Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, 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("8045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.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: | \(64.2396484261\) |
Analytic rank: | \(0\) |
Dimension: | \(141\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41054 | −1.70451 | −0.852254 | − | 0.523129i | \(-0.824765\pi\) | ||||
−0.852254 | + | 0.523129i | \(0.824765\pi\) | |||||||
\(3\) | 1.33575 | 0.771198 | 0.385599 | − | 0.922666i | \(-0.373995\pi\) | ||||
0.385599 | + | 0.922666i | \(0.373995\pi\) | |||||||
\(4\) | 3.81069 | 1.90534 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.21988 | −1.31451 | ||||||||
\(7\) | −0.579711 | −0.219110 | −0.109555 | − | 0.993981i | \(-0.534943\pi\) | ||||
−0.109555 | + | 0.993981i | \(0.534943\pi\) | |||||||
\(8\) | −4.36473 | −1.54317 | ||||||||
\(9\) | −1.21576 | −0.405254 | ||||||||
\(10\) | 2.41054 | 0.762279 | ||||||||
\(11\) | 5.70925 | 1.72140 | 0.860702 | − | 0.509108i | \(-0.170025\pi\) | ||||
0.860702 | + | 0.509108i | \(0.170025\pi\) | |||||||
\(12\) | 5.09014 | 1.46940 | ||||||||
\(13\) | −1.30078 | −0.360771 | −0.180385 | − | 0.983596i | \(-0.557734\pi\) | ||||
−0.180385 | + | 0.983596i | \(0.557734\pi\) | |||||||
\(14\) | 1.39741 | 0.373475 | ||||||||
\(15\) | −1.33575 | −0.344890 | ||||||||
\(16\) | 2.89997 | 0.724993 | ||||||||
\(17\) | −6.86388 | −1.66474 | −0.832368 | − | 0.554224i | \(-0.813015\pi\) | ||||
−0.832368 | + | 0.554224i | \(0.813015\pi\) | |||||||
\(18\) | 2.93064 | 0.690758 | ||||||||
\(19\) | 5.70841 | 1.30960 | 0.654800 | − | 0.755802i | \(-0.272753\pi\) | ||||
0.654800 | + | 0.755802i | \(0.272753\pi\) | |||||||
\(20\) | −3.81069 | −0.852096 | ||||||||
\(21\) | −0.774351 | −0.168977 | ||||||||
\(22\) | −13.7624 | −2.93415 | ||||||||
\(23\) | 4.02978 | 0.840267 | 0.420134 | − | 0.907462i | \(-0.361983\pi\) | ||||
0.420134 | + | 0.907462i | \(0.361983\pi\) | |||||||
\(24\) | −5.83021 | −1.19009 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.13557 | 0.614936 | ||||||||
\(27\) | −5.63122 | −1.08373 | ||||||||
\(28\) | −2.20910 | −0.417480 | ||||||||
\(29\) | 0.140171 | 0.0260290 | 0.0130145 | − | 0.999915i | \(-0.495857\pi\) | ||||
0.0130145 | + | 0.999915i | \(0.495857\pi\) | |||||||
\(30\) | 3.21988 | 0.587868 | ||||||||
\(31\) | 6.35534 | 1.14145 | 0.570726 | − | 0.821141i | \(-0.306662\pi\) | ||||
0.570726 | + | 0.821141i | \(0.306662\pi\) | |||||||
\(32\) | 1.73898 | 0.307410 | ||||||||
\(33\) | 7.62616 | 1.32754 | ||||||||
\(34\) | 16.5456 | 2.83755 | ||||||||
\(35\) | 0.579711 | 0.0979890 | ||||||||
\(36\) | −4.63289 | −0.772148 | ||||||||
\(37\) | −6.11193 | −1.00480 | −0.502398 | − | 0.864637i | \(-0.667549\pi\) | ||||
−0.502398 | + | 0.864637i | \(0.667549\pi\) | |||||||
\(38\) | −13.7603 | −2.23222 | ||||||||
\(39\) | −1.73752 | −0.278225 | ||||||||
\(40\) | 4.36473 | 0.690125 | ||||||||
\(41\) | 1.11713 | 0.174466 | 0.0872329 | − | 0.996188i | \(-0.472198\pi\) | ||||
0.0872329 | + | 0.996188i | \(0.472198\pi\) | |||||||
\(42\) | 1.86660 | 0.288023 | ||||||||
\(43\) | 3.75806 | 0.573099 | 0.286549 | − | 0.958065i | \(-0.407492\pi\) | ||||
0.286549 | + | 0.958065i | \(0.407492\pi\) | |||||||
\(44\) | 21.7562 | 3.27987 | ||||||||
\(45\) | 1.21576 | 0.181235 | ||||||||
\(46\) | −9.71393 | −1.43224 | ||||||||
\(47\) | −9.17145 | −1.33779 | −0.668897 | − | 0.743355i | \(-0.733233\pi\) | ||||
−0.668897 | + | 0.743355i | \(0.733233\pi\) | |||||||
\(48\) | 3.87365 | 0.559113 | ||||||||
\(49\) | −6.66394 | −0.951991 | ||||||||
\(50\) | −2.41054 | −0.340901 | ||||||||
\(51\) | −9.16845 | −1.28384 | ||||||||
\(52\) | −4.95686 | −0.687392 | ||||||||
\(53\) | 0.869216 | 0.119396 | 0.0596980 | − | 0.998216i | \(-0.480986\pi\) | ||||
0.0596980 | + | 0.998216i | \(0.480986\pi\) | |||||||
\(54\) | 13.5743 | 1.84722 | ||||||||
\(55\) | −5.70925 | −0.769836 | ||||||||
\(56\) | 2.53028 | 0.338123 | ||||||||
\(57\) | 7.62503 | 1.00996 | ||||||||
\(58\) | −0.337886 | −0.0443666 | ||||||||
\(59\) | 10.5599 | 1.37478 | 0.687391 | − | 0.726288i | \(-0.258756\pi\) | ||||
0.687391 | + | 0.726288i | \(0.258756\pi\) | |||||||
\(60\) | −5.09014 | −0.657135 | ||||||||
\(61\) | 12.3740 | 1.58433 | 0.792167 | − | 0.610305i | \(-0.208953\pi\) | ||||
0.792167 | + | 0.610305i | \(0.208953\pi\) | |||||||
\(62\) | −15.3198 | −1.94561 | ||||||||
\(63\) | 0.704790 | 0.0887952 | ||||||||
\(64\) | −9.99181 | −1.24898 | ||||||||
\(65\) | 1.30078 | 0.161341 | ||||||||
\(66\) | −18.3831 | −2.26281 | ||||||||
\(67\) | 3.52300 | 0.430403 | 0.215201 | − | 0.976570i | \(-0.430959\pi\) | ||||
0.215201 | + | 0.976570i | \(0.430959\pi\) | |||||||
\(68\) | −26.1561 | −3.17189 | ||||||||
\(69\) | 5.38279 | 0.648012 | ||||||||
\(70\) | −1.39741 | −0.167023 | ||||||||
\(71\) | −2.15319 | −0.255537 | −0.127768 | − | 0.991804i | \(-0.540781\pi\) | ||||
−0.127768 | + | 0.991804i | \(0.540781\pi\) | |||||||
\(72\) | 5.30647 | 0.625374 | ||||||||
\(73\) | −1.33394 | −0.156126 | −0.0780632 | − | 0.996948i | \(-0.524874\pi\) | ||||
−0.0780632 | + | 0.996948i | \(0.524874\pi\) | |||||||
\(74\) | 14.7330 | 1.71268 | ||||||||
\(75\) | 1.33575 | 0.154240 | ||||||||
\(76\) | 21.7530 | 2.49524 | ||||||||
\(77\) | −3.30972 | −0.377177 | ||||||||
\(78\) | 4.18835 | 0.474237 | ||||||||
\(79\) | 6.29460 | 0.708198 | 0.354099 | − | 0.935208i | \(-0.384788\pi\) | ||||
0.354099 | + | 0.935208i | \(0.384788\pi\) | |||||||
\(80\) | −2.89997 | −0.324227 | ||||||||
\(81\) | −3.87464 | −0.430516 | ||||||||
\(82\) | −2.69288 | −0.297378 | ||||||||
\(83\) | −12.6133 | −1.38449 | −0.692246 | − | 0.721662i | \(-0.743378\pi\) | ||||
−0.692246 | + | 0.721662i | \(0.743378\pi\) | |||||||
\(84\) | −2.95081 | −0.321960 | ||||||||
\(85\) | 6.86388 | 0.744492 | ||||||||
\(86\) | −9.05894 | −0.976851 | ||||||||
\(87\) | 0.187233 | 0.0200735 | ||||||||
\(88\) | −24.9194 | −2.65641 | ||||||||
\(89\) | 0.459166 | 0.0486715 | 0.0243357 | − | 0.999704i | \(-0.492253\pi\) | ||||
0.0243357 | + | 0.999704i | \(0.492253\pi\) | |||||||
\(90\) | −2.93064 | −0.308916 | ||||||||
\(91\) | 0.754074 | 0.0790484 | ||||||||
\(92\) | 15.3562 | 1.60100 | ||||||||
\(93\) | 8.48917 | 0.880286 | ||||||||
\(94\) | 22.1081 | 2.28028 | ||||||||
\(95\) | −5.70841 | −0.585671 | ||||||||
\(96\) | 2.32284 | 0.237074 | ||||||||
\(97\) | 1.65456 | 0.167995 | 0.0839973 | − | 0.996466i | \(-0.473231\pi\) | ||||
0.0839973 | + | 0.996466i | \(0.473231\pi\) | |||||||
\(98\) | 16.0637 | 1.62268 | ||||||||
\(99\) | −6.94109 | −0.697606 | ||||||||
\(100\) | 3.81069 | 0.381069 | ||||||||
\(101\) | −17.9101 | −1.78212 | −0.891060 | − | 0.453885i | \(-0.850038\pi\) | ||||
−0.891060 | + | 0.453885i | \(0.850038\pi\) | |||||||
\(102\) | 22.1009 | 2.18832 | ||||||||
\(103\) | 2.57010 | 0.253240 | 0.126620 | − | 0.991951i | \(-0.459587\pi\) | ||||
0.126620 | + | 0.991951i | \(0.459587\pi\) | |||||||
\(104\) | 5.67754 | 0.556729 | ||||||||
\(105\) | 0.774351 | 0.0755689 | ||||||||
\(106\) | −2.09528 | −0.203511 | ||||||||
\(107\) | 16.4936 | 1.59450 | 0.797250 | − | 0.603650i | \(-0.206287\pi\) | ||||
0.797250 | + | 0.603650i | \(0.206287\pi\) | |||||||
\(108\) | −21.4588 | −2.06488 | ||||||||
\(109\) | −5.84389 | −0.559743 | −0.279872 | − | 0.960037i | \(-0.590292\pi\) | ||||
−0.279872 | + | 0.960037i | \(0.590292\pi\) | |||||||
\(110\) | 13.7624 | 1.31219 | ||||||||
\(111\) | −8.16404 | −0.774896 | ||||||||
\(112\) | −1.68114 | −0.158853 | ||||||||
\(113\) | 15.5070 | 1.45878 | 0.729389 | − | 0.684099i | \(-0.239804\pi\) | ||||
0.729389 | + | 0.684099i | \(0.239804\pi\) | |||||||
\(114\) | −18.3804 | −1.72148 | ||||||||
\(115\) | −4.02978 | −0.375779 | ||||||||
\(116\) | 0.534146 | 0.0495942 | ||||||||
\(117\) | 1.58143 | 0.146204 | ||||||||
\(118\) | −25.4550 | −2.34332 | ||||||||
\(119\) | 3.97906 | 0.364760 | ||||||||
\(120\) | 5.83021 | 0.532223 | ||||||||
\(121\) | 21.5956 | 1.96323 | ||||||||
\(122\) | −29.8281 | −2.70051 | ||||||||
\(123\) | 1.49221 | 0.134548 | ||||||||
\(124\) | 24.2182 | 2.17486 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.69892 | −0.151352 | ||||||||
\(127\) | 15.4325 | 1.36941 | 0.684707 | − | 0.728819i | \(-0.259930\pi\) | ||||
0.684707 | + | 0.728819i | \(0.259930\pi\) | |||||||
\(128\) | 20.6077 | 1.82148 | ||||||||
\(129\) | 5.01984 | 0.441972 | ||||||||
\(130\) | −3.13557 | −0.275008 | ||||||||
\(131\) | 0.915298 | 0.0799699 | 0.0399850 | − | 0.999200i | \(-0.487269\pi\) | ||||
0.0399850 | + | 0.999200i | \(0.487269\pi\) | |||||||
\(132\) | 29.0609 | 2.52943 | ||||||||
\(133\) | −3.30923 | −0.286946 | ||||||||
\(134\) | −8.49232 | −0.733624 | ||||||||
\(135\) | 5.63122 | 0.484658 | ||||||||
\(136\) | 29.9590 | 2.56896 | ||||||||
\(137\) | −6.65133 | −0.568262 | −0.284131 | − | 0.958785i | \(-0.591705\pi\) | ||||
−0.284131 | + | 0.958785i | \(0.591705\pi\) | |||||||
\(138\) | −12.9754 | −1.10454 | ||||||||
\(139\) | −12.4453 | −1.05560 | −0.527799 | − | 0.849369i | \(-0.676983\pi\) | ||||
−0.527799 | + | 0.849369i | \(0.676983\pi\) | |||||||
\(140\) | 2.20910 | 0.186703 | ||||||||
\(141\) | −12.2508 | −1.03170 | ||||||||
\(142\) | 5.19035 | 0.435564 | ||||||||
\(143\) | −7.42646 | −0.621032 | ||||||||
\(144\) | −3.52567 | −0.293806 | ||||||||
\(145\) | −0.140171 | −0.0116405 | ||||||||
\(146\) | 3.21552 | 0.266119 | ||||||||
\(147\) | −8.90138 | −0.734173 | ||||||||
\(148\) | −23.2907 | −1.91448 | ||||||||
\(149\) | −5.49516 | −0.450181 | −0.225090 | − | 0.974338i | \(-0.572268\pi\) | ||||
−0.225090 | + | 0.974338i | \(0.572268\pi\) | |||||||
\(150\) | −3.21988 | −0.262902 | ||||||||
\(151\) | −15.8564 | −1.29038 | −0.645189 | − | 0.764023i | \(-0.723221\pi\) | ||||
−0.645189 | + | 0.764023i | \(0.723221\pi\) | |||||||
\(152\) | −24.9157 | −2.02093 | ||||||||
\(153\) | 8.34484 | 0.674640 | ||||||||
\(154\) | 7.97819 | 0.642901 | ||||||||
\(155\) | −6.35534 | −0.510473 | ||||||||
\(156\) | −6.62114 | −0.530115 | ||||||||
\(157\) | −16.1043 | −1.28526 | −0.642631 | − | 0.766176i | \(-0.722157\pi\) | ||||
−0.642631 | + | 0.766176i | \(0.722157\pi\) | |||||||
\(158\) | −15.1734 | −1.20713 | ||||||||
\(159\) | 1.16106 | 0.0920779 | ||||||||
\(160\) | −1.73898 | −0.137478 | ||||||||
\(161\) | −2.33611 | −0.184111 | ||||||||
\(162\) | 9.33996 | 0.733817 | ||||||||
\(163\) | 10.0309 | 0.785679 | 0.392839 | − | 0.919607i | \(-0.371493\pi\) | ||||
0.392839 | + | 0.919607i | \(0.371493\pi\) | |||||||
\(164\) | 4.25702 | 0.332418 | ||||||||
\(165\) | −7.62616 | −0.593696 | ||||||||
\(166\) | 30.4049 | 2.35987 | ||||||||
\(167\) | −7.43019 | −0.574966 | −0.287483 | − | 0.957786i | \(-0.592818\pi\) | ||||
−0.287483 | + | 0.957786i | \(0.592818\pi\) | |||||||
\(168\) | 3.37983 | 0.260760 | ||||||||
\(169\) | −11.3080 | −0.869845 | ||||||||
\(170\) | −16.5456 | −1.26899 | ||||||||
\(171\) | −6.94007 | −0.530720 | ||||||||
\(172\) | 14.3208 | 1.09195 | ||||||||
\(173\) | 1.24346 | 0.0945388 | 0.0472694 | − | 0.998882i | \(-0.484948\pi\) | ||||
0.0472694 | + | 0.998882i | \(0.484948\pi\) | |||||||
\(174\) | −0.451333 | −0.0342155 | ||||||||
\(175\) | −0.579711 | −0.0438220 | ||||||||
\(176\) | 16.5567 | 1.24801 | ||||||||
\(177\) | 14.1054 | 1.06023 | ||||||||
\(178\) | −1.10684 | −0.0829609 | ||||||||
\(179\) | 25.9239 | 1.93764 | 0.968821 | − | 0.247764i | \(-0.0796956\pi\) | ||||
0.968821 | + | 0.247764i | \(0.0796956\pi\) | |||||||
\(180\) | 4.63289 | 0.345315 | ||||||||
\(181\) | 16.8986 | 1.25607 | 0.628033 | − | 0.778187i | \(-0.283860\pi\) | ||||
0.628033 | + | 0.778187i | \(0.283860\pi\) | |||||||
\(182\) | −1.81772 | −0.134739 | ||||||||
\(183\) | 16.5287 | 1.22183 | ||||||||
\(184\) | −17.5889 | −1.29667 | ||||||||
\(185\) | 6.11193 | 0.449358 | ||||||||
\(186\) | −20.4634 | −1.50045 | ||||||||
\(187\) | −39.1876 | −2.86568 | ||||||||
\(188\) | −34.9495 | −2.54896 | ||||||||
\(189\) | 3.26448 | 0.237456 | ||||||||
\(190\) | 13.7603 | 0.998280 | ||||||||
\(191\) | 1.13415 | 0.0820642 | 0.0410321 | − | 0.999158i | \(-0.486935\pi\) | ||||
0.0410321 | + | 0.999158i | \(0.486935\pi\) | |||||||
\(192\) | −13.3466 | −0.963208 | ||||||||
\(193\) | 10.1469 | 0.730386 | 0.365193 | − | 0.930932i | \(-0.381003\pi\) | ||||
0.365193 | + | 0.930932i | \(0.381003\pi\) | |||||||
\(194\) | −3.98837 | −0.286348 | ||||||||
\(195\) | 1.73752 | 0.124426 | ||||||||
\(196\) | −25.3942 | −1.81387 | ||||||||
\(197\) | −13.6503 | −0.972543 | −0.486272 | − | 0.873808i | \(-0.661643\pi\) | ||||
−0.486272 | + | 0.873808i | \(0.661643\pi\) | |||||||
\(198\) | 16.7318 | 1.18907 | ||||||||
\(199\) | −11.7669 | −0.834135 | −0.417068 | − | 0.908875i | \(-0.636942\pi\) | ||||
−0.417068 | + | 0.908875i | \(0.636942\pi\) | |||||||
\(200\) | −4.36473 | −0.308633 | ||||||||
\(201\) | 4.70586 | 0.331926 | ||||||||
\(202\) | 43.1729 | 3.03764 | ||||||||
\(203\) | −0.0812584 | −0.00570322 | ||||||||
\(204\) | −34.9381 | −2.44616 | ||||||||
\(205\) | −1.11713 | −0.0780235 | ||||||||
\(206\) | −6.19532 | −0.431649 | ||||||||
\(207\) | −4.89925 | −0.340521 | ||||||||
\(208\) | −3.77222 | −0.261556 | ||||||||
\(209\) | 32.5908 | 2.25435 | ||||||||
\(210\) | −1.86660 | −0.128808 | ||||||||
\(211\) | 27.5331 | 1.89546 | 0.947728 | − | 0.319080i | \(-0.103374\pi\) | ||||
0.947728 | + | 0.319080i | \(0.103374\pi\) | |||||||
\(212\) | 3.31231 | 0.227490 | ||||||||
\(213\) | −2.87613 | −0.197070 | ||||||||
\(214\) | −39.7585 | −2.71784 | ||||||||
\(215\) | −3.75806 | −0.256298 | ||||||||
\(216\) | 24.5788 | 1.67237 | ||||||||
\(217\) | −3.68426 | −0.250104 | ||||||||
\(218\) | 14.0869 | 0.954086 | ||||||||
\(219\) | −1.78182 | −0.120404 | ||||||||
\(220\) | −21.7562 | −1.46680 | ||||||||
\(221\) | 8.92837 | 0.600587 | ||||||||
\(222\) | 19.6797 | 1.32082 | ||||||||
\(223\) | −5.28037 | −0.353599 | −0.176800 | − | 0.984247i | \(-0.556574\pi\) | ||||
−0.176800 | + | 0.984247i | \(0.556574\pi\) | |||||||
\(224\) | −1.00810 | −0.0673567 | ||||||||
\(225\) | −1.21576 | −0.0810508 | ||||||||
\(226\) | −37.3803 | −2.48650 | ||||||||
\(227\) | 11.7070 | 0.777023 | 0.388511 | − | 0.921444i | \(-0.372989\pi\) | ||||
0.388511 | + | 0.921444i | \(0.372989\pi\) | |||||||
\(228\) | 29.0566 | 1.92432 | ||||||||
\(229\) | 21.7015 | 1.43408 | 0.717039 | − | 0.697033i | \(-0.245497\pi\) | ||||
0.717039 | + | 0.697033i | \(0.245497\pi\) | |||||||
\(230\) | 9.71393 | 0.640518 | ||||||||
\(231\) | −4.42097 | −0.290878 | ||||||||
\(232\) | −0.611807 | −0.0401671 | ||||||||
\(233\) | −4.91197 | −0.321794 | −0.160897 | − | 0.986971i | \(-0.551439\pi\) | ||||
−0.160897 | + | 0.986971i | \(0.551439\pi\) | |||||||
\(234\) | −3.81211 | −0.249205 | ||||||||
\(235\) | 9.17145 | 0.598279 | ||||||||
\(236\) | 40.2405 | 2.61943 | ||||||||
\(237\) | 8.40804 | 0.546161 | ||||||||
\(238\) | −9.59168 | −0.621736 | ||||||||
\(239\) | −25.4102 | −1.64365 | −0.821824 | − | 0.569741i | \(-0.807043\pi\) | ||||
−0.821824 | + | 0.569741i | \(0.807043\pi\) | |||||||
\(240\) | −3.87365 | −0.250043 | ||||||||
\(241\) | −0.552882 | −0.0356143 | −0.0178071 | − | 0.999841i | \(-0.505668\pi\) | ||||
−0.0178071 | + | 0.999841i | \(0.505668\pi\) | |||||||
\(242\) | −52.0570 | −3.34635 | ||||||||
\(243\) | 11.7181 | 0.751716 | ||||||||
\(244\) | 47.1536 | 3.01870 | ||||||||
\(245\) | 6.66394 | 0.425743 | ||||||||
\(246\) | −3.59702 | −0.229338 | ||||||||
\(247\) | −7.42537 | −0.472465 | ||||||||
\(248\) | −27.7393 | −1.76145 | ||||||||
\(249\) | −16.8483 | −1.06772 | ||||||||
\(250\) | 2.41054 | 0.152456 | ||||||||
\(251\) | −1.11420 | −0.0703277 | −0.0351639 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351639 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(252\) | 2.68573 | 0.169185 | ||||||||
\(253\) | 23.0070 | 1.44644 | ||||||||
\(254\) | −37.2006 | −2.33418 | ||||||||
\(255\) | 9.16845 | 0.574151 | ||||||||
\(256\) | −29.6919 | −1.85575 | ||||||||
\(257\) | 14.6434 | 0.913430 | 0.456715 | − | 0.889613i | \(-0.349026\pi\) | ||||
0.456715 | + | 0.889613i | \(0.349026\pi\) | |||||||
\(258\) | −12.1005 | −0.753345 | ||||||||
\(259\) | 3.54315 | 0.220161 | ||||||||
\(260\) | 4.95686 | 0.307411 | ||||||||
\(261\) | −0.170414 | −0.0105484 | ||||||||
\(262\) | −2.20636 | −0.136309 | ||||||||
\(263\) | 20.0453 | 1.23604 | 0.618022 | − | 0.786161i | \(-0.287934\pi\) | ||||
0.618022 | + | 0.786161i | \(0.287934\pi\) | |||||||
\(264\) | −33.2861 | −2.04862 | ||||||||
\(265\) | −0.869216 | −0.0533955 | ||||||||
\(266\) | 7.97702 | 0.489102 | ||||||||
\(267\) | 0.613332 | 0.0375353 | ||||||||
\(268\) | 13.4250 | 0.820065 | ||||||||
\(269\) | 9.60367 | 0.585546 | 0.292773 | − | 0.956182i | \(-0.405422\pi\) | ||||
0.292773 | + | 0.956182i | \(0.405422\pi\) | |||||||
\(270\) | −13.5743 | −0.826103 | ||||||||
\(271\) | 6.36441 | 0.386610 | 0.193305 | − | 0.981139i | \(-0.438079\pi\) | ||||
0.193305 | + | 0.981139i | \(0.438079\pi\) | |||||||
\(272\) | −19.9051 | −1.20692 | ||||||||
\(273\) | 1.00726 | 0.0609620 | ||||||||
\(274\) | 16.0333 | 0.968606 | ||||||||
\(275\) | 5.70925 | 0.344281 | ||||||||
\(276\) | 20.5122 | 1.23469 | ||||||||
\(277\) | 12.2752 | 0.737547 | 0.368774 | − | 0.929519i | \(-0.379778\pi\) | ||||
0.368774 | + | 0.929519i | \(0.379778\pi\) | |||||||
\(278\) | 29.9999 | 1.79928 | ||||||||
\(279\) | −7.72657 | −0.462578 | ||||||||
\(280\) | −2.53028 | −0.151213 | ||||||||
\(281\) | −10.2846 | −0.613529 | −0.306764 | − | 0.951785i | \(-0.599246\pi\) | ||||
−0.306764 | + | 0.951785i | \(0.599246\pi\) | |||||||
\(282\) | 29.5310 | 1.75855 | ||||||||
\(283\) | 11.0051 | 0.654188 | 0.327094 | − | 0.944992i | \(-0.393931\pi\) | ||||
0.327094 | + | 0.944992i | \(0.393931\pi\) | |||||||
\(284\) | −8.20515 | −0.486886 | ||||||||
\(285\) | −7.62503 | −0.451668 | ||||||||
\(286\) | 17.9018 | 1.05855 | ||||||||
\(287\) | −0.647610 | −0.0382272 | ||||||||
\(288\) | −2.11418 | −0.124579 | ||||||||
\(289\) | 30.1128 | 1.77134 | ||||||||
\(290\) | 0.337886 | 0.0198414 | ||||||||
\(291\) | 2.21008 | 0.129557 | ||||||||
\(292\) | −5.08325 | −0.297475 | ||||||||
\(293\) | 4.93739 | 0.288445 | 0.144223 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144223 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(294\) | 21.4571 | 1.25140 | ||||||||
\(295\) | −10.5599 | −0.614821 | ||||||||
\(296\) | 26.6769 | 1.55057 | ||||||||
\(297\) | −32.1501 | −1.86554 | ||||||||
\(298\) | 13.2463 | 0.767336 | ||||||||
\(299\) | −5.24184 | −0.303144 | ||||||||
\(300\) | 5.09014 | 0.293880 | ||||||||
\(301\) | −2.17859 | −0.125572 | ||||||||
\(302\) | 38.2225 | 2.19946 | ||||||||
\(303\) | −23.9235 | −1.37437 | ||||||||
\(304\) | 16.5542 | 0.949451 | ||||||||
\(305\) | −12.3740 | −0.708536 | ||||||||
\(306\) | −20.1155 | −1.14993 | ||||||||
\(307\) | 20.4369 | 1.16640 | 0.583199 | − | 0.812329i | \(-0.301801\pi\) | ||||
0.583199 | + | 0.812329i | \(0.301801\pi\) | |||||||
\(308\) | −12.6123 | −0.718652 | ||||||||
\(309\) | 3.43302 | 0.195298 | ||||||||
\(310\) | 15.3198 | 0.870105 | ||||||||
\(311\) | −7.90496 | −0.448249 | −0.224124 | − | 0.974561i | \(-0.571952\pi\) | ||||
−0.224124 | + | 0.974561i | \(0.571952\pi\) | |||||||
\(312\) | 7.58380 | 0.429348 | ||||||||
\(313\) | 24.8828 | 1.40646 | 0.703230 | − | 0.710963i | \(-0.251741\pi\) | ||||
0.703230 | + | 0.710963i | \(0.251741\pi\) | |||||||
\(314\) | 38.8200 | 2.19074 | ||||||||
\(315\) | −0.704790 | −0.0397104 | ||||||||
\(316\) | 23.9868 | 1.34936 | ||||||||
\(317\) | −23.2173 | −1.30402 | −0.652008 | − | 0.758212i | \(-0.726073\pi\) | ||||
−0.652008 | + | 0.758212i | \(0.726073\pi\) | |||||||
\(318\) | −2.79877 | −0.156947 | ||||||||
\(319\) | 0.800269 | 0.0448065 | ||||||||
\(320\) | 9.99181 | 0.558559 | ||||||||
\(321\) | 22.0314 | 1.22967 | ||||||||
\(322\) | 5.63127 | 0.313818 | ||||||||
\(323\) | −39.1819 | −2.18014 | ||||||||
\(324\) | −14.7650 | −0.820281 | ||||||||
\(325\) | −1.30078 | −0.0721541 | ||||||||
\(326\) | −24.1798 | −1.33920 | ||||||||
\(327\) | −7.80600 | −0.431673 | ||||||||
\(328\) | −4.87596 | −0.269230 | ||||||||
\(329\) | 5.31679 | 0.293124 | ||||||||
\(330\) | 18.3831 | 1.01196 | ||||||||
\(331\) | 10.5504 | 0.579901 | 0.289951 | − | 0.957042i | \(-0.406361\pi\) | ||||
0.289951 | + | 0.957042i | \(0.406361\pi\) | |||||||
\(332\) | −48.0654 | −2.63793 | ||||||||
\(333\) | 7.43065 | 0.407197 | ||||||||
\(334\) | 17.9108 | 0.980033 | ||||||||
\(335\) | −3.52300 | −0.192482 | ||||||||
\(336\) | −2.24560 | −0.122507 | ||||||||
\(337\) | −28.9734 | −1.57828 | −0.789142 | − | 0.614211i | \(-0.789475\pi\) | ||||
−0.789142 | + | 0.614211i | \(0.789475\pi\) | |||||||
\(338\) | 27.2583 | 1.48266 | ||||||||
\(339\) | 20.7136 | 1.12501 | ||||||||
\(340\) | 26.1561 | 1.41851 | ||||||||
\(341\) | 36.2842 | 1.96490 | ||||||||
\(342\) | 16.7293 | 0.904616 | ||||||||
\(343\) | 7.92113 | 0.427701 | ||||||||
\(344\) | −16.4029 | −0.884386 | ||||||||
\(345\) | −5.38279 | −0.289800 | ||||||||
\(346\) | −2.99741 | −0.161142 | ||||||||
\(347\) | −28.3134 | −1.51994 | −0.759971 | − | 0.649957i | \(-0.774787\pi\) | ||||
−0.759971 | + | 0.649957i | \(0.774787\pi\) | |||||||
\(348\) | 0.713488 | 0.0382470 | ||||||||
\(349\) | 36.0563 | 1.93005 | 0.965025 | − | 0.262156i | \(-0.0844336\pi\) | ||||
0.965025 | + | 0.262156i | \(0.0844336\pi\) | |||||||
\(350\) | 1.39741 | 0.0746949 | ||||||||
\(351\) | 7.32496 | 0.390977 | ||||||||
\(352\) | 9.92825 | 0.529178 | ||||||||
\(353\) | 34.5113 | 1.83685 | 0.918426 | − | 0.395592i | \(-0.129461\pi\) | ||||
0.918426 | + | 0.395592i | \(0.129461\pi\) | |||||||
\(354\) | −34.0016 | −1.80717 | ||||||||
\(355\) | 2.15319 | 0.114280 | ||||||||
\(356\) | 1.74974 | 0.0927359 | ||||||||
\(357\) | 5.31505 | 0.281302 | ||||||||
\(358\) | −62.4905 | −3.30272 | ||||||||
\(359\) | −8.45269 | −0.446116 | −0.223058 | − | 0.974805i | \(-0.571604\pi\) | ||||
−0.223058 | + | 0.974805i | \(0.571604\pi\) | |||||||
\(360\) | −5.30647 | −0.279676 | ||||||||
\(361\) | 13.5860 | 0.715051 | ||||||||
\(362\) | −40.7348 | −2.14097 | ||||||||
\(363\) | 28.8464 | 1.51404 | ||||||||
\(364\) | 2.87354 | 0.150615 | ||||||||
\(365\) | 1.33394 | 0.0698219 | ||||||||
\(366\) | −39.8430 | −2.08263 | ||||||||
\(367\) | 25.5447 | 1.33342 | 0.666710 | − | 0.745317i | \(-0.267702\pi\) | ||||
0.666710 | + | 0.745317i | \(0.267702\pi\) | |||||||
\(368\) | 11.6862 | 0.609188 | ||||||||
\(369\) | −1.35816 | −0.0707030 | ||||||||
\(370\) | −14.7330 | −0.765934 | ||||||||
\(371\) | −0.503894 | −0.0261609 | ||||||||
\(372\) | 32.3496 | 1.67725 | ||||||||
\(373\) | 30.0540 | 1.55614 | 0.778069 | − | 0.628178i | \(-0.216199\pi\) | ||||
0.778069 | + | 0.628178i | \(0.216199\pi\) | |||||||
\(374\) | 94.4632 | 4.88458 | ||||||||
\(375\) | −1.33575 | −0.0689780 | ||||||||
\(376\) | 40.0309 | 2.06444 | ||||||||
\(377\) | −0.182331 | −0.00939050 | ||||||||
\(378\) | −7.86915 | −0.404745 | ||||||||
\(379\) | −2.24607 | −0.115373 | −0.0576864 | − | 0.998335i | \(-0.518372\pi\) | ||||
−0.0576864 | + | 0.998335i | \(0.518372\pi\) | |||||||
\(380\) | −21.7530 | −1.11590 | ||||||||
\(381\) | 20.6140 | 1.05609 | ||||||||
\(382\) | −2.73391 | −0.139879 | ||||||||
\(383\) | −19.8384 | −1.01369 | −0.506847 | − | 0.862036i | \(-0.669189\pi\) | ||||
−0.506847 | + | 0.862036i | \(0.669189\pi\) | |||||||
\(384\) | 27.5268 | 1.40472 | ||||||||
\(385\) | 3.30972 | 0.168679 | ||||||||
\(386\) | −24.4594 | −1.24495 | ||||||||
\(387\) | −4.56890 | −0.232250 | ||||||||
\(388\) | 6.30500 | 0.320088 | ||||||||
\(389\) | −29.4296 | −1.49214 | −0.746069 | − | 0.665869i | \(-0.768061\pi\) | ||||
−0.746069 | + | 0.665869i | \(0.768061\pi\) | |||||||
\(390\) | −4.18835 | −0.212085 | ||||||||
\(391\) | −27.6599 | −1.39882 | ||||||||
\(392\) | 29.0863 | 1.46908 | ||||||||
\(393\) | 1.22261 | 0.0616727 | ||||||||
\(394\) | 32.9045 | 1.65771 | ||||||||
\(395\) | −6.29460 | −0.316716 | ||||||||
\(396\) | −26.4503 | −1.32918 | ||||||||
\(397\) | 5.48517 | 0.275293 | 0.137646 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137646 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(398\) | 28.3646 | 1.42179 | ||||||||
\(399\) | −4.42031 | −0.221292 | ||||||||
\(400\) | 2.89997 | 0.144999 | ||||||||
\(401\) | −15.2511 | −0.761606 | −0.380803 | − | 0.924656i | \(-0.624352\pi\) | ||||
−0.380803 | + | 0.924656i | \(0.624352\pi\) | |||||||
\(402\) | −11.3436 | −0.565770 | ||||||||
\(403\) | −8.26687 | −0.411802 | ||||||||
\(404\) | −68.2498 | −3.39555 | ||||||||
\(405\) | 3.87464 | 0.192532 | ||||||||
\(406\) | 0.195876 | 0.00972118 | ||||||||
\(407\) | −34.8946 | −1.72966 | ||||||||
\(408\) | 40.0179 | 1.98118 | ||||||||
\(409\) | 33.6003 | 1.66143 | 0.830714 | − | 0.556700i | \(-0.187933\pi\) | ||||
0.830714 | + | 0.556700i | \(0.187933\pi\) | |||||||
\(410\) | 2.69288 | 0.132992 | ||||||||
\(411\) | −8.88455 | −0.438242 | ||||||||
\(412\) | 9.79386 | 0.482509 | ||||||||
\(413\) | −6.12168 | −0.301228 | ||||||||
\(414\) | 11.8098 | 0.580421 | ||||||||
\(415\) | 12.6133 | 0.619163 | ||||||||
\(416\) | −2.26202 | −0.110905 | ||||||||
\(417\) | −16.6239 | −0.814076 | ||||||||
\(418\) | −78.5613 | −3.84256 | ||||||||
\(419\) | 10.2645 | 0.501455 | 0.250728 | − | 0.968058i | \(-0.419330\pi\) | ||||
0.250728 | + | 0.968058i | \(0.419330\pi\) | |||||||
\(420\) | 2.95081 | 0.143985 | ||||||||
\(421\) | −3.18192 | −0.155077 | −0.0775386 | − | 0.996989i | \(-0.524706\pi\) | ||||
−0.0775386 | + | 0.996989i | \(0.524706\pi\) | |||||||
\(422\) | −66.3695 | −3.23082 | ||||||||
\(423\) | 11.1503 | 0.542146 | ||||||||
\(424\) | −3.79389 | −0.184248 | ||||||||
\(425\) | −6.86388 | −0.332947 | ||||||||
\(426\) | 6.93303 | 0.335906 | ||||||||
\(427\) | −7.17336 | −0.347143 | ||||||||
\(428\) | 62.8521 | 3.03807 | ||||||||
\(429\) | −9.91993 | −0.478939 | ||||||||
\(430\) | 9.05894 | 0.436861 | ||||||||
\(431\) | 37.5920 | 1.81074 | 0.905372 | − | 0.424618i | \(-0.139592\pi\) | ||||
0.905372 | + | 0.424618i | \(0.139592\pi\) | |||||||
\(432\) | −16.3304 | −0.785696 | ||||||||
\(433\) | −19.1518 | −0.920376 | −0.460188 | − | 0.887822i | \(-0.652218\pi\) | ||||
−0.460188 | + | 0.887822i | \(0.652218\pi\) | |||||||
\(434\) | 8.88104 | 0.426303 | ||||||||
\(435\) | −0.187233 | −0.00897715 | ||||||||
\(436\) | −22.2692 | −1.06650 | ||||||||
\(437\) | 23.0036 | 1.10041 | ||||||||
\(438\) | 4.29515 | 0.205230 | ||||||||
\(439\) | 8.78346 | 0.419212 | 0.209606 | − | 0.977786i | \(-0.432782\pi\) | ||||
0.209606 | + | 0.977786i | \(0.432782\pi\) | |||||||
\(440\) | 24.9194 | 1.18798 | ||||||||
\(441\) | 8.10176 | 0.385798 | ||||||||
\(442\) | −21.5222 | −1.02371 | ||||||||
\(443\) | −31.7253 | −1.50731 | −0.753657 | − | 0.657268i | \(-0.771712\pi\) | ||||
−0.753657 | + | 0.657268i | \(0.771712\pi\) | |||||||
\(444\) | −31.1106 | −1.47644 | ||||||||
\(445\) | −0.459166 | −0.0217665 | ||||||||
\(446\) | 12.7285 | 0.602713 | ||||||||
\(447\) | −7.34018 | −0.347178 | ||||||||
\(448\) | 5.79236 | 0.273663 | ||||||||
\(449\) | 7.74859 | 0.365679 | 0.182839 | − | 0.983143i | \(-0.441471\pi\) | ||||
0.182839 | + | 0.983143i | \(0.441471\pi\) | |||||||
\(450\) | 2.93064 | 0.138152 | ||||||||
\(451\) | 6.37796 | 0.300326 | ||||||||
\(452\) | 59.0925 | 2.77948 | ||||||||
\(453\) | −21.1803 | −0.995136 | ||||||||
\(454\) | −28.2202 | −1.32444 | ||||||||
\(455\) | −0.754074 | −0.0353515 | ||||||||
\(456\) | −33.2812 | −1.55854 | ||||||||
\(457\) | 4.64336 | 0.217207 | 0.108604 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108604 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(458\) | −52.3124 | −2.44440 | ||||||||
\(459\) | 38.6520 | 1.80412 | ||||||||
\(460\) | −15.3562 | −0.715988 | ||||||||
\(461\) | 39.4625 | 1.83795 | 0.918976 | − | 0.394314i | \(-0.129018\pi\) | ||||
0.918976 | + | 0.394314i | \(0.129018\pi\) | |||||||
\(462\) | 10.6569 | 0.495804 | ||||||||
\(463\) | 5.01227 | 0.232940 | 0.116470 | − | 0.993194i | \(-0.462842\pi\) | ||||
0.116470 | + | 0.993194i | \(0.462842\pi\) | |||||||
\(464\) | 0.406491 | 0.0188709 | ||||||||
\(465\) | −8.48917 | −0.393676 | ||||||||
\(466\) | 11.8405 | 0.548500 | ||||||||
\(467\) | 1.54960 | 0.0717067 | 0.0358534 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358534 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(468\) | 6.02635 | 0.278568 | ||||||||
\(469\) | −2.04232 | −0.0943055 | ||||||||
\(470\) | −22.1081 | −1.01977 | ||||||||
\(471\) | −21.5114 | −0.991192 | ||||||||
\(472\) | −46.0911 | −2.12152 | ||||||||
\(473\) | 21.4557 | 0.986535 | ||||||||
\(474\) | −20.2679 | −0.930935 | ||||||||
\(475\) | 5.70841 | 0.261920 | ||||||||
\(476\) | 15.1630 | 0.694994 | ||||||||
\(477\) | −1.05676 | −0.0483857 | ||||||||
\(478\) | 61.2522 | 2.80161 | ||||||||
\(479\) | −24.6773 | −1.12754 | −0.563768 | − | 0.825933i | \(-0.690649\pi\) | ||||
−0.563768 | + | 0.825933i | \(0.690649\pi\) | |||||||
\(480\) | −2.32284 | −0.106023 | ||||||||
\(481\) | 7.95026 | 0.362501 | ||||||||
\(482\) | 1.33274 | 0.0607048 | ||||||||
\(483\) | −3.12046 | −0.141986 | ||||||||
\(484\) | 82.2940 | 3.74064 | ||||||||
\(485\) | −1.65456 | −0.0751295 | ||||||||
\(486\) | −28.2469 | −1.28131 | ||||||||
\(487\) | 37.8051 | 1.71311 | 0.856556 | − | 0.516054i | \(-0.172600\pi\) | ||||
0.856556 | + | 0.516054i | \(0.172600\pi\) | |||||||
\(488\) | −54.0094 | −2.44489 | ||||||||
\(489\) | 13.3988 | 0.605914 | ||||||||
\(490\) | −16.0637 | −0.725682 | ||||||||
\(491\) | −35.2010 | −1.58860 | −0.794300 | − | 0.607526i | \(-0.792162\pi\) | ||||
−0.794300 | + | 0.607526i | \(0.792162\pi\) | |||||||
\(492\) | 5.68633 | 0.256360 | ||||||||
\(493\) | −0.962114 | −0.0433314 | ||||||||
\(494\) | 17.8991 | 0.805320 | ||||||||
\(495\) | 6.94109 | 0.311979 | ||||||||
\(496\) | 18.4303 | 0.827545 | ||||||||
\(497\) | 1.24823 | 0.0559907 | ||||||||
\(498\) | 40.6134 | 1.81993 | ||||||||
\(499\) | −20.7551 | −0.929125 | −0.464563 | − | 0.885540i | \(-0.653788\pi\) | ||||
−0.464563 | + | 0.885540i | \(0.653788\pi\) | |||||||
\(500\) | −3.81069 | −0.170419 | ||||||||
\(501\) | −9.92491 | −0.443412 | ||||||||
\(502\) | 2.68582 | 0.119874 | ||||||||
\(503\) | −34.6591 | −1.54537 | −0.772687 | − | 0.634787i | \(-0.781088\pi\) | ||||
−0.772687 | + | 0.634787i | \(0.781088\pi\) | |||||||
\(504\) | −3.07622 | −0.137026 | ||||||||
\(505\) | 17.9101 | 0.796989 | ||||||||
\(506\) | −55.4593 | −2.46547 | ||||||||
\(507\) | −15.1047 | −0.670822 | ||||||||
\(508\) | 58.8085 | 2.60921 | ||||||||
\(509\) | 35.0177 | 1.55213 | 0.776065 | − | 0.630652i | \(-0.217213\pi\) | ||||
0.776065 | + | 0.630652i | \(0.217213\pi\) | |||||||
\(510\) | −22.1009 | −0.978644 | ||||||||
\(511\) | 0.773302 | 0.0342089 | ||||||||
\(512\) | 30.3582 | 1.34165 | ||||||||
\(513\) | −32.1453 | −1.41925 | ||||||||
\(514\) | −35.2985 | −1.55695 | ||||||||
\(515\) | −2.57010 | −0.113252 | ||||||||
\(516\) | 19.1291 | 0.842110 | ||||||||
\(517\) | −52.3621 | −2.30288 | ||||||||
\(518\) | −8.54090 | −0.375266 | ||||||||
\(519\) | 1.66096 | 0.0729081 | ||||||||
\(520\) | −5.67754 | −0.248977 | ||||||||
\(521\) | −15.5454 | −0.681057 | −0.340528 | − | 0.940234i | \(-0.610606\pi\) | ||||
−0.340528 | + | 0.940234i | \(0.610606\pi\) | |||||||
\(522\) | 0.410789 | 0.0179798 | ||||||||
\(523\) | 19.2984 | 0.843860 | 0.421930 | − | 0.906628i | \(-0.361353\pi\) | ||||
0.421930 | + | 0.906628i | \(0.361353\pi\) | |||||||
\(524\) | 3.48792 | 0.152370 | ||||||||
\(525\) | −0.774351 | −0.0337954 | ||||||||
\(526\) | −48.3198 | −2.10684 | ||||||||
\(527\) | −43.6223 | −1.90022 | ||||||||
\(528\) | 22.1156 | 0.962460 | ||||||||
\(529\) | −6.76088 | −0.293951 | ||||||||
\(530\) | 2.09528 | 0.0910130 | ||||||||
\(531\) | −12.8383 | −0.557135 | ||||||||
\(532\) | −12.6104 | −0.546732 | ||||||||
\(533\) | −1.45313 | −0.0629422 | ||||||||
\(534\) | −1.47846 | −0.0639792 | ||||||||
\(535\) | −16.4936 | −0.713082 | ||||||||
\(536\) | −15.3769 | −0.664183 | ||||||||
\(537\) | 34.6279 | 1.49430 | ||||||||
\(538\) | −23.1500 | −0.998067 | ||||||||
\(539\) | −38.0461 | −1.63876 | ||||||||
\(540\) | 21.4588 | 0.923441 | ||||||||
\(541\) | −6.66798 | −0.286679 | −0.143340 | − | 0.989674i | \(-0.545784\pi\) | ||||
−0.143340 | + | 0.989674i | \(0.545784\pi\) | |||||||
\(542\) | −15.3416 | −0.658980 | ||||||||
\(543\) | 22.5724 | 0.968676 | ||||||||
\(544\) | −11.9361 | −0.511757 | ||||||||
\(545\) | 5.84389 | 0.250325 | ||||||||
\(546\) | −2.42803 | −0.103910 | ||||||||
\(547\) | −35.4767 | −1.51687 | −0.758437 | − | 0.651746i | \(-0.774037\pi\) | ||||
−0.758437 | + | 0.651746i | \(0.774037\pi\) | |||||||
\(548\) | −25.3462 | −1.08273 | ||||||||
\(549\) | −15.0439 | −0.642057 | ||||||||
\(550\) | −13.7624 | −0.586829 | ||||||||
\(551\) | 0.800151 | 0.0340876 | ||||||||
\(552\) | −23.4945 | −0.999990 | ||||||||
\(553\) | −3.64905 | −0.155173 | ||||||||
\(554\) | −29.5899 | −1.25715 | ||||||||
\(555\) | 8.16404 | 0.346544 | ||||||||
\(556\) | −47.4253 | −2.01128 | ||||||||
\(557\) | 25.5149 | 1.08110 | 0.540551 | − | 0.841311i | \(-0.318216\pi\) | ||||
0.540551 | + | 0.841311i | \(0.318216\pi\) | |||||||
\(558\) | 18.6252 | 0.788467 | ||||||||
\(559\) | −4.88840 | −0.206757 | ||||||||
\(560\) | 1.68114 | 0.0710413 | ||||||||
\(561\) | −52.3450 | −2.21001 | ||||||||
\(562\) | 24.7914 | 1.04576 | ||||||||
\(563\) | −25.2270 | −1.06319 | −0.531597 | − | 0.846998i | \(-0.678408\pi\) | ||||
−0.531597 | + | 0.846998i | \(0.678408\pi\) | |||||||
\(564\) | −46.6840 | −1.96575 | ||||||||
\(565\) | −15.5070 | −0.652386 | ||||||||
\(566\) | −26.5283 | −1.11507 | ||||||||
\(567\) | 2.24617 | 0.0943303 | ||||||||
\(568\) | 9.39811 | 0.394336 | ||||||||
\(569\) | −31.1301 | −1.30504 | −0.652520 | − | 0.757771i | \(-0.726288\pi\) | ||||
−0.652520 | + | 0.757771i | \(0.726288\pi\) | |||||||
\(570\) | 18.3804 | 0.769871 | ||||||||
\(571\) | −18.6652 | −0.781113 | −0.390557 | − | 0.920579i | \(-0.627717\pi\) | ||||
−0.390557 | + | 0.920579i | \(0.627717\pi\) | |||||||
\(572\) | −28.2999 | −1.18328 | ||||||||
\(573\) | 1.51495 | 0.0632877 | ||||||||
\(574\) | 1.56109 | 0.0651586 | ||||||||
\(575\) | 4.02978 | 0.168053 | ||||||||
\(576\) | 12.1477 | 0.506152 | ||||||||
\(577\) | −44.4690 | −1.85127 | −0.925634 | − | 0.378421i | \(-0.876467\pi\) | ||||
−0.925634 | + | 0.378421i | \(0.876467\pi\) | |||||||
\(578\) | −72.5881 | −3.01927 | ||||||||
\(579\) | 13.5537 | 0.563272 | ||||||||
\(580\) | −0.534146 | −0.0221792 | ||||||||
\(581\) | 7.31207 | 0.303356 | ||||||||
\(582\) | −5.32748 | −0.220831 | ||||||||
\(583\) | 4.96257 | 0.205529 | ||||||||
\(584\) | 5.82231 | 0.240929 | ||||||||
\(585\) | −1.58143 | −0.0653842 | ||||||||
\(586\) | −11.9018 | −0.491657 | ||||||||
\(587\) | −1.52790 | −0.0630633 | −0.0315316 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315316 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(588\) | −33.9204 | −1.39885 | ||||||||
\(589\) | 36.2789 | 1.49485 | ||||||||
\(590\) | 25.4550 | 1.04797 | ||||||||
\(591\) | −18.2334 | −0.750023 | ||||||||
\(592\) | −17.7244 | −0.728469 | ||||||||
\(593\) | 43.7258 | 1.79560 | 0.897801 | − | 0.440402i | \(-0.145164\pi\) | ||||
0.897801 | + | 0.440402i | \(0.145164\pi\) | |||||||
\(594\) | 77.4989 | 3.17982 | ||||||||
\(595\) | −3.97906 | −0.163126 | ||||||||
\(596\) | −20.9403 | −0.857749 | ||||||||
\(597\) | −15.7177 | −0.643283 | ||||||||
\(598\) | 12.6357 | 0.516710 | ||||||||
\(599\) | 34.3780 | 1.40465 | 0.702323 | − | 0.711858i | \(-0.252146\pi\) | ||||
0.702323 | + | 0.711858i | \(0.252146\pi\) | |||||||
\(600\) | −5.83021 | −0.238017 | ||||||||
\(601\) | 31.5603 | 1.28737 | 0.643687 | − | 0.765289i | \(-0.277404\pi\) | ||||
0.643687 | + | 0.765289i | \(0.277404\pi\) | |||||||
\(602\) | 5.25156 | 0.214038 | ||||||||
\(603\) | −4.28312 | −0.174422 | ||||||||
\(604\) | −60.4239 | −2.45861 | ||||||||
\(605\) | −21.5956 | −0.877985 | ||||||||
\(606\) | 57.6684 | 2.34262 | ||||||||
\(607\) | −4.85283 | −0.196970 | −0.0984852 | − | 0.995139i | \(-0.531400\pi\) | ||||
−0.0984852 | + | 0.995139i | \(0.531400\pi\) | |||||||
\(608\) | 9.92679 | 0.402584 | ||||||||
\(609\) | −0.108541 | −0.00439831 | ||||||||
\(610\) | 29.8281 | 1.20770 | ||||||||
\(611\) | 11.9300 | 0.482636 | ||||||||
\(612\) | 31.7996 | 1.28542 | ||||||||
\(613\) | 10.0307 | 0.405134 | 0.202567 | − | 0.979268i | \(-0.435072\pi\) | ||||
0.202567 | + | 0.979268i | \(0.435072\pi\) | |||||||
\(614\) | −49.2640 | −1.98813 | ||||||||
\(615\) | −1.49221 | −0.0601716 | ||||||||
\(616\) | 14.4460 | 0.582047 | ||||||||
\(617\) | 24.5548 | 0.988540 | 0.494270 | − | 0.869309i | \(-0.335435\pi\) | ||||
0.494270 | + | 0.869309i | \(0.335435\pi\) | |||||||
\(618\) | −8.27543 | −0.332887 | ||||||||
\(619\) | −8.06974 | −0.324350 | −0.162175 | − | 0.986762i | \(-0.551851\pi\) | ||||
−0.162175 | + | 0.986762i | \(0.551851\pi\) | |||||||
\(620\) | −24.2182 | −0.972627 | ||||||||
\(621\) | −22.6926 | −0.910622 | ||||||||
\(622\) | 19.0552 | 0.764044 | ||||||||
\(623\) | −0.266183 | −0.0106644 | ||||||||
\(624\) | −5.03875 | −0.201712 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −59.9809 | −2.39732 | ||||||||
\(627\) | 43.5333 | 1.73855 | ||||||||
\(628\) | −61.3685 | −2.44887 | ||||||||
\(629\) | 41.9516 | 1.67272 | ||||||||
\(630\) | 1.69892 | 0.0676867 | ||||||||
\(631\) | −10.7421 | −0.427637 | −0.213819 | − | 0.976873i | \(-0.568590\pi\) | ||||
−0.213819 | + | 0.976873i | \(0.568590\pi\) | |||||||
\(632\) | −27.4742 | −1.09287 | ||||||||
\(633\) | 36.7774 | 1.46177 | ||||||||
\(634\) | 55.9662 | 2.22270 | ||||||||
\(635\) | −15.4325 | −0.612421 | ||||||||
\(636\) | 4.42443 | 0.175440 | ||||||||
\(637\) | 8.66829 | 0.343450 | ||||||||
\(638\) | −1.92908 | −0.0763730 | ||||||||
\(639\) | 2.61777 | 0.103557 | ||||||||
\(640\) | −20.6077 | −0.814590 | ||||||||
\(641\) | −1.84518 | −0.0728802 | −0.0364401 | − | 0.999336i | \(-0.511602\pi\) | ||||
−0.0364401 | + | 0.999336i | \(0.511602\pi\) | |||||||
\(642\) | −53.1076 | −2.09599 | ||||||||
\(643\) | 33.9688 | 1.33960 | 0.669799 | − | 0.742543i | \(-0.266380\pi\) | ||||
0.669799 | + | 0.742543i | \(0.266380\pi\) | |||||||
\(644\) | −8.90217 | −0.350795 | ||||||||
\(645\) | −5.01984 | −0.197656 | ||||||||
\(646\) | 94.4493 | 3.71606 | ||||||||
\(647\) | −16.3951 | −0.644558 | −0.322279 | − | 0.946645i | \(-0.604449\pi\) | ||||
−0.322279 | + | 0.946645i | \(0.604449\pi\) | |||||||
\(648\) | 16.9118 | 0.664357 | ||||||||
\(649\) | 60.2891 | 2.36656 | ||||||||
\(650\) | 3.13557 | 0.122987 | ||||||||
\(651\) | −4.92126 | −0.192879 | ||||||||
\(652\) | 38.2246 | 1.49699 | ||||||||
\(653\) | −44.1211 | −1.72659 | −0.863296 | − | 0.504697i | \(-0.831604\pi\) | ||||
−0.863296 | + | 0.504697i | \(0.831604\pi\) | |||||||
\(654\) | 18.8167 | 0.735789 | ||||||||
\(655\) | −0.915298 | −0.0357636 | ||||||||
\(656\) | 3.23964 | 0.126487 | ||||||||
\(657\) | 1.62176 | 0.0632708 | ||||||||
\(658\) | −12.8163 | −0.499632 | ||||||||
\(659\) | −31.5331 | −1.22835 | −0.614177 | − | 0.789168i | \(-0.710512\pi\) | ||||
−0.614177 | + | 0.789168i | \(0.710512\pi\) | |||||||
\(660\) | −29.0609 | −1.13119 | ||||||||
\(661\) | 29.1323 | 1.13312 | 0.566558 | − | 0.824022i | \(-0.308275\pi\) | ||||
0.566558 | + | 0.824022i | \(0.308275\pi\) | |||||||
\(662\) | −25.4321 | −0.988446 | ||||||||
\(663\) | 11.9261 | 0.463172 | ||||||||
\(664\) | 55.0537 | 2.13650 | ||||||||
\(665\) | 3.30923 | 0.128326 | ||||||||
\(666\) | −17.9119 | −0.694070 | ||||||||
\(667\) | 0.564856 | 0.0218713 | ||||||||
\(668\) | −28.3142 | −1.09551 | ||||||||
\(669\) | −7.05327 | −0.272695 | ||||||||
\(670\) | 8.49232 | 0.328087 | ||||||||
\(671\) | 70.6465 | 2.72728 | ||||||||
\(672\) | −1.34658 | −0.0519453 | ||||||||
\(673\) | 34.3259 | 1.32317 | 0.661584 | − | 0.749871i | \(-0.269885\pi\) | ||||
0.661584 | + | 0.749871i | \(0.269885\pi\) | |||||||
\(674\) | 69.8416 | 2.69020 | ||||||||
\(675\) | −5.63122 | −0.216746 | ||||||||
\(676\) | −43.0912 | −1.65735 | ||||||||
\(677\) | 37.0080 | 1.42233 | 0.711167 | − | 0.703023i | \(-0.248167\pi\) | ||||
0.711167 | + | 0.703023i | \(0.248167\pi\) | |||||||
\(678\) | −49.9308 | −1.91758 | ||||||||
\(679\) | −0.959163 | −0.0368093 | ||||||||
\(680\) | −29.9590 | −1.14888 | ||||||||
\(681\) | 15.6377 | 0.599238 | ||||||||
\(682\) | −87.4645 | −3.34919 | ||||||||
\(683\) | 26.5191 | 1.01472 | 0.507362 | − | 0.861733i | \(-0.330621\pi\) | ||||
0.507362 | + | 0.861733i | \(0.330621\pi\) | |||||||
\(684\) | −26.4464 | −1.01120 | ||||||||
\(685\) | 6.65133 | 0.254134 | ||||||||
\(686\) | −19.0942 | −0.729019 | ||||||||
\(687\) | 28.9879 | 1.10596 | ||||||||
\(688\) | 10.8983 | 0.415493 | ||||||||
\(689\) | −1.13066 | −0.0430746 | ||||||||
\(690\) | 12.9754 | 0.493966 | ||||||||
\(691\) | −31.4022 | −1.19460 | −0.597298 | − | 0.802019i | \(-0.703759\pi\) | ||||
−0.597298 | + | 0.802019i | \(0.703759\pi\) | |||||||
\(692\) | 4.73845 | 0.180129 | ||||||||
\(693\) | 4.02382 | 0.152852 | ||||||||
\(694\) | 68.2505 | 2.59075 | ||||||||
\(695\) | 12.4453 | 0.472078 | ||||||||
\(696\) | −0.817224 | −0.0309768 | ||||||||
\(697\) | −7.66782 | −0.290440 | ||||||||
\(698\) | −86.9151 | −3.28979 | ||||||||
\(699\) | −6.56119 | −0.248167 | ||||||||
\(700\) | −2.20910 | −0.0834960 | ||||||||
\(701\) | 9.82011 | 0.370900 | 0.185450 | − | 0.982654i | \(-0.440626\pi\) | ||||
0.185450 | + | 0.982654i | \(0.440626\pi\) | |||||||
\(702\) | −17.6571 | −0.666424 | ||||||||
\(703\) | −34.8894 | −1.31588 | ||||||||
\(704\) | −57.0458 | −2.14999 | ||||||||
\(705\) | 12.2508 | 0.461392 | ||||||||
\(706\) | −83.1908 | −3.13093 | ||||||||
\(707\) | 10.3827 | 0.390481 | ||||||||
\(708\) | 53.7514 | 2.02010 | ||||||||
\(709\) | −13.1889 | −0.495321 | −0.247661 | − | 0.968847i | \(-0.579662\pi\) | ||||
−0.247661 | + | 0.968847i | \(0.579662\pi\) | |||||||
\(710\) | −5.19035 | −0.194790 | ||||||||
\(711\) | −7.65273 | −0.287000 | ||||||||
\(712\) | −2.00414 | −0.0751081 | ||||||||
\(713\) | 25.6106 | 0.959125 | ||||||||
\(714\) | −12.8121 | −0.479482 | ||||||||
\(715\) | 7.42646 | 0.277734 | ||||||||
\(716\) | 98.7878 | 3.69187 | ||||||||
\(717\) | −33.9418 | −1.26758 | ||||||||
\(718\) | 20.3755 | 0.760408 | ||||||||
\(719\) | −19.4729 | −0.726218 | −0.363109 | − | 0.931747i | \(-0.618285\pi\) | ||||
−0.363109 | + | 0.931747i | \(0.618285\pi\) | |||||||
\(720\) | 3.52567 | 0.131394 | ||||||||
\(721\) | −1.48992 | −0.0554873 | ||||||||
\(722\) | −32.7495 | −1.21881 | ||||||||
\(723\) | −0.738515 | −0.0274657 | ||||||||
\(724\) | 64.3955 | 2.39324 | ||||||||
\(725\) | 0.140171 | 0.00520580 | ||||||||
\(726\) | −69.5353 | −2.58070 | ||||||||
\(727\) | 43.4526 | 1.61157 | 0.805783 | − | 0.592211i | \(-0.201745\pi\) | ||||
0.805783 | + | 0.592211i | \(0.201745\pi\) | |||||||
\(728\) | −3.29133 | −0.121985 | ||||||||
\(729\) | 27.2764 | 1.01024 | ||||||||
\(730\) | −3.21552 | −0.119012 | ||||||||
\(731\) | −25.7949 | −0.954058 | ||||||||
\(732\) | 62.9856 | 2.32802 | ||||||||
\(733\) | 10.0034 | 0.369484 | 0.184742 | − | 0.982787i | \(-0.440855\pi\) | ||||
0.184742 | + | 0.982787i | \(0.440855\pi\) | |||||||
\(734\) | −61.5764 | −2.27283 | ||||||||
\(735\) | 8.90138 | 0.328332 | ||||||||
\(736\) | 7.00769 | 0.258307 | ||||||||
\(737\) | 20.1137 | 0.740897 | ||||||||
\(738\) | 3.27389 | 0.120514 | ||||||||
\(739\) | 7.88510 | 0.290058 | 0.145029 | − | 0.989427i | \(-0.453672\pi\) | ||||
0.145029 | + | 0.989427i | \(0.453672\pi\) | |||||||
\(740\) | 23.2907 | 0.856182 | ||||||||
\(741\) | −9.91847 | −0.364364 | ||||||||
\(742\) | 1.21465 | 0.0445914 | ||||||||
\(743\) | 27.1428 | 0.995773 | 0.497887 | − | 0.867242i | \(-0.334110\pi\) | ||||
0.497887 | + | 0.867242i | \(0.334110\pi\) | |||||||
\(744\) | −37.0529 | −1.35843 | ||||||||
\(745\) | 5.49516 | 0.201327 | ||||||||
\(746\) | −72.4463 | −2.65245 | ||||||||
\(747\) | 15.3348 | 0.561070 | ||||||||
\(748\) | −149.332 | −5.46011 | ||||||||
\(749\) | −9.56153 | −0.349371 | ||||||||
\(750\) | 3.21988 | 0.117574 | ||||||||
\(751\) | 52.1710 | 1.90375 | 0.951873 | − | 0.306493i | \(-0.0991556\pi\) | ||||
0.951873 | + | 0.306493i | \(0.0991556\pi\) | |||||||
\(752\) | −26.5969 | −0.969891 | ||||||||
\(753\) | −1.48830 | −0.0542366 | ||||||||
\(754\) | 0.439515 | 0.0160062 | ||||||||
\(755\) | 15.8564 | 0.577074 | ||||||||
\(756\) | 12.4399 | 0.452435 | ||||||||
\(757\) | −30.3129 | −1.10174 | −0.550871 | − | 0.834590i | \(-0.685704\pi\) | ||||
−0.550871 | + | 0.834590i | \(0.685704\pi\) | |||||||
\(758\) | 5.41423 | 0.196654 | ||||||||
\(759\) | 30.7317 | 1.11549 | ||||||||
\(760\) | 24.9157 | 0.903787 | ||||||||
\(761\) | −15.0889 | −0.546973 | −0.273486 | − | 0.961876i | \(-0.588177\pi\) | ||||
−0.273486 | + | 0.961876i | \(0.588177\pi\) | |||||||
\(762\) | −49.6909 | −1.80011 | ||||||||
\(763\) | 3.38777 | 0.122645 | ||||||||
\(764\) | 4.32189 | 0.156361 | ||||||||
\(765\) | −8.34484 | −0.301708 | ||||||||
\(766\) | 47.8212 | 1.72785 | ||||||||
\(767\) | −13.7361 | −0.495981 | ||||||||
\(768\) | −39.6611 | −1.43115 | ||||||||
\(769\) | 48.8197 | 1.76048 | 0.880242 | − | 0.474525i | \(-0.157380\pi\) | ||||
0.880242 | + | 0.474525i | \(0.157380\pi\) | |||||||
\(770\) | −7.97819 | −0.287514 | ||||||||
\(771\) | 19.5600 | 0.704435 | ||||||||
\(772\) | 38.6665 | 1.39164 | ||||||||
\(773\) | −24.2575 | −0.872480 | −0.436240 | − | 0.899830i | \(-0.643690\pi\) | ||||
−0.436240 | + | 0.899830i | \(0.643690\pi\) | |||||||
\(774\) | 11.0135 | 0.395872 | ||||||||
\(775\) | 6.35534 | 0.228290 | ||||||||
\(776\) | −7.22169 | −0.259244 | ||||||||
\(777\) | 4.73278 | 0.169787 | ||||||||
\(778\) | 70.9410 | 2.54336 | ||||||||
\(779\) | 6.37702 | 0.228480 | ||||||||
\(780\) | 6.62114 | 0.237075 | ||||||||
\(781\) | −12.2931 | −0.439882 | ||||||||
\(782\) | 66.6753 | 2.38430 | ||||||||
\(783\) | −0.789331 | −0.0282084 | ||||||||
\(784\) | −19.3252 | −0.690187 | ||||||||
\(785\) | 16.1043 | 0.574787 | ||||||||
\(786\) | −2.94715 | −0.105121 | ||||||||
\(787\) | −33.7528 | −1.20316 | −0.601579 | − | 0.798813i | \(-0.705462\pi\) | ||||
−0.601579 | + | 0.798813i | \(0.705462\pi\) | |||||||
\(788\) | −52.0170 | −1.85303 | ||||||||
\(789\) | 26.7755 | 0.953234 | ||||||||
\(790\) | 15.1734 | 0.539844 | ||||||||
\(791\) | −8.98959 | −0.319633 | ||||||||
\(792\) | 30.2960 | 1.07652 | ||||||||
\(793\) | −16.0959 | −0.571581 | ||||||||
\(794\) | −13.2222 | −0.469238 | ||||||||
\(795\) | −1.16106 | −0.0411785 | ||||||||
\(796\) | −44.8401 | −1.58932 | ||||||||
\(797\) | 52.6570 | 1.86521 | 0.932603 | − | 0.360905i | \(-0.117532\pi\) | ||||
0.932603 | + | 0.360905i | \(0.117532\pi\) | |||||||
\(798\) | 10.6553 | 0.377195 | ||||||||
\(799\) | 62.9517 | 2.22707 | ||||||||
\(800\) | 1.73898 | 0.0614821 | ||||||||
\(801\) | −0.558236 | −0.0197243 | ||||||||
\(802\) | 36.7635 | 1.29816 | ||||||||
\(803\) | −7.61583 | −0.268757 | ||||||||
\(804\) | 17.9326 | 0.632433 | ||||||||
\(805\) | 2.33611 | 0.0823369 | ||||||||
\(806\) | 19.9276 | 0.701920 | ||||||||
\(807\) | 12.8281 | 0.451572 | ||||||||
\(808\) | 78.1728 | 2.75011 | ||||||||
\(809\) | 0.0319325 | 0.00112269 | 0.000561343 | − | 1.00000i | \(-0.499821\pi\) | ||||
0.000561343 | 1.00000i | \(0.499821\pi\) | ||||||||
\(810\) | −9.33996 | −0.328173 | ||||||||
\(811\) | 22.3795 | 0.785851 | 0.392926 | − | 0.919570i | \(-0.371463\pi\) | ||||
0.392926 | + | 0.919570i | \(0.371463\pi\) | |||||||
\(812\) | −0.309650 | −0.0108666 | ||||||||
\(813\) | 8.50129 | 0.298153 | ||||||||
\(814\) | 84.1146 | 2.94822 | ||||||||
\(815\) | −10.0309 | −0.351366 | ||||||||
\(816\) | −26.5883 | −0.930775 | ||||||||
\(817\) | 21.4526 | 0.750530 | ||||||||
\(818\) | −80.9948 | −2.83192 | ||||||||
\(819\) | −0.916774 | −0.0320347 | ||||||||
\(820\) | −4.25702 | −0.148662 | ||||||||
\(821\) | 36.1927 | 1.26313 | 0.631567 | − | 0.775321i | \(-0.282412\pi\) | ||||
0.631567 | + | 0.775321i | \(0.282412\pi\) | |||||||
\(822\) | 21.4165 | 0.746987 | ||||||||
\(823\) | 5.49059 | 0.191390 | 0.0956949 | − | 0.995411i | \(-0.469493\pi\) | ||||
0.0956949 | + | 0.995411i | \(0.469493\pi\) | |||||||
\(824\) | −11.2178 | −0.390791 | ||||||||
\(825\) | 7.62616 | 0.265509 | ||||||||
\(826\) | 14.7565 | 0.513446 | ||||||||
\(827\) | 43.7052 | 1.51978 | 0.759889 | − | 0.650053i | \(-0.225253\pi\) | ||||
0.759889 | + | 0.650053i | \(0.225253\pi\) | |||||||
\(828\) | −18.6695 | −0.648811 | ||||||||
\(829\) | 52.9404 | 1.83870 | 0.919349 | − | 0.393444i | \(-0.128716\pi\) | ||||
0.919349 | + | 0.393444i | \(0.128716\pi\) | |||||||
\(830\) | −30.4049 | −1.05537 | ||||||||
\(831\) | 16.3967 | 0.568795 | ||||||||
\(832\) | 12.9971 | 0.450594 | ||||||||
\(833\) | 45.7405 | 1.58481 | ||||||||
\(834\) | 40.0725 | 1.38760 | ||||||||
\(835\) | 7.43019 | 0.257132 | ||||||||
\(836\) | 124.193 | 4.29532 | ||||||||
\(837\) | −35.7883 | −1.23702 | ||||||||
\(838\) | −24.7430 | −0.854734 | ||||||||
\(839\) | 18.5850 | 0.641625 | 0.320812 | − | 0.947143i | \(-0.396044\pi\) | ||||
0.320812 | + | 0.947143i | \(0.396044\pi\) | |||||||
\(840\) | −3.37983 | −0.116615 | ||||||||
\(841\) | −28.9804 | −0.999322 | ||||||||
\(842\) | 7.67013 | 0.264330 | ||||||||
\(843\) | −13.7377 | −0.473152 | ||||||||
\(844\) | 104.920 | 3.61150 | ||||||||
\(845\) | 11.3080 | 0.389006 | ||||||||
\(846\) | −26.8782 | −0.924091 | ||||||||
\(847\) | −12.5192 | −0.430164 | ||||||||
\(848\) | 2.52070 | 0.0865612 | ||||||||
\(849\) | 14.7002 | 0.504508 | ||||||||
\(850\) | 16.5456 | 0.567511 | ||||||||
\(851\) | −24.6297 | −0.844296 | ||||||||
\(852\) | −10.9601 | −0.375485 | ||||||||
\(853\) | 15.7908 | 0.540667 | 0.270333 | − | 0.962767i | \(-0.412866\pi\) | ||||
0.270333 | + | 0.962767i | \(0.412866\pi\) | |||||||
\(854\) | 17.2917 | 0.591708 | ||||||||
\(855\) | 6.94007 | 0.237345 | ||||||||
\(856\) | −71.9903 | −2.46058 | ||||||||
\(857\) | 39.4878 | 1.34888 | 0.674438 | − | 0.738331i | \(-0.264386\pi\) | ||||
0.674438 | + | 0.738331i | \(0.264386\pi\) | |||||||
\(858\) | 23.9124 | 0.816354 | ||||||||
\(859\) | 10.1549 | 0.346482 | 0.173241 | − | 0.984879i | \(-0.444576\pi\) | ||||
0.173241 | + | 0.984879i | \(0.444576\pi\) | |||||||
\(860\) | −14.3208 | −0.488335 | ||||||||
\(861\) | −0.865048 | −0.0294808 | ||||||||
\(862\) | −90.6170 | −3.08643 | ||||||||
\(863\) | −8.91836 | −0.303584 | −0.151792 | − | 0.988412i | \(-0.548504\pi\) | ||||
−0.151792 | + | 0.988412i | \(0.548504\pi\) | |||||||
\(864\) | −9.79255 | −0.333149 | ||||||||
\(865\) | −1.24346 | −0.0422790 | ||||||||
\(866\) | 46.1661 | 1.56879 | ||||||||
\(867\) | 40.2233 | 1.36606 | ||||||||
\(868\) | −14.0396 | −0.476534 | ||||||||
\(869\) | 35.9375 | 1.21909 | ||||||||
\(870\) | 0.451333 | 0.0153016 | ||||||||
\(871\) | −4.58263 | −0.155277 | ||||||||
\(872\) | 25.5070 | 0.863777 | ||||||||
\(873\) | −2.01154 | −0.0680805 | ||||||||
\(874\) | −55.4511 | −1.87566 | ||||||||
\(875\) | 0.579711 | 0.0195978 | ||||||||
\(876\) | −6.78997 | −0.229412 | ||||||||
\(877\) | 28.2114 | 0.952633 | 0.476316 | − | 0.879274i | \(-0.341972\pi\) | ||||
0.476316 | + | 0.879274i | \(0.341972\pi\) | |||||||
\(878\) | −21.1728 | −0.714549 | ||||||||
\(879\) | 6.59513 | 0.222448 | ||||||||
\(880\) | −16.5567 | −0.558125 | ||||||||
\(881\) | 41.2054 | 1.38825 | 0.694123 | − | 0.719856i | \(-0.255792\pi\) | ||||
0.694123 | + | 0.719856i | \(0.255792\pi\) | |||||||
\(882\) | −19.5296 | −0.657595 | ||||||||
\(883\) | −48.1849 | −1.62155 | −0.810776 | − | 0.585357i | \(-0.800955\pi\) | ||||
−0.810776 | + | 0.585357i | \(0.800955\pi\) | |||||||
\(884\) | 34.0233 | 1.14433 | ||||||||
\(885\) | −14.1054 | −0.474149 | ||||||||
\(886\) | 76.4749 | 2.56923 | ||||||||
\(887\) | 41.4084 | 1.39036 | 0.695180 | − | 0.718836i | \(-0.255325\pi\) | ||||
0.695180 | + | 0.718836i | \(0.255325\pi\) | |||||||
\(888\) | 35.6338 | 1.19579 | ||||||||
\(889\) | −8.94639 | −0.300052 | ||||||||
\(890\) | 1.10684 | 0.0371012 | ||||||||
\(891\) | −22.1213 | −0.741092 | ||||||||
\(892\) | −20.1218 | −0.673729 | ||||||||
\(893\) | −52.3544 | −1.75197 | ||||||||
\(894\) | 17.6938 | 0.591768 | ||||||||
\(895\) | −25.9239 | −0.866539 | ||||||||
\(896\) | −11.9465 | −0.399104 | ||||||||
\(897\) | −7.00181 | −0.233784 | ||||||||
\(898\) | −18.6783 | −0.623302 | ||||||||
\(899\) | 0.890831 | 0.0297109 | ||||||||
\(900\) | −4.63289 | −0.154430 | ||||||||
\(901\) | −5.96619 | −0.198763 | ||||||||
\(902\) | −15.3743 | −0.511909 | ||||||||
\(903\) | −2.91006 | −0.0968406 | ||||||||
\(904\) | −67.6840 | −2.25114 | ||||||||
\(905\) | −16.8986 | −0.561730 | ||||||||
\(906\) | 51.0558 | 1.69622 | ||||||||
\(907\) | 36.4098 | 1.20897 | 0.604484 | − | 0.796617i | \(-0.293379\pi\) | ||||
0.604484 | + | 0.796617i | \(0.293379\pi\) | |||||||
\(908\) | 44.6118 | 1.48050 | ||||||||
\(909\) | 21.7744 | 0.722211 | ||||||||
\(910\) | 1.81772 | 0.0602570 | ||||||||
\(911\) | 9.79543 | 0.324537 | 0.162268 | − | 0.986747i | \(-0.448119\pi\) | ||||
0.162268 | + | 0.986747i | \(0.448119\pi\) | |||||||
\(912\) | 22.1124 | 0.732214 | ||||||||
\(913\) | −72.0126 | −2.38327 | ||||||||
\(914\) | −11.1930 | −0.370231 | ||||||||
\(915\) | −16.5287 | −0.546421 | ||||||||
\(916\) | 82.6978 | 2.73241 | ||||||||
\(917\) | −0.530608 | −0.0175222 | ||||||||
\(918\) | −93.1721 | −3.07514 | ||||||||
\(919\) | 16.5519 | 0.545997 | 0.272999 | − | 0.962014i | \(-0.411985\pi\) | ||||
0.272999 | + | 0.962014i | \(0.411985\pi\) | |||||||
\(920\) | 17.5889 | 0.579889 | ||||||||
\(921\) | 27.2987 | 0.899524 | ||||||||
\(922\) | −95.1258 | −3.13280 | ||||||||
\(923\) | 2.80082 | 0.0921902 | ||||||||
\(924\) | −16.8469 | −0.554223 | ||||||||
\(925\) | −6.11193 | −0.200959 | ||||||||
\(926\) | −12.0823 | −0.397048 | ||||||||
\(927\) | −3.12463 | −0.102626 | ||||||||
\(928\) | 0.243753 | 0.00800159 | ||||||||
\(929\) | 12.9098 | 0.423556 | 0.211778 | − | 0.977318i | \(-0.432075\pi\) | ||||
0.211778 | + | 0.977318i | \(0.432075\pi\) | |||||||
\(930\) | 20.4634 | 0.671023 | ||||||||
\(931\) | −38.0405 | −1.24673 | ||||||||
\(932\) | −18.7180 | −0.613129 | ||||||||
\(933\) | −10.5591 | −0.345689 | ||||||||
\(934\) | −3.73536 | −0.122225 | ||||||||
\(935\) | 39.1876 | 1.28157 | ||||||||
\(936\) | −6.90254 | −0.225616 | ||||||||
\(937\) | 34.1648 | 1.11612 | 0.558058 | − | 0.829802i | \(-0.311547\pi\) | ||||
0.558058 | + | 0.829802i | \(0.311547\pi\) | |||||||
\(938\) | 4.92309 | 0.160744 | ||||||||
\(939\) | 33.2373 | 1.08466 | ||||||||
\(940\) | 34.9495 | 1.13993 | ||||||||
\(941\) | −10.5660 | −0.344441 | −0.172221 | − | 0.985058i | \(-0.555094\pi\) | ||||
−0.172221 | + | 0.985058i | \(0.555094\pi\) | |||||||
\(942\) | 51.8540 | 1.68949 | ||||||||
\(943\) | 4.50177 | 0.146598 | ||||||||
\(944\) | 30.6234 | 0.996707 | ||||||||
\(945\) | −3.26448 | −0.106193 | ||||||||
\(946\) | −51.7198 | −1.68156 | ||||||||
\(947\) | 1.38108 | 0.0448791 | 0.0224396 | − | 0.999748i | \(-0.492857\pi\) | ||||
0.0224396 | + | 0.999748i | \(0.492857\pi\) | |||||||
\(948\) | 32.0404 | 1.04062 | ||||||||
\(949\) | 1.73516 | 0.0563258 | ||||||||
\(950\) | −13.7603 | −0.446444 | ||||||||
\(951\) | −31.0126 | −1.00565 | ||||||||
\(952\) | −17.3676 | −0.562886 | ||||||||
\(953\) | −33.2565 | −1.07728 | −0.538642 | − | 0.842535i | \(-0.681062\pi\) | ||||
−0.538642 | + | 0.842535i | \(0.681062\pi\) | |||||||
\(954\) | 2.54736 | 0.0824737 | ||||||||
\(955\) | −1.13415 | −0.0367002 | ||||||||
\(956\) | −96.8303 | −3.13172 | ||||||||
\(957\) | 1.06896 | 0.0345547 | ||||||||
\(958\) | 59.4856 | 1.92189 | ||||||||
\(959\) | 3.85585 | 0.124512 | ||||||||
\(960\) | 13.3466 | 0.430760 | ||||||||
\(961\) | 9.39030 | 0.302913 | ||||||||
\(962\) | −19.1644 | −0.617885 | ||||||||
\(963\) | −20.0523 | −0.646177 | ||||||||
\(964\) | −2.10686 | −0.0678575 | ||||||||
\(965\) | −10.1469 | −0.326639 | ||||||||
\(966\) | 7.52199 | 0.242016 | ||||||||
\(967\) | 0.916683 | 0.0294785 | 0.0147393 | − | 0.999891i | \(-0.495308\pi\) | ||||
0.0147393 | + | 0.999891i | \(0.495308\pi\) | |||||||
\(968\) | −94.2589 | −3.02960 | ||||||||
\(969\) | −52.3373 | −1.68132 | ||||||||
\(970\) | 3.98837 | 0.128059 | ||||||||
\(971\) | 55.9817 | 1.79654 | 0.898270 | − | 0.439444i | \(-0.144825\pi\) | ||||
0.898270 | + | 0.439444i | \(0.144825\pi\) | |||||||
\(972\) | 44.6540 | 1.43228 | ||||||||
\(973\) | 7.21469 | 0.231292 | ||||||||
\(974\) | −91.1306 | −2.92001 | ||||||||
\(975\) | −1.73752 | −0.0556451 | ||||||||
\(976\) | 35.8844 | 1.14863 | ||||||||
\(977\) | −8.05021 | −0.257549 | −0.128774 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128774 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(978\) | −32.2983 | −1.03278 | ||||||||
\(979\) | 2.62149 | 0.0837833 | ||||||||
\(980\) | 25.3942 | 0.811187 | ||||||||
\(981\) | 7.10478 | 0.226838 | ||||||||
\(982\) | 84.8533 | 2.70778 | ||||||||
\(983\) | −20.2213 | −0.644960 | −0.322480 | − | 0.946576i | \(-0.604517\pi\) | ||||
−0.322480 | + | 0.946576i | \(0.604517\pi\) | |||||||
\(984\) | −6.51308 | −0.207629 | ||||||||
\(985\) | 13.6503 | 0.434934 | ||||||||
\(986\) | 2.31921 | 0.0738587 | ||||||||
\(987\) | 7.10192 | 0.226057 | ||||||||
\(988\) | −28.2958 | −0.900208 | ||||||||
\(989\) | 15.1441 | 0.481556 | ||||||||
\(990\) | −16.7318 | −0.531770 | ||||||||
\(991\) | −47.8187 | −1.51901 | −0.759505 | − | 0.650501i | \(-0.774559\pi\) | ||||
−0.759505 | + | 0.650501i | \(0.774559\pi\) | |||||||
\(992\) | 11.0518 | 0.350894 | ||||||||
\(993\) | 14.0927 | 0.447219 | ||||||||
\(994\) | −3.00890 | −0.0954365 | ||||||||
\(995\) | 11.7669 | 0.373037 | ||||||||
\(996\) | −64.2036 | −2.03437 | ||||||||
\(997\) | 18.9245 | 0.599346 | 0.299673 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299673 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(998\) | 50.0309 | 1.58370 | ||||||||
\(999\) | 34.4176 | 1.08893 |
(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 | 8045.2.a.d.1.16 | ✓ | 141 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8045.2.a.d.1.16 | ✓ | 141 | 1.1 | even | 1 | trivial |