Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
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: | \( x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.60802\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60802 | −1.84415 | −0.922074 | − | 0.387015i | \(-0.873506\pi\) | ||||
−0.922074 | + | 0.387015i | \(0.873506\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.80176 | 2.40088 | ||||||||
\(5\) | 1.50528 | 0.673181 | 0.336590 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336590 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(6\) | −2.60802 | −1.06472 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.30704 | −2.58343 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.92579 | −1.24144 | ||||||||
\(11\) | −0.0869524 | −0.0262171 | −0.0131086 | − | 0.999914i | \(-0.504173\pi\) | ||||
−0.0131086 | + | 0.999914i | \(0.504173\pi\) | |||||||
\(12\) | 4.80176 | 1.38615 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.60802 | 0.697022 | ||||||||
\(15\) | 1.50528 | 0.388661 | ||||||||
\(16\) | 9.45336 | 2.36334 | ||||||||
\(17\) | 6.49464 | 1.57518 | 0.787591 | − | 0.616199i | \(-0.211328\pi\) | ||||
0.787591 | + | 0.616199i | \(0.211328\pi\) | |||||||
\(18\) | −2.60802 | −0.614716 | ||||||||
\(19\) | −5.29220 | −1.21411 | −0.607057 | − | 0.794658i | \(-0.707650\pi\) | ||||
−0.607057 | + | 0.794658i | \(0.707650\pi\) | |||||||
\(20\) | 7.22798 | 1.61623 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.226773 | 0.0483482 | ||||||||
\(23\) | −5.20221 | −1.08473 | −0.542367 | − | 0.840141i | \(-0.682472\pi\) | ||||
−0.542367 | + | 0.840141i | \(0.682472\pi\) | |||||||
\(24\) | −7.30704 | −1.49154 | ||||||||
\(25\) | −2.73414 | −0.546828 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.80176 | −0.907447 | ||||||||
\(29\) | −5.97602 | −1.10972 | −0.554859 | − | 0.831944i | \(-0.687228\pi\) | ||||
−0.554859 | + | 0.831944i | \(0.687228\pi\) | |||||||
\(30\) | −3.92579 | −0.716748 | ||||||||
\(31\) | −2.00289 | −0.359730 | −0.179865 | − | 0.983691i | \(-0.557566\pi\) | ||||
−0.179865 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(32\) | −10.0405 | −1.77492 | ||||||||
\(33\) | −0.0869524 | −0.0151365 | ||||||||
\(34\) | −16.9381 | −2.90487 | ||||||||
\(35\) | −1.50528 | −0.254438 | ||||||||
\(36\) | 4.80176 | 0.800293 | ||||||||
\(37\) | −9.52127 | −1.56529 | −0.782643 | − | 0.622470i | \(-0.786129\pi\) | ||||
−0.782643 | + | 0.622470i | \(0.786129\pi\) | |||||||
\(38\) | 13.8022 | 2.23901 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.9991 | −1.73911 | ||||||||
\(41\) | 6.43896 | 1.00560 | 0.502799 | − | 0.864404i | \(-0.332304\pi\) | ||||
0.502799 | + | 0.864404i | \(0.332304\pi\) | |||||||
\(42\) | 2.60802 | 0.402426 | ||||||||
\(43\) | 6.81071 | 1.03862 | 0.519312 | − | 0.854585i | \(-0.326188\pi\) | ||||
0.519312 | + | 0.854585i | \(0.326188\pi\) | |||||||
\(44\) | −0.417524 | −0.0629441 | ||||||||
\(45\) | 1.50528 | 0.224394 | ||||||||
\(46\) | 13.5674 | 2.00041 | ||||||||
\(47\) | 1.83051 | 0.267008 | 0.133504 | − | 0.991048i | \(-0.457377\pi\) | ||||
0.133504 | + | 0.991048i | \(0.457377\pi\) | |||||||
\(48\) | 9.45336 | 1.36448 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.13069 | 1.00843 | ||||||||
\(51\) | 6.49464 | 0.909431 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.28476 | −0.451197 | −0.225598 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225598 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(54\) | −2.60802 | −0.354906 | ||||||||
\(55\) | −0.130887 | −0.0176489 | ||||||||
\(56\) | 7.30704 | 0.976444 | ||||||||
\(57\) | −5.29220 | −0.700969 | ||||||||
\(58\) | 15.5856 | 2.04649 | ||||||||
\(59\) | −2.67509 | −0.348267 | −0.174133 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174133 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(60\) | 7.22798 | 0.933128 | ||||||||
\(61\) | −6.54557 | −0.838074 | −0.419037 | − | 0.907969i | \(-0.637632\pi\) | ||||
−0.419037 | + | 0.907969i | \(0.637632\pi\) | |||||||
\(62\) | 5.22357 | 0.663394 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 7.27901 | 0.909876 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.226773 | 0.0279139 | ||||||||
\(67\) | −8.29459 | −1.01335 | −0.506673 | − | 0.862138i | \(-0.669125\pi\) | ||||
−0.506673 | + | 0.862138i | \(0.669125\pi\) | |||||||
\(68\) | 31.1857 | 3.78182 | ||||||||
\(69\) | −5.20221 | −0.626272 | ||||||||
\(70\) | 3.92579 | 0.469222 | ||||||||
\(71\) | 12.9178 | 1.53307 | 0.766533 | − | 0.642205i | \(-0.221980\pi\) | ||||
0.766533 | + | 0.642205i | \(0.221980\pi\) | |||||||
\(72\) | −7.30704 | −0.861142 | ||||||||
\(73\) | −14.5507 | −1.70303 | −0.851513 | − | 0.524334i | \(-0.824314\pi\) | ||||
−0.851513 | + | 0.524334i | \(0.824314\pi\) | |||||||
\(74\) | 24.8316 | 2.88662 | ||||||||
\(75\) | −2.73414 | −0.315711 | ||||||||
\(76\) | −25.4119 | −2.91494 | ||||||||
\(77\) | 0.0869524 | 0.00990914 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6780 | −1.31387 | −0.656936 | − | 0.753946i | \(-0.728148\pi\) | ||||
−0.656936 | + | 0.753946i | \(0.728148\pi\) | |||||||
\(80\) | 14.2299 | 1.59096 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.7929 | −1.85447 | ||||||||
\(83\) | −1.29310 | −0.141937 | −0.0709683 | − | 0.997479i | \(-0.522609\pi\) | ||||
−0.0709683 | + | 0.997479i | \(0.522609\pi\) | |||||||
\(84\) | −4.80176 | −0.523915 | ||||||||
\(85\) | 9.77623 | 1.06038 | ||||||||
\(86\) | −17.7625 | −1.91538 | ||||||||
\(87\) | −5.97602 | −0.640697 | ||||||||
\(88\) | 0.635364 | 0.0677300 | ||||||||
\(89\) | −15.8454 | −1.67961 | −0.839805 | − | 0.542889i | \(-0.817331\pi\) | ||||
−0.839805 | + | 0.542889i | \(0.817331\pi\) | |||||||
\(90\) | −3.92579 | −0.413815 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −24.9797 | −2.60432 | ||||||||
\(93\) | −2.00289 | −0.207690 | ||||||||
\(94\) | −4.77401 | −0.492402 | ||||||||
\(95\) | −7.96623 | −0.817318 | ||||||||
\(96\) | −10.0405 | −1.02475 | ||||||||
\(97\) | 5.86980 | 0.595988 | 0.297994 | − | 0.954568i | \(-0.403682\pi\) | ||||
0.297994 | + | 0.954568i | \(0.403682\pi\) | |||||||
\(98\) | −2.60802 | −0.263450 | ||||||||
\(99\) | −0.0869524 | −0.00873904 | ||||||||
\(100\) | −13.1287 | −1.31287 | ||||||||
\(101\) | −6.68172 | −0.664856 | −0.332428 | − | 0.943129i | \(-0.607868\pi\) | ||||
−0.332428 | + | 0.943129i | \(0.607868\pi\) | |||||||
\(102\) | −16.9381 | −1.67713 | ||||||||
\(103\) | −4.52273 | −0.445637 | −0.222819 | − | 0.974860i | \(-0.571526\pi\) | ||||
−0.222819 | + | 0.974860i | \(0.571526\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.50528 | −0.146900 | ||||||||
\(106\) | 8.56672 | 0.832073 | ||||||||
\(107\) | −10.2448 | −0.990404 | −0.495202 | − | 0.868778i | \(-0.664906\pi\) | ||||
−0.495202 | + | 0.868778i | \(0.664906\pi\) | |||||||
\(108\) | 4.80176 | 0.462049 | ||||||||
\(109\) | 13.5552 | 1.29835 | 0.649177 | − | 0.760637i | \(-0.275113\pi\) | ||||
0.649177 | + | 0.760637i | \(0.275113\pi\) | |||||||
\(110\) | 0.341357 | 0.0325471 | ||||||||
\(111\) | −9.52127 | −0.903719 | ||||||||
\(112\) | −9.45336 | −0.893259 | ||||||||
\(113\) | 13.3874 | 1.25938 | 0.629691 | − | 0.776846i | \(-0.283182\pi\) | ||||
0.629691 | + | 0.776846i | \(0.283182\pi\) | |||||||
\(114\) | 13.8022 | 1.29269 | ||||||||
\(115\) | −7.83076 | −0.730222 | ||||||||
\(116\) | −28.6954 | −2.66430 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.97667 | 0.642255 | ||||||||
\(119\) | −6.49464 | −0.595363 | ||||||||
\(120\) | −10.9991 | −1.00408 | ||||||||
\(121\) | −10.9924 | −0.999313 | ||||||||
\(122\) | 17.0710 | 1.54553 | ||||||||
\(123\) | 6.43896 | 0.580582 | ||||||||
\(124\) | −9.61739 | −0.863667 | ||||||||
\(125\) | −11.6420 | −1.04129 | ||||||||
\(126\) | 2.60802 | 0.232341 | ||||||||
\(127\) | 12.9447 | 1.14866 | 0.574328 | − | 0.818626i | \(-0.305264\pi\) | ||||
0.574328 | + | 0.818626i | \(0.305264\pi\) | |||||||
\(128\) | 1.09716 | 0.0969765 | ||||||||
\(129\) | 6.81071 | 0.599650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.84887 | 0.511018 | 0.255509 | − | 0.966807i | \(-0.417757\pi\) | ||||
0.255509 | + | 0.966807i | \(0.417757\pi\) | |||||||
\(132\) | −0.417524 | −0.0363408 | ||||||||
\(133\) | 5.29220 | 0.458892 | ||||||||
\(134\) | 21.6324 | 1.86876 | ||||||||
\(135\) | 1.50528 | 0.129554 | ||||||||
\(136\) | −47.4566 | −4.06937 | ||||||||
\(137\) | −5.11089 | −0.436653 | −0.218327 | − | 0.975876i | \(-0.570060\pi\) | ||||
−0.218327 | + | 0.975876i | \(0.570060\pi\) | |||||||
\(138\) | 13.5674 | 1.15494 | ||||||||
\(139\) | −19.3275 | −1.63934 | −0.819669 | − | 0.572837i | \(-0.805843\pi\) | ||||
−0.819669 | + | 0.572837i | \(0.805843\pi\) | |||||||
\(140\) | −7.22798 | −0.610876 | ||||||||
\(141\) | 1.83051 | 0.154157 | ||||||||
\(142\) | −33.6900 | −2.82720 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.45336 | 0.787780 | ||||||||
\(145\) | −8.99557 | −0.747041 | ||||||||
\(146\) | 37.9484 | 3.14063 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −45.7188 | −3.75806 | ||||||||
\(149\) | 9.51027 | 0.779112 | 0.389556 | − | 0.921003i | \(-0.372628\pi\) | ||||
0.389556 | + | 0.921003i | \(0.372628\pi\) | |||||||
\(150\) | 7.13069 | 0.582218 | ||||||||
\(151\) | 12.7770 | 1.03977 | 0.519887 | − | 0.854235i | \(-0.325974\pi\) | ||||
0.519887 | + | 0.854235i | \(0.325974\pi\) | |||||||
\(152\) | 38.6703 | 3.13658 | ||||||||
\(153\) | 6.49464 | 0.525060 | ||||||||
\(154\) | −0.226773 | −0.0182739 | ||||||||
\(155\) | −3.01490 | −0.242163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.57466 | −0.205480 | −0.102740 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102740 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(158\) | 30.4563 | 2.42297 | ||||||||
\(159\) | −3.28476 | −0.260499 | ||||||||
\(160\) | −15.1137 | −1.19484 | ||||||||
\(161\) | 5.20221 | 0.409991 | ||||||||
\(162\) | −2.60802 | −0.204905 | ||||||||
\(163\) | −19.5300 | −1.52971 | −0.764853 | − | 0.644205i | \(-0.777188\pi\) | ||||
−0.764853 | + | 0.644205i | \(0.777188\pi\) | |||||||
\(164\) | 30.9183 | 2.41432 | ||||||||
\(165\) | −0.130887 | −0.0101896 | ||||||||
\(166\) | 3.37244 | 0.261752 | ||||||||
\(167\) | 1.39652 | 0.108066 | 0.0540331 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540331 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(168\) | 7.30704 | 0.563750 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −25.4966 | −1.95550 | ||||||||
\(171\) | −5.29220 | −0.404705 | ||||||||
\(172\) | 32.7034 | 2.49361 | ||||||||
\(173\) | 17.1814 | 1.30628 | 0.653138 | − | 0.757238i | \(-0.273452\pi\) | ||||
0.653138 | + | 0.757238i | \(0.273452\pi\) | |||||||
\(174\) | 15.5856 | 1.18154 | ||||||||
\(175\) | 2.73414 | 0.206682 | ||||||||
\(176\) | −0.821992 | −0.0619600 | ||||||||
\(177\) | −2.67509 | −0.201072 | ||||||||
\(178\) | 41.3251 | 3.09745 | ||||||||
\(179\) | −1.43708 | −0.107412 | −0.0537061 | − | 0.998557i | \(-0.517103\pi\) | ||||
−0.0537061 | + | 0.998557i | \(0.517103\pi\) | |||||||
\(180\) | 7.22798 | 0.538742 | ||||||||
\(181\) | −4.31882 | −0.321015 | −0.160508 | − | 0.987035i | \(-0.551313\pi\) | ||||
−0.160508 | + | 0.987035i | \(0.551313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.54557 | −0.483862 | ||||||||
\(184\) | 38.0127 | 2.80233 | ||||||||
\(185\) | −14.3321 | −1.05372 | ||||||||
\(186\) | 5.22357 | 0.383011 | ||||||||
\(187\) | −0.564724 | −0.0412967 | ||||||||
\(188\) | 8.78969 | 0.641054 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 20.7761 | 1.50726 | ||||||||
\(191\) | −6.78719 | −0.491104 | −0.245552 | − | 0.969383i | \(-0.578969\pi\) | ||||
−0.245552 | + | 0.969383i | \(0.578969\pi\) | |||||||
\(192\) | 7.27901 | 0.525317 | ||||||||
\(193\) | 21.3749 | 1.53860 | 0.769300 | − | 0.638887i | \(-0.220605\pi\) | ||||
0.769300 | + | 0.638887i | \(0.220605\pi\) | |||||||
\(194\) | −15.3085 | −1.09909 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.80176 | 0.342983 | ||||||||
\(197\) | 22.7982 | 1.62431 | 0.812153 | − | 0.583444i | \(-0.198295\pi\) | ||||
0.812153 | + | 0.583444i | \(0.198295\pi\) | |||||||
\(198\) | 0.226773 | 0.0161161 | ||||||||
\(199\) | 2.66365 | 0.188821 | 0.0944107 | − | 0.995533i | \(-0.469903\pi\) | ||||
0.0944107 | + | 0.995533i | \(0.469903\pi\) | |||||||
\(200\) | 19.9785 | 1.41269 | ||||||||
\(201\) | −8.29459 | −0.585055 | ||||||||
\(202\) | 17.4260 | 1.22609 | ||||||||
\(203\) | 5.97602 | 0.419434 | ||||||||
\(204\) | 31.1857 | 2.18343 | ||||||||
\(205\) | 9.69243 | 0.676948 | ||||||||
\(206\) | 11.7953 | 0.821821 | ||||||||
\(207\) | −5.20221 | −0.361578 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.460170 | 0.0318306 | ||||||||
\(210\) | 3.92579 | 0.270905 | ||||||||
\(211\) | −24.1832 | −1.66484 | −0.832419 | − | 0.554147i | \(-0.813045\pi\) | ||||
−0.832419 | + | 0.554147i | \(0.813045\pi\) | |||||||
\(212\) | −15.7726 | −1.08327 | ||||||||
\(213\) | 12.9178 | 0.885116 | ||||||||
\(214\) | 26.7187 | 1.82645 | ||||||||
\(215\) | 10.2520 | 0.699181 | ||||||||
\(216\) | −7.30704 | −0.497181 | ||||||||
\(217\) | 2.00289 | 0.135965 | ||||||||
\(218\) | −35.3523 | −2.39436 | ||||||||
\(219\) | −14.5507 | −0.983242 | ||||||||
\(220\) | −0.628490 | −0.0423728 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.8316 | 1.66659 | ||||||||
\(223\) | −16.9080 | −1.13224 | −0.566122 | − | 0.824322i | \(-0.691557\pi\) | ||||
−0.566122 | + | 0.824322i | \(0.691557\pi\) | |||||||
\(224\) | 10.0405 | 0.670857 | ||||||||
\(225\) | −2.73414 | −0.182276 | ||||||||
\(226\) | −34.9146 | −2.32248 | ||||||||
\(227\) | −11.6431 | −0.772782 | −0.386391 | − | 0.922335i | \(-0.626278\pi\) | ||||
−0.386391 | + | 0.922335i | \(0.626278\pi\) | |||||||
\(228\) | −25.4119 | −1.68294 | ||||||||
\(229\) | 7.90801 | 0.522576 | 0.261288 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261288 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(230\) | 20.4228 | 1.34664 | ||||||||
\(231\) | 0.0869524 | 0.00572105 | ||||||||
\(232\) | 43.6670 | 2.86688 | ||||||||
\(233\) | −24.0854 | −1.57789 | −0.788945 | − | 0.614464i | \(-0.789372\pi\) | ||||
−0.788945 | + | 0.614464i | \(0.789372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.75543 | 0.179745 | ||||||||
\(236\) | −12.8451 | −0.836146 | ||||||||
\(237\) | −11.6780 | −0.758565 | ||||||||
\(238\) | 16.9381 | 1.09794 | ||||||||
\(239\) | 10.9354 | 0.707352 | 0.353676 | − | 0.935368i | \(-0.384932\pi\) | ||||
0.353676 | + | 0.935368i | \(0.384932\pi\) | |||||||
\(240\) | 14.2299 | 0.918538 | ||||||||
\(241\) | 19.9054 | 1.28222 | 0.641108 | − | 0.767450i | \(-0.278475\pi\) | ||||
0.641108 | + | 0.767450i | \(0.278475\pi\) | |||||||
\(242\) | 28.6685 | 1.84288 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −31.4302 | −2.01212 | ||||||||
\(245\) | 1.50528 | 0.0961687 | ||||||||
\(246\) | −16.7929 | −1.07068 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.6352 | 0.929335 | ||||||||
\(249\) | −1.29310 | −0.0819471 | ||||||||
\(250\) | 30.3626 | 1.92030 | ||||||||
\(251\) | −23.3883 | −1.47626 | −0.738129 | − | 0.674659i | \(-0.764290\pi\) | ||||
−0.738129 | + | 0.674659i | \(0.764290\pi\) | |||||||
\(252\) | −4.80176 | −0.302482 | ||||||||
\(253\) | 0.452344 | 0.0284386 | ||||||||
\(254\) | −33.7600 | −2.11829 | ||||||||
\(255\) | 9.77623 | 0.612212 | ||||||||
\(256\) | −17.4194 | −1.08871 | ||||||||
\(257\) | 12.0595 | 0.752251 | 0.376125 | − | 0.926569i | \(-0.377256\pi\) | ||||
0.376125 | + | 0.926569i | \(0.377256\pi\) | |||||||
\(258\) | −17.7625 | −1.10584 | ||||||||
\(259\) | 9.52127 | 0.591623 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.97602 | −0.369906 | ||||||||
\(262\) | −15.2540 | −0.942393 | ||||||||
\(263\) | 4.53226 | 0.279471 | 0.139736 | − | 0.990189i | \(-0.455375\pi\) | ||||
0.139736 | + | 0.990189i | \(0.455375\pi\) | |||||||
\(264\) | 0.635364 | 0.0391039 | ||||||||
\(265\) | −4.94448 | −0.303737 | ||||||||
\(266\) | −13.8022 | −0.846265 | ||||||||
\(267\) | −15.8454 | −0.969723 | ||||||||
\(268\) | −39.8286 | −2.43292 | ||||||||
\(269\) | −27.9600 | −1.70475 | −0.852375 | − | 0.522931i | \(-0.824838\pi\) | ||||
−0.852375 | + | 0.522931i | \(0.824838\pi\) | |||||||
\(270\) | −3.92579 | −0.238916 | ||||||||
\(271\) | −4.18954 | −0.254496 | −0.127248 | − | 0.991871i | \(-0.540614\pi\) | ||||
−0.127248 | + | 0.991871i | \(0.540614\pi\) | |||||||
\(272\) | 61.3962 | 3.72269 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.3293 | 0.805252 | ||||||||
\(275\) | 0.237740 | 0.0143363 | ||||||||
\(276\) | −24.9797 | −1.50360 | ||||||||
\(277\) | 9.86805 | 0.592913 | 0.296457 | − | 0.955046i | \(-0.404195\pi\) | ||||
0.296457 | + | 0.955046i | \(0.404195\pi\) | |||||||
\(278\) | 50.4065 | 3.02318 | ||||||||
\(279\) | −2.00289 | −0.119910 | ||||||||
\(280\) | 10.9991 | 0.657323 | ||||||||
\(281\) | 2.76496 | 0.164944 | 0.0824719 | − | 0.996593i | \(-0.473719\pi\) | ||||
0.0824719 | + | 0.996593i | \(0.473719\pi\) | |||||||
\(282\) | −4.77401 | −0.284288 | ||||||||
\(283\) | −5.74079 | −0.341255 | −0.170627 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170627 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(284\) | 62.0284 | 3.68071 | ||||||||
\(285\) | −7.96623 | −0.471879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.43896 | −0.380080 | ||||||||
\(288\) | −10.0405 | −0.591641 | ||||||||
\(289\) | 25.1803 | 1.48120 | ||||||||
\(290\) | 23.4606 | 1.37765 | ||||||||
\(291\) | 5.86980 | 0.344094 | ||||||||
\(292\) | −69.8687 | −4.08876 | ||||||||
\(293\) | 15.8014 | 0.923131 | 0.461565 | − | 0.887106i | \(-0.347288\pi\) | ||||
0.461565 | + | 0.887106i | \(0.347288\pi\) | |||||||
\(294\) | −2.60802 | −0.152103 | ||||||||
\(295\) | −4.02675 | −0.234446 | ||||||||
\(296\) | 69.5722 | 4.04380 | ||||||||
\(297\) | −0.0869524 | −0.00504549 | ||||||||
\(298\) | −24.8030 | −1.43680 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.1287 | −0.757985 | ||||||||
\(301\) | −6.81071 | −0.392563 | ||||||||
\(302\) | −33.3226 | −1.91750 | ||||||||
\(303\) | −6.68172 | −0.383855 | ||||||||
\(304\) | −50.0291 | −2.86937 | ||||||||
\(305\) | −9.85290 | −0.564175 | ||||||||
\(306\) | −16.9381 | −0.968289 | ||||||||
\(307\) | 10.1195 | 0.577549 | 0.288774 | − | 0.957397i | \(-0.406752\pi\) | ||||
0.288774 | + | 0.957397i | \(0.406752\pi\) | |||||||
\(308\) | 0.417524 | 0.0237906 | ||||||||
\(309\) | −4.52273 | −0.257289 | ||||||||
\(310\) | 7.86293 | 0.446584 | ||||||||
\(311\) | 14.4989 | 0.822155 | 0.411077 | − | 0.911600i | \(-0.365153\pi\) | ||||
0.411077 | + | 0.911600i | \(0.365153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2670 | 0.749897 | 0.374948 | − | 0.927046i | \(-0.377660\pi\) | ||||
0.374948 | + | 0.927046i | \(0.377660\pi\) | |||||||
\(314\) | 6.71477 | 0.378936 | ||||||||
\(315\) | −1.50528 | −0.0848128 | ||||||||
\(316\) | −56.0747 | −3.15445 | ||||||||
\(317\) | 30.4190 | 1.70850 | 0.854252 | − | 0.519860i | \(-0.174016\pi\) | ||||
0.854252 | + | 0.519860i | \(0.174016\pi\) | |||||||
\(318\) | 8.56672 | 0.480398 | ||||||||
\(319\) | 0.519629 | 0.0290936 | ||||||||
\(320\) | 10.9569 | 0.612511 | ||||||||
\(321\) | −10.2448 | −0.571810 | ||||||||
\(322\) | −13.5674 | −0.756084 | ||||||||
\(323\) | −34.3710 | −1.91245 | ||||||||
\(324\) | 4.80176 | 0.266764 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 50.9345 | 2.82100 | ||||||||
\(327\) | 13.5552 | 0.749605 | ||||||||
\(328\) | −47.0497 | −2.59789 | ||||||||
\(329\) | −1.83051 | −0.100920 | ||||||||
\(330\) | 0.341357 | 0.0187911 | ||||||||
\(331\) | −9.30294 | −0.511336 | −0.255668 | − | 0.966765i | \(-0.582295\pi\) | ||||
−0.255668 | + | 0.966765i | \(0.582295\pi\) | |||||||
\(332\) | −6.20917 | −0.340773 | ||||||||
\(333\) | −9.52127 | −0.521762 | ||||||||
\(334\) | −3.64216 | −0.199290 | ||||||||
\(335\) | −12.4857 | −0.682165 | ||||||||
\(336\) | −9.45336 | −0.515723 | ||||||||
\(337\) | 13.3054 | 0.724789 | 0.362395 | − | 0.932025i | \(-0.381959\pi\) | ||||
0.362395 | + | 0.932025i | \(0.381959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3874 | 0.727104 | ||||||||
\(340\) | 46.9431 | 2.54585 | ||||||||
\(341\) | 0.174156 | 0.00943108 | ||||||||
\(342\) | 13.8022 | 0.746335 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −49.7661 | −2.68321 | ||||||||
\(345\) | −7.83076 | −0.421594 | ||||||||
\(346\) | −44.8094 | −2.40897 | ||||||||
\(347\) | −16.8760 | −0.905953 | −0.452976 | − | 0.891523i | \(-0.649638\pi\) | ||||
−0.452976 | + | 0.891523i | \(0.649638\pi\) | |||||||
\(348\) | −28.6954 | −1.53823 | ||||||||
\(349\) | 2.40720 | 0.128854 | 0.0644271 | − | 0.997922i | \(-0.479478\pi\) | ||||
0.0644271 | + | 0.997922i | \(0.479478\pi\) | |||||||
\(350\) | −7.13069 | −0.381151 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.873043 | 0.0465333 | ||||||||
\(353\) | −30.7137 | −1.63472 | −0.817361 | − | 0.576125i | \(-0.804564\pi\) | ||||
−0.817361 | + | 0.576125i | \(0.804564\pi\) | |||||||
\(354\) | 6.97667 | 0.370806 | ||||||||
\(355\) | 19.4449 | 1.03203 | ||||||||
\(356\) | −76.0858 | −4.03254 | ||||||||
\(357\) | −6.49464 | −0.343733 | ||||||||
\(358\) | 3.74792 | 0.198084 | ||||||||
\(359\) | −10.6322 | −0.561145 | −0.280572 | − | 0.959833i | \(-0.590524\pi\) | ||||
−0.280572 | + | 0.959833i | \(0.590524\pi\) | |||||||
\(360\) | −10.9991 | −0.579704 | ||||||||
\(361\) | 9.00742 | 0.474075 | ||||||||
\(362\) | 11.2636 | 0.592000 | ||||||||
\(363\) | −10.9924 | −0.576953 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.9028 | −1.14644 | ||||||||
\(366\) | 17.0710 | 0.892314 | ||||||||
\(367\) | 26.2062 | 1.36795 | 0.683977 | − | 0.729503i | \(-0.260249\pi\) | ||||
0.683977 | + | 0.729503i | \(0.260249\pi\) | |||||||
\(368\) | −49.1784 | −2.56360 | ||||||||
\(369\) | 6.43896 | 0.335199 | ||||||||
\(370\) | 37.3785 | 1.94322 | ||||||||
\(371\) | 3.28476 | 0.170536 | ||||||||
\(372\) | −9.61739 | −0.498639 | ||||||||
\(373\) | 18.2102 | 0.942888 | 0.471444 | − | 0.881896i | \(-0.343733\pi\) | ||||
0.471444 | + | 0.881896i | \(0.343733\pi\) | |||||||
\(374\) | 1.47281 | 0.0761572 | ||||||||
\(375\) | −11.6420 | −0.601192 | ||||||||
\(376\) | −13.3756 | −0.689796 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.60802 | 0.134142 | ||||||||
\(379\) | −28.8947 | −1.48422 | −0.742110 | − | 0.670278i | \(-0.766175\pi\) | ||||
−0.742110 | + | 0.670278i | \(0.766175\pi\) | |||||||
\(380\) | −38.2519 | −1.96228 | ||||||||
\(381\) | 12.9447 | 0.663176 | ||||||||
\(382\) | 17.7011 | 0.905668 | ||||||||
\(383\) | 17.3262 | 0.885329 | 0.442665 | − | 0.896687i | \(-0.354033\pi\) | ||||
0.442665 | + | 0.896687i | \(0.354033\pi\) | |||||||
\(384\) | 1.09716 | 0.0559894 | ||||||||
\(385\) | 0.130887 | 0.00667064 | ||||||||
\(386\) | −55.7462 | −2.83741 | ||||||||
\(387\) | 6.81071 | 0.346208 | ||||||||
\(388\) | 28.1854 | 1.43090 | ||||||||
\(389\) | 13.6737 | 0.693282 | 0.346641 | − | 0.937998i | \(-0.387322\pi\) | ||||
0.346641 | + | 0.937998i | \(0.387322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.7865 | −1.70865 | ||||||||
\(392\) | −7.30704 | −0.369061 | ||||||||
\(393\) | 5.84887 | 0.295037 | ||||||||
\(394\) | −59.4582 | −2.99546 | ||||||||
\(395\) | −17.5786 | −0.884473 | ||||||||
\(396\) | −0.417524 | −0.0209814 | ||||||||
\(397\) | −15.4433 | −0.775079 | −0.387540 | − | 0.921853i | \(-0.626675\pi\) | ||||
−0.387540 | + | 0.921853i | \(0.626675\pi\) | |||||||
\(398\) | −6.94686 | −0.348215 | ||||||||
\(399\) | 5.29220 | 0.264942 | ||||||||
\(400\) | −25.8468 | −1.29234 | ||||||||
\(401\) | −14.2334 | −0.710783 | −0.355391 | − | 0.934718i | \(-0.615652\pi\) | ||||
−0.355391 | + | 0.934718i | \(0.615652\pi\) | |||||||
\(402\) | 21.6324 | 1.07893 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −32.0840 | −1.59624 | ||||||||
\(405\) | 1.50528 | 0.0747978 | ||||||||
\(406\) | −15.5856 | −0.773499 | ||||||||
\(407\) | 0.827897 | 0.0410373 | ||||||||
\(408\) | −47.4566 | −2.34945 | ||||||||
\(409\) | −14.0858 | −0.696499 | −0.348249 | − | 0.937402i | \(-0.613224\pi\) | ||||
−0.348249 | + | 0.937402i | \(0.613224\pi\) | |||||||
\(410\) | −25.2780 | −1.24839 | ||||||||
\(411\) | −5.11089 | −0.252102 | ||||||||
\(412\) | −21.7170 | −1.06992 | ||||||||
\(413\) | 2.67509 | 0.131632 | ||||||||
\(414\) | 13.5674 | 0.666804 | ||||||||
\(415\) | −1.94648 | −0.0955489 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.3275 | −0.946473 | ||||||||
\(418\) | −1.20013 | −0.0587003 | ||||||||
\(419\) | −37.6723 | −1.84041 | −0.920207 | − | 0.391432i | \(-0.871980\pi\) | ||||
−0.920207 | + | 0.391432i | \(0.871980\pi\) | |||||||
\(420\) | −7.22798 | −0.352689 | ||||||||
\(421\) | −2.28615 | −0.111420 | −0.0557101 | − | 0.998447i | \(-0.517742\pi\) | ||||
−0.0557101 | + | 0.998447i | \(0.517742\pi\) | |||||||
\(422\) | 63.0701 | 3.07021 | ||||||||
\(423\) | 1.83051 | 0.0890026 | ||||||||
\(424\) | 24.0019 | 1.16563 | ||||||||
\(425\) | −17.7573 | −0.861353 | ||||||||
\(426\) | −33.6900 | −1.63228 | ||||||||
\(427\) | 6.54557 | 0.316762 | ||||||||
\(428\) | −49.1931 | −2.37784 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.7374 | −1.28939 | ||||||||
\(431\) | 1.98118 | 0.0954301 | 0.0477150 | − | 0.998861i | \(-0.484806\pi\) | ||||
0.0477150 | + | 0.998861i | \(0.484806\pi\) | |||||||
\(432\) | 9.45336 | 0.454825 | ||||||||
\(433\) | −5.89088 | −0.283098 | −0.141549 | − | 0.989931i | \(-0.545208\pi\) | ||||
−0.141549 | + | 0.989931i | \(0.545208\pi\) | |||||||
\(434\) | −5.22357 | −0.250740 | ||||||||
\(435\) | −8.99557 | −0.431304 | ||||||||
\(436\) | 65.0889 | 3.11719 | ||||||||
\(437\) | 27.5311 | 1.31699 | ||||||||
\(438\) | 37.9484 | 1.81324 | ||||||||
\(439\) | −8.06563 | −0.384951 | −0.192476 | − | 0.981302i | \(-0.561652\pi\) | ||||
−0.192476 | + | 0.981302i | \(0.561652\pi\) | |||||||
\(440\) | 0.956399 | 0.0455945 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.65984 | 0.316419 | 0.158209 | − | 0.987406i | \(-0.449428\pi\) | ||||
0.158209 | + | 0.987406i | \(0.449428\pi\) | |||||||
\(444\) | −45.7188 | −2.16972 | ||||||||
\(445\) | −23.8517 | −1.13068 | ||||||||
\(446\) | 44.0964 | 2.08802 | ||||||||
\(447\) | 9.51027 | 0.449821 | ||||||||
\(448\) | −7.27901 | −0.343901 | ||||||||
\(449\) | −19.8491 | −0.936738 | −0.468369 | − | 0.883533i | \(-0.655158\pi\) | ||||
−0.468369 | + | 0.883533i | \(0.655158\pi\) | |||||||
\(450\) | 7.13069 | 0.336144 | ||||||||
\(451\) | −0.559883 | −0.0263639 | ||||||||
\(452\) | 64.2831 | 3.02362 | ||||||||
\(453\) | 12.7770 | 0.600314 | ||||||||
\(454\) | 30.3655 | 1.42512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6703 | 1.81090 | ||||||||
\(457\) | 2.58884 | 0.121101 | 0.0605505 | − | 0.998165i | \(-0.480714\pi\) | ||||
0.0605505 | + | 0.998165i | \(0.480714\pi\) | |||||||
\(458\) | −20.6242 | −0.963708 | ||||||||
\(459\) | 6.49464 | 0.303144 | ||||||||
\(460\) | −37.6014 | −1.75318 | ||||||||
\(461\) | −26.3667 | −1.22802 | −0.614010 | − | 0.789298i | \(-0.710445\pi\) | ||||
−0.614010 | + | 0.789298i | \(0.710445\pi\) | |||||||
\(462\) | −0.226773 | −0.0105504 | ||||||||
\(463\) | −29.3082 | −1.36207 | −0.681034 | − | 0.732252i | \(-0.738469\pi\) | ||||
−0.681034 | + | 0.732252i | \(0.738469\pi\) | |||||||
\(464\) | −56.4935 | −2.62264 | ||||||||
\(465\) | −3.01490 | −0.139813 | ||||||||
\(466\) | 62.8153 | 2.90986 | ||||||||
\(467\) | 3.23005 | 0.149469 | 0.0747345 | − | 0.997203i | \(-0.476189\pi\) | ||||
0.0747345 | + | 0.997203i | \(0.476189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.29459 | 0.383009 | ||||||||
\(470\) | −7.18622 | −0.331475 | ||||||||
\(471\) | −2.57466 | −0.118634 | ||||||||
\(472\) | 19.5470 | 0.899721 | ||||||||
\(473\) | −0.592207 | −0.0272297 | ||||||||
\(474\) | 30.4563 | 1.39890 | ||||||||
\(475\) | 14.4696 | 0.663912 | ||||||||
\(476\) | −31.1857 | −1.42939 | ||||||||
\(477\) | −3.28476 | −0.150399 | ||||||||
\(478\) | −28.5197 | −1.30446 | ||||||||
\(479\) | −7.91296 | −0.361552 | −0.180776 | − | 0.983524i | \(-0.557861\pi\) | ||||
−0.180776 | + | 0.983524i | \(0.557861\pi\) | |||||||
\(480\) | −15.1137 | −0.689843 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −51.9135 | −2.36460 | ||||||||
\(483\) | 5.20221 | 0.236709 | ||||||||
\(484\) | −52.7830 | −2.39923 | ||||||||
\(485\) | 8.83568 | 0.401208 | ||||||||
\(486\) | −2.60802 | −0.118302 | ||||||||
\(487\) | 15.4451 | 0.699883 | 0.349941 | − | 0.936772i | \(-0.386201\pi\) | ||||
0.349941 | + | 0.936772i | \(0.386201\pi\) | |||||||
\(488\) | 47.8287 | 2.16510 | ||||||||
\(489\) | −19.5300 | −0.883176 | ||||||||
\(490\) | −3.92579 | −0.177349 | ||||||||
\(491\) | −14.9062 | −0.672708 | −0.336354 | − | 0.941736i | \(-0.609194\pi\) | ||||
−0.336354 | + | 0.941736i | \(0.609194\pi\) | |||||||
\(492\) | 30.9183 | 1.39391 | ||||||||
\(493\) | −38.8121 | −1.74801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.130887 | −0.00588295 | ||||||||
\(496\) | −18.9340 | −0.850164 | ||||||||
\(497\) | −12.9178 | −0.579445 | ||||||||
\(498\) | 3.37244 | 0.151123 | ||||||||
\(499\) | −25.4306 | −1.13843 | −0.569214 | − | 0.822189i | \(-0.692752\pi\) | ||||
−0.569214 | + | 0.822189i | \(0.692752\pi\) | |||||||
\(500\) | −55.9022 | −2.50002 | ||||||||
\(501\) | 1.39652 | 0.0623920 | ||||||||
\(502\) | 60.9972 | 2.72244 | ||||||||
\(503\) | 28.7912 | 1.28373 | 0.641867 | − | 0.766816i | \(-0.278160\pi\) | ||||
0.641867 | + | 0.766816i | \(0.278160\pi\) | |||||||
\(504\) | 7.30704 | 0.325481 | ||||||||
\(505\) | −10.0578 | −0.447568 | ||||||||
\(506\) | −1.17972 | −0.0524450 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 62.1573 | 2.75778 | ||||||||
\(509\) | −15.6649 | −0.694334 | −0.347167 | − | 0.937803i | \(-0.612856\pi\) | ||||
−0.347167 | + | 0.937803i | \(0.612856\pi\) | |||||||
\(510\) | −25.4966 | −1.12901 | ||||||||
\(511\) | 14.5507 | 0.643683 | ||||||||
\(512\) | 43.2359 | 1.91077 | ||||||||
\(513\) | −5.29220 | −0.233656 | ||||||||
\(514\) | −31.4514 | −1.38726 | ||||||||
\(515\) | −6.80796 | −0.299994 | ||||||||
\(516\) | 32.7034 | 1.43969 | ||||||||
\(517\) | −0.159168 | −0.00700018 | ||||||||
\(518\) | −24.8316 | −1.09104 | ||||||||
\(519\) | 17.1814 | 0.754179 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.38082 | 0.191927 | 0.0959636 | − | 0.995385i | \(-0.469407\pi\) | ||||
0.0959636 | + | 0.995385i | \(0.469407\pi\) | |||||||
\(522\) | 15.5856 | 0.682162 | ||||||||
\(523\) | −21.3207 | −0.932289 | −0.466144 | − | 0.884709i | \(-0.654357\pi\) | ||||
−0.466144 | + | 0.884709i | \(0.654357\pi\) | |||||||
\(524\) | 28.0849 | 1.22689 | ||||||||
\(525\) | 2.73414 | 0.119328 | ||||||||
\(526\) | −11.8202 | −0.515386 | ||||||||
\(527\) | −13.0080 | −0.566639 | ||||||||
\(528\) | −0.821992 | −0.0357726 | ||||||||
\(529\) | 4.06295 | 0.176650 | ||||||||
\(530\) | 12.8953 | 0.560136 | ||||||||
\(531\) | −2.67509 | −0.116089 | ||||||||
\(532\) | 25.4119 | 1.10174 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 41.3251 | 1.78831 | ||||||||
\(535\) | −15.4213 | −0.666720 | ||||||||
\(536\) | 60.6089 | 2.61791 | ||||||||
\(537\) | −1.43708 | −0.0620144 | ||||||||
\(538\) | 72.9201 | 3.14381 | ||||||||
\(539\) | −0.0869524 | −0.00374530 | ||||||||
\(540\) | 7.22798 | 0.311043 | ||||||||
\(541\) | −18.7093 | −0.804374 | −0.402187 | − | 0.915557i | \(-0.631750\pi\) | ||||
−0.402187 | + | 0.915557i | \(0.631750\pi\) | |||||||
\(542\) | 10.9264 | 0.469329 | ||||||||
\(543\) | −4.31882 | −0.185338 | ||||||||
\(544\) | −65.2093 | −2.79582 | ||||||||
\(545\) | 20.4044 | 0.874027 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4218 | 1.12972 | 0.564858 | − | 0.825188i | \(-0.308931\pi\) | ||||
0.564858 | + | 0.825188i | \(0.308931\pi\) | |||||||
\(548\) | −24.5413 | −1.04835 | ||||||||
\(549\) | −6.54557 | −0.279358 | ||||||||
\(550\) | −0.620030 | −0.0264382 | ||||||||
\(551\) | 31.6263 | 1.34733 | ||||||||
\(552\) | 38.0127 | 1.61793 | ||||||||
\(553\) | 11.6780 | 0.496597 | ||||||||
\(554\) | −25.7360 | −1.09342 | ||||||||
\(555\) | −14.3321 | −0.608366 | ||||||||
\(556\) | −92.8061 | −3.93585 | ||||||||
\(557\) | −18.0656 | −0.765462 | −0.382731 | − | 0.923860i | \(-0.625016\pi\) | ||||
−0.382731 | + | 0.923860i | \(0.625016\pi\) | |||||||
\(558\) | 5.22357 | 0.221131 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −14.2299 | −0.601325 | ||||||||
\(561\) | −0.564724 | −0.0238427 | ||||||||
\(562\) | −7.21107 | −0.304181 | ||||||||
\(563\) | −32.9515 | −1.38874 | −0.694371 | − | 0.719617i | \(-0.744317\pi\) | ||||
−0.694371 | + | 0.719617i | \(0.744317\pi\) | |||||||
\(564\) | 8.78969 | 0.370113 | ||||||||
\(565\) | 20.1518 | 0.847791 | ||||||||
\(566\) | 14.9721 | 0.629324 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −94.3912 | −3.96057 | ||||||||
\(569\) | 6.66475 | 0.279401 | 0.139700 | − | 0.990194i | \(-0.455386\pi\) | ||||
0.139700 | + | 0.990194i | \(0.455386\pi\) | |||||||
\(570\) | 20.7761 | 0.870214 | ||||||||
\(571\) | −40.5063 | −1.69513 | −0.847567 | − | 0.530688i | \(-0.821934\pi\) | ||||
−0.847567 | + | 0.530688i | \(0.821934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.78719 | −0.283539 | ||||||||
\(574\) | 16.7929 | 0.700923 | ||||||||
\(575\) | 14.2236 | 0.593163 | ||||||||
\(576\) | 7.27901 | 0.303292 | ||||||||
\(577\) | 16.2052 | 0.674632 | 0.337316 | − | 0.941391i | \(-0.390481\pi\) | ||||
0.337316 | + | 0.941391i | \(0.390481\pi\) | |||||||
\(578\) | −65.6708 | −2.73154 | ||||||||
\(579\) | 21.3749 | 0.888312 | ||||||||
\(580\) | −43.1945 | −1.79356 | ||||||||
\(581\) | 1.29310 | 0.0536470 | ||||||||
\(582\) | −15.3085 | −0.634560 | ||||||||
\(583\) | 0.285618 | 0.0118291 | ||||||||
\(584\) | 106.322 | 4.39964 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.2105 | −1.70239 | ||||||||
\(587\) | 17.9423 | 0.740557 | 0.370278 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370278 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(588\) | 4.80176 | 0.198021 | ||||||||
\(589\) | 10.5997 | 0.436753 | ||||||||
\(590\) | 10.5018 | 0.432354 | ||||||||
\(591\) | 22.7982 | 0.937794 | ||||||||
\(592\) | −90.0080 | −3.69931 | ||||||||
\(593\) | 34.1889 | 1.40397 | 0.701984 | − | 0.712193i | \(-0.252298\pi\) | ||||
0.701984 | + | 0.712193i | \(0.252298\pi\) | |||||||
\(594\) | 0.226773 | 0.00930462 | ||||||||
\(595\) | −9.77623 | −0.400787 | ||||||||
\(596\) | 45.6660 | 1.87055 | ||||||||
\(597\) | 2.66365 | 0.109016 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.68405 | −0.395680 | −0.197840 | − | 0.980234i | \(-0.563393\pi\) | ||||
−0.197840 | + | 0.980234i | \(0.563393\pi\) | |||||||
\(600\) | 19.9785 | 0.815617 | ||||||||
\(601\) | 12.8886 | 0.525738 | 0.262869 | − | 0.964832i | \(-0.415331\pi\) | ||||
0.262869 | + | 0.964832i | \(0.415331\pi\) | |||||||
\(602\) | 17.7625 | 0.723944 | ||||||||
\(603\) | −8.29459 | −0.337782 | ||||||||
\(604\) | 61.3519 | 2.49637 | ||||||||
\(605\) | −16.5467 | −0.672718 | ||||||||
\(606\) | 17.4260 | 0.707884 | ||||||||
\(607\) | 15.8179 | 0.642029 | 0.321014 | − | 0.947074i | \(-0.395976\pi\) | ||||
0.321014 | + | 0.947074i | \(0.395976\pi\) | |||||||
\(608\) | 53.1362 | 2.15496 | ||||||||
\(609\) | 5.97602 | 0.242161 | ||||||||
\(610\) | 25.6965 | 1.04042 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 31.1857 | 1.26061 | ||||||||
\(613\) | −26.1313 | −1.05543 | −0.527716 | − | 0.849421i | \(-0.676951\pi\) | ||||
−0.527716 | + | 0.849421i | \(0.676951\pi\) | |||||||
\(614\) | −26.3918 | −1.06509 | ||||||||
\(615\) | 9.69243 | 0.390836 | ||||||||
\(616\) | −0.635364 | −0.0255995 | ||||||||
\(617\) | −22.8276 | −0.919003 | −0.459502 | − | 0.888177i | \(-0.651972\pi\) | ||||
−0.459502 | + | 0.888177i | \(0.651972\pi\) | |||||||
\(618\) | 11.7953 | 0.474479 | ||||||||
\(619\) | 25.4700 | 1.02373 | 0.511863 | − | 0.859067i | \(-0.328956\pi\) | ||||
0.511863 | + | 0.859067i | \(0.328956\pi\) | |||||||
\(620\) | −14.4768 | −0.581404 | ||||||||
\(621\) | −5.20221 | −0.208757 | ||||||||
\(622\) | −37.8133 | −1.51617 | ||||||||
\(623\) | 15.8454 | 0.634833 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.85378 | −0.154151 | ||||||||
\(626\) | −34.6006 | −1.38292 | ||||||||
\(627\) | 0.460170 | 0.0183774 | ||||||||
\(628\) | −12.3629 | −0.493334 | ||||||||
\(629\) | −61.8372 | −2.46561 | ||||||||
\(630\) | 3.92579 | 0.156407 | ||||||||
\(631\) | 15.4599 | 0.615448 | 0.307724 | − | 0.951476i | \(-0.400433\pi\) | ||||
0.307724 | + | 0.951476i | \(0.400433\pi\) | |||||||
\(632\) | 85.3312 | 3.39429 | ||||||||
\(633\) | −24.1832 | −0.961195 | ||||||||
\(634\) | −79.3334 | −3.15073 | ||||||||
\(635\) | 19.4853 | 0.773252 | ||||||||
\(636\) | −15.7726 | −0.625426 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.35520 | −0.0536529 | ||||||||
\(639\) | 12.9178 | 0.511022 | ||||||||
\(640\) | 1.65154 | 0.0652827 | ||||||||
\(641\) | −23.3837 | −0.923600 | −0.461800 | − | 0.886984i | \(-0.652796\pi\) | ||||
−0.461800 | + | 0.886984i | \(0.652796\pi\) | |||||||
\(642\) | 26.7187 | 1.05450 | ||||||||
\(643\) | 1.22303 | 0.0482316 | 0.0241158 | − | 0.999709i | \(-0.492323\pi\) | ||||
0.0241158 | + | 0.999709i | \(0.492323\pi\) | |||||||
\(644\) | 24.9797 | 0.984339 | ||||||||
\(645\) | 10.2520 | 0.403673 | ||||||||
\(646\) | 89.6401 | 3.52684 | ||||||||
\(647\) | 12.3618 | 0.485993 | 0.242996 | − | 0.970027i | \(-0.421870\pi\) | ||||
0.242996 | + | 0.970027i | \(0.421870\pi\) | |||||||
\(648\) | −7.30704 | −0.287047 | ||||||||
\(649\) | 0.232605 | 0.00913055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.00289 | 0.0784994 | ||||||||
\(652\) | −93.7782 | −3.67264 | ||||||||
\(653\) | 9.86309 | 0.385972 | 0.192986 | − | 0.981201i | \(-0.438183\pi\) | ||||
0.192986 | + | 0.981201i | \(0.438183\pi\) | |||||||
\(654\) | −35.3523 | −1.38238 | ||||||||
\(655\) | 8.80417 | 0.344008 | ||||||||
\(656\) | 60.8699 | 2.37657 | ||||||||
\(657\) | −14.5507 | −0.567675 | ||||||||
\(658\) | 4.77401 | 0.186110 | ||||||||
\(659\) | 14.5491 | 0.566753 | 0.283376 | − | 0.959009i | \(-0.408545\pi\) | ||||
0.283376 | + | 0.959009i | \(0.408545\pi\) | |||||||
\(660\) | −0.628490 | −0.0244639 | ||||||||
\(661\) | −19.4099 | −0.754958 | −0.377479 | − | 0.926018i | \(-0.623209\pi\) | ||||
−0.377479 | + | 0.926018i | \(0.623209\pi\) | |||||||
\(662\) | 24.2622 | 0.942979 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.44876 | 0.366683 | ||||||||
\(665\) | 7.96623 | 0.308917 | ||||||||
\(666\) | 24.8316 | 0.962206 | ||||||||
\(667\) | 31.0885 | 1.20375 | ||||||||
\(668\) | 6.70577 | 0.259454 | ||||||||
\(669\) | −16.9080 | −0.653701 | ||||||||
\(670\) | 32.5628 | 1.25801 | ||||||||
\(671\) | 0.569153 | 0.0219719 | ||||||||
\(672\) | 10.0405 | 0.387320 | ||||||||
\(673\) | 35.3779 | 1.36372 | 0.681859 | − | 0.731484i | \(-0.261172\pi\) | ||||
0.681859 | + | 0.731484i | \(0.261172\pi\) | |||||||
\(674\) | −34.7006 | −1.33662 | ||||||||
\(675\) | −2.73414 | −0.105237 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.9841 | 0.422154 | 0.211077 | − | 0.977469i | \(-0.432303\pi\) | ||||
0.211077 | + | 0.977469i | \(0.432303\pi\) | |||||||
\(678\) | −34.9146 | −1.34089 | ||||||||
\(679\) | −5.86980 | −0.225262 | ||||||||
\(680\) | −71.4353 | −2.73942 | ||||||||
\(681\) | −11.6431 | −0.446166 | ||||||||
\(682\) | −0.454202 | −0.0173923 | ||||||||
\(683\) | 6.41924 | 0.245625 | 0.122813 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122813 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(684\) | −25.4119 | −0.971648 | ||||||||
\(685\) | −7.69331 | −0.293946 | ||||||||
\(686\) | 2.60802 | 0.0995746 | ||||||||
\(687\) | 7.90801 | 0.301710 | ||||||||
\(688\) | 64.3841 | 2.45462 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 20.4228 | 0.777482 | ||||||||
\(691\) | −27.6062 | −1.05019 | −0.525094 | − | 0.851044i | \(-0.675970\pi\) | ||||
−0.525094 | + | 0.851044i | \(0.675970\pi\) | |||||||
\(692\) | 82.5009 | 3.13621 | ||||||||
\(693\) | 0.0869524 | 0.00330305 | ||||||||
\(694\) | 44.0130 | 1.67071 | ||||||||
\(695\) | −29.0933 | −1.10357 | ||||||||
\(696\) | 43.6670 | 1.65519 | ||||||||
\(697\) | 41.8187 | 1.58400 | ||||||||
\(698\) | −6.27801 | −0.237626 | ||||||||
\(699\) | −24.0854 | −0.910995 | ||||||||
\(700\) | 13.1287 | 0.496217 | ||||||||
\(701\) | 15.9426 | 0.602144 | 0.301072 | − | 0.953601i | \(-0.402656\pi\) | ||||
0.301072 | + | 0.953601i | \(0.402656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.3885 | 1.90044 | ||||||||
\(704\) | −0.632927 | −0.0238543 | ||||||||
\(705\) | 2.75543 | 0.103776 | ||||||||
\(706\) | 80.1018 | 3.01467 | ||||||||
\(707\) | 6.68172 | 0.251292 | ||||||||
\(708\) | −12.8451 | −0.482749 | ||||||||
\(709\) | −12.5273 | −0.470472 | −0.235236 | − | 0.971938i | \(-0.575586\pi\) | ||||
−0.235236 | + | 0.971938i | \(0.575586\pi\) | |||||||
\(710\) | −50.7128 | −1.90322 | ||||||||
\(711\) | −11.6780 | −0.437958 | ||||||||
\(712\) | 115.783 | 4.33915 | ||||||||
\(713\) | 10.4194 | 0.390211 | ||||||||
\(714\) | 16.9381 | 0.633894 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.90049 | −0.257883 | ||||||||
\(717\) | 10.9354 | 0.408390 | ||||||||
\(718\) | 27.7289 | 1.03483 | ||||||||
\(719\) | −42.5632 | −1.58734 | −0.793670 | − | 0.608348i | \(-0.791832\pi\) | ||||
−0.793670 | + | 0.608348i | \(0.791832\pi\) | |||||||
\(720\) | 14.2299 | 0.530318 | ||||||||
\(721\) | 4.52273 | 0.168435 | ||||||||
\(722\) | −23.4915 | −0.874263 | ||||||||
\(723\) | 19.9054 | 0.740288 | ||||||||
\(724\) | −20.7379 | −0.770719 | ||||||||
\(725\) | 16.3393 | 0.606825 | ||||||||
\(726\) | 28.6685 | 1.06399 | ||||||||
\(727\) | −25.1186 | −0.931596 | −0.465798 | − | 0.884891i | \(-0.654233\pi\) | ||||
−0.465798 | + | 0.884891i | \(0.654233\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 57.1228 | 2.11421 | ||||||||
\(731\) | 44.2331 | 1.63602 | ||||||||
\(732\) | −31.4302 | −1.16170 | ||||||||
\(733\) | −2.32992 | −0.0860574 | −0.0430287 | − | 0.999074i | \(-0.513701\pi\) | ||||
−0.0430287 | + | 0.999074i | \(0.513701\pi\) | |||||||
\(734\) | −68.3463 | −2.52271 | ||||||||
\(735\) | 1.50528 | 0.0555230 | ||||||||
\(736\) | 52.2326 | 1.92532 | ||||||||
\(737\) | 0.721234 | 0.0265670 | ||||||||
\(738\) | −16.7929 | −0.618156 | ||||||||
\(739\) | −26.8170 | −0.986478 | −0.493239 | − | 0.869894i | \(-0.664187\pi\) | ||||
−0.493239 | + | 0.869894i | \(0.664187\pi\) | |||||||
\(740\) | −68.8195 | −2.52986 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.56672 | −0.314494 | ||||||||
\(743\) | −49.8687 | −1.82951 | −0.914753 | − | 0.404014i | \(-0.867615\pi\) | ||||
−0.914753 | + | 0.404014i | \(0.867615\pi\) | |||||||
\(744\) | 14.6352 | 0.536552 | ||||||||
\(745\) | 14.3156 | 0.524483 | ||||||||
\(746\) | −47.4925 | −1.73882 | ||||||||
\(747\) | −1.29310 | −0.0473122 | ||||||||
\(748\) | −2.71167 | −0.0991484 | ||||||||
\(749\) | 10.2448 | 0.374337 | ||||||||
\(750\) | 30.3626 | 1.10869 | ||||||||
\(751\) | 2.78782 | 0.101729 | 0.0508645 | − | 0.998706i | \(-0.483802\pi\) | ||||
0.0508645 | + | 0.998706i | \(0.483802\pi\) | |||||||
\(752\) | 17.3045 | 0.631031 | ||||||||
\(753\) | −23.3883 | −0.852318 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.2329 | 0.699956 | ||||||||
\(756\) | −4.80176 | −0.174638 | ||||||||
\(757\) | 13.8497 | 0.503374 | 0.251687 | − | 0.967809i | \(-0.419015\pi\) | ||||
0.251687 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(758\) | 75.3579 | 2.73712 | ||||||||
\(759\) | 0.452344 | 0.0164191 | ||||||||
\(760\) | 58.2096 | 2.11148 | ||||||||
\(761\) | −44.7203 | −1.62111 | −0.810555 | − | 0.585663i | \(-0.800834\pi\) | ||||
−0.810555 | + | 0.585663i | \(0.800834\pi\) | |||||||
\(762\) | −33.7600 | −1.22299 | ||||||||
\(763\) | −13.5552 | −0.490732 | ||||||||
\(764\) | −32.5904 | −1.17908 | ||||||||
\(765\) | 9.77623 | 0.353461 | ||||||||
\(766\) | −45.1871 | −1.63268 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −17.4194 | −0.628570 | ||||||||
\(769\) | −12.8746 | −0.464268 | −0.232134 | − | 0.972684i | \(-0.574571\pi\) | ||||
−0.232134 | + | 0.972684i | \(0.574571\pi\) | |||||||
\(770\) | −0.341357 | −0.0123016 | ||||||||
\(771\) | 12.0595 | 0.434312 | ||||||||
\(772\) | 102.637 | 3.69399 | ||||||||
\(773\) | 14.7887 | 0.531913 | 0.265957 | − | 0.963985i | \(-0.414312\pi\) | ||||
0.265957 | + | 0.963985i | \(0.414312\pi\) | |||||||
\(774\) | −17.7625 | −0.638458 | ||||||||
\(775\) | 5.47618 | 0.196710 | ||||||||
\(776\) | −42.8909 | −1.53969 | ||||||||
\(777\) | 9.52127 | 0.341574 | ||||||||
\(778\) | −35.6611 | −1.27851 | ||||||||
\(779\) | −34.0763 | −1.22091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.12324 | −0.0401926 | ||||||||
\(782\) | 88.1157 | 3.15101 | ||||||||
\(783\) | −5.97602 | −0.213566 | ||||||||
\(784\) | 9.45336 | 0.337620 | ||||||||
\(785\) | −3.87558 | −0.138325 | ||||||||
\(786\) | −15.2540 | −0.544091 | ||||||||
\(787\) | 19.9581 | 0.711428 | 0.355714 | − | 0.934595i | \(-0.384238\pi\) | ||||
0.355714 | + | 0.934595i | \(0.384238\pi\) | |||||||
\(788\) | 109.472 | 3.89976 | ||||||||
\(789\) | 4.53226 | 0.161353 | ||||||||
\(790\) | 45.8452 | 1.63110 | ||||||||
\(791\) | −13.3874 | −0.476001 | ||||||||
\(792\) | 0.635364 | 0.0225767 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 40.2765 | 1.42936 | ||||||||
\(795\) | −4.94448 | −0.175363 | ||||||||
\(796\) | 12.7902 | 0.453337 | ||||||||
\(797\) | 11.4612 | 0.405977 | 0.202989 | − | 0.979181i | \(-0.434935\pi\) | ||||
0.202989 | + | 0.979181i | \(0.434935\pi\) | |||||||
\(798\) | −13.8022 | −0.488591 | ||||||||
\(799\) | 11.8885 | 0.420586 | ||||||||
\(800\) | 27.4521 | 0.970577 | ||||||||
\(801\) | −15.8454 | −0.559870 | ||||||||
\(802\) | 37.1210 | 1.31079 | ||||||||
\(803\) | 1.26521 | 0.0446484 | ||||||||
\(804\) | −39.8286 | −1.40465 | ||||||||
\(805\) | 7.83076 | 0.275998 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.9600 | −0.984238 | ||||||||
\(808\) | 48.8235 | 1.71761 | ||||||||
\(809\) | 21.4851 | 0.755375 | 0.377688 | − | 0.925933i | \(-0.376719\pi\) | ||||
0.377688 | + | 0.925933i | \(0.376719\pi\) | |||||||
\(810\) | −3.92579 | −0.137938 | ||||||||
\(811\) | −25.8937 | −0.909249 | −0.454625 | − | 0.890683i | \(-0.650227\pi\) | ||||
−0.454625 | + | 0.890683i | \(0.650227\pi\) | |||||||
\(812\) | 28.6954 | 1.00701 | ||||||||
\(813\) | −4.18954 | −0.146934 | ||||||||
\(814\) | −2.15917 | −0.0756788 | ||||||||
\(815\) | −29.3980 | −1.02977 | ||||||||
\(816\) | 61.3962 | 2.14930 | ||||||||
\(817\) | −36.0437 | −1.26101 | ||||||||
\(818\) | 36.7361 | 1.28445 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 46.5407 | 1.62527 | ||||||||
\(821\) | 54.8269 | 1.91347 | 0.956736 | − | 0.290959i | \(-0.0939743\pi\) | ||||
0.956736 | + | 0.290959i | \(0.0939743\pi\) | |||||||
\(822\) | 13.3293 | 0.464913 | ||||||||
\(823\) | −5.98811 | −0.208732 | −0.104366 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104366 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(824\) | 33.0477 | 1.15127 | ||||||||
\(825\) | 0.237740 | 0.00827704 | ||||||||
\(826\) | −6.97667 | −0.242750 | ||||||||
\(827\) | −13.1913 | −0.458705 | −0.229353 | − | 0.973343i | \(-0.573661\pi\) | ||||
−0.229353 | + | 0.973343i | \(0.573661\pi\) | |||||||
\(828\) | −24.9797 | −0.868106 | ||||||||
\(829\) | 55.5439 | 1.92912 | 0.964559 | − | 0.263866i | \(-0.0849975\pi\) | ||||
0.964559 | + | 0.263866i | \(0.0849975\pi\) | |||||||
\(830\) | 5.07645 | 0.176206 | ||||||||
\(831\) | 9.86805 | 0.342319 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.49464 | 0.225026 | ||||||||
\(834\) | 50.4065 | 1.74544 | ||||||||
\(835\) | 2.10215 | 0.0727481 | ||||||||
\(836\) | 2.20962 | 0.0764214 | ||||||||
\(837\) | −2.00289 | −0.0692300 | ||||||||
\(838\) | 98.2501 | 3.39399 | ||||||||
\(839\) | −1.28875 | −0.0444928 | −0.0222464 | − | 0.999753i | \(-0.507082\pi\) | ||||
−0.0222464 | + | 0.999753i | \(0.507082\pi\) | |||||||
\(840\) | 10.9991 | 0.379506 | ||||||||
\(841\) | 6.71280 | 0.231476 | ||||||||
\(842\) | 5.96233 | 0.205475 | ||||||||
\(843\) | 2.76496 | 0.0952304 | ||||||||
\(844\) | −116.122 | −3.99707 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.77401 | −0.164134 | ||||||||
\(847\) | 10.9924 | 0.377705 | ||||||||
\(848\) | −31.0521 | −1.06633 | ||||||||
\(849\) | −5.74079 | −0.197024 | ||||||||
\(850\) | 46.3112 | 1.58846 | ||||||||
\(851\) | 49.5316 | 1.69792 | ||||||||
\(852\) | 62.0284 | 2.12506 | ||||||||
\(853\) | −25.6774 | −0.879178 | −0.439589 | − | 0.898199i | \(-0.644876\pi\) | ||||
−0.439589 | + | 0.898199i | \(0.644876\pi\) | |||||||
\(854\) | −17.0710 | −0.584156 | ||||||||
\(855\) | −7.96623 | −0.272439 | ||||||||
\(856\) | 74.8592 | 2.55864 | ||||||||
\(857\) | 32.7226 | 1.11778 | 0.558891 | − | 0.829241i | \(-0.311227\pi\) | ||||
0.558891 | + | 0.829241i | \(0.311227\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4087 | 0.696335 | 0.348168 | − | 0.937432i | \(-0.386804\pi\) | ||||
0.348168 | + | 0.937432i | \(0.386804\pi\) | |||||||
\(860\) | 49.2277 | 1.67865 | ||||||||
\(861\) | −6.43896 | −0.219439 | ||||||||
\(862\) | −5.16695 | −0.175987 | ||||||||
\(863\) | 11.1079 | 0.378117 | 0.189059 | − | 0.981966i | \(-0.439456\pi\) | ||||
0.189059 | + | 0.981966i | \(0.439456\pi\) | |||||||
\(864\) | −10.0405 | −0.341584 | ||||||||
\(865\) | 25.8628 | 0.879360 | ||||||||
\(866\) | 15.3635 | 0.522074 | ||||||||
\(867\) | 25.1803 | 0.855169 | ||||||||
\(868\) | 9.61739 | 0.326436 | ||||||||
\(869\) | 1.01543 | 0.0344460 | ||||||||
\(870\) | 23.4606 | 0.795389 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −99.0485 | −3.35420 | ||||||||
\(873\) | 5.86980 | 0.198663 | ||||||||
\(874\) | −71.8017 | −2.42873 | ||||||||
\(875\) | 11.6420 | 0.393572 | ||||||||
\(876\) | −69.8687 | −2.36065 | ||||||||
\(877\) | −28.5938 | −0.965545 | −0.482772 | − | 0.875746i | \(-0.660370\pi\) | ||||
−0.482772 | + | 0.875746i | \(0.660370\pi\) | |||||||
\(878\) | 21.0353 | 0.709907 | ||||||||
\(879\) | 15.8014 | 0.532970 | ||||||||
\(880\) | −1.23733 | −0.0417103 | ||||||||
\(881\) | 22.3516 | 0.753046 | 0.376523 | − | 0.926407i | \(-0.377120\pi\) | ||||
0.376523 | + | 0.926407i | \(0.377120\pi\) | |||||||
\(882\) | −2.60802 | −0.0878165 | ||||||||
\(883\) | −2.58792 | −0.0870905 | −0.0435453 | − | 0.999051i | \(-0.513865\pi\) | ||||
−0.0435453 | + | 0.999051i | \(0.513865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.02675 | −0.135358 | ||||||||
\(886\) | −17.3690 | −0.583523 | ||||||||
\(887\) | −36.1778 | −1.21473 | −0.607365 | − | 0.794423i | \(-0.707774\pi\) | ||||
−0.607365 | + | 0.794423i | \(0.707774\pi\) | |||||||
\(888\) | 69.5722 | 2.33469 | ||||||||
\(889\) | −12.9447 | −0.434151 | ||||||||
\(890\) | 62.2057 | 2.08514 | ||||||||
\(891\) | −0.0869524 | −0.00291301 | ||||||||
\(892\) | −81.1881 | −2.71838 | ||||||||
\(893\) | −9.68745 | −0.324178 | ||||||||
\(894\) | −24.8030 | −0.829535 | ||||||||
\(895\) | −2.16320 | −0.0723077 | ||||||||
\(896\) | −1.09716 | −0.0366537 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51.7669 | 1.72748 | ||||||||
\(899\) | 11.9693 | 0.399199 | ||||||||
\(900\) | −13.1287 | −0.437623 | ||||||||
\(901\) | −21.3333 | −0.710717 | ||||||||
\(902\) | 1.46019 | 0.0486188 | ||||||||
\(903\) | −6.81071 | −0.226646 | ||||||||
\(904\) | −97.8223 | −3.25352 | ||||||||
\(905\) | −6.50102 | −0.216101 | ||||||||
\(906\) | −33.3226 | −1.10707 | ||||||||
\(907\) | 40.9607 | 1.36008 | 0.680039 | − | 0.733176i | \(-0.261963\pi\) | ||||
0.680039 | + | 0.733176i | \(0.261963\pi\) | |||||||
\(908\) | −55.9075 | −1.85536 | ||||||||
\(909\) | −6.68172 | −0.221619 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.19307 | 0.0726595 | 0.0363298 | − | 0.999340i | \(-0.488433\pi\) | ||||
0.0363298 | + | 0.999340i | \(0.488433\pi\) | |||||||
\(912\) | −50.0291 | −1.65663 | ||||||||
\(913\) | 0.112438 | 0.00372117 | ||||||||
\(914\) | −6.75175 | −0.223328 | ||||||||
\(915\) | −9.85290 | −0.325727 | ||||||||
\(916\) | 37.9724 | 1.25464 | ||||||||
\(917\) | −5.84887 | −0.193147 | ||||||||
\(918\) | −16.9381 | −0.559042 | ||||||||
\(919\) | 51.0323 | 1.68340 | 0.841700 | − | 0.539945i | \(-0.181555\pi\) | ||||
0.841700 | + | 0.539945i | \(0.181555\pi\) | |||||||
\(920\) | 57.2197 | 1.88648 | ||||||||
\(921\) | 10.1195 | 0.333448 | ||||||||
\(922\) | 68.7649 | 2.26465 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.417524 | 0.0137355 | ||||||||
\(925\) | 26.0325 | 0.855942 | ||||||||
\(926\) | 76.4363 | 2.51185 | ||||||||
\(927\) | −4.52273 | −0.148546 | ||||||||
\(928\) | 60.0021 | 1.96966 | ||||||||
\(929\) | 34.1988 | 1.12203 | 0.561014 | − | 0.827806i | \(-0.310411\pi\) | ||||
0.561014 | + | 0.827806i | \(0.310411\pi\) | |||||||
\(930\) | 7.86293 | 0.257836 | ||||||||
\(931\) | −5.29220 | −0.173445 | ||||||||
\(932\) | −115.652 | −3.78832 | ||||||||
\(933\) | 14.4989 | 0.474671 | ||||||||
\(934\) | −8.42404 | −0.275643 | ||||||||
\(935\) | −0.850067 | −0.0278002 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.0430 | −1.83084 | −0.915422 | − | 0.402496i | \(-0.868143\pi\) | ||||
−0.915422 | + | 0.402496i | \(0.868143\pi\) | |||||||
\(938\) | −21.6324 | −0.706324 | ||||||||
\(939\) | 13.2670 | 0.432953 | ||||||||
\(940\) | 13.2309 | 0.431545 | ||||||||
\(941\) | 31.6322 | 1.03118 | 0.515591 | − | 0.856835i | \(-0.327573\pi\) | ||||
0.515591 | + | 0.856835i | \(0.327573\pi\) | |||||||
\(942\) | 6.71477 | 0.218779 | ||||||||
\(943\) | −33.4968 | −1.09081 | ||||||||
\(944\) | −25.2886 | −0.823073 | ||||||||
\(945\) | −1.50528 | −0.0489667 | ||||||||
\(946\) | 1.54449 | 0.0502156 | ||||||||
\(947\) | −46.5004 | −1.51106 | −0.755529 | − | 0.655115i | \(-0.772620\pi\) | ||||
−0.755529 | + | 0.655115i | \(0.772620\pi\) | |||||||
\(948\) | −56.0747 | −1.82122 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −37.7370 | −1.22435 | ||||||||
\(951\) | 30.4190 | 0.986405 | ||||||||
\(952\) | 47.4566 | 1.53808 | ||||||||
\(953\) | −23.2511 | −0.753178 | −0.376589 | − | 0.926380i | \(-0.622903\pi\) | ||||
−0.376589 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(954\) | 8.56672 | 0.277358 | ||||||||
\(955\) | −10.2166 | −0.330601 | ||||||||
\(956\) | 52.5091 | 1.69827 | ||||||||
\(957\) | 0.519629 | 0.0167972 | ||||||||
\(958\) | 20.6371 | 0.666756 | ||||||||
\(959\) | 5.11089 | 0.165039 | ||||||||
\(960\) | 10.9569 | 0.353633 | ||||||||
\(961\) | −26.9884 | −0.870595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2448 | −0.330135 | ||||||||
\(964\) | 95.5807 | 3.07845 | ||||||||
\(965\) | 32.1752 | 1.03576 | ||||||||
\(966\) | −13.5674 | −0.436525 | ||||||||
\(967\) | −13.6117 | −0.437723 | −0.218861 | − | 0.975756i | \(-0.570234\pi\) | ||||
−0.218861 | + | 0.975756i | \(0.570234\pi\) | |||||||
\(968\) | 80.3221 | 2.58165 | ||||||||
\(969\) | −34.3710 | −1.10415 | ||||||||
\(970\) | −23.0436 | −0.739886 | ||||||||
\(971\) | −9.93417 | −0.318803 | −0.159401 | − | 0.987214i | \(-0.550956\pi\) | ||||
−0.159401 | + | 0.987214i | \(0.550956\pi\) | |||||||
\(972\) | 4.80176 | 0.154016 | ||||||||
\(973\) | 19.3275 | 0.619612 | ||||||||
\(974\) | −40.2810 | −1.29069 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.8777 | −1.98066 | ||||||||
\(977\) | 39.1543 | 1.25266 | 0.626328 | − | 0.779559i | \(-0.284557\pi\) | ||||
0.626328 | + | 0.779559i | \(0.284557\pi\) | |||||||
\(978\) | 50.9345 | 1.62871 | ||||||||
\(979\) | 1.37780 | 0.0440345 | ||||||||
\(980\) | 7.22798 | 0.230889 | ||||||||
\(981\) | 13.5552 | 0.432785 | ||||||||
\(982\) | 38.8757 | 1.24057 | ||||||||
\(983\) | −4.01341 | −0.128008 | −0.0640039 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640039 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(984\) | −47.0497 | −1.49989 | ||||||||
\(985\) | 34.3177 | 1.09345 | ||||||||
\(986\) | 101.223 | 3.22359 | ||||||||
\(987\) | −1.83051 | −0.0582659 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.4307 | −1.12663 | ||||||||
\(990\) | 0.341357 | 0.0108490 | ||||||||
\(991\) | −34.3760 | −1.09199 | −0.545995 | − | 0.837789i | \(-0.683848\pi\) | ||||
−0.545995 | + | 0.837789i | \(0.683848\pi\) | |||||||
\(992\) | 20.1100 | 0.638492 | ||||||||
\(993\) | −9.30294 | −0.295220 | ||||||||
\(994\) | 33.6900 | 1.06858 | ||||||||
\(995\) | 4.00954 | 0.127111 | ||||||||
\(996\) | −6.20917 | −0.196745 | ||||||||
\(997\) | 4.46643 | 0.141453 | 0.0707266 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707266 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(998\) | 66.3233 | 2.09943 | ||||||||
\(999\) | −9.52127 | −0.301240 |
(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 | 3549.2.a.bb.1.1 | 8 | ||
13.2 | odd | 12 | 273.2.bd.a.43.1 | ✓ | 16 | ||
13.7 | odd | 12 | 273.2.bd.a.127.1 | yes | 16 | ||
13.12 | even | 2 | 3549.2.a.bd.1.8 | 8 | |||
39.2 | even | 12 | 819.2.ct.b.316.8 | 16 | |||
39.20 | even | 12 | 819.2.ct.b.127.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bd.a.43.1 | ✓ | 16 | 13.2 | odd | 12 | ||
273.2.bd.a.127.1 | yes | 16 | 13.7 | odd | 12 | ||
819.2.ct.b.127.8 | 16 | 39.20 | even | 12 | |||
819.2.ct.b.316.8 | 16 | 39.2 | even | 12 | |||
3549.2.a.bb.1.1 | 8 | 1.1 | even | 1 | trivial | ||
3549.2.a.bd.1.8 | 8 | 13.12 | even | 2 |