Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81914 | −1.28633 | −0.643163 | − | 0.765729i | \(-0.722378\pi\) | ||||
−0.643163 | + | 0.765729i | \(0.722378\pi\) | |||||||
\(3\) | −2.58004 | −1.48958 | −0.744792 | − | 0.667296i | \(-0.767451\pi\) | ||||
−0.744792 | + | 0.667296i | \(0.767451\pi\) | |||||||
\(4\) | 1.30927 | 0.654636 | ||||||||
\(5\) | −0.309884 | −0.138585 | −0.0692923 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692923 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(6\) | 4.69345 | 1.91609 | ||||||||
\(7\) | 2.19724 | 0.830479 | 0.415239 | − | 0.909712i | \(-0.363698\pi\) | ||||
0.415239 | + | 0.909712i | \(0.363698\pi\) | |||||||
\(8\) | 1.25653 | 0.444250 | ||||||||
\(9\) | 3.65659 | 1.21886 | ||||||||
\(10\) | 0.563723 | 0.178265 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.37797 | −0.975136 | ||||||||
\(13\) | −1.15152 | −0.319373 | −0.159687 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159687 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(14\) | −3.99709 | −1.06827 | ||||||||
\(15\) | 0.799513 | 0.206433 | ||||||||
\(16\) | −4.90435 | −1.22609 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −6.65184 | −1.56785 | ||||||||
\(19\) | 7.06291 | 1.62034 | 0.810171 | − | 0.586194i | \(-0.199374\pi\) | ||||
0.810171 | + | 0.586194i | \(0.199374\pi\) | |||||||
\(20\) | −0.405723 | −0.0907225 | ||||||||
\(21\) | −5.66896 | −1.23707 | ||||||||
\(22\) | −1.81914 | −0.387842 | ||||||||
\(23\) | 7.05132 | 1.47030 | 0.735151 | − | 0.677903i | \(-0.237111\pi\) | ||||
0.735151 | + | 0.677903i | \(0.237111\pi\) | |||||||
\(24\) | −3.24189 | −0.661748 | ||||||||
\(25\) | −4.90397 | −0.980794 | ||||||||
\(26\) | 2.09477 | 0.410818 | ||||||||
\(27\) | −1.69401 | −0.326013 | ||||||||
\(28\) | 2.87679 | 0.543662 | ||||||||
\(29\) | −5.56845 | −1.03403 | −0.517017 | − | 0.855975i | \(-0.672958\pi\) | ||||
−0.517017 | + | 0.855975i | \(0.672958\pi\) | |||||||
\(30\) | −1.45443 | −0.265541 | ||||||||
\(31\) | 4.78411 | 0.859251 | 0.429626 | − | 0.903007i | \(-0.358646\pi\) | ||||
0.429626 | + | 0.903007i | \(0.358646\pi\) | |||||||
\(32\) | 6.40864 | 1.13290 | ||||||||
\(33\) | −2.58004 | −0.449127 | ||||||||
\(34\) | 1.81914 | 0.311980 | ||||||||
\(35\) | −0.680890 | −0.115091 | ||||||||
\(36\) | 4.78747 | 0.797911 | ||||||||
\(37\) | 3.05148 | 0.501661 | 0.250830 | − | 0.968031i | \(-0.419296\pi\) | ||||
0.250830 | + | 0.968031i | \(0.419296\pi\) | |||||||
\(38\) | −12.8484 | −2.08429 | ||||||||
\(39\) | 2.97095 | 0.475733 | ||||||||
\(40\) | −0.389379 | −0.0615662 | ||||||||
\(41\) | 8.46839 | 1.32254 | 0.661270 | − | 0.750148i | \(-0.270018\pi\) | ||||
0.661270 | + | 0.750148i | \(0.270018\pi\) | |||||||
\(42\) | 10.3126 | 1.59127 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.30927 | 0.197380 | ||||||||
\(45\) | −1.13312 | −0.168915 | ||||||||
\(46\) | −12.8274 | −1.89129 | ||||||||
\(47\) | −6.45625 | −0.941740 | −0.470870 | − | 0.882203i | \(-0.656060\pi\) | ||||
−0.470870 | + | 0.882203i | \(0.656060\pi\) | |||||||
\(48\) | 12.6534 | 1.82636 | ||||||||
\(49\) | −2.17214 | −0.310305 | ||||||||
\(50\) | 8.92101 | 1.26162 | ||||||||
\(51\) | 2.58004 | 0.361277 | ||||||||
\(52\) | −1.50765 | −0.209073 | ||||||||
\(53\) | −8.12081 | −1.11548 | −0.557740 | − | 0.830016i | \(-0.688331\pi\) | ||||
−0.557740 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(54\) | 3.08165 | 0.419359 | ||||||||
\(55\) | −0.309884 | −0.0417848 | ||||||||
\(56\) | 2.76090 | 0.368940 | ||||||||
\(57\) | −18.2226 | −2.41364 | ||||||||
\(58\) | 10.1298 | 1.33011 | ||||||||
\(59\) | 6.52889 | 0.849989 | 0.424994 | − | 0.905196i | \(-0.360276\pi\) | ||||
0.424994 | + | 0.905196i | \(0.360276\pi\) | |||||||
\(60\) | 1.04678 | 0.135139 | ||||||||
\(61\) | −10.0154 | −1.28234 | −0.641171 | − | 0.767398i | \(-0.721551\pi\) | ||||
−0.641171 | + | 0.767398i | \(0.721551\pi\) | |||||||
\(62\) | −8.70297 | −1.10528 | ||||||||
\(63\) | 8.03439 | 1.01224 | ||||||||
\(64\) | −1.84952 | −0.231191 | ||||||||
\(65\) | 0.356837 | 0.0442602 | ||||||||
\(66\) | 4.69345 | 0.577724 | ||||||||
\(67\) | 0.220738 | 0.0269674 | 0.0134837 | − | 0.999909i | \(-0.495708\pi\) | ||||
0.0134837 | + | 0.999909i | \(0.495708\pi\) | |||||||
\(68\) | −1.30927 | −0.158773 | ||||||||
\(69\) | −18.1927 | −2.19014 | ||||||||
\(70\) | 1.23864 | 0.148045 | ||||||||
\(71\) | −8.42059 | −0.999340 | −0.499670 | − | 0.866216i | \(-0.666545\pi\) | ||||
−0.499670 | + | 0.866216i | \(0.666545\pi\) | |||||||
\(72\) | 4.59461 | 0.541480 | ||||||||
\(73\) | −9.74501 | −1.14057 | −0.570284 | − | 0.821448i | \(-0.693167\pi\) | ||||
−0.570284 | + | 0.821448i | \(0.693167\pi\) | |||||||
\(74\) | −5.55108 | −0.645300 | ||||||||
\(75\) | 12.6524 | 1.46098 | ||||||||
\(76\) | 9.24727 | 1.06073 | ||||||||
\(77\) | 2.19724 | 0.250399 | ||||||||
\(78\) | −5.40458 | −0.611948 | ||||||||
\(79\) | −0.647122 | −0.0728069 | −0.0364034 | − | 0.999337i | \(-0.511590\pi\) | ||||
−0.0364034 | + | 0.999337i | \(0.511590\pi\) | |||||||
\(80\) | 1.51978 | 0.169917 | ||||||||
\(81\) | −6.59914 | −0.733238 | ||||||||
\(82\) | −15.4052 | −1.70122 | ||||||||
\(83\) | 3.78465 | 0.415419 | 0.207710 | − | 0.978191i | \(-0.433399\pi\) | ||||
0.207710 | + | 0.978191i | \(0.433399\pi\) | |||||||
\(84\) | −7.42221 | −0.809830 | ||||||||
\(85\) | 0.309884 | 0.0336117 | ||||||||
\(86\) | −1.81914 | −0.196163 | ||||||||
\(87\) | 14.3668 | 1.54028 | ||||||||
\(88\) | 1.25653 | 0.133947 | ||||||||
\(89\) | −16.2048 | −1.71771 | −0.858853 | − | 0.512222i | \(-0.828822\pi\) | ||||
−0.858853 | + | 0.512222i | \(0.828822\pi\) | |||||||
\(90\) | 2.06130 | 0.217280 | ||||||||
\(91\) | −2.53016 | −0.265233 | ||||||||
\(92\) | 9.23211 | 0.962514 | ||||||||
\(93\) | −12.3432 | −1.27993 | ||||||||
\(94\) | 11.7448 | 1.21139 | ||||||||
\(95\) | −2.18868 | −0.224554 | ||||||||
\(96\) | −16.5345 | −1.68755 | ||||||||
\(97\) | −4.94827 | −0.502421 | −0.251210 | − | 0.967932i | \(-0.580829\pi\) | ||||
−0.251210 | + | 0.967932i | \(0.580829\pi\) | |||||||
\(98\) | 3.95142 | 0.399154 | ||||||||
\(99\) | 3.65659 | 0.367501 | ||||||||
\(100\) | −6.42064 | −0.642064 | ||||||||
\(101\) | −1.26342 | −0.125715 | −0.0628576 | − | 0.998023i | \(-0.520021\pi\) | ||||
−0.0628576 | + | 0.998023i | \(0.520021\pi\) | |||||||
\(102\) | −4.69345 | −0.464721 | ||||||||
\(103\) | −14.3964 | −1.41852 | −0.709258 | − | 0.704949i | \(-0.750970\pi\) | ||||
−0.709258 | + | 0.704949i | \(0.750970\pi\) | |||||||
\(104\) | −1.44691 | −0.141882 | ||||||||
\(105\) | 1.75672 | 0.171438 | ||||||||
\(106\) | 14.7729 | 1.43487 | ||||||||
\(107\) | −12.9363 | −1.25060 | −0.625301 | − | 0.780384i | \(-0.715024\pi\) | ||||
−0.625301 | + | 0.780384i | \(0.715024\pi\) | |||||||
\(108\) | −2.21793 | −0.213420 | ||||||||
\(109\) | 2.36293 | 0.226328 | 0.113164 | − | 0.993576i | \(-0.463901\pi\) | ||||
0.113164 | + | 0.993576i | \(0.463901\pi\) | |||||||
\(110\) | 0.563723 | 0.0537489 | ||||||||
\(111\) | −7.87294 | −0.747266 | ||||||||
\(112\) | −10.7760 | −1.01824 | ||||||||
\(113\) | 10.4000 | 0.978352 | 0.489176 | − | 0.872185i | \(-0.337298\pi\) | ||||
0.489176 | + | 0.872185i | \(0.337298\pi\) | |||||||
\(114\) | 33.1494 | 3.10472 | ||||||||
\(115\) | −2.18510 | −0.203761 | ||||||||
\(116\) | −7.29062 | −0.676917 | ||||||||
\(117\) | −4.21062 | −0.389272 | ||||||||
\(118\) | −11.8770 | −1.09336 | ||||||||
\(119\) | −2.19724 | −0.201421 | ||||||||
\(120\) | 1.00461 | 0.0917081 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 18.2194 | 1.64951 | ||||||||
\(123\) | −21.8488 | −1.97004 | ||||||||
\(124\) | 6.26370 | 0.562497 | ||||||||
\(125\) | 3.06909 | 0.274507 | ||||||||
\(126\) | −14.6157 | −1.30207 | ||||||||
\(127\) | 20.7064 | 1.83740 | 0.918699 | − | 0.394958i | \(-0.129241\pi\) | ||||
0.918699 | + | 0.394958i | \(0.129241\pi\) | |||||||
\(128\) | −9.45274 | −0.835512 | ||||||||
\(129\) | −2.58004 | −0.227159 | ||||||||
\(130\) | −0.649136 | −0.0569330 | ||||||||
\(131\) | −7.31949 | −0.639506 | −0.319753 | − | 0.947501i | \(-0.603600\pi\) | ||||
−0.319753 | + | 0.947501i | \(0.603600\pi\) | |||||||
\(132\) | −3.37797 | −0.294015 | ||||||||
\(133\) | 15.5189 | 1.34566 | ||||||||
\(134\) | −0.401553 | −0.0346889 | ||||||||
\(135\) | 0.524948 | 0.0451804 | ||||||||
\(136\) | −1.25653 | −0.107747 | ||||||||
\(137\) | 2.06747 | 0.176636 | 0.0883181 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883181 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(138\) | 33.0950 | 2.81724 | ||||||||
\(139\) | −4.04796 | −0.343343 | −0.171672 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171672 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(140\) | −0.891471 | −0.0753431 | ||||||||
\(141\) | 16.6573 | 1.40280 | ||||||||
\(142\) | 15.3182 | 1.28548 | ||||||||
\(143\) | −1.15152 | −0.0962946 | ||||||||
\(144\) | −17.9332 | −1.49443 | ||||||||
\(145\) | 1.72557 | 0.143301 | ||||||||
\(146\) | 17.7275 | 1.46714 | ||||||||
\(147\) | 5.60419 | 0.462226 | ||||||||
\(148\) | 3.99523 | 0.328406 | ||||||||
\(149\) | −22.5253 | −1.84534 | −0.922671 | − | 0.385587i | \(-0.873999\pi\) | ||||
−0.922671 | + | 0.385587i | \(0.873999\pi\) | |||||||
\(150\) | −23.0165 | −1.87929 | ||||||||
\(151\) | −19.1427 | −1.55781 | −0.778904 | − | 0.627143i | \(-0.784224\pi\) | ||||
−0.778904 | + | 0.627143i | \(0.784224\pi\) | |||||||
\(152\) | 8.87475 | 0.719837 | ||||||||
\(153\) | −3.65659 | −0.295617 | ||||||||
\(154\) | −3.99709 | −0.322095 | ||||||||
\(155\) | −1.48252 | −0.119079 | ||||||||
\(156\) | 3.88979 | 0.311432 | ||||||||
\(157\) | 17.4530 | 1.39290 | 0.696449 | − | 0.717606i | \(-0.254762\pi\) | ||||
0.696449 | + | 0.717606i | \(0.254762\pi\) | |||||||
\(158\) | 1.17721 | 0.0936534 | ||||||||
\(159\) | 20.9520 | 1.66160 | ||||||||
\(160\) | −1.98594 | −0.157002 | ||||||||
\(161\) | 15.4935 | 1.22105 | ||||||||
\(162\) | 12.0048 | 0.943183 | ||||||||
\(163\) | 12.8036 | 1.00286 | 0.501428 | − | 0.865199i | \(-0.332808\pi\) | ||||
0.501428 | + | 0.865199i | \(0.332808\pi\) | |||||||
\(164\) | 11.0874 | 0.865783 | ||||||||
\(165\) | 0.799513 | 0.0622420 | ||||||||
\(166\) | −6.88481 | −0.534365 | ||||||||
\(167\) | −5.74237 | −0.444358 | −0.222179 | − | 0.975006i | \(-0.571317\pi\) | ||||
−0.222179 | + | 0.975006i | \(0.571317\pi\) | |||||||
\(168\) | −7.12321 | −0.549568 | ||||||||
\(169\) | −11.6740 | −0.898001 | ||||||||
\(170\) | −0.563723 | −0.0432356 | ||||||||
\(171\) | 25.8261 | 1.97497 | ||||||||
\(172\) | 1.30927 | 0.0998311 | ||||||||
\(173\) | 2.08421 | 0.158460 | 0.0792298 | − | 0.996856i | \(-0.474754\pi\) | ||||
0.0792298 | + | 0.996856i | \(0.474754\pi\) | |||||||
\(174\) | −26.1352 | −1.98131 | ||||||||
\(175\) | −10.7752 | −0.814529 | ||||||||
\(176\) | −4.90435 | −0.369679 | ||||||||
\(177\) | −16.8448 | −1.26613 | ||||||||
\(178\) | 29.4788 | 2.20953 | ||||||||
\(179\) | 12.4408 | 0.929867 | 0.464934 | − | 0.885346i | \(-0.346078\pi\) | ||||
0.464934 | + | 0.885346i | \(0.346078\pi\) | |||||||
\(180\) | −1.48356 | −0.110578 | ||||||||
\(181\) | −11.4110 | −0.848176 | −0.424088 | − | 0.905621i | \(-0.639405\pi\) | ||||
−0.424088 | + | 0.905621i | \(0.639405\pi\) | |||||||
\(182\) | 4.60271 | 0.341176 | ||||||||
\(183\) | 25.8401 | 1.91016 | ||||||||
\(184\) | 8.86020 | 0.653183 | ||||||||
\(185\) | −0.945607 | −0.0695224 | ||||||||
\(186\) | 22.4540 | 1.64640 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −8.45299 | −0.616498 | ||||||||
\(189\) | −3.72215 | −0.270747 | ||||||||
\(190\) | 3.98152 | 0.288850 | ||||||||
\(191\) | −20.9231 | −1.51394 | −0.756971 | − | 0.653449i | \(-0.773321\pi\) | ||||
−0.756971 | + | 0.653449i | \(0.773321\pi\) | |||||||
\(192\) | 4.77184 | 0.344378 | ||||||||
\(193\) | 19.8474 | 1.42865 | 0.714324 | − | 0.699816i | \(-0.246735\pi\) | ||||
0.714324 | + | 0.699816i | \(0.246735\pi\) | |||||||
\(194\) | 9.00160 | 0.646277 | ||||||||
\(195\) | −0.920652 | −0.0659293 | ||||||||
\(196\) | −2.84392 | −0.203137 | ||||||||
\(197\) | −21.6962 | −1.54579 | −0.772895 | − | 0.634534i | \(-0.781192\pi\) | ||||
−0.772895 | + | 0.634534i | \(0.781192\pi\) | |||||||
\(198\) | −6.65184 | −0.472726 | ||||||||
\(199\) | 7.73062 | 0.548009 | 0.274005 | − | 0.961728i | \(-0.411652\pi\) | ||||
0.274005 | + | 0.961728i | \(0.411652\pi\) | |||||||
\(200\) | −6.16199 | −0.435718 | ||||||||
\(201\) | −0.569512 | −0.0401703 | ||||||||
\(202\) | 2.29834 | 0.161711 | ||||||||
\(203\) | −12.2352 | −0.858744 | ||||||||
\(204\) | 3.37797 | 0.236505 | ||||||||
\(205\) | −2.62422 | −0.183284 | ||||||||
\(206\) | 26.1890 | 1.82468 | ||||||||
\(207\) | 25.7838 | 1.79210 | ||||||||
\(208\) | 5.64744 | 0.391579 | ||||||||
\(209\) | 7.06291 | 0.488551 | ||||||||
\(210\) | −3.19572 | −0.220526 | ||||||||
\(211\) | 25.6799 | 1.76787 | 0.883937 | − | 0.467606i | \(-0.154883\pi\) | ||||
0.883937 | + | 0.467606i | \(0.154883\pi\) | |||||||
\(212\) | −10.6324 | −0.730233 | ||||||||
\(213\) | 21.7254 | 1.48860 | ||||||||
\(214\) | 23.5330 | 1.60868 | ||||||||
\(215\) | −0.309884 | −0.0211339 | ||||||||
\(216\) | −2.12858 | −0.144831 | ||||||||
\(217\) | 10.5118 | 0.713590 | ||||||||
\(218\) | −4.29851 | −0.291132 | ||||||||
\(219\) | 25.1425 | 1.69897 | ||||||||
\(220\) | −0.405723 | −0.0273539 | ||||||||
\(221\) | 1.15152 | 0.0774594 | ||||||||
\(222\) | 14.3220 | 0.961229 | ||||||||
\(223\) | 1.68734 | 0.112993 | 0.0564965 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564965 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(224\) | 14.0813 | 0.940848 | ||||||||
\(225\) | −17.9318 | −1.19545 | ||||||||
\(226\) | −18.9191 | −1.25848 | ||||||||
\(227\) | −3.37453 | −0.223975 | −0.111988 | − | 0.993710i | \(-0.535722\pi\) | ||||
−0.111988 | + | 0.993710i | \(0.535722\pi\) | |||||||
\(228\) | −23.8583 | −1.58005 | ||||||||
\(229\) | 2.96964 | 0.196239 | 0.0981196 | − | 0.995175i | \(-0.468717\pi\) | ||||
0.0981196 | + | 0.995175i | \(0.468717\pi\) | |||||||
\(230\) | 3.97500 | 0.262103 | ||||||||
\(231\) | −5.66896 | −0.372990 | ||||||||
\(232\) | −6.99692 | −0.459370 | ||||||||
\(233\) | 15.7798 | 1.03377 | 0.516886 | − | 0.856055i | \(-0.327091\pi\) | ||||
0.516886 | + | 0.856055i | \(0.327091\pi\) | |||||||
\(234\) | 7.65970 | 0.500731 | ||||||||
\(235\) | 2.00069 | 0.130511 | ||||||||
\(236\) | 8.54809 | 0.556434 | ||||||||
\(237\) | 1.66960 | 0.108452 | ||||||||
\(238\) | 3.99709 | 0.259093 | ||||||||
\(239\) | 16.3491 | 1.05754 | 0.528768 | − | 0.848767i | \(-0.322654\pi\) | ||||
0.528768 | + | 0.848767i | \(0.322654\pi\) | |||||||
\(240\) | −3.92109 | −0.253105 | ||||||||
\(241\) | −10.0483 | −0.647270 | −0.323635 | − | 0.946182i | \(-0.604905\pi\) | ||||
−0.323635 | + | 0.946182i | \(0.604905\pi\) | |||||||
\(242\) | −1.81914 | −0.116939 | ||||||||
\(243\) | 22.1081 | 1.41823 | ||||||||
\(244\) | −13.1129 | −0.839467 | ||||||||
\(245\) | 0.673112 | 0.0430035 | ||||||||
\(246\) | 39.7460 | 2.53411 | ||||||||
\(247\) | −8.13305 | −0.517494 | ||||||||
\(248\) | 6.01137 | 0.381723 | ||||||||
\(249\) | −9.76453 | −0.618802 | ||||||||
\(250\) | −5.58310 | −0.353106 | ||||||||
\(251\) | 13.3650 | 0.843590 | 0.421795 | − | 0.906691i | \(-0.361400\pi\) | ||||
0.421795 | + | 0.906691i | \(0.361400\pi\) | |||||||
\(252\) | 10.5192 | 0.662648 | ||||||||
\(253\) | 7.05132 | 0.443313 | ||||||||
\(254\) | −37.6679 | −2.36349 | ||||||||
\(255\) | −0.799513 | −0.0500674 | ||||||||
\(256\) | 20.8949 | 1.30593 | ||||||||
\(257\) | −14.5126 | −0.905268 | −0.452634 | − | 0.891696i | \(-0.649516\pi\) | ||||
−0.452634 | + | 0.891696i | \(0.649516\pi\) | |||||||
\(258\) | 4.69345 | 0.292201 | ||||||||
\(259\) | 6.70484 | 0.416619 | ||||||||
\(260\) | 0.467197 | 0.0289743 | ||||||||
\(261\) | −20.3615 | −1.26035 | ||||||||
\(262\) | 13.3152 | 0.822614 | ||||||||
\(263\) | 10.7646 | 0.663775 | 0.331887 | − | 0.943319i | \(-0.392315\pi\) | ||||
0.331887 | + | 0.943319i | \(0.392315\pi\) | |||||||
\(264\) | −3.24189 | −0.199525 | ||||||||
\(265\) | 2.51651 | 0.154588 | ||||||||
\(266\) | −28.2311 | −1.73096 | ||||||||
\(267\) | 41.8090 | 2.55867 | ||||||||
\(268\) | 0.289006 | 0.0176539 | ||||||||
\(269\) | −1.97714 | −0.120549 | −0.0602743 | − | 0.998182i | \(-0.519198\pi\) | ||||
−0.0602743 | + | 0.998182i | \(0.519198\pi\) | |||||||
\(270\) | −0.954955 | −0.0581167 | ||||||||
\(271\) | 23.6165 | 1.43460 | 0.717299 | − | 0.696765i | \(-0.245378\pi\) | ||||
0.717299 | + | 0.696765i | \(0.245378\pi\) | |||||||
\(272\) | 4.90435 | 0.297370 | ||||||||
\(273\) | 6.52790 | 0.395086 | ||||||||
\(274\) | −3.76103 | −0.227212 | ||||||||
\(275\) | −4.90397 | −0.295721 | ||||||||
\(276\) | −23.8192 | −1.43375 | ||||||||
\(277\) | −0.440317 | −0.0264561 | −0.0132281 | − | 0.999913i | \(-0.504211\pi\) | ||||
−0.0132281 | + | 0.999913i | \(0.504211\pi\) | |||||||
\(278\) | 7.36380 | 0.441651 | ||||||||
\(279\) | 17.4935 | 1.04731 | ||||||||
\(280\) | −0.855559 | −0.0511294 | ||||||||
\(281\) | −23.9393 | −1.42810 | −0.714048 | − | 0.700097i | \(-0.753140\pi\) | ||||
−0.714048 | + | 0.700097i | \(0.753140\pi\) | |||||||
\(282\) | −30.3021 | −1.80446 | ||||||||
\(283\) | −23.6663 | −1.40682 | −0.703408 | − | 0.710786i | \(-0.748339\pi\) | ||||
−0.703408 | + | 0.710786i | \(0.748339\pi\) | |||||||
\(284\) | −11.0249 | −0.654205 | ||||||||
\(285\) | 5.64688 | 0.334493 | ||||||||
\(286\) | 2.09477 | 0.123866 | ||||||||
\(287\) | 18.6071 | 1.09834 | ||||||||
\(288\) | 23.4338 | 1.38085 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.13906 | −0.184332 | ||||||||
\(291\) | 12.7667 | 0.748398 | ||||||||
\(292\) | −12.7589 | −0.746657 | ||||||||
\(293\) | −12.5915 | −0.735604 | −0.367802 | − | 0.929904i | \(-0.619890\pi\) | ||||
−0.367802 | + | 0.929904i | \(0.619890\pi\) | |||||||
\(294\) | −10.1948 | −0.594574 | ||||||||
\(295\) | −2.02320 | −0.117795 | ||||||||
\(296\) | 3.83428 | 0.222863 | ||||||||
\(297\) | −1.69401 | −0.0982966 | ||||||||
\(298\) | 40.9767 | 2.37371 | ||||||||
\(299\) | −8.11971 | −0.469575 | ||||||||
\(300\) | 16.5655 | 0.956408 | ||||||||
\(301\) | 2.19724 | 0.126647 | ||||||||
\(302\) | 34.8232 | 2.00385 | ||||||||
\(303\) | 3.25967 | 0.187263 | ||||||||
\(304\) | −34.6390 | −1.98668 | ||||||||
\(305\) | 3.10362 | 0.177713 | ||||||||
\(306\) | 6.65184 | 0.380261 | ||||||||
\(307\) | −10.5981 | −0.604866 | −0.302433 | − | 0.953171i | \(-0.597799\pi\) | ||||
−0.302433 | + | 0.953171i | \(0.597799\pi\) | |||||||
\(308\) | 2.87679 | 0.163920 | ||||||||
\(309\) | 37.1432 | 2.11300 | ||||||||
\(310\) | 2.69691 | 0.153174 | ||||||||
\(311\) | 11.1184 | 0.630464 | 0.315232 | − | 0.949015i | \(-0.397918\pi\) | ||||
0.315232 | + | 0.949015i | \(0.397918\pi\) | |||||||
\(312\) | 3.73309 | 0.211345 | ||||||||
\(313\) | −21.0730 | −1.19112 | −0.595559 | − | 0.803312i | \(-0.703069\pi\) | ||||
−0.595559 | + | 0.803312i | \(0.703069\pi\) | |||||||
\(314\) | −31.7494 | −1.79172 | ||||||||
\(315\) | −2.48973 | −0.140281 | ||||||||
\(316\) | −0.847259 | −0.0476620 | ||||||||
\(317\) | 2.66256 | 0.149544 | 0.0747720 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747720 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(318\) | −38.1146 | −2.13736 | ||||||||
\(319\) | −5.56845 | −0.311773 | ||||||||
\(320\) | 0.573139 | 0.0320394 | ||||||||
\(321\) | 33.3762 | 1.86288 | ||||||||
\(322\) | −28.1848 | −1.57068 | ||||||||
\(323\) | −7.06291 | −0.392991 | ||||||||
\(324\) | −8.64008 | −0.480004 | ||||||||
\(325\) | 5.64700 | 0.313239 | ||||||||
\(326\) | −23.2916 | −1.29000 | ||||||||
\(327\) | −6.09645 | −0.337135 | ||||||||
\(328\) | 10.6408 | 0.587539 | ||||||||
\(329\) | −14.1859 | −0.782095 | ||||||||
\(330\) | −1.45443 | −0.0800635 | ||||||||
\(331\) | 17.9004 | 0.983895 | 0.491947 | − | 0.870625i | \(-0.336285\pi\) | ||||
0.491947 | + | 0.870625i | \(0.336285\pi\) | |||||||
\(332\) | 4.95514 | 0.271949 | ||||||||
\(333\) | 11.1580 | 0.611455 | ||||||||
\(334\) | 10.4462 | 0.571589 | ||||||||
\(335\) | −0.0684033 | −0.00373727 | ||||||||
\(336\) | 27.8026 | 1.51675 | ||||||||
\(337\) | 14.0098 | 0.763160 | 0.381580 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381580 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(338\) | 21.2367 | 1.15512 | ||||||||
\(339\) | −26.8324 | −1.45734 | ||||||||
\(340\) | 0.405723 | 0.0220034 | ||||||||
\(341\) | 4.78411 | 0.259074 | ||||||||
\(342\) | −46.9813 | −2.54046 | ||||||||
\(343\) | −20.1534 | −1.08818 | ||||||||
\(344\) | 1.25653 | 0.0677475 | ||||||||
\(345\) | 5.63763 | 0.303520 | ||||||||
\(346\) | −3.79147 | −0.203831 | ||||||||
\(347\) | 22.3568 | 1.20018 | 0.600089 | − | 0.799934i | \(-0.295132\pi\) | ||||
0.600089 | + | 0.799934i | \(0.295132\pi\) | |||||||
\(348\) | 18.8101 | 1.00832 | ||||||||
\(349\) | 1.92500 | 0.103043 | 0.0515214 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515214 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(350\) | 19.6016 | 1.04775 | ||||||||
\(351\) | 1.95068 | 0.104120 | ||||||||
\(352\) | 6.40864 | 0.341582 | ||||||||
\(353\) | 11.9600 | 0.636568 | 0.318284 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318284 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(354\) | 30.6430 | 1.62866 | ||||||||
\(355\) | 2.60941 | 0.138493 | ||||||||
\(356\) | −21.2165 | −1.12447 | ||||||||
\(357\) | 5.66896 | 0.300033 | ||||||||
\(358\) | −22.6315 | −1.19611 | ||||||||
\(359\) | −28.6711 | −1.51320 | −0.756602 | − | 0.653876i | \(-0.773142\pi\) | ||||
−0.756602 | + | 0.653876i | \(0.773142\pi\) | |||||||
\(360\) | −1.42380 | −0.0750407 | ||||||||
\(361\) | 30.8846 | 1.62551 | ||||||||
\(362\) | 20.7583 | 1.09103 | ||||||||
\(363\) | −2.58004 | −0.135417 | ||||||||
\(364\) | −3.31267 | −0.173631 | ||||||||
\(365\) | 3.01983 | 0.158065 | ||||||||
\(366\) | −47.0068 | −2.45708 | ||||||||
\(367\) | −10.8826 | −0.568066 | −0.284033 | − | 0.958815i | \(-0.591673\pi\) | ||||
−0.284033 | + | 0.958815i | \(0.591673\pi\) | |||||||
\(368\) | −34.5822 | −1.80272 | ||||||||
\(369\) | 30.9654 | 1.61199 | ||||||||
\(370\) | 1.72019 | 0.0894286 | ||||||||
\(371\) | −17.8434 | −0.926382 | ||||||||
\(372\) | −16.1606 | −0.837887 | ||||||||
\(373\) | −22.0617 | −1.14231 | −0.571156 | − | 0.820842i | \(-0.693505\pi\) | ||||
−0.571156 | + | 0.820842i | \(0.693505\pi\) | |||||||
\(374\) | 1.81914 | 0.0940655 | ||||||||
\(375\) | −7.91835 | −0.408902 | ||||||||
\(376\) | −8.11246 | −0.418368 | ||||||||
\(377\) | 6.41216 | 0.330243 | ||||||||
\(378\) | 6.77112 | 0.348269 | ||||||||
\(379\) | 26.8791 | 1.38069 | 0.690343 | − | 0.723482i | \(-0.257460\pi\) | ||||
0.690343 | + | 0.723482i | \(0.257460\pi\) | |||||||
\(380\) | −2.86559 | −0.147001 | ||||||||
\(381\) | −53.4233 | −2.73696 | ||||||||
\(382\) | 38.0620 | 1.94742 | ||||||||
\(383\) | 23.1962 | 1.18527 | 0.592634 | − | 0.805472i | \(-0.298088\pi\) | ||||
0.592634 | + | 0.805472i | \(0.298088\pi\) | |||||||
\(384\) | 24.3884 | 1.24457 | ||||||||
\(385\) | −0.680890 | −0.0347014 | ||||||||
\(386\) | −36.1052 | −1.83771 | ||||||||
\(387\) | 3.65659 | 0.185875 | ||||||||
\(388\) | −6.47864 | −0.328903 | ||||||||
\(389\) | −18.8278 | −0.954608 | −0.477304 | − | 0.878738i | \(-0.658386\pi\) | ||||
−0.477304 | + | 0.878738i | \(0.658386\pi\) | |||||||
\(390\) | 1.67480 | 0.0848066 | ||||||||
\(391\) | −7.05132 | −0.356601 | ||||||||
\(392\) | −2.72936 | −0.137853 | ||||||||
\(393\) | 18.8845 | 0.952599 | ||||||||
\(394\) | 39.4684 | 1.98839 | ||||||||
\(395\) | 0.200533 | 0.0100899 | ||||||||
\(396\) | 4.78747 | 0.240579 | ||||||||
\(397\) | −13.1898 | −0.661979 | −0.330989 | − | 0.943634i | \(-0.607382\pi\) | ||||
−0.330989 | + | 0.943634i | \(0.607382\pi\) | |||||||
\(398\) | −14.0631 | −0.704919 | ||||||||
\(399\) | −40.0393 | −2.00447 | ||||||||
\(400\) | 24.0508 | 1.20254 | ||||||||
\(401\) | −0.392752 | −0.0196131 | −0.00980656 | − | 0.999952i | \(-0.503122\pi\) | ||||
−0.00980656 | + | 0.999952i | \(0.503122\pi\) | |||||||
\(402\) | 1.03602 | 0.0516721 | ||||||||
\(403\) | −5.50898 | −0.274422 | ||||||||
\(404\) | −1.65416 | −0.0822977 | ||||||||
\(405\) | 2.04497 | 0.101615 | ||||||||
\(406\) | 22.2576 | 1.10462 | ||||||||
\(407\) | 3.05148 | 0.151256 | ||||||||
\(408\) | 3.24189 | 0.160498 | ||||||||
\(409\) | −15.5698 | −0.769880 | −0.384940 | − | 0.922942i | \(-0.625778\pi\) | ||||
−0.384940 | + | 0.922942i | \(0.625778\pi\) | |||||||
\(410\) | 4.77383 | 0.235763 | ||||||||
\(411\) | −5.33416 | −0.263115 | ||||||||
\(412\) | −18.8488 | −0.928613 | ||||||||
\(413\) | 14.3455 | 0.705897 | ||||||||
\(414\) | −46.9043 | −2.30522 | ||||||||
\(415\) | −1.17280 | −0.0575707 | ||||||||
\(416\) | −7.37966 | −0.361817 | ||||||||
\(417\) | 10.4439 | 0.511439 | ||||||||
\(418\) | −12.8484 | −0.628437 | ||||||||
\(419\) | 31.4633 | 1.53708 | 0.768542 | − | 0.639799i | \(-0.220982\pi\) | ||||
0.768542 | + | 0.639799i | \(0.220982\pi\) | |||||||
\(420\) | 2.30003 | 0.112230 | ||||||||
\(421\) | 25.4469 | 1.24021 | 0.620103 | − | 0.784520i | \(-0.287091\pi\) | ||||
0.620103 | + | 0.784520i | \(0.287091\pi\) | |||||||
\(422\) | −46.7153 | −2.27406 | ||||||||
\(423\) | −23.6078 | −1.14785 | ||||||||
\(424\) | −10.2040 | −0.495552 | ||||||||
\(425\) | 4.90397 | 0.237878 | ||||||||
\(426\) | −39.5216 | −1.91483 | ||||||||
\(427\) | −22.0062 | −1.06496 | ||||||||
\(428\) | −16.9372 | −0.818690 | ||||||||
\(429\) | 2.97095 | 0.143439 | ||||||||
\(430\) | 0.563723 | 0.0271852 | ||||||||
\(431\) | −18.6120 | −0.896508 | −0.448254 | − | 0.893906i | \(-0.647954\pi\) | ||||
−0.448254 | + | 0.893906i | \(0.647954\pi\) | |||||||
\(432\) | 8.30804 | 0.399721 | ||||||||
\(433\) | 11.8804 | 0.570934 | 0.285467 | − | 0.958389i | \(-0.407851\pi\) | ||||
0.285467 | + | 0.958389i | \(0.407851\pi\) | |||||||
\(434\) | −19.1225 | −0.917910 | ||||||||
\(435\) | −4.45204 | −0.213459 | ||||||||
\(436\) | 3.09372 | 0.148163 | ||||||||
\(437\) | 49.8028 | 2.38239 | ||||||||
\(438\) | −45.7377 | −2.18543 | ||||||||
\(439\) | −6.86067 | −0.327442 | −0.163721 | − | 0.986507i | \(-0.552350\pi\) | ||||
−0.163721 | + | 0.986507i | \(0.552350\pi\) | |||||||
\(440\) | −0.389379 | −0.0185629 | ||||||||
\(441\) | −7.94261 | −0.378219 | ||||||||
\(442\) | −2.09477 | −0.0996380 | ||||||||
\(443\) | −27.2426 | −1.29434 | −0.647168 | − | 0.762348i | \(-0.724047\pi\) | ||||
−0.647168 | + | 0.762348i | \(0.724047\pi\) | |||||||
\(444\) | −10.3078 | −0.489188 | ||||||||
\(445\) | 5.02162 | 0.238047 | ||||||||
\(446\) | −3.06952 | −0.145346 | ||||||||
\(447\) | 58.1160 | 2.74879 | ||||||||
\(448\) | −4.06385 | −0.191999 | ||||||||
\(449\) | −13.2869 | −0.627049 | −0.313524 | − | 0.949580i | \(-0.601510\pi\) | ||||
−0.313524 | + | 0.949580i | \(0.601510\pi\) | |||||||
\(450\) | 32.6205 | 1.53774 | ||||||||
\(451\) | 8.46839 | 0.398761 | ||||||||
\(452\) | 13.6165 | 0.640465 | ||||||||
\(453\) | 49.3888 | 2.32049 | ||||||||
\(454\) | 6.13874 | 0.288105 | ||||||||
\(455\) | 0.784056 | 0.0367571 | ||||||||
\(456\) | −22.8972 | −1.07226 | ||||||||
\(457\) | 0.235046 | 0.0109950 | 0.00549749 | − | 0.999985i | \(-0.498250\pi\) | ||||
0.00549749 | + | 0.999985i | \(0.498250\pi\) | |||||||
\(458\) | −5.40219 | −0.252428 | ||||||||
\(459\) | 1.69401 | 0.0790698 | ||||||||
\(460\) | −2.86089 | −0.133390 | ||||||||
\(461\) | 22.2093 | 1.03439 | 0.517196 | − | 0.855867i | \(-0.326976\pi\) | ||||
0.517196 | + | 0.855867i | \(0.326976\pi\) | |||||||
\(462\) | 10.3126 | 0.479787 | ||||||||
\(463\) | −24.2188 | −1.12554 | −0.562772 | − | 0.826612i | \(-0.690265\pi\) | ||||
−0.562772 | + | 0.826612i | \(0.690265\pi\) | |||||||
\(464\) | 27.3096 | 1.26782 | ||||||||
\(465\) | 3.82496 | 0.177378 | ||||||||
\(466\) | −28.7057 | −1.32977 | ||||||||
\(467\) | 0.578902 | 0.0267884 | 0.0133942 | − | 0.999910i | \(-0.495736\pi\) | ||||
0.0133942 | + | 0.999910i | \(0.495736\pi\) | |||||||
\(468\) | −5.51285 | −0.254831 | ||||||||
\(469\) | 0.485014 | 0.0223959 | ||||||||
\(470\) | −3.63954 | −0.167879 | ||||||||
\(471\) | −45.0293 | −2.07484 | ||||||||
\(472\) | 8.20374 | 0.377608 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −3.03723 | −0.139505 | ||||||||
\(475\) | −34.6363 | −1.58922 | ||||||||
\(476\) | −2.87679 | −0.131857 | ||||||||
\(477\) | −29.6944 | −1.35962 | ||||||||
\(478\) | −29.7413 | −1.36034 | ||||||||
\(479\) | −14.7416 | −0.673562 | −0.336781 | − | 0.941583i | \(-0.609338\pi\) | ||||
−0.336781 | + | 0.941583i | \(0.609338\pi\) | |||||||
\(480\) | 5.12379 | 0.233868 | ||||||||
\(481\) | −3.51383 | −0.160217 | ||||||||
\(482\) | 18.2793 | 0.832600 | ||||||||
\(483\) | −39.9737 | −1.81886 | ||||||||
\(484\) | 1.30927 | 0.0595124 | ||||||||
\(485\) | 1.53339 | 0.0696278 | ||||||||
\(486\) | −40.2177 | −1.82431 | ||||||||
\(487\) | 28.9754 | 1.31300 | 0.656500 | − | 0.754326i | \(-0.272036\pi\) | ||||
0.656500 | + | 0.754326i | \(0.272036\pi\) | |||||||
\(488\) | −12.5847 | −0.569681 | ||||||||
\(489\) | −33.0338 | −1.49384 | ||||||||
\(490\) | −1.22448 | −0.0553166 | ||||||||
\(491\) | −21.2332 | −0.958239 | −0.479120 | − | 0.877750i | \(-0.659044\pi\) | ||||
−0.479120 | + | 0.877750i | \(0.659044\pi\) | |||||||
\(492\) | −28.6060 | −1.28966 | ||||||||
\(493\) | 5.56845 | 0.250790 | ||||||||
\(494\) | 14.7952 | 0.665666 | ||||||||
\(495\) | −1.13312 | −0.0509299 | ||||||||
\(496\) | −23.4629 | −1.05352 | ||||||||
\(497\) | −18.5021 | −0.829931 | ||||||||
\(498\) | 17.7631 | 0.795982 | ||||||||
\(499\) | −9.13575 | −0.408972 | −0.204486 | − | 0.978869i | \(-0.565552\pi\) | ||||
−0.204486 | + | 0.978869i | \(0.565552\pi\) | |||||||
\(500\) | 4.01827 | 0.179703 | ||||||||
\(501\) | 14.8155 | 0.661908 | ||||||||
\(502\) | −24.3128 | −1.08513 | ||||||||
\(503\) | −19.3213 | −0.861494 | −0.430747 | − | 0.902473i | \(-0.641750\pi\) | ||||
−0.430747 | + | 0.902473i | \(0.641750\pi\) | |||||||
\(504\) | 10.0955 | 0.449687 | ||||||||
\(505\) | 0.391515 | 0.0174222 | ||||||||
\(506\) | −12.8274 | −0.570245 | ||||||||
\(507\) | 30.1194 | 1.33765 | ||||||||
\(508\) | 27.1104 | 1.20283 | ||||||||
\(509\) | −32.9010 | −1.45831 | −0.729156 | − | 0.684347i | \(-0.760087\pi\) | ||||
−0.729156 | + | 0.684347i | \(0.760087\pi\) | |||||||
\(510\) | 1.45443 | 0.0644031 | ||||||||
\(511\) | −21.4121 | −0.947217 | ||||||||
\(512\) | −19.1053 | −0.844343 | ||||||||
\(513\) | −11.9647 | −0.528253 | ||||||||
\(514\) | 26.4004 | 1.16447 | ||||||||
\(515\) | 4.46121 | 0.196584 | ||||||||
\(516\) | −3.37797 | −0.148707 | ||||||||
\(517\) | −6.45625 | −0.283945 | ||||||||
\(518\) | −12.1971 | −0.535908 | ||||||||
\(519\) | −5.37734 | −0.236039 | ||||||||
\(520\) | 0.448376 | 0.0196626 | ||||||||
\(521\) | 3.89339 | 0.170573 | 0.0852863 | − | 0.996356i | \(-0.472819\pi\) | ||||
0.0852863 | + | 0.996356i | \(0.472819\pi\) | |||||||
\(522\) | 37.0404 | 1.62122 | ||||||||
\(523\) | −22.0813 | −0.965548 | −0.482774 | − | 0.875745i | \(-0.660371\pi\) | ||||
−0.482774 | + | 0.875745i | \(0.660371\pi\) | |||||||
\(524\) | −9.58320 | −0.418644 | ||||||||
\(525\) | 27.8004 | 1.21331 | ||||||||
\(526\) | −19.5823 | −0.853831 | ||||||||
\(527\) | −4.78411 | −0.208399 | ||||||||
\(528\) | 12.6534 | 0.550669 | ||||||||
\(529\) | 26.7212 | 1.16179 | ||||||||
\(530\) | −4.57789 | −0.198851 | ||||||||
\(531\) | 23.8734 | 1.03602 | ||||||||
\(532\) | 20.3185 | 0.880918 | ||||||||
\(533\) | −9.75149 | −0.422384 | ||||||||
\(534\) | −76.0564 | −3.29128 | ||||||||
\(535\) | 4.00877 | 0.173314 | ||||||||
\(536\) | 0.277364 | 0.0119803 | ||||||||
\(537\) | −32.0977 | −1.38512 | ||||||||
\(538\) | 3.59670 | 0.155065 | ||||||||
\(539\) | −2.17214 | −0.0935606 | ||||||||
\(540\) | 0.687301 | 0.0295767 | ||||||||
\(541\) | 11.3058 | 0.486073 | 0.243036 | − | 0.970017i | \(-0.421857\pi\) | ||||
0.243036 | + | 0.970017i | \(0.421857\pi\) | |||||||
\(542\) | −42.9617 | −1.84536 | ||||||||
\(543\) | 29.4409 | 1.26343 | ||||||||
\(544\) | −6.40864 | −0.274768 | ||||||||
\(545\) | −0.732236 | −0.0313656 | ||||||||
\(546\) | −11.8752 | −0.508210 | ||||||||
\(547\) | 3.12396 | 0.133571 | 0.0667855 | − | 0.997767i | \(-0.478726\pi\) | ||||
0.0667855 | + | 0.997767i | \(0.478726\pi\) | |||||||
\(548\) | 2.70689 | 0.115633 | ||||||||
\(549\) | −36.6222 | −1.56300 | ||||||||
\(550\) | 8.92101 | 0.380393 | ||||||||
\(551\) | −39.3294 | −1.67549 | ||||||||
\(552\) | −22.8596 | −0.972971 | ||||||||
\(553\) | −1.42188 | −0.0604646 | ||||||||
\(554\) | 0.800999 | 0.0340312 | ||||||||
\(555\) | 2.43970 | 0.103560 | ||||||||
\(556\) | −5.29988 | −0.224765 | ||||||||
\(557\) | 23.5934 | 0.999684 | 0.499842 | − | 0.866117i | \(-0.333391\pi\) | ||||
0.499842 | + | 0.866117i | \(0.333391\pi\) | |||||||
\(558\) | −31.8231 | −1.34718 | ||||||||
\(559\) | −1.15152 | −0.0487039 | ||||||||
\(560\) | 3.33932 | 0.141112 | ||||||||
\(561\) | 2.58004 | 0.108929 | ||||||||
\(562\) | 43.5489 | 1.83700 | ||||||||
\(563\) | −44.1143 | −1.85919 | −0.929597 | − | 0.368577i | \(-0.879845\pi\) | ||||
−0.929597 | + | 0.368577i | \(0.879845\pi\) | |||||||
\(564\) | 21.8090 | 0.918325 | ||||||||
\(565\) | −3.22280 | −0.135584 | ||||||||
\(566\) | 43.0524 | 1.80963 | ||||||||
\(567\) | −14.4999 | −0.608938 | ||||||||
\(568\) | −10.5807 | −0.443957 | ||||||||
\(569\) | −34.9418 | −1.46484 | −0.732418 | − | 0.680855i | \(-0.761608\pi\) | ||||
−0.732418 | + | 0.680855i | \(0.761608\pi\) | |||||||
\(570\) | −10.2725 | −0.430267 | ||||||||
\(571\) | −36.0562 | −1.50890 | −0.754452 | − | 0.656355i | \(-0.772097\pi\) | ||||
−0.754452 | + | 0.656355i | \(0.772097\pi\) | |||||||
\(572\) | −1.50765 | −0.0630380 | ||||||||
\(573\) | 53.9823 | 2.25514 | ||||||||
\(574\) | −33.8489 | −1.41283 | ||||||||
\(575\) | −34.5795 | −1.44206 | ||||||||
\(576\) | −6.76294 | −0.281789 | ||||||||
\(577\) | 20.8119 | 0.866412 | 0.433206 | − | 0.901295i | \(-0.357382\pi\) | ||||
0.433206 | + | 0.901295i | \(0.357382\pi\) | |||||||
\(578\) | −1.81914 | −0.0756663 | ||||||||
\(579\) | −51.2070 | −2.12809 | ||||||||
\(580\) | 2.25925 | 0.0938102 | ||||||||
\(581\) | 8.31578 | 0.344997 | ||||||||
\(582\) | −23.2245 | −0.962685 | ||||||||
\(583\) | −8.12081 | −0.336330 | ||||||||
\(584\) | −12.2449 | −0.506697 | ||||||||
\(585\) | 1.30480 | 0.0539470 | ||||||||
\(586\) | 22.9057 | 0.946228 | ||||||||
\(587\) | −22.4810 | −0.927889 | −0.463945 | − | 0.885864i | \(-0.653566\pi\) | ||||
−0.463945 | + | 0.885864i | \(0.653566\pi\) | |||||||
\(588\) | 7.33742 | 0.302590 | ||||||||
\(589\) | 33.7897 | 1.39228 | ||||||||
\(590\) | 3.68049 | 0.151523 | ||||||||
\(591\) | 55.9770 | 2.30259 | ||||||||
\(592\) | −14.9655 | −0.615080 | ||||||||
\(593\) | 3.62206 | 0.148740 | 0.0743701 | − | 0.997231i | \(-0.476305\pi\) | ||||
0.0743701 | + | 0.997231i | \(0.476305\pi\) | |||||||
\(594\) | 3.08165 | 0.126442 | ||||||||
\(595\) | 0.680890 | 0.0279138 | ||||||||
\(596\) | −29.4917 | −1.20803 | ||||||||
\(597\) | −19.9453 | −0.816306 | ||||||||
\(598\) | 14.7709 | 0.604027 | ||||||||
\(599\) | −19.8201 | −0.809827 | −0.404913 | − | 0.914355i | \(-0.632698\pi\) | ||||
−0.404913 | + | 0.914355i | \(0.632698\pi\) | |||||||
\(600\) | 15.8981 | 0.649039 | ||||||||
\(601\) | −16.7579 | −0.683568 | −0.341784 | − | 0.939779i | \(-0.611031\pi\) | ||||
−0.341784 | + | 0.939779i | \(0.611031\pi\) | |||||||
\(602\) | −3.99709 | −0.162909 | ||||||||
\(603\) | 0.807147 | 0.0328696 | ||||||||
\(604\) | −25.0630 | −1.01980 | ||||||||
\(605\) | −0.309884 | −0.0125986 | ||||||||
\(606\) | −5.92981 | −0.240882 | ||||||||
\(607\) | −12.1182 | −0.491861 | −0.245930 | − | 0.969287i | \(-0.579093\pi\) | ||||
−0.245930 | + | 0.969287i | \(0.579093\pi\) | |||||||
\(608\) | 45.2636 | 1.83568 | ||||||||
\(609\) | 31.5673 | 1.27917 | ||||||||
\(610\) | −5.64592 | −0.228597 | ||||||||
\(611\) | 7.43447 | 0.300767 | ||||||||
\(612\) | −4.78747 | −0.193522 | ||||||||
\(613\) | −5.54652 | −0.224022 | −0.112011 | − | 0.993707i | \(-0.535729\pi\) | ||||
−0.112011 | + | 0.993707i | \(0.535729\pi\) | |||||||
\(614\) | 19.2795 | 0.778055 | ||||||||
\(615\) | 6.77059 | 0.273016 | ||||||||
\(616\) | 2.76090 | 0.111240 | ||||||||
\(617\) | −23.0873 | −0.929462 | −0.464731 | − | 0.885452i | \(-0.653849\pi\) | ||||
−0.464731 | + | 0.885452i | \(0.653849\pi\) | |||||||
\(618\) | −67.5686 | −2.71801 | ||||||||
\(619\) | 3.92856 | 0.157902 | 0.0789511 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789511 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(620\) | −1.94102 | −0.0779534 | ||||||||
\(621\) | −11.9450 | −0.479338 | ||||||||
\(622\) | −20.2258 | −0.810983 | ||||||||
\(623\) | −35.6058 | −1.42652 | ||||||||
\(624\) | −14.5706 | −0.583291 | ||||||||
\(625\) | 23.5688 | 0.942752 | ||||||||
\(626\) | 38.3348 | 1.53217 | ||||||||
\(627\) | −18.2226 | −0.727739 | ||||||||
\(628\) | 22.8507 | 0.911842 | ||||||||
\(629\) | −3.05148 | −0.121671 | ||||||||
\(630\) | 4.52918 | 0.180447 | ||||||||
\(631\) | −29.9224 | −1.19119 | −0.595595 | − | 0.803285i | \(-0.703084\pi\) | ||||
−0.595595 | + | 0.803285i | \(0.703084\pi\) | |||||||
\(632\) | −0.813128 | −0.0323445 | ||||||||
\(633\) | −66.2550 | −2.63340 | ||||||||
\(634\) | −4.84356 | −0.192362 | ||||||||
\(635\) | −6.41660 | −0.254635 | ||||||||
\(636\) | 27.4319 | 1.08774 | ||||||||
\(637\) | 2.50125 | 0.0991032 | ||||||||
\(638\) | 10.1298 | 0.401042 | ||||||||
\(639\) | −30.7906 | −1.21806 | ||||||||
\(640\) | 2.92926 | 0.115789 | ||||||||
\(641\) | 7.91602 | 0.312664 | 0.156332 | − | 0.987705i | \(-0.450033\pi\) | ||||
0.156332 | + | 0.987705i | \(0.450033\pi\) | |||||||
\(642\) | −60.7160 | −2.39627 | ||||||||
\(643\) | 33.3893 | 1.31674 | 0.658372 | − | 0.752693i | \(-0.271245\pi\) | ||||
0.658372 | + | 0.752693i | \(0.271245\pi\) | |||||||
\(644\) | 20.2852 | 0.799347 | ||||||||
\(645\) | 0.799513 | 0.0314808 | ||||||||
\(646\) | 12.8484 | 0.505514 | ||||||||
\(647\) | 45.2258 | 1.77801 | 0.889006 | − | 0.457896i | \(-0.151397\pi\) | ||||
0.889006 | + | 0.457896i | \(0.151397\pi\) | |||||||
\(648\) | −8.29202 | −0.325741 | ||||||||
\(649\) | 6.52889 | 0.256281 | ||||||||
\(650\) | −10.2727 | −0.402928 | ||||||||
\(651\) | −27.1209 | −1.06295 | ||||||||
\(652\) | 16.7634 | 0.656506 | ||||||||
\(653\) | 41.5869 | 1.62742 | 0.813710 | − | 0.581270i | \(-0.197444\pi\) | ||||
0.813710 | + | 0.581270i | \(0.197444\pi\) | |||||||
\(654\) | 11.0903 | 0.433665 | ||||||||
\(655\) | 2.26819 | 0.0886257 | ||||||||
\(656\) | −41.5320 | −1.62155 | ||||||||
\(657\) | −35.6335 | −1.39019 | ||||||||
\(658\) | 25.8062 | 1.00603 | ||||||||
\(659\) | 14.5441 | 0.566559 | 0.283280 | − | 0.959037i | \(-0.408578\pi\) | ||||
0.283280 | + | 0.959037i | \(0.408578\pi\) | |||||||
\(660\) | 1.04678 | 0.0407459 | ||||||||
\(661\) | 7.00903 | 0.272620 | 0.136310 | − | 0.990666i | \(-0.456476\pi\) | ||||
0.136310 | + | 0.990666i | \(0.456476\pi\) | |||||||
\(662\) | −32.5633 | −1.26561 | ||||||||
\(663\) | −2.97095 | −0.115382 | ||||||||
\(664\) | 4.75553 | 0.184550 | ||||||||
\(665\) | −4.80906 | −0.186488 | ||||||||
\(666\) | −20.2980 | −0.786531 | ||||||||
\(667\) | −39.2649 | −1.52034 | ||||||||
\(668\) | −7.51832 | −0.290893 | ||||||||
\(669\) | −4.35341 | −0.168312 | ||||||||
\(670\) | 0.124435 | 0.00480735 | ||||||||
\(671\) | −10.0154 | −0.386640 | ||||||||
\(672\) | −36.3303 | −1.40147 | ||||||||
\(673\) | 30.6146 | 1.18010 | 0.590052 | − | 0.807365i | \(-0.299107\pi\) | ||||
0.590052 | + | 0.807365i | \(0.299107\pi\) | |||||||
\(674\) | −25.4857 | −0.981673 | ||||||||
\(675\) | 8.30739 | 0.319752 | ||||||||
\(676\) | −15.2845 | −0.587864 | ||||||||
\(677\) | −27.0109 | −1.03811 | −0.519056 | − | 0.854740i | \(-0.673717\pi\) | ||||
−0.519056 | + | 0.854740i | \(0.673717\pi\) | |||||||
\(678\) | 48.8120 | 1.87461 | ||||||||
\(679\) | −10.8725 | −0.417250 | ||||||||
\(680\) | 0.389379 | 0.0149320 | ||||||||
\(681\) | 8.70640 | 0.333630 | ||||||||
\(682\) | −8.70297 | −0.333254 | ||||||||
\(683\) | −25.6333 | −0.980832 | −0.490416 | − | 0.871488i | \(-0.663155\pi\) | ||||
−0.490416 | + | 0.871488i | \(0.663155\pi\) | |||||||
\(684\) | 33.8134 | 1.29289 | ||||||||
\(685\) | −0.640678 | −0.0244790 | ||||||||
\(686\) | 36.6618 | 1.39976 | ||||||||
\(687\) | −7.66177 | −0.292315 | ||||||||
\(688\) | −4.90435 | −0.186977 | ||||||||
\(689\) | 9.35125 | 0.356254 | ||||||||
\(690\) | −10.2556 | −0.390425 | ||||||||
\(691\) | 36.1227 | 1.37417 | 0.687086 | − | 0.726576i | \(-0.258889\pi\) | ||||
0.687086 | + | 0.726576i | \(0.258889\pi\) | |||||||
\(692\) | 2.72880 | 0.103733 | ||||||||
\(693\) | 8.03439 | 0.305201 | ||||||||
\(694\) | −40.6702 | −1.54382 | ||||||||
\(695\) | 1.25440 | 0.0475820 | ||||||||
\(696\) | 18.0523 | 0.684271 | ||||||||
\(697\) | −8.46839 | −0.320763 | ||||||||
\(698\) | −3.50184 | −0.132547 | ||||||||
\(699\) | −40.7125 | −1.53989 | ||||||||
\(700\) | −14.1077 | −0.533220 | ||||||||
\(701\) | −43.6549 | −1.64882 | −0.824411 | − | 0.565992i | \(-0.808493\pi\) | ||||
−0.824411 | + | 0.565992i | \(0.808493\pi\) | |||||||
\(702\) | −3.54857 | −0.133932 | ||||||||
\(703\) | 21.5523 | 0.812862 | ||||||||
\(704\) | −1.84952 | −0.0697066 | ||||||||
\(705\) | −5.16185 | −0.194407 | ||||||||
\(706\) | −21.7570 | −0.818835 | ||||||||
\(707\) | −2.77604 | −0.104404 | ||||||||
\(708\) | −22.0544 | −0.828855 | ||||||||
\(709\) | −24.9206 | −0.935912 | −0.467956 | − | 0.883752i | \(-0.655009\pi\) | ||||
−0.467956 | + | 0.883752i | \(0.655009\pi\) | |||||||
\(710\) | −4.74688 | −0.178147 | ||||||||
\(711\) | −2.36626 | −0.0887415 | ||||||||
\(712\) | −20.3618 | −0.763091 | ||||||||
\(713\) | 33.7343 | 1.26336 | ||||||||
\(714\) | −10.3126 | −0.385941 | ||||||||
\(715\) | 0.356837 | 0.0133449 | ||||||||
\(716\) | 16.2884 | 0.608725 | ||||||||
\(717\) | −42.1813 | −1.57529 | ||||||||
\(718\) | 52.1568 | 1.94647 | ||||||||
\(719\) | −35.3816 | −1.31951 | −0.659755 | − | 0.751481i | \(-0.729340\pi\) | ||||
−0.659755 | + | 0.751481i | \(0.729340\pi\) | |||||||
\(720\) | 5.55721 | 0.207105 | ||||||||
\(721\) | −31.6323 | −1.17805 | ||||||||
\(722\) | −56.1835 | −2.09093 | ||||||||
\(723\) | 25.9250 | 0.964163 | ||||||||
\(724\) | −14.9402 | −0.555247 | ||||||||
\(725\) | 27.3075 | 1.01418 | ||||||||
\(726\) | 4.69345 | 0.174190 | ||||||||
\(727\) | 5.80904 | 0.215445 | 0.107723 | − | 0.994181i | \(-0.465644\pi\) | ||||
0.107723 | + | 0.994181i | \(0.465644\pi\) | |||||||
\(728\) | −3.17922 | −0.117830 | ||||||||
\(729\) | −37.2422 | −1.37934 | ||||||||
\(730\) | −5.49349 | −0.203323 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 33.8318 | 1.25046 | ||||||||
\(733\) | 42.7645 | 1.57954 | 0.789771 | − | 0.613402i | \(-0.210199\pi\) | ||||
0.789771 | + | 0.613402i | \(0.210199\pi\) | |||||||
\(734\) | 19.7969 | 0.730718 | ||||||||
\(735\) | −1.73665 | −0.0640574 | ||||||||
\(736\) | 45.1894 | 1.66570 | ||||||||
\(737\) | 0.220738 | 0.00813099 | ||||||||
\(738\) | −56.3304 | −2.07355 | ||||||||
\(739\) | 38.9973 | 1.43454 | 0.717270 | − | 0.696796i | \(-0.245392\pi\) | ||||
0.717270 | + | 0.696796i | \(0.245392\pi\) | |||||||
\(740\) | −1.23806 | −0.0455119 | ||||||||
\(741\) | 20.9836 | 0.770850 | ||||||||
\(742\) | 32.4596 | 1.19163 | ||||||||
\(743\) | 20.6670 | 0.758200 | 0.379100 | − | 0.925356i | \(-0.376234\pi\) | ||||
0.379100 | + | 0.925356i | \(0.376234\pi\) | |||||||
\(744\) | −15.5096 | −0.568608 | ||||||||
\(745\) | 6.98023 | 0.255736 | ||||||||
\(746\) | 40.1333 | 1.46939 | ||||||||
\(747\) | 13.8389 | 0.506339 | ||||||||
\(748\) | −1.30927 | −0.0478718 | ||||||||
\(749\) | −28.4242 | −1.03860 | ||||||||
\(750\) | 14.4046 | 0.525982 | ||||||||
\(751\) | −35.3895 | −1.29138 | −0.645690 | − | 0.763599i | \(-0.723430\pi\) | ||||
−0.645690 | + | 0.763599i | \(0.723430\pi\) | |||||||
\(752\) | 31.6637 | 1.15466 | ||||||||
\(753\) | −34.4821 | −1.25660 | ||||||||
\(754\) | −11.6646 | −0.424800 | ||||||||
\(755\) | 5.93201 | 0.215888 | ||||||||
\(756\) | −4.87332 | −0.177241 | ||||||||
\(757\) | −16.7523 | −0.608871 | −0.304436 | − | 0.952533i | \(-0.598468\pi\) | ||||
−0.304436 | + | 0.952533i | \(0.598468\pi\) | |||||||
\(758\) | −48.8969 | −1.77601 | ||||||||
\(759\) | −18.1927 | −0.660352 | ||||||||
\(760\) | −2.75015 | −0.0997583 | ||||||||
\(761\) | 47.7997 | 1.73274 | 0.866370 | − | 0.499404i | \(-0.166447\pi\) | ||||
0.866370 | + | 0.499404i | \(0.166447\pi\) | |||||||
\(762\) | 97.1845 | 3.52062 | ||||||||
\(763\) | 5.19193 | 0.187961 | ||||||||
\(764\) | −27.3940 | −0.991081 | ||||||||
\(765\) | 1.13312 | 0.0409680 | ||||||||
\(766\) | −42.1971 | −1.52464 | ||||||||
\(767\) | −7.51812 | −0.271464 | ||||||||
\(768\) | −53.9096 | −1.94530 | ||||||||
\(769\) | 30.1859 | 1.08853 | 0.544266 | − | 0.838912i | \(-0.316808\pi\) | ||||
0.544266 | + | 0.838912i | \(0.316808\pi\) | |||||||
\(770\) | 1.23864 | 0.0446373 | ||||||||
\(771\) | 37.4429 | 1.34847 | ||||||||
\(772\) | 25.9857 | 0.935244 | ||||||||
\(773\) | 4.00349 | 0.143996 | 0.0719979 | − | 0.997405i | \(-0.477063\pi\) | ||||
0.0719979 | + | 0.997405i | \(0.477063\pi\) | |||||||
\(774\) | −6.65184 | −0.239096 | ||||||||
\(775\) | −23.4611 | −0.842749 | ||||||||
\(776\) | −6.21765 | −0.223201 | ||||||||
\(777\) | −17.2987 | −0.620589 | ||||||||
\(778\) | 34.2504 | 1.22794 | ||||||||
\(779\) | 59.8115 | 2.14297 | ||||||||
\(780\) | −1.20538 | −0.0431597 | ||||||||
\(781\) | −8.42059 | −0.301312 | ||||||||
\(782\) | 12.8274 | 0.458705 | ||||||||
\(783\) | 9.43302 | 0.337109 | ||||||||
\(784\) | 10.6529 | 0.380462 | ||||||||
\(785\) | −5.40840 | −0.193034 | ||||||||
\(786\) | −34.3536 | −1.22535 | ||||||||
\(787\) | −39.0476 | −1.39190 | −0.695949 | − | 0.718091i | \(-0.745016\pi\) | ||||
−0.695949 | + | 0.718091i | \(0.745016\pi\) | |||||||
\(788\) | −28.4063 | −1.01193 | ||||||||
\(789\) | −27.7731 | −0.988748 | ||||||||
\(790\) | −0.364798 | −0.0129789 | ||||||||
\(791\) | 22.8513 | 0.812500 | ||||||||
\(792\) | 4.59461 | 0.163262 | ||||||||
\(793\) | 11.5329 | 0.409545 | ||||||||
\(794\) | 23.9942 | 0.851521 | ||||||||
\(795\) | −6.49269 | −0.230272 | ||||||||
\(796\) | 10.1215 | 0.358747 | ||||||||
\(797\) | −6.61123 | −0.234182 | −0.117091 | − | 0.993121i | \(-0.537357\pi\) | ||||
−0.117091 | + | 0.993121i | \(0.537357\pi\) | |||||||
\(798\) | 72.8371 | 2.57841 | ||||||||
\(799\) | 6.45625 | 0.228406 | ||||||||
\(800\) | −31.4278 | −1.11114 | ||||||||
\(801\) | −59.2542 | −2.09365 | ||||||||
\(802\) | 0.714472 | 0.0252289 | ||||||||
\(803\) | −9.74501 | −0.343894 | ||||||||
\(804\) | −0.745646 | −0.0262969 | ||||||||
\(805\) | −4.80118 | −0.169219 | ||||||||
\(806\) | 10.0216 | 0.352996 | ||||||||
\(807\) | 5.10110 | 0.179567 | ||||||||
\(808\) | −1.58753 | −0.0558490 | ||||||||
\(809\) | −54.5466 | −1.91775 | −0.958877 | − | 0.283820i | \(-0.908398\pi\) | ||||
−0.958877 | + | 0.283820i | \(0.908398\pi\) | |||||||
\(810\) | −3.72009 | −0.130711 | ||||||||
\(811\) | −0.537046 | −0.0188582 | −0.00942912 | − | 0.999956i | \(-0.503001\pi\) | ||||
−0.00942912 | + | 0.999956i | \(0.503001\pi\) | |||||||
\(812\) | −16.0192 | −0.562165 | ||||||||
\(813\) | −60.9313 | −2.13696 | ||||||||
\(814\) | −5.55108 | −0.194565 | ||||||||
\(815\) | −3.96764 | −0.138980 | ||||||||
\(816\) | −12.6534 | −0.442958 | ||||||||
\(817\) | 7.06291 | 0.247100 | ||||||||
\(818\) | 28.3237 | 0.990317 | ||||||||
\(819\) | −9.25173 | −0.323282 | ||||||||
\(820\) | −3.43582 | −0.119984 | ||||||||
\(821\) | 3.05513 | 0.106625 | 0.0533123 | − | 0.998578i | \(-0.483022\pi\) | ||||
0.0533123 | + | 0.998578i | \(0.483022\pi\) | |||||||
\(822\) | 9.70358 | 0.338451 | ||||||||
\(823\) | −23.1245 | −0.806071 | −0.403035 | − | 0.915184i | \(-0.632045\pi\) | ||||
−0.403035 | + | 0.915184i | \(0.632045\pi\) | |||||||
\(824\) | −18.0895 | −0.630176 | ||||||||
\(825\) | 12.6524 | 0.440501 | ||||||||
\(826\) | −26.0965 | −0.908015 | ||||||||
\(827\) | 27.8644 | 0.968942 | 0.484471 | − | 0.874807i | \(-0.339012\pi\) | ||||
0.484471 | + | 0.874807i | \(0.339012\pi\) | |||||||
\(828\) | 33.7580 | 1.17317 | ||||||||
\(829\) | −7.16435 | −0.248828 | −0.124414 | − | 0.992230i | \(-0.539705\pi\) | ||||
−0.124414 | + | 0.992230i | \(0.539705\pi\) | |||||||
\(830\) | 2.13350 | 0.0740547 | ||||||||
\(831\) | 1.13603 | 0.0394086 | ||||||||
\(832\) | 2.12976 | 0.0738361 | ||||||||
\(833\) | 2.17214 | 0.0752601 | ||||||||
\(834\) | −18.9989 | −0.657877 | ||||||||
\(835\) | 1.77947 | 0.0615811 | ||||||||
\(836\) | 9.24727 | 0.319824 | ||||||||
\(837\) | −8.10434 | −0.280127 | ||||||||
\(838\) | −57.2363 | −1.97719 | ||||||||
\(839\) | 11.5562 | 0.398965 | 0.199482 | − | 0.979901i | \(-0.436074\pi\) | ||||
0.199482 | + | 0.979901i | \(0.436074\pi\) | |||||||
\(840\) | 2.20737 | 0.0761616 | ||||||||
\(841\) | 2.00760 | 0.0692276 | ||||||||
\(842\) | −46.2915 | −1.59531 | ||||||||
\(843\) | 61.7641 | 2.12727 | ||||||||
\(844\) | 33.6219 | 1.15732 | ||||||||
\(845\) | 3.61759 | 0.124449 | ||||||||
\(846\) | 42.9459 | 1.47651 | ||||||||
\(847\) | 2.19724 | 0.0754980 | ||||||||
\(848\) | 39.8273 | 1.36768 | ||||||||
\(849\) | 61.0600 | 2.09557 | ||||||||
\(850\) | −8.92101 | −0.305988 | ||||||||
\(851\) | 21.5170 | 0.737594 | ||||||||
\(852\) | 28.4445 | 0.974493 | ||||||||
\(853\) | 43.4723 | 1.48846 | 0.744232 | − | 0.667921i | \(-0.232816\pi\) | ||||
0.744232 | + | 0.667921i | \(0.232816\pi\) | |||||||
\(854\) | 40.0325 | 1.36988 | ||||||||
\(855\) | −8.00311 | −0.273701 | ||||||||
\(856\) | −16.2549 | −0.555580 | ||||||||
\(857\) | −15.1271 | −0.516732 | −0.258366 | − | 0.966047i | \(-0.583184\pi\) | ||||
−0.258366 | + | 0.966047i | \(0.583184\pi\) | |||||||
\(858\) | −5.40458 | −0.184509 | ||||||||
\(859\) | 46.6582 | 1.59196 | 0.795978 | − | 0.605326i | \(-0.206957\pi\) | ||||
0.795978 | + | 0.605326i | \(0.206957\pi\) | |||||||
\(860\) | −0.405723 | −0.0138350 | ||||||||
\(861\) | −48.0070 | −1.63607 | ||||||||
\(862\) | 33.8578 | 1.15320 | ||||||||
\(863\) | −30.6550 | −1.04351 | −0.521754 | − | 0.853096i | \(-0.674722\pi\) | ||||
−0.521754 | + | 0.853096i | \(0.674722\pi\) | |||||||
\(864\) | −10.8563 | −0.369340 | ||||||||
\(865\) | −0.645864 | −0.0219600 | ||||||||
\(866\) | −21.6121 | −0.734408 | ||||||||
\(867\) | −2.58004 | −0.0876226 | ||||||||
\(868\) | 13.7629 | 0.467142 | ||||||||
\(869\) | −0.647122 | −0.0219521 | ||||||||
\(870\) | 8.09890 | 0.274578 | ||||||||
\(871\) | −0.254183 | −0.00861267 | ||||||||
\(872\) | 2.96910 | 0.100546 | ||||||||
\(873\) | −18.0938 | −0.612382 | ||||||||
\(874\) | −90.5984 | −3.06454 | ||||||||
\(875\) | 6.74352 | 0.227973 | ||||||||
\(876\) | 32.9184 | 1.11221 | ||||||||
\(877\) | 36.1948 | 1.22221 | 0.611105 | − | 0.791550i | \(-0.290725\pi\) | ||||
0.611105 | + | 0.791550i | \(0.290725\pi\) | |||||||
\(878\) | 12.4805 | 0.421198 | ||||||||
\(879\) | 32.4866 | 1.09574 | ||||||||
\(880\) | 1.51978 | 0.0512318 | ||||||||
\(881\) | −30.6032 | −1.03105 | −0.515524 | − | 0.856875i | \(-0.672403\pi\) | ||||
−0.515524 | + | 0.856875i | \(0.672403\pi\) | |||||||
\(882\) | 14.4487 | 0.486514 | ||||||||
\(883\) | 32.5655 | 1.09592 | 0.547959 | − | 0.836505i | \(-0.315405\pi\) | ||||
0.547959 | + | 0.836505i | \(0.315405\pi\) | |||||||
\(884\) | 1.50765 | 0.0507077 | ||||||||
\(885\) | 5.21993 | 0.175466 | ||||||||
\(886\) | 49.5581 | 1.66494 | ||||||||
\(887\) | −26.4979 | −0.889711 | −0.444856 | − | 0.895602i | \(-0.646745\pi\) | ||||
−0.444856 | + | 0.895602i | \(0.646745\pi\) | |||||||
\(888\) | −9.89258 | −0.331973 | ||||||||
\(889\) | 45.4970 | 1.52592 | ||||||||
\(890\) | −9.13503 | −0.306207 | ||||||||
\(891\) | −6.59914 | −0.221080 | ||||||||
\(892\) | 2.20919 | 0.0739693 | ||||||||
\(893\) | −45.5999 | −1.52594 | ||||||||
\(894\) | −105.721 | −3.53585 | ||||||||
\(895\) | −3.85520 | −0.128865 | ||||||||
\(896\) | −20.7699 | −0.693875 | ||||||||
\(897\) | 20.9492 | 0.699472 | ||||||||
\(898\) | 24.1708 | 0.806589 | ||||||||
\(899\) | −26.6401 | −0.888496 | ||||||||
\(900\) | −23.4776 | −0.782587 | ||||||||
\(901\) | 8.12081 | 0.270543 | ||||||||
\(902\) | −15.4052 | −0.512937 | ||||||||
\(903\) | −5.66896 | −0.188651 | ||||||||
\(904\) | 13.0679 | 0.434633 | ||||||||
\(905\) | 3.53610 | 0.117544 | ||||||||
\(906\) | −89.8451 | −2.98490 | ||||||||
\(907\) | 45.0243 | 1.49501 | 0.747504 | − | 0.664257i | \(-0.231252\pi\) | ||||
0.747504 | + | 0.664257i | \(0.231252\pi\) | |||||||
\(908\) | −4.41818 | −0.146622 | ||||||||
\(909\) | −4.61981 | −0.153229 | ||||||||
\(910\) | −1.42631 | −0.0472817 | ||||||||
\(911\) | −12.9460 | −0.428921 | −0.214460 | − | 0.976733i | \(-0.568799\pi\) | ||||
−0.214460 | + | 0.976733i | \(0.568799\pi\) | |||||||
\(912\) | 89.3698 | 2.95933 | ||||||||
\(913\) | 3.78465 | 0.125254 | ||||||||
\(914\) | −0.427581 | −0.0141431 | ||||||||
\(915\) | −8.00745 | −0.264718 | ||||||||
\(916\) | 3.88807 | 0.128465 | ||||||||
\(917\) | −16.0827 | −0.531096 | ||||||||
\(918\) | −3.08165 | −0.101710 | ||||||||
\(919\) | 4.57273 | 0.150840 | 0.0754202 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754202 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(920\) | −2.74564 | −0.0905210 | ||||||||
\(921\) | 27.3435 | 0.900999 | ||||||||
\(922\) | −40.4019 | −1.33057 | ||||||||
\(923\) | 9.69645 | 0.319162 | ||||||||
\(924\) | −7.42221 | −0.244173 | ||||||||
\(925\) | −14.9644 | −0.492026 | ||||||||
\(926\) | 44.0575 | 1.44782 | ||||||||
\(927\) | −52.6416 | −1.72898 | ||||||||
\(928\) | −35.6862 | −1.17146 | ||||||||
\(929\) | −8.75389 | −0.287206 | −0.143603 | − | 0.989635i | \(-0.545869\pi\) | ||||
−0.143603 | + | 0.989635i | \(0.545869\pi\) | |||||||
\(930\) | −6.95813 | −0.228166 | ||||||||
\(931\) | −15.3416 | −0.502801 | ||||||||
\(932\) | 20.6601 | 0.676744 | ||||||||
\(933\) | −28.6858 | −0.939129 | ||||||||
\(934\) | −1.05310 | −0.0344586 | ||||||||
\(935\) | 0.309884 | 0.0101343 | ||||||||
\(936\) | −5.29076 | −0.172934 | ||||||||
\(937\) | 21.8245 | 0.712976 | 0.356488 | − | 0.934300i | \(-0.383974\pi\) | ||||
0.356488 | + | 0.934300i | \(0.383974\pi\) | |||||||
\(938\) | −0.882309 | −0.0288084 | ||||||||
\(939\) | 54.3692 | 1.77427 | ||||||||
\(940\) | 2.61945 | 0.0854370 | ||||||||
\(941\) | −22.7396 | −0.741291 | −0.370646 | − | 0.928774i | \(-0.620864\pi\) | ||||
−0.370646 | + | 0.928774i | \(0.620864\pi\) | |||||||
\(942\) | 81.9146 | 2.66892 | ||||||||
\(943\) | 59.7134 | 1.94454 | ||||||||
\(944\) | −32.0199 | −1.04216 | ||||||||
\(945\) | 1.15344 | 0.0375213 | ||||||||
\(946\) | −1.81914 | −0.0591454 | ||||||||
\(947\) | −2.67403 | −0.0868944 | −0.0434472 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434472 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(948\) | 2.18596 | 0.0709966 | ||||||||
\(949\) | 11.2215 | 0.364266 | ||||||||
\(950\) | 63.0083 | 2.04426 | ||||||||
\(951\) | −6.86949 | −0.222758 | ||||||||
\(952\) | −2.76090 | −0.0894812 | ||||||||
\(953\) | 29.6142 | 0.959297 | 0.479648 | − | 0.877461i | \(-0.340764\pi\) | ||||
0.479648 | + | 0.877461i | \(0.340764\pi\) | |||||||
\(954\) | 54.0184 | 1.74891 | ||||||||
\(955\) | 6.48374 | 0.209809 | ||||||||
\(956\) | 21.4054 | 0.692301 | ||||||||
\(957\) | 14.3668 | 0.464412 | ||||||||
\(958\) | 26.8171 | 0.866421 | ||||||||
\(959\) | 4.54274 | 0.146693 | ||||||||
\(960\) | −1.47872 | −0.0477254 | ||||||||
\(961\) | −8.11230 | −0.261687 | ||||||||
\(962\) | 6.39216 | 0.206091 | ||||||||
\(963\) | −47.3028 | −1.52431 | ||||||||
\(964\) | −13.1560 | −0.423726 | ||||||||
\(965\) | −6.15040 | −0.197988 | ||||||||
\(966\) | 72.7177 | 2.33965 | ||||||||
\(967\) | −36.5168 | −1.17430 | −0.587150 | − | 0.809478i | \(-0.699750\pi\) | ||||
−0.587150 | + | 0.809478i | \(0.699750\pi\) | |||||||
\(968\) | 1.25653 | 0.0403864 | ||||||||
\(969\) | 18.2226 | 0.585393 | ||||||||
\(970\) | −2.78946 | −0.0895640 | ||||||||
\(971\) | −34.3183 | −1.10133 | −0.550664 | − | 0.834727i | \(-0.685625\pi\) | ||||
−0.550664 | + | 0.834727i | \(0.685625\pi\) | |||||||
\(972\) | 28.9455 | 0.928427 | ||||||||
\(973\) | −8.89433 | −0.285139 | ||||||||
\(974\) | −52.7103 | −1.68895 | ||||||||
\(975\) | −14.5695 | −0.466596 | ||||||||
\(976\) | 49.1191 | 1.57226 | ||||||||
\(977\) | −5.34626 | −0.171042 | −0.0855209 | − | 0.996336i | \(-0.527255\pi\) | ||||
−0.0855209 | + | 0.996336i | \(0.527255\pi\) | |||||||
\(978\) | 60.0931 | 1.92156 | ||||||||
\(979\) | −16.2048 | −0.517908 | ||||||||
\(980\) | 0.881287 | 0.0281517 | ||||||||
\(981\) | 8.64027 | 0.275863 | ||||||||
\(982\) | 38.6261 | 1.23261 | ||||||||
\(983\) | 5.35795 | 0.170892 | 0.0854460 | − | 0.996343i | \(-0.472768\pi\) | ||||
0.0854460 | + | 0.996343i | \(0.472768\pi\) | |||||||
\(984\) | −27.4536 | −0.875189 | ||||||||
\(985\) | 6.72331 | 0.214223 | ||||||||
\(986\) | −10.1298 | −0.322598 | ||||||||
\(987\) | 36.6002 | 1.16500 | ||||||||
\(988\) | −10.6484 | −0.338770 | ||||||||
\(989\) | 7.05132 | 0.224219 | ||||||||
\(990\) | 2.06130 | 0.0655125 | ||||||||
\(991\) | −19.3325 | −0.614118 | −0.307059 | − | 0.951690i | \(-0.599345\pi\) | ||||
−0.307059 | + | 0.951690i | \(0.599345\pi\) | |||||||
\(992\) | 30.6596 | 0.973445 | ||||||||
\(993\) | −46.1837 | −1.46559 | ||||||||
\(994\) | 33.6578 | 1.06756 | ||||||||
\(995\) | −2.39560 | −0.0759456 | ||||||||
\(996\) | −12.7844 | −0.405091 | ||||||||
\(997\) | −14.1636 | −0.448567 | −0.224284 | − | 0.974524i | \(-0.572004\pi\) | ||||
−0.224284 | + | 0.974524i | \(0.572004\pi\) | |||||||
\(998\) | 16.6192 | 0.526072 | ||||||||
\(999\) | −5.16926 | −0.163548 |
(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 | 8041.2.a.d.1.14 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.d.1.14 | ✓ | 62 | 1.1 | even | 1 | trivial |