Properties

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

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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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{3} +25.0000 q^{5} +62.0000 q^{7} -239.000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} +25.0000 q^{5} +62.0000 q^{7} -239.000 q^{9} -144.000 q^{11} +654.000 q^{13} -50.0000 q^{15} -1190.00 q^{17} +556.000 q^{19} -124.000 q^{21} -2182.00 q^{23} +625.000 q^{25} +964.000 q^{27} +1578.00 q^{29} -9660.00 q^{31} +288.000 q^{33} +1550.00 q^{35} +3534.00 q^{37} -1308.00 q^{39} +7462.00 q^{41} -7114.00 q^{43} -5975.00 q^{45} +28294.0 q^{47} -12963.0 q^{49} +2380.00 q^{51} +13046.0 q^{53} -3600.00 q^{55} -1112.00 q^{57} -37092.0 q^{59} -39570.0 q^{61} -14818.0 q^{63} +16350.0 q^{65} -56734.0 q^{67} +4364.00 q^{69} -45588.0 q^{71} +11842.0 q^{73} -1250.00 q^{75} -8928.00 q^{77} -94216.0 q^{79} +56149.0 q^{81} -31482.0 q^{83} -29750.0 q^{85} -3156.00 q^{87} -94054.0 q^{89} +40548.0 q^{91} +19320.0 q^{93} +13900.0 q^{95} +23714.0 q^{97} +34416.0 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −0.128300 −0.0641500 0.997940i \(-0.520434\pi\)
−0.0641500 + 0.997940i \(0.520434\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 62.0000 0.478241 0.239120 0.970990i \(-0.423141\pi\)
0.239120 + 0.970990i \(0.423141\pi\)
\(8\) 0 0
\(9\) −239.000 −0.983539
\(10\) 0 0
\(11\) −144.000 −0.358823 −0.179412 0.983774i \(-0.557419\pi\)
−0.179412 + 0.983774i \(0.557419\pi\)
\(12\) 0 0
\(13\) 654.000 1.07330 0.536648 0.843806i \(-0.319690\pi\)
0.536648 + 0.843806i \(0.319690\pi\)
\(14\) 0 0
\(15\) −50.0000 −0.0573775
\(16\) 0 0
\(17\) −1190.00 −0.998676 −0.499338 0.866407i \(-0.666423\pi\)
−0.499338 + 0.866407i \(0.666423\pi\)
\(18\) 0 0
\(19\) 556.000 0.353338 0.176669 0.984270i \(-0.443468\pi\)
0.176669 + 0.984270i \(0.443468\pi\)
\(20\) 0 0
\(21\) −124.000 −0.0613583
\(22\) 0 0
\(23\) −2182.00 −0.860073 −0.430036 0.902812i \(-0.641499\pi\)
−0.430036 + 0.902812i \(0.641499\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 964.000 0.254488
\(28\) 0 0
\(29\) 1578.00 0.348427 0.174214 0.984708i \(-0.444262\pi\)
0.174214 + 0.984708i \(0.444262\pi\)
\(30\) 0 0
\(31\) −9660.00 −1.80540 −0.902699 0.430273i \(-0.858417\pi\)
−0.902699 + 0.430273i \(0.858417\pi\)
\(32\) 0 0
\(33\) 288.000 0.0460371
\(34\) 0 0
\(35\) 1550.00 0.213876
\(36\) 0 0
\(37\) 3534.00 0.424387 0.212194 0.977228i \(-0.431939\pi\)
0.212194 + 0.977228i \(0.431939\pi\)
\(38\) 0 0
\(39\) −1308.00 −0.137704
\(40\) 0 0
\(41\) 7462.00 0.693259 0.346630 0.938002i \(-0.387326\pi\)
0.346630 + 0.938002i \(0.387326\pi\)
\(42\) 0 0
\(43\) −7114.00 −0.586736 −0.293368 0.956000i \(-0.594776\pi\)
−0.293368 + 0.956000i \(0.594776\pi\)
\(44\) 0 0
\(45\) −5975.00 −0.439852
\(46\) 0 0
\(47\) 28294.0 1.86831 0.934157 0.356863i \(-0.116154\pi\)
0.934157 + 0.356863i \(0.116154\pi\)
\(48\) 0 0
\(49\) −12963.0 −0.771286
\(50\) 0 0
\(51\) 2380.00 0.128130
\(52\) 0 0
\(53\) 13046.0 0.637952 0.318976 0.947763i \(-0.396661\pi\)
0.318976 + 0.947763i \(0.396661\pi\)
\(54\) 0 0
\(55\) −3600.00 −0.160471
\(56\) 0 0
\(57\) −1112.00 −0.0453333
\(58\) 0 0
\(59\) −37092.0 −1.38724 −0.693618 0.720343i \(-0.743984\pi\)
−0.693618 + 0.720343i \(0.743984\pi\)
\(60\) 0 0
\(61\) −39570.0 −1.36157 −0.680787 0.732481i \(-0.738362\pi\)
−0.680787 + 0.732481i \(0.738362\pi\)
\(62\) 0 0
\(63\) −14818.0 −0.470368
\(64\) 0 0
\(65\) 16350.0 0.479992
\(66\) 0 0
\(67\) −56734.0 −1.54403 −0.772016 0.635603i \(-0.780752\pi\)
−0.772016 + 0.635603i \(0.780752\pi\)
\(68\) 0 0
\(69\) 4364.00 0.110347
\(70\) 0 0
\(71\) −45588.0 −1.07326 −0.536630 0.843818i \(-0.680303\pi\)
−0.536630 + 0.843818i \(0.680303\pi\)
\(72\) 0 0
\(73\) 11842.0 0.260087 0.130043 0.991508i \(-0.458488\pi\)
0.130043 + 0.991508i \(0.458488\pi\)
\(74\) 0 0
\(75\) −1250.00 −0.0256600
\(76\) 0 0
\(77\) −8928.00 −0.171604
\(78\) 0 0
\(79\) −94216.0 −1.69847 −0.849233 0.528018i \(-0.822935\pi\)
−0.849233 + 0.528018i \(0.822935\pi\)
\(80\) 0 0
\(81\) 56149.0 0.950888
\(82\) 0 0
\(83\) −31482.0 −0.501611 −0.250806 0.968037i \(-0.580695\pi\)
−0.250806 + 0.968037i \(0.580695\pi\)
\(84\) 0 0
\(85\) −29750.0 −0.446622
\(86\) 0 0
\(87\) −3156.00 −0.0447032
\(88\) 0 0
\(89\) −94054.0 −1.25864 −0.629321 0.777145i \(-0.716667\pi\)
−0.629321 + 0.777145i \(0.716667\pi\)
\(90\) 0 0
\(91\) 40548.0 0.513294
\(92\) 0 0
\(93\) 19320.0 0.231633
\(94\) 0 0
\(95\) 13900.0 0.158018
\(96\) 0 0
\(97\) 23714.0 0.255903 0.127952 0.991780i \(-0.459160\pi\)
0.127952 + 0.991780i \(0.459160\pi\)
\(98\) 0 0
\(99\) 34416.0 0.352917
\(100\) 0 0
\(101\) 129674. 1.26488 0.632440 0.774609i \(-0.282053\pi\)
0.632440 + 0.774609i \(0.282053\pi\)
\(102\) 0 0
\(103\) −136846. −1.27098 −0.635490 0.772109i \(-0.719202\pi\)
−0.635490 + 0.772109i \(0.719202\pi\)
\(104\) 0 0
\(105\) −3100.00 −0.0274403
\(106\) 0 0
\(107\) −193190. −1.63127 −0.815634 0.578569i \(-0.803612\pi\)
−0.815634 + 0.578569i \(0.803612\pi\)
\(108\) 0 0
\(109\) 120046. 0.967791 0.483895 0.875126i \(-0.339222\pi\)
0.483895 + 0.875126i \(0.339222\pi\)
\(110\) 0 0
\(111\) −7068.00 −0.0544489
\(112\) 0 0
\(113\) −152646. −1.12458 −0.562289 0.826941i \(-0.690079\pi\)
−0.562289 + 0.826941i \(0.690079\pi\)
\(114\) 0 0
\(115\) −54550.0 −0.384636
\(116\) 0 0
\(117\) −156306. −1.05563
\(118\) 0 0
\(119\) −73780.0 −0.477608
\(120\) 0 0
\(121\) −140315. −0.871246
\(122\) 0 0
\(123\) −14924.0 −0.0889452
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −107906. −0.593658 −0.296829 0.954931i \(-0.595929\pi\)
−0.296829 + 0.954931i \(0.595929\pi\)
\(128\) 0 0
\(129\) 14228.0 0.0752783
\(130\) 0 0
\(131\) −233072. −1.18662 −0.593310 0.804974i \(-0.702179\pi\)
−0.593310 + 0.804974i \(0.702179\pi\)
\(132\) 0 0
\(133\) 34472.0 0.168981
\(134\) 0 0
\(135\) 24100.0 0.113811
\(136\) 0 0
\(137\) 356082. 1.62087 0.810436 0.585827i \(-0.199230\pi\)
0.810436 + 0.585827i \(0.199230\pi\)
\(138\) 0 0
\(139\) 312204. 1.37057 0.685285 0.728275i \(-0.259677\pi\)
0.685285 + 0.728275i \(0.259677\pi\)
\(140\) 0 0
\(141\) −56588.0 −0.239705
\(142\) 0 0
\(143\) −94176.0 −0.385124
\(144\) 0 0
\(145\) 39450.0 0.155821
\(146\) 0 0
\(147\) 25926.0 0.0989560
\(148\) 0 0
\(149\) −27498.0 −0.101469 −0.0507347 0.998712i \(-0.516156\pi\)
−0.0507347 + 0.998712i \(0.516156\pi\)
\(150\) 0 0
\(151\) 136908. 0.488637 0.244319 0.969695i \(-0.421436\pi\)
0.244319 + 0.969695i \(0.421436\pi\)
\(152\) 0 0
\(153\) 284410. 0.982237
\(154\) 0 0
\(155\) −241500. −0.807398
\(156\) 0 0
\(157\) −406714. −1.31686 −0.658431 0.752641i \(-0.728779\pi\)
−0.658431 + 0.752641i \(0.728779\pi\)
\(158\) 0 0
\(159\) −26092.0 −0.0818492
\(160\) 0 0
\(161\) −135284. −0.411322
\(162\) 0 0
\(163\) −13642.0 −0.0402169 −0.0201085 0.999798i \(-0.506401\pi\)
−0.0201085 + 0.999798i \(0.506401\pi\)
\(164\) 0 0
\(165\) 7200.00 0.0205884
\(166\) 0 0
\(167\) 203438. 0.564470 0.282235 0.959345i \(-0.408924\pi\)
0.282235 + 0.959345i \(0.408924\pi\)
\(168\) 0 0
\(169\) 56423.0 0.151964
\(170\) 0 0
\(171\) −132884. −0.347522
\(172\) 0 0
\(173\) −127242. −0.323233 −0.161616 0.986854i \(-0.551671\pi\)
−0.161616 + 0.986854i \(0.551671\pi\)
\(174\) 0 0
\(175\) 38750.0 0.0956482
\(176\) 0 0
\(177\) 74184.0 0.177982
\(178\) 0 0
\(179\) −94684.0 −0.220874 −0.110437 0.993883i \(-0.535225\pi\)
−0.110437 + 0.993883i \(0.535225\pi\)
\(180\) 0 0
\(181\) 517018. 1.17303 0.586515 0.809938i \(-0.300499\pi\)
0.586515 + 0.809938i \(0.300499\pi\)
\(182\) 0 0
\(183\) 79140.0 0.174690
\(184\) 0 0
\(185\) 88350.0 0.189792
\(186\) 0 0
\(187\) 171360. 0.358348
\(188\) 0 0
\(189\) 59768.0 0.121707
\(190\) 0 0
\(191\) 412300. 0.817768 0.408884 0.912586i \(-0.365918\pi\)
0.408884 + 0.912586i \(0.365918\pi\)
\(192\) 0 0
\(193\) −771654. −1.49118 −0.745589 0.666406i \(-0.767832\pi\)
−0.745589 + 0.666406i \(0.767832\pi\)
\(194\) 0 0
\(195\) −32700.0 −0.0615831
\(196\) 0 0
\(197\) 190238. 0.349246 0.174623 0.984635i \(-0.444129\pi\)
0.174623 + 0.984635i \(0.444129\pi\)
\(198\) 0 0
\(199\) −132072. −0.236417 −0.118208 0.992989i \(-0.537715\pi\)
−0.118208 + 0.992989i \(0.537715\pi\)
\(200\) 0 0
\(201\) 113468. 0.198099
\(202\) 0 0
\(203\) 97836.0 0.166632
\(204\) 0 0
\(205\) 186550. 0.310035
\(206\) 0 0
\(207\) 521498. 0.845915
\(208\) 0 0
\(209\) −80064.0 −0.126786
\(210\) 0 0
\(211\) 928704. 1.43606 0.718028 0.696015i \(-0.245045\pi\)
0.718028 + 0.696015i \(0.245045\pi\)
\(212\) 0 0
\(213\) 91176.0 0.137699
\(214\) 0 0
\(215\) −177850. −0.262396
\(216\) 0 0
\(217\) −598920. −0.863415
\(218\) 0 0
\(219\) −23684.0 −0.0333691
\(220\) 0 0
\(221\) −778260. −1.07187
\(222\) 0 0
\(223\) −421494. −0.567583 −0.283791 0.958886i \(-0.591592\pi\)
−0.283791 + 0.958886i \(0.591592\pi\)
\(224\) 0 0
\(225\) −149375. −0.196708
\(226\) 0 0
\(227\) 991962. 1.27770 0.638852 0.769329i \(-0.279410\pi\)
0.638852 + 0.769329i \(0.279410\pi\)
\(228\) 0 0
\(229\) 266946. 0.336384 0.168192 0.985754i \(-0.446207\pi\)
0.168192 + 0.985754i \(0.446207\pi\)
\(230\) 0 0
\(231\) 17856.0 0.0220168
\(232\) 0 0
\(233\) 960314. 1.15884 0.579420 0.815029i \(-0.303279\pi\)
0.579420 + 0.815029i \(0.303279\pi\)
\(234\) 0 0
\(235\) 707350. 0.835535
\(236\) 0 0
\(237\) 188432. 0.217913
\(238\) 0 0
\(239\) 492696. 0.557936 0.278968 0.960300i \(-0.410008\pi\)
0.278968 + 0.960300i \(0.410008\pi\)
\(240\) 0 0
\(241\) 56078.0 0.0621942 0.0310971 0.999516i \(-0.490100\pi\)
0.0310971 + 0.999516i \(0.490100\pi\)
\(242\) 0 0
\(243\) −346550. −0.376487
\(244\) 0 0
\(245\) −324075. −0.344929
\(246\) 0 0
\(247\) 363624. 0.379237
\(248\) 0 0
\(249\) 62964.0 0.0643567
\(250\) 0 0
\(251\) 1.96792e6 1.97162 0.985810 0.167866i \(-0.0536876\pi\)
0.985810 + 0.167866i \(0.0536876\pi\)
\(252\) 0 0
\(253\) 314208. 0.308614
\(254\) 0 0
\(255\) 59500.0 0.0573016
\(256\) 0 0
\(257\) −971910. −0.917896 −0.458948 0.888463i \(-0.651773\pi\)
−0.458948 + 0.888463i \(0.651773\pi\)
\(258\) 0 0
\(259\) 219108. 0.202959
\(260\) 0 0
\(261\) −377142. −0.342692
\(262\) 0 0
\(263\) 154770. 0.137974 0.0689870 0.997618i \(-0.478023\pi\)
0.0689870 + 0.997618i \(0.478023\pi\)
\(264\) 0 0
\(265\) 326150. 0.285301
\(266\) 0 0
\(267\) 188108. 0.161484
\(268\) 0 0
\(269\) −1.02371e6 −0.862577 −0.431289 0.902214i \(-0.641941\pi\)
−0.431289 + 0.902214i \(0.641941\pi\)
\(270\) 0 0
\(271\) 1.14776e6 0.949350 0.474675 0.880161i \(-0.342566\pi\)
0.474675 + 0.880161i \(0.342566\pi\)
\(272\) 0 0
\(273\) −81096.0 −0.0658556
\(274\) 0 0
\(275\) −90000.0 −0.0717647
\(276\) 0 0
\(277\) 2.49676e6 1.95514 0.977568 0.210619i \(-0.0675481\pi\)
0.977568 + 0.210619i \(0.0675481\pi\)
\(278\) 0 0
\(279\) 2.30874e6 1.77568
\(280\) 0 0
\(281\) 1.69540e6 1.28087 0.640436 0.768011i \(-0.278754\pi\)
0.640436 + 0.768011i \(0.278754\pi\)
\(282\) 0 0
\(283\) −2.12395e6 −1.57645 −0.788223 0.615390i \(-0.788999\pi\)
−0.788223 + 0.615390i \(0.788999\pi\)
\(284\) 0 0
\(285\) −27800.0 −0.0202737
\(286\) 0 0
\(287\) 462644. 0.331545
\(288\) 0 0
\(289\) −3757.00 −0.00264604
\(290\) 0 0
\(291\) −47428.0 −0.0328324
\(292\) 0 0
\(293\) −992722. −0.675552 −0.337776 0.941227i \(-0.609675\pi\)
−0.337776 + 0.941227i \(0.609675\pi\)
\(294\) 0 0
\(295\) −927300. −0.620391
\(296\) 0 0
\(297\) −138816. −0.0913163
\(298\) 0 0
\(299\) −1.42703e6 −0.923112
\(300\) 0 0
\(301\) −441068. −0.280601
\(302\) 0 0
\(303\) −259348. −0.162284
\(304\) 0 0
\(305\) −989250. −0.608915
\(306\) 0 0
\(307\) 487522. 0.295222 0.147611 0.989046i \(-0.452842\pi\)
0.147611 + 0.989046i \(0.452842\pi\)
\(308\) 0 0
\(309\) 273692. 0.163067
\(310\) 0 0
\(311\) 444116. 0.260373 0.130186 0.991490i \(-0.458442\pi\)
0.130186 + 0.991490i \(0.458442\pi\)
\(312\) 0 0
\(313\) 47242.0 0.0272563 0.0136282 0.999907i \(-0.495662\pi\)
0.0136282 + 0.999907i \(0.495662\pi\)
\(314\) 0 0
\(315\) −370450. −0.210355
\(316\) 0 0
\(317\) −694058. −0.387925 −0.193962 0.981009i \(-0.562134\pi\)
−0.193962 + 0.981009i \(0.562134\pi\)
\(318\) 0 0
\(319\) −227232. −0.125024
\(320\) 0 0
\(321\) 386380. 0.209292
\(322\) 0 0
\(323\) −661640. −0.352871
\(324\) 0 0
\(325\) 408750. 0.214659
\(326\) 0 0
\(327\) −240092. −0.124168
\(328\) 0 0
\(329\) 1.75423e6 0.893504
\(330\) 0 0
\(331\) 82168.0 0.0412223 0.0206112 0.999788i \(-0.493439\pi\)
0.0206112 + 0.999788i \(0.493439\pi\)
\(332\) 0 0
\(333\) −844626. −0.417401
\(334\) 0 0
\(335\) −1.41835e6 −0.690512
\(336\) 0 0
\(337\) −727934. −0.349154 −0.174577 0.984644i \(-0.555856\pi\)
−0.174577 + 0.984644i \(0.555856\pi\)
\(338\) 0 0
\(339\) 305292. 0.144283
\(340\) 0 0
\(341\) 1.39104e6 0.647819
\(342\) 0 0
\(343\) −1.84574e6 −0.847101
\(344\) 0 0
\(345\) 109100. 0.0493488
\(346\) 0 0
\(347\) 2.02298e6 0.901919 0.450959 0.892544i \(-0.351082\pi\)
0.450959 + 0.892544i \(0.351082\pi\)
\(348\) 0 0
\(349\) −4.40858e6 −1.93747 −0.968736 0.248095i \(-0.920196\pi\)
−0.968736 + 0.248095i \(0.920196\pi\)
\(350\) 0 0
\(351\) 630456. 0.273141
\(352\) 0 0
\(353\) 1.06965e6 0.456883 0.228441 0.973558i \(-0.426637\pi\)
0.228441 + 0.973558i \(0.426637\pi\)
\(354\) 0 0
\(355\) −1.13970e6 −0.479976
\(356\) 0 0
\(357\) 147560. 0.0612771
\(358\) 0 0
\(359\) 32968.0 0.0135007 0.00675035 0.999977i \(-0.497851\pi\)
0.00675035 + 0.999977i \(0.497851\pi\)
\(360\) 0 0
\(361\) −2.16696e6 −0.875152
\(362\) 0 0
\(363\) 280630. 0.111781
\(364\) 0 0
\(365\) 296050. 0.116314
\(366\) 0 0
\(367\) −3.64081e6 −1.41102 −0.705509 0.708700i \(-0.749282\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) 0 0
\(369\) −1.78342e6 −0.681847
\(370\) 0 0
\(371\) 808852. 0.305094
\(372\) 0 0
\(373\) 3.17311e6 1.18090 0.590450 0.807074i \(-0.298950\pi\)
0.590450 + 0.807074i \(0.298950\pi\)
\(374\) 0 0
\(375\) −31250.0 −0.0114755
\(376\) 0 0
\(377\) 1.03201e6 0.373965
\(378\) 0 0
\(379\) 1.60498e6 0.573947 0.286973 0.957939i \(-0.407351\pi\)
0.286973 + 0.957939i \(0.407351\pi\)
\(380\) 0 0
\(381\) 215812. 0.0761664
\(382\) 0 0
\(383\) −1.98925e6 −0.692936 −0.346468 0.938062i \(-0.612619\pi\)
−0.346468 + 0.938062i \(0.612619\pi\)
\(384\) 0 0
\(385\) −223200. −0.0767436
\(386\) 0 0
\(387\) 1.70025e6 0.577078
\(388\) 0 0
\(389\) 5.16495e6 1.73058 0.865291 0.501270i \(-0.167134\pi\)
0.865291 + 0.501270i \(0.167134\pi\)
\(390\) 0 0
\(391\) 2.59658e6 0.858934
\(392\) 0 0
\(393\) 466144. 0.152243
\(394\) 0 0
\(395\) −2.35540e6 −0.759577
\(396\) 0 0
\(397\) −937586. −0.298562 −0.149281 0.988795i \(-0.547696\pi\)
−0.149281 + 0.988795i \(0.547696\pi\)
\(398\) 0 0
\(399\) −68944.0 −0.0216802
\(400\) 0 0
\(401\) −5.63657e6 −1.75047 −0.875234 0.483699i \(-0.839293\pi\)
−0.875234 + 0.483699i \(0.839293\pi\)
\(402\) 0 0
\(403\) −6.31764e6 −1.93773
\(404\) 0 0
\(405\) 1.40373e6 0.425250
\(406\) 0 0
\(407\) −508896. −0.152280
\(408\) 0 0
\(409\) 4.06137e6 1.20051 0.600254 0.799810i \(-0.295066\pi\)
0.600254 + 0.799810i \(0.295066\pi\)
\(410\) 0 0
\(411\) −712164. −0.207958
\(412\) 0 0
\(413\) −2.29970e6 −0.663433
\(414\) 0 0
\(415\) −787050. −0.224327
\(416\) 0 0
\(417\) −624408. −0.175844
\(418\) 0 0
\(419\) −976108. −0.271621 −0.135810 0.990735i \(-0.543364\pi\)
−0.135810 + 0.990735i \(0.543364\pi\)
\(420\) 0 0
\(421\) 1.62706e6 0.447403 0.223701 0.974658i \(-0.428186\pi\)
0.223701 + 0.974658i \(0.428186\pi\)
\(422\) 0 0
\(423\) −6.76227e6 −1.83756
\(424\) 0 0
\(425\) −743750. −0.199735
\(426\) 0 0
\(427\) −2.45334e6 −0.651161
\(428\) 0 0
\(429\) 188352. 0.0494114
\(430\) 0 0
\(431\) 4.27900e6 1.10956 0.554778 0.831998i \(-0.312803\pi\)
0.554778 + 0.831998i \(0.312803\pi\)
\(432\) 0 0
\(433\) −3.20195e6 −0.820720 −0.410360 0.911924i \(-0.634597\pi\)
−0.410360 + 0.911924i \(0.634597\pi\)
\(434\) 0 0
\(435\) −78900.0 −0.0199919
\(436\) 0 0
\(437\) −1.21319e6 −0.303897
\(438\) 0 0
\(439\) −5.09246e6 −1.26115 −0.630574 0.776129i \(-0.717180\pi\)
−0.630574 + 0.776129i \(0.717180\pi\)
\(440\) 0 0
\(441\) 3.09816e6 0.758590
\(442\) 0 0
\(443\) −5.43551e6 −1.31593 −0.657963 0.753050i \(-0.728582\pi\)
−0.657963 + 0.753050i \(0.728582\pi\)
\(444\) 0 0
\(445\) −2.35135e6 −0.562882
\(446\) 0 0
\(447\) 54996.0 0.0130185
\(448\) 0 0
\(449\) −2.99007e6 −0.699948 −0.349974 0.936759i \(-0.613810\pi\)
−0.349974 + 0.936759i \(0.613810\pi\)
\(450\) 0 0
\(451\) −1.07453e6 −0.248758
\(452\) 0 0
\(453\) −273816. −0.0626922
\(454\) 0 0
\(455\) 1.01370e6 0.229552
\(456\) 0 0
\(457\) 8.01759e6 1.79578 0.897891 0.440218i \(-0.145099\pi\)
0.897891 + 0.440218i \(0.145099\pi\)
\(458\) 0 0
\(459\) −1.14716e6 −0.254151
\(460\) 0 0
\(461\) −2.58462e6 −0.566428 −0.283214 0.959057i \(-0.591401\pi\)
−0.283214 + 0.959057i \(0.591401\pi\)
\(462\) 0 0
\(463\) −6.14261e6 −1.33168 −0.665840 0.746094i \(-0.731927\pi\)
−0.665840 + 0.746094i \(0.731927\pi\)
\(464\) 0 0
\(465\) 483000. 0.103589
\(466\) 0 0
\(467\) −1.59270e6 −0.337942 −0.168971 0.985621i \(-0.554044\pi\)
−0.168971 + 0.985621i \(0.554044\pi\)
\(468\) 0 0
\(469\) −3.51751e6 −0.738419
\(470\) 0 0
\(471\) 813428. 0.168953
\(472\) 0 0
\(473\) 1.02442e6 0.210535
\(474\) 0 0
\(475\) 347500. 0.0706677
\(476\) 0 0
\(477\) −3.11799e6 −0.627450
\(478\) 0 0
\(479\) −863592. −0.171977 −0.0859884 0.996296i \(-0.527405\pi\)
−0.0859884 + 0.996296i \(0.527405\pi\)
\(480\) 0 0
\(481\) 2.31124e6 0.455493
\(482\) 0 0
\(483\) 270568. 0.0527726
\(484\) 0 0
\(485\) 592850. 0.114443
\(486\) 0 0
\(487\) 8.20714e6 1.56808 0.784042 0.620707i \(-0.213154\pi\)
0.784042 + 0.620707i \(0.213154\pi\)
\(488\) 0 0
\(489\) 27284.0 0.00515984
\(490\) 0 0
\(491\) 8.93394e6 1.67240 0.836198 0.548428i \(-0.184773\pi\)
0.836198 + 0.548428i \(0.184773\pi\)
\(492\) 0 0
\(493\) −1.87782e6 −0.347966
\(494\) 0 0
\(495\) 860400. 0.157829
\(496\) 0 0
\(497\) −2.82646e6 −0.513276
\(498\) 0 0
\(499\) 1.11960e6 0.201284 0.100642 0.994923i \(-0.467910\pi\)
0.100642 + 0.994923i \(0.467910\pi\)
\(500\) 0 0
\(501\) −406876. −0.0724215
\(502\) 0 0
\(503\) −3.68177e6 −0.648839 −0.324420 0.945913i \(-0.605169\pi\)
−0.324420 + 0.945913i \(0.605169\pi\)
\(504\) 0 0
\(505\) 3.24185e6 0.565672
\(506\) 0 0
\(507\) −112846. −0.0194969
\(508\) 0 0
\(509\) 6.73483e6 1.15221 0.576105 0.817375i \(-0.304572\pi\)
0.576105 + 0.817375i \(0.304572\pi\)
\(510\) 0 0
\(511\) 734204. 0.124384
\(512\) 0 0
\(513\) 535984. 0.0899204
\(514\) 0 0
\(515\) −3.42115e6 −0.568400
\(516\) 0 0
\(517\) −4.07434e6 −0.670395
\(518\) 0 0
\(519\) 254484. 0.0414708
\(520\) 0 0
\(521\) 441370. 0.0712375 0.0356187 0.999365i \(-0.488660\pi\)
0.0356187 + 0.999365i \(0.488660\pi\)
\(522\) 0 0
\(523\) −1.17300e7 −1.87518 −0.937589 0.347744i \(-0.886948\pi\)
−0.937589 + 0.347744i \(0.886948\pi\)
\(524\) 0 0
\(525\) −77500.0 −0.0122717
\(526\) 0 0
\(527\) 1.14954e7 1.80301
\(528\) 0 0
\(529\) −1.67522e6 −0.260275
\(530\) 0 0
\(531\) 8.86499e6 1.36440
\(532\) 0 0
\(533\) 4.88015e6 0.744072
\(534\) 0 0
\(535\) −4.82975e6 −0.729525
\(536\) 0 0
\(537\) 189368. 0.0283381
\(538\) 0 0
\(539\) 1.86667e6 0.276755
\(540\) 0 0
\(541\) −744158. −0.109313 −0.0546565 0.998505i \(-0.517406\pi\)
−0.0546565 + 0.998505i \(0.517406\pi\)
\(542\) 0 0
\(543\) −1.03404e6 −0.150500
\(544\) 0 0
\(545\) 3.00115e6 0.432809
\(546\) 0 0
\(547\) −3.24801e6 −0.464139 −0.232070 0.972699i \(-0.574550\pi\)
−0.232070 + 0.972699i \(0.574550\pi\)
\(548\) 0 0
\(549\) 9.45723e6 1.33916
\(550\) 0 0
\(551\) 877368. 0.123113
\(552\) 0 0
\(553\) −5.84139e6 −0.812276
\(554\) 0 0
\(555\) −176700. −0.0243503
\(556\) 0 0
\(557\) 9.94446e6 1.35814 0.679068 0.734075i \(-0.262384\pi\)
0.679068 + 0.734075i \(0.262384\pi\)
\(558\) 0 0
\(559\) −4.65256e6 −0.629741
\(560\) 0 0
\(561\) −342720. −0.0459761
\(562\) 0 0
\(563\) 3.89374e6 0.517721 0.258861 0.965915i \(-0.416653\pi\)
0.258861 + 0.965915i \(0.416653\pi\)
\(564\) 0 0
\(565\) −3.81615e6 −0.502926
\(566\) 0 0
\(567\) 3.48124e6 0.454754
\(568\) 0 0
\(569\) −1.11951e7 −1.44960 −0.724801 0.688958i \(-0.758068\pi\)
−0.724801 + 0.688958i \(0.758068\pi\)
\(570\) 0 0
\(571\) −844040. −0.108336 −0.0541680 0.998532i \(-0.517251\pi\)
−0.0541680 + 0.998532i \(0.517251\pi\)
\(572\) 0 0
\(573\) −824600. −0.104920
\(574\) 0 0
\(575\) −1.36375e6 −0.172015
\(576\) 0 0
\(577\) −5.13378e6 −0.641945 −0.320973 0.947088i \(-0.604010\pi\)
−0.320973 + 0.947088i \(0.604010\pi\)
\(578\) 0 0
\(579\) 1.54331e6 0.191318
\(580\) 0 0
\(581\) −1.95188e6 −0.239891
\(582\) 0 0
\(583\) −1.87862e6 −0.228912
\(584\) 0 0
\(585\) −3.90765e6 −0.472091
\(586\) 0 0
\(587\) 9.76156e6 1.16929 0.584647 0.811287i \(-0.301233\pi\)
0.584647 + 0.811287i \(0.301233\pi\)
\(588\) 0 0
\(589\) −5.37096e6 −0.637916
\(590\) 0 0
\(591\) −380476. −0.0448083
\(592\) 0 0
\(593\) 966226. 0.112835 0.0564173 0.998407i \(-0.482032\pi\)
0.0564173 + 0.998407i \(0.482032\pi\)
\(594\) 0 0
\(595\) −1.84450e6 −0.213593
\(596\) 0 0
\(597\) 264144. 0.0303323
\(598\) 0 0
\(599\) 7.90000e6 0.899622 0.449811 0.893124i \(-0.351491\pi\)
0.449811 + 0.893124i \(0.351491\pi\)
\(600\) 0 0
\(601\) 1.03126e7 1.16461 0.582307 0.812969i \(-0.302150\pi\)
0.582307 + 0.812969i \(0.302150\pi\)
\(602\) 0 0
\(603\) 1.35594e7 1.51862
\(604\) 0 0
\(605\) −3.50788e6 −0.389633
\(606\) 0 0
\(607\) 9.70767e6 1.06941 0.534704 0.845040i \(-0.320423\pi\)
0.534704 + 0.845040i \(0.320423\pi\)
\(608\) 0 0
\(609\) −195672. −0.0213789
\(610\) 0 0
\(611\) 1.85043e7 2.00525
\(612\) 0 0
\(613\) 1.10568e7 1.18844 0.594219 0.804304i \(-0.297461\pi\)
0.594219 + 0.804304i \(0.297461\pi\)
\(614\) 0 0
\(615\) −373100. −0.0397775
\(616\) 0 0
\(617\) 8.31174e6 0.878980 0.439490 0.898248i \(-0.355159\pi\)
0.439490 + 0.898248i \(0.355159\pi\)
\(618\) 0 0
\(619\) 1.15451e7 1.21108 0.605539 0.795816i \(-0.292958\pi\)
0.605539 + 0.795816i \(0.292958\pi\)
\(620\) 0 0
\(621\) −2.10345e6 −0.218878
\(622\) 0 0
\(623\) −5.83135e6 −0.601934
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 160128. 0.0162667
\(628\) 0 0
\(629\) −4.20546e6 −0.423825
\(630\) 0 0
\(631\) 8.20262e6 0.820123 0.410062 0.912058i \(-0.365507\pi\)
0.410062 + 0.912058i \(0.365507\pi\)
\(632\) 0 0
\(633\) −1.85741e6 −0.184246
\(634\) 0 0
\(635\) −2.69765e6 −0.265492
\(636\) 0 0
\(637\) −8.47780e6 −0.827818
\(638\) 0 0
\(639\) 1.08955e7 1.05559
\(640\) 0 0
\(641\) −5.39695e6 −0.518804 −0.259402 0.965769i \(-0.583525\pi\)
−0.259402 + 0.965769i \(0.583525\pi\)
\(642\) 0 0
\(643\) −1.33896e7 −1.27715 −0.638573 0.769561i \(-0.720475\pi\)
−0.638573 + 0.769561i \(0.720475\pi\)
\(644\) 0 0
\(645\) 355700. 0.0336655
\(646\) 0 0
\(647\) −6.48254e6 −0.608814 −0.304407 0.952542i \(-0.598458\pi\)
−0.304407 + 0.952542i \(0.598458\pi\)
\(648\) 0 0
\(649\) 5.34125e6 0.497773
\(650\) 0 0
\(651\) 1.19784e6 0.110776
\(652\) 0 0
\(653\) −1.44907e7 −1.32986 −0.664931 0.746904i \(-0.731539\pi\)
−0.664931 + 0.746904i \(0.731539\pi\)
\(654\) 0 0
\(655\) −5.82680e6 −0.530673
\(656\) 0 0
\(657\) −2.83024e6 −0.255805
\(658\) 0 0
\(659\) 6.59080e6 0.591187 0.295593 0.955314i \(-0.404483\pi\)
0.295593 + 0.955314i \(0.404483\pi\)
\(660\) 0 0
\(661\) 3.25233e6 0.289528 0.144764 0.989466i \(-0.453758\pi\)
0.144764 + 0.989466i \(0.453758\pi\)
\(662\) 0 0
\(663\) 1.55652e6 0.137522
\(664\) 0 0
\(665\) 861800. 0.0755705
\(666\) 0 0
\(667\) −3.44320e6 −0.299673
\(668\) 0 0
\(669\) 842988. 0.0728209
\(670\) 0 0
\(671\) 5.69808e6 0.488565
\(672\) 0 0
\(673\) 3.86655e6 0.329068 0.164534 0.986371i \(-0.447388\pi\)
0.164534 + 0.986371i \(0.447388\pi\)
\(674\) 0 0
\(675\) 602500. 0.0508976
\(676\) 0 0
\(677\) −1.23856e6 −0.103859 −0.0519297 0.998651i \(-0.516537\pi\)
−0.0519297 + 0.998651i \(0.516537\pi\)
\(678\) 0 0
\(679\) 1.47027e6 0.122383
\(680\) 0 0
\(681\) −1.98392e6 −0.163930
\(682\) 0 0
\(683\) −1.31376e7 −1.07762 −0.538810 0.842427i \(-0.681126\pi\)
−0.538810 + 0.842427i \(0.681126\pi\)
\(684\) 0 0
\(685\) 8.90205e6 0.724876
\(686\) 0 0
\(687\) −533892. −0.0431580
\(688\) 0 0
\(689\) 8.53208e6 0.684711
\(690\) 0 0
\(691\) −1.23841e7 −0.986664 −0.493332 0.869841i \(-0.664221\pi\)
−0.493332 + 0.869841i \(0.664221\pi\)
\(692\) 0 0
\(693\) 2.13379e6 0.168779
\(694\) 0 0
\(695\) 7.80510e6 0.612938
\(696\) 0 0
\(697\) −8.87978e6 −0.692341
\(698\) 0 0
\(699\) −1.92063e6 −0.148679
\(700\) 0 0
\(701\) 9.78952e6 0.752430 0.376215 0.926532i \(-0.377225\pi\)
0.376215 + 0.926532i \(0.377225\pi\)
\(702\) 0 0
\(703\) 1.96490e6 0.149952
\(704\) 0 0
\(705\) −1.41470e6 −0.107199
\(706\) 0 0
\(707\) 8.03979e6 0.604917
\(708\) 0 0
\(709\) −1.22257e7 −0.913397 −0.456699 0.889622i \(-0.650968\pi\)
−0.456699 + 0.889622i \(0.650968\pi\)
\(710\) 0 0
\(711\) 2.25176e7 1.67051
\(712\) 0 0
\(713\) 2.10781e7 1.55277
\(714\) 0 0
\(715\) −2.35440e6 −0.172233
\(716\) 0 0
\(717\) −985392. −0.0715832
\(718\) 0 0
\(719\) 1.35053e7 0.974276 0.487138 0.873325i \(-0.338041\pi\)
0.487138 + 0.873325i \(0.338041\pi\)
\(720\) 0 0
\(721\) −8.48445e6 −0.607835
\(722\) 0 0
\(723\) −112156. −0.00797952
\(724\) 0 0
\(725\) 986250. 0.0696854
\(726\) 0 0
\(727\) −1.17271e7 −0.822916 −0.411458 0.911429i \(-0.634980\pi\)
−0.411458 + 0.911429i \(0.634980\pi\)
\(728\) 0 0
\(729\) −1.29511e7 −0.902585
\(730\) 0 0
\(731\) 8.46566e6 0.585959
\(732\) 0 0
\(733\) 1.16512e7 0.800960 0.400480 0.916305i \(-0.368843\pi\)
0.400480 + 0.916305i \(0.368843\pi\)
\(734\) 0 0
\(735\) 648150. 0.0442545
\(736\) 0 0
\(737\) 8.16970e6 0.554035
\(738\) 0 0
\(739\) −1.26808e7 −0.854155 −0.427077 0.904215i \(-0.640457\pi\)
−0.427077 + 0.904215i \(0.640457\pi\)
\(740\) 0 0
\(741\) −727248. −0.0486561
\(742\) 0 0
\(743\) 197370. 0.0131162 0.00655812 0.999978i \(-0.497912\pi\)
0.00655812 + 0.999978i \(0.497912\pi\)
\(744\) 0 0
\(745\) −687450. −0.0453785
\(746\) 0 0
\(747\) 7.52420e6 0.493354
\(748\) 0 0
\(749\) −1.19778e7 −0.780139
\(750\) 0 0
\(751\) 1.33282e7 0.862326 0.431163 0.902274i \(-0.358103\pi\)
0.431163 + 0.902274i \(0.358103\pi\)
\(752\) 0 0
\(753\) −3.93584e6 −0.252959
\(754\) 0 0
\(755\) 3.42270e6 0.218525
\(756\) 0 0
\(757\) 3.86122e6 0.244898 0.122449 0.992475i \(-0.460925\pi\)
0.122449 + 0.992475i \(0.460925\pi\)
\(758\) 0 0
\(759\) −628416. −0.0395952
\(760\) 0 0
\(761\) −8.31756e6 −0.520636 −0.260318 0.965523i \(-0.583827\pi\)
−0.260318 + 0.965523i \(0.583827\pi\)
\(762\) 0 0
\(763\) 7.44285e6 0.462837
\(764\) 0 0
\(765\) 7.11025e6 0.439270
\(766\) 0 0
\(767\) −2.42582e7 −1.48891
\(768\) 0 0
\(769\) 2.76358e7 1.68522 0.842609 0.538527i \(-0.181019\pi\)
0.842609 + 0.538527i \(0.181019\pi\)
\(770\) 0 0
\(771\) 1.94382e6 0.117766
\(772\) 0 0
\(773\) −1.78842e7 −1.07652 −0.538259 0.842780i \(-0.680918\pi\)
−0.538259 + 0.842780i \(0.680918\pi\)
\(774\) 0 0
\(775\) −6.03750e6 −0.361080
\(776\) 0 0
\(777\) −438216. −0.0260397
\(778\) 0 0
\(779\) 4.14887e6 0.244955
\(780\) 0 0
\(781\) 6.56467e6 0.385111
\(782\) 0 0
\(783\) 1.52119e6 0.0886706
\(784\) 0 0
\(785\) −1.01679e7 −0.588918
\(786\) 0 0
\(787\) 2.15691e7 1.24135 0.620676 0.784067i \(-0.286858\pi\)
0.620676 + 0.784067i \(0.286858\pi\)
\(788\) 0 0
\(789\) −309540. −0.0177021
\(790\) 0 0
\(791\) −9.46405e6 −0.537819
\(792\) 0 0
\(793\) −2.58788e7 −1.46137
\(794\) 0 0
\(795\) −652300. −0.0366041
\(796\) 0 0
\(797\) 1.03060e7 0.574705 0.287353 0.957825i \(-0.407225\pi\)
0.287353 + 0.957825i \(0.407225\pi\)
\(798\) 0 0
\(799\) −3.36699e7 −1.86584
\(800\) 0 0
\(801\) 2.24789e7 1.23792
\(802\) 0 0
\(803\) −1.70525e6 −0.0933251
\(804\) 0 0
\(805\) −3.38210e6 −0.183949
\(806\) 0 0
\(807\) 2.04743e6 0.110669
\(808\) 0 0
\(809\) 372378. 0.0200038 0.0100019 0.999950i \(-0.496816\pi\)
0.0100019 + 0.999950i \(0.496816\pi\)
\(810\) 0 0
\(811\) −1.94795e7 −1.03998 −0.519990 0.854173i \(-0.674064\pi\)
−0.519990 + 0.854173i \(0.674064\pi\)
\(812\) 0 0
\(813\) −2.29551e6 −0.121802
\(814\) 0 0
\(815\) −341050. −0.0179856
\(816\) 0 0
\(817\) −3.95538e6 −0.207316
\(818\) 0 0
\(819\) −9.69097e6 −0.504844
\(820\) 0 0
\(821\) 469318. 0.0243002 0.0121501 0.999926i \(-0.496132\pi\)
0.0121501 + 0.999926i \(0.496132\pi\)
\(822\) 0 0
\(823\) −1.78622e7 −0.919253 −0.459626 0.888112i \(-0.652017\pi\)
−0.459626 + 0.888112i \(0.652017\pi\)
\(824\) 0 0
\(825\) 180000. 0.00920741
\(826\) 0 0
\(827\) 9.42560e6 0.479231 0.239616 0.970868i \(-0.422979\pi\)
0.239616 + 0.970868i \(0.422979\pi\)
\(828\) 0 0
\(829\) 1.48622e7 0.751098 0.375549 0.926803i \(-0.377454\pi\)
0.375549 + 0.926803i \(0.377454\pi\)
\(830\) 0 0
\(831\) −4.99352e6 −0.250844
\(832\) 0 0
\(833\) 1.54260e7 0.770265
\(834\) 0 0
\(835\) 5.08595e6 0.252439
\(836\) 0 0
\(837\) −9.31224e6 −0.459452
\(838\) 0 0
\(839\) 4.71170e6 0.231085 0.115543 0.993303i \(-0.463139\pi\)
0.115543 + 0.993303i \(0.463139\pi\)
\(840\) 0 0
\(841\) −1.80211e7 −0.878599
\(842\) 0 0
\(843\) −3.39080e6 −0.164336
\(844\) 0 0
\(845\) 1.41058e6 0.0679602
\(846\) 0 0
\(847\) −8.69953e6 −0.416665
\(848\) 0 0
\(849\) 4.24791e6 0.202258
\(850\) 0 0
\(851\) −7.71119e6 −0.365004
\(852\) 0 0
\(853\) −1.62685e7 −0.765552 −0.382776 0.923841i \(-0.625032\pi\)
−0.382776 + 0.923841i \(0.625032\pi\)
\(854\) 0 0
\(855\) −3.32210e6 −0.155417
\(856\) 0 0
\(857\) −2.92667e7 −1.36120 −0.680600 0.732656i \(-0.738281\pi\)
−0.680600 + 0.732656i \(0.738281\pi\)
\(858\) 0 0
\(859\) −3.31062e7 −1.53083 −0.765413 0.643539i \(-0.777465\pi\)
−0.765413 + 0.643539i \(0.777465\pi\)
\(860\) 0 0
\(861\) −925288. −0.0425372
\(862\) 0 0
\(863\) 1.58052e7 0.722391 0.361196 0.932490i \(-0.382369\pi\)
0.361196 + 0.932490i \(0.382369\pi\)
\(864\) 0 0
\(865\) −3.18105e6 −0.144554
\(866\) 0 0
\(867\) 7514.00 0.000339487 0
\(868\) 0 0
\(869\) 1.35671e7 0.609449
\(870\) 0 0
\(871\) −3.71040e7 −1.65720
\(872\) 0 0
\(873\) −5.66765e6 −0.251691
\(874\) 0 0
\(875\) 968750. 0.0427752
\(876\) 0 0
\(877\) 4.26834e7 1.87396 0.936980 0.349384i \(-0.113609\pi\)
0.936980 + 0.349384i \(0.113609\pi\)
\(878\) 0 0
\(879\) 1.98544e6 0.0866733
\(880\) 0 0
\(881\) −3.57397e6 −0.155135 −0.0775677 0.996987i \(-0.524715\pi\)
−0.0775677 + 0.996987i \(0.524715\pi\)
\(882\) 0 0
\(883\) −1.68471e7 −0.727149 −0.363574 0.931565i \(-0.618444\pi\)
−0.363574 + 0.931565i \(0.618444\pi\)
\(884\) 0 0
\(885\) 1.85460e6 0.0795962
\(886\) 0 0
\(887\) 8.36792e6 0.357115 0.178558 0.983929i \(-0.442857\pi\)
0.178558 + 0.983929i \(0.442857\pi\)
\(888\) 0 0
\(889\) −6.69017e6 −0.283911
\(890\) 0 0
\(891\) −8.08546e6 −0.341201
\(892\) 0 0
\(893\) 1.57315e7 0.660147
\(894\) 0 0
\(895\) −2.36710e6 −0.0987777
\(896\) 0 0
\(897\) 2.85406e6 0.118435
\(898\) 0 0
\(899\) −1.52435e7 −0.629050
\(900\) 0 0
\(901\) −1.55247e7 −0.637107
\(902\) 0 0
\(903\) 882136. 0.0360011
\(904\) 0 0
\(905\) 1.29255e7 0.524595
\(906\) 0 0
\(907\) −2.57230e7 −1.03825 −0.519127 0.854697i \(-0.673743\pi\)
−0.519127 + 0.854697i \(0.673743\pi\)
\(908\) 0 0
\(909\) −3.09921e7 −1.24406
\(910\) 0 0
\(911\) −3.42108e7 −1.36574 −0.682869 0.730540i \(-0.739268\pi\)
−0.682869 + 0.730540i \(0.739268\pi\)
\(912\) 0 0
\(913\) 4.53341e6 0.179990
\(914\) 0 0
\(915\) 1.97850e6 0.0781238
\(916\) 0 0
\(917\) −1.44505e7 −0.567490
\(918\) 0 0
\(919\) −2.44034e6 −0.0953149 −0.0476575 0.998864i \(-0.515176\pi\)
−0.0476575 + 0.998864i \(0.515176\pi\)
\(920\) 0 0
\(921\) −975044. −0.0378770
\(922\) 0 0
\(923\) −2.98146e7 −1.15192
\(924\) 0 0
\(925\) 2.20875e6 0.0848774
\(926\) 0 0
\(927\) 3.27062e7 1.25006
\(928\) 0 0
\(929\) 1.34361e7 0.510781 0.255390 0.966838i \(-0.417796\pi\)
0.255390 + 0.966838i \(0.417796\pi\)
\(930\) 0 0
\(931\) −7.20743e6 −0.272525
\(932\) 0 0
\(933\) −888232. −0.0334058
\(934\) 0 0
\(935\) 4.28400e6 0.160258
\(936\) 0 0
\(937\) 7.96529e6 0.296383 0.148191 0.988959i \(-0.452655\pi\)
0.148191 + 0.988959i \(0.452655\pi\)
\(938\) 0 0
\(939\) −94484.0 −0.00349699
\(940\) 0 0
\(941\) −9.08025e6 −0.334290 −0.167145 0.985932i \(-0.553455\pi\)
−0.167145 + 0.985932i \(0.553455\pi\)
\(942\) 0 0
\(943\) −1.62821e7 −0.596253
\(944\) 0 0
\(945\) 1.49420e6 0.0544289
\(946\) 0 0
\(947\) −3.21769e7 −1.16592 −0.582961 0.812500i \(-0.698106\pi\)
−0.582961 + 0.812500i \(0.698106\pi\)
\(948\) 0 0
\(949\) 7.74467e6 0.279150
\(950\) 0 0
\(951\) 1.38812e6 0.0497708
\(952\) 0 0
\(953\) 5.33807e6 0.190394 0.0951968 0.995458i \(-0.469652\pi\)
0.0951968 + 0.995458i \(0.469652\pi\)
\(954\) 0 0
\(955\) 1.03075e7 0.365717
\(956\) 0 0
\(957\) 454464. 0.0160406
\(958\) 0 0
\(959\) 2.20771e7 0.775167
\(960\) 0 0
\(961\) 6.46864e7 2.25946
\(962\) 0 0
\(963\) 4.61724e7 1.60442
\(964\) 0 0
\(965\) −1.92914e7 −0.666875
\(966\) 0 0
\(967\) −3.71522e7 −1.27767 −0.638834 0.769345i \(-0.720583\pi\)
−0.638834 + 0.769345i \(0.720583\pi\)
\(968\) 0 0
\(969\) 1.32328e6 0.0452733
\(970\) 0 0
\(971\) −1.09865e7 −0.373949 −0.186975 0.982365i \(-0.559868\pi\)
−0.186975 + 0.982365i \(0.559868\pi\)
\(972\) 0 0
\(973\) 1.93566e7 0.655463
\(974\) 0 0
\(975\) −817500. −0.0275408
\(976\) 0 0
\(977\) −2.65054e7 −0.888379 −0.444190 0.895933i \(-0.646508\pi\)
−0.444190 + 0.895933i \(0.646508\pi\)
\(978\) 0 0
\(979\) 1.35438e7 0.451630
\(980\) 0 0
\(981\) −2.86910e7 −0.951860
\(982\) 0 0
\(983\) 4.75726e7 1.57027 0.785133 0.619327i \(-0.212594\pi\)
0.785133 + 0.619327i \(0.212594\pi\)
\(984\) 0 0
\(985\) 4.75595e6 0.156188
\(986\) 0 0
\(987\) −3.50846e6 −0.114637
\(988\) 0 0
\(989\) 1.55227e7 0.504636
\(990\) 0 0
\(991\) −3.22149e7 −1.04201 −0.521006 0.853553i \(-0.674443\pi\)
−0.521006 + 0.853553i \(0.674443\pi\)
\(992\) 0 0
\(993\) −164336. −0.00528883
\(994\) 0 0
\(995\) −3.30180e6 −0.105729
\(996\) 0 0
\(997\) −3.87072e7 −1.23326 −0.616630 0.787253i \(-0.711502\pi\)
−0.616630 + 0.787253i \(0.711502\pi\)
\(998\) 0 0
\(999\) 3.40678e6 0.108002
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.h.1.1 1
4.3 odd 2 320.6.a.i.1.1 1
8.3 odd 2 40.6.a.c.1.1 1
8.5 even 2 80.6.a.d.1.1 1
24.5 odd 2 720.6.a.t.1.1 1
24.11 even 2 360.6.a.f.1.1 1
40.3 even 4 200.6.c.d.49.1 2
40.13 odd 4 400.6.c.k.49.2 2
40.19 odd 2 200.6.a.b.1.1 1
40.27 even 4 200.6.c.d.49.2 2
40.29 even 2 400.6.a.h.1.1 1
40.37 odd 4 400.6.c.k.49.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.c.1.1 1 8.3 odd 2
80.6.a.d.1.1 1 8.5 even 2
200.6.a.b.1.1 1 40.19 odd 2
200.6.c.d.49.1 2 40.3 even 4
200.6.c.d.49.2 2 40.27 even 4
320.6.a.h.1.1 1 1.1 even 1 trivial
320.6.a.i.1.1 1 4.3 odd 2
360.6.a.f.1.1 1 24.11 even 2
400.6.a.h.1.1 1 40.29 even 2
400.6.c.k.49.1 2 40.37 odd 4
400.6.c.k.49.2 2 40.13 odd 4
720.6.a.t.1.1 1 24.5 odd 2