Properties

Label 504.6.a.d.1.1
Level $504$
Weight $6$
Character 504.1
Self dual yes
Analytic conductor $80.833$
Analytic rank $1$
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] = [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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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)
 
\(f(q)\) \(=\) \(q-4.00000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-4.00000 q^{5} -49.0000 q^{7} -370.000 q^{11} +122.000 q^{13} +1428.00 q^{17} +1724.00 q^{19} +2670.00 q^{23} -3109.00 q^{25} -4302.00 q^{29} +3104.00 q^{31} +196.000 q^{35} -14318.0 q^{37} +12272.0 q^{41} -21652.0 q^{43} +2644.00 q^{47} +2401.00 q^{49} +24342.0 q^{53} +1480.00 q^{55} +14088.0 q^{59} -24474.0 q^{61} -488.000 q^{65} +7208.00 q^{67} -54302.0 q^{71} -48962.0 q^{73} +18130.0 q^{77} -33332.0 q^{79} +4004.00 q^{83} -5712.00 q^{85} -64752.0 q^{89} -5978.00 q^{91} -6896.00 q^{95} +7038.00 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −4.00000 −0.0715542 −0.0357771 0.999360i \(-0.511391\pi\)
−0.0357771 + 0.999360i \(0.511391\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −370.000 −0.921977 −0.460988 0.887406i \(-0.652505\pi\)
−0.460988 + 0.887406i \(0.652505\pi\)
\(12\) 0 0
\(13\) 122.000 0.200217 0.100109 0.994977i \(-0.468081\pi\)
0.100109 + 0.994977i \(0.468081\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1428.00 1.19841 0.599206 0.800595i \(-0.295483\pi\)
0.599206 + 0.800595i \(0.295483\pi\)
\(18\) 0 0
\(19\) 1724.00 1.09560 0.547802 0.836608i \(-0.315465\pi\)
0.547802 + 0.836608i \(0.315465\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2670.00 1.05243 0.526213 0.850353i \(-0.323611\pi\)
0.526213 + 0.850353i \(0.323611\pi\)
\(24\) 0 0
\(25\) −3109.00 −0.994880
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4302.00 −0.949895 −0.474947 0.880014i \(-0.657533\pi\)
−0.474947 + 0.880014i \(0.657533\pi\)
\(30\) 0 0
\(31\) 3104.00 0.580120 0.290060 0.957009i \(-0.406325\pi\)
0.290060 + 0.957009i \(0.406325\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 196.000 0.0270449
\(36\) 0 0
\(37\) −14318.0 −1.71940 −0.859702 0.510796i \(-0.829351\pi\)
−0.859702 + 0.510796i \(0.829351\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 12272.0 1.14013 0.570067 0.821598i \(-0.306917\pi\)
0.570067 + 0.821598i \(0.306917\pi\)
\(42\) 0 0
\(43\) −21652.0 −1.78578 −0.892888 0.450279i \(-0.851324\pi\)
−0.892888 + 0.450279i \(0.851324\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2644.00 0.174589 0.0872945 0.996183i \(-0.472178\pi\)
0.0872945 + 0.996183i \(0.472178\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 24342.0 1.19033 0.595164 0.803604i \(-0.297087\pi\)
0.595164 + 0.803604i \(0.297087\pi\)
\(54\) 0 0
\(55\) 1480.00 0.0659713
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 14088.0 0.526889 0.263445 0.964675i \(-0.415141\pi\)
0.263445 + 0.964675i \(0.415141\pi\)
\(60\) 0 0
\(61\) −24474.0 −0.842132 −0.421066 0.907030i \(-0.638344\pi\)
−0.421066 + 0.907030i \(0.638344\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −488.000 −0.0143264
\(66\) 0 0
\(67\) 7208.00 0.196168 0.0980839 0.995178i \(-0.468729\pi\)
0.0980839 + 0.995178i \(0.468729\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −54302.0 −1.27841 −0.639205 0.769037i \(-0.720736\pi\)
−0.639205 + 0.769037i \(0.720736\pi\)
\(72\) 0 0
\(73\) −48962.0 −1.07536 −0.537678 0.843150i \(-0.680698\pi\)
−0.537678 + 0.843150i \(0.680698\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18130.0 0.348474
\(78\) 0 0
\(79\) −33332.0 −0.600888 −0.300444 0.953799i \(-0.597135\pi\)
−0.300444 + 0.953799i \(0.597135\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4004.00 0.0637968 0.0318984 0.999491i \(-0.489845\pi\)
0.0318984 + 0.999491i \(0.489845\pi\)
\(84\) 0 0
\(85\) −5712.00 −0.0857513
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −64752.0 −0.866519 −0.433260 0.901269i \(-0.642637\pi\)
−0.433260 + 0.901269i \(0.642637\pi\)
\(90\) 0 0
\(91\) −5978.00 −0.0756750
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6896.00 −0.0783950
\(96\) 0 0
\(97\) 7038.00 0.0759486 0.0379743 0.999279i \(-0.487909\pi\)
0.0379743 + 0.999279i \(0.487909\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −24784.0 −0.241751 −0.120875 0.992668i \(-0.538570\pi\)
−0.120875 + 0.992668i \(0.538570\pi\)
\(102\) 0 0
\(103\) 108080. 1.00381 0.501906 0.864922i \(-0.332632\pi\)
0.501906 + 0.864922i \(0.332632\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −108834. −0.918978 −0.459489 0.888183i \(-0.651967\pi\)
−0.459489 + 0.888183i \(0.651967\pi\)
\(108\) 0 0
\(109\) −202642. −1.63367 −0.816833 0.576874i \(-0.804272\pi\)
−0.816833 + 0.576874i \(0.804272\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 50198.0 0.369820 0.184910 0.982755i \(-0.440801\pi\)
0.184910 + 0.982755i \(0.440801\pi\)
\(114\) 0 0
\(115\) −10680.0 −0.0753055
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −69972.0 −0.452957
\(120\) 0 0
\(121\) −24151.0 −0.149959
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 24936.0 0.142742
\(126\) 0 0
\(127\) 3052.00 0.0167909 0.00839547 0.999965i \(-0.497328\pi\)
0.00839547 + 0.999965i \(0.497328\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −218788. −1.11390 −0.556949 0.830547i \(-0.688028\pi\)
−0.556949 + 0.830547i \(0.688028\pi\)
\(132\) 0 0
\(133\) −84476.0 −0.414099
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −203070. −0.924367 −0.462183 0.886784i \(-0.652934\pi\)
−0.462183 + 0.886784i \(0.652934\pi\)
\(138\) 0 0
\(139\) 49540.0 0.217480 0.108740 0.994070i \(-0.465318\pi\)
0.108740 + 0.994070i \(0.465318\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −45140.0 −0.184596
\(144\) 0 0
\(145\) 17208.0 0.0679689
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −93354.0 −0.344483 −0.172241 0.985055i \(-0.555101\pi\)
−0.172241 + 0.985055i \(0.555101\pi\)
\(150\) 0 0
\(151\) 70872.0 0.252949 0.126474 0.991970i \(-0.459634\pi\)
0.126474 + 0.991970i \(0.459634\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12416.0 −0.0415100
\(156\) 0 0
\(157\) −374898. −1.21385 −0.606924 0.794760i \(-0.707597\pi\)
−0.606924 + 0.794760i \(0.707597\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −130830. −0.397780
\(162\) 0 0
\(163\) −125184. −0.369045 −0.184523 0.982828i \(-0.559074\pi\)
−0.184523 + 0.982828i \(0.559074\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −444068. −1.23214 −0.616068 0.787693i \(-0.711275\pi\)
−0.616068 + 0.787693i \(0.711275\pi\)
\(168\) 0 0
\(169\) −356409. −0.959913
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −544368. −1.38286 −0.691429 0.722445i \(-0.743018\pi\)
−0.691429 + 0.722445i \(0.743018\pi\)
\(174\) 0 0
\(175\) 152341. 0.376029
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 616130. 1.43727 0.718637 0.695385i \(-0.244766\pi\)
0.718637 + 0.695385i \(0.244766\pi\)
\(180\) 0 0
\(181\) 98266.0 0.222950 0.111475 0.993767i \(-0.464443\pi\)
0.111475 + 0.993767i \(0.464443\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 57272.0 0.123031
\(186\) 0 0
\(187\) −528360. −1.10491
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 515138. 1.02174 0.510870 0.859658i \(-0.329323\pi\)
0.510870 + 0.859658i \(0.329323\pi\)
\(192\) 0 0
\(193\) −449930. −0.869464 −0.434732 0.900560i \(-0.643157\pi\)
−0.434732 + 0.900560i \(0.643157\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 404934. 0.743393 0.371697 0.928354i \(-0.378776\pi\)
0.371697 + 0.928354i \(0.378776\pi\)
\(198\) 0 0
\(199\) −342576. −0.613231 −0.306616 0.951833i \(-0.599197\pi\)
−0.306616 + 0.951833i \(0.599197\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 210798. 0.359026
\(204\) 0 0
\(205\) −49088.0 −0.0815813
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −637880. −1.01012
\(210\) 0 0
\(211\) −812820. −1.25686 −0.628432 0.777865i \(-0.716303\pi\)
−0.628432 + 0.777865i \(0.716303\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 86608.0 0.127780
\(216\) 0 0
\(217\) −152096. −0.219265
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 174216. 0.239943
\(222\) 0 0
\(223\) −655320. −0.882452 −0.441226 0.897396i \(-0.645456\pi\)
−0.441226 + 0.897396i \(0.645456\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.19258e6 1.53611 0.768053 0.640386i \(-0.221226\pi\)
0.768053 + 0.640386i \(0.221226\pi\)
\(228\) 0 0
\(229\) 374506. 0.471922 0.235961 0.971763i \(-0.424176\pi\)
0.235961 + 0.971763i \(0.424176\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.47249e6 −1.77690 −0.888452 0.458970i \(-0.848218\pi\)
−0.888452 + 0.458970i \(0.848218\pi\)
\(234\) 0 0
\(235\) −10576.0 −0.0124926
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.28908e6 1.45977 0.729885 0.683570i \(-0.239574\pi\)
0.729885 + 0.683570i \(0.239574\pi\)
\(240\) 0 0
\(241\) 174478. 0.193508 0.0967538 0.995308i \(-0.469154\pi\)
0.0967538 + 0.995308i \(0.469154\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9604.00 −0.0102220
\(246\) 0 0
\(247\) 210328. 0.219359
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 875928. 0.877575 0.438787 0.898591i \(-0.355408\pi\)
0.438787 + 0.898591i \(0.355408\pi\)
\(252\) 0 0
\(253\) −987900. −0.970313
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 674408. 0.636927 0.318464 0.947935i \(-0.396833\pi\)
0.318464 + 0.947935i \(0.396833\pi\)
\(258\) 0 0
\(259\) 701582. 0.649874
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.47155e6 −1.31186 −0.655929 0.754823i \(-0.727723\pi\)
−0.655929 + 0.754823i \(0.727723\pi\)
\(264\) 0 0
\(265\) −97368.0 −0.0851729
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.12577e6 −1.79117 −0.895583 0.444894i \(-0.853241\pi\)
−0.895583 + 0.444894i \(0.853241\pi\)
\(270\) 0 0
\(271\) 1.10940e6 0.917624 0.458812 0.888533i \(-0.348275\pi\)
0.458812 + 0.888533i \(0.348275\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.15033e6 0.917256
\(276\) 0 0
\(277\) −229094. −0.179397 −0.0896983 0.995969i \(-0.528590\pi\)
−0.0896983 + 0.995969i \(0.528590\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 625962. 0.472914 0.236457 0.971642i \(-0.424014\pi\)
0.236457 + 0.971642i \(0.424014\pi\)
\(282\) 0 0
\(283\) −2.04374e6 −1.51691 −0.758455 0.651726i \(-0.774045\pi\)
−0.758455 + 0.651726i \(0.774045\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −601328. −0.430930
\(288\) 0 0
\(289\) 619327. 0.436190
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.96838e6 −1.33949 −0.669747 0.742589i \(-0.733597\pi\)
−0.669747 + 0.742589i \(0.733597\pi\)
\(294\) 0 0
\(295\) −56352.0 −0.0377011
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 325740. 0.210714
\(300\) 0 0
\(301\) 1.06095e6 0.674960
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 97896.0 0.0602581
\(306\) 0 0
\(307\) 3.04359e6 1.84306 0.921531 0.388305i \(-0.126939\pi\)
0.921531 + 0.388305i \(0.126939\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 325724. 0.190963 0.0954814 0.995431i \(-0.469561\pi\)
0.0954814 + 0.995431i \(0.469561\pi\)
\(312\) 0 0
\(313\) 2.28769e6 1.31989 0.659943 0.751316i \(-0.270580\pi\)
0.659943 + 0.751316i \(0.270580\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −902562. −0.504463 −0.252231 0.967667i \(-0.581164\pi\)
−0.252231 + 0.967667i \(0.581164\pi\)
\(318\) 0 0
\(319\) 1.59174e6 0.875781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.46187e6 1.31298
\(324\) 0 0
\(325\) −379298. −0.199192
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −129556. −0.0659884
\(330\) 0 0
\(331\) 1.56194e6 0.783600 0.391800 0.920050i \(-0.371853\pi\)
0.391800 + 0.920050i \(0.371853\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −28832.0 −0.0140366
\(336\) 0 0
\(337\) −572230. −0.274471 −0.137235 0.990538i \(-0.543822\pi\)
−0.137235 + 0.990538i \(0.543822\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.14848e6 −0.534857
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.88039e6 0.838350 0.419175 0.907906i \(-0.362319\pi\)
0.419175 + 0.907906i \(0.362319\pi\)
\(348\) 0 0
\(349\) 1.43343e6 0.629960 0.314980 0.949098i \(-0.398002\pi\)
0.314980 + 0.949098i \(0.398002\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.09802e6 1.32327 0.661633 0.749827i \(-0.269864\pi\)
0.661633 + 0.749827i \(0.269864\pi\)
\(354\) 0 0
\(355\) 217208. 0.0914755
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −663918. −0.271881 −0.135940 0.990717i \(-0.543406\pi\)
−0.135940 + 0.990717i \(0.543406\pi\)
\(360\) 0 0
\(361\) 496077. 0.200346
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 195848. 0.0769462
\(366\) 0 0
\(367\) 4.33787e6 1.68117 0.840585 0.541680i \(-0.182211\pi\)
0.840585 + 0.541680i \(0.182211\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.19276e6 −0.449902
\(372\) 0 0
\(373\) 4.49537e6 1.67299 0.836494 0.547976i \(-0.184601\pi\)
0.836494 + 0.547976i \(0.184601\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −524844. −0.190185
\(378\) 0 0
\(379\) −1.44910e6 −0.518203 −0.259102 0.965850i \(-0.583426\pi\)
−0.259102 + 0.965850i \(0.583426\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.62465e6 −1.26261 −0.631305 0.775535i \(-0.717480\pi\)
−0.631305 + 0.775535i \(0.717480\pi\)
\(384\) 0 0
\(385\) −72520.0 −0.0249348
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 585274. 0.196103 0.0980517 0.995181i \(-0.468739\pi\)
0.0980517 + 0.995181i \(0.468739\pi\)
\(390\) 0 0
\(391\) 3.81276e6 1.26124
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 133328. 0.0429961
\(396\) 0 0
\(397\) −4.36239e6 −1.38915 −0.694573 0.719422i \(-0.744407\pi\)
−0.694573 + 0.719422i \(0.744407\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.16168e6 −1.29243 −0.646216 0.763155i \(-0.723649\pi\)
−0.646216 + 0.763155i \(0.723649\pi\)
\(402\) 0 0
\(403\) 378688. 0.116150
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.29766e6 1.58525
\(408\) 0 0
\(409\) −4.54131e6 −1.34237 −0.671185 0.741290i \(-0.734215\pi\)
−0.671185 + 0.741290i \(0.734215\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −690312. −0.199145
\(414\) 0 0
\(415\) −16016.0 −0.00456493
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.93357e6 0.538052 0.269026 0.963133i \(-0.413298\pi\)
0.269026 + 0.963133i \(0.413298\pi\)
\(420\) 0 0
\(421\) −2.16777e6 −0.596084 −0.298042 0.954553i \(-0.596333\pi\)
−0.298042 + 0.954553i \(0.596333\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.43965e6 −1.19228
\(426\) 0 0
\(427\) 1.19923e6 0.318296
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.36421e6 0.872348 0.436174 0.899862i \(-0.356333\pi\)
0.436174 + 0.899862i \(0.356333\pi\)
\(432\) 0 0
\(433\) 6.09510e6 1.56229 0.781144 0.624351i \(-0.214637\pi\)
0.781144 + 0.624351i \(0.214637\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.60308e6 1.15304
\(438\) 0 0
\(439\) 7.65252e6 1.89515 0.947574 0.319536i \(-0.103527\pi\)
0.947574 + 0.319536i \(0.103527\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 762570. 0.184616 0.0923082 0.995730i \(-0.470575\pi\)
0.0923082 + 0.995730i \(0.470575\pi\)
\(444\) 0 0
\(445\) 259008. 0.0620031
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.44504e6 1.04054 0.520271 0.854001i \(-0.325831\pi\)
0.520271 + 0.854001i \(0.325831\pi\)
\(450\) 0 0
\(451\) −4.54064e6 −1.05118
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 23912.0 0.00541486
\(456\) 0 0
\(457\) −6.00527e6 −1.34506 −0.672531 0.740069i \(-0.734793\pi\)
−0.672531 + 0.740069i \(0.734793\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.86783e6 0.628494 0.314247 0.949341i \(-0.398248\pi\)
0.314247 + 0.949341i \(0.398248\pi\)
\(462\) 0 0
\(463\) 4.45140e6 0.965037 0.482518 0.875886i \(-0.339722\pi\)
0.482518 + 0.875886i \(0.339722\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.34522e6 0.497613 0.248807 0.968553i \(-0.419962\pi\)
0.248807 + 0.968553i \(0.419962\pi\)
\(468\) 0 0
\(469\) −353192. −0.0741445
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.01124e6 1.64644
\(474\) 0 0
\(475\) −5.35992e6 −1.08999
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.16154e6 −0.231311 −0.115655 0.993289i \(-0.536897\pi\)
−0.115655 + 0.993289i \(0.536897\pi\)
\(480\) 0 0
\(481\) −1.74680e6 −0.344254
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −28152.0 −0.00543444
\(486\) 0 0
\(487\) −17776.0 −0.00339634 −0.00169817 0.999999i \(-0.500541\pi\)
−0.00169817 + 0.999999i \(0.500541\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.09827e6 0.392787 0.196393 0.980525i \(-0.437077\pi\)
0.196393 + 0.980525i \(0.437077\pi\)
\(492\) 0 0
\(493\) −6.14326e6 −1.13836
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.66080e6 0.483193
\(498\) 0 0
\(499\) −8.44714e6 −1.51865 −0.759326 0.650710i \(-0.774471\pi\)
−0.759326 + 0.650710i \(0.774471\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.42743e6 −1.30894 −0.654468 0.756089i \(-0.727108\pi\)
−0.654468 + 0.756089i \(0.727108\pi\)
\(504\) 0 0
\(505\) 99136.0 0.0172983
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.06342e6 −0.353015 −0.176508 0.984299i \(-0.556480\pi\)
−0.176508 + 0.984299i \(0.556480\pi\)
\(510\) 0 0
\(511\) 2.39914e6 0.406446
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −432320. −0.0718269
\(516\) 0 0
\(517\) −978280. −0.160967
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −233724. −0.0377232 −0.0188616 0.999822i \(-0.506004\pi\)
−0.0188616 + 0.999822i \(0.506004\pi\)
\(522\) 0 0
\(523\) 1.15859e7 1.85214 0.926071 0.377350i \(-0.123165\pi\)
0.926071 + 0.377350i \(0.123165\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.43251e6 0.695222
\(528\) 0 0
\(529\) 692557. 0.107601
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.49718e6 0.228274
\(534\) 0 0
\(535\) 435336. 0.0657567
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −888370. −0.131711
\(540\) 0 0
\(541\) 8.75141e6 1.28554 0.642769 0.766060i \(-0.277786\pi\)
0.642769 + 0.766060i \(0.277786\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 810568. 0.116896
\(546\) 0 0
\(547\) −1.29193e7 −1.84617 −0.923084 0.384598i \(-0.874340\pi\)
−0.923084 + 0.384598i \(0.874340\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.41665e6 −1.04071
\(552\) 0 0
\(553\) 1.63327e6 0.227114
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.28030e6 −0.721141 −0.360571 0.932732i \(-0.617418\pi\)
−0.360571 + 0.932732i \(0.617418\pi\)
\(558\) 0 0
\(559\) −2.64154e6 −0.357543
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.48097e6 −1.12765 −0.563825 0.825894i \(-0.690671\pi\)
−0.563825 + 0.825894i \(0.690671\pi\)
\(564\) 0 0
\(565\) −200792. −0.0264622
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.01798e6 −0.908723 −0.454362 0.890817i \(-0.650133\pi\)
−0.454362 + 0.890817i \(0.650133\pi\)
\(570\) 0 0
\(571\) 4.79490e6 0.615446 0.307723 0.951476i \(-0.400433\pi\)
0.307723 + 0.951476i \(0.400433\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.30103e6 −1.04704
\(576\) 0 0
\(577\) −6.39709e6 −0.799914 −0.399957 0.916534i \(-0.630975\pi\)
−0.399957 + 0.916534i \(0.630975\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −196196. −0.0241129
\(582\) 0 0
\(583\) −9.00654e6 −1.09745
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.49917e6 0.658721 0.329361 0.944204i \(-0.393167\pi\)
0.329361 + 0.944204i \(0.393167\pi\)
\(588\) 0 0
\(589\) 5.35130e6 0.635581
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.34543e7 1.57118 0.785588 0.618750i \(-0.212361\pi\)
0.785588 + 0.618750i \(0.212361\pi\)
\(594\) 0 0
\(595\) 279888. 0.0324110
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.57493e6 −0.520976 −0.260488 0.965477i \(-0.583883\pi\)
−0.260488 + 0.965477i \(0.583883\pi\)
\(600\) 0 0
\(601\) 1.07837e7 1.21782 0.608910 0.793240i \(-0.291607\pi\)
0.608910 + 0.793240i \(0.291607\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 96604.0 0.0107302
\(606\) 0 0
\(607\) −1.28728e7 −1.41808 −0.709041 0.705167i \(-0.750872\pi\)
−0.709041 + 0.705167i \(0.750872\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 322568. 0.0349557
\(612\) 0 0
\(613\) −1.13805e7 −1.22323 −0.611616 0.791155i \(-0.709480\pi\)
−0.611616 + 0.791155i \(0.709480\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.15644e7 −1.22295 −0.611477 0.791263i \(-0.709424\pi\)
−0.611477 + 0.791263i \(0.709424\pi\)
\(618\) 0 0
\(619\) 641356. 0.0672779 0.0336390 0.999434i \(-0.489290\pi\)
0.0336390 + 0.999434i \(0.489290\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.17285e6 0.327513
\(624\) 0 0
\(625\) 9.61588e6 0.984666
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.04461e7 −2.06055
\(630\) 0 0
\(631\) 1.18685e7 1.18665 0.593323 0.804964i \(-0.297816\pi\)
0.593323 + 0.804964i \(0.297816\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12208.0 −0.00120146
\(636\) 0 0
\(637\) 292922. 0.0286025
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.80700e6 −0.269834 −0.134917 0.990857i \(-0.543077\pi\)
−0.134917 + 0.990857i \(0.543077\pi\)
\(642\) 0 0
\(643\) −3.23109e6 −0.308192 −0.154096 0.988056i \(-0.549247\pi\)
−0.154096 + 0.988056i \(0.549247\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.13192e7 −1.06305 −0.531527 0.847041i \(-0.678382\pi\)
−0.531527 + 0.847041i \(0.678382\pi\)
\(648\) 0 0
\(649\) −5.21256e6 −0.485780
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.54002e6 −0.416653 −0.208327 0.978059i \(-0.566802\pi\)
−0.208327 + 0.978059i \(0.566802\pi\)
\(654\) 0 0
\(655\) 875152. 0.0797040
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.24941e7 1.12070 0.560352 0.828254i \(-0.310666\pi\)
0.560352 + 0.828254i \(0.310666\pi\)
\(660\) 0 0
\(661\) −1.61074e7 −1.43391 −0.716954 0.697121i \(-0.754464\pi\)
−0.716954 + 0.697121i \(0.754464\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 337904. 0.0296305
\(666\) 0 0
\(667\) −1.14863e7 −0.999694
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.05538e6 0.776427
\(672\) 0 0
\(673\) 1.42956e7 1.21665 0.608326 0.793688i \(-0.291841\pi\)
0.608326 + 0.793688i \(0.291841\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.53658e6 −0.212705 −0.106352 0.994328i \(-0.533917\pi\)
−0.106352 + 0.994328i \(0.533917\pi\)
\(678\) 0 0
\(679\) −344862. −0.0287059
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.58174e6 −0.539870 −0.269935 0.962879i \(-0.587002\pi\)
−0.269935 + 0.962879i \(0.587002\pi\)
\(684\) 0 0
\(685\) 812280. 0.0661423
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.96972e6 0.238324
\(690\) 0 0
\(691\) −8.68272e6 −0.691768 −0.345884 0.938277i \(-0.612421\pi\)
−0.345884 + 0.938277i \(0.612421\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −198160. −0.0155616
\(696\) 0 0
\(697\) 1.75244e7 1.36635
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.22777e6 −0.324950 −0.162475 0.986713i \(-0.551948\pi\)
−0.162475 + 0.986713i \(0.551948\pi\)
\(702\) 0 0
\(703\) −2.46842e7 −1.88378
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.21442e6 0.0913732
\(708\) 0 0
\(709\) −9.66791e6 −0.722299 −0.361150 0.932508i \(-0.617616\pi\)
−0.361150 + 0.932508i \(0.617616\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.28768e6 0.610533
\(714\) 0 0
\(715\) 180560. 0.0132086
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.23997e7 −1.61592 −0.807962 0.589235i \(-0.799429\pi\)
−0.807962 + 0.589235i \(0.799429\pi\)
\(720\) 0 0
\(721\) −5.29592e6 −0.379405
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.33749e7 0.945031
\(726\) 0 0
\(727\) −1.06700e7 −0.748735 −0.374368 0.927280i \(-0.622140\pi\)
−0.374368 + 0.927280i \(0.622140\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.09191e7 −2.14009
\(732\) 0 0
\(733\) −1.30456e7 −0.896818 −0.448409 0.893828i \(-0.648009\pi\)
−0.448409 + 0.893828i \(0.648009\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.66696e6 −0.180862
\(738\) 0 0
\(739\) −2.77150e6 −0.186683 −0.0933414 0.995634i \(-0.529755\pi\)
−0.0933414 + 0.995634i \(0.529755\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.37895e7 0.916381 0.458191 0.888854i \(-0.348498\pi\)
0.458191 + 0.888854i \(0.348498\pi\)
\(744\) 0 0
\(745\) 373416. 0.0246492
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.33287e6 0.347341
\(750\) 0 0
\(751\) −1.84892e7 −1.19624 −0.598118 0.801408i \(-0.704085\pi\)
−0.598118 + 0.801408i \(0.704085\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −283488. −0.0180995
\(756\) 0 0
\(757\) 2.05745e7 1.30494 0.652469 0.757816i \(-0.273733\pi\)
0.652469 + 0.757816i \(0.273733\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.75512e7 1.09862 0.549309 0.835620i \(-0.314891\pi\)
0.549309 + 0.835620i \(0.314891\pi\)
\(762\) 0 0
\(763\) 9.92946e6 0.617468
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.71874e6 0.105492
\(768\) 0 0
\(769\) 1.47910e6 0.0901947 0.0450974 0.998983i \(-0.485640\pi\)
0.0450974 + 0.998983i \(0.485640\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.71423e6 −0.584736 −0.292368 0.956306i \(-0.594443\pi\)
−0.292368 + 0.956306i \(0.594443\pi\)
\(774\) 0 0
\(775\) −9.65034e6 −0.577149
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.11569e7 1.24913
\(780\) 0 0
\(781\) 2.00917e7 1.17866
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.49959e6 0.0868558
\(786\) 0 0
\(787\) 1.45994e7 0.840231 0.420115 0.907471i \(-0.361990\pi\)
0.420115 + 0.907471i \(0.361990\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.45970e6 −0.139779
\(792\) 0 0
\(793\) −2.98583e6 −0.168609
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.46095e7 1.37233 0.686163 0.727448i \(-0.259294\pi\)
0.686163 + 0.727448i \(0.259294\pi\)
\(798\) 0 0
\(799\) 3.77563e6 0.209229
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.81159e7 0.991453
\(804\) 0 0
\(805\) 523320. 0.0284628
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.00982e7 1.07966 0.539828 0.841776i \(-0.318489\pi\)
0.539828 + 0.841776i \(0.318489\pi\)
\(810\) 0 0
\(811\) −1.12008e7 −0.597993 −0.298996 0.954254i \(-0.596652\pi\)
−0.298996 + 0.954254i \(0.596652\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 500736. 0.0264067
\(816\) 0 0
\(817\) −3.73280e7 −1.95650
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.38971e7 −1.23733 −0.618667 0.785653i \(-0.712327\pi\)
−0.618667 + 0.785653i \(0.712327\pi\)
\(822\) 0 0
\(823\) 9.17972e6 0.472422 0.236211 0.971702i \(-0.424094\pi\)
0.236211 + 0.971702i \(0.424094\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.82018e7 −1.43388 −0.716939 0.697135i \(-0.754458\pi\)
−0.716939 + 0.697135i \(0.754458\pi\)
\(828\) 0 0
\(829\) −1.81930e7 −0.919429 −0.459714 0.888067i \(-0.652048\pi\)
−0.459714 + 0.888067i \(0.652048\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.42863e6 0.171202
\(834\) 0 0
\(835\) 1.77627e6 0.0881644
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.97349e6 0.145835 0.0729175 0.997338i \(-0.476769\pi\)
0.0729175 + 0.997338i \(0.476769\pi\)
\(840\) 0 0
\(841\) −2.00394e6 −0.0977003
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.42564e6 0.0686858
\(846\) 0 0
\(847\) 1.18340e6 0.0566791
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.82291e7 −1.80955
\(852\) 0 0
\(853\) −1.43801e7 −0.676690 −0.338345 0.941022i \(-0.609867\pi\)
−0.338345 + 0.941022i \(0.609867\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.74223e7 1.27542 0.637708 0.770278i \(-0.279883\pi\)
0.637708 + 0.770278i \(0.279883\pi\)
\(858\) 0 0
\(859\) −2.79786e7 −1.29373 −0.646864 0.762606i \(-0.723920\pi\)
−0.646864 + 0.762606i \(0.723920\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 5.67312e6 0.259295 0.129648 0.991560i \(-0.458615\pi\)
0.129648 + 0.991560i \(0.458615\pi\)
\(864\) 0 0
\(865\) 2.17747e6 0.0989492
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.23328e7 0.554005
\(870\) 0 0
\(871\) 879376. 0.0392762
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.22186e6 −0.0539514
\(876\) 0 0
\(877\) −1.09211e7 −0.479478 −0.239739 0.970837i \(-0.577062\pi\)
−0.239739 + 0.970837i \(0.577062\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.72031e7 1.61488 0.807438 0.589952i \(-0.200854\pi\)
0.807438 + 0.589952i \(0.200854\pi\)
\(882\) 0 0
\(883\) 3.57619e7 1.54355 0.771773 0.635898i \(-0.219370\pi\)
0.771773 + 0.635898i \(0.219370\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.25301e7 0.961510 0.480755 0.876855i \(-0.340363\pi\)
0.480755 + 0.876855i \(0.340363\pi\)
\(888\) 0 0
\(889\) −149548. −0.00634638
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.55826e6 0.191280
\(894\) 0 0
\(895\) −2.46452e6 −0.102843
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.33534e7 −0.551052
\(900\) 0 0
\(901\) 3.47604e7 1.42650
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −393064. −0.0159530
\(906\) 0 0
\(907\) 3.18871e7 1.28705 0.643526 0.765424i \(-0.277471\pi\)
0.643526 + 0.765424i \(0.277471\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.21745e7 −0.885233 −0.442617 0.896711i \(-0.645950\pi\)
−0.442617 + 0.896711i \(0.645950\pi\)
\(912\) 0 0
\(913\) −1.48148e6 −0.0588192
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.07206e7 0.421014
\(918\) 0 0
\(919\) −2.87465e7 −1.12279 −0.561393 0.827549i \(-0.689734\pi\)
−0.561393 + 0.827549i \(0.689734\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −6.62484e6 −0.255960
\(924\) 0 0
\(925\) 4.45147e7 1.71060
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.58792e7 0.983810 0.491905 0.870649i \(-0.336301\pi\)
0.491905 + 0.870649i \(0.336301\pi\)
\(930\) 0 0
\(931\) 4.13932e6 0.156515
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.11344e6 0.0790607
\(936\) 0 0
\(937\) 4.35364e7 1.61996 0.809979 0.586459i \(-0.199478\pi\)
0.809979 + 0.586459i \(0.199478\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.20702e7 −1.54882 −0.774410 0.632684i \(-0.781953\pi\)
−0.774410 + 0.632684i \(0.781953\pi\)
\(942\) 0 0
\(943\) 3.27662e7 1.19991
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −505082. −0.0183015 −0.00915076 0.999958i \(-0.502913\pi\)
−0.00915076 + 0.999958i \(0.502913\pi\)
\(948\) 0 0
\(949\) −5.97336e6 −0.215305
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.18755e7 −0.780234 −0.390117 0.920765i \(-0.627566\pi\)
−0.390117 + 0.920765i \(0.627566\pi\)
\(954\) 0 0
\(955\) −2.06055e6 −0.0731097
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 9.95043e6 0.349378
\(960\) 0 0
\(961\) −1.89943e7 −0.663461
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.79972e6 0.0622138
\(966\) 0 0
\(967\) 2.79738e7 0.962024 0.481012 0.876714i \(-0.340269\pi\)
0.481012 + 0.876714i \(0.340269\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.37517e7 −1.48918 −0.744590 0.667522i \(-0.767355\pi\)
−0.744590 + 0.667522i \(0.767355\pi\)
\(972\) 0 0
\(973\) −2.42746e6 −0.0821997
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.53190e7 1.51895 0.759476 0.650535i \(-0.225455\pi\)
0.759476 + 0.650535i \(0.225455\pi\)
\(978\) 0 0
\(979\) 2.39582e7 0.798911
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.15059e7 −1.37002 −0.685009 0.728534i \(-0.740202\pi\)
−0.685009 + 0.728534i \(0.740202\pi\)
\(984\) 0 0
\(985\) −1.61974e6 −0.0531929
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.78108e7 −1.87940
\(990\) 0 0
\(991\) 3.40757e7 1.10220 0.551101 0.834439i \(-0.314208\pi\)
0.551101 + 0.834439i \(0.314208\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.37030e6 0.0438793
\(996\) 0 0
\(997\) −4.22181e7 −1.34512 −0.672560 0.740042i \(-0.734805\pi\)
−0.672560 + 0.740042i \(0.734805\pi\)
\(998\) 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.d.1.1 1
3.2 odd 2 168.6.a.b.1.1 1
4.3 odd 2 1008.6.a.q.1.1 1
12.11 even 2 336.6.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.b.1.1 1 3.2 odd 2
336.6.a.m.1.1 1 12.11 even 2
504.6.a.d.1.1 1 1.1 even 1 trivial
1008.6.a.q.1.1 1 4.3 odd 2