Properties

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

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{57}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 7)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.27492\) 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)
 
\(f(q)\) \(=\) \(q-28.7492 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-28.7492 q^{5} -49.0000 q^{7} -270.090 q^{11} +300.640 q^{13} -613.106 q^{17} +1700.95 q^{19} +3188.15 q^{23} -2298.49 q^{25} -4299.28 q^{29} -2028.46 q^{31} +1408.71 q^{35} +5154.46 q^{37} +7146.21 q^{41} +19584.3 q^{43} +19998.4 q^{47} +2401.00 q^{49} -3948.82 q^{53} +7764.86 q^{55} -29707.6 q^{59} -50519.3 q^{61} -8643.14 q^{65} -5053.56 q^{67} +32853.3 q^{71} -11115.0 q^{73} +13234.4 q^{77} -81889.4 q^{79} +118234. q^{83} +17626.3 q^{85} +41695.4 q^{89} -14731.3 q^{91} -48900.9 q^{95} +43682.8 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 18 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 18 q^{5} - 98 q^{7} + 396 q^{11} - 350 q^{13} - 1800 q^{17} + 3266 q^{19} + 2088 q^{23} - 3238 q^{25} - 6696 q^{29} + 20 q^{31} - 882 q^{35} + 6232 q^{37} + 6048 q^{41} + 3020 q^{43} + 11700 q^{47} + 4802 q^{49} - 9468 q^{53} + 38904 q^{55} - 43938 q^{59} - 64754 q^{61} - 39060 q^{65} - 24784 q^{67} + 97416 q^{71} + 17452 q^{73} - 19404 q^{77} - 51256 q^{79} + 117558 q^{83} - 37860 q^{85} - 84276 q^{89} + 17150 q^{91} + 24264 q^{95} + 20776 q^{97}+O(q^{100}) \) 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
\(5\) −28.7492 −0.514281 −0.257140 0.966374i \(-0.582780\pi\)
−0.257140 + 0.966374i \(0.582780\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −270.090 −0.673018 −0.336509 0.941680i \(-0.609246\pi\)
−0.336509 + 0.941680i \(0.609246\pi\)
\(12\) 0 0
\(13\) 300.640 0.493387 0.246694 0.969094i \(-0.420656\pi\)
0.246694 + 0.969094i \(0.420656\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −613.106 −0.514533 −0.257267 0.966340i \(-0.582822\pi\)
−0.257267 + 0.966340i \(0.582822\pi\)
\(18\) 0 0
\(19\) 1700.95 1.08095 0.540477 0.841359i \(-0.318244\pi\)
0.540477 + 0.841359i \(0.318244\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3188.15 1.25667 0.628333 0.777945i \(-0.283738\pi\)
0.628333 + 0.777945i \(0.283738\pi\)
\(24\) 0 0
\(25\) −2298.49 −0.735515
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4299.28 −0.949294 −0.474647 0.880176i \(-0.657424\pi\)
−0.474647 + 0.880176i \(0.657424\pi\)
\(30\) 0 0
\(31\) −2028.46 −0.379106 −0.189553 0.981870i \(-0.560704\pi\)
−0.189553 + 0.981870i \(0.560704\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1408.71 0.194380
\(36\) 0 0
\(37\) 5154.46 0.618983 0.309491 0.950902i \(-0.399841\pi\)
0.309491 + 0.950902i \(0.399841\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7146.21 0.663921 0.331960 0.943293i \(-0.392290\pi\)
0.331960 + 0.943293i \(0.392290\pi\)
\(42\) 0 0
\(43\) 19584.3 1.61524 0.807620 0.589703i \(-0.200755\pi\)
0.807620 + 0.589703i \(0.200755\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 19998.4 1.32054 0.660268 0.751030i \(-0.270443\pi\)
0.660268 + 0.751030i \(0.270443\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3948.82 −0.193098 −0.0965489 0.995328i \(-0.530780\pi\)
−0.0965489 + 0.995328i \(0.530780\pi\)
\(54\) 0 0
\(55\) 7764.86 0.346120
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −29707.6 −1.11106 −0.555530 0.831497i \(-0.687484\pi\)
−0.555530 + 0.831497i \(0.687484\pi\)
\(60\) 0 0
\(61\) −50519.3 −1.73833 −0.869165 0.494522i \(-0.835343\pi\)
−0.869165 + 0.494522i \(0.835343\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8643.14 −0.253740
\(66\) 0 0
\(67\) −5053.56 −0.137534 −0.0687671 0.997633i \(-0.521907\pi\)
−0.0687671 + 0.997633i \(0.521907\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 32853.3 0.773453 0.386726 0.922195i \(-0.373606\pi\)
0.386726 + 0.922195i \(0.373606\pi\)
\(72\) 0 0
\(73\) −11115.0 −0.244119 −0.122059 0.992523i \(-0.538950\pi\)
−0.122059 + 0.992523i \(0.538950\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13234.4 0.254377
\(78\) 0 0
\(79\) −81889.4 −1.47625 −0.738125 0.674664i \(-0.764288\pi\)
−0.738125 + 0.674664i \(0.764288\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 118234. 1.88385 0.941926 0.335819i \(-0.109013\pi\)
0.941926 + 0.335819i \(0.109013\pi\)
\(84\) 0 0
\(85\) 17626.3 0.264615
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 41695.4 0.557972 0.278986 0.960295i \(-0.410002\pi\)
0.278986 + 0.960295i \(0.410002\pi\)
\(90\) 0 0
\(91\) −14731.3 −0.186483
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −48900.9 −0.555914
\(96\) 0 0
\(97\) 43682.8 0.471391 0.235695 0.971827i \(-0.424263\pi\)
0.235695 + 0.971827i \(0.424263\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −25648.1 −0.250179 −0.125090 0.992145i \(-0.539922\pi\)
−0.125090 + 0.992145i \(0.539922\pi\)
\(102\) 0 0
\(103\) 14320.0 0.133000 0.0664999 0.997786i \(-0.478817\pi\)
0.0664999 + 0.997786i \(0.478817\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17201.8 0.145249 0.0726247 0.997359i \(-0.476862\pi\)
0.0726247 + 0.997359i \(0.476862\pi\)
\(108\) 0 0
\(109\) −86017.6 −0.693459 −0.346730 0.937965i \(-0.612708\pi\)
−0.346730 + 0.937965i \(0.612708\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −137568. −1.01349 −0.506745 0.862096i \(-0.669152\pi\)
−0.506745 + 0.862096i \(0.669152\pi\)
\(114\) 0 0
\(115\) −91656.8 −0.646279
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 30042.2 0.194475
\(120\) 0 0
\(121\) −88102.5 −0.547047
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 155921. 0.892542
\(126\) 0 0
\(127\) 70567.1 0.388233 0.194117 0.980978i \(-0.437816\pi\)
0.194117 + 0.980978i \(0.437816\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −173712. −0.884408 −0.442204 0.896914i \(-0.645803\pi\)
−0.442204 + 0.896914i \(0.645803\pi\)
\(132\) 0 0
\(133\) −83346.5 −0.408562
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1989.94 0.00905813 0.00452907 0.999990i \(-0.498558\pi\)
0.00452907 + 0.999990i \(0.498558\pi\)
\(138\) 0 0
\(139\) −366409. −1.60853 −0.804264 0.594272i \(-0.797440\pi\)
−0.804264 + 0.594272i \(0.797440\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −81199.7 −0.332058
\(144\) 0 0
\(145\) 123601. 0.488204
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −140719. −0.519261 −0.259631 0.965708i \(-0.583601\pi\)
−0.259631 + 0.965708i \(0.583601\pi\)
\(150\) 0 0
\(151\) −50064.6 −0.178685 −0.0893425 0.996001i \(-0.528477\pi\)
−0.0893425 + 0.996001i \(0.528477\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 58316.4 0.194967
\(156\) 0 0
\(157\) −89794.6 −0.290738 −0.145369 0.989378i \(-0.546437\pi\)
−0.145369 + 0.989378i \(0.546437\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −156219. −0.474975
\(162\) 0 0
\(163\) 481230. 1.41868 0.709339 0.704867i \(-0.248994\pi\)
0.709339 + 0.704867i \(0.248994\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −86572.7 −0.240209 −0.120105 0.992761i \(-0.538323\pi\)
−0.120105 + 0.992761i \(0.538323\pi\)
\(168\) 0 0
\(169\) −280909. −0.756569
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 58137.4 0.147686 0.0738432 0.997270i \(-0.476474\pi\)
0.0738432 + 0.997270i \(0.476474\pi\)
\(174\) 0 0
\(175\) 112626. 0.277999
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −209380. −0.488431 −0.244215 0.969721i \(-0.578530\pi\)
−0.244215 + 0.969721i \(0.578530\pi\)
\(180\) 0 0
\(181\) 278996. 0.632996 0.316498 0.948593i \(-0.397493\pi\)
0.316498 + 0.948593i \(0.397493\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −148186. −0.318331
\(186\) 0 0
\(187\) 165594. 0.346290
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −445132. −0.882888 −0.441444 0.897289i \(-0.645534\pi\)
−0.441444 + 0.897289i \(0.645534\pi\)
\(192\) 0 0
\(193\) −726811. −1.40452 −0.702260 0.711920i \(-0.747826\pi\)
−0.702260 + 0.711920i \(0.747826\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 364897. 0.669892 0.334946 0.942237i \(-0.391282\pi\)
0.334946 + 0.942237i \(0.391282\pi\)
\(198\) 0 0
\(199\) −289307. −0.517877 −0.258938 0.965894i \(-0.583373\pi\)
−0.258938 + 0.965894i \(0.583373\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 210665. 0.358799
\(204\) 0 0
\(205\) −205448. −0.341442
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −459409. −0.727501
\(210\) 0 0
\(211\) −750147. −1.15995 −0.579976 0.814633i \(-0.696938\pi\)
−0.579976 + 0.814633i \(0.696938\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −563033. −0.830687
\(216\) 0 0
\(217\) 99394.3 0.143289
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −184324. −0.253864
\(222\) 0 0
\(223\) −534398. −0.719619 −0.359810 0.933026i \(-0.617158\pi\)
−0.359810 + 0.933026i \(0.617158\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −410624. −0.528907 −0.264453 0.964398i \(-0.585192\pi\)
−0.264453 + 0.964398i \(0.585192\pi\)
\(228\) 0 0
\(229\) 1.03036e6 1.29838 0.649189 0.760627i \(-0.275108\pi\)
0.649189 + 0.760627i \(0.275108\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 119211. 0.143856 0.0719278 0.997410i \(-0.477085\pi\)
0.0719278 + 0.997410i \(0.477085\pi\)
\(234\) 0 0
\(235\) −574937. −0.679127
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −254090. −0.287735 −0.143868 0.989597i \(-0.545954\pi\)
−0.143868 + 0.989597i \(0.545954\pi\)
\(240\) 0 0
\(241\) 1.41251e6 1.56656 0.783282 0.621667i \(-0.213544\pi\)
0.783282 + 0.621667i \(0.213544\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −69026.8 −0.0734687
\(246\) 0 0
\(247\) 511372. 0.533329
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.67542e6 −1.67857 −0.839286 0.543690i \(-0.817027\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(252\) 0 0
\(253\) −861087. −0.845758
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −726996. −0.686593 −0.343296 0.939227i \(-0.611544\pi\)
−0.343296 + 0.939227i \(0.611544\pi\)
\(258\) 0 0
\(259\) −252568. −0.233953
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −225880. −0.201367 −0.100684 0.994918i \(-0.532103\pi\)
−0.100684 + 0.994918i \(0.532103\pi\)
\(264\) 0 0
\(265\) 113525. 0.0993065
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.80527e6 −1.52111 −0.760557 0.649272i \(-0.775074\pi\)
−0.760557 + 0.649272i \(0.775074\pi\)
\(270\) 0 0
\(271\) 1.71380e6 1.41754 0.708771 0.705439i \(-0.249250\pi\)
0.708771 + 0.705439i \(0.249250\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 620797. 0.495015
\(276\) 0 0
\(277\) 2.23055e6 1.74668 0.873338 0.487115i \(-0.161951\pi\)
0.873338 + 0.487115i \(0.161951\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.67140e6 −1.26274 −0.631371 0.775481i \(-0.717507\pi\)
−0.631371 + 0.775481i \(0.717507\pi\)
\(282\) 0 0
\(283\) 396152. 0.294033 0.147016 0.989134i \(-0.453033\pi\)
0.147016 + 0.989134i \(0.453033\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −350164. −0.250938
\(288\) 0 0
\(289\) −1.04396e6 −0.735256
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 929465. 0.632505 0.316252 0.948675i \(-0.397575\pi\)
0.316252 + 0.948675i \(0.397575\pi\)
\(294\) 0 0
\(295\) 854068. 0.571397
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 958485. 0.620022
\(300\) 0 0
\(301\) −959631. −0.610503
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.45239e6 0.893990
\(306\) 0 0
\(307\) −1.83295e6 −1.10995 −0.554976 0.831866i \(-0.687273\pi\)
−0.554976 + 0.831866i \(0.687273\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.29685e6 −1.34658 −0.673289 0.739379i \(-0.735119\pi\)
−0.673289 + 0.739379i \(0.735119\pi\)
\(312\) 0 0
\(313\) −3.42470e6 −1.97589 −0.987943 0.154817i \(-0.950521\pi\)
−0.987943 + 0.154817i \(0.950521\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.94305e6 −1.64494 −0.822470 0.568808i \(-0.807405\pi\)
−0.822470 + 0.568808i \(0.807405\pi\)
\(318\) 0 0
\(319\) 1.16119e6 0.638891
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.04286e6 −0.556187
\(324\) 0 0
\(325\) −691016. −0.362894
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −979921. −0.499116
\(330\) 0 0
\(331\) −966164. −0.484709 −0.242354 0.970188i \(-0.577920\pi\)
−0.242354 + 0.970188i \(0.577920\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 145286. 0.0707312
\(336\) 0 0
\(337\) 136417. 0.0654327 0.0327163 0.999465i \(-0.489584\pi\)
0.0327163 + 0.999465i \(0.489584\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 547865. 0.255145
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 355408. 0.158454 0.0792270 0.996857i \(-0.474755\pi\)
0.0792270 + 0.996857i \(0.474755\pi\)
\(348\) 0 0
\(349\) −140128. −0.0615830 −0.0307915 0.999526i \(-0.509803\pi\)
−0.0307915 + 0.999526i \(0.509803\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.48141e6 −1.48703 −0.743514 0.668721i \(-0.766842\pi\)
−0.743514 + 0.668721i \(0.766842\pi\)
\(354\) 0 0
\(355\) −944507. −0.397772
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.75285e6 0.717810 0.358905 0.933374i \(-0.383150\pi\)
0.358905 + 0.933374i \(0.383150\pi\)
\(360\) 0 0
\(361\) 417127. 0.168461
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 319546. 0.125546
\(366\) 0 0
\(367\) 1.76939e6 0.685738 0.342869 0.939383i \(-0.388601\pi\)
0.342869 + 0.939383i \(0.388601\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 193492. 0.0729841
\(372\) 0 0
\(373\) −4.16212e6 −1.54897 −0.774485 0.632592i \(-0.781991\pi\)
−0.774485 + 0.632592i \(0.781991\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.29253e6 −0.468369
\(378\) 0 0
\(379\) −618163. −0.221057 −0.110529 0.993873i \(-0.535254\pi\)
−0.110529 + 0.993873i \(0.535254\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.11163e6 −1.43225 −0.716123 0.697974i \(-0.754085\pi\)
−0.716123 + 0.697974i \(0.754085\pi\)
\(384\) 0 0
\(385\) −380478. −0.130821
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.62076e6 −1.54824 −0.774122 0.633037i \(-0.781808\pi\)
−0.774122 + 0.633037i \(0.781808\pi\)
\(390\) 0 0
\(391\) −1.95468e6 −0.646596
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.35425e6 0.759207
\(396\) 0 0
\(397\) 5.07349e6 1.61559 0.807794 0.589465i \(-0.200661\pi\)
0.807794 + 0.589465i \(0.200661\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.48056e6 0.459795 0.229898 0.973215i \(-0.426161\pi\)
0.229898 + 0.973215i \(0.426161\pi\)
\(402\) 0 0
\(403\) −609834. −0.187046
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.39217e6 −0.416586
\(408\) 0 0
\(409\) −4.53379e6 −1.34015 −0.670075 0.742294i \(-0.733738\pi\)
−0.670075 + 0.742294i \(0.733738\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.45567e6 0.419941
\(414\) 0 0
\(415\) −3.39913e6 −0.968829
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 111026. 0.0308952 0.0154476 0.999881i \(-0.495083\pi\)
0.0154476 + 0.999881i \(0.495083\pi\)
\(420\) 0 0
\(421\) −1.41151e6 −0.388132 −0.194066 0.980988i \(-0.562168\pi\)
−0.194066 + 0.980988i \(0.562168\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.40922e6 0.378447
\(426\) 0 0
\(427\) 2.47544e6 0.657027
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.07640e6 0.279113 0.139557 0.990214i \(-0.455432\pi\)
0.139557 + 0.990214i \(0.455432\pi\)
\(432\) 0 0
\(433\) −310172. −0.0795029 −0.0397515 0.999210i \(-0.512657\pi\)
−0.0397515 + 0.999210i \(0.512657\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.42288e6 1.35840
\(438\) 0 0
\(439\) −5.67650e6 −1.40579 −0.702893 0.711296i \(-0.748109\pi\)
−0.702893 + 0.711296i \(0.748109\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.05966e6 0.982834 0.491417 0.870924i \(-0.336479\pi\)
0.491417 + 0.870924i \(0.336479\pi\)
\(444\) 0 0
\(445\) −1.19871e6 −0.286955
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.96544e6 1.63054 0.815272 0.579078i \(-0.196587\pi\)
0.815272 + 0.579078i \(0.196587\pi\)
\(450\) 0 0
\(451\) −1.93012e6 −0.446830
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 423514. 0.0959045
\(456\) 0 0
\(457\) 1.79523e6 0.402096 0.201048 0.979581i \(-0.435565\pi\)
0.201048 + 0.979581i \(0.435565\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.11294e6 0.463058 0.231529 0.972828i \(-0.425627\pi\)
0.231529 + 0.972828i \(0.425627\pi\)
\(462\) 0 0
\(463\) −1.26223e6 −0.273643 −0.136822 0.990596i \(-0.543689\pi\)
−0.136822 + 0.990596i \(0.543689\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.58926e6 −0.761576 −0.380788 0.924662i \(-0.624347\pi\)
−0.380788 + 0.924662i \(0.624347\pi\)
\(468\) 0 0
\(469\) 247624. 0.0519830
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.28952e6 −1.08708
\(474\) 0 0
\(475\) −3.90960e6 −0.795058
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.41693e6 −0.481311 −0.240655 0.970611i \(-0.577362\pi\)
−0.240655 + 0.970611i \(0.577362\pi\)
\(480\) 0 0
\(481\) 1.54963e6 0.305398
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.25584e6 −0.242427
\(486\) 0 0
\(487\) 5.19403e6 0.992388 0.496194 0.868212i \(-0.334730\pi\)
0.496194 + 0.868212i \(0.334730\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.38961e6 1.00891 0.504456 0.863437i \(-0.331693\pi\)
0.504456 + 0.863437i \(0.331693\pi\)
\(492\) 0 0
\(493\) 2.63592e6 0.488443
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.60981e6 −0.292338
\(498\) 0 0
\(499\) 3.29606e6 0.592576 0.296288 0.955099i \(-0.404251\pi\)
0.296288 + 0.955099i \(0.404251\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.06512e7 −1.87706 −0.938528 0.345204i \(-0.887810\pi\)
−0.938528 + 0.345204i \(0.887810\pi\)
\(504\) 0 0
\(505\) 737361. 0.128662
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.74268e6 0.469225 0.234612 0.972089i \(-0.424618\pi\)
0.234612 + 0.972089i \(0.424618\pi\)
\(510\) 0 0
\(511\) 544633. 0.0922682
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −411689. −0.0683992
\(516\) 0 0
\(517\) −5.40136e6 −0.888744
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.97077e6 −0.802286 −0.401143 0.916015i \(-0.631387\pi\)
−0.401143 + 0.916015i \(0.631387\pi\)
\(522\) 0 0
\(523\) −2.41579e6 −0.386193 −0.193096 0.981180i \(-0.561853\pi\)
−0.193096 + 0.981180i \(0.561853\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.24366e6 0.195063
\(528\) 0 0
\(529\) 3.72798e6 0.579207
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.14843e6 0.327570
\(534\) 0 0
\(535\) −494537. −0.0746989
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −648485. −0.0961454
\(540\) 0 0
\(541\) 472165. 0.0693587 0.0346794 0.999398i \(-0.488959\pi\)
0.0346794 + 0.999398i \(0.488959\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.47293e6 0.356633
\(546\) 0 0
\(547\) −7.63716e6 −1.09135 −0.545675 0.837997i \(-0.683727\pi\)
−0.545675 + 0.837997i \(0.683727\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.31285e6 −1.02614
\(552\) 0 0
\(553\) 4.01258e6 0.557970
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.48807e6 0.612946 0.306473 0.951879i \(-0.400851\pi\)
0.306473 + 0.951879i \(0.400851\pi\)
\(558\) 0 0
\(559\) 5.88782e6 0.796938
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.16500e6 −0.287864 −0.143932 0.989588i \(-0.545975\pi\)
−0.143932 + 0.989588i \(0.545975\pi\)
\(564\) 0 0
\(565\) 3.95495e6 0.521219
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.13325e7 1.46739 0.733696 0.679478i \(-0.237794\pi\)
0.733696 + 0.679478i \(0.237794\pi\)
\(570\) 0 0
\(571\) 843773. 0.108302 0.0541509 0.998533i \(-0.482755\pi\)
0.0541509 + 0.998533i \(0.482755\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7.32792e6 −0.924296
\(576\) 0 0
\(577\) −2.23784e6 −0.279827 −0.139914 0.990164i \(-0.544682\pi\)
−0.139914 + 0.990164i \(0.544682\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.79346e6 −0.712029
\(582\) 0 0
\(583\) 1.06653e6 0.129958
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.21190e7 1.45168 0.725839 0.687864i \(-0.241452\pi\)
0.725839 + 0.687864i \(0.241452\pi\)
\(588\) 0 0
\(589\) −3.45030e6 −0.409797
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.00167e6 −0.934424 −0.467212 0.884145i \(-0.654742\pi\)
−0.467212 + 0.884145i \(0.654742\pi\)
\(594\) 0 0
\(595\) −863689. −0.100015
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.45899e7 1.66144 0.830719 0.556692i \(-0.187930\pi\)
0.830719 + 0.556692i \(0.187930\pi\)
\(600\) 0 0
\(601\) −8.67178e6 −0.979314 −0.489657 0.871915i \(-0.662878\pi\)
−0.489657 + 0.871915i \(0.662878\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.53287e6 0.281336
\(606\) 0 0
\(607\) 1.33059e7 1.46580 0.732898 0.680339i \(-0.238167\pi\)
0.732898 + 0.680339i \(0.238167\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.01231e6 0.651536
\(612\) 0 0
\(613\) 2.35101e6 0.252699 0.126350 0.991986i \(-0.459674\pi\)
0.126350 + 0.991986i \(0.459674\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.63523e6 −1.01894 −0.509470 0.860488i \(-0.670159\pi\)
−0.509470 + 0.860488i \(0.670159\pi\)
\(618\) 0 0
\(619\) 4.86148e6 0.509967 0.254983 0.966945i \(-0.417930\pi\)
0.254983 + 0.966945i \(0.417930\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.04307e6 −0.210894
\(624\) 0 0
\(625\) 2.70017e6 0.276498
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.16023e6 −0.318487
\(630\) 0 0
\(631\) 6.59770e6 0.659659 0.329829 0.944041i \(-0.393009\pi\)
0.329829 + 0.944041i \(0.393009\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.02874e6 −0.199661
\(636\) 0 0
\(637\) 721836. 0.0704839
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.44525e7 −1.38930 −0.694651 0.719347i \(-0.744441\pi\)
−0.694651 + 0.719347i \(0.744441\pi\)
\(642\) 0 0
\(643\) 1.54720e7 1.47577 0.737886 0.674926i \(-0.235824\pi\)
0.737886 + 0.674926i \(0.235824\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.66647e7 1.56508 0.782540 0.622601i \(-0.213924\pi\)
0.782540 + 0.622601i \(0.213924\pi\)
\(648\) 0 0
\(649\) 8.02371e6 0.747762
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.33451e7 1.22472 0.612361 0.790578i \(-0.290220\pi\)
0.612361 + 0.790578i \(0.290220\pi\)
\(654\) 0 0
\(655\) 4.99409e6 0.454834
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.00667e6 −0.359393 −0.179697 0.983722i \(-0.557512\pi\)
−0.179697 + 0.983722i \(0.557512\pi\)
\(660\) 0 0
\(661\) 1.08005e7 0.961478 0.480739 0.876864i \(-0.340368\pi\)
0.480739 + 0.876864i \(0.340368\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.39614e6 0.210116
\(666\) 0 0
\(667\) −1.37068e7 −1.19294
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.36447e7 1.16993
\(672\) 0 0
\(673\) 1.09119e7 0.928676 0.464338 0.885658i \(-0.346292\pi\)
0.464338 + 0.885658i \(0.346292\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.35765e7 1.13846 0.569229 0.822179i \(-0.307242\pi\)
0.569229 + 0.822179i \(0.307242\pi\)
\(678\) 0 0
\(679\) −2.14046e6 −0.178169
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.26726e7 −1.03948 −0.519738 0.854326i \(-0.673970\pi\)
−0.519738 + 0.854326i \(0.673970\pi\)
\(684\) 0 0
\(685\) −57209.2 −0.00465843
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.18717e6 −0.0952720
\(690\) 0 0
\(691\) −7.11964e6 −0.567235 −0.283617 0.958938i \(-0.591535\pi\)
−0.283617 + 0.958938i \(0.591535\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.05339e7 0.827235
\(696\) 0 0
\(697\) −4.38139e6 −0.341609
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.00155e7 0.769803 0.384902 0.922958i \(-0.374235\pi\)
0.384902 + 0.922958i \(0.374235\pi\)
\(702\) 0 0
\(703\) 8.76746e6 0.669092
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.25676e6 0.0945589
\(708\) 0 0
\(709\) −8.84454e6 −0.660784 −0.330392 0.943844i \(-0.607181\pi\)
−0.330392 + 0.943844i \(0.607181\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.46703e6 −0.476410
\(714\) 0 0
\(715\) 2.33442e6 0.170771
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.58086e6 0.474745 0.237373 0.971419i \(-0.423714\pi\)
0.237373 + 0.971419i \(0.423714\pi\)
\(720\) 0 0
\(721\) −701682. −0.0502692
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.88183e6 0.698220
\(726\) 0 0
\(727\) −1.88401e7 −1.32205 −0.661023 0.750365i \(-0.729878\pi\)
−0.661023 + 0.750365i \(0.729878\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.20073e7 −0.831095
\(732\) 0 0
\(733\) −2.78330e6 −0.191337 −0.0956687 0.995413i \(-0.530499\pi\)
−0.0956687 + 0.995413i \(0.530499\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.36491e6 0.0925629
\(738\) 0 0
\(739\) 2.48970e7 1.67701 0.838505 0.544894i \(-0.183430\pi\)
0.838505 + 0.544894i \(0.183430\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.86085e6 −0.256573 −0.128286 0.991737i \(-0.540948\pi\)
−0.128286 + 0.991737i \(0.540948\pi\)
\(744\) 0 0
\(745\) 4.04554e6 0.267046
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −842888. −0.0548991
\(750\) 0 0
\(751\) −6.72737e6 −0.435257 −0.217628 0.976032i \(-0.569832\pi\)
−0.217628 + 0.976032i \(0.569832\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.43932e6 0.0918943
\(756\) 0 0
\(757\) 2.17782e7 1.38128 0.690642 0.723197i \(-0.257328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.57074e7 1.60915 0.804575 0.593851i \(-0.202393\pi\)
0.804575 + 0.593851i \(0.202393\pi\)
\(762\) 0 0
\(763\) 4.21486e6 0.262103
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.93127e6 −0.548182
\(768\) 0 0
\(769\) −1.34375e7 −0.819413 −0.409706 0.912217i \(-0.634369\pi\)
−0.409706 + 0.912217i \(0.634369\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.05572e7 −1.83935 −0.919674 0.392682i \(-0.871547\pi\)
−0.919674 + 0.392682i \(0.871547\pi\)
\(774\) 0 0
\(775\) 4.66237e6 0.278839
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.21553e7 0.717667
\(780\) 0 0
\(781\) −8.87335e6 −0.520547
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.58152e6 0.149521
\(786\) 0 0
\(787\) 2.07672e6 0.119520 0.0597602 0.998213i \(-0.480966\pi\)
0.0597602 + 0.998213i \(0.480966\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6.74081e6 0.383064
\(792\) 0 0
\(793\) −1.51881e7 −0.857670
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.98563e6 0.333783 0.166892 0.985975i \(-0.446627\pi\)
0.166892 + 0.985975i \(0.446627\pi\)
\(798\) 0 0
\(799\) −1.22611e7 −0.679460
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.00204e6 0.164296
\(804\) 0 0
\(805\) 4.49118e6 0.244270
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.96864e7 −1.05754 −0.528769 0.848766i \(-0.677346\pi\)
−0.528769 + 0.848766i \(0.677346\pi\)
\(810\) 0 0
\(811\) −8.50101e6 −0.453856 −0.226928 0.973912i \(-0.572868\pi\)
−0.226928 + 0.973912i \(0.572868\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.38350e7 −0.729599
\(816\) 0 0
\(817\) 3.33119e7 1.74600
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.36199e6 0.0705204 0.0352602 0.999378i \(-0.488774\pi\)
0.0352602 + 0.999378i \(0.488774\pi\)
\(822\) 0 0
\(823\) 1.35934e6 0.0699566 0.0349783 0.999388i \(-0.488864\pi\)
0.0349783 + 0.999388i \(0.488864\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.00727e7 0.512132 0.256066 0.966659i \(-0.417574\pi\)
0.256066 + 0.966659i \(0.417574\pi\)
\(828\) 0 0
\(829\) −5.63984e6 −0.285023 −0.142512 0.989793i \(-0.545518\pi\)
−0.142512 + 0.989793i \(0.545518\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.47207e6 −0.0735048
\(834\) 0 0
\(835\) 2.48889e6 0.123535
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.16351e7 −0.570642 −0.285321 0.958432i \(-0.592100\pi\)
−0.285321 + 0.958432i \(0.592100\pi\)
\(840\) 0 0
\(841\) −2.02735e6 −0.0988413
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.07590e6 0.389089
\(846\) 0 0
\(847\) 4.31702e6 0.206764
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.64332e7 0.777854
\(852\) 0 0
\(853\) 2.85205e7 1.34210 0.671049 0.741413i \(-0.265844\pi\)
0.671049 + 0.741413i \(0.265844\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 9.95725e6 0.463113 0.231557 0.972821i \(-0.425618\pi\)
0.231557 + 0.972821i \(0.425618\pi\)
\(858\) 0 0
\(859\) 1.49322e7 0.690463 0.345232 0.938517i \(-0.387800\pi\)
0.345232 + 0.938517i \(0.387800\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.84933e7 1.75937 0.879687 0.475553i \(-0.157752\pi\)
0.879687 + 0.475553i \(0.157752\pi\)
\(864\) 0 0
\(865\) −1.67140e6 −0.0759523
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.21175e7 0.993542
\(870\) 0 0
\(871\) −1.51930e6 −0.0678576
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −7.64011e6 −0.337349
\(876\) 0 0
\(877\) 9.40311e6 0.412831 0.206416 0.978464i \(-0.433820\pi\)
0.206416 + 0.978464i \(0.433820\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.10395e6 −0.0479194 −0.0239597 0.999713i \(-0.507627\pi\)
−0.0239597 + 0.999713i \(0.507627\pi\)
\(882\) 0 0
\(883\) −8.06579e6 −0.348133 −0.174067 0.984734i \(-0.555691\pi\)
−0.174067 + 0.984734i \(0.555691\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.49902e7 −0.639732 −0.319866 0.947463i \(-0.603638\pi\)
−0.319866 + 0.947463i \(0.603638\pi\)
\(888\) 0 0
\(889\) −3.45779e6 −0.146738
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.40162e7 1.42744
\(894\) 0 0
\(895\) 6.01950e6 0.251190
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.72090e6 0.359883
\(900\) 0 0
\(901\) 2.42104e6 0.0993553
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8.02089e6 −0.325538
\(906\) 0 0
\(907\) −4.12622e6 −0.166546 −0.0832730 0.996527i \(-0.526537\pi\)
−0.0832730 + 0.996527i \(0.526537\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.04272e7 1.61391 0.806953 0.590616i \(-0.201115\pi\)
0.806953 + 0.590616i \(0.201115\pi\)
\(912\) 0 0
\(913\) −3.19338e7 −1.26787
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.51191e6 0.334275
\(918\) 0 0
\(919\) −2.18546e7 −0.853600 −0.426800 0.904346i \(-0.640359\pi\)
−0.426800 + 0.904346i \(0.640359\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9.87702e6 0.381612
\(924\) 0 0
\(925\) −1.18474e7 −0.455271
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.06843e7 −0.406169 −0.203085 0.979161i \(-0.565097\pi\)
−0.203085 + 0.979161i \(0.565097\pi\)
\(930\) 0 0
\(931\) 4.08398e6 0.154422
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.76068e6 −0.178090
\(936\) 0 0
\(937\) −3.99105e7 −1.48504 −0.742521 0.669823i \(-0.766370\pi\)
−0.742521 + 0.669823i \(0.766370\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.32350e6 −0.0487248 −0.0243624 0.999703i \(-0.507756\pi\)
−0.0243624 + 0.999703i \(0.507756\pi\)
\(942\) 0 0
\(943\) 2.27832e7 0.834326
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.76322e7 −1.00124 −0.500622 0.865666i \(-0.666895\pi\)
−0.500622 + 0.865666i \(0.666895\pi\)
\(948\) 0 0
\(949\) −3.34160e6 −0.120445
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.07901e7 1.09819 0.549096 0.835759i \(-0.314972\pi\)
0.549096 + 0.835759i \(0.314972\pi\)
\(954\) 0 0
\(955\) 1.27972e7 0.454053
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −97507.1 −0.00342365
\(960\) 0 0
\(961\) −2.45145e7 −0.856278
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.08952e7 0.722318
\(966\) 0 0
\(967\) −2.92557e6 −0.100611 −0.0503055 0.998734i \(-0.516019\pi\)
−0.0503055 + 0.998734i \(0.516019\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.78109e6 0.0946601 0.0473301 0.998879i \(-0.484929\pi\)
0.0473301 + 0.998879i \(0.484929\pi\)
\(972\) 0 0
\(973\) 1.79540e7 0.607967
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −7.48673e6 −0.250932 −0.125466 0.992098i \(-0.540043\pi\)
−0.125466 + 0.992098i \(0.540043\pi\)
\(978\) 0 0
\(979\) −1.12615e7 −0.375525
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.79815e7 0.593528 0.296764 0.954951i \(-0.404093\pi\)
0.296764 + 0.954951i \(0.404093\pi\)
\(984\) 0 0
\(985\) −1.04905e7 −0.344512
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.24378e7 2.02982
\(990\) 0 0
\(991\) −3.72778e7 −1.20578 −0.602888 0.797826i \(-0.705983\pi\)
−0.602888 + 0.797826i \(0.705983\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8.31734e6 0.266334
\(996\) 0 0
\(997\) 4.87422e7 1.55298 0.776492 0.630128i \(-0.216997\pi\)
0.776492 + 0.630128i \(0.216997\pi\)
\(998\) 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.bq.1.1 2
3.2 odd 2 112.6.a.h.1.2 2
4.3 odd 2 63.6.a.f.1.1 2
12.11 even 2 7.6.a.b.1.2 2
21.20 even 2 784.6.a.v.1.1 2
24.5 odd 2 448.6.a.u.1.1 2
24.11 even 2 448.6.a.w.1.2 2
28.27 even 2 441.6.a.l.1.1 2
60.23 odd 4 175.6.b.c.99.1 4
60.47 odd 4 175.6.b.c.99.4 4
60.59 even 2 175.6.a.c.1.1 2
84.11 even 6 49.6.c.e.30.1 4
84.23 even 6 49.6.c.e.18.1 4
84.47 odd 6 49.6.c.d.18.1 4
84.59 odd 6 49.6.c.d.30.1 4
84.83 odd 2 49.6.a.f.1.2 2
132.131 odd 2 847.6.a.c.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.6.a.b.1.2 2 12.11 even 2
49.6.a.f.1.2 2 84.83 odd 2
49.6.c.d.18.1 4 84.47 odd 6
49.6.c.d.30.1 4 84.59 odd 6
49.6.c.e.18.1 4 84.23 even 6
49.6.c.e.30.1 4 84.11 even 6
63.6.a.f.1.1 2 4.3 odd 2
112.6.a.h.1.2 2 3.2 odd 2
175.6.a.c.1.1 2 60.59 even 2
175.6.b.c.99.1 4 60.23 odd 4
175.6.b.c.99.4 4 60.47 odd 4
441.6.a.l.1.1 2 28.27 even 2
448.6.a.u.1.1 2 24.5 odd 2
448.6.a.w.1.2 2 24.11 even 2
784.6.a.v.1.1 2 21.20 even 2
847.6.a.c.1.1 2 132.131 odd 2
1008.6.a.bq.1.1 2 1.1 even 1 trivial