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Properties

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

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
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)
 
\(f(q)\) \(=\) \(q-54.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-54.0000 q^{5} -49.0000 q^{7} +594.000 q^{11} +26.0000 q^{13} +534.000 q^{17} +3004.00 q^{19} +3510.00 q^{23} -209.000 q^{25} -4296.00 q^{29} -8036.00 q^{31} +2646.00 q^{35} -502.000 q^{37} -9870.00 q^{41} -9068.00 q^{43} +1140.00 q^{47} +2401.00 q^{49} -28356.0 q^{53} -32076.0 q^{55} -8196.00 q^{59} +29822.0 q^{61} -1404.00 q^{65} +62884.0 q^{67} -34398.0 q^{71} +56990.0 q^{73} -29106.0 q^{77} -49496.0 q^{79} -52512.0 q^{83} -28836.0 q^{85} +48282.0 q^{89} -1274.00 q^{91} -162216. q^{95} -83938.0 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −54.0000 −0.965981 −0.482991 − 0.875625i \(-0.660450\pi\)
−0.482991 + 0.875625i \(0.660450\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 594.000 1.48015 0.740073 − 0.672526i \(-0.234791\pi\)
0.740073 + 0.672526i \(0.234791\pi\)
\(12\) 0 0
\(13\) 26.0000 0.0426692 0.0213346 − 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 534.000 0.448145 0.224073 − 0.974572i \(-0.428065\pi\)
0.224073 + 0.974572i \(0.428065\pi\)
\(18\) 0 0
\(19\) 3004.00 1.90904 0.954522 − 0.298141i \(-0.0963664\pi\)
0.954522 + 0.298141i \(0.0963664\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3510.00 1.38353 0.691763 − 0.722124i \(-0.256834\pi\)
0.691763 + 0.722124i \(0.256834\pi\)
\(24\) 0 0
\(25\) −209.000 −0.0668800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4296.00 −0.948570 −0.474285 − 0.880371i \(-0.657293\pi\)
−0.474285 + 0.880371i \(0.657293\pi\)
\(30\) 0 0
\(31\) −8036.00 −1.50188 −0.750941 − 0.660370i \(-0.770400\pi\)
−0.750941 + 0.660370i \(0.770400\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2646.00 0.365107
\(36\) 0 0
\(37\) −502.000 −0.0602836 −0.0301418 − 0.999546i \(-0.509596\pi\)
−0.0301418 + 0.999546i \(0.509596\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9870.00 −0.916975 −0.458488 − 0.888701i \(-0.651609\pi\)
−0.458488 + 0.888701i \(0.651609\pi\)
\(42\) 0 0
\(43\) −9068.00 −0.747895 −0.373947 − 0.927450i \(-0.621996\pi\)
−0.373947 + 0.927450i \(0.621996\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1140.00 0.0752766 0.0376383 − 0.999291i \(-0.488017\pi\)
0.0376383 + 0.999291i \(0.488017\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −28356.0 −1.38661 −0.693307 − 0.720643i \(-0.743847\pi\)
−0.693307 + 0.720643i \(0.743847\pi\)
\(54\) 0 0
\(55\) −32076.0 −1.42979
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8196.00 −0.306529 −0.153265 − 0.988185i \(-0.548979\pi\)
−0.153265 + 0.988185i \(0.548979\pi\)
\(60\) 0 0
\(61\) 29822.0 1.02615 0.513077 − 0.858343i \(-0.328506\pi\)
0.513077 + 0.858343i \(0.328506\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1404.00 −0.0412177
\(66\) 0 0
\(67\) 62884.0 1.71141 0.855703 − 0.517467i \(-0.173125\pi\)
0.855703 + 0.517467i \(0.173125\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −34398.0 −0.809818 −0.404909 − 0.914357i \(-0.632697\pi\)
−0.404909 + 0.914357i \(0.632697\pi\)
\(72\) 0 0
\(73\) 56990.0 1.25167 0.625837 − 0.779954i \(-0.284757\pi\)
0.625837 + 0.779954i \(0.284757\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −29106.0 −0.559443
\(78\) 0 0
\(79\) −49496.0 −0.892282 −0.446141 − 0.894963i \(-0.647202\pi\)
−0.446141 + 0.894963i \(0.647202\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −52512.0 −0.836688 −0.418344 − 0.908289i \(-0.637389\pi\)
−0.418344 + 0.908289i \(0.637389\pi\)
\(84\) 0 0
\(85\) −28836.0 −0.432900
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 48282.0 0.646116 0.323058 − 0.946379i \(-0.395289\pi\)
0.323058 + 0.946379i \(0.395289\pi\)
\(90\) 0 0
\(91\) −1274.00 −0.0161275
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −162216. −1.84410
\(96\) 0 0
\(97\) −83938.0 −0.905794 −0.452897 − 0.891563i \(-0.649609\pi\)
−0.452897 + 0.891563i \(0.649609\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 62694.0 0.611537 0.305768 − 0.952106i \(-0.401087\pi\)
0.305768 + 0.952106i \(0.401087\pi\)
\(102\) 0 0
\(103\) 30988.0 0.287806 0.143903 − 0.989592i \(-0.454035\pi\)
0.143903 + 0.989592i \(0.454035\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 118218. 0.998215 0.499108 − 0.866540i \(-0.333661\pi\)
0.499108 + 0.866540i \(0.333661\pi\)
\(108\) 0 0
\(109\) 207362. 1.67172 0.835859 − 0.548944i \(-0.184970\pi\)
0.835859 + 0.548944i \(0.184970\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 136416. 1.00501 0.502504 − 0.864575i \(-0.332412\pi\)
0.502504 + 0.864575i \(0.332412\pi\)
\(114\) 0 0
\(115\) −189540. −1.33646
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −26166.0 −0.169383
\(120\) 0 0
\(121\) 191785. 1.19083
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 180036. 1.03059
\(126\) 0 0
\(127\) 128248. 0.705572 0.352786 − 0.935704i \(-0.385234\pi\)
0.352786 + 0.935704i \(0.385234\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 370296. 1.88526 0.942629 − 0.333842i \(-0.108345\pi\)
0.942629 + 0.333842i \(0.108345\pi\)
\(132\) 0 0
\(133\) −147196. −0.721551
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12924.0 −0.0588296 −0.0294148 − 0.999567i \(-0.509364\pi\)
−0.0294148 + 0.999567i \(0.509364\pi\)
\(138\) 0 0
\(139\) 177760. 0.780364 0.390182 − 0.920738i \(-0.372412\pi\)
0.390182 + 0.920738i \(0.372412\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 15444.0 0.0631567
\(144\) 0 0
\(145\) 231984. 0.916301
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −309564. −1.14231 −0.571156 − 0.820841i \(-0.693505\pi\)
−0.571156 + 0.820841i \(0.693505\pi\)
\(150\) 0 0
\(151\) 300136. 1.07121 0.535606 − 0.844468i \(-0.320083\pi\)
0.535606 + 0.844468i \(0.320083\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 433944. 1.45079
\(156\) 0 0
\(157\) 11726.0 0.0379665 0.0189833 − 0.999820i \(-0.493957\pi\)
0.0189833 + 0.999820i \(0.493957\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −171990. −0.522924
\(162\) 0 0
\(163\) 269260. 0.793785 0.396892 − 0.917865i \(-0.370089\pi\)
0.396892 + 0.917865i \(0.370089\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 41604.0 0.115437 0.0577184 − 0.998333i \(-0.481617\pi\)
0.0577184 + 0.998333i \(0.481617\pi\)
\(168\) 0 0
\(169\) −370617. −0.998179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −286962. −0.728969 −0.364485 − 0.931209i \(-0.618755\pi\)
−0.364485 + 0.931209i \(0.618755\pi\)
\(174\) 0 0
\(175\) 10241.0 0.0252783
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −420186. −0.980187 −0.490094 − 0.871670i \(-0.663037\pi\)
−0.490094 + 0.871670i \(0.663037\pi\)
\(180\) 0 0
\(181\) −16918.0 −0.0383842 −0.0191921 − 0.999816i \(-0.506109\pi\)
−0.0191921 + 0.999816i \(0.506109\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 27108.0 0.0582329
\(186\) 0 0
\(187\) 317196. 0.663321
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −134742. −0.267251 −0.133626 − 0.991032i \(-0.542662\pi\)
−0.133626 + 0.991032i \(0.542662\pi\)
\(192\) 0 0
\(193\) −314650. −0.608043 −0.304022 − 0.952665i \(-0.598330\pi\)
−0.304022 + 0.952665i \(0.598330\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −596628. −1.09531 −0.547656 − 0.836703i \(-0.684480\pi\)
−0.547656 + 0.836703i \(0.684480\pi\)
\(198\) 0 0
\(199\) 10096.0 0.0180724 0.00903622 − 0.999959i \(-0.497124\pi\)
0.00903622 + 0.999959i \(0.497124\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 210504. 0.358526
\(204\) 0 0
\(205\) 532980. 0.885781
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.78438e6 2.82566
\(210\) 0 0
\(211\) 721324. 1.11538 0.557692 − 0.830048i \(-0.311687\pi\)
0.557692 + 0.830048i \(0.311687\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 489672. 0.722452
\(216\) 0 0
\(217\) 393764. 0.567658
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13884.0 0.0191220
\(222\) 0 0
\(223\) 536584. 0.722563 0.361281 − 0.932457i \(-0.382339\pi\)
0.361281 + 0.932457i \(0.382339\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.48698e6 −1.91532 −0.957658 − 0.287908i \(-0.907040\pi\)
−0.957658 + 0.287908i \(0.907040\pi\)
\(228\) 0 0
\(229\) −1.10957e6 −1.39818 −0.699092 − 0.715032i \(-0.746412\pi\)
−0.699092 + 0.715032i \(0.746412\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.38796e6 −1.67489 −0.837444 − 0.546523i \(-0.815951\pi\)
−0.837444 + 0.546523i \(0.815951\pi\)
\(234\) 0 0
\(235\) −61560.0 −0.0727158
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.56406e6 1.77117 0.885583 − 0.464481i \(-0.153759\pi\)
0.885583 + 0.464481i \(0.153759\pi\)
\(240\) 0 0
\(241\) 1.36319e6 1.51187 0.755934 − 0.654648i \(-0.227183\pi\)
0.755934 + 0.654648i \(0.227183\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −129654. −0.137997
\(246\) 0 0
\(247\) 78104.0 0.0814575
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.54847e6 −1.55138 −0.775690 − 0.631115i \(-0.782598\pi\)
−0.775690 + 0.631115i \(0.782598\pi\)
\(252\) 0 0
\(253\) 2.08494e6 2.04782
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.54147e6 1.45580 0.727899 − 0.685684i \(-0.240497\pi\)
0.727899 + 0.685684i \(0.240497\pi\)
\(258\) 0 0
\(259\) 24598.0 0.0227851
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.13251e6 −1.90109 −0.950545 − 0.310588i \(-0.899474\pi\)
−0.950545 + 0.310588i \(0.899474\pi\)
\(264\) 0 0
\(265\) 1.53122e6 1.33944
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −386142. −0.325362 −0.162681 − 0.986679i \(-0.552014\pi\)
−0.162681 + 0.986679i \(0.552014\pi\)
\(270\) 0 0
\(271\) 1.17581e6 0.972556 0.486278 − 0.873804i \(-0.338354\pi\)
0.486278 + 0.873804i \(0.338354\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −124146. −0.0989922
\(276\) 0 0
\(277\) 417038. 0.326570 0.163285 − 0.986579i \(-0.447791\pi\)
0.163285 + 0.986579i \(0.447791\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 523932. 0.395830 0.197915 − 0.980219i \(-0.436583\pi\)
0.197915 + 0.980219i \(0.436583\pi\)
\(282\) 0 0
\(283\) 2.36724e6 1.75702 0.878510 − 0.477723i \(-0.158538\pi\)
0.878510 + 0.477723i \(0.158538\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 483630. 0.346584
\(288\) 0 0
\(289\) −1.13470e6 −0.799166
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.44630e6 1.66472 0.832360 − 0.554236i \(-0.186989\pi\)
0.832360 + 0.554236i \(0.186989\pi\)
\(294\) 0 0
\(295\) 442584. 0.296102
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 91260.0 0.0590340
\(300\) 0 0
\(301\) 444332. 0.282678
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.61039e6 −0.991245
\(306\) 0 0
\(307\) 969316. 0.586975 0.293487 − 0.955963i \(-0.405184\pi\)
0.293487 + 0.955963i \(0.405184\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.44765e6 1.43499 0.717495 − 0.696564i \(-0.245289\pi\)
0.717495 + 0.696564i \(0.245289\pi\)
\(312\) 0 0
\(313\) 2.02541e6 1.16856 0.584281 − 0.811551i \(-0.301376\pi\)
0.584281 + 0.811551i \(0.301376\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.50379e6 −1.39942 −0.699712 − 0.714425i \(-0.746688\pi\)
−0.699712 + 0.714425i \(0.746688\pi\)
\(318\) 0 0
\(319\) −2.55182e6 −1.40402
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.60414e6 0.855529
\(324\) 0 0
\(325\) −5434.00 −0.00285372
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −55860.0 −0.0284519
\(330\) 0 0
\(331\) −1.28700e6 −0.645665 −0.322832 − 0.946456i \(-0.604635\pi\)
−0.322832 + 0.946456i \(0.604635\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.39574e6 −1.65319
\(336\) 0 0
\(337\) −1.40639e6 −0.674574 −0.337287 − 0.941402i \(-0.609509\pi\)
−0.337287 + 0.941402i \(0.609509\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.77338e6 −2.22300
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.25313e6 −0.558692 −0.279346 − 0.960191i \(-0.590118\pi\)
−0.279346 + 0.960191i \(0.590118\pi\)
\(348\) 0 0
\(349\) 1.66876e6 0.733381 0.366691 − 0.930343i \(-0.380491\pi\)
0.366691 + 0.930343i \(0.380491\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.13687e6 0.912728 0.456364 − 0.889793i \(-0.349152\pi\)
0.456364 + 0.889793i \(0.349152\pi\)
\(354\) 0 0
\(355\) 1.85749e6 0.782269
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.60907e6 1.47795 0.738973 − 0.673735i \(-0.235311\pi\)
0.738973 + 0.673735i \(0.235311\pi\)
\(360\) 0 0
\(361\) 6.54792e6 2.64445
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.07746e6 −1.20909
\(366\) 0 0
\(367\) 1.88190e6 0.729344 0.364672 − 0.931136i \(-0.381181\pi\)
0.364672 + 0.931136i \(0.381181\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.38944e6 0.524090
\(372\) 0 0
\(373\) 4.86186e6 1.80938 0.904692 − 0.426067i \(-0.140101\pi\)
0.904692 + 0.426067i \(0.140101\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −111696. −0.0404748
\(378\) 0 0
\(379\) −251300. −0.0898658 −0.0449329 − 0.998990i \(-0.514307\pi\)
−0.0449329 + 0.998990i \(0.514307\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −567720. −0.197759 −0.0988797 − 0.995099i \(-0.531526\pi\)
−0.0988797 + 0.995099i \(0.531526\pi\)
\(384\) 0 0
\(385\) 1.57172e6 0.540411
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.34547e6 0.785880 0.392940 − 0.919564i \(-0.371458\pi\)
0.392940 + 0.919564i \(0.371458\pi\)
\(390\) 0 0
\(391\) 1.87434e6 0.620021
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.67278e6 0.861928
\(396\) 0 0
\(397\) −5.25719e6 −1.67408 −0.837042 − 0.547139i \(-0.815717\pi\)
−0.837042 + 0.547139i \(0.815717\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.34140e6 0.727136 0.363568 − 0.931568i \(-0.381558\pi\)
0.363568 + 0.931568i \(0.381558\pi\)
\(402\) 0 0
\(403\) −208936. −0.0640842
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −298188. −0.0892286
\(408\) 0 0
\(409\) 662318. 0.195775 0.0978877 − 0.995197i \(-0.468791\pi\)
0.0978877 + 0.995197i \(0.468791\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 401604. 0.115857
\(414\) 0 0
\(415\) 2.83565e6 0.808225
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.27752e6 1.46857 0.734285 − 0.678842i \(-0.237518\pi\)
0.734285 + 0.678842i \(0.237518\pi\)
\(420\) 0 0
\(421\) 1.74817e6 0.480706 0.240353 − 0.970686i \(-0.422737\pi\)
0.240353 + 0.970686i \(0.422737\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −111606. −0.0299720
\(426\) 0 0
\(427\) −1.46128e6 −0.387849
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.65575e6 −0.688643 −0.344321 − 0.938852i \(-0.611891\pi\)
−0.344321 + 0.938852i \(0.611891\pi\)
\(432\) 0 0
\(433\) −3.12026e6 −0.799781 −0.399891 − 0.916563i \(-0.630952\pi\)
−0.399891 + 0.916563i \(0.630952\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.05440e7 2.64121
\(438\) 0 0
\(439\) 4.02131e6 0.995879 0.497939 − 0.867212i \(-0.334090\pi\)
0.497939 + 0.867212i \(0.334090\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −766146. −0.185482 −0.0927411 − 0.995690i \(-0.529563\pi\)
−0.0927411 + 0.995690i \(0.529563\pi\)
\(444\) 0 0
\(445\) −2.60723e6 −0.624136
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.01961e6 0.706862 0.353431 − 0.935461i \(-0.385015\pi\)
0.353431 + 0.935461i \(0.385015\pi\)
\(450\) 0 0
\(451\) −5.86278e6 −1.35726
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 68796.0 0.0155788
\(456\) 0 0
\(457\) −223114. −0.0499731 −0.0249866 − 0.999688i \(-0.507954\pi\)
−0.0249866 + 0.999688i \(0.507954\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.58050e6 1.00383 0.501916 − 0.864917i \(-0.332629\pi\)
0.501916 + 0.864917i \(0.332629\pi\)
\(462\) 0 0
\(463\) 4.23654e6 0.918458 0.459229 − 0.888318i \(-0.348126\pi\)
0.459229 + 0.888318i \(0.348126\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.74499e6 −0.582436 −0.291218 − 0.956657i \(-0.594061\pi\)
−0.291218 + 0.956657i \(0.594061\pi\)
\(468\) 0 0
\(469\) −3.08132e6 −0.646851
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.38639e6 −1.10699
\(474\) 0 0
\(475\) −627836. −0.127677
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.67628e6 −0.532957 −0.266478 − 0.963841i \(-0.585860\pi\)
−0.266478 + 0.963841i \(0.585860\pi\)
\(480\) 0 0
\(481\) −13052.0 −0.00257226
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.53265e6 0.874980
\(486\) 0 0
\(487\) 7.92959e6 1.51506 0.757528 − 0.652803i \(-0.226407\pi\)
0.757528 + 0.652803i \(0.226407\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.10567e6 −1.33015 −0.665076 − 0.746775i \(-0.731601\pi\)
−0.665076 + 0.746775i \(0.731601\pi\)
\(492\) 0 0
\(493\) −2.29406e6 −0.425097
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.68550e6 0.306082
\(498\) 0 0
\(499\) 1.31352e6 0.236149 0.118075 − 0.993005i \(-0.462328\pi\)
0.118075 + 0.993005i \(0.462328\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.64608e6 0.642549 0.321274 − 0.946986i \(-0.395889\pi\)
0.321274 + 0.946986i \(0.395889\pi\)
\(504\) 0 0
\(505\) −3.38548e6 −0.590733
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.65410e6 −1.65165 −0.825824 − 0.563928i \(-0.809289\pi\)
−0.825824 + 0.563928i \(0.809289\pi\)
\(510\) 0 0
\(511\) −2.79251e6 −0.473089
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.67335e6 −0.278016
\(516\) 0 0
\(517\) 677160. 0.111420
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.67870e6 −1.23935 −0.619674 − 0.784859i \(-0.712735\pi\)
−0.619674 + 0.784859i \(0.712735\pi\)
\(522\) 0 0
\(523\) 9.06510e6 1.44917 0.724584 − 0.689187i \(-0.242032\pi\)
0.724584 + 0.689187i \(0.242032\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.29122e6 −0.673061
\(528\) 0 0
\(529\) 5.88376e6 0.914146
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −256620. −0.0391266
\(534\) 0 0
\(535\) −6.38377e6 −0.964257
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.42619e6 0.211450
\(540\) 0 0
\(541\) 7.33108e6 1.07690 0.538449 − 0.842658i \(-0.319010\pi\)
0.538449 + 0.842658i \(0.319010\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.11975e7 −1.61485
\(546\) 0 0
\(547\) 3.16498e6 0.452275 0.226138 − 0.974095i \(-0.427390\pi\)
0.226138 + 0.974095i \(0.427390\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.29052e7 −1.81086
\(552\) 0 0
\(553\) 2.42530e6 0.337251
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 118092. 0.0161281 0.00806404 − 0.999967i \(-0.497433\pi\)
0.00806404 + 0.999967i \(0.497433\pi\)
\(558\) 0 0
\(559\) −235768. −0.0319121
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.43544e6 0.855672 0.427836 − 0.903856i \(-0.359276\pi\)
0.427836 + 0.903856i \(0.359276\pi\)
\(564\) 0 0
\(565\) −7.36646e6 −0.970818
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.22976e6 −0.418206 −0.209103 − 0.977894i \(-0.567054\pi\)
−0.209103 + 0.977894i \(0.567054\pi\)
\(570\) 0 0
\(571\) 228556. 0.0293361 0.0146680 − 0.999892i \(-0.495331\pi\)
0.0146680 + 0.999892i \(0.495331\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −733590. −0.0925303
\(576\) 0 0
\(577\) 1.50817e7 1.88587 0.942933 − 0.332983i \(-0.108055\pi\)
0.942933 + 0.332983i \(0.108055\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.57309e6 0.316238
\(582\) 0 0
\(583\) −1.68435e7 −2.05239
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.90044e6 1.06614 0.533072 − 0.846070i \(-0.321037\pi\)
0.533072 + 0.846070i \(0.321037\pi\)
\(588\) 0 0
\(589\) −2.41401e7 −2.86716
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.34870e6 −0.157499 −0.0787495 − 0.996894i \(-0.525093\pi\)
−0.0787495 + 0.996894i \(0.525093\pi\)
\(594\) 0 0
\(595\) 1.41296e6 0.163621
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.18444e7 1.34879 0.674395 − 0.738371i \(-0.264405\pi\)
0.674395 + 0.738371i \(0.264405\pi\)
\(600\) 0 0
\(601\) −9.62671e6 −1.08716 −0.543578 − 0.839359i \(-0.682931\pi\)
−0.543578 + 0.839359i \(0.682931\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.03564e7 −1.15032
\(606\) 0 0
\(607\) 641512. 0.0706697 0.0353348 − 0.999376i \(-0.488750\pi\)
0.0353348 + 0.999376i \(0.488750\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29640.0 0.00321200
\(612\) 0 0
\(613\) 3.72964e6 0.400881 0.200441 − 0.979706i \(-0.435763\pi\)
0.200441 + 0.979706i \(0.435763\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.18580e7 1.25400 0.627000 − 0.779019i \(-0.284282\pi\)
0.627000 + 0.779019i \(0.284282\pi\)
\(618\) 0 0
\(619\) −2.60636e6 −0.273406 −0.136703 − 0.990612i \(-0.543651\pi\)
−0.136703 + 0.990612i \(0.543651\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.36582e6 −0.244209
\(624\) 0 0
\(625\) −9.06882e6 −0.928647
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −268068. −0.0270158
\(630\) 0 0
\(631\) −5.15540e6 −0.515453 −0.257726 − 0.966218i \(-0.582973\pi\)
−0.257726 + 0.966218i \(0.582973\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.92539e6 −0.681569
\(636\) 0 0
\(637\) 62426.0 0.00609561
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.42517e7 −1.37000 −0.685002 − 0.728541i \(-0.740199\pi\)
−0.685002 + 0.728541i \(0.740199\pi\)
\(642\) 0 0
\(643\) 1.24310e7 1.18571 0.592857 − 0.805308i \(-0.298000\pi\)
0.592857 + 0.805308i \(0.298000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.71643e6 0.536864 0.268432 − 0.963299i \(-0.413495\pi\)
0.268432 + 0.963299i \(0.413495\pi\)
\(648\) 0 0
\(649\) −4.86842e6 −0.453708
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.48479e6 0.228038 0.114019 − 0.993479i \(-0.463628\pi\)
0.114019 + 0.993479i \(0.463628\pi\)
\(654\) 0 0
\(655\) −1.99960e7 −1.82112
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.87481e6 0.257867 0.128933 − 0.991653i \(-0.458845\pi\)
0.128933 + 0.991653i \(0.458845\pi\)
\(660\) 0 0
\(661\) −8.18274e6 −0.728442 −0.364221 − 0.931313i \(-0.618665\pi\)
−0.364221 + 0.931313i \(0.618665\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.94858e6 0.697005
\(666\) 0 0
\(667\) −1.50790e7 −1.31237
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.77143e7 1.51886
\(672\) 0 0
\(673\) 1.52187e7 1.29521 0.647603 − 0.761978i \(-0.275772\pi\)
0.647603 + 0.761978i \(0.275772\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.85942e7 1.55922 0.779609 − 0.626266i \(-0.215418\pi\)
0.779609 + 0.626266i \(0.215418\pi\)
\(678\) 0 0
\(679\) 4.11296e6 0.342358
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1362.00 −0.000111719 0 −5.58593e−5 − 1.00000i \(-0.500018\pi\)
−5.58593e−5 1.00000i \(0.500018\pi\)
\(684\) 0 0
\(685\) 697896. 0.0568282
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −737256. −0.0591657
\(690\) 0 0
\(691\) −1.83515e7 −1.46210 −0.731048 − 0.682327i \(-0.760968\pi\)
−0.731048 + 0.682327i \(0.760968\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.59904e6 −0.753817
\(696\) 0 0
\(697\) −5.27058e6 −0.410938
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.00448e7 0.772051 0.386025 − 0.922488i \(-0.373848\pi\)
0.386025 + 0.922488i \(0.373848\pi\)
\(702\) 0 0
\(703\) −1.50801e6 −0.115084
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.07201e6 −0.231139
\(708\) 0 0
\(709\) −2.11149e6 −0.157752 −0.0788759 − 0.996884i \(-0.525133\pi\)
−0.0788759 + 0.996884i \(0.525133\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.82064e7 −2.07789
\(714\) 0 0
\(715\) −833976. −0.0610082
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −296016. −0.0213547 −0.0106773 − 0.999943i \(-0.503399\pi\)
−0.0106773 + 0.999943i \(0.503399\pi\)
\(720\) 0 0
\(721\) −1.51841e6 −0.108781
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 897864. 0.0634403
\(726\) 0 0
\(727\) 90220.0 0.00633092 0.00316546 − 0.999995i \(-0.498992\pi\)
0.00316546 + 0.999995i \(0.498992\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.84231e6 −0.335166
\(732\) 0 0
\(733\) −1.40664e7 −0.966992 −0.483496 − 0.875347i \(-0.660633\pi\)
−0.483496 + 0.875347i \(0.660633\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.73531e7 2.53313
\(738\) 0 0
\(739\) −2.20018e7 −1.48199 −0.740997 − 0.671508i \(-0.765647\pi\)
−0.740997 + 0.671508i \(0.765647\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.42981e6 0.626658 0.313329 − 0.949645i \(-0.398556\pi\)
0.313329 + 0.949645i \(0.398556\pi\)
\(744\) 0 0
\(745\) 1.67165e7 1.10345
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.79268e6 −0.377290
\(750\) 0 0
\(751\) −5.06420e6 −0.327651 −0.163825 − 0.986489i \(-0.552383\pi\)
−0.163825 + 0.986489i \(0.552383\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.62073e7 −1.03477
\(756\) 0 0
\(757\) −9.41479e6 −0.597133 −0.298566 − 0.954389i \(-0.596508\pi\)
−0.298566 + 0.954389i \(0.596508\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.81025e7 1.13313 0.566563 − 0.824019i \(-0.308273\pi\)
0.566563 + 0.824019i \(0.308273\pi\)
\(762\) 0 0
\(763\) −1.01607e7 −0.631850
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −213096. −0.0130794
\(768\) 0 0
\(769\) 2.37970e7 1.45113 0.725566 − 0.688152i \(-0.241578\pi\)
0.725566 + 0.688152i \(0.241578\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.76453e6 0.587763 0.293882 − 0.955842i \(-0.405053\pi\)
0.293882 + 0.955842i \(0.405053\pi\)
\(774\) 0 0
\(775\) 1.67952e6 0.100446
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.96495e7 −1.75055
\(780\) 0 0
\(781\) −2.04324e7 −1.19865
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −633204. −0.0366749
\(786\) 0 0
\(787\) 2.69301e6 0.154989 0.0774945 − 0.996993i \(-0.475308\pi\)
0.0774945 + 0.996993i \(0.475308\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.68438e6 −0.379857
\(792\) 0 0
\(793\) 775372. 0.0437852
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.69834e7 1.50470 0.752352 − 0.658762i \(-0.228919\pi\)
0.752352 + 0.658762i \(0.228919\pi\)
\(798\) 0 0
\(799\) 608760. 0.0337349
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.38521e7 1.85266
\(804\) 0 0
\(805\) 9.28746e6 0.505135
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.30813e7 −0.702718 −0.351359 − 0.936241i \(-0.614280\pi\)
−0.351359 + 0.936241i \(0.614280\pi\)
\(810\) 0 0
\(811\) −2.12063e7 −1.13217 −0.566086 − 0.824346i \(-0.691543\pi\)
−0.566086 + 0.824346i \(0.691543\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.45400e7 −0.766781
\(816\) 0 0
\(817\) −2.72403e7 −1.42776
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.76237e7 −1.94806 −0.974032 − 0.226411i \(-0.927301\pi\)
−0.974032 + 0.226411i \(0.927301\pi\)
\(822\) 0 0
\(823\) −4.75582e6 −0.244752 −0.122376 − 0.992484i \(-0.539051\pi\)
−0.122376 + 0.992484i \(0.539051\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.26167e7 −1.14991 −0.574957 − 0.818184i \(-0.694981\pi\)
−0.574957 + 0.818184i \(0.694981\pi\)
\(828\) 0 0
\(829\) −2.44896e7 −1.23764 −0.618821 − 0.785532i \(-0.712389\pi\)
−0.618821 + 0.785532i \(0.712389\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.28213e6 0.0640208
\(834\) 0 0
\(835\) −2.24662e6 −0.111510
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.13107e7 1.53563 0.767816 − 0.640670i \(-0.221343\pi\)
0.767816 + 0.640670i \(0.221343\pi\)
\(840\) 0 0
\(841\) −2.05553e6 −0.100215
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.00133e7 0.964223
\(846\) 0 0
\(847\) −9.39746e6 −0.450093
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.76202e6 −0.0834040
\(852\) 0 0
\(853\) −1.59565e7 −0.750870 −0.375435 − 0.926849i \(-0.622507\pi\)
−0.375435 + 0.926849i \(0.622507\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.51800e6 −0.303153 −0.151577 − 0.988446i \(-0.548435\pi\)
−0.151577 + 0.988446i \(0.548435\pi\)
\(858\) 0 0
\(859\) 1.77405e7 0.820321 0.410161 − 0.912013i \(-0.365473\pi\)
0.410161 + 0.912013i \(0.365473\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.57437e6 0.391900 0.195950 − 0.980614i \(-0.437221\pi\)
0.195950 + 0.980614i \(0.437221\pi\)
\(864\) 0 0
\(865\) 1.54959e7 0.704171
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.94006e7 −1.32071
\(870\) 0 0
\(871\) 1.63498e6 0.0730244
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.82176e6 −0.389525
\(876\) 0 0
\(877\) −3.83551e7 −1.68393 −0.841964 − 0.539533i \(-0.818601\pi\)
−0.841964 + 0.539533i \(0.818601\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.91651e7 −1.70004 −0.850020 − 0.526751i \(-0.823410\pi\)
−0.850020 + 0.526751i \(0.823410\pi\)
\(882\) 0 0
\(883\) −1.72766e7 −0.745688 −0.372844 − 0.927894i \(-0.621617\pi\)
−0.372844 + 0.927894i \(0.621617\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.33351e7 0.995865 0.497932 − 0.867216i \(-0.334093\pi\)
0.497932 + 0.867216i \(0.334093\pi\)
\(888\) 0 0
\(889\) −6.28415e6 −0.266681
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.42456e6 0.143706
\(894\) 0 0
\(895\) 2.26900e7 0.946843
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.45227e7 1.42464
\(900\) 0 0
\(901\) −1.51421e7 −0.621404
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 913572. 0.0370784
\(906\) 0 0
\(907\) 3.16449e7 1.27728 0.638640 − 0.769506i \(-0.279497\pi\)
0.638640 + 0.769506i \(0.279497\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.29551e6 −0.0916396 −0.0458198 − 0.998950i \(-0.514590\pi\)
−0.0458198 + 0.998950i \(0.514590\pi\)
\(912\) 0 0
\(913\) −3.11921e7 −1.23842
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.81445e7 −0.712561
\(918\) 0 0
\(919\) 2.80612e7 1.09602 0.548008 − 0.836473i \(-0.315386\pi\)
0.548008 + 0.836473i \(0.315386\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −894348. −0.0345543
\(924\) 0 0
\(925\) 104918. 0.00403177
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.79025e6 −0.258135 −0.129067 − 0.991636i \(-0.541198\pi\)
−0.129067 + 0.991636i \(0.541198\pi\)
\(930\) 0 0
\(931\) 7.21260e6 0.272721
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.71286e7 −0.640756
\(936\) 0 0
\(937\) 3.83161e7 1.42571 0.712857 − 0.701310i \(-0.247401\pi\)
0.712857 + 0.701310i \(0.247401\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.16868e7 −0.430250 −0.215125 − 0.976587i \(-0.569016\pi\)
−0.215125 + 0.976587i \(0.569016\pi\)
\(942\) 0 0
\(943\) −3.46437e7 −1.26866
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.08201e7 0.754410 0.377205 − 0.926130i \(-0.376885\pi\)
0.377205 + 0.926130i \(0.376885\pi\)
\(948\) 0 0
\(949\) 1.48174e6 0.0534080
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.41556e7 0.504888 0.252444 − 0.967612i \(-0.418766\pi\)
0.252444 + 0.967612i \(0.418766\pi\)
\(954\) 0 0
\(955\) 7.27607e6 0.258160
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 633276. 0.0222355
\(960\) 0 0
\(961\) 3.59481e7 1.25565
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.69911e7 0.587358
\(966\) 0 0
\(967\) −5.29558e7 −1.82116 −0.910578 − 0.413337i \(-0.864363\pi\)
−0.910578 + 0.413337i \(0.864363\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.07845e7 0.367072 0.183536 − 0.983013i \(-0.441246\pi\)
0.183536 + 0.983013i \(0.441246\pi\)
\(972\) 0 0
\(973\) −8.71024e6 −0.294950
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.78226e7 1.60286 0.801432 − 0.598086i \(-0.204072\pi\)
0.801432 + 0.598086i \(0.204072\pi\)
\(978\) 0 0
\(979\) 2.86795e7 0.956346
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.96662e7 −0.979216 −0.489608 − 0.871943i \(-0.662860\pi\)
−0.489608 + 0.871943i \(0.662860\pi\)
\(984\) 0 0
\(985\) 3.22179e7 1.05805
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.18287e7 −1.03473
\(990\) 0 0
\(991\) 1.39263e7 0.450456 0.225228 − 0.974306i \(-0.427687\pi\)
0.225228 + 0.974306i \(0.427687\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −545184. −0.0174576
\(996\) 0 0
\(997\) −3.59999e6 −0.114700 −0.0573499 − 0.998354i \(-0.518265\pi\)
−0.0573499 + 0.998354i \(0.518265\pi\)
\(998\) 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.f.1.1 1
3.2 odd 2 1008.6.a.w.1.1 1
4.3 odd 2 126.6.a.g.1.1 yes 1
12.11 even 2 126.6.a.e.1.1 ✓ 1
28.27 even 2 882.6.a.w.1.1 1
84.83 odd 2 882.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.6.a.e.1.1 ✓ 1 12.11 even 2
126.6.a.g.1.1 yes 1 4.3 odd 2
882.6.a.b.1.1 1 84.83 odd 2
882.6.a.w.1.1 1 28.27 even 2
1008.6.a.f.1.1 1 1.1 even 1 trivial
1008.6.a.w.1.1 1 3.2 odd 2