Properties

Label 588.6.a.e.1.1
Level $588$
Weight $6$
Character 588.1
Self dual yes
Analytic conductor $94.306$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,6,Mod(1,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, 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("588.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 588.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: \(94.3056860500\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 588.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{3} -6.00000 q^{5} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} -6.00000 q^{5} +81.0000 q^{9} -108.000 q^{11} +346.000 q^{13} -54.0000 q^{15} +1398.00 q^{17} +1012.00 q^{19} -1536.00 q^{23} -3089.00 q^{25} +729.000 q^{27} -3762.00 q^{29} +736.000 q^{31} -972.000 q^{33} +2054.00 q^{37} +3114.00 q^{39} +15534.0 q^{41} +11036.0 q^{43} -486.000 q^{45} -4560.00 q^{47} +12582.0 q^{51} -7962.00 q^{53} +648.000 q^{55} +9108.00 q^{57} +7020.00 q^{59} -26870.0 q^{61} -2076.00 q^{65} +52148.0 q^{67} -13824.0 q^{69} -2544.00 q^{71} +9766.00 q^{73} -27801.0 q^{75} +68672.0 q^{79} +6561.00 q^{81} +61668.0 q^{83} -8388.00 q^{85} -33858.0 q^{87} +41454.0 q^{89} +6624.00 q^{93} -6072.00 q^{95} +111262. q^{97} -8748.00 q^{99} +O(q^{100})\)

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
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) −6.00000 −0.107331 −0.0536656 0.998559i \(-0.517091\pi\)
−0.0536656 + 0.998559i \(0.517091\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −108.000 −0.269118 −0.134559 0.990906i \(-0.542962\pi\)
−0.134559 + 0.990906i \(0.542962\pi\)
\(12\) 0 0
\(13\) 346.000 0.567829 0.283915 0.958850i \(-0.408367\pi\)
0.283915 + 0.958850i \(0.408367\pi\)
\(14\) 0 0
\(15\) −54.0000 −0.0619677
\(16\) 0 0
\(17\) 1398.00 1.17323 0.586617 0.809864i \(-0.300459\pi\)
0.586617 + 0.809864i \(0.300459\pi\)
\(18\) 0 0
\(19\) 1012.00 0.643127 0.321563 0.946888i \(-0.395792\pi\)
0.321563 + 0.946888i \(0.395792\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1536.00 −0.605441 −0.302720 0.953079i \(-0.597895\pi\)
−0.302720 + 0.953079i \(0.597895\pi\)
\(24\) 0 0
\(25\) −3089.00 −0.988480
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −3762.00 −0.830661 −0.415330 0.909671i \(-0.636334\pi\)
−0.415330 + 0.909671i \(0.636334\pi\)
\(30\) 0 0
\(31\) 736.000 0.137554 0.0687771 0.997632i \(-0.478090\pi\)
0.0687771 + 0.997632i \(0.478090\pi\)
\(32\) 0 0
\(33\) −972.000 −0.155375
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2054.00 0.246659 0.123329 0.992366i \(-0.460643\pi\)
0.123329 + 0.992366i \(0.460643\pi\)
\(38\) 0 0
\(39\) 3114.00 0.327836
\(40\) 0 0
\(41\) 15534.0 1.44319 0.721595 0.692315i \(-0.243409\pi\)
0.721595 + 0.692315i \(0.243409\pi\)
\(42\) 0 0
\(43\) 11036.0 0.910208 0.455104 0.890438i \(-0.349602\pi\)
0.455104 + 0.890438i \(0.349602\pi\)
\(44\) 0 0
\(45\) −486.000 −0.0357771
\(46\) 0 0
\(47\) −4560.00 −0.301107 −0.150553 0.988602i \(-0.548106\pi\)
−0.150553 + 0.988602i \(0.548106\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 12582.0 0.677367
\(52\) 0 0
\(53\) −7962.00 −0.389343 −0.194672 0.980868i \(-0.562364\pi\)
−0.194672 + 0.980868i \(0.562364\pi\)
\(54\) 0 0
\(55\) 648.000 0.0288847
\(56\) 0 0
\(57\) 9108.00 0.371309
\(58\) 0 0
\(59\) 7020.00 0.262547 0.131274 0.991346i \(-0.458093\pi\)
0.131274 + 0.991346i \(0.458093\pi\)
\(60\) 0 0
\(61\) −26870.0 −0.924577 −0.462288 0.886730i \(-0.652972\pi\)
−0.462288 + 0.886730i \(0.652972\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2076.00 −0.0609458
\(66\) 0 0
\(67\) 52148.0 1.41922 0.709612 0.704593i \(-0.248870\pi\)
0.709612 + 0.704593i \(0.248870\pi\)
\(68\) 0 0
\(69\) −13824.0 −0.349551
\(70\) 0 0
\(71\) −2544.00 −0.0598923 −0.0299462 0.999552i \(-0.509534\pi\)
−0.0299462 + 0.999552i \(0.509534\pi\)
\(72\) 0 0
\(73\) 9766.00 0.214491 0.107246 0.994233i \(-0.465797\pi\)
0.107246 + 0.994233i \(0.465797\pi\)
\(74\) 0 0
\(75\) −27801.0 −0.570699
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 68672.0 1.23798 0.618988 0.785401i \(-0.287543\pi\)
0.618988 + 0.785401i \(0.287543\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) 61668.0 0.982573 0.491286 0.870998i \(-0.336527\pi\)
0.491286 + 0.870998i \(0.336527\pi\)
\(84\) 0 0
\(85\) −8388.00 −0.125925
\(86\) 0 0
\(87\) −33858.0 −0.479582
\(88\) 0 0
\(89\) 41454.0 0.554742 0.277371 0.960763i \(-0.410537\pi\)
0.277371 + 0.960763i \(0.410537\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 6624.00 0.0794169
\(94\) 0 0
\(95\) −6072.00 −0.0690276
\(96\) 0 0
\(97\) 111262. 1.20065 0.600327 0.799755i \(-0.295037\pi\)
0.600327 + 0.799755i \(0.295037\pi\)
\(98\) 0 0
\(99\) −8748.00 −0.0897059
\(100\) 0 0
\(101\) 180426. 1.75993 0.879966 0.475037i \(-0.157565\pi\)
0.879966 + 0.475037i \(0.157565\pi\)
\(102\) 0 0
\(103\) −35912.0 −0.333539 −0.166769 0.985996i \(-0.553334\pi\)
−0.166769 + 0.985996i \(0.553334\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −30492.0 −0.257470 −0.128735 0.991679i \(-0.541092\pi\)
−0.128735 + 0.991679i \(0.541092\pi\)
\(108\) 0 0
\(109\) 82382.0 0.664150 0.332075 0.943253i \(-0.392251\pi\)
0.332075 + 0.943253i \(0.392251\pi\)
\(110\) 0 0
\(111\) 18486.0 0.142408
\(112\) 0 0
\(113\) −160398. −1.18169 −0.590844 0.806786i \(-0.701205\pi\)
−0.590844 + 0.806786i \(0.701205\pi\)
\(114\) 0 0
\(115\) 9216.00 0.0649827
\(116\) 0 0
\(117\) 28026.0 0.189276
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −149387. −0.927576
\(122\) 0 0
\(123\) 139806. 0.833226
\(124\) 0 0
\(125\) 37284.0 0.213426
\(126\) 0 0
\(127\) −80896.0 −0.445059 −0.222530 0.974926i \(-0.571431\pi\)
−0.222530 + 0.974926i \(0.571431\pi\)
\(128\) 0 0
\(129\) 99324.0 0.525509
\(130\) 0 0
\(131\) −173676. −0.884223 −0.442111 0.896960i \(-0.645770\pi\)
−0.442111 + 0.896960i \(0.645770\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4374.00 −0.0206559
\(136\) 0 0
\(137\) 390426. 1.77720 0.888602 0.458679i \(-0.151677\pi\)
0.888602 + 0.458679i \(0.151677\pi\)
\(138\) 0 0
\(139\) −83204.0 −0.365264 −0.182632 0.983181i \(-0.558462\pi\)
−0.182632 + 0.983181i \(0.558462\pi\)
\(140\) 0 0
\(141\) −41040.0 −0.173844
\(142\) 0 0
\(143\) −37368.0 −0.152813
\(144\) 0 0
\(145\) 22572.0 0.0891559
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 140358. 0.517931 0.258965 0.965887i \(-0.416618\pi\)
0.258965 + 0.965887i \(0.416618\pi\)
\(150\) 0 0
\(151\) 320360. 1.14339 0.571697 0.820465i \(-0.306285\pi\)
0.571697 + 0.820465i \(0.306285\pi\)
\(152\) 0 0
\(153\) 113238. 0.391078
\(154\) 0 0
\(155\) −4416.00 −0.0147639
\(156\) 0 0
\(157\) 158266. 0.512435 0.256217 0.966619i \(-0.417524\pi\)
0.256217 + 0.966619i \(0.417524\pi\)
\(158\) 0 0
\(159\) −71658.0 −0.224787
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 345476. 1.01847 0.509236 0.860627i \(-0.329928\pi\)
0.509236 + 0.860627i \(0.329928\pi\)
\(164\) 0 0
\(165\) 5832.00 0.0166766
\(166\) 0 0
\(167\) 20568.0 0.0570691 0.0285345 0.999593i \(-0.490916\pi\)
0.0285345 + 0.999593i \(0.490916\pi\)
\(168\) 0 0
\(169\) −251577. −0.677570
\(170\) 0 0
\(171\) 81972.0 0.214376
\(172\) 0 0
\(173\) −732558. −1.86092 −0.930458 0.366399i \(-0.880591\pi\)
−0.930458 + 0.366399i \(0.880591\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 63180.0 0.151582
\(178\) 0 0
\(179\) 572220. 1.33484 0.667422 0.744680i \(-0.267398\pi\)
0.667422 + 0.744680i \(0.267398\pi\)
\(180\) 0 0
\(181\) 352402. 0.799543 0.399772 0.916615i \(-0.369089\pi\)
0.399772 + 0.916615i \(0.369089\pi\)
\(182\) 0 0
\(183\) −241830. −0.533805
\(184\) 0 0
\(185\) −12324.0 −0.0264742
\(186\) 0 0
\(187\) −150984. −0.315738
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18456.0 −0.0366062 −0.0183031 0.999832i \(-0.505826\pi\)
−0.0183031 + 0.999832i \(0.505826\pi\)
\(192\) 0 0
\(193\) 832322. 1.60841 0.804207 0.594349i \(-0.202590\pi\)
0.804207 + 0.594349i \(0.202590\pi\)
\(194\) 0 0
\(195\) −18684.0 −0.0351871
\(196\) 0 0
\(197\) 612438. 1.12434 0.562169 0.827023i \(-0.309967\pi\)
0.562169 + 0.827023i \(0.309967\pi\)
\(198\) 0 0
\(199\) 501352. 0.897450 0.448725 0.893670i \(-0.351878\pi\)
0.448725 + 0.893670i \(0.351878\pi\)
\(200\) 0 0
\(201\) 469332. 0.819389
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −93204.0 −0.154899
\(206\) 0 0
\(207\) −124416. −0.201814
\(208\) 0 0
\(209\) −109296. −0.173077
\(210\) 0 0
\(211\) −556588. −0.860652 −0.430326 0.902673i \(-0.641601\pi\)
−0.430326 + 0.902673i \(0.641601\pi\)
\(212\) 0 0
\(213\) −22896.0 −0.0345789
\(214\) 0 0
\(215\) −66216.0 −0.0976938
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 87894.0 0.123837
\(220\) 0 0
\(221\) 483708. 0.666197
\(222\) 0 0
\(223\) 1.25680e6 1.69240 0.846202 0.532862i \(-0.178884\pi\)
0.846202 + 0.532862i \(0.178884\pi\)
\(224\) 0 0
\(225\) −250209. −0.329493
\(226\) 0 0
\(227\) 700932. 0.902841 0.451420 0.892311i \(-0.350917\pi\)
0.451420 + 0.892311i \(0.350917\pi\)
\(228\) 0 0
\(229\) −153374. −0.193269 −0.0966347 0.995320i \(-0.530808\pi\)
−0.0966347 + 0.995320i \(0.530808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 154266. 0.186157 0.0930787 0.995659i \(-0.470329\pi\)
0.0930787 + 0.995659i \(0.470329\pi\)
\(234\) 0 0
\(235\) 27360.0 0.0323181
\(236\) 0 0
\(237\) 618048. 0.714745
\(238\) 0 0
\(239\) −926376. −1.04904 −0.524521 0.851398i \(-0.675755\pi\)
−0.524521 + 0.851398i \(0.675755\pi\)
\(240\) 0 0
\(241\) 1.05662e6 1.17186 0.585932 0.810360i \(-0.300729\pi\)
0.585932 + 0.810360i \(0.300729\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 350152. 0.365186
\(248\) 0 0
\(249\) 555012. 0.567289
\(250\) 0 0
\(251\) 1.45984e6 1.46258 0.731290 0.682066i \(-0.238919\pi\)
0.731290 + 0.682066i \(0.238919\pi\)
\(252\) 0 0
\(253\) 165888. 0.162935
\(254\) 0 0
\(255\) −75492.0 −0.0727027
\(256\) 0 0
\(257\) −1.57142e6 −1.48409 −0.742043 0.670353i \(-0.766143\pi\)
−0.742043 + 0.670353i \(0.766143\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −304722. −0.276887
\(262\) 0 0
\(263\) −1.46275e6 −1.30401 −0.652006 0.758214i \(-0.726072\pi\)
−0.652006 + 0.758214i \(0.726072\pi\)
\(264\) 0 0
\(265\) 47772.0 0.0417887
\(266\) 0 0
\(267\) 373086. 0.320281
\(268\) 0 0
\(269\) 230850. 0.194513 0.0972566 0.995259i \(-0.468993\pi\)
0.0972566 + 0.995259i \(0.468993\pi\)
\(270\) 0 0
\(271\) 574432. 0.475133 0.237567 0.971371i \(-0.423650\pi\)
0.237567 + 0.971371i \(0.423650\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 333612. 0.266017
\(276\) 0 0
\(277\) 510950. 0.400110 0.200055 0.979785i \(-0.435888\pi\)
0.200055 + 0.979785i \(0.435888\pi\)
\(278\) 0 0
\(279\) 59616.0 0.0458514
\(280\) 0 0
\(281\) 931146. 0.703480 0.351740 0.936098i \(-0.385590\pi\)
0.351740 + 0.936098i \(0.385590\pi\)
\(282\) 0 0
\(283\) −2.15560e6 −1.59994 −0.799969 0.600042i \(-0.795151\pi\)
−0.799969 + 0.600042i \(0.795151\pi\)
\(284\) 0 0
\(285\) −54648.0 −0.0398531
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 534547. 0.376479
\(290\) 0 0
\(291\) 1.00136e6 0.693197
\(292\) 0 0
\(293\) −962070. −0.654693 −0.327346 0.944904i \(-0.606154\pi\)
−0.327346 + 0.944904i \(0.606154\pi\)
\(294\) 0 0
\(295\) −42120.0 −0.0281795
\(296\) 0 0
\(297\) −78732.0 −0.0517917
\(298\) 0 0
\(299\) −531456. −0.343787
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.62383e6 1.01610
\(304\) 0 0
\(305\) 161220. 0.0992360
\(306\) 0 0
\(307\) −1.71988e6 −1.04149 −0.520743 0.853714i \(-0.674345\pi\)
−0.520743 + 0.853714i \(0.674345\pi\)
\(308\) 0 0
\(309\) −323208. −0.192569
\(310\) 0 0
\(311\) 2.38121e6 1.39604 0.698018 0.716081i \(-0.254066\pi\)
0.698018 + 0.716081i \(0.254066\pi\)
\(312\) 0 0
\(313\) 293494. 0.169332 0.0846659 0.996409i \(-0.473018\pi\)
0.0846659 + 0.996409i \(0.473018\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.94642e6 −1.08790 −0.543949 0.839118i \(-0.683071\pi\)
−0.543949 + 0.839118i \(0.683071\pi\)
\(318\) 0 0
\(319\) 406296. 0.223545
\(320\) 0 0
\(321\) −274428. −0.148650
\(322\) 0 0
\(323\) 1.41478e6 0.754538
\(324\) 0 0
\(325\) −1.06879e6 −0.561288
\(326\) 0 0
\(327\) 741438. 0.383447
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.25184e6 0.628026 0.314013 0.949419i \(-0.398326\pi\)
0.314013 + 0.949419i \(0.398326\pi\)
\(332\) 0 0
\(333\) 166374. 0.0822195
\(334\) 0 0
\(335\) −312888. −0.152327
\(336\) 0 0
\(337\) 297458. 0.142676 0.0713380 0.997452i \(-0.477273\pi\)
0.0713380 + 0.997452i \(0.477273\pi\)
\(338\) 0 0
\(339\) −1.44358e6 −0.682248
\(340\) 0 0
\(341\) −79488.0 −0.0370182
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 82944.0 0.0375178
\(346\) 0 0
\(347\) −3.40657e6 −1.51878 −0.759388 0.650638i \(-0.774502\pi\)
−0.759388 + 0.650638i \(0.774502\pi\)
\(348\) 0 0
\(349\) 420826. 0.184943 0.0924717 0.995715i \(-0.470523\pi\)
0.0924717 + 0.995715i \(0.470523\pi\)
\(350\) 0 0
\(351\) 252234. 0.109279
\(352\) 0 0
\(353\) −1.39435e6 −0.595571 −0.297786 0.954633i \(-0.596248\pi\)
−0.297786 + 0.954633i \(0.596248\pi\)
\(354\) 0 0
\(355\) 15264.0 0.00642832
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.55037e6 −1.45391 −0.726955 0.686686i \(-0.759065\pi\)
−0.726955 + 0.686686i \(0.759065\pi\)
\(360\) 0 0
\(361\) −1.45196e6 −0.586388
\(362\) 0 0
\(363\) −1.34448e6 −0.535536
\(364\) 0 0
\(365\) −58596.0 −0.0230216
\(366\) 0 0
\(367\) 391696. 0.151804 0.0759021 0.997115i \(-0.475816\pi\)
0.0759021 + 0.997115i \(0.475816\pi\)
\(368\) 0 0
\(369\) 1.25825e6 0.481063
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −163834. −0.0609722 −0.0304861 0.999535i \(-0.509706\pi\)
−0.0304861 + 0.999535i \(0.509706\pi\)
\(374\) 0 0
\(375\) 335556. 0.123222
\(376\) 0 0
\(377\) −1.30165e6 −0.471674
\(378\) 0 0
\(379\) 206156. 0.0737221 0.0368611 0.999320i \(-0.488264\pi\)
0.0368611 + 0.999320i \(0.488264\pi\)
\(380\) 0 0
\(381\) −728064. −0.256955
\(382\) 0 0
\(383\) −484176. −0.168658 −0.0843289 0.996438i \(-0.526875\pi\)
−0.0843289 + 0.996438i \(0.526875\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 893916. 0.303403
\(388\) 0 0
\(389\) −4.17479e6 −1.39882 −0.699409 0.714722i \(-0.746553\pi\)
−0.699409 + 0.714722i \(0.746553\pi\)
\(390\) 0 0
\(391\) −2.14733e6 −0.710324
\(392\) 0 0
\(393\) −1.56308e6 −0.510506
\(394\) 0 0
\(395\) −412032. −0.132873
\(396\) 0 0
\(397\) 4.39998e6 1.40112 0.700558 0.713595i \(-0.252934\pi\)
0.700558 + 0.713595i \(0.252934\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.45917e6 −1.69537 −0.847687 0.530497i \(-0.822005\pi\)
−0.847687 + 0.530497i \(0.822005\pi\)
\(402\) 0 0
\(403\) 254656. 0.0781072
\(404\) 0 0
\(405\) −39366.0 −0.0119257
\(406\) 0 0
\(407\) −221832. −0.0663801
\(408\) 0 0
\(409\) −2.18307e6 −0.645295 −0.322648 0.946519i \(-0.604573\pi\)
−0.322648 + 0.946519i \(0.604573\pi\)
\(410\) 0 0
\(411\) 3.51383e6 1.02607
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −370008. −0.105461
\(416\) 0 0
\(417\) −748836. −0.210885
\(418\) 0 0
\(419\) −5.44561e6 −1.51535 −0.757673 0.652635i \(-0.773664\pi\)
−0.757673 + 0.652635i \(0.773664\pi\)
\(420\) 0 0
\(421\) −4.83054e6 −1.32828 −0.664141 0.747607i \(-0.731203\pi\)
−0.664141 + 0.747607i \(0.731203\pi\)
\(422\) 0 0
\(423\) −369360. −0.100369
\(424\) 0 0
\(425\) −4.31842e6 −1.15972
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −336312. −0.0882265
\(430\) 0 0
\(431\) −7.58182e6 −1.96598 −0.982992 0.183647i \(-0.941210\pi\)
−0.982992 + 0.183647i \(0.941210\pi\)
\(432\) 0 0
\(433\) 99838.0 0.0255903 0.0127952 0.999918i \(-0.495927\pi\)
0.0127952 + 0.999918i \(0.495927\pi\)
\(434\) 0 0
\(435\) 203148. 0.0514742
\(436\) 0 0
\(437\) −1.55443e6 −0.389375
\(438\) 0 0
\(439\) 7.77690e6 1.92595 0.962976 0.269587i \(-0.0868873\pi\)
0.962976 + 0.269587i \(0.0868873\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.15488e6 0.763790 0.381895 0.924206i \(-0.375272\pi\)
0.381895 + 0.924206i \(0.375272\pi\)
\(444\) 0 0
\(445\) −248724. −0.0595412
\(446\) 0 0
\(447\) 1.26322e6 0.299027
\(448\) 0 0
\(449\) 4.91450e6 1.15044 0.575219 0.817999i \(-0.304917\pi\)
0.575219 + 0.817999i \(0.304917\pi\)
\(450\) 0 0
\(451\) −1.67767e6 −0.388388
\(452\) 0 0
\(453\) 2.88324e6 0.660139
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.77001e6 −1.29237 −0.646183 0.763182i \(-0.723636\pi\)
−0.646183 + 0.763182i \(0.723636\pi\)
\(458\) 0 0
\(459\) 1.01914e6 0.225789
\(460\) 0 0
\(461\) −1.65272e6 −0.362198 −0.181099 0.983465i \(-0.557965\pi\)
−0.181099 + 0.983465i \(0.557965\pi\)
\(462\) 0 0
\(463\) 7.69146e6 1.66746 0.833731 0.552170i \(-0.186200\pi\)
0.833731 + 0.552170i \(0.186200\pi\)
\(464\) 0 0
\(465\) −39744.0 −0.00852392
\(466\) 0 0
\(467\) −4.95880e6 −1.05217 −0.526083 0.850433i \(-0.676340\pi\)
−0.526083 + 0.850433i \(0.676340\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.42439e6 0.295854
\(472\) 0 0
\(473\) −1.19189e6 −0.244953
\(474\) 0 0
\(475\) −3.12607e6 −0.635718
\(476\) 0 0
\(477\) −644922. −0.129781
\(478\) 0 0
\(479\) 1.46899e6 0.292537 0.146268 0.989245i \(-0.453274\pi\)
0.146268 + 0.989245i \(0.453274\pi\)
\(480\) 0 0
\(481\) 710684. 0.140060
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −667572. −0.128868
\(486\) 0 0
\(487\) −6.46679e6 −1.23557 −0.617784 0.786348i \(-0.711969\pi\)
−0.617784 + 0.786348i \(0.711969\pi\)
\(488\) 0 0
\(489\) 3.10928e6 0.588015
\(490\) 0 0
\(491\) 8.94479e6 1.67443 0.837214 0.546876i \(-0.184183\pi\)
0.837214 + 0.546876i \(0.184183\pi\)
\(492\) 0 0
\(493\) −5.25928e6 −0.974560
\(494\) 0 0
\(495\) 52488.0 0.00962824
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.05052e7 1.88866 0.944329 0.329004i \(-0.106713\pi\)
0.944329 + 0.329004i \(0.106713\pi\)
\(500\) 0 0
\(501\) 185112. 0.0329488
\(502\) 0 0
\(503\) −7.97993e6 −1.40630 −0.703152 0.711040i \(-0.748225\pi\)
−0.703152 + 0.711040i \(0.748225\pi\)
\(504\) 0 0
\(505\) −1.08256e6 −0.188896
\(506\) 0 0
\(507\) −2.26419e6 −0.391195
\(508\) 0 0
\(509\) −8.13425e6 −1.39163 −0.695814 0.718222i \(-0.744956\pi\)
−0.695814 + 0.718222i \(0.744956\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 737748. 0.123770
\(514\) 0 0
\(515\) 215472. 0.0357992
\(516\) 0 0
\(517\) 492480. 0.0810331
\(518\) 0 0
\(519\) −6.59302e6 −1.07440
\(520\) 0 0
\(521\) −1.76800e6 −0.285357 −0.142678 0.989769i \(-0.545571\pi\)
−0.142678 + 0.989769i \(0.545571\pi\)
\(522\) 0 0
\(523\) 4.07211e6 0.650976 0.325488 0.945546i \(-0.394471\pi\)
0.325488 + 0.945546i \(0.394471\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.02893e6 0.161383
\(528\) 0 0
\(529\) −4.07705e6 −0.633442
\(530\) 0 0
\(531\) 568620. 0.0875157
\(532\) 0 0
\(533\) 5.37476e6 0.819486
\(534\) 0 0
\(535\) 182952. 0.0276346
\(536\) 0 0
\(537\) 5.14998e6 0.770672
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4.60904e6 −0.677045 −0.338522 0.940958i \(-0.609927\pi\)
−0.338522 + 0.940958i \(0.609927\pi\)
\(542\) 0 0
\(543\) 3.17162e6 0.461616
\(544\) 0 0
\(545\) −494292. −0.0712840
\(546\) 0 0
\(547\) −5.81091e6 −0.830378 −0.415189 0.909735i \(-0.636285\pi\)
−0.415189 + 0.909735i \(0.636285\pi\)
\(548\) 0 0
\(549\) −2.17647e6 −0.308192
\(550\) 0 0
\(551\) −3.80714e6 −0.534220
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −110916. −0.0152849
\(556\) 0 0
\(557\) −9.59949e6 −1.31102 −0.655511 0.755185i \(-0.727547\pi\)
−0.655511 + 0.755185i \(0.727547\pi\)
\(558\) 0 0
\(559\) 3.81846e6 0.516843
\(560\) 0 0
\(561\) −1.35886e6 −0.182291
\(562\) 0 0
\(563\) 3.21152e6 0.427012 0.213506 0.976942i \(-0.431512\pi\)
0.213506 + 0.976942i \(0.431512\pi\)
\(564\) 0 0
\(565\) 962388. 0.126832
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.23573e6 −1.19589 −0.597944 0.801538i \(-0.704016\pi\)
−0.597944 + 0.801538i \(0.704016\pi\)
\(570\) 0 0
\(571\) 2.81683e6 0.361551 0.180776 0.983524i \(-0.442139\pi\)
0.180776 + 0.983524i \(0.442139\pi\)
\(572\) 0 0
\(573\) −166104. −0.0211346
\(574\) 0 0
\(575\) 4.74470e6 0.598466
\(576\) 0 0
\(577\) −4.13415e6 −0.516947 −0.258474 0.966018i \(-0.583220\pi\)
−0.258474 + 0.966018i \(0.583220\pi\)
\(578\) 0 0
\(579\) 7.49090e6 0.928619
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 859896. 0.104779
\(584\) 0 0
\(585\) −168156. −0.0203153
\(586\) 0 0
\(587\) 4.38155e6 0.524847 0.262423 0.964953i \(-0.415478\pi\)
0.262423 + 0.964953i \(0.415478\pi\)
\(588\) 0 0
\(589\) 744832. 0.0884647
\(590\) 0 0
\(591\) 5.51194e6 0.649136
\(592\) 0 0
\(593\) −1.22971e7 −1.43604 −0.718020 0.696023i \(-0.754951\pi\)
−0.718020 + 0.696023i \(0.754951\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.51217e6 0.518143
\(598\) 0 0
\(599\) −9.20928e6 −1.04872 −0.524359 0.851497i \(-0.675695\pi\)
−0.524359 + 0.851497i \(0.675695\pi\)
\(600\) 0 0
\(601\) 1.63394e7 1.84522 0.922612 0.385730i \(-0.126050\pi\)
0.922612 + 0.385730i \(0.126050\pi\)
\(602\) 0 0
\(603\) 4.22399e6 0.473074
\(604\) 0 0
\(605\) 896322. 0.0995579
\(606\) 0 0
\(607\) 3.73082e6 0.410991 0.205495 0.978658i \(-0.434119\pi\)
0.205495 + 0.978658i \(0.434119\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.57776e6 −0.170977
\(612\) 0 0
\(613\) 1.46503e7 1.57469 0.787346 0.616511i \(-0.211455\pi\)
0.787346 + 0.616511i \(0.211455\pi\)
\(614\) 0 0
\(615\) −838836. −0.0894312
\(616\) 0 0
\(617\) −4.33527e6 −0.458462 −0.229231 0.973372i \(-0.573621\pi\)
−0.229231 + 0.973372i \(0.573621\pi\)
\(618\) 0 0
\(619\) 1.79095e7 1.87869 0.939346 0.342970i \(-0.111433\pi\)
0.939346 + 0.342970i \(0.111433\pi\)
\(620\) 0 0
\(621\) −1.11974e6 −0.116517
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.42942e6 0.965573
\(626\) 0 0
\(627\) −983664. −0.0999259
\(628\) 0 0
\(629\) 2.87149e6 0.289388
\(630\) 0 0
\(631\) −7.13615e6 −0.713495 −0.356747 0.934201i \(-0.616114\pi\)
−0.356747 + 0.934201i \(0.616114\pi\)
\(632\) 0 0
\(633\) −5.00929e6 −0.496898
\(634\) 0 0
\(635\) 485376. 0.0477688
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −206064. −0.0199641
\(640\) 0 0
\(641\) −2.47025e6 −0.237463 −0.118732 0.992926i \(-0.537883\pi\)
−0.118732 + 0.992926i \(0.537883\pi\)
\(642\) 0 0
\(643\) −1.13717e7 −1.08467 −0.542337 0.840161i \(-0.682460\pi\)
−0.542337 + 0.840161i \(0.682460\pi\)
\(644\) 0 0
\(645\) −595944. −0.0564035
\(646\) 0 0
\(647\) 1.69812e7 1.59480 0.797402 0.603449i \(-0.206207\pi\)
0.797402 + 0.603449i \(0.206207\pi\)
\(648\) 0 0
\(649\) −758160. −0.0706560
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.56724e7 −1.43831 −0.719157 0.694847i \(-0.755472\pi\)
−0.719157 + 0.694847i \(0.755472\pi\)
\(654\) 0 0
\(655\) 1.04206e6 0.0949047
\(656\) 0 0
\(657\) 791046. 0.0714971
\(658\) 0 0
\(659\) 2.85424e6 0.256021 0.128011 0.991773i \(-0.459141\pi\)
0.128011 + 0.991773i \(0.459141\pi\)
\(660\) 0 0
\(661\) −1.56396e7 −1.39226 −0.696131 0.717915i \(-0.745097\pi\)
−0.696131 + 0.717915i \(0.745097\pi\)
\(662\) 0 0
\(663\) 4.35337e6 0.384629
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.77843e6 0.502916
\(668\) 0 0
\(669\) 1.13112e7 0.977110
\(670\) 0 0
\(671\) 2.90196e6 0.248820
\(672\) 0 0
\(673\) −3.01209e6 −0.256349 −0.128174 0.991752i \(-0.540912\pi\)
−0.128174 + 0.991752i \(0.540912\pi\)
\(674\) 0 0
\(675\) −2.25188e6 −0.190233
\(676\) 0 0
\(677\) −8.98733e6 −0.753632 −0.376816 0.926288i \(-0.622981\pi\)
−0.376816 + 0.926288i \(0.622981\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.30839e6 0.521255
\(682\) 0 0
\(683\) 7.13932e6 0.585605 0.292803 0.956173i \(-0.405412\pi\)
0.292803 + 0.956173i \(0.405412\pi\)
\(684\) 0 0
\(685\) −2.34256e6 −0.190750
\(686\) 0 0
\(687\) −1.38037e6 −0.111584
\(688\) 0 0
\(689\) −2.75485e6 −0.221080
\(690\) 0 0
\(691\) 1.55104e7 1.23575 0.617873 0.786278i \(-0.287995\pi\)
0.617873 + 0.786278i \(0.287995\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 499224. 0.0392043
\(696\) 0 0
\(697\) 2.17165e7 1.69320
\(698\) 0 0
\(699\) 1.38839e6 0.107478
\(700\) 0 0
\(701\) −2.22948e7 −1.71359 −0.856797 0.515654i \(-0.827549\pi\)
−0.856797 + 0.515654i \(0.827549\pi\)
\(702\) 0 0
\(703\) 2.07865e6 0.158633
\(704\) 0 0
\(705\) 246240. 0.0186589
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2534.00 0.000189318 0 9.46588e−5 1.00000i \(-0.499970\pi\)
9.46588e−5 1.00000i \(0.499970\pi\)
\(710\) 0 0
\(711\) 5.56243e6 0.412658
\(712\) 0 0
\(713\) −1.13050e6 −0.0832809
\(714\) 0 0
\(715\) 224208. 0.0164016
\(716\) 0 0
\(717\) −8.33738e6 −0.605664
\(718\) 0 0
\(719\) −1.66728e7 −1.20278 −0.601390 0.798955i \(-0.705386\pi\)
−0.601390 + 0.798955i \(0.705386\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 9.50960e6 0.676576
\(724\) 0 0
\(725\) 1.16208e7 0.821092
\(726\) 0 0
\(727\) 940648. 0.0660072 0.0330036 0.999455i \(-0.489493\pi\)
0.0330036 + 0.999455i \(0.489493\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 1.54283e7 1.06789
\(732\) 0 0
\(733\) −2.76783e7 −1.90274 −0.951369 0.308053i \(-0.900323\pi\)
−0.951369 + 0.308053i \(0.900323\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.63198e6 −0.381938
\(738\) 0 0
\(739\) 1.00351e7 0.675947 0.337973 0.941156i \(-0.390259\pi\)
0.337973 + 0.941156i \(0.390259\pi\)
\(740\) 0 0
\(741\) 3.15137e6 0.210840
\(742\) 0 0
\(743\) 1.67202e7 1.11114 0.555572 0.831469i \(-0.312499\pi\)
0.555572 + 0.831469i \(0.312499\pi\)
\(744\) 0 0
\(745\) −842148. −0.0555901
\(746\) 0 0
\(747\) 4.99511e6 0.327524
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 9.81728e6 0.635172 0.317586 0.948229i \(-0.397128\pi\)
0.317586 + 0.948229i \(0.397128\pi\)
\(752\) 0 0
\(753\) 1.31385e7 0.844421
\(754\) 0 0
\(755\) −1.92216e6 −0.122722
\(756\) 0 0
\(757\) −2.72948e6 −0.173117 −0.0865587 0.996247i \(-0.527587\pi\)
−0.0865587 + 0.996247i \(0.527587\pi\)
\(758\) 0 0
\(759\) 1.49299e6 0.0940704
\(760\) 0 0
\(761\) −2.78176e6 −0.174124 −0.0870619 0.996203i \(-0.527748\pi\)
−0.0870619 + 0.996203i \(0.527748\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −679428. −0.0419749
\(766\) 0 0
\(767\) 2.42892e6 0.149082
\(768\) 0 0
\(769\) −5.04331e6 −0.307539 −0.153769 0.988107i \(-0.549141\pi\)
−0.153769 + 0.988107i \(0.549141\pi\)
\(770\) 0 0
\(771\) −1.41428e7 −0.856837
\(772\) 0 0
\(773\) 1.49824e7 0.901845 0.450923 0.892563i \(-0.351095\pi\)
0.450923 + 0.892563i \(0.351095\pi\)
\(774\) 0 0
\(775\) −2.27350e6 −0.135969
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.57204e7 0.928154
\(780\) 0 0
\(781\) 274752. 0.0161181
\(782\) 0 0
\(783\) −2.74250e6 −0.159861
\(784\) 0 0
\(785\) −949596. −0.0550003
\(786\) 0 0
\(787\) −4.82851e6 −0.277892 −0.138946 0.990300i \(-0.544371\pi\)
−0.138946 + 0.990300i \(0.544371\pi\)
\(788\) 0 0
\(789\) −1.31648e7 −0.752871
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.29702e6 −0.525002
\(794\) 0 0
\(795\) 429948. 0.0241267
\(796\) 0 0
\(797\) 2.22125e7 1.23866 0.619331 0.785130i \(-0.287404\pi\)
0.619331 + 0.785130i \(0.287404\pi\)
\(798\) 0 0
\(799\) −6.37488e6 −0.353269
\(800\) 0 0
\(801\) 3.35777e6 0.184914
\(802\) 0 0
\(803\) −1.05473e6 −0.0577234
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.07765e6 0.112302
\(808\) 0 0
\(809\) 1.34312e7 0.721512 0.360756 0.932660i \(-0.382519\pi\)
0.360756 + 0.932660i \(0.382519\pi\)
\(810\) 0 0
\(811\) 1.99673e7 1.06602 0.533012 0.846107i \(-0.321060\pi\)
0.533012 + 0.846107i \(0.321060\pi\)
\(812\) 0 0
\(813\) 5.16989e6 0.274318
\(814\) 0 0
\(815\) −2.07286e6 −0.109314
\(816\) 0 0
\(817\) 1.11684e7 0.585379
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.90063e7 −1.50188 −0.750939 0.660372i \(-0.770399\pi\)
−0.750939 + 0.660372i \(0.770399\pi\)
\(822\) 0 0
\(823\) 2.38801e7 1.22896 0.614478 0.788934i \(-0.289366\pi\)
0.614478 + 0.788934i \(0.289366\pi\)
\(824\) 0 0
\(825\) 3.00251e6 0.153585
\(826\) 0 0
\(827\) −9.58724e6 −0.487450 −0.243725 0.969844i \(-0.578369\pi\)
−0.243725 + 0.969844i \(0.578369\pi\)
\(828\) 0 0
\(829\) 2.66835e7 1.34852 0.674260 0.738494i \(-0.264463\pi\)
0.674260 + 0.738494i \(0.264463\pi\)
\(830\) 0 0
\(831\) 4.59855e6 0.231003
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −123408. −0.00612530
\(836\) 0 0
\(837\) 536544. 0.0264723
\(838\) 0 0
\(839\) −5.41870e6 −0.265760 −0.132880 0.991132i \(-0.542423\pi\)
−0.132880 + 0.991132i \(0.542423\pi\)
\(840\) 0 0
\(841\) −6.35850e6 −0.310002
\(842\) 0 0
\(843\) 8.38031e6 0.406155
\(844\) 0 0
\(845\) 1.50946e6 0.0727244
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1.94004e7 −0.923724
\(850\) 0 0
\(851\) −3.15494e6 −0.149337
\(852\) 0 0
\(853\) 2.02323e7 0.952079 0.476040 0.879424i \(-0.342072\pi\)
0.476040 + 0.879424i \(0.342072\pi\)
\(854\) 0 0
\(855\) −491832. −0.0230092
\(856\) 0 0
\(857\) −7.16071e6 −0.333046 −0.166523 0.986038i \(-0.553254\pi\)
−0.166523 + 0.986038i \(0.553254\pi\)
\(858\) 0 0
\(859\) 1.24840e7 0.577258 0.288629 0.957441i \(-0.406801\pi\)
0.288629 + 0.957441i \(0.406801\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.32731e7 1.52078 0.760391 0.649466i \(-0.225007\pi\)
0.760391 + 0.649466i \(0.225007\pi\)
\(864\) 0 0
\(865\) 4.39535e6 0.199734
\(866\) 0 0
\(867\) 4.81092e6 0.217361
\(868\) 0 0
\(869\) −7.41658e6 −0.333161
\(870\) 0 0
\(871\) 1.80432e7 0.805876
\(872\) 0 0
\(873\) 9.01222e6 0.400218
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 4.10248e6 0.180114 0.0900570 0.995937i \(-0.471295\pi\)
0.0900570 + 0.995937i \(0.471295\pi\)
\(878\) 0 0
\(879\) −8.65863e6 −0.377987
\(880\) 0 0
\(881\) 2.99636e6 0.130063 0.0650315 0.997883i \(-0.479285\pi\)
0.0650315 + 0.997883i \(0.479285\pi\)
\(882\) 0 0
\(883\) −1.07514e7 −0.464049 −0.232024 0.972710i \(-0.574535\pi\)
−0.232024 + 0.972710i \(0.574535\pi\)
\(884\) 0 0
\(885\) −379080. −0.0162694
\(886\) 0 0
\(887\) −2.04970e7 −0.874744 −0.437372 0.899281i \(-0.644091\pi\)
−0.437372 + 0.899281i \(0.644091\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −708588. −0.0299020
\(892\) 0 0
\(893\) −4.61472e6 −0.193650
\(894\) 0 0
\(895\) −3.43332e6 −0.143270
\(896\) 0 0
\(897\) −4.78310e6 −0.198485
\(898\) 0 0
\(899\) −2.76883e6 −0.114261
\(900\) 0 0
\(901\) −1.11309e7 −0.456791
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.11441e6 −0.0858160
\(906\) 0 0
\(907\) −1.97520e7 −0.797245 −0.398623 0.917115i \(-0.630512\pi\)
−0.398623 + 0.917115i \(0.630512\pi\)
\(908\) 0 0
\(909\) 1.46145e7 0.586644
\(910\) 0 0
\(911\) 2.48511e7 0.992087 0.496044 0.868298i \(-0.334786\pi\)
0.496044 + 0.868298i \(0.334786\pi\)
\(912\) 0 0
\(913\) −6.66014e6 −0.264428
\(914\) 0 0
\(915\) 1.45098e6 0.0572939
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.54864e7 0.604869 0.302435 0.953170i \(-0.402201\pi\)
0.302435 + 0.953170i \(0.402201\pi\)
\(920\) 0 0
\(921\) −1.54790e7 −0.601302
\(922\) 0 0
\(923\) −880224. −0.0340086
\(924\) 0 0
\(925\) −6.34481e6 −0.243817
\(926\) 0 0
\(927\) −2.90887e6 −0.111180
\(928\) 0 0
\(929\) −1.73849e7 −0.660895 −0.330447 0.943824i \(-0.607200\pi\)
−0.330447 + 0.943824i \(0.607200\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2.14309e7 0.806001
\(934\) 0 0
\(935\) 905904. 0.0338886
\(936\) 0 0
\(937\) 2.72897e7 1.01543 0.507714 0.861526i \(-0.330491\pi\)
0.507714 + 0.861526i \(0.330491\pi\)
\(938\) 0 0
\(939\) 2.64145e6 0.0977637
\(940\) 0 0
\(941\) 1.20400e7 0.443256 0.221628 0.975131i \(-0.428863\pi\)
0.221628 + 0.975131i \(0.428863\pi\)
\(942\) 0 0
\(943\) −2.38602e7 −0.873766
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.82808e7 1.38710 0.693548 0.720411i \(-0.256047\pi\)
0.693548 + 0.720411i \(0.256047\pi\)
\(948\) 0 0
\(949\) 3.37904e6 0.121794
\(950\) 0 0
\(951\) −1.75178e7 −0.628098
\(952\) 0 0
\(953\) 1.83655e7 0.655043 0.327521 0.944844i \(-0.393787\pi\)
0.327521 + 0.944844i \(0.393787\pi\)
\(954\) 0 0
\(955\) 110736. 0.00392899
\(956\) 0 0
\(957\) 3.65666e6 0.129064
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2.80875e7 −0.981079
\(962\) 0 0
\(963\) −2.46985e6 −0.0858233
\(964\) 0 0
\(965\) −4.99393e6 −0.172633
\(966\) 0 0
\(967\) 1.83781e7 0.632024 0.316012 0.948755i \(-0.397656\pi\)
0.316012 + 0.948755i \(0.397656\pi\)
\(968\) 0 0
\(969\) 1.27330e7 0.435633
\(970\) 0 0
\(971\) 1.90795e7 0.649411 0.324706 0.945815i \(-0.394735\pi\)
0.324706 + 0.945815i \(0.394735\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −9.61915e6 −0.324060
\(976\) 0 0
\(977\) 3.37407e7 1.13088 0.565442 0.824788i \(-0.308706\pi\)
0.565442 + 0.824788i \(0.308706\pi\)
\(978\) 0 0
\(979\) −4.47703e6 −0.149291
\(980\) 0 0
\(981\) 6.67294e6 0.221383
\(982\) 0 0
\(983\) −1.56535e7 −0.516689 −0.258344 0.966053i \(-0.583177\pi\)
−0.258344 + 0.966053i \(0.583177\pi\)
\(984\) 0 0
\(985\) −3.67463e6 −0.120677
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.69513e7 −0.551077
\(990\) 0 0
\(991\) −1.10122e7 −0.356198 −0.178099 0.984013i \(-0.556995\pi\)
−0.178099 + 0.984013i \(0.556995\pi\)
\(992\) 0 0
\(993\) 1.12665e7 0.362591
\(994\) 0 0
\(995\) −3.00811e6 −0.0963244
\(996\) 0 0
\(997\) −2.38356e7 −0.759431 −0.379716 0.925103i \(-0.623978\pi\)
−0.379716 + 0.925103i \(0.623978\pi\)
\(998\) 0 0
\(999\) 1.49737e6 0.0474695
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 588.6.a.e.1.1 1
7.2 even 3 588.6.i.b.361.1 2
7.3 odd 6 588.6.i.f.373.1 2
7.4 even 3 588.6.i.b.373.1 2
7.5 odd 6 588.6.i.f.361.1 2
7.6 odd 2 84.6.a.a.1.1 1
21.20 even 2 252.6.a.b.1.1 1
28.27 even 2 336.6.a.n.1.1 1
84.83 odd 2 1008.6.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.a.1.1 1 7.6 odd 2
252.6.a.b.1.1 1 21.20 even 2
336.6.a.n.1.1 1 28.27 even 2
588.6.a.e.1.1 1 1.1 even 1 trivial
588.6.i.b.361.1 2 7.2 even 3
588.6.i.b.373.1 2 7.4 even 3
588.6.i.f.361.1 2 7.5 odd 6
588.6.i.f.373.1 2 7.3 odd 6
1008.6.a.o.1.1 1 84.83 odd 2