Properties

Label 1008.6.a.t.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 21)
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)
 
\(f(q)\) \(=\) \(q+34.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+34.0000 q^{5} +49.0000 q^{7} -340.000 q^{11} +454.000 q^{13} +798.000 q^{17} -892.000 q^{19} -3192.00 q^{23} -1969.00 q^{25} +8242.00 q^{29} +2496.00 q^{31} +1666.00 q^{35} +9798.00 q^{37} -19834.0 q^{41} +17236.0 q^{43} +8928.00 q^{47} +2401.00 q^{49} -150.000 q^{53} -11560.0 q^{55} -42396.0 q^{59} +14758.0 q^{61} +15436.0 q^{65} +1676.00 q^{67} +14568.0 q^{71} +78378.0 q^{73} -16660.0 q^{77} +2272.00 q^{79} -37764.0 q^{83} +27132.0 q^{85} +117286. q^{89} +22246.0 q^{91} -30328.0 q^{95} +10002.0 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 34.0000 0.608210 0.304105 0.952638i \(-0.401643\pi\)
0.304105 + 0.952638i \(0.401643\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −340.000 −0.847222 −0.423611 0.905844i \(-0.639238\pi\)
−0.423611 + 0.905844i \(0.639238\pi\)
\(12\) 0 0
\(13\) 454.000 0.745071 0.372535 0.928018i \(-0.378489\pi\)
0.372535 + 0.928018i \(0.378489\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 798.000 0.669700 0.334850 0.942271i \(-0.391314\pi\)
0.334850 + 0.942271i \(0.391314\pi\)
\(18\) 0 0
\(19\) −892.000 −0.566867 −0.283433 0.958992i \(-0.591473\pi\)
−0.283433 + 0.958992i \(0.591473\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3192.00 −1.25818 −0.629091 0.777332i \(-0.716573\pi\)
−0.629091 + 0.777332i \(0.716573\pi\)
\(24\) 0 0
\(25\) −1969.00 −0.630080
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8242.00 1.81986 0.909929 0.414764i \(-0.136136\pi\)
0.909929 + 0.414764i \(0.136136\pi\)
\(30\) 0 0
\(31\) 2496.00 0.466488 0.233244 0.972418i \(-0.425066\pi\)
0.233244 + 0.972418i \(0.425066\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1666.00 0.229882
\(36\) 0 0
\(37\) 9798.00 1.17661 0.588306 0.808639i \(-0.299795\pi\)
0.588306 + 0.808639i \(0.299795\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −19834.0 −1.84268 −0.921342 0.388754i \(-0.872906\pi\)
−0.921342 + 0.388754i \(0.872906\pi\)
\(42\) 0 0
\(43\) 17236.0 1.42156 0.710780 0.703414i \(-0.248342\pi\)
0.710780 + 0.703414i \(0.248342\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8928.00 0.589535 0.294767 0.955569i \(-0.404758\pi\)
0.294767 + 0.955569i \(0.404758\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −150.000 −0.00733502 −0.00366751 0.999993i \(-0.501167\pi\)
−0.00366751 + 0.999993i \(0.501167\pi\)
\(54\) 0 0
\(55\) −11560.0 −0.515289
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −42396.0 −1.58560 −0.792802 0.609479i \(-0.791379\pi\)
−0.792802 + 0.609479i \(0.791379\pi\)
\(60\) 0 0
\(61\) 14758.0 0.507812 0.253906 0.967229i \(-0.418285\pi\)
0.253906 + 0.967229i \(0.418285\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 15436.0 0.453160
\(66\) 0 0
\(67\) 1676.00 0.0456128 0.0228064 0.999740i \(-0.492740\pi\)
0.0228064 + 0.999740i \(0.492740\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14568.0 0.342968 0.171484 0.985187i \(-0.445144\pi\)
0.171484 + 0.985187i \(0.445144\pi\)
\(72\) 0 0
\(73\) 78378.0 1.72142 0.860710 0.509095i \(-0.170020\pi\)
0.860710 + 0.509095i \(0.170020\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16660.0 −0.320220
\(78\) 0 0
\(79\) 2272.00 0.0409582 0.0204791 0.999790i \(-0.493481\pi\)
0.0204791 + 0.999790i \(0.493481\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −37764.0 −0.601704 −0.300852 0.953671i \(-0.597271\pi\)
−0.300852 + 0.953671i \(0.597271\pi\)
\(84\) 0 0
\(85\) 27132.0 0.407319
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 117286. 1.56954 0.784768 0.619790i \(-0.212782\pi\)
0.784768 + 0.619790i \(0.212782\pi\)
\(90\) 0 0
\(91\) 22246.0 0.281610
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −30328.0 −0.344774
\(96\) 0 0
\(97\) 10002.0 0.107934 0.0539669 0.998543i \(-0.482813\pi\)
0.0539669 + 0.998543i \(0.482813\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 108770. 1.06098 0.530488 0.847692i \(-0.322009\pi\)
0.530488 + 0.847692i \(0.322009\pi\)
\(102\) 0 0
\(103\) 199192. 1.85003 0.925015 0.379930i \(-0.124052\pi\)
0.925015 + 0.379930i \(0.124052\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −79972.0 −0.675272 −0.337636 0.941277i \(-0.609627\pi\)
−0.337636 + 0.941277i \(0.609627\pi\)
\(108\) 0 0
\(109\) −46098.0 −0.371634 −0.185817 0.982584i \(-0.559493\pi\)
−0.185817 + 0.982584i \(0.559493\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −262706. −1.93541 −0.967707 0.252078i \(-0.918886\pi\)
−0.967707 + 0.252078i \(0.918886\pi\)
\(114\) 0 0
\(115\) −108528. −0.765239
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 39102.0 0.253123
\(120\) 0 0
\(121\) −45451.0 −0.282215
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −173196. −0.991432
\(126\) 0 0
\(127\) −196608. −1.08166 −0.540831 0.841131i \(-0.681890\pi\)
−0.540831 + 0.841131i \(0.681890\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −77140.0 −0.392737 −0.196368 0.980530i \(-0.562915\pi\)
−0.196368 + 0.980530i \(0.562915\pi\)
\(132\) 0 0
\(133\) −43708.0 −0.214255
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −208170. −0.947582 −0.473791 0.880637i \(-0.657115\pi\)
−0.473791 + 0.880637i \(0.657115\pi\)
\(138\) 0 0
\(139\) 275580. 1.20979 0.604896 0.796304i \(-0.293215\pi\)
0.604896 + 0.796304i \(0.293215\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −154360. −0.631240
\(144\) 0 0
\(145\) 280228. 1.10686
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 296106. 1.09265 0.546326 0.837573i \(-0.316026\pi\)
0.546326 + 0.837573i \(0.316026\pi\)
\(150\) 0 0
\(151\) 426472. 1.52212 0.761059 0.648683i \(-0.224680\pi\)
0.761059 + 0.648683i \(0.224680\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 84864.0 0.283723
\(156\) 0 0
\(157\) 178486. 0.577903 0.288952 0.957344i \(-0.406693\pi\)
0.288952 + 0.957344i \(0.406693\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −156408. −0.475548
\(162\) 0 0
\(163\) −252772. −0.745178 −0.372589 0.927996i \(-0.621530\pi\)
−0.372589 + 0.927996i \(0.621530\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 508088. 1.40977 0.704884 0.709322i \(-0.250999\pi\)
0.704884 + 0.709322i \(0.250999\pi\)
\(168\) 0 0
\(169\) −165177. −0.444870
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 221834. 0.563525 0.281762 0.959484i \(-0.409081\pi\)
0.281762 + 0.959484i \(0.409081\pi\)
\(174\) 0 0
\(175\) −96481.0 −0.238148
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −113564. −0.264916 −0.132458 0.991189i \(-0.542287\pi\)
−0.132458 + 0.991189i \(0.542287\pi\)
\(180\) 0 0
\(181\) 663118. 1.50451 0.752254 0.658873i \(-0.228967\pi\)
0.752254 + 0.658873i \(0.228967\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 333132. 0.715628
\(186\) 0 0
\(187\) −271320. −0.567385
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 505664. 1.00295 0.501474 0.865173i \(-0.332791\pi\)
0.501474 + 0.865173i \(0.332791\pi\)
\(192\) 0 0
\(193\) −432382. −0.835554 −0.417777 0.908550i \(-0.637191\pi\)
−0.417777 + 0.908550i \(0.637191\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 131962. 0.242261 0.121130 0.992637i \(-0.461348\pi\)
0.121130 + 0.992637i \(0.461348\pi\)
\(198\) 0 0
\(199\) −298536. −0.534397 −0.267199 0.963642i \(-0.586098\pi\)
−0.267199 + 0.963642i \(0.586098\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 403858. 0.687842
\(204\) 0 0
\(205\) −674356. −1.12074
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 303280. 0.480262
\(210\) 0 0
\(211\) 1.17062e6 1.81013 0.905065 0.425273i \(-0.139822\pi\)
0.905065 + 0.425273i \(0.139822\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 586024. 0.864608
\(216\) 0 0
\(217\) 122304. 0.176316
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 362292. 0.498974
\(222\) 0 0
\(223\) −399376. −0.537799 −0.268899 0.963168i \(-0.586660\pi\)
−0.268899 + 0.963168i \(0.586660\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 707916. 0.911837 0.455918 0.890022i \(-0.349311\pi\)
0.455918 + 0.890022i \(0.349311\pi\)
\(228\) 0 0
\(229\) −735778. −0.927167 −0.463584 0.886053i \(-0.653437\pi\)
−0.463584 + 0.886053i \(0.653437\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 208758. 0.251915 0.125957 0.992036i \(-0.459800\pi\)
0.125957 + 0.992036i \(0.459800\pi\)
\(234\) 0 0
\(235\) 303552. 0.358561
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 713376. 0.807837 0.403919 0.914795i \(-0.367648\pi\)
0.403919 + 0.914795i \(0.367648\pi\)
\(240\) 0 0
\(241\) −505246. −0.560351 −0.280176 0.959949i \(-0.590393\pi\)
−0.280176 + 0.959949i \(0.590393\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 81634.0 0.0868872
\(246\) 0 0
\(247\) −404968. −0.422356
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 317108. 0.317704 0.158852 0.987302i \(-0.449221\pi\)
0.158852 + 0.987302i \(0.449221\pi\)
\(252\) 0 0
\(253\) 1.08528e6 1.06596
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.44285e6 1.36266 0.681329 0.731977i \(-0.261402\pi\)
0.681329 + 0.731977i \(0.261402\pi\)
\(258\) 0 0
\(259\) 480102. 0.444717
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 271496. 0.242033 0.121016 0.992651i \(-0.461385\pi\)
0.121016 + 0.992651i \(0.461385\pi\)
\(264\) 0 0
\(265\) −5100.00 −0.00446124
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −850614. −0.716724 −0.358362 0.933583i \(-0.616665\pi\)
−0.358362 + 0.933583i \(0.616665\pi\)
\(270\) 0 0
\(271\) 540128. 0.446759 0.223380 0.974732i \(-0.428291\pi\)
0.223380 + 0.974732i \(0.428291\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 669460. 0.533818
\(276\) 0 0
\(277\) 513574. 0.402164 0.201082 0.979574i \(-0.435554\pi\)
0.201082 + 0.979574i \(0.435554\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.35642e6 1.02478 0.512388 0.858754i \(-0.328761\pi\)
0.512388 + 0.858754i \(0.328761\pi\)
\(282\) 0 0
\(283\) −286756. −0.212837 −0.106418 0.994321i \(-0.533938\pi\)
−0.106418 + 0.994321i \(0.533938\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −971866. −0.696469
\(288\) 0 0
\(289\) −783053. −0.551501
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.70727e6 1.16180 0.580901 0.813974i \(-0.302700\pi\)
0.580901 + 0.813974i \(0.302700\pi\)
\(294\) 0 0
\(295\) −1.44146e6 −0.964381
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.44917e6 −0.937434
\(300\) 0 0
\(301\) 844564. 0.537299
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 501772. 0.308857
\(306\) 0 0
\(307\) 546788. 0.331111 0.165555 0.986201i \(-0.447058\pi\)
0.165555 + 0.986201i \(0.447058\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.23426e6 1.89616 0.948079 0.318035i \(-0.103023\pi\)
0.948079 + 0.318035i \(0.103023\pi\)
\(312\) 0 0
\(313\) 1.81313e6 1.04609 0.523044 0.852306i \(-0.324796\pi\)
0.523044 + 0.852306i \(0.324796\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.27658e6 0.713509 0.356754 0.934198i \(-0.383883\pi\)
0.356754 + 0.934198i \(0.383883\pi\)
\(318\) 0 0
\(319\) −2.80228e6 −1.54182
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −711816. −0.379631
\(324\) 0 0
\(325\) −893926. −0.469454
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 437472. 0.222823
\(330\) 0 0
\(331\) 1.73621e6 0.871029 0.435515 0.900182i \(-0.356566\pi\)
0.435515 + 0.900182i \(0.356566\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 56984.0 0.0277422
\(336\) 0 0
\(337\) 2.07215e6 0.993907 0.496953 0.867777i \(-0.334452\pi\)
0.496953 + 0.867777i \(0.334452\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −848640. −0.395219
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.65146e6 −0.736282 −0.368141 0.929770i \(-0.620006\pi\)
−0.368141 + 0.929770i \(0.620006\pi\)
\(348\) 0 0
\(349\) 1.26645e6 0.556578 0.278289 0.960497i \(-0.410233\pi\)
0.278289 + 0.960497i \(0.410233\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −573218. −0.244840 −0.122420 0.992478i \(-0.539066\pi\)
−0.122420 + 0.992478i \(0.539066\pi\)
\(354\) 0 0
\(355\) 495312. 0.208597
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.46322e6 1.82773 0.913866 0.406016i \(-0.133082\pi\)
0.913866 + 0.406016i \(0.133082\pi\)
\(360\) 0 0
\(361\) −1.68044e6 −0.678662
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.66485e6 1.04699
\(366\) 0 0
\(367\) 4.50797e6 1.74709 0.873546 0.486742i \(-0.161815\pi\)
0.873546 + 0.486742i \(0.161815\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7350.00 −0.00277238
\(372\) 0 0
\(373\) 1.66535e6 0.619774 0.309887 0.950773i \(-0.399709\pi\)
0.309887 + 0.950773i \(0.399709\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.74187e6 1.35592
\(378\) 0 0
\(379\) 2.53232e6 0.905568 0.452784 0.891620i \(-0.350431\pi\)
0.452784 + 0.891620i \(0.350431\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 796368. 0.277407 0.138703 0.990334i \(-0.455707\pi\)
0.138703 + 0.990334i \(0.455707\pi\)
\(384\) 0 0
\(385\) −566440. −0.194761
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.94799e6 −0.652699 −0.326349 0.945249i \(-0.605819\pi\)
−0.326349 + 0.945249i \(0.605819\pi\)
\(390\) 0 0
\(391\) −2.54722e6 −0.842605
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 77248.0 0.0249112
\(396\) 0 0
\(397\) 1.08116e6 0.344281 0.172140 0.985072i \(-0.444932\pi\)
0.172140 + 0.985072i \(0.444932\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.76770e6 −0.859524 −0.429762 0.902942i \(-0.641402\pi\)
−0.429762 + 0.902942i \(0.641402\pi\)
\(402\) 0 0
\(403\) 1.13318e6 0.347566
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.33132e6 −0.996851
\(408\) 0 0
\(409\) 2.36350e6 0.698630 0.349315 0.937005i \(-0.386414\pi\)
0.349315 + 0.937005i \(0.386414\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.07740e6 −0.599302
\(414\) 0 0
\(415\) −1.28398e6 −0.365963
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.98669e6 −0.831104 −0.415552 0.909569i \(-0.636412\pi\)
−0.415552 + 0.909569i \(0.636412\pi\)
\(420\) 0 0
\(421\) −3.46331e6 −0.952326 −0.476163 0.879357i \(-0.657973\pi\)
−0.476163 + 0.879357i \(0.657973\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.57126e6 −0.421965
\(426\) 0 0
\(427\) 723142. 0.191935
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.33693e6 0.605971 0.302986 0.952995i \(-0.402017\pi\)
0.302986 + 0.952995i \(0.402017\pi\)
\(432\) 0 0
\(433\) −3.50838e6 −0.899264 −0.449632 0.893214i \(-0.648445\pi\)
−0.449632 + 0.893214i \(0.648445\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.84726e6 0.713221
\(438\) 0 0
\(439\) −3.54833e6 −0.878744 −0.439372 0.898305i \(-0.644799\pi\)
−0.439372 + 0.898305i \(0.644799\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.76833e6 0.428109 0.214055 0.976822i \(-0.431333\pi\)
0.214055 + 0.976822i \(0.431333\pi\)
\(444\) 0 0
\(445\) 3.98772e6 0.954608
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.52579e6 1.29354 0.646768 0.762687i \(-0.276120\pi\)
0.646768 + 0.762687i \(0.276120\pi\)
\(450\) 0 0
\(451\) 6.74356e6 1.56116
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 756364. 0.171278
\(456\) 0 0
\(457\) −2.96226e6 −0.663488 −0.331744 0.943369i \(-0.607637\pi\)
−0.331744 + 0.943369i \(0.607637\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.11884e6 −0.464350 −0.232175 0.972674i \(-0.574584\pi\)
−0.232175 + 0.972674i \(0.574584\pi\)
\(462\) 0 0
\(463\) −3.19226e6 −0.692062 −0.346031 0.938223i \(-0.612471\pi\)
−0.346031 + 0.938223i \(0.612471\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.42621e6 −1.57571 −0.787853 0.615863i \(-0.788807\pi\)
−0.787853 + 0.615863i \(0.788807\pi\)
\(468\) 0 0
\(469\) 82124.0 0.0172400
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.86024e6 −1.20438
\(474\) 0 0
\(475\) 1.75635e6 0.357171
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.39685e6 −0.676453 −0.338226 0.941065i \(-0.609827\pi\)
−0.338226 + 0.941065i \(0.609827\pi\)
\(480\) 0 0
\(481\) 4.44829e6 0.876659
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 340068. 0.0656465
\(486\) 0 0
\(487\) 3.71382e6 0.709574 0.354787 0.934947i \(-0.384553\pi\)
0.354787 + 0.934947i \(0.384553\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.57494e6 1.04361 0.521803 0.853066i \(-0.325260\pi\)
0.521803 + 0.853066i \(0.325260\pi\)
\(492\) 0 0
\(493\) 6.57712e6 1.21876
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 713832. 0.129630
\(498\) 0 0
\(499\) −3.92698e6 −0.706004 −0.353002 0.935623i \(-0.614839\pi\)
−0.353002 + 0.935623i \(0.614839\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.42079e6 1.13154 0.565768 0.824564i \(-0.308580\pi\)
0.565768 + 0.824564i \(0.308580\pi\)
\(504\) 0 0
\(505\) 3.69818e6 0.645297
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −146278. −0.0250256 −0.0125128 0.999922i \(-0.503983\pi\)
−0.0125128 + 0.999922i \(0.503983\pi\)
\(510\) 0 0
\(511\) 3.84052e6 0.650636
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.77253e6 1.12521
\(516\) 0 0
\(517\) −3.03552e6 −0.499467
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.70937e6 −1.24430 −0.622149 0.782899i \(-0.713740\pi\)
−0.622149 + 0.782899i \(0.713740\pi\)
\(522\) 0 0
\(523\) 569420. 0.0910287 0.0455144 0.998964i \(-0.485507\pi\)
0.0455144 + 0.998964i \(0.485507\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.99181e6 0.312407
\(528\) 0 0
\(529\) 3.75252e6 0.583021
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00464e6 −1.37293
\(534\) 0 0
\(535\) −2.71905e6 −0.410707
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −816340. −0.121032
\(540\) 0 0
\(541\) −9.44802e6 −1.38787 −0.693933 0.720040i \(-0.744124\pi\)
−0.693933 + 0.720040i \(0.744124\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.56733e6 −0.226032
\(546\) 0 0
\(547\) 1.35321e6 0.193374 0.0966869 0.995315i \(-0.469175\pi\)
0.0966869 + 0.995315i \(0.469175\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.35186e6 −1.03162
\(552\) 0 0
\(553\) 111328. 0.0154807
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.19390e6 −1.11906 −0.559529 0.828811i \(-0.689018\pi\)
−0.559529 + 0.828811i \(0.689018\pi\)
\(558\) 0 0
\(559\) 7.82514e6 1.05916
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.05796e7 −1.40669 −0.703347 0.710847i \(-0.748312\pi\)
−0.703347 + 0.710847i \(0.748312\pi\)
\(564\) 0 0
\(565\) −8.93200e6 −1.17714
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.20205e7 1.55648 0.778238 0.627969i \(-0.216114\pi\)
0.778238 + 0.627969i \(0.216114\pi\)
\(570\) 0 0
\(571\) 2.48948e6 0.319534 0.159767 0.987155i \(-0.448926\pi\)
0.159767 + 0.987155i \(0.448926\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.28505e6 0.792755
\(576\) 0 0
\(577\) 8.21322e6 1.02701 0.513504 0.858087i \(-0.328347\pi\)
0.513504 + 0.858087i \(0.328347\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.85044e6 −0.227423
\(582\) 0 0
\(583\) 51000.0 0.00621439
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.21827e6 −0.145931 −0.0729655 0.997334i \(-0.523246\pi\)
−0.0729655 + 0.997334i \(0.523246\pi\)
\(588\) 0 0
\(589\) −2.22643e6 −0.264436
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.42379e6 0.983718 0.491859 0.870675i \(-0.336317\pi\)
0.491859 + 0.870675i \(0.336317\pi\)
\(594\) 0 0
\(595\) 1.32947e6 0.153952
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.21254e6 0.935212 0.467606 0.883937i \(-0.345117\pi\)
0.467606 + 0.883937i \(0.345117\pi\)
\(600\) 0 0
\(601\) 3.25478e6 0.367566 0.183783 0.982967i \(-0.441166\pi\)
0.183783 + 0.982967i \(0.441166\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.54533e6 −0.171646
\(606\) 0 0
\(607\) −7.82101e6 −0.861571 −0.430785 0.902454i \(-0.641763\pi\)
−0.430785 + 0.902454i \(0.641763\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.05331e6 0.439245
\(612\) 0 0
\(613\) −9.51670e6 −1.02290 −0.511452 0.859312i \(-0.670892\pi\)
−0.511452 + 0.859312i \(0.670892\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.04895e6 0.745438 0.372719 0.927944i \(-0.378426\pi\)
0.372719 + 0.927944i \(0.378426\pi\)
\(618\) 0 0
\(619\) 6.32174e6 0.663147 0.331574 0.943429i \(-0.392420\pi\)
0.331574 + 0.943429i \(0.392420\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.74701e6 0.593229
\(624\) 0 0
\(625\) 264461. 0.0270808
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.81880e6 0.787977
\(630\) 0 0
\(631\) −8.61236e6 −0.861090 −0.430545 0.902569i \(-0.641679\pi\)
−0.430545 + 0.902569i \(0.641679\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.68467e6 −0.657879
\(636\) 0 0
\(637\) 1.09005e6 0.106439
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.22829e6 0.502590 0.251295 0.967910i \(-0.419143\pi\)
0.251295 + 0.967910i \(0.419143\pi\)
\(642\) 0 0
\(643\) −1.61373e7 −1.53923 −0.769615 0.638508i \(-0.779552\pi\)
−0.769615 + 0.638508i \(0.779552\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.58749e7 −1.49090 −0.745451 0.666560i \(-0.767766\pi\)
−0.745451 + 0.666560i \(0.767766\pi\)
\(648\) 0 0
\(649\) 1.44146e7 1.34336
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.94112e6 0.545237 0.272619 0.962122i \(-0.412110\pi\)
0.272619 + 0.962122i \(0.412110\pi\)
\(654\) 0 0
\(655\) −2.62276e6 −0.238867
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.64430e6 −0.685684 −0.342842 0.939393i \(-0.611390\pi\)
−0.342842 + 0.939393i \(0.611390\pi\)
\(660\) 0 0
\(661\) −7.58688e6 −0.675398 −0.337699 0.941254i \(-0.609649\pi\)
−0.337699 + 0.941254i \(0.609649\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.48607e6 −0.130312
\(666\) 0 0
\(667\) −2.63085e7 −2.28971
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.01772e6 −0.430229
\(672\) 0 0
\(673\) −2.06681e7 −1.75899 −0.879494 0.475910i \(-0.842119\pi\)
−0.879494 + 0.475910i \(0.842119\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.89541e6 −0.662068 −0.331034 0.943619i \(-0.607398\pi\)
−0.331034 + 0.943619i \(0.607398\pi\)
\(678\) 0 0
\(679\) 490098. 0.0407951
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.96015e7 −1.60782 −0.803911 0.594750i \(-0.797251\pi\)
−0.803911 + 0.594750i \(0.797251\pi\)
\(684\) 0 0
\(685\) −7.07778e6 −0.576329
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −68100.0 −0.00546511
\(690\) 0 0
\(691\) 1.72710e7 1.37601 0.688005 0.725706i \(-0.258487\pi\)
0.688005 + 0.725706i \(0.258487\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.36972e6 0.735808
\(696\) 0 0
\(697\) −1.58275e7 −1.23405
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.36344e6 0.412238 0.206119 0.978527i \(-0.433917\pi\)
0.206119 + 0.978527i \(0.433917\pi\)
\(702\) 0 0
\(703\) −8.73982e6 −0.666982
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.32973e6 0.401011
\(708\) 0 0
\(709\) −1.73733e7 −1.29798 −0.648988 0.760798i \(-0.724808\pi\)
−0.648988 + 0.760798i \(0.724808\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.96723e6 −0.586926
\(714\) 0 0
\(715\) −5.24824e6 −0.383927
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 424608. 0.0306313 0.0153157 0.999883i \(-0.495125\pi\)
0.0153157 + 0.999883i \(0.495125\pi\)
\(720\) 0 0
\(721\) 9.76041e6 0.699246
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.62285e7 −1.14666
\(726\) 0 0
\(727\) −2.18290e7 −1.53179 −0.765893 0.642968i \(-0.777703\pi\)
−0.765893 + 0.642968i \(0.777703\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.37543e7 0.952020
\(732\) 0 0
\(733\) 2.17675e7 1.49640 0.748202 0.663470i \(-0.230917\pi\)
0.748202 + 0.663470i \(0.230917\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −569840. −0.0386442
\(738\) 0 0
\(739\) −6.21786e6 −0.418822 −0.209411 0.977828i \(-0.567155\pi\)
−0.209411 + 0.977828i \(0.567155\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.77647e6 0.250966 0.125483 0.992096i \(-0.459952\pi\)
0.125483 + 0.992096i \(0.459952\pi\)
\(744\) 0 0
\(745\) 1.00676e7 0.664562
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.91863e6 −0.255229
\(750\) 0 0
\(751\) 2.88795e6 0.186849 0.0934244 0.995626i \(-0.470219\pi\)
0.0934244 + 0.995626i \(0.470219\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.45000e7 0.925768
\(756\) 0 0
\(757\) 1.25519e6 0.0796104 0.0398052 0.999207i \(-0.487326\pi\)
0.0398052 + 0.999207i \(0.487326\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.42623e7 0.892746 0.446373 0.894847i \(-0.352716\pi\)
0.446373 + 0.894847i \(0.352716\pi\)
\(762\) 0 0
\(763\) −2.25880e6 −0.140465
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.92478e7 −1.18139
\(768\) 0 0
\(769\) −2.02261e7 −1.23338 −0.616689 0.787207i \(-0.711526\pi\)
−0.616689 + 0.787207i \(0.711526\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.62288e7 −1.57881 −0.789406 0.613872i \(-0.789611\pi\)
−0.789406 + 0.613872i \(0.789611\pi\)
\(774\) 0 0
\(775\) −4.91462e6 −0.293925
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.76919e7 1.04456
\(780\) 0 0
\(781\) −4.95312e6 −0.290570
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.06852e6 0.351487
\(786\) 0 0
\(787\) 9.92829e6 0.571397 0.285698 0.958320i \(-0.407774\pi\)
0.285698 + 0.958320i \(0.407774\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.28726e7 −0.731518
\(792\) 0 0
\(793\) 6.70013e6 0.378356
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.09033e7 −0.608014 −0.304007 0.952670i \(-0.598325\pi\)
−0.304007 + 0.952670i \(0.598325\pi\)
\(798\) 0 0
\(799\) 7.12454e6 0.394812
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.66485e7 −1.45843
\(804\) 0 0
\(805\) −5.31787e6 −0.289233
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.06398e6 −0.325751 −0.162876 0.986647i \(-0.552077\pi\)
−0.162876 + 0.986647i \(0.552077\pi\)
\(810\) 0 0
\(811\) 8.59438e6 0.458841 0.229421 0.973327i \(-0.426317\pi\)
0.229421 + 0.973327i \(0.426317\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.59425e6 −0.453225
\(816\) 0 0
\(817\) −1.53745e7 −0.805835
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.01396e6 0.104278 0.0521391 0.998640i \(-0.483396\pi\)
0.0521391 + 0.998640i \(0.483396\pi\)
\(822\) 0 0
\(823\) 2.64679e7 1.36213 0.681067 0.732221i \(-0.261516\pi\)
0.681067 + 0.732221i \(0.261516\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.90229e6 −0.198407 −0.0992033 0.995067i \(-0.531629\pi\)
−0.0992033 + 0.995067i \(0.531629\pi\)
\(828\) 0 0
\(829\) −1.95595e7 −0.988487 −0.494244 0.869323i \(-0.664555\pi\)
−0.494244 + 0.869323i \(0.664555\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.91600e6 0.0956715
\(834\) 0 0
\(835\) 1.72750e7 0.857436
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.45448e7 −1.20380 −0.601901 0.798570i \(-0.705590\pi\)
−0.601901 + 0.798570i \(0.705590\pi\)
\(840\) 0 0
\(841\) 4.74194e7 2.31188
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5.61602e6 −0.270574
\(846\) 0 0
\(847\) −2.22710e6 −0.106667
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.12752e7 −1.48039
\(852\) 0 0
\(853\) 3.38305e7 1.59197 0.795987 0.605314i \(-0.206952\pi\)
0.795987 + 0.605314i \(0.206952\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.18009e7 −1.47907 −0.739534 0.673120i \(-0.764954\pi\)
−0.739534 + 0.673120i \(0.764954\pi\)
\(858\) 0 0
\(859\) −638420. −0.0295205 −0.0147602 0.999891i \(-0.504699\pi\)
−0.0147602 + 0.999891i \(0.504699\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.22256e6 −0.192996 −0.0964981 0.995333i \(-0.530764\pi\)
−0.0964981 + 0.995333i \(0.530764\pi\)
\(864\) 0 0
\(865\) 7.54236e6 0.342742
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −772480. −0.0347007
\(870\) 0 0
\(871\) 760904. 0.0339848
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.48660e6 −0.374726
\(876\) 0 0
\(877\) −2.45043e7 −1.07583 −0.537915 0.842999i \(-0.680788\pi\)
−0.537915 + 0.842999i \(0.680788\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.77630e7 1.20511 0.602555 0.798078i \(-0.294150\pi\)
0.602555 + 0.798078i \(0.294150\pi\)
\(882\) 0 0
\(883\) −3.30170e7 −1.42507 −0.712534 0.701638i \(-0.752452\pi\)
−0.712534 + 0.701638i \(0.752452\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4.34462e6 0.185414 0.0927070 0.995693i \(-0.470448\pi\)
0.0927070 + 0.995693i \(0.470448\pi\)
\(888\) 0 0
\(889\) −9.63379e6 −0.408830
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7.96378e6 −0.334188
\(894\) 0 0
\(895\) −3.86118e6 −0.161125
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.05720e7 0.848942
\(900\) 0 0
\(901\) −119700. −0.00491227
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.25460e7 0.915057
\(906\) 0 0
\(907\) −1.96499e7 −0.793128 −0.396564 0.918007i \(-0.629797\pi\)
−0.396564 + 0.918007i \(0.629797\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −7.26518e6 −0.290035 −0.145018 0.989429i \(-0.546324\pi\)
−0.145018 + 0.989429i \(0.546324\pi\)
\(912\) 0 0
\(913\) 1.28398e7 0.509777
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.77986e6 −0.148440
\(918\) 0 0
\(919\) −9.82532e6 −0.383758 −0.191879 0.981419i \(-0.561458\pi\)
−0.191879 + 0.981419i \(0.561458\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 6.61387e6 0.255536
\(924\) 0 0
\(925\) −1.92923e7 −0.741359
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.71152e7 −1.03080 −0.515399 0.856951i \(-0.672356\pi\)
−0.515399 + 0.856951i \(0.672356\pi\)
\(930\) 0 0
\(931\) −2.14169e6 −0.0809809
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.22488e6 −0.345089
\(936\) 0 0
\(937\) −4.53522e7 −1.68752 −0.843761 0.536720i \(-0.819663\pi\)
−0.843761 + 0.536720i \(0.819663\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.65780e7 −1.71477 −0.857387 0.514672i \(-0.827914\pi\)
−0.857387 + 0.514672i \(0.827914\pi\)
\(942\) 0 0
\(943\) 6.33101e7 2.31843
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.53799e7 0.919632 0.459816 0.888014i \(-0.347915\pi\)
0.459816 + 0.888014i \(0.347915\pi\)
\(948\) 0 0
\(949\) 3.55836e7 1.28258
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.52948e7 −0.545520 −0.272760 0.962082i \(-0.587937\pi\)
−0.272760 + 0.962082i \(0.587937\pi\)
\(954\) 0 0
\(955\) 1.71926e7 0.610004
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.02003e7 −0.358152
\(960\) 0 0
\(961\) −2.23991e7 −0.782389
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.47010e7 −0.508192
\(966\) 0 0
\(967\) 5.71465e6 0.196527 0.0982637 0.995160i \(-0.468671\pi\)
0.0982637 + 0.995160i \(0.468671\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.30250e7 0.443332 0.221666 0.975123i \(-0.428851\pi\)
0.221666 + 0.975123i \(0.428851\pi\)
\(972\) 0 0
\(973\) 1.35034e7 0.457258
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.70360e7 0.570992 0.285496 0.958380i \(-0.407842\pi\)
0.285496 + 0.958380i \(0.407842\pi\)
\(978\) 0 0
\(979\) −3.98772e7 −1.32974
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.36985e7 −0.452156 −0.226078 0.974109i \(-0.572590\pi\)
−0.226078 + 0.974109i \(0.572590\pi\)
\(984\) 0 0
\(985\) 4.48671e6 0.147346
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.50173e7 −1.78858
\(990\) 0 0
\(991\) 3.49088e7 1.12915 0.564574 0.825383i \(-0.309041\pi\)
0.564574 + 0.825383i \(0.309041\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.01502e7 −0.325026
\(996\) 0 0
\(997\) 875662. 0.0278996 0.0139498 0.999903i \(-0.495559\pi\)
0.0139498 + 0.999903i \(0.495559\pi\)
\(998\) 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.t.1.1 1
3.2 odd 2 336.6.a.l.1.1 1
4.3 odd 2 63.6.a.c.1.1 1
12.11 even 2 21.6.a.b.1.1 1
28.27 even 2 441.6.a.d.1.1 1
60.23 odd 4 525.6.d.d.274.1 2
60.47 odd 4 525.6.d.d.274.2 2
60.59 even 2 525.6.a.c.1.1 1
84.11 even 6 147.6.e.f.79.1 2
84.23 even 6 147.6.e.f.67.1 2
84.47 odd 6 147.6.e.e.67.1 2
84.59 odd 6 147.6.e.e.79.1 2
84.83 odd 2 147.6.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.a.b.1.1 1 12.11 even 2
63.6.a.c.1.1 1 4.3 odd 2
147.6.a.e.1.1 1 84.83 odd 2
147.6.e.e.67.1 2 84.47 odd 6
147.6.e.e.79.1 2 84.59 odd 6
147.6.e.f.67.1 2 84.23 even 6
147.6.e.f.79.1 2 84.11 even 6
336.6.a.l.1.1 1 3.2 odd 2
441.6.a.d.1.1 1 28.27 even 2
525.6.a.c.1.1 1 60.59 even 2
525.6.d.d.274.1 2 60.23 odd 4
525.6.d.d.274.2 2 60.47 odd 4
1008.6.a.t.1.1 1 1.1 even 1 trivial