Properties

Label 2200.4.a.e.1.1
Level $2200$
Weight $4$
Character 2200.1
Self dual yes
Analytic conductor $129.804$
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] = [2200,4,Mod(1,2200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2200.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: \(129.804202013\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-16.0000 q^{7} -27.0000 q^{9} +O(q^{10})\) \(q-16.0000 q^{7} -27.0000 q^{9} -11.0000 q^{11} +70.0000 q^{13} +10.0000 q^{17} -12.0000 q^{19} +84.0000 q^{23} +30.0000 q^{29} -72.0000 q^{31} -310.000 q^{37} +18.0000 q^{41} +388.000 q^{43} +516.000 q^{47} -87.0000 q^{49} +298.000 q^{53} +204.000 q^{59} -210.000 q^{61} +432.000 q^{63} +432.000 q^{67} -440.000 q^{71} -46.0000 q^{73} +176.000 q^{77} -616.000 q^{79} +729.000 q^{81} -740.000 q^{83} -6.00000 q^{89} -1120.00 q^{91} -490.000 q^{97} +297.000 q^{99} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −16.0000 −0.863919 −0.431959 0.901893i \(-0.642178\pi\)
−0.431959 + 0.901893i \(0.642178\pi\)
\(8\) 0 0
\(9\) −27.0000 −1.00000
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 70.0000 1.49342 0.746712 0.665148i \(-0.231631\pi\)
0.746712 + 0.665148i \(0.231631\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 10.0000 0.142668 0.0713340 0.997452i \(-0.477274\pi\)
0.0713340 + 0.997452i \(0.477274\pi\)
\(18\) 0 0
\(19\) −12.0000 −0.144894 −0.0724471 0.997372i \(-0.523081\pi\)
−0.0724471 + 0.997372i \(0.523081\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 84.0000 0.761531 0.380765 0.924672i \(-0.375661\pi\)
0.380765 + 0.924672i \(0.375661\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 30.0000 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) 0 0
\(31\) −72.0000 −0.417148 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −310.000 −1.37740 −0.688698 0.725048i \(-0.741818\pi\)
−0.688698 + 0.725048i \(0.741818\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 18.0000 0.0685641 0.0342820 0.999412i \(-0.489086\pi\)
0.0342820 + 0.999412i \(0.489086\pi\)
\(42\) 0 0
\(43\) 388.000 1.37603 0.688017 0.725695i \(-0.258482\pi\)
0.688017 + 0.725695i \(0.258482\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 516.000 1.60141 0.800706 0.599058i \(-0.204458\pi\)
0.800706 + 0.599058i \(0.204458\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 298.000 0.772329 0.386165 0.922430i \(-0.373800\pi\)
0.386165 + 0.922430i \(0.373800\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 204.000 0.450145 0.225072 0.974342i \(-0.427738\pi\)
0.225072 + 0.974342i \(0.427738\pi\)
\(60\) 0 0
\(61\) −210.000 −0.440783 −0.220391 0.975412i \(-0.570733\pi\)
−0.220391 + 0.975412i \(0.570733\pi\)
\(62\) 0 0
\(63\) 432.000 0.863919
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 432.000 0.787719 0.393860 0.919171i \(-0.371140\pi\)
0.393860 + 0.919171i \(0.371140\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −440.000 −0.735470 −0.367735 0.929931i \(-0.619867\pi\)
−0.367735 + 0.929931i \(0.619867\pi\)
\(72\) 0 0
\(73\) −46.0000 −0.0737520 −0.0368760 0.999320i \(-0.511741\pi\)
−0.0368760 + 0.999320i \(0.511741\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 176.000 0.260481
\(78\) 0 0
\(79\) −616.000 −0.877284 −0.438642 0.898662i \(-0.644540\pi\)
−0.438642 + 0.898662i \(0.644540\pi\)
\(80\) 0 0
\(81\) 729.000 1.00000
\(82\) 0 0
\(83\) −740.000 −0.978621 −0.489311 0.872110i \(-0.662752\pi\)
−0.489311 + 0.872110i \(0.662752\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.00714605 −0.00357303 0.999994i \(-0.501137\pi\)
−0.00357303 + 0.999994i \(0.501137\pi\)
\(90\) 0 0
\(91\) −1120.00 −1.29020
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −490.000 −0.512907 −0.256453 0.966557i \(-0.582554\pi\)
−0.256453 + 0.966557i \(0.582554\pi\)
\(98\) 0 0
\(99\) 297.000 0.301511
\(100\) 0 0
\(101\) −1506.00 −1.48369 −0.741845 0.670572i \(-0.766049\pi\)
−0.741845 + 0.670572i \(0.766049\pi\)
\(102\) 0 0
\(103\) −148.000 −0.141581 −0.0707906 0.997491i \(-0.522552\pi\)
−0.0707906 + 0.997491i \(0.522552\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 396.000 0.357783 0.178891 0.983869i \(-0.442749\pi\)
0.178891 + 0.983869i \(0.442749\pi\)
\(108\) 0 0
\(109\) −58.0000 −0.0509669 −0.0254835 0.999675i \(-0.508113\pi\)
−0.0254835 + 0.999675i \(0.508113\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −890.000 −0.740922 −0.370461 0.928848i \(-0.620800\pi\)
−0.370461 + 0.928848i \(0.620800\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1890.00 −1.49342
\(118\) 0 0
\(119\) −160.000 −0.123254
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 160.000 0.111793 0.0558965 0.998437i \(-0.482198\pi\)
0.0558965 + 0.998437i \(0.482198\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 956.000 0.637604 0.318802 0.947821i \(-0.396720\pi\)
0.318802 + 0.947821i \(0.396720\pi\)
\(132\) 0 0
\(133\) 192.000 0.125177
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 126.000 0.0785760 0.0392880 0.999228i \(-0.487491\pi\)
0.0392880 + 0.999228i \(0.487491\pi\)
\(138\) 0 0
\(139\) −2556.00 −1.55969 −0.779846 0.625972i \(-0.784702\pi\)
−0.779846 + 0.625972i \(0.784702\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −770.000 −0.450284
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1854.00 1.01937 0.509683 0.860362i \(-0.329763\pi\)
0.509683 + 0.860362i \(0.329763\pi\)
\(150\) 0 0
\(151\) −2152.00 −1.15978 −0.579892 0.814694i \(-0.696905\pi\)
−0.579892 + 0.814694i \(0.696905\pi\)
\(152\) 0 0
\(153\) −270.000 −0.142668
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2502.00 −1.27186 −0.635928 0.771749i \(-0.719382\pi\)
−0.635928 + 0.771749i \(0.719382\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1344.00 −0.657901
\(162\) 0 0
\(163\) −144.000 −0.0691960 −0.0345980 0.999401i \(-0.511015\pi\)
−0.0345980 + 0.999401i \(0.511015\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1080.00 −0.500437 −0.250218 0.968189i \(-0.580502\pi\)
−0.250218 + 0.968189i \(0.580502\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) 0 0
\(171\) 324.000 0.144894
\(172\) 0 0
\(173\) −2994.00 −1.31578 −0.657889 0.753115i \(-0.728550\pi\)
−0.657889 + 0.753115i \(0.728550\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −820.000 −0.342400 −0.171200 0.985236i \(-0.554764\pi\)
−0.171200 + 0.985236i \(0.554764\pi\)
\(180\) 0 0
\(181\) −754.000 −0.309637 −0.154819 0.987943i \(-0.549479\pi\)
−0.154819 + 0.987943i \(0.549479\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −110.000 −0.0430160
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2520.00 −0.954664 −0.477332 0.878723i \(-0.658396\pi\)
−0.477332 + 0.878723i \(0.658396\pi\)
\(192\) 0 0
\(193\) −246.000 −0.0917485 −0.0458743 0.998947i \(-0.514607\pi\)
−0.0458743 + 0.998947i \(0.514607\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4906.00 −1.77430 −0.887152 0.461477i \(-0.847320\pi\)
−0.887152 + 0.461477i \(0.847320\pi\)
\(198\) 0 0
\(199\) 4496.00 1.60157 0.800786 0.598950i \(-0.204415\pi\)
0.800786 + 0.598950i \(0.204415\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −480.000 −0.165958
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2268.00 −0.761531
\(208\) 0 0
\(209\) 132.000 0.0436872
\(210\) 0 0
\(211\) 2764.00 0.901809 0.450904 0.892572i \(-0.351102\pi\)
0.450904 + 0.892572i \(0.351102\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1152.00 0.360382
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 700.000 0.213064
\(222\) 0 0
\(223\) 2828.00 0.849224 0.424612 0.905375i \(-0.360411\pi\)
0.424612 + 0.905375i \(0.360411\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2164.00 −0.632730 −0.316365 0.948638i \(-0.602462\pi\)
−0.316365 + 0.948638i \(0.602462\pi\)
\(228\) 0 0
\(229\) 3374.00 0.973625 0.486813 0.873506i \(-0.338159\pi\)
0.486813 + 0.873506i \(0.338159\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3642.00 1.02401 0.512007 0.858981i \(-0.328902\pi\)
0.512007 + 0.858981i \(0.328902\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6072.00 1.64337 0.821684 0.569943i \(-0.193035\pi\)
0.821684 + 0.569943i \(0.193035\pi\)
\(240\) 0 0
\(241\) −3478.00 −0.929617 −0.464808 0.885411i \(-0.653877\pi\)
−0.464808 + 0.885411i \(0.653877\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −840.000 −0.216388
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5564.00 −1.39919 −0.699595 0.714540i \(-0.746636\pi\)
−0.699595 + 0.714540i \(0.746636\pi\)
\(252\) 0 0
\(253\) −924.000 −0.229610
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6126.00 1.48688 0.743442 0.668800i \(-0.233192\pi\)
0.743442 + 0.668800i \(0.233192\pi\)
\(258\) 0 0
\(259\) 4960.00 1.18996
\(260\) 0 0
\(261\) −810.000 −0.192099
\(262\) 0 0
\(263\) −2520.00 −0.590836 −0.295418 0.955368i \(-0.595459\pi\)
−0.295418 + 0.955368i \(0.595459\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3274.00 −0.742079 −0.371040 0.928617i \(-0.620999\pi\)
−0.371040 + 0.928617i \(0.620999\pi\)
\(270\) 0 0
\(271\) 1312.00 0.294090 0.147045 0.989130i \(-0.453024\pi\)
0.147045 + 0.989130i \(0.453024\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8274.00 −1.79472 −0.897358 0.441303i \(-0.854516\pi\)
−0.897358 + 0.441303i \(0.854516\pi\)
\(278\) 0 0
\(279\) 1944.00 0.417148
\(280\) 0 0
\(281\) 2722.00 0.577868 0.288934 0.957349i \(-0.406699\pi\)
0.288934 + 0.957349i \(0.406699\pi\)
\(282\) 0 0
\(283\) 420.000 0.0882205 0.0441103 0.999027i \(-0.485955\pi\)
0.0441103 + 0.999027i \(0.485955\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −288.000 −0.0592338
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7122.00 −1.42004 −0.710020 0.704182i \(-0.751314\pi\)
−0.710020 + 0.704182i \(0.751314\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5880.00 1.13729
\(300\) 0 0
\(301\) −6208.00 −1.18878
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2252.00 −0.418659 −0.209330 0.977845i \(-0.567128\pi\)
−0.209330 + 0.977845i \(0.567128\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4920.00 −0.897066 −0.448533 0.893766i \(-0.648053\pi\)
−0.448533 + 0.893766i \(0.648053\pi\)
\(312\) 0 0
\(313\) −922.000 −0.166500 −0.0832500 0.996529i \(-0.526530\pi\)
−0.0832500 + 0.996529i \(0.526530\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9078.00 −1.60843 −0.804213 0.594341i \(-0.797413\pi\)
−0.804213 + 0.594341i \(0.797413\pi\)
\(318\) 0 0
\(319\) −330.000 −0.0579199
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −120.000 −0.0206718
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8256.00 −1.38349
\(330\) 0 0
\(331\) −6260.00 −1.03952 −0.519759 0.854313i \(-0.673978\pi\)
−0.519759 + 0.854313i \(0.673978\pi\)
\(332\) 0 0
\(333\) 8370.00 1.37740
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5974.00 −0.965651 −0.482826 0.875716i \(-0.660390\pi\)
−0.482826 + 0.875716i \(0.660390\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 792.000 0.125775
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2500.00 −0.386764 −0.193382 0.981124i \(-0.561946\pi\)
−0.193382 + 0.981124i \(0.561946\pi\)
\(348\) 0 0
\(349\) −12146.0 −1.86292 −0.931462 0.363839i \(-0.881466\pi\)
−0.931462 + 0.363839i \(0.881466\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 878.000 0.132383 0.0661915 0.997807i \(-0.478915\pi\)
0.0661915 + 0.997807i \(0.478915\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2368.00 −0.348129 −0.174064 0.984734i \(-0.555690\pi\)
−0.174064 + 0.984734i \(0.555690\pi\)
\(360\) 0 0
\(361\) −6715.00 −0.979006
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6388.00 0.908586 0.454293 0.890852i \(-0.349892\pi\)
0.454293 + 0.890852i \(0.349892\pi\)
\(368\) 0 0
\(369\) −486.000 −0.0685641
\(370\) 0 0
\(371\) −4768.00 −0.667230
\(372\) 0 0
\(373\) 13222.0 1.83541 0.917707 0.397259i \(-0.130038\pi\)
0.917707 + 0.397259i \(0.130038\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2100.00 0.286885
\(378\) 0 0
\(379\) −5380.00 −0.729161 −0.364581 0.931172i \(-0.618788\pi\)
−0.364581 + 0.931172i \(0.618788\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11292.0 −1.50651 −0.753256 0.657727i \(-0.771518\pi\)
−0.753256 + 0.657727i \(0.771518\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −10476.0 −1.37603
\(388\) 0 0
\(389\) 6558.00 0.854766 0.427383 0.904071i \(-0.359436\pi\)
0.427383 + 0.904071i \(0.359436\pi\)
\(390\) 0 0
\(391\) 840.000 0.108646
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 442.000 0.0558774 0.0279387 0.999610i \(-0.491106\pi\)
0.0279387 + 0.999610i \(0.491106\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12318.0 −1.53399 −0.766997 0.641651i \(-0.778250\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(402\) 0 0
\(403\) −5040.00 −0.622978
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3410.00 0.415301
\(408\) 0 0
\(409\) −4534.00 −0.548146 −0.274073 0.961709i \(-0.588371\pi\)
−0.274073 + 0.961709i \(0.588371\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3264.00 −0.388888
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5580.00 0.650599 0.325299 0.945611i \(-0.394535\pi\)
0.325299 + 0.945611i \(0.394535\pi\)
\(420\) 0 0
\(421\) −10146.0 −1.17455 −0.587275 0.809387i \(-0.699799\pi\)
−0.587275 + 0.809387i \(0.699799\pi\)
\(422\) 0 0
\(423\) −13932.0 −1.60141
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3360.00 0.380800
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8968.00 −1.00226 −0.501129 0.865372i \(-0.667082\pi\)
−0.501129 + 0.865372i \(0.667082\pi\)
\(432\) 0 0
\(433\) 14358.0 1.59354 0.796768 0.604285i \(-0.206541\pi\)
0.796768 + 0.604285i \(0.206541\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1008.00 −0.110341
\(438\) 0 0
\(439\) 1064.00 0.115676 0.0578382 0.998326i \(-0.481579\pi\)
0.0578382 + 0.998326i \(0.481579\pi\)
\(440\) 0 0
\(441\) 2349.00 0.253644
\(442\) 0 0
\(443\) −16088.0 −1.72543 −0.862713 0.505693i \(-0.831237\pi\)
−0.862713 + 0.505693i \(0.831237\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7554.00 0.793976 0.396988 0.917824i \(-0.370055\pi\)
0.396988 + 0.917824i \(0.370055\pi\)
\(450\) 0 0
\(451\) −198.000 −0.0206729
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4614.00 −0.472284 −0.236142 0.971719i \(-0.575883\pi\)
−0.236142 + 0.971719i \(0.575883\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10710.0 1.08203 0.541013 0.841014i \(-0.318041\pi\)
0.541013 + 0.841014i \(0.318041\pi\)
\(462\) 0 0
\(463\) 11340.0 1.13826 0.569130 0.822247i \(-0.307280\pi\)
0.569130 + 0.822247i \(0.307280\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13248.0 1.31273 0.656364 0.754444i \(-0.272093\pi\)
0.656364 + 0.754444i \(0.272093\pi\)
\(468\) 0 0
\(469\) −6912.00 −0.680526
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4268.00 −0.414890
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −8046.00 −0.772329
\(478\) 0 0
\(479\) 17960.0 1.71318 0.856590 0.515997i \(-0.172579\pi\)
0.856590 + 0.515997i \(0.172579\pi\)
\(480\) 0 0
\(481\) −21700.0 −2.05704
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7628.00 0.709769 0.354885 0.934910i \(-0.384520\pi\)
0.354885 + 0.934910i \(0.384520\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8876.00 0.815821 0.407911 0.913022i \(-0.366257\pi\)
0.407911 + 0.913022i \(0.366257\pi\)
\(492\) 0 0
\(493\) 300.000 0.0274063
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7040.00 0.635387
\(498\) 0 0
\(499\) 2836.00 0.254422 0.127211 0.991876i \(-0.459397\pi\)
0.127211 + 0.991876i \(0.459397\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12768.0 1.13180 0.565902 0.824473i \(-0.308528\pi\)
0.565902 + 0.824473i \(0.308528\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14646.0 1.27539 0.637694 0.770290i \(-0.279888\pi\)
0.637694 + 0.770290i \(0.279888\pi\)
\(510\) 0 0
\(511\) 736.000 0.0637157
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5676.00 −0.482844
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12918.0 −1.08627 −0.543136 0.839645i \(-0.682763\pi\)
−0.543136 + 0.839645i \(0.682763\pi\)
\(522\) 0 0
\(523\) −19092.0 −1.59624 −0.798121 0.602497i \(-0.794173\pi\)
−0.798121 + 0.602497i \(0.794173\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −720.000 −0.0595136
\(528\) 0 0
\(529\) −5111.00 −0.420071
\(530\) 0 0
\(531\) −5508.00 −0.450145
\(532\) 0 0
\(533\) 1260.00 0.102395
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 957.000 0.0764766
\(540\) 0 0
\(541\) 5078.00 0.403549 0.201775 0.979432i \(-0.435329\pi\)
0.201775 + 0.979432i \(0.435329\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12300.0 0.961444 0.480722 0.876873i \(-0.340375\pi\)
0.480722 + 0.876873i \(0.340375\pi\)
\(548\) 0 0
\(549\) 5670.00 0.440783
\(550\) 0 0
\(551\) −360.000 −0.0278340
\(552\) 0 0
\(553\) 9856.00 0.757902
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12066.0 −0.917869 −0.458934 0.888470i \(-0.651769\pi\)
−0.458934 + 0.888470i \(0.651769\pi\)
\(558\) 0 0
\(559\) 27160.0 2.05500
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6436.00 0.481785 0.240893 0.970552i \(-0.422560\pi\)
0.240893 + 0.970552i \(0.422560\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −11664.0 −0.863919
\(568\) 0 0
\(569\) −16214.0 −1.19460 −0.597299 0.802019i \(-0.703759\pi\)
−0.597299 + 0.802019i \(0.703759\pi\)
\(570\) 0 0
\(571\) −1588.00 −0.116385 −0.0581924 0.998305i \(-0.518534\pi\)
−0.0581924 + 0.998305i \(0.518534\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −13386.0 −0.965800 −0.482900 0.875676i \(-0.660417\pi\)
−0.482900 + 0.875676i \(0.660417\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11840.0 0.845449
\(582\) 0 0
\(583\) −3278.00 −0.232866
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3064.00 −0.215443 −0.107721 0.994181i \(-0.534355\pi\)
−0.107721 + 0.994181i \(0.534355\pi\)
\(588\) 0 0
\(589\) 864.000 0.0604423
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4506.00 0.312039 0.156020 0.987754i \(-0.450134\pi\)
0.156020 + 0.987754i \(0.450134\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10856.0 −0.740508 −0.370254 0.928931i \(-0.620729\pi\)
−0.370254 + 0.928931i \(0.620729\pi\)
\(600\) 0 0
\(601\) −15726.0 −1.06735 −0.533675 0.845690i \(-0.679189\pi\)
−0.533675 + 0.845690i \(0.679189\pi\)
\(602\) 0 0
\(603\) −11664.0 −0.787719
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11376.0 0.760688 0.380344 0.924845i \(-0.375806\pi\)
0.380344 + 0.924845i \(0.375806\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 36120.0 2.39159
\(612\) 0 0
\(613\) −15658.0 −1.03168 −0.515841 0.856685i \(-0.672520\pi\)
−0.515841 + 0.856685i \(0.672520\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27890.0 −1.81979 −0.909894 0.414841i \(-0.863837\pi\)
−0.909894 + 0.414841i \(0.863837\pi\)
\(618\) 0 0
\(619\) −20956.0 −1.36073 −0.680366 0.732873i \(-0.738179\pi\)
−0.680366 + 0.732873i \(0.738179\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 96.0000 0.00617361
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3100.00 −0.196510
\(630\) 0 0
\(631\) 7720.00 0.487050 0.243525 0.969895i \(-0.421696\pi\)
0.243525 + 0.969895i \(0.421696\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6090.00 −0.378798
\(638\) 0 0
\(639\) 11880.0 0.735470
\(640\) 0 0
\(641\) 2210.00 0.136177 0.0680887 0.997679i \(-0.478310\pi\)
0.0680887 + 0.997679i \(0.478310\pi\)
\(642\) 0 0
\(643\) 17840.0 1.09415 0.547077 0.837082i \(-0.315741\pi\)
0.547077 + 0.837082i \(0.315741\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14716.0 −0.894197 −0.447099 0.894485i \(-0.647543\pi\)
−0.447099 + 0.894485i \(0.647543\pi\)
\(648\) 0 0
\(649\) −2244.00 −0.135724
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3582.00 −0.214662 −0.107331 0.994223i \(-0.534231\pi\)
−0.107331 + 0.994223i \(0.534231\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1242.00 0.0737520
\(658\) 0 0
\(659\) 4940.00 0.292011 0.146005 0.989284i \(-0.453358\pi\)
0.146005 + 0.989284i \(0.453358\pi\)
\(660\) 0 0
\(661\) 31726.0 1.86687 0.933433 0.358752i \(-0.116798\pi\)
0.933433 + 0.358752i \(0.116798\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2520.00 0.146289
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2310.00 0.132901
\(672\) 0 0
\(673\) −11894.0 −0.681248 −0.340624 0.940200i \(-0.610638\pi\)
−0.340624 + 0.940200i \(0.610638\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29282.0 −1.66233 −0.831166 0.556024i \(-0.812326\pi\)
−0.831166 + 0.556024i \(0.812326\pi\)
\(678\) 0 0
\(679\) 7840.00 0.443110
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21712.0 1.21638 0.608189 0.793792i \(-0.291896\pi\)
0.608189 + 0.793792i \(0.291896\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20860.0 1.15341
\(690\) 0 0
\(691\) −10516.0 −0.578940 −0.289470 0.957187i \(-0.593479\pi\)
−0.289470 + 0.957187i \(0.593479\pi\)
\(692\) 0 0
\(693\) −4752.00 −0.260481
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 180.000 0.00978190
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21134.0 1.13869 0.569344 0.822099i \(-0.307197\pi\)
0.569344 + 0.822099i \(0.307197\pi\)
\(702\) 0 0
\(703\) 3720.00 0.199577
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 24096.0 1.28179
\(708\) 0 0
\(709\) −23570.0 −1.24850 −0.624252 0.781223i \(-0.714596\pi\)
−0.624252 + 0.781223i \(0.714596\pi\)
\(710\) 0 0
\(711\) 16632.0 0.877284
\(712\) 0 0
\(713\) −6048.00 −0.317671
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −28816.0 −1.49465 −0.747326 0.664457i \(-0.768663\pi\)
−0.747326 + 0.664457i \(0.768663\pi\)
\(720\) 0 0
\(721\) 2368.00 0.122315
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 26884.0 1.37149 0.685744 0.727842i \(-0.259477\pi\)
0.685744 + 0.727842i \(0.259477\pi\)
\(728\) 0 0
\(729\) −19683.0 −1.00000
\(730\) 0 0
\(731\) 3880.00 0.196316
\(732\) 0 0
\(733\) −20802.0 −1.04821 −0.524106 0.851653i \(-0.675600\pi\)
−0.524106 + 0.851653i \(0.675600\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4752.00 −0.237506
\(738\) 0 0
\(739\) 36460.0 1.81489 0.907444 0.420172i \(-0.138030\pi\)
0.907444 + 0.420172i \(0.138030\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2072.00 0.102307 0.0511536 0.998691i \(-0.483710\pi\)
0.0511536 + 0.998691i \(0.483710\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 19980.0 0.978621
\(748\) 0 0
\(749\) −6336.00 −0.309095
\(750\) 0 0
\(751\) −24448.0 −1.18791 −0.593955 0.804498i \(-0.702434\pi\)
−0.593955 + 0.804498i \(0.702434\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 27458.0 1.31833 0.659166 0.751997i \(-0.270909\pi\)
0.659166 + 0.751997i \(0.270909\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23770.0 1.13228 0.566138 0.824311i \(-0.308437\pi\)
0.566138 + 0.824311i \(0.308437\pi\)
\(762\) 0 0
\(763\) 928.000 0.0440313
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14280.0 0.672257
\(768\) 0 0
\(769\) −23574.0 −1.10546 −0.552731 0.833360i \(-0.686414\pi\)
−0.552731 + 0.833360i \(0.686414\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 26746.0 1.24448 0.622242 0.782825i \(-0.286222\pi\)
0.622242 + 0.782825i \(0.286222\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −216.000 −0.00993454
\(780\) 0 0
\(781\) 4840.00 0.221753
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −17516.0 −0.793365 −0.396682 0.917956i \(-0.629839\pi\)
−0.396682 + 0.917956i \(0.629839\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14240.0 0.640096
\(792\) 0 0
\(793\) −14700.0 −0.658275
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15226.0 0.676703 0.338352 0.941020i \(-0.390131\pi\)
0.338352 + 0.941020i \(0.390131\pi\)
\(798\) 0 0
\(799\) 5160.00 0.228470
\(800\) 0 0
\(801\) 162.000 0.00714605
\(802\) 0 0
\(803\) 506.000 0.0222371
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3422.00 −0.148716 −0.0743579 0.997232i \(-0.523691\pi\)
−0.0743579 + 0.997232i \(0.523691\pi\)
\(810\) 0 0
\(811\) 4220.00 0.182718 0.0913590 0.995818i \(-0.470879\pi\)
0.0913590 + 0.995818i \(0.470879\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −4656.00 −0.199379
\(818\) 0 0
\(819\) 30240.0 1.29020
\(820\) 0 0
\(821\) 6006.00 0.255312 0.127656 0.991819i \(-0.459255\pi\)
0.127656 + 0.991819i \(0.459255\pi\)
\(822\) 0 0
\(823\) −30836.0 −1.30605 −0.653023 0.757338i \(-0.726499\pi\)
−0.653023 + 0.757338i \(0.726499\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29164.0 1.22628 0.613139 0.789975i \(-0.289907\pi\)
0.613139 + 0.789975i \(0.289907\pi\)
\(828\) 0 0
\(829\) −17146.0 −0.718342 −0.359171 0.933272i \(-0.616940\pi\)
−0.359171 + 0.933272i \(0.616940\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −870.000 −0.0361869
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −14640.0 −0.602418 −0.301209 0.953558i \(-0.597390\pi\)
−0.301209 + 0.953558i \(0.597390\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1936.00 −0.0785381
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −26040.0 −1.04893
\(852\) 0 0
\(853\) 24918.0 1.00021 0.500103 0.865966i \(-0.333295\pi\)
0.500103 + 0.865966i \(0.333295\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 434.000 0.0172989 0.00864945 0.999963i \(-0.497247\pi\)
0.00864945 + 0.999963i \(0.497247\pi\)
\(858\) 0 0
\(859\) −27020.0 −1.07324 −0.536618 0.843825i \(-0.680299\pi\)
−0.536618 + 0.843825i \(0.680299\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −5164.00 −0.203690 −0.101845 0.994800i \(-0.532475\pi\)
−0.101845 + 0.994800i \(0.532475\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6776.00 0.264511
\(870\) 0 0
\(871\) 30240.0 1.17640
\(872\) 0 0
\(873\) 13230.0 0.512907
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 39870.0 1.53514 0.767568 0.640968i \(-0.221467\pi\)
0.767568 + 0.640968i \(0.221467\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25138.0 0.961318 0.480659 0.876908i \(-0.340398\pi\)
0.480659 + 0.876908i \(0.340398\pi\)
\(882\) 0 0
\(883\) 39472.0 1.50435 0.752174 0.658965i \(-0.229005\pi\)
0.752174 + 0.658965i \(0.229005\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 45768.0 1.73251 0.866257 0.499600i \(-0.166519\pi\)
0.866257 + 0.499600i \(0.166519\pi\)
\(888\) 0 0
\(889\) −2560.00 −0.0965800
\(890\) 0 0
\(891\) −8019.00 −0.301511
\(892\) 0 0
\(893\) −6192.00 −0.232035
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2160.00 −0.0801335
\(900\) 0 0
\(901\) 2980.00 0.110187
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 35224.0 1.28952 0.644759 0.764386i \(-0.276958\pi\)
0.644759 + 0.764386i \(0.276958\pi\)
\(908\) 0 0
\(909\) 40662.0 1.48369
\(910\) 0 0
\(911\) 10568.0 0.384340 0.192170 0.981362i \(-0.438448\pi\)
0.192170 + 0.981362i \(0.438448\pi\)
\(912\) 0 0
\(913\) 8140.00 0.295065
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15296.0 −0.550838
\(918\) 0 0
\(919\) −11128.0 −0.399433 −0.199716 0.979854i \(-0.564002\pi\)
−0.199716 + 0.979854i \(0.564002\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −30800.0 −1.09837
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3996.00 0.141581
\(928\) 0 0
\(929\) −33422.0 −1.18034 −0.590172 0.807277i \(-0.700940\pi\)
−0.590172 + 0.807277i \(0.700940\pi\)
\(930\) 0 0
\(931\) 1044.00 0.0367516
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 18490.0 0.644655 0.322328 0.946628i \(-0.395535\pi\)
0.322328 + 0.946628i \(0.395535\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8790.00 0.304512 0.152256 0.988341i \(-0.451346\pi\)
0.152256 + 0.988341i \(0.451346\pi\)
\(942\) 0 0
\(943\) 1512.00 0.0522137
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 19104.0 0.655540 0.327770 0.944758i \(-0.393703\pi\)
0.327770 + 0.944758i \(0.393703\pi\)
\(948\) 0 0
\(949\) −3220.00 −0.110143
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −6294.00 −0.213938 −0.106969 0.994262i \(-0.534115\pi\)
−0.106969 + 0.994262i \(0.534115\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2016.00 −0.0678832
\(960\) 0 0
\(961\) −24607.0 −0.825988
\(962\) 0 0
\(963\) −10692.0 −0.357783
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 34328.0 1.14159 0.570793 0.821094i \(-0.306636\pi\)
0.570793 + 0.821094i \(0.306636\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −23700.0 −0.783284 −0.391642 0.920118i \(-0.628093\pi\)
−0.391642 + 0.920118i \(0.628093\pi\)
\(972\) 0 0
\(973\) 40896.0 1.34745
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −30026.0 −0.983231 −0.491616 0.870812i \(-0.663593\pi\)
−0.491616 + 0.870812i \(0.663593\pi\)
\(978\) 0 0
\(979\) 66.0000 0.00215462
\(980\) 0 0
\(981\) 1566.00 0.0509669
\(982\) 0 0
\(983\) 34572.0 1.12175 0.560873 0.827902i \(-0.310466\pi\)
0.560873 + 0.827902i \(0.310466\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 32592.0 1.04789
\(990\) 0 0
\(991\) −36824.0 −1.18038 −0.590188 0.807266i \(-0.700946\pi\)
−0.590188 + 0.807266i \(0.700946\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −25402.0 −0.806910 −0.403455 0.914999i \(-0.632191\pi\)
−0.403455 + 0.914999i \(0.632191\pi\)
\(998\) 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 2200.4.a.e.1.1 1
5.4 even 2 440.4.a.c.1.1 1
20.19 odd 2 880.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.4.a.c.1.1 1 5.4 even 2
880.4.a.i.1.1 1 20.19 odd 2
2200.4.a.e.1.1 1 1.1 even 1 trivial