↑

Properties

Label 576.6.a.j.1.1
Level $576$
Weight $6$
Character 576.1
Self dual yes
Analytic conductor $92.381$
Analytic rank $0$
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] = [576,6,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, 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("576.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(92.3810802123\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-66.0000 q^{5} +176.000 q^{7} +O(q^{10})\) \(q-66.0000 q^{5} +176.000 q^{7} -60.0000 q^{11} +658.000 q^{13} +414.000 q^{17} -956.000 q^{19} -600.000 q^{23} +1231.00 q^{25} +5574.00 q^{29} -3592.00 q^{31} -11616.0 q^{35} +8458.00 q^{37} -19194.0 q^{41} -13316.0 q^{43} +19680.0 q^{47} +14169.0 q^{49} -31266.0 q^{53} +3960.00 q^{55} +26340.0 q^{59} +31090.0 q^{61} -43428.0 q^{65} +16804.0 q^{67} -6120.00 q^{71} -25558.0 q^{73} -10560.0 q^{77} +74408.0 q^{79} -6468.00 q^{83} -27324.0 q^{85} +32742.0 q^{89} +115808. q^{91} +63096.0 q^{95} +166082. q^{97} +O(q^{100})\)

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
\(5\) −66.0000 −1.18064 −0.590322 − 0.807168i \(-0.700999\pi\)
−0.590322 + 0.807168i \(0.700999\pi\)
\(6\) 0 0
\(7\) 176.000 1.35759 0.678793 − 0.734329i \(-0.262503\pi\)
0.678793 + 0.734329i \(0.262503\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −60.0000 −0.149510 −0.0747549 − 0.997202i \(-0.523817\pi\)
−0.0747549 + 0.997202i \(0.523817\pi\)
\(12\) 0 0
\(13\) 658.000 1.07986 0.539930 − 0.841710i \(-0.318451\pi\)
0.539930 + 0.841710i \(0.318451\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 414.000 0.347439 0.173719 − 0.984795i \(-0.444421\pi\)
0.173719 + 0.984795i \(0.444421\pi\)
\(18\) 0 0
\(19\) −956.000 −0.607539 −0.303769 − 0.952746i \(-0.598245\pi\)
−0.303769 + 0.952746i \(0.598245\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −600.000 −0.236500 −0.118250 − 0.992984i \(-0.537728\pi\)
−0.118250 + 0.992984i \(0.537728\pi\)
\(24\) 0 0
\(25\) 1231.00 0.393920
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5574.00 1.23076 0.615378 − 0.788232i \(-0.289003\pi\)
0.615378 + 0.788232i \(0.289003\pi\)
\(30\) 0 0
\(31\) −3592.00 −0.671324 −0.335662 − 0.941983i \(-0.608960\pi\)
−0.335662 + 0.941983i \(0.608960\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11616.0 −1.60283
\(36\) 0 0
\(37\) 8458.00 1.01570 0.507848 − 0.861447i \(-0.330441\pi\)
0.507848 + 0.861447i \(0.330441\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −19194.0 −1.78322 −0.891612 − 0.452800i \(-0.850425\pi\)
−0.891612 + 0.452800i \(0.850425\pi\)
\(42\) 0 0
\(43\) −13316.0 −1.09825 −0.549127 − 0.835739i \(-0.685040\pi\)
−0.549127 + 0.835739i \(0.685040\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 19680.0 1.29951 0.649756 − 0.760143i \(-0.274871\pi\)
0.649756 + 0.760143i \(0.274871\pi\)
\(48\) 0 0
\(49\) 14169.0 0.843042
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −31266.0 −1.52891 −0.764456 − 0.644676i \(-0.776992\pi\)
−0.764456 + 0.644676i \(0.776992\pi\)
\(54\) 0 0
\(55\) 3960.00 0.176518
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 26340.0 0.985112 0.492556 − 0.870281i \(-0.336063\pi\)
0.492556 + 0.870281i \(0.336063\pi\)
\(60\) 0 0
\(61\) 31090.0 1.06978 0.534892 − 0.844920i \(-0.320352\pi\)
0.534892 + 0.844920i \(0.320352\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −43428.0 −1.27493
\(66\) 0 0
\(67\) 16804.0 0.457326 0.228663 − 0.973506i \(-0.426565\pi\)
0.228663 + 0.973506i \(0.426565\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6120.00 −0.144081 −0.0720403 − 0.997402i \(-0.522951\pi\)
−0.0720403 + 0.997402i \(0.522951\pi\)
\(72\) 0 0
\(73\) −25558.0 −0.561332 −0.280666 − 0.959806i \(-0.590555\pi\)
−0.280666 + 0.959806i \(0.590555\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10560.0 −0.202972
\(78\) 0 0
\(79\) 74408.0 1.34138 0.670690 − 0.741738i \(-0.265998\pi\)
0.670690 + 0.741738i \(0.265998\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6468.00 −0.103056 −0.0515282 − 0.998672i \(-0.516409\pi\)
−0.0515282 + 0.998672i \(0.516409\pi\)
\(84\) 0 0
\(85\) −27324.0 −0.410201
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 32742.0 0.438157 0.219079 − 0.975707i \(-0.429695\pi\)
0.219079 + 0.975707i \(0.429695\pi\)
\(90\) 0 0
\(91\) 115808. 1.46600
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 63096.0 0.717287
\(96\) 0 0
\(97\) 166082. 1.79223 0.896114 − 0.443824i \(-0.146378\pi\)
0.896114 + 0.443824i \(0.146378\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −22002.0 −0.214614 −0.107307 − 0.994226i \(-0.534223\pi\)
−0.107307 + 0.994226i \(0.534223\pi\)
\(102\) 0 0
\(103\) −79264.0 −0.736178 −0.368089 − 0.929791i \(-0.619988\pi\)
−0.368089 + 0.929791i \(0.619988\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 227988. 1.92510 0.962548 − 0.271110i \(-0.0873908\pi\)
0.962548 + 0.271110i \(0.0873908\pi\)
\(108\) 0 0
\(109\) 8530.00 0.0687674 0.0343837 − 0.999409i \(-0.489053\pi\)
0.0343837 + 0.999409i \(0.489053\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 195438. 1.43984 0.719918 − 0.694059i \(-0.244179\pi\)
0.719918 + 0.694059i \(0.244179\pi\)
\(114\) 0 0
\(115\) 39600.0 0.279223
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 72864.0 0.471678
\(120\) 0 0
\(121\) −157451. −0.977647
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125004. 0.715565
\(126\) 0 0
\(127\) 173000. 0.951780 0.475890 − 0.879505i \(-0.342126\pi\)
0.475890 + 0.879505i \(0.342126\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 151260. 0.770098 0.385049 − 0.922896i \(-0.374185\pi\)
0.385049 + 0.922896i \(0.374185\pi\)
\(132\) 0 0
\(133\) −168256. −0.824786
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 128454. 0.584718 0.292359 − 0.956309i \(-0.405560\pi\)
0.292359 + 0.956309i \(0.405560\pi\)
\(138\) 0 0
\(139\) −154196. −0.676918 −0.338459 − 0.940981i \(-0.609906\pi\)
−0.338459 + 0.940981i \(0.609906\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −39480.0 −0.161450
\(144\) 0 0
\(145\) −367884. −1.45308
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 29454.0 0.108687 0.0543436 − 0.998522i \(-0.482693\pi\)
0.0543436 + 0.998522i \(0.482693\pi\)
\(150\) 0 0
\(151\) −203872. −0.727638 −0.363819 − 0.931470i \(-0.618527\pi\)
−0.363819 + 0.931470i \(0.618527\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 237072. 0.792594
\(156\) 0 0
\(157\) −136142. −0.440801 −0.220401 − 0.975409i \(-0.570737\pi\)
−0.220401 + 0.975409i \(0.570737\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −105600. −0.321070
\(162\) 0 0
\(163\) 171124. 0.504478 0.252239 − 0.967665i \(-0.418833\pi\)
0.252239 + 0.967665i \(0.418833\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 676200. 1.87622 0.938110 − 0.346336i \(-0.112574\pi\)
0.938110 + 0.346336i \(0.112574\pi\)
\(168\) 0 0
\(169\) 61671.0 0.166098
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 133158. 0.338261 0.169131 − 0.985594i \(-0.445904\pi\)
0.169131 + 0.985594i \(0.445904\pi\)
\(174\) 0 0
\(175\) 216656. 0.534781
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −693396. −1.61752 −0.808758 − 0.588141i \(-0.799860\pi\)
−0.808758 + 0.588141i \(0.799860\pi\)
\(180\) 0 0
\(181\) −377174. −0.855747 −0.427873 − 0.903839i \(-0.640737\pi\)
−0.427873 + 0.903839i \(0.640737\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −558228. −1.19917
\(186\) 0 0
\(187\) −24840.0 −0.0519455
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 265344. 0.526291 0.263145 − 0.964756i \(-0.415240\pi\)
0.263145 + 0.964756i \(0.415240\pi\)
\(192\) 0 0
\(193\) 295298. 0.570647 0.285323 − 0.958431i \(-0.407899\pi\)
0.285323 + 0.958431i \(0.407899\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 201294. 0.369543 0.184772 − 0.982781i \(-0.440845\pi\)
0.184772 + 0.982781i \(0.440845\pi\)
\(198\) 0 0
\(199\) 652448. 1.16792 0.583960 − 0.811782i \(-0.301502\pi\)
0.583960 + 0.811782i \(0.301502\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 981024. 1.67086
\(204\) 0 0
\(205\) 1.26680e6 2.10535
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 57360.0 0.0908330
\(210\) 0 0
\(211\) 1.14706e6 1.77370 0.886850 − 0.462058i \(-0.152889\pi\)
0.886850 + 0.462058i \(0.152889\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 878856. 1.29665
\(216\) 0 0
\(217\) −632192. −0.911380
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 272412. 0.375185
\(222\) 0 0
\(223\) 701960. 0.945258 0.472629 − 0.881262i \(-0.343305\pi\)
0.472629 + 0.881262i \(0.343305\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.23611e6 1.59218 0.796089 − 0.605179i \(-0.206899\pi\)
0.796089 + 0.605179i \(0.206899\pi\)
\(228\) 0 0
\(229\) −105830. −0.133358 −0.0666792 − 0.997774i \(-0.521240\pi\)
−0.0666792 + 0.997774i \(0.521240\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 438678. 0.529366 0.264683 − 0.964335i \(-0.414733\pi\)
0.264683 + 0.964335i \(0.414733\pi\)
\(234\) 0 0
\(235\) −1.29888e6 −1.53426
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −28464.0 −0.0322330 −0.0161165 − 0.999870i \(-0.505130\pi\)
−0.0161165 + 0.999870i \(0.505130\pi\)
\(240\) 0 0
\(241\) 892562. 0.989910 0.494955 − 0.868919i \(-0.335185\pi\)
0.494955 + 0.868919i \(0.335185\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −935154. −0.995332
\(246\) 0 0
\(247\) −629048. −0.656057
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −110124. −0.110331 −0.0551655 − 0.998477i \(-0.517569\pi\)
−0.0551655 + 0.998477i \(0.517569\pi\)
\(252\) 0 0
\(253\) 36000.0 0.0353591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −140802. −0.132977 −0.0664884 − 0.997787i \(-0.521180\pi\)
−0.0664884 + 0.997787i \(0.521180\pi\)
\(258\) 0 0
\(259\) 1.48861e6 1.37889
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 938760. 0.836884 0.418442 − 0.908244i \(-0.362576\pi\)
0.418442 + 0.908244i \(0.362576\pi\)
\(264\) 0 0
\(265\) 2.06356e6 1.80510
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.11451e6 −0.939078 −0.469539 − 0.882912i \(-0.655580\pi\)
−0.469539 + 0.882912i \(0.655580\pi\)
\(270\) 0 0
\(271\) 567704. 0.469568 0.234784 − 0.972048i \(-0.424562\pi\)
0.234784 + 0.972048i \(0.424562\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −73860.0 −0.0588949
\(276\) 0 0
\(277\) 1.21326e6 0.950066 0.475033 − 0.879968i \(-0.342436\pi\)
0.475033 + 0.879968i \(0.342436\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −687738. −0.519586 −0.259793 − 0.965664i \(-0.583654\pi\)
−0.259793 + 0.965664i \(0.583654\pi\)
\(282\) 0 0
\(283\) 830908. 0.616718 0.308359 − 0.951270i \(-0.400220\pi\)
0.308359 + 0.951270i \(0.400220\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.37814e6 −2.42088
\(288\) 0 0
\(289\) −1.24846e6 −0.879286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.31263e6 −0.893248 −0.446624 − 0.894722i \(-0.647374\pi\)
−0.446624 + 0.894722i \(0.647374\pi\)
\(294\) 0 0
\(295\) −1.73844e6 −1.16307
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −394800. −0.255387
\(300\) 0 0
\(301\) −2.34362e6 −1.49097
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.05194e6 −1.26303
\(306\) 0 0
\(307\) −1.69022e6 −1.02352 −0.511761 − 0.859128i \(-0.671007\pi\)
−0.511761 + 0.859128i \(0.671007\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.50204e6 0.880604 0.440302 − 0.897850i \(-0.354871\pi\)
0.440302 + 0.897850i \(0.354871\pi\)
\(312\) 0 0
\(313\) 810842. 0.467816 0.233908 − 0.972259i \(-0.424848\pi\)
0.233908 + 0.972259i \(0.424848\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 903558. 0.505019 0.252510 − 0.967594i \(-0.418744\pi\)
0.252510 + 0.967594i \(0.418744\pi\)
\(318\) 0 0
\(319\) −334440. −0.184010
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −395784. −0.211082
\(324\) 0 0
\(325\) 809998. 0.425379
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.46368e6 1.76420
\(330\) 0 0
\(331\) −1.12197e6 −0.562875 −0.281438 − 0.959580i \(-0.590811\pi\)
−0.281438 + 0.959580i \(0.590811\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.10906e6 −0.539939
\(336\) 0 0
\(337\) −2.75217e6 −1.32008 −0.660041 − 0.751229i \(-0.729461\pi\)
−0.660041 + 0.751229i \(0.729461\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 215520. 0.100369
\(342\) 0 0
\(343\) −464288. −0.213085
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.91749e6 0.854889 0.427445 − 0.904042i \(-0.359414\pi\)
0.427445 + 0.904042i \(0.359414\pi\)
\(348\) 0 0
\(349\) −1.83659e6 −0.807140 −0.403570 − 0.914949i \(-0.632231\pi\)
−0.403570 + 0.914949i \(0.632231\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 622014. 0.265683 0.132841 − 0.991137i \(-0.457590\pi\)
0.132841 + 0.991137i \(0.457590\pi\)
\(354\) 0 0
\(355\) 403920. 0.170108
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.74062e6 −1.53182 −0.765909 − 0.642949i \(-0.777711\pi\)
−0.765909 + 0.642949i \(0.777711\pi\)
\(360\) 0 0
\(361\) −1.56216e6 −0.630897
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.68683e6 0.662733
\(366\) 0 0
\(367\) 16232.0 0.00629081 0.00314541 − 0.999995i \(-0.498999\pi\)
0.00314541 + 0.999995i \(0.498999\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.50282e6 −2.07563
\(372\) 0 0
\(373\) −293606. −0.109268 −0.0546340 − 0.998506i \(-0.517399\pi\)
−0.0546340 + 0.998506i \(0.517399\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.66769e6 1.32904
\(378\) 0 0
\(379\) −3.18012e6 −1.13722 −0.568611 − 0.822607i \(-0.692519\pi\)
−0.568611 + 0.822607i \(0.692519\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.97984e6 1.03800 0.518998 − 0.854775i \(-0.326305\pi\)
0.518998 + 0.854775i \(0.326305\pi\)
\(384\) 0 0
\(385\) 696960. 0.239638
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.45977e6 1.15924 0.579620 − 0.814887i \(-0.303201\pi\)
0.579620 + 0.814887i \(0.303201\pi\)
\(390\) 0 0
\(391\) −248400. −0.0821693
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.91093e6 −1.58369
\(396\) 0 0
\(397\) 3.90416e6 1.24323 0.621615 − 0.783323i \(-0.286477\pi\)
0.621615 + 0.783323i \(0.286477\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.44115e6 −1.68978 −0.844890 − 0.534940i \(-0.820334\pi\)
−0.844890 + 0.534940i \(0.820334\pi\)
\(402\) 0 0
\(403\) −2.36354e6 −0.724936
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −507480. −0.151856
\(408\) 0 0
\(409\) 1.96995e6 0.582299 0.291150 − 0.956678i \(-0.405962\pi\)
0.291150 + 0.956678i \(0.405962\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.63584e6 1.33738
\(414\) 0 0
\(415\) 426888. 0.121673
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 139020. 0.0386850 0.0193425 − 0.999813i \(-0.493843\pi\)
0.0193425 + 0.999813i \(0.493843\pi\)
\(420\) 0 0
\(421\) −4.32743e6 −1.18994 −0.594970 − 0.803748i \(-0.702836\pi\)
−0.594970 + 0.803748i \(0.702836\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 509634. 0.136863
\(426\) 0 0
\(427\) 5.47184e6 1.45232
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.79936e6 0.725881 0.362941 − 0.931812i \(-0.381773\pi\)
0.362941 + 0.931812i \(0.381773\pi\)
\(432\) 0 0
\(433\) −5.90241e6 −1.51290 −0.756449 − 0.654052i \(-0.773068\pi\)
−0.756449 + 0.654052i \(0.773068\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 573600. 0.143683
\(438\) 0 0
\(439\) −446512. −0.110579 −0.0552894 − 0.998470i \(-0.517608\pi\)
−0.0552894 + 0.998470i \(0.517608\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.49525e6 0.846193 0.423096 − 0.906085i \(-0.360943\pi\)
0.423096 + 0.906085i \(0.360943\pi\)
\(444\) 0 0
\(445\) −2.16097e6 −0.517308
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.20613e6 0.282343 0.141171 − 0.989985i \(-0.454913\pi\)
0.141171 + 0.989985i \(0.454913\pi\)
\(450\) 0 0
\(451\) 1.15164e6 0.266609
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.64333e6 −1.73083
\(456\) 0 0
\(457\) 233546. 0.0523097 0.0261548 − 0.999658i \(-0.491674\pi\)
0.0261548 + 0.999658i \(0.491674\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.74489e6 −0.382398 −0.191199 − 0.981551i \(-0.561238\pi\)
−0.191199 + 0.981551i \(0.561238\pi\)
\(462\) 0 0
\(463\) −2.91786e6 −0.632576 −0.316288 − 0.948663i \(-0.602437\pi\)
−0.316288 + 0.948663i \(0.602437\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.31076e6 −1.12684 −0.563422 − 0.826169i \(-0.690516\pi\)
−0.563422 + 0.826169i \(0.690516\pi\)
\(468\) 0 0
\(469\) 2.95750e6 0.620859
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 798960. 0.164200
\(474\) 0 0
\(475\) −1.17684e6 −0.239322
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.34466e6 −0.466918 −0.233459 − 0.972367i \(-0.575004\pi\)
−0.233459 + 0.972367i \(0.575004\pi\)
\(480\) 0 0
\(481\) 5.56536e6 1.09681
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.09614e7 −2.11598
\(486\) 0 0
\(487\) 9.81531e6 1.87535 0.937674 − 0.347517i \(-0.112975\pi\)
0.937674 + 0.347517i \(0.112975\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.94520e6 −1.11292 −0.556458 − 0.830876i \(-0.687840\pi\)
−0.556458 + 0.830876i \(0.687840\pi\)
\(492\) 0 0
\(493\) 2.30764e6 0.427612
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.07712e6 −0.195602
\(498\) 0 0
\(499\) −6.47832e6 −1.16469 −0.582346 − 0.812941i \(-0.697865\pi\)
−0.582346 + 0.812941i \(0.697865\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.71794e6 −0.831444 −0.415722 − 0.909492i \(-0.636471\pi\)
−0.415722 + 0.909492i \(0.636471\pi\)
\(504\) 0 0
\(505\) 1.45213e6 0.253383
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.90771e6 −0.326375 −0.163188 − 0.986595i \(-0.552178\pi\)
−0.163188 + 0.986595i \(0.552178\pi\)
\(510\) 0 0
\(511\) −4.49821e6 −0.762057
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.23142e6 0.869164
\(516\) 0 0
\(517\) −1.18080e6 −0.194290
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.01974e6 −1.29439 −0.647196 − 0.762324i \(-0.724059\pi\)
−0.647196 + 0.762324i \(0.724059\pi\)
\(522\) 0 0
\(523\) −1.91162e6 −0.305596 −0.152798 − 0.988257i \(-0.548828\pi\)
−0.152798 + 0.988257i \(0.548828\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.48709e6 −0.233244
\(528\) 0 0
\(529\) −6.07634e6 −0.944068
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.26297e7 −1.92563
\(534\) 0 0
\(535\) −1.50472e7 −2.27285
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −850140. −0.126043
\(540\) 0 0
\(541\) 1.19900e7 1.76128 0.880639 − 0.473788i \(-0.157114\pi\)
0.880639 + 0.473788i \(0.157114\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −562980. −0.0811898
\(546\) 0 0
\(547\) −4.45809e6 −0.637061 −0.318530 − 0.947913i \(-0.603189\pi\)
−0.318530 + 0.947913i \(0.603189\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.32874e6 −0.747732
\(552\) 0 0
\(553\) 1.30958e7 1.82104
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.02612e6 1.23272 0.616358 − 0.787466i \(-0.288607\pi\)
0.616358 + 0.787466i \(0.288607\pi\)
\(558\) 0 0
\(559\) −8.76193e6 −1.18596
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.84899e6 0.910658 0.455329 − 0.890323i \(-0.349522\pi\)
0.455329 + 0.890323i \(0.349522\pi\)
\(564\) 0 0
\(565\) −1.28989e7 −1.69993
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.46322e6 0.707405 0.353703 − 0.935358i \(-0.384923\pi\)
0.353703 + 0.935358i \(0.384923\pi\)
\(570\) 0 0
\(571\) 1.02324e7 1.31337 0.656684 − 0.754166i \(-0.271959\pi\)
0.656684 + 0.754166i \(0.271959\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −738600. −0.0931622
\(576\) 0 0
\(577\) 1.59437e7 1.99365 0.996825 − 0.0796186i \(-0.0253702\pi\)
0.996825 + 0.0796186i \(0.0253702\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.13837e6 −0.139908
\(582\) 0 0
\(583\) 1.87596e6 0.228587
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.47713e6 −1.13522 −0.567612 − 0.823296i \(-0.692133\pi\)
−0.567612 + 0.823296i \(0.692133\pi\)
\(588\) 0 0
\(589\) 3.43395e6 0.407855
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.45349e6 −0.286515 −0.143258 − 0.989685i \(-0.545758\pi\)
−0.143258 + 0.989685i \(0.545758\pi\)
\(594\) 0 0
\(595\) −4.80902e6 −0.556884
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.29978e6 1.05902 0.529512 − 0.848302i \(-0.322375\pi\)
0.529512 + 0.848302i \(0.322375\pi\)
\(600\) 0 0
\(601\) −1.14617e7 −1.29438 −0.647192 − 0.762327i \(-0.724057\pi\)
−0.647192 + 0.762327i \(0.724057\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.03918e7 1.15425
\(606\) 0 0
\(607\) 1.12784e7 1.24244 0.621219 − 0.783637i \(-0.286638\pi\)
0.621219 + 0.783637i \(0.286638\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.29494e7 1.40329
\(612\) 0 0
\(613\) −93782.0 −0.0100802 −0.00504009 − 0.999987i \(-0.501604\pi\)
−0.00504009 + 0.999987i \(0.501604\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.49642e7 1.58248 0.791242 − 0.611504i \(-0.209435\pi\)
0.791242 + 0.611504i \(0.209435\pi\)
\(618\) 0 0
\(619\) 5.06888e6 0.531723 0.265861 − 0.964011i \(-0.414344\pi\)
0.265861 + 0.964011i \(0.414344\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.76259e6 0.594837
\(624\) 0 0
\(625\) −1.20971e7 −1.23875
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.50161e6 0.352892
\(630\) 0 0
\(631\) 1.55919e7 1.55892 0.779462 − 0.626450i \(-0.215493\pi\)
0.779462 + 0.626450i \(0.215493\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.14180e7 −1.12371
\(636\) 0 0
\(637\) 9.32320e6 0.910367
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.09701e7 −1.05455 −0.527274 − 0.849695i \(-0.676786\pi\)
−0.527274 + 0.849695i \(0.676786\pi\)
\(642\) 0 0
\(643\) 2.83704e6 0.270607 0.135303 − 0.990804i \(-0.456799\pi\)
0.135303 + 0.990804i \(0.456799\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.05686e6 0.568835 0.284418 − 0.958700i \(-0.408200\pi\)
0.284418 + 0.958700i \(0.408200\pi\)
\(648\) 0 0
\(649\) −1.58040e6 −0.147284
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.08892e6 −0.0999341 −0.0499671 − 0.998751i \(-0.515912\pi\)
−0.0499671 + 0.998751i \(0.515912\pi\)
\(654\) 0 0
\(655\) −9.98316e6 −0.909211
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.41803e6 0.665388 0.332694 − 0.943035i \(-0.392042\pi\)
0.332694 + 0.943035i \(0.392042\pi\)
\(660\) 0 0
\(661\) −767654. −0.0683379 −0.0341690 − 0.999416i \(-0.510878\pi\)
−0.0341690 + 0.999416i \(0.510878\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.11049e7 0.973779
\(666\) 0 0
\(667\) −3.34440e6 −0.291074
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.86540e6 −0.159943
\(672\) 0 0
\(673\) 1.42263e6 0.121075 0.0605373 − 0.998166i \(-0.480719\pi\)
0.0605373 + 0.998166i \(0.480719\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.16231e6 −0.516739 −0.258370 − 0.966046i \(-0.583185\pi\)
−0.258370 + 0.966046i \(0.583185\pi\)
\(678\) 0 0
\(679\) 2.92304e7 2.43310
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.50621e7 1.23548 0.617739 − 0.786383i \(-0.288049\pi\)
0.617739 + 0.786383i \(0.288049\pi\)
\(684\) 0 0
\(685\) −8.47796e6 −0.690343
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.05730e7 −1.65101
\(690\) 0 0
\(691\) 5.87636e6 0.468180 0.234090 − 0.972215i \(-0.424789\pi\)
0.234090 + 0.972215i \(0.424789\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.01769e7 0.799199
\(696\) 0 0
\(697\) −7.94632e6 −0.619561
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 3.60077e6 0.276758 0.138379 − 0.990379i \(-0.455811\pi\)
0.138379 + 0.990379i \(0.455811\pi\)
\(702\) 0 0
\(703\) −8.08585e6 −0.617074
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.87235e6 −0.291358
\(708\) 0 0
\(709\) −9.22516e6 −0.689221 −0.344610 − 0.938746i \(-0.611989\pi\)
−0.344610 + 0.938746i \(0.611989\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.15520e6 0.158768
\(714\) 0 0
\(715\) 2.60568e6 0.190615
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.63923e7 1.90395 0.951975 − 0.306177i \(-0.0990500\pi\)
0.951975 + 0.306177i \(0.0990500\pi\)
\(720\) 0 0
\(721\) −1.39505e7 −0.999426
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.86159e6 0.484819
\(726\) 0 0
\(727\) −9.79485e6 −0.687324 −0.343662 − 0.939093i \(-0.611667\pi\)
−0.343662 + 0.939093i \(0.611667\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.51282e6 −0.381576
\(732\) 0 0
\(733\) −4.07584e6 −0.280193 −0.140096 − 0.990138i \(-0.544741\pi\)
−0.140096 + 0.990138i \(0.544741\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.00824e6 −0.0683747
\(738\) 0 0
\(739\) 1.65709e7 1.11618 0.558089 − 0.829781i \(-0.311535\pi\)
0.558089 + 0.829781i \(0.311535\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.44141e7 −0.957892 −0.478946 − 0.877844i \(-0.658981\pi\)
−0.478946 + 0.877844i \(0.658981\pi\)
\(744\) 0 0
\(745\) −1.94396e6 −0.128321
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.01259e7 2.61349
\(750\) 0 0
\(751\) 1.67944e7 1.08659 0.543295 − 0.839542i \(-0.317177\pi\)
0.543295 + 0.839542i \(0.317177\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.34556e7 0.859081
\(756\) 0 0
\(757\) −1.32943e7 −0.843188 −0.421594 − 0.906785i \(-0.638529\pi\)
−0.421594 + 0.906785i \(0.638529\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.14786e6 0.134445 0.0672225 − 0.997738i \(-0.478586\pi\)
0.0672225 + 0.997738i \(0.478586\pi\)
\(762\) 0 0
\(763\) 1.50128e6 0.0933577
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.73317e7 1.06378
\(768\) 0 0
\(769\) −1.31059e7 −0.799193 −0.399596 − 0.916691i \(-0.630850\pi\)
−0.399596 + 0.916691i \(0.630850\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.37154e7 −1.42752 −0.713759 − 0.700392i \(-0.753009\pi\)
−0.713759 + 0.700392i \(0.753009\pi\)
\(774\) 0 0
\(775\) −4.42175e6 −0.264448
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.83495e7 1.08338
\(780\) 0 0
\(781\) 367200. 0.0215415
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.98537e6 0.520430
\(786\) 0 0
\(787\) 8.40048e6 0.483468 0.241734 − 0.970343i \(-0.422284\pi\)
0.241734 + 0.970343i \(0.422284\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.43971e7 1.95470
\(792\) 0 0
\(793\) 2.04572e7 1.15522
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.41023e6 0.301696 0.150848 − 0.988557i \(-0.451800\pi\)
0.150848 + 0.988557i \(0.451800\pi\)
\(798\) 0 0
\(799\) 8.14752e6 0.451501
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.53348e6 0.0839246
\(804\) 0 0
\(805\) 6.96960e6 0.379069
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.60777e7 1.40087 0.700436 − 0.713715i \(-0.252989\pi\)
0.700436 + 0.713715i \(0.252989\pi\)
\(810\) 0 0
\(811\) −1.90021e7 −1.01449 −0.507247 − 0.861800i \(-0.669337\pi\)
−0.507247 + 0.861800i \(0.669337\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.12942e7 −0.595608
\(816\) 0 0
\(817\) 1.27301e7 0.667231
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.10173e7 −1.60600 −0.803001 − 0.595978i \(-0.796764\pi\)
−0.803001 + 0.595978i \(0.796764\pi\)
\(822\) 0 0
\(823\) −1.56290e7 −0.804323 −0.402162 − 0.915569i \(-0.631741\pi\)
−0.402162 + 0.915569i \(0.631741\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.58421e7 0.805467 0.402733 − 0.915317i \(-0.368060\pi\)
0.402733 + 0.915317i \(0.368060\pi\)
\(828\) 0 0
\(829\) −2.06176e6 −0.104196 −0.0520980 − 0.998642i \(-0.516591\pi\)
−0.0520980 + 0.998642i \(0.516591\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.86597e6 0.292905
\(834\) 0 0
\(835\) −4.46292e7 −2.21515
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.03900e7 −1.49048 −0.745240 − 0.666796i \(-0.767665\pi\)
−0.745240 + 0.666796i \(0.767665\pi\)
\(840\) 0 0
\(841\) 1.05583e7 0.514760
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.07029e6 −0.196103
\(846\) 0 0
\(847\) −2.77114e7 −1.32724
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.07480e6 −0.240212
\(852\) 0 0
\(853\) 2.97738e7 1.40108 0.700538 − 0.713615i \(-0.252944\pi\)
0.700538 + 0.713615i \(0.252944\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8.64100e6 −0.401894 −0.200947 − 0.979602i \(-0.564402\pi\)
−0.200947 + 0.979602i \(0.564402\pi\)
\(858\) 0 0
\(859\) 3.35663e7 1.55210 0.776051 − 0.630670i \(-0.217220\pi\)
0.776051 + 0.630670i \(0.217220\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.90191e7 −1.78341 −0.891703 − 0.452621i \(-0.850489\pi\)
−0.891703 + 0.452621i \(0.850489\pi\)
\(864\) 0 0
\(865\) −8.78843e6 −0.399366
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4.46448e6 −0.200549
\(870\) 0 0
\(871\) 1.10570e7 0.493848
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.20007e7 0.971441
\(876\) 0 0
\(877\) 1.81382e7 0.796333 0.398166 − 0.917313i \(-0.369647\pi\)
0.398166 + 0.917313i \(0.369647\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.05312e7 −1.32527 −0.662634 − 0.748943i \(-0.730562\pi\)
−0.662634 + 0.748943i \(0.730562\pi\)
\(882\) 0 0
\(883\) 4.35533e7 1.87983 0.939916 − 0.341405i \(-0.110903\pi\)
0.939916 + 0.341405i \(0.110903\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.34152e7 0.572515 0.286257 − 0.958153i \(-0.407589\pi\)
0.286257 + 0.958153i \(0.407589\pi\)
\(888\) 0 0
\(889\) 3.04480e7 1.29212
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.88141e7 −0.789504
\(894\) 0 0
\(895\) 4.57641e7 1.90971
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.00218e7 −0.826236
\(900\) 0 0
\(901\) −1.29441e7 −0.531203
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.48935e7 1.01033
\(906\) 0 0
\(907\) −3.10816e6 −0.125454 −0.0627272 − 0.998031i \(-0.519980\pi\)
−0.0627272 + 0.998031i \(0.519980\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.19035e6 −0.0475203 −0.0237602 − 0.999718i \(-0.507564\pi\)
−0.0237602 + 0.999718i \(0.507564\pi\)
\(912\) 0 0
\(913\) 388080. 0.0154079
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.66218e7 1.04547
\(918\) 0 0
\(919\) −4.71996e7 −1.84353 −0.921764 − 0.387752i \(-0.873252\pi\)
−0.921764 + 0.387752i \(0.873252\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.02696e6 −0.155587
\(924\) 0 0
\(925\) 1.04118e7 0.400103
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.33595e6 −0.0507870 −0.0253935 − 0.999678i \(-0.508084\pi\)
−0.0253935 + 0.999678i \(0.508084\pi\)
\(930\) 0 0
\(931\) −1.35456e7 −0.512180
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.63944e6 0.0613291
\(936\) 0 0
\(937\) 1.47238e7 0.547861 0.273931 − 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.69196e7 −0.991049 −0.495525 − 0.868594i \(-0.665024\pi\)
−0.495525 + 0.868594i \(0.665024\pi\)
\(942\) 0 0
\(943\) 1.15164e7 0.421733
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.73160e6 −0.135214 −0.0676068 − 0.997712i \(-0.521536\pi\)
−0.0676068 + 0.997712i \(0.521536\pi\)
\(948\) 0 0
\(949\) −1.68172e7 −0.606160
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.18735e7 −0.780166 −0.390083 − 0.920780i \(-0.627554\pi\)
−0.390083 + 0.920780i \(0.627554\pi\)
\(954\) 0 0
\(955\) −1.75127e7 −0.621362
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.26079e7 0.793805
\(960\) 0 0
\(961\) −1.57267e7 −0.549324
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.94897e7 −0.673730
\(966\) 0 0
\(967\) 1.76025e7 0.605352 0.302676 − 0.953093i \(-0.402120\pi\)
0.302676 + 0.953093i \(0.402120\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.67317e7 0.569497 0.284749 − 0.958602i \(-0.408090\pi\)
0.284749 + 0.958602i \(0.408090\pi\)
\(972\) 0 0
\(973\) −2.71385e7 −0.918975
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.55382e7 −1.86147 −0.930733 − 0.365699i \(-0.880830\pi\)
−0.930733 + 0.365699i \(0.880830\pi\)
\(978\) 0 0
\(979\) −1.96452e6 −0.0655088
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.86784e7 1.27669 0.638344 − 0.769751i \(-0.279620\pi\)
0.638344 + 0.769751i \(0.279620\pi\)
\(984\) 0 0
\(985\) −1.32854e7 −0.436299
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.98960e6 0.259737
\(990\) 0 0
\(991\) 9.58498e6 0.310033 0.155016 − 0.987912i \(-0.450457\pi\)
0.155016 + 0.987912i \(0.450457\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.30616e7 −1.37890
\(996\) 0 0
\(997\) 1.03650e7 0.330242 0.165121 − 0.986273i \(-0.447198\pi\)
0.165121 + 0.986273i \(0.447198\pi\)
\(998\) 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 576.6.a.j.1.1 1
3.2 odd 2 192.6.a.o.1.1 1
4.3 odd 2 576.6.a.i.1.1 1
8.3 odd 2 144.6.a.j.1.1 1
8.5 even 2 18.6.a.b.1.1 1
12.11 even 2 192.6.a.g.1.1 1
24.5 odd 2 6.6.a.a.1.1 ✓ 1
24.11 even 2 48.6.a.c.1.1 1
40.13 odd 4 450.6.c.j.199.2 2
40.29 even 2 450.6.a.m.1.1 1
40.37 odd 4 450.6.c.j.199.1 2
48.5 odd 4 768.6.d.c.385.1 2
48.11 even 4 768.6.d.p.385.2 2
48.29 odd 4 768.6.d.c.385.2 2
48.35 even 4 768.6.d.p.385.1 2
56.13 odd 2 882.6.a.a.1.1 1
72.5 odd 6 162.6.c.e.55.1 2
72.13 even 6 162.6.c.h.55.1 2
72.29 odd 6 162.6.c.e.109.1 2
72.61 even 6 162.6.c.h.109.1 2
120.29 odd 2 150.6.a.d.1.1 1
120.53 even 4 150.6.c.b.49.1 2
120.77 even 4 150.6.c.b.49.2 2
168.5 even 6 294.6.e.a.67.1 2
168.53 odd 6 294.6.e.g.79.1 2
168.101 even 6 294.6.e.a.79.1 2
168.125 even 2 294.6.a.m.1.1 1
168.149 odd 6 294.6.e.g.67.1 2
264.197 even 2 726.6.a.a.1.1 1
312.77 odd 2 1014.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.6.a.a.1.1 ✓ 1 24.5 odd 2
18.6.a.b.1.1 1 8.5 even 2
48.6.a.c.1.1 1 24.11 even 2
144.6.a.j.1.1 1 8.3 odd 2
150.6.a.d.1.1 1 120.29 odd 2
150.6.c.b.49.1 2 120.53 even 4
150.6.c.b.49.2 2 120.77 even 4
162.6.c.e.55.1 2 72.5 odd 6
162.6.c.e.109.1 2 72.29 odd 6
162.6.c.h.55.1 2 72.13 even 6
162.6.c.h.109.1 2 72.61 even 6
192.6.a.g.1.1 1 12.11 even 2
192.6.a.o.1.1 1 3.2 odd 2
294.6.a.m.1.1 1 168.125 even 2
294.6.e.a.67.1 2 168.5 even 6
294.6.e.a.79.1 2 168.101 even 6
294.6.e.g.67.1 2 168.149 odd 6
294.6.e.g.79.1 2 168.53 odd 6
450.6.a.m.1.1 1 40.29 even 2
450.6.c.j.199.1 2 40.37 odd 4
450.6.c.j.199.2 2 40.13 odd 4
576.6.a.i.1.1 1 4.3 odd 2
576.6.a.j.1.1 1 1.1 even 1 trivial
726.6.a.a.1.1 1 264.197 even 2
768.6.d.c.385.1 2 48.5 odd 4
768.6.d.c.385.2 2 48.29 odd 4
768.6.d.p.385.1 2 48.35 even 4
768.6.d.p.385.2 2 48.11 even 4
882.6.a.a.1.1 1 56.13 odd 2
1014.6.a.c.1.1 1 312.77 odd 2