Properties

Label 1008.4.a.g.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.00000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-6.00000 q^{5} -7.00000 q^{7} +30.0000 q^{11} +2.00000 q^{13} -66.0000 q^{17} +52.0000 q^{19} +114.000 q^{23} -89.0000 q^{25} -72.0000 q^{29} +196.000 q^{31} +42.0000 q^{35} -286.000 q^{37} +378.000 q^{41} -164.000 q^{43} -228.000 q^{47} +49.0000 q^{49} +348.000 q^{53} -180.000 q^{55} -348.000 q^{59} -106.000 q^{61} -12.0000 q^{65} -596.000 q^{67} +630.000 q^{71} -1042.00 q^{73} -210.000 q^{77} +88.0000 q^{79} -1440.00 q^{83} +396.000 q^{85} -1374.00 q^{89} -14.0000 q^{91} -312.000 q^{95} -34.0000 q^{97} +O(q^{100})\)

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
\(5\) −6.00000 −0.536656 −0.268328 0.963328i \(-0.586471\pi\)
−0.268328 + 0.963328i \(0.586471\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 30.0000 0.822304 0.411152 0.911567i \(-0.365127\pi\)
0.411152 + 0.911567i \(0.365127\pi\)
\(12\) 0 0
\(13\) 2.00000 0.0426692 0.0213346 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −66.0000 −0.941609 −0.470804 0.882238i \(-0.656036\pi\)
−0.470804 + 0.882238i \(0.656036\pi\)
\(18\) 0 0
\(19\) 52.0000 0.627875 0.313937 0.949444i \(-0.398352\pi\)
0.313937 + 0.949444i \(0.398352\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 114.000 1.03351 0.516753 0.856134i \(-0.327141\pi\)
0.516753 + 0.856134i \(0.327141\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −72.0000 −0.461037 −0.230518 0.973068i \(-0.574042\pi\)
−0.230518 + 0.973068i \(0.574042\pi\)
\(30\) 0 0
\(31\) 196.000 1.13557 0.567785 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 42.0000 0.202837
\(36\) 0 0
\(37\) −286.000 −1.27076 −0.635380 0.772200i \(-0.719156\pi\)
−0.635380 + 0.772200i \(0.719156\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 378.000 1.43985 0.719923 0.694054i \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −228.000 −0.707600 −0.353800 0.935321i \(-0.615111\pi\)
−0.353800 + 0.935321i \(0.615111\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 348.000 0.901915 0.450957 0.892546i \(-0.351083\pi\)
0.450957 + 0.892546i \(0.351083\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −348.000 −0.767894 −0.383947 0.923355i \(-0.625435\pi\)
−0.383947 + 0.923355i \(0.625435\pi\)
\(60\) 0 0
\(61\) −106.000 −0.222490 −0.111245 0.993793i \(-0.535484\pi\)
−0.111245 + 0.993793i \(0.535484\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.0000 −0.0228987
\(66\) 0 0
\(67\) −596.000 −1.08676 −0.543381 0.839487i \(-0.682856\pi\)
−0.543381 + 0.839487i \(0.682856\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 630.000 1.05306 0.526530 0.850157i \(-0.323493\pi\)
0.526530 + 0.850157i \(0.323493\pi\)
\(72\) 0 0
\(73\) −1042.00 −1.67064 −0.835321 0.549762i \(-0.814718\pi\)
−0.835321 + 0.549762i \(0.814718\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −210.000 −0.310802
\(78\) 0 0
\(79\) 88.0000 0.125326 0.0626631 0.998035i \(-0.480041\pi\)
0.0626631 + 0.998035i \(0.480041\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1440.00 −1.90434 −0.952172 0.305563i \(-0.901155\pi\)
−0.952172 + 0.305563i \(0.901155\pi\)
\(84\) 0 0
\(85\) 396.000 0.505320
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1374.00 −1.63645 −0.818223 0.574901i \(-0.805041\pi\)
−0.818223 + 0.574901i \(0.805041\pi\)
\(90\) 0 0
\(91\) −14.0000 −0.0161275
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −312.000 −0.336953
\(96\) 0 0
\(97\) −34.0000 −0.0355895 −0.0177947 0.999842i \(-0.505665\pi\)
−0.0177947 + 0.999842i \(0.505665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 438.000 0.431511 0.215756 0.976447i \(-0.430779\pi\)
0.215756 + 0.976447i \(0.430779\pi\)
\(102\) 0 0
\(103\) −1676.00 −1.60331 −0.801656 0.597785i \(-0.796048\pi\)
−0.801656 + 0.597785i \(0.796048\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2022.00 1.82686 0.913430 0.406995i \(-0.133423\pi\)
0.913430 + 0.406995i \(0.133423\pi\)
\(108\) 0 0
\(109\) −502.000 −0.441127 −0.220564 0.975373i \(-0.570790\pi\)
−0.220564 + 0.975373i \(0.570790\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2016.00 −1.67831 −0.839156 0.543890i \(-0.816951\pi\)
−0.839156 + 0.543890i \(0.816951\pi\)
\(114\) 0 0
\(115\) −684.000 −0.554638
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 462.000 0.355895
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1284.00 0.918756
\(126\) 0 0
\(127\) −1784.00 −1.24649 −0.623246 0.782026i \(-0.714186\pi\)
−0.623246 + 0.782026i \(0.714186\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1608.00 1.07246 0.536228 0.844073i \(-0.319849\pi\)
0.536228 + 0.844073i \(0.319849\pi\)
\(132\) 0 0
\(133\) −364.000 −0.237314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2580.00 1.60894 0.804468 0.593996i \(-0.202450\pi\)
0.804468 + 0.593996i \(0.202450\pi\)
\(138\) 0 0
\(139\) −2144.00 −1.30829 −0.654143 0.756371i \(-0.726970\pi\)
−0.654143 + 0.756371i \(0.726970\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 60.0000 0.0350871
\(144\) 0 0
\(145\) 432.000 0.247418
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1500.00 −0.824730 −0.412365 0.911019i \(-0.635297\pi\)
−0.412365 + 0.911019i \(0.635297\pi\)
\(150\) 0 0
\(151\) 1240.00 0.668277 0.334138 0.942524i \(-0.391555\pi\)
0.334138 + 0.942524i \(0.391555\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1176.00 −0.609410
\(156\) 0 0
\(157\) 614.000 0.312118 0.156059 0.987748i \(-0.450121\pi\)
0.156059 + 0.987748i \(0.450121\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −798.000 −0.390629
\(162\) 0 0
\(163\) −92.0000 −0.0442086 −0.0221043 0.999756i \(-0.507037\pi\)
−0.0221043 + 0.999756i \(0.507037\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3924.00 −1.81825 −0.909126 0.416520i \(-0.863250\pi\)
−0.909126 + 0.416520i \(0.863250\pi\)
\(168\) 0 0
\(169\) −2193.00 −0.998179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1902.00 0.835875 0.417938 0.908476i \(-0.362753\pi\)
0.417938 + 0.908476i \(0.362753\pi\)
\(174\) 0 0
\(175\) 623.000 0.269111
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.00000 −0.00250537 −0.00125268 0.999999i \(-0.500399\pi\)
−0.00125268 + 0.999999i \(0.500399\pi\)
\(180\) 0 0
\(181\) −2878.00 −1.18188 −0.590939 0.806716i \(-0.701243\pi\)
−0.590939 + 0.806716i \(0.701243\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1716.00 0.681961
\(186\) 0 0
\(187\) −1980.00 −0.774288
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −354.000 −0.134108 −0.0670538 0.997749i \(-0.521360\pi\)
−0.0670538 + 0.997749i \(0.521360\pi\)
\(192\) 0 0
\(193\) −4858.00 −1.81185 −0.905924 0.423441i \(-0.860822\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 396.000 0.143217 0.0716087 0.997433i \(-0.477187\pi\)
0.0716087 + 0.997433i \(0.477187\pi\)
\(198\) 0 0
\(199\) −1712.00 −0.609852 −0.304926 0.952376i \(-0.598632\pi\)
−0.304926 + 0.952376i \(0.598632\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 504.000 0.174255
\(204\) 0 0
\(205\) −2268.00 −0.772702
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1560.00 0.516304
\(210\) 0 0
\(211\) 772.000 0.251880 0.125940 0.992038i \(-0.459805\pi\)
0.125940 + 0.992038i \(0.459805\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 984.000 0.312131
\(216\) 0 0
\(217\) −1372.00 −0.429205
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −132.000 −0.0401777
\(222\) 0 0
\(223\) −776.000 −0.233026 −0.116513 0.993189i \(-0.537172\pi\)
−0.116513 + 0.993189i \(0.537172\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1788.00 −0.522792 −0.261396 0.965232i \(-0.584183\pi\)
−0.261396 + 0.965232i \(0.584183\pi\)
\(228\) 0 0
\(229\) 5402.00 1.55884 0.779420 0.626502i \(-0.215514\pi\)
0.779420 + 0.626502i \(0.215514\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3012.00 −0.846878 −0.423439 0.905925i \(-0.639177\pi\)
−0.423439 + 0.905925i \(0.639177\pi\)
\(234\) 0 0
\(235\) 1368.00 0.379738
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3546.00 0.959714 0.479857 0.877347i \(-0.340689\pi\)
0.479857 + 0.877347i \(0.340689\pi\)
\(240\) 0 0
\(241\) −3562.00 −0.952069 −0.476034 0.879427i \(-0.657926\pi\)
−0.476034 + 0.879427i \(0.657926\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −294.000 −0.0766652
\(246\) 0 0
\(247\) 104.000 0.0267909
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3348.00 0.841928 0.420964 0.907077i \(-0.361692\pi\)
0.420964 + 0.907077i \(0.361692\pi\)
\(252\) 0 0
\(253\) 3420.00 0.849856
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −366.000 −0.0888344 −0.0444172 0.999013i \(-0.514143\pi\)
−0.0444172 + 0.999013i \(0.514143\pi\)
\(258\) 0 0
\(259\) 2002.00 0.480302
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4170.00 0.977693 0.488846 0.872370i \(-0.337418\pi\)
0.488846 + 0.872370i \(0.337418\pi\)
\(264\) 0 0
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6078.00 −1.37763 −0.688814 0.724938i \(-0.741869\pi\)
−0.688814 + 0.724938i \(0.741869\pi\)
\(270\) 0 0
\(271\) −2468.00 −0.553212 −0.276606 0.960983i \(-0.589210\pi\)
−0.276606 + 0.960983i \(0.589210\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2670.00 −0.585480
\(276\) 0 0
\(277\) −394.000 −0.0854627 −0.0427313 0.999087i \(-0.513606\pi\)
−0.0427313 + 0.999087i \(0.513606\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 396.000 0.0840690 0.0420345 0.999116i \(-0.486616\pi\)
0.0420345 + 0.999116i \(0.486616\pi\)
\(282\) 0 0
\(283\) 1348.00 0.283146 0.141573 0.989928i \(-0.454784\pi\)
0.141573 + 0.989928i \(0.454784\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2646.00 −0.544211
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7506.00 −1.49660 −0.748302 0.663358i \(-0.769131\pi\)
−0.748302 + 0.663358i \(0.769131\pi\)
\(294\) 0 0
\(295\) 2088.00 0.412095
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 228.000 0.0440989
\(300\) 0 0
\(301\) 1148.00 0.219833
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 636.000 0.119401
\(306\) 0 0
\(307\) −1748.00 −0.324963 −0.162481 0.986712i \(-0.551950\pi\)
−0.162481 + 0.986712i \(0.551950\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1140.00 −0.207857 −0.103928 0.994585i \(-0.533141\pi\)
−0.103928 + 0.994585i \(0.533141\pi\)
\(312\) 0 0
\(313\) 146.000 0.0263655 0.0131828 0.999913i \(-0.495804\pi\)
0.0131828 + 0.999913i \(0.495804\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8148.00 1.44365 0.721825 0.692075i \(-0.243303\pi\)
0.721825 + 0.692075i \(0.243303\pi\)
\(318\) 0 0
\(319\) −2160.00 −0.379112
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3432.00 −0.591212
\(324\) 0 0
\(325\) −178.000 −0.0303805
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1596.00 0.267448
\(330\) 0 0
\(331\) 9700.00 1.61076 0.805378 0.592762i \(-0.201962\pi\)
0.805378 + 0.592762i \(0.201962\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3576.00 0.583217
\(336\) 0 0
\(337\) 8174.00 1.32126 0.660632 0.750710i \(-0.270288\pi\)
0.660632 + 0.750710i \(0.270288\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5880.00 0.933783
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4038.00 −0.624701 −0.312350 0.949967i \(-0.601116\pi\)
−0.312350 + 0.949967i \(0.601116\pi\)
\(348\) 0 0
\(349\) 10766.0 1.65126 0.825631 0.564210i \(-0.190819\pi\)
0.825631 + 0.564210i \(0.190819\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3666.00 −0.552752 −0.276376 0.961050i \(-0.589134\pi\)
−0.276376 + 0.961050i \(0.589134\pi\)
\(354\) 0 0
\(355\) −3780.00 −0.565131
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5106.00 −0.750653 −0.375326 0.926893i \(-0.622469\pi\)
−0.375326 + 0.926893i \(0.622469\pi\)
\(360\) 0 0
\(361\) −4155.00 −0.605773
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6252.00 0.896561
\(366\) 0 0
\(367\) 5776.00 0.821539 0.410769 0.911739i \(-0.365260\pi\)
0.410769 + 0.911739i \(0.365260\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2436.00 −0.340892
\(372\) 0 0
\(373\) 8462.00 1.17465 0.587327 0.809350i \(-0.300180\pi\)
0.587327 + 0.809350i \(0.300180\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −144.000 −0.0196721
\(378\) 0 0
\(379\) −6860.00 −0.929748 −0.464874 0.885377i \(-0.653900\pi\)
−0.464874 + 0.885377i \(0.653900\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −696.000 −0.0928562 −0.0464281 0.998922i \(-0.514784\pi\)
−0.0464281 + 0.998922i \(0.514784\pi\)
\(384\) 0 0
\(385\) 1260.00 0.166794
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11136.0 −1.45146 −0.725730 0.687980i \(-0.758498\pi\)
−0.725730 + 0.687980i \(0.758498\pi\)
\(390\) 0 0
\(391\) −7524.00 −0.973159
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −528.000 −0.0672571
\(396\) 0 0
\(397\) 10838.0 1.37014 0.685068 0.728480i \(-0.259773\pi\)
0.685068 + 0.728480i \(0.259773\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8364.00 1.04159 0.520796 0.853681i \(-0.325635\pi\)
0.520796 + 0.853681i \(0.325635\pi\)
\(402\) 0 0
\(403\) 392.000 0.0484539
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8580.00 −1.04495
\(408\) 0 0
\(409\) −1762.00 −0.213020 −0.106510 0.994312i \(-0.533968\pi\)
−0.106510 + 0.994312i \(0.533968\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2436.00 0.290237
\(414\) 0 0
\(415\) 8640.00 1.02198
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14580.0 1.69995 0.849976 0.526822i \(-0.176617\pi\)
0.849976 + 0.526822i \(0.176617\pi\)
\(420\) 0 0
\(421\) 8534.00 0.987938 0.493969 0.869480i \(-0.335546\pi\)
0.493969 + 0.869480i \(0.335546\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5874.00 0.670426
\(426\) 0 0
\(427\) 742.000 0.0840934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5934.00 0.663180 0.331590 0.943424i \(-0.392415\pi\)
0.331590 + 0.943424i \(0.392415\pi\)
\(432\) 0 0
\(433\) −14758.0 −1.63793 −0.818966 0.573843i \(-0.805452\pi\)
−0.818966 + 0.573843i \(0.805452\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5928.00 0.648912
\(438\) 0 0
\(439\) 11392.0 1.23852 0.619260 0.785186i \(-0.287433\pi\)
0.619260 + 0.785186i \(0.287433\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7026.00 0.753533 0.376767 0.926308i \(-0.377036\pi\)
0.376767 + 0.926308i \(0.377036\pi\)
\(444\) 0 0
\(445\) 8244.00 0.878209
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3384.00 0.355681 0.177841 0.984059i \(-0.443089\pi\)
0.177841 + 0.984059i \(0.443089\pi\)
\(450\) 0 0
\(451\) 11340.0 1.18399
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 84.0000 0.00865490
\(456\) 0 0
\(457\) −4282.00 −0.438301 −0.219150 0.975691i \(-0.570329\pi\)
−0.219150 + 0.975691i \(0.570329\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16650.0 −1.68214 −0.841071 0.540924i \(-0.818075\pi\)
−0.841071 + 0.540924i \(0.818075\pi\)
\(462\) 0 0
\(463\) 9664.00 0.970031 0.485015 0.874506i \(-0.338814\pi\)
0.485015 + 0.874506i \(0.338814\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12324.0 −1.22117 −0.610585 0.791950i \(-0.709066\pi\)
−0.610585 + 0.791950i \(0.709066\pi\)
\(468\) 0 0
\(469\) 4172.00 0.410757
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4920.00 −0.478270
\(474\) 0 0
\(475\) −4628.00 −0.447047
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18660.0 1.77995 0.889976 0.456007i \(-0.150721\pi\)
0.889976 + 0.456007i \(0.150721\pi\)
\(480\) 0 0
\(481\) −572.000 −0.0542224
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 204.000 0.0190993
\(486\) 0 0
\(487\) 3400.00 0.316363 0.158181 0.987410i \(-0.449437\pi\)
0.158181 + 0.987410i \(0.449437\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2970.00 0.272982 0.136491 0.990641i \(-0.456418\pi\)
0.136491 + 0.990641i \(0.456418\pi\)
\(492\) 0 0
\(493\) 4752.00 0.434116
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4410.00 −0.398019
\(498\) 0 0
\(499\) 988.000 0.0886352 0.0443176 0.999017i \(-0.485889\pi\)
0.0443176 + 0.999017i \(0.485889\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5184.00 0.459529 0.229765 0.973246i \(-0.426204\pi\)
0.229765 + 0.973246i \(0.426204\pi\)
\(504\) 0 0
\(505\) −2628.00 −0.231573
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16854.0 −1.46766 −0.733831 0.679332i \(-0.762270\pi\)
−0.733831 + 0.679332i \(0.762270\pi\)
\(510\) 0 0
\(511\) 7294.00 0.631443
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10056.0 0.860428
\(516\) 0 0
\(517\) −6840.00 −0.581862
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4398.00 0.369827 0.184914 0.982755i \(-0.440800\pi\)
0.184914 + 0.982755i \(0.440800\pi\)
\(522\) 0 0
\(523\) 10672.0 0.892264 0.446132 0.894967i \(-0.352801\pi\)
0.446132 + 0.894967i \(0.352801\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12936.0 −1.06926
\(528\) 0 0
\(529\) 829.000 0.0681351
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 756.000 0.0614371
\(534\) 0 0
\(535\) −12132.0 −0.980396
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1470.00 0.117472
\(540\) 0 0
\(541\) 20702.0 1.64519 0.822596 0.568627i \(-0.192525\pi\)
0.822596 + 0.568627i \(0.192525\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3012.00 0.236734
\(546\) 0 0
\(547\) 22876.0 1.78813 0.894065 0.447937i \(-0.147841\pi\)
0.894065 + 0.447937i \(0.147841\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3744.00 −0.289473
\(552\) 0 0
\(553\) −616.000 −0.0473689
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12876.0 0.979486 0.489743 0.871867i \(-0.337091\pi\)
0.489743 + 0.871867i \(0.337091\pi\)
\(558\) 0 0
\(559\) −328.000 −0.0248174
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6900.00 −0.516519 −0.258260 0.966076i \(-0.583149\pi\)
−0.258260 + 0.966076i \(0.583149\pi\)
\(564\) 0 0
\(565\) 12096.0 0.900677
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14676.0 −1.08128 −0.540641 0.841253i \(-0.681818\pi\)
−0.540641 + 0.841253i \(0.681818\pi\)
\(570\) 0 0
\(571\) −380.000 −0.0278503 −0.0139251 0.999903i \(-0.504433\pi\)
−0.0139251 + 0.999903i \(0.504433\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10146.0 −0.735856
\(576\) 0 0
\(577\) −11806.0 −0.851803 −0.425901 0.904770i \(-0.640043\pi\)
−0.425901 + 0.904770i \(0.640043\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10080.0 0.719774
\(582\) 0 0
\(583\) 10440.0 0.741648
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19188.0 −1.34919 −0.674594 0.738189i \(-0.735681\pi\)
−0.674594 + 0.738189i \(0.735681\pi\)
\(588\) 0 0
\(589\) 10192.0 0.712995
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −690.000 −0.0477823 −0.0238912 0.999715i \(-0.507606\pi\)
−0.0238912 + 0.999715i \(0.507606\pi\)
\(594\) 0 0
\(595\) −2772.00 −0.190993
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20490.0 −1.39766 −0.698830 0.715287i \(-0.746296\pi\)
−0.698830 + 0.715287i \(0.746296\pi\)
\(600\) 0 0
\(601\) −11590.0 −0.786632 −0.393316 0.919403i \(-0.628672\pi\)
−0.393316 + 0.919403i \(0.628672\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2586.00 0.173778
\(606\) 0 0
\(607\) 6424.00 0.429559 0.214779 0.976663i \(-0.431097\pi\)
0.214779 + 0.976663i \(0.431097\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −456.000 −0.0301928
\(612\) 0 0
\(613\) −9682.00 −0.637932 −0.318966 0.947766i \(-0.603336\pi\)
−0.318966 + 0.947766i \(0.603336\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5076.00 −0.331203 −0.165601 0.986193i \(-0.552956\pi\)
−0.165601 + 0.986193i \(0.552956\pi\)
\(618\) 0 0
\(619\) −22664.0 −1.47164 −0.735818 0.677179i \(-0.763202\pi\)
−0.735818 + 0.677179i \(0.763202\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9618.00 0.618519
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 18876.0 1.19656
\(630\) 0 0
\(631\) 8584.00 0.541559 0.270779 0.962641i \(-0.412719\pi\)
0.270779 + 0.962641i \(0.412719\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10704.0 0.668937
\(636\) 0 0
\(637\) 98.0000 0.00609561
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −372.000 −0.0229222 −0.0114611 0.999934i \(-0.503648\pi\)
−0.0114611 + 0.999934i \(0.503648\pi\)
\(642\) 0 0
\(643\) −3188.00 −0.195525 −0.0977624 0.995210i \(-0.531169\pi\)
−0.0977624 + 0.995210i \(0.531169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12732.0 −0.773642 −0.386821 0.922155i \(-0.626427\pi\)
−0.386821 + 0.922155i \(0.626427\pi\)
\(648\) 0 0
\(649\) −10440.0 −0.631442
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3576.00 0.214303 0.107151 0.994243i \(-0.465827\pi\)
0.107151 + 0.994243i \(0.465827\pi\)
\(654\) 0 0
\(655\) −9648.00 −0.575540
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11430.0 0.675644 0.337822 0.941210i \(-0.390310\pi\)
0.337822 + 0.941210i \(0.390310\pi\)
\(660\) 0 0
\(661\) 22646.0 1.33257 0.666284 0.745698i \(-0.267884\pi\)
0.666284 + 0.745698i \(0.267884\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2184.00 0.127356
\(666\) 0 0
\(667\) −8208.00 −0.476484
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3180.00 −0.182955
\(672\) 0 0
\(673\) −13570.0 −0.777244 −0.388622 0.921397i \(-0.627049\pi\)
−0.388622 + 0.921397i \(0.627049\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2838.00 0.161113 0.0805563 0.996750i \(-0.474330\pi\)
0.0805563 + 0.996750i \(0.474330\pi\)
\(678\) 0 0
\(679\) 238.000 0.0134515
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6558.00 −0.367401 −0.183701 0.982982i \(-0.558808\pi\)
−0.183701 + 0.982982i \(0.558808\pi\)
\(684\) 0 0
\(685\) −15480.0 −0.863446
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 696.000 0.0384840
\(690\) 0 0
\(691\) 21832.0 1.20192 0.600961 0.799278i \(-0.294785\pi\)
0.600961 + 0.799278i \(0.294785\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12864.0 0.702100
\(696\) 0 0
\(697\) −24948.0 −1.35577
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −16200.0 −0.872847 −0.436423 0.899741i \(-0.643755\pi\)
−0.436423 + 0.899741i \(0.643755\pi\)
\(702\) 0 0
\(703\) −14872.0 −0.797878
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3066.00 −0.163096
\(708\) 0 0
\(709\) 36722.0 1.94517 0.972584 0.232553i \(-0.0747080\pi\)
0.972584 + 0.232553i \(0.0747080\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 22344.0 1.17362
\(714\) 0 0
\(715\) −360.000 −0.0188297
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13776.0 0.714545 0.357273 0.934000i \(-0.383707\pi\)
0.357273 + 0.934000i \(0.383707\pi\)
\(720\) 0 0
\(721\) 11732.0 0.605995
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6408.00 0.328258
\(726\) 0 0
\(727\) −34220.0 −1.74574 −0.872868 0.487957i \(-0.837742\pi\)
−0.872868 + 0.487957i \(0.837742\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 10824.0 0.547661
\(732\) 0 0
\(733\) −13750.0 −0.692862 −0.346431 0.938075i \(-0.612607\pi\)
−0.346431 + 0.938075i \(0.612607\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −17880.0 −0.893648
\(738\) 0 0
\(739\) −39836.0 −1.98294 −0.991469 0.130344i \(-0.958392\pi\)
−0.991469 + 0.130344i \(0.958392\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 34470.0 1.70199 0.850997 0.525170i \(-0.175998\pi\)
0.850997 + 0.525170i \(0.175998\pi\)
\(744\) 0 0
\(745\) 9000.00 0.442597
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14154.0 −0.690489
\(750\) 0 0
\(751\) −5240.00 −0.254608 −0.127304 0.991864i \(-0.540632\pi\)
−0.127304 + 0.991864i \(0.540632\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7440.00 −0.358635
\(756\) 0 0
\(757\) 18578.0 0.891980 0.445990 0.895038i \(-0.352852\pi\)
0.445990 + 0.895038i \(0.352852\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −30534.0 −1.45448 −0.727238 0.686385i \(-0.759196\pi\)
−0.727238 + 0.686385i \(0.759196\pi\)
\(762\) 0 0
\(763\) 3514.00 0.166730
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −696.000 −0.0327655
\(768\) 0 0
\(769\) −39958.0 −1.87376 −0.936881 0.349650i \(-0.886301\pi\)
−0.936881 + 0.349650i \(0.886301\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3966.00 0.184537 0.0922685 0.995734i \(-0.470588\pi\)
0.0922685 + 0.995734i \(0.470588\pi\)
\(774\) 0 0
\(775\) −17444.0 −0.808525
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19656.0 0.904043
\(780\) 0 0
\(781\) 18900.0 0.865935
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3684.00 −0.167500
\(786\) 0 0
\(787\) 3760.00 0.170304 0.0851522 0.996368i \(-0.472862\pi\)
0.0851522 + 0.996368i \(0.472862\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14112.0 0.634343
\(792\) 0 0
\(793\) −212.000 −0.00949349
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24102.0 1.07119 0.535594 0.844476i \(-0.320088\pi\)
0.535594 + 0.844476i \(0.320088\pi\)
\(798\) 0 0
\(799\) 15048.0 0.666283
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −31260.0 −1.37378
\(804\) 0 0
\(805\) 4788.00 0.209633
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −11712.0 −0.508989 −0.254494 0.967074i \(-0.581909\pi\)
−0.254494 + 0.967074i \(0.581909\pi\)
\(810\) 0 0
\(811\) −37424.0 −1.62039 −0.810194 0.586162i \(-0.800638\pi\)
−0.810194 + 0.586162i \(0.800638\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 552.000 0.0237248
\(816\) 0 0
\(817\) −8528.00 −0.365186
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −13452.0 −0.571837 −0.285918 0.958254i \(-0.592299\pi\)
−0.285918 + 0.958254i \(0.592299\pi\)
\(822\) 0 0
\(823\) −20432.0 −0.865389 −0.432694 0.901541i \(-0.642437\pi\)
−0.432694 + 0.901541i \(0.642437\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 24390.0 1.02554 0.512771 0.858525i \(-0.328619\pi\)
0.512771 + 0.858525i \(0.328619\pi\)
\(828\) 0 0
\(829\) −28510.0 −1.19444 −0.597221 0.802076i \(-0.703729\pi\)
−0.597221 + 0.802076i \(0.703729\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3234.00 −0.134516
\(834\) 0 0
\(835\) 23544.0 0.975777
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −36972.0 −1.52135 −0.760677 0.649131i \(-0.775133\pi\)
−0.760677 + 0.649131i \(0.775133\pi\)
\(840\) 0 0
\(841\) −19205.0 −0.787445
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 13158.0 0.535679
\(846\) 0 0
\(847\) 3017.00 0.122391
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −32604.0 −1.31334
\(852\) 0 0
\(853\) −14074.0 −0.564929 −0.282465 0.959278i \(-0.591152\pi\)
−0.282465 + 0.959278i \(0.591152\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8826.00 0.351797 0.175899 0.984408i \(-0.443717\pi\)
0.175899 + 0.984408i \(0.443717\pi\)
\(858\) 0 0
\(859\) 20500.0 0.814262 0.407131 0.913370i \(-0.366529\pi\)
0.407131 + 0.913370i \(0.366529\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7674.00 0.302695 0.151348 0.988481i \(-0.451639\pi\)
0.151348 + 0.988481i \(0.451639\pi\)
\(864\) 0 0
\(865\) −11412.0 −0.448578
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2640.00 0.103056
\(870\) 0 0
\(871\) −1192.00 −0.0463713
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8988.00 −0.347257
\(876\) 0 0
\(877\) −8890.00 −0.342296 −0.171148 0.985245i \(-0.554748\pi\)
−0.171148 + 0.985245i \(0.554748\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −738.000 −0.0282223 −0.0141112 0.999900i \(-0.504492\pi\)
−0.0141112 + 0.999900i \(0.504492\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.000762235 0 −0.000381118 1.00000i \(-0.500121\pi\)
−0.000381118 1.00000i \(0.500121\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 39804.0 1.50675 0.753375 0.657591i \(-0.228424\pi\)
0.753375 + 0.657591i \(0.228424\pi\)
\(888\) 0 0
\(889\) 12488.0 0.471129
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −11856.0 −0.444284
\(894\) 0 0
\(895\) 36.0000 0.00134452
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −14112.0 −0.523539
\(900\) 0 0
\(901\) −22968.0 −0.849251
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 17268.0 0.634263
\(906\) 0 0
\(907\) −29180.0 −1.06825 −0.534127 0.845404i \(-0.679360\pi\)
−0.534127 + 0.845404i \(0.679360\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −48258.0 −1.75506 −0.877530 0.479523i \(-0.840810\pi\)
−0.877530 + 0.479523i \(0.840810\pi\)
\(912\) 0 0
\(913\) −43200.0 −1.56595
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −11256.0 −0.405350
\(918\) 0 0
\(919\) −25760.0 −0.924640 −0.462320 0.886713i \(-0.652983\pi\)
−0.462320 + 0.886713i \(0.652983\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1260.00 0.0449333
\(924\) 0 0
\(925\) 25454.0 0.904781
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 44778.0 1.58140 0.790699 0.612205i \(-0.209717\pi\)
0.790699 + 0.612205i \(0.209717\pi\)
\(930\) 0 0
\(931\) 2548.00 0.0896964
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11880.0 0.415527
\(936\) 0 0
\(937\) −44494.0 −1.55129 −0.775643 0.631171i \(-0.782574\pi\)
−0.775643 + 0.631171i \(0.782574\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 7458.00 0.258368 0.129184 0.991621i \(-0.458764\pi\)
0.129184 + 0.991621i \(0.458764\pi\)
\(942\) 0 0
\(943\) 43092.0 1.48809
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17790.0 0.610451 0.305226 0.952280i \(-0.401268\pi\)
0.305226 + 0.952280i \(0.401268\pi\)
\(948\) 0 0
\(949\) −2084.00 −0.0712850
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5832.00 0.198234 0.0991170 0.995076i \(-0.468398\pi\)
0.0991170 + 0.995076i \(0.468398\pi\)
\(954\) 0 0
\(955\) 2124.00 0.0719697
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18060.0 −0.608121
\(960\) 0 0
\(961\) 8625.00 0.289517
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 29148.0 0.972339
\(966\) 0 0
\(967\) 13264.0 0.441098 0.220549 0.975376i \(-0.429215\pi\)
0.220549 + 0.975376i \(0.429215\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3984.00 0.131671 0.0658356 0.997830i \(-0.479029\pi\)
0.0658356 + 0.997830i \(0.479029\pi\)
\(972\) 0 0
\(973\) 15008.0 0.494485
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 38940.0 1.27513 0.637564 0.770397i \(-0.279942\pi\)
0.637564 + 0.770397i \(0.279942\pi\)
\(978\) 0 0
\(979\) −41220.0 −1.34566
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8808.00 −0.285790 −0.142895 0.989738i \(-0.545641\pi\)
−0.142895 + 0.989738i \(0.545641\pi\)
\(984\) 0 0
\(985\) −2376.00 −0.0768585
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18696.0 −0.601110
\(990\) 0 0
\(991\) −18488.0 −0.592624 −0.296312 0.955091i \(-0.595757\pi\)
−0.296312 + 0.955091i \(0.595757\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 10272.0 0.327281
\(996\) 0 0
\(997\) −5002.00 −0.158892 −0.0794458 0.996839i \(-0.525315\pi\)
−0.0794458 + 0.996839i \(0.525315\pi\)
\(998\) 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 1008.4.a.g.1.1 1
3.2 odd 2 1008.4.a.n.1.1 1
4.3 odd 2 126.4.a.b.1.1 1
12.11 even 2 126.4.a.g.1.1 yes 1
28.3 even 6 882.4.g.q.667.1 2
28.11 odd 6 882.4.g.t.667.1 2
28.19 even 6 882.4.g.q.361.1 2
28.23 odd 6 882.4.g.t.361.1 2
28.27 even 2 882.4.a.e.1.1 1
84.11 even 6 882.4.g.e.667.1 2
84.23 even 6 882.4.g.e.361.1 2
84.47 odd 6 882.4.g.h.361.1 2
84.59 odd 6 882.4.g.h.667.1 2
84.83 odd 2 882.4.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.4.a.b.1.1 1 4.3 odd 2
126.4.a.g.1.1 yes 1 12.11 even 2
882.4.a.e.1.1 1 28.27 even 2
882.4.a.m.1.1 1 84.83 odd 2
882.4.g.e.361.1 2 84.23 even 6
882.4.g.e.667.1 2 84.11 even 6
882.4.g.h.361.1 2 84.47 odd 6
882.4.g.h.667.1 2 84.59 odd 6
882.4.g.q.361.1 2 28.19 even 6
882.4.g.q.667.1 2 28.3 even 6
882.4.g.t.361.1 2 28.23 odd 6
882.4.g.t.667.1 2 28.11 odd 6
1008.4.a.g.1.1 1 1.1 even 1 trivial
1008.4.a.n.1.1 1 3.2 odd 2