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Properties

Label 288.6.a.d.1.1
Level $288$
Weight $6$
Character 288.1
Self dual yes
Analytic conductor $46.191$
Analytic rank $1$
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] = [288,6,Mod(1,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, 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("288.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 288.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: \(46.1905401061\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 288.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-14.0000 q^{5} -208.000 q^{7} +O(q^{10})\) \(q-14.0000 q^{5} -208.000 q^{7} +536.000 q^{11} +694.000 q^{13} +1278.00 q^{17} +1112.00 q^{19} -3216.00 q^{23} -2929.00 q^{25} -2918.00 q^{29} -2624.00 q^{31} +2912.00 q^{35} -9458.00 q^{37} -170.000 q^{41} -19928.0 q^{43} -32.0000 q^{47} +26457.0 q^{49} +22178.0 q^{53} -7504.00 q^{55} -41480.0 q^{59} +15462.0 q^{61} -9716.00 q^{65} -20744.0 q^{67} -28592.0 q^{71} -53670.0 q^{73} -111488. q^{77} -69152.0 q^{79} +37800.0 q^{83} -17892.0 q^{85} +126806. q^{89} -144352. q^{91} -15568.0 q^{95} +62290.0 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −14.0000 −0.250440 −0.125220 − 0.992129i \(-0.539964\pi\)
−0.125220 + 0.992129i \(0.539964\pi\)
\(6\) 0 0
\(7\) −208.000 −1.60442 −0.802210 − 0.597042i \(-0.796343\pi\)
−0.802210 + 0.597042i \(0.796343\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 536.000 1.33562 0.667810 − 0.744332i \(-0.267232\pi\)
0.667810 + 0.744332i \(0.267232\pi\)
\(12\) 0 0
\(13\) 694.000 1.13894 0.569470 − 0.822012i \(-0.307148\pi\)
0.569470 + 0.822012i \(0.307148\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1278.00 1.07253 0.536264 − 0.844050i \(-0.319835\pi\)
0.536264 + 0.844050i \(0.319835\pi\)
\(18\) 0 0
\(19\) 1112.00 0.706677 0.353338 − 0.935496i \(-0.385046\pi\)
0.353338 + 0.935496i \(0.385046\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3216.00 −1.26764 −0.633821 − 0.773480i \(-0.718514\pi\)
−0.633821 + 0.773480i \(0.718514\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2918.00 −0.644303 −0.322152 − 0.946688i \(-0.604406\pi\)
−0.322152 + 0.946688i \(0.604406\pi\)
\(30\) 0 0
\(31\) −2624.00 −0.490410 −0.245205 − 0.969471i \(-0.578855\pi\)
−0.245205 + 0.969471i \(0.578855\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2912.00 0.401810
\(36\) 0 0
\(37\) −9458.00 −1.13578 −0.567891 − 0.823104i \(-0.692241\pi\)
−0.567891 + 0.823104i \(0.692241\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −170.000 −0.0157939 −0.00789695 − 0.999969i \(-0.502514\pi\)
−0.00789695 + 0.999969i \(0.502514\pi\)
\(42\) 0 0
\(43\) −19928.0 −1.64359 −0.821793 − 0.569786i \(-0.807026\pi\)
−0.821793 + 0.569786i \(0.807026\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −32.0000 −0.00211303 −0.00105651 − 0.999999i \(-0.500336\pi\)
−0.00105651 + 0.999999i \(0.500336\pi\)
\(48\) 0 0
\(49\) 26457.0 1.57417
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 22178.0 1.08451 0.542254 − 0.840215i \(-0.317571\pi\)
0.542254 + 0.840215i \(0.317571\pi\)
\(54\) 0 0
\(55\) −7504.00 −0.334492
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −41480.0 −1.55135 −0.775673 − 0.631135i \(-0.782589\pi\)
−0.775673 + 0.631135i \(0.782589\pi\)
\(60\) 0 0
\(61\) 15462.0 0.532036 0.266018 − 0.963968i \(-0.414292\pi\)
0.266018 + 0.963968i \(0.414292\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9716.00 −0.285236
\(66\) 0 0
\(67\) −20744.0 −0.564554 −0.282277 − 0.959333i \(-0.591090\pi\)
−0.282277 + 0.959333i \(0.591090\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −28592.0 −0.673130 −0.336565 − 0.941660i \(-0.609265\pi\)
−0.336565 + 0.941660i \(0.609265\pi\)
\(72\) 0 0
\(73\) −53670.0 −1.17876 −0.589379 − 0.807857i \(-0.700627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −111488. −2.14290
\(78\) 0 0
\(79\) −69152.0 −1.24663 −0.623314 − 0.781971i \(-0.714214\pi\)
−0.623314 + 0.781971i \(0.714214\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 37800.0 0.602277 0.301139 − 0.953580i \(-0.402633\pi\)
0.301139 + 0.953580i \(0.402633\pi\)
\(84\) 0 0
\(85\) −17892.0 −0.268603
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 126806. 1.69693 0.848467 − 0.529249i \(-0.177526\pi\)
0.848467 + 0.529249i \(0.177526\pi\)
\(90\) 0 0
\(91\) −144352. −1.82734
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15568.0 −0.176980
\(96\) 0 0
\(97\) 62290.0 0.672185 0.336093 − 0.941829i \(-0.390894\pi\)
0.336093 + 0.941829i \(0.390894\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6414.00 −0.0625641 −0.0312821 − 0.999511i \(-0.509959\pi\)
−0.0312821 + 0.999511i \(0.509959\pi\)
\(102\) 0 0
\(103\) −108432. −1.00708 −0.503541 − 0.863972i \(-0.667970\pi\)
−0.503541 + 0.863972i \(0.667970\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −103976. −0.877958 −0.438979 − 0.898497i \(-0.644660\pi\)
−0.438979 + 0.898497i \(0.644660\pi\)
\(108\) 0 0
\(109\) 2486.00 0.0200417 0.0100209 − 0.999950i \(-0.496810\pi\)
0.0100209 + 0.999950i \(0.496810\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15794.0 −0.116358 −0.0581790 − 0.998306i \(-0.518529\pi\)
−0.0581790 + 0.998306i \(0.518529\pi\)
\(114\) 0 0
\(115\) 45024.0 0.317468
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −265824. −1.72079
\(120\) 0 0
\(121\) 126245. 0.783882
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 84756.0 0.485172
\(126\) 0 0
\(127\) 1024.00 0.00563366 0.00281683 − 0.999996i \(-0.499103\pi\)
0.00281683 + 0.999996i \(0.499103\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 22664.0 0.115387 0.0576937 − 0.998334i \(-0.481625\pi\)
0.0576937 + 0.998334i \(0.481625\pi\)
\(132\) 0 0
\(133\) −231296. −1.13381
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 53238.0 0.242337 0.121169 − 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(138\) 0 0
\(139\) 19816.0 0.0869919 0.0434960 − 0.999054i \(-0.486150\pi\)
0.0434960 + 0.999054i \(0.486150\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 371984. 1.52119
\(144\) 0 0
\(145\) 40852.0 0.161359
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −452190. −1.66861 −0.834306 − 0.551302i \(-0.814131\pi\)
−0.834306 + 0.551302i \(0.814131\pi\)
\(150\) 0 0
\(151\) −263280. −0.939670 −0.469835 − 0.882754i \(-0.655687\pi\)
−0.469835 + 0.882754i \(0.655687\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 36736.0 0.122818
\(156\) 0 0
\(157\) −353530. −1.14466 −0.572331 − 0.820023i \(-0.693961\pi\)
−0.572331 + 0.820023i \(0.693961\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 668928. 2.03383
\(162\) 0 0
\(163\) −100936. −0.297562 −0.148781 − 0.988870i \(-0.547535\pi\)
−0.148781 + 0.988870i \(0.547535\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 284944. 0.790621 0.395310 − 0.918548i \(-0.370637\pi\)
0.395310 + 0.918548i \(0.370637\pi\)
\(168\) 0 0
\(169\) 110343. 0.297186
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −484374. −1.23045 −0.615227 − 0.788350i \(-0.710936\pi\)
−0.615227 + 0.788350i \(0.710936\pi\)
\(174\) 0 0
\(175\) 609232. 1.50379
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −406680. −0.948681 −0.474341 − 0.880341i \(-0.657313\pi\)
−0.474341 + 0.880341i \(0.657313\pi\)
\(180\) 0 0
\(181\) 570302. 1.29392 0.646962 − 0.762523i \(-0.276039\pi\)
0.646962 + 0.762523i \(0.276039\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 132412. 0.284445
\(186\) 0 0
\(187\) 685008. 1.43249
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −138624. −0.274951 −0.137475 − 0.990505i \(-0.543899\pi\)
−0.137475 + 0.990505i \(0.543899\pi\)
\(192\) 0 0
\(193\) 34482.0 0.0666345 0.0333173 − 0.999445i \(-0.489393\pi\)
0.0333173 + 0.999445i \(0.489393\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −643598. −1.18154 −0.590771 − 0.806839i \(-0.701176\pi\)
−0.590771 + 0.806839i \(0.701176\pi\)
\(198\) 0 0
\(199\) 1.10738e6 1.98227 0.991134 − 0.132865i \(-0.0424178\pi\)
0.991134 + 0.132865i \(0.0424178\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 606944. 1.03373
\(204\) 0 0
\(205\) 2380.00 0.00395542
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 596032. 0.943852
\(210\) 0 0
\(211\) 229976. 0.355612 0.177806 − 0.984066i \(-0.443100\pi\)
0.177806 + 0.984066i \(0.443100\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 278992. 0.411619
\(216\) 0 0
\(217\) 545792. 0.786824
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 886932. 1.22155
\(222\) 0 0
\(223\) −1.08947e6 −1.46708 −0.733540 − 0.679646i \(-0.762133\pi\)
−0.733540 + 0.679646i \(0.762133\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 687048. 0.884958 0.442479 − 0.896779i \(-0.354099\pi\)
0.442479 + 0.896779i \(0.354099\pi\)
\(228\) 0 0
\(229\) −699730. −0.881743 −0.440871 − 0.897570i \(-0.645330\pi\)
−0.440871 + 0.897570i \(0.645330\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −937722. −1.13158 −0.565789 − 0.824550i \(-0.691428\pi\)
−0.565789 + 0.824550i \(0.691428\pi\)
\(234\) 0 0
\(235\) 448.000 0.000529186 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −643488. −0.728695 −0.364347 − 0.931263i \(-0.618708\pi\)
−0.364347 + 0.931263i \(0.618708\pi\)
\(240\) 0 0
\(241\) 157282. 0.174436 0.0872181 − 0.996189i \(-0.472202\pi\)
0.0872181 + 0.996189i \(0.472202\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −370398. −0.394233
\(246\) 0 0
\(247\) 771728. 0.804863
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.58604e6 1.58902 0.794511 − 0.607250i \(-0.207727\pi\)
0.794511 + 0.607250i \(0.207727\pi\)
\(252\) 0 0
\(253\) −1.72378e6 −1.69309
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 654334. 0.617969 0.308984 − 0.951067i \(-0.400011\pi\)
0.308984 + 0.951067i \(0.400011\pi\)
\(258\) 0 0
\(259\) 1.96726e6 1.82227
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 330192. 0.294359 0.147179 − 0.989110i \(-0.452981\pi\)
0.147179 + 0.989110i \(0.452981\pi\)
\(264\) 0 0
\(265\) −310492. −0.271604
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.56956e6 −1.32250 −0.661252 − 0.750164i \(-0.729974\pi\)
−0.661252 + 0.750164i \(0.729974\pi\)
\(270\) 0 0
\(271\) 957792. 0.792224 0.396112 − 0.918202i \(-0.370359\pi\)
0.396112 + 0.918202i \(0.370359\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.56994e6 −1.25185
\(276\) 0 0
\(277\) 565438. 0.442778 0.221389 − 0.975186i \(-0.428941\pi\)
0.221389 + 0.975186i \(0.428941\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.34127e6 1.01333 0.506664 − 0.862143i \(-0.330878\pi\)
0.506664 + 0.862143i \(0.330878\pi\)
\(282\) 0 0
\(283\) −734264. −0.544987 −0.272494 − 0.962158i \(-0.587848\pi\)
−0.272494 + 0.962158i \(0.587848\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 35360.0 0.0253401
\(288\) 0 0
\(289\) 213427. 0.150316
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.13320e6 0.771149 0.385574 − 0.922677i \(-0.374003\pi\)
0.385574 + 0.922677i \(0.374003\pi\)
\(294\) 0 0
\(295\) 580720. 0.388519
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.23190e6 −1.44377
\(300\) 0 0
\(301\) 4.14502e6 2.63700
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −216468. −0.133243
\(306\) 0 0
\(307\) −2.91377e6 −1.76445 −0.882224 − 0.470829i \(-0.843955\pi\)
−0.882224 + 0.470829i \(0.843955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.43813e6 0.843134 0.421567 − 0.906797i \(-0.361480\pi\)
0.421567 + 0.906797i \(0.361480\pi\)
\(312\) 0 0
\(313\) −1.37601e6 −0.793888 −0.396944 − 0.917843i \(-0.629929\pi\)
−0.396944 + 0.917843i \(0.629929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.23494e6 0.690235 0.345118 − 0.938559i \(-0.387839\pi\)
0.345118 + 0.938559i \(0.387839\pi\)
\(318\) 0 0
\(319\) −1.56405e6 −0.860545
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.42114e6 0.757930
\(324\) 0 0
\(325\) −2.03273e6 −1.06751
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6656.00 0.00339019
\(330\) 0 0
\(331\) −1.48930e6 −0.747160 −0.373580 − 0.927598i \(-0.621870\pi\)
−0.373580 + 0.927598i \(0.621870\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 290416. 0.141387
\(336\) 0 0
\(337\) 838226. 0.402056 0.201028 − 0.979586i \(-0.435572\pi\)
0.201028 + 0.979586i \(0.435572\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.40646e6 −0.655002
\(342\) 0 0
\(343\) −2.00720e6 −0.921203
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 350008. 0.156047 0.0780233 − 0.996952i \(-0.475139\pi\)
0.0780233 + 0.996952i \(0.475139\pi\)
\(348\) 0 0
\(349\) −383642. −0.168602 −0.0843010 − 0.996440i \(-0.526866\pi\)
−0.0843010 + 0.996440i \(0.526866\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.09309e6 −1.74829 −0.874147 − 0.485661i \(-0.838579\pi\)
−0.874147 + 0.485661i \(0.838579\pi\)
\(354\) 0 0
\(355\) 400288. 0.168578
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.14430e6 −1.28762 −0.643811 − 0.765185i \(-0.722648\pi\)
−0.643811 + 0.765185i \(0.722648\pi\)
\(360\) 0 0
\(361\) −1.23955e6 −0.500608
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 751380. 0.295208
\(366\) 0 0
\(367\) −1.47619e6 −0.572108 −0.286054 − 0.958214i \(-0.592344\pi\)
−0.286054 + 0.958214i \(0.592344\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.61302e6 −1.74001
\(372\) 0 0
\(373\) −3.73981e6 −1.39180 −0.695901 − 0.718138i \(-0.744995\pi\)
−0.695901 + 0.718138i \(0.744995\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.02509e6 −0.733823
\(378\) 0 0
\(379\) 1.89966e6 0.679324 0.339662 − 0.940548i \(-0.389687\pi\)
0.339662 + 0.940548i \(0.389687\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.74310e6 −0.607192 −0.303596 − 0.952801i \(-0.598187\pi\)
−0.303596 + 0.952801i \(0.598187\pi\)
\(384\) 0 0
\(385\) 1.56083e6 0.536666
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.69147e6 0.901812 0.450906 − 0.892571i \(-0.351101\pi\)
0.450906 + 0.892571i \(0.351101\pi\)
\(390\) 0 0
\(391\) −4.11005e6 −1.35958
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 968128. 0.312205
\(396\) 0 0
\(397\) 5.37353e6 1.71113 0.855565 − 0.517695i \(-0.173210\pi\)
0.855565 + 0.517695i \(0.173210\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −156418. −0.0485765 −0.0242882 − 0.999705i \(-0.507732\pi\)
−0.0242882 + 0.999705i \(0.507732\pi\)
\(402\) 0 0
\(403\) −1.82106e6 −0.558548
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.06949e6 −1.51697
\(408\) 0 0
\(409\) −306086. −0.0904764 −0.0452382 − 0.998976i \(-0.514405\pi\)
−0.0452382 + 0.998976i \(0.514405\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.62784e6 2.48901
\(414\) 0 0
\(415\) −529200. −0.150834
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.70868e6 1.86682 0.933409 − 0.358814i \(-0.116819\pi\)
0.933409 + 0.358814i \(0.116819\pi\)
\(420\) 0 0
\(421\) 4.02347e6 1.10636 0.553179 − 0.833063i \(-0.313415\pi\)
0.553179 + 0.833063i \(0.313415\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.74326e6 −1.00526
\(426\) 0 0
\(427\) −3.21610e6 −0.853610
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.04304e6 1.82628 0.913139 − 0.407648i \(-0.133651\pi\)
0.913139 + 0.407648i \(0.133651\pi\)
\(432\) 0 0
\(433\) −1.25142e6 −0.320763 −0.160381 − 0.987055i \(-0.551272\pi\)
−0.160381 + 0.987055i \(0.551272\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.57619e6 −0.895813
\(438\) 0 0
\(439\) −1.25406e6 −0.310569 −0.155285 − 0.987870i \(-0.549629\pi\)
−0.155285 + 0.987870i \(0.549629\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.18081e6 −1.25426 −0.627131 − 0.778914i \(-0.715771\pi\)
−0.627131 + 0.778914i \(0.715771\pi\)
\(444\) 0 0
\(445\) −1.77528e6 −0.424979
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.73064e6 1.34149 0.670745 − 0.741688i \(-0.265975\pi\)
0.670745 + 0.741688i \(0.265975\pi\)
\(450\) 0 0
\(451\) −91120.0 −0.0210947
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.02093e6 0.457638
\(456\) 0 0
\(457\) −5.24153e6 −1.17400 −0.586999 − 0.809588i \(-0.699691\pi\)
−0.586999 + 0.809588i \(0.699691\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 173994. 0.0381313 0.0190657 − 0.999818i \(-0.493931\pi\)
0.0190657 + 0.999818i \(0.493931\pi\)
\(462\) 0 0
\(463\) 4.01277e6 0.869945 0.434972 − 0.900444i \(-0.356758\pi\)
0.434972 + 0.900444i \(0.356758\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −774616. −0.164359 −0.0821796 − 0.996618i \(-0.526188\pi\)
−0.0821796 + 0.996618i \(0.526188\pi\)
\(468\) 0 0
\(469\) 4.31475e6 0.905782
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.06814e7 −2.19521
\(474\) 0 0
\(475\) −3.25705e6 −0.662354
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.33530e6 −0.465054 −0.232527 − 0.972590i \(-0.574699\pi\)
−0.232527 + 0.972590i \(0.574699\pi\)
\(480\) 0 0
\(481\) −6.56385e6 −1.29359
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −872060. −0.168342
\(486\) 0 0
\(487\) 1.03947e6 0.198605 0.0993025 − 0.995057i \(-0.468339\pi\)
0.0993025 + 0.995057i \(0.468339\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.85092e6 −1.46966 −0.734830 − 0.678251i \(-0.762738\pi\)
−0.734830 + 0.678251i \(0.762738\pi\)
\(492\) 0 0
\(493\) −3.72920e6 −0.691033
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.94714e6 1.07998
\(498\) 0 0
\(499\) 2.71644e6 0.488370 0.244185 − 0.969729i \(-0.421480\pi\)
0.244185 + 0.969729i \(0.421480\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.62034e6 0.814242 0.407121 − 0.913374i \(-0.366533\pi\)
0.407121 + 0.913374i \(0.366533\pi\)
\(504\) 0 0
\(505\) 89796.0 0.0156685
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.46198e6 0.763366 0.381683 − 0.924293i \(-0.375345\pi\)
0.381683 + 0.924293i \(0.375345\pi\)
\(510\) 0 0
\(511\) 1.11634e7 1.89122
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.51805e6 0.252213
\(516\) 0 0
\(517\) −17152.0 −0.00282220
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.74375e6 −0.604245 −0.302122 − 0.953269i \(-0.597695\pi\)
−0.302122 + 0.953269i \(0.597695\pi\)
\(522\) 0 0
\(523\) 9.28433e6 1.48421 0.742107 − 0.670282i \(-0.233827\pi\)
0.742107 + 0.670282i \(0.233827\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.35347e6 −0.525979
\(528\) 0 0
\(529\) 3.90631e6 0.606915
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −117980. −0.0179883
\(534\) 0 0
\(535\) 1.45566e6 0.219875
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.41810e7 2.10249
\(540\) 0 0
\(541\) 862150. 0.126645 0.0633227 − 0.997993i \(-0.479830\pi\)
0.0633227 + 0.997993i \(0.479830\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −34804.0 −0.00501924
\(546\) 0 0
\(547\) 1.75442e6 0.250707 0.125353 − 0.992112i \(-0.459994\pi\)
0.125353 + 0.992112i \(0.459994\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.24482e6 −0.455314
\(552\) 0 0
\(553\) 1.43836e7 2.00012
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00292e7 1.36971 0.684856 − 0.728678i \(-0.259865\pi\)
0.684856 + 0.728678i \(0.259865\pi\)
\(558\) 0 0
\(559\) −1.38300e7 −1.87195
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.27460e6 0.701324 0.350662 − 0.936502i \(-0.385957\pi\)
0.350662 + 0.936502i \(0.385957\pi\)
\(564\) 0 0
\(565\) 221116. 0.0291406
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.36940e6 −1.08371 −0.541856 − 0.840471i \(-0.682278\pi\)
−0.541856 + 0.840471i \(0.682278\pi\)
\(570\) 0 0
\(571\) 4.02702e6 0.516884 0.258442 − 0.966027i \(-0.416791\pi\)
0.258442 + 0.966027i \(0.416791\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.41966e6 1.18814
\(576\) 0 0
\(577\) 2.37568e6 0.297063 0.148532 − 0.988908i \(-0.452545\pi\)
0.148532 + 0.988908i \(0.452545\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7.86240e6 −0.966306
\(582\) 0 0
\(583\) 1.18874e7 1.44849
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.44028e6 0.412096 0.206048 − 0.978542i \(-0.433940\pi\)
0.206048 + 0.978542i \(0.433940\pi\)
\(588\) 0 0
\(589\) −2.91789e6 −0.346562
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.22942e6 0.377127 0.188564 − 0.982061i \(-0.439617\pi\)
0.188564 + 0.982061i \(0.439617\pi\)
\(594\) 0 0
\(595\) 3.72154e6 0.430953
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.29714e6 1.05872 0.529361 − 0.848397i \(-0.322432\pi\)
0.529361 + 0.848397i \(0.322432\pi\)
\(600\) 0 0
\(601\) −1.12782e7 −1.27366 −0.636828 − 0.771006i \(-0.719754\pi\)
−0.636828 + 0.771006i \(0.719754\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.76743e6 −0.196315
\(606\) 0 0
\(607\) 7.00115e6 0.771255 0.385627 − 0.922655i \(-0.373985\pi\)
0.385627 + 0.922655i \(0.373985\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −22208.0 −0.00240661
\(612\) 0 0
\(613\) −6.19432e6 −0.665798 −0.332899 − 0.942962i \(-0.608027\pi\)
−0.332899 + 0.942962i \(0.608027\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.62407e6 0.277500 0.138750 − 0.990327i \(-0.455692\pi\)
0.138750 + 0.990327i \(0.455692\pi\)
\(618\) 0 0
\(619\) −2.83721e6 −0.297622 −0.148811 − 0.988866i \(-0.547545\pi\)
−0.148811 + 0.988866i \(0.547545\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.63756e7 −2.72259
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.20873e7 −1.21816
\(630\) 0 0
\(631\) 1.29656e7 1.29634 0.648170 − 0.761496i \(-0.275535\pi\)
0.648170 + 0.761496i \(0.275535\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14336.0 −0.00141089
\(636\) 0 0
\(637\) 1.83612e7 1.79288
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.16798e7 1.12276 0.561382 − 0.827557i \(-0.310270\pi\)
0.561382 + 0.827557i \(0.310270\pi\)
\(642\) 0 0
\(643\) 7.02732e6 0.670289 0.335145 − 0.942167i \(-0.391215\pi\)
0.335145 + 0.942167i \(0.391215\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.72821e6 0.913634 0.456817 − 0.889561i \(-0.348989\pi\)
0.456817 + 0.889561i \(0.348989\pi\)
\(648\) 0 0
\(649\) −2.22333e7 −2.07201
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.81425e6 0.900688 0.450344 − 0.892855i \(-0.351301\pi\)
0.450344 + 0.892855i \(0.351301\pi\)
\(654\) 0 0
\(655\) −317296. −0.0288976
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.46652e7 −1.31545 −0.657724 − 0.753259i \(-0.728481\pi\)
−0.657724 + 0.753259i \(0.728481\pi\)
\(660\) 0 0
\(661\) −1.41836e7 −1.26265 −0.631327 − 0.775517i \(-0.717489\pi\)
−0.631327 + 0.775517i \(0.717489\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.23814e6 0.283950
\(666\) 0 0
\(667\) 9.38429e6 0.816745
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.28763e6 0.710598
\(672\) 0 0
\(673\) 5.49941e6 0.468035 0.234018 − 0.972232i \(-0.424813\pi\)
0.234018 + 0.972232i \(0.424813\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.77375e7 −1.48737 −0.743687 − 0.668528i \(-0.766925\pi\)
−0.743687 + 0.668528i \(0.766925\pi\)
\(678\) 0 0
\(679\) −1.29563e7 −1.07847
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.39670e6 0.770768 0.385384 − 0.922756i \(-0.374069\pi\)
0.385384 + 0.922756i \(0.374069\pi\)
\(684\) 0 0
\(685\) −745332. −0.0606909
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.53915e7 1.23519
\(690\) 0 0
\(691\) −1.34767e7 −1.07371 −0.536857 − 0.843673i \(-0.680389\pi\)
−0.536857 + 0.843673i \(0.680389\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −277424. −0.0217862
\(696\) 0 0
\(697\) −217260. −0.0169394
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.15594e7 −1.65707 −0.828536 − 0.559935i \(-0.810826\pi\)
−0.828536 + 0.559935i \(0.810826\pi\)
\(702\) 0 0
\(703\) −1.05173e7 −0.802631
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.33411e6 0.100379
\(708\) 0 0
\(709\) −6.38165e6 −0.476779 −0.238390 − 0.971170i \(-0.576620\pi\)
−0.238390 + 0.971170i \(0.576620\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.43878e6 0.621664
\(714\) 0 0
\(715\) −5.20778e6 −0.380967
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.63566e7 1.17997 0.589986 − 0.807413i \(-0.299133\pi\)
0.589986 + 0.807413i \(0.299133\pi\)
\(720\) 0 0
\(721\) 2.25539e7 1.61578
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 8.54682e6 0.603893
\(726\) 0 0
\(727\) −2.13130e7 −1.49558 −0.747788 − 0.663937i \(-0.768884\pi\)
−0.747788 + 0.663937i \(0.768884\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.54680e7 −1.76279
\(732\) 0 0
\(733\) 1.21571e7 0.835737 0.417869 − 0.908507i \(-0.362777\pi\)
0.417869 + 0.908507i \(0.362777\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.11188e7 −0.754030
\(738\) 0 0
\(739\) −1.92337e7 −1.29555 −0.647773 − 0.761834i \(-0.724299\pi\)
−0.647773 + 0.761834i \(0.724299\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.66565e6 −0.110691 −0.0553454 − 0.998467i \(-0.517626\pi\)
−0.0553454 + 0.998467i \(0.517626\pi\)
\(744\) 0 0
\(745\) 6.33066e6 0.417886
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.16270e7 1.40861
\(750\) 0 0
\(751\) 9.81290e6 0.634888 0.317444 − 0.948277i \(-0.397175\pi\)
0.317444 + 0.948277i \(0.397175\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.68592e6 0.235331
\(756\) 0 0
\(757\) −1.92753e7 −1.22254 −0.611269 − 0.791423i \(-0.709341\pi\)
−0.611269 + 0.791423i \(0.709341\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.17863e7 0.737762 0.368881 − 0.929477i \(-0.379741\pi\)
0.368881 + 0.929477i \(0.379741\pi\)
\(762\) 0 0
\(763\) −517088. −0.0321553
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.87871e7 −1.76689
\(768\) 0 0
\(769\) 1.22941e7 0.749690 0.374845 − 0.927087i \(-0.377696\pi\)
0.374845 + 0.927087i \(0.377696\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.57086e6 −0.154750 −0.0773749 − 0.997002i \(-0.524654\pi\)
−0.0773749 + 0.997002i \(0.524654\pi\)
\(774\) 0 0
\(775\) 7.68570e6 0.459652
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −189040. −0.0111612
\(780\) 0 0
\(781\) −1.53253e7 −0.899046
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.94942e6 0.286669
\(786\) 0 0
\(787\) 5.54594e6 0.319182 0.159591 − 0.987183i \(-0.448982\pi\)
0.159591 + 0.987183i \(0.448982\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.28515e6 0.186687
\(792\) 0 0
\(793\) 1.07306e7 0.605958
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.09610e7 −1.16887 −0.584436 − 0.811440i \(-0.698684\pi\)
−0.584436 + 0.811440i \(0.698684\pi\)
\(798\) 0 0
\(799\) −40896.0 −0.00226628
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.87671e7 −1.57437
\(804\) 0 0
\(805\) −9.36499e6 −0.509352
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.70297e7 −1.45201 −0.726005 − 0.687690i \(-0.758625\pi\)
−0.726005 + 0.687690i \(0.758625\pi\)
\(810\) 0 0
\(811\) −2.13052e6 −0.113745 −0.0568727 − 0.998381i \(-0.518113\pi\)
−0.0568727 + 0.998381i \(0.518113\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.41310e6 0.0745212
\(816\) 0 0
\(817\) −2.21599e7 −1.16148
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.58060e7 −0.818396 −0.409198 − 0.912446i \(-0.634191\pi\)
−0.409198 + 0.912446i \(0.634191\pi\)
\(822\) 0 0
\(823\) −2.28848e7 −1.17773 −0.588867 − 0.808230i \(-0.700426\pi\)
−0.588867 + 0.808230i \(0.700426\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.55336e7 1.29822 0.649109 − 0.760695i \(-0.275142\pi\)
0.649109 + 0.760695i \(0.275142\pi\)
\(828\) 0 0
\(829\) 8.31786e6 0.420364 0.210182 − 0.977662i \(-0.432594\pi\)
0.210182 + 0.977662i \(0.432594\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.38120e7 1.68834
\(834\) 0 0
\(835\) −3.98922e6 −0.198003
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.66261e7 −1.79633 −0.898164 − 0.439660i \(-0.855099\pi\)
−0.898164 + 0.439660i \(0.855099\pi\)
\(840\) 0 0
\(841\) −1.19964e7 −0.584873
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.54480e6 −0.0744271
\(846\) 0 0
\(847\) −2.62590e7 −1.25768
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.04169e7 1.43976
\(852\) 0 0
\(853\) 1.74802e7 0.822571 0.411286 − 0.911507i \(-0.365080\pi\)
0.411286 + 0.911507i \(0.365080\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.31062e6 −0.433038 −0.216519 − 0.976278i \(-0.569470\pi\)
−0.216519 + 0.976278i \(0.569470\pi\)
\(858\) 0 0
\(859\) −3.49525e7 −1.61620 −0.808101 − 0.589045i \(-0.799504\pi\)
−0.808101 + 0.589045i \(0.799504\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.02349e7 0.924858 0.462429 − 0.886656i \(-0.346978\pi\)
0.462429 + 0.886656i \(0.346978\pi\)
\(864\) 0 0
\(865\) 6.78124e6 0.308155
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −3.70655e7 −1.66502
\(870\) 0 0
\(871\) −1.43963e7 −0.642994
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.76292e7 −0.778419
\(876\) 0 0
\(877\) −1.98342e7 −0.870797 −0.435398 − 0.900238i \(-0.643392\pi\)
−0.435398 + 0.900238i \(0.643392\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.81023e7 1.65391 0.826954 − 0.562270i \(-0.190072\pi\)
0.826954 + 0.562270i \(0.190072\pi\)
\(882\) 0 0
\(883\) −2.41560e7 −1.04261 −0.521307 − 0.853369i \(-0.674555\pi\)
−0.521307 + 0.853369i \(0.674555\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.02368e7 −0.863638 −0.431819 − 0.901960i \(-0.642128\pi\)
−0.431819 + 0.901960i \(0.642128\pi\)
\(888\) 0 0
\(889\) −212992. −0.00903876
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −35584.0 −0.00149323
\(894\) 0 0
\(895\) 5.69352e6 0.237587
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.65683e6 0.315973
\(900\) 0 0
\(901\) 2.83435e7 1.16316
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.98423e6 −0.324050
\(906\) 0 0
\(907\) 1.97976e7 0.799088 0.399544 − 0.916714i \(-0.369169\pi\)
0.399544 + 0.916714i \(0.369169\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.13242e7 0.851288 0.425644 − 0.904891i \(-0.360048\pi\)
0.425644 + 0.904891i \(0.360048\pi\)
\(912\) 0 0
\(913\) 2.02608e7 0.804414
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.71411e6 −0.185130
\(918\) 0 0
\(919\) 3.49941e7 1.36680 0.683401 − 0.730043i \(-0.260500\pi\)
0.683401 + 0.730043i \(0.260500\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.98428e7 −0.766655
\(924\) 0 0
\(925\) 2.77025e7 1.06455
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.88107e7 1.09525 0.547627 − 0.836722i \(-0.315531\pi\)
0.547627 + 0.836722i \(0.315531\pi\)
\(930\) 0 0
\(931\) 2.94202e7 1.11243
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.59011e6 −0.358752
\(936\) 0 0
\(937\) 1.28854e7 0.479457 0.239729 − 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.27615e7 1.94242 0.971210 − 0.238227i \(-0.0765662\pi\)
0.971210 + 0.238227i \(0.0765662\pi\)
\(942\) 0 0
\(943\) 546720. 0.0200210
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.53961e6 −0.200726 −0.100363 − 0.994951i \(-0.532000\pi\)
−0.100363 + 0.994951i \(0.532000\pi\)
\(948\) 0 0
\(949\) −3.72470e7 −1.34253
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 228102. 0.00813574 0.00406787 − 0.999992i \(-0.498705\pi\)
0.00406787 + 0.999992i \(0.498705\pi\)
\(954\) 0 0
\(955\) 1.94074e6 0.0688586
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.10735e7 −0.388811
\(960\) 0 0
\(961\) −2.17438e7 −0.759498
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −482748. −0.0166879
\(966\) 0 0
\(967\) 7.36709e6 0.253355 0.126678 − 0.991944i \(-0.459569\pi\)
0.126678 + 0.991944i \(0.459569\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.91161e7 0.650654 0.325327 − 0.945602i \(-0.394526\pi\)
0.325327 + 0.945602i \(0.394526\pi\)
\(972\) 0 0
\(973\) −4.12173e6 −0.139572
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.57040e7 −1.86702 −0.933512 − 0.358546i \(-0.883273\pi\)
−0.933512 + 0.358546i \(0.883273\pi\)
\(978\) 0 0
\(979\) 6.79680e7 2.26646
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.55469e7 0.513167 0.256584 − 0.966522i \(-0.417403\pi\)
0.256584 + 0.966522i \(0.417403\pi\)
\(984\) 0 0
\(985\) 9.01037e6 0.295905
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.40884e7 2.08348
\(990\) 0 0
\(991\) 2.36890e7 0.766237 0.383118 − 0.923699i \(-0.374850\pi\)
0.383118 + 0.923699i \(0.374850\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.55033e7 −0.496438
\(996\) 0 0
\(997\) 3.71720e6 0.118434 0.0592172 − 0.998245i \(-0.481140\pi\)
0.0592172 + 0.998245i \(0.481140\pi\)
\(998\) 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 288.6.a.d.1.1 1
3.2 odd 2 32.6.a.a.1.1 ✓ 1
4.3 odd 2 288.6.a.e.1.1 1
8.3 odd 2 576.6.a.v.1.1 1
8.5 even 2 576.6.a.u.1.1 1
12.11 even 2 32.6.a.c.1.1 yes 1
15.2 even 4 800.6.c.a.449.2 2
15.8 even 4 800.6.c.a.449.1 2
15.14 odd 2 800.6.a.e.1.1 1
24.5 odd 2 64.6.a.e.1.1 1
24.11 even 2 64.6.a.c.1.1 1
48.5 odd 4 256.6.b.h.129.2 2
48.11 even 4 256.6.b.b.129.1 2
48.29 odd 4 256.6.b.h.129.1 2
48.35 even 4 256.6.b.b.129.2 2
60.23 odd 4 800.6.c.b.449.2 2
60.47 odd 4 800.6.c.b.449.1 2
60.59 even 2 800.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.6.a.a.1.1 ✓ 1 3.2 odd 2
32.6.a.c.1.1 yes 1 12.11 even 2
64.6.a.c.1.1 1 24.11 even 2
64.6.a.e.1.1 1 24.5 odd 2
256.6.b.b.129.1 2 48.11 even 4
256.6.b.b.129.2 2 48.35 even 4
256.6.b.h.129.1 2 48.29 odd 4
256.6.b.h.129.2 2 48.5 odd 4
288.6.a.d.1.1 1 1.1 even 1 trivial
288.6.a.e.1.1 1 4.3 odd 2
576.6.a.u.1.1 1 8.5 even 2
576.6.a.v.1.1 1 8.3 odd 2
800.6.a.a.1.1 1 60.59 even 2
800.6.a.e.1.1 1 15.14 odd 2
800.6.c.a.449.1 2 15.8 even 4
800.6.c.a.449.2 2 15.2 even 4
800.6.c.b.449.1 2 60.47 odd 4
800.6.c.b.449.2 2 60.23 odd 4