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Properties

Label 11.11.b.a.10.1
Level $11$
Weight $11$
Character 11.10
Self dual yes
Analytic conductor $6.989$
Analytic rank $0$
Dimension $1$
CM discriminant -11
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [11,11,Mod(10,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 11.b (of order \(2\), degree \(1\), minimal)

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: \(6.98892977941\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 10.1
Character \(\chi\) \(=\) 11.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+475.000 q^{3} +1024.00 q^{4} -3001.00 q^{5} +166576. q^{9} +O(q^{10})\) \(q+475.000 q^{3} +1024.00 q^{4} -3001.00 q^{5} +166576. q^{9} -161051. q^{11} +486400. q^{12} -1.42548e6 q^{15} +1.04858e6 q^{16} -3.07302e6 q^{20} -1.19103e7 q^{23} -759624. q^{25} +5.10753e7 q^{27} +3.19232e6 q^{31} -7.64992e7 q^{33} +1.70574e8 q^{36} -1.37083e8 q^{37} -1.64916e8 q^{44} -4.99895e8 q^{45} +1.51795e8 q^{47} +4.98074e8 q^{48} +2.82475e8 q^{49} +3.75067e8 q^{53} +4.83314e8 q^{55} -8.13568e8 q^{59} -1.45969e9 q^{60} +1.07374e9 q^{64} +2.61664e9 q^{67} -5.65740e9 q^{69} +7.83652e8 q^{71} -3.60821e8 q^{75} -3.14678e9 q^{80} +1.44246e10 q^{81} -2.87091e9 q^{89} -1.21962e10 q^{92} +1.51635e9 q^{93} +9.45401e9 q^{97} -2.68272e10 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 475.000 1.95473 0.977366 − 0.211554i \(-0.0678525\pi\)
0.977366 + 0.211554i \(0.0678525\pi\)
\(4\) 1024.00 1.00000
\(5\) −3001.00 −0.960320 −0.480160 − 0.877181i \(-0.659421\pi\)
−0.480160 + 0.877181i \(0.659421\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 166576. 2.82098
\(10\) 0 0
\(11\) −161051. −1.00000
\(12\) 486400. 1.95473
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.42548e6 −1.87717
\(16\) 1.04858e6 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −3.07302e6 −0.960320
\(21\) 0 0
\(22\) 0 0
\(23\) −1.19103e7 −1.85048 −0.925240 − 0.379382i \(-0.876137\pi\)
−0.925240 + 0.379382i \(0.876137\pi\)
\(24\) 0 0
\(25\) −759624. −0.0777855
\(26\) 0 0
\(27\) 5.10753e7 3.55953
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 3.19232e6 0.111506 0.0557530 − 0.998445i \(-0.482244\pi\)
0.0557530 + 0.998445i \(0.482244\pi\)
\(32\) 0 0
\(33\) −7.64992e7 −1.95473
\(34\) 0 0
\(35\) 0 0
\(36\) 1.70574e8 2.82098
\(37\) −1.37083e8 −1.97685 −0.988425 − 0.151709i \(-0.951522\pi\)
−0.988425 + 0.151709i \(0.951522\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.64916e8 −1.00000
\(45\) −4.99895e8 −2.70904
\(46\) 0 0
\(47\) 1.51795e8 0.661864 0.330932 − 0.943655i \(-0.392637\pi\)
0.330932 + 0.943655i \(0.392637\pi\)
\(48\) 4.98074e8 1.95473
\(49\) 2.82475e8 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.75067e8 0.896869 0.448435 − 0.893816i \(-0.351982\pi\)
0.448435 + 0.893816i \(0.351982\pi\)
\(54\) 0 0
\(55\) 4.83314e8 0.960320
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.13568e8 −1.13798 −0.568989 − 0.822345i \(-0.692665\pi\)
−0.568989 + 0.822345i \(0.692665\pi\)
\(60\) −1.45969e9 −1.87717
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.07374e9 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.61664e9 1.93807 0.969036 − 0.246921i \(-0.0794188\pi\)
0.969036 + 0.246921i \(0.0794188\pi\)
\(68\) 0 0
\(69\) −5.65740e9 −3.61719
\(70\) 0 0
\(71\) 7.83652e8 0.434342 0.217171 − 0.976134i \(-0.430317\pi\)
0.217171 + 0.976134i \(0.430317\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −3.60821e8 −0.152050
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −3.14678e9 −0.960320
\(81\) 1.44246e10 4.13694
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.87091e9 −0.514127 −0.257063 − 0.966395i \(-0.582755\pi\)
−0.257063 + 0.966395i \(0.582755\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.21962e10 −1.85048
\(93\) 1.51635e9 0.217964
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.45401e9 1.10092 0.550462 − 0.834860i \(-0.314452\pi\)
0.550462 + 0.834860i \(0.314452\pi\)
\(98\) 0 0
\(99\) −2.68272e10 −2.82098
\(100\) −7.77855e8 −0.0777855
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 9.30242e9 0.802435 0.401217 − 0.915983i \(-0.368587\pi\)
0.401217 + 0.915983i \(0.368587\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 5.23011e10 3.55953
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −6.51142e10 −3.86421
\(112\) 0 0
\(113\) 1.61746e8 0.00877890 0.00438945 − 0.999990i \(-0.498603\pi\)
0.00438945 + 0.999990i \(0.498603\pi\)
\(114\) 0 0
\(115\) 3.57429e10 1.77705
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.59374e10 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 3.26894e9 0.111506
\(125\) 3.15863e10 1.03502
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −7.83352e10 −1.95473
\(133\) 0 0
\(134\) 0 0
\(135\) −1.53277e11 −3.41829
\(136\) 0 0
\(137\) −2.72055e10 −0.563708 −0.281854 − 0.959457i \(-0.590949\pi\)
−0.281854 + 0.959457i \(0.590949\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 7.21027e10 1.29377
\(142\) 0 0
\(143\) 0 0
\(144\) 1.74668e11 2.82098
\(145\) 0 0
\(146\) 0 0
\(147\) 1.34176e11 1.95473
\(148\) −1.40373e11 −1.97685
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.58016e9 −0.107081
\(156\) 0 0
\(157\) −1.12312e11 −1.17742 −0.588708 − 0.808346i \(-0.700363\pi\)
−0.588708 + 0.808346i \(0.700363\pi\)
\(158\) 0 0
\(159\) 1.78157e11 1.75314
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.03184e11 −1.76584 −0.882920 − 0.469523i \(-0.844426\pi\)
−0.882920 + 0.469523i \(0.844426\pi\)
\(164\) 0 0
\(165\) 2.29574e11 1.87717
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.37858e11 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.68874e11 −1.00000
\(177\) −3.86445e11 −2.22444
\(178\) 0 0
\(179\) 3.38386e11 1.84139 0.920697 − 0.390278i \(-0.127621\pi\)
0.920697 + 0.390278i \(0.127621\pi\)
\(180\) −5.11892e11 −2.70904
\(181\) −3.10198e11 −1.59679 −0.798393 − 0.602137i \(-0.794316\pi\)
−0.798393 + 0.602137i \(0.794316\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.11385e11 1.89841
\(186\) 0 0
\(187\) 0 0
\(188\) 1.55438e11 0.661864
\(189\) 0 0
\(190\) 0 0
\(191\) −4.34229e11 −1.70825 −0.854126 − 0.520066i \(-0.825907\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(192\) 5.10027e11 1.95473
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.89255e11 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 1.56808e10 0.0502462 0.0251231 − 0.999684i \(-0.492002\pi\)
0.0251231 + 0.999684i \(0.492002\pi\)
\(200\) 0 0
\(201\) 1.24290e12 3.78841
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.98397e12 −5.22017
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 3.84068e11 0.896869
\(213\) 3.72235e11 0.849022
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 4.94914e11 0.960320
\(221\) 0 0
\(222\) 0 0
\(223\) −1.04167e12 −1.88889 −0.944447 − 0.328663i \(-0.893402\pi\)
−0.944447 + 0.328663i \(0.893402\pi\)
\(224\) 0 0
\(225\) −1.26535e11 −0.219431
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 1.11773e11 0.177484 0.0887419 − 0.996055i \(-0.471715\pi\)
0.0887419 + 0.996055i \(0.471715\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −4.55538e11 −0.635601
\(236\) −8.33094e11 −1.13798
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.49472e12 −1.87717
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 3.83575e12 4.52709
\(244\) 0 0
\(245\) −8.47708e11 −0.960320
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.42306e12 1.42841 0.714207 − 0.699935i \(-0.246788\pi\)
0.714207 + 0.699935i \(0.246788\pi\)
\(252\) 0 0
\(253\) 1.91817e12 1.85048
\(254\) 0 0
\(255\) 0 0
\(256\) 1.09951e12 1.00000
\(257\) −2.12681e12 −1.89698 −0.948489 − 0.316810i \(-0.897388\pi\)
−0.948489 + 0.316810i \(0.897388\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −1.12558e12 −0.861281
\(266\) 0 0
\(267\) −1.36368e12 −1.00498
\(268\) 2.67944e12 1.93807
\(269\) −1.46946e12 −1.04327 −0.521633 − 0.853170i \(-0.674677\pi\)
−0.521633 + 0.853170i \(0.674677\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.22338e11 0.0777855
\(276\) −5.79318e12 −3.61719
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 5.31764e11 0.314556
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 8.02459e11 0.434342
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.01599e12 1.00000
\(290\) 0 0
\(291\) 4.49066e12 2.15201
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 2.44152e12 1.09282
\(296\) 0 0
\(297\) −8.22573e12 −3.55953
\(298\) 0 0
\(299\) 0 0
\(300\) −3.69481e11 −0.152050
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 4.41865e12 1.56855
\(310\) 0 0
\(311\) 5.50479e12 1.89208 0.946039 − 0.324052i \(-0.105045\pi\)
0.946039 + 0.324052i \(0.105045\pi\)
\(312\) 0 0
\(313\) −4.90828e12 −1.63383 −0.816916 − 0.576756i \(-0.804318\pi\)
−0.816916 + 0.576756i \(0.804318\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.37352e12 1.36627 0.683133 − 0.730294i \(-0.260617\pi\)
0.683133 + 0.730294i \(0.260617\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −3.22230e12 −0.960320
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.47708e13 4.13694
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.40333e12 −1.86332 −0.931660 − 0.363332i \(-0.881639\pi\)
−0.931660 + 0.363332i \(0.881639\pi\)
\(332\) 0 0
\(333\) −2.28347e13 −5.57665
\(334\) 0 0
\(335\) −7.85253e12 −1.86117
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 7.68291e10 0.0171604
\(340\) 0 0
\(341\) −5.14127e11 −0.111506
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.69779e13 3.47366
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.22003e12 1.49968 0.749842 − 0.661617i \(-0.230129\pi\)
0.749842 + 0.661617i \(0.230129\pi\)
\(354\) 0 0
\(355\) −2.35174e12 −0.417107
\(356\) −2.93981e12 −0.514127
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 6.13107e12 1.00000
\(362\) 0 0
\(363\) 1.23203e13 1.95473
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.15912e13 −1.74099 −0.870497 − 0.492174i \(-0.836203\pi\)
−0.870497 + 0.492174i \(0.836203\pi\)
\(368\) −1.24889e13 −1.85048
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.55275e12 0.217964
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.50035e13 2.02319
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.20727e13 −1.54386 −0.771931 − 0.635706i \(-0.780709\pi\)
−0.771931 + 0.635706i \(0.780709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.08983e13 1.32241 0.661203 − 0.750207i \(-0.270046\pi\)
0.661203 + 0.750207i \(0.270046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 9.68091e12 1.10092
\(389\) 1.29221e13 1.45072 0.725362 − 0.688368i \(-0.241672\pi\)
0.725362 + 0.688368i \(0.241672\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −2.74711e13 −2.82098
\(397\) −1.72891e13 −1.75315 −0.876575 − 0.481264i \(-0.840178\pi\)
−0.876575 + 0.481264i \(0.840178\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −7.96523e11 −0.0777855
\(401\) 1.19222e13 1.14984 0.574918 − 0.818211i \(-0.305034\pi\)
0.574918 + 0.818211i \(0.305034\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −4.32883e13 −3.97279
\(406\) 0 0
\(407\) 2.20773e13 1.97685
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −1.29226e13 −1.10190
\(412\) 9.52568e12 0.802435
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.58238e13 −1.99963 −0.999817 − 0.0191062i \(-0.993918\pi\)
−0.999817 + 0.0191062i \(0.993918\pi\)
\(420\) 0 0
\(421\) 2.05682e13 1.55520 0.777600 − 0.628759i \(-0.216437\pi\)
0.777600 + 0.628759i \(0.216437\pi\)
\(422\) 0 0
\(423\) 2.52854e13 1.86711
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 5.35564e13 3.55953
\(433\) −4.37938e12 −0.287722 −0.143861 − 0.989598i \(-0.545952\pi\)
−0.143861 + 0.989598i \(0.545952\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 4.70536e13 2.82098
\(442\) 0 0
\(443\) −1.66747e13 −0.977325 −0.488663 − 0.872473i \(-0.662515\pi\)
−0.488663 + 0.872473i \(0.662515\pi\)
\(444\) −6.66770e13 −3.86421
\(445\) 8.61561e12 0.493726
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.32859e13 −1.27603 −0.638015 − 0.770024i \(-0.720244\pi\)
−0.638015 + 0.770024i \(0.720244\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.65627e11 0.00877890
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 3.66007e13 1.77705
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 7.99606e12 0.375812 0.187906 − 0.982187i \(-0.439830\pi\)
0.187906 + 0.982187i \(0.439830\pi\)
\(464\) 0 0
\(465\) −4.55058e12 −0.209316
\(466\) 0 0
\(467\) −3.41290e13 −1.53652 −0.768261 − 0.640136i \(-0.778878\pi\)
−0.768261 + 0.640136i \(0.778878\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.33484e13 −2.30153
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.24771e13 2.53005
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2.65599e13 1.00000
\(485\) −2.83715e13 −1.05724
\(486\) 0 0
\(487\) −3.54246e13 −1.29318 −0.646592 − 0.762836i \(-0.723806\pi\)
−0.646592 + 0.762836i \(0.723806\pi\)
\(488\) 0 0
\(489\) −9.65124e13 −3.45175
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 8.05085e13 2.70904
\(496\) 3.34739e12 0.111506
\(497\) 0 0
\(498\) 0 0
\(499\) −5.93009e12 −0.191672 −0.0958359 − 0.995397i \(-0.530552\pi\)
−0.0958359 + 0.995397i \(0.530552\pi\)
\(500\) 3.23443e13 1.03502
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.54828e13 1.95473
\(508\) 0 0
\(509\) 5.06582e13 1.48273 0.741363 − 0.671104i \(-0.234180\pi\)
0.741363 + 0.671104i \(0.234180\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.79166e13 −0.770594
\(516\) 0 0
\(517\) −2.44468e13 −0.661864
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.51450e13 1.95754 0.978772 − 0.204952i \(-0.0657038\pi\)
0.978772 + 0.204952i \(0.0657038\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −8.02153e13 −1.95473
\(529\) 1.00429e14 2.42428
\(530\) 0 0
\(531\) −1.35521e14 −3.21021
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.60733e14 3.59943
\(538\) 0 0
\(539\) −4.54929e13 −1.00000
\(540\) −1.56956e14 −3.41829
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −1.47344e14 −3.12129
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −2.78584e13 −0.563708
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.95408e14 3.71088
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 7.38332e13 1.29377
\(565\) −4.85398e11 −0.00843055
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −2.06259e14 −3.33918
\(574\) 0 0
\(575\) 9.04737e12 0.143941
\(576\) 1.78860e14 2.82098
\(577\) −6.30450e13 −0.985760 −0.492880 − 0.870097i \(-0.664056\pi\)
−0.492880 + 0.870097i \(0.664056\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.04049e13 −0.896869
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.73593e13 0.392568 0.196284 − 0.980547i \(-0.437113\pi\)
0.196284 + 0.980547i \(0.437113\pi\)
\(588\) 1.37396e14 1.95473
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.43742e14 −1.97685
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.44838e12 0.0982178
\(598\) 0 0
\(599\) 6.14022e13 0.796251 0.398126 − 0.917331i \(-0.369661\pi\)
0.398126 + 0.917331i \(0.369661\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 4.35869e14 5.46726
\(604\) 0 0
\(605\) −7.78382e13 −0.960320
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.42489e14 1.59352 0.796758 − 0.604299i \(-0.206547\pi\)
0.796758 + 0.604299i \(0.206547\pi\)
\(618\) 0 0
\(619\) −1.78095e14 −1.95974 −0.979871 − 0.199630i \(-0.936026\pi\)
−0.979871 + 0.199630i \(0.936026\pi\)
\(620\) −9.81009e12 −0.107081
\(621\) −6.08324e14 −6.58683
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −8.73722e13 −0.916164
\(626\) 0 0
\(627\) 0 0
\(628\) −1.15008e14 −1.17742
\(629\) 0 0
\(630\) 0 0
\(631\) −3.44236e13 −0.344119 −0.172060 − 0.985087i \(-0.555042\pi\)
−0.172060 + 0.985087i \(0.555042\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.82432e14 1.75314
\(637\) 0 0
\(638\) 0 0
\(639\) 1.30538e14 1.22527
\(640\) 0 0
\(641\) 1.09532e13 0.101216 0.0506082 − 0.998719i \(-0.483884\pi\)
0.0506082 + 0.998719i \(0.483884\pi\)
\(642\) 0 0
\(643\) 2.19818e14 1.99990 0.999952 − 0.00979126i \(-0.00311670\pi\)
0.999952 + 0.00979126i \(0.00311670\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.75105e14 −1.54446 −0.772229 − 0.635344i \(-0.780858\pi\)
−0.772229 + 0.635344i \(0.780858\pi\)
\(648\) 0 0
\(649\) 1.31026e14 1.13798
\(650\) 0 0
\(651\) 0 0
\(652\) −2.08060e14 −1.76584
\(653\) 1.89126e14 1.59289 0.796444 − 0.604712i \(-0.206712\pi\)
0.796444 + 0.604712i \(0.206712\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 2.35084e14 1.87717
\(661\) 2.10313e14 1.66671 0.833355 − 0.552739i \(-0.186417\pi\)
0.833355 + 0.552739i \(0.186417\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −4.94795e14 −3.69228
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −3.87980e13 −0.276880
\(676\) 1.41167e14 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.72866e13 −0.116307 −0.0581537 − 0.998308i \(-0.518521\pi\)
−0.0581537 + 0.998308i \(0.518521\pi\)
\(684\) 0 0
\(685\) 8.16437e13 0.541340
\(686\) 0 0
\(687\) 5.30921e13 0.346933
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 3.11488e14 1.97720 0.988600 − 0.150563i \(-0.0481087\pi\)
0.988600 + 0.150563i \(0.0481087\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.72927e14 −1.00000
\(705\) −2.16380e14 −1.24243
\(706\) 0 0
\(707\) 0 0
\(708\) −3.95719e14 −2.22444
\(709\) 3.13308e14 1.74880 0.874402 − 0.485203i \(-0.161254\pi\)
0.874402 + 0.485203i \(0.161254\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.80216e13 −0.206340
\(714\) 0 0
\(715\) 0 0
\(716\) 3.46507e14 1.84139
\(717\) 0 0
\(718\) 0 0
\(719\) −3.84303e14 −2.00000 −0.999998 − 0.00216702i \(-0.999310\pi\)
−0.999998 + 0.00216702i \(0.999310\pi\)
\(720\) −5.24177e14 −2.70904
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −3.17643e14 −1.59679
\(725\) 0 0
\(726\) 0 0
\(727\) −1.14172e14 −0.562197 −0.281098 − 0.959679i \(-0.590699\pi\)
−0.281098 + 0.959679i \(0.590699\pi\)
\(728\) 0 0
\(729\) 9.70223e14 4.71231
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −4.02661e14 −1.87717
\(736\) 0 0
\(737\) −4.21412e14 −1.93807
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 4.21258e14 1.89841
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.78058e14 0.745353 0.372677 − 0.927961i \(-0.378440\pi\)
0.372677 + 0.927961i \(0.378440\pi\)
\(752\) 1.59169e14 0.661864
\(753\) 6.75952e14 2.79217
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.13954e14 −0.458405 −0.229202 − 0.973379i \(-0.573612\pi\)
−0.229202 + 0.973379i \(0.573612\pi\)
\(758\) 0 0
\(759\) 9.11131e14 3.61719
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.44650e14 −1.70825
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 5.22268e14 1.95473
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −1.01023e15 −3.70808
\(772\) 0 0
\(773\) −4.10387e14 −1.48695 −0.743475 − 0.668764i \(-0.766824\pi\)
−0.743475 + 0.668764i \(0.766824\pi\)
\(774\) 0 0
\(775\) −2.42497e12 −0.00867355
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −1.26208e14 −0.434342
\(782\) 0 0
\(783\) 0 0
\(784\) 2.96197e14 1.00000
\(785\) 3.37050e14 1.13070
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −5.34648e14 −1.68357
\(796\) 1.60571e13 0.0502462
\(797\) −5.54413e14 −1.72402 −0.862008 − 0.506894i \(-0.830794\pi\)
−0.862008 + 0.506894i \(0.830794\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −4.78225e14 −1.45034
\(802\) 0 0
\(803\) 0 0
\(804\) 1.27273e15 3.78841
\(805\) 0 0
\(806\) 0 0
\(807\) −6.97992e14 −2.03931
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.09755e14 1.69577
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 5.19688e14 1.37640 0.688199 − 0.725522i \(-0.258402\pi\)
0.688199 + 0.725522i \(0.258402\pi\)
\(824\) 0 0
\(825\) 5.81106e13 0.152050
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −2.03159e15 −5.22017
\(829\) −4.19459e14 −1.07131 −0.535657 − 0.844436i \(-0.679936\pi\)
−0.535657 + 0.844436i \(0.679936\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.63049e14 0.396909
\(838\) 0 0
\(839\) 7.17676e14 1.72631 0.863154 − 0.504940i \(-0.168485\pi\)
0.863154 + 0.504940i \(0.168485\pi\)
\(840\) 0 0
\(841\) 4.20707e14 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.13713e14 −0.960320
\(846\) 0 0
\(847\) 0 0
\(848\) 3.93286e14 0.896869
\(849\) 0 0
\(850\) 0 0
\(851\) 1.63270e15 3.65812
\(852\) 3.81168e14 0.849022
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −7.08943e14 −1.51581 −0.757907 − 0.652363i \(-0.773778\pi\)
−0.757907 + 0.652363i \(0.773778\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.11193e14 −1.90352 −0.951758 − 0.306851i \(-0.900725\pi\)
−0.951758 + 0.306851i \(0.900725\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 9.57597e14 1.95473
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.57481e15 3.10568
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 5.06792e14 0.960320
\(881\) −1.01074e15 −1.90441 −0.952204 − 0.305462i \(-0.901189\pi\)
−0.952204 + 0.305462i \(0.901189\pi\)
\(882\) 0 0
\(883\) −1.03389e15 −1.92606 −0.963031 − 0.269391i \(-0.913178\pi\)
−0.963031 + 0.269391i \(0.913178\pi\)
\(884\) 0 0
\(885\) 1.15972e15 2.13618
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −2.32310e15 −4.13694
\(892\) −1.06667e15 −1.88889
\(893\) 0 0
\(894\) 0 0
\(895\) −1.01550e15 −1.76833
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.29572e14 −0.219431
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 9.30906e14 1.53343
\(906\) 0 0
\(907\) −2.90238e14 −0.472844 −0.236422 − 0.971650i \(-0.575975\pi\)
−0.236422 + 0.971650i \(0.575975\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 5.68037e14 0.905284 0.452642 − 0.891692i \(-0.350482\pi\)
0.452642 + 0.891692i \(0.350482\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.14455e14 0.177484
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.04131e14 0.153770
\(926\) 0 0
\(927\) 1.54956e15 2.26365
\(928\) 0 0
\(929\) −5.80692e14 −0.839203 −0.419601 − 0.907708i \(-0.637830\pi\)
−0.419601 + 0.907708i \(0.637830\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2.61478e15 3.69851
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −2.33143e15 −3.19371
\(940\) −4.66470e14 −0.635601
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −8.53088e14 −1.13798
\(945\) 0 0
\(946\) 0 0
\(947\) −1.13888e15 −1.49529 −0.747647 − 0.664096i \(-0.768816\pi\)
−0.747647 + 0.664096i \(0.768816\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 2.07742e15 2.67068
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 1.30312e15 1.64047
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −1.53059e15 −1.87717
\(961\) −8.09437e14 −0.987566
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.66222e14 0.424276 0.212138 − 0.977240i \(-0.431957\pi\)
0.212138 + 0.977240i \(0.431957\pi\)
\(972\) 3.92781e15 4.52709
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.34198e14 0.487769 0.243885 − 0.969804i \(-0.421578\pi\)
0.243885 + 0.969804i \(0.421578\pi\)
\(978\) 0 0
\(979\) 4.62363e14 0.514127
\(980\) −8.68053e14 −0.960320
\(981\) 0 0
\(982\) 0 0
\(983\) 1.83071e15 1.99458 0.997290 − 0.0735772i \(-0.0234415\pi\)
0.997290 + 0.0735772i \(0.0234415\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.90369e15 1.99172 0.995861 − 0.0908931i \(-0.0289722\pi\)
0.995861 + 0.0908931i \(0.0289722\pi\)
\(992\) 0 0
\(993\) −3.51658e15 −3.64229
\(994\) 0 0
\(995\) −4.70581e13 −0.0482524
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) −7.00154e15 −7.03665
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 11.11.b.a.10.1 ✓ 1
3.2 odd 2 99.11.c.a.10.1 1
4.3 odd 2 176.11.h.a.65.1 1
11.10 odd 2 CM 11.11.b.a.10.1 ✓ 1
33.32 even 2 99.11.c.a.10.1 1
44.43 even 2 176.11.h.a.65.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.11.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.11.b.a.10.1 ✓ 1 11.10 odd 2 CM
99.11.c.a.10.1 1 3.2 odd 2
99.11.c.a.10.1 1 33.32 even 2
176.11.h.a.65.1 1 4.3 odd 2
176.11.h.a.65.1 1 44.43 even 2