Properties

Label 704.6.a.f.1.1
Level $704$
Weight $6$
Character 704.1
Self dual yes
Analytic conductor $112.910$
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] = [704,6,Mod(1,704)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(704, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("704.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 704 = 2^{6} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 704.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: \(112.910209148\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 22)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 704.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +51.0000 q^{5} +166.000 q^{7} -242.000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +51.0000 q^{5} +166.000 q^{7} -242.000 q^{9} -121.000 q^{11} -692.000 q^{13} +51.0000 q^{15} -738.000 q^{17} +1424.00 q^{19} +166.000 q^{21} +1779.00 q^{23} -524.000 q^{25} -485.000 q^{27} +2064.00 q^{29} -6245.00 q^{31} -121.000 q^{33} +8466.00 q^{35} +14785.0 q^{37} -692.000 q^{39} +5304.00 q^{41} +17798.0 q^{43} -12342.0 q^{45} +17184.0 q^{47} +10749.0 q^{49} -738.000 q^{51} +30726.0 q^{53} -6171.00 q^{55} +1424.00 q^{57} -34989.0 q^{59} +45940.0 q^{61} -40172.0 q^{63} -35292.0 q^{65} +25343.0 q^{67} +1779.00 q^{69} -13311.0 q^{71} -53260.0 q^{73} -524.000 q^{75} -20086.0 q^{77} -77234.0 q^{79} +58321.0 q^{81} +55014.0 q^{83} -37638.0 q^{85} +2064.00 q^{87} +125415. q^{89} -114872. q^{91} -6245.00 q^{93} +72624.0 q^{95} -88807.0 q^{97} +29282.0 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.0641500 0.0320750 0.999485i \(-0.489788\pi\)
0.0320750 + 0.999485i \(0.489788\pi\)
\(4\) 0 0
\(5\) 51.0000 0.912316 0.456158 0.889899i \(-0.349225\pi\)
0.456158 + 0.889899i \(0.349225\pi\)
\(6\) 0 0
\(7\) 166.000 1.28045 0.640226 0.768187i \(-0.278841\pi\)
0.640226 + 0.768187i \(0.278841\pi\)
\(8\) 0 0
\(9\) −242.000 −0.995885
\(10\) 0 0
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) −692.000 −1.13566 −0.567829 0.823146i \(-0.692217\pi\)
−0.567829 + 0.823146i \(0.692217\pi\)
\(14\) 0 0
\(15\) 51.0000 0.0585251
\(16\) 0 0
\(17\) −738.000 −0.619347 −0.309674 0.950843i \(-0.600220\pi\)
−0.309674 + 0.950843i \(0.600220\pi\)
\(18\) 0 0
\(19\) 1424.00 0.904953 0.452476 0.891776i \(-0.350541\pi\)
0.452476 + 0.891776i \(0.350541\pi\)
\(20\) 0 0
\(21\) 166.000 0.0821410
\(22\) 0 0
\(23\) 1779.00 0.701223 0.350612 0.936521i \(-0.385974\pi\)
0.350612 + 0.936521i \(0.385974\pi\)
\(24\) 0 0
\(25\) −524.000 −0.167680
\(26\) 0 0
\(27\) −485.000 −0.128036
\(28\) 0 0
\(29\) 2064.00 0.455737 0.227869 0.973692i \(-0.426824\pi\)
0.227869 + 0.973692i \(0.426824\pi\)
\(30\) 0 0
\(31\) −6245.00 −1.16715 −0.583577 0.812058i \(-0.698347\pi\)
−0.583577 + 0.812058i \(0.698347\pi\)
\(32\) 0 0
\(33\) −121.000 −0.0193420
\(34\) 0 0
\(35\) 8466.00 1.16818
\(36\) 0 0
\(37\) 14785.0 1.77549 0.887743 0.460340i \(-0.152273\pi\)
0.887743 + 0.460340i \(0.152273\pi\)
\(38\) 0 0
\(39\) −692.000 −0.0728525
\(40\) 0 0
\(41\) 5304.00 0.492770 0.246385 0.969172i \(-0.420757\pi\)
0.246385 + 0.969172i \(0.420757\pi\)
\(42\) 0 0
\(43\) 17798.0 1.46791 0.733956 0.679197i \(-0.237672\pi\)
0.733956 + 0.679197i \(0.237672\pi\)
\(44\) 0 0
\(45\) −12342.0 −0.908561
\(46\) 0 0
\(47\) 17184.0 1.13470 0.567348 0.823478i \(-0.307969\pi\)
0.567348 + 0.823478i \(0.307969\pi\)
\(48\) 0 0
\(49\) 10749.0 0.639555
\(50\) 0 0
\(51\) −738.000 −0.0397311
\(52\) 0 0
\(53\) 30726.0 1.50251 0.751253 0.660014i \(-0.229450\pi\)
0.751253 + 0.660014i \(0.229450\pi\)
\(54\) 0 0
\(55\) −6171.00 −0.275074
\(56\) 0 0
\(57\) 1424.00 0.0580528
\(58\) 0 0
\(59\) −34989.0 −1.30858 −0.654292 0.756242i \(-0.727033\pi\)
−0.654292 + 0.756242i \(0.727033\pi\)
\(60\) 0 0
\(61\) 45940.0 1.58076 0.790381 0.612616i \(-0.209883\pi\)
0.790381 + 0.612616i \(0.209883\pi\)
\(62\) 0 0
\(63\) −40172.0 −1.27518
\(64\) 0 0
\(65\) −35292.0 −1.03608
\(66\) 0 0
\(67\) 25343.0 0.689717 0.344859 0.938655i \(-0.387927\pi\)
0.344859 + 0.938655i \(0.387927\pi\)
\(68\) 0 0
\(69\) 1779.00 0.0449835
\(70\) 0 0
\(71\) −13311.0 −0.313375 −0.156688 0.987648i \(-0.550082\pi\)
−0.156688 + 0.987648i \(0.550082\pi\)
\(72\) 0 0
\(73\) −53260.0 −1.16975 −0.584876 0.811123i \(-0.698857\pi\)
−0.584876 + 0.811123i \(0.698857\pi\)
\(74\) 0 0
\(75\) −524.000 −0.0107567
\(76\) 0 0
\(77\) −20086.0 −0.386071
\(78\) 0 0
\(79\) −77234.0 −1.39233 −0.696163 0.717884i \(-0.745111\pi\)
−0.696163 + 0.717884i \(0.745111\pi\)
\(80\) 0 0
\(81\) 58321.0 0.987671
\(82\) 0 0
\(83\) 55014.0 0.876553 0.438276 0.898840i \(-0.355589\pi\)
0.438276 + 0.898840i \(0.355589\pi\)
\(84\) 0 0
\(85\) −37638.0 −0.565040
\(86\) 0 0
\(87\) 2064.00 0.0292356
\(88\) 0 0
\(89\) 125415. 1.67832 0.839159 0.543886i \(-0.183047\pi\)
0.839159 + 0.543886i \(0.183047\pi\)
\(90\) 0 0
\(91\) −114872. −1.45416
\(92\) 0 0
\(93\) −6245.00 −0.0748730
\(94\) 0 0
\(95\) 72624.0 0.825603
\(96\) 0 0
\(97\) −88807.0 −0.958336 −0.479168 0.877723i \(-0.659062\pi\)
−0.479168 + 0.877723i \(0.659062\pi\)
\(98\) 0 0
\(99\) 29282.0 0.300271
\(100\) 0 0
\(101\) −1482.00 −0.0144559 −0.00722794 0.999974i \(-0.502301\pi\)
−0.00722794 + 0.999974i \(0.502301\pi\)
\(102\) 0 0
\(103\) 117496. 1.09126 0.545632 0.838025i \(-0.316290\pi\)
0.545632 + 0.838025i \(0.316290\pi\)
\(104\) 0 0
\(105\) 8466.00 0.0749385
\(106\) 0 0
\(107\) −79362.0 −0.670121 −0.335060 0.942197i \(-0.608757\pi\)
−0.335060 + 0.942197i \(0.608757\pi\)
\(108\) 0 0
\(109\) −87842.0 −0.708167 −0.354084 0.935214i \(-0.615207\pi\)
−0.354084 + 0.935214i \(0.615207\pi\)
\(110\) 0 0
\(111\) 14785.0 0.113897
\(112\) 0 0
\(113\) −47247.0 −0.348079 −0.174040 0.984739i \(-0.555682\pi\)
−0.174040 + 0.984739i \(0.555682\pi\)
\(114\) 0 0
\(115\) 90729.0 0.639737
\(116\) 0 0
\(117\) 167464. 1.13098
\(118\) 0 0
\(119\) −122508. −0.793044
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) 0 0
\(123\) 5304.00 0.0316112
\(124\) 0 0
\(125\) −186099. −1.06529
\(126\) 0 0
\(127\) 239416. 1.31718 0.658588 0.752504i \(-0.271154\pi\)
0.658588 + 0.752504i \(0.271154\pi\)
\(128\) 0 0
\(129\) 17798.0 0.0941666
\(130\) 0 0
\(131\) −98142.0 −0.499662 −0.249831 0.968289i \(-0.580375\pi\)
−0.249831 + 0.968289i \(0.580375\pi\)
\(132\) 0 0
\(133\) 236384. 1.15875
\(134\) 0 0
\(135\) −24735.0 −0.116809
\(136\) 0 0
\(137\) 400137. 1.82141 0.910704 0.413059i \(-0.135540\pi\)
0.910704 + 0.413059i \(0.135540\pi\)
\(138\) 0 0
\(139\) 205766. 0.903310 0.451655 0.892193i \(-0.350834\pi\)
0.451655 + 0.892193i \(0.350834\pi\)
\(140\) 0 0
\(141\) 17184.0 0.0727908
\(142\) 0 0
\(143\) 83732.0 0.342414
\(144\) 0 0
\(145\) 105264. 0.415776
\(146\) 0 0
\(147\) 10749.0 0.0410275
\(148\) 0 0
\(149\) −87726.0 −0.323715 −0.161857 0.986814i \(-0.551748\pi\)
−0.161857 + 0.986814i \(0.551748\pi\)
\(150\) 0 0
\(151\) 432778. 1.54462 0.772312 0.635243i \(-0.219100\pi\)
0.772312 + 0.635243i \(0.219100\pi\)
\(152\) 0 0
\(153\) 178596. 0.616798
\(154\) 0 0
\(155\) −318495. −1.06481
\(156\) 0 0
\(157\) 34075.0 0.110328 0.0551641 0.998477i \(-0.482432\pi\)
0.0551641 + 0.998477i \(0.482432\pi\)
\(158\) 0 0
\(159\) 30726.0 0.0963858
\(160\) 0 0
\(161\) 295314. 0.897882
\(162\) 0 0
\(163\) 45020.0 0.132720 0.0663600 0.997796i \(-0.478861\pi\)
0.0663600 + 0.997796i \(0.478861\pi\)
\(164\) 0 0
\(165\) −6171.00 −0.0176460
\(166\) 0 0
\(167\) −482556. −1.33893 −0.669463 0.742845i \(-0.733476\pi\)
−0.669463 + 0.742845i \(0.733476\pi\)
\(168\) 0 0
\(169\) 107571. 0.289720
\(170\) 0 0
\(171\) −344608. −0.901229
\(172\) 0 0
\(173\) 766254. 1.94651 0.973257 0.229719i \(-0.0737808\pi\)
0.973257 + 0.229719i \(0.0737808\pi\)
\(174\) 0 0
\(175\) −86984.0 −0.214706
\(176\) 0 0
\(177\) −34989.0 −0.0839457
\(178\) 0 0
\(179\) 303399. 0.707753 0.353876 0.935292i \(-0.384863\pi\)
0.353876 + 0.935292i \(0.384863\pi\)
\(180\) 0 0
\(181\) 285181. 0.647030 0.323515 0.946223i \(-0.395135\pi\)
0.323515 + 0.946223i \(0.395135\pi\)
\(182\) 0 0
\(183\) 45940.0 0.101406
\(184\) 0 0
\(185\) 754035. 1.61980
\(186\) 0 0
\(187\) 89298.0 0.186740
\(188\) 0 0
\(189\) −80510.0 −0.163944
\(190\) 0 0
\(191\) −767067. −1.52142 −0.760711 0.649090i \(-0.775150\pi\)
−0.760711 + 0.649090i \(0.775150\pi\)
\(192\) 0 0
\(193\) 411668. 0.795525 0.397763 0.917488i \(-0.369787\pi\)
0.397763 + 0.917488i \(0.369787\pi\)
\(194\) 0 0
\(195\) −35292.0 −0.0664645
\(196\) 0 0
\(197\) 759258. 1.39387 0.696937 0.717132i \(-0.254545\pi\)
0.696937 + 0.717132i \(0.254545\pi\)
\(198\) 0 0
\(199\) 46600.0 0.0834167 0.0417084 0.999130i \(-0.486720\pi\)
0.0417084 + 0.999130i \(0.486720\pi\)
\(200\) 0 0
\(201\) 25343.0 0.0442454
\(202\) 0 0
\(203\) 342624. 0.583549
\(204\) 0 0
\(205\) 270504. 0.449561
\(206\) 0 0
\(207\) −430518. −0.698338
\(208\) 0 0
\(209\) −172304. −0.272854
\(210\) 0 0
\(211\) −932428. −1.44181 −0.720907 0.693032i \(-0.756274\pi\)
−0.720907 + 0.693032i \(0.756274\pi\)
\(212\) 0 0
\(213\) −13311.0 −0.0201030
\(214\) 0 0
\(215\) 907698. 1.33920
\(216\) 0 0
\(217\) −1.03667e6 −1.49448
\(218\) 0 0
\(219\) −53260.0 −0.0750397
\(220\) 0 0
\(221\) 510696. 0.703367
\(222\) 0 0
\(223\) −169745. −0.228578 −0.114289 0.993448i \(-0.536459\pi\)
−0.114289 + 0.993448i \(0.536459\pi\)
\(224\) 0 0
\(225\) 126808. 0.166990
\(226\) 0 0
\(227\) 198078. 0.255136 0.127568 0.991830i \(-0.459283\pi\)
0.127568 + 0.991830i \(0.459283\pi\)
\(228\) 0 0
\(229\) 849997. 1.07110 0.535548 0.844505i \(-0.320105\pi\)
0.535548 + 0.844505i \(0.320105\pi\)
\(230\) 0 0
\(231\) −20086.0 −0.0247664
\(232\) 0 0
\(233\) −401832. −0.484903 −0.242451 0.970164i \(-0.577952\pi\)
−0.242451 + 0.970164i \(0.577952\pi\)
\(234\) 0 0
\(235\) 876384. 1.03520
\(236\) 0 0
\(237\) −77234.0 −0.0893177
\(238\) 0 0
\(239\) −855174. −0.968411 −0.484206 0.874954i \(-0.660891\pi\)
−0.484206 + 0.874954i \(0.660891\pi\)
\(240\) 0 0
\(241\) 1.12546e6 1.24821 0.624107 0.781339i \(-0.285463\pi\)
0.624107 + 0.781339i \(0.285463\pi\)
\(242\) 0 0
\(243\) 176176. 0.191395
\(244\) 0 0
\(245\) 548199. 0.583476
\(246\) 0 0
\(247\) −985408. −1.02772
\(248\) 0 0
\(249\) 55014.0 0.0562309
\(250\) 0 0
\(251\) −1.19751e6 −1.19976 −0.599882 0.800088i \(-0.704786\pi\)
−0.599882 + 0.800088i \(0.704786\pi\)
\(252\) 0 0
\(253\) −215259. −0.211427
\(254\) 0 0
\(255\) −37638.0 −0.0362473
\(256\) 0 0
\(257\) 37758.0 0.0356596 0.0178298 0.999841i \(-0.494324\pi\)
0.0178298 + 0.999841i \(0.494324\pi\)
\(258\) 0 0
\(259\) 2.45431e6 2.27342
\(260\) 0 0
\(261\) −499488. −0.453862
\(262\) 0 0
\(263\) 631254. 0.562749 0.281375 0.959598i \(-0.409210\pi\)
0.281375 + 0.959598i \(0.409210\pi\)
\(264\) 0 0
\(265\) 1.56703e6 1.37076
\(266\) 0 0
\(267\) 125415. 0.107664
\(268\) 0 0
\(269\) 1.08034e6 0.910292 0.455146 0.890417i \(-0.349587\pi\)
0.455146 + 0.890417i \(0.349587\pi\)
\(270\) 0 0
\(271\) 816100. 0.675025 0.337513 0.941321i \(-0.390414\pi\)
0.337513 + 0.941321i \(0.390414\pi\)
\(272\) 0 0
\(273\) −114872. −0.0932841
\(274\) 0 0
\(275\) 63404.0 0.0505574
\(276\) 0 0
\(277\) −1.68820e6 −1.32198 −0.660989 0.750396i \(-0.729863\pi\)
−0.660989 + 0.750396i \(0.729863\pi\)
\(278\) 0 0
\(279\) 1.51129e6 1.16235
\(280\) 0 0
\(281\) −879042. −0.664116 −0.332058 0.943259i \(-0.607743\pi\)
−0.332058 + 0.943259i \(0.607743\pi\)
\(282\) 0 0
\(283\) 1.54027e6 1.14322 0.571611 0.820525i \(-0.306319\pi\)
0.571611 + 0.820525i \(0.306319\pi\)
\(284\) 0 0
\(285\) 72624.0 0.0529624
\(286\) 0 0
\(287\) 880464. 0.630967
\(288\) 0 0
\(289\) −875213. −0.616409
\(290\) 0 0
\(291\) −88807.0 −0.0614773
\(292\) 0 0
\(293\) −720840. −0.490535 −0.245267 0.969455i \(-0.578876\pi\)
−0.245267 + 0.969455i \(0.578876\pi\)
\(294\) 0 0
\(295\) −1.78444e6 −1.19384
\(296\) 0 0
\(297\) 58685.0 0.0386043
\(298\) 0 0
\(299\) −1.23107e6 −0.796350
\(300\) 0 0
\(301\) 2.95447e6 1.87959
\(302\) 0 0
\(303\) −1482.00 −0.000927346 0
\(304\) 0 0
\(305\) 2.34294e6 1.44215
\(306\) 0 0
\(307\) −1.03905e6 −0.629201 −0.314601 0.949224i \(-0.601871\pi\)
−0.314601 + 0.949224i \(0.601871\pi\)
\(308\) 0 0
\(309\) 117496. 0.0700046
\(310\) 0 0
\(311\) 1.25135e6 0.733630 0.366815 0.930294i \(-0.380448\pi\)
0.366815 + 0.930294i \(0.380448\pi\)
\(312\) 0 0
\(313\) −1.44336e6 −0.832749 −0.416375 0.909193i \(-0.636699\pi\)
−0.416375 + 0.909193i \(0.636699\pi\)
\(314\) 0 0
\(315\) −2.04877e6 −1.16337
\(316\) 0 0
\(317\) 2.01208e6 1.12460 0.562298 0.826934i \(-0.309917\pi\)
0.562298 + 0.826934i \(0.309917\pi\)
\(318\) 0 0
\(319\) −249744. −0.137410
\(320\) 0 0
\(321\) −79362.0 −0.0429883
\(322\) 0 0
\(323\) −1.05091e6 −0.560480
\(324\) 0 0
\(325\) 362608. 0.190427
\(326\) 0 0
\(327\) −87842.0 −0.0454290
\(328\) 0 0
\(329\) 2.85254e6 1.45292
\(330\) 0 0
\(331\) 2.01734e6 1.01207 0.506033 0.862514i \(-0.331112\pi\)
0.506033 + 0.862514i \(0.331112\pi\)
\(332\) 0 0
\(333\) −3.57797e6 −1.76818
\(334\) 0 0
\(335\) 1.29249e6 0.629240
\(336\) 0 0
\(337\) 264122. 0.126686 0.0633432 0.997992i \(-0.479824\pi\)
0.0633432 + 0.997992i \(0.479824\pi\)
\(338\) 0 0
\(339\) −47247.0 −0.0223293
\(340\) 0 0
\(341\) 755645. 0.351910
\(342\) 0 0
\(343\) −1.00563e6 −0.461532
\(344\) 0 0
\(345\) 90729.0 0.0410392
\(346\) 0 0
\(347\) −1.71049e6 −0.762601 −0.381300 0.924451i \(-0.624524\pi\)
−0.381300 + 0.924451i \(0.624524\pi\)
\(348\) 0 0
\(349\) −218822. −0.0961673 −0.0480836 0.998843i \(-0.515311\pi\)
−0.0480836 + 0.998843i \(0.515311\pi\)
\(350\) 0 0
\(351\) 335620. 0.145405
\(352\) 0 0
\(353\) 3.68192e6 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(354\) 0 0
\(355\) −678861. −0.285897
\(356\) 0 0
\(357\) −122508. −0.0508738
\(358\) 0 0
\(359\) −1.88528e6 −0.772042 −0.386021 0.922490i \(-0.626151\pi\)
−0.386021 + 0.922490i \(0.626151\pi\)
\(360\) 0 0
\(361\) −448323. −0.181060
\(362\) 0 0
\(363\) 14641.0 0.00583182
\(364\) 0 0
\(365\) −2.71626e6 −1.06718
\(366\) 0 0
\(367\) 3.11666e6 1.20788 0.603940 0.797029i \(-0.293596\pi\)
0.603940 + 0.797029i \(0.293596\pi\)
\(368\) 0 0
\(369\) −1.28357e6 −0.490742
\(370\) 0 0
\(371\) 5.10052e6 1.92389
\(372\) 0 0
\(373\) −1.39441e6 −0.518943 −0.259471 0.965751i \(-0.583548\pi\)
−0.259471 + 0.965751i \(0.583548\pi\)
\(374\) 0 0
\(375\) −186099. −0.0683386
\(376\) 0 0
\(377\) −1.42829e6 −0.517562
\(378\) 0 0
\(379\) −4.26036e6 −1.52352 −0.761759 0.647860i \(-0.775664\pi\)
−0.761759 + 0.647860i \(0.775664\pi\)
\(380\) 0 0
\(381\) 239416. 0.0844969
\(382\) 0 0
\(383\) −201765. −0.0702828 −0.0351414 0.999382i \(-0.511188\pi\)
−0.0351414 + 0.999382i \(0.511188\pi\)
\(384\) 0 0
\(385\) −1.02439e6 −0.352218
\(386\) 0 0
\(387\) −4.30712e6 −1.46187
\(388\) 0 0
\(389\) −1.94882e6 −0.652977 −0.326489 0.945201i \(-0.605865\pi\)
−0.326489 + 0.945201i \(0.605865\pi\)
\(390\) 0 0
\(391\) −1.31290e6 −0.434301
\(392\) 0 0
\(393\) −98142.0 −0.0320534
\(394\) 0 0
\(395\) −3.93893e6 −1.27024
\(396\) 0 0
\(397\) 1.46826e6 0.467548 0.233774 0.972291i \(-0.424892\pi\)
0.233774 + 0.972291i \(0.424892\pi\)
\(398\) 0 0
\(399\) 236384. 0.0743337
\(400\) 0 0
\(401\) 2.24618e6 0.697563 0.348781 0.937204i \(-0.386596\pi\)
0.348781 + 0.937204i \(0.386596\pi\)
\(402\) 0 0
\(403\) 4.32154e6 1.32549
\(404\) 0 0
\(405\) 2.97437e6 0.901068
\(406\) 0 0
\(407\) −1.78898e6 −0.535329
\(408\) 0 0
\(409\) −3.61488e6 −1.06853 −0.534263 0.845318i \(-0.679411\pi\)
−0.534263 + 0.845318i \(0.679411\pi\)
\(410\) 0 0
\(411\) 400137. 0.116843
\(412\) 0 0
\(413\) −5.80817e6 −1.67558
\(414\) 0 0
\(415\) 2.80571e6 0.799693
\(416\) 0 0
\(417\) 205766. 0.0579473
\(418\) 0 0
\(419\) −3.81239e6 −1.06087 −0.530435 0.847726i \(-0.677971\pi\)
−0.530435 + 0.847726i \(0.677971\pi\)
\(420\) 0 0
\(421\) −1.97346e6 −0.542655 −0.271327 0.962487i \(-0.587463\pi\)
−0.271327 + 0.962487i \(0.587463\pi\)
\(422\) 0 0
\(423\) −4.15853e6 −1.13003
\(424\) 0 0
\(425\) 386712. 0.103852
\(426\) 0 0
\(427\) 7.62604e6 2.02409
\(428\) 0 0
\(429\) 83732.0 0.0219659
\(430\) 0 0
\(431\) 2.08359e6 0.540280 0.270140 0.962821i \(-0.412930\pi\)
0.270140 + 0.962821i \(0.412930\pi\)
\(432\) 0 0
\(433\) −72691.0 −0.0186321 −0.00931603 0.999957i \(-0.502965\pi\)
−0.00931603 + 0.999957i \(0.502965\pi\)
\(434\) 0 0
\(435\) 105264. 0.0266721
\(436\) 0 0
\(437\) 2.53330e6 0.634574
\(438\) 0 0
\(439\) −594392. −0.147201 −0.0736007 0.997288i \(-0.523449\pi\)
−0.0736007 + 0.997288i \(0.523449\pi\)
\(440\) 0 0
\(441\) −2.60126e6 −0.636923
\(442\) 0 0
\(443\) 4.56651e6 1.10554 0.552770 0.833334i \(-0.313571\pi\)
0.552770 + 0.833334i \(0.313571\pi\)
\(444\) 0 0
\(445\) 6.39616e6 1.53116
\(446\) 0 0
\(447\) −87726.0 −0.0207663
\(448\) 0 0
\(449\) −5.44382e6 −1.27435 −0.637174 0.770720i \(-0.719897\pi\)
−0.637174 + 0.770720i \(0.719897\pi\)
\(450\) 0 0
\(451\) −641784. −0.148576
\(452\) 0 0
\(453\) 432778. 0.0990877
\(454\) 0 0
\(455\) −5.85847e6 −1.32665
\(456\) 0 0
\(457\) 6.70312e6 1.50137 0.750683 0.660662i \(-0.229724\pi\)
0.750683 + 0.660662i \(0.229724\pi\)
\(458\) 0 0
\(459\) 357930. 0.0792988
\(460\) 0 0
\(461\) 1.25994e6 0.276120 0.138060 0.990424i \(-0.455913\pi\)
0.138060 + 0.990424i \(0.455913\pi\)
\(462\) 0 0
\(463\) 5.02308e6 1.08897 0.544487 0.838769i \(-0.316724\pi\)
0.544487 + 0.838769i \(0.316724\pi\)
\(464\) 0 0
\(465\) −318495. −0.0683078
\(466\) 0 0
\(467\) −2.35660e6 −0.500028 −0.250014 0.968242i \(-0.580435\pi\)
−0.250014 + 0.968242i \(0.580435\pi\)
\(468\) 0 0
\(469\) 4.20694e6 0.883149
\(470\) 0 0
\(471\) 34075.0 0.00707756
\(472\) 0 0
\(473\) −2.15356e6 −0.442592
\(474\) 0 0
\(475\) −746176. −0.151743
\(476\) 0 0
\(477\) −7.43569e6 −1.49632
\(478\) 0 0
\(479\) 6.72258e6 1.33874 0.669371 0.742928i \(-0.266563\pi\)
0.669371 + 0.742928i \(0.266563\pi\)
\(480\) 0 0
\(481\) −1.02312e7 −2.01634
\(482\) 0 0
\(483\) 295314. 0.0575992
\(484\) 0 0
\(485\) −4.52916e6 −0.874305
\(486\) 0 0
\(487\) −1.96001e6 −0.374487 −0.187243 0.982314i \(-0.559955\pi\)
−0.187243 + 0.982314i \(0.559955\pi\)
\(488\) 0 0
\(489\) 45020.0 0.00851399
\(490\) 0 0
\(491\) −579624. −0.108503 −0.0542516 0.998527i \(-0.517277\pi\)
−0.0542516 + 0.998527i \(0.517277\pi\)
\(492\) 0 0
\(493\) −1.52323e6 −0.282260
\(494\) 0 0
\(495\) 1.49338e6 0.273942
\(496\) 0 0
\(497\) −2.20963e6 −0.401262
\(498\) 0 0
\(499\) 1.36905e6 0.246132 0.123066 0.992398i \(-0.460727\pi\)
0.123066 + 0.992398i \(0.460727\pi\)
\(500\) 0 0
\(501\) −482556. −0.0858921
\(502\) 0 0
\(503\) −1.83343e6 −0.323105 −0.161552 0.986864i \(-0.551650\pi\)
−0.161552 + 0.986864i \(0.551650\pi\)
\(504\) 0 0
\(505\) −75582.0 −0.0131883
\(506\) 0 0
\(507\) 107571. 0.0185855
\(508\) 0 0
\(509\) 1.71266e6 0.293006 0.146503 0.989210i \(-0.453198\pi\)
0.146503 + 0.989210i \(0.453198\pi\)
\(510\) 0 0
\(511\) −8.84116e6 −1.49781
\(512\) 0 0
\(513\) −690640. −0.115867
\(514\) 0 0
\(515\) 5.99230e6 0.995578
\(516\) 0 0
\(517\) −2.07926e6 −0.342124
\(518\) 0 0
\(519\) 766254. 0.124869
\(520\) 0 0
\(521\) −789435. −0.127415 −0.0637077 0.997969i \(-0.520293\pi\)
−0.0637077 + 0.997969i \(0.520293\pi\)
\(522\) 0 0
\(523\) 627392. 0.100296 0.0501481 0.998742i \(-0.484031\pi\)
0.0501481 + 0.998742i \(0.484031\pi\)
\(524\) 0 0
\(525\) −86984.0 −0.0137734
\(526\) 0 0
\(527\) 4.60881e6 0.722873
\(528\) 0 0
\(529\) −3.27150e6 −0.508286
\(530\) 0 0
\(531\) 8.46734e6 1.30320
\(532\) 0 0
\(533\) −3.67037e6 −0.559618
\(534\) 0 0
\(535\) −4.04746e6 −0.611362
\(536\) 0 0
\(537\) 303399. 0.0454024
\(538\) 0 0
\(539\) −1.30063e6 −0.192833
\(540\) 0 0
\(541\) −3.20895e6 −0.471379 −0.235689 0.971828i \(-0.575735\pi\)
−0.235689 + 0.971828i \(0.575735\pi\)
\(542\) 0 0
\(543\) 285181. 0.0415070
\(544\) 0 0
\(545\) −4.47994e6 −0.646072
\(546\) 0 0
\(547\) 3.42658e6 0.489658 0.244829 0.969566i \(-0.421268\pi\)
0.244829 + 0.969566i \(0.421268\pi\)
\(548\) 0 0
\(549\) −1.11175e7 −1.57426
\(550\) 0 0
\(551\) 2.93914e6 0.412421
\(552\) 0 0
\(553\) −1.28208e7 −1.78280
\(554\) 0 0
\(555\) 754035. 0.103910
\(556\) 0 0
\(557\) −1.05198e7 −1.43672 −0.718358 0.695674i \(-0.755106\pi\)
−0.718358 + 0.695674i \(0.755106\pi\)
\(558\) 0 0
\(559\) −1.23162e7 −1.66705
\(560\) 0 0
\(561\) 89298.0 0.0119794
\(562\) 0 0
\(563\) 5.47288e6 0.727687 0.363844 0.931460i \(-0.381464\pi\)
0.363844 + 0.931460i \(0.381464\pi\)
\(564\) 0 0
\(565\) −2.40960e6 −0.317558
\(566\) 0 0
\(567\) 9.68129e6 1.26466
\(568\) 0 0
\(569\) −1.17787e7 −1.52516 −0.762580 0.646893i \(-0.776068\pi\)
−0.762580 + 0.646893i \(0.776068\pi\)
\(570\) 0 0
\(571\) −8.35628e6 −1.07256 −0.536281 0.844039i \(-0.680171\pi\)
−0.536281 + 0.844039i \(0.680171\pi\)
\(572\) 0 0
\(573\) −767067. −0.0975993
\(574\) 0 0
\(575\) −932196. −0.117581
\(576\) 0 0
\(577\) −1.37758e7 −1.72258 −0.861288 0.508117i \(-0.830342\pi\)
−0.861288 + 0.508117i \(0.830342\pi\)
\(578\) 0 0
\(579\) 411668. 0.0510330
\(580\) 0 0
\(581\) 9.13232e6 1.12238
\(582\) 0 0
\(583\) −3.71785e6 −0.453023
\(584\) 0 0
\(585\) 8.54066e6 1.03182
\(586\) 0 0
\(587\) −1.27093e7 −1.52239 −0.761196 0.648522i \(-0.775388\pi\)
−0.761196 + 0.648522i \(0.775388\pi\)
\(588\) 0 0
\(589\) −8.89288e6 −1.05622
\(590\) 0 0
\(591\) 759258. 0.0894171
\(592\) 0 0
\(593\) 1.00825e6 0.117742 0.0588711 0.998266i \(-0.481250\pi\)
0.0588711 + 0.998266i \(0.481250\pi\)
\(594\) 0 0
\(595\) −6.24791e6 −0.723506
\(596\) 0 0
\(597\) 46600.0 0.00535119
\(598\) 0 0
\(599\) −1.05100e7 −1.19684 −0.598421 0.801182i \(-0.704205\pi\)
−0.598421 + 0.801182i \(0.704205\pi\)
\(600\) 0 0
\(601\) −199390. −0.0225173 −0.0112587 0.999937i \(-0.503584\pi\)
−0.0112587 + 0.999937i \(0.503584\pi\)
\(602\) 0 0
\(603\) −6.13301e6 −0.686879
\(604\) 0 0
\(605\) 746691. 0.0829378
\(606\) 0 0
\(607\) −16190.0 −0.00178351 −0.000891754 1.00000i \(-0.500284\pi\)
−0.000891754 1.00000i \(0.500284\pi\)
\(608\) 0 0
\(609\) 342624. 0.0374347
\(610\) 0 0
\(611\) −1.18913e7 −1.28863
\(612\) 0 0
\(613\) 1.15253e7 1.23880 0.619402 0.785074i \(-0.287375\pi\)
0.619402 + 0.785074i \(0.287375\pi\)
\(614\) 0 0
\(615\) 270504. 0.0288394
\(616\) 0 0
\(617\) 1.69974e7 1.79750 0.898751 0.438459i \(-0.144476\pi\)
0.898751 + 0.438459i \(0.144476\pi\)
\(618\) 0 0
\(619\) −1.84875e7 −1.93933 −0.969663 0.244445i \(-0.921394\pi\)
−0.969663 + 0.244445i \(0.921394\pi\)
\(620\) 0 0
\(621\) −862815. −0.0897819
\(622\) 0 0
\(623\) 2.08189e7 2.14901
\(624\) 0 0
\(625\) −7.85355e6 −0.804203
\(626\) 0 0
\(627\) −172304. −0.0175036
\(628\) 0 0
\(629\) −1.09113e7 −1.09964
\(630\) 0 0
\(631\) 4.54281e6 0.454204 0.227102 0.973871i \(-0.427075\pi\)
0.227102 + 0.973871i \(0.427075\pi\)
\(632\) 0 0
\(633\) −932428. −0.0924924
\(634\) 0 0
\(635\) 1.22102e7 1.20168
\(636\) 0 0
\(637\) −7.43831e6 −0.726316
\(638\) 0 0
\(639\) 3.22126e6 0.312086
\(640\) 0 0
\(641\) 1.84286e7 1.77153 0.885764 0.464136i \(-0.153635\pi\)
0.885764 + 0.464136i \(0.153635\pi\)
\(642\) 0 0
\(643\) 9.66604e6 0.921979 0.460989 0.887406i \(-0.347495\pi\)
0.460989 + 0.887406i \(0.347495\pi\)
\(644\) 0 0
\(645\) 907698. 0.0859097
\(646\) 0 0
\(647\) 4.51430e6 0.423965 0.211982 0.977273i \(-0.432008\pi\)
0.211982 + 0.977273i \(0.432008\pi\)
\(648\) 0 0
\(649\) 4.23367e6 0.394553
\(650\) 0 0
\(651\) −1.03667e6 −0.0958712
\(652\) 0 0
\(653\) 5.37235e6 0.493039 0.246519 0.969138i \(-0.420713\pi\)
0.246519 + 0.969138i \(0.420713\pi\)
\(654\) 0 0
\(655\) −5.00524e6 −0.455850
\(656\) 0 0
\(657\) 1.28889e7 1.16494
\(658\) 0 0
\(659\) 9.87956e6 0.886184 0.443092 0.896476i \(-0.353881\pi\)
0.443092 + 0.896476i \(0.353881\pi\)
\(660\) 0 0
\(661\) −1.08052e7 −0.961898 −0.480949 0.876748i \(-0.659708\pi\)
−0.480949 + 0.876748i \(0.659708\pi\)
\(662\) 0 0
\(663\) 510696. 0.0451210
\(664\) 0 0
\(665\) 1.20556e7 1.05714
\(666\) 0 0
\(667\) 3.67186e6 0.319574
\(668\) 0 0
\(669\) −169745. −0.0146633
\(670\) 0 0
\(671\) −5.55874e6 −0.476618
\(672\) 0 0
\(673\) 1.13275e7 0.964042 0.482021 0.876160i \(-0.339903\pi\)
0.482021 + 0.876160i \(0.339903\pi\)
\(674\) 0 0
\(675\) 254140. 0.0214691
\(676\) 0 0
\(677\) 1.20595e7 1.01125 0.505624 0.862754i \(-0.331262\pi\)
0.505624 + 0.862754i \(0.331262\pi\)
\(678\) 0 0
\(679\) −1.47420e7 −1.22710
\(680\) 0 0
\(681\) 198078. 0.0163670
\(682\) 0 0
\(683\) −5.14166e6 −0.421747 −0.210873 0.977513i \(-0.567631\pi\)
−0.210873 + 0.977513i \(0.567631\pi\)
\(684\) 0 0
\(685\) 2.04070e7 1.66170
\(686\) 0 0
\(687\) 849997. 0.0687109
\(688\) 0 0
\(689\) −2.12624e7 −1.70633
\(690\) 0 0
\(691\) 1.31243e7 1.04563 0.522817 0.852445i \(-0.324881\pi\)
0.522817 + 0.852445i \(0.324881\pi\)
\(692\) 0 0
\(693\) 4.86081e6 0.384482
\(694\) 0 0
\(695\) 1.04941e7 0.824104
\(696\) 0 0
\(697\) −3.91435e6 −0.305195
\(698\) 0 0
\(699\) −401832. −0.0311065
\(700\) 0 0
\(701\) −3.65956e6 −0.281277 −0.140638 0.990061i \(-0.544916\pi\)
−0.140638 + 0.990061i \(0.544916\pi\)
\(702\) 0 0
\(703\) 2.10538e7 1.60673
\(704\) 0 0
\(705\) 876384. 0.0664082
\(706\) 0 0
\(707\) −246012. −0.0185101
\(708\) 0 0
\(709\) −1.02252e7 −0.763935 −0.381968 0.924176i \(-0.624753\pi\)
−0.381968 + 0.924176i \(0.624753\pi\)
\(710\) 0 0
\(711\) 1.86906e7 1.38660
\(712\) 0 0
\(713\) −1.11099e7 −0.818436
\(714\) 0 0
\(715\) 4.27033e6 0.312390
\(716\) 0 0
\(717\) −855174. −0.0621236
\(718\) 0 0
\(719\) −2.41683e7 −1.74351 −0.871753 0.489945i \(-0.837017\pi\)
−0.871753 + 0.489945i \(0.837017\pi\)
\(720\) 0 0
\(721\) 1.95043e7 1.39731
\(722\) 0 0
\(723\) 1.12546e6 0.0800730
\(724\) 0 0
\(725\) −1.08154e6 −0.0764181
\(726\) 0 0
\(727\) −1.68246e7 −1.18062 −0.590310 0.807177i \(-0.700994\pi\)
−0.590310 + 0.807177i \(0.700994\pi\)
\(728\) 0 0
\(729\) −1.39958e7 −0.975393
\(730\) 0 0
\(731\) −1.31349e7 −0.909147
\(732\) 0 0
\(733\) 5.04168e6 0.346590 0.173295 0.984870i \(-0.444559\pi\)
0.173295 + 0.984870i \(0.444559\pi\)
\(734\) 0 0
\(735\) 548199. 0.0374300
\(736\) 0 0
\(737\) −3.06650e6 −0.207958
\(738\) 0 0
\(739\) −6.26375e6 −0.421913 −0.210957 0.977495i \(-0.567658\pi\)
−0.210957 + 0.977495i \(0.567658\pi\)
\(740\) 0 0
\(741\) −985408. −0.0659281
\(742\) 0 0
\(743\) −3.63976e6 −0.241880 −0.120940 0.992660i \(-0.538591\pi\)
−0.120940 + 0.992660i \(0.538591\pi\)
\(744\) 0 0
\(745\) −4.47403e6 −0.295330
\(746\) 0 0
\(747\) −1.33134e7 −0.872945
\(748\) 0 0
\(749\) −1.31741e7 −0.858057
\(750\) 0 0
\(751\) 1.87370e7 1.21227 0.606135 0.795362i \(-0.292719\pi\)
0.606135 + 0.795362i \(0.292719\pi\)
\(752\) 0 0
\(753\) −1.19751e6 −0.0769649
\(754\) 0 0
\(755\) 2.20717e7 1.40918
\(756\) 0 0
\(757\) −489242. −0.0310302 −0.0155151 0.999880i \(-0.504939\pi\)
−0.0155151 + 0.999880i \(0.504939\pi\)
\(758\) 0 0
\(759\) −215259. −0.0135630
\(760\) 0 0
\(761\) 1.46969e7 0.919952 0.459976 0.887931i \(-0.347858\pi\)
0.459976 + 0.887931i \(0.347858\pi\)
\(762\) 0 0
\(763\) −1.45818e7 −0.906774
\(764\) 0 0
\(765\) 9.10840e6 0.562715
\(766\) 0 0
\(767\) 2.42124e7 1.48610
\(768\) 0 0
\(769\) 2.42072e7 1.47615 0.738073 0.674721i \(-0.235736\pi\)
0.738073 + 0.674721i \(0.235736\pi\)
\(770\) 0 0
\(771\) 37758.0 0.00228756
\(772\) 0 0
\(773\) −1.35260e7 −0.814181 −0.407091 0.913388i \(-0.633457\pi\)
−0.407091 + 0.913388i \(0.633457\pi\)
\(774\) 0 0
\(775\) 3.27238e6 0.195708
\(776\) 0 0
\(777\) 2.45431e6 0.145840
\(778\) 0 0
\(779\) 7.55290e6 0.445933
\(780\) 0 0
\(781\) 1.61063e6 0.0944862
\(782\) 0 0
\(783\) −1.00104e6 −0.0583508
\(784\) 0 0
\(785\) 1.73782e6 0.100654
\(786\) 0 0
\(787\) 1.42094e7 0.817786 0.408893 0.912582i \(-0.365915\pi\)
0.408893 + 0.912582i \(0.365915\pi\)
\(788\) 0 0
\(789\) 631254. 0.0361004
\(790\) 0 0
\(791\) −7.84300e6 −0.445698
\(792\) 0 0
\(793\) −3.17905e7 −1.79521
\(794\) 0 0
\(795\) 1.56703e6 0.0879343
\(796\) 0 0
\(797\) 7.93333e6 0.442395 0.221197 0.975229i \(-0.429003\pi\)
0.221197 + 0.975229i \(0.429003\pi\)
\(798\) 0 0
\(799\) −1.26818e7 −0.702771
\(800\) 0 0
\(801\) −3.03504e7 −1.67141
\(802\) 0 0
\(803\) 6.44446e6 0.352694
\(804\) 0 0
\(805\) 1.50610e7 0.819152
\(806\) 0 0
\(807\) 1.08034e6 0.0583952
\(808\) 0 0
\(809\) −1.04685e7 −0.562359 −0.281180 0.959655i \(-0.590726\pi\)
−0.281180 + 0.959655i \(0.590726\pi\)
\(810\) 0 0
\(811\) 1.19147e7 0.636110 0.318055 0.948072i \(-0.396970\pi\)
0.318055 + 0.948072i \(0.396970\pi\)
\(812\) 0 0
\(813\) 816100. 0.0433029
\(814\) 0 0
\(815\) 2.29602e6 0.121083
\(816\) 0 0
\(817\) 2.53444e7 1.32839
\(818\) 0 0
\(819\) 2.77990e7 1.44817
\(820\) 0 0
\(821\) 1.86112e6 0.0963645 0.0481822 0.998839i \(-0.484657\pi\)
0.0481822 + 0.998839i \(0.484657\pi\)
\(822\) 0 0
\(823\) −2.30153e7 −1.18445 −0.592225 0.805773i \(-0.701750\pi\)
−0.592225 + 0.805773i \(0.701750\pi\)
\(824\) 0 0
\(825\) 63404.0 0.00324326
\(826\) 0 0
\(827\) −1.68351e7 −0.855959 −0.427980 0.903788i \(-0.640775\pi\)
−0.427980 + 0.903788i \(0.640775\pi\)
\(828\) 0 0
\(829\) 2.35299e7 1.18914 0.594570 0.804044i \(-0.297322\pi\)
0.594570 + 0.804044i \(0.297322\pi\)
\(830\) 0 0
\(831\) −1.68820e6 −0.0848049
\(832\) 0 0
\(833\) −7.93276e6 −0.396106
\(834\) 0 0
\(835\) −2.46104e7 −1.22152
\(836\) 0 0
\(837\) 3.02882e6 0.149438
\(838\) 0 0
\(839\) −2.91549e7 −1.42990 −0.714952 0.699173i \(-0.753552\pi\)
−0.714952 + 0.699173i \(0.753552\pi\)
\(840\) 0 0
\(841\) −1.62511e7 −0.792303
\(842\) 0 0
\(843\) −879042. −0.0426030
\(844\) 0 0
\(845\) 5.48612e6 0.264316
\(846\) 0 0
\(847\) 2.43041e6 0.116405
\(848\) 0 0
\(849\) 1.54027e6 0.0733377
\(850\) 0 0
\(851\) 2.63025e7 1.24501
\(852\) 0 0
\(853\) 9.49052e6 0.446599 0.223299 0.974750i \(-0.428317\pi\)
0.223299 + 0.974750i \(0.428317\pi\)
\(854\) 0 0
\(855\) −1.75750e7 −0.822205
\(856\) 0 0
\(857\) −1.81553e6 −0.0844405 −0.0422203 0.999108i \(-0.513443\pi\)
−0.0422203 + 0.999108i \(0.513443\pi\)
\(858\) 0 0
\(859\) −1.07812e7 −0.498522 −0.249261 0.968436i \(-0.580188\pi\)
−0.249261 + 0.968436i \(0.580188\pi\)
\(860\) 0 0
\(861\) 880464. 0.0404766
\(862\) 0 0
\(863\) 2.83355e7 1.29510 0.647550 0.762023i \(-0.275794\pi\)
0.647550 + 0.762023i \(0.275794\pi\)
\(864\) 0 0
\(865\) 3.90790e7 1.77584
\(866\) 0 0
\(867\) −875213. −0.0395427
\(868\) 0 0
\(869\) 9.34531e6 0.419802
\(870\) 0 0
\(871\) −1.75374e7 −0.783283
\(872\) 0 0
\(873\) 2.14913e7 0.954392
\(874\) 0 0
\(875\) −3.08924e7 −1.36406
\(876\) 0 0
\(877\) 2.68919e7 1.18065 0.590326 0.807165i \(-0.298999\pi\)
0.590326 + 0.807165i \(0.298999\pi\)
\(878\) 0 0
\(879\) −720840. −0.0314678
\(880\) 0 0
\(881\) −1.92132e7 −0.833989 −0.416995 0.908909i \(-0.636917\pi\)
−0.416995 + 0.908909i \(0.636917\pi\)
\(882\) 0 0
\(883\) 1.15931e7 0.500378 0.250189 0.968197i \(-0.419507\pi\)
0.250189 + 0.968197i \(0.419507\pi\)
\(884\) 0 0
\(885\) −1.78444e6 −0.0765850
\(886\) 0 0
\(887\) −1.31857e7 −0.562721 −0.281361 0.959602i \(-0.590786\pi\)
−0.281361 + 0.959602i \(0.590786\pi\)
\(888\) 0 0
\(889\) 3.97431e7 1.68658
\(890\) 0 0
\(891\) −7.05684e6 −0.297794
\(892\) 0 0
\(893\) 2.44700e7 1.02685
\(894\) 0 0
\(895\) 1.54733e7 0.645694
\(896\) 0 0
\(897\) −1.23107e6 −0.0510859
\(898\) 0 0
\(899\) −1.28897e7 −0.531916
\(900\) 0 0
\(901\) −2.26758e7 −0.930573
\(902\) 0 0
\(903\) 2.95447e6 0.120576
\(904\) 0 0
\(905\) 1.45442e7 0.590295
\(906\) 0 0
\(907\) 2.98195e6 0.120360 0.0601800 0.998188i \(-0.480833\pi\)
0.0601800 + 0.998188i \(0.480833\pi\)
\(908\) 0 0
\(909\) 358644. 0.0143964
\(910\) 0 0
\(911\) −2.96579e7 −1.18398 −0.591989 0.805946i \(-0.701657\pi\)
−0.591989 + 0.805946i \(0.701657\pi\)
\(912\) 0 0
\(913\) −6.65669e6 −0.264291
\(914\) 0 0
\(915\) 2.34294e6 0.0925142
\(916\) 0 0
\(917\) −1.62916e7 −0.639793
\(918\) 0 0
\(919\) −3.18057e7 −1.24227 −0.621135 0.783704i \(-0.713328\pi\)
−0.621135 + 0.783704i \(0.713328\pi\)
\(920\) 0 0
\(921\) −1.03905e6 −0.0403633
\(922\) 0 0
\(923\) 9.21121e6 0.355887
\(924\) 0 0
\(925\) −7.74734e6 −0.297713
\(926\) 0 0
\(927\) −2.84340e7 −1.08677
\(928\) 0 0
\(929\) −2.33444e7 −0.887451 −0.443725 0.896163i \(-0.646343\pi\)
−0.443725 + 0.896163i \(0.646343\pi\)
\(930\) 0 0
\(931\) 1.53066e7 0.578767
\(932\) 0 0
\(933\) 1.25135e6 0.0470624
\(934\) 0 0
\(935\) 4.55420e6 0.170366
\(936\) 0 0
\(937\) 2.07372e7 0.771616 0.385808 0.922579i \(-0.373923\pi\)
0.385808 + 0.922579i \(0.373923\pi\)
\(938\) 0 0
\(939\) −1.44336e6 −0.0534209
\(940\) 0 0
\(941\) −2.69193e7 −0.991036 −0.495518 0.868598i \(-0.665022\pi\)
−0.495518 + 0.868598i \(0.665022\pi\)
\(942\) 0 0
\(943\) 9.43582e6 0.345542
\(944\) 0 0
\(945\) −4.10601e6 −0.149569
\(946\) 0 0
\(947\) 1.01896e7 0.369216 0.184608 0.982812i \(-0.440898\pi\)
0.184608 + 0.982812i \(0.440898\pi\)
\(948\) 0 0
\(949\) 3.68559e7 1.32844
\(950\) 0 0
\(951\) 2.01208e6 0.0721429
\(952\) 0 0
\(953\) 1.03924e7 0.370665 0.185333 0.982676i \(-0.440664\pi\)
0.185333 + 0.982676i \(0.440664\pi\)
\(954\) 0 0
\(955\) −3.91204e7 −1.38802
\(956\) 0 0
\(957\) −249744. −0.00881486
\(958\) 0 0
\(959\) 6.64227e7 2.33222
\(960\) 0 0
\(961\) 1.03709e7 0.362249
\(962\) 0 0
\(963\) 1.92056e7 0.667363
\(964\) 0 0
\(965\) 2.09951e7 0.725770
\(966\) 0 0
\(967\) 8.18877e6 0.281613 0.140806 0.990037i \(-0.455030\pi\)
0.140806 + 0.990037i \(0.455030\pi\)
\(968\) 0 0
\(969\) −1.05091e6 −0.0359548
\(970\) 0 0
\(971\) −1.73274e7 −0.589775 −0.294887 0.955532i \(-0.595282\pi\)
−0.294887 + 0.955532i \(0.595282\pi\)
\(972\) 0 0
\(973\) 3.41572e7 1.15664
\(974\) 0 0
\(975\) 362608. 0.0122159
\(976\) 0 0
\(977\) −438963. −0.0147127 −0.00735634 0.999973i \(-0.502342\pi\)
−0.00735634 + 0.999973i \(0.502342\pi\)
\(978\) 0 0
\(979\) −1.51752e7 −0.506032
\(980\) 0 0
\(981\) 2.12578e7 0.705253
\(982\) 0 0
\(983\) 2.79124e7 0.921326 0.460663 0.887575i \(-0.347612\pi\)
0.460663 + 0.887575i \(0.347612\pi\)
\(984\) 0 0
\(985\) 3.87222e7 1.27165
\(986\) 0 0
\(987\) 2.85254e6 0.0932051
\(988\) 0 0
\(989\) 3.16626e7 1.02933
\(990\) 0 0
\(991\) 4.26846e7 1.38066 0.690331 0.723494i \(-0.257465\pi\)
0.690331 + 0.723494i \(0.257465\pi\)
\(992\) 0 0
\(993\) 2.01734e6 0.0649240
\(994\) 0 0
\(995\) 2.37660e6 0.0761024
\(996\) 0 0
\(997\) 2.21044e7 0.704273 0.352137 0.935949i \(-0.385455\pi\)
0.352137 + 0.935949i \(0.385455\pi\)
\(998\) 0 0
\(999\) −7.17072e6 −0.227326
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 704.6.a.f.1.1 1
4.3 odd 2 704.6.a.e.1.1 1
8.3 odd 2 22.6.a.b.1.1 1
8.5 even 2 176.6.a.b.1.1 1
24.11 even 2 198.6.a.i.1.1 1
40.3 even 4 550.6.b.f.199.2 2
40.19 odd 2 550.6.a.f.1.1 1
40.27 even 4 550.6.b.f.199.1 2
56.27 even 2 1078.6.a.a.1.1 1
88.43 even 2 242.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.6.a.b.1.1 1 8.3 odd 2
176.6.a.b.1.1 1 8.5 even 2
198.6.a.i.1.1 1 24.11 even 2
242.6.a.d.1.1 1 88.43 even 2
550.6.a.f.1.1 1 40.19 odd 2
550.6.b.f.199.1 2 40.27 even 4
550.6.b.f.199.2 2 40.3 even 4
704.6.a.e.1.1 1 4.3 odd 2
704.6.a.f.1.1 1 1.1 even 1 trivial
1078.6.a.a.1.1 1 56.27 even 2