Properties

Label 1008.6.a.bx.1.1
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 1.1
Root \(10.8562\) 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 \(-0.504056\pi\)
−0.0127423 + 0.999919i \(0.504056\pi\)
\(6\) 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 \(-0.536457\pi\)
−0.114283 + 0.993448i \(0.536457\pi\)
\(12\) 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 \(-0.644543\pi\)
−0.438649 + 0.898658i \(0.644543\pi\)
\(18\) 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 \(-0.322176\pi\)
0.530041 + 0.847972i \(0.322176\pi\)
\(24\) 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 \(-0.179209\pi\)
0.845657 + 0.533727i \(0.179209\pi\)
\(30\) 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 \(-0.823588\pi\)
−0.850314 + 0.526275i \(0.823588\pi\)
\(42\) 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 \(-0.551221\pi\)
−0.160221 + 0.987081i \(0.551221\pi\)
\(48\) 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 \(-0.507317\pi\)
−0.0229846 + 0.999736i \(0.507317\pi\)
\(54\) 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 \(-0.579384\pi\)
−0.246815 + 0.969063i \(0.579384\pi\)
\(60\) 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 \(-0.139953\pi\)
0.904890 + 0.425645i \(0.139953\pi\)
\(72\) 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 \(-0.464927\pi\)
0.109963 + 0.993936i \(0.464927\pi\)
\(84\) 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 \(-0.566501\pi\)
−0.207401 + 0.978256i \(0.566501\pi\)
\(90\) 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 \(-0.878320\pi\)
−0.927821 + 0.373027i \(0.878320\pi\)
\(102\) 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 \(-0.294972\pi\)
0.600491 + 0.799632i \(0.294972\pi\)
\(108\) 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 \(-0.558692\pi\)
−0.183343 + 0.983049i \(0.558692\pi\)
\(114\) 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 \(-0.361589\pi\)
0.421256 + 0.906942i \(0.361589\pi\)
\(132\) 0 0
\(133\) −49647.1 −0.243369
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −224888. −1.02368 −0.511842 0.859080i \(-0.671037\pi\)
−0.511842 + 0.859080i \(0.671037\pi\)
\(138\) 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 \(-0.516539\pi\)
−0.0519363 + 0.998650i \(0.516539\pi\)
\(150\) 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 \(-0.119106\pi\)
0.930807 + 0.365512i \(0.119106\pi\)
\(168\) 0 0
\(169\) −320761. −0.863902
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −425338. −1.08049 −0.540243 0.841509i \(-0.681668\pi\)
−0.540243 + 0.841509i \(0.681668\pi\)
\(174\) 0 0
\(175\) 153026. 0.377719
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 457231. 1.06660 0.533301 0.845925i \(-0.320951\pi\)
0.533301 + 0.845925i \(0.320951\pi\)
\(180\) 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 \(-0.513442\pi\)
−0.0422173 + 0.999108i \(0.513442\pi\)
\(192\) 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 \(-0.634063\pi\)
−0.408829 + 0.912611i \(0.634063\pi\)
\(198\) 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 \(-0.301017\pi\)
0.585197 + 0.810891i \(0.301017\pi\)
\(228\) 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 \(-0.650830\pi\)
−0.456311 + 0.889820i \(0.650830\pi\)
\(234\) 0 0
\(235\) 6913.47 0.00816633
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 530659. 0.600926 0.300463 0.953794i \(-0.402859\pi\)
0.300463 + 0.953794i \(0.402859\pi\)
\(240\) 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 \(-0.725525\pi\)
−0.650701 + 0.759334i \(0.725525\pi\)
\(252\) 0 0
\(253\) −246690. −0.242299
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.05589e6 0.997208 0.498604 0.866830i \(-0.333846\pi\)
0.498604 + 0.866830i \(0.333846\pi\)
\(258\) 0 0
\(259\) −446328. −0.413433
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −461318. −0.411255 −0.205627 0.978630i \(-0.565923\pi\)
−0.205627 + 0.978630i \(0.565923\pi\)
\(264\) 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 \(-0.280949\pi\)
0.635123 + 0.772411i \(0.280949\pi\)
\(270\) 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 \(-0.446278\pi\)
0.167971 + 0.985792i \(0.446278\pi\)
\(282\) 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 \(-0.615543\pi\)
−0.355069 + 0.934840i \(0.615543\pi\)
\(294\) 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 \(-0.812816\pi\)
−0.832021 + 0.554744i \(0.812816\pi\)
\(312\) 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 \(-0.323835\pi\)
0.525615 + 0.850723i \(0.323835\pi\)
\(318\) 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 \(-0.602136\pi\)
−0.315391 + 0.948962i \(0.602136\pi\)
\(348\) 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 \(-0.536772\pi\)
−0.115266 + 0.993335i \(0.536772\pi\)
\(354\) 0 0
\(355\) −109515. −0.0461215
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.43124e6 −1.40512 −0.702562 0.711623i \(-0.747961\pi\)
−0.702562 + 0.711623i \(0.747961\pi\)
\(360\) 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 \(-0.573295\pi\)
−0.228234 + 0.973606i \(0.573295\pi\)
\(384\) 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 \(-0.343385\pi\)
0.472408 + 0.881380i \(0.343385\pi\)
\(390\) 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 \(-0.421498\pi\)
0.244130 + 0.969743i \(0.421498\pi\)
\(402\) 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 \(-0.521151\pi\)
−0.0663975 + 0.997793i \(0.521151\pi\)
\(420\) 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 \(-0.297603\pi\)
0.593860 + 0.804569i \(0.297603\pi\)
\(432\) 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 \(-0.655870\pi\)
−0.470343 + 0.882484i \(0.655870\pi\)
\(444\) 0 0
\(445\) 44158.9 0.0105710
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 590043. 0.138124 0.0690618 0.997612i \(-0.477999\pi\)
0.0690618 + 0.997612i \(0.477999\pi\)
\(450\) 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 \(-0.482828\pi\)
0.0539213 + 0.998545i \(0.482828\pi\)
\(462\) 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 \(-0.849741\pi\)
−0.890637 + 0.454715i \(0.849741\pi\)
\(468\) 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 \(-0.793973\pi\)
−0.797744 + 0.602996i \(0.793973\pi\)
\(480\) 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 \(-0.219868\pi\)
0.770777 + 0.637105i \(0.219868\pi\)
\(492\) 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 \(-0.408434\pi\)
0.283713 + 0.958909i \(0.408434\pi\)
\(504\) 0 0
\(505\) 271019. 0.0472902
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.87503e6 −1.34728 −0.673640 0.739060i \(-0.735270\pi\)
−0.673640 + 0.739060i \(0.735270\pi\)
\(510\) 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 \(-0.230128\pi\)
0.749846 + 0.661613i \(0.230128\pi\)
\(522\) 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 \(-0.580534\pi\)
−0.250314 + 0.968165i \(0.580534\pi\)
\(558\) 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 \(-0.529123\pi\)
−0.0913656 + 0.995817i \(0.529123\pi\)
\(564\) 0 0
\(565\) 70907.7 0.00934484
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 640716. 0.0829631 0.0414815 0.999139i \(-0.486792\pi\)
0.0414815 + 0.999139i \(0.486792\pi\)
\(570\) 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 \(-0.345788\pi\)
0.465741 + 0.884921i \(0.345788\pi\)
\(588\) 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 \(-0.527585\pi\)
−0.0865521 + 0.996247i \(0.527585\pi\)
\(594\) 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 \(-0.454505\pi\)
0.142441 + 0.989803i \(0.454505\pi\)
\(600\) 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 \(-0.761645\pi\)
−0.732497 + 0.680770i \(0.761645\pi\)
\(618\) 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 \(-0.786231\pi\)
−0.782843 + 0.622219i \(0.786231\pi\)
\(642\) 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 \(-0.473013\pi\)
0.0846794 + 0.996408i \(0.473013\pi\)
\(648\) 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 \(-0.247526\pi\)
0.712581 + 0.701590i \(0.247526\pi\)
\(654\) 0 0
\(655\) −235753. −0.0214711
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.05891e7 1.84682 0.923409 0.383816i \(-0.125390\pi\)
0.923409 + 0.383816i \(0.125390\pi\)
\(660\) 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 \(-0.214227\pi\)
0.781947 + 0.623345i \(0.214227\pi\)
\(678\) 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 \(-0.254033\pi\)
0.698091 + 0.716009i \(0.254033\pi\)
\(684\) 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 \(-0.627216\pi\)
−0.389106 + 0.921193i \(0.627216\pi\)
\(702\) 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 \(-0.484212\pi\)
0.0495794 + 0.998770i \(0.484212\pi\)
\(720\) 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 \(-0.319650\pi\)
0.536754 + 0.843739i \(0.319650\pi\)
\(744\) 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 \(-0.608680\pi\)
−0.334832 + 0.942278i \(0.608680\pi\)
\(762\) 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 \(-0.242021\pi\)
0.724607 + 0.689162i \(0.242021\pi\)
\(774\) 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 \(-0.579751\pi\)
−0.247932 + 0.968777i \(0.579751\pi\)
\(798\) 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 \(-0.125081\pi\)
0.923782 + 0.382918i \(0.125081\pi\)
\(810\) 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 \(-0.729314\pi\)
−0.659694 + 0.751535i \(0.729314\pi\)
\(822\) 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 \(-0.457963\pi\)
0.131680 + 0.991292i \(0.457963\pi\)
\(828\) 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 \(-0.351617\pi\)
0.449457 + 0.893302i \(0.351617\pi\)
\(840\) 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 \(-0.216996\pi\)
0.776494 + 0.630124i \(0.216996\pi\)
\(858\) 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 \(-0.739683\pi\)
−0.683821 + 0.729649i \(0.739683\pi\)
\(864\) 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 \(-0.238825\pi\)
0.731490 + 0.681852i \(0.238825\pi\)
\(882\) 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 \(-0.690836\pi\)
−0.564253 + 0.825602i \(0.690836\pi\)
\(888\) 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 \(-0.404642\pi\)
0.295115 + 0.955462i \(0.404642\pi\)
\(912\) 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 \(-0.373328\pi\)
0.387531 + 0.921857i \(0.373328\pi\)
\(930\) 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 \(-0.331105\pi\)
0.506049 + 0.862504i \(0.331105\pi\)
\(942\) 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 \(-0.615224\pi\)
−0.354133 + 0.935195i \(0.615224\pi\)
\(948\) 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 \(-0.747895\pi\)
−0.702416 + 0.711767i \(0.747895\pi\)
\(954\) 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 \(-0.668311\pi\)
−0.504466 + 0.863431i \(0.668311\pi\)
\(972\) 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 \(-0.831330\pi\)
−0.862861 + 0.505441i \(0.831330\pi\)
\(978\) 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 \(-0.743762\pi\)
−0.693114 + 0.720828i \(0.743762\pi\)
\(984\) 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.bx.1.1 2
3.2 odd 2 1008.6.a.be.1.2 2
4.3 odd 2 504.6.a.w.1.1 yes 2
12.11 even 2 504.6.a.j.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.j.1.2 2 12.11 even 2
504.6.a.w.1.1 yes 2 4.3 odd 2
1008.6.a.be.1.2 2 3.2 odd 2
1008.6.a.bx.1.1 2 1.1 even 1 trivial