Properties

Label 1008.6.a.bb.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
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)
 
\(f(q)\) \(=\) \(q+96.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+96.0000 q^{5} -49.0000 q^{7} -720.000 q^{11} +572.000 q^{13} -1254.00 q^{17} +94.0000 q^{19} +96.0000 q^{23} +6091.00 q^{25} +4374.00 q^{29} +6244.00 q^{31} -4704.00 q^{35} -10798.0 q^{37} -12006.0 q^{41} +9160.00 q^{43} -25836.0 q^{47} +2401.00 q^{49} -1014.00 q^{53} -69120.0 q^{55} +1242.00 q^{59} +7592.00 q^{61} +54912.0 q^{65} -41132.0 q^{67} -37632.0 q^{71} -13438.0 q^{73} +35280.0 q^{77} -6248.00 q^{79} -25254.0 q^{83} -120384. q^{85} +45126.0 q^{89} -28028.0 q^{91} +9024.00 q^{95} +107222. q^{97} +O(q^{100})\)

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
\(5\) 96.0000 1.71730 0.858650 0.512562i \(-0.171304\pi\)
0.858650 + 0.512562i \(0.171304\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −720.000 −1.79412 −0.897059 0.441912i \(-0.854300\pi\)
−0.897059 + 0.441912i \(0.854300\pi\)
\(12\) 0 0
\(13\) 572.000 0.938723 0.469362 0.883006i \(-0.344484\pi\)
0.469362 + 0.883006i \(0.344484\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1254.00 −1.05239 −0.526193 0.850365i \(-0.676381\pi\)
−0.526193 + 0.850365i \(0.676381\pi\)
\(18\) 0 0
\(19\) 94.0000 0.0597371 0.0298685 0.999554i \(-0.490491\pi\)
0.0298685 + 0.999554i \(0.490491\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 96.0000 0.0378400 0.0189200 0.999821i \(-0.493977\pi\)
0.0189200 + 0.999821i \(0.493977\pi\)
\(24\) 0 0
\(25\) 6091.00 1.94912
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4374.00 0.965792 0.482896 0.875678i \(-0.339585\pi\)
0.482896 + 0.875678i \(0.339585\pi\)
\(30\) 0 0
\(31\) 6244.00 1.16697 0.583484 0.812125i \(-0.301689\pi\)
0.583484 + 0.812125i \(0.301689\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4704.00 −0.649078
\(36\) 0 0
\(37\) −10798.0 −1.29670 −0.648349 0.761343i \(-0.724540\pi\)
−0.648349 + 0.761343i \(0.724540\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12006.0 −1.11542 −0.557710 0.830036i \(-0.688320\pi\)
−0.557710 + 0.830036i \(0.688320\pi\)
\(42\) 0 0
\(43\) 9160.00 0.755482 0.377741 0.925911i \(-0.376701\pi\)
0.377741 + 0.925911i \(0.376701\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −25836.0 −1.70601 −0.853003 0.521906i \(-0.825221\pi\)
−0.853003 + 0.521906i \(0.825221\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1014.00 −0.0495848 −0.0247924 0.999693i \(-0.507892\pi\)
−0.0247924 + 0.999693i \(0.507892\pi\)
\(54\) 0 0
\(55\) −69120.0 −3.08104
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1242.00 0.0464506 0.0232253 0.999730i \(-0.492606\pi\)
0.0232253 + 0.999730i \(0.492606\pi\)
\(60\) 0 0
\(61\) 7592.00 0.261235 0.130618 0.991433i \(-0.458304\pi\)
0.130618 + 0.991433i \(0.458304\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 54912.0 1.61207
\(66\) 0 0
\(67\) −41132.0 −1.11942 −0.559710 0.828689i \(-0.689087\pi\)
−0.559710 + 0.828689i \(0.689087\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −37632.0 −0.885955 −0.442977 0.896533i \(-0.646078\pi\)
−0.442977 + 0.896533i \(0.646078\pi\)
\(72\) 0 0
\(73\) −13438.0 −0.295140 −0.147570 0.989052i \(-0.547145\pi\)
−0.147570 + 0.989052i \(0.547145\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 35280.0 0.678113
\(78\) 0 0
\(79\) −6248.00 −0.112635 −0.0563175 0.998413i \(-0.517936\pi\)
−0.0563175 + 0.998413i \(0.517936\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −25254.0 −0.402379 −0.201189 0.979552i \(-0.564481\pi\)
−0.201189 + 0.979552i \(0.564481\pi\)
\(84\) 0 0
\(85\) −120384. −1.80726
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 45126.0 0.603882 0.301941 0.953327i \(-0.402365\pi\)
0.301941 + 0.953327i \(0.402365\pi\)
\(90\) 0 0
\(91\) −28028.0 −0.354804
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9024.00 0.102586
\(96\) 0 0
\(97\) 107222. 1.15706 0.578528 0.815662i \(-0.303627\pi\)
0.578528 + 0.815662i \(0.303627\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −47136.0 −0.459779 −0.229890 0.973217i \(-0.573837\pi\)
−0.229890 + 0.973217i \(0.573837\pi\)
\(102\) 0 0
\(103\) −122204. −1.13499 −0.567495 0.823377i \(-0.692088\pi\)
−0.567495 + 0.823377i \(0.692088\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −129636. −1.09463 −0.547314 0.836928i \(-0.684349\pi\)
−0.547314 + 0.836928i \(0.684349\pi\)
\(108\) 0 0
\(109\) −220558. −1.77810 −0.889051 0.457809i \(-0.848635\pi\)
−0.889051 + 0.457809i \(0.848635\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −170694. −1.25754 −0.628770 0.777591i \(-0.716441\pi\)
−0.628770 + 0.777591i \(0.716441\pi\)
\(114\) 0 0
\(115\) 9216.00 0.0649827
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 61446.0 0.397765
\(120\) 0 0
\(121\) 357349. 2.21886
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 284736. 1.62992
\(126\) 0 0
\(127\) 249808. 1.37435 0.687175 0.726492i \(-0.258851\pi\)
0.687175 + 0.726492i \(0.258851\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12210.0 0.0621638 0.0310819 0.999517i \(-0.490105\pi\)
0.0310819 + 0.999517i \(0.490105\pi\)
\(132\) 0 0
\(133\) −4606.00 −0.0225785
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13902.0 0.0632814 0.0316407 0.999499i \(-0.489927\pi\)
0.0316407 + 0.999499i \(0.489927\pi\)
\(138\) 0 0
\(139\) 431794. 1.89557 0.947785 0.318911i \(-0.103317\pi\)
0.947785 + 0.318911i \(0.103317\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −411840. −1.68418
\(144\) 0 0
\(145\) 419904. 1.65856
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −326814. −1.20597 −0.602983 0.797754i \(-0.706021\pi\)
−0.602983 + 0.797754i \(0.706021\pi\)
\(150\) 0 0
\(151\) −173480. −0.619166 −0.309583 0.950872i \(-0.600189\pi\)
−0.309583 + 0.950872i \(0.600189\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 599424. 2.00403
\(156\) 0 0
\(157\) −54532.0 −0.176564 −0.0882820 0.996096i \(-0.528138\pi\)
−0.0882820 + 0.996096i \(0.528138\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4704.00 −0.0143022
\(162\) 0 0
\(163\) −104960. −0.309425 −0.154712 0.987960i \(-0.549445\pi\)
−0.154712 + 0.987960i \(0.549445\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 160788. 0.446131 0.223066 0.974803i \(-0.428394\pi\)
0.223066 + 0.974803i \(0.428394\pi\)
\(168\) 0 0
\(169\) −44109.0 −0.118798
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −360564. −0.915940 −0.457970 0.888968i \(-0.651423\pi\)
−0.457970 + 0.888968i \(0.651423\pi\)
\(174\) 0 0
\(175\) −298459. −0.736698
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −312732. −0.729524 −0.364762 0.931101i \(-0.618850\pi\)
−0.364762 + 0.931101i \(0.618850\pi\)
\(180\) 0 0
\(181\) −123820. −0.280928 −0.140464 0.990086i \(-0.544859\pi\)
−0.140464 + 0.990086i \(0.544859\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.03661e6 −2.22682
\(186\) 0 0
\(187\) 902880. 1.88810
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 323448. 0.641536 0.320768 0.947158i \(-0.396059\pi\)
0.320768 + 0.947158i \(0.396059\pi\)
\(192\) 0 0
\(193\) −619954. −1.19803 −0.599013 0.800739i \(-0.704440\pi\)
−0.599013 + 0.800739i \(0.704440\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 499362. 0.916748 0.458374 0.888759i \(-0.348432\pi\)
0.458374 + 0.888759i \(0.348432\pi\)
\(198\) 0 0
\(199\) 785932. 1.40686 0.703432 0.710762i \(-0.251650\pi\)
0.703432 + 0.710762i \(0.251650\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −214326. −0.365035
\(204\) 0 0
\(205\) −1.15258e6 −1.91551
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −67680.0 −0.107175
\(210\) 0 0
\(211\) −1.06276e6 −1.64335 −0.821676 0.569955i \(-0.806961\pi\)
−0.821676 + 0.569955i \(0.806961\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 879360. 1.29739
\(216\) 0 0
\(217\) −305956. −0.441072
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −717288. −0.987900
\(222\) 0 0
\(223\) −707720. −0.953014 −0.476507 0.879171i \(-0.658097\pi\)
−0.476507 + 0.879171i \(0.658097\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.04437e6 −1.34520 −0.672602 0.740005i \(-0.734823\pi\)
−0.672602 + 0.740005i \(0.734823\pi\)
\(228\) 0 0
\(229\) −539716. −0.680106 −0.340053 0.940406i \(-0.610445\pi\)
−0.340053 + 0.940406i \(0.610445\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −177114. −0.213729 −0.106864 0.994274i \(-0.534081\pi\)
−0.106864 + 0.994274i \(0.534081\pi\)
\(234\) 0 0
\(235\) −2.48026e6 −2.92972
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −655464. −0.742257 −0.371128 0.928582i \(-0.621029\pi\)
−0.371128 + 0.928582i \(0.621029\pi\)
\(240\) 0 0
\(241\) 1.38709e6 1.53838 0.769189 0.639021i \(-0.220660\pi\)
0.769189 + 0.639021i \(0.220660\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 230496. 0.245329
\(246\) 0 0
\(247\) 53768.0 0.0560766
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.88811e6 1.89166 0.945830 0.324663i \(-0.105251\pi\)
0.945830 + 0.324663i \(0.105251\pi\)
\(252\) 0 0
\(253\) −69120.0 −0.0678895
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −346194. −0.326954 −0.163477 0.986547i \(-0.552271\pi\)
−0.163477 + 0.986547i \(0.552271\pi\)
\(258\) 0 0
\(259\) 529102. 0.490106
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −929088. −0.828262 −0.414131 0.910217i \(-0.635914\pi\)
−0.414131 + 0.910217i \(0.635914\pi\)
\(264\) 0 0
\(265\) −97344.0 −0.0851519
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −382068. −0.321929 −0.160964 0.986960i \(-0.551460\pi\)
−0.160964 + 0.986960i \(0.551460\pi\)
\(270\) 0 0
\(271\) 1.58056e6 1.30734 0.653669 0.756781i \(-0.273229\pi\)
0.653669 + 0.756781i \(0.273229\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.38552e6 −3.49695
\(276\) 0 0
\(277\) −1.36911e6 −1.07211 −0.536056 0.844182i \(-0.680086\pi\)
−0.536056 + 0.844182i \(0.680086\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 394854. 0.298312 0.149156 0.988814i \(-0.452344\pi\)
0.149156 + 0.988814i \(0.452344\pi\)
\(282\) 0 0
\(283\) −673034. −0.499541 −0.249770 0.968305i \(-0.580355\pi\)
−0.249770 + 0.968305i \(0.580355\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 588294. 0.421589
\(288\) 0 0
\(289\) 152659. 0.107517
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.83468e6 −1.24851 −0.624254 0.781222i \(-0.714597\pi\)
−0.624254 + 0.781222i \(0.714597\pi\)
\(294\) 0 0
\(295\) 119232. 0.0797697
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 54912.0 0.0355213
\(300\) 0 0
\(301\) −448840. −0.285545
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 728832. 0.448619
\(306\) 0 0
\(307\) 1.51056e6 0.914727 0.457363 0.889280i \(-0.348794\pi\)
0.457363 + 0.889280i \(0.348794\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.87529e6 −1.09943 −0.549714 0.835353i \(-0.685263\pi\)
−0.549714 + 0.835353i \(0.685263\pi\)
\(312\) 0 0
\(313\) −1.51076e6 −0.871636 −0.435818 0.900035i \(-0.643541\pi\)
−0.435818 + 0.900035i \(0.643541\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.02709e6 −1.13299 −0.566495 0.824065i \(-0.691701\pi\)
−0.566495 + 0.824065i \(0.691701\pi\)
\(318\) 0 0
\(319\) −3.14928e6 −1.73274
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −117876. −0.0628665
\(324\) 0 0
\(325\) 3.48405e6 1.82968
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.26596e6 0.644810
\(330\) 0 0
\(331\) −1.54009e6 −0.772637 −0.386319 0.922365i \(-0.626253\pi\)
−0.386319 + 0.922365i \(0.626253\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.94867e6 −1.92238
\(336\) 0 0
\(337\) 1.01166e6 0.485245 0.242622 0.970121i \(-0.421992\pi\)
0.242622 + 0.970121i \(0.421992\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.49568e6 −2.09368
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.15748e6 −0.961885 −0.480942 0.876752i \(-0.659705\pi\)
−0.480942 + 0.876752i \(0.659705\pi\)
\(348\) 0 0
\(349\) −1.15798e6 −0.508906 −0.254453 0.967085i \(-0.581895\pi\)
−0.254453 + 0.967085i \(0.581895\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.17566e6 1.35643 0.678215 0.734863i \(-0.262754\pi\)
0.678215 + 0.734863i \(0.262754\pi\)
\(354\) 0 0
\(355\) −3.61267e6 −1.52145
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −74616.0 −0.0305560 −0.0152780 0.999883i \(-0.504863\pi\)
−0.0152780 + 0.999883i \(0.504863\pi\)
\(360\) 0 0
\(361\) −2.46726e6 −0.996431
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.29005e6 −0.506843
\(366\) 0 0
\(367\) 1.79807e6 0.696854 0.348427 0.937336i \(-0.386716\pi\)
0.348427 + 0.937336i \(0.386716\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 49686.0 0.0187413
\(372\) 0 0
\(373\) 2.20461e6 0.820463 0.410231 0.911981i \(-0.365448\pi\)
0.410231 + 0.911981i \(0.365448\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.50193e6 0.906612
\(378\) 0 0
\(379\) 177568. 0.0634990 0.0317495 0.999496i \(-0.489892\pi\)
0.0317495 + 0.999496i \(0.489892\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.87468e6 −1.00137 −0.500683 0.865630i \(-0.666918\pi\)
−0.500683 + 0.865630i \(0.666918\pi\)
\(384\) 0 0
\(385\) 3.38688e6 1.16452
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.79965e6 1.60818 0.804091 0.594506i \(-0.202652\pi\)
0.804091 + 0.594506i \(0.202652\pi\)
\(390\) 0 0
\(391\) −120384. −0.0398223
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −599808. −0.193428
\(396\) 0 0
\(397\) −2.81643e6 −0.896855 −0.448428 0.893819i \(-0.648016\pi\)
−0.448428 + 0.893819i \(0.648016\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.83797e6 0.881347 0.440673 0.897667i \(-0.354740\pi\)
0.440673 + 0.897667i \(0.354740\pi\)
\(402\) 0 0
\(403\) 3.57157e6 1.09546
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.77456e6 2.32643
\(408\) 0 0
\(409\) 154286. 0.0456056 0.0228028 0.999740i \(-0.492741\pi\)
0.0228028 + 0.999740i \(0.492741\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −60858.0 −0.0175567
\(414\) 0 0
\(415\) −2.42438e6 −0.691005
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.72865e6 1.03757 0.518783 0.854906i \(-0.326385\pi\)
0.518783 + 0.854906i \(0.326385\pi\)
\(420\) 0 0
\(421\) −2.32623e6 −0.639658 −0.319829 0.947475i \(-0.603626\pi\)
−0.319829 + 0.947475i \(0.603626\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.63811e6 −2.05123
\(426\) 0 0
\(427\) −372008. −0.0987376
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.61482e6 −0.678031 −0.339015 0.940781i \(-0.610094\pi\)
−0.339015 + 0.940781i \(0.610094\pi\)
\(432\) 0 0
\(433\) −1.19226e6 −0.305598 −0.152799 0.988257i \(-0.548829\pi\)
−0.152799 + 0.988257i \(0.548829\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9024.00 0.00226045
\(438\) 0 0
\(439\) −1.05793e6 −0.261996 −0.130998 0.991383i \(-0.541818\pi\)
−0.130998 + 0.991383i \(0.541818\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.12756e6 0.999272 0.499636 0.866235i \(-0.333467\pi\)
0.499636 + 0.866235i \(0.333467\pi\)
\(444\) 0 0
\(445\) 4.33210e6 1.03705
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.75823e6 −0.879766 −0.439883 0.898055i \(-0.644980\pi\)
−0.439883 + 0.898055i \(0.644980\pi\)
\(450\) 0 0
\(451\) 8.64432e6 2.00120
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.69069e6 −0.609305
\(456\) 0 0
\(457\) −451114. −0.101041 −0.0505203 0.998723i \(-0.516088\pi\)
−0.0505203 + 0.998723i \(0.516088\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.95186e6 0.427756 0.213878 0.976860i \(-0.431390\pi\)
0.213878 + 0.976860i \(0.431390\pi\)
\(462\) 0 0
\(463\) 7.20218e6 1.56139 0.780695 0.624913i \(-0.214865\pi\)
0.780695 + 0.624913i \(0.214865\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.17801e6 1.52304 0.761521 0.648140i \(-0.224453\pi\)
0.761521 + 0.648140i \(0.224453\pi\)
\(468\) 0 0
\(469\) 2.01547e6 0.423101
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.59520e6 −1.35542
\(474\) 0 0
\(475\) 572554. 0.116435
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.17632e6 1.22996 0.614980 0.788543i \(-0.289164\pi\)
0.614980 + 0.788543i \(0.289164\pi\)
\(480\) 0 0
\(481\) −6.17646e6 −1.21724
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.02933e7 1.98701
\(486\) 0 0
\(487\) −7.59330e6 −1.45080 −0.725401 0.688327i \(-0.758345\pi\)
−0.725401 + 0.688327i \(0.758345\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.51878e6 −0.284309 −0.142155 0.989844i \(-0.545403\pi\)
−0.142155 + 0.989844i \(0.545403\pi\)
\(492\) 0 0
\(493\) −5.48500e6 −1.01639
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.84397e6 0.334859
\(498\) 0 0
\(499\) −1.47576e6 −0.265316 −0.132658 0.991162i \(-0.542351\pi\)
−0.132658 + 0.991162i \(0.542351\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.31309e6 −0.231406 −0.115703 0.993284i \(-0.536912\pi\)
−0.115703 + 0.993284i \(0.536912\pi\)
\(504\) 0 0
\(505\) −4.52506e6 −0.789579
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.40932e6 −0.754357 −0.377178 0.926141i \(-0.623106\pi\)
−0.377178 + 0.926141i \(0.623106\pi\)
\(510\) 0 0
\(511\) 658462. 0.111552
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.17316e7 −1.94912
\(516\) 0 0
\(517\) 1.86019e7 3.06078
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.97629e6 −0.480376 −0.240188 0.970726i \(-0.577209\pi\)
−0.240188 + 0.970726i \(0.577209\pi\)
\(522\) 0 0
\(523\) −6.34627e6 −1.01453 −0.507265 0.861790i \(-0.669343\pi\)
−0.507265 + 0.861790i \(0.669343\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.82998e6 −1.22810
\(528\) 0 0
\(529\) −6.42713e6 −0.998568
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.86743e6 −1.04707
\(534\) 0 0
\(535\) −1.24451e7 −1.87980
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.72872e6 −0.256302
\(540\) 0 0
\(541\) −1.36667e6 −0.200756 −0.100378 0.994949i \(-0.532005\pi\)
−0.100378 + 0.994949i \(0.532005\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.11736e7 −3.05353
\(546\) 0 0
\(547\) 9.55818e6 1.36586 0.682931 0.730483i \(-0.260705\pi\)
0.682931 + 0.730483i \(0.260705\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 411156. 0.0576936
\(552\) 0 0
\(553\) 306152. 0.0425720
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.94287e6 −0.948202 −0.474101 0.880470i \(-0.657227\pi\)
−0.474101 + 0.880470i \(0.657227\pi\)
\(558\) 0 0
\(559\) 5.23952e6 0.709189
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.24662e6 0.697604 0.348802 0.937196i \(-0.386589\pi\)
0.348802 + 0.937196i \(0.386589\pi\)
\(564\) 0 0
\(565\) −1.63866e7 −2.15958
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.46551e6 −0.448731 −0.224366 0.974505i \(-0.572031\pi\)
−0.224366 + 0.974505i \(0.572031\pi\)
\(570\) 0 0
\(571\) −4.90069e6 −0.629023 −0.314512 0.949254i \(-0.601841\pi\)
−0.314512 + 0.949254i \(0.601841\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 584736. 0.0737548
\(576\) 0 0
\(577\) 2.28346e6 0.285531 0.142766 0.989757i \(-0.454401\pi\)
0.142766 + 0.989757i \(0.454401\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.23745e6 0.152085
\(582\) 0 0
\(583\) 730080. 0.0889609
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.03157e7 1.23568 0.617838 0.786305i \(-0.288009\pi\)
0.617838 + 0.786305i \(0.288009\pi\)
\(588\) 0 0
\(589\) 586936. 0.0697112
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.52838e6 −0.412039 −0.206020 0.978548i \(-0.566051\pi\)
−0.206020 + 0.978548i \(0.566051\pi\)
\(594\) 0 0
\(595\) 5.89882e6 0.683081
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.92260e6 0.332815 0.166407 0.986057i \(-0.446783\pi\)
0.166407 + 0.986057i \(0.446783\pi\)
\(600\) 0 0
\(601\) −1.17567e7 −1.32770 −0.663849 0.747866i \(-0.731078\pi\)
−0.663849 + 0.747866i \(0.731078\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.43055e7 3.81044
\(606\) 0 0
\(607\) 4.71491e6 0.519400 0.259700 0.965689i \(-0.416376\pi\)
0.259700 + 0.965689i \(0.416376\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.47782e7 −1.60147
\(612\) 0 0
\(613\) 213842. 0.0229849 0.0114924 0.999934i \(-0.496342\pi\)
0.0114924 + 0.999934i \(0.496342\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 336666. 0.0356030 0.0178015 0.999842i \(-0.494333\pi\)
0.0178015 + 0.999842i \(0.494333\pi\)
\(618\) 0 0
\(619\) −1.42655e7 −1.49645 −0.748223 0.663447i \(-0.769093\pi\)
−0.748223 + 0.663447i \(0.769093\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.21117e6 −0.228246
\(624\) 0 0
\(625\) 8.30028e6 0.849949
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.35407e7 1.36463
\(630\) 0 0
\(631\) 6.59637e6 0.659525 0.329763 0.944064i \(-0.393031\pi\)
0.329763 + 0.944064i \(0.393031\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.39816e7 2.36017
\(636\) 0 0
\(637\) 1.37337e6 0.134103
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.02490e7 0.985225 0.492613 0.870249i \(-0.336042\pi\)
0.492613 + 0.870249i \(0.336042\pi\)
\(642\) 0 0
\(643\) 4.16543e6 0.397312 0.198656 0.980069i \(-0.436342\pi\)
0.198656 + 0.980069i \(0.436342\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3.35051e6 −0.314666 −0.157333 0.987546i \(-0.550290\pi\)
−0.157333 + 0.987546i \(0.550290\pi\)
\(648\) 0 0
\(649\) −894240. −0.0833379
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.05408e6 0.830924 0.415462 0.909611i \(-0.363620\pi\)
0.415462 + 0.909611i \(0.363620\pi\)
\(654\) 0 0
\(655\) 1.17216e6 0.106754
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.45382e6 0.578899 0.289450 0.957193i \(-0.406528\pi\)
0.289450 + 0.957193i \(0.406528\pi\)
\(660\) 0 0
\(661\) 1.43167e7 1.27450 0.637250 0.770657i \(-0.280072\pi\)
0.637250 + 0.770657i \(0.280072\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −442176. −0.0387740
\(666\) 0 0
\(667\) 419904. 0.0365456
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.46624e6 −0.468686
\(672\) 0 0
\(673\) 2.27250e7 1.93404 0.967020 0.254701i \(-0.0819771\pi\)
0.967020 + 0.254701i \(0.0819771\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.53249e6 0.715491 0.357746 0.933819i \(-0.383546\pi\)
0.357746 + 0.933819i \(0.383546\pi\)
\(678\) 0 0
\(679\) −5.25388e6 −0.437326
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −2.24921e7 −1.84492 −0.922461 0.386090i \(-0.873825\pi\)
−0.922461 + 0.386090i \(0.873825\pi\)
\(684\) 0 0
\(685\) 1.33459e6 0.108673
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −580008. −0.0465464
\(690\) 0 0
\(691\) 1.26894e7 1.01099 0.505495 0.862830i \(-0.331310\pi\)
0.505495 + 0.862830i \(0.331310\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.14522e7 3.25526
\(696\) 0 0
\(697\) 1.50555e7 1.17385
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.13939e6 0.395018 0.197509 0.980301i \(-0.436715\pi\)
0.197509 + 0.980301i \(0.436715\pi\)
\(702\) 0 0
\(703\) −1.01501e6 −0.0774610
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.30966e6 0.173780
\(708\) 0 0
\(709\) −1.16065e7 −0.867132 −0.433566 0.901122i \(-0.642745\pi\)
−0.433566 + 0.901122i \(0.642745\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 599424. 0.0441581
\(714\) 0 0
\(715\) −3.95366e7 −2.89224
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.50998e7 1.08930 0.544650 0.838663i \(-0.316662\pi\)
0.544650 + 0.838663i \(0.316662\pi\)
\(720\) 0 0
\(721\) 5.98800e6 0.428986
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.66420e7 1.88245
\(726\) 0 0
\(727\) 2.32536e7 1.63175 0.815874 0.578229i \(-0.196256\pi\)
0.815874 + 0.578229i \(0.196256\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.14866e7 −0.795059
\(732\) 0 0
\(733\) 2.37814e7 1.63485 0.817423 0.576038i \(-0.195402\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.96150e7 2.00837
\(738\) 0 0
\(739\) 2.51392e6 0.169333 0.0846663 0.996409i \(-0.473018\pi\)
0.0846663 + 0.996409i \(0.473018\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.22646e7 −1.47959 −0.739797 0.672830i \(-0.765078\pi\)
−0.739797 + 0.672830i \(0.765078\pi\)
\(744\) 0 0
\(745\) −3.13741e7 −2.07101
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.35216e6 0.413730
\(750\) 0 0
\(751\) −2.30108e7 −1.48878 −0.744392 0.667743i \(-0.767260\pi\)
−0.744392 + 0.667743i \(0.767260\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.66541e7 −1.06329
\(756\) 0 0
\(757\) 1.59335e7 1.01058 0.505290 0.862950i \(-0.331386\pi\)
0.505290 + 0.862950i \(0.331386\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.68629e7 −1.05553 −0.527764 0.849391i \(-0.676969\pi\)
−0.527764 + 0.849391i \(0.676969\pi\)
\(762\) 0 0
\(763\) 1.08073e7 0.672059
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 710424. 0.0436043
\(768\) 0 0
\(769\) −2.75402e7 −1.67939 −0.839694 0.543060i \(-0.817265\pi\)
−0.839694 + 0.543060i \(0.817265\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.26820e7 −1.36532 −0.682658 0.730738i \(-0.739176\pi\)
−0.682658 + 0.730738i \(0.739176\pi\)
\(774\) 0 0
\(775\) 3.80322e7 2.27456
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.12856e6 −0.0666320
\(780\) 0 0
\(781\) 2.70950e7 1.58951
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5.23507e6 −0.303213
\(786\) 0 0
\(787\) 2.34266e7 1.34826 0.674129 0.738614i \(-0.264519\pi\)
0.674129 + 0.738614i \(0.264519\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.36401e6 0.475306
\(792\) 0 0
\(793\) 4.34262e6 0.245228
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.82051e7 1.01519 0.507594 0.861596i \(-0.330535\pi\)
0.507594 + 0.861596i \(0.330535\pi\)
\(798\) 0 0
\(799\) 3.23983e7 1.79538
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.67536e6 0.529515
\(804\) 0 0
\(805\) −451584. −0.0245612
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.47411e7 −0.791878 −0.395939 0.918277i \(-0.629581\pi\)
−0.395939 + 0.918277i \(0.629581\pi\)
\(810\) 0 0
\(811\) −1.69629e7 −0.905625 −0.452812 0.891606i \(-0.649579\pi\)
−0.452812 + 0.891606i \(0.649579\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.00762e7 −0.531375
\(816\) 0 0
\(817\) 861040. 0.0451303
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −8.03929e6 −0.416255 −0.208128 0.978102i \(-0.566737\pi\)
−0.208128 + 0.978102i \(0.566737\pi\)
\(822\) 0 0
\(823\) −386648. −0.0198983 −0.00994915 0.999951i \(-0.503167\pi\)
−0.00994915 + 0.999951i \(0.503167\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.55021e7 1.80505 0.902526 0.430635i \(-0.141710\pi\)
0.902526 + 0.430635i \(0.141710\pi\)
\(828\) 0 0
\(829\) 2.48814e7 1.25745 0.628723 0.777630i \(-0.283578\pi\)
0.628723 + 0.777630i \(0.283578\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.01085e6 −0.150341
\(834\) 0 0
\(835\) 1.54356e7 0.766141
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.41458e7 1.67468 0.837340 0.546682i \(-0.184109\pi\)
0.837340 + 0.546682i \(0.184109\pi\)
\(840\) 0 0
\(841\) −1.37927e6 −0.0672450
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.23446e6 −0.204012
\(846\) 0 0
\(847\) −1.75101e7 −0.838649
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.03661e6 −0.0490671
\(852\) 0 0
\(853\) 2.50701e7 1.17973 0.589865 0.807502i \(-0.299181\pi\)
0.589865 + 0.807502i \(0.299181\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.81938e7 0.846199 0.423099 0.906083i \(-0.360942\pi\)
0.423099 + 0.906083i \(0.360942\pi\)
\(858\) 0 0
\(859\) −6.91797e6 −0.319886 −0.159943 0.987126i \(-0.551131\pi\)
−0.159943 + 0.987126i \(0.551131\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.78069e7 −1.27094 −0.635471 0.772125i \(-0.719194\pi\)
−0.635471 + 0.772125i \(0.719194\pi\)
\(864\) 0 0
\(865\) −3.46141e7 −1.57294
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.49856e6 0.202080
\(870\) 0 0
\(871\) −2.35275e7 −1.05083
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.39521e7 −0.616053
\(876\) 0 0
\(877\) 3.79587e6 0.166653 0.0833263 0.996522i \(-0.473446\pi\)
0.0833263 + 0.996522i \(0.473446\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.48904e7 −1.08042 −0.540210 0.841530i \(-0.681655\pi\)
−0.540210 + 0.841530i \(0.681655\pi\)
\(882\) 0 0
\(883\) 3.13568e6 0.135341 0.0676705 0.997708i \(-0.478443\pi\)
0.0676705 + 0.997708i \(0.478443\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.02437e7 −0.863933 −0.431966 0.901890i \(-0.642180\pi\)
−0.431966 + 0.901890i \(0.642180\pi\)
\(888\) 0 0
\(889\) −1.22406e7 −0.519455
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.42858e6 −0.101912
\(894\) 0 0
\(895\) −3.00223e7 −1.25281
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.73113e7 1.12705
\(900\) 0 0
\(901\) 1.27156e6 0.0521823
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.18867e7 −0.482437
\(906\) 0 0
\(907\) 6.86324e6 0.277020 0.138510 0.990361i \(-0.455769\pi\)
0.138510 + 0.990361i \(0.455769\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −9.40661e6 −0.375523 −0.187762 0.982215i \(-0.560123\pi\)
−0.187762 + 0.982215i \(0.560123\pi\)
\(912\) 0 0
\(913\) 1.81829e7 0.721914
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −598290. −0.0234957
\(918\) 0 0
\(919\) 2.10280e7 0.821313 0.410656 0.911790i \(-0.365300\pi\)
0.410656 + 0.911790i \(0.365300\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.15255e7 −0.831666
\(924\) 0 0
\(925\) −6.57706e7 −2.52742
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.30928e7 1.63819 0.819096 0.573656i \(-0.194475\pi\)
0.819096 + 0.573656i \(0.194475\pi\)
\(930\) 0 0
\(931\) 225694. 0.00853387
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 8.66765e7 3.24244
\(936\) 0 0
\(937\) −3.85862e6 −0.143576 −0.0717882 0.997420i \(-0.522871\pi\)
−0.0717882 + 0.997420i \(0.522871\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.59601e7 −0.587572 −0.293786 0.955871i \(-0.594915\pi\)
−0.293786 + 0.955871i \(0.594915\pi\)
\(942\) 0 0
\(943\) −1.15258e6 −0.0422076
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.66831e6 −0.169155 −0.0845775 0.996417i \(-0.526954\pi\)
−0.0845775 + 0.996417i \(0.526954\pi\)
\(948\) 0 0
\(949\) −7.68654e6 −0.277054
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.43457e7 1.22501 0.612505 0.790466i \(-0.290162\pi\)
0.612505 + 0.790466i \(0.290162\pi\)
\(954\) 0 0
\(955\) 3.10510e7 1.10171
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −681198. −0.0239181
\(960\) 0 0
\(961\) 1.03584e7 0.361813
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.95156e7 −2.05737
\(966\) 0 0
\(967\) 2.28181e7 0.784718 0.392359 0.919812i \(-0.371659\pi\)
0.392359 + 0.919812i \(0.371659\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.94042e7 1.68157 0.840786 0.541367i \(-0.182093\pi\)
0.840786 + 0.541367i \(0.182093\pi\)
\(972\) 0 0
\(973\) −2.11579e7 −0.716458
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −7.17542e6 −0.240498 −0.120249 0.992744i \(-0.538369\pi\)
−0.120249 + 0.992744i \(0.538369\pi\)
\(978\) 0 0
\(979\) −3.24907e7 −1.08343
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.22279e6 −0.139385 −0.0696924 0.997569i \(-0.522202\pi\)
−0.0696924 + 0.997569i \(0.522202\pi\)
\(984\) 0 0
\(985\) 4.79388e7 1.57433
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 879360. 0.0285875
\(990\) 0 0
\(991\) −1.65645e7 −0.535789 −0.267895 0.963448i \(-0.586328\pi\)
−0.267895 + 0.963448i \(0.586328\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7.54495e7 2.41601
\(996\) 0 0
\(997\) −4.40973e7 −1.40499 −0.702496 0.711687i \(-0.747931\pi\)
−0.702496 + 0.711687i \(0.747931\pi\)
\(998\) 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.bb.1.1 1
3.2 odd 2 112.6.a.e.1.1 1
4.3 odd 2 252.6.a.d.1.1 1
12.11 even 2 28.6.a.a.1.1 1
21.20 even 2 784.6.a.f.1.1 1
24.5 odd 2 448.6.a.h.1.1 1
24.11 even 2 448.6.a.i.1.1 1
60.23 odd 4 700.6.e.d.449.1 2
60.47 odd 4 700.6.e.d.449.2 2
60.59 even 2 700.6.a.d.1.1 1
84.11 even 6 196.6.e.f.177.1 2
84.23 even 6 196.6.e.f.165.1 2
84.47 odd 6 196.6.e.e.165.1 2
84.59 odd 6 196.6.e.e.177.1 2
84.83 odd 2 196.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.6.a.a.1.1 1 12.11 even 2
112.6.a.e.1.1 1 3.2 odd 2
196.6.a.d.1.1 1 84.83 odd 2
196.6.e.e.165.1 2 84.47 odd 6
196.6.e.e.177.1 2 84.59 odd 6
196.6.e.f.165.1 2 84.23 even 6
196.6.e.f.177.1 2 84.11 even 6
252.6.a.d.1.1 1 4.3 odd 2
448.6.a.h.1.1 1 24.5 odd 2
448.6.a.i.1.1 1 24.11 even 2
700.6.a.d.1.1 1 60.59 even 2
700.6.e.d.449.1 2 60.23 odd 4
700.6.e.d.449.2 2 60.47 odd 4
784.6.a.f.1.1 1 21.20 even 2
1008.6.a.bb.1.1 1 1.1 even 1 trivial