Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(115.883063137\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.0000 | 0.972272 | 0.486136 | − | 0.873883i | \(-0.338406\pi\) | ||||
0.486136 | + | 0.873883i | \(0.338406\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −28.0000 | −0.0546875 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5988.00 | 0.942629 | 0.471314 | − | 0.881965i | \(-0.343780\pi\) | ||||
0.471314 | + | 0.881965i | \(0.343780\pi\) | |||||||
\(8\) | −11880.0 | −1.02544 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14648.0 | 0.301655 | 0.150828 | − | 0.988560i | \(-0.451806\pi\) | ||||
0.150828 | + | 0.988560i | \(0.451806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37906.0 | −0.368098 | −0.184049 | − | 0.982917i | \(-0.558920\pi\) | ||||
−0.184049 | + | 0.982917i | \(0.558920\pi\) | |||||||
\(14\) | 131736. | 0.916491 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −247024. | −0.942322 | ||||||||
\(17\) | −441098. | −1.28090 | −0.640450 | − | 0.768000i | \(-0.721252\pi\) | ||||
−0.640450 | + | 0.768000i | \(0.721252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 441820. | 0.777775 | 0.388888 | − | 0.921285i | \(-0.372859\pi\) | ||||
0.388888 | + | 0.921285i | \(0.372859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 322256. | 0.293291 | ||||||||
\(23\) | 2.26414e6 | 1.68705 | 0.843524 | − | 0.537092i | \(-0.180477\pi\) | ||||
0.843524 | + | 0.537092i | \(0.180477\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −833932. | −0.357891 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −167664. | −0.0515500 | ||||||||
\(29\) | 1.04935e6 | 0.275505 | 0.137752 | − | 0.990467i | \(-0.456012\pi\) | ||||
0.137752 | + | 0.990467i | \(0.456012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.91057e6 | −1.53844 | −0.769219 | − | 0.638985i | \(-0.779355\pi\) | ||||
−0.769219 | + | 0.638985i | \(0.779355\pi\) | |||||||
\(32\) | 648032. | 0.109250 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.70416e6 | −1.24538 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.09926e7 | 1.84144 | 0.920720 | − | 0.390224i | \(-0.127602\pi\) | ||||
0.920720 | + | 0.390224i | \(0.127602\pi\) | |||||||
\(38\) | 9.72004e6 | 0.756209 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.32856e7 | −0.734265 | −0.367132 | − | 0.930169i | \(-0.619660\pi\) | ||||
−0.367132 | + | 0.930169i | \(0.619660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.31308e7 | 1.03177 | 0.515884 | − | 0.856659i | \(-0.327464\pi\) | ||||
0.515884 | + | 0.856659i | \(0.327464\pi\) | |||||||
\(44\) | −410144. | −0.0164968 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.98110e7 | 1.64027 | ||||||||
\(47\) | −1.38737e7 | −0.414717 | −0.207358 | − | 0.978265i | \(-0.566487\pi\) | ||||
−0.207358 | + | 0.978265i | \(0.566487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.49746e6 | −0.111451 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.06137e6 | 0.0201303 | ||||||||
\(53\) | −5.76352e7 | −1.00334 | −0.501668 | − | 0.865060i | \(-0.667280\pi\) | ||||
−0.501668 | + | 0.865060i | \(0.667280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.11374e7 | −0.966612 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.30857e7 | 0.267866 | ||||||||
\(59\) | 3.20421e7 | 0.344260 | 0.172130 | − | 0.985074i | \(-0.444935\pi\) | ||||
0.172130 | + | 0.985074i | \(0.444935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.10664e8 | 1.02335 | 0.511673 | − | 0.859180i | \(-0.329026\pi\) | ||||
0.511673 | + | 0.859180i | \(0.329026\pi\) | |||||||
\(62\) | −1.74032e8 | −1.49578 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.40733e8 | 1.04854 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.18568e8 | 0.718839 | 0.359420 | − | 0.933176i | \(-0.382975\pi\) | ||||
0.359420 | + | 0.933176i | \(0.382975\pi\) | |||||||
\(68\) | 1.23507e7 | 0.0700492 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.76680e8 | −1.29216 | −0.646078 | − | 0.763272i | \(-0.723592\pi\) | ||||
−0.646078 | + | 0.763272i | \(0.723592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.64023e8 | 1.08815 | 0.544076 | − | 0.839036i | \(-0.316880\pi\) | ||||
0.544076 | + | 0.839036i | \(0.316880\pi\) | |||||||
\(74\) | 4.61836e8 | 1.79038 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23710e7 | −0.0425346 | ||||||||
\(77\) | 8.77122e7 | 0.284349 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.48203e8 | 1.29465 | 0.647325 | − | 0.762214i | \(-0.275888\pi\) | ||||
0.647325 | + | 0.762214i | \(0.275888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.92282e8 | −0.713905 | ||||||||
\(83\) | 8.51016e8 | 1.96828 | 0.984138 | − | 0.177402i | \(-0.0567693\pi\) | ||||
0.984138 | + | 0.177402i | \(0.0567693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.08877e8 | 1.00316 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.74018e8 | −0.309331 | ||||||||
\(89\) | −1.89895e8 | −0.320818 | −0.160409 | − | 0.987051i | \(-0.551281\pi\) | ||||
−0.160409 | + | 0.987051i | \(0.551281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.26981e8 | −0.346979 | ||||||||
\(92\) | −6.33958e7 | −0.0922604 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.05221e8 | −0.403217 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01415e9 | 1.16313 | 0.581566 | − | 0.813499i | \(-0.302440\pi\) | ||||
0.581566 | + | 0.813499i | \(0.302440\pi\) | |||||||
\(98\) | −9.89442e7 | −0.108361 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.31537e9 | 1.25777 | 0.628885 | − | 0.777498i | \(-0.283512\pi\) | ||||
0.628885 | + | 0.777498i | \(0.283512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.82797e9 | 1.60030 | 0.800151 | − | 0.599798i | \(-0.204752\pi\) | ||||
0.800151 | + | 0.599798i | \(0.204752\pi\) | |||||||
\(104\) | 4.50323e8 | 0.377463 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.26797e9 | −0.975515 | ||||||||
\(107\) | 1.85367e8 | 0.136712 | 0.0683559 | − | 0.997661i | \(-0.478225\pi\) | ||||
0.0683559 | + | 0.997661i | \(0.478225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.97869e9 | 1.34264 | 0.671318 | − | 0.741169i | \(-0.265728\pi\) | ||||
0.671318 | + | 0.741169i | \(0.265728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.47918e9 | −0.888259 | ||||||||
\(113\) | 1.57875e9 | 0.910876 | 0.455438 | − | 0.890267i | \(-0.349483\pi\) | ||||
0.455438 | + | 0.890267i | \(0.349483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.93818e7 | −0.0150667 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.04927e8 | 0.334715 | ||||||||
\(119\) | −2.64129e9 | −1.20741 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14338e9 | −0.909004 | ||||||||
\(122\) | 2.43461e9 | 0.994970 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.21496e8 | 0.0841333 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.40001e9 | −0.818645 | −0.409322 | − | 0.912390i | \(-0.634235\pi\) | ||||
−0.409322 | + | 0.912390i | \(0.634235\pi\) | |||||||
\(128\) | 2.76433e9 | 0.910218 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.96840e9 | 0.583971 | 0.291986 | − | 0.956423i | \(-0.405684\pi\) | ||||
0.291986 | + | 0.956423i | \(0.405684\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64562e9 | 0.733153 | ||||||||
\(134\) | 2.60850e9 | 0.698907 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.24024e9 | 1.31349 | ||||||||
\(137\) | −2.02909e9 | −0.492107 | −0.246054 | − | 0.969256i | \(-0.579134\pi\) | ||||
−0.246054 | + | 0.969256i | \(0.579134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.13673e9 | −0.258280 | −0.129140 | − | 0.991626i | \(-0.541222\pi\) | ||||
−0.129140 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.08695e9 | −1.25633 | ||||||||
\(143\) | −5.55247e8 | −0.111039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.80851e9 | 1.05798 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.87792e8 | −0.100704 | ||||||||
\(149\) | 4.73854e9 | 0.787601 | 0.393800 | − | 0.919196i | \(-0.371160\pi\) | ||||
0.393800 | + | 0.919196i | \(0.371160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26216e9 | 0.354101 | 0.177051 | − | 0.984202i | \(-0.443344\pi\) | ||||
0.177051 | + | 0.984202i | \(0.443344\pi\) | |||||||
\(152\) | −5.24882e9 | −0.797564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.92967e9 | 0.276465 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.17889e10 | 1.54854 | 0.774272 | − | 0.632853i | \(-0.218116\pi\) | ||||
0.774272 | + | 0.632853i | \(0.218116\pi\) | |||||||
\(158\) | 9.86046e9 | 1.25875 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.35576e10 | 1.59026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.14608e10 | −1.27166 | −0.635829 | − | 0.771830i | \(-0.719342\pi\) | ||||
−0.635829 | + | 0.771830i | \(0.719342\pi\) | |||||||
\(164\) | 3.71996e8 | 0.0401551 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.87223e10 | 1.91370 | ||||||||
\(167\) | −1.33707e10 | −1.33024 | −0.665118 | − | 0.746738i | \(-0.731619\pi\) | ||||
−0.665118 | + | 0.746738i | \(0.731619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.16763e9 | −0.864504 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.47661e8 | −0.0564248 | ||||||||
\(173\) | 1.06264e10 | 0.901939 | 0.450970 | − | 0.892539i | \(-0.351078\pi\) | ||||
0.450970 | + | 0.892539i | \(0.351078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.61841e9 | −0.284257 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.17769e9 | −0.311922 | ||||||||
\(179\) | −2.61254e10 | −1.90206 | −0.951031 | − | 0.309094i | \(-0.899974\pi\) | ||||
−0.951031 | + | 0.309094i | \(0.899974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34689e9 | 0.162532 | 0.0812660 | − | 0.996692i | \(-0.474104\pi\) | ||||
0.0812660 | + | 0.996692i | \(0.474104\pi\) | |||||||
\(182\) | −4.99358e9 | −0.337358 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.68979e10 | −1.72997 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.46120e9 | −0.386390 | ||||||||
\(188\) | 3.88463e8 | 0.0226798 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.24064e10 | −1.21821 | −0.609105 | − | 0.793089i | \(-0.708471\pi\) | ||||
−0.609105 | + | 0.793089i | \(0.708471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65959e10 | 1.89856 | 0.949282 | − | 0.314427i | \(-0.101812\pi\) | ||||
0.949282 | + | 0.314427i | \(0.101812\pi\) | |||||||
\(194\) | 2.23113e10 | 1.13088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.25929e8 | 0.00609499 | ||||||||
\(197\) | −5.41546e9 | −0.256175 | −0.128088 | − | 0.991763i | \(-0.540884\pi\) | ||||
−0.128088 | + | 0.991763i | \(0.540884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.62714e8 | 0.0118753 | 0.00593764 | − | 0.999982i | \(-0.498110\pi\) | ||||
0.00593764 | + | 0.999982i | \(0.498110\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.89381e10 | 1.22289 | ||||||||
\(203\) | 6.28351e9 | 0.259699 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.02154e10 | 1.55593 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.36369e9 | 0.346866 | ||||||||
\(209\) | 6.47178e9 | 0.234620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34493e10 | 0.467121 | 0.233560 | − | 0.972342i | \(-0.424962\pi\) | ||||
0.233560 | + | 0.972342i | \(0.424962\pi\) | |||||||
\(212\) | 1.61378e9 | 0.0548699 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.07808e9 | 0.132921 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.73685e10 | −1.45018 | ||||||||
\(218\) | 4.35312e10 | 1.30541 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.67203e10 | 0.471496 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.66463e10 | 0.721547 | 0.360773 | − | 0.932654i | \(-0.382513\pi\) | ||||
0.360773 | + | 0.932654i | \(0.382513\pi\) | |||||||
\(224\) | 3.88042e9 | 0.102982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.47324e10 | 0.885619 | ||||||||
\(227\) | 3.36318e10 | 0.840686 | 0.420343 | − | 0.907365i | \(-0.361910\pi\) | ||||
0.420343 | + | 0.907365i | \(0.361910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00453e10 | 1.20255 | 0.601276 | − | 0.799042i | \(-0.294659\pi\) | ||||
0.601276 | + | 0.799042i | \(0.294659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.24663e10 | −0.282515 | ||||||||
\(233\) | −3.29626e10 | −0.732688 | −0.366344 | − | 0.930479i | \(-0.619391\pi\) | ||||
−0.366344 | + | 0.930479i | \(0.619391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.97179e8 | −0.0188267 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.81085e10 | −1.17393 | ||||||||
\(239\) | 7.95422e9 | 0.157691 | 0.0788455 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788455 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.52477e10 | −1.43687 | −0.718434 | − | 0.695595i | \(-0.755141\pi\) | ||||
−0.718434 | + | 0.695595i | \(0.755141\pi\) | |||||||
\(242\) | −4.71544e10 | −0.883799 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.09859e9 | −0.0559642 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.67476e10 | −0.286297 | ||||||||
\(248\) | 9.39775e10 | 1.57758 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.84631e10 | 1.56582 | 0.782910 | − | 0.622135i | \(-0.213734\pi\) | ||||
0.782910 | + | 0.622135i | \(0.213734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.31651e10 | 0.508907 | ||||||||
\(254\) | −5.28001e10 | −0.795945 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.12400e10 | −0.163563 | ||||||||
\(257\) | 8.52399e9 | 0.121883 | 0.0609416 | − | 0.998141i | \(-0.480590\pi\) | ||||
0.0609416 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.25703e11 | 1.73579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.33047e10 | 0.567779 | ||||||||
\(263\) | 5.90654e9 | 0.0761259 | 0.0380630 | − | 0.999275i | \(-0.487881\pi\) | ||||
0.0380630 | + | 0.999275i | \(0.487881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.82036e10 | 0.712824 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.31991e9 | −0.0393115 | ||||||||
\(269\) | 7.15961e10 | 0.833689 | 0.416845 | − | 0.908978i | \(-0.363136\pi\) | ||||
0.416845 | + | 0.908978i | \(0.363136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24755e11 | −1.40506 | −0.702530 | − | 0.711654i | \(-0.747946\pi\) | ||||
−0.702530 | + | 0.711654i | \(0.747946\pi\) | |||||||
\(272\) | 1.08962e11 | 1.20702 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.46401e10 | −0.478462 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12824e11 | −1.15145 | −0.575723 | − | 0.817645i | \(-0.695279\pi\) | ||||
−0.575723 | + | 0.817645i | \(0.695279\pi\) | |||||||
\(278\) | −2.50080e10 | −0.251118 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.70208e10 | −0.832616 | −0.416308 | − | 0.909224i | \(-0.636676\pi\) | ||||
−0.416308 | + | 0.909224i | \(0.636676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.27696e9 | −0.0303692 | −0.0151846 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151846 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(284\) | 7.74703e9 | 0.0706647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.22154e10 | −0.107960 | ||||||||
\(287\) | −7.95539e10 | −0.692139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.59796e10 | 0.640703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.39265e9 | −0.0595083 | ||||||||
\(293\) | −1.49860e11 | −1.18791 | −0.593953 | − | 0.804500i | \(-0.702433\pi\) | ||||
−0.593953 | + | 0.804500i | \(0.702433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.49392e11 | −1.88829 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.04248e11 | 0.765762 | ||||||||
\(299\) | −8.58243e10 | −0.620998 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38507e11 | 0.972574 | ||||||||
\(302\) | 4.97676e10 | 0.344283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.09140e11 | −0.732915 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.84570e11 | 1.18587 | 0.592937 | − | 0.805249i | \(-0.297968\pi\) | ||||
0.592937 | + | 0.805249i | \(0.297968\pi\) | |||||||
\(308\) | −2.45594e9 | −0.0155503 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.04650e10 | −0.548351 | −0.274176 | − | 0.961680i | \(-0.588405\pi\) | ||||
−0.274176 | + | 0.961680i | \(0.588405\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.07930e10 | −0.0635615 | −0.0317808 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317808 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(314\) | 2.59355e11 | 1.50560 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.25497e10 | −0.0708012 | ||||||||
\(317\) | 4.18319e10 | 0.232670 | 0.116335 | − | 0.993210i | \(-0.462885\pi\) | ||||
0.116335 | + | 0.993210i | \(0.462885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.53709e10 | 0.0831076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.98268e11 | 1.54616 | ||||||||
\(323\) | −1.94886e11 | −0.996252 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.52137e11 | −1.23640 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.57832e11 | 0.752946 | ||||||||
\(329\) | −8.30756e10 | −0.390924 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23310e10 | −0.0564640 | −0.0282320 | − | 0.999601i | \(-0.508988\pi\) | ||||
−0.0282320 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(332\) | −2.38284e10 | −0.107640 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.94154e11 | −1.29335 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17976e10 | 0.0920606 | 0.0460303 | − | 0.998940i | \(-0.485343\pi\) | ||||
0.0460303 | + | 0.998940i | \(0.485343\pi\) | |||||||
\(338\) | −2.01688e11 | −0.840533 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.15874e11 | −0.464078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.68568e11 | −1.04769 | ||||||||
\(344\) | −2.74793e11 | −1.05802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.33780e11 | 0.876930 | ||||||||
\(347\) | −8.43613e10 | −0.312364 | −0.156182 | − | 0.987728i | \(-0.549919\pi\) | ||||
−0.156182 | + | 0.987728i | \(0.549919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.23295e9 | −0.00444867 | −0.00222434 | − | 0.999998i | \(-0.500708\pi\) | ||||
−0.00222434 | + | 0.999998i | \(0.500708\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.49237e9 | 0.0329559 | ||||||||
\(353\) | 1.73388e11 | 0.594336 | 0.297168 | − | 0.954825i | \(-0.403958\pi\) | ||||
0.297168 | + | 0.954825i | \(0.403958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.31706e9 | 0.0175447 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.74760e11 | −1.84932 | ||||||||
\(359\) | −6.38159e10 | −0.202770 | −0.101385 | − | 0.994847i | \(-0.532327\pi\) | ||||
−0.101385 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.27483e11 | −0.395066 | ||||||||
\(362\) | 5.16316e10 | 0.158025 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.35547e9 | 0.0189754 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.12242e11 | −0.322966 | −0.161483 | − | 0.986876i | \(-0.551628\pi\) | ||||
−0.161483 | + | 0.986876i | \(0.551628\pi\) | |||||||
\(368\) | −5.59296e11 | −1.58974 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.45119e11 | −0.945773 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.21004e11 | −1.92863 | −0.964313 | − | 0.264766i | \(-0.914705\pi\) | ||||
−0.964313 | + | 0.264766i | \(0.914705\pi\) | |||||||
\(374\) | −1.42146e11 | −0.375676 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.64819e11 | 0.425268 | ||||||||
\(377\) | −3.97767e10 | −0.101413 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.04331e11 | −0.508695 | −0.254348 | − | 0.967113i | \(-0.581861\pi\) | ||||
−0.254348 | + | 0.967113i | \(0.581861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.92941e11 | −1.18443 | ||||||||
\(383\) | −5.47180e11 | −1.29938 | −0.649689 | − | 0.760200i | \(-0.725101\pi\) | ||||
−0.649689 | + | 0.760200i | \(0.725101\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.05111e11 | 1.84592 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.83962e10 | −0.0636088 | ||||||||
\(389\) | 3.46262e11 | 0.766711 | 0.383356 | − | 0.923601i | \(-0.374768\pi\) | ||||
0.383356 | + | 0.923601i | \(0.374768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.98706e11 | −2.16094 | ||||||||
\(392\) | 5.34299e10 | 0.114287 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.19140e11 | −0.249072 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.56758e11 | −0.518760 | −0.259380 | − | 0.965775i | \(-0.583518\pi\) | ||||
−0.259380 | + | 0.965775i | \(0.583518\pi\) | |||||||
\(398\) | 5.77971e9 | 0.0115460 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.01679e10 | −0.0389504 | −0.0194752 | − | 0.999810i | \(-0.506200\pi\) | ||||
−0.0194752 | + | 0.999810i | \(0.506200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.99858e11 | 0.566295 | ||||||||
\(404\) | −3.68303e10 | −0.0687843 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38237e11 | 0.252498 | ||||||||
\(407\) | 3.07499e11 | 0.555481 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.33405e10 | −0.0765842 | −0.0382921 | − | 0.999267i | \(-0.512192\pi\) | ||||
−0.0382921 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.11832e10 | −0.0875166 | ||||||||
\(413\) | 1.91868e11 | 0.324510 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.45643e10 | −0.0402147 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.42379e11 | 0.228115 | ||||||||
\(419\) | −5.10680e11 | −0.809443 | −0.404721 | − | 0.914440i | \(-0.632631\pi\) | ||||
−0.404721 | + | 0.914440i | \(0.632631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.21228e11 | 0.498361 | 0.249181 | − | 0.968457i | \(-0.419839\pi\) | ||||
0.249181 | + | 0.968457i | \(0.419839\pi\) | |||||||
\(422\) | 2.95885e11 | 0.454168 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.84706e11 | 1.02886 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.62656e11 | 0.964635 | ||||||||
\(428\) | −5.19029e9 | −0.00747643 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.47617e11 | −0.624826 | −0.312413 | − | 0.949946i | \(-0.601137\pi\) | ||||
−0.312413 | + | 0.949946i | \(0.601137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.41186e11 | 0.193017 | 0.0965085 | − | 0.995332i | \(-0.469233\pi\) | ||||
0.0965085 | + | 0.995332i | \(0.469233\pi\) | |||||||
\(434\) | −1.04211e12 | −1.40997 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.54033e10 | −0.0734254 | ||||||||
\(437\) | 1.00034e12 | 1.31214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.50498e11 | −1.09291 | −0.546453 | − | 0.837490i | \(-0.684022\pi\) | ||||
−0.546453 | + | 0.837490i | \(0.684022\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.67846e11 | 0.458422 | ||||||||
\(443\) | 3.03188e11 | 0.374020 | 0.187010 | − | 0.982358i | \(-0.440120\pi\) | ||||
0.187010 | + | 0.982358i | \(0.440120\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.86218e11 | 0.701540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.42709e11 | 0.988386 | ||||||||
\(449\) | 1.40328e12 | 1.62943 | 0.814714 | − | 0.579863i | \(-0.196894\pi\) | ||||
0.814714 | + | 0.579863i | \(0.196894\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.94607e11 | −0.221495 | ||||||||
\(452\) | −4.42049e10 | −0.0498136 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.39899e11 | 0.817375 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.35354e11 | −0.359650 | −0.179825 | − | 0.983699i | \(-0.557553\pi\) | ||||
−0.179825 | + | 0.983699i | \(0.557553\pi\) | |||||||
\(458\) | 1.10100e12 | 1.16921 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.04275e12 | −1.07529 | −0.537645 | − | 0.843171i | \(-0.680686\pi\) | ||||
−0.537645 | + | 0.843171i | \(0.680686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.74084e11 | 0.985103 | 0.492552 | − | 0.870283i | \(-0.336064\pi\) | ||||
0.492552 | + | 0.870283i | \(0.336064\pi\) | |||||||
\(464\) | −2.59215e11 | −0.259614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.25176e11 | −0.712372 | ||||||||
\(467\) | −1.97851e11 | −0.192492 | −0.0962458 | − | 0.995358i | \(-0.530683\pi\) | ||||
−0.0962458 | + | 0.995358i | \(0.530683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.09987e11 | 0.677599 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.80660e11 | −0.353019 | ||||||||
\(473\) | 3.38819e11 | 0.311238 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.39563e10 | 0.0660304 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.74993e11 | 0.153319 | ||||||||
\(479\) | 9.08731e11 | 0.788725 | 0.394362 | − | 0.918955i | \(-0.370965\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.95744e11 | −0.677830 | ||||||||
\(482\) | −1.65545e12 | −1.39703 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.00147e10 | 0.0497112 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.16963e12 | −0.942254 | −0.471127 | − | 0.882065i | \(-0.656153\pi\) | ||||
−0.471127 | + | 0.882065i | \(0.656153\pi\) | |||||||
\(488\) | −1.31469e12 | −1.04938 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.49149e12 | 1.93460 | 0.967301 | − | 0.253630i | \(-0.0816246\pi\) | ||||
0.967301 | + | 0.253630i | \(0.0816246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.62866e11 | −0.352894 | ||||||||
\(494\) | −3.68448e11 | −0.278359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.95410e12 | 1.44970 | ||||||||
\(497\) | −1.65676e12 | −1.21802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.57571e11 | −0.402576 | −0.201288 | − | 0.979532i | \(-0.564513\pi\) | ||||
−0.201288 | + | 0.979532i | \(0.564513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.16619e12 | 1.52240 | ||||||||
\(503\) | 1.80137e12 | 1.25472 | 0.627359 | − | 0.778730i | \(-0.284136\pi\) | ||||
0.627359 | + | 0.778730i | \(0.284136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.29631e11 | 0.494796 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.72001e10 | 0.0447696 | ||||||||
\(509\) | 2.40110e12 | 1.58555 | 0.792774 | − | 0.609515i | \(-0.208636\pi\) | ||||
0.792774 | + | 0.609515i | \(0.208636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58097e12 | 1.02572 | ||||||||
\(512\) | −1.66262e12 | −1.06925 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.87528e11 | 0.118504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.03222e11 | −0.125102 | ||||||||
\(518\) | 2.76548e12 | 1.68766 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.03008e12 | −0.612491 | −0.306246 | − | 0.951953i | \(-0.599073\pi\) | ||||
−0.306246 | + | 0.951953i | \(0.599073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.06637e12 | −0.623232 | −0.311616 | − | 0.950208i | \(-0.600870\pi\) | ||||
−0.311616 | + | 0.950208i | \(0.600870\pi\) | |||||||
\(524\) | −5.51151e10 | −0.0319359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.29944e11 | 0.0740151 | ||||||||
\(527\) | 3.48934e12 | 1.97058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.32516e12 | 1.84613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.40773e10 | −0.0400943 | ||||||||
\(533\) | 5.03603e11 | 0.270281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.40859e12 | −0.737129 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.57511e12 | 0.810572 | ||||||||
\(539\) | −6.58788e10 | −0.0336199 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.51749e12 | 1.26351 | 0.631756 | − | 0.775167i | \(-0.282334\pi\) | ||||
0.631756 | + | 0.775167i | \(0.282334\pi\) | |||||||
\(542\) | −2.74460e12 | −1.36610 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.85846e11 | −0.139938 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10353e12 | 0.527037 | 0.263518 | − | 0.964654i | \(-0.415117\pi\) | ||||
0.263518 | + | 0.964654i | \(0.415117\pi\) | |||||||
\(548\) | 5.68146e10 | 0.0269121 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.63624e11 | 0.214281 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.68384e12 | 1.22037 | ||||||||
\(554\) | −2.48213e12 | −1.11952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.18284e10 | 0.0141247 | ||||||||
\(557\) | −1.09072e12 | −0.480137 | −0.240068 | − | 0.970756i | \(-0.577170\pi\) | ||||
−0.240068 | + | 0.970756i | \(0.577170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.76795e11 | −0.379791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.91446e12 | −0.809529 | ||||||||
\(563\) | 1.03081e12 | 0.432403 | 0.216202 | − | 0.976349i | \(-0.430633\pi\) | ||||
0.216202 | + | 0.976349i | \(0.430633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.20932e10 | −0.0295271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.28695e12 | 1.32503 | ||||||||
\(569\) | 4.06618e12 | 1.62623 | 0.813113 | − | 0.582106i | \(-0.197771\pi\) | ||||
0.813113 | + | 0.582106i | \(0.197771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.86144e11 | 0.388220 | 0.194110 | − | 0.980980i | \(-0.437818\pi\) | ||||
0.194110 | + | 0.980980i | \(0.437818\pi\) | |||||||
\(572\) | 1.55469e10 | 0.00607243 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.75019e12 | −0.672947 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.86947e12 | 1.07773 | 0.538866 | − | 0.842391i | \(-0.318853\pi\) | ||||
0.538866 | + | 0.842391i | \(0.318853\pi\) | |||||||
\(578\) | 1.67155e12 | 0.622937 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.09588e12 | 1.85535 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.44240e11 | −0.302662 | ||||||||
\(584\) | −3.13660e12 | −1.11584 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.29692e12 | −1.15497 | ||||||||
\(587\) | 1.14169e12 | 0.396898 | 0.198449 | − | 0.980111i | \(-0.436410\pi\) | ||||
0.198449 | + | 0.980111i | \(0.436410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.49505e12 | −1.19656 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.18567e12 | −1.73523 | ||||||||
\(593\) | −2.97176e12 | −0.986888 | −0.493444 | − | 0.869777i | \(-0.664262\pi\) | ||||
−0.493444 | + | 0.869777i | \(0.664262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.32679e11 | −0.0430719 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.88814e12 | −0.603779 | ||||||||
\(599\) | −1.77262e12 | −0.562593 | −0.281297 | − | 0.959621i | \(-0.590764\pi\) | ||||
−0.281297 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.25838e12 | 0.393439 | 0.196719 | − | 0.980460i | \(-0.436971\pi\) | ||||
0.196719 | + | 0.980460i | \(0.436971\pi\) | |||||||
\(602\) | 3.04715e12 | 0.945606 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.33405e10 | −0.0193649 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.74535e11 | −0.0521834 | −0.0260917 | − | 0.999660i | \(-0.508306\pi\) | ||||
−0.0260917 | + | 0.999660i | \(0.508306\pi\) | |||||||
\(608\) | 2.86313e11 | 0.0849720 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.25896e11 | 0.152656 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.63037e12 | −1.32447 | −0.662237 | − | 0.749294i | \(-0.730393\pi\) | ||||
−0.662237 | + | 0.749294i | \(0.730393\pi\) | |||||||
\(614\) | 4.06054e12 | 1.15299 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.04202e12 | −0.291584 | ||||||||
\(617\) | 2.50518e12 | 0.695914 | 0.347957 | − | 0.937511i | \(-0.386876\pi\) | ||||
0.347957 | + | 0.937511i | \(0.386876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.44228e11 | 0.148995 | 0.0744977 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744977 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.99023e12 | −0.533146 | ||||||||
\(623\) | −1.13709e12 | −0.302412 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.37447e11 | −0.0617991 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.30088e11 | −0.0846860 | ||||||||
\(629\) | −9.25978e12 | −2.35870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.51975e12 | −1.63719 | −0.818594 | − | 0.574372i | \(-0.805246\pi\) | ||||
−0.818594 | + | 0.574372i | \(0.805246\pi\) | |||||||
\(632\) | −5.32465e12 | −1.32759 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.20303e11 | 0.226219 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.70481e11 | 0.0410250 | ||||||||
\(638\) | 3.38159e11 | 0.0808032 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.36297e12 | 0.786794 | 0.393397 | − | 0.919369i | \(-0.371300\pi\) | ||||
0.393397 | + | 0.919369i | \(0.371300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.18082e12 | −0.272417 | −0.136208 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136208 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(644\) | −3.79614e11 | −0.0869673 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.28749e12 | −0.968628 | ||||||||
\(647\) | 6.63176e12 | 1.48785 | 0.743926 | − | 0.668262i | \(-0.232962\pi\) | ||||
0.743926 | + | 0.668262i | \(0.232962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.69353e11 | 0.103848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.20902e11 | 0.0695438 | ||||||||
\(653\) | 8.25189e11 | 0.177601 | 0.0888003 | − | 0.996049i | \(-0.471697\pi\) | ||||
0.0888003 | + | 0.996049i | \(0.471697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.28185e12 | 0.691913 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.82766e12 | −0.380084 | ||||||||
\(659\) | 4.40214e11 | 0.0909242 | 0.0454621 | − | 0.998966i | \(-0.485524\pi\) | ||||
0.0454621 | + | 0.998966i | \(0.485524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.77788e12 | 1.99222 | 0.996112 | − | 0.0880914i | \(-0.0280767\pi\) | ||||
0.996112 | + | 0.0880914i | \(0.0280767\pi\) | |||||||
\(662\) | −2.71281e11 | −0.0548983 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.01101e13 | −2.01836 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.37587e12 | 0.464790 | ||||||||
\(668\) | 3.74378e11 | 0.0727473 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.62101e12 | 0.308698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.22591e12 | −0.794058 | −0.397029 | − | 0.917806i | \(-0.629959\pi\) | ||||
−0.397029 | + | 0.917806i | \(0.629959\pi\) | |||||||
\(674\) | 4.79547e11 | 0.0895079 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.56694e11 | 0.0472776 | ||||||||
\(677\) | −7.56977e12 | −1.38495 | −0.692474 | − | 0.721442i | \(-0.743479\pi\) | ||||
−0.692474 | + | 0.721442i | \(0.743479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.07273e12 | 1.09640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.54923e12 | −0.451210 | ||||||||
\(683\) | −1.92029e12 | −0.337655 | −0.168827 | − | 0.985646i | \(-0.553998\pi\) | ||||
−0.168827 | + | 0.985646i | \(0.553998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.90850e12 | −1.01864 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.71385e12 | −0.972257 | ||||||||
\(689\) | 2.18472e12 | 0.369325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.99839e12 | −0.667166 | −0.333583 | − | 0.942721i | \(-0.608258\pi\) | ||||
−0.333583 | + | 0.942721i | \(0.608258\pi\) | |||||||
\(692\) | −2.97538e11 | −0.0493248 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.85595e12 | −0.303702 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.86023e12 | 0.940519 | ||||||||
\(698\) | −2.71249e10 | −0.00432532 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.12736e13 | −1.76332 | −0.881662 | − | 0.471881i | \(-0.843575\pi\) | ||||
−0.881662 | + | 0.471881i | \(0.843575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.27493e12 | 1.43223 | ||||||||
\(704\) | 2.06146e12 | 0.316299 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.81453e12 | 0.577856 | ||||||||
\(707\) | 7.87643e12 | 1.18561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.12679e13 | 1.67469 | 0.837346 | − | 0.546673i | \(-0.184106\pi\) | ||||
0.837346 | + | 0.546673i | \(0.184106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.25595e12 | 0.328980 | ||||||||
\(713\) | −1.79106e13 | −2.59542 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.31512e11 | 0.104019 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.40395e12 | −0.197148 | ||||||||
\(719\) | 9.05247e12 | 1.26324 | 0.631622 | − | 0.775277i | \(-0.282390\pi\) | ||||
0.631622 | + | 0.775277i | \(0.282390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.09459e13 | 1.50849 | ||||||||
\(722\) | −2.80462e12 | −0.384111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.57129e10 | −0.00888847 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.34408e12 | −0.178452 | −0.0892260 | − | 0.996011i | \(-0.528439\pi\) | ||||
−0.0892260 | + | 0.996011i | \(0.528439\pi\) | |||||||
\(728\) | 2.69654e12 | 0.355807 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.02029e13 | −1.32159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.57401e11 | −0.0841129 | −0.0420564 | − | 0.999115i | \(-0.513391\pi\) | ||||
−0.0420564 | + | 0.999115i | \(0.513391\pi\) | |||||||
\(734\) | −2.46932e12 | −0.314011 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.46723e12 | 0.184310 | ||||||||
\(737\) | 1.73679e12 | 0.216842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.15587e12 | 0.265903 | 0.132951 | − | 0.991123i | \(-0.457555\pi\) | ||||
0.132951 | + | 0.991123i | \(0.457555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.59263e12 | −0.919548 | ||||||||
\(743\) | −7.73594e12 | −0.931244 | −0.465622 | − | 0.884984i | \(-0.654169\pi\) | ||||
−0.465622 | + | 0.884984i | \(0.654169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.58621e13 | −1.87515 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.80914e11 | 0.0211307 | ||||||||
\(749\) | 1.10998e12 | 0.128869 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.12448e13 | −1.28995 | −0.644974 | − | 0.764205i | \(-0.723132\pi\) | ||||
−0.644974 | + | 0.764205i | \(0.723132\pi\) | |||||||
\(752\) | 3.42713e12 | 0.390797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.75087e11 | −0.0986007 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.18544e13 | 1.31205 | 0.656024 | − | 0.754740i | \(-0.272237\pi\) | ||||
0.656024 | + | 0.754740i | \(0.272237\pi\) | |||||||
\(758\) | −4.49528e12 | −0.494590 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.24765e12 | 0.242939 | 0.121470 | − | 0.992595i | \(-0.461239\pi\) | ||||
0.121470 | + | 0.992595i | \(0.461239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.18484e13 | 1.26561 | ||||||||
\(764\) | 6.27380e11 | 0.0666209 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20380e13 | −1.26335 | ||||||||
\(767\) | −1.21459e12 | −0.126721 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.44505e13 | −1.49010 | −0.745049 | − | 0.667009i | \(-0.767574\pi\) | ||||
−0.745049 | + | 0.667009i | \(0.767574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.02469e12 | −0.103828 | ||||||||
\(773\) | 5.19022e12 | 0.522852 | 0.261426 | − | 0.965224i | \(-0.415807\pi\) | ||||
0.261426 | + | 0.965224i | \(0.415807\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.20481e13 | −1.19273 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.61777e12 | 0.745452 | ||||||||
\(779\) | −5.86983e12 | −0.571093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.05280e12 | −0.389786 | ||||||||
\(782\) | −2.19715e13 | −2.10102 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.11098e12 | 0.105023 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.39938e13 | 1.30032 | 0.650161 | − | 0.759797i | \(-0.274701\pi\) | ||||
0.650161 | + | 0.759797i | \(0.274701\pi\) | |||||||
\(788\) | 1.51633e11 | 0.0140096 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.45354e12 | 0.858618 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.19483e12 | −0.376691 | ||||||||
\(794\) | −5.64867e12 | −0.504375 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.35599e9 | −0.000649430 0 | ||||||||
\(797\) | 2.01269e13 | 1.76691 | 0.883454 | − | 0.468518i | \(-0.155212\pi\) | ||||
0.883454 | + | 0.468518i | \(0.155212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.11966e12 | 0.531210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.43695e11 | −0.0378704 | ||||||||
\(803\) | 3.86741e12 | 0.328247 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.59688e12 | 0.550593 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.56266e13 | −1.28977 | ||||||||
\(809\) | 8.95775e12 | 0.735242 | 0.367621 | − | 0.929976i | \(-0.380172\pi\) | ||||
0.367621 | + | 0.929976i | \(0.380172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.76446e12 | −0.143225 | −0.0716123 | − | 0.997433i | \(-0.522814\pi\) | ||||
−0.0716123 | + | 0.997433i | \(0.522814\pi\) | |||||||
\(812\) | −1.75938e11 | −0.0142023 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.76498e12 | 0.540078 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.02196e13 | 0.802483 | ||||||||
\(818\) | −9.53491e11 | −0.0744607 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48082e13 | −1.13752 | −0.568758 | − | 0.822505i | \(-0.692576\pi\) | ||||
−0.568758 | + | 0.822505i | \(0.692576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.39651e12 | 0.258067 | 0.129034 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129034 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(824\) | −2.17163e13 | −1.64102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.22110e12 | 0.315512 | ||||||||
\(827\) | 1.88344e13 | 1.40016 | 0.700080 | − | 0.714065i | \(-0.253148\pi\) | ||||
0.700080 | + | 0.714065i | \(0.253148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.18947e13 | 0.874695 | 0.437348 | − | 0.899292i | \(-0.355918\pi\) | ||||
0.437348 | + | 0.899292i | \(0.355918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.33462e12 | −0.385966 | ||||||||
\(833\) | 1.98382e12 | 0.142758 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.81210e11 | −0.0128308 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.12350e13 | −0.786998 | ||||||||
\(839\) | 1.22881e13 | 0.856165 | 0.428083 | − | 0.903740i | \(-0.359189\pi\) | ||||
0.428083 | + | 0.903740i | \(0.359189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34060e13 | −0.924097 | ||||||||
\(842\) | 7.06702e12 | 0.484543 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.76581e11 | −0.0255457 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.28346e13 | −0.856853 | ||||||||
\(848\) | 1.42373e13 | 0.945465 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.75300e13 | 3.10660 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.61355e12 | 0.298376 | 0.149188 | − | 0.988809i | \(-0.452334\pi\) | ||||
0.149188 | + | 0.988809i | \(0.452334\pi\) | |||||||
\(854\) | 1.45784e13 | 0.937887 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.20216e12 | −0.140190 | ||||||||
\(857\) | −4.29363e12 | −0.271901 | −0.135950 | − | 0.990716i | \(-0.543409\pi\) | ||||
−0.135950 | + | 0.990716i | \(0.543409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.40428e12 | −0.401330 | −0.200665 | − | 0.979660i | \(-0.564310\pi\) | ||||
−0.200665 | + | 0.979660i | \(0.564310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.84758e12 | −0.607501 | ||||||||
\(863\) | −3.24421e12 | −0.199095 | −0.0995474 | − | 0.995033i | \(-0.531740\pi\) | ||||
−0.0995474 | + | 0.995033i | \(0.531740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.10609e12 | 0.187665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.32632e12 | 0.0793065 | ||||||||
\(869\) | 6.56527e12 | 0.390539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.49445e12 | −0.264603 | ||||||||
\(872\) | −2.35068e13 | −1.37680 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.20075e13 | 1.27576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.89711e13 | −1.65374 | −0.826871 | − | 0.562392i | \(-0.809881\pi\) | ||||
−0.826871 | + | 0.562392i | \(0.809881\pi\) | |||||||
\(878\) | −1.87109e13 | −1.06260 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.50447e12 | −0.419690 | −0.209845 | − | 0.977735i | \(-0.567296\pi\) | ||||
−0.209845 | + | 0.977735i | \(0.567296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.87141e13 | −1.58954 | −0.794772 | − | 0.606908i | \(-0.792410\pi\) | ||||
−0.794772 | + | 0.606908i | \(0.792410\pi\) | |||||||
\(884\) | −4.68167e11 | −0.0257849 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.67013e12 | 0.363649 | ||||||||
\(887\) | 9.99825e12 | 0.542335 | 0.271168 | − | 0.962532i | \(-0.412590\pi\) | ||||
0.271168 | + | 0.962532i | \(0.412590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.43712e13 | −0.771678 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.46095e11 | −0.0394596 | ||||||||
\(893\) | −6.12967e12 | −0.322556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.65528e13 | 0.857998 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.08721e13 | 1.58425 | ||||||||
\(899\) | −8.30095e12 | −0.423847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.54228e13 | 1.28517 | ||||||||
\(902\) | −4.28135e12 | −0.215353 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.87555e13 | −0.934052 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.70846e12 | −0.231018 | −0.115509 | − | 0.993306i | \(-0.536850\pi\) | ||||
−0.115509 | + | 0.993306i | \(0.536850\pi\) | |||||||
\(908\) | −9.41690e11 | −0.0459750 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.69663e13 | −1.29714 | −0.648572 | − | 0.761154i | \(-0.724633\pi\) | ||||
−0.648572 | + | 0.761154i | \(0.724633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.24657e13 | 0.593742 | ||||||||
\(914\) | −7.37778e12 | −0.349678 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.40127e12 | −0.0657645 | ||||||||
\(917\) | 1.17868e13 | 0.550468 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.96618e12 | −0.183422 | −0.0917112 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917112 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.29405e13 | −1.04547 | ||||||||
\(923\) | 1.04878e13 | 0.475639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.14298e13 | 0.957788 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.80012e11 | 0.0300989 | ||||||||
\(929\) | −1.96912e13 | −0.867365 | −0.433683 | − | 0.901066i | \(-0.642786\pi\) | ||||
−0.433683 | + | 0.901066i | \(0.642786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.98707e12 | −0.0866841 | ||||||||
\(932\) | 9.22952e11 | 0.0400689 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.35271e12 | −0.187154 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.11305e13 | 0.895532 | 0.447766 | − | 0.894151i | \(-0.352220\pi\) | ||||
0.447766 | + | 0.894151i | \(0.352220\pi\) | |||||||
\(938\) | 1.56197e13 | 0.658810 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.41072e12 | −0.224958 | −0.112479 | − | 0.993654i | \(-0.535879\pi\) | ||||
−0.112479 | + | 0.993654i | \(0.535879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.00803e13 | −1.23874 | ||||||||
\(944\) | −7.91517e12 | −0.324404 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.45403e12 | 0.302608 | ||||||||
\(947\) | 3.44259e12 | 0.139095 | 0.0695473 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695473 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00081e13 | −0.400546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.13786e13 | 1.23813 | ||||||||
\(953\) | −4.18440e12 | −0.164329 | −0.0821647 | − | 0.996619i | \(-0.526183\pi\) | ||||
−0.0821647 | + | 0.996619i | \(0.526183\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.22718e11 | −0.00862373 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.99921e13 | 0.766855 | ||||||||
\(959\) | −1.21502e13 | −0.463874 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.61375e13 | 1.36679 | ||||||||
\(962\) | −1.75064e13 | −0.659035 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.10694e12 | 0.0785787 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.49800e13 | −0.550926 | −0.275463 | − | 0.961312i | \(-0.588831\pi\) | ||||
−0.275463 | + | 0.961312i | \(0.588831\pi\) | |||||||
\(968\) | 2.54634e13 | 0.932132 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82460e13 | 1.01970 | 0.509848 | − | 0.860264i | \(-0.329701\pi\) | ||||
0.509848 | + | 0.860264i | \(0.329701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.80673e12 | −0.243462 | ||||||||
\(974\) | −2.57318e13 | −0.916127 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.73367e13 | −0.964321 | ||||||||
\(977\) | −4.62242e13 | −1.62309 | −0.811547 | − | 0.584287i | \(-0.801374\pi\) | ||||
−0.811547 | + | 0.584287i | \(0.801374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.78158e12 | −0.0967764 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.48127e13 | 1.88096 | ||||||||
\(983\) | 4.80363e13 | 1.64089 | 0.820443 | − | 0.571728i | \(-0.193727\pi\) | ||||
0.820443 | + | 0.571728i | \(0.193727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.01831e13 | −0.343109 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.68934e11 | 0.0156569 | ||||||||
\(989\) | 5.23712e13 | 1.74064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.31211e13 | 0.761512 | 0.380756 | − | 0.924675i | \(-0.375664\pi\) | ||||
0.380756 | + | 0.924675i | \(0.375664\pi\) | |||||||
\(992\) | −5.12630e12 | −0.168074 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.64487e13 | −1.18425 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.35362e13 | 0.433878 | 0.216939 | − | 0.976185i | \(-0.430393\pi\) | ||||
0.216939 | + | 0.976185i | \(0.430393\pi\) | |||||||
\(998\) | −1.22666e13 | −0.391413 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.10.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 75.10.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.10.b.b.199.2 | 2 | |||
5.3 | odd | 4 | 225.10.b.b.199.1 | 2 | |||
5.4 | even | 2 | 45.10.a.a.1.1 | 1 | |||
15.2 | even | 4 | 75.10.b.b.49.1 | 2 | |||
15.8 | even | 4 | 75.10.b.b.49.2 | 2 | |||
15.14 | odd | 2 | 15.10.a.b.1.1 | ✓ | 1 | ||
60.59 | even | 2 | 240.10.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.b.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.10.a.a.1.1 | 1 | 5.4 | even | 2 | |||
75.10.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
75.10.b.b.49.1 | 2 | 15.2 | even | 4 | |||
75.10.b.b.49.2 | 2 | 15.8 | even | 4 | |||
225.10.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.10.b.b.199.1 | 2 | 5.3 | odd | 4 | |||
225.10.b.b.199.2 | 2 | 5.2 | odd | 4 | |||
240.10.a.g.1.1 | 1 | 60.59 | even | 2 |