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: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75814 | −1.95030 | −0.975148 | − | 0.221553i | \(-0.928888\pi\) | ||||
−0.975148 | + | 0.221553i | \(0.928888\pi\) | |||||||
\(3\) | 1.25704 | 0.725751 | 0.362875 | − | 0.931838i | \(-0.381795\pi\) | ||||
0.362875 | + | 0.931838i | \(0.381795\pi\) | |||||||
\(4\) | 5.60732 | 2.80366 | ||||||||
\(5\) | 1.25507 | 0.561286 | 0.280643 | − | 0.959812i | \(-0.409452\pi\) | ||||
0.280643 | + | 0.959812i | \(0.409452\pi\) | |||||||
\(6\) | −3.46708 | −1.41543 | ||||||||
\(7\) | 2.38515 | 0.901501 | 0.450751 | − | 0.892650i | \(-0.351156\pi\) | ||||
0.450751 | + | 0.892650i | \(0.351156\pi\) | |||||||
\(8\) | −9.94947 | −3.51767 | ||||||||
\(9\) | −1.41986 | −0.473286 | ||||||||
\(10\) | −3.46166 | −1.09467 | ||||||||
\(11\) | −4.34393 | −1.30975 | −0.654873 | − | 0.755739i | \(-0.727278\pi\) | ||||
−0.654873 | + | 0.755739i | \(0.727278\pi\) | |||||||
\(12\) | 7.04861 | 2.03476 | ||||||||
\(13\) | −4.19052 | −1.16224 | −0.581121 | − | 0.813818i | \(-0.697386\pi\) | ||||
−0.581121 | + | 0.813818i | \(0.697386\pi\) | |||||||
\(14\) | −6.57856 | −1.75820 | ||||||||
\(15\) | 1.57767 | 0.407353 | ||||||||
\(16\) | 16.2274 | 4.05684 | ||||||||
\(17\) | 6.23808 | 1.51296 | 0.756478 | − | 0.654019i | \(-0.226918\pi\) | ||||
0.756478 | + | 0.654019i | \(0.226918\pi\) | |||||||
\(18\) | 3.91616 | 0.923048 | ||||||||
\(19\) | −8.62095 | −1.97778 | −0.988891 | − | 0.148641i | \(-0.952510\pi\) | ||||
−0.988891 | + | 0.148641i | \(0.952510\pi\) | |||||||
\(20\) | 7.03759 | 1.57365 | ||||||||
\(21\) | 2.99822 | 0.654265 | ||||||||
\(22\) | 11.9812 | 2.55439 | ||||||||
\(23\) | 1.33700 | 0.278784 | 0.139392 | − | 0.990237i | \(-0.455485\pi\) | ||||
0.139392 | + | 0.990237i | \(0.455485\pi\) | |||||||
\(24\) | −12.5069 | −2.55295 | ||||||||
\(25\) | −3.42479 | −0.684959 | ||||||||
\(26\) | 11.5580 | 2.26671 | ||||||||
\(27\) | −5.55593 | −1.06924 | ||||||||
\(28\) | 13.3743 | 2.52750 | ||||||||
\(29\) | 8.63999 | 1.60441 | 0.802203 | − | 0.597051i | \(-0.203661\pi\) | ||||
0.802203 | + | 0.597051i | \(0.203661\pi\) | |||||||
\(30\) | −4.35144 | −0.794460 | ||||||||
\(31\) | 2.64779 | 0.475557 | 0.237778 | − | 0.971319i | \(-0.423581\pi\) | ||||
0.237778 | + | 0.971319i | \(0.423581\pi\) | |||||||
\(32\) | −24.8583 | −4.39437 | ||||||||
\(33\) | −5.46049 | −0.950549 | ||||||||
\(34\) | −17.2055 | −2.95072 | ||||||||
\(35\) | 2.99353 | 0.506000 | ||||||||
\(36\) | −7.96159 | −1.32693 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 23.7778 | 3.85726 | ||||||||
\(39\) | −5.26764 | −0.843497 | ||||||||
\(40\) | −12.4873 | −1.97442 | ||||||||
\(41\) | 5.54332 | 0.865722 | 0.432861 | − | 0.901461i | \(-0.357504\pi\) | ||||
0.432861 | + | 0.901461i | \(0.357504\pi\) | |||||||
\(42\) | −8.26950 | −1.27601 | ||||||||
\(43\) | 0.869458 | 0.132591 | 0.0662956 | − | 0.997800i | \(-0.478882\pi\) | ||||
0.0662956 | + | 0.997800i | \(0.478882\pi\) | |||||||
\(44\) | −24.3578 | −3.67208 | ||||||||
\(45\) | −1.78202 | −0.265648 | ||||||||
\(46\) | −3.68764 | −0.543712 | ||||||||
\(47\) | 4.50020 | 0.656421 | 0.328211 | − | 0.944605i | \(-0.393554\pi\) | ||||
0.328211 | + | 0.944605i | \(0.393554\pi\) | |||||||
\(48\) | 20.3984 | 2.94425 | ||||||||
\(49\) | −1.31107 | −0.187295 | ||||||||
\(50\) | 9.44604 | 1.33587 | ||||||||
\(51\) | 7.84150 | 1.09803 | ||||||||
\(52\) | −23.4976 | −3.25853 | ||||||||
\(53\) | −9.77876 | −1.34322 | −0.671608 | − | 0.740907i | \(-0.734396\pi\) | ||||
−0.671608 | + | 0.740907i | \(0.734396\pi\) | |||||||
\(54\) | 15.3240 | 2.08533 | ||||||||
\(55\) | −5.45195 | −0.735141 | ||||||||
\(56\) | −23.7310 | −3.17118 | ||||||||
\(57\) | −10.8369 | −1.43538 | ||||||||
\(58\) | −23.8303 | −3.12907 | ||||||||
\(59\) | 7.40026 | 0.963432 | 0.481716 | − | 0.876327i | \(-0.340014\pi\) | ||||
0.481716 | + | 0.876327i | \(0.340014\pi\) | |||||||
\(60\) | 8.84651 | 1.14208 | ||||||||
\(61\) | 4.66071 | 0.596743 | 0.298372 | − | 0.954450i | \(-0.403557\pi\) | ||||
0.298372 | + | 0.954450i | \(0.403557\pi\) | |||||||
\(62\) | −7.30296 | −0.927476 | ||||||||
\(63\) | −3.38657 | −0.426668 | ||||||||
\(64\) | 36.1079 | 4.51349 | ||||||||
\(65\) | −5.25941 | −0.652349 | ||||||||
\(66\) | 15.0608 | 1.85385 | ||||||||
\(67\) | −1.17172 | −0.143148 | −0.0715741 | − | 0.997435i | \(-0.522802\pi\) | ||||
−0.0715741 | + | 0.997435i | \(0.522802\pi\) | |||||||
\(68\) | 34.9789 | 4.24181 | ||||||||
\(69\) | 1.68066 | 0.202328 | ||||||||
\(70\) | −8.25658 | −0.986850 | ||||||||
\(71\) | 14.2401 | 1.68999 | 0.844997 | − | 0.534771i | \(-0.179602\pi\) | ||||
0.844997 | + | 0.534771i | \(0.179602\pi\) | |||||||
\(72\) | 14.1268 | 1.66486 | ||||||||
\(73\) | 5.38858 | 0.630686 | 0.315343 | − | 0.948978i | \(-0.397880\pi\) | ||||
0.315343 | + | 0.948978i | \(0.397880\pi\) | |||||||
\(74\) | 2.75814 | 0.320627 | ||||||||
\(75\) | −4.30509 | −0.497109 | ||||||||
\(76\) | −48.3404 | −5.54502 | ||||||||
\(77\) | −10.3609 | −1.18074 | ||||||||
\(78\) | 14.5289 | 1.64507 | ||||||||
\(79\) | 7.54515 | 0.848896 | 0.424448 | − | 0.905452i | \(-0.360468\pi\) | ||||
0.424448 | + | 0.905452i | \(0.360468\pi\) | |||||||
\(80\) | 20.3665 | 2.27705 | ||||||||
\(81\) | −2.72443 | −0.302715 | ||||||||
\(82\) | −15.2892 | −1.68841 | ||||||||
\(83\) | 5.13075 | 0.563172 | 0.281586 | − | 0.959536i | \(-0.409139\pi\) | ||||
0.281586 | + | 0.959536i | \(0.409139\pi\) | |||||||
\(84\) | 16.8120 | 1.83434 | ||||||||
\(85\) | 7.82924 | 0.849201 | ||||||||
\(86\) | −2.39808 | −0.258592 | ||||||||
\(87\) | 10.8608 | 1.16440 | ||||||||
\(88\) | 43.2198 | 4.60725 | ||||||||
\(89\) | 18.6815 | 1.98024 | 0.990119 | − | 0.140229i | \(-0.0447840\pi\) | ||||
0.990119 | + | 0.140229i | \(0.0447840\pi\) | |||||||
\(90\) | 4.91506 | 0.518093 | ||||||||
\(91\) | −9.99501 | −1.04776 | ||||||||
\(92\) | 7.49700 | 0.781616 | ||||||||
\(93\) | 3.32837 | 0.345136 | ||||||||
\(94\) | −12.4122 | −1.28022 | ||||||||
\(95\) | −10.8199 | −1.11010 | ||||||||
\(96\) | −31.2478 | −3.18922 | ||||||||
\(97\) | 4.65603 | 0.472748 | 0.236374 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236374 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(98\) | 3.61610 | 0.365281 | ||||||||
\(99\) | 6.16776 | 0.619884 | ||||||||
\(100\) | −19.2039 | −1.92039 | ||||||||
\(101\) | −0.116683 | −0.0116104 | −0.00580521 | − | 0.999983i | \(-0.501848\pi\) | ||||
−0.00580521 | + | 0.999983i | \(0.501848\pi\) | |||||||
\(102\) | −21.6279 | −2.14148 | ||||||||
\(103\) | 14.2705 | 1.40611 | 0.703057 | − | 0.711133i | \(-0.251818\pi\) | ||||
0.703057 | + | 0.711133i | \(0.251818\pi\) | |||||||
\(104\) | 41.6934 | 4.08838 | ||||||||
\(105\) | 3.76298 | 0.367230 | ||||||||
\(106\) | 26.9711 | 2.61967 | ||||||||
\(107\) | 2.82254 | 0.272865 | 0.136432 | − | 0.990649i | \(-0.456436\pi\) | ||||
0.136432 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(108\) | −31.1538 | −2.99778 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 15.0372 | 1.43374 | ||||||||
\(111\) | −1.25704 | −0.119313 | ||||||||
\(112\) | 38.7047 | 3.65725 | ||||||||
\(113\) | 19.0646 | 1.79345 | 0.896725 | − | 0.442588i | \(-0.145940\pi\) | ||||
0.896725 | + | 0.442588i | \(0.145940\pi\) | |||||||
\(114\) | 29.8895 | 2.79941 | ||||||||
\(115\) | 1.67804 | 0.156478 | ||||||||
\(116\) | 48.4472 | 4.49821 | ||||||||
\(117\) | 5.94994 | 0.550072 | ||||||||
\(118\) | −20.4109 | −1.87898 | ||||||||
\(119\) | 14.8787 | 1.36393 | ||||||||
\(120\) | −15.6970 | −1.43293 | ||||||||
\(121\) | 7.86976 | 0.715432 | ||||||||
\(122\) | −12.8549 | −1.16383 | ||||||||
\(123\) | 6.96816 | 0.628298 | ||||||||
\(124\) | 14.8470 | 1.33330 | ||||||||
\(125\) | −10.5737 | −0.945743 | ||||||||
\(126\) | 9.34062 | 0.832129 | ||||||||
\(127\) | −0.232971 | −0.0206728 | −0.0103364 | − | 0.999947i | \(-0.503290\pi\) | ||||
−0.0103364 | + | 0.999947i | \(0.503290\pi\) | |||||||
\(128\) | −49.8740 | −4.40828 | ||||||||
\(129\) | 1.09294 | 0.0962281 | ||||||||
\(130\) | 14.5062 | 1.27227 | ||||||||
\(131\) | −3.82136 | −0.333874 | −0.166937 | − | 0.985968i | \(-0.553388\pi\) | ||||
−0.166937 | + | 0.985968i | \(0.553388\pi\) | |||||||
\(132\) | −30.6187 | −2.66501 | ||||||||
\(133\) | −20.5623 | −1.78297 | ||||||||
\(134\) | 3.23176 | 0.279182 | ||||||||
\(135\) | −6.97309 | −0.600148 | ||||||||
\(136\) | −62.0656 | −5.32208 | ||||||||
\(137\) | −4.97380 | −0.424941 | −0.212470 | − | 0.977168i | \(-0.568151\pi\) | ||||
−0.212470 | + | 0.977168i | \(0.568151\pi\) | |||||||
\(138\) | −4.63550 | −0.394600 | ||||||||
\(139\) | −0.185802 | −0.0157595 | −0.00787977 | − | 0.999969i | \(-0.502508\pi\) | ||||
−0.00787977 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(140\) | 16.7857 | 1.41865 | ||||||||
\(141\) | 5.65691 | 0.476398 | ||||||||
\(142\) | −39.2763 | −3.29599 | ||||||||
\(143\) | 18.2033 | 1.52224 | ||||||||
\(144\) | −23.0405 | −1.92004 | ||||||||
\(145\) | 10.8438 | 0.900530 | ||||||||
\(146\) | −14.8624 | −1.23002 | ||||||||
\(147\) | −1.64806 | −0.135930 | ||||||||
\(148\) | −5.60732 | −0.460919 | ||||||||
\(149\) | 14.1196 | 1.15672 | 0.578359 | − | 0.815782i | \(-0.303693\pi\) | ||||
0.578359 | + | 0.815782i | \(0.303693\pi\) | |||||||
\(150\) | 11.8740 | 0.969511 | ||||||||
\(151\) | 3.38384 | 0.275373 | 0.137686 | − | 0.990476i | \(-0.456033\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456033\pi\) | |||||||
\(152\) | 85.7739 | 6.95718 | ||||||||
\(153\) | −8.85718 | −0.716061 | ||||||||
\(154\) | 28.5768 | 2.30279 | ||||||||
\(155\) | 3.32316 | 0.266923 | ||||||||
\(156\) | −29.5373 | −2.36488 | ||||||||
\(157\) | 17.0998 | 1.36472 | 0.682358 | − | 0.731018i | \(-0.260954\pi\) | ||||
0.682358 | + | 0.731018i | \(0.260954\pi\) | |||||||
\(158\) | −20.8106 | −1.65560 | ||||||||
\(159\) | −12.2923 | −0.974840 | ||||||||
\(160\) | −31.1990 | −2.46650 | ||||||||
\(161\) | 3.18895 | 0.251325 | ||||||||
\(162\) | 7.51436 | 0.590384 | ||||||||
\(163\) | 23.7820 | 1.86275 | 0.931375 | − | 0.364061i | \(-0.118610\pi\) | ||||
0.931375 | + | 0.364061i | \(0.118610\pi\) | |||||||
\(164\) | 31.0832 | 2.42719 | ||||||||
\(165\) | −6.85331 | −0.533529 | ||||||||
\(166\) | −14.1513 | −1.09835 | ||||||||
\(167\) | 11.0745 | 0.856972 | 0.428486 | − | 0.903548i | \(-0.359047\pi\) | ||||
0.428486 | + | 0.903548i | \(0.359047\pi\) | |||||||
\(168\) | −29.8307 | −2.30149 | ||||||||
\(169\) | 4.56045 | 0.350804 | ||||||||
\(170\) | −21.5941 | −1.65619 | ||||||||
\(171\) | 12.2405 | 0.936056 | ||||||||
\(172\) | 4.87533 | 0.371740 | ||||||||
\(173\) | 4.24058 | 0.322406 | 0.161203 | − | 0.986921i | \(-0.448463\pi\) | ||||
0.161203 | + | 0.986921i | \(0.448463\pi\) | |||||||
\(174\) | −29.9555 | −2.27092 | ||||||||
\(175\) | −8.16864 | −0.617491 | ||||||||
\(176\) | −70.4906 | −5.31343 | ||||||||
\(177\) | 9.30241 | 0.699212 | ||||||||
\(178\) | −51.5262 | −3.86205 | ||||||||
\(179\) | 18.3809 | 1.37385 | 0.686927 | − | 0.726726i | \(-0.258959\pi\) | ||||
0.686927 | + | 0.726726i | \(0.258959\pi\) | |||||||
\(180\) | −9.99237 | −0.744787 | ||||||||
\(181\) | −9.67304 | −0.718991 | −0.359496 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359496 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(182\) | 27.5676 | 2.04345 | ||||||||
\(183\) | 5.85869 | 0.433087 | ||||||||
\(184\) | −13.3025 | −0.980671 | ||||||||
\(185\) | −1.25507 | −0.0922748 | ||||||||
\(186\) | −9.18009 | −0.673117 | ||||||||
\(187\) | −27.0978 | −1.98159 | ||||||||
\(188\) | 25.2340 | 1.84038 | ||||||||
\(189\) | −13.2517 | −0.963920 | ||||||||
\(190\) | 29.8428 | 2.16503 | ||||||||
\(191\) | −10.5585 | −0.763989 | −0.381995 | − | 0.924165i | \(-0.624763\pi\) | ||||
−0.381995 | + | 0.924165i | \(0.624763\pi\) | |||||||
\(192\) | 45.3890 | 3.27567 | ||||||||
\(193\) | −26.1904 | −1.88523 | −0.942613 | − | 0.333887i | \(-0.891639\pi\) | ||||
−0.942613 | + | 0.333887i | \(0.891639\pi\) | |||||||
\(194\) | −12.8420 | −0.921999 | ||||||||
\(195\) | −6.61127 | −0.473443 | ||||||||
\(196\) | −7.35157 | −0.525112 | ||||||||
\(197\) | −15.6977 | −1.11842 | −0.559208 | − | 0.829027i | \(-0.688895\pi\) | ||||
−0.559208 | + | 0.829027i | \(0.688895\pi\) | |||||||
\(198\) | −17.0115 | −1.20896 | ||||||||
\(199\) | 0.0502232 | 0.00356023 | 0.00178012 | − | 0.999998i | \(-0.499433\pi\) | ||||
0.00178012 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(200\) | 34.0749 | 2.40946 | ||||||||
\(201\) | −1.47289 | −0.103890 | ||||||||
\(202\) | 0.321828 | 0.0226438 | ||||||||
\(203\) | 20.6077 | 1.44637 | ||||||||
\(204\) | 43.9698 | 3.07850 | ||||||||
\(205\) | 6.95727 | 0.485917 | ||||||||
\(206\) | −39.3600 | −2.74234 | ||||||||
\(207\) | −1.89835 | −0.131945 | ||||||||
\(208\) | −68.0011 | −4.71502 | ||||||||
\(209\) | 37.4488 | 2.59039 | ||||||||
\(210\) | −10.3788 | −0.716207 | ||||||||
\(211\) | −11.7141 | −0.806435 | −0.403218 | − | 0.915104i | \(-0.632108\pi\) | ||||
−0.403218 | + | 0.915104i | \(0.632108\pi\) | |||||||
\(212\) | −54.8326 | −3.76592 | ||||||||
\(213\) | 17.9004 | 1.22651 | ||||||||
\(214\) | −7.78494 | −0.532167 | ||||||||
\(215\) | 1.09123 | 0.0744215 | ||||||||
\(216\) | 55.2785 | 3.76123 | ||||||||
\(217\) | 6.31536 | 0.428715 | ||||||||
\(218\) | −2.75814 | −0.186805 | ||||||||
\(219\) | 6.77365 | 0.457721 | ||||||||
\(220\) | −30.5708 | −2.06108 | ||||||||
\(221\) | −26.1408 | −1.75842 | ||||||||
\(222\) | 3.46708 | 0.232695 | ||||||||
\(223\) | 18.4652 | 1.23652 | 0.618259 | − | 0.785974i | \(-0.287838\pi\) | ||||
0.618259 | + | 0.785974i | \(0.287838\pi\) | |||||||
\(224\) | −59.2908 | −3.96153 | ||||||||
\(225\) | 4.86272 | 0.324181 | ||||||||
\(226\) | −52.5829 | −3.49776 | ||||||||
\(227\) | −16.8565 | −1.11881 | −0.559404 | − | 0.828895i | \(-0.688970\pi\) | ||||
−0.559404 | + | 0.828895i | \(0.688970\pi\) | |||||||
\(228\) | −60.7657 | −4.02431 | ||||||||
\(229\) | −18.7728 | −1.24054 | −0.620271 | − | 0.784388i | \(-0.712977\pi\) | ||||
−0.620271 | + | 0.784388i | \(0.712977\pi\) | |||||||
\(230\) | −4.62825 | −0.305178 | ||||||||
\(231\) | −13.0241 | −0.856921 | ||||||||
\(232\) | −85.9633 | −5.64377 | ||||||||
\(233\) | 10.8932 | 0.713634 | 0.356817 | − | 0.934174i | \(-0.383862\pi\) | ||||
0.356817 | + | 0.934174i | \(0.383862\pi\) | |||||||
\(234\) | −16.4107 | −1.07280 | ||||||||
\(235\) | 5.64807 | 0.368440 | ||||||||
\(236\) | 41.4956 | 2.70113 | ||||||||
\(237\) | 9.48454 | 0.616087 | ||||||||
\(238\) | −41.0376 | −2.66007 | ||||||||
\(239\) | 3.78859 | 0.245063 | 0.122532 | − | 0.992465i | \(-0.460899\pi\) | ||||
0.122532 | + | 0.992465i | \(0.460899\pi\) | |||||||
\(240\) | 25.6015 | 1.65257 | ||||||||
\(241\) | −13.2201 | −0.851579 | −0.425789 | − | 0.904822i | \(-0.640004\pi\) | ||||
−0.425789 | + | 0.904822i | \(0.640004\pi\) | |||||||
\(242\) | −21.7059 | −1.39531 | ||||||||
\(243\) | 13.2431 | 0.849543 | ||||||||
\(244\) | 26.1341 | 1.67306 | ||||||||
\(245\) | −1.64548 | −0.105126 | ||||||||
\(246\) | −19.2191 | −1.22537 | ||||||||
\(247\) | 36.1263 | 2.29866 | ||||||||
\(248\) | −26.3441 | −1.67285 | ||||||||
\(249\) | 6.44954 | 0.408723 | ||||||||
\(250\) | 29.1638 | 1.84448 | ||||||||
\(251\) | 20.4228 | 1.28908 | 0.644538 | − | 0.764572i | \(-0.277050\pi\) | ||||
0.644538 | + | 0.764572i | \(0.277050\pi\) | |||||||
\(252\) | −18.9896 | −1.19623 | ||||||||
\(253\) | −5.80785 | −0.365137 | ||||||||
\(254\) | 0.642566 | 0.0403182 | ||||||||
\(255\) | 9.84165 | 0.616308 | ||||||||
\(256\) | 65.3433 | 4.08396 | ||||||||
\(257\) | −18.0816 | −1.12790 | −0.563950 | − | 0.825809i | \(-0.690719\pi\) | ||||
−0.563950 | + | 0.825809i | \(0.690719\pi\) | |||||||
\(258\) | −3.01448 | −0.187673 | ||||||||
\(259\) | −2.38515 | −0.148206 | ||||||||
\(260\) | −29.4912 | −1.82896 | ||||||||
\(261\) | −12.2676 | −0.759343 | ||||||||
\(262\) | 10.5398 | 0.651153 | ||||||||
\(263\) | 6.03079 | 0.371874 | 0.185937 | − | 0.982562i | \(-0.440468\pi\) | ||||
0.185937 | + | 0.982562i | \(0.440468\pi\) | |||||||
\(264\) | 54.3289 | 3.34371 | ||||||||
\(265\) | −12.2730 | −0.753927 | ||||||||
\(266\) | 56.7135 | 3.47733 | ||||||||
\(267\) | 23.4834 | 1.43716 | ||||||||
\(268\) | −6.57020 | −0.401339 | ||||||||
\(269\) | −1.57224 | −0.0958611 | −0.0479305 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479305 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(270\) | 19.2327 | 1.17047 | ||||||||
\(271\) | −25.9927 | −1.57895 | −0.789473 | − | 0.613785i | \(-0.789646\pi\) | ||||
−0.789473 | + | 0.613785i | \(0.789646\pi\) | |||||||
\(272\) | 101.228 | 6.13782 | ||||||||
\(273\) | −12.5641 | −0.760414 | ||||||||
\(274\) | 13.7184 | 0.828761 | ||||||||
\(275\) | 14.8771 | 0.897121 | ||||||||
\(276\) | 9.42401 | 0.567259 | ||||||||
\(277\) | 15.3266 | 0.920888 | 0.460444 | − | 0.887689i | \(-0.347690\pi\) | ||||
0.460444 | + | 0.887689i | \(0.347690\pi\) | |||||||
\(278\) | 0.512468 | 0.0307358 | ||||||||
\(279\) | −3.75948 | −0.225074 | ||||||||
\(280\) | −29.7841 | −1.77994 | ||||||||
\(281\) | −24.7496 | −1.47644 | −0.738218 | − | 0.674563i | \(-0.764332\pi\) | ||||
−0.738218 | + | 0.674563i | \(0.764332\pi\) | |||||||
\(282\) | −15.6025 | −0.929118 | ||||||||
\(283\) | 11.3790 | 0.676410 | 0.338205 | − | 0.941073i | \(-0.390180\pi\) | ||||
0.338205 | + | 0.941073i | \(0.390180\pi\) | |||||||
\(284\) | 79.8490 | 4.73817 | ||||||||
\(285\) | −13.6010 | −0.805657 | ||||||||
\(286\) | −50.2073 | −2.96882 | ||||||||
\(287\) | 13.2216 | 0.780449 | ||||||||
\(288\) | 35.2953 | 2.07979 | ||||||||
\(289\) | 21.9137 | 1.28904 | ||||||||
\(290\) | −29.9087 | −1.75630 | ||||||||
\(291\) | 5.85280 | 0.343097 | ||||||||
\(292\) | 30.2155 | 1.76823 | ||||||||
\(293\) | −18.9512 | −1.10714 | −0.553569 | − | 0.832803i | \(-0.686735\pi\) | ||||
−0.553569 | + | 0.832803i | \(0.686735\pi\) | |||||||
\(294\) | 4.54558 | 0.265103 | ||||||||
\(295\) | 9.28787 | 0.540761 | ||||||||
\(296\) | 9.94947 | 0.578301 | ||||||||
\(297\) | 24.1346 | 1.40043 | ||||||||
\(298\) | −38.9437 | −2.25595 | ||||||||
\(299\) | −5.60274 | −0.324015 | ||||||||
\(300\) | −24.1400 | −1.39372 | ||||||||
\(301\) | 2.07379 | 0.119531 | ||||||||
\(302\) | −9.33308 | −0.537059 | ||||||||
\(303\) | −0.146675 | −0.00842627 | ||||||||
\(304\) | −139.895 | −8.02355 | ||||||||
\(305\) | 5.84953 | 0.334943 | ||||||||
\(306\) | 24.4293 | 1.39653 | ||||||||
\(307\) | −4.17983 | −0.238555 | −0.119278 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119278 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(308\) | −58.0970 | −3.31038 | ||||||||
\(309\) | 17.9386 | 1.02049 | ||||||||
\(310\) | −9.16574 | −0.520579 | ||||||||
\(311\) | −23.1985 | −1.31547 | −0.657734 | − | 0.753250i | \(-0.728485\pi\) | ||||
−0.657734 | + | 0.753250i | \(0.728485\pi\) | |||||||
\(312\) | 52.4102 | 2.96714 | ||||||||
\(313\) | 20.3327 | 1.14927 | 0.574637 | − | 0.818408i | \(-0.305143\pi\) | ||||
0.574637 | + | 0.818408i | \(0.305143\pi\) | |||||||
\(314\) | −47.1637 | −2.66160 | ||||||||
\(315\) | −4.25039 | −0.239482 | ||||||||
\(316\) | 42.3081 | 2.38001 | ||||||||
\(317\) | −23.6398 | −1.32775 | −0.663873 | − | 0.747845i | \(-0.731088\pi\) | ||||
−0.663873 | + | 0.747845i | \(0.731088\pi\) | |||||||
\(318\) | 33.9037 | 1.90123 | ||||||||
\(319\) | −37.5315 | −2.10136 | ||||||||
\(320\) | 45.3181 | 2.53336 | ||||||||
\(321\) | 3.54803 | 0.198032 | ||||||||
\(322\) | −8.79556 | −0.490158 | ||||||||
\(323\) | −53.7782 | −2.99230 | ||||||||
\(324\) | −15.2768 | −0.848709 | ||||||||
\(325\) | 14.3517 | 0.796087 | ||||||||
\(326\) | −65.5940 | −3.63292 | ||||||||
\(327\) | 1.25704 | 0.0695143 | ||||||||
\(328\) | −55.1531 | −3.04532 | ||||||||
\(329\) | 10.7336 | 0.591765 | ||||||||
\(330\) | 18.9024 | 1.04054 | ||||||||
\(331\) | 27.4345 | 1.50794 | 0.753969 | − | 0.656910i | \(-0.228137\pi\) | ||||
0.753969 | + | 0.656910i | \(0.228137\pi\) | |||||||
\(332\) | 28.7697 | 1.57894 | ||||||||
\(333\) | 1.41986 | 0.0778077 | ||||||||
\(334\) | −30.5450 | −1.67135 | ||||||||
\(335\) | −1.47059 | −0.0803470 | ||||||||
\(336\) | 48.6532 | 2.65425 | ||||||||
\(337\) | −6.73198 | −0.366714 | −0.183357 | − | 0.983046i | \(-0.558696\pi\) | ||||
−0.183357 | + | 0.983046i | \(0.558696\pi\) | |||||||
\(338\) | −12.5784 | −0.684172 | ||||||||
\(339\) | 23.9650 | 1.30160 | ||||||||
\(340\) | 43.9010 | 2.38087 | ||||||||
\(341\) | −11.5018 | −0.622858 | ||||||||
\(342\) | −33.7610 | −1.82559 | ||||||||
\(343\) | −19.8231 | −1.07035 | ||||||||
\(344\) | −8.65065 | −0.466412 | ||||||||
\(345\) | 2.10935 | 0.113564 | ||||||||
\(346\) | −11.6961 | −0.628787 | ||||||||
\(347\) | 16.7341 | 0.898334 | 0.449167 | − | 0.893448i | \(-0.351721\pi\) | ||||
0.449167 | + | 0.893448i | \(0.351721\pi\) | |||||||
\(348\) | 60.8999 | 3.26458 | ||||||||
\(349\) | −21.8942 | −1.17197 | −0.585986 | − | 0.810321i | \(-0.699293\pi\) | ||||
−0.585986 | + | 0.810321i | \(0.699293\pi\) | |||||||
\(350\) | 22.5302 | 1.20429 | ||||||||
\(351\) | 23.2822 | 1.24271 | ||||||||
\(352\) | 107.983 | 5.75551 | ||||||||
\(353\) | 2.21935 | 0.118124 | 0.0590620 | − | 0.998254i | \(-0.481189\pi\) | ||||
0.0590620 | + | 0.998254i | \(0.481189\pi\) | |||||||
\(354\) | −25.6573 | −1.36367 | ||||||||
\(355\) | 17.8724 | 0.948569 | ||||||||
\(356\) | 104.753 | 5.55191 | ||||||||
\(357\) | 18.7031 | 0.989875 | ||||||||
\(358\) | −50.6971 | −2.67943 | ||||||||
\(359\) | −16.8065 | −0.887014 | −0.443507 | − | 0.896271i | \(-0.646266\pi\) | ||||
−0.443507 | + | 0.896271i | \(0.646266\pi\) | |||||||
\(360\) | 17.7302 | 0.934463 | ||||||||
\(361\) | 55.3208 | 2.91162 | ||||||||
\(362\) | 26.6796 | 1.40225 | ||||||||
\(363\) | 9.89258 | 0.519226 | ||||||||
\(364\) | −56.0452 | −2.93757 | ||||||||
\(365\) | 6.76306 | 0.353995 | ||||||||
\(366\) | −16.1591 | −0.844648 | ||||||||
\(367\) | 31.7140 | 1.65546 | 0.827728 | − | 0.561129i | \(-0.189633\pi\) | ||||
0.827728 | + | 0.561129i | \(0.189633\pi\) | |||||||
\(368\) | 21.6960 | 1.13098 | ||||||||
\(369\) | −7.87073 | −0.409734 | ||||||||
\(370\) | 3.46166 | 0.179963 | ||||||||
\(371\) | −23.3238 | −1.21091 | ||||||||
\(372\) | 18.6632 | 0.967642 | ||||||||
\(373\) | 6.16915 | 0.319426 | 0.159713 | − | 0.987163i | \(-0.448943\pi\) | ||||
0.159713 | + | 0.987163i | \(0.448943\pi\) | |||||||
\(374\) | 74.7394 | 3.86468 | ||||||||
\(375\) | −13.2916 | −0.686374 | ||||||||
\(376\) | −44.7746 | −2.30907 | ||||||||
\(377\) | −36.2061 | −1.86471 | ||||||||
\(378\) | 36.5500 | 1.87993 | ||||||||
\(379\) | 5.69260 | 0.292409 | 0.146205 | − | 0.989254i | \(-0.453294\pi\) | ||||
0.146205 | + | 0.989254i | \(0.453294\pi\) | |||||||
\(380\) | −60.6707 | −3.11234 | ||||||||
\(381\) | −0.292853 | −0.0150033 | ||||||||
\(382\) | 29.1219 | 1.49001 | ||||||||
\(383\) | −18.1379 | −0.926801 | −0.463401 | − | 0.886149i | \(-0.653371\pi\) | ||||
−0.463401 | + | 0.886149i | \(0.653371\pi\) | |||||||
\(384\) | −62.6934 | −3.19931 | ||||||||
\(385\) | −13.0037 | −0.662731 | ||||||||
\(386\) | 72.2367 | 3.67675 | ||||||||
\(387\) | −1.23451 | −0.0627535 | ||||||||
\(388\) | 26.1078 | 1.32542 | ||||||||
\(389\) | 18.5628 | 0.941171 | 0.470585 | − | 0.882354i | \(-0.344043\pi\) | ||||
0.470585 | + | 0.882354i | \(0.344043\pi\) | |||||||
\(390\) | 18.2348 | 0.923354 | ||||||||
\(391\) | 8.34033 | 0.421789 | ||||||||
\(392\) | 13.0444 | 0.658843 | ||||||||
\(393\) | −4.80359 | −0.242309 | ||||||||
\(394\) | 43.2965 | 2.18124 | ||||||||
\(395\) | 9.46972 | 0.476473 | ||||||||
\(396\) | 34.5846 | 1.73794 | ||||||||
\(397\) | −24.7674 | −1.24304 | −0.621520 | − | 0.783398i | \(-0.713484\pi\) | ||||
−0.621520 | + | 0.783398i | \(0.713484\pi\) | |||||||
\(398\) | −0.138522 | −0.00694351 | ||||||||
\(399\) | −25.8475 | −1.29399 | ||||||||
\(400\) | −55.5753 | −2.77877 | ||||||||
\(401\) | −8.11149 | −0.405069 | −0.202534 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202534 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(402\) | 4.06244 | 0.202616 | ||||||||
\(403\) | −11.0956 | −0.552711 | ||||||||
\(404\) | −0.654280 | −0.0325517 | ||||||||
\(405\) | −3.41936 | −0.169910 | ||||||||
\(406\) | −56.8387 | −2.82086 | ||||||||
\(407\) | 4.34393 | 0.215321 | ||||||||
\(408\) | −78.0188 | −3.86250 | ||||||||
\(409\) | −8.69395 | −0.429888 | −0.214944 | − | 0.976626i | \(-0.568957\pi\) | ||||
−0.214944 | + | 0.976626i | \(0.568957\pi\) | |||||||
\(410\) | −19.1891 | −0.947682 | ||||||||
\(411\) | −6.25226 | −0.308401 | ||||||||
\(412\) | 80.0192 | 3.94226 | ||||||||
\(413\) | 17.6507 | 0.868536 | ||||||||
\(414\) | 5.23592 | 0.257331 | ||||||||
\(415\) | 6.43946 | 0.316101 | ||||||||
\(416\) | 104.169 | 5.10732 | ||||||||
\(417\) | −0.233560 | −0.0114375 | ||||||||
\(418\) | −103.289 | −5.05203 | ||||||||
\(419\) | −16.0386 | −0.783539 | −0.391770 | − | 0.920063i | \(-0.628137\pi\) | ||||
−0.391770 | + | 0.920063i | \(0.628137\pi\) | |||||||
\(420\) | 21.1002 | 1.02959 | ||||||||
\(421\) | −19.7347 | −0.961810 | −0.480905 | − | 0.876773i | \(-0.659692\pi\) | ||||
−0.480905 | + | 0.876773i | \(0.659692\pi\) | |||||||
\(422\) | 32.3092 | 1.57279 | ||||||||
\(423\) | −6.38964 | −0.310675 | ||||||||
\(424\) | 97.2934 | 4.72499 | ||||||||
\(425\) | −21.3641 | −1.03631 | ||||||||
\(426\) | −49.3717 | −2.39207 | ||||||||
\(427\) | 11.1165 | 0.537965 | ||||||||
\(428\) | 15.8269 | 0.765020 | ||||||||
\(429\) | 22.8823 | 1.10477 | ||||||||
\(430\) | −3.00977 | −0.145144 | ||||||||
\(431\) | −11.1196 | −0.535614 | −0.267807 | − | 0.963473i | \(-0.586299\pi\) | ||||
−0.267807 | + | 0.963473i | \(0.586299\pi\) | |||||||
\(432\) | −90.1580 | −4.33773 | ||||||||
\(433\) | 19.6937 | 0.946419 | 0.473210 | − | 0.880950i | \(-0.343095\pi\) | ||||
0.473210 | + | 0.880950i | \(0.343095\pi\) | |||||||
\(434\) | −17.4186 | −0.836121 | ||||||||
\(435\) | 13.6311 | 0.653560 | ||||||||
\(436\) | 5.60732 | 0.268542 | ||||||||
\(437\) | −11.5262 | −0.551375 | ||||||||
\(438\) | −18.6827 | −0.892692 | ||||||||
\(439\) | −14.2216 | −0.678758 | −0.339379 | − | 0.940650i | \(-0.610217\pi\) | ||||
−0.339379 | + | 0.940650i | \(0.610217\pi\) | |||||||
\(440\) | 54.2440 | 2.58598 | ||||||||
\(441\) | 1.86153 | 0.0886442 | ||||||||
\(442\) | 72.0999 | 3.42944 | ||||||||
\(443\) | −15.1748 | −0.720976 | −0.360488 | − | 0.932764i | \(-0.617390\pi\) | ||||
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(444\) | −7.04861 | −0.334512 | ||||||||
\(445\) | 23.4467 | 1.11148 | ||||||||
\(446\) | −50.9294 | −2.41158 | ||||||||
\(447\) | 17.7488 | 0.839490 | ||||||||
\(448\) | 86.1228 | 4.06892 | ||||||||
\(449\) | 31.6796 | 1.49505 | 0.747527 | − | 0.664232i | \(-0.231241\pi\) | ||||
0.747527 | + | 0.664232i | \(0.231241\pi\) | |||||||
\(450\) | −13.4120 | −0.632249 | ||||||||
\(451\) | −24.0798 | −1.13387 | ||||||||
\(452\) | 106.901 | 5.02822 | ||||||||
\(453\) | 4.25361 | 0.199852 | ||||||||
\(454\) | 46.4926 | 2.18201 | ||||||||
\(455\) | −12.5445 | −0.588094 | ||||||||
\(456\) | 107.821 | 5.04918 | ||||||||
\(457\) | −12.0030 | −0.561478 | −0.280739 | − | 0.959784i | \(-0.590580\pi\) | ||||
−0.280739 | + | 0.959784i | \(0.590580\pi\) | |||||||
\(458\) | 51.7779 | 2.41942 | ||||||||
\(459\) | −34.6583 | −1.61771 | ||||||||
\(460\) | 9.40928 | 0.438710 | ||||||||
\(461\) | −17.3015 | −0.805812 | −0.402906 | − | 0.915241i | \(-0.632000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(462\) | 35.9222 | 1.67125 | ||||||||
\(463\) | 35.2855 | 1.63986 | 0.819928 | − | 0.572466i | \(-0.194013\pi\) | ||||
0.819928 | + | 0.572466i | \(0.194013\pi\) | |||||||
\(464\) | 140.204 | 6.50882 | ||||||||
\(465\) | 4.17734 | 0.193720 | ||||||||
\(466\) | −30.0448 | −1.39180 | ||||||||
\(467\) | −0.544554 | −0.0251990 | −0.0125995 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0125995 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(468\) | 33.3632 | 1.54221 | ||||||||
\(469\) | −2.79472 | −0.129048 | ||||||||
\(470\) | −15.5782 | −0.718567 | ||||||||
\(471\) | 21.4951 | 0.990444 | ||||||||
\(472\) | −73.6287 | −3.38904 | ||||||||
\(473\) | −3.77687 | −0.173661 | ||||||||
\(474\) | −26.1597 | −1.20155 | ||||||||
\(475\) | 29.5250 | 1.35470 | ||||||||
\(476\) | 83.4298 | 3.82400 | ||||||||
\(477\) | 13.8844 | 0.635725 | ||||||||
\(478\) | −10.4494 | −0.477946 | ||||||||
\(479\) | −3.63708 | −0.166182 | −0.0830912 | − | 0.996542i | \(-0.526479\pi\) | ||||
−0.0830912 | + | 0.996542i | \(0.526479\pi\) | |||||||
\(480\) | −39.2183 | −1.79006 | ||||||||
\(481\) | 4.19052 | 0.191071 | ||||||||
\(482\) | 36.4627 | 1.66083 | ||||||||
\(483\) | 4.00863 | 0.182399 | ||||||||
\(484\) | 44.1282 | 2.00583 | ||||||||
\(485\) | 5.84365 | 0.265347 | ||||||||
\(486\) | −36.5262 | −1.65686 | ||||||||
\(487\) | 10.5889 | 0.479830 | 0.239915 | − | 0.970794i | \(-0.422880\pi\) | ||||
0.239915 | + | 0.970794i | \(0.422880\pi\) | |||||||
\(488\) | −46.3716 | −2.09914 | ||||||||
\(489\) | 29.8949 | 1.35189 | ||||||||
\(490\) | 4.53847 | 0.205027 | ||||||||
\(491\) | 5.80992 | 0.262198 | 0.131099 | − | 0.991369i | \(-0.458149\pi\) | ||||
0.131099 | + | 0.991369i | \(0.458149\pi\) | |||||||
\(492\) | 39.0727 | 1.76153 | ||||||||
\(493\) | 53.8970 | 2.42740 | ||||||||
\(494\) | −99.6412 | −4.48307 | ||||||||
\(495\) | 7.74099 | 0.347932 | ||||||||
\(496\) | 42.9666 | 1.92926 | ||||||||
\(497\) | 33.9649 | 1.52353 | ||||||||
\(498\) | −17.7887 | −0.797131 | ||||||||
\(499\) | −38.8583 | −1.73954 | −0.869768 | − | 0.493461i | \(-0.835732\pi\) | ||||
−0.869768 | + | 0.493461i | \(0.835732\pi\) | |||||||
\(500\) | −59.2902 | −2.65154 | ||||||||
\(501\) | 13.9211 | 0.621948 | ||||||||
\(502\) | −56.3289 | −2.51408 | ||||||||
\(503\) | −3.68776 | −0.164429 | −0.0822146 | − | 0.996615i | \(-0.526199\pi\) | ||||
−0.0822146 | + | 0.996615i | \(0.526199\pi\) | |||||||
\(504\) | 33.6946 | 1.50088 | ||||||||
\(505\) | −0.146446 | −0.00651676 | ||||||||
\(506\) | 16.0189 | 0.712125 | ||||||||
\(507\) | 5.73266 | 0.254596 | ||||||||
\(508\) | −1.30634 | −0.0579596 | ||||||||
\(509\) | −13.3060 | −0.589780 | −0.294890 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294890 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(510\) | −27.1446 | −1.20198 | ||||||||
\(511\) | 12.8526 | 0.568564 | ||||||||
\(512\) | −80.4778 | −3.55665 | ||||||||
\(513\) | 47.8974 | 2.11472 | ||||||||
\(514\) | 49.8715 | 2.19974 | ||||||||
\(515\) | 17.9105 | 0.789232 | ||||||||
\(516\) | 6.12847 | 0.269791 | ||||||||
\(517\) | −19.5486 | −0.859744 | ||||||||
\(518\) | 6.57856 | 0.289046 | ||||||||
\(519\) | 5.33057 | 0.233986 | ||||||||
\(520\) | 52.3283 | 2.29475 | ||||||||
\(521\) | 30.5432 | 1.33812 | 0.669061 | − | 0.743208i | \(-0.266697\pi\) | ||||
0.669061 | + | 0.743208i | \(0.266697\pi\) | |||||||
\(522\) | 33.8356 | 1.48094 | ||||||||
\(523\) | 7.34207 | 0.321046 | 0.160523 | − | 0.987032i | \(-0.448682\pi\) | ||||
0.160523 | + | 0.987032i | \(0.448682\pi\) | |||||||
\(524\) | −21.4276 | −0.936068 | ||||||||
\(525\) | −10.2683 | −0.448145 | ||||||||
\(526\) | −16.6337 | −0.725265 | ||||||||
\(527\) | 16.5171 | 0.719497 | ||||||||
\(528\) | −88.6093 | −3.85622 | ||||||||
\(529\) | −21.2124 | −0.922279 | ||||||||
\(530\) | 33.8507 | 1.47038 | ||||||||
\(531\) | −10.5073 | −0.455979 | ||||||||
\(532\) | −115.299 | −4.99885 | ||||||||
\(533\) | −23.2294 | −1.00618 | ||||||||
\(534\) | −64.7704 | −2.80289 | ||||||||
\(535\) | 3.54249 | 0.153155 | ||||||||
\(536\) | 11.6580 | 0.503548 | ||||||||
\(537\) | 23.1055 | 0.997076 | ||||||||
\(538\) | 4.33645 | 0.186958 | ||||||||
\(539\) | 5.69519 | 0.245309 | ||||||||
\(540\) | −39.1003 | −1.68261 | ||||||||
\(541\) | −1.26386 | −0.0543377 | −0.0271688 | − | 0.999631i | \(-0.508649\pi\) | ||||
−0.0271688 | + | 0.999631i | \(0.508649\pi\) | |||||||
\(542\) | 71.6915 | 3.07941 | ||||||||
\(543\) | −12.1594 | −0.521809 | ||||||||
\(544\) | −155.068 | −6.64850 | ||||||||
\(545\) | 1.25507 | 0.0537614 | ||||||||
\(546\) | 34.6535 | 1.48303 | ||||||||
\(547\) | −4.31002 | −0.184283 | −0.0921416 | − | 0.995746i | \(-0.529371\pi\) | ||||
−0.0921416 | + | 0.995746i | \(0.529371\pi\) | |||||||
\(548\) | −27.8897 | −1.19139 | ||||||||
\(549\) | −6.61755 | −0.282430 | ||||||||
\(550\) | −41.0330 | −1.74965 | ||||||||
\(551\) | −74.4850 | −3.17317 | ||||||||
\(552\) | −16.7217 | −0.711723 | ||||||||
\(553\) | 17.9963 | 0.765281 | ||||||||
\(554\) | −42.2729 | −1.79601 | ||||||||
\(555\) | −1.57767 | −0.0669685 | ||||||||
\(556\) | −1.04185 | −0.0441844 | ||||||||
\(557\) | 16.1442 | 0.684052 | 0.342026 | − | 0.939691i | \(-0.388887\pi\) | ||||
0.342026 | + | 0.939691i | \(0.388887\pi\) | |||||||
\(558\) | 10.3692 | 0.438961 | ||||||||
\(559\) | −3.64348 | −0.154103 | ||||||||
\(560\) | 48.5772 | 2.05276 | ||||||||
\(561\) | −34.0630 | −1.43814 | ||||||||
\(562\) | 68.2627 | 2.87949 | ||||||||
\(563\) | 10.8722 | 0.458209 | 0.229105 | − | 0.973402i | \(-0.426420\pi\) | ||||
0.229105 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(564\) | 31.7201 | 1.33566 | ||||||||
\(565\) | 23.9275 | 1.00664 | ||||||||
\(566\) | −31.3848 | −1.31920 | ||||||||
\(567\) | −6.49818 | −0.272898 | ||||||||
\(568\) | −141.682 | −5.94484 | ||||||||
\(569\) | −24.2218 | −1.01543 | −0.507716 | − | 0.861524i | \(-0.669510\pi\) | ||||
−0.507716 | + | 0.861524i | \(0.669510\pi\) | |||||||
\(570\) | 37.5135 | 1.57127 | ||||||||
\(571\) | 2.55600 | 0.106965 | 0.0534827 | − | 0.998569i | \(-0.482968\pi\) | ||||
0.0534827 | + | 0.998569i | \(0.482968\pi\) | |||||||
\(572\) | 102.072 | 4.26784 | ||||||||
\(573\) | −13.2725 | −0.554466 | ||||||||
\(574\) | −36.4671 | −1.52211 | ||||||||
\(575\) | −4.57896 | −0.190956 | ||||||||
\(576\) | −51.2681 | −2.13617 | ||||||||
\(577\) | −5.45630 | −0.227149 | −0.113574 | − | 0.993529i | \(-0.536230\pi\) | ||||
−0.113574 | + | 0.993529i | \(0.536230\pi\) | |||||||
\(578\) | −60.4408 | −2.51401 | ||||||||
\(579\) | −32.9223 | −1.36820 | ||||||||
\(580\) | 60.8047 | 2.52478 | ||||||||
\(581\) | 12.2376 | 0.507701 | ||||||||
\(582\) | −16.1428 | −0.669141 | ||||||||
\(583\) | 42.4783 | 1.75927 | ||||||||
\(584\) | −53.6135 | −2.21854 | ||||||||
\(585\) | 7.46761 | 0.308748 | ||||||||
\(586\) | 52.2699 | 2.15925 | ||||||||
\(587\) | 31.2694 | 1.29063 | 0.645313 | − | 0.763918i | \(-0.276727\pi\) | ||||
0.645313 | + | 0.763918i | \(0.276727\pi\) | |||||||
\(588\) | −9.24120 | −0.381100 | ||||||||
\(589\) | −22.8264 | −0.940547 | ||||||||
\(590\) | −25.6172 | −1.05464 | ||||||||
\(591\) | −19.7326 | −0.811692 | ||||||||
\(592\) | −16.2274 | −0.666940 | ||||||||
\(593\) | 23.6951 | 0.973043 | 0.486522 | − | 0.873669i | \(-0.338266\pi\) | ||||
0.486522 | + | 0.873669i | \(0.338266\pi\) | |||||||
\(594\) | −66.5664 | −2.73125 | ||||||||
\(595\) | 18.6739 | 0.765556 | ||||||||
\(596\) | 79.1728 | 3.24304 | ||||||||
\(597\) | 0.0631325 | 0.00258384 | ||||||||
\(598\) | 15.4531 | 0.631925 | ||||||||
\(599\) | 8.60870 | 0.351742 | 0.175871 | − | 0.984413i | \(-0.443726\pi\) | ||||
0.175871 | + | 0.984413i | \(0.443726\pi\) | |||||||
\(600\) | 42.8334 | 1.74867 | ||||||||
\(601\) | 34.4352 | 1.40464 | 0.702321 | − | 0.711861i | \(-0.252147\pi\) | ||||
0.702321 | + | 0.711861i | \(0.252147\pi\) | |||||||
\(602\) | −5.71979 | −0.233121 | ||||||||
\(603\) | 1.66367 | 0.0677500 | ||||||||
\(604\) | 18.9742 | 0.772051 | ||||||||
\(605\) | 9.87711 | 0.401562 | ||||||||
\(606\) | 0.404550 | 0.0164337 | ||||||||
\(607\) | −30.6085 | −1.24236 | −0.621179 | − | 0.783668i | \(-0.713346\pi\) | ||||
−0.621179 | + | 0.783668i | \(0.713346\pi\) | |||||||
\(608\) | 214.302 | 8.69111 | ||||||||
\(609\) | 25.9046 | 1.04971 | ||||||||
\(610\) | −16.1338 | −0.653239 | ||||||||
\(611\) | −18.8582 | −0.762920 | ||||||||
\(612\) | −49.6650 | −2.00759 | ||||||||
\(613\) | 26.4882 | 1.06985 | 0.534925 | − | 0.844900i | \(-0.320340\pi\) | ||||
0.534925 | + | 0.844900i | \(0.320340\pi\) | |||||||
\(614\) | 11.5285 | 0.465253 | ||||||||
\(615\) | 8.74555 | 0.352655 | ||||||||
\(616\) | 103.086 | 4.15344 | ||||||||
\(617\) | −19.6697 | −0.791874 | −0.395937 | − | 0.918278i | \(-0.629580\pi\) | ||||
−0.395937 | + | 0.918278i | \(0.629580\pi\) | |||||||
\(618\) | −49.4770 | −1.99026 | ||||||||
\(619\) | −33.6407 | −1.35213 | −0.676067 | − | 0.736840i | \(-0.736317\pi\) | ||||
−0.676067 | + | 0.736840i | \(0.736317\pi\) | |||||||
\(620\) | 18.6340 | 0.748361 | ||||||||
\(621\) | −7.42829 | −0.298087 | ||||||||
\(622\) | 63.9847 | 2.56555 | ||||||||
\(623\) | 44.5582 | 1.78519 | ||||||||
\(624\) | −85.4799 | −3.42193 | ||||||||
\(625\) | 3.85317 | 0.154127 | ||||||||
\(626\) | −56.0804 | −2.24143 | ||||||||
\(627\) | 47.0746 | 1.87998 | ||||||||
\(628\) | 95.8842 | 3.82620 | ||||||||
\(629\) | −6.23808 | −0.248729 | ||||||||
\(630\) | 11.7232 | 0.467062 | ||||||||
\(631\) | −0.123738 | −0.00492594 | −0.00246297 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246297 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(632\) | −75.0703 | −2.98614 | ||||||||
\(633\) | −14.7251 | −0.585271 | ||||||||
\(634\) | 65.2019 | 2.58950 | ||||||||
\(635\) | −0.292396 | −0.0116034 | ||||||||
\(636\) | −68.9266 | −2.73312 | ||||||||
\(637\) | 5.49405 | 0.217682 | ||||||||
\(638\) | 103.517 | 4.09828 | ||||||||
\(639\) | −20.2190 | −0.799850 | ||||||||
\(640\) | −62.5954 | −2.47430 | ||||||||
\(641\) | −45.9698 | −1.81570 | −0.907849 | − | 0.419298i | \(-0.862276\pi\) | ||||
−0.907849 | + | 0.419298i | \(0.862276\pi\) | |||||||
\(642\) | −9.78596 | −0.386221 | ||||||||
\(643\) | −16.7281 | −0.659692 | −0.329846 | − | 0.944035i | \(-0.606997\pi\) | ||||
−0.329846 | + | 0.944035i | \(0.606997\pi\) | |||||||
\(644\) | 17.8815 | 0.704628 | ||||||||
\(645\) | 1.37172 | 0.0540115 | ||||||||
\(646\) | 148.328 | 5.83587 | ||||||||
\(647\) | 1.42017 | 0.0558328 | 0.0279164 | − | 0.999610i | \(-0.491113\pi\) | ||||
0.0279164 | + | 0.999610i | \(0.491113\pi\) | |||||||
\(648\) | 27.1067 | 1.06485 | ||||||||
\(649\) | −32.1463 | −1.26185 | ||||||||
\(650\) | −39.5838 | −1.55261 | ||||||||
\(651\) | 7.93865 | 0.311140 | ||||||||
\(652\) | 133.353 | 5.22252 | ||||||||
\(653\) | 39.9174 | 1.56209 | 0.781045 | − | 0.624475i | \(-0.214687\pi\) | ||||
0.781045 | + | 0.624475i | \(0.214687\pi\) | |||||||
\(654\) | −3.46708 | −0.135574 | ||||||||
\(655\) | −4.79608 | −0.187399 | ||||||||
\(656\) | 89.9535 | 3.51209 | ||||||||
\(657\) | −7.65102 | −0.298495 | ||||||||
\(658\) | −29.6048 | −1.15412 | ||||||||
\(659\) | −33.7434 | −1.31445 | −0.657227 | − | 0.753692i | \(-0.728271\pi\) | ||||
−0.657227 | + | 0.753692i | \(0.728271\pi\) | |||||||
\(660\) | −38.4287 | −1.49583 | ||||||||
\(661\) | 18.8057 | 0.731455 | 0.365728 | − | 0.930722i | \(-0.380820\pi\) | ||||
0.365728 | + | 0.930722i | \(0.380820\pi\) | |||||||
\(662\) | −75.6681 | −2.94093 | ||||||||
\(663\) | −32.8600 | −1.27618 | ||||||||
\(664\) | −51.0482 | −1.98105 | ||||||||
\(665\) | −25.8071 | −1.00076 | ||||||||
\(666\) | −3.91616 | −0.151748 | ||||||||
\(667\) | 11.5517 | 0.447284 | ||||||||
\(668\) | 62.0984 | 2.40266 | ||||||||
\(669\) | 23.2114 | 0.897404 | ||||||||
\(670\) | 4.05609 | 0.156701 | ||||||||
\(671\) | −20.2458 | −0.781581 | ||||||||
\(672\) | −74.5307 | −2.87509 | ||||||||
\(673\) | 45.1145 | 1.73904 | 0.869518 | − | 0.493901i | \(-0.164430\pi\) | ||||
0.869518 | + | 0.493901i | \(0.164430\pi\) | |||||||
\(674\) | 18.5677 | 0.715202 | ||||||||
\(675\) | 19.0279 | 0.732384 | ||||||||
\(676\) | 25.5719 | 0.983535 | ||||||||
\(677\) | −9.06201 | −0.348281 | −0.174141 | − | 0.984721i | \(-0.555715\pi\) | ||||
−0.174141 | + | 0.984721i | \(0.555715\pi\) | |||||||
\(678\) | −66.0986 | −2.53850 | ||||||||
\(679\) | 11.1053 | 0.426183 | ||||||||
\(680\) | −77.8968 | −2.98721 | ||||||||
\(681\) | −21.1893 | −0.811976 | ||||||||
\(682\) | 31.7236 | 1.21476 | ||||||||
\(683\) | 38.2738 | 1.46451 | 0.732254 | − | 0.681032i | \(-0.238469\pi\) | ||||
0.732254 | + | 0.681032i | \(0.238469\pi\) | |||||||
\(684\) | 68.6365 | 2.62438 | ||||||||
\(685\) | −6.24249 | −0.238513 | ||||||||
\(686\) | 54.6749 | 2.08750 | ||||||||
\(687\) | −23.5981 | −0.900324 | ||||||||
\(688\) | 14.1090 | 0.537901 | ||||||||
\(689\) | 40.9781 | 1.56114 | ||||||||
\(690\) | −5.81789 | −0.221483 | ||||||||
\(691\) | −6.52529 | −0.248234 | −0.124117 | − | 0.992268i | \(-0.539610\pi\) | ||||
−0.124117 | + | 0.992268i | \(0.539610\pi\) | |||||||
\(692\) | 23.7783 | 0.903915 | ||||||||
\(693\) | 14.7110 | 0.558826 | ||||||||
\(694\) | −46.1550 | −1.75202 | ||||||||
\(695\) | −0.233195 | −0.00884561 | ||||||||
\(696\) | −108.059 | −4.09597 | ||||||||
\(697\) | 34.5797 | 1.30980 | ||||||||
\(698\) | 60.3873 | 2.28569 | ||||||||
\(699\) | 13.6931 | 0.517921 | ||||||||
\(700\) | −45.8041 | −1.73123 | ||||||||
\(701\) | −12.1342 | −0.458303 | −0.229151 | − | 0.973391i | \(-0.573595\pi\) | ||||
−0.229151 | + | 0.973391i | \(0.573595\pi\) | |||||||
\(702\) | −64.2155 | −2.42366 | ||||||||
\(703\) | 8.62095 | 0.325145 | ||||||||
\(704\) | −156.850 | −5.91152 | ||||||||
\(705\) | 7.09984 | 0.267395 | ||||||||
\(706\) | −6.12126 | −0.230377 | ||||||||
\(707\) | −0.278307 | −0.0104668 | ||||||||
\(708\) | 52.1615 | 1.96035 | ||||||||
\(709\) | −27.4134 | −1.02953 | −0.514766 | − | 0.857331i | \(-0.672121\pi\) | ||||
−0.514766 | + | 0.857331i | \(0.672121\pi\) | |||||||
\(710\) | −49.2946 | −1.84999 | ||||||||
\(711\) | −10.7130 | −0.401770 | ||||||||
\(712\) | −185.871 | −6.96582 | ||||||||
\(713\) | 3.54010 | 0.132578 | ||||||||
\(714\) | −51.5858 | −1.93055 | ||||||||
\(715\) | 22.8465 | 0.854411 | ||||||||
\(716\) | 103.068 | 3.85182 | ||||||||
\(717\) | 4.76239 | 0.177855 | ||||||||
\(718\) | 46.3547 | 1.72994 | ||||||||
\(719\) | 8.65479 | 0.322769 | 0.161385 | − | 0.986892i | \(-0.448404\pi\) | ||||
0.161385 | + | 0.986892i | \(0.448404\pi\) | |||||||
\(720\) | −28.9175 | −1.07769 | ||||||||
\(721\) | 34.0373 | 1.26761 | ||||||||
\(722\) | −152.582 | −5.67853 | ||||||||
\(723\) | −16.6181 | −0.618034 | ||||||||
\(724\) | −54.2398 | −2.01581 | ||||||||
\(725\) | −29.5902 | −1.09895 | ||||||||
\(726\) | −27.2851 | −1.01264 | ||||||||
\(727\) | −23.4223 | −0.868684 | −0.434342 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434342 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(728\) | 99.4450 | 3.68568 | ||||||||
\(729\) | 24.8203 | 0.919271 | ||||||||
\(730\) | −18.6535 | −0.690395 | ||||||||
\(731\) | 5.42375 | 0.200605 | ||||||||
\(732\) | 32.8515 | 1.21423 | ||||||||
\(733\) | 9.11720 | 0.336751 | 0.168376 | − | 0.985723i | \(-0.446148\pi\) | ||||
0.168376 | + | 0.985723i | \(0.446148\pi\) | |||||||
\(734\) | −87.4715 | −3.22863 | ||||||||
\(735\) | −2.06844 | −0.0762954 | ||||||||
\(736\) | −33.2357 | −1.22508 | ||||||||
\(737\) | 5.08987 | 0.187488 | ||||||||
\(738\) | 21.7085 | 0.799102 | ||||||||
\(739\) | −20.8406 | −0.766634 | −0.383317 | − | 0.923617i | \(-0.625218\pi\) | ||||
−0.383317 | + | 0.923617i | \(0.625218\pi\) | |||||||
\(740\) | −7.03759 | −0.258707 | ||||||||
\(741\) | 45.4121 | 1.66825 | ||||||||
\(742\) | 64.3302 | 2.36164 | ||||||||
\(743\) | −31.8288 | −1.16768 | −0.583842 | − | 0.811867i | \(-0.698451\pi\) | ||||
−0.583842 | + | 0.811867i | \(0.698451\pi\) | |||||||
\(744\) | −33.1155 | −1.21407 | ||||||||
\(745\) | 17.7211 | 0.649250 | ||||||||
\(746\) | −17.0154 | −0.622976 | ||||||||
\(747\) | −7.28493 | −0.266541 | ||||||||
\(748\) | −151.946 | −5.55569 | ||||||||
\(749\) | 6.73217 | 0.245988 | ||||||||
\(750\) | 36.6600 | 1.33863 | ||||||||
\(751\) | 42.5080 | 1.55114 | 0.775569 | − | 0.631263i | \(-0.217463\pi\) | ||||
0.775569 | + | 0.631263i | \(0.217463\pi\) | |||||||
\(752\) | 73.0263 | 2.66299 | ||||||||
\(753\) | 25.6722 | 0.935548 | ||||||||
\(754\) | 99.8612 | 3.63673 | ||||||||
\(755\) | 4.24696 | 0.154563 | ||||||||
\(756\) | −74.3065 | −2.70250 | ||||||||
\(757\) | −11.0716 | −0.402404 | −0.201202 | − | 0.979550i | \(-0.564485\pi\) | ||||
−0.201202 | + | 0.979550i | \(0.564485\pi\) | |||||||
\(758\) | −15.7010 | −0.570285 | ||||||||
\(759\) | −7.30069 | −0.264998 | ||||||||
\(760\) | 107.652 | 3.90497 | ||||||||
\(761\) | 38.4906 | 1.39528 | 0.697642 | − | 0.716447i | \(-0.254233\pi\) | ||||
0.697642 | + | 0.716447i | \(0.254233\pi\) | |||||||
\(762\) | 0.807729 | 0.0292609 | ||||||||
\(763\) | 2.38515 | 0.0863482 | ||||||||
\(764\) | −59.2051 | −2.14196 | ||||||||
\(765\) | −11.1164 | −0.401915 | ||||||||
\(766\) | 50.0267 | 1.80754 | ||||||||
\(767\) | −31.0110 | −1.11974 | ||||||||
\(768\) | 82.1390 | 2.96393 | ||||||||
\(769\) | −15.8554 | −0.571759 | −0.285880 | − | 0.958266i | \(-0.592286\pi\) | ||||
−0.285880 | + | 0.958266i | \(0.592286\pi\) | |||||||
\(770\) | 35.8660 | 1.29252 | ||||||||
\(771\) | −22.7293 | −0.818574 | ||||||||
\(772\) | −146.858 | −5.28553 | ||||||||
\(773\) | 50.2707 | 1.80811 | 0.904056 | − | 0.427415i | \(-0.140576\pi\) | ||||
0.904056 | + | 0.427415i | \(0.140576\pi\) | |||||||
\(774\) | 3.40494 | 0.122388 | ||||||||
\(775\) | −9.06812 | −0.325737 | ||||||||
\(776\) | −46.3250 | −1.66297 | ||||||||
\(777\) | −2.99822 | −0.107561 | ||||||||
\(778\) | −51.1987 | −1.83556 | ||||||||
\(779\) | −47.7887 | −1.71221 | ||||||||
\(780\) | −37.0715 | −1.32737 | ||||||||
\(781\) | −61.8582 | −2.21346 | ||||||||
\(782\) | −23.0038 | −0.822614 | ||||||||
\(783\) | −48.0032 | −1.71549 | ||||||||
\(784\) | −21.2752 | −0.759827 | ||||||||
\(785\) | 21.4616 | 0.765996 | ||||||||
\(786\) | 13.2490 | 0.472575 | ||||||||
\(787\) | 11.2433 | 0.400779 | 0.200390 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200390 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(788\) | −88.0221 | −3.13566 | ||||||||
\(789\) | 7.58093 | 0.269888 | ||||||||
\(790\) | −26.1188 | −0.929264 | ||||||||
\(791\) | 45.4720 | 1.61680 | ||||||||
\(792\) | −61.3660 | −2.18054 | ||||||||
\(793\) | −19.5308 | −0.693559 | ||||||||
\(794\) | 68.3118 | 2.42430 | ||||||||
\(795\) | −15.4277 | −0.547163 | ||||||||
\(796\) | 0.281617 | 0.00998167 | ||||||||
\(797\) | 10.8114 | 0.382960 | 0.191480 | − | 0.981497i | \(-0.438671\pi\) | ||||
0.191480 | + | 0.981497i | \(0.438671\pi\) | |||||||
\(798\) | 71.2910 | 2.52367 | ||||||||
\(799\) | 28.0726 | 0.993137 | ||||||||
\(800\) | 85.1346 | 3.00996 | ||||||||
\(801\) | −26.5251 | −0.937218 | ||||||||
\(802\) | 22.3726 | 0.790004 | ||||||||
\(803\) | −23.4076 | −0.826038 | ||||||||
\(804\) | −8.25898 | −0.291272 | ||||||||
\(805\) | 4.00237 | 0.141065 | ||||||||
\(806\) | 30.6032 | 1.07795 | ||||||||
\(807\) | −1.97636 | −0.0695712 | ||||||||
\(808\) | 1.16094 | 0.0408416 | ||||||||
\(809\) | 44.0854 | 1.54996 | 0.774980 | − | 0.631986i | \(-0.217760\pi\) | ||||
0.774980 | + | 0.631986i | \(0.217760\pi\) | |||||||
\(810\) | 9.43107 | 0.331374 | ||||||||
\(811\) | −39.3783 | −1.38276 | −0.691379 | − | 0.722492i | \(-0.742996\pi\) | ||||
−0.691379 | + | 0.722492i | \(0.742996\pi\) | |||||||
\(812\) | 115.554 | 4.05514 | ||||||||
\(813\) | −32.6738 | −1.14592 | ||||||||
\(814\) | −11.9812 | −0.419939 | ||||||||
\(815\) | 29.8481 | 1.04553 | ||||||||
\(816\) | 127.247 | 4.45453 | ||||||||
\(817\) | −7.49556 | −0.262236 | ||||||||
\(818\) | 23.9791 | 0.838410 | ||||||||
\(819\) | 14.1915 | 0.495891 | ||||||||
\(820\) | 39.0116 | 1.36234 | ||||||||
\(821\) | −44.5103 | −1.55342 | −0.776711 | − | 0.629858i | \(-0.783113\pi\) | ||||
−0.776711 | + | 0.629858i | \(0.783113\pi\) | |||||||
\(822\) | 17.2446 | 0.601474 | ||||||||
\(823\) | 10.5105 | 0.366374 | 0.183187 | − | 0.983078i | \(-0.441359\pi\) | ||||
0.183187 | + | 0.983078i | \(0.441359\pi\) | |||||||
\(824\) | −141.984 | −4.94625 | ||||||||
\(825\) | 18.7010 | 0.651086 | ||||||||
\(826\) | −48.6831 | −1.69390 | ||||||||
\(827\) | −39.5348 | −1.37476 | −0.687380 | − | 0.726298i | \(-0.741239\pi\) | ||||
−0.687380 | + | 0.726298i | \(0.741239\pi\) | |||||||
\(828\) | −10.6447 | −0.369928 | ||||||||
\(829\) | 6.04907 | 0.210093 | 0.105047 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105047 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(830\) | −17.7609 | −0.616490 | ||||||||
\(831\) | 19.2661 | 0.668335 | ||||||||
\(832\) | −151.311 | −5.24577 | ||||||||
\(833\) | −8.17854 | −0.283370 | ||||||||
\(834\) | 0.644192 | 0.0223065 | ||||||||
\(835\) | 13.8993 | 0.481006 | ||||||||
\(836\) | 209.987 | 7.26257 | ||||||||
\(837\) | −14.7109 | −0.508483 | ||||||||
\(838\) | 44.2368 | 1.52813 | ||||||||
\(839\) | 13.1688 | 0.454638 | 0.227319 | − | 0.973820i | \(-0.427004\pi\) | ||||
0.227319 | + | 0.973820i | \(0.427004\pi\) | |||||||
\(840\) | −37.4397 | −1.29179 | ||||||||
\(841\) | 45.6495 | 1.57412 | ||||||||
\(842\) | 54.4310 | 1.87581 | ||||||||
\(843\) | −31.1111 | −1.07152 | ||||||||
\(844\) | −65.6849 | −2.26097 | ||||||||
\(845\) | 5.72370 | 0.196901 | ||||||||
\(846\) | 17.6235 | 0.605908 | ||||||||
\(847\) | 18.7705 | 0.644963 | ||||||||
\(848\) | −158.683 | −5.44921 | ||||||||
\(849\) | 14.3038 | 0.490905 | ||||||||
\(850\) | 58.9252 | 2.02112 | ||||||||
\(851\) | −1.33700 | −0.0458319 | ||||||||
\(852\) | 100.373 | 3.43873 | ||||||||
\(853\) | 5.63477 | 0.192931 | 0.0964655 | − | 0.995336i | \(-0.469246\pi\) | ||||
0.0964655 | + | 0.995336i | \(0.469246\pi\) | |||||||
\(854\) | −30.6608 | −1.04919 | ||||||||
\(855\) | 15.3627 | 0.525395 | ||||||||
\(856\) | −28.0827 | −0.959848 | ||||||||
\(857\) | −18.2956 | −0.624965 | −0.312482 | − | 0.949924i | \(-0.601161\pi\) | ||||
−0.312482 | + | 0.949924i | \(0.601161\pi\) | |||||||
\(858\) | −63.1124 | −2.15462 | ||||||||
\(859\) | 10.3210 | 0.352147 | 0.176073 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176073 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(860\) | 6.11889 | 0.208652 | ||||||||
\(861\) | 16.6201 | 0.566412 | ||||||||
\(862\) | 30.6695 | 1.04461 | ||||||||
\(863\) | 4.08768 | 0.139146 | 0.0695731 | − | 0.997577i | \(-0.477836\pi\) | ||||
0.0695731 | + | 0.997577i | \(0.477836\pi\) | |||||||
\(864\) | 138.111 | 4.69863 | ||||||||
\(865\) | 5.32224 | 0.180962 | ||||||||
\(866\) | −54.3179 | −1.84580 | ||||||||
\(867\) | 27.5463 | 0.935521 | ||||||||
\(868\) | 35.4122 | 1.20197 | ||||||||
\(869\) | −32.7756 | −1.11184 | ||||||||
\(870\) | −37.5964 | −1.27464 | ||||||||
\(871\) | 4.91011 | 0.166373 | ||||||||
\(872\) | −9.94947 | −0.336931 | ||||||||
\(873\) | −6.61089 | −0.223745 | ||||||||
\(874\) | 31.7909 | 1.07534 | ||||||||
\(875\) | −25.2199 | −0.852588 | ||||||||
\(876\) | 37.9820 | 1.28329 | ||||||||
\(877\) | −57.1754 | −1.93068 | −0.965338 | − | 0.261002i | \(-0.915947\pi\) | ||||
−0.965338 | + | 0.261002i | \(0.915947\pi\) | |||||||
\(878\) | 39.2250 | 1.32378 | ||||||||
\(879\) | −23.8223 | −0.803507 | ||||||||
\(880\) | −88.4708 | −2.98235 | ||||||||
\(881\) | 25.4426 | 0.857183 | 0.428592 | − | 0.903498i | \(-0.359010\pi\) | ||||
0.428592 | + | 0.903498i | \(0.359010\pi\) | |||||||
\(882\) | −5.13435 | −0.172882 | ||||||||
\(883\) | −6.35425 | −0.213838 | −0.106919 | − | 0.994268i | \(-0.534098\pi\) | ||||
−0.106919 | + | 0.994268i | \(0.534098\pi\) | |||||||
\(884\) | −146.580 | −4.93001 | ||||||||
\(885\) | 11.6752 | 0.392458 | ||||||||
\(886\) | 41.8542 | 1.40612 | ||||||||
\(887\) | −19.1155 | −0.641834 | −0.320917 | − | 0.947107i | \(-0.603991\pi\) | ||||
−0.320917 | + | 0.947107i | \(0.603991\pi\) | |||||||
\(888\) | 12.5069 | 0.419702 | ||||||||
\(889\) | −0.555671 | −0.0186366 | ||||||||
\(890\) | −64.6691 | −2.16771 | ||||||||
\(891\) | 11.8348 | 0.396479 | ||||||||
\(892\) | 103.540 | 3.46677 | ||||||||
\(893\) | −38.7960 | −1.29826 | ||||||||
\(894\) | −48.9536 | −1.63725 | ||||||||
\(895\) | 23.0694 | 0.771125 | ||||||||
\(896\) | −118.957 | −3.97407 | ||||||||
\(897\) | −7.04285 | −0.235154 | ||||||||
\(898\) | −87.3767 | −2.91580 | ||||||||
\(899\) | 22.8769 | 0.762986 | ||||||||
\(900\) | 27.2668 | 0.908893 | ||||||||
\(901\) | −61.0007 | −2.03223 | ||||||||
\(902\) | 66.4154 | 2.21139 | ||||||||
\(903\) | 2.60683 | 0.0867498 | ||||||||
\(904\) | −189.683 | −6.30876 | ||||||||
\(905\) | −12.1404 | −0.403559 | ||||||||
\(906\) | −11.7320 | −0.389771 | ||||||||
\(907\) | 49.0647 | 1.62917 | 0.814583 | − | 0.580047i | \(-0.196966\pi\) | ||||
0.814583 | + | 0.580047i | \(0.196966\pi\) | |||||||
\(908\) | −94.5199 | −3.13675 | ||||||||
\(909\) | 0.165674 | 0.00549505 | ||||||||
\(910\) | 34.5993 | 1.14696 | ||||||||
\(911\) | 32.4699 | 1.07578 | 0.537888 | − | 0.843017i | \(-0.319222\pi\) | ||||
0.537888 | + | 0.843017i | \(0.319222\pi\) | |||||||
\(912\) | −175.854 | −5.82309 | ||||||||
\(913\) | −22.2876 | −0.737612 | ||||||||
\(914\) | 33.1060 | 1.09505 | ||||||||
\(915\) | 7.35308 | 0.243085 | ||||||||
\(916\) | −105.265 | −3.47805 | ||||||||
\(917\) | −9.11451 | −0.300988 | ||||||||
\(918\) | 95.5923 | 3.15502 | ||||||||
\(919\) | −6.78879 | −0.223941 | −0.111971 | − | 0.993712i | \(-0.535716\pi\) | ||||
−0.111971 | + | 0.993712i | \(0.535716\pi\) | |||||||
\(920\) | −16.6956 | −0.550437 | ||||||||
\(921\) | −5.25420 | −0.173132 | ||||||||
\(922\) | 47.7200 | 1.57157 | ||||||||
\(923\) | −59.6736 | −1.96418 | ||||||||
\(924\) | −73.0301 | −2.40251 | ||||||||
\(925\) | 3.42479 | 0.112606 | ||||||||
\(926\) | −97.3222 | −3.19821 | ||||||||
\(927\) | −20.2621 | −0.665494 | ||||||||
\(928\) | −214.776 | −7.05036 | ||||||||
\(929\) | 10.9723 | 0.359991 | 0.179996 | − | 0.983667i | \(-0.442392\pi\) | ||||
0.179996 | + | 0.983667i | \(0.442392\pi\) | |||||||
\(930\) | −11.5217 | −0.377811 | ||||||||
\(931\) | 11.3026 | 0.370429 | ||||||||
\(932\) | 61.0814 | 2.00079 | ||||||||
\(933\) | −29.1614 | −0.954703 | ||||||||
\(934\) | 1.50195 | 0.0491455 | ||||||||
\(935\) | −34.0097 | −1.11224 | ||||||||
\(936\) | −59.1987 | −1.93497 | ||||||||
\(937\) | −58.6047 | −1.91453 | −0.957266 | − | 0.289211i | \(-0.906607\pi\) | ||||
−0.957266 | + | 0.289211i | \(0.906607\pi\) | |||||||
\(938\) | 7.70823 | 0.251683 | ||||||||
\(939\) | 25.5590 | 0.834087 | ||||||||
\(940\) | 31.6705 | 1.03298 | ||||||||
\(941\) | 45.3489 | 1.47833 | 0.739166 | − | 0.673523i | \(-0.235220\pi\) | ||||
0.739166 | + | 0.673523i | \(0.235220\pi\) | |||||||
\(942\) | −59.2865 | −1.93166 | ||||||||
\(943\) | 7.41144 | 0.241350 | ||||||||
\(944\) | 120.087 | 3.90849 | ||||||||
\(945\) | −16.6319 | −0.541034 | ||||||||
\(946\) | 10.4171 | 0.338690 | ||||||||
\(947\) | −4.94163 | −0.160581 | −0.0802907 | − | 0.996771i | \(-0.525585\pi\) | ||||
−0.0802907 | + | 0.996771i | \(0.525585\pi\) | |||||||
\(948\) | 53.1828 | 1.72730 | ||||||||
\(949\) | −22.5810 | −0.733009 | ||||||||
\(950\) | −81.4339 | −2.64206 | ||||||||
\(951\) | −29.7162 | −0.963613 | ||||||||
\(952\) | −148.036 | −4.79786 | ||||||||
\(953\) | −2.57723 | −0.0834848 | −0.0417424 | − | 0.999128i | \(-0.513291\pi\) | ||||
−0.0417424 | + | 0.999128i | \(0.513291\pi\) | |||||||
\(954\) | −38.2952 | −1.23985 | ||||||||
\(955\) | −13.2517 | −0.428816 | ||||||||
\(956\) | 21.2438 | 0.687074 | ||||||||
\(957\) | −47.1786 | −1.52507 | ||||||||
\(958\) | 10.0316 | 0.324105 | ||||||||
\(959\) | −11.8633 | −0.383085 | ||||||||
\(960\) | 56.9665 | 1.83859 | ||||||||
\(961\) | −23.9892 | −0.773846 | ||||||||
\(962\) | −11.5580 | −0.372646 | ||||||||
\(963\) | −4.00760 | −0.129143 | ||||||||
\(964\) | −74.1290 | −2.38754 | ||||||||
\(965\) | −32.8708 | −1.05815 | ||||||||
\(966\) | −11.0564 | −0.355732 | ||||||||
\(967\) | 29.2183 | 0.939596 | 0.469798 | − | 0.882774i | \(-0.344327\pi\) | ||||
0.469798 | + | 0.882774i | \(0.344327\pi\) | |||||||
\(968\) | −78.2999 | −2.51665 | ||||||||
\(969\) | −67.6012 | −2.17166 | ||||||||
\(970\) | −16.1176 | −0.517504 | ||||||||
\(971\) | 37.9966 | 1.21937 | 0.609684 | − | 0.792645i | \(-0.291296\pi\) | ||||
0.609684 | + | 0.792645i | \(0.291296\pi\) | |||||||
\(972\) | 74.2580 | 2.38183 | ||||||||
\(973\) | −0.443166 | −0.0142073 | ||||||||
\(974\) | −29.2057 | −0.935811 | ||||||||
\(975\) | 18.0406 | 0.577761 | ||||||||
\(976\) | 75.6310 | 2.42089 | ||||||||
\(977\) | 41.0347 | 1.31281 | 0.656407 | − | 0.754407i | \(-0.272075\pi\) | ||||
0.656407 | + | 0.754407i | \(0.272075\pi\) | |||||||
\(978\) | −82.4541 | −2.63659 | ||||||||
\(979\) | −81.1513 | −2.59361 | ||||||||
\(980\) | −9.22675 | −0.294738 | ||||||||
\(981\) | −1.41986 | −0.0453325 | ||||||||
\(982\) | −16.0246 | −0.511364 | ||||||||
\(983\) | 29.4434 | 0.939099 | 0.469550 | − | 0.882906i | \(-0.344416\pi\) | ||||
0.469550 | + | 0.882906i | \(0.344416\pi\) | |||||||
\(984\) | −69.3295 | −2.21014 | ||||||||
\(985\) | −19.7018 | −0.627751 | ||||||||
\(986\) | −148.655 | −4.73415 | ||||||||
\(987\) | 13.4926 | 0.429474 | ||||||||
\(988\) | 202.571 | 6.44466 | ||||||||
\(989\) | 1.16247 | 0.0369643 | ||||||||
\(990\) | −21.3507 | −0.678570 | ||||||||
\(991\) | −1.49719 | −0.0475599 | −0.0237800 | − | 0.999717i | \(-0.507570\pi\) | ||||
−0.0237800 | + | 0.999717i | \(0.507570\pi\) | |||||||
\(992\) | −65.8195 | −2.08977 | ||||||||
\(993\) | 34.4862 | 1.09439 | ||||||||
\(994\) | −93.6797 | −2.97134 | ||||||||
\(995\) | 0.0630338 | 0.00199831 | ||||||||
\(996\) | 36.1646 | 1.14592 | ||||||||
\(997\) | 15.4718 | 0.489996 | 0.244998 | − | 0.969524i | \(-0.421213\pi\) | ||||
0.244998 | + | 0.969524i | \(0.421213\pi\) | |||||||
\(998\) | 107.176 | 3.39261 | ||||||||
\(999\) | 5.55593 | 0.175782 |
(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.e.1.1 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.e.1.1 | ✓ | 82 | 1.1 | even | 1 | trivial |