Properties

Label 1008.6.a.h.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $2$
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: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
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)
 
\(f(q)\) \(=\) \(q-32.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-32.0000 q^{5} -49.0000 q^{7} -624.000 q^{11} -708.000 q^{13} -934.000 q^{17} -1858.00 q^{19} -1120.00 q^{23} -2101.00 q^{25} +1174.00 q^{29} -2908.00 q^{31} +1568.00 q^{35} -12462.0 q^{37} -2662.00 q^{41} +7144.00 q^{43} -7468.00 q^{47} +2401.00 q^{49} +27274.0 q^{53} +19968.0 q^{55} +2490.00 q^{59} -11096.0 q^{61} +22656.0 q^{65} -39756.0 q^{67} -69888.0 q^{71} +16450.0 q^{73} +30576.0 q^{77} -78376.0 q^{79} +109818. q^{83} +29888.0 q^{85} +56966.0 q^{89} +34692.0 q^{91} +59456.0 q^{95} -115946. q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −32.0000 −0.572433 −0.286217 0.958165i \(-0.592398\pi\)
−0.286217 + 0.958165i \(0.592398\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −624.000 −1.55490 −0.777451 0.628944i \(-0.783488\pi\)
−0.777451 + 0.628944i \(0.783488\pi\)
\(12\) 0 0
\(13\) −708.000 −1.16192 −0.580958 0.813933i \(-0.697322\pi\)
−0.580958 + 0.813933i \(0.697322\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −934.000 −0.783835 −0.391917 0.920000i \(-0.628188\pi\)
−0.391917 + 0.920000i \(0.628188\pi\)
\(18\) 0 0
\(19\) −1858.00 −1.18076 −0.590380 0.807125i \(-0.701022\pi\)
−0.590380 + 0.807125i \(0.701022\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1120.00 −0.441467 −0.220734 0.975334i \(-0.570845\pi\)
−0.220734 + 0.975334i \(0.570845\pi\)
\(24\) 0 0
\(25\) −2101.00 −0.672320
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1174.00 0.259223 0.129611 0.991565i \(-0.458627\pi\)
0.129611 + 0.991565i \(0.458627\pi\)
\(30\) 0 0
\(31\) −2908.00 −0.543488 −0.271744 0.962370i \(-0.587600\pi\)
−0.271744 + 0.962370i \(0.587600\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1568.00 0.216359
\(36\) 0 0
\(37\) −12462.0 −1.49652 −0.748262 0.663404i \(-0.769111\pi\)
−0.748262 + 0.663404i \(0.769111\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2662.00 −0.247314 −0.123657 0.992325i \(-0.539462\pi\)
−0.123657 + 0.992325i \(0.539462\pi\)
\(42\) 0 0
\(43\) 7144.00 0.589210 0.294605 0.955619i \(-0.404812\pi\)
0.294605 + 0.955619i \(0.404812\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7468.00 −0.493128 −0.246564 0.969127i \(-0.579302\pi\)
−0.246564 + 0.969127i \(0.579302\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 27274.0 1.33370 0.666852 0.745191i \(-0.267642\pi\)
0.666852 + 0.745191i \(0.267642\pi\)
\(54\) 0 0
\(55\) 19968.0 0.890078
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2490.00 0.0931257 0.0465628 0.998915i \(-0.485173\pi\)
0.0465628 + 0.998915i \(0.485173\pi\)
\(60\) 0 0
\(61\) −11096.0 −0.381805 −0.190903 0.981609i \(-0.561141\pi\)
−0.190903 + 0.981609i \(0.561141\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 22656.0 0.665120
\(66\) 0 0
\(67\) −39756.0 −1.08197 −0.540986 0.841032i \(-0.681949\pi\)
−0.540986 + 0.841032i \(0.681949\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −69888.0 −1.64534 −0.822672 0.568516i \(-0.807518\pi\)
−0.822672 + 0.568516i \(0.807518\pi\)
\(72\) 0 0
\(73\) 16450.0 0.361292 0.180646 0.983548i \(-0.442181\pi\)
0.180646 + 0.983548i \(0.442181\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 30576.0 0.587698
\(78\) 0 0
\(79\) −78376.0 −1.41291 −0.706456 0.707757i \(-0.749707\pi\)
−0.706456 + 0.707757i \(0.749707\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 109818. 1.74976 0.874880 0.484340i \(-0.160940\pi\)
0.874880 + 0.484340i \(0.160940\pi\)
\(84\) 0 0
\(85\) 29888.0 0.448693
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56966.0 0.762326 0.381163 0.924508i \(-0.375524\pi\)
0.381163 + 0.924508i \(0.375524\pi\)
\(90\) 0 0
\(91\) 34692.0 0.439163
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 59456.0 0.675907
\(96\) 0 0
\(97\) −115946. −1.25120 −0.625600 0.780144i \(-0.715146\pi\)
−0.625600 + 0.780144i \(0.715146\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8352.00 −0.0814680 −0.0407340 0.999170i \(-0.512970\pi\)
−0.0407340 + 0.999170i \(0.512970\pi\)
\(102\) 0 0
\(103\) −179484. −1.66699 −0.833494 0.552528i \(-0.813663\pi\)
−0.833494 + 0.552528i \(0.813663\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −53892.0 −0.455056 −0.227528 0.973772i \(-0.573064\pi\)
−0.227528 + 0.973772i \(0.573064\pi\)
\(108\) 0 0
\(109\) 105970. 0.854312 0.427156 0.904178i \(-0.359515\pi\)
0.427156 + 0.904178i \(0.359515\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2502.00 −0.0184328 −0.00921640 0.999958i \(-0.502934\pi\)
−0.00921640 + 0.999958i \(0.502934\pi\)
\(114\) 0 0
\(115\) 35840.0 0.252711
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 45766.0 0.296262
\(120\) 0 0
\(121\) 228325. 1.41772
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 167232. 0.957292
\(126\) 0 0
\(127\) −287792. −1.58332 −0.791661 0.610960i \(-0.790784\pi\)
−0.791661 + 0.610960i \(0.790784\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −47662.0 −0.242658 −0.121329 0.992612i \(-0.538716\pi\)
−0.121329 + 0.992612i \(0.538716\pi\)
\(132\) 0 0
\(133\) 91042.0 0.446285
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −223154. −1.01579 −0.507894 0.861419i \(-0.669576\pi\)
−0.507894 + 0.861419i \(0.669576\pi\)
\(138\) 0 0
\(139\) −250542. −1.09988 −0.549938 0.835206i \(-0.685349\pi\)
−0.549938 + 0.835206i \(0.685349\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 441792. 1.80667
\(144\) 0 0
\(145\) −37568.0 −0.148388
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 487394. 1.79852 0.899258 0.437418i \(-0.144107\pi\)
0.899258 + 0.437418i \(0.144107\pi\)
\(150\) 0 0
\(151\) 54680.0 0.195158 0.0975790 0.995228i \(-0.468890\pi\)
0.0975790 + 0.995228i \(0.468890\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 93056.0 0.311111
\(156\) 0 0
\(157\) 211068. 0.683397 0.341699 0.939810i \(-0.388998\pi\)
0.341699 + 0.939810i \(0.388998\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 54880.0 0.166859
\(162\) 0 0
\(163\) 20192.0 0.0595265 0.0297632 0.999557i \(-0.490525\pi\)
0.0297632 + 0.999557i \(0.490525\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4524.00 −0.0125525 −0.00627627 0.999980i \(-0.501998\pi\)
−0.00627627 + 0.999980i \(0.501998\pi\)
\(168\) 0 0
\(169\) 129971. 0.350050
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 104332. 0.265034 0.132517 0.991181i \(-0.457694\pi\)
0.132517 + 0.991181i \(0.457694\pi\)
\(174\) 0 0
\(175\) 102949. 0.254113
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −201724. −0.470571 −0.235285 0.971926i \(-0.575602\pi\)
−0.235285 + 0.971926i \(0.575602\pi\)
\(180\) 0 0
\(181\) 655700. 1.48768 0.743839 0.668359i \(-0.233003\pi\)
0.743839 + 0.668359i \(0.233003\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 398784. 0.856660
\(186\) 0 0
\(187\) 582816. 1.21879
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −151496. −0.300482 −0.150241 0.988649i \(-0.548005\pi\)
−0.150241 + 0.988649i \(0.548005\pi\)
\(192\) 0 0
\(193\) 229326. 0.443159 0.221580 0.975142i \(-0.428879\pi\)
0.221580 + 0.975142i \(0.428879\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −421086. −0.773046 −0.386523 0.922280i \(-0.626324\pi\)
−0.386523 + 0.922280i \(0.626324\pi\)
\(198\) 0 0
\(199\) −197300. −0.353179 −0.176589 0.984285i \(-0.556506\pi\)
−0.176589 + 0.984285i \(0.556506\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −57526.0 −0.0979770
\(204\) 0 0
\(205\) 85184.0 0.141571
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.15939e6 1.83597
\(210\) 0 0
\(211\) −679052. −1.05002 −0.525009 0.851097i \(-0.675938\pi\)
−0.525009 + 0.851097i \(0.675938\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −228608. −0.337284
\(216\) 0 0
\(217\) 142492. 0.205419
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 661272. 0.910751
\(222\) 0 0
\(223\) 184440. 0.248366 0.124183 0.992259i \(-0.460369\pi\)
0.124183 + 0.992259i \(0.460369\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −868078. −1.11813 −0.559067 0.829122i \(-0.688841\pi\)
−0.559067 + 0.829122i \(0.688841\pi\)
\(228\) 0 0
\(229\) −593860. −0.748334 −0.374167 0.927361i \(-0.622071\pi\)
−0.374167 + 0.927361i \(0.622071\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −48218.0 −0.0581861 −0.0290931 0.999577i \(-0.509262\pi\)
−0.0290931 + 0.999577i \(0.509262\pi\)
\(234\) 0 0
\(235\) 238976. 0.282283
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 241688. 0.273691 0.136845 0.990592i \(-0.456304\pi\)
0.136845 + 0.990592i \(0.456304\pi\)
\(240\) 0 0
\(241\) 565270. 0.626922 0.313461 0.949601i \(-0.398512\pi\)
0.313461 + 0.949601i \(0.398512\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −76832.0 −0.0817762
\(246\) 0 0
\(247\) 1.31546e6 1.37194
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.43775e6 −1.44045 −0.720224 0.693741i \(-0.755961\pi\)
−0.720224 + 0.693741i \(0.755961\pi\)
\(252\) 0 0
\(253\) 698880. 0.686438
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −494802. −0.467303 −0.233652 0.972320i \(-0.575067\pi\)
−0.233652 + 0.972320i \(0.575067\pi\)
\(258\) 0 0
\(259\) 610638. 0.565633
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.55654e6 1.38762 0.693812 0.720156i \(-0.255930\pi\)
0.693812 + 0.720156i \(0.255930\pi\)
\(264\) 0 0
\(265\) −872768. −0.763456
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.36204e6 −1.14765 −0.573823 0.818979i \(-0.694540\pi\)
−0.573823 + 0.818979i \(0.694540\pi\)
\(270\) 0 0
\(271\) −558320. −0.461806 −0.230903 0.972977i \(-0.574168\pi\)
−0.230903 + 0.972977i \(0.574168\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.31102e6 1.04539
\(276\) 0 0
\(277\) 586342. 0.459147 0.229573 0.973291i \(-0.426267\pi\)
0.229573 + 0.973291i \(0.426267\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −606234. −0.458010 −0.229005 0.973425i \(-0.573547\pi\)
−0.229005 + 0.973425i \(0.573547\pi\)
\(282\) 0 0
\(283\) 865174. 0.642151 0.321076 0.947054i \(-0.395956\pi\)
0.321076 + 0.947054i \(0.395956\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 130438. 0.0934758
\(288\) 0 0
\(289\) −547501. −0.385603
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 353352. 0.240458 0.120229 0.992746i \(-0.461637\pi\)
0.120229 + 0.992746i \(0.461637\pi\)
\(294\) 0 0
\(295\) −79680.0 −0.0533082
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 792960. 0.512948
\(300\) 0 0
\(301\) −350056. −0.222701
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 355072. 0.218558
\(306\) 0 0
\(307\) 1.95904e6 1.18631 0.593153 0.805090i \(-0.297883\pi\)
0.593153 + 0.805090i \(0.297883\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.06257e6 1.79550 0.897749 0.440508i \(-0.145202\pi\)
0.897749 + 0.440508i \(0.145202\pi\)
\(312\) 0 0
\(313\) −582634. −0.336151 −0.168076 0.985774i \(-0.553755\pi\)
−0.168076 + 0.985774i \(0.553755\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.09585e6 1.73034 0.865171 0.501478i \(-0.167210\pi\)
0.865171 + 0.501478i \(0.167210\pi\)
\(318\) 0 0
\(319\) −732576. −0.403066
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.73537e6 0.925521
\(324\) 0 0
\(325\) 1.48751e6 0.781180
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 365932. 0.186385
\(330\) 0 0
\(331\) −625496. −0.313801 −0.156901 0.987614i \(-0.550150\pi\)
−0.156901 + 0.987614i \(0.550150\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.27219e6 0.619356
\(336\) 0 0
\(337\) 2.32494e6 1.11516 0.557580 0.830123i \(-0.311730\pi\)
0.557580 + 0.830123i \(0.311730\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.81459e6 0.845071
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −781128. −0.348256 −0.174128 0.984723i \(-0.555711\pi\)
−0.174128 + 0.984723i \(0.555711\pi\)
\(348\) 0 0
\(349\) 1.48586e6 0.653002 0.326501 0.945197i \(-0.394130\pi\)
0.326501 + 0.945197i \(0.394130\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.44463e6 −0.617048 −0.308524 0.951217i \(-0.599835\pi\)
−0.308524 + 0.951217i \(0.599835\pi\)
\(354\) 0 0
\(355\) 2.23642e6 0.941850
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 404040. 0.165458 0.0827291 0.996572i \(-0.473636\pi\)
0.0827291 + 0.996572i \(0.473636\pi\)
\(360\) 0 0
\(361\) 976065. 0.394195
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −526400. −0.206816
\(366\) 0 0
\(367\) 2.71698e6 1.05298 0.526492 0.850180i \(-0.323507\pi\)
0.526492 + 0.850180i \(0.323507\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.33643e6 −0.504092
\(372\) 0 0
\(373\) −1.79399e6 −0.667647 −0.333824 0.942636i \(-0.608339\pi\)
−0.333824 + 0.942636i \(0.608339\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −831192. −0.301195
\(378\) 0 0
\(379\) 18624.0 0.00666001 0.00333001 0.999994i \(-0.498940\pi\)
0.00333001 + 0.999994i \(0.498940\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.33004e6 −0.463307 −0.231654 0.972798i \(-0.574414\pi\)
−0.231654 + 0.972798i \(0.574414\pi\)
\(384\) 0 0
\(385\) −978432. −0.336418
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.26506e6 −0.758936 −0.379468 0.925205i \(-0.623893\pi\)
−0.379468 + 0.925205i \(0.623893\pi\)
\(390\) 0 0
\(391\) 1.04608e6 0.346037
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.50803e6 0.808798
\(396\) 0 0
\(397\) −4.48900e6 −1.42947 −0.714733 0.699398i \(-0.753452\pi\)
−0.714733 + 0.699398i \(0.753452\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 95442.0 0.0296400 0.0148200 0.999890i \(-0.495282\pi\)
0.0148200 + 0.999890i \(0.495282\pi\)
\(402\) 0 0
\(403\) 2.05886e6 0.631488
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.77629e6 2.32695
\(408\) 0 0
\(409\) −2.99003e6 −0.883828 −0.441914 0.897057i \(-0.645700\pi\)
−0.441914 + 0.897057i \(0.645700\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −122010. −0.0351982
\(414\) 0 0
\(415\) −3.51418e6 −1.00162
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.39037e6 0.943436 0.471718 0.881749i \(-0.343634\pi\)
0.471718 + 0.881749i \(0.343634\pi\)
\(420\) 0 0
\(421\) 3.38397e6 0.930512 0.465256 0.885176i \(-0.345962\pi\)
0.465256 + 0.885176i \(0.345962\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.96233e6 0.526988
\(426\) 0 0
\(427\) 543704. 0.144309
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.98353e6 −0.514334 −0.257167 0.966367i \(-0.582789\pi\)
−0.257167 + 0.966367i \(0.582789\pi\)
\(432\) 0 0
\(433\) −7.17581e6 −1.83929 −0.919647 0.392746i \(-0.871525\pi\)
−0.919647 + 0.392746i \(0.871525\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.08096e6 0.521267
\(438\) 0 0
\(439\) 2.44390e6 0.605231 0.302616 0.953113i \(-0.402140\pi\)
0.302616 + 0.953113i \(0.402140\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 231716. 0.0560979 0.0280490 0.999607i \(-0.491071\pi\)
0.0280490 + 0.999607i \(0.491071\pi\)
\(444\) 0 0
\(445\) −1.82291e6 −0.436381
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.73637e6 1.10874 0.554370 0.832271i \(-0.312959\pi\)
0.554370 + 0.832271i \(0.312959\pi\)
\(450\) 0 0
\(451\) 1.66109e6 0.384549
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.11014e6 −0.251392
\(456\) 0 0
\(457\) −7.87486e6 −1.76381 −0.881906 0.471426i \(-0.843740\pi\)
−0.881906 + 0.471426i \(0.843740\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.23218e6 1.80411 0.902054 0.431623i \(-0.142059\pi\)
0.902054 + 0.431623i \(0.142059\pi\)
\(462\) 0 0
\(463\) −2.36038e6 −0.511717 −0.255859 0.966714i \(-0.582358\pi\)
−0.255859 + 0.966714i \(0.582358\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.31700e6 −1.34035 −0.670175 0.742203i \(-0.733781\pi\)
−0.670175 + 0.742203i \(0.733781\pi\)
\(468\) 0 0
\(469\) 1.94804e6 0.408947
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.45786e6 −0.916164
\(474\) 0 0
\(475\) 3.90366e6 0.793849
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.45856e6 0.290459 0.145229 0.989398i \(-0.453608\pi\)
0.145229 + 0.989398i \(0.453608\pi\)
\(480\) 0 0
\(481\) 8.82310e6 1.73883
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.71027e6 0.716228
\(486\) 0 0
\(487\) −9.28782e6 −1.77456 −0.887282 0.461228i \(-0.847409\pi\)
−0.887282 + 0.461228i \(0.847409\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −234972. −0.0439858 −0.0219929 0.999758i \(-0.507001\pi\)
−0.0219929 + 0.999758i \(0.507001\pi\)
\(492\) 0 0
\(493\) −1.09652e6 −0.203188
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.42451e6 0.621882
\(498\) 0 0
\(499\) 7.00792e6 1.25991 0.629953 0.776633i \(-0.283074\pi\)
0.629953 + 0.776633i \(0.283074\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.94752e6 0.871902 0.435951 0.899970i \(-0.356412\pi\)
0.435951 + 0.899970i \(0.356412\pi\)
\(504\) 0 0
\(505\) 267264. 0.0466350
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.50640e6 −0.942049 −0.471025 0.882120i \(-0.656116\pi\)
−0.471025 + 0.882120i \(0.656116\pi\)
\(510\) 0 0
\(511\) −806050. −0.136556
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.74349e6 0.954240
\(516\) 0 0
\(517\) 4.66003e6 0.766765
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.63076e6 −0.263206 −0.131603 0.991303i \(-0.542012\pi\)
−0.131603 + 0.991303i \(0.542012\pi\)
\(522\) 0 0
\(523\) 1.00765e7 1.61086 0.805429 0.592692i \(-0.201935\pi\)
0.805429 + 0.592692i \(0.201935\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.71607e6 0.426005
\(528\) 0 0
\(529\) −5.18194e6 −0.805107
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.88470e6 0.287358
\(534\) 0 0
\(535\) 1.72454e6 0.260489
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.49822e6 −0.222129
\(540\) 0 0
\(541\) −1.25225e7 −1.83949 −0.919746 0.392513i \(-0.871606\pi\)
−0.919746 + 0.392513i \(0.871606\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.39104e6 −0.489037
\(546\) 0 0
\(547\) −6.67430e6 −0.953756 −0.476878 0.878970i \(-0.658232\pi\)
−0.476878 + 0.878970i \(0.658232\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.18129e6 −0.306080
\(552\) 0 0
\(553\) 3.84042e6 0.534031
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.61643e6 0.630475 0.315238 0.949013i \(-0.397916\pi\)
0.315238 + 0.949013i \(0.397916\pi\)
\(558\) 0 0
\(559\) −5.05795e6 −0.684613
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.84218e6 −1.17568 −0.587839 0.808978i \(-0.700021\pi\)
−0.587839 + 0.808978i \(0.700021\pi\)
\(564\) 0 0
\(565\) 80064.0 0.0105515
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.15771e7 −1.49906 −0.749532 0.661968i \(-0.769721\pi\)
−0.749532 + 0.661968i \(0.769721\pi\)
\(570\) 0 0
\(571\) −4.48069e6 −0.575115 −0.287557 0.957763i \(-0.592843\pi\)
−0.287557 + 0.957763i \(0.592843\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.35312e6 0.296807
\(576\) 0 0
\(577\) 1.32788e7 1.66042 0.830212 0.557448i \(-0.188220\pi\)
0.830212 + 0.557448i \(0.188220\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.38108e6 −0.661347
\(582\) 0 0
\(583\) −1.70190e7 −2.07378
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.11188e7 −1.33187 −0.665936 0.746009i \(-0.731968\pi\)
−0.665936 + 0.746009i \(0.731968\pi\)
\(588\) 0 0
\(589\) 5.40306e6 0.641729
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.92737e6 0.458632 0.229316 0.973352i \(-0.426351\pi\)
0.229316 + 0.973352i \(0.426351\pi\)
\(594\) 0 0
\(595\) −1.46451e6 −0.169590
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.74099e7 −1.98258 −0.991289 0.131704i \(-0.957955\pi\)
−0.991289 + 0.131704i \(0.957955\pi\)
\(600\) 0 0
\(601\) 7.46243e6 0.842740 0.421370 0.906889i \(-0.361549\pi\)
0.421370 + 0.906889i \(0.361549\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.30640e6 −0.811549
\(606\) 0 0
\(607\) −701152. −0.0772397 −0.0386198 0.999254i \(-0.512296\pi\)
−0.0386198 + 0.999254i \(0.512296\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.28734e6 0.572974
\(612\) 0 0
\(613\) 1.09575e7 1.17777 0.588886 0.808216i \(-0.299567\pi\)
0.588886 + 0.808216i \(0.299567\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.90666e6 −0.201633 −0.100816 0.994905i \(-0.532145\pi\)
−0.100816 + 0.994905i \(0.532145\pi\)
\(618\) 0 0
\(619\) 2.22346e6 0.233240 0.116620 0.993177i \(-0.462794\pi\)
0.116620 + 0.993177i \(0.462794\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.79133e6 −0.288132
\(624\) 0 0
\(625\) 1.21420e6 0.124334
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.16395e7 1.17303
\(630\) 0 0
\(631\) −752624. −0.0752497 −0.0376248 0.999292i \(-0.511979\pi\)
−0.0376248 + 0.999292i \(0.511979\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.20934e6 0.906347
\(636\) 0 0
\(637\) −1.69991e6 −0.165988
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.45429e6 0.235929 0.117964 0.993018i \(-0.462363\pi\)
0.117964 + 0.993018i \(0.462363\pi\)
\(642\) 0 0
\(643\) −1.58237e7 −1.50932 −0.754660 0.656116i \(-0.772198\pi\)
−0.754660 + 0.656116i \(0.772198\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.65489e6 −0.249337 −0.124668 0.992198i \(-0.539787\pi\)
−0.124668 + 0.992198i \(0.539787\pi\)
\(648\) 0 0
\(649\) −1.55376e6 −0.144801
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.26899e6 −0.850648 −0.425324 0.905041i \(-0.639840\pi\)
−0.425324 + 0.905041i \(0.639840\pi\)
\(654\) 0 0
\(655\) 1.52518e6 0.138905
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.68242e7 −1.50911 −0.754556 0.656235i \(-0.772148\pi\)
−0.754556 + 0.656235i \(0.772148\pi\)
\(660\) 0 0
\(661\) −6.77217e6 −0.602871 −0.301435 0.953487i \(-0.597466\pi\)
−0.301435 + 0.953487i \(0.597466\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.91334e6 −0.255469
\(666\) 0 0
\(667\) −1.31488e6 −0.114438
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.92390e6 0.593669
\(672\) 0 0
\(673\) 7.61315e6 0.647928 0.323964 0.946069i \(-0.394984\pi\)
0.323964 + 0.946069i \(0.394984\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.11672e6 −0.512917 −0.256459 0.966555i \(-0.582556\pi\)
−0.256459 + 0.966555i \(0.582556\pi\)
\(678\) 0 0
\(679\) 5.68135e6 0.472909
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.12588e7 −0.923511 −0.461755 0.887007i \(-0.652780\pi\)
−0.461755 + 0.887007i \(0.652780\pi\)
\(684\) 0 0
\(685\) 7.14093e6 0.581471
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.93100e7 −1.54965
\(690\) 0 0
\(691\) −9.50952e6 −0.757641 −0.378821 0.925470i \(-0.623670\pi\)
−0.378821 + 0.925470i \(0.623670\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.01734e6 0.629605
\(696\) 0 0
\(697\) 2.48631e6 0.193853
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.53868e7 −1.18264 −0.591322 0.806436i \(-0.701394\pi\)
−0.591322 + 0.806436i \(0.701394\pi\)
\(702\) 0 0
\(703\) 2.31544e7 1.76703
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 409248. 0.0307920
\(708\) 0 0
\(709\) −1.21379e6 −0.0906834 −0.0453417 0.998972i \(-0.514438\pi\)
−0.0453417 + 0.998972i \(0.514438\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.25696e6 0.239932
\(714\) 0 0
\(715\) −1.41373e7 −1.03420
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.00002e7 −0.721418 −0.360709 0.932678i \(-0.617465\pi\)
−0.360709 + 0.932678i \(0.617465\pi\)
\(720\) 0 0
\(721\) 8.79472e6 0.630063
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.46657e6 −0.174281
\(726\) 0 0
\(727\) −1.33745e7 −0.938514 −0.469257 0.883062i \(-0.655478\pi\)
−0.469257 + 0.883062i \(0.655478\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.67250e6 −0.461844
\(732\) 0 0
\(733\) 1.61380e7 1.10940 0.554701 0.832050i \(-0.312833\pi\)
0.554701 + 0.832050i \(0.312833\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.48077e7 1.68236
\(738\) 0 0
\(739\) −8.61059e6 −0.579992 −0.289996 0.957028i \(-0.593654\pi\)
−0.289996 + 0.957028i \(0.593654\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.85027e7 −1.89415 −0.947075 0.321012i \(-0.895977\pi\)
−0.947075 + 0.321012i \(0.895977\pi\)
\(744\) 0 0
\(745\) −1.55966e7 −1.02953
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.64071e6 0.171995
\(750\) 0 0
\(751\) 7.28721e6 0.471478 0.235739 0.971816i \(-0.424249\pi\)
0.235739 + 0.971816i \(0.424249\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.74976e6 −0.111715
\(756\) 0 0
\(757\) −2.77165e7 −1.75792 −0.878958 0.476899i \(-0.841761\pi\)
−0.878958 + 0.476899i \(0.841761\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.07625e7 −1.92557 −0.962787 0.270262i \(-0.912890\pi\)
−0.962787 + 0.270262i \(0.912890\pi\)
\(762\) 0 0
\(763\) −5.19253e6 −0.322900
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.76292e6 −0.108204
\(768\) 0 0
\(769\) −1.83665e7 −1.11998 −0.559990 0.828499i \(-0.689195\pi\)
−0.559990 + 0.828499i \(0.689195\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.01397e7 0.610348 0.305174 0.952297i \(-0.401285\pi\)
0.305174 + 0.952297i \(0.401285\pi\)
\(774\) 0 0
\(775\) 6.10971e6 0.365398
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.94600e6 0.292018
\(780\) 0 0
\(781\) 4.36101e7 2.55835
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.75418e6 −0.391199
\(786\) 0 0
\(787\) 1.89442e7 1.09028 0.545140 0.838345i \(-0.316476\pi\)
0.545140 + 0.838345i \(0.316476\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 122598. 0.00696694
\(792\) 0 0
\(793\) 7.85597e6 0.443626
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.19835e7 0.668248 0.334124 0.942529i \(-0.391560\pi\)
0.334124 + 0.942529i \(0.391560\pi\)
\(798\) 0 0
\(799\) 6.97511e6 0.386531
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.02648e7 −0.561774
\(804\) 0 0
\(805\) −1.75616e6 −0.0955156
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.31823e6 0.339410 0.169705 0.985495i \(-0.445719\pi\)
0.169705 + 0.985495i \(0.445719\pi\)
\(810\) 0 0
\(811\) −1.47079e6 −0.0785231 −0.0392615 0.999229i \(-0.512501\pi\)
−0.0392615 + 0.999229i \(0.512501\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −646144. −0.0340750
\(816\) 0 0
\(817\) −1.32736e7 −0.695716
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.10138e7 1.08804 0.544022 0.839071i \(-0.316901\pi\)
0.544022 + 0.839071i \(0.316901\pi\)
\(822\) 0 0
\(823\) 1.35856e7 0.699163 0.349582 0.936906i \(-0.386324\pi\)
0.349582 + 0.936906i \(0.386324\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.62070e7 −1.33246 −0.666230 0.745747i \(-0.732093\pi\)
−0.666230 + 0.745747i \(0.732093\pi\)
\(828\) 0 0
\(829\) −1.17710e7 −0.594876 −0.297438 0.954741i \(-0.596132\pi\)
−0.297438 + 0.954741i \(0.596132\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.24253e6 −0.111976
\(834\) 0 0
\(835\) 144768. 0.00718549
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.44898e7 0.710651 0.355326 0.934743i \(-0.384370\pi\)
0.355326 + 0.934743i \(0.384370\pi\)
\(840\) 0 0
\(841\) −1.91329e7 −0.932804
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.15907e6 −0.200380
\(846\) 0 0
\(847\) −1.11879e7 −0.535847
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.39574e7 0.660666
\(852\) 0 0
\(853\) 1.77865e7 0.836984 0.418492 0.908220i \(-0.362559\pi\)
0.418492 + 0.908220i \(0.362559\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.79124e7 −1.76331 −0.881656 0.471893i \(-0.843571\pi\)
−0.881656 + 0.471893i \(0.843571\pi\)
\(858\) 0 0
\(859\) −3.32376e7 −1.53690 −0.768451 0.639909i \(-0.778972\pi\)
−0.768451 + 0.639909i \(0.778972\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.33166e6 0.106571 0.0532853 0.998579i \(-0.483031\pi\)
0.0532853 + 0.998579i \(0.483031\pi\)
\(864\) 0 0
\(865\) −3.33862e6 −0.151715
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.89066e7 2.19694
\(870\) 0 0
\(871\) 2.81472e7 1.25716
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.19437e6 −0.361822
\(876\) 0 0
\(877\) −3.38189e7 −1.48477 −0.742386 0.669972i \(-0.766306\pi\)
−0.742386 + 0.669972i \(0.766306\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.65707e7 −1.15336 −0.576678 0.816972i \(-0.695651\pi\)
−0.576678 + 0.816972i \(0.695651\pi\)
\(882\) 0 0
\(883\) −1.74913e7 −0.754954 −0.377477 0.926019i \(-0.623208\pi\)
−0.377477 + 0.926019i \(0.623208\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.77452e7 −0.757305 −0.378652 0.925539i \(-0.623612\pi\)
−0.378652 + 0.925539i \(0.623612\pi\)
\(888\) 0 0
\(889\) 1.41018e7 0.598440
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.38755e7 0.582266
\(894\) 0 0
\(895\) 6.45517e6 0.269370
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.41399e6 −0.140885
\(900\) 0 0
\(901\) −2.54739e7 −1.04540
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.09824e7 −0.851596
\(906\) 0 0
\(907\) 2.82335e7 1.13958 0.569792 0.821789i \(-0.307024\pi\)
0.569792 + 0.821789i \(0.307024\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.71757e7 0.685674 0.342837 0.939395i \(-0.388612\pi\)
0.342837 + 0.939395i \(0.388612\pi\)
\(912\) 0 0
\(913\) −6.85264e7 −2.72070
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.33544e6 0.0917160
\(918\) 0 0
\(919\) −2.42273e7 −0.946273 −0.473137 0.880989i \(-0.656878\pi\)
−0.473137 + 0.880989i \(0.656878\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.94807e7 1.91175
\(924\) 0 0
\(925\) 2.61827e7 1.00614
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.45919e7 −0.934874 −0.467437 0.884026i \(-0.654822\pi\)
−0.467437 + 0.884026i \(0.654822\pi\)
\(930\) 0 0
\(931\) −4.46106e6 −0.168680
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.86501e7 −0.697674
\(936\) 0 0
\(937\) −1.31199e7 −0.488181 −0.244090 0.969753i \(-0.578489\pi\)
−0.244090 + 0.969753i \(0.578489\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −640776. −0.0235902 −0.0117951 0.999930i \(-0.503755\pi\)
−0.0117951 + 0.999930i \(0.503755\pi\)
\(942\) 0 0
\(943\) 2.98144e6 0.109181
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.01502e7 0.730135 0.365068 0.930981i \(-0.381046\pi\)
0.365068 + 0.930981i \(0.381046\pi\)
\(948\) 0 0
\(949\) −1.16466e7 −0.419791
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.33217e7 1.18849 0.594244 0.804285i \(-0.297451\pi\)
0.594244 + 0.804285i \(0.297451\pi\)
\(954\) 0 0
\(955\) 4.84787e6 0.172006
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.09345e7 0.383932
\(960\) 0 0
\(961\) −2.01727e7 −0.704621
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −7.33843e6 −0.253679
\(966\) 0 0
\(967\) −4.51857e7 −1.55394 −0.776970 0.629537i \(-0.783245\pi\)
−0.776970 + 0.629537i \(0.783245\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.62935e7 0.894953 0.447477 0.894296i \(-0.352323\pi\)
0.447477 + 0.894296i \(0.352323\pi\)
\(972\) 0 0
\(973\) 1.22766e7 0.415714
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.02548e7 −0.678879 −0.339440 0.940628i \(-0.610237\pi\)
−0.339440 + 0.940628i \(0.610237\pi\)
\(978\) 0 0
\(979\) −3.55468e7 −1.18534
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 9.43782e6 0.311521 0.155761 0.987795i \(-0.450217\pi\)
0.155761 + 0.987795i \(0.450217\pi\)
\(984\) 0 0
\(985\) 1.34748e7 0.442517
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00128e6 −0.260117
\(990\) 0 0
\(991\) −1.53265e7 −0.495747 −0.247874 0.968792i \(-0.579732\pi\)
−0.247874 + 0.968792i \(0.579732\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 6.31360e6 0.202171
\(996\) 0 0
\(997\) −2.16514e6 −0.0689841 −0.0344920 0.999405i \(-0.510981\pi\)
−0.0344920 + 0.999405i \(0.510981\pi\)
\(998\) 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.h.1.1 1
3.2 odd 2 112.6.a.a.1.1 1
4.3 odd 2 504.6.a.b.1.1 1
12.11 even 2 56.6.a.b.1.1 1
21.20 even 2 784.6.a.n.1.1 1
24.5 odd 2 448.6.a.p.1.1 1
24.11 even 2 448.6.a.a.1.1 1
84.11 even 6 392.6.i.a.177.1 2
84.23 even 6 392.6.i.a.361.1 2
84.47 odd 6 392.6.i.f.361.1 2
84.59 odd 6 392.6.i.f.177.1 2
84.83 odd 2 392.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.b.1.1 1 12.11 even 2
112.6.a.a.1.1 1 3.2 odd 2
392.6.a.a.1.1 1 84.83 odd 2
392.6.i.a.177.1 2 84.11 even 6
392.6.i.a.361.1 2 84.23 even 6
392.6.i.f.177.1 2 84.59 odd 6
392.6.i.f.361.1 2 84.47 odd 6
448.6.a.a.1.1 1 24.11 even 2
448.6.a.p.1.1 1 24.5 odd 2
504.6.a.b.1.1 1 4.3 odd 2
784.6.a.n.1.1 1 21.20 even 2
1008.6.a.h.1.1 1 1.1 even 1 trivial