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Properties

Label 432.6.a.b.1.1
Level $432$
Weight $6$
Character 432.1
Self dual yes
Analytic conductor $69.286$
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] = [432,6,Mod(1,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, 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("432.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.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: \(69.2858101592\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 432.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-33.0000 q^{5} -59.0000 q^{7} +O(q^{10})\) \(q-33.0000 q^{5} -59.0000 q^{7} +147.000 q^{11} +836.000 q^{13} +1080.00 q^{17} -2882.00 q^{19} -4386.00 q^{23} -2036.00 q^{25} -1866.00 q^{29} +3295.00 q^{31} +1947.00 q^{35} -3958.00 q^{37} +20586.0 q^{41} +8770.00 q^{43} +12666.0 q^{47} -13326.0 q^{49} +9621.00 q^{53} -4851.00 q^{55} -21468.0 q^{59} +36248.0 q^{61} -27588.0 q^{65} -5174.00 q^{67} +63720.0 q^{71} +57953.0 q^{73} -8673.00 q^{77} -16448.0 q^{79} +69267.0 q^{83} -35640.0 q^{85} +54198.0 q^{89} -49324.0 q^{91} +95106.0 q^{95} -132961. q^{97} +O(q^{100})\)

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
\(5\) −33.0000 −0.590322 −0.295161 − 0.955448i \(-0.595373\pi\)
−0.295161 + 0.955448i \(0.595373\pi\)
\(6\) 0 0
\(7\) −59.0000 −0.455100 −0.227550 − 0.973766i \(-0.573072\pi\)
−0.227550 + 0.973766i \(0.573072\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 147.000 0.366299 0.183149 − 0.983085i \(-0.441371\pi\)
0.183149 + 0.983085i \(0.441371\pi\)
\(12\) 0 0
\(13\) 836.000 1.37198 0.685990 − 0.727611i \(-0.259369\pi\)
0.685990 + 0.727611i \(0.259369\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1080.00 0.906362 0.453181 − 0.891419i \(-0.350289\pi\)
0.453181 + 0.891419i \(0.350289\pi\)
\(18\) 0 0
\(19\) −2882.00 −1.83151 −0.915756 − 0.401734i \(-0.868408\pi\)
−0.915756 + 0.401734i \(0.868408\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4386.00 −1.72882 −0.864409 − 0.502790i \(-0.832307\pi\)
−0.864409 + 0.502790i \(0.832307\pi\)
\(24\) 0 0
\(25\) −2036.00 −0.651520
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1866.00 −0.412018 −0.206009 − 0.978550i \(-0.566048\pi\)
−0.206009 + 0.978550i \(0.566048\pi\)
\(30\) 0 0
\(31\) 3295.00 0.615816 0.307908 − 0.951416i \(-0.400371\pi\)
0.307908 + 0.951416i \(0.400371\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1947.00 0.268656
\(36\) 0 0
\(37\) −3958.00 −0.475304 −0.237652 − 0.971350i \(-0.576378\pi\)
−0.237652 + 0.971350i \(0.576378\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 20586.0 1.91255 0.956274 − 0.292472i \(-0.0944780\pi\)
0.956274 + 0.292472i \(0.0944780\pi\)
\(42\) 0 0
\(43\) 8770.00 0.723317 0.361658 − 0.932311i \(-0.382211\pi\)
0.361658 + 0.932311i \(0.382211\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12666.0 0.836363 0.418182 − 0.908363i \(-0.362668\pi\)
0.418182 + 0.908363i \(0.362668\pi\)
\(48\) 0 0
\(49\) −13326.0 −0.792884
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9621.00 0.470468 0.235234 − 0.971939i \(-0.424414\pi\)
0.235234 + 0.971939i \(0.424414\pi\)
\(54\) 0 0
\(55\) −4851.00 −0.216234
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −21468.0 −0.802900 −0.401450 − 0.915881i \(-0.631494\pi\)
−0.401450 + 0.915881i \(0.631494\pi\)
\(60\) 0 0
\(61\) 36248.0 1.24727 0.623634 − 0.781717i \(-0.285656\pi\)
0.623634 + 0.781717i \(0.285656\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −27588.0 −0.809910
\(66\) 0 0
\(67\) −5174.00 −0.140812 −0.0704060 − 0.997518i \(-0.522429\pi\)
−0.0704060 + 0.997518i \(0.522429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 63720.0 1.50013 0.750067 − 0.661362i \(-0.230021\pi\)
0.750067 + 0.661362i \(0.230021\pi\)
\(72\) 0 0
\(73\) 57953.0 1.27283 0.636413 − 0.771349i \(-0.280418\pi\)
0.636413 + 0.771349i \(0.280418\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8673.00 −0.166703
\(78\) 0 0
\(79\) −16448.0 −0.296514 −0.148257 − 0.988949i \(-0.547366\pi\)
−0.148257 + 0.988949i \(0.547366\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 69267.0 1.10365 0.551825 − 0.833960i \(-0.313932\pi\)
0.551825 + 0.833960i \(0.313932\pi\)
\(84\) 0 0
\(85\) −35640.0 −0.535045
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 54198.0 0.725284 0.362642 − 0.931928i \(-0.381875\pi\)
0.362642 + 0.931928i \(0.381875\pi\)
\(90\) 0 0
\(91\) −49324.0 −0.624388
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 95106.0 1.08118
\(96\) 0 0
\(97\) −132961. −1.43481 −0.717406 − 0.696655i \(-0.754671\pi\)
−0.717406 + 0.696655i \(0.754671\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 171033. 1.66831 0.834154 − 0.551531i \(-0.185956\pi\)
0.834154 + 0.551531i \(0.185956\pi\)
\(102\) 0 0
\(103\) 120844. 1.12236 0.561180 − 0.827694i \(-0.310348\pi\)
0.561180 + 0.827694i \(0.310348\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 30879.0 0.260738 0.130369 − 0.991466i \(-0.458384\pi\)
0.130369 + 0.991466i \(0.458384\pi\)
\(108\) 0 0
\(109\) 39962.0 0.322167 0.161083 − 0.986941i \(-0.448501\pi\)
0.161083 + 0.986941i \(0.448501\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −70134.0 −0.516693 −0.258346 − 0.966052i \(-0.583178\pi\)
−0.258346 + 0.966052i \(0.583178\pi\)
\(114\) 0 0
\(115\) 144738. 1.02056
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −63720.0 −0.412485
\(120\) 0 0
\(121\) −139442. −0.865825
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 170313. 0.974929
\(126\) 0 0
\(127\) −181613. −0.999166 −0.499583 − 0.866266i \(-0.666513\pi\)
−0.499583 + 0.866266i \(0.666513\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 320055. 1.62947 0.814735 − 0.579833i \(-0.196882\pi\)
0.814735 + 0.579833i \(0.196882\pi\)
\(132\) 0 0
\(133\) 170038. 0.833522
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 312414. 1.42210 0.711048 − 0.703143i \(-0.248221\pi\)
0.711048 + 0.703143i \(0.248221\pi\)
\(138\) 0 0
\(139\) −205676. −0.902914 −0.451457 − 0.892293i \(-0.649096\pi\)
−0.451457 + 0.892293i \(0.649096\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 122892. 0.502555
\(144\) 0 0
\(145\) 61578.0 0.243224
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 346647. 1.27915 0.639575 − 0.768728i \(-0.279110\pi\)
0.639575 + 0.768728i \(0.279110\pi\)
\(150\) 0 0
\(151\) −185117. −0.660699 −0.330350 − 0.943859i \(-0.607167\pi\)
−0.330350 + 0.943859i \(0.607167\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −108735. −0.363530
\(156\) 0 0
\(157\) 65996.0 0.213682 0.106841 − 0.994276i \(-0.465926\pi\)
0.106841 + 0.994276i \(0.465926\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 258774. 0.786785
\(162\) 0 0
\(163\) 271060. 0.799091 0.399546 − 0.916713i \(-0.369168\pi\)
0.399546 + 0.916713i \(0.369168\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −104826. −0.290856 −0.145428 − 0.989369i \(-0.546456\pi\)
−0.145428 + 0.989369i \(0.546456\pi\)
\(168\) 0 0
\(169\) 327603. 0.882330
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −210405. −0.534491 −0.267246 − 0.963628i \(-0.586114\pi\)
−0.267246 + 0.963628i \(0.586114\pi\)
\(174\) 0 0
\(175\) 120124. 0.296507
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 74961.0 0.174865 0.0874325 − 0.996170i \(-0.472134\pi\)
0.0874325 + 0.996170i \(0.472134\pi\)
\(180\) 0 0
\(181\) 30944.0 0.0702069 0.0351035 − 0.999384i \(-0.488824\pi\)
0.0351035 + 0.999384i \(0.488824\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 130614. 0.280582
\(186\) 0 0
\(187\) 158760. 0.331999
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 936948. 1.85837 0.929185 − 0.369616i \(-0.120511\pi\)
0.929185 + 0.369616i \(0.120511\pi\)
\(192\) 0 0
\(193\) −335395. −0.648132 −0.324066 − 0.946035i \(-0.605050\pi\)
−0.324066 + 0.946035i \(0.605050\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −445059. −0.817056 −0.408528 − 0.912746i \(-0.633958\pi\)
−0.408528 + 0.912746i \(0.633958\pi\)
\(198\) 0 0
\(199\) 616867. 1.10423 0.552114 − 0.833769i \(-0.313821\pi\)
0.552114 + 0.833769i \(0.313821\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 110094. 0.187510
\(204\) 0 0
\(205\) −679338. −1.12902
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −423654. −0.670881
\(210\) 0 0
\(211\) −655658. −1.01384 −0.506922 − 0.861992i \(-0.669217\pi\)
−0.506922 + 0.861992i \(0.669217\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −289410. −0.426990
\(216\) 0 0
\(217\) −194405. −0.280258
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 902880. 1.24351
\(222\) 0 0
\(223\) 906592. 1.22081 0.610407 − 0.792088i \(-0.291006\pi\)
0.610407 + 0.792088i \(0.291006\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 449868. 0.579456 0.289728 − 0.957109i \(-0.406435\pi\)
0.289728 + 0.957109i \(0.406435\pi\)
\(228\) 0 0
\(229\) −218386. −0.275192 −0.137596 − 0.990488i \(-0.543938\pi\)
−0.137596 + 0.990488i \(0.543938\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.05860e6 −1.27744 −0.638721 − 0.769438i \(-0.720536\pi\)
−0.638721 + 0.769438i \(0.720536\pi\)
\(234\) 0 0
\(235\) −417978. −0.493723
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −699510. −0.792135 −0.396067 − 0.918221i \(-0.629625\pi\)
−0.396067 + 0.918221i \(0.629625\pi\)
\(240\) 0 0
\(241\) 1.56839e6 1.73945 0.869724 − 0.493538i \(-0.164297\pi\)
0.869724 + 0.493538i \(0.164297\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 439758. 0.468057
\(246\) 0 0
\(247\) −2.40935e6 −2.51280
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 568080. 0.569148 0.284574 − 0.958654i \(-0.408148\pi\)
0.284574 + 0.958654i \(0.408148\pi\)
\(252\) 0 0
\(253\) −644742. −0.633264
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −843612. −0.796728 −0.398364 − 0.917227i \(-0.630422\pi\)
−0.398364 + 0.917227i \(0.630422\pi\)
\(258\) 0 0
\(259\) 233522. 0.216311
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −751290. −0.669759 −0.334879 − 0.942261i \(-0.608696\pi\)
−0.334879 + 0.942261i \(0.608696\pi\)
\(264\) 0 0
\(265\) −317493. −0.277728
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.48088e6 1.24778 0.623891 − 0.781512i \(-0.285551\pi\)
0.623891 + 0.781512i \(0.285551\pi\)
\(270\) 0 0
\(271\) −12395.0 −0.0102523 −0.00512617 − 0.999987i \(-0.501632\pi\)
−0.00512617 + 0.999987i \(0.501632\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −299292. −0.238651
\(276\) 0 0
\(277\) 1.87225e6 1.46610 0.733051 − 0.680174i \(-0.238096\pi\)
0.733051 + 0.680174i \(0.238096\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.89422e6 −1.43109 −0.715543 − 0.698569i \(-0.753821\pi\)
−0.715543 + 0.698569i \(0.753821\pi\)
\(282\) 0 0
\(283\) 676306. 0.501969 0.250985 − 0.967991i \(-0.419246\pi\)
0.250985 + 0.967991i \(0.419246\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.21457e6 −0.870401
\(288\) 0 0
\(289\) −253457. −0.178509
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.98821e6 −1.35299 −0.676494 − 0.736448i \(-0.736502\pi\)
−0.676494 + 0.736448i \(0.736502\pi\)
\(294\) 0 0
\(295\) 708444. 0.473970
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.66670e6 −2.37190
\(300\) 0 0
\(301\) −517430. −0.329181
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.19618e6 −0.736289
\(306\) 0 0
\(307\) 1.57214e6 0.952016 0.476008 − 0.879441i \(-0.342083\pi\)
0.476008 + 0.879441i \(0.342083\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −185826. −0.108945 −0.0544723 − 0.998515i \(-0.517348\pi\)
−0.0544723 + 0.998515i \(0.517348\pi\)
\(312\) 0 0
\(313\) −1.06718e6 −0.615710 −0.307855 − 0.951433i \(-0.599611\pi\)
−0.307855 + 0.951433i \(0.599611\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.39367e6 1.33788 0.668939 − 0.743317i \(-0.266749\pi\)
0.668939 + 0.743317i \(0.266749\pi\)
\(318\) 0 0
\(319\) −274302. −0.150922
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.11256e6 −1.66001
\(324\) 0 0
\(325\) −1.70210e6 −0.893873
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −747294. −0.380629
\(330\) 0 0
\(331\) 396850. 0.199093 0.0995466 − 0.995033i \(-0.468261\pi\)
0.0995466 + 0.995033i \(0.468261\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 170742. 0.0831244
\(336\) 0 0
\(337\) −1.28762e6 −0.617609 −0.308805 − 0.951126i \(-0.599929\pi\)
−0.308805 + 0.951126i \(0.599929\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 484365. 0.225573
\(342\) 0 0
\(343\) 1.77785e6 0.815942
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.33329e6 0.594432 0.297216 − 0.954810i \(-0.403942\pi\)
0.297216 + 0.954810i \(0.403942\pi\)
\(348\) 0 0
\(349\) 1.69259e6 0.743855 0.371927 − 0.928262i \(-0.378697\pi\)
0.371927 + 0.928262i \(0.378697\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −798906. −0.341239 −0.170620 − 0.985337i \(-0.554577\pi\)
−0.170620 + 0.985337i \(0.554577\pi\)
\(354\) 0 0
\(355\) −2.10276e6 −0.885562
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.72080e6 1.52370 0.761851 − 0.647752i \(-0.224291\pi\)
0.761851 + 0.647752i \(0.224291\pi\)
\(360\) 0 0
\(361\) 5.82982e6 2.35444
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.91245e6 −0.751377
\(366\) 0 0
\(367\) 2.34640e6 0.909363 0.454682 − 0.890654i \(-0.349753\pi\)
0.454682 + 0.890654i \(0.349753\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −567639. −0.214110
\(372\) 0 0
\(373\) −4.47321e6 −1.66474 −0.832371 − 0.554219i \(-0.813017\pi\)
−0.832371 + 0.554219i \(0.813017\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.55998e6 −0.565281
\(378\) 0 0
\(379\) −3.40850e6 −1.21889 −0.609446 − 0.792828i \(-0.708608\pi\)
−0.609446 + 0.792828i \(0.708608\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.94982e6 −1.37588 −0.687940 − 0.725767i \(-0.741485\pi\)
−0.687940 + 0.725767i \(0.741485\pi\)
\(384\) 0 0
\(385\) 286209. 0.0984082
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.50501e6 −0.839335 −0.419667 − 0.907678i \(-0.637853\pi\)
−0.419667 + 0.907678i \(0.637853\pi\)
\(390\) 0 0
\(391\) −4.73688e6 −1.56693
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 542784. 0.175039
\(396\) 0 0
\(397\) 4.42550e6 1.40924 0.704622 − 0.709583i \(-0.251117\pi\)
0.704622 + 0.709583i \(0.251117\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.63557e6 −1.75016 −0.875079 − 0.483981i \(-0.839190\pi\)
−0.875079 + 0.483981i \(0.839190\pi\)
\(402\) 0 0
\(403\) 2.75462e6 0.844888
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −581826. −0.174103
\(408\) 0 0
\(409\) −4.52038e6 −1.33618 −0.668092 − 0.744079i \(-0.732889\pi\)
−0.668092 + 0.744079i \(0.732889\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.26661e6 0.365400
\(414\) 0 0
\(415\) −2.28581e6 −0.651508
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −488028. −0.135803 −0.0679015 − 0.997692i \(-0.521630\pi\)
−0.0679015 + 0.997692i \(0.521630\pi\)
\(420\) 0 0
\(421\) 3.54769e6 0.975529 0.487764 − 0.872975i \(-0.337812\pi\)
0.487764 + 0.872975i \(0.337812\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.19888e6 −0.590513
\(426\) 0 0
\(427\) −2.13863e6 −0.567631
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.90608e6 −0.753555 −0.376777 − 0.926304i \(-0.622968\pi\)
−0.376777 + 0.926304i \(0.622968\pi\)
\(432\) 0 0
\(433\) −4.07157e6 −1.04362 −0.521810 − 0.853062i \(-0.674743\pi\)
−0.521810 + 0.853062i \(0.674743\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.26405e7 3.16635
\(438\) 0 0
\(439\) 121999. 0.0302131 0.0151065 − 0.999886i \(-0.495191\pi\)
0.0151065 + 0.999886i \(0.495191\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.59731e6 1.83929 0.919645 − 0.392750i \(-0.128476\pi\)
0.919645 + 0.392750i \(0.128476\pi\)
\(444\) 0 0
\(445\) −1.78853e6 −0.428151
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.09200e6 −1.19199 −0.595995 − 0.802988i \(-0.703242\pi\)
−0.595995 + 0.802988i \(0.703242\pi\)
\(450\) 0 0
\(451\) 3.02614e6 0.700564
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.62769e6 0.368590
\(456\) 0 0
\(457\) 1.36968e6 0.306781 0.153390 − 0.988166i \(-0.450981\pi\)
0.153390 + 0.988166i \(0.450981\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 659391. 0.144508 0.0722538 − 0.997386i \(-0.476981\pi\)
0.0722538 + 0.997386i \(0.476981\pi\)
\(462\) 0 0
\(463\) 7.32679e6 1.58841 0.794203 − 0.607653i \(-0.207889\pi\)
0.794203 + 0.607653i \(0.207889\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.45508e6 0.520924 0.260462 − 0.965484i \(-0.416125\pi\)
0.260462 + 0.965484i \(0.416125\pi\)
\(468\) 0 0
\(469\) 305266. 0.0640835
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.28919e6 0.264950
\(474\) 0 0
\(475\) 5.86775e6 1.19327
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.24387e6 0.247705 0.123853 − 0.992301i \(-0.460475\pi\)
0.123853 + 0.992301i \(0.460475\pi\)
\(480\) 0 0
\(481\) −3.30889e6 −0.652108
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.38771e6 0.847001
\(486\) 0 0
\(487\) −1.15882e6 −0.221409 −0.110704 − 0.993853i \(-0.535311\pi\)
−0.110704 + 0.993853i \(0.535311\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.98739e6 −0.559227 −0.279614 − 0.960113i \(-0.590206\pi\)
−0.279614 + 0.960113i \(0.590206\pi\)
\(492\) 0 0
\(493\) −2.01528e6 −0.373438
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.75948e6 −0.682711
\(498\) 0 0
\(499\) −3.98173e6 −0.715848 −0.357924 − 0.933751i \(-0.616515\pi\)
−0.357924 + 0.933751i \(0.616515\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.90964e6 −0.336536 −0.168268 − 0.985741i \(-0.553817\pi\)
−0.168268 + 0.985741i \(0.553817\pi\)
\(504\) 0 0
\(505\) −5.64409e6 −0.984839
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.29440e6 1.07686 0.538431 − 0.842669i \(-0.319017\pi\)
0.538431 + 0.842669i \(0.319017\pi\)
\(510\) 0 0
\(511\) −3.41923e6 −0.579263
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.98785e6 −0.662554
\(516\) 0 0
\(517\) 1.86190e6 0.306359
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.34932e6 −0.217781 −0.108890 − 0.994054i \(-0.534730\pi\)
−0.108890 + 0.994054i \(0.534730\pi\)
\(522\) 0 0
\(523\) −5.18866e6 −0.829471 −0.414736 − 0.909942i \(-0.636126\pi\)
−0.414736 + 0.909942i \(0.636126\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.55860e6 0.558152
\(528\) 0 0
\(529\) 1.28007e7 1.98881
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.72099e7 2.62398
\(534\) 0 0
\(535\) −1.01901e6 −0.153919
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.95892e6 −0.290433
\(540\) 0 0
\(541\) 9.40250e6 1.38118 0.690590 − 0.723247i \(-0.257351\pi\)
0.690590 + 0.723247i \(0.257351\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.31875e6 −0.190182
\(546\) 0 0
\(547\) 6.46643e6 0.924052 0.462026 − 0.886866i \(-0.347123\pi\)
0.462026 + 0.886866i \(0.347123\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.37781e6 0.754617
\(552\) 0 0
\(553\) 970432. 0.134944
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.12306e7 1.53379 0.766895 − 0.641773i \(-0.221801\pi\)
0.766895 + 0.641773i \(0.221801\pi\)
\(558\) 0 0
\(559\) 7.33172e6 0.992376
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.15199e7 1.53171 0.765854 − 0.643015i \(-0.222317\pi\)
0.765854 + 0.643015i \(0.222317\pi\)
\(564\) 0 0
\(565\) 2.31442e6 0.305015
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.00381e6 0.129979 0.0649893 − 0.997886i \(-0.479299\pi\)
0.0649893 + 0.997886i \(0.479299\pi\)
\(570\) 0 0
\(571\) −1.35620e7 −1.74074 −0.870371 − 0.492396i \(-0.836121\pi\)
−0.870371 + 0.492396i \(0.836121\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.92990e6 1.12636
\(576\) 0 0
\(577\) 1.66252e6 0.207887 0.103943 − 0.994583i \(-0.466854\pi\)
0.103943 + 0.994583i \(0.466854\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.08675e6 −0.502271
\(582\) 0 0
\(583\) 1.41429e6 0.172332
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.83917e6 −0.340092 −0.170046 − 0.985436i \(-0.554392\pi\)
−0.170046 + 0.985436i \(0.554392\pi\)
\(588\) 0 0
\(589\) −9.49619e6 −1.12788
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.56588e6 0.299640 0.149820 − 0.988713i \(-0.452131\pi\)
0.149820 + 0.988713i \(0.452131\pi\)
\(594\) 0 0
\(595\) 2.10276e6 0.243499
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.72454e6 0.538012 0.269006 − 0.963138i \(-0.413305\pi\)
0.269006 + 0.963138i \(0.413305\pi\)
\(600\) 0 0
\(601\) −6.60032e6 −0.745382 −0.372691 − 0.927955i \(-0.621565\pi\)
−0.372691 + 0.927955i \(0.621565\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.60159e6 0.511116
\(606\) 0 0
\(607\) −1.48098e7 −1.63147 −0.815734 − 0.578428i \(-0.803667\pi\)
−0.815734 + 0.578428i \(0.803667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.05888e7 1.14747
\(612\) 0 0
\(613\) −6.44259e6 −0.692484 −0.346242 − 0.938145i \(-0.612542\pi\)
−0.346242 + 0.938145i \(0.612542\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.02261e7 −1.08142 −0.540711 − 0.841208i \(-0.681845\pi\)
−0.540711 + 0.841208i \(0.681845\pi\)
\(618\) 0 0
\(619\) 5.70327e6 0.598270 0.299135 − 0.954211i \(-0.403302\pi\)
0.299135 + 0.954211i \(0.403302\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.19768e6 −0.330077
\(624\) 0 0
\(625\) 742171. 0.0759983
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.27464e6 −0.430797
\(630\) 0 0
\(631\) 5.09132e6 0.509046 0.254523 − 0.967067i \(-0.418081\pi\)
0.254523 + 0.967067i \(0.418081\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.99323e6 0.589830
\(636\) 0 0
\(637\) −1.11405e7 −1.08782
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.81898e6 −0.367115 −0.183558 − 0.983009i \(-0.558761\pi\)
−0.183558 + 0.983009i \(0.558761\pi\)
\(642\) 0 0
\(643\) 1.36716e7 1.30404 0.652022 − 0.758200i \(-0.273921\pi\)
0.652022 + 0.758200i \(0.273921\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.93384e6 −0.932946 −0.466473 − 0.884535i \(-0.654476\pi\)
−0.466473 + 0.884535i \(0.654476\pi\)
\(648\) 0 0
\(649\) −3.15580e6 −0.294101
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.31301e6 0.304046 0.152023 − 0.988377i \(-0.451421\pi\)
0.152023 + 0.988377i \(0.451421\pi\)
\(654\) 0 0
\(655\) −1.05618e7 −0.961912
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.77763e6 0.159451 0.0797256 − 0.996817i \(-0.474596\pi\)
0.0797256 + 0.996817i \(0.474596\pi\)
\(660\) 0 0
\(661\) −55306.0 −0.00492344 −0.00246172 − 0.999997i \(-0.500784\pi\)
−0.00246172 + 0.999997i \(0.500784\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.61125e6 −0.492046
\(666\) 0 0
\(667\) 8.18428e6 0.712304
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.32846e6 0.456873
\(672\) 0 0
\(673\) 4.65070e6 0.395805 0.197902 − 0.980222i \(-0.436587\pi\)
0.197902 + 0.980222i \(0.436587\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.49270e6 0.376735 0.188367 − 0.982099i \(-0.439680\pi\)
0.188367 + 0.982099i \(0.439680\pi\)
\(678\) 0 0
\(679\) 7.84470e6 0.652983
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.68760e6 −0.384502 −0.192251 − 0.981346i \(-0.561579\pi\)
−0.192251 + 0.981346i \(0.561579\pi\)
\(684\) 0 0
\(685\) −1.03097e7 −0.839495
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.04316e6 0.645474
\(690\) 0 0
\(691\) −8.09452e6 −0.644906 −0.322453 − 0.946586i \(-0.604507\pi\)
−0.322453 + 0.946586i \(0.604507\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.78731e6 0.533010
\(696\) 0 0
\(697\) 2.22329e7 1.73346
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.62894e6 0.509506 0.254753 − 0.967006i \(-0.418006\pi\)
0.254753 + 0.967006i \(0.418006\pi\)
\(702\) 0 0
\(703\) 1.14070e7 0.870525
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.00909e7 −0.759248
\(708\) 0 0
\(709\) 1.23483e7 0.922552 0.461276 − 0.887257i \(-0.347392\pi\)
0.461276 + 0.887257i \(0.347392\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.44519e7 −1.06463
\(714\) 0 0
\(715\) −4.05544e6 −0.296669
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.91464e6 0.570964 0.285482 − 0.958384i \(-0.407846\pi\)
0.285482 + 0.958384i \(0.407846\pi\)
\(720\) 0 0
\(721\) −7.12980e6 −0.510786
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.79918e6 0.268438
\(726\) 0 0
\(727\) −1.19607e7 −0.839306 −0.419653 − 0.907685i \(-0.637848\pi\)
−0.419653 + 0.907685i \(0.637848\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.47160e6 0.655586
\(732\) 0 0
\(733\) 1.84911e7 1.27117 0.635585 − 0.772031i \(-0.280759\pi\)
0.635585 + 0.772031i \(0.280759\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −760578. −0.0515793
\(738\) 0 0
\(739\) −2.86031e7 −1.92664 −0.963322 − 0.268348i \(-0.913522\pi\)
−0.963322 + 0.268348i \(0.913522\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.08559e6 −0.337963 −0.168981 − 0.985619i \(-0.554048\pi\)
−0.168981 + 0.985619i \(0.554048\pi\)
\(744\) 0 0
\(745\) −1.14394e7 −0.755111
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.82186e6 −0.118662
\(750\) 0 0
\(751\) 1.40296e7 0.907705 0.453853 − 0.891077i \(-0.350049\pi\)
0.453853 + 0.891077i \(0.350049\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.10886e6 0.390025
\(756\) 0 0
\(757\) −1.23984e6 −0.0786367 −0.0393183 − 0.999227i \(-0.512519\pi\)
−0.0393183 + 0.999227i \(0.512519\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.50752e7 −0.943627 −0.471814 − 0.881698i \(-0.656401\pi\)
−0.471814 + 0.881698i \(0.656401\pi\)
\(762\) 0 0
\(763\) −2.35776e6 −0.146618
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.79472e7 −1.10156
\(768\) 0 0
\(769\) −1.99071e6 −0.121393 −0.0606963 − 0.998156i \(-0.519332\pi\)
−0.0606963 + 0.998156i \(0.519332\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.24623e7 0.750153 0.375077 − 0.926994i \(-0.377616\pi\)
0.375077 + 0.926994i \(0.377616\pi\)
\(774\) 0 0
\(775\) −6.70862e6 −0.401217
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.93289e7 −3.50286
\(780\) 0 0
\(781\) 9.36684e6 0.549497
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.17787e6 −0.126141
\(786\) 0 0
\(787\) 6.30237e6 0.362716 0.181358 − 0.983417i \(-0.441951\pi\)
0.181358 + 0.983417i \(0.441951\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.13791e6 0.235147
\(792\) 0 0
\(793\) 3.03033e7 1.71123
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.95260e7 1.08885 0.544423 − 0.838811i \(-0.316748\pi\)
0.544423 + 0.838811i \(0.316748\pi\)
\(798\) 0 0
\(799\) 1.36793e7 0.758047
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.51909e6 0.466234
\(804\) 0 0
\(805\) −8.53954e6 −0.464456
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.56364e7 −0.839975 −0.419988 − 0.907530i \(-0.637966\pi\)
−0.419988 + 0.907530i \(0.637966\pi\)
\(810\) 0 0
\(811\) 1.53900e7 0.821649 0.410825 − 0.911714i \(-0.365241\pi\)
0.410825 + 0.911714i \(0.365241\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.94498e6 −0.471721
\(816\) 0 0
\(817\) −2.52751e7 −1.32476
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.65043e6 −0.396121 −0.198060 − 0.980190i \(-0.563464\pi\)
−0.198060 + 0.980190i \(0.563464\pi\)
\(822\) 0 0
\(823\) −7.11099e6 −0.365957 −0.182979 − 0.983117i \(-0.558574\pi\)
−0.182979 + 0.983117i \(0.558574\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.50690e7 −1.27460 −0.637298 − 0.770617i \(-0.719948\pi\)
−0.637298 + 0.770617i \(0.719948\pi\)
\(828\) 0 0
\(829\) −9.64584e6 −0.487476 −0.243738 − 0.969841i \(-0.578374\pi\)
−0.243738 + 0.969841i \(0.578374\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.43921e7 −0.718639
\(834\) 0 0
\(835\) 3.45926e6 0.171699
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.41135e7 −0.692199 −0.346099 − 0.938198i \(-0.612494\pi\)
−0.346099 + 0.938198i \(0.612494\pi\)
\(840\) 0 0
\(841\) −1.70292e7 −0.830241
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.08109e7 −0.520859
\(846\) 0 0
\(847\) 8.22708e6 0.394037
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.73598e7 0.821714
\(852\) 0 0
\(853\) −3.62546e7 −1.70605 −0.853024 − 0.521872i \(-0.825234\pi\)
−0.853024 + 0.521872i \(0.825234\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.65814e7 −0.771205 −0.385603 − 0.922665i \(-0.626006\pi\)
−0.385603 + 0.922665i \(0.626006\pi\)
\(858\) 0 0
\(859\) 2.77808e7 1.28458 0.642290 − 0.766462i \(-0.277984\pi\)
0.642290 + 0.766462i \(0.277984\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.94274e7 −0.887950 −0.443975 − 0.896039i \(-0.646432\pi\)
−0.443975 + 0.896039i \(0.646432\pi\)
\(864\) 0 0
\(865\) 6.94336e6 0.315522
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.41786e6 −0.108613
\(870\) 0 0
\(871\) −4.32546e6 −0.193191
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.00485e7 −0.443690
\(876\) 0 0
\(877\) 4.12534e6 0.181118 0.0905588 − 0.995891i \(-0.471135\pi\)
0.0905588 + 0.995891i \(0.471135\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.32293e7 −1.00832 −0.504158 − 0.863611i \(-0.668197\pi\)
−0.504158 + 0.863611i \(0.668197\pi\)
\(882\) 0 0
\(883\) −3.86906e7 −1.66995 −0.834976 − 0.550286i \(-0.814519\pi\)
−0.834976 + 0.550286i \(0.814519\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.52681e7 0.651592 0.325796 − 0.945440i \(-0.394368\pi\)
0.325796 + 0.945440i \(0.394368\pi\)
\(888\) 0 0
\(889\) 1.07152e7 0.454721
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.65034e7 −1.53181
\(894\) 0 0
\(895\) −2.47371e6 −0.103227
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6.14847e6 −0.253728
\(900\) 0 0
\(901\) 1.03907e7 0.426415
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.02115e6 −0.0414447
\(906\) 0 0
\(907\) 3.19149e6 0.128818 0.0644089 − 0.997924i \(-0.479484\pi\)
0.0644089 + 0.997924i \(0.479484\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.33880e7 −0.534465 −0.267232 − 0.963632i \(-0.586109\pi\)
−0.267232 + 0.963632i \(0.586109\pi\)
\(912\) 0 0
\(913\) 1.01822e7 0.404266
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.88832e7 −0.741572
\(918\) 0 0
\(919\) −5.44593e6 −0.212708 −0.106354 − 0.994328i \(-0.533918\pi\)
−0.106354 + 0.994328i \(0.533918\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5.32699e7 2.05815
\(924\) 0 0
\(925\) 8.05849e6 0.309670
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.44241e7 1.68881 0.844403 − 0.535709i \(-0.179956\pi\)
0.844403 + 0.535709i \(0.179956\pi\)
\(930\) 0 0
\(931\) 3.84055e7 1.45218
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.23908e6 −0.195986
\(936\) 0 0
\(937\) −2.42388e7 −0.901907 −0.450954 − 0.892547i \(-0.648916\pi\)
−0.450954 + 0.892547i \(0.648916\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.67337e7 −1.35235 −0.676177 − 0.736739i \(-0.736365\pi\)
−0.676177 + 0.736739i \(0.736365\pi\)
\(942\) 0 0
\(943\) −9.02902e7 −3.30645
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −215259. −0.00779985 −0.00389993 − 0.999992i \(-0.501241\pi\)
−0.00389993 + 0.999992i \(0.501241\pi\)
\(948\) 0 0
\(949\) 4.84487e7 1.74629
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.04947e7 1.80100 0.900500 − 0.434856i \(-0.143201\pi\)
0.900500 + 0.434856i \(0.143201\pi\)
\(954\) 0 0
\(955\) −3.09193e7 −1.09704
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.84324e7 −0.647196
\(960\) 0 0
\(961\) −1.77721e7 −0.620770
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.10680e7 0.382606
\(966\) 0 0
\(967\) 5.08587e7 1.74904 0.874518 − 0.484993i \(-0.161178\pi\)
0.874518 + 0.484993i \(0.161178\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.81634e7 0.958599 0.479300 − 0.877651i \(-0.340891\pi\)
0.479300 + 0.877651i \(0.340891\pi\)
\(972\) 0 0
\(973\) 1.21349e7 0.410916
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.89210e6 −0.231002 −0.115501 − 0.993307i \(-0.536847\pi\)
−0.115501 + 0.993307i \(0.536847\pi\)
\(978\) 0 0
\(979\) 7.96711e6 0.265671
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.47833e7 −0.487965 −0.243982 − 0.969780i \(-0.578454\pi\)
−0.243982 + 0.969780i \(0.578454\pi\)
\(984\) 0 0
\(985\) 1.46869e7 0.482326
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.84652e7 −1.25048
\(990\) 0 0
\(991\) 1.62721e7 0.526333 0.263166 − 0.964750i \(-0.415233\pi\)
0.263166 + 0.964750i \(0.415233\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.03566e7 −0.651850
\(996\) 0 0
\(997\) −1.05805e7 −0.337109 −0.168554 − 0.985692i \(-0.553910\pi\)
−0.168554 + 0.985692i \(0.553910\pi\)
\(998\) 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 432.6.a.b.1.1 1
3.2 odd 2 432.6.a.i.1.1 1
4.3 odd 2 54.6.a.a.1.1 ✓ 1
12.11 even 2 54.6.a.f.1.1 yes 1
36.7 odd 6 162.6.c.k.109.1 2
36.11 even 6 162.6.c.b.109.1 2
36.23 even 6 162.6.c.b.55.1 2
36.31 odd 6 162.6.c.k.55.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.6.a.a.1.1 ✓ 1 4.3 odd 2
54.6.a.f.1.1 yes 1 12.11 even 2
162.6.c.b.55.1 2 36.23 even 6
162.6.c.b.109.1 2 36.11 even 6
162.6.c.k.55.1 2 36.31 odd 6
162.6.c.k.109.1 2 36.7 odd 6
432.6.a.b.1.1 1 1.1 even 1 trivial
432.6.a.i.1.1 1 3.2 odd 2