Properties

Label 2496.4.a.d.1.1
Level $2496$
Weight $4$
Character 2496.1
Self dual yes
Analytic conductor $147.269$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2496,4,Mod(1,2496)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2496, 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("2496.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2496.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: \(147.268767374\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 156)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2496.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} +2.00000 q^{5} -32.0000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} +2.00000 q^{5} -32.0000 q^{7} +9.00000 q^{9} +68.0000 q^{11} -13.0000 q^{13} -6.00000 q^{15} -14.0000 q^{17} -4.00000 q^{19} +96.0000 q^{21} +72.0000 q^{23} -121.000 q^{25} -27.0000 q^{27} -102.000 q^{29} -136.000 q^{31} -204.000 q^{33} -64.0000 q^{35} +386.000 q^{37} +39.0000 q^{39} +250.000 q^{41} +140.000 q^{43} +18.0000 q^{45} -296.000 q^{47} +681.000 q^{49} +42.0000 q^{51} -526.000 q^{53} +136.000 q^{55} +12.0000 q^{57} -332.000 q^{59} +410.000 q^{61} -288.000 q^{63} -26.0000 q^{65} -596.000 q^{67} -216.000 q^{69} -880.000 q^{71} +506.000 q^{73} +363.000 q^{75} -2176.00 q^{77} -640.000 q^{79} +81.0000 q^{81} -1380.00 q^{83} -28.0000 q^{85} +306.000 q^{87} +1450.00 q^{89} +416.000 q^{91} +408.000 q^{93} -8.00000 q^{95} -446.000 q^{97} +612.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) 2.00000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) −32.0000 −1.72784 −0.863919 0.503631i \(-0.831997\pi\)
−0.863919 + 0.503631i \(0.831997\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 68.0000 1.86389 0.931944 0.362602i \(-0.118111\pi\)
0.931944 + 0.362602i \(0.118111\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) −6.00000 −0.103280
\(16\) 0 0
\(17\) −14.0000 −0.199735 −0.0998676 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) 96.0000 0.997567
\(22\) 0 0
\(23\) 72.0000 0.652741 0.326370 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −102.000 −0.653135 −0.326568 0.945174i \(-0.605892\pi\)
−0.326568 + 0.945174i \(0.605892\pi\)
\(30\) 0 0
\(31\) −136.000 −0.787946 −0.393973 0.919122i \(-0.628900\pi\)
−0.393973 + 0.919122i \(0.628900\pi\)
\(32\) 0 0
\(33\) −204.000 −1.07612
\(34\) 0 0
\(35\) −64.0000 −0.309085
\(36\) 0 0
\(37\) 386.000 1.71508 0.857541 0.514416i \(-0.171991\pi\)
0.857541 + 0.514416i \(0.171991\pi\)
\(38\) 0 0
\(39\) 39.0000 0.160128
\(40\) 0 0
\(41\) 250.000 0.952279 0.476140 0.879370i \(-0.342036\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(42\) 0 0
\(43\) 140.000 0.496507 0.248253 0.968695i \(-0.420143\pi\)
0.248253 + 0.968695i \(0.420143\pi\)
\(44\) 0 0
\(45\) 18.0000 0.0596285
\(46\) 0 0
\(47\) −296.000 −0.918639 −0.459320 0.888271i \(-0.651907\pi\)
−0.459320 + 0.888271i \(0.651907\pi\)
\(48\) 0 0
\(49\) 681.000 1.98542
\(50\) 0 0
\(51\) 42.0000 0.115317
\(52\) 0 0
\(53\) −526.000 −1.36324 −0.681619 0.731707i \(-0.738724\pi\)
−0.681619 + 0.731707i \(0.738724\pi\)
\(54\) 0 0
\(55\) 136.000 0.333422
\(56\) 0 0
\(57\) 12.0000 0.0278849
\(58\) 0 0
\(59\) −332.000 −0.732588 −0.366294 0.930499i \(-0.619374\pi\)
−0.366294 + 0.930499i \(0.619374\pi\)
\(60\) 0 0
\(61\) 410.000 0.860576 0.430288 0.902692i \(-0.358412\pi\)
0.430288 + 0.902692i \(0.358412\pi\)
\(62\) 0 0
\(63\) −288.000 −0.575946
\(64\) 0 0
\(65\) −26.0000 −0.0496139
\(66\) 0 0
\(67\) −596.000 −1.08676 −0.543381 0.839487i \(-0.682856\pi\)
−0.543381 + 0.839487i \(0.682856\pi\)
\(68\) 0 0
\(69\) −216.000 −0.376860
\(70\) 0 0
\(71\) −880.000 −1.47094 −0.735470 0.677557i \(-0.763039\pi\)
−0.735470 + 0.677557i \(0.763039\pi\)
\(72\) 0 0
\(73\) 506.000 0.811272 0.405636 0.914035i \(-0.367050\pi\)
0.405636 + 0.914035i \(0.367050\pi\)
\(74\) 0 0
\(75\) 363.000 0.558875
\(76\) 0 0
\(77\) −2176.00 −3.22050
\(78\) 0 0
\(79\) −640.000 −0.911464 −0.455732 0.890117i \(-0.650622\pi\)
−0.455732 + 0.890117i \(0.650622\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −1380.00 −1.82500 −0.912498 0.409081i \(-0.865849\pi\)
−0.912498 + 0.409081i \(0.865849\pi\)
\(84\) 0 0
\(85\) −28.0000 −0.0357297
\(86\) 0 0
\(87\) 306.000 0.377088
\(88\) 0 0
\(89\) 1450.00 1.72696 0.863481 0.504381i \(-0.168279\pi\)
0.863481 + 0.504381i \(0.168279\pi\)
\(90\) 0 0
\(91\) 416.000 0.479216
\(92\) 0 0
\(93\) 408.000 0.454921
\(94\) 0 0
\(95\) −8.00000 −0.00863982
\(96\) 0 0
\(97\) −446.000 −0.466850 −0.233425 0.972375i \(-0.574993\pi\)
−0.233425 + 0.972375i \(0.574993\pi\)
\(98\) 0 0
\(99\) 612.000 0.621296
\(100\) 0 0
\(101\) 610.000 0.600963 0.300482 0.953788i \(-0.402853\pi\)
0.300482 + 0.953788i \(0.402853\pi\)
\(102\) 0 0
\(103\) −1352.00 −1.29336 −0.646682 0.762760i \(-0.723844\pi\)
−0.646682 + 0.762760i \(0.723844\pi\)
\(104\) 0 0
\(105\) 192.000 0.178450
\(106\) 0 0
\(107\) 732.000 0.661356 0.330678 0.943744i \(-0.392723\pi\)
0.330678 + 0.943744i \(0.392723\pi\)
\(108\) 0 0
\(109\) 1514.00 1.33041 0.665206 0.746660i \(-0.268344\pi\)
0.665206 + 0.746660i \(0.268344\pi\)
\(110\) 0 0
\(111\) −1158.00 −0.990203
\(112\) 0 0
\(113\) −1518.00 −1.26373 −0.631865 0.775079i \(-0.717710\pi\)
−0.631865 + 0.775079i \(0.717710\pi\)
\(114\) 0 0
\(115\) 144.000 0.116766
\(116\) 0 0
\(117\) −117.000 −0.0924500
\(118\) 0 0
\(119\) 448.000 0.345110
\(120\) 0 0
\(121\) 3293.00 2.47408
\(122\) 0 0
\(123\) −750.000 −0.549799
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) −96.0000 −0.0670758 −0.0335379 0.999437i \(-0.510677\pi\)
−0.0335379 + 0.999437i \(0.510677\pi\)
\(128\) 0 0
\(129\) −420.000 −0.286658
\(130\) 0 0
\(131\) 2548.00 1.69939 0.849694 0.527276i \(-0.176787\pi\)
0.849694 + 0.527276i \(0.176787\pi\)
\(132\) 0 0
\(133\) 128.000 0.0834512
\(134\) 0 0
\(135\) −54.0000 −0.0344265
\(136\) 0 0
\(137\) −230.000 −0.143432 −0.0717162 0.997425i \(-0.522848\pi\)
−0.0717162 + 0.997425i \(0.522848\pi\)
\(138\) 0 0
\(139\) −516.000 −0.314867 −0.157434 0.987530i \(-0.550322\pi\)
−0.157434 + 0.987530i \(0.550322\pi\)
\(140\) 0 0
\(141\) 888.000 0.530377
\(142\) 0 0
\(143\) −884.000 −0.516950
\(144\) 0 0
\(145\) −204.000 −0.116836
\(146\) 0 0
\(147\) −2043.00 −1.14628
\(148\) 0 0
\(149\) 1842.00 1.01277 0.506384 0.862308i \(-0.330982\pi\)
0.506384 + 0.862308i \(0.330982\pi\)
\(150\) 0 0
\(151\) −528.000 −0.284556 −0.142278 0.989827i \(-0.545443\pi\)
−0.142278 + 0.989827i \(0.545443\pi\)
\(152\) 0 0
\(153\) −126.000 −0.0665784
\(154\) 0 0
\(155\) −272.000 −0.140952
\(156\) 0 0
\(157\) 1306.00 0.663886 0.331943 0.943299i \(-0.392296\pi\)
0.331943 + 0.943299i \(0.392296\pi\)
\(158\) 0 0
\(159\) 1578.00 0.787066
\(160\) 0 0
\(161\) −2304.00 −1.12783
\(162\) 0 0
\(163\) 3772.00 1.81255 0.906276 0.422687i \(-0.138913\pi\)
0.906276 + 0.422687i \(0.138913\pi\)
\(164\) 0 0
\(165\) −408.000 −0.192502
\(166\) 0 0
\(167\) 384.000 0.177933 0.0889665 0.996035i \(-0.471644\pi\)
0.0889665 + 0.996035i \(0.471644\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) −36.0000 −0.0160993
\(172\) 0 0
\(173\) −1462.00 −0.642508 −0.321254 0.946993i \(-0.604104\pi\)
−0.321254 + 0.946993i \(0.604104\pi\)
\(174\) 0 0
\(175\) 3872.00 1.67255
\(176\) 0 0
\(177\) 996.000 0.422960
\(178\) 0 0
\(179\) 1332.00 0.556192 0.278096 0.960553i \(-0.410297\pi\)
0.278096 + 0.960553i \(0.410297\pi\)
\(180\) 0 0
\(181\) −2030.00 −0.833639 −0.416820 0.908989i \(-0.636855\pi\)
−0.416820 + 0.908989i \(0.636855\pi\)
\(182\) 0 0
\(183\) −1230.00 −0.496854
\(184\) 0 0
\(185\) 772.000 0.306803
\(186\) 0 0
\(187\) −952.000 −0.372284
\(188\) 0 0
\(189\) 864.000 0.332522
\(190\) 0 0
\(191\) −16.0000 −0.00606136 −0.00303068 0.999995i \(-0.500965\pi\)
−0.00303068 + 0.999995i \(0.500965\pi\)
\(192\) 0 0
\(193\) −2078.00 −0.775014 −0.387507 0.921867i \(-0.626664\pi\)
−0.387507 + 0.921867i \(0.626664\pi\)
\(194\) 0 0
\(195\) 78.0000 0.0286446
\(196\) 0 0
\(197\) −3486.00 −1.26075 −0.630374 0.776292i \(-0.717098\pi\)
−0.630374 + 0.776292i \(0.717098\pi\)
\(198\) 0 0
\(199\) 568.000 0.202334 0.101167 0.994869i \(-0.467742\pi\)
0.101167 + 0.994869i \(0.467742\pi\)
\(200\) 0 0
\(201\) 1788.00 0.627442
\(202\) 0 0
\(203\) 3264.00 1.12851
\(204\) 0 0
\(205\) 500.000 0.170349
\(206\) 0 0
\(207\) 648.000 0.217580
\(208\) 0 0
\(209\) −272.000 −0.0900222
\(210\) 0 0
\(211\) −3804.00 −1.24113 −0.620564 0.784156i \(-0.713096\pi\)
−0.620564 + 0.784156i \(0.713096\pi\)
\(212\) 0 0
\(213\) 2640.00 0.849248
\(214\) 0 0
\(215\) 280.000 0.0888179
\(216\) 0 0
\(217\) 4352.00 1.36144
\(218\) 0 0
\(219\) −1518.00 −0.468388
\(220\) 0 0
\(221\) 182.000 0.0553966
\(222\) 0 0
\(223\) 5912.00 1.77532 0.887661 0.460498i \(-0.152329\pi\)
0.887661 + 0.460498i \(0.152329\pi\)
\(224\) 0 0
\(225\) −1089.00 −0.322667
\(226\) 0 0
\(227\) 3308.00 0.967223 0.483612 0.875283i \(-0.339325\pi\)
0.483612 + 0.875283i \(0.339325\pi\)
\(228\) 0 0
\(229\) 6050.00 1.74583 0.872915 0.487872i \(-0.162227\pi\)
0.872915 + 0.487872i \(0.162227\pi\)
\(230\) 0 0
\(231\) 6528.00 1.85935
\(232\) 0 0
\(233\) 4794.00 1.34792 0.673960 0.738768i \(-0.264592\pi\)
0.673960 + 0.738768i \(0.264592\pi\)
\(234\) 0 0
\(235\) −592.000 −0.164331
\(236\) 0 0
\(237\) 1920.00 0.526234
\(238\) 0 0
\(239\) −4440.00 −1.20167 −0.600836 0.799372i \(-0.705166\pi\)
−0.600836 + 0.799372i \(0.705166\pi\)
\(240\) 0 0
\(241\) 1330.00 0.355489 0.177744 0.984077i \(-0.443120\pi\)
0.177744 + 0.984077i \(0.443120\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 1362.00 0.355163
\(246\) 0 0
\(247\) 52.0000 0.0133955
\(248\) 0 0
\(249\) 4140.00 1.05366
\(250\) 0 0
\(251\) 5116.00 1.28653 0.643265 0.765644i \(-0.277579\pi\)
0.643265 + 0.765644i \(0.277579\pi\)
\(252\) 0 0
\(253\) 4896.00 1.21664
\(254\) 0 0
\(255\) 84.0000 0.0206286
\(256\) 0 0
\(257\) 642.000 0.155824 0.0779122 0.996960i \(-0.475175\pi\)
0.0779122 + 0.996960i \(0.475175\pi\)
\(258\) 0 0
\(259\) −12352.0 −2.96338
\(260\) 0 0
\(261\) −918.000 −0.217712
\(262\) 0 0
\(263\) 4264.00 0.999732 0.499866 0.866103i \(-0.333383\pi\)
0.499866 + 0.866103i \(0.333383\pi\)
\(264\) 0 0
\(265\) −1052.00 −0.243864
\(266\) 0 0
\(267\) −4350.00 −0.997062
\(268\) 0 0
\(269\) 3850.00 0.872634 0.436317 0.899793i \(-0.356283\pi\)
0.436317 + 0.899793i \(0.356283\pi\)
\(270\) 0 0
\(271\) 2936.00 0.658115 0.329058 0.944310i \(-0.393269\pi\)
0.329058 + 0.944310i \(0.393269\pi\)
\(272\) 0 0
\(273\) −1248.00 −0.276675
\(274\) 0 0
\(275\) −8228.00 −1.80424
\(276\) 0 0
\(277\) 2066.00 0.448137 0.224068 0.974573i \(-0.428066\pi\)
0.224068 + 0.974573i \(0.428066\pi\)
\(278\) 0 0
\(279\) −1224.00 −0.262649
\(280\) 0 0
\(281\) −214.000 −0.0454312 −0.0227156 0.999742i \(-0.507231\pi\)
−0.0227156 + 0.999742i \(0.507231\pi\)
\(282\) 0 0
\(283\) 2620.00 0.550328 0.275164 0.961397i \(-0.411268\pi\)
0.275164 + 0.961397i \(0.411268\pi\)
\(284\) 0 0
\(285\) 24.0000 0.00498820
\(286\) 0 0
\(287\) −8000.00 −1.64538
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) 0 0
\(291\) 1338.00 0.269536
\(292\) 0 0
\(293\) 1154.00 0.230094 0.115047 0.993360i \(-0.463298\pi\)
0.115047 + 0.993360i \(0.463298\pi\)
\(294\) 0 0
\(295\) −664.000 −0.131049
\(296\) 0 0
\(297\) −1836.00 −0.358705
\(298\) 0 0
\(299\) −936.000 −0.181038
\(300\) 0 0
\(301\) −4480.00 −0.857883
\(302\) 0 0
\(303\) −1830.00 −0.346966
\(304\) 0 0
\(305\) 820.000 0.153944
\(306\) 0 0
\(307\) 4076.00 0.757751 0.378876 0.925448i \(-0.376311\pi\)
0.378876 + 0.925448i \(0.376311\pi\)
\(308\) 0 0
\(309\) 4056.00 0.746724
\(310\) 0 0
\(311\) −6456.00 −1.17713 −0.588563 0.808451i \(-0.700306\pi\)
−0.588563 + 0.808451i \(0.700306\pi\)
\(312\) 0 0
\(313\) −5526.00 −0.997917 −0.498958 0.866626i \(-0.666284\pi\)
−0.498958 + 0.866626i \(0.666284\pi\)
\(314\) 0 0
\(315\) −576.000 −0.103028
\(316\) 0 0
\(317\) 10458.0 1.85293 0.926467 0.376377i \(-0.122830\pi\)
0.926467 + 0.376377i \(0.122830\pi\)
\(318\) 0 0
\(319\) −6936.00 −1.21737
\(320\) 0 0
\(321\) −2196.00 −0.381834
\(322\) 0 0
\(323\) 56.0000 0.00964682
\(324\) 0 0
\(325\) 1573.00 0.268475
\(326\) 0 0
\(327\) −4542.00 −0.768114
\(328\) 0 0
\(329\) 9472.00 1.58726
\(330\) 0 0
\(331\) −2348.00 −0.389903 −0.194951 0.980813i \(-0.562455\pi\)
−0.194951 + 0.980813i \(0.562455\pi\)
\(332\) 0 0
\(333\) 3474.00 0.571694
\(334\) 0 0
\(335\) −1192.00 −0.194406
\(336\) 0 0
\(337\) 5298.00 0.856381 0.428191 0.903688i \(-0.359151\pi\)
0.428191 + 0.903688i \(0.359151\pi\)
\(338\) 0 0
\(339\) 4554.00 0.729615
\(340\) 0 0
\(341\) −9248.00 −1.46864
\(342\) 0 0
\(343\) −10816.0 −1.70265
\(344\) 0 0
\(345\) −432.000 −0.0674148
\(346\) 0 0
\(347\) −9876.00 −1.52787 −0.763936 0.645292i \(-0.776736\pi\)
−0.763936 + 0.645292i \(0.776736\pi\)
\(348\) 0 0
\(349\) 5370.00 0.823638 0.411819 0.911266i \(-0.364894\pi\)
0.411819 + 0.911266i \(0.364894\pi\)
\(350\) 0 0
\(351\) 351.000 0.0533761
\(352\) 0 0
\(353\) 7330.00 1.10520 0.552601 0.833446i \(-0.313635\pi\)
0.552601 + 0.833446i \(0.313635\pi\)
\(354\) 0 0
\(355\) −1760.00 −0.263130
\(356\) 0 0
\(357\) −1344.00 −0.199249
\(358\) 0 0
\(359\) 7488.00 1.10084 0.550420 0.834888i \(-0.314468\pi\)
0.550420 + 0.834888i \(0.314468\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) −9879.00 −1.42841
\(364\) 0 0
\(365\) 1012.00 0.145125
\(366\) 0 0
\(367\) 1504.00 0.213919 0.106959 0.994263i \(-0.465889\pi\)
0.106959 + 0.994263i \(0.465889\pi\)
\(368\) 0 0
\(369\) 2250.00 0.317426
\(370\) 0 0
\(371\) 16832.0 2.35546
\(372\) 0 0
\(373\) −6702.00 −0.930339 −0.465169 0.885222i \(-0.654007\pi\)
−0.465169 + 0.885222i \(0.654007\pi\)
\(374\) 0 0
\(375\) 1476.00 0.203254
\(376\) 0 0
\(377\) 1326.00 0.181147
\(378\) 0 0
\(379\) 5700.00 0.772531 0.386266 0.922388i \(-0.373765\pi\)
0.386266 + 0.922388i \(0.373765\pi\)
\(380\) 0 0
\(381\) 288.000 0.0387262
\(382\) 0 0
\(383\) 2328.00 0.310588 0.155294 0.987868i \(-0.450367\pi\)
0.155294 + 0.987868i \(0.450367\pi\)
\(384\) 0 0
\(385\) −4352.00 −0.576100
\(386\) 0 0
\(387\) 1260.00 0.165502
\(388\) 0 0
\(389\) 11554.0 1.50594 0.752971 0.658054i \(-0.228620\pi\)
0.752971 + 0.658054i \(0.228620\pi\)
\(390\) 0 0
\(391\) −1008.00 −0.130375
\(392\) 0 0
\(393\) −7644.00 −0.981142
\(394\) 0 0
\(395\) −1280.00 −0.163048
\(396\) 0 0
\(397\) −6486.00 −0.819957 −0.409979 0.912095i \(-0.634464\pi\)
−0.409979 + 0.912095i \(0.634464\pi\)
\(398\) 0 0
\(399\) −384.000 −0.0481806
\(400\) 0 0
\(401\) 7698.00 0.958653 0.479326 0.877637i \(-0.340881\pi\)
0.479326 + 0.877637i \(0.340881\pi\)
\(402\) 0 0
\(403\) 1768.00 0.218537
\(404\) 0 0
\(405\) 162.000 0.0198762
\(406\) 0 0
\(407\) 26248.0 3.19672
\(408\) 0 0
\(409\) 3338.00 0.403554 0.201777 0.979432i \(-0.435328\pi\)
0.201777 + 0.979432i \(0.435328\pi\)
\(410\) 0 0
\(411\) 690.000 0.0828107
\(412\) 0 0
\(413\) 10624.0 1.26579
\(414\) 0 0
\(415\) −2760.00 −0.326465
\(416\) 0 0
\(417\) 1548.00 0.181789
\(418\) 0 0
\(419\) 52.0000 0.00606293 0.00303146 0.999995i \(-0.499035\pi\)
0.00303146 + 0.999995i \(0.499035\pi\)
\(420\) 0 0
\(421\) 5858.00 0.678151 0.339075 0.940759i \(-0.389886\pi\)
0.339075 + 0.940759i \(0.389886\pi\)
\(422\) 0 0
\(423\) −2664.00 −0.306213
\(424\) 0 0
\(425\) 1694.00 0.193344
\(426\) 0 0
\(427\) −13120.0 −1.48694
\(428\) 0 0
\(429\) 2652.00 0.298461
\(430\) 0 0
\(431\) 8840.00 0.987953 0.493977 0.869475i \(-0.335543\pi\)
0.493977 + 0.869475i \(0.335543\pi\)
\(432\) 0 0
\(433\) 11346.0 1.25925 0.629624 0.776900i \(-0.283209\pi\)
0.629624 + 0.776900i \(0.283209\pi\)
\(434\) 0 0
\(435\) 612.000 0.0674555
\(436\) 0 0
\(437\) −288.000 −0.0315261
\(438\) 0 0
\(439\) 16456.0 1.78907 0.894535 0.446997i \(-0.147507\pi\)
0.894535 + 0.446997i \(0.147507\pi\)
\(440\) 0 0
\(441\) 6129.00 0.661808
\(442\) 0 0
\(443\) 3788.00 0.406260 0.203130 0.979152i \(-0.434889\pi\)
0.203130 + 0.979152i \(0.434889\pi\)
\(444\) 0 0
\(445\) 2900.00 0.308929
\(446\) 0 0
\(447\) −5526.00 −0.584722
\(448\) 0 0
\(449\) 546.000 0.0573883 0.0286941 0.999588i \(-0.490865\pi\)
0.0286941 + 0.999588i \(0.490865\pi\)
\(450\) 0 0
\(451\) 17000.0 1.77494
\(452\) 0 0
\(453\) 1584.00 0.164289
\(454\) 0 0
\(455\) 832.000 0.0857248
\(456\) 0 0
\(457\) 3546.00 0.362965 0.181482 0.983394i \(-0.441910\pi\)
0.181482 + 0.983394i \(0.441910\pi\)
\(458\) 0 0
\(459\) 378.000 0.0384391
\(460\) 0 0
\(461\) −12918.0 −1.30510 −0.652550 0.757746i \(-0.726301\pi\)
−0.652550 + 0.757746i \(0.726301\pi\)
\(462\) 0 0
\(463\) 18328.0 1.83969 0.919843 0.392287i \(-0.128316\pi\)
0.919843 + 0.392287i \(0.128316\pi\)
\(464\) 0 0
\(465\) 816.000 0.0813787
\(466\) 0 0
\(467\) −11980.0 −1.18708 −0.593542 0.804803i \(-0.702271\pi\)
−0.593542 + 0.804803i \(0.702271\pi\)
\(468\) 0 0
\(469\) 19072.0 1.87775
\(470\) 0 0
\(471\) −3918.00 −0.383295
\(472\) 0 0
\(473\) 9520.00 0.925434
\(474\) 0 0
\(475\) 484.000 0.0467525
\(476\) 0 0
\(477\) −4734.00 −0.454413
\(478\) 0 0
\(479\) −12344.0 −1.17748 −0.588739 0.808323i \(-0.700375\pi\)
−0.588739 + 0.808323i \(0.700375\pi\)
\(480\) 0 0
\(481\) −5018.00 −0.475678
\(482\) 0 0
\(483\) 6912.00 0.651153
\(484\) 0 0
\(485\) −892.000 −0.0835126
\(486\) 0 0
\(487\) −80.0000 −0.00744383 −0.00372192 0.999993i \(-0.501185\pi\)
−0.00372192 + 0.999993i \(0.501185\pi\)
\(488\) 0 0
\(489\) −11316.0 −1.04648
\(490\) 0 0
\(491\) 15660.0 1.43936 0.719680 0.694306i \(-0.244288\pi\)
0.719680 + 0.694306i \(0.244288\pi\)
\(492\) 0 0
\(493\) 1428.00 0.130454
\(494\) 0 0
\(495\) 1224.00 0.111141
\(496\) 0 0
\(497\) 28160.0 2.54155
\(498\) 0 0
\(499\) 60.0000 0.00538270 0.00269135 0.999996i \(-0.499143\pi\)
0.00269135 + 0.999996i \(0.499143\pi\)
\(500\) 0 0
\(501\) −1152.00 −0.102730
\(502\) 0 0
\(503\) 12248.0 1.08571 0.542854 0.839827i \(-0.317344\pi\)
0.542854 + 0.839827i \(0.317344\pi\)
\(504\) 0 0
\(505\) 1220.00 0.107504
\(506\) 0 0
\(507\) −507.000 −0.0444116
\(508\) 0 0
\(509\) 90.0000 0.00783729 0.00391864 0.999992i \(-0.498753\pi\)
0.00391864 + 0.999992i \(0.498753\pi\)
\(510\) 0 0
\(511\) −16192.0 −1.40175
\(512\) 0 0
\(513\) 108.000 0.00929496
\(514\) 0 0
\(515\) −2704.00 −0.231364
\(516\) 0 0
\(517\) −20128.0 −1.71224
\(518\) 0 0
\(519\) 4386.00 0.370952
\(520\) 0 0
\(521\) 9818.00 0.825594 0.412797 0.910823i \(-0.364552\pi\)
0.412797 + 0.910823i \(0.364552\pi\)
\(522\) 0 0
\(523\) 20252.0 1.69323 0.846614 0.532208i \(-0.178637\pi\)
0.846614 + 0.532208i \(0.178637\pi\)
\(524\) 0 0
\(525\) −11616.0 −0.965645
\(526\) 0 0
\(527\) 1904.00 0.157381
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) 0 0
\(531\) −2988.00 −0.244196
\(532\) 0 0
\(533\) −3250.00 −0.264115
\(534\) 0 0
\(535\) 1464.00 0.118307
\(536\) 0 0
\(537\) −3996.00 −0.321118
\(538\) 0 0
\(539\) 46308.0 3.70061
\(540\) 0 0
\(541\) 12634.0 1.00403 0.502013 0.864860i \(-0.332593\pi\)
0.502013 + 0.864860i \(0.332593\pi\)
\(542\) 0 0
\(543\) 6090.00 0.481302
\(544\) 0 0
\(545\) 3028.00 0.237991
\(546\) 0 0
\(547\) −11756.0 −0.918922 −0.459461 0.888198i \(-0.651957\pi\)
−0.459461 + 0.888198i \(0.651957\pi\)
\(548\) 0 0
\(549\) 3690.00 0.286859
\(550\) 0 0
\(551\) 408.000 0.0315452
\(552\) 0 0
\(553\) 20480.0 1.57486
\(554\) 0 0
\(555\) −2316.00 −0.177133
\(556\) 0 0
\(557\) −17622.0 −1.34052 −0.670259 0.742128i \(-0.733817\pi\)
−0.670259 + 0.742128i \(0.733817\pi\)
\(558\) 0 0
\(559\) −1820.00 −0.137706
\(560\) 0 0
\(561\) 2856.00 0.214938
\(562\) 0 0
\(563\) 23092.0 1.72862 0.864309 0.502961i \(-0.167756\pi\)
0.864309 + 0.502961i \(0.167756\pi\)
\(564\) 0 0
\(565\) −3036.00 −0.226063
\(566\) 0 0
\(567\) −2592.00 −0.191982
\(568\) 0 0
\(569\) −1302.00 −0.0959274 −0.0479637 0.998849i \(-0.515273\pi\)
−0.0479637 + 0.998849i \(0.515273\pi\)
\(570\) 0 0
\(571\) −24868.0 −1.82258 −0.911290 0.411765i \(-0.864913\pi\)
−0.911290 + 0.411765i \(0.864913\pi\)
\(572\) 0 0
\(573\) 48.0000 0.00349953
\(574\) 0 0
\(575\) −8712.00 −0.631853
\(576\) 0 0
\(577\) 2562.00 0.184848 0.0924241 0.995720i \(-0.470538\pi\)
0.0924241 + 0.995720i \(0.470538\pi\)
\(578\) 0 0
\(579\) 6234.00 0.447455
\(580\) 0 0
\(581\) 44160.0 3.15330
\(582\) 0 0
\(583\) −35768.0 −2.54092
\(584\) 0 0
\(585\) −234.000 −0.0165380
\(586\) 0 0
\(587\) −13484.0 −0.948116 −0.474058 0.880494i \(-0.657211\pi\)
−0.474058 + 0.880494i \(0.657211\pi\)
\(588\) 0 0
\(589\) 544.000 0.0380562
\(590\) 0 0
\(591\) 10458.0 0.727893
\(592\) 0 0
\(593\) −16974.0 −1.17544 −0.587722 0.809063i \(-0.699975\pi\)
−0.587722 + 0.809063i \(0.699975\pi\)
\(594\) 0 0
\(595\) 896.000 0.0617352
\(596\) 0 0
\(597\) −1704.00 −0.116818
\(598\) 0 0
\(599\) 3864.00 0.263571 0.131785 0.991278i \(-0.457929\pi\)
0.131785 + 0.991278i \(0.457929\pi\)
\(600\) 0 0
\(601\) 17546.0 1.19088 0.595438 0.803401i \(-0.296979\pi\)
0.595438 + 0.803401i \(0.296979\pi\)
\(602\) 0 0
\(603\) −5364.00 −0.362254
\(604\) 0 0
\(605\) 6586.00 0.442577
\(606\) 0 0
\(607\) 9296.00 0.621603 0.310801 0.950475i \(-0.399403\pi\)
0.310801 + 0.950475i \(0.399403\pi\)
\(608\) 0 0
\(609\) −9792.00 −0.651547
\(610\) 0 0
\(611\) 3848.00 0.254785
\(612\) 0 0
\(613\) 6914.00 0.455553 0.227776 0.973713i \(-0.426854\pi\)
0.227776 + 0.973713i \(0.426854\pi\)
\(614\) 0 0
\(615\) −1500.00 −0.0983510
\(616\) 0 0
\(617\) −25446.0 −1.66032 −0.830160 0.557525i \(-0.811751\pi\)
−0.830160 + 0.557525i \(0.811751\pi\)
\(618\) 0 0
\(619\) 11236.0 0.729585 0.364792 0.931089i \(-0.381140\pi\)
0.364792 + 0.931089i \(0.381140\pi\)
\(620\) 0 0
\(621\) −1944.00 −0.125620
\(622\) 0 0
\(623\) −46400.0 −2.98391
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 816.000 0.0519743
\(628\) 0 0
\(629\) −5404.00 −0.342562
\(630\) 0 0
\(631\) −29424.0 −1.85634 −0.928170 0.372156i \(-0.878619\pi\)
−0.928170 + 0.372156i \(0.878619\pi\)
\(632\) 0 0
\(633\) 11412.0 0.716566
\(634\) 0 0
\(635\) −192.000 −0.0119989
\(636\) 0 0
\(637\) −8853.00 −0.550657
\(638\) 0 0
\(639\) −7920.00 −0.490314
\(640\) 0 0
\(641\) −5054.00 −0.311421 −0.155711 0.987803i \(-0.549767\pi\)
−0.155711 + 0.987803i \(0.549767\pi\)
\(642\) 0 0
\(643\) 1132.00 0.0694273 0.0347136 0.999397i \(-0.488948\pi\)
0.0347136 + 0.999397i \(0.488948\pi\)
\(644\) 0 0
\(645\) −840.000 −0.0512790
\(646\) 0 0
\(647\) 1464.00 0.0889579 0.0444790 0.999010i \(-0.485837\pi\)
0.0444790 + 0.999010i \(0.485837\pi\)
\(648\) 0 0
\(649\) −22576.0 −1.36546
\(650\) 0 0
\(651\) −13056.0 −0.786029
\(652\) 0 0
\(653\) −5494.00 −0.329245 −0.164622 0.986357i \(-0.552641\pi\)
−0.164622 + 0.986357i \(0.552641\pi\)
\(654\) 0 0
\(655\) 5096.00 0.303996
\(656\) 0 0
\(657\) 4554.00 0.270424
\(658\) 0 0
\(659\) −11580.0 −0.684511 −0.342256 0.939607i \(-0.611191\pi\)
−0.342256 + 0.939607i \(0.611191\pi\)
\(660\) 0 0
\(661\) 1298.00 0.0763787 0.0381894 0.999271i \(-0.487841\pi\)
0.0381894 + 0.999271i \(0.487841\pi\)
\(662\) 0 0
\(663\) −546.000 −0.0319832
\(664\) 0 0
\(665\) 256.000 0.0149282
\(666\) 0 0
\(667\) −7344.00 −0.426328
\(668\) 0 0
\(669\) −17736.0 −1.02498
\(670\) 0 0
\(671\) 27880.0 1.60402
\(672\) 0 0
\(673\) 16162.0 0.925705 0.462852 0.886435i \(-0.346826\pi\)
0.462852 + 0.886435i \(0.346826\pi\)
\(674\) 0 0
\(675\) 3267.00 0.186292
\(676\) 0 0
\(677\) 9890.00 0.561453 0.280726 0.959788i \(-0.409425\pi\)
0.280726 + 0.959788i \(0.409425\pi\)
\(678\) 0 0
\(679\) 14272.0 0.806641
\(680\) 0 0
\(681\) −9924.00 −0.558427
\(682\) 0 0
\(683\) −27100.0 −1.51823 −0.759116 0.650955i \(-0.774369\pi\)
−0.759116 + 0.650955i \(0.774369\pi\)
\(684\) 0 0
\(685\) −460.000 −0.0256580
\(686\) 0 0
\(687\) −18150.0 −1.00796
\(688\) 0 0
\(689\) 6838.00 0.378094
\(690\) 0 0
\(691\) 11132.0 0.612853 0.306426 0.951894i \(-0.400867\pi\)
0.306426 + 0.951894i \(0.400867\pi\)
\(692\) 0 0
\(693\) −19584.0 −1.07350
\(694\) 0 0
\(695\) −1032.00 −0.0563252
\(696\) 0 0
\(697\) −3500.00 −0.190204
\(698\) 0 0
\(699\) −14382.0 −0.778222
\(700\) 0 0
\(701\) −1862.00 −0.100323 −0.0501617 0.998741i \(-0.515974\pi\)
−0.0501617 + 0.998741i \(0.515974\pi\)
\(702\) 0 0
\(703\) −1544.00 −0.0828351
\(704\) 0 0
\(705\) 1776.00 0.0948766
\(706\) 0 0
\(707\) −19520.0 −1.03837
\(708\) 0 0
\(709\) 7938.00 0.420477 0.210238 0.977650i \(-0.432576\pi\)
0.210238 + 0.977650i \(0.432576\pi\)
\(710\) 0 0
\(711\) −5760.00 −0.303821
\(712\) 0 0
\(713\) −9792.00 −0.514324
\(714\) 0 0
\(715\) −1768.00 −0.0924748
\(716\) 0 0
\(717\) 13320.0 0.693786
\(718\) 0 0
\(719\) −24240.0 −1.25730 −0.628651 0.777688i \(-0.716392\pi\)
−0.628651 + 0.777688i \(0.716392\pi\)
\(720\) 0 0
\(721\) 43264.0 2.23472
\(722\) 0 0
\(723\) −3990.00 −0.205242
\(724\) 0 0
\(725\) 12342.0 0.632235
\(726\) 0 0
\(727\) −13720.0 −0.699927 −0.349963 0.936763i \(-0.613806\pi\)
−0.349963 + 0.936763i \(0.613806\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −1960.00 −0.0991699
\(732\) 0 0
\(733\) −21958.0 −1.10646 −0.553231 0.833028i \(-0.686605\pi\)
−0.553231 + 0.833028i \(0.686605\pi\)
\(734\) 0 0
\(735\) −4086.00 −0.205054
\(736\) 0 0
\(737\) −40528.0 −2.02560
\(738\) 0 0
\(739\) −13348.0 −0.664430 −0.332215 0.943204i \(-0.607796\pi\)
−0.332215 + 0.943204i \(0.607796\pi\)
\(740\) 0 0
\(741\) −156.000 −0.00773388
\(742\) 0 0
\(743\) 20304.0 1.00253 0.501266 0.865293i \(-0.332868\pi\)
0.501266 + 0.865293i \(0.332868\pi\)
\(744\) 0 0
\(745\) 3684.00 0.181170
\(746\) 0 0
\(747\) −12420.0 −0.608332
\(748\) 0 0
\(749\) −23424.0 −1.14272
\(750\) 0 0
\(751\) −3952.00 −0.192025 −0.0960123 0.995380i \(-0.530609\pi\)
−0.0960123 + 0.995380i \(0.530609\pi\)
\(752\) 0 0
\(753\) −15348.0 −0.742779
\(754\) 0 0
\(755\) −1056.00 −0.0509030
\(756\) 0 0
\(757\) 22386.0 1.07481 0.537406 0.843324i \(-0.319404\pi\)
0.537406 + 0.843324i \(0.319404\pi\)
\(758\) 0 0
\(759\) −14688.0 −0.702425
\(760\) 0 0
\(761\) 12458.0 0.593433 0.296716 0.954966i \(-0.404108\pi\)
0.296716 + 0.954966i \(0.404108\pi\)
\(762\) 0 0
\(763\) −48448.0 −2.29874
\(764\) 0 0
\(765\) −252.000 −0.0119099
\(766\) 0 0
\(767\) 4316.00 0.203183
\(768\) 0 0
\(769\) −28126.0 −1.31892 −0.659460 0.751740i \(-0.729215\pi\)
−0.659460 + 0.751740i \(0.729215\pi\)
\(770\) 0 0
\(771\) −1926.00 −0.0899652
\(772\) 0 0
\(773\) 35778.0 1.66474 0.832371 0.554219i \(-0.186983\pi\)
0.832371 + 0.554219i \(0.186983\pi\)
\(774\) 0 0
\(775\) 16456.0 0.762732
\(776\) 0 0
\(777\) 37056.0 1.71091
\(778\) 0 0
\(779\) −1000.00 −0.0459932
\(780\) 0 0
\(781\) −59840.0 −2.74167
\(782\) 0 0
\(783\) 2754.00 0.125696
\(784\) 0 0
\(785\) 2612.00 0.118760
\(786\) 0 0
\(787\) −7252.00 −0.328470 −0.164235 0.986421i \(-0.552516\pi\)
−0.164235 + 0.986421i \(0.552516\pi\)
\(788\) 0 0
\(789\) −12792.0 −0.577196
\(790\) 0 0
\(791\) 48576.0 2.18352
\(792\) 0 0
\(793\) −5330.00 −0.238681
\(794\) 0 0
\(795\) 3156.00 0.140795
\(796\) 0 0
\(797\) −4454.00 −0.197953 −0.0989766 0.995090i \(-0.531557\pi\)
−0.0989766 + 0.995090i \(0.531557\pi\)
\(798\) 0 0
\(799\) 4144.00 0.183485
\(800\) 0 0
\(801\) 13050.0 0.575654
\(802\) 0 0
\(803\) 34408.0 1.51212
\(804\) 0 0
\(805\) −4608.00 −0.201752
\(806\) 0 0
\(807\) −11550.0 −0.503816
\(808\) 0 0
\(809\) −34118.0 −1.48273 −0.741363 0.671104i \(-0.765820\pi\)
−0.741363 + 0.671104i \(0.765820\pi\)
\(810\) 0 0
\(811\) −16428.0 −0.711301 −0.355650 0.934619i \(-0.615741\pi\)
−0.355650 + 0.934619i \(0.615741\pi\)
\(812\) 0 0
\(813\) −8808.00 −0.379963
\(814\) 0 0
\(815\) 7544.00 0.324239
\(816\) 0 0
\(817\) −560.000 −0.0239803
\(818\) 0 0
\(819\) 3744.00 0.159739
\(820\) 0 0
\(821\) 18738.0 0.796542 0.398271 0.917268i \(-0.369610\pi\)
0.398271 + 0.917268i \(0.369610\pi\)
\(822\) 0 0
\(823\) 13928.0 0.589914 0.294957 0.955510i \(-0.404695\pi\)
0.294957 + 0.955510i \(0.404695\pi\)
\(824\) 0 0
\(825\) 24684.0 1.04168
\(826\) 0 0
\(827\) −41804.0 −1.75776 −0.878880 0.477043i \(-0.841709\pi\)
−0.878880 + 0.477043i \(0.841709\pi\)
\(828\) 0 0
\(829\) 43226.0 1.81098 0.905489 0.424369i \(-0.139504\pi\)
0.905489 + 0.424369i \(0.139504\pi\)
\(830\) 0 0
\(831\) −6198.00 −0.258732
\(832\) 0 0
\(833\) −9534.00 −0.396559
\(834\) 0 0
\(835\) 768.000 0.0318296
\(836\) 0 0
\(837\) 3672.00 0.151640
\(838\) 0 0
\(839\) 10240.0 0.421364 0.210682 0.977555i \(-0.432432\pi\)
0.210682 + 0.977555i \(0.432432\pi\)
\(840\) 0 0
\(841\) −13985.0 −0.573414
\(842\) 0 0
\(843\) 642.000 0.0262297
\(844\) 0 0
\(845\) 338.000 0.0137604
\(846\) 0 0
\(847\) −105376. −4.27481
\(848\) 0 0
\(849\) −7860.00 −0.317732
\(850\) 0 0
\(851\) 27792.0 1.11950
\(852\) 0 0
\(853\) 25682.0 1.03087 0.515437 0.856928i \(-0.327630\pi\)
0.515437 + 0.856928i \(0.327630\pi\)
\(854\) 0 0
\(855\) −72.0000 −0.00287994
\(856\) 0 0
\(857\) −21558.0 −0.859285 −0.429643 0.902999i \(-0.641360\pi\)
−0.429643 + 0.902999i \(0.641360\pi\)
\(858\) 0 0
\(859\) 14060.0 0.558465 0.279232 0.960224i \(-0.409920\pi\)
0.279232 + 0.960224i \(0.409920\pi\)
\(860\) 0 0
\(861\) 24000.0 0.949963
\(862\) 0 0
\(863\) 42008.0 1.65697 0.828487 0.560008i \(-0.189202\pi\)
0.828487 + 0.560008i \(0.189202\pi\)
\(864\) 0 0
\(865\) −2924.00 −0.114935
\(866\) 0 0
\(867\) 14151.0 0.554317
\(868\) 0 0
\(869\) −43520.0 −1.69887
\(870\) 0 0
\(871\) 7748.00 0.301413
\(872\) 0 0
\(873\) −4014.00 −0.155617
\(874\) 0 0
\(875\) 15744.0 0.608279
\(876\) 0 0
\(877\) −23734.0 −0.913843 −0.456921 0.889507i \(-0.651048\pi\)
−0.456921 + 0.889507i \(0.651048\pi\)
\(878\) 0 0
\(879\) −3462.00 −0.132845
\(880\) 0 0
\(881\) −37550.0 −1.43597 −0.717986 0.696057i \(-0.754936\pi\)
−0.717986 + 0.696057i \(0.754936\pi\)
\(882\) 0 0
\(883\) −12556.0 −0.478531 −0.239266 0.970954i \(-0.576907\pi\)
−0.239266 + 0.970954i \(0.576907\pi\)
\(884\) 0 0
\(885\) 1992.00 0.0756614
\(886\) 0 0
\(887\) 37368.0 1.41454 0.707269 0.706945i \(-0.249927\pi\)
0.707269 + 0.706945i \(0.249927\pi\)
\(888\) 0 0
\(889\) 3072.00 0.115896
\(890\) 0 0
\(891\) 5508.00 0.207099
\(892\) 0 0
\(893\) 1184.00 0.0443685
\(894\) 0 0
\(895\) 2664.00 0.0994946
\(896\) 0 0
\(897\) 2808.00 0.104522
\(898\) 0 0
\(899\) 13872.0 0.514635
\(900\) 0 0
\(901\) 7364.00 0.272287
\(902\) 0 0
\(903\) 13440.0 0.495299
\(904\) 0 0
\(905\) −4060.00 −0.149126
\(906\) 0 0
\(907\) −33364.0 −1.22143 −0.610713 0.791852i \(-0.709117\pi\)
−0.610713 + 0.791852i \(0.709117\pi\)
\(908\) 0 0
\(909\) 5490.00 0.200321
\(910\) 0 0
\(911\) 50432.0 1.83412 0.917062 0.398745i \(-0.130554\pi\)
0.917062 + 0.398745i \(0.130554\pi\)
\(912\) 0 0
\(913\) −93840.0 −3.40159
\(914\) 0 0
\(915\) −2460.00 −0.0888799
\(916\) 0 0
\(917\) −81536.0 −2.93627
\(918\) 0 0
\(919\) 11864.0 0.425851 0.212926 0.977068i \(-0.431701\pi\)
0.212926 + 0.977068i \(0.431701\pi\)
\(920\) 0 0
\(921\) −12228.0 −0.437488
\(922\) 0 0
\(923\) 11440.0 0.407966
\(924\) 0 0
\(925\) −46706.0 −1.66020
\(926\) 0 0
\(927\) −12168.0 −0.431121
\(928\) 0 0
\(929\) −5950.00 −0.210133 −0.105066 0.994465i \(-0.533505\pi\)
−0.105066 + 0.994465i \(0.533505\pi\)
\(930\) 0 0
\(931\) −2724.00 −0.0958920
\(932\) 0 0
\(933\) 19368.0 0.679614
\(934\) 0 0
\(935\) −1904.00 −0.0665962
\(936\) 0 0
\(937\) −20806.0 −0.725403 −0.362701 0.931905i \(-0.618146\pi\)
−0.362701 + 0.931905i \(0.618146\pi\)
\(938\) 0 0
\(939\) 16578.0 0.576148
\(940\) 0 0
\(941\) 22346.0 0.774133 0.387066 0.922052i \(-0.373488\pi\)
0.387066 + 0.922052i \(0.373488\pi\)
\(942\) 0 0
\(943\) 18000.0 0.621591
\(944\) 0 0
\(945\) 1728.00 0.0594834
\(946\) 0 0
\(947\) −31636.0 −1.08557 −0.542783 0.839873i \(-0.682630\pi\)
−0.542783 + 0.839873i \(0.682630\pi\)
\(948\) 0 0
\(949\) −6578.00 −0.225006
\(950\) 0 0
\(951\) −31374.0 −1.06979
\(952\) 0 0
\(953\) −23190.0 −0.788245 −0.394123 0.919058i \(-0.628951\pi\)
−0.394123 + 0.919058i \(0.628951\pi\)
\(954\) 0 0
\(955\) −32.0000 −0.00108429
\(956\) 0 0
\(957\) 20808.0 0.702850
\(958\) 0 0
\(959\) 7360.00 0.247828
\(960\) 0 0
\(961\) −11295.0 −0.379141
\(962\) 0 0
\(963\) 6588.00 0.220452
\(964\) 0 0
\(965\) −4156.00 −0.138639
\(966\) 0 0
\(967\) 304.000 0.0101096 0.00505480 0.999987i \(-0.498391\pi\)
0.00505480 + 0.999987i \(0.498391\pi\)
\(968\) 0 0
\(969\) −168.000 −0.00556960
\(970\) 0 0
\(971\) 53372.0 1.76394 0.881972 0.471302i \(-0.156216\pi\)
0.881972 + 0.471302i \(0.156216\pi\)
\(972\) 0 0
\(973\) 16512.0 0.544039
\(974\) 0 0
\(975\) −4719.00 −0.155004
\(976\) 0 0
\(977\) 13650.0 0.446983 0.223491 0.974706i \(-0.428255\pi\)
0.223491 + 0.974706i \(0.428255\pi\)
\(978\) 0 0
\(979\) 98600.0 3.21887
\(980\) 0 0
\(981\) 13626.0 0.443471
\(982\) 0 0
\(983\) 34992.0 1.13537 0.567686 0.823245i \(-0.307839\pi\)
0.567686 + 0.823245i \(0.307839\pi\)
\(984\) 0 0
\(985\) −6972.00 −0.225529
\(986\) 0 0
\(987\) −28416.0 −0.916405
\(988\) 0 0
\(989\) 10080.0 0.324090
\(990\) 0 0
\(991\) 18096.0 0.580059 0.290029 0.957018i \(-0.406335\pi\)
0.290029 + 0.957018i \(0.406335\pi\)
\(992\) 0 0
\(993\) 7044.00 0.225110
\(994\) 0 0
\(995\) 1136.00 0.0361946
\(996\) 0 0
\(997\) 18914.0 0.600815 0.300407 0.953811i \(-0.402877\pi\)
0.300407 + 0.953811i \(0.402877\pi\)
\(998\) 0 0
\(999\) −10422.0 −0.330068
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 2496.4.a.d.1.1 1
4.3 odd 2 2496.4.a.m.1.1 1
8.3 odd 2 624.4.a.b.1.1 1
8.5 even 2 156.4.a.b.1.1 1
24.5 odd 2 468.4.a.a.1.1 1
24.11 even 2 1872.4.a.i.1.1 1
104.5 odd 4 2028.4.b.d.337.2 2
104.21 odd 4 2028.4.b.d.337.1 2
104.77 even 2 2028.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.4.a.b.1.1 1 8.5 even 2
468.4.a.a.1.1 1 24.5 odd 2
624.4.a.b.1.1 1 8.3 odd 2
1872.4.a.i.1.1 1 24.11 even 2
2028.4.a.b.1.1 1 104.77 even 2
2028.4.b.d.337.1 2 104.21 odd 4
2028.4.b.d.337.2 2 104.5 odd 4
2496.4.a.d.1.1 1 1.1 even 1 trivial
2496.4.a.m.1.1 1 4.3 odd 2