Properties

Label 504.6.a.t.1.2
Level $504$
Weight $6$
Character 504.1
Self dual yes
Analytic conductor $80.833$
Analytic rank $1$
Dimension $2$
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] = [504,6,Mod(1,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 504.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: \(80.8334451857\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{249}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 62 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-7.38987\) of defining polynomial
Character \(\chi\) \(=\) 504.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+63.5595 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+63.5595 q^{5} +49.0000 q^{7} -743.392 q^{11} +606.951 q^{13} +1457.53 q^{17} -2895.40 q^{19} -1770.72 q^{23} +914.806 q^{25} -150.405 q^{29} -6752.26 q^{31} +3114.41 q^{35} -5552.80 q^{37} -15482.1 q^{41} -11432.3 q^{43} +10111.4 q^{47} +2401.00 q^{49} +13596.3 q^{53} -47249.6 q^{55} +41467.6 q^{59} +10243.9 q^{61} +38577.5 q^{65} +45980.1 q^{67} +48272.0 q^{71} -27340.3 q^{73} -36426.2 q^{77} -87096.9 q^{79} -91629.1 q^{83} +92640.0 q^{85} +56598.5 q^{89} +29740.6 q^{91} -184030. q^{95} -131388. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 64 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 64 q^{5} + 98 q^{7} - 540 q^{11} + 204 q^{13} - 304 q^{17} - 1120 q^{19} + 940 q^{23} - 2210 q^{25} - 932 q^{29} - 16408 q^{31} + 3136 q^{35} - 1764 q^{37} + 2552 q^{41} - 24632 q^{43} + 36760 q^{47} + 4802 q^{49} - 9164 q^{53} - 47160 q^{55} + 39888 q^{59} - 25084 q^{61} + 38400 q^{65} - 2592 q^{67} + 35508 q^{71} - 17188 q^{73} - 26460 q^{77} - 95800 q^{79} - 65352 q^{83} + 91864 q^{85} + 23000 q^{89} + 9996 q^{91} - 183248 q^{95} - 108388 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 63.5595 1.13699 0.568493 0.822688i \(-0.307527\pi\)
0.568493 + 0.822688i \(0.307527\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −743.392 −1.85241 −0.926203 0.377025i \(-0.876947\pi\)
−0.926203 + 0.377025i \(0.876947\pi\)
\(12\) 0 0
\(13\) 606.951 0.996083 0.498042 0.867153i \(-0.334053\pi\)
0.498042 + 0.867153i \(0.334053\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1457.53 1.22320 0.611598 0.791169i \(-0.290527\pi\)
0.611598 + 0.791169i \(0.290527\pi\)
\(18\) 0 0
\(19\) −2895.40 −1.84003 −0.920014 0.391884i \(-0.871823\pi\)
−0.920014 + 0.391884i \(0.871823\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1770.72 −0.697960 −0.348980 0.937130i \(-0.613472\pi\)
−0.348980 + 0.937130i \(0.613472\pi\)
\(24\) 0 0
\(25\) 914.806 0.292738
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −150.405 −0.0332099 −0.0166050 0.999862i \(-0.505286\pi\)
−0.0166050 + 0.999862i \(0.505286\pi\)
\(30\) 0 0
\(31\) −6752.26 −1.26196 −0.630979 0.775800i \(-0.717347\pi\)
−0.630979 + 0.775800i \(0.717347\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3114.41 0.429740
\(36\) 0 0
\(37\) −5552.80 −0.666819 −0.333409 0.942782i \(-0.608199\pi\)
−0.333409 + 0.942782i \(0.608199\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −15482.1 −1.43837 −0.719183 0.694820i \(-0.755484\pi\)
−0.719183 + 0.694820i \(0.755484\pi\)
\(42\) 0 0
\(43\) −11432.3 −0.942896 −0.471448 0.881894i \(-0.656269\pi\)
−0.471448 + 0.881894i \(0.656269\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10111.4 0.667679 0.333839 0.942630i \(-0.391656\pi\)
0.333839 + 0.942630i \(0.391656\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13596.3 0.664859 0.332430 0.943128i \(-0.392132\pi\)
0.332430 + 0.943128i \(0.392132\pi\)
\(54\) 0 0
\(55\) −47249.6 −2.10616
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 41467.6 1.55088 0.775440 0.631421i \(-0.217528\pi\)
0.775440 + 0.631421i \(0.217528\pi\)
\(60\) 0 0
\(61\) 10243.9 0.352486 0.176243 0.984347i \(-0.443605\pi\)
0.176243 + 0.984347i \(0.443605\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 38577.5 1.13253
\(66\) 0 0
\(67\) 45980.1 1.25136 0.625681 0.780079i \(-0.284821\pi\)
0.625681 + 0.780079i \(0.284821\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 48272.0 1.13645 0.568224 0.822874i \(-0.307631\pi\)
0.568224 + 0.822874i \(0.307631\pi\)
\(72\) 0 0
\(73\) −27340.3 −0.600477 −0.300239 0.953864i \(-0.597066\pi\)
−0.300239 + 0.953864i \(0.597066\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −36426.2 −0.700144
\(78\) 0 0
\(79\) −87096.9 −1.57013 −0.785063 0.619415i \(-0.787370\pi\)
−0.785063 + 0.619415i \(0.787370\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −91629.1 −1.45995 −0.729975 0.683474i \(-0.760468\pi\)
−0.729975 + 0.683474i \(0.760468\pi\)
\(84\) 0 0
\(85\) 92640.0 1.39076
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56598.5 0.757408 0.378704 0.925518i \(-0.376370\pi\)
0.378704 + 0.925518i \(0.376370\pi\)
\(90\) 0 0
\(91\) 29740.6 0.376484
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −184030. −2.09209
\(96\) 0 0
\(97\) −131388. −1.41784 −0.708921 0.705288i \(-0.750818\pi\)
−0.708921 + 0.705288i \(0.750818\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −189888. −1.85223 −0.926114 0.377243i \(-0.876872\pi\)
−0.926114 + 0.377243i \(0.876872\pi\)
\(102\) 0 0
\(103\) −179030. −1.66277 −0.831384 0.555698i \(-0.812451\pi\)
−0.831384 + 0.555698i \(0.812451\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 139871. 1.18105 0.590526 0.807018i \(-0.298920\pi\)
0.590526 + 0.807018i \(0.298920\pi\)
\(108\) 0 0
\(109\) −27077.8 −0.218297 −0.109148 0.994025i \(-0.534812\pi\)
−0.109148 + 0.994025i \(0.534812\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3694.91 0.0272212 0.0136106 0.999907i \(-0.495667\pi\)
0.0136106 + 0.999907i \(0.495667\pi\)
\(114\) 0 0
\(115\) −112546. −0.793572
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 71419.1 0.462325
\(120\) 0 0
\(121\) 391581. 2.43141
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −140479. −0.804147
\(126\) 0 0
\(127\) −162019. −0.891365 −0.445683 0.895191i \(-0.647039\pi\)
−0.445683 + 0.895191i \(0.647039\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 23429.5 0.119285 0.0596424 0.998220i \(-0.481004\pi\)
0.0596424 + 0.998220i \(0.481004\pi\)
\(132\) 0 0
\(133\) −141875. −0.695466
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −220081. −1.00180 −0.500901 0.865505i \(-0.666998\pi\)
−0.500901 + 0.865505i \(0.666998\pi\)
\(138\) 0 0
\(139\) 164108. 0.720431 0.360216 0.932869i \(-0.382703\pi\)
0.360216 + 0.932869i \(0.382703\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −451203. −1.84515
\(144\) 0 0
\(145\) −9559.68 −0.0377593
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −130408. −0.481215 −0.240607 0.970623i \(-0.577347\pi\)
−0.240607 + 0.970623i \(0.577347\pi\)
\(150\) 0 0
\(151\) −316560. −1.12983 −0.564915 0.825149i \(-0.691091\pi\)
−0.564915 + 0.825149i \(0.691091\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −429170. −1.43483
\(156\) 0 0
\(157\) −249308. −0.807212 −0.403606 0.914933i \(-0.632243\pi\)
−0.403606 + 0.914933i \(0.632243\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −86765.4 −0.263804
\(162\) 0 0
\(163\) 241804. 0.712843 0.356422 0.934325i \(-0.383997\pi\)
0.356422 + 0.934325i \(0.383997\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 394733. 1.09525 0.547624 0.836724i \(-0.315532\pi\)
0.547624 + 0.836724i \(0.315532\pi\)
\(168\) 0 0
\(169\) −2902.90 −0.00781835
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −55967.7 −0.142175 −0.0710873 0.997470i \(-0.522647\pi\)
−0.0710873 + 0.997470i \(0.522647\pi\)
\(174\) 0 0
\(175\) 44825.5 0.110645
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −283606. −0.661580 −0.330790 0.943704i \(-0.607315\pi\)
−0.330790 + 0.943704i \(0.607315\pi\)
\(180\) 0 0
\(181\) −381796. −0.866234 −0.433117 0.901338i \(-0.642586\pi\)
−0.433117 + 0.901338i \(0.642586\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −352933. −0.758164
\(186\) 0 0
\(187\) −1.08352e6 −2.26586
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 773789. 1.53476 0.767378 0.641195i \(-0.221561\pi\)
0.767378 + 0.641195i \(0.221561\pi\)
\(192\) 0 0
\(193\) −580648. −1.12207 −0.561035 0.827792i \(-0.689597\pi\)
−0.561035 + 0.827792i \(0.689597\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 301110. 0.552789 0.276395 0.961044i \(-0.410860\pi\)
0.276395 + 0.961044i \(0.410860\pi\)
\(198\) 0 0
\(199\) 901241. 1.61327 0.806637 0.591047i \(-0.201285\pi\)
0.806637 + 0.591047i \(0.201285\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7369.86 −0.0125522
\(204\) 0 0
\(205\) −984033. −1.63540
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.15242e6 3.40848
\(210\) 0 0
\(211\) −163082. −0.252173 −0.126087 0.992019i \(-0.540242\pi\)
−0.126087 + 0.992019i \(0.540242\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −726633. −1.07206
\(216\) 0 0
\(217\) −330861. −0.476976
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 884652. 1.21840
\(222\) 0 0
\(223\) −565625. −0.761669 −0.380835 0.924643i \(-0.624363\pi\)
−0.380835 + 0.924643i \(0.624363\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −334254. −0.430538 −0.215269 0.976555i \(-0.569063\pi\)
−0.215269 + 0.976555i \(0.569063\pi\)
\(228\) 0 0
\(229\) 188123. 0.237058 0.118529 0.992951i \(-0.462182\pi\)
0.118529 + 0.992951i \(0.462182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 588574. 0.710250 0.355125 0.934819i \(-0.384438\pi\)
0.355125 + 0.934819i \(0.384438\pi\)
\(234\) 0 0
\(235\) 642676. 0.759141
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.15364e6 −1.30640 −0.653201 0.757185i \(-0.726574\pi\)
−0.653201 + 0.757185i \(0.726574\pi\)
\(240\) 0 0
\(241\) 599210. 0.664564 0.332282 0.943180i \(-0.392181\pi\)
0.332282 + 0.943180i \(0.392181\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 152606. 0.162427
\(246\) 0 0
\(247\) −1.75737e6 −1.83282
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −442325. −0.443156 −0.221578 0.975143i \(-0.571121\pi\)
−0.221578 + 0.975143i \(0.571121\pi\)
\(252\) 0 0
\(253\) 1.31634e6 1.29291
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 177887. 0.168001 0.0840003 0.996466i \(-0.473230\pi\)
0.0840003 + 0.996466i \(0.473230\pi\)
\(258\) 0 0
\(259\) −272087. −0.252034
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.26234e6 −1.12535 −0.562674 0.826679i \(-0.690227\pi\)
−0.562674 + 0.826679i \(0.690227\pi\)
\(264\) 0 0
\(265\) 864171. 0.755936
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 969188. 0.816634 0.408317 0.912840i \(-0.366116\pi\)
0.408317 + 0.912840i \(0.366116\pi\)
\(270\) 0 0
\(271\) −1.17860e6 −0.974860 −0.487430 0.873162i \(-0.662066\pi\)
−0.487430 + 0.873162i \(0.662066\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −680059. −0.542269
\(276\) 0 0
\(277\) −158674. −0.124253 −0.0621265 0.998068i \(-0.519788\pi\)
−0.0621265 + 0.998068i \(0.519788\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −696402. −0.526132 −0.263066 0.964778i \(-0.584734\pi\)
−0.263066 + 0.964778i \(0.584734\pi\)
\(282\) 0 0
\(283\) −951366. −0.706125 −0.353062 0.935600i \(-0.614860\pi\)
−0.353062 + 0.935600i \(0.614860\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −758622. −0.543651
\(288\) 0 0
\(289\) 704545. 0.496208
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −798149. −0.543144 −0.271572 0.962418i \(-0.587543\pi\)
−0.271572 + 0.962418i \(0.587543\pi\)
\(294\) 0 0
\(295\) 2.63566e6 1.76333
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.07474e6 −0.695227
\(300\) 0 0
\(301\) −560184. −0.356381
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 651099. 0.400772
\(306\) 0 0
\(307\) 253169. 0.153308 0.0766540 0.997058i \(-0.475576\pi\)
0.0766540 + 0.997058i \(0.475576\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 704729. 0.413163 0.206581 0.978429i \(-0.433766\pi\)
0.206581 + 0.978429i \(0.433766\pi\)
\(312\) 0 0
\(313\) −9154.82 −0.00528189 −0.00264094 0.999997i \(-0.500841\pi\)
−0.00264094 + 0.999997i \(0.500841\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.26957e6 0.709594 0.354797 0.934943i \(-0.384550\pi\)
0.354797 + 0.934943i \(0.384550\pi\)
\(318\) 0 0
\(319\) 111810. 0.0615183
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.22014e6 −2.25072
\(324\) 0 0
\(325\) 555243. 0.291591
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 495460. 0.252359
\(330\) 0 0
\(331\) 3.52407e6 1.76797 0.883985 0.467515i \(-0.154851\pi\)
0.883985 + 0.467515i \(0.154851\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.92247e6 1.42278
\(336\) 0 0
\(337\) 1.72795e6 0.828815 0.414407 0.910092i \(-0.363989\pi\)
0.414407 + 0.910092i \(0.363989\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.01958e6 2.33766
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −620429. −0.276610 −0.138305 0.990390i \(-0.544165\pi\)
−0.138305 + 0.990390i \(0.544165\pi\)
\(348\) 0 0
\(349\) −561993. −0.246983 −0.123492 0.992346i \(-0.539409\pi\)
−0.123492 + 0.992346i \(0.539409\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.30385e6 −0.984051 −0.492025 0.870581i \(-0.663743\pi\)
−0.492025 + 0.870581i \(0.663743\pi\)
\(354\) 0 0
\(355\) 3.06814e6 1.29213
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.45173e6 1.82303 0.911513 0.411272i \(-0.134915\pi\)
0.911513 + 0.411272i \(0.134915\pi\)
\(360\) 0 0
\(361\) 5.90725e6 2.38571
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.73774e6 −0.682734
\(366\) 0 0
\(367\) 929818. 0.360357 0.180178 0.983634i \(-0.442332\pi\)
0.180178 + 0.983634i \(0.442332\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 666216. 0.251293
\(372\) 0 0
\(373\) 1.91861e6 0.714026 0.357013 0.934099i \(-0.383795\pi\)
0.357013 + 0.934099i \(0.383795\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −91288.7 −0.0330799
\(378\) 0 0
\(379\) 3.71768e6 1.32946 0.664728 0.747086i \(-0.268548\pi\)
0.664728 + 0.747086i \(0.268548\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −236982. −0.0825502 −0.0412751 0.999148i \(-0.513142\pi\)
−0.0412751 + 0.999148i \(0.513142\pi\)
\(384\) 0 0
\(385\) −2.31523e6 −0.796054
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.31064e6 −1.10927 −0.554636 0.832093i \(-0.687142\pi\)
−0.554636 + 0.832093i \(0.687142\pi\)
\(390\) 0 0
\(391\) −2.58089e6 −0.853742
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.53583e6 −1.78521
\(396\) 0 0
\(397\) 159806. 0.0508881 0.0254441 0.999676i \(-0.491900\pi\)
0.0254441 + 0.999676i \(0.491900\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.39976e6 1.36637 0.683184 0.730246i \(-0.260595\pi\)
0.683184 + 0.730246i \(0.260595\pi\)
\(402\) 0 0
\(403\) −4.09830e6 −1.25702
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.12791e6 1.23522
\(408\) 0 0
\(409\) 3.20429e6 0.947161 0.473581 0.880751i \(-0.342961\pi\)
0.473581 + 0.880751i \(0.342961\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.03191e6 0.586178
\(414\) 0 0
\(415\) −5.82390e6 −1.65994
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −836895. −0.232882 −0.116441 0.993198i \(-0.537149\pi\)
−0.116441 + 0.993198i \(0.537149\pi\)
\(420\) 0 0
\(421\) 397324. 0.109255 0.0546273 0.998507i \(-0.482603\pi\)
0.0546273 + 0.998507i \(0.482603\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.33336e6 0.358076
\(426\) 0 0
\(427\) 501953. 0.133227
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −693656. −0.179867 −0.0899334 0.995948i \(-0.528665\pi\)
−0.0899334 + 0.995948i \(0.528665\pi\)
\(432\) 0 0
\(433\) −3.19992e6 −0.820200 −0.410100 0.912041i \(-0.634506\pi\)
−0.410100 + 0.912041i \(0.634506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.12695e6 1.28427
\(438\) 0 0
\(439\) −3.58657e6 −0.888215 −0.444107 0.895974i \(-0.646479\pi\)
−0.444107 + 0.895974i \(0.646479\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.11515e6 0.269975 0.134988 0.990847i \(-0.456900\pi\)
0.134988 + 0.990847i \(0.456900\pi\)
\(444\) 0 0
\(445\) 3.59737e6 0.861162
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.44703e6 −1.50919 −0.754595 0.656191i \(-0.772167\pi\)
−0.754595 + 0.656191i \(0.772167\pi\)
\(450\) 0 0
\(451\) 1.15093e7 2.66444
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.89030e6 0.428057
\(456\) 0 0
\(457\) 7.98008e6 1.78738 0.893690 0.448685i \(-0.148107\pi\)
0.893690 + 0.448685i \(0.148107\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.43839e6 −0.753533 −0.376767 0.926308i \(-0.622964\pi\)
−0.376767 + 0.926308i \(0.622964\pi\)
\(462\) 0 0
\(463\) 2.36232e6 0.512137 0.256069 0.966659i \(-0.417573\pi\)
0.256069 + 0.966659i \(0.417573\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.00471e6 1.69845 0.849227 0.528029i \(-0.177069\pi\)
0.849227 + 0.528029i \(0.177069\pi\)
\(468\) 0 0
\(469\) 2.25302e6 0.472970
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.49871e6 1.74663
\(474\) 0 0
\(475\) −2.64873e6 −0.538646
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.36957e6 1.06930 0.534651 0.845073i \(-0.320443\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(480\) 0 0
\(481\) −3.37028e6 −0.664207
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.35098e6 −1.61207
\(486\) 0 0
\(487\) −8.29649e6 −1.58516 −0.792578 0.609770i \(-0.791262\pi\)
−0.792578 + 0.609770i \(0.791262\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.94205e6 0.737936 0.368968 0.929442i \(-0.379711\pi\)
0.368968 + 0.929442i \(0.379711\pi\)
\(492\) 0 0
\(493\) −219221. −0.0406223
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.36533e6 0.429537
\(498\) 0 0
\(499\) −9.47204e6 −1.70291 −0.851456 0.524426i \(-0.824280\pi\)
−0.851456 + 0.524426i \(0.824280\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 739396. 0.130304 0.0651519 0.997875i \(-0.479247\pi\)
0.0651519 + 0.997875i \(0.479247\pi\)
\(504\) 0 0
\(505\) −1.20692e7 −2.10596
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.12834e7 1.93039 0.965195 0.261532i \(-0.0842277\pi\)
0.965195 + 0.261532i \(0.0842277\pi\)
\(510\) 0 0
\(511\) −1.33968e6 −0.226959
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.13790e7 −1.89054
\(516\) 0 0
\(517\) −7.51675e6 −1.23681
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.31103e6 −1.01860 −0.509302 0.860588i \(-0.670097\pi\)
−0.509302 + 0.860588i \(0.670097\pi\)
\(522\) 0 0
\(523\) 1.24140e6 0.198453 0.0992265 0.995065i \(-0.468363\pi\)
0.0992265 + 0.995065i \(0.468363\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.84165e6 −1.54362
\(528\) 0 0
\(529\) −3.30089e6 −0.512851
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.39687e6 −1.43273
\(534\) 0 0
\(535\) 8.89015e6 1.34284
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.78488e6 −0.264629
\(540\) 0 0
\(541\) 7.19933e6 1.05755 0.528773 0.848764i \(-0.322652\pi\)
0.528773 + 0.848764i \(0.322652\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.72105e6 −0.248200
\(546\) 0 0
\(547\) −5.09875e6 −0.728610 −0.364305 0.931280i \(-0.618693\pi\)
−0.364305 + 0.931280i \(0.618693\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 435484. 0.0611073
\(552\) 0 0
\(553\) −4.26775e6 −0.593452
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.08006e7 1.47506 0.737528 0.675317i \(-0.235993\pi\)
0.737528 + 0.675317i \(0.235993\pi\)
\(558\) 0 0
\(559\) −6.93887e6 −0.939203
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −165192. −0.0219643 −0.0109822 0.999940i \(-0.503496\pi\)
−0.0109822 + 0.999940i \(0.503496\pi\)
\(564\) 0 0
\(565\) 234846. 0.0309501
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.21706e7 −1.57590 −0.787952 0.615737i \(-0.788858\pi\)
−0.787952 + 0.615737i \(0.788858\pi\)
\(570\) 0 0
\(571\) 2.30513e6 0.295873 0.147936 0.988997i \(-0.452737\pi\)
0.147936 + 0.988997i \(0.452737\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.61987e6 −0.204319
\(576\) 0 0
\(577\) 3.54323e6 0.443058 0.221529 0.975154i \(-0.428895\pi\)
0.221529 + 0.975154i \(0.428895\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.48983e6 −0.551809
\(582\) 0 0
\(583\) −1.01073e7 −1.23159
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.26253e6 1.10952 0.554759 0.832011i \(-0.312810\pi\)
0.554759 + 0.832011i \(0.312810\pi\)
\(588\) 0 0
\(589\) 1.95505e7 2.32204
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.00317e7 −1.17149 −0.585743 0.810497i \(-0.699197\pi\)
−0.585743 + 0.810497i \(0.699197\pi\)
\(594\) 0 0
\(595\) 4.53936e6 0.525657
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.22306e6 −0.822535 −0.411267 0.911515i \(-0.634914\pi\)
−0.411267 + 0.911515i \(0.634914\pi\)
\(600\) 0 0
\(601\) 1.34318e7 1.51687 0.758434 0.651749i \(-0.225965\pi\)
0.758434 + 0.651749i \(0.225965\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.48887e7 2.76448
\(606\) 0 0
\(607\) 1.63035e7 1.79602 0.898008 0.439979i \(-0.145014\pi\)
0.898008 + 0.439979i \(0.145014\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.13714e6 0.665063
\(612\) 0 0
\(613\) 4.13783e6 0.444755 0.222378 0.974961i \(-0.428618\pi\)
0.222378 + 0.974961i \(0.428618\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.91918e6 0.625962 0.312981 0.949759i \(-0.398672\pi\)
0.312981 + 0.949759i \(0.398672\pi\)
\(618\) 0 0
\(619\) 9.91507e6 1.04009 0.520043 0.854140i \(-0.325916\pi\)
0.520043 + 0.854140i \(0.325916\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.77333e6 0.286273
\(624\) 0 0
\(625\) −1.17875e7 −1.20704
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.09339e6 −0.815650
\(630\) 0 0
\(631\) −1.19832e7 −1.19812 −0.599058 0.800705i \(-0.704458\pi\)
−0.599058 + 0.800705i \(0.704458\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.02978e7 −1.01347
\(636\) 0 0
\(637\) 1.45729e6 0.142298
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.49041e7 −1.43272 −0.716359 0.697732i \(-0.754193\pi\)
−0.716359 + 0.697732i \(0.754193\pi\)
\(642\) 0 0
\(643\) 8.98754e6 0.857261 0.428631 0.903480i \(-0.358996\pi\)
0.428631 + 0.903480i \(0.358996\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.81362e6 0.358160 0.179080 0.983835i \(-0.442688\pi\)
0.179080 + 0.983835i \(0.442688\pi\)
\(648\) 0 0
\(649\) −3.08267e7 −2.87286
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.78785e6 0.164077 0.0820387 0.996629i \(-0.473857\pi\)
0.0820387 + 0.996629i \(0.473857\pi\)
\(654\) 0 0
\(655\) 1.48917e6 0.135625
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.09551e7 −0.982657 −0.491328 0.870974i \(-0.663489\pi\)
−0.491328 + 0.870974i \(0.663489\pi\)
\(660\) 0 0
\(661\) −1.95795e7 −1.74300 −0.871499 0.490397i \(-0.836852\pi\)
−0.871499 + 0.490397i \(0.836852\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.01748e6 −0.790735
\(666\) 0 0
\(667\) 266326. 0.0231792
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.61526e6 −0.652948
\(672\) 0 0
\(673\) −1.28996e7 −1.09784 −0.548918 0.835876i \(-0.684960\pi\)
−0.548918 + 0.835876i \(0.684960\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.21099e6 −0.185402 −0.0927011 0.995694i \(-0.529550\pi\)
−0.0927011 + 0.995694i \(0.529550\pi\)
\(678\) 0 0
\(679\) −6.43803e6 −0.535894
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.34237e6 0.438210 0.219105 0.975701i \(-0.429686\pi\)
0.219105 + 0.975701i \(0.429686\pi\)
\(684\) 0 0
\(685\) −1.39883e7 −1.13904
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.25227e6 0.662255
\(690\) 0 0
\(691\) 4.07335e6 0.324531 0.162266 0.986747i \(-0.448120\pi\)
0.162266 + 0.986747i \(0.448120\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.04306e7 0.819120
\(696\) 0 0
\(697\) −2.25656e7 −1.75940
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.55148e7 −1.19248 −0.596241 0.802805i \(-0.703340\pi\)
−0.596241 + 0.802805i \(0.703340\pi\)
\(702\) 0 0
\(703\) 1.60776e7 1.22697
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.30452e6 −0.700077
\(708\) 0 0
\(709\) 2.11958e7 1.58356 0.791778 0.610809i \(-0.209156\pi\)
0.791778 + 0.610809i \(0.209156\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.19564e7 0.880797
\(714\) 0 0
\(715\) −2.86782e7 −2.09791
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.50416e6 −0.685632 −0.342816 0.939403i \(-0.611381\pi\)
−0.342816 + 0.939403i \(0.611381\pi\)
\(720\) 0 0
\(721\) −8.77245e6 −0.628467
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −137592. −0.00972181
\(726\) 0 0
\(727\) 4.70101e6 0.329879 0.164940 0.986304i \(-0.447257\pi\)
0.164940 + 0.986304i \(0.447257\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.66630e7 −1.15335
\(732\) 0 0
\(733\) 2.14755e7 1.47633 0.738163 0.674622i \(-0.235693\pi\)
0.738163 + 0.674622i \(0.235693\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.41812e7 −2.31803
\(738\) 0 0
\(739\) 1.32038e7 0.889379 0.444690 0.895685i \(-0.353314\pi\)
0.444690 + 0.895685i \(0.353314\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.48906e6 0.431231 0.215616 0.976478i \(-0.430824\pi\)
0.215616 + 0.976478i \(0.430824\pi\)
\(744\) 0 0
\(745\) −8.28867e6 −0.547135
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.85370e6 0.446396
\(750\) 0 0
\(751\) 2.01859e7 1.30601 0.653007 0.757352i \(-0.273507\pi\)
0.653007 + 0.757352i \(0.273507\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.01204e7 −1.28460
\(756\) 0 0
\(757\) −2.86038e7 −1.81420 −0.907098 0.420920i \(-0.861707\pi\)
−0.907098 + 0.420920i \(0.861707\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.98907e6 −0.562669 −0.281335 0.959610i \(-0.590777\pi\)
−0.281335 + 0.959610i \(0.590777\pi\)
\(762\) 0 0
\(763\) −1.32681e6 −0.0825084
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.51688e7 1.54481
\(768\) 0 0
\(769\) −2.58860e6 −0.157851 −0.0789257 0.996880i \(-0.525149\pi\)
−0.0789257 + 0.996880i \(0.525149\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.40322e6 0.505821 0.252911 0.967490i \(-0.418612\pi\)
0.252911 + 0.967490i \(0.418612\pi\)
\(774\) 0 0
\(775\) −6.17701e6 −0.369423
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.48268e7 2.64664
\(780\) 0 0
\(781\) −3.58850e7 −2.10516
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.58459e7 −0.917789
\(786\) 0 0
\(787\) −2.46380e7 −1.41798 −0.708988 0.705221i \(-0.750848\pi\)
−0.708988 + 0.705221i \(0.750848\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 181050. 0.0102886
\(792\) 0 0
\(793\) 6.21757e6 0.351106
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.18021e7 −0.658131 −0.329066 0.944307i \(-0.606734\pi\)
−0.329066 + 0.944307i \(0.606734\pi\)
\(798\) 0 0
\(799\) 1.47377e7 0.816702
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.03246e7 1.11233
\(804\) 0 0
\(805\) −5.51476e6 −0.299942
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.24938e6 −0.120834 −0.0604172 0.998173i \(-0.519243\pi\)
−0.0604172 + 0.998173i \(0.519243\pi\)
\(810\) 0 0
\(811\) −2.67498e7 −1.42813 −0.714065 0.700080i \(-0.753148\pi\)
−0.714065 + 0.700080i \(0.753148\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.53689e7 0.810493
\(816\) 0 0
\(817\) 3.31012e7 1.73496
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 7.87167e6 0.407577 0.203788 0.979015i \(-0.434675\pi\)
0.203788 + 0.979015i \(0.434675\pi\)
\(822\) 0 0
\(823\) −2.72796e7 −1.40390 −0.701952 0.712224i \(-0.747688\pi\)
−0.701952 + 0.712224i \(0.747688\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.31252e7 1.17577 0.587884 0.808945i \(-0.299961\pi\)
0.587884 + 0.808945i \(0.299961\pi\)
\(828\) 0 0
\(829\) 8.79851e6 0.444655 0.222327 0.974972i \(-0.428635\pi\)
0.222327 + 0.974972i \(0.428635\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.49954e6 0.174742
\(834\) 0 0
\(835\) 2.50890e7 1.24528
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.78911e6 0.185837 0.0929185 0.995674i \(-0.470380\pi\)
0.0929185 + 0.995674i \(0.470380\pi\)
\(840\) 0 0
\(841\) −2.04885e7 −0.998897
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −184507. −0.00888935
\(846\) 0 0
\(847\) 1.91875e7 0.918986
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.83247e6 0.465413
\(852\) 0 0
\(853\) 2.19644e7 1.03358 0.516792 0.856111i \(-0.327126\pi\)
0.516792 + 0.856111i \(0.327126\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.36376e7 0.634289 0.317145 0.948377i \(-0.397276\pi\)
0.317145 + 0.948377i \(0.397276\pi\)
\(858\) 0 0
\(859\) 2.89922e7 1.34060 0.670299 0.742091i \(-0.266166\pi\)
0.670299 + 0.742091i \(0.266166\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.76372e7 1.72024 0.860122 0.510088i \(-0.170387\pi\)
0.860122 + 0.510088i \(0.170387\pi\)
\(864\) 0 0
\(865\) −3.55728e6 −0.161651
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.47471e7 2.90851
\(870\) 0 0
\(871\) 2.79077e7 1.24646
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.88346e6 −0.303939
\(876\) 0 0
\(877\) −7.58400e6 −0.332966 −0.166483 0.986044i \(-0.553241\pi\)
−0.166483 + 0.986044i \(0.553241\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.08299e7 −1.33823 −0.669117 0.743157i \(-0.733328\pi\)
−0.669117 + 0.743157i \(0.733328\pi\)
\(882\) 0 0
\(883\) −4.38308e7 −1.89181 −0.945905 0.324444i \(-0.894823\pi\)
−0.945905 + 0.324444i \(0.894823\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.19743e7 −1.36456 −0.682279 0.731092i \(-0.739011\pi\)
−0.682279 + 0.731092i \(0.739011\pi\)
\(888\) 0 0
\(889\) −7.93892e6 −0.336904
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.92766e7 −1.22855
\(894\) 0 0
\(895\) −1.80258e7 −0.752207
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.01558e6 0.0419096
\(900\) 0 0
\(901\) 1.98170e7 0.813253
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.42668e7 −0.984897
\(906\) 0 0
\(907\) −1.24543e7 −0.502693 −0.251346 0.967897i \(-0.580873\pi\)
−0.251346 + 0.967897i \(0.580873\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.91131e7 0.763021 0.381510 0.924365i \(-0.375404\pi\)
0.381510 + 0.924365i \(0.375404\pi\)
\(912\) 0 0
\(913\) 6.81163e7 2.70442
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.14805e6 0.0450854
\(918\) 0 0
\(919\) 1.34330e6 0.0524667 0.0262334 0.999656i \(-0.491649\pi\)
0.0262334 + 0.999656i \(0.491649\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.92988e7 1.13200
\(924\) 0 0
\(925\) −5.07974e6 −0.195203
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.01419e7 0.385551 0.192775 0.981243i \(-0.438251\pi\)
0.192775 + 0.981243i \(0.438251\pi\)
\(930\) 0 0
\(931\) −6.95186e6 −0.262861
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.88678e7 −2.57625
\(936\) 0 0
\(937\) 3.85233e7 1.43342 0.716711 0.697370i \(-0.245647\pi\)
0.716711 + 0.697370i \(0.245647\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.36272e6 −0.197429 −0.0987146 0.995116i \(-0.531473\pi\)
−0.0987146 + 0.995116i \(0.531473\pi\)
\(942\) 0 0
\(943\) 2.74145e7 1.00392
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.51394e7 0.548572 0.274286 0.961648i \(-0.411559\pi\)
0.274286 + 0.961648i \(0.411559\pi\)
\(948\) 0 0
\(949\) −1.65943e7 −0.598125
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 602459. 0.0214880 0.0107440 0.999942i \(-0.496580\pi\)
0.0107440 + 0.999942i \(0.496580\pi\)
\(954\) 0 0
\(955\) 4.91816e7 1.74500
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.07840e7 −0.378646
\(960\) 0 0
\(961\) 1.69639e7 0.592540
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.69057e7 −1.27578
\(966\) 0 0
\(967\) −3.51834e7 −1.20996 −0.604981 0.796240i \(-0.706819\pi\)
−0.604981 + 0.796240i \(0.706819\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.86560e7 −0.975365 −0.487683 0.873021i \(-0.662158\pi\)
−0.487683 + 0.873021i \(0.662158\pi\)
\(972\) 0 0
\(973\) 8.04129e6 0.272297
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.68769e7 0.900829 0.450414 0.892820i \(-0.351276\pi\)
0.450414 + 0.892820i \(0.351276\pi\)
\(978\) 0 0
\(979\) −4.20749e7 −1.40303
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −7.59729e6 −0.250770 −0.125385 0.992108i \(-0.540017\pi\)
−0.125385 + 0.992108i \(0.540017\pi\)
\(984\) 0 0
\(985\) 1.91384e7 0.628514
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.02435e7 0.658104
\(990\) 0 0
\(991\) 4.52583e7 1.46391 0.731954 0.681354i \(-0.238609\pi\)
0.731954 + 0.681354i \(0.238609\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 5.72824e7 1.83427
\(996\) 0 0
\(997\) 2.37777e7 0.757587 0.378793 0.925481i \(-0.376339\pi\)
0.378793 + 0.925481i \(0.376339\pi\)
\(998\) 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 504.6.a.t.1.2 2
3.2 odd 2 168.6.a.h.1.1 2
4.3 odd 2 1008.6.a.bu.1.2 2
12.11 even 2 336.6.a.w.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.h.1.1 2 3.2 odd 2
336.6.a.w.1.1 2 12.11 even 2
504.6.a.t.1.2 2 1.1 even 1 trivial
1008.6.a.bu.1.2 2 4.3 odd 2