Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + 5237 x^{4} - 12206 x^{3} - 7876 x^{2} + 9264 x + 4048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(4.49493\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.49493 | 1.56298 | 0.781490 | − | 0.623918i | \(-0.214460\pi\) | ||||
0.781490 | + | 0.623918i | \(0.214460\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.415035 | 0.156869 | 0.0784343 | − | 0.996919i | \(-0.475008\pi\) | ||||
0.0784343 | + | 0.996919i | \(0.475008\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.49493 | −1.10519 | ||||||||
\(11\) | −4.08684 | −1.23223 | −0.616114 | − | 0.787657i | \(-0.711294\pi\) | ||||
−0.616114 | + | 0.787657i | \(0.711294\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.91017 | −1.36184 | −0.680918 | − | 0.732360i | \(-0.738419\pi\) | ||||
−0.680918 | + | 0.732360i | \(0.738419\pi\) | |||||||
\(14\) | −0.415035 | −0.110923 | ||||||||
\(15\) | 3.49493 | 0.902387 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.09702 | 1.23621 | 0.618105 | − | 0.786096i | \(-0.287901\pi\) | ||||
0.618105 | + | 0.786096i | \(0.287901\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.49493 | 0.781490 | ||||||||
\(21\) | 0.415035 | 0.0905681 | ||||||||
\(22\) | 4.08684 | 0.871317 | ||||||||
\(23\) | 1.96030 | 0.408751 | 0.204376 | − | 0.978893i | \(-0.434484\pi\) | ||||
0.204376 | + | 0.978893i | \(0.434484\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.21452 | 1.44290 | ||||||||
\(26\) | 4.91017 | 0.962963 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.415035 | 0.0784343 | ||||||||
\(29\) | 7.83262 | 1.45448 | 0.727241 | − | 0.686383i | \(-0.240802\pi\) | ||||
0.727241 | + | 0.686383i | \(0.240802\pi\) | |||||||
\(30\) | −3.49493 | −0.638084 | ||||||||
\(31\) | 4.64876 | 0.834941 | 0.417471 | − | 0.908690i | \(-0.362917\pi\) | ||||
0.417471 | + | 0.908690i | \(0.362917\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.08684 | −0.711428 | ||||||||
\(34\) | −5.09702 | −0.874132 | ||||||||
\(35\) | 1.45052 | 0.245182 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.20548 | 0.526978 | 0.263489 | − | 0.964662i | \(-0.415127\pi\) | ||||
0.263489 | + | 0.964662i | \(0.415127\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −4.91017 | −0.786256 | ||||||||
\(40\) | −3.49493 | −0.552597 | ||||||||
\(41\) | 0.147607 | 0.0230524 | 0.0115262 | − | 0.999934i | \(-0.496331\pi\) | ||||
0.0115262 | + | 0.999934i | \(0.496331\pi\) | |||||||
\(42\) | −0.415035 | −0.0640413 | ||||||||
\(43\) | 0.0396988 | 0.00605401 | 0.00302700 | − | 0.999995i | \(-0.499036\pi\) | ||||
0.00302700 | + | 0.999995i | \(0.499036\pi\) | |||||||
\(44\) | −4.08684 | −0.616114 | ||||||||
\(45\) | 3.49493 | 0.520993 | ||||||||
\(46\) | −1.96030 | −0.289031 | ||||||||
\(47\) | −0.0503944 | −0.00735077 | −0.00367539 | − | 0.999993i | \(-0.501170\pi\) | ||||
−0.00367539 | + | 0.999993i | \(0.501170\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.82775 | −0.975392 | ||||||||
\(50\) | −7.21452 | −1.02029 | ||||||||
\(51\) | 5.09702 | 0.713726 | ||||||||
\(52\) | −4.91017 | −0.680918 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −14.2832 | −1.92595 | ||||||||
\(56\) | −0.415035 | −0.0554614 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −7.83262 | −1.02847 | ||||||||
\(59\) | −11.4052 | −1.48483 | −0.742417 | − | 0.669938i | \(-0.766321\pi\) | ||||
−0.742417 | + | 0.669938i | \(0.766321\pi\) | |||||||
\(60\) | 3.49493 | 0.451193 | ||||||||
\(61\) | 6.82283 | 0.873574 | 0.436787 | − | 0.899565i | \(-0.356116\pi\) | ||||
0.436787 | + | 0.899565i | \(0.356116\pi\) | |||||||
\(62\) | −4.64876 | −0.590393 | ||||||||
\(63\) | 0.415035 | 0.0522895 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −17.1607 | −2.12852 | ||||||||
\(66\) | 4.08684 | 0.503055 | ||||||||
\(67\) | 2.20770 | 0.269714 | 0.134857 | − | 0.990865i | \(-0.456942\pi\) | ||||
0.134857 | + | 0.990865i | \(0.456942\pi\) | |||||||
\(68\) | 5.09702 | 0.618105 | ||||||||
\(69\) | 1.96030 | 0.235993 | ||||||||
\(70\) | −1.45052 | −0.173370 | ||||||||
\(71\) | 13.8103 | 1.63899 | 0.819493 | − | 0.573089i | \(-0.194255\pi\) | ||||
0.819493 | + | 0.573089i | \(0.194255\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −16.3320 | −1.91151 | −0.955757 | − | 0.294157i | \(-0.904961\pi\) | ||||
−0.955757 | + | 0.294157i | \(0.904961\pi\) | |||||||
\(74\) | −3.20548 | −0.372630 | ||||||||
\(75\) | 7.21452 | 0.833061 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −1.69618 | −0.193298 | ||||||||
\(78\) | 4.91017 | 0.555967 | ||||||||
\(79\) | 15.7254 | 1.76925 | 0.884624 | − | 0.466305i | \(-0.154415\pi\) | ||||
0.884624 | + | 0.466305i | \(0.154415\pi\) | |||||||
\(80\) | 3.49493 | 0.390745 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.147607 | −0.0163005 | ||||||||
\(83\) | 8.45796 | 0.928382 | 0.464191 | − | 0.885735i | \(-0.346345\pi\) | ||||
0.464191 | + | 0.885735i | \(0.346345\pi\) | |||||||
\(84\) | 0.415035 | 0.0452841 | ||||||||
\(85\) | 17.8137 | 1.93217 | ||||||||
\(86\) | −0.0396988 | −0.00428083 | ||||||||
\(87\) | 7.83262 | 0.839745 | ||||||||
\(88\) | 4.08684 | 0.435659 | ||||||||
\(89\) | −9.19983 | −0.975180 | −0.487590 | − | 0.873073i | \(-0.662124\pi\) | ||||
−0.487590 | + | 0.873073i | \(0.662124\pi\) | |||||||
\(90\) | −3.49493 | −0.368398 | ||||||||
\(91\) | −2.03789 | −0.213629 | ||||||||
\(92\) | 1.96030 | 0.204376 | ||||||||
\(93\) | 4.64876 | 0.482054 | ||||||||
\(94\) | 0.0503944 | 0.00519778 | ||||||||
\(95\) | 3.49493 | 0.358572 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.2553 | −1.14280 | −0.571400 | − | 0.820672i | \(-0.693600\pi\) | ||||
−0.571400 | + | 0.820672i | \(0.693600\pi\) | |||||||
\(98\) | 6.82775 | 0.689706 | ||||||||
\(99\) | −4.08684 | −0.410743 | ||||||||
\(100\) | 7.21452 | 0.721452 | ||||||||
\(101\) | −5.72812 | −0.569969 | −0.284985 | − | 0.958532i | \(-0.591988\pi\) | ||||
−0.284985 | + | 0.958532i | \(0.591988\pi\) | |||||||
\(102\) | −5.09702 | −0.504680 | ||||||||
\(103\) | 16.7849 | 1.65386 | 0.826932 | − | 0.562302i | \(-0.190084\pi\) | ||||
0.826932 | + | 0.562302i | \(0.190084\pi\) | |||||||
\(104\) | 4.91017 | 0.481482 | ||||||||
\(105\) | 1.45052 | 0.141556 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 13.4762 | 1.30279 | 0.651396 | − | 0.758738i | \(-0.274184\pi\) | ||||
0.651396 | + | 0.758738i | \(0.274184\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.89315 | −0.468679 | −0.234340 | − | 0.972155i | \(-0.575293\pi\) | ||||
−0.234340 | + | 0.972155i | \(0.575293\pi\) | |||||||
\(110\) | 14.2832 | 1.36185 | ||||||||
\(111\) | 3.20548 | 0.304251 | ||||||||
\(112\) | 0.415035 | 0.0392171 | ||||||||
\(113\) | 14.2894 | 1.34424 | 0.672119 | − | 0.740443i | \(-0.265384\pi\) | ||||
0.672119 | + | 0.740443i | \(0.265384\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 6.85111 | 0.638869 | ||||||||
\(116\) | 7.83262 | 0.727241 | ||||||||
\(117\) | −4.91017 | −0.453945 | ||||||||
\(118\) | 11.4052 | 1.04994 | ||||||||
\(119\) | 2.11544 | 0.193922 | ||||||||
\(120\) | −3.49493 | −0.319042 | ||||||||
\(121\) | 5.70226 | 0.518388 | ||||||||
\(122\) | −6.82283 | −0.617710 | ||||||||
\(123\) | 0.147607 | 0.0133093 | ||||||||
\(124\) | 4.64876 | 0.417471 | ||||||||
\(125\) | 7.73960 | 0.692251 | ||||||||
\(126\) | −0.415035 | −0.0369743 | ||||||||
\(127\) | 14.7621 | 1.30992 | 0.654962 | − | 0.755661i | \(-0.272684\pi\) | ||||
0.654962 | + | 0.755661i | \(0.272684\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.0396988 | 0.00349528 | ||||||||
\(130\) | 17.1607 | 1.50509 | ||||||||
\(131\) | 10.9973 | 0.960836 | 0.480418 | − | 0.877040i | \(-0.340485\pi\) | ||||
0.480418 | + | 0.877040i | \(0.340485\pi\) | |||||||
\(132\) | −4.08684 | −0.355714 | ||||||||
\(133\) | 0.415035 | 0.0359881 | ||||||||
\(134\) | −2.20770 | −0.190717 | ||||||||
\(135\) | 3.49493 | 0.300796 | ||||||||
\(136\) | −5.09702 | −0.437066 | ||||||||
\(137\) | −16.6482 | −1.42235 | −0.711176 | − | 0.703014i | \(-0.751837\pi\) | ||||
−0.711176 | + | 0.703014i | \(0.751837\pi\) | |||||||
\(138\) | −1.96030 | −0.166872 | ||||||||
\(139\) | 4.76043 | 0.403775 | 0.201887 | − | 0.979409i | \(-0.435293\pi\) | ||||
0.201887 | + | 0.979409i | \(0.435293\pi\) | |||||||
\(140\) | 1.45052 | 0.122591 | ||||||||
\(141\) | −0.0503944 | −0.00424397 | ||||||||
\(142\) | −13.8103 | −1.15894 | ||||||||
\(143\) | 20.0671 | 1.67809 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 27.3745 | 2.27332 | ||||||||
\(146\) | 16.3320 | 1.35164 | ||||||||
\(147\) | −6.82775 | −0.563143 | ||||||||
\(148\) | 3.20548 | 0.263489 | ||||||||
\(149\) | −17.0799 | −1.39924 | −0.699620 | − | 0.714515i | \(-0.746647\pi\) | ||||
−0.699620 | + | 0.714515i | \(0.746647\pi\) | |||||||
\(150\) | −7.21452 | −0.589063 | ||||||||
\(151\) | 14.1138 | 1.14857 | 0.574284 | − | 0.818656i | \(-0.305281\pi\) | ||||
0.574284 | + | 0.818656i | \(0.305281\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.09702 | 0.412070 | ||||||||
\(154\) | 1.69618 | 0.136682 | ||||||||
\(155\) | 16.2471 | 1.30500 | ||||||||
\(156\) | −4.91017 | −0.393128 | ||||||||
\(157\) | 9.41661 | 0.751527 | 0.375764 | − | 0.926716i | \(-0.377380\pi\) | ||||
0.375764 | + | 0.926716i | \(0.377380\pi\) | |||||||
\(158\) | −15.7254 | −1.25105 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | −3.49493 | −0.276298 | ||||||||
\(161\) | 0.813594 | 0.0641202 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −17.2516 | −1.35125 | −0.675627 | − | 0.737244i | \(-0.736127\pi\) | ||||
−0.675627 | + | 0.737244i | \(0.736127\pi\) | |||||||
\(164\) | 0.147607 | 0.0115262 | ||||||||
\(165\) | −14.2832 | −1.11195 | ||||||||
\(166\) | −8.45796 | −0.656465 | ||||||||
\(167\) | −3.67750 | −0.284573 | −0.142287 | − | 0.989825i | \(-0.545445\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545445\pi\) | |||||||
\(168\) | −0.415035 | −0.0320207 | ||||||||
\(169\) | 11.1098 | 0.854596 | ||||||||
\(170\) | −17.8137 | −1.36625 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0.0396988 | 0.00302700 | ||||||||
\(173\) | 21.5612 | 1.63927 | 0.819635 | − | 0.572886i | \(-0.194176\pi\) | ||||
0.819635 | + | 0.572886i | \(0.194176\pi\) | |||||||
\(174\) | −7.83262 | −0.593790 | ||||||||
\(175\) | 2.99428 | 0.226346 | ||||||||
\(176\) | −4.08684 | −0.308057 | ||||||||
\(177\) | −11.4052 | −0.857269 | ||||||||
\(178\) | 9.19983 | 0.689556 | ||||||||
\(179\) | −15.5774 | −1.16431 | −0.582153 | − | 0.813079i | \(-0.697790\pi\) | ||||
−0.582153 | + | 0.813079i | \(0.697790\pi\) | |||||||
\(180\) | 3.49493 | 0.260497 | ||||||||
\(181\) | −5.32170 | −0.395559 | −0.197779 | − | 0.980247i | \(-0.563373\pi\) | ||||
−0.197779 | + | 0.980247i | \(0.563373\pi\) | |||||||
\(182\) | 2.03789 | 0.151059 | ||||||||
\(183\) | 6.82283 | 0.504358 | ||||||||
\(184\) | −1.96030 | −0.144515 | ||||||||
\(185\) | 11.2029 | 0.823656 | ||||||||
\(186\) | −4.64876 | −0.340863 | ||||||||
\(187\) | −20.8307 | −1.52329 | ||||||||
\(188\) | −0.0503944 | −0.00367539 | ||||||||
\(189\) | 0.415035 | 0.0301894 | ||||||||
\(190\) | −3.49493 | −0.253549 | ||||||||
\(191\) | −10.8987 | −0.788599 | −0.394300 | − | 0.918982i | \(-0.629013\pi\) | ||||
−0.394300 | + | 0.918982i | \(0.629013\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 9.27849 | 0.667880 | 0.333940 | − | 0.942594i | \(-0.391622\pi\) | ||||
0.333940 | + | 0.942594i | \(0.391622\pi\) | |||||||
\(194\) | 11.2553 | 0.808082 | ||||||||
\(195\) | −17.1607 | −1.22890 | ||||||||
\(196\) | −6.82775 | −0.487696 | ||||||||
\(197\) | 0.0491723 | 0.00350338 | 0.00175169 | − | 0.999998i | \(-0.499442\pi\) | ||||
0.00175169 | + | 0.999998i | \(0.499442\pi\) | |||||||
\(198\) | 4.08684 | 0.290439 | ||||||||
\(199\) | 20.2449 | 1.43512 | 0.717562 | − | 0.696495i | \(-0.245258\pi\) | ||||
0.717562 | + | 0.696495i | \(0.245258\pi\) | |||||||
\(200\) | −7.21452 | −0.510144 | ||||||||
\(201\) | 2.20770 | 0.155719 | ||||||||
\(202\) | 5.72812 | 0.403029 | ||||||||
\(203\) | 3.25081 | 0.228162 | ||||||||
\(204\) | 5.09702 | 0.356863 | ||||||||
\(205\) | 0.515877 | 0.0360304 | ||||||||
\(206\) | −16.7849 | −1.16946 | ||||||||
\(207\) | 1.96030 | 0.136250 | ||||||||
\(208\) | −4.91017 | −0.340459 | ||||||||
\(209\) | −4.08684 | −0.282693 | ||||||||
\(210\) | −1.45052 | −0.100095 | ||||||||
\(211\) | 19.2314 | 1.32394 | 0.661972 | − | 0.749528i | \(-0.269720\pi\) | ||||
0.661972 | + | 0.749528i | \(0.269720\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | 13.8103 | 0.946269 | ||||||||
\(214\) | −13.4762 | −0.921213 | ||||||||
\(215\) | 0.138744 | 0.00946229 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 1.92940 | 0.130976 | ||||||||
\(218\) | 4.89315 | 0.331406 | ||||||||
\(219\) | −16.3320 | −1.10361 | ||||||||
\(220\) | −14.2832 | −0.962974 | ||||||||
\(221\) | −25.0272 | −1.68351 | ||||||||
\(222\) | −3.20548 | −0.215138 | ||||||||
\(223\) | −8.05779 | −0.539589 | −0.269795 | − | 0.962918i | \(-0.586956\pi\) | ||||
−0.269795 | + | 0.962918i | \(0.586956\pi\) | |||||||
\(224\) | −0.415035 | −0.0277307 | ||||||||
\(225\) | 7.21452 | 0.480968 | ||||||||
\(226\) | −14.2894 | −0.950520 | ||||||||
\(227\) | 16.8358 | 1.11743 | 0.558714 | − | 0.829360i | \(-0.311295\pi\) | ||||
0.558714 | + | 0.829360i | \(0.311295\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 9.71143 | 0.641750 | 0.320875 | − | 0.947122i | \(-0.396023\pi\) | ||||
0.320875 | + | 0.947122i | \(0.396023\pi\) | |||||||
\(230\) | −6.85111 | −0.451749 | ||||||||
\(231\) | −1.69618 | −0.111601 | ||||||||
\(232\) | −7.83262 | −0.514237 | ||||||||
\(233\) | 12.5612 | 0.822913 | 0.411457 | − | 0.911429i | \(-0.365020\pi\) | ||||
0.411457 | + | 0.911429i | \(0.365020\pi\) | |||||||
\(234\) | 4.91017 | 0.320988 | ||||||||
\(235\) | −0.176125 | −0.0114891 | ||||||||
\(236\) | −11.4052 | −0.742417 | ||||||||
\(237\) | 15.7254 | 1.02148 | ||||||||
\(238\) | −2.11544 | −0.137124 | ||||||||
\(239\) | 0.440965 | 0.0285236 | 0.0142618 | − | 0.999898i | \(-0.495460\pi\) | ||||
0.0142618 | + | 0.999898i | \(0.495460\pi\) | |||||||
\(240\) | 3.49493 | 0.225597 | ||||||||
\(241\) | 5.43948 | 0.350388 | 0.175194 | − | 0.984534i | \(-0.443945\pi\) | ||||
0.175194 | + | 0.984534i | \(0.443945\pi\) | |||||||
\(242\) | −5.70226 | −0.366555 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.82283 | 0.436787 | ||||||||
\(245\) | −23.8625 | −1.52452 | ||||||||
\(246\) | −0.147607 | −0.00941110 | ||||||||
\(247\) | −4.91017 | −0.312427 | ||||||||
\(248\) | −4.64876 | −0.295196 | ||||||||
\(249\) | 8.45796 | 0.536002 | ||||||||
\(250\) | −7.73960 | −0.489495 | ||||||||
\(251\) | −3.56968 | −0.225316 | −0.112658 | − | 0.993634i | \(-0.535936\pi\) | ||||
−0.112658 | + | 0.993634i | \(0.535936\pi\) | |||||||
\(252\) | 0.415035 | 0.0261448 | ||||||||
\(253\) | −8.01144 | −0.503675 | ||||||||
\(254\) | −14.7621 | −0.926257 | ||||||||
\(255\) | 17.8137 | 1.11554 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.34972 | −0.583220 | −0.291610 | − | 0.956537i | \(-0.594191\pi\) | ||||
−0.291610 | + | 0.956537i | \(0.594191\pi\) | |||||||
\(258\) | −0.0396988 | −0.00247154 | ||||||||
\(259\) | 1.33039 | 0.0826664 | ||||||||
\(260\) | −17.1607 | −1.06426 | ||||||||
\(261\) | 7.83262 | 0.484827 | ||||||||
\(262\) | −10.9973 | −0.679414 | ||||||||
\(263\) | 21.4780 | 1.32439 | 0.662194 | − | 0.749332i | \(-0.269625\pi\) | ||||
0.662194 | + | 0.749332i | \(0.269625\pi\) | |||||||
\(264\) | 4.08684 | 0.251528 | ||||||||
\(265\) | 3.49493 | 0.214692 | ||||||||
\(266\) | −0.415035 | −0.0254474 | ||||||||
\(267\) | −9.19983 | −0.563020 | ||||||||
\(268\) | 2.20770 | 0.134857 | ||||||||
\(269\) | 4.13801 | 0.252299 | 0.126149 | − | 0.992011i | \(-0.459738\pi\) | ||||
0.126149 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(270\) | −3.49493 | −0.212695 | ||||||||
\(271\) | −16.8861 | −1.02576 | −0.512880 | − | 0.858460i | \(-0.671421\pi\) | ||||
−0.512880 | + | 0.858460i | \(0.671421\pi\) | |||||||
\(272\) | 5.09702 | 0.309052 | ||||||||
\(273\) | −2.03789 | −0.123339 | ||||||||
\(274\) | 16.6482 | 1.00575 | ||||||||
\(275\) | −29.4846 | −1.77799 | ||||||||
\(276\) | 1.96030 | 0.117996 | ||||||||
\(277\) | 3.23480 | 0.194361 | 0.0971803 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971803 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(278\) | −4.76043 | −0.285512 | ||||||||
\(279\) | 4.64876 | 0.278314 | ||||||||
\(280\) | −1.45052 | −0.0866851 | ||||||||
\(281\) | −30.2443 | −1.80422 | −0.902111 | − | 0.431505i | \(-0.857983\pi\) | ||||
−0.902111 | + | 0.431505i | \(0.857983\pi\) | |||||||
\(282\) | 0.0503944 | 0.00300094 | ||||||||
\(283\) | −16.9773 | −1.00920 | −0.504599 | − | 0.863354i | \(-0.668359\pi\) | ||||
−0.504599 | + | 0.863354i | \(0.668359\pi\) | |||||||
\(284\) | 13.8103 | 0.819493 | ||||||||
\(285\) | 3.49493 | 0.207022 | ||||||||
\(286\) | −20.0671 | −1.18659 | ||||||||
\(287\) | 0.0612622 | 0.00361619 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.97963 | 0.528214 | ||||||||
\(290\) | −27.3745 | −1.60748 | ||||||||
\(291\) | −11.2553 | −0.659796 | ||||||||
\(292\) | −16.3320 | −0.955757 | ||||||||
\(293\) | −9.13408 | −0.533619 | −0.266809 | − | 0.963749i | \(-0.585969\pi\) | ||||
−0.266809 | + | 0.963749i | \(0.585969\pi\) | |||||||
\(294\) | 6.82775 | 0.398202 | ||||||||
\(295\) | −39.8604 | −2.32076 | ||||||||
\(296\) | −3.20548 | −0.186315 | ||||||||
\(297\) | −4.08684 | −0.237143 | ||||||||
\(298\) | 17.0799 | 0.989412 | ||||||||
\(299\) | −9.62541 | −0.556652 | ||||||||
\(300\) | 7.21452 | 0.416531 | ||||||||
\(301\) | 0.0164764 | 0.000949683 0 | ||||||||
\(302\) | −14.1138 | −0.812160 | ||||||||
\(303\) | −5.72812 | −0.329072 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 23.8453 | 1.36538 | ||||||||
\(306\) | −5.09702 | −0.291377 | ||||||||
\(307\) | 23.8662 | 1.36212 | 0.681059 | − | 0.732229i | \(-0.261520\pi\) | ||||
0.681059 | + | 0.732229i | \(0.261520\pi\) | |||||||
\(308\) | −1.69618 | −0.0966490 | ||||||||
\(309\) | 16.7849 | 0.954859 | ||||||||
\(310\) | −16.2471 | −0.922772 | ||||||||
\(311\) | 6.45660 | 0.366120 | 0.183060 | − | 0.983102i | \(-0.441400\pi\) | ||||
0.183060 | + | 0.983102i | \(0.441400\pi\) | |||||||
\(312\) | 4.91017 | 0.277984 | ||||||||
\(313\) | −10.2086 | −0.577021 | −0.288511 | − | 0.957477i | \(-0.593160\pi\) | ||||
−0.288511 | + | 0.957477i | \(0.593160\pi\) | |||||||
\(314\) | −9.41661 | −0.531410 | ||||||||
\(315\) | 1.45052 | 0.0817275 | ||||||||
\(316\) | 15.7254 | 0.884624 | ||||||||
\(317\) | −15.9024 | −0.893168 | −0.446584 | − | 0.894742i | \(-0.647360\pi\) | ||||
−0.446584 | + | 0.894742i | \(0.647360\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −32.0107 | −1.79225 | ||||||||
\(320\) | 3.49493 | 0.195372 | ||||||||
\(321\) | 13.4762 | 0.752167 | ||||||||
\(322\) | −0.813594 | −0.0453398 | ||||||||
\(323\) | 5.09702 | 0.283606 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −35.4245 | −1.96500 | ||||||||
\(326\) | 17.2516 | 0.955480 | ||||||||
\(327\) | −4.89315 | −0.270592 | ||||||||
\(328\) | −0.147607 | −0.00815025 | ||||||||
\(329\) | −0.0209154 | −0.00115311 | ||||||||
\(330\) | 14.2832 | 0.786265 | ||||||||
\(331\) | 24.0475 | 1.32177 | 0.660886 | − | 0.750487i | \(-0.270181\pi\) | ||||
0.660886 | + | 0.750487i | \(0.270181\pi\) | |||||||
\(332\) | 8.45796 | 0.464191 | ||||||||
\(333\) | 3.20548 | 0.175659 | ||||||||
\(334\) | 3.67750 | 0.201224 | ||||||||
\(335\) | 7.71577 | 0.421558 | ||||||||
\(336\) | 0.415035 | 0.0226420 | ||||||||
\(337\) | 3.33476 | 0.181656 | 0.0908280 | − | 0.995867i | \(-0.471049\pi\) | ||||
0.0908280 | + | 0.995867i | \(0.471049\pi\) | |||||||
\(338\) | −11.1098 | −0.604291 | ||||||||
\(339\) | 14.2894 | 0.776096 | ||||||||
\(340\) | 17.8137 | 0.966085 | ||||||||
\(341\) | −18.9987 | −1.02884 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −5.73900 | −0.309877 | ||||||||
\(344\) | −0.0396988 | −0.00214041 | ||||||||
\(345\) | 6.85111 | 0.368851 | ||||||||
\(346\) | −21.5612 | −1.15914 | ||||||||
\(347\) | −35.8949 | −1.92694 | −0.963469 | − | 0.267819i | \(-0.913697\pi\) | ||||
−0.963469 | + | 0.267819i | \(0.913697\pi\) | |||||||
\(348\) | 7.83262 | 0.419873 | ||||||||
\(349\) | 17.3197 | 0.927100 | 0.463550 | − | 0.886071i | \(-0.346575\pi\) | ||||
0.463550 | + | 0.886071i | \(0.346575\pi\) | |||||||
\(350\) | −2.99428 | −0.160051 | ||||||||
\(351\) | −4.91017 | −0.262085 | ||||||||
\(352\) | 4.08684 | 0.217829 | ||||||||
\(353\) | −15.9809 | −0.850575 | −0.425288 | − | 0.905058i | \(-0.639827\pi\) | ||||
−0.425288 | + | 0.905058i | \(0.639827\pi\) | |||||||
\(354\) | 11.4052 | 0.606181 | ||||||||
\(355\) | 48.2662 | 2.56170 | ||||||||
\(356\) | −9.19983 | −0.487590 | ||||||||
\(357\) | 2.11544 | 0.111961 | ||||||||
\(358\) | 15.5774 | 0.823289 | ||||||||
\(359\) | −19.6405 | −1.03659 | −0.518294 | − | 0.855203i | \(-0.673433\pi\) | ||||
−0.518294 | + | 0.855203i | \(0.673433\pi\) | |||||||
\(360\) | −3.49493 | −0.184199 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.32170 | 0.279702 | ||||||||
\(363\) | 5.70226 | 0.299291 | ||||||||
\(364\) | −2.03789 | −0.106815 | ||||||||
\(365\) | −57.0791 | −2.98766 | ||||||||
\(366\) | −6.82283 | −0.356635 | ||||||||
\(367\) | −5.75736 | −0.300532 | −0.150266 | − | 0.988646i | \(-0.548013\pi\) | ||||
−0.150266 | + | 0.988646i | \(0.548013\pi\) | |||||||
\(368\) | 1.96030 | 0.102188 | ||||||||
\(369\) | 0.147607 | 0.00768413 | ||||||||
\(370\) | −11.2029 | −0.582413 | ||||||||
\(371\) | 0.415035 | 0.0215476 | ||||||||
\(372\) | 4.64876 | 0.241027 | ||||||||
\(373\) | 27.0308 | 1.39960 | 0.699801 | − | 0.714338i | \(-0.253272\pi\) | ||||
0.699801 | + | 0.714338i | \(0.253272\pi\) | |||||||
\(374\) | 20.8307 | 1.07713 | ||||||||
\(375\) | 7.73960 | 0.399671 | ||||||||
\(376\) | 0.0503944 | 0.00259889 | ||||||||
\(377\) | −38.4595 | −1.98076 | ||||||||
\(378\) | −0.415035 | −0.0213471 | ||||||||
\(379\) | 16.1485 | 0.829494 | 0.414747 | − | 0.909937i | \(-0.363870\pi\) | ||||
0.414747 | + | 0.909937i | \(0.363870\pi\) | |||||||
\(380\) | 3.49493 | 0.179286 | ||||||||
\(381\) | 14.7621 | 0.756285 | ||||||||
\(382\) | 10.8987 | 0.557624 | ||||||||
\(383\) | 28.1444 | 1.43811 | 0.719057 | − | 0.694951i | \(-0.244574\pi\) | ||||
0.719057 | + | 0.694951i | \(0.244574\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −5.92804 | −0.302121 | ||||||||
\(386\) | −9.27849 | −0.472263 | ||||||||
\(387\) | 0.0396988 | 0.00201800 | ||||||||
\(388\) | −11.2553 | −0.571400 | ||||||||
\(389\) | 26.2108 | 1.32894 | 0.664469 | − | 0.747316i | \(-0.268658\pi\) | ||||
0.664469 | + | 0.747316i | \(0.268658\pi\) | |||||||
\(390\) | 17.1607 | 0.868965 | ||||||||
\(391\) | 9.99170 | 0.505302 | ||||||||
\(392\) | 6.82775 | 0.344853 | ||||||||
\(393\) | 10.9973 | 0.554739 | ||||||||
\(394\) | −0.0491723 | −0.00247727 | ||||||||
\(395\) | 54.9592 | 2.76530 | ||||||||
\(396\) | −4.08684 | −0.205371 | ||||||||
\(397\) | 10.5870 | 0.531348 | 0.265674 | − | 0.964063i | \(-0.414405\pi\) | ||||
0.265674 | + | 0.964063i | \(0.414405\pi\) | |||||||
\(398\) | −20.2449 | −1.01479 | ||||||||
\(399\) | 0.415035 | 0.0207778 | ||||||||
\(400\) | 7.21452 | 0.360726 | ||||||||
\(401\) | −3.50880 | −0.175221 | −0.0876105 | − | 0.996155i | \(-0.527923\pi\) | ||||
−0.0876105 | + | 0.996155i | \(0.527923\pi\) | |||||||
\(402\) | −2.20770 | −0.110110 | ||||||||
\(403\) | −22.8262 | −1.13705 | ||||||||
\(404\) | −5.72812 | −0.284985 | ||||||||
\(405\) | 3.49493 | 0.173664 | ||||||||
\(406\) | −3.25081 | −0.161335 | ||||||||
\(407\) | −13.1003 | −0.649358 | ||||||||
\(408\) | −5.09702 | −0.252340 | ||||||||
\(409\) | −15.8684 | −0.784644 | −0.392322 | − | 0.919828i | \(-0.628328\pi\) | ||||
−0.392322 | + | 0.919828i | \(0.628328\pi\) | |||||||
\(410\) | −0.515877 | −0.0254773 | ||||||||
\(411\) | −16.6482 | −0.821195 | ||||||||
\(412\) | 16.7849 | 0.826932 | ||||||||
\(413\) | −4.73357 | −0.232924 | ||||||||
\(414\) | −1.96030 | −0.0963435 | ||||||||
\(415\) | 29.5600 | 1.45104 | ||||||||
\(416\) | 4.91017 | 0.240741 | ||||||||
\(417\) | 4.76043 | 0.233119 | ||||||||
\(418\) | 4.08684 | 0.199894 | ||||||||
\(419\) | 37.5886 | 1.83632 | 0.918162 | − | 0.396205i | \(-0.129673\pi\) | ||||
0.918162 | + | 0.396205i | \(0.129673\pi\) | |||||||
\(420\) | 1.45052 | 0.0707781 | ||||||||
\(421\) | 8.13549 | 0.396500 | 0.198250 | − | 0.980152i | \(-0.436474\pi\) | ||||
0.198250 | + | 0.980152i | \(0.436474\pi\) | |||||||
\(422\) | −19.2314 | −0.936170 | ||||||||
\(423\) | −0.0503944 | −0.00245026 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 36.7726 | 1.78373 | ||||||||
\(426\) | −13.8103 | −0.669113 | ||||||||
\(427\) | 2.83172 | 0.137036 | ||||||||
\(428\) | 13.4762 | 0.651396 | ||||||||
\(429\) | 20.0671 | 0.968847 | ||||||||
\(430\) | −0.138744 | −0.00669085 | ||||||||
\(431\) | −20.9723 | −1.01020 | −0.505100 | − | 0.863061i | \(-0.668544\pi\) | ||||
−0.505100 | + | 0.863061i | \(0.668544\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 24.2854 | 1.16708 | 0.583540 | − | 0.812084i | \(-0.301667\pi\) | ||||
0.583540 | + | 0.812084i | \(0.301667\pi\) | |||||||
\(434\) | −1.92940 | −0.0926141 | ||||||||
\(435\) | 27.3745 | 1.31250 | ||||||||
\(436\) | −4.89315 | −0.234340 | ||||||||
\(437\) | 1.96030 | 0.0937739 | ||||||||
\(438\) | 16.3320 | 0.780373 | ||||||||
\(439\) | 10.4349 | 0.498033 | 0.249016 | − | 0.968499i | \(-0.419893\pi\) | ||||
0.249016 | + | 0.968499i | \(0.419893\pi\) | |||||||
\(440\) | 14.2832 | 0.680925 | ||||||||
\(441\) | −6.82775 | −0.325131 | ||||||||
\(442\) | 25.0272 | 1.19042 | ||||||||
\(443\) | −36.6413 | −1.74088 | −0.870440 | − | 0.492275i | \(-0.836165\pi\) | ||||
−0.870440 | + | 0.492275i | \(0.836165\pi\) | |||||||
\(444\) | 3.20548 | 0.152126 | ||||||||
\(445\) | −32.1527 | −1.52419 | ||||||||
\(446\) | 8.05779 | 0.381547 | ||||||||
\(447\) | −17.0799 | −0.807852 | ||||||||
\(448\) | 0.415035 | 0.0196086 | ||||||||
\(449\) | −23.7926 | −1.12284 | −0.561421 | − | 0.827530i | \(-0.689745\pi\) | ||||
−0.561421 | + | 0.827530i | \(0.689745\pi\) | |||||||
\(450\) | −7.21452 | −0.340096 | ||||||||
\(451\) | −0.603247 | −0.0284058 | ||||||||
\(452\) | 14.2894 | 0.672119 | ||||||||
\(453\) | 14.1138 | 0.663126 | ||||||||
\(454\) | −16.8358 | −0.790141 | ||||||||
\(455\) | −7.12229 | −0.333898 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −22.5476 | −1.05473 | −0.527367 | − | 0.849638i | \(-0.676821\pi\) | ||||
−0.527367 | + | 0.849638i | \(0.676821\pi\) | |||||||
\(458\) | −9.71143 | −0.453785 | ||||||||
\(459\) | 5.09702 | 0.237909 | ||||||||
\(460\) | 6.85111 | 0.319435 | ||||||||
\(461\) | 9.76411 | 0.454760 | 0.227380 | − | 0.973806i | \(-0.426984\pi\) | ||||
0.227380 | + | 0.973806i | \(0.426984\pi\) | |||||||
\(462\) | 1.69618 | 0.0789136 | ||||||||
\(463\) | −15.7547 | −0.732183 | −0.366091 | − | 0.930579i | \(-0.619304\pi\) | ||||
−0.366091 | + | 0.930579i | \(0.619304\pi\) | |||||||
\(464\) | 7.83262 | 0.363620 | ||||||||
\(465\) | 16.2471 | 0.753440 | ||||||||
\(466\) | −12.5612 | −0.581887 | ||||||||
\(467\) | 2.92445 | 0.135327 | 0.0676636 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676636 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(468\) | −4.91017 | −0.226973 | ||||||||
\(469\) | 0.916275 | 0.0423097 | ||||||||
\(470\) | 0.176125 | 0.00812403 | ||||||||
\(471\) | 9.41661 | 0.433894 | ||||||||
\(472\) | 11.4052 | 0.524968 | ||||||||
\(473\) | −0.162243 | −0.00745992 | ||||||||
\(474\) | −15.7254 | −0.722292 | ||||||||
\(475\) | 7.21452 | 0.331025 | ||||||||
\(476\) | 2.11544 | 0.0969612 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | −0.440965 | −0.0201693 | ||||||||
\(479\) | −8.66304 | −0.395825 | −0.197912 | − | 0.980220i | \(-0.563416\pi\) | ||||
−0.197912 | + | 0.980220i | \(0.563416\pi\) | |||||||
\(480\) | −3.49493 | −0.159521 | ||||||||
\(481\) | −15.7395 | −0.717658 | ||||||||
\(482\) | −5.43948 | −0.247762 | ||||||||
\(483\) | 0.813594 | 0.0370198 | ||||||||
\(484\) | 5.70226 | 0.259194 | ||||||||
\(485\) | −39.3364 | −1.78617 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −36.4364 | −1.65109 | −0.825544 | − | 0.564337i | \(-0.809132\pi\) | ||||
−0.825544 | + | 0.564337i | \(0.809132\pi\) | |||||||
\(488\) | −6.82283 | −0.308855 | ||||||||
\(489\) | −17.2516 | −0.780146 | ||||||||
\(490\) | 23.8625 | 1.07800 | ||||||||
\(491\) | 19.8059 | 0.893830 | 0.446915 | − | 0.894577i | \(-0.352523\pi\) | ||||
0.446915 | + | 0.894577i | \(0.352523\pi\) | |||||||
\(492\) | 0.147607 | 0.00665465 | ||||||||
\(493\) | 39.9230 | 1.79804 | ||||||||
\(494\) | 4.91017 | 0.220919 | ||||||||
\(495\) | −14.2832 | −0.641983 | ||||||||
\(496\) | 4.64876 | 0.208735 | ||||||||
\(497\) | 5.73178 | 0.257105 | ||||||||
\(498\) | −8.45796 | −0.379010 | ||||||||
\(499\) | 25.2560 | 1.13061 | 0.565306 | − | 0.824881i | \(-0.308758\pi\) | ||||
0.565306 | + | 0.824881i | \(0.308758\pi\) | |||||||
\(500\) | 7.73960 | 0.346125 | ||||||||
\(501\) | −3.67750 | −0.164299 | ||||||||
\(502\) | 3.56968 | 0.159322 | ||||||||
\(503\) | −9.35473 | −0.417107 | −0.208553 | − | 0.978011i | \(-0.566875\pi\) | ||||
−0.208553 | + | 0.978011i | \(0.566875\pi\) | |||||||
\(504\) | −0.415035 | −0.0184871 | ||||||||
\(505\) | −20.0194 | −0.890850 | ||||||||
\(506\) | 8.01144 | 0.356152 | ||||||||
\(507\) | 11.1098 | 0.493401 | ||||||||
\(508\) | 14.7621 | 0.654962 | ||||||||
\(509\) | −32.3109 | −1.43216 | −0.716078 | − | 0.698021i | \(-0.754064\pi\) | ||||
−0.716078 | + | 0.698021i | \(0.754064\pi\) | |||||||
\(510\) | −17.8137 | −0.788805 | ||||||||
\(511\) | −6.77835 | −0.299857 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 9.34972 | 0.412398 | ||||||||
\(515\) | 58.6620 | 2.58496 | ||||||||
\(516\) | 0.0396988 | 0.00174764 | ||||||||
\(517\) | 0.205954 | 0.00905783 | ||||||||
\(518\) | −1.33039 | −0.0584539 | ||||||||
\(519\) | 21.5612 | 0.946433 | ||||||||
\(520\) | 17.1607 | 0.752546 | ||||||||
\(521\) | 18.3558 | 0.804184 | 0.402092 | − | 0.915599i | \(-0.368283\pi\) | ||||
0.402092 | + | 0.915599i | \(0.368283\pi\) | |||||||
\(522\) | −7.83262 | −0.342825 | ||||||||
\(523\) | 2.38320 | 0.104210 | 0.0521050 | − | 0.998642i | \(-0.483407\pi\) | ||||
0.0521050 | + | 0.998642i | \(0.483407\pi\) | |||||||
\(524\) | 10.9973 | 0.480418 | ||||||||
\(525\) | 2.99428 | 0.130681 | ||||||||
\(526\) | −21.4780 | −0.936484 | ||||||||
\(527\) | 23.6948 | 1.03216 | ||||||||
\(528\) | −4.08684 | −0.177857 | ||||||||
\(529\) | −19.1572 | −0.832923 | ||||||||
\(530\) | −3.49493 | −0.151810 | ||||||||
\(531\) | −11.4052 | −0.494945 | ||||||||
\(532\) | 0.415035 | 0.0179941 | ||||||||
\(533\) | −0.724776 | −0.0313936 | ||||||||
\(534\) | 9.19983 | 0.398116 | ||||||||
\(535\) | 47.0983 | 2.03624 | ||||||||
\(536\) | −2.20770 | −0.0953583 | ||||||||
\(537\) | −15.5774 | −0.672212 | ||||||||
\(538\) | −4.13801 | −0.178402 | ||||||||
\(539\) | 27.9039 | 1.20191 | ||||||||
\(540\) | 3.49493 | 0.150398 | ||||||||
\(541\) | 14.3594 | 0.617357 | 0.308679 | − | 0.951166i | \(-0.400113\pi\) | ||||
0.308679 | + | 0.951166i | \(0.400113\pi\) | |||||||
\(542\) | 16.8861 | 0.725322 | ||||||||
\(543\) | −5.32170 | −0.228376 | ||||||||
\(544\) | −5.09702 | −0.218533 | ||||||||
\(545\) | −17.1012 | −0.732536 | ||||||||
\(546\) | 2.03789 | 0.0872138 | ||||||||
\(547\) | 5.70761 | 0.244040 | 0.122020 | − | 0.992528i | \(-0.461063\pi\) | ||||
0.122020 | + | 0.992528i | \(0.461063\pi\) | |||||||
\(548\) | −16.6482 | −0.711176 | ||||||||
\(549\) | 6.82283 | 0.291191 | ||||||||
\(550\) | 29.4846 | 1.25723 | ||||||||
\(551\) | 7.83262 | 0.333681 | ||||||||
\(552\) | −1.96030 | −0.0834360 | ||||||||
\(553\) | 6.52660 | 0.277539 | ||||||||
\(554\) | −3.23480 | −0.137434 | ||||||||
\(555\) | 11.2029 | 0.475538 | ||||||||
\(556\) | 4.76043 | 0.201887 | ||||||||
\(557\) | −5.10258 | −0.216203 | −0.108102 | − | 0.994140i | \(-0.534477\pi\) | ||||
−0.108102 | + | 0.994140i | \(0.534477\pi\) | |||||||
\(558\) | −4.64876 | −0.196798 | ||||||||
\(559\) | −0.194928 | −0.00824456 | ||||||||
\(560\) | 1.45052 | 0.0612956 | ||||||||
\(561\) | −20.8307 | −0.879473 | ||||||||
\(562\) | 30.2443 | 1.27578 | ||||||||
\(563\) | −13.6236 | −0.574168 | −0.287084 | − | 0.957905i | \(-0.592686\pi\) | ||||
−0.287084 | + | 0.957905i | \(0.592686\pi\) | |||||||
\(564\) | −0.0503944 | −0.00212199 | ||||||||
\(565\) | 49.9406 | 2.10102 | ||||||||
\(566\) | 16.9773 | 0.713610 | ||||||||
\(567\) | 0.415035 | 0.0174298 | ||||||||
\(568\) | −13.8103 | −0.579469 | ||||||||
\(569\) | −45.5719 | −1.91047 | −0.955236 | − | 0.295844i | \(-0.904399\pi\) | ||||
−0.955236 | + | 0.295844i | \(0.904399\pi\) | |||||||
\(570\) | −3.49493 | −0.146386 | ||||||||
\(571\) | −31.6212 | −1.32331 | −0.661653 | − | 0.749810i | \(-0.730145\pi\) | ||||
−0.661653 | + | 0.749810i | \(0.730145\pi\) | |||||||
\(572\) | 20.0671 | 0.839046 | ||||||||
\(573\) | −10.8987 | −0.455298 | ||||||||
\(574\) | −0.0612622 | −0.00255704 | ||||||||
\(575\) | 14.1426 | 0.589789 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.6238 | 0.608797 | 0.304399 | − | 0.952545i | \(-0.401545\pi\) | ||||
0.304399 | + | 0.952545i | \(0.401545\pi\) | |||||||
\(578\) | −8.97963 | −0.373504 | ||||||||
\(579\) | 9.27849 | 0.385601 | ||||||||
\(580\) | 27.3745 | 1.13666 | ||||||||
\(581\) | 3.51035 | 0.145634 | ||||||||
\(582\) | 11.2553 | 0.466546 | ||||||||
\(583\) | −4.08684 | −0.169260 | ||||||||
\(584\) | 16.3320 | 0.675822 | ||||||||
\(585\) | −17.1607 | −0.709507 | ||||||||
\(586\) | 9.13408 | 0.377325 | ||||||||
\(587\) | 40.3285 | 1.66453 | 0.832267 | − | 0.554375i | \(-0.187043\pi\) | ||||
0.832267 | + | 0.554375i | \(0.187043\pi\) | |||||||
\(588\) | −6.82775 | −0.281571 | ||||||||
\(589\) | 4.64876 | 0.191549 | ||||||||
\(590\) | 39.8604 | 1.64103 | ||||||||
\(591\) | 0.0491723 | 0.00202268 | ||||||||
\(592\) | 3.20548 | 0.131745 | ||||||||
\(593\) | −35.4019 | −1.45378 | −0.726890 | − | 0.686754i | \(-0.759035\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(594\) | 4.08684 | 0.167685 | ||||||||
\(595\) | 7.39332 | 0.303097 | ||||||||
\(596\) | −17.0799 | −0.699620 | ||||||||
\(597\) | 20.2449 | 0.828569 | ||||||||
\(598\) | 9.62541 | 0.393612 | ||||||||
\(599\) | −17.6271 | −0.720225 | −0.360112 | − | 0.932909i | \(-0.617262\pi\) | ||||
−0.360112 | + | 0.932909i | \(0.617262\pi\) | |||||||
\(600\) | −7.21452 | −0.294532 | ||||||||
\(601\) | 21.5204 | 0.877837 | 0.438919 | − | 0.898527i | \(-0.355362\pi\) | ||||
0.438919 | + | 0.898527i | \(0.355362\pi\) | |||||||
\(602\) | −0.0164764 | −0.000671528 0 | ||||||||
\(603\) | 2.20770 | 0.0899047 | ||||||||
\(604\) | 14.1138 | 0.574284 | ||||||||
\(605\) | 19.9290 | 0.810229 | ||||||||
\(606\) | 5.72812 | 0.232689 | ||||||||
\(607\) | −34.7096 | −1.40882 | −0.704410 | − | 0.709793i | \(-0.748788\pi\) | ||||
−0.704410 | + | 0.709793i | \(0.748788\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 3.25081 | 0.131730 | ||||||||
\(610\) | −23.8453 | −0.965468 | ||||||||
\(611\) | 0.247445 | 0.0100105 | ||||||||
\(612\) | 5.09702 | 0.206035 | ||||||||
\(613\) | −0.984912 | −0.0397802 | −0.0198901 | − | 0.999802i | \(-0.506332\pi\) | ||||
−0.0198901 | + | 0.999802i | \(0.506332\pi\) | |||||||
\(614\) | −23.8662 | −0.963162 | ||||||||
\(615\) | 0.515877 | 0.0208022 | ||||||||
\(616\) | 1.69618 | 0.0683412 | ||||||||
\(617\) | 15.1661 | 0.610566 | 0.305283 | − | 0.952262i | \(-0.401249\pi\) | ||||
0.305283 | + | 0.952262i | \(0.401249\pi\) | |||||||
\(618\) | −16.7849 | −0.675187 | ||||||||
\(619\) | −35.1489 | −1.41275 | −0.706377 | − | 0.707836i | \(-0.749671\pi\) | ||||
−0.706377 | + | 0.707836i | \(0.749671\pi\) | |||||||
\(620\) | 16.2471 | 0.652498 | ||||||||
\(621\) | 1.96030 | 0.0786642 | ||||||||
\(622\) | −6.45660 | −0.258886 | ||||||||
\(623\) | −3.81825 | −0.152975 | ||||||||
\(624\) | −4.91017 | −0.196564 | ||||||||
\(625\) | −9.02327 | −0.360931 | ||||||||
\(626\) | 10.2086 | 0.408016 | ||||||||
\(627\) | −4.08684 | −0.163213 | ||||||||
\(628\) | 9.41661 | 0.375764 | ||||||||
\(629\) | 16.3384 | 0.651456 | ||||||||
\(630\) | −1.45052 | −0.0577900 | ||||||||
\(631\) | 0.181817 | 0.00723803 | 0.00361902 | − | 0.999993i | \(-0.498848\pi\) | ||||
0.00361902 | + | 0.999993i | \(0.498848\pi\) | |||||||
\(632\) | −15.7254 | −0.625523 | ||||||||
\(633\) | 19.2314 | 0.764380 | ||||||||
\(634\) | 15.9024 | 0.631565 | ||||||||
\(635\) | 51.5925 | 2.04739 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | 33.5254 | 1.32832 | ||||||||
\(638\) | 32.0107 | 1.26731 | ||||||||
\(639\) | 13.8103 | 0.546329 | ||||||||
\(640\) | −3.49493 | −0.138149 | ||||||||
\(641\) | −9.50673 | −0.375493 | −0.187747 | − | 0.982217i | \(-0.560118\pi\) | ||||
−0.187747 | + | 0.982217i | \(0.560118\pi\) | |||||||
\(642\) | −13.4762 | −0.531862 | ||||||||
\(643\) | −10.1644 | −0.400846 | −0.200423 | − | 0.979709i | \(-0.564232\pi\) | ||||
−0.200423 | + | 0.979709i | \(0.564232\pi\) | |||||||
\(644\) | 0.813594 | 0.0320601 | ||||||||
\(645\) | 0.138744 | 0.00546305 | ||||||||
\(646\) | −5.09702 | −0.200540 | ||||||||
\(647\) | −40.2766 | −1.58343 | −0.791717 | − | 0.610887i | \(-0.790813\pi\) | ||||
−0.791717 | + | 0.610887i | \(0.790813\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 46.6113 | 1.82965 | ||||||||
\(650\) | 35.4245 | 1.38946 | ||||||||
\(651\) | 1.92940 | 0.0756191 | ||||||||
\(652\) | −17.2516 | −0.675627 | ||||||||
\(653\) | −46.0722 | −1.80294 | −0.901472 | − | 0.432837i | \(-0.857513\pi\) | ||||
−0.901472 | + | 0.432837i | \(0.857513\pi\) | |||||||
\(654\) | 4.89315 | 0.191337 | ||||||||
\(655\) | 38.4347 | 1.50177 | ||||||||
\(656\) | 0.147607 | 0.00576310 | ||||||||
\(657\) | −16.3320 | −0.637171 | ||||||||
\(658\) | 0.0209154 | 0.000815369 0 | ||||||||
\(659\) | −27.5267 | −1.07229 | −0.536143 | − | 0.844127i | \(-0.680119\pi\) | ||||
−0.536143 | + | 0.844127i | \(0.680119\pi\) | |||||||
\(660\) | −14.2832 | −0.555973 | ||||||||
\(661\) | −40.7418 | −1.58467 | −0.792336 | − | 0.610086i | \(-0.791135\pi\) | ||||
−0.792336 | + | 0.610086i | \(0.791135\pi\) | |||||||
\(662\) | −24.0475 | −0.934633 | ||||||||
\(663\) | −25.0272 | −0.971977 | ||||||||
\(664\) | −8.45796 | −0.328233 | ||||||||
\(665\) | 1.45052 | 0.0562487 | ||||||||
\(666\) | −3.20548 | −0.124210 | ||||||||
\(667\) | 15.3543 | 0.594521 | ||||||||
\(668\) | −3.67750 | −0.142287 | ||||||||
\(669\) | −8.05779 | −0.311532 | ||||||||
\(670\) | −7.71577 | −0.298086 | ||||||||
\(671\) | −27.8838 | −1.07644 | ||||||||
\(672\) | −0.415035 | −0.0160103 | ||||||||
\(673\) | 48.9819 | 1.88811 | 0.944056 | − | 0.329786i | \(-0.106977\pi\) | ||||
0.944056 | + | 0.329786i | \(0.106977\pi\) | |||||||
\(674\) | −3.33476 | −0.128450 | ||||||||
\(675\) | 7.21452 | 0.277687 | ||||||||
\(676\) | 11.1098 | 0.427298 | ||||||||
\(677\) | 39.5360 | 1.51949 | 0.759745 | − | 0.650221i | \(-0.225324\pi\) | ||||
0.759745 | + | 0.650221i | \(0.225324\pi\) | |||||||
\(678\) | −14.2894 | −0.548783 | ||||||||
\(679\) | −4.67134 | −0.179269 | ||||||||
\(680\) | −17.8137 | −0.683125 | ||||||||
\(681\) | 16.8358 | 0.645147 | ||||||||
\(682\) | 18.9987 | 0.727499 | ||||||||
\(683\) | 8.82629 | 0.337729 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −58.1843 | −2.22311 | ||||||||
\(686\) | 5.73900 | 0.219116 | ||||||||
\(687\) | 9.71143 | 0.370514 | ||||||||
\(688\) | 0.0396988 | 0.00151350 | ||||||||
\(689\) | −4.91017 | −0.187063 | ||||||||
\(690\) | −6.85111 | −0.260817 | ||||||||
\(691\) | 18.2774 | 0.695305 | 0.347652 | − | 0.937624i | \(-0.386979\pi\) | ||||
0.347652 | + | 0.937624i | \(0.386979\pi\) | |||||||
\(692\) | 21.5612 | 0.819635 | ||||||||
\(693\) | −1.69618 | −0.0644327 | ||||||||
\(694\) | 35.8949 | 1.36255 | ||||||||
\(695\) | 16.6374 | 0.631091 | ||||||||
\(696\) | −7.83262 | −0.296895 | ||||||||
\(697\) | 0.752357 | 0.0284976 | ||||||||
\(698\) | −17.3197 | −0.655559 | ||||||||
\(699\) | 12.5612 | 0.475109 | ||||||||
\(700\) | 2.99428 | 0.113173 | ||||||||
\(701\) | −3.92380 | −0.148200 | −0.0741000 | − | 0.997251i | \(-0.523608\pi\) | ||||
−0.0741000 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(702\) | 4.91017 | 0.185322 | ||||||||
\(703\) | 3.20548 | 0.120897 | ||||||||
\(704\) | −4.08684 | −0.154029 | ||||||||
\(705\) | −0.176125 | −0.00663324 | ||||||||
\(706\) | 15.9809 | 0.601447 | ||||||||
\(707\) | −2.37737 | −0.0894103 | ||||||||
\(708\) | −11.4052 | −0.428635 | ||||||||
\(709\) | 6.36341 | 0.238983 | 0.119491 | − | 0.992835i | \(-0.461874\pi\) | ||||
0.119491 | + | 0.992835i | \(0.461874\pi\) | |||||||
\(710\) | −48.2662 | −1.81140 | ||||||||
\(711\) | 15.7254 | 0.589749 | ||||||||
\(712\) | 9.19983 | 0.344778 | ||||||||
\(713\) | 9.11296 | 0.341283 | ||||||||
\(714\) | −2.11544 | −0.0791685 | ||||||||
\(715\) | 70.1330 | 2.62282 | ||||||||
\(716\) | −15.5774 | −0.582153 | ||||||||
\(717\) | 0.440965 | 0.0164681 | ||||||||
\(718\) | 19.6405 | 0.732978 | ||||||||
\(719\) | −47.5181 | −1.77212 | −0.886062 | − | 0.463566i | \(-0.846570\pi\) | ||||
−0.886062 | + | 0.463566i | \(0.846570\pi\) | |||||||
\(720\) | 3.49493 | 0.130248 | ||||||||
\(721\) | 6.96632 | 0.259439 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 5.43948 | 0.202297 | ||||||||
\(724\) | −5.32170 | −0.197779 | ||||||||
\(725\) | 56.5086 | 2.09868 | ||||||||
\(726\) | −5.70226 | −0.211631 | ||||||||
\(727\) | −43.0459 | −1.59649 | −0.798243 | − | 0.602336i | \(-0.794237\pi\) | ||||
−0.798243 | + | 0.602336i | \(0.794237\pi\) | |||||||
\(728\) | 2.03789 | 0.0755293 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 57.0791 | 2.11259 | ||||||||
\(731\) | 0.202346 | 0.00748402 | ||||||||
\(732\) | 6.82283 | 0.252179 | ||||||||
\(733\) | 51.3459 | 1.89650 | 0.948251 | − | 0.317521i | \(-0.102850\pi\) | ||||
0.948251 | + | 0.317521i | \(0.102850\pi\) | |||||||
\(734\) | 5.75736 | 0.212508 | ||||||||
\(735\) | −23.8625 | −0.880181 | ||||||||
\(736\) | −1.96030 | −0.0722577 | ||||||||
\(737\) | −9.02254 | −0.332349 | ||||||||
\(738\) | −0.147607 | −0.00543350 | ||||||||
\(739\) | 37.7221 | 1.38763 | 0.693815 | − | 0.720153i | \(-0.255928\pi\) | ||||
0.693815 | + | 0.720153i | \(0.255928\pi\) | |||||||
\(740\) | 11.2029 | 0.411828 | ||||||||
\(741\) | −4.91017 | −0.180380 | ||||||||
\(742\) | −0.415035 | −0.0152364 | ||||||||
\(743\) | −0.497714 | −0.0182594 | −0.00912969 | − | 0.999958i | \(-0.502906\pi\) | ||||
−0.00912969 | + | 0.999958i | \(0.502906\pi\) | |||||||
\(744\) | −4.64876 | −0.170432 | ||||||||
\(745\) | −59.6931 | −2.18698 | ||||||||
\(746\) | −27.0308 | −0.989668 | ||||||||
\(747\) | 8.45796 | 0.309461 | ||||||||
\(748\) | −20.8307 | −0.761646 | ||||||||
\(749\) | 5.59309 | 0.204367 | ||||||||
\(750\) | −7.73960 | −0.282610 | ||||||||
\(751\) | −19.6513 | −0.717087 | −0.358543 | − | 0.933513i | \(-0.616726\pi\) | ||||
−0.358543 | + | 0.933513i | \(0.616726\pi\) | |||||||
\(752\) | −0.0503944 | −0.00183769 | ||||||||
\(753\) | −3.56968 | −0.130086 | ||||||||
\(754\) | 38.4595 | 1.40061 | ||||||||
\(755\) | 49.3268 | 1.79519 | ||||||||
\(756\) | 0.415035 | 0.0150947 | ||||||||
\(757\) | −21.4267 | −0.778766 | −0.389383 | − | 0.921076i | \(-0.627312\pi\) | ||||
−0.389383 | + | 0.921076i | \(0.627312\pi\) | |||||||
\(758\) | −16.1485 | −0.586541 | ||||||||
\(759\) | −8.01144 | −0.290797 | ||||||||
\(760\) | −3.49493 | −0.126774 | ||||||||
\(761\) | −34.3057 | −1.24358 | −0.621790 | − | 0.783184i | \(-0.713594\pi\) | ||||
−0.621790 | + | 0.783184i | \(0.713594\pi\) | |||||||
\(762\) | −14.7621 | −0.534775 | ||||||||
\(763\) | −2.03083 | −0.0735210 | ||||||||
\(764\) | −10.8987 | −0.394300 | ||||||||
\(765\) | 17.8137 | 0.644057 | ||||||||
\(766\) | −28.1444 | −1.01690 | ||||||||
\(767\) | 56.0016 | 2.02210 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −19.5776 | −0.705987 | −0.352993 | − | 0.935626i | \(-0.614836\pi\) | ||||
−0.352993 | + | 0.935626i | \(0.614836\pi\) | |||||||
\(770\) | 5.92804 | 0.213632 | ||||||||
\(771\) | −9.34972 | −0.336722 | ||||||||
\(772\) | 9.27849 | 0.333940 | ||||||||
\(773\) | 7.30683 | 0.262808 | 0.131404 | − | 0.991329i | \(-0.458051\pi\) | ||||
0.131404 | + | 0.991329i | \(0.458051\pi\) | |||||||
\(774\) | −0.0396988 | −0.00142694 | ||||||||
\(775\) | 33.5386 | 1.20474 | ||||||||
\(776\) | 11.2553 | 0.404041 | ||||||||
\(777\) | 1.33039 | 0.0477274 | ||||||||
\(778\) | −26.2108 | −0.939701 | ||||||||
\(779\) | 0.147607 | 0.00528858 | ||||||||
\(780\) | −17.1607 | −0.614451 | ||||||||
\(781\) | −56.4407 | −2.01961 | ||||||||
\(782\) | −9.99170 | −0.357302 | ||||||||
\(783\) | 7.83262 | 0.279915 | ||||||||
\(784\) | −6.82775 | −0.243848 | ||||||||
\(785\) | 32.9104 | 1.17462 | ||||||||
\(786\) | −10.9973 | −0.392260 | ||||||||
\(787\) | 18.3602 | 0.654472 | 0.327236 | − | 0.944943i | \(-0.393883\pi\) | ||||
0.327236 | + | 0.944943i | \(0.393883\pi\) | |||||||
\(788\) | 0.0491723 | 0.00175169 | ||||||||
\(789\) | 21.4780 | 0.764636 | ||||||||
\(790\) | −54.9592 | −1.95536 | ||||||||
\(791\) | 5.93062 | 0.210869 | ||||||||
\(792\) | 4.08684 | 0.145220 | ||||||||
\(793\) | −33.5012 | −1.18966 | ||||||||
\(794\) | −10.5870 | −0.375720 | ||||||||
\(795\) | 3.49493 | 0.123952 | ||||||||
\(796\) | 20.2449 | 0.717562 | ||||||||
\(797\) | −49.4087 | −1.75015 | −0.875074 | − | 0.483990i | \(-0.839187\pi\) | ||||
−0.875074 | + | 0.483990i | \(0.839187\pi\) | |||||||
\(798\) | −0.415035 | −0.0146921 | ||||||||
\(799\) | −0.256861 | −0.00908710 | ||||||||
\(800\) | −7.21452 | −0.255072 | ||||||||
\(801\) | −9.19983 | −0.325060 | ||||||||
\(802\) | 3.50880 | 0.123900 | ||||||||
\(803\) | 66.7462 | 2.35542 | ||||||||
\(804\) | 2.20770 | 0.0778597 | ||||||||
\(805\) | 2.84345 | 0.100219 | ||||||||
\(806\) | 22.8262 | 0.804018 | ||||||||
\(807\) | 4.13801 | 0.145665 | ||||||||
\(808\) | 5.72812 | 0.201515 | ||||||||
\(809\) | 31.0964 | 1.09329 | 0.546645 | − | 0.837364i | \(-0.315905\pi\) | ||||
0.546645 | + | 0.837364i | \(0.315905\pi\) | |||||||
\(810\) | −3.49493 | −0.122799 | ||||||||
\(811\) | −35.9571 | −1.26262 | −0.631312 | − | 0.775529i | \(-0.717483\pi\) | ||||
−0.631312 | + | 0.775529i | \(0.717483\pi\) | |||||||
\(812\) | 3.25081 | 0.114081 | ||||||||
\(813\) | −16.8861 | −0.592223 | ||||||||
\(814\) | 13.1003 | 0.459165 | ||||||||
\(815\) | −60.2933 | −2.11198 | ||||||||
\(816\) | 5.09702 | 0.178431 | ||||||||
\(817\) | 0.0396988 | 0.00138888 | ||||||||
\(818\) | 15.8684 | 0.554827 | ||||||||
\(819\) | −2.03789 | −0.0712097 | ||||||||
\(820\) | 0.515877 | 0.0180152 | ||||||||
\(821\) | 1.89421 | 0.0661083 | 0.0330542 | − | 0.999454i | \(-0.489477\pi\) | ||||
0.0330542 | + | 0.999454i | \(0.489477\pi\) | |||||||
\(822\) | 16.6482 | 0.580673 | ||||||||
\(823\) | 40.1468 | 1.39943 | 0.699715 | − | 0.714422i | \(-0.253310\pi\) | ||||
0.699715 | + | 0.714422i | \(0.253310\pi\) | |||||||
\(824\) | −16.7849 | −0.584729 | ||||||||
\(825\) | −29.4846 | −1.02652 | ||||||||
\(826\) | 4.73357 | 0.164702 | ||||||||
\(827\) | −30.1148 | −1.04719 | −0.523597 | − | 0.851966i | \(-0.675410\pi\) | ||||
−0.523597 | + | 0.851966i | \(0.675410\pi\) | |||||||
\(828\) | 1.96030 | 0.0681252 | ||||||||
\(829\) | −37.0113 | −1.28546 | −0.642728 | − | 0.766094i | \(-0.722197\pi\) | ||||
−0.642728 | + | 0.766094i | \(0.722197\pi\) | |||||||
\(830\) | −29.5600 | −1.02604 | ||||||||
\(831\) | 3.23480 | 0.112214 | ||||||||
\(832\) | −4.91017 | −0.170229 | ||||||||
\(833\) | −34.8012 | −1.20579 | ||||||||
\(834\) | −4.76043 | −0.164840 | ||||||||
\(835\) | −12.8526 | −0.444782 | ||||||||
\(836\) | −4.08684 | −0.141346 | ||||||||
\(837\) | 4.64876 | 0.160685 | ||||||||
\(838\) | −37.5886 | −1.29848 | ||||||||
\(839\) | 12.9499 | 0.447078 | 0.223539 | − | 0.974695i | \(-0.428239\pi\) | ||||
0.223539 | + | 0.974695i | \(0.428239\pi\) | |||||||
\(840\) | −1.45052 | −0.0500476 | ||||||||
\(841\) | 32.3500 | 1.11552 | ||||||||
\(842\) | −8.13549 | −0.280368 | ||||||||
\(843\) | −30.2443 | −1.04167 | ||||||||
\(844\) | 19.2314 | 0.661972 | ||||||||
\(845\) | 38.8278 | 1.33572 | ||||||||
\(846\) | 0.0503944 | 0.00173259 | ||||||||
\(847\) | 2.36664 | 0.0813187 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −16.9773 | −0.582660 | ||||||||
\(850\) | −36.7726 | −1.26129 | ||||||||
\(851\) | 6.28372 | 0.215403 | ||||||||
\(852\) | 13.8103 | 0.473135 | ||||||||
\(853\) | 35.2445 | 1.20675 | 0.603375 | − | 0.797458i | \(-0.293822\pi\) | ||||
0.603375 | + | 0.797458i | \(0.293822\pi\) | |||||||
\(854\) | −2.83172 | −0.0968993 | ||||||||
\(855\) | 3.49493 | 0.119524 | ||||||||
\(856\) | −13.4762 | −0.460606 | ||||||||
\(857\) | −15.4683 | −0.528385 | −0.264193 | − | 0.964470i | \(-0.585105\pi\) | ||||
−0.264193 | + | 0.964470i | \(0.585105\pi\) | |||||||
\(858\) | −20.0671 | −0.685079 | ||||||||
\(859\) | 6.42187 | 0.219111 | 0.109556 | − | 0.993981i | \(-0.465057\pi\) | ||||
0.109556 | + | 0.993981i | \(0.465057\pi\) | |||||||
\(860\) | 0.138744 | 0.00473114 | ||||||||
\(861\) | 0.0612622 | 0.00208781 | ||||||||
\(862\) | 20.9723 | 0.714320 | ||||||||
\(863\) | −11.5249 | −0.392311 | −0.196155 | − | 0.980573i | \(-0.562846\pi\) | ||||
−0.196155 | + | 0.980573i | \(0.562846\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 75.3550 | 2.56215 | ||||||||
\(866\) | −24.2854 | −0.825251 | ||||||||
\(867\) | 8.97963 | 0.304964 | ||||||||
\(868\) | 1.92940 | 0.0654880 | ||||||||
\(869\) | −64.2673 | −2.18012 | ||||||||
\(870\) | −27.3745 | −0.928081 | ||||||||
\(871\) | −10.8402 | −0.367306 | ||||||||
\(872\) | 4.89315 | 0.165703 | ||||||||
\(873\) | −11.2553 | −0.380933 | ||||||||
\(874\) | −1.96030 | −0.0663082 | ||||||||
\(875\) | 3.21221 | 0.108592 | ||||||||
\(876\) | −16.3320 | −0.551807 | ||||||||
\(877\) | 0.664469 | 0.0224375 | 0.0112188 | − | 0.999937i | \(-0.496429\pi\) | ||||
0.0112188 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(878\) | −10.4349 | −0.352162 | ||||||||
\(879\) | −9.13408 | −0.308085 | ||||||||
\(880\) | −14.2832 | −0.481487 | ||||||||
\(881\) | 4.43302 | 0.149352 | 0.0746761 | − | 0.997208i | \(-0.476208\pi\) | ||||
0.0746761 | + | 0.997208i | \(0.476208\pi\) | |||||||
\(882\) | 6.82775 | 0.229902 | ||||||||
\(883\) | −5.55256 | −0.186858 | −0.0934292 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934292 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(884\) | −25.0272 | −0.841757 | ||||||||
\(885\) | −39.8604 | −1.33989 | ||||||||
\(886\) | 36.6413 | 1.23099 | ||||||||
\(887\) | −20.7613 | −0.697097 | −0.348549 | − | 0.937291i | \(-0.613325\pi\) | ||||
−0.348549 | + | 0.937291i | \(0.613325\pi\) | |||||||
\(888\) | −3.20548 | −0.107569 | ||||||||
\(889\) | 6.12679 | 0.205486 | ||||||||
\(890\) | 32.1527 | 1.07776 | ||||||||
\(891\) | −4.08684 | −0.136914 | ||||||||
\(892\) | −8.05779 | −0.269795 | ||||||||
\(893\) | −0.0503944 | −0.00168638 | ||||||||
\(894\) | 17.0799 | 0.571238 | ||||||||
\(895\) | −54.4417 | −1.81979 | ||||||||
\(896\) | −0.415035 | −0.0138654 | ||||||||
\(897\) | −9.62541 | −0.321383 | ||||||||
\(898\) | 23.7926 | 0.793969 | ||||||||
\(899\) | 36.4120 | 1.21441 | ||||||||
\(900\) | 7.21452 | 0.240484 | ||||||||
\(901\) | 5.09702 | 0.169806 | ||||||||
\(902\) | 0.603247 | 0.0200859 | ||||||||
\(903\) | 0.0164764 | 0.000548300 0 | ||||||||
\(904\) | −14.2894 | −0.475260 | ||||||||
\(905\) | −18.5990 | −0.618250 | ||||||||
\(906\) | −14.1138 | −0.468901 | ||||||||
\(907\) | −38.1089 | −1.26538 | −0.632692 | − | 0.774404i | \(-0.718050\pi\) | ||||
−0.632692 | + | 0.774404i | \(0.718050\pi\) | |||||||
\(908\) | 16.8358 | 0.558714 | ||||||||
\(909\) | −5.72812 | −0.189990 | ||||||||
\(910\) | 7.12229 | 0.236102 | ||||||||
\(911\) | 32.5119 | 1.07717 | 0.538583 | − | 0.842573i | \(-0.318960\pi\) | ||||
0.538583 | + | 0.842573i | \(0.318960\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −34.5663 | −1.14398 | ||||||||
\(914\) | 22.5476 | 0.745809 | ||||||||
\(915\) | 23.8453 | 0.788301 | ||||||||
\(916\) | 9.71143 | 0.320875 | ||||||||
\(917\) | 4.56425 | 0.150725 | ||||||||
\(918\) | −5.09702 | −0.168227 | ||||||||
\(919\) | 46.8658 | 1.54596 | 0.772979 | − | 0.634431i | \(-0.218766\pi\) | ||||
0.772979 | + | 0.634431i | \(0.218766\pi\) | |||||||
\(920\) | −6.85111 | −0.225874 | ||||||||
\(921\) | 23.8662 | 0.786419 | ||||||||
\(922\) | −9.76411 | −0.321564 | ||||||||
\(923\) | −67.8111 | −2.23203 | ||||||||
\(924\) | −1.69618 | −0.0558003 | ||||||||
\(925\) | 23.1260 | 0.760380 | ||||||||
\(926\) | 15.7547 | 0.517731 | ||||||||
\(927\) | 16.7849 | 0.551288 | ||||||||
\(928\) | −7.83262 | −0.257118 | ||||||||
\(929\) | −29.7878 | −0.977306 | −0.488653 | − | 0.872478i | \(-0.662512\pi\) | ||||
−0.488653 | + | 0.872478i | \(0.662512\pi\) | |||||||
\(930\) | −16.2471 | −0.532762 | ||||||||
\(931\) | −6.82775 | −0.223770 | ||||||||
\(932\) | 12.5612 | 0.411457 | ||||||||
\(933\) | 6.45660 | 0.211380 | ||||||||
\(934\) | −2.92445 | −0.0956908 | ||||||||
\(935\) | −72.8019 | −2.38088 | ||||||||
\(936\) | 4.91017 | 0.160494 | ||||||||
\(937\) | 22.5070 | 0.735273 | 0.367636 | − | 0.929970i | \(-0.380167\pi\) | ||||
0.367636 | + | 0.929970i | \(0.380167\pi\) | |||||||
\(938\) | −0.916275 | −0.0299174 | ||||||||
\(939\) | −10.2086 | −0.333143 | ||||||||
\(940\) | −0.176125 | −0.00574455 | ||||||||
\(941\) | 6.56150 | 0.213899 | 0.106949 | − | 0.994264i | \(-0.465892\pi\) | ||||
0.106949 | + | 0.994264i | \(0.465892\pi\) | |||||||
\(942\) | −9.41661 | −0.306810 | ||||||||
\(943\) | 0.289355 | 0.00942269 | ||||||||
\(944\) | −11.4052 | −0.371208 | ||||||||
\(945\) | 1.45052 | 0.0471854 | ||||||||
\(946\) | 0.162243 | 0.00527496 | ||||||||
\(947\) | 2.22644 | 0.0723495 | 0.0361748 | − | 0.999345i | \(-0.488483\pi\) | ||||
0.0361748 | + | 0.999345i | \(0.488483\pi\) | |||||||
\(948\) | 15.7254 | 0.510738 | ||||||||
\(949\) | 80.1928 | 2.60317 | ||||||||
\(950\) | −7.21452 | −0.234070 | ||||||||
\(951\) | −15.9024 | −0.515671 | ||||||||
\(952\) | −2.11544 | −0.0685619 | ||||||||
\(953\) | 2.24347 | 0.0726733 | 0.0363366 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363366 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −38.0900 | −1.23256 | ||||||||
\(956\) | 0.440965 | 0.0142618 | ||||||||
\(957\) | −32.0107 | −1.03476 | ||||||||
\(958\) | 8.66304 | 0.279890 | ||||||||
\(959\) | −6.90959 | −0.223122 | ||||||||
\(960\) | 3.49493 | 0.112798 | ||||||||
\(961\) | −9.38906 | −0.302873 | ||||||||
\(962\) | 15.7395 | 0.507461 | ||||||||
\(963\) | 13.4762 | 0.434264 | ||||||||
\(964\) | 5.43948 | 0.175194 | ||||||||
\(965\) | 32.4277 | 1.04388 | ||||||||
\(966\) | −0.813594 | −0.0261770 | ||||||||
\(967\) | 25.0956 | 0.807020 | 0.403510 | − | 0.914975i | \(-0.367790\pi\) | ||||
0.403510 | + | 0.914975i | \(0.367790\pi\) | |||||||
\(968\) | −5.70226 | −0.183278 | ||||||||
\(969\) | 5.09702 | 0.163740 | ||||||||
\(970\) | 39.3364 | 1.26302 | ||||||||
\(971\) | −23.8720 | −0.766090 | −0.383045 | − | 0.923730i | \(-0.625125\pi\) | ||||
−0.383045 | + | 0.923730i | \(0.625125\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.97575 | 0.0633396 | ||||||||
\(974\) | 36.4364 | 1.16750 | ||||||||
\(975\) | −35.4245 | −1.13449 | ||||||||
\(976\) | 6.82283 | 0.218393 | ||||||||
\(977\) | 3.52776 | 0.112863 | 0.0564315 | − | 0.998406i | \(-0.482028\pi\) | ||||
0.0564315 | + | 0.998406i | \(0.482028\pi\) | |||||||
\(978\) | 17.2516 | 0.551647 | ||||||||
\(979\) | 37.5982 | 1.20164 | ||||||||
\(980\) | −23.8625 | −0.762259 | ||||||||
\(981\) | −4.89315 | −0.156226 | ||||||||
\(982\) | −19.8059 | −0.632033 | ||||||||
\(983\) | −21.2352 | −0.677299 | −0.338649 | − | 0.940913i | \(-0.609970\pi\) | ||||
−0.338649 | + | 0.940913i | \(0.609970\pi\) | |||||||
\(984\) | −0.147607 | −0.00470555 | ||||||||
\(985\) | 0.171854 | 0.00547571 | ||||||||
\(986\) | −39.9230 | −1.27141 | ||||||||
\(987\) | −0.0209154 | −0.000665746 0 | ||||||||
\(988\) | −4.91017 | −0.156213 | ||||||||
\(989\) | 0.0778216 | 0.00247458 | ||||||||
\(990\) | 14.2832 | 0.453950 | ||||||||
\(991\) | −22.1328 | −0.703073 | −0.351537 | − | 0.936174i | \(-0.614341\pi\) | ||||
−0.351537 | + | 0.936174i | \(0.614341\pi\) | |||||||
\(992\) | −4.64876 | −0.147598 | ||||||||
\(993\) | 24.0475 | 0.763125 | ||||||||
\(994\) | −5.73178 | −0.181801 | ||||||||
\(995\) | 70.7545 | 2.24307 | ||||||||
\(996\) | 8.45796 | 0.268001 | ||||||||
\(997\) | 46.0248 | 1.45762 | 0.728810 | − | 0.684716i | \(-0.240074\pi\) | ||||
0.728810 | + | 0.684716i | \(0.240074\pi\) | |||||||
\(998\) | −25.2560 | −0.799464 | ||||||||
\(999\) | 3.20548 | 0.101417 |
(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 | 6042.2.a.bf.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bf.1.12 | ✓ | 12 | 1.1 | even | 1 | trivial |