Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.15742 | −1.24559 | −0.622794 | − | 0.782386i | \(-0.714002\pi\) | ||||
−0.622794 | + | 0.782386i | \(0.714002\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.78011 | −1.24330 | −0.621652 | − | 0.783294i | \(-0.713538\pi\) | ||||
−0.621652 | + | 0.783294i | \(0.713538\pi\) | |||||||
\(6\) | 2.15742 | 0.880763 | ||||||||
\(7\) | −1.33229 | −0.503560 | −0.251780 | − | 0.967784i | \(-0.581016\pi\) | ||||
−0.251780 | + | 0.967784i | \(0.581016\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.65446 | 0.551488 | ||||||||
\(10\) | 2.78011 | 0.879148 | ||||||||
\(11\) | −5.50011 | −1.65835 | −0.829173 | − | 0.558992i | \(-0.811188\pi\) | ||||
−0.829173 | + | 0.558992i | \(0.811188\pi\) | |||||||
\(12\) | −2.15742 | −0.622794 | ||||||||
\(13\) | −5.88689 | −1.63273 | −0.816365 | − | 0.577536i | \(-0.804014\pi\) | ||||
−0.816365 | + | 0.577536i | \(0.804014\pi\) | |||||||
\(14\) | 1.33229 | 0.356071 | ||||||||
\(15\) | 5.99787 | 1.54864 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.24200 | −0.543764 | −0.271882 | − | 0.962331i | \(-0.587646\pi\) | ||||
−0.271882 | + | 0.962331i | \(0.587646\pi\) | |||||||
\(18\) | −1.65446 | −0.389961 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.78011 | −0.621652 | ||||||||
\(21\) | 2.87432 | 0.627228 | ||||||||
\(22\) | 5.50011 | 1.17263 | ||||||||
\(23\) | −6.52318 | −1.36018 | −0.680089 | − | 0.733130i | \(-0.738059\pi\) | ||||
−0.680089 | + | 0.733130i | \(0.738059\pi\) | |||||||
\(24\) | 2.15742 | 0.440382 | ||||||||
\(25\) | 2.72902 | 0.545804 | ||||||||
\(26\) | 5.88689 | 1.15451 | ||||||||
\(27\) | 2.90289 | 0.558661 | ||||||||
\(28\) | −1.33229 | −0.251780 | ||||||||
\(29\) | 7.17506 | 1.33238 | 0.666188 | − | 0.745784i | \(-0.267925\pi\) | ||||
0.666188 | + | 0.745784i | \(0.267925\pi\) | |||||||
\(30\) | −5.99787 | −1.09506 | ||||||||
\(31\) | 3.81787 | 0.685710 | 0.342855 | − | 0.939388i | \(-0.388606\pi\) | ||||
0.342855 | + | 0.939388i | \(0.388606\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 11.8661 | 2.06562 | ||||||||
\(34\) | 2.24200 | 0.384499 | ||||||||
\(35\) | 3.70393 | 0.626078 | ||||||||
\(36\) | 1.65446 | 0.275744 | ||||||||
\(37\) | 0.00121348 | 0.000199495 0 | 9.97474e−5 | − | 1.00000i | \(-0.499968\pi\) | ||||
9.97474e−5 | 1.00000i | \(0.499968\pi\) | ||||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 12.7005 | 2.03371 | ||||||||
\(40\) | 2.78011 | 0.439574 | ||||||||
\(41\) | −0.0230918 | −0.00360634 | −0.00180317 | − | 0.999998i | \(-0.500574\pi\) | ||||
−0.00180317 | + | 0.999998i | \(0.500574\pi\) | |||||||
\(42\) | −2.87432 | −0.443517 | ||||||||
\(43\) | −10.2247 | −1.55926 | −0.779628 | − | 0.626243i | \(-0.784592\pi\) | ||||
−0.779628 | + | 0.626243i | \(0.784592\pi\) | |||||||
\(44\) | −5.50011 | −0.829173 | ||||||||
\(45\) | −4.59959 | −0.685667 | ||||||||
\(46\) | 6.52318 | 0.961791 | ||||||||
\(47\) | −1.06053 | −0.154695 | −0.0773474 | − | 0.997004i | \(-0.524645\pi\) | ||||
−0.0773474 | + | 0.997004i | \(0.524645\pi\) | |||||||
\(48\) | −2.15742 | −0.311397 | ||||||||
\(49\) | −5.22499 | −0.746427 | ||||||||
\(50\) | −2.72902 | −0.385941 | ||||||||
\(51\) | 4.83693 | 0.677306 | ||||||||
\(52\) | −5.88689 | −0.816365 | ||||||||
\(53\) | 10.3892 | 1.42707 | 0.713534 | − | 0.700621i | \(-0.247094\pi\) | ||||
0.713534 | + | 0.700621i | \(0.247094\pi\) | |||||||
\(54\) | −2.90289 | −0.395033 | ||||||||
\(55\) | 15.2909 | 2.06183 | ||||||||
\(56\) | 1.33229 | 0.178035 | ||||||||
\(57\) | 2.15742 | 0.285757 | ||||||||
\(58\) | −7.17506 | −0.942132 | ||||||||
\(59\) | 13.1194 | 1.70800 | 0.853998 | − | 0.520276i | \(-0.174171\pi\) | ||||
0.853998 | + | 0.520276i | \(0.174171\pi\) | |||||||
\(60\) | 5.99787 | 0.774322 | ||||||||
\(61\) | 2.45924 | 0.314874 | 0.157437 | − | 0.987529i | \(-0.449677\pi\) | ||||
0.157437 | + | 0.987529i | \(0.449677\pi\) | |||||||
\(62\) | −3.81787 | −0.484870 | ||||||||
\(63\) | −2.20423 | −0.277707 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.3662 | 2.02998 | ||||||||
\(66\) | −11.8661 | −1.46061 | ||||||||
\(67\) | 6.44973 | 0.787960 | 0.393980 | − | 0.919119i | \(-0.371098\pi\) | ||||
0.393980 | + | 0.919119i | \(0.371098\pi\) | |||||||
\(68\) | −2.24200 | −0.271882 | ||||||||
\(69\) | 14.0732 | 1.69422 | ||||||||
\(70\) | −3.70393 | −0.442704 | ||||||||
\(71\) | 2.95646 | 0.350868 | 0.175434 | − | 0.984491i | \(-0.443867\pi\) | ||||
0.175434 | + | 0.984491i | \(0.443867\pi\) | |||||||
\(72\) | −1.65446 | −0.194980 | ||||||||
\(73\) | −7.06136 | −0.826470 | −0.413235 | − | 0.910624i | \(-0.635601\pi\) | ||||
−0.413235 | + | 0.910624i | \(0.635601\pi\) | |||||||
\(74\) | −0.00121348 | −0.000141064 0 | ||||||||
\(75\) | −5.88764 | −0.679846 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 7.32777 | 0.835077 | ||||||||
\(78\) | −12.7005 | −1.43805 | ||||||||
\(79\) | 4.54943 | 0.511850 | 0.255925 | − | 0.966697i | \(-0.417620\pi\) | ||||
0.255925 | + | 0.966697i | \(0.417620\pi\) | |||||||
\(80\) | −2.78011 | −0.310826 | ||||||||
\(81\) | −11.2261 | −1.24735 | ||||||||
\(82\) | 0.0230918 | 0.00255006 | ||||||||
\(83\) | −2.00252 | −0.219806 | −0.109903 | − | 0.993942i | \(-0.535054\pi\) | ||||
−0.109903 | + | 0.993942i | \(0.535054\pi\) | |||||||
\(84\) | 2.87432 | 0.313614 | ||||||||
\(85\) | 6.23300 | 0.676064 | ||||||||
\(86\) | 10.2247 | 1.10256 | ||||||||
\(87\) | −15.4796 | −1.65959 | ||||||||
\(88\) | 5.50011 | 0.586314 | ||||||||
\(89\) | 10.2497 | 1.08647 | 0.543235 | − | 0.839581i | \(-0.317199\pi\) | ||||
0.543235 | + | 0.839581i | \(0.317199\pi\) | |||||||
\(90\) | 4.59959 | 0.484840 | ||||||||
\(91\) | 7.84307 | 0.822178 | ||||||||
\(92\) | −6.52318 | −0.680089 | ||||||||
\(93\) | −8.23675 | −0.854112 | ||||||||
\(94\) | 1.06053 | 0.109386 | ||||||||
\(95\) | 2.78011 | 0.285233 | ||||||||
\(96\) | 2.15742 | 0.220191 | ||||||||
\(97\) | 3.39933 | 0.345150 | 0.172575 | − | 0.984996i | \(-0.444791\pi\) | ||||
0.172575 | + | 0.984996i | \(0.444791\pi\) | |||||||
\(98\) | 5.22499 | 0.527804 | ||||||||
\(99\) | −9.09974 | −0.914558 | ||||||||
\(100\) | 2.72902 | 0.272902 | ||||||||
\(101\) | −4.60039 | −0.457756 | −0.228878 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228878 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(102\) | −4.83693 | −0.478927 | ||||||||
\(103\) | −11.1268 | −1.09636 | −0.548180 | − | 0.836360i | \(-0.684679\pi\) | ||||
−0.548180 | + | 0.836360i | \(0.684679\pi\) | |||||||
\(104\) | 5.88689 | 0.577257 | ||||||||
\(105\) | −7.99093 | −0.779835 | ||||||||
\(106\) | −10.3892 | −1.00909 | ||||||||
\(107\) | 0.319302 | 0.0308681 | 0.0154340 | − | 0.999881i | \(-0.495087\pi\) | ||||
0.0154340 | + | 0.999881i | \(0.495087\pi\) | |||||||
\(108\) | 2.90289 | 0.279331 | ||||||||
\(109\) | −8.01354 | −0.767558 | −0.383779 | − | 0.923425i | \(-0.625378\pi\) | ||||
−0.383779 | + | 0.923425i | \(0.625378\pi\) | |||||||
\(110\) | −15.2909 | −1.45793 | ||||||||
\(111\) | −0.00261799 | −0.000248488 0 | ||||||||
\(112\) | −1.33229 | −0.125890 | ||||||||
\(113\) | 7.93918 | 0.746855 | 0.373428 | − | 0.927659i | \(-0.378182\pi\) | ||||
0.373428 | + | 0.927659i | \(0.378182\pi\) | |||||||
\(114\) | −2.15742 | −0.202061 | ||||||||
\(115\) | 18.1352 | 1.69111 | ||||||||
\(116\) | 7.17506 | 0.666188 | ||||||||
\(117\) | −9.73965 | −0.900431 | ||||||||
\(118\) | −13.1194 | −1.20774 | ||||||||
\(119\) | 2.98700 | 0.273818 | ||||||||
\(120\) | −5.99787 | −0.547528 | ||||||||
\(121\) | 19.2512 | 1.75011 | ||||||||
\(122\) | −2.45924 | −0.222649 | ||||||||
\(123\) | 0.0498188 | 0.00449201 | ||||||||
\(124\) | 3.81787 | 0.342855 | ||||||||
\(125\) | 6.31358 | 0.564704 | ||||||||
\(126\) | 2.20423 | 0.196369 | ||||||||
\(127\) | −15.8788 | −1.40902 | −0.704509 | − | 0.709695i | \(-0.748833\pi\) | ||||
−0.704509 | + | 0.709695i | \(0.748833\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.0590 | 1.94219 | ||||||||
\(130\) | −16.3662 | −1.43541 | ||||||||
\(131\) | 11.8312 | 1.03369 | 0.516847 | − | 0.856078i | \(-0.327106\pi\) | ||||
0.516847 | + | 0.856078i | \(0.327106\pi\) | |||||||
\(132\) | 11.8661 | 1.03281 | ||||||||
\(133\) | 1.33229 | 0.115525 | ||||||||
\(134\) | −6.44973 | −0.557172 | ||||||||
\(135\) | −8.07035 | −0.694585 | ||||||||
\(136\) | 2.24200 | 0.192250 | ||||||||
\(137\) | −13.9862 | −1.19492 | −0.597459 | − | 0.801899i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801899i | \(0.703823\pi\) | |||||||
\(138\) | −14.0732 | −1.19799 | ||||||||
\(139\) | 5.22721 | 0.443366 | 0.221683 | − | 0.975119i | \(-0.428845\pi\) | ||||
0.221683 | + | 0.975119i | \(0.428845\pi\) | |||||||
\(140\) | 3.70393 | 0.313039 | ||||||||
\(141\) | 2.28802 | 0.192686 | ||||||||
\(142\) | −2.95646 | −0.248101 | ||||||||
\(143\) | 32.3786 | 2.70763 | ||||||||
\(144\) | 1.65446 | 0.137872 | ||||||||
\(145\) | −19.9475 | −1.65655 | ||||||||
\(146\) | 7.06136 | 0.584403 | ||||||||
\(147\) | 11.2725 | 0.929740 | ||||||||
\(148\) | 0.00121348 | 9.97474e−5 0 | ||||||||
\(149\) | −12.7346 | −1.04326 | −0.521630 | − | 0.853172i | \(-0.674676\pi\) | ||||
−0.521630 | + | 0.853172i | \(0.674676\pi\) | |||||||
\(150\) | 5.88764 | 0.480724 | ||||||||
\(151\) | −15.3227 | −1.24694 | −0.623471 | − | 0.781846i | \(-0.714278\pi\) | ||||
−0.623471 | + | 0.781846i | \(0.714278\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −3.70930 | −0.299879 | ||||||||
\(154\) | −7.32777 | −0.590489 | ||||||||
\(155\) | −10.6141 | −0.852546 | ||||||||
\(156\) | 12.7005 | 1.01685 | ||||||||
\(157\) | 9.36503 | 0.747411 | 0.373705 | − | 0.927547i | \(-0.378087\pi\) | ||||
0.373705 | + | 0.927547i | \(0.378087\pi\) | |||||||
\(158\) | −4.54943 | −0.361933 | ||||||||
\(159\) | −22.4139 | −1.77754 | ||||||||
\(160\) | 2.78011 | 0.219787 | ||||||||
\(161\) | 8.69080 | 0.684931 | ||||||||
\(162\) | 11.2261 | 0.882009 | ||||||||
\(163\) | −10.5985 | −0.830135 | −0.415068 | − | 0.909791i | \(-0.636242\pi\) | ||||
−0.415068 | + | 0.909791i | \(0.636242\pi\) | |||||||
\(164\) | −0.0230918 | −0.00180317 | ||||||||
\(165\) | −32.9890 | −2.56819 | ||||||||
\(166\) | 2.00252 | 0.155426 | ||||||||
\(167\) | −24.5651 | −1.90091 | −0.950453 | − | 0.310869i | \(-0.899380\pi\) | ||||
−0.950453 | + | 0.310869i | \(0.899380\pi\) | |||||||
\(168\) | −2.87432 | −0.221759 | ||||||||
\(169\) | 21.6555 | 1.66581 | ||||||||
\(170\) | −6.23300 | −0.478049 | ||||||||
\(171\) | −1.65446 | −0.126520 | ||||||||
\(172\) | −10.2247 | −0.779628 | ||||||||
\(173\) | 18.5003 | 1.40655 | 0.703274 | − | 0.710919i | \(-0.251721\pi\) | ||||
0.703274 | + | 0.710919i | \(0.251721\pi\) | |||||||
\(174\) | 15.4796 | 1.17351 | ||||||||
\(175\) | −3.63586 | −0.274845 | ||||||||
\(176\) | −5.50011 | −0.414587 | ||||||||
\(177\) | −28.3040 | −2.12746 | ||||||||
\(178\) | −10.2497 | −0.768250 | ||||||||
\(179\) | 21.2926 | 1.59149 | 0.795743 | − | 0.605634i | \(-0.207080\pi\) | ||||
0.795743 | + | 0.605634i | \(0.207080\pi\) | |||||||
\(180\) | −4.59959 | −0.342833 | ||||||||
\(181\) | −17.1761 | −1.27669 | −0.638346 | − | 0.769750i | \(-0.720381\pi\) | ||||
−0.638346 | + | 0.769750i | \(0.720381\pi\) | |||||||
\(182\) | −7.84307 | −0.581367 | ||||||||
\(183\) | −5.30562 | −0.392203 | ||||||||
\(184\) | 6.52318 | 0.480895 | ||||||||
\(185\) | −0.00337361 | −0.000248033 0 | ||||||||
\(186\) | 8.23675 | 0.603948 | ||||||||
\(187\) | 12.3312 | 0.901749 | ||||||||
\(188\) | −1.06053 | −0.0773474 | ||||||||
\(189\) | −3.86750 | −0.281319 | ||||||||
\(190\) | −2.78011 | −0.201690 | ||||||||
\(191\) | 8.30885 | 0.601208 | 0.300604 | − | 0.953749i | \(-0.402812\pi\) | ||||
0.300604 | + | 0.953749i | \(0.402812\pi\) | |||||||
\(192\) | −2.15742 | −0.155698 | ||||||||
\(193\) | 25.4097 | 1.82903 | 0.914515 | − | 0.404551i | \(-0.132572\pi\) | ||||
0.914515 | + | 0.404551i | \(0.132572\pi\) | |||||||
\(194\) | −3.39933 | −0.244058 | ||||||||
\(195\) | −35.3088 | −2.52852 | ||||||||
\(196\) | −5.22499 | −0.373214 | ||||||||
\(197\) | 1.65567 | 0.117962 | 0.0589808 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589808 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(198\) | 9.09974 | 0.646690 | ||||||||
\(199\) | −13.4727 | −0.955057 | −0.477529 | − | 0.878616i | \(-0.658467\pi\) | ||||
−0.477529 | + | 0.878616i | \(0.658467\pi\) | |||||||
\(200\) | −2.72902 | −0.192971 | ||||||||
\(201\) | −13.9148 | −0.981473 | ||||||||
\(202\) | 4.60039 | 0.323682 | ||||||||
\(203\) | −9.55930 | −0.670931 | ||||||||
\(204\) | 4.83693 | 0.338653 | ||||||||
\(205\) | 0.0641978 | 0.00448377 | ||||||||
\(206\) | 11.1268 | 0.775243 | ||||||||
\(207\) | −10.7924 | −0.750121 | ||||||||
\(208\) | −5.88689 | −0.408182 | ||||||||
\(209\) | 5.50011 | 0.380451 | ||||||||
\(210\) | 7.99093 | 0.551427 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 10.3892 | 0.713534 | ||||||||
\(213\) | −6.37833 | −0.437036 | ||||||||
\(214\) | −0.319302 | −0.0218270 | ||||||||
\(215\) | 28.4259 | 1.93863 | ||||||||
\(216\) | −2.90289 | −0.197517 | ||||||||
\(217\) | −5.08653 | −0.345296 | ||||||||
\(218\) | 8.01354 | 0.542746 | ||||||||
\(219\) | 15.2343 | 1.02944 | ||||||||
\(220\) | 15.2909 | 1.03091 | ||||||||
\(221\) | 13.1984 | 0.887820 | ||||||||
\(222\) | 0.00261799 | 0.000175708 0 | ||||||||
\(223\) | −2.73815 | −0.183360 | −0.0916802 | − | 0.995789i | \(-0.529224\pi\) | ||||
−0.0916802 | + | 0.995789i | \(0.529224\pi\) | |||||||
\(224\) | 1.33229 | 0.0890177 | ||||||||
\(225\) | 4.51506 | 0.301004 | ||||||||
\(226\) | −7.93918 | −0.528106 | ||||||||
\(227\) | 11.9544 | 0.793440 | 0.396720 | − | 0.917940i | \(-0.370148\pi\) | ||||
0.396720 | + | 0.917940i | \(0.370148\pi\) | |||||||
\(228\) | 2.15742 | 0.142879 | ||||||||
\(229\) | 23.1719 | 1.53124 | 0.765620 | − | 0.643293i | \(-0.222432\pi\) | ||||
0.765620 | + | 0.643293i | \(0.222432\pi\) | |||||||
\(230\) | −18.1352 | −1.19580 | ||||||||
\(231\) | −15.8091 | −1.04016 | ||||||||
\(232\) | −7.17506 | −0.471066 | ||||||||
\(233\) | 0.0624516 | 0.00409134 | 0.00204567 | − | 0.999998i | \(-0.499349\pi\) | ||||
0.00204567 | + | 0.999998i | \(0.499349\pi\) | |||||||
\(234\) | 9.73965 | 0.636701 | ||||||||
\(235\) | 2.94840 | 0.192333 | ||||||||
\(236\) | 13.1194 | 0.853998 | ||||||||
\(237\) | −9.81503 | −0.637554 | ||||||||
\(238\) | −2.98700 | −0.193618 | ||||||||
\(239\) | 4.02893 | 0.260610 | 0.130305 | − | 0.991474i | \(-0.458404\pi\) | ||||
0.130305 | + | 0.991474i | \(0.458404\pi\) | |||||||
\(240\) | 5.99787 | 0.387161 | ||||||||
\(241\) | −15.1865 | −0.978246 | −0.489123 | − | 0.872215i | \(-0.662683\pi\) | ||||
−0.489123 | + | 0.872215i | \(0.662683\pi\) | |||||||
\(242\) | −19.2512 | −1.23752 | ||||||||
\(243\) | 15.5108 | 0.995021 | ||||||||
\(244\) | 2.45924 | 0.157437 | ||||||||
\(245\) | 14.5261 | 0.928036 | ||||||||
\(246\) | −0.0498188 | −0.00317633 | ||||||||
\(247\) | 5.88689 | 0.374574 | ||||||||
\(248\) | −3.81787 | −0.242435 | ||||||||
\(249\) | 4.32029 | 0.273787 | ||||||||
\(250\) | −6.31358 | −0.399306 | ||||||||
\(251\) | 8.49005 | 0.535887 | 0.267944 | − | 0.963435i | \(-0.413656\pi\) | ||||
0.267944 | + | 0.963435i | \(0.413656\pi\) | |||||||
\(252\) | −2.20423 | −0.138854 | ||||||||
\(253\) | 35.8782 | 2.25565 | ||||||||
\(254\) | 15.8788 | 0.996327 | ||||||||
\(255\) | −13.4472 | −0.842097 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.782274 | 0.0487969 | 0.0243985 | − | 0.999702i | \(-0.492233\pi\) | ||||
0.0243985 | + | 0.999702i | \(0.492233\pi\) | |||||||
\(258\) | −22.0590 | −1.37333 | ||||||||
\(259\) | −0.00161671 | −0.000100458 0 | ||||||||
\(260\) | 16.3662 | 1.01499 | ||||||||
\(261\) | 11.8709 | 0.734789 | ||||||||
\(262\) | −11.8312 | −0.730932 | ||||||||
\(263\) | 29.1044 | 1.79465 | 0.897327 | − | 0.441366i | \(-0.145506\pi\) | ||||
0.897327 | + | 0.441366i | \(0.145506\pi\) | |||||||
\(264\) | −11.8661 | −0.730305 | ||||||||
\(265\) | −28.8832 | −1.77428 | ||||||||
\(266\) | −1.33229 | −0.0816882 | ||||||||
\(267\) | −22.1130 | −1.35329 | ||||||||
\(268\) | 6.44973 | 0.393980 | ||||||||
\(269\) | 9.47053 | 0.577428 | 0.288714 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288714 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(270\) | 8.07035 | 0.491146 | ||||||||
\(271\) | 10.9255 | 0.663675 | 0.331838 | − | 0.943336i | \(-0.392331\pi\) | ||||
0.331838 | + | 0.943336i | \(0.392331\pi\) | |||||||
\(272\) | −2.24200 | −0.135941 | ||||||||
\(273\) | −16.9208 | −1.02409 | ||||||||
\(274\) | 13.9862 | 0.844935 | ||||||||
\(275\) | −15.0099 | −0.905131 | ||||||||
\(276\) | 14.0732 | 0.847110 | ||||||||
\(277\) | 25.6386 | 1.54047 | 0.770236 | − | 0.637759i | \(-0.220138\pi\) | ||||
0.770236 | + | 0.637759i | \(0.220138\pi\) | |||||||
\(278\) | −5.22721 | −0.313507 | ||||||||
\(279\) | 6.31653 | 0.378161 | ||||||||
\(280\) | −3.70393 | −0.221352 | ||||||||
\(281\) | 1.68999 | 0.100817 | 0.0504083 | − | 0.998729i | \(-0.483948\pi\) | ||||
0.0504083 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(282\) | −2.28802 | −0.136249 | ||||||||
\(283\) | 0.713173 | 0.0423937 | 0.0211969 | − | 0.999775i | \(-0.493252\pi\) | ||||
0.0211969 | + | 0.999775i | \(0.493252\pi\) | |||||||
\(284\) | 2.95646 | 0.175434 | ||||||||
\(285\) | −5.99787 | −0.355283 | ||||||||
\(286\) | −32.3786 | −1.91458 | ||||||||
\(287\) | 0.0307651 | 0.00181601 | ||||||||
\(288\) | −1.65446 | −0.0974902 | ||||||||
\(289\) | −11.9735 | −0.704321 | ||||||||
\(290\) | 19.9475 | 1.17136 | ||||||||
\(291\) | −7.33379 | −0.429914 | ||||||||
\(292\) | −7.06136 | −0.413235 | ||||||||
\(293\) | 2.86164 | 0.167179 | 0.0835894 | − | 0.996500i | \(-0.473362\pi\) | ||||
0.0835894 | + | 0.996500i | \(0.473362\pi\) | |||||||
\(294\) | −11.2725 | −0.657426 | ||||||||
\(295\) | −36.4733 | −2.12356 | ||||||||
\(296\) | −0.00121348 | −7.05321e−5 0 | ||||||||
\(297\) | −15.9662 | −0.926454 | ||||||||
\(298\) | 12.7346 | 0.737696 | ||||||||
\(299\) | 38.4013 | 2.22080 | ||||||||
\(300\) | −5.88764 | −0.339923 | ||||||||
\(301\) | 13.6223 | 0.785179 | ||||||||
\(302\) | 15.3227 | 0.881722 | ||||||||
\(303\) | 9.92498 | 0.570175 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −6.83697 | −0.391484 | ||||||||
\(306\) | 3.70930 | 0.212047 | ||||||||
\(307\) | −1.59554 | −0.0910623 | −0.0455311 | − | 0.998963i | \(-0.514498\pi\) | ||||
−0.0455311 | + | 0.998963i | \(0.514498\pi\) | |||||||
\(308\) | 7.32777 | 0.417539 | ||||||||
\(309\) | 24.0053 | 1.36561 | ||||||||
\(310\) | 10.6141 | 0.602841 | ||||||||
\(311\) | −15.4563 | −0.876446 | −0.438223 | − | 0.898866i | \(-0.644392\pi\) | ||||
−0.438223 | + | 0.898866i | \(0.644392\pi\) | |||||||
\(312\) | −12.7005 | −0.719024 | ||||||||
\(313\) | −20.3537 | −1.15046 | −0.575230 | − | 0.817992i | \(-0.695087\pi\) | ||||
−0.575230 | + | 0.817992i | \(0.695087\pi\) | |||||||
\(314\) | −9.36503 | −0.528499 | ||||||||
\(315\) | 6.12801 | 0.345274 | ||||||||
\(316\) | 4.54943 | 0.255925 | ||||||||
\(317\) | 15.3337 | 0.861225 | 0.430612 | − | 0.902537i | \(-0.358298\pi\) | ||||
0.430612 | + | 0.902537i | \(0.358298\pi\) | |||||||
\(318\) | 22.4139 | 1.25691 | ||||||||
\(319\) | −39.4636 | −2.20954 | ||||||||
\(320\) | −2.78011 | −0.155413 | ||||||||
\(321\) | −0.688869 | −0.0384489 | ||||||||
\(322\) | −8.69080 | −0.484319 | ||||||||
\(323\) | 2.24200 | 0.124748 | ||||||||
\(324\) | −11.2261 | −0.623675 | ||||||||
\(325\) | −16.0654 | −0.891150 | ||||||||
\(326\) | 10.5985 | 0.586994 | ||||||||
\(327\) | 17.2886 | 0.956061 | ||||||||
\(328\) | 0.0230918 | 0.00127503 | ||||||||
\(329\) | 1.41294 | 0.0778981 | ||||||||
\(330\) | 32.9890 | 1.81598 | ||||||||
\(331\) | 19.1231 | 1.05110 | 0.525552 | − | 0.850762i | \(-0.323859\pi\) | ||||
0.525552 | + | 0.850762i | \(0.323859\pi\) | |||||||
\(332\) | −2.00252 | −0.109903 | ||||||||
\(333\) | 0.00200766 | 0.000110019 0 | ||||||||
\(334\) | 24.5651 | 1.34414 | ||||||||
\(335\) | −17.9310 | −0.979673 | ||||||||
\(336\) | 2.87432 | 0.156807 | ||||||||
\(337\) | 12.7409 | 0.694042 | 0.347021 | − | 0.937857i | \(-0.387193\pi\) | ||||
0.347021 | + | 0.937857i | \(0.387193\pi\) | |||||||
\(338\) | −21.6555 | −1.17790 | ||||||||
\(339\) | −17.1281 | −0.930273 | ||||||||
\(340\) | 6.23300 | 0.338032 | ||||||||
\(341\) | −20.9987 | −1.13714 | ||||||||
\(342\) | 1.65446 | 0.0894631 | ||||||||
\(343\) | 16.2873 | 0.879431 | ||||||||
\(344\) | 10.2247 | 0.551280 | ||||||||
\(345\) | −39.1252 | −2.10643 | ||||||||
\(346\) | −18.5003 | −0.994580 | ||||||||
\(347\) | −13.0802 | −0.702179 | −0.351090 | − | 0.936342i | \(-0.614189\pi\) | ||||
−0.351090 | + | 0.936342i | \(0.614189\pi\) | |||||||
\(348\) | −15.4796 | −0.829795 | ||||||||
\(349\) | −14.1564 | −0.757774 | −0.378887 | − | 0.925443i | \(-0.623693\pi\) | ||||
−0.378887 | + | 0.925443i | \(0.623693\pi\) | |||||||
\(350\) | 3.63586 | 0.194345 | ||||||||
\(351\) | −17.0890 | −0.912143 | ||||||||
\(352\) | 5.50011 | 0.293157 | ||||||||
\(353\) | −15.0701 | −0.802102 | −0.401051 | − | 0.916056i | \(-0.631355\pi\) | ||||
−0.401051 | + | 0.916056i | \(0.631355\pi\) | |||||||
\(354\) | 28.3040 | 1.50434 | ||||||||
\(355\) | −8.21929 | −0.436235 | ||||||||
\(356\) | 10.2497 | 0.543235 | ||||||||
\(357\) | −6.44422 | −0.341064 | ||||||||
\(358\) | −21.2926 | −1.12535 | ||||||||
\(359\) | 22.9899 | 1.21336 | 0.606679 | − | 0.794947i | \(-0.292501\pi\) | ||||
0.606679 | + | 0.794947i | \(0.292501\pi\) | |||||||
\(360\) | 4.59959 | 0.242420 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.1761 | 0.902758 | ||||||||
\(363\) | −41.5330 | −2.17992 | ||||||||
\(364\) | 7.84307 | 0.411089 | ||||||||
\(365\) | 19.6314 | 1.02755 | ||||||||
\(366\) | 5.30562 | 0.277329 | ||||||||
\(367\) | −27.3145 | −1.42581 | −0.712903 | − | 0.701263i | \(-0.752620\pi\) | ||||
−0.712903 | + | 0.701263i | \(0.752620\pi\) | |||||||
\(368\) | −6.52318 | −0.340044 | ||||||||
\(369\) | −0.0382046 | −0.00198885 | ||||||||
\(370\) | 0.00337361 | 0.000175386 0 | ||||||||
\(371\) | −13.8415 | −0.718614 | ||||||||
\(372\) | −8.23675 | −0.427056 | ||||||||
\(373\) | 21.8061 | 1.12908 | 0.564538 | − | 0.825407i | \(-0.309054\pi\) | ||||
0.564538 | + | 0.825407i | \(0.309054\pi\) | |||||||
\(374\) | −12.3312 | −0.637633 | ||||||||
\(375\) | −13.6211 | −0.703388 | ||||||||
\(376\) | 1.06053 | 0.0546929 | ||||||||
\(377\) | −42.2388 | −2.17541 | ||||||||
\(378\) | 3.86750 | 0.198923 | ||||||||
\(379\) | −30.5595 | −1.56973 | −0.784867 | − | 0.619664i | \(-0.787269\pi\) | ||||
−0.784867 | + | 0.619664i | \(0.787269\pi\) | |||||||
\(380\) | 2.78011 | 0.142617 | ||||||||
\(381\) | 34.2573 | 1.75506 | ||||||||
\(382\) | −8.30885 | −0.425118 | ||||||||
\(383\) | 11.4871 | 0.586963 | 0.293481 | − | 0.955965i | \(-0.405186\pi\) | ||||
0.293481 | + | 0.955965i | \(0.405186\pi\) | |||||||
\(384\) | 2.15742 | 0.110095 | ||||||||
\(385\) | −20.3720 | −1.03825 | ||||||||
\(386\) | −25.4097 | −1.29332 | ||||||||
\(387\) | −16.9164 | −0.859910 | ||||||||
\(388\) | 3.39933 | 0.172575 | ||||||||
\(389\) | −15.0418 | −0.762651 | −0.381326 | − | 0.924441i | \(-0.624532\pi\) | ||||
−0.381326 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(390\) | 35.3088 | 1.78793 | ||||||||
\(391\) | 14.6250 | 0.739616 | ||||||||
\(392\) | 5.22499 | 0.263902 | ||||||||
\(393\) | −25.5248 | −1.28756 | ||||||||
\(394\) | −1.65567 | −0.0834115 | ||||||||
\(395\) | −12.6479 | −0.636385 | ||||||||
\(396\) | −9.09974 | −0.457279 | ||||||||
\(397\) | 28.2545 | 1.41805 | 0.709026 | − | 0.705182i | \(-0.249135\pi\) | ||||
0.709026 | + | 0.705182i | \(0.249135\pi\) | |||||||
\(398\) | 13.4727 | 0.675328 | ||||||||
\(399\) | −2.87432 | −0.143896 | ||||||||
\(400\) | 2.72902 | 0.136451 | ||||||||
\(401\) | −0.492403 | −0.0245894 | −0.0122947 | − | 0.999924i | \(-0.503914\pi\) | ||||
−0.0122947 | + | 0.999924i | \(0.503914\pi\) | |||||||
\(402\) | 13.9148 | 0.694006 | ||||||||
\(403\) | −22.4754 | −1.11958 | ||||||||
\(404\) | −4.60039 | −0.228878 | ||||||||
\(405\) | 31.2099 | 1.55083 | ||||||||
\(406\) | 9.55930 | 0.474420 | ||||||||
\(407\) | −0.00667427 | −0.000330831 0 | ||||||||
\(408\) | −4.83693 | −0.239464 | ||||||||
\(409\) | 8.21722 | 0.406316 | 0.203158 | − | 0.979146i | \(-0.434880\pi\) | ||||
0.203158 | + | 0.979146i | \(0.434880\pi\) | |||||||
\(410\) | −0.0641978 | −0.00317050 | ||||||||
\(411\) | 30.1740 | 1.48838 | ||||||||
\(412\) | −11.1268 | −0.548180 | ||||||||
\(413\) | −17.4789 | −0.860079 | ||||||||
\(414\) | 10.7924 | 0.530416 | ||||||||
\(415\) | 5.56724 | 0.273285 | ||||||||
\(416\) | 5.88689 | 0.288629 | ||||||||
\(417\) | −11.2773 | −0.552251 | ||||||||
\(418\) | −5.50011 | −0.269019 | ||||||||
\(419\) | −26.8072 | −1.30962 | −0.654808 | − | 0.755795i | \(-0.727251\pi\) | ||||
−0.654808 | + | 0.755795i | \(0.727251\pi\) | |||||||
\(420\) | −7.99093 | −0.389917 | ||||||||
\(421\) | −29.2489 | −1.42550 | −0.712752 | − | 0.701416i | \(-0.752552\pi\) | ||||
−0.712752 | + | 0.701416i | \(0.752552\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −1.75461 | −0.0853123 | ||||||||
\(424\) | −10.3892 | −0.504545 | ||||||||
\(425\) | −6.11845 | −0.296788 | ||||||||
\(426\) | 6.37833 | 0.309031 | ||||||||
\(427\) | −3.27644 | −0.158558 | ||||||||
\(428\) | 0.319302 | 0.0154340 | ||||||||
\(429\) | −69.8542 | −3.37259 | ||||||||
\(430\) | −28.4259 | −1.37082 | ||||||||
\(431\) | 0.974703 | 0.0469498 | 0.0234749 | − | 0.999724i | \(-0.492527\pi\) | ||||
0.0234749 | + | 0.999724i | \(0.492527\pi\) | |||||||
\(432\) | 2.90289 | 0.139665 | ||||||||
\(433\) | −7.32945 | −0.352231 | −0.176115 | − | 0.984370i | \(-0.556353\pi\) | ||||
−0.176115 | + | 0.984370i | \(0.556353\pi\) | |||||||
\(434\) | 5.08653 | 0.244161 | ||||||||
\(435\) | 43.0351 | 2.06337 | ||||||||
\(436\) | −8.01354 | −0.383779 | ||||||||
\(437\) | 6.52318 | 0.312046 | ||||||||
\(438\) | −15.2343 | −0.727924 | ||||||||
\(439\) | −19.3320 | −0.922665 | −0.461333 | − | 0.887227i | \(-0.652629\pi\) | ||||
−0.461333 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(440\) | −15.2909 | −0.728966 | ||||||||
\(441\) | −8.64456 | −0.411646 | ||||||||
\(442\) | −13.1984 | −0.627783 | ||||||||
\(443\) | −30.3823 | −1.44350 | −0.721752 | − | 0.692152i | \(-0.756663\pi\) | ||||
−0.721752 | + | 0.692152i | \(0.756663\pi\) | |||||||
\(444\) | −0.00261799 | −0.000124244 0 | ||||||||
\(445\) | −28.4954 | −1.35081 | ||||||||
\(446\) | 2.73815 | 0.129655 | ||||||||
\(447\) | 27.4739 | 1.29947 | ||||||||
\(448\) | −1.33229 | −0.0629450 | ||||||||
\(449\) | 38.4172 | 1.81302 | 0.906509 | − | 0.422186i | \(-0.138737\pi\) | ||||
0.906509 | + | 0.422186i | \(0.138737\pi\) | |||||||
\(450\) | −4.51506 | −0.212842 | ||||||||
\(451\) | 0.127008 | 0.00598055 | ||||||||
\(452\) | 7.93918 | 0.373428 | ||||||||
\(453\) | 33.0575 | 1.55318 | ||||||||
\(454\) | −11.9544 | −0.561047 | ||||||||
\(455\) | −21.8046 | −1.02222 | ||||||||
\(456\) | −2.15742 | −0.101030 | ||||||||
\(457\) | −1.48137 | −0.0692958 | −0.0346479 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346479 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(458\) | −23.1719 | −1.08275 | ||||||||
\(459\) | −6.50827 | −0.303780 | ||||||||
\(460\) | 18.1352 | 0.845557 | ||||||||
\(461\) | −38.6136 | −1.79841 | −0.899207 | − | 0.437523i | \(-0.855856\pi\) | ||||
−0.899207 | + | 0.437523i | \(0.855856\pi\) | |||||||
\(462\) | 15.8091 | 0.735505 | ||||||||
\(463\) | −4.78767 | −0.222502 | −0.111251 | − | 0.993792i | \(-0.535486\pi\) | ||||
−0.111251 | + | 0.993792i | \(0.535486\pi\) | |||||||
\(464\) | 7.17506 | 0.333094 | ||||||||
\(465\) | 22.8991 | 1.06192 | ||||||||
\(466\) | −0.0624516 | −0.00289301 | ||||||||
\(467\) | −16.0814 | −0.744157 | −0.372078 | − | 0.928201i | \(-0.621355\pi\) | ||||
−0.372078 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(468\) | −9.73965 | −0.450215 | ||||||||
\(469\) | −8.59294 | −0.396785 | ||||||||
\(470\) | −2.94840 | −0.136000 | ||||||||
\(471\) | −20.2043 | −0.930966 | ||||||||
\(472\) | −13.1194 | −0.603868 | ||||||||
\(473\) | 56.2371 | 2.58579 | ||||||||
\(474\) | 9.81503 | 0.450819 | ||||||||
\(475\) | −2.72902 | −0.125216 | ||||||||
\(476\) | 2.98700 | 0.136909 | ||||||||
\(477\) | 17.1886 | 0.787010 | ||||||||
\(478\) | −4.02893 | −0.184279 | ||||||||
\(479\) | 5.35999 | 0.244904 | 0.122452 | − | 0.992474i | \(-0.460924\pi\) | ||||
0.122452 | + | 0.992474i | \(0.460924\pi\) | |||||||
\(480\) | −5.99787 | −0.273764 | ||||||||
\(481\) | −0.00714362 | −0.000325721 0 | ||||||||
\(482\) | 15.1865 | 0.691725 | ||||||||
\(483\) | −18.7497 | −0.853141 | ||||||||
\(484\) | 19.2512 | 0.875056 | ||||||||
\(485\) | −9.45052 | −0.429126 | ||||||||
\(486\) | −15.5108 | −0.703586 | ||||||||
\(487\) | −1.50511 | −0.0682029 | −0.0341014 | − | 0.999418i | \(-0.510857\pi\) | ||||
−0.0341014 | + | 0.999418i | \(0.510857\pi\) | |||||||
\(488\) | −2.45924 | −0.111325 | ||||||||
\(489\) | 22.8653 | 1.03401 | ||||||||
\(490\) | −14.5261 | −0.656220 | ||||||||
\(491\) | 10.0401 | 0.453102 | 0.226551 | − | 0.973999i | \(-0.427255\pi\) | ||||
0.226551 | + | 0.973999i | \(0.427255\pi\) | |||||||
\(492\) | 0.0498188 | 0.00224600 | ||||||||
\(493\) | −16.0865 | −0.724498 | ||||||||
\(494\) | −5.88689 | −0.264864 | ||||||||
\(495\) | 25.2983 | 1.13707 | ||||||||
\(496\) | 3.81787 | 0.171427 | ||||||||
\(497\) | −3.93888 | −0.176683 | ||||||||
\(498\) | −4.32029 | −0.193597 | ||||||||
\(499\) | 15.9373 | 0.713453 | 0.356727 | − | 0.934209i | \(-0.383893\pi\) | ||||
0.356727 | + | 0.934209i | \(0.383893\pi\) | |||||||
\(500\) | 6.31358 | 0.282352 | ||||||||
\(501\) | 52.9973 | 2.36774 | ||||||||
\(502\) | −8.49005 | −0.378929 | ||||||||
\(503\) | 41.3289 | 1.84277 | 0.921383 | − | 0.388656i | \(-0.127061\pi\) | ||||
0.921383 | + | 0.388656i | \(0.127061\pi\) | |||||||
\(504\) | 2.20423 | 0.0981843 | ||||||||
\(505\) | 12.7896 | 0.569130 | ||||||||
\(506\) | −35.8782 | −1.59498 | ||||||||
\(507\) | −46.7200 | −2.07491 | ||||||||
\(508\) | −15.8788 | −0.704509 | ||||||||
\(509\) | 18.4331 | 0.817031 | 0.408516 | − | 0.912751i | \(-0.366047\pi\) | ||||
0.408516 | + | 0.912751i | \(0.366047\pi\) | |||||||
\(510\) | 13.4472 | 0.595452 | ||||||||
\(511\) | 9.40782 | 0.416177 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.90289 | −0.128166 | ||||||||
\(514\) | −0.782274 | −0.0345046 | ||||||||
\(515\) | 30.9338 | 1.36311 | ||||||||
\(516\) | 22.0590 | 0.971094 | ||||||||
\(517\) | 5.83306 | 0.256538 | ||||||||
\(518\) | 0.00161671 | 7.10343e−5 0 | ||||||||
\(519\) | −39.9128 | −1.75198 | ||||||||
\(520\) | −16.3662 | −0.717706 | ||||||||
\(521\) | −40.0811 | −1.75599 | −0.877993 | − | 0.478674i | \(-0.841118\pi\) | ||||
−0.877993 | + | 0.478674i | \(0.841118\pi\) | |||||||
\(522\) | −11.8709 | −0.519574 | ||||||||
\(523\) | −3.41281 | −0.149232 | −0.0746158 | − | 0.997212i | \(-0.523773\pi\) | ||||
−0.0746158 | + | 0.997212i | \(0.523773\pi\) | |||||||
\(524\) | 11.8312 | 0.516847 | ||||||||
\(525\) | 7.84407 | 0.342343 | ||||||||
\(526\) | −29.1044 | −1.26901 | ||||||||
\(527\) | −8.55965 | −0.372864 | ||||||||
\(528\) | 11.8661 | 0.516404 | ||||||||
\(529\) | 19.5519 | 0.850082 | ||||||||
\(530\) | 28.8832 | 1.25460 | ||||||||
\(531\) | 21.7055 | 0.941939 | ||||||||
\(532\) | 1.33229 | 0.0577623 | ||||||||
\(533\) | 0.135939 | 0.00588817 | ||||||||
\(534\) | 22.1130 | 0.956922 | ||||||||
\(535\) | −0.887695 | −0.0383784 | ||||||||
\(536\) | −6.44973 | −0.278586 | ||||||||
\(537\) | −45.9372 | −1.98234 | ||||||||
\(538\) | −9.47053 | −0.408304 | ||||||||
\(539\) | 28.7380 | 1.23783 | ||||||||
\(540\) | −8.07035 | −0.347293 | ||||||||
\(541\) | 38.3046 | 1.64684 | 0.823422 | − | 0.567430i | \(-0.192062\pi\) | ||||
0.823422 | + | 0.567430i | \(0.192062\pi\) | |||||||
\(542\) | −10.9255 | −0.469289 | ||||||||
\(543\) | 37.0561 | 1.59023 | ||||||||
\(544\) | 2.24200 | 0.0961248 | ||||||||
\(545\) | 22.2785 | 0.954308 | ||||||||
\(546\) | 16.9208 | 0.724144 | ||||||||
\(547\) | −2.03295 | −0.0869226 | −0.0434613 | − | 0.999055i | \(-0.513839\pi\) | ||||
−0.0434613 | + | 0.999055i | \(0.513839\pi\) | |||||||
\(548\) | −13.9862 | −0.597459 | ||||||||
\(549\) | 4.06873 | 0.173649 | ||||||||
\(550\) | 15.0099 | 0.640025 | ||||||||
\(551\) | −7.17506 | −0.305668 | ||||||||
\(552\) | −14.0732 | −0.598997 | ||||||||
\(553\) | −6.06118 | −0.257747 | ||||||||
\(554\) | −25.6386 | −1.08928 | ||||||||
\(555\) | 0.00727829 | 0.000308946 0 | ||||||||
\(556\) | 5.22721 | 0.221683 | ||||||||
\(557\) | −26.4962 | −1.12268 | −0.561339 | − | 0.827586i | \(-0.689714\pi\) | ||||
−0.561339 | + | 0.827586i | \(0.689714\pi\) | |||||||
\(558\) | −6.31653 | −0.267400 | ||||||||
\(559\) | 60.1918 | 2.54584 | ||||||||
\(560\) | 3.70393 | 0.156520 | ||||||||
\(561\) | −26.6037 | −1.12321 | ||||||||
\(562\) | −1.68999 | −0.0712881 | ||||||||
\(563\) | −7.76923 | −0.327434 | −0.163717 | − | 0.986507i | \(-0.552348\pi\) | ||||
−0.163717 | + | 0.986507i | \(0.552348\pi\) | |||||||
\(564\) | 2.28802 | 0.0963429 | ||||||||
\(565\) | −22.0718 | −0.928568 | ||||||||
\(566\) | −0.713173 | −0.0299769 | ||||||||
\(567\) | 14.9565 | 0.628115 | ||||||||
\(568\) | −2.95646 | −0.124050 | ||||||||
\(569\) | 13.2614 | 0.555949 | 0.277974 | − | 0.960588i | \(-0.410337\pi\) | ||||
0.277974 | + | 0.960588i | \(0.410337\pi\) | |||||||
\(570\) | 5.99787 | 0.251223 | ||||||||
\(571\) | −9.12816 | −0.382002 | −0.191001 | − | 0.981590i | \(-0.561173\pi\) | ||||
−0.191001 | + | 0.981590i | \(0.561173\pi\) | |||||||
\(572\) | 32.3786 | 1.35382 | ||||||||
\(573\) | −17.9257 | −0.748857 | ||||||||
\(574\) | −0.0307651 | −0.00128411 | ||||||||
\(575\) | −17.8019 | −0.742390 | ||||||||
\(576\) | 1.65446 | 0.0689360 | ||||||||
\(577\) | −18.3659 | −0.764581 | −0.382291 | − | 0.924042i | \(-0.624865\pi\) | ||||
−0.382291 | + | 0.924042i | \(0.624865\pi\) | |||||||
\(578\) | 11.9735 | 0.498030 | ||||||||
\(579\) | −54.8194 | −2.27822 | ||||||||
\(580\) | −19.9475 | −0.828273 | ||||||||
\(581\) | 2.66795 | 0.110685 | ||||||||
\(582\) | 7.33379 | 0.303995 | ||||||||
\(583\) | −57.1418 | −2.36657 | ||||||||
\(584\) | 7.06136 | 0.292201 | ||||||||
\(585\) | 27.0773 | 1.11951 | ||||||||
\(586\) | −2.86164 | −0.118213 | ||||||||
\(587\) | 14.5419 | 0.600210 | 0.300105 | − | 0.953906i | \(-0.402978\pi\) | ||||
0.300105 | + | 0.953906i | \(0.402978\pi\) | |||||||
\(588\) | 11.2725 | 0.464870 | ||||||||
\(589\) | −3.81787 | −0.157313 | ||||||||
\(590\) | 36.4733 | 1.50158 | ||||||||
\(591\) | −3.57198 | −0.146932 | ||||||||
\(592\) | 0.00121348 | 4.98737e−5 0 | ||||||||
\(593\) | −12.0601 | −0.495249 | −0.247625 | − | 0.968856i | \(-0.579650\pi\) | ||||
−0.247625 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(594\) | 15.9662 | 0.655102 | ||||||||
\(595\) | −8.30419 | −0.340439 | ||||||||
\(596\) | −12.7346 | −0.521630 | ||||||||
\(597\) | 29.0664 | 1.18961 | ||||||||
\(598\) | −38.4013 | −1.57034 | ||||||||
\(599\) | −9.07245 | −0.370690 | −0.185345 | − | 0.982673i | \(-0.559340\pi\) | ||||
−0.185345 | + | 0.982673i | \(0.559340\pi\) | |||||||
\(600\) | 5.88764 | 0.240362 | ||||||||
\(601\) | −0.942780 | −0.0384568 | −0.0192284 | − | 0.999815i | \(-0.506121\pi\) | ||||
−0.0192284 | + | 0.999815i | \(0.506121\pi\) | |||||||
\(602\) | −13.6223 | −0.555205 | ||||||||
\(603\) | 10.6708 | 0.434550 | ||||||||
\(604\) | −15.3227 | −0.623471 | ||||||||
\(605\) | −53.5206 | −2.17592 | ||||||||
\(606\) | −9.92498 | −0.403175 | ||||||||
\(607\) | 22.7710 | 0.924245 | 0.462122 | − | 0.886816i | \(-0.347088\pi\) | ||||
0.462122 | + | 0.886816i | \(0.347088\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 20.6234 | 0.835703 | ||||||||
\(610\) | 6.83697 | 0.276821 | ||||||||
\(611\) | 6.24325 | 0.252575 | ||||||||
\(612\) | −3.70930 | −0.149940 | ||||||||
\(613\) | 48.0768 | 1.94180 | 0.970902 | − | 0.239476i | \(-0.0769755\pi\) | ||||
0.970902 | + | 0.239476i | \(0.0769755\pi\) | |||||||
\(614\) | 1.59554 | 0.0643908 | ||||||||
\(615\) | −0.138502 | −0.00558493 | ||||||||
\(616\) | −7.32777 | −0.295244 | ||||||||
\(617\) | 8.23906 | 0.331692 | 0.165846 | − | 0.986152i | \(-0.446965\pi\) | ||||
0.165846 | + | 0.986152i | \(0.446965\pi\) | |||||||
\(618\) | −24.0053 | −0.965633 | ||||||||
\(619\) | −1.67620 | −0.0673721 | −0.0336860 | − | 0.999432i | \(-0.510725\pi\) | ||||
−0.0336860 | + | 0.999432i | \(0.510725\pi\) | |||||||
\(620\) | −10.6141 | −0.426273 | ||||||||
\(621\) | −18.9361 | −0.759878 | ||||||||
\(622\) | 15.4563 | 0.619741 | ||||||||
\(623\) | −13.6557 | −0.547103 | ||||||||
\(624\) | 12.7005 | 0.508427 | ||||||||
\(625\) | −31.1976 | −1.24790 | ||||||||
\(626\) | 20.3537 | 0.813498 | ||||||||
\(627\) | −11.8661 | −0.473885 | ||||||||
\(628\) | 9.36503 | 0.373705 | ||||||||
\(629\) | −0.00272062 | −0.000108478 0 | ||||||||
\(630\) | −6.12801 | −0.244146 | ||||||||
\(631\) | −40.8749 | −1.62721 | −0.813603 | − | 0.581421i | \(-0.802497\pi\) | ||||
−0.813603 | + | 0.581421i | \(0.802497\pi\) | |||||||
\(632\) | −4.54943 | −0.180966 | ||||||||
\(633\) | 2.15742 | 0.0857498 | ||||||||
\(634\) | −15.3337 | −0.608978 | ||||||||
\(635\) | 44.1449 | 1.75184 | ||||||||
\(636\) | −22.4139 | −0.888769 | ||||||||
\(637\) | 30.7590 | 1.21871 | ||||||||
\(638\) | 39.4636 | 1.56238 | ||||||||
\(639\) | 4.89136 | 0.193499 | ||||||||
\(640\) | 2.78011 | 0.109894 | ||||||||
\(641\) | −26.2565 | −1.03707 | −0.518535 | − | 0.855056i | \(-0.673522\pi\) | ||||
−0.518535 | + | 0.855056i | \(0.673522\pi\) | |||||||
\(642\) | 0.688869 | 0.0271875 | ||||||||
\(643\) | −24.4264 | −0.963282 | −0.481641 | − | 0.876369i | \(-0.659959\pi\) | ||||
−0.481641 | + | 0.876369i | \(0.659959\pi\) | |||||||
\(644\) | 8.69080 | 0.342466 | ||||||||
\(645\) | −61.3265 | −2.41473 | ||||||||
\(646\) | −2.24200 | −0.0882102 | ||||||||
\(647\) | −29.1756 | −1.14701 | −0.573505 | − | 0.819202i | \(-0.694417\pi\) | ||||
−0.573505 | + | 0.819202i | \(0.694417\pi\) | |||||||
\(648\) | 11.2261 | 0.441004 | ||||||||
\(649\) | −72.1580 | −2.83245 | ||||||||
\(650\) | 16.0654 | 0.630138 | ||||||||
\(651\) | 10.9738 | 0.430097 | ||||||||
\(652\) | −10.5985 | −0.415068 | ||||||||
\(653\) | −36.8413 | −1.44171 | −0.720855 | − | 0.693086i | \(-0.756251\pi\) | ||||
−0.720855 | + | 0.693086i | \(0.756251\pi\) | |||||||
\(654\) | −17.2886 | −0.676037 | ||||||||
\(655\) | −32.8919 | −1.28519 | ||||||||
\(656\) | −0.0230918 | −0.000901584 0 | ||||||||
\(657\) | −11.6828 | −0.455788 | ||||||||
\(658\) | −1.41294 | −0.0550823 | ||||||||
\(659\) | −16.2993 | −0.634930 | −0.317465 | − | 0.948270i | \(-0.602832\pi\) | ||||
−0.317465 | + | 0.948270i | \(0.602832\pi\) | |||||||
\(660\) | −32.9890 | −1.28409 | ||||||||
\(661\) | 45.4371 | 1.76730 | 0.883648 | − | 0.468151i | \(-0.155080\pi\) | ||||
0.883648 | + | 0.468151i | \(0.155080\pi\) | |||||||
\(662\) | −19.1231 | −0.743242 | ||||||||
\(663\) | −28.4745 | −1.10586 | ||||||||
\(664\) | 2.00252 | 0.0777130 | ||||||||
\(665\) | −3.70393 | −0.143632 | ||||||||
\(666\) | −0.00200766 | −7.77951e−5 0 | ||||||||
\(667\) | −46.8042 | −1.81227 | ||||||||
\(668\) | −24.5651 | −0.950453 | ||||||||
\(669\) | 5.90735 | 0.228391 | ||||||||
\(670\) | 17.9310 | 0.692734 | ||||||||
\(671\) | −13.5261 | −0.522170 | ||||||||
\(672\) | −2.87432 | −0.110879 | ||||||||
\(673\) | −42.1124 | −1.62331 | −0.811657 | − | 0.584134i | \(-0.801434\pi\) | ||||
−0.811657 | + | 0.584134i | \(0.801434\pi\) | |||||||
\(674\) | −12.7409 | −0.490762 | ||||||||
\(675\) | 7.92203 | 0.304919 | ||||||||
\(676\) | 21.6555 | 0.832903 | ||||||||
\(677\) | −31.4073 | −1.20708 | −0.603539 | − | 0.797333i | \(-0.706243\pi\) | ||||
−0.603539 | + | 0.797333i | \(0.706243\pi\) | |||||||
\(678\) | 17.1281 | 0.657803 | ||||||||
\(679\) | −4.52891 | −0.173804 | ||||||||
\(680\) | −6.23300 | −0.239025 | ||||||||
\(681\) | −25.7906 | −0.988299 | ||||||||
\(682\) | 20.9987 | 0.804083 | ||||||||
\(683\) | 9.75667 | 0.373329 | 0.186664 | − | 0.982424i | \(-0.440232\pi\) | ||||
0.186664 | + | 0.982424i | \(0.440232\pi\) | |||||||
\(684\) | −1.65446 | −0.0632600 | ||||||||
\(685\) | 38.8831 | 1.48565 | ||||||||
\(686\) | −16.2873 | −0.621852 | ||||||||
\(687\) | −49.9914 | −1.90729 | ||||||||
\(688\) | −10.2247 | −0.389814 | ||||||||
\(689\) | −61.1601 | −2.33002 | ||||||||
\(690\) | 39.1252 | 1.48947 | ||||||||
\(691\) | 21.8118 | 0.829761 | 0.414881 | − | 0.909876i | \(-0.363823\pi\) | ||||
0.414881 | + | 0.909876i | \(0.363823\pi\) | |||||||
\(692\) | 18.5003 | 0.703274 | ||||||||
\(693\) | 12.1235 | 0.460535 | ||||||||
\(694\) | 13.0802 | 0.496516 | ||||||||
\(695\) | −14.5322 | −0.551239 | ||||||||
\(696\) | 15.4796 | 0.586754 | ||||||||
\(697\) | 0.0517718 | 0.00196100 | ||||||||
\(698\) | 14.1564 | 0.535827 | ||||||||
\(699\) | −0.134734 | −0.00509612 | ||||||||
\(700\) | −3.63586 | −0.137422 | ||||||||
\(701\) | −4.43796 | −0.167620 | −0.0838098 | − | 0.996482i | \(-0.526709\pi\) | ||||
−0.0838098 | + | 0.996482i | \(0.526709\pi\) | |||||||
\(702\) | 17.0890 | 0.644982 | ||||||||
\(703\) | −0.00121348 | −4.57672e−5 0 | ||||||||
\(704\) | −5.50011 | −0.207293 | ||||||||
\(705\) | −6.36094 | −0.239567 | ||||||||
\(706\) | 15.0701 | 0.567172 | ||||||||
\(707\) | 6.12908 | 0.230508 | ||||||||
\(708\) | −28.3040 | −1.06373 | ||||||||
\(709\) | −18.3684 | −0.689839 | −0.344920 | − | 0.938632i | \(-0.612094\pi\) | ||||
−0.344920 | + | 0.938632i | \(0.612094\pi\) | |||||||
\(710\) | 8.21929 | 0.308465 | ||||||||
\(711\) | 7.52686 | 0.282279 | ||||||||
\(712\) | −10.2497 | −0.384125 | ||||||||
\(713\) | −24.9047 | −0.932687 | ||||||||
\(714\) | 6.44422 | 0.241169 | ||||||||
\(715\) | −90.0160 | −3.36641 | ||||||||
\(716\) | 21.2926 | 0.795743 | ||||||||
\(717\) | −8.69210 | −0.324612 | ||||||||
\(718\) | −22.9899 | −0.857974 | ||||||||
\(719\) | 41.4738 | 1.54671 | 0.773356 | − | 0.633972i | \(-0.218577\pi\) | ||||
0.773356 | + | 0.633972i | \(0.218577\pi\) | |||||||
\(720\) | −4.59959 | −0.171417 | ||||||||
\(721\) | 14.8242 | 0.552083 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 32.7636 | 1.21849 | ||||||||
\(724\) | −17.1761 | −0.638346 | ||||||||
\(725\) | 19.5809 | 0.727215 | ||||||||
\(726\) | 41.5330 | 1.54144 | ||||||||
\(727\) | 20.1418 | 0.747018 | 0.373509 | − | 0.927627i | \(-0.378155\pi\) | ||||
0.373509 | + | 0.927627i | \(0.378155\pi\) | |||||||
\(728\) | −7.84307 | −0.290684 | ||||||||
\(729\) | 0.215012 | 0.00796340 | ||||||||
\(730\) | −19.6314 | −0.726590 | ||||||||
\(731\) | 22.9238 | 0.847867 | ||||||||
\(732\) | −5.30562 | −0.196101 | ||||||||
\(733\) | 51.9726 | 1.91965 | 0.959825 | − | 0.280599i | \(-0.0905330\pi\) | ||||
0.959825 | + | 0.280599i | \(0.0905330\pi\) | |||||||
\(734\) | 27.3145 | 1.00820 | ||||||||
\(735\) | −31.3388 | −1.15595 | ||||||||
\(736\) | 6.52318 | 0.240448 | ||||||||
\(737\) | −35.4742 | −1.30671 | ||||||||
\(738\) | 0.0382046 | 0.00140633 | ||||||||
\(739\) | −37.8111 | −1.39090 | −0.695452 | − | 0.718573i | \(-0.744796\pi\) | ||||
−0.695452 | + | 0.718573i | \(0.744796\pi\) | |||||||
\(740\) | −0.00337361 | −0.000124016 0 | ||||||||
\(741\) | −12.7005 | −0.466565 | ||||||||
\(742\) | 13.8415 | 0.508137 | ||||||||
\(743\) | 0.661684 | 0.0242748 | 0.0121374 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121374 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(744\) | 8.23675 | 0.301974 | ||||||||
\(745\) | 35.4036 | 1.29709 | ||||||||
\(746\) | −21.8061 | −0.798378 | ||||||||
\(747\) | −3.31310 | −0.121220 | ||||||||
\(748\) | 12.3312 | 0.450875 | ||||||||
\(749\) | −0.425404 | −0.0155439 | ||||||||
\(750\) | 13.6211 | 0.497371 | ||||||||
\(751\) | −1.74926 | −0.0638315 | −0.0319158 | − | 0.999491i | \(-0.510161\pi\) | ||||
−0.0319158 | + | 0.999491i | \(0.510161\pi\) | |||||||
\(752\) | −1.06053 | −0.0386737 | ||||||||
\(753\) | −18.3166 | −0.667494 | ||||||||
\(754\) | 42.2388 | 1.53825 | ||||||||
\(755\) | 42.5988 | 1.55033 | ||||||||
\(756\) | −3.86750 | −0.140660 | ||||||||
\(757\) | −28.9312 | −1.05152 | −0.525761 | − | 0.850632i | \(-0.676220\pi\) | ||||
−0.525761 | + | 0.850632i | \(0.676220\pi\) | |||||||
\(758\) | 30.5595 | 1.10997 | ||||||||
\(759\) | −77.4044 | −2.80960 | ||||||||
\(760\) | −2.78011 | −0.100845 | ||||||||
\(761\) | 14.8160 | 0.537079 | 0.268540 | − | 0.963269i | \(-0.413459\pi\) | ||||
0.268540 | + | 0.963269i | \(0.413459\pi\) | |||||||
\(762\) | −34.2573 | −1.24101 | ||||||||
\(763\) | 10.6764 | 0.386512 | ||||||||
\(764\) | 8.30885 | 0.300604 | ||||||||
\(765\) | 10.3123 | 0.372841 | ||||||||
\(766\) | −11.4871 | −0.415045 | ||||||||
\(767\) | −77.2323 | −2.78870 | ||||||||
\(768\) | −2.15742 | −0.0778492 | ||||||||
\(769\) | 33.2703 | 1.19976 | 0.599880 | − | 0.800090i | \(-0.295215\pi\) | ||||
0.599880 | + | 0.800090i | \(0.295215\pi\) | |||||||
\(770\) | 20.3720 | 0.734157 | ||||||||
\(771\) | −1.68769 | −0.0607808 | ||||||||
\(772\) | 25.4097 | 0.914515 | ||||||||
\(773\) | 11.0643 | 0.397957 | 0.198978 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198978 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(774\) | 16.9164 | 0.608048 | ||||||||
\(775\) | 10.4190 | 0.374263 | ||||||||
\(776\) | −3.39933 | −0.122029 | ||||||||
\(777\) | 0.00348793 | 0.000125129 0 | ||||||||
\(778\) | 15.0418 | 0.539276 | ||||||||
\(779\) | 0.0230918 | 0.000827350 0 | ||||||||
\(780\) | −35.3088 | −1.26426 | ||||||||
\(781\) | −16.2609 | −0.581860 | ||||||||
\(782\) | −14.6250 | −0.522987 | ||||||||
\(783\) | 20.8284 | 0.744346 | ||||||||
\(784\) | −5.22499 | −0.186607 | ||||||||
\(785\) | −26.0358 | −0.929259 | ||||||||
\(786\) | 25.5248 | 0.910439 | ||||||||
\(787\) | 16.0464 | 0.571993 | 0.285996 | − | 0.958231i | \(-0.407675\pi\) | ||||
0.285996 | + | 0.958231i | \(0.407675\pi\) | |||||||
\(788\) | 1.65567 | 0.0589808 | ||||||||
\(789\) | −62.7904 | −2.23540 | ||||||||
\(790\) | 12.6479 | 0.449992 | ||||||||
\(791\) | −10.5773 | −0.376086 | ||||||||
\(792\) | 9.09974 | 0.323345 | ||||||||
\(793\) | −14.4773 | −0.514104 | ||||||||
\(794\) | −28.2545 | −1.00271 | ||||||||
\(795\) | 62.3131 | 2.21002 | ||||||||
\(796\) | −13.4727 | −0.477529 | ||||||||
\(797\) | 41.5438 | 1.47156 | 0.735778 | − | 0.677223i | \(-0.236817\pi\) | ||||
0.735778 | + | 0.677223i | \(0.236817\pi\) | |||||||
\(798\) | 2.87432 | 0.101750 | ||||||||
\(799\) | 2.37771 | 0.0841175 | ||||||||
\(800\) | −2.72902 | −0.0964854 | ||||||||
\(801\) | 16.9578 | 0.599175 | ||||||||
\(802\) | 0.492403 | 0.0173874 | ||||||||
\(803\) | 38.8383 | 1.37057 | ||||||||
\(804\) | −13.9148 | −0.490736 | ||||||||
\(805\) | −24.1614 | −0.851577 | ||||||||
\(806\) | 22.4754 | 0.791662 | ||||||||
\(807\) | −20.4319 | −0.719238 | ||||||||
\(808\) | 4.60039 | 0.161841 | ||||||||
\(809\) | 29.7877 | 1.04728 | 0.523641 | − | 0.851939i | \(-0.324573\pi\) | ||||
0.523641 | + | 0.851939i | \(0.324573\pi\) | |||||||
\(810\) | −31.2099 | −1.09660 | ||||||||
\(811\) | 46.3916 | 1.62903 | 0.814515 | − | 0.580142i | \(-0.197003\pi\) | ||||
0.814515 | + | 0.580142i | \(0.197003\pi\) | |||||||
\(812\) | −9.55930 | −0.335466 | ||||||||
\(813\) | −23.5708 | −0.826666 | ||||||||
\(814\) | 0.00667427 | 0.000233933 0 | ||||||||
\(815\) | 29.4649 | 1.03211 | ||||||||
\(816\) | 4.83693 | 0.169326 | ||||||||
\(817\) | 10.2247 | 0.357718 | ||||||||
\(818\) | −8.21722 | −0.287309 | ||||||||
\(819\) | 12.9761 | 0.453421 | ||||||||
\(820\) | 0.0641978 | 0.00224188 | ||||||||
\(821\) | 0.984358 | 0.0343543 | 0.0171772 | − | 0.999852i | \(-0.494532\pi\) | ||||
0.0171772 | + | 0.999852i | \(0.494532\pi\) | |||||||
\(822\) | −30.1740 | −1.05244 | ||||||||
\(823\) | −11.9961 | −0.418157 | −0.209078 | − | 0.977899i | \(-0.567046\pi\) | ||||
−0.209078 | + | 0.977899i | \(0.567046\pi\) | |||||||
\(824\) | 11.1268 | 0.387622 | ||||||||
\(825\) | 32.3827 | 1.12742 | ||||||||
\(826\) | 17.4789 | 0.608168 | ||||||||
\(827\) | −17.9525 | −0.624270 | −0.312135 | − | 0.950038i | \(-0.601044\pi\) | ||||
−0.312135 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(828\) | −10.7924 | −0.375061 | ||||||||
\(829\) | 33.9311 | 1.17848 | 0.589239 | − | 0.807959i | \(-0.299428\pi\) | ||||
0.589239 | + | 0.807959i | \(0.299428\pi\) | |||||||
\(830\) | −5.56724 | −0.193242 | ||||||||
\(831\) | −55.3132 | −1.91879 | ||||||||
\(832\) | −5.88689 | −0.204091 | ||||||||
\(833\) | 11.7144 | 0.405880 | ||||||||
\(834\) | 11.2773 | 0.390501 | ||||||||
\(835\) | 68.2937 | 2.36340 | ||||||||
\(836\) | 5.50011 | 0.190225 | ||||||||
\(837\) | 11.0829 | 0.383079 | ||||||||
\(838\) | 26.8072 | 0.926039 | ||||||||
\(839\) | −20.1454 | −0.695496 | −0.347748 | − | 0.937588i | \(-0.613054\pi\) | ||||
−0.347748 | + | 0.937588i | \(0.613054\pi\) | |||||||
\(840\) | 7.99093 | 0.275713 | ||||||||
\(841\) | 22.4815 | 0.775224 | ||||||||
\(842\) | 29.2489 | 1.00798 | ||||||||
\(843\) | −3.64603 | −0.125576 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −60.2047 | −2.07110 | ||||||||
\(846\) | 1.75461 | 0.0603249 | ||||||||
\(847\) | −25.6483 | −0.881287 | ||||||||
\(848\) | 10.3892 | 0.356767 | ||||||||
\(849\) | −1.53861 | −0.0528051 | ||||||||
\(850\) | 6.11845 | 0.209861 | ||||||||
\(851\) | −0.00791575 | −0.000271348 0 | ||||||||
\(852\) | −6.37833 | −0.218518 | ||||||||
\(853\) | 9.31580 | 0.318967 | 0.159483 | − | 0.987201i | \(-0.449017\pi\) | ||||
0.159483 | + | 0.987201i | \(0.449017\pi\) | |||||||
\(854\) | 3.27644 | 0.112117 | ||||||||
\(855\) | 4.59959 | 0.157303 | ||||||||
\(856\) | −0.319302 | −0.0109135 | ||||||||
\(857\) | 13.1804 | 0.450233 | 0.225116 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225116 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(858\) | 69.8542 | 2.38478 | ||||||||
\(859\) | 15.0053 | 0.511975 | 0.255987 | − | 0.966680i | \(-0.417599\pi\) | ||||
0.255987 | + | 0.966680i | \(0.417599\pi\) | |||||||
\(860\) | 28.4259 | 0.969314 | ||||||||
\(861\) | −0.0663733 | −0.00226199 | ||||||||
\(862\) | −0.974703 | −0.0331985 | ||||||||
\(863\) | −47.7992 | −1.62710 | −0.813552 | − | 0.581493i | \(-0.802469\pi\) | ||||
−0.813552 | + | 0.581493i | \(0.802469\pi\) | |||||||
\(864\) | −2.90289 | −0.0987583 | ||||||||
\(865\) | −51.4328 | −1.74877 | ||||||||
\(866\) | 7.32945 | 0.249065 | ||||||||
\(867\) | 25.8318 | 0.877293 | ||||||||
\(868\) | −5.08653 | −0.172648 | ||||||||
\(869\) | −25.0224 | −0.848825 | ||||||||
\(870\) | −43.0351 | −1.45903 | ||||||||
\(871\) | −37.9689 | −1.28653 | ||||||||
\(872\) | 8.01354 | 0.271373 | ||||||||
\(873\) | 5.62407 | 0.190346 | ||||||||
\(874\) | −6.52318 | −0.220650 | ||||||||
\(875\) | −8.41155 | −0.284362 | ||||||||
\(876\) | 15.2343 | 0.514720 | ||||||||
\(877\) | −37.1911 | −1.25585 | −0.627927 | − | 0.778273i | \(-0.716096\pi\) | ||||
−0.627927 | + | 0.778273i | \(0.716096\pi\) | |||||||
\(878\) | 19.3320 | 0.652423 | ||||||||
\(879\) | −6.17376 | −0.208236 | ||||||||
\(880\) | 15.2909 | 0.515457 | ||||||||
\(881\) | 7.44719 | 0.250902 | 0.125451 | − | 0.992100i | \(-0.459962\pi\) | ||||
0.125451 | + | 0.992100i | \(0.459962\pi\) | |||||||
\(882\) | 8.64456 | 0.291077 | ||||||||
\(883\) | −15.0947 | −0.507976 | −0.253988 | − | 0.967207i | \(-0.581742\pi\) | ||||
−0.253988 | + | 0.967207i | \(0.581742\pi\) | |||||||
\(884\) | 13.1984 | 0.443910 | ||||||||
\(885\) | 78.6883 | 2.64508 | ||||||||
\(886\) | 30.3823 | 1.02071 | ||||||||
\(887\) | −6.63936 | −0.222928 | −0.111464 | − | 0.993768i | \(-0.535554\pi\) | ||||
−0.111464 | + | 0.993768i | \(0.535554\pi\) | |||||||
\(888\) | 0.00261799 | 8.78538e−5 0 | ||||||||
\(889\) | 21.1553 | 0.709526 | ||||||||
\(890\) | 28.4954 | 0.955168 | ||||||||
\(891\) | 61.7450 | 2.06854 | ||||||||
\(892\) | −2.73815 | −0.0916802 | ||||||||
\(893\) | 1.06053 | 0.0354894 | ||||||||
\(894\) | −27.4739 | −0.918864 | ||||||||
\(895\) | −59.1959 | −1.97870 | ||||||||
\(896\) | 1.33229 | 0.0445088 | ||||||||
\(897\) | −82.8477 | −2.76620 | ||||||||
\(898\) | −38.4172 | −1.28200 | ||||||||
\(899\) | 27.3935 | 0.913623 | ||||||||
\(900\) | 4.51506 | 0.150502 | ||||||||
\(901\) | −23.2926 | −0.775988 | ||||||||
\(902\) | −0.127008 | −0.00422889 | ||||||||
\(903\) | −29.3891 | −0.978009 | ||||||||
\(904\) | −7.93918 | −0.264053 | ||||||||
\(905\) | 47.7516 | 1.58732 | ||||||||
\(906\) | −33.0575 | −1.09826 | ||||||||
\(907\) | −7.26465 | −0.241219 | −0.120609 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120609 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(908\) | 11.9544 | 0.396720 | ||||||||
\(909\) | −7.61118 | −0.252447 | ||||||||
\(910\) | 21.8046 | 0.722816 | ||||||||
\(911\) | 24.7731 | 0.820770 | 0.410385 | − | 0.911912i | \(-0.365394\pi\) | ||||
0.410385 | + | 0.911912i | \(0.365394\pi\) | |||||||
\(912\) | 2.15742 | 0.0714393 | ||||||||
\(913\) | 11.0141 | 0.364514 | ||||||||
\(914\) | 1.48137 | 0.0489995 | ||||||||
\(915\) | 14.7502 | 0.487627 | ||||||||
\(916\) | 23.1719 | 0.765620 | ||||||||
\(917\) | −15.7626 | −0.520527 | ||||||||
\(918\) | 6.50827 | 0.214805 | ||||||||
\(919\) | −21.0392 | −0.694019 | −0.347009 | − | 0.937862i | \(-0.612803\pi\) | ||||
−0.347009 | + | 0.937862i | \(0.612803\pi\) | |||||||
\(920\) | −18.1352 | −0.597899 | ||||||||
\(921\) | 3.44225 | 0.113426 | ||||||||
\(922\) | 38.6136 | 1.27167 | ||||||||
\(923\) | −17.4044 | −0.572872 | ||||||||
\(924\) | −15.8091 | −0.520081 | ||||||||
\(925\) | 0.00331161 | 0.000108885 0 | ||||||||
\(926\) | 4.78767 | 0.157333 | ||||||||
\(927\) | −18.4089 | −0.604629 | ||||||||
\(928\) | −7.17506 | −0.235533 | ||||||||
\(929\) | −0.464932 | −0.0152539 | −0.00762697 | − | 0.999971i | \(-0.502428\pi\) | ||||
−0.00762697 | + | 0.999971i | \(0.502428\pi\) | |||||||
\(930\) | −22.8991 | −0.750891 | ||||||||
\(931\) | 5.22499 | 0.171242 | ||||||||
\(932\) | 0.0624516 | 0.00204567 | ||||||||
\(933\) | 33.3457 | 1.09169 | ||||||||
\(934\) | 16.0814 | 0.526198 | ||||||||
\(935\) | −34.2822 | −1.12115 | ||||||||
\(936\) | 9.73965 | 0.318350 | ||||||||
\(937\) | 39.4858 | 1.28995 | 0.644973 | − | 0.764206i | \(-0.276869\pi\) | ||||
0.644973 | + | 0.764206i | \(0.276869\pi\) | |||||||
\(938\) | 8.59294 | 0.280569 | ||||||||
\(939\) | 43.9115 | 1.43300 | ||||||||
\(940\) | 2.94840 | 0.0961663 | ||||||||
\(941\) | 49.5049 | 1.61381 | 0.806907 | − | 0.590678i | \(-0.201140\pi\) | ||||
0.806907 | + | 0.590678i | \(0.201140\pi\) | |||||||
\(942\) | 20.2043 | 0.658292 | ||||||||
\(943\) | 0.150632 | 0.00490526 | ||||||||
\(944\) | 13.1194 | 0.426999 | ||||||||
\(945\) | 10.7521 | 0.349765 | ||||||||
\(946\) | −56.2371 | −1.82843 | ||||||||
\(947\) | −49.1586 | −1.59744 | −0.798720 | − | 0.601703i | \(-0.794489\pi\) | ||||
−0.798720 | + | 0.601703i | \(0.794489\pi\) | |||||||
\(948\) | −9.81503 | −0.318777 | ||||||||
\(949\) | 41.5695 | 1.34940 | ||||||||
\(950\) | 2.72902 | 0.0885410 | ||||||||
\(951\) | −33.0812 | −1.07273 | ||||||||
\(952\) | −2.98700 | −0.0968092 | ||||||||
\(953\) | 12.7431 | 0.412791 | 0.206395 | − | 0.978469i | \(-0.433827\pi\) | ||||
0.206395 | + | 0.978469i | \(0.433827\pi\) | |||||||
\(954\) | −17.1886 | −0.556500 | ||||||||
\(955\) | −23.0995 | −0.747484 | ||||||||
\(956\) | 4.02893 | 0.130305 | ||||||||
\(957\) | 85.1397 | 2.75217 | ||||||||
\(958\) | −5.35999 | −0.173174 | ||||||||
\(959\) | 18.6337 | 0.601713 | ||||||||
\(960\) | 5.99787 | 0.193580 | ||||||||
\(961\) | −16.4239 | −0.529802 | ||||||||
\(962\) | 0.00714362 | 0.000230320 0 | ||||||||
\(963\) | 0.528274 | 0.0170234 | ||||||||
\(964\) | −15.1865 | −0.489123 | ||||||||
\(965\) | −70.6418 | −2.27404 | ||||||||
\(966\) | 18.7497 | 0.603262 | ||||||||
\(967\) | −39.0003 | −1.25417 | −0.627083 | − | 0.778953i | \(-0.715751\pi\) | ||||
−0.627083 | + | 0.778953i | \(0.715751\pi\) | |||||||
\(968\) | −19.2512 | −0.618758 | ||||||||
\(969\) | −4.83693 | −0.155385 | ||||||||
\(970\) | 9.45052 | 0.303438 | ||||||||
\(971\) | −6.69225 | −0.214764 | −0.107382 | − | 0.994218i | \(-0.534247\pi\) | ||||
−0.107382 | + | 0.994218i | \(0.534247\pi\) | |||||||
\(972\) | 15.5108 | 0.497511 | ||||||||
\(973\) | −6.96419 | −0.223262 | ||||||||
\(974\) | 1.50511 | 0.0482267 | ||||||||
\(975\) | 34.6599 | 1.11001 | ||||||||
\(976\) | 2.45924 | 0.0787185 | ||||||||
\(977\) | 35.5370 | 1.13693 | 0.568465 | − | 0.822707i | \(-0.307537\pi\) | ||||
0.568465 | + | 0.822707i | \(0.307537\pi\) | |||||||
\(978\) | −22.8653 | −0.731153 | ||||||||
\(979\) | −56.3747 | −1.80174 | ||||||||
\(980\) | 14.5261 | 0.464018 | ||||||||
\(981\) | −13.2581 | −0.423299 | ||||||||
\(982\) | −10.0401 | −0.320392 | ||||||||
\(983\) | −21.5663 | −0.687857 | −0.343928 | − | 0.938996i | \(-0.611758\pi\) | ||||
−0.343928 | + | 0.938996i | \(0.611758\pi\) | |||||||
\(984\) | −0.0498188 | −0.00158816 | ||||||||
\(985\) | −4.60295 | −0.146662 | ||||||||
\(986\) | 16.0865 | 0.512297 | ||||||||
\(987\) | −3.04831 | −0.0970289 | ||||||||
\(988\) | 5.88689 | 0.187287 | ||||||||
\(989\) | 66.6977 | 2.12086 | ||||||||
\(990\) | −25.2983 | −0.804032 | ||||||||
\(991\) | 23.0864 | 0.733365 | 0.366682 | − | 0.930346i | \(-0.380494\pi\) | ||||
0.366682 | + | 0.930346i | \(0.380494\pi\) | |||||||
\(992\) | −3.81787 | −0.121218 | ||||||||
\(993\) | −41.2567 | −1.30924 | ||||||||
\(994\) | 3.93888 | 0.124934 | ||||||||
\(995\) | 37.4557 | 1.18743 | ||||||||
\(996\) | 4.32029 | 0.136894 | ||||||||
\(997\) | −43.6392 | −1.38207 | −0.691034 | − | 0.722823i | \(-0.742844\pi\) | ||||
−0.691034 | + | 0.722823i | \(0.742844\pi\) | |||||||
\(998\) | −15.9373 | −0.504488 | ||||||||
\(999\) | 0.00352260 | 0.000111450 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.f.1.8 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.8 | ✓ | 34 | 1.1 | even | 1 | trivial |