Properties

Label 1008.6.a.bq.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: \(\Q(\sqrt{57}) \)
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 1.2
Root \(4.27492\) 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)
 
\(f(q)\) \(=\) \(q+46.7492 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+46.7492 q^{5} -49.0000 q^{7} +666.090 q^{11} -650.640 q^{13} -1186.89 q^{17} +1565.05 q^{19} -1100.15 q^{23} -939.515 q^{25} -2396.72 q^{29} +2048.46 q^{31} -2290.71 q^{35} +1077.54 q^{37} -1098.21 q^{41} -16564.3 q^{43} -8298.39 q^{47} +2401.00 q^{49} -5519.18 q^{53} +31139.1 q^{55} -14230.4 q^{59} -14234.7 q^{61} -30416.9 q^{65} -19730.4 q^{67} +64562.7 q^{71} +28567.0 q^{73} -32638.4 q^{77} +30633.4 q^{79} -675.946 q^{83} -55486.3 q^{85} -125971. q^{89} +31881.3 q^{91} +73164.9 q^{95} -22906.8 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 18 q^{5} - 98 q^{7}+O(q^{10}) \) 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
\(5\) 46.7492 0.836275 0.418137 0.908384i \(-0.362683\pi\)
0.418137 + 0.908384i \(0.362683\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 666.090 1.65978 0.829891 0.557926i \(-0.188403\pi\)
0.829891 + 0.557926i \(0.188403\pi\)
\(12\) 0 0
\(13\) −650.640 −1.06778 −0.533890 0.845554i \(-0.679271\pi\)
−0.533890 + 0.845554i \(0.679271\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1186.89 −0.996069 −0.498035 0.867157i \(-0.665945\pi\)
−0.498035 + 0.867157i \(0.665945\pi\)
\(18\) 0 0
\(19\) 1565.05 0.994591 0.497296 0.867581i \(-0.334326\pi\)
0.497296 + 0.867581i \(0.334326\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1100.15 −0.433644 −0.216822 0.976211i \(-0.569569\pi\)
−0.216822 + 0.976211i \(0.569569\pi\)
\(24\) 0 0
\(25\) −939.515 −0.300645
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2396.72 −0.529203 −0.264602 0.964358i \(-0.585240\pi\)
−0.264602 + 0.964358i \(0.585240\pi\)
\(30\) 0 0
\(31\) 2048.46 0.382844 0.191422 0.981508i \(-0.438690\pi\)
0.191422 + 0.981508i \(0.438690\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2290.71 −0.316082
\(36\) 0 0
\(37\) 1077.54 0.129399 0.0646995 0.997905i \(-0.479391\pi\)
0.0646995 + 0.997905i \(0.479391\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1098.21 −0.102029 −0.0510147 0.998698i \(-0.516246\pi\)
−0.0510147 + 0.998698i \(0.516246\pi\)
\(42\) 0 0
\(43\) −16564.3 −1.36616 −0.683081 0.730343i \(-0.739360\pi\)
−0.683081 + 0.730343i \(0.739360\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8298.39 −0.547960 −0.273980 0.961735i \(-0.588340\pi\)
−0.273980 + 0.961735i \(0.588340\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5519.18 −0.269889 −0.134944 0.990853i \(-0.543086\pi\)
−0.134944 + 0.990853i \(0.543086\pi\)
\(54\) 0 0
\(55\) 31139.1 1.38803
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −14230.4 −0.532216 −0.266108 0.963943i \(-0.585738\pi\)
−0.266108 + 0.963943i \(0.585738\pi\)
\(60\) 0 0
\(61\) −14234.7 −0.489807 −0.244904 0.969547i \(-0.578756\pi\)
−0.244904 + 0.969547i \(0.578756\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −30416.9 −0.892958
\(66\) 0 0
\(67\) −19730.4 −0.536970 −0.268485 0.963284i \(-0.586523\pi\)
−0.268485 + 0.963284i \(0.586523\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 64562.7 1.51997 0.759986 0.649940i \(-0.225206\pi\)
0.759986 + 0.649940i \(0.225206\pi\)
\(72\) 0 0
\(73\) 28567.0 0.627418 0.313709 0.949519i \(-0.398428\pi\)
0.313709 + 0.949519i \(0.398428\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −32638.4 −0.627339
\(78\) 0 0
\(79\) 30633.4 0.552239 0.276119 0.961123i \(-0.410951\pi\)
0.276119 + 0.961123i \(0.410951\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −675.946 −0.0107700 −0.00538501 0.999986i \(-0.501714\pi\)
−0.00538501 + 0.999986i \(0.501714\pi\)
\(84\) 0 0
\(85\) −55486.3 −0.832987
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −125971. −1.68576 −0.842882 0.538098i \(-0.819143\pi\)
−0.842882 + 0.538098i \(0.819143\pi\)
\(90\) 0 0
\(91\) 31881.3 0.403583
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 73164.9 0.831751
\(96\) 0 0
\(97\) −22906.8 −0.247192 −0.123596 0.992333i \(-0.539443\pi\)
−0.123596 + 0.992333i \(0.539443\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 181474. 1.77015 0.885077 0.465444i \(-0.154105\pi\)
0.885077 + 0.465444i \(0.154105\pi\)
\(102\) 0 0
\(103\) −64772.0 −0.601581 −0.300791 0.953690i \(-0.597251\pi\)
−0.300791 + 0.953690i \(0.597251\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −148170. −1.25112 −0.625562 0.780175i \(-0.715130\pi\)
−0.625562 + 0.780175i \(0.715130\pi\)
\(108\) 0 0
\(109\) −111294. −0.897237 −0.448618 0.893723i \(-0.648084\pi\)
−0.448618 + 0.893723i \(0.648084\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 43175.5 0.318084 0.159042 0.987272i \(-0.449160\pi\)
0.159042 + 0.987272i \(0.449160\pi\)
\(114\) 0 0
\(115\) −51431.2 −0.362646
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 58157.8 0.376479
\(120\) 0 0
\(121\) 282625. 1.75488
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −190013. −1.08770
\(126\) 0 0
\(127\) 131449. 0.723182 0.361591 0.932337i \(-0.382234\pi\)
0.361591 + 0.932337i \(0.382234\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −349458. −1.77916 −0.889582 0.456775i \(-0.849005\pi\)
−0.889582 + 0.456775i \(0.849005\pi\)
\(132\) 0 0
\(133\) −76687.5 −0.375920
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −386434. −1.75903 −0.879516 0.475869i \(-0.842134\pi\)
−0.879516 + 0.475869i \(0.842134\pi\)
\(138\) 0 0
\(139\) −17289.3 −0.0758997 −0.0379498 0.999280i \(-0.512083\pi\)
−0.0379498 + 0.999280i \(0.512083\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −433384. −1.77228
\(144\) 0 0
\(145\) −112045. −0.442559
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 112171. 0.413917 0.206959 0.978350i \(-0.433643\pi\)
0.206959 + 0.978350i \(0.433643\pi\)
\(150\) 0 0
\(151\) −30495.4 −0.108841 −0.0544205 0.998518i \(-0.517331\pi\)
−0.0544205 + 0.998518i \(0.517331\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 95763.6 0.320163
\(156\) 0 0
\(157\) 523509. 1.69502 0.847510 0.530780i \(-0.178101\pi\)
0.847510 + 0.530780i \(0.178101\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 53907.5 0.163902
\(162\) 0 0
\(163\) 439646. 1.29609 0.648043 0.761604i \(-0.275588\pi\)
0.648043 + 0.761604i \(0.275588\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 279353. 0.775107 0.387554 0.921847i \(-0.373320\pi\)
0.387554 + 0.921847i \(0.373320\pi\)
\(168\) 0 0
\(169\) 52038.8 0.140156
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −99699.4 −0.253266 −0.126633 0.991950i \(-0.540417\pi\)
−0.126633 + 0.991950i \(0.540417\pi\)
\(174\) 0 0
\(175\) 46036.2 0.113633
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 329980. 0.769760 0.384880 0.922967i \(-0.374243\pi\)
0.384880 + 0.922967i \(0.374243\pi\)
\(180\) 0 0
\(181\) −505810. −1.14760 −0.573800 0.818995i \(-0.694531\pi\)
−0.573800 + 0.818995i \(0.694531\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 50374.3 0.108213
\(186\) 0 0
\(187\) −790578. −1.65326
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −63835.6 −0.126613 −0.0633067 0.997994i \(-0.520165\pi\)
−0.0633067 + 0.997994i \(0.520165\pi\)
\(192\) 0 0
\(193\) 469355. 0.907001 0.453501 0.891256i \(-0.350175\pi\)
0.453501 + 0.891256i \(0.350175\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −268021. −0.492043 −0.246021 0.969264i \(-0.579123\pi\)
−0.246021 + 0.969264i \(0.579123\pi\)
\(198\) 0 0
\(199\) 605167. 1.08328 0.541642 0.840609i \(-0.317803\pi\)
0.541642 + 0.840609i \(0.317803\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 117439. 0.200020
\(204\) 0 0
\(205\) −51340.4 −0.0853246
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.04246e6 1.65080
\(210\) 0 0
\(211\) −335389. −0.518612 −0.259306 0.965795i \(-0.583494\pi\)
−0.259306 + 0.965795i \(0.583494\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −774367. −1.14249
\(216\) 0 0
\(217\) −100374. −0.144702
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 772240. 1.06358
\(222\) 0 0
\(223\) −1.02526e6 −1.38061 −0.690305 0.723518i \(-0.742524\pi\)
−0.690305 + 0.723518i \(0.742524\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −504226. −0.649473 −0.324736 0.945805i \(-0.605276\pi\)
−0.324736 + 0.945805i \(0.605276\pi\)
\(228\) 0 0
\(229\) −1.11939e6 −1.41057 −0.705283 0.708925i \(-0.749180\pi\)
−0.705283 + 0.708925i \(0.749180\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −770703. −0.930031 −0.465015 0.885303i \(-0.653951\pi\)
−0.465015 + 0.885303i \(0.653951\pi\)
\(234\) 0 0
\(235\) −387943. −0.458245
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −171646. −0.194374 −0.0971871 0.995266i \(-0.530985\pi\)
−0.0971871 + 0.995266i \(0.530985\pi\)
\(240\) 0 0
\(241\) −383779. −0.425637 −0.212818 0.977092i \(-0.568264\pi\)
−0.212818 + 0.977092i \(0.568264\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 112245. 0.119468
\(246\) 0 0
\(247\) −1.01828e6 −1.06201
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.57046e6 −1.57342 −0.786708 0.617325i \(-0.788216\pi\)
−0.786708 + 0.617325i \(0.788216\pi\)
\(252\) 0 0
\(253\) −732801. −0.719755
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −790656. −0.746715 −0.373357 0.927688i \(-0.621793\pi\)
−0.373357 + 0.927688i \(0.621793\pi\)
\(258\) 0 0
\(259\) −52799.7 −0.0489082
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 464416. 0.414017 0.207008 0.978339i \(-0.433627\pi\)
0.207008 + 0.978339i \(0.433627\pi\)
\(264\) 0 0
\(265\) −258017. −0.225701
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.99959e6 −1.68484 −0.842422 0.538818i \(-0.818871\pi\)
−0.842422 + 0.538818i \(0.818871\pi\)
\(270\) 0 0
\(271\) −1.61296e6 −1.33414 −0.667070 0.744995i \(-0.732452\pi\)
−0.667070 + 0.744995i \(0.732452\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −625801. −0.499005
\(276\) 0 0
\(277\) −2.08119e6 −1.62972 −0.814860 0.579658i \(-0.803186\pi\)
−0.814860 + 0.579658i \(0.803186\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 982035. 0.741927 0.370964 0.928647i \(-0.379027\pi\)
0.370964 + 0.928647i \(0.379027\pi\)
\(282\) 0 0
\(283\) 1.39622e6 1.03630 0.518152 0.855289i \(-0.326620\pi\)
0.518152 + 0.855289i \(0.326620\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 53812.3 0.0385635
\(288\) 0 0
\(289\) −11140.3 −0.00784609
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.56205e6 −1.74348 −0.871742 0.489965i \(-0.837010\pi\)
−0.871742 + 0.489965i \(0.837010\pi\)
\(294\) 0 0
\(295\) −665260. −0.445078
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 715803. 0.463037
\(300\) 0 0
\(301\) 811651. 0.516361
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −665463. −0.409613
\(306\) 0 0
\(307\) 884855. 0.535829 0.267915 0.963443i \(-0.413666\pi\)
0.267915 + 0.963443i \(0.413666\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.80120e6 1.05599 0.527997 0.849246i \(-0.322943\pi\)
0.527997 + 0.849246i \(0.322943\pi\)
\(312\) 0 0
\(313\) 950366. 0.548315 0.274158 0.961685i \(-0.411601\pi\)
0.274158 + 0.961685i \(0.411601\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.04277e6 −1.70068 −0.850338 0.526237i \(-0.823602\pi\)
−0.850338 + 0.526237i \(0.823602\pi\)
\(318\) 0 0
\(319\) −1.59643e6 −0.878362
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.85755e6 −0.990682
\(324\) 0 0
\(325\) 611286. 0.321023
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 406621. 0.207110
\(330\) 0 0
\(331\) 2.19616e6 1.10178 0.550889 0.834579i \(-0.314289\pi\)
0.550889 + 0.834579i \(0.314289\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −922382. −0.449054
\(336\) 0 0
\(337\) −2.41491e6 −1.15832 −0.579158 0.815216i \(-0.696618\pi\)
−0.579158 + 0.815216i \(0.696618\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.36446e6 0.635438
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.08833e6 −0.485219 −0.242609 0.970124i \(-0.578003\pi\)
−0.242609 + 0.970124i \(0.578003\pi\)
\(348\) 0 0
\(349\) 2.79267e6 1.22731 0.613657 0.789573i \(-0.289698\pi\)
0.613657 + 0.789573i \(0.289698\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.53134e6 −1.08122 −0.540610 0.841273i \(-0.681807\pi\)
−0.540610 + 0.841273i \(0.681807\pi\)
\(354\) 0 0
\(355\) 3.01825e6 1.27111
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.09028e6 0.446480 0.223240 0.974763i \(-0.428337\pi\)
0.223240 + 0.974763i \(0.428337\pi\)
\(360\) 0 0
\(361\) −26712.8 −0.0107883
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.33548e6 0.524694
\(366\) 0 0
\(367\) −188070. −0.0728879 −0.0364439 0.999336i \(-0.511603\pi\)
−0.0364439 + 0.999336i \(0.511603\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 270440. 0.102008
\(372\) 0 0
\(373\) −1.79371e6 −0.667545 −0.333772 0.942654i \(-0.608322\pi\)
−0.333772 + 0.942654i \(0.608322\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.55940e6 0.565073
\(378\) 0 0
\(379\) −3.58806e6 −1.28310 −0.641551 0.767080i \(-0.721709\pi\)
−0.641551 + 0.767080i \(0.721709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.42457e6 −1.19291 −0.596457 0.802645i \(-0.703425\pi\)
−0.596457 + 0.802645i \(0.703425\pi\)
\(384\) 0 0
\(385\) −1.52582e6 −0.524627
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8625.27 −0.00289001 −0.00144500 0.999999i \(-0.500460\pi\)
−0.00144500 + 0.999999i \(0.500460\pi\)
\(390\) 0 0
\(391\) 1.30576e6 0.431940
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.43208e6 0.461823
\(396\) 0 0
\(397\) 1.25709e6 0.400306 0.200153 0.979765i \(-0.435856\pi\)
0.200153 + 0.979765i \(0.435856\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.42670e6 −0.443070 −0.221535 0.975152i \(-0.571107\pi\)
−0.221535 + 0.975152i \(0.571107\pi\)
\(402\) 0 0
\(403\) −1.33281e6 −0.408794
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 717741. 0.214774
\(408\) 0 0
\(409\) −3.06529e6 −0.906073 −0.453036 0.891492i \(-0.649659\pi\)
−0.453036 + 0.891492i \(0.649659\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 697291. 0.201159
\(414\) 0 0
\(415\) −31599.9 −0.00900670
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −248240. −0.0690776 −0.0345388 0.999403i \(-0.510996\pi\)
−0.0345388 + 0.999403i \(0.510996\pi\)
\(420\) 0 0
\(421\) 5.96280e6 1.63963 0.819814 0.572630i \(-0.194077\pi\)
0.819814 + 0.572630i \(0.194077\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.11510e6 0.299463
\(426\) 0 0
\(427\) 697503. 0.185130
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.93538e6 −1.27976 −0.639879 0.768476i \(-0.721015\pi\)
−0.639879 + 0.768476i \(0.721015\pi\)
\(432\) 0 0
\(433\) 4.15513e6 1.06504 0.532519 0.846418i \(-0.321245\pi\)
0.532519 + 0.846418i \(0.321245\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.72180e6 −0.431299
\(438\) 0 0
\(439\) 227955. 0.0564531 0.0282265 0.999602i \(-0.491014\pi\)
0.0282265 + 0.999602i \(0.491014\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.98462e6 −0.480472 −0.240236 0.970715i \(-0.577225\pi\)
−0.240236 + 0.970715i \(0.577225\pi\)
\(444\) 0 0
\(445\) −5.88906e6 −1.40976
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.61077e6 −0.611157 −0.305579 0.952167i \(-0.598850\pi\)
−0.305579 + 0.952167i \(0.598850\pi\)
\(450\) 0 0
\(451\) −731506. −0.169347
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.49043e6 0.337506
\(456\) 0 0
\(457\) −4.09917e6 −0.918132 −0.459066 0.888402i \(-0.651816\pi\)
−0.459066 + 0.888402i \(0.651816\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.62378e6 0.575009 0.287505 0.957779i \(-0.407174\pi\)
0.287505 + 0.957779i \(0.407174\pi\)
\(462\) 0 0
\(463\) 4.28563e6 0.929100 0.464550 0.885547i \(-0.346216\pi\)
0.464550 + 0.885547i \(0.346216\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 990118. 0.210085 0.105042 0.994468i \(-0.466502\pi\)
0.105042 + 0.994468i \(0.466502\pi\)
\(468\) 0 0
\(469\) 966792. 0.202955
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.10333e7 −2.26753
\(474\) 0 0
\(475\) −1.47039e6 −0.299019
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.57976e6 0.513737 0.256868 0.966446i \(-0.417309\pi\)
0.256868 + 0.966446i \(0.417309\pi\)
\(480\) 0 0
\(481\) −701093. −0.138170
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.07087e6 −0.206720
\(486\) 0 0
\(487\) −3.21474e6 −0.614219 −0.307109 0.951674i \(-0.599362\pi\)
−0.307109 + 0.951674i \(0.599362\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.86108e6 −1.47156 −0.735781 0.677220i \(-0.763185\pi\)
−0.735781 + 0.677220i \(0.763185\pi\)
\(492\) 0 0
\(493\) 2.84465e6 0.527123
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.16357e6 −0.574495
\(498\) 0 0
\(499\) 1.35382e6 0.243395 0.121697 0.992567i \(-0.461166\pi\)
0.121697 + 0.992567i \(0.461166\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.85775e6 0.679851 0.339926 0.940452i \(-0.389598\pi\)
0.339926 + 0.940452i \(0.389598\pi\)
\(504\) 0 0
\(505\) 8.48376e6 1.48034
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.06060e7 1.81451 0.907253 0.420585i \(-0.138175\pi\)
0.907253 + 0.420585i \(0.138175\pi\)
\(510\) 0 0
\(511\) −1.39978e6 −0.237142
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.02804e6 −0.503087
\(516\) 0 0
\(517\) −5.52747e6 −0.909495
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.17989e6 1.48164 0.740821 0.671703i \(-0.234437\pi\)
0.740821 + 0.671703i \(0.234437\pi\)
\(522\) 0 0
\(523\) −9.05585e6 −1.44769 −0.723844 0.689964i \(-0.757627\pi\)
−0.723844 + 0.689964i \(0.757627\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.43130e6 −0.381339
\(528\) 0 0
\(529\) −5.22601e6 −0.811953
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 714539. 0.108945
\(534\) 0 0
\(535\) −6.92681e6 −1.04628
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.59928e6 0.237112
\(540\) 0 0
\(541\) 1.21783e7 1.78894 0.894468 0.447132i \(-0.147555\pi\)
0.894468 + 0.447132i \(0.147555\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.20292e6 −0.750336
\(546\) 0 0
\(547\) 9.00451e6 1.28674 0.643372 0.765554i \(-0.277535\pi\)
0.643372 + 0.765554i \(0.277535\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.75099e6 −0.526341
\(552\) 0 0
\(553\) −1.50103e6 −0.208727
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.54461e6 −0.210950 −0.105475 0.994422i \(-0.533636\pi\)
−0.105475 + 0.994422i \(0.533636\pi\)
\(558\) 0 0
\(559\) 1.07774e7 1.45876
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.18748e7 −1.57890 −0.789449 0.613816i \(-0.789634\pi\)
−0.789449 + 0.613816i \(0.789634\pi\)
\(564\) 0 0
\(565\) 2.01842e6 0.266005
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.54308e6 0.199806 0.0999031 0.994997i \(-0.468147\pi\)
0.0999031 + 0.994997i \(0.468147\pi\)
\(570\) 0 0
\(571\) 7.01812e6 0.900804 0.450402 0.892826i \(-0.351281\pi\)
0.450402 + 0.892826i \(0.351281\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.03361e6 0.130373
\(576\) 0 0
\(577\) −5.37543e6 −0.672162 −0.336081 0.941833i \(-0.609102\pi\)
−0.336081 + 0.941833i \(0.609102\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 33121.4 0.00407069
\(582\) 0 0
\(583\) −3.67627e6 −0.447957
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.06682e6 −0.247575 −0.123788 0.992309i \(-0.539504\pi\)
−0.123788 + 0.992309i \(0.539504\pi\)
\(588\) 0 0
\(589\) 3.20594e6 0.380774
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.46947e6 0.638717 0.319358 0.947634i \(-0.396533\pi\)
0.319358 + 0.947634i \(0.396533\pi\)
\(594\) 0 0
\(595\) 2.71883e6 0.314840
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.09943e7 1.25199 0.625996 0.779826i \(-0.284693\pi\)
0.625996 + 0.779826i \(0.284693\pi\)
\(600\) 0 0
\(601\) 1.58788e7 1.79322 0.896608 0.442826i \(-0.146024\pi\)
0.896608 + 0.442826i \(0.146024\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.32125e7 1.46756
\(606\) 0 0
\(607\) −5.33262e6 −0.587447 −0.293724 0.955890i \(-0.594895\pi\)
−0.293724 + 0.955890i \(0.594895\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.39926e6 0.585102
\(612\) 0 0
\(613\) −8.91838e6 −0.958594 −0.479297 0.877653i \(-0.659108\pi\)
−0.479297 + 0.877653i \(0.659108\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.63586e6 −1.01901 −0.509504 0.860468i \(-0.670171\pi\)
−0.509504 + 0.860468i \(0.670171\pi\)
\(618\) 0 0
\(619\) −1.21747e7 −1.27712 −0.638560 0.769572i \(-0.720470\pi\)
−0.638560 + 0.769572i \(0.720470\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.17260e6 0.637159
\(624\) 0 0
\(625\) −5.94695e6 −0.608968
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.27893e6 −0.128890
\(630\) 0 0
\(631\) 1.30854e7 1.30832 0.654161 0.756356i \(-0.273022\pi\)
0.654161 + 0.756356i \(0.273022\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.14513e6 0.604779
\(636\) 0 0
\(637\) −1.56219e6 −0.152540
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 441107. 0.0424032 0.0212016 0.999775i \(-0.493251\pi\)
0.0212016 + 0.999775i \(0.493251\pi\)
\(642\) 0 0
\(643\) 4.18888e6 0.399550 0.199775 0.979842i \(-0.435979\pi\)
0.199775 + 0.979842i \(0.435979\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.87822e7 1.76395 0.881973 0.471300i \(-0.156215\pi\)
0.881973 + 0.471300i \(0.156215\pi\)
\(648\) 0 0
\(649\) −9.47874e6 −0.883362
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.51733e6 0.139251 0.0696254 0.997573i \(-0.477820\pi\)
0.0696254 + 0.997573i \(0.477820\pi\)
\(654\) 0 0
\(655\) −1.63368e7 −1.48787
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.84809e7 1.65772 0.828859 0.559458i \(-0.188991\pi\)
0.828859 + 0.559458i \(0.188991\pi\)
\(660\) 0 0
\(661\) −1.03952e7 −0.925403 −0.462702 0.886514i \(-0.653120\pi\)
−0.462702 + 0.886514i \(0.653120\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.58508e6 −0.314372
\(666\) 0 0
\(667\) 2.63676e6 0.229486
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.48162e6 −0.812973
\(672\) 0 0
\(673\) −1.10398e7 −0.939556 −0.469778 0.882785i \(-0.655666\pi\)
−0.469778 + 0.882785i \(0.655666\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.23485e6 0.690532 0.345266 0.938505i \(-0.387789\pi\)
0.345266 + 0.938505i \(0.387789\pi\)
\(678\) 0 0
\(679\) 1.12243e6 0.0934298
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.98437e7 1.62768 0.813842 0.581086i \(-0.197372\pi\)
0.813842 + 0.581086i \(0.197372\pi\)
\(684\) 0 0
\(685\) −1.80655e7 −1.47103
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.59100e6 0.288182
\(690\) 0 0
\(691\) 2.37019e6 0.188837 0.0944185 0.995533i \(-0.469901\pi\)
0.0944185 + 0.995533i \(0.469901\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −808259. −0.0634730
\(696\) 0 0
\(697\) 1.30346e6 0.101628
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.56833e7 1.20543 0.602714 0.797957i \(-0.294086\pi\)
0.602714 + 0.797957i \(0.294086\pi\)
\(702\) 0 0
\(703\) 1.68641e6 0.128699
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.89223e6 −0.669056
\(708\) 0 0
\(709\) 3.68544e6 0.275343 0.137671 0.990478i \(-0.456038\pi\)
0.137671 + 0.990478i \(0.456038\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.25361e6 −0.166018
\(714\) 0 0
\(715\) −2.02604e7 −1.48212
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.56427e7 −1.12847 −0.564233 0.825615i \(-0.690828\pi\)
−0.564233 + 0.825615i \(0.690828\pi\)
\(720\) 0 0
\(721\) 3.17383e6 0.227376
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.25175e6 0.159102
\(726\) 0 0
\(727\) −1.85908e7 −1.30456 −0.652279 0.757979i \(-0.726187\pi\)
−0.652279 + 0.757979i \(0.726187\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.96601e7 1.36079
\(732\) 0 0
\(733\) 2.49466e7 1.71495 0.857476 0.514524i \(-0.172031\pi\)
0.857476 + 0.514524i \(0.172031\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.31422e7 −0.891253
\(738\) 0 0
\(739\) 2.42944e7 1.63642 0.818211 0.574918i \(-0.194966\pi\)
0.818211 + 0.574918i \(0.194966\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.16541e6 0.276812 0.138406 0.990376i \(-0.455802\pi\)
0.138406 + 0.990376i \(0.455802\pi\)
\(744\) 0 0
\(745\) 5.24388e6 0.346148
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.26032e6 0.472880
\(750\) 0 0
\(751\) 2.36434e7 1.52972 0.764858 0.644199i \(-0.222809\pi\)
0.764858 + 0.644199i \(0.222809\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.42564e6 −0.0910209
\(756\) 0 0
\(757\) 1.50108e7 0.952062 0.476031 0.879429i \(-0.342075\pi\)
0.476031 + 0.879429i \(0.342075\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.92191e6 −0.182897 −0.0914483 0.995810i \(-0.529150\pi\)
−0.0914483 + 0.995810i \(0.529150\pi\)
\(762\) 0 0
\(763\) 5.45343e6 0.339124
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.25887e6 0.568290
\(768\) 0 0
\(769\) 1.42847e7 0.871073 0.435536 0.900171i \(-0.356559\pi\)
0.435536 + 0.900171i \(0.356559\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.09012e7 0.656186 0.328093 0.944645i \(-0.393594\pi\)
0.328093 + 0.944645i \(0.393594\pi\)
\(774\) 0 0
\(775\) −1.92455e6 −0.115100
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.71875e6 −0.101478
\(780\) 0 0
\(781\) 4.30045e7 2.52282
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.44736e7 1.41750
\(786\) 0 0
\(787\) 2.56449e7 1.47593 0.737963 0.674841i \(-0.235788\pi\)
0.737963 + 0.674841i \(0.235788\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.11560e6 −0.120224
\(792\) 0 0
\(793\) 9.26169e6 0.523007
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.73086e6 −0.431104 −0.215552 0.976492i \(-0.569155\pi\)
−0.215552 + 0.976492i \(0.569155\pi\)
\(798\) 0 0
\(799\) 9.84931e6 0.545807
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.90282e7 1.04138
\(804\) 0 0
\(805\) 2.52013e6 0.137067
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.87811e7 1.00890 0.504452 0.863440i \(-0.331695\pi\)
0.504452 + 0.863440i \(0.331695\pi\)
\(810\) 0 0
\(811\) 9.00729e6 0.480886 0.240443 0.970663i \(-0.422707\pi\)
0.240443 + 0.970663i \(0.422707\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.05531e7 1.08388
\(816\) 0 0
\(817\) −2.59240e7 −1.35877
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 9.27965e6 0.480478 0.240239 0.970714i \(-0.422774\pi\)
0.240239 + 0.970714i \(0.422774\pi\)
\(822\) 0 0
\(823\) 1.08308e7 0.557393 0.278697 0.960379i \(-0.410098\pi\)
0.278697 + 0.960379i \(0.410098\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.05230e7 −1.04346 −0.521731 0.853110i \(-0.674714\pi\)
−0.521731 + 0.853110i \(0.674714\pi\)
\(828\) 0 0
\(829\) −1.42216e7 −0.718724 −0.359362 0.933198i \(-0.617006\pi\)
−0.359362 + 0.933198i \(0.617006\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.84973e6 −0.142296
\(834\) 0 0
\(835\) 1.30595e7 0.648202
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −9.29934e6 −0.456087 −0.228043 0.973651i \(-0.573233\pi\)
−0.228043 + 0.973651i \(0.573233\pi\)
\(840\) 0 0
\(841\) −1.47669e7 −0.719944
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.43277e6 0.117209
\(846\) 0 0
\(847\) −1.38486e7 −0.663281
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.18546e6 −0.0561131
\(852\) 0 0
\(853\) −3.07436e6 −0.144671 −0.0723357 0.997380i \(-0.523045\pi\)
−0.0723357 + 0.997380i \(0.523045\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.45835e7 −1.60848 −0.804242 0.594302i \(-0.797428\pi\)
−0.804242 + 0.594302i \(0.797428\pi\)
\(858\) 0 0
\(859\) −1.63022e7 −0.753814 −0.376907 0.926251i \(-0.623012\pi\)
−0.376907 + 0.926251i \(0.623012\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.56962e7 1.17447 0.587235 0.809416i \(-0.300216\pi\)
0.587235 + 0.809416i \(0.300216\pi\)
\(864\) 0 0
\(865\) −4.66087e6 −0.211800
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.04046e7 0.916596
\(870\) 0 0
\(871\) 1.28374e7 0.573366
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.31062e6 0.411111
\(876\) 0 0
\(877\) 3.30060e7 1.44908 0.724542 0.689230i \(-0.242051\pi\)
0.724542 + 0.689230i \(0.242051\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.26705e6 −0.0984060 −0.0492030 0.998789i \(-0.515668\pi\)
−0.0492030 + 0.998789i \(0.515668\pi\)
\(882\) 0 0
\(883\) −1.97779e7 −0.853649 −0.426825 0.904334i \(-0.640368\pi\)
−0.426825 + 0.904334i \(0.640368\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −36468.3 −0.00155635 −0.000778173 1.00000i \(-0.500248\pi\)
−0.000778173 1.00000i \(0.500248\pi\)
\(888\) 0 0
\(889\) −6.44100e6 −0.273337
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.29874e7 −0.544997
\(894\) 0 0
\(895\) 1.54263e7 0.643730
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.90958e6 −0.202602
\(900\) 0 0
\(901\) 6.55068e6 0.268828
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.36462e7 −0.959709
\(906\) 0 0
\(907\) −1.62298e7 −0.655079 −0.327540 0.944837i \(-0.606219\pi\)
−0.327540 + 0.944837i \(0.606219\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.61699e7 −1.04474 −0.522368 0.852720i \(-0.674951\pi\)
−0.522368 + 0.852720i \(0.674951\pi\)
\(912\) 0 0
\(913\) −450241. −0.0178759
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.71234e7 0.672461
\(918\) 0 0
\(919\) −4.05973e6 −0.158565 −0.0792826 0.996852i \(-0.525263\pi\)
−0.0792826 + 0.996852i \(0.525263\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.20070e7 −1.62300
\(924\) 0 0
\(925\) −1.01237e6 −0.0389031
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.69518e6 −0.140474 −0.0702370 0.997530i \(-0.522376\pi\)
−0.0702370 + 0.997530i \(0.522376\pi\)
\(930\) 0 0
\(931\) 3.75769e6 0.142084
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3.69589e7 −1.38258
\(936\) 0 0
\(937\) −1.91384e7 −0.712126 −0.356063 0.934462i \(-0.615881\pi\)
−0.356063 + 0.934462i \(0.615881\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.20954e7 −0.445294 −0.222647 0.974899i \(-0.571470\pi\)
−0.222647 + 0.974899i \(0.571470\pi\)
\(942\) 0 0
\(943\) 1.20820e6 0.0442445
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.95969e7 −0.710087 −0.355044 0.934850i \(-0.615534\pi\)
−0.355044 + 0.934850i \(0.615534\pi\)
\(948\) 0 0
\(949\) −1.85868e7 −0.669945
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −4.23265e7 −1.50966 −0.754832 0.655918i \(-0.772282\pi\)
−0.754832 + 0.655918i \(0.772282\pi\)
\(954\) 0 0
\(955\) −2.98426e6 −0.105884
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.89353e7 0.664852
\(960\) 0 0
\(961\) −2.44330e7 −0.853430
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.19419e7 0.758502
\(966\) 0 0
\(967\) −1.39211e6 −0.0478749 −0.0239375 0.999713i \(-0.507620\pi\)
−0.0239375 + 0.999713i \(0.507620\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.41877e7 1.50402 0.752009 0.659153i \(-0.229085\pi\)
0.752009 + 0.659153i \(0.229085\pi\)
\(972\) 0 0
\(973\) 847175. 0.0286874
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.60457e7 1.87848 0.939239 0.343264i \(-0.111533\pi\)
0.939239 + 0.343264i \(0.111533\pi\)
\(978\) 0 0
\(979\) −8.39082e7 −2.79800
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −5.00560e7 −1.65224 −0.826118 0.563497i \(-0.809456\pi\)
−0.826118 + 0.563497i \(0.809456\pi\)
\(984\) 0 0
\(985\) −1.25298e7 −0.411483
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.82233e7 0.592428
\(990\) 0 0
\(991\) −1.59116e7 −0.514670 −0.257335 0.966322i \(-0.582844\pi\)
−0.257335 + 0.966322i \(0.582844\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.82911e7 0.905924
\(996\) 0 0
\(997\) 4.25995e7 1.35727 0.678635 0.734476i \(-0.262572\pi\)
0.678635 + 0.734476i \(0.262572\pi\)
\(998\) 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.1.2 2
3.2 odd 2 112.6.a.h.1.1 2
4.3 odd 2 63.6.a.f.1.2 2
12.11 even 2 7.6.a.b.1.1 2
21.20 even 2 784.6.a.v.1.2 2
24.5 odd 2 448.6.a.u.1.2 2
24.11 even 2 448.6.a.w.1.1 2
28.27 even 2 441.6.a.l.1.2 2
60.23 odd 4 175.6.b.c.99.2 4
60.47 odd 4 175.6.b.c.99.3 4
60.59 even 2 175.6.a.c.1.2 2
84.11 even 6 49.6.c.e.30.2 4
84.23 even 6 49.6.c.e.18.2 4
84.47 odd 6 49.6.c.d.18.2 4
84.59 odd 6 49.6.c.d.30.2 4
84.83 odd 2 49.6.a.f.1.1 2
132.131 odd 2 847.6.a.c.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.6.a.b.1.1 2 12.11 even 2
49.6.a.f.1.1 2 84.83 odd 2
49.6.c.d.18.2 4 84.47 odd 6
49.6.c.d.30.2 4 84.59 odd 6
49.6.c.e.18.2 4 84.23 even 6
49.6.c.e.30.2 4 84.11 even 6
63.6.a.f.1.2 2 4.3 odd 2
112.6.a.h.1.1 2 3.2 odd 2
175.6.a.c.1.2 2 60.59 even 2
175.6.b.c.99.2 4 60.23 odd 4
175.6.b.c.99.3 4 60.47 odd 4
441.6.a.l.1.2 2 28.27 even 2
448.6.a.u.1.2 2 24.5 odd 2
448.6.a.w.1.1 2 24.11 even 2
784.6.a.v.1.2 2 21.20 even 2
847.6.a.c.1.2 2 132.131 odd 2
1008.6.a.bq.1.2 2 1.1 even 1 trivial