Properties

Label 1008.6.a.be.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $2$
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] = [1008,6,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, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{429}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 107 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-9.85616\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q+1.42463 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+1.42463 q^{5} -49.0000 q^{7} +91.7261 q^{11} +224.794 q^{13} +1045.37 q^{17} +1013.21 q^{19} -2689.42 q^{23} -3122.97 q^{25} -7659.83 q^{29} -8188.32 q^{31} -69.8069 q^{35} +9108.73 q^{37} +18305.0 q^{41} +22387.1 q^{43} +4852.82 q^{47} +2401.00 q^{49} +940.063 q^{53} +130.676 q^{55} +13198.7 q^{59} +2987.79 q^{61} +320.248 q^{65} -37064.7 q^{67} -76872.6 q^{71} -50245.5 q^{73} -4494.58 q^{77} +10646.9 q^{79} -13803.0 q^{83} +1489.27 q^{85} +30996.7 q^{89} -11014.9 q^{91} +1443.44 q^{95} +99406.6 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 80 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 80 q^{5} - 98 q^{7} + 432 q^{11} - 876 q^{13} + 848 q^{17} + 3352 q^{19} - 5296 q^{23} + 382 q^{25} + 256 q^{29} + 856 q^{31} + 3920 q^{35} + 3636 q^{37} + 3056 q^{41} + 26216 q^{43} + 2912 q^{47} + 4802 q^{49} + 27232 q^{53} - 27576 q^{55} + 59040 q^{59} - 40420 q^{61} + 89952 q^{65} - 52920 q^{67} - 52752 q^{71} + 18812 q^{73} - 21168 q^{77} - 50288 q^{79} - 66048 q^{83} + 17560 q^{85} + 131504 q^{89} + 42924 q^{91} - 188992 q^{95} + 164348 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 1.42463 0.0254846 0.0127423 0.999919i \(-0.495944\pi\)
0.0127423 + 0.999919i \(0.495944\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 91.7261 0.228566 0.114283 0.993448i \(-0.463543\pi\)
0.114283 + 0.993448i \(0.463543\pi\)
\(12\) 0 0
\(13\) 224.794 0.368915 0.184458 0.982840i \(-0.440947\pi\)
0.184458 + 0.982840i \(0.440947\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1045.37 0.877299 0.438649 0.898658i \(-0.355457\pi\)
0.438649 + 0.898658i \(0.355457\pi\)
\(18\) 0 0
\(19\) 1013.21 0.643893 0.321947 0.946758i \(-0.395663\pi\)
0.321947 + 0.946758i \(0.395663\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2689.42 −1.06008 −0.530041 0.847972i \(-0.677824\pi\)
−0.530041 + 0.847972i \(0.677824\pi\)
\(24\) 0 0
\(25\) −3122.97 −0.999351
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7659.83 −1.69131 −0.845657 0.533727i \(-0.820791\pi\)
−0.845657 + 0.533727i \(0.820791\pi\)
\(30\) 0 0
\(31\) −8188.32 −1.53035 −0.765175 0.643822i \(-0.777348\pi\)
−0.765175 + 0.643822i \(0.777348\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −69.8069 −0.00963226
\(36\) 0 0
\(37\) 9108.73 1.09384 0.546920 0.837185i \(-0.315800\pi\)
0.546920 + 0.837185i \(0.315800\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 18305.0 1.70063 0.850314 0.526275i \(-0.176412\pi\)
0.850314 + 0.526275i \(0.176412\pi\)
\(42\) 0 0
\(43\) 22387.1 1.84641 0.923203 0.384314i \(-0.125562\pi\)
0.923203 + 0.384314i \(0.125562\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4852.82 0.320442 0.160221 0.987081i \(-0.448779\pi\)
0.160221 + 0.987081i \(0.448779\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 940.063 0.0459692 0.0229846 0.999736i \(-0.492683\pi\)
0.0229846 + 0.999736i \(0.492683\pi\)
\(54\) 0 0
\(55\) 130.676 0.00582490
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13198.7 0.493629 0.246815 0.969063i \(-0.420616\pi\)
0.246815 + 0.969063i \(0.420616\pi\)
\(60\) 0 0
\(61\) 2987.79 0.102808 0.0514039 0.998678i \(-0.483630\pi\)
0.0514039 + 0.998678i \(0.483630\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 320.248 0.00940164
\(66\) 0 0
\(67\) −37064.7 −1.00873 −0.504363 0.863492i \(-0.668273\pi\)
−0.504363 + 0.863492i \(0.668273\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −76872.6 −1.80978 −0.904890 0.425645i \(-0.860047\pi\)
−0.904890 + 0.425645i \(0.860047\pi\)
\(72\) 0 0
\(73\) −50245.5 −1.10354 −0.551772 0.833995i \(-0.686048\pi\)
−0.551772 + 0.833995i \(0.686048\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4494.58 −0.0863898
\(78\) 0 0
\(79\) 10646.9 0.191935 0.0959676 0.995384i \(-0.469405\pi\)
0.0959676 + 0.995384i \(0.469405\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −13803.0 −0.219926 −0.109963 0.993936i \(-0.535073\pi\)
−0.109963 + 0.993936i \(0.535073\pi\)
\(84\) 0 0
\(85\) 1489.27 0.0223576
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 30996.7 0.414802 0.207401 0.978256i \(-0.433499\pi\)
0.207401 + 0.978256i \(0.433499\pi\)
\(90\) 0 0
\(91\) −11014.9 −0.139437
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1443.44 0.0164093
\(96\) 0 0
\(97\) 99406.6 1.07272 0.536360 0.843990i \(-0.319799\pi\)
0.536360 + 0.843990i \(0.319799\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 190238. 1.85564 0.927821 0.373027i \(-0.121680\pi\)
0.927821 + 0.373027i \(0.121680\pi\)
\(102\) 0 0
\(103\) −24516.0 −0.227697 −0.113848 0.993498i \(-0.536318\pi\)
−0.113848 + 0.993498i \(0.536318\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −142231. −1.20098 −0.600491 0.799632i \(-0.705028\pi\)
−0.600491 + 0.799632i \(0.705028\pi\)
\(108\) 0 0
\(109\) −123869. −0.998612 −0.499306 0.866426i \(-0.666412\pi\)
−0.499306 + 0.866426i \(0.666412\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 49772.7 0.366686 0.183343 0.983049i \(-0.441308\pi\)
0.183343 + 0.983049i \(0.441308\pi\)
\(114\) 0 0
\(115\) −3831.44 −0.0270157
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −51223.1 −0.331588
\(120\) 0 0
\(121\) −152637. −0.947758
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8901.05 −0.0509526
\(126\) 0 0
\(127\) −168621. −0.927687 −0.463844 0.885917i \(-0.653530\pi\)
−0.463844 + 0.885917i \(0.653530\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −165483. −0.842512 −0.421256 0.906942i \(-0.638411\pi\)
−0.421256 + 0.906942i \(0.638411\pi\)
\(132\) 0 0
\(133\) −49647.1 −0.243369
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 224888. 1.02368 0.511842 0.859080i \(-0.328963\pi\)
0.511842 + 0.859080i \(0.328963\pi\)
\(138\) 0 0
\(139\) 81205.3 0.356490 0.178245 0.983986i \(-0.442958\pi\)
0.178245 + 0.983986i \(0.442958\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 20619.5 0.0843214
\(144\) 0 0
\(145\) −10912.4 −0.0431024
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 28149.2 0.103873 0.0519363 0.998650i \(-0.483461\pi\)
0.0519363 + 0.998650i \(0.483461\pi\)
\(150\) 0 0
\(151\) −159410. −0.568948 −0.284474 0.958684i \(-0.591819\pi\)
−0.284474 + 0.958684i \(0.591819\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11665.3 −0.0390003
\(156\) 0 0
\(157\) 301600. 0.976522 0.488261 0.872698i \(-0.337631\pi\)
0.488261 + 0.872698i \(0.337631\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 131782. 0.400674
\(162\) 0 0
\(163\) −259215. −0.764173 −0.382086 0.924127i \(-0.624794\pi\)
−0.382086 + 0.924127i \(0.624794\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −670935. −1.86161 −0.930807 0.365512i \(-0.880894\pi\)
−0.930807 + 0.365512i \(0.880894\pi\)
\(168\) 0 0
\(169\) −320761. −0.863902
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 425338. 1.08049 0.540243 0.841509i \(-0.318332\pi\)
0.540243 + 0.841509i \(0.318332\pi\)
\(174\) 0 0
\(175\) 153026. 0.377719
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −457231. −1.06660 −0.533301 0.845925i \(-0.679049\pi\)
−0.533301 + 0.845925i \(0.679049\pi\)
\(180\) 0 0
\(181\) −622087. −1.41141 −0.705707 0.708504i \(-0.749371\pi\)
−0.705707 + 0.708504i \(0.749371\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12976.6 0.0278760
\(186\) 0 0
\(187\) 95887.7 0.200520
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 42570.1 0.0844347 0.0422173 0.999108i \(-0.486558\pi\)
0.0422173 + 0.999108i \(0.486558\pi\)
\(192\) 0 0
\(193\) 108849. 0.210345 0.105173 0.994454i \(-0.466460\pi\)
0.105173 + 0.994454i \(0.466460\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 445387. 0.817658 0.408829 0.912611i \(-0.365937\pi\)
0.408829 + 0.912611i \(0.365937\pi\)
\(198\) 0 0
\(199\) −203894. −0.364983 −0.182492 0.983207i \(-0.558416\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 375332. 0.639256
\(204\) 0 0
\(205\) 26077.8 0.0433398
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 92937.4 0.147172
\(210\) 0 0
\(211\) −442304. −0.683934 −0.341967 0.939712i \(-0.611093\pi\)
−0.341967 + 0.939712i \(0.611093\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 31893.4 0.0470548
\(216\) 0 0
\(217\) 401228. 0.578418
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 234993. 0.323649
\(222\) 0 0
\(223\) −988850. −1.33158 −0.665792 0.746138i \(-0.731906\pi\)
−0.665792 + 0.746138i \(0.731906\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −908650. −1.17039 −0.585197 0.810891i \(-0.698983\pi\)
−0.585197 + 0.810891i \(0.698983\pi\)
\(228\) 0 0
\(229\) −822273. −1.03616 −0.518080 0.855332i \(-0.673353\pi\)
−0.518080 + 0.855332i \(0.673353\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 756277. 0.912623 0.456311 0.889820i \(-0.349170\pi\)
0.456311 + 0.889820i \(0.349170\pi\)
\(234\) 0 0
\(235\) 6913.47 0.00816633
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −530659. −0.600926 −0.300463 0.953794i \(-0.597141\pi\)
−0.300463 + 0.953794i \(0.597141\pi\)
\(240\) 0 0
\(241\) −1.67683e6 −1.85972 −0.929858 0.367919i \(-0.880070\pi\)
−0.929858 + 0.367919i \(0.880070\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3420.54 0.00364065
\(246\) 0 0
\(247\) 227763. 0.237542
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.29896e6 1.30140 0.650701 0.759334i \(-0.274475\pi\)
0.650701 + 0.759334i \(0.274475\pi\)
\(252\) 0 0
\(253\) −246690. −0.242299
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.05589e6 −0.997208 −0.498604 0.866830i \(-0.666154\pi\)
−0.498604 + 0.866830i \(0.666154\pi\)
\(258\) 0 0
\(259\) −446328. −0.413433
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 461318. 0.411255 0.205627 0.978630i \(-0.434077\pi\)
0.205627 + 0.978630i \(0.434077\pi\)
\(264\) 0 0
\(265\) 1339.24 0.00117151
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.50754e6 −1.27025 −0.635123 0.772411i \(-0.719051\pi\)
−0.635123 + 0.772411i \(0.719051\pi\)
\(270\) 0 0
\(271\) −1.80207e6 −1.49056 −0.745278 0.666754i \(-0.767683\pi\)
−0.745278 + 0.666754i \(0.767683\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −286458. −0.228417
\(276\) 0 0
\(277\) −827961. −0.648352 −0.324176 0.945997i \(-0.605087\pi\)
−0.324176 + 0.945997i \(0.605087\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −444663. −0.335943 −0.167971 0.985792i \(-0.553722\pi\)
−0.167971 + 0.985792i \(0.553722\pi\)
\(282\) 0 0
\(283\) −1.30880e6 −0.971422 −0.485711 0.874119i \(-0.661439\pi\)
−0.485711 + 0.874119i \(0.661439\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −896944. −0.642777
\(288\) 0 0
\(289\) −327060. −0.230347
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.04355e6 0.710138 0.355069 0.934840i \(-0.384457\pi\)
0.355069 + 0.934840i \(0.384457\pi\)
\(294\) 0 0
\(295\) 18803.3 0.0125799
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −604567. −0.391081
\(300\) 0 0
\(301\) −1.09697e6 −0.697876
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4256.50 0.00262001
\(306\) 0 0
\(307\) 609911. 0.369335 0.184668 0.982801i \(-0.440879\pi\)
0.184668 + 0.982801i \(0.440879\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.83834e6 1.66404 0.832021 0.554744i \(-0.187184\pi\)
0.832021 + 0.554744i \(0.187184\pi\)
\(312\) 0 0
\(313\) 966888. 0.557847 0.278924 0.960313i \(-0.410022\pi\)
0.278924 + 0.960313i \(0.410022\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.88081e6 −1.05123 −0.525615 0.850723i \(-0.676165\pi\)
−0.525615 + 0.850723i \(0.676165\pi\)
\(318\) 0 0
\(319\) −702606. −0.386576
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.05917e6 0.564887
\(324\) 0 0
\(325\) −702025. −0.368676
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −237788. −0.121116
\(330\) 0 0
\(331\) −1.80336e6 −0.904717 −0.452359 0.891836i \(-0.649417\pi\)
−0.452359 + 0.891836i \(0.649417\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −52803.5 −0.0257070
\(336\) 0 0
\(337\) −2.08491e6 −1.00003 −0.500015 0.866017i \(-0.666672\pi\)
−0.500015 + 0.866017i \(0.666672\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −751083. −0.349786
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.41483e6 0.630783 0.315391 0.948962i \(-0.397864\pi\)
0.315391 + 0.948962i \(0.397864\pi\)
\(348\) 0 0
\(349\) −929394. −0.408447 −0.204224 0.978924i \(-0.565467\pi\)
−0.204224 + 0.978924i \(0.565467\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 539719. 0.230532 0.115266 0.993335i \(-0.463228\pi\)
0.115266 + 0.993335i \(0.463228\pi\)
\(354\) 0 0
\(355\) −109515. −0.0461215
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.43124e6 1.40512 0.702562 0.711623i \(-0.252039\pi\)
0.702562 + 0.711623i \(0.252039\pi\)
\(360\) 0 0
\(361\) −1.44951e6 −0.585402
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −71581.2 −0.0281233
\(366\) 0 0
\(367\) −757163. −0.293443 −0.146722 0.989178i \(-0.546872\pi\)
−0.146722 + 0.989178i \(0.546872\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −46063.1 −0.0173747
\(372\) 0 0
\(373\) −1.81560e6 −0.675690 −0.337845 0.941202i \(-0.609698\pi\)
−0.337845 + 0.941202i \(0.609698\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.72188e6 −0.623951
\(378\) 0 0
\(379\) −1.95161e6 −0.697903 −0.348951 0.937141i \(-0.613462\pi\)
−0.348951 + 0.937141i \(0.613462\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.31041e6 0.456467 0.228234 0.973606i \(-0.426705\pi\)
0.228234 + 0.973606i \(0.426705\pi\)
\(384\) 0 0
\(385\) −6403.11 −0.00220161
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.81982e6 −0.944816 −0.472408 0.881380i \(-0.656615\pi\)
−0.472408 + 0.881380i \(0.656615\pi\)
\(390\) 0 0
\(391\) −2.81144e6 −0.930009
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15167.9 0.00489138
\(396\) 0 0
\(397\) −3.74747e6 −1.19334 −0.596668 0.802489i \(-0.703509\pi\)
−0.596668 + 0.802489i \(0.703509\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.57222e6 −0.488260 −0.244130 0.969743i \(-0.578502\pi\)
−0.244130 + 0.969743i \(0.578502\pi\)
\(402\) 0 0
\(403\) −1.84069e6 −0.564569
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 835509. 0.250014
\(408\) 0 0
\(409\) 3.65811e6 1.08130 0.540652 0.841246i \(-0.318178\pi\)
0.540652 + 0.841246i \(0.318178\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −646736. −0.186574
\(414\) 0 0
\(415\) −19664.1 −0.00560473
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 477218. 0.132795 0.0663975 0.997793i \(-0.478849\pi\)
0.0663975 + 0.997793i \(0.478849\pi\)
\(420\) 0 0
\(421\) 3.78986e6 1.04212 0.521060 0.853520i \(-0.325537\pi\)
0.521060 + 0.853520i \(0.325537\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.26466e6 −0.876729
\(426\) 0 0
\(427\) −146402. −0.0388577
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.58044e6 −1.18772 −0.593860 0.804569i \(-0.702397\pi\)
−0.593860 + 0.804569i \(0.702397\pi\)
\(432\) 0 0
\(433\) −3.45781e6 −0.886301 −0.443150 0.896447i \(-0.646139\pi\)
−0.443150 + 0.896447i \(0.646139\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.72494e6 −0.682580
\(438\) 0 0
\(439\) 4.95610e6 1.22738 0.613689 0.789548i \(-0.289685\pi\)
0.613689 + 0.789548i \(0.289685\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.88556e6 0.940685 0.470343 0.882484i \(-0.344130\pi\)
0.470343 + 0.882484i \(0.344130\pi\)
\(444\) 0 0
\(445\) 44158.9 0.0105710
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −590043. −0.138124 −0.0690618 0.997612i \(-0.522001\pi\)
−0.0690618 + 0.997612i \(0.522001\pi\)
\(450\) 0 0
\(451\) 1.67904e6 0.388706
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15692.2 −0.00355349
\(456\) 0 0
\(457\) −2.08724e6 −0.467501 −0.233750 0.972297i \(-0.575100\pi\)
−0.233750 + 0.972297i \(0.575100\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −492088. −0.107843 −0.0539213 0.998545i \(-0.517172\pi\)
−0.0539213 + 0.998545i \(0.517172\pi\)
\(462\) 0 0
\(463\) 2.51852e6 0.546000 0.273000 0.962014i \(-0.411984\pi\)
0.273000 + 0.962014i \(0.411984\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.39504e6 1.78127 0.890637 0.454715i \(-0.150259\pi\)
0.890637 + 0.454715i \(0.150259\pi\)
\(468\) 0 0
\(469\) 1.81617e6 0.381263
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.05348e6 0.422025
\(474\) 0 0
\(475\) −3.16421e6 −0.643475
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.01184e6 1.59549 0.797744 0.602996i \(-0.206027\pi\)
0.797744 + 0.602996i \(0.206027\pi\)
\(480\) 0 0
\(481\) 2.04759e6 0.403534
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 141618. 0.0273378
\(486\) 0 0
\(487\) −5.72223e6 −1.09331 −0.546654 0.837358i \(-0.684099\pi\)
−0.546654 + 0.837358i \(0.684099\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.23498e6 −1.54155 −0.770777 0.637105i \(-0.780132\pi\)
−0.770777 + 0.637105i \(0.780132\pi\)
\(492\) 0 0
\(493\) −8.00735e6 −1.48379
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.76676e6 0.684033
\(498\) 0 0
\(499\) −1.23344e6 −0.221752 −0.110876 0.993834i \(-0.535366\pi\)
−0.110876 + 0.993834i \(0.535366\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.21980e6 −0.567425 −0.283713 0.958909i \(-0.591566\pi\)
−0.283713 + 0.958909i \(0.591566\pi\)
\(504\) 0 0
\(505\) 271019. 0.0472902
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.87503e6 1.34728 0.673640 0.739060i \(-0.264730\pi\)
0.673640 + 0.739060i \(0.264730\pi\)
\(510\) 0 0
\(511\) 2.46203e6 0.417101
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −34926.3 −0.00580276
\(516\) 0 0
\(517\) 445130. 0.0732421
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.29172e6 −1.49969 −0.749846 0.661613i \(-0.769872\pi\)
−0.749846 + 0.661613i \(0.769872\pi\)
\(522\) 0 0
\(523\) −8.51310e6 −1.36092 −0.680461 0.732784i \(-0.738221\pi\)
−0.680461 + 0.732784i \(0.738221\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.55982e6 −1.34257
\(528\) 0 0
\(529\) 796662. 0.123776
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.11485e6 0.627388
\(534\) 0 0
\(535\) −202627. −0.0306065
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 220234. 0.0326523
\(540\) 0 0
\(541\) 2.50333e6 0.367727 0.183864 0.982952i \(-0.441140\pi\)
0.183864 + 0.982952i \(0.441140\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −176468. −0.0254492
\(546\) 0 0
\(547\) 1.58615e6 0.226661 0.113330 0.993557i \(-0.463848\pi\)
0.113330 + 0.993557i \(0.463848\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.76099e6 −1.08903
\(552\) 0 0
\(553\) −521697. −0.0725447
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.66566e6 0.500627 0.250314 0.968165i \(-0.419466\pi\)
0.250314 + 0.968165i \(0.419466\pi\)
\(558\) 0 0
\(559\) 5.03249e6 0.681167
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.37431e6 0.182731 0.0913656 0.995817i \(-0.470877\pi\)
0.0913656 + 0.995817i \(0.470877\pi\)
\(564\) 0 0
\(565\) 70907.7 0.00934484
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −640716. −0.0829631 −0.0414815 0.999139i \(-0.513208\pi\)
−0.0414815 + 0.999139i \(0.513208\pi\)
\(570\) 0 0
\(571\) 1.50255e7 1.92858 0.964289 0.264852i \(-0.0853230\pi\)
0.964289 + 0.264852i \(0.0853230\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.39899e6 1.05939
\(576\) 0 0
\(577\) 1.14721e7 1.43451 0.717253 0.696813i \(-0.245399\pi\)
0.717253 + 0.696813i \(0.245399\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 676346. 0.0831244
\(582\) 0 0
\(583\) 86228.3 0.0105070
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.77624e6 −0.931482 −0.465741 0.884921i \(-0.654212\pi\)
−0.465741 + 0.884921i \(0.654212\pi\)
\(588\) 0 0
\(589\) −8.29646e6 −0.985382
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.48233e6 0.173104 0.0865521 0.996247i \(-0.472415\pi\)
0.0865521 + 0.996247i \(0.472415\pi\)
\(594\) 0 0
\(595\) −72974.0 −0.00845037
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.50168e6 −0.284882 −0.142441 0.989803i \(-0.545495\pi\)
−0.142441 + 0.989803i \(0.545495\pi\)
\(600\) 0 0
\(601\) 7.48878e6 0.845717 0.422858 0.906196i \(-0.361027\pi\)
0.422858 + 0.906196i \(0.361027\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −217452. −0.0241532
\(606\) 0 0
\(607\) −6.14962e6 −0.677449 −0.338724 0.940886i \(-0.609995\pi\)
−0.338724 + 0.940886i \(0.609995\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.09089e6 0.118216
\(612\) 0 0
\(613\) −6.50878e6 −0.699598 −0.349799 0.936825i \(-0.613750\pi\)
−0.349799 + 0.936825i \(0.613750\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.38532e7 1.46499 0.732497 0.680770i \(-0.238355\pi\)
0.732497 + 0.680770i \(0.238355\pi\)
\(618\) 0 0
\(619\) −1.19631e6 −0.125492 −0.0627459 0.998030i \(-0.519986\pi\)
−0.0627459 + 0.998030i \(0.519986\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.51884e6 −0.156780
\(624\) 0 0
\(625\) 9.74660e6 0.998052
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.52199e6 0.959624
\(630\) 0 0
\(631\) 2.25678e6 0.225640 0.112820 0.993615i \(-0.464012\pi\)
0.112820 + 0.993615i \(0.464012\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −240222. −0.0236417
\(636\) 0 0
\(637\) 539731. 0.0527022
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.62873e7 1.56569 0.782843 0.622219i \(-0.213769\pi\)
0.782843 + 0.622219i \(0.213769\pi\)
\(642\) 0 0
\(643\) 1.68780e6 0.160988 0.0804942 0.996755i \(-0.474350\pi\)
0.0804942 + 0.996755i \(0.474350\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.80330e6 −0.169359 −0.0846794 0.996408i \(-0.526987\pi\)
−0.0846794 + 0.996408i \(0.526987\pi\)
\(648\) 0 0
\(649\) 1.21066e6 0.112827
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.55291e7 −1.42516 −0.712581 0.701590i \(-0.752474\pi\)
−0.712581 + 0.701590i \(0.752474\pi\)
\(654\) 0 0
\(655\) −235753. −0.0214711
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.05891e7 −1.84682 −0.923409 0.383816i \(-0.874610\pi\)
−0.923409 + 0.383816i \(0.874610\pi\)
\(660\) 0 0
\(661\) −8.11279e6 −0.722215 −0.361108 0.932524i \(-0.617601\pi\)
−0.361108 + 0.932524i \(0.617601\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −70728.8 −0.00620214
\(666\) 0 0
\(667\) 2.06005e7 1.79293
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 274059. 0.0234983
\(672\) 0 0
\(673\) 1.86442e7 1.58674 0.793370 0.608740i \(-0.208325\pi\)
0.793370 + 0.608740i \(0.208325\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.86500e7 −1.56389 −0.781947 0.623345i \(-0.785773\pi\)
−0.781947 + 0.623345i \(0.785773\pi\)
\(678\) 0 0
\(679\) −4.87093e6 −0.405450
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.70213e7 −1.39618 −0.698091 0.716009i \(-0.745967\pi\)
−0.698091 + 0.716009i \(0.745967\pi\)
\(684\) 0 0
\(685\) 320383. 0.0260881
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 211321. 0.0169587
\(690\) 0 0
\(691\) 2.22823e7 1.77527 0.887636 0.460546i \(-0.152347\pi\)
0.887636 + 0.460546i \(0.152347\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 115688. 0.00908500
\(696\) 0 0
\(697\) 1.91355e7 1.49196
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.01249e7 0.778212 0.389106 0.921193i \(-0.372784\pi\)
0.389106 + 0.921193i \(0.372784\pi\)
\(702\) 0 0
\(703\) 9.22902e6 0.704316
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.32167e6 −0.701366
\(708\) 0 0
\(709\) 1.39102e7 1.03924 0.519622 0.854396i \(-0.326073\pi\)
0.519622 + 0.854396i \(0.326073\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.20219e7 1.62230
\(714\) 0 0
\(715\) 29375.1 0.00214889
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.37453e6 −0.0991589 −0.0495794 0.998770i \(-0.515788\pi\)
−0.0495794 + 0.998770i \(0.515788\pi\)
\(720\) 0 0
\(721\) 1.20129e6 0.0860613
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.39214e7 1.69022
\(726\) 0 0
\(727\) 5.92812e6 0.415988 0.207994 0.978130i \(-0.433307\pi\)
0.207994 + 0.978130i \(0.433307\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.34028e7 1.61985
\(732\) 0 0
\(733\) 1.21732e7 0.836844 0.418422 0.908253i \(-0.362583\pi\)
0.418422 + 0.908253i \(0.362583\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.39980e6 −0.230560
\(738\) 0 0
\(739\) −1.91339e7 −1.28882 −0.644409 0.764681i \(-0.722897\pi\)
−0.644409 + 0.764681i \(0.722897\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.61539e7 −1.07351 −0.536754 0.843739i \(-0.680350\pi\)
−0.536754 + 0.843739i \(0.680350\pi\)
\(744\) 0 0
\(745\) 40102.2 0.00264715
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.96934e6 0.453928
\(750\) 0 0
\(751\) 886544. 0.0573589 0.0286794 0.999589i \(-0.490870\pi\)
0.0286794 + 0.999589i \(0.490870\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −227100. −0.0144994
\(756\) 0 0
\(757\) −7.32720e6 −0.464727 −0.232364 0.972629i \(-0.574646\pi\)
−0.232364 + 0.972629i \(0.574646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.06984e7 0.669664 0.334832 0.942278i \(-0.391320\pi\)
0.334832 + 0.942278i \(0.391320\pi\)
\(762\) 0 0
\(763\) 6.06959e6 0.377440
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.96699e6 0.182107
\(768\) 0 0
\(769\) −1.55599e7 −0.948835 −0.474418 0.880300i \(-0.657341\pi\)
−0.474418 + 0.880300i \(0.657341\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.40758e7 −1.44921 −0.724607 0.689162i \(-0.757979\pi\)
−0.724607 + 0.689162i \(0.757979\pi\)
\(774\) 0 0
\(775\) 2.55719e7 1.52936
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.85467e7 1.09502
\(780\) 0 0
\(781\) −7.05123e6 −0.413654
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 429668. 0.0248862
\(786\) 0 0
\(787\) −2.82983e6 −0.162863 −0.0814316 0.996679i \(-0.525949\pi\)
−0.0814316 + 0.996679i \(0.525949\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.43886e6 −0.138594
\(792\) 0 0
\(793\) 671638. 0.0379273
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.89218e6 0.495864 0.247932 0.968777i \(-0.420249\pi\)
0.247932 + 0.968777i \(0.420249\pi\)
\(798\) 0 0
\(799\) 5.07299e6 0.281123
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.60882e6 −0.252232
\(804\) 0 0
\(805\) 187740. 0.0102110
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.43931e7 −1.84756 −0.923782 0.382918i \(-0.874919\pi\)
−0.923782 + 0.382918i \(0.874919\pi\)
\(810\) 0 0
\(811\) −2.07305e7 −1.10677 −0.553384 0.832926i \(-0.686664\pi\)
−0.553384 + 0.832926i \(0.686664\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −369286. −0.0194746
\(816\) 0 0
\(817\) 2.26828e7 1.18889
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.54818e7 1.31939 0.659694 0.751535i \(-0.270686\pi\)
0.659694 + 0.751535i \(0.270686\pi\)
\(822\) 0 0
\(823\) 1.43584e7 0.738933 0.369467 0.929244i \(-0.379540\pi\)
0.369467 + 0.929244i \(0.379540\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5.17982e6 −0.263361 −0.131680 0.991292i \(-0.542037\pi\)
−0.131680 + 0.991292i \(0.542037\pi\)
\(828\) 0 0
\(829\) 1.98018e7 1.00073 0.500366 0.865814i \(-0.333199\pi\)
0.500366 + 0.865814i \(0.333199\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.50993e6 0.125328
\(834\) 0 0
\(835\) −955835. −0.0474424
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.83283e7 −0.898914 −0.449457 0.893302i \(-0.648383\pi\)
−0.449457 + 0.893302i \(0.648383\pi\)
\(840\) 0 0
\(841\) 3.81619e7 1.86054
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −456965. −0.0220162
\(846\) 0 0
\(847\) 7.47923e6 0.358219
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.44973e7 −1.15956
\(852\) 0 0
\(853\) −1.30941e7 −0.616175 −0.308087 0.951358i \(-0.599689\pi\)
−0.308087 + 0.951358i \(0.599689\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.33903e7 −1.55299 −0.776494 0.630124i \(-0.783004\pi\)
−0.776494 + 0.630124i \(0.783004\pi\)
\(858\) 0 0
\(859\) 1.20144e7 0.555545 0.277772 0.960647i \(-0.410404\pi\)
0.277772 + 0.960647i \(0.410404\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.99226e7 1.36764 0.683821 0.729649i \(-0.260317\pi\)
0.683821 + 0.729649i \(0.260317\pi\)
\(864\) 0 0
\(865\) 605950. 0.0275357
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 976597. 0.0438698
\(870\) 0 0
\(871\) −8.33193e6 −0.372135
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 436151. 0.0192583
\(876\) 0 0
\(877\) −2.48936e7 −1.09292 −0.546460 0.837485i \(-0.684025\pi\)
−0.546460 + 0.837485i \(0.684025\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.37037e7 −1.46298 −0.731490 0.681852i \(-0.761175\pi\)
−0.731490 + 0.681852i \(0.761175\pi\)
\(882\) 0 0
\(883\) 2.47973e7 1.07029 0.535147 0.844759i \(-0.320256\pi\)
0.535147 + 0.844759i \(0.320256\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.64431e7 1.12851 0.564253 0.825602i \(-0.309164\pi\)
0.564253 + 0.825602i \(0.309164\pi\)
\(888\) 0 0
\(889\) 8.26241e6 0.350633
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.91691e6 0.206330
\(894\) 0 0
\(895\) −651385. −0.0271819
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.27212e7 2.58830
\(900\) 0 0
\(901\) 982713. 0.0403288
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −886244. −0.0359693
\(906\) 0 0
\(907\) 2.96507e7 1.19679 0.598393 0.801203i \(-0.295806\pi\)
0.598393 + 0.801203i \(0.295806\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.47849e7 −0.590230 −0.295115 0.955462i \(-0.595358\pi\)
−0.295115 + 0.955462i \(0.595358\pi\)
\(912\) 0 0
\(913\) −1.26609e6 −0.0502677
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.10869e6 0.318440
\(918\) 0 0
\(919\) 1.87883e6 0.0733837 0.0366918 0.999327i \(-0.488318\pi\)
0.0366918 + 0.999327i \(0.488318\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.72805e7 −0.667655
\(924\) 0 0
\(925\) −2.84463e7 −1.09313
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.03881e7 −0.775062 −0.387531 0.921857i \(-0.626672\pi\)
−0.387531 + 0.921857i \(0.626672\pi\)
\(930\) 0 0
\(931\) 2.43271e6 0.0919847
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 136604. 0.00511018
\(936\) 0 0
\(937\) 4.20402e7 1.56429 0.782143 0.623099i \(-0.214127\pi\)
0.782143 + 0.623099i \(0.214127\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.74914e7 −1.01210 −0.506049 0.862504i \(-0.668895\pi\)
−0.506049 + 0.862504i \(0.668895\pi\)
\(942\) 0 0
\(943\) −4.92299e7 −1.80281
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.95466e7 0.708266 0.354133 0.935195i \(-0.384776\pi\)
0.354133 + 0.935195i \(0.384776\pi\)
\(948\) 0 0
\(949\) −1.12949e7 −0.407114
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.93873e7 1.40483 0.702416 0.711767i \(-0.252105\pi\)
0.702416 + 0.711767i \(0.252105\pi\)
\(954\) 0 0
\(955\) 60646.6 0.00215178
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.10195e7 −0.386916
\(960\) 0 0
\(961\) 3.84195e7 1.34197
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 155070. 0.00536056
\(966\) 0 0
\(967\) −245882. −0.00845591 −0.00422796 0.999991i \(-0.501346\pi\)
−0.00422796 + 0.999991i \(0.501346\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.96422e7 1.00893 0.504466 0.863431i \(-0.331689\pi\)
0.504466 + 0.863431i \(0.331689\pi\)
\(972\) 0 0
\(973\) −3.97906e6 −0.134741
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.14882e7 1.72572 0.862861 0.505441i \(-0.168670\pi\)
0.862861 + 0.505441i \(0.168670\pi\)
\(978\) 0 0
\(979\) 2.84321e6 0.0948096
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.19970e7 1.38623 0.693114 0.720828i \(-0.256238\pi\)
0.693114 + 0.720828i \(0.256238\pi\)
\(984\) 0 0
\(985\) 634511. 0.0208377
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.02085e7 −1.95734
\(990\) 0 0
\(991\) −2.14353e7 −0.693339 −0.346670 0.937987i \(-0.612687\pi\)
−0.346670 + 0.937987i \(0.612687\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −290474. −0.00930143
\(996\) 0 0
\(997\) −1.94096e7 −0.618413 −0.309207 0.950995i \(-0.600063\pi\)
−0.309207 + 0.950995i \(0.600063\pi\)
\(998\) 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 1008.6.a.be.1.2 2
3.2 odd 2 1008.6.a.bx.1.1 2
4.3 odd 2 504.6.a.j.1.2 2
12.11 even 2 504.6.a.w.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.j.1.2 2 4.3 odd 2
504.6.a.w.1.1 yes 2 12.11 even 2
1008.6.a.be.1.2 2 1.1 even 1 trivial
1008.6.a.bx.1.1 2 3.2 odd 2