Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.64 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.63648 | 1.15716 | 0.578581 | − | 0.815625i | \(-0.303607\pi\) | ||||
0.578581 | + | 0.815625i | \(0.303607\pi\) | |||||||
\(3\) | 1.67074 | 0.964600 | 0.482300 | − | 0.876006i | \(-0.339802\pi\) | ||||
0.482300 | + | 0.876006i | \(0.339802\pi\) | |||||||
\(4\) | 0.678051 | 0.339026 | ||||||||
\(5\) | 1.47944 | 0.661625 | 0.330812 | − | 0.943697i | \(-0.392677\pi\) | ||||
0.330812 | + | 0.943697i | \(0.392677\pi\) | |||||||
\(6\) | 2.73412 | 1.11620 | ||||||||
\(7\) | −2.83994 | −1.07340 | −0.536698 | − | 0.843774i | \(-0.680329\pi\) | ||||
−0.536698 | + | 0.843774i | \(0.680329\pi\) | |||||||
\(8\) | −2.16334 | −0.764855 | ||||||||
\(9\) | −0.208643 | −0.0695476 | ||||||||
\(10\) | 2.42106 | 0.765608 | ||||||||
\(11\) | 1.80916 | 0.545483 | 0.272742 | − | 0.962087i | \(-0.412070\pi\) | ||||
0.272742 | + | 0.962087i | \(0.412070\pi\) | |||||||
\(12\) | 1.13284 | 0.327024 | ||||||||
\(13\) | −4.94134 | −1.37048 | −0.685240 | − | 0.728317i | \(-0.740303\pi\) | ||||
−0.685240 | + | 0.728317i | \(0.740303\pi\) | |||||||
\(14\) | −4.64749 | −1.24209 | ||||||||
\(15\) | 2.47175 | 0.638203 | ||||||||
\(16\) | −4.89635 | −1.22409 | ||||||||
\(17\) | −1.34129 | −0.325310 | −0.162655 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162655 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(18\) | −0.341439 | −0.0804779 | ||||||||
\(19\) | 2.42257 | 0.555776 | 0.277888 | − | 0.960613i | \(-0.410366\pi\) | ||||
0.277888 | + | 0.960613i | \(0.410366\pi\) | |||||||
\(20\) | 1.00313 | 0.224308 | ||||||||
\(21\) | −4.74479 | −1.03540 | ||||||||
\(22\) | 2.96065 | 0.631213 | ||||||||
\(23\) | −1.31284 | −0.273746 | −0.136873 | − | 0.990589i | \(-0.543705\pi\) | ||||
−0.136873 | + | 0.990589i | \(0.543705\pi\) | |||||||
\(24\) | −3.61436 | −0.737779 | ||||||||
\(25\) | −2.81126 | −0.562253 | ||||||||
\(26\) | −8.08637 | −1.58587 | ||||||||
\(27\) | −5.36079 | −1.03169 | ||||||||
\(28\) | −1.92562 | −0.363909 | ||||||||
\(29\) | −9.70408 | −1.80200 | −0.901001 | − | 0.433816i | \(-0.857167\pi\) | ||||
−0.901001 | + | 0.433816i | \(0.857167\pi\) | |||||||
\(30\) | 4.04496 | 0.738505 | ||||||||
\(31\) | 3.85932 | 0.693153 | 0.346577 | − | 0.938022i | \(-0.387344\pi\) | ||||
0.346577 | + | 0.938022i | \(0.387344\pi\) | |||||||
\(32\) | −3.68608 | −0.651613 | ||||||||
\(33\) | 3.02263 | 0.526173 | ||||||||
\(34\) | −2.19498 | −0.376437 | ||||||||
\(35\) | −4.20151 | −0.710185 | ||||||||
\(36\) | −0.141471 | −0.0235784 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 3.96448 | 0.643124 | ||||||||
\(39\) | −8.25567 | −1.32196 | ||||||||
\(40\) | −3.20052 | −0.506047 | ||||||||
\(41\) | −4.26082 | −0.665428 | −0.332714 | − | 0.943028i | \(-0.607964\pi\) | ||||
−0.332714 | + | 0.943028i | \(0.607964\pi\) | |||||||
\(42\) | −7.76473 | −1.19812 | ||||||||
\(43\) | 1.97772 | 0.301599 | 0.150800 | − | 0.988564i | \(-0.451815\pi\) | ||||
0.150800 | + | 0.988564i | \(0.451815\pi\) | |||||||
\(44\) | 1.22670 | 0.184933 | ||||||||
\(45\) | −0.308674 | −0.0460144 | ||||||||
\(46\) | −2.14843 | −0.316769 | ||||||||
\(47\) | 12.1650 | 1.77445 | 0.887226 | − | 0.461336i | \(-0.152630\pi\) | ||||
0.887226 | + | 0.461336i | \(0.152630\pi\) | |||||||
\(48\) | −8.18050 | −1.18075 | ||||||||
\(49\) | 1.06525 | 0.152179 | ||||||||
\(50\) | −4.60056 | −0.650618 | ||||||||
\(51\) | −2.24094 | −0.313794 | ||||||||
\(52\) | −3.35048 | −0.464628 | ||||||||
\(53\) | −11.6517 | −1.60048 | −0.800240 | − | 0.599680i | \(-0.795295\pi\) | ||||
−0.800240 | + | 0.599680i | \(0.795295\pi\) | |||||||
\(54\) | −8.77281 | −1.19383 | ||||||||
\(55\) | 2.67654 | 0.360905 | ||||||||
\(56\) | 6.14374 | 0.820992 | ||||||||
\(57\) | 4.04748 | 0.536102 | ||||||||
\(58\) | −15.8805 | −2.08521 | ||||||||
\(59\) | 4.85443 | 0.631994 | 0.315997 | − | 0.948760i | \(-0.397661\pi\) | ||||
0.315997 | + | 0.948760i | \(0.397661\pi\) | |||||||
\(60\) | 1.67597 | 0.216367 | ||||||||
\(61\) | −6.17621 | −0.790782 | −0.395391 | − | 0.918513i | \(-0.629391\pi\) | ||||
−0.395391 | + | 0.918513i | \(0.629391\pi\) | |||||||
\(62\) | 6.31567 | 0.802091 | ||||||||
\(63\) | 0.592533 | 0.0746522 | ||||||||
\(64\) | 3.76052 | 0.470065 | ||||||||
\(65\) | −7.31040 | −0.906744 | ||||||||
\(66\) | 4.94646 | 0.608867 | ||||||||
\(67\) | −9.53293 | −1.16463 | −0.582317 | − | 0.812962i | \(-0.697854\pi\) | ||||
−0.582317 | + | 0.812962i | \(0.697854\pi\) | |||||||
\(68\) | −0.909462 | −0.110288 | ||||||||
\(69\) | −2.19341 | −0.264056 | ||||||||
\(70\) | −6.87567 | −0.821800 | ||||||||
\(71\) | 7.27131 | 0.862946 | 0.431473 | − | 0.902126i | \(-0.357994\pi\) | ||||
0.431473 | + | 0.902126i | \(0.357994\pi\) | |||||||
\(72\) | 0.451365 | 0.0531939 | ||||||||
\(73\) | 15.8618 | 1.85648 | 0.928239 | − | 0.371984i | \(-0.121323\pi\) | ||||
0.928239 | + | 0.371984i | \(0.121323\pi\) | |||||||
\(74\) | −1.63648 | −0.190236 | ||||||||
\(75\) | −4.69688 | −0.542349 | ||||||||
\(76\) | 1.64263 | 0.188422 | ||||||||
\(77\) | −5.13791 | −0.585519 | ||||||||
\(78\) | −13.5102 | −1.52973 | ||||||||
\(79\) | 8.53665 | 0.960449 | 0.480224 | − | 0.877146i | \(-0.340555\pi\) | ||||
0.480224 | + | 0.877146i | \(0.340555\pi\) | |||||||
\(80\) | −7.24384 | −0.809886 | ||||||||
\(81\) | −8.33054 | −0.925615 | ||||||||
\(82\) | −6.97272 | −0.770008 | ||||||||
\(83\) | 0.979738 | 0.107540 | 0.0537701 | − | 0.998553i | \(-0.482876\pi\) | ||||
0.0537701 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(84\) | −3.21721 | −0.351026 | ||||||||
\(85\) | −1.98435 | −0.215233 | ||||||||
\(86\) | 3.23649 | 0.348999 | ||||||||
\(87\) | −16.2130 | −1.73821 | ||||||||
\(88\) | −3.91383 | −0.417215 | ||||||||
\(89\) | 0.458112 | 0.0485597 | 0.0242799 | − | 0.999705i | \(-0.492271\pi\) | ||||
0.0242799 | + | 0.999705i | \(0.492271\pi\) | |||||||
\(90\) | −0.505138 | −0.0532462 | ||||||||
\(91\) | 14.0331 | 1.47107 | ||||||||
\(92\) | −0.890173 | −0.0928070 | ||||||||
\(93\) | 6.44789 | 0.668616 | ||||||||
\(94\) | 19.9078 | 2.05333 | ||||||||
\(95\) | 3.58405 | 0.367715 | ||||||||
\(96\) | −6.15846 | −0.628546 | ||||||||
\(97\) | −18.0435 | −1.83204 | −0.916020 | − | 0.401132i | \(-0.868617\pi\) | ||||
−0.916020 | + | 0.401132i | \(0.868617\pi\) | |||||||
\(98\) | 1.74326 | 0.176096 | ||||||||
\(99\) | −0.377469 | −0.0379371 | ||||||||
\(100\) | −1.90618 | −0.190618 | ||||||||
\(101\) | 7.48057 | 0.744345 | 0.372172 | − | 0.928164i | \(-0.378613\pi\) | ||||
0.372172 | + | 0.928164i | \(0.378613\pi\) | |||||||
\(102\) | −3.66724 | −0.363111 | ||||||||
\(103\) | 7.66146 | 0.754906 | 0.377453 | − | 0.926029i | \(-0.376800\pi\) | ||||
0.377453 | + | 0.926029i | \(0.376800\pi\) | |||||||
\(104\) | 10.6898 | 1.04822 | ||||||||
\(105\) | −7.01962 | −0.685045 | ||||||||
\(106\) | −19.0677 | −1.85202 | ||||||||
\(107\) | −15.6190 | −1.50995 | −0.754975 | − | 0.655754i | \(-0.772351\pi\) | ||||
−0.754975 | + | 0.655754i | \(0.772351\pi\) | |||||||
\(108\) | −3.63489 | −0.349768 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 4.38010 | 0.417626 | ||||||||
\(111\) | −1.67074 | −0.158579 | ||||||||
\(112\) | 13.9053 | 1.31393 | ||||||||
\(113\) | −7.46276 | −0.702037 | −0.351019 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351019 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(114\) | 6.62360 | 0.620357 | ||||||||
\(115\) | −1.94227 | −0.181117 | ||||||||
\(116\) | −6.57986 | −0.610925 | ||||||||
\(117\) | 1.03097 | 0.0953137 | ||||||||
\(118\) | 7.94416 | 0.731319 | ||||||||
\(119\) | 3.80918 | 0.349187 | ||||||||
\(120\) | −5.34723 | −0.488133 | ||||||||
\(121\) | −7.72693 | −0.702448 | ||||||||
\(122\) | −10.1072 | −0.915064 | ||||||||
\(123\) | −7.11870 | −0.641872 | ||||||||
\(124\) | 2.61681 | 0.234997 | ||||||||
\(125\) | −11.5563 | −1.03363 | ||||||||
\(126\) | 0.969666 | 0.0863847 | ||||||||
\(127\) | 11.0196 | 0.977832 | 0.488916 | − | 0.872331i | \(-0.337393\pi\) | ||||
0.488916 | + | 0.872331i | \(0.337393\pi\) | |||||||
\(128\) | 13.5262 | 1.19555 | ||||||||
\(129\) | 3.30425 | 0.290923 | ||||||||
\(130\) | −11.9633 | −1.04925 | ||||||||
\(131\) | 2.23657 | 0.195410 | 0.0977049 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977049 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(132\) | 2.04950 | 0.178386 | ||||||||
\(133\) | −6.87996 | −0.596568 | ||||||||
\(134\) | −15.6004 | −1.34767 | ||||||||
\(135\) | −7.93096 | −0.682588 | ||||||||
\(136\) | 2.90166 | 0.248815 | ||||||||
\(137\) | −8.04851 | −0.687631 | −0.343816 | − | 0.939037i | \(-0.611719\pi\) | ||||
−0.343816 | + | 0.939037i | \(0.611719\pi\) | |||||||
\(138\) | −3.58946 | −0.305555 | ||||||||
\(139\) | 21.9618 | 1.86277 | 0.931387 | − | 0.364030i | \(-0.118599\pi\) | ||||
0.931387 | + | 0.364030i | \(0.118599\pi\) | |||||||
\(140\) | −2.84884 | −0.240771 | ||||||||
\(141\) | 20.3245 | 1.71164 | ||||||||
\(142\) | 11.8993 | 0.998569 | ||||||||
\(143\) | −8.93968 | −0.747574 | ||||||||
\(144\) | 1.02159 | 0.0851324 | ||||||||
\(145\) | −14.3566 | −1.19225 | ||||||||
\(146\) | 25.9574 | 2.14825 | ||||||||
\(147\) | 1.77975 | 0.146792 | ||||||||
\(148\) | −0.678051 | −0.0557355 | ||||||||
\(149\) | −10.2006 | −0.835667 | −0.417833 | − | 0.908524i | \(-0.637210\pi\) | ||||
−0.417833 | + | 0.908524i | \(0.637210\pi\) | |||||||
\(150\) | −7.68632 | −0.627586 | ||||||||
\(151\) | −16.1784 | −1.31658 | −0.658289 | − | 0.752765i | \(-0.728719\pi\) | ||||
−0.658289 | + | 0.752765i | \(0.728719\pi\) | |||||||
\(152\) | −5.24084 | −0.425088 | ||||||||
\(153\) | 0.279850 | 0.0226246 | ||||||||
\(154\) | −8.40806 | −0.677541 | ||||||||
\(155\) | 5.70962 | 0.458607 | ||||||||
\(156\) | −5.59776 | −0.448180 | ||||||||
\(157\) | 12.1022 | 0.965859 | 0.482929 | − | 0.875659i | \(-0.339573\pi\) | ||||
0.482929 | + | 0.875659i | \(0.339573\pi\) | |||||||
\(158\) | 13.9700 | 1.11140 | ||||||||
\(159\) | −19.4669 | −1.54382 | ||||||||
\(160\) | −5.45333 | −0.431123 | ||||||||
\(161\) | 3.72839 | 0.293838 | ||||||||
\(162\) | −13.6327 | −1.07109 | ||||||||
\(163\) | 5.05421 | 0.395877 | 0.197938 | − | 0.980214i | \(-0.436575\pi\) | ||||
0.197938 | + | 0.980214i | \(0.436575\pi\) | |||||||
\(164\) | −2.88905 | −0.225597 | ||||||||
\(165\) | 4.47180 | 0.348129 | ||||||||
\(166\) | 1.60332 | 0.124442 | ||||||||
\(167\) | −0.659764 | −0.0510541 | −0.0255270 | − | 0.999674i | \(-0.508126\pi\) | ||||
−0.0255270 | + | 0.999674i | \(0.508126\pi\) | |||||||
\(168\) | 10.2646 | 0.791929 | ||||||||
\(169\) | 11.4168 | 0.878215 | ||||||||
\(170\) | −3.24734 | −0.249060 | ||||||||
\(171\) | −0.505453 | −0.0386529 | ||||||||
\(172\) | 1.34099 | 0.102250 | ||||||||
\(173\) | 13.8511 | 1.05308 | 0.526540 | − | 0.850150i | \(-0.323489\pi\) | ||||
0.526540 | + | 0.850150i | \(0.323489\pi\) | |||||||
\(174\) | −26.5321 | −2.01139 | ||||||||
\(175\) | 7.98382 | 0.603520 | ||||||||
\(176\) | −8.85829 | −0.667719 | ||||||||
\(177\) | 8.11048 | 0.609621 | ||||||||
\(178\) | 0.749688 | 0.0561915 | ||||||||
\(179\) | −7.27609 | −0.543840 | −0.271920 | − | 0.962320i | \(-0.587659\pi\) | ||||
−0.271920 | + | 0.962320i | \(0.587659\pi\) | |||||||
\(180\) | −0.209297 | −0.0156001 | ||||||||
\(181\) | −4.51957 | −0.335937 | −0.167968 | − | 0.985792i | \(-0.553721\pi\) | ||||
−0.167968 | + | 0.985792i | \(0.553721\pi\) | |||||||
\(182\) | 22.9648 | 1.70226 | ||||||||
\(183\) | −10.3188 | −0.762788 | ||||||||
\(184\) | 2.84012 | 0.209376 | ||||||||
\(185\) | −1.47944 | −0.108770 | ||||||||
\(186\) | 10.5518 | 0.773697 | ||||||||
\(187\) | −2.42661 | −0.177451 | ||||||||
\(188\) | 8.24851 | 0.601584 | ||||||||
\(189\) | 15.2243 | 1.10741 | ||||||||
\(190\) | 5.86520 | 0.425507 | ||||||||
\(191\) | −8.53849 | −0.617824 | −0.308912 | − | 0.951091i | \(-0.599965\pi\) | ||||
−0.308912 | + | 0.951091i | \(0.599965\pi\) | |||||||
\(192\) | 6.28283 | 0.453424 | ||||||||
\(193\) | −6.57047 | −0.472952 | −0.236476 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236476 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(194\) | −29.5278 | −2.11997 | ||||||||
\(195\) | −12.2137 | −0.874644 | ||||||||
\(196\) | 0.722295 | 0.0515925 | ||||||||
\(197\) | −9.97993 | −0.711041 | −0.355520 | − | 0.934669i | \(-0.615696\pi\) | ||||
−0.355520 | + | 0.934669i | \(0.615696\pi\) | |||||||
\(198\) | −0.617719 | −0.0438994 | ||||||||
\(199\) | −17.9787 | −1.27448 | −0.637240 | − | 0.770666i | \(-0.719924\pi\) | ||||
−0.637240 | + | 0.770666i | \(0.719924\pi\) | |||||||
\(200\) | 6.08171 | 0.430042 | ||||||||
\(201\) | −15.9270 | −1.12340 | ||||||||
\(202\) | 12.2418 | 0.861328 | ||||||||
\(203\) | 27.5590 | 1.93426 | ||||||||
\(204\) | −1.51947 | −0.106384 | ||||||||
\(205\) | −6.30362 | −0.440264 | ||||||||
\(206\) | 12.5378 | 0.873549 | ||||||||
\(207\) | 0.273915 | 0.0190384 | ||||||||
\(208\) | 24.1945 | 1.67759 | ||||||||
\(209\) | 4.38283 | 0.303167 | ||||||||
\(210\) | −11.4874 | −0.792708 | ||||||||
\(211\) | −6.82591 | −0.469915 | −0.234957 | − | 0.972006i | \(-0.575495\pi\) | ||||
−0.234957 | + | 0.972006i | \(0.575495\pi\) | |||||||
\(212\) | −7.90043 | −0.542604 | ||||||||
\(213\) | 12.1484 | 0.832397 | ||||||||
\(214\) | −25.5602 | −1.74726 | ||||||||
\(215\) | 2.92591 | 0.199546 | ||||||||
\(216\) | 11.5972 | 0.789090 | ||||||||
\(217\) | −10.9602 | −0.744028 | ||||||||
\(218\) | −1.63648 | −0.110836 | ||||||||
\(219\) | 26.5008 | 1.79076 | ||||||||
\(220\) | 1.81483 | 0.122356 | ||||||||
\(221\) | 6.62775 | 0.445831 | ||||||||
\(222\) | −2.73412 | −0.183502 | ||||||||
\(223\) | −3.65951 | −0.245059 | −0.122530 | − | 0.992465i | \(-0.539101\pi\) | ||||
−0.122530 | + | 0.992465i | \(0.539101\pi\) | |||||||
\(224\) | 10.4682 | 0.699439 | ||||||||
\(225\) | 0.586550 | 0.0391033 | ||||||||
\(226\) | −12.2126 | −0.812372 | ||||||||
\(227\) | 18.1893 | 1.20727 | 0.603634 | − | 0.797262i | \(-0.293719\pi\) | ||||
0.603634 | + | 0.797262i | \(0.293719\pi\) | |||||||
\(228\) | 2.74440 | 0.181752 | ||||||||
\(229\) | −7.02896 | −0.464486 | −0.232243 | − | 0.972658i | \(-0.574607\pi\) | ||||
−0.232243 | + | 0.972658i | \(0.574607\pi\) | |||||||
\(230\) | −3.17847 | −0.209582 | ||||||||
\(231\) | −8.58409 | −0.564792 | ||||||||
\(232\) | 20.9932 | 1.37827 | ||||||||
\(233\) | 14.4277 | 0.945188 | 0.472594 | − | 0.881280i | \(-0.343318\pi\) | ||||
0.472594 | + | 0.881280i | \(0.343318\pi\) | |||||||
\(234\) | 1.68716 | 0.110293 | ||||||||
\(235\) | 17.9974 | 1.17402 | ||||||||
\(236\) | 3.29155 | 0.214262 | ||||||||
\(237\) | 14.2625 | 0.926448 | ||||||||
\(238\) | 6.23362 | 0.404066 | ||||||||
\(239\) | −13.0374 | −0.843316 | −0.421658 | − | 0.906755i | \(-0.638552\pi\) | ||||
−0.421658 | + | 0.906755i | \(0.638552\pi\) | |||||||
\(240\) | −12.1025 | −0.781216 | ||||||||
\(241\) | 8.67524 | 0.558821 | 0.279411 | − | 0.960172i | \(-0.409861\pi\) | ||||
0.279411 | + | 0.960172i | \(0.409861\pi\) | |||||||
\(242\) | −12.6449 | −0.812847 | ||||||||
\(243\) | 2.16425 | 0.138837 | ||||||||
\(244\) | −4.18778 | −0.268095 | ||||||||
\(245\) | 1.57597 | 0.100685 | ||||||||
\(246\) | −11.6496 | −0.742750 | ||||||||
\(247\) | −11.9707 | −0.761681 | ||||||||
\(248\) | −8.34900 | −0.530162 | ||||||||
\(249\) | 1.63688 | 0.103733 | ||||||||
\(250\) | −18.9116 | −1.19607 | ||||||||
\(251\) | 21.2054 | 1.33848 | 0.669238 | − | 0.743048i | \(-0.266621\pi\) | ||||
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(252\) | 0.401768 | 0.0253090 | ||||||||
\(253\) | −2.37514 | −0.149324 | ||||||||
\(254\) | 18.0333 | 1.13151 | ||||||||
\(255\) | −3.31533 | −0.207614 | ||||||||
\(256\) | 14.6142 | 0.913386 | ||||||||
\(257\) | 14.1597 | 0.883260 | 0.441630 | − | 0.897197i | \(-0.354400\pi\) | ||||
0.441630 | + | 0.897197i | \(0.354400\pi\) | |||||||
\(258\) | 5.40732 | 0.336645 | ||||||||
\(259\) | 2.83994 | 0.176465 | ||||||||
\(260\) | −4.95682 | −0.307409 | ||||||||
\(261\) | 2.02469 | 0.125325 | ||||||||
\(262\) | 3.66009 | 0.226121 | ||||||||
\(263\) | 15.7356 | 0.970299 | 0.485149 | − | 0.874431i | \(-0.338765\pi\) | ||||
0.485149 | + | 0.874431i | \(0.338765\pi\) | |||||||
\(264\) | −6.53897 | −0.402446 | ||||||||
\(265\) | −17.2379 | −1.05892 | ||||||||
\(266\) | −11.2589 | −0.690326 | ||||||||
\(267\) | 0.765383 | 0.0468407 | ||||||||
\(268\) | −6.46382 | −0.394840 | ||||||||
\(269\) | −5.11460 | −0.311843 | −0.155921 | − | 0.987769i | \(-0.549835\pi\) | ||||
−0.155921 | + | 0.987769i | \(0.549835\pi\) | |||||||
\(270\) | −12.9788 | −0.789866 | ||||||||
\(271\) | −18.6072 | −1.13031 | −0.565153 | − | 0.824986i | \(-0.691183\pi\) | ||||
−0.565153 | + | 0.824986i | \(0.691183\pi\) | |||||||
\(272\) | 6.56741 | 0.398208 | ||||||||
\(273\) | 23.4456 | 1.41899 | ||||||||
\(274\) | −13.1712 | −0.795701 | ||||||||
\(275\) | −5.08603 | −0.306699 | ||||||||
\(276\) | −1.48724 | −0.0895216 | ||||||||
\(277\) | −9.02972 | −0.542543 | −0.271272 | − | 0.962503i | \(-0.587444\pi\) | ||||
−0.271272 | + | 0.962503i | \(0.587444\pi\) | |||||||
\(278\) | 35.9399 | 2.15553 | ||||||||
\(279\) | −0.805219 | −0.0482072 | ||||||||
\(280\) | 9.08929 | 0.543189 | ||||||||
\(281\) | 13.5343 | 0.807391 | 0.403696 | − | 0.914893i | \(-0.367725\pi\) | ||||
0.403696 | + | 0.914893i | \(0.367725\pi\) | |||||||
\(282\) | 33.2606 | 1.98064 | ||||||||
\(283\) | 21.0111 | 1.24898 | 0.624491 | − | 0.781032i | \(-0.285306\pi\) | ||||
0.624491 | + | 0.781032i | \(0.285306\pi\) | |||||||
\(284\) | 4.93032 | 0.292561 | ||||||||
\(285\) | 5.98799 | 0.354698 | ||||||||
\(286\) | −14.6296 | −0.865064 | ||||||||
\(287\) | 12.1005 | 0.714268 | ||||||||
\(288\) | 0.769075 | 0.0453182 | ||||||||
\(289\) | −15.2009 | −0.894173 | ||||||||
\(290\) | −23.4942 | −1.37963 | ||||||||
\(291\) | −30.1459 | −1.76719 | ||||||||
\(292\) | 10.7551 | 0.629393 | ||||||||
\(293\) | 0.185923 | 0.0108617 | 0.00543086 | − | 0.999985i | \(-0.498271\pi\) | ||||
0.00543086 | + | 0.999985i | \(0.498271\pi\) | |||||||
\(294\) | 2.91252 | 0.169862 | ||||||||
\(295\) | 7.18184 | 0.418143 | ||||||||
\(296\) | 2.16334 | 0.125741 | ||||||||
\(297\) | −9.69855 | −0.562767 | ||||||||
\(298\) | −16.6931 | −0.967003 | ||||||||
\(299\) | 6.48719 | 0.375164 | ||||||||
\(300\) | −3.18472 | −0.183870 | ||||||||
\(301\) | −5.61660 | −0.323736 | ||||||||
\(302\) | −26.4755 | −1.52349 | ||||||||
\(303\) | 12.4981 | 0.717995 | ||||||||
\(304\) | −11.8618 | −0.680319 | ||||||||
\(305\) | −9.13732 | −0.523201 | ||||||||
\(306\) | 0.457968 | 0.0261803 | ||||||||
\(307\) | −24.9431 | −1.42358 | −0.711788 | − | 0.702395i | \(-0.752114\pi\) | ||||
−0.711788 | + | 0.702395i | \(0.752114\pi\) | |||||||
\(308\) | −3.48377 | −0.198506 | ||||||||
\(309\) | 12.8003 | 0.728182 | ||||||||
\(310\) | 9.34365 | 0.530683 | ||||||||
\(311\) | −6.04246 | −0.342637 | −0.171318 | − | 0.985216i | \(-0.554803\pi\) | ||||
−0.171318 | + | 0.985216i | \(0.554803\pi\) | |||||||
\(312\) | 17.8598 | 1.01111 | ||||||||
\(313\) | −16.0560 | −0.907538 | −0.453769 | − | 0.891119i | \(-0.649921\pi\) | ||||
−0.453769 | + | 0.891119i | \(0.649921\pi\) | |||||||
\(314\) | 19.8049 | 1.11766 | ||||||||
\(315\) | 0.876616 | 0.0493917 | ||||||||
\(316\) | 5.78829 | 0.325617 | ||||||||
\(317\) | −6.02432 | −0.338359 | −0.169180 | − | 0.985585i | \(-0.554112\pi\) | ||||
−0.169180 | + | 0.985585i | \(0.554112\pi\) | |||||||
\(318\) | −31.8570 | −1.78645 | ||||||||
\(319\) | −17.5563 | −0.982962 | ||||||||
\(320\) | 5.56346 | 0.311007 | ||||||||
\(321\) | −26.0953 | −1.45650 | ||||||||
\(322\) | 6.10141 | 0.340018 | ||||||||
\(323\) | −3.24937 | −0.180800 | ||||||||
\(324\) | −5.64853 | −0.313807 | ||||||||
\(325\) | 13.8914 | 0.770556 | ||||||||
\(326\) | 8.27110 | 0.458094 | ||||||||
\(327\) | −1.67074 | −0.0923919 | ||||||||
\(328\) | 9.21758 | 0.508956 | ||||||||
\(329\) | −34.5479 | −1.90469 | ||||||||
\(330\) | 7.31798 | 0.402842 | ||||||||
\(331\) | 25.6176 | 1.40807 | 0.704034 | − | 0.710166i | \(-0.251380\pi\) | ||||
0.704034 | + | 0.710166i | \(0.251380\pi\) | |||||||
\(332\) | 0.664313 | 0.0364589 | ||||||||
\(333\) | 0.208643 | 0.0114336 | ||||||||
\(334\) | −1.07969 | −0.0590779 | ||||||||
\(335\) | −14.1034 | −0.770550 | ||||||||
\(336\) | 23.2321 | 1.26742 | ||||||||
\(337\) | −18.0292 | −0.982111 | −0.491056 | − | 0.871128i | \(-0.663389\pi\) | ||||
−0.491056 | + | 0.871128i | \(0.663389\pi\) | |||||||
\(338\) | 18.6833 | 1.01624 | ||||||||
\(339\) | −12.4683 | −0.677185 | ||||||||
\(340\) | −1.34549 | −0.0729696 | ||||||||
\(341\) | 6.98213 | 0.378103 | ||||||||
\(342\) | −0.827161 | −0.0447277 | ||||||||
\(343\) | 16.8543 | 0.910048 | ||||||||
\(344\) | −4.27847 | −0.230680 | ||||||||
\(345\) | −3.24501 | −0.174706 | ||||||||
\(346\) | 22.6670 | 1.21859 | ||||||||
\(347\) | −9.82600 | −0.527487 | −0.263744 | − | 0.964593i | \(-0.584957\pi\) | ||||
−0.263744 | + | 0.964593i | \(0.584957\pi\) | |||||||
\(348\) | −10.9932 | −0.589298 | ||||||||
\(349\) | 18.2946 | 0.979285 | 0.489643 | − | 0.871923i | \(-0.337127\pi\) | ||||
0.489643 | + | 0.871923i | \(0.337127\pi\) | |||||||
\(350\) | 13.0653 | 0.698371 | ||||||||
\(351\) | 26.4895 | 1.41390 | ||||||||
\(352\) | −6.66872 | −0.355444 | ||||||||
\(353\) | −15.0098 | −0.798889 | −0.399445 | − | 0.916757i | \(-0.630797\pi\) | ||||
−0.399445 | + | 0.916757i | \(0.630797\pi\) | |||||||
\(354\) | 13.2726 | 0.705430 | ||||||||
\(355\) | 10.7575 | 0.570946 | ||||||||
\(356\) | 0.310623 | 0.0164630 | ||||||||
\(357\) | 6.36413 | 0.336825 | ||||||||
\(358\) | −11.9071 | −0.629312 | ||||||||
\(359\) | 19.5629 | 1.03249 | 0.516246 | − | 0.856440i | \(-0.327329\pi\) | ||||
0.516246 | + | 0.856440i | \(0.327329\pi\) | |||||||
\(360\) | 0.667766 | 0.0351944 | ||||||||
\(361\) | −13.1311 | −0.691113 | ||||||||
\(362\) | −7.39616 | −0.388734 | ||||||||
\(363\) | −12.9097 | −0.677581 | ||||||||
\(364\) | 9.51515 | 0.498729 | ||||||||
\(365\) | 23.4665 | 1.22829 | ||||||||
\(366\) | −16.8865 | −0.882670 | ||||||||
\(367\) | −7.55573 | −0.394406 | −0.197203 | − | 0.980363i | \(-0.563186\pi\) | ||||
−0.197203 | + | 0.980363i | \(0.563186\pi\) | |||||||
\(368\) | 6.42813 | 0.335089 | ||||||||
\(369\) | 0.888990 | 0.0462790 | ||||||||
\(370\) | −2.42106 | −0.125865 | ||||||||
\(371\) | 33.0900 | 1.71795 | ||||||||
\(372\) | 4.37200 | 0.226678 | ||||||||
\(373\) | 22.9616 | 1.18891 | 0.594455 | − | 0.804129i | \(-0.297368\pi\) | ||||
0.594455 | + | 0.804129i | \(0.297368\pi\) | |||||||
\(374\) | −3.97108 | −0.205340 | ||||||||
\(375\) | −19.3075 | −0.997034 | ||||||||
\(376\) | −26.3170 | −1.35720 | ||||||||
\(377\) | 47.9511 | 2.46961 | ||||||||
\(378\) | 24.9142 | 1.28145 | ||||||||
\(379\) | 8.67330 | 0.445518 | 0.222759 | − | 0.974874i | \(-0.428494\pi\) | ||||
0.222759 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(380\) | 2.43017 | 0.124665 | ||||||||
\(381\) | 18.4108 | 0.943216 | ||||||||
\(382\) | −13.9730 | −0.714922 | ||||||||
\(383\) | 4.82530 | 0.246561 | 0.123281 | − | 0.992372i | \(-0.460658\pi\) | ||||
0.123281 | + | 0.992372i | \(0.460658\pi\) | |||||||
\(384\) | 22.5986 | 1.15323 | ||||||||
\(385\) | −7.60122 | −0.387394 | ||||||||
\(386\) | −10.7524 | −0.547283 | ||||||||
\(387\) | −0.412637 | −0.0209755 | ||||||||
\(388\) | −12.2344 | −0.621109 | ||||||||
\(389\) | 2.87282 | 0.145658 | 0.0728289 | − | 0.997344i | \(-0.476797\pi\) | ||||
0.0728289 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(390\) | −19.9875 | −1.01211 | ||||||||
\(391\) | 1.76090 | 0.0890524 | ||||||||
\(392\) | −2.30450 | −0.116395 | ||||||||
\(393\) | 3.73671 | 0.188492 | ||||||||
\(394\) | −16.3319 | −0.822790 | ||||||||
\(395\) | 12.6295 | 0.635457 | ||||||||
\(396\) | −0.255943 | −0.0128616 | ||||||||
\(397\) | −30.1383 | −1.51260 | −0.756299 | − | 0.654227i | \(-0.772994\pi\) | ||||
−0.756299 | + | 0.654227i | \(0.772994\pi\) | |||||||
\(398\) | −29.4218 | −1.47478 | ||||||||
\(399\) | −11.4946 | −0.575449 | ||||||||
\(400\) | 13.7649 | 0.688246 | ||||||||
\(401\) | 28.5336 | 1.42490 | 0.712450 | − | 0.701723i | \(-0.247586\pi\) | ||||
0.712450 | + | 0.701723i | \(0.247586\pi\) | |||||||
\(402\) | −26.0642 | −1.29996 | ||||||||
\(403\) | −19.0702 | −0.949953 | ||||||||
\(404\) | 5.07221 | 0.252352 | ||||||||
\(405\) | −12.3245 | −0.612410 | ||||||||
\(406\) | 45.0996 | 2.23826 | ||||||||
\(407\) | −1.80916 | −0.0896769 | ||||||||
\(408\) | 4.84790 | 0.240007 | ||||||||
\(409\) | −2.35976 | −0.116683 | −0.0583413 | − | 0.998297i | \(-0.518581\pi\) | ||||
−0.0583413 | + | 0.998297i | \(0.518581\pi\) | |||||||
\(410\) | −10.3157 | −0.509457 | ||||||||
\(411\) | −13.4469 | −0.663289 | ||||||||
\(412\) | 5.19486 | 0.255932 | ||||||||
\(413\) | −13.7863 | −0.678379 | ||||||||
\(414\) | 0.448255 | 0.0220305 | ||||||||
\(415\) | 1.44946 | 0.0711513 | ||||||||
\(416\) | 18.2142 | 0.893023 | ||||||||
\(417\) | 36.6923 | 1.79683 | ||||||||
\(418\) | 7.17239 | 0.350813 | ||||||||
\(419\) | 27.9186 | 1.36391 | 0.681957 | − | 0.731392i | \(-0.261129\pi\) | ||||
0.681957 | + | 0.731392i | \(0.261129\pi\) | |||||||
\(420\) | −4.75966 | −0.232248 | ||||||||
\(421\) | −27.9350 | −1.36147 | −0.680733 | − | 0.732531i | \(-0.738339\pi\) | ||||
−0.680733 | + | 0.732531i | \(0.738339\pi\) | |||||||
\(422\) | −11.1704 | −0.543768 | ||||||||
\(423\) | −2.53815 | −0.123409 | ||||||||
\(424\) | 25.2065 | 1.22414 | ||||||||
\(425\) | 3.77071 | 0.182906 | ||||||||
\(426\) | 19.8806 | 0.963219 | ||||||||
\(427\) | 17.5401 | 0.848823 | ||||||||
\(428\) | −10.5905 | −0.511911 | ||||||||
\(429\) | −14.9358 | −0.721109 | ||||||||
\(430\) | 4.78818 | 0.230907 | ||||||||
\(431\) | −14.8397 | −0.714803 | −0.357402 | − | 0.933951i | \(-0.616337\pi\) | ||||
−0.357402 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(432\) | 26.2483 | 1.26287 | ||||||||
\(433\) | 1.35115 | 0.0649323 | 0.0324662 | − | 0.999473i | \(-0.489664\pi\) | ||||
0.0324662 | + | 0.999473i | \(0.489664\pi\) | |||||||
\(434\) | −17.9361 | −0.860962 | ||||||||
\(435\) | −23.9861 | −1.15004 | ||||||||
\(436\) | −0.678051 | −0.0324728 | ||||||||
\(437\) | −3.18045 | −0.152142 | ||||||||
\(438\) | 43.3679 | 2.07220 | ||||||||
\(439\) | −2.43036 | −0.115995 | −0.0579973 | − | 0.998317i | \(-0.518471\pi\) | ||||
−0.0579973 | + | 0.998317i | \(0.518471\pi\) | |||||||
\(440\) | −5.79027 | −0.276040 | ||||||||
\(441\) | −0.222257 | −0.0105837 | ||||||||
\(442\) | 10.8462 | 0.515899 | ||||||||
\(443\) | −19.7248 | −0.937155 | −0.468577 | − | 0.883422i | \(-0.655233\pi\) | ||||
−0.468577 | + | 0.883422i | \(0.655233\pi\) | |||||||
\(444\) | −1.13284 | −0.0537624 | ||||||||
\(445\) | 0.677748 | 0.0321283 | ||||||||
\(446\) | −5.98870 | −0.283573 | ||||||||
\(447\) | −17.0425 | −0.806084 | ||||||||
\(448\) | −10.6796 | −0.504566 | ||||||||
\(449\) | 11.3367 | 0.535011 | 0.267505 | − | 0.963556i | \(-0.413801\pi\) | ||||
0.267505 | + | 0.963556i | \(0.413801\pi\) | |||||||
\(450\) | 0.959875 | 0.0452489 | ||||||||
\(451\) | −7.70851 | −0.362980 | ||||||||
\(452\) | −5.06013 | −0.238009 | ||||||||
\(453\) | −27.0298 | −1.26997 | ||||||||
\(454\) | 29.7664 | 1.39700 | ||||||||
\(455\) | 20.7611 | 0.973295 | ||||||||
\(456\) | −8.75606 | −0.410040 | ||||||||
\(457\) | −12.9011 | −0.603488 | −0.301744 | − | 0.953389i | \(-0.597569\pi\) | ||||
−0.301744 | + | 0.953389i | \(0.597569\pi\) | |||||||
\(458\) | −11.5027 | −0.537486 | ||||||||
\(459\) | 7.19037 | 0.335618 | ||||||||
\(460\) | −1.31696 | −0.0614034 | ||||||||
\(461\) | 13.0158 | 0.606206 | 0.303103 | − | 0.952958i | \(-0.401977\pi\) | ||||
0.303103 | + | 0.952958i | \(0.401977\pi\) | |||||||
\(462\) | −14.0477 | −0.653556 | ||||||||
\(463\) | −28.5795 | −1.32820 | −0.664100 | − | 0.747644i | \(-0.731185\pi\) | ||||
−0.664100 | + | 0.747644i | \(0.731185\pi\) | |||||||
\(464\) | 47.5146 | 2.20581 | ||||||||
\(465\) | 9.53926 | 0.442373 | ||||||||
\(466\) | 23.6105 | 1.09374 | ||||||||
\(467\) | −4.93454 | −0.228343 | −0.114172 | − | 0.993461i | \(-0.536421\pi\) | ||||
−0.114172 | + | 0.993461i | \(0.536421\pi\) | |||||||
\(468\) | 0.699054 | 0.0323138 | ||||||||
\(469\) | 27.0729 | 1.25011 | ||||||||
\(470\) | 29.4523 | 1.35853 | ||||||||
\(471\) | 20.2195 | 0.931667 | ||||||||
\(472\) | −10.5018 | −0.483383 | ||||||||
\(473\) | 3.57802 | 0.164517 | ||||||||
\(474\) | 23.3402 | 1.07205 | ||||||||
\(475\) | −6.81049 | −0.312487 | ||||||||
\(476\) | 2.58282 | 0.118383 | ||||||||
\(477\) | 2.43104 | 0.111310 | ||||||||
\(478\) | −21.3353 | −0.975854 | ||||||||
\(479\) | −32.8105 | −1.49915 | −0.749576 | − | 0.661919i | \(-0.769742\pi\) | ||||
−0.749576 | + | 0.661919i | \(0.769742\pi\) | |||||||
\(480\) | −9.11107 | −0.415861 | ||||||||
\(481\) | 4.94134 | 0.225306 | ||||||||
\(482\) | 14.1968 | 0.646647 | ||||||||
\(483\) | 6.22915 | 0.283436 | ||||||||
\(484\) | −5.23925 | −0.238148 | ||||||||
\(485\) | −26.6943 | −1.21212 | ||||||||
\(486\) | 3.54175 | 0.160657 | ||||||||
\(487\) | −10.5021 | −0.475897 | −0.237948 | − | 0.971278i | \(-0.576475\pi\) | ||||
−0.237948 | + | 0.971278i | \(0.576475\pi\) | |||||||
\(488\) | 13.3612 | 0.604834 | ||||||||
\(489\) | 8.44426 | 0.381862 | ||||||||
\(490\) | 2.57904 | 0.116509 | ||||||||
\(491\) | −0.536109 | −0.0241943 | −0.0120971 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120971 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(492\) | −4.82684 | −0.217611 | ||||||||
\(493\) | 13.0160 | 0.586210 | ||||||||
\(494\) | −19.5898 | −0.881388 | ||||||||
\(495\) | −0.558442 | −0.0251001 | ||||||||
\(496\) | −18.8966 | −0.848480 | ||||||||
\(497\) | −20.6501 | −0.926282 | ||||||||
\(498\) | 2.67872 | 0.120036 | ||||||||
\(499\) | −14.5312 | −0.650507 | −0.325253 | − | 0.945627i | \(-0.605450\pi\) | ||||
−0.325253 | + | 0.945627i | \(0.605450\pi\) | |||||||
\(500\) | −7.83575 | −0.350425 | ||||||||
\(501\) | −1.10229 | −0.0492467 | ||||||||
\(502\) | 34.7022 | 1.54883 | ||||||||
\(503\) | −11.3529 | −0.506202 | −0.253101 | − | 0.967440i | \(-0.581450\pi\) | ||||
−0.253101 | + | 0.967440i | \(0.581450\pi\) | |||||||
\(504\) | −1.28185 | −0.0570981 | ||||||||
\(505\) | 11.0670 | 0.492477 | ||||||||
\(506\) | −3.88686 | −0.172792 | ||||||||
\(507\) | 19.0745 | 0.847126 | ||||||||
\(508\) | 7.47185 | 0.331510 | ||||||||
\(509\) | 1.34841 | 0.0597673 | 0.0298836 | − | 0.999553i | \(-0.490486\pi\) | ||||
0.0298836 | + | 0.999553i | \(0.490486\pi\) | |||||||
\(510\) | −5.42545 | −0.240243 | ||||||||
\(511\) | −45.0464 | −1.99274 | ||||||||
\(512\) | −3.13657 | −0.138618 | ||||||||
\(513\) | −12.9869 | −0.573386 | ||||||||
\(514\) | 23.1721 | 1.02208 | ||||||||
\(515\) | 11.3347 | 0.499464 | ||||||||
\(516\) | 2.24045 | 0.0986302 | ||||||||
\(517\) | 22.0085 | 0.967933 | ||||||||
\(518\) | 4.64749 | 0.204199 | ||||||||
\(519\) | 23.1415 | 1.01580 | ||||||||
\(520\) | 15.8149 | 0.693527 | ||||||||
\(521\) | 4.02602 | 0.176383 | 0.0881915 | − | 0.996104i | \(-0.471891\pi\) | ||||
0.0881915 | + | 0.996104i | \(0.471891\pi\) | |||||||
\(522\) | 3.31335 | 0.145021 | ||||||||
\(523\) | 33.0997 | 1.44735 | 0.723673 | − | 0.690143i | \(-0.242452\pi\) | ||||
0.723673 | + | 0.690143i | \(0.242452\pi\) | |||||||
\(524\) | 1.51651 | 0.0662489 | ||||||||
\(525\) | 13.3388 | 0.582155 | ||||||||
\(526\) | 25.7509 | 1.12279 | ||||||||
\(527\) | −5.17645 | −0.225490 | ||||||||
\(528\) | −14.7999 | −0.644081 | ||||||||
\(529\) | −21.2764 | −0.925063 | ||||||||
\(530\) | −28.2094 | −1.22534 | ||||||||
\(531\) | −1.01284 | −0.0439537 | ||||||||
\(532\) | −4.66496 | −0.202252 | ||||||||
\(533\) | 21.0541 | 0.911956 | ||||||||
\(534\) | 1.25253 | 0.0542023 | ||||||||
\(535\) | −23.1074 | −0.999020 | ||||||||
\(536\) | 20.6229 | 0.890776 | ||||||||
\(537\) | −12.1564 | −0.524588 | ||||||||
\(538\) | −8.36992 | −0.360853 | ||||||||
\(539\) | 1.92721 | 0.0830110 | ||||||||
\(540\) | −5.37760 | −0.231415 | ||||||||
\(541\) | −8.07535 | −0.347186 | −0.173593 | − | 0.984817i | \(-0.555538\pi\) | ||||
−0.173593 | + | 0.984817i | \(0.555538\pi\) | |||||||
\(542\) | −30.4502 | −1.30795 | ||||||||
\(543\) | −7.55101 | −0.324045 | ||||||||
\(544\) | 4.94409 | 0.211976 | ||||||||
\(545\) | −1.47944 | −0.0633722 | ||||||||
\(546\) | 38.3681 | 1.64200 | ||||||||
\(547\) | 12.5640 | 0.537198 | 0.268599 | − | 0.963252i | \(-0.413439\pi\) | ||||
0.268599 | + | 0.963252i | \(0.413439\pi\) | |||||||
\(548\) | −5.45730 | −0.233124 | ||||||||
\(549\) | 1.28862 | 0.0549971 | ||||||||
\(550\) | −8.32317 | −0.354901 | ||||||||
\(551\) | −23.5088 | −1.00151 | ||||||||
\(552\) | 4.74508 | 0.201964 | ||||||||
\(553\) | −24.2436 | −1.03094 | ||||||||
\(554\) | −14.7769 | −0.627811 | ||||||||
\(555\) | −2.47175 | −0.104920 | ||||||||
\(556\) | 14.8912 | 0.631528 | ||||||||
\(557\) | −32.4676 | −1.37570 | −0.687848 | − | 0.725855i | \(-0.741444\pi\) | ||||
−0.687848 | + | 0.725855i | \(0.741444\pi\) | |||||||
\(558\) | −1.31772 | −0.0557836 | ||||||||
\(559\) | −9.77257 | −0.413336 | ||||||||
\(560\) | 20.5721 | 0.869329 | ||||||||
\(561\) | −4.05422 | −0.171169 | ||||||||
\(562\) | 22.1486 | 0.934283 | ||||||||
\(563\) | −29.7715 | −1.25472 | −0.627360 | − | 0.778729i | \(-0.715865\pi\) | ||||
−0.627360 | + | 0.778729i | \(0.715865\pi\) | |||||||
\(564\) | 13.7811 | 0.580288 | ||||||||
\(565\) | −11.0407 | −0.464485 | ||||||||
\(566\) | 34.3842 | 1.44528 | ||||||||
\(567\) | 23.6582 | 0.993552 | ||||||||
\(568\) | −15.7303 | −0.660028 | ||||||||
\(569\) | 14.3759 | 0.602669 | 0.301334 | − | 0.953519i | \(-0.402568\pi\) | ||||
0.301334 | + | 0.953519i | \(0.402568\pi\) | |||||||
\(570\) | 9.79920 | 0.410444 | ||||||||
\(571\) | −25.9384 | −1.08549 | −0.542744 | − | 0.839898i | \(-0.682614\pi\) | ||||
−0.542744 | + | 0.839898i | \(0.682614\pi\) | |||||||
\(572\) | −6.06156 | −0.253447 | ||||||||
\(573\) | −14.2656 | −0.595952 | ||||||||
\(574\) | 19.8021 | 0.826524 | ||||||||
\(575\) | 3.69074 | 0.153915 | ||||||||
\(576\) | −0.784606 | −0.0326919 | ||||||||
\(577\) | 30.4494 | 1.26763 | 0.633814 | − | 0.773486i | \(-0.281489\pi\) | ||||
0.633814 | + | 0.773486i | \(0.281489\pi\) | |||||||
\(578\) | −24.8760 | −1.03470 | ||||||||
\(579\) | −10.9775 | −0.456210 | ||||||||
\(580\) | −9.73450 | −0.404203 | ||||||||
\(581\) | −2.78240 | −0.115433 | ||||||||
\(582\) | −49.3331 | −2.04492 | ||||||||
\(583\) | −21.0798 | −0.873035 | ||||||||
\(584\) | −34.3143 | −1.41994 | ||||||||
\(585\) | 1.52526 | 0.0630619 | ||||||||
\(586\) | 0.304258 | 0.0125688 | ||||||||
\(587\) | −6.23333 | −0.257277 | −0.128638 | − | 0.991692i | \(-0.541061\pi\) | ||||
−0.128638 | + | 0.991692i | \(0.541061\pi\) | |||||||
\(588\) | 1.20676 | 0.0497661 | ||||||||
\(589\) | 9.34947 | 0.385238 | ||||||||
\(590\) | 11.7529 | 0.483859 | ||||||||
\(591\) | −16.6738 | −0.685869 | ||||||||
\(592\) | 4.89635 | 0.201239 | ||||||||
\(593\) | −13.0033 | −0.533984 | −0.266992 | − | 0.963699i | \(-0.586030\pi\) | ||||
−0.266992 | + | 0.963699i | \(0.586030\pi\) | |||||||
\(594\) | −15.8714 | −0.651213 | ||||||||
\(595\) | 5.63544 | 0.231030 | ||||||||
\(596\) | −6.91654 | −0.283312 | ||||||||
\(597\) | −30.0377 | −1.22936 | ||||||||
\(598\) | 10.6161 | 0.434125 | ||||||||
\(599\) | −1.27850 | −0.0522379 | −0.0261190 | − | 0.999659i | \(-0.508315\pi\) | ||||
−0.0261190 | + | 0.999659i | \(0.508315\pi\) | |||||||
\(600\) | 10.1609 | 0.414818 | ||||||||
\(601\) | 21.5189 | 0.877775 | 0.438887 | − | 0.898542i | \(-0.355373\pi\) | ||||
0.438887 | + | 0.898542i | \(0.355373\pi\) | |||||||
\(602\) | −9.19143 | −0.374615 | ||||||||
\(603\) | 1.98898 | 0.0809975 | ||||||||
\(604\) | −10.9698 | −0.446353 | ||||||||
\(605\) | −11.4315 | −0.464757 | ||||||||
\(606\) | 20.4528 | 0.830836 | ||||||||
\(607\) | −12.4158 | −0.503940 | −0.251970 | − | 0.967735i | \(-0.581078\pi\) | ||||
−0.251970 | + | 0.967735i | \(0.581078\pi\) | |||||||
\(608\) | −8.92980 | −0.362151 | ||||||||
\(609\) | 46.0438 | 1.86579 | ||||||||
\(610\) | −14.9530 | −0.605429 | ||||||||
\(611\) | −60.1115 | −2.43185 | ||||||||
\(612\) | 0.189753 | 0.00767030 | ||||||||
\(613\) | −29.1464 | −1.17721 | −0.588605 | − | 0.808421i | \(-0.700323\pi\) | ||||
−0.588605 | + | 0.808421i | \(0.700323\pi\) | |||||||
\(614\) | −40.8187 | −1.64731 | ||||||||
\(615\) | −10.5317 | −0.424678 | ||||||||
\(616\) | 11.1150 | 0.447837 | ||||||||
\(617\) | 24.0892 | 0.969794 | 0.484897 | − | 0.874571i | \(-0.338857\pi\) | ||||
0.484897 | + | 0.874571i | \(0.338857\pi\) | |||||||
\(618\) | 20.9473 | 0.842625 | ||||||||
\(619\) | −4.05177 | −0.162854 | −0.0814272 | − | 0.996679i | \(-0.525948\pi\) | ||||
−0.0814272 | + | 0.996679i | \(0.525948\pi\) | |||||||
\(620\) | 3.87141 | 0.155480 | ||||||||
\(621\) | 7.03787 | 0.282420 | ||||||||
\(622\) | −9.88834 | −0.396486 | ||||||||
\(623\) | −1.30101 | −0.0521238 | ||||||||
\(624\) | 40.4226 | 1.61820 | ||||||||
\(625\) | −3.04048 | −0.121619 | ||||||||
\(626\) | −26.2752 | −1.05017 | ||||||||
\(627\) | 7.32255 | 0.292434 | ||||||||
\(628\) | 8.20589 | 0.327451 | ||||||||
\(629\) | 1.34129 | 0.0534807 | ||||||||
\(630\) | 1.43456 | 0.0571543 | ||||||||
\(631\) | −24.8491 | −0.989226 | −0.494613 | − | 0.869113i | \(-0.664690\pi\) | ||||
−0.494613 | + | 0.869113i | \(0.664690\pi\) | |||||||
\(632\) | −18.4677 | −0.734604 | ||||||||
\(633\) | −11.4043 | −0.453280 | ||||||||
\(634\) | −9.85864 | −0.391537 | ||||||||
\(635\) | 16.3028 | 0.646958 | ||||||||
\(636\) | −13.1995 | −0.523395 | ||||||||
\(637\) | −5.26377 | −0.208558 | ||||||||
\(638\) | −28.7304 | −1.13745 | ||||||||
\(639\) | −1.51711 | −0.0600158 | ||||||||
\(640\) | 20.0111 | 0.791009 | ||||||||
\(641\) | 6.24215 | 0.246550 | 0.123275 | − | 0.992373i | \(-0.460660\pi\) | ||||
0.123275 | + | 0.992373i | \(0.460660\pi\) | |||||||
\(642\) | −42.7043 | −1.68540 | ||||||||
\(643\) | 19.7930 | 0.780560 | 0.390280 | − | 0.920696i | \(-0.372378\pi\) | ||||
0.390280 | + | 0.920696i | \(0.372378\pi\) | |||||||
\(644\) | 2.52804 | 0.0996186 | ||||||||
\(645\) | 4.88843 | 0.192482 | ||||||||
\(646\) | −5.31751 | −0.209215 | ||||||||
\(647\) | −2.46432 | −0.0968826 | −0.0484413 | − | 0.998826i | \(-0.515425\pi\) | ||||
−0.0484413 | + | 0.998826i | \(0.515425\pi\) | |||||||
\(648\) | 18.0218 | 0.707962 | ||||||||
\(649\) | 8.78246 | 0.344742 | ||||||||
\(650\) | 22.7329 | 0.891659 | ||||||||
\(651\) | −18.3116 | −0.717689 | ||||||||
\(652\) | 3.42702 | 0.134212 | ||||||||
\(653\) | −33.9536 | −1.32871 | −0.664354 | − | 0.747418i | \(-0.731293\pi\) | ||||
−0.664354 | + | 0.747418i | \(0.731293\pi\) | |||||||
\(654\) | −2.73412 | −0.106912 | ||||||||
\(655\) | 3.30886 | 0.129288 | ||||||||
\(656\) | 20.8625 | 0.814542 | ||||||||
\(657\) | −3.30944 | −0.129114 | ||||||||
\(658\) | −56.5368 | −2.20403 | ||||||||
\(659\) | −17.8783 | −0.696438 | −0.348219 | − | 0.937413i | \(-0.613213\pi\) | ||||
−0.348219 | + | 0.937413i | \(0.613213\pi\) | |||||||
\(660\) | 3.03211 | 0.118025 | ||||||||
\(661\) | −4.66432 | −0.181421 | −0.0907105 | − | 0.995877i | \(-0.528914\pi\) | ||||
−0.0907105 | + | 0.995877i | \(0.528914\pi\) | |||||||
\(662\) | 41.9225 | 1.62936 | ||||||||
\(663\) | 11.0732 | 0.430048 | ||||||||
\(664\) | −2.11950 | −0.0822527 | ||||||||
\(665\) | −10.1785 | −0.394704 | ||||||||
\(666\) | 0.341439 | 0.0132305 | ||||||||
\(667\) | 12.7399 | 0.493291 | ||||||||
\(668\) | −0.447354 | −0.0173086 | ||||||||
\(669\) | −6.11408 | −0.236384 | ||||||||
\(670\) | −23.0798 | −0.891652 | ||||||||
\(671\) | −11.1738 | −0.431358 | ||||||||
\(672\) | 17.4897 | 0.674678 | ||||||||
\(673\) | 35.8891 | 1.38342 | 0.691712 | − | 0.722173i | \(-0.256857\pi\) | ||||
0.691712 | + | 0.722173i | \(0.256857\pi\) | |||||||
\(674\) | −29.5043 | −1.13646 | ||||||||
\(675\) | 15.0706 | 0.580068 | ||||||||
\(676\) | 7.74117 | 0.297737 | ||||||||
\(677\) | −35.7238 | −1.37298 | −0.686488 | − | 0.727141i | \(-0.740849\pi\) | ||||
−0.686488 | + | 0.727141i | \(0.740849\pi\) | |||||||
\(678\) | −20.4041 | −0.783613 | ||||||||
\(679\) | 51.2425 | 1.96651 | ||||||||
\(680\) | 4.29282 | 0.164622 | ||||||||
\(681\) | 30.3895 | 1.16453 | ||||||||
\(682\) | 11.4261 | 0.437527 | ||||||||
\(683\) | 4.17252 | 0.159657 | 0.0798285 | − | 0.996809i | \(-0.474563\pi\) | ||||
0.0798285 | + | 0.996809i | \(0.474563\pi\) | |||||||
\(684\) | −0.342723 | −0.0131043 | ||||||||
\(685\) | −11.9073 | −0.454954 | ||||||||
\(686\) | 27.5817 | 1.05307 | ||||||||
\(687\) | −11.7435 | −0.448043 | ||||||||
\(688\) | −9.68360 | −0.369184 | ||||||||
\(689\) | 57.5748 | 2.19343 | ||||||||
\(690\) | −5.31038 | −0.202163 | ||||||||
\(691\) | 50.3769 | 1.91643 | 0.958213 | − | 0.286054i | \(-0.0923437\pi\) | ||||
0.958213 | + | 0.286054i | \(0.0923437\pi\) | |||||||
\(692\) | 9.39176 | 0.357021 | ||||||||
\(693\) | 1.07199 | 0.0407215 | ||||||||
\(694\) | −16.0800 | −0.610389 | ||||||||
\(695\) | 32.4911 | 1.23246 | ||||||||
\(696\) | 35.0741 | 1.32948 | ||||||||
\(697\) | 5.71498 | 0.216470 | ||||||||
\(698\) | 29.9386 | 1.13319 | ||||||||
\(699\) | 24.1048 | 0.911728 | ||||||||
\(700\) | 5.41343 | 0.204609 | ||||||||
\(701\) | 37.4057 | 1.41279 | 0.706396 | − | 0.707817i | \(-0.250320\pi\) | ||||
0.706396 | + | 0.707817i | \(0.250320\pi\) | |||||||
\(702\) | 43.3494 | 1.63612 | ||||||||
\(703\) | −2.42257 | −0.0913691 | ||||||||
\(704\) | 6.80339 | 0.256412 | ||||||||
\(705\) | 30.0689 | 1.13246 | ||||||||
\(706\) | −24.5631 | −0.924445 | ||||||||
\(707\) | −21.2444 | −0.798977 | ||||||||
\(708\) | 5.49932 | 0.206677 | ||||||||
\(709\) | −14.8459 | −0.557549 | −0.278774 | − | 0.960357i | \(-0.589928\pi\) | ||||
−0.278774 | + | 0.960357i | \(0.589928\pi\) | |||||||
\(710\) | 17.6043 | 0.660678 | ||||||||
\(711\) | −1.78111 | −0.0667969 | ||||||||
\(712\) | −0.991050 | −0.0371412 | ||||||||
\(713\) | −5.06667 | −0.189748 | ||||||||
\(714\) | 10.4147 | 0.389762 | ||||||||
\(715\) | −13.2257 | −0.494613 | ||||||||
\(716\) | −4.93356 | −0.184376 | ||||||||
\(717\) | −21.7820 | −0.813463 | ||||||||
\(718\) | 32.0142 | 1.19476 | ||||||||
\(719\) | −42.5704 | −1.58761 | −0.793803 | − | 0.608174i | \(-0.791902\pi\) | ||||
−0.793803 | + | 0.608174i | \(0.791902\pi\) | |||||||
\(720\) | 1.51138 | 0.0563257 | ||||||||
\(721\) | −21.7581 | −0.810313 | ||||||||
\(722\) | −21.4888 | −0.799730 | ||||||||
\(723\) | 14.4940 | 0.539039 | ||||||||
\(724\) | −3.06450 | −0.113891 | ||||||||
\(725\) | 27.2807 | 1.01318 | ||||||||
\(726\) | −21.1263 | −0.784072 | ||||||||
\(727\) | 4.34883 | 0.161289 | 0.0806446 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806446 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(728\) | −30.3583 | −1.12515 | ||||||||
\(729\) | 28.6075 | 1.05954 | ||||||||
\(730\) | 38.4023 | 1.42133 | ||||||||
\(731\) | −2.65269 | −0.0981133 | ||||||||
\(732\) | −6.99668 | −0.258605 | ||||||||
\(733\) | −11.9813 | −0.442538 | −0.221269 | − | 0.975213i | \(-0.571020\pi\) | ||||
−0.221269 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(734\) | −12.3648 | −0.456392 | ||||||||
\(735\) | 2.63304 | 0.0971210 | ||||||||
\(736\) | 4.83924 | 0.178377 | ||||||||
\(737\) | −17.2466 | −0.635288 | ||||||||
\(738\) | 1.45481 | 0.0535523 | ||||||||
\(739\) | −5.30437 | −0.195124 | −0.0975622 | − | 0.995229i | \(-0.531104\pi\) | ||||
−0.0975622 | + | 0.995229i | \(0.531104\pi\) | |||||||
\(740\) | −1.00313 | −0.0368760 | ||||||||
\(741\) | −20.0000 | −0.734717 | ||||||||
\(742\) | 54.1510 | 1.98795 | ||||||||
\(743\) | 15.6795 | 0.575226 | 0.287613 | − | 0.957747i | \(-0.407138\pi\) | ||||
0.287613 | + | 0.957747i | \(0.407138\pi\) | |||||||
\(744\) | −13.9490 | −0.511394 | ||||||||
\(745\) | −15.0912 | −0.552898 | ||||||||
\(746\) | 37.5762 | 1.37576 | ||||||||
\(747\) | −0.204415 | −0.00747917 | ||||||||
\(748\) | −1.64536 | −0.0601605 | ||||||||
\(749\) | 44.3571 | 1.62077 | ||||||||
\(750\) | −31.5962 | −1.15373 | ||||||||
\(751\) | −1.42456 | −0.0519828 | −0.0259914 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259914 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(752\) | −59.5642 | −2.17208 | ||||||||
\(753\) | 35.4287 | 1.29109 | ||||||||
\(754\) | 78.4708 | 2.85774 | ||||||||
\(755\) | −23.9349 | −0.871080 | ||||||||
\(756\) | 10.3229 | 0.375439 | ||||||||
\(757\) | −36.6098 | −1.33061 | −0.665303 | − | 0.746574i | \(-0.731698\pi\) | ||||
−0.665303 | + | 0.746574i | \(0.731698\pi\) | |||||||
\(758\) | 14.1936 | 0.515536 | ||||||||
\(759\) | −3.96823 | −0.144038 | ||||||||
\(760\) | −7.75350 | −0.281249 | ||||||||
\(761\) | 43.5188 | 1.57755 | 0.788777 | − | 0.614679i | \(-0.210715\pi\) | ||||
0.788777 | + | 0.614679i | \(0.210715\pi\) | |||||||
\(762\) | 30.1289 | 1.09145 | ||||||||
\(763\) | 2.83994 | 0.102813 | ||||||||
\(764\) | −5.78953 | −0.209458 | ||||||||
\(765\) | 0.414021 | 0.0149690 | ||||||||
\(766\) | 7.89648 | 0.285311 | ||||||||
\(767\) | −23.9874 | −0.866135 | ||||||||
\(768\) | 24.4164 | 0.881052 | ||||||||
\(769\) | −6.95070 | −0.250649 | −0.125324 | − | 0.992116i | \(-0.539997\pi\) | ||||
−0.125324 | + | 0.992116i | \(0.539997\pi\) | |||||||
\(770\) | −12.4392 | −0.448278 | ||||||||
\(771\) | 23.6572 | 0.851992 | ||||||||
\(772\) | −4.45511 | −0.160343 | ||||||||
\(773\) | 1.98872 | 0.0715292 | 0.0357646 | − | 0.999360i | \(-0.488613\pi\) | ||||
0.0357646 | + | 0.999360i | \(0.488613\pi\) | |||||||
\(774\) | −0.675270 | −0.0242721 | ||||||||
\(775\) | −10.8496 | −0.389727 | ||||||||
\(776\) | 39.0342 | 1.40125 | ||||||||
\(777\) | 4.74479 | 0.170218 | ||||||||
\(778\) | 4.70130 | 0.168550 | ||||||||
\(779\) | −10.3221 | −0.369829 | ||||||||
\(780\) | −8.28154 | −0.296527 | ||||||||
\(781\) | 13.1550 | 0.470722 | ||||||||
\(782\) | 2.88167 | 0.103048 | ||||||||
\(783\) | 52.0216 | 1.85910 | ||||||||
\(784\) | −5.21585 | −0.186280 | ||||||||
\(785\) | 17.9044 | 0.639036 | ||||||||
\(786\) | 6.11504 | 0.218116 | ||||||||
\(787\) | 31.5429 | 1.12438 | 0.562192 | − | 0.827006i | \(-0.309958\pi\) | ||||
0.562192 | + | 0.827006i | \(0.309958\pi\) | |||||||
\(788\) | −6.76690 | −0.241061 | ||||||||
\(789\) | 26.2900 | 0.935950 | ||||||||
\(790\) | 20.6678 | 0.735327 | ||||||||
\(791\) | 21.1938 | 0.753564 | ||||||||
\(792\) | 0.816593 | 0.0290164 | ||||||||
\(793\) | 30.5187 | 1.08375 | ||||||||
\(794\) | −49.3206 | −1.75032 | ||||||||
\(795\) | −28.8000 | −1.02143 | ||||||||
\(796\) | −12.1905 | −0.432081 | ||||||||
\(797\) | 0.669871 | 0.0237280 | 0.0118640 | − | 0.999930i | \(-0.496223\pi\) | ||||
0.0118640 | + | 0.999930i | \(0.496223\pi\) | |||||||
\(798\) | −18.8106 | −0.665889 | ||||||||
\(799\) | −16.3168 | −0.577247 | ||||||||
\(800\) | 10.3625 | 0.366371 | ||||||||
\(801\) | −0.0955818 | −0.00337722 | ||||||||
\(802\) | 46.6945 | 1.64884 | ||||||||
\(803\) | 28.6965 | 1.01268 | ||||||||
\(804\) | −10.7993 | −0.380863 | ||||||||
\(805\) | 5.51592 | 0.194411 | ||||||||
\(806\) | −31.2079 | −1.09925 | ||||||||
\(807\) | −8.54514 | −0.300803 | ||||||||
\(808\) | −16.1830 | −0.569316 | ||||||||
\(809\) | −6.02851 | −0.211951 | −0.105976 | − | 0.994369i | \(-0.533797\pi\) | ||||
−0.105976 | + | 0.994369i | \(0.533797\pi\) | |||||||
\(810\) | −20.1688 | −0.708658 | ||||||||
\(811\) | 26.2163 | 0.920578 | 0.460289 | − | 0.887769i | \(-0.347746\pi\) | ||||
0.460289 | + | 0.887769i | \(0.347746\pi\) | |||||||
\(812\) | 18.6864 | 0.655764 | ||||||||
\(813\) | −31.0877 | −1.09029 | ||||||||
\(814\) | −2.96065 | −0.103771 | ||||||||
\(815\) | 7.47740 | 0.261922 | ||||||||
\(816\) | 10.9724 | 0.384111 | ||||||||
\(817\) | 4.79117 | 0.167622 | ||||||||
\(818\) | −3.86169 | −0.135021 | ||||||||
\(819\) | −2.92791 | −0.102309 | ||||||||
\(820\) | −4.27417 | −0.149261 | ||||||||
\(821\) | 29.2765 | 1.02176 | 0.510878 | − | 0.859653i | \(-0.329320\pi\) | ||||
0.510878 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(822\) | −22.0056 | −0.767533 | ||||||||
\(823\) | 31.3133 | 1.09151 | 0.545757 | − | 0.837944i | \(-0.316242\pi\) | ||||
0.545757 | + | 0.837944i | \(0.316242\pi\) | |||||||
\(824\) | −16.5743 | −0.577394 | ||||||||
\(825\) | −8.49741 | −0.295842 | ||||||||
\(826\) | −22.5609 | −0.784995 | ||||||||
\(827\) | 25.5755 | 0.889348 | 0.444674 | − | 0.895693i | \(-0.353320\pi\) | ||||
0.444674 | + | 0.895693i | \(0.353320\pi\) | |||||||
\(828\) | 0.185728 | 0.00645451 | ||||||||
\(829\) | 1.80238 | 0.0625991 | 0.0312995 | − | 0.999510i | \(-0.490035\pi\) | ||||
0.0312995 | + | 0.999510i | \(0.490035\pi\) | |||||||
\(830\) | 2.37201 | 0.0823336 | ||||||||
\(831\) | −15.0863 | −0.523337 | ||||||||
\(832\) | −18.5820 | −0.644215 | ||||||||
\(833\) | −1.42881 | −0.0495053 | ||||||||
\(834\) | 60.0461 | 2.07923 | ||||||||
\(835\) | −0.976080 | −0.0337786 | ||||||||
\(836\) | 2.97178 | 0.102781 | ||||||||
\(837\) | −20.6890 | −0.715116 | ||||||||
\(838\) | 45.6881 | 1.57827 | ||||||||
\(839\) | −23.5344 | −0.812498 | −0.406249 | − | 0.913762i | \(-0.633163\pi\) | ||||
−0.406249 | + | 0.913762i | \(0.633163\pi\) | |||||||
\(840\) | 15.1858 | 0.523960 | ||||||||
\(841\) | 65.1692 | 2.24721 | ||||||||
\(842\) | −45.7149 | −1.57544 | ||||||||
\(843\) | 22.6123 | 0.778809 | ||||||||
\(844\) | −4.62831 | −0.159313 | ||||||||
\(845\) | 16.8904 | 0.581049 | ||||||||
\(846\) | −4.15361 | −0.142804 | ||||||||
\(847\) | 21.9440 | 0.754005 | ||||||||
\(848\) | 57.0506 | 1.95913 | ||||||||
\(849\) | 35.1040 | 1.20477 | ||||||||
\(850\) | 6.17068 | 0.211653 | ||||||||
\(851\) | 1.31284 | 0.0450036 | ||||||||
\(852\) | 8.23726 | 0.282204 | ||||||||
\(853\) | −12.2079 | −0.417990 | −0.208995 | − | 0.977917i | \(-0.567019\pi\) | ||||
−0.208995 | + | 0.977917i | \(0.567019\pi\) | |||||||
\(854\) | 28.7039 | 0.982226 | ||||||||
\(855\) | −0.747786 | −0.0255737 | ||||||||
\(856\) | 33.7892 | 1.15489 | ||||||||
\(857\) | −34.3583 | −1.17366 | −0.586828 | − | 0.809711i | \(-0.699624\pi\) | ||||
−0.586828 | + | 0.809711i | \(0.699624\pi\) | |||||||
\(858\) | −24.4421 | −0.834441 | ||||||||
\(859\) | 11.1492 | 0.380404 | 0.190202 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190202 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(860\) | 1.98392 | 0.0676510 | ||||||||
\(861\) | 20.2167 | 0.688982 | ||||||||
\(862\) | −24.2848 | −0.827144 | ||||||||
\(863\) | −4.12069 | −0.140270 | −0.0701349 | − | 0.997538i | \(-0.522343\pi\) | ||||
−0.0701349 | + | 0.997538i | \(0.522343\pi\) | |||||||
\(864\) | 19.7603 | 0.672260 | ||||||||
\(865\) | 20.4919 | 0.696744 | ||||||||
\(866\) | 2.21113 | 0.0751373 | ||||||||
\(867\) | −25.3968 | −0.862519 | ||||||||
\(868\) | −7.43159 | −0.252245 | ||||||||
\(869\) | 15.4442 | 0.523908 | ||||||||
\(870\) | −39.2526 | −1.33079 | ||||||||
\(871\) | 47.1054 | 1.59611 | ||||||||
\(872\) | 2.16334 | 0.0732598 | ||||||||
\(873\) | 3.76465 | 0.127414 | ||||||||
\(874\) | −5.20473 | −0.176053 | ||||||||
\(875\) | 32.8191 | 1.10949 | ||||||||
\(876\) | 17.9689 | 0.607113 | ||||||||
\(877\) | −25.2253 | −0.851797 | −0.425898 | − | 0.904771i | \(-0.640042\pi\) | ||||
−0.425898 | + | 0.904771i | \(0.640042\pi\) | |||||||
\(878\) | −3.97722 | −0.134225 | ||||||||
\(879\) | 0.310628 | 0.0104772 | ||||||||
\(880\) | −13.1053 | −0.441779 | ||||||||
\(881\) | 38.0767 | 1.28284 | 0.641418 | − | 0.767192i | \(-0.278347\pi\) | ||||
0.641418 | + | 0.767192i | \(0.278347\pi\) | |||||||
\(882\) | −0.363719 | −0.0122470 | ||||||||
\(883\) | −40.7554 | −1.37153 | −0.685765 | − | 0.727823i | \(-0.740532\pi\) | ||||
−0.685765 | + | 0.727823i | \(0.740532\pi\) | |||||||
\(884\) | 4.49396 | 0.151148 | ||||||||
\(885\) | 11.9989 | 0.403340 | ||||||||
\(886\) | −32.2792 | −1.08444 | ||||||||
\(887\) | −1.36291 | −0.0457620 | −0.0228810 | − | 0.999738i | \(-0.507284\pi\) | ||||
−0.0228810 | + | 0.999738i | \(0.507284\pi\) | |||||||
\(888\) | 3.61436 | 0.121290 | ||||||||
\(889\) | −31.2950 | −1.04960 | ||||||||
\(890\) | 1.10912 | 0.0371777 | ||||||||
\(891\) | −15.0713 | −0.504908 | ||||||||
\(892\) | −2.48134 | −0.0830813 | ||||||||
\(893\) | 29.4707 | 0.986198 | ||||||||
\(894\) | −27.8897 | −0.932770 | ||||||||
\(895\) | −10.7645 | −0.359818 | ||||||||
\(896\) | −38.4135 | −1.28330 | ||||||||
\(897\) | 10.8384 | 0.361883 | ||||||||
\(898\) | 18.5522 | 0.619094 | ||||||||
\(899\) | −37.4511 | −1.24906 | ||||||||
\(900\) | 0.397711 | 0.0132570 | ||||||||
\(901\) | 15.6282 | 0.520652 | ||||||||
\(902\) | −12.6148 | −0.420027 | ||||||||
\(903\) | −9.38385 | −0.312275 | ||||||||
\(904\) | 16.1445 | 0.536957 | ||||||||
\(905\) | −6.68642 | −0.222264 | ||||||||
\(906\) | −44.2336 | −1.46956 | ||||||||
\(907\) | −37.9353 | −1.25962 | −0.629811 | − | 0.776748i | \(-0.716868\pi\) | ||||
−0.629811 | + | 0.776748i | \(0.716868\pi\) | |||||||
\(908\) | 12.3333 | 0.409294 | ||||||||
\(909\) | −1.56077 | −0.0517674 | ||||||||
\(910\) | 33.9750 | 1.12626 | ||||||||
\(911\) | 24.9675 | 0.827209 | 0.413605 | − | 0.910457i | \(-0.364270\pi\) | ||||
0.413605 | + | 0.910457i | \(0.364270\pi\) | |||||||
\(912\) | −19.8179 | −0.656235 | ||||||||
\(913\) | 1.77251 | 0.0586614 | ||||||||
\(914\) | −21.1123 | −0.698334 | ||||||||
\(915\) | −15.2660 | −0.504680 | ||||||||
\(916\) | −4.76599 | −0.157473 | ||||||||
\(917\) | −6.35171 | −0.209752 | ||||||||
\(918\) | 11.7669 | 0.388364 | ||||||||
\(919\) | 4.93453 | 0.162775 | 0.0813876 | − | 0.996683i | \(-0.474065\pi\) | ||||
0.0813876 | + | 0.996683i | \(0.474065\pi\) | |||||||
\(920\) | 4.20178 | 0.138528 | ||||||||
\(921\) | −41.6732 | −1.37318 | ||||||||
\(922\) | 21.3000 | 0.701479 | ||||||||
\(923\) | −35.9300 | −1.18265 | ||||||||
\(924\) | −5.82045 | −0.191479 | ||||||||
\(925\) | 2.81126 | 0.0924338 | ||||||||
\(926\) | −46.7696 | −1.53694 | ||||||||
\(927\) | −1.59851 | −0.0525019 | ||||||||
\(928\) | 35.7700 | 1.17421 | ||||||||
\(929\) | −33.6674 | −1.10459 | −0.552295 | − | 0.833649i | \(-0.686248\pi\) | ||||
−0.552295 | + | 0.833649i | \(0.686248\pi\) | |||||||
\(930\) | 15.6108 | 0.511897 | ||||||||
\(931\) | 2.58065 | 0.0845775 | ||||||||
\(932\) | 9.78269 | 0.320443 | ||||||||
\(933\) | −10.0954 | −0.330507 | ||||||||
\(934\) | −8.07526 | −0.264231 | ||||||||
\(935\) | −3.59002 | −0.117406 | ||||||||
\(936\) | −2.23035 | −0.0729011 | ||||||||
\(937\) | −9.86172 | −0.322168 | −0.161084 | − | 0.986941i | \(-0.551499\pi\) | ||||
−0.161084 | + | 0.986941i | \(0.551499\pi\) | |||||||
\(938\) | 44.3042 | 1.44658 | ||||||||
\(939\) | −26.8253 | −0.875410 | ||||||||
\(940\) | 12.2032 | 0.398023 | ||||||||
\(941\) | −6.24530 | −0.203591 | −0.101795 | − | 0.994805i | \(-0.532459\pi\) | ||||
−0.101795 | + | 0.994805i | \(0.532459\pi\) | |||||||
\(942\) | 33.0888 | 1.07809 | ||||||||
\(943\) | 5.59378 | 0.182158 | ||||||||
\(944\) | −23.7690 | −0.773615 | ||||||||
\(945\) | 22.5234 | 0.732688 | ||||||||
\(946\) | 5.85533 | 0.190373 | ||||||||
\(947\) | 31.0889 | 1.01025 | 0.505127 | − | 0.863045i | \(-0.331446\pi\) | ||||
0.505127 | + | 0.863045i | \(0.331446\pi\) | |||||||
\(948\) | 9.67070 | 0.314090 | ||||||||
\(949\) | −78.3783 | −2.54427 | ||||||||
\(950\) | −11.1452 | −0.361598 | ||||||||
\(951\) | −10.0650 | −0.326381 | ||||||||
\(952\) | −8.24053 | −0.267077 | ||||||||
\(953\) | −46.4637 | −1.50511 | −0.752553 | − | 0.658532i | \(-0.771178\pi\) | ||||
−0.752553 | + | 0.658532i | \(0.771178\pi\) | |||||||
\(954\) | 3.97834 | 0.128803 | ||||||||
\(955\) | −12.6322 | −0.408767 | ||||||||
\(956\) | −8.83999 | −0.285906 | ||||||||
\(957\) | −29.3319 | −0.948165 | ||||||||
\(958\) | −53.6936 | −1.73476 | ||||||||
\(959\) | 22.8573 | 0.738100 | ||||||||
\(960\) | 9.29506 | 0.299997 | ||||||||
\(961\) | −16.1057 | −0.519538 | ||||||||
\(962\) | 8.08637 | 0.260715 | ||||||||
\(963\) | 3.25880 | 0.105013 | ||||||||
\(964\) | 5.88226 | 0.189455 | ||||||||
\(965\) | −9.72060 | −0.312917 | ||||||||
\(966\) | 10.1938 | 0.327982 | ||||||||
\(967\) | −55.1039 | −1.77202 | −0.886011 | − | 0.463663i | \(-0.846535\pi\) | ||||
−0.886011 | + | 0.463663i | \(0.846535\pi\) | |||||||
\(968\) | 16.7160 | 0.537271 | ||||||||
\(969\) | −5.42884 | −0.174399 | ||||||||
\(970\) | −43.6845 | −1.40262 | ||||||||
\(971\) | 39.3443 | 1.26262 | 0.631310 | − | 0.775531i | \(-0.282518\pi\) | ||||
0.631310 | + | 0.775531i | \(0.282518\pi\) | |||||||
\(972\) | 1.46747 | 0.0470693 | ||||||||
\(973\) | −62.3701 | −1.99949 | ||||||||
\(974\) | −17.1865 | −0.550690 | ||||||||
\(975\) | 23.2088 | 0.743278 | ||||||||
\(976\) | 30.2409 | 0.967987 | ||||||||
\(977\) | 10.7406 | 0.343623 | 0.171811 | − | 0.985130i | \(-0.445038\pi\) | ||||
0.171811 | + | 0.985130i | \(0.445038\pi\) | |||||||
\(978\) | 13.8188 | 0.441877 | ||||||||
\(979\) | 0.828798 | 0.0264885 | ||||||||
\(980\) | 1.06859 | 0.0341349 | ||||||||
\(981\) | 0.208643 | 0.00666146 | ||||||||
\(982\) | −0.877329 | −0.0279967 | ||||||||
\(983\) | 6.02893 | 0.192293 | 0.0961465 | − | 0.995367i | \(-0.469348\pi\) | ||||
0.0961465 | + | 0.995367i | \(0.469348\pi\) | |||||||
\(984\) | 15.4001 | 0.490939 | ||||||||
\(985\) | −14.7647 | −0.470442 | ||||||||
\(986\) | 21.3003 | 0.678340 | ||||||||
\(987\) | −57.7204 | −1.83726 | ||||||||
\(988\) | −8.11678 | −0.258229 | ||||||||
\(989\) | −2.59643 | −0.0825617 | ||||||||
\(990\) | −0.913876 | −0.0290449 | ||||||||
\(991\) | −41.9959 | −1.33404 | −0.667021 | − | 0.745039i | \(-0.732431\pi\) | ||||
−0.667021 | + | 0.745039i | \(0.732431\pi\) | |||||||
\(992\) | −14.2257 | −0.451668 | ||||||||
\(993\) | 42.8002 | 1.35822 | ||||||||
\(994\) | −33.7933 | −1.07186 | ||||||||
\(995\) | −26.5984 | −0.843227 | ||||||||
\(996\) | 1.10989 | 0.0351682 | ||||||||
\(997\) | 7.27669 | 0.230455 | 0.115228 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115228 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(998\) | −23.7800 | −0.752742 | ||||||||
\(999\) | 5.36079 | 0.169608 |
(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 | 4033.2.a.d.1.64 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.64 | ✓ | 79 | 1.1 | even | 1 | trivial |