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Properties

Label 252.6.a.d.1.1
Level $252$
Weight $6$
Character 252.1
Self dual yes
Analytic conductor $40.417$
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] = [252,6,Mod(1,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 252.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: \(40.4167225929\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 252.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+96.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+96.0000 q^{5} +49.0000 q^{7} +720.000 q^{11} +572.000 q^{13} -1254.00 q^{17} -94.0000 q^{19} -96.0000 q^{23} +6091.00 q^{25} +4374.00 q^{29} -6244.00 q^{31} +4704.00 q^{35} -10798.0 q^{37} -12006.0 q^{41} -9160.00 q^{43} +25836.0 q^{47} +2401.00 q^{49} -1014.00 q^{53} +69120.0 q^{55} -1242.00 q^{59} +7592.00 q^{61} +54912.0 q^{65} +41132.0 q^{67} +37632.0 q^{71} -13438.0 q^{73} +35280.0 q^{77} +6248.00 q^{79} +25254.0 q^{83} -120384. q^{85} +45126.0 q^{89} +28028.0 q^{91} -9024.00 q^{95} +107222. q^{97} +O(q^{100})\)

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
\(5\) 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 \(-0.145700\pi\)
0.897059 + 0.441912i \(0.145700\pi\)
\(12\) 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 \(-0.509509\pi\)
−0.0298685 + 0.999554i \(0.509509\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −96.0000 −0.0378400 −0.0189200 − 0.999821i \(-0.506023\pi\)
−0.0189200 + 0.999821i \(0.506023\pi\)
\(24\) 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 \(-0.698311\pi\)
−0.583484 + 0.812125i \(0.698311\pi\)
\(32\) 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 \(-0.623299\pi\)
−0.377741 + 0.925911i \(0.623299\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 25836.0 1.70601 0.853003 − 0.521906i \(-0.174779\pi\)
0.853003 + 0.521906i \(0.174779\pi\)
\(48\) 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 \(-0.507394\pi\)
−0.0232253 + 0.999730i \(0.507394\pi\)
\(60\) 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 \(-0.310913\pi\)
0.559710 + 0.828689i \(0.310913\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 37632.0 0.885955 0.442977 − 0.896533i \(-0.353922\pi\)
0.442977 + 0.896533i \(0.353922\pi\)
\(72\) 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 \(-0.482064\pi\)
0.0563175 + 0.998413i \(0.482064\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 25254.0 0.402379 0.201189 − 0.979552i \(-0.435519\pi\)
0.201189 + 0.979552i \(0.435519\pi\)
\(84\) 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 \(-0.307912\pi\)
0.567495 + 0.823377i \(0.307912\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 129636. 1.09463 0.547314 − 0.836928i \(-0.315651\pi\)
0.547314 + 0.836928i \(0.315651\pi\)
\(108\) 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 \(-0.741149\pi\)
−0.687175 + 0.726492i \(0.741149\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12210.0 −0.0621638 −0.0310819 − 0.999517i \(-0.509895\pi\)
−0.0310819 + 0.999517i \(0.509895\pi\)
\(132\) 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 \(-0.896683\pi\)
−0.947785 + 0.318911i \(0.896683\pi\)
\(140\) 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 \(-0.399811\pi\)
0.309583 + 0.950872i \(0.399811\pi\)
\(152\) 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 \(-0.450555\pi\)
0.154712 + 0.987960i \(0.450555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −160788. −0.446131 −0.223066 − 0.974803i \(-0.571606\pi\)
−0.223066 + 0.974803i \(0.571606\pi\)
\(168\) 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 \(-0.381150\pi\)
0.364762 + 0.931101i \(0.381150\pi\)
\(180\) 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 \(-0.603941\pi\)
−0.320768 + 0.947158i \(0.603941\pi\)
\(192\) 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 \(-0.748350\pi\)
−0.703432 + 0.710762i \(0.748350\pi\)
\(200\) 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 \(-0.193039\pi\)
0.821676 + 0.569955i \(0.193039\pi\)
\(212\) 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 \(-0.341903\pi\)
0.476507 + 0.879171i \(0.341903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.04437e6 1.34520 0.672602 − 0.740005i \(-0.265177\pi\)
0.672602 + 0.740005i \(0.265177\pi\)
\(228\) 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 \(-0.378971\pi\)
0.371128 + 0.928582i \(0.378971\pi\)
\(240\) 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 \(-0.894749\pi\)
−0.945830 + 0.324663i \(0.894749\pi\)
\(252\) 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 \(-0.364086\pi\)
0.414131 + 0.910217i \(0.364086\pi\)
\(264\) 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 \(-0.726771\pi\)
−0.653669 + 0.756781i \(0.726771\pi\)
\(272\) 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 \(-0.419645\pi\)
0.249770 + 0.968305i \(0.419645\pi\)
\(284\) 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 \(-0.651206\pi\)
−0.457363 + 0.889280i \(0.651206\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.87529e6 1.09943 0.549714 − 0.835353i \(-0.314737\pi\)
0.549714 + 0.835353i \(0.314737\pi\)
\(312\) 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 \(-0.373747\pi\)
0.386319 + 0.922365i \(0.373747\pi\)
\(332\) 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 \(-0.340295\pi\)
0.480942 + 0.876752i \(0.340295\pi\)
\(348\) 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 \(-0.495137\pi\)
0.0152780 + 0.999883i \(0.495137\pi\)
\(360\) 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 \(-0.613284\pi\)
−0.348427 + 0.937336i \(0.613284\pi\)
\(368\) 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 \(-0.510108\pi\)
−0.0317495 + 0.999496i \(0.510108\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.87468e6 1.00137 0.500683 − 0.865630i \(-0.333082\pi\)
0.500683 + 0.865630i \(0.333082\pi\)
\(384\) 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 \(-0.673615\pi\)
−0.518783 + 0.854906i \(0.673615\pi\)
\(420\) 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 \(-0.389906\pi\)
0.339015 + 0.940781i \(0.389906\pi\)
\(432\) 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 \(-0.458182\pi\)
0.130998 + 0.991383i \(0.458182\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.12756e6 −0.999272 −0.499636 − 0.866235i \(-0.666533\pi\)
−0.499636 + 0.866235i \(0.666533\pi\)
\(444\) 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 \(-0.785135\pi\)
−0.780695 + 0.624913i \(0.785135\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.17801e6 −1.52304 −0.761521 − 0.648140i \(-0.775547\pi\)
−0.761521 + 0.648140i \(0.775547\pi\)
\(468\) 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 \(-0.710836\pi\)
−0.614980 + 0.788543i \(0.710836\pi\)
\(480\) 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 \(-0.241655\pi\)
0.725401 + 0.688327i \(0.241655\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.51878e6 0.284309 0.142155 − 0.989844i \(-0.454597\pi\)
0.142155 + 0.989844i \(0.454597\pi\)
\(492\) 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 \(-0.457649\pi\)
0.132658 + 0.991162i \(0.457649\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.31309e6 0.231406 0.115703 − 0.993284i \(-0.463088\pi\)
0.115703 + 0.993284i \(0.463088\pi\)
\(504\) 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 \(-0.330657\pi\)
0.507265 + 0.861790i \(0.330657\pi\)
\(524\) 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 \(-0.739295\pi\)
−0.682931 + 0.730483i \(0.739295\pi\)
\(548\) 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 \(-0.613411\pi\)
−0.348802 + 0.937196i \(0.613411\pi\)
\(564\) 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 \(-0.398159\pi\)
0.314512 + 0.949254i \(0.398159\pi\)
\(572\) 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 \(-0.711991\pi\)
−0.617838 + 0.786305i \(0.711991\pi\)
\(588\) 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 \(-0.553217\pi\)
−0.166407 + 0.986057i \(0.553217\pi\)
\(600\) 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 \(-0.583624\pi\)
−0.259700 + 0.965689i \(0.583624\pi\)
\(608\) 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 \(-0.230907\pi\)
0.748223 + 0.663447i \(0.230907\pi\)
\(620\) 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 \(-0.606969\pi\)
−0.329763 + 0.944064i \(0.606969\pi\)
\(632\) 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 \(-0.563658\pi\)
−0.198656 + 0.980069i \(0.563658\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.35051e6 0.314666 0.157333 − 0.987546i \(-0.449710\pi\)
0.157333 + 0.987546i \(0.449710\pi\)
\(648\) 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 \(-0.593472\pi\)
−0.289450 + 0.957193i \(0.593472\pi\)
\(660\) 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 \(-0.126175\pi\)
0.922461 + 0.386090i \(0.126175\pi\)
\(684\) 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 \(-0.668690\pi\)
−0.505495 + 0.862830i \(0.668690\pi\)
\(692\) 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 \(-0.683338\pi\)
−0.544650 + 0.838663i \(0.683338\pi\)
\(720\) 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 \(-0.803744\pi\)
−0.815874 + 0.578229i \(0.803744\pi\)
\(728\) 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 \(-0.526982\pi\)
−0.0846663 + 0.996409i \(0.526982\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.22646e7 1.47959 0.739797 − 0.672830i \(-0.234922\pi\)
0.739797 + 0.672830i \(0.234922\pi\)
\(744\) 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 \(-0.232740\pi\)
0.744392 + 0.667743i \(0.232740\pi\)
\(752\) 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 \(-0.735481\pi\)
−0.674129 + 0.738614i \(0.735481\pi\)
\(788\) 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 \(-0.350421\pi\)
0.452812 + 0.891606i \(0.350421\pi\)
\(812\) 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 \(-0.496833\pi\)
0.00994915 + 0.999951i \(0.496833\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.55021e7 −1.80505 −0.902526 − 0.430635i \(-0.858290\pi\)
−0.902526 + 0.430635i \(0.858290\pi\)
\(828\) 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 \(-0.815891\pi\)
−0.837340 + 0.546682i \(0.815891\pi\)
\(840\) 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 \(-0.448869\pi\)
0.159943 + 0.987126i \(0.448869\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.78069e7 1.27094 0.635471 − 0.772125i \(-0.280806\pi\)
0.635471 + 0.772125i \(0.280806\pi\)
\(864\) 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 \(-0.521557\pi\)
−0.0676705 + 0.997708i \(0.521557\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.02437e7 0.863933 0.431966 − 0.901890i \(-0.357820\pi\)
0.431966 + 0.901890i \(0.357820\pi\)
\(888\) 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 \(-0.544231\pi\)
−0.138510 + 0.990361i \(0.544231\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.40661e6 0.375523 0.187762 − 0.982215i \(-0.439877\pi\)
0.187762 + 0.982215i \(0.439877\pi\)
\(912\) 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 \(-0.634700\pi\)
−0.410656 + 0.911790i \(0.634700\pi\)
\(920\) 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 \(-0.473046\pi\)
0.0845775 + 0.996417i \(0.473046\pi\)
\(948\) 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 \(-0.628341\pi\)
−0.392359 + 0.919812i \(0.628341\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.94042e7 −1.68157 −0.840786 − 0.541367i \(-0.817907\pi\)
−0.840786 + 0.541367i \(0.817907\pi\)
\(972\) 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 \(-0.477798\pi\)
0.0696924 + 0.997569i \(0.477798\pi\)
\(984\) 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 \(-0.413672\pi\)
0.267895 + 0.963448i \(0.413672\pi\)
\(992\) 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 252.6.a.d.1.1 1
3.2 odd 2 28.6.a.a.1.1 ✓ 1
4.3 odd 2 1008.6.a.bb.1.1 1
12.11 even 2 112.6.a.e.1.1 1
15.2 even 4 700.6.e.d.449.2 2
15.8 even 4 700.6.e.d.449.1 2
15.14 odd 2 700.6.a.d.1.1 1
21.2 odd 6 196.6.e.f.165.1 2
21.5 even 6 196.6.e.e.165.1 2
21.11 odd 6 196.6.e.f.177.1 2
21.17 even 6 196.6.e.e.177.1 2
21.20 even 2 196.6.a.d.1.1 1
24.5 odd 2 448.6.a.i.1.1 1
24.11 even 2 448.6.a.h.1.1 1
84.83 odd 2 784.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.6.a.a.1.1 ✓ 1 3.2 odd 2
112.6.a.e.1.1 1 12.11 even 2
196.6.a.d.1.1 1 21.20 even 2
196.6.e.e.165.1 2 21.5 even 6
196.6.e.e.177.1 2 21.17 even 6
196.6.e.f.165.1 2 21.2 odd 6
196.6.e.f.177.1 2 21.11 odd 6
252.6.a.d.1.1 1 1.1 even 1 trivial
448.6.a.h.1.1 1 24.11 even 2
448.6.a.i.1.1 1 24.5 odd 2
700.6.a.d.1.1 1 15.14 odd 2
700.6.e.d.449.1 2 15.8 even 4
700.6.e.d.449.2 2 15.2 even 4
784.6.a.f.1.1 1 84.83 odd 2
1008.6.a.bb.1.1 1 4.3 odd 2