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Properties

Label 1008.6.a.j.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 42)
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)
 
\(f(q)\) \(=\) \(q-26.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-26.0000 q^{5} +49.0000 q^{7} +664.000 q^{11} +318.000 q^{13} -1582.00 q^{17} -236.000 q^{19} +2212.00 q^{23} -2449.00 q^{25} +4954.00 q^{29} +7128.00 q^{31} -1274.00 q^{35} +4358.00 q^{37} -10542.0 q^{41} +8452.00 q^{43} +5352.00 q^{47} +2401.00 q^{49} +33354.0 q^{53} -17264.0 q^{55} -15436.0 q^{59} -36762.0 q^{61} -8268.00 q^{65} -40972.0 q^{67} -9092.00 q^{71} -73454.0 q^{73} +32536.0 q^{77} -89400.0 q^{79} -6428.00 q^{83} +41132.0 q^{85} +122658. q^{89} +15582.0 q^{91} +6136.00 q^{95} +21370.0 q^{97} +O(q^{100})\)

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
\(5\) −26.0000 −0.465102 −0.232551 − 0.972584i \(-0.574707\pi\)
−0.232551 + 0.972584i \(0.574707\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 664.000 1.65457 0.827287 − 0.561779i \(-0.189883\pi\)
0.827287 + 0.561779i \(0.189883\pi\)
\(12\) 0 0
\(13\) 318.000 0.521878 0.260939 − 0.965355i \(-0.415968\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1582.00 −1.32765 −0.663826 − 0.747887i \(-0.731068\pi\)
−0.663826 + 0.747887i \(0.731068\pi\)
\(18\) 0 0
\(19\) −236.000 −0.149978 −0.0749891 − 0.997184i \(-0.523892\pi\)
−0.0749891 + 0.997184i \(0.523892\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2212.00 0.871898 0.435949 − 0.899971i \(-0.356413\pi\)
0.435949 + 0.899971i \(0.356413\pi\)
\(24\) 0 0
\(25\) −2449.00 −0.783680
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4954.00 1.09386 0.546929 − 0.837179i \(-0.315797\pi\)
0.546929 + 0.837179i \(0.315797\pi\)
\(30\) 0 0
\(31\) 7128.00 1.33218 0.666091 − 0.745871i \(-0.267966\pi\)
0.666091 + 0.745871i \(0.267966\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1274.00 −0.175792
\(36\) 0 0
\(37\) 4358.00 0.523339 0.261669 − 0.965158i \(-0.415727\pi\)
0.261669 + 0.965158i \(0.415727\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10542.0 −0.979407 −0.489704 − 0.871889i \(-0.662895\pi\)
−0.489704 + 0.871889i \(0.662895\pi\)
\(42\) 0 0
\(43\) 8452.00 0.697089 0.348545 − 0.937292i \(-0.386676\pi\)
0.348545 + 0.937292i \(0.386676\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5352.00 0.353404 0.176702 − 0.984264i \(-0.443457\pi\)
0.176702 + 0.984264i \(0.443457\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 33354.0 1.63102 0.815508 − 0.578746i \(-0.196458\pi\)
0.815508 + 0.578746i \(0.196458\pi\)
\(54\) 0 0
\(55\) −17264.0 −0.769546
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −15436.0 −0.577304 −0.288652 − 0.957434i \(-0.593207\pi\)
−0.288652 + 0.957434i \(0.593207\pi\)
\(60\) 0 0
\(61\) −36762.0 −1.26495 −0.632477 − 0.774579i \(-0.717962\pi\)
−0.632477 + 0.774579i \(0.717962\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8268.00 −0.242726
\(66\) 0 0
\(67\) −40972.0 −1.11506 −0.557532 − 0.830155i \(-0.688252\pi\)
−0.557532 + 0.830155i \(0.688252\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9092.00 −0.214049 −0.107025 − 0.994256i \(-0.534132\pi\)
−0.107025 + 0.994256i \(0.534132\pi\)
\(72\) 0 0
\(73\) −73454.0 −1.61327 −0.806637 − 0.591047i \(-0.798715\pi\)
−0.806637 + 0.591047i \(0.798715\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 32536.0 0.625370
\(78\) 0 0
\(79\) −89400.0 −1.61165 −0.805823 − 0.592156i \(-0.798277\pi\)
−0.805823 + 0.592156i \(0.798277\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6428.00 −0.102419 −0.0512095 − 0.998688i \(-0.516308\pi\)
−0.0512095 + 0.998688i \(0.516308\pi\)
\(84\) 0 0
\(85\) 41132.0 0.617494
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 122658. 1.64142 0.820712 − 0.571342i \(-0.193577\pi\)
0.820712 + 0.571342i \(0.193577\pi\)
\(90\) 0 0
\(91\) 15582.0 0.197251
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6136.00 0.0697552
\(96\) 0 0
\(97\) 21370.0 0.230608 0.115304 − 0.993330i \(-0.463216\pi\)
0.115304 + 0.993330i \(0.463216\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 36814.0 0.359095 0.179548 − 0.983749i \(-0.442537\pi\)
0.179548 + 0.983749i \(0.442537\pi\)
\(102\) 0 0
\(103\) −104528. −0.970822 −0.485411 − 0.874286i \(-0.661330\pi\)
−0.485411 + 0.874286i \(0.661330\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 214440. 1.81070 0.905350 − 0.424667i \(-0.139609\pi\)
0.905350 + 0.424667i \(0.139609\pi\)
\(108\) 0 0
\(109\) 28798.0 0.232165 0.116082 − 0.993240i \(-0.462966\pi\)
0.116082 + 0.993240i \(0.462966\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 56014.0 0.412668 0.206334 − 0.978482i \(-0.433847\pi\)
0.206334 + 0.978482i \(0.433847\pi\)
\(114\) 0 0
\(115\) −57512.0 −0.405521
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −77518.0 −0.501805
\(120\) 0 0
\(121\) 279845. 1.73762
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 144924. 0.829593
\(126\) 0 0
\(127\) −185400. −1.02000 −0.510000 − 0.860174i \(-0.670355\pi\)
−0.510000 + 0.860174i \(0.670355\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 64532.0 0.328547 0.164273 − 0.986415i \(-0.447472\pi\)
0.164273 + 0.986415i \(0.447472\pi\)
\(132\) 0 0
\(133\) −11564.0 −0.0566864
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −152930. −0.696131 −0.348066 − 0.937470i \(-0.613161\pi\)
−0.348066 + 0.937470i \(0.613161\pi\)
\(138\) 0 0
\(139\) 343460. 1.50778 0.753892 − 0.656998i \(-0.228174\pi\)
0.753892 + 0.656998i \(0.228174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 211152. 0.863486
\(144\) 0 0
\(145\) −128804. −0.508756
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 174858. 0.645238 0.322619 − 0.946529i \(-0.395437\pi\)
0.322619 + 0.946529i \(0.395437\pi\)
\(150\) 0 0
\(151\) 452552. 1.61520 0.807600 − 0.589731i \(-0.200766\pi\)
0.807600 + 0.589731i \(0.200766\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −185328. −0.619601
\(156\) 0 0
\(157\) −499066. −1.61588 −0.807940 − 0.589265i \(-0.799417\pi\)
−0.807940 + 0.589265i \(0.799417\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 108388. 0.329546
\(162\) 0 0
\(163\) 475588. 1.40204 0.701022 − 0.713139i \(-0.252727\pi\)
0.701022 + 0.713139i \(0.252727\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 120224. 0.333580 0.166790 − 0.985992i \(-0.446660\pi\)
0.166790 + 0.985992i \(0.446660\pi\)
\(168\) 0 0
\(169\) −270169. −0.727644
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −508874. −1.29269 −0.646346 − 0.763045i \(-0.723704\pi\)
−0.646346 + 0.763045i \(0.723704\pi\)
\(174\) 0 0
\(175\) −120001. −0.296203
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 487560. 1.13735 0.568677 − 0.822561i \(-0.307456\pi\)
0.568677 + 0.822561i \(0.307456\pi\)
\(180\) 0 0
\(181\) −544410. −1.23518 −0.617589 − 0.786501i \(-0.711891\pi\)
−0.617589 + 0.786501i \(0.711891\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −113308. −0.243406
\(186\) 0 0
\(187\) −1.05045e6 −2.19670
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 376404. 0.746570 0.373285 − 0.927717i \(-0.378231\pi\)
0.373285 + 0.927717i \(0.378231\pi\)
\(192\) 0 0
\(193\) 844946. 1.63281 0.816405 − 0.577480i \(-0.195964\pi\)
0.816405 + 0.577480i \(0.195964\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 492794. 0.904690 0.452345 − 0.891843i \(-0.350588\pi\)
0.452345 + 0.891843i \(0.350588\pi\)
\(198\) 0 0
\(199\) 914776. 1.63750 0.818751 − 0.574148i \(-0.194667\pi\)
0.818751 + 0.574148i \(0.194667\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 242746. 0.413440
\(204\) 0 0
\(205\) 274092. 0.455524
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −156704. −0.248150
\(210\) 0 0
\(211\) −311780. −0.482106 −0.241053 − 0.970512i \(-0.577493\pi\)
−0.241053 + 0.970512i \(0.577493\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −219752. −0.324218
\(216\) 0 0
\(217\) 349272. 0.503517
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −503076. −0.692872
\(222\) 0 0
\(223\) 1.28776e6 1.73409 0.867047 − 0.498226i \(-0.166015\pi\)
0.867047 + 0.498226i \(0.166015\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.28905e6 1.66037 0.830187 − 0.557485i \(-0.188234\pi\)
0.830187 + 0.557485i \(0.188234\pi\)
\(228\) 0 0
\(229\) 678214. 0.854630 0.427315 − 0.904103i \(-0.359460\pi\)
0.427315 + 0.904103i \(0.359460\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.11731e6 1.34829 0.674146 − 0.738598i \(-0.264512\pi\)
0.674146 + 0.738598i \(0.264512\pi\)
\(234\) 0 0
\(235\) −139152. −0.164369
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.26196e6 −1.42906 −0.714528 − 0.699606i \(-0.753359\pi\)
−0.714528 + 0.699606i \(0.753359\pi\)
\(240\) 0 0
\(241\) 948218. 1.05164 0.525818 − 0.850597i \(-0.323759\pi\)
0.525818 + 0.850597i \(0.323759\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −62426.0 −0.0664432
\(246\) 0 0
\(247\) −75048.0 −0.0782703
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −486396. −0.487310 −0.243655 − 0.969862i \(-0.578347\pi\)
−0.243655 + 0.969862i \(0.578347\pi\)
\(252\) 0 0
\(253\) 1.46877e6 1.44262
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.03910e6 0.981349 0.490675 − 0.871343i \(-0.336750\pi\)
0.490675 + 0.871343i \(0.336750\pi\)
\(258\) 0 0
\(259\) 213542. 0.197803
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.35104e6 1.20443 0.602213 − 0.798335i \(-0.294286\pi\)
0.602213 + 0.798335i \(0.294286\pi\)
\(264\) 0 0
\(265\) −867204. −0.758589
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.11811e6 0.942115 0.471057 − 0.882103i \(-0.343872\pi\)
0.471057 + 0.882103i \(0.343872\pi\)
\(270\) 0 0
\(271\) 190104. 0.157242 0.0786209 − 0.996905i \(-0.474948\pi\)
0.0786209 + 0.996905i \(0.474948\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.62614e6 −1.29666
\(276\) 0 0
\(277\) −200506. −0.157010 −0.0785051 − 0.996914i \(-0.525015\pi\)
−0.0785051 + 0.996914i \(0.525015\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.09237e6 −0.825285 −0.412643 − 0.910893i \(-0.635394\pi\)
−0.412643 + 0.910893i \(0.635394\pi\)
\(282\) 0 0
\(283\) −1.81258e6 −1.34534 −0.672669 − 0.739944i \(-0.734852\pi\)
−0.672669 + 0.739944i \(0.734852\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −516558. −0.370181
\(288\) 0 0
\(289\) 1.08287e6 0.762659
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.10031e6 −1.42927 −0.714634 − 0.699499i \(-0.753407\pi\)
−0.714634 + 0.699499i \(0.753407\pi\)
\(294\) 0 0
\(295\) 401336. 0.268505
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 703416. 0.455024
\(300\) 0 0
\(301\) 414148. 0.263475
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 955812. 0.588333
\(306\) 0 0
\(307\) 1.64104e6 0.993743 0.496872 − 0.867824i \(-0.334482\pi\)
0.496872 + 0.867824i \(0.334482\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −945232. −0.554163 −0.277081 − 0.960846i \(-0.589367\pi\)
−0.277081 + 0.960846i \(0.589367\pi\)
\(312\) 0 0
\(313\) 415354. 0.239639 0.119820 − 0.992796i \(-0.461768\pi\)
0.119820 + 0.992796i \(0.461768\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.18481e6 −0.662220 −0.331110 − 0.943592i \(-0.607423\pi\)
−0.331110 + 0.943592i \(0.607423\pi\)
\(318\) 0 0
\(319\) 3.28946e6 1.80987
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 373352. 0.199119
\(324\) 0 0
\(325\) −778782. −0.408985
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 262248. 0.133574
\(330\) 0 0
\(331\) −1.37155e6 −0.688083 −0.344042 − 0.938954i \(-0.611796\pi\)
−0.344042 + 0.938954i \(0.611796\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.06527e6 0.518619
\(336\) 0 0
\(337\) 963522. 0.462154 0.231077 − 0.972935i \(-0.425775\pi\)
0.231077 + 0.972935i \(0.425775\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.73299e6 2.20419
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.57731e6 1.14906 0.574531 − 0.818483i \(-0.305185\pi\)
0.574531 + 0.818483i \(0.305185\pi\)
\(348\) 0 0
\(349\) −3.06751e6 −1.34810 −0.674051 − 0.738684i \(-0.735447\pi\)
−0.674051 + 0.738684i \(0.735447\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.10144e6 1.32473 0.662364 − 0.749182i \(-0.269553\pi\)
0.662364 + 0.749182i \(0.269553\pi\)
\(354\) 0 0
\(355\) 236392. 0.0995547
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −327508. −0.134118 −0.0670588 − 0.997749i \(-0.521362\pi\)
−0.0670588 + 0.997749i \(0.521362\pi\)
\(360\) 0 0
\(361\) −2.42040e6 −0.977507
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.90980e6 0.750337
\(366\) 0 0
\(367\) 2.86739e6 1.11128 0.555638 − 0.831424i \(-0.312474\pi\)
0.555638 + 0.831424i \(0.312474\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.63435e6 0.616466
\(372\) 0 0
\(373\) 3.58029e6 1.33244 0.666218 − 0.745757i \(-0.267912\pi\)
0.666218 + 0.745757i \(0.267912\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.57537e6 0.570860
\(378\) 0 0
\(379\) −1.64235e6 −0.587310 −0.293655 − 0.955912i \(-0.594872\pi\)
−0.293655 + 0.955912i \(0.594872\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.05698e6 −0.716527 −0.358263 − 0.933621i \(-0.616631\pi\)
−0.358263 + 0.933621i \(0.616631\pi\)
\(384\) 0 0
\(385\) −845936. −0.290861
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −616142. −0.206446 −0.103223 − 0.994658i \(-0.532916\pi\)
−0.103223 + 0.994658i \(0.532916\pi\)
\(390\) 0 0
\(391\) −3.49938e6 −1.15758
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.32440e6 0.749580
\(396\) 0 0
\(397\) 2.19212e6 0.698052 0.349026 − 0.937113i \(-0.386513\pi\)
0.349026 + 0.937113i \(0.386513\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.28454e6 −1.02003 −0.510015 − 0.860165i \(-0.670360\pi\)
−0.510015 + 0.860165i \(0.670360\pi\)
\(402\) 0 0
\(403\) 2.26670e6 0.695236
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.89371e6 0.865903
\(408\) 0 0
\(409\) −3.61219e6 −1.06773 −0.533866 − 0.845569i \(-0.679261\pi\)
−0.533866 + 0.845569i \(0.679261\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −756364. −0.218200
\(414\) 0 0
\(415\) 167128. 0.0476353
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.41489e6 1.50680 0.753398 − 0.657564i \(-0.228413\pi\)
0.753398 + 0.657564i \(0.228413\pi\)
\(420\) 0 0
\(421\) 3.60629e6 0.991644 0.495822 − 0.868424i \(-0.334867\pi\)
0.495822 + 0.868424i \(0.334867\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.87432e6 1.04045
\(426\) 0 0
\(427\) −1.80134e6 −0.478107
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.78214e6 −0.721416 −0.360708 − 0.932679i \(-0.617465\pi\)
−0.360708 + 0.932679i \(0.617465\pi\)
\(432\) 0 0
\(433\) 6.27619e6 1.60871 0.804353 − 0.594152i \(-0.202512\pi\)
0.804353 + 0.594152i \(0.202512\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −522032. −0.130766
\(438\) 0 0
\(439\) −641592. −0.158890 −0.0794452 − 0.996839i \(-0.525315\pi\)
−0.0794452 + 0.996839i \(0.525315\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.05546e6 1.46601 0.733006 − 0.680222i \(-0.238117\pi\)
0.733006 + 0.680222i \(0.238117\pi\)
\(444\) 0 0
\(445\) −3.18911e6 −0.763430
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.16681e6 1.20950 0.604752 − 0.796414i \(-0.293272\pi\)
0.604752 + 0.796414i \(0.293272\pi\)
\(450\) 0 0
\(451\) −6.99989e6 −1.62050
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −405132. −0.0917420
\(456\) 0 0
\(457\) −227798. −0.0510222 −0.0255111 − 0.999675i \(-0.508121\pi\)
−0.0255111 + 0.999675i \(0.508121\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −585146. −0.128237 −0.0641183 − 0.997942i \(-0.520423\pi\)
−0.0641183 + 0.997942i \(0.520423\pi\)
\(462\) 0 0
\(463\) 3.41454e6 0.740251 0.370126 − 0.928982i \(-0.379315\pi\)
0.370126 + 0.928982i \(0.379315\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 716300. 0.151986 0.0759929 − 0.997108i \(-0.475787\pi\)
0.0759929 + 0.997108i \(0.475787\pi\)
\(468\) 0 0
\(469\) −2.00763e6 −0.421455
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.61213e6 1.15339
\(474\) 0 0
\(475\) 577964. 0.117535
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.24092e6 1.04368 0.521842 − 0.853042i \(-0.325245\pi\)
0.521842 + 0.853042i \(0.325245\pi\)
\(480\) 0 0
\(481\) 1.38584e6 0.273119
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −555620. −0.107256
\(486\) 0 0
\(487\) −1.11702e6 −0.213421 −0.106710 − 0.994290i \(-0.534032\pi\)
−0.106710 + 0.994290i \(0.534032\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.34458e6 0.251699 0.125850 − 0.992049i \(-0.459834\pi\)
0.125850 + 0.992049i \(0.459834\pi\)
\(492\) 0 0
\(493\) −7.83723e6 −1.45226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −445508. −0.0809030
\(498\) 0 0
\(499\) 6.54648e6 1.17695 0.588473 − 0.808517i \(-0.299729\pi\)
0.588473 + 0.808517i \(0.299729\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8.22050e6 −1.44870 −0.724350 − 0.689432i \(-0.757860\pi\)
−0.724350 + 0.689432i \(0.757860\pi\)
\(504\) 0 0
\(505\) −957164. −0.167016
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.11045e6 0.874308 0.437154 − 0.899387i \(-0.355987\pi\)
0.437154 + 0.899387i \(0.355987\pi\)
\(510\) 0 0
\(511\) −3.59925e6 −0.609760
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.71773e6 0.451531
\(516\) 0 0
\(517\) 3.55373e6 0.584733
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.69999e6 −1.56559 −0.782793 − 0.622282i \(-0.786206\pi\)
−0.782793 + 0.622282i \(0.786206\pi\)
\(522\) 0 0
\(523\) 3.17295e6 0.507234 0.253617 − 0.967305i \(-0.418380\pi\)
0.253617 + 0.967305i \(0.418380\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.12765e7 −1.76867
\(528\) 0 0
\(529\) −1.54340e6 −0.239794
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.35236e6 −0.511131
\(534\) 0 0
\(535\) −5.57544e6 −0.842160
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.59426e6 0.236368
\(540\) 0 0
\(541\) −6.62575e6 −0.973289 −0.486644 − 0.873600i \(-0.661779\pi\)
−0.486644 + 0.873600i \(0.661779\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −748748. −0.107980
\(546\) 0 0
\(547\) −3.84707e6 −0.549745 −0.274873 − 0.961481i \(-0.588636\pi\)
−0.274873 + 0.961481i \(0.588636\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.16914e6 −0.164055
\(552\) 0 0
\(553\) −4.38060e6 −0.609145
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.00176e6 −0.683101 −0.341550 − 0.939863i \(-0.610952\pi\)
−0.341550 + 0.939863i \(0.610952\pi\)
\(558\) 0 0
\(559\) 2.68774e6 0.363795
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.27772e6 0.302852 0.151426 − 0.988469i \(-0.451614\pi\)
0.151426 + 0.988469i \(0.451614\pi\)
\(564\) 0 0
\(565\) −1.45636e6 −0.191933
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.86979e6 −1.14850 −0.574252 − 0.818678i \(-0.694707\pi\)
−0.574252 + 0.818678i \(0.694707\pi\)
\(570\) 0 0
\(571\) −1.40102e7 −1.79826 −0.899132 − 0.437678i \(-0.855801\pi\)
−0.899132 + 0.437678i \(0.855801\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.41719e6 −0.683289
\(576\) 0 0
\(577\) 8.75327e6 1.09454 0.547269 − 0.836957i \(-0.315668\pi\)
0.547269 + 0.836957i \(0.315668\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −314972. −0.0387108
\(582\) 0 0
\(583\) 2.21471e7 2.69864
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.06117e7 −1.27113 −0.635564 − 0.772048i \(-0.719232\pi\)
−0.635564 + 0.772048i \(0.719232\pi\)
\(588\) 0 0
\(589\) −1.68221e6 −0.199798
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.88552e6 −0.220188 −0.110094 − 0.993921i \(-0.535115\pi\)
−0.110094 + 0.993921i \(0.535115\pi\)
\(594\) 0 0
\(595\) 2.01547e6 0.233391
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.27256e7 1.44915 0.724573 − 0.689198i \(-0.242037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(600\) 0 0
\(601\) 7.18846e6 0.811801 0.405900 − 0.913917i \(-0.366958\pi\)
0.405900 + 0.913917i \(0.366958\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.27597e6 −0.808170
\(606\) 0 0
\(607\) −1.08494e7 −1.19519 −0.597593 − 0.801800i \(-0.703876\pi\)
−0.597593 + 0.801800i \(0.703876\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.70194e6 0.184434
\(612\) 0 0
\(613\) −4.90511e6 −0.527227 −0.263614 − 0.964628i \(-0.584914\pi\)
−0.263614 + 0.964628i \(0.584914\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.58445e6 −0.273310 −0.136655 − 0.990619i \(-0.543635\pi\)
−0.136655 + 0.990619i \(0.543635\pi\)
\(618\) 0 0
\(619\) 4.99336e6 0.523801 0.261901 − 0.965095i \(-0.415651\pi\)
0.261901 + 0.965095i \(0.415651\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.01024e6 0.620400
\(624\) 0 0
\(625\) 3.88510e6 0.397834
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.89436e6 −0.694812
\(630\) 0 0
\(631\) 1.18219e7 1.18199 0.590997 − 0.806674i \(-0.298735\pi\)
0.590997 + 0.806674i \(0.298735\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.82040e6 0.474404
\(636\) 0 0
\(637\) 763518. 0.0745540
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.47007e6 0.525833 0.262916 − 0.964819i \(-0.415316\pi\)
0.262916 + 0.964819i \(0.415316\pi\)
\(642\) 0 0
\(643\) −9.64934e6 −0.920386 −0.460193 − 0.887819i \(-0.652220\pi\)
−0.460193 + 0.887819i \(0.652220\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 292368. 0.0274580 0.0137290 − 0.999906i \(-0.495630\pi\)
0.0137290 + 0.999906i \(0.495630\pi\)
\(648\) 0 0
\(649\) −1.02495e7 −0.955193
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.94081e6 −0.636982 −0.318491 − 0.947926i \(-0.603176\pi\)
−0.318491 + 0.947926i \(0.603176\pi\)
\(654\) 0 0
\(655\) −1.67783e6 −0.152808
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.32912e7 −1.19221 −0.596104 − 0.802908i \(-0.703285\pi\)
−0.596104 + 0.802908i \(0.703285\pi\)
\(660\) 0 0
\(661\) 2.05219e6 0.182690 0.0913448 − 0.995819i \(-0.470883\pi\)
0.0913448 + 0.995819i \(0.470883\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 300664. 0.0263650
\(666\) 0 0
\(667\) 1.09582e7 0.953732
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.44100e7 −2.09296
\(672\) 0 0
\(673\) −1.57039e7 −1.33650 −0.668252 − 0.743935i \(-0.732957\pi\)
−0.668252 + 0.743935i \(0.732957\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 969534. 0.0813002 0.0406501 − 0.999173i \(-0.487057\pi\)
0.0406501 + 0.999173i \(0.487057\pi\)
\(678\) 0 0
\(679\) 1.04713e6 0.0871618
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.49908e7 −1.22962 −0.614812 − 0.788673i \(-0.710768\pi\)
−0.614812 + 0.788673i \(0.710768\pi\)
\(684\) 0 0
\(685\) 3.97618e6 0.323772
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.06066e7 0.851191
\(690\) 0 0
\(691\) 7.16038e6 0.570481 0.285240 − 0.958456i \(-0.407927\pi\)
0.285240 + 0.958456i \(0.407927\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.92996e6 −0.701274
\(696\) 0 0
\(697\) 1.66774e7 1.30031
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 91834.0 0.00705844 0.00352922 − 0.999994i \(-0.498877\pi\)
0.00352922 + 0.999994i \(0.498877\pi\)
\(702\) 0 0
\(703\) −1.02849e6 −0.0784894
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.80389e6 0.135725
\(708\) 0 0
\(709\) 2.20981e7 1.65097 0.825487 − 0.564422i \(-0.190901\pi\)
0.825487 + 0.564422i \(0.190901\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.57671e7 1.16153
\(714\) 0 0
\(715\) −5.48995e6 −0.401609
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.58388e7 1.14262 0.571308 − 0.820736i \(-0.306436\pi\)
0.571308 + 0.820736i \(0.306436\pi\)
\(720\) 0 0
\(721\) −5.12187e6 −0.366936
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.21323e7 −0.857235
\(726\) 0 0
\(727\) −6.31418e6 −0.443078 −0.221539 − 0.975151i \(-0.571108\pi\)
−0.221539 + 0.975151i \(0.571108\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.33711e7 −0.925492
\(732\) 0 0
\(733\) 6.93003e6 0.476404 0.238202 − 0.971216i \(-0.423442\pi\)
0.238202 + 0.971216i \(0.423442\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.72054e7 −1.84496
\(738\) 0 0
\(739\) −1.42331e7 −0.958714 −0.479357 − 0.877620i \(-0.659130\pi\)
−0.479357 + 0.877620i \(0.659130\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.94460e6 −0.395048 −0.197524 − 0.980298i \(-0.563290\pi\)
−0.197524 + 0.980298i \(0.563290\pi\)
\(744\) 0 0
\(745\) −4.54631e6 −0.300102
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.05076e7 0.684380
\(750\) 0 0
\(751\) 682752. 0.0441736 0.0220868 − 0.999756i \(-0.492969\pi\)
0.0220868 + 0.999756i \(0.492969\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.17664e7 −0.751233
\(756\) 0 0
\(757\) 1.46333e7 0.928116 0.464058 − 0.885805i \(-0.346393\pi\)
0.464058 + 0.885805i \(0.346393\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.16367e7 0.728399 0.364200 − 0.931321i \(-0.381343\pi\)
0.364200 + 0.931321i \(0.381343\pi\)
\(762\) 0 0
\(763\) 1.41110e6 0.0877500
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.90865e6 −0.301282
\(768\) 0 0
\(769\) 1.91472e7 1.16759 0.583793 − 0.811902i \(-0.301568\pi\)
0.583793 + 0.811902i \(0.301568\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.39261e6 0.324601 0.162301 − 0.986741i \(-0.448109\pi\)
0.162301 + 0.986741i \(0.448109\pi\)
\(774\) 0 0
\(775\) −1.74565e7 −1.04400
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.48791e6 0.146890
\(780\) 0 0
\(781\) −6.03709e6 −0.354160
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.29757e7 0.751549
\(786\) 0 0
\(787\) −3.04348e6 −0.175159 −0.0875796 − 0.996158i \(-0.527913\pi\)
−0.0875796 + 0.996158i \(0.527913\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.74469e6 0.155974
\(792\) 0 0
\(793\) −1.16903e7 −0.660151
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.29652e7 −1.28063 −0.640316 − 0.768111i \(-0.721197\pi\)
−0.640316 + 0.768111i \(0.721197\pi\)
\(798\) 0 0
\(799\) −8.46686e6 −0.469197
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.87735e7 −2.66928
\(804\) 0 0
\(805\) −2.81809e6 −0.153273
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.90787e7 −1.02489 −0.512445 − 0.858720i \(-0.671260\pi\)
−0.512445 + 0.858720i \(0.671260\pi\)
\(810\) 0 0
\(811\) −1.09414e7 −0.584147 −0.292074 − 0.956396i \(-0.594345\pi\)
−0.292074 + 0.956396i \(0.594345\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.23653e7 −0.652094
\(816\) 0 0
\(817\) −1.99467e6 −0.104548
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.12594e7 −1.10076 −0.550380 − 0.834914i \(-0.685517\pi\)
−0.550380 + 0.834914i \(0.685517\pi\)
\(822\) 0 0
\(823\) 1.42256e7 0.732103 0.366052 − 0.930595i \(-0.380709\pi\)
0.366052 + 0.930595i \(0.380709\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.76103e6 0.140381 0.0701904 − 0.997534i \(-0.477639\pi\)
0.0701904 + 0.997534i \(0.477639\pi\)
\(828\) 0 0
\(829\) −3.82147e7 −1.93127 −0.965637 − 0.259895i \(-0.916312\pi\)
−0.965637 + 0.259895i \(0.916312\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.79838e6 −0.189665
\(834\) 0 0
\(835\) −3.12582e6 −0.155149
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.06044e7 0.520094 0.260047 − 0.965596i \(-0.416262\pi\)
0.260047 + 0.965596i \(0.416262\pi\)
\(840\) 0 0
\(841\) 4.03097e6 0.196526
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.02439e6 0.338429
\(846\) 0 0
\(847\) 1.37124e7 0.656758
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.63990e6 0.456298
\(852\) 0 0
\(853\) −4.07009e7 −1.91527 −0.957637 − 0.287977i \(-0.907017\pi\)
−0.957637 + 0.287977i \(0.907017\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.10120e7 1.44237 0.721187 − 0.692741i \(-0.243597\pi\)
0.721187 + 0.692741i \(0.243597\pi\)
\(858\) 0 0
\(859\) −1.09104e7 −0.504495 −0.252247 − 0.967663i \(-0.581170\pi\)
−0.252247 + 0.967663i \(0.581170\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.04089e7 0.475751 0.237875 − 0.971296i \(-0.423549\pi\)
0.237875 + 0.971296i \(0.423549\pi\)
\(864\) 0 0
\(865\) 1.32307e7 0.601234
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.93616e7 −2.66659
\(870\) 0 0
\(871\) −1.30291e7 −0.581928
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 7.10128e6 0.313557
\(876\) 0 0
\(877\) 1.64064e7 0.720299 0.360150 − 0.932895i \(-0.382726\pi\)
0.360150 + 0.932895i \(0.382726\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.48577e7 −0.644927 −0.322464 − 0.946582i \(-0.604511\pi\)
−0.322464 + 0.946582i \(0.604511\pi\)
\(882\) 0 0
\(883\) 2.72018e7 1.17407 0.587037 − 0.809560i \(-0.300294\pi\)
0.587037 + 0.809560i \(0.300294\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.71242e7 1.15757 0.578785 − 0.815480i \(-0.303527\pi\)
0.578785 + 0.815480i \(0.303527\pi\)
\(888\) 0 0
\(889\) −9.08460e6 −0.385524
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.26307e6 −0.0530029
\(894\) 0 0
\(895\) −1.26766e7 −0.528986
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.53121e7 1.45722
\(900\) 0 0
\(901\) −5.27660e7 −2.16542
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.41547e7 0.574484
\(906\) 0 0
\(907\) 8.42269e6 0.339964 0.169982 − 0.985447i \(-0.445629\pi\)
0.169982 + 0.985447i \(0.445629\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.08637e7 1.23212 0.616060 − 0.787700i \(-0.288728\pi\)
0.616060 + 0.787700i \(0.288728\pi\)
\(912\) 0 0
\(913\) −4.26819e6 −0.169460
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.16207e6 0.124179
\(918\) 0 0
\(919\) −4.93895e6 −0.192906 −0.0964531 − 0.995338i \(-0.530750\pi\)
−0.0964531 + 0.995338i \(0.530750\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.89126e6 −0.111707
\(924\) 0 0
\(925\) −1.06727e7 −0.410130
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −5.62575e6 −0.213866 −0.106933 − 0.994266i \(-0.534103\pi\)
−0.106933 + 0.994266i \(0.534103\pi\)
\(930\) 0 0
\(931\) −566636. −0.0214255
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.73116e7 1.02169
\(936\) 0 0
\(937\) 2.60073e7 0.967714 0.483857 − 0.875147i \(-0.339236\pi\)
0.483857 + 0.875147i \(0.339236\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.02160e6 −0.111241 −0.0556203 − 0.998452i \(-0.517714\pi\)
−0.0556203 + 0.998452i \(0.517714\pi\)
\(942\) 0 0
\(943\) −2.33189e7 −0.853943
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.48282e7 −1.26199 −0.630995 − 0.775787i \(-0.717353\pi\)
−0.630995 + 0.775787i \(0.717353\pi\)
\(948\) 0 0
\(949\) −2.33584e7 −0.841932
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.39009e6 0.334917 0.167459 − 0.985879i \(-0.446444\pi\)
0.167459 + 0.985879i \(0.446444\pi\)
\(954\) 0 0
\(955\) −9.78650e6 −0.347232
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.49357e6 −0.263113
\(960\) 0 0
\(961\) 2.21792e7 0.774708
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.19686e7 −0.759423
\(966\) 0 0
\(967\) −1.44768e7 −0.497860 −0.248930 − 0.968521i \(-0.580079\pi\)
−0.248930 + 0.968521i \(0.580079\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 9.24976e6 0.314834 0.157417 − 0.987532i \(-0.449683\pi\)
0.157417 + 0.987532i \(0.449683\pi\)
\(972\) 0 0
\(973\) 1.68295e7 0.569889
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.97780e7 1.66840 0.834202 − 0.551459i \(-0.185929\pi\)
0.834202 + 0.551459i \(0.185929\pi\)
\(978\) 0 0
\(979\) 8.14449e7 2.71586
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8.95601e6 −0.295618 −0.147809 − 0.989016i \(-0.547222\pi\)
−0.147809 + 0.989016i \(0.547222\pi\)
\(984\) 0 0
\(985\) −1.28126e7 −0.420773
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.86958e7 0.607790
\(990\) 0 0
\(991\) −2.62400e7 −0.848751 −0.424376 − 0.905486i \(-0.639506\pi\)
−0.424376 + 0.905486i \(0.639506\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.37842e7 −0.761606
\(996\) 0 0
\(997\) 2.80506e7 0.893727 0.446863 − 0.894602i \(-0.352541\pi\)
0.446863 + 0.894602i \(0.352541\pi\)
\(998\) 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.j.1.1 1
3.2 odd 2 336.6.a.h.1.1 1
4.3 odd 2 126.6.a.i.1.1 1
12.11 even 2 42.6.a.d.1.1 ✓ 1
28.27 even 2 882.6.a.s.1.1 1
60.23 odd 4 1050.6.g.i.799.2 2
60.47 odd 4 1050.6.g.i.799.1 2
60.59 even 2 1050.6.a.k.1.1 1
84.11 even 6 294.6.e.i.79.1 2
84.23 even 6 294.6.e.i.67.1 2
84.47 odd 6 294.6.e.p.67.1 2
84.59 odd 6 294.6.e.p.79.1 2
84.83 odd 2 294.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.d.1.1 ✓ 1 12.11 even 2
126.6.a.i.1.1 1 4.3 odd 2
294.6.a.b.1.1 1 84.83 odd 2
294.6.e.i.67.1 2 84.23 even 6
294.6.e.i.79.1 2 84.11 even 6
294.6.e.p.67.1 2 84.47 odd 6
294.6.e.p.79.1 2 84.59 odd 6
336.6.a.h.1.1 1 3.2 odd 2
882.6.a.s.1.1 1 28.27 even 2
1008.6.a.j.1.1 1 1.1 even 1 trivial
1050.6.a.k.1.1 1 60.59 even 2
1050.6.g.i.799.1 2 60.47 odd 4
1050.6.g.i.799.2 2 60.23 odd 4