Properties

Label 1008.6.a.br.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{114}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 114 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-10.6771\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-50.0625 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-50.0625 q^{5} +49.0000 q^{7} -150.437 q^{11} +522.250 q^{13} +345.313 q^{17} +2140.75 q^{19} +484.688 q^{23} -618.749 q^{25} -3947.50 q^{29} +3905.75 q^{31} -2453.06 q^{35} -5574.75 q^{37} -7703.56 q^{41} -2565.00 q^{43} -20901.9 q^{47} +2401.00 q^{49} +29684.9 q^{53} +7531.26 q^{55} -14887.6 q^{59} +4981.74 q^{61} -26145.1 q^{65} -35931.5 q^{67} -13176.9 q^{71} +49108.5 q^{73} -7371.43 q^{77} +17296.5 q^{79} +17900.5 q^{83} -17287.2 q^{85} +71460.7 q^{89} +25590.2 q^{91} -107171. q^{95} +74744.5 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 28 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 28 q^{5} + 98 q^{7} + 596 q^{11} + 532 q^{13} + 2100 q^{17} + 2744 q^{19} + 3660 q^{23} + 2350 q^{25} - 720 q^{29} - 3976 q^{31} + 1372 q^{35} + 6788 q^{37} - 4004 q^{41} - 19480 q^{43} - 21560 q^{47} + 4802 q^{49} + 57576 q^{53} + 65800 q^{55} - 22344 q^{59} - 38724 q^{61} - 25384 q^{65} - 7288 q^{67} - 3932 q^{71} + 19292 q^{73} + 29204 q^{77} - 15632 q^{79} - 22624 q^{83} + 119688 q^{85} + 112812 q^{89} + 26068 q^{91} - 60080 q^{95} - 36036 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −50.0625 −0.895545 −0.447772 0.894148i \(-0.647782\pi\)
−0.447772 + 0.894148i \(0.647782\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −150.437 −0.374864 −0.187432 0.982278i \(-0.560016\pi\)
−0.187432 + 0.982278i \(0.560016\pi\)
\(12\) 0 0
\(13\) 522.250 0.857077 0.428539 0.903523i \(-0.359029\pi\)
0.428539 + 0.903523i \(0.359029\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 345.313 0.289795 0.144897 0.989447i \(-0.453715\pi\)
0.144897 + 0.989447i \(0.453715\pi\)
\(18\) 0 0
\(19\) 2140.75 1.36045 0.680224 0.733004i \(-0.261883\pi\)
0.680224 + 0.733004i \(0.261883\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 484.688 0.191048 0.0955241 0.995427i \(-0.469547\pi\)
0.0955241 + 0.995427i \(0.469547\pi\)
\(24\) 0 0
\(25\) −618.749 −0.198000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3947.50 −0.871620 −0.435810 0.900039i \(-0.643538\pi\)
−0.435810 + 0.900039i \(0.643538\pi\)
\(30\) 0 0
\(31\) 3905.75 0.729961 0.364981 0.931015i \(-0.381076\pi\)
0.364981 + 0.931015i \(0.381076\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2453.06 −0.338484
\(36\) 0 0
\(37\) −5574.75 −0.669454 −0.334727 0.942315i \(-0.608644\pi\)
−0.334727 + 0.942315i \(0.608644\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7703.56 −0.715701 −0.357851 0.933779i \(-0.616490\pi\)
−0.357851 + 0.933779i \(0.616490\pi\)
\(42\) 0 0
\(43\) −2565.00 −0.211552 −0.105776 0.994390i \(-0.533733\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −20901.9 −1.38020 −0.690098 0.723716i \(-0.742432\pi\)
−0.690098 + 0.723716i \(0.742432\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 29684.9 1.45160 0.725798 0.687908i \(-0.241471\pi\)
0.725798 + 0.687908i \(0.241471\pi\)
\(54\) 0 0
\(55\) 7531.26 0.335707
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −14887.6 −0.556795 −0.278398 0.960466i \(-0.589803\pi\)
−0.278398 + 0.960466i \(0.589803\pi\)
\(60\) 0 0
\(61\) 4981.74 0.171418 0.0857090 0.996320i \(-0.472684\pi\)
0.0857090 + 0.996320i \(0.472684\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −26145.1 −0.767551
\(66\) 0 0
\(67\) −35931.5 −0.977886 −0.488943 0.872316i \(-0.662617\pi\)
−0.488943 + 0.872316i \(0.662617\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13176.9 −0.310219 −0.155110 0.987897i \(-0.549573\pi\)
−0.155110 + 0.987897i \(0.549573\pi\)
\(72\) 0 0
\(73\) 49108.5 1.07857 0.539286 0.842123i \(-0.318694\pi\)
0.539286 + 0.842123i \(0.318694\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7371.43 −0.141685
\(78\) 0 0
\(79\) 17296.5 0.311810 0.155905 0.987772i \(-0.450171\pi\)
0.155905 + 0.987772i \(0.450171\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17900.5 0.285213 0.142607 0.989779i \(-0.454452\pi\)
0.142607 + 0.989779i \(0.454452\pi\)
\(84\) 0 0
\(85\) −17287.2 −0.259524
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 71460.7 0.956296 0.478148 0.878279i \(-0.341308\pi\)
0.478148 + 0.878279i \(0.341308\pi\)
\(90\) 0 0
\(91\) 25590.2 0.323945
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −107171. −1.21834
\(96\) 0 0
\(97\) 74744.5 0.806584 0.403292 0.915071i \(-0.367866\pi\)
0.403292 + 0.915071i \(0.367866\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 24726.6 0.241191 0.120595 0.992702i \(-0.461520\pi\)
0.120595 + 0.992702i \(0.461520\pi\)
\(102\) 0 0
\(103\) −1889.77 −0.0175516 −0.00877580 0.999961i \(-0.502793\pi\)
−0.00877580 + 0.999961i \(0.502793\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −176838. −1.49319 −0.746596 0.665278i \(-0.768313\pi\)
−0.746596 + 0.665278i \(0.768313\pi\)
\(108\) 0 0
\(109\) −76023.5 −0.612889 −0.306444 0.951889i \(-0.599139\pi\)
−0.306444 + 0.951889i \(0.599139\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 70053.5 0.516100 0.258050 0.966132i \(-0.416920\pi\)
0.258050 + 0.966132i \(0.416920\pi\)
\(114\) 0 0
\(115\) −24264.7 −0.171092
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 16920.3 0.109532
\(120\) 0 0
\(121\) −138420. −0.859477
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 187421. 1.07286
\(126\) 0 0
\(127\) 90666.0 0.498810 0.249405 0.968399i \(-0.419765\pi\)
0.249405 + 0.968399i \(0.419765\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 26597.2 0.135412 0.0677060 0.997705i \(-0.478432\pi\)
0.0677060 + 0.997705i \(0.478432\pi\)
\(132\) 0 0
\(133\) 104897. 0.514201
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 130412. 0.593632 0.296816 0.954935i \(-0.404075\pi\)
0.296816 + 0.954935i \(0.404075\pi\)
\(138\) 0 0
\(139\) 295933. 1.29914 0.649572 0.760300i \(-0.274948\pi\)
0.649572 + 0.760300i \(0.274948\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −78565.9 −0.321287
\(144\) 0 0
\(145\) 197622. 0.780574
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 441885. 1.63059 0.815293 0.579049i \(-0.196576\pi\)
0.815293 + 0.579049i \(0.196576\pi\)
\(150\) 0 0
\(151\) −247605. −0.883726 −0.441863 0.897083i \(-0.645682\pi\)
−0.441863 + 0.897083i \(0.645682\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −195531. −0.653713
\(156\) 0 0
\(157\) 67662.2 0.219077 0.109539 0.993983i \(-0.465063\pi\)
0.109539 + 0.993983i \(0.465063\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 23749.7 0.0722094
\(162\) 0 0
\(163\) 595355. 1.75512 0.877561 0.479466i \(-0.159169\pi\)
0.877561 + 0.479466i \(0.159169\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −541587. −1.50272 −0.751358 0.659895i \(-0.770601\pi\)
−0.751358 + 0.659895i \(0.770601\pi\)
\(168\) 0 0
\(169\) −98548.1 −0.265419
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 407207. 1.03443 0.517213 0.855857i \(-0.326969\pi\)
0.517213 + 0.855857i \(0.326969\pi\)
\(174\) 0 0
\(175\) −30318.7 −0.0748369
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 309285. 0.721483 0.360742 0.932666i \(-0.382524\pi\)
0.360742 + 0.932666i \(0.382524\pi\)
\(180\) 0 0
\(181\) 300949. 0.682804 0.341402 0.939917i \(-0.389098\pi\)
0.341402 + 0.939917i \(0.389098\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 279086. 0.599526
\(186\) 0 0
\(187\) −51947.9 −0.108634
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 41016.3 0.0813529 0.0406764 0.999172i \(-0.487049\pi\)
0.0406764 + 0.999172i \(0.487049\pi\)
\(192\) 0 0
\(193\) 454328. 0.877963 0.438982 0.898496i \(-0.355339\pi\)
0.438982 + 0.898496i \(0.355339\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 477754. 0.877078 0.438539 0.898712i \(-0.355496\pi\)
0.438539 + 0.898712i \(0.355496\pi\)
\(198\) 0 0
\(199\) −260092. −0.465580 −0.232790 0.972527i \(-0.574785\pi\)
−0.232790 + 0.972527i \(0.574785\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −193427. −0.329441
\(204\) 0 0
\(205\) 385659. 0.640943
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −322049. −0.509983
\(210\) 0 0
\(211\) −74213.3 −0.114756 −0.0573780 0.998353i \(-0.518274\pi\)
−0.0573780 + 0.998353i \(0.518274\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 128410. 0.189454
\(216\) 0 0
\(217\) 191382. 0.275899
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 180340. 0.248376
\(222\) 0 0
\(223\) 792373. 1.06701 0.533504 0.845798i \(-0.320875\pi\)
0.533504 + 0.845798i \(0.320875\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.32051e6 −1.70090 −0.850449 0.526058i \(-0.823670\pi\)
−0.850449 + 0.526058i \(0.823670\pi\)
\(228\) 0 0
\(229\) 1.03037e6 1.29839 0.649197 0.760620i \(-0.275105\pi\)
0.649197 + 0.760620i \(0.275105\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −809463. −0.976804 −0.488402 0.872619i \(-0.662420\pi\)
−0.488402 + 0.872619i \(0.662420\pi\)
\(234\) 0 0
\(235\) 1.04640e6 1.23603
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −46281.9 −0.0524103 −0.0262052 0.999657i \(-0.508342\pi\)
−0.0262052 + 0.999657i \(0.508342\pi\)
\(240\) 0 0
\(241\) 1.16053e6 1.28711 0.643554 0.765401i \(-0.277459\pi\)
0.643554 + 0.765401i \(0.277459\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −120200. −0.127935
\(246\) 0 0
\(247\) 1.11801e6 1.16601
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −52898.3 −0.0529978 −0.0264989 0.999649i \(-0.508436\pi\)
−0.0264989 + 0.999649i \(0.508436\pi\)
\(252\) 0 0
\(253\) −72915.2 −0.0716171
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 315247. 0.297727 0.148863 0.988858i \(-0.452439\pi\)
0.148863 + 0.988858i \(0.452439\pi\)
\(258\) 0 0
\(259\) −273163. −0.253030
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −222707. −0.198538 −0.0992692 0.995061i \(-0.531651\pi\)
−0.0992692 + 0.995061i \(0.531651\pi\)
\(264\) 0 0
\(265\) −1.48610e6 −1.29997
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10498.1 −0.00884563 −0.00442281 0.999990i \(-0.501408\pi\)
−0.00442281 + 0.999990i \(0.501408\pi\)
\(270\) 0 0
\(271\) 933583. 0.772200 0.386100 0.922457i \(-0.373822\pi\)
0.386100 + 0.922457i \(0.373822\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 93082.9 0.0742230
\(276\) 0 0
\(277\) 1.36264e6 1.06704 0.533522 0.845786i \(-0.320868\pi\)
0.533522 + 0.845786i \(0.320868\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.56211e6 −1.18018 −0.590088 0.807339i \(-0.700907\pi\)
−0.590088 + 0.807339i \(0.700907\pi\)
\(282\) 0 0
\(283\) 191256. 0.141954 0.0709772 0.997478i \(-0.477388\pi\)
0.0709772 + 0.997478i \(0.477388\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −377474. −0.270510
\(288\) 0 0
\(289\) −1.30062e6 −0.916019
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −462576. −0.314785 −0.157393 0.987536i \(-0.550309\pi\)
−0.157393 + 0.987536i \(0.550309\pi\)
\(294\) 0 0
\(295\) 745311. 0.498635
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 253128. 0.163743
\(300\) 0 0
\(301\) −125685. −0.0799591
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −249398. −0.153512
\(306\) 0 0
\(307\) −221395. −0.134067 −0.0670335 0.997751i \(-0.521353\pi\)
−0.0670335 + 0.997751i \(0.521353\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.03372e6 0.606039 0.303019 0.952984i \(-0.402005\pi\)
0.303019 + 0.952984i \(0.402005\pi\)
\(312\) 0 0
\(313\) 1.71162e6 0.987519 0.493759 0.869599i \(-0.335622\pi\)
0.493759 + 0.869599i \(0.335622\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 872214. 0.487500 0.243750 0.969838i \(-0.421622\pi\)
0.243750 + 0.969838i \(0.421622\pi\)
\(318\) 0 0
\(319\) 593851. 0.326739
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 739228. 0.394251
\(324\) 0 0
\(325\) −323142. −0.169701
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.02419e6 −0.521665
\(330\) 0 0
\(331\) 999733. 0.501550 0.250775 0.968045i \(-0.419315\pi\)
0.250775 + 0.968045i \(0.419315\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.79882e6 0.875740
\(336\) 0 0
\(337\) 1.96881e6 0.944340 0.472170 0.881507i \(-0.343471\pi\)
0.472170 + 0.881507i \(0.343471\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −587570. −0.273636
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.48114e6 1.55202 0.776011 0.630719i \(-0.217240\pi\)
0.776011 + 0.630719i \(0.217240\pi\)
\(348\) 0 0
\(349\) 2.38332e6 1.04741 0.523707 0.851899i \(-0.324549\pi\)
0.523707 + 0.851899i \(0.324549\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.12172e6 −1.33339 −0.666696 0.745330i \(-0.732292\pi\)
−0.666696 + 0.745330i \(0.732292\pi\)
\(354\) 0 0
\(355\) 659670. 0.277815
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 607472. 0.248765 0.124383 0.992234i \(-0.460305\pi\)
0.124383 + 0.992234i \(0.460305\pi\)
\(360\) 0 0
\(361\) 2.10671e6 0.850818
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.45849e6 −0.965910
\(366\) 0 0
\(367\) 1.65712e6 0.642229 0.321115 0.947040i \(-0.395943\pi\)
0.321115 + 0.947040i \(0.395943\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.45456e6 0.548651
\(372\) 0 0
\(373\) 3.92072e6 1.45913 0.729564 0.683913i \(-0.239723\pi\)
0.729564 + 0.683913i \(0.239723\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.06158e6 −0.747045
\(378\) 0 0
\(379\) 2.50020e6 0.894082 0.447041 0.894513i \(-0.352478\pi\)
0.447041 + 0.894513i \(0.352478\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.61937e6 0.564091 0.282045 0.959401i \(-0.408987\pi\)
0.282045 + 0.959401i \(0.408987\pi\)
\(384\) 0 0
\(385\) 369032. 0.126886
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.18930e6 1.06861 0.534307 0.845290i \(-0.320573\pi\)
0.534307 + 0.845290i \(0.320573\pi\)
\(390\) 0 0
\(391\) 167369. 0.0553647
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −865905. −0.279240
\(396\) 0 0
\(397\) −1.98115e6 −0.630870 −0.315435 0.948947i \(-0.602150\pi\)
−0.315435 + 0.948947i \(0.602150\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.95405e6 0.917396 0.458698 0.888592i \(-0.348316\pi\)
0.458698 + 0.888592i \(0.348316\pi\)
\(402\) 0 0
\(403\) 2.03978e6 0.625633
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 838650. 0.250954
\(408\) 0 0
\(409\) 2.63901e6 0.780067 0.390034 0.920801i \(-0.372463\pi\)
0.390034 + 0.920801i \(0.372463\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −729494. −0.210449
\(414\) 0 0
\(415\) −896143. −0.255421
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −625639. −0.174096 −0.0870480 0.996204i \(-0.527743\pi\)
−0.0870480 + 0.996204i \(0.527743\pi\)
\(420\) 0 0
\(421\) 3.30853e6 0.909767 0.454883 0.890551i \(-0.349681\pi\)
0.454883 + 0.890551i \(0.349681\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −213662. −0.0573793
\(426\) 0 0
\(427\) 244105. 0.0647899
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.27141e6 1.88549 0.942747 0.333508i \(-0.108232\pi\)
0.942747 + 0.333508i \(0.108232\pi\)
\(432\) 0 0
\(433\) 922867. 0.236548 0.118274 0.992981i \(-0.462264\pi\)
0.118274 + 0.992981i \(0.462264\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.03760e6 0.259911
\(438\) 0 0
\(439\) −1.17979e6 −0.292176 −0.146088 0.989272i \(-0.546668\pi\)
−0.146088 + 0.989272i \(0.546668\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.45194e6 0.351512 0.175756 0.984434i \(-0.443763\pi\)
0.175756 + 0.984434i \(0.443763\pi\)
\(444\) 0 0
\(445\) −3.57750e6 −0.856405
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.52131e6 −0.356126 −0.178063 0.984019i \(-0.556983\pi\)
−0.178063 + 0.984019i \(0.556983\pi\)
\(450\) 0 0
\(451\) 1.15890e6 0.268291
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.28111e6 −0.290107
\(456\) 0 0
\(457\) −2.65993e6 −0.595771 −0.297886 0.954602i \(-0.596281\pi\)
−0.297886 + 0.954602i \(0.596281\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.26417e6 −1.81112 −0.905559 0.424220i \(-0.860548\pi\)
−0.905559 + 0.424220i \(0.860548\pi\)
\(462\) 0 0
\(463\) 5.76340e6 1.24947 0.624736 0.780836i \(-0.285207\pi\)
0.624736 + 0.780836i \(0.285207\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.44068e6 0.730050 0.365025 0.930998i \(-0.381061\pi\)
0.365025 + 0.930998i \(0.381061\pi\)
\(468\) 0 0
\(469\) −1.76064e6 −0.369606
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 385872. 0.0793032
\(474\) 0 0
\(475\) −1.32459e6 −0.269368
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.39817e6 −1.27414 −0.637070 0.770806i \(-0.719854\pi\)
−0.637070 + 0.770806i \(0.719854\pi\)
\(480\) 0 0
\(481\) −2.91141e6 −0.573774
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.74189e6 −0.722332
\(486\) 0 0
\(487\) −5.01077e6 −0.957375 −0.478687 0.877985i \(-0.658887\pi\)
−0.478687 + 0.877985i \(0.658887\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.92530e6 0.547603 0.273802 0.961786i \(-0.411719\pi\)
0.273802 + 0.961786i \(0.411719\pi\)
\(492\) 0 0
\(493\) −1.36312e6 −0.252591
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −645670. −0.117252
\(498\) 0 0
\(499\) −3.75480e6 −0.675050 −0.337525 0.941317i \(-0.609590\pi\)
−0.337525 + 0.941317i \(0.609590\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.49794e6 −0.792673 −0.396337 0.918105i \(-0.629719\pi\)
−0.396337 + 0.918105i \(0.629719\pi\)
\(504\) 0 0
\(505\) −1.23787e6 −0.215997
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.89885e6 0.838107 0.419054 0.907962i \(-0.362362\pi\)
0.419054 + 0.907962i \(0.362362\pi\)
\(510\) 0 0
\(511\) 2.40632e6 0.407662
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 94606.8 0.0157182
\(516\) 0 0
\(517\) 3.14442e6 0.517386
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.46792e6 1.36673 0.683364 0.730077i \(-0.260516\pi\)
0.683364 + 0.730077i \(0.260516\pi\)
\(522\) 0 0
\(523\) 4.23571e6 0.677130 0.338565 0.940943i \(-0.390059\pi\)
0.338565 + 0.940943i \(0.390059\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.34870e6 0.211539
\(528\) 0 0
\(529\) −6.20142e6 −0.963501
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.02318e6 −0.613411
\(534\) 0 0
\(535\) 8.85293e6 1.33722
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −361200. −0.0535520
\(540\) 0 0
\(541\) 1.26890e7 1.86395 0.931977 0.362517i \(-0.118082\pi\)
0.931977 + 0.362517i \(0.118082\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.80593e6 0.548869
\(546\) 0 0
\(547\) −8.45389e6 −1.20806 −0.604030 0.796962i \(-0.706439\pi\)
−0.604030 + 0.796962i \(0.706439\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8.45061e6 −1.18579
\(552\) 0 0
\(553\) 847528. 0.117853
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.19598e6 −1.11934 −0.559671 0.828715i \(-0.689072\pi\)
−0.559671 + 0.828715i \(0.689072\pi\)
\(558\) 0 0
\(559\) −1.33957e6 −0.181316
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.06213e6 −1.20492 −0.602462 0.798148i \(-0.705813\pi\)
−0.602462 + 0.798148i \(0.705813\pi\)
\(564\) 0 0
\(565\) −3.50705e6 −0.462191
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.51890e6 0.455645 0.227822 0.973703i \(-0.426839\pi\)
0.227822 + 0.973703i \(0.426839\pi\)
\(570\) 0 0
\(571\) 912516. 0.117125 0.0585626 0.998284i \(-0.481348\pi\)
0.0585626 + 0.998284i \(0.481348\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −299900. −0.0378275
\(576\) 0 0
\(577\) −5.44889e6 −0.681347 −0.340674 0.940182i \(-0.610655\pi\)
−0.340674 + 0.940182i \(0.610655\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 877124. 0.107800
\(582\) 0 0
\(583\) −4.46571e6 −0.544151
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −482435. −0.0577888 −0.0288944 0.999582i \(-0.509199\pi\)
−0.0288944 + 0.999582i \(0.509199\pi\)
\(588\) 0 0
\(589\) 8.36123e6 0.993074
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.60547e6 0.187484 0.0937422 0.995597i \(-0.470117\pi\)
0.0937422 + 0.995597i \(0.470117\pi\)
\(594\) 0 0
\(595\) −847073. −0.0980909
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.66288e6 0.644867 0.322434 0.946592i \(-0.395499\pi\)
0.322434 + 0.946592i \(0.395499\pi\)
\(600\) 0 0
\(601\) −6.72653e6 −0.759635 −0.379817 0.925062i \(-0.624013\pi\)
−0.379817 + 0.925062i \(0.624013\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.92963e6 0.769700
\(606\) 0 0
\(607\) −5.25145e6 −0.578505 −0.289253 0.957253i \(-0.593407\pi\)
−0.289253 + 0.957253i \(0.593407\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.09160e7 −1.18293
\(612\) 0 0
\(613\) 325286. 0.0349634 0.0174817 0.999847i \(-0.494435\pi\)
0.0174817 + 0.999847i \(0.494435\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.46400e6 −0.366324 −0.183162 0.983083i \(-0.558633\pi\)
−0.183162 + 0.983083i \(0.558633\pi\)
\(618\) 0 0
\(619\) −8.92401e6 −0.936124 −0.468062 0.883696i \(-0.655048\pi\)
−0.468062 + 0.883696i \(0.655048\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.50157e6 0.361446
\(624\) 0 0
\(625\) −7.44918e6 −0.762796
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.92503e6 −0.194004
\(630\) 0 0
\(631\) −1.00882e7 −1.00865 −0.504325 0.863514i \(-0.668259\pi\)
−0.504325 + 0.863514i \(0.668259\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.53896e6 −0.446706
\(636\) 0 0
\(637\) 1.25392e6 0.122440
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.18337e7 1.13756 0.568781 0.822489i \(-0.307415\pi\)
0.568781 + 0.822489i \(0.307415\pi\)
\(642\) 0 0
\(643\) −1.13185e7 −1.07959 −0.539797 0.841795i \(-0.681499\pi\)
−0.539797 + 0.841795i \(0.681499\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.59034e7 −1.49359 −0.746793 0.665056i \(-0.768408\pi\)
−0.746793 + 0.665056i \(0.768408\pi\)
\(648\) 0 0
\(649\) 2.23965e6 0.208722
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.03780e7 1.87016 0.935082 0.354432i \(-0.115326\pi\)
0.935082 + 0.354432i \(0.115326\pi\)
\(654\) 0 0
\(655\) −1.33152e6 −0.121267
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.51593e7 −1.35977 −0.679884 0.733319i \(-0.737970\pi\)
−0.679884 + 0.733319i \(0.737970\pi\)
\(660\) 0 0
\(661\) −4.02611e6 −0.358412 −0.179206 0.983812i \(-0.557353\pi\)
−0.179206 + 0.983812i \(0.557353\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.25139e6 −0.460490
\(666\) 0 0
\(667\) −1.91331e6 −0.166521
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −749439. −0.0642584
\(672\) 0 0
\(673\) −2.19098e7 −1.86466 −0.932330 0.361608i \(-0.882228\pi\)
−0.932330 + 0.361608i \(0.882228\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 406122. 0.0340553 0.0170277 0.999855i \(-0.494580\pi\)
0.0170277 + 0.999855i \(0.494580\pi\)
\(678\) 0 0
\(679\) 3.66248e6 0.304860
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8.99699e6 0.737981 0.368991 0.929433i \(-0.379703\pi\)
0.368991 + 0.929433i \(0.379703\pi\)
\(684\) 0 0
\(685\) −6.52877e6 −0.531624
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.55029e7 1.24413
\(690\) 0 0
\(691\) 1.13549e7 0.904669 0.452335 0.891848i \(-0.350591\pi\)
0.452335 + 0.891848i \(0.350591\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.48152e7 −1.16344
\(696\) 0 0
\(697\) −2.66014e6 −0.207406
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.70090e6 −0.361315 −0.180657 0.983546i \(-0.557823\pi\)
−0.180657 + 0.983546i \(0.557823\pi\)
\(702\) 0 0
\(703\) −1.19341e7 −0.910757
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.21160e6 0.0911615
\(708\) 0 0
\(709\) 1.51946e6 0.113520 0.0567602 0.998388i \(-0.481923\pi\)
0.0567602 + 0.998388i \(0.481923\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.89307e6 0.139458
\(714\) 0 0
\(715\) 3.93320e6 0.287727
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.03946e6 0.363548 0.181774 0.983340i \(-0.441816\pi\)
0.181774 + 0.983340i \(0.441816\pi\)
\(720\) 0 0
\(721\) −92599.0 −0.00663388
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.44251e6 0.172580
\(726\) 0 0
\(727\) 1.81583e6 0.127420 0.0637101 0.997968i \(-0.479707\pi\)
0.0637101 + 0.997968i \(0.479707\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −885729. −0.0613066
\(732\) 0 0
\(733\) 9.26839e6 0.637154 0.318577 0.947897i \(-0.396795\pi\)
0.318577 + 0.947897i \(0.396795\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.40544e6 0.366574
\(738\) 0 0
\(739\) 9.41597e6 0.634241 0.317120 0.948385i \(-0.397284\pi\)
0.317120 + 0.948385i \(0.397284\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.68590e7 1.78491 0.892457 0.451132i \(-0.148980\pi\)
0.892457 + 0.451132i \(0.148980\pi\)
\(744\) 0 0
\(745\) −2.21219e7 −1.46026
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.66505e6 −0.564373
\(750\) 0 0
\(751\) −4.29030e6 −0.277580 −0.138790 0.990322i \(-0.544321\pi\)
−0.138790 + 0.990322i \(0.544321\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.23957e7 0.791416
\(756\) 0 0
\(757\) −2.68729e6 −0.170442 −0.0852208 0.996362i \(-0.527160\pi\)
−0.0852208 + 0.996362i \(0.527160\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.65935e7 1.66461 0.832307 0.554315i \(-0.187020\pi\)
0.832307 + 0.554315i \(0.187020\pi\)
\(762\) 0 0
\(763\) −3.72515e6 −0.231650
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.77506e6 −0.477216
\(768\) 0 0
\(769\) −2.18614e7 −1.33310 −0.666549 0.745461i \(-0.732229\pi\)
−0.666549 + 0.745461i \(0.732229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7.17747e6 0.432039 0.216019 0.976389i \(-0.430693\pi\)
0.216019 + 0.976389i \(0.430693\pi\)
\(774\) 0 0
\(775\) −2.41668e6 −0.144532
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.64914e7 −0.973674
\(780\) 0 0
\(781\) 1.98230e6 0.116290
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.38734e6 −0.196193
\(786\) 0 0
\(787\) −1.34004e7 −0.771225 −0.385612 0.922661i \(-0.626010\pi\)
−0.385612 + 0.922661i \(0.626010\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.43262e6 0.195067
\(792\) 0 0
\(793\) 2.60171e6 0.146918
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −503745. −0.0280909 −0.0140454 0.999901i \(-0.504471\pi\)
−0.0140454 + 0.999901i \(0.504471\pi\)
\(798\) 0 0
\(799\) −7.21768e6 −0.399973
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7.38775e6 −0.404318
\(804\) 0 0
\(805\) −1.18897e6 −0.0646668
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.36891e7 −1.27256 −0.636279 0.771459i \(-0.719527\pi\)
−0.636279 + 0.771459i \(0.719527\pi\)
\(810\) 0 0
\(811\) −1.47421e7 −0.787057 −0.393528 0.919312i \(-0.628746\pi\)
−0.393528 + 0.919312i \(0.628746\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.98050e7 −1.57179
\(816\) 0 0
\(817\) −5.49103e6 −0.287805
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6.54488e6 0.338878 0.169439 0.985541i \(-0.445804\pi\)
0.169439 + 0.985541i \(0.445804\pi\)
\(822\) 0 0
\(823\) −3.14409e7 −1.61806 −0.809031 0.587766i \(-0.800008\pi\)
−0.809031 + 0.587766i \(0.800008\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.94944e7 1.49960 0.749801 0.661663i \(-0.230149\pi\)
0.749801 + 0.661663i \(0.230149\pi\)
\(828\) 0 0
\(829\) 8.27844e6 0.418371 0.209186 0.977876i \(-0.432919\pi\)
0.209186 + 0.977876i \(0.432919\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 829096. 0.0413992
\(834\) 0 0
\(835\) 2.71132e7 1.34575
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.53550e7 1.24353 0.621767 0.783202i \(-0.286415\pi\)
0.621767 + 0.783202i \(0.286415\pi\)
\(840\) 0 0
\(841\) −4.92841e6 −0.240279
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.93356e6 0.237694
\(846\) 0 0
\(847\) −6.78256e6 −0.324852
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.70201e6 −0.127898
\(852\) 0 0
\(853\) 6.68641e6 0.314645 0.157322 0.987547i \(-0.449714\pi\)
0.157322 + 0.987547i \(0.449714\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.50753e7 1.63136 0.815678 0.578506i \(-0.196364\pi\)
0.815678 + 0.578506i \(0.196364\pi\)
\(858\) 0 0
\(859\) −2.38202e7 −1.10144 −0.550722 0.834689i \(-0.685647\pi\)
−0.550722 + 0.834689i \(0.685647\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.18907e7 1.00054 0.500269 0.865870i \(-0.333235\pi\)
0.500269 + 0.865870i \(0.333235\pi\)
\(864\) 0 0
\(865\) −2.03858e7 −0.926375
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.60204e6 −0.116886
\(870\) 0 0
\(871\) −1.87652e7 −0.838124
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.18365e6 0.405504
\(876\) 0 0
\(877\) −2.55178e7 −1.12032 −0.560162 0.828383i \(-0.689261\pi\)
−0.560162 + 0.828383i \(0.689261\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.08125e7 −0.903410 −0.451705 0.892167i \(-0.649184\pi\)
−0.451705 + 0.892167i \(0.649184\pi\)
\(882\) 0 0
\(883\) −4.62199e6 −0.199493 −0.0997465 0.995013i \(-0.531803\pi\)
−0.0997465 + 0.995013i \(0.531803\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.37519e7 −1.44042 −0.720210 0.693756i \(-0.755955\pi\)
−0.720210 + 0.693756i \(0.755955\pi\)
\(888\) 0 0
\(889\) 4.44263e6 0.188532
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −4.47457e7 −1.87768
\(894\) 0 0
\(895\) −1.54836e7 −0.646121
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.54179e7 −0.636249
\(900\) 0 0
\(901\) 1.02506e7 0.420665
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.50662e7 −0.611482
\(906\) 0 0
\(907\) −1.55386e7 −0.627183 −0.313591 0.949558i \(-0.601532\pi\)
−0.313591 + 0.949558i \(0.601532\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.69477e7 1.07578 0.537892 0.843014i \(-0.319221\pi\)
0.537892 + 0.843014i \(0.319221\pi\)
\(912\) 0 0
\(913\) −2.69290e6 −0.106916
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.30326e6 0.0511809
\(918\) 0 0
\(919\) 2.77206e7 1.08272 0.541358 0.840792i \(-0.317910\pi\)
0.541358 + 0.840792i \(0.317910\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −6.88165e6 −0.265882
\(924\) 0 0
\(925\) 3.44937e6 0.132552
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4.06274e7 −1.54447 −0.772236 0.635336i \(-0.780862\pi\)
−0.772236 + 0.635336i \(0.780862\pi\)
\(930\) 0 0
\(931\) 5.13994e6 0.194350
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.60064e6 0.0972862
\(936\) 0 0
\(937\) −2.23464e7 −0.831493 −0.415747 0.909480i \(-0.636480\pi\)
−0.415747 + 0.909480i \(0.636480\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.05299e7 1.12396 0.561981 0.827150i \(-0.310039\pi\)
0.561981 + 0.827150i \(0.310039\pi\)
\(942\) 0 0
\(943\) −3.73382e6 −0.136733
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9.02758e6 −0.327112 −0.163556 0.986534i \(-0.552296\pi\)
−0.163556 + 0.986534i \(0.552296\pi\)
\(948\) 0 0
\(949\) 2.56469e7 0.924420
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.20115e7 −1.85510 −0.927550 0.373699i \(-0.878089\pi\)
−0.927550 + 0.373699i \(0.878089\pi\)
\(954\) 0 0
\(955\) −2.05338e6 −0.0728551
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.39021e6 0.224372
\(960\) 0 0
\(961\) −1.33743e7 −0.467156
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.27448e7 −0.786255
\(966\) 0 0
\(967\) 3.40751e7 1.17185 0.585924 0.810366i \(-0.300732\pi\)
0.585924 + 0.810366i \(0.300732\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.90682e7 0.989396 0.494698 0.869065i \(-0.335279\pi\)
0.494698 + 0.869065i \(0.335279\pi\)
\(972\) 0 0
\(973\) 1.45007e7 0.491030
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −4.11776e7 −1.38015 −0.690073 0.723740i \(-0.742422\pi\)
−0.690073 + 0.723740i \(0.742422\pi\)
\(978\) 0 0
\(979\) −1.07504e7 −0.358481
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −3.65465e7 −1.20632 −0.603160 0.797621i \(-0.706092\pi\)
−0.603160 + 0.797621i \(0.706092\pi\)
\(984\) 0 0
\(985\) −2.39175e7 −0.785463
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.24323e6 −0.0404166
\(990\) 0 0
\(991\) −1.79164e7 −0.579518 −0.289759 0.957100i \(-0.593575\pi\)
−0.289759 + 0.957100i \(0.593575\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.30208e7 0.416947
\(996\) 0 0
\(997\) 4.44808e7 1.41721 0.708606 0.705604i \(-0.249324\pi\)
0.708606 + 0.705604i \(0.249324\pi\)
\(998\) 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.br.1.1 2
3.2 odd 2 1008.6.a.bj.1.2 2
4.3 odd 2 504.6.a.q.1.1 yes 2
12.11 even 2 504.6.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.n.1.2 2 12.11 even 2
504.6.a.q.1.1 yes 2 4.3 odd 2
1008.6.a.bj.1.2 2 3.2 odd 2
1008.6.a.br.1.1 2 1.1 even 1 trivial