843e6 −0.259970
\(616\) 0 0
\(617\) 1.15522e6 0.122166 0.0610831 0.998133i \(-0.480545\pi\)
0.0610831 + 0.998133i \(0.480545\pi\)
\(618\) 0 0
\(619\) −1.76853e7 −1.85517 −0.927587 0.373606i \(-0.878121\pi\)
−0.927587 + 0.373606i \(0.878121\pi\)
\(620\) 0 0
\(621\) 1.08140e7 1.12528
\(622\) 0 0
\(623\) −1.49159e7 −1.53967
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −3.36162e6 −0.341491
\(628\) 0 0
\(629\) −1.32468e6 −0.133501
\(630\) 0 0
\(631\) −5.42541e6 −0.542449 −0.271225 0.962516i \(-0.587429\pi\)
−0.271225 + 0.962516i \(0.587429\pi\)
\(632\) 0 0
\(633\) −6.07932e6 −0.603039
\(634\) 0 0
\(635\) −3.93425e6 −0.387193
\(636\) 0 0
\(637\) −371602. −0.0362852
\(638\) 0 0
\(639\) −3.40855e6 −0.330230
\(640\) 0 0
\(641\) 1.16005e7 1.11515 0.557573 0.830128i \(-0.311733\pi\)
0.557573 + 0.830128i \(0.311733\pi\)
\(642\) 0 0
\(643\) 9.57873e6 0.913651 0.456826 0.889556i \(-0.348986\pi\)
0.456826 + 0.889556i \(0.348986\pi\)
\(644\) 0 0
\(645\) −6.00750e6 −0.568584
\(646\) 0 0
\(647\) 1.28130e7 1.20334 0.601671 0.798744i \(-0.294502\pi\)
0.601671 + 0.798744i \(0.294502\pi\)
\(648\) 0 0
\(649\) 8.82992e6 0.822896
\(650\) 0 0
\(651\) −5.87263e6 −0.543100
\(652\) 0 0
\(653\) 1.58665e6 0.145613 0.0728064 0.997346i \(-0.476804\pi\)
0.0728064 + 0.997346i \(0.476804\pi\)
\(654\) 0 0
\(655\) 6.69322e6 0.609582
\(656\) 0 0
\(657\) 1.16764e6 0.105535
\(658\) 0 0
\(659\) 1.95559e7 1.75414 0.877071 0.480361i \(-0.159494\pi\)
0.877071 + 0.480361i \(0.159494\pi\)
\(660\) 0 0
\(661\) 7.46471e6 0.664522 0.332261 0.943188i \(-0.392189\pi\)
0.332261 + 0.943188i \(0.392189\pi\)
\(662\) 0 0
\(663\) 367771. 0.0324933
\(664\) 0 0
\(665\) −3.34800e6 −0.293583
\(666\) 0 0
\(667\) −1.08261e7 −0.942231
\(668\) 0 0
\(669\) 5.77386e6 0.498771
\(670\) 0 0
\(671\) 6.94371e6 0.595367
\(672\) 0 0
\(673\) −1.09694e7 −0.933568 −0.466784 0.884371i \(-0.654587\pi\)
−0.466784 + 0.884371i \(0.654587\pi\)
\(674\) 0 0
\(675\) 2.56589e6 0.216760
\(676\) 0 0
\(677\) 6.52708e6 0.547327 0.273664 0.961825i \(-0.411764\pi\)
0.273664 + 0.961825i \(0.411764\pi\)
\(678\) 0 0
\(679\) −1.50889e7 −1.25598
\(680\) 0 0
\(681\) 1.50805e7 1.24608
\(682\) 0 0
\(683\) 1.54389e7 1.26638 0.633191 0.773995i \(-0.281745\pi\)
0.633191 + 0.773995i \(0.281745\pi\)
\(684\) 0 0
\(685\) −2.80395e6 −0.228320
\(686\) 0 0
\(687\) −1.08996e7 −0.881089
\(688\) 0 0
\(689\) 4.96280e6 0.398271
\(690\) 0 0
\(691\) 4.78757e6 0.381435 0.190717 0.981645i \(-0.438919\pi\)
0.190717 + 0.981645i \(0.438919\pi\)
\(692\) 0 0
\(693\) 2.26548e6 0.179196
\(694\) 0 0
\(695\) −3.68370e6 −0.289282
\(696\) 0 0
\(697\) 1.29406e6 0.100896
\(698\) 0 0
\(699\) −1.13529e7 −0.878847
\(700\) 0 0
\(701\) 3.31891e6 0.255094 0.127547 0.991833i \(-0.459290\pi\)
0.127547 + 0.991833i \(0.459290\pi\)
\(702\) 0 0
\(703\) 7.18883e6 0.548618
\(704\) 0 0
\(705\) 2.48550e6 0.188339
\(706\) 0 0
\(707\) −8.20699e6 −0.617497
\(708\) 0 0
\(709\) −1.60044e7 −1.19570 −0.597852 0.801607i \(-0.703979\pi\)
−0.597852 + 0.801607i \(0.703979\pi\)
\(710\) 0 0
\(711\) 5.46472e6 0.405409
\(712\) 0 0
\(713\) 8.31668e6 0.612669
\(714\) 0 0
\(715\) 998628. 0.0730531
\(716\) 0 0
\(717\) 760560. 0.0552504
\(718\) 0 0
\(719\) 1.56006e7 1.12543 0.562715 0.826651i \(-0.309757\pi\)
0.562715 + 0.826651i \(0.309757\pi\)
\(720\) 0 0
\(721\) −1.56531e7 −1.12141
\(722\) 0 0
\(723\) −1.71154e7 −1.21771
\(724\) 0 0
\(725\) −2.56875e6 −0.181500
\(726\) 0 0
\(727\) 1.14545e7 0.803783 0.401891 0.915687i \(-0.368353\pi\)
0.401891 + 0.915687i \(0.368353\pi\)
\(728\) 0 0
\(729\) 1.58900e7 1.10740
\(730\) 0 0
\(731\) 3.18814e6 0.220670
\(732\) 0 0
\(733\) −1.13267e7 −0.778650 −0.389325 0.921101i \(-0.627292\pi\)
−0.389325 + 0.921101i \(0.627292\pi\)
\(734\) 0 0
\(735\) −809345. −0.0552606
\(736\) 0 0
\(737\) 1.29189e7 0.876108
\(738\) 0 0
\(739\) 1.31055e7 0.882756 0.441378 0.897321i \(-0.354490\pi\)
0.441378 + 0.897321i \(0.354490\pi\)
\(740\) 0 0
\(741\) −1.99584e6 −0.133530
\(742\) 0 0
\(743\) −4.16787e6 −0.276976 −0.138488 0.990364i \(-0.544224\pi\)
−0.138488 + 0.990364i \(0.544224\pi\)
\(744\) 0 0
\(745\) 4.36415e6 0.288077
\(746\) 0 0
\(747\) −4.95448e6 −0.324860
\(748\) 0 0
\(749\) −5.55086e6 −0.361539
\(750\) 0 0
\(751\) 2.89308e7 1.87180 0.935902 0.352260i \(-0.114587\pi\)
0.935902 + 0.352260i \(0.114587\pi\)
\(752\) 0 0
\(753\) −683400. −0.0439225
\(754\) 0 0
\(755\) 8.63145e6 0.551082
\(756\) 0 0
\(757\) −8.32870e6 −0.528247 −0.264124 0.964489i \(-0.585083\pi\)
−0.264124 + 0.964489i \(0.585083\pi\)
\(758\) 0 0
\(759\) 9.16663e6 0.577571
\(760\) 0 0
\(761\) 4.48292e6 0.280608 0.140304 0.990108i \(-0.455192\pi\)
0.140304 + 0.990108i \(0.455192\pi\)
\(762\) 0 0
\(763\) 1.93556e7 1.20363
\(764\) 0 0
\(765\) −280350. −0.0173200
\(766\) 0 0
\(767\) 5.24245e6 0.321770
\(768\) 0 0
\(769\) 1.32141e6 0.0805790 0.0402895 0.999188i \(-0.487172\pi\)
0.0402895 + 0.999188i \(0.487172\pi\)
\(770\) 0 0
\(771\) −2.21110e7 −1.33959
\(772\) 0 0
\(773\) 7.24897e6 0.436342 0.218171 0.975911i \(-0.429991\pi\)
0.218171 + 0.975911i \(0.429991\pi\)
\(774\) 0 0
\(775\) 1.97333e6 0.118017
\(776\) 0 0
\(777\) 1.38421e7 0.822527
\(778\) 0 0
\(779\) −7.02268e6 −0.414629
\(780\) 0 0
\(781\) −1.40337e7 −0.823273
\(782\) 0 0
\(783\) −1.68733e7 −0.983547
\(784\) 0 0
\(785\) 662550. 0.0383747
\(786\) 0 0
\(787\) −4.98037e6 −0.286632 −0.143316 0.989677i \(-0.545777\pi\)
−0.143316 + 0.989677i \(0.545777\pi\)
\(788\) 0 0
\(789\) −7.01670e6 −0.401273
\(790\) 0 0
\(791\) −5.96773e6 −0.339132
\(792\) 0 0
\(793\) 4.12258e6 0.232802
\(794\) 0 0
\(795\) 1.08089e7 0.606548
\(796\) 0 0
\(797\) −1.48673e7 −0.829061 −0.414530 0.910036i \(-0.636054\pi\)
−0.414530 + 0.910036i \(0.636054\pi\)
\(798\) 0 0
\(799\) −1.31904e6 −0.0730955
\(800\) 0 0
\(801\) 6.77817e6 0.373277
\(802\) 0 0
\(803\) 4.80742e6 0.263101
\(804\) 0 0
\(805\) 9.12950e6 0.496543
\(806\) 0 0
\(807\) −2.59995e7 −1.40534
\(808\) 0 0
\(809\) −684390. −0.0367648 −0.0183824 0.999831i \(-0.505852\pi\)
−0.0183824 + 0.999831i \(0.505852\pi\)
\(810\) 0 0
\(811\) 3.27890e7 1.75056 0.875279 0.483618i \(-0.160677\pi\)
0.875279 + 0.483618i \(0.160677\pi\)
\(812\) 0 0
\(813\) −1.34341e7 −0.712825
\(814\) 0 0
\(815\) −3.54271e6 −0.186828
\(816\) 0 0
\(817\) −1.73016e7 −0.906841
\(818\) 0 0
\(819\) 1.34505e6 0.0700694
\(820\) 0 0
\(821\) −7.17265e6 −0.371383 −0.185691 0.982608i \(-0.559452\pi\)
−0.185691 + 0.982608i \(0.559452\pi\)
\(822\) 0 0
\(823\) 1.32939e6 0.0684153 0.0342077 0.999415i \(-0.489109\pi\)
0.0342077 + 0.999415i \(0.489109\pi\)
\(824\) 0 0
\(825\) 2.17500e6 0.111256
\(826\) 0 0
\(827\) 1.92964e7 0.981099 0.490550 0.871413i \(-0.336796\pi\)
0.490550 + 0.871413i \(0.336796\pi\)
\(828\) 0 0
\(829\) −7.10811e6 −0.359226 −0.179613 0.983737i \(-0.557485\pi\)
−0.179613 + 0.983737i \(0.557485\pi\)
\(830\) 0 0
\(831\) −5.97972e6 −0.300385
\(832\) 0 0
\(833\) 429514. 0.0214469
\(834\) 0 0
\(835\) −1.02762e7 −0.510054
\(836\) 0 0
\(837\) 1.29622e7 0.639534
\(838\) 0 0
\(839\) −8.24538e6 −0.404395 −0.202198 0.979345i \(-0.564808\pi\)
−0.202198 + 0.979345i \(0.564808\pi\)
\(840\) 0 0
\(841\) −3.61905e6 −0.176443
\(842\) 0 0
\(843\) −1.67231e7 −0.810493
\(844\) 0 0
\(845\) −8.68942e6 −0.418648
\(846\) 0 0
\(847\) −1.30001e7 −0.622640
\(848\) 0 0
\(849\) −3.05761e7 −1.45584
\(850\) 0 0
\(851\) −1.96029e7 −0.927889
\(852\) 0 0
\(853\) −1.86921e7 −0.879599 −0.439800 0.898096i \(-0.644951\pi\)
−0.439800 + 0.898096i \(0.644951\pi\)
\(854\) 0 0
\(855\) 1.52142e6 0.0711761
\(856\) 0 0
\(857\) −2.24473e7 −1.04403 −0.522013 0.852937i \(-0.674819\pi\)
−0.522013 + 0.852937i \(0.674819\pi\)
\(858\) 0 0
\(859\) −3.24436e6 −0.150019 −0.0750094 0.997183i \(-0.523899\pi\)
−0.0750094 + 0.997183i \(0.523899\pi\)
\(860\) 0 0
\(861\) −1.35222e7 −0.621641
\(862\) 0 0
\(863\) −1.01542e6 −0.0464108 −0.0232054 0.999731i \(-0.507387\pi\)
−0.0232054 + 0.999731i \(0.507387\pi\)
\(864\) 0 0
\(865\) −1.48986e7 −0.677028
\(866\) 0 0
\(867\) 1.86243e7 0.841457
\(868\) 0 0
\(869\) 2.24994e7 1.01070
\(870\) 0 0
\(871\) 7.67015e6 0.342577
\(872\) 0 0
\(873\) 6.85679e6 0.304499
\(874\) 0 0
\(875\) 2.16619e6 0.0956482
\(876\) 0 0
\(877\) −3.96764e7 −1.74194 −0.870970 0.491337i \(-0.836508\pi\)
−0.870970 + 0.491337i \(0.836508\pi\)
\(878\) 0 0
\(879\) 3.29275e7 1.43743
\(880\) 0 0
\(881\) −2.44584e7 −1.06167 −0.530833 0.847477i \(-0.678121\pi\)
−0.530833 + 0.847477i \(0.678121\pi\)
\(882\) 0 0
\(883\) −3.11179e7 −1.34310 −0.671549 0.740960i \(-0.734371\pi\)
−0.671549 + 0.740960i \(0.734371\pi\)
\(884\) 0 0
\(885\) 1.14180e7 0.490040
\(886\) 0 0
\(887\) 1.87514e7 0.800249 0.400124 0.916461i \(-0.368967\pi\)
0.400124 + 0.916461i \(0.368967\pi\)
\(888\) 0 0
\(889\) −2.18172e7 −0.925858
\(890\) 0 0
\(891\) 1.03160e7 0.435327
\(892\) 0 0
\(893\) 7.15824e6 0.300385
\(894\) 0 0
\(895\) 7.52347e6 0.313950
\(896\) 0 0
\(897\) 5.44236e6 0.225843
\(898\) 0 0
\(899\) −1.29766e7 −0.535503
\(900\) 0 0
\(901\) −5.73623e6 −0.235404
\(902\) 0 0
\(903\) −3.33143e7 −1.35960
\(904\) 0 0
\(905\) −5.42555e6 −0.220203
\(906\) 0 0
\(907\) −5.07504e6 −0.204843 −0.102421 0.994741i \(-0.532659\pi\)
−0.102421 + 0.994741i \(0.532659\pi\)
\(908\) 0 0
\(909\) 3.72947e6 0.149706
\(910\) 0 0
\(911\) −2.83599e7 −1.13216 −0.566082 0.824349i \(-0.691541\pi\)
−0.566082 + 0.824349i \(0.691541\pi\)
\(912\) 0 0
\(913\) −2.03986e7 −0.809885
\(914\) 0 0
\(915\) 8.97893e6 0.354545
\(916\) 0 0
\(917\) 3.71169e7 1.45763
\(918\) 0 0
\(919\) 9.58570e6 0.374399 0.187200 0.982322i \(-0.440059\pi\)
0.187200 + 0.982322i \(0.440059\pi\)
\(920\) 0 0
\(921\) −277860. −0.0107939
\(922\) 0 0
\(923\) −8.33200e6 −0.321918
\(924\) 0 0
\(925\) −4.65125e6 −0.178737
\(926\) 0 0
\(927\) 7.11321e6 0.271873
\(928\) 0 0
\(929\) −3.82212e7 −1.45300 −0.726500 0.687167i \(-0.758854\pi\)
−0.726500 + 0.687167i \(0.758854\pi\)
\(930\) 0 0
\(931\) −2.33091e6 −0.0881357
\(932\) 0 0
\(933\) 634200. 0.0238519
\(934\) 0 0
\(935\) −1.15426e6 −0.0431791
\(936\) 0 0
\(937\) −9.37422e6 −0.348808 −0.174404 0.984674i \(-0.555800\pi\)
−0.174404 + 0.984674i \(0.555800\pi\)
\(938\) 0 0
\(939\) 3.74544e7 1.38624
\(940\) 0 0
\(941\) −3.04898e6 −0.112249 −0.0561243 0.998424i \(-0.517874\pi\)
−0.0561243 + 0.998424i \(0.517874\pi\)
\(942\) 0 0
\(943\) 1.91498e7 0.701270
\(944\) 0 0
\(945\) 1.42290e7 0.518316
\(946\) 0 0
\(947\) −2.95948e7 −1.07236 −0.536180 0.844104i \(-0.680133\pi\)
−0.536180 + 0.844104i \(0.680133\pi\)
\(948\) 0 0
\(949\) 2.85424e6 0.102878
\(950\) 0 0
\(951\) −6.32694e6 −0.226852
\(952\) 0 0
\(953\) 1.58338e7 0.564744 0.282372 0.959305i \(-0.408879\pi\)
0.282372 + 0.959305i \(0.408879\pi\)
\(954\) 0 0
\(955\) −2.29065e7 −0.812738
\(956\) 0 0
\(957\) −1.43028e7 −0.504825
\(958\) 0 0
\(959\) −1.55492e7 −0.545960
\(960\) 0 0
\(961\) −1.86604e7 −0.651798
\(962\) 0 0
\(963\) 2.52246e6 0.0876513
\(964\) 0 0
\(965\) 2.16028e7 0.746780
\(966\) 0 0
\(967\) 8.69009e6 0.298853 0.149427 0.988773i \(-0.452257\pi\)
0.149427 + 0.988773i \(0.452257\pi\)
\(968\) 0 0
\(969\) 2.30688e6 0.0789252
\(970\) 0 0
\(971\) −2.81474e7 −0.958054 −0.479027 0.877800i \(-0.659010\pi\)
−0.479027 + 0.877800i \(0.659010\pi\)
\(972\) 0 0
\(973\) −2.04278e7 −0.691733
\(974\) 0 0
\(975\) 1.29133e6 0.0435036
\(976\) 0 0
\(977\) −4.34090e7 −1.45493 −0.727467 0.686143i \(-0.759303\pi\)
−0.727467 + 0.686143i \(0.759303\pi\)
\(978\) 0 0
\(979\) 2.79071e7 0.930590
\(980\) 0 0
\(981\) −8.79568e6 −0.291808
\(982\) 0 0
\(983\) 4.64172e7 1.53213 0.766065 0.642763i \(-0.222212\pi\)
0.766065 + 0.642763i \(0.222212\pi\)
\(984\) 0 0
\(985\) −1.08130e7 −0.355106
\(986\) 0 0
\(987\) 1.37832e7 0.450358
\(988\) 0 0
\(989\) 4.71789e7 1.53376
\(990\) 0 0
\(991\) −4.64577e7 −1.50271 −0.751353 0.659901i \(-0.770598\pi\)
−0.751353 + 0.659901i \(0.770598\pi\)
\(992\) 0 0
\(993\) 4.14690e7 1.33460
\(994\) 0 0
\(995\) −1.98795e7 −0.636574
\(996\) 0 0
\(997\) −1.35968e7 −0.433211 −0.216605 0.976259i \(-0.569499\pi\)
−0.216605 + 0.976259i \(0.569499\pi\)
\(998\) 0 0
\(999\) −3.05525e7 −0.968576
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 320.6.a.t.1.1 2
4.3 odd 2 inner 320.6.a.t.1.2 2
8.3 odd 2 160.6.a.b.1.1 2
8.5 even 2 160.6.a.b.1.2 yes 2
40.3 even 4 800.6.c.h.449.1 4
40.13 odd 4 800.6.c.h.449.4 4
40.19 odd 2 800.6.a.i.1.2 2
40.27 even 4 800.6.c.h.449.3 4
40.29 even 2 800.6.a.i.1.1 2
40.37 odd 4 800.6.c.h.449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.b.1.1 2 8.3 odd 2
160.6.a.b.1.2 yes 2 8.5 even 2
320.6.a.t.1.1 2 1.1 even 1 trivial
320.6.a.t.1.2 2 4.3 odd 2 inner
800.6.a.i.1.1 2 40.29 even 2
800.6.a.i.1.2 2 40.19 odd 2
800.6.c.h.449.1 4 40.3 even 4
800.6.c.h.449.2 4 40.37 odd 4
800.6.c.h.449.3 4 40.27 even 4
800.6.c.h.449.4 4 40.13 odd 4