Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 12x^{7} + 14x^{6} + 35x^{5} - 35x^{4} - 28x^{3} + 10x^{2} + 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.97314\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.04618 | 0.604011 | 0.302006 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302006 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.929245 | 0.415571 | 0.207785 | − | 0.978174i | \(-0.433374\pi\) | ||||
0.207785 | + | 0.978174i | \(0.433374\pi\) | |||||||
\(6\) | 1.04618 | 0.427101 | ||||||||
\(7\) | −2.89421 | −1.09391 | −0.546954 | − | 0.837162i | \(-0.684213\pi\) | ||||
−0.546954 | + | 0.837162i | \(0.684213\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.90551 | −0.635170 | ||||||||
\(10\) | 0.929245 | 0.293853 | ||||||||
\(11\) | 3.97504 | 1.19852 | 0.599259 | − | 0.800555i | \(-0.295462\pi\) | ||||
0.599259 | + | 0.800555i | \(0.295462\pi\) | |||||||
\(12\) | 1.04618 | 0.302006 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.89421 | −0.773510 | ||||||||
\(15\) | 0.972156 | 0.251010 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.54056 | −1.10125 | −0.550623 | − | 0.834754i | \(-0.685610\pi\) | ||||
−0.550623 | + | 0.834754i | \(0.685610\pi\) | |||||||
\(18\) | −1.90551 | −0.449133 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.929245 | 0.207785 | ||||||||
\(21\) | −3.02786 | −0.660733 | ||||||||
\(22\) | 3.97504 | 0.847480 | ||||||||
\(23\) | −4.09689 | −0.854262 | −0.427131 | − | 0.904190i | \(-0.640476\pi\) | ||||
−0.427131 | + | 0.904190i | \(0.640476\pi\) | |||||||
\(24\) | 1.04618 | 0.213550 | ||||||||
\(25\) | −4.13650 | −0.827301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.13204 | −0.987662 | ||||||||
\(28\) | −2.89421 | −0.546954 | ||||||||
\(29\) | 1.64963 | 0.306329 | 0.153164 | − | 0.988201i | \(-0.451054\pi\) | ||||
0.153164 | + | 0.988201i | \(0.451054\pi\) | |||||||
\(30\) | 0.972156 | 0.177491 | ||||||||
\(31\) | −7.79245 | −1.39957 | −0.699783 | − | 0.714356i | \(-0.746720\pi\) | ||||
−0.699783 | + | 0.714356i | \(0.746720\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.15860 | 0.723919 | ||||||||
\(34\) | −4.54056 | −0.778699 | ||||||||
\(35\) | −2.68943 | −0.454597 | ||||||||
\(36\) | −1.90551 | −0.317585 | ||||||||
\(37\) | 2.85188 | 0.468847 | 0.234423 | − | 0.972135i | \(-0.424680\pi\) | ||||
0.234423 | + | 0.972135i | \(0.424680\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.929245 | 0.146926 | ||||||||
\(41\) | −0.453243 | −0.0707847 | −0.0353923 | − | 0.999373i | \(-0.511268\pi\) | ||||
−0.0353923 | + | 0.999373i | \(0.511268\pi\) | |||||||
\(42\) | −3.02786 | −0.467209 | ||||||||
\(43\) | 4.16877 | 0.635732 | 0.317866 | − | 0.948136i | \(-0.397034\pi\) | ||||
0.317866 | + | 0.948136i | \(0.397034\pi\) | |||||||
\(44\) | 3.97504 | 0.599259 | ||||||||
\(45\) | −1.77069 | −0.263958 | ||||||||
\(46\) | −4.09689 | −0.604054 | ||||||||
\(47\) | −9.08685 | −1.32545 | −0.662727 | − | 0.748862i | \(-0.730601\pi\) | ||||
−0.662727 | + | 0.748862i | \(0.730601\pi\) | |||||||
\(48\) | 1.04618 | 0.151003 | ||||||||
\(49\) | 1.37645 | 0.196636 | ||||||||
\(50\) | −4.13650 | −0.584990 | ||||||||
\(51\) | −4.75023 | −0.665166 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.63605 | −0.499450 | −0.249725 | − | 0.968317i | \(-0.580340\pi\) | ||||
−0.249725 | + | 0.968317i | \(0.580340\pi\) | |||||||
\(54\) | −5.13204 | −0.698382 | ||||||||
\(55\) | 3.69378 | 0.498069 | ||||||||
\(56\) | −2.89421 | −0.386755 | ||||||||
\(57\) | −1.04618 | −0.138570 | ||||||||
\(58\) | 1.64963 | 0.216607 | ||||||||
\(59\) | 9.02326 | 1.17473 | 0.587364 | − | 0.809323i | \(-0.300166\pi\) | ||||
0.587364 | + | 0.809323i | \(0.300166\pi\) | |||||||
\(60\) | 0.972156 | 0.125505 | ||||||||
\(61\) | 4.87261 | 0.623874 | 0.311937 | − | 0.950103i | \(-0.399022\pi\) | ||||
0.311937 | + | 0.950103i | \(0.399022\pi\) | |||||||
\(62\) | −7.79245 | −0.989642 | ||||||||
\(63\) | 5.51495 | 0.694818 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.15860 | 0.511888 | ||||||||
\(67\) | −14.2461 | −1.74043 | −0.870217 | − | 0.492669i | \(-0.836021\pi\) | ||||
−0.870217 | + | 0.492669i | \(0.836021\pi\) | |||||||
\(68\) | −4.54056 | −0.550623 | ||||||||
\(69\) | −4.28608 | −0.515984 | ||||||||
\(70\) | −2.68943 | −0.321448 | ||||||||
\(71\) | −10.8788 | −1.29107 | −0.645535 | − | 0.763731i | \(-0.723366\pi\) | ||||
−0.645535 | + | 0.763731i | \(0.723366\pi\) | |||||||
\(72\) | −1.90551 | −0.224567 | ||||||||
\(73\) | −11.6900 | −1.36821 | −0.684105 | − | 0.729384i | \(-0.739807\pi\) | ||||
−0.684105 | + | 0.729384i | \(0.739807\pi\) | |||||||
\(74\) | 2.85188 | 0.331525 | ||||||||
\(75\) | −4.32752 | −0.499699 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −11.5046 | −1.31107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.60591 | 1.08075 | 0.540375 | − | 0.841425i | \(-0.318283\pi\) | ||||
0.540375 | + | 0.841425i | \(0.318283\pi\) | |||||||
\(80\) | 0.929245 | 0.103893 | ||||||||
\(81\) | 0.347501 | 0.0386112 | ||||||||
\(82\) | −0.453243 | −0.0500523 | ||||||||
\(83\) | −4.33877 | −0.476242 | −0.238121 | − | 0.971235i | \(-0.576531\pi\) | ||||
−0.238121 | + | 0.971235i | \(0.576531\pi\) | |||||||
\(84\) | −3.02786 | −0.330367 | ||||||||
\(85\) | −4.21929 | −0.457646 | ||||||||
\(86\) | 4.16877 | 0.449530 | ||||||||
\(87\) | 1.72581 | 0.185026 | ||||||||
\(88\) | 3.97504 | 0.423740 | ||||||||
\(89\) | 6.23045 | 0.660427 | 0.330213 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330213 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(90\) | −1.77069 | −0.186647 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.09689 | −0.427131 | ||||||||
\(93\) | −8.15229 | −0.845354 | ||||||||
\(94\) | −9.08685 | −0.937237 | ||||||||
\(95\) | −0.929245 | −0.0953385 | ||||||||
\(96\) | 1.04618 | 0.106775 | ||||||||
\(97\) | −11.5845 | −1.17623 | −0.588116 | − | 0.808777i | \(-0.700130\pi\) | ||||
−0.588116 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(98\) | 1.37645 | 0.139043 | ||||||||
\(99\) | −7.57447 | −0.761263 | ||||||||
\(100\) | −4.13650 | −0.413650 | ||||||||
\(101\) | 9.68495 | 0.963689 | 0.481844 | − | 0.876257i | \(-0.339967\pi\) | ||||
0.481844 | + | 0.876257i | \(0.339967\pi\) | |||||||
\(102\) | −4.75023 | −0.470343 | ||||||||
\(103\) | −0.0784942 | −0.00773427 | −0.00386713 | − | 0.999993i | \(-0.501231\pi\) | ||||
−0.00386713 | + | 0.999993i | \(0.501231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.81362 | −0.274582 | ||||||||
\(106\) | −3.63605 | −0.353165 | ||||||||
\(107\) | 1.97833 | 0.191253 | 0.0956264 | − | 0.995417i | \(-0.469515\pi\) | ||||
0.0956264 | + | 0.995417i | \(0.469515\pi\) | |||||||
\(108\) | −5.13204 | −0.493831 | ||||||||
\(109\) | 17.0468 | 1.63279 | 0.816395 | − | 0.577494i | \(-0.195969\pi\) | ||||
0.816395 | + | 0.577494i | \(0.195969\pi\) | |||||||
\(110\) | 3.69378 | 0.352188 | ||||||||
\(111\) | 2.98358 | 0.283189 | ||||||||
\(112\) | −2.89421 | −0.273477 | ||||||||
\(113\) | 7.23739 | 0.680836 | 0.340418 | − | 0.940274i | \(-0.389431\pi\) | ||||
0.340418 | + | 0.940274i | \(0.389431\pi\) | |||||||
\(114\) | −1.04618 | −0.0979836 | ||||||||
\(115\) | −3.80702 | −0.355006 | ||||||||
\(116\) | 1.64963 | 0.153164 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.02326 | 0.830659 | ||||||||
\(119\) | 13.1413 | 1.20466 | ||||||||
\(120\) | 0.972156 | 0.0887453 | ||||||||
\(121\) | 4.80091 | 0.436446 | ||||||||
\(122\) | 4.87261 | 0.441145 | ||||||||
\(123\) | −0.474173 | −0.0427547 | ||||||||
\(124\) | −7.79245 | −0.699783 | ||||||||
\(125\) | −8.49005 | −0.759373 | ||||||||
\(126\) | 5.51495 | 0.491311 | ||||||||
\(127\) | −10.6484 | −0.944893 | −0.472447 | − | 0.881359i | \(-0.656629\pi\) | ||||
−0.472447 | + | 0.881359i | \(0.656629\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.36128 | 0.383989 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6085 | 1.53846 | 0.769232 | − | 0.638970i | \(-0.220639\pi\) | ||||
0.769232 | + | 0.638970i | \(0.220639\pi\) | |||||||
\(132\) | 4.15860 | 0.361959 | ||||||||
\(133\) | 2.89421 | 0.250960 | ||||||||
\(134\) | −14.2461 | −1.23067 | ||||||||
\(135\) | −4.76892 | −0.410443 | ||||||||
\(136\) | −4.54056 | −0.389349 | ||||||||
\(137\) | −10.1912 | −0.870689 | −0.435345 | − | 0.900264i | \(-0.643374\pi\) | ||||
−0.435345 | + | 0.900264i | \(0.643374\pi\) | |||||||
\(138\) | −4.28608 | −0.364856 | ||||||||
\(139\) | 18.1509 | 1.53954 | 0.769771 | − | 0.638320i | \(-0.220370\pi\) | ||||
0.769771 | + | 0.638320i | \(0.220370\pi\) | |||||||
\(140\) | −2.68943 | −0.227298 | ||||||||
\(141\) | −9.50647 | −0.800589 | ||||||||
\(142\) | −10.8788 | −0.912924 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.90551 | −0.158793 | ||||||||
\(145\) | 1.53291 | 0.127301 | ||||||||
\(146\) | −11.6900 | −0.967470 | ||||||||
\(147\) | 1.44002 | 0.118771 | ||||||||
\(148\) | 2.85188 | 0.234423 | ||||||||
\(149\) | −2.69811 | −0.221038 | −0.110519 | − | 0.993874i | \(-0.535251\pi\) | ||||
−0.110519 | + | 0.993874i | \(0.535251\pi\) | |||||||
\(150\) | −4.32752 | −0.353341 | ||||||||
\(151\) | 5.24220 | 0.426604 | 0.213302 | − | 0.976986i | \(-0.431578\pi\) | ||||
0.213302 | + | 0.976986i | \(0.431578\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 8.65208 | 0.699479 | ||||||||
\(154\) | −11.5046 | −0.927066 | ||||||||
\(155\) | −7.24109 | −0.581619 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.20220 | 0.175755 | 0.0878774 | − | 0.996131i | \(-0.471992\pi\) | ||||
0.0878774 | + | 0.996131i | \(0.471992\pi\) | |||||||
\(158\) | 9.60591 | 0.764205 | ||||||||
\(159\) | −3.80396 | −0.301674 | ||||||||
\(160\) | 0.929245 | 0.0734632 | ||||||||
\(161\) | 11.8573 | 0.934484 | ||||||||
\(162\) | 0.347501 | 0.0273022 | ||||||||
\(163\) | −21.2249 | −1.66246 | −0.831232 | − | 0.555926i | \(-0.812364\pi\) | ||||
−0.831232 | + | 0.555926i | \(0.812364\pi\) | |||||||
\(164\) | −0.453243 | −0.0353923 | ||||||||
\(165\) | 3.86435 | 0.300840 | ||||||||
\(166\) | −4.33877 | −0.336754 | ||||||||
\(167\) | −16.6096 | −1.28529 | −0.642645 | − | 0.766164i | \(-0.722163\pi\) | ||||
−0.642645 | + | 0.766164i | \(0.722163\pi\) | |||||||
\(168\) | −3.02786 | −0.233605 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.21929 | −0.323605 | ||||||||
\(171\) | 1.90551 | 0.145718 | ||||||||
\(172\) | 4.16877 | 0.317866 | ||||||||
\(173\) | −5.22082 | −0.396932 | −0.198466 | − | 0.980108i | \(-0.563596\pi\) | ||||
−0.198466 | + | 0.980108i | \(0.563596\pi\) | |||||||
\(174\) | 1.72581 | 0.130833 | ||||||||
\(175\) | 11.9719 | 0.904992 | ||||||||
\(176\) | 3.97504 | 0.299630 | ||||||||
\(177\) | 9.43994 | 0.709550 | ||||||||
\(178\) | 6.23045 | 0.466992 | ||||||||
\(179\) | −3.64551 | −0.272478 | −0.136239 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136239 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(180\) | −1.77069 | −0.131979 | ||||||||
\(181\) | −14.4527 | −1.07426 | −0.537131 | − | 0.843499i | \(-0.680492\pi\) | ||||
−0.537131 | + | 0.843499i | \(0.680492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.09762 | 0.376827 | ||||||||
\(184\) | −4.09689 | −0.302027 | ||||||||
\(185\) | 2.65010 | 0.194839 | ||||||||
\(186\) | −8.15229 | −0.597755 | ||||||||
\(187\) | −18.0489 | −1.31986 | ||||||||
\(188\) | −9.08685 | −0.662727 | ||||||||
\(189\) | 14.8532 | 1.08041 | ||||||||
\(190\) | −0.929245 | −0.0674145 | ||||||||
\(191\) | −7.34389 | −0.531386 | −0.265693 | − | 0.964058i | \(-0.585601\pi\) | ||||
−0.265693 | + | 0.964058i | \(0.585601\pi\) | |||||||
\(192\) | 1.04618 | 0.0755014 | ||||||||
\(193\) | 9.57969 | 0.689561 | 0.344781 | − | 0.938683i | \(-0.387953\pi\) | ||||
0.344781 | + | 0.938683i | \(0.387953\pi\) | |||||||
\(194\) | −11.5845 | −0.831722 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.37645 | 0.0983182 | ||||||||
\(197\) | 1.25654 | 0.0895246 | 0.0447623 | − | 0.998998i | \(-0.485747\pi\) | ||||
0.0447623 | + | 0.998998i | \(0.485747\pi\) | |||||||
\(198\) | −7.57447 | −0.538294 | ||||||||
\(199\) | 5.97439 | 0.423513 | 0.211757 | − | 0.977322i | \(-0.432082\pi\) | ||||
0.211757 | + | 0.977322i | \(0.432082\pi\) | |||||||
\(200\) | −4.13650 | −0.292495 | ||||||||
\(201\) | −14.9039 | −1.05124 | ||||||||
\(202\) | 9.68495 | 0.681431 | ||||||||
\(203\) | −4.77438 | −0.335096 | ||||||||
\(204\) | −4.75023 | −0.332583 | ||||||||
\(205\) | −0.421174 | −0.0294160 | ||||||||
\(206\) | −0.0784942 | −0.00546895 | ||||||||
\(207\) | 7.80668 | 0.542601 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.97504 | −0.274959 | ||||||||
\(210\) | −2.81362 | −0.194158 | ||||||||
\(211\) | −2.93090 | −0.201772 | −0.100886 | − | 0.994898i | \(-0.532168\pi\) | ||||
−0.100886 | + | 0.994898i | \(0.532168\pi\) | |||||||
\(212\) | −3.63605 | −0.249725 | ||||||||
\(213\) | −11.3811 | −0.779821 | ||||||||
\(214\) | 1.97833 | 0.135236 | ||||||||
\(215\) | 3.87381 | 0.264192 | ||||||||
\(216\) | −5.13204 | −0.349191 | ||||||||
\(217\) | 22.5530 | 1.53100 | ||||||||
\(218\) | 17.0468 | 1.15456 | ||||||||
\(219\) | −12.2298 | −0.826414 | ||||||||
\(220\) | 3.69378 | 0.249035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.98358 | 0.200245 | ||||||||
\(223\) | 21.7936 | 1.45941 | 0.729705 | − | 0.683762i | \(-0.239657\pi\) | ||||
0.729705 | + | 0.683762i | \(0.239657\pi\) | |||||||
\(224\) | −2.89421 | −0.193378 | ||||||||
\(225\) | 7.88215 | 0.525477 | ||||||||
\(226\) | 7.23739 | 0.481424 | ||||||||
\(227\) | −18.0721 | −1.19949 | −0.599743 | − | 0.800192i | \(-0.704731\pi\) | ||||
−0.599743 | + | 0.800192i | \(0.704731\pi\) | |||||||
\(228\) | −1.04618 | −0.0692849 | ||||||||
\(229\) | −20.7571 | −1.37167 | −0.685833 | − | 0.727759i | \(-0.740562\pi\) | ||||
−0.685833 | + | 0.727759i | \(0.740562\pi\) | |||||||
\(230\) | −3.80702 | −0.251027 | ||||||||
\(231\) | −12.0359 | −0.791901 | ||||||||
\(232\) | 1.64963 | 0.108304 | ||||||||
\(233\) | −26.8846 | −1.76127 | −0.880636 | − | 0.473794i | \(-0.842884\pi\) | ||||
−0.880636 | + | 0.473794i | \(0.842884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.44390 | −0.550820 | ||||||||
\(236\) | 9.02326 | 0.587364 | ||||||||
\(237\) | 10.0495 | 0.652785 | ||||||||
\(238\) | 13.1413 | 0.851826 | ||||||||
\(239\) | 12.0208 | 0.777559 | 0.388779 | − | 0.921331i | \(-0.372897\pi\) | ||||
0.388779 | + | 0.921331i | \(0.372897\pi\) | |||||||
\(240\) | 0.972156 | 0.0627524 | ||||||||
\(241\) | −16.9086 | −1.08918 | −0.544588 | − | 0.838704i | \(-0.683314\pi\) | ||||
−0.544588 | + | 0.838704i | \(0.683314\pi\) | |||||||
\(242\) | 4.80091 | 0.308614 | ||||||||
\(243\) | 15.7597 | 1.01098 | ||||||||
\(244\) | 4.87261 | 0.311937 | ||||||||
\(245\) | 1.27906 | 0.0817163 | ||||||||
\(246\) | −0.474173 | −0.0302322 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.79245 | −0.494821 | ||||||||
\(249\) | −4.53913 | −0.287656 | ||||||||
\(250\) | −8.49005 | −0.536958 | ||||||||
\(251\) | 24.5896 | 1.55208 | 0.776041 | − | 0.630682i | \(-0.217225\pi\) | ||||
0.776041 | + | 0.630682i | \(0.217225\pi\) | |||||||
\(252\) | 5.51495 | 0.347409 | ||||||||
\(253\) | −16.2853 | −1.02385 | ||||||||
\(254\) | −10.6484 | −0.668140 | ||||||||
\(255\) | −4.41413 | −0.276423 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.6988 | −1.29115 | −0.645577 | − | 0.763695i | \(-0.723383\pi\) | ||||
−0.645577 | + | 0.763695i | \(0.723383\pi\) | |||||||
\(258\) | 4.36128 | 0.271521 | ||||||||
\(259\) | −8.25395 | −0.512876 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.14339 | −0.194571 | ||||||||
\(262\) | 17.6085 | 1.08786 | ||||||||
\(263\) | −24.3236 | −1.49986 | −0.749930 | − | 0.661517i | \(-0.769913\pi\) | ||||
−0.749930 | + | 0.661517i | \(0.769913\pi\) | |||||||
\(264\) | 4.15860 | 0.255944 | ||||||||
\(265\) | −3.37878 | −0.207557 | ||||||||
\(266\) | 2.89421 | 0.177455 | ||||||||
\(267\) | 6.51817 | 0.398905 | ||||||||
\(268\) | −14.2461 | −0.870217 | ||||||||
\(269\) | −0.385169 | −0.0234842 | −0.0117421 | − | 0.999931i | \(-0.503738\pi\) | ||||
−0.0117421 | + | 0.999931i | \(0.503738\pi\) | |||||||
\(270\) | −4.76892 | −0.290227 | ||||||||
\(271\) | 21.8256 | 1.32581 | 0.662906 | − | 0.748702i | \(-0.269323\pi\) | ||||
0.662906 | + | 0.748702i | \(0.269323\pi\) | |||||||
\(272\) | −4.54056 | −0.275312 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1912 | −0.615670 | ||||||||
\(275\) | −16.4428 | −0.991535 | ||||||||
\(276\) | −4.28608 | −0.257992 | ||||||||
\(277\) | −12.9100 | −0.775687 | −0.387843 | − | 0.921725i | \(-0.626780\pi\) | ||||
−0.387843 | + | 0.921725i | \(0.626780\pi\) | |||||||
\(278\) | 18.1509 | 1.08862 | ||||||||
\(279\) | 14.8486 | 0.888962 | ||||||||
\(280\) | −2.68943 | −0.160724 | ||||||||
\(281\) | −6.07209 | −0.362230 | −0.181115 | − | 0.983462i | \(-0.557971\pi\) | ||||
−0.181115 | + | 0.983462i | \(0.557971\pi\) | |||||||
\(282\) | −9.50647 | −0.566102 | ||||||||
\(283\) | 12.3131 | 0.731940 | 0.365970 | − | 0.930627i | \(-0.380737\pi\) | ||||
0.365970 | + | 0.930627i | \(0.380737\pi\) | |||||||
\(284\) | −10.8788 | −0.645535 | ||||||||
\(285\) | −0.972156 | −0.0575855 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.31178 | 0.0774320 | ||||||||
\(288\) | −1.90551 | −0.112283 | ||||||||
\(289\) | 3.61665 | 0.212744 | ||||||||
\(290\) | 1.53291 | 0.0900156 | ||||||||
\(291\) | −12.1195 | −0.710458 | ||||||||
\(292\) | −11.6900 | −0.684105 | ||||||||
\(293\) | −7.44576 | −0.434986 | −0.217493 | − | 0.976062i | \(-0.569788\pi\) | ||||
−0.217493 | + | 0.976062i | \(0.569788\pi\) | |||||||
\(294\) | 1.44002 | 0.0839835 | ||||||||
\(295\) | 8.38482 | 0.488183 | ||||||||
\(296\) | 2.85188 | 0.165762 | ||||||||
\(297\) | −20.4000 | −1.18373 | ||||||||
\(298\) | −2.69811 | −0.156297 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.32752 | −0.249850 | ||||||||
\(301\) | −12.0653 | −0.695433 | ||||||||
\(302\) | 5.24220 | 0.301655 | ||||||||
\(303\) | 10.1322 | 0.582079 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 4.52785 | 0.259264 | ||||||||
\(306\) | 8.65208 | 0.494606 | ||||||||
\(307\) | 18.8708 | 1.07701 | 0.538506 | − | 0.842622i | \(-0.318989\pi\) | ||||
0.538506 | + | 0.842622i | \(0.318989\pi\) | |||||||
\(308\) | −11.5046 | −0.655535 | ||||||||
\(309\) | −0.0821190 | −0.00467159 | ||||||||
\(310\) | −7.24109 | −0.411266 | ||||||||
\(311\) | 5.01837 | 0.284566 | 0.142283 | − | 0.989826i | \(-0.454556\pi\) | ||||
0.142283 | + | 0.989826i | \(0.454556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5284 | −1.27338 | −0.636689 | − | 0.771121i | \(-0.719696\pi\) | ||||
−0.636689 | + | 0.771121i | \(0.719696\pi\) | |||||||
\(314\) | 2.20220 | 0.124277 | ||||||||
\(315\) | 5.12474 | 0.288746 | ||||||||
\(316\) | 9.60591 | 0.540375 | ||||||||
\(317\) | 17.2007 | 0.966086 | 0.483043 | − | 0.875597i | \(-0.339532\pi\) | ||||
0.483043 | + | 0.875597i | \(0.339532\pi\) | |||||||
\(318\) | −3.80396 | −0.213316 | ||||||||
\(319\) | 6.55734 | 0.367141 | ||||||||
\(320\) | 0.929245 | 0.0519464 | ||||||||
\(321\) | 2.06969 | 0.115519 | ||||||||
\(322\) | 11.8573 | 0.660780 | ||||||||
\(323\) | 4.54056 | 0.252643 | ||||||||
\(324\) | 0.347501 | 0.0193056 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.2249 | −1.17554 | ||||||||
\(327\) | 17.8340 | 0.986224 | ||||||||
\(328\) | −0.453243 | −0.0250262 | ||||||||
\(329\) | 26.2993 | 1.44992 | ||||||||
\(330\) | 3.86435 | 0.212726 | ||||||||
\(331\) | −7.57755 | −0.416500 | −0.208250 | − | 0.978076i | \(-0.566777\pi\) | ||||
−0.208250 | + | 0.978076i | \(0.566777\pi\) | |||||||
\(332\) | −4.33877 | −0.238121 | ||||||||
\(333\) | −5.43429 | −0.297797 | ||||||||
\(334\) | −16.6096 | −0.908837 | ||||||||
\(335\) | −13.2381 | −0.723273 | ||||||||
\(336\) | −3.02786 | −0.165183 | ||||||||
\(337\) | 12.4953 | 0.680665 | 0.340333 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340333 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.57160 | 0.411233 | ||||||||
\(340\) | −4.21929 | −0.228823 | ||||||||
\(341\) | −30.9753 | −1.67740 | ||||||||
\(342\) | 1.90551 | 0.103038 | ||||||||
\(343\) | 16.2757 | 0.878807 | ||||||||
\(344\) | 4.16877 | 0.224765 | ||||||||
\(345\) | −3.98282 | −0.214428 | ||||||||
\(346\) | −5.22082 | −0.280673 | ||||||||
\(347\) | −9.64219 | −0.517620 | −0.258810 | − | 0.965928i | \(-0.583330\pi\) | ||||
−0.258810 | + | 0.965928i | \(0.583330\pi\) | |||||||
\(348\) | 1.72581 | 0.0925130 | ||||||||
\(349\) | 30.2434 | 1.61889 | 0.809446 | − | 0.587195i | \(-0.199768\pi\) | ||||
0.809446 | + | 0.587195i | \(0.199768\pi\) | |||||||
\(350\) | 11.9719 | 0.639926 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.97504 | 0.211870 | ||||||||
\(353\) | 11.1133 | 0.591500 | 0.295750 | − | 0.955265i | \(-0.404431\pi\) | ||||
0.295750 | + | 0.955265i | \(0.404431\pi\) | |||||||
\(354\) | 9.43994 | 0.501727 | ||||||||
\(355\) | −10.1090 | −0.536531 | ||||||||
\(356\) | 6.23045 | 0.330213 | ||||||||
\(357\) | 13.7482 | 0.727631 | ||||||||
\(358\) | −3.64551 | −0.192671 | ||||||||
\(359\) | −29.5541 | −1.55981 | −0.779904 | − | 0.625899i | \(-0.784732\pi\) | ||||
−0.779904 | + | 0.625899i | \(0.784732\pi\) | |||||||
\(360\) | −1.77069 | −0.0933233 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.4527 | −0.759618 | ||||||||
\(363\) | 5.02261 | 0.263618 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8629 | −0.568588 | ||||||||
\(366\) | 5.09762 | 0.266457 | ||||||||
\(367\) | 30.4669 | 1.59036 | 0.795179 | − | 0.606375i | \(-0.207377\pi\) | ||||
0.795179 | + | 0.606375i | \(0.207377\pi\) | |||||||
\(368\) | −4.09689 | −0.213565 | ||||||||
\(369\) | 0.863659 | 0.0449603 | ||||||||
\(370\) | 2.65010 | 0.137772 | ||||||||
\(371\) | 10.5235 | 0.546353 | ||||||||
\(372\) | −8.15229 | −0.422677 | ||||||||
\(373\) | 28.9669 | 1.49985 | 0.749924 | − | 0.661524i | \(-0.230090\pi\) | ||||
0.749924 | + | 0.661524i | \(0.230090\pi\) | |||||||
\(374\) | −18.0489 | −0.933285 | ||||||||
\(375\) | −8.88211 | −0.458670 | ||||||||
\(376\) | −9.08685 | −0.468618 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 14.8532 | 0.763966 | ||||||||
\(379\) | −32.9190 | −1.69094 | −0.845468 | − | 0.534026i | \(-0.820679\pi\) | ||||
−0.845468 | + | 0.534026i | \(0.820679\pi\) | |||||||
\(380\) | −0.929245 | −0.0476692 | ||||||||
\(381\) | −11.1401 | −0.570726 | ||||||||
\(382\) | −7.34389 | −0.375746 | ||||||||
\(383\) | −17.1752 | −0.877610 | −0.438805 | − | 0.898582i | \(-0.644598\pi\) | ||||
−0.438805 | + | 0.898582i | \(0.644598\pi\) | |||||||
\(384\) | 1.04618 | 0.0533876 | ||||||||
\(385\) | −10.6906 | −0.544842 | ||||||||
\(386\) | 9.57969 | 0.487593 | ||||||||
\(387\) | −7.94364 | −0.403798 | ||||||||
\(388\) | −11.5845 | −0.588116 | ||||||||
\(389\) | 1.10030 | 0.0557876 | 0.0278938 | − | 0.999611i | \(-0.491120\pi\) | ||||
0.0278938 | + | 0.999611i | \(0.491120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.6022 | 0.940753 | ||||||||
\(392\) | 1.37645 | 0.0695214 | ||||||||
\(393\) | 18.4217 | 0.929250 | ||||||||
\(394\) | 1.25654 | 0.0633035 | ||||||||
\(395\) | 8.92624 | 0.449128 | ||||||||
\(396\) | −7.57447 | −0.380631 | ||||||||
\(397\) | 23.3055 | 1.16967 | 0.584836 | − | 0.811152i | \(-0.301159\pi\) | ||||
0.584836 | + | 0.811152i | \(0.301159\pi\) | |||||||
\(398\) | 5.97439 | 0.299469 | ||||||||
\(399\) | 3.02786 | 0.151583 | ||||||||
\(400\) | −4.13650 | −0.206825 | ||||||||
\(401\) | 27.1581 | 1.35621 | 0.678106 | − | 0.734964i | \(-0.262801\pi\) | ||||
0.678106 | + | 0.734964i | \(0.262801\pi\) | |||||||
\(402\) | −14.9039 | −0.743340 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.68495 | 0.481844 | ||||||||
\(405\) | 0.322913 | 0.0160457 | ||||||||
\(406\) | −4.77438 | −0.236948 | ||||||||
\(407\) | 11.3363 | 0.561921 | ||||||||
\(408\) | −4.75023 | −0.235172 | ||||||||
\(409\) | −4.47035 | −0.221044 | −0.110522 | − | 0.993874i | \(-0.535252\pi\) | ||||
−0.110522 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(410\) | −0.421174 | −0.0208003 | ||||||||
\(411\) | −10.6618 | −0.525906 | ||||||||
\(412\) | −0.0784942 | −0.00386713 | ||||||||
\(413\) | −26.1152 | −1.28505 | ||||||||
\(414\) | 7.80668 | 0.383677 | ||||||||
\(415\) | −4.03178 | −0.197912 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.9891 | 0.929901 | ||||||||
\(418\) | −3.97504 | −0.194425 | ||||||||
\(419\) | 7.62391 | 0.372453 | 0.186226 | − | 0.982507i | \(-0.440374\pi\) | ||||
0.186226 | + | 0.982507i | \(0.440374\pi\) | |||||||
\(420\) | −2.81362 | −0.137291 | ||||||||
\(421\) | −31.6349 | −1.54179 | −0.770896 | − | 0.636962i | \(-0.780191\pi\) | ||||
−0.770896 | + | 0.636962i | \(0.780191\pi\) | |||||||
\(422\) | −2.93090 | −0.142674 | ||||||||
\(423\) | 17.3151 | 0.841888 | ||||||||
\(424\) | −3.63605 | −0.176582 | ||||||||
\(425\) | 18.7820 | 0.911062 | ||||||||
\(426\) | −11.3811 | −0.551417 | ||||||||
\(427\) | −14.1024 | −0.682461 | ||||||||
\(428\) | 1.97833 | 0.0956264 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.87381 | 0.186812 | ||||||||
\(431\) | −5.99194 | −0.288621 | −0.144311 | − | 0.989532i | \(-0.546096\pi\) | ||||
−0.144311 | + | 0.989532i | \(0.546096\pi\) | |||||||
\(432\) | −5.13204 | −0.246915 | ||||||||
\(433\) | 22.3035 | 1.07184 | 0.535919 | − | 0.844270i | \(-0.319965\pi\) | ||||
0.535919 | + | 0.844270i | \(0.319965\pi\) | |||||||
\(434\) | 22.5530 | 1.08258 | ||||||||
\(435\) | 1.60370 | 0.0768914 | ||||||||
\(436\) | 17.0468 | 0.816395 | ||||||||
\(437\) | 4.09689 | 0.195981 | ||||||||
\(438\) | −12.2298 | −0.584363 | ||||||||
\(439\) | −8.13560 | −0.388291 | −0.194146 | − | 0.980973i | \(-0.562193\pi\) | ||||
−0.194146 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(440\) | 3.69378 | 0.176094 | ||||||||
\(441\) | −2.62285 | −0.124898 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.37320 | 0.445334 | 0.222667 | − | 0.974895i | \(-0.428524\pi\) | ||||
0.222667 | + | 0.974895i | \(0.428524\pi\) | |||||||
\(444\) | 2.98358 | 0.141594 | ||||||||
\(445\) | 5.78961 | 0.274454 | ||||||||
\(446\) | 21.7936 | 1.03196 | ||||||||
\(447\) | −2.82271 | −0.133509 | ||||||||
\(448\) | −2.89421 | −0.136739 | ||||||||
\(449\) | 23.5049 | 1.10926 | 0.554632 | − | 0.832096i | \(-0.312859\pi\) | ||||
0.554632 | + | 0.832096i | \(0.312859\pi\) | |||||||
\(450\) | 7.88215 | 0.371568 | ||||||||
\(451\) | −1.80166 | −0.0848367 | ||||||||
\(452\) | 7.23739 | 0.340418 | ||||||||
\(453\) | 5.48428 | 0.257674 | ||||||||
\(454\) | −18.0721 | −0.848165 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.04618 | −0.0489918 | ||||||||
\(457\) | 7.02736 | 0.328726 | 0.164363 | − | 0.986400i | \(-0.447443\pi\) | ||||
0.164363 | + | 0.986400i | \(0.447443\pi\) | |||||||
\(458\) | −20.7571 | −0.969915 | ||||||||
\(459\) | 23.3023 | 1.08766 | ||||||||
\(460\) | −3.80702 | −0.177503 | ||||||||
\(461\) | 2.09583 | 0.0976127 | 0.0488064 | − | 0.998808i | \(-0.484458\pi\) | ||||
0.0488064 | + | 0.998808i | \(0.484458\pi\) | |||||||
\(462\) | −12.0359 | −0.559959 | ||||||||
\(463\) | −22.3671 | −1.03949 | −0.519743 | − | 0.854323i | \(-0.673972\pi\) | ||||
−0.519743 | + | 0.854323i | \(0.673972\pi\) | |||||||
\(464\) | 1.64963 | 0.0765822 | ||||||||
\(465\) | −7.57548 | −0.351304 | ||||||||
\(466\) | −26.8846 | −1.24541 | ||||||||
\(467\) | 36.8013 | 1.70296 | 0.851480 | − | 0.524387i | \(-0.175705\pi\) | ||||
0.851480 | + | 0.524387i | \(0.175705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.2311 | 1.90388 | ||||||||
\(470\) | −8.44390 | −0.389488 | ||||||||
\(471\) | 2.30390 | 0.106158 | ||||||||
\(472\) | 9.02326 | 0.415329 | ||||||||
\(473\) | 16.5710 | 0.761936 | ||||||||
\(474\) | 10.0495 | 0.461589 | ||||||||
\(475\) | 4.13650 | 0.189796 | ||||||||
\(476\) | 13.1413 | 0.602332 | ||||||||
\(477\) | 6.92854 | 0.317236 | ||||||||
\(478\) | 12.0208 | 0.549817 | ||||||||
\(479\) | −18.0660 | −0.825459 | −0.412729 | − | 0.910854i | \(-0.635424\pi\) | ||||
−0.412729 | + | 0.910854i | \(0.635424\pi\) | |||||||
\(480\) | 0.972156 | 0.0443726 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.9086 | −0.770164 | ||||||||
\(483\) | 12.4048 | 0.564439 | ||||||||
\(484\) | 4.80091 | 0.218223 | ||||||||
\(485\) | −10.7649 | −0.488808 | ||||||||
\(486\) | 15.7597 | 0.714873 | ||||||||
\(487\) | 19.7205 | 0.893622 | 0.446811 | − | 0.894628i | \(-0.352560\pi\) | ||||
0.446811 | + | 0.894628i | \(0.352560\pi\) | |||||||
\(488\) | 4.87261 | 0.220573 | ||||||||
\(489\) | −22.2050 | −1.00415 | ||||||||
\(490\) | 1.27906 | 0.0577822 | ||||||||
\(491\) | −26.6062 | −1.20072 | −0.600360 | − | 0.799730i | \(-0.704976\pi\) | ||||
−0.600360 | + | 0.799730i | \(0.704976\pi\) | |||||||
\(492\) | −0.474173 | −0.0213774 | ||||||||
\(493\) | −7.49024 | −0.337343 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.03854 | −0.316359 | ||||||||
\(496\) | −7.79245 | −0.349891 | ||||||||
\(497\) | 31.4854 | 1.41231 | ||||||||
\(498\) | −4.53913 | −0.203403 | ||||||||
\(499\) | −5.10306 | −0.228444 | −0.114222 | − | 0.993455i | \(-0.536438\pi\) | ||||
−0.114222 | + | 0.993455i | \(0.536438\pi\) | |||||||
\(500\) | −8.49005 | −0.379686 | ||||||||
\(501\) | −17.3766 | −0.776330 | ||||||||
\(502\) | 24.5896 | 1.09749 | ||||||||
\(503\) | 27.0694 | 1.20697 | 0.603483 | − | 0.797376i | \(-0.293779\pi\) | ||||
0.603483 | + | 0.797376i | \(0.293779\pi\) | |||||||
\(504\) | 5.51495 | 0.245655 | ||||||||
\(505\) | 8.99969 | 0.400481 | ||||||||
\(506\) | −16.2853 | −0.723970 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.6484 | −0.472447 | ||||||||
\(509\) | 9.16648 | 0.406297 | 0.203148 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203148 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(510\) | −4.41413 | −0.195461 | ||||||||
\(511\) | 33.8333 | 1.49670 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.13204 | 0.226585 | ||||||||
\(514\) | −20.6988 | −0.912984 | ||||||||
\(515\) | −0.0729404 | −0.00321414 | ||||||||
\(516\) | 4.36128 | 0.191995 | ||||||||
\(517\) | −36.1205 | −1.58858 | ||||||||
\(518\) | −8.25395 | −0.362658 | ||||||||
\(519\) | −5.46191 | −0.239751 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1666 | −1.32162 | −0.660811 | − | 0.750553i | \(-0.729787\pi\) | ||||
−0.660811 | + | 0.750553i | \(0.729787\pi\) | |||||||
\(522\) | −3.14339 | −0.137582 | ||||||||
\(523\) | −9.39066 | −0.410625 | −0.205312 | − | 0.978697i | \(-0.565821\pi\) | ||||
−0.205312 | + | 0.978697i | \(0.565821\pi\) | |||||||
\(524\) | 17.6085 | 0.769232 | ||||||||
\(525\) | 12.5248 | 0.546625 | ||||||||
\(526\) | −24.3236 | −1.06056 | ||||||||
\(527\) | 35.3821 | 1.54127 | ||||||||
\(528\) | 4.15860 | 0.180980 | ||||||||
\(529\) | −6.21545 | −0.270237 | ||||||||
\(530\) | −3.37878 | −0.146765 | ||||||||
\(531\) | −17.1939 | −0.746153 | ||||||||
\(532\) | 2.89421 | 0.125480 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.51817 | 0.282069 | ||||||||
\(535\) | 1.83836 | 0.0794791 | ||||||||
\(536\) | −14.2461 | −0.615336 | ||||||||
\(537\) | −3.81385 | −0.164580 | ||||||||
\(538\) | −0.385169 | −0.0166058 | ||||||||
\(539\) | 5.47145 | 0.235672 | ||||||||
\(540\) | −4.76892 | −0.205222 | ||||||||
\(541\) | 13.6802 | 0.588160 | 0.294080 | − | 0.955781i | \(-0.404987\pi\) | ||||
0.294080 | + | 0.955781i | \(0.404987\pi\) | |||||||
\(542\) | 21.8256 | 0.937491 | ||||||||
\(543\) | −15.1201 | −0.648866 | ||||||||
\(544\) | −4.54056 | −0.194675 | ||||||||
\(545\) | 15.8407 | 0.678540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.13964 | −0.262512 | −0.131256 | − | 0.991349i | \(-0.541901\pi\) | ||||
−0.131256 | + | 0.991349i | \(0.541901\pi\) | |||||||
\(548\) | −10.1912 | −0.435345 | ||||||||
\(549\) | −9.28481 | −0.396266 | ||||||||
\(550\) | −16.4428 | −0.701121 | ||||||||
\(551\) | −1.64963 | −0.0702766 | ||||||||
\(552\) | −4.28608 | −0.182428 | ||||||||
\(553\) | −27.8015 | −1.18224 | ||||||||
\(554\) | −12.9100 | −0.548494 | ||||||||
\(555\) | 2.77248 | 0.117685 | ||||||||
\(556\) | 18.1509 | 0.769771 | ||||||||
\(557\) | 12.9201 | 0.547444 | 0.273722 | − | 0.961809i | \(-0.411745\pi\) | ||||
0.273722 | + | 0.961809i | \(0.411745\pi\) | |||||||
\(558\) | 14.8486 | 0.628591 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.68943 | −0.113649 | ||||||||
\(561\) | −18.8823 | −0.797213 | ||||||||
\(562\) | −6.07209 | −0.256136 | ||||||||
\(563\) | −39.3705 | −1.65927 | −0.829634 | − | 0.558307i | \(-0.811451\pi\) | ||||
−0.829634 | + | 0.558307i | \(0.811451\pi\) | |||||||
\(564\) | −9.50647 | −0.400294 | ||||||||
\(565\) | 6.72530 | 0.282936 | ||||||||
\(566\) | 12.3131 | 0.517560 | ||||||||
\(567\) | −1.00574 | −0.0422371 | ||||||||
\(568\) | −10.8788 | −0.456462 | ||||||||
\(569\) | 27.7960 | 1.16527 | 0.582634 | − | 0.812734i | \(-0.302022\pi\) | ||||
0.582634 | + | 0.812734i | \(0.302022\pi\) | |||||||
\(570\) | −0.972156 | −0.0407191 | ||||||||
\(571\) | −4.79328 | −0.200592 | −0.100296 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100296 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.68303 | −0.320963 | ||||||||
\(574\) | 1.31178 | 0.0547527 | ||||||||
\(575\) | 16.9468 | 0.706731 | ||||||||
\(576\) | −1.90551 | −0.0793963 | ||||||||
\(577\) | 19.1405 | 0.796829 | 0.398415 | − | 0.917205i | \(-0.369561\pi\) | ||||
0.398415 | + | 0.917205i | \(0.369561\pi\) | |||||||
\(578\) | 3.61665 | 0.150433 | ||||||||
\(579\) | 10.0221 | 0.416503 | ||||||||
\(580\) | 1.53291 | 0.0636506 | ||||||||
\(581\) | 12.5573 | 0.520965 | ||||||||
\(582\) | −12.1195 | −0.502369 | ||||||||
\(583\) | −14.4534 | −0.598600 | ||||||||
\(584\) | −11.6900 | −0.483735 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.44576 | −0.307582 | ||||||||
\(587\) | −15.8721 | −0.655110 | −0.327555 | − | 0.944832i | \(-0.606225\pi\) | ||||
−0.327555 | + | 0.944832i | \(0.606225\pi\) | |||||||
\(588\) | 1.44002 | 0.0593853 | ||||||||
\(589\) | 7.79245 | 0.321082 | ||||||||
\(590\) | 8.38482 | 0.345198 | ||||||||
\(591\) | 1.31456 | 0.0540739 | ||||||||
\(592\) | 2.85188 | 0.117212 | ||||||||
\(593\) | 10.8277 | 0.444642 | 0.222321 | − | 0.974973i | \(-0.428637\pi\) | ||||
0.222321 | + | 0.974973i | \(0.428637\pi\) | |||||||
\(594\) | −20.4000 | −0.837024 | ||||||||
\(595\) | 12.2115 | 0.500623 | ||||||||
\(596\) | −2.69811 | −0.110519 | ||||||||
\(597\) | 6.25028 | 0.255807 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.831670 | −0.0339811 | −0.0169906 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169906 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(600\) | −4.32752 | −0.176670 | ||||||||
\(601\) | 35.6665 | 1.45487 | 0.727433 | − | 0.686179i | \(-0.240713\pi\) | ||||
0.727433 | + | 0.686179i | \(0.240713\pi\) | |||||||
\(602\) | −12.0653 | −0.491745 | ||||||||
\(603\) | 27.1460 | 1.10547 | ||||||||
\(604\) | 5.24220 | 0.213302 | ||||||||
\(605\) | 4.46122 | 0.181374 | ||||||||
\(606\) | 10.1322 | 0.411592 | ||||||||
\(607\) | 16.8104 | 0.682311 | 0.341156 | − | 0.940007i | \(-0.389182\pi\) | ||||
0.341156 | + | 0.940007i | \(0.389182\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −4.99485 | −0.202402 | ||||||||
\(610\) | 4.52785 | 0.183327 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.65208 | 0.349739 | ||||||||
\(613\) | 27.5552 | 1.11294 | 0.556471 | − | 0.830867i | \(-0.312155\pi\) | ||||
0.556471 | + | 0.830867i | \(0.312155\pi\) | |||||||
\(614\) | 18.8708 | 0.761563 | ||||||||
\(615\) | −0.440623 | −0.0177676 | ||||||||
\(616\) | −11.5046 | −0.463533 | ||||||||
\(617\) | −40.6943 | −1.63829 | −0.819145 | − | 0.573586i | \(-0.805552\pi\) | ||||
−0.819145 | + | 0.573586i | \(0.805552\pi\) | |||||||
\(618\) | −0.0821190 | −0.00330331 | ||||||||
\(619\) | −1.84653 | −0.0742183 | −0.0371092 | − | 0.999311i | \(-0.511815\pi\) | ||||
−0.0371092 | + | 0.999311i | \(0.511815\pi\) | |||||||
\(620\) | −7.24109 | −0.290809 | ||||||||
\(621\) | 21.0254 | 0.843721 | ||||||||
\(622\) | 5.01837 | 0.201218 | ||||||||
\(623\) | −18.0322 | −0.722446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7932 | 0.511728 | ||||||||
\(626\) | −22.5284 | −0.900414 | ||||||||
\(627\) | −4.15860 | −0.166078 | ||||||||
\(628\) | 2.20220 | 0.0878774 | ||||||||
\(629\) | −12.9491 | −0.516316 | ||||||||
\(630\) | 5.12474 | 0.204174 | ||||||||
\(631\) | −4.53563 | −0.180560 | −0.0902802 | − | 0.995916i | \(-0.528776\pi\) | ||||
−0.0902802 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(632\) | 9.60591 | 0.382103 | ||||||||
\(633\) | −3.06625 | −0.121872 | ||||||||
\(634\) | 17.2007 | 0.683126 | ||||||||
\(635\) | −9.89497 | −0.392670 | ||||||||
\(636\) | −3.80396 | −0.150837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.55734 | 0.259608 | ||||||||
\(639\) | 20.7296 | 0.820049 | ||||||||
\(640\) | 0.929245 | 0.0367316 | ||||||||
\(641\) | −7.09568 | −0.280263 | −0.140131 | − | 0.990133i | \(-0.544752\pi\) | ||||
−0.140131 | + | 0.990133i | \(0.544752\pi\) | |||||||
\(642\) | 2.06969 | 0.0816842 | ||||||||
\(643\) | 31.5892 | 1.24576 | 0.622879 | − | 0.782318i | \(-0.285963\pi\) | ||||
0.622879 | + | 0.782318i | \(0.285963\pi\) | |||||||
\(644\) | 11.8573 | 0.467242 | ||||||||
\(645\) | 4.05270 | 0.159575 | ||||||||
\(646\) | 4.54056 | 0.178646 | ||||||||
\(647\) | 3.99801 | 0.157178 | 0.0785891 | − | 0.996907i | \(-0.474959\pi\) | ||||
0.0785891 | + | 0.996907i | \(0.474959\pi\) | |||||||
\(648\) | 0.347501 | 0.0136511 | ||||||||
\(649\) | 35.8678 | 1.40793 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.5945 | 0.924740 | ||||||||
\(652\) | −21.2249 | −0.831232 | ||||||||
\(653\) | 21.4463 | 0.839258 | 0.419629 | − | 0.907696i | \(-0.362160\pi\) | ||||
0.419629 | + | 0.907696i | \(0.362160\pi\) | |||||||
\(654\) | 17.8340 | 0.697366 | ||||||||
\(655\) | 16.3626 | 0.639341 | ||||||||
\(656\) | −0.453243 | −0.0176962 | ||||||||
\(657\) | 22.2754 | 0.869045 | ||||||||
\(658\) | 26.2993 | 1.02525 | ||||||||
\(659\) | −21.7818 | −0.848497 | −0.424248 | − | 0.905546i | \(-0.639462\pi\) | ||||
−0.424248 | + | 0.905546i | \(0.639462\pi\) | |||||||
\(660\) | 3.86435 | 0.150420 | ||||||||
\(661\) | −10.0216 | −0.389795 | −0.194898 | − | 0.980824i | \(-0.562437\pi\) | ||||
−0.194898 | + | 0.980824i | \(0.562437\pi\) | |||||||
\(662\) | −7.57755 | −0.294510 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.33877 | −0.168377 | ||||||||
\(665\) | 2.68943 | 0.104292 | ||||||||
\(666\) | −5.43429 | −0.210575 | ||||||||
\(667\) | −6.75836 | −0.261685 | ||||||||
\(668\) | −16.6096 | −0.642645 | ||||||||
\(669\) | 22.8000 | 0.881501 | ||||||||
\(670\) | −13.2381 | −0.511431 | ||||||||
\(671\) | 19.3688 | 0.747724 | ||||||||
\(672\) | −3.02786 | −0.116802 | ||||||||
\(673\) | −2.72873 | −0.105185 | −0.0525925 | − | 0.998616i | \(-0.516748\pi\) | ||||
−0.0525925 | + | 0.998616i | \(0.516748\pi\) | |||||||
\(674\) | 12.4953 | 0.481303 | ||||||||
\(675\) | 21.2287 | 0.817093 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.2469 | 0.970315 | 0.485158 | − | 0.874427i | \(-0.338762\pi\) | ||||
0.485158 | + | 0.874427i | \(0.338762\pi\) | |||||||
\(678\) | 7.57160 | 0.290786 | ||||||||
\(679\) | 33.5281 | 1.28669 | ||||||||
\(680\) | −4.21929 | −0.161802 | ||||||||
\(681\) | −18.9066 | −0.724504 | ||||||||
\(682\) | −30.9753 | −1.18610 | ||||||||
\(683\) | −42.1086 | −1.61124 | −0.805620 | − | 0.592432i | \(-0.798168\pi\) | ||||
−0.805620 | + | 0.592432i | \(0.798168\pi\) | |||||||
\(684\) | 1.90551 | 0.0728590 | ||||||||
\(685\) | −9.47008 | −0.361833 | ||||||||
\(686\) | 16.2757 | 0.621410 | ||||||||
\(687\) | −21.7156 | −0.828502 | ||||||||
\(688\) | 4.16877 | 0.158933 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.98282 | −0.151623 | ||||||||
\(691\) | −39.6111 | −1.50688 | −0.753438 | − | 0.657519i | \(-0.771606\pi\) | ||||
−0.753438 | + | 0.657519i | \(0.771606\pi\) | |||||||
\(692\) | −5.22082 | −0.198466 | ||||||||
\(693\) | 21.9221 | 0.832752 | ||||||||
\(694\) | −9.64219 | −0.366013 | ||||||||
\(695\) | 16.8667 | 0.639789 | ||||||||
\(696\) | 1.72581 | 0.0654166 | ||||||||
\(697\) | 2.05798 | 0.0779514 | ||||||||
\(698\) | 30.2434 | 1.14473 | ||||||||
\(699\) | −28.1261 | −1.06383 | ||||||||
\(700\) | 11.9719 | 0.452496 | ||||||||
\(701\) | 36.4844 | 1.37800 | 0.688998 | − | 0.724764i | \(-0.258051\pi\) | ||||
0.688998 | + | 0.724764i | \(0.258051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.85188 | −0.107561 | ||||||||
\(704\) | 3.97504 | 0.149815 | ||||||||
\(705\) | −8.83383 | −0.332701 | ||||||||
\(706\) | 11.1133 | 0.418253 | ||||||||
\(707\) | −28.0303 | −1.05419 | ||||||||
\(708\) | 9.43994 | 0.354775 | ||||||||
\(709\) | 38.2462 | 1.43637 | 0.718183 | − | 0.695854i | \(-0.244974\pi\) | ||||
0.718183 | + | 0.695854i | \(0.244974\pi\) | |||||||
\(710\) | −10.1090 | −0.379385 | ||||||||
\(711\) | −18.3042 | −0.686460 | ||||||||
\(712\) | 6.23045 | 0.233496 | ||||||||
\(713\) | 31.9248 | 1.19559 | ||||||||
\(714\) | 13.7482 | 0.514512 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.64551 | −0.136239 | ||||||||
\(717\) | 12.5759 | 0.469654 | ||||||||
\(718\) | −29.5541 | −1.10295 | ||||||||
\(719\) | 36.6382 | 1.36637 | 0.683187 | − | 0.730244i | \(-0.260593\pi\) | ||||
0.683187 | + | 0.730244i | \(0.260593\pi\) | |||||||
\(720\) | −1.77069 | −0.0659895 | ||||||||
\(721\) | 0.227179 | 0.00846058 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −17.6894 | −0.657875 | ||||||||
\(724\) | −14.4527 | −0.537131 | ||||||||
\(725\) | −6.82370 | −0.253426 | ||||||||
\(726\) | 5.02261 | 0.186406 | ||||||||
\(727\) | −25.0966 | −0.930781 | −0.465391 | − | 0.885105i | \(-0.654086\pi\) | ||||
−0.465391 | + | 0.885105i | \(0.654086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4449 | 0.572034 | ||||||||
\(730\) | −10.8629 | −0.402052 | ||||||||
\(731\) | −18.9285 | −0.700097 | ||||||||
\(732\) | 5.09762 | 0.188413 | ||||||||
\(733\) | −10.8948 | −0.402410 | −0.201205 | − | 0.979549i | \(-0.564486\pi\) | ||||
−0.201205 | + | 0.979549i | \(0.564486\pi\) | |||||||
\(734\) | 30.4669 | 1.12455 | ||||||||
\(735\) | 1.33813 | 0.0493576 | ||||||||
\(736\) | −4.09689 | −0.151014 | ||||||||
\(737\) | −56.6286 | −2.08594 | ||||||||
\(738\) | 0.863659 | 0.0317917 | ||||||||
\(739\) | 7.22806 | 0.265888 | 0.132944 | − | 0.991124i | \(-0.457557\pi\) | ||||
0.132944 | + | 0.991124i | \(0.457557\pi\) | |||||||
\(740\) | 2.65010 | 0.0974195 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.5235 | 0.386330 | ||||||||
\(743\) | −53.9055 | −1.97760 | −0.988801 | − | 0.149239i | \(-0.952318\pi\) | ||||
−0.988801 | + | 0.149239i | \(0.952318\pi\) | |||||||
\(744\) | −8.15229 | −0.298878 | ||||||||
\(745\) | −2.50720 | −0.0918569 | ||||||||
\(746\) | 28.9669 | 1.06055 | ||||||||
\(747\) | 8.26757 | 0.302495 | ||||||||
\(748\) | −18.0489 | −0.659932 | ||||||||
\(749\) | −5.72572 | −0.209213 | ||||||||
\(750\) | −8.88211 | −0.324329 | ||||||||
\(751\) | −15.8038 | −0.576689 | −0.288344 | − | 0.957527i | \(-0.593105\pi\) | ||||
−0.288344 | + | 0.957527i | \(0.593105\pi\) | |||||||
\(752\) | −9.08685 | −0.331363 | ||||||||
\(753\) | 25.7251 | 0.937475 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.87129 | 0.177284 | ||||||||
\(756\) | 14.8532 | 0.540206 | ||||||||
\(757\) | −19.9728 | −0.725925 | −0.362963 | − | 0.931804i | \(-0.618235\pi\) | ||||
−0.362963 | + | 0.931804i | \(0.618235\pi\) | |||||||
\(758\) | −32.9190 | −1.19567 | ||||||||
\(759\) | −17.0373 | −0.618416 | ||||||||
\(760\) | −0.929245 | −0.0337072 | ||||||||
\(761\) | 13.8528 | 0.502164 | 0.251082 | − | 0.967966i | \(-0.419214\pi\) | ||||
0.251082 | + | 0.967966i | \(0.419214\pi\) | |||||||
\(762\) | −11.1401 | −0.403564 | ||||||||
\(763\) | −49.3371 | −1.78612 | ||||||||
\(764\) | −7.34389 | −0.265693 | ||||||||
\(765\) | 8.03990 | 0.290683 | ||||||||
\(766\) | −17.1752 | −0.620564 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.04618 | 0.0377507 | ||||||||
\(769\) | 18.3743 | 0.662594 | 0.331297 | − | 0.943526i | \(-0.392514\pi\) | ||||
0.331297 | + | 0.943526i | \(0.392514\pi\) | |||||||
\(770\) | −10.6906 | −0.385262 | ||||||||
\(771\) | −21.6546 | −0.779872 | ||||||||
\(772\) | 9.57969 | 0.344781 | ||||||||
\(773\) | −26.3325 | −0.947115 | −0.473558 | − | 0.880763i | \(-0.657030\pi\) | ||||
−0.473558 | + | 0.880763i | \(0.657030\pi\) | |||||||
\(774\) | −7.94364 | −0.285528 | ||||||||
\(775\) | 32.2335 | 1.15786 | ||||||||
\(776\) | −11.5845 | −0.415861 | ||||||||
\(777\) | −8.63511 | −0.309783 | ||||||||
\(778\) | 1.10030 | 0.0394478 | ||||||||
\(779\) | 0.453243 | 0.0162391 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.2434 | −1.54737 | ||||||||
\(782\) | 18.6022 | 0.665213 | ||||||||
\(783\) | −8.46597 | −0.302549 | ||||||||
\(784\) | 1.37645 | 0.0491591 | ||||||||
\(785\) | 2.04638 | 0.0730386 | ||||||||
\(786\) | 18.4217 | 0.657079 | ||||||||
\(787\) | −54.9301 | −1.95805 | −0.979023 | − | 0.203748i | \(-0.934688\pi\) | ||||
−0.979023 | + | 0.203748i | \(0.934688\pi\) | |||||||
\(788\) | 1.25654 | 0.0447623 | ||||||||
\(789\) | −25.4469 | −0.905932 | ||||||||
\(790\) | 8.92624 | 0.317581 | ||||||||
\(791\) | −20.9465 | −0.744773 | ||||||||
\(792\) | −7.57447 | −0.269147 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 23.3055 | 0.827083 | ||||||||
\(795\) | −3.53481 | −0.125367 | ||||||||
\(796\) | 5.97439 | 0.211757 | ||||||||
\(797\) | −25.0272 | −0.886510 | −0.443255 | − | 0.896396i | \(-0.646176\pi\) | ||||
−0.443255 | + | 0.896396i | \(0.646176\pi\) | |||||||
\(798\) | 3.02786 | 0.107185 | ||||||||
\(799\) | 41.2593 | 1.45965 | ||||||||
\(800\) | −4.13650 | −0.146248 | ||||||||
\(801\) | −11.8722 | −0.419483 | ||||||||
\(802\) | 27.1581 | 0.958986 | ||||||||
\(803\) | −46.4681 | −1.63982 | ||||||||
\(804\) | −14.9039 | −0.525621 | ||||||||
\(805\) | 11.0183 | 0.388344 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.402955 | −0.0141847 | ||||||||
\(808\) | 9.68495 | 0.340716 | ||||||||
\(809\) | −16.4556 | −0.578549 | −0.289275 | − | 0.957246i | \(-0.593414\pi\) | ||||
−0.289275 | + | 0.957246i | \(0.593414\pi\) | |||||||
\(810\) | 0.322913 | 0.0113460 | ||||||||
\(811\) | −18.3589 | −0.644667 | −0.322334 | − | 0.946626i | \(-0.604467\pi\) | ||||
−0.322334 | + | 0.946626i | \(0.604467\pi\) | |||||||
\(812\) | −4.77438 | −0.167548 | ||||||||
\(813\) | 22.8335 | 0.800806 | ||||||||
\(814\) | 11.3363 | 0.397338 | ||||||||
\(815\) | −19.7231 | −0.690871 | ||||||||
\(816\) | −4.75023 | −0.166291 | ||||||||
\(817\) | −4.16877 | −0.145847 | ||||||||
\(818\) | −4.47035 | −0.156302 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.421174 | −0.0147080 | ||||||||
\(821\) | −56.5259 | −1.97277 | −0.986384 | − | 0.164460i | \(-0.947412\pi\) | ||||
−0.986384 | + | 0.164460i | \(0.947412\pi\) | |||||||
\(822\) | −10.6618 | −0.371872 | ||||||||
\(823\) | −22.1382 | −0.771690 | −0.385845 | − | 0.922564i | \(-0.626090\pi\) | ||||
−0.385845 | + | 0.922564i | \(0.626090\pi\) | |||||||
\(824\) | −0.0784942 | −0.00273448 | ||||||||
\(825\) | −17.2021 | −0.598899 | ||||||||
\(826\) | −26.1152 | −0.908665 | ||||||||
\(827\) | 14.6709 | 0.510157 | 0.255078 | − | 0.966920i | \(-0.417899\pi\) | ||||
0.255078 | + | 0.966920i | \(0.417899\pi\) | |||||||
\(828\) | 7.80668 | 0.271301 | ||||||||
\(829\) | 32.7680 | 1.13808 | 0.569040 | − | 0.822310i | \(-0.307315\pi\) | ||||
0.569040 | + | 0.822310i | \(0.307315\pi\) | |||||||
\(830\) | −4.03178 | −0.139945 | ||||||||
\(831\) | −13.5062 | −0.468524 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.24987 | −0.216545 | ||||||||
\(834\) | 18.9891 | 0.657539 | ||||||||
\(835\) | −15.4344 | −0.534129 | ||||||||
\(836\) | −3.97504 | −0.137479 | ||||||||
\(837\) | 39.9912 | 1.38230 | ||||||||
\(838\) | 7.62391 | 0.263364 | ||||||||
\(839\) | −13.6785 | −0.472234 | −0.236117 | − | 0.971725i | \(-0.575875\pi\) | ||||
−0.236117 | + | 0.971725i | \(0.575875\pi\) | |||||||
\(840\) | −2.81362 | −0.0970792 | ||||||||
\(841\) | −26.2787 | −0.906163 | ||||||||
\(842\) | −31.6349 | −1.09021 | ||||||||
\(843\) | −6.35249 | −0.218791 | ||||||||
\(844\) | −2.93090 | −0.100886 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.3151 | 0.595305 | ||||||||
\(847\) | −13.8948 | −0.477432 | ||||||||
\(848\) | −3.63605 | −0.124863 | ||||||||
\(849\) | 12.8817 | 0.442100 | ||||||||
\(850\) | 18.7820 | 0.644218 | ||||||||
\(851\) | −11.6839 | −0.400518 | ||||||||
\(852\) | −11.3811 | −0.389911 | ||||||||
\(853\) | −41.0799 | −1.40655 | −0.703274 | − | 0.710919i | \(-0.748279\pi\) | ||||
−0.703274 | + | 0.710919i | \(0.748279\pi\) | |||||||
\(854\) | −14.1024 | −0.482573 | ||||||||
\(855\) | 1.77069 | 0.0605562 | ||||||||
\(856\) | 1.97833 | 0.0676181 | ||||||||
\(857\) | 11.4735 | 0.391929 | 0.195964 | − | 0.980611i | \(-0.437216\pi\) | ||||
0.195964 | + | 0.980611i | \(0.437216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.2630 | −0.350170 | −0.175085 | − | 0.984553i | \(-0.556020\pi\) | ||||
−0.175085 | + | 0.984553i | \(0.556020\pi\) | |||||||
\(860\) | 3.87381 | 0.132096 | ||||||||
\(861\) | 1.37236 | 0.0467698 | ||||||||
\(862\) | −5.99194 | −0.204086 | ||||||||
\(863\) | −53.9995 | −1.83816 | −0.919082 | − | 0.394067i | \(-0.871068\pi\) | ||||
−0.919082 | + | 0.394067i | \(0.871068\pi\) | |||||||
\(864\) | −5.13204 | −0.174596 | ||||||||
\(865\) | −4.85142 | −0.164953 | ||||||||
\(866\) | 22.3035 | 0.757904 | ||||||||
\(867\) | 3.78366 | 0.128500 | ||||||||
\(868\) | 22.5530 | 0.765498 | ||||||||
\(869\) | 38.1838 | 1.29530 | ||||||||
\(870\) | 1.60370 | 0.0543705 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17.0468 | 0.577278 | ||||||||
\(873\) | 22.0745 | 0.747107 | ||||||||
\(874\) | 4.09689 | 0.138580 | ||||||||
\(875\) | 24.5720 | 0.830685 | ||||||||
\(876\) | −12.2298 | −0.413207 | ||||||||
\(877\) | 46.9344 | 1.58486 | 0.792431 | − | 0.609962i | \(-0.208815\pi\) | ||||
0.792431 | + | 0.609962i | \(0.208815\pi\) | |||||||
\(878\) | −8.13560 | −0.274563 | ||||||||
\(879\) | −7.78960 | −0.262737 | ||||||||
\(880\) | 3.69378 | 0.124517 | ||||||||
\(881\) | 36.7205 | 1.23714 | 0.618572 | − | 0.785728i | \(-0.287712\pi\) | ||||
0.618572 | + | 0.785728i | \(0.287712\pi\) | |||||||
\(882\) | −2.62285 | −0.0883159 | ||||||||
\(883\) | −40.7395 | −1.37099 | −0.685497 | − | 0.728076i | \(-0.740415\pi\) | ||||
−0.685497 | + | 0.728076i | \(0.740415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.77202 | 0.294868 | ||||||||
\(886\) | 9.37320 | 0.314899 | ||||||||
\(887\) | 38.9664 | 1.30836 | 0.654182 | − | 0.756337i | \(-0.273013\pi\) | ||||
0.654182 | + | 0.756337i | \(0.273013\pi\) | |||||||
\(888\) | 2.98358 | 0.100122 | ||||||||
\(889\) | 30.8187 | 1.03363 | ||||||||
\(890\) | 5.78961 | 0.194068 | ||||||||
\(891\) | 1.38133 | 0.0462762 | ||||||||
\(892\) | 21.7936 | 0.729705 | ||||||||
\(893\) | 9.08685 | 0.304080 | ||||||||
\(894\) | −2.82271 | −0.0944054 | ||||||||
\(895\) | −3.38757 | −0.113234 | ||||||||
\(896\) | −2.89421 | −0.0966888 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.5049 | 0.784368 | ||||||||
\(899\) | −12.8547 | −0.428727 | ||||||||
\(900\) | 7.88215 | 0.262738 | ||||||||
\(901\) | 16.5097 | 0.550018 | ||||||||
\(902\) | −1.80166 | −0.0599886 | ||||||||
\(903\) | −12.6225 | −0.420049 | ||||||||
\(904\) | 7.23739 | 0.240712 | ||||||||
\(905\) | −13.4301 | −0.446432 | ||||||||
\(906\) | 5.48428 | 0.182203 | ||||||||
\(907\) | 57.5459 | 1.91078 | 0.955391 | − | 0.295345i | \(-0.0954347\pi\) | ||||
0.955391 | + | 0.295345i | \(0.0954347\pi\) | |||||||
\(908\) | −18.0721 | −0.599743 | ||||||||
\(909\) | −18.4548 | −0.612106 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3410 | 0.475140 | 0.237570 | − | 0.971370i | \(-0.423649\pi\) | ||||
0.237570 | + | 0.971370i | \(0.423649\pi\) | |||||||
\(912\) | −1.04618 | −0.0346424 | ||||||||
\(913\) | −17.2468 | −0.570785 | ||||||||
\(914\) | 7.02736 | 0.232445 | ||||||||
\(915\) | 4.73694 | 0.156598 | ||||||||
\(916\) | −20.7571 | −0.685833 | ||||||||
\(917\) | −50.9628 | −1.68294 | ||||||||
\(918\) | 23.3023 | 0.769091 | ||||||||
\(919\) | −9.88857 | −0.326194 | −0.163097 | − | 0.986610i | \(-0.552148\pi\) | ||||
−0.163097 | + | 0.986610i | \(0.552148\pi\) | |||||||
\(920\) | −3.80702 | −0.125514 | ||||||||
\(921\) | 19.7422 | 0.650528 | ||||||||
\(922\) | 2.09583 | 0.0690226 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.0359 | −0.395951 | ||||||||
\(925\) | −11.7968 | −0.387877 | ||||||||
\(926\) | −22.3671 | −0.735028 | ||||||||
\(927\) | 0.149572 | 0.00491258 | ||||||||
\(928\) | 1.64963 | 0.0541518 | ||||||||
\(929\) | −29.4749 | −0.967041 | −0.483521 | − | 0.875333i | \(-0.660642\pi\) | ||||
−0.483521 | + | 0.875333i | \(0.660642\pi\) | |||||||
\(930\) | −7.57548 | −0.248410 | ||||||||
\(931\) | −1.37645 | −0.0451115 | ||||||||
\(932\) | −26.8846 | −0.880636 | ||||||||
\(933\) | 5.25011 | 0.171881 | ||||||||
\(934\) | 36.8013 | 1.20417 | ||||||||
\(935\) | −16.7718 | −0.548497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6698 | −0.381237 | −0.190619 | − | 0.981664i | \(-0.561049\pi\) | ||||
−0.190619 | + | 0.981664i | \(0.561049\pi\) | |||||||
\(938\) | 41.2311 | 1.34624 | ||||||||
\(939\) | −23.5687 | −0.769135 | ||||||||
\(940\) | −8.44390 | −0.275410 | ||||||||
\(941\) | 14.3074 | 0.466407 | 0.233203 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233203 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(942\) | 2.30390 | 0.0750650 | ||||||||
\(943\) | 1.85689 | 0.0604686 | ||||||||
\(944\) | 9.02326 | 0.293682 | ||||||||
\(945\) | 13.8023 | 0.448988 | ||||||||
\(946\) | 16.5710 | 0.538770 | ||||||||
\(947\) | 26.7816 | 0.870285 | 0.435142 | − | 0.900362i | \(-0.356698\pi\) | ||||
0.435142 | + | 0.900362i | \(0.356698\pi\) | |||||||
\(948\) | 10.0495 | 0.326392 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.13650 | 0.134206 | ||||||||
\(951\) | 17.9950 | 0.583527 | ||||||||
\(952\) | 13.1413 | 0.425913 | ||||||||
\(953\) | 37.3685 | 1.21048 | 0.605242 | − | 0.796042i | \(-0.293076\pi\) | ||||
0.605242 | + | 0.796042i | \(0.293076\pi\) | |||||||
\(954\) | 6.92854 | 0.224320 | ||||||||
\(955\) | −6.82427 | −0.220828 | ||||||||
\(956\) | 12.0208 | 0.388779 | ||||||||
\(957\) | 6.86015 | 0.221757 | ||||||||
\(958\) | −18.0660 | −0.583687 | ||||||||
\(959\) | 29.4954 | 0.952455 | ||||||||
\(960\) | 0.972156 | 0.0313762 | ||||||||
\(961\) | 29.7223 | 0.958783 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.76974 | −0.121478 | ||||||||
\(964\) | −16.9086 | −0.544588 | ||||||||
\(965\) | 8.90188 | 0.286562 | ||||||||
\(966\) | 12.4048 | 0.399119 | ||||||||
\(967\) | −23.2450 | −0.747508 | −0.373754 | − | 0.927528i | \(-0.621930\pi\) | ||||
−0.373754 | + | 0.927528i | \(0.621930\pi\) | |||||||
\(968\) | 4.80091 | 0.154307 | ||||||||
\(969\) | 4.75023 | 0.152599 | ||||||||
\(970\) | −10.7649 | −0.345639 | ||||||||
\(971\) | −3.68714 | −0.118326 | −0.0591630 | − | 0.998248i | \(-0.518843\pi\) | ||||
−0.0591630 | + | 0.998248i | \(0.518843\pi\) | |||||||
\(972\) | 15.7597 | 0.505492 | ||||||||
\(973\) | −52.5326 | −1.68412 | ||||||||
\(974\) | 19.7205 | 0.631886 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.87261 | 0.155968 | ||||||||
\(977\) | 29.2065 | 0.934399 | 0.467200 | − | 0.884152i | \(-0.345263\pi\) | ||||
0.467200 | + | 0.884152i | \(0.345263\pi\) | |||||||
\(978\) | −22.2050 | −0.710039 | ||||||||
\(979\) | 24.7663 | 0.791533 | ||||||||
\(980\) | 1.27906 | 0.0408582 | ||||||||
\(981\) | −32.4829 | −1.03710 | ||||||||
\(982\) | −26.6062 | −0.849037 | ||||||||
\(983\) | −10.6377 | −0.339291 | −0.169646 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169646 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(984\) | −0.474173 | −0.0151161 | ||||||||
\(985\) | 1.16763 | 0.0372038 | ||||||||
\(986\) | −7.49024 | −0.238538 | ||||||||
\(987\) | 27.5137 | 0.875771 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0790 | −0.543081 | ||||||||
\(990\) | −7.03854 | −0.223699 | ||||||||
\(991\) | 35.2488 | 1.11972 | 0.559858 | − | 0.828589i | \(-0.310856\pi\) | ||||
0.559858 | + | 0.828589i | \(0.310856\pi\) | |||||||
\(992\) | −7.79245 | −0.247411 | ||||||||
\(993\) | −7.92747 | −0.251571 | ||||||||
\(994\) | 31.4854 | 0.998656 | ||||||||
\(995\) | 5.55167 | 0.176000 | ||||||||
\(996\) | −4.53913 | −0.143828 | ||||||||
\(997\) | 34.8962 | 1.10517 | 0.552586 | − | 0.833456i | \(-0.313641\pi\) | ||||
0.552586 | + | 0.833456i | \(0.313641\pi\) | |||||||
\(998\) | −5.10306 | −0.161534 | ||||||||
\(999\) | −14.6360 | −0.463062 |
(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 | 6422.2.a.bl.1.6 | yes | 9 | |
13.12 | even | 2 | 6422.2.a.bj.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6422.2.a.bj.1.6 | ✓ | 9 | 13.12 | even | 2 | ||
6422.2.a.bl.1.6 | yes | 9 | 1.1 | even | 1 | trivial |