Properties

Label 1008.6.a.v.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(161.666890371\)
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 \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+38.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+38.0000 q^{5} +49.0000 q^{7} +600.000 q^{11} -674.000 q^{13} -78.0000 q^{17} +916.000 q^{19} -4604.00 q^{23} -1681.00 q^{25} +6810.00 q^{29} -7912.00 q^{31} +1862.00 q^{35} -9274.00 q^{37} +242.000 q^{41} -1116.00 q^{43} -28312.0 q^{47} +2401.00 q^{49} -10230.0 q^{53} +22800.0 q^{55} -4108.00 q^{59} +15878.0 q^{61} -25612.0 q^{65} +67668.0 q^{67} -67492.0 q^{71} +1106.00 q^{73} +29400.0 q^{77} -84152.0 q^{79} -2908.00 q^{83} -2964.00 q^{85} +8322.00 q^{89} -33026.0 q^{91} +34808.0 q^{95} +130810. q^{97} +O(q^{100})\)

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
\(5\) 38.0000 0.679765 0.339882 0.940468i \(-0.389613\pi\)
0.339882 + 0.940468i \(0.389613\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 600.000 1.49510 0.747549 0.664207i \(-0.231231\pi\)
0.747549 + 0.664207i \(0.231231\pi\)
\(12\) 0 0
\(13\) −674.000 −1.10612 −0.553059 0.833142i \(-0.686540\pi\)
−0.553059 + 0.833142i \(0.686540\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −78.0000 −0.0654594 −0.0327297 0.999464i \(-0.510420\pi\)
−0.0327297 + 0.999464i \(0.510420\pi\)
\(18\) 0 0
\(19\) 916.000 0.582119 0.291059 0.956705i \(-0.405992\pi\)
0.291059 + 0.956705i \(0.405992\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4604.00 −1.81475 −0.907373 0.420327i \(-0.861915\pi\)
−0.907373 + 0.420327i \(0.861915\pi\)
\(24\) 0 0
\(25\) −1681.00 −0.537920
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6810.00 1.50367 0.751834 0.659352i \(-0.229169\pi\)
0.751834 + 0.659352i \(0.229169\pi\)
\(30\) 0 0
\(31\) −7912.00 −1.47871 −0.739353 0.673318i \(-0.764869\pi\)
−0.739353 + 0.673318i \(0.764869\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1862.00 0.256927
\(36\) 0 0
\(37\) −9274.00 −1.11369 −0.556843 0.830618i \(-0.687988\pi\)
−0.556843 + 0.830618i \(0.687988\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 242.000 0.0224831 0.0112415 0.999937i \(-0.496422\pi\)
0.0112415 + 0.999937i \(0.496422\pi\)
\(42\) 0 0
\(43\) −1116.00 −0.0920435 −0.0460217 0.998940i \(-0.514654\pi\)
−0.0460217 + 0.998940i \(0.514654\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −28312.0 −1.86950 −0.934751 0.355304i \(-0.884377\pi\)
−0.934751 + 0.355304i \(0.884377\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10230.0 −0.500249 −0.250124 0.968214i \(-0.580472\pi\)
−0.250124 + 0.968214i \(0.580472\pi\)
\(54\) 0 0
\(55\) 22800.0 1.01631
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4108.00 −0.153639 −0.0768193 0.997045i \(-0.524476\pi\)
−0.0768193 + 0.997045i \(0.524476\pi\)
\(60\) 0 0
\(61\) 15878.0 0.546350 0.273175 0.961964i \(-0.411926\pi\)
0.273175 + 0.961964i \(0.411926\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −25612.0 −0.751900
\(66\) 0 0
\(67\) 67668.0 1.84160 0.920802 0.390030i \(-0.127535\pi\)
0.920802 + 0.390030i \(0.127535\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −67492.0 −1.58894 −0.794468 0.607306i \(-0.792250\pi\)
−0.794468 + 0.607306i \(0.792250\pi\)
\(72\) 0 0
\(73\) 1106.00 0.0242911 0.0121456 0.999926i \(-0.496134\pi\)
0.0121456 + 0.999926i \(0.496134\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 29400.0 0.565094
\(78\) 0 0
\(79\) −84152.0 −1.51704 −0.758519 0.651650i \(-0.774077\pi\)
−0.758519 + 0.651650i \(0.774077\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −2908.00 −0.0463339 −0.0231670 0.999732i \(-0.507375\pi\)
−0.0231670 + 0.999732i \(0.507375\pi\)
\(84\) 0 0
\(85\) −2964.00 −0.0444970
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8322.00 0.111366 0.0556830 0.998448i \(-0.482266\pi\)
0.0556830 + 0.998448i \(0.482266\pi\)
\(90\) 0 0
\(91\) −33026.0 −0.418073
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 34808.0 0.395704
\(96\) 0 0
\(97\) 130810. 1.41160 0.705800 0.708411i \(-0.250588\pi\)
0.705800 + 0.708411i \(0.250588\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −159794. −1.55868 −0.779340 0.626601i \(-0.784446\pi\)
−0.779340 + 0.626601i \(0.784446\pi\)
\(102\) 0 0
\(103\) 91440.0 0.849265 0.424632 0.905366i \(-0.360403\pi\)
0.424632 + 0.905366i \(0.360403\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −139480. −1.17775 −0.588874 0.808225i \(-0.700429\pi\)
−0.588874 + 0.808225i \(0.700429\pi\)
\(108\) 0 0
\(109\) 141758. 1.14283 0.571415 0.820662i \(-0.306395\pi\)
0.571415 + 0.820662i \(0.306395\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 81742.0 0.602212 0.301106 0.953591i \(-0.402644\pi\)
0.301106 + 0.953591i \(0.402644\pi\)
\(114\) 0 0
\(115\) −174952. −1.23360
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3822.00 −0.0247413
\(120\) 0 0
\(121\) 198949. 1.23532
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −182628. −1.04542
\(126\) 0 0
\(127\) −90488.0 −0.497831 −0.248915 0.968525i \(-0.580074\pi\)
−0.248915 + 0.968525i \(0.580074\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 187476. 0.954481 0.477241 0.878773i \(-0.341637\pi\)
0.477241 + 0.878773i \(0.341637\pi\)
\(132\) 0 0
\(133\) 44884.0 0.220020
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −168482. −0.766924 −0.383462 0.923557i \(-0.625268\pi\)
−0.383462 + 0.923557i \(0.625268\pi\)
\(138\) 0 0
\(139\) −668.000 −0.00293251 −0.00146625 0.999999i \(-0.500467\pi\)
−0.00146625 + 0.999999i \(0.500467\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −404400. −1.65375
\(144\) 0 0
\(145\) 258780. 1.02214
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 300618. 1.10930 0.554650 0.832084i \(-0.312852\pi\)
0.554650 + 0.832084i \(0.312852\pi\)
\(150\) 0 0
\(151\) −359032. −1.28142 −0.640709 0.767784i \(-0.721359\pi\)
−0.640709 + 0.767784i \(0.721359\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −300656. −1.00517
\(156\) 0 0
\(157\) 110822. 0.358820 0.179410 0.983774i \(-0.442581\pi\)
0.179410 + 0.983774i \(0.442581\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −225596. −0.685909
\(162\) 0 0
\(163\) −372380. −1.09779 −0.548893 0.835893i \(-0.684950\pi\)
−0.548893 + 0.835893i \(0.684950\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −109600. −0.304102 −0.152051 0.988373i \(-0.548588\pi\)
−0.152051 + 0.988373i \(0.548588\pi\)
\(168\) 0 0
\(169\) 82983.0 0.223497
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 388598. 0.987155 0.493577 0.869702i \(-0.335689\pi\)
0.493577 + 0.869702i \(0.335689\pi\)
\(174\) 0 0
\(175\) −82369.0 −0.203315
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −241656. −0.563722 −0.281861 0.959455i \(-0.590952\pi\)
−0.281861 + 0.959455i \(0.590952\pi\)
\(180\) 0 0
\(181\) 190854. 0.433017 0.216508 0.976281i \(-0.430533\pi\)
0.216508 + 0.976281i \(0.430533\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −352412. −0.757044
\(186\) 0 0
\(187\) −46800.0 −0.0978683
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 253300. 0.502402 0.251201 0.967935i \(-0.419174\pi\)
0.251201 + 0.967935i \(0.419174\pi\)
\(192\) 0 0
\(193\) −712302. −1.37648 −0.688242 0.725482i \(-0.741617\pi\)
−0.688242 + 0.725482i \(0.741617\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 107194. 0.196791 0.0983954 0.995147i \(-0.468629\pi\)
0.0983954 + 0.995147i \(0.468629\pi\)
\(198\) 0 0
\(199\) 956952. 1.71300 0.856500 0.516147i \(-0.172634\pi\)
0.856500 + 0.516147i \(0.172634\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 333690. 0.568333
\(204\) 0 0
\(205\) 9196.00 0.0152832
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 549600. 0.870324
\(210\) 0 0
\(211\) 320700. 0.495899 0.247949 0.968773i \(-0.420243\pi\)
0.247949 + 0.968773i \(0.420243\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −42408.0 −0.0625679
\(216\) 0 0
\(217\) −387688. −0.558899
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 52572.0 0.0724059
\(222\) 0 0
\(223\) −1.06840e6 −1.43870 −0.719352 0.694645i \(-0.755561\pi\)
−0.719352 + 0.694645i \(0.755561\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −806820. −1.03923 −0.519615 0.854400i \(-0.673925\pi\)
−0.519615 + 0.854400i \(0.673925\pi\)
\(228\) 0 0
\(229\) 1.21661e6 1.53308 0.766539 0.642198i \(-0.221977\pi\)
0.766539 + 0.642198i \(0.221977\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −214722. −0.259112 −0.129556 0.991572i \(-0.541355\pi\)
−0.129556 + 0.991572i \(0.541355\pi\)
\(234\) 0 0
\(235\) −1.07586e6 −1.27082
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −615780. −0.697318 −0.348659 0.937250i \(-0.613363\pi\)
−0.348659 + 0.937250i \(0.613363\pi\)
\(240\) 0 0
\(241\) −995590. −1.10418 −0.552088 0.833786i \(-0.686169\pi\)
−0.552088 + 0.833786i \(0.686169\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 91238.0 0.0971092
\(246\) 0 0
\(247\) −617384. −0.643892
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −169340. −0.169658 −0.0848292 0.996396i \(-0.527034\pi\)
−0.0848292 + 0.996396i \(0.527034\pi\)
\(252\) 0 0
\(253\) −2.76240e6 −2.71322
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.67825e6 −1.58498 −0.792488 0.609887i \(-0.791215\pi\)
−0.792488 + 0.609887i \(0.791215\pi\)
\(258\) 0 0
\(259\) −454426. −0.420934
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.77507e6 −1.58243 −0.791217 0.611535i \(-0.790552\pi\)
−0.791217 + 0.611535i \(0.790552\pi\)
\(264\) 0 0
\(265\) −388740. −0.340051
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15646.0 0.0131833 0.00659163 0.999978i \(-0.497902\pi\)
0.00659163 + 0.999978i \(0.497902\pi\)
\(270\) 0 0
\(271\) 635672. 0.525787 0.262894 0.964825i \(-0.415323\pi\)
0.262894 + 0.964825i \(0.415323\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00860e6 −0.804243
\(276\) 0 0
\(277\) −92218.0 −0.0722131 −0.0361066 0.999348i \(-0.511496\pi\)
−0.0361066 + 0.999348i \(0.511496\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.15678e6 0.873948 0.436974 0.899474i \(-0.356050\pi\)
0.436974 + 0.899474i \(0.356050\pi\)
\(282\) 0 0
\(283\) −1.97380e6 −1.46500 −0.732498 0.680770i \(-0.761645\pi\)
−0.732498 + 0.680770i \(0.761645\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11858.0 0.00849780
\(288\) 0 0
\(289\) −1.41377e6 −0.995715
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 113966. 0.0775544 0.0387772 0.999248i \(-0.487654\pi\)
0.0387772 + 0.999248i \(0.487654\pi\)
\(294\) 0 0
\(295\) −156104. −0.104438
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.10310e6 2.00732
\(300\) 0 0
\(301\) −54684.0 −0.0347892
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 603364. 0.371390
\(306\) 0 0
\(307\) −2.18500e6 −1.32314 −0.661571 0.749883i \(-0.730110\pi\)
−0.661571 + 0.749883i \(0.730110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −365520. −0.214294 −0.107147 0.994243i \(-0.534172\pi\)
−0.107147 + 0.994243i \(0.534172\pi\)
\(312\) 0 0
\(313\) 1.24550e6 0.718592 0.359296 0.933224i \(-0.383017\pi\)
0.359296 + 0.933224i \(0.383017\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.79646e6 −1.00408 −0.502042 0.864843i \(-0.667418\pi\)
−0.502042 + 0.864843i \(0.667418\pi\)
\(318\) 0 0
\(319\) 4.08600e6 2.24813
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −71448.0 −0.0381052
\(324\) 0 0
\(325\) 1.13299e6 0.595003
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.38729e6 −0.706605
\(330\) 0 0
\(331\) −1.55840e6 −0.781822 −0.390911 0.920428i \(-0.627840\pi\)
−0.390911 + 0.920428i \(0.627840\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.57138e6 1.25186
\(336\) 0 0
\(337\) −1.33472e6 −0.640199 −0.320099 0.947384i \(-0.603716\pi\)
−0.320099 + 0.947384i \(0.603716\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.74720e6 −2.21081
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.56086e6 1.58757 0.793783 0.608201i \(-0.208109\pi\)
0.793783 + 0.608201i \(0.208109\pi\)
\(348\) 0 0
\(349\) −1.60451e6 −0.705144 −0.352572 0.935785i \(-0.614693\pi\)
−0.352572 + 0.935785i \(0.614693\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 384290. 0.164143 0.0820715 0.996626i \(-0.473846\pi\)
0.0820715 + 0.996626i \(0.473846\pi\)
\(354\) 0 0
\(355\) −2.56470e6 −1.08010
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −500532. −0.204973 −0.102486 0.994734i \(-0.532680\pi\)
−0.102486 + 0.994734i \(0.532680\pi\)
\(360\) 0 0
\(361\) −1.63704e6 −0.661138
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 42028.0 0.0165123
\(366\) 0 0
\(367\) 4.13210e6 1.60142 0.800710 0.599052i \(-0.204456\pi\)
0.800710 + 0.599052i \(0.204456\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −501270. −0.189076
\(372\) 0 0
\(373\) 3.41287e6 1.27013 0.635064 0.772459i \(-0.280974\pi\)
0.635064 + 0.772459i \(0.280974\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.58994e6 −1.66324
\(378\) 0 0
\(379\) 3.16959e6 1.13346 0.566728 0.823905i \(-0.308209\pi\)
0.566728 + 0.823905i \(0.308209\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.07848e6 −1.76904 −0.884518 0.466506i \(-0.845513\pi\)
−0.884518 + 0.466506i \(0.845513\pi\)
\(384\) 0 0
\(385\) 1.11720e6 0.384131
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.57224e6 −0.526798 −0.263399 0.964687i \(-0.584844\pi\)
−0.263399 + 0.964687i \(0.584844\pi\)
\(390\) 0 0
\(391\) 359112. 0.118792
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.19778e6 −1.03123
\(396\) 0 0
\(397\) −3.00804e6 −0.957872 −0.478936 0.877850i \(-0.658977\pi\)
−0.478936 + 0.877850i \(0.658977\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 54406.0 0.0168961 0.00844804 0.999964i \(-0.497311\pi\)
0.00844804 + 0.999964i \(0.497311\pi\)
\(402\) 0 0
\(403\) 5.33269e6 1.63562
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.56440e6 −1.66507
\(408\) 0 0
\(409\) −2.07030e6 −0.611963 −0.305982 0.952037i \(-0.598985\pi\)
−0.305982 + 0.952037i \(0.598985\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −201292. −0.0580699
\(414\) 0 0
\(415\) −110504. −0.0314962
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.48062e6 0.412011 0.206005 0.978551i \(-0.433954\pi\)
0.206005 + 0.978551i \(0.433954\pi\)
\(420\) 0 0
\(421\) −2.22283e6 −0.611224 −0.305612 0.952156i \(-0.598861\pi\)
−0.305612 + 0.952156i \(0.598861\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 131118. 0.0352119
\(426\) 0 0
\(427\) 778022. 0.206501
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.96259e6 −0.508904 −0.254452 0.967085i \(-0.581895\pi\)
−0.254452 + 0.967085i \(0.581895\pi\)
\(432\) 0 0
\(433\) 1.92503e6 0.493420 0.246710 0.969089i \(-0.420650\pi\)
0.246710 + 0.969089i \(0.420650\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.21726e6 −1.05640
\(438\) 0 0
\(439\) −1.68838e6 −0.418127 −0.209063 0.977902i \(-0.567041\pi\)
−0.209063 + 0.977902i \(0.567041\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.37277e6 1.78493 0.892465 0.451116i \(-0.148974\pi\)
0.892465 + 0.451116i \(0.148974\pi\)
\(444\) 0 0
\(445\) 316236. 0.0757027
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.61309e6 1.07988 0.539940 0.841703i \(-0.318447\pi\)
0.539940 + 0.841703i \(0.318447\pi\)
\(450\) 0 0
\(451\) 145200. 0.0336144
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.25499e6 −0.284191
\(456\) 0 0
\(457\) −5.75663e6 −1.28937 −0.644685 0.764448i \(-0.723012\pi\)
−0.644685 + 0.764448i \(0.723012\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.67782e6 −1.24431 −0.622156 0.782893i \(-0.713743\pi\)
−0.622156 + 0.782893i \(0.713743\pi\)
\(462\) 0 0
\(463\) 8.06452e6 1.74834 0.874170 0.485619i \(-0.161406\pi\)
0.874170 + 0.485619i \(0.161406\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.92248e6 −1.46882 −0.734412 0.678704i \(-0.762542\pi\)
−0.734412 + 0.678704i \(0.762542\pi\)
\(468\) 0 0
\(469\) 3.31573e6 0.696061
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −669600. −0.137614
\(474\) 0 0
\(475\) −1.53980e6 −0.313133
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.33297e6 −1.65944 −0.829719 0.558182i \(-0.811499\pi\)
−0.829719 + 0.558182i \(0.811499\pi\)
\(480\) 0 0
\(481\) 6.25068e6 1.23187
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.97078e6 0.959556
\(486\) 0 0
\(487\) −496792. −0.0949188 −0.0474594 0.998873i \(-0.515112\pi\)
−0.0474594 + 0.998873i \(0.515112\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −760704. −0.142401 −0.0712003 0.997462i \(-0.522683\pi\)
−0.0712003 + 0.997462i \(0.522683\pi\)
\(492\) 0 0
\(493\) −531180. −0.0984293
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.30711e6 −0.600561
\(498\) 0 0
\(499\) −2.19192e6 −0.394071 −0.197035 0.980396i \(-0.563131\pi\)
−0.197035 + 0.980396i \(0.563131\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −790680. −0.139342 −0.0696708 0.997570i \(-0.522195\pi\)
−0.0696708 + 0.997570i \(0.522195\pi\)
\(504\) 0 0
\(505\) −6.07217e6 −1.05954
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.75272e6 −0.470943 −0.235471 0.971881i \(-0.575663\pi\)
−0.235471 + 0.971881i \(0.575663\pi\)
\(510\) 0 0
\(511\) 54194.0 0.00918119
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.47472e6 0.577300
\(516\) 0 0
\(517\) −1.69872e7 −2.79509
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.27911e6 1.01345 0.506727 0.862107i \(-0.330855\pi\)
0.506727 + 0.862107i \(0.330855\pi\)
\(522\) 0 0
\(523\) 5.60610e6 0.896203 0.448102 0.893983i \(-0.352100\pi\)
0.448102 + 0.893983i \(0.352100\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 617136. 0.0967953
\(528\) 0 0
\(529\) 1.47605e7 2.29330
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −163108. −0.0248689
\(534\) 0 0
\(535\) −5.30024e6 −0.800592
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.44060e6 0.213585
\(540\) 0 0
\(541\) 3.31128e6 0.486410 0.243205 0.969975i \(-0.421801\pi\)
0.243205 + 0.969975i \(0.421801\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.38680e6 0.776855
\(546\) 0 0
\(547\) −5.66566e6 −0.809622 −0.404811 0.914400i \(-0.632663\pi\)
−0.404811 + 0.914400i \(0.632663\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.23796e6 0.875313
\(552\) 0 0
\(553\) −4.12345e6 −0.573387
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.36880e6 0.869801 0.434900 0.900479i \(-0.356784\pi\)
0.434900 + 0.900479i \(0.356784\pi\)
\(558\) 0 0
\(559\) 752184. 0.101811
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 181404. 0.0241199 0.0120600 0.999927i \(-0.496161\pi\)
0.0120600 + 0.999927i \(0.496161\pi\)
\(564\) 0 0
\(565\) 3.10620e6 0.409362
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.02851e6 0.651116 0.325558 0.945522i \(-0.394448\pi\)
0.325558 + 0.945522i \(0.394448\pi\)
\(570\) 0 0
\(571\) 7.57430e6 0.972192 0.486096 0.873905i \(-0.338420\pi\)
0.486096 + 0.873905i \(0.338420\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7.73932e6 0.976188
\(576\) 0 0
\(577\) 1.52011e7 1.90080 0.950400 0.311029i \(-0.100674\pi\)
0.950400 + 0.311029i \(0.100674\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −142492. −0.0175126
\(582\) 0 0
\(583\) −6.13800e6 −0.747921
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.64015e6 0.555823 0.277912 0.960607i \(-0.410358\pi\)
0.277912 + 0.960607i \(0.410358\pi\)
\(588\) 0 0
\(589\) −7.24739e6 −0.860783
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.18658e6 0.488903 0.244451 0.969662i \(-0.421392\pi\)
0.244451 + 0.969662i \(0.421392\pi\)
\(594\) 0 0
\(595\) −145236. −0.0168183
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.02901e7 −1.17180 −0.585898 0.810385i \(-0.699258\pi\)
−0.585898 + 0.810385i \(0.699258\pi\)
\(600\) 0 0
\(601\) 1.43512e7 1.62070 0.810349 0.585947i \(-0.199277\pi\)
0.810349 + 0.585947i \(0.199277\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.56006e6 0.839725
\(606\) 0 0
\(607\) −1.09870e7 −1.21034 −0.605169 0.796097i \(-0.706894\pi\)
−0.605169 + 0.796097i \(0.706894\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.90823e7 2.06789
\(612\) 0 0
\(613\) 3.00637e6 0.323141 0.161570 0.986861i \(-0.448344\pi\)
0.161570 + 0.986861i \(0.448344\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.82040e7 −1.92510 −0.962550 0.271105i \(-0.912611\pi\)
−0.962550 + 0.271105i \(0.912611\pi\)
\(618\) 0 0
\(619\) −6.45803e6 −0.677444 −0.338722 0.940887i \(-0.609995\pi\)
−0.338722 + 0.940887i \(0.609995\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 407778. 0.0420924
\(624\) 0 0
\(625\) −1.68674e6 −0.172722
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 723372. 0.0729013
\(630\) 0 0
\(631\) −3.59598e6 −0.359538 −0.179769 0.983709i \(-0.557535\pi\)
−0.179769 + 0.983709i \(0.557535\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.43854e6 −0.338408
\(636\) 0 0
\(637\) −1.61827e6 −0.158017
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.54433e6 −0.629101 −0.314550 0.949241i \(-0.601854\pi\)
−0.314550 + 0.949241i \(0.601854\pi\)
\(642\) 0 0
\(643\) −1.48417e7 −1.41565 −0.707827 0.706386i \(-0.750324\pi\)
−0.707827 + 0.706386i \(0.750324\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.34043e6 0.407636 0.203818 0.979009i \(-0.434665\pi\)
0.203818 + 0.979009i \(0.434665\pi\)
\(648\) 0 0
\(649\) −2.46480e6 −0.229705
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.31207e6 −0.487507 −0.243753 0.969837i \(-0.578379\pi\)
−0.243753 + 0.969837i \(0.578379\pi\)
\(654\) 0 0
\(655\) 7.12409e6 0.648823
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.78371e6 −0.249696 −0.124848 0.992176i \(-0.539844\pi\)
−0.124848 + 0.992176i \(0.539844\pi\)
\(660\) 0 0
\(661\) 2.01522e7 1.79398 0.896992 0.442047i \(-0.145747\pi\)
0.896992 + 0.442047i \(0.145747\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.70559e6 0.149562
\(666\) 0 0
\(667\) −3.13532e7 −2.72878
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.52680e6 0.816847
\(672\) 0 0
\(673\) −1.26277e7 −1.07470 −0.537349 0.843360i \(-0.680574\pi\)
−0.537349 + 0.843360i \(0.680574\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.94541e6 0.582406 0.291203 0.956661i \(-0.405944\pi\)
0.291203 + 0.956661i \(0.405944\pi\)
\(678\) 0 0
\(679\) 6.40969e6 0.533535
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −278144. −0.0228149 −0.0114074 0.999935i \(-0.503631\pi\)
−0.0114074 + 0.999935i \(0.503631\pi\)
\(684\) 0 0
\(685\) −6.40232e6 −0.521328
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.89502e6 0.553334
\(690\) 0 0
\(691\) 6.38656e6 0.508829 0.254414 0.967095i \(-0.418117\pi\)
0.254414 + 0.967095i \(0.418117\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25384.0 −0.00199342
\(696\) 0 0
\(697\) −18876.0 −0.00147173
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.26602e7 0.973075 0.486537 0.873660i \(-0.338260\pi\)
0.486537 + 0.873660i \(0.338260\pi\)
\(702\) 0 0
\(703\) −8.49498e6 −0.648297
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.82991e6 −0.589126
\(708\) 0 0
\(709\) −1.29990e7 −0.971169 −0.485585 0.874190i \(-0.661393\pi\)
−0.485585 + 0.874190i \(0.661393\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.64268e7 2.68348
\(714\) 0 0
\(715\) −1.53672e7 −1.12416
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.27912e6 0.0922761 0.0461380 0.998935i \(-0.485309\pi\)
0.0461380 + 0.998935i \(0.485309\pi\)
\(720\) 0 0
\(721\) 4.48056e6 0.320992
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.14476e7 −0.808853
\(726\) 0 0
\(727\) 2.01247e7 1.41219 0.706097 0.708115i \(-0.250454\pi\)
0.706097 + 0.708115i \(0.250454\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 87048.0 0.00602512
\(732\) 0 0
\(733\) 2.59171e7 1.78167 0.890835 0.454328i \(-0.150121\pi\)
0.890835 + 0.454328i \(0.150121\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.06008e7 2.75338
\(738\) 0 0
\(739\) −2.57638e6 −0.173540 −0.0867698 0.996228i \(-0.527654\pi\)
−0.0867698 + 0.996228i \(0.527654\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.36046e7 1.56865 0.784323 0.620353i \(-0.213010\pi\)
0.784323 + 0.620353i \(0.213010\pi\)
\(744\) 0 0
\(745\) 1.14235e7 0.754063
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.83452e6 −0.445147
\(750\) 0 0
\(751\) 9.32237e6 0.603151 0.301576 0.953442i \(-0.402487\pi\)
0.301576 + 0.953442i \(0.402487\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.36432e7 −0.871063
\(756\) 0 0
\(757\) 1.90696e7 1.20949 0.604744 0.796420i \(-0.293276\pi\)
0.604744 + 0.796420i \(0.293276\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.87530e6 0.430358 0.215179 0.976575i \(-0.430967\pi\)
0.215179 + 0.976575i \(0.430967\pi\)
\(762\) 0 0
\(763\) 6.94614e6 0.431949
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.76879e6 0.169942
\(768\) 0 0
\(769\) 1.90337e7 1.16067 0.580334 0.814379i \(-0.302922\pi\)
0.580334 + 0.814379i \(0.302922\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.64278e7 −0.988851 −0.494426 0.869220i \(-0.664622\pi\)
−0.494426 + 0.869220i \(0.664622\pi\)
\(774\) 0 0
\(775\) 1.33001e7 0.795426
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 221672. 0.0130878
\(780\) 0 0
\(781\) −4.04952e7 −2.37561
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.21124e6 0.243913
\(786\) 0 0
\(787\) 4.19153e6 0.241233 0.120616 0.992699i \(-0.461513\pi\)
0.120616 + 0.992699i \(0.461513\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.00536e6 0.227615
\(792\) 0 0
\(793\) −1.07018e7 −0.604328
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.28046e7 0.714035 0.357018 0.934098i \(-0.383794\pi\)
0.357018 + 0.934098i \(0.383794\pi\)
\(798\) 0 0
\(799\) 2.20834e6 0.122377
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 663600. 0.0363176
\(804\) 0 0
\(805\) −8.57265e6 −0.466257
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.33669e7 0.718057 0.359029 0.933327i \(-0.383108\pi\)
0.359029 + 0.933327i \(0.383108\pi\)
\(810\) 0 0
\(811\) 3.51226e7 1.87514 0.937571 0.347794i \(-0.113069\pi\)
0.937571 + 0.347794i \(0.113069\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.41504e7 −0.746236
\(816\) 0 0
\(817\) −1.02226e6 −0.0535802
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.66290e7 1.37878 0.689392 0.724389i \(-0.257878\pi\)
0.689392 + 0.724389i \(0.257878\pi\)
\(822\) 0 0
\(823\) 1.11835e7 0.575545 0.287773 0.957699i \(-0.407085\pi\)
0.287773 + 0.957699i \(0.407085\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.56108e6 −0.130215 −0.0651073 0.997878i \(-0.520739\pi\)
−0.0651073 + 0.997878i \(0.520739\pi\)
\(828\) 0 0
\(829\) 2.27188e7 1.14815 0.574076 0.818802i \(-0.305362\pi\)
0.574076 + 0.818802i \(0.305362\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −187278. −0.00935135
\(834\) 0 0
\(835\) −4.16480e6 −0.206718
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.94627e7 1.93545 0.967725 0.252007i \(-0.0810907\pi\)
0.967725 + 0.252007i \(0.0810907\pi\)
\(840\) 0 0
\(841\) 2.58650e7 1.26102
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.15335e6 0.151926
\(846\) 0 0
\(847\) 9.74850e6 0.466906
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.26975e7 2.02106
\(852\) 0 0
\(853\) −2.87657e7 −1.35364 −0.676818 0.736150i \(-0.736642\pi\)
−0.676818 + 0.736150i \(0.736642\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.40799e7 0.654860 0.327430 0.944875i \(-0.393817\pi\)
0.327430 + 0.944875i \(0.393817\pi\)
\(858\) 0 0
\(859\) 3.10876e7 1.43749 0.718744 0.695275i \(-0.244718\pi\)
0.718744 + 0.695275i \(0.244718\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.66226e6 −0.441623 −0.220812 0.975316i \(-0.570871\pi\)
−0.220812 + 0.975316i \(0.570871\pi\)
\(864\) 0 0
\(865\) 1.47667e7 0.671033
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.04912e7 −2.26812
\(870\) 0 0
\(871\) −4.56082e7 −2.03703
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.94877e6 −0.395133
\(876\) 0 0
\(877\) −1.98937e7 −0.873409 −0.436704 0.899605i \(-0.643854\pi\)
−0.436704 + 0.899605i \(0.643854\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.03248e6 0.0882240 0.0441120 0.999027i \(-0.485954\pi\)
0.0441120 + 0.999027i \(0.485954\pi\)
\(882\) 0 0
\(883\) 3.69655e7 1.59549 0.797747 0.602993i \(-0.206025\pi\)
0.797747 + 0.602993i \(0.206025\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.75837e7 −1.17718 −0.588591 0.808431i \(-0.700317\pi\)
−0.588591 + 0.808431i \(0.700317\pi\)
\(888\) 0 0
\(889\) −4.43391e6 −0.188162
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.59338e7 −1.08827
\(894\) 0 0
\(895\) −9.18293e6 −0.383198
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.38807e7 −2.22348
\(900\) 0 0
\(901\) 797940. 0.0327460
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.25245e6 0.294350
\(906\) 0 0
\(907\) 1.73426e7 0.699997 0.349998 0.936750i \(-0.386182\pi\)
0.349998 + 0.936750i \(0.386182\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.98913e7 1.59251 0.796255 0.604961i \(-0.206811\pi\)
0.796255 + 0.604961i \(0.206811\pi\)
\(912\) 0 0
\(913\) −1.74480e6 −0.0692738
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 9.18632e6 0.360760
\(918\) 0 0
\(919\) −4.01774e7 −1.56925 −0.784626 0.619970i \(-0.787145\pi\)
−0.784626 + 0.619970i \(0.787145\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.54896e7 1.75755
\(924\) 0 0
\(925\) 1.55896e7 0.599074
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.03389e7 −1.15335 −0.576675 0.816974i \(-0.695650\pi\)
−0.576675 + 0.816974i \(0.695650\pi\)
\(930\) 0 0
\(931\) 2.19932e6 0.0831598
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.77840e6 −0.0665274
\(936\) 0 0
\(937\) −4.32143e7 −1.60797 −0.803986 0.594648i \(-0.797291\pi\)
−0.803986 + 0.594648i \(0.797291\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.39045e7 −1.61635 −0.808174 0.588944i \(-0.799544\pi\)
−0.808174 + 0.588944i \(0.799544\pi\)
\(942\) 0 0
\(943\) −1.11417e6 −0.0408011
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.80030e7 −1.73937 −0.869687 0.493603i \(-0.835680\pi\)
−0.869687 + 0.493603i \(0.835680\pi\)
\(948\) 0 0
\(949\) −745444. −0.0268689
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.26010e6 0.0806113 0.0403056 0.999187i \(-0.487167\pi\)
0.0403056 + 0.999187i \(0.487167\pi\)
\(954\) 0 0
\(955\) 9.62540e6 0.341515
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.25562e6 −0.289870
\(960\) 0 0
\(961\) 3.39706e7 1.18657
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.70675e7 −0.935685
\(966\) 0 0
\(967\) −2.43715e6 −0.0838140 −0.0419070 0.999122i \(-0.513343\pi\)
−0.0419070 + 0.999122i \(0.513343\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.15303e7 −1.41357 −0.706784 0.707429i \(-0.749855\pi\)
−0.706784 + 0.707429i \(0.749855\pi\)
\(972\) 0 0
\(973\) −32732.0 −0.00110838
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.59151e6 −0.120376 −0.0601882 0.998187i \(-0.519170\pi\)
−0.0601882 + 0.998187i \(0.519170\pi\)
\(978\) 0 0
\(979\) 4.99320e6 0.166503
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.84268e7 1.26838 0.634191 0.773176i \(-0.281333\pi\)
0.634191 + 0.773176i \(0.281333\pi\)
\(984\) 0 0
\(985\) 4.07337e6 0.133771
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.13806e6 0.167035
\(990\) 0 0
\(991\) −7.96056e6 −0.257489 −0.128745 0.991678i \(-0.541095\pi\)
−0.128745 + 0.991678i \(0.541095\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.63642e7 1.16444
\(996\) 0 0
\(997\) 2.67858e7 0.853427 0.426713 0.904387i \(-0.359671\pi\)
0.426713 + 0.904387i \(0.359671\pi\)
\(998\) 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 1008.6.a.v.1.1 1
3.2 odd 2 336.6.a.d.1.1 1
4.3 odd 2 504.6.a.g.1.1 1
12.11 even 2 168.6.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.e.1.1 1 12.11 even 2
336.6.a.d.1.1 1 3.2 odd 2
504.6.a.g.1.1 1 4.3 odd 2
1008.6.a.v.1.1 1 1.1 even 1 trivial