Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
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, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(6.43791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.43791 | 0.657425 | 0.328712 | − | 0.944430i | \(-0.393385\pi\) | ||||
0.328712 | + | 0.944430i | \(0.393385\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −72.6775 | −0.567793 | ||||||||
\(5\) | 171.827 | 0.614747 | 0.307374 | − | 0.951589i | \(-0.400550\pi\) | ||||
0.307374 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(6\) | 200.824 | 0.379564 | ||||||||
\(7\) | 1529.87 | 1.68582 | 0.842909 | − | 0.538056i | \(-0.180841\pi\) | ||||
0.842909 | + | 0.538056i | \(0.180841\pi\) | |||||||
\(8\) | −1492.62 | −1.03071 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1278.03 | 0.404150 | ||||||||
\(11\) | −1638.92 | −0.371263 | −0.185632 | − | 0.982619i | \(-0.559433\pi\) | ||||
−0.185632 | + | 0.982619i | \(0.559433\pi\) | |||||||
\(12\) | −1962.29 | −0.327815 | ||||||||
\(13\) | −7315.98 | −0.923572 | −0.461786 | − | 0.886991i | \(-0.652791\pi\) | ||||
−0.461786 | + | 0.886991i | \(0.652791\pi\) | |||||||
\(14\) | 11379.0 | 1.10830 | ||||||||
\(15\) | 4639.33 | 0.354924 | ||||||||
\(16\) | −1799.27 | −0.109818 | ||||||||
\(17\) | 33214.7 | 1.63968 | 0.819841 | − | 0.572592i | \(-0.194062\pi\) | ||||
0.819841 | + | 0.572592i | \(0.194062\pi\) | |||||||
\(18\) | 5422.24 | 0.219142 | ||||||||
\(19\) | 55570.3 | 1.85868 | 0.929342 | − | 0.369221i | \(-0.120375\pi\) | ||||
0.929342 | + | 0.369221i | \(0.120375\pi\) | |||||||
\(20\) | −12488.0 | −0.349049 | ||||||||
\(21\) | 41306.4 | 0.973308 | ||||||||
\(22\) | −12190.1 | −0.244078 | ||||||||
\(23\) | −51886.9 | −0.889222 | −0.444611 | − | 0.895724i | \(-0.646658\pi\) | ||||
−0.444611 | + | 0.895724i | \(0.646658\pi\) | |||||||
\(24\) | −40300.8 | −0.595078 | ||||||||
\(25\) | −48600.5 | −0.622086 | ||||||||
\(26\) | −54415.6 | −0.607179 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −111187. | −0.957196 | ||||||||
\(29\) | 10383.5 | 0.0790591 | 0.0395296 | − | 0.999218i | \(-0.487414\pi\) | ||||
0.0395296 | + | 0.999218i | \(0.487414\pi\) | |||||||
\(30\) | 34506.9 | 0.233336 | ||||||||
\(31\) | 92770.0 | 0.559296 | 0.279648 | − | 0.960103i | \(-0.409782\pi\) | ||||
0.279648 | + | 0.960103i | \(0.409782\pi\) | |||||||
\(32\) | 177673. | 0.958508 | ||||||||
\(33\) | −44250.7 | −0.214349 | ||||||||
\(34\) | 247048. | 1.07797 | ||||||||
\(35\) | 262873. | 1.03635 | ||||||||
\(36\) | −52981.9 | −0.189264 | ||||||||
\(37\) | −504232. | −1.63653 | −0.818266 | − | 0.574840i | \(-0.805064\pi\) | ||||
−0.818266 | + | 0.574840i | \(0.805064\pi\) | |||||||
\(38\) | 413327. | 1.22194 | ||||||||
\(39\) | −197531. | −0.533224 | ||||||||
\(40\) | −256473. | −0.633623 | ||||||||
\(41\) | 635489. | 1.44001 | 0.720003 | − | 0.693971i | \(-0.244140\pi\) | ||||
0.720003 | + | 0.693971i | \(0.244140\pi\) | |||||||
\(42\) | 307234. | 0.639877 | ||||||||
\(43\) | 101770. | 0.195200 | 0.0976002 | − | 0.995226i | \(-0.468883\pi\) | ||||
0.0976002 | + | 0.995226i | \(0.468883\pi\) | |||||||
\(44\) | 119112. | 0.210801 | ||||||||
\(45\) | 125262. | 0.204916 | ||||||||
\(46\) | −385930. | −0.584597 | ||||||||
\(47\) | −72413.1 | −0.101736 | −0.0508680 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508680 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(48\) | −48580.2 | −0.0634037 | ||||||||
\(49\) | 1.51695e6 | 1.84198 | ||||||||
\(50\) | −361486. | −0.408975 | ||||||||
\(51\) | 896798. | 0.946671 | ||||||||
\(52\) | 531707. | 0.524397 | ||||||||
\(53\) | 1.67234e6 | 1.54297 | 0.771487 | − | 0.636245i | \(-0.219513\pi\) | ||||
0.771487 | + | 0.636245i | \(0.219513\pi\) | |||||||
\(54\) | 146400. | 0.126521 | ||||||||
\(55\) | −281610. | −0.228233 | ||||||||
\(56\) | −2.28351e6 | −1.73758 | ||||||||
\(57\) | 1.50040e6 | 1.07311 | ||||||||
\(58\) | 77231.8 | 0.0519754 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −337175. | −0.201524 | ||||||||
\(61\) | 727353. | 0.410290 | 0.205145 | − | 0.978732i | \(-0.434233\pi\) | ||||
0.205145 | + | 0.978732i | \(0.434233\pi\) | |||||||
\(62\) | 690015. | 0.367695 | ||||||||
\(63\) | 1.11527e6 | 0.561940 | ||||||||
\(64\) | 1.55182e6 | 0.739965 | ||||||||
\(65\) | −1.25708e6 | −0.567763 | ||||||||
\(66\) | −329133. | −0.140918 | ||||||||
\(67\) | 2.81505e6 | 1.14347 | 0.571735 | − | 0.820439i | \(-0.306271\pi\) | ||||
0.571735 | + | 0.820439i | \(0.306271\pi\) | |||||||
\(68\) | −2.41396e6 | −0.930999 | ||||||||
\(69\) | −1.40095e6 | −0.513393 | ||||||||
\(70\) | 1.95522e6 | 0.681323 | ||||||||
\(71\) | −850222. | −0.281921 | −0.140961 | − | 0.990015i | \(-0.545019\pi\) | ||||
−0.140961 | + | 0.990015i | \(0.545019\pi\) | |||||||
\(72\) | −1.08812e6 | −0.343569 | ||||||||
\(73\) | 5.84245e6 | 1.75778 | 0.878891 | − | 0.477023i | \(-0.158284\pi\) | ||||
0.878891 | + | 0.477023i | \(0.158284\pi\) | |||||||
\(74\) | −3.75043e6 | −1.07590 | ||||||||
\(75\) | −1.31221e6 | −0.359161 | ||||||||
\(76\) | −4.03871e6 | −1.05535 | ||||||||
\(77\) | −2.50732e6 | −0.625883 | ||||||||
\(78\) | −1.46922e6 | −0.350555 | ||||||||
\(79\) | 2.74755e6 | 0.626977 | 0.313488 | − | 0.949592i | \(-0.398502\pi\) | ||||
0.313488 | + | 0.949592i | \(0.398502\pi\) | |||||||
\(80\) | −309162. | −0.0675106 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 4.72671e6 | 0.946695 | ||||||||
\(83\) | 2.78632e6 | 0.534882 | 0.267441 | − | 0.963574i | \(-0.413822\pi\) | ||||
0.267441 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(84\) | −3.00205e6 | −0.552637 | ||||||||
\(85\) | 5.70719e6 | 1.00799 | ||||||||
\(86\) | 756957. | 0.128330 | ||||||||
\(87\) | 280355. | 0.0456448 | ||||||||
\(88\) | 2.44628e6 | 0.382663 | ||||||||
\(89\) | −6.16092e6 | −0.926361 | −0.463181 | − | 0.886264i | \(-0.653292\pi\) | ||||
−0.463181 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(90\) | 931687. | 0.134717 | ||||||||
\(91\) | −1.11925e7 | −1.55697 | ||||||||
\(92\) | 3.77101e6 | 0.504894 | ||||||||
\(93\) | 2.50479e6 | 0.322910 | ||||||||
\(94\) | −538602. | −0.0668838 | ||||||||
\(95\) | 9.54849e6 | 1.14262 | ||||||||
\(96\) | 4.79716e6 | 0.553395 | ||||||||
\(97\) | −1.67686e7 | −1.86550 | −0.932751 | − | 0.360521i | \(-0.882599\pi\) | ||||
−0.932751 | + | 0.360521i | \(0.882599\pi\) | |||||||
\(98\) | 1.12830e7 | 1.21097 | ||||||||
\(99\) | −1.19477e6 | −0.123754 | ||||||||
\(100\) | 3.53216e6 | 0.353216 | ||||||||
\(101\) | 7.93944e6 | 0.766770 | 0.383385 | − | 0.923589i | \(-0.374758\pi\) | ||||
0.383385 | + | 0.923589i | \(0.374758\pi\) | |||||||
\(102\) | 6.67030e6 | 0.622365 | ||||||||
\(103\) | 1.76750e7 | 1.59378 | 0.796889 | − | 0.604125i | \(-0.206477\pi\) | ||||
0.796889 | + | 0.604125i | \(0.206477\pi\) | |||||||
\(104\) | 1.09200e7 | 0.951931 | ||||||||
\(105\) | 7.09756e6 | 0.598338 | ||||||||
\(106\) | 1.24387e7 | 1.01439 | ||||||||
\(107\) | −9.16951e6 | −0.723607 | −0.361803 | − | 0.932254i | \(-0.617839\pi\) | ||||
−0.361803 | + | 0.932254i | \(0.617839\pi\) | |||||||
\(108\) | −1.43051e6 | −0.109272 | ||||||||
\(109\) | 1.32228e7 | 0.977982 | 0.488991 | − | 0.872289i | \(-0.337365\pi\) | ||||
0.488991 | + | 0.872289i | \(0.337365\pi\) | |||||||
\(110\) | −2.09459e6 | −0.150046 | ||||||||
\(111\) | −1.36143e7 | −0.944852 | ||||||||
\(112\) | −2.75264e6 | −0.185134 | ||||||||
\(113\) | −2.66031e7 | −1.73443 | −0.867216 | − | 0.497932i | \(-0.834093\pi\) | ||||
−0.867216 | + | 0.497932i | \(0.834093\pi\) | |||||||
\(114\) | 1.11598e7 | 0.705490 | ||||||||
\(115\) | −8.91557e6 | −0.546647 | ||||||||
\(116\) | −754649. | −0.0448892 | ||||||||
\(117\) | −5.33335e6 | −0.307857 | ||||||||
\(118\) | 1.52759e6 | 0.0855894 | ||||||||
\(119\) | 5.08142e7 | 2.76421 | ||||||||
\(120\) | −6.92476e6 | −0.365823 | ||||||||
\(121\) | −1.68011e7 | −0.862163 | ||||||||
\(122\) | 5.40999e6 | 0.269735 | ||||||||
\(123\) | 1.71582e7 | 0.831388 | ||||||||
\(124\) | −6.74229e6 | −0.317564 | ||||||||
\(125\) | −2.17749e7 | −0.997173 | ||||||||
\(126\) | 8.29531e6 | 0.369433 | ||||||||
\(127\) | −2.04342e7 | −0.885209 | −0.442604 | − | 0.896717i | \(-0.645945\pi\) | ||||
−0.442604 | + | 0.896717i | \(0.645945\pi\) | |||||||
\(128\) | −1.11998e7 | −0.472037 | ||||||||
\(129\) | 2.74779e6 | 0.112699 | ||||||||
\(130\) | −9.35007e6 | −0.373261 | ||||||||
\(131\) | −4.18739e7 | −1.62740 | −0.813699 | − | 0.581286i | \(-0.802550\pi\) | ||||
−0.813699 | + | 0.581286i | \(0.802550\pi\) | |||||||
\(132\) | 3.21603e6 | 0.121706 | ||||||||
\(133\) | 8.50153e7 | 3.13340 | ||||||||
\(134\) | 2.09381e7 | 0.751745 | ||||||||
\(135\) | 3.38207e6 | 0.118308 | ||||||||
\(136\) | −4.95770e7 | −1.69003 | ||||||||
\(137\) | 5.60709e7 | 1.86301 | 0.931506 | − | 0.363725i | \(-0.118495\pi\) | ||||
0.931506 | + | 0.363725i | \(0.118495\pi\) | |||||||
\(138\) | −1.04201e7 | −0.337517 | ||||||||
\(139\) | −3.90420e7 | −1.23305 | −0.616524 | − | 0.787336i | \(-0.711460\pi\) | ||||
−0.616524 | + | 0.787336i | \(0.711460\pi\) | |||||||
\(140\) | −1.91049e7 | −0.588433 | ||||||||
\(141\) | −1.95515e6 | −0.0587373 | ||||||||
\(142\) | −6.32387e6 | −0.185342 | ||||||||
\(143\) | 1.19903e7 | 0.342888 | ||||||||
\(144\) | −1.31166e6 | −0.0366062 | ||||||||
\(145\) | 1.78417e6 | 0.0486014 | ||||||||
\(146\) | 4.34556e7 | 1.15561 | ||||||||
\(147\) | 4.09577e7 | 1.06347 | ||||||||
\(148\) | 3.66463e7 | 0.929211 | ||||||||
\(149\) | 5.58520e7 | 1.38320 | 0.691602 | − | 0.722278i | \(-0.256905\pi\) | ||||
0.691602 | + | 0.722278i | \(0.256905\pi\) | |||||||
\(150\) | −9.76012e6 | −0.236122 | ||||||||
\(151\) | −6.78120e7 | −1.60283 | −0.801414 | − | 0.598110i | \(-0.795919\pi\) | ||||
−0.801414 | + | 0.598110i | \(0.795919\pi\) | |||||||
\(152\) | −8.29455e7 | −1.91576 | ||||||||
\(153\) | 2.42135e7 | 0.546561 | ||||||||
\(154\) | −1.86493e7 | −0.411471 | ||||||||
\(155\) | 1.59404e7 | 0.343826 | ||||||||
\(156\) | 1.43561e7 | 0.302761 | ||||||||
\(157\) | 4.45770e7 | 0.919310 | 0.459655 | − | 0.888098i | \(-0.347973\pi\) | ||||
0.459655 | + | 0.888098i | \(0.347973\pi\) | |||||||
\(158\) | 2.04361e7 | 0.412190 | ||||||||
\(159\) | 4.51532e7 | 0.890837 | ||||||||
\(160\) | 3.05290e7 | 0.589240 | ||||||||
\(161\) | −7.93801e7 | −1.49907 | ||||||||
\(162\) | 3.95281e6 | 0.0730472 | ||||||||
\(163\) | −9.62679e7 | −1.74111 | −0.870553 | − | 0.492075i | \(-0.836238\pi\) | ||||
−0.870553 | + | 0.492075i | \(0.836238\pi\) | |||||||
\(164\) | −4.61857e7 | −0.817625 | ||||||||
\(165\) | −7.60347e6 | −0.131770 | ||||||||
\(166\) | 2.07244e7 | 0.351645 | ||||||||
\(167\) | −3.06157e7 | −0.508671 | −0.254335 | − | 0.967116i | \(-0.581857\pi\) | ||||
−0.254335 | + | 0.967116i | \(0.581857\pi\) | |||||||
\(168\) | −6.16549e7 | −1.00319 | ||||||||
\(169\) | −9.22500e6 | −0.147015 | ||||||||
\(170\) | 4.24496e7 | 0.662677 | ||||||||
\(171\) | 4.05108e7 | 0.619561 | ||||||||
\(172\) | −7.39640e6 | −0.110833 | ||||||||
\(173\) | −1.60370e7 | −0.235484 | −0.117742 | − | 0.993044i | \(-0.537566\pi\) | ||||
−0.117742 | + | 0.993044i | \(0.537566\pi\) | |||||||
\(174\) | 2.08526e6 | 0.0300080 | ||||||||
\(175\) | −7.43523e7 | −1.04872 | ||||||||
\(176\) | 2.94884e6 | 0.0407716 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −4.58244e7 | −0.609013 | ||||||||
\(179\) | −2.33939e7 | −0.304872 | −0.152436 | − | 0.988313i | \(-0.548712\pi\) | ||||
−0.152436 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(180\) | −9.10372e6 | −0.116350 | ||||||||
\(181\) | −9.84290e7 | −1.23381 | −0.616904 | − | 0.787038i | \(-0.711614\pi\) | ||||
−0.616904 | + | 0.787038i | \(0.711614\pi\) | |||||||
\(182\) | −8.32487e7 | −1.02359 | ||||||||
\(183\) | 1.96385e7 | 0.236881 | ||||||||
\(184\) | 7.74475e7 | 0.916527 | ||||||||
\(185\) | −8.66407e7 | −1.00605 | ||||||||
\(186\) | 1.86304e7 | 0.212289 | ||||||||
\(187\) | −5.44361e7 | −0.608754 | ||||||||
\(188\) | 5.26280e6 | 0.0577650 | ||||||||
\(189\) | 3.01124e7 | 0.324436 | ||||||||
\(190\) | 7.10208e7 | 0.751187 | ||||||||
\(191\) | 3.21552e7 | 0.333914 | 0.166957 | − | 0.985964i | \(-0.446606\pi\) | ||||
0.166957 | + | 0.985964i | \(0.446606\pi\) | |||||||
\(192\) | 4.18991e7 | 0.427219 | ||||||||
\(193\) | 2.59381e7 | 0.259709 | 0.129854 | − | 0.991533i | \(-0.458549\pi\) | ||||
0.129854 | + | 0.991533i | \(0.458549\pi\) | |||||||
\(194\) | −1.24723e8 | −1.22643 | ||||||||
\(195\) | −3.39412e7 | −0.327798 | ||||||||
\(196\) | −1.10248e8 | −1.04587 | ||||||||
\(197\) | −1.60676e7 | −0.149733 | −0.0748666 | − | 0.997194i | \(-0.523853\pi\) | ||||
−0.0748666 | + | 0.997194i | \(0.523853\pi\) | |||||||
\(198\) | −8.88659e6 | −0.0813592 | ||||||||
\(199\) | 6.47444e7 | 0.582394 | 0.291197 | − | 0.956663i | \(-0.405947\pi\) | ||||
0.291197 | + | 0.956663i | \(0.405947\pi\) | |||||||
\(200\) | 7.25421e7 | 0.641187 | ||||||||
\(201\) | 7.60064e7 | 0.660182 | ||||||||
\(202\) | 5.90529e7 | 0.504094 | ||||||||
\(203\) | 1.58854e7 | 0.133279 | ||||||||
\(204\) | −6.51770e7 | −0.537513 | ||||||||
\(205\) | 1.09194e8 | 0.885240 | ||||||||
\(206\) | 1.31465e8 | 1.04779 | ||||||||
\(207\) | −3.78256e7 | −0.296407 | ||||||||
\(208\) | 1.31634e7 | 0.101425 | ||||||||
\(209\) | −9.10751e7 | −0.690061 | ||||||||
\(210\) | 5.27910e7 | 0.393362 | ||||||||
\(211\) | −4.05485e7 | −0.297157 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(212\) | −1.21541e8 | −0.876090 | ||||||||
\(213\) | −2.29560e7 | −0.162767 | ||||||||
\(214\) | −6.82020e7 | −0.475717 | ||||||||
\(215\) | 1.74869e7 | 0.119999 | ||||||||
\(216\) | −2.93793e7 | −0.198359 | ||||||||
\(217\) | 1.41926e8 | 0.942872 | ||||||||
\(218\) | 9.83501e7 | 0.642950 | ||||||||
\(219\) | 1.57746e8 | 1.01486 | ||||||||
\(220\) | 2.04667e7 | 0.129589 | ||||||||
\(221\) | −2.42998e8 | −1.51436 | ||||||||
\(222\) | −1.01262e8 | −0.621169 | ||||||||
\(223\) | −6.68937e7 | −0.403941 | −0.201971 | − | 0.979392i | \(-0.564735\pi\) | ||||
−0.201971 | + | 0.979392i | \(0.564735\pi\) | |||||||
\(224\) | 2.71816e8 | 1.61587 | ||||||||
\(225\) | −3.54297e7 | −0.207362 | ||||||||
\(226\) | −1.97871e8 | −1.14026 | ||||||||
\(227\) | 1.22298e8 | 0.693949 | 0.346975 | − | 0.937875i | \(-0.387209\pi\) | ||||
0.346975 | + | 0.937875i | \(0.387209\pi\) | |||||||
\(228\) | −1.09045e8 | −0.609305 | ||||||||
\(229\) | −2.32389e8 | −1.27876 | −0.639382 | − | 0.768889i | \(-0.720810\pi\) | ||||
−0.639382 | + | 0.768889i | \(0.720810\pi\) | |||||||
\(230\) | −6.63132e7 | −0.359379 | ||||||||
\(231\) | −6.76978e7 | −0.361354 | ||||||||
\(232\) | −1.54987e7 | −0.0814867 | ||||||||
\(233\) | 7.69697e7 | 0.398634 | 0.199317 | − | 0.979935i | \(-0.436128\pi\) | ||||
0.199317 | + | 0.979935i | \(0.436128\pi\) | |||||||
\(234\) | −3.96690e7 | −0.202393 | ||||||||
\(235\) | −1.24425e7 | −0.0625419 | ||||||||
\(236\) | −1.49264e7 | −0.0739203 | ||||||||
\(237\) | 7.41839e7 | 0.361985 | ||||||||
\(238\) | 3.77951e8 | 1.81726 | ||||||||
\(239\) | −1.06849e7 | −0.0506264 | −0.0253132 | − | 0.999680i | \(-0.508058\pi\) | ||||
−0.0253132 | + | 0.999680i | \(0.508058\pi\) | |||||||
\(240\) | −8.34739e6 | −0.0389773 | ||||||||
\(241\) | −3.74132e8 | −1.72173 | −0.860866 | − | 0.508831i | \(-0.830078\pi\) | ||||
−0.860866 | + | 0.508831i | \(0.830078\pi\) | |||||||
\(242\) | −1.24965e8 | −0.566808 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −5.28622e7 | −0.232960 | ||||||||
\(245\) | 2.60654e8 | 1.13235 | ||||||||
\(246\) | 1.27621e8 | 0.546575 | ||||||||
\(247\) | −4.06551e8 | −1.71663 | ||||||||
\(248\) | −1.38470e8 | −0.576470 | ||||||||
\(249\) | 7.52307e7 | 0.308814 | ||||||||
\(250\) | −1.61959e8 | −0.655566 | ||||||||
\(251\) | 2.63434e8 | 1.05151 | 0.525755 | − | 0.850636i | \(-0.323783\pi\) | ||||
0.525755 | + | 0.850636i | \(0.323783\pi\) | |||||||
\(252\) | −8.10553e7 | −0.319065 | ||||||||
\(253\) | 8.50383e7 | 0.330136 | ||||||||
\(254\) | −1.51988e8 | −0.581958 | ||||||||
\(255\) | 1.54094e8 | 0.581963 | ||||||||
\(256\) | −2.81936e8 | −1.05029 | ||||||||
\(257\) | −3.92808e8 | −1.44349 | −0.721746 | − | 0.692158i | \(-0.756660\pi\) | ||||
−0.721746 | + | 0.692158i | \(0.756660\pi\) | |||||||
\(258\) | 2.04378e7 | 0.0740911 | ||||||||
\(259\) | −7.71409e8 | −2.75890 | ||||||||
\(260\) | 9.13616e7 | 0.322372 | ||||||||
\(261\) | 7.56959e6 | 0.0263530 | ||||||||
\(262\) | −3.11454e8 | −1.06989 | ||||||||
\(263\) | −2.41410e8 | −0.818297 | −0.409148 | − | 0.912468i | \(-0.634174\pi\) | ||||
−0.409148 | + | 0.912468i | \(0.634174\pi\) | |||||||
\(264\) | 6.60496e7 | 0.220931 | ||||||||
\(265\) | 2.87353e8 | 0.948539 | ||||||||
\(266\) | 6.32336e8 | 2.05998 | ||||||||
\(267\) | −1.66345e8 | −0.534835 | ||||||||
\(268\) | −2.04591e8 | −0.649254 | ||||||||
\(269\) | 2.35755e8 | 0.738463 | 0.369231 | − | 0.929337i | \(-0.379621\pi\) | ||||
0.369231 | + | 0.929337i | \(0.379621\pi\) | |||||||
\(270\) | 2.51555e7 | 0.0777787 | ||||||||
\(271\) | −1.49957e8 | −0.457692 | −0.228846 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228846 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(272\) | −5.97621e7 | −0.180067 | ||||||||
\(273\) | −3.02197e8 | −0.898920 | ||||||||
\(274\) | 4.17051e8 | 1.22479 | ||||||||
\(275\) | 7.96521e7 | 0.230958 | ||||||||
\(276\) | 1.01817e8 | 0.291501 | ||||||||
\(277\) | −9.52984e7 | −0.269406 | −0.134703 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134703 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(278\) | −2.90391e8 | −0.810637 | ||||||||
\(279\) | 6.76293e7 | 0.186432 | ||||||||
\(280\) | −3.92369e8 | −1.06817 | ||||||||
\(281\) | −7.30263e7 | −0.196339 | −0.0981696 | − | 0.995170i | \(-0.531299\pi\) | ||||
−0.0981696 | + | 0.995170i | \(0.531299\pi\) | |||||||
\(282\) | −1.45423e7 | −0.0386154 | ||||||||
\(283\) | 1.79740e8 | 0.471404 | 0.235702 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235702 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(284\) | 6.17920e7 | 0.160073 | ||||||||
\(285\) | 2.57809e8 | 0.659692 | ||||||||
\(286\) | 8.91825e7 | 0.225423 | ||||||||
\(287\) | 9.72214e8 | 2.42759 | ||||||||
\(288\) | 1.29523e8 | 0.319503 | ||||||||
\(289\) | 6.92880e8 | 1.68856 | ||||||||
\(290\) | 1.32705e7 | 0.0319517 | ||||||||
\(291\) | −4.52752e8 | −1.07705 | ||||||||
\(292\) | −4.24614e8 | −0.998056 | ||||||||
\(293\) | 8.12673e8 | 1.88747 | 0.943733 | − | 0.330709i | \(-0.107288\pi\) | ||||
0.943733 | + | 0.330709i | \(0.107288\pi\) | |||||||
\(294\) | 3.04640e8 | 0.699152 | ||||||||
\(295\) | 3.52897e7 | 0.0800333 | ||||||||
\(296\) | 7.52628e8 | 1.68678 | ||||||||
\(297\) | −3.22588e7 | −0.0714497 | ||||||||
\(298\) | 4.15422e8 | 0.909353 | ||||||||
\(299\) | 3.79603e8 | 0.821261 | ||||||||
\(300\) | 9.53683e7 | 0.203929 | ||||||||
\(301\) | 1.55695e8 | 0.329073 | ||||||||
\(302\) | −5.04379e8 | −1.05374 | ||||||||
\(303\) | 2.14365e8 | 0.442695 | ||||||||
\(304\) | −9.99858e7 | −0.204118 | ||||||||
\(305\) | 1.24979e8 | 0.252225 | ||||||||
\(306\) | 1.80098e8 | 0.359322 | ||||||||
\(307\) | −1.93647e8 | −0.381968 | −0.190984 | − | 0.981593i | \(-0.561168\pi\) | ||||
−0.190984 | + | 0.981593i | \(0.561168\pi\) | |||||||
\(308\) | 1.82226e8 | 0.355372 | ||||||||
\(309\) | 4.77224e8 | 0.920168 | ||||||||
\(310\) | 1.18563e8 | 0.226039 | ||||||||
\(311\) | 1.76764e8 | 0.333220 | 0.166610 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166610 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(312\) | 2.94840e8 | 0.549597 | ||||||||
\(313\) | 1.36535e8 | 0.251675 | 0.125837 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125837 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(314\) | 3.31560e8 | 0.604377 | ||||||||
\(315\) | 1.91634e8 | 0.345451 | ||||||||
\(316\) | −1.99685e8 | −0.355993 | ||||||||
\(317\) | −1.67078e8 | −0.294586 | −0.147293 | − | 0.989093i | \(-0.547056\pi\) | ||||
−0.147293 | + | 0.989093i | \(0.547056\pi\) | |||||||
\(318\) | 3.35845e8 | 0.585658 | ||||||||
\(319\) | −1.70177e7 | −0.0293518 | ||||||||
\(320\) | 2.66645e8 | 0.454892 | ||||||||
\(321\) | −2.47577e8 | −0.417775 | ||||||||
\(322\) | −5.90422e8 | −0.985524 | ||||||||
\(323\) | 1.84575e9 | 3.04765 | ||||||||
\(324\) | −3.86238e7 | −0.0630881 | ||||||||
\(325\) | 3.55560e8 | 0.574541 | ||||||||
\(326\) | −7.16032e8 | −1.14465 | ||||||||
\(327\) | 3.57016e8 | 0.564638 | ||||||||
\(328\) | −9.48544e8 | −1.48422 | ||||||||
\(329\) | −1.10783e8 | −0.171508 | ||||||||
\(330\) | −5.65539e7 | −0.0866291 | ||||||||
\(331\) | 3.82887e8 | 0.580327 | 0.290163 | − | 0.956977i | \(-0.406290\pi\) | ||||
0.290163 | + | 0.956977i | \(0.406290\pi\) | |||||||
\(332\) | −2.02503e8 | −0.303702 | ||||||||
\(333\) | −3.67585e8 | −0.545511 | ||||||||
\(334\) | −2.27717e8 | −0.334413 | ||||||||
\(335\) | 4.83702e8 | 0.702944 | ||||||||
\(336\) | −7.43213e7 | −0.106887 | ||||||||
\(337\) | 7.71340e8 | 1.09785 | 0.548923 | − | 0.835873i | \(-0.315038\pi\) | ||||
0.548923 | + | 0.835873i | \(0.315038\pi\) | |||||||
\(338\) | −6.86147e7 | −0.0966515 | ||||||||
\(339\) | −7.18283e8 | −1.00137 | ||||||||
\(340\) | −4.14784e8 | −0.572329 | ||||||||
\(341\) | −1.52042e8 | −0.207646 | ||||||||
\(342\) | 3.01316e8 | 0.407315 | ||||||||
\(343\) | 1.06083e9 | 1.41943 | ||||||||
\(344\) | −1.51904e8 | −0.201194 | ||||||||
\(345\) | −2.40721e8 | −0.315607 | ||||||||
\(346\) | −1.19281e8 | −0.154813 | ||||||||
\(347\) | −1.31263e9 | −1.68651 | −0.843257 | − | 0.537511i | \(-0.819365\pi\) | ||||
−0.843257 | + | 0.537511i | \(0.819365\pi\) | |||||||
\(348\) | −2.03755e7 | −0.0259168 | ||||||||
\(349\) | −5.67291e8 | −0.714360 | −0.357180 | − | 0.934036i | \(-0.616262\pi\) | ||||
−0.357180 | + | 0.934036i | \(0.616262\pi\) | |||||||
\(350\) | −5.53026e8 | −0.689457 | ||||||||
\(351\) | −1.44000e8 | −0.177741 | ||||||||
\(352\) | −2.91191e8 | −0.355859 | ||||||||
\(353\) | 1.79304e8 | 0.216959 | 0.108480 | − | 0.994099i | \(-0.465402\pi\) | ||||
0.108480 | + | 0.994099i | \(0.465402\pi\) | |||||||
\(354\) | 4.12449e7 | 0.0494151 | ||||||||
\(355\) | −1.46091e8 | −0.173310 | ||||||||
\(356\) | 4.47760e8 | 0.525981 | ||||||||
\(357\) | 1.37198e9 | 1.59592 | ||||||||
\(358\) | −1.74002e8 | −0.200430 | ||||||||
\(359\) | −1.28294e9 | −1.46344 | −0.731722 | − | 0.681603i | \(-0.761283\pi\) | ||||
−0.731722 | + | 0.681603i | \(0.761283\pi\) | |||||||
\(360\) | −1.86969e8 | −0.211208 | ||||||||
\(361\) | 2.19419e9 | 2.45470 | ||||||||
\(362\) | −7.32106e8 | −0.811136 | ||||||||
\(363\) | −4.53630e8 | −0.497770 | ||||||||
\(364\) | 8.13441e8 | 0.884039 | ||||||||
\(365\) | 1.00389e9 | 1.08059 | ||||||||
\(366\) | 1.46070e8 | 0.155731 | ||||||||
\(367\) | 1.71884e7 | 0.0181512 | 0.00907560 | − | 0.999959i | \(-0.497111\pi\) | ||||
0.00907560 | + | 0.999959i | \(0.497111\pi\) | |||||||
\(368\) | 9.33583e7 | 0.0976530 | ||||||||
\(369\) | 4.63271e8 | 0.480002 | ||||||||
\(370\) | −6.44426e8 | −0.661404 | ||||||||
\(371\) | 2.55846e9 | 2.60118 | ||||||||
\(372\) | −1.82042e8 | −0.183346 | ||||||||
\(373\) | −8.02127e8 | −0.800318 | −0.400159 | − | 0.916446i | \(-0.631045\pi\) | ||||
−0.400159 | + | 0.916446i | \(0.631045\pi\) | |||||||
\(374\) | −4.04891e8 | −0.400210 | ||||||||
\(375\) | −5.87921e8 | −0.575718 | ||||||||
\(376\) | 1.08085e8 | 0.104860 | ||||||||
\(377\) | −7.59657e7 | −0.0730168 | ||||||||
\(378\) | 2.23973e8 | 0.213292 | ||||||||
\(379\) | 9.63664e6 | 0.00909261 | 0.00454630 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454630 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(380\) | −6.93960e8 | −0.648772 | ||||||||
\(381\) | −5.51725e8 | −0.511075 | ||||||||
\(382\) | 2.39168e8 | 0.219523 | ||||||||
\(383\) | 8.26495e8 | 0.751700 | 0.375850 | − | 0.926681i | \(-0.377351\pi\) | ||||
0.375850 | + | 0.926681i | \(0.377351\pi\) | |||||||
\(384\) | −3.02395e8 | −0.272531 | ||||||||
\(385\) | −4.30826e8 | −0.384760 | ||||||||
\(386\) | 1.92925e8 | 0.170739 | ||||||||
\(387\) | 7.41904e7 | 0.0650668 | ||||||||
\(388\) | 1.21870e9 | 1.05922 | ||||||||
\(389\) | 7.27469e8 | 0.626601 | 0.313300 | − | 0.949654i | \(-0.398565\pi\) | ||||
0.313300 | + | 0.949654i | \(0.398565\pi\) | |||||||
\(390\) | −2.52452e8 | −0.215503 | ||||||||
\(391\) | −1.72341e9 | −1.45804 | ||||||||
\(392\) | −2.26424e9 | −1.89854 | ||||||||
\(393\) | −1.13060e9 | −0.939579 | ||||||||
\(394\) | −1.19509e8 | −0.0984383 | ||||||||
\(395\) | 4.72104e8 | 0.385432 | ||||||||
\(396\) | 8.68328e7 | 0.0702669 | ||||||||
\(397\) | −1.15679e9 | −0.927871 | −0.463936 | − | 0.885869i | \(-0.653563\pi\) | ||||
−0.463936 | + | 0.885869i | \(0.653563\pi\) | |||||||
\(398\) | 4.81563e8 | 0.382880 | ||||||||
\(399\) | 2.29541e9 | 1.80907 | ||||||||
\(400\) | 8.74451e7 | 0.0683165 | ||||||||
\(401\) | 9.57807e7 | 0.0741776 | 0.0370888 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370888 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(402\) | 5.65329e8 | 0.434020 | ||||||||
\(403\) | −6.78703e8 | −0.516550 | ||||||||
\(404\) | −5.77019e8 | −0.435367 | ||||||||
\(405\) | 9.13159e7 | 0.0683052 | ||||||||
\(406\) | 1.18154e8 | 0.0876211 | ||||||||
\(407\) | 8.26394e8 | 0.607585 | ||||||||
\(408\) | −1.33858e9 | −0.975739 | ||||||||
\(409\) | −1.12641e9 | −0.814079 | −0.407040 | − | 0.913410i | \(-0.633439\pi\) | ||||
−0.407040 | + | 0.913410i | \(0.633439\pi\) | |||||||
\(410\) | 8.12176e8 | 0.581978 | ||||||||
\(411\) | 1.51392e9 | 1.07561 | ||||||||
\(412\) | −1.28457e9 | −0.904936 | ||||||||
\(413\) | 3.14203e8 | 0.219475 | ||||||||
\(414\) | −2.81343e8 | −0.194866 | ||||||||
\(415\) | 4.78766e8 | 0.328817 | ||||||||
\(416\) | −1.29985e9 | −0.885251 | ||||||||
\(417\) | −1.05413e9 | −0.711901 | ||||||||
\(418\) | −6.77408e8 | −0.453663 | ||||||||
\(419\) | −2.46333e9 | −1.63596 | −0.817981 | − | 0.575245i | \(-0.804907\pi\) | ||||
−0.817981 | + | 0.575245i | \(0.804907\pi\) | |||||||
\(420\) | −5.15833e8 | −0.339732 | ||||||||
\(421\) | 6.02698e8 | 0.393652 | 0.196826 | − | 0.980438i | \(-0.436937\pi\) | ||||
0.196826 | + | 0.980438i | \(0.436937\pi\) | |||||||
\(422\) | −3.01596e8 | −0.195358 | ||||||||
\(423\) | −5.27892e7 | −0.0339120 | ||||||||
\(424\) | −2.49617e9 | −1.59035 | ||||||||
\(425\) | −1.61425e9 | −1.02002 | ||||||||
\(426\) | −1.70745e8 | −0.107007 | ||||||||
\(427\) | 1.11275e9 | 0.691674 | ||||||||
\(428\) | 6.66417e8 | 0.410859 | ||||||||
\(429\) | 3.23737e8 | 0.197967 | ||||||||
\(430\) | 1.30066e8 | 0.0788902 | ||||||||
\(431\) | 1.69548e9 | 1.02005 | 0.510027 | − | 0.860159i | \(-0.329636\pi\) | ||||
0.510027 | + | 0.860159i | \(0.329636\pi\) | |||||||
\(432\) | −3.54149e7 | −0.0211346 | ||||||||
\(433\) | −5.31537e8 | −0.314649 | −0.157324 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157324 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(434\) | 1.05563e9 | 0.619867 | ||||||||
\(435\) | 4.81726e7 | 0.0280600 | ||||||||
\(436\) | −9.61000e8 | −0.555291 | ||||||||
\(437\) | −2.88337e9 | −1.65278 | ||||||||
\(438\) | 1.17330e9 | 0.667191 | ||||||||
\(439\) | −2.39663e9 | −1.35200 | −0.675998 | − | 0.736904i | \(-0.736287\pi\) | ||||
−0.675998 | + | 0.736904i | \(0.736287\pi\) | |||||||
\(440\) | 4.20337e8 | 0.235241 | ||||||||
\(441\) | 1.10586e9 | 0.613995 | ||||||||
\(442\) | −1.80740e9 | −0.995580 | ||||||||
\(443\) | −2.03310e9 | −1.11108 | −0.555542 | − | 0.831489i | \(-0.687489\pi\) | ||||
−0.555542 | + | 0.831489i | \(0.687489\pi\) | |||||||
\(444\) | 9.89451e8 | 0.536480 | ||||||||
\(445\) | −1.05861e9 | −0.569478 | ||||||||
\(446\) | −4.97550e8 | −0.265561 | ||||||||
\(447\) | 1.50800e9 | 0.798594 | ||||||||
\(448\) | 2.37408e9 | 1.24745 | ||||||||
\(449\) | 3.46417e9 | 1.80608 | 0.903040 | − | 0.429557i | \(-0.141330\pi\) | ||||
0.903040 | + | 0.429557i | \(0.141330\pi\) | |||||||
\(450\) | −2.63523e8 | −0.136325 | ||||||||
\(451\) | −1.04151e9 | −0.534622 | ||||||||
\(452\) | 1.93344e9 | 0.984798 | ||||||||
\(453\) | −1.83092e9 | −0.925393 | ||||||||
\(454\) | 9.09639e8 | 0.456219 | ||||||||
\(455\) | −1.92317e9 | −0.957146 | ||||||||
\(456\) | −2.23953e9 | −1.10606 | ||||||||
\(457\) | −2.70035e8 | −0.132347 | −0.0661735 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661735 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(458\) | −1.72849e9 | −0.840692 | ||||||||
\(459\) | 6.53766e8 | 0.315557 | ||||||||
\(460\) | 6.47962e8 | 0.310382 | ||||||||
\(461\) | −1.94305e9 | −0.923698 | −0.461849 | − | 0.886959i | \(-0.652814\pi\) | ||||
−0.461849 | + | 0.886959i | \(0.652814\pi\) | |||||||
\(462\) | −5.03530e8 | −0.237563 | ||||||||
\(463\) | −1.57266e8 | −0.0736378 | −0.0368189 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368189 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(464\) | −1.86827e7 | −0.00868215 | ||||||||
\(465\) | 4.30391e8 | 0.198508 | ||||||||
\(466\) | 5.72494e8 | 0.262072 | ||||||||
\(467\) | −1.00777e9 | −0.457881 | −0.228941 | − | 0.973440i | \(-0.573526\pi\) | ||||
−0.228941 | + | 0.973440i | \(0.573526\pi\) | |||||||
\(468\) | 3.87614e8 | 0.174799 | ||||||||
\(469\) | 4.30666e9 | 1.92768 | ||||||||
\(470\) | −9.25465e7 | −0.0411166 | ||||||||
\(471\) | 1.20358e9 | 0.530764 | ||||||||
\(472\) | −3.06553e8 | −0.134186 | ||||||||
\(473\) | −1.66793e8 | −0.0724708 | ||||||||
\(474\) | 5.51773e8 | 0.237978 | ||||||||
\(475\) | −2.70074e9 | −1.15626 | ||||||||
\(476\) | −3.69305e9 | −1.56950 | ||||||||
\(477\) | 1.21914e9 | 0.514325 | ||||||||
\(478\) | −7.94732e7 | −0.0332830 | ||||||||
\(479\) | 1.14824e9 | 0.477372 | 0.238686 | − | 0.971097i | \(-0.423283\pi\) | ||||
0.238686 | + | 0.971097i | \(0.423283\pi\) | |||||||
\(480\) | 8.24283e8 | 0.340198 | ||||||||
\(481\) | 3.68895e9 | 1.51145 | ||||||||
\(482\) | −2.78276e9 | −1.13191 | ||||||||
\(483\) | −2.14326e9 | −0.865487 | ||||||||
\(484\) | 1.22106e9 | 0.489530 | ||||||||
\(485\) | −2.88130e9 | −1.14681 | ||||||||
\(486\) | 1.06726e8 | 0.0421738 | ||||||||
\(487\) | 2.65456e9 | 1.04146 | 0.520729 | − | 0.853722i | \(-0.325660\pi\) | ||||
0.520729 | + | 0.853722i | \(0.325660\pi\) | |||||||
\(488\) | −1.08566e9 | −0.422888 | ||||||||
\(489\) | −2.59923e9 | −1.00523 | ||||||||
\(490\) | 1.93872e9 | 0.744438 | ||||||||
\(491\) | −2.25039e9 | −0.857971 | −0.428986 | − | 0.903311i | \(-0.641129\pi\) | ||||
−0.428986 | + | 0.903311i | \(0.641129\pi\) | |||||||
\(492\) | −1.24701e9 | −0.472056 | ||||||||
\(493\) | 3.44886e8 | 0.129632 | ||||||||
\(494\) | −3.02389e9 | −1.12855 | ||||||||
\(495\) | −2.05294e8 | −0.0760777 | ||||||||
\(496\) | −1.66918e8 | −0.0614210 | ||||||||
\(497\) | −1.30073e9 | −0.475268 | ||||||||
\(498\) | 5.59559e8 | 0.203022 | ||||||||
\(499\) | 7.47962e8 | 0.269481 | 0.134740 | − | 0.990881i | \(-0.456980\pi\) | ||||
0.134740 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(500\) | 1.58254e9 | 0.566188 | ||||||||
\(501\) | −8.26624e8 | −0.293681 | ||||||||
\(502\) | 1.95940e9 | 0.691288 | ||||||||
\(503\) | 5.29706e9 | 1.85587 | 0.927933 | − | 0.372746i | \(-0.121584\pi\) | ||||
0.927933 | + | 0.372746i | \(0.121584\pi\) | |||||||
\(504\) | −1.66468e9 | −0.579194 | ||||||||
\(505\) | 1.36421e9 | 0.471370 | ||||||||
\(506\) | 6.32507e8 | 0.217039 | ||||||||
\(507\) | −2.49075e8 | −0.0848794 | ||||||||
\(508\) | 1.48511e9 | 0.502615 | ||||||||
\(509\) | 2.52094e9 | 0.847327 | 0.423663 | − | 0.905820i | \(-0.360744\pi\) | ||||
0.423663 | + | 0.905820i | \(0.360744\pi\) | |||||||
\(510\) | 1.14614e9 | 0.382597 | ||||||||
\(511\) | 8.93818e9 | 2.96330 | ||||||||
\(512\) | −6.63440e8 | −0.218452 | ||||||||
\(513\) | 1.09379e9 | 0.357704 | ||||||||
\(514\) | −2.92167e9 | −0.948988 | ||||||||
\(515\) | 3.03703e9 | 0.979771 | ||||||||
\(516\) | −1.99703e8 | −0.0639897 | ||||||||
\(517\) | 1.18679e8 | 0.0377709 | ||||||||
\(518\) | −5.73767e9 | −1.81377 | ||||||||
\(519\) | −4.32998e8 | −0.135957 | ||||||||
\(520\) | 1.87635e9 | 0.585197 | ||||||||
\(521\) | 6.27028e9 | 1.94247 | 0.971236 | − | 0.238118i | \(-0.0765305\pi\) | ||||
0.971236 | + | 0.238118i | \(0.0765305\pi\) | |||||||
\(522\) | 5.63020e7 | 0.0173251 | ||||||||
\(523\) | −6.45997e8 | −0.197458 | −0.0987289 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987289 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(524\) | 3.04329e9 | 0.924025 | ||||||||
\(525\) | −2.00751e9 | −0.605481 | ||||||||
\(526\) | −1.79559e9 | −0.537969 | ||||||||
\(527\) | 3.08133e9 | 0.917067 | ||||||||
\(528\) | 7.96188e7 | 0.0235395 | ||||||||
\(529\) | −7.12574e8 | −0.209284 | ||||||||
\(530\) | 2.13731e9 | 0.623593 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | −6.17870e9 | −1.77912 | ||||||||
\(533\) | −4.64922e9 | −1.32995 | ||||||||
\(534\) | −1.23726e9 | −0.351614 | ||||||||
\(535\) | −1.57557e9 | −0.444835 | ||||||||
\(536\) | −4.20181e9 | −1.17858 | ||||||||
\(537\) | −6.31635e8 | −0.176018 | ||||||||
\(538\) | 1.75353e9 | 0.485484 | ||||||||
\(539\) | −2.48616e9 | −0.683861 | ||||||||
\(540\) | −2.45800e8 | −0.0671745 | ||||||||
\(541\) | −3.10398e9 | −0.842807 | −0.421404 | − | 0.906873i | \(-0.638462\pi\) | ||||
−0.421404 | + | 0.906873i | \(0.638462\pi\) | |||||||
\(542\) | −1.11536e9 | −0.300898 | ||||||||
\(543\) | −2.65758e9 | −0.712340 | ||||||||
\(544\) | 5.90135e9 | 1.57165 | ||||||||
\(545\) | 2.27204e9 | 0.601212 | ||||||||
\(546\) | −2.24771e9 | −0.590972 | ||||||||
\(547\) | −2.73990e9 | −0.715779 | −0.357890 | − | 0.933764i | \(-0.616504\pi\) | ||||
−0.357890 | + | 0.933764i | \(0.616504\pi\) | |||||||
\(548\) | −4.07509e9 | −1.05781 | ||||||||
\(549\) | 5.30240e8 | 0.136763 | ||||||||
\(550\) | 5.92445e8 | 0.151837 | ||||||||
\(551\) | 5.77016e8 | 0.146946 | ||||||||
\(552\) | 2.09108e9 | 0.529157 | ||||||||
\(553\) | 4.20339e9 | 1.05697 | ||||||||
\(554\) | −7.08821e8 | −0.177114 | ||||||||
\(555\) | −2.33930e9 | −0.580845 | ||||||||
\(556\) | 2.83747e9 | 0.700116 | ||||||||
\(557\) | 2.13952e9 | 0.524595 | 0.262297 | − | 0.964987i | \(-0.415520\pi\) | ||||
0.262297 | + | 0.964987i | \(0.415520\pi\) | |||||||
\(558\) | 5.03021e8 | 0.122565 | ||||||||
\(559\) | −7.44548e8 | −0.180282 | ||||||||
\(560\) | −4.72978e8 | −0.113811 | ||||||||
\(561\) | −1.46978e9 | −0.351464 | ||||||||
\(562\) | −5.43163e8 | −0.129078 | ||||||||
\(563\) | −2.85723e9 | −0.674786 | −0.337393 | − | 0.941364i | \(-0.609545\pi\) | ||||
−0.337393 | + | 0.941364i | \(0.609545\pi\) | |||||||
\(564\) | 1.42096e8 | 0.0333506 | ||||||||
\(565\) | −4.57113e9 | −1.06624 | ||||||||
\(566\) | 1.33689e9 | 0.309912 | ||||||||
\(567\) | 8.13035e8 | 0.187313 | ||||||||
\(568\) | 1.26906e9 | 0.290578 | ||||||||
\(569\) | −3.13031e9 | −0.712352 | −0.356176 | − | 0.934419i | \(-0.615920\pi\) | ||||
−0.356176 | + | 0.934419i | \(0.615920\pi\) | |||||||
\(570\) | 1.91756e9 | 0.433698 | ||||||||
\(571\) | −4.57416e9 | −1.02822 | −0.514109 | − | 0.857725i | \(-0.671877\pi\) | ||||
−0.514109 | + | 0.857725i | \(0.671877\pi\) | |||||||
\(572\) | −8.71422e8 | −0.194690 | ||||||||
\(573\) | 8.68191e8 | 0.192785 | ||||||||
\(574\) | 7.23124e9 | 1.59596 | ||||||||
\(575\) | 2.52173e9 | 0.553173 | ||||||||
\(576\) | 1.13128e9 | 0.246655 | ||||||||
\(577\) | −5.19496e9 | −1.12581 | −0.562907 | − | 0.826520i | \(-0.690317\pi\) | ||||
−0.562907 | + | 0.826520i | \(0.690317\pi\) | |||||||
\(578\) | 5.15358e9 | 1.11010 | ||||||||
\(579\) | 7.00328e8 | 0.149943 | ||||||||
\(580\) | −1.29669e8 | −0.0275955 | ||||||||
\(581\) | 4.26271e9 | 0.901714 | ||||||||
\(582\) | −3.36753e9 | −0.708078 | ||||||||
\(583\) | −2.74082e9 | −0.572850 | ||||||||
\(584\) | −8.72056e9 | −1.81176 | ||||||||
\(585\) | −9.16413e8 | −0.189254 | ||||||||
\(586\) | 6.04459e9 | 1.24087 | ||||||||
\(587\) | 2.60032e9 | 0.530632 | 0.265316 | − | 0.964162i | \(-0.414524\pi\) | ||||
0.265316 | + | 0.964162i | \(0.414524\pi\) | |||||||
\(588\) | −2.97671e9 | −0.603831 | ||||||||
\(589\) | 5.15526e9 | 1.03955 | ||||||||
\(590\) | 2.62481e8 | 0.0526158 | ||||||||
\(591\) | −4.33824e8 | −0.0864485 | ||||||||
\(592\) | 9.07248e8 | 0.179721 | ||||||||
\(593\) | 7.30947e9 | 1.43944 | 0.719721 | − | 0.694263i | \(-0.244269\pi\) | ||||
0.719721 | + | 0.694263i | \(0.244269\pi\) | |||||||
\(594\) | −2.39938e8 | −0.0469728 | ||||||||
\(595\) | 8.73125e9 | 1.69929 | ||||||||
\(596\) | −4.05918e9 | −0.785374 | ||||||||
\(597\) | 1.74810e9 | 0.336245 | ||||||||
\(598\) | 2.82346e9 | 0.539917 | ||||||||
\(599\) | 1.02859e9 | 0.195545 | 0.0977725 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977725 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(600\) | 1.95864e9 | 0.370190 | ||||||||
\(601\) | −2.84013e9 | −0.533676 | −0.266838 | − | 0.963741i | \(-0.585979\pi\) | ||||
−0.266838 | + | 0.963741i | \(0.585979\pi\) | |||||||
\(602\) | 1.15804e9 | 0.216340 | ||||||||
\(603\) | 2.05217e9 | 0.381156 | ||||||||
\(604\) | 4.92840e9 | 0.910074 | ||||||||
\(605\) | −2.88689e9 | −0.530013 | ||||||||
\(606\) | 1.59443e9 | 0.291039 | ||||||||
\(607\) | 8.39067e9 | 1.52278 | 0.761388 | − | 0.648296i | \(-0.224518\pi\) | ||||
0.761388 | + | 0.648296i | \(0.224518\pi\) | |||||||
\(608\) | 9.87333e9 | 1.78156 | ||||||||
\(609\) | 4.28907e8 | 0.0769489 | ||||||||
\(610\) | 9.29582e8 | 0.165819 | ||||||||
\(611\) | 5.29773e8 | 0.0939605 | ||||||||
\(612\) | −1.75978e9 | −0.310333 | ||||||||
\(613\) | −2.69978e9 | −0.473388 | −0.236694 | − | 0.971584i | \(-0.576064\pi\) | ||||
−0.236694 | + | 0.971584i | \(0.576064\pi\) | |||||||
\(614\) | −1.44033e9 | −0.251115 | ||||||||
\(615\) | 2.94824e9 | 0.511093 | ||||||||
\(616\) | 3.74249e9 | 0.645101 | ||||||||
\(617\) | 3.54215e9 | 0.607112 | 0.303556 | − | 0.952814i | \(-0.401826\pi\) | ||||
0.303556 | + | 0.952814i | \(0.401826\pi\) | |||||||
\(618\) | 3.54955e9 | 0.604941 | ||||||||
\(619\) | −7.53401e9 | −1.27676 | −0.638380 | − | 0.769721i | \(-0.720395\pi\) | ||||
−0.638380 | + | 0.769721i | \(0.720395\pi\) | |||||||
\(620\) | −1.15851e9 | −0.195222 | ||||||||
\(621\) | −1.02129e9 | −0.171131 | ||||||||
\(622\) | 1.31475e9 | 0.219067 | ||||||||
\(623\) | −9.42539e9 | −1.56168 | ||||||||
\(624\) | 3.55411e8 | 0.0585579 | ||||||||
\(625\) | 5.54007e7 | 0.00907685 | ||||||||
\(626\) | 1.01554e9 | 0.165457 | ||||||||
\(627\) | −2.45903e9 | −0.398407 | ||||||||
\(628\) | −3.23974e9 | −0.521978 | ||||||||
\(629\) | −1.67479e10 | −2.68339 | ||||||||
\(630\) | 1.42536e9 | 0.227108 | ||||||||
\(631\) | 1.21541e10 | 1.92584 | 0.962920 | − | 0.269787i | \(-0.0869533\pi\) | ||||
0.962920 | + | 0.269787i | \(0.0869533\pi\) | |||||||
\(632\) | −4.10106e9 | −0.646228 | ||||||||
\(633\) | −1.09481e9 | −0.171564 | ||||||||
\(634\) | −1.24271e9 | −0.193668 | ||||||||
\(635\) | −3.51116e9 | −0.544179 | ||||||||
\(636\) | −3.28162e9 | −0.505811 | ||||||||
\(637\) | −1.10980e10 | −1.70120 | ||||||||
\(638\) | −1.26576e8 | −0.0192966 | ||||||||
\(639\) | −6.19812e8 | −0.0939738 | ||||||||
\(640\) | −1.92443e9 | −0.290183 | ||||||||
\(641\) | 6.74739e9 | 1.01189 | 0.505944 | − | 0.862566i | \(-0.331144\pi\) | ||||
0.505944 | + | 0.862566i | \(0.331144\pi\) | |||||||
\(642\) | −1.84145e9 | −0.274655 | ||||||||
\(643\) | −8.85998e9 | −1.31430 | −0.657150 | − | 0.753760i | \(-0.728238\pi\) | ||||
−0.657150 | + | 0.753760i | \(0.728238\pi\) | |||||||
\(644\) | 5.76915e9 | 0.851160 | ||||||||
\(645\) | 4.72145e8 | 0.0692814 | ||||||||
\(646\) | 1.37286e10 | 2.00360 | ||||||||
\(647\) | −5.90409e9 | −0.857015 | −0.428507 | − | 0.903538i | \(-0.640960\pi\) | ||||
−0.428507 | + | 0.903538i | \(0.640960\pi\) | |||||||
\(648\) | −7.93240e8 | −0.114523 | ||||||||
\(649\) | −3.36599e8 | −0.0483344 | ||||||||
\(650\) | 2.64462e9 | 0.377717 | ||||||||
\(651\) | 3.83200e9 | 0.544367 | ||||||||
\(652\) | 6.99651e9 | 0.988587 | ||||||||
\(653\) | −8.95278e9 | −1.25823 | −0.629117 | − | 0.777310i | \(-0.716584\pi\) | ||||
−0.629117 | + | 0.777310i | \(0.716584\pi\) | |||||||
\(654\) | 2.65545e9 | 0.371207 | ||||||||
\(655\) | −7.19507e9 | −1.00044 | ||||||||
\(656\) | −1.14341e9 | −0.158139 | ||||||||
\(657\) | 4.25914e9 | 0.585927 | ||||||||
\(658\) | −8.23991e8 | −0.112754 | ||||||||
\(659\) | 1.19309e10 | 1.62396 | 0.811979 | − | 0.583687i | \(-0.198391\pi\) | ||||
0.811979 | + | 0.583687i | \(0.198391\pi\) | |||||||
\(660\) | 5.52601e8 | 0.0748183 | ||||||||
\(661\) | −3.52536e9 | −0.474786 | −0.237393 | − | 0.971414i | \(-0.576293\pi\) | ||||
−0.237393 | + | 0.971414i | \(0.576293\pi\) | |||||||
\(662\) | 2.84788e9 | 0.381521 | ||||||||
\(663\) | −6.56095e9 | −0.874318 | ||||||||
\(664\) | −4.15892e9 | −0.551306 | ||||||||
\(665\) | 1.46079e10 | 1.92625 | ||||||||
\(666\) | −2.73407e9 | −0.358632 | ||||||||
\(667\) | −5.38769e8 | −0.0703011 | ||||||||
\(668\) | 2.22507e9 | 0.288820 | ||||||||
\(669\) | −1.80613e9 | −0.233216 | ||||||||
\(670\) | 3.59773e9 | 0.462133 | ||||||||
\(671\) | −1.19207e9 | −0.152326 | ||||||||
\(672\) | 7.33903e9 | 0.932924 | ||||||||
\(673\) | 2.13472e9 | 0.269953 | 0.134976 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134976 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(674\) | 5.73716e9 | 0.721751 | ||||||||
\(675\) | −9.56603e8 | −0.119720 | ||||||||
\(676\) | 6.70450e8 | 0.0834743 | ||||||||
\(677\) | 1.03034e10 | 1.27621 | 0.638103 | − | 0.769951i | \(-0.279719\pi\) | ||||
0.638103 | + | 0.769951i | \(0.279719\pi\) | |||||||
\(678\) | −5.34253e9 | −0.658329 | ||||||||
\(679\) | −2.56537e10 | −3.14490 | ||||||||
\(680\) | −8.51867e9 | −1.03894 | ||||||||
\(681\) | 3.30204e9 | 0.400652 | ||||||||
\(682\) | −1.13088e9 | −0.136512 | ||||||||
\(683\) | 4.34566e9 | 0.521895 | 0.260947 | − | 0.965353i | \(-0.415965\pi\) | ||||
0.260947 | + | 0.965353i | \(0.415965\pi\) | |||||||
\(684\) | −2.94422e9 | −0.351782 | ||||||||
\(685\) | 9.63450e9 | 1.14528 | ||||||||
\(686\) | 7.89033e9 | 0.933170 | ||||||||
\(687\) | −6.27449e9 | −0.738295 | ||||||||
\(688\) | −1.83112e8 | −0.0214366 | ||||||||
\(689\) | −1.22348e10 | −1.42505 | ||||||||
\(690\) | −1.79046e9 | −0.207488 | ||||||||
\(691\) | 1.26968e9 | 0.146393 | 0.0731965 | − | 0.997318i | \(-0.476680\pi\) | ||||
0.0731965 | + | 0.997318i | \(0.476680\pi\) | |||||||
\(692\) | 1.16553e9 | 0.133706 | ||||||||
\(693\) | −1.82784e9 | −0.208628 | ||||||||
\(694\) | −9.76324e9 | −1.10876 | ||||||||
\(695\) | −6.70847e9 | −0.758013 | ||||||||
\(696\) | −4.18464e8 | −0.0470464 | ||||||||
\(697\) | 2.11076e10 | 2.36115 | ||||||||
\(698\) | −4.21946e9 | −0.469638 | ||||||||
\(699\) | 2.07818e9 | 0.230151 | ||||||||
\(700\) | 5.40374e9 | 0.595458 | ||||||||
\(701\) | −1.71178e9 | −0.187687 | −0.0938435 | − | 0.995587i | \(-0.529915\pi\) | ||||
−0.0938435 | + | 0.995587i | \(0.529915\pi\) | |||||||
\(702\) | −1.07106e9 | −0.116852 | ||||||||
\(703\) | −2.80204e10 | −3.04180 | ||||||||
\(704\) | −2.54330e9 | −0.274722 | ||||||||
\(705\) | −3.35948e8 | −0.0361086 | ||||||||
\(706\) | 1.33365e9 | 0.142634 | ||||||||
\(707\) | 1.21463e10 | 1.29264 | ||||||||
\(708\) | −4.03014e8 | −0.0426779 | ||||||||
\(709\) | 1.22235e10 | 1.28805 | 0.644025 | − | 0.765004i | \(-0.277263\pi\) | ||||
0.644025 | + | 0.765004i | \(0.277263\pi\) | |||||||
\(710\) | −1.08661e9 | −0.113938 | ||||||||
\(711\) | 2.00297e9 | 0.208992 | ||||||||
\(712\) | 9.19592e9 | 0.954806 | ||||||||
\(713\) | −4.81355e9 | −0.497338 | ||||||||
\(714\) | 1.02047e10 | 1.04919 | ||||||||
\(715\) | 2.06025e9 | 0.210790 | ||||||||
\(716\) | 1.70021e9 | 0.173104 | ||||||||
\(717\) | −2.88492e8 | −0.0292292 | ||||||||
\(718\) | −9.54240e9 | −0.962104 | ||||||||
\(719\) | −5.76282e8 | −0.0578207 | −0.0289104 | − | 0.999582i | \(-0.509204\pi\) | ||||
−0.0289104 | + | 0.999582i | \(0.509204\pi\) | |||||||
\(720\) | −2.25379e8 | −0.0225035 | ||||||||
\(721\) | 2.70403e10 | 2.68682 | ||||||||
\(722\) | 1.63202e10 | 1.61378 | ||||||||
\(723\) | −1.01016e10 | −0.994043 | ||||||||
\(724\) | 7.15357e9 | 0.700548 | ||||||||
\(725\) | −5.04644e8 | −0.0491816 | ||||||||
\(726\) | −3.37406e9 | −0.327246 | ||||||||
\(727\) | 3.68604e9 | 0.355787 | 0.177894 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177894 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(728\) | 1.67061e10 | 1.60478 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 7.46685e9 | 0.710407 | ||||||||
\(731\) | 3.38027e9 | 0.320067 | ||||||||
\(732\) | −1.42728e9 | −0.134499 | ||||||||
\(733\) | −5.75370e9 | −0.539614 | −0.269807 | − | 0.962914i | \(-0.586960\pi\) | ||||
−0.269807 | + | 0.962914i | \(0.586960\pi\) | |||||||
\(734\) | 1.27846e8 | 0.0119331 | ||||||||
\(735\) | 7.03765e9 | 0.653765 | ||||||||
\(736\) | −9.21889e9 | −0.852327 | ||||||||
\(737\) | −4.61363e9 | −0.424528 | ||||||||
\(738\) | 3.44577e9 | 0.315565 | ||||||||
\(739\) | −7.57514e9 | −0.690455 | −0.345227 | − | 0.938519i | \(-0.612198\pi\) | ||||
−0.345227 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(740\) | 6.29683e9 | 0.571230 | ||||||||
\(741\) | −1.09769e10 | −0.991095 | ||||||||
\(742\) | 1.90296e10 | 1.71008 | ||||||||
\(743\) | 9.30976e9 | 0.832679 | 0.416340 | − | 0.909209i | \(-0.363313\pi\) | ||||
0.416340 | + | 0.909209i | \(0.363313\pi\) | |||||||
\(744\) | −3.73870e9 | −0.332825 | ||||||||
\(745\) | 9.59688e9 | 0.850321 | ||||||||
\(746\) | −5.96615e9 | −0.526149 | ||||||||
\(747\) | 2.03123e9 | 0.178294 | ||||||||
\(748\) | 3.95628e9 | 0.345646 | ||||||||
\(749\) | −1.40281e10 | −1.21987 | ||||||||
\(750\) | −4.37291e9 | −0.378491 | ||||||||
\(751\) | 1.04130e10 | 0.897091 | 0.448546 | − | 0.893760i | \(-0.351942\pi\) | ||||
0.448546 | + | 0.893760i | \(0.351942\pi\) | |||||||
\(752\) | 1.30290e8 | 0.0111725 | ||||||||
\(753\) | 7.11271e9 | 0.607089 | ||||||||
\(754\) | −5.65026e8 | −0.0480030 | ||||||||
\(755\) | −1.16519e10 | −0.985334 | ||||||||
\(756\) | −2.18849e9 | −0.184212 | ||||||||
\(757\) | −5.37115e9 | −0.450020 | −0.225010 | − | 0.974356i | \(-0.572241\pi\) | ||||
−0.225010 | + | 0.974356i | \(0.572241\pi\) | |||||||
\(758\) | 7.16765e7 | 0.00597771 | ||||||||
\(759\) | 2.29603e9 | 0.190604 | ||||||||
\(760\) | −1.42523e10 | −1.17771 | ||||||||
\(761\) | −2.00035e10 | −1.64535 | −0.822677 | − | 0.568509i | \(-0.807521\pi\) | ||||
−0.822677 | + | 0.568509i | \(0.807521\pi\) | |||||||
\(762\) | −4.10368e9 | −0.335994 | ||||||||
\(763\) | 2.02292e10 | 1.64870 | ||||||||
\(764\) | −2.33696e9 | −0.189594 | ||||||||
\(765\) | 4.16054e9 | 0.335997 | ||||||||
\(766\) | 6.14740e9 | 0.494186 | ||||||||
\(767\) | −1.50255e9 | −0.120239 | ||||||||
\(768\) | −7.61228e9 | −0.606388 | ||||||||
\(769\) | −1.99672e10 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(770\) | −3.20445e9 | −0.252950 | ||||||||
\(771\) | −1.06058e10 | −0.833401 | ||||||||
\(772\) | −1.88511e9 | −0.147461 | ||||||||
\(773\) | −1.32942e10 | −1.03522 | −0.517611 | − | 0.855616i | \(-0.673179\pi\) | ||||
−0.517611 | + | 0.855616i | \(0.673179\pi\) | |||||||
\(774\) | 5.51822e8 | 0.0427765 | ||||||||
\(775\) | −4.50867e9 | −0.347930 | ||||||||
\(776\) | 2.50292e10 | 1.92278 | ||||||||
\(777\) | −2.08280e10 | −1.59285 | ||||||||
\(778\) | 5.41085e9 | 0.411943 | ||||||||
\(779\) | 3.53143e10 | 2.67652 | ||||||||
\(780\) | 2.46676e9 | 0.186121 | ||||||||
\(781\) | 1.39344e9 | 0.104667 | ||||||||
\(782\) | −1.28186e10 | −0.958552 | ||||||||
\(783\) | 2.04379e8 | 0.0152149 | ||||||||
\(784\) | −2.72940e9 | −0.202284 | ||||||||
\(785\) | 7.65954e9 | 0.565143 | ||||||||
\(786\) | −8.40927e9 | −0.617702 | ||||||||
\(787\) | −1.67731e10 | −1.22659 | −0.613297 | − | 0.789853i | \(-0.710157\pi\) | ||||
−0.613297 | + | 0.789853i | \(0.710157\pi\) | |||||||
\(788\) | 1.16775e9 | 0.0850174 | ||||||||
\(789\) | −6.51808e9 | −0.472444 | ||||||||
\(790\) | 3.51147e9 | 0.253393 | ||||||||
\(791\) | −4.06992e10 | −2.92394 | ||||||||
\(792\) | 1.78334e9 | 0.127554 | ||||||||
\(793\) | −5.32130e9 | −0.378932 | ||||||||
\(794\) | −8.60410e9 | −0.610005 | ||||||||
\(795\) | 7.75854e9 | 0.547640 | ||||||||
\(796\) | −4.70546e9 | −0.330679 | ||||||||
\(797\) | −1.36721e10 | −0.956603 | −0.478301 | − | 0.878196i | \(-0.658747\pi\) | ||||
−0.478301 | + | 0.878196i | \(0.658747\pi\) | |||||||
\(798\) | 1.70731e10 | 1.18933 | ||||||||
\(799\) | −2.40518e9 | −0.166815 | ||||||||
\(800\) | −8.63498e9 | −0.596275 | ||||||||
\(801\) | −4.49131e9 | −0.308787 | ||||||||
\(802\) | 7.12408e8 | 0.0487662 | ||||||||
\(803\) | −9.57528e9 | −0.652600 | ||||||||
\(804\) | −5.52395e9 | −0.374847 | ||||||||
\(805\) | −1.36397e10 | −0.921548 | ||||||||
\(806\) | −5.04813e9 | −0.339593 | ||||||||
\(807\) | 6.36540e9 | 0.426352 | ||||||||
\(808\) | −1.18506e10 | −0.790314 | ||||||||
\(809\) | 2.47296e10 | 1.64209 | 0.821046 | − | 0.570862i | \(-0.193391\pi\) | ||||
0.821046 | + | 0.570862i | \(0.193391\pi\) | |||||||
\(810\) | 6.79200e8 | 0.0449055 | ||||||||
\(811\) | −5.97641e9 | −0.393430 | −0.196715 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196715 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(812\) | −1.15451e9 | −0.0756751 | ||||||||
\(813\) | −4.04883e9 | −0.264248 | ||||||||
\(814\) | 6.14664e9 | 0.399441 | ||||||||
\(815\) | −1.65414e10 | −1.07034 | ||||||||
\(816\) | −1.61358e9 | −0.103962 | ||||||||
\(817\) | 5.65540e9 | 0.362816 | ||||||||
\(818\) | −8.37817e9 | −0.535196 | ||||||||
\(819\) | −8.15932e9 | −0.518991 | ||||||||
\(820\) | −7.93596e9 | −0.502633 | ||||||||
\(821\) | 6.86651e9 | 0.433047 | 0.216523 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216523 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(822\) | 1.12604e10 | 0.707133 | ||||||||
\(823\) | −1.06812e10 | −0.667916 | −0.333958 | − | 0.942588i | \(-0.608384\pi\) | ||||
−0.333958 | + | 0.942588i | \(0.608384\pi\) | |||||||
\(824\) | −2.63820e10 | −1.64272 | ||||||||
\(825\) | 2.15061e9 | 0.133344 | ||||||||
\(826\) | 2.33701e9 | 0.144288 | ||||||||
\(827\) | 1.28871e10 | 0.792291 | 0.396146 | − | 0.918188i | \(-0.370348\pi\) | ||||
0.396146 | + | 0.918188i | \(0.370348\pi\) | |||||||
\(828\) | 2.74907e9 | 0.168298 | ||||||||
\(829\) | 2.54525e10 | 1.55164 | 0.775819 | − | 0.630956i | \(-0.217337\pi\) | ||||
0.775819 | + | 0.630956i | \(0.217337\pi\) | |||||||
\(830\) | 3.56102e9 | 0.216173 | ||||||||
\(831\) | −2.57306e9 | −0.155541 | ||||||||
\(832\) | −1.13531e10 | −0.683411 | ||||||||
\(833\) | 5.03852e10 | 3.02027 | ||||||||
\(834\) | −7.84056e9 | −0.468021 | ||||||||
\(835\) | −5.26061e9 | −0.312704 | ||||||||
\(836\) | 6.61911e9 | 0.391812 | ||||||||
\(837\) | 1.82599e9 | 0.107637 | ||||||||
\(838\) | −1.83220e10 | −1.07552 | ||||||||
\(839\) | 1.16543e10 | 0.681269 | 0.340635 | − | 0.940196i | \(-0.389358\pi\) | ||||
0.340635 | + | 0.940196i | \(0.389358\pi\) | |||||||
\(840\) | −1.05940e10 | −0.616711 | ||||||||
\(841\) | −1.71421e10 | −0.993750 | ||||||||
\(842\) | 4.48282e9 | 0.258797 | ||||||||
\(843\) | −1.97171e9 | −0.113356 | ||||||||
\(844\) | 2.94696e9 | 0.168724 | ||||||||
\(845\) | −1.58510e9 | −0.0903773 | ||||||||
\(846\) | −3.92641e8 | −0.0222946 | ||||||||
\(847\) | −2.57035e10 | −1.45345 | ||||||||
\(848\) | −3.00898e9 | −0.169447 | ||||||||
\(849\) | 4.85299e9 | 0.272165 | ||||||||
\(850\) | −1.20067e10 | −0.670588 | ||||||||
\(851\) | 2.61631e10 | 1.45524 | ||||||||
\(852\) | 1.66838e9 | 0.0924181 | ||||||||
\(853\) | −8.84397e9 | −0.487894 | −0.243947 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243947 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(854\) | 8.27657e9 | 0.454724 | ||||||||
\(855\) | 6.96085e9 | 0.380873 | ||||||||
\(856\) | 1.36866e10 | 0.745826 | ||||||||
\(857\) | −9.53214e9 | −0.517318 | −0.258659 | − | 0.965969i | \(-0.583281\pi\) | ||||
−0.258659 | + | 0.965969i | \(0.583281\pi\) | |||||||
\(858\) | 2.40793e9 | 0.130148 | ||||||||
\(859\) | −1.01239e10 | −0.544971 | −0.272485 | − | 0.962160i | \(-0.587846\pi\) | ||||
−0.272485 | + | 0.962160i | \(0.587846\pi\) | |||||||
\(860\) | −1.27090e9 | −0.0681345 | ||||||||
\(861\) | 2.62498e10 | 1.40157 | ||||||||
\(862\) | 1.26108e10 | 0.670608 | ||||||||
\(863\) | 3.34111e9 | 0.176951 | 0.0884755 | − | 0.996078i | \(-0.471801\pi\) | ||||
0.0884755 | + | 0.996078i | \(0.471801\pi\) | |||||||
\(864\) | 3.49713e9 | 0.184465 | ||||||||
\(865\) | −2.75558e9 | −0.144763 | ||||||||
\(866\) | −3.95353e9 | −0.206858 | ||||||||
\(867\) | 1.87078e10 | 0.974888 | ||||||||
\(868\) | −1.03148e10 | −0.535356 | ||||||||
\(869\) | −4.50301e9 | −0.232773 | ||||||||
\(870\) | 3.58304e8 | 0.0184473 | ||||||||
\(871\) | −2.05948e10 | −1.05608 | ||||||||
\(872\) | −1.97366e10 | −1.00801 | ||||||||
\(873\) | −1.22243e10 | −0.621834 | ||||||||
\(874\) | −2.14463e10 | −1.08658 | ||||||||
\(875\) | −3.33127e10 | −1.68105 | ||||||||
\(876\) | −1.14646e10 | −0.576228 | ||||||||
\(877\) | −1.70327e10 | −0.852679 | −0.426339 | − | 0.904563i | \(-0.640197\pi\) | ||||
−0.426339 | + | 0.904563i | \(0.640197\pi\) | |||||||
\(878\) | −1.78259e10 | −0.888835 | ||||||||
\(879\) | 2.19422e10 | 1.08973 | ||||||||
\(880\) | 5.06691e8 | 0.0250642 | ||||||||
\(881\) | −6.92335e9 | −0.341115 | −0.170558 | − | 0.985348i | \(-0.554557\pi\) | ||||
−0.170558 | + | 0.985348i | \(0.554557\pi\) | |||||||
\(882\) | 8.22528e9 | 0.403655 | ||||||||
\(883\) | −2.45719e9 | −0.120109 | −0.0600547 | − | 0.998195i | \(-0.519128\pi\) | ||||
−0.0600547 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(884\) | 1.76605e10 | 0.859845 | ||||||||
\(885\) | 9.52821e8 | 0.0462072 | ||||||||
\(886\) | −1.51220e10 | −0.730453 | ||||||||
\(887\) | 1.99592e10 | 0.960307 | 0.480154 | − | 0.877184i | \(-0.340581\pi\) | ||||
0.480154 | + | 0.877184i | \(0.340581\pi\) | |||||||
\(888\) | 2.03209e10 | 0.973865 | ||||||||
\(889\) | −3.12617e10 | −1.49230 | ||||||||
\(890\) | −7.87387e9 | −0.374389 | ||||||||
\(891\) | −8.70987e8 | −0.0412515 | ||||||||
\(892\) | 4.86167e9 | 0.229355 | ||||||||
\(893\) | −4.02402e9 | −0.189095 | ||||||||
\(894\) | 1.12164e10 | 0.525015 | ||||||||
\(895\) | −4.01971e9 | −0.187419 | ||||||||
\(896\) | −1.71342e10 | −0.795768 | ||||||||
\(897\) | 1.02493e10 | 0.474155 | ||||||||
\(898\) | 2.57662e10 | 1.18736 | ||||||||
\(899\) | 9.63280e8 | 0.0442174 | ||||||||
\(900\) | 2.57494e9 | 0.117739 | ||||||||
\(901\) | 5.55463e10 | 2.52999 | ||||||||
\(902\) | −7.74667e9 | −0.351473 | ||||||||
\(903\) | 4.20376e9 | 0.189990 | ||||||||
\(904\) | 3.97083e10 | 1.78769 | ||||||||
\(905\) | −1.69128e10 | −0.758481 | ||||||||
\(906\) | −1.36182e10 | −0.608376 | ||||||||
\(907\) | 1.22070e10 | 0.543227 | 0.271614 | − | 0.962406i | \(-0.412443\pi\) | ||||
0.271614 | + | 0.962406i | \(0.412443\pi\) | |||||||
\(908\) | −8.88829e9 | −0.394019 | ||||||||
\(909\) | 5.78785e9 | 0.255590 | ||||||||
\(910\) | −1.43044e10 | −0.629251 | ||||||||
\(911\) | 1.78824e10 | 0.783629 | 0.391815 | − | 0.920044i | \(-0.371847\pi\) | ||||
0.391815 | + | 0.920044i | \(0.371847\pi\) | |||||||
\(912\) | −2.69962e9 | −0.117847 | ||||||||
\(913\) | −4.56655e9 | −0.198582 | ||||||||
\(914\) | −2.00850e9 | −0.0870081 | ||||||||
\(915\) | 3.37443e9 | 0.145622 | ||||||||
\(916\) | 1.68894e10 | 0.726074 | ||||||||
\(917\) | −6.40616e10 | −2.74350 | ||||||||
\(918\) | 4.86265e9 | 0.207455 | ||||||||
\(919\) | −1.01138e10 | −0.429843 | −0.214921 | − | 0.976631i | \(-0.568949\pi\) | ||||
−0.214921 | + | 0.976631i | \(0.568949\pi\) | |||||||
\(920\) | 1.33076e10 | 0.563432 | ||||||||
\(921\) | −5.22847e9 | −0.220529 | ||||||||
\(922\) | −1.44522e10 | −0.607262 | ||||||||
\(923\) | 6.22020e9 | 0.260375 | ||||||||
\(924\) | 4.92010e9 | 0.205174 | ||||||||
\(925\) | 2.45059e10 | 1.01806 | ||||||||
\(926\) | −1.16973e9 | −0.0484113 | ||||||||
\(927\) | 1.28850e10 | 0.531259 | ||||||||
\(928\) | 1.84487e9 | 0.0757788 | ||||||||
\(929\) | 7.28094e9 | 0.297942 | 0.148971 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148971 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(930\) | 3.20121e9 | 0.130504 | ||||||||
\(931\) | 8.42976e10 | 3.42367 | ||||||||
\(932\) | −5.59397e9 | −0.226342 | ||||||||
\(933\) | 4.77262e9 | 0.192385 | ||||||||
\(934\) | −7.49571e9 | −0.301022 | ||||||||
\(935\) | −9.35360e9 | −0.374230 | ||||||||
\(936\) | 7.96067e9 | 0.317310 | ||||||||
\(937\) | −2.64374e10 | −1.04986 | −0.524928 | − | 0.851147i | \(-0.675908\pi\) | ||||
−0.524928 | + | 0.851147i | \(0.675908\pi\) | |||||||
\(938\) | 3.20325e10 | 1.26731 | ||||||||
\(939\) | 3.68645e9 | 0.145304 | ||||||||
\(940\) | 9.04292e8 | 0.0355109 | ||||||||
\(941\) | −7.30500e9 | −0.285796 | −0.142898 | − | 0.989737i | \(-0.545642\pi\) | ||||
−0.142898 | + | 0.989737i | \(0.545642\pi\) | |||||||
\(942\) | 8.95211e9 | 0.348937 | ||||||||
\(943\) | −3.29735e10 | −1.28049 | ||||||||
\(944\) | −3.69531e8 | −0.0142971 | ||||||||
\(945\) | 5.17412e9 | 0.199446 | ||||||||
\(946\) | −1.24059e9 | −0.0476441 | ||||||||
\(947\) | 6.35717e9 | 0.243242 | 0.121621 | − | 0.992577i | \(-0.461191\pi\) | ||||
0.121621 | + | 0.992577i | \(0.461191\pi\) | |||||||
\(948\) | −5.39150e9 | −0.205533 | ||||||||
\(949\) | −4.27432e10 | −1.62344 | ||||||||
\(950\) | −2.00879e10 | −0.760154 | ||||||||
\(951\) | −4.51111e9 | −0.170079 | ||||||||
\(952\) | −7.58463e10 | −2.84908 | ||||||||
\(953\) | −6.22176e9 | −0.232856 | −0.116428 | − | 0.993199i | \(-0.537144\pi\) | ||||
−0.116428 | + | 0.993199i | \(0.537144\pi\) | |||||||
\(954\) | 9.06782e9 | 0.338130 | ||||||||
\(955\) | 5.52514e9 | 0.205273 | ||||||||
\(956\) | 7.76550e8 | 0.0287453 | ||||||||
\(957\) | −4.59479e8 | −0.0169462 | ||||||||
\(958\) | 8.54047e9 | 0.313836 | ||||||||
\(959\) | 8.57811e10 | 3.14070 | ||||||||
\(960\) | 7.19941e9 | 0.262632 | ||||||||
\(961\) | −1.89063e10 | −0.687188 | ||||||||
\(962\) | 2.74381e10 | 0.993668 | ||||||||
\(963\) | −6.68457e9 | −0.241202 | ||||||||
\(964\) | 2.71910e10 | 0.977587 | ||||||||
\(965\) | 4.45686e9 | 0.159655 | ||||||||
\(966\) | −1.59414e10 | −0.568993 | ||||||||
\(967\) | −3.37902e10 | −1.20171 | −0.600853 | − | 0.799360i | \(-0.705172\pi\) | ||||
−0.600853 | + | 0.799360i | \(0.705172\pi\) | |||||||
\(968\) | 2.50777e10 | 0.888637 | ||||||||
\(969\) | 4.98354e10 | 1.75956 | ||||||||
\(970\) | −2.14308e10 | −0.753943 | ||||||||
\(971\) | −4.96021e10 | −1.73873 | −0.869366 | − | 0.494169i | \(-0.835472\pi\) | ||||
−0.869366 | + | 0.494169i | \(0.835472\pi\) | |||||||
\(972\) | −1.04284e9 | −0.0364239 | ||||||||
\(973\) | −5.97291e10 | −2.07870 | ||||||||
\(974\) | 1.97444e10 | 0.684680 | ||||||||
\(975\) | 9.60012e9 | 0.331711 | ||||||||
\(976\) | −1.30870e9 | −0.0450574 | ||||||||
\(977\) | −3.46137e10 | −1.18745 | −0.593727 | − | 0.804667i | \(-0.702344\pi\) | ||||
−0.593727 | + | 0.804667i | \(0.702344\pi\) | |||||||
\(978\) | −1.93329e10 | −0.660861 | ||||||||
\(979\) | 1.00972e10 | 0.343924 | ||||||||
\(980\) | −1.89437e10 | −0.642943 | ||||||||
\(981\) | 9.63943e9 | 0.325994 | ||||||||
\(982\) | −1.67382e10 | −0.564052 | ||||||||
\(983\) | −9.52456e9 | −0.319822 | −0.159911 | − | 0.987131i | \(-0.551121\pi\) | ||||
−0.159911 | + | 0.987131i | \(0.551121\pi\) | |||||||
\(984\) | −2.56107e10 | −0.856916 | ||||||||
\(985\) | −2.76084e9 | −0.0920480 | ||||||||
\(986\) | 2.56523e9 | 0.0852231 | ||||||||
\(987\) | −2.99113e9 | −0.0990205 | ||||||||
\(988\) | 2.95471e10 | 0.974689 | ||||||||
\(989\) | −5.28054e9 | −0.173577 | ||||||||
\(990\) | −1.52696e9 | −0.0500154 | ||||||||
\(991\) | 4.31860e10 | 1.40956 | 0.704782 | − | 0.709424i | \(-0.251045\pi\) | ||||
0.704782 | + | 0.709424i | \(0.251045\pi\) | |||||||
\(992\) | 1.64827e10 | 0.536090 | ||||||||
\(993\) | 1.03379e10 | 0.335052 | ||||||||
\(994\) | −9.67469e9 | −0.312453 | ||||||||
\(995\) | 1.11248e10 | 0.358025 | ||||||||
\(996\) | −5.46758e9 | −0.175343 | ||||||||
\(997\) | 5.74177e9 | 0.183490 | 0.0917451 | − | 0.995783i | \(-0.470755\pi\) | ||||
0.0917451 | + | 0.995783i | \(0.470755\pi\) | |||||||
\(998\) | 5.56327e9 | 0.177163 | ||||||||
\(999\) | −9.92480e9 | −0.314951 |
(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 | 177.8.a.d.1.11 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.11 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.8 | 18 | 3.2 | odd | 2 |