Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.30594\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.30594 | −1.90869 | −0.954343 | − | 0.298714i | \(-0.903442\pi\) | ||||
−0.954343 | + | 0.298714i | \(0.903442\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.60566 | 0.718071 | 0.359035 | − | 0.933324i | \(-0.383106\pi\) | ||||
0.359035 | + | 0.933324i | \(0.383106\pi\) | |||||||
\(6\) | 3.30594 | 1.34964 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.92924 | 2.64308 | ||||||||
\(10\) | −1.60566 | −0.507753 | ||||||||
\(11\) | −1.00497 | −0.303011 | −0.151506 | − | 0.988456i | \(-0.548412\pi\) | ||||
−0.151506 | + | 0.988456i | \(0.548412\pi\) | |||||||
\(12\) | −3.30594 | −0.954343 | ||||||||
\(13\) | −3.99407 | −1.10776 | −0.553878 | − | 0.832598i | \(-0.686853\pi\) | ||||
−0.553878 | + | 0.832598i | \(0.686853\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −5.30820 | −1.37057 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.17047 | 1.01149 | 0.505744 | − | 0.862684i | \(-0.331218\pi\) | ||||
0.505744 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(18\) | −7.92924 | −1.86894 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.60566 | 0.359035 | ||||||||
\(21\) | 3.30594 | 0.721415 | ||||||||
\(22\) | 1.00497 | 0.214261 | ||||||||
\(23\) | −3.41425 | −0.711920 | −0.355960 | − | 0.934501i | \(-0.615846\pi\) | ||||
−0.355960 | + | 0.934501i | \(0.615846\pi\) | |||||||
\(24\) | 3.30594 | 0.674822 | ||||||||
\(25\) | −2.42187 | −0.484374 | ||||||||
\(26\) | 3.99407 | 0.783302 | ||||||||
\(27\) | −16.2958 | −3.13612 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 9.28749 | 1.72464 | 0.862322 | − | 0.506360i | \(-0.169009\pi\) | ||||
0.862322 | + | 0.506360i | \(0.169009\pi\) | |||||||
\(30\) | 5.30820 | 0.969140 | ||||||||
\(31\) | −3.52169 | −0.632515 | −0.316257 | − | 0.948673i | \(-0.602426\pi\) | ||||
−0.316257 | + | 0.948673i | \(0.602426\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.32238 | 0.578353 | ||||||||
\(34\) | −4.17047 | −0.715230 | ||||||||
\(35\) | −1.60566 | −0.271405 | ||||||||
\(36\) | 7.92924 | 1.32154 | ||||||||
\(37\) | −6.29853 | −1.03547 | −0.517736 | − | 0.855540i | \(-0.673225\pi\) | ||||
−0.517736 | + | 0.855540i | \(0.673225\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.2042 | 2.11436 | ||||||||
\(40\) | −1.60566 | −0.253876 | ||||||||
\(41\) | 11.8943 | 1.85759 | 0.928793 | − | 0.370600i | \(-0.120848\pi\) | ||||
0.928793 | + | 0.370600i | \(0.120848\pi\) | |||||||
\(42\) | −3.30594 | −0.510118 | ||||||||
\(43\) | −3.45997 | −0.527640 | −0.263820 | − | 0.964572i | \(-0.584982\pi\) | ||||
−0.263820 | + | 0.964572i | \(0.584982\pi\) | |||||||
\(44\) | −1.00497 | −0.151506 | ||||||||
\(45\) | 12.7316 | 1.89792 | ||||||||
\(46\) | 3.41425 | 0.503404 | ||||||||
\(47\) | −6.77599 | −0.988380 | −0.494190 | − | 0.869354i | \(-0.664535\pi\) | ||||
−0.494190 | + | 0.869354i | \(0.664535\pi\) | |||||||
\(48\) | −3.30594 | −0.477171 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.42187 | 0.342504 | ||||||||
\(51\) | −13.7873 | −1.93061 | ||||||||
\(52\) | −3.99407 | −0.553878 | ||||||||
\(53\) | 0.844502 | 0.116001 | 0.0580006 | − | 0.998317i | \(-0.481527\pi\) | ||||
0.0580006 | + | 0.998317i | \(0.481527\pi\) | |||||||
\(54\) | 16.2958 | 2.21757 | ||||||||
\(55\) | −1.61364 | −0.217583 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.28749 | −1.21951 | ||||||||
\(59\) | 13.3841 | 1.74247 | 0.871234 | − | 0.490868i | \(-0.163320\pi\) | ||||
0.871234 | + | 0.490868i | \(0.163320\pi\) | |||||||
\(60\) | −5.30820 | −0.685286 | ||||||||
\(61\) | −2.17110 | −0.277981 | −0.138991 | − | 0.990294i | \(-0.544386\pi\) | ||||
−0.138991 | + | 0.990294i | \(0.544386\pi\) | |||||||
\(62\) | 3.52169 | 0.447255 | ||||||||
\(63\) | −7.92924 | −0.998990 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.41311 | −0.795448 | ||||||||
\(66\) | −3.32238 | −0.408957 | ||||||||
\(67\) | −1.83197 | −0.223811 | −0.111905 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111905 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(68\) | 4.17047 | 0.505744 | ||||||||
\(69\) | 11.2873 | 1.35883 | ||||||||
\(70\) | 1.60566 | 0.191913 | ||||||||
\(71\) | −1.00901 | −0.119748 | −0.0598738 | − | 0.998206i | \(-0.519070\pi\) | ||||
−0.0598738 | + | 0.998206i | \(0.519070\pi\) | |||||||
\(72\) | −7.92924 | −0.934470 | ||||||||
\(73\) | 4.42347 | 0.517728 | 0.258864 | − | 0.965914i | \(-0.416652\pi\) | ||||
0.258864 | + | 0.965914i | \(0.416652\pi\) | |||||||
\(74\) | 6.29853 | 0.732189 | ||||||||
\(75\) | 8.00656 | 0.924518 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00497 | 0.114527 | ||||||||
\(78\) | −13.2042 | −1.49508 | ||||||||
\(79\) | −3.58891 | −0.403783 | −0.201892 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201892 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(80\) | 1.60566 | 0.179518 | ||||||||
\(81\) | 30.0851 | 3.34279 | ||||||||
\(82\) | −11.8943 | −1.31351 | ||||||||
\(83\) | 9.90796 | 1.08754 | 0.543770 | − | 0.839234i | \(-0.316996\pi\) | ||||
0.543770 | + | 0.839234i | \(0.316996\pi\) | |||||||
\(84\) | 3.30594 | 0.360708 | ||||||||
\(85\) | 6.69634 | 0.726320 | ||||||||
\(86\) | 3.45997 | 0.373098 | ||||||||
\(87\) | −30.7039 | −3.29180 | ||||||||
\(88\) | 1.00497 | 0.107131 | ||||||||
\(89\) | −0.861489 | −0.0913176 | −0.0456588 | − | 0.998957i | \(-0.514539\pi\) | ||||
−0.0456588 | + | 0.998957i | \(0.514539\pi\) | |||||||
\(90\) | −12.7316 | −1.34203 | ||||||||
\(91\) | 3.99407 | 0.418693 | ||||||||
\(92\) | −3.41425 | −0.355960 | ||||||||
\(93\) | 11.6425 | 1.20727 | ||||||||
\(94\) | 6.77599 | 0.698890 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.30594 | 0.337411 | ||||||||
\(97\) | 14.3251 | 1.45450 | 0.727248 | − | 0.686374i | \(-0.240799\pi\) | ||||
0.727248 | + | 0.686374i | \(0.240799\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −7.96868 | −0.800883 | ||||||||
\(100\) | −2.42187 | −0.242187 | ||||||||
\(101\) | −7.44763 | −0.741067 | −0.370533 | − | 0.928819i | \(-0.620825\pi\) | ||||
−0.370533 | + | 0.928819i | \(0.620825\pi\) | |||||||
\(102\) | 13.7873 | 1.36515 | ||||||||
\(103\) | 0.208292 | 0.0205236 | 0.0102618 | − | 0.999947i | \(-0.496734\pi\) | ||||
0.0102618 | + | 0.999947i | \(0.496734\pi\) | |||||||
\(104\) | 3.99407 | 0.391651 | ||||||||
\(105\) | 5.30820 | 0.518027 | ||||||||
\(106\) | −0.844502 | −0.0820252 | ||||||||
\(107\) | 1.35041 | 0.130549 | 0.0652747 | − | 0.997867i | \(-0.479208\pi\) | ||||
0.0652747 | + | 0.997867i | \(0.479208\pi\) | |||||||
\(108\) | −16.2958 | −1.56806 | ||||||||
\(109\) | −17.4667 | −1.67301 | −0.836505 | − | 0.547960i | \(-0.815405\pi\) | ||||
−0.836505 | + | 0.547960i | \(0.815405\pi\) | |||||||
\(110\) | 1.61364 | 0.153855 | ||||||||
\(111\) | 20.8226 | 1.97639 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −5.83241 | −0.548667 | −0.274334 | − | 0.961635i | \(-0.588457\pi\) | ||||
−0.274334 | + | 0.961635i | \(0.588457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.48211 | −0.511209 | ||||||||
\(116\) | 9.28749 | 0.862322 | ||||||||
\(117\) | −31.6700 | −2.92789 | ||||||||
\(118\) | −13.3841 | −1.23211 | ||||||||
\(119\) | −4.17047 | −0.382306 | ||||||||
\(120\) | 5.30820 | 0.484570 | ||||||||
\(121\) | −9.99003 | −0.908184 | ||||||||
\(122\) | 2.17110 | 0.196562 | ||||||||
\(123\) | −39.3220 | −3.54555 | ||||||||
\(124\) | −3.52169 | −0.316257 | ||||||||
\(125\) | −11.9170 | −1.06589 | ||||||||
\(126\) | 7.92924 | 0.706393 | ||||||||
\(127\) | 1.15749 | 0.102710 | 0.0513552 | − | 0.998680i | \(-0.483646\pi\) | ||||
0.0513552 | + | 0.998680i | \(0.483646\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.4384 | 1.00710 | ||||||||
\(130\) | 6.41311 | 0.562467 | ||||||||
\(131\) | −17.2178 | −1.50432 | −0.752161 | − | 0.658979i | \(-0.770988\pi\) | ||||
−0.752161 | + | 0.658979i | \(0.770988\pi\) | |||||||
\(132\) | 3.32238 | 0.289176 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.83197 | 0.158258 | ||||||||
\(135\) | −26.1654 | −2.25196 | ||||||||
\(136\) | −4.17047 | −0.357615 | ||||||||
\(137\) | −6.98319 | −0.596614 | −0.298307 | − | 0.954470i | \(-0.596422\pi\) | ||||
−0.298307 | + | 0.954470i | \(0.596422\pi\) | |||||||
\(138\) | −11.2873 | −0.960839 | ||||||||
\(139\) | 21.5790 | 1.83031 | 0.915154 | − | 0.403104i | \(-0.132069\pi\) | ||||
0.915154 | + | 0.403104i | \(0.132069\pi\) | |||||||
\(140\) | −1.60566 | −0.135703 | ||||||||
\(141\) | 22.4010 | 1.88651 | ||||||||
\(142\) | 1.00901 | 0.0846743 | ||||||||
\(143\) | 4.01394 | 0.335663 | ||||||||
\(144\) | 7.92924 | 0.660770 | ||||||||
\(145\) | 14.9125 | 1.23842 | ||||||||
\(146\) | −4.42347 | −0.366089 | ||||||||
\(147\) | −3.30594 | −0.272669 | ||||||||
\(148\) | −6.29853 | −0.517736 | ||||||||
\(149\) | −17.3627 | −1.42241 | −0.711205 | − | 0.702984i | \(-0.751850\pi\) | ||||
−0.711205 | + | 0.702984i | \(0.751850\pi\) | |||||||
\(150\) | −8.00656 | −0.653733 | ||||||||
\(151\) | −19.3294 | −1.57300 | −0.786500 | − | 0.617590i | \(-0.788109\pi\) | ||||
−0.786500 | + | 0.617590i | \(0.788109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.0687 | 2.67344 | ||||||||
\(154\) | −1.00497 | −0.0809831 | ||||||||
\(155\) | −5.65462 | −0.454190 | ||||||||
\(156\) | 13.2042 | 1.05718 | ||||||||
\(157\) | 12.3453 | 0.985262 | 0.492631 | − | 0.870238i | \(-0.336035\pi\) | ||||
0.492631 | + | 0.870238i | \(0.336035\pi\) | |||||||
\(158\) | 3.58891 | 0.285518 | ||||||||
\(159\) | −2.79187 | −0.221410 | ||||||||
\(160\) | −1.60566 | −0.126938 | ||||||||
\(161\) | 3.41425 | 0.269081 | ||||||||
\(162\) | −30.0851 | −2.36371 | ||||||||
\(163\) | 10.6114 | 0.831146 | 0.415573 | − | 0.909560i | \(-0.363581\pi\) | ||||
0.415573 | + | 0.909560i | \(0.363581\pi\) | |||||||
\(164\) | 11.8943 | 0.928793 | ||||||||
\(165\) | 5.33460 | 0.415298 | ||||||||
\(166\) | −9.90796 | −0.769007 | ||||||||
\(167\) | −12.3986 | −0.959435 | −0.479717 | − | 0.877423i | \(-0.659261\pi\) | ||||
−0.479717 | + | 0.877423i | \(0.659261\pi\) | |||||||
\(168\) | −3.30594 | −0.255059 | ||||||||
\(169\) | 2.95263 | 0.227125 | ||||||||
\(170\) | −6.69634 | −0.513586 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.45997 | −0.263820 | ||||||||
\(173\) | −11.8515 | −0.901053 | −0.450527 | − | 0.892763i | \(-0.648764\pi\) | ||||
−0.450527 | + | 0.892763i | \(0.648764\pi\) | |||||||
\(174\) | 30.7039 | 2.32766 | ||||||||
\(175\) | 2.42187 | 0.183076 | ||||||||
\(176\) | −1.00497 | −0.0757528 | ||||||||
\(177\) | −44.2472 | −3.32582 | ||||||||
\(178\) | 0.861489 | 0.0645713 | ||||||||
\(179\) | 5.57373 | 0.416600 | 0.208300 | − | 0.978065i | \(-0.433207\pi\) | ||||
0.208300 | + | 0.978065i | \(0.433207\pi\) | |||||||
\(180\) | 12.7316 | 0.948959 | ||||||||
\(181\) | 0.503474 | 0.0374230 | 0.0187115 | − | 0.999825i | \(-0.494044\pi\) | ||||
0.0187115 | + | 0.999825i | \(0.494044\pi\) | |||||||
\(182\) | −3.99407 | −0.296060 | ||||||||
\(183\) | 7.17754 | 0.530579 | ||||||||
\(184\) | 3.41425 | 0.251702 | ||||||||
\(185\) | −10.1133 | −0.743542 | ||||||||
\(186\) | −11.6425 | −0.853670 | ||||||||
\(187\) | −4.19121 | −0.306492 | ||||||||
\(188\) | −6.77599 | −0.494190 | ||||||||
\(189\) | 16.2958 | 1.18534 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5992 | 1.49051 | 0.745255 | − | 0.666780i | \(-0.232328\pi\) | ||||
0.745255 | + | 0.666780i | \(0.232328\pi\) | |||||||
\(192\) | −3.30594 | −0.238586 | ||||||||
\(193\) | 9.42217 | 0.678223 | 0.339111 | − | 0.940746i | \(-0.389874\pi\) | ||||
0.339111 | + | 0.940746i | \(0.389874\pi\) | |||||||
\(194\) | −14.3251 | −1.02848 | ||||||||
\(195\) | 21.2013 | 1.51826 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.10840 | −0.435205 | −0.217603 | − | 0.976037i | \(-0.569824\pi\) | ||||
−0.217603 | + | 0.976037i | \(0.569824\pi\) | |||||||
\(198\) | 7.96868 | 0.566310 | ||||||||
\(199\) | 20.0890 | 1.42407 | 0.712036 | − | 0.702143i | \(-0.247773\pi\) | ||||
0.712036 | + | 0.702143i | \(0.247773\pi\) | |||||||
\(200\) | 2.42187 | 0.171252 | ||||||||
\(201\) | 6.05639 | 0.427185 | ||||||||
\(202\) | 7.44763 | 0.524013 | ||||||||
\(203\) | −9.28749 | −0.651854 | ||||||||
\(204\) | −13.7873 | −0.965306 | ||||||||
\(205\) | 19.0982 | 1.33388 | ||||||||
\(206\) | −0.208292 | −0.0145124 | ||||||||
\(207\) | −27.0724 | −1.88166 | ||||||||
\(208\) | −3.99407 | −0.276939 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.30820 | −0.366301 | ||||||||
\(211\) | −16.5622 | −1.14019 | −0.570095 | − | 0.821579i | \(-0.693094\pi\) | ||||
−0.570095 | + | 0.821579i | \(0.693094\pi\) | |||||||
\(212\) | 0.844502 | 0.0580006 | ||||||||
\(213\) | 3.33573 | 0.228560 | ||||||||
\(214\) | −1.35041 | −0.0923124 | ||||||||
\(215\) | −5.55551 | −0.378883 | ||||||||
\(216\) | 16.2958 | 1.10879 | ||||||||
\(217\) | 3.52169 | 0.239068 | ||||||||
\(218\) | 17.4667 | 1.18300 | ||||||||
\(219\) | −14.6237 | −0.988180 | ||||||||
\(220\) | −1.61364 | −0.108792 | ||||||||
\(221\) | −16.6572 | −1.12048 | ||||||||
\(222\) | −20.8226 | −1.39752 | ||||||||
\(223\) | 9.06669 | 0.607150 | 0.303575 | − | 0.952807i | \(-0.401820\pi\) | ||||
0.303575 | + | 0.952807i | \(0.401820\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −19.2036 | −1.28024 | ||||||||
\(226\) | 5.83241 | 0.387966 | ||||||||
\(227\) | −14.1539 | −0.939426 | −0.469713 | − | 0.882819i | \(-0.655643\pi\) | ||||
−0.469713 | + | 0.882819i | \(0.655643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.9957 | −1.91609 | −0.958044 | − | 0.286622i | \(-0.907468\pi\) | ||||
−0.958044 | + | 0.286622i | \(0.907468\pi\) | |||||||
\(230\) | 5.48211 | 0.361480 | ||||||||
\(231\) | −3.32238 | −0.218597 | ||||||||
\(232\) | −9.28749 | −0.609754 | ||||||||
\(233\) | 22.3353 | 1.46323 | 0.731617 | − | 0.681716i | \(-0.238766\pi\) | ||||
0.731617 | + | 0.681716i | \(0.238766\pi\) | |||||||
\(234\) | 31.6700 | 2.07033 | ||||||||
\(235\) | −10.8799 | −0.709727 | ||||||||
\(236\) | 13.3841 | 0.871234 | ||||||||
\(237\) | 11.8647 | 0.770696 | ||||||||
\(238\) | 4.17047 | 0.270331 | ||||||||
\(239\) | 0.263228 | 0.0170268 | 0.00851340 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851340 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(240\) | −5.30820 | −0.342643 | ||||||||
\(241\) | 13.7704 | 0.887033 | 0.443516 | − | 0.896266i | \(-0.353731\pi\) | ||||
0.443516 | + | 0.896266i | \(0.353731\pi\) | |||||||
\(242\) | 9.99003 | 0.642183 | ||||||||
\(243\) | −50.5723 | −3.24422 | ||||||||
\(244\) | −2.17110 | −0.138991 | ||||||||
\(245\) | 1.60566 | 0.102582 | ||||||||
\(246\) | 39.3220 | 2.50708 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.52169 | 0.223628 | ||||||||
\(249\) | −32.7551 | −2.07577 | ||||||||
\(250\) | 11.9170 | 0.753695 | ||||||||
\(251\) | 5.64849 | 0.356530 | 0.178265 | − | 0.983983i | \(-0.442952\pi\) | ||||
0.178265 | + | 0.983983i | \(0.442952\pi\) | |||||||
\(252\) | −7.92924 | −0.499495 | ||||||||
\(253\) | 3.43123 | 0.215720 | ||||||||
\(254\) | −1.15749 | −0.0726272 | ||||||||
\(255\) | −22.1377 | −1.38632 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.93091 | 0.369960 | 0.184980 | − | 0.982742i | \(-0.440778\pi\) | ||||
0.184980 | + | 0.982742i | \(0.440778\pi\) | |||||||
\(258\) | −11.4384 | −0.712126 | ||||||||
\(259\) | 6.29853 | 0.391372 | ||||||||
\(260\) | −6.41311 | −0.397724 | ||||||||
\(261\) | 73.6428 | 4.55837 | ||||||||
\(262\) | 17.2178 | 1.06372 | ||||||||
\(263\) | 25.1607 | 1.55148 | 0.775738 | − | 0.631056i | \(-0.217378\pi\) | ||||
0.775738 | + | 0.631056i | \(0.217378\pi\) | |||||||
\(264\) | −3.32238 | −0.204479 | ||||||||
\(265\) | 1.35598 | 0.0832971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.84803 | 0.174297 | ||||||||
\(268\) | −1.83197 | −0.111905 | ||||||||
\(269\) | 20.2771 | 1.23632 | 0.618160 | − | 0.786053i | \(-0.287879\pi\) | ||||
0.618160 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(270\) | 26.1654 | 1.59238 | ||||||||
\(271\) | 14.3611 | 0.872373 | 0.436187 | − | 0.899856i | \(-0.356329\pi\) | ||||
0.436187 | + | 0.899856i | \(0.356329\pi\) | |||||||
\(272\) | 4.17047 | 0.252872 | ||||||||
\(273\) | −13.2042 | −0.799153 | ||||||||
\(274\) | 6.98319 | 0.421870 | ||||||||
\(275\) | 2.43392 | 0.146771 | ||||||||
\(276\) | 11.2873 | 0.679416 | ||||||||
\(277\) | −4.45484 | −0.267665 | −0.133833 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133833 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(278\) | −21.5790 | −1.29422 | ||||||||
\(279\) | −27.9243 | −1.67179 | ||||||||
\(280\) | 1.60566 | 0.0959563 | ||||||||
\(281\) | 22.9154 | 1.36702 | 0.683508 | − | 0.729943i | \(-0.260454\pi\) | ||||
0.683508 | + | 0.729943i | \(0.260454\pi\) | |||||||
\(282\) | −22.4010 | −1.33396 | ||||||||
\(283\) | −3.90540 | −0.232152 | −0.116076 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116076 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(284\) | −1.00901 | −0.0598738 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.01394 | −0.237349 | ||||||||
\(287\) | −11.8943 | −0.702101 | ||||||||
\(288\) | −7.92924 | −0.467235 | ||||||||
\(289\) | 0.392821 | 0.0231071 | ||||||||
\(290\) | −14.9125 | −0.875693 | ||||||||
\(291\) | −47.3580 | −2.77618 | ||||||||
\(292\) | 4.42347 | 0.258864 | ||||||||
\(293\) | −9.18435 | −0.536555 | −0.268278 | − | 0.963342i | \(-0.586454\pi\) | ||||
−0.268278 | + | 0.963342i | \(0.586454\pi\) | |||||||
\(294\) | 3.30594 | 0.192806 | ||||||||
\(295\) | 21.4903 | 1.25122 | ||||||||
\(296\) | 6.29853 | 0.366095 | ||||||||
\(297\) | 16.3768 | 0.950280 | ||||||||
\(298\) | 17.3627 | 1.00580 | ||||||||
\(299\) | 13.6368 | 0.788635 | ||||||||
\(300\) | 8.00656 | 0.462259 | ||||||||
\(301\) | 3.45997 | 0.199429 | ||||||||
\(302\) | 19.3294 | 1.11228 | ||||||||
\(303\) | 24.6214 | 1.41446 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.48604 | −0.199610 | ||||||||
\(306\) | −33.0687 | −1.89041 | ||||||||
\(307\) | 18.8767 | 1.07735 | 0.538675 | − | 0.842514i | \(-0.318925\pi\) | ||||
0.538675 | + | 0.842514i | \(0.318925\pi\) | |||||||
\(308\) | 1.00497 | 0.0572637 | ||||||||
\(309\) | −0.688601 | −0.0391731 | ||||||||
\(310\) | 5.65462 | 0.321161 | ||||||||
\(311\) | −14.2998 | −0.810867 | −0.405433 | − | 0.914125i | \(-0.632879\pi\) | ||||
−0.405433 | + | 0.914125i | \(0.632879\pi\) | |||||||
\(312\) | −13.2042 | −0.747539 | ||||||||
\(313\) | −9.27385 | −0.524189 | −0.262095 | − | 0.965042i | \(-0.584413\pi\) | ||||
−0.262095 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(314\) | −12.3453 | −0.696686 | ||||||||
\(315\) | −12.7316 | −0.717346 | ||||||||
\(316\) | −3.58891 | −0.201892 | ||||||||
\(317\) | 15.0866 | 0.847350 | 0.423675 | − | 0.905814i | \(-0.360740\pi\) | ||||
0.423675 | + | 0.905814i | \(0.360740\pi\) | |||||||
\(318\) | 2.79187 | 0.156560 | ||||||||
\(319\) | −9.33369 | −0.522586 | ||||||||
\(320\) | 1.60566 | 0.0897589 | ||||||||
\(321\) | −4.46439 | −0.249178 | ||||||||
\(322\) | −3.41425 | −0.190269 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 30.0851 | 1.67140 | ||||||||
\(325\) | 9.67313 | 0.536569 | ||||||||
\(326\) | −10.6114 | −0.587709 | ||||||||
\(327\) | 57.7440 | 3.19325 | ||||||||
\(328\) | −11.8943 | −0.656755 | ||||||||
\(329\) | 6.77599 | 0.373572 | ||||||||
\(330\) | −5.33460 | −0.293660 | ||||||||
\(331\) | 32.9502 | 1.81110 | 0.905552 | − | 0.424235i | \(-0.139457\pi\) | ||||
0.905552 | + | 0.424235i | \(0.139457\pi\) | |||||||
\(332\) | 9.90796 | 0.543770 | ||||||||
\(333\) | −49.9426 | −2.73684 | ||||||||
\(334\) | 12.3986 | 0.678423 | ||||||||
\(335\) | −2.94151 | −0.160712 | ||||||||
\(336\) | 3.30594 | 0.180354 | ||||||||
\(337\) | 5.29047 | 0.288190 | 0.144095 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144095 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(338\) | −2.95263 | −0.160602 | ||||||||
\(339\) | 19.2816 | 1.04723 | ||||||||
\(340\) | 6.69634 | 0.363160 | ||||||||
\(341\) | 3.53921 | 0.191659 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.45997 | 0.186549 | ||||||||
\(345\) | 18.1235 | 0.975738 | ||||||||
\(346\) | 11.8515 | 0.637141 | ||||||||
\(347\) | 26.6940 | 1.43301 | 0.716505 | − | 0.697582i | \(-0.245741\pi\) | ||||
0.716505 | + | 0.697582i | \(0.245741\pi\) | |||||||
\(348\) | −30.7039 | −1.64590 | ||||||||
\(349\) | 18.5294 | 0.991859 | 0.495929 | − | 0.868363i | \(-0.334828\pi\) | ||||
0.495929 | + | 0.868363i | \(0.334828\pi\) | |||||||
\(350\) | −2.42187 | −0.129454 | ||||||||
\(351\) | 65.0865 | 3.47406 | ||||||||
\(352\) | 1.00497 | 0.0535653 | ||||||||
\(353\) | 15.1656 | 0.807184 | 0.403592 | − | 0.914939i | \(-0.367762\pi\) | ||||
0.403592 | + | 0.914939i | \(0.367762\pi\) | |||||||
\(354\) | 44.2472 | 2.35171 | ||||||||
\(355\) | −1.62012 | −0.0859872 | ||||||||
\(356\) | −0.861489 | −0.0456588 | ||||||||
\(357\) | 13.7873 | 0.729703 | ||||||||
\(358\) | −5.57373 | −0.294581 | ||||||||
\(359\) | 4.86384 | 0.256704 | 0.128352 | − | 0.991729i | \(-0.459031\pi\) | ||||
0.128352 | + | 0.991729i | \(0.459031\pi\) | |||||||
\(360\) | −12.7316 | −0.671016 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −0.503474 | −0.0264620 | ||||||||
\(363\) | 33.0264 | 1.73344 | ||||||||
\(364\) | 3.99407 | 0.209346 | ||||||||
\(365\) | 7.10257 | 0.371765 | ||||||||
\(366\) | −7.17754 | −0.375176 | ||||||||
\(367\) | −15.1487 | −0.790753 | −0.395377 | − | 0.918519i | \(-0.629386\pi\) | ||||
−0.395377 | + | 0.918519i | \(0.629386\pi\) | |||||||
\(368\) | −3.41425 | −0.177980 | ||||||||
\(369\) | 94.3131 | 4.90975 | ||||||||
\(370\) | 10.1133 | 0.525764 | ||||||||
\(371\) | −0.844502 | −0.0438443 | ||||||||
\(372\) | 11.6425 | 0.603636 | ||||||||
\(373\) | −12.0889 | −0.625940 | −0.312970 | − | 0.949763i | \(-0.601324\pi\) | ||||
−0.312970 | + | 0.949763i | \(0.601324\pi\) | |||||||
\(374\) | 4.19121 | 0.216723 | ||||||||
\(375\) | 39.3968 | 2.03444 | ||||||||
\(376\) | 6.77599 | 0.349445 | ||||||||
\(377\) | −37.0949 | −1.91049 | ||||||||
\(378\) | −16.2958 | −0.838164 | ||||||||
\(379\) | 2.53167 | 0.130043 | 0.0650215 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650215 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.82658 | −0.196042 | ||||||||
\(382\) | −20.5992 | −1.05395 | ||||||||
\(383\) | 17.7672 | 0.907861 | 0.453931 | − | 0.891037i | \(-0.350021\pi\) | ||||
0.453931 | + | 0.891037i | \(0.350021\pi\) | |||||||
\(384\) | 3.30594 | 0.168706 | ||||||||
\(385\) | 1.61364 | 0.0822388 | ||||||||
\(386\) | −9.42217 | −0.479576 | ||||||||
\(387\) | −27.4349 | −1.39459 | ||||||||
\(388\) | 14.3251 | 0.727248 | ||||||||
\(389\) | −7.41576 | −0.375994 | −0.187997 | − | 0.982170i | \(-0.560200\pi\) | ||||
−0.187997 | + | 0.982170i | \(0.560200\pi\) | |||||||
\(390\) | −21.2013 | −1.07357 | ||||||||
\(391\) | −14.2390 | −0.720099 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 56.9209 | 2.87128 | ||||||||
\(394\) | 6.10840 | 0.307737 | ||||||||
\(395\) | −5.76255 | −0.289945 | ||||||||
\(396\) | −7.96868 | −0.400441 | ||||||||
\(397\) | 23.0391 | 1.15630 | 0.578149 | − | 0.815931i | \(-0.303775\pi\) | ||||
0.578149 | + | 0.815931i | \(0.303775\pi\) | |||||||
\(398\) | −20.0890 | −1.00697 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.42187 | −0.121094 | ||||||||
\(401\) | 21.7693 | 1.08711 | 0.543554 | − | 0.839374i | \(-0.317078\pi\) | ||||
0.543554 | + | 0.839374i | \(0.317078\pi\) | |||||||
\(402\) | −6.05639 | −0.302065 | ||||||||
\(403\) | 14.0659 | 0.700672 | ||||||||
\(404\) | −7.44763 | −0.370533 | ||||||||
\(405\) | 48.3064 | 2.40036 | ||||||||
\(406\) | 9.28749 | 0.460930 | ||||||||
\(407\) | 6.32986 | 0.313760 | ||||||||
\(408\) | 13.7873 | 0.682574 | ||||||||
\(409\) | 10.8461 | 0.536303 | 0.268152 | − | 0.963377i | \(-0.413587\pi\) | ||||
0.268152 | + | 0.963377i | \(0.413587\pi\) | |||||||
\(410\) | −19.0982 | −0.943194 | ||||||||
\(411\) | 23.0860 | 1.13875 | ||||||||
\(412\) | 0.208292 | 0.0102618 | ||||||||
\(413\) | −13.3841 | −0.658591 | ||||||||
\(414\) | 27.0724 | 1.33054 | ||||||||
\(415\) | 15.9088 | 0.780931 | ||||||||
\(416\) | 3.99407 | 0.195826 | ||||||||
\(417\) | −71.3389 | −3.49348 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3984 | −0.507994 | −0.253997 | − | 0.967205i | \(-0.581745\pi\) | ||||
−0.253997 | + | 0.967205i | \(0.581745\pi\) | |||||||
\(420\) | 5.30820 | 0.259014 | ||||||||
\(421\) | −7.23504 | −0.352614 | −0.176307 | − | 0.984335i | \(-0.556415\pi\) | ||||
−0.176307 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(422\) | 16.5622 | 0.806236 | ||||||||
\(423\) | −53.7285 | −2.61237 | ||||||||
\(424\) | −0.844502 | −0.0410126 | ||||||||
\(425\) | −10.1003 | −0.489938 | ||||||||
\(426\) | −3.33573 | −0.161617 | ||||||||
\(427\) | 2.17110 | 0.105067 | ||||||||
\(428\) | 1.35041 | 0.0652747 | ||||||||
\(429\) | −13.2699 | −0.640674 | ||||||||
\(430\) | 5.55551 | 0.267911 | ||||||||
\(431\) | −11.2858 | −0.543616 | −0.271808 | − | 0.962352i | \(-0.587622\pi\) | ||||
−0.271808 | + | 0.962352i | \(0.587622\pi\) | |||||||
\(432\) | −16.2958 | −0.784031 | ||||||||
\(433\) | 27.7278 | 1.33251 | 0.666257 | − | 0.745722i | \(-0.267895\pi\) | ||||
0.666257 | + | 0.745722i | \(0.267895\pi\) | |||||||
\(434\) | −3.52169 | −0.169047 | ||||||||
\(435\) | −49.2999 | −2.36375 | ||||||||
\(436\) | −17.4667 | −0.836505 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 14.6237 | 0.698749 | ||||||||
\(439\) | 16.1949 | 0.772942 | 0.386471 | − | 0.922301i | \(-0.373694\pi\) | ||||
0.386471 | + | 0.922301i | \(0.373694\pi\) | |||||||
\(440\) | 1.61364 | 0.0769274 | ||||||||
\(441\) | 7.92924 | 0.377583 | ||||||||
\(442\) | 16.6572 | 0.792301 | ||||||||
\(443\) | −1.92143 | −0.0912898 | −0.0456449 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456449 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(444\) | 20.8226 | 0.988195 | ||||||||
\(445\) | −1.38325 | −0.0655725 | ||||||||
\(446\) | −9.06669 | −0.429320 | ||||||||
\(447\) | 57.4002 | 2.71493 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −7.10807 | −0.335450 | −0.167725 | − | 0.985834i | \(-0.553642\pi\) | ||||
−0.167725 | + | 0.985834i | \(0.553642\pi\) | |||||||
\(450\) | 19.2036 | 0.905266 | ||||||||
\(451\) | −11.9535 | −0.562869 | ||||||||
\(452\) | −5.83241 | −0.274334 | ||||||||
\(453\) | 63.9017 | 3.00236 | ||||||||
\(454\) | 14.1539 | 0.664274 | ||||||||
\(455\) | 6.41311 | 0.300651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4257 | 1.00225 | 0.501126 | − | 0.865374i | \(-0.332919\pi\) | ||||
0.501126 | + | 0.865374i | \(0.332919\pi\) | |||||||
\(458\) | 28.9957 | 1.35488 | ||||||||
\(459\) | −67.9610 | −3.17215 | ||||||||
\(460\) | −5.48211 | −0.255605 | ||||||||
\(461\) | 1.92191 | 0.0895122 | 0.0447561 | − | 0.998998i | \(-0.485749\pi\) | ||||
0.0447561 | + | 0.998998i | \(0.485749\pi\) | |||||||
\(462\) | 3.32238 | 0.154571 | ||||||||
\(463\) | 13.3363 | 0.619792 | 0.309896 | − | 0.950770i | \(-0.399706\pi\) | ||||
0.309896 | + | 0.950770i | \(0.399706\pi\) | |||||||
\(464\) | 9.28749 | 0.431161 | ||||||||
\(465\) | 18.6938 | 0.866906 | ||||||||
\(466\) | −22.3353 | −1.03466 | ||||||||
\(467\) | 12.5501 | 0.580751 | 0.290375 | − | 0.956913i | \(-0.406220\pi\) | ||||
0.290375 | + | 0.956913i | \(0.406220\pi\) | |||||||
\(468\) | −31.6700 | −1.46395 | ||||||||
\(469\) | 1.83197 | 0.0845926 | ||||||||
\(470\) | 10.8799 | 0.501853 | ||||||||
\(471\) | −40.8128 | −1.88056 | ||||||||
\(472\) | −13.3841 | −0.616055 | ||||||||
\(473\) | 3.47718 | 0.159881 | ||||||||
\(474\) | −11.8647 | −0.544964 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.17047 | −0.191153 | ||||||||
\(477\) | 6.69626 | 0.306601 | ||||||||
\(478\) | −0.263228 | −0.0120398 | ||||||||
\(479\) | −14.6582 | −0.669752 | −0.334876 | − | 0.942262i | \(-0.608694\pi\) | ||||
−0.334876 | + | 0.942262i | \(0.608694\pi\) | |||||||
\(480\) | 5.30820 | 0.242285 | ||||||||
\(481\) | 25.1568 | 1.14705 | ||||||||
\(482\) | −13.7704 | −0.627227 | ||||||||
\(483\) | −11.2873 | −0.513590 | ||||||||
\(484\) | −9.99003 | −0.454092 | ||||||||
\(485\) | 23.0012 | 1.04443 | ||||||||
\(486\) | 50.5723 | 2.29401 | ||||||||
\(487\) | −27.0128 | −1.22407 | −0.612033 | − | 0.790832i | \(-0.709648\pi\) | ||||
−0.612033 | + | 0.790832i | \(0.709648\pi\) | |||||||
\(488\) | 2.17110 | 0.0982812 | ||||||||
\(489\) | −35.0805 | −1.58640 | ||||||||
\(490\) | −1.60566 | −0.0725361 | ||||||||
\(491\) | 13.6444 | 0.615764 | 0.307882 | − | 0.951424i | \(-0.400380\pi\) | ||||
0.307882 | + | 0.951424i | \(0.400380\pi\) | |||||||
\(492\) | −39.3220 | −1.77277 | ||||||||
\(493\) | 38.7332 | 1.74446 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7950 | −0.575091 | ||||||||
\(496\) | −3.52169 | −0.158129 | ||||||||
\(497\) | 1.00901 | 0.0452603 | ||||||||
\(498\) | 32.7551 | 1.46779 | ||||||||
\(499\) | −17.1149 | −0.766168 | −0.383084 | − | 0.923714i | \(-0.625138\pi\) | ||||
−0.383084 | + | 0.923714i | \(0.625138\pi\) | |||||||
\(500\) | −11.9170 | −0.532943 | ||||||||
\(501\) | 40.9891 | 1.83126 | ||||||||
\(502\) | −5.64849 | −0.252104 | ||||||||
\(503\) | 21.6483 | 0.965251 | 0.482625 | − | 0.875827i | \(-0.339683\pi\) | ||||
0.482625 | + | 0.875827i | \(0.339683\pi\) | |||||||
\(504\) | 7.92924 | 0.353196 | ||||||||
\(505\) | −11.9583 | −0.532139 | ||||||||
\(506\) | −3.43123 | −0.152537 | ||||||||
\(507\) | −9.76122 | −0.433511 | ||||||||
\(508\) | 1.15749 | 0.0513552 | ||||||||
\(509\) | 3.87595 | 0.171799 | 0.0858993 | − | 0.996304i | \(-0.472624\pi\) | ||||
0.0858993 | + | 0.996304i | \(0.472624\pi\) | |||||||
\(510\) | 22.1377 | 0.980273 | ||||||||
\(511\) | −4.42347 | −0.195683 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.93091 | −0.261601 | ||||||||
\(515\) | 0.334445 | 0.0147374 | ||||||||
\(516\) | 11.4384 | 0.503549 | ||||||||
\(517\) | 6.80970 | 0.299490 | ||||||||
\(518\) | −6.29853 | −0.276742 | ||||||||
\(519\) | 39.1804 | 1.71983 | ||||||||
\(520\) | 6.41311 | 0.281233 | ||||||||
\(521\) | 33.3837 | 1.46257 | 0.731283 | − | 0.682074i | \(-0.238922\pi\) | ||||
0.731283 | + | 0.682074i | \(0.238922\pi\) | |||||||
\(522\) | −73.6428 | −3.22326 | ||||||||
\(523\) | −28.0440 | −1.22628 | −0.613140 | − | 0.789974i | \(-0.710094\pi\) | ||||
−0.613140 | + | 0.789974i | \(0.710094\pi\) | |||||||
\(524\) | −17.2178 | −0.752161 | ||||||||
\(525\) | −8.00656 | −0.349435 | ||||||||
\(526\) | −25.1607 | −1.09706 | ||||||||
\(527\) | −14.6871 | −0.639781 | ||||||||
\(528\) | 3.32238 | 0.144588 | ||||||||
\(529\) | −11.3429 | −0.493169 | ||||||||
\(530\) | −1.35598 | −0.0588999 | ||||||||
\(531\) | 106.126 | 4.60548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.5069 | −2.05775 | ||||||||
\(534\) | −2.84803 | −0.123246 | ||||||||
\(535\) | 2.16830 | 0.0937438 | ||||||||
\(536\) | 1.83197 | 0.0791291 | ||||||||
\(537\) | −18.4264 | −0.795158 | ||||||||
\(538\) | −20.2771 | −0.874210 | ||||||||
\(539\) | −1.00497 | −0.0432873 | ||||||||
\(540\) | −26.1654 | −1.12598 | ||||||||
\(541\) | 7.34681 | 0.315864 | 0.157932 | − | 0.987450i | \(-0.449517\pi\) | ||||
0.157932 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(542\) | −14.3611 | −0.616861 | ||||||||
\(543\) | −1.66446 | −0.0714287 | ||||||||
\(544\) | −4.17047 | −0.178807 | ||||||||
\(545\) | −28.0455 | −1.20134 | ||||||||
\(546\) | 13.2042 | 0.565086 | ||||||||
\(547\) | 28.7382 | 1.22876 | 0.614378 | − | 0.789012i | \(-0.289407\pi\) | ||||
0.614378 | + | 0.789012i | \(0.289407\pi\) | |||||||
\(548\) | −6.98319 | −0.298307 | ||||||||
\(549\) | −17.2152 | −0.734727 | ||||||||
\(550\) | −2.43392 | −0.103783 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −11.2873 | −0.480420 | ||||||||
\(553\) | 3.58891 | 0.152616 | ||||||||
\(554\) | 4.45484 | 0.189268 | ||||||||
\(555\) | 33.4339 | 1.41919 | ||||||||
\(556\) | 21.5790 | 0.915154 | ||||||||
\(557\) | −44.1857 | −1.87221 | −0.936104 | − | 0.351724i | \(-0.885596\pi\) | ||||
−0.936104 | + | 0.351724i | \(0.885596\pi\) | |||||||
\(558\) | 27.9243 | 1.18213 | ||||||||
\(559\) | 13.8194 | 0.584497 | ||||||||
\(560\) | −1.60566 | −0.0678513 | ||||||||
\(561\) | 13.8559 | 0.584997 | ||||||||
\(562\) | −22.9154 | −0.966626 | ||||||||
\(563\) | 19.8387 | 0.836103 | 0.418051 | − | 0.908423i | \(-0.362713\pi\) | ||||
0.418051 | + | 0.908423i | \(0.362713\pi\) | |||||||
\(564\) | 22.4010 | 0.943253 | ||||||||
\(565\) | −9.36484 | −0.393982 | ||||||||
\(566\) | 3.90540 | 0.164156 | ||||||||
\(567\) | −30.0851 | −1.26346 | ||||||||
\(568\) | 1.00901 | 0.0423372 | ||||||||
\(569\) | −10.2122 | −0.428119 | −0.214060 | − | 0.976821i | \(-0.568669\pi\) | ||||
−0.214060 | + | 0.976821i | \(0.568669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.1274 | −1.21894 | −0.609472 | − | 0.792808i | \(-0.708619\pi\) | ||||
−0.609472 | + | 0.792808i | \(0.708619\pi\) | |||||||
\(572\) | 4.01394 | 0.167831 | ||||||||
\(573\) | −68.0999 | −2.84491 | ||||||||
\(574\) | 11.8943 | 0.496460 | ||||||||
\(575\) | 8.26887 | 0.344836 | ||||||||
\(576\) | 7.92924 | 0.330385 | ||||||||
\(577\) | 41.9370 | 1.74586 | 0.872930 | − | 0.487845i | \(-0.162217\pi\) | ||||
0.872930 | + | 0.487845i | \(0.162217\pi\) | |||||||
\(578\) | −0.392821 | −0.0163392 | ||||||||
\(579\) | −31.1491 | −1.29451 | ||||||||
\(580\) | 14.9125 | 0.619208 | ||||||||
\(581\) | −9.90796 | −0.411052 | ||||||||
\(582\) | 47.3580 | 1.96305 | ||||||||
\(583\) | −0.848702 | −0.0351497 | ||||||||
\(584\) | −4.42347 | −0.183044 | ||||||||
\(585\) | −50.8511 | −2.10243 | ||||||||
\(586\) | 9.18435 | 0.379402 | ||||||||
\(587\) | 12.9226 | 0.533371 | 0.266686 | − | 0.963784i | \(-0.414071\pi\) | ||||
0.266686 | + | 0.963784i | \(0.414071\pi\) | |||||||
\(588\) | −3.30594 | −0.136335 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −21.4903 | −0.884743 | ||||||||
\(591\) | 20.1940 | 0.830670 | ||||||||
\(592\) | −6.29853 | −0.258868 | ||||||||
\(593\) | 1.46902 | 0.0603254 | 0.0301627 | − | 0.999545i | \(-0.490397\pi\) | ||||
0.0301627 | + | 0.999545i | \(0.490397\pi\) | |||||||
\(594\) | −16.3768 | −0.671950 | ||||||||
\(595\) | −6.69634 | −0.274523 | ||||||||
\(596\) | −17.3627 | −0.711205 | ||||||||
\(597\) | −66.4131 | −2.71811 | ||||||||
\(598\) | −13.6368 | −0.557649 | ||||||||
\(599\) | 28.7788 | 1.17587 | 0.587935 | − | 0.808909i | \(-0.299941\pi\) | ||||
0.587935 | + | 0.808909i | \(0.299941\pi\) | |||||||
\(600\) | −8.00656 | −0.326866 | ||||||||
\(601\) | 46.1978 | 1.88445 | 0.942224 | − | 0.334983i | \(-0.108731\pi\) | ||||
0.942224 | + | 0.334983i | \(0.108731\pi\) | |||||||
\(602\) | −3.45997 | −0.141018 | ||||||||
\(603\) | −14.5261 | −0.591550 | ||||||||
\(604\) | −19.3294 | −0.786500 | ||||||||
\(605\) | −16.0405 | −0.652141 | ||||||||
\(606\) | −24.6214 | −1.00018 | ||||||||
\(607\) | −24.3713 | −0.989202 | −0.494601 | − | 0.869120i | \(-0.664686\pi\) | ||||
−0.494601 | + | 0.869120i | \(0.664686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.7039 | 1.24418 | ||||||||
\(610\) | 3.48604 | 0.141146 | ||||||||
\(611\) | 27.0638 | 1.09488 | ||||||||
\(612\) | 33.0687 | 1.33672 | ||||||||
\(613\) | −6.03281 | −0.243663 | −0.121831 | − | 0.992551i | \(-0.538877\pi\) | ||||
−0.121831 | + | 0.992551i | \(0.538877\pi\) | |||||||
\(614\) | −18.8767 | −0.761801 | ||||||||
\(615\) | −63.1376 | −2.54595 | ||||||||
\(616\) | −1.00497 | −0.0404916 | ||||||||
\(617\) | 23.8645 | 0.960749 | 0.480374 | − | 0.877064i | \(-0.340501\pi\) | ||||
0.480374 | + | 0.877064i | \(0.340501\pi\) | |||||||
\(618\) | 0.688601 | 0.0276996 | ||||||||
\(619\) | −22.9388 | −0.921987 | −0.460994 | − | 0.887403i | \(-0.652507\pi\) | ||||
−0.460994 | + | 0.887403i | \(0.652507\pi\) | |||||||
\(620\) | −5.65462 | −0.227095 | ||||||||
\(621\) | 55.6378 | 2.23267 | ||||||||
\(622\) | 14.2998 | 0.573369 | ||||||||
\(623\) | 0.861489 | 0.0345148 | ||||||||
\(624\) | 13.2042 | 0.528590 | ||||||||
\(625\) | −7.02519 | −0.281007 | ||||||||
\(626\) | 9.27385 | 0.370658 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.3453 | 0.492631 | ||||||||
\(629\) | −26.2678 | −1.04737 | ||||||||
\(630\) | 12.7316 | 0.507240 | ||||||||
\(631\) | −41.7210 | −1.66089 | −0.830444 | − | 0.557102i | \(-0.811913\pi\) | ||||
−0.830444 | + | 0.557102i | \(0.811913\pi\) | |||||||
\(632\) | 3.58891 | 0.142759 | ||||||||
\(633\) | 54.7537 | 2.17627 | ||||||||
\(634\) | −15.0866 | −0.599167 | ||||||||
\(635\) | 1.85853 | 0.0737534 | ||||||||
\(636\) | −2.79187 | −0.110705 | ||||||||
\(637\) | −3.99407 | −0.158251 | ||||||||
\(638\) | 9.33369 | 0.369524 | ||||||||
\(639\) | −8.00069 | −0.316502 | ||||||||
\(640\) | −1.60566 | −0.0634691 | ||||||||
\(641\) | 19.6493 | 0.776101 | 0.388051 | − | 0.921638i | \(-0.373149\pi\) | ||||
0.388051 | + | 0.921638i | \(0.373149\pi\) | |||||||
\(642\) | 4.46439 | 0.176195 | ||||||||
\(643\) | 4.88804 | 0.192765 | 0.0963827 | − | 0.995344i | \(-0.469273\pi\) | ||||
0.0963827 | + | 0.995344i | \(0.469273\pi\) | |||||||
\(644\) | 3.41425 | 0.134540 | ||||||||
\(645\) | 18.3662 | 0.723168 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2737 | 1.11155 | 0.555777 | − | 0.831331i | \(-0.312421\pi\) | ||||
0.555777 | + | 0.831331i | \(0.312421\pi\) | |||||||
\(648\) | −30.0851 | −1.18186 | ||||||||
\(649\) | −13.4507 | −0.527987 | ||||||||
\(650\) | −9.67313 | −0.379411 | ||||||||
\(651\) | −11.6425 | −0.456306 | ||||||||
\(652\) | 10.6114 | 0.415573 | ||||||||
\(653\) | 0.457000 | 0.0178838 | 0.00894190 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894190 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(654\) | −57.7440 | −2.25797 | ||||||||
\(655\) | −27.6458 | −1.08021 | ||||||||
\(656\) | 11.8943 | 0.464396 | ||||||||
\(657\) | 35.0748 | 1.36840 | ||||||||
\(658\) | −6.77599 | −0.264156 | ||||||||
\(659\) | −34.6704 | −1.35057 | −0.675284 | − | 0.737557i | \(-0.735979\pi\) | ||||
−0.675284 | + | 0.737557i | \(0.735979\pi\) | |||||||
\(660\) | 5.33460 | 0.207649 | ||||||||
\(661\) | 49.5022 | 1.92541 | 0.962706 | − | 0.270551i | \(-0.0872059\pi\) | ||||
0.962706 | + | 0.270551i | \(0.0872059\pi\) | |||||||
\(662\) | −32.9502 | −1.28064 | ||||||||
\(663\) | 55.0676 | 2.13865 | ||||||||
\(664\) | −9.90796 | −0.384504 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 49.9426 | 1.93523 | ||||||||
\(667\) | −31.7098 | −1.22781 | ||||||||
\(668\) | −12.3986 | −0.479717 | ||||||||
\(669\) | −29.9739 | −1.15886 | ||||||||
\(670\) | 2.94151 | 0.113641 | ||||||||
\(671\) | 2.18190 | 0.0842314 | ||||||||
\(672\) | −3.30594 | −0.127529 | ||||||||
\(673\) | 34.6829 | 1.33693 | 0.668463 | − | 0.743745i | \(-0.266953\pi\) | ||||
0.668463 | + | 0.743745i | \(0.266953\pi\) | |||||||
\(674\) | −5.29047 | −0.203781 | ||||||||
\(675\) | 39.4663 | 1.51906 | ||||||||
\(676\) | 2.95263 | 0.113563 | ||||||||
\(677\) | −7.08968 | −0.272478 | −0.136239 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136239 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(678\) | −19.2816 | −0.740506 | ||||||||
\(679\) | −14.3251 | −0.549748 | ||||||||
\(680\) | −6.69634 | −0.256793 | ||||||||
\(681\) | 46.7919 | 1.79307 | ||||||||
\(682\) | −3.53921 | −0.135523 | ||||||||
\(683\) | −6.70433 | −0.256534 | −0.128267 | − | 0.991740i | \(-0.540941\pi\) | ||||
−0.128267 | + | 0.991740i | \(0.540941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2126 | −0.428411 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 95.8579 | 3.65721 | ||||||||
\(688\) | −3.45997 | −0.131910 | ||||||||
\(689\) | −3.37300 | −0.128501 | ||||||||
\(690\) | −18.1235 | −0.689951 | ||||||||
\(691\) | 9.62186 | 0.366033 | 0.183016 | − | 0.983110i | \(-0.441414\pi\) | ||||
0.183016 | + | 0.983110i | \(0.441414\pi\) | |||||||
\(692\) | −11.8515 | −0.450527 | ||||||||
\(693\) | 7.96868 | 0.302705 | ||||||||
\(694\) | −26.6940 | −1.01329 | ||||||||
\(695\) | 34.6485 | 1.31429 | ||||||||
\(696\) | 30.7039 | 1.16383 | ||||||||
\(697\) | 49.6050 | 1.87892 | ||||||||
\(698\) | −18.5294 | −0.701350 | ||||||||
\(699\) | −73.8391 | −2.79285 | ||||||||
\(700\) | 2.42187 | 0.0915381 | ||||||||
\(701\) | −47.0077 | −1.77546 | −0.887728 | − | 0.460369i | \(-0.847717\pi\) | ||||
−0.887728 | + | 0.460369i | \(0.847717\pi\) | |||||||
\(702\) | −65.0865 | −2.45653 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00497 | −0.0378764 | ||||||||
\(705\) | 35.9683 | 1.35465 | ||||||||
\(706\) | −15.1656 | −0.570765 | ||||||||
\(707\) | 7.44763 | 0.280097 | ||||||||
\(708\) | −44.2472 | −1.66291 | ||||||||
\(709\) | 30.3987 | 1.14165 | 0.570823 | − | 0.821073i | \(-0.306624\pi\) | ||||
0.570823 | + | 0.821073i | \(0.306624\pi\) | |||||||
\(710\) | 1.62012 | 0.0608022 | ||||||||
\(711\) | −28.4573 | −1.06723 | ||||||||
\(712\) | 0.861489 | 0.0322857 | ||||||||
\(713\) | 12.0239 | 0.450300 | ||||||||
\(714\) | −13.7873 | −0.515978 | ||||||||
\(715\) | 6.44501 | 0.241030 | ||||||||
\(716\) | 5.57373 | 0.208300 | ||||||||
\(717\) | −0.870215 | −0.0324988 | ||||||||
\(718\) | −4.86384 | −0.181517 | ||||||||
\(719\) | 7.66631 | 0.285905 | 0.142953 | − | 0.989730i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989730i | \(0.454340\pi\) | |||||||
\(720\) | 12.7316 | 0.474480 | ||||||||
\(721\) | −0.208292 | −0.00775720 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.5243 | −1.69307 | ||||||||
\(724\) | 0.503474 | 0.0187115 | ||||||||
\(725\) | −22.4931 | −0.835373 | ||||||||
\(726\) | −33.0264 | −1.22573 | ||||||||
\(727\) | 6.99220 | 0.259326 | 0.129663 | − | 0.991558i | \(-0.458610\pi\) | ||||
0.129663 | + | 0.991558i | \(0.458610\pi\) | |||||||
\(728\) | −3.99407 | −0.148030 | ||||||||
\(729\) | 76.9337 | 2.84940 | ||||||||
\(730\) | −7.10257 | −0.262878 | ||||||||
\(731\) | −14.4297 | −0.533701 | ||||||||
\(732\) | 7.17754 | 0.265289 | ||||||||
\(733\) | 14.7249 | 0.543878 | 0.271939 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271939 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(734\) | 15.1487 | 0.559147 | ||||||||
\(735\) | −5.30820 | −0.195796 | ||||||||
\(736\) | 3.41425 | 0.125851 | ||||||||
\(737\) | 1.84108 | 0.0678172 | ||||||||
\(738\) | −94.3131 | −3.47171 | ||||||||
\(739\) | 45.0688 | 1.65788 | 0.828941 | − | 0.559337i | \(-0.188944\pi\) | ||||
0.828941 | + | 0.559337i | \(0.188944\pi\) | |||||||
\(740\) | −10.1133 | −0.371771 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.844502 | 0.0310026 | ||||||||
\(743\) | 37.5977 | 1.37932 | 0.689662 | − | 0.724131i | \(-0.257759\pi\) | ||||
0.689662 | + | 0.724131i | \(0.257759\pi\) | |||||||
\(744\) | −11.6425 | −0.426835 | ||||||||
\(745\) | −27.8786 | −1.02139 | ||||||||
\(746\) | 12.0889 | 0.442606 | ||||||||
\(747\) | 78.5626 | 2.87446 | ||||||||
\(748\) | −4.19121 | −0.153246 | ||||||||
\(749\) | −1.35041 | −0.0493431 | ||||||||
\(750\) | −39.3968 | −1.43857 | ||||||||
\(751\) | 1.17468 | 0.0428647 | 0.0214324 | − | 0.999770i | \(-0.493177\pi\) | ||||
0.0214324 | + | 0.999770i | \(0.493177\pi\) | |||||||
\(752\) | −6.77599 | −0.247095 | ||||||||
\(753\) | −18.6736 | −0.680503 | ||||||||
\(754\) | 37.0949 | 1.35092 | ||||||||
\(755\) | −31.0363 | −1.12953 | ||||||||
\(756\) | 16.2958 | 0.592672 | ||||||||
\(757\) | 26.3197 | 0.956605 | 0.478302 | − | 0.878195i | \(-0.341252\pi\) | ||||
0.478302 | + | 0.878195i | \(0.341252\pi\) | |||||||
\(758\) | −2.53167 | −0.0919542 | ||||||||
\(759\) | −11.3435 | −0.411741 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0097 | 0.652850 | 0.326425 | − | 0.945223i | \(-0.394156\pi\) | ||||
0.326425 | + | 0.945223i | \(0.394156\pi\) | |||||||
\(762\) | 3.82658 | 0.138623 | ||||||||
\(763\) | 17.4667 | 0.632338 | ||||||||
\(764\) | 20.5992 | 0.745255 | ||||||||
\(765\) | 53.0969 | 1.91972 | ||||||||
\(766\) | −17.7672 | −0.641955 | ||||||||
\(767\) | −53.4573 | −1.93023 | ||||||||
\(768\) | −3.30594 | −0.119293 | ||||||||
\(769\) | 1.24078 | 0.0447437 | 0.0223719 | − | 0.999750i | \(-0.492878\pi\) | ||||
0.0223719 | + | 0.999750i | \(0.492878\pi\) | |||||||
\(770\) | −1.61364 | −0.0581516 | ||||||||
\(771\) | −19.6072 | −0.706137 | ||||||||
\(772\) | 9.42217 | 0.339111 | ||||||||
\(773\) | −30.1364 | −1.08393 | −0.541966 | − | 0.840400i | \(-0.682320\pi\) | ||||
−0.541966 | + | 0.840400i | \(0.682320\pi\) | |||||||
\(774\) | 27.4349 | 0.986127 | ||||||||
\(775\) | 8.52908 | 0.306374 | ||||||||
\(776\) | −14.3251 | −0.514242 | ||||||||
\(777\) | −20.8226 | −0.747005 | ||||||||
\(778\) | 7.41576 | 0.265868 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 21.2013 | 0.759130 | ||||||||
\(781\) | 1.01403 | 0.0362848 | ||||||||
\(782\) | 14.2390 | 0.509187 | ||||||||
\(783\) | −151.347 | −5.40870 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 19.8223 | 0.707488 | ||||||||
\(786\) | −56.9209 | −2.03030 | ||||||||
\(787\) | −31.8145 | −1.13407 | −0.567033 | − | 0.823695i | \(-0.691909\pi\) | ||||
−0.567033 | + | 0.823695i | \(0.691909\pi\) | |||||||
\(788\) | −6.10840 | −0.217603 | ||||||||
\(789\) | −83.1798 | −2.96128 | ||||||||
\(790\) | 5.76255 | 0.205022 | ||||||||
\(791\) | 5.83241 | 0.207377 | ||||||||
\(792\) | 7.96868 | 0.283155 | ||||||||
\(793\) | 8.67155 | 0.307936 | ||||||||
\(794\) | −23.0391 | −0.817626 | ||||||||
\(795\) | −4.48278 | −0.158988 | ||||||||
\(796\) | 20.0890 | 0.712036 | ||||||||
\(797\) | −2.40659 | −0.0852458 | −0.0426229 | − | 0.999091i | \(-0.513571\pi\) | ||||
−0.0426229 | + | 0.999091i | \(0.513571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2591 | −0.999734 | ||||||||
\(800\) | 2.42187 | 0.0856261 | ||||||||
\(801\) | −6.83095 | −0.241360 | ||||||||
\(802\) | −21.7693 | −0.768701 | ||||||||
\(803\) | −4.44547 | −0.156877 | ||||||||
\(804\) | 6.05639 | 0.213592 | ||||||||
\(805\) | 5.48211 | 0.193219 | ||||||||
\(806\) | −14.0659 | −0.495450 | ||||||||
\(807\) | −67.0350 | −2.35974 | ||||||||
\(808\) | 7.44763 | 0.262007 | ||||||||
\(809\) | 50.5604 | 1.77761 | 0.888805 | − | 0.458286i | \(-0.151536\pi\) | ||||
0.888805 | + | 0.458286i | \(0.151536\pi\) | |||||||
\(810\) | −48.3064 | −1.69731 | ||||||||
\(811\) | 6.03456 | 0.211902 | 0.105951 | − | 0.994371i | \(-0.466211\pi\) | ||||
0.105951 | + | 0.994371i | \(0.466211\pi\) | |||||||
\(812\) | −9.28749 | −0.325927 | ||||||||
\(813\) | −47.4769 | −1.66509 | ||||||||
\(814\) | −6.32986 | −0.221861 | ||||||||
\(815\) | 17.0382 | 0.596822 | ||||||||
\(816\) | −13.7873 | −0.482653 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −10.8461 | −0.379224 | ||||||||
\(819\) | 31.6700 | 1.10664 | ||||||||
\(820\) | 19.0982 | 0.666939 | ||||||||
\(821\) | 22.9676 | 0.801573 | 0.400787 | − | 0.916171i | \(-0.368737\pi\) | ||||
0.400787 | + | 0.916171i | \(0.368737\pi\) | |||||||
\(822\) | −23.0860 | −0.805217 | ||||||||
\(823\) | 20.7187 | 0.722209 | 0.361104 | − | 0.932525i | \(-0.382400\pi\) | ||||
0.361104 | + | 0.932525i | \(0.382400\pi\) | |||||||
\(824\) | −0.208292 | −0.00725619 | ||||||||
\(825\) | −8.04639 | −0.280139 | ||||||||
\(826\) | 13.3841 | 0.465694 | ||||||||
\(827\) | 14.5464 | 0.505827 | 0.252913 | − | 0.967489i | \(-0.418611\pi\) | ||||
0.252913 | + | 0.967489i | \(0.418611\pi\) | |||||||
\(828\) | −27.0724 | −0.940831 | ||||||||
\(829\) | −41.2656 | −1.43321 | −0.716607 | − | 0.697477i | \(-0.754306\pi\) | ||||
−0.716607 | + | 0.697477i | \(0.754306\pi\) | |||||||
\(830\) | −15.9088 | −0.552202 | ||||||||
\(831\) | 14.7274 | 0.510889 | ||||||||
\(832\) | −3.99407 | −0.138470 | ||||||||
\(833\) | 4.17047 | 0.144498 | ||||||||
\(834\) | 71.3389 | 2.47026 | ||||||||
\(835\) | −19.9079 | −0.688942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 57.3887 | 1.98364 | ||||||||
\(838\) | 10.3984 | 0.359206 | ||||||||
\(839\) | −17.9654 | −0.620233 | −0.310117 | − | 0.950699i | \(-0.600368\pi\) | ||||
−0.310117 | + | 0.950699i | \(0.600368\pi\) | |||||||
\(840\) | −5.30820 | −0.183150 | ||||||||
\(841\) | 57.2575 | 1.97440 | ||||||||
\(842\) | 7.23504 | 0.249336 | ||||||||
\(843\) | −75.7568 | −2.60920 | ||||||||
\(844\) | −16.5622 | −0.570095 | ||||||||
\(845\) | 4.74091 | 0.163092 | ||||||||
\(846\) | 53.7285 | 1.84722 | ||||||||
\(847\) | 9.99003 | 0.343261 | ||||||||
\(848\) | 0.844502 | 0.0290003 | ||||||||
\(849\) | 12.9110 | 0.443105 | ||||||||
\(850\) | 10.1003 | 0.346439 | ||||||||
\(851\) | 21.5048 | 0.737174 | ||||||||
\(852\) | 3.33573 | 0.114280 | ||||||||
\(853\) | 53.2831 | 1.82438 | 0.912189 | − | 0.409771i | \(-0.134391\pi\) | ||||
0.912189 | + | 0.409771i | \(0.134391\pi\) | |||||||
\(854\) | −2.17110 | −0.0742936 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.35041 | −0.0461562 | ||||||||
\(857\) | −20.3916 | −0.696564 | −0.348282 | − | 0.937390i | \(-0.613235\pi\) | ||||
−0.348282 | + | 0.937390i | \(0.613235\pi\) | |||||||
\(858\) | 13.2699 | 0.453025 | ||||||||
\(859\) | 12.2523 | 0.418043 | 0.209022 | − | 0.977911i | \(-0.432972\pi\) | ||||
0.209022 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(860\) | −5.55551 | −0.189441 | ||||||||
\(861\) | 39.3220 | 1.34009 | ||||||||
\(862\) | 11.2858 | 0.384394 | ||||||||
\(863\) | −38.4927 | −1.31031 | −0.655154 | − | 0.755496i | \(-0.727396\pi\) | ||||
−0.655154 | + | 0.755496i | \(0.727396\pi\) | |||||||
\(864\) | 16.2958 | 0.554394 | ||||||||
\(865\) | −19.0294 | −0.647020 | ||||||||
\(866\) | −27.7278 | −0.942230 | ||||||||
\(867\) | −1.29864 | −0.0441042 | ||||||||
\(868\) | 3.52169 | 0.119534 | ||||||||
\(869\) | 3.60676 | 0.122351 | ||||||||
\(870\) | 49.2999 | 1.67142 | ||||||||
\(871\) | 7.31703 | 0.247928 | ||||||||
\(872\) | 17.4667 | 0.591498 | ||||||||
\(873\) | 113.587 | 3.84435 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.9170 | 0.402867 | ||||||||
\(876\) | −14.6237 | −0.494090 | ||||||||
\(877\) | −32.9843 | −1.11380 | −0.556901 | − | 0.830579i | \(-0.688010\pi\) | ||||
−0.556901 | + | 0.830579i | \(0.688010\pi\) | |||||||
\(878\) | −16.1949 | −0.546553 | ||||||||
\(879\) | 30.3629 | 1.02412 | ||||||||
\(880\) | −1.61364 | −0.0543959 | ||||||||
\(881\) | 5.07102 | 0.170847 | 0.0854236 | − | 0.996345i | \(-0.472776\pi\) | ||||
0.0854236 | + | 0.996345i | \(0.472776\pi\) | |||||||
\(882\) | −7.92924 | −0.266991 | ||||||||
\(883\) | 27.6866 | 0.931728 | 0.465864 | − | 0.884856i | \(-0.345744\pi\) | ||||
0.465864 | + | 0.884856i | \(0.345744\pi\) | |||||||
\(884\) | −16.6572 | −0.560241 | ||||||||
\(885\) | −71.0457 | −2.38818 | ||||||||
\(886\) | 1.92143 | 0.0645516 | ||||||||
\(887\) | −35.2956 | −1.18511 | −0.592556 | − | 0.805530i | \(-0.701881\pi\) | ||||
−0.592556 | + | 0.805530i | \(0.701881\pi\) | |||||||
\(888\) | −20.8226 | −0.698760 | ||||||||
\(889\) | −1.15749 | −0.0388209 | ||||||||
\(890\) | 1.38325 | 0.0463668 | ||||||||
\(891\) | −30.2348 | −1.01290 | ||||||||
\(892\) | 9.06669 | 0.303575 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −57.4002 | −1.91975 | ||||||||
\(895\) | 8.94949 | 0.299148 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −45.0823 | −1.50526 | ||||||||
\(898\) | 7.10807 | 0.237199 | ||||||||
\(899\) | −32.7077 | −1.09086 | ||||||||
\(900\) | −19.2036 | −0.640120 | ||||||||
\(901\) | 3.52197 | 0.117334 | ||||||||
\(902\) | 11.9535 | 0.398008 | ||||||||
\(903\) | −11.4384 | −0.380647 | ||||||||
\(904\) | 5.83241 | 0.193983 | ||||||||
\(905\) | 0.808406 | 0.0268723 | ||||||||
\(906\) | −63.9017 | −2.12299 | ||||||||
\(907\) | −25.1085 | −0.833715 | −0.416857 | − | 0.908972i | \(-0.636869\pi\) | ||||
−0.416857 | + | 0.908972i | \(0.636869\pi\) | |||||||
\(908\) | −14.1539 | −0.469713 | ||||||||
\(909\) | −59.0540 | −1.95870 | ||||||||
\(910\) | −6.41311 | −0.212592 | ||||||||
\(911\) | −18.6010 | −0.616278 | −0.308139 | − | 0.951341i | \(-0.599706\pi\) | ||||
−0.308139 | + | 0.951341i | \(0.599706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.95725 | −0.329537 | ||||||||
\(914\) | −21.4257 | −0.708700 | ||||||||
\(915\) | 11.5247 | 0.380993 | ||||||||
\(916\) | −28.9957 | −0.958044 | ||||||||
\(917\) | 17.2178 | 0.568580 | ||||||||
\(918\) | 67.9610 | 2.24305 | ||||||||
\(919\) | 16.9273 | 0.558381 | 0.279191 | − | 0.960236i | \(-0.409934\pi\) | ||||
0.279191 | + | 0.960236i | \(0.409934\pi\) | |||||||
\(920\) | 5.48211 | 0.180740 | ||||||||
\(921\) | −62.4052 | −2.05632 | ||||||||
\(922\) | −1.92191 | −0.0632947 | ||||||||
\(923\) | 4.03006 | 0.132651 | ||||||||
\(924\) | −3.32238 | −0.109298 | ||||||||
\(925\) | 15.2542 | 0.501556 | ||||||||
\(926\) | −13.3363 | −0.438259 | ||||||||
\(927\) | 1.65160 | 0.0542456 | ||||||||
\(928\) | −9.28749 | −0.304877 | ||||||||
\(929\) | 4.96916 | 0.163033 | 0.0815164 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815164 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(930\) | −18.6938 | −0.612995 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.3353 | 0.731617 | ||||||||
\(933\) | 47.2742 | 1.54769 | ||||||||
\(934\) | −12.5501 | −0.410653 | ||||||||
\(935\) | −6.72965 | −0.220083 | ||||||||
\(936\) | 31.6700 | 1.03517 | ||||||||
\(937\) | −13.5173 | −0.441592 | −0.220796 | − | 0.975320i | \(-0.570865\pi\) | ||||
−0.220796 | + | 0.975320i | \(0.570865\pi\) | |||||||
\(938\) | −1.83197 | −0.0598160 | ||||||||
\(939\) | 30.6588 | 1.00051 | ||||||||
\(940\) | −10.8799 | −0.354863 | ||||||||
\(941\) | 20.5294 | 0.669239 | 0.334619 | − | 0.942353i | \(-0.391392\pi\) | ||||
0.334619 | + | 0.942353i | \(0.391392\pi\) | |||||||
\(942\) | 40.8128 | 1.32975 | ||||||||
\(943\) | −40.6103 | −1.32245 | ||||||||
\(944\) | 13.3841 | 0.435617 | ||||||||
\(945\) | 26.1654 | 0.851160 | ||||||||
\(946\) | −3.47718 | −0.113053 | ||||||||
\(947\) | 0.960158 | 0.0312009 | 0.0156005 | − | 0.999878i | \(-0.495034\pi\) | ||||
0.0156005 | + | 0.999878i | \(0.495034\pi\) | |||||||
\(948\) | 11.8647 | 0.385348 | ||||||||
\(949\) | −17.6677 | −0.573517 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.8755 | −1.61732 | ||||||||
\(952\) | 4.17047 | 0.135166 | ||||||||
\(953\) | −14.1493 | −0.458342 | −0.229171 | − | 0.973386i | \(-0.573602\pi\) | ||||
−0.229171 | + | 0.973386i | \(0.573602\pi\) | |||||||
\(954\) | −6.69626 | −0.216799 | ||||||||
\(955\) | 33.0753 | 1.07029 | ||||||||
\(956\) | 0.263228 | 0.00851340 | ||||||||
\(957\) | 30.8566 | 0.997453 | ||||||||
\(958\) | 14.6582 | 0.473586 | ||||||||
\(959\) | 6.98319 | 0.225499 | ||||||||
\(960\) | −5.30820 | −0.171321 | ||||||||
\(961\) | −18.5977 | −0.599925 | ||||||||
\(962\) | −25.1568 | −0.811088 | ||||||||
\(963\) | 10.7078 | 0.345053 | ||||||||
\(964\) | 13.7704 | 0.443516 | ||||||||
\(965\) | 15.1288 | 0.487012 | ||||||||
\(966\) | 11.2873 | 0.363163 | ||||||||
\(967\) | 5.94491 | 0.191175 | 0.0955877 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955877 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(968\) | 9.99003 | 0.321092 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.0012 | −0.738525 | ||||||||
\(971\) | −20.5310 | −0.658872 | −0.329436 | − | 0.944178i | \(-0.606859\pi\) | ||||
−0.329436 | + | 0.944178i | \(0.606859\pi\) | |||||||
\(972\) | −50.5723 | −1.62211 | ||||||||
\(973\) | −21.5790 | −0.691791 | ||||||||
\(974\) | 27.0128 | 0.865545 | ||||||||
\(975\) | −31.9788 | −1.02414 | ||||||||
\(976\) | −2.17110 | −0.0694953 | ||||||||
\(977\) | −19.7977 | −0.633384 | −0.316692 | − | 0.948528i | \(-0.602572\pi\) | ||||
−0.316692 | + | 0.948528i | \(0.602572\pi\) | |||||||
\(978\) | 35.0805 | 1.12175 | ||||||||
\(979\) | 0.865774 | 0.0276703 | ||||||||
\(980\) | 1.60566 | 0.0512908 | ||||||||
\(981\) | −138.498 | −4.42190 | ||||||||
\(982\) | −13.6444 | −0.435411 | ||||||||
\(983\) | 58.6875 | 1.87184 | 0.935920 | − | 0.352213i | \(-0.114571\pi\) | ||||
0.935920 | + | 0.352213i | \(0.114571\pi\) | |||||||
\(984\) | 39.3220 | 1.25354 | ||||||||
\(985\) | −9.80798 | −0.312508 | ||||||||
\(986\) | −38.7332 | −1.23352 | ||||||||
\(987\) | −22.4010 | −0.713032 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.8132 | 0.375638 | ||||||||
\(990\) | 12.7950 | 0.406650 | ||||||||
\(991\) | −17.2451 | −0.547808 | −0.273904 | − | 0.961757i | \(-0.588315\pi\) | ||||
−0.273904 | + | 0.961757i | \(0.588315\pi\) | |||||||
\(992\) | 3.52169 | 0.111814 | ||||||||
\(993\) | −108.931 | −3.45683 | ||||||||
\(994\) | −1.00901 | −0.0320039 | ||||||||
\(995\) | 32.2560 | 1.02258 | ||||||||
\(996\) | −32.7551 | −1.03789 | ||||||||
\(997\) | −11.9959 | −0.379915 | −0.189957 | − | 0.981792i | \(-0.560835\pi\) | ||||
−0.189957 | + | 0.981792i | \(0.560835\pi\) | |||||||
\(998\) | 17.1149 | 0.541763 | ||||||||
\(999\) | 102.639 | 3.24737 |
(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 | 5054.2.a.bj.1.1 | 9 | ||
19.3 | odd | 18 | 266.2.u.c.85.3 | ✓ | 18 | ||
19.13 | odd | 18 | 266.2.u.c.169.3 | yes | 18 | ||
19.18 | odd | 2 | 5054.2.a.bk.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.u.c.85.3 | ✓ | 18 | 19.3 | odd | 18 | ||
266.2.u.c.169.3 | yes | 18 | 19.13 | odd | 18 | ||
5054.2.a.bj.1.1 | 9 | 1.1 | even | 1 | trivial | ||
5054.2.a.bk.1.9 | 9 | 19.18 | odd | 2 |