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Properties

Label 1008.6.a.s.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+34.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+34.0000 q^{5} -49.0000 q^{7} -756.000 q^{11} +678.000 q^{13} +1838.00 q^{17} -604.000 q^{19} +2840.00 q^{23} -1969.00 q^{25} -6878.00 q^{29} -3568.00 q^{31} -1666.00 q^{35} +14598.0 q^{37} -5962.00 q^{41} +676.000 q^{43} -20800.0 q^{47} +2401.00 q^{49} -32390.0 q^{53} -25704.0 q^{55} +42948.0 q^{59} +44806.0 q^{61} +23052.0 q^{65} +39708.0 q^{67} -25800.0 q^{71} +58954.0 q^{73} +37044.0 q^{77} +77648.0 q^{79} +35964.0 q^{83} +62492.0 q^{85} -80842.0 q^{89} -33222.0 q^{91} -20536.0 q^{95} -64334.0 q^{97} +O(q^{100})\)

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
\(5\) 34.0000 0.608210 0.304105 − 0.952638i \(-0.401643\pi\)
0.304105 + 0.952638i \(0.401643\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −756.000 −1.88382 −0.941911 − 0.335861i \(-0.890973\pi\)
−0.941911 + 0.335861i \(0.890973\pi\)
\(12\) 0 0
\(13\) 678.000 1.11268 0.556341 − 0.830954i \(-0.312205\pi\)
0.556341 + 0.830954i \(0.312205\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1838.00 1.54249 0.771247 − 0.636537i \(-0.219634\pi\)
0.771247 + 0.636537i \(0.219634\pi\)
\(18\) 0 0
\(19\) −604.000 −0.383842 −0.191921 − 0.981410i \(-0.561472\pi\)
−0.191921 + 0.981410i \(0.561472\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2840.00 1.11943 0.559717 − 0.828684i \(-0.310910\pi\)
0.559717 + 0.828684i \(0.310910\pi\)
\(24\) 0 0
\(25\) −1969.00 −0.630080
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6878.00 −1.51868 −0.759342 − 0.650692i \(-0.774479\pi\)
−0.759342 + 0.650692i \(0.774479\pi\)
\(30\) 0 0
\(31\) −3568.00 −0.666838 −0.333419 − 0.942779i \(-0.608202\pi\)
−0.333419 + 0.942779i \(0.608202\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1666.00 −0.229882
\(36\) 0 0
\(37\) 14598.0 1.75303 0.876514 − 0.481376i \(-0.159863\pi\)
0.876514 + 0.481376i \(0.159863\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5962.00 −0.553901 −0.276951 − 0.960884i \(-0.589324\pi\)
−0.276951 + 0.960884i \(0.589324\pi\)
\(42\) 0 0
\(43\) 676.000 0.0557539 0.0278770 − 0.999611i \(-0.491125\pi\)
0.0278770 + 0.999611i \(0.491125\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −20800.0 −1.37347 −0.686734 − 0.726909i \(-0.740956\pi\)
−0.686734 + 0.726909i \(0.740956\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −32390.0 −1.58388 −0.791938 − 0.610601i \(-0.790928\pi\)
−0.791938 + 0.610601i \(0.790928\pi\)
\(54\) 0 0
\(55\) −25704.0 −1.14576
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 42948.0 1.60625 0.803125 − 0.595811i \(-0.203169\pi\)
0.803125 + 0.595811i \(0.203169\pi\)
\(60\) 0 0
\(61\) 44806.0 1.54174 0.770871 − 0.636992i \(-0.219821\pi\)
0.770871 + 0.636992i \(0.219821\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 23052.0 0.676745
\(66\) 0 0
\(67\) 39708.0 1.08066 0.540332 − 0.841452i \(-0.318299\pi\)
0.540332 + 0.841452i \(0.318299\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −25800.0 −0.607399 −0.303699 − 0.952768i \(-0.598222\pi\)
−0.303699 + 0.952768i \(0.598222\pi\)
\(72\) 0 0
\(73\) 58954.0 1.29481 0.647405 − 0.762146i \(-0.275854\pi\)
0.647405 + 0.762146i \(0.275854\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 37044.0 0.712018
\(78\) 0 0
\(79\) 77648.0 1.39979 0.699894 − 0.714246i \(-0.253230\pi\)
0.699894 + 0.714246i \(0.253230\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 35964.0 0.573024 0.286512 − 0.958077i \(-0.407504\pi\)
0.286512 + 0.958077i \(0.407504\pi\)
\(84\) 0 0
\(85\) 62492.0 0.938160
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −80842.0 −1.08184 −0.540919 − 0.841075i \(-0.681923\pi\)
−0.540919 + 0.841075i \(0.681923\pi\)
\(90\) 0 0
\(91\) −33222.0 −0.420555
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −20536.0 −0.233457
\(96\) 0 0
\(97\) −64334.0 −0.694243 −0.347121 − 0.937820i \(-0.612841\pi\)
−0.347121 + 0.937820i \(0.612841\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 40290.0 0.393001 0.196501 − 0.980504i \(-0.437042\pi\)
0.196501 + 0.980504i \(0.437042\pi\)
\(102\) 0 0
\(103\) −132888. −1.23422 −0.617110 − 0.786877i \(-0.711697\pi\)
−0.617110 + 0.786877i \(0.711697\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −119364. −1.00789 −0.503946 − 0.863735i \(-0.668119\pi\)
−0.503946 + 0.863735i \(0.668119\pi\)
\(108\) 0 0
\(109\) −47282.0 −0.381180 −0.190590 − 0.981670i \(-0.561040\pi\)
−0.190590 + 0.981670i \(0.561040\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 186126. 1.37123 0.685616 − 0.727963i \(-0.259533\pi\)
0.685616 + 0.727963i \(0.259533\pi\)
\(114\) 0 0
\(115\) 96560.0 0.680852
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −90062.0 −0.583008
\(120\) 0 0
\(121\) 410485. 2.54879
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −173196. −0.991432
\(126\) 0 0
\(127\) −43856.0 −0.241279 −0.120640 − 0.992696i \(-0.538495\pi\)
−0.120640 + 0.992696i \(0.538495\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −172468. −0.878072 −0.439036 − 0.898469i \(-0.644680\pi\)
−0.439036 + 0.898469i \(0.644680\pi\)
\(132\) 0 0
\(133\) 29596.0 0.145079
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 362134. 1.64842 0.824210 − 0.566284i \(-0.191620\pi\)
0.824210 + 0.566284i \(0.191620\pi\)
\(138\) 0 0
\(139\) −60132.0 −0.263979 −0.131989 − 0.991251i \(-0.542136\pi\)
−0.131989 + 0.991251i \(0.542136\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −512568. −2.09610
\(144\) 0 0
\(145\) −233852. −0.923679
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 33050.0 0.121957 0.0609784 − 0.998139i \(-0.480578\pi\)
0.0609784 + 0.998139i \(0.480578\pi\)
\(150\) 0 0
\(151\) −3400.00 −0.0121349 −0.00606745 − 0.999982i \(-0.501931\pi\)
−0.00606745 + 0.999982i \(0.501931\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −121312. −0.405578
\(156\) 0 0
\(157\) 80982.0 0.262204 0.131102 − 0.991369i \(-0.458148\pi\)
0.131102 + 0.991369i \(0.458148\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −139160. −0.423107
\(162\) 0 0
\(163\) 402860. 1.18764 0.593820 − 0.804598i \(-0.297619\pi\)
0.593820 + 0.804598i \(0.297619\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 384216. 1.06607 0.533033 − 0.846094i \(-0.321052\pi\)
0.533033 + 0.846094i \(0.321052\pi\)
\(168\) 0 0
\(169\) 88391.0 0.238063
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −270614. −0.687440 −0.343720 − 0.939072i \(-0.611687\pi\)
−0.343720 + 0.939072i \(0.611687\pi\)
\(174\) 0 0
\(175\) 96481.0 0.238148
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 351620. 0.820240 0.410120 − 0.912032i \(-0.365487\pi\)
0.410120 + 0.912032i \(0.365487\pi\)
\(180\) 0 0
\(181\) 641774. 1.45608 0.728041 − 0.685534i \(-0.240431\pi\)
0.728041 + 0.685534i \(0.240431\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 496332. 1.06621
\(186\) 0 0
\(187\) −1.38953e6 −2.90578
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 605392. 1.20075 0.600376 − 0.799718i \(-0.295018\pi\)
0.600376 + 0.799718i \(0.295018\pi\)
\(192\) 0 0
\(193\) 784386. 1.51578 0.757891 − 0.652382i \(-0.226230\pi\)
0.757891 + 0.652382i \(0.226230\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 395466. 0.726012 0.363006 − 0.931787i \(-0.381751\pi\)
0.363006 + 0.931787i \(0.381751\pi\)
\(198\) 0 0
\(199\) 96136.0 0.172089 0.0860445 − 0.996291i \(-0.472577\pi\)
0.0860445 + 0.996291i \(0.472577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 337022. 0.574008
\(204\) 0 0
\(205\) −202708. −0.336889
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 456624. 0.723091
\(210\) 0 0
\(211\) 131692. 0.203635 0.101818 − 0.994803i \(-0.467534\pi\)
0.101818 + 0.994803i \(0.467534\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 22984.0 0.0339101
\(216\) 0 0
\(217\) 174832. 0.252041
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.24616e6 1.71631
\(222\) 0 0
\(223\) −589344. −0.793609 −0.396805 − 0.917903i \(-0.629881\pi\)
−0.396805 + 0.917903i \(0.629881\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.12651e6 1.45101 0.725504 − 0.688218i \(-0.241607\pi\)
0.725504 + 0.688218i \(0.241607\pi\)
\(228\) 0 0
\(229\) 576254. 0.726148 0.363074 − 0.931760i \(-0.381727\pi\)
0.363074 + 0.931760i \(0.381727\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.11742e6 −1.34842 −0.674211 − 0.738539i \(-0.735516\pi\)
−0.674211 + 0.738539i \(0.735516\pi\)
\(234\) 0 0
\(235\) −707200. −0.835358
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 797936. 0.903594 0.451797 − 0.892121i \(-0.350783\pi\)
0.451797 + 0.892121i \(0.350783\pi\)
\(240\) 0 0
\(241\) 118978. 0.131954 0.0659772 − 0.997821i \(-0.478984\pi\)
0.0659772 + 0.997821i \(0.478984\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 81634.0 0.0868872
\(246\) 0 0
\(247\) −409512. −0.427095
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −485036. −0.485948 −0.242974 − 0.970033i \(-0.578123\pi\)
−0.242974 + 0.970033i \(0.578123\pi\)
\(252\) 0 0
\(253\) −2.14704e6 −2.10882
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 121902. 0.115127 0.0575636 − 0.998342i \(-0.481667\pi\)
0.0575636 + 0.998342i \(0.481667\pi\)
\(258\) 0 0
\(259\) −715302. −0.662583
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 161304. 0.143799 0.0718995 − 0.997412i \(-0.477094\pi\)
0.0718995 + 0.997412i \(0.477094\pi\)
\(264\) 0 0
\(265\) −1.10126e6 −0.963330
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.11633e6 0.940615 0.470307 − 0.882503i \(-0.344143\pi\)
0.470307 + 0.882503i \(0.344143\pi\)
\(270\) 0 0
\(271\) 1.73003e6 1.43097 0.715486 − 0.698627i \(-0.246205\pi\)
0.715486 + 0.698627i \(0.246205\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.48856e6 1.18696
\(276\) 0 0
\(277\) 940102. 0.736166 0.368083 − 0.929793i \(-0.380014\pi\)
0.368083 + 0.929793i \(0.380014\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.50577e6 1.13761 0.568803 − 0.822474i \(-0.307407\pi\)
0.568803 + 0.822474i \(0.307407\pi\)
\(282\) 0 0
\(283\) 957244. 0.710488 0.355244 − 0.934774i \(-0.384398\pi\)
0.355244 + 0.934774i \(0.384398\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 292138. 0.209355
\(288\) 0 0
\(289\) 1.95839e6 1.37928
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 247554. 0.168462 0.0842308 − 0.996446i \(-0.473157\pi\)
0.0842308 + 0.996446i \(0.473157\pi\)
\(294\) 0 0
\(295\) 1.46023e6 0.976938
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.92552e6 1.24558
\(300\) 0 0
\(301\) −33124.0 −0.0210730
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.52340e6 0.937703
\(306\) 0 0
\(307\) −2.56150e6 −1.55113 −0.775565 − 0.631267i \(-0.782535\pi\)
−0.775565 + 0.631267i \(0.782535\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.65194e6 −0.968488 −0.484244 − 0.874933i \(-0.660905\pi\)
−0.484244 + 0.874933i \(0.660905\pi\)
\(312\) 0 0
\(313\) 396938. 0.229014 0.114507 − 0.993422i \(-0.463471\pi\)
0.114507 + 0.993422i \(0.463471\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −749838. −0.419102 −0.209551 − 0.977798i \(-0.567200\pi\)
−0.209551 + 0.977798i \(0.567200\pi\)
\(318\) 0 0
\(319\) 5.19977e6 2.86093
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.11015e6 −0.592074
\(324\) 0 0
\(325\) −1.33498e6 −0.701079
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.01920e6 0.519122
\(330\) 0 0
\(331\) 1.89716e6 0.951772 0.475886 − 0.879507i \(-0.342127\pi\)
0.475886 + 0.879507i \(0.342127\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.35007e6 0.657272
\(336\) 0 0
\(337\) −2.76696e6 −1.32717 −0.663587 − 0.748099i \(-0.730967\pi\)
−0.663587 + 0.748099i \(0.730967\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.69741e6 1.25621
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.94137e6 0.865536 0.432768 − 0.901505i \(-0.357537\pi\)
0.432768 + 0.901505i \(0.357537\pi\)
\(348\) 0 0
\(349\) 1.57938e6 0.694103 0.347051 − 0.937846i \(-0.387183\pi\)
0.347051 + 0.937846i \(0.387183\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 110862. 0.0473528 0.0236764 − 0.999720i \(-0.492463\pi\)
0.0236764 + 0.999720i \(0.492463\pi\)
\(354\) 0 0
\(355\) −877200. −0.369426
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −942360. −0.385905 −0.192953 − 0.981208i \(-0.561806\pi\)
−0.192953 + 0.981208i \(0.561806\pi\)
\(360\) 0 0
\(361\) −2.11128e6 −0.852665
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00444e6 0.787517
\(366\) 0 0
\(367\) 1.44002e6 0.558087 0.279044 − 0.960278i \(-0.409983\pi\)
0.279044 + 0.960278i \(0.409983\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.58711e6 0.598649
\(372\) 0 0
\(373\) −1.39667e6 −0.519781 −0.259891 − 0.965638i \(-0.583686\pi\)
−0.259891 + 0.965638i \(0.583686\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.66328e6 −1.68981
\(378\) 0 0
\(379\) 2.91378e6 1.04198 0.520989 − 0.853563i \(-0.325563\pi\)
0.520989 + 0.853563i \(0.325563\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.74130e6 1.65158 0.825791 − 0.563976i \(-0.190729\pi\)
0.825791 + 0.563976i \(0.190729\pi\)
\(384\) 0 0
\(385\) 1.25950e6 0.433057
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.03917e6 −0.348188 −0.174094 − 0.984729i \(-0.555700\pi\)
−0.174094 + 0.984729i \(0.555700\pi\)
\(390\) 0 0
\(391\) 5.21992e6 1.72672
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.64003e6 0.851366
\(396\) 0 0
\(397\) −1.40067e6 −0.446024 −0.223012 − 0.974816i \(-0.571589\pi\)
−0.223012 + 0.974816i \(0.571589\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −545682. −0.169464 −0.0847322 − 0.996404i \(-0.527003\pi\)
−0.0847322 + 0.996404i \(0.527003\pi\)
\(402\) 0 0
\(403\) −2.41910e6 −0.741980
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.10361e7 −3.30240
\(408\) 0 0
\(409\) −2.13797e6 −0.631967 −0.315983 − 0.948765i \(-0.602334\pi\)
−0.315983 + 0.948765i \(0.602334\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.10445e6 −0.607105
\(414\) 0 0
\(415\) 1.22278e6 0.348519
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.34675e6 0.931296 0.465648 − 0.884970i \(-0.345821\pi\)
0.465648 + 0.884970i \(0.345821\pi\)
\(420\) 0 0
\(421\) 3.12578e6 0.859515 0.429757 − 0.902944i \(-0.358599\pi\)
0.429757 + 0.902944i \(0.358599\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.61902e6 −0.971894
\(426\) 0 0
\(427\) −2.19549e6 −0.582724
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.06699e6 0.276674 0.138337 − 0.990385i \(-0.455824\pi\)
0.138337 + 0.990385i \(0.455824\pi\)
\(432\) 0 0
\(433\) 2.44976e6 0.627920 0.313960 − 0.949436i \(-0.398344\pi\)
0.313960 + 0.949436i \(0.398344\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.71536e6 −0.429686
\(438\) 0 0
\(439\) 1.31134e6 0.324753 0.162376 − 0.986729i \(-0.448084\pi\)
0.162376 + 0.986729i \(0.448084\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −67924.0 −0.0164442 −0.00822212 − 0.999966i \(-0.502617\pi\)
−0.00822212 + 0.999966i \(0.502617\pi\)
\(444\) 0 0
\(445\) −2.74863e6 −0.657985
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.63757e6 0.617430 0.308715 − 0.951155i \(-0.400101\pi\)
0.308715 + 0.951155i \(0.400101\pi\)
\(450\) 0 0
\(451\) 4.50727e6 1.04345
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.12955e6 −0.255786
\(456\) 0 0
\(457\) 1.93393e6 0.433162 0.216581 − 0.976265i \(-0.430509\pi\)
0.216581 + 0.976265i \(0.430509\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.15285e6 −0.471805 −0.235902 − 0.971777i \(-0.575805\pi\)
−0.235902 + 0.971777i \(0.575805\pi\)
\(462\) 0 0
\(463\) −4.04523e6 −0.876983 −0.438491 − 0.898735i \(-0.644487\pi\)
−0.438491 + 0.898735i \(0.644487\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.36134e6 0.925396 0.462698 − 0.886516i \(-0.346881\pi\)
0.462698 + 0.886516i \(0.346881\pi\)
\(468\) 0 0
\(469\) −1.94569e6 −0.408453
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −511056. −0.105031
\(474\) 0 0
\(475\) 1.18928e6 0.241851
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.80808e6 −0.559205 −0.279602 − 0.960116i \(-0.590203\pi\)
−0.279602 + 0.960116i \(0.590203\pi\)
\(480\) 0 0
\(481\) 9.89744e6 1.95056
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.18736e6 −0.422246
\(486\) 0 0
\(487\) −5.50338e6 −1.05150 −0.525748 − 0.850641i \(-0.676214\pi\)
−0.525748 + 0.850641i \(0.676214\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.60656e6 1.04952 0.524762 − 0.851249i \(-0.324154\pi\)
0.524762 + 0.851249i \(0.324154\pi\)
\(492\) 0 0
\(493\) −1.26418e7 −2.34256
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.26420e6 0.229575
\(498\) 0 0
\(499\) −3.35170e6 −0.602579 −0.301289 − 0.953533i \(-0.597417\pi\)
−0.301289 + 0.953533i \(0.597417\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 890104. 0.156863 0.0784315 − 0.996920i \(-0.475009\pi\)
0.0784315 + 0.996920i \(0.475009\pi\)
\(504\) 0 0
\(505\) 1.36986e6 0.239027
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.77043e6 0.302889 0.151444 − 0.988466i \(-0.451608\pi\)
0.151444 + 0.988466i \(0.451608\pi\)
\(510\) 0 0
\(511\) −2.88875e6 −0.489392
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.51819e6 −0.750666
\(516\) 0 0
\(517\) 1.57248e7 2.58737
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 892950. 0.144123 0.0720614 − 0.997400i \(-0.477042\pi\)
0.0720614 + 0.997400i \(0.477042\pi\)
\(522\) 0 0
\(523\) 3.53086e6 0.564451 0.282226 − 0.959348i \(-0.408927\pi\)
0.282226 + 0.959348i \(0.408927\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.55798e6 −1.02859
\(528\) 0 0
\(529\) 1.62926e6 0.253134
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.04224e6 −0.616316
\(534\) 0 0
\(535\) −4.05838e6 −0.613010
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.81516e6 −0.269118
\(540\) 0 0
\(541\) 1.08729e7 1.59718 0.798588 − 0.601878i \(-0.205581\pi\)
0.798588 + 0.601878i \(0.205581\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.60759e6 −0.231837
\(546\) 0 0
\(547\) 1.04837e7 1.49812 0.749061 − 0.662501i \(-0.230505\pi\)
0.749061 + 0.662501i \(0.230505\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.15431e6 0.582935
\(552\) 0 0
\(553\) −3.80475e6 −0.529070
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.28781e6 0.858739 0.429370 − 0.903129i \(-0.358736\pi\)
0.429370 + 0.903129i \(0.358736\pi\)
\(558\) 0 0
\(559\) 458328. 0.0620364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.07513e7 1.42952 0.714760 − 0.699370i \(-0.246536\pi\)
0.714760 + 0.699370i \(0.246536\pi\)
\(564\) 0 0
\(565\) 6.32828e6 0.833998
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.48777e6 −0.451614 −0.225807 − 0.974172i \(-0.572502\pi\)
−0.225807 + 0.974172i \(0.572502\pi\)
\(570\) 0 0
\(571\) 2.42568e6 0.311346 0.155673 − 0.987809i \(-0.450245\pi\)
0.155673 + 0.987809i \(0.450245\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.59196e6 −0.705333
\(576\) 0 0
\(577\) −1.51118e7 −1.88963 −0.944813 − 0.327610i \(-0.893757\pi\)
−0.944813 + 0.327610i \(0.893757\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.76224e6 −0.216583
\(582\) 0 0
\(583\) 2.44868e7 2.98374
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.22473e6 −0.386277 −0.193138 − 0.981172i \(-0.561867\pi\)
−0.193138 + 0.981172i \(0.561867\pi\)
\(588\) 0 0
\(589\) 2.15507e6 0.255961
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.40022e6 0.630630 0.315315 − 0.948987i \(-0.397890\pi\)
0.315315 + 0.948987i \(0.397890\pi\)
\(594\) 0 0
\(595\) −3.06211e6 −0.354591
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −683960. −0.0778868 −0.0389434 − 0.999241i \(-0.512399\pi\)
−0.0389434 + 0.999241i \(0.512399\pi\)
\(600\) 0 0
\(601\) −1.40895e7 −1.59114 −0.795571 − 0.605861i \(-0.792829\pi\)
−0.795571 + 0.605861i \(0.792829\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.39565e7 1.55020
\(606\) 0 0
\(607\) −1.12823e7 −1.24287 −0.621434 − 0.783467i \(-0.713450\pi\)
−0.621434 + 0.783467i \(0.713450\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.41024e7 −1.52823
\(612\) 0 0
\(613\) 1.42254e7 1.52903 0.764513 − 0.644609i \(-0.222980\pi\)
0.764513 + 0.644609i \(0.222980\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.53527e6 −0.796868 −0.398434 − 0.917197i \(-0.630446\pi\)
−0.398434 + 0.917197i \(0.630446\pi\)
\(618\) 0 0
\(619\) −1.57737e7 −1.65466 −0.827329 − 0.561718i \(-0.810141\pi\)
−0.827329 + 0.561718i \(0.810141\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.96126e6 0.408896
\(624\) 0 0
\(625\) 264461. 0.0270808
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.68311e7 2.70403
\(630\) 0 0
\(631\) −2.73183e6 −0.273137 −0.136569 − 0.990631i \(-0.543607\pi\)
−0.136569 + 0.990631i \(0.543607\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.49110e6 −0.146748
\(636\) 0 0
\(637\) 1.62788e6 0.158955
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.98163e6 0.286621 0.143311 − 0.989678i \(-0.454225\pi\)
0.143311 + 0.989678i \(0.454225\pi\)
\(642\) 0 0
\(643\) −1.60808e7 −1.53384 −0.766920 − 0.641743i \(-0.778212\pi\)
−0.766920 + 0.641743i \(0.778212\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.27375e7 1.19625 0.598127 − 0.801401i \(-0.295912\pi\)
0.598127 + 0.801401i \(0.295912\pi\)
\(648\) 0 0
\(649\) −3.24687e7 −3.02589
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.00216e6 −0.642612 −0.321306 − 0.946975i \(-0.604122\pi\)
−0.321306 + 0.946975i \(0.604122\pi\)
\(654\) 0 0
\(655\) −5.86391e6 −0.534053
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.49512e6 0.134111 0.0670554 − 0.997749i \(-0.478640\pi\)
0.0670554 + 0.997749i \(0.478640\pi\)
\(660\) 0 0
\(661\) −9.48061e6 −0.843981 −0.421990 − 0.906600i \(-0.638668\pi\)
−0.421990 + 0.906600i \(0.638668\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00626e6 0.0882384
\(666\) 0 0
\(667\) −1.95335e7 −1.70007
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.38733e7 −2.90437
\(672\) 0 0
\(673\) 1.68756e7 1.43622 0.718110 − 0.695929i \(-0.245007\pi\)
0.718110 + 0.695929i \(0.245007\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.26500e7 −1.06076 −0.530382 − 0.847759i \(-0.677951\pi\)
−0.530382 + 0.847759i \(0.677951\pi\)
\(678\) 0 0
\(679\) 3.15237e6 0.262399
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.33743e7 −1.09703 −0.548515 − 0.836141i \(-0.684807\pi\)
−0.548515 + 0.836141i \(0.684807\pi\)
\(684\) 0 0
\(685\) 1.23126e7 1.00259
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.19604e7 −1.76235
\(690\) 0 0
\(691\) −8.43168e6 −0.671767 −0.335884 − 0.941904i \(-0.609035\pi\)
−0.335884 + 0.941904i \(0.609035\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.04449e6 −0.160555
\(696\) 0 0
\(697\) −1.09582e7 −0.854389
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.07968e7 0.829853 0.414927 − 0.909855i \(-0.363807\pi\)
0.414927 + 0.909855i \(0.363807\pi\)
\(702\) 0 0
\(703\) −8.81719e6 −0.672887
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.97421e6 −0.148540
\(708\) 0 0
\(709\) −1.93853e7 −1.44830 −0.724148 − 0.689645i \(-0.757767\pi\)
−0.724148 + 0.689645i \(0.757767\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.01331e7 −0.746482
\(714\) 0 0
\(715\) −1.74273e7 −1.27487
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.01782e6 0.361987 0.180994 − 0.983484i \(-0.442069\pi\)
0.180994 + 0.983484i \(0.442069\pi\)
\(720\) 0 0
\(721\) 6.51151e6 0.466491
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.35428e7 0.956892
\(726\) 0 0
\(727\) −1.32402e7 −0.929094 −0.464547 − 0.885549i \(-0.653783\pi\)
−0.464547 + 0.885549i \(0.653783\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.24249e6 0.0860001
\(732\) 0 0
\(733\) −1.91362e7 −1.31551 −0.657757 − 0.753230i \(-0.728495\pi\)
−0.657757 + 0.753230i \(0.728495\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.00192e7 −2.03578
\(738\) 0 0
\(739\) −2.43530e7 −1.64037 −0.820186 − 0.572097i \(-0.806130\pi\)
−0.820186 + 0.572097i \(0.806130\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.33449e6 −0.0886835 −0.0443417 − 0.999016i \(-0.514119\pi\)
−0.0443417 + 0.999016i \(0.514119\pi\)
\(744\) 0 0
\(745\) 1.12370e6 0.0741754
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.84884e6 0.380947
\(750\) 0 0
\(751\) 2.23022e7 1.44294 0.721470 − 0.692446i \(-0.243467\pi\)
0.721470 + 0.692446i \(0.243467\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −115600. −0.00738058
\(756\) 0 0
\(757\) 1.34941e7 0.855861 0.427931 − 0.903812i \(-0.359243\pi\)
0.427931 + 0.903812i \(0.359243\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.96938e7 1.23273 0.616366 − 0.787460i \(-0.288604\pi\)
0.616366 + 0.787460i \(0.288604\pi\)
\(762\) 0 0
\(763\) 2.31682e6 0.144072
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.91187e7 1.78725
\(768\) 0 0
\(769\) −1.42494e6 −0.0868923 −0.0434462 − 0.999056i \(-0.513834\pi\)
−0.0434462 + 0.999056i \(0.513834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.90912e7 1.14917 0.574586 − 0.818444i \(-0.305163\pi\)
0.574586 + 0.818444i \(0.305163\pi\)
\(774\) 0 0
\(775\) 7.02539e6 0.420162
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.60105e6 0.212611
\(780\) 0 0
\(781\) 1.95048e7 1.14423
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.75339e6 0.159475
\(786\) 0 0
\(787\) 2.99080e7 1.72128 0.860638 − 0.509217i \(-0.170065\pi\)
0.860638 + 0.509217i \(0.170065\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.12017e6 −0.518277
\(792\) 0 0
\(793\) 3.03785e7 1.71547
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.78726e7 −1.55429 −0.777146 − 0.629321i \(-0.783333\pi\)
−0.777146 + 0.629321i \(0.783333\pi\)
\(798\) 0 0
\(799\) −3.82304e7 −2.11857
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.45692e7 −2.43919
\(804\) 0 0
\(805\) −4.73144e6 −0.257338
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.65275e6 −0.357380 −0.178690 − 0.983905i \(-0.557186\pi\)
−0.178690 + 0.983905i \(0.557186\pi\)
\(810\) 0 0
\(811\) 3.02403e7 1.61448 0.807242 − 0.590220i \(-0.200959\pi\)
0.807242 + 0.590220i \(0.200959\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.36972e7 0.722336
\(816\) 0 0
\(817\) −408304. −0.0214007
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.16228e7 −1.11958 −0.559788 − 0.828636i \(-0.689117\pi\)
−0.559788 + 0.828636i \(0.689117\pi\)
\(822\) 0 0
\(823\) −3.54169e6 −0.182268 −0.0911341 − 0.995839i \(-0.529049\pi\)
−0.0911341 + 0.995839i \(0.529049\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.36075e7 −1.70872 −0.854362 − 0.519678i \(-0.826052\pi\)
−0.854362 + 0.519678i \(0.826052\pi\)
\(828\) 0 0
\(829\) 2.23805e7 1.13106 0.565528 − 0.824729i \(-0.308673\pi\)
0.565528 + 0.824729i \(0.308673\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.41304e6 0.220356
\(834\) 0 0
\(835\) 1.30633e7 0.648393
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.50796e6 0.466318 0.233159 − 0.972439i \(-0.425094\pi\)
0.233159 + 0.972439i \(0.425094\pi\)
\(840\) 0 0
\(841\) 2.67957e7 1.30640
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.00529e6 0.144792
\(846\) 0 0
\(847\) −2.01138e7 −0.963352
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.14583e7 1.96240
\(852\) 0 0
\(853\) 1.64803e7 0.775518 0.387759 − 0.921761i \(-0.373249\pi\)
0.387759 + 0.921761i \(0.373249\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.49736e7 −1.16153 −0.580764 − 0.814072i \(-0.697246\pi\)
−0.580764 + 0.814072i \(0.697246\pi\)
\(858\) 0 0
\(859\) −4.01823e6 −0.185803 −0.0929013 − 0.995675i \(-0.529614\pi\)
−0.0929013 + 0.995675i \(0.529614\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.78866e7 −1.27458 −0.637292 − 0.770623i \(-0.719945\pi\)
−0.637292 + 0.770623i \(0.719945\pi\)
\(864\) 0 0
\(865\) −9.20088e6 −0.418108
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.87019e7 −2.63695
\(870\) 0 0
\(871\) 2.69220e7 1.20244
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.48660e6 0.374726
\(876\) 0 0
\(877\) −3.05699e7 −1.34213 −0.671067 − 0.741397i \(-0.734164\pi\)
−0.671067 + 0.741397i \(0.734164\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −9.75786e6 −0.423560 −0.211780 − 0.977317i \(-0.567926\pi\)
−0.211780 + 0.977317i \(0.567926\pi\)
\(882\) 0 0
\(883\) −1.53777e7 −0.663728 −0.331864 − 0.943327i \(-0.607677\pi\)
−0.331864 + 0.943327i \(0.607677\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.69364e7 0.722790 0.361395 − 0.932413i \(-0.382301\pi\)
0.361395 + 0.932413i \(0.382301\pi\)
\(888\) 0 0
\(889\) 2.14894e6 0.0911949
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.25632e7 0.527195
\(894\) 0 0
\(895\) 1.19551e7 0.498879
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.45407e7 1.01272
\(900\) 0 0
\(901\) −5.95328e7 −2.44312
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.18203e7 0.885604
\(906\) 0 0
\(907\) 1.44015e6 0.0581285 0.0290642 − 0.999578i \(-0.490747\pi\)
0.0290642 + 0.999578i \(0.490747\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.04883e7 0.817920 0.408960 − 0.912552i \(-0.365892\pi\)
0.408960 + 0.912552i \(0.365892\pi\)
\(912\) 0 0
\(913\) −2.71888e7 −1.07948
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.45093e6 0.331880
\(918\) 0 0
\(919\) 2.71154e7 1.05908 0.529538 − 0.848286i \(-0.322365\pi\)
0.529538 + 0.848286i \(0.322365\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.74924e7 −0.675842
\(924\) 0 0
\(925\) −2.87435e7 −1.10455
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.21981e7 −1.22403 −0.612014 − 0.790847i \(-0.709641\pi\)
−0.612014 + 0.790847i \(0.709641\pi\)
\(930\) 0 0
\(931\) −1.45020e6 −0.0548346
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.72440e7 −1.76733
\(936\) 0 0
\(937\) −4.35134e7 −1.61910 −0.809551 − 0.587050i \(-0.800289\pi\)
−0.809551 + 0.587050i \(0.800289\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.49194e6 −0.165371 −0.0826856 − 0.996576i \(-0.526350\pi\)
−0.0826856 + 0.996576i \(0.526350\pi\)
\(942\) 0 0
\(943\) −1.69321e7 −0.620056
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.65260e7 −1.32351 −0.661755 − 0.749720i \(-0.730188\pi\)
−0.661755 + 0.749720i \(0.730188\pi\)
\(948\) 0 0
\(949\) 3.99708e7 1.44071
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.10606e7 −1.82118 −0.910592 − 0.413306i \(-0.864374\pi\)
−0.910592 + 0.413306i \(0.864374\pi\)
\(954\) 0 0
\(955\) 2.05833e7 0.730310
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.77446e7 −0.623044
\(960\) 0 0
\(961\) −1.58985e7 −0.555327
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.66691e7 0.921914
\(966\) 0 0
\(967\) −4.41431e7 −1.51809 −0.759044 − 0.651039i \(-0.774333\pi\)
−0.759044 + 0.651039i \(0.774333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.16730e7 −1.41843 −0.709213 − 0.704995i \(-0.750949\pi\)
−0.709213 + 0.704995i \(0.750949\pi\)
\(972\) 0 0
\(973\) 2.94647e6 0.0997745
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.78673e7 −0.934024 −0.467012 − 0.884251i \(-0.654670\pi\)
−0.467012 + 0.884251i \(0.654670\pi\)
\(978\) 0 0
\(979\) 6.11166e7 2.03799
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.08251e7 0.687389 0.343694 − 0.939082i \(-0.388322\pi\)
0.343694 + 0.939082i \(0.388322\pi\)
\(984\) 0 0
\(985\) 1.34458e7 0.441568
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.91984e6 0.0624129
\(990\) 0 0
\(991\) −2.00484e7 −0.648480 −0.324240 − 0.945975i \(-0.605109\pi\)
−0.324240 + 0.945975i \(0.605109\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.26862e6 0.104666
\(996\) 0 0
\(997\) −2.38869e7 −0.761064 −0.380532 − 0.924768i \(-0.624259\pi\)
−0.380532 + 0.924768i \(0.624259\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.6.a.s.1.1 1
3.2 odd 2 336.6.a.k.1.1 1
4.3 odd 2 504.6.a.f.1.1 1
12.11 even 2 168.6.a.a.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.a.1.1 ✓ 1 12.11 even 2
336.6.a.k.1.1 1 3.2 odd 2
504.6.a.f.1.1 1 4.3 odd 2
1008.6.a.s.1.1 1 1.1 even 1 trivial