Properties

Label 280.6.a.e.1.1
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 463 x - 1890\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(23.3245\) of defining polynomial
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q-21.3245 q^{3} -25.0000 q^{5} +49.0000 q^{7} +211.733 q^{9} +O(q^{10})\) \(q-21.3245 q^{3} -25.0000 q^{5} +49.0000 q^{7} +211.733 q^{9} -381.382 q^{11} +372.295 q^{13} +533.112 q^{15} -1099.55 q^{17} +2859.15 q^{19} -1044.90 q^{21} +2943.73 q^{23} +625.000 q^{25} +666.754 q^{27} +2410.16 q^{29} -463.669 q^{31} +8132.76 q^{33} -1225.00 q^{35} +1806.73 q^{37} -7938.99 q^{39} -9019.08 q^{41} -33.7132 q^{43} -5293.32 q^{45} -15132.0 q^{47} +2401.00 q^{49} +23447.4 q^{51} -31344.7 q^{53} +9534.55 q^{55} -60969.9 q^{57} -30247.3 q^{59} -10021.8 q^{61} +10374.9 q^{63} -9307.37 q^{65} +52832.9 q^{67} -62773.5 q^{69} -11610.0 q^{71} -4765.45 q^{73} -13327.8 q^{75} -18687.7 q^{77} -28256.2 q^{79} -65669.3 q^{81} +36453.8 q^{83} +27488.9 q^{85} -51395.4 q^{87} -132386. q^{89} +18242.4 q^{91} +9887.49 q^{93} -71478.8 q^{95} -98024.6 q^{97} -80751.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 6 q^{3} - 75 q^{5} + 147 q^{7} + 209 q^{9} + O(q^{10}) \) \( 3 q + 6 q^{3} - 75 q^{5} + 147 q^{7} + 209 q^{9} - 578 q^{11} + 80 q^{13} - 150 q^{15} - 1244 q^{17} + 944 q^{19} + 294 q^{21} + 1096 q^{23} + 1875 q^{25} - 3006 q^{27} + 1868 q^{29} - 6620 q^{31} + 2662 q^{33} - 3675 q^{35} - 4058 q^{37} - 20910 q^{39} - 9602 q^{41} - 12340 q^{43} - 5225 q^{45} - 41026 q^{47} + 7203 q^{49} + 10006 q^{51} - 37610 q^{53} + 14450 q^{55} - 95456 q^{57} - 37664 q^{59} - 8386 q^{61} + 10241 q^{63} - 2000 q^{65} + 69340 q^{67} - 37712 q^{69} - 34016 q^{71} - 45314 q^{73} + 3750 q^{75} - 28322 q^{77} + 1382 q^{79} - 101005 q^{81} - 10128 q^{83} + 31100 q^{85} - 41510 q^{87} - 222810 q^{89} + 3920 q^{91} - 174292 q^{93} - 23600 q^{95} - 159476 q^{97} - 156568 q^{99} + O(q^{100}) \)

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
\(3\) −21.3245 −1.36797 −0.683983 0.729498i \(-0.739754\pi\)
−0.683983 + 0.729498i \(0.739754\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 211.733 0.871329
\(10\) 0 0
\(11\) −381.382 −0.950338 −0.475169 0.879894i \(-0.657613\pi\)
−0.475169 + 0.879894i \(0.657613\pi\)
\(12\) 0 0
\(13\) 372.295 0.610982 0.305491 0.952195i \(-0.401179\pi\)
0.305491 + 0.952195i \(0.401179\pi\)
\(14\) 0 0
\(15\) 533.112 0.611773
\(16\) 0 0
\(17\) −1099.55 −0.922772 −0.461386 0.887200i \(-0.652648\pi\)
−0.461386 + 0.887200i \(0.652648\pi\)
\(18\) 0 0
\(19\) 2859.15 1.81699 0.908497 0.417892i \(-0.137231\pi\)
0.908497 + 0.417892i \(0.137231\pi\)
\(20\) 0 0
\(21\) −1044.90 −0.517042
\(22\) 0 0
\(23\) 2943.73 1.16032 0.580161 0.814502i \(-0.302990\pi\)
0.580161 + 0.814502i \(0.302990\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 666.754 0.176018
\(28\) 0 0
\(29\) 2410.16 0.532171 0.266086 0.963949i \(-0.414270\pi\)
0.266086 + 0.963949i \(0.414270\pi\)
\(30\) 0 0
\(31\) −463.669 −0.0866570 −0.0433285 0.999061i \(-0.513796\pi\)
−0.0433285 + 0.999061i \(0.513796\pi\)
\(32\) 0 0
\(33\) 8132.76 1.30003
\(34\) 0 0
\(35\) −1225.00 −0.169031
\(36\) 0 0
\(37\) 1806.73 0.216965 0.108483 0.994098i \(-0.465401\pi\)
0.108483 + 0.994098i \(0.465401\pi\)
\(38\) 0 0
\(39\) −7938.99 −0.835802
\(40\) 0 0
\(41\) −9019.08 −0.837920 −0.418960 0.908005i \(-0.637605\pi\)
−0.418960 + 0.908005i \(0.637605\pi\)
\(42\) 0 0
\(43\) −33.7132 −0.00278054 −0.00139027 0.999999i \(-0.500443\pi\)
−0.00139027 + 0.999999i \(0.500443\pi\)
\(44\) 0 0
\(45\) −5293.32 −0.389670
\(46\) 0 0
\(47\) −15132.0 −0.999199 −0.499600 0.866256i \(-0.666520\pi\)
−0.499600 + 0.866256i \(0.666520\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 23447.4 1.26232
\(52\) 0 0
\(53\) −31344.7 −1.53276 −0.766381 0.642386i \(-0.777945\pi\)
−0.766381 + 0.642386i \(0.777945\pi\)
\(54\) 0 0
\(55\) 9534.55 0.425004
\(56\) 0 0
\(57\) −60969.9 −2.48558
\(58\) 0 0
\(59\) −30247.3 −1.13125 −0.565623 0.824664i \(-0.691364\pi\)
−0.565623 + 0.824664i \(0.691364\pi\)
\(60\) 0 0
\(61\) −10021.8 −0.344841 −0.172421 0.985023i \(-0.555159\pi\)
−0.172421 + 0.985023i \(0.555159\pi\)
\(62\) 0 0
\(63\) 10374.9 0.329331
\(64\) 0 0
\(65\) −9307.37 −0.273240
\(66\) 0 0
\(67\) 52832.9 1.43786 0.718931 0.695081i \(-0.244632\pi\)
0.718931 + 0.695081i \(0.244632\pi\)
\(68\) 0 0
\(69\) −62773.5 −1.58728
\(70\) 0 0
\(71\) −11610.0 −0.273330 −0.136665 0.990617i \(-0.543638\pi\)
−0.136665 + 0.990617i \(0.543638\pi\)
\(72\) 0 0
\(73\) −4765.45 −0.104664 −0.0523320 0.998630i \(-0.516665\pi\)
−0.0523320 + 0.998630i \(0.516665\pi\)
\(74\) 0 0
\(75\) −13327.8 −0.273593
\(76\) 0 0
\(77\) −18687.7 −0.359194
\(78\) 0 0
\(79\) −28256.2 −0.509385 −0.254693 0.967022i \(-0.581974\pi\)
−0.254693 + 0.967022i \(0.581974\pi\)
\(80\) 0 0
\(81\) −65669.3 −1.11211
\(82\) 0 0
\(83\) 36453.8 0.580828 0.290414 0.956901i \(-0.406207\pi\)
0.290414 + 0.956901i \(0.406207\pi\)
\(84\) 0 0
\(85\) 27488.9 0.412676
\(86\) 0 0
\(87\) −51395.4 −0.727992
\(88\) 0 0
\(89\) −132386. −1.77160 −0.885802 0.464063i \(-0.846391\pi\)
−0.885802 + 0.464063i \(0.846391\pi\)
\(90\) 0 0
\(91\) 18242.4 0.230930
\(92\) 0 0
\(93\) 9887.49 0.118544
\(94\) 0 0
\(95\) −71478.8 −0.812584
\(96\) 0 0
\(97\) −98024.6 −1.05780 −0.528902 0.848683i \(-0.677396\pi\)
−0.528902 + 0.848683i \(0.677396\pi\)
\(98\) 0 0
\(99\) −80751.1 −0.828057
\(100\) 0 0
\(101\) 34873.5 0.340167 0.170083 0.985430i \(-0.445596\pi\)
0.170083 + 0.985430i \(0.445596\pi\)
\(102\) 0 0
\(103\) −93279.1 −0.866346 −0.433173 0.901311i \(-0.642606\pi\)
−0.433173 + 0.901311i \(0.642606\pi\)
\(104\) 0 0
\(105\) 26122.5 0.231228
\(106\) 0 0
\(107\) 193063. 1.63020 0.815098 0.579324i \(-0.196683\pi\)
0.815098 + 0.579324i \(0.196683\pi\)
\(108\) 0 0
\(109\) −34782.7 −0.280412 −0.140206 0.990122i \(-0.544776\pi\)
−0.140206 + 0.990122i \(0.544776\pi\)
\(110\) 0 0
\(111\) −38527.6 −0.296801
\(112\) 0 0
\(113\) 54953.9 0.404858 0.202429 0.979297i \(-0.435116\pi\)
0.202429 + 0.979297i \(0.435116\pi\)
\(114\) 0 0
\(115\) −73593.3 −0.518912
\(116\) 0 0
\(117\) 78827.1 0.532366
\(118\) 0 0
\(119\) −53878.1 −0.348775
\(120\) 0 0
\(121\) −15598.9 −0.0968568
\(122\) 0 0
\(123\) 192327. 1.14625
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 312973. 1.72186 0.860930 0.508723i \(-0.169882\pi\)
0.860930 + 0.508723i \(0.169882\pi\)
\(128\) 0 0
\(129\) 718.916 0.00380368
\(130\) 0 0
\(131\) 112963. 0.575118 0.287559 0.957763i \(-0.407156\pi\)
0.287559 + 0.957763i \(0.407156\pi\)
\(132\) 0 0
\(133\) 140099. 0.686759
\(134\) 0 0
\(135\) −16668.8 −0.0787175
\(136\) 0 0
\(137\) −41357.4 −0.188257 −0.0941287 0.995560i \(-0.530007\pi\)
−0.0941287 + 0.995560i \(0.530007\pi\)
\(138\) 0 0
\(139\) −391228. −1.71749 −0.858743 0.512407i \(-0.828754\pi\)
−0.858743 + 0.512407i \(0.828754\pi\)
\(140\) 0 0
\(141\) 322682. 1.36687
\(142\) 0 0
\(143\) −141986. −0.580640
\(144\) 0 0
\(145\) −60254.1 −0.237994
\(146\) 0 0
\(147\) −51200.0 −0.195424
\(148\) 0 0
\(149\) −303054. −1.11829 −0.559144 0.829071i \(-0.688870\pi\)
−0.559144 + 0.829071i \(0.688870\pi\)
\(150\) 0 0
\(151\) −112954. −0.403144 −0.201572 0.979474i \(-0.564605\pi\)
−0.201572 + 0.979474i \(0.564605\pi\)
\(152\) 0 0
\(153\) −232812. −0.804038
\(154\) 0 0
\(155\) 11591.7 0.0387542
\(156\) 0 0
\(157\) −23023.9 −0.0745470 −0.0372735 0.999305i \(-0.511867\pi\)
−0.0372735 + 0.999305i \(0.511867\pi\)
\(158\) 0 0
\(159\) 668410. 2.09677
\(160\) 0 0
\(161\) 144243. 0.438560
\(162\) 0 0
\(163\) 212947. 0.627774 0.313887 0.949460i \(-0.398369\pi\)
0.313887 + 0.949460i \(0.398369\pi\)
\(164\) 0 0
\(165\) −203319. −0.581391
\(166\) 0 0
\(167\) −509533. −1.41378 −0.706889 0.707325i \(-0.749902\pi\)
−0.706889 + 0.707325i \(0.749902\pi\)
\(168\) 0 0
\(169\) −232690. −0.626701
\(170\) 0 0
\(171\) 605377. 1.58320
\(172\) 0 0
\(173\) 251973. 0.640088 0.320044 0.947403i \(-0.396302\pi\)
0.320044 + 0.947403i \(0.396302\pi\)
\(174\) 0 0
\(175\) 30625.0 0.0755929
\(176\) 0 0
\(177\) 645008. 1.54750
\(178\) 0 0
\(179\) −187246. −0.436797 −0.218398 0.975860i \(-0.570083\pi\)
−0.218398 + 0.975860i \(0.570083\pi\)
\(180\) 0 0
\(181\) −547053. −1.24117 −0.620587 0.784138i \(-0.713106\pi\)
−0.620587 + 0.784138i \(0.713106\pi\)
\(182\) 0 0
\(183\) 213709. 0.471731
\(184\) 0 0
\(185\) −45168.3 −0.0970297
\(186\) 0 0
\(187\) 419350. 0.876945
\(188\) 0 0
\(189\) 32670.9 0.0665284
\(190\) 0 0
\(191\) 82048.2 0.162737 0.0813684 0.996684i \(-0.474071\pi\)
0.0813684 + 0.996684i \(0.474071\pi\)
\(192\) 0 0
\(193\) 834554. 1.61273 0.806364 0.591419i \(-0.201432\pi\)
0.806364 + 0.591419i \(0.201432\pi\)
\(194\) 0 0
\(195\) 198475. 0.373782
\(196\) 0 0
\(197\) −801077. −1.47065 −0.735324 0.677716i \(-0.762970\pi\)
−0.735324 + 0.677716i \(0.762970\pi\)
\(198\) 0 0
\(199\) −728144. −1.30342 −0.651710 0.758468i \(-0.725948\pi\)
−0.651710 + 0.758468i \(0.725948\pi\)
\(200\) 0 0
\(201\) −1.12663e6 −1.96695
\(202\) 0 0
\(203\) 118098. 0.201142
\(204\) 0 0
\(205\) 225477. 0.374729
\(206\) 0 0
\(207\) 623285. 1.01102
\(208\) 0 0
\(209\) −1.09043e6 −1.72676
\(210\) 0 0
\(211\) 737969. 1.14112 0.570561 0.821255i \(-0.306726\pi\)
0.570561 + 0.821255i \(0.306726\pi\)
\(212\) 0 0
\(213\) 247578. 0.373906
\(214\) 0 0
\(215\) 842.830 0.00124349
\(216\) 0 0
\(217\) −22719.8 −0.0327533
\(218\) 0 0
\(219\) 101621. 0.143177
\(220\) 0 0
\(221\) −409358. −0.563797
\(222\) 0 0
\(223\) −504580. −0.679466 −0.339733 0.940522i \(-0.610337\pi\)
−0.339733 + 0.940522i \(0.610337\pi\)
\(224\) 0 0
\(225\) 132333. 0.174266
\(226\) 0 0
\(227\) 793643. 1.02226 0.511129 0.859504i \(-0.329228\pi\)
0.511129 + 0.859504i \(0.329228\pi\)
\(228\) 0 0
\(229\) 533635. 0.672444 0.336222 0.941783i \(-0.390851\pi\)
0.336222 + 0.941783i \(0.390851\pi\)
\(230\) 0 0
\(231\) 398505. 0.491365
\(232\) 0 0
\(233\) 1.56974e6 1.89425 0.947125 0.320863i \(-0.103973\pi\)
0.947125 + 0.320863i \(0.103973\pi\)
\(234\) 0 0
\(235\) 378300. 0.446856
\(236\) 0 0
\(237\) 602549. 0.696821
\(238\) 0 0
\(239\) 318353. 0.360507 0.180253 0.983620i \(-0.442308\pi\)
0.180253 + 0.983620i \(0.442308\pi\)
\(240\) 0 0
\(241\) −719047. −0.797471 −0.398736 0.917066i \(-0.630551\pi\)
−0.398736 + 0.917066i \(0.630551\pi\)
\(242\) 0 0
\(243\) 1.23834e6 1.34532
\(244\) 0 0
\(245\) −60025.0 −0.0638877
\(246\) 0 0
\(247\) 1.06445e6 1.11015
\(248\) 0 0
\(249\) −777358. −0.794553
\(250\) 0 0
\(251\) 1.63688e6 1.63995 0.819977 0.572397i \(-0.193986\pi\)
0.819977 + 0.572397i \(0.193986\pi\)
\(252\) 0 0
\(253\) −1.12269e6 −1.10270
\(254\) 0 0
\(255\) −586185. −0.564526
\(256\) 0 0
\(257\) 713835. 0.674163 0.337082 0.941475i \(-0.390560\pi\)
0.337082 + 0.941475i \(0.390560\pi\)
\(258\) 0 0
\(259\) 88530.0 0.0820051
\(260\) 0 0
\(261\) 510311. 0.463696
\(262\) 0 0
\(263\) −1.93481e6 −1.72484 −0.862419 0.506195i \(-0.831052\pi\)
−0.862419 + 0.506195i \(0.831052\pi\)
\(264\) 0 0
\(265\) 783618. 0.685472
\(266\) 0 0
\(267\) 2.82306e6 2.42349
\(268\) 0 0
\(269\) 104742. 0.0882554 0.0441277 0.999026i \(-0.485949\pi\)
0.0441277 + 0.999026i \(0.485949\pi\)
\(270\) 0 0
\(271\) 1.09108e6 0.902471 0.451235 0.892405i \(-0.350983\pi\)
0.451235 + 0.892405i \(0.350983\pi\)
\(272\) 0 0
\(273\) −389010. −0.315904
\(274\) 0 0
\(275\) −238364. −0.190068
\(276\) 0 0
\(277\) 328777. 0.257455 0.128728 0.991680i \(-0.458911\pi\)
0.128728 + 0.991680i \(0.458911\pi\)
\(278\) 0 0
\(279\) −98174.0 −0.0755067
\(280\) 0 0
\(281\) −37359.3 −0.0282249 −0.0141125 0.999900i \(-0.504492\pi\)
−0.0141125 + 0.999900i \(0.504492\pi\)
\(282\) 0 0
\(283\) −1.80297e6 −1.33820 −0.669101 0.743172i \(-0.733321\pi\)
−0.669101 + 0.743172i \(0.733321\pi\)
\(284\) 0 0
\(285\) 1.52425e6 1.11159
\(286\) 0 0
\(287\) −441935. −0.316704
\(288\) 0 0
\(289\) −210838. −0.148492
\(290\) 0 0
\(291\) 2.09032e6 1.44704
\(292\) 0 0
\(293\) −1.56997e6 −1.06837 −0.534185 0.845368i \(-0.679381\pi\)
−0.534185 + 0.845368i \(0.679381\pi\)
\(294\) 0 0
\(295\) 756183. 0.505908
\(296\) 0 0
\(297\) −254288. −0.167276
\(298\) 0 0
\(299\) 1.09594e6 0.708936
\(300\) 0 0
\(301\) −1651.95 −0.00105094
\(302\) 0 0
\(303\) −743658. −0.465336
\(304\) 0 0
\(305\) 250544. 0.154218
\(306\) 0 0
\(307\) −2.27153e6 −1.37554 −0.687769 0.725930i \(-0.741410\pi\)
−0.687769 + 0.725930i \(0.741410\pi\)
\(308\) 0 0
\(309\) 1.98913e6 1.18513
\(310\) 0 0
\(311\) −2.71344e6 −1.59082 −0.795408 0.606074i \(-0.792743\pi\)
−0.795408 + 0.606074i \(0.792743\pi\)
\(312\) 0 0
\(313\) −3.03548e6 −1.75132 −0.875661 0.482926i \(-0.839574\pi\)
−0.875661 + 0.482926i \(0.839574\pi\)
\(314\) 0 0
\(315\) −259373. −0.147281
\(316\) 0 0
\(317\) 655683. 0.366476 0.183238 0.983069i \(-0.441342\pi\)
0.183238 + 0.983069i \(0.441342\pi\)
\(318\) 0 0
\(319\) −919192. −0.505743
\(320\) 0 0
\(321\) −4.11697e6 −2.23005
\(322\) 0 0
\(323\) −3.14379e6 −1.67667
\(324\) 0 0
\(325\) 232684. 0.122196
\(326\) 0 0
\(327\) 741722. 0.383594
\(328\) 0 0
\(329\) −741469. −0.377662
\(330\) 0 0
\(331\) −3.77092e6 −1.89181 −0.945904 0.324447i \(-0.894822\pi\)
−0.945904 + 0.324447i \(0.894822\pi\)
\(332\) 0 0
\(333\) 382545. 0.189048
\(334\) 0 0
\(335\) −1.32082e6 −0.643032
\(336\) 0 0
\(337\) −1.44388e6 −0.692557 −0.346278 0.938132i \(-0.612555\pi\)
−0.346278 + 0.938132i \(0.612555\pi\)
\(338\) 0 0
\(339\) −1.17186e6 −0.553831
\(340\) 0 0
\(341\) 176835. 0.0823535
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 1.56934e6 0.709853
\(346\) 0 0
\(347\) −2.00100e6 −0.892120 −0.446060 0.895003i \(-0.647173\pi\)
−0.446060 + 0.895003i \(0.647173\pi\)
\(348\) 0 0
\(349\) 688692. 0.302664 0.151332 0.988483i \(-0.451644\pi\)
0.151332 + 0.988483i \(0.451644\pi\)
\(350\) 0 0
\(351\) 248229. 0.107544
\(352\) 0 0
\(353\) 805367. 0.343999 0.172000 0.985097i \(-0.444977\pi\)
0.172000 + 0.985097i \(0.444977\pi\)
\(354\) 0 0
\(355\) 290251. 0.122237
\(356\) 0 0
\(357\) 1.14892e6 0.477112
\(358\) 0 0
\(359\) −1.80310e6 −0.738386 −0.369193 0.929353i \(-0.620366\pi\)
−0.369193 + 0.929353i \(0.620366\pi\)
\(360\) 0 0
\(361\) 5.69866e6 2.30147
\(362\) 0 0
\(363\) 332638. 0.132497
\(364\) 0 0
\(365\) 119136. 0.0468071
\(366\) 0 0
\(367\) 2.17144e6 0.841554 0.420777 0.907164i \(-0.361757\pi\)
0.420777 + 0.907164i \(0.361757\pi\)
\(368\) 0 0
\(369\) −1.90964e6 −0.730104
\(370\) 0 0
\(371\) −1.53589e6 −0.579330
\(372\) 0 0
\(373\) 2.31643e6 0.862080 0.431040 0.902333i \(-0.358147\pi\)
0.431040 + 0.902333i \(0.358147\pi\)
\(374\) 0 0
\(375\) 333195. 0.122355
\(376\) 0 0
\(377\) 897291. 0.325147
\(378\) 0 0
\(379\) −4.28068e6 −1.53079 −0.765393 0.643563i \(-0.777455\pi\)
−0.765393 + 0.643563i \(0.777455\pi\)
\(380\) 0 0
\(381\) −6.67399e6 −2.35544
\(382\) 0 0
\(383\) −5.33887e6 −1.85974 −0.929871 0.367886i \(-0.880082\pi\)
−0.929871 + 0.367886i \(0.880082\pi\)
\(384\) 0 0
\(385\) 467193. 0.160637
\(386\) 0 0
\(387\) −7138.19 −0.00242276
\(388\) 0 0
\(389\) 1.66287e6 0.557167 0.278584 0.960412i \(-0.410135\pi\)
0.278584 + 0.960412i \(0.410135\pi\)
\(390\) 0 0
\(391\) −3.23679e6 −1.07071
\(392\) 0 0
\(393\) −2.40887e6 −0.786741
\(394\) 0 0
\(395\) 706405. 0.227804
\(396\) 0 0
\(397\) 274923. 0.0875458 0.0437729 0.999042i \(-0.486062\pi\)
0.0437729 + 0.999042i \(0.486062\pi\)
\(398\) 0 0
\(399\) −2.98753e6 −0.939462
\(400\) 0 0
\(401\) −1.99036e6 −0.618118 −0.309059 0.951043i \(-0.600014\pi\)
−0.309059 + 0.951043i \(0.600014\pi\)
\(402\) 0 0
\(403\) −172621. −0.0529459
\(404\) 0 0
\(405\) 1.64173e6 0.497353
\(406\) 0 0
\(407\) −689055. −0.206190
\(408\) 0 0
\(409\) 2.80249e6 0.828391 0.414196 0.910188i \(-0.364063\pi\)
0.414196 + 0.910188i \(0.364063\pi\)
\(410\) 0 0
\(411\) 881925. 0.257530
\(412\) 0 0
\(413\) −1.48212e6 −0.427570
\(414\) 0 0
\(415\) −911345. −0.259754
\(416\) 0 0
\(417\) 8.34273e6 2.34946
\(418\) 0 0
\(419\) −574142. −0.159766 −0.0798830 0.996804i \(-0.525455\pi\)
−0.0798830 + 0.996804i \(0.525455\pi\)
\(420\) 0 0
\(421\) −3.80048e6 −1.04504 −0.522520 0.852627i \(-0.675008\pi\)
−0.522520 + 0.852627i \(0.675008\pi\)
\(422\) 0 0
\(423\) −3.20395e6 −0.870631
\(424\) 0 0
\(425\) −687221. −0.184554
\(426\) 0 0
\(427\) −491066. −0.130338
\(428\) 0 0
\(429\) 3.02779e6 0.794295
\(430\) 0 0
\(431\) 2.21830e6 0.575211 0.287606 0.957749i \(-0.407141\pi\)
0.287606 + 0.957749i \(0.407141\pi\)
\(432\) 0 0
\(433\) −1.16997e6 −0.299886 −0.149943 0.988695i \(-0.547909\pi\)
−0.149943 + 0.988695i \(0.547909\pi\)
\(434\) 0 0
\(435\) 1.28489e6 0.325568
\(436\) 0 0
\(437\) 8.41658e6 2.10830
\(438\) 0 0
\(439\) 4.00014e6 0.990636 0.495318 0.868712i \(-0.335051\pi\)
0.495318 + 0.868712i \(0.335051\pi\)
\(440\) 0 0
\(441\) 508371. 0.124476
\(442\) 0 0
\(443\) −2.94996e6 −0.714179 −0.357089 0.934070i \(-0.616231\pi\)
−0.357089 + 0.934070i \(0.616231\pi\)
\(444\) 0 0
\(445\) 3.30965e6 0.792286
\(446\) 0 0
\(447\) 6.46246e6 1.52978
\(448\) 0 0
\(449\) −3.44945e6 −0.807483 −0.403742 0.914873i \(-0.632291\pi\)
−0.403742 + 0.914873i \(0.632291\pi\)
\(450\) 0 0
\(451\) 3.43971e6 0.796307
\(452\) 0 0
\(453\) 2.40869e6 0.551486
\(454\) 0 0
\(455\) −456061. −0.103275
\(456\) 0 0
\(457\) −6.94632e6 −1.55584 −0.777919 0.628365i \(-0.783724\pi\)
−0.777919 + 0.628365i \(0.783724\pi\)
\(458\) 0 0
\(459\) −733132. −0.162424
\(460\) 0 0
\(461\) 3.63913e6 0.797527 0.398764 0.917054i \(-0.369439\pi\)
0.398764 + 0.917054i \(0.369439\pi\)
\(462\) 0 0
\(463\) 5.29061e6 1.14697 0.573486 0.819215i \(-0.305591\pi\)
0.573486 + 0.819215i \(0.305591\pi\)
\(464\) 0 0
\(465\) −247187. −0.0530144
\(466\) 0 0
\(467\) 7.01082e6 1.48757 0.743783 0.668421i \(-0.233029\pi\)
0.743783 + 0.668421i \(0.233029\pi\)
\(468\) 0 0
\(469\) 2.58881e6 0.543461
\(470\) 0 0
\(471\) 490973. 0.101978
\(472\) 0 0
\(473\) 12857.6 0.00264245
\(474\) 0 0
\(475\) 1.78697e6 0.363399
\(476\) 0 0
\(477\) −6.63671e6 −1.33554
\(478\) 0 0
\(479\) −9.33895e6 −1.85977 −0.929885 0.367850i \(-0.880094\pi\)
−0.929885 + 0.367850i \(0.880094\pi\)
\(480\) 0 0
\(481\) 672638. 0.132562
\(482\) 0 0
\(483\) −3.07590e6 −0.599935
\(484\) 0 0
\(485\) 2.45061e6 0.473065
\(486\) 0 0
\(487\) 3.02941e6 0.578809 0.289404 0.957207i \(-0.406543\pi\)
0.289404 + 0.957207i \(0.406543\pi\)
\(488\) 0 0
\(489\) −4.54099e6 −0.858773
\(490\) 0 0
\(491\) −5.58970e6 −1.04637 −0.523185 0.852219i \(-0.675256\pi\)
−0.523185 + 0.852219i \(0.675256\pi\)
\(492\) 0 0
\(493\) −2.65010e6 −0.491072
\(494\) 0 0
\(495\) 2.01878e6 0.370319
\(496\) 0 0
\(497\) −568892. −0.103309
\(498\) 0 0
\(499\) −3.82995e6 −0.688561 −0.344280 0.938867i \(-0.611877\pi\)
−0.344280 + 0.938867i \(0.611877\pi\)
\(500\) 0 0
\(501\) 1.08655e7 1.93400
\(502\) 0 0
\(503\) 6.93999e6 1.22304 0.611518 0.791231i \(-0.290559\pi\)
0.611518 + 0.791231i \(0.290559\pi\)
\(504\) 0 0
\(505\) −871837. −0.152127
\(506\) 0 0
\(507\) 4.96198e6 0.857305
\(508\) 0 0
\(509\) −4.13814e6 −0.707963 −0.353981 0.935252i \(-0.615172\pi\)
−0.353981 + 0.935252i \(0.615172\pi\)
\(510\) 0 0
\(511\) −233507. −0.0395592
\(512\) 0 0
\(513\) 1.90635e6 0.319823
\(514\) 0 0
\(515\) 2.33198e6 0.387442
\(516\) 0 0
\(517\) 5.77108e6 0.949578
\(518\) 0 0
\(519\) −5.37320e6 −0.875618
\(520\) 0 0
\(521\) −1.43012e6 −0.230823 −0.115411 0.993318i \(-0.536819\pi\)
−0.115411 + 0.993318i \(0.536819\pi\)
\(522\) 0 0
\(523\) 1.67112e6 0.267149 0.133574 0.991039i \(-0.457354\pi\)
0.133574 + 0.991039i \(0.457354\pi\)
\(524\) 0 0
\(525\) −653062. −0.103408
\(526\) 0 0
\(527\) 509829. 0.0799646
\(528\) 0 0
\(529\) 2.22921e6 0.346347
\(530\) 0 0
\(531\) −6.40435e6 −0.985687
\(532\) 0 0
\(533\) −3.35776e6 −0.511954
\(534\) 0 0
\(535\) −4.82658e6 −0.729046
\(536\) 0 0
\(537\) 3.99292e6 0.597523
\(538\) 0 0
\(539\) −915698. −0.135763
\(540\) 0 0
\(541\) 2.14416e6 0.314966 0.157483 0.987522i \(-0.449662\pi\)
0.157483 + 0.987522i \(0.449662\pi\)
\(542\) 0 0
\(543\) 1.16656e7 1.69788
\(544\) 0 0
\(545\) 869566. 0.125404
\(546\) 0 0
\(547\) 3.69979e6 0.528700 0.264350 0.964427i \(-0.414843\pi\)
0.264350 + 0.964427i \(0.414843\pi\)
\(548\) 0 0
\(549\) −2.12194e6 −0.300470
\(550\) 0 0
\(551\) 6.89102e6 0.966952
\(552\) 0 0
\(553\) −1.38455e6 −0.192529
\(554\) 0 0
\(555\) 963191. 0.132733
\(556\) 0 0
\(557\) 5.12724e6 0.700238 0.350119 0.936705i \(-0.386141\pi\)
0.350119 + 0.936705i \(0.386141\pi\)
\(558\) 0 0
\(559\) −12551.2 −0.00169886
\(560\) 0 0
\(561\) −8.94241e6 −1.19963
\(562\) 0 0
\(563\) −7.94546e6 −1.05645 −0.528224 0.849105i \(-0.677142\pi\)
−0.528224 + 0.849105i \(0.677142\pi\)
\(564\) 0 0
\(565\) −1.37385e6 −0.181058
\(566\) 0 0
\(567\) −3.21779e6 −0.420340
\(568\) 0 0
\(569\) −1.76137e6 −0.228071 −0.114035 0.993477i \(-0.536378\pi\)
−0.114035 + 0.993477i \(0.536378\pi\)
\(570\) 0 0
\(571\) −286582. −0.0367840 −0.0183920 0.999831i \(-0.505855\pi\)
−0.0183920 + 0.999831i \(0.505855\pi\)
\(572\) 0 0
\(573\) −1.74963e6 −0.222618
\(574\) 0 0
\(575\) 1.83983e6 0.232064
\(576\) 0 0
\(577\) −4.12433e6 −0.515720 −0.257860 0.966182i \(-0.583017\pi\)
−0.257860 + 0.966182i \(0.583017\pi\)
\(578\) 0 0
\(579\) −1.77964e7 −2.20616
\(580\) 0 0
\(581\) 1.78624e6 0.219532
\(582\) 0 0
\(583\) 1.19543e7 1.45664
\(584\) 0 0
\(585\) −1.97068e6 −0.238082
\(586\) 0 0
\(587\) −1.43423e7 −1.71800 −0.859000 0.511975i \(-0.828914\pi\)
−0.859000 + 0.511975i \(0.828914\pi\)
\(588\) 0 0
\(589\) −1.32570e6 −0.157455
\(590\) 0 0
\(591\) 1.70825e7 2.01180
\(592\) 0 0
\(593\) −8.67127e6 −1.01262 −0.506309 0.862352i \(-0.668991\pi\)
−0.506309 + 0.862352i \(0.668991\pi\)
\(594\) 0 0
\(595\) 1.34695e6 0.155977
\(596\) 0 0
\(597\) 1.55273e7 1.78303
\(598\) 0 0
\(599\) 1.14786e7 1.30714 0.653571 0.756866i \(-0.273270\pi\)
0.653571 + 0.756866i \(0.273270\pi\)
\(600\) 0 0
\(601\) 1.21619e7 1.37346 0.686728 0.726914i \(-0.259046\pi\)
0.686728 + 0.726914i \(0.259046\pi\)
\(602\) 0 0
\(603\) 1.11865e7 1.25285
\(604\) 0 0
\(605\) 389972. 0.0433157
\(606\) 0 0
\(607\) 9.05671e6 0.997697 0.498849 0.866689i \(-0.333756\pi\)
0.498849 + 0.866689i \(0.333756\pi\)
\(608\) 0 0
\(609\) −2.51838e6 −0.275155
\(610\) 0 0
\(611\) −5.63357e6 −0.610493
\(612\) 0 0
\(613\) 5.57609e6 0.599347 0.299673 0.954042i \(-0.403122\pi\)
0.299673 + 0.954042i \(0.403122\pi\)
\(614\) 0 0
\(615\) −4.80818e6 −0.512616
\(616\) 0 0
\(617\) 1.88756e6 0.199612 0.0998062 0.995007i \(-0.468178\pi\)
0.0998062 + 0.995007i \(0.468178\pi\)
\(618\) 0 0
\(619\) −353063. −0.0370361 −0.0185181 0.999829i \(-0.505895\pi\)
−0.0185181 + 0.999829i \(0.505895\pi\)
\(620\) 0 0
\(621\) 1.96274e6 0.204237
\(622\) 0 0
\(623\) −6.48691e6 −0.669604
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 2.32528e7 2.36215
\(628\) 0 0
\(629\) −1.98660e6 −0.200209
\(630\) 0 0
\(631\) 9.14879e6 0.914724 0.457362 0.889281i \(-0.348794\pi\)
0.457362 + 0.889281i \(0.348794\pi\)
\(632\) 0 0
\(633\) −1.57368e7 −1.56102
\(634\) 0 0
\(635\) −7.82433e6 −0.770039
\(636\) 0 0
\(637\) 893880. 0.0872832
\(638\) 0 0
\(639\) −2.45823e6 −0.238161
\(640\) 0 0
\(641\) −8.33065e6 −0.800818 −0.400409 0.916336i \(-0.631132\pi\)
−0.400409 + 0.916336i \(0.631132\pi\)
\(642\) 0 0
\(643\) 8.59733e6 0.820042 0.410021 0.912076i \(-0.365521\pi\)
0.410021 + 0.912076i \(0.365521\pi\)
\(644\) 0 0
\(645\) −17972.9 −0.00170106
\(646\) 0 0
\(647\) −1.65094e7 −1.55050 −0.775248 0.631657i \(-0.782375\pi\)
−0.775248 + 0.631657i \(0.782375\pi\)
\(648\) 0 0
\(649\) 1.15358e7 1.07507
\(650\) 0 0
\(651\) 484487. 0.0448053
\(652\) 0 0
\(653\) 7.65233e6 0.702280 0.351140 0.936323i \(-0.385794\pi\)
0.351140 + 0.936323i \(0.385794\pi\)
\(654\) 0 0
\(655\) −2.82407e6 −0.257200
\(656\) 0 0
\(657\) −1.00900e6 −0.0911967
\(658\) 0 0
\(659\) −1.28219e7 −1.15011 −0.575056 0.818114i \(-0.695020\pi\)
−0.575056 + 0.818114i \(0.695020\pi\)
\(660\) 0 0
\(661\) 1.20104e7 1.06918 0.534592 0.845110i \(-0.320465\pi\)
0.534592 + 0.845110i \(0.320465\pi\)
\(662\) 0 0
\(663\) 8.72935e6 0.771255
\(664\) 0 0
\(665\) −3.50246e6 −0.307128
\(666\) 0 0
\(667\) 7.09487e6 0.617490
\(668\) 0 0
\(669\) 1.07599e7 0.929486
\(670\) 0 0
\(671\) 3.82211e6 0.327716
\(672\) 0 0
\(673\) −6.31342e6 −0.537312 −0.268656 0.963236i \(-0.586580\pi\)
−0.268656 + 0.963236i \(0.586580\pi\)
\(674\) 0 0
\(675\) 416721. 0.0352035
\(676\) 0 0
\(677\) 1.43615e6 0.120428 0.0602142 0.998185i \(-0.480822\pi\)
0.0602142 + 0.998185i \(0.480822\pi\)
\(678\) 0 0
\(679\) −4.80320e6 −0.399813
\(680\) 0 0
\(681\) −1.69240e7 −1.39841
\(682\) 0 0
\(683\) 1.90641e7 1.56374 0.781871 0.623441i \(-0.214266\pi\)
0.781871 + 0.623441i \(0.214266\pi\)
\(684\) 0 0
\(685\) 1.03394e6 0.0841913
\(686\) 0 0
\(687\) −1.13795e7 −0.919880
\(688\) 0 0
\(689\) −1.16695e7 −0.936491
\(690\) 0 0
\(691\) 1.58516e7 1.26292 0.631462 0.775407i \(-0.282455\pi\)
0.631462 + 0.775407i \(0.282455\pi\)
\(692\) 0 0
\(693\) −3.95680e6 −0.312976
\(694\) 0 0
\(695\) 9.78070e6 0.768083
\(696\) 0 0
\(697\) 9.91696e6 0.773209
\(698\) 0 0
\(699\) −3.34738e7 −2.59127
\(700\) 0 0
\(701\) 870113. 0.0668776 0.0334388 0.999441i \(-0.489354\pi\)
0.0334388 + 0.999441i \(0.489354\pi\)
\(702\) 0 0
\(703\) 5.16573e6 0.394224
\(704\) 0 0
\(705\) −8.06705e6 −0.611283
\(706\) 0 0
\(707\) 1.70880e6 0.128571
\(708\) 0 0
\(709\) 1.14645e7 0.856524 0.428262 0.903655i \(-0.359126\pi\)
0.428262 + 0.903655i \(0.359126\pi\)
\(710\) 0 0
\(711\) −5.98277e6 −0.443842
\(712\) 0 0
\(713\) −1.36492e6 −0.100550
\(714\) 0 0
\(715\) 3.54966e6 0.259670
\(716\) 0 0
\(717\) −6.78870e6 −0.493161
\(718\) 0 0
\(719\) −1.00675e7 −0.726273 −0.363137 0.931736i \(-0.618294\pi\)
−0.363137 + 0.931736i \(0.618294\pi\)
\(720\) 0 0
\(721\) −4.57068e6 −0.327448
\(722\) 0 0
\(723\) 1.53333e7 1.09091
\(724\) 0 0
\(725\) 1.50635e6 0.106434
\(726\) 0 0
\(727\) −1.42656e7 −1.00104 −0.500522 0.865724i \(-0.666858\pi\)
−0.500522 + 0.865724i \(0.666858\pi\)
\(728\) 0 0
\(729\) −1.04493e7 −0.728232
\(730\) 0 0
\(731\) 37069.5 0.00256580
\(732\) 0 0
\(733\) 7.44090e6 0.511524 0.255762 0.966740i \(-0.417674\pi\)
0.255762 + 0.966740i \(0.417674\pi\)
\(734\) 0 0
\(735\) 1.28000e6 0.0873961
\(736\) 0 0
\(737\) −2.01495e7 −1.36646
\(738\) 0 0
\(739\) −2.73511e6 −0.184231 −0.0921156 0.995748i \(-0.529363\pi\)
−0.0921156 + 0.995748i \(0.529363\pi\)
\(740\) 0 0
\(741\) −2.26988e7 −1.51865
\(742\) 0 0
\(743\) 2.09318e7 1.39102 0.695511 0.718515i \(-0.255178\pi\)
0.695511 + 0.718515i \(0.255178\pi\)
\(744\) 0 0
\(745\) 7.57634e6 0.500114
\(746\) 0 0
\(747\) 7.71847e6 0.506093
\(748\) 0 0
\(749\) 9.46009e6 0.616156
\(750\) 0 0
\(751\) −2.73024e7 −1.76645 −0.883225 0.468950i \(-0.844632\pi\)
−0.883225 + 0.468950i \(0.844632\pi\)
\(752\) 0 0
\(753\) −3.49055e7 −2.24340
\(754\) 0 0
\(755\) 2.82385e6 0.180291
\(756\) 0 0
\(757\) 1.28294e7 0.813703 0.406851 0.913494i \(-0.366627\pi\)
0.406851 + 0.913494i \(0.366627\pi\)
\(758\) 0 0
\(759\) 2.39407e7 1.50845
\(760\) 0 0
\(761\) 2.04401e7 1.27945 0.639723 0.768606i \(-0.279049\pi\)
0.639723 + 0.768606i \(0.279049\pi\)
\(762\) 0 0
\(763\) −1.70435e6 −0.105986
\(764\) 0 0
\(765\) 5.82029e6 0.359577
\(766\) 0 0
\(767\) −1.12609e7 −0.691171
\(768\) 0 0
\(769\) −1.17270e7 −0.715109 −0.357555 0.933892i \(-0.616389\pi\)
−0.357555 + 0.933892i \(0.616389\pi\)
\(770\) 0 0
\(771\) −1.52221e7 −0.922232
\(772\) 0 0
\(773\) −2.63342e7 −1.58515 −0.792576 0.609773i \(-0.791260\pi\)
−0.792576 + 0.609773i \(0.791260\pi\)
\(774\) 0 0
\(775\) −289793. −0.0173314
\(776\) 0 0
\(777\) −1.88785e6 −0.112180
\(778\) 0 0
\(779\) −2.57869e7 −1.52250
\(780\) 0 0
\(781\) 4.42786e6 0.259756
\(782\) 0 0
\(783\) 1.60699e6 0.0936715
\(784\) 0 0
\(785\) 575598. 0.0333384
\(786\) 0 0
\(787\) −32107.6 −0.00184787 −0.000923933 1.00000i \(-0.500294\pi\)
−0.000923933 1.00000i \(0.500294\pi\)
\(788\) 0 0
\(789\) 4.12587e7 2.35952
\(790\) 0 0
\(791\) 2.69274e6 0.153022
\(792\) 0 0
\(793\) −3.73105e6 −0.210692
\(794\) 0 0
\(795\) −1.67102e7 −0.937702
\(796\) 0 0
\(797\) −1.60617e7 −0.895665 −0.447832 0.894118i \(-0.647804\pi\)
−0.447832 + 0.894118i \(0.647804\pi\)
\(798\) 0 0
\(799\) 1.66385e7 0.922033
\(800\) 0 0
\(801\) −2.80305e7 −1.54365
\(802\) 0 0
\(803\) 1.81746e6 0.0994662
\(804\) 0 0
\(805\) −3.60607e6 −0.196130
\(806\) 0 0
\(807\) −2.23357e6 −0.120730
\(808\) 0 0
\(809\) 9.71020e6 0.521623 0.260812 0.965390i \(-0.416010\pi\)
0.260812 + 0.965390i \(0.416010\pi\)
\(810\) 0 0
\(811\) −2.95547e7 −1.57788 −0.788942 0.614468i \(-0.789371\pi\)
−0.788942 + 0.614468i \(0.789371\pi\)
\(812\) 0 0
\(813\) −2.32667e7 −1.23455
\(814\) 0 0
\(815\) −5.32369e6 −0.280749
\(816\) 0 0
\(817\) −96391.2 −0.00505222
\(818\) 0 0
\(819\) 3.86253e6 0.201216
\(820\) 0 0
\(821\) 3.69239e6 0.191183 0.0955915 0.995421i \(-0.469526\pi\)
0.0955915 + 0.995421i \(0.469526\pi\)
\(822\) 0 0
\(823\) −1.37549e7 −0.707878 −0.353939 0.935268i \(-0.615158\pi\)
−0.353939 + 0.935268i \(0.615158\pi\)
\(824\) 0 0
\(825\) 5.08298e6 0.260006
\(826\) 0 0
\(827\) 4.94189e6 0.251263 0.125632 0.992077i \(-0.459904\pi\)
0.125632 + 0.992077i \(0.459904\pi\)
\(828\) 0 0
\(829\) −3.72295e7 −1.88149 −0.940743 0.339119i \(-0.889871\pi\)
−0.940743 + 0.339119i \(0.889871\pi\)
\(830\) 0 0
\(831\) −7.01099e6 −0.352190
\(832\) 0 0
\(833\) −2.64003e6 −0.131825
\(834\) 0 0
\(835\) 1.27383e7 0.632260
\(836\) 0 0
\(837\) −309153. −0.0152532
\(838\) 0 0
\(839\) −1.90655e7 −0.935066 −0.467533 0.883976i \(-0.654857\pi\)
−0.467533 + 0.883976i \(0.654857\pi\)
\(840\) 0 0
\(841\) −1.47023e7 −0.716794
\(842\) 0 0
\(843\) 796667. 0.0386107
\(844\) 0 0
\(845\) 5.81724e6 0.280269
\(846\) 0 0
\(847\) −764345. −0.0366084
\(848\) 0 0
\(849\) 3.84473e7 1.83061
\(850\) 0 0
\(851\) 5.31854e6 0.251749
\(852\) 0 0
\(853\) −2.09785e7 −0.987193 −0.493596 0.869691i \(-0.664318\pi\)
−0.493596 + 0.869691i \(0.664318\pi\)
\(854\) 0 0
\(855\) −1.51344e7 −0.708028
\(856\) 0 0
\(857\) −2.97938e7 −1.38571 −0.692857 0.721075i \(-0.743648\pi\)
−0.692857 + 0.721075i \(0.743648\pi\)
\(858\) 0 0
\(859\) 1.86748e6 0.0863520 0.0431760 0.999067i \(-0.486252\pi\)
0.0431760 + 0.999067i \(0.486252\pi\)
\(860\) 0 0
\(861\) 9.42402e6 0.433240
\(862\) 0 0
\(863\) 2.28328e7 1.04359 0.521797 0.853070i \(-0.325262\pi\)
0.521797 + 0.853070i \(0.325262\pi\)
\(864\) 0 0
\(865\) −6.29934e6 −0.286256
\(866\) 0 0
\(867\) 4.49601e6 0.203132
\(868\) 0 0
\(869\) 1.07764e7 0.484088
\(870\) 0 0
\(871\) 1.96694e7 0.878508
\(872\) 0 0
\(873\) −2.07550e7 −0.921696
\(874\) 0 0
\(875\) −765625. −0.0338062
\(876\) 0 0
\(877\) −4.10654e7 −1.80292 −0.901462 0.432858i \(-0.857505\pi\)
−0.901462 + 0.432858i \(0.857505\pi\)
\(878\) 0 0
\(879\) 3.34787e7 1.46149
\(880\) 0 0
\(881\) −3.94268e7 −1.71140 −0.855700 0.517472i \(-0.826873\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(882\) 0 0
\(883\) 1.49358e7 0.644654 0.322327 0.946628i \(-0.395535\pi\)
0.322327 + 0.946628i \(0.395535\pi\)
\(884\) 0 0
\(885\) −1.61252e7 −0.692065
\(886\) 0 0
\(887\) −2.44515e7 −1.04351 −0.521754 0.853096i \(-0.674722\pi\)
−0.521754 + 0.853096i \(0.674722\pi\)
\(888\) 0 0
\(889\) 1.53357e7 0.650802
\(890\) 0 0
\(891\) 2.50451e7 1.05689
\(892\) 0 0
\(893\) −4.32647e7 −1.81554
\(894\) 0 0
\(895\) 4.68115e6 0.195342
\(896\) 0 0
\(897\) −2.33702e7 −0.969800
\(898\) 0 0
\(899\) −1.11752e6 −0.0461164
\(900\) 0 0
\(901\) 3.44652e7 1.41439
\(902\) 0 0
\(903\) 35226.9 0.00143766
\(904\) 0 0
\(905\) 1.36763e7 0.555070
\(906\) 0 0
\(907\) 2.77487e7 1.12002 0.560009 0.828487i \(-0.310798\pi\)
0.560009 + 0.828487i \(0.310798\pi\)
\(908\) 0 0
\(909\) 7.38386e6 0.296397
\(910\) 0 0
\(911\) −1.04000e6 −0.0415181 −0.0207591 0.999785i \(-0.506608\pi\)
−0.0207591 + 0.999785i \(0.506608\pi\)
\(912\) 0 0
\(913\) −1.39028e7 −0.551984
\(914\) 0 0
\(915\) −5.34271e6 −0.210964
\(916\) 0 0
\(917\) 5.53517e6 0.217374
\(918\) 0 0
\(919\) 2.58322e7 1.00896 0.504479 0.863424i \(-0.331685\pi\)
0.504479 + 0.863424i \(0.331685\pi\)
\(920\) 0 0
\(921\) 4.84392e7 1.88169
\(922\) 0 0
\(923\) −4.32236e6 −0.167000
\(924\) 0 0
\(925\) 1.12921e6 0.0433930
\(926\) 0 0
\(927\) −1.97503e7 −0.754872
\(928\) 0 0
\(929\) 1.92846e7 0.733114 0.366557 0.930396i \(-0.380536\pi\)
0.366557 + 0.930396i \(0.380536\pi\)
\(930\) 0 0
\(931\) 6.86483e6 0.259571
\(932\) 0 0
\(933\) 5.78628e7 2.17618
\(934\) 0 0
\(935\) −1.04837e7 −0.392182
\(936\) 0 0
\(937\) 8.79237e6 0.327158 0.163579 0.986530i \(-0.447696\pi\)
0.163579 + 0.986530i \(0.447696\pi\)
\(938\) 0 0
\(939\) 6.47299e7 2.39575
\(940\) 0 0
\(941\) 5.04584e7 1.85763 0.928816 0.370542i \(-0.120828\pi\)
0.928816 + 0.370542i \(0.120828\pi\)
\(942\) 0 0
\(943\) −2.65497e7 −0.972257
\(944\) 0 0
\(945\) −816773. −0.0297524
\(946\) 0 0
\(947\) −6.48456e6 −0.234966 −0.117483 0.993075i \(-0.537483\pi\)
−0.117483 + 0.993075i \(0.537483\pi\)
\(948\) 0 0
\(949\) −1.77415e6 −0.0639478
\(950\) 0 0
\(951\) −1.39821e7 −0.501327
\(952\) 0 0
\(953\) −1.67568e7 −0.597666 −0.298833 0.954305i \(-0.596597\pi\)
−0.298833 + 0.954305i \(0.596597\pi\)
\(954\) 0 0
\(955\) −2.05121e6 −0.0727781
\(956\) 0 0
\(957\) 1.96013e7 0.691838
\(958\) 0 0
\(959\) −2.02651e6 −0.0711546
\(960\) 0 0
\(961\) −2.84142e7 −0.992491
\(962\) 0 0
\(963\) 4.08778e7 1.42044
\(964\) 0 0
\(965\) −2.08639e7 −0.721234
\(966\) 0 0
\(967\) 1.12777e7 0.387843 0.193921 0.981017i \(-0.437879\pi\)
0.193921 + 0.981017i \(0.437879\pi\)
\(968\) 0 0
\(969\) 6.70397e7 2.29363
\(970\) 0 0
\(971\) −2.36109e7 −0.803644 −0.401822 0.915718i \(-0.631623\pi\)
−0.401822 + 0.915718i \(0.631623\pi\)
\(972\) 0 0
\(973\) −1.91702e7 −0.649149
\(974\) 0 0
\(975\) −4.96187e6 −0.167160
\(976\) 0 0
\(977\) −4.36268e7 −1.46223 −0.731117 0.682252i \(-0.761001\pi\)
−0.731117 + 0.682252i \(0.761001\pi\)
\(978\) 0 0
\(979\) 5.04896e7 1.68362
\(980\) 0 0
\(981\) −7.36463e6 −0.244331
\(982\) 0 0
\(983\) −1.23492e7 −0.407618 −0.203809 0.979011i \(-0.565332\pi\)
−0.203809 + 0.979011i \(0.565332\pi\)
\(984\) 0 0
\(985\) 2.00269e7 0.657694
\(986\) 0 0
\(987\) 1.58114e7 0.516628
\(988\) 0 0
\(989\) −99242.6 −0.00322632
\(990\) 0 0
\(991\) 5.32915e7 1.72375 0.861874 0.507122i \(-0.169291\pi\)
0.861874 + 0.507122i \(0.169291\pi\)
\(992\) 0 0
\(993\) 8.04128e7 2.58793
\(994\) 0 0
\(995\) 1.82036e7 0.582907
\(996\) 0 0
\(997\) 6.43068e6 0.204889 0.102445 0.994739i \(-0.467334\pi\)
0.102445 + 0.994739i \(0.467334\pi\)
\(998\) 0 0
\(999\) 1.20465e6 0.0381897
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 280.6.a.e.1.1 3
4.3 odd 2 560.6.a.s.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.e.1.1 3 1.1 even 1 trivial
560.6.a.s.1.3 3 4.3 odd 2