Properties

Label 80.6.a.e.1.1
Level $80$
Weight $6$
Character 80.1
Self dual yes
Analytic conductor $12.831$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.8307055850\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 80.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{3} +25.0000 q^{5} -192.000 q^{7} -227.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{3} +25.0000 q^{5} -192.000 q^{7} -227.000 q^{9} +148.000 q^{11} +286.000 q^{13} +100.000 q^{15} -1678.00 q^{17} -1060.00 q^{19} -768.000 q^{21} -2976.00 q^{23} +625.000 q^{25} -1880.00 q^{27} -3410.00 q^{29} +2448.00 q^{31} +592.000 q^{33} -4800.00 q^{35} +182.000 q^{37} +1144.00 q^{39} -9398.00 q^{41} +1244.00 q^{43} -5675.00 q^{45} +12088.0 q^{47} +20057.0 q^{49} -6712.00 q^{51} +23846.0 q^{53} +3700.00 q^{55} -4240.00 q^{57} +20020.0 q^{59} +32302.0 q^{61} +43584.0 q^{63} +7150.00 q^{65} -60972.0 q^{67} -11904.0 q^{69} +32648.0 q^{71} -38774.0 q^{73} +2500.00 q^{75} -28416.0 q^{77} +33360.0 q^{79} +47641.0 q^{81} -16716.0 q^{83} -41950.0 q^{85} -13640.0 q^{87} +101370. q^{89} -54912.0 q^{91} +9792.00 q^{93} -26500.0 q^{95} -119038. q^{97} -33596.0 q^{99} +O(q^{100})\)

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
\(3\) 4.00000 0.256600 0.128300 0.991735i \(-0.459048\pi\)
0.128300 + 0.991735i \(0.459048\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −192.000 −1.48100 −0.740502 0.672054i \(-0.765412\pi\)
−0.740502 + 0.672054i \(0.765412\pi\)
\(8\) 0 0
\(9\) −227.000 −0.934156
\(10\) 0 0
\(11\) 148.000 0.368791 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(12\) 0 0
\(13\) 286.000 0.469362 0.234681 0.972072i \(-0.424595\pi\)
0.234681 + 0.972072i \(0.424595\pi\)
\(14\) 0 0
\(15\) 100.000 0.114755
\(16\) 0 0
\(17\) −1678.00 −1.40822 −0.704109 0.710092i \(-0.748653\pi\)
−0.704109 + 0.710092i \(0.748653\pi\)
\(18\) 0 0
\(19\) −1060.00 −0.673631 −0.336815 0.941571i \(-0.609350\pi\)
−0.336815 + 0.941571i \(0.609350\pi\)
\(20\) 0 0
\(21\) −768.000 −0.380026
\(22\) 0 0
\(23\) −2976.00 −1.17304 −0.586521 0.809934i \(-0.699503\pi\)
−0.586521 + 0.809934i \(0.699503\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −1880.00 −0.496305
\(28\) 0 0
\(29\) −3410.00 −0.752938 −0.376469 0.926429i \(-0.622862\pi\)
−0.376469 + 0.926429i \(0.622862\pi\)
\(30\) 0 0
\(31\) 2448.00 0.457517 0.228758 0.973483i \(-0.426533\pi\)
0.228758 + 0.973483i \(0.426533\pi\)
\(32\) 0 0
\(33\) 592.000 0.0946317
\(34\) 0 0
\(35\) −4800.00 −0.662325
\(36\) 0 0
\(37\) 182.000 0.0218558 0.0109279 0.999940i \(-0.496521\pi\)
0.0109279 + 0.999940i \(0.496521\pi\)
\(38\) 0 0
\(39\) 1144.00 0.120438
\(40\) 0 0
\(41\) −9398.00 −0.873124 −0.436562 0.899674i \(-0.643804\pi\)
−0.436562 + 0.899674i \(0.643804\pi\)
\(42\) 0 0
\(43\) 1244.00 0.102600 0.0513002 0.998683i \(-0.483663\pi\)
0.0513002 + 0.998683i \(0.483663\pi\)
\(44\) 0 0
\(45\) −5675.00 −0.417767
\(46\) 0 0
\(47\) 12088.0 0.798196 0.399098 0.916908i \(-0.369323\pi\)
0.399098 + 0.916908i \(0.369323\pi\)
\(48\) 0 0
\(49\) 20057.0 1.19337
\(50\) 0 0
\(51\) −6712.00 −0.361349
\(52\) 0 0
\(53\) 23846.0 1.16607 0.583037 0.812446i \(-0.301864\pi\)
0.583037 + 0.812446i \(0.301864\pi\)
\(54\) 0 0
\(55\) 3700.00 0.164928
\(56\) 0 0
\(57\) −4240.00 −0.172854
\(58\) 0 0
\(59\) 20020.0 0.748745 0.374373 0.927278i \(-0.377858\pi\)
0.374373 + 0.927278i \(0.377858\pi\)
\(60\) 0 0
\(61\) 32302.0 1.11149 0.555744 0.831353i \(-0.312433\pi\)
0.555744 + 0.831353i \(0.312433\pi\)
\(62\) 0 0
\(63\) 43584.0 1.38349
\(64\) 0 0
\(65\) 7150.00 0.209905
\(66\) 0 0
\(67\) −60972.0 −1.65937 −0.829685 0.558231i \(-0.811480\pi\)
−0.829685 + 0.558231i \(0.811480\pi\)
\(68\) 0 0
\(69\) −11904.0 −0.301003
\(70\) 0 0
\(71\) 32648.0 0.768618 0.384309 0.923204i \(-0.374440\pi\)
0.384309 + 0.923204i \(0.374440\pi\)
\(72\) 0 0
\(73\) −38774.0 −0.851596 −0.425798 0.904818i \(-0.640007\pi\)
−0.425798 + 0.904818i \(0.640007\pi\)
\(74\) 0 0
\(75\) 2500.00 0.0513200
\(76\) 0 0
\(77\) −28416.0 −0.546180
\(78\) 0 0
\(79\) 33360.0 0.601393 0.300696 0.953720i \(-0.402781\pi\)
0.300696 + 0.953720i \(0.402781\pi\)
\(80\) 0 0
\(81\) 47641.0 0.806805
\(82\) 0 0
\(83\) −16716.0 −0.266340 −0.133170 0.991093i \(-0.542516\pi\)
−0.133170 + 0.991093i \(0.542516\pi\)
\(84\) 0 0
\(85\) −41950.0 −0.629774
\(86\) 0 0
\(87\) −13640.0 −0.193204
\(88\) 0 0
\(89\) 101370. 1.35655 0.678273 0.734810i \(-0.262729\pi\)
0.678273 + 0.734810i \(0.262729\pi\)
\(90\) 0 0
\(91\) −54912.0 −0.695126
\(92\) 0 0
\(93\) 9792.00 0.117399
\(94\) 0 0
\(95\) −26500.0 −0.301257
\(96\) 0 0
\(97\) −119038. −1.28457 −0.642283 0.766468i \(-0.722013\pi\)
−0.642283 + 0.766468i \(0.722013\pi\)
\(98\) 0 0
\(99\) −33596.0 −0.344508
\(100\) 0 0
\(101\) −89898.0 −0.876893 −0.438446 0.898757i \(-0.644471\pi\)
−0.438446 + 0.898757i \(0.644471\pi\)
\(102\) 0 0
\(103\) 19504.0 0.181147 0.0905734 0.995890i \(-0.471130\pi\)
0.0905734 + 0.995890i \(0.471130\pi\)
\(104\) 0 0
\(105\) −19200.0 −0.169953
\(106\) 0 0
\(107\) −158292. −1.33659 −0.668297 0.743895i \(-0.732976\pi\)
−0.668297 + 0.743895i \(0.732976\pi\)
\(108\) 0 0
\(109\) 36830.0 0.296917 0.148459 0.988919i \(-0.452569\pi\)
0.148459 + 0.988919i \(0.452569\pi\)
\(110\) 0 0
\(111\) 728.000 0.00560821
\(112\) 0 0
\(113\) 11186.0 0.0824098 0.0412049 0.999151i \(-0.486880\pi\)
0.0412049 + 0.999151i \(0.486880\pi\)
\(114\) 0 0
\(115\) −74400.0 −0.524600
\(116\) 0 0
\(117\) −64922.0 −0.438457
\(118\) 0 0
\(119\) 322176. 2.08557
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 0 0
\(123\) −37592.0 −0.224044
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −70552.0 −0.388150 −0.194075 0.980987i \(-0.562171\pi\)
−0.194075 + 0.980987i \(0.562171\pi\)
\(128\) 0 0
\(129\) 4976.00 0.0263273
\(130\) 0 0
\(131\) −76452.0 −0.389234 −0.194617 0.980879i \(-0.562346\pi\)
−0.194617 + 0.980879i \(0.562346\pi\)
\(132\) 0 0
\(133\) 203520. 0.997650
\(134\) 0 0
\(135\) −47000.0 −0.221954
\(136\) 0 0
\(137\) −144918. −0.659661 −0.329831 0.944040i \(-0.606992\pi\)
−0.329831 + 0.944040i \(0.606992\pi\)
\(138\) 0 0
\(139\) −112220. −0.492644 −0.246322 0.969188i \(-0.579222\pi\)
−0.246322 + 0.969188i \(0.579222\pi\)
\(140\) 0 0
\(141\) 48352.0 0.204817
\(142\) 0 0
\(143\) 42328.0 0.173096
\(144\) 0 0
\(145\) −85250.0 −0.336724
\(146\) 0 0
\(147\) 80228.0 0.306219
\(148\) 0 0
\(149\) 403750. 1.48986 0.744932 0.667140i \(-0.232482\pi\)
0.744932 + 0.667140i \(0.232482\pi\)
\(150\) 0 0
\(151\) 446648. 1.59413 0.797064 0.603895i \(-0.206385\pi\)
0.797064 + 0.603895i \(0.206385\pi\)
\(152\) 0 0
\(153\) 380906. 1.31550
\(154\) 0 0
\(155\) 61200.0 0.204608
\(156\) 0 0
\(157\) −262258. −0.849141 −0.424570 0.905395i \(-0.639575\pi\)
−0.424570 + 0.905395i \(0.639575\pi\)
\(158\) 0 0
\(159\) 95384.0 0.299215
\(160\) 0 0
\(161\) 571392. 1.73728
\(162\) 0 0
\(163\) 154564. 0.455658 0.227829 0.973701i \(-0.426837\pi\)
0.227829 + 0.973701i \(0.426837\pi\)
\(164\) 0 0
\(165\) 14800.0 0.0423206
\(166\) 0 0
\(167\) −396672. −1.10063 −0.550314 0.834958i \(-0.685492\pi\)
−0.550314 + 0.834958i \(0.685492\pi\)
\(168\) 0 0
\(169\) −289497. −0.779700
\(170\) 0 0
\(171\) 240620. 0.629276
\(172\) 0 0
\(173\) −573474. −1.45680 −0.728398 0.685155i \(-0.759735\pi\)
−0.728398 + 0.685155i \(0.759735\pi\)
\(174\) 0 0
\(175\) −120000. −0.296201
\(176\) 0 0
\(177\) 80080.0 0.192128
\(178\) 0 0
\(179\) 594460. 1.38672 0.693362 0.720589i \(-0.256129\pi\)
0.693362 + 0.720589i \(0.256129\pi\)
\(180\) 0 0
\(181\) −107098. −0.242988 −0.121494 0.992592i \(-0.538769\pi\)
−0.121494 + 0.992592i \(0.538769\pi\)
\(182\) 0 0
\(183\) 129208. 0.285208
\(184\) 0 0
\(185\) 4550.00 0.00977422
\(186\) 0 0
\(187\) −248344. −0.519337
\(188\) 0 0
\(189\) 360960. 0.735029
\(190\) 0 0
\(191\) −469552. −0.931323 −0.465661 0.884963i \(-0.654184\pi\)
−0.465661 + 0.884963i \(0.654184\pi\)
\(192\) 0 0
\(193\) 52706.0 0.101851 0.0509257 0.998702i \(-0.483783\pi\)
0.0509257 + 0.998702i \(0.483783\pi\)
\(194\) 0 0
\(195\) 28600.0 0.0538616
\(196\) 0 0
\(197\) 455862. 0.836889 0.418444 0.908242i \(-0.362575\pi\)
0.418444 + 0.908242i \(0.362575\pi\)
\(198\) 0 0
\(199\) −865000. −1.54840 −0.774200 0.632940i \(-0.781848\pi\)
−0.774200 + 0.632940i \(0.781848\pi\)
\(200\) 0 0
\(201\) −243888. −0.425795
\(202\) 0 0
\(203\) 654720. 1.11510
\(204\) 0 0
\(205\) −234950. −0.390473
\(206\) 0 0
\(207\) 675552. 1.09580
\(208\) 0 0
\(209\) −156880. −0.248429
\(210\) 0 0
\(211\) −1.10565e6 −1.70967 −0.854835 0.518900i \(-0.826342\pi\)
−0.854835 + 0.518900i \(0.826342\pi\)
\(212\) 0 0
\(213\) 130592. 0.197228
\(214\) 0 0
\(215\) 31100.0 0.0458843
\(216\) 0 0
\(217\) −470016. −0.677584
\(218\) 0 0
\(219\) −155096. −0.218520
\(220\) 0 0
\(221\) −479908. −0.660963
\(222\) 0 0
\(223\) −1.12158e6 −1.51031 −0.755156 0.655545i \(-0.772439\pi\)
−0.755156 + 0.655545i \(0.772439\pi\)
\(224\) 0 0
\(225\) −141875. −0.186831
\(226\) 0 0
\(227\) 23348.0 0.0300736 0.0150368 0.999887i \(-0.495213\pi\)
0.0150368 + 0.999887i \(0.495213\pi\)
\(228\) 0 0
\(229\) −596010. −0.751043 −0.375522 0.926814i \(-0.622536\pi\)
−0.375522 + 0.926814i \(0.622536\pi\)
\(230\) 0 0
\(231\) −113664. −0.140150
\(232\) 0 0
\(233\) −485334. −0.585667 −0.292834 0.956163i \(-0.594598\pi\)
−0.292834 + 0.956163i \(0.594598\pi\)
\(234\) 0 0
\(235\) 302200. 0.356964
\(236\) 0 0
\(237\) 133440. 0.154317
\(238\) 0 0
\(239\) 48880.0 0.0553524 0.0276762 0.999617i \(-0.491189\pi\)
0.0276762 + 0.999617i \(0.491189\pi\)
\(240\) 0 0
\(241\) −110798. −0.122882 −0.0614411 0.998111i \(-0.519570\pi\)
−0.0614411 + 0.998111i \(0.519570\pi\)
\(242\) 0 0
\(243\) 647404. 0.703331
\(244\) 0 0
\(245\) 501425. 0.533692
\(246\) 0 0
\(247\) −303160. −0.316176
\(248\) 0 0
\(249\) −66864.0 −0.0683430
\(250\) 0 0
\(251\) 1.64375e6 1.64684 0.823419 0.567434i \(-0.192064\pi\)
0.823419 + 0.567434i \(0.192064\pi\)
\(252\) 0 0
\(253\) −440448. −0.432607
\(254\) 0 0
\(255\) −167800. −0.161600
\(256\) 0 0
\(257\) 1.30624e6 1.23365 0.616823 0.787102i \(-0.288419\pi\)
0.616823 + 0.787102i \(0.288419\pi\)
\(258\) 0 0
\(259\) −34944.0 −0.0323685
\(260\) 0 0
\(261\) 774070. 0.703362
\(262\) 0 0
\(263\) −2.12834e6 −1.89736 −0.948682 0.316231i \(-0.897583\pi\)
−0.948682 + 0.316231i \(0.897583\pi\)
\(264\) 0 0
\(265\) 596150. 0.521484
\(266\) 0 0
\(267\) 405480. 0.348090
\(268\) 0 0
\(269\) −1.44109e6 −1.21426 −0.607128 0.794604i \(-0.707679\pi\)
−0.607128 + 0.794604i \(0.707679\pi\)
\(270\) 0 0
\(271\) 93248.0 0.0771288 0.0385644 0.999256i \(-0.487722\pi\)
0.0385644 + 0.999256i \(0.487722\pi\)
\(272\) 0 0
\(273\) −219648. −0.178370
\(274\) 0 0
\(275\) 92500.0 0.0737581
\(276\) 0 0
\(277\) −110298. −0.0863711 −0.0431855 0.999067i \(-0.513751\pi\)
−0.0431855 + 0.999067i \(0.513751\pi\)
\(278\) 0 0
\(279\) −555696. −0.427392
\(280\) 0 0
\(281\) −192198. −0.145205 −0.0726027 0.997361i \(-0.523131\pi\)
−0.0726027 + 0.997361i \(0.523131\pi\)
\(282\) 0 0
\(283\) 331884. 0.246332 0.123166 0.992386i \(-0.460695\pi\)
0.123166 + 0.992386i \(0.460695\pi\)
\(284\) 0 0
\(285\) −106000. −0.0773025
\(286\) 0 0
\(287\) 1.80442e6 1.29310
\(288\) 0 0
\(289\) 1.39583e6 0.983076
\(290\) 0 0
\(291\) −476152. −0.329620
\(292\) 0 0
\(293\) 2.19481e6 1.49358 0.746788 0.665063i \(-0.231595\pi\)
0.746788 + 0.665063i \(0.231595\pi\)
\(294\) 0 0
\(295\) 500500. 0.334849
\(296\) 0 0
\(297\) −278240. −0.183033
\(298\) 0 0
\(299\) −851136. −0.550581
\(300\) 0 0
\(301\) −238848. −0.151952
\(302\) 0 0
\(303\) −359592. −0.225011
\(304\) 0 0
\(305\) 807550. 0.497073
\(306\) 0 0
\(307\) 2.37751e6 1.43971 0.719857 0.694123i \(-0.244207\pi\)
0.719857 + 0.694123i \(0.244207\pi\)
\(308\) 0 0
\(309\) 78016.0 0.0464823
\(310\) 0 0
\(311\) 2.37305e6 1.39125 0.695626 0.718405i \(-0.255127\pi\)
0.695626 + 0.718405i \(0.255127\pi\)
\(312\) 0 0
\(313\) −1.42941e6 −0.824702 −0.412351 0.911025i \(-0.635292\pi\)
−0.412351 + 0.911025i \(0.635292\pi\)
\(314\) 0 0
\(315\) 1.08960e6 0.618715
\(316\) 0 0
\(317\) 2.12462e6 1.18750 0.593750 0.804650i \(-0.297647\pi\)
0.593750 + 0.804650i \(0.297647\pi\)
\(318\) 0 0
\(319\) −504680. −0.277677
\(320\) 0 0
\(321\) −633168. −0.342970
\(322\) 0 0
\(323\) 1.77868e6 0.948618
\(324\) 0 0
\(325\) 178750. 0.0938723
\(326\) 0 0
\(327\) 147320. 0.0761890
\(328\) 0 0
\(329\) −2.32090e6 −1.18213
\(330\) 0 0
\(331\) −3.09985e6 −1.55515 −0.777573 0.628793i \(-0.783549\pi\)
−0.777573 + 0.628793i \(0.783549\pi\)
\(332\) 0 0
\(333\) −41314.0 −0.0204168
\(334\) 0 0
\(335\) −1.52430e6 −0.742093
\(336\) 0 0
\(337\) 2.40008e6 1.15120 0.575601 0.817731i \(-0.304768\pi\)
0.575601 + 0.817731i \(0.304768\pi\)
\(338\) 0 0
\(339\) 44744.0 0.0211464
\(340\) 0 0
\(341\) 362304. 0.168728
\(342\) 0 0
\(343\) −624000. −0.286384
\(344\) 0 0
\(345\) −297600. −0.134612
\(346\) 0 0
\(347\) −1.77741e6 −0.792436 −0.396218 0.918156i \(-0.629678\pi\)
−0.396218 + 0.918156i \(0.629678\pi\)
\(348\) 0 0
\(349\) −2.14805e6 −0.944019 −0.472010 0.881593i \(-0.656471\pi\)
−0.472010 + 0.881593i \(0.656471\pi\)
\(350\) 0 0
\(351\) −537680. −0.232946
\(352\) 0 0
\(353\) −661854. −0.282700 −0.141350 0.989960i \(-0.545144\pi\)
−0.141350 + 0.989960i \(0.545144\pi\)
\(354\) 0 0
\(355\) 816200. 0.343737
\(356\) 0 0
\(357\) 1.28870e6 0.535159
\(358\) 0 0
\(359\) 259320. 0.106194 0.0530970 0.998589i \(-0.483091\pi\)
0.0530970 + 0.998589i \(0.483091\pi\)
\(360\) 0 0
\(361\) −1.35250e6 −0.546222
\(362\) 0 0
\(363\) −556588. −0.221701
\(364\) 0 0
\(365\) −969350. −0.380845
\(366\) 0 0
\(367\) 1.49993e6 0.581307 0.290653 0.956828i \(-0.406127\pi\)
0.290653 + 0.956828i \(0.406127\pi\)
\(368\) 0 0
\(369\) 2.13335e6 0.815634
\(370\) 0 0
\(371\) −4.57843e6 −1.72696
\(372\) 0 0
\(373\) −2.23807e6 −0.832918 −0.416459 0.909154i \(-0.636729\pi\)
−0.416459 + 0.909154i \(0.636729\pi\)
\(374\) 0 0
\(375\) 62500.0 0.0229510
\(376\) 0 0
\(377\) −975260. −0.353400
\(378\) 0 0
\(379\) −3.15934e6 −1.12979 −0.564896 0.825162i \(-0.691084\pi\)
−0.564896 + 0.825162i \(0.691084\pi\)
\(380\) 0 0
\(381\) −282208. −0.0995994
\(382\) 0 0
\(383\) −342216. −0.119207 −0.0596037 0.998222i \(-0.518984\pi\)
−0.0596037 + 0.998222i \(0.518984\pi\)
\(384\) 0 0
\(385\) −710400. −0.244259
\(386\) 0 0
\(387\) −282388. −0.0958449
\(388\) 0 0
\(389\) 88470.0 0.0296430 0.0148215 0.999890i \(-0.495282\pi\)
0.0148215 + 0.999890i \(0.495282\pi\)
\(390\) 0 0
\(391\) 4.99373e6 1.65190
\(392\) 0 0
\(393\) −305808. −0.0998775
\(394\) 0 0
\(395\) 834000. 0.268951
\(396\) 0 0
\(397\) −5.45674e6 −1.73763 −0.868814 0.495138i \(-0.835117\pi\)
−0.868814 + 0.495138i \(0.835117\pi\)
\(398\) 0 0
\(399\) 814080. 0.255997
\(400\) 0 0
\(401\) 4.04680e6 1.25676 0.628378 0.777908i \(-0.283719\pi\)
0.628378 + 0.777908i \(0.283719\pi\)
\(402\) 0 0
\(403\) 700128. 0.214741
\(404\) 0 0
\(405\) 1.19102e6 0.360814
\(406\) 0 0
\(407\) 26936.0 0.00806022
\(408\) 0 0
\(409\) −2.71207e6 −0.801664 −0.400832 0.916151i \(-0.631279\pi\)
−0.400832 + 0.916151i \(0.631279\pi\)
\(410\) 0 0
\(411\) −579672. −0.169269
\(412\) 0 0
\(413\) −3.84384e6 −1.10889
\(414\) 0 0
\(415\) −417900. −0.119111
\(416\) 0 0
\(417\) −448880. −0.126413
\(418\) 0 0
\(419\) −3.71746e6 −1.03445 −0.517227 0.855848i \(-0.673036\pi\)
−0.517227 + 0.855848i \(0.673036\pi\)
\(420\) 0 0
\(421\) 3.55250e6 0.976853 0.488426 0.872605i \(-0.337571\pi\)
0.488426 + 0.872605i \(0.337571\pi\)
\(422\) 0 0
\(423\) −2.74398e6 −0.745640
\(424\) 0 0
\(425\) −1.04875e6 −0.281643
\(426\) 0 0
\(427\) −6.20198e6 −1.64612
\(428\) 0 0
\(429\) 169312. 0.0444165
\(430\) 0 0
\(431\) 4.06205e6 1.05330 0.526650 0.850082i \(-0.323448\pi\)
0.526650 + 0.850082i \(0.323448\pi\)
\(432\) 0 0
\(433\) 7.26287e6 1.86161 0.930804 0.365518i \(-0.119108\pi\)
0.930804 + 0.365518i \(0.119108\pi\)
\(434\) 0 0
\(435\) −341000. −0.0864035
\(436\) 0 0
\(437\) 3.15456e6 0.790197
\(438\) 0 0
\(439\) 5.41028e6 1.33986 0.669928 0.742426i \(-0.266325\pi\)
0.669928 + 0.742426i \(0.266325\pi\)
\(440\) 0 0
\(441\) −4.55294e6 −1.11480
\(442\) 0 0
\(443\) 6.51524e6 1.57733 0.788663 0.614826i \(-0.210774\pi\)
0.788663 + 0.614826i \(0.210774\pi\)
\(444\) 0 0
\(445\) 2.53425e6 0.606666
\(446\) 0 0
\(447\) 1.61500e6 0.382299
\(448\) 0 0
\(449\) −509950. −0.119375 −0.0596873 0.998217i \(-0.519010\pi\)
−0.0596873 + 0.998217i \(0.519010\pi\)
\(450\) 0 0
\(451\) −1.39090e6 −0.322000
\(452\) 0 0
\(453\) 1.78659e6 0.409053
\(454\) 0 0
\(455\) −1.37280e6 −0.310870
\(456\) 0 0
\(457\) 1.22084e6 0.273444 0.136722 0.990609i \(-0.456343\pi\)
0.136722 + 0.990609i \(0.456343\pi\)
\(458\) 0 0
\(459\) 3.15464e6 0.698905
\(460\) 0 0
\(461\) −4.07210e6 −0.892413 −0.446207 0.894930i \(-0.647225\pi\)
−0.446207 + 0.894930i \(0.647225\pi\)
\(462\) 0 0
\(463\) −2.02294e6 −0.438561 −0.219280 0.975662i \(-0.570371\pi\)
−0.219280 + 0.975662i \(0.570371\pi\)
\(464\) 0 0
\(465\) 244800. 0.0525024
\(466\) 0 0
\(467\) −3.25097e6 −0.689797 −0.344898 0.938640i \(-0.612087\pi\)
−0.344898 + 0.938640i \(0.612087\pi\)
\(468\) 0 0
\(469\) 1.17066e7 2.45753
\(470\) 0 0
\(471\) −1.04903e6 −0.217890
\(472\) 0 0
\(473\) 184112. 0.0378381
\(474\) 0 0
\(475\) −662500. −0.134726
\(476\) 0 0
\(477\) −5.41304e6 −1.08929
\(478\) 0 0
\(479\) 3.27936e6 0.653056 0.326528 0.945188i \(-0.394121\pi\)
0.326528 + 0.945188i \(0.394121\pi\)
\(480\) 0 0
\(481\) 52052.0 0.0102583
\(482\) 0 0
\(483\) 2.28557e6 0.445786
\(484\) 0 0
\(485\) −2.97595e6 −0.574475
\(486\) 0 0
\(487\) 8.53197e6 1.63015 0.815074 0.579357i \(-0.196696\pi\)
0.815074 + 0.579357i \(0.196696\pi\)
\(488\) 0 0
\(489\) 618256. 0.116922
\(490\) 0 0
\(491\) −1.51265e6 −0.283162 −0.141581 0.989927i \(-0.545219\pi\)
−0.141581 + 0.989927i \(0.545219\pi\)
\(492\) 0 0
\(493\) 5.72198e6 1.06030
\(494\) 0 0
\(495\) −839900. −0.154069
\(496\) 0 0
\(497\) −6.26842e6 −1.13833
\(498\) 0 0
\(499\) 6.49190e6 1.16713 0.583567 0.812065i \(-0.301657\pi\)
0.583567 + 0.812065i \(0.301657\pi\)
\(500\) 0 0
\(501\) −1.58669e6 −0.282421
\(502\) 0 0
\(503\) −8.61770e6 −1.51870 −0.759349 0.650684i \(-0.774482\pi\)
−0.759349 + 0.650684i \(0.774482\pi\)
\(504\) 0 0
\(505\) −2.24745e6 −0.392158
\(506\) 0 0
\(507\) −1.15799e6 −0.200071
\(508\) 0 0
\(509\) 2.67323e6 0.457343 0.228671 0.973504i \(-0.426562\pi\)
0.228671 + 0.973504i \(0.426562\pi\)
\(510\) 0 0
\(511\) 7.44461e6 1.26122
\(512\) 0 0
\(513\) 1.99280e6 0.334326
\(514\) 0 0
\(515\) 487600. 0.0810113
\(516\) 0 0
\(517\) 1.78902e6 0.294367
\(518\) 0 0
\(519\) −2.29390e6 −0.373814
\(520\) 0 0
\(521\) 6.18500e6 0.998264 0.499132 0.866526i \(-0.333652\pi\)
0.499132 + 0.866526i \(0.333652\pi\)
\(522\) 0 0
\(523\) 6.89452e6 1.10217 0.551087 0.834448i \(-0.314213\pi\)
0.551087 + 0.834448i \(0.314213\pi\)
\(524\) 0 0
\(525\) −480000. −0.0760051
\(526\) 0 0
\(527\) −4.10774e6 −0.644283
\(528\) 0 0
\(529\) 2.42023e6 0.376026
\(530\) 0 0
\(531\) −4.54454e6 −0.699445
\(532\) 0 0
\(533\) −2.68783e6 −0.409811
\(534\) 0 0
\(535\) −3.95730e6 −0.597743
\(536\) 0 0
\(537\) 2.37784e6 0.355834
\(538\) 0 0
\(539\) 2.96844e6 0.440104
\(540\) 0 0
\(541\) 155502. 0.0228425 0.0114212 0.999935i \(-0.496364\pi\)
0.0114212 + 0.999935i \(0.496364\pi\)
\(542\) 0 0
\(543\) −428392. −0.0623508
\(544\) 0 0
\(545\) 920750. 0.132785
\(546\) 0 0
\(547\) −1.26544e7 −1.80831 −0.904157 0.427201i \(-0.859500\pi\)
−0.904157 + 0.427201i \(0.859500\pi\)
\(548\) 0 0
\(549\) −7.33255e6 −1.03830
\(550\) 0 0
\(551\) 3.61460e6 0.507202
\(552\) 0 0
\(553\) −6.40512e6 −0.890665
\(554\) 0 0
\(555\) 18200.0 0.00250807
\(556\) 0 0
\(557\) −7.07786e6 −0.966638 −0.483319 0.875444i \(-0.660569\pi\)
−0.483319 + 0.875444i \(0.660569\pi\)
\(558\) 0 0
\(559\) 355784. 0.0481567
\(560\) 0 0
\(561\) −993376. −0.133262
\(562\) 0 0
\(563\) −846636. −0.112571 −0.0562854 0.998415i \(-0.517926\pi\)
−0.0562854 + 0.998415i \(0.517926\pi\)
\(564\) 0 0
\(565\) 279650. 0.0368548
\(566\) 0 0
\(567\) −9.14707e6 −1.19488
\(568\) 0 0
\(569\) 4.96041e6 0.642299 0.321149 0.947029i \(-0.395931\pi\)
0.321149 + 0.947029i \(0.395931\pi\)
\(570\) 0 0
\(571\) −8.96505e6 −1.15070 −0.575351 0.817907i \(-0.695134\pi\)
−0.575351 + 0.817907i \(0.695134\pi\)
\(572\) 0 0
\(573\) −1.87821e6 −0.238978
\(574\) 0 0
\(575\) −1.86000e6 −0.234608
\(576\) 0 0
\(577\) −2.86080e6 −0.357724 −0.178862 0.983874i \(-0.557242\pi\)
−0.178862 + 0.983874i \(0.557242\pi\)
\(578\) 0 0
\(579\) 210824. 0.0261351
\(580\) 0 0
\(581\) 3.20947e6 0.394451
\(582\) 0 0
\(583\) 3.52921e6 0.430037
\(584\) 0 0
\(585\) −1.62305e6 −0.196084
\(586\) 0 0
\(587\) 6.74027e6 0.807387 0.403694 0.914894i \(-0.367726\pi\)
0.403694 + 0.914894i \(0.367726\pi\)
\(588\) 0 0
\(589\) −2.59488e6 −0.308197
\(590\) 0 0
\(591\) 1.82345e6 0.214746
\(592\) 0 0
\(593\) −1.78609e6 −0.208578 −0.104289 0.994547i \(-0.533257\pi\)
−0.104289 + 0.994547i \(0.533257\pi\)
\(594\) 0 0
\(595\) 8.05440e6 0.932697
\(596\) 0 0
\(597\) −3.46000e6 −0.397320
\(598\) 0 0
\(599\) −4.94620e6 −0.563254 −0.281627 0.959524i \(-0.590874\pi\)
−0.281627 + 0.959524i \(0.590874\pi\)
\(600\) 0 0
\(601\) −4.58100e6 −0.517337 −0.258669 0.965966i \(-0.583284\pi\)
−0.258669 + 0.965966i \(0.583284\pi\)
\(602\) 0 0
\(603\) 1.38406e7 1.55011
\(604\) 0 0
\(605\) −3.47868e6 −0.386390
\(606\) 0 0
\(607\) −7.07999e6 −0.779940 −0.389970 0.920828i \(-0.627515\pi\)
−0.389970 + 0.920828i \(0.627515\pi\)
\(608\) 0 0
\(609\) 2.61888e6 0.286136
\(610\) 0 0
\(611\) 3.45717e6 0.374643
\(612\) 0 0
\(613\) 5.09609e6 0.547754 0.273877 0.961765i \(-0.411694\pi\)
0.273877 + 0.961765i \(0.411694\pi\)
\(614\) 0 0
\(615\) −939800. −0.100195
\(616\) 0 0
\(617\) −1.30003e7 −1.37480 −0.687400 0.726279i \(-0.741248\pi\)
−0.687400 + 0.726279i \(0.741248\pi\)
\(618\) 0 0
\(619\) −4.84406e6 −0.508139 −0.254070 0.967186i \(-0.581769\pi\)
−0.254070 + 0.967186i \(0.581769\pi\)
\(620\) 0 0
\(621\) 5.59488e6 0.582186
\(622\) 0 0
\(623\) −1.94630e7 −2.00905
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −627520. −0.0637468
\(628\) 0 0
\(629\) −305396. −0.0307777
\(630\) 0 0
\(631\) −6.22775e6 −0.622670 −0.311335 0.950300i \(-0.600776\pi\)
−0.311335 + 0.950300i \(0.600776\pi\)
\(632\) 0 0
\(633\) −4.42261e6 −0.438702
\(634\) 0 0
\(635\) −1.76380e6 −0.173586
\(636\) 0 0
\(637\) 5.73630e6 0.560123
\(638\) 0 0
\(639\) −7.41110e6 −0.718010
\(640\) 0 0
\(641\) 1.53280e6 0.147347 0.0736734 0.997282i \(-0.476528\pi\)
0.0736734 + 0.997282i \(0.476528\pi\)
\(642\) 0 0
\(643\) 1.74382e7 1.66332 0.831659 0.555287i \(-0.187391\pi\)
0.831659 + 0.555287i \(0.187391\pi\)
\(644\) 0 0
\(645\) 124400. 0.0117739
\(646\) 0 0
\(647\) 4.25469e6 0.399583 0.199792 0.979838i \(-0.435974\pi\)
0.199792 + 0.979838i \(0.435974\pi\)
\(648\) 0 0
\(649\) 2.96296e6 0.276130
\(650\) 0 0
\(651\) −1.88006e6 −0.173868
\(652\) 0 0
\(653\) 3.01085e6 0.276316 0.138158 0.990410i \(-0.455882\pi\)
0.138158 + 0.990410i \(0.455882\pi\)
\(654\) 0 0
\(655\) −1.91130e6 −0.174071
\(656\) 0 0
\(657\) 8.80170e6 0.795524
\(658\) 0 0
\(659\) 8.11462e6 0.727871 0.363936 0.931424i \(-0.381433\pi\)
0.363936 + 0.931424i \(0.381433\pi\)
\(660\) 0 0
\(661\) 2.47370e6 0.220213 0.110107 0.993920i \(-0.464881\pi\)
0.110107 + 0.993920i \(0.464881\pi\)
\(662\) 0 0
\(663\) −1.91963e6 −0.169603
\(664\) 0 0
\(665\) 5.08800e6 0.446162
\(666\) 0 0
\(667\) 1.01482e7 0.883228
\(668\) 0 0
\(669\) −4.48630e6 −0.387546
\(670\) 0 0
\(671\) 4.78070e6 0.409907
\(672\) 0 0
\(673\) 5.77063e6 0.491117 0.245559 0.969382i \(-0.421029\pi\)
0.245559 + 0.969382i \(0.421029\pi\)
\(674\) 0 0
\(675\) −1.17500e6 −0.0992610
\(676\) 0 0
\(677\) 1.67197e7 1.40203 0.701014 0.713147i \(-0.252731\pi\)
0.701014 + 0.713147i \(0.252731\pi\)
\(678\) 0 0
\(679\) 2.28553e7 1.90245
\(680\) 0 0
\(681\) 93392.0 0.00771688
\(682\) 0 0
\(683\) −7.14532e6 −0.586097 −0.293049 0.956098i \(-0.594670\pi\)
−0.293049 + 0.956098i \(0.594670\pi\)
\(684\) 0 0
\(685\) −3.62295e6 −0.295009
\(686\) 0 0
\(687\) −2.38404e6 −0.192718
\(688\) 0 0
\(689\) 6.81996e6 0.547310
\(690\) 0 0
\(691\) 8.78395e6 0.699833 0.349917 0.936781i \(-0.386210\pi\)
0.349917 + 0.936781i \(0.386210\pi\)
\(692\) 0 0
\(693\) 6.45043e6 0.510218
\(694\) 0 0
\(695\) −2.80550e6 −0.220317
\(696\) 0 0
\(697\) 1.57698e7 1.22955
\(698\) 0 0
\(699\) −1.94134e6 −0.150282
\(700\) 0 0
\(701\) −1.60141e7 −1.23086 −0.615428 0.788193i \(-0.711017\pi\)
−0.615428 + 0.788193i \(0.711017\pi\)
\(702\) 0 0
\(703\) −192920. −0.0147228
\(704\) 0 0
\(705\) 1.20880e6 0.0915971
\(706\) 0 0
\(707\) 1.72604e7 1.29868
\(708\) 0 0
\(709\) −1.91354e7 −1.42962 −0.714811 0.699318i \(-0.753487\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(710\) 0 0
\(711\) −7.57272e6 −0.561795
\(712\) 0 0
\(713\) −7.28525e6 −0.536686
\(714\) 0 0
\(715\) 1.05820e6 0.0774110
\(716\) 0 0
\(717\) 195520. 0.0142034
\(718\) 0 0
\(719\) −1.02934e7 −0.742566 −0.371283 0.928520i \(-0.621082\pi\)
−0.371283 + 0.928520i \(0.621082\pi\)
\(720\) 0 0
\(721\) −3.74477e6 −0.268279
\(722\) 0 0
\(723\) −443192. −0.0315316
\(724\) 0 0
\(725\) −2.13125e6 −0.150588
\(726\) 0 0
\(727\) 1.93264e7 1.35618 0.678088 0.734981i \(-0.262809\pi\)
0.678088 + 0.734981i \(0.262809\pi\)
\(728\) 0 0
\(729\) −8.98715e6 −0.626330
\(730\) 0 0
\(731\) −2.08743e6 −0.144484
\(732\) 0 0
\(733\) 5.26197e6 0.361733 0.180866 0.983508i \(-0.442110\pi\)
0.180866 + 0.983508i \(0.442110\pi\)
\(734\) 0 0
\(735\) 2.00570e6 0.136945
\(736\) 0 0
\(737\) −9.02386e6 −0.611961
\(738\) 0 0
\(739\) −2.82944e7 −1.90585 −0.952927 0.303199i \(-0.901945\pi\)
−0.952927 + 0.303199i \(0.901945\pi\)
\(740\) 0 0
\(741\) −1.21264e6 −0.0811309
\(742\) 0 0
\(743\) −2.09863e7 −1.39464 −0.697321 0.716759i \(-0.745625\pi\)
−0.697321 + 0.716759i \(0.745625\pi\)
\(744\) 0 0
\(745\) 1.00938e7 0.666288
\(746\) 0 0
\(747\) 3.79453e6 0.248804
\(748\) 0 0
\(749\) 3.03921e7 1.97950
\(750\) 0 0
\(751\) 1.89668e7 1.22714 0.613572 0.789639i \(-0.289732\pi\)
0.613572 + 0.789639i \(0.289732\pi\)
\(752\) 0 0
\(753\) 6.57499e6 0.422579
\(754\) 0 0
\(755\) 1.11662e7 0.712915
\(756\) 0 0
\(757\) −1.08257e7 −0.686617 −0.343309 0.939223i \(-0.611548\pi\)
−0.343309 + 0.939223i \(0.611548\pi\)
\(758\) 0 0
\(759\) −1.76179e6 −0.111007
\(760\) 0 0
\(761\) 1.90534e7 1.19264 0.596322 0.802745i \(-0.296628\pi\)
0.596322 + 0.802745i \(0.296628\pi\)
\(762\) 0 0
\(763\) −7.07136e6 −0.439736
\(764\) 0 0
\(765\) 9.52265e6 0.588307
\(766\) 0 0
\(767\) 5.72572e6 0.351432
\(768\) 0 0
\(769\) −1.57826e7 −0.962415 −0.481208 0.876607i \(-0.659802\pi\)
−0.481208 + 0.876607i \(0.659802\pi\)
\(770\) 0 0
\(771\) 5.22497e6 0.316554
\(772\) 0 0
\(773\) −2.44049e7 −1.46902 −0.734510 0.678598i \(-0.762588\pi\)
−0.734510 + 0.678598i \(0.762588\pi\)
\(774\) 0 0
\(775\) 1.53000e6 0.0915034
\(776\) 0 0
\(777\) −139776. −0.00830577
\(778\) 0 0
\(779\) 9.96188e6 0.588163
\(780\) 0 0
\(781\) 4.83190e6 0.283459
\(782\) 0 0
\(783\) 6.41080e6 0.373687
\(784\) 0 0
\(785\) −6.55645e6 −0.379747
\(786\) 0 0
\(787\) −3.37607e7 −1.94301 −0.971505 0.237019i \(-0.923830\pi\)
−0.971505 + 0.237019i \(0.923830\pi\)
\(788\) 0 0
\(789\) −8.51334e6 −0.486864
\(790\) 0 0
\(791\) −2.14771e6 −0.122049
\(792\) 0 0
\(793\) 9.23837e6 0.521690
\(794\) 0 0
\(795\) 2.38460e6 0.133813
\(796\) 0 0
\(797\) 2.19885e7 1.22617 0.613083 0.790019i \(-0.289929\pi\)
0.613083 + 0.790019i \(0.289929\pi\)
\(798\) 0 0
\(799\) −2.02837e7 −1.12403
\(800\) 0 0
\(801\) −2.30110e7 −1.26723
\(802\) 0 0
\(803\) −5.73855e6 −0.314061
\(804\) 0 0
\(805\) 1.42848e7 0.776935
\(806\) 0 0
\(807\) −5.76436e6 −0.311578
\(808\) 0 0
\(809\) −2.93597e7 −1.57717 −0.788587 0.614923i \(-0.789187\pi\)
−0.788587 + 0.614923i \(0.789187\pi\)
\(810\) 0 0
\(811\) −3.17703e7 −1.69617 −0.848083 0.529863i \(-0.822243\pi\)
−0.848083 + 0.529863i \(0.822243\pi\)
\(812\) 0 0
\(813\) 372992. 0.0197912
\(814\) 0 0
\(815\) 3.86410e6 0.203777
\(816\) 0 0
\(817\) −1.31864e6 −0.0691148
\(818\) 0 0
\(819\) 1.24650e7 0.649357
\(820\) 0 0
\(821\) −2.71430e6 −0.140540 −0.0702699 0.997528i \(-0.522386\pi\)
−0.0702699 + 0.997528i \(0.522386\pi\)
\(822\) 0 0
\(823\) 1.25866e7 0.647753 0.323877 0.946099i \(-0.395014\pi\)
0.323877 + 0.946099i \(0.395014\pi\)
\(824\) 0 0
\(825\) 370000. 0.0189263
\(826\) 0 0
\(827\) 8.72355e6 0.443537 0.221768 0.975099i \(-0.428817\pi\)
0.221768 + 0.975099i \(0.428817\pi\)
\(828\) 0 0
\(829\) −1.06178e7 −0.536597 −0.268299 0.963336i \(-0.586461\pi\)
−0.268299 + 0.963336i \(0.586461\pi\)
\(830\) 0 0
\(831\) −441192. −0.0221628
\(832\) 0 0
\(833\) −3.36556e7 −1.68053
\(834\) 0 0
\(835\) −9.91680e6 −0.492216
\(836\) 0 0
\(837\) −4.60224e6 −0.227068
\(838\) 0 0
\(839\) −1.67765e7 −0.822805 −0.411403 0.911454i \(-0.634961\pi\)
−0.411403 + 0.911454i \(0.634961\pi\)
\(840\) 0 0
\(841\) −8.88305e6 −0.433084
\(842\) 0 0
\(843\) −768792. −0.0372597
\(844\) 0 0
\(845\) −7.23742e6 −0.348692
\(846\) 0 0
\(847\) 2.67162e7 1.27958
\(848\) 0 0
\(849\) 1.32754e6 0.0632087
\(850\) 0 0
\(851\) −541632. −0.0256378
\(852\) 0 0
\(853\) −2.20186e7 −1.03613 −0.518067 0.855340i \(-0.673348\pi\)
−0.518067 + 0.855340i \(0.673348\pi\)
\(854\) 0 0
\(855\) 6.01550e6 0.281421
\(856\) 0 0
\(857\) 3.16676e7 1.47287 0.736434 0.676510i \(-0.236508\pi\)
0.736434 + 0.676510i \(0.236508\pi\)
\(858\) 0 0
\(859\) −1.58064e7 −0.730886 −0.365443 0.930834i \(-0.619082\pi\)
−0.365443 + 0.930834i \(0.619082\pi\)
\(860\) 0 0
\(861\) 7.21766e6 0.331809
\(862\) 0 0
\(863\) 1.44287e7 0.659476 0.329738 0.944072i \(-0.393040\pi\)
0.329738 + 0.944072i \(0.393040\pi\)
\(864\) 0 0
\(865\) −1.43368e7 −0.651499
\(866\) 0 0
\(867\) 5.58331e6 0.252257
\(868\) 0 0
\(869\) 4.93728e6 0.221788
\(870\) 0 0
\(871\) −1.74380e7 −0.778845
\(872\) 0 0
\(873\) 2.70216e7 1.19999
\(874\) 0 0
\(875\) −3.00000e6 −0.132465
\(876\) 0 0
\(877\) 247902. 0.0108838 0.00544191 0.999985i \(-0.498268\pi\)
0.00544191 + 0.999985i \(0.498268\pi\)
\(878\) 0 0
\(879\) 8.77922e6 0.383252
\(880\) 0 0
\(881\) 4.10268e7 1.78085 0.890426 0.455128i \(-0.150406\pi\)
0.890426 + 0.455128i \(0.150406\pi\)
\(882\) 0 0
\(883\) −4.18015e7 −1.80422 −0.902112 0.431503i \(-0.857984\pi\)
−0.902112 + 0.431503i \(0.857984\pi\)
\(884\) 0 0
\(885\) 2.00200e6 0.0859223
\(886\) 0 0
\(887\) 2.10476e7 0.898241 0.449120 0.893471i \(-0.351737\pi\)
0.449120 + 0.893471i \(0.351737\pi\)
\(888\) 0 0
\(889\) 1.35460e7 0.574852
\(890\) 0 0
\(891\) 7.05087e6 0.297542
\(892\) 0 0
\(893\) −1.28133e7 −0.537690
\(894\) 0 0
\(895\) 1.48615e7 0.620162
\(896\) 0 0
\(897\) −3.40454e6 −0.141279
\(898\) 0 0
\(899\) −8.34768e6 −0.344482
\(900\) 0 0
\(901\) −4.00136e7 −1.64208
\(902\) 0 0
\(903\) −955392. −0.0389908
\(904\) 0 0
\(905\) −2.67745e6 −0.108668
\(906\) 0 0
\(907\) −7.48309e6 −0.302039 −0.151019 0.988531i \(-0.548256\pi\)
−0.151019 + 0.988531i \(0.548256\pi\)
\(908\) 0 0
\(909\) 2.04068e7 0.819155
\(910\) 0 0
\(911\) 6.63165e6 0.264744 0.132372 0.991200i \(-0.457741\pi\)
0.132372 + 0.991200i \(0.457741\pi\)
\(912\) 0 0
\(913\) −2.47397e6 −0.0982239
\(914\) 0 0
\(915\) 3.23020e6 0.127549
\(916\) 0 0
\(917\) 1.46788e7 0.576457
\(918\) 0 0
\(919\) 1.68976e7 0.659990 0.329995 0.943983i \(-0.392953\pi\)
0.329995 + 0.943983i \(0.392953\pi\)
\(920\) 0 0
\(921\) 9.51003e6 0.369431
\(922\) 0 0
\(923\) 9.33733e6 0.360760
\(924\) 0 0
\(925\) 113750. 0.00437116
\(926\) 0 0
\(927\) −4.42741e6 −0.169219
\(928\) 0 0
\(929\) −1.28653e7 −0.489081 −0.244541 0.969639i \(-0.578637\pi\)
−0.244541 + 0.969639i \(0.578637\pi\)
\(930\) 0 0
\(931\) −2.12604e7 −0.803892
\(932\) 0 0
\(933\) 9.49219e6 0.356995
\(934\) 0 0
\(935\) −6.20860e6 −0.232255
\(936\) 0 0
\(937\) 1.06887e7 0.397718 0.198859 0.980028i \(-0.436276\pi\)
0.198859 + 0.980028i \(0.436276\pi\)
\(938\) 0 0
\(939\) −5.71766e6 −0.211619
\(940\) 0 0
\(941\) 2.82455e7 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(942\) 0 0
\(943\) 2.79684e7 1.02421
\(944\) 0 0
\(945\) 9.02400e6 0.328715
\(946\) 0 0
\(947\) 1.70892e7 0.619222 0.309611 0.950863i \(-0.399801\pi\)
0.309611 + 0.950863i \(0.399801\pi\)
\(948\) 0 0
\(949\) −1.10894e7 −0.399706
\(950\) 0 0
\(951\) 8.49849e6 0.304713
\(952\) 0 0
\(953\) 2.22259e7 0.792735 0.396367 0.918092i \(-0.370271\pi\)
0.396367 + 0.918092i \(0.370271\pi\)
\(954\) 0 0
\(955\) −1.17388e7 −0.416500
\(956\) 0 0
\(957\) −2.01872e6 −0.0712519
\(958\) 0 0
\(959\) 2.78243e7 0.976961
\(960\) 0 0
\(961\) −2.26364e7 −0.790678
\(962\) 0 0
\(963\) 3.59323e7 1.24859
\(964\) 0 0
\(965\) 1.31765e6 0.0455493
\(966\) 0 0
\(967\) −2.41551e7 −0.830696 −0.415348 0.909663i \(-0.636340\pi\)
−0.415348 + 0.909663i \(0.636340\pi\)
\(968\) 0 0
\(969\) 7.11472e6 0.243416
\(970\) 0 0
\(971\) 5.48313e7 1.86630 0.933149 0.359491i \(-0.117050\pi\)
0.933149 + 0.359491i \(0.117050\pi\)
\(972\) 0 0
\(973\) 2.15462e7 0.729608
\(974\) 0 0
\(975\) 715000. 0.0240877
\(976\) 0 0
\(977\) −1.56612e7 −0.524915 −0.262457 0.964944i \(-0.584533\pi\)
−0.262457 + 0.964944i \(0.584533\pi\)
\(978\) 0 0
\(979\) 1.50028e7 0.500281
\(980\) 0 0
\(981\) −8.36041e6 −0.277367
\(982\) 0 0
\(983\) 1.63420e7 0.539412 0.269706 0.962943i \(-0.413073\pi\)
0.269706 + 0.962943i \(0.413073\pi\)
\(984\) 0 0
\(985\) 1.13966e7 0.374268
\(986\) 0 0
\(987\) −9.28358e6 −0.303335
\(988\) 0 0
\(989\) −3.70214e6 −0.120355
\(990\) 0 0
\(991\) −1.37576e7 −0.444997 −0.222498 0.974933i \(-0.571421\pi\)
−0.222498 + 0.974933i \(0.571421\pi\)
\(992\) 0 0
\(993\) −1.23994e7 −0.399050
\(994\) 0 0
\(995\) −2.16250e7 −0.692466
\(996\) 0 0
\(997\) −1.29097e7 −0.411320 −0.205660 0.978624i \(-0.565934\pi\)
−0.205660 + 0.978624i \(0.565934\pi\)
\(998\) 0 0
\(999\) −342160. −0.0108471
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 80.6.a.e.1.1 1
3.2 odd 2 720.6.a.a.1.1 1
4.3 odd 2 5.6.a.a.1.1 1
5.2 odd 4 400.6.c.j.49.1 2
5.3 odd 4 400.6.c.j.49.2 2
5.4 even 2 400.6.a.g.1.1 1
8.3 odd 2 320.6.a.j.1.1 1
8.5 even 2 320.6.a.g.1.1 1
12.11 even 2 45.6.a.b.1.1 1
20.3 even 4 25.6.b.a.24.1 2
20.7 even 4 25.6.b.a.24.2 2
20.19 odd 2 25.6.a.a.1.1 1
28.27 even 2 245.6.a.b.1.1 1
44.43 even 2 605.6.a.a.1.1 1
52.51 odd 2 845.6.a.b.1.1 1
60.23 odd 4 225.6.b.e.199.2 2
60.47 odd 4 225.6.b.e.199.1 2
60.59 even 2 225.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.6.a.a.1.1 1 4.3 odd 2
25.6.a.a.1.1 1 20.19 odd 2
25.6.b.a.24.1 2 20.3 even 4
25.6.b.a.24.2 2 20.7 even 4
45.6.a.b.1.1 1 12.11 even 2
80.6.a.e.1.1 1 1.1 even 1 trivial
225.6.a.f.1.1 1 60.59 even 2
225.6.b.e.199.1 2 60.47 odd 4
225.6.b.e.199.2 2 60.23 odd 4
245.6.a.b.1.1 1 28.27 even 2
320.6.a.g.1.1 1 8.5 even 2
320.6.a.j.1.1 1 8.3 odd 2
400.6.a.g.1.1 1 5.4 even 2
400.6.c.j.49.1 2 5.2 odd 4
400.6.c.j.49.2 2 5.3 odd 4
605.6.a.a.1.1 1 44.43 even 2
720.6.a.a.1.1 1 3.2 odd 2
845.6.a.b.1.1 1 52.51 odd 2