Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.131407\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.131407 | −0.0929185 | −0.0464592 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464592 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(3\) | 1.32082 | 0.762575 | 0.381288 | − | 0.924456i | \(-0.375481\pi\) | ||||
0.381288 | + | 0.924456i | \(0.375481\pi\) | |||||||
\(4\) | −1.98273 | −0.991366 | ||||||||
\(5\) | 1.78074 | 0.796369 | 0.398185 | − | 0.917305i | \(-0.369640\pi\) | ||||
0.398185 | + | 0.917305i | \(0.369640\pi\) | |||||||
\(6\) | −0.173564 | −0.0708573 | ||||||||
\(7\) | 0.0149856 | 0.00566403 | 0.00283201 | − | 0.999996i | \(-0.499099\pi\) | ||||
0.00283201 | + | 0.999996i | \(0.499099\pi\) | |||||||
\(8\) | 0.523357 | 0.185035 | ||||||||
\(9\) | −1.25544 | −0.418479 | ||||||||
\(10\) | −0.234000 | −0.0739974 | ||||||||
\(11\) | −2.07972 | −0.627061 | −0.313530 | − | 0.949578i | \(-0.601512\pi\) | ||||
−0.313530 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(12\) | −2.61883 | −0.755991 | ||||||||
\(13\) | −1.62441 | −0.450531 | −0.225265 | − | 0.974297i | \(-0.572325\pi\) | ||||
−0.225265 | + | 0.974297i | \(0.572325\pi\) | |||||||
\(14\) | −0.00196921 | −0.000526293 0 | ||||||||
\(15\) | 2.35203 | 0.607292 | ||||||||
\(16\) | 3.89669 | 0.974173 | ||||||||
\(17\) | −6.03444 | −1.46357 | −0.731783 | − | 0.681537i | \(-0.761312\pi\) | ||||
−0.731783 | + | 0.681537i | \(0.761312\pi\) | |||||||
\(18\) | 0.164973 | 0.0388844 | ||||||||
\(19\) | 7.62293 | 1.74882 | 0.874410 | − | 0.485188i | \(-0.161249\pi\) | ||||
0.874410 | + | 0.485188i | \(0.161249\pi\) | |||||||
\(20\) | −3.53072 | −0.789494 | ||||||||
\(21\) | 0.0197933 | 0.00431925 | ||||||||
\(22\) | 0.273289 | 0.0582655 | ||||||||
\(23\) | −5.30206 | −1.10556 | −0.552778 | − | 0.833329i | \(-0.686432\pi\) | ||||
−0.552778 | + | 0.833329i | \(0.686432\pi\) | |||||||
\(24\) | 0.691260 | 0.141103 | ||||||||
\(25\) | −1.82898 | −0.365796 | ||||||||
\(26\) | 0.213458 | 0.0418626 | ||||||||
\(27\) | −5.62066 | −1.08170 | ||||||||
\(28\) | −0.0297125 | −0.00561513 | ||||||||
\(29\) | −7.17687 | −1.33271 | −0.666356 | − | 0.745634i | \(-0.732147\pi\) | ||||
−0.666356 | + | 0.745634i | \(0.732147\pi\) | |||||||
\(30\) | −0.309072 | −0.0564286 | ||||||||
\(31\) | 2.38527 | 0.428407 | 0.214203 | − | 0.976789i | \(-0.431284\pi\) | ||||
0.214203 | + | 0.976789i | \(0.431284\pi\) | |||||||
\(32\) | −1.55877 | −0.275553 | ||||||||
\(33\) | −2.74694 | −0.478181 | ||||||||
\(34\) | 0.792965 | 0.135992 | ||||||||
\(35\) | 0.0266854 | 0.00451066 | ||||||||
\(36\) | 2.48919 | 0.414866 | ||||||||
\(37\) | 5.04085 | 0.828711 | 0.414356 | − | 0.910115i | \(-0.364007\pi\) | ||||
0.414356 | + | 0.910115i | \(0.364007\pi\) | |||||||
\(38\) | −1.00170 | −0.162498 | ||||||||
\(39\) | −2.14555 | −0.343563 | ||||||||
\(40\) | 0.931961 | 0.147356 | ||||||||
\(41\) | 3.55296 | 0.554879 | 0.277439 | − | 0.960743i | \(-0.410514\pi\) | ||||
0.277439 | + | 0.960743i | \(0.410514\pi\) | |||||||
\(42\) | −0.00260097 | −0.000401338 0 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 4.12354 | 0.621647 | ||||||||
\(45\) | −2.23560 | −0.333264 | ||||||||
\(46\) | 0.696725 | 0.102727 | ||||||||
\(47\) | −10.0228 | −1.46198 | −0.730988 | − | 0.682390i | \(-0.760940\pi\) | ||||
−0.730988 | + | 0.682390i | \(0.760940\pi\) | |||||||
\(48\) | 5.14683 | 0.742880 | ||||||||
\(49\) | −6.99978 | −0.999968 | ||||||||
\(50\) | 0.240340 | 0.0339892 | ||||||||
\(51\) | −7.97041 | −1.11608 | ||||||||
\(52\) | 3.22077 | 0.446641 | ||||||||
\(53\) | −6.85699 | −0.941881 | −0.470940 | − | 0.882165i | \(-0.656085\pi\) | ||||
−0.470940 | + | 0.882165i | \(0.656085\pi\) | |||||||
\(54\) | 0.738592 | 0.100510 | ||||||||
\(55\) | −3.70344 | −0.499372 | ||||||||
\(56\) | 0.00784283 | 0.00104804 | ||||||||
\(57\) | 10.0685 | 1.33361 | ||||||||
\(58\) | 0.943088 | 0.123833 | ||||||||
\(59\) | −1.66670 | −0.216986 | −0.108493 | − | 0.994097i | \(-0.534602\pi\) | ||||
−0.108493 | + | 0.994097i | \(0.534602\pi\) | |||||||
\(60\) | −4.66345 | −0.602048 | ||||||||
\(61\) | −6.05120 | −0.774777 | −0.387389 | − | 0.921916i | \(-0.626623\pi\) | ||||
−0.387389 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(62\) | −0.313440 | −0.0398069 | ||||||||
\(63\) | −0.0188135 | −0.00237028 | ||||||||
\(64\) | −7.58855 | −0.948569 | ||||||||
\(65\) | −2.89265 | −0.358789 | ||||||||
\(66\) | 0.360966 | 0.0444318 | ||||||||
\(67\) | 1.43303 | 0.175073 | 0.0875363 | − | 0.996161i | \(-0.472101\pi\) | ||||
0.0875363 | + | 0.996161i | \(0.472101\pi\) | |||||||
\(68\) | 11.9647 | 1.45093 | ||||||||
\(69\) | −7.00306 | −0.843070 | ||||||||
\(70\) | −0.00350664 | −0.000419124 0 | ||||||||
\(71\) | −7.04548 | −0.836144 | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418072 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(72\) | −0.657042 | −0.0774331 | ||||||||
\(73\) | 9.76187 | 1.14254 | 0.571270 | − | 0.820762i | \(-0.306451\pi\) | ||||
0.571270 | + | 0.820762i | \(0.306451\pi\) | |||||||
\(74\) | −0.662401 | −0.0770026 | ||||||||
\(75\) | −2.41575 | −0.278947 | ||||||||
\(76\) | −15.1142 | −1.73372 | ||||||||
\(77\) | −0.0311659 | −0.00355169 | ||||||||
\(78\) | 0.281940 | 0.0319234 | ||||||||
\(79\) | 12.0115 | 1.35139 | 0.675697 | − | 0.737179i | \(-0.263843\pi\) | ||||
0.675697 | + | 0.737179i | \(0.263843\pi\) | |||||||
\(80\) | 6.93898 | 0.775802 | ||||||||
\(81\) | −3.65757 | −0.406397 | ||||||||
\(82\) | −0.466882 | −0.0515585 | ||||||||
\(83\) | 9.06798 | 0.995340 | 0.497670 | − | 0.867366i | \(-0.334189\pi\) | ||||
0.497670 | + | 0.867366i | \(0.334189\pi\) | |||||||
\(84\) | −0.0392448 | −0.00428196 | ||||||||
\(85\) | −10.7457 | −1.16554 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.47935 | −1.01629 | ||||||||
\(88\) | −1.08844 | −0.116028 | ||||||||
\(89\) | −15.9043 | −1.68585 | −0.842925 | − | 0.538031i | \(-0.819168\pi\) | ||||
−0.842925 | + | 0.538031i | \(0.819168\pi\) | |||||||
\(90\) | 0.293773 | 0.0309664 | ||||||||
\(91\) | −0.0243428 | −0.00255182 | ||||||||
\(92\) | 10.5126 | 1.09601 | ||||||||
\(93\) | 3.15051 | 0.326692 | ||||||||
\(94\) | 1.31706 | 0.135845 | ||||||||
\(95\) | 13.5744 | 1.39271 | ||||||||
\(96\) | −2.05885 | −0.210130 | ||||||||
\(97\) | 13.5487 | 1.37566 | 0.687832 | − | 0.725870i | \(-0.258563\pi\) | ||||
0.687832 | + | 0.725870i | \(0.258563\pi\) | |||||||
\(98\) | 0.919817 | 0.0929155 | ||||||||
\(99\) | 2.61096 | 0.262412 | ||||||||
\(100\) | 3.62637 | 0.362637 | ||||||||
\(101\) | 3.12321 | 0.310771 | 0.155385 | − | 0.987854i | \(-0.450338\pi\) | ||||
0.155385 | + | 0.987854i | \(0.450338\pi\) | |||||||
\(102\) | 1.04736 | 0.103704 | ||||||||
\(103\) | −0.527236 | −0.0519501 | −0.0259751 | − | 0.999663i | \(-0.508269\pi\) | ||||
−0.0259751 | + | 0.999663i | \(0.508269\pi\) | |||||||
\(104\) | −0.850147 | −0.0833638 | ||||||||
\(105\) | 0.0352466 | 0.00343972 | ||||||||
\(106\) | 0.901054 | 0.0875181 | ||||||||
\(107\) | 1.13567 | 0.109789 | 0.0548945 | − | 0.998492i | \(-0.482518\pi\) | ||||
0.0548945 | + | 0.998492i | \(0.482518\pi\) | |||||||
\(108\) | 11.1443 | 1.07236 | ||||||||
\(109\) | −12.2005 | −1.16859 | −0.584297 | − | 0.811540i | \(-0.698630\pi\) | ||||
−0.584297 | + | 0.811540i | \(0.698630\pi\) | |||||||
\(110\) | 0.486657 | 0.0464009 | ||||||||
\(111\) | 6.65806 | 0.631955 | ||||||||
\(112\) | 0.0583943 | 0.00551774 | ||||||||
\(113\) | −4.40928 | −0.414790 | −0.207395 | − | 0.978257i | \(-0.566499\pi\) | ||||
−0.207395 | + | 0.978257i | \(0.566499\pi\) | |||||||
\(114\) | −1.32307 | −0.123917 | ||||||||
\(115\) | −9.44157 | −0.880431 | ||||||||
\(116\) | 14.2298 | 1.32120 | ||||||||
\(117\) | 2.03934 | 0.188538 | ||||||||
\(118\) | 0.219015 | 0.0201620 | ||||||||
\(119\) | −0.0904298 | −0.00828968 | ||||||||
\(120\) | 1.23095 | 0.112370 | ||||||||
\(121\) | −6.67475 | −0.606795 | ||||||||
\(122\) | 0.795168 | 0.0719911 | ||||||||
\(123\) | 4.69281 | 0.423137 | ||||||||
\(124\) | −4.72935 | −0.424708 | ||||||||
\(125\) | −12.1606 | −1.08768 | ||||||||
\(126\) | 0.00247222 | 0.000220242 0 | ||||||||
\(127\) | −9.00820 | −0.799348 | −0.399674 | − | 0.916657i | \(-0.630877\pi\) | ||||
−0.399674 | + | 0.916657i | \(0.630877\pi\) | |||||||
\(128\) | 4.11472 | 0.363693 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.380113 | 0.0333381 | ||||||||
\(131\) | −4.56448 | −0.398801 | −0.199400 | − | 0.979918i | \(-0.563899\pi\) | ||||
−0.199400 | + | 0.979918i | \(0.563899\pi\) | |||||||
\(132\) | 5.44645 | 0.474052 | ||||||||
\(133\) | 0.114234 | 0.00990537 | ||||||||
\(134\) | −0.188310 | −0.0162675 | ||||||||
\(135\) | −10.0089 | −0.861430 | ||||||||
\(136\) | −3.15817 | −0.270811 | ||||||||
\(137\) | −15.5552 | −1.32897 | −0.664484 | − | 0.747302i | \(-0.731349\pi\) | ||||
−0.664484 | + | 0.747302i | \(0.731349\pi\) | |||||||
\(138\) | 0.920248 | 0.0783367 | ||||||||
\(139\) | −6.85934 | −0.581802 | −0.290901 | − | 0.956753i | \(-0.593955\pi\) | ||||
−0.290901 | + | 0.956753i | \(0.593955\pi\) | |||||||
\(140\) | −0.0529101 | −0.00447172 | ||||||||
\(141\) | −13.2383 | −1.11487 | ||||||||
\(142\) | 0.925822 | 0.0776933 | ||||||||
\(143\) | 3.37833 | 0.282510 | ||||||||
\(144\) | −4.89205 | −0.407671 | ||||||||
\(145\) | −12.7801 | −1.06133 | ||||||||
\(146\) | −1.28277 | −0.106163 | ||||||||
\(147\) | −9.24544 | −0.762551 | ||||||||
\(148\) | −9.99466 | −0.821556 | ||||||||
\(149\) | 20.6396 | 1.69087 | 0.845433 | − | 0.534082i | \(-0.179343\pi\) | ||||
0.845433 | + | 0.534082i | \(0.179343\pi\) | |||||||
\(150\) | 0.317445 | 0.0259193 | ||||||||
\(151\) | −3.87910 | −0.315676 | −0.157838 | − | 0.987465i | \(-0.550452\pi\) | ||||
−0.157838 | + | 0.987465i | \(0.550452\pi\) | |||||||
\(152\) | 3.98951 | 0.323592 | ||||||||
\(153\) | 7.57586 | 0.612472 | ||||||||
\(154\) | 0.00409541 | 0.000330018 0 | ||||||||
\(155\) | 4.24753 | 0.341170 | ||||||||
\(156\) | 4.25406 | 0.340597 | ||||||||
\(157\) | 1.37891 | 0.110049 | 0.0550244 | − | 0.998485i | \(-0.482476\pi\) | ||||
0.0550244 | + | 0.998485i | \(0.482476\pi\) | |||||||
\(158\) | −1.57838 | −0.125570 | ||||||||
\(159\) | −9.05685 | −0.718255 | ||||||||
\(160\) | −2.77575 | −0.219442 | ||||||||
\(161\) | −0.0794546 | −0.00626190 | ||||||||
\(162\) | 0.480629 | 0.0377618 | ||||||||
\(163\) | −3.27038 | −0.256156 | −0.128078 | − | 0.991764i | \(-0.540881\pi\) | ||||
−0.128078 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(164\) | −7.04456 | −0.550088 | ||||||||
\(165\) | −4.89158 | −0.380809 | ||||||||
\(166\) | −1.19159 | −0.0924855 | ||||||||
\(167\) | 3.47025 | 0.268536 | 0.134268 | − | 0.990945i | \(-0.457132\pi\) | ||||
0.134268 | + | 0.990945i | \(0.457132\pi\) | |||||||
\(168\) | 0.0103590 | 0.000799211 0 | ||||||||
\(169\) | −10.3613 | −0.797022 | ||||||||
\(170\) | 1.41206 | 0.108300 | ||||||||
\(171\) | −9.57010 | −0.731844 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9268 | 1.28692 | 0.643459 | − | 0.765480i | \(-0.277499\pi\) | ||||
0.643459 | + | 0.765480i | \(0.277499\pi\) | |||||||
\(174\) | 1.24565 | 0.0944324 | ||||||||
\(175\) | −0.0274084 | −0.00207188 | ||||||||
\(176\) | −8.10405 | −0.610865 | ||||||||
\(177\) | −2.20141 | −0.165468 | ||||||||
\(178\) | 2.08993 | 0.156647 | ||||||||
\(179\) | 9.43773 | 0.705409 | 0.352705 | − | 0.935735i | \(-0.385262\pi\) | ||||
0.352705 | + | 0.935735i | \(0.385262\pi\) | |||||||
\(180\) | 4.43260 | 0.330386 | ||||||||
\(181\) | −7.36950 | −0.547771 | −0.273885 | − | 0.961762i | \(-0.588309\pi\) | ||||
−0.273885 | + | 0.961762i | \(0.588309\pi\) | |||||||
\(182\) | 0.00319880 | 0.000237111 0 | ||||||||
\(183\) | −7.99255 | −0.590826 | ||||||||
\(184\) | −2.77487 | −0.204566 | ||||||||
\(185\) | 8.97643 | 0.659960 | ||||||||
\(186\) | −0.413997 | −0.0303558 | ||||||||
\(187\) | 12.5500 | 0.917745 | ||||||||
\(188\) | 19.8725 | 1.44935 | ||||||||
\(189\) | −0.0842291 | −0.00612676 | ||||||||
\(190\) | −1.78377 | −0.129408 | ||||||||
\(191\) | 19.3203 | 1.39797 | 0.698983 | − | 0.715138i | \(-0.253636\pi\) | ||||
0.698983 | + | 0.715138i | \(0.253636\pi\) | |||||||
\(192\) | −10.0231 | −0.723355 | ||||||||
\(193\) | 2.11851 | 0.152493 | 0.0762467 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762467 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(194\) | −1.78039 | −0.127825 | ||||||||
\(195\) | −3.82066 | −0.273603 | ||||||||
\(196\) | 13.8787 | 0.991334 | ||||||||
\(197\) | −18.5821 | −1.32392 | −0.661960 | − | 0.749539i | \(-0.730275\pi\) | ||||
−0.661960 | + | 0.749539i | \(0.730275\pi\) | |||||||
\(198\) | −0.343098 | −0.0243829 | ||||||||
\(199\) | −7.88855 | −0.559204 | −0.279602 | − | 0.960116i | \(-0.590203\pi\) | ||||
−0.279602 | + | 0.960116i | \(0.590203\pi\) | |||||||
\(200\) | −0.957209 | −0.0676849 | ||||||||
\(201\) | 1.89277 | 0.133506 | ||||||||
\(202\) | −0.410410 | −0.0288764 | ||||||||
\(203\) | −0.107550 | −0.00754851 | ||||||||
\(204\) | 15.8032 | 1.10644 | ||||||||
\(205\) | 6.32688 | 0.441888 | ||||||||
\(206\) | 0.0692823 | 0.00482713 | ||||||||
\(207\) | 6.65640 | 0.462652 | ||||||||
\(208\) | −6.32983 | −0.438895 | ||||||||
\(209\) | −15.8536 | −1.09662 | ||||||||
\(210\) | −0.00463164 | −0.000319613 0 | ||||||||
\(211\) | 8.05765 | 0.554711 | 0.277356 | − | 0.960767i | \(-0.410542\pi\) | ||||
0.277356 | + | 0.960767i | \(0.410542\pi\) | |||||||
\(212\) | 13.5956 | 0.933749 | ||||||||
\(213\) | −9.30580 | −0.637623 | ||||||||
\(214\) | −0.149234 | −0.0102014 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.94161 | −0.200151 | ||||||||
\(217\) | 0.0357447 | 0.00242651 | ||||||||
\(218\) | 1.60322 | 0.108584 | ||||||||
\(219\) | 12.8937 | 0.871273 | ||||||||
\(220\) | 7.34293 | 0.495060 | ||||||||
\(221\) | 9.80241 | 0.659382 | ||||||||
\(222\) | −0.874912 | −0.0587203 | ||||||||
\(223\) | 20.3361 | 1.36180 | 0.680902 | − | 0.732374i | \(-0.261588\pi\) | ||||
0.680902 | + | 0.732374i | \(0.261588\pi\) | |||||||
\(224\) | −0.0233591 | −0.00156074 | ||||||||
\(225\) | 2.29617 | 0.153078 | ||||||||
\(226\) | 0.579408 | 0.0385416 | ||||||||
\(227\) | 5.13351 | 0.340723 | 0.170361 | − | 0.985382i | \(-0.445506\pi\) | ||||
0.170361 | + | 0.985382i | \(0.445506\pi\) | |||||||
\(228\) | −19.9632 | −1.32209 | ||||||||
\(229\) | −2.86288 | −0.189185 | −0.0945923 | − | 0.995516i | \(-0.530155\pi\) | ||||
−0.0945923 | + | 0.995516i | \(0.530155\pi\) | |||||||
\(230\) | 1.24068 | 0.0818083 | ||||||||
\(231\) | −0.0411646 | −0.00270843 | ||||||||
\(232\) | −3.75607 | −0.246598 | ||||||||
\(233\) | 12.4178 | 0.813518 | 0.406759 | − | 0.913535i | \(-0.366659\pi\) | ||||
0.406759 | + | 0.913535i | \(0.366659\pi\) | |||||||
\(234\) | −0.267983 | −0.0175186 | ||||||||
\(235\) | −17.8480 | −1.16427 | ||||||||
\(236\) | 3.30461 | 0.215112 | ||||||||
\(237\) | 15.8650 | 1.03054 | ||||||||
\(238\) | 0.0118831 | 0.000770265 0 | ||||||||
\(239\) | −23.2734 | −1.50543 | −0.752716 | − | 0.658345i | \(-0.771257\pi\) | ||||
−0.752716 | + | 0.658345i | \(0.771257\pi\) | |||||||
\(240\) | 9.16514 | 0.591607 | ||||||||
\(241\) | 3.51552 | 0.226455 | 0.113227 | − | 0.993569i | \(-0.463881\pi\) | ||||
0.113227 | + | 0.993569i | \(0.463881\pi\) | |||||||
\(242\) | 0.877105 | 0.0563825 | ||||||||
\(243\) | 12.0310 | 0.771789 | ||||||||
\(244\) | 11.9979 | 0.768088 | ||||||||
\(245\) | −12.4648 | −0.796344 | ||||||||
\(246\) | −0.616667 | −0.0393172 | ||||||||
\(247\) | −12.3828 | −0.787897 | ||||||||
\(248\) | 1.24835 | 0.0792701 | ||||||||
\(249\) | 11.9772 | 0.759022 | ||||||||
\(250\) | 1.59798 | 0.101065 | ||||||||
\(251\) | −13.8483 | −0.874097 | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(252\) | 0.0373021 | 0.00234981 | ||||||||
\(253\) | 11.0268 | 0.693250 | ||||||||
\(254\) | 1.18374 | 0.0742742 | ||||||||
\(255\) | −14.1932 | −0.888812 | ||||||||
\(256\) | 14.6364 | 0.914775 | ||||||||
\(257\) | 24.5832 | 1.53346 | 0.766728 | − | 0.641972i | \(-0.221883\pi\) | ||||
0.766728 | + | 0.641972i | \(0.221883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0755403 | 0.00469384 | ||||||||
\(260\) | 5.73535 | 0.355691 | ||||||||
\(261\) | 9.01010 | 0.557711 | ||||||||
\(262\) | 0.599803 | 0.0370560 | ||||||||
\(263\) | −7.08052 | −0.436603 | −0.218302 | − | 0.975881i | \(-0.570052\pi\) | ||||
−0.218302 | + | 0.975881i | \(0.570052\pi\) | |||||||
\(264\) | −1.43763 | −0.0884801 | ||||||||
\(265\) | −12.2105 | −0.750085 | ||||||||
\(266\) | −0.0150111 | −0.000920392 0 | ||||||||
\(267\) | −21.0067 | −1.28559 | ||||||||
\(268\) | −2.84132 | −0.173561 | ||||||||
\(269\) | −9.15068 | −0.557927 | −0.278963 | − | 0.960302i | \(-0.589991\pi\) | ||||
−0.278963 | + | 0.960302i | \(0.589991\pi\) | |||||||
\(270\) | 1.31524 | 0.0800428 | ||||||||
\(271\) | 3.31695 | 0.201490 | 0.100745 | − | 0.994912i | \(-0.467877\pi\) | ||||
0.100745 | + | 0.994912i | \(0.467877\pi\) | |||||||
\(272\) | −23.5144 | −1.42577 | ||||||||
\(273\) | −0.0321524 | −0.00194595 | ||||||||
\(274\) | 2.04405 | 0.123486 | ||||||||
\(275\) | 3.80377 | 0.229376 | ||||||||
\(276\) | 13.8852 | 0.835791 | ||||||||
\(277\) | −1.91138 | −0.114844 | −0.0574218 | − | 0.998350i | \(-0.518288\pi\) | ||||
−0.0574218 | + | 0.998350i | \(0.518288\pi\) | |||||||
\(278\) | 0.901363 | 0.0540602 | ||||||||
\(279\) | −2.99455 | −0.179279 | ||||||||
\(280\) | 0.0139660 | 0.000834629 0 | ||||||||
\(281\) | 19.7462 | 1.17796 | 0.588981 | − | 0.808147i | \(-0.299529\pi\) | ||||
0.588981 | + | 0.808147i | \(0.299529\pi\) | |||||||
\(282\) | 1.73960 | 0.103592 | ||||||||
\(283\) | −17.5592 | −1.04378 | −0.521892 | − | 0.853012i | \(-0.674773\pi\) | ||||
−0.521892 | + | 0.853012i | \(0.674773\pi\) | |||||||
\(284\) | 13.9693 | 0.828925 | ||||||||
\(285\) | 17.9294 | 1.06204 | ||||||||
\(286\) | −0.443934 | −0.0262504 | ||||||||
\(287\) | 0.0532432 | 0.00314285 | ||||||||
\(288\) | 1.95693 | 0.115313 | ||||||||
\(289\) | 19.4145 | 1.14203 | ||||||||
\(290\) | 1.67939 | 0.0986172 | ||||||||
\(291\) | 17.8954 | 1.04905 | ||||||||
\(292\) | −19.3552 | −1.13268 | ||||||||
\(293\) | 5.75228 | 0.336052 | 0.168026 | − | 0.985783i | \(-0.446261\pi\) | ||||
0.168026 | + | 0.985783i | \(0.446261\pi\) | |||||||
\(294\) | 1.21491 | 0.0708551 | ||||||||
\(295\) | −2.96795 | −0.172801 | ||||||||
\(296\) | 2.63817 | 0.153340 | ||||||||
\(297\) | 11.6894 | 0.678290 | ||||||||
\(298\) | −2.71218 | −0.157113 | ||||||||
\(299\) | 8.61272 | 0.498087 | ||||||||
\(300\) | 4.78978 | 0.276538 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.509739 | 0.0293322 | ||||||||
\(303\) | 4.12519 | 0.236986 | ||||||||
\(304\) | 29.7042 | 1.70365 | ||||||||
\(305\) | −10.7756 | −0.617009 | ||||||||
\(306\) | −0.995517 | −0.0569099 | ||||||||
\(307\) | −15.2358 | −0.869552 | −0.434776 | − | 0.900539i | \(-0.643172\pi\) | ||||
−0.434776 | + | 0.900539i | \(0.643172\pi\) | |||||||
\(308\) | 0.0617937 | 0.00352102 | ||||||||
\(309\) | −0.696384 | −0.0396159 | ||||||||
\(310\) | −0.558154 | −0.0317010 | ||||||||
\(311\) | 32.8205 | 1.86108 | 0.930541 | − | 0.366189i | \(-0.119338\pi\) | ||||
0.930541 | + | 0.366189i | \(0.119338\pi\) | |||||||
\(312\) | −1.12289 | −0.0635712 | ||||||||
\(313\) | 19.4958 | 1.10197 | 0.550984 | − | 0.834516i | \(-0.314252\pi\) | ||||
0.550984 | + | 0.834516i | \(0.314252\pi\) | |||||||
\(314\) | −0.181197 | −0.0102256 | ||||||||
\(315\) | −0.0335019 | −0.00188762 | ||||||||
\(316\) | −23.8155 | −1.33973 | ||||||||
\(317\) | −16.8983 | −0.949102 | −0.474551 | − | 0.880228i | \(-0.657390\pi\) | ||||
−0.474551 | + | 0.880228i | \(0.657390\pi\) | |||||||
\(318\) | 1.19013 | 0.0667392 | ||||||||
\(319\) | 14.9259 | 0.835691 | ||||||||
\(320\) | −13.5132 | −0.755411 | ||||||||
\(321\) | 1.50001 | 0.0837223 | ||||||||
\(322\) | 0.0104409 | 0.000581846 0 | ||||||||
\(323\) | −46.0001 | −2.55951 | ||||||||
\(324\) | 7.25198 | 0.402888 | ||||||||
\(325\) | 2.97101 | 0.164802 | ||||||||
\(326\) | 0.429749 | 0.0238016 | ||||||||
\(327\) | −16.1146 | −0.891141 | ||||||||
\(328\) | 1.85947 | 0.102672 | ||||||||
\(329\) | −0.150198 | −0.00828067 | ||||||||
\(330\) | 0.642785 | 0.0353842 | ||||||||
\(331\) | −28.7420 | −1.57980 | −0.789901 | − | 0.613235i | \(-0.789868\pi\) | ||||
−0.789901 | + | 0.613235i | \(0.789868\pi\) | |||||||
\(332\) | −17.9794 | −0.986746 | ||||||||
\(333\) | −6.32847 | −0.346798 | ||||||||
\(334\) | −0.456013 | −0.0249519 | ||||||||
\(335\) | 2.55185 | 0.139422 | ||||||||
\(336\) | 0.0771283 | 0.00420770 | ||||||||
\(337\) | 17.0393 | 0.928190 | 0.464095 | − | 0.885786i | \(-0.346380\pi\) | ||||
0.464095 | + | 0.885786i | \(0.346380\pi\) | |||||||
\(338\) | 1.36154 | 0.0740581 | ||||||||
\(339\) | −5.82386 | −0.316309 | ||||||||
\(340\) | 21.3059 | 1.15548 | ||||||||
\(341\) | −4.96070 | −0.268637 | ||||||||
\(342\) | 1.25757 | 0.0680018 | ||||||||
\(343\) | −0.209795 | −0.0113279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.4706 | −0.671395 | ||||||||
\(346\) | −2.22429 | −0.119578 | ||||||||
\(347\) | −27.8145 | −1.49316 | −0.746579 | − | 0.665296i | \(-0.768305\pi\) | ||||
−0.746579 | + | 0.665296i | \(0.768305\pi\) | |||||||
\(348\) | 18.7950 | 1.00752 | ||||||||
\(349\) | −12.5352 | −0.670995 | −0.335498 | − | 0.942041i | \(-0.608904\pi\) | ||||
−0.335498 | + | 0.942041i | \(0.608904\pi\) | |||||||
\(350\) | 0.00360164 | 0.000192516 0 | ||||||||
\(351\) | 9.13027 | 0.487338 | ||||||||
\(352\) | 3.24180 | 0.172789 | ||||||||
\(353\) | −0.747503 | −0.0397856 | −0.0198928 | − | 0.999802i | \(-0.506332\pi\) | ||||
−0.0198928 | + | 0.999802i | \(0.506332\pi\) | |||||||
\(354\) | 0.289279 | 0.0153750 | ||||||||
\(355\) | −12.5461 | −0.665880 | ||||||||
\(356\) | 31.5339 | 1.67129 | ||||||||
\(357\) | −0.119441 | −0.00632151 | ||||||||
\(358\) | −1.24018 | −0.0655455 | ||||||||
\(359\) | 0.379130 | 0.0200097 | 0.0100049 | − | 0.999950i | \(-0.496815\pi\) | ||||
0.0100049 | + | 0.999950i | \(0.496815\pi\) | |||||||
\(360\) | −1.17002 | −0.0616654 | ||||||||
\(361\) | 39.1090 | 2.05837 | ||||||||
\(362\) | 0.968401 | 0.0508980 | ||||||||
\(363\) | −8.81613 | −0.462727 | ||||||||
\(364\) | 0.0482652 | 0.00252979 | ||||||||
\(365\) | 17.3833 | 0.909884 | ||||||||
\(366\) | 1.05027 | 0.0548987 | ||||||||
\(367\) | 17.2647 | 0.901207 | 0.450604 | − | 0.892724i | \(-0.351209\pi\) | ||||
0.450604 | + | 0.892724i | \(0.351209\pi\) | |||||||
\(368\) | −20.6605 | −1.07700 | ||||||||
\(369\) | −4.46051 | −0.232205 | ||||||||
\(370\) | −1.17956 | −0.0613225 | ||||||||
\(371\) | −0.102756 | −0.00533484 | ||||||||
\(372\) | −6.24661 | −0.323872 | ||||||||
\(373\) | 28.8028 | 1.49135 | 0.745675 | − | 0.666310i | \(-0.232127\pi\) | ||||
0.745675 | + | 0.666310i | \(0.232127\pi\) | |||||||
\(374\) | −1.64915 | −0.0852755 | ||||||||
\(375\) | −16.0620 | −0.829436 | ||||||||
\(376\) | −5.24550 | −0.270516 | ||||||||
\(377\) | 11.6582 | 0.600427 | ||||||||
\(378\) | 0.0110683 | 0.000569289 0 | ||||||||
\(379\) | 19.2545 | 0.989039 | 0.494519 | − | 0.869167i | \(-0.335344\pi\) | ||||
0.494519 | + | 0.869167i | \(0.335344\pi\) | |||||||
\(380\) | −26.9145 | −1.38068 | ||||||||
\(381\) | −11.8982 | −0.609563 | ||||||||
\(382\) | −2.53881 | −0.129897 | ||||||||
\(383\) | −13.7094 | −0.700515 | −0.350258 | − | 0.936653i | \(-0.613906\pi\) | ||||
−0.350258 | + | 0.936653i | \(0.613906\pi\) | |||||||
\(384\) | 5.43480 | 0.277343 | ||||||||
\(385\) | −0.0554983 | −0.00282846 | ||||||||
\(386\) | −0.278386 | −0.0141695 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −26.8635 | −1.36379 | ||||||||
\(389\) | 29.2387 | 1.48246 | 0.741229 | − | 0.671252i | \(-0.234243\pi\) | ||||
0.741229 | + | 0.671252i | \(0.234243\pi\) | |||||||
\(390\) | 0.502060 | 0.0254228 | ||||||||
\(391\) | 31.9950 | 1.61805 | ||||||||
\(392\) | −3.66338 | −0.185029 | ||||||||
\(393\) | −6.02886 | −0.304116 | ||||||||
\(394\) | 2.44181 | 0.123017 | ||||||||
\(395\) | 21.3892 | 1.07621 | ||||||||
\(396\) | −5.17684 | −0.260146 | ||||||||
\(397\) | 18.6986 | 0.938457 | 0.469229 | − | 0.883077i | \(-0.344532\pi\) | ||||
0.469229 | + | 0.883077i | \(0.344532\pi\) | |||||||
\(398\) | 1.03661 | 0.0519604 | ||||||||
\(399\) | 0.150883 | 0.00755359 | ||||||||
\(400\) | −7.12696 | −0.356348 | ||||||||
\(401\) | −5.29723 | −0.264531 | −0.132265 | − | 0.991214i | \(-0.542225\pi\) | ||||
−0.132265 | + | 0.991214i | \(0.542225\pi\) | |||||||
\(402\) | −0.248723 | −0.0124052 | ||||||||
\(403\) | −3.87465 | −0.193010 | ||||||||
\(404\) | −6.19249 | −0.308088 | ||||||||
\(405\) | −6.51317 | −0.323642 | ||||||||
\(406\) | 0.0141327 | 0.000701397 0 | ||||||||
\(407\) | −10.4836 | −0.519652 | ||||||||
\(408\) | −4.17137 | −0.206514 | ||||||||
\(409\) | 6.09599 | 0.301427 | 0.150714 | − | 0.988577i | \(-0.451843\pi\) | ||||
0.150714 | + | 0.988577i | \(0.451843\pi\) | |||||||
\(410\) | −0.831394 | −0.0410596 | ||||||||
\(411\) | −20.5456 | −1.01344 | ||||||||
\(412\) | 1.04537 | 0.0515016 | ||||||||
\(413\) | −0.0249765 | −0.00122901 | ||||||||
\(414\) | −0.874695 | −0.0429889 | ||||||||
\(415\) | 16.1477 | 0.792658 | ||||||||
\(416\) | 2.53208 | 0.124145 | ||||||||
\(417\) | −9.05995 | −0.443668 | ||||||||
\(418\) | 2.08327 | 0.101896 | ||||||||
\(419\) | 5.38564 | 0.263106 | 0.131553 | − | 0.991309i | \(-0.458004\pi\) | ||||
0.131553 | + | 0.991309i | \(0.458004\pi\) | |||||||
\(420\) | −0.0698846 | −0.00341002 | ||||||||
\(421\) | 35.8102 | 1.74528 | 0.872641 | − | 0.488362i | \(-0.162405\pi\) | ||||
0.872641 | + | 0.488362i | \(0.162405\pi\) | |||||||
\(422\) | −1.05883 | −0.0515429 | ||||||||
\(423\) | 12.5830 | 0.611806 | ||||||||
\(424\) | −3.58866 | −0.174281 | ||||||||
\(425\) | 11.0369 | 0.535366 | ||||||||
\(426\) | 1.22284 | 0.0592470 | ||||||||
\(427\) | −0.0906810 | −0.00438836 | ||||||||
\(428\) | −2.25172 | −0.108841 | ||||||||
\(429\) | 4.46216 | 0.215435 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.38810 | 0.115031 | 0.0575153 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575153 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(432\) | −21.9020 | −1.05376 | ||||||||
\(433\) | −8.45324 | −0.406237 | −0.203119 | − | 0.979154i | \(-0.565108\pi\) | ||||
−0.203119 | + | 0.979154i | \(0.565108\pi\) | |||||||
\(434\) | −0.00469709 | −0.000225467 0 | ||||||||
\(435\) | −16.8802 | −0.809345 | ||||||||
\(436\) | 24.1903 | 1.15850 | ||||||||
\(437\) | −40.4172 | −1.93342 | ||||||||
\(438\) | −1.69431 | −0.0809573 | ||||||||
\(439\) | 3.89988 | 0.186131 | 0.0930655 | − | 0.995660i | \(-0.470333\pi\) | ||||
0.0930655 | + | 0.995660i | \(0.470333\pi\) | |||||||
\(440\) | −1.93822 | −0.0924011 | ||||||||
\(441\) | 8.78777 | 0.418465 | ||||||||
\(442\) | −1.28810 | −0.0612687 | ||||||||
\(443\) | 25.3153 | 1.20276 | 0.601382 | − | 0.798962i | \(-0.294617\pi\) | ||||
0.601382 | + | 0.798962i | \(0.294617\pi\) | |||||||
\(444\) | −13.2011 | −0.626499 | ||||||||
\(445\) | −28.3213 | −1.34256 | ||||||||
\(446\) | −2.67229 | −0.126537 | ||||||||
\(447\) | 27.2612 | 1.28941 | ||||||||
\(448\) | −0.113719 | −0.00537272 | ||||||||
\(449\) | −35.7482 | −1.68706 | −0.843531 | − | 0.537080i | \(-0.819527\pi\) | ||||
−0.843531 | + | 0.537080i | \(0.819527\pi\) | |||||||
\(450\) | −0.301731 | −0.0142238 | ||||||||
\(451\) | −7.38917 | −0.347943 | ||||||||
\(452\) | 8.74242 | 0.411209 | ||||||||
\(453\) | −5.12359 | −0.240727 | ||||||||
\(454\) | −0.674577 | −0.0316594 | ||||||||
\(455\) | −0.0433481 | −0.00203219 | ||||||||
\(456\) | 5.26943 | 0.246764 | ||||||||
\(457\) | 18.9542 | 0.886641 | 0.443321 | − | 0.896363i | \(-0.353800\pi\) | ||||
0.443321 | + | 0.896363i | \(0.353800\pi\) | |||||||
\(458\) | 0.376202 | 0.0175787 | ||||||||
\(459\) | 33.9176 | 1.58314 | ||||||||
\(460\) | 18.7201 | 0.872829 | ||||||||
\(461\) | 14.0800 | 0.655773 | 0.327887 | − | 0.944717i | \(-0.393664\pi\) | ||||
0.327887 | + | 0.944717i | \(0.393664\pi\) | |||||||
\(462\) | 0.00540930 | 0.000251663 0 | ||||||||
\(463\) | 18.7262 | 0.870282 | 0.435141 | − | 0.900362i | \(-0.356699\pi\) | ||||
0.435141 | + | 0.900362i | \(0.356699\pi\) | |||||||
\(464\) | −27.9661 | −1.29829 | ||||||||
\(465\) | 5.61022 | 0.260168 | ||||||||
\(466\) | −1.63178 | −0.0755909 | ||||||||
\(467\) | −2.15149 | −0.0995592 | −0.0497796 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497796 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(468\) | −4.04348 | −0.186910 | ||||||||
\(469\) | 0.0214748 | 0.000991616 0 | ||||||||
\(470\) | 2.34534 | 0.108182 | ||||||||
\(471\) | 1.82129 | 0.0839205 | ||||||||
\(472\) | −0.872278 | −0.0401499 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.08476 | −0.0957562 | ||||||||
\(475\) | −13.9422 | −0.639711 | ||||||||
\(476\) | 0.179298 | 0.00821811 | ||||||||
\(477\) | 8.60852 | 0.394157 | ||||||||
\(478\) | 3.05828 | 0.139882 | ||||||||
\(479\) | 28.0982 | 1.28384 | 0.641919 | − | 0.766772i | \(-0.278138\pi\) | ||||
0.641919 | + | 0.766772i | \(0.278138\pi\) | |||||||
\(480\) | −3.66626 | −0.167341 | ||||||||
\(481\) | −8.18842 | −0.373360 | ||||||||
\(482\) | −0.461962 | −0.0210418 | ||||||||
\(483\) | −0.104945 | −0.00477517 | ||||||||
\(484\) | 13.2342 | 0.601556 | ||||||||
\(485\) | 24.1267 | 1.09554 | ||||||||
\(486\) | −1.58095 | −0.0717135 | ||||||||
\(487\) | −18.8948 | −0.856206 | −0.428103 | − | 0.903730i | \(-0.640818\pi\) | ||||
−0.428103 | + | 0.903730i | \(0.640818\pi\) | |||||||
\(488\) | −3.16694 | −0.143361 | ||||||||
\(489\) | −4.31958 | −0.195338 | ||||||||
\(490\) | 1.63795 | 0.0739951 | ||||||||
\(491\) | −27.0470 | −1.22061 | −0.610306 | − | 0.792166i | \(-0.708954\pi\) | ||||
−0.610306 | + | 0.792166i | \(0.708954\pi\) | |||||||
\(492\) | −9.30459 | −0.419483 | ||||||||
\(493\) | 43.3084 | 1.95051 | ||||||||
\(494\) | 1.62718 | 0.0732102 | ||||||||
\(495\) | 4.64944 | 0.208977 | ||||||||
\(496\) | 9.29465 | 0.417342 | ||||||||
\(497\) | −0.105581 | −0.00473595 | ||||||||
\(498\) | −1.57388 | −0.0705271 | ||||||||
\(499\) | 7.10029 | 0.317853 | 0.158926 | − | 0.987290i | \(-0.449197\pi\) | ||||
0.158926 | + | 0.987290i | \(0.449197\pi\) | |||||||
\(500\) | 24.1112 | 1.07829 | ||||||||
\(501\) | 4.58357 | 0.204779 | ||||||||
\(502\) | 1.81976 | 0.0812197 | ||||||||
\(503\) | −19.3911 | −0.864608 | −0.432304 | − | 0.901728i | \(-0.642299\pi\) | ||||
−0.432304 | + | 0.901728i | \(0.642299\pi\) | |||||||
\(504\) | −0.00984617 | −0.000438583 0 | ||||||||
\(505\) | 5.56161 | 0.247488 | ||||||||
\(506\) | −1.44900 | −0.0644158 | ||||||||
\(507\) | −13.6854 | −0.607789 | ||||||||
\(508\) | 17.8608 | 0.792447 | ||||||||
\(509\) | −24.1473 | −1.07031 | −0.535156 | − | 0.844754i | \(-0.679747\pi\) | ||||
−0.535156 | + | 0.844754i | \(0.679747\pi\) | |||||||
\(510\) | 1.86508 | 0.0825871 | ||||||||
\(511\) | 0.146288 | 0.00647138 | ||||||||
\(512\) | −10.1528 | −0.448693 | ||||||||
\(513\) | −42.8459 | −1.89169 | ||||||||
\(514\) | −3.23039 | −0.142486 | ||||||||
\(515\) | −0.938868 | −0.0413715 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.8447 | 0.916747 | ||||||||
\(518\) | −0.00992649 | −0.000436145 0 | ||||||||
\(519\) | 22.3572 | 0.981372 | ||||||||
\(520\) | −1.51389 | −0.0663884 | ||||||||
\(521\) | 2.26759 | 0.0993450 | 0.0496725 | − | 0.998766i | \(-0.484182\pi\) | ||||
0.0496725 | + | 0.998766i | \(0.484182\pi\) | |||||||
\(522\) | −1.18399 | −0.0518217 | ||||||||
\(523\) | 31.4577 | 1.37555 | 0.687775 | − | 0.725923i | \(-0.258587\pi\) | ||||
0.687775 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(524\) | 9.05015 | 0.395358 | ||||||||
\(525\) | −0.0362015 | −0.00157996 | ||||||||
\(526\) | 0.930427 | 0.0405685 | ||||||||
\(527\) | −14.3938 | −0.627002 | ||||||||
\(528\) | −10.7040 | −0.465831 | ||||||||
\(529\) | 5.11183 | 0.222254 | ||||||||
\(530\) | 1.60454 | 0.0696968 | ||||||||
\(531\) | 2.09243 | 0.0908038 | ||||||||
\(532\) | −0.226496 | −0.00981984 | ||||||||
\(533\) | −5.77146 | −0.249990 | ||||||||
\(534\) | 2.76042 | 0.119455 | ||||||||
\(535\) | 2.02232 | 0.0874325 | ||||||||
\(536\) | 0.749987 | 0.0323945 | ||||||||
\(537\) | 12.4655 | 0.537928 | ||||||||
\(538\) | 1.20246 | 0.0518417 | ||||||||
\(539\) | 14.5576 | 0.627040 | ||||||||
\(540\) | 19.8450 | 0.853993 | ||||||||
\(541\) | −0.910849 | −0.0391605 | −0.0195802 | − | 0.999808i | \(-0.506233\pi\) | ||||
−0.0195802 | + | 0.999808i | \(0.506233\pi\) | |||||||
\(542\) | −0.435869 | −0.0187222 | ||||||||
\(543\) | −9.73378 | −0.417717 | ||||||||
\(544\) | 9.40628 | 0.403291 | ||||||||
\(545\) | −21.7258 | −0.930632 | ||||||||
\(546\) | 0.00422504 | 0.000180815 0 | ||||||||
\(547\) | −37.6312 | −1.60900 | −0.804498 | − | 0.593956i | \(-0.797565\pi\) | ||||
−0.804498 | + | 0.593956i | \(0.797565\pi\) | |||||||
\(548\) | 30.8417 | 1.31749 | ||||||||
\(549\) | 7.59690 | 0.324228 | ||||||||
\(550\) | −0.499841 | −0.0213133 | ||||||||
\(551\) | −54.7088 | −2.33067 | ||||||||
\(552\) | −3.66510 | −0.155997 | ||||||||
\(553\) | 0.179999 | 0.00765434 | ||||||||
\(554\) | 0.251168 | 0.0106711 | ||||||||
\(555\) | 11.8562 | 0.503269 | ||||||||
\(556\) | 13.6002 | 0.576779 | ||||||||
\(557\) | −41.4304 | −1.75546 | −0.877732 | − | 0.479153i | \(-0.840944\pi\) | ||||
−0.877732 | + | 0.479153i | \(0.840944\pi\) | |||||||
\(558\) | 0.393504 | 0.0166583 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.103985 | 0.00439416 | ||||||||
\(561\) | 16.5762 | 0.699850 | ||||||||
\(562\) | −2.59478 | −0.109454 | ||||||||
\(563\) | 23.6741 | 0.997743 | 0.498872 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498872 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(564\) | 26.2480 | 1.10524 | ||||||||
\(565\) | −7.85176 | −0.330326 | ||||||||
\(566\) | 2.30739 | 0.0969868 | ||||||||
\(567\) | −0.0548109 | −0.00230184 | ||||||||
\(568\) | −3.68730 | −0.154716 | ||||||||
\(569\) | 4.74494 | 0.198918 | 0.0994591 | − | 0.995042i | \(-0.468289\pi\) | ||||
0.0994591 | + | 0.995042i | \(0.468289\pi\) | |||||||
\(570\) | −2.35604 | −0.0986835 | ||||||||
\(571\) | −36.2166 | −1.51562 | −0.757809 | − | 0.652477i | \(-0.773730\pi\) | ||||
−0.757809 | + | 0.652477i | \(0.773730\pi\) | |||||||
\(572\) | −6.69832 | −0.280071 | ||||||||
\(573\) | 25.5186 | 1.06606 | ||||||||
\(574\) | −0.00699651 | −0.000292029 0 | ||||||||
\(575\) | 9.69735 | 0.404408 | ||||||||
\(576\) | 9.52695 | 0.396956 | ||||||||
\(577\) | 20.7025 | 0.861855 | 0.430927 | − | 0.902387i | \(-0.358186\pi\) | ||||
0.430927 | + | 0.902387i | \(0.358186\pi\) | |||||||
\(578\) | −2.55119 | −0.106115 | ||||||||
\(579\) | 2.79816 | 0.116288 | ||||||||
\(580\) | 25.3395 | 1.05217 | ||||||||
\(581\) | 0.135889 | 0.00563763 | ||||||||
\(582\) | −2.35157 | −0.0974759 | ||||||||
\(583\) | 14.2607 | 0.590616 | ||||||||
\(584\) | 5.10894 | 0.211410 | ||||||||
\(585\) | 3.63154 | 0.150146 | ||||||||
\(586\) | −0.755888 | −0.0312254 | ||||||||
\(587\) | −22.7426 | −0.938687 | −0.469344 | − | 0.883016i | \(-0.655509\pi\) | ||||
−0.469344 | + | 0.883016i | \(0.655509\pi\) | |||||||
\(588\) | 18.3312 | 0.755967 | ||||||||
\(589\) | 18.1827 | 0.749206 | ||||||||
\(590\) | 0.390008 | 0.0160564 | ||||||||
\(591\) | −24.5436 | −1.00959 | ||||||||
\(592\) | 19.6427 | 0.807308 | ||||||||
\(593\) | −8.73804 | −0.358828 | −0.179414 | − | 0.983774i | \(-0.557420\pi\) | ||||
−0.179414 | + | 0.983774i | \(0.557420\pi\) | |||||||
\(594\) | −1.53607 | −0.0630256 | ||||||||
\(595\) | −0.161032 | −0.00660165 | ||||||||
\(596\) | −40.9229 | −1.67627 | ||||||||
\(597\) | −10.4193 | −0.426435 | ||||||||
\(598\) | −1.13177 | −0.0462815 | ||||||||
\(599\) | 21.0835 | 0.861446 | 0.430723 | − | 0.902484i | \(-0.358259\pi\) | ||||
0.430723 | + | 0.902484i | \(0.358259\pi\) | |||||||
\(600\) | −1.26430 | −0.0516148 | ||||||||
\(601\) | −9.25003 | −0.377316 | −0.188658 | − | 0.982043i | \(-0.560414\pi\) | ||||
−0.188658 | + | 0.982043i | \(0.560414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.79908 | −0.0732641 | ||||||||
\(604\) | 7.69121 | 0.312951 | ||||||||
\(605\) | −11.8860 | −0.483233 | ||||||||
\(606\) | −0.542078 | −0.0220204 | ||||||||
\(607\) | −36.0062 | −1.46145 | −0.730723 | − | 0.682674i | \(-0.760817\pi\) | ||||
−0.730723 | + | 0.682674i | \(0.760817\pi\) | |||||||
\(608\) | −11.8824 | −0.481893 | ||||||||
\(609\) | −0.142054 | −0.00575631 | ||||||||
\(610\) | 1.41598 | 0.0573315 | ||||||||
\(611\) | 16.2811 | 0.658665 | ||||||||
\(612\) | −15.0209 | −0.607184 | ||||||||
\(613\) | −7.55326 | −0.305073 | −0.152537 | − | 0.988298i | \(-0.548744\pi\) | ||||
−0.152537 | + | 0.988298i | \(0.548744\pi\) | |||||||
\(614\) | 2.00208 | 0.0807974 | ||||||||
\(615\) | 8.35666 | 0.336973 | ||||||||
\(616\) | −0.0163109 | −0.000657186 0 | ||||||||
\(617\) | 14.0622 | 0.566121 | 0.283061 | − | 0.959102i | \(-0.408650\pi\) | ||||
0.283061 | + | 0.959102i | \(0.408650\pi\) | |||||||
\(618\) | 0.0915094 | 0.00368105 | ||||||||
\(619\) | −6.15010 | −0.247194 | −0.123597 | − | 0.992333i | \(-0.539443\pi\) | ||||
−0.123597 | + | 0.992333i | \(0.539443\pi\) | |||||||
\(620\) | −8.42172 | −0.338224 | ||||||||
\(621\) | 29.8011 | 1.19588 | ||||||||
\(622\) | −4.31283 | −0.172929 | ||||||||
\(623\) | −0.238335 | −0.00954870 | ||||||||
\(624\) | −8.36056 | −0.334690 | ||||||||
\(625\) | −12.5099 | −0.500398 | ||||||||
\(626\) | −2.56188 | −0.102393 | ||||||||
\(627\) | −20.9397 | −0.836252 | ||||||||
\(628\) | −2.73400 | −0.109099 | ||||||||
\(629\) | −30.4187 | −1.21287 | ||||||||
\(630\) | 0.00440236 | 0.000175394 0 | ||||||||
\(631\) | −31.1395 | −1.23965 | −0.619823 | − | 0.784742i | \(-0.712796\pi\) | ||||
−0.619823 | + | 0.784742i | \(0.712796\pi\) | |||||||
\(632\) | 6.28628 | 0.250055 | ||||||||
\(633\) | 10.6427 | 0.423009 | ||||||||
\(634\) | 2.22055 | 0.0881891 | ||||||||
\(635\) | −16.0412 | −0.636577 | ||||||||
\(636\) | 17.9573 | 0.712054 | ||||||||
\(637\) | 11.3705 | 0.450516 | ||||||||
\(638\) | −1.96136 | −0.0776511 | ||||||||
\(639\) | 8.84515 | 0.349909 | ||||||||
\(640\) | 7.32722 | 0.289634 | ||||||||
\(641\) | −26.4675 | −1.04540 | −0.522701 | − | 0.852516i | \(-0.675076\pi\) | ||||
−0.522701 | + | 0.852516i | \(0.675076\pi\) | |||||||
\(642\) | −0.197111 | −0.00777935 | ||||||||
\(643\) | 16.8687 | 0.665236 | 0.332618 | − | 0.943062i | \(-0.392068\pi\) | ||||
0.332618 | + | 0.943062i | \(0.392068\pi\) | |||||||
\(644\) | 0.157537 | 0.00620784 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.04472 | 0.237826 | ||||||||
\(647\) | 8.85456 | 0.348109 | 0.174054 | − | 0.984736i | \(-0.444313\pi\) | ||||
0.174054 | + | 0.984736i | \(0.444313\pi\) | |||||||
\(648\) | −1.91422 | −0.0751975 | ||||||||
\(649\) | 3.46627 | 0.136063 | ||||||||
\(650\) | −0.390411 | −0.0153132 | ||||||||
\(651\) | 0.0472123 | 0.00185040 | ||||||||
\(652\) | 6.48429 | 0.253944 | ||||||||
\(653\) | 4.27841 | 0.167427 | 0.0837135 | − | 0.996490i | \(-0.473322\pi\) | ||||
0.0837135 | + | 0.996490i | \(0.473322\pi\) | |||||||
\(654\) | 2.11757 | 0.0828035 | ||||||||
\(655\) | −8.12814 | −0.317593 | ||||||||
\(656\) | 13.8448 | 0.540548 | ||||||||
\(657\) | −12.2554 | −0.478129 | ||||||||
\(658\) | 0.0197370 | 0.000769427 0 | ||||||||
\(659\) | −21.9991 | −0.856963 | −0.428481 | − | 0.903551i | \(-0.640951\pi\) | ||||
−0.428481 | + | 0.903551i | \(0.640951\pi\) | |||||||
\(660\) | 9.69869 | 0.377521 | ||||||||
\(661\) | −15.1722 | −0.590131 | −0.295066 | − | 0.955477i | \(-0.595342\pi\) | ||||
−0.295066 | + | 0.955477i | \(0.595342\pi\) | |||||||
\(662\) | 3.77688 | 0.146793 | ||||||||
\(663\) | 12.9472 | 0.502828 | ||||||||
\(664\) | 4.74579 | 0.184172 | ||||||||
\(665\) | 0.203421 | 0.00788833 | ||||||||
\(666\) | 0.831603 | 0.0322240 | ||||||||
\(667\) | 38.0522 | 1.47339 | ||||||||
\(668\) | −6.88057 | −0.266217 | ||||||||
\(669\) | 26.8603 | 1.03848 | ||||||||
\(670\) | −0.335330 | −0.0129549 | ||||||||
\(671\) | 12.5848 | 0.485832 | ||||||||
\(672\) | −0.0308531 | −0.00119018 | ||||||||
\(673\) | 18.4425 | 0.710905 | 0.355453 | − | 0.934694i | \(-0.384327\pi\) | ||||
0.355453 | + | 0.934694i | \(0.384327\pi\) | |||||||
\(674\) | −2.23908 | −0.0862460 | ||||||||
\(675\) | 10.2801 | 0.395680 | ||||||||
\(676\) | 20.5437 | 0.790141 | ||||||||
\(677\) | 23.0579 | 0.886186 | 0.443093 | − | 0.896476i | \(-0.353881\pi\) | ||||
0.443093 | + | 0.896476i | \(0.353881\pi\) | |||||||
\(678\) | 0.765293 | 0.0293909 | ||||||||
\(679\) | 0.203036 | 0.00779180 | ||||||||
\(680\) | −5.62386 | −0.215665 | ||||||||
\(681\) | 6.78043 | 0.259827 | ||||||||
\(682\) | 0.651869 | 0.0249613 | ||||||||
\(683\) | 47.6757 | 1.82426 | 0.912129 | − | 0.409903i | \(-0.134437\pi\) | ||||
0.912129 | + | 0.409903i | \(0.134437\pi\) | |||||||
\(684\) | 18.9750 | 0.725525 | ||||||||
\(685\) | −27.6997 | −1.05835 | ||||||||
\(686\) | 0.0275685 | 0.00105257 | ||||||||
\(687\) | −3.78135 | −0.144268 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.1386 | 0.424346 | ||||||||
\(690\) | 1.63872 | 0.0623850 | ||||||||
\(691\) | 16.1924 | 0.615988 | 0.307994 | − | 0.951388i | \(-0.400342\pi\) | ||||
0.307994 | + | 0.951388i | \(0.400342\pi\) | |||||||
\(692\) | −33.5612 | −1.27581 | ||||||||
\(693\) | 0.0391269 | 0.00148631 | ||||||||
\(694\) | 3.65500 | 0.138742 | ||||||||
\(695\) | −12.2147 | −0.463329 | ||||||||
\(696\) | −4.96108 | −0.188049 | ||||||||
\(697\) | −21.4401 | −0.812102 | ||||||||
\(698\) | 1.64721 | 0.0623478 | ||||||||
\(699\) | 16.4017 | 0.620369 | ||||||||
\(700\) | 0.0543434 | 0.00205399 | ||||||||
\(701\) | −29.5981 | −1.11790 | −0.558952 | − | 0.829200i | \(-0.688796\pi\) | ||||
−0.558952 | + | 0.829200i | \(0.688796\pi\) | |||||||
\(702\) | −1.19978 | −0.0452827 | ||||||||
\(703\) | 38.4261 | 1.44927 | ||||||||
\(704\) | 15.7821 | 0.594810 | ||||||||
\(705\) | −23.5739 | −0.887846 | ||||||||
\(706\) | 0.0982268 | 0.00369682 | ||||||||
\(707\) | 0.0468032 | 0.00176022 | ||||||||
\(708\) | 4.36480 | 0.164039 | ||||||||
\(709\) | −18.1434 | −0.681388 | −0.340694 | − | 0.940174i | \(-0.610662\pi\) | ||||
−0.340694 | + | 0.940174i | \(0.610662\pi\) | |||||||
\(710\) | 1.64865 | 0.0618726 | ||||||||
\(711\) | −15.0796 | −0.565530 | ||||||||
\(712\) | −8.32362 | −0.311941 | ||||||||
\(713\) | −12.6468 | −0.473628 | ||||||||
\(714\) | 0.0156954 | 0.000587385 0 | ||||||||
\(715\) | 6.01591 | 0.224982 | ||||||||
\(716\) | −18.7125 | −0.699319 | ||||||||
\(717\) | −30.7400 | −1.14801 | ||||||||
\(718\) | −0.0498202 | −0.00185927 | ||||||||
\(719\) | 17.9498 | 0.669414 | 0.334707 | − | 0.942322i | \(-0.391363\pi\) | ||||
0.334707 | + | 0.942322i | \(0.391363\pi\) | |||||||
\(720\) | −8.71145 | −0.324657 | ||||||||
\(721\) | −0.00790095 | −0.000294247 0 | ||||||||
\(722\) | −5.13919 | −0.191261 | ||||||||
\(723\) | 4.64337 | 0.172689 | ||||||||
\(724\) | 14.6118 | 0.543042 | ||||||||
\(725\) | 13.1263 | 0.487500 | ||||||||
\(726\) | 1.15850 | 0.0429959 | ||||||||
\(727\) | 12.3726 | 0.458876 | 0.229438 | − | 0.973323i | \(-0.426311\pi\) | ||||
0.229438 | + | 0.973323i | \(0.426311\pi\) | |||||||
\(728\) | −0.0127400 | −0.000472175 0 | ||||||||
\(729\) | 26.8635 | 0.994944 | ||||||||
\(730\) | −2.28428 | −0.0845450 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 15.8471 | 0.585725 | ||||||||
\(733\) | −19.8125 | −0.731790 | −0.365895 | − | 0.930656i | \(-0.619237\pi\) | ||||
−0.365895 | + | 0.930656i | \(0.619237\pi\) | |||||||
\(734\) | −2.26869 | −0.0837388 | ||||||||
\(735\) | −16.4637 | −0.607272 | ||||||||
\(736\) | 8.26467 | 0.304640 | ||||||||
\(737\) | −2.98031 | −0.109781 | ||||||||
\(738\) | 0.586141 | 0.0215761 | ||||||||
\(739\) | −29.2367 | −1.07549 | −0.537745 | − | 0.843108i | \(-0.680724\pi\) | ||||
−0.537745 | + | 0.843108i | \(0.680724\pi\) | |||||||
\(740\) | −17.7979 | −0.654262 | ||||||||
\(741\) | −16.3554 | −0.600831 | ||||||||
\(742\) | 0.0135028 | 0.000495705 0 | ||||||||
\(743\) | −18.5545 | −0.680698 | −0.340349 | − | 0.940299i | \(-0.610545\pi\) | ||||
−0.340349 | + | 0.940299i | \(0.610545\pi\) | |||||||
\(744\) | 1.64884 | 0.0604494 | ||||||||
\(745\) | 36.7538 | 1.34655 | ||||||||
\(746\) | −3.78487 | −0.138574 | ||||||||
\(747\) | −11.3843 | −0.416529 | ||||||||
\(748\) | −24.8832 | −0.909821 | ||||||||
\(749\) | 0.0170186 | 0.000621848 0 | ||||||||
\(750\) | 2.11065 | 0.0770700 | ||||||||
\(751\) | −41.5635 | −1.51668 | −0.758338 | − | 0.651862i | \(-0.773988\pi\) | ||||
−0.758338 | + | 0.651862i | \(0.773988\pi\) | |||||||
\(752\) | −39.0558 | −1.42422 | ||||||||
\(753\) | −18.2911 | −0.666565 | ||||||||
\(754\) | −1.53196 | −0.0557908 | ||||||||
\(755\) | −6.90765 | −0.251395 | ||||||||
\(756\) | 0.167004 | 0.00607387 | ||||||||
\(757\) | −25.1239 | −0.913143 | −0.456572 | − | 0.889687i | \(-0.650923\pi\) | ||||
−0.456572 | + | 0.889687i | \(0.650923\pi\) | |||||||
\(758\) | −2.53017 | −0.0919000 | ||||||||
\(759\) | 14.5644 | 0.528656 | ||||||||
\(760\) | 7.10427 | 0.257699 | ||||||||
\(761\) | 2.67135 | 0.0968363 | 0.0484182 | − | 0.998827i | \(-0.484582\pi\) | ||||
0.0484182 | + | 0.998827i | \(0.484582\pi\) | |||||||
\(762\) | 1.56350 | 0.0566397 | ||||||||
\(763\) | −0.182832 | −0.00661895 | ||||||||
\(764\) | −38.3070 | −1.38590 | ||||||||
\(765\) | 13.4906 | 0.487754 | ||||||||
\(766\) | 1.80150 | 0.0650908 | ||||||||
\(767\) | 2.70740 | 0.0977586 | ||||||||
\(768\) | 19.3320 | 0.697585 | ||||||||
\(769\) | −37.0496 | −1.33604 | −0.668022 | − | 0.744142i | \(-0.732859\pi\) | ||||
−0.668022 | + | 0.744142i | \(0.732859\pi\) | |||||||
\(770\) | 0.00729285 | 0.000262816 0 | ||||||||
\(771\) | 32.4699 | 1.16938 | ||||||||
\(772\) | −4.20043 | −0.151177 | ||||||||
\(773\) | 46.2293 | 1.66275 | 0.831376 | − | 0.555711i | \(-0.187554\pi\) | ||||
0.831376 | + | 0.555711i | \(0.187554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.36260 | −0.156709 | ||||||||
\(776\) | 7.09082 | 0.254546 | ||||||||
\(777\) | 0.0997750 | 0.00357941 | ||||||||
\(778\) | −3.84215 | −0.137748 | ||||||||
\(779\) | 27.0839 | 0.970383 | ||||||||
\(780\) | 7.57536 | 0.271241 | ||||||||
\(781\) | 14.6527 | 0.524313 | ||||||||
\(782\) | −4.20435 | −0.150347 | ||||||||
\(783\) | 40.3388 | 1.44159 | ||||||||
\(784\) | −27.2760 | −0.974142 | ||||||||
\(785\) | 2.45547 | 0.0876395 | ||||||||
\(786\) | 0.792232 | 0.0282580 | ||||||||
\(787\) | 12.9148 | 0.460364 | 0.230182 | − | 0.973148i | \(-0.426068\pi\) | ||||
0.230182 | + | 0.973148i | \(0.426068\pi\) | |||||||
\(788\) | 36.8433 | 1.31249 | ||||||||
\(789\) | −9.35208 | −0.332943 | ||||||||
\(790\) | −2.81069 | −0.0999997 | ||||||||
\(791\) | −0.0660757 | −0.00234938 | ||||||||
\(792\) | 1.36647 | 0.0485553 | ||||||||
\(793\) | 9.82964 | 0.349061 | ||||||||
\(794\) | −2.45712 | −0.0872000 | ||||||||
\(795\) | −16.1279 | −0.571996 | ||||||||
\(796\) | 15.6409 | 0.554376 | ||||||||
\(797\) | 34.9960 | 1.23962 | 0.619811 | − | 0.784751i | \(-0.287209\pi\) | ||||
0.619811 | + | 0.784751i | \(0.287209\pi\) | |||||||
\(798\) | −0.0198270 | −0.000701868 0 | ||||||||
\(799\) | 60.4820 | 2.13970 | ||||||||
\(800\) | 2.85095 | 0.100796 | ||||||||
\(801\) | 19.9668 | 0.705493 | ||||||||
\(802\) | 0.696091 | 0.0245798 | ||||||||
\(803\) | −20.3020 | −0.716442 | ||||||||
\(804\) | −3.75286 | −0.132353 | ||||||||
\(805\) | −0.141488 | −0.00498679 | ||||||||
\(806\) | 0.509155 | 0.0179342 | ||||||||
\(807\) | −12.0864 | −0.425461 | ||||||||
\(808\) | 1.63455 | 0.0575034 | ||||||||
\(809\) | −20.2894 | −0.713339 | −0.356669 | − | 0.934231i | \(-0.616088\pi\) | ||||
−0.356669 | + | 0.934231i | \(0.616088\pi\) | |||||||
\(810\) | 0.855873 | 0.0300723 | ||||||||
\(811\) | 7.05661 | 0.247791 | 0.123896 | − | 0.992295i | \(-0.460461\pi\) | ||||
0.123896 | + | 0.992295i | \(0.460461\pi\) | |||||||
\(812\) | 0.213242 | 0.00748334 | ||||||||
\(813\) | 4.38109 | 0.153651 | ||||||||
\(814\) | 1.37761 | 0.0482853 | ||||||||
\(815\) | −5.82369 | −0.203995 | ||||||||
\(816\) | −31.0582 | −1.08726 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.801053 | −0.0280082 | ||||||||
\(819\) | 0.0305608 | 0.00106788 | ||||||||
\(820\) | −12.5445 | −0.438073 | ||||||||
\(821\) | −29.1585 | −1.01764 | −0.508819 | − | 0.860874i | \(-0.669918\pi\) | ||||
−0.508819 | + | 0.860874i | \(0.669918\pi\) | |||||||
\(822\) | 2.69982 | 0.0941672 | ||||||||
\(823\) | −49.0909 | −1.71120 | −0.855600 | − | 0.517637i | \(-0.826812\pi\) | ||||
−0.855600 | + | 0.517637i | \(0.826812\pi\) | |||||||
\(824\) | −0.275933 | −0.00961257 | ||||||||
\(825\) | 5.02409 | 0.174917 | ||||||||
\(826\) | 0.00328207 | 0.000114198 0 | ||||||||
\(827\) | 4.85202 | 0.168721 | 0.0843606 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843606 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(828\) | −13.1979 | −0.458657 | ||||||||
\(829\) | 30.6618 | 1.06493 | 0.532465 | − | 0.846452i | \(-0.321266\pi\) | ||||
0.532465 | + | 0.846452i | \(0.321266\pi\) | |||||||
\(830\) | −2.12191 | −0.0736526 | ||||||||
\(831\) | −2.52459 | −0.0875770 | ||||||||
\(832\) | 12.3269 | 0.427359 | ||||||||
\(833\) | 42.2397 | 1.46352 | ||||||||
\(834\) | 1.19054 | 0.0412249 | ||||||||
\(835\) | 6.17960 | 0.213854 | ||||||||
\(836\) | 31.4334 | 1.08715 | ||||||||
\(837\) | −13.4068 | −0.463406 | ||||||||
\(838\) | −0.707709 | −0.0244474 | ||||||||
\(839\) | −31.9485 | −1.10299 | −0.551493 | − | 0.834180i | \(-0.685941\pi\) | ||||
−0.551493 | + | 0.834180i | \(0.685941\pi\) | |||||||
\(840\) | 0.0184466 | 0.000636467 0 | ||||||||
\(841\) | 22.5075 | 0.776119 | ||||||||
\(842\) | −4.70570 | −0.162169 | ||||||||
\(843\) | 26.0812 | 0.898284 | ||||||||
\(844\) | −15.9762 | −0.549922 | ||||||||
\(845\) | −18.4507 | −0.634724 | ||||||||
\(846\) | −1.65349 | −0.0568481 | ||||||||
\(847\) | −0.100025 | −0.00343690 | ||||||||
\(848\) | −26.7196 | −0.917555 | ||||||||
\(849\) | −23.1925 | −0.795963 | ||||||||
\(850\) | −1.45032 | −0.0497454 | ||||||||
\(851\) | −26.7269 | −0.916187 | ||||||||
\(852\) | 18.4509 | 0.632118 | ||||||||
\(853\) | 24.1240 | 0.825991 | 0.412996 | − | 0.910733i | \(-0.364482\pi\) | ||||
0.412996 | + | 0.910733i | \(0.364482\pi\) | |||||||
\(854\) | 0.0119161 | 0.000407760 0 | ||||||||
\(855\) | −17.0418 | −0.582818 | ||||||||
\(856\) | 0.594359 | 0.0203148 | ||||||||
\(857\) | 45.7278 | 1.56203 | 0.781016 | − | 0.624511i | \(-0.214702\pi\) | ||||
0.781016 | + | 0.624511i | \(0.214702\pi\) | |||||||
\(858\) | −0.586357 | −0.0200179 | ||||||||
\(859\) | −31.4601 | −1.07341 | −0.536703 | − | 0.843771i | \(-0.680330\pi\) | ||||
−0.536703 | + | 0.843771i | \(0.680330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0703247 | 0.00239666 | ||||||||
\(862\) | −0.313811 | −0.0106885 | ||||||||
\(863\) | −9.07754 | −0.309003 | −0.154501 | − | 0.987993i | \(-0.549377\pi\) | ||||
−0.154501 | + | 0.987993i | \(0.549377\pi\) | |||||||
\(864\) | 8.76129 | 0.298065 | ||||||||
\(865\) | 30.1421 | 1.02486 | ||||||||
\(866\) | 1.11081 | 0.0377469 | ||||||||
\(867\) | 25.6430 | 0.870882 | ||||||||
\(868\) | −0.0708722 | −0.00240556 | ||||||||
\(869\) | −24.9805 | −0.847406 | ||||||||
\(870\) | 2.21817 | 0.0752031 | ||||||||
\(871\) | −2.32783 | −0.0788755 | ||||||||
\(872\) | −6.38521 | −0.216230 | ||||||||
\(873\) | −17.0096 | −0.575686 | ||||||||
\(874\) | 5.31109 | 0.179650 | ||||||||
\(875\) | −0.182234 | −0.00616064 | ||||||||
\(876\) | −25.5647 | −0.863750 | ||||||||
\(877\) | −43.9606 | −1.48444 | −0.742221 | − | 0.670155i | \(-0.766228\pi\) | ||||
−0.742221 | + | 0.670155i | \(0.766228\pi\) | |||||||
\(878\) | −0.512469 | −0.0172950 | ||||||||
\(879\) | 7.59772 | 0.256265 | ||||||||
\(880\) | −14.4312 | −0.486475 | ||||||||
\(881\) | 20.8194 | 0.701424 | 0.350712 | − | 0.936483i | \(-0.385940\pi\) | ||||
0.350712 | + | 0.936483i | \(0.385940\pi\) | |||||||
\(882\) | −1.15477 | −0.0388832 | ||||||||
\(883\) | −50.5651 | −1.70165 | −0.850825 | − | 0.525448i | \(-0.823898\pi\) | ||||
−0.850825 | + | 0.525448i | \(0.823898\pi\) | |||||||
\(884\) | −19.4356 | −0.653689 | ||||||||
\(885\) | −3.92012 | −0.131774 | ||||||||
\(886\) | −3.32659 | −0.111759 | ||||||||
\(887\) | −55.7000 | −1.87022 | −0.935111 | − | 0.354355i | \(-0.884700\pi\) | ||||
−0.935111 | + | 0.354355i | \(0.884700\pi\) | |||||||
\(888\) | 3.48454 | 0.116934 | ||||||||
\(889\) | −0.134993 | −0.00452753 | ||||||||
\(890\) | 3.72161 | 0.124749 | ||||||||
\(891\) | 7.60674 | 0.254835 | ||||||||
\(892\) | −40.3210 | −1.35005 | ||||||||
\(893\) | −76.4031 | −2.55673 | ||||||||
\(894\) | −3.58231 | −0.119810 | ||||||||
\(895\) | 16.8061 | 0.561766 | ||||||||
\(896\) | 0.0616615 | 0.00205997 | ||||||||
\(897\) | 11.3759 | 0.379829 | ||||||||
\(898\) | 4.69755 | 0.156759 | ||||||||
\(899\) | −17.1188 | −0.570942 | ||||||||
\(900\) | −4.55268 | −0.151756 | ||||||||
\(901\) | 41.3781 | 1.37851 | ||||||||
\(902\) | 0.970986 | 0.0323303 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.30763 | −0.0767505 | ||||||||
\(905\) | −13.1231 | −0.436228 | ||||||||
\(906\) | 0.673273 | 0.0223680 | ||||||||
\(907\) | −42.1173 | −1.39848 | −0.699241 | − | 0.714886i | \(-0.746479\pi\) | ||||
−0.699241 | + | 0.714886i | \(0.746479\pi\) | |||||||
\(908\) | −10.1784 | −0.337781 | ||||||||
\(909\) | −3.92099 | −0.130051 | ||||||||
\(910\) | 0.00569622 | 0.000188828 0 | ||||||||
\(911\) | −15.7963 | −0.523353 | −0.261677 | − | 0.965156i | \(-0.584275\pi\) | ||||
−0.261677 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(912\) | 39.2339 | 1.29916 | ||||||||
\(913\) | −18.8589 | −0.624138 | ||||||||
\(914\) | −2.49071 | −0.0823854 | ||||||||
\(915\) | −14.2326 | −0.470516 | ||||||||
\(916\) | 5.67633 | 0.187551 | ||||||||
\(917\) | −0.0684016 | −0.00225882 | ||||||||
\(918\) | −4.45699 | −0.147103 | ||||||||
\(919\) | 28.4300 | 0.937819 | 0.468909 | − | 0.883246i | \(-0.344647\pi\) | ||||
0.468909 | + | 0.883246i | \(0.344647\pi\) | |||||||
\(920\) | −4.94131 | −0.162910 | ||||||||
\(921\) | −20.1237 | −0.663099 | ||||||||
\(922\) | −1.85021 | −0.0609335 | ||||||||
\(923\) | 11.4448 | 0.376709 | ||||||||
\(924\) | 0.0816183 | 0.00268505 | ||||||||
\(925\) | −9.21961 | −0.303139 | ||||||||
\(926\) | −2.46075 | −0.0808653 | ||||||||
\(927\) | 0.661911 | 0.0217400 | ||||||||
\(928\) | 11.1871 | 0.367233 | ||||||||
\(929\) | −44.3206 | −1.45411 | −0.727056 | − | 0.686578i | \(-0.759112\pi\) | ||||
−0.727056 | + | 0.686578i | \(0.759112\pi\) | |||||||
\(930\) | −0.737220 | −0.0241744 | ||||||||
\(931\) | −53.3588 | −1.74876 | ||||||||
\(932\) | −24.6212 | −0.806495 | ||||||||
\(933\) | 43.3500 | 1.41921 | ||||||||
\(934\) | 0.282720 | 0.00925089 | ||||||||
\(935\) | 22.3482 | 0.730864 | ||||||||
\(936\) | 1.06731 | 0.0348860 | ||||||||
\(937\) | 30.6555 | 1.00147 | 0.500736 | − | 0.865600i | \(-0.333063\pi\) | ||||
0.500736 | + | 0.865600i | \(0.333063\pi\) | |||||||
\(938\) | −0.00282193 | −9.21394e−5 0 | ||||||||
\(939\) | 25.7504 | 0.840334 | ||||||||
\(940\) | 35.3877 | 1.15422 | ||||||||
\(941\) | −35.7206 | −1.16446 | −0.582229 | − | 0.813025i | \(-0.697819\pi\) | ||||
−0.582229 | + | 0.813025i | \(0.697819\pi\) | |||||||
\(942\) | −0.239329 | −0.00779776 | ||||||||
\(943\) | −18.8380 | −0.613449 | ||||||||
\(944\) | −6.49461 | −0.211381 | ||||||||
\(945\) | −0.149990 | −0.00487917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.7779 | −1.32510 | −0.662552 | − | 0.749016i | \(-0.730527\pi\) | ||||
−0.662552 | + | 0.749016i | \(0.730527\pi\) | |||||||
\(948\) | −31.4560 | −1.02164 | ||||||||
\(949\) | −15.8573 | −0.514749 | ||||||||
\(950\) | 1.83209 | 0.0594409 | ||||||||
\(951\) | −22.3196 | −0.723762 | ||||||||
\(952\) | −0.0473271 | −0.00153388 | ||||||||
\(953\) | −24.8562 | −0.805172 | −0.402586 | − | 0.915382i | \(-0.631889\pi\) | ||||
−0.402586 | + | 0.915382i | \(0.631889\pi\) | |||||||
\(954\) | −1.13122 | −0.0366245 | ||||||||
\(955\) | 34.4043 | 1.11330 | ||||||||
\(956\) | 46.1450 | 1.49243 | ||||||||
\(957\) | 19.7144 | 0.637277 | ||||||||
\(958\) | −3.69228 | −0.119292 | ||||||||
\(959\) | −0.233104 | −0.00752732 | ||||||||
\(960\) | −17.8485 | −0.576058 | ||||||||
\(961\) | −25.3105 | −0.816468 | ||||||||
\(962\) | 1.07601 | 0.0346920 | ||||||||
\(963\) | −1.42576 | −0.0459443 | ||||||||
\(964\) | −6.97034 | −0.224499 | ||||||||
\(965\) | 3.77250 | 0.121441 | ||||||||
\(966\) | 0.0137905 | 0.000443702 0 | ||||||||
\(967\) | −12.4470 | −0.400269 | −0.200135 | − | 0.979768i | \(-0.564138\pi\) | ||||
−0.200135 | + | 0.979768i | \(0.564138\pi\) | |||||||
\(968\) | −3.49328 | −0.112278 | ||||||||
\(969\) | −60.7578 | −1.95182 | ||||||||
\(970\) | −3.17041 | −0.101796 | ||||||||
\(971\) | 30.2774 | 0.971648 | 0.485824 | − | 0.874057i | \(-0.338520\pi\) | ||||
0.485824 | + | 0.874057i | \(0.338520\pi\) | |||||||
\(972\) | −23.8543 | −0.765125 | ||||||||
\(973\) | −0.102791 | −0.00329534 | ||||||||
\(974\) | 2.48290 | 0.0795574 | ||||||||
\(975\) | 3.92417 | 0.125674 | ||||||||
\(976\) | −23.5797 | −0.754767 | ||||||||
\(977\) | 35.9146 | 1.14901 | 0.574505 | − | 0.818501i | \(-0.305195\pi\) | ||||
0.574505 | + | 0.818501i | \(0.305195\pi\) | |||||||
\(978\) | 0.567621 | 0.0181505 | ||||||||
\(979\) | 33.0765 | 1.05713 | ||||||||
\(980\) | 24.7143 | 0.789468 | ||||||||
\(981\) | 15.3169 | 0.489032 | ||||||||
\(982\) | 3.55415 | 0.113417 | ||||||||
\(983\) | 48.3080 | 1.54078 | 0.770392 | − | 0.637570i | \(-0.220060\pi\) | ||||
0.770392 | + | 0.637570i | \(0.220060\pi\) | |||||||
\(984\) | 2.45602 | 0.0782950 | ||||||||
\(985\) | −33.0898 | −1.05433 | ||||||||
\(986\) | −5.69101 | −0.181239 | ||||||||
\(987\) | −0.198384 | −0.00631464 | ||||||||
\(988\) | 24.5517 | 0.781094 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.610966 | −0.0194178 | ||||||||
\(991\) | −11.1406 | −0.353893 | −0.176946 | − | 0.984220i | \(-0.556622\pi\) | ||||
−0.176946 | + | 0.984220i | \(0.556622\pi\) | |||||||
\(992\) | −3.71807 | −0.118049 | ||||||||
\(993\) | −37.9629 | −1.20472 | ||||||||
\(994\) | 0.0138740 | 0.000440057 0 | ||||||||
\(995\) | −14.0474 | −0.445333 | ||||||||
\(996\) | −23.7475 | −0.752468 | ||||||||
\(997\) | −39.5782 | −1.25346 | −0.626728 | − | 0.779238i | \(-0.715606\pi\) | ||||
−0.626728 | + | 0.779238i | \(0.715606\pi\) | |||||||
\(998\) | −0.933024 | −0.0295344 | ||||||||
\(999\) | −28.3329 | −0.896414 |
(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 | 1849.2.a.n.1.10 | 18 | ||
43.17 | even | 21 | 43.2.g.a.31.2 | yes | 36 | ||
43.38 | even | 21 | 43.2.g.a.25.2 | ✓ | 36 | ||
43.42 | odd | 2 | 1849.2.a.o.1.9 | 18 | |||
129.17 | odd | 42 | 387.2.y.c.289.2 | 36 | |||
129.38 | odd | 42 | 387.2.y.c.154.2 | 36 | |||
172.103 | odd | 42 | 688.2.bg.c.289.1 | 36 | |||
172.167 | odd | 42 | 688.2.bg.c.369.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.25.2 | ✓ | 36 | 43.38 | even | 21 | ||
43.2.g.a.31.2 | yes | 36 | 43.17 | even | 21 | ||
387.2.y.c.154.2 | 36 | 129.38 | odd | 42 | |||
387.2.y.c.289.2 | 36 | 129.17 | odd | 42 | |||
688.2.bg.c.289.1 | 36 | 172.103 | odd | 42 | |||
688.2.bg.c.369.1 | 36 | 172.167 | odd | 42 | |||
1849.2.a.n.1.10 | 18 | 1.1 | even | 1 | trivial | ||
1849.2.a.o.1.9 | 18 | 43.42 | odd | 2 |