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Properties

Label 576.6.a.b.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 $1$

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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 18)
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)
 
\(f(q)\) \(=\) \(q-96.0000 q^{5} +148.000 q^{7} +O(q^{10})\) \(q-96.0000 q^{5} +148.000 q^{7} -384.000 q^{11} +334.000 q^{13} -576.000 q^{17} -664.000 q^{19} -3840.00 q^{23} +6091.00 q^{25} +96.0000 q^{29} +4564.00 q^{31} -14208.0 q^{35} -5798.00 q^{37} +6720.00 q^{41} -14872.0 q^{43} -19200.0 q^{47} +5097.00 q^{49} +7776.00 q^{53} +36864.0 q^{55} +13056.0 q^{59} -42782.0 q^{61} -32064.0 q^{65} +36656.0 q^{67} +64512.0 q^{71} -16810.0 q^{73} -56832.0 q^{77} -28076.0 q^{79} +66432.0 q^{83} +55296.0 q^{85} +81792.0 q^{89} +49432.0 q^{91} +63744.0 q^{95} -29938.0 q^{97} +O(q^{100})\)

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
\(5\) −96.0000 −1.71730 −0.858650 − 0.512562i \(-0.828696\pi\)
−0.858650 + 0.512562i \(0.828696\pi\)
\(6\) 0 0
\(7\) 148.000 1.14161 0.570803 − 0.821087i \(-0.306632\pi\)
0.570803 + 0.821087i \(0.306632\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −384.000 −0.956862 −0.478431 − 0.878125i \(-0.658794\pi\)
−0.478431 + 0.878125i \(0.658794\pi\)
\(12\) 0 0
\(13\) 334.000 0.548136 0.274068 − 0.961710i \(-0.411631\pi\)
0.274068 + 0.961710i \(0.411631\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −576.000 −0.483393 −0.241696 − 0.970352i \(-0.577704\pi\)
−0.241696 + 0.970352i \(0.577704\pi\)
\(18\) 0 0
\(19\) −664.000 −0.421972 −0.210986 − 0.977489i \(-0.567668\pi\)
−0.210986 + 0.977489i \(0.567668\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3840.00 −1.51360 −0.756801 − 0.653645i \(-0.773239\pi\)
−0.756801 + 0.653645i \(0.773239\pi\)
\(24\) 0 0
\(25\) 6091.00 1.94912
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 96.0000 0.0211971 0.0105985 − 0.999944i \(-0.496626\pi\)
0.0105985 + 0.999944i \(0.496626\pi\)
\(30\) 0 0
\(31\) 4564.00 0.852985 0.426493 − 0.904491i \(-0.359749\pi\)
0.426493 + 0.904491i \(0.359749\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14208.0 −1.96048
\(36\) 0 0
\(37\) −5798.00 −0.696264 −0.348132 − 0.937446i \(-0.613184\pi\)
−0.348132 + 0.937446i \(0.613184\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6720.00 0.624323 0.312162 − 0.950029i \(-0.398947\pi\)
0.312162 + 0.950029i \(0.398947\pi\)
\(42\) 0 0
\(43\) −14872.0 −1.22659 −0.613293 − 0.789855i \(-0.710156\pi\)
−0.613293 + 0.789855i \(0.710156\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −19200.0 −1.26782 −0.633909 − 0.773408i \(-0.718550\pi\)
−0.633909 + 0.773408i \(0.718550\pi\)
\(48\) 0 0
\(49\) 5097.00 0.303266
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7776.00 0.380248 0.190124 − 0.981760i \(-0.439111\pi\)
0.190124 + 0.981760i \(0.439111\pi\)
\(54\) 0 0
\(55\) 36864.0 1.64322
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13056.0 0.488293 0.244146 − 0.969738i \(-0.421492\pi\)
0.244146 + 0.969738i \(0.421492\pi\)
\(60\) 0 0
\(61\) −42782.0 −1.47210 −0.736049 − 0.676929i \(-0.763311\pi\)
−0.736049 + 0.676929i \(0.763311\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −32064.0 −0.941314
\(66\) 0 0
\(67\) 36656.0 0.997604 0.498802 − 0.866716i \(-0.333774\pi\)
0.498802 + 0.866716i \(0.333774\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 64512.0 1.51878 0.759390 − 0.650636i \(-0.225498\pi\)
0.759390 + 0.650636i \(0.225498\pi\)
\(72\) 0 0
\(73\) −16810.0 −0.369199 −0.184600 − 0.982814i \(-0.559099\pi\)
−0.184600 + 0.982814i \(0.559099\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −56832.0 −1.09236
\(78\) 0 0
\(79\) −28076.0 −0.506136 −0.253068 − 0.967448i \(-0.581440\pi\)
−0.253068 + 0.967448i \(0.581440\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 66432.0 1.05848 0.529239 − 0.848473i \(-0.322477\pi\)
0.529239 + 0.848473i \(0.322477\pi\)
\(84\) 0 0
\(85\) 55296.0 0.830131
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 81792.0 1.09455 0.547275 − 0.836953i \(-0.315665\pi\)
0.547275 + 0.836953i \(0.315665\pi\)
\(90\) 0 0
\(91\) 49432.0 0.625756
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 63744.0 0.724653
\(96\) 0 0
\(97\) −29938.0 −0.323068 −0.161534 − 0.986867i \(-0.551644\pi\)
−0.161534 + 0.986867i \(0.551644\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 178656. 1.74267 0.871333 − 0.490692i \(-0.163256\pi\)
0.871333 + 0.490692i \(0.163256\pi\)
\(102\) 0 0
\(103\) 115228. 1.07020 0.535100 − 0.844789i \(-0.320274\pi\)
0.535100 + 0.844789i \(0.320274\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 76032.0 0.642003 0.321001 − 0.947079i \(-0.395981\pi\)
0.321001 + 0.947079i \(0.395981\pi\)
\(108\) 0 0
\(109\) 231118. 1.86323 0.931617 − 0.363441i \(-0.118398\pi\)
0.931617 + 0.363441i \(0.118398\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −142464. −1.04956 −0.524782 − 0.851237i \(-0.675853\pi\)
−0.524782 + 0.851237i \(0.675853\pi\)
\(114\) 0 0
\(115\) 368640. 2.59931
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −85248.0 −0.551845
\(120\) 0 0
\(121\) −13595.0 −0.0844143
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −284736. −1.62992
\(126\) 0 0
\(127\) 988.000 0.00543560 0.00271780 − 0.999996i \(-0.499135\pi\)
0.00271780 + 0.999996i \(0.499135\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −224256. −1.14174 −0.570868 − 0.821042i \(-0.693393\pi\)
−0.570868 + 0.821042i \(0.693393\pi\)
\(132\) 0 0
\(133\) −98272.0 −0.481727
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 278976. 1.26989 0.634944 − 0.772558i \(-0.281023\pi\)
0.634944 + 0.772558i \(0.281023\pi\)
\(138\) 0 0
\(139\) 177200. 0.777905 0.388953 − 0.921258i \(-0.372837\pi\)
0.388953 + 0.921258i \(0.372837\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −128256. −0.524490
\(144\) 0 0
\(145\) −9216.00 −0.0364018
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 236064. 0.871092 0.435546 − 0.900166i \(-0.356555\pi\)
0.435546 + 0.900166i \(0.356555\pi\)
\(150\) 0 0
\(151\) 482836. 1.72329 0.861643 − 0.507515i \(-0.169436\pi\)
0.861643 + 0.507515i \(0.169436\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −438144. −1.46483
\(156\) 0 0
\(157\) −381086. −1.23388 −0.616941 − 0.787009i \(-0.711628\pi\)
−0.616941 + 0.787009i \(0.711628\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −568320. −1.72794
\(162\) 0 0
\(163\) 162920. 0.480292 0.240146 − 0.970737i \(-0.422805\pi\)
0.240146 + 0.970737i \(0.422805\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −566016. −1.57050 −0.785249 − 0.619180i \(-0.787465\pi\)
−0.785249 + 0.619180i \(0.787465\pi\)
\(168\) 0 0
\(169\) −259737. −0.699547
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −218208. −0.554313 −0.277157 − 0.960825i \(-0.589392\pi\)
−0.277157 + 0.960825i \(0.589392\pi\)
\(174\) 0 0
\(175\) 901468. 2.22513
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 412416. 0.962062 0.481031 − 0.876704i \(-0.340262\pi\)
0.481031 + 0.876704i \(0.340262\pi\)
\(180\) 0 0
\(181\) 25558.0 0.0579870 0.0289935 − 0.999580i \(-0.490770\pi\)
0.0289935 + 0.999580i \(0.490770\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 556608. 1.19569
\(186\) 0 0
\(187\) 221184. 0.462540
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 400128. 0.793625 0.396813 − 0.917900i \(-0.370116\pi\)
0.396813 + 0.917900i \(0.370116\pi\)
\(192\) 0 0
\(193\) 699650. 1.35203 0.676017 − 0.736886i \(-0.263705\pi\)
0.676017 + 0.736886i \(0.263705\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 406368. 0.746026 0.373013 − 0.927826i \(-0.378325\pi\)
0.373013 + 0.927826i \(0.378325\pi\)
\(198\) 0 0
\(199\) 361996. 0.647994 0.323997 − 0.946058i \(-0.394973\pi\)
0.323997 + 0.946058i \(0.394973\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 14208.0 0.0241987
\(204\) 0 0
\(205\) −645120. −1.07215
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 254976. 0.403770
\(210\) 0 0
\(211\) 151856. 0.234815 0.117407 − 0.993084i \(-0.462542\pi\)
0.117407 + 0.993084i \(0.462542\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.42771e6 2.10642
\(216\) 0 0
\(217\) 675472. 0.973774
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −192384. −0.264965
\(222\) 0 0
\(223\) 1.09332e6 1.47227 0.736134 − 0.676836i \(-0.236649\pi\)
0.736134 + 0.676836i \(0.236649\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 566400. 0.729556 0.364778 − 0.931095i \(-0.381145\pi\)
0.364778 + 0.931095i \(0.381145\pi\)
\(228\) 0 0
\(229\) 587206. 0.739949 0.369974 − 0.929042i \(-0.379366\pi\)
0.369974 + 0.929042i \(0.379366\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −579456. −0.699247 −0.349624 − 0.936890i \(-0.613691\pi\)
−0.349624 + 0.936890i \(0.613691\pi\)
\(234\) 0 0
\(235\) 1.84320e6 2.17722
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −584448. −0.661837 −0.330919 − 0.943659i \(-0.607359\pi\)
−0.330919 + 0.943659i \(0.607359\pi\)
\(240\) 0 0
\(241\) −414130. −0.459298 −0.229649 − 0.973274i \(-0.573758\pi\)
−0.229649 + 0.973274i \(0.573758\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −489312. −0.520800
\(246\) 0 0
\(247\) −221776. −0.231298
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.89965e6 1.90322 0.951610 − 0.307309i \(-0.0994287\pi\)
0.951610 + 0.307309i \(0.0994287\pi\)
\(252\) 0 0
\(253\) 1.47456e6 1.44831
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −447744. −0.422860 −0.211430 − 0.977393i \(-0.567812\pi\)
−0.211430 + 0.977393i \(0.567812\pi\)
\(258\) 0 0
\(259\) −858104. −0.794860
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −67584.0 −0.0602496 −0.0301248 − 0.999546i \(-0.509590\pi\)
−0.0301248 + 0.999546i \(0.509590\pi\)
\(264\) 0 0
\(265\) −746496. −0.652999
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 564192. 0.475386 0.237693 − 0.971340i \(-0.423609\pi\)
0.237693 + 0.971340i \(0.423609\pi\)
\(270\) 0 0
\(271\) −720308. −0.595792 −0.297896 − 0.954598i \(-0.596285\pi\)
−0.297896 + 0.954598i \(0.596285\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.33894e6 −1.86504
\(276\) 0 0
\(277\) 141142. 0.110524 0.0552620 − 0.998472i \(-0.482401\pi\)
0.0552620 + 0.998472i \(0.482401\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −584448. −0.441550 −0.220775 − 0.975325i \(-0.570859\pi\)
−0.220775 + 0.975325i \(0.570859\pi\)
\(282\) 0 0
\(283\) 177056. 0.131415 0.0657074 − 0.997839i \(-0.479070\pi\)
0.0657074 + 0.997839i \(0.479070\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 994560. 0.712732
\(288\) 0 0
\(289\) −1.08808e6 −0.766331
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −956832. −0.651128 −0.325564 − 0.945520i \(-0.605554\pi\)
−0.325564 + 0.945520i \(0.605554\pi\)
\(294\) 0 0
\(295\) −1.25338e6 −0.838545
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.28256e6 −0.829659
\(300\) 0 0
\(301\) −2.20106e6 −1.40028
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.10707e6 2.52803
\(306\) 0 0
\(307\) 2.88286e6 1.74573 0.872867 − 0.487958i \(-0.162258\pi\)
0.872867 + 0.487958i \(0.162258\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.60045e6 −1.52457 −0.762285 − 0.647242i \(-0.775922\pi\)
−0.762285 + 0.647242i \(0.775922\pi\)
\(312\) 0 0
\(313\) −2.58079e6 −1.48899 −0.744495 − 0.667628i \(-0.767310\pi\)
−0.744495 + 0.667628i \(0.767310\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.31101e6 1.29168 0.645838 − 0.763475i \(-0.276508\pi\)
0.645838 + 0.763475i \(0.276508\pi\)
\(318\) 0 0
\(319\) −36864.0 −0.0202827
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 382464. 0.203978
\(324\) 0 0
\(325\) 2.03439e6 1.06838
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.84160e6 −1.44735
\(330\) 0 0
\(331\) −637024. −0.319585 −0.159792 − 0.987151i \(-0.551082\pi\)
−0.159792 + 0.987151i \(0.551082\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.51898e6 −1.71319
\(336\) 0 0
\(337\) 3.38665e6 1.62441 0.812206 − 0.583371i \(-0.198267\pi\)
0.812206 + 0.583371i \(0.198267\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.75258e6 −0.816189
\(342\) 0 0
\(343\) −1.73308e6 −0.795396
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.77824e6 −1.23864 −0.619321 − 0.785138i \(-0.712592\pi\)
−0.619321 + 0.785138i \(0.712592\pi\)
\(348\) 0 0
\(349\) −1.55536e6 −0.683545 −0.341772 − 0.939783i \(-0.611027\pi\)
−0.341772 + 0.939783i \(0.611027\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.11776e6 −0.904565 −0.452283 − 0.891875i \(-0.649390\pi\)
−0.452283 + 0.891875i \(0.649390\pi\)
\(354\) 0 0
\(355\) −6.19315e6 −2.60820
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.17498e6 0.890673 0.445337 − 0.895363i \(-0.353084\pi\)
0.445337 + 0.895363i \(0.353084\pi\)
\(360\) 0 0
\(361\) −2.03520e6 −0.821939
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.61376e6 0.634026
\(366\) 0 0
\(367\) −1.05336e6 −0.408235 −0.204117 − 0.978946i \(-0.565432\pi\)
−0.204117 + 0.978946i \(0.565432\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.15085e6 0.434093
\(372\) 0 0
\(373\) 677098. 0.251988 0.125994 − 0.992031i \(-0.459788\pi\)
0.125994 + 0.992031i \(0.459788\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 32064.0 0.0116189
\(378\) 0 0
\(379\) −5.10748e6 −1.82645 −0.913227 − 0.407452i \(-0.866418\pi\)
−0.913227 + 0.407452i \(0.866418\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.63200e6 0.568491 0.284245 − 0.958752i \(-0.408257\pi\)
0.284245 + 0.958752i \(0.408257\pi\)
\(384\) 0 0
\(385\) 5.45587e6 1.87591
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.46563e6 −1.49627 −0.748133 − 0.663549i \(-0.769050\pi\)
−0.748133 + 0.663549i \(0.769050\pi\)
\(390\) 0 0
\(391\) 2.21184e6 0.731664
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.69530e6 0.869188
\(396\) 0 0
\(397\) 611026. 0.194573 0.0972867 − 0.995256i \(-0.468984\pi\)
0.0972867 + 0.995256i \(0.468984\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.09158e6 1.89177 0.945887 − 0.324496i \(-0.105195\pi\)
0.945887 + 0.324496i \(0.105195\pi\)
\(402\) 0 0
\(403\) 1.52438e6 0.467552
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.22643e6 0.666229
\(408\) 0 0
\(409\) 2.89108e6 0.854578 0.427289 − 0.904115i \(-0.359469\pi\)
0.427289 + 0.904115i \(0.359469\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.93229e6 0.557438
\(414\) 0 0
\(415\) −6.37747e6 −1.81773
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.98406e6 0.830373 0.415186 − 0.909736i \(-0.363716\pi\)
0.415186 + 0.909736i \(0.363716\pi\)
\(420\) 0 0
\(421\) −822074. −0.226051 −0.113025 − 0.993592i \(-0.536054\pi\)
−0.113025 + 0.993592i \(0.536054\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.50842e6 −0.942191
\(426\) 0 0
\(427\) −6.33174e6 −1.68056
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.32448e6 1.63995 0.819977 − 0.572397i \(-0.193986\pi\)
0.819977 + 0.572397i \(0.193986\pi\)
\(432\) 0 0
\(433\) −851902. −0.218358 −0.109179 − 0.994022i \(-0.534822\pi\)
−0.109179 + 0.994022i \(0.534822\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.54976e6 0.638698
\(438\) 0 0
\(439\) 334732. 0.0828964 0.0414482 − 0.999141i \(-0.486803\pi\)
0.0414482 + 0.999141i \(0.486803\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.76218e6 0.426619 0.213309 − 0.976985i \(-0.431576\pi\)
0.213309 + 0.976985i \(0.431576\pi\)
\(444\) 0 0
\(445\) −7.85203e6 −1.87967
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.51859e6 −1.52594 −0.762971 − 0.646433i \(-0.776260\pi\)
−0.762971 + 0.646433i \(0.776260\pi\)
\(450\) 0 0
\(451\) −2.58048e6 −0.597392
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.74547e6 −1.07461
\(456\) 0 0
\(457\) −92074.0 −0.0206227 −0.0103114 − 0.999947i \(-0.503282\pi\)
−0.0103114 + 0.999947i \(0.503282\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 257568. 0.0564468 0.0282234 − 0.999602i \(-0.491015\pi\)
0.0282234 + 0.999602i \(0.491015\pi\)
\(462\) 0 0
\(463\) −3.96228e6 −0.858998 −0.429499 − 0.903067i \(-0.641310\pi\)
−0.429499 + 0.903067i \(0.641310\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.48941e6 0.740388 0.370194 − 0.928954i \(-0.379291\pi\)
0.370194 + 0.928954i \(0.379291\pi\)
\(468\) 0 0
\(469\) 5.42509e6 1.13887
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.71085e6 1.17367
\(474\) 0 0
\(475\) −4.04442e6 −0.822475
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 513024. 0.102164 0.0510821 − 0.998694i \(-0.483733\pi\)
0.0510821 + 0.998694i \(0.483733\pi\)
\(480\) 0 0
\(481\) −1.93653e6 −0.381647
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.87405e6 0.554804
\(486\) 0 0
\(487\) −4.14499e6 −0.791956 −0.395978 − 0.918260i \(-0.629594\pi\)
−0.395978 + 0.918260i \(0.629594\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.75866e6 −0.516409 −0.258205 − 0.966090i \(-0.583131\pi\)
−0.258205 + 0.966090i \(0.583131\pi\)
\(492\) 0 0
\(493\) −55296.0 −0.0102465
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.54778e6 1.73385
\(498\) 0 0
\(499\) 660896. 0.118818 0.0594089 − 0.998234i \(-0.481078\pi\)
0.0594089 + 0.998234i \(0.481078\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −944640. −0.166474 −0.0832370 − 0.996530i \(-0.526526\pi\)
−0.0832370 + 0.996530i \(0.526526\pi\)
\(504\) 0 0
\(505\) −1.71510e7 −2.99268
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.83773e6 −1.34090 −0.670449 − 0.741956i \(-0.733898\pi\)
−0.670449 + 0.741956i \(0.733898\pi\)
\(510\) 0 0
\(511\) −2.48788e6 −0.421480
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.10619e7 −1.83785
\(516\) 0 0
\(517\) 7.37280e6 1.21313
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.29645e6 −0.532049 −0.266025 − 0.963966i \(-0.585710\pi\)
−0.266025 + 0.963966i \(0.585710\pi\)
\(522\) 0 0
\(523\) 6.50238e6 1.03948 0.519742 − 0.854323i \(-0.326028\pi\)
0.519742 + 0.854323i \(0.326028\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.62886e6 −0.412327
\(528\) 0 0
\(529\) 8.30926e6 1.29099
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.24448e6 0.342214
\(534\) 0 0
\(535\) −7.29907e6 −1.10251
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.95725e6 −0.290184
\(540\) 0 0
\(541\) −9.82714e6 −1.44356 −0.721778 − 0.692124i \(-0.756675\pi\)
−0.721778 + 0.692124i \(0.756675\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.21873e7 −3.19973
\(546\) 0 0
\(547\) −3.42580e6 −0.489546 −0.244773 − 0.969580i \(-0.578713\pi\)
−0.244773 + 0.969580i \(0.578713\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −63744.0 −0.00894459
\(552\) 0 0
\(553\) −4.15525e6 −0.577809
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.43363e6 −0.878655 −0.439327 − 0.898327i \(-0.644783\pi\)
−0.439327 + 0.898327i \(0.644783\pi\)
\(558\) 0 0
\(559\) −4.96725e6 −0.672336
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −753024. −0.100124 −0.0500620 − 0.998746i \(-0.515942\pi\)
−0.0500620 + 0.998746i \(0.515942\pi\)
\(564\) 0 0
\(565\) 1.36765e7 1.80242
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.11481e7 1.44351 0.721755 − 0.692148i \(-0.243336\pi\)
0.721755 + 0.692148i \(0.243336\pi\)
\(570\) 0 0
\(571\) 191024. 0.0245187 0.0122594 − 0.999925i \(-0.496098\pi\)
0.0122594 + 0.999925i \(0.496098\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.33894e7 −2.95019
\(576\) 0 0
\(577\) 1.03722e7 1.29697 0.648486 − 0.761227i \(-0.275403\pi\)
0.648486 + 0.761227i \(0.275403\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 9.83194e6 1.20837
\(582\) 0 0
\(583\) −2.98598e6 −0.363845
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.97062e6 0.355838 0.177919 − 0.984045i \(-0.443063\pi\)
0.177919 + 0.984045i \(0.443063\pi\)
\(588\) 0 0
\(589\) −3.03050e6 −0.359936
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.55827e6 0.882644 0.441322 − 0.897349i \(-0.354510\pi\)
0.441322 + 0.897349i \(0.354510\pi\)
\(594\) 0 0
\(595\) 8.18381e6 0.947683
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.69158e6 0.762012 0.381006 − 0.924573i \(-0.375578\pi\)
0.381006 + 0.924573i \(0.375578\pi\)
\(600\) 0 0
\(601\) −3.20359e6 −0.361785 −0.180893 − 0.983503i \(-0.557899\pi\)
−0.180893 + 0.983503i \(0.557899\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.30512e6 0.144965
\(606\) 0 0
\(607\) 1.35585e7 1.49362 0.746809 − 0.665038i \(-0.231585\pi\)
0.746809 + 0.665038i \(0.231585\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.41280e6 −0.694936
\(612\) 0 0
\(613\) 1.07654e7 1.15712 0.578561 − 0.815639i \(-0.303615\pi\)
0.578561 + 0.815639i \(0.303615\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.33504e6 0.987196 0.493598 − 0.869690i \(-0.335681\pi\)
0.493598 + 0.869690i \(0.335681\pi\)
\(618\) 0 0
\(619\) 9.07664e6 0.952135 0.476067 − 0.879409i \(-0.342062\pi\)
0.476067 + 0.879409i \(0.342062\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.21052e7 1.24955
\(624\) 0 0
\(625\) 8.30028e6 0.849949
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.33965e6 0.336569
\(630\) 0 0
\(631\) 1.13367e7 1.13348 0.566741 − 0.823896i \(-0.308204\pi\)
0.566741 + 0.823896i \(0.308204\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −94848.0 −0.00933456
\(636\) 0 0
\(637\) 1.70240e6 0.166231
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.55449e7 −1.49432 −0.747159 − 0.664646i \(-0.768582\pi\)
−0.747159 + 0.664646i \(0.768582\pi\)
\(642\) 0 0
\(643\) −8.80026e6 −0.839399 −0.419699 − 0.907663i \(-0.637864\pi\)
−0.419699 + 0.907663i \(0.637864\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.08449e7 1.01851 0.509256 − 0.860615i \(-0.329921\pi\)
0.509256 + 0.860615i \(0.329921\pi\)
\(648\) 0 0
\(649\) −5.01350e6 −0.467229
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.88771e6 −0.907429 −0.453715 − 0.891147i \(-0.649901\pi\)
−0.453715 + 0.891147i \(0.649901\pi\)
\(654\) 0 0
\(655\) 2.15286e7 1.96070
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.46150e7 1.31095 0.655476 − 0.755216i \(-0.272468\pi\)
0.655476 + 0.755216i \(0.272468\pi\)
\(660\) 0 0
\(661\) −1.57792e7 −1.40469 −0.702347 − 0.711834i \(-0.747865\pi\)
−0.702347 + 0.711834i \(0.747865\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9.43411e6 0.827269
\(666\) 0 0
\(667\) −368640. −0.0320840
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.64283e7 1.40859
\(672\) 0 0
\(673\) 6.64939e6 0.565906 0.282953 − 0.959134i \(-0.408686\pi\)
0.282953 + 0.959134i \(0.408686\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.42550e6 0.371100 0.185550 − 0.982635i \(-0.440593\pi\)
0.185550 + 0.982635i \(0.440593\pi\)
\(678\) 0 0
\(679\) −4.43082e6 −0.368816
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.67827e6 0.383737 0.191869 − 0.981421i \(-0.438545\pi\)
0.191869 + 0.981421i \(0.438545\pi\)
\(684\) 0 0
\(685\) −2.67817e7 −2.18078
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.59718e6 0.208427
\(690\) 0 0
\(691\) −5.54102e6 −0.441463 −0.220731 − 0.975335i \(-0.570844\pi\)
−0.220731 + 0.975335i \(0.570844\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.70112e7 −1.33590
\(696\) 0 0
\(697\) −3.87072e6 −0.301793
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.53443e6 −0.502242 −0.251121 − 0.967956i \(-0.580799\pi\)
−0.251121 + 0.967956i \(0.580799\pi\)
\(702\) 0 0
\(703\) 3.84987e6 0.293804
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.64411e7 1.98944
\(708\) 0 0
\(709\) 3.86541e6 0.288789 0.144394 − 0.989520i \(-0.453877\pi\)
0.144394 + 0.989520i \(0.453877\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.75258e7 −1.29108
\(714\) 0 0
\(715\) 1.23126e7 0.900708
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.80614e6 0.346717 0.173358 − 0.984859i \(-0.444538\pi\)
0.173358 + 0.984859i \(0.444538\pi\)
\(720\) 0 0
\(721\) 1.70537e7 1.22175
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 584736. 0.0413157
\(726\) 0 0
\(727\) 1.90590e7 1.33741 0.668704 − 0.743529i \(-0.266850\pi\)
0.668704 + 0.743529i \(0.266850\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.56627e6 0.592923
\(732\) 0 0
\(733\) −5.69616e6 −0.391582 −0.195791 − 0.980646i \(-0.562727\pi\)
−0.195791 + 0.980646i \(0.562727\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.40759e7 −0.954570
\(738\) 0 0
\(739\) 1.84902e7 1.24546 0.622730 − 0.782437i \(-0.286024\pi\)
0.622730 + 0.782437i \(0.286024\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.90336e6 0.658128 0.329064 − 0.944308i \(-0.393267\pi\)
0.329064 + 0.944308i \(0.393267\pi\)
\(744\) 0 0
\(745\) −2.26621e7 −1.49593
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.12527e7 0.732915
\(750\) 0 0
\(751\) 9.05914e6 0.586121 0.293060 − 0.956094i \(-0.405326\pi\)
0.293060 + 0.956094i \(0.405326\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.63523e7 −2.95940
\(756\) 0 0
\(757\) 1.16677e7 0.740022 0.370011 − 0.929027i \(-0.379354\pi\)
0.370011 + 0.929027i \(0.379354\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.27398e7 0.797444 0.398722 − 0.917072i \(-0.369454\pi\)
0.398722 + 0.917072i \(0.369454\pi\)
\(762\) 0 0
\(763\) 3.42055e7 2.12708
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.36070e6 0.267651
\(768\) 0 0
\(769\) 1.06783e7 0.651156 0.325578 − 0.945515i \(-0.394441\pi\)
0.325578 + 0.945515i \(0.394441\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.18634e6 −0.552960 −0.276480 − 0.961020i \(-0.589168\pi\)
−0.276480 + 0.961020i \(0.589168\pi\)
\(774\) 0 0
\(775\) 2.77993e7 1.66257
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.46208e6 −0.263447
\(780\) 0 0
\(781\) −2.47726e7 −1.45326
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.65843e7 2.11895
\(786\) 0 0
\(787\) −9.28209e6 −0.534206 −0.267103 − 0.963668i \(-0.586066\pi\)
−0.267103 + 0.963668i \(0.586066\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.10847e7 −1.19819
\(792\) 0 0
\(793\) −1.42892e7 −0.806909
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21792.0 0.00121521 0.000607605 − 1.00000i \(-0.499807\pi\)
0.000607605 1.00000i \(0.499807\pi\)
\(798\) 0 0
\(799\) 1.10592e7 0.612854
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.45504e6 0.353273
\(804\) 0 0
\(805\) 5.45587e7 2.96739
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.23085e7 −0.661204 −0.330602 − 0.943770i \(-0.607252\pi\)
−0.330602 + 0.943770i \(0.607252\pi\)
\(810\) 0 0
\(811\) −2.34636e7 −1.25269 −0.626343 − 0.779547i \(-0.715449\pi\)
−0.626343 + 0.779547i \(0.715449\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.56403e7 −0.824806
\(816\) 0 0
\(817\) 9.87501e6 0.517586
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.44206e7 −0.746666 −0.373333 − 0.927697i \(-0.621785\pi\)
−0.373333 + 0.927697i \(0.621785\pi\)
\(822\) 0 0
\(823\) −3.43419e7 −1.76736 −0.883679 − 0.468093i \(-0.844941\pi\)
−0.883679 + 0.468093i \(0.844941\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.13327e7 −1.08463 −0.542316 − 0.840174i \(-0.682453\pi\)
−0.542316 + 0.840174i \(0.682453\pi\)
\(828\) 0 0
\(829\) −2.63751e6 −0.133293 −0.0666465 − 0.997777i \(-0.521230\pi\)
−0.0666465 + 0.997777i \(0.521230\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.93587e6 −0.146597
\(834\) 0 0
\(835\) 5.43375e7 2.69702
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.00577e7 −0.493282 −0.246641 − 0.969107i \(-0.579327\pi\)
−0.246641 + 0.969107i \(0.579327\pi\)
\(840\) 0 0
\(841\) −2.05019e7 −0.999551
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.49348e7 1.20133
\(846\) 0 0
\(847\) −2.01206e6 −0.0963679
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.22643e7 1.05387
\(852\) 0 0
\(853\) 2.30748e7 1.08584 0.542919 − 0.839785i \(-0.317319\pi\)
0.542919 + 0.839785i \(0.317319\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.51646e7 −1.63551 −0.817756 − 0.575565i \(-0.804782\pi\)
−0.817756 + 0.575565i \(0.804782\pi\)
\(858\) 0 0
\(859\) 1.66022e7 0.767684 0.383842 − 0.923399i \(-0.374601\pi\)
0.383842 + 0.923399i \(0.374601\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.97009e7 −1.35751 −0.678754 − 0.734366i \(-0.737480\pi\)
−0.678754 + 0.734366i \(0.737480\pi\)
\(864\) 0 0
\(865\) 2.09480e7 0.951923
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.07812e7 0.484303
\(870\) 0 0
\(871\) 1.22431e7 0.546822
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.21409e7 −1.86073
\(876\) 0 0
\(877\) 1.17943e7 0.517811 0.258906 − 0.965903i \(-0.416638\pi\)
0.258906 + 0.965903i \(0.416638\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.10378e7 0.913190 0.456595 − 0.889675i \(-0.349069\pi\)
0.456595 + 0.889675i \(0.349069\pi\)
\(882\) 0 0
\(883\) 2.12192e7 0.915855 0.457928 − 0.888990i \(-0.348592\pi\)
0.457928 + 0.888990i \(0.348592\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.28818e7 0.976520 0.488260 − 0.872698i \(-0.337632\pi\)
0.488260 + 0.872698i \(0.337632\pi\)
\(888\) 0 0
\(889\) 146224. 0.00620532
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.27488e7 0.534984
\(894\) 0 0
\(895\) −3.95919e7 −1.65215
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 438144. 0.0180808
\(900\) 0 0
\(901\) −4.47898e6 −0.183809
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.45357e6 −0.0995810
\(906\) 0 0
\(907\) −9.68692e6 −0.390992 −0.195496 − 0.980705i \(-0.562632\pi\)
−0.195496 + 0.980705i \(0.562632\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.38112e6 0.374506 0.187253 − 0.982312i \(-0.440042\pi\)
0.187253 + 0.982312i \(0.440042\pi\)
\(912\) 0 0
\(913\) −2.55099e7 −1.01282
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.31899e7 −1.30341
\(918\) 0 0
\(919\) 4.21870e7 1.64774 0.823872 − 0.566775i \(-0.191809\pi\)
0.823872 + 0.566775i \(0.191809\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.15470e7 0.832497
\(924\) 0 0
\(925\) −3.53156e7 −1.35710
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.04556e7 1.15779 0.578893 − 0.815404i \(-0.303485\pi\)
0.578893 + 0.815404i \(0.303485\pi\)
\(930\) 0 0
\(931\) −3.38441e6 −0.127970
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.12337e7 −0.794321
\(936\) 0 0
\(937\) 1.47847e7 0.550128 0.275064 − 0.961426i \(-0.411301\pi\)
0.275064 + 0.961426i \(0.411301\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −9.91997e6 −0.365205 −0.182602 − 0.983187i \(-0.558452\pi\)
−0.182602 + 0.983187i \(0.558452\pi\)
\(942\) 0 0
\(943\) −2.58048e7 −0.944977
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.91610e6 −0.105664 −0.0528320 − 0.998603i \(-0.516825\pi\)
−0.0528320 + 0.998603i \(0.516825\pi\)
\(948\) 0 0
\(949\) −5.61454e6 −0.202371
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.40861e7 −0.502410 −0.251205 − 0.967934i \(-0.580827\pi\)
−0.251205 + 0.967934i \(0.580827\pi\)
\(954\) 0 0
\(955\) −3.84123e7 −1.36289
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.12884e7 1.44971
\(960\) 0 0
\(961\) −7.79906e6 −0.272417
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −6.71664e7 −2.32185
\(966\) 0 0
\(967\) −1.51949e7 −0.522553 −0.261276 − 0.965264i \(-0.584143\pi\)
−0.261276 + 0.965264i \(0.584143\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 5.61220e7 1.91023 0.955113 − 0.296240i \(-0.0957329\pi\)
0.955113 + 0.296240i \(0.0957329\pi\)
\(972\) 0 0
\(973\) 2.62256e7 0.888062
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.45625e7 −1.15843 −0.579214 − 0.815176i \(-0.696640\pi\)
−0.579214 + 0.815176i \(0.696640\pi\)
\(978\) 0 0
\(979\) −3.14081e7 −1.04733
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5.56385e7 1.83650 0.918252 − 0.395997i \(-0.129601\pi\)
0.918252 + 0.395997i \(0.129601\pi\)
\(984\) 0 0
\(985\) −3.90113e7 −1.28115
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.71085e7 1.85656
\(990\) 0 0
\(991\) 3.60028e7 1.16453 0.582267 − 0.812998i \(-0.302166\pi\)
0.582267 + 0.812998i \(0.302166\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.47516e7 −1.11280
\(996\) 0 0
\(997\) −2.35811e7 −0.751322 −0.375661 − 0.926757i \(-0.622584\pi\)
−0.375661 + 0.926757i \(0.622584\pi\)
\(998\) 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.b.1.1 1
3.2 odd 2 576.6.a.bi.1.1 1
4.3 odd 2 576.6.a.a.1.1 1
8.3 odd 2 18.6.a.c.1.1 yes 1
8.5 even 2 144.6.a.l.1.1 1
12.11 even 2 576.6.a.bh.1.1 1
24.5 odd 2 144.6.a.a.1.1 1
24.11 even 2 18.6.a.a.1.1 ✓ 1
40.3 even 4 450.6.c.c.199.1 2
40.19 odd 2 450.6.a.k.1.1 1
40.27 even 4 450.6.c.c.199.2 2
56.27 even 2 882.6.a.l.1.1 1
72.11 even 6 162.6.c.l.109.1 2
72.43 odd 6 162.6.c.a.109.1 2
72.59 even 6 162.6.c.l.55.1 2
72.67 odd 6 162.6.c.a.55.1 2
120.59 even 2 450.6.a.v.1.1 1
120.83 odd 4 450.6.c.m.199.2 2
120.107 odd 4 450.6.c.m.199.1 2
168.83 odd 2 882.6.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.6.a.a.1.1 ✓ 1 24.11 even 2
18.6.a.c.1.1 yes 1 8.3 odd 2
144.6.a.a.1.1 1 24.5 odd 2
144.6.a.l.1.1 1 8.5 even 2
162.6.c.a.55.1 2 72.67 odd 6
162.6.c.a.109.1 2 72.43 odd 6
162.6.c.l.55.1 2 72.59 even 6
162.6.c.l.109.1 2 72.11 even 6
450.6.a.k.1.1 1 40.19 odd 2
450.6.a.v.1.1 1 120.59 even 2
450.6.c.c.199.1 2 40.3 even 4
450.6.c.c.199.2 2 40.27 even 4
450.6.c.m.199.1 2 120.107 odd 4
450.6.c.m.199.2 2 120.83 odd 4
576.6.a.a.1.1 1 4.3 odd 2
576.6.a.b.1.1 1 1.1 even 1 trivial
576.6.a.bh.1.1 1 12.11 even 2
576.6.a.bi.1.1 1 3.2 odd 2
882.6.a.k.1.1 1 168.83 odd 2
882.6.a.l.1.1 1 56.27 even 2