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Properties

Label 1008.4.a.u.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
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] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+16.0000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+16.0000 q^{5} +7.00000 q^{7} +24.0000 q^{11} -68.0000 q^{13} -54.0000 q^{17} +46.0000 q^{19} +176.000 q^{23} +131.000 q^{25} +174.000 q^{29} +116.000 q^{31} +112.000 q^{35} +74.0000 q^{37} +10.0000 q^{41} +480.000 q^{43} -572.000 q^{47} +49.0000 q^{49} +162.000 q^{53} +384.000 q^{55} -86.0000 q^{59} -904.000 q^{61} -1088.00 q^{65} -660.000 q^{67} +1024.00 q^{71} +770.000 q^{73} +168.000 q^{77} +904.000 q^{79} +682.000 q^{83} -864.000 q^{85} +102.000 q^{89} -476.000 q^{91} +736.000 q^{95} -218.000 q^{97} +O(q^{100})\)

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
\(5\) 16.0000 1.43108 0.715542 − 0.698570i \(-0.246180\pi\)
0.715542 + 0.698570i \(0.246180\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 24.0000 0.657843 0.328921 − 0.944357i \(-0.393315\pi\)
0.328921 + 0.944357i \(0.393315\pi\)
\(12\) 0 0
\(13\) −68.0000 −1.45075 −0.725377 − 0.688352i \(-0.758335\pi\)
−0.725377 + 0.688352i \(0.758335\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −54.0000 −0.770407 −0.385204 − 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 0 0
\(19\) 46.0000 0.555428 0.277714 − 0.960664i \(-0.410423\pi\)
0.277714 + 0.960664i \(0.410423\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 176.000 1.59559 0.797794 − 0.602930i \(-0.206000\pi\)
0.797794 + 0.602930i \(0.206000\pi\)
\(24\) 0 0
\(25\) 131.000 1.04800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 174.000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 116.000 0.672071 0.336036 − 0.941849i \(-0.390914\pi\)
0.336036 + 0.941849i \(0.390914\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 112.000 0.540899
\(36\) 0 0
\(37\) 74.0000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.0000 0.0380912 0.0190456 − 0.999819i \(-0.493937\pi\)
0.0190456 + 0.999819i \(0.493937\pi\)
\(42\) 0 0
\(43\) 480.000 1.70231 0.851155 − 0.524915i \(-0.175903\pi\)
0.851155 + 0.524915i \(0.175903\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −572.000 −1.77521 −0.887604 − 0.460607i \(-0.847632\pi\)
−0.887604 + 0.460607i \(0.847632\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 162.000 0.419857 0.209928 − 0.977717i \(-0.432677\pi\)
0.209928 + 0.977717i \(0.432677\pi\)
\(54\) 0 0
\(55\) 384.000 0.941428
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −86.0000 −0.189767 −0.0948834 − 0.995488i \(-0.530248\pi\)
−0.0948834 + 0.995488i \(0.530248\pi\)
\(60\) 0 0
\(61\) −904.000 −1.89746 −0.948732 − 0.316081i \(-0.897633\pi\)
−0.948732 + 0.316081i \(0.897633\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1088.00 −2.07615
\(66\) 0 0
\(67\) −660.000 −1.20346 −0.601730 − 0.798699i \(-0.705522\pi\)
−0.601730 + 0.798699i \(0.705522\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1024.00 1.71164 0.855820 − 0.517274i \(-0.173053\pi\)
0.855820 + 0.517274i \(0.173053\pi\)
\(72\) 0 0
\(73\) 770.000 1.23454 0.617272 − 0.786750i \(-0.288238\pi\)
0.617272 + 0.786750i \(0.288238\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 168.000 0.248641
\(78\) 0 0
\(79\) 904.000 1.28744 0.643721 − 0.765260i \(-0.277390\pi\)
0.643721 + 0.765260i \(0.277390\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 682.000 0.901918 0.450959 − 0.892545i \(-0.351082\pi\)
0.450959 + 0.892545i \(0.351082\pi\)
\(84\) 0 0
\(85\) −864.000 −1.10252
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 102.000 0.121483 0.0607415 − 0.998154i \(-0.480653\pi\)
0.0607415 + 0.998154i \(0.480653\pi\)
\(90\) 0 0
\(91\) −476.000 −0.548334
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 736.000 0.794863
\(96\) 0 0
\(97\) −218.000 −0.228191 −0.114096 − 0.993470i \(-0.536397\pi\)
−0.114096 + 0.993470i \(0.536397\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 80.0000 0.0788148 0.0394074 − 0.999223i \(-0.487453\pi\)
0.0394074 + 0.999223i \(0.487453\pi\)
\(102\) 0 0
\(103\) −108.000 −0.103316 −0.0516580 − 0.998665i \(-0.516451\pi\)
−0.0516580 + 0.998665i \(0.516451\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1492.00 1.34801 0.674005 − 0.738727i \(-0.264573\pi\)
0.674005 + 0.738727i \(0.264573\pi\)
\(108\) 0 0
\(109\) −1510.00 −1.32690 −0.663448 − 0.748222i \(-0.730908\pi\)
−0.663448 + 0.748222i \(0.730908\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2138.00 1.77988 0.889939 − 0.456080i \(-0.150747\pi\)
0.889939 + 0.456080i \(0.150747\pi\)
\(114\) 0 0
\(115\) 2816.00 2.28342
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −378.000 −0.291187
\(120\) 0 0
\(121\) −755.000 −0.567243
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 96.0000 0.0686920
\(126\) 0 0
\(127\) −1616.00 −1.12911 −0.564554 − 0.825396i \(-0.690952\pi\)
−0.564554 + 0.825396i \(0.690952\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −414.000 −0.276117 −0.138059 − 0.990424i \(-0.544086\pi\)
−0.138059 + 0.990424i \(0.544086\pi\)
\(132\) 0 0
\(133\) 322.000 0.209932
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 926.000 0.577471 0.288735 − 0.957409i \(-0.406765\pi\)
0.288735 + 0.957409i \(0.406765\pi\)
\(138\) 0 0
\(139\) −494.000 −0.301443 −0.150721 − 0.988576i \(-0.548160\pi\)
−0.150721 + 0.988576i \(0.548160\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1632.00 −0.954369
\(144\) 0 0
\(145\) 2784.00 1.59447
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 474.000 0.260615 0.130307 − 0.991474i \(-0.458404\pi\)
0.130307 + 0.991474i \(0.458404\pi\)
\(150\) 0 0
\(151\) −88.0000 −0.0474261 −0.0237130 − 0.999719i \(-0.507549\pi\)
−0.0237130 + 0.999719i \(0.507549\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1856.00 0.961790
\(156\) 0 0
\(157\) 2972.00 1.51077 0.755387 − 0.655279i \(-0.227449\pi\)
0.755387 + 0.655279i \(0.227449\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1232.00 0.603076
\(162\) 0 0
\(163\) 1480.00 0.711181 0.355591 − 0.934642i \(-0.384280\pi\)
0.355591 + 0.934642i \(0.384280\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2500.00 1.15842 0.579209 − 0.815179i \(-0.303362\pi\)
0.579209 + 0.815179i \(0.303362\pi\)
\(168\) 0 0
\(169\) 2427.00 1.10469
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −980.000 −0.430682 −0.215341 − 0.976539i \(-0.569086\pi\)
−0.215341 + 0.976539i \(0.569086\pi\)
\(174\) 0 0
\(175\) 917.000 0.396107
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2580.00 −1.07731 −0.538654 − 0.842527i \(-0.681067\pi\)
−0.538654 + 0.842527i \(0.681067\pi\)
\(180\) 0 0
\(181\) 2388.00 0.980655 0.490328 − 0.871538i \(-0.336877\pi\)
0.490328 + 0.871538i \(0.336877\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1184.00 0.470537
\(186\) 0 0
\(187\) −1296.00 −0.506807
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1912.00 −0.724332 −0.362166 − 0.932114i \(-0.617963\pi\)
−0.362166 + 0.932114i \(0.617963\pi\)
\(192\) 0 0
\(193\) −1938.00 −0.722799 −0.361400 − 0.932411i \(-0.617701\pi\)
−0.361400 + 0.932411i \(0.617701\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 122.000 0.0441225 0.0220613 − 0.999757i \(-0.492977\pi\)
0.0220613 + 0.999757i \(0.492977\pi\)
\(198\) 0 0
\(199\) 3900.00 1.38926 0.694632 − 0.719365i \(-0.255567\pi\)
0.694632 + 0.719365i \(0.255567\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1218.00 0.421117
\(204\) 0 0
\(205\) 160.000 0.0545116
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1104.00 0.365384
\(210\) 0 0
\(211\) 1164.00 0.379778 0.189889 − 0.981806i \(-0.439187\pi\)
0.189889 + 0.981806i \(0.439187\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7680.00 2.43615
\(216\) 0 0
\(217\) 812.000 0.254019
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3672.00 1.11767
\(222\) 0 0
\(223\) −1480.00 −0.444431 −0.222216 − 0.974998i \(-0.571329\pi\)
−0.222216 + 0.974998i \(0.571329\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3906.00 1.14207 0.571036 − 0.820925i \(-0.306542\pi\)
0.571036 + 0.820925i \(0.306542\pi\)
\(228\) 0 0
\(229\) 252.000 0.0727189 0.0363595 − 0.999339i \(-0.488424\pi\)
0.0363595 + 0.999339i \(0.488424\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2070.00 0.582018 0.291009 − 0.956720i \(-0.406009\pi\)
0.291009 + 0.956720i \(0.406009\pi\)
\(234\) 0 0
\(235\) −9152.00 −2.54047
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5352.00 −1.44850 −0.724251 − 0.689536i \(-0.757814\pi\)
−0.724251 + 0.689536i \(0.757814\pi\)
\(240\) 0 0
\(241\) −6298.00 −1.68336 −0.841680 − 0.539976i \(-0.818433\pi\)
−0.841680 + 0.539976i \(0.818433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 784.000 0.204441
\(246\) 0 0
\(247\) −3128.00 −0.805789
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1810.00 −0.455164 −0.227582 − 0.973759i \(-0.573082\pi\)
−0.227582 + 0.973759i \(0.573082\pi\)
\(252\) 0 0
\(253\) 4224.00 1.04965
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 334.000 0.0810675 0.0405338 − 0.999178i \(-0.487094\pi\)
0.0405338 + 0.999178i \(0.487094\pi\)
\(258\) 0 0
\(259\) 518.000 0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3488.00 −0.817792 −0.408896 − 0.912581i \(-0.634086\pi\)
−0.408896 + 0.912581i \(0.634086\pi\)
\(264\) 0 0
\(265\) 2592.00 0.600850
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3796.00 −0.860395 −0.430197 − 0.902735i \(-0.641556\pi\)
−0.430197 + 0.902735i \(0.641556\pi\)
\(270\) 0 0
\(271\) −2416.00 −0.541556 −0.270778 − 0.962642i \(-0.587281\pi\)
−0.270778 + 0.962642i \(0.587281\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3144.00 0.689419
\(276\) 0 0
\(277\) 6734.00 1.46067 0.730337 − 0.683087i \(-0.239363\pi\)
0.730337 + 0.683087i \(0.239363\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2250.00 −0.477665 −0.238832 − 0.971061i \(-0.576765\pi\)
−0.238832 + 0.971061i \(0.576765\pi\)
\(282\) 0 0
\(283\) −3642.00 −0.764998 −0.382499 − 0.923956i \(-0.624936\pi\)
−0.382499 + 0.923956i \(0.624936\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 70.0000 0.0143971
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7288.00 1.45314 0.726569 − 0.687093i \(-0.241114\pi\)
0.726569 + 0.687093i \(0.241114\pi\)
\(294\) 0 0
\(295\) −1376.00 −0.271572
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −11968.0 −2.31481
\(300\) 0 0
\(301\) 3360.00 0.643413
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −14464.0 −2.71543
\(306\) 0 0
\(307\) 3790.00 0.704582 0.352291 − 0.935890i \(-0.385403\pi\)
0.352291 + 0.935890i \(0.385403\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2760.00 0.503232 0.251616 − 0.967827i \(-0.419038\pi\)
0.251616 + 0.967827i \(0.419038\pi\)
\(312\) 0 0
\(313\) −6714.00 −1.21245 −0.606226 − 0.795292i \(-0.707317\pi\)
−0.606226 + 0.795292i \(0.707317\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6386.00 1.13146 0.565731 − 0.824590i \(-0.308594\pi\)
0.565731 + 0.824590i \(0.308594\pi\)
\(318\) 0 0
\(319\) 4176.00 0.732950
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2484.00 −0.427905
\(324\) 0 0
\(325\) −8908.00 −1.52039
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4004.00 −0.670966
\(330\) 0 0
\(331\) −7168.00 −1.19030 −0.595149 − 0.803615i \(-0.702907\pi\)
−0.595149 + 0.803615i \(0.702907\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10560.0 −1.72225
\(336\) 0 0
\(337\) 2478.00 0.400550 0.200275 − 0.979740i \(-0.435816\pi\)
0.200275 + 0.979740i \(0.435816\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2784.00 0.442117
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2144.00 −0.331689 −0.165844 − 0.986152i \(-0.553035\pi\)
−0.165844 + 0.986152i \(0.553035\pi\)
\(348\) 0 0
\(349\) 7652.00 1.17365 0.586823 − 0.809716i \(-0.300379\pi\)
0.586823 + 0.809716i \(0.300379\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7442.00 −1.12209 −0.561045 − 0.827785i \(-0.689600\pi\)
−0.561045 + 0.827785i \(0.689600\pi\)
\(354\) 0 0
\(355\) 16384.0 2.44950
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2616.00 0.384588 0.192294 − 0.981337i \(-0.438407\pi\)
0.192294 + 0.981337i \(0.438407\pi\)
\(360\) 0 0
\(361\) −4743.00 −0.691500
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 12320.0 1.76673
\(366\) 0 0
\(367\) 6616.00 0.941015 0.470507 − 0.882396i \(-0.344071\pi\)
0.470507 + 0.882396i \(0.344071\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1134.00 0.158691
\(372\) 0 0
\(373\) −3770.00 −0.523333 −0.261666 − 0.965158i \(-0.584272\pi\)
−0.261666 + 0.965158i \(0.584272\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −11832.0 −1.61639
\(378\) 0 0
\(379\) 6232.00 0.844634 0.422317 − 0.906448i \(-0.361217\pi\)
0.422317 + 0.906448i \(0.361217\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12212.0 1.62925 0.814627 − 0.579986i \(-0.196942\pi\)
0.814627 + 0.579986i \(0.196942\pi\)
\(384\) 0 0
\(385\) 2688.00 0.355826
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7706.00 −1.00440 −0.502198 − 0.864753i \(-0.667475\pi\)
−0.502198 + 0.864753i \(0.667475\pi\)
\(390\) 0 0
\(391\) −9504.00 −1.22925
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14464.0 1.84244
\(396\) 0 0
\(397\) −9260.00 −1.17065 −0.585323 − 0.810801i \(-0.699032\pi\)
−0.585323 + 0.810801i \(0.699032\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2638.00 −0.328517 −0.164259 − 0.986417i \(-0.552523\pi\)
−0.164259 + 0.986417i \(0.552523\pi\)
\(402\) 0 0
\(403\) −7888.00 −0.975011
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1776.00 0.216297
\(408\) 0 0
\(409\) −9122.00 −1.10282 −0.551411 − 0.834234i \(-0.685910\pi\)
−0.551411 + 0.834234i \(0.685910\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −602.000 −0.0717251
\(414\) 0 0
\(415\) 10912.0 1.29072
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5370.00 −0.626114 −0.313057 − 0.949734i \(-0.601353\pi\)
−0.313057 + 0.949734i \(0.601353\pi\)
\(420\) 0 0
\(421\) 8046.00 0.931444 0.465722 − 0.884931i \(-0.345795\pi\)
0.465722 + 0.884931i \(0.345795\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7074.00 −0.807387
\(426\) 0 0
\(427\) −6328.00 −0.717174
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5064.00 −0.565950 −0.282975 − 0.959127i \(-0.591321\pi\)
−0.282975 + 0.959127i \(0.591321\pi\)
\(432\) 0 0
\(433\) −7922.00 −0.879231 −0.439616 − 0.898186i \(-0.644885\pi\)
−0.439616 + 0.898186i \(0.644885\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8096.00 0.886234
\(438\) 0 0
\(439\) 1080.00 0.117416 0.0587080 − 0.998275i \(-0.481302\pi\)
0.0587080 + 0.998275i \(0.481302\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3740.00 0.401112 0.200556 − 0.979682i \(-0.435725\pi\)
0.200556 + 0.979682i \(0.435725\pi\)
\(444\) 0 0
\(445\) 1632.00 0.173852
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5458.00 −0.573672 −0.286836 − 0.957980i \(-0.592604\pi\)
−0.286836 + 0.957980i \(0.592604\pi\)
\(450\) 0 0
\(451\) 240.000 0.0250580
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7616.00 −0.784711
\(456\) 0 0
\(457\) −3674.00 −0.376067 −0.188033 − 0.982163i \(-0.560211\pi\)
−0.188033 + 0.982163i \(0.560211\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6252.00 −0.631637 −0.315819 − 0.948820i \(-0.602279\pi\)
−0.315819 + 0.948820i \(0.602279\pi\)
\(462\) 0 0
\(463\) −19472.0 −1.95452 −0.977258 − 0.212055i \(-0.931984\pi\)
−0.977258 + 0.212055i \(0.931984\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2806.00 −0.278043 −0.139022 − 0.990289i \(-0.544396\pi\)
−0.139022 + 0.990289i \(0.544396\pi\)
\(468\) 0 0
\(469\) −4620.00 −0.454865
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11520.0 1.11985
\(474\) 0 0
\(475\) 6026.00 0.582088
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 588.000 0.0560885 0.0280443 − 0.999607i \(-0.491072\pi\)
0.0280443 + 0.999607i \(0.491072\pi\)
\(480\) 0 0
\(481\) −5032.00 −0.477005
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3488.00 −0.326561
\(486\) 0 0
\(487\) 7136.00 0.663990 0.331995 − 0.943281i \(-0.392278\pi\)
0.331995 + 0.943281i \(0.392278\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7140.00 −0.656260 −0.328130 − 0.944633i \(-0.606418\pi\)
−0.328130 + 0.944633i \(0.606418\pi\)
\(492\) 0 0
\(493\) −9396.00 −0.858366
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7168.00 0.646939
\(498\) 0 0
\(499\) 12908.0 1.15800 0.578999 − 0.815328i \(-0.303443\pi\)
0.578999 + 0.815328i \(0.303443\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12192.0 −1.08074 −0.540372 − 0.841426i \(-0.681717\pi\)
−0.540372 + 0.841426i \(0.681717\pi\)
\(504\) 0 0
\(505\) 1280.00 0.112791
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −420.000 −0.0365740 −0.0182870 − 0.999833i \(-0.505821\pi\)
−0.0182870 + 0.999833i \(0.505821\pi\)
\(510\) 0 0
\(511\) 5390.00 0.466614
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1728.00 −0.147854
\(516\) 0 0
\(517\) −13728.0 −1.16781
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −18582.0 −1.56256 −0.781279 − 0.624183i \(-0.785432\pi\)
−0.781279 + 0.624183i \(0.785432\pi\)
\(522\) 0 0
\(523\) −17106.0 −1.43020 −0.715099 − 0.699024i \(-0.753618\pi\)
−0.715099 + 0.699024i \(0.753618\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6264.00 −0.517769
\(528\) 0 0
\(529\) 18809.0 1.54590
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −680.000 −0.0552609
\(534\) 0 0
\(535\) 23872.0 1.92912
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1176.00 0.0939776
\(540\) 0 0
\(541\) −8786.00 −0.698225 −0.349112 − 0.937081i \(-0.613517\pi\)
−0.349112 + 0.937081i \(0.613517\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −24160.0 −1.89890
\(546\) 0 0
\(547\) 7952.00 0.621578 0.310789 − 0.950479i \(-0.399407\pi\)
0.310789 + 0.950479i \(0.399407\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8004.00 0.618842
\(552\) 0 0
\(553\) 6328.00 0.486607
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9042.00 0.687831 0.343915 − 0.939001i \(-0.388247\pi\)
0.343915 + 0.939001i \(0.388247\pi\)
\(558\) 0 0
\(559\) −32640.0 −2.46963
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22818.0 −1.70811 −0.854053 − 0.520185i \(-0.825863\pi\)
−0.854053 + 0.520185i \(0.825863\pi\)
\(564\) 0 0
\(565\) 34208.0 2.54715
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −726.000 −0.0534895 −0.0267447 − 0.999642i \(-0.508514\pi\)
−0.0267447 + 0.999642i \(0.508514\pi\)
\(570\) 0 0
\(571\) 2504.00 0.183519 0.0917593 − 0.995781i \(-0.470751\pi\)
0.0917593 + 0.995781i \(0.470751\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 23056.0 1.67218
\(576\) 0 0
\(577\) −16158.0 −1.16580 −0.582900 − 0.812544i \(-0.698082\pi\)
−0.582900 + 0.812544i \(0.698082\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4774.00 0.340893
\(582\) 0 0
\(583\) 3888.00 0.276200
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2070.00 0.145550 0.0727752 − 0.997348i \(-0.476814\pi\)
0.0727752 + 0.997348i \(0.476814\pi\)
\(588\) 0 0
\(589\) 5336.00 0.373287
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7002.00 −0.484886 −0.242443 − 0.970166i \(-0.577949\pi\)
−0.242443 + 0.970166i \(0.577949\pi\)
\(594\) 0 0
\(595\) −6048.00 −0.416712
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13272.0 −0.905308 −0.452654 − 0.891686i \(-0.649523\pi\)
−0.452654 + 0.891686i \(0.649523\pi\)
\(600\) 0 0
\(601\) −25990.0 −1.76398 −0.881992 − 0.471265i \(-0.843798\pi\)
−0.881992 + 0.471265i \(0.843798\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12080.0 −0.811772
\(606\) 0 0
\(607\) −448.000 −0.0299568 −0.0149784 − 0.999888i \(-0.504768\pi\)
−0.0149784 + 0.999888i \(0.504768\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 38896.0 2.57539
\(612\) 0 0
\(613\) 11018.0 0.725959 0.362979 − 0.931797i \(-0.381760\pi\)
0.362979 + 0.931797i \(0.381760\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3786.00 0.247032 0.123516 − 0.992343i \(-0.460583\pi\)
0.123516 + 0.992343i \(0.460583\pi\)
\(618\) 0 0
\(619\) 342.000 0.0222070 0.0111035 − 0.999938i \(-0.496466\pi\)
0.0111035 + 0.999938i \(0.496466\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 714.000 0.0459162
\(624\) 0 0
\(625\) −14839.0 −0.949696
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3996.00 −0.253308
\(630\) 0 0
\(631\) −26992.0 −1.70291 −0.851454 − 0.524430i \(-0.824279\pi\)
−0.851454 + 0.524430i \(0.824279\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −25856.0 −1.61585
\(636\) 0 0
\(637\) −3332.00 −0.207251
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16978.0 1.04616 0.523082 − 0.852283i \(-0.324782\pi\)
0.523082 + 0.852283i \(0.324782\pi\)
\(642\) 0 0
\(643\) −22510.0 −1.38057 −0.690286 − 0.723537i \(-0.742515\pi\)
−0.690286 + 0.723537i \(0.742515\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9404.00 −0.571421 −0.285711 − 0.958316i \(-0.592230\pi\)
−0.285711 + 0.958316i \(0.592230\pi\)
\(648\) 0 0
\(649\) −2064.00 −0.124837
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4182.00 0.250619 0.125310 − 0.992118i \(-0.460008\pi\)
0.125310 + 0.992118i \(0.460008\pi\)
\(654\) 0 0
\(655\) −6624.00 −0.395147
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6096.00 0.360344 0.180172 − 0.983635i \(-0.442335\pi\)
0.180172 + 0.983635i \(0.442335\pi\)
\(660\) 0 0
\(661\) 6632.00 0.390249 0.195125 − 0.980778i \(-0.437489\pi\)
0.195125 + 0.980778i \(0.437489\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5152.00 0.300430
\(666\) 0 0
\(667\) 30624.0 1.77776
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −21696.0 −1.24823
\(672\) 0 0
\(673\) −1990.00 −0.113980 −0.0569902 − 0.998375i \(-0.518150\pi\)
−0.0569902 + 0.998375i \(0.518150\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22124.0 1.25597 0.627987 − 0.778224i \(-0.283879\pi\)
0.627987 + 0.778224i \(0.283879\pi\)
\(678\) 0 0
\(679\) −1526.00 −0.0862482
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6428.00 0.360118 0.180059 − 0.983656i \(-0.442371\pi\)
0.180059 + 0.983656i \(0.442371\pi\)
\(684\) 0 0
\(685\) 14816.0 0.826409
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11016.0 −0.609109
\(690\) 0 0
\(691\) 23838.0 1.31236 0.656180 − 0.754605i \(-0.272171\pi\)
0.656180 + 0.754605i \(0.272171\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7904.00 −0.431390
\(696\) 0 0
\(697\) −540.000 −0.0293457
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 886.000 0.0477372 0.0238686 − 0.999715i \(-0.492402\pi\)
0.0238686 + 0.999715i \(0.492402\pi\)
\(702\) 0 0
\(703\) 3404.00 0.182623
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 560.000 0.0297892
\(708\) 0 0
\(709\) 16602.0 0.879409 0.439705 − 0.898142i \(-0.355083\pi\)
0.439705 + 0.898142i \(0.355083\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20416.0 1.07235
\(714\) 0 0
\(715\) −26112.0 −1.36578
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 27260.0 1.41394 0.706972 − 0.707241i \(-0.250060\pi\)
0.706972 + 0.707241i \(0.250060\pi\)
\(720\) 0 0
\(721\) −756.000 −0.0390498
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 22794.0 1.16765
\(726\) 0 0
\(727\) 3652.00 0.186307 0.0931535 − 0.995652i \(-0.470305\pi\)
0.0931535 + 0.995652i \(0.470305\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −25920.0 −1.31147
\(732\) 0 0
\(733\) −13432.0 −0.676838 −0.338419 − 0.940996i \(-0.609892\pi\)
−0.338419 + 0.940996i \(0.609892\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15840.0 −0.791688
\(738\) 0 0
\(739\) −34360.0 −1.71036 −0.855178 − 0.518334i \(-0.826552\pi\)
−0.855178 + 0.518334i \(0.826552\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5624.00 −0.277691 −0.138846 − 0.990314i \(-0.544339\pi\)
−0.138846 + 0.990314i \(0.544339\pi\)
\(744\) 0 0
\(745\) 7584.00 0.372961
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10444.0 0.509500
\(750\) 0 0
\(751\) −10392.0 −0.504939 −0.252470 − 0.967605i \(-0.581243\pi\)
−0.252470 + 0.967605i \(0.581243\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1408.00 −0.0678707
\(756\) 0 0
\(757\) 2666.00 0.128002 0.0640009 − 0.997950i \(-0.479614\pi\)
0.0640009 + 0.997950i \(0.479614\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3138.00 0.149478 0.0747388 − 0.997203i \(-0.476188\pi\)
0.0747388 + 0.997203i \(0.476188\pi\)
\(762\) 0 0
\(763\) −10570.0 −0.501520
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5848.00 0.275305
\(768\) 0 0
\(769\) 38878.0 1.82312 0.911558 − 0.411171i \(-0.134880\pi\)
0.911558 + 0.411171i \(0.134880\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3976.00 −0.185002 −0.0925012 − 0.995713i \(-0.529486\pi\)
−0.0925012 + 0.995713i \(0.529486\pi\)
\(774\) 0 0
\(775\) 15196.0 0.704331
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 460.000 0.0211569
\(780\) 0 0
\(781\) 24576.0 1.12599
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 47552.0 2.16204
\(786\) 0 0
\(787\) −23258.0 −1.05344 −0.526721 − 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14966.0 0.672730
\(792\) 0 0
\(793\) 61472.0 2.75276
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2604.00 0.115732 0.0578660 − 0.998324i \(-0.481570\pi\)
0.0578660 + 0.998324i \(0.481570\pi\)
\(798\) 0 0
\(799\) 30888.0 1.36763
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 18480.0 0.812136
\(804\) 0 0
\(805\) 19712.0 0.863052
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −39926.0 −1.73513 −0.867567 − 0.497320i \(-0.834317\pi\)
−0.867567 + 0.497320i \(0.834317\pi\)
\(810\) 0 0
\(811\) 17422.0 0.754339 0.377170 − 0.926144i \(-0.376897\pi\)
0.377170 + 0.926144i \(0.376897\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 23680.0 1.01776
\(816\) 0 0
\(817\) 22080.0 0.945510
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3870.00 −0.164511 −0.0822557 − 0.996611i \(-0.526212\pi\)
−0.0822557 + 0.996611i \(0.526212\pi\)
\(822\) 0 0
\(823\) 22120.0 0.936883 0.468442 − 0.883495i \(-0.344816\pi\)
0.468442 + 0.883495i \(0.344816\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −13724.0 −0.577062 −0.288531 − 0.957471i \(-0.593167\pi\)
−0.288531 + 0.957471i \(0.593167\pi\)
\(828\) 0 0
\(829\) −11320.0 −0.474258 −0.237129 − 0.971478i \(-0.576206\pi\)
−0.237129 + 0.971478i \(0.576206\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2646.00 −0.110058
\(834\) 0 0
\(835\) 40000.0 1.65779
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 18876.0 0.776725 0.388362 − 0.921507i \(-0.373041\pi\)
0.388362 + 0.921507i \(0.373041\pi\)
\(840\) 0 0
\(841\) 5887.00 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 38832.0 1.58090
\(846\) 0 0
\(847\) −5285.00 −0.214398
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 13024.0 0.524626
\(852\) 0 0
\(853\) −33748.0 −1.35464 −0.677321 − 0.735688i \(-0.736859\pi\)
−0.677321 + 0.735688i \(0.736859\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3230.00 −0.128745 −0.0643726 − 0.997926i \(-0.520505\pi\)
−0.0643726 + 0.997926i \(0.520505\pi\)
\(858\) 0 0
\(859\) 43922.0 1.74459 0.872293 − 0.488984i \(-0.162632\pi\)
0.872293 + 0.488984i \(0.162632\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26968.0 1.06373 0.531866 − 0.846828i \(-0.321491\pi\)
0.531866 + 0.846828i \(0.321491\pi\)
\(864\) 0 0
\(865\) −15680.0 −0.616342
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 21696.0 0.846935
\(870\) 0 0
\(871\) 44880.0 1.74593
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 672.000 0.0259631
\(876\) 0 0
\(877\) −11486.0 −0.442252 −0.221126 − 0.975245i \(-0.570973\pi\)
−0.221126 + 0.975245i \(0.570973\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −22026.0 −0.842310 −0.421155 − 0.906989i \(-0.638375\pi\)
−0.421155 + 0.906989i \(0.638375\pi\)
\(882\) 0 0
\(883\) −8428.00 −0.321206 −0.160603 − 0.987019i \(-0.551344\pi\)
−0.160603 + 0.987019i \(0.551344\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −18996.0 −0.719079 −0.359540 − 0.933130i \(-0.617066\pi\)
−0.359540 + 0.933130i \(0.617066\pi\)
\(888\) 0 0
\(889\) −11312.0 −0.426763
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −26312.0 −0.985999
\(894\) 0 0
\(895\) −41280.0 −1.54172
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 20184.0 0.748803
\(900\) 0 0
\(901\) −8748.00 −0.323461
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 38208.0 1.40340
\(906\) 0 0
\(907\) −20948.0 −0.766887 −0.383444 − 0.923564i \(-0.625262\pi\)
−0.383444 + 0.923564i \(0.625262\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1392.00 −0.0506246 −0.0253123 − 0.999680i \(-0.508058\pi\)
−0.0253123 + 0.999680i \(0.508058\pi\)
\(912\) 0 0
\(913\) 16368.0 0.593321
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2898.00 −0.104362
\(918\) 0 0
\(919\) −41432.0 −1.48718 −0.743588 − 0.668638i \(-0.766878\pi\)
−0.743588 + 0.668638i \(0.766878\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −69632.0 −2.48317
\(924\) 0 0
\(925\) 9694.00 0.344580
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 25674.0 0.906713 0.453357 − 0.891329i \(-0.350226\pi\)
0.453357 + 0.891329i \(0.350226\pi\)
\(930\) 0 0
\(931\) 2254.00 0.0793468
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −20736.0 −0.725283
\(936\) 0 0
\(937\) −46238.0 −1.61209 −0.806046 − 0.591853i \(-0.798396\pi\)
−0.806046 + 0.591853i \(0.798396\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −17432.0 −0.603897 −0.301948 − 0.953324i \(-0.597637\pi\)
−0.301948 + 0.953324i \(0.597637\pi\)
\(942\) 0 0
\(943\) 1760.00 0.0607778
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26880.0 0.922368 0.461184 − 0.887304i \(-0.347425\pi\)
0.461184 + 0.887304i \(0.347425\pi\)
\(948\) 0 0
\(949\) −52360.0 −1.79102
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −30970.0 −1.05269 −0.526347 − 0.850270i \(-0.676439\pi\)
−0.526347 + 0.850270i \(0.676439\pi\)
\(954\) 0 0
\(955\) −30592.0 −1.03658
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6482.00 0.218264
\(960\) 0 0
\(961\) −16335.0 −0.548320
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −31008.0 −1.03439
\(966\) 0 0
\(967\) 19344.0 0.643290 0.321645 − 0.946860i \(-0.395764\pi\)
0.321645 + 0.946860i \(0.395764\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 50122.0 1.65653 0.828265 − 0.560336i \(-0.189328\pi\)
0.828265 + 0.560336i \(0.189328\pi\)
\(972\) 0 0
\(973\) −3458.00 −0.113935
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −25850.0 −0.846484 −0.423242 − 0.906017i \(-0.639108\pi\)
−0.423242 + 0.906017i \(0.639108\pi\)
\(978\) 0 0
\(979\) 2448.00 0.0799167
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 32012.0 1.03868 0.519341 − 0.854567i \(-0.326177\pi\)
0.519341 + 0.854567i \(0.326177\pi\)
\(984\) 0 0
\(985\) 1952.00 0.0631430
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 84480.0 2.71619
\(990\) 0 0
\(991\) −18240.0 −0.584675 −0.292337 − 0.956315i \(-0.594433\pi\)
−0.292337 + 0.956315i \(0.594433\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 62400.0 1.98815
\(996\) 0 0
\(997\) −23144.0 −0.735183 −0.367592 − 0.929987i \(-0.619818\pi\)
−0.367592 + 0.929987i \(0.619818\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.4.a.u.1.1 1
3.2 odd 2 112.4.a.d.1.1 1
4.3 odd 2 504.4.a.g.1.1 1
12.11 even 2 56.4.a.a.1.1 ✓ 1
21.20 even 2 784.4.a.i.1.1 1
24.5 odd 2 448.4.a.h.1.1 1
24.11 even 2 448.4.a.l.1.1 1
60.23 odd 4 1400.4.g.f.449.1 2
60.47 odd 4 1400.4.g.f.449.2 2
60.59 even 2 1400.4.a.f.1.1 1
84.11 even 6 392.4.i.e.177.1 2
84.23 even 6 392.4.i.e.361.1 2
84.47 odd 6 392.4.i.d.361.1 2
84.59 odd 6 392.4.i.d.177.1 2
84.83 odd 2 392.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.4.a.a.1.1 ✓ 1 12.11 even 2
112.4.a.d.1.1 1 3.2 odd 2
392.4.a.c.1.1 1 84.83 odd 2
392.4.i.d.177.1 2 84.59 odd 6
392.4.i.d.361.1 2 84.47 odd 6
392.4.i.e.177.1 2 84.11 even 6
392.4.i.e.361.1 2 84.23 even 6
448.4.a.h.1.1 1 24.5 odd 2
448.4.a.l.1.1 1 24.11 even 2
504.4.a.g.1.1 1 4.3 odd 2
784.4.a.i.1.1 1 21.20 even 2
1008.4.a.u.1.1 1 1.1 even 1 trivial
1400.4.a.f.1.1 1 60.59 even 2
1400.4.g.f.449.1 2 60.23 odd 4
1400.4.g.f.449.2 2 60.47 odd 4