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Properties

Label 648.4.a.a.1.1
Level $648$
Weight $4$
Character 648.1
Self dual yes
Analytic conductor $38.233$
Analytic rank $0$
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] = [648,4,Mod(1,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("648.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.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: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 648.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +36.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +36.0000 q^{7} +64.0000 q^{11} -65.0000 q^{13} +59.0000 q^{17} -28.0000 q^{19} +160.000 q^{23} -100.000 q^{25} -57.0000 q^{29} +164.000 q^{31} -180.000 q^{35} -321.000 q^{37} -246.000 q^{41} -8.00000 q^{43} +84.0000 q^{47} +953.000 q^{49} +478.000 q^{53} -320.000 q^{55} -32.0000 q^{59} +415.000 q^{61} +325.000 q^{65} -220.000 q^{67} +884.000 q^{71} -77.0000 q^{73} +2304.00 q^{77} -80.0000 q^{79} +1268.00 q^{83} -295.000 q^{85} +123.000 q^{89} -2340.00 q^{91} +140.000 q^{95} +1346.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −5.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 36.0000 1.94382 0.971909 − 0.235358i \(-0.0756264\pi\)
0.971909 + 0.235358i \(0.0756264\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 64.0000 1.75425 0.877124 − 0.480264i \(-0.159459\pi\)
0.877124 + 0.480264i \(0.159459\pi\)
\(12\) 0 0
\(13\) −65.0000 −1.38675 −0.693375 − 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 59.0000 0.841741 0.420871 − 0.907121i \(-0.361725\pi\)
0.420871 + 0.907121i \(0.361725\pi\)
\(18\) 0 0
\(19\) −28.0000 −0.338086 −0.169043 − 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 160.000 1.45054 0.725268 − 0.688467i \(-0.241716\pi\)
0.725268 + 0.688467i \(0.241716\pi\)
\(24\) 0 0
\(25\) −100.000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −57.0000 −0.364987 −0.182494 − 0.983207i \(-0.558417\pi\)
−0.182494 + 0.983207i \(0.558417\pi\)
\(30\) 0 0
\(31\) 164.000 0.950170 0.475085 − 0.879940i \(-0.342417\pi\)
0.475085 + 0.879940i \(0.342417\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −180.000 −0.869302
\(36\) 0 0
\(37\) −321.000 −1.42627 −0.713136 − 0.701026i \(-0.752726\pi\)
−0.713136 + 0.701026i \(0.752726\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −246.000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −8.00000 −0.0283718 −0.0141859 − 0.999899i \(-0.504516\pi\)
−0.0141859 + 0.999899i \(0.504516\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 84.0000 0.260695 0.130347 − 0.991468i \(-0.458391\pi\)
0.130347 + 0.991468i \(0.458391\pi\)
\(48\) 0 0
\(49\) 953.000 2.77843
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 478.000 1.23884 0.619418 − 0.785061i \(-0.287368\pi\)
0.619418 + 0.785061i \(0.287368\pi\)
\(54\) 0 0
\(55\) −320.000 −0.784523
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −32.0000 −0.0706109 −0.0353055 − 0.999377i \(-0.511240\pi\)
−0.0353055 + 0.999377i \(0.511240\pi\)
\(60\) 0 0
\(61\) 415.000 0.871071 0.435535 − 0.900172i \(-0.356559\pi\)
0.435535 + 0.900172i \(0.356559\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 325.000 0.620174
\(66\) 0 0
\(67\) −220.000 −0.401153 −0.200577 − 0.979678i \(-0.564282\pi\)
−0.200577 + 0.979678i \(0.564282\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 884.000 1.47763 0.738813 − 0.673910i \(-0.235386\pi\)
0.738813 + 0.673910i \(0.235386\pi\)
\(72\) 0 0
\(73\) −77.0000 −0.123454 −0.0617272 − 0.998093i \(-0.519661\pi\)
−0.0617272 + 0.998093i \(0.519661\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2304.00 3.40994
\(78\) 0 0
\(79\) −80.0000 −0.113933 −0.0569665 − 0.998376i \(-0.518143\pi\)
−0.0569665 + 0.998376i \(0.518143\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1268.00 1.67688 0.838440 − 0.544994i \(-0.183468\pi\)
0.838440 + 0.544994i \(0.183468\pi\)
\(84\) 0 0
\(85\) −295.000 −0.376438
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 123.000 0.146494 0.0732470 − 0.997314i \(-0.476664\pi\)
0.0732470 + 0.997314i \(0.476664\pi\)
\(90\) 0 0
\(91\) −2340.00 −2.69559
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 140.000 0.151197
\(96\) 0 0
\(97\) 1346.00 1.40892 0.704462 − 0.709742i \(-0.251188\pi\)
0.704462 + 0.709742i \(0.251188\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −834.000 −0.821645 −0.410822 − 0.911715i \(-0.634758\pi\)
−0.410822 + 0.911715i \(0.634758\pi\)
\(102\) 0 0
\(103\) 1060.00 1.01403 0.507014 − 0.861938i \(-0.330749\pi\)
0.507014 + 0.861938i \(0.330749\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 300.000 0.271048 0.135524 − 0.990774i \(-0.456728\pi\)
0.135524 + 0.990774i \(0.456728\pi\)
\(108\) 0 0
\(109\) −557.000 −0.489458 −0.244729 − 0.969592i \(-0.578699\pi\)
−0.244729 + 0.969592i \(0.578699\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1617.00 −1.34615 −0.673073 − 0.739576i \(-0.735026\pi\)
−0.673073 + 0.739576i \(0.735026\pi\)
\(114\) 0 0
\(115\) −800.000 −0.648699
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2124.00 1.63619
\(120\) 0 0
\(121\) 2765.00 2.07739
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1125.00 0.804984
\(126\) 0 0
\(127\) −1136.00 −0.793730 −0.396865 − 0.917877i \(-0.629902\pi\)
−0.396865 + 0.917877i \(0.629902\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 116.000 0.0773662 0.0386831 − 0.999252i \(-0.487684\pi\)
0.0386831 + 0.999252i \(0.487684\pi\)
\(132\) 0 0
\(133\) −1008.00 −0.657178
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 615.000 0.383526 0.191763 − 0.981441i \(-0.438580\pi\)
0.191763 + 0.981441i \(0.438580\pi\)
\(138\) 0 0
\(139\) 1452.00 0.886022 0.443011 − 0.896516i \(-0.353910\pi\)
0.443011 + 0.896516i \(0.353910\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4160.00 −2.43270
\(144\) 0 0
\(145\) 285.000 0.163227
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 839.000 0.461299 0.230650 − 0.973037i \(-0.425915\pi\)
0.230650 + 0.973037i \(0.425915\pi\)
\(150\) 0 0
\(151\) −2056.00 −1.10805 −0.554023 − 0.832501i \(-0.686908\pi\)
−0.554023 + 0.832501i \(0.686908\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −820.000 −0.424929
\(156\) 0 0
\(157\) 1099.00 0.558661 0.279330 − 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5760.00 2.81958
\(162\) 0 0
\(163\) −72.0000 −0.0345980 −0.0172990 − 0.999850i \(-0.505507\pi\)
−0.0172990 + 0.999850i \(0.505507\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2124.00 0.984192 0.492096 − 0.870541i \(-0.336231\pi\)
0.492096 + 0.870541i \(0.336231\pi\)
\(168\) 0 0
\(169\) 2028.00 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4005.00 −1.76008 −0.880042 − 0.474896i \(-0.842486\pi\)
−0.880042 + 0.474896i \(0.842486\pi\)
\(174\) 0 0
\(175\) −3600.00 −1.55505
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1428.00 −0.596278 −0.298139 − 0.954522i \(-0.596366\pi\)
−0.298139 + 0.954522i \(0.596366\pi\)
\(180\) 0 0
\(181\) −2226.00 −0.914129 −0.457064 − 0.889434i \(-0.651099\pi\)
−0.457064 + 0.889434i \(0.651099\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1605.00 0.637848
\(186\) 0 0
\(187\) 3776.00 1.47662
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3756.00 1.42290 0.711452 − 0.702735i \(-0.248038\pi\)
0.711452 + 0.702735i \(0.248038\pi\)
\(192\) 0 0
\(193\) −3637.00 −1.35646 −0.678231 − 0.734849i \(-0.737253\pi\)
−0.678231 + 0.734849i \(0.737253\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 795.000 0.287520 0.143760 − 0.989613i \(-0.454081\pi\)
0.143760 + 0.989613i \(0.454081\pi\)
\(198\) 0 0
\(199\) 2500.00 0.890554 0.445277 − 0.895393i \(-0.353105\pi\)
0.445277 + 0.895393i \(0.353105\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2052.00 −0.709469
\(204\) 0 0
\(205\) 1230.00 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1792.00 −0.593087
\(210\) 0 0
\(211\) −3944.00 −1.28681 −0.643403 − 0.765527i \(-0.722478\pi\)
−0.643403 + 0.765527i \(0.722478\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 40.0000 0.0126883
\(216\) 0 0
\(217\) 5904.00 1.84696
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3835.00 −1.16729
\(222\) 0 0
\(223\) −680.000 −0.204198 −0.102099 − 0.994774i \(-0.532556\pi\)
−0.102099 + 0.994774i \(0.532556\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3924.00 1.14733 0.573667 − 0.819088i \(-0.305520\pi\)
0.573667 + 0.819088i \(0.305520\pi\)
\(228\) 0 0
\(229\) 4615.00 1.33174 0.665869 − 0.746069i \(-0.268061\pi\)
0.665869 + 0.746069i \(0.268061\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4493.00 −1.26329 −0.631644 − 0.775258i \(-0.717620\pi\)
−0.631644 + 0.775258i \(0.717620\pi\)
\(234\) 0 0
\(235\) −420.000 −0.116586
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3124.00 −0.845501 −0.422751 − 0.906246i \(-0.638935\pi\)
−0.422751 + 0.906246i \(0.638935\pi\)
\(240\) 0 0
\(241\) −309.000 −0.0825910 −0.0412955 − 0.999147i \(-0.513149\pi\)
−0.0412955 + 0.999147i \(0.513149\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4765.00 −1.24255
\(246\) 0 0
\(247\) 1820.00 0.468841
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1352.00 0.339990 0.169995 − 0.985445i \(-0.445625\pi\)
0.169995 + 0.985445i \(0.445625\pi\)
\(252\) 0 0
\(253\) 10240.0 2.54460
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3695.00 0.896840 0.448420 − 0.893823i \(-0.351987\pi\)
0.448420 + 0.893823i \(0.351987\pi\)
\(258\) 0 0
\(259\) −11556.0 −2.77241
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −980.000 −0.229770 −0.114885 − 0.993379i \(-0.536650\pi\)
−0.114885 + 0.993379i \(0.536650\pi\)
\(264\) 0 0
\(265\) −2390.00 −0.554025
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5293.00 −1.19970 −0.599851 − 0.800112i \(-0.704774\pi\)
−0.599851 + 0.800112i \(0.704774\pi\)
\(270\) 0 0
\(271\) −4912.00 −1.10104 −0.550522 − 0.834821i \(-0.685571\pi\)
−0.550522 + 0.834821i \(0.685571\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6400.00 −1.40340
\(276\) 0 0
\(277\) −1394.00 −0.302373 −0.151187 − 0.988505i \(-0.548309\pi\)
−0.151187 + 0.988505i \(0.548309\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7165.00 −1.52110 −0.760548 − 0.649282i \(-0.775070\pi\)
−0.760548 + 0.649282i \(0.775070\pi\)
\(282\) 0 0
\(283\) −9340.00 −1.96186 −0.980928 − 0.194370i \(-0.937734\pi\)
−0.980928 + 0.194370i \(0.937734\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8856.00 −1.82144
\(288\) 0 0
\(289\) −1432.00 −0.291472
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6873.00 −1.37039 −0.685196 − 0.728359i \(-0.740284\pi\)
−0.685196 + 0.728359i \(0.740284\pi\)
\(294\) 0 0
\(295\) 160.000 0.0315782
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10400.0 −2.01153
\(300\) 0 0
\(301\) −288.000 −0.0551496
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2075.00 −0.389555
\(306\) 0 0
\(307\) 204.000 0.0379247 0.0189624 − 0.999820i \(-0.493964\pi\)
0.0189624 + 0.999820i \(0.493964\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4056.00 0.739533 0.369766 − 0.929125i \(-0.379438\pi\)
0.369766 + 0.929125i \(0.379438\pi\)
\(312\) 0 0
\(313\) 1095.00 0.197741 0.0988707 − 0.995100i \(-0.468477\pi\)
0.0988707 + 0.995100i \(0.468477\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10419.0 1.84602 0.923012 − 0.384772i \(-0.125720\pi\)
0.923012 + 0.384772i \(0.125720\pi\)
\(318\) 0 0
\(319\) −3648.00 −0.640278
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1652.00 −0.284581
\(324\) 0 0
\(325\) 6500.00 1.10940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3024.00 0.506743
\(330\) 0 0
\(331\) 3596.00 0.597142 0.298571 − 0.954387i \(-0.403490\pi\)
0.298571 + 0.954387i \(0.403490\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1100.00 0.179401
\(336\) 0 0
\(337\) −2910.00 −0.470379 −0.235190 − 0.971950i \(-0.575571\pi\)
−0.235190 + 0.971950i \(0.575571\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10496.0 1.66683
\(342\) 0 0
\(343\) 21960.0 3.45693
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5076.00 −0.785285 −0.392643 − 0.919691i \(-0.628439\pi\)
−0.392643 + 0.919691i \(0.628439\pi\)
\(348\) 0 0
\(349\) 8118.00 1.24512 0.622560 − 0.782572i \(-0.286093\pi\)
0.622560 + 0.782572i \(0.286093\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9262.00 −1.39651 −0.698253 − 0.715851i \(-0.746039\pi\)
−0.698253 + 0.715851i \(0.746039\pi\)
\(354\) 0 0
\(355\) −4420.00 −0.660815
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1248.00 0.183473 0.0917367 − 0.995783i \(-0.470758\pi\)
0.0917367 + 0.995783i \(0.470758\pi\)
\(360\) 0 0
\(361\) −6075.00 −0.885698
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 385.000 0.0552105
\(366\) 0 0
\(367\) 9880.00 1.40526 0.702632 − 0.711554i \(-0.252008\pi\)
0.702632 + 0.711554i \(0.252008\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 17208.0 2.40807
\(372\) 0 0
\(373\) −9778.00 −1.35733 −0.678667 − 0.734446i \(-0.737442\pi\)
−0.678667 + 0.734446i \(0.737442\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3705.00 0.506146
\(378\) 0 0
\(379\) 3260.00 0.441834 0.220917 − 0.975293i \(-0.429095\pi\)
0.220917 + 0.975293i \(0.429095\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1620.00 0.216131 0.108065 − 0.994144i \(-0.465534\pi\)
0.108065 + 0.994144i \(0.465534\pi\)
\(384\) 0 0
\(385\) −11520.0 −1.52497
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6910.00 0.900645 0.450323 − 0.892866i \(-0.351309\pi\)
0.450323 + 0.892866i \(0.351309\pi\)
\(390\) 0 0
\(391\) 9440.00 1.22098
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 400.000 0.0509524
\(396\) 0 0
\(397\) −1705.00 −0.215545 −0.107773 − 0.994176i \(-0.534372\pi\)
−0.107773 + 0.994176i \(0.534372\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4005.00 −0.498754 −0.249377 − 0.968407i \(-0.580226\pi\)
−0.249377 + 0.968407i \(0.580226\pi\)
\(402\) 0 0
\(403\) −10660.0 −1.31765
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −20544.0 −2.50204
\(408\) 0 0
\(409\) −5385.00 −0.651030 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1152.00 −0.137255
\(414\) 0 0
\(415\) −6340.00 −0.749924
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5640.00 0.657594 0.328797 − 0.944401i \(-0.393357\pi\)
0.328797 + 0.944401i \(0.393357\pi\)
\(420\) 0 0
\(421\) 4331.00 0.501378 0.250689 − 0.968068i \(-0.419343\pi\)
0.250689 + 0.968068i \(0.419343\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5900.00 −0.673393
\(426\) 0 0
\(427\) 14940.0 1.69320
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11596.0 −1.29596 −0.647981 − 0.761656i \(-0.724386\pi\)
−0.647981 + 0.761656i \(0.724386\pi\)
\(432\) 0 0
\(433\) −2765.00 −0.306876 −0.153438 − 0.988158i \(-0.549035\pi\)
−0.153438 + 0.988158i \(0.549035\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4480.00 −0.490406
\(438\) 0 0
\(439\) 7932.00 0.862355 0.431177 − 0.902267i \(-0.358098\pi\)
0.431177 + 0.902267i \(0.358098\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12268.0 −1.31573 −0.657867 − 0.753134i \(-0.728541\pi\)
−0.657867 + 0.753134i \(0.728541\pi\)
\(444\) 0 0
\(445\) −615.000 −0.0655141
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10478.0 −1.10131 −0.550654 − 0.834734i \(-0.685622\pi\)
−0.550654 + 0.834734i \(0.685622\pi\)
\(450\) 0 0
\(451\) −15744.0 −1.64380
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11700.0 1.20550
\(456\) 0 0
\(457\) −16129.0 −1.65095 −0.825474 − 0.564441i \(-0.809092\pi\)
−0.825474 + 0.564441i \(0.809092\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1034.00 −0.104465 −0.0522323 − 0.998635i \(-0.516634\pi\)
−0.0522323 + 0.998635i \(0.516634\pi\)
\(462\) 0 0
\(463\) 9080.00 0.911411 0.455706 − 0.890131i \(-0.349387\pi\)
0.455706 + 0.890131i \(0.349387\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18504.0 1.83354 0.916770 − 0.399416i \(-0.130787\pi\)
0.916770 + 0.399416i \(0.130787\pi\)
\(468\) 0 0
\(469\) −7920.00 −0.779769
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −512.000 −0.0497712
\(474\) 0 0
\(475\) 2800.00 0.270469
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17012.0 1.62275 0.811376 − 0.584525i \(-0.198719\pi\)
0.811376 + 0.584525i \(0.198719\pi\)
\(480\) 0 0
\(481\) 20865.0 1.97788
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6730.00 −0.630090
\(486\) 0 0
\(487\) −6140.00 −0.571314 −0.285657 − 0.958332i \(-0.592212\pi\)
−0.285657 + 0.958332i \(0.592212\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10944.0 −1.00590 −0.502949 − 0.864316i \(-0.667752\pi\)
−0.502949 + 0.864316i \(0.667752\pi\)
\(492\) 0 0
\(493\) −3363.00 −0.307225
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 31824.0 2.87224
\(498\) 0 0
\(499\) −5208.00 −0.467219 −0.233609 − 0.972331i \(-0.575054\pi\)
−0.233609 + 0.972331i \(0.575054\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1440.00 0.127647 0.0638235 − 0.997961i \(-0.479671\pi\)
0.0638235 + 0.997961i \(0.479671\pi\)
\(504\) 0 0
\(505\) 4170.00 0.367451
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2310.00 0.201157 0.100579 − 0.994929i \(-0.467931\pi\)
0.100579 + 0.994929i \(0.467931\pi\)
\(510\) 0 0
\(511\) −2772.00 −0.239973
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5300.00 −0.453487
\(516\) 0 0
\(517\) 5376.00 0.457323
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9910.00 −0.833330 −0.416665 − 0.909060i \(-0.636801\pi\)
−0.416665 + 0.909060i \(0.636801\pi\)
\(522\) 0 0
\(523\) 6640.00 0.555157 0.277578 − 0.960703i \(-0.410468\pi\)
0.277578 + 0.960703i \(0.410468\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9676.00 0.799797
\(528\) 0 0
\(529\) 13433.0 1.10405
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 15990.0 1.29944
\(534\) 0 0
\(535\) −1500.00 −0.121216
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 60992.0 4.87405
\(540\) 0 0
\(541\) −15969.0 −1.26906 −0.634530 − 0.772899i \(-0.718806\pi\)
−0.634530 + 0.772899i \(0.718806\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2785.00 0.218892
\(546\) 0 0
\(547\) 500.000 0.0390831 0.0195416 − 0.999809i \(-0.493779\pi\)
0.0195416 + 0.999809i \(0.493779\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1596.00 0.123397
\(552\) 0 0
\(553\) −2880.00 −0.221465
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3845.00 −0.292492 −0.146246 − 0.989248i \(-0.546719\pi\)
−0.146246 + 0.989248i \(0.546719\pi\)
\(558\) 0 0
\(559\) 520.000 0.0393446
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3188.00 −0.238647 −0.119323 − 0.992855i \(-0.538073\pi\)
−0.119323 + 0.992855i \(0.538073\pi\)
\(564\) 0 0
\(565\) 8085.00 0.602015
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17263.0 1.27189 0.635943 − 0.771736i \(-0.280612\pi\)
0.635943 + 0.771736i \(0.280612\pi\)
\(570\) 0 0
\(571\) −4656.00 −0.341239 −0.170620 − 0.985337i \(-0.554577\pi\)
−0.170620 + 0.985337i \(0.554577\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16000.0 −1.16043
\(576\) 0 0
\(577\) −23209.0 −1.67453 −0.837265 − 0.546798i \(-0.815847\pi\)
−0.837265 + 0.546798i \(0.815847\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 45648.0 3.25955
\(582\) 0 0
\(583\) 30592.0 2.17323
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17624.0 −1.23922 −0.619608 − 0.784911i \(-0.712709\pi\)
−0.619608 + 0.784911i \(0.712709\pi\)
\(588\) 0 0
\(589\) −4592.00 −0.321239
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17695.0 1.22537 0.612687 − 0.790326i \(-0.290089\pi\)
0.612687 + 0.790326i \(0.290089\pi\)
\(594\) 0 0
\(595\) −10620.0 −0.731727
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2748.00 0.187446 0.0937231 − 0.995598i \(-0.470123\pi\)
0.0937231 + 0.995598i \(0.470123\pi\)
\(600\) 0 0
\(601\) 19579.0 1.32886 0.664429 − 0.747351i \(-0.268675\pi\)
0.664429 + 0.747351i \(0.268675\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13825.0 −0.929035
\(606\) 0 0
\(607\) 17804.0 1.19051 0.595257 − 0.803535i \(-0.297050\pi\)
0.595257 + 0.803535i \(0.297050\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5460.00 −0.361519
\(612\) 0 0
\(613\) −22690.0 −1.49501 −0.747504 − 0.664257i \(-0.768748\pi\)
−0.747504 + 0.664257i \(0.768748\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1755.00 0.114512 0.0572558 − 0.998360i \(-0.481765\pi\)
0.0572558 + 0.998360i \(0.481765\pi\)
\(618\) 0 0
\(619\) −6920.00 −0.449335 −0.224667 − 0.974436i \(-0.572130\pi\)
−0.224667 + 0.974436i \(0.572130\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4428.00 0.284758
\(624\) 0 0
\(625\) 6875.00 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −18939.0 −1.20055
\(630\) 0 0
\(631\) 10744.0 0.677832 0.338916 − 0.940817i \(-0.389940\pi\)
0.338916 + 0.940817i \(0.389940\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5680.00 0.354967
\(636\) 0 0
\(637\) −61945.0 −3.85298
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9931.00 0.611936 0.305968 − 0.952042i \(-0.401020\pi\)
0.305968 + 0.952042i \(0.401020\pi\)
\(642\) 0 0
\(643\) 4068.00 0.249497 0.124748 − 0.992188i \(-0.460188\pi\)
0.124748 + 0.992188i \(0.460188\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17540.0 1.06579 0.532897 − 0.846180i \(-0.321103\pi\)
0.532897 + 0.846180i \(0.321103\pi\)
\(648\) 0 0
\(649\) −2048.00 −0.123869
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30090.0 −1.80324 −0.901618 − 0.432534i \(-0.857620\pi\)
−0.901618 + 0.432534i \(0.857620\pi\)
\(654\) 0 0
\(655\) −580.000 −0.0345992
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8820.00 −0.521363 −0.260682 − 0.965425i \(-0.583947\pi\)
−0.260682 + 0.965425i \(0.583947\pi\)
\(660\) 0 0
\(661\) 13319.0 0.783735 0.391868 − 0.920022i \(-0.371829\pi\)
0.391868 + 0.920022i \(0.371829\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5040.00 0.293899
\(666\) 0 0
\(667\) −9120.00 −0.529427
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 26560.0 1.52807
\(672\) 0 0
\(673\) 14035.0 0.803877 0.401939 − 0.915667i \(-0.368336\pi\)
0.401939 + 0.915667i \(0.368336\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9410.00 −0.534203 −0.267102 − 0.963668i \(-0.586066\pi\)
−0.267102 + 0.963668i \(0.586066\pi\)
\(678\) 0 0
\(679\) 48456.0 2.73869
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1060.00 0.0593847 0.0296924 − 0.999559i \(-0.490547\pi\)
0.0296924 + 0.999559i \(0.490547\pi\)
\(684\) 0 0
\(685\) −3075.00 −0.171518
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −31070.0 −1.71796
\(690\) 0 0
\(691\) 8540.00 0.470155 0.235077 − 0.971977i \(-0.424466\pi\)
0.235077 + 0.971977i \(0.424466\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7260.00 −0.396241
\(696\) 0 0
\(697\) −14514.0 −0.788747
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17259.0 0.929905 0.464953 − 0.885336i \(-0.346071\pi\)
0.464953 + 0.885336i \(0.346071\pi\)
\(702\) 0 0
\(703\) 8988.00 0.482203
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −30024.0 −1.59713
\(708\) 0 0
\(709\) −24145.0 −1.27896 −0.639481 − 0.768807i \(-0.720851\pi\)
−0.639481 + 0.768807i \(0.720851\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 26240.0 1.37825
\(714\) 0 0
\(715\) 20800.0 1.08794
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17792.0 −0.922851 −0.461425 − 0.887179i \(-0.652662\pi\)
−0.461425 + 0.887179i \(0.652662\pi\)
\(720\) 0 0
\(721\) 38160.0 1.97109
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5700.00 0.291990
\(726\) 0 0
\(727\) 10620.0 0.541780 0.270890 − 0.962610i \(-0.412682\pi\)
0.270890 + 0.962610i \(0.412682\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −472.000 −0.0238817
\(732\) 0 0
\(733\) −8650.00 −0.435873 −0.217937 − 0.975963i \(-0.569933\pi\)
−0.217937 + 0.975963i \(0.569933\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −14080.0 −0.703722
\(738\) 0 0
\(739\) 4652.00 0.231565 0.115783 − 0.993275i \(-0.463062\pi\)
0.115783 + 0.993275i \(0.463062\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33868.0 1.67227 0.836135 − 0.548524i \(-0.184810\pi\)
0.836135 + 0.548524i \(0.184810\pi\)
\(744\) 0 0
\(745\) −4195.00 −0.206299
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10800.0 0.526867
\(750\) 0 0
\(751\) −12852.0 −0.624469 −0.312234 − 0.950005i \(-0.601077\pi\)
−0.312234 + 0.950005i \(0.601077\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10280.0 0.495533
\(756\) 0 0
\(757\) −9730.00 −0.467164 −0.233582 − 0.972337i \(-0.575045\pi\)
−0.233582 + 0.972337i \(0.575045\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −33361.0 −1.58914 −0.794570 − 0.607173i \(-0.792304\pi\)
−0.794570 + 0.607173i \(0.792304\pi\)
\(762\) 0 0
\(763\) −20052.0 −0.951417
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2080.00 0.0979197
\(768\) 0 0
\(769\) −26557.0 −1.24534 −0.622672 − 0.782483i \(-0.713953\pi\)
−0.622672 + 0.782483i \(0.713953\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18333.0 −0.853030 −0.426515 − 0.904480i \(-0.640259\pi\)
−0.426515 + 0.904480i \(0.640259\pi\)
\(774\) 0 0
\(775\) −16400.0 −0.760136
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6888.00 0.316801
\(780\) 0 0
\(781\) 56576.0 2.59212
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5495.00 −0.249841
\(786\) 0 0
\(787\) −37376.0 −1.69290 −0.846449 − 0.532470i \(-0.821264\pi\)
−0.846449 + 0.532470i \(0.821264\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −58212.0 −2.61666
\(792\) 0 0
\(793\) −26975.0 −1.20796
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16075.0 0.714436 0.357218 − 0.934021i \(-0.383725\pi\)
0.357218 + 0.934021i \(0.383725\pi\)
\(798\) 0 0
\(799\) 4956.00 0.219438
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4928.00 −0.216570
\(804\) 0 0
\(805\) −28800.0 −1.26095
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 32183.0 1.39863 0.699316 − 0.714812i \(-0.253488\pi\)
0.699316 + 0.714812i \(0.253488\pi\)
\(810\) 0 0
\(811\) −1424.00 −0.0616565 −0.0308282 − 0.999525i \(-0.509814\pi\)
−0.0308282 + 0.999525i \(0.509814\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 360.000 0.0154727
\(816\) 0 0
\(817\) 224.000 0.00959213
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −26961.0 −1.14610 −0.573048 − 0.819522i \(-0.694239\pi\)
−0.573048 + 0.819522i \(0.694239\pi\)
\(822\) 0 0
\(823\) −21100.0 −0.893681 −0.446841 − 0.894614i \(-0.647451\pi\)
−0.446841 + 0.894614i \(0.647451\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 35120.0 1.47671 0.738357 − 0.674410i \(-0.235602\pi\)
0.738357 + 0.674410i \(0.235602\pi\)
\(828\) 0 0
\(829\) 21238.0 0.889778 0.444889 − 0.895586i \(-0.353243\pi\)
0.444889 + 0.895586i \(0.353243\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 56227.0 2.33872
\(834\) 0 0
\(835\) −10620.0 −0.440144
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26088.0 −1.07349 −0.536745 − 0.843745i \(-0.680346\pi\)
−0.536745 + 0.843745i \(0.680346\pi\)
\(840\) 0 0
\(841\) −21140.0 −0.866784
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10140.0 −0.412813
\(846\) 0 0
\(847\) 99540.0 4.03806
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −51360.0 −2.06886
\(852\) 0 0
\(853\) −11122.0 −0.446436 −0.223218 − 0.974769i \(-0.571656\pi\)
−0.223218 + 0.974769i \(0.571656\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2985.00 −0.118980 −0.0594899 − 0.998229i \(-0.518947\pi\)
−0.0594899 + 0.998229i \(0.518947\pi\)
\(858\) 0 0
\(859\) −49548.0 −1.96805 −0.984026 − 0.178027i \(-0.943029\pi\)
−0.984026 + 0.178027i \(0.943029\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 21688.0 0.855467 0.427734 − 0.903905i \(-0.359312\pi\)
0.427734 + 0.903905i \(0.359312\pi\)
\(864\) 0 0
\(865\) 20025.0 0.787133
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5120.00 −0.199867
\(870\) 0 0
\(871\) 14300.0 0.556300
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 40500.0 1.56474
\(876\) 0 0
\(877\) 10935.0 0.421036 0.210518 − 0.977590i \(-0.432485\pi\)
0.210518 + 0.977590i \(0.432485\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −40126.0 −1.53448 −0.767241 − 0.641358i \(-0.778371\pi\)
−0.767241 + 0.641358i \(0.778371\pi\)
\(882\) 0 0
\(883\) −42748.0 −1.62920 −0.814601 − 0.580022i \(-0.803044\pi\)
−0.814601 + 0.580022i \(0.803044\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −27496.0 −1.04084 −0.520420 − 0.853910i \(-0.674225\pi\)
−0.520420 + 0.853910i \(0.674225\pi\)
\(888\) 0 0
\(889\) −40896.0 −1.54287
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2352.00 −0.0881374
\(894\) 0 0
\(895\) 7140.00 0.266664
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −9348.00 −0.346800
\(900\) 0 0
\(901\) 28202.0 1.04278
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 11130.0 0.408811
\(906\) 0 0
\(907\) −21680.0 −0.793685 −0.396843 − 0.917887i \(-0.629894\pi\)
−0.396843 + 0.917887i \(0.629894\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −6824.00 −0.248177 −0.124088 − 0.992271i \(-0.539601\pi\)
−0.124088 + 0.992271i \(0.539601\pi\)
\(912\) 0 0
\(913\) 81152.0 2.94166
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4176.00 0.150386
\(918\) 0 0
\(919\) 26512.0 0.951632 0.475816 − 0.879545i \(-0.342153\pi\)
0.475816 + 0.879545i \(0.342153\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −57460.0 −2.04910
\(924\) 0 0
\(925\) 32100.0 1.14102
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −22597.0 −0.798045 −0.399022 − 0.916941i \(-0.630650\pi\)
−0.399022 + 0.916941i \(0.630650\pi\)
\(930\) 0 0
\(931\) −26684.0 −0.939348
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18880.0 −0.660366
\(936\) 0 0
\(937\) 38115.0 1.32888 0.664441 − 0.747341i \(-0.268670\pi\)
0.664441 + 0.747341i \(0.268670\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −43485.0 −1.50645 −0.753226 − 0.657762i \(-0.771503\pi\)
−0.753226 + 0.657762i \(0.771503\pi\)
\(942\) 0 0
\(943\) −39360.0 −1.35921
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −45420.0 −1.55856 −0.779278 − 0.626679i \(-0.784414\pi\)
−0.779278 + 0.626679i \(0.784414\pi\)
\(948\) 0 0
\(949\) 5005.00 0.171200
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −32505.0 −1.10487 −0.552435 − 0.833556i \(-0.686301\pi\)
−0.552435 + 0.833556i \(0.686301\pi\)
\(954\) 0 0
\(955\) −18780.0 −0.636342
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22140.0 0.745504
\(960\) 0 0
\(961\) −2895.00 −0.0971770
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18185.0 0.606628
\(966\) 0 0
\(967\) 14276.0 0.474752 0.237376 − 0.971418i \(-0.423713\pi\)
0.237376 + 0.971418i \(0.423713\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −35844.0 −1.18464 −0.592322 − 0.805702i \(-0.701789\pi\)
−0.592322 + 0.805702i \(0.701789\pi\)
\(972\) 0 0
\(973\) 52272.0 1.72226
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24270.0 −0.794745 −0.397373 − 0.917657i \(-0.630078\pi\)
−0.397373 + 0.917657i \(0.630078\pi\)
\(978\) 0 0
\(979\) 7872.00 0.256987
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 19152.0 0.621418 0.310709 − 0.950505i \(-0.399434\pi\)
0.310709 + 0.950505i \(0.399434\pi\)
\(984\) 0 0
\(985\) −3975.00 −0.128583
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1280.00 −0.0411543
\(990\) 0 0
\(991\) −9164.00 −0.293748 −0.146874 − 0.989155i \(-0.546921\pi\)
−0.146874 + 0.989155i \(0.546921\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12500.0 −0.398268
\(996\) 0 0
\(997\) 36259.0 1.15179 0.575895 − 0.817524i \(-0.304654\pi\)
0.575895 + 0.817524i \(0.304654\pi\)
\(998\) 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 648.4.a.a.1.1 ✓ 1
3.2 odd 2 648.4.a.b.1.1 yes 1
4.3 odd 2 1296.4.a.c.1.1 1
9.2 odd 6 648.4.i.c.433.1 2
9.4 even 3 648.4.i.j.217.1 2
9.5 odd 6 648.4.i.c.217.1 2
9.7 even 3 648.4.i.j.433.1 2
12.11 even 2 1296.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.4.a.a.1.1 ✓ 1 1.1 even 1 trivial
648.4.a.b.1.1 yes 1 3.2 odd 2
648.4.i.c.217.1 2 9.5 odd 6
648.4.i.c.433.1 2 9.2 odd 6
648.4.i.j.217.1 2 9.4 even 3
648.4.i.j.433.1 2 9.7 even 3
1296.4.a.c.1.1 1 4.3 odd 2
1296.4.a.f.1.1 1 12.11 even 2