Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,36,Mod(1,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.1");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(31.0380522535\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 1597028177x + 23572260890640 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{4}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19173.3\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.83743e8 | −1.26854 | −0.634268 | − | 0.773114i | \(-0.718698\pi\) | ||||
−0.634268 | + | 0.773114i | \(0.718698\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.90658e11 | 0.287610 | 0.143805 | − | 0.989606i | \(-0.454066\pi\) | ||||
0.143805 | + | 0.989606i | \(0.454066\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.46684e14 | −0.400798 | −0.200399 | − | 0.979714i | \(-0.564224\pi\) | ||||
−0.200399 | + | 0.979714i | \(0.564224\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.04783e16 | 0.609182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.33450e18 | 1.39258 | 0.696291 | − | 0.717759i | \(-0.254832\pi\) | ||||
0.696291 | + | 0.717759i | \(0.254832\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.81916e19 | 1.22450 | 0.612251 | − | 0.790663i | \(-0.290264\pi\) | ||||
0.612251 | + | 0.790663i | \(0.290264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.39220e20 | −0.364843 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.45028e21 | −1.30476 | −0.652381 | − | 0.757891i | \(-0.726230\pi\) | ||||
−0.652381 | + | 0.757891i | \(0.726230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.08695e22 | 0.873623 | 0.436812 | − | 0.899553i | \(-0.356108\pi\) | ||||
0.436812 | + | 0.899553i | \(0.356108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.99948e22 | 0.508427 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.20235e23 | −0.621234 | −0.310617 | − | 0.950535i | \(-0.600536\pi\) | ||||
−0.310617 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.66964e24 | −0.917281 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.54809e24 | 0.495767 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.50471e24 | −0.192030 | −0.0960150 | − | 0.995380i | \(-0.530610\pi\) | ||||
−0.0960150 | + | 0.995380i | \(0.530610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.91757e26 | −1.52729 | −0.763646 | − | 0.645635i | \(-0.776593\pi\) | ||||
−0.763646 | + | 0.645635i | \(0.776593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.62396e26 | −1.76654 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.21037e26 | −0.115273 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.21127e27 | −1.15650 | −0.578252 | − | 0.815858i | \(-0.696265\pi\) | ||||
−0.578252 | + | 0.815858i | \(0.696265\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.08366e28 | −1.55332 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.18713e28 | −1.30664 | −0.653322 | − | 0.757080i | \(-0.726625\pi\) | ||||
−0.653322 | + | 0.757080i | \(0.726625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.51246e28 | 0.911829 | 0.455914 | − | 0.890024i | \(-0.349312\pi\) | ||||
0.455914 | + | 0.890024i | \(0.349312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.49544e28 | 0.175207 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.90248e29 | 1.58875 | 0.794377 | − | 0.607426i | \(-0.207798\pi\) | ||||
0.794377 | + | 0.607426i | \(0.207798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.17966e29 | −0.839361 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.26273e30 | 1.65514 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.28287e30 | 0.857739 | 0.428869 | − | 0.903367i | \(-0.358912\pi\) | ||||
0.428869 | + | 0.903367i | \(0.358912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14544e30 | 0.400520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.92157e30 | −1.10822 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.49203e31 | −1.52710 | −0.763549 | − | 0.645750i | \(-0.776545\pi\) | ||||
−0.763549 | + | 0.645750i | \(0.776545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.52662e30 | −0.258525 | −0.129262 | − | 0.991610i | \(-0.541261\pi\) | ||||
−0.129262 | + | 0.991610i | \(0.541261\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.51852e30 | −0.244159 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.87390e31 | 0.352179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.01659e32 | −1.12418 | −0.562090 | − | 0.827076i | \(-0.690002\pi\) | ||||
−0.562090 | + | 0.827076i | \(0.690002\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.19239e32 | 0.788058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.79692e32 | 0.720290 | 0.360145 | − | 0.932896i | \(-0.382727\pi\) | ||||
0.360145 | + | 0.932896i | \(0.382727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.54379e32 | 1.12013 | 0.560064 | − | 0.828449i | \(-0.310776\pi\) | ||||
0.560064 | + | 0.828449i | \(0.310776\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.57490e32 | 1.16360 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.75883e32 | −0.558145 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.10706e33 | −0.685009 | −0.342505 | − | 0.939516i | \(-0.611275\pi\) | ||||
−0.342505 | + | 0.939516i | \(0.611275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.09911e33 | −1.23808 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.18064e32 | 0.161126 | 0.0805632 | − | 0.996750i | \(-0.474328\pi\) | ||||
0.0805632 | + | 0.996750i | \(0.474328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.18356e33 | −0.375262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.12941e33 | 0.243597 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41163e34 | −1.08492 | −0.542459 | − | 0.840082i | \(-0.682507\pi\) | ||||
−0.542459 | + | 0.840082i | \(0.682507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.42127e33 | −0.490778 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.44097e34 | 1.93742 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.02398e34 | 0.251262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.64379e34 | 1.13217 | 0.566083 | − | 0.824348i | \(-0.308458\pi\) | ||||
0.566083 | + | 0.824348i | \(0.308458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.11515e34 | 0.848336 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.14029e35 | −0.958056 | −0.479028 | − | 0.877800i | \(-0.659011\pi\) | ||||
−0.479028 | + | 0.877800i | \(0.659011\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.30990e35 | −1.37702 | −0.688512 | − | 0.725225i | \(-0.741736\pi\) | ||||
−0.688512 | + | 0.725225i | \(0.741736\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.43435e34 | 0.146228 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.27204e34 | 0.100139 | 0.0500693 | − | 0.998746i | \(-0.484056\pi\) | ||||
0.0500693 | + | 0.998746i | \(0.484056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.12314e35 | −1.57655 | −0.788275 | − | 0.615323i | \(-0.789026\pi\) | ||||
−0.788275 | + | 0.615323i | \(0.789026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.11175e35 | 1.46707 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.11897e36 | −1.31810 | −0.659048 | − | 0.752101i | \(-0.729040\pi\) | ||||
−0.659048 | + | 0.752101i | \(0.729040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.06192e35 | −0.178673 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.16402e36 | 0.745944 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.09781e36 | 0.522946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.63963e36 | 0.939287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.20582e36 | 1.65752 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.73788e36 | −0.551428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.48154e36 | −0.836253 | −0.418126 | − | 0.908389i | \(-0.637313\pi\) | ||||
−0.418126 | + | 0.908389i | \(0.637313\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.96634e36 | −1.15669 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.03882e36 | −0.180772 | −0.0903859 | − | 0.995907i | \(-0.528810\pi\) | ||||
−0.0903859 | + | 0.995907i | \(0.528810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.14818e36 | −0.350147 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.72221e36 | 0.142587 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.05428e37 | −0.426921 | −0.213461 | − | 0.976952i | \(-0.568474\pi\) | ||||
−0.213461 | + | 0.976952i | \(0.568474\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.83397e37 | 0.890504 | 0.445252 | − | 0.895405i | \(-0.353114\pi\) | ||||
0.445252 | + | 0.895405i | \(0.353114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.23557e37 | −2.01539 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.91582e37 | 1.70522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.68224e36 | −0.0552296 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.02204e37 | 1.06476 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.84255e37 | 0.264818 | 0.132409 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132409 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.11776e38 | 1.56235 | 0.781177 | − | 0.624310i | \(-0.214620\pi\) | ||||
0.781177 | + | 0.624310i | \(0.214620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.35637e38 | −0.794837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.40872e37 | −0.439264 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.38275e38 | −1.26190 | −0.630951 | − | 0.775823i | \(-0.717335\pi\) | ||||
−0.630951 | + | 0.775823i | \(0.717335\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.64005e38 | −1.08807 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.03665e38 | 0.248990 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.02228e37 | 0.0971891 | 0.0485946 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485946 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.25009e38 | −0.508074 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.10664e38 | 0.519934 | 0.259967 | − | 0.965618i | \(-0.416288\pi\) | ||||
0.259967 | + | 0.965618i | \(0.416288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.85814e38 | 0.499405 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.36067e38 | 0.532195 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.96129e39 | −1.33886 | −0.669431 | − | 0.742874i | \(-0.733462\pi\) | ||||
−0.669431 | + | 0.742874i | \(0.733462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.58558e38 | 0.367644 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.23352e39 | 1.93718 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.30177e39 | 0.865235 | 0.432618 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432618 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.13992e39 | −0.662251 | −0.331126 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331126 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.28440e39 | 0.327948 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.57564e39 | −0.332622 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03892e40 | −1.81699 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.36863e39 | −0.198702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.38915e40 | −1.67751 | −0.838757 | − | 0.544506i | \(-0.816717\pi\) | ||||
−0.838757 | + | 0.544506i | \(0.816717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.41314e40 | 1.42211 | 0.711055 | − | 0.703137i | \(-0.248218\pi\) | ||||
0.711055 | + | 0.703137i | \(0.248218\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.31706e39 | −0.446751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.36956e39 | 0.588225 | 0.294113 | − | 0.955771i | \(-0.404976\pi\) | ||||
0.294113 | + | 0.955771i | \(0.404976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.43229e39 | −0.261035 | −0.130518 | − | 0.991446i | \(-0.541664\pi\) | ||||
−0.130518 | + | 0.991446i | \(0.541664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.88449e40 | 1.42606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.85129e39 | 0.0769652 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07313e40 | −0.375803 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.28081e40 | −0.378445 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.87198e40 | 1.21659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.98494e40 | 0.842323 | 0.421161 | − | 0.906986i | \(-0.361623\pi\) | ||||
0.421161 | + | 0.906986i | \(0.361623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.09862e40 | −0.913713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.72341e40 | 0.262251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.73035e40 | 0.612136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.28927e41 | −1.42092 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.69963e41 | −1.59768 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.82214e40 | −0.306882 | −0.153441 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153441 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.13661e40 | −0.558791 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.02193e40 | 0.236582 | 0.118291 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118291 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.36117e41 | 0.686738 | 0.343369 | − | 0.939201i | \(-0.388432\pi\) | ||||
0.343369 | + | 0.939201i | \(0.388432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.63403e41 | 0.708026 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.52213e41 | 0.567184 | 0.283592 | − | 0.958945i | \(-0.408474\pi\) | ||||
0.283592 | + | 0.958945i | \(0.408474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.42412e41 | 0.456941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.14120e41 | 0.868959 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.23009e40 | −0.0771349 | −0.0385675 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385675 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.01250e41 | −1.65375 | −0.826875 | − | 0.562386i | \(-0.809884\pi\) | ||||
−0.826875 | + | 0.562386i | \(0.809884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.01769e41 | 1.07478 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.56012e41 | −0.241408 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.97040e41 | 1.06975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.75371e41 | −0.204394 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.02698e41 | −0.914644 | −0.457322 | − | 0.889301i | \(-0.651191\pi\) | ||||
−0.457322 | + | 0.889301i | \(0.651191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.81038e41 | −0.865120 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.19570e41 | 0.476033 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.85219e42 | −1.91139 | −0.955693 | − | 0.294367i | \(-0.904891\pi\) | ||||
−0.955693 | + | 0.294367i | \(0.904891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.92171e41 | 0.463525 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.28731e41 | −0.116981 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.38534e42 | −0.619911 | −0.309956 | − | 0.950751i | \(-0.600314\pi\) | ||||
−0.309956 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.29450e41 | 0.246694 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00541e42 | 1.37626 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.48754e42 | 1.95621 | 0.978105 | − | 0.208112i | \(-0.0667319\pi\) | ||||
0.978105 | + | 0.208112i | \(0.0667319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.20669e42 | −0.319619 | −0.159810 | − | 0.987148i | \(-0.551088\pi\) | ||||
−0.159810 | + | 0.987148i | \(0.551088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.67322e42 | 0.622569 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.23226e42 | −1.27739 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.45964e42 | 1.70796 | 0.853982 | − | 0.520303i | \(-0.174181\pi\) | ||||
0.853982 | + | 0.520303i | \(0.174181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.84444e42 | −0.930399 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.02911e43 | −1.44577 | −0.722887 | − | 0.690966i | \(-0.757185\pi\) | ||||
−0.722887 | + | 0.690966i | \(0.757185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.37988e42 | 0.171230 | 0.0856149 | − | 0.996328i | \(-0.472715\pi\) | ||||
0.0856149 | + | 0.996328i | \(0.472715\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.90546e42 | −0.318735 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.39530e42 | 0.523700 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17144e42 | 0.702403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.88513e43 | −1.43619 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.01953e42 | −0.609538 | −0.304769 | − | 0.952426i | \(-0.598579\pi\) | ||||
−0.304769 | + | 0.952426i | \(0.598579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.32075e42 | −0.439208 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.29520e43 | 0.690396 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.60495e43 | −0.760703 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.66468e42 | −0.365459 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.23549e43 | 1.21533 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.22102e42 | −0.0743542 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.42879e43 | 1.91959 | 0.959793 | − | 0.280708i | \(-0.0905694\pi\) | ||||
0.959793 | + | 0.280708i | \(0.0905694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.55416e43 | 1.74680 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.61324e43 | −1.81244 | −0.906218 | − | 0.422810i | \(-0.861044\pi\) | ||||
−0.906218 | + | 0.422810i | \(0.861044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.53058e43 | 1.17691 | 0.588457 | − | 0.808529i | \(-0.299736\pi\) | ||||
0.588457 | + | 0.808529i | \(0.299736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.68902e42 | −0.0702225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.88573e43 | −1.34371 | −0.671854 | − | 0.740684i | \(-0.734502\pi\) | ||||
−0.671854 | + | 0.740684i | \(0.734502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.75197e43 | −0.267418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.28416e42 | −0.127029 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.28751e43 | −1.13987 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.01958e44 | −1.12321 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.02114e44 | 1.99991 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.15995e43 | −0.636769 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.05747e42 | −0.0564493 | −0.0282247 | − | 0.999602i | \(-0.508985\pi\) | ||||
−0.0282247 | + | 0.999602i | \(0.508985\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.78742e43 | −0.704522 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98796e43 | −0.323325 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.23271e44 | 0.720007 | 0.360003 | − | 0.932951i | \(-0.382776\pi\) | ||||
0.360003 | + | 0.932951i | \(0.382776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.17500e44 | 1.67205 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.47657e44 | −2.12688 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.71886e44 | 0.737212 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.85053e43 | 0.226653 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.42984e43 | 0.330171 | 0.165085 | − | 0.986279i | \(-0.447210\pi\) | ||||
0.165085 | + | 0.986279i | \(0.447210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.06575e44 | 1.60398 | 0.801989 | − | 0.597339i | \(-0.203775\pi\) | ||||
0.801989 | + | 0.597339i | \(0.203775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.11890e44 | 0.607067 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.03174e43 | 0.182392 | 0.0911960 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911960 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.81672e43 | 0.207162 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.11497e44 | −0.663375 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.55482e44 | −1.65218 | −0.826091 | − | 0.563536i | \(-0.809440\pi\) | ||||
−0.826091 | + | 0.563536i | \(0.809440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35122e44 | −0.236783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.48974e44 | −1.19152 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.22944e44 | 0.322160 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.84210e44 | −0.373236 | −0.186618 | − | 0.982433i | \(-0.559753\pi\) | ||||
−0.186618 | + | 0.982433i | \(0.559753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.66600e44 | −0.795983 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.16464e44 | −0.343780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.75086e45 | 1.73120 | 0.865600 | − | 0.500735i | \(-0.166937\pi\) | ||||
0.865600 | + | 0.500735i | \(0.166937\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.76853e44 | 0.699506 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.86617e44 | −0.235141 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.12102e44 | −0.457760 | −0.228880 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228880 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55535e45 | 1.06082 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.71048e44 | −0.479847 | −0.239923 | − | 0.970792i | \(-0.577122\pi\) | ||||
−0.239923 | + | 0.970792i | \(0.577122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.82561e44 | −0.160528 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.07054e45 | 0.555469 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.82937e44 | 0.228967 | 0.114483 | − | 0.993425i | \(-0.463479\pi\) | ||||
0.114483 | + | 0.993425i | \(0.463479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.87016e45 | 0.810563 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.78499e44 | 0.229315 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.43187e44 | −0.197015 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.75288e44 | −0.290615 | −0.145307 | − | 0.989387i | \(-0.546417\pi\) | ||||
−0.145307 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.46076e45 | 0.444173 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.22212e45 | 0.619071 | 0.309535 | − | 0.950888i | \(-0.399827\pi\) | ||||
0.309535 | + | 0.950888i | \(0.399827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.32352e45 | −1.87017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.52060e45 | −0.356084 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.49671e45 | −1.61053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.00647e45 | −0.789958 | −0.394979 | − | 0.918690i | \(-0.629248\pi\) | ||||
−0.394979 | + | 0.918690i | \(0.629248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.99145e45 | 0.541565 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.68060e45 | 0.612058 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.03258e44 | 0.0463415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.04117e45 | −1.12964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.97513e45 | 1.03037 | 0.515184 | − | 0.857080i | \(-0.327724\pi\) | ||||
0.515184 | + | 0.857080i | \(0.327724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.79872e45 | 1.04588 | 0.522941 | − | 0.852369i | \(-0.324835\pi\) | ||||
0.522941 | + | 0.852369i | \(0.324835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.84626e45 | 0.967840 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.18806e46 | 1.19683 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.11665e45 | 0.103616 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.52980e46 | −2.16313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.04764e46 | 1.61399 | 0.806994 | − | 0.590559i | \(-0.201093\pi\) | ||||
0.806994 | + | 0.590559i | \(0.201093\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.27229e45 | −0.455920 | −0.227960 | − | 0.973671i | \(-0.573205\pi\) | ||||
−0.227960 | + | 0.973671i | \(0.573205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.04481e45 | 0.0700608 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.77010e45 | −0.542725 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.80675e45 | 0.217483 | 0.108742 | − | 0.994070i | \(-0.465318\pi\) | ||||
0.108742 | + | 0.994070i | \(0.465318\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.69105e45 | −0.511323 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.94774e46 | 0.949436 | 0.474718 | − | 0.880138i | \(-0.342550\pi\) | ||||
0.474718 | + | 0.880138i | \(0.342550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.92629e45 | −0.312033 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.06551e45 | −0.335931 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.66259e46 | 1.02564 | 0.512819 | − | 0.858497i | \(-0.328601\pi\) | ||||
0.512819 | + | 0.858497i | \(0.328601\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.10585e46 | −1.81961 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.00898e46 | −1.98190 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.62262e45 | −0.141152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.37152e46 | 0.670647 | 0.335323 | − | 0.942103i | \(-0.391154\pi\) | ||||
0.335323 | + | 0.942103i | \(0.391154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.46905e46 | −0.646857 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.97091e46 | 1.20690 | 0.603448 | − | 0.797402i | \(-0.293793\pi\) | ||||
0.603448 | + | 0.797402i | \(0.293793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14163e45 | −0.115727 | −0.0578633 | − | 0.998325i | \(-0.518429\pi\) | ||||
−0.0578633 | + | 0.998325i | \(0.518429\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.66965e46 | 0.557222 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.98000e45 | 0.135148 | 0.0675740 | − | 0.997714i | \(-0.478474\pi\) | ||||
0.0675740 | + | 0.997714i | \(0.478474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.50776e46 | 0.450569 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.59829e46 | 1.60077 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.19982e46 | 1.26980 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.57140e46 | −0.801358 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.90997e46 | 0.522519 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.34782e46 | −0.540007 | −0.270004 | − | 0.962859i | \(-0.587025\pi\) | ||||
−0.270004 | + | 0.962859i | \(0.587025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.22644e47 | −1.41614 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.94143e46 | −0.315852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.25982e46 | 0.325622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.39946e46 | 0.130078 | 0.0650391 | − | 0.997883i | \(-0.479283\pi\) | ||||
0.0650391 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.42503e46 | −0.123288 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.70380e47 | −1.37244 | −0.686218 | − | 0.727396i | \(-0.740730\pi\) | ||||
−0.686218 | + | 0.727396i | \(0.740730\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.33981e46 | 0.250553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.49110e46 | 0.243990 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.43272e46 | −0.288691 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00476e46 | 0.303825 | 0.151913 | − | 0.988394i | \(-0.451457\pi\) | ||||
0.151913 | + | 0.988394i | \(0.451457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.16523e47 | −0.659554 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.79753e46 | 0.200476 | 0.100238 | − | 0.994964i | \(-0.468040\pi\) | ||||
0.100238 | + | 0.994964i | \(0.468040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.59491e46 | −0.275546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.37846e47 | −0.633513 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.61088e47 | 0.691039 | 0.345520 | − | 0.938412i | \(-0.387703\pi\) | ||||
0.345520 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.12088e47 | −0.448945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.15786e47 | 0.433113 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13337e47 | −0.396045 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.77582e47 | 2.21247 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.56502e47 | 1.69839 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.24063e47 | −0.924634 | −0.462317 | − | 0.886715i | \(-0.652982\pi\) | ||||
−0.462317 | + | 0.886715i | \(0.652982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.80294e46 | 0.261563 | 0.130782 | − | 0.991411i | \(-0.458251\pi\) | ||||
0.130782 | + | 0.991411i | \(0.458251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.86861e47 | −0.466370 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.53374e47 | 1.99275 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.80990e47 | −0.614068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.54745e47 | −0.930280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.35301e47 | −1.59999 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.60545e46 | 0.0288008 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.53111e47 | −1.09758 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.42289e47 | −1.16888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.29578e47 | 0.338827 | 0.169413 | − | 0.985545i | \(-0.445813\pi\) | ||||
0.169413 | + | 0.985545i | \(0.445813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.07187e47 | 0.840089 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.49502e47 | −0.453431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.20054e47 | 0.754486 | 0.377243 | − | 0.926114i | \(-0.376872\pi\) | ||||
0.377243 | + | 0.926114i | \(0.376872\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.37964e47 | −0.157489 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.56620e47 | −0.167762 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.73094e47 | 0.274550 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.47075e47 | 0.421943 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.00082e48 | −1.77313 | −0.886567 | − | 0.462601i | \(-0.846916\pi\) | ||||
−0.886567 | + | 0.462601i | \(0.846916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.34147e48 | 1.11654 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.94785e48 | 2.30491 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.18076e48 | −1.60218 | −0.801091 | − | 0.598543i | \(-0.795747\pi\) | ||||
−0.801091 | + | 0.598543i | \(0.795747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.49033e47 | −0.379097 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.64500e47 | 0.496220 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.95181e48 | 1.19116 | 0.595582 | − | 0.803294i | \(-0.296921\pi\) | ||||
0.595582 | + | 0.803294i | \(0.296921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.74335e48 | −1.00058 | −0.500292 | − | 0.865857i | \(-0.666774\pi\) | ||||
−0.500292 | + | 0.865857i | \(0.666774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.94162e48 | 2.12798 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.12188e48 | 0.569846 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.93777e47 | −0.283822 | −0.141911 | − | 0.989879i | \(-0.545325\pi\) | ||||
−0.141911 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.00969e48 | −1.80400 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.52467e47 | −0.0645791 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.99485e48 | 1.19447 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.71133e47 | 0.214541 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.95184e48 | −1.75227 | −0.876133 | − | 0.482069i | \(-0.839886\pi\) | ||||
−0.876133 | + | 0.482069i | \(0.839886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00188e48 | −1.33428 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.37480e48 | −0.746184 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.92884e48 | −1.16361 | −0.581804 | − | 0.813329i | \(-0.697653\pi\) | ||||
−0.581804 | + | 0.813329i | \(0.697653\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.38651e47 | 0.150404 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.25763e48 | 0.331132 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.36641e48 | 0.835982 | 0.417991 | − | 0.908451i | \(-0.362734\pi\) | ||||
0.417991 | + | 0.908451i | \(0.362734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.17376e48 | 1.21200 | 0.606001 | − | 0.795464i | \(-0.292773\pi\) | ||||
0.606001 | + | 0.795464i | \(0.292773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.09839e48 | −0.684830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.29515e48 | 0.270148 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.08661e47 | 0.178896 | 0.0894478 | − | 0.995992i | \(-0.471490\pi\) | ||||
0.0894478 | + | 0.995992i | \(0.471490\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.25291e47 | −0.0976331 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10850e49 | 1.94543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.25008e47 | −0.0538686 | −0.0269343 | − | 0.999637i | \(-0.508574\pi\) | ||||
−0.0269343 | + | 0.999637i | \(0.508574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.04493e48 | 0.476720 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.17292e47 | 0.120889 | 0.0604445 | − | 0.998172i | \(-0.480748\pi\) | ||||
0.0604445 | + | 0.998172i | \(0.480748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.02467e49 | −1.43217 | −0.716087 | − | 0.698011i | \(-0.754069\pi\) | ||||
−0.716087 | + | 0.698011i | \(0.754069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.33150e48 | −0.307987 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.48228e48 | 0.434833 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.42631e48 | 0.758685 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.38239e49 | −1.54329 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.42911e49 | 1.50896 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.46353e49 | 1.46180 | 0.730898 | − | 0.682487i | \(-0.239101\pi\) | ||||
0.730898 | + | 0.682487i | \(0.239101\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.13070e49 | −1.06852 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.68956e48 | −0.240514 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21436e49 | −1.02780 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.47670e48 | 0.438788 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.87013e49 | −1.41859 | −0.709294 | − | 0.704913i | \(-0.750986\pi\) | ||||
−0.709294 | + | 0.704913i | \(0.750986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.63269e48 | −0.332768 | −0.166384 | − | 0.986061i | \(-0.553209\pi\) | ||||
−0.166384 | + | 0.986061i | \(0.553209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.89006e48 | −0.332674 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.11401e49 | 0.717898 | 0.358949 | − | 0.933357i | \(-0.383135\pi\) | ||||
0.358949 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.48313e49 | −2.12661 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.34220e49 | −0.776516 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.45552e49 | 1.34637 | 0.673184 | − | 0.739475i | \(-0.264926\pi\) | ||||
0.673184 | + | 0.739475i | \(0.264926\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00036e48 | −0.0519917 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.38487e49 | 0.682362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.88794e49 | 1.34925 | 0.674627 | − | 0.738159i | \(-0.264304\pi\) | ||||
0.674627 | + | 0.738159i | \(0.264304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.16569e49 | −0.516487 | −0.258243 | − | 0.966080i | \(-0.583144\pi\) | ||||
−0.258243 | + | 0.966080i | \(0.583144\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.82259e49 | 2.02672 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.52599e48 | −0.100705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.15374e48 | 0.119296 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.08450e49 | 0.389290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05674e49 | −0.360017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.78400e49 | 0.576940 | 0.288470 | − | 0.957489i | \(-0.406853\pi\) | ||||
0.288470 | + | 0.957489i | \(0.406853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.48114e49 | −0.454757 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.09002e49 | 0.317786 | 0.158893 | − | 0.987296i | \(-0.449208\pi\) | ||||
0.158893 | + | 0.987296i | \(0.449208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.63892e49 | −0.453770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.14119e49 | −0.300113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.96392e49 | −0.740465 | −0.370233 | − | 0.928939i | \(-0.620722\pi\) | ||||
−0.370233 | + | 0.928939i | \(0.620722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.17292e48 | −0.122787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.86221e49 | −0.871151 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.89949e49 | 1.05030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.67650e49 | −0.952916 | −0.476458 | − | 0.879197i | \(-0.658080\pi\) | ||||
−0.476458 | + | 0.879197i | \(0.658080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.75519e49 | −0.340012 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.39051e49 | 0.256117 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.73334e49 | 1.70486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.31894e49 | −0.719494 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.43229e49 | −1.01930 | −0.509648 | − | 0.860383i | \(-0.670224\pi\) | ||||
−0.509648 | + | 0.860383i | \(0.670224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.70177e49 | −1.01035 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.04084e49 | −0.579645 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.81291e49 | 0.383987 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.40300e49 | 0.182284 | 0.0911419 | − | 0.995838i | \(-0.470948\pi\) | ||||
0.0911419 | + | 0.995838i | \(0.470948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.37413e49 | −0.417295 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.05832e49 | 0.948807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.37461e49 | 0.490438 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.16513e48 | 0.0978484 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.96213e47 | 0.0101297 | 0.00506485 | − | 0.999987i | \(-0.498388\pi\) | ||||
0.00506485 | + | 0.999987i | \(0.498388\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.69815e49 | 0.551908 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.27349e50 | 2.09784 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00349e49 | 0.176145 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.68047e49 | 0.811043 | 0.405522 | − | 0.914085i | \(-0.367090\pi\) | ||||
0.405522 | + | 0.914085i | \(0.367090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.56944e49 | −0.125318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.56314e50 | −1.18972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.44337e49 | 0.394956 | 0.197478 | − | 0.980307i | \(-0.436725\pi\) | ||||
0.197478 | + | 0.980307i | \(0.436725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.42673e49 | 0.306235 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.37322e50 | −1.56551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56111e49 | 0.349852 | 0.174926 | − | 0.984582i | \(-0.444031\pi\) | ||||
0.174926 | + | 0.984582i | \(0.444031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.26154e50 | −1.35702 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.67574e50 | −0.959185 | −0.479593 | − | 0.877491i | \(-0.659216\pi\) | ||||
−0.479593 | + | 0.877491i | \(0.659216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.39472e49 | 0.0761642 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.88375e49 | 0.0981553 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.07160e48 | −0.0401354 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.20459e50 | −1.52081 | −0.760403 | − | 0.649451i | \(-0.774999\pi\) | ||||
−0.760403 | + | 0.649451i | \(0.774999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.56134e50 | 1.16026 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.03909e50 | 0.449348 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.86478e49 | −0.159568 | −0.0797842 | − | 0.996812i | \(-0.525423\pi\) | ||||
−0.0797842 | + | 0.996812i | \(0.525423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.78362e50 | 1.09744 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.82364e50 | −0.686607 | −0.343303 | − | 0.939225i | \(-0.611546\pi\) | ||||
−0.343303 | + | 0.939225i | \(0.611546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.75717e50 | 0.631878 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.65513e49 | −0.228603 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.69830e50 | −1.86993 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.28112e50 | −1.02875 | −0.514376 | − | 0.857565i | \(-0.671976\pi\) | ||||
−0.514376 | + | 0.857565i | \(0.671976\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.09287e50 | 2.42466 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.84696e50 | 0.815156 | 0.407578 | − | 0.913170i | \(-0.366373\pi\) | ||||
0.407578 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.11923e50 | 1.40096 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.24773e50 | −0.587998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.56443e50 | −1.14151 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.19490e50 | 1.00306 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.16368e49 | −0.0952020 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.65977e50 | −0.362935 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.44639e50 | 1.55736 | 0.778678 | − | 0.627423i | \(-0.215890\pi\) | ||||
0.778678 | + | 0.627423i | \(0.215890\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.93079e50 | 0.786379 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.76033e50 | 0.528290 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.72879e50 | −0.316564 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.78602e50 | −0.312940 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.39179e50 | −1.07177 | −0.535885 | − | 0.844291i | \(-0.680022\pi\) | ||||
−0.535885 | + | 0.844291i | \(0.680022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.29168e51 | −2.07294 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.30242e50 | −0.660912 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.06075e51 | 1.55987 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.08642e49 | 0.0716118 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.84079e51 | −2.48152 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71253e50 | 0.221074 | 0.110537 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110537 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.82188e50 | −1.09068 | −0.545338 | − | 0.838216i | \(-0.683599\pi\) | ||||
−0.545338 | + | 0.838216i | \(0.683599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.42389e50 | 0.405449 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.46422e49 | 0.0279525 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.33033e50 | 0.796595 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.87144e50 | −0.298973 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.26416e50 | 0.525199 | 0.262600 | − | 0.964905i | \(-0.415420\pi\) | ||||
0.262600 | + | 0.964905i | \(0.415420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.49543e50 | 0.907857 | 0.453929 | − | 0.891038i | \(-0.350022\pi\) | ||||
0.453929 | + | 0.891038i | \(0.350022\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.76836e51 | 1.62041 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.29171e48 | −0.00376950 | −0.00188475 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188475 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.30923e50 | 0.699611 | 0.349805 | − | 0.936822i | \(-0.386248\pi\) | ||||
0.349805 | + | 0.936822i | \(0.386248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.68410e51 | −2.16661 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.41504e51 | 1.09517 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.01495e50 | 0.149538 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.06389e51 | −0.757181 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.65560e50 | 0.590831 | 0.295415 | − | 0.955369i | \(-0.404542\pi\) | ||||
0.295415 | + | 0.955369i | \(0.404542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47100e51 | −0.963125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.92002e51 | 1.83402 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.38369e50 | 0.143634 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.51154e50 | −0.376465 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.91531e50 | −0.217211 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.34949e51 | 0.718460 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.25142e51 | −0.639433 | −0.319716 | − | 0.947513i | \(-0.603588\pi\) | ||||
−0.319716 | + | 0.947513i | \(0.603588\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.12091e50 | 0.153065 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.39052e50 | 0.0654656 | 0.0327328 | − | 0.999464i | \(-0.489579\pi\) | ||||
0.0327328 | + | 0.999464i | \(0.489579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.12695e50 | −0.231728 | −0.115864 | − | 0.993265i | \(-0.536964\pi\) | ||||
−0.115864 | + | 0.993265i | \(0.536964\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.53088e51 | −0.664332 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.92641e50 | 0.163609 | 0.0818045 | − | 0.996648i | \(-0.473932\pi\) | ||||
0.0818045 | + | 0.996648i | \(0.473932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.62323e50 | −0.385069 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.31859e51 | −0.891023 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.58442e51 | −0.953932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.88251e51 | −1.37656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.02491e51 | 0.689695 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.75392e50 | 0.221011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.47786e51 | −1.09350 | −0.546750 | − | 0.837296i | \(-0.684135\pi\) | ||||
−0.546750 | + | 0.837296i | \(0.684135\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.55922e51 | 0.773220 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.02605e51 | −0.588264 | −0.294132 | − | 0.955765i | \(-0.595031\pi\) | ||||
−0.294132 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.52091e51 | 1.54063 | 0.770315 | − | 0.637663i | \(-0.220099\pi\) | ||||
0.770315 | + | 0.637663i | \(0.220099\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.07721e51 | 0.557151 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.31525e51 | 1.88611 | 0.943053 | − | 0.332643i | \(-0.107940\pi\) | ||||
0.943053 | + | 0.332643i | \(0.107940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.35221e51 | 0.335169 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.23485e51 | −1.72413 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.05733e51 | 1.38797 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.12938e51 | 0.248850 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.55392e51 | 0.964978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.43908e51 | 0.293286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.70913e51 | −1.11914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.45854e51 | 0.463598 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.04997e51 | −0.190470 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.23219e50 | 0.0215055 | 0.0107528 | − | 0.999942i | \(-0.496577\pi\) | ||||
0.0107528 | + | 0.999942i | \(0.496577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.47541e51 | −0.583630 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.49346e51 | −1.04931 | −0.524656 | − | 0.851314i | \(-0.675806\pi\) | ||||
−0.524656 | + | 0.851314i | \(0.675806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.44287e51 | 0.224382 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.30199e50 | 0.0943210 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.02944e50 | 0.0724530 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.52733e51 | 0.627799 | 0.313899 | − | 0.949456i | \(-0.398365\pi\) | ||||
0.313899 | + | 0.949456i | \(0.398365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.82412e52 | −2.43506 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.86273e51 | 0.881997 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.57294e51 | 1.06084 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.04018e51 | −0.838857 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.76706e51 | −0.776471 | −0.388235 | − | 0.921560i | \(-0.626915\pi\) | ||||
−0.388235 | + | 0.921560i | \(0.626915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.63578e51 | −0.733285 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.16020e52 | 2.29914 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.09752e51 | −0.522583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.49743e51 | −0.444142 | −0.222071 | − | 0.975030i | \(-0.571282\pi\) | ||||
−0.222071 | + | 0.975030i | \(0.571282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.56926e52 | −1.49296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.33504e52 | −1.22370 | −0.611850 | − | 0.790974i | \(-0.709574\pi\) | ||||
−0.611850 | + | 0.790974i | \(0.709574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.19109e51 | 0.811732 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.71526e50 | −0.0571487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.72665e51 | −0.797698 | −0.398849 | − | 0.917017i | \(-0.630590\pi\) | ||||
−0.398849 | + | 0.917017i | \(0.630590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.73535e52 | 1.37160 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.23752e52 | 1.70454 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.57100e52 | 1.15358 | 0.576792 | − | 0.816891i | \(-0.304304\pi\) | ||||
0.576792 | + | 0.816891i | \(0.304304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.81598e51 | −0.482469 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.97109e51 | 0.339229 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.60075e51 | 0.171109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.10071e52 | 1.33262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.97261e50 | 0.0610027 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.93369e51 | 0.409012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.31887e52 | −0.750307 | −0.375154 | − | 0.926963i | \(-0.622410\pi\) | ||||
−0.375154 | + | 0.926963i | \(0.622410\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.63526e52 | 1.44597 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.45878e52 | −1.83057 | −0.915285 | − | 0.402806i | \(-0.868035\pi\) | ||||
−0.915285 | + | 0.402806i | \(0.868035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.99095e51 | −0.356912 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.89298e52 | 1.42483 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.79825e52 | −1.80480 | −0.902400 | − | 0.430900i | \(-0.858196\pi\) | ||||
−0.902400 | + | 0.430900i | \(0.858196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.29545e52 | −1.51084 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.17101e52 | −0.960406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.22067e51 | −0.222864 | −0.111432 | − | 0.993772i | \(-0.535544\pi\) | ||||
−0.111432 | + | 0.993772i | \(0.535544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.10659e51 | 0.169179 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.03158e52 | 0.807764 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.47606e52 | −0.566459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.70299e52 | 1.00128 | 0.500639 | − | 0.865656i | \(-0.333098\pi\) | ||||
0.500639 | + | 0.865656i | \(0.333098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00250e51 | 0.0716080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.17474e51 | −0.0750762 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14317e52 | −1.38092 | −0.690459 | − | 0.723372i | \(-0.742591\pi\) | ||||
−0.690459 | + | 0.723372i | \(0.742591\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.78164e52 | −0.573356 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 4.36.a.a.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 16.36.a.c.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.36.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.36.a.c.1.3 | 3 | 4.3 | odd | 2 |