Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.10 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.91 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 54.8156i | − | 1.71299i | −0.516158 | − | 0.856493i | \(-0.672638\pi\) | ||
0.516158 | − | 0.856493i | \(-0.327362\pi\) | |||||||
\(3\) | −140.296 | −0.577350 | ||||||||
\(4\) | −1980.75 | −1.93432 | ||||||||
\(5\) | −4481.58 | −1.43410 | −0.717052 | − | 0.697019i | \(-0.754509\pi\) | ||||
−0.717052 | + | 0.697019i | \(0.754509\pi\) | |||||||
\(6\) | 7690.41i | 0.988993i | ||||||||
\(7\) | −27371.2 | −1.62856 | −0.814280 | − | 0.580472i | \(-0.802868\pi\) | ||||
−0.814280 | + | 0.580472i | \(0.802868\pi\) | |||||||
\(8\) | 52444.5i | 1.60048i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | 245660.i | 2.45660i | ||||||||
\(11\) | − | 21424.0i | − | 0.133026i | −0.997786 | − | 0.0665130i | \(-0.978813\pi\) | ||
0.997786 | − | 0.0665130i | \(-0.0211874\pi\) | |||||||
\(12\) | 277891. | 1.11678 | ||||||||
\(13\) | − | 309118.i | − | 0.832544i | −0.909240 | − | 0.416272i | \(-0.863336\pi\) | ||
0.909240 | − | 0.416272i | \(-0.136664\pi\) | |||||||
\(14\) | 1.50037e6i | 2.78970i | ||||||||
\(15\) | 628748. | 0.827981 | ||||||||
\(16\) | 846494. | 0.807279 | ||||||||
\(17\) | 1.91085e6 | 1.34581 | 0.672904 | − | 0.739730i | \(-0.265047\pi\) | ||||
0.672904 | + | 0.739730i | \(0.265047\pi\) | |||||||
\(18\) | − | 1.07893e6i | − | 0.570995i | ||||||
\(19\) | −675482. | −0.272801 | −0.136400 | − | 0.990654i | \(-0.543553\pi\) | ||||
−0.136400 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(20\) | 8.87686e6 | 2.77402 | ||||||||
\(21\) | 3.84007e6 | 0.940249 | ||||||||
\(22\) | −1.17437e6 | −0.227872 | ||||||||
\(23\) | − | 4.00666e6i | − | 0.622505i | −0.950327 | − | 0.311253i | \(-0.899251\pi\) | ||
0.950327 | − | 0.311253i | \(-0.100749\pi\) | |||||||
\(24\) | − | 7.35777e6i | − | 0.924038i | ||||||
\(25\) | 1.03189e7 | 1.05666 | ||||||||
\(26\) | −1.69445e7 | −1.42614 | ||||||||
\(27\) | −2.76145e6 | −0.192450 | ||||||||
\(28\) | 5.42154e7 | 3.15016 | ||||||||
\(29\) | 1.18366e7 | 0.577080 | 0.288540 | − | 0.957468i | \(-0.406830\pi\) | ||||
0.288540 | + | 0.957468i | \(0.406830\pi\) | |||||||
\(30\) | − | 3.44652e7i | − | 1.41832i | ||||||
\(31\) | − | 1.59663e7i | − | 0.557694i | −0.960336 | − | 0.278847i | \(-0.910048\pi\) | ||
0.960336 | − | 0.278847i | \(-0.0899522\pi\) | |||||||
\(32\) | 7.30219e6i | 0.217622i | ||||||||
\(33\) | 3.00570e6i | 0.0768026i | ||||||||
\(34\) | − | 1.04745e8i | − | 2.30535i | ||||||
\(35\) | 1.22666e8 | 2.33553 | ||||||||
\(36\) | −3.89870e7 | −0.644774 | ||||||||
\(37\) | − | 7.63595e7i | − | 1.10117i | −0.834779 | − | 0.550585i | \(-0.814405\pi\) | ||
0.834779 | − | 0.550585i | \(-0.185595\pi\) | |||||||
\(38\) | 3.70269e7i | 0.467304i | ||||||||
\(39\) | 4.33680e7i | 0.480669i | ||||||||
\(40\) | − | 2.35034e8i | − | 2.29526i | ||||||
\(41\) | 4.81846e7 | 0.415900 | 0.207950 | − | 0.978139i | \(-0.433321\pi\) | ||||
0.207950 | + | 0.978139i | \(0.433321\pi\) | |||||||
\(42\) | − | 2.10496e8i | − | 1.61063i | ||||||
\(43\) | 1.47581e8i | 1.00389i | 0.864899 | + | 0.501946i | \(0.167383\pi\) | ||||
−0.864899 | + | 0.501946i | \(0.832617\pi\) | |||||||
\(44\) | 4.24354e7i | 0.257315i | ||||||||
\(45\) | −8.82109e7 | −0.478035 | ||||||||
\(46\) | −2.19627e8 | −1.06634 | ||||||||
\(47\) | − | 8.31364e7i | − | 0.362495i | −0.983438 | − | 0.181248i | \(-0.941986\pi\) | ||
0.983438 | − | 0.181248i | \(-0.0580135\pi\) | |||||||
\(48\) | −1.18760e8 | −0.466083 | ||||||||
\(49\) | 4.66708e8 | 1.65221 | ||||||||
\(50\) | − | 5.65637e8i | − | 1.81004i | ||||||
\(51\) | −2.68085e8 | −0.777002 | ||||||||
\(52\) | 6.12284e8i | 1.61041i | ||||||||
\(53\) | 5.12608e8 | 1.22576 | 0.612881 | − | 0.790176i | \(-0.290011\pi\) | ||||
0.612881 | + | 0.790176i | \(0.290011\pi\) | |||||||
\(54\) | 1.51370e8i | 0.329664i | ||||||||
\(55\) | 9.60132e7i | 0.190773i | ||||||||
\(56\) | − | 1.43547e9i | − | 2.60648i | ||||||
\(57\) | 9.47675e7 | 0.157502 | ||||||||
\(58\) | − | 6.48828e8i | − | 0.988529i | ||||||
\(59\) | 4.98252e8 | + | 5.12701e8i | 0.696929 | + | 0.717140i | ||||
\(60\) | −1.24539e9 | −1.60158 | ||||||||
\(61\) | 2.96707e8i | 0.351301i | 0.984453 | + | 0.175650i | \(0.0562028\pi\) | ||||
−0.984453 | + | 0.175650i | \(0.943797\pi\) | |||||||
\(62\) | −8.75202e8 | −0.955322 | ||||||||
\(63\) | −5.38747e8 | −0.542853 | ||||||||
\(64\) | 1.26708e9 | 1.18006 | ||||||||
\(65\) | 1.38533e9i | 1.19396i | ||||||||
\(66\) | 1.64759e8 | 0.131562 | ||||||||
\(67\) | 5.57657e8i | 0.413041i | 0.978442 | + | 0.206520i | \(0.0662140\pi\) | ||||
−0.978442 | + | 0.206520i | \(0.933786\pi\) | |||||||
\(68\) | −3.78492e9 | −2.60322 | ||||||||
\(69\) | 5.62119e8i | 0.359404i | ||||||||
\(70\) | − | 6.72401e9i | − | 4.00072i | ||||||
\(71\) | −6.33242e8 | −0.350976 | −0.175488 | − | 0.984482i | \(-0.556150\pi\) | ||||
−0.175488 | + | 0.984482i | \(0.556150\pi\) | |||||||
\(72\) | 1.03227e9i | 0.533493i | ||||||||
\(73\) | − | 6.09409e8i | − | 0.293964i | −0.989139 | − | 0.146982i | \(-0.953044\pi\) | ||
0.989139 | − | 0.146982i | \(-0.0469560\pi\) | |||||||
\(74\) | −4.18569e9 | −1.88629 | ||||||||
\(75\) | −1.44770e9 | −0.610061 | ||||||||
\(76\) | 1.33796e9 | 0.527685 | ||||||||
\(77\) | 5.86400e8i | 0.216641i | ||||||||
\(78\) | 2.37724e9 | 0.823380 | ||||||||
\(79\) | −1.56682e9 | −0.509196 | −0.254598 | − | 0.967047i | \(-0.581943\pi\) | ||||
−0.254598 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(80\) | −3.79363e9 | −1.15772 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | − | 2.64126e9i | − | 0.712431i | ||||||
\(83\) | − | 1.79188e9i | − | 0.454903i | −0.973789 | − | 0.227451i | \(-0.926961\pi\) | ||
0.973789 | − | 0.227451i | \(-0.0730393\pi\) | |||||||
\(84\) | −7.60621e9 | −1.81875 | ||||||||
\(85\) | −8.56364e9 | −1.93003 | ||||||||
\(86\) | 8.08972e9 | 1.71965 | ||||||||
\(87\) | −1.66062e9 | −0.333177 | ||||||||
\(88\) | 1.12357e9 | 0.212906 | ||||||||
\(89\) | 9.80823e9i | 1.75647i | 0.478230 | + | 0.878235i | \(0.341279\pi\) | ||||
−0.478230 | + | 0.878235i | \(0.658721\pi\) | |||||||
\(90\) | 4.83533e9i | 0.818867i | ||||||||
\(91\) | 8.46093e9i | 1.35585i | ||||||||
\(92\) | 7.93617e9i | 1.20413i | ||||||||
\(93\) | 2.24001e9i | 0.321985i | ||||||||
\(94\) | −4.55717e9 | −0.620949 | ||||||||
\(95\) | 3.02722e9 | 0.391225 | ||||||||
\(96\) | − | 1.02447e9i | − | 0.125644i | ||||||
\(97\) | − | 7.87880e9i | − | 0.917490i | −0.888568 | − | 0.458745i | \(-0.848299\pi\) | ||
0.888568 | − | 0.458745i | \(-0.151701\pi\) | |||||||
\(98\) | − | 2.55828e10i | − | 2.83021i | ||||||
\(99\) | − | 4.21688e8i | − | 0.0443420i | ||||||
\(100\) | −2.04391e10 | −2.04391 | ||||||||
\(101\) | − | 1.38657e10i | − | 1.31927i | −0.751584 | − | 0.659637i | \(-0.770710\pi\) | ||
0.751584 | − | 0.659637i | \(-0.229290\pi\) | |||||||
\(102\) | 1.46952e10i | 1.33099i | ||||||||
\(103\) | − | 7.33673e9i | − | 0.632872i | −0.948614 | − | 0.316436i | \(-0.897514\pi\) | ||
0.948614 | − | 0.316436i | \(-0.102486\pi\) | |||||||
\(104\) | 1.62115e10 | 1.33247 | ||||||||
\(105\) | −1.72096e10 | −1.34842 | ||||||||
\(106\) | − | 2.80989e10i | − | 2.09971i | ||||||
\(107\) | −1.43613e10 | −1.02394 | −0.511971 | − | 0.859003i | \(-0.671085\pi\) | ||||
−0.511971 | + | 0.859003i | \(0.671085\pi\) | |||||||
\(108\) | 5.46973e9 | 0.372260 | ||||||||
\(109\) | − | 1.28408e10i | − | 0.834562i | −0.908777 | − | 0.417281i | \(-0.862983\pi\) | ||
0.908777 | − | 0.417281i | \(-0.137017\pi\) | |||||||
\(110\) | 5.26302e9 | 0.326792 | ||||||||
\(111\) | 1.07129e10i | 0.635761i | ||||||||
\(112\) | −2.31696e10 | −1.31470 | ||||||||
\(113\) | 4.19928e9i | 0.227920i | 0.993485 | + | 0.113960i | \(0.0363536\pi\) | ||||
−0.993485 | + | 0.113960i | \(0.963646\pi\) | |||||||
\(114\) | − | 5.19473e9i | − | 0.269798i | ||||||
\(115\) | 1.79561e10i | 0.892738i | ||||||||
\(116\) | −2.34452e10 | −1.11626 | ||||||||
\(117\) | − | 6.08436e9i | − | 0.277515i | ||||||
\(118\) | 2.81040e10 | − | 2.73119e10i | 1.22845 | − | 1.19383i | ||||
\(119\) | −5.23024e10 | −2.19173 | ||||||||
\(120\) | 3.29744e10i | 1.32517i | ||||||||
\(121\) | 2.54784e10 | 0.982304 | ||||||||
\(122\) | 1.62642e10 | 0.601773 | ||||||||
\(123\) | −6.76011e9 | −0.240120 | ||||||||
\(124\) | 3.16252e10i | 1.07876i | ||||||||
\(125\) | −2.47957e9 | −0.0812505 | ||||||||
\(126\) | 2.95317e10i | 0.929900i | ||||||||
\(127\) | 4.28326e10 | 1.29645 | 0.648225 | − | 0.761449i | \(-0.275511\pi\) | ||||
0.648225 | + | 0.761449i | \(0.275511\pi\) | |||||||
\(128\) | − | 6.19784e10i | − | 1.80381i | ||||||
\(129\) | − | 2.07050e10i | − | 0.579598i | ||||||
\(130\) | 7.59379e10 | 2.04523 | ||||||||
\(131\) | 7.08750e10i | 1.83712i | 0.395285 | + | 0.918558i | \(0.370646\pi\) | ||||
−0.395285 | + | 0.918558i | \(0.629354\pi\) | |||||||
\(132\) | − | 5.95353e9i | − | 0.148561i | ||||||
\(133\) | 1.84888e10 | 0.444272 | ||||||||
\(134\) | 3.05683e10 | 0.707534 | ||||||||
\(135\) | 1.23756e10 | 0.275994 | ||||||||
\(136\) | 1.00214e11i | 2.15394i | ||||||||
\(137\) | 6.98990e10 | 1.44833 | 0.724166 | − | 0.689625i | \(-0.242225\pi\) | ||||
0.724166 | + | 0.689625i | \(0.242225\pi\) | |||||||
\(138\) | 3.08128e10 | 0.615654 | ||||||||
\(139\) | 1.83568e7 | 0.000353771 | 0.000176886 | − | 1.00000i | \(-0.499944\pi\) | ||||
0.000176886 | 1.00000i | \(0.499944\pi\) | ||||||||
\(140\) | −2.42970e11 | −4.51766 | ||||||||
\(141\) | 1.16637e10i | 0.209287i | ||||||||
\(142\) | 3.47115e10i | 0.601218i | ||||||||
\(143\) | −6.62253e9 | −0.110750 | ||||||||
\(144\) | 1.66615e10 | 0.269093 | ||||||||
\(145\) | −5.30465e10 | −0.827593 | ||||||||
\(146\) | −3.34051e10 | −0.503556 | ||||||||
\(147\) | −6.54773e10 | −0.953902 | ||||||||
\(148\) | 1.51249e11i | 2.13002i | ||||||||
\(149\) | − | 6.81370e10i | − | 0.927795i | −0.885889 | − | 0.463897i | \(-0.846451\pi\) | ||
0.885889 | − | 0.463897i | \(-0.153549\pi\) | |||||||
\(150\) | 7.93566e10i | 1.04503i | ||||||||
\(151\) | 1.12413e11i | 1.43196i | 0.698119 | + | 0.715981i | \(0.254020\pi\) | ||||
−0.698119 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(152\) | − | 3.54253e10i | − | 0.436612i | ||||||
\(153\) | 3.76113e10 | 0.448602 | ||||||||
\(154\) | 3.21438e10 | 0.371103 | ||||||||
\(155\) | 7.15542e10i | 0.799791i | ||||||||
\(156\) | − | 8.59010e10i | − | 0.929769i | ||||||
\(157\) | 1.54822e11i | 1.62306i | 0.584313 | + | 0.811528i | \(0.301364\pi\) | ||||
−0.584313 | + | 0.811528i | \(0.698636\pi\) | |||||||
\(158\) | 8.58864e10i | 0.872246i | ||||||||
\(159\) | −7.19169e10 | −0.707693 | ||||||||
\(160\) | − | 3.27253e10i | − | 0.312093i | ||||||
\(161\) | 1.09667e11i | 1.01379i | ||||||||
\(162\) | − | 2.12367e10i | − | 0.190332i | ||||||
\(163\) | 2.52617e10 | 0.219545 | 0.109773 | − | 0.993957i | \(-0.464988\pi\) | ||||
0.109773 | + | 0.993957i | \(0.464988\pi\) | |||||||
\(164\) | −9.54414e10 | −0.804484 | ||||||||
\(165\) | − | 1.34703e10i | − | 0.110143i | ||||||
\(166\) | −9.82229e10 | −0.779242 | ||||||||
\(167\) | −8.02086e9 | −0.0617502 | −0.0308751 | − | 0.999523i | \(-0.509829\pi\) | ||||
−0.0308751 | + | 0.999523i | \(0.509829\pi\) | |||||||
\(168\) | 2.01391e11i | 1.50485i | ||||||||
\(169\) | 4.23047e10 | 0.306871 | ||||||||
\(170\) | 4.69421e11i | 3.30611i | ||||||||
\(171\) | −1.32955e10 | −0.0909336 | ||||||||
\(172\) | − | 2.92320e11i | − | 1.94185i | ||||||
\(173\) | − | 2.51337e11i | − | 1.62190i | −0.585113 | − | 0.810952i | \(-0.698950\pi\) | ||
0.585113 | − | 0.810952i | \(-0.301050\pi\) | |||||||
\(174\) | 9.10280e10i | 0.570728i | ||||||||
\(175\) | −2.82441e11 | −1.72083 | ||||||||
\(176\) | − | 1.81353e10i | − | 0.107389i | ||||||
\(177\) | −6.99028e10 | − | 7.19299e10i | −0.402372 | − | 0.414041i | ||||
\(178\) | 5.37644e11 | 3.00881 | ||||||||
\(179\) | 1.16008e11i | 0.631283i | 0.948878 | + | 0.315642i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315642i | \(0.897780\pi\) | |||||||
\(180\) | 1.74723e11 | 0.924673 | ||||||||
\(181\) | 1.96522e11 | 1.01162 | 0.505811 | − | 0.862644i | \(-0.331193\pi\) | ||||
0.505811 | + | 0.862644i | \(0.331193\pi\) | |||||||
\(182\) | 4.63790e11 | 2.32255 | ||||||||
\(183\) | − | 4.16269e10i | − | 0.202824i | ||||||
\(184\) | 2.10127e11 | 0.996308 | ||||||||
\(185\) | 3.42211e11i | 1.57919i | ||||||||
\(186\) | 1.22787e11 | 0.551555 | ||||||||
\(187\) | − | 4.09381e10i | − | 0.179027i | ||||||
\(188\) | 1.64672e11i | 0.701182i | ||||||||
\(189\) | 7.55842e10 | 0.313416 | ||||||||
\(190\) | − | 1.65939e11i | − | 0.670163i | ||||||
\(191\) | − | 4.12495e11i | − | 1.62275i | −0.584524 | − | 0.811376i | \(-0.698719\pi\) | ||
0.584524 | − | 0.811376i | \(-0.301281\pi\) | |||||||
\(192\) | −1.77767e11 | −0.681310 | ||||||||
\(193\) | −2.45939e11 | −0.918418 | −0.459209 | − | 0.888328i | \(-0.651867\pi\) | ||||
−0.459209 | + | 0.888328i | \(0.651867\pi\) | |||||||
\(194\) | −4.31881e11 | −1.57165 | ||||||||
\(195\) | − | 1.94357e11i | − | 0.689330i | ||||||
\(196\) | −9.24429e11 | −3.19590 | ||||||||
\(197\) | −3.72976e10 | −0.125704 | −0.0628521 | − | 0.998023i | \(-0.520020\pi\) | ||||
−0.0628521 | + | 0.998023i | \(0.520020\pi\) | |||||||
\(198\) | −2.31151e10 | −0.0759573 | ||||||||
\(199\) | 4.63716e11 | 1.48589 | 0.742946 | − | 0.669352i | \(-0.233428\pi\) | ||||
0.742946 | + | 0.669352i | \(0.233428\pi\) | |||||||
\(200\) | 5.41170e11i | 1.69116i | ||||||||
\(201\) | − | 7.82371e10i | − | 0.238469i | ||||||
\(202\) | −7.60056e11 | −2.25990 | ||||||||
\(203\) | −3.23981e11 | −0.939809 | ||||||||
\(204\) | 5.31009e11 | 1.50297 | ||||||||
\(205\) | −2.15943e11 | −0.596444 | ||||||||
\(206\) | −4.02167e11 | −1.08410 | ||||||||
\(207\) | − | 7.88631e10i | − | 0.207502i | ||||||
\(208\) | − | 2.61666e11i | − | 0.672095i | ||||||
\(209\) | 1.44715e10i | 0.0362896i | ||||||||
\(210\) | 9.43353e11i | 2.30982i | ||||||||
\(211\) | − | 7.10941e11i | − | 1.69989i | −0.526871 | − | 0.849946i | \(-0.676635\pi\) | ||
0.526871 | − | 0.849946i | \(-0.323365\pi\) | |||||||
\(212\) | −1.01535e12 | −2.37102 | ||||||||
\(213\) | 8.88414e10 | 0.202636 | ||||||||
\(214\) | 7.87224e11i | 1.75400i | ||||||||
\(215\) | − | 6.61394e11i | − | 1.43969i | ||||||
\(216\) | − | 1.44823e11i | − | 0.308013i | ||||||
\(217\) | 4.37017e11i | 0.908238i | ||||||||
\(218\) | −7.03874e11 | −1.42959 | ||||||||
\(219\) | 8.54977e10i | 0.169720i | ||||||||
\(220\) | − | 1.90178e11i | − | 0.369017i | ||||||
\(221\) | − | 5.90679e11i | − | 1.12044i | ||||||
\(222\) | 5.87236e11 | 1.08905 | ||||||||
\(223\) | 8.81026e11 | 1.59759 | 0.798794 | − | 0.601605i | \(-0.205472\pi\) | ||||
0.798794 | + | 0.601605i | \(0.205472\pi\) | |||||||
\(224\) | − | 1.99870e11i | − | 0.354411i | ||||||
\(225\) | 2.03107e11 | 0.352219 | ||||||||
\(226\) | 2.30186e11 | 0.390424 | ||||||||
\(227\) | − | 5.30184e11i | − | 0.879625i | −0.898090 | − | 0.439813i | \(-0.855045\pi\) | ||
0.898090 | − | 0.439813i | \(-0.144955\pi\) | |||||||
\(228\) | −1.87710e11 | −0.304659 | ||||||||
\(229\) | 5.38590e11i | 0.855226i | 0.903962 | + | 0.427613i | \(0.140645\pi\) | ||||
−0.903962 | + | 0.427613i | \(0.859355\pi\) | |||||||
\(230\) | 9.84276e11 | 1.52925 | ||||||||
\(231\) | − | 8.22697e10i | − | 0.125078i | ||||||
\(232\) | 6.20763e11i | 0.923605i | ||||||||
\(233\) | − | 3.84999e11i | − | 0.560635i | −0.959907 | − | 0.280318i | \(-0.909560\pi\) | ||
0.959907 | − | 0.280318i | \(-0.0904398\pi\) | |||||||
\(234\) | −3.33518e11 | −0.475379 | ||||||||
\(235\) | 3.72582e11i | 0.519856i | ||||||||
\(236\) | −9.86910e11 | − | 1.01553e12i | −1.34809 | − | 1.38718i | ||||
\(237\) | 2.19819e11 | 0.293984 | ||||||||
\(238\) | 2.86698e12i | 3.75440i | ||||||||
\(239\) | −1.14818e12 | −1.47238 | −0.736190 | − | 0.676775i | \(-0.763377\pi\) | ||||
−0.736190 | + | 0.676775i | \(0.763377\pi\) | |||||||
\(240\) | 5.32231e11 | 0.668412 | ||||||||
\(241\) | −4.12541e11 | −0.507436 | −0.253718 | − | 0.967278i | \(-0.581654\pi\) | ||||
−0.253718 | + | 0.967278i | \(0.581654\pi\) | |||||||
\(242\) | − | 1.39661e12i | − | 1.68267i | ||||||
\(243\) | −5.43536e10 | −0.0641500 | ||||||||
\(244\) | − | 5.87702e11i | − | 0.679529i | ||||||
\(245\) | −2.09159e12 | −2.36944 | ||||||||
\(246\) | 3.70559e11i | 0.411322i | ||||||||
\(247\) | 2.08803e11i | 0.227119i | ||||||||
\(248\) | 8.37345e11 | 0.892578 | ||||||||
\(249\) | 2.51394e11i | 0.262638i | ||||||||
\(250\) | 1.35919e11i | 0.139181i | ||||||||
\(251\) | −7.38749e11 | −0.741530 | −0.370765 | − | 0.928727i | \(-0.620904\pi\) | ||||
−0.370765 | + | 0.928727i | \(0.620904\pi\) | |||||||
\(252\) | 1.06712e12 | 1.05005 | ||||||||
\(253\) | −8.58386e10 | −0.0828094 | ||||||||
\(254\) | − | 2.34789e12i | − | 2.22080i | ||||||
\(255\) | 1.20145e12 | 1.11430 | ||||||||
\(256\) | −2.09989e12 | −1.90984 | ||||||||
\(257\) | 1.59405e12 | 1.42180 | 0.710898 | − | 0.703296i | \(-0.248289\pi\) | ||||
0.710898 | + | 0.703296i | \(0.248289\pi\) | |||||||
\(258\) | −1.13496e12 | −0.992843 | ||||||||
\(259\) | 2.09005e12i | 1.79332i | ||||||||
\(260\) | − | 2.74400e12i | − | 2.30949i | ||||||
\(261\) | 2.32979e11 | 0.192360 | ||||||||
\(262\) | 3.88505e12 | 3.14696 | ||||||||
\(263\) | −1.52501e12 | −1.21197 | −0.605987 | − | 0.795475i | \(-0.707222\pi\) | ||||
−0.605987 | + | 0.795475i | \(0.707222\pi\) | |||||||
\(264\) | −1.57633e11 | −0.122921 | ||||||||
\(265\) | −2.29729e12 | −1.75787 | ||||||||
\(266\) | − | 1.01347e12i | − | 0.761033i | ||||||
\(267\) | − | 1.37606e12i | − | 1.01410i | ||||||
\(268\) | − | 1.10458e12i | − | 0.798954i | ||||||
\(269\) | − | 2.61925e12i | − | 1.85959i | −0.368083 | − | 0.929793i | \(-0.619986\pi\) | ||
0.368083 | − | 0.929793i | \(-0.380014\pi\) | |||||||
\(270\) | − | 6.78378e11i | − | 0.472773i | ||||||
\(271\) | −2.22168e12 | −1.51997 | −0.759984 | − | 0.649942i | \(-0.774793\pi\) | ||||
−0.759984 | + | 0.649942i | \(0.774793\pi\) | |||||||
\(272\) | 1.61753e12 | 1.08644 | ||||||||
\(273\) | − | 1.18703e12i | − | 0.782799i | ||||||
\(274\) | − | 3.83155e12i | − | 2.48097i | ||||||
\(275\) | − | 2.21072e11i | − | 0.140563i | ||||||
\(276\) | − | 1.11341e12i | − | 0.695202i | ||||||
\(277\) | 1.07104e12 | 0.656758 | 0.328379 | − | 0.944546i | \(-0.393498\pi\) | ||||
0.328379 | + | 0.944546i | \(0.393498\pi\) | |||||||
\(278\) | − | 1.00624e9i | − | 0.000606006i | ||||||
\(279\) | − | 3.14265e11i | − | 0.185898i | ||||||
\(280\) | 6.43317e12i | 3.73796i | ||||||||
\(281\) | −9.21119e11 | −0.525756 | −0.262878 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262878 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(282\) | 6.39353e11 | 0.358505 | ||||||||
\(283\) | 1.71565e12i | 0.945142i | 0.881293 | + | 0.472571i | \(0.156674\pi\) | ||||
−0.881293 | + | 0.472571i | \(0.843326\pi\) | |||||||
\(284\) | 1.25429e12 | 0.678901 | ||||||||
\(285\) | −4.24708e11 | −0.225874 | ||||||||
\(286\) | 3.63018e11i | 0.189713i | ||||||||
\(287\) | −1.31887e12 | −0.677318 | ||||||||
\(288\) | 1.43729e11i | 0.0725408i | ||||||||
\(289\) | 1.63537e12 | 0.811197 | ||||||||
\(290\) | 2.90777e12i | 1.41765i | ||||||||
\(291\) | 1.10536e12i | 0.529713i | ||||||||
\(292\) | 1.20708e12i | 0.568621i | ||||||||
\(293\) | 9.31552e10 | 0.0431389 | 0.0215694 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215694 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(294\) | 3.58917e12i | 1.63402i | ||||||||
\(295\) | −2.23295e12 | − | 2.29771e12i | −0.999470 | − | 1.02845i | ||||
\(296\) | 4.00464e12 | 1.76240 | ||||||||
\(297\) | 5.91612e10i | 0.0256009i | ||||||||
\(298\) | −3.73497e12 | −1.58930 | ||||||||
\(299\) | −1.23853e12 | −0.518263 | ||||||||
\(300\) | 2.86753e12 | 1.18005 | ||||||||
\(301\) | − | 4.03946e12i | − | 1.63490i | ||||||
\(302\) | 6.16198e12 | 2.45293 | ||||||||
\(303\) | 1.94530e12i | 0.761683i | ||||||||
\(304\) | −5.71791e11 | −0.220226 | ||||||||
\(305\) | − | 1.32972e12i | − | 0.503802i | ||||||
\(306\) | − | 2.06169e12i | − | 0.768450i | ||||||
\(307\) | −1.27727e12 | −0.468374 | −0.234187 | − | 0.972192i | \(-0.575243\pi\) | ||||
−0.234187 | + | 0.972192i | \(0.575243\pi\) | |||||||
\(308\) | − | 1.16151e12i | − | 0.419053i | ||||||
\(309\) | 1.02931e12i | 0.365389i | ||||||||
\(310\) | 3.92228e12 | 1.37003 | ||||||||
\(311\) | 2.75148e12 | 0.945723 | 0.472862 | − | 0.881137i | \(-0.343221\pi\) | ||||
0.472862 | + | 0.881137i | \(0.343221\pi\) | |||||||
\(312\) | −2.27442e12 | −0.769302 | ||||||||
\(313\) | 2.13941e12i | 0.712151i | 0.934457 | + | 0.356075i | \(0.115885\pi\) | ||||
−0.934457 | + | 0.356075i | \(0.884115\pi\) | |||||||
\(314\) | 8.48664e12 | 2.78027 | ||||||||
\(315\) | 2.41444e12 | 0.778508 | ||||||||
\(316\) | 3.10348e12 | 0.984949 | ||||||||
\(317\) | 1.34809e12 | 0.421137 | 0.210568 | − | 0.977579i | \(-0.432469\pi\) | ||||
0.210568 | + | 0.977579i | \(0.432469\pi\) | |||||||
\(318\) | 3.94216e12i | 1.21227i | ||||||||
\(319\) | − | 2.53586e11i | − | 0.0767666i | ||||||
\(320\) | −5.67853e12 | −1.69233 | ||||||||
\(321\) | 2.01484e12 | 0.591174 | ||||||||
\(322\) | 6.01146e12 | 1.73660 | ||||||||
\(323\) | −1.29075e12 | −0.367137 | ||||||||
\(324\) | −7.67381e11 | −0.214925 | ||||||||
\(325\) | − | 3.18976e12i | − | 0.879712i | ||||||
\(326\) | − | 1.38473e12i | − | 0.376078i | ||||||
\(327\) | 1.80151e12i | 0.481835i | ||||||||
\(328\) | 2.52702e12i | 0.665639i | ||||||||
\(329\) | 2.27554e12i | 0.590345i | ||||||||
\(330\) | −7.38381e11 | −0.188673 | ||||||||
\(331\) | 5.34528e12 | 1.34534 | 0.672668 | − | 0.739944i | \(-0.265148\pi\) | ||||
0.672668 | + | 0.739944i | \(0.265148\pi\) | |||||||
\(332\) | 3.54926e12i | 0.879928i | ||||||||
\(333\) | − | 1.50298e12i | − | 0.367057i | ||||||
\(334\) | 4.39668e11i | 0.105777i | ||||||||
\(335\) | − | 2.49918e12i | − | 0.592344i | ||||||
\(336\) | 3.25060e12 | 0.759044 | ||||||||
\(337\) | 5.65028e11i | 0.129993i | 0.997885 | + | 0.0649965i | \(0.0207036\pi\) | ||||
−0.997885 | + | 0.0649965i | \(0.979296\pi\) | |||||||
\(338\) | − | 2.31896e12i | − | 0.525665i | ||||||
\(339\) | − | 5.89143e11i | − | 0.131590i | ||||||
\(340\) | 1.69624e13 | 3.73330 | ||||||||
\(341\) | −3.42062e11 | −0.0741878 | ||||||||
\(342\) | 7.28801e11i | 0.155768i | ||||||||
\(343\) | −5.04266e12 | −1.06216 | ||||||||
\(344\) | −7.73980e12 | −1.60671 | ||||||||
\(345\) | − | 2.51918e12i | − | 0.515422i | ||||||
\(346\) | −1.37772e13 | −2.77830 | ||||||||
\(347\) | 3.89130e12i | 0.773476i | 0.922190 | + | 0.386738i | \(0.126398\pi\) | ||||
−0.922190 | + | 0.386738i | \(0.873602\pi\) | |||||||
\(348\) | 3.28927e12 | 0.644472 | ||||||||
\(349\) | − | 1.06678e12i | − | 0.206039i | −0.994679 | − | 0.103020i | \(-0.967150\pi\) | ||
0.994679 | − | 0.103020i | \(-0.0328504\pi\) | |||||||
\(350\) | 1.54822e13i | 2.94775i | ||||||||
\(351\) | 8.53613e11i | 0.160223i | ||||||||
\(352\) | 1.56442e11 | 0.0289494 | ||||||||
\(353\) | − | 4.84504e11i | − | 0.0883942i | −0.999023 | − | 0.0441971i | \(-0.985927\pi\) | ||
0.999023 | − | 0.0441971i | \(-0.0140730\pi\) | |||||||
\(354\) | −3.94288e12 | + | 3.83176e12i | −0.709246 | + | 0.689258i | ||||
\(355\) | 2.83792e12 | 0.503337 | ||||||||
\(356\) | − | 1.94276e13i | − | 3.39758i | ||||||
\(357\) | 7.33782e12 | 1.26539 | ||||||||
\(358\) | 6.35907e12 | 1.08138 | ||||||||
\(359\) | 1.04808e13 | 1.75762 | 0.878808 | − | 0.477175i | \(-0.158339\pi\) | ||||
0.878808 | + | 0.477175i | \(0.158339\pi\) | |||||||
\(360\) | − | 4.62618e12i | − | 0.765085i | ||||||
\(361\) | −5.67479e12 | −0.925580 | ||||||||
\(362\) | − | 1.07725e13i | − | 1.73290i | ||||||
\(363\) | −3.57453e12 | −0.567134 | ||||||||
\(364\) | − | 1.67589e13i | − | 2.62265i | ||||||
\(365\) | 2.73111e12i | 0.421575i | ||||||||
\(366\) | −2.28180e12 | −0.347434 | ||||||||
\(367\) | − | 8.72911e12i | − | 1.31111i | −0.755147 | − | 0.655555i | \(-0.772435\pi\) | ||
0.755147 | − | 0.655555i | \(-0.227565\pi\) | |||||||
\(368\) | − | 3.39161e12i | − | 0.502536i | ||||||
\(369\) | 9.48417e11 | 0.138633 | ||||||||
\(370\) | 1.87585e13 | 2.70514 | ||||||||
\(371\) | −1.40307e13 | −1.99623 | ||||||||
\(372\) | − | 4.43689e12i | − | 0.622822i | ||||||
\(373\) | 7.39620e12 | 1.02439 | 0.512194 | − | 0.858870i | \(-0.328833\pi\) | ||||
0.512194 | + | 0.858870i | \(0.328833\pi\) | |||||||
\(374\) | −2.24404e12 | −0.306671 | ||||||||
\(375\) | 3.47874e11 | 0.0469100 | ||||||||
\(376\) | 4.36005e12 | 0.580166 | ||||||||
\(377\) | − | 3.65889e12i | − | 0.480444i | ||||||
\(378\) | − | 4.14319e12i | − | 0.536878i | ||||||
\(379\) | −2.11206e12 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(380\) | −5.99616e12 | −0.756755 | ||||||||
\(381\) | −6.00925e12 | −0.748506 | ||||||||
\(382\) | −2.26112e13 | −2.77975 | ||||||||
\(383\) | −1.52770e12 | −0.185372 | −0.0926862 | − | 0.995695i | \(-0.529545\pi\) | ||||
−0.0926862 | + | 0.995695i | \(0.529545\pi\) | |||||||
\(384\) | 8.69533e12i | 1.04143i | ||||||||
\(385\) | − | 2.62800e12i | − | 0.310686i | ||||||
\(386\) | 1.34813e13i | 1.57324i | ||||||||
\(387\) | 2.90483e12i | 0.334631i | ||||||||
\(388\) | 1.56059e13i | 1.77472i | ||||||||
\(389\) | −6.15791e12 | −0.691329 | −0.345665 | − | 0.938358i | \(-0.612347\pi\) | ||||
−0.345665 | + | 0.938358i | \(0.612347\pi\) | |||||||
\(390\) | −1.06538e13 | −1.18081 | ||||||||
\(391\) | − | 7.65614e12i | − | 0.837772i | ||||||
\(392\) | 2.44763e13i | 2.64433i | ||||||||
\(393\) | − | 9.94349e12i | − | 1.06066i | ||||||
\(394\) | 2.04449e12i | 0.215330i | ||||||||
\(395\) | 7.02185e12 | 0.730240 | ||||||||
\(396\) | 8.35257e11i | 0.0857717i | ||||||||
\(397\) | 2.95400e12i | 0.299543i | 0.988721 | + | 0.149771i | \(0.0478537\pi\) | ||||
−0.988721 | + | 0.149771i | \(0.952146\pi\) | |||||||
\(398\) | − | 2.54189e13i | − | 2.54531i | ||||||
\(399\) | −2.59390e12 | −0.256501 | ||||||||
\(400\) | 8.73489e12 | 0.853016 | ||||||||
\(401\) | 1.10122e13i | 1.06206i | 0.847352 | + | 0.531032i | \(0.178196\pi\) | ||||
−0.847352 | + | 0.531032i | \(0.821804\pi\) | |||||||
\(402\) | −4.28861e12 | −0.408495 | ||||||||
\(403\) | −4.93547e12 | −0.464305 | ||||||||
\(404\) | 2.74644e13i | 2.55190i | ||||||||
\(405\) | −1.73625e12 | −0.159345 | ||||||||
\(406\) | 1.77592e13i | 1.60988i | ||||||||
\(407\) | −1.63592e12 | −0.146484 | ||||||||
\(408\) | − | 1.40596e13i | − | 1.24358i | ||||||
\(409\) | − | 1.11556e13i | − | 0.974708i | −0.873204 | − | 0.487354i | \(-0.837962\pi\) | ||
0.873204 | − | 0.487354i | \(-0.162038\pi\) | |||||||
\(410\) | 1.18370e13i | 1.02170i | ||||||||
\(411\) | −9.80656e12 | −0.836195 | ||||||||
\(412\) | 1.45322e13i | 1.22418i | ||||||||
\(413\) | −1.36378e13 | − | 1.40332e13i | −1.13499 | − | 1.16791i | ||||
\(414\) | −4.32292e12 | −0.355448 | ||||||||
\(415\) | 8.03045e12i | 0.652378i | ||||||||
\(416\) | 2.25724e12 | 0.181180 | ||||||||
\(417\) | −2.57539e9 | −0.000204250 | ||||||||
\(418\) | 7.93264e11 | 0.0621636 | ||||||||
\(419\) | 5.63550e12i | 0.436377i | 0.975907 | + | 0.218189i | \(0.0700148\pi\) | ||||
−0.975907 | + | 0.218189i | \(0.929985\pi\) | |||||||
\(420\) | 3.40878e13 | 2.60827 | ||||||||
\(421\) | 1.37108e12i | 0.103670i | 0.998656 | + | 0.0518349i | \(0.0165070\pi\) | ||||
−0.998656 | + | 0.0518349i | \(0.983493\pi\) | |||||||
\(422\) | −3.89706e13 | −2.91189 | ||||||||
\(423\) | − | 1.63637e12i | − | 0.120832i | ||||||
\(424\) | 2.68835e13i | 1.96181i | ||||||||
\(425\) | 1.97179e13 | 1.42206 | ||||||||
\(426\) | − | 4.86989e12i | − | 0.347113i | ||||||
\(427\) | − | 8.12124e12i | − | 0.572114i | ||||||
\(428\) | 2.84461e13 | 1.98063 | ||||||||
\(429\) | 9.29115e11 | 0.0639416 | ||||||||
\(430\) | −3.62547e13 | −2.46616 | ||||||||
\(431\) | 2.81455e13i | 1.89244i | 0.323525 | + | 0.946219i | \(0.395132\pi\) | ||||
−0.323525 | + | 0.946219i | \(0.604868\pi\) | |||||||
\(432\) | −2.33755e12 | −0.155361 | ||||||||
\(433\) | −1.64021e13 | −1.07760 | −0.538802 | − | 0.842432i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(434\) | 2.39553e13 | 1.55580 | ||||||||
\(435\) | 7.44221e12 | 0.477811 | ||||||||
\(436\) | 2.54343e13i | 1.61431i | ||||||||
\(437\) | 2.70642e12i | 0.169820i | ||||||||
\(438\) | 4.68660e12 | 0.290728 | ||||||||
\(439\) | −2.05239e13 | −1.25875 | −0.629373 | − | 0.777103i | \(-0.716688\pi\) | ||||
−0.629373 | + | 0.777103i | \(0.716688\pi\) | |||||||
\(440\) | −5.03537e12 | −0.305329 | ||||||||
\(441\) | 9.18621e12 | 0.550736 | ||||||||
\(442\) | −3.23784e13 | −1.91930 | ||||||||
\(443\) | − | 3.21792e13i | − | 1.88606i | −0.332704 | − | 0.943031i | \(-0.607961\pi\) | ||
0.332704 | − | 0.943031i | \(-0.392039\pi\) | |||||||
\(444\) | − | 2.12196e13i | − | 1.22977i | ||||||
\(445\) | − | 4.39563e13i | − | 2.51896i | ||||||
\(446\) | − | 4.82940e13i | − | 2.73665i | ||||||
\(447\) | 9.55936e12i | 0.535662i | ||||||||
\(448\) | −3.46816e13 | −1.92180 | ||||||||
\(449\) | −2.00652e13 | −1.09954 | −0.549772 | − | 0.835315i | \(-0.685285\pi\) | ||||
−0.549772 | + | 0.835315i | \(0.685285\pi\) | |||||||
\(450\) | − | 1.11334e13i | − | 0.603346i | ||||||
\(451\) | − | 1.03231e12i | − | 0.0553255i | ||||||
\(452\) | − | 8.31771e12i | − | 0.440871i | ||||||
\(453\) | − | 1.57711e13i | − | 0.826744i | ||||||
\(454\) | −2.90624e13 | −1.50679 | ||||||||
\(455\) | − | 3.79183e13i | − | 1.94443i | ||||||
\(456\) | 4.97004e12i | 0.252078i | ||||||||
\(457\) | − | 1.86358e13i | − | 0.934905i | −0.884018 | − | 0.467453i | \(-0.845172\pi\) | ||
0.884018 | − | 0.467453i | \(-0.154828\pi\) | |||||||
\(458\) | 2.95231e13 | 1.46499 | ||||||||
\(459\) | −5.27672e12 | −0.259001 | ||||||||
\(460\) | − | 3.55666e13i | − | 1.72684i | ||||||
\(461\) | −1.98467e13 | −0.953201 | −0.476601 | − | 0.879120i | \(-0.658131\pi\) | ||||
−0.476601 | + | 0.879120i | \(0.658131\pi\) | |||||||
\(462\) | −4.50966e12 | −0.214256 | ||||||||
\(463\) | − | 9.83106e12i | − | 0.462057i | −0.972947 | − | 0.231028i | \(-0.925791\pi\) | ||
0.972947 | − | 0.231028i | \(-0.0742090\pi\) | |||||||
\(464\) | 1.00196e13 | 0.465864 | ||||||||
\(465\) | − | 1.00388e13i | − | 0.461760i | ||||||
\(466\) | −2.11040e13 | −0.960361 | ||||||||
\(467\) | 7.05766e12i | 0.317743i | 0.987299 | + | 0.158872i | \(0.0507856\pi\) | ||||
−0.987299 | + | 0.158872i | \(0.949214\pi\) | |||||||
\(468\) | 1.20516e13i | 0.536803i | ||||||||
\(469\) | − | 1.52637e13i | − | 0.672662i | ||||||
\(470\) | 2.04233e13 | 0.890506 | ||||||||
\(471\) | − | 2.17209e13i | − | 0.937072i | ||||||
\(472\) | −2.68884e13 | + | 2.61306e13i | −1.14777 | + | 1.11542i | ||||
\(473\) | 3.16177e12 | 0.133544 | ||||||||
\(474\) | − | 1.20495e13i | − | 0.503591i | ||||||
\(475\) | −6.97023e12 | −0.288257 | ||||||||
\(476\) | 1.03598e14 | 4.23951 | ||||||||
\(477\) | 1.00897e13 | 0.408587 | ||||||||
\(478\) | 6.29380e13i | 2.52217i | ||||||||
\(479\) | −1.57057e13 | −0.622844 | −0.311422 | − | 0.950272i | \(-0.600805\pi\) | ||||
−0.311422 | + | 0.950272i | \(0.600805\pi\) | |||||||
\(480\) | 4.59124e12i | 0.180187i | ||||||||
\(481\) | −2.36041e13 | −0.916773 | ||||||||
\(482\) | 2.26136e13i | 0.869231i | ||||||||
\(483\) | − | 1.53859e13i | − | 0.585310i | ||||||
\(484\) | −5.04663e13 | −1.90009 | ||||||||
\(485\) | 3.53094e13i | 1.31578i | ||||||||
\(486\) | 2.97942e12i | 0.109888i | ||||||||
\(487\) | 3.55340e13 | 1.29718 | 0.648589 | − | 0.761139i | \(-0.275359\pi\) | ||||
0.648589 | + | 0.761139i | \(0.275359\pi\) | |||||||
\(488\) | −1.55607e13 | −0.562250 | ||||||||
\(489\) | −3.54412e12 | −0.126755 | ||||||||
\(490\) | 1.14651e14i | 4.05881i | ||||||||
\(491\) | 4.49539e13 | 1.57529 | 0.787644 | − | 0.616131i | \(-0.211301\pi\) | ||||
0.787644 | + | 0.616131i | \(0.211301\pi\) | |||||||
\(492\) | 1.33901e13 | 0.464469 | ||||||||
\(493\) | 2.26179e13 | 0.776638 | ||||||||
\(494\) | 1.14457e13 | 0.389051 | ||||||||
\(495\) | 1.88983e12i | 0.0635911i | ||||||||
\(496\) | − | 1.35154e13i | − | 0.450215i | ||||||
\(497\) | 1.73326e13 | 0.571586 | ||||||||
\(498\) | 1.37803e13 | 0.449896 | ||||||||
\(499\) | 5.61991e13 | 1.81646 | 0.908232 | − | 0.418467i | \(-0.137432\pi\) | ||||
0.908232 | + | 0.418467i | \(0.137432\pi\) | |||||||
\(500\) | 4.91139e12 | 0.157165 | ||||||||
\(501\) | 1.12529e12 | 0.0356515 | ||||||||
\(502\) | 4.04950e13i | 1.27023i | ||||||||
\(503\) | 1.85153e12i | 0.0575030i | 0.999587 | + | 0.0287515i | \(0.00915316\pi\) | ||||
−0.999587 | + | 0.0287515i | \(0.990847\pi\) | |||||||
\(504\) | − | 2.82544e13i | − | 0.868826i | ||||||
\(505\) | 6.21402e13i | 1.89198i | ||||||||
\(506\) | 4.70529e12i | 0.141851i | ||||||||
\(507\) | −5.93519e12 | −0.177172 | ||||||||
\(508\) | −8.48405e13 | −2.50775 | ||||||||
\(509\) | 6.65068e13i | 1.94660i | 0.229530 | + | 0.973302i | \(0.426281\pi\) | ||||
−0.229530 | + | 0.973302i | \(0.573719\pi\) | |||||||
\(510\) | − | 6.58579e13i | − | 1.90878i | ||||||
\(511\) | 1.66802e13i | 0.478738i | ||||||||
\(512\) | 5.16407e13i | 1.46772i | ||||||||
\(513\) | 1.86531e12 | 0.0525005 | ||||||||
\(514\) | − | 8.73789e13i | − | 2.43552i | ||||||
\(515\) | 3.28801e13i | 0.907605i | ||||||||
\(516\) | 4.10113e13i | 1.12113i | ||||||||
\(517\) | −1.78111e12 | −0.0482213 | ||||||||
\(518\) | 1.14567e14 | 3.07193 | ||||||||
\(519\) | 3.52615e13i | 0.936407i | ||||||||
\(520\) | −7.26533e13 | −1.91090 | ||||||||
\(521\) | 7.49443e13 | 1.95232 | 0.976158 | − | 0.217060i | \(-0.0696467\pi\) | ||||
0.976158 | + | 0.217060i | \(0.0696467\pi\) | |||||||
\(522\) | − | 1.27709e13i | − | 0.329510i | ||||||
\(523\) | −2.65517e13 | −0.678554 | −0.339277 | − | 0.940686i | \(-0.610182\pi\) | ||||
−0.339277 | + | 0.940686i | \(0.610182\pi\) | |||||||
\(524\) | − | 1.40385e14i | − | 3.55358i | ||||||
\(525\) | 3.96254e13 | 0.993520 | ||||||||
\(526\) | 8.35941e13i | 2.07609i | ||||||||
\(527\) | − | 3.05093e13i | − | 0.750548i | ||||||
\(528\) | 2.54431e12i | 0.0620012i | ||||||||
\(529\) | 2.53732e13 | 0.612487 | ||||||||
\(530\) | 1.25927e14i | 3.01121i | ||||||||
\(531\) | 9.80709e12 | + | 1.00915e13i | 0.232310 | + | 0.239047i | ||||
\(532\) | −3.66215e13 | −0.859366 | ||||||||
\(533\) | − | 1.48947e13i | − | 0.346255i | ||||||
\(534\) | −7.54293e13 | −1.73714 | ||||||||
\(535\) | 6.43614e13 | 1.46844 | ||||||||
\(536\) | −2.92461e13 | −0.661064 | ||||||||
\(537\) | − | 1.62755e13i | − | 0.364472i | ||||||
\(538\) | −1.43576e14 | −3.18544 | ||||||||
\(539\) | − | 9.99873e12i | − | 0.219787i | ||||||
\(540\) | −2.45130e13 | −0.533860 | ||||||||
\(541\) | 8.54421e13i | 1.84368i | 0.387570 | + | 0.921840i | \(0.373315\pi\) | ||||
−0.387570 | + | 0.921840i | \(0.626685\pi\) | |||||||
\(542\) | 1.21782e14i | 2.60368i | ||||||||
\(543\) | −2.75713e13 | −0.584061 | ||||||||
\(544\) | 1.39534e13i | 0.292878i | ||||||||
\(545\) | 5.75469e13i | 1.19685i | ||||||||
\(546\) | −6.50680e13 | −1.34092 | ||||||||
\(547\) | −3.36039e13 | −0.686205 | −0.343102 | − | 0.939298i | \(-0.611478\pi\) | ||||
−0.343102 | + | 0.939298i | \(0.611478\pi\) | |||||||
\(548\) | −1.38452e14 | −2.80154 | ||||||||
\(549\) | 5.84009e12i | 0.117100i | ||||||||
\(550\) | −1.21182e13 | −0.240782 | ||||||||
\(551\) | −7.99539e12 | −0.157428 | ||||||||
\(552\) | −2.94801e13 | −0.575219 | ||||||||
\(553\) | 4.28859e13 | 0.829256 | ||||||||
\(554\) | − | 5.87095e13i | − | 1.12502i | ||||||
\(555\) | − | 4.80109e13i | − | 0.911748i | ||||||
\(556\) | −3.63601e10 | −0.000684308 | ||||||||
\(557\) | −6.37800e13 | −1.18962 | −0.594810 | − | 0.803866i | \(-0.702773\pi\) | ||||
−0.594810 | + | 0.803866i | \(0.702773\pi\) | |||||||
\(558\) | −1.72266e13 | −0.318441 | ||||||||
\(559\) | 4.56198e13 | 0.835785 | ||||||||
\(560\) | 1.03836e14 | 1.88542 | ||||||||
\(561\) | 5.74345e12i | 0.103362i | ||||||||
\(562\) | 5.04917e13i | 0.900613i | ||||||||
\(563\) | − | 5.16188e13i | − | 0.912570i | −0.889834 | − | 0.456285i | \(-0.849180\pi\) | ||
0.889834 | − | 0.456285i | \(-0.150820\pi\) | |||||||
\(564\) | − | 2.31029e13i | − | 0.404828i | ||||||
\(565\) | − | 1.88194e13i | − | 0.326862i | ||||||
\(566\) | 9.40445e13 | 1.61902 | ||||||||
\(567\) | −1.06042e13 | −0.180951 | ||||||||
\(568\) | − | 3.32101e13i | − | 0.561731i | ||||||
\(569\) | − | 1.06813e14i | − | 1.79087i | −0.445190 | − | 0.895436i | \(-0.646864\pi\) | ||
0.445190 | − | 0.895436i | \(-0.353136\pi\) | |||||||
\(570\) | 2.32806e13i | 0.386919i | ||||||||
\(571\) | 5.47878e13i | 0.902616i | 0.892368 | + | 0.451308i | \(0.149042\pi\) | ||||
−0.892368 | + | 0.451308i | \(0.850958\pi\) | |||||||
\(572\) | 1.31175e13 | 0.214226 | ||||||||
\(573\) | 5.78715e13i | 0.936896i | ||||||||
\(574\) | 7.22946e13i | 1.16024i | ||||||||
\(575\) | − | 4.13443e13i | − | 0.657774i | ||||||
\(576\) | 2.49400e13 | 0.393354 | ||||||||
\(577\) | 7.67946e13 | 1.20075 | 0.600373 | − | 0.799720i | \(-0.295019\pi\) | ||||
0.600373 | + | 0.799720i | \(0.295019\pi\) | |||||||
\(578\) | − | 8.96436e13i | − | 1.38957i | ||||||
\(579\) | 3.45042e13 | 0.530249 | ||||||||
\(580\) | 1.05072e14 | 1.60083 | ||||||||
\(581\) | 4.90459e13i | 0.740836i | ||||||||
\(582\) | 6.05912e13 | 0.907391 | ||||||||
\(583\) | − | 1.09821e13i | − | 0.163058i | ||||||
\(584\) | 3.19602e13 | 0.470484 | ||||||||
\(585\) | 2.72675e13i | 0.397985i | ||||||||
\(586\) | − | 5.10635e12i | − | 0.0738963i | ||||||
\(587\) | − | 2.35646e13i | − | 0.338119i | −0.985606 | − | 0.169059i | \(-0.945927\pi\) | ||
0.985606 | − | 0.169059i | \(-0.0540729\pi\) | |||||||
\(588\) | 1.29694e14 | 1.84515 | ||||||||
\(589\) | 1.07849e13i | 0.152139i | ||||||||
\(590\) | −1.25950e14 | + | 1.22401e14i | −1.76173 | + | 1.71208i | ||||
\(591\) | 5.23271e12 | 0.0725754 | ||||||||
\(592\) | − | 6.46378e13i | − | 0.888952i | ||||||
\(593\) | −3.97416e12 | −0.0541966 | −0.0270983 | − | 0.999633i | \(-0.508627\pi\) | ||||
−0.0270983 | + | 0.999633i | \(0.508627\pi\) | |||||||
\(594\) | 3.24295e12 | 0.0438539 | ||||||||
\(595\) | 2.34397e14 | 3.14317 | ||||||||
\(596\) | 1.34962e14i | 1.79465i | ||||||||
\(597\) | −6.50576e13 | −0.857880 | ||||||||
\(598\) | 6.78907e13i | 0.887778i | ||||||||
\(599\) | 9.56501e13 | 1.24037 | 0.620185 | − | 0.784455i | \(-0.287057\pi\) | ||||
0.620185 | + | 0.784455i | \(0.287057\pi\) | |||||||
\(600\) | − | 7.59241e13i | − | 0.976390i | ||||||
\(601\) | − | 1.19763e14i | − | 1.52739i | −0.645578 | − | 0.763694i | \(-0.723384\pi\) | ||
0.645578 | − | 0.763694i | \(-0.276616\pi\) | |||||||
\(602\) | −2.21425e14 | −2.80056 | ||||||||
\(603\) | 1.09764e13i | 0.137680i | ||||||||
\(604\) | − | 2.22662e14i | − | 2.76988i | ||||||
\(605\) | −1.14184e14 | −1.40873 | ||||||||
\(606\) | 1.06633e14 | 1.30475 | ||||||||
\(607\) | 9.12510e13 | 1.10737 | 0.553687 | − | 0.832725i | \(-0.313221\pi\) | ||||
0.553687 | + | 0.832725i | \(0.313221\pi\) | |||||||
\(608\) | − | 4.93250e12i | − | 0.0593675i | ||||||
\(609\) | 4.54533e13 | 0.542599 | ||||||||
\(610\) | −7.28892e13 | −0.863006 | ||||||||
\(611\) | −2.56989e13 | −0.301793 | ||||||||
\(612\) | −7.44985e13 | −0.867741 | ||||||||
\(613\) | 1.62743e14i | 1.88018i | 0.340928 | + | 0.940089i | \(0.389259\pi\) | ||||
−0.340928 | + | 0.940089i | \(0.610741\pi\) | |||||||
\(614\) | 7.00145e13i | 0.802317i | ||||||||
\(615\) | 3.02959e13 | 0.344357 | ||||||||
\(616\) | −3.07535e13 | −0.346729 | ||||||||
\(617\) | −1.37883e13 | −0.154200 | −0.0771002 | − | 0.997023i | \(-0.524566\pi\) | ||||
−0.0771002 | + | 0.997023i | \(0.524566\pi\) | |||||||
\(618\) | 5.64224e13 | 0.625906 | ||||||||
\(619\) | 2.94466e13 | 0.324028 | 0.162014 | − | 0.986788i | \(-0.448201\pi\) | ||||
0.162014 | + | 0.986788i | \(0.448201\pi\) | |||||||
\(620\) | − | 1.41731e14i | − | 1.54705i | ||||||
\(621\) | 1.10642e13i | 0.119801i | ||||||||
\(622\) | − | 1.50824e14i | − | 1.62001i | ||||||
\(623\) | − | 2.68463e14i | − | 2.86052i | ||||||
\(624\) | 3.67108e13i | 0.388034i | ||||||||
\(625\) | −8.96582e13 | −0.940134 | ||||||||
\(626\) | 1.17273e14 | 1.21990 | ||||||||
\(627\) | − | 2.03030e12i | − | 0.0209518i | ||||||
\(628\) | − | 3.06662e14i | − | 3.13951i | ||||||
\(629\) | − | 1.45912e14i | − | 1.48196i | ||||||
\(630\) | − | 1.32349e14i | − | 1.33357i | ||||||
\(631\) | 5.81855e13 | 0.581658 | 0.290829 | − | 0.956775i | \(-0.406069\pi\) | ||||
0.290829 | + | 0.956775i | \(0.406069\pi\) | |||||||
\(632\) | − | 8.21714e13i | − | 0.814958i | ||||||
\(633\) | 9.97422e13i | 0.981433i | ||||||||
\(634\) | − | 7.38964e13i | − | 0.721402i | ||||||
\(635\) | −1.91958e14 | −1.85925 | ||||||||
\(636\) | 1.42449e14 | 1.36891 | ||||||||
\(637\) | − | 1.44268e14i | − | 1.37554i | ||||||
\(638\) | −1.39005e13 | −0.131500 | ||||||||
\(639\) | −1.24641e13 | −0.116992 | ||||||||
\(640\) | 2.77761e14i | 2.58685i | ||||||||
\(641\) | 7.38506e13 | 0.682439 | 0.341219 | − | 0.939984i | \(-0.389160\pi\) | ||||
0.341219 | + | 0.939984i | \(0.389160\pi\) | |||||||
\(642\) | − | 1.10444e14i | − | 1.01267i | ||||||
\(643\) | −8.30666e13 | −0.755739 | −0.377869 | − | 0.925859i | \(-0.623343\pi\) | ||||
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(644\) | − | 2.17223e14i | − | 1.96099i | ||||||
\(645\) | 9.27910e13i | 0.831204i | ||||||||
\(646\) | 7.07530e13i | 0.628901i | ||||||||
\(647\) | 1.99383e14 | 1.75860 | 0.879300 | − | 0.476268i | \(-0.158011\pi\) | ||||
0.879300 | + | 0.476268i | \(0.158011\pi\) | |||||||
\(648\) | 2.03181e13i | 0.177831i | ||||||||
\(649\) | 1.09841e13 | − | 1.06745e13i | 0.0953983 | − | 0.0927097i | ||||
\(650\) | −1.74848e14 | −1.50694 | ||||||||
\(651\) | − | 6.13118e13i | − | 0.524371i | ||||||
\(652\) | −5.00370e13 | −0.424671 | ||||||||
\(653\) | 4.42893e13 | 0.373021 | 0.186510 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186510 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(654\) | 9.87508e13 | 0.825376 | ||||||||
\(655\) | − | 3.17632e14i | − | 2.63462i | ||||||
\(656\) | 4.07879e13 | 0.335747 | ||||||||
\(657\) | − | 1.19950e13i | − | 0.0979880i | ||||||
\(658\) | 1.24735e14 | 1.01125 | ||||||||
\(659\) | 9.75611e13i | 0.784964i | 0.919760 | + | 0.392482i | \(0.128383\pi\) | ||||
−0.919760 | + | 0.392482i | \(0.871617\pi\) | |||||||
\(660\) | 2.66812e13i | 0.213052i | ||||||||
\(661\) | 6.45464e12 | 0.0511523 | 0.0255761 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255761 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(662\) | − | 2.93005e14i | − | 2.30454i | ||||||
\(663\) | 8.28699e13i | 0.646888i | ||||||||
\(664\) | 9.39743e13 | 0.728063 | ||||||||
\(665\) | −8.28588e13 | −0.637133 | ||||||||
\(666\) | −8.23869e13 | −0.628763 | ||||||||
\(667\) | − | 4.74251e13i | − | 0.359235i | ||||||
\(668\) | 1.58873e13 | 0.119445 | ||||||||
\(669\) | −1.23605e14 | −0.922367 | ||||||||
\(670\) | −1.36994e14 | −1.01468 | ||||||||
\(671\) | 6.35665e12 | 0.0467322 | ||||||||
\(672\) | 2.80410e13i | 0.204619i | ||||||||
\(673\) | 4.61819e13i | 0.334500i | 0.985914 | + | 0.167250i | \(0.0534887\pi\) | ||||
−0.985914 | + | 0.167250i | \(0.946511\pi\) | |||||||
\(674\) | 3.09723e13 | 0.222676 | ||||||||
\(675\) | −2.84951e13 | −0.203354 | ||||||||
\(676\) | −8.37949e13 | −0.593586 | ||||||||
\(677\) | 8.77618e13 | 0.617110 | 0.308555 | − | 0.951207i | \(-0.400155\pi\) | ||||
0.308555 | + | 0.951207i | \(0.400155\pi\) | |||||||
\(678\) | −3.22942e13 | −0.225412 | ||||||||
\(679\) | 2.15652e14i | 1.49419i | ||||||||
\(680\) | − | 4.49116e14i | − | 3.08897i | ||||||
\(681\) | 7.43828e13i | 0.507852i | ||||||||
\(682\) | 1.87503e13i | 0.127083i | ||||||||
\(683\) | 2.02710e14i | 1.36387i | 0.731414 | + | 0.681933i | \(0.238861\pi\) | ||||
−0.731414 | + | 0.681933i | \(0.761139\pi\) | |||||||
\(684\) | 2.63350e13 | 0.175895 | ||||||||
\(685\) | −3.13258e14 | −2.07706 | ||||||||
\(686\) | 2.76416e14i | 1.81946i | ||||||||
\(687\) | − | 7.55621e13i | − | 0.493765i | ||||||
\(688\) | 1.24926e14i | 0.810422i | ||||||||
\(689\) | − | 1.58456e14i | − | 1.02050i | ||||||
\(690\) | −1.38090e14 | −0.882912 | ||||||||
\(691\) | − | 2.19696e14i | − | 1.39454i | −0.716806 | − | 0.697272i | \(-0.754397\pi\) | ||
0.716806 | − | 0.697272i | \(-0.245603\pi\) | |||||||
\(692\) | 4.97834e14i | 3.13728i | ||||||||
\(693\) | 1.15421e13i | 0.0722136i | ||||||||
\(694\) | 2.13304e14 | 1.32495 | ||||||||
\(695\) | −8.22674e10 | −0.000507345 | ||||||||
\(696\) | − | 8.70907e13i | − | 0.533243i | ||||||
\(697\) | 9.20737e13 | 0.559721 | ||||||||
\(698\) | −5.84764e13 | −0.352942 | ||||||||
\(699\) | 5.40139e13i | 0.323683i | ||||||||
\(700\) | 5.59444e14 | 3.32863 | ||||||||
\(701\) | 3.01975e14i | 1.78394i | 0.452091 | + | 0.891972i | \(0.350678\pi\) | ||||
−0.452091 | + | 0.891972i | \(0.649322\pi\) | |||||||
\(702\) | 4.67913e13 | 0.274460 | ||||||||
\(703\) | 5.15794e13i | 0.300400i | ||||||||
\(704\) | − | 2.71460e13i | − | 0.156979i | ||||||
\(705\) | − | 5.22718e13i | − | 0.300139i | ||||||
\(706\) | −2.65583e13 | −0.151418 | ||||||||
\(707\) | 3.79521e14i | 2.14852i | ||||||||
\(708\) | 1.38460e14 | + | 1.42475e14i | 0.778318 | + | 0.800888i | ||||
\(709\) | −7.73009e13 | −0.431473 | −0.215736 | − | 0.976452i | \(-0.569215\pi\) | ||||
−0.215736 | + | 0.976452i | \(0.569215\pi\) | |||||||
\(710\) | − | 1.55562e14i | − | 0.862209i | ||||||
\(711\) | −3.08398e13 | −0.169732 | ||||||||
\(712\) | −5.14388e14 | −2.81120 | ||||||||
\(713\) | −6.39715e13 | −0.347167 | ||||||||
\(714\) | − | 4.02227e14i | − | 2.16760i | ||||||
\(715\) | 2.96794e13 | 0.158827 | ||||||||
\(716\) | − | 2.29783e14i | − | 1.22111i | ||||||
\(717\) | 1.61085e14 | 0.850079 | ||||||||
\(718\) | − | 5.74514e14i | − | 3.01077i | ||||||
\(719\) | − | 2.62216e14i | − | 1.36463i | −0.731059 | − | 0.682314i | \(-0.760974\pi\) | ||
0.731059 | − | 0.682314i | \(-0.239026\pi\) | |||||||
\(720\) | −7.46699e13 | −0.385908 | ||||||||
\(721\) | 2.00815e14i | 1.03067i | ||||||||
\(722\) | 3.11067e14i | 1.58551i | ||||||||
\(723\) | 5.78778e13 | 0.292968 | ||||||||
\(724\) | −3.89260e14 | −1.95680 | ||||||||
\(725\) | 1.22140e14 | 0.609775 | ||||||||
\(726\) | 1.95940e14i | 0.971492i | ||||||||
\(727\) | −1.80737e14 | −0.889970 | −0.444985 | − | 0.895538i | \(-0.646791\pi\) | ||||
−0.444985 | + | 0.895538i | \(0.646791\pi\) | |||||||
\(728\) | −4.43729e14 | −2.17001 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 1.49707e14 | 0.722153 | ||||||||
\(731\) | 2.82005e14i | 1.35105i | ||||||||
\(732\) | 8.24523e13i | 0.392326i | ||||||||
\(733\) | 3.23004e14 | 1.52647 | 0.763236 | − | 0.646120i | \(-0.223610\pi\) | ||||
0.763236 | + | 0.646120i | \(0.223610\pi\) | |||||||
\(734\) | −4.78491e14 | −2.24591 | ||||||||
\(735\) | 2.93441e14 | 1.36800 | ||||||||
\(736\) | 2.92574e13 | 0.135471 | ||||||||
\(737\) | 1.19472e13 | 0.0549452 | ||||||||
\(738\) | − | 5.19880e13i | − | 0.237477i | ||||||
\(739\) | 7.65366e13i | 0.347254i | 0.984812 | + | 0.173627i | \(0.0555486\pi\) | ||||
−0.984812 | + | 0.173627i | \(0.944451\pi\) | |||||||
\(740\) | − | 6.77833e14i | − | 3.05467i | ||||||
\(741\) | − | 2.92943e13i | − | 0.131127i | ||||||
\(742\) | 7.69100e14i | 3.41951i | ||||||||
\(743\) | −2.02718e14 | −0.895257 | −0.447629 | − | 0.894220i | \(-0.647731\pi\) | ||||
−0.447629 | + | 0.894220i | \(0.647731\pi\) | |||||||
\(744\) | −1.17476e14 | −0.515330 | ||||||||
\(745\) | 3.05361e14i | 1.33055i | ||||||||
\(746\) | − | 4.05427e14i | − | 1.75476i | ||||||
\(747\) | − | 3.52696e13i | − | 0.151634i | ||||||
\(748\) | 8.10879e13i | 0.346297i | ||||||||
\(749\) | 3.93087e14 | 1.66755 | ||||||||
\(750\) | − | 1.90689e13i | − | 0.0803562i | ||||||
\(751\) | 4.55437e14i | 1.90647i | 0.302238 | + | 0.953233i | \(0.402266\pi\) | ||||
−0.302238 | + | 0.953233i | \(0.597734\pi\) | |||||||
\(752\) | − | 7.03745e13i | − | 0.292635i | ||||||
\(753\) | 1.03644e14 | 0.428122 | ||||||||
\(754\) | −2.00564e14 | −0.822994 | ||||||||
\(755\) | − | 5.03787e14i | − | 2.05358i | ||||||
\(756\) | −1.49713e14 | −0.606248 | ||||||||
\(757\) | 1.19767e14 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(758\) | 1.15774e14i | 0.462662i | ||||||||
\(759\) | 1.20428e13 | 0.0478100 | ||||||||
\(760\) | 1.58761e14i | 0.626148i | ||||||||
\(761\) | −3.20270e14 | −1.25485 | −0.627427 | − | 0.778676i | \(-0.715892\pi\) | ||||
−0.627427 | + | 0.778676i | \(0.715892\pi\) | |||||||
\(762\) | 3.29400e14i | 1.28218i | ||||||||
\(763\) | 3.51468e14i | 1.35913i | ||||||||
\(764\) | 8.17048e14i | 3.13893i | ||||||||
\(765\) | −1.68558e14 | −0.643343 | ||||||||
\(766\) | 8.37419e13i | 0.317540i | ||||||||
\(767\) | 1.58485e14 | − | 1.54018e14i | 0.597050 | − | 0.580224i | ||||
\(768\) | 2.94606e14 | 1.10265 | ||||||||
\(769\) | 1.47981e14i | 0.550268i | 0.961406 | + | 0.275134i | \(0.0887223\pi\) | ||||
−0.961406 | + | 0.275134i | \(0.911278\pi\) | |||||||
\(770\) | −1.44055e14 | −0.532200 | ||||||||
\(771\) | −2.23639e14 | −0.820874 | ||||||||
\(772\) | 4.87142e14 | 1.77652 | ||||||||
\(773\) | − | 4.29167e13i | − | 0.155500i | −0.996973 | − | 0.0777498i | \(-0.975226\pi\) | ||
0.996973 | − | 0.0777498i | \(-0.0247735\pi\) | |||||||
\(774\) | 1.59230e14 | 0.573218 | ||||||||
\(775\) | − | 1.64755e14i | − | 0.589290i | ||||||
\(776\) | 4.13200e14 | 1.46842 | ||||||||
\(777\) | − | 2.93226e14i | − | 1.03537i | ||||||
\(778\) | 3.37549e14i | 1.18424i | ||||||||
\(779\) | −3.25478e13 | −0.113458 | ||||||||
\(780\) | 3.84972e14i | 1.33339i | ||||||||
\(781\) | 1.35666e13i | 0.0466890i | ||||||||
\(782\) | −4.19676e14 | −1.43509 | ||||||||
\(783\) | −3.26861e13 | −0.111059 | ||||||||
\(784\) | 3.95065e14 | 1.33379 | ||||||||
\(785\) | − | 6.93846e14i | − | 2.32763i | ||||||
\(786\) | −5.45058e14 | −1.81690 | ||||||||
\(787\) | 4.61361e14 | 1.52815 | 0.764077 | − | 0.645125i | \(-0.223195\pi\) | ||||
0.764077 | + | 0.645125i | \(0.223195\pi\) | |||||||
\(788\) | 7.38771e13 | 0.243153 | ||||||||
\(789\) | 2.13953e14 | 0.699733 | ||||||||
\(790\) | − | 3.84906e14i | − | 1.25089i | ||||||
\(791\) | − | 1.14939e14i | − | 0.371182i | ||||||
\(792\) | 2.21152e13 | 0.0709685 | ||||||||
\(793\) | 9.17175e13 | 0.292473 | ||||||||
\(794\) | 1.61925e14 | 0.513112 | ||||||||
\(795\) | 3.22301e14 | 1.01491 | ||||||||
\(796\) | −9.18504e14 | −2.87419 | ||||||||
\(797\) | 1.44143e14i | 0.448231i | 0.974563 | + | 0.224116i | \(0.0719493\pi\) | ||||
−0.974563 | + | 0.224116i | \(0.928051\pi\) | |||||||
\(798\) | 1.42186e14i | 0.439382i | ||||||||
\(799\) | − | 1.58862e14i | − | 0.487848i | ||||||
\(800\) | 7.53506e13i | 0.229952i | ||||||||
\(801\) | 1.93055e14i | 0.585490i | ||||||||
\(802\) | 6.03638e14 | 1.81930 | ||||||||
\(803\) | −1.30560e13 | −0.0391049 | ||||||||
\(804\) | 1.54968e14i | 0.461276i | ||||||||
\(805\) | − | 4.91481e14i | − | 1.45388i | ||||||
\(806\) | 2.70540e14i | 0.795347i | ||||||||
\(807\) | 3.67471e14i | 1.07363i | ||||||||
\(808\) | 7.27181e14 | 2.11147 | ||||||||
\(809\) | − | 6.54583e14i | − | 1.88896i | −0.328573 | − | 0.944478i | \(-0.606568\pi\) | ||
0.328573 | − | 0.944478i | \(-0.393432\pi\) | |||||||
\(810\) | 9.51738e13i | 0.272956i | ||||||||
\(811\) | 9.01373e13i | 0.256921i | 0.991715 | + | 0.128461i | \(0.0410036\pi\) | ||||
−0.991715 | + | 0.128461i | \(0.958996\pi\) | |||||||
\(812\) | 6.41724e14 | 1.81789 | ||||||||
\(813\) | 3.11693e14 | 0.877554 | ||||||||
\(814\) | 8.96741e13i | 0.250926i | ||||||||
\(815\) | −1.13212e14 | −0.314851 | ||||||||
\(816\) | −2.26933e14 | −0.627258 | ||||||||
\(817\) | − | 9.96881e13i | − | 0.273863i | ||||||
\(818\) | −6.11498e14 | −1.66966 | ||||||||
\(819\) | 1.66536e14i | 0.451949i | ||||||||
\(820\) | 4.27728e14 | 1.15371 | ||||||||
\(821\) | − | 5.37663e14i | − | 1.44143i | −0.693230 | − | 0.720716i | \(-0.743813\pi\) | ||
0.693230 | − | 0.720716i | \(-0.256187\pi\) | |||||||
\(822\) | 5.37552e14i | 1.43239i | ||||||||
\(823\) | − | 2.77563e14i | − | 0.735127i | −0.929998 | − | 0.367564i | \(-0.880192\pi\) | ||
0.929998 | − | 0.367564i | \(-0.119808\pi\) | |||||||
\(824\) | 3.84771e14 | 1.01290 | ||||||||
\(825\) | 3.10155e13i | 0.0811539i | ||||||||
\(826\) | −7.69240e14 | + | 7.47561e14i | −2.00061 | + | 1.94422i | ||||
\(827\) | 1.24917e14 | 0.322920 | 0.161460 | − | 0.986879i | \(-0.448380\pi\) | ||||
0.161460 | + | 0.986879i | \(0.448380\pi\) | |||||||
\(828\) | 1.56208e14i | 0.401375i | ||||||||
\(829\) | −1.50300e14 | −0.383873 | −0.191936 | − | 0.981407i | \(-0.561477\pi\) | ||||
−0.191936 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(830\) | 4.40194e14 | 1.11751 | ||||||||
\(831\) | −1.50262e14 | −0.379179 | ||||||||
\(832\) | − | 3.91678e14i | − | 0.982455i | ||||||
\(833\) | 8.91810e14 | 2.22355 | ||||||||
\(834\) | 1.41171e11i | 0.000349878i | ||||||||
\(835\) | 3.59461e13 | 0.0885562 | ||||||||
\(836\) | − | 2.86644e13i | − | 0.0701958i | ||||||
\(837\) | 4.40901e13i | 0.107328i | ||||||||
\(838\) | 3.08913e14 | 0.747508 | ||||||||
\(839\) | − | 3.68858e14i | − | 0.887257i | −0.896211 | − | 0.443629i | \(-0.853691\pi\) | ||
0.896211 | − | 0.443629i | \(-0.146309\pi\) | |||||||
\(840\) | − | 9.02549e14i | − | 2.15811i | ||||||
\(841\) | −2.80603e14 | −0.666979 | ||||||||
\(842\) | 7.51565e13 | 0.177585 | ||||||||
\(843\) | 1.29229e14 | 0.303545 | ||||||||
\(844\) | 1.40819e15i | 3.28814i | ||||||||
\(845\) | −1.89592e14 | −0.440084 | ||||||||
\(846\) | −8.96988e13 | −0.206983 | ||||||||
\(847\) | −6.97376e14 | −1.59974 | ||||||||
\(848\) | 4.33919e14 | 0.989531 | ||||||||
\(849\) | − | 2.40699e14i | − | 0.545678i | ||||||
\(850\) | − | 1.08085e15i | − | 2.43596i | ||||||
\(851\) | −3.05946e14 | −0.685484 | ||||||||
\(852\) | −1.75972e14 | −0.391964 | ||||||||
\(853\) | −5.87151e14 | −1.30018 | −0.650092 | − | 0.759855i | \(-0.725270\pi\) | ||||
−0.650092 | + | 0.759855i | \(0.725270\pi\) | |||||||
\(854\) | −4.45170e14 | −0.980024 | ||||||||
\(855\) | 5.95848e13 | 0.130408 | ||||||||
\(856\) | − | 7.53173e14i | − | 1.63880i | ||||||
\(857\) | 8.93692e13i | 0.193323i | 0.995317 | + | 0.0966616i | \(0.0308164\pi\) | ||||
−0.995317 | + | 0.0966616i | \(0.969184\pi\) | |||||||
\(858\) | − | 5.09300e13i | − | 0.109531i | ||||||
\(859\) | − | 8.25451e14i | − | 1.76492i | −0.470386 | − | 0.882461i | \(-0.655885\pi\) | ||
0.470386 | − | 0.882461i | \(-0.344115\pi\) | |||||||
\(860\) | 1.31005e15i | 2.78482i | ||||||||
\(861\) | 1.85032e14 | 0.391050 | ||||||||
\(862\) | 1.54281e15 | 3.24172 | ||||||||
\(863\) | − | 9.45516e11i | − | 0.00197522i | −1.00000 | 0.000987609i | \(-0.999686\pi\) | |||
1.00000 | 0.000987609i | \(-0.000314366\pi\) | ||||||||
\(864\) | − | 2.01646e13i | − | 0.0418814i | ||||||
\(865\) | 1.12638e15i | 2.32598i | ||||||||
\(866\) | 8.99089e14i | 1.84592i | ||||||||
\(867\) | −2.29436e14 | −0.468345 | ||||||||
\(868\) | − | 8.65619e14i | − | 1.75682i | ||||||
\(869\) | 3.35676e13i | 0.0677363i | ||||||||
\(870\) | − | 4.07949e14i | − | 0.818483i | ||||||
\(871\) | 1.72382e14 | 0.343875 | ||||||||
\(872\) | 6.73429e14 | 1.33570 | ||||||||
\(873\) | − | 1.55078e14i | − | 0.305830i | ||||||
\(874\) | 1.48354e14 | 0.290899 | ||||||||
\(875\) | 6.78688e13 | 0.132321 | ||||||||
\(876\) | − | 1.69349e14i | − | 0.328294i | ||||||
\(877\) | 5.57499e13 | 0.107460 | 0.0537299 | − | 0.998556i | \(-0.482889\pi\) | ||||
0.0537299 | + | 0.998556i | \(0.482889\pi\) | |||||||
\(878\) | 1.12503e15i | 2.15621i | ||||||||
\(879\) | −1.30693e13 | −0.0249063 | ||||||||
\(880\) | 8.12746e13i | 0.154007i | ||||||||
\(881\) | − | 1.10028e14i | − | 0.207312i | −0.994613 | − | 0.103656i | \(-0.966946\pi\) | ||
0.994613 | − | 0.103656i | \(-0.0330541\pi\) | |||||||
\(882\) | − | 5.03547e14i | − | 0.943403i | ||||||
\(883\) | 2.09051e14 | 0.389448 | 0.194724 | − | 0.980858i | \(-0.437619\pi\) | ||||
0.194724 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(884\) | 1.16998e15i | 2.16730i | ||||||||
\(885\) | 3.13275e14 | + | 3.22359e14i | 0.577044 | + | 0.593778i | ||||
\(886\) | −1.76392e15 | −3.23080 | ||||||||
\(887\) | − | 1.47493e14i | − | 0.268630i | −0.990939 | − | 0.134315i | \(-0.957117\pi\) | ||
0.990939 | − | 0.134315i | \(-0.0428833\pi\) | |||||||
\(888\) | −5.61835e14 | −1.01752 | ||||||||
\(889\) | −1.17238e15 | −2.11135 | ||||||||
\(890\) | −2.40949e15 | −4.31495 | ||||||||
\(891\) | − | 8.30009e12i | − | 0.0147807i | ||||||
\(892\) | −1.74509e15 | −3.09025 | ||||||||
\(893\) | 5.61571e13i | 0.0988889i | ||||||||
\(894\) | 5.24002e14 | 0.917582 | ||||||||
\(895\) | − | 5.19901e14i | − | 0.905326i | ||||||
\(896\) | 1.69642e15i | 2.93761i | ||||||||
\(897\) | 1.73761e14 | 0.299219 | ||||||||
\(898\) | 1.09989e15i | 1.88350i | ||||||||
\(899\) | − | 1.88986e14i | − | 0.321834i | ||||||
\(900\) | −4.02303e14 | −0.681304 | ||||||||
\(901\) | 9.79518e14 | 1.64964 | ||||||||
\(902\) | −5.65864e13 | −0.0947718 | ||||||||
\(903\) | 5.66721e14i | 0.943910i | ||||||||
\(904\) | −2.20230e14 | −0.364782 | ||||||||
\(905\) | −8.80729e14 | −1.45077 | ||||||||
\(906\) | −8.64502e14 | −1.41620 | ||||||||
\(907\) | 1.13791e15 | 1.85384 | 0.926922 | − | 0.375254i | \(-0.122444\pi\) | ||||
0.926922 | + | 0.375254i | \(0.122444\pi\) | |||||||
\(908\) | 1.05016e15i | 1.70148i | ||||||||
\(909\) | − | 2.72919e14i | − | 0.439758i | ||||||
\(910\) | −2.07851e15 | −3.33078 | ||||||||
\(911\) | 4.19526e14 | 0.668601 | 0.334301 | − | 0.942466i | \(-0.391500\pi\) | ||||
0.334301 | + | 0.942466i | \(0.391500\pi\) | |||||||
\(912\) | 8.02201e13 | 0.127148 | ||||||||
\(913\) | −3.83892e13 | −0.0605139 | ||||||||
\(914\) | −1.02153e15 | −1.60148 | ||||||||
\(915\) | 1.86554e14i | 0.290870i | ||||||||
\(916\) | − | 1.06681e15i | − | 1.65428i | ||||||
\(917\) | − | 1.93994e15i | − | 2.99185i | ||||||
\(918\) | 2.89247e14i | 0.443665i | ||||||||
\(919\) | − | 5.23381e14i | − | 0.798436i | −0.916856 | − | 0.399218i | \(-0.869282\pi\) | ||
0.916856 | − | 0.399218i | \(-0.130718\pi\) | |||||||
\(920\) | −9.41702e14 | −1.42881 | ||||||||
\(921\) | 1.79197e14 | 0.270416 | ||||||||
\(922\) | 1.08791e15i | 1.63282i | ||||||||
\(923\) | 1.95746e14i | 0.292203i | ||||||||
\(924\) | 1.62955e14i | 0.241940i | ||||||||
\(925\) | − | 7.87946e14i | − | 1.16356i | ||||||
\(926\) | −5.38895e14 | −0.791497 | ||||||||
\(927\) | − | 1.44409e14i | − | 0.210957i | ||||||
\(928\) | 8.64329e13i | 0.125585i | ||||||||
\(929\) | 1.48309e14i | 0.214333i | 0.994241 | + | 0.107166i | \(0.0341778\pi\) | ||||
−0.994241 | + | 0.107166i | \(0.965822\pi\) | |||||||
\(930\) | −5.50281e14 | −0.790988 | ||||||||
\(931\) | −3.15253e14 | −0.450723 | ||||||||
\(932\) | 7.62586e14i | 1.08445i | ||||||||
\(933\) | −3.86022e14 | −0.546014 | ||||||||
\(934\) | 3.86869e14 | 0.544290 | ||||||||
\(935\) | 1.83467e14i | 0.256744i | ||||||||
\(936\) | 3.19092e14 | 0.444157 | ||||||||
\(937\) | − | 4.43050e14i | − | 0.613415i | −0.951804 | − | 0.306708i | \(-0.900773\pi\) | ||
0.951804 | − | 0.306708i | \(-0.0992273\pi\) | |||||||
\(938\) | −8.36691e14 | −1.15226 | ||||||||
\(939\) | − | 3.00151e14i | − | 0.411160i | ||||||
\(940\) | − | 7.37991e14i | − | 1.00557i | ||||||
\(941\) | − | 9.43694e14i | − | 1.27904i | −0.768776 | − | 0.639518i | \(-0.779134\pi\) | ||
0.768776 | − | 0.639518i | \(-0.220866\pi\) | |||||||
\(942\) | −1.19064e15 | −1.60519 | ||||||||
\(943\) | − | 1.93059e14i | − | 0.258900i | ||||||
\(944\) | 4.21767e14 | + | 4.33998e14i | 0.562617 | + | 0.578932i | ||||
\(945\) | −3.38736e14 | −0.449472 | ||||||||
\(946\) | − | 1.73314e14i | − | 0.228759i | ||||||
\(947\) | −6.06562e13 | −0.0796389 | −0.0398195 | − | 0.999207i | \(-0.512678\pi\) | ||||
−0.0398195 | + | 0.999207i | \(0.512678\pi\) | |||||||
\(948\) | −4.35406e14 | −0.568661 | ||||||||
\(949\) | −1.88379e14 | −0.244738 | ||||||||
\(950\) | 3.82077e14i | 0.493780i | ||||||||
\(951\) | −1.89132e14 | −0.243143 | ||||||||
\(952\) | − | 2.74297e15i | − | 3.50782i | ||||||
\(953\) | 4.11774e14 | 0.523835 | 0.261918 | − | 0.965090i | \(-0.415645\pi\) | ||||
0.261918 | + | 0.965090i | \(0.415645\pi\) | |||||||
\(954\) | − | 5.53070e14i | − | 0.699904i | ||||||
\(955\) | 1.84863e15i | 2.32720i | ||||||||
\(956\) | 2.27425e15 | 2.84806 | ||||||||
\(957\) | 3.55772e13i | 0.0443212i | ||||||||
\(958\) | 8.60916e14i | 1.06692i | ||||||||
\(959\) | −1.91322e15 | −2.35870 | ||||||||
\(960\) | 7.96676e14 | 0.977070 | ||||||||
\(961\) | 5.64706e14 | 0.688978 | ||||||||
\(962\) | 1.29387e15i | 1.57042i | ||||||||
\(963\) | −2.82674e14 | −0.341314 | ||||||||
\(964\) | 8.17138e14 | 0.981545 | ||||||||
\(965\) | 1.10219e15 | 1.31711 | ||||||||
\(966\) | −8.43385e14 | −1.00263 | ||||||||
\(967\) | − | 5.62073e14i | − | 0.664753i | −0.943147 | − | 0.332376i | \(-0.892150\pi\) | ||
0.943147 | − | 0.332376i | \(-0.107850\pi\) | |||||||
\(968\) | 1.33621e15i | 1.57216i | ||||||||
\(969\) | 1.81087e14 | 0.211967 | ||||||||
\(970\) | 1.93551e15 | 2.25391 | ||||||||
\(971\) | −1.20236e15 | −1.39296 | −0.696481 | − | 0.717575i | \(-0.745252\pi\) | ||||
−0.696481 | + | 0.717575i | \(0.745252\pi\) | |||||||
\(972\) | 1.07661e14 | 0.124087 | ||||||||
\(973\) | −5.02448e11 | −0.000576138 | ||||||||
\(974\) | − | 1.94782e15i | − | 2.22205i | ||||||
\(975\) | 4.47510e14i | 0.507902i | ||||||||
\(976\) | 2.51161e14i | 0.283598i | ||||||||
\(977\) | 3.27645e13i | 0.0368070i | 0.999831 | + | 0.0184035i | \(0.00585835\pi\) | ||||
−0.999831 | + | 0.0184035i | \(0.994142\pi\) | |||||||
\(978\) | 1.94273e14i | 0.217129i | ||||||||
\(979\) | 2.10131e14 | 0.233656 | ||||||||
\(980\) | 4.14290e15 | 4.58326 | ||||||||
\(981\) | − | 2.52745e14i | − | 0.278187i | ||||||
\(982\) | − | 2.46417e15i | − | 2.69845i | ||||||
\(983\) | 3.08300e14i | 0.335897i | 0.985796 | + | 0.167948i | \(0.0537142\pi\) | ||||
−0.985796 | + | 0.167948i | \(0.946286\pi\) | |||||||
\(984\) | − | 3.54531e14i | − | 0.384307i | ||||||
\(985\) | 1.67152e14 | 0.180273 | ||||||||
\(986\) | − | 1.23982e15i | − | 1.33037i | ||||||
\(987\) | − | 3.19250e14i | − | 0.340836i | ||||||
\(988\) | − | 4.13586e14i | − | 0.439321i | ||||||
\(989\) | 5.91305e14 | 0.624929 | ||||||||
\(990\) | 1.03592e14 | 0.108931 | ||||||||
\(991\) | − | 6.90032e13i | − | 0.0721940i | −0.999348 | − | 0.0360970i | \(-0.988507\pi\) | ||
0.999348 | − | 0.0360970i | \(-0.0114925\pi\) | |||||||
\(992\) | 1.16589e14 | 0.121367 | ||||||||
\(993\) | −7.49922e14 | −0.776730 | ||||||||
\(994\) | − | 9.50096e14i | − | 0.979119i | ||||||
\(995\) | −2.07818e15 | −2.13092 | ||||||||
\(996\) | − | 4.97947e14i | − | 0.508027i | ||||||
\(997\) | 1.52386e15 | 1.54693 | 0.773464 | − | 0.633841i | \(-0.218523\pi\) | ||||
0.773464 | + | 0.633841i | \(0.218523\pi\) | |||||||
\(998\) | − | 3.08059e15i | − | 3.11158i | ||||||
\(999\) | 2.10863e14i | 0.211920i |
(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 | 177.11.c.a.58.10 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.91 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.10 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.91 | yes | 100 | 59.58 | odd | 2 | inner |