Properties

Label 720.6.a.r.1.1
Level $720$
Weight $6$
Character 720.1
Self dual yes
Analytic conductor $115.476$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,6,Mod(1,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(115.476350265\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.0000 q^{5} +22.0000 q^{7} +O(q^{10})\) \(q+25.0000 q^{5} +22.0000 q^{7} -768.000 q^{11} -46.0000 q^{13} -378.000 q^{17} -1100.00 q^{19} -1986.00 q^{23} +625.000 q^{25} +5610.00 q^{29} +3988.00 q^{31} +550.000 q^{35} -142.000 q^{37} -1542.00 q^{41} +5026.00 q^{43} +24738.0 q^{47} -16323.0 q^{49} +14166.0 q^{53} -19200.0 q^{55} +28380.0 q^{59} +5522.00 q^{61} -1150.00 q^{65} +24742.0 q^{67} +42372.0 q^{71} -52126.0 q^{73} -16896.0 q^{77} +39640.0 q^{79} -59826.0 q^{83} -9450.00 q^{85} -57690.0 q^{89} -1012.00 q^{91} -27500.0 q^{95} -144382. q^{97} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 22.0000 0.169698 0.0848492 0.996394i \(-0.472959\pi\)
0.0848492 + 0.996394i \(0.472959\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −768.000 −1.91372 −0.956862 0.290541i \(-0.906165\pi\)
−0.956862 + 0.290541i \(0.906165\pi\)
\(12\) 0 0
\(13\) −46.0000 −0.0754917 −0.0377459 0.999287i \(-0.512018\pi\)
−0.0377459 + 0.999287i \(0.512018\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −378.000 −0.317227 −0.158613 0.987341i \(-0.550702\pi\)
−0.158613 + 0.987341i \(0.550702\pi\)
\(18\) 0 0
\(19\) −1100.00 −0.699051 −0.349525 0.936927i \(-0.613657\pi\)
−0.349525 + 0.936927i \(0.613657\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1986.00 −0.782816 −0.391408 0.920217i \(-0.628012\pi\)
−0.391408 + 0.920217i \(0.628012\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5610.00 1.23870 0.619352 0.785113i \(-0.287395\pi\)
0.619352 + 0.785113i \(0.287395\pi\)
\(30\) 0 0
\(31\) 3988.00 0.745334 0.372667 0.927965i \(-0.378443\pi\)
0.372667 + 0.927965i \(0.378443\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 550.000 0.0758914
\(36\) 0 0
\(37\) −142.000 −0.0170523 −0.00852617 0.999964i \(-0.502714\pi\)
−0.00852617 + 0.999964i \(0.502714\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1542.00 −0.143260 −0.0716300 0.997431i \(-0.522820\pi\)
−0.0716300 + 0.997431i \(0.522820\pi\)
\(42\) 0 0
\(43\) 5026.00 0.414526 0.207263 0.978285i \(-0.433544\pi\)
0.207263 + 0.978285i \(0.433544\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 24738.0 1.63350 0.816752 0.576990i \(-0.195773\pi\)
0.816752 + 0.576990i \(0.195773\pi\)
\(48\) 0 0
\(49\) −16323.0 −0.971202
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14166.0 0.692720 0.346360 0.938102i \(-0.387418\pi\)
0.346360 + 0.938102i \(0.387418\pi\)
\(54\) 0 0
\(55\) −19200.0 −0.855844
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 28380.0 1.06141 0.530704 0.847557i \(-0.321928\pi\)
0.530704 + 0.847557i \(0.321928\pi\)
\(60\) 0 0
\(61\) 5522.00 0.190008 0.0950040 0.995477i \(-0.469714\pi\)
0.0950040 + 0.995477i \(0.469714\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1150.00 −0.0337609
\(66\) 0 0
\(67\) 24742.0 0.673361 0.336680 0.941619i \(-0.390696\pi\)
0.336680 + 0.941619i \(0.390696\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 42372.0 0.997546 0.498773 0.866733i \(-0.333784\pi\)
0.498773 + 0.866733i \(0.333784\pi\)
\(72\) 0 0
\(73\) −52126.0 −1.14485 −0.572423 0.819958i \(-0.693997\pi\)
−0.572423 + 0.819958i \(0.693997\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16896.0 −0.324756
\(78\) 0 0
\(79\) 39640.0 0.714605 0.357302 0.933989i \(-0.383697\pi\)
0.357302 + 0.933989i \(0.383697\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −59826.0 −0.953223 −0.476612 0.879114i \(-0.658135\pi\)
−0.476612 + 0.879114i \(0.658135\pi\)
\(84\) 0 0
\(85\) −9450.00 −0.141868
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −57690.0 −0.772015 −0.386007 0.922496i \(-0.626146\pi\)
−0.386007 + 0.922496i \(0.626146\pi\)
\(90\) 0 0
\(91\) −1012.00 −0.0128108
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −27500.0 −0.312625
\(96\) 0 0
\(97\) −144382. −1.55806 −0.779029 0.626988i \(-0.784288\pi\)
−0.779029 + 0.626988i \(0.784288\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 141258. 1.37787 0.688937 0.724821i \(-0.258078\pi\)
0.688937 + 0.724821i \(0.258078\pi\)
\(102\) 0 0
\(103\) −139814. −1.29855 −0.649273 0.760555i \(-0.724927\pi\)
−0.649273 + 0.760555i \(0.724927\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 86418.0 0.729701 0.364850 0.931066i \(-0.381120\pi\)
0.364850 + 0.931066i \(0.381120\pi\)
\(108\) 0 0
\(109\) 218450. 1.76111 0.880554 0.473947i \(-0.157171\pi\)
0.880554 + 0.473947i \(0.157171\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 28806.0 0.212220 0.106110 0.994354i \(-0.466160\pi\)
0.106110 + 0.994354i \(0.466160\pi\)
\(114\) 0 0
\(115\) −49650.0 −0.350086
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8316.00 −0.0538328
\(120\) 0 0
\(121\) 428773. 2.66234
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 216502. 1.19111 0.595556 0.803314i \(-0.296932\pi\)
0.595556 + 0.803314i \(0.296932\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −244608. −1.24535 −0.622676 0.782479i \(-0.713955\pi\)
−0.622676 + 0.782479i \(0.713955\pi\)
\(132\) 0 0
\(133\) −24200.0 −0.118628
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 239502. 1.09020 0.545102 0.838370i \(-0.316491\pi\)
0.545102 + 0.838370i \(0.316491\pi\)
\(138\) 0 0
\(139\) −30860.0 −0.135475 −0.0677375 0.997703i \(-0.521578\pi\)
−0.0677375 + 0.997703i \(0.521578\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 35328.0 0.144470
\(144\) 0 0
\(145\) 140250. 0.553966
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 100950. 0.372512 0.186256 0.982501i \(-0.440365\pi\)
0.186256 + 0.982501i \(0.440365\pi\)
\(150\) 0 0
\(151\) −12452.0 −0.0444423 −0.0222212 0.999753i \(-0.507074\pi\)
−0.0222212 + 0.999753i \(0.507074\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 99700.0 0.333323
\(156\) 0 0
\(157\) −6022.00 −0.0194981 −0.00974903 0.999952i \(-0.503103\pi\)
−0.00974903 + 0.999952i \(0.503103\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −43692.0 −0.132843
\(162\) 0 0
\(163\) 500866. 1.47656 0.738282 0.674492i \(-0.235637\pi\)
0.738282 + 0.674492i \(0.235637\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 555258. 1.54065 0.770324 0.637652i \(-0.220094\pi\)
0.770324 + 0.637652i \(0.220094\pi\)
\(168\) 0 0
\(169\) −369177. −0.994301
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −417354. −1.06020 −0.530102 0.847934i \(-0.677846\pi\)
−0.530102 + 0.847934i \(0.677846\pi\)
\(174\) 0 0
\(175\) 13750.0 0.0339397
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −52380.0 −0.122189 −0.0610946 0.998132i \(-0.519459\pi\)
−0.0610946 + 0.998132i \(0.519459\pi\)
\(180\) 0 0
\(181\) 546662. 1.24029 0.620144 0.784488i \(-0.287074\pi\)
0.620144 + 0.784488i \(0.287074\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3550.00 −0.00762604
\(186\) 0 0
\(187\) 290304. 0.607084
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −452028. −0.896565 −0.448283 0.893892i \(-0.647964\pi\)
−0.448283 + 0.893892i \(0.647964\pi\)
\(192\) 0 0
\(193\) 485594. 0.938383 0.469191 0.883097i \(-0.344545\pi\)
0.469191 + 0.883097i \(0.344545\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.01018e6 −1.85452 −0.927262 0.374414i \(-0.877844\pi\)
−0.927262 + 0.374414i \(0.877844\pi\)
\(198\) 0 0
\(199\) 807640. 1.44572 0.722862 0.690993i \(-0.242826\pi\)
0.722862 + 0.690993i \(0.242826\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 123420. 0.210206
\(204\) 0 0
\(205\) −38550.0 −0.0640678
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 844800. 1.33779
\(210\) 0 0
\(211\) −149552. −0.231252 −0.115626 0.993293i \(-0.536887\pi\)
−0.115626 + 0.993293i \(0.536887\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 125650. 0.185381
\(216\) 0 0
\(217\) 87736.0 0.126482
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17388.0 0.0239480
\(222\) 0 0
\(223\) 443506. 0.597224 0.298612 0.954375i \(-0.403476\pi\)
0.298612 + 0.954375i \(0.403476\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 420018. 0.541007 0.270504 0.962719i \(-0.412810\pi\)
0.270504 + 0.962719i \(0.412810\pi\)
\(228\) 0 0
\(229\) 1.05875e6 1.33415 0.667075 0.744990i \(-0.267546\pi\)
0.667075 + 0.744990i \(0.267546\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.27345e6 1.53671 0.768353 0.640026i \(-0.221077\pi\)
0.768353 + 0.640026i \(0.221077\pi\)
\(234\) 0 0
\(235\) 618450. 0.730525
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −370680. −0.419763 −0.209882 0.977727i \(-0.567308\pi\)
−0.209882 + 0.977727i \(0.567308\pi\)
\(240\) 0 0
\(241\) −561298. −0.622517 −0.311258 0.950325i \(-0.600750\pi\)
−0.311258 + 0.950325i \(0.600750\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −408075. −0.434335
\(246\) 0 0
\(247\) 50600.0 0.0527726
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 577152. 0.578237 0.289119 0.957293i \(-0.406638\pi\)
0.289119 + 0.957293i \(0.406638\pi\)
\(252\) 0 0
\(253\) 1.52525e6 1.49809
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 651462. 0.615257 0.307628 0.951507i \(-0.400465\pi\)
0.307628 + 0.951507i \(0.400465\pi\)
\(258\) 0 0
\(259\) −3124.00 −0.00289375
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 917574. 0.817997 0.408999 0.912535i \(-0.365878\pi\)
0.408999 + 0.912535i \(0.365878\pi\)
\(264\) 0 0
\(265\) 354150. 0.309794
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 735390. 0.619637 0.309818 0.950796i \(-0.399732\pi\)
0.309818 + 0.950796i \(0.399732\pi\)
\(270\) 0 0
\(271\) 1.12131e6 0.927474 0.463737 0.885973i \(-0.346508\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −480000. −0.382745
\(276\) 0 0
\(277\) −1.66034e6 −1.30016 −0.650082 0.759864i \(-0.725265\pi\)
−0.650082 + 0.759864i \(0.725265\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.45210e6 −1.09706 −0.548531 0.836130i \(-0.684813\pi\)
−0.548531 + 0.836130i \(0.684813\pi\)
\(282\) 0 0
\(283\) −309014. −0.229357 −0.114679 0.993403i \(-0.536584\pi\)
−0.114679 + 0.993403i \(0.536584\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −33924.0 −0.0243110
\(288\) 0 0
\(289\) −1.27697e6 −0.899367
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.59301e6 1.08405 0.542024 0.840363i \(-0.317658\pi\)
0.542024 + 0.840363i \(0.317658\pi\)
\(294\) 0 0
\(295\) 709500. 0.474676
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 91356.0 0.0590961
\(300\) 0 0
\(301\) 110572. 0.0703443
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 138050. 0.0849741
\(306\) 0 0
\(307\) −1.24726e6 −0.755284 −0.377642 0.925952i \(-0.623265\pi\)
−0.377642 + 0.925952i \(0.623265\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −665988. −0.390450 −0.195225 0.980758i \(-0.562544\pi\)
−0.195225 + 0.980758i \(0.562544\pi\)
\(312\) 0 0
\(313\) −591286. −0.341143 −0.170572 0.985345i \(-0.554561\pi\)
−0.170572 + 0.985345i \(0.554561\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 516342. 0.288595 0.144298 0.989534i \(-0.453908\pi\)
0.144298 + 0.989534i \(0.453908\pi\)
\(318\) 0 0
\(319\) −4.30848e6 −2.37054
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 415800. 0.221757
\(324\) 0 0
\(325\) −28750.0 −0.0150983
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 544236. 0.277203
\(330\) 0 0
\(331\) 3.29577e6 1.65343 0.826717 0.562619i \(-0.190206\pi\)
0.826717 + 0.562619i \(0.190206\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 618550. 0.301136
\(336\) 0 0
\(337\) 1.91098e6 0.916602 0.458301 0.888797i \(-0.348458\pi\)
0.458301 + 0.888797i \(0.348458\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.06278e6 −1.42636
\(342\) 0 0
\(343\) −728860. −0.334510
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.42006e6 1.07895 0.539476 0.842001i \(-0.318622\pi\)
0.539476 + 0.842001i \(0.318622\pi\)
\(348\) 0 0
\(349\) 2.50727e6 1.10189 0.550944 0.834542i \(-0.314268\pi\)
0.550944 + 0.834542i \(0.314268\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 413166. 0.176477 0.0882384 0.996099i \(-0.471876\pi\)
0.0882384 + 0.996099i \(0.471876\pi\)
\(354\) 0 0
\(355\) 1.05930e6 0.446116
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.73772e6 0.711613 0.355806 0.934560i \(-0.384206\pi\)
0.355806 + 0.934560i \(0.384206\pi\)
\(360\) 0 0
\(361\) −1.26610e6 −0.511328
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.30315e6 −0.511991
\(366\) 0 0
\(367\) −1.16098e6 −0.449944 −0.224972 0.974365i \(-0.572229\pi\)
−0.224972 + 0.974365i \(0.572229\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 311652. 0.117553
\(372\) 0 0
\(373\) 343754. 0.127931 0.0639655 0.997952i \(-0.479625\pi\)
0.0639655 + 0.997952i \(0.479625\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −258060. −0.0935120
\(378\) 0 0
\(379\) −573140. −0.204957 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.88055e6 −1.00341 −0.501704 0.865039i \(-0.667293\pi\)
−0.501704 + 0.865039i \(0.667293\pi\)
\(384\) 0 0
\(385\) −422400. −0.145235
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.08559e6 1.03387 0.516933 0.856026i \(-0.327074\pi\)
0.516933 + 0.856026i \(0.327074\pi\)
\(390\) 0 0
\(391\) 750708. 0.248330
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 991000. 0.319581
\(396\) 0 0
\(397\) 885458. 0.281963 0.140981 0.990012i \(-0.454974\pi\)
0.140981 + 0.990012i \(0.454974\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.75344e6 1.16565 0.582825 0.812598i \(-0.301947\pi\)
0.582825 + 0.812598i \(0.301947\pi\)
\(402\) 0 0
\(403\) −183448. −0.0562666
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 109056. 0.0326335
\(408\) 0 0
\(409\) −1.94653e6 −0.575377 −0.287689 0.957724i \(-0.592887\pi\)
−0.287689 + 0.957724i \(0.592887\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 624360. 0.180119
\(414\) 0 0
\(415\) −1.49565e6 −0.426295
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.99166e6 −0.832486 −0.416243 0.909253i \(-0.636654\pi\)
−0.416243 + 0.909253i \(0.636654\pi\)
\(420\) 0 0
\(421\) 3.96660e6 1.09072 0.545360 0.838202i \(-0.316393\pi\)
0.545360 + 0.838202i \(0.316393\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −236250. −0.0634453
\(426\) 0 0
\(427\) 121484. 0.0322440
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.17115e6 −1.34089 −0.670446 0.741958i \(-0.733897\pi\)
−0.670446 + 0.741958i \(0.733897\pi\)
\(432\) 0 0
\(433\) −4.53485e6 −1.16237 −0.581183 0.813773i \(-0.697410\pi\)
−0.581183 + 0.813773i \(0.697410\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.18460e6 0.547228
\(438\) 0 0
\(439\) 1.08220e6 0.268007 0.134004 0.990981i \(-0.457217\pi\)
0.134004 + 0.990981i \(0.457217\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.08079e6 −0.261656 −0.130828 0.991405i \(-0.541764\pi\)
−0.130828 + 0.991405i \(0.541764\pi\)
\(444\) 0 0
\(445\) −1.44225e6 −0.345255
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.61783e6 −0.612810 −0.306405 0.951901i \(-0.599126\pi\)
−0.306405 + 0.951901i \(0.599126\pi\)
\(450\) 0 0
\(451\) 1.18426e6 0.274160
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −25300.0 −0.00572917
\(456\) 0 0
\(457\) 1.59046e6 0.356231 0.178115 0.984010i \(-0.443000\pi\)
0.178115 + 0.984010i \(0.443000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.25470e6 −0.932431 −0.466216 0.884671i \(-0.654383\pi\)
−0.466216 + 0.884671i \(0.654383\pi\)
\(462\) 0 0
\(463\) −3.26605e6 −0.708061 −0.354031 0.935234i \(-0.615189\pi\)
−0.354031 + 0.935234i \(0.615189\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −601542. −0.127636 −0.0638181 0.997962i \(-0.520328\pi\)
−0.0638181 + 0.997962i \(0.520328\pi\)
\(468\) 0 0
\(469\) 544324. 0.114268
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.85997e6 −0.793288
\(474\) 0 0
\(475\) −687500. −0.139810
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.57932e6 −0.911931 −0.455966 0.889997i \(-0.650706\pi\)
−0.455966 + 0.889997i \(0.650706\pi\)
\(480\) 0 0
\(481\) 6532.00 0.00128731
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.60955e6 −0.696785
\(486\) 0 0
\(487\) −7.05226e6 −1.34743 −0.673714 0.738992i \(-0.735302\pi\)
−0.673714 + 0.738992i \(0.735302\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.62349e6 −0.491106 −0.245553 0.969383i \(-0.578970\pi\)
−0.245553 + 0.969383i \(0.578970\pi\)
\(492\) 0 0
\(493\) −2.12058e6 −0.392950
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 932184. 0.169282
\(498\) 0 0
\(499\) 3.61234e6 0.649437 0.324719 0.945811i \(-0.394730\pi\)
0.324719 + 0.945811i \(0.394730\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.15629e6 1.61361 0.806807 0.590815i \(-0.201194\pi\)
0.806807 + 0.590815i \(0.201194\pi\)
\(504\) 0 0
\(505\) 3.53145e6 0.616204
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.26159e6 −1.24233 −0.621165 0.783679i \(-0.713340\pi\)
−0.621165 + 0.783679i \(0.713340\pi\)
\(510\) 0 0
\(511\) −1.14677e6 −0.194279
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.49535e6 −0.580728
\(516\) 0 0
\(517\) −1.89988e7 −3.12608
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.81020e6 −0.937771 −0.468886 0.883259i \(-0.655344\pi\)
−0.468886 + 0.883259i \(0.655344\pi\)
\(522\) 0 0
\(523\) 8.17067e6 1.30618 0.653090 0.757280i \(-0.273472\pi\)
0.653090 + 0.757280i \(0.273472\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.50746e6 −0.236440
\(528\) 0 0
\(529\) −2.49215e6 −0.387199
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 70932.0 0.0108149
\(534\) 0 0
\(535\) 2.16045e6 0.326332
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.25361e7 1.85861
\(540\) 0 0
\(541\) −817378. −0.120069 −0.0600343 0.998196i \(-0.519121\pi\)
−0.0600343 + 0.998196i \(0.519121\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.46125e6 0.787591
\(546\) 0 0
\(547\) 3.50750e6 0.501221 0.250611 0.968088i \(-0.419369\pi\)
0.250611 + 0.968088i \(0.419369\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.17100e6 −0.865918
\(552\) 0 0
\(553\) 872080. 0.121267
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.61490e6 −1.31313 −0.656563 0.754271i \(-0.727991\pi\)
−0.656563 + 0.754271i \(0.727991\pi\)
\(558\) 0 0
\(559\) −231196. −0.0312933
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.01941e6 0.268506 0.134253 0.990947i \(-0.457136\pi\)
0.134253 + 0.990947i \(0.457136\pi\)
\(564\) 0 0
\(565\) 720150. 0.0949078
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.37859e6 −0.178507 −0.0892533 0.996009i \(-0.528448\pi\)
−0.0892533 + 0.996009i \(0.528448\pi\)
\(570\) 0 0
\(571\) −8.54295e6 −1.09652 −0.548261 0.836307i \(-0.684710\pi\)
−0.548261 + 0.836307i \(0.684710\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.24125e6 −0.156563
\(576\) 0 0
\(577\) −2.31458e6 −0.289423 −0.144711 0.989474i \(-0.546225\pi\)
−0.144711 + 0.989474i \(0.546225\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.31617e6 −0.161760
\(582\) 0 0
\(583\) −1.08795e7 −1.32568
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 928338. 0.111202 0.0556008 0.998453i \(-0.482293\pi\)
0.0556008 + 0.998453i \(0.482293\pi\)
\(588\) 0 0
\(589\) −4.38680e6 −0.521026
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 909486. 0.106209 0.0531043 0.998589i \(-0.483088\pi\)
0.0531043 + 0.998589i \(0.483088\pi\)
\(594\) 0 0
\(595\) −207900. −0.0240748
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.51136e6 −0.969241 −0.484621 0.874724i \(-0.661042\pi\)
−0.484621 + 0.874724i \(0.661042\pi\)
\(600\) 0 0
\(601\) 6.12498e6 0.691701 0.345851 0.938290i \(-0.387590\pi\)
0.345851 + 0.938290i \(0.387590\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.07193e7 1.19064
\(606\) 0 0
\(607\) 4.51646e6 0.497538 0.248769 0.968563i \(-0.419974\pi\)
0.248769 + 0.968563i \(0.419974\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.13795e6 −0.123316
\(612\) 0 0
\(613\) 9.63979e6 1.03614 0.518068 0.855340i \(-0.326651\pi\)
0.518068 + 0.855340i \(0.326651\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.92650e6 1.04974 0.524872 0.851181i \(-0.324113\pi\)
0.524872 + 0.851181i \(0.324113\pi\)
\(618\) 0 0
\(619\) −7.63322e6 −0.800721 −0.400360 0.916358i \(-0.631115\pi\)
−0.400360 + 0.916358i \(0.631115\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.26918e6 −0.131010
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 53676.0 0.00540946
\(630\) 0 0
\(631\) −1.80314e7 −1.80284 −0.901418 0.432949i \(-0.857473\pi\)
−0.901418 + 0.432949i \(0.857473\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.41255e6 0.532681
\(636\) 0 0
\(637\) 750858. 0.0733178
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.30190e6 −0.894184 −0.447092 0.894488i \(-0.647540\pi\)
−0.447092 + 0.894488i \(0.647540\pi\)
\(642\) 0 0
\(643\) 1.38332e7 1.31946 0.659730 0.751503i \(-0.270671\pi\)
0.659730 + 0.751503i \(0.270671\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.48997e7 −1.39932 −0.699658 0.714478i \(-0.746664\pi\)
−0.699658 + 0.714478i \(0.746664\pi\)
\(648\) 0 0
\(649\) −2.17958e7 −2.03124
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.93306e7 1.77403 0.887016 0.461738i \(-0.152774\pi\)
0.887016 + 0.461738i \(0.152774\pi\)
\(654\) 0 0
\(655\) −6.11520e6 −0.556939
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.06110e6 −0.364276 −0.182138 0.983273i \(-0.558302\pi\)
−0.182138 + 0.983273i \(0.558302\pi\)
\(660\) 0 0
\(661\) −1.35152e7 −1.20315 −0.601575 0.798816i \(-0.705460\pi\)
−0.601575 + 0.798816i \(0.705460\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −605000. −0.0530519
\(666\) 0 0
\(667\) −1.11415e7 −0.969678
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.24090e6 −0.363623
\(672\) 0 0
\(673\) 1.43520e7 1.22144 0.610722 0.791845i \(-0.290879\pi\)
0.610722 + 0.791845i \(0.290879\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.89530e6 −0.158930 −0.0794650 0.996838i \(-0.525321\pi\)
−0.0794650 + 0.996838i \(0.525321\pi\)
\(678\) 0 0
\(679\) −3.17640e6 −0.264400
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.91641e6 0.239220 0.119610 0.992821i \(-0.461836\pi\)
0.119610 + 0.992821i \(0.461836\pi\)
\(684\) 0 0
\(685\) 5.98755e6 0.487554
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −651636. −0.0522946
\(690\) 0 0
\(691\) −1.44278e7 −1.14949 −0.574743 0.818334i \(-0.694898\pi\)
−0.574743 + 0.818334i \(0.694898\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −771500. −0.0605862
\(696\) 0 0
\(697\) 582876. 0.0454458
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.58679e7 1.21962 0.609811 0.792547i \(-0.291246\pi\)
0.609811 + 0.792547i \(0.291246\pi\)
\(702\) 0 0
\(703\) 156200. 0.0119205
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.10768e6 0.233823
\(708\) 0 0
\(709\) −301810. −0.0225485 −0.0112743 0.999936i \(-0.503589\pi\)
−0.0112743 + 0.999936i \(0.503589\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.92017e6 −0.583459
\(714\) 0 0
\(715\) 883200. 0.0646091
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.12677e7 1.53426 0.767130 0.641492i \(-0.221684\pi\)
0.767130 + 0.641492i \(0.221684\pi\)
\(720\) 0 0
\(721\) −3.07591e6 −0.220361
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.50625e6 0.247741
\(726\) 0 0
\(727\) −1.55009e7 −1.08773 −0.543863 0.839174i \(-0.683039\pi\)
−0.543863 + 0.839174i \(0.683039\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.89983e6 −0.131499
\(732\) 0 0
\(733\) −1.21850e7 −0.837653 −0.418827 0.908066i \(-0.637559\pi\)
−0.418827 + 0.908066i \(0.637559\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.90019e7 −1.28863
\(738\) 0 0
\(739\) 2.90282e7 1.95528 0.977641 0.210282i \(-0.0674382\pi\)
0.977641 + 0.210282i \(0.0674382\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.61145e7 1.07089 0.535445 0.844570i \(-0.320144\pi\)
0.535445 + 0.844570i \(0.320144\pi\)
\(744\) 0 0
\(745\) 2.52375e6 0.166593
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.90120e6 0.123829
\(750\) 0 0
\(751\) 2.92431e6 0.189201 0.0946005 0.995515i \(-0.469843\pi\)
0.0946005 + 0.995515i \(0.469843\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −311300. −0.0198752
\(756\) 0 0
\(757\) 2.60325e7 1.65111 0.825557 0.564319i \(-0.190861\pi\)
0.825557 + 0.564319i \(0.190861\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.63263e7 −1.02194 −0.510970 0.859598i \(-0.670714\pi\)
−0.510970 + 0.859598i \(0.670714\pi\)
\(762\) 0 0
\(763\) 4.80590e6 0.298857
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.30548e6 −0.0801275
\(768\) 0 0
\(769\) 2.58132e7 1.57408 0.787040 0.616902i \(-0.211612\pi\)
0.787040 + 0.616902i \(0.211612\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.90592e7 1.14725 0.573624 0.819119i \(-0.305537\pi\)
0.573624 + 0.819119i \(0.305537\pi\)
\(774\) 0 0
\(775\) 2.49250e6 0.149067
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.69620e6 0.100146
\(780\) 0 0
\(781\) −3.25417e7 −1.90903
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −150550. −0.00871980
\(786\) 0 0
\(787\) 1.73411e7 0.998021 0.499011 0.866596i \(-0.333697\pi\)
0.499011 + 0.866596i \(0.333697\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 633732. 0.0360134
\(792\) 0 0
\(793\) −254012. −0.0143440
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.58169e7 1.43965 0.719827 0.694153i \(-0.244221\pi\)
0.719827 + 0.694153i \(0.244221\pi\)
\(798\) 0 0
\(799\) −9.35096e6 −0.518190
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.00328e7 2.19092
\(804\) 0 0
\(805\) −1.09230e6 −0.0594090
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.88489e6 −0.477288 −0.238644 0.971107i \(-0.576703\pi\)
−0.238644 + 0.971107i \(0.576703\pi\)
\(810\) 0 0
\(811\) 2.46396e7 1.31547 0.657735 0.753249i \(-0.271515\pi\)
0.657735 + 0.753249i \(0.271515\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.25216e7 0.660340
\(816\) 0 0
\(817\) −5.52860e6 −0.289774
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.13768e7 −0.589062 −0.294531 0.955642i \(-0.595163\pi\)
−0.294531 + 0.955642i \(0.595163\pi\)
\(822\) 0 0
\(823\) 1.30783e7 0.673057 0.336529 0.941673i \(-0.390747\pi\)
0.336529 + 0.941673i \(0.390747\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.57188e7 −1.81607 −0.908037 0.418891i \(-0.862419\pi\)
−0.908037 + 0.418891i \(0.862419\pi\)
\(828\) 0 0
\(829\) 1.61880e7 0.818103 0.409052 0.912511i \(-0.365860\pi\)
0.409052 + 0.912511i \(0.365860\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6.17009e6 0.308091
\(834\) 0 0
\(835\) 1.38814e7 0.688999
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.55497e7 −1.25309 −0.626543 0.779387i \(-0.715531\pi\)
−0.626543 + 0.779387i \(0.715531\pi\)
\(840\) 0 0
\(841\) 1.09610e7 0.534390
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.22942e6 −0.444665
\(846\) 0 0
\(847\) 9.43301e6 0.451795
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 282012. 0.0133488
\(852\) 0 0
\(853\) −2.22953e7 −1.04916 −0.524579 0.851362i \(-0.675777\pi\)
−0.524579 + 0.851362i \(0.675777\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.96872e7 −0.915656 −0.457828 0.889041i \(-0.651372\pi\)
−0.457828 + 0.889041i \(0.651372\pi\)
\(858\) 0 0
\(859\) −6.77582e6 −0.313313 −0.156657 0.987653i \(-0.550072\pi\)
−0.156657 + 0.987653i \(0.550072\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.63804e7 −1.20574 −0.602871 0.797839i \(-0.705977\pi\)
−0.602871 + 0.797839i \(0.705977\pi\)
\(864\) 0 0
\(865\) −1.04338e7 −0.474138
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −3.04435e7 −1.36756
\(870\) 0 0
\(871\) −1.13813e6 −0.0508332
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 343750. 0.0151783
\(876\) 0 0
\(877\) 2.95161e7 1.29587 0.647934 0.761697i \(-0.275633\pi\)
0.647934 + 0.761697i \(0.275633\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.48565e7 0.644877 0.322438 0.946590i \(-0.395498\pi\)
0.322438 + 0.946590i \(0.395498\pi\)
\(882\) 0 0
\(883\) 1.45340e7 0.627313 0.313656 0.949537i \(-0.398446\pi\)
0.313656 + 0.949537i \(0.398446\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.72028e7 −0.734160 −0.367080 0.930189i \(-0.619642\pi\)
−0.367080 + 0.930189i \(0.619642\pi\)
\(888\) 0 0
\(889\) 4.76304e6 0.202130
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.72118e7 −1.14190
\(894\) 0 0
\(895\) −1.30950e6 −0.0546447
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.23727e7 0.923249
\(900\) 0 0
\(901\) −5.35475e6 −0.219749
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.36666e7 0.554674
\(906\) 0 0
\(907\) 3.44434e7 1.39023 0.695116 0.718897i \(-0.255353\pi\)
0.695116 + 0.718897i \(0.255353\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −983748. −0.0392724 −0.0196362 0.999807i \(-0.506251\pi\)
−0.0196362 + 0.999807i \(0.506251\pi\)
\(912\) 0 0
\(913\) 4.59464e7 1.82421
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5.38138e6 −0.211334
\(918\) 0 0
\(919\) −3.08857e7 −1.20634 −0.603168 0.797614i \(-0.706095\pi\)
−0.603168 + 0.797614i \(0.706095\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.94911e6 −0.0753065
\(924\) 0 0
\(925\) −88750.0 −0.00341047
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.20874e7 1.21982 0.609909 0.792472i \(-0.291206\pi\)
0.609909 + 0.792472i \(0.291206\pi\)
\(930\) 0 0
\(931\) 1.79553e7 0.678920
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.25760e6 0.271496
\(936\) 0 0
\(937\) 1.52520e7 0.567515 0.283757 0.958896i \(-0.408419\pi\)
0.283757 + 0.958896i \(0.408419\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.48166e6 −0.128178 −0.0640889 0.997944i \(-0.520414\pi\)
−0.0640889 + 0.997944i \(0.520414\pi\)
\(942\) 0 0
\(943\) 3.06241e6 0.112146
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.54010e7 −0.920398 −0.460199 0.887816i \(-0.652222\pi\)
−0.460199 + 0.887816i \(0.652222\pi\)
\(948\) 0 0
\(949\) 2.39780e6 0.0864265
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.97352e7 1.77391 0.886955 0.461856i \(-0.152816\pi\)
0.886955 + 0.461856i \(0.152816\pi\)
\(954\) 0 0
\(955\) −1.13007e7 −0.400956
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 5.26904e6 0.185006
\(960\) 0 0
\(961\) −1.27250e7 −0.444477
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.21398e7 0.419658
\(966\) 0 0
\(967\) −3.05173e7 −1.04949 −0.524747 0.851258i \(-0.675840\pi\)
−0.524747 + 0.851258i \(0.675840\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.19854e7 1.08869 0.544344 0.838862i \(-0.316779\pi\)
0.544344 + 0.838862i \(0.316779\pi\)
\(972\) 0 0
\(973\) −678920. −0.0229899
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.90786e6 −0.0974623 −0.0487312 0.998812i \(-0.515518\pi\)
−0.0487312 + 0.998812i \(0.515518\pi\)
\(978\) 0 0
\(979\) 4.43059e7 1.47742
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.49621e7 1.15402 0.577010 0.816737i \(-0.304219\pi\)
0.577010 + 0.816737i \(0.304219\pi\)
\(984\) 0 0
\(985\) −2.52544e7 −0.829368
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.98164e6 −0.324497
\(990\) 0 0
\(991\) −3.00465e6 −0.0971874 −0.0485937 0.998819i \(-0.515474\pi\)
−0.0485937 + 0.998819i \(0.515474\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.01910e7 0.646547
\(996\) 0 0
\(997\) 3.20789e7 1.02207 0.511035 0.859560i \(-0.329262\pi\)
0.511035 + 0.859560i \(0.329262\pi\)
\(998\) 0 0
\(999\) 0 0
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 720.6.a.r.1.1 1
3.2 odd 2 80.6.a.h.1.1 1
4.3 odd 2 90.6.a.f.1.1 1
12.11 even 2 10.6.a.a.1.1 1
15.2 even 4 400.6.c.a.49.1 2
15.8 even 4 400.6.c.a.49.2 2
15.14 odd 2 400.6.a.a.1.1 1
20.3 even 4 450.6.c.o.199.1 2
20.7 even 4 450.6.c.o.199.2 2
20.19 odd 2 450.6.a.h.1.1 1
24.5 odd 2 320.6.a.a.1.1 1
24.11 even 2 320.6.a.p.1.1 1
60.23 odd 4 50.6.b.d.49.2 2
60.47 odd 4 50.6.b.d.49.1 2
60.59 even 2 50.6.a.g.1.1 1
84.83 odd 2 490.6.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.a.1.1 1 12.11 even 2
50.6.a.g.1.1 1 60.59 even 2
50.6.b.d.49.1 2 60.47 odd 4
50.6.b.d.49.2 2 60.23 odd 4
80.6.a.h.1.1 1 3.2 odd 2
90.6.a.f.1.1 1 4.3 odd 2
320.6.a.a.1.1 1 24.5 odd 2
320.6.a.p.1.1 1 24.11 even 2
400.6.a.a.1.1 1 15.14 odd 2
400.6.c.a.49.1 2 15.2 even 4
400.6.c.a.49.2 2 15.8 even 4
450.6.a.h.1.1 1 20.19 odd 2
450.6.c.o.199.1 2 20.3 even 4
450.6.c.o.199.2 2 20.7 even 4
490.6.a.j.1.1 1 84.83 odd 2
720.6.a.r.1.1 1 1.1 even 1 trivial