Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.226007\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22601 | −0.866918 | −0.433459 | − | 0.901173i | \(-0.642707\pi\) | ||||
−0.433459 | + | 0.901173i | \(0.642707\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.496906 | −0.248453 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.451695 | 0.170725 | 0.0853623 | − | 0.996350i | \(-0.472795\pi\) | ||||
0.0853623 | + | 0.996350i | \(0.472795\pi\) | |||||||
\(8\) | 3.06123 | 1.08231 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.22601 | −0.387698 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.84034 | 1.34247 | 0.671235 | − | 0.741245i | \(-0.265764\pi\) | ||||
0.671235 | + | 0.741245i | \(0.265764\pi\) | |||||||
\(14\) | −0.553781 | −0.148004 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.75927 | −0.689818 | ||||||||
\(17\) | 0.740078 | 0.179495 | 0.0897477 | − | 0.995965i | \(-0.471394\pi\) | ||||
0.0897477 | + | 0.995965i | \(0.471394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.80375 | −1.56089 | −0.780443 | − | 0.625227i | \(-0.785007\pi\) | ||||
−0.780443 | + | 0.625227i | \(0.785007\pi\) | |||||||
\(20\) | −0.496906 | −0.111112 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.00634166 | 0.00132233 | 0.000661164 | − | 1.00000i | \(-0.499790\pi\) | ||||
0.000661164 | 1.00000i | \(0.499790\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.93429 | −1.16381 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.224450 | −0.0424171 | ||||||||
\(29\) | −0.323900 | −0.0601468 | −0.0300734 | − | 0.999548i | \(-0.509574\pi\) | ||||
−0.0300734 | + | 0.999548i | \(0.509574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60583 | −1.00684 | −0.503419 | − | 0.864043i | \(-0.667925\pi\) | ||||
−0.503419 | + | 0.864043i | \(0.667925\pi\) | |||||||
\(32\) | −2.73956 | −0.484291 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.907341 | −0.155608 | ||||||||
\(35\) | 0.451695 | 0.0763504 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.36894 | 1.21145 | 0.605723 | − | 0.795675i | \(-0.292884\pi\) | ||||
0.605723 | + | 0.795675i | \(0.292884\pi\) | |||||||
\(38\) | 8.34144 | 1.35316 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06123 | 0.484022 | ||||||||
\(41\) | −10.9705 | −1.71330 | −0.856649 | − | 0.515900i | \(-0.827457\pi\) | ||||
−0.856649 | + | 0.515900i | \(0.827457\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80668 | 0.275516 | 0.137758 | − | 0.990466i | \(-0.456010\pi\) | ||||
0.137758 | + | 0.990466i | \(0.456010\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.00777492 | −0.00114635 | ||||||||
\(47\) | 1.67948 | 0.244978 | 0.122489 | − | 0.992470i | \(-0.460912\pi\) | ||||
0.122489 | + | 0.992470i | \(0.460912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79597 | −0.970853 | ||||||||
\(50\) | −1.22601 | −0.173384 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.40520 | −0.333541 | ||||||||
\(53\) | −8.63948 | −1.18672 | −0.593362 | − | 0.804936i | \(-0.702200\pi\) | ||||
−0.593362 | + | 0.804936i | \(0.702200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.38274 | 0.184776 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.397104 | 0.0521423 | ||||||||
\(59\) | 1.50054 | 0.195353 | 0.0976766 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976766 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0454 | −1.67029 | −0.835147 | − | 0.550027i | \(-0.814617\pi\) | ||||
−0.835147 | + | 0.550027i | \(0.814617\pi\) | |||||||
\(62\) | 6.87279 | 0.872845 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.87727 | 1.10966 | ||||||||
\(65\) | 4.84034 | 0.600371 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.60773 | 1.17377 | 0.586885 | − | 0.809670i | \(-0.300354\pi\) | ||||
0.586885 | + | 0.809670i | \(0.300354\pi\) | |||||||
\(68\) | −0.367750 | −0.0445962 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.553781 | −0.0661895 | ||||||||
\(71\) | −11.4126 | −1.35442 | −0.677211 | − | 0.735789i | \(-0.736812\pi\) | ||||
−0.677211 | + | 0.735789i | \(0.736812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2399 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(74\) | −9.03438 | −1.05023 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.38083 | 0.387807 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.09965 | 0.236229 | 0.118115 | − | 0.993000i | \(-0.462315\pi\) | ||||
0.118115 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(80\) | −2.75927 | −0.308496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.4499 | 1.48529 | ||||||||
\(83\) | −15.8945 | −1.74465 | −0.872323 | − | 0.488929i | \(-0.837388\pi\) | ||||
−0.872323 | + | 0.488929i | \(0.837388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.740078 | 0.0802727 | ||||||||
\(86\) | −2.21500 | −0.238850 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.36925 | 0.993138 | 0.496569 | − | 0.867997i | \(-0.334593\pi\) | ||||
0.496569 | + | 0.867997i | \(0.334593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.18636 | 0.229193 | ||||||||
\(92\) | −0.00315121 | −0.000328536 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.05906 | −0.212375 | ||||||||
\(95\) | −6.80375 | −0.698050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.87983 | 0.597007 | 0.298503 | − | 0.954409i | \(-0.403513\pi\) | ||||
0.298503 | + | 0.954409i | \(0.403513\pi\) | |||||||
\(98\) | 8.33191 | 0.841650 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.496906 | −0.0496906 | ||||||||
\(101\) | −2.20797 | −0.219701 | −0.109851 | − | 0.993948i | \(-0.535037\pi\) | ||||
−0.109851 | + | 0.993948i | \(0.535037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.67943 | 0.953743 | 0.476871 | − | 0.878973i | \(-0.341771\pi\) | ||||
0.476871 | + | 0.878973i | \(0.341771\pi\) | |||||||
\(104\) | 14.8174 | 1.45296 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.5921 | 1.02879 | ||||||||
\(107\) | −11.7564 | −1.13654 | −0.568269 | − | 0.822843i | \(-0.692387\pi\) | ||||
−0.568269 | + | 0.822843i | \(0.692387\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5091 | 1.19816 | 0.599078 | − | 0.800691i | \(-0.295534\pi\) | ||||
0.599078 | + | 0.800691i | \(0.295534\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.24635 | −0.117769 | ||||||||
\(113\) | −9.90608 | −0.931885 | −0.465943 | − | 0.884815i | \(-0.654285\pi\) | ||||
−0.465943 | + | 0.884815i | \(0.654285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.00634166 | 0.000591363 0 | ||||||||
\(116\) | 0.160948 | 0.0149437 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.83967 | −0.169355 | ||||||||
\(119\) | 0.334290 | 0.0306443 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 15.9938 | 1.44801 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.78557 | 0.250152 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.561561 | 0.0498304 | 0.0249152 | − | 0.999690i | \(-0.492068\pi\) | ||||
0.0249152 | + | 0.999690i | \(0.492068\pi\) | |||||||
\(128\) | −5.40447 | −0.477692 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.93429 | −0.520472 | ||||||||
\(131\) | 3.03500 | 0.265170 | 0.132585 | − | 0.991172i | \(-0.457672\pi\) | ||||
0.132585 | + | 0.991172i | \(0.457672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.07322 | −0.266482 | ||||||||
\(134\) | −11.7791 | −1.01756 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.26555 | 0.194269 | ||||||||
\(137\) | 20.7004 | 1.76855 | 0.884275 | − | 0.466966i | \(-0.154653\pi\) | ||||
0.884275 | + | 0.466966i | \(0.154653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.54873 | −0.300999 | −0.150500 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150500 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(140\) | −0.224450 | −0.0189695 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.9919 | 1.17417 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.323900 | −0.0268985 | ||||||||
\(146\) | 12.5542 | 1.03899 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.66168 | −0.300988 | ||||||||
\(149\) | 6.30459 | 0.516492 | 0.258246 | − | 0.966079i | \(-0.416855\pi\) | ||||
0.258246 | + | 0.966079i | \(0.416855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.68432 | 0.299826 | 0.149913 | − | 0.988699i | \(-0.452101\pi\) | ||||
0.149913 | + | 0.988699i | \(0.452101\pi\) | |||||||
\(152\) | −20.8278 | −1.68936 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.60583 | −0.450271 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82869 | 0.225754 | 0.112877 | − | 0.993609i | \(-0.463993\pi\) | ||||
0.112877 | + | 0.993609i | \(0.463993\pi\) | |||||||
\(158\) | −2.57419 | −0.204792 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.73956 | −0.216582 | ||||||||
\(161\) | 0.00286450 | 0.000225754 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.85141 | 0.693296 | 0.346648 | − | 0.937995i | \(-0.387320\pi\) | ||||
0.346648 | + | 0.937995i | \(0.387320\pi\) | |||||||
\(164\) | 5.45129 | 0.425674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.4868 | 1.51247 | ||||||||
\(167\) | −19.6842 | −1.52321 | −0.761605 | − | 0.648042i | \(-0.775588\pi\) | ||||
−0.761605 | + | 0.648042i | \(0.775588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4289 | 0.802224 | ||||||||
\(170\) | −0.907341 | −0.0695899 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.897750 | −0.0684528 | ||||||||
\(173\) | −2.91136 | −0.221347 | −0.110673 | − | 0.993857i | \(-0.535301\pi\) | ||||
−0.110673 | + | 0.993857i | \(0.535301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.451695 | 0.0341449 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4868 | −0.860969 | ||||||||
\(179\) | −6.29309 | −0.470368 | −0.235184 | − | 0.971951i | \(-0.575569\pi\) | ||||
−0.235184 | + | 0.971951i | \(0.575569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1642 | −0.829826 | −0.414913 | − | 0.909861i | \(-0.636188\pi\) | ||||
−0.414913 | + | 0.909861i | \(0.636188\pi\) | |||||||
\(182\) | −2.68049 | −0.198691 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0194132 | 0.00143116 | ||||||||
\(185\) | 7.36894 | 0.541776 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.834545 | −0.0608655 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.34144 | 0.605152 | ||||||||
\(191\) | −20.3946 | −1.47570 | −0.737851 | − | 0.674964i | \(-0.764159\pi\) | ||||
−0.737851 | + | 0.674964i | \(0.764159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.97433 | 0.214097 | 0.107049 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107049 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(194\) | −7.20872 | −0.517556 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.37696 | 0.241212 | ||||||||
\(197\) | −5.20127 | −0.370575 | −0.185288 | − | 0.982684i | \(-0.559322\pi\) | ||||
−0.185288 | + | 0.982684i | \(0.559322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.10264 | 0.574381 | 0.287191 | − | 0.957873i | \(-0.407279\pi\) | ||||
0.287191 | + | 0.957873i | \(0.407279\pi\) | |||||||
\(200\) | 3.06123 | 0.216461 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.70699 | 0.190463 | ||||||||
\(203\) | −0.146304 | −0.0102685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.9705 | −0.766210 | ||||||||
\(206\) | −11.8671 | −0.826817 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.3558 | −0.926059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.31335 | 0.0904146 | 0.0452073 | − | 0.998978i | \(-0.485605\pi\) | ||||
0.0452073 | + | 0.998978i | \(0.485605\pi\) | |||||||
\(212\) | 4.29301 | 0.294845 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.4135 | 0.985286 | ||||||||
\(215\) | 1.80668 | 0.123214 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.53213 | −0.171892 | ||||||||
\(218\) | −15.3363 | −1.03870 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.58223 | 0.240967 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.6347 | 1.91752 | 0.958761 | − | 0.284214i | \(-0.0917325\pi\) | ||||
0.958761 | + | 0.284214i | \(0.0917325\pi\) | |||||||
\(224\) | −1.23745 | −0.0826804 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.1449 | 0.807868 | ||||||||
\(227\) | 7.86603 | 0.522087 | 0.261043 | − | 0.965327i | \(-0.415933\pi\) | ||||
0.261043 | + | 0.965327i | \(0.415933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1510 | −1.06729 | −0.533644 | − | 0.845710i | \(-0.679178\pi\) | ||||
−0.533644 | + | 0.845710i | \(0.679178\pi\) | |||||||
\(230\) | −0.00777492 | −0.000512663 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.991532 | −0.0650973 | ||||||||
\(233\) | −18.4345 | −1.20768 | −0.603841 | − | 0.797105i | \(-0.706364\pi\) | ||||
−0.603841 | + | 0.797105i | \(0.706364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.67948 | 0.109557 | ||||||||
\(236\) | −0.745626 | −0.0485361 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.409841 | −0.0265661 | ||||||||
\(239\) | −22.3638 | −1.44660 | −0.723298 | − | 0.690536i | \(-0.757375\pi\) | ||||
−0.723298 | + | 0.690536i | \(0.757375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2213 | 0.851662 | 0.425831 | − | 0.904803i | \(-0.359982\pi\) | ||||
0.425831 | + | 0.904803i | \(0.359982\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.48235 | 0.414990 | ||||||||
\(245\) | −6.79597 | −0.434179 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.9325 | −2.09544 | ||||||||
\(248\) | −17.1607 | −1.08971 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.22601 | −0.0775395 | ||||||||
\(251\) | −21.0032 | −1.32571 | −0.662854 | − | 0.748749i | \(-0.730655\pi\) | ||||
−0.662854 | + | 0.748749i | \(0.730655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.688477 | −0.0431989 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.1286 | −0.695539 | ||||||||
\(257\) | −3.36772 | −0.210073 | −0.105036 | − | 0.994468i | \(-0.533496\pi\) | ||||
−0.105036 | + | 0.994468i | \(0.533496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.32852 | 0.206824 | ||||||||
\(260\) | −2.40520 | −0.149164 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.72094 | −0.229880 | ||||||||
\(263\) | −21.0450 | −1.29769 | −0.648845 | − | 0.760920i | \(-0.724748\pi\) | ||||
−0.648845 | + | 0.760920i | \(0.724748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.63948 | −0.530719 | ||||||||
\(266\) | 3.76779 | 0.231018 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.77414 | −0.291627 | ||||||||
\(269\) | 23.3816 | 1.42560 | 0.712800 | − | 0.701367i | \(-0.247427\pi\) | ||||
0.712800 | + | 0.701367i | \(0.247427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5474 | 1.24817 | 0.624084 | − | 0.781357i | \(-0.285472\pi\) | ||||
0.624084 | + | 0.781357i | \(0.285472\pi\) | |||||||
\(272\) | −2.04208 | −0.123819 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.3788 | −1.53319 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5818 | 1.17656 | 0.588280 | − | 0.808658i | \(-0.299805\pi\) | ||||
0.588280 | + | 0.808658i | \(0.299805\pi\) | |||||||
\(278\) | 4.35077 | 0.260942 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.38274 | 0.0826345 | ||||||||
\(281\) | −13.7926 | −0.822800 | −0.411400 | − | 0.911455i | \(-0.634960\pi\) | ||||
−0.411400 | + | 0.911455i | \(0.634960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.5177 | −1.87353 | −0.936765 | − | 0.349958i | \(-0.886196\pi\) | ||||
−0.936765 | + | 0.349958i | \(0.886196\pi\) | |||||||
\(284\) | 5.67098 | 0.336511 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.95530 | −0.292502 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4523 | −0.967781 | ||||||||
\(290\) | 0.397104 | 0.0233188 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.08826 | 0.297768 | ||||||||
\(293\) | 23.3131 | 1.36196 | 0.680982 | − | 0.732300i | \(-0.261553\pi\) | ||||
0.680982 | + | 0.732300i | \(0.261553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50054 | 0.0873646 | ||||||||
\(296\) | 22.5580 | 1.31116 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.72948 | −0.447757 | ||||||||
\(299\) | 0.0306958 | 0.00177518 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.816068 | 0.0470374 | ||||||||
\(302\) | −4.51700 | −0.259924 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.7734 | 1.07673 | ||||||||
\(305\) | −13.0454 | −0.746978 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0938 | 0.576083 | 0.288042 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288042 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.87279 | 0.390348 | ||||||||
\(311\) | −13.3254 | −0.755614 | −0.377807 | − | 0.925884i | \(-0.623322\pi\) | ||||
−0.377807 | + | 0.925884i | \(0.623322\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.1682 | 1.30955 | 0.654773 | − | 0.755825i | \(-0.272764\pi\) | ||||
0.654773 | + | 0.755825i | \(0.272764\pi\) | |||||||
\(314\) | −3.46799 | −0.195710 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04333 | −0.0586920 | ||||||||
\(317\) | 6.93189 | 0.389334 | 0.194667 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194667 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.87727 | 0.496254 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.00351189 | −0.000195710 0 | ||||||||
\(323\) | −5.03530 | −0.280172 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.84034 | 0.268494 | ||||||||
\(326\) | −10.8519 | −0.601031 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −33.5830 | −1.85431 | ||||||||
\(329\) | 0.758613 | 0.0418237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5717 | −0.581075 | −0.290538 | − | 0.956864i | \(-0.593834\pi\) | ||||
−0.290538 | + | 0.956864i | \(0.593834\pi\) | |||||||
\(332\) | 7.89807 | 0.433463 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.1330 | 1.32050 | ||||||||
\(335\) | 9.60773 | 0.524926 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.34668 | 0.345726 | 0.172863 | − | 0.984946i | \(-0.444698\pi\) | ||||
0.172863 | + | 0.984946i | \(0.444698\pi\) | |||||||
\(338\) | −12.7859 | −0.695463 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.367750 | −0.0199440 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.23157 | −0.336473 | ||||||||
\(344\) | 5.53065 | 0.298193 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.56935 | 0.191890 | ||||||||
\(347\) | −25.2417 | −1.35505 | −0.677524 | − | 0.735501i | \(-0.736947\pi\) | ||||
−0.677524 | + | 0.735501i | \(0.736947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1035 | 0.594359 | 0.297179 | − | 0.954822i | \(-0.403954\pi\) | ||||
0.297179 | + | 0.954822i | \(0.403954\pi\) | |||||||
\(350\) | −0.553781 | −0.0296009 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8552 | 1.00356 | 0.501780 | − | 0.864996i | \(-0.332679\pi\) | ||||
0.501780 | + | 0.864996i | \(0.332679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4126 | −0.605716 | ||||||||
\(356\) | −4.65564 | −0.246748 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.71537 | 0.407770 | ||||||||
\(359\) | −21.2928 | −1.12379 | −0.561895 | − | 0.827208i | \(-0.689928\pi\) | ||||
−0.561895 | + | 0.827208i | \(0.689928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.2910 | 1.43637 | ||||||||
\(362\) | 13.6873 | 0.719391 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.08642 | −0.0569437 | ||||||||
\(365\) | −10.2399 | −0.535980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.2857 | −1.63310 | −0.816550 | − | 0.577275i | \(-0.804116\pi\) | ||||
−0.816550 | + | 0.577275i | \(0.804116\pi\) | |||||||
\(368\) | −0.0174984 | −0.000912165 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.03438 | −0.469675 | ||||||||
\(371\) | −3.90241 | −0.202603 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.39368 | −0.486386 | −0.243193 | − | 0.969978i | \(-0.578195\pi\) | ||||
−0.243193 | + | 0.969978i | \(0.578195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.14127 | 0.265141 | ||||||||
\(377\) | −1.56779 | −0.0807452 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.19727 | −0.421065 | −0.210533 | − | 0.977587i | \(-0.567520\pi\) | ||||
−0.210533 | + | 0.977587i | \(0.567520\pi\) | |||||||
\(380\) | 3.38083 | 0.173433 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.0039 | 1.27931 | ||||||||
\(383\) | −33.6830 | −1.72112 | −0.860560 | − | 0.509349i | \(-0.829886\pi\) | ||||
−0.860560 | + | 0.509349i | \(0.829886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.64656 | −0.185605 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.92173 | −0.148328 | ||||||||
\(389\) | 32.9338 | 1.66981 | 0.834905 | − | 0.550395i | \(-0.185523\pi\) | ||||
0.834905 | + | 0.550395i | \(0.185523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.00469332 | 0.000237352 0 | ||||||||
\(392\) | −20.8040 | −1.05076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.37680 | 0.321259 | ||||||||
\(395\) | 2.09965 | 0.105645 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3865 | −0.772228 | −0.386114 | − | 0.922451i | \(-0.626183\pi\) | ||||
−0.386114 | + | 0.922451i | \(0.626183\pi\) | |||||||
\(398\) | −9.93390 | −0.497941 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.75927 | −0.137964 | ||||||||
\(401\) | 6.64295 | 0.331733 | 0.165866 | − | 0.986148i | \(-0.446958\pi\) | ||||
0.165866 | + | 0.986148i | \(0.446958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.1341 | −1.35165 | ||||||||
\(404\) | 1.09715 | 0.0545855 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.179370 | 0.00890198 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.4850 | −1.21071 | −0.605353 | − | 0.795957i | \(-0.706968\pi\) | ||||
−0.605353 | + | 0.795957i | \(0.706968\pi\) | |||||||
\(410\) | 13.4499 | 0.664241 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.80977 | −0.236960 | ||||||||
\(413\) | 0.677784 | 0.0333516 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.8945 | −0.780230 | ||||||||
\(416\) | −13.2604 | −0.650146 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.8656 | 1.01935 | 0.509676 | − | 0.860367i | \(-0.329765\pi\) | ||||
0.509676 | + | 0.860367i | \(0.329765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9311 | −0.825172 | −0.412586 | − | 0.910919i | \(-0.635374\pi\) | ||||
−0.412586 | + | 0.910919i | \(0.635374\pi\) | |||||||
\(422\) | −1.61017 | −0.0783821 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.4474 | −1.28440 | ||||||||
\(425\) | 0.740078 | 0.0358991 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.89255 | −0.285160 | ||||||||
\(428\) | 5.84186 | 0.282377 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.21500 | −0.106817 | ||||||||
\(431\) | −26.1647 | −1.26031 | −0.630154 | − | 0.776470i | \(-0.717008\pi\) | ||||
−0.630154 | + | 0.776470i | \(0.717008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0593 | −1.20427 | −0.602137 | − | 0.798393i | \(-0.705684\pi\) | ||||
−0.602137 | + | 0.798393i | \(0.705684\pi\) | |||||||
\(434\) | 3.10440 | 0.149016 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.21586 | −0.297686 | ||||||||
\(437\) | −0.0431470 | −0.00206400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.11234 | −0.243999 | −0.121999 | − | 0.992530i | \(-0.538931\pi\) | ||||
−0.121999 | + | 0.992530i | \(0.538931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.39184 | −0.208899 | ||||||||
\(443\) | 28.0773 | 1.33399 | 0.666995 | − | 0.745062i | \(-0.267580\pi\) | ||||
0.666995 | + | 0.745062i | \(0.267580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.36925 | 0.444145 | ||||||||
\(446\) | −35.1064 | −1.66233 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00982 | 0.189446 | ||||||||
\(449\) | 36.9951 | 1.74591 | 0.872953 | − | 0.487804i | \(-0.162202\pi\) | ||||
0.872953 | + | 0.487804i | \(0.162202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.92239 | 0.231530 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.64381 | −0.452606 | ||||||||
\(455\) | 2.18636 | 0.102498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.8462 | −1.72359 | −0.861795 | − | 0.507256i | \(-0.830660\pi\) | ||||
−0.861795 | + | 0.507256i | \(0.830660\pi\) | |||||||
\(458\) | 19.8012 | 0.925250 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.00315121 | −0.000146926 0 | ||||||||
\(461\) | −23.0013 | −1.07128 | −0.535640 | − | 0.844447i | \(-0.679929\pi\) | ||||
−0.535640 | + | 0.844447i | \(0.679929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.1571 | −1.68036 | −0.840181 | − | 0.542306i | \(-0.817551\pi\) | ||||
−0.840181 | + | 0.542306i | \(0.817551\pi\) | |||||||
\(464\) | 0.893729 | 0.0414903 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.6008 | 1.04696 | ||||||||
\(467\) | −2.26498 | −0.104811 | −0.0524053 | − | 0.998626i | \(-0.516689\pi\) | ||||
−0.0524053 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.33976 | 0.200392 | ||||||||
\(470\) | −2.05906 | −0.0949772 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.59348 | 0.211432 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.80375 | −0.312177 | ||||||||
\(476\) | −0.166111 | −0.00761367 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.4182 | 1.25408 | ||||||||
\(479\) | 30.5308 | 1.39499 | 0.697495 | − | 0.716590i | \(-0.254298\pi\) | ||||
0.697495 | + | 0.716590i | \(0.254298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.6682 | 1.62633 | ||||||||
\(482\) | −16.2095 | −0.738321 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.87983 | 0.266989 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1543 | −0.732021 | −0.366010 | − | 0.930611i | \(-0.619277\pi\) | ||||
−0.366010 | + | 0.930611i | \(0.619277\pi\) | |||||||
\(488\) | −39.9349 | −1.80777 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.33191 | 0.376397 | ||||||||
\(491\) | 11.6766 | 0.526960 | 0.263480 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263480 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.239712 | −0.0107961 | ||||||||
\(494\) | 40.3754 | 1.81658 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.4680 | 0.694534 | ||||||||
\(497\) | −5.15500 | −0.231233 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.9366 | −1.83257 | −0.916287 | − | 0.400522i | \(-0.868829\pi\) | ||||
−0.916287 | + | 0.400522i | \(0.868829\pi\) | |||||||
\(500\) | −0.496906 | −0.0222223 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.7500 | 1.14928 | ||||||||
\(503\) | 0.424478 | 0.0189266 | 0.00946328 | − | 0.999955i | \(-0.496988\pi\) | ||||
0.00946328 | + | 0.999955i | \(0.496988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.20797 | −0.0982533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.279043 | −0.0123805 | ||||||||
\(509\) | −19.8053 | −0.877854 | −0.438927 | − | 0.898523i | \(-0.644641\pi\) | ||||
−0.438927 | + | 0.898523i | \(0.644641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.62530 | −0.204611 | ||||||||
\(512\) | 24.4527 | 1.08067 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.12885 | 0.182116 | ||||||||
\(515\) | 9.67943 | 0.426527 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.08078 | −0.179299 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.8174 | 0.649785 | ||||||||
\(521\) | 36.8095 | 1.61265 | 0.806327 | − | 0.591470i | \(-0.201452\pi\) | ||||
0.806327 | + | 0.591470i | \(0.201452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5015 | 0.459198 | 0.229599 | − | 0.973285i | \(-0.426258\pi\) | ||||
0.229599 | + | 0.973285i | \(0.426258\pi\) | |||||||
\(524\) | −1.50811 | −0.0658822 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8013 | 1.12499 | ||||||||
\(527\) | −4.14875 | −0.180723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −0.999998 | ||||||||
\(530\) | 10.5921 | 0.460090 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.52710 | 0.0662083 | ||||||||
\(533\) | −53.1008 | −2.30005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7564 | −0.508276 | ||||||||
\(536\) | 29.4114 | 1.27038 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.6660 | −1.23588 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.654613 | −0.0281440 | −0.0140720 | − | 0.999901i | \(-0.504479\pi\) | ||||
−0.0140720 | + | 0.999901i | \(0.504479\pi\) | |||||||
\(542\) | −25.1913 | −1.08206 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.02749 | −0.0869280 | ||||||||
\(545\) | 12.5091 | 0.535832 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4159 | 0.573621 | 0.286810 | − | 0.957987i | \(-0.407405\pi\) | ||||
0.286810 | + | 0.957987i | \(0.407405\pi\) | |||||||
\(548\) | −10.2861 | −0.439402 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.20374 | 0.0938823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.948403 | 0.0403302 | ||||||||
\(554\) | −24.0075 | −1.01998 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.76339 | 0.0747843 | ||||||||
\(557\) | 13.2421 | 0.561087 | 0.280544 | − | 0.959841i | \(-0.409485\pi\) | ||||
0.280544 | + | 0.959841i | \(0.409485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.74494 | 0.369872 | ||||||||
\(560\) | −1.24635 | −0.0526679 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.9099 | 0.713300 | ||||||||
\(563\) | 21.3619 | 0.900297 | 0.450149 | − | 0.892954i | \(-0.351371\pi\) | ||||
0.450149 | + | 0.892954i | \(0.351371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.90608 | −0.416752 | ||||||||
\(566\) | 38.6409 | 1.62420 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −34.9364 | −1.46590 | ||||||||
\(569\) | −45.3375 | −1.90065 | −0.950323 | − | 0.311267i | \(-0.899247\pi\) | ||||
−0.950323 | + | 0.311267i | \(0.899247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1544 | 1.05268 | 0.526339 | − | 0.850275i | \(-0.323564\pi\) | ||||
0.526339 | + | 0.850275i | \(0.323564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.07523 | 0.253575 | ||||||||
\(575\) | 0.00634166 | 0.000264465 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.62653 | 0.317496 | 0.158748 | − | 0.987319i | \(-0.449254\pi\) | ||||
0.158748 | + | 0.987319i | \(0.449254\pi\) | |||||||
\(578\) | 20.1706 | 0.838987 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.160948 | 0.00668301 | ||||||||
\(581\) | −7.17946 | −0.297854 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −31.3466 | −1.29713 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.5820 | −1.18071 | ||||||||
\(587\) | −7.88825 | −0.325583 | −0.162791 | − | 0.986660i | \(-0.552050\pi\) | ||||
−0.162791 | + | 0.986660i | \(0.552050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.1407 | 1.57156 | ||||||||
\(590\) | −1.83967 | −0.0757379 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.3329 | −0.835678 | ||||||||
\(593\) | −8.68507 | −0.356653 | −0.178327 | − | 0.983971i | \(-0.557068\pi\) | ||||
−0.178327 | + | 0.983971i | \(0.557068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.334290 | 0.0137045 | ||||||||
\(596\) | −3.13279 | −0.128324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0376333 | −0.00153894 | ||||||||
\(599\) | 14.0016 | 0.572088 | 0.286044 | − | 0.958216i | \(-0.407660\pi\) | ||||
0.286044 | + | 0.958216i | \(0.407660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2936 | 0.419886 | 0.209943 | − | 0.977714i | \(-0.432672\pi\) | ||||
0.209943 | + | 0.977714i | \(0.432672\pi\) | |||||||
\(602\) | −1.00050 | −0.0407775 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.83076 | −0.0744927 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.4756 | −1.11520 | −0.557599 | − | 0.830110i | \(-0.688277\pi\) | ||||
−0.557599 | + | 0.830110i | \(0.688277\pi\) | |||||||
\(608\) | 18.6393 | 0.755923 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.9938 | 0.647569 | ||||||||
\(611\) | 8.12926 | 0.328875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8580 | 0.438550 | 0.219275 | − | 0.975663i | \(-0.429631\pi\) | ||||
0.219275 | + | 0.975663i | \(0.429631\pi\) | |||||||
\(614\) | −12.3751 | −0.499417 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2404 | −0.734330 | −0.367165 | − | 0.930156i | \(-0.619671\pi\) | ||||
−0.367165 | + | 0.930156i | \(0.619671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6799 | 0.791004 | 0.395502 | − | 0.918465i | \(-0.370571\pi\) | ||||
0.395502 | + | 0.918465i | \(0.370571\pi\) | |||||||
\(620\) | 2.78557 | 0.111871 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.3370 | 0.655056 | ||||||||
\(623\) | 4.23204 | 0.169553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.4044 | −1.13527 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.40559 | −0.0560893 | ||||||||
\(629\) | 5.45359 | 0.217449 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.4249 | −1.21120 | −0.605598 | − | 0.795771i | \(-0.707066\pi\) | ||||
−0.605598 | + | 0.795771i | \(0.707066\pi\) | |||||||
\(632\) | 6.42751 | 0.255673 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.49854 | −0.337520 | ||||||||
\(635\) | 0.561561 | 0.0222849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.8948 | −1.30334 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.40447 | −0.213630 | ||||||||
\(641\) | −37.3528 | −1.47535 | −0.737674 | − | 0.675157i | \(-0.764076\pi\) | ||||
−0.737674 | + | 0.675157i | \(0.764076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.06494 | 0.0419971 | 0.0209986 | − | 0.999780i | \(-0.493315\pi\) | ||||
0.0209986 | + | 0.999780i | \(0.493315\pi\) | |||||||
\(644\) | −0.00142339 | −5.60893e−5 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.17332 | 0.242886 | ||||||||
\(647\) | 15.8049 | 0.621354 | 0.310677 | − | 0.950516i | \(-0.399444\pi\) | ||||
0.310677 | + | 0.950516i | \(0.399444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.93429 | −0.232762 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.39832 | −0.172252 | ||||||||
\(653\) | −35.3513 | −1.38340 | −0.691701 | − | 0.722184i | \(-0.743138\pi\) | ||||
−0.691701 | + | 0.722184i | \(0.743138\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.03500 | 0.118587 | ||||||||
\(656\) | 30.2705 | 1.18186 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.930065 | −0.0362577 | ||||||||
\(659\) | −28.4474 | −1.10815 | −0.554077 | − | 0.832465i | \(-0.686929\pi\) | ||||
−0.554077 | + | 0.832465i | \(0.686929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.5989 | 1.54022 | 0.770110 | − | 0.637911i | \(-0.220201\pi\) | ||||
0.770110 | + | 0.637911i | \(0.220201\pi\) | |||||||
\(662\) | 12.9610 | 0.503745 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −48.6566 | −1.88824 | ||||||||
\(665\) | −3.07322 | −0.119174 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.00205407 | −7.95337e−5 0 | ||||||||
\(668\) | 9.78121 | 0.378446 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.7791 | −0.455068 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.5621 | 0.676969 | 0.338484 | − | 0.940972i | \(-0.390086\pi\) | ||||
0.338484 | + | 0.940972i | \(0.390086\pi\) | |||||||
\(674\) | −7.78108 | −0.299716 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.18220 | −0.199315 | ||||||||
\(677\) | −45.0690 | −1.73214 | −0.866071 | − | 0.499922i | \(-0.833362\pi\) | ||||
−0.866071 | + | 0.499922i | \(0.833362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.65589 | 0.101924 | ||||||||
\(680\) | 2.26555 | 0.0868797 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7677 | −0.603334 | −0.301667 | − | 0.953413i | \(-0.597543\pi\) | ||||
−0.301667 | + | 0.953413i | \(0.597543\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7004 | 0.790920 | ||||||||
\(686\) | 7.63995 | 0.291695 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.98512 | −0.190056 | ||||||||
\(689\) | −41.8180 | −1.59314 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.96619 | 0.112839 | 0.0564197 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564197 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(692\) | 1.44668 | 0.0549944 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.9465 | 1.17471 | ||||||||
\(695\) | −3.54873 | −0.134611 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.11899 | −0.307529 | ||||||||
\(698\) | −13.6130 | −0.515260 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.224450 | −0.00848342 | ||||||||
\(701\) | 37.1301 | 1.40238 | 0.701192 | − | 0.712973i | \(-0.252652\pi\) | ||||
0.701192 | + | 0.712973i | \(0.252652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.1364 | −1.89093 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1166 | −0.870003 | ||||||||
\(707\) | −0.997329 | −0.0375084 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7505 | −1.19241 | −0.596207 | − | 0.802831i | \(-0.703326\pi\) | ||||
−0.596207 | + | 0.802831i | \(0.703326\pi\) | |||||||
\(710\) | 13.9919 | 0.525106 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.6814 | 1.07488 | ||||||||
\(713\) | −0.0355503 | −0.00133137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.12708 | 0.116864 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.1051 | 0.974234 | ||||||||
\(719\) | 31.8772 | 1.18882 | 0.594409 | − | 0.804163i | \(-0.297386\pi\) | ||||
0.594409 | + | 0.804163i | \(0.297386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.37215 | 0.162827 | ||||||||
\(722\) | −33.4589 | −1.24521 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.54755 | 0.206173 | ||||||||
\(725\) | −0.323900 | −0.0120294 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.4129 | 1.53592 | 0.767959 | − | 0.640499i | \(-0.221272\pi\) | ||||
0.767959 | + | 0.640499i | \(0.221272\pi\) | |||||||
\(728\) | 6.69294 | 0.248057 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.5542 | 0.464650 | ||||||||
\(731\) | 1.33708 | 0.0494538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.6920 | −1.76155 | −0.880773 | − | 0.473540i | \(-0.842976\pi\) | ||||
−0.880773 | + | 0.473540i | \(0.842976\pi\) | |||||||
\(734\) | 38.3565 | 1.41576 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0173734 | −0.000640391 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.4567 | 0.458228 | 0.229114 | − | 0.973400i | \(-0.426417\pi\) | ||||
0.229114 | + | 0.973400i | \(0.426417\pi\) | |||||||
\(740\) | −3.66168 | −0.134606 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.78438 | 0.175640 | ||||||||
\(743\) | −27.3723 | −1.00419 | −0.502095 | − | 0.864812i | \(-0.667437\pi\) | ||||
−0.502095 | + | 0.864812i | \(0.667437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.30459 | 0.230982 | ||||||||
\(746\) | 11.5167 | 0.421657 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.31033 | −0.194035 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.8725 | −1.52795 | −0.763975 | − | 0.645246i | \(-0.776755\pi\) | ||||
−0.763975 | + | 0.645246i | \(0.776755\pi\) | |||||||
\(752\) | −4.63414 | −0.168990 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.92212 | 0.0699995 | ||||||||
\(755\) | 3.68432 | 0.134086 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1192 | 0.585863 | 0.292932 | − | 0.956133i | \(-0.405369\pi\) | ||||
0.292932 | + | 0.956133i | \(0.405369\pi\) | |||||||
\(758\) | 10.0499 | 0.365029 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.8278 | −0.755504 | ||||||||
\(761\) | 10.9239 | 0.395990 | 0.197995 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197995 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.65030 | 0.204555 | ||||||||
\(764\) | 10.1342 | 0.366643 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.2956 | 1.49207 | ||||||||
\(767\) | 7.26311 | 0.262256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.2074 | 1.23355 | 0.616775 | − | 0.787139i | \(-0.288439\pi\) | ||||
0.616775 | + | 0.787139i | \(0.288439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.47797 | −0.0531932 | ||||||||
\(773\) | 8.63688 | 0.310647 | 0.155323 | − | 0.987864i | \(-0.450358\pi\) | ||||
0.155323 | + | 0.987864i | \(0.450358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.60583 | −0.201367 | ||||||||
\(776\) | 17.9995 | 0.646144 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.3771 | −1.44759 | ||||||||
\(779\) | 74.6402 | 2.67426 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.00575405 | −0.000205764 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.7519 | 0.669712 | ||||||||
\(785\) | 2.82869 | 0.100960 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1043 | 0.823581 | 0.411790 | − | 0.911279i | \(-0.364904\pi\) | ||||
0.411790 | + | 0.911279i | \(0.364904\pi\) | |||||||
\(788\) | 2.58455 | 0.0920707 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.57419 | −0.0915856 | ||||||||
\(791\) | −4.47453 | −0.159096 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63.1443 | −2.24232 | ||||||||
\(794\) | 18.8640 | 0.669458 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.02626 | −0.142707 | ||||||||
\(797\) | −39.7333 | −1.40743 | −0.703714 | − | 0.710484i | \(-0.748476\pi\) | ||||
−0.703714 | + | 0.710484i | \(0.748476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24295 | 0.0439723 | ||||||||
\(800\) | −2.73956 | −0.0968582 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.14430 | −0.287585 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00286450 | 0.000100960 0 | ||||||||
\(806\) | 33.2667 | 1.17177 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.75909 | −0.237784 | ||||||||
\(809\) | 31.0140 | 1.09039 | 0.545197 | − | 0.838308i | \(-0.316455\pi\) | ||||
0.545197 | + | 0.838308i | \(0.316455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.45922 | −0.261929 | −0.130964 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130964 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(812\) | 0.0726995 | 0.00255125 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.85141 | 0.310051 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.2922 | −0.430049 | ||||||||
\(818\) | 30.0188 | 1.04958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.45129 | 0.190367 | ||||||||
\(821\) | 12.6556 | 0.441683 | 0.220841 | − | 0.975310i | \(-0.429120\pi\) | ||||
0.220841 | + | 0.975310i | \(0.429120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2890 | −0.951234 | −0.475617 | − | 0.879652i | \(-0.657775\pi\) | ||||
−0.475617 | + | 0.879652i | \(0.657775\pi\) | |||||||
\(824\) | 29.6309 | 1.03224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.830969 | −0.0289131 | ||||||||
\(827\) | 16.9544 | 0.589563 | 0.294781 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294781 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.7794 | 0.686967 | 0.343483 | − | 0.939159i | \(-0.388393\pi\) | ||||
0.343483 | + | 0.939159i | \(0.388393\pi\) | |||||||
\(830\) | 19.4868 | 0.676395 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42.9690 | 1.48968 | ||||||||
\(833\) | −5.02955 | −0.174264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.6842 | −0.681200 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.5814 | −0.883694 | ||||||||
\(839\) | −4.97974 | −0.171920 | −0.0859598 | − | 0.996299i | \(-0.527396\pi\) | ||||
−0.0859598 | + | 0.996299i | \(0.527396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8951 | −0.996382 | ||||||||
\(842\) | 20.7577 | 0.715357 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.652611 | −0.0224638 | ||||||||
\(845\) | 10.4289 | 0.358766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.8387 | 0.818623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.907341 | −0.0311215 | ||||||||
\(851\) | 0.0467313 | 0.00160193 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.2464 | 0.795943 | 0.397971 | − | 0.917398i | \(-0.369714\pi\) | ||||
0.397971 | + | 0.917398i | \(0.369714\pi\) | |||||||
\(854\) | 7.22430 | 0.247211 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.9891 | −1.23008 | ||||||||
\(857\) | 30.6976 | 1.04861 | 0.524306 | − | 0.851530i | \(-0.324325\pi\) | ||||
0.524306 | + | 0.851530i | \(0.324325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1830 | −0.381560 | −0.190780 | − | 0.981633i | \(-0.561102\pi\) | ||||
−0.190780 | + | 0.981633i | \(0.561102\pi\) | |||||||
\(860\) | −0.897750 | −0.0306130 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.0781 | 1.09258 | ||||||||
\(863\) | −3.66335 | −0.124702 | −0.0623510 | − | 0.998054i | \(-0.519860\pi\) | ||||
−0.0623510 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.91136 | −0.0989894 | ||||||||
\(866\) | 30.7229 | 1.04401 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.25823 | 0.0427071 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5047 | 1.57575 | ||||||||
\(872\) | 38.2932 | 1.29677 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.0528986 | 0.00178932 | ||||||||
\(875\) | 0.451695 | 0.0152701 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.36271 | −0.248621 | −0.124310 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124310 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(878\) | 6.26776 | 0.211527 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.07165 | 0.204559 | 0.102280 | − | 0.994756i | \(-0.467386\pi\) | ||||
0.102280 | + | 0.994756i | \(0.467386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1767 | 1.04918 | 0.524589 | − | 0.851356i | \(-0.324219\pi\) | ||||
0.524589 | + | 0.851356i | \(0.324219\pi\) | |||||||
\(884\) | −1.78003 | −0.0598690 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.4229 | −1.15646 | ||||||||
\(887\) | 5.68999 | 0.191051 | 0.0955255 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955255 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.253654 | 0.00850729 | ||||||||
\(890\) | −11.4868 | −0.385037 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.2288 | −0.476414 | ||||||||
\(893\) | −11.4268 | −0.382382 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.29309 | −0.210355 | ||||||||
\(896\) | −2.44117 | −0.0815538 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.3563 | −1.51356 | ||||||||
\(899\) | 1.81573 | 0.0605580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.39389 | −0.213011 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.3247 | −1.00859 | ||||||||
\(905\) | −11.1642 | −0.371109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.4917 | 1.41091 | 0.705456 | − | 0.708754i | \(-0.250742\pi\) | ||||
0.705456 | + | 0.708754i | \(0.250742\pi\) | |||||||
\(908\) | −3.90868 | −0.129714 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.68049 | −0.0888574 | ||||||||
\(911\) | −2.14405 | −0.0710356 | −0.0355178 | − | 0.999369i | \(-0.511308\pi\) | ||||
−0.0355178 | + | 0.999369i | \(0.511308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 45.1737 | 1.49421 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.02553 | 0.265171 | ||||||||
\(917\) | 1.37090 | 0.0452710 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0683 | −0.530044 | −0.265022 | − | 0.964242i | \(-0.585379\pi\) | ||||
−0.265022 | + | 0.964242i | \(0.585379\pi\) | |||||||
\(920\) | 0.0194132 | 0.000640036 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.1998 | 0.928711 | ||||||||
\(923\) | −55.2407 | −1.81827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.36894 | 0.242289 | ||||||||
\(926\) | 44.3289 | 1.45674 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.887346 | 0.0291286 | ||||||||
\(929\) | −37.4770 | −1.22958 | −0.614791 | − | 0.788690i | \(-0.710760\pi\) | ||||
−0.614791 | + | 0.788690i | \(0.710760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.2381 | 1.51539 | ||||||||
\(932\) | 9.16021 | 0.300053 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.77688 | 0.0908621 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0054 | 0.849560 | 0.424780 | − | 0.905297i | \(-0.360351\pi\) | ||||
0.424780 | + | 0.905297i | \(0.360351\pi\) | |||||||
\(938\) | −5.32058 | −0.173723 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.834545 | −0.0272199 | ||||||||
\(941\) | −8.58482 | −0.279857 | −0.139929 | − | 0.990162i | \(-0.544687\pi\) | ||||
−0.139929 | + | 0.990162i | \(0.544687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0695709 | −0.00226554 | ||||||||
\(944\) | −4.14038 | −0.134758 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.0304 | −1.17083 | −0.585416 | − | 0.810733i | \(-0.699069\pi\) | ||||
−0.585416 | + | 0.810733i | \(0.699069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.5645 | −1.60893 | ||||||||
\(950\) | 8.34144 | 0.270632 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.02334 | 0.0331665 | ||||||||
\(953\) | 43.8525 | 1.42052 | 0.710261 | − | 0.703938i | \(-0.248577\pi\) | ||||
0.710261 | + | 0.703938i | \(0.248577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.3946 | −0.659954 | ||||||||
\(956\) | 11.1127 | 0.359412 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.4310 | −1.20934 | ||||||||
\(959\) | 9.35025 | 0.301935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.425347 | 0.0137209 | ||||||||
\(962\) | −43.7295 | −1.40990 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.56977 | −0.211598 | ||||||||
\(965\) | 2.97433 | 0.0957472 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.1271 | 1.54766 | 0.773831 | − | 0.633392i | \(-0.218338\pi\) | ||||
0.773831 | + | 0.633392i | \(0.218338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.20872 | −0.231458 | ||||||||
\(971\) | 31.7334 | 1.01837 | 0.509187 | − | 0.860656i | \(-0.329946\pi\) | ||||
0.509187 | + | 0.860656i | \(0.329946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.60294 | −0.0513880 | ||||||||
\(974\) | 19.8053 | 0.634602 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.9958 | 1.15220 | ||||||||
\(977\) | 43.1280 | 1.37979 | 0.689893 | − | 0.723911i | \(-0.257658\pi\) | ||||
0.689893 | + | 0.723911i | \(0.257658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.37696 | 0.107873 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.3156 | −0.456831 | ||||||||
\(983\) | 44.6922 | 1.42546 | 0.712729 | − | 0.701439i | \(-0.247459\pi\) | ||||
0.712729 | + | 0.701439i | \(0.247459\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.20127 | −0.165726 | ||||||||
\(986\) | 0.293888 | 0.00935931 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.3644 | 0.520619 | ||||||||
\(989\) | 0.0114573 | 0.000364322 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7657 | 0.437282 | 0.218641 | − | 0.975805i | \(-0.429838\pi\) | ||||
0.218641 | + | 0.975805i | \(0.429838\pi\) | |||||||
\(992\) | 15.3575 | 0.487602 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.32007 | 0.200460 | ||||||||
\(995\) | 8.10264 | 0.256871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.89609 | −0.155061 | −0.0775303 | − | 0.996990i | \(-0.524703\pi\) | ||||
−0.0775303 | + | 0.996990i | \(0.524703\pi\) | |||||||
\(998\) | 50.1886 | 1.58869 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.cb.1.3 | 8 | ||
3.2 | odd | 2 | 5445.2.a.cc.1.6 | 8 | |||
11.2 | odd | 10 | 495.2.n.g.136.2 | yes | 16 | ||
11.6 | odd | 10 | 495.2.n.g.91.2 | ✓ | 16 | ||
11.10 | odd | 2 | 5445.2.a.cd.1.6 | 8 | |||
33.2 | even | 10 | 495.2.n.h.136.3 | yes | 16 | ||
33.17 | even | 10 | 495.2.n.h.91.3 | yes | 16 | ||
33.32 | even | 2 | 5445.2.a.ca.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.91.2 | ✓ | 16 | 11.6 | odd | 10 | ||
495.2.n.g.136.2 | yes | 16 | 11.2 | odd | 10 | ||
495.2.n.h.91.3 | yes | 16 | 33.17 | even | 10 | ||
495.2.n.h.136.3 | yes | 16 | 33.2 | even | 10 | ||
5445.2.a.ca.1.3 | 8 | 33.32 | even | 2 | |||
5445.2.a.cb.1.3 | 8 | 1.1 | even | 1 | trivial | ||
5445.2.a.cc.1.6 | 8 | 3.2 | odd | 2 | |||
5445.2.a.cd.1.6 | 8 | 11.10 | odd | 2 |