Properties

Label 1008.6.a.bi.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{193}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-6.44622\) 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)
 
\(f(q)\) \(=\) \(q+48.4622 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+48.4622 q^{5} +49.0000 q^{7} -163.506 q^{11} -120.828 q^{13} -78.1920 q^{17} +2265.00 q^{19} -2451.95 q^{23} -776.413 q^{25} -6985.27 q^{29} -2794.03 q^{31} +2374.65 q^{35} +9459.44 q^{37} -10088.5 q^{41} +6934.29 q^{43} +1165.76 q^{47} +2401.00 q^{49} -8562.42 q^{53} -7923.85 q^{55} +6220.26 q^{59} -41928.9 q^{61} -5855.62 q^{65} -1812.09 q^{67} -56823.3 q^{71} -44299.5 q^{73} -8011.78 q^{77} -34912.4 q^{79} -39652.9 q^{83} -3789.36 q^{85} +126299. q^{89} -5920.59 q^{91} +109767. q^{95} -145513. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 42 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 42 q^{5} + 98 q^{7} - 716 q^{11} - 714 q^{13} + 1344 q^{17} + 1946 q^{19} - 1792 q^{23} + 4282 q^{25} + 1200 q^{29} + 6804 q^{31} - 2058 q^{35} + 14640 q^{37} - 7896 q^{41} - 524 q^{43} - 18396 q^{47} + 4802 q^{49} - 45132 q^{53} + 42056 q^{55} + 22582 q^{59} - 52822 q^{61} + 47804 q^{65} - 9848 q^{67} - 840 q^{71} - 122052 q^{73} - 35084 q^{77} - 31704 q^{79} + 36974 q^{83} - 132444 q^{85} + 210588 q^{89} - 34986 q^{91} + 138624 q^{95} - 44240 q^{97}+O(q^{100}) \) 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
\(5\) 48.4622 0.866919 0.433459 0.901173i \(-0.357293\pi\)
0.433459 + 0.901173i \(0.357293\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −163.506 −0.407429 −0.203714 0.979030i \(-0.565301\pi\)
−0.203714 + 0.979030i \(0.565301\pi\)
\(12\) 0 0
\(13\) −120.828 −0.198295 −0.0991473 0.995073i \(-0.531611\pi\)
−0.0991473 + 0.995073i \(0.531611\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −78.1920 −0.0656206 −0.0328103 0.999462i \(-0.510446\pi\)
−0.0328103 + 0.999462i \(0.510446\pi\)
\(18\) 0 0
\(19\) 2265.00 1.43941 0.719704 0.694281i \(-0.244278\pi\)
0.719704 + 0.694281i \(0.244278\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2451.95 −0.966480 −0.483240 0.875488i \(-0.660540\pi\)
−0.483240 + 0.875488i \(0.660540\pi\)
\(24\) 0 0
\(25\) −776.413 −0.248452
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6985.27 −1.54237 −0.771185 0.636611i \(-0.780336\pi\)
−0.771185 + 0.636611i \(0.780336\pi\)
\(30\) 0 0
\(31\) −2794.03 −0.522188 −0.261094 0.965313i \(-0.584083\pi\)
−0.261094 + 0.965313i \(0.584083\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2374.65 0.327664
\(36\) 0 0
\(37\) 9459.44 1.13595 0.567977 0.823044i \(-0.307726\pi\)
0.567977 + 0.823044i \(0.307726\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10088.5 −0.937271 −0.468636 0.883392i \(-0.655254\pi\)
−0.468636 + 0.883392i \(0.655254\pi\)
\(42\) 0 0
\(43\) 6934.29 0.571914 0.285957 0.958242i \(-0.407689\pi\)
0.285957 + 0.958242i \(0.407689\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1165.76 0.0769778 0.0384889 0.999259i \(-0.487746\pi\)
0.0384889 + 0.999259i \(0.487746\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8562.42 −0.418704 −0.209352 0.977840i \(-0.567135\pi\)
−0.209352 + 0.977840i \(0.567135\pi\)
\(54\) 0 0
\(55\) −7923.85 −0.353207
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6220.26 0.232637 0.116318 0.993212i \(-0.462891\pi\)
0.116318 + 0.993212i \(0.462891\pi\)
\(60\) 0 0
\(61\) −41928.9 −1.44274 −0.721371 0.692549i \(-0.756488\pi\)
−0.721371 + 0.692549i \(0.756488\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5855.62 −0.171905
\(66\) 0 0
\(67\) −1812.09 −0.0493166 −0.0246583 0.999696i \(-0.507850\pi\)
−0.0246583 + 0.999696i \(0.507850\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −56823.3 −1.33777 −0.668884 0.743367i \(-0.733228\pi\)
−0.668884 + 0.743367i \(0.733228\pi\)
\(72\) 0 0
\(73\) −44299.5 −0.972953 −0.486476 0.873694i \(-0.661718\pi\)
−0.486476 + 0.873694i \(0.661718\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8011.78 −0.153993
\(78\) 0 0
\(79\) −34912.4 −0.629379 −0.314690 0.949195i \(-0.601900\pi\)
−0.314690 + 0.949195i \(0.601900\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −39652.9 −0.631800 −0.315900 0.948793i \(-0.602306\pi\)
−0.315900 + 0.948793i \(0.602306\pi\)
\(84\) 0 0
\(85\) −3789.36 −0.0568877
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 126299. 1.69015 0.845077 0.534645i \(-0.179555\pi\)
0.845077 + 0.534645i \(0.179555\pi\)
\(90\) 0 0
\(91\) −5920.59 −0.0749483
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 109767. 1.24785
\(96\) 0 0
\(97\) −145513. −1.57026 −0.785130 0.619331i \(-0.787404\pi\)
−0.785130 + 0.619331i \(0.787404\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −99545.5 −0.970998 −0.485499 0.874237i \(-0.661362\pi\)
−0.485499 + 0.874237i \(0.661362\pi\)
\(102\) 0 0
\(103\) 129791. 1.20546 0.602729 0.797946i \(-0.294080\pi\)
0.602729 + 0.797946i \(0.294080\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 218811. 1.84761 0.923804 0.382865i \(-0.125062\pi\)
0.923804 + 0.382865i \(0.125062\pi\)
\(108\) 0 0
\(109\) 201627. 1.62549 0.812743 0.582623i \(-0.197974\pi\)
0.812743 + 0.582623i \(0.197974\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −31803.9 −0.234306 −0.117153 0.993114i \(-0.537377\pi\)
−0.117153 + 0.993114i \(0.537377\pi\)
\(114\) 0 0
\(115\) −118827. −0.837859
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3831.41 −0.0248022
\(120\) 0 0
\(121\) −134317. −0.834002
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −189071. −1.08231
\(126\) 0 0
\(127\) 318115. 1.75015 0.875075 0.483988i \(-0.160812\pi\)
0.875075 + 0.483988i \(0.160812\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −305194. −1.55381 −0.776905 0.629618i \(-0.783212\pi\)
−0.776905 + 0.629618i \(0.783212\pi\)
\(132\) 0 0
\(133\) 110985. 0.544045
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −180045. −0.819556 −0.409778 0.912185i \(-0.634394\pi\)
−0.409778 + 0.912185i \(0.634394\pi\)
\(138\) 0 0
\(139\) 323204. 1.41886 0.709430 0.704776i \(-0.248953\pi\)
0.709430 + 0.704776i \(0.248953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 19756.2 0.0807909
\(144\) 0 0
\(145\) −338522. −1.33711
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −294159. −1.08547 −0.542733 0.839905i \(-0.682610\pi\)
−0.542733 + 0.839905i \(0.682610\pi\)
\(150\) 0 0
\(151\) 334962. 1.19551 0.597754 0.801679i \(-0.296060\pi\)
0.597754 + 0.801679i \(0.296060\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −135405. −0.452694
\(156\) 0 0
\(157\) −145150. −0.469967 −0.234984 0.971999i \(-0.575504\pi\)
−0.234984 + 0.971999i \(0.575504\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −120146. −0.365295
\(162\) 0 0
\(163\) 176221. 0.519504 0.259752 0.965675i \(-0.416359\pi\)
0.259752 + 0.965675i \(0.416359\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −45460.7 −0.126138 −0.0630689 0.998009i \(-0.520089\pi\)
−0.0630689 + 0.998009i \(0.520089\pi\)
\(168\) 0 0
\(169\) −356693. −0.960679
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 205842. 0.522900 0.261450 0.965217i \(-0.415799\pi\)
0.261450 + 0.965217i \(0.415799\pi\)
\(174\) 0 0
\(175\) −38044.2 −0.0939061
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −199205. −0.464695 −0.232348 0.972633i \(-0.574641\pi\)
−0.232348 + 0.972633i \(0.574641\pi\)
\(180\) 0 0
\(181\) 198411. 0.450162 0.225081 0.974340i \(-0.427735\pi\)
0.225081 + 0.974340i \(0.427735\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 458425. 0.984780
\(186\) 0 0
\(187\) 12784.8 0.0267357
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 372947. 0.739714 0.369857 0.929089i \(-0.379407\pi\)
0.369857 + 0.929089i \(0.379407\pi\)
\(192\) 0 0
\(193\) 175020. 0.338215 0.169108 0.985598i \(-0.445911\pi\)
0.169108 + 0.985598i \(0.445911\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −883770. −1.62246 −0.811229 0.584728i \(-0.801201\pi\)
−0.811229 + 0.584728i \(0.801201\pi\)
\(198\) 0 0
\(199\) −785843. −1.40671 −0.703353 0.710841i \(-0.748314\pi\)
−0.703353 + 0.710841i \(0.748314\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −342278. −0.582961
\(204\) 0 0
\(205\) −488909. −0.812538
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −370340. −0.586456
\(210\) 0 0
\(211\) −763861. −1.18116 −0.590579 0.806980i \(-0.701101\pi\)
−0.590579 + 0.806980i \(0.701101\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 336051. 0.495803
\(216\) 0 0
\(217\) −136907. −0.197368
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9447.82 0.0130122
\(222\) 0 0
\(223\) 204400. 0.275245 0.137623 0.990485i \(-0.456054\pi\)
0.137623 + 0.990485i \(0.456054\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.00806e6 1.29844 0.649218 0.760603i \(-0.275096\pi\)
0.649218 + 0.760603i \(0.275096\pi\)
\(228\) 0 0
\(229\) −244324. −0.307877 −0.153938 0.988080i \(-0.549196\pi\)
−0.153938 + 0.988080i \(0.549196\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20822.9 −0.0251276 −0.0125638 0.999921i \(-0.503999\pi\)
−0.0125638 + 0.999921i \(0.503999\pi\)
\(234\) 0 0
\(235\) 56495.5 0.0667335
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −474033. −0.536801 −0.268401 0.963307i \(-0.586495\pi\)
−0.268401 + 0.963307i \(0.586495\pi\)
\(240\) 0 0
\(241\) −1.70390e6 −1.88974 −0.944869 0.327450i \(-0.893811\pi\)
−0.944869 + 0.327450i \(0.893811\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 116358. 0.123846
\(246\) 0 0
\(247\) −273676. −0.285427
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −810918. −0.812442 −0.406221 0.913775i \(-0.633154\pi\)
−0.406221 + 0.913775i \(0.633154\pi\)
\(252\) 0 0
\(253\) 400909. 0.393771
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.26657e6 −1.19618 −0.598088 0.801431i \(-0.704073\pi\)
−0.598088 + 0.801431i \(0.704073\pi\)
\(258\) 0 0
\(259\) 463512. 0.429350
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.96048e6 −1.74773 −0.873863 0.486172i \(-0.838393\pi\)
−0.873863 + 0.486172i \(0.838393\pi\)
\(264\) 0 0
\(265\) −414954. −0.362982
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.49358e6 1.25848 0.629242 0.777209i \(-0.283365\pi\)
0.629242 + 0.777209i \(0.283365\pi\)
\(270\) 0 0
\(271\) −1.23626e6 −1.02255 −0.511275 0.859417i \(-0.670827\pi\)
−0.511275 + 0.859417i \(0.670827\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 126948. 0.101227
\(276\) 0 0
\(277\) −170150. −0.133239 −0.0666197 0.997778i \(-0.521221\pi\)
−0.0666197 + 0.997778i \(0.521221\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.29957e6 −0.981824 −0.490912 0.871209i \(-0.663336\pi\)
−0.490912 + 0.871209i \(0.663336\pi\)
\(282\) 0 0
\(283\) 374032. 0.277615 0.138807 0.990319i \(-0.455673\pi\)
0.138807 + 0.990319i \(0.455673\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −494335. −0.354255
\(288\) 0 0
\(289\) −1.41374e6 −0.995694
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.15022e6 −0.782728 −0.391364 0.920236i \(-0.627997\pi\)
−0.391364 + 0.920236i \(0.627997\pi\)
\(294\) 0 0
\(295\) 301448. 0.201677
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 296266. 0.191648
\(300\) 0 0
\(301\) 339780. 0.216163
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.03197e6 −1.25074
\(306\) 0 0
\(307\) −2.61214e6 −1.58179 −0.790897 0.611949i \(-0.790386\pi\)
−0.790897 + 0.611949i \(0.790386\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.40646e6 −0.824566 −0.412283 0.911056i \(-0.635269\pi\)
−0.412283 + 0.911056i \(0.635269\pi\)
\(312\) 0 0
\(313\) 2.37930e6 1.37274 0.686369 0.727253i \(-0.259203\pi\)
0.686369 + 0.727253i \(0.259203\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 563199. 0.314785 0.157393 0.987536i \(-0.449691\pi\)
0.157393 + 0.987536i \(0.449691\pi\)
\(318\) 0 0
\(319\) 1.14213e6 0.628405
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −177105. −0.0944547
\(324\) 0 0
\(325\) 93812.8 0.0492667
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 57122.4 0.0290949
\(330\) 0 0
\(331\) 850649. 0.426757 0.213378 0.976970i \(-0.431553\pi\)
0.213378 + 0.976970i \(0.431553\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −87818.0 −0.0427535
\(336\) 0 0
\(337\) 4.01506e6 1.92582 0.962912 0.269814i \(-0.0869623\pi\)
0.962912 + 0.269814i \(0.0869623\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 456840. 0.212754
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.39961e6 −1.06984 −0.534918 0.844904i \(-0.679657\pi\)
−0.534918 + 0.844904i \(0.679657\pi\)
\(348\) 0 0
\(349\) −919171. −0.403955 −0.201977 0.979390i \(-0.564737\pi\)
−0.201977 + 0.979390i \(0.564737\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.07684e6 −0.459953 −0.229976 0.973196i \(-0.573865\pi\)
−0.229976 + 0.973196i \(0.573865\pi\)
\(354\) 0 0
\(355\) −2.75378e6 −1.15974
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.24219e6 −0.508688 −0.254344 0.967114i \(-0.581860\pi\)
−0.254344 + 0.967114i \(0.581860\pi\)
\(360\) 0 0
\(361\) 2.65411e6 1.07189
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.14685e6 −0.843471
\(366\) 0 0
\(367\) −4.17293e6 −1.61725 −0.808624 0.588326i \(-0.799787\pi\)
−0.808624 + 0.588326i \(0.799787\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −419558. −0.158255
\(372\) 0 0
\(373\) −1.72238e6 −0.640999 −0.320500 0.947249i \(-0.603851\pi\)
−0.320500 + 0.947249i \(0.603851\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 844020. 0.305844
\(378\) 0 0
\(379\) −1.72998e6 −0.618647 −0.309324 0.950957i \(-0.600103\pi\)
−0.309324 + 0.950957i \(0.600103\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.34881e6 −1.16652 −0.583262 0.812284i \(-0.698224\pi\)
−0.583262 + 0.812284i \(0.698224\pi\)
\(384\) 0 0
\(385\) −388269. −0.133500
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.18691e6 1.73794 0.868970 0.494864i \(-0.164782\pi\)
0.868970 + 0.494864i \(0.164782\pi\)
\(390\) 0 0
\(391\) 191723. 0.0634209
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.69193e6 −0.545621
\(396\) 0 0
\(397\) −1.30271e6 −0.414830 −0.207415 0.978253i \(-0.566505\pi\)
−0.207415 + 0.978253i \(0.566505\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.53036e6 0.475261 0.237631 0.971356i \(-0.423629\pi\)
0.237631 + 0.971356i \(0.423629\pi\)
\(402\) 0 0
\(403\) 337598. 0.103547
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.54667e6 −0.462820
\(408\) 0 0
\(409\) −2.93690e6 −0.868123 −0.434062 0.900883i \(-0.642920\pi\)
−0.434062 + 0.900883i \(0.642920\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 304793. 0.0879284
\(414\) 0 0
\(415\) −1.92167e6 −0.547719
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.16465e6 −0.324085 −0.162043 0.986784i \(-0.551808\pi\)
−0.162043 + 0.986784i \(0.551808\pi\)
\(420\) 0 0
\(421\) −1.58204e6 −0.435022 −0.217511 0.976058i \(-0.569794\pi\)
−0.217511 + 0.976058i \(0.569794\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 60709.3 0.0163036
\(426\) 0 0
\(427\) −2.05451e6 −0.545305
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.10233e6 1.58235 0.791174 0.611591i \(-0.209470\pi\)
0.791174 + 0.611591i \(0.209470\pi\)
\(432\) 0 0
\(433\) 1.08115e6 0.277118 0.138559 0.990354i \(-0.455753\pi\)
0.138559 + 0.990354i \(0.455753\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.55367e6 −1.39116
\(438\) 0 0
\(439\) 7.04807e6 1.74546 0.872728 0.488207i \(-0.162349\pi\)
0.872728 + 0.488207i \(0.162349\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.32031e6 −0.561742 −0.280871 0.959746i \(-0.590623\pi\)
−0.280871 + 0.959746i \(0.590623\pi\)
\(444\) 0 0
\(445\) 6.12075e6 1.46523
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.45039e6 1.27589 0.637943 0.770084i \(-0.279786\pi\)
0.637943 + 0.770084i \(0.279786\pi\)
\(450\) 0 0
\(451\) 1.64952e6 0.381871
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −286925. −0.0649741
\(456\) 0 0
\(457\) 6.62676e6 1.48426 0.742132 0.670254i \(-0.233815\pi\)
0.742132 + 0.670254i \(0.233815\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −606397. −0.132894 −0.0664469 0.997790i \(-0.521166\pi\)
−0.0664469 + 0.997790i \(0.521166\pi\)
\(462\) 0 0
\(463\) −3.65855e6 −0.793153 −0.396576 0.918002i \(-0.629802\pi\)
−0.396576 + 0.918002i \(0.629802\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.62712e6 1.19397 0.596986 0.802252i \(-0.296365\pi\)
0.596986 + 0.802252i \(0.296365\pi\)
\(468\) 0 0
\(469\) −88792.5 −0.0186399
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.13380e6 −0.233014
\(474\) 0 0
\(475\) −1.75857e6 −0.357624
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.25107e6 0.846563 0.423281 0.905998i \(-0.360878\pi\)
0.423281 + 0.905998i \(0.360878\pi\)
\(480\) 0 0
\(481\) −1.14297e6 −0.225254
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.05187e6 −1.36129
\(486\) 0 0
\(487\) −5.28756e6 −1.01026 −0.505130 0.863043i \(-0.668555\pi\)
−0.505130 + 0.863043i \(0.668555\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.33842e6 −0.624939 −0.312469 0.949928i \(-0.601156\pi\)
−0.312469 + 0.949928i \(0.601156\pi\)
\(492\) 0 0
\(493\) 546192. 0.101211
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.78434e6 −0.505629
\(498\) 0 0
\(499\) −2.52847e6 −0.454576 −0.227288 0.973828i \(-0.572986\pi\)
−0.227288 + 0.973828i \(0.572986\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5.94498e6 −1.04768 −0.523842 0.851815i \(-0.675502\pi\)
−0.523842 + 0.851815i \(0.675502\pi\)
\(504\) 0 0
\(505\) −4.82420e6 −0.841776
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 603525. 0.103253 0.0516263 0.998666i \(-0.483560\pi\)
0.0516263 + 0.998666i \(0.483560\pi\)
\(510\) 0 0
\(511\) −2.17068e6 −0.367741
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.28997e6 1.04503
\(516\) 0 0
\(517\) −190609. −0.0313630
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.03389e7 −1.66870 −0.834350 0.551235i \(-0.814157\pi\)
−0.834350 + 0.551235i \(0.814157\pi\)
\(522\) 0 0
\(523\) 8.82310e6 1.41048 0.705240 0.708968i \(-0.250839\pi\)
0.705240 + 0.708968i \(0.250839\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 218471. 0.0342663
\(528\) 0 0
\(529\) −424266. −0.0659172
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.21897e6 0.185856
\(534\) 0 0
\(535\) 1.06041e7 1.60173
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −392577. −0.0582041
\(540\) 0 0
\(541\) 1.16811e6 0.171590 0.0857949 0.996313i \(-0.472657\pi\)
0.0857949 + 0.996313i \(0.472657\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.77130e6 1.40916
\(546\) 0 0
\(547\) −9.17075e6 −1.31050 −0.655249 0.755413i \(-0.727436\pi\)
−0.655249 + 0.755413i \(0.727436\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.58216e7 −2.22010
\(552\) 0 0
\(553\) −1.71071e6 −0.237883
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.22421e6 −0.850054 −0.425027 0.905181i \(-0.639735\pi\)
−0.425027 + 0.905181i \(0.639735\pi\)
\(558\) 0 0
\(559\) −837859. −0.113407
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.64042e6 −0.749964 −0.374982 0.927032i \(-0.622351\pi\)
−0.374982 + 0.927032i \(0.622351\pi\)
\(564\) 0 0
\(565\) −1.54129e6 −0.203125
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.05286e7 1.36330 0.681650 0.731678i \(-0.261263\pi\)
0.681650 + 0.731678i \(0.261263\pi\)
\(570\) 0 0
\(571\) 7.31395e6 0.938776 0.469388 0.882992i \(-0.344475\pi\)
0.469388 + 0.882992i \(0.344475\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.90373e6 0.240124
\(576\) 0 0
\(577\) 2.66534e6 0.333282 0.166641 0.986018i \(-0.446708\pi\)
0.166641 + 0.986018i \(0.446708\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.94299e6 −0.238798
\(582\) 0 0
\(583\) 1.40000e6 0.170592
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.92431e6 0.589861 0.294931 0.955519i \(-0.404703\pi\)
0.294931 + 0.955519i \(0.404703\pi\)
\(588\) 0 0
\(589\) −6.32847e6 −0.751641
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.08735e6 0.594094 0.297047 0.954863i \(-0.403998\pi\)
0.297047 + 0.954863i \(0.403998\pi\)
\(594\) 0 0
\(595\) −185678. −0.0215015
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.64678e6 0.529157 0.264579 0.964364i \(-0.414767\pi\)
0.264579 + 0.964364i \(0.414767\pi\)
\(600\) 0 0
\(601\) −4.35424e6 −0.491730 −0.245865 0.969304i \(-0.579072\pi\)
−0.245865 + 0.969304i \(0.579072\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.50929e6 −0.723012
\(606\) 0 0
\(607\) 1.25461e7 1.38209 0.691043 0.722813i \(-0.257151\pi\)
0.691043 + 0.722813i \(0.257151\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −140857. −0.0152643
\(612\) 0 0
\(613\) −4.07637e6 −0.438149 −0.219075 0.975708i \(-0.570304\pi\)
−0.219075 + 0.975708i \(0.570304\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.88533e6 0.939639 0.469819 0.882763i \(-0.344319\pi\)
0.469819 + 0.882763i \(0.344319\pi\)
\(618\) 0 0
\(619\) 1.28530e7 1.34827 0.674136 0.738607i \(-0.264516\pi\)
0.674136 + 0.738607i \(0.264516\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.18867e6 0.638818
\(624\) 0 0
\(625\) −6.73652e6 −0.689819
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −739652. −0.0745420
\(630\) 0 0
\(631\) 288616. 0.0288567 0.0144283 0.999896i \(-0.495407\pi\)
0.0144283 + 0.999896i \(0.495407\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.54166e7 1.51724
\(636\) 0 0
\(637\) −290109. −0.0283278
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.94591e7 1.87058 0.935291 0.353880i \(-0.115138\pi\)
0.935291 + 0.353880i \(0.115138\pi\)
\(642\) 0 0
\(643\) −1.30171e7 −1.24161 −0.620805 0.783965i \(-0.713194\pi\)
−0.620805 + 0.783965i \(0.713194\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.42864e6 0.603751 0.301876 0.953347i \(-0.402387\pi\)
0.301876 + 0.953347i \(0.402387\pi\)
\(648\) 0 0
\(649\) −1.01705e6 −0.0947829
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.00202e7 −0.919592 −0.459796 0.888025i \(-0.652077\pi\)
−0.459796 + 0.888025i \(0.652077\pi\)
\(654\) 0 0
\(655\) −1.47904e7 −1.34703
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.49356e7 1.33971 0.669854 0.742493i \(-0.266357\pi\)
0.669854 + 0.742493i \(0.266357\pi\)
\(660\) 0 0
\(661\) −1.35055e6 −0.120229 −0.0601143 0.998191i \(-0.519147\pi\)
−0.0601143 + 0.998191i \(0.519147\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.37857e6 0.471643
\(666\) 0 0
\(667\) 1.71276e7 1.49067
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.85561e6 0.587814
\(672\) 0 0
\(673\) 6.59401e6 0.561193 0.280596 0.959826i \(-0.409468\pi\)
0.280596 + 0.959826i \(0.409468\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.42517e7 −1.19508 −0.597538 0.801840i \(-0.703854\pi\)
−0.597538 + 0.801840i \(0.703854\pi\)
\(678\) 0 0
\(679\) −7.13012e6 −0.593502
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.65006e6 −0.627499 −0.313749 0.949506i \(-0.601585\pi\)
−0.313749 + 0.949506i \(0.601585\pi\)
\(684\) 0 0
\(685\) −8.72536e6 −0.710489
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.03458e6 0.0830266
\(690\) 0 0
\(691\) −1.38655e7 −1.10469 −0.552344 0.833616i \(-0.686267\pi\)
−0.552344 + 0.833616i \(0.686267\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.56632e7 1.23004
\(696\) 0 0
\(697\) 788837. 0.0615042
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.38825e6 0.183563 0.0917814 0.995779i \(-0.470744\pi\)
0.0917814 + 0.995779i \(0.470744\pi\)
\(702\) 0 0
\(703\) 2.14256e7 1.63510
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.87773e6 −0.367003
\(708\) 0 0
\(709\) −1.55641e7 −1.16281 −0.581404 0.813615i \(-0.697496\pi\)
−0.581404 + 0.813615i \(0.697496\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.85083e6 0.504684
\(714\) 0 0
\(715\) 957427. 0.0700391
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.82555e7 1.31696 0.658478 0.752600i \(-0.271200\pi\)
0.658478 + 0.752600i \(0.271200\pi\)
\(720\) 0 0
\(721\) 6.35977e6 0.455620
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.42346e6 0.383205
\(726\) 0 0
\(727\) 2.11427e6 0.148362 0.0741812 0.997245i \(-0.476366\pi\)
0.0741812 + 0.997245i \(0.476366\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −542206. −0.0375293
\(732\) 0 0
\(733\) 2.12932e6 0.146380 0.0731898 0.997318i \(-0.476682\pi\)
0.0731898 + 0.997318i \(0.476682\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 296288. 0.0200930
\(738\) 0 0
\(739\) 8.08671e6 0.544704 0.272352 0.962198i \(-0.412198\pi\)
0.272352 + 0.962198i \(0.412198\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.18944e7 −0.790442 −0.395221 0.918586i \(-0.629332\pi\)
−0.395221 + 0.918586i \(0.629332\pi\)
\(744\) 0 0
\(745\) −1.42556e7 −0.941010
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.07217e7 0.698331
\(750\) 0 0
\(751\) 1.85538e7 1.20042 0.600211 0.799842i \(-0.295083\pi\)
0.600211 + 0.799842i \(0.295083\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.62330e7 1.03641
\(756\) 0 0
\(757\) 9.32534e6 0.591459 0.295730 0.955272i \(-0.404437\pi\)
0.295730 + 0.955272i \(0.404437\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.00756e6 −0.501232 −0.250616 0.968087i \(-0.580633\pi\)
−0.250616 + 0.968087i \(0.580633\pi\)
\(762\) 0 0
\(763\) 9.87974e6 0.614376
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −751584. −0.0461306
\(768\) 0 0
\(769\) 2.02720e7 1.23618 0.618089 0.786108i \(-0.287907\pi\)
0.618089 + 0.786108i \(0.287907\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.87881e6 −0.173286 −0.0866431 0.996239i \(-0.527614\pi\)
−0.0866431 + 0.996239i \(0.527614\pi\)
\(774\) 0 0
\(775\) 2.16932e6 0.129739
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.28503e7 −1.34911
\(780\) 0 0
\(781\) 9.29094e6 0.545045
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.03428e6 −0.407423
\(786\) 0 0
\(787\) 2.03508e7 1.17124 0.585618 0.810587i \(-0.300852\pi\)
0.585618 + 0.810587i \(0.300852\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.55839e6 −0.0885595
\(792\) 0 0
\(793\) 5.06620e6 0.286088
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.24765e7 1.25338 0.626689 0.779269i \(-0.284410\pi\)
0.626689 + 0.779269i \(0.284410\pi\)
\(798\) 0 0
\(799\) −91153.3 −0.00505133
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.24322e6 0.396409
\(804\) 0 0
\(805\) −5.82253e6 −0.316681
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.15427e6 0.0620062 0.0310031 0.999519i \(-0.490130\pi\)
0.0310031 + 0.999519i \(0.490130\pi\)
\(810\) 0 0
\(811\) 2.26698e7 1.21031 0.605154 0.796108i \(-0.293112\pi\)
0.605154 + 0.796108i \(0.293112\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8.54007e6 0.450368
\(816\) 0 0
\(817\) 1.57061e7 0.823217
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.41657e6 0.125124 0.0625622 0.998041i \(-0.480073\pi\)
0.0625622 + 0.998041i \(0.480073\pi\)
\(822\) 0 0
\(823\) 2.10169e6 0.108161 0.0540804 0.998537i \(-0.482777\pi\)
0.0540804 + 0.998537i \(0.482777\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.53997e7 0.782977 0.391489 0.920183i \(-0.371960\pi\)
0.391489 + 0.920183i \(0.371960\pi\)
\(828\) 0 0
\(829\) −2.33839e7 −1.18177 −0.590883 0.806757i \(-0.701221\pi\)
−0.590883 + 0.806757i \(0.701221\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −187739. −0.00937436
\(834\) 0 0
\(835\) −2.20313e6 −0.109351
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.03016e7 0.995695 0.497848 0.867265i \(-0.334124\pi\)
0.497848 + 0.867265i \(0.334124\pi\)
\(840\) 0 0
\(841\) 2.82829e7 1.37890
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.72862e7 −0.832831
\(846\) 0 0
\(847\) −6.58153e6 −0.315223
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.31941e7 −1.09788
\(852\) 0 0
\(853\) 3.35163e7 1.57719 0.788594 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.30661e7 1.07281 0.536405 0.843961i \(-0.319782\pi\)
0.536405 + 0.843961i \(0.319782\pi\)
\(858\) 0 0
\(859\) −3.85609e7 −1.78305 −0.891527 0.452968i \(-0.850365\pi\)
−0.891527 + 0.452968i \(0.850365\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.86892e7 1.76833 0.884163 0.467179i \(-0.154729\pi\)
0.884163 + 0.467179i \(0.154729\pi\)
\(864\) 0 0
\(865\) 9.97555e6 0.453311
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.70838e6 0.256427
\(870\) 0 0
\(871\) 218952. 0.00977922
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −9.26449e6 −0.409073
\(876\) 0 0
\(877\) −2.17369e7 −0.954332 −0.477166 0.878813i \(-0.658336\pi\)
−0.477166 + 0.878813i \(0.658336\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −8.42086e6 −0.365525 −0.182762 0.983157i \(-0.558504\pi\)
−0.182762 + 0.983157i \(0.558504\pi\)
\(882\) 0 0
\(883\) −3.22954e7 −1.39392 −0.696962 0.717108i \(-0.745465\pi\)
−0.696962 + 0.717108i \(0.745465\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.21800e7 −1.80010 −0.900052 0.435782i \(-0.856472\pi\)
−0.900052 + 0.435782i \(0.856472\pi\)
\(888\) 0 0
\(889\) 1.55876e7 0.661494
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.64045e6 0.110802
\(894\) 0 0
\(895\) −9.65393e6 −0.402853
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.95171e7 0.805407
\(900\) 0 0
\(901\) 669512. 0.0274756
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 9.61542e6 0.390254
\(906\) 0 0
\(907\) 7.64517e6 0.308581 0.154291 0.988026i \(-0.450691\pi\)
0.154291 + 0.988026i \(0.450691\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.93310e7 −1.57014 −0.785072 0.619405i \(-0.787374\pi\)
−0.785072 + 0.619405i \(0.787374\pi\)
\(912\) 0 0
\(913\) 6.48347e6 0.257413
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.49545e7 −0.587285
\(918\) 0 0
\(919\) −3.52204e7 −1.37564 −0.687822 0.725880i \(-0.741433\pi\)
−0.687822 + 0.725880i \(0.741433\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 6.86587e6 0.265272
\(924\) 0 0
\(925\) −7.34443e6 −0.282230
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.66300e7 0.632199 0.316099 0.948726i \(-0.397627\pi\)
0.316099 + 0.948726i \(0.397627\pi\)
\(930\) 0 0
\(931\) 5.43826e6 0.205630
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 619582. 0.0231777
\(936\) 0 0
\(937\) 2.07121e7 0.770681 0.385341 0.922774i \(-0.374084\pi\)
0.385341 + 0.922774i \(0.374084\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.09797e7 0.404219 0.202110 0.979363i \(-0.435220\pi\)
0.202110 + 0.979363i \(0.435220\pi\)
\(942\) 0 0
\(943\) 2.47364e7 0.905853
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.71723e6 0.0984581 0.0492290 0.998788i \(-0.484324\pi\)
0.0492290 + 0.998788i \(0.484324\pi\)
\(948\) 0 0
\(949\) 5.35264e6 0.192931
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.24083e6 0.329594 0.164797 0.986328i \(-0.447303\pi\)
0.164797 + 0.986328i \(0.447303\pi\)
\(954\) 0 0
\(955\) 1.80739e7 0.641272
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.82219e6 −0.309763
\(960\) 0 0
\(961\) −2.08225e7 −0.727320
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 8.48183e6 0.293205
\(966\) 0 0
\(967\) 1.50444e7 0.517379 0.258690 0.965960i \(-0.416709\pi\)
0.258690 + 0.965960i \(0.416709\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.27894e7 0.775685 0.387842 0.921726i \(-0.373220\pi\)
0.387842 + 0.921726i \(0.373220\pi\)
\(972\) 0 0
\(973\) 1.58370e7 0.536279
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.96682e7 1.32955 0.664777 0.747042i \(-0.268526\pi\)
0.664777 + 0.747042i \(0.268526\pi\)
\(978\) 0 0
\(979\) −2.06507e7 −0.688617
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.77093e7 0.914621 0.457310 0.889307i \(-0.348813\pi\)
0.457310 + 0.889307i \(0.348813\pi\)
\(984\) 0 0
\(985\) −4.28294e7 −1.40654
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.70025e7 −0.552743
\(990\) 0 0
\(991\) −4.78535e7 −1.54785 −0.773926 0.633276i \(-0.781710\pi\)
−0.773926 + 0.633276i \(0.781710\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.80837e7 −1.21950
\(996\) 0 0
\(997\) −5.48289e7 −1.74691 −0.873457 0.486902i \(-0.838127\pi\)
−0.873457 + 0.486902i \(0.838127\pi\)
\(998\) 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.bi.1.2 2
3.2 odd 2 112.6.a.j.1.1 2
4.3 odd 2 504.6.a.m.1.2 2
12.11 even 2 56.6.a.d.1.2 2
21.20 even 2 784.6.a.q.1.2 2
24.5 odd 2 448.6.a.r.1.2 2
24.11 even 2 448.6.a.x.1.1 2
84.11 even 6 392.6.i.k.177.1 4
84.23 even 6 392.6.i.k.361.1 4
84.47 odd 6 392.6.i.h.361.2 4
84.59 odd 6 392.6.i.h.177.2 4
84.83 odd 2 392.6.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.d.1.2 2 12.11 even 2
112.6.a.j.1.1 2 3.2 odd 2
392.6.a.e.1.1 2 84.83 odd 2
392.6.i.h.177.2 4 84.59 odd 6
392.6.i.h.361.2 4 84.47 odd 6
392.6.i.k.177.1 4 84.11 even 6
392.6.i.k.361.1 4 84.23 even 6
448.6.a.r.1.2 2 24.5 odd 2
448.6.a.x.1.1 2 24.11 even 2
504.6.a.m.1.2 2 4.3 odd 2
784.6.a.q.1.2 2 21.20 even 2
1008.6.a.bi.1.2 2 1.1 even 1 trivial