Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.145 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92587 | 1.36180 | 0.680899 | − | 0.732377i | \(-0.261589\pi\) | ||||
0.680899 | + | 0.732377i | \(0.261589\pi\) | |||||||
\(3\) | 1.55925 | 0.900231 | 0.450115 | − | 0.892970i | \(-0.351383\pi\) | ||||
0.450115 | + | 0.892970i | \(0.351383\pi\) | |||||||
\(4\) | 1.70899 | 0.854494 | ||||||||
\(5\) | −3.80552 | −1.70188 | −0.850940 | − | 0.525263i | \(-0.823967\pi\) | ||||
−0.850940 | + | 0.525263i | \(0.823967\pi\) | |||||||
\(6\) | 3.00291 | 1.22593 | ||||||||
\(7\) | −0.241535 | −0.0912915 | −0.0456457 | − | 0.998958i | \(-0.514535\pi\) | ||||
−0.0456457 | + | 0.998958i | \(0.514535\pi\) | |||||||
\(8\) | −0.560450 | −0.198149 | ||||||||
\(9\) | −0.568752 | −0.189584 | ||||||||
\(10\) | −7.32895 | −2.31762 | ||||||||
\(11\) | 4.51627 | 1.36171 | 0.680853 | − | 0.732420i | \(-0.261609\pi\) | ||||
0.680853 | + | 0.732420i | \(0.261609\pi\) | |||||||
\(12\) | 2.66473 | 0.769242 | ||||||||
\(13\) | −2.64004 | −0.732215 | −0.366107 | − | 0.930573i | \(-0.619310\pi\) | ||||
−0.366107 | + | 0.930573i | \(0.619310\pi\) | |||||||
\(14\) | −0.465165 | −0.124321 | ||||||||
\(15\) | −5.93374 | −1.53209 | ||||||||
\(16\) | −4.49733 | −1.12433 | ||||||||
\(17\) | −0.0403322 | −0.00978199 | −0.00489100 | − | 0.999988i | \(-0.501557\pi\) | ||||
−0.00489100 | + | 0.999988i | \(0.501557\pi\) | |||||||
\(18\) | −1.09535 | −0.258175 | ||||||||
\(19\) | 7.82018 | 1.79407 | 0.897036 | − | 0.441958i | \(-0.145716\pi\) | ||||
0.897036 | + | 0.441958i | \(0.145716\pi\) | |||||||
\(20\) | −6.50359 | −1.45425 | ||||||||
\(21\) | −0.376612 | −0.0821834 | ||||||||
\(22\) | 8.69777 | 1.85437 | ||||||||
\(23\) | 9.16320 | 1.91066 | 0.955330 | − | 0.295542i | \(-0.0955003\pi\) | ||||
0.955330 | + | 0.295542i | \(0.0955003\pi\) | |||||||
\(24\) | −0.873880 | −0.178380 | ||||||||
\(25\) | 9.48199 | 1.89640 | ||||||||
\(26\) | −5.08438 | −0.997129 | ||||||||
\(27\) | −5.56456 | −1.07090 | ||||||||
\(28\) | −0.412780 | −0.0780081 | ||||||||
\(29\) | 4.49399 | 0.834512 | 0.417256 | − | 0.908789i | \(-0.362992\pi\) | ||||
0.417256 | + | 0.908789i | \(0.362992\pi\) | |||||||
\(30\) | −11.4276 | −2.08639 | ||||||||
\(31\) | 7.37396 | 1.32440 | 0.662201 | − | 0.749326i | \(-0.269622\pi\) | ||||
0.662201 | + | 0.749326i | \(0.269622\pi\) | |||||||
\(32\) | −7.54040 | −1.33297 | ||||||||
\(33\) | 7.04198 | 1.22585 | ||||||||
\(34\) | −0.0776747 | −0.0133211 | ||||||||
\(35\) | 0.919165 | 0.155367 | ||||||||
\(36\) | −0.971992 | −0.161999 | ||||||||
\(37\) | 4.70117 | 0.772867 | 0.386433 | − | 0.922317i | \(-0.373707\pi\) | ||||
0.386433 | + | 0.922317i | \(0.373707\pi\) | |||||||
\(38\) | 15.0607 | 2.44316 | ||||||||
\(39\) | −4.11647 | −0.659162 | ||||||||
\(40\) | 2.13281 | 0.337226 | ||||||||
\(41\) | 0.360772 | 0.0563431 | 0.0281716 | − | 0.999603i | \(-0.491032\pi\) | ||||
0.0281716 | + | 0.999603i | \(0.491032\pi\) | |||||||
\(42\) | −0.725306 | −0.111917 | ||||||||
\(43\) | −8.36820 | −1.27614 | −0.638069 | − | 0.769979i | \(-0.720267\pi\) | ||||
−0.638069 | + | 0.769979i | \(0.720267\pi\) | |||||||
\(44\) | 7.71826 | 1.16357 | ||||||||
\(45\) | 2.16440 | 0.322650 | ||||||||
\(46\) | 17.6472 | 2.60193 | ||||||||
\(47\) | 9.02076 | 1.31581 | 0.657906 | − | 0.753100i | \(-0.271442\pi\) | ||||
0.657906 | + | 0.753100i | \(0.271442\pi\) | |||||||
\(48\) | −7.01245 | −1.01216 | ||||||||
\(49\) | −6.94166 | −0.991666 | ||||||||
\(50\) | 18.2611 | 2.58251 | ||||||||
\(51\) | −0.0628878 | −0.00880605 | ||||||||
\(52\) | −4.51179 | −0.625673 | ||||||||
\(53\) | −10.8528 | −1.49074 | −0.745372 | − | 0.666649i | \(-0.767728\pi\) | ||||
−0.745372 | + | 0.666649i | \(0.767728\pi\) | |||||||
\(54\) | −10.7166 | −1.45835 | ||||||||
\(55\) | −17.1868 | −2.31746 | ||||||||
\(56\) | 0.135368 | 0.0180893 | ||||||||
\(57\) | 12.1936 | 1.61508 | ||||||||
\(58\) | 8.65485 | 1.13644 | ||||||||
\(59\) | −2.84122 | −0.369895 | −0.184948 | − | 0.982748i | \(-0.559212\pi\) | ||||
−0.184948 | + | 0.982748i | \(0.559212\pi\) | |||||||
\(60\) | −10.1407 | −1.30916 | ||||||||
\(61\) | −13.0672 | −1.67308 | −0.836540 | − | 0.547906i | \(-0.815425\pi\) | ||||
−0.836540 | + | 0.547906i | \(0.815425\pi\) | |||||||
\(62\) | 14.2013 | 1.80357 | ||||||||
\(63\) | 0.137373 | 0.0173074 | ||||||||
\(64\) | −5.52718 | −0.690898 | ||||||||
\(65\) | 10.0467 | 1.24614 | ||||||||
\(66\) | 13.5620 | 1.66936 | ||||||||
\(67\) | 4.86140 | 0.593914 | 0.296957 | − | 0.954891i | \(-0.404028\pi\) | ||||
0.296957 | + | 0.954891i | \(0.404028\pi\) | |||||||
\(68\) | −0.0689273 | −0.00835866 | ||||||||
\(69\) | 14.2877 | 1.72003 | ||||||||
\(70\) | 1.77019 | 0.211579 | ||||||||
\(71\) | 13.0255 | 1.54584 | 0.772922 | − | 0.634501i | \(-0.218794\pi\) | ||||
0.772922 | + | 0.634501i | \(0.218794\pi\) | |||||||
\(72\) | 0.318758 | 0.0375659 | ||||||||
\(73\) | 13.0676 | 1.52945 | 0.764725 | − | 0.644357i | \(-0.222875\pi\) | ||||
0.764725 | + | 0.644357i | \(0.222875\pi\) | |||||||
\(74\) | 9.05385 | 1.05249 | ||||||||
\(75\) | 14.7847 | 1.70720 | ||||||||
\(76\) | 13.3646 | 1.53302 | ||||||||
\(77\) | −1.09084 | −0.124312 | ||||||||
\(78\) | −7.92780 | −0.897646 | ||||||||
\(79\) | 17.0816 | 1.92184 | 0.960918 | − | 0.276834i | \(-0.0892852\pi\) | ||||
0.960918 | + | 0.276834i | \(0.0892852\pi\) | |||||||
\(80\) | 17.1147 | 1.91348 | ||||||||
\(81\) | −6.97026 | −0.774474 | ||||||||
\(82\) | 0.694801 | 0.0767280 | ||||||||
\(83\) | 2.70398 | 0.296801 | 0.148400 | − | 0.988927i | \(-0.452588\pi\) | ||||
0.148400 | + | 0.988927i | \(0.452588\pi\) | |||||||
\(84\) | −0.643625 | −0.0702253 | ||||||||
\(85\) | 0.153485 | 0.0166478 | ||||||||
\(86\) | −16.1161 | −1.73784 | ||||||||
\(87\) | 7.00723 | 0.751254 | ||||||||
\(88\) | −2.53115 | −0.269821 | ||||||||
\(89\) | 17.9898 | 1.90692 | 0.953459 | − | 0.301522i | \(-0.0974946\pi\) | ||||
0.953459 | + | 0.301522i | \(0.0974946\pi\) | |||||||
\(90\) | 4.16836 | 0.439384 | ||||||||
\(91\) | 0.637660 | 0.0668450 | ||||||||
\(92\) | 15.6598 | 1.63265 | ||||||||
\(93\) | 11.4978 | 1.19227 | ||||||||
\(94\) | 17.3728 | 1.79187 | ||||||||
\(95\) | −29.7598 | −3.05330 | ||||||||
\(96\) | −11.7573 | −1.19998 | ||||||||
\(97\) | −10.9780 | −1.11465 | −0.557325 | − | 0.830295i | \(-0.688172\pi\) | ||||
−0.557325 | + | 0.830295i | \(0.688172\pi\) | |||||||
\(98\) | −13.3688 | −1.35045 | ||||||||
\(99\) | −2.56864 | −0.258158 | ||||||||
\(100\) | 16.2046 | 1.62046 | ||||||||
\(101\) | 10.4638 | 1.04119 | 0.520593 | − | 0.853805i | \(-0.325711\pi\) | ||||
0.520593 | + | 0.853805i | \(0.325711\pi\) | |||||||
\(102\) | −0.121114 | −0.0119921 | ||||||||
\(103\) | 16.5376 | 1.62950 | 0.814749 | − | 0.579814i | \(-0.196875\pi\) | ||||
0.814749 | + | 0.579814i | \(0.196875\pi\) | |||||||
\(104\) | 1.47961 | 0.145088 | ||||||||
\(105\) | 1.43320 | 0.139866 | ||||||||
\(106\) | −20.9011 | −2.03009 | ||||||||
\(107\) | −0.407451 | −0.0393897 | −0.0196949 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196949 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(108\) | −9.50978 | −0.915079 | ||||||||
\(109\) | 2.61906 | 0.250860 | 0.125430 | − | 0.992102i | \(-0.459969\pi\) | ||||
0.125430 | + | 0.992102i | \(0.459969\pi\) | |||||||
\(110\) | −33.0995 | −3.15592 | ||||||||
\(111\) | 7.33027 | 0.695759 | ||||||||
\(112\) | 1.08626 | 0.102642 | ||||||||
\(113\) | −19.9364 | −1.87546 | −0.937729 | − | 0.347367i | \(-0.887076\pi\) | ||||
−0.937729 | + | 0.347367i | \(0.887076\pi\) | |||||||
\(114\) | 23.4833 | 2.19941 | ||||||||
\(115\) | −34.8707 | −3.25171 | ||||||||
\(116\) | 7.68017 | 0.713086 | ||||||||
\(117\) | 1.50153 | 0.138816 | ||||||||
\(118\) | −5.47183 | −0.503723 | ||||||||
\(119\) | 0.00974161 | 0.000893012 0 | ||||||||
\(120\) | 3.32557 | 0.303581 | ||||||||
\(121\) | 9.39670 | 0.854245 | ||||||||
\(122\) | −25.1657 | −2.27840 | ||||||||
\(123\) | 0.562532 | 0.0507218 | ||||||||
\(124\) | 12.6020 | 1.13169 | ||||||||
\(125\) | −17.0563 | −1.52556 | ||||||||
\(126\) | 0.264564 | 0.0235692 | ||||||||
\(127\) | 2.61364 | 0.231923 | 0.115961 | − | 0.993254i | \(-0.463005\pi\) | ||||
0.115961 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(128\) | 4.43614 | 0.392103 | ||||||||
\(129\) | −13.0481 | −1.14882 | ||||||||
\(130\) | 19.3487 | 1.69699 | ||||||||
\(131\) | 3.31099 | 0.289282 | 0.144641 | − | 0.989484i | \(-0.453797\pi\) | ||||
0.144641 | + | 0.989484i | \(0.453797\pi\) | |||||||
\(132\) | 12.0347 | 1.04748 | ||||||||
\(133\) | −1.88884 | −0.163783 | ||||||||
\(134\) | 9.36244 | 0.808792 | ||||||||
\(135\) | 21.1761 | 1.82254 | ||||||||
\(136\) | 0.0226042 | 0.00193829 | ||||||||
\(137\) | 1.88103 | 0.160707 | 0.0803537 | − | 0.996766i | \(-0.474395\pi\) | ||||
0.0803537 | + | 0.996766i | \(0.474395\pi\) | |||||||
\(138\) | 27.5163 | 2.34234 | ||||||||
\(139\) | 1.86057 | 0.157811 | 0.0789057 | − | 0.996882i | \(-0.474857\pi\) | ||||
0.0789057 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(140\) | 1.57084 | 0.132760 | ||||||||
\(141\) | 14.0656 | 1.18454 | ||||||||
\(142\) | 25.0855 | 2.10513 | ||||||||
\(143\) | −11.9231 | −0.997062 | ||||||||
\(144\) | 2.55787 | 0.213156 | ||||||||
\(145\) | −17.1020 | −1.42024 | ||||||||
\(146\) | 25.1666 | 2.08280 | ||||||||
\(147\) | −10.8238 | −0.892728 | ||||||||
\(148\) | 8.03424 | 0.660410 | ||||||||
\(149\) | −12.7440 | −1.04403 | −0.522015 | − | 0.852936i | \(-0.674819\pi\) | ||||
−0.522015 | + | 0.852936i | \(0.674819\pi\) | |||||||
\(150\) | 28.4736 | 2.32486 | ||||||||
\(151\) | −6.49721 | −0.528736 | −0.264368 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264368 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(152\) | −4.38282 | −0.355494 | ||||||||
\(153\) | 0.0229390 | 0.00185451 | ||||||||
\(154\) | −2.10081 | −0.169288 | ||||||||
\(155\) | −28.0618 | −2.25398 | ||||||||
\(156\) | −7.03500 | −0.563251 | ||||||||
\(157\) | 17.2640 | 1.37782 | 0.688908 | − | 0.724849i | \(-0.258090\pi\) | ||||
0.688908 | + | 0.724849i | \(0.258090\pi\) | |||||||
\(158\) | 32.8971 | 2.61715 | ||||||||
\(159\) | −16.9222 | −1.34201 | ||||||||
\(160\) | 28.6951 | 2.26855 | ||||||||
\(161\) | −2.21323 | −0.174427 | ||||||||
\(162\) | −13.4238 | −1.05468 | ||||||||
\(163\) | 4.02890 | 0.315568 | 0.157784 | − | 0.987474i | \(-0.449565\pi\) | ||||
0.157784 | + | 0.987474i | \(0.449565\pi\) | |||||||
\(164\) | 0.616556 | 0.0481449 | ||||||||
\(165\) | −26.7984 | −2.08625 | ||||||||
\(166\) | 5.20753 | 0.404183 | ||||||||
\(167\) | 8.20389 | 0.634836 | 0.317418 | − | 0.948286i | \(-0.397184\pi\) | ||||
0.317418 | + | 0.948286i | \(0.397184\pi\) | |||||||
\(168\) | 0.211072 | 0.0162846 | ||||||||
\(169\) | −6.03020 | −0.463862 | ||||||||
\(170\) | 0.295593 | 0.0226709 | ||||||||
\(171\) | −4.44775 | −0.340128 | ||||||||
\(172\) | −14.3012 | −1.09045 | ||||||||
\(173\) | −1.73616 | −0.131998 | −0.0659989 | − | 0.997820i | \(-0.521023\pi\) | ||||
−0.0659989 | + | 0.997820i | \(0.521023\pi\) | |||||||
\(174\) | 13.4950 | 1.02306 | ||||||||
\(175\) | −2.29023 | −0.173125 | ||||||||
\(176\) | −20.3112 | −1.53101 | ||||||||
\(177\) | −4.43016 | −0.332991 | ||||||||
\(178\) | 34.6461 | 2.59684 | ||||||||
\(179\) | −21.9604 | −1.64140 | −0.820700 | − | 0.571360i | \(-0.806416\pi\) | ||||
−0.820700 | + | 0.571360i | \(0.806416\pi\) | |||||||
\(180\) | 3.69893 | 0.275702 | ||||||||
\(181\) | −11.8627 | −0.881750 | −0.440875 | − | 0.897569i | \(-0.645332\pi\) | ||||
−0.440875 | + | 0.897569i | \(0.645332\pi\) | |||||||
\(182\) | 1.22805 | 0.0910293 | ||||||||
\(183\) | −20.3749 | −1.50616 | ||||||||
\(184\) | −5.13552 | −0.378596 | ||||||||
\(185\) | −17.8904 | −1.31533 | ||||||||
\(186\) | 22.1433 | 1.62363 | ||||||||
\(187\) | −0.182151 | −0.0133202 | ||||||||
\(188\) | 15.4164 | 1.12435 | ||||||||
\(189\) | 1.34403 | 0.0977641 | ||||||||
\(190\) | −57.3137 | −4.15797 | ||||||||
\(191\) | −12.0032 | −0.868521 | −0.434261 | − | 0.900787i | \(-0.642990\pi\) | ||||
−0.434261 | + | 0.900787i | \(0.642990\pi\) | |||||||
\(192\) | −8.61823 | −0.621968 | ||||||||
\(193\) | −8.16426 | −0.587677 | −0.293838 | − | 0.955855i | \(-0.594933\pi\) | ||||
−0.293838 | + | 0.955855i | \(0.594933\pi\) | |||||||
\(194\) | −21.1423 | −1.51793 | ||||||||
\(195\) | 15.6653 | 1.12182 | ||||||||
\(196\) | −11.8632 | −0.847373 | ||||||||
\(197\) | −11.6872 | −0.832679 | −0.416339 | − | 0.909209i | \(-0.636687\pi\) | ||||
−0.416339 | + | 0.909209i | \(0.636687\pi\) | |||||||
\(198\) | −4.94688 | −0.351559 | ||||||||
\(199\) | 10.1338 | 0.718364 | 0.359182 | − | 0.933268i | \(-0.383056\pi\) | ||||
0.359182 | + | 0.933268i | \(0.383056\pi\) | |||||||
\(200\) | −5.31418 | −0.375770 | ||||||||
\(201\) | 7.58012 | 0.534660 | ||||||||
\(202\) | 20.1519 | 1.41788 | ||||||||
\(203\) | −1.08545 | −0.0761839 | ||||||||
\(204\) | −0.107475 | −0.00752472 | ||||||||
\(205\) | −1.37293 | −0.0958893 | ||||||||
\(206\) | 31.8493 | 2.21905 | ||||||||
\(207\) | −5.21159 | −0.362231 | ||||||||
\(208\) | 11.8731 | 0.823254 | ||||||||
\(209\) | 35.3180 | 2.44300 | ||||||||
\(210\) | 2.76017 | 0.190470 | ||||||||
\(211\) | −19.8357 | −1.36555 | −0.682774 | − | 0.730629i | \(-0.739227\pi\) | ||||
−0.682774 | + | 0.730629i | \(0.739227\pi\) | |||||||
\(212\) | −18.5473 | −1.27383 | ||||||||
\(213\) | 20.3100 | 1.39162 | ||||||||
\(214\) | −0.784699 | −0.0536409 | ||||||||
\(215\) | 31.8454 | 2.17184 | ||||||||
\(216\) | 3.11866 | 0.212198 | ||||||||
\(217\) | −1.78107 | −0.120907 | ||||||||
\(218\) | 5.04397 | 0.341621 | ||||||||
\(219\) | 20.3756 | 1.37686 | ||||||||
\(220\) | −29.3720 | −1.98026 | ||||||||
\(221\) | 0.106478 | 0.00716252 | ||||||||
\(222\) | 14.1172 | 0.947483 | ||||||||
\(223\) | −17.8267 | −1.19377 | −0.596883 | − | 0.802328i | \(-0.703594\pi\) | ||||
−0.596883 | + | 0.802328i | \(0.703594\pi\) | |||||||
\(224\) | 1.82127 | 0.121688 | ||||||||
\(225\) | −5.39290 | −0.359527 | ||||||||
\(226\) | −38.3950 | −2.55400 | ||||||||
\(227\) | −21.2212 | −1.40850 | −0.704252 | − | 0.709950i | \(-0.748717\pi\) | ||||
−0.704252 | + | 0.709950i | \(0.748717\pi\) | |||||||
\(228\) | 20.8387 | 1.38008 | ||||||||
\(229\) | −2.74103 | −0.181132 | −0.0905660 | − | 0.995890i | \(-0.528868\pi\) | ||||
−0.0905660 | + | 0.995890i | \(0.528868\pi\) | |||||||
\(230\) | −67.1566 | −4.42818 | ||||||||
\(231\) | −1.70088 | −0.111910 | ||||||||
\(232\) | −2.51866 | −0.165358 | ||||||||
\(233\) | −5.03032 | −0.329547 | −0.164773 | − | 0.986331i | \(-0.552689\pi\) | ||||
−0.164773 | + | 0.986331i | \(0.552689\pi\) | |||||||
\(234\) | 2.89175 | 0.189040 | ||||||||
\(235\) | −34.3287 | −2.23936 | ||||||||
\(236\) | −4.85561 | −0.316073 | ||||||||
\(237\) | 26.6345 | 1.73010 | ||||||||
\(238\) | 0.0187611 | 0.00121610 | ||||||||
\(239\) | 1.48484 | 0.0960464 | 0.0480232 | − | 0.998846i | \(-0.484708\pi\) | ||||
0.0480232 | + | 0.998846i | \(0.484708\pi\) | |||||||
\(240\) | 26.6860 | 1.72258 | ||||||||
\(241\) | 9.91003 | 0.638361 | 0.319180 | − | 0.947694i | \(-0.396592\pi\) | ||||
0.319180 | + | 0.947694i | \(0.396592\pi\) | |||||||
\(242\) | 18.0969 | 1.16331 | ||||||||
\(243\) | 5.82533 | 0.373695 | ||||||||
\(244\) | −22.3317 | −1.42964 | ||||||||
\(245\) | 26.4166 | 1.68770 | ||||||||
\(246\) | 1.08337 | 0.0690729 | ||||||||
\(247\) | −20.6456 | −1.31365 | ||||||||
\(248\) | −4.13274 | −0.262429 | ||||||||
\(249\) | 4.21618 | 0.267189 | ||||||||
\(250\) | −32.8483 | −2.07751 | ||||||||
\(251\) | −15.4192 | −0.973249 | −0.486624 | − | 0.873611i | \(-0.661772\pi\) | ||||
−0.486624 | + | 0.873611i | \(0.661772\pi\) | |||||||
\(252\) | 0.234770 | 0.0147891 | ||||||||
\(253\) | 41.3835 | 2.60176 | ||||||||
\(254\) | 5.03353 | 0.315832 | ||||||||
\(255\) | 0.239321 | 0.0149868 | ||||||||
\(256\) | 19.5978 | 1.22486 | ||||||||
\(257\) | 21.1289 | 1.31799 | 0.658993 | − | 0.752149i | \(-0.270983\pi\) | ||||
0.658993 | + | 0.752149i | \(0.270983\pi\) | |||||||
\(258\) | −25.1290 | −1.56446 | ||||||||
\(259\) | −1.13549 | −0.0705562 | ||||||||
\(260\) | 17.1697 | 1.06482 | ||||||||
\(261\) | −2.55597 | −0.158210 | ||||||||
\(262\) | 6.37654 | 0.393944 | ||||||||
\(263\) | −9.18975 | −0.566664 | −0.283332 | − | 0.959022i | \(-0.591440\pi\) | ||||
−0.283332 | + | 0.959022i | \(0.591440\pi\) | |||||||
\(264\) | −3.94668 | −0.242901 | ||||||||
\(265\) | 41.3005 | 2.53707 | ||||||||
\(266\) | −3.63767 | −0.223040 | ||||||||
\(267\) | 28.0506 | 1.71667 | ||||||||
\(268\) | 8.30808 | 0.507497 | ||||||||
\(269\) | −19.5231 | −1.19034 | −0.595171 | − | 0.803599i | \(-0.702916\pi\) | ||||
−0.595171 | + | 0.803599i | \(0.702916\pi\) | |||||||
\(270\) | 40.7824 | 2.48194 | ||||||||
\(271\) | 11.9398 | 0.725292 | 0.362646 | − | 0.931927i | \(-0.381873\pi\) | ||||
0.362646 | + | 0.931927i | \(0.381873\pi\) | |||||||
\(272\) | 0.181387 | 0.0109982 | ||||||||
\(273\) | 0.994269 | 0.0601759 | ||||||||
\(274\) | 3.62263 | 0.218851 | ||||||||
\(275\) | 42.8232 | 2.58234 | ||||||||
\(276\) | 24.4175 | 1.46976 | ||||||||
\(277\) | −15.0490 | −0.904204 | −0.452102 | − | 0.891966i | \(-0.649326\pi\) | ||||
−0.452102 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(278\) | 3.58322 | 0.214907 | ||||||||
\(279\) | −4.19396 | −0.251086 | ||||||||
\(280\) | −0.515146 | −0.0307859 | ||||||||
\(281\) | 31.0218 | 1.85061 | 0.925303 | − | 0.379228i | \(-0.123810\pi\) | ||||
0.925303 | + | 0.379228i | \(0.123810\pi\) | |||||||
\(282\) | 27.0885 | 1.61310 | ||||||||
\(283\) | 4.60383 | 0.273669 | 0.136835 | − | 0.990594i | \(-0.456307\pi\) | ||||
0.136835 | + | 0.990594i | \(0.456307\pi\) | |||||||
\(284\) | 22.2605 | 1.32091 | ||||||||
\(285\) | −46.4029 | −2.74867 | ||||||||
\(286\) | −22.9624 | −1.35780 | ||||||||
\(287\) | −0.0871389 | −0.00514365 | ||||||||
\(288\) | 4.28862 | 0.252709 | ||||||||
\(289\) | −16.9984 | −0.999904 | ||||||||
\(290\) | −32.9362 | −1.93408 | ||||||||
\(291\) | −17.1174 | −1.00344 | ||||||||
\(292\) | 22.3324 | 1.30691 | ||||||||
\(293\) | 31.2883 | 1.82788 | 0.913940 | − | 0.405848i | \(-0.133024\pi\) | ||||
0.913940 | + | 0.405848i | \(0.133024\pi\) | |||||||
\(294\) | −20.8452 | −1.21572 | ||||||||
\(295\) | 10.8123 | 0.629518 | ||||||||
\(296\) | −2.63477 | −0.153143 | ||||||||
\(297\) | −25.1311 | −1.45825 | ||||||||
\(298\) | −24.5433 | −1.42176 | ||||||||
\(299\) | −24.1912 | −1.39901 | ||||||||
\(300\) | 25.2670 | 1.45879 | ||||||||
\(301\) | 2.02121 | 0.116501 | ||||||||
\(302\) | −12.5128 | −0.720031 | ||||||||
\(303\) | 16.3156 | 0.937307 | ||||||||
\(304\) | −35.1700 | −2.01714 | ||||||||
\(305\) | 49.7274 | 2.84738 | ||||||||
\(306\) | 0.0441777 | 0.00252547 | ||||||||
\(307\) | 0.0701815 | 0.00400547 | 0.00200273 | − | 0.999998i | \(-0.499363\pi\) | ||||
0.00200273 | + | 0.999998i | \(0.499363\pi\) | |||||||
\(308\) | −1.86423 | −0.106224 | ||||||||
\(309\) | 25.7862 | 1.46692 | ||||||||
\(310\) | −54.0434 | −3.06946 | ||||||||
\(311\) | −20.7286 | −1.17541 | −0.587705 | − | 0.809075i | \(-0.699968\pi\) | ||||
−0.587705 | + | 0.809075i | \(0.699968\pi\) | |||||||
\(312\) | 2.30708 | 0.130612 | ||||||||
\(313\) | 6.24610 | 0.353051 | 0.176525 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176525 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(314\) | 33.2483 | 1.87631 | ||||||||
\(315\) | −0.522777 | −0.0294552 | ||||||||
\(316\) | 29.1923 | 1.64220 | ||||||||
\(317\) | 2.10936 | 0.118473 | 0.0592366 | − | 0.998244i | \(-0.481133\pi\) | ||||
0.0592366 | + | 0.998244i | \(0.481133\pi\) | |||||||
\(318\) | −32.5899 | −1.82755 | ||||||||
\(319\) | 20.2961 | 1.13636 | ||||||||
\(320\) | 21.0338 | 1.17583 | ||||||||
\(321\) | −0.635316 | −0.0354599 | ||||||||
\(322\) | −4.26240 | −0.237534 | ||||||||
\(323\) | −0.315405 | −0.0175496 | ||||||||
\(324\) | −11.9121 | −0.661783 | ||||||||
\(325\) | −25.0328 | −1.38857 | ||||||||
\(326\) | 7.75916 | 0.429740 | ||||||||
\(327\) | 4.08375 | 0.225832 | ||||||||
\(328\) | −0.202195 | −0.0111643 | ||||||||
\(329\) | −2.17882 | −0.120122 | ||||||||
\(330\) | −51.6103 | −2.84105 | ||||||||
\(331\) | 20.8793 | 1.14763 | 0.573814 | − | 0.818986i | \(-0.305463\pi\) | ||||
0.573814 | + | 0.818986i | \(0.305463\pi\) | |||||||
\(332\) | 4.62108 | 0.253615 | ||||||||
\(333\) | −2.67380 | −0.146523 | ||||||||
\(334\) | 15.7997 | 0.864519 | ||||||||
\(335\) | −18.5002 | −1.01077 | ||||||||
\(336\) | 1.69375 | 0.0924016 | ||||||||
\(337\) | −15.8906 | −0.865618 | −0.432809 | − | 0.901486i | \(-0.642478\pi\) | ||||
−0.432809 | + | 0.901486i | \(0.642478\pi\) | |||||||
\(338\) | −11.6134 | −0.631686 | ||||||||
\(339\) | −31.0857 | −1.68835 | ||||||||
\(340\) | 0.262304 | 0.0142254 | ||||||||
\(341\) | 33.3028 | 1.80345 | ||||||||
\(342\) | −8.56579 | −0.463185 | ||||||||
\(343\) | 3.36739 | 0.181822 | ||||||||
\(344\) | 4.68996 | 0.252866 | ||||||||
\(345\) | −54.3721 | −2.92729 | ||||||||
\(346\) | −3.34363 | −0.179754 | ||||||||
\(347\) | −2.36350 | −0.126879 | −0.0634397 | − | 0.997986i | \(-0.520207\pi\) | ||||
−0.0634397 | + | 0.997986i | \(0.520207\pi\) | |||||||
\(348\) | 11.9753 | 0.641942 | ||||||||
\(349\) | 1.27289 | 0.0681362 | 0.0340681 | − | 0.999420i | \(-0.489154\pi\) | ||||
0.0340681 | + | 0.999420i | \(0.489154\pi\) | |||||||
\(350\) | −4.41069 | −0.235761 | ||||||||
\(351\) | 14.6907 | 0.784129 | ||||||||
\(352\) | −34.0545 | −1.81511 | ||||||||
\(353\) | −17.5982 | −0.936657 | −0.468328 | − | 0.883554i | \(-0.655144\pi\) | ||||
−0.468328 | + | 0.883554i | \(0.655144\pi\) | |||||||
\(354\) | −8.53193 | −0.453467 | ||||||||
\(355\) | −49.5688 | −2.63084 | ||||||||
\(356\) | 30.7444 | 1.62945 | ||||||||
\(357\) | 0.0151896 | 0.000803917 0 | ||||||||
\(358\) | −42.2930 | −2.23525 | ||||||||
\(359\) | 16.9880 | 0.896592 | 0.448296 | − | 0.893885i | \(-0.352031\pi\) | ||||
0.448296 | + | 0.893885i | \(0.352031\pi\) | |||||||
\(360\) | −1.21304 | −0.0639327 | ||||||||
\(361\) | 42.1552 | 2.21869 | ||||||||
\(362\) | −22.8461 | −1.20076 | ||||||||
\(363\) | 14.6518 | 0.769018 | ||||||||
\(364\) | 1.08975 | 0.0571186 | ||||||||
\(365\) | −49.7291 | −2.60294 | ||||||||
\(366\) | −39.2395 | −2.05108 | ||||||||
\(367\) | −5.49070 | −0.286612 | −0.143306 | − | 0.989678i | \(-0.545773\pi\) | ||||
−0.143306 | + | 0.989678i | \(0.545773\pi\) | |||||||
\(368\) | −41.2100 | −2.14822 | ||||||||
\(369\) | −0.205190 | −0.0106818 | ||||||||
\(370\) | −34.4546 | −1.79121 | ||||||||
\(371\) | 2.62132 | 0.136092 | ||||||||
\(372\) | 19.6496 | 1.01879 | ||||||||
\(373\) | 17.0082 | 0.880652 | 0.440326 | − | 0.897838i | \(-0.354863\pi\) | ||||
0.440326 | + | 0.897838i | \(0.354863\pi\) | |||||||
\(374\) | −0.350800 | −0.0181394 | ||||||||
\(375\) | −26.5949 | −1.37336 | ||||||||
\(376\) | −5.05569 | −0.260727 | ||||||||
\(377\) | −11.8643 | −0.611042 | ||||||||
\(378\) | 2.58844 | 0.133135 | ||||||||
\(379\) | 1.87958 | 0.0965477 | 0.0482739 | − | 0.998834i | \(-0.484628\pi\) | ||||
0.0482739 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(380\) | −50.8592 | −2.60902 | ||||||||
\(381\) | 4.07530 | 0.208784 | ||||||||
\(382\) | −23.1166 | −1.18275 | ||||||||
\(383\) | 31.8719 | 1.62858 | 0.814289 | − | 0.580459i | \(-0.197127\pi\) | ||||
0.814289 | + | 0.580459i | \(0.197127\pi\) | |||||||
\(384\) | 6.91703 | 0.352983 | ||||||||
\(385\) | 4.15120 | 0.211565 | ||||||||
\(386\) | −15.7233 | −0.800297 | ||||||||
\(387\) | 4.75943 | 0.241936 | ||||||||
\(388\) | −18.7613 | −0.952462 | ||||||||
\(389\) | 27.7644 | 1.40771 | 0.703854 | − | 0.710344i | \(-0.251461\pi\) | ||||
0.703854 | + | 0.710344i | \(0.251461\pi\) | |||||||
\(390\) | 30.1694 | 1.52769 | ||||||||
\(391\) | −0.369572 | −0.0186901 | ||||||||
\(392\) | 3.89046 | 0.196498 | ||||||||
\(393\) | 5.16264 | 0.260421 | ||||||||
\(394\) | −22.5081 | −1.13394 | ||||||||
\(395\) | −65.0046 | −3.27073 | ||||||||
\(396\) | −4.38978 | −0.220595 | ||||||||
\(397\) | 6.86918 | 0.344754 | 0.172377 | − | 0.985031i | \(-0.444855\pi\) | ||||
0.172377 | + | 0.985031i | \(0.444855\pi\) | |||||||
\(398\) | 19.5164 | 0.978267 | ||||||||
\(399\) | −2.94517 | −0.147443 | ||||||||
\(400\) | −42.6437 | −2.13218 | ||||||||
\(401\) | −26.3264 | −1.31468 | −0.657339 | − | 0.753595i | \(-0.728318\pi\) | ||||
−0.657339 | + | 0.753595i | \(0.728318\pi\) | |||||||
\(402\) | 14.5983 | 0.728099 | ||||||||
\(403\) | −19.4675 | −0.969747 | ||||||||
\(404\) | 17.8825 | 0.889687 | ||||||||
\(405\) | 26.5255 | 1.31806 | ||||||||
\(406\) | −2.09044 | −0.103747 | ||||||||
\(407\) | 21.2317 | 1.05242 | ||||||||
\(408\) | 0.0352455 | 0.00174491 | ||||||||
\(409\) | 2.97792 | 0.147249 | 0.0736244 | − | 0.997286i | \(-0.476543\pi\) | ||||
0.0736244 | + | 0.997286i | \(0.476543\pi\) | |||||||
\(410\) | −2.64408 | −0.130582 | ||||||||
\(411\) | 2.93299 | 0.144674 | ||||||||
\(412\) | 28.2626 | 1.39240 | ||||||||
\(413\) | 0.686253 | 0.0337683 | ||||||||
\(414\) | −10.0369 | −0.493285 | ||||||||
\(415\) | −10.2901 | −0.505120 | ||||||||
\(416\) | 19.9069 | 0.976018 | ||||||||
\(417\) | 2.90108 | 0.142067 | ||||||||
\(418\) | 68.0181 | 3.32687 | ||||||||
\(419\) | 11.6573 | 0.569495 | 0.284748 | − | 0.958603i | \(-0.408090\pi\) | ||||
0.284748 | + | 0.958603i | \(0.408090\pi\) | |||||||
\(420\) | 2.44933 | 0.119515 | ||||||||
\(421\) | 12.1251 | 0.590942 | 0.295471 | − | 0.955352i | \(-0.404523\pi\) | ||||
0.295471 | + | 0.955352i | \(0.404523\pi\) | |||||||
\(422\) | −38.2011 | −1.85960 | ||||||||
\(423\) | −5.13058 | −0.249457 | ||||||||
\(424\) | 6.08245 | 0.295390 | ||||||||
\(425\) | −0.382429 | −0.0185505 | ||||||||
\(426\) | 39.1144 | 1.89510 | ||||||||
\(427\) | 3.15617 | 0.152738 | ||||||||
\(428\) | −0.696329 | −0.0336583 | ||||||||
\(429\) | −18.5911 | −0.897586 | ||||||||
\(430\) | 61.3301 | 2.95760 | ||||||||
\(431\) | −15.2477 | −0.734458 | −0.367229 | − | 0.930131i | \(-0.619693\pi\) | ||||
−0.367229 | + | 0.930131i | \(0.619693\pi\) | |||||||
\(432\) | 25.0257 | 1.20405 | ||||||||
\(433\) | 10.6963 | 0.514033 | 0.257016 | − | 0.966407i | \(-0.417261\pi\) | ||||
0.257016 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(434\) | −3.43011 | −0.164650 | ||||||||
\(435\) | −26.6662 | −1.27854 | ||||||||
\(436\) | 4.47594 | 0.214359 | ||||||||
\(437\) | 71.6579 | 3.42786 | ||||||||
\(438\) | 39.2409 | 1.87500 | ||||||||
\(439\) | 18.3356 | 0.875109 | 0.437554 | − | 0.899192i | \(-0.355845\pi\) | ||||
0.437554 | + | 0.899192i | \(0.355845\pi\) | |||||||
\(440\) | 9.63233 | 0.459203 | ||||||||
\(441\) | 3.94809 | 0.188004 | ||||||||
\(442\) | 0.205064 | 0.00975390 | ||||||||
\(443\) | 1.65444 | 0.0786048 | 0.0393024 | − | 0.999227i | \(-0.487486\pi\) | ||||
0.0393024 | + | 0.999227i | \(0.487486\pi\) | |||||||
\(444\) | 12.5274 | 0.594522 | ||||||||
\(445\) | −68.4607 | −3.24535 | ||||||||
\(446\) | −34.3320 | −1.62567 | ||||||||
\(447\) | −19.8710 | −0.939868 | ||||||||
\(448\) | 1.33501 | 0.0630731 | ||||||||
\(449\) | 25.7870 | 1.21696 | 0.608482 | − | 0.793568i | \(-0.291779\pi\) | ||||
0.608482 | + | 0.793568i | \(0.291779\pi\) | |||||||
\(450\) | −10.3860 | −0.489603 | ||||||||
\(451\) | 1.62934 | 0.0767228 | ||||||||
\(452\) | −34.0711 | −1.60257 | ||||||||
\(453\) | −10.1308 | −0.475984 | ||||||||
\(454\) | −40.8694 | −1.91810 | ||||||||
\(455\) | −2.42663 | −0.113762 | ||||||||
\(456\) | −6.83390 | −0.320027 | ||||||||
\(457\) | −0.922525 | −0.0431539 | −0.0215770 | − | 0.999767i | \(-0.506869\pi\) | ||||
−0.0215770 | + | 0.999767i | \(0.506869\pi\) | |||||||
\(458\) | −5.27887 | −0.246665 | ||||||||
\(459\) | 0.224431 | 0.0104755 | ||||||||
\(460\) | −59.5937 | −2.77857 | ||||||||
\(461\) | −36.6179 | −1.70547 | −0.852734 | − | 0.522346i | \(-0.825057\pi\) | ||||
−0.852734 | + | 0.522346i | \(0.825057\pi\) | |||||||
\(462\) | −3.27568 | −0.152398 | ||||||||
\(463\) | −15.5084 | −0.720737 | −0.360369 | − | 0.932810i | \(-0.617349\pi\) | ||||
−0.360369 | + | 0.932810i | \(0.617349\pi\) | |||||||
\(464\) | −20.2110 | −0.938270 | ||||||||
\(465\) | −43.7552 | −2.02910 | ||||||||
\(466\) | −9.68775 | −0.448776 | ||||||||
\(467\) | −23.7761 | −1.10023 | −0.550113 | − | 0.835090i | \(-0.685415\pi\) | ||||
−0.550113 | + | 0.835090i | \(0.685415\pi\) | |||||||
\(468\) | 2.56609 | 0.118618 | ||||||||
\(469\) | −1.17420 | −0.0542193 | ||||||||
\(470\) | −66.1127 | −3.04955 | ||||||||
\(471\) | 26.9188 | 1.24035 | ||||||||
\(472\) | 1.59236 | 0.0732944 | ||||||||
\(473\) | −37.7931 | −1.73773 | ||||||||
\(474\) | 51.2947 | 2.35604 | ||||||||
\(475\) | 74.1508 | 3.40227 | ||||||||
\(476\) | 0.0166483 | 0.000763074 0 | ||||||||
\(477\) | 6.17255 | 0.282621 | ||||||||
\(478\) | 2.85962 | 0.130796 | ||||||||
\(479\) | 26.2354 | 1.19872 | 0.599362 | − | 0.800478i | \(-0.295421\pi\) | ||||
0.599362 | + | 0.800478i | \(0.295421\pi\) | |||||||
\(480\) | 44.7428 | 2.04222 | ||||||||
\(481\) | −12.4113 | −0.565904 | ||||||||
\(482\) | 19.0855 | 0.869319 | ||||||||
\(483\) | −3.45097 | −0.157024 | ||||||||
\(484\) | 16.0589 | 0.729948 | ||||||||
\(485\) | 41.7771 | 1.89700 | ||||||||
\(486\) | 11.2189 | 0.508898 | ||||||||
\(487\) | 4.40302 | 0.199520 | 0.0997599 | − | 0.995012i | \(-0.468193\pi\) | ||||
0.0997599 | + | 0.995012i | \(0.468193\pi\) | |||||||
\(488\) | 7.32350 | 0.331519 | ||||||||
\(489\) | 6.28205 | 0.284084 | ||||||||
\(490\) | 50.8751 | 2.29830 | ||||||||
\(491\) | −31.2403 | −1.40985 | −0.704927 | − | 0.709280i | \(-0.749020\pi\) | ||||
−0.704927 | + | 0.709280i | \(0.749020\pi\) | |||||||
\(492\) | 0.961362 | 0.0433415 | ||||||||
\(493\) | −0.181252 | −0.00816319 | ||||||||
\(494\) | −39.7607 | −1.78892 | ||||||||
\(495\) | 9.77501 | 0.439354 | ||||||||
\(496\) | −33.1632 | −1.48907 | ||||||||
\(497\) | −3.14611 | −0.141122 | ||||||||
\(498\) | 8.11982 | 0.363858 | ||||||||
\(499\) | −1.12984 | −0.0505786 | −0.0252893 | − | 0.999680i | \(-0.508051\pi\) | ||||
−0.0252893 | + | 0.999680i | \(0.508051\pi\) | |||||||
\(500\) | −29.1490 | −1.30358 | ||||||||
\(501\) | 12.7919 | 0.571499 | ||||||||
\(502\) | −29.6953 | −1.32537 | ||||||||
\(503\) | −17.4507 | −0.778089 | −0.389045 | − | 0.921219i | \(-0.627195\pi\) | ||||
−0.389045 | + | 0.921219i | \(0.627195\pi\) | |||||||
\(504\) | −0.0769910 | −0.00342945 | ||||||||
\(505\) | −39.8201 | −1.77197 | ||||||||
\(506\) | 79.6994 | 3.54307 | ||||||||
\(507\) | −9.40257 | −0.417583 | ||||||||
\(508\) | 4.46668 | 0.198177 | ||||||||
\(509\) | 33.0181 | 1.46350 | 0.731750 | − | 0.681573i | \(-0.238704\pi\) | ||||
0.731750 | + | 0.681573i | \(0.238704\pi\) | |||||||
\(510\) | 0.460902 | 0.0204091 | ||||||||
\(511\) | −3.15628 | −0.139626 | ||||||||
\(512\) | 28.8706 | 1.27591 | ||||||||
\(513\) | −43.5159 | −1.92127 | ||||||||
\(514\) | 40.6916 | 1.79483 | ||||||||
\(515\) | −62.9342 | −2.77321 | ||||||||
\(516\) | −22.2990 | −0.981660 | ||||||||
\(517\) | 40.7402 | 1.79175 | ||||||||
\(518\) | −2.18682 | −0.0960832 | ||||||||
\(519\) | −2.70710 | −0.118829 | ||||||||
\(520\) | −5.63069 | −0.246922 | ||||||||
\(521\) | 1.55627 | 0.0681815 | 0.0340908 | − | 0.999419i | \(-0.489146\pi\) | ||||
0.0340908 | + | 0.999419i | \(0.489146\pi\) | |||||||
\(522\) | −4.92247 | −0.215451 | ||||||||
\(523\) | −26.4168 | −1.15513 | −0.577563 | − | 0.816346i | \(-0.695996\pi\) | ||||
−0.577563 | + | 0.816346i | \(0.695996\pi\) | |||||||
\(524\) | 5.65844 | 0.247190 | ||||||||
\(525\) | −3.57103 | −0.155852 | ||||||||
\(526\) | −17.6983 | −0.771682 | ||||||||
\(527\) | −0.297408 | −0.0129553 | ||||||||
\(528\) | −31.6701 | −1.37827 | ||||||||
\(529\) | 60.9642 | 2.65062 | ||||||||
\(530\) | 79.5395 | 3.45497 | ||||||||
\(531\) | 1.61595 | 0.0701263 | ||||||||
\(532\) | −3.22801 | −0.139952 | ||||||||
\(533\) | −0.952452 | −0.0412553 | ||||||||
\(534\) | 54.0219 | 2.33775 | ||||||||
\(535\) | 1.55056 | 0.0670366 | ||||||||
\(536\) | −2.72457 | −0.117684 | ||||||||
\(537\) | −34.2417 | −1.47764 | ||||||||
\(538\) | −37.5990 | −1.62101 | ||||||||
\(539\) | −31.3504 | −1.35036 | ||||||||
\(540\) | 36.1896 | 1.55735 | ||||||||
\(541\) | −0.463213 | −0.0199151 | −0.00995755 | − | 0.999950i | \(-0.503170\pi\) | ||||
−0.00995755 | + | 0.999950i | \(0.503170\pi\) | |||||||
\(542\) | 22.9946 | 0.987701 | ||||||||
\(543\) | −18.4969 | −0.793778 | ||||||||
\(544\) | 0.304121 | 0.0130391 | ||||||||
\(545\) | −9.96688 | −0.426934 | ||||||||
\(546\) | 1.91484 | 0.0819474 | ||||||||
\(547\) | −4.41548 | −0.188792 | −0.0943961 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943961 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(548\) | 3.21466 | 0.137324 | ||||||||
\(549\) | 7.43199 | 0.317189 | ||||||||
\(550\) | 82.4721 | 3.51662 | ||||||||
\(551\) | 35.1438 | 1.49718 | ||||||||
\(552\) | −8.00754 | −0.340823 | ||||||||
\(553\) | −4.12581 | −0.175447 | ||||||||
\(554\) | −28.9824 | −1.23134 | ||||||||
\(555\) | −27.8955 | −1.18410 | ||||||||
\(556\) | 3.17969 | 0.134849 | ||||||||
\(557\) | −30.7259 | −1.30190 | −0.650949 | − | 0.759121i | \(-0.725629\pi\) | ||||
−0.650949 | + | 0.759121i | \(0.725629\pi\) | |||||||
\(558\) | −8.07703 | −0.341928 | ||||||||
\(559\) | 22.0924 | 0.934407 | ||||||||
\(560\) | −4.13379 | −0.174685 | ||||||||
\(561\) | −0.284018 | −0.0119913 | ||||||||
\(562\) | 59.7441 | 2.52015 | ||||||||
\(563\) | 11.0243 | 0.464617 | 0.232309 | − | 0.972642i | \(-0.425372\pi\) | ||||
0.232309 | + | 0.972642i | \(0.425372\pi\) | |||||||
\(564\) | 24.0379 | 1.01218 | ||||||||
\(565\) | 75.8684 | 3.19181 | ||||||||
\(566\) | 8.86639 | 0.372682 | ||||||||
\(567\) | 1.68356 | 0.0707028 | ||||||||
\(568\) | −7.30015 | −0.306308 | ||||||||
\(569\) | −2.47167 | −0.103618 | −0.0518090 | − | 0.998657i | \(-0.516499\pi\) | ||||
−0.0518090 | + | 0.998657i | \(0.516499\pi\) | |||||||
\(570\) | −89.3661 | −3.74314 | ||||||||
\(571\) | 6.15024 | 0.257380 | 0.128690 | − | 0.991685i | \(-0.458923\pi\) | ||||
0.128690 | + | 0.991685i | \(0.458923\pi\) | |||||||
\(572\) | −20.3765 | −0.851984 | ||||||||
\(573\) | −18.7159 | −0.781870 | ||||||||
\(574\) | −0.167819 | −0.00700461 | ||||||||
\(575\) | 86.8853 | 3.62337 | ||||||||
\(576\) | 3.14360 | 0.130983 | ||||||||
\(577\) | −1.34304 | −0.0559114 | −0.0279557 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279557 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(578\) | −32.7367 | −1.36167 | ||||||||
\(579\) | −12.7301 | −0.529045 | ||||||||
\(580\) | −29.2271 | −1.21359 | ||||||||
\(581\) | −0.653106 | −0.0270954 | ||||||||
\(582\) | −32.9660 | −1.36649 | ||||||||
\(583\) | −49.0141 | −2.02996 | ||||||||
\(584\) | −7.32376 | −0.303059 | ||||||||
\(585\) | −5.71409 | −0.236249 | ||||||||
\(586\) | 60.2573 | 2.48920 | ||||||||
\(587\) | −28.5062 | −1.17658 | −0.588288 | − | 0.808651i | \(-0.700198\pi\) | ||||
−0.588288 | + | 0.808651i | \(0.700198\pi\) | |||||||
\(588\) | −18.4977 | −0.762831 | ||||||||
\(589\) | 57.6657 | 2.37607 | ||||||||
\(590\) | 20.8232 | 0.857276 | ||||||||
\(591\) | −18.2232 | −0.749603 | ||||||||
\(592\) | −21.1427 | −0.868960 | ||||||||
\(593\) | 25.6786 | 1.05449 | 0.527247 | − | 0.849712i | \(-0.323224\pi\) | ||||
0.527247 | + | 0.849712i | \(0.323224\pi\) | |||||||
\(594\) | −48.3993 | −1.98585 | ||||||||
\(595\) | −0.0370719 | −0.00151980 | ||||||||
\(596\) | −21.7794 | −0.892118 | ||||||||
\(597\) | 15.8010 | 0.646693 | ||||||||
\(598\) | −46.5892 | −1.90517 | ||||||||
\(599\) | −10.4424 | −0.426664 | −0.213332 | − | 0.976980i | \(-0.568432\pi\) | ||||
−0.213332 | + | 0.976980i | \(0.568432\pi\) | |||||||
\(600\) | −8.28612 | −0.338279 | ||||||||
\(601\) | 17.4730 | 0.712739 | 0.356369 | − | 0.934345i | \(-0.384014\pi\) | ||||
0.356369 | + | 0.934345i | \(0.384014\pi\) | |||||||
\(602\) | 3.89259 | 0.158650 | ||||||||
\(603\) | −2.76493 | −0.112597 | ||||||||
\(604\) | −11.1037 | −0.451802 | ||||||||
\(605\) | −35.7593 | −1.45382 | ||||||||
\(606\) | 31.4218 | 1.27642 | ||||||||
\(607\) | 13.8759 | 0.563205 | 0.281602 | − | 0.959531i | \(-0.409134\pi\) | ||||
0.281602 | + | 0.959531i | \(0.409134\pi\) | |||||||
\(608\) | −58.9672 | −2.39144 | ||||||||
\(609\) | −1.69249 | −0.0685831 | ||||||||
\(610\) | 95.7687 | 3.87756 | ||||||||
\(611\) | −23.8151 | −0.963457 | ||||||||
\(612\) | 0.0392025 | 0.00158467 | ||||||||
\(613\) | 30.8506 | 1.24605 | 0.623023 | − | 0.782204i | \(-0.285904\pi\) | ||||
0.623023 | + | 0.782204i | \(0.285904\pi\) | |||||||
\(614\) | 0.135161 | 0.00545464 | ||||||||
\(615\) | −2.14073 | −0.0863225 | ||||||||
\(616\) | 0.611359 | 0.0246324 | ||||||||
\(617\) | 42.6931 | 1.71876 | 0.859379 | − | 0.511339i | \(-0.170850\pi\) | ||||
0.859379 | + | 0.511339i | \(0.170850\pi\) | |||||||
\(618\) | 49.6609 | 1.99766 | ||||||||
\(619\) | 31.4285 | 1.26322 | 0.631610 | − | 0.775286i | \(-0.282394\pi\) | ||||
0.631610 | + | 0.775286i | \(0.282394\pi\) | |||||||
\(620\) | −47.9572 | −1.92601 | ||||||||
\(621\) | −50.9892 | −2.04613 | ||||||||
\(622\) | −39.9206 | −1.60067 | ||||||||
\(623\) | −4.34517 | −0.174085 | ||||||||
\(624\) | 18.5131 | 0.741118 | ||||||||
\(625\) | 17.4981 | 0.699925 | ||||||||
\(626\) | 12.0292 | 0.480784 | ||||||||
\(627\) | 55.0695 | 2.19926 | ||||||||
\(628\) | 29.5040 | 1.17734 | ||||||||
\(629\) | −0.189608 | −0.00756018 | ||||||||
\(630\) | −1.00680 | −0.0401120 | ||||||||
\(631\) | 43.0799 | 1.71498 | 0.857492 | − | 0.514497i | \(-0.172021\pi\) | ||||
0.857492 | + | 0.514497i | \(0.172021\pi\) | |||||||
\(632\) | −9.57342 | −0.380810 | ||||||||
\(633\) | −30.9288 | −1.22931 | ||||||||
\(634\) | 4.06235 | 0.161337 | ||||||||
\(635\) | −9.94625 | −0.394705 | ||||||||
\(636\) | −28.9198 | −1.14674 | ||||||||
\(637\) | 18.3262 | 0.726112 | ||||||||
\(638\) | 39.0876 | 1.54749 | ||||||||
\(639\) | −7.40829 | −0.293067 | ||||||||
\(640\) | −16.8818 | −0.667313 | ||||||||
\(641\) | −12.1718 | −0.480758 | −0.240379 | − | 0.970679i | \(-0.577272\pi\) | ||||
−0.240379 | + | 0.970679i | \(0.577272\pi\) | |||||||
\(642\) | −1.22354 | −0.0482892 | ||||||||
\(643\) | 3.48617 | 0.137481 | 0.0687406 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687406 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(644\) | −3.78238 | −0.149047 | ||||||||
\(645\) | 49.6547 | 1.95515 | ||||||||
\(646\) | −0.607430 | −0.0238990 | ||||||||
\(647\) | −11.6664 | −0.458653 | −0.229326 | − | 0.973350i | \(-0.573652\pi\) | ||||
−0.229326 | + | 0.973350i | \(0.573652\pi\) | |||||||
\(648\) | 3.90649 | 0.153461 | ||||||||
\(649\) | −12.8317 | −0.503689 | ||||||||
\(650\) | −48.2100 | −1.89095 | ||||||||
\(651\) | −2.77712 | −0.108844 | ||||||||
\(652\) | 6.88535 | 0.269651 | ||||||||
\(653\) | 0.538774 | 0.0210838 | 0.0105419 | − | 0.999944i | \(-0.496644\pi\) | ||||
0.0105419 | + | 0.999944i | \(0.496644\pi\) | |||||||
\(654\) | 7.86480 | 0.307538 | ||||||||
\(655\) | −12.6000 | −0.492324 | ||||||||
\(656\) | −1.62251 | −0.0633485 | ||||||||
\(657\) | −7.43224 | −0.289959 | ||||||||
\(658\) | −4.19614 | −0.163583 | ||||||||
\(659\) | −13.1889 | −0.513766 | −0.256883 | − | 0.966442i | \(-0.582696\pi\) | ||||
−0.256883 | + | 0.966442i | \(0.582696\pi\) | |||||||
\(660\) | −45.7981 | −1.78269 | ||||||||
\(661\) | 3.19662 | 0.124334 | 0.0621670 | − | 0.998066i | \(-0.480199\pi\) | ||||
0.0621670 | + | 0.998066i | \(0.480199\pi\) | |||||||
\(662\) | 40.2108 | 1.56284 | ||||||||
\(663\) | 0.166026 | 0.00644792 | ||||||||
\(664\) | −1.51545 | −0.0588108 | ||||||||
\(665\) | 7.18803 | 0.278740 | ||||||||
\(666\) | −5.14940 | −0.199535 | ||||||||
\(667\) | 41.1793 | 1.59447 | ||||||||
\(668\) | 14.0204 | 0.542464 | ||||||||
\(669\) | −27.7963 | −1.07467 | ||||||||
\(670\) | −35.6290 | −1.37647 | ||||||||
\(671\) | −59.0149 | −2.27824 | ||||||||
\(672\) | 2.83980 | 0.109548 | ||||||||
\(673\) | 41.2058 | 1.58837 | 0.794183 | − | 0.607679i | \(-0.207899\pi\) | ||||
0.794183 | + | 0.607679i | \(0.207899\pi\) | |||||||
\(674\) | −30.6033 | −1.17880 | ||||||||
\(675\) | −52.7631 | −2.03085 | ||||||||
\(676\) | −10.3055 | −0.396367 | ||||||||
\(677\) | −12.6571 | −0.486452 | −0.243226 | − | 0.969970i | \(-0.578206\pi\) | ||||
−0.243226 | + | 0.969970i | \(0.578206\pi\) | |||||||
\(678\) | −59.8672 | −2.29919 | ||||||||
\(679\) | 2.65157 | 0.101758 | ||||||||
\(680\) | −0.0860207 | −0.00329874 | ||||||||
\(681\) | −33.0891 | −1.26798 | ||||||||
\(682\) | 64.1370 | 2.45593 | ||||||||
\(683\) | −24.6882 | −0.944667 | −0.472334 | − | 0.881420i | \(-0.656588\pi\) | ||||
−0.472334 | + | 0.881420i | \(0.656588\pi\) | |||||||
\(684\) | −7.60115 | −0.290637 | ||||||||
\(685\) | −7.15831 | −0.273505 | ||||||||
\(686\) | 6.48517 | 0.247605 | ||||||||
\(687\) | −4.27393 | −0.163061 | ||||||||
\(688\) | 37.6346 | 1.43481 | ||||||||
\(689\) | 28.6517 | 1.09154 | ||||||||
\(690\) | −104.714 | −3.98638 | ||||||||
\(691\) | 12.2157 | 0.464708 | 0.232354 | − | 0.972631i | \(-0.425357\pi\) | ||||
0.232354 | + | 0.972631i | \(0.425357\pi\) | |||||||
\(692\) | −2.96708 | −0.112791 | ||||||||
\(693\) | 0.620415 | 0.0235676 | ||||||||
\(694\) | −4.55180 | −0.172784 | ||||||||
\(695\) | −7.08043 | −0.268576 | ||||||||
\(696\) | −3.92721 | −0.148860 | ||||||||
\(697\) | −0.0145507 | −0.000551148 0 | ||||||||
\(698\) | 2.45142 | 0.0927878 | ||||||||
\(699\) | −7.84350 | −0.296668 | ||||||||
\(700\) | −3.91397 | −0.147934 | ||||||||
\(701\) | −22.5837 | −0.852974 | −0.426487 | − | 0.904494i | \(-0.640249\pi\) | ||||
−0.426487 | + | 0.904494i | \(0.640249\pi\) | |||||||
\(702\) | 28.2923 | 1.06783 | ||||||||
\(703\) | 36.7640 | 1.38658 | ||||||||
\(704\) | −24.9622 | −0.940800 | ||||||||
\(705\) | −53.5268 | −2.01594 | ||||||||
\(706\) | −33.8919 | −1.27554 | ||||||||
\(707\) | −2.52736 | −0.0950513 | ||||||||
\(708\) | −7.57109 | −0.284539 | ||||||||
\(709\) | −10.8886 | −0.408930 | −0.204465 | − | 0.978874i | \(-0.565546\pi\) | ||||
−0.204465 | + | 0.978874i | \(0.565546\pi\) | |||||||
\(710\) | −95.4633 | −3.58267 | ||||||||
\(711\) | −9.71523 | −0.364350 | ||||||||
\(712\) | −10.0824 | −0.377854 | ||||||||
\(713\) | 67.5691 | 2.53048 | ||||||||
\(714\) | 0.0292532 | 0.00109477 | ||||||||
\(715\) | 45.3737 | 1.69688 | ||||||||
\(716\) | −37.5301 | −1.40257 | ||||||||
\(717\) | 2.31523 | 0.0864640 | ||||||||
\(718\) | 32.7167 | 1.22098 | ||||||||
\(719\) | 11.7301 | 0.437459 | 0.218729 | − | 0.975786i | \(-0.429809\pi\) | ||||
0.218729 | + | 0.975786i | \(0.429809\pi\) | |||||||
\(720\) | −9.73403 | −0.362766 | ||||||||
\(721\) | −3.99440 | −0.148759 | ||||||||
\(722\) | 81.1855 | 3.02141 | ||||||||
\(723\) | 15.4522 | 0.574672 | ||||||||
\(724\) | −20.2733 | −0.753450 | ||||||||
\(725\) | 42.6119 | 1.58257 | ||||||||
\(726\) | 28.2174 | 1.04725 | ||||||||
\(727\) | 0.372335 | 0.0138091 | 0.00690457 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690457 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(728\) | −0.357377 | −0.0132453 | ||||||||
\(729\) | 29.9939 | 1.11089 | ||||||||
\(730\) | −95.7720 | −3.54468 | ||||||||
\(731\) | 0.337508 | 0.0124832 | ||||||||
\(732\) | −34.8205 | −1.28700 | ||||||||
\(733\) | −25.9204 | −0.957393 | −0.478696 | − | 0.877980i | \(-0.658891\pi\) | ||||
−0.478696 | + | 0.877980i | \(0.658891\pi\) | |||||||
\(734\) | −10.5744 | −0.390308 | ||||||||
\(735\) | 41.1900 | 1.51932 | ||||||||
\(736\) | −69.0942 | −2.54684 | ||||||||
\(737\) | 21.9554 | 0.808737 | ||||||||
\(738\) | −0.395170 | −0.0145464 | ||||||||
\(739\) | 4.69958 | 0.172877 | 0.0864385 | − | 0.996257i | \(-0.472451\pi\) | ||||
0.0864385 | + | 0.996257i | \(0.472451\pi\) | |||||||
\(740\) | −30.5745 | −1.12394 | ||||||||
\(741\) | −32.1915 | −1.18258 | ||||||||
\(742\) | 5.04833 | 0.185330 | ||||||||
\(743\) | −43.9654 | −1.61294 | −0.806468 | − | 0.591278i | \(-0.798624\pi\) | ||||
−0.806468 | + | 0.591278i | \(0.798624\pi\) | |||||||
\(744\) | −6.44396 | −0.236247 | ||||||||
\(745\) | 48.4976 | 1.77681 | ||||||||
\(746\) | 32.7557 | 1.19927 | ||||||||
\(747\) | −1.53790 | −0.0562687 | ||||||||
\(748\) | −0.311294 | −0.0113820 | ||||||||
\(749\) | 0.0984134 | 0.00359595 | ||||||||
\(750\) | −51.2185 | −1.87024 | ||||||||
\(751\) | −2.88688 | −0.105344 | −0.0526719 | − | 0.998612i | \(-0.516774\pi\) | ||||
−0.0526719 | + | 0.998612i | \(0.516774\pi\) | |||||||
\(752\) | −40.5694 | −1.47941 | ||||||||
\(753\) | −24.0423 | −0.876149 | ||||||||
\(754\) | −22.8491 | −0.832116 | ||||||||
\(755\) | 24.7253 | 0.899845 | ||||||||
\(756\) | 2.29694 | 0.0835389 | ||||||||
\(757\) | −19.7532 | −0.717943 | −0.358971 | − | 0.933349i | \(-0.616872\pi\) | ||||
−0.358971 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(758\) | 3.61984 | 0.131479 | ||||||||
\(759\) | 64.5270 | 2.34218 | ||||||||
\(760\) | 16.6789 | 0.605008 | ||||||||
\(761\) | 7.29433 | 0.264419 | 0.132210 | − | 0.991222i | \(-0.457793\pi\) | ||||
0.132210 | + | 0.991222i | \(0.457793\pi\) | |||||||
\(762\) | 7.84852 | 0.284322 | ||||||||
\(763\) | −0.632593 | −0.0229014 | ||||||||
\(764\) | −20.5133 | −0.742146 | ||||||||
\(765\) | −0.0872949 | −0.00315615 | ||||||||
\(766\) | 61.3813 | 2.21780 | ||||||||
\(767\) | 7.50093 | 0.270843 | ||||||||
\(768\) | 30.5578 | 1.10266 | ||||||||
\(769\) | −14.7248 | −0.530988 | −0.265494 | − | 0.964112i | \(-0.585535\pi\) | ||||
−0.265494 | + | 0.964112i | \(0.585535\pi\) | |||||||
\(770\) | 7.99468 | 0.288108 | ||||||||
\(771\) | 32.9452 | 1.18649 | ||||||||
\(772\) | −13.9526 | −0.502166 | ||||||||
\(773\) | −43.4277 | −1.56199 | −0.780993 | − | 0.624540i | \(-0.785287\pi\) | ||||
−0.780993 | + | 0.624540i | \(0.785287\pi\) | |||||||
\(774\) | 9.16607 | 0.329468 | ||||||||
\(775\) | 69.9198 | 2.51159 | ||||||||
\(776\) | 6.15264 | 0.220867 | ||||||||
\(777\) | −1.77051 | −0.0635168 | ||||||||
\(778\) | 53.4706 | 1.91702 | ||||||||
\(779\) | 2.82130 | 0.101084 | ||||||||
\(780\) | 26.7718 | 0.958585 | ||||||||
\(781\) | 58.8267 | 2.10499 | ||||||||
\(782\) | −0.711749 | −0.0254521 | ||||||||
\(783\) | −25.0071 | −0.893680 | ||||||||
\(784\) | 31.2190 | 1.11496 | ||||||||
\(785\) | −65.6985 | −2.34488 | ||||||||
\(786\) | 9.94260 | 0.354641 | ||||||||
\(787\) | 2.36935 | 0.0844583 | 0.0422292 | − | 0.999108i | \(-0.486554\pi\) | ||||
0.0422292 | + | 0.999108i | \(0.486554\pi\) | |||||||
\(788\) | −19.9733 | −0.711519 | ||||||||
\(789\) | −14.3291 | −0.510129 | ||||||||
\(790\) | −125.191 | −4.45408 | ||||||||
\(791\) | 4.81533 | 0.171213 | ||||||||
\(792\) | 1.43960 | 0.0511538 | ||||||||
\(793\) | 34.4978 | 1.22505 | ||||||||
\(794\) | 13.2292 | 0.469486 | ||||||||
\(795\) | 64.3976 | 2.28395 | ||||||||
\(796\) | 17.3185 | 0.613838 | ||||||||
\(797\) | 16.0573 | 0.568778 | 0.284389 | − | 0.958709i | \(-0.408209\pi\) | ||||
0.284389 | + | 0.958709i | \(0.408209\pi\) | |||||||
\(798\) | −5.67203 | −0.200788 | ||||||||
\(799\) | −0.363827 | −0.0128713 | ||||||||
\(800\) | −71.4979 | −2.52783 | ||||||||
\(801\) | −10.2318 | −0.361522 | ||||||||
\(802\) | −50.7013 | −1.79033 | ||||||||
\(803\) | 59.0169 | 2.08266 | ||||||||
\(804\) | 12.9543 | 0.456864 | ||||||||
\(805\) | 8.42249 | 0.296854 | ||||||||
\(806\) | −37.4920 | −1.32060 | ||||||||
\(807\) | −30.4413 | −1.07158 | ||||||||
\(808\) | −5.86443 | −0.206310 | ||||||||
\(809\) | −52.1316 | −1.83285 | −0.916424 | − | 0.400208i | \(-0.868938\pi\) | ||||
−0.916424 | + | 0.400208i | \(0.868938\pi\) | |||||||
\(810\) | 51.0847 | 1.79493 | ||||||||
\(811\) | −18.6496 | −0.654875 | −0.327438 | − | 0.944873i | \(-0.606185\pi\) | ||||
−0.327438 | + | 0.944873i | \(0.606185\pi\) | |||||||
\(812\) | −1.85503 | −0.0650987 | ||||||||
\(813\) | 18.6171 | 0.652930 | ||||||||
\(814\) | 40.8896 | 1.43318 | ||||||||
\(815\) | −15.3321 | −0.537059 | ||||||||
\(816\) | 0.282827 | 0.00990094 | ||||||||
\(817\) | −65.4408 | −2.28948 | ||||||||
\(818\) | 5.73510 | 0.200523 | ||||||||
\(819\) | −0.362671 | −0.0126727 | ||||||||
\(820\) | −2.34631 | −0.0819369 | ||||||||
\(821\) | −23.9677 | −0.836479 | −0.418239 | − | 0.908337i | \(-0.637353\pi\) | ||||
−0.418239 | + | 0.908337i | \(0.637353\pi\) | |||||||
\(822\) | 5.64857 | 0.197017 | ||||||||
\(823\) | −12.1227 | −0.422569 | −0.211285 | − | 0.977425i | \(-0.567765\pi\) | ||||
−0.211285 | + | 0.977425i | \(0.567765\pi\) | |||||||
\(824\) | −9.26851 | −0.322884 | ||||||||
\(825\) | 66.7719 | 2.32470 | ||||||||
\(826\) | 1.32164 | 0.0459856 | ||||||||
\(827\) | 8.86514 | 0.308271 | 0.154136 | − | 0.988050i | \(-0.450741\pi\) | ||||
0.154136 | + | 0.988050i | \(0.450741\pi\) | |||||||
\(828\) | −8.90655 | −0.309524 | ||||||||
\(829\) | 32.7052 | 1.13590 | 0.567949 | − | 0.823064i | \(-0.307737\pi\) | ||||
0.567949 | + | 0.823064i | \(0.307737\pi\) | |||||||
\(830\) | −19.8174 | −0.687871 | ||||||||
\(831\) | −23.4650 | −0.813992 | ||||||||
\(832\) | 14.5920 | 0.505885 | ||||||||
\(833\) | 0.279972 | 0.00970047 | ||||||||
\(834\) | 5.58712 | 0.193466 | ||||||||
\(835\) | −31.2201 | −1.08042 | ||||||||
\(836\) | 60.3581 | 2.08753 | ||||||||
\(837\) | −41.0329 | −1.41830 | ||||||||
\(838\) | 22.4504 | 0.775537 | ||||||||
\(839\) | 14.2915 | 0.493396 | 0.246698 | − | 0.969092i | \(-0.420654\pi\) | ||||
0.246698 | + | 0.969092i | \(0.420654\pi\) | |||||||
\(840\) | −0.803240 | −0.0277144 | ||||||||
\(841\) | −8.80409 | −0.303589 | ||||||||
\(842\) | 23.3515 | 0.804744 | ||||||||
\(843\) | 48.3706 | 1.66597 | ||||||||
\(844\) | −33.8991 | −1.16685 | ||||||||
\(845\) | 22.9481 | 0.789437 | ||||||||
\(846\) | −9.88084 | −0.339710 | ||||||||
\(847\) | −2.26963 | −0.0779853 | ||||||||
\(848\) | 48.8086 | 1.67609 | ||||||||
\(849\) | 7.17850 | 0.246365 | ||||||||
\(850\) | −0.736510 | −0.0252621 | ||||||||
\(851\) | 43.0777 | 1.47669 | ||||||||
\(852\) | 34.7095 | 1.18913 | ||||||||
\(853\) | −9.49025 | −0.324940 | −0.162470 | − | 0.986713i | \(-0.551946\pi\) | ||||
−0.162470 | + | 0.986713i | \(0.551946\pi\) | |||||||
\(854\) | 6.07839 | 0.207998 | ||||||||
\(855\) | 16.9260 | 0.578856 | ||||||||
\(856\) | 0.228356 | 0.00780505 | ||||||||
\(857\) | −19.5854 | −0.669025 | −0.334513 | − | 0.942391i | \(-0.608572\pi\) | ||||
−0.334513 | + | 0.942391i | \(0.608572\pi\) | |||||||
\(858\) | −35.8041 | −1.22233 | ||||||||
\(859\) | 35.4819 | 1.21063 | 0.605313 | − | 0.795987i | \(-0.293048\pi\) | ||||
0.605313 | + | 0.795987i | \(0.293048\pi\) | |||||||
\(860\) | 54.4234 | 1.85582 | ||||||||
\(861\) | −0.135871 | −0.00463047 | ||||||||
\(862\) | −29.3652 | −1.00018 | ||||||||
\(863\) | −13.4238 | −0.456952 | −0.228476 | − | 0.973550i | \(-0.573374\pi\) | ||||
−0.228476 | + | 0.973550i | \(0.573374\pi\) | |||||||
\(864\) | 41.9590 | 1.42747 | ||||||||
\(865\) | 6.60699 | 0.224645 | ||||||||
\(866\) | 20.5998 | 0.700009 | ||||||||
\(867\) | −26.5046 | −0.900145 | ||||||||
\(868\) | −3.04382 | −0.103314 | ||||||||
\(869\) | 77.1453 | 2.61698 | ||||||||
\(870\) | −51.3556 | −1.74112 | ||||||||
\(871\) | −12.8343 | −0.434873 | ||||||||
\(872\) | −1.46785 | −0.0497077 | ||||||||
\(873\) | 6.24378 | 0.211320 | ||||||||
\(874\) | 138.004 | 4.66805 | ||||||||
\(875\) | 4.11968 | 0.139271 | ||||||||
\(876\) | 34.8217 | 1.17652 | ||||||||
\(877\) | −3.75641 | −0.126845 | −0.0634225 | − | 0.997987i | \(-0.520202\pi\) | ||||
−0.0634225 | + | 0.997987i | \(0.520202\pi\) | |||||||
\(878\) | 35.3120 | 1.19172 | ||||||||
\(879\) | 48.7861 | 1.64552 | ||||||||
\(880\) | 77.2946 | 2.60560 | ||||||||
\(881\) | −49.4564 | −1.66623 | −0.833114 | − | 0.553101i | \(-0.813444\pi\) | ||||
−0.833114 | + | 0.553101i | \(0.813444\pi\) | |||||||
\(882\) | 7.60352 | 0.256024 | ||||||||
\(883\) | −14.2351 | −0.479049 | −0.239524 | − | 0.970890i | \(-0.576991\pi\) | ||||
−0.239524 | + | 0.970890i | \(0.576991\pi\) | |||||||
\(884\) | 0.181971 | 0.00612033 | ||||||||
\(885\) | 16.8591 | 0.566711 | ||||||||
\(886\) | 3.18624 | 0.107044 | ||||||||
\(887\) | −2.67754 | −0.0899031 | −0.0449516 | − | 0.998989i | \(-0.514313\pi\) | ||||
−0.0449516 | + | 0.998989i | \(0.514313\pi\) | |||||||
\(888\) | −4.10826 | −0.137864 | ||||||||
\(889\) | −0.631283 | −0.0211726 | ||||||||
\(890\) | −131.847 | −4.41951 | ||||||||
\(891\) | −31.4796 | −1.05461 | ||||||||
\(892\) | −30.4657 | −1.02007 | ||||||||
\(893\) | 70.5439 | 2.36066 | ||||||||
\(894\) | −38.2691 | −1.27991 | ||||||||
\(895\) | 83.5708 | 2.79347 | ||||||||
\(896\) | −1.07148 | −0.0357957 | ||||||||
\(897\) | −37.7200 | −1.25943 | ||||||||
\(898\) | 49.6625 | 1.65726 | ||||||||
\(899\) | 33.1385 | 1.10523 | ||||||||
\(900\) | −9.21641 | −0.307214 | ||||||||
\(901\) | 0.437716 | 0.0145824 | ||||||||
\(902\) | 3.13791 | 0.104481 | ||||||||
\(903\) | 3.15156 | 0.104877 | ||||||||
\(904\) | 11.1734 | 0.371621 | ||||||||
\(905\) | 45.1438 | 1.50063 | ||||||||
\(906\) | −19.5105 | −0.648194 | ||||||||
\(907\) | 12.0947 | 0.401598 | 0.200799 | − | 0.979632i | \(-0.435646\pi\) | ||||
0.200799 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(908\) | −36.2669 | −1.20356 | ||||||||
\(909\) | −5.95130 | −0.197392 | ||||||||
\(910\) | −4.67338 | −0.154921 | ||||||||
\(911\) | −0.443134 | −0.0146817 | −0.00734083 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734083 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(912\) | −54.8386 | −1.81589 | ||||||||
\(913\) | 12.2119 | 0.404156 | ||||||||
\(914\) | −1.77667 | −0.0587669 | ||||||||
\(915\) | 77.5372 | 2.56330 | ||||||||
\(916\) | −4.68438 | −0.154776 | ||||||||
\(917\) | −0.799718 | −0.0264090 | ||||||||
\(918\) | 0.432226 | 0.0142656 | ||||||||
\(919\) | −37.4751 | −1.23619 | −0.618094 | − | 0.786104i | \(-0.712095\pi\) | ||||
−0.618094 | + | 0.786104i | \(0.712095\pi\) | |||||||
\(920\) | 19.5433 | 0.644324 | ||||||||
\(921\) | 0.109430 | 0.00360585 | ||||||||
\(922\) | −70.5215 | −2.32250 | ||||||||
\(923\) | −34.3878 | −1.13189 | ||||||||
\(924\) | −2.90679 | −0.0956262 | ||||||||
\(925\) | 44.5764 | 1.46566 | ||||||||
\(926\) | −29.8673 | −0.981499 | ||||||||
\(927\) | −9.40580 | −0.308927 | ||||||||
\(928\) | −33.8864 | −1.11238 | ||||||||
\(929\) | 45.4912 | 1.49252 | 0.746259 | − | 0.665656i | \(-0.231848\pi\) | ||||
0.746259 | + | 0.665656i | \(0.231848\pi\) | |||||||
\(930\) | −84.2670 | −2.76322 | ||||||||
\(931\) | −54.2850 | −1.77912 | ||||||||
\(932\) | −8.59675 | −0.281596 | ||||||||
\(933\) | −32.3210 | −1.05814 | ||||||||
\(934\) | −45.7897 | −1.49829 | ||||||||
\(935\) | 0.693179 | 0.0226694 | ||||||||
\(936\) | −0.841532 | −0.0275063 | ||||||||
\(937\) | −38.7947 | −1.26737 | −0.633684 | − | 0.773592i | \(-0.718458\pi\) | ||||
−0.633684 | + | 0.773592i | \(0.718458\pi\) | |||||||
\(938\) | −2.26135 | −0.0738358 | ||||||||
\(939\) | 9.73921 | 0.317827 | ||||||||
\(940\) | −58.6673 | −1.91352 | ||||||||
\(941\) | 29.6821 | 0.967607 | 0.483804 | − | 0.875177i | \(-0.339255\pi\) | ||||
0.483804 | + | 0.875177i | \(0.339255\pi\) | |||||||
\(942\) | 51.8422 | 1.68911 | ||||||||
\(943\) | 3.30583 | 0.107653 | ||||||||
\(944\) | 12.7779 | 0.415886 | ||||||||
\(945\) | −5.11475 | −0.166383 | ||||||||
\(946\) | −72.7846 | −2.36643 | ||||||||
\(947\) | 13.4750 | 0.437880 | 0.218940 | − | 0.975738i | \(-0.429740\pi\) | ||||
0.218940 | + | 0.975738i | \(0.429740\pi\) | |||||||
\(948\) | 45.5180 | 1.47836 | ||||||||
\(949\) | −34.4990 | −1.11989 | ||||||||
\(950\) | 142.805 | 4.63321 | ||||||||
\(951\) | 3.28900 | 0.106653 | ||||||||
\(952\) | −0.00545969 | −0.000176950 0 | ||||||||
\(953\) | −22.8306 | −0.739557 | −0.369779 | − | 0.929120i | \(-0.620566\pi\) | ||||
−0.369779 | + | 0.929120i | \(0.620566\pi\) | |||||||
\(954\) | 11.8875 | 0.384873 | ||||||||
\(955\) | 45.6784 | 1.47812 | ||||||||
\(956\) | 2.53758 | 0.0820711 | ||||||||
\(957\) | 31.6465 | 1.02299 | ||||||||
\(958\) | 50.5260 | 1.63242 | ||||||||
\(959\) | −0.454334 | −0.0146712 | ||||||||
\(960\) | 32.7969 | 1.05851 | ||||||||
\(961\) | 23.3753 | 0.754042 | ||||||||
\(962\) | −23.9025 | −0.770648 | ||||||||
\(963\) | 0.231739 | 0.00746767 | ||||||||
\(964\) | 16.9361 | 0.545476 | ||||||||
\(965\) | 31.0693 | 1.00016 | ||||||||
\(966\) | −6.64613 | −0.213836 | ||||||||
\(967\) | 38.8447 | 1.24916 | 0.624581 | − | 0.780960i | \(-0.285270\pi\) | ||||
0.624581 | + | 0.780960i | \(0.285270\pi\) | |||||||
\(968\) | −5.26638 | −0.169268 | ||||||||
\(969\) | −0.491794 | −0.0157987 | ||||||||
\(970\) | 80.4574 | 2.58333 | ||||||||
\(971\) | −29.8372 | −0.957521 | −0.478761 | − | 0.877945i | \(-0.658914\pi\) | ||||
−0.478761 | + | 0.877945i | \(0.658914\pi\) | |||||||
\(972\) | 9.95543 | 0.319321 | ||||||||
\(973\) | −0.449392 | −0.0144068 | ||||||||
\(974\) | 8.47966 | 0.271706 | ||||||||
\(975\) | −39.0323 | −1.25003 | ||||||||
\(976\) | 58.7674 | 1.88110 | ||||||||
\(977\) | −3.35840 | −0.107445 | −0.0537224 | − | 0.998556i | \(-0.517109\pi\) | ||||
−0.0537224 | + | 0.998556i | \(0.517109\pi\) | |||||||
\(978\) | 12.0984 | 0.386865 | ||||||||
\(979\) | 81.2470 | 2.59666 | ||||||||
\(980\) | 45.1457 | 1.44213 | ||||||||
\(981\) | −1.48960 | −0.0475591 | ||||||||
\(982\) | −60.1648 | −1.91994 | ||||||||
\(983\) | 16.5818 | 0.528876 | 0.264438 | − | 0.964403i | \(-0.414814\pi\) | ||||
0.264438 | + | 0.964403i | \(0.414814\pi\) | |||||||
\(984\) | −0.315272 | −0.0100505 | ||||||||
\(985\) | 44.4759 | 1.41712 | ||||||||
\(986\) | −0.349069 | −0.0111166 | ||||||||
\(987\) | −3.39732 | −0.108138 | ||||||||
\(988\) | −35.2830 | −1.12250 | ||||||||
\(989\) | −76.6795 | −2.43827 | ||||||||
\(990\) | 18.8254 | 0.598312 | ||||||||
\(991\) | 27.2203 | 0.864681 | 0.432341 | − | 0.901710i | \(-0.357688\pi\) | ||||
0.432341 | + | 0.901710i | \(0.357688\pi\) | |||||||
\(992\) | −55.6026 | −1.76538 | ||||||||
\(993\) | 32.5559 | 1.03313 | ||||||||
\(994\) | −6.05901 | −0.192180 | ||||||||
\(995\) | −38.5643 | −1.22257 | ||||||||
\(996\) | 7.20540 | 0.228312 | ||||||||
\(997\) | 7.36253 | 0.233174 | 0.116587 | − | 0.993181i | \(-0.462805\pi\) | ||||
0.116587 | + | 0.993181i | \(0.462805\pi\) | |||||||
\(998\) | −2.17593 | −0.0688778 | ||||||||
\(999\) | −26.1599 | −0.827664 |
(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 | 4001.2.a.b.1.145 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.145 | ✓ | 184 | 1.1 | even | 1 | trivial |