↑

Properties

Label 900.6.a.g.1.1
Level $900$
Weight $6$
Character 900.1
Self dual yes
Analytic conductor $144.345$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [900,6,Mod(1,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("900.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.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: \(144.345437832\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+16.0000 q^{7} +O(q^{10})\) \(q+16.0000 q^{7} +564.000 q^{11} +370.000 q^{13} -1086.00 q^{17} -2860.00 q^{19} +1584.00 q^{23} -1134.00 q^{29} -6016.00 q^{31} +538.000 q^{37} -11370.0 q^{41} -5444.00 q^{43} +10296.0 q^{47} -16551.0 q^{49} +34758.0 q^{53} +26196.0 q^{59} +9422.00 q^{61} +51124.0 q^{67} -14520.0 q^{71} +22678.0 q^{73} +9024.00 q^{77} -97312.0 q^{79} -7956.00 q^{83} +47910.0 q^{89} +5920.00 q^{91} -140738. q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) 0 0
\(6\) 0 0
\(7\) 16.0000 0.123417 0.0617085 − 0.998094i \(-0.480345\pi\)
0.0617085 + 0.998094i \(0.480345\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 564.000 1.40539 0.702696 − 0.711490i \(-0.251979\pi\)
0.702696 + 0.711490i \(0.251979\pi\)
\(12\) 0 0
\(13\) 370.000 0.607216 0.303608 − 0.952797i \(-0.401809\pi\)
0.303608 + 0.952797i \(0.401809\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1086.00 −0.911397 −0.455698 − 0.890134i \(-0.650610\pi\)
−0.455698 + 0.890134i \(0.650610\pi\)
\(18\) 0 0
\(19\) −2860.00 −1.81753 −0.908766 − 0.417306i \(-0.862974\pi\)
−0.908766 + 0.417306i \(0.862974\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1584.00 0.624361 0.312180 − 0.950023i \(-0.398941\pi\)
0.312180 + 0.950023i \(0.398941\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1134.00 −0.250391 −0.125195 − 0.992132i \(-0.539956\pi\)
−0.125195 + 0.992132i \(0.539956\pi\)
\(30\) 0 0
\(31\) −6016.00 −1.12436 −0.562178 − 0.827016i \(-0.690036\pi\)
−0.562178 + 0.827016i \(0.690036\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 538.000 0.0646068 0.0323034 − 0.999478i \(-0.489716\pi\)
0.0323034 + 0.999478i \(0.489716\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11370.0 −1.05633 −0.528166 − 0.849141i \(-0.677120\pi\)
−0.528166 + 0.849141i \(0.677120\pi\)
\(42\) 0 0
\(43\) −5444.00 −0.449001 −0.224500 − 0.974474i \(-0.572075\pi\)
−0.224500 + 0.974474i \(0.572075\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10296.0 0.679867 0.339933 − 0.940449i \(-0.389595\pi\)
0.339933 + 0.940449i \(0.389595\pi\)
\(48\) 0 0
\(49\) −16551.0 −0.984768
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 34758.0 1.69967 0.849836 − 0.527047i \(-0.176701\pi\)
0.849836 + 0.527047i \(0.176701\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 26196.0 0.979727 0.489863 − 0.871799i \(-0.337047\pi\)
0.489863 + 0.871799i \(0.337047\pi\)
\(60\) 0 0
\(61\) 9422.00 0.324204 0.162102 − 0.986774i \(-0.448173\pi\)
0.162102 + 0.986774i \(0.448173\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 51124.0 1.39135 0.695677 − 0.718354i \(-0.255104\pi\)
0.695677 + 0.718354i \(0.255104\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14520.0 −0.341838 −0.170919 − 0.985285i \(-0.554674\pi\)
−0.170919 + 0.985285i \(0.554674\pi\)
\(72\) 0 0
\(73\) 22678.0 0.498078 0.249039 − 0.968493i \(-0.419885\pi\)
0.249039 + 0.968493i \(0.419885\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9024.00 0.173449
\(78\) 0 0
\(79\) −97312.0 −1.75428 −0.877140 − 0.480236i \(-0.840551\pi\)
−0.877140 + 0.480236i \(0.840551\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7956.00 −0.126765 −0.0633825 − 0.997989i \(-0.520189\pi\)
−0.0633825 + 0.997989i \(0.520189\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 47910.0 0.641137 0.320569 − 0.947225i \(-0.396126\pi\)
0.320569 + 0.947225i \(0.396126\pi\)
\(90\) 0 0
\(91\) 5920.00 0.0749408
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −140738. −1.51874 −0.759368 − 0.650662i \(-0.774492\pi\)
−0.759368 + 0.650662i \(0.774492\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −85398.0 −0.832999 −0.416499 − 0.909136i \(-0.636743\pi\)
−0.416499 + 0.909136i \(0.636743\pi\)
\(102\) 0 0
\(103\) −198656. −1.84505 −0.922526 − 0.385935i \(-0.873879\pi\)
−0.922526 + 0.385935i \(0.873879\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −116268. −0.981750 −0.490875 − 0.871230i \(-0.663323\pi\)
−0.490875 + 0.871230i \(0.663323\pi\)
\(108\) 0 0
\(109\) −146722. −1.18285 −0.591424 − 0.806361i \(-0.701434\pi\)
−0.591424 + 0.806361i \(0.701434\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 210882. 1.55361 0.776807 − 0.629738i \(-0.216838\pi\)
0.776807 + 0.629738i \(0.216838\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −17376.0 −0.112482
\(120\) 0 0
\(121\) 157045. 0.975126
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −244424. −1.34473 −0.672364 − 0.740221i \(-0.734721\pi\)
−0.672364 + 0.740221i \(0.734721\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 145308. 0.739795 0.369897 − 0.929073i \(-0.379393\pi\)
0.369897 + 0.929073i \(0.379393\pi\)
\(132\) 0 0
\(133\) −45760.0 −0.224314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −125478. −0.571171 −0.285586 − 0.958353i \(-0.592188\pi\)
−0.285586 + 0.958353i \(0.592188\pi\)
\(138\) 0 0
\(139\) 251756. 1.10520 0.552602 − 0.833445i \(-0.313635\pi\)
0.552602 + 0.833445i \(0.313635\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 208680. 0.853377
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 167322. 0.617430 0.308715 − 0.951155i \(-0.400101\pi\)
0.308715 + 0.951155i \(0.400101\pi\)
\(150\) 0 0
\(151\) 68120.0 0.243126 0.121563 − 0.992584i \(-0.461209\pi\)
0.121563 + 0.992584i \(0.461209\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 361762. 1.17132 0.585658 − 0.810559i \(-0.300836\pi\)
0.585658 + 0.810559i \(0.300836\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 25344.0 0.0770567
\(162\) 0 0
\(163\) −121820. −0.359128 −0.179564 − 0.983746i \(-0.557469\pi\)
−0.179564 + 0.983746i \(0.557469\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −409008. −1.13486 −0.567428 − 0.823423i \(-0.692061\pi\)
−0.567428 + 0.823423i \(0.692061\pi\)
\(168\) 0 0
\(169\) −234393. −0.631288
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −729954. −1.85430 −0.927151 − 0.374689i \(-0.877749\pi\)
−0.927151 + 0.374689i \(0.877749\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −704484. −1.64338 −0.821691 − 0.569933i \(-0.806969\pi\)
−0.821691 + 0.569933i \(0.806969\pi\)
\(180\) 0 0
\(181\) −405850. −0.920808 −0.460404 − 0.887709i \(-0.652295\pi\)
−0.460404 + 0.887709i \(0.652295\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −612504. −1.28087
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −183024. −0.363015 −0.181508 − 0.983390i \(-0.558098\pi\)
−0.181508 + 0.983390i \(0.558098\pi\)
\(192\) 0 0
\(193\) 853054. 1.64848 0.824239 − 0.566242i \(-0.191603\pi\)
0.824239 + 0.566242i \(0.191603\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −476394. −0.874582 −0.437291 − 0.899320i \(-0.644062\pi\)
−0.437291 + 0.899320i \(0.644062\pi\)
\(198\) 0 0
\(199\) 470648. 0.842488 0.421244 − 0.906947i \(-0.361594\pi\)
0.421244 + 0.906947i \(0.361594\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −18144.0 −0.0309025
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.61304e6 −2.55434
\(210\) 0 0
\(211\) −14140.0 −0.0218647 −0.0109323 − 0.999940i \(-0.503480\pi\)
−0.0109323 + 0.999940i \(0.503480\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −96256.0 −0.138765
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −401820. −0.553415
\(222\) 0 0
\(223\) 1.08052e6 1.45503 0.727513 − 0.686094i \(-0.240676\pi\)
0.727513 + 0.686094i \(0.240676\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −340500. −0.438584 −0.219292 − 0.975659i \(-0.570375\pi\)
−0.219292 + 0.975659i \(0.570375\pi\)
\(228\) 0 0
\(229\) −787594. −0.992462 −0.496231 − 0.868191i \(-0.665283\pi\)
−0.496231 + 0.868191i \(0.665283\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.51881e6 1.83279 0.916397 − 0.400271i \(-0.131084\pi\)
0.916397 + 0.400271i \(0.131084\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.18181e6 −1.33830 −0.669148 − 0.743129i \(-0.733341\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(240\) 0 0
\(241\) −523342. −0.580421 −0.290210 − 0.956963i \(-0.593725\pi\)
−0.290210 + 0.956963i \(0.593725\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.05820e6 −1.10363
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.27741e6 1.27981 0.639907 − 0.768453i \(-0.278973\pi\)
0.639907 + 0.768453i \(0.278973\pi\)
\(252\) 0 0
\(253\) 893376. 0.877471
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.93112e6 −1.82379 −0.911897 − 0.410418i \(-0.865383\pi\)
−0.911897 + 0.410418i \(0.865383\pi\)
\(258\) 0 0
\(259\) 8608.00 0.00797357
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −822336. −0.733094 −0.366547 − 0.930399i \(-0.619460\pi\)
−0.366547 + 0.930399i \(0.619460\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.59181e6 −1.34125 −0.670625 − 0.741797i \(-0.733974\pi\)
−0.670625 + 0.741797i \(0.733974\pi\)
\(270\) 0 0
\(271\) −1.21106e6 −1.00171 −0.500854 − 0.865532i \(-0.666981\pi\)
−0.500854 + 0.865532i \(0.666981\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.34356e6 1.83517 0.917587 − 0.397536i \(-0.130135\pi\)
0.917587 + 0.397536i \(0.130135\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.86211e6 −1.40682 −0.703410 − 0.710784i \(-0.748340\pi\)
−0.703410 + 0.710784i \(0.748340\pi\)
\(282\) 0 0
\(283\) −108212. −0.0803173 −0.0401587 − 0.999193i \(-0.512786\pi\)
−0.0401587 + 0.999193i \(0.512786\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −181920. −0.130369
\(288\) 0 0
\(289\) −240461. −0.169356
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −959658. −0.653052 −0.326526 − 0.945188i \(-0.605878\pi\)
−0.326526 + 0.945188i \(0.605878\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 586080. 0.379122
\(300\) 0 0
\(301\) −87104.0 −0.0554143
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.62729e6 −0.985416 −0.492708 − 0.870195i \(-0.663993\pi\)
−0.492708 + 0.870195i \(0.663993\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.84086e6 1.66551 0.832757 − 0.553639i \(-0.186761\pi\)
0.832757 + 0.553639i \(0.186761\pi\)
\(312\) 0 0
\(313\) −1.61715e6 −0.933014 −0.466507 − 0.884517i \(-0.654488\pi\)
−0.466507 + 0.884517i \(0.654488\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.04367e6 −1.14225 −0.571126 − 0.820863i \(-0.693493\pi\)
−0.571126 + 0.820863i \(0.693493\pi\)
\(318\) 0 0
\(319\) −639576. −0.351897
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.10596e6 1.65649
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 164736. 0.0839071
\(330\) 0 0
\(331\) 1.00425e6 0.503817 0.251908 − 0.967751i \(-0.418942\pi\)
0.251908 + 0.967751i \(0.418942\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2.91960e6 −1.40039 −0.700195 − 0.713952i \(-0.746904\pi\)
−0.700195 + 0.713952i \(0.746904\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.39302e6 −1.58016
\(342\) 0 0
\(343\) −533728. −0.244954
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.21075e6 −0.985634 −0.492817 − 0.870133i \(-0.664033\pi\)
−0.492817 + 0.870133i \(0.664033\pi\)
\(348\) 0 0
\(349\) 375566. 0.165053 0.0825264 − 0.996589i \(-0.473701\pi\)
0.0825264 + 0.996589i \(0.473701\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.49992e6 0.640666 0.320333 − 0.947305i \(-0.396205\pi\)
0.320333 + 0.947305i \(0.396205\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.49626e6 −1.02224 −0.511122 − 0.859508i \(-0.670770\pi\)
−0.511122 + 0.859508i \(0.670770\pi\)
\(360\) 0 0
\(361\) 5.70350e6 2.30342
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.09714e6 −1.58787 −0.793937 − 0.608000i \(-0.791972\pi\)
−0.793937 + 0.608000i \(0.791972\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 556128. 0.209768
\(372\) 0 0
\(373\) −1.24213e6 −0.462271 −0.231135 − 0.972922i \(-0.574244\pi\)
−0.231135 + 0.972922i \(0.574244\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −419580. −0.152041
\(378\) 0 0
\(379\) −2.28413e6 −0.816814 −0.408407 − 0.912800i \(-0.633916\pi\)
−0.408407 + 0.912800i \(0.633916\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −565128. −0.196857 −0.0984283 − 0.995144i \(-0.531382\pi\)
−0.0984283 + 0.995144i \(0.531382\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.37367e6 1.13039 0.565196 − 0.824957i \(-0.308801\pi\)
0.565196 + 0.824957i \(0.308801\pi\)
\(390\) 0 0
\(391\) −1.72022e6 −0.569040
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 745138. 0.237280 0.118640 − 0.992937i \(-0.462147\pi\)
0.118640 + 0.992937i \(0.462147\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −864786. −0.268564 −0.134282 − 0.990943i \(-0.542873\pi\)
−0.134282 + 0.990943i \(0.542873\pi\)
\(402\) 0 0
\(403\) −2.22592e6 −0.682727
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 303432. 0.0907978
\(408\) 0 0
\(409\) −5.70189e6 −1.68543 −0.842715 − 0.538359i \(-0.819044\pi\)
−0.842715 + 0.538359i \(0.819044\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 419136. 0.120915
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.91947e6 0.812398 0.406199 − 0.913785i \(-0.366854\pi\)
0.406199 + 0.913785i \(0.366854\pi\)
\(420\) 0 0
\(421\) 1.08815e6 0.299215 0.149608 − 0.988745i \(-0.452199\pi\)
0.149608 + 0.988745i \(0.452199\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 150752. 0.0400123
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.64573e6 −1.20465 −0.602325 − 0.798251i \(-0.705759\pi\)
−0.602325 + 0.798251i \(0.705759\pi\)
\(432\) 0 0
\(433\) 702094. 0.179960 0.0899799 − 0.995944i \(-0.471320\pi\)
0.0899799 + 0.995944i \(0.471320\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.53024e6 −1.13480
\(438\) 0 0
\(439\) −1.63343e6 −0.404520 −0.202260 − 0.979332i \(-0.564829\pi\)
−0.202260 + 0.979332i \(0.564829\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.39500e6 1.30612 0.653058 − 0.757308i \(-0.273486\pi\)
0.653058 + 0.757308i \(0.273486\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 918462. 0.215003 0.107502 − 0.994205i \(-0.465715\pi\)
0.107502 + 0.994205i \(0.465715\pi\)
\(450\) 0 0
\(451\) −6.41268e6 −1.48456
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.55695e6 0.348726 0.174363 − 0.984681i \(-0.444213\pi\)
0.174363 + 0.984681i \(0.444213\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.19299e6 1.13806 0.569030 − 0.822316i \(-0.307319\pi\)
0.569030 + 0.822316i \(0.307319\pi\)
\(462\) 0 0
\(463\) 665848. 0.144352 0.0721760 − 0.997392i \(-0.477006\pi\)
0.0721760 + 0.997392i \(0.477006\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.84073e6 1.45148 0.725739 − 0.687970i \(-0.241498\pi\)
0.725739 + 0.687970i \(0.241498\pi\)
\(468\) 0 0
\(469\) 817984. 0.171717
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.07042e6 −0.631022
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.26214e6 −0.450486 −0.225243 − 0.974303i \(-0.572318\pi\)
−0.225243 + 0.974303i \(0.572318\pi\)
\(480\) 0 0
\(481\) 199060. 0.0392303
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.78443e6 1.29626 0.648128 − 0.761531i \(-0.275552\pi\)
0.648128 + 0.761531i \(0.275552\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.75964e6 1.26538 0.632688 − 0.774407i \(-0.281952\pi\)
0.632688 + 0.774407i \(0.281952\pi\)
\(492\) 0 0
\(493\) 1.23152e6 0.228205
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −232320. −0.0421886
\(498\) 0 0
\(499\) 8.73256e6 1.56997 0.784983 − 0.619517i \(-0.212671\pi\)
0.784983 + 0.619517i \(0.212671\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.75426e6 0.837843 0.418921 − 0.908022i \(-0.362408\pi\)
0.418921 + 0.908022i \(0.362408\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.13074e6 0.364532 0.182266 − 0.983249i \(-0.441657\pi\)
0.182266 + 0.983249i \(0.441657\pi\)
\(510\) 0 0
\(511\) 362848. 0.0614713
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.80694e6 0.955479
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.10967e7 −1.79101 −0.895507 − 0.445048i \(-0.853187\pi\)
−0.895507 + 0.445048i \(0.853187\pi\)
\(522\) 0 0
\(523\) −941252. −0.150471 −0.0752353 − 0.997166i \(-0.523971\pi\)
−0.0752353 + 0.997166i \(0.523971\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.53338e6 1.02473
\(528\) 0 0
\(529\) −3.92729e6 −0.610174
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.20690e6 −0.641422
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.33476e6 −1.38399
\(540\) 0 0
\(541\) 2.39896e6 0.352395 0.176197 − 0.984355i \(-0.443620\pi\)
0.176197 + 0.984355i \(0.443620\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.55851e6 −0.222711 −0.111355 − 0.993781i \(-0.535519\pi\)
−0.111355 + 0.993781i \(0.535519\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.24324e6 0.455093
\(552\) 0 0
\(553\) −1.55699e6 −0.216508
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.19451e7 1.63137 0.815685 − 0.578496i \(-0.196360\pi\)
0.815685 + 0.578496i \(0.196360\pi\)
\(558\) 0 0
\(559\) −2.01428e6 −0.272640
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.63906e6 −1.28163 −0.640817 − 0.767694i \(-0.721404\pi\)
−0.640817 + 0.767694i \(0.721404\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −830106. −0.107486 −0.0537431 − 0.998555i \(-0.517115\pi\)
−0.0537431 + 0.998555i \(0.517115\pi\)
\(570\) 0 0
\(571\) −3.32914e6 −0.427309 −0.213654 − 0.976909i \(-0.568537\pi\)
−0.213654 + 0.976909i \(0.568537\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −4.40026e6 −0.550223 −0.275111 − 0.961412i \(-0.588715\pi\)
−0.275111 + 0.961412i \(0.588715\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −127296. −0.0156450
\(582\) 0 0
\(583\) 1.96035e7 2.38870
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.25848e6 −0.869461 −0.434731 − 0.900561i \(-0.643156\pi\)
−0.434731 + 0.900561i \(0.643156\pi\)
\(588\) 0 0
\(589\) 1.72058e7 2.04355
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.55171e7 −1.81206 −0.906032 − 0.423210i \(-0.860903\pi\)
−0.906032 + 0.423210i \(0.860903\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.02670e7 1.16917 0.584583 − 0.811334i \(-0.301258\pi\)
0.584583 + 0.811334i \(0.301258\pi\)
\(600\) 0 0
\(601\) −9.42362e6 −1.06422 −0.532110 − 0.846675i \(-0.678601\pi\)
−0.532110 + 0.846675i \(0.678601\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.67289e6 0.845254 0.422627 − 0.906304i \(-0.361108\pi\)
0.422627 + 0.906304i \(0.361108\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.80952e6 0.412826
\(612\) 0 0
\(613\) 2.30598e6 0.247859 0.123929 − 0.992291i \(-0.460450\pi\)
0.123929 + 0.992291i \(0.460450\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −505254. −0.0534314 −0.0267157 − 0.999643i \(-0.508505\pi\)
−0.0267157 + 0.999643i \(0.508505\pi\)
\(618\) 0 0
\(619\) 4.61380e6 0.483986 0.241993 − 0.970278i \(-0.422199\pi\)
0.241993 + 0.970278i \(0.422199\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 766560. 0.0791272
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −584268. −0.0588824
\(630\) 0 0
\(631\) 4.77327e6 0.477247 0.238623 − 0.971112i \(-0.423304\pi\)
0.238623 + 0.971112i \(0.423304\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.12387e6 −0.597967
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.09254e7 1.05025 0.525125 − 0.851025i \(-0.324019\pi\)
0.525125 + 0.851025i \(0.324019\pi\)
\(642\) 0 0
\(643\) −1.13952e6 −0.108691 −0.0543454 − 0.998522i \(-0.517307\pi\)
−0.0543454 + 0.998522i \(0.517307\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.10955e6 0.479868 0.239934 − 0.970789i \(-0.422874\pi\)
0.239934 + 0.970789i \(0.422874\pi\)
\(648\) 0 0
\(649\) 1.47745e7 1.37690
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.81591e6 −0.717293 −0.358646 − 0.933474i \(-0.616762\pi\)
−0.358646 + 0.933474i \(0.616762\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.05905e7 0.949954 0.474977 − 0.879998i \(-0.342456\pi\)
0.474977 + 0.879998i \(0.342456\pi\)
\(660\) 0 0
\(661\) 4.67092e6 0.415814 0.207907 − 0.978149i \(-0.433335\pi\)
0.207907 + 0.978149i \(0.433335\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.79626e6 −0.156334
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.31401e6 0.455634
\(672\) 0 0
\(673\) −2.07728e7 −1.76790 −0.883948 − 0.467585i \(-0.845124\pi\)
−0.883948 + 0.467585i \(0.845124\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.67497e7 1.40454 0.702270 − 0.711911i \(-0.252170\pi\)
0.702270 + 0.711911i \(0.252170\pi\)
\(678\) 0 0
\(679\) −2.25181e6 −0.187438
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.41700e6 0.362306 0.181153 − 0.983455i \(-0.442017\pi\)
0.181153 + 0.983455i \(0.442017\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.28605e7 1.03207
\(690\) 0 0
\(691\) 1.86481e7 1.48573 0.742863 − 0.669443i \(-0.233467\pi\)
0.742863 + 0.669443i \(0.233467\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.23478e7 0.962739
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7.28389e6 −0.559845 −0.279923 − 0.960023i \(-0.590309\pi\)
−0.279923 + 0.960023i \(0.590309\pi\)
\(702\) 0 0
\(703\) −1.53868e6 −0.117425
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.36637e6 −0.102806
\(708\) 0 0
\(709\) 1.82063e7 1.36021 0.680105 − 0.733115i \(-0.261934\pi\)
0.680105 + 0.733115i \(0.261934\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9.52934e6 −0.702003
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.46901e6 −0.466676 −0.233338 − 0.972396i \(-0.574965\pi\)
−0.233338 + 0.972396i \(0.574965\pi\)
\(720\) 0 0
\(721\) −3.17850e6 −0.227711
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.39991e7 0.982343 0.491172 − 0.871063i \(-0.336569\pi\)
0.491172 + 0.871063i \(0.336569\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.91218e6 0.409218
\(732\) 0 0
\(733\) −2.51019e7 −1.72562 −0.862811 − 0.505526i \(-0.831298\pi\)
−0.862811 + 0.505526i \(0.831298\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.88339e7 1.95540
\(738\) 0 0
\(739\) 9.73514e6 0.655739 0.327870 − 0.944723i \(-0.393669\pi\)
0.327870 + 0.944723i \(0.393669\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.03370e6 0.201604 0.100802 − 0.994906i \(-0.467859\pi\)
0.100802 + 0.994906i \(0.467859\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.86029e6 −0.121165
\(750\) 0 0
\(751\) −6.07557e6 −0.393086 −0.196543 − 0.980495i \(-0.562971\pi\)
−0.196543 + 0.980495i \(0.562971\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 4.82103e6 0.305774 0.152887 − 0.988244i \(-0.451143\pi\)
0.152887 + 0.988244i \(0.451143\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5.82748e6 −0.364770 −0.182385 − 0.983227i \(-0.558382\pi\)
−0.182385 + 0.983227i \(0.558382\pi\)
\(762\) 0 0
\(763\) −2.34755e6 −0.145984
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.69252e6 0.594906
\(768\) 0 0
\(769\) −2.71546e7 −1.65587 −0.827936 − 0.560822i \(-0.810485\pi\)
−0.827936 + 0.560822i \(0.810485\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6678.00 0.000401974 0 0.000200987 − 1.00000i \(-0.499936\pi\)
0.000200987 1.00000i \(0.499936\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.25182e7 1.91992
\(780\) 0 0
\(781\) −8.18928e6 −0.480417
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.44352e7 −0.830781 −0.415391 − 0.909643i \(-0.636355\pi\)
−0.415391 + 0.909643i \(0.636355\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.37411e6 0.191742
\(792\) 0 0
\(793\) 3.48614e6 0.196862
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.90792e6 −0.106393 −0.0531967 − 0.998584i \(-0.516941\pi\)
−0.0531967 + 0.998584i \(0.516941\pi\)
\(798\) 0 0
\(799\) −1.11815e7 −0.619629
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.27904e7 0.699995
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3.48543e7 1.87234 0.936171 − 0.351546i \(-0.114344\pi\)
0.936171 + 0.351546i \(0.114344\pi\)
\(810\) 0 0
\(811\) 1.41263e7 0.754182 0.377091 − 0.926176i \(-0.376924\pi\)
0.377091 + 0.926176i \(0.376924\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.55698e7 0.816073
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.78858e7 −0.926082 −0.463041 − 0.886337i \(-0.653242\pi\)
−0.463041 + 0.886337i \(0.653242\pi\)
\(822\) 0 0
\(823\) 1.73695e7 0.893897 0.446948 − 0.894560i \(-0.352511\pi\)
0.446948 + 0.894560i \(0.352511\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.84745e7 −0.939310 −0.469655 − 0.882850i \(-0.655622\pi\)
−0.469655 + 0.882850i \(0.655622\pi\)
\(828\) 0 0
\(829\) −3.02647e7 −1.52950 −0.764750 − 0.644327i \(-0.777138\pi\)
−0.764750 + 0.644327i \(0.777138\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.79744e7 0.897515
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.10237e7 1.03111 0.515555 − 0.856856i \(-0.327586\pi\)
0.515555 + 0.856856i \(0.327586\pi\)
\(840\) 0 0
\(841\) −1.92252e7 −0.937305
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.51272e6 0.120347
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 852192. 0.0403379
\(852\) 0 0
\(853\) 2.60690e7 1.22674 0.613369 − 0.789796i \(-0.289814\pi\)
0.613369 + 0.789796i \(0.289814\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 489738. 0.0227778 0.0113889 − 0.999935i \(-0.496375\pi\)
0.0113889 + 0.999935i \(0.496375\pi\)
\(858\) 0 0
\(859\) −2.17067e7 −1.00371 −0.501857 − 0.864951i \(-0.667350\pi\)
−0.501857 + 0.864951i \(0.667350\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.91038e7 1.33022 0.665108 − 0.746747i \(-0.268385\pi\)
0.665108 + 0.746747i \(0.268385\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.48840e7 −2.46545
\(870\) 0 0
\(871\) 1.89159e7 0.844853
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.11648e7 −0.929215 −0.464607 − 0.885517i \(-0.653805\pi\)
−0.464607 + 0.885517i \(0.653805\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.60651e6 0.416990 0.208495 − 0.978023i \(-0.433143\pi\)
0.208495 + 0.978023i \(0.433143\pi\)
\(882\) 0 0
\(883\) −2.58825e7 −1.11713 −0.558566 − 0.829460i \(-0.688648\pi\)
−0.558566 + 0.829460i \(0.688648\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.43249e7 1.03811 0.519053 − 0.854742i \(-0.326285\pi\)
0.519053 + 0.854742i \(0.326285\pi\)
\(888\) 0 0
\(889\) −3.91078e6 −0.165962
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.94466e7 −1.23568
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.82214e6 0.281528
\(900\) 0 0
\(901\) −3.77472e7 −1.54908
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 7.87371e6 0.317805 0.158903 − 0.987294i \(-0.449204\pi\)
0.158903 + 0.987294i \(0.449204\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −4.74478e7 −1.89418 −0.947088 − 0.320975i \(-0.895990\pi\)
−0.947088 + 0.320975i \(0.895990\pi\)
\(912\) 0 0
\(913\) −4.48718e6 −0.178155
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.32493e6 0.0913032
\(918\) 0 0
\(919\) 605288. 0.0236414 0.0118207 − 0.999930i \(-0.496237\pi\)
0.0118207 + 0.999930i \(0.496237\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.37240e6 −0.207570
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 9.52438e6 0.362074 0.181037 − 0.983476i \(-0.442055\pi\)
0.181037 + 0.983476i \(0.442055\pi\)
\(930\) 0 0
\(931\) 4.73359e7 1.78985
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 9.15708e6 0.340728 0.170364 − 0.985381i \(-0.445506\pi\)
0.170364 + 0.985381i \(0.445506\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.46291e6 −0.0906723 −0.0453361 − 0.998972i \(-0.514436\pi\)
−0.0453361 + 0.998972i \(0.514436\pi\)
\(942\) 0 0
\(943\) −1.80101e7 −0.659533
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.13961e6 0.294937 0.147468 − 0.989067i \(-0.452888\pi\)
0.147468 + 0.989067i \(0.452888\pi\)
\(948\) 0 0
\(949\) 8.39086e6 0.302441
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.65014e7 0.588557 0.294278 − 0.955720i \(-0.404921\pi\)
0.294278 + 0.955720i \(0.404921\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2.00765e6 −0.0704922
\(960\) 0 0
\(961\) 7.56310e6 0.264175
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 2.72505e7 0.937148 0.468574 − 0.883424i \(-0.344768\pi\)
0.468574 + 0.883424i \(0.344768\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.77172e7 0.603040 0.301520 − 0.953460i \(-0.402506\pi\)
0.301520 + 0.953460i \(0.402506\pi\)
\(972\) 0 0
\(973\) 4.02810e6 0.136401
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.57062e7 0.861591 0.430795 − 0.902450i \(-0.358233\pi\)
0.430795 + 0.902450i \(0.358233\pi\)
\(978\) 0 0
\(979\) 2.70212e7 0.901049
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.05067e6 0.133704 0.0668518 − 0.997763i \(-0.478705\pi\)
0.0668518 + 0.997763i \(0.478705\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.62330e6 −0.280338
\(990\) 0 0
\(991\) −1.71299e6 −0.0554078 −0.0277039 − 0.999616i \(-0.508820\pi\)
−0.0277039 + 0.999616i \(0.508820\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −2.09874e7 −0.668683 −0.334341 − 0.942452i \(-0.608514\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(998\) 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 900.6.a.g.1.1 1
3.2 odd 2 300.6.a.e.1.1 1
5.2 odd 4 900.6.d.i.649.2 2
5.3 odd 4 900.6.d.i.649.1 2
5.4 even 2 180.6.a.a.1.1 1
15.2 even 4 300.6.d.a.49.1 2
15.8 even 4 300.6.d.a.49.2 2
15.14 odd 2 60.6.a.b.1.1 ✓ 1
20.19 odd 2 720.6.a.f.1.1 1
60.59 even 2 240.6.a.m.1.1 1
120.29 odd 2 960.6.a.r.1.1 1
120.59 even 2 960.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.6.a.b.1.1 ✓ 1 15.14 odd 2
180.6.a.a.1.1 1 5.4 even 2
240.6.a.m.1.1 1 60.59 even 2
300.6.a.e.1.1 1 3.2 odd 2
300.6.d.a.49.1 2 15.2 even 4
300.6.d.a.49.2 2 15.8 even 4
720.6.a.f.1.1 1 20.19 odd 2
900.6.a.g.1.1 1 1.1 even 1 trivial
900.6.d.i.649.1 2 5.3 odd 4
900.6.d.i.649.2 2 5.2 odd 4
960.6.a.c.1.1 1 120.59 even 2
960.6.a.r.1.1 1 120.29 odd 2