Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(1\) |
Dimension: | \(205\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58762 | −1.82972 | −0.914861 | − | 0.403769i | \(-0.867700\pi\) | ||||
−0.914861 | + | 0.403769i | \(0.867700\pi\) | |||||||
\(3\) | 0.766219 | 0.442377 | 0.221188 | − | 0.975231i | \(-0.429006\pi\) | ||||
0.221188 | + | 0.975231i | \(0.429006\pi\) | |||||||
\(4\) | 4.69576 | 2.34788 | ||||||||
\(5\) | 1.84822 | 0.826548 | 0.413274 | − | 0.910607i | \(-0.364385\pi\) | ||||
0.413274 | + | 0.910607i | \(0.364385\pi\) | |||||||
\(6\) | −1.98268 | −0.809426 | ||||||||
\(7\) | −5.04954 | −1.90855 | −0.954274 | − | 0.298933i | \(-0.903369\pi\) | ||||
−0.954274 | + | 0.298933i | \(0.903369\pi\) | |||||||
\(8\) | −6.97561 | −2.46625 | ||||||||
\(9\) | −2.41291 | −0.804303 | ||||||||
\(10\) | −4.78248 | −1.51235 | ||||||||
\(11\) | −4.49504 | −1.35530 | −0.677652 | − | 0.735382i | \(-0.737003\pi\) | ||||
−0.677652 | + | 0.735382i | \(0.737003\pi\) | |||||||
\(12\) | 3.59798 | 1.03865 | ||||||||
\(13\) | 5.95124 | 1.65058 | 0.825288 | − | 0.564711i | \(-0.191013\pi\) | ||||
0.825288 | + | 0.564711i | \(0.191013\pi\) | |||||||
\(14\) | 13.0663 | 3.49211 | ||||||||
\(15\) | 1.41614 | 0.365646 | ||||||||
\(16\) | 8.65867 | 2.16467 | ||||||||
\(17\) | 5.94585 | 1.44208 | 0.721040 | − | 0.692893i | \(-0.243664\pi\) | ||||
0.721040 | + | 0.692893i | \(0.243664\pi\) | |||||||
\(18\) | 6.24368 | 1.47165 | ||||||||
\(19\) | −2.59001 | −0.594189 | −0.297094 | − | 0.954848i | \(-0.596018\pi\) | ||||
−0.297094 | + | 0.954848i | \(0.596018\pi\) | |||||||
\(20\) | 8.67880 | 1.94064 | ||||||||
\(21\) | −3.86906 | −0.844297 | ||||||||
\(22\) | 11.6314 | 2.47983 | ||||||||
\(23\) | 5.07878 | 1.05900 | 0.529499 | − | 0.848310i | \(-0.322380\pi\) | ||||
0.529499 | + | 0.848310i | \(0.322380\pi\) | |||||||
\(24\) | −5.34484 | −1.09101 | ||||||||
\(25\) | −1.58409 | −0.316818 | ||||||||
\(26\) | −15.3995 | −3.02010 | ||||||||
\(27\) | −4.14747 | −0.798182 | ||||||||
\(28\) | −23.7115 | −4.48105 | ||||||||
\(29\) | 6.37999 | 1.18474 | 0.592368 | − | 0.805668i | \(-0.298193\pi\) | ||||
0.592368 | + | 0.805668i | \(0.298193\pi\) | |||||||
\(30\) | −3.66443 | −0.669030 | ||||||||
\(31\) | −1.63544 | −0.293733 | −0.146867 | − | 0.989156i | \(-0.546919\pi\) | ||||
−0.146867 | + | 0.989156i | \(0.546919\pi\) | |||||||
\(32\) | −8.45412 | −1.49449 | ||||||||
\(33\) | −3.44418 | −0.599555 | ||||||||
\(34\) | −15.3856 | −2.63861 | ||||||||
\(35\) | −9.33266 | −1.57751 | ||||||||
\(36\) | −11.3304 | −1.88841 | ||||||||
\(37\) | −0.397533 | −0.0653541 | −0.0326770 | − | 0.999466i | \(-0.510403\pi\) | ||||
−0.0326770 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(38\) | 6.70195 | 1.08720 | ||||||||
\(39\) | 4.55995 | 0.730177 | ||||||||
\(40\) | −12.8924 | −2.03847 | ||||||||
\(41\) | −6.87961 | −1.07442 | −0.537208 | − | 0.843450i | \(-0.680521\pi\) | ||||
−0.537208 | + | 0.843450i | \(0.680521\pi\) | |||||||
\(42\) | 10.0116 | 1.54483 | ||||||||
\(43\) | −3.03051 | −0.462149 | −0.231075 | − | 0.972936i | \(-0.574224\pi\) | ||||
−0.231075 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(44\) | −21.1076 | −3.18210 | ||||||||
\(45\) | −4.45958 | −0.664795 | ||||||||
\(46\) | −13.1419 | −1.93767 | ||||||||
\(47\) | 1.80977 | 0.263982 | 0.131991 | − | 0.991251i | \(-0.457863\pi\) | ||||
0.131991 | + | 0.991251i | \(0.457863\pi\) | |||||||
\(48\) | 6.63444 | 0.957599 | ||||||||
\(49\) | 18.4979 | 2.64256 | ||||||||
\(50\) | 4.09902 | 0.579688 | ||||||||
\(51\) | 4.55582 | 0.637943 | ||||||||
\(52\) | 27.9456 | 3.87536 | ||||||||
\(53\) | −2.78340 | −0.382330 | −0.191165 | − | 0.981558i | \(-0.561226\pi\) | ||||
−0.191165 | + | 0.981558i | \(0.561226\pi\) | |||||||
\(54\) | 10.7321 | 1.46045 | ||||||||
\(55\) | −8.30781 | −1.12023 | ||||||||
\(56\) | 35.2236 | 4.70696 | ||||||||
\(57\) | −1.98451 | −0.262855 | ||||||||
\(58\) | −16.5090 | −2.16774 | ||||||||
\(59\) | −4.71105 | −0.613327 | −0.306663 | − | 0.951818i | \(-0.599213\pi\) | ||||
−0.306663 | + | 0.951818i | \(0.599213\pi\) | |||||||
\(60\) | 6.64986 | 0.858493 | ||||||||
\(61\) | 11.2088 | 1.43514 | 0.717568 | − | 0.696488i | \(-0.245255\pi\) | ||||
0.717568 | + | 0.696488i | \(0.245255\pi\) | |||||||
\(62\) | 4.23189 | 0.537450 | ||||||||
\(63\) | 12.1841 | 1.53505 | ||||||||
\(64\) | 4.55869 | 0.569836 | ||||||||
\(65\) | 10.9992 | 1.36428 | ||||||||
\(66\) | 8.91223 | 1.09702 | ||||||||
\(67\) | 11.8469 | 1.44733 | 0.723665 | − | 0.690151i | \(-0.242456\pi\) | ||||
0.723665 | + | 0.690151i | \(0.242456\pi\) | |||||||
\(68\) | 27.9203 | 3.38584 | ||||||||
\(69\) | 3.89146 | 0.468476 | ||||||||
\(70\) | 24.1494 | 2.88640 | ||||||||
\(71\) | −5.94805 | −0.705904 | −0.352952 | − | 0.935642i | \(-0.614822\pi\) | ||||
−0.352952 | + | 0.935642i | \(0.614822\pi\) | |||||||
\(72\) | 16.8315 | 1.98361 | ||||||||
\(73\) | −5.36688 | −0.628145 | −0.314073 | − | 0.949399i | \(-0.601694\pi\) | ||||
−0.314073 | + | 0.949399i | \(0.601694\pi\) | |||||||
\(74\) | 1.02866 | 0.119580 | ||||||||
\(75\) | −1.21376 | −0.140153 | ||||||||
\(76\) | −12.1621 | −1.39508 | ||||||||
\(77\) | 22.6979 | 2.58666 | ||||||||
\(78\) | −11.7994 | −1.33602 | ||||||||
\(79\) | −16.0823 | −1.80940 | −0.904698 | − | 0.426054i | \(-0.859903\pi\) | ||||
−0.904698 | + | 0.426054i | \(0.859903\pi\) | |||||||
\(80\) | 16.0031 | 1.78920 | ||||||||
\(81\) | 4.06085 | 0.451206 | ||||||||
\(82\) | 17.8018 | 1.96588 | ||||||||
\(83\) | −0.0257040 | −0.00282138 | −0.00141069 | − | 0.999999i | \(-0.500449\pi\) | ||||
−0.00141069 | + | 0.999999i | \(0.500449\pi\) | |||||||
\(84\) | −18.1682 | −1.98231 | ||||||||
\(85\) | 10.9892 | 1.19195 | ||||||||
\(86\) | 7.84181 | 0.845604 | ||||||||
\(87\) | 4.88847 | 0.524099 | ||||||||
\(88\) | 31.3556 | 3.34252 | ||||||||
\(89\) | −2.46316 | −0.261094 | −0.130547 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130547 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(90\) | 11.5397 | 1.21639 | ||||||||
\(91\) | −30.0510 | −3.15021 | ||||||||
\(92\) | 23.8488 | 2.48640 | ||||||||
\(93\) | −1.25310 | −0.129941 | ||||||||
\(94\) | −4.68299 | −0.483014 | ||||||||
\(95\) | −4.78690 | −0.491126 | ||||||||
\(96\) | −6.47771 | −0.661129 | ||||||||
\(97\) | 11.7916 | 1.19725 | 0.598626 | − | 0.801028i | \(-0.295713\pi\) | ||||
0.598626 | + | 0.801028i | \(0.295713\pi\) | |||||||
\(98\) | −47.8655 | −4.83514 | ||||||||
\(99\) | 10.8461 | 1.09008 | ||||||||
\(100\) | −7.43851 | −0.743851 | ||||||||
\(101\) | 10.2893 | 1.02383 | 0.511914 | − | 0.859037i | \(-0.328937\pi\) | ||||
0.511914 | + | 0.859037i | \(0.328937\pi\) | |||||||
\(102\) | −11.7887 | −1.16726 | ||||||||
\(103\) | −8.38960 | −0.826652 | −0.413326 | − | 0.910583i | \(-0.635633\pi\) | ||||
−0.413326 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(104\) | −41.5135 | −4.07073 | ||||||||
\(105\) | −7.15086 | −0.697853 | ||||||||
\(106\) | 7.20238 | 0.699557 | ||||||||
\(107\) | 2.89861 | 0.280219 | 0.140110 | − | 0.990136i | \(-0.455254\pi\) | ||||
0.140110 | + | 0.990136i | \(0.455254\pi\) | |||||||
\(108\) | −19.4756 | −1.87404 | ||||||||
\(109\) | 8.51618 | 0.815702 | 0.407851 | − | 0.913049i | \(-0.366278\pi\) | ||||
0.407851 | + | 0.913049i | \(0.366278\pi\) | |||||||
\(110\) | 21.4974 | 2.04970 | ||||||||
\(111\) | −0.304598 | −0.0289111 | ||||||||
\(112\) | −43.7224 | −4.13137 | ||||||||
\(113\) | −20.3099 | −1.91059 | −0.955296 | − | 0.295650i | \(-0.904464\pi\) | ||||
−0.955296 | + | 0.295650i | \(0.904464\pi\) | |||||||
\(114\) | 5.13516 | 0.480952 | ||||||||
\(115\) | 9.38669 | 0.875314 | ||||||||
\(116\) | 29.9590 | 2.78162 | ||||||||
\(117\) | −14.3598 | −1.32756 | ||||||||
\(118\) | 12.1904 | 1.12222 | ||||||||
\(119\) | −30.0238 | −2.75228 | ||||||||
\(120\) | −9.87844 | −0.901774 | ||||||||
\(121\) | 9.20537 | 0.836852 | ||||||||
\(122\) | −29.0040 | −2.62590 | ||||||||
\(123\) | −5.27129 | −0.475296 | ||||||||
\(124\) | −7.67963 | −0.689651 | ||||||||
\(125\) | −12.1688 | −1.08841 | ||||||||
\(126\) | −31.5278 | −2.80872 | ||||||||
\(127\) | 4.52126 | 0.401197 | 0.200598 | − | 0.979674i | \(-0.435711\pi\) | ||||
0.200598 | + | 0.979674i | \(0.435711\pi\) | |||||||
\(128\) | 5.11210 | 0.451850 | ||||||||
\(129\) | −2.32204 | −0.204444 | ||||||||
\(130\) | −28.4617 | −2.49626 | ||||||||
\(131\) | 5.51783 | 0.482095 | 0.241048 | − | 0.970513i | \(-0.422509\pi\) | ||||
0.241048 | + | 0.970513i | \(0.422509\pi\) | |||||||
\(132\) | −16.1731 | −1.40769 | ||||||||
\(133\) | 13.0784 | 1.13404 | ||||||||
\(134\) | −30.6553 | −2.64821 | ||||||||
\(135\) | −7.66544 | −0.659736 | ||||||||
\(136\) | −41.4759 | −3.55653 | ||||||||
\(137\) | −2.64880 | −0.226302 | −0.113151 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113151 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(138\) | −10.0696 | −0.857182 | ||||||||
\(139\) | 14.4666 | 1.22704 | 0.613521 | − | 0.789678i | \(-0.289752\pi\) | ||||
0.613521 | + | 0.789678i | \(0.289752\pi\) | |||||||
\(140\) | −43.8240 | −3.70380 | ||||||||
\(141\) | 1.38668 | 0.116779 | ||||||||
\(142\) | 15.3913 | 1.29161 | ||||||||
\(143\) | −26.7510 | −2.23703 | ||||||||
\(144\) | −20.8926 | −1.74105 | ||||||||
\(145\) | 11.7916 | 0.979241 | ||||||||
\(146\) | 13.8874 | 1.14933 | ||||||||
\(147\) | 14.1734 | 1.16901 | ||||||||
\(148\) | −1.86672 | −0.153444 | ||||||||
\(149\) | −2.95291 | −0.241912 | −0.120956 | − | 0.992658i | \(-0.538596\pi\) | ||||
−0.120956 | + | 0.992658i | \(0.538596\pi\) | |||||||
\(150\) | 3.14074 | 0.256441 | ||||||||
\(151\) | 3.33749 | 0.271601 | 0.135801 | − | 0.990736i | \(-0.456639\pi\) | ||||
0.135801 | + | 0.990736i | \(0.456639\pi\) | |||||||
\(152\) | 18.0669 | 1.46542 | ||||||||
\(153\) | −14.3468 | −1.15987 | ||||||||
\(154\) | −58.7335 | −4.73288 | ||||||||
\(155\) | −3.02265 | −0.242785 | ||||||||
\(156\) | 21.4125 | 1.71437 | ||||||||
\(157\) | −12.6950 | −1.01317 | −0.506585 | − | 0.862190i | \(-0.669093\pi\) | ||||
−0.506585 | + | 0.862190i | \(0.669093\pi\) | |||||||
\(158\) | 41.6147 | 3.31069 | ||||||||
\(159\) | −2.13269 | −0.169134 | ||||||||
\(160\) | −15.6251 | −1.23527 | ||||||||
\(161\) | −25.6455 | −2.02115 | ||||||||
\(162\) | −10.5079 | −0.825581 | ||||||||
\(163\) | 11.8635 | 0.929223 | 0.464611 | − | 0.885515i | \(-0.346194\pi\) | ||||
0.464611 | + | 0.885515i | \(0.346194\pi\) | |||||||
\(164\) | −32.3050 | −2.52260 | ||||||||
\(165\) | −6.36560 | −0.495562 | ||||||||
\(166\) | 0.0665120 | 0.00516233 | ||||||||
\(167\) | −24.0347 | −1.85986 | −0.929930 | − | 0.367736i | \(-0.880133\pi\) | ||||
−0.929930 | + | 0.367736i | \(0.880133\pi\) | |||||||
\(168\) | 26.9890 | 2.08225 | ||||||||
\(169\) | 22.4172 | 1.72440 | ||||||||
\(170\) | −28.4359 | −2.18094 | ||||||||
\(171\) | 6.24945 | 0.477908 | ||||||||
\(172\) | −14.2306 | −1.08507 | ||||||||
\(173\) | −10.4947 | −0.797899 | −0.398950 | − | 0.916973i | \(-0.630625\pi\) | ||||
−0.398950 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(174\) | −12.6495 | −0.958956 | ||||||||
\(175\) | 7.99893 | 0.604662 | ||||||||
\(176\) | −38.9211 | −2.93379 | ||||||||
\(177\) | −3.60970 | −0.271321 | ||||||||
\(178\) | 6.37370 | 0.477729 | ||||||||
\(179\) | −9.95085 | −0.743762 | −0.371881 | − | 0.928280i | \(-0.621287\pi\) | ||||
−0.371881 | + | 0.928280i | \(0.621287\pi\) | |||||||
\(180\) | −20.9411 | −1.56086 | ||||||||
\(181\) | −23.0790 | −1.71545 | −0.857723 | − | 0.514112i | \(-0.828122\pi\) | ||||
−0.857723 | + | 0.514112i | \(0.828122\pi\) | |||||||
\(182\) | 77.7606 | 5.76400 | ||||||||
\(183\) | 8.58837 | 0.634871 | ||||||||
\(184\) | −35.4276 | −2.61176 | ||||||||
\(185\) | −0.734729 | −0.0540183 | ||||||||
\(186\) | 3.24255 | 0.237755 | ||||||||
\(187\) | −26.7268 | −1.95446 | ||||||||
\(188\) | 8.49825 | 0.619799 | ||||||||
\(189\) | 20.9428 | 1.52337 | ||||||||
\(190\) | 12.3867 | 0.898623 | ||||||||
\(191\) | 23.8289 | 1.72420 | 0.862100 | − | 0.506737i | \(-0.169149\pi\) | ||||
0.862100 | + | 0.506737i | \(0.169149\pi\) | |||||||
\(192\) | 3.49295 | 0.252082 | ||||||||
\(193\) | −19.2071 | −1.38256 | −0.691279 | − | 0.722588i | \(-0.742952\pi\) | ||||
−0.691279 | + | 0.722588i | \(0.742952\pi\) | |||||||
\(194\) | −30.5121 | −2.19064 | ||||||||
\(195\) | 8.42779 | 0.603526 | ||||||||
\(196\) | 86.8618 | 6.20441 | ||||||||
\(197\) | −7.10233 | −0.506020 | −0.253010 | − | 0.967464i | \(-0.581421\pi\) | ||||
−0.253010 | + | 0.967464i | \(0.581421\pi\) | |||||||
\(198\) | −28.0656 | −1.99454 | ||||||||
\(199\) | 13.2520 | 0.939406 | 0.469703 | − | 0.882825i | \(-0.344361\pi\) | ||||
0.469703 | + | 0.882825i | \(0.344361\pi\) | |||||||
\(200\) | 11.0500 | 0.781352 | ||||||||
\(201\) | 9.07733 | 0.640266 | ||||||||
\(202\) | −26.6249 | −1.87332 | ||||||||
\(203\) | −32.2161 | −2.26112 | ||||||||
\(204\) | 21.3931 | 1.49781 | ||||||||
\(205\) | −12.7150 | −0.888056 | ||||||||
\(206\) | 21.7091 | 1.51254 | ||||||||
\(207\) | −12.2546 | −0.851756 | ||||||||
\(208\) | 51.5298 | 3.57295 | ||||||||
\(209\) | 11.6422 | 0.805307 | ||||||||
\(210\) | 18.5037 | 1.27688 | ||||||||
\(211\) | 16.1986 | 1.11516 | 0.557578 | − | 0.830125i | \(-0.311731\pi\) | ||||
0.557578 | + | 0.830125i | \(0.311731\pi\) | |||||||
\(212\) | −13.0702 | −0.897665 | ||||||||
\(213\) | −4.55751 | −0.312275 | ||||||||
\(214\) | −7.50050 | −0.512723 | ||||||||
\(215\) | −5.60105 | −0.381989 | ||||||||
\(216\) | 28.9311 | 1.96852 | ||||||||
\(217\) | 8.25821 | 0.560604 | ||||||||
\(218\) | −22.0366 | −1.49251 | ||||||||
\(219\) | −4.11220 | −0.277877 | ||||||||
\(220\) | −39.0115 | −2.63016 | ||||||||
\(221\) | 35.3852 | 2.38026 | ||||||||
\(222\) | 0.788182 | 0.0528993 | ||||||||
\(223\) | −23.5131 | −1.57456 | −0.787278 | − | 0.616599i | \(-0.788510\pi\) | ||||
−0.787278 | + | 0.616599i | \(0.788510\pi\) | |||||||
\(224\) | 42.6895 | 2.85231 | ||||||||
\(225\) | 3.82226 | 0.254817 | ||||||||
\(226\) | 52.5542 | 3.49585 | ||||||||
\(227\) | −9.57054 | −0.635219 | −0.317609 | − | 0.948222i | \(-0.602880\pi\) | ||||
−0.317609 | + | 0.948222i | \(0.602880\pi\) | |||||||
\(228\) | −9.31881 | −0.617153 | ||||||||
\(229\) | 9.91149 | 0.654970 | 0.327485 | − | 0.944856i | \(-0.393799\pi\) | ||||
0.327485 | + | 0.944856i | \(0.393799\pi\) | |||||||
\(230\) | −24.2892 | −1.60158 | ||||||||
\(231\) | 17.3916 | 1.14428 | ||||||||
\(232\) | −44.5043 | −2.92185 | ||||||||
\(233\) | 6.39402 | 0.418886 | 0.209443 | − | 0.977821i | \(-0.432835\pi\) | ||||
0.209443 | + | 0.977821i | \(0.432835\pi\) | |||||||
\(234\) | 37.1577 | 2.42907 | ||||||||
\(235\) | 3.34485 | 0.218194 | ||||||||
\(236\) | −22.1220 | −1.44002 | ||||||||
\(237\) | −12.3225 | −0.800434 | ||||||||
\(238\) | 77.6902 | 5.03591 | ||||||||
\(239\) | −19.3926 | −1.25440 | −0.627201 | − | 0.778857i | \(-0.715800\pi\) | ||||
−0.627201 | + | 0.778857i | \(0.715800\pi\) | |||||||
\(240\) | 12.2619 | 0.791502 | ||||||||
\(241\) | −10.5814 | −0.681608 | −0.340804 | − | 0.940134i | \(-0.610699\pi\) | ||||
−0.340804 | + | 0.940134i | \(0.610699\pi\) | |||||||
\(242\) | −23.8200 | −1.53121 | ||||||||
\(243\) | 15.5539 | 0.997785 | ||||||||
\(244\) | 52.6337 | 3.36953 | ||||||||
\(245\) | 34.1881 | 2.18420 | ||||||||
\(246\) | 13.6401 | 0.869660 | ||||||||
\(247\) | −15.4138 | −0.980754 | ||||||||
\(248\) | 11.4082 | 0.724419 | ||||||||
\(249\) | −0.0196949 | −0.00124811 | ||||||||
\(250\) | 31.4883 | 1.99149 | ||||||||
\(251\) | −16.8151 | −1.06136 | −0.530681 | − | 0.847572i | \(-0.678064\pi\) | ||||
−0.530681 | + | 0.847572i | \(0.678064\pi\) | |||||||
\(252\) | 57.2136 | 3.60412 | ||||||||
\(253\) | −22.8293 | −1.43527 | ||||||||
\(254\) | −11.6993 | −0.734079 | ||||||||
\(255\) | 8.42016 | 0.527291 | ||||||||
\(256\) | −22.3455 | −1.39660 | ||||||||
\(257\) | −8.44417 | −0.526733 | −0.263366 | − | 0.964696i | \(-0.584833\pi\) | ||||
−0.263366 | + | 0.964696i | \(0.584833\pi\) | |||||||
\(258\) | 6.00855 | 0.374076 | ||||||||
\(259\) | 2.00736 | 0.124731 | ||||||||
\(260\) | 51.6496 | 3.20317 | ||||||||
\(261\) | −15.3943 | −0.952886 | ||||||||
\(262\) | −14.2780 | −0.882101 | ||||||||
\(263\) | 4.55204 | 0.280691 | 0.140345 | − | 0.990103i | \(-0.455179\pi\) | ||||
0.140345 | + | 0.990103i | \(0.455179\pi\) | |||||||
\(264\) | 24.0253 | 1.47865 | ||||||||
\(265\) | −5.14433 | −0.316014 | ||||||||
\(266\) | −33.8418 | −2.07497 | ||||||||
\(267\) | −1.88732 | −0.115502 | ||||||||
\(268\) | 55.6303 | 3.39816 | ||||||||
\(269\) | −31.9921 | −1.95059 | −0.975297 | − | 0.220898i | \(-0.929101\pi\) | ||||
−0.975297 | + | 0.220898i | \(0.929101\pi\) | |||||||
\(270\) | 19.8352 | 1.20713 | ||||||||
\(271\) | −19.1585 | −1.16380 | −0.581899 | − | 0.813261i | \(-0.697690\pi\) | ||||
−0.581899 | + | 0.813261i | \(0.697690\pi\) | |||||||
\(272\) | 51.4832 | 3.12163 | ||||||||
\(273\) | −23.0257 | −1.39358 | ||||||||
\(274\) | 6.85408 | 0.414070 | ||||||||
\(275\) | 7.12054 | 0.429385 | ||||||||
\(276\) | 18.2734 | 1.09993 | ||||||||
\(277\) | −4.98781 | −0.299688 | −0.149844 | − | 0.988710i | \(-0.547877\pi\) | ||||
−0.149844 | + | 0.988710i | \(0.547877\pi\) | |||||||
\(278\) | −37.4341 | −2.24515 | ||||||||
\(279\) | 3.94616 | 0.236250 | ||||||||
\(280\) | 65.1010 | 3.89053 | ||||||||
\(281\) | 24.3252 | 1.45112 | 0.725560 | − | 0.688159i | \(-0.241581\pi\) | ||||
0.725560 | + | 0.688159i | \(0.241581\pi\) | |||||||
\(282\) | −3.58820 | −0.213674 | ||||||||
\(283\) | 0.750252 | 0.0445979 | 0.0222989 | − | 0.999751i | \(-0.492901\pi\) | ||||
0.0222989 | + | 0.999751i | \(0.492901\pi\) | |||||||
\(284\) | −27.9306 | −1.65738 | ||||||||
\(285\) | −3.66781 | −0.217263 | ||||||||
\(286\) | 69.2215 | 4.09315 | ||||||||
\(287\) | 34.7389 | 2.05057 | ||||||||
\(288\) | 20.3990 | 1.20202 | ||||||||
\(289\) | 18.3531 | 1.07960 | ||||||||
\(290\) | −30.5122 | −1.79174 | ||||||||
\(291\) | 9.03493 | 0.529637 | ||||||||
\(292\) | −25.2016 | −1.47481 | ||||||||
\(293\) | 13.9289 | 0.813737 | 0.406869 | − | 0.913487i | \(-0.366621\pi\) | ||||
0.406869 | + | 0.913487i | \(0.366621\pi\) | |||||||
\(294\) | −36.6754 | −2.13895 | ||||||||
\(295\) | −8.70705 | −0.506944 | ||||||||
\(296\) | 2.77304 | 0.161179 | ||||||||
\(297\) | 18.6431 | 1.08178 | ||||||||
\(298\) | 7.64100 | 0.442631 | ||||||||
\(299\) | 30.2250 | 1.74796 | ||||||||
\(300\) | −5.69953 | −0.329062 | ||||||||
\(301\) | 15.3027 | 0.882034 | ||||||||
\(302\) | −8.63615 | −0.496954 | ||||||||
\(303\) | 7.88389 | 0.452918 | ||||||||
\(304\) | −22.4260 | −1.28622 | ||||||||
\(305\) | 20.7163 | 1.18621 | ||||||||
\(306\) | 37.1240 | 2.12224 | ||||||||
\(307\) | −4.03565 | −0.230327 | −0.115163 | − | 0.993347i | \(-0.536739\pi\) | ||||
−0.115163 | + | 0.993347i | \(0.536739\pi\) | |||||||
\(308\) | 106.584 | 6.07318 | ||||||||
\(309\) | −6.42827 | −0.365692 | ||||||||
\(310\) | 7.82145 | 0.444229 | ||||||||
\(311\) | −16.1657 | −0.916671 | −0.458336 | − | 0.888779i | \(-0.651554\pi\) | ||||
−0.458336 | + | 0.888779i | \(0.651554\pi\) | |||||||
\(312\) | −31.8084 | −1.80080 | ||||||||
\(313\) | −11.4098 | −0.644922 | −0.322461 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322461 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(314\) | 32.8498 | 1.85382 | ||||||||
\(315\) | 22.5189 | 1.26879 | ||||||||
\(316\) | −75.5185 | −4.24825 | ||||||||
\(317\) | −21.5803 | −1.21207 | −0.606036 | − | 0.795437i | \(-0.707241\pi\) | ||||
−0.606036 | + | 0.795437i | \(0.707241\pi\) | |||||||
\(318\) | 5.51860 | 0.309468 | ||||||||
\(319\) | −28.6783 | −1.60568 | ||||||||
\(320\) | 8.42545 | 0.470997 | ||||||||
\(321\) | 2.22097 | 0.123963 | ||||||||
\(322\) | 66.3608 | 3.69814 | ||||||||
\(323\) | −15.3998 | −0.856868 | ||||||||
\(324\) | 19.0688 | 1.05938 | ||||||||
\(325\) | −9.42729 | −0.522932 | ||||||||
\(326\) | −30.6982 | −1.70022 | ||||||||
\(327\) | 6.52526 | 0.360848 | ||||||||
\(328\) | 47.9895 | 2.64978 | ||||||||
\(329\) | −9.13851 | −0.503822 | ||||||||
\(330\) | 16.4717 | 0.906740 | ||||||||
\(331\) | 19.4107 | 1.06691 | 0.533453 | − | 0.845830i | \(-0.320894\pi\) | ||||
0.533453 | + | 0.845830i | \(0.320894\pi\) | |||||||
\(332\) | −0.120700 | −0.00662426 | ||||||||
\(333\) | 0.959212 | 0.0525645 | ||||||||
\(334\) | 62.1926 | 3.40303 | ||||||||
\(335\) | 21.8957 | 1.19629 | ||||||||
\(336\) | −33.5009 | −1.82762 | ||||||||
\(337\) | 14.9979 | 0.816987 | 0.408494 | − | 0.912761i | \(-0.366054\pi\) | ||||
0.408494 | + | 0.912761i | \(0.366054\pi\) | |||||||
\(338\) | −58.0073 | −3.15518 | ||||||||
\(339\) | −15.5618 | −0.845202 | ||||||||
\(340\) | 51.6028 | 2.79856 | ||||||||
\(341\) | 7.35135 | 0.398098 | ||||||||
\(342\) | −16.1712 | −0.874438 | ||||||||
\(343\) | −58.0591 | −3.13490 | ||||||||
\(344\) | 21.1397 | 1.13978 | ||||||||
\(345\) | 7.19226 | 0.387218 | ||||||||
\(346\) | 27.1563 | 1.45993 | ||||||||
\(347\) | −21.1969 | −1.13791 | −0.568955 | − | 0.822369i | \(-0.692652\pi\) | ||||
−0.568955 | + | 0.822369i | \(0.692652\pi\) | |||||||
\(348\) | 22.9551 | 1.23052 | ||||||||
\(349\) | −23.6881 | −1.26800 | −0.633998 | − | 0.773335i | \(-0.718587\pi\) | ||||
−0.633998 | + | 0.773335i | \(0.718587\pi\) | |||||||
\(350\) | −20.6982 | −1.10636 | ||||||||
\(351\) | −24.6826 | −1.31746 | ||||||||
\(352\) | 38.0016 | 2.02549 | ||||||||
\(353\) | −11.5168 | −0.612976 | −0.306488 | − | 0.951875i | \(-0.599154\pi\) | ||||
−0.306488 | + | 0.951875i | \(0.599154\pi\) | |||||||
\(354\) | 9.34052 | 0.496443 | ||||||||
\(355\) | −10.9933 | −0.583463 | ||||||||
\(356\) | −11.5664 | −0.613018 | ||||||||
\(357\) | −23.0048 | −1.21754 | ||||||||
\(358\) | 25.7490 | 1.36088 | ||||||||
\(359\) | −8.13803 | −0.429509 | −0.214754 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214754 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(360\) | 31.1083 | 1.63955 | ||||||||
\(361\) | −12.2919 | −0.646940 | ||||||||
\(362\) | 59.7195 | 3.13879 | ||||||||
\(363\) | 7.05333 | 0.370204 | ||||||||
\(364\) | −141.113 | −7.39631 | ||||||||
\(365\) | −9.91916 | −0.519192 | ||||||||
\(366\) | −22.2234 | −1.16164 | ||||||||
\(367\) | −3.28415 | −0.171431 | −0.0857156 | − | 0.996320i | \(-0.527318\pi\) | ||||
−0.0857156 | + | 0.996320i | \(0.527318\pi\) | |||||||
\(368\) | 43.9755 | 2.29238 | ||||||||
\(369\) | 16.5999 | 0.864155 | ||||||||
\(370\) | 1.90120 | 0.0988385 | ||||||||
\(371\) | 14.0549 | 0.729694 | ||||||||
\(372\) | −5.88428 | −0.305086 | ||||||||
\(373\) | 20.7088 | 1.07226 | 0.536131 | − | 0.844135i | \(-0.319885\pi\) | ||||
0.536131 | + | 0.844135i | \(0.319885\pi\) | |||||||
\(374\) | 69.1588 | 3.57612 | ||||||||
\(375\) | −9.32399 | −0.481489 | ||||||||
\(376\) | −12.6242 | −0.651045 | ||||||||
\(377\) | 37.9689 | 1.95550 | ||||||||
\(378\) | −54.1921 | −2.78734 | ||||||||
\(379\) | −6.08202 | −0.312412 | −0.156206 | − | 0.987724i | \(-0.549926\pi\) | ||||
−0.156206 | + | 0.987724i | \(0.549926\pi\) | |||||||
\(380\) | −22.4782 | −1.15311 | ||||||||
\(381\) | 3.46428 | 0.177480 | ||||||||
\(382\) | −61.6602 | −3.15481 | ||||||||
\(383\) | −31.1342 | −1.59088 | −0.795441 | − | 0.606031i | \(-0.792761\pi\) | ||||
−0.795441 | + | 0.606031i | \(0.792761\pi\) | |||||||
\(384\) | 3.91699 | 0.199888 | ||||||||
\(385\) | 41.9507 | 2.13800 | ||||||||
\(386\) | 49.7006 | 2.52970 | ||||||||
\(387\) | 7.31235 | 0.371708 | ||||||||
\(388\) | 55.3705 | 2.81101 | ||||||||
\(389\) | 13.6895 | 0.694087 | 0.347044 | − | 0.937849i | \(-0.387186\pi\) | ||||
0.347044 | + | 0.937849i | \(0.387186\pi\) | |||||||
\(390\) | −21.8079 | −1.10429 | ||||||||
\(391\) | 30.1977 | 1.52716 | ||||||||
\(392\) | −129.034 | −6.51720 | ||||||||
\(393\) | 4.22787 | 0.213268 | ||||||||
\(394\) | 18.3781 | 0.925876 | ||||||||
\(395\) | −29.7235 | −1.49555 | ||||||||
\(396\) | 50.9308 | 2.55937 | ||||||||
\(397\) | 12.8676 | 0.645805 | 0.322903 | − | 0.946432i | \(-0.395341\pi\) | ||||
0.322903 | + | 0.946432i | \(0.395341\pi\) | |||||||
\(398\) | −34.2910 | −1.71885 | ||||||||
\(399\) | 10.0209 | 0.501672 | ||||||||
\(400\) | −13.7161 | −0.685806 | ||||||||
\(401\) | −22.9024 | −1.14369 | −0.571846 | − | 0.820361i | \(-0.693772\pi\) | ||||
−0.571846 | + | 0.820361i | \(0.693772\pi\) | |||||||
\(402\) | −23.4887 | −1.17151 | ||||||||
\(403\) | −9.73288 | −0.484829 | ||||||||
\(404\) | 48.3163 | 2.40383 | ||||||||
\(405\) | 7.50534 | 0.372943 | ||||||||
\(406\) | 83.3628 | 4.13723 | ||||||||
\(407\) | 1.78693 | 0.0885747 | ||||||||
\(408\) | −31.7796 | −1.57333 | ||||||||
\(409\) | 4.74393 | 0.234572 | 0.117286 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117286 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(410\) | 32.9016 | 1.62490 | ||||||||
\(411\) | −2.02956 | −0.100111 | ||||||||
\(412\) | −39.3956 | −1.94088 | ||||||||
\(413\) | 23.7887 | 1.17056 | ||||||||
\(414\) | 31.7103 | 1.55848 | ||||||||
\(415\) | −0.0475065 | −0.00233200 | ||||||||
\(416\) | −50.3125 | −2.46677 | ||||||||
\(417\) | 11.0846 | 0.542815 | ||||||||
\(418\) | −30.1255 | −1.47349 | ||||||||
\(419\) | −14.7035 | −0.718314 | −0.359157 | − | 0.933277i | \(-0.616936\pi\) | ||||
−0.359157 | + | 0.933277i | \(0.616936\pi\) | |||||||
\(420\) | −33.5788 | −1.63848 | ||||||||
\(421\) | −24.5200 | −1.19503 | −0.597517 | − | 0.801857i | \(-0.703846\pi\) | ||||
−0.597517 | + | 0.801857i | \(0.703846\pi\) | |||||||
\(422\) | −41.9157 | −2.04042 | ||||||||
\(423\) | −4.36681 | −0.212321 | ||||||||
\(424\) | 19.4159 | 0.942920 | ||||||||
\(425\) | −9.41876 | −0.456877 | ||||||||
\(426\) | 11.7931 | 0.571377 | ||||||||
\(427\) | −56.5992 | −2.73903 | ||||||||
\(428\) | 13.6112 | 0.657922 | ||||||||
\(429\) | −20.4972 | −0.989612 | ||||||||
\(430\) | 14.4934 | 0.698933 | ||||||||
\(431\) | 26.4517 | 1.27414 | 0.637068 | − | 0.770808i | \(-0.280147\pi\) | ||||
0.637068 | + | 0.770808i | \(0.280147\pi\) | |||||||
\(432\) | −35.9116 | −1.72780 | ||||||||
\(433\) | −22.5495 | −1.08366 | −0.541829 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541829 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(434\) | −21.3691 | −1.02575 | ||||||||
\(435\) | 9.03497 | 0.433193 | ||||||||
\(436\) | 39.9900 | 1.91517 | ||||||||
\(437\) | −13.1541 | −0.629245 | ||||||||
\(438\) | 10.6408 | 0.508437 | ||||||||
\(439\) | −23.6058 | −1.12664 | −0.563321 | − | 0.826238i | \(-0.690477\pi\) | ||||
−0.563321 | + | 0.826238i | \(0.690477\pi\) | |||||||
\(440\) | 57.9520 | 2.76275 | ||||||||
\(441\) | −44.6337 | −2.12542 | ||||||||
\(442\) | −91.5633 | −4.35522 | ||||||||
\(443\) | −33.9437 | −1.61271 | −0.806356 | − | 0.591430i | \(-0.798563\pi\) | ||||
−0.806356 | + | 0.591430i | \(0.798563\pi\) | |||||||
\(444\) | −1.43032 | −0.0678799 | ||||||||
\(445\) | −4.55245 | −0.215807 | ||||||||
\(446\) | 60.8430 | 2.88100 | ||||||||
\(447\) | −2.26258 | −0.107016 | ||||||||
\(448\) | −23.0193 | −1.08756 | ||||||||
\(449\) | 15.4000 | 0.726770 | 0.363385 | − | 0.931639i | \(-0.381621\pi\) | ||||
0.363385 | + | 0.931639i | \(0.381621\pi\) | |||||||
\(450\) | −9.89055 | −0.466245 | ||||||||
\(451\) | 30.9241 | 1.45616 | ||||||||
\(452\) | −95.3704 | −4.48585 | ||||||||
\(453\) | 2.55725 | 0.120150 | ||||||||
\(454\) | 24.7649 | 1.16227 | ||||||||
\(455\) | −55.5409 | −2.60380 | ||||||||
\(456\) | 13.8432 | 0.648267 | ||||||||
\(457\) | −3.99425 | −0.186843 | −0.0934215 | − | 0.995627i | \(-0.529780\pi\) | ||||
−0.0934215 | + | 0.995627i | \(0.529780\pi\) | |||||||
\(458\) | −25.6471 | −1.19841 | ||||||||
\(459\) | −24.6603 | −1.15104 | ||||||||
\(460\) | 44.0777 | 2.05513 | ||||||||
\(461\) | −29.3465 | −1.36680 | −0.683401 | − | 0.730044i | \(-0.739500\pi\) | ||||
−0.683401 | + | 0.730044i | \(0.739500\pi\) | |||||||
\(462\) | −45.0027 | −2.09371 | ||||||||
\(463\) | 42.1482 | 1.95879 | 0.979396 | − | 0.201948i | \(-0.0647273\pi\) | ||||
0.979396 | + | 0.201948i | \(0.0647273\pi\) | |||||||
\(464\) | 55.2423 | 2.56456 | ||||||||
\(465\) | −2.31601 | −0.107402 | ||||||||
\(466\) | −16.5453 | −0.766445 | ||||||||
\(467\) | −34.7270 | −1.60697 | −0.803487 | − | 0.595323i | \(-0.797024\pi\) | ||||
−0.803487 | + | 0.595323i | \(0.797024\pi\) | |||||||
\(468\) | −67.4302 | −3.11696 | ||||||||
\(469\) | −59.8215 | −2.76230 | ||||||||
\(470\) | −8.65519 | −0.399234 | ||||||||
\(471\) | −9.72715 | −0.448203 | ||||||||
\(472\) | 32.8624 | 1.51262 | ||||||||
\(473\) | 13.6223 | 0.626353 | ||||||||
\(474\) | 31.8860 | 1.46457 | ||||||||
\(475\) | 4.10280 | 0.188249 | ||||||||
\(476\) | −140.985 | −6.46203 | ||||||||
\(477\) | 6.71609 | 0.307509 | ||||||||
\(478\) | 50.1806 | 2.29521 | ||||||||
\(479\) | −1.66170 | −0.0759252 | −0.0379626 | − | 0.999279i | \(-0.512087\pi\) | ||||
−0.0379626 | + | 0.999279i | \(0.512087\pi\) | |||||||
\(480\) | −11.9722 | −0.546455 | ||||||||
\(481\) | −2.36582 | −0.107872 | ||||||||
\(482\) | 27.3806 | 1.24715 | ||||||||
\(483\) | −19.6501 | −0.894110 | ||||||||
\(484\) | 43.2262 | 1.96483 | ||||||||
\(485\) | 21.7934 | 0.989587 | ||||||||
\(486\) | −40.2476 | −1.82567 | ||||||||
\(487\) | −6.63744 | −0.300771 | −0.150385 | − | 0.988627i | \(-0.548051\pi\) | ||||
−0.150385 | + | 0.988627i | \(0.548051\pi\) | |||||||
\(488\) | −78.1880 | −3.53940 | ||||||||
\(489\) | 9.09005 | 0.411066 | ||||||||
\(490\) | −88.4659 | −3.99648 | ||||||||
\(491\) | −17.7654 | −0.801743 | −0.400871 | − | 0.916134i | \(-0.631293\pi\) | ||||
−0.400871 | + | 0.916134i | \(0.631293\pi\) | |||||||
\(492\) | −24.7527 | −1.11594 | ||||||||
\(493\) | 37.9345 | 1.70848 | ||||||||
\(494\) | 39.8849 | 1.79451 | ||||||||
\(495\) | 20.0460 | 0.901000 | ||||||||
\(496\) | −14.1607 | −0.635835 | ||||||||
\(497\) | 30.0349 | 1.34725 | ||||||||
\(498\) | 0.0509628 | 0.00228370 | ||||||||
\(499\) | −13.1513 | −0.588734 | −0.294367 | − | 0.955692i | \(-0.595109\pi\) | ||||
−0.294367 | + | 0.955692i | \(0.595109\pi\) | |||||||
\(500\) | −57.1420 | −2.55547 | ||||||||
\(501\) | −18.4158 | −0.822759 | ||||||||
\(502\) | 43.5111 | 1.94200 | ||||||||
\(503\) | −12.7272 | −0.567477 | −0.283739 | − | 0.958902i | \(-0.591575\pi\) | ||||
−0.283739 | + | 0.958902i | \(0.591575\pi\) | |||||||
\(504\) | −84.9914 | −3.78582 | ||||||||
\(505\) | 19.0170 | 0.846243 | ||||||||
\(506\) | 59.0735 | 2.62614 | ||||||||
\(507\) | 17.1765 | 0.762836 | ||||||||
\(508\) | 21.2308 | 0.941963 | ||||||||
\(509\) | 18.4125 | 0.816118 | 0.408059 | − | 0.912955i | \(-0.366206\pi\) | ||||
0.408059 | + | 0.912955i | \(0.366206\pi\) | |||||||
\(510\) | −21.7881 | −0.964795 | ||||||||
\(511\) | 27.1003 | 1.19885 | ||||||||
\(512\) | 47.5975 | 2.10353 | ||||||||
\(513\) | 10.7420 | 0.474270 | ||||||||
\(514\) | 21.8503 | 0.963774 | ||||||||
\(515\) | −15.5058 | −0.683268 | ||||||||
\(516\) | −10.9037 | −0.480011 | ||||||||
\(517\) | −8.13498 | −0.357776 | ||||||||
\(518\) | −5.19429 | −0.228224 | ||||||||
\(519\) | −8.04126 | −0.352972 | ||||||||
\(520\) | −76.7260 | −3.36466 | ||||||||
\(521\) | 39.5624 | 1.73326 | 0.866630 | − | 0.498952i | \(-0.166282\pi\) | ||||
0.866630 | + | 0.498952i | \(0.166282\pi\) | |||||||
\(522\) | 39.8347 | 1.74352 | ||||||||
\(523\) | −30.7335 | −1.34388 | −0.671941 | − | 0.740605i | \(-0.734539\pi\) | ||||
−0.671941 | + | 0.740605i | \(0.734539\pi\) | |||||||
\(524\) | 25.9104 | 1.13190 | ||||||||
\(525\) | 6.12893 | 0.267488 | ||||||||
\(526\) | −11.7789 | −0.513586 | ||||||||
\(527\) | −9.72407 | −0.423587 | ||||||||
\(528\) | −29.8221 | −1.29784 | ||||||||
\(529\) | 2.79400 | 0.121478 | ||||||||
\(530\) | 13.3116 | 0.578217 | ||||||||
\(531\) | 11.3673 | 0.493300 | ||||||||
\(532\) | 61.4129 | 2.66259 | ||||||||
\(533\) | −40.9422 | −1.77340 | ||||||||
\(534\) | 4.88365 | 0.211336 | ||||||||
\(535\) | 5.35727 | 0.231615 | ||||||||
\(536\) | −82.6394 | −3.56948 | ||||||||
\(537\) | −7.62453 | −0.329023 | ||||||||
\(538\) | 82.7834 | 3.56904 | ||||||||
\(539\) | −83.1487 | −3.58147 | ||||||||
\(540\) | −35.9951 | −1.54898 | ||||||||
\(541\) | 3.56507 | 0.153274 | 0.0766371 | − | 0.997059i | \(-0.475582\pi\) | ||||
0.0766371 | + | 0.997059i | \(0.475582\pi\) | |||||||
\(542\) | 49.5750 | 2.12943 | ||||||||
\(543\) | −17.6835 | −0.758874 | ||||||||
\(544\) | −50.2670 | −2.15518 | ||||||||
\(545\) | 15.7398 | 0.674217 | ||||||||
\(546\) | 59.5817 | 2.54986 | ||||||||
\(547\) | 19.7788 | 0.845678 | 0.422839 | − | 0.906205i | \(-0.361034\pi\) | ||||
0.422839 | + | 0.906205i | \(0.361034\pi\) | |||||||
\(548\) | −12.4381 | −0.531331 | ||||||||
\(549\) | −27.0457 | −1.15428 | ||||||||
\(550\) | −18.4252 | −0.785655 | ||||||||
\(551\) | −16.5242 | −0.703956 | ||||||||
\(552\) | −27.1453 | −1.15538 | ||||||||
\(553\) | 81.2081 | 3.45332 | ||||||||
\(554\) | 12.9065 | 0.548346 | ||||||||
\(555\) | −0.562963 | −0.0238964 | ||||||||
\(556\) | 67.9318 | 2.88095 | ||||||||
\(557\) | −19.7703 | −0.837694 | −0.418847 | − | 0.908057i | \(-0.637566\pi\) | ||||
−0.418847 | + | 0.908057i | \(0.637566\pi\) | |||||||
\(558\) | −10.2112 | −0.432273 | ||||||||
\(559\) | −18.0353 | −0.762813 | ||||||||
\(560\) | −80.8085 | −3.41478 | ||||||||
\(561\) | −20.4786 | −0.864607 | ||||||||
\(562\) | −62.9443 | −2.65515 | ||||||||
\(563\) | −5.67918 | −0.239349 | −0.119674 | − | 0.992813i | \(-0.538185\pi\) | ||||
−0.119674 | + | 0.992813i | \(0.538185\pi\) | |||||||
\(564\) | 6.51152 | 0.274184 | ||||||||
\(565\) | −37.5371 | −1.57920 | ||||||||
\(566\) | −1.94137 | −0.0816017 | ||||||||
\(567\) | −20.5055 | −0.861148 | ||||||||
\(568\) | 41.4913 | 1.74093 | ||||||||
\(569\) | 18.0978 | 0.758701 | 0.379350 | − | 0.925253i | \(-0.376147\pi\) | ||||
0.379350 | + | 0.925253i | \(0.376147\pi\) | |||||||
\(570\) | 9.49090 | 0.397530 | ||||||||
\(571\) | 43.1172 | 1.80440 | 0.902200 | − | 0.431318i | \(-0.141951\pi\) | ||||
0.902200 | + | 0.431318i | \(0.141951\pi\) | |||||||
\(572\) | −125.617 | −5.25229 | ||||||||
\(573\) | 18.2582 | 0.762746 | ||||||||
\(574\) | −89.8910 | −3.75198 | ||||||||
\(575\) | −8.04524 | −0.335510 | ||||||||
\(576\) | −10.9997 | −0.458321 | ||||||||
\(577\) | 21.7848 | 0.906914 | 0.453457 | − | 0.891278i | \(-0.350191\pi\) | ||||
0.453457 | + | 0.891278i | \(0.350191\pi\) | |||||||
\(578\) | −47.4909 | −1.97536 | ||||||||
\(579\) | −14.7168 | −0.611611 | ||||||||
\(580\) | 55.3707 | 2.29914 | ||||||||
\(581\) | 0.129793 | 0.00538473 | ||||||||
\(582\) | −23.3789 | −0.969088 | ||||||||
\(583\) | 12.5115 | 0.518173 | ||||||||
\(584\) | 37.4372 | 1.54916 | ||||||||
\(585\) | −26.5400 | −1.09730 | ||||||||
\(586\) | −36.0428 | −1.48891 | ||||||||
\(587\) | 22.6747 | 0.935886 | 0.467943 | − | 0.883759i | \(-0.344995\pi\) | ||||
0.467943 | + | 0.883759i | \(0.344995\pi\) | |||||||
\(588\) | 66.5551 | 2.74469 | ||||||||
\(589\) | 4.23580 | 0.174533 | ||||||||
\(590\) | 22.5305 | 0.927567 | ||||||||
\(591\) | −5.44194 | −0.223851 | ||||||||
\(592\) | −3.44211 | −0.141470 | ||||||||
\(593\) | −18.9771 | −0.779296 | −0.389648 | − | 0.920964i | \(-0.627403\pi\) | ||||
−0.389648 | + | 0.920964i | \(0.627403\pi\) | |||||||
\(594\) | −48.2411 | −1.97936 | ||||||||
\(595\) | −55.4906 | −2.27489 | ||||||||
\(596\) | −13.8662 | −0.567980 | ||||||||
\(597\) | 10.1539 | 0.415571 | ||||||||
\(598\) | −78.2108 | −3.19828 | ||||||||
\(599\) | −25.6169 | −1.04668 | −0.523339 | − | 0.852125i | \(-0.675314\pi\) | ||||
−0.523339 | + | 0.852125i | \(0.675314\pi\) | |||||||
\(600\) | 8.46671 | 0.345652 | ||||||||
\(601\) | 12.9796 | 0.529449 | 0.264724 | − | 0.964324i | \(-0.414719\pi\) | ||||
0.264724 | + | 0.964324i | \(0.414719\pi\) | |||||||
\(602\) | −39.5976 | −1.61388 | ||||||||
\(603\) | −28.5855 | −1.16409 | ||||||||
\(604\) | 15.6721 | 0.637687 | ||||||||
\(605\) | 17.0135 | 0.691698 | ||||||||
\(606\) | −20.4005 | −0.828713 | ||||||||
\(607\) | 13.2246 | 0.536768 | 0.268384 | − | 0.963312i | \(-0.413510\pi\) | ||||
0.268384 | + | 0.963312i | \(0.413510\pi\) | |||||||
\(608\) | 21.8962 | 0.888010 | ||||||||
\(609\) | −24.6846 | −1.00027 | ||||||||
\(610\) | −53.6057 | −2.17043 | ||||||||
\(611\) | 10.7704 | 0.435723 | ||||||||
\(612\) | −67.3692 | −2.72324 | ||||||||
\(613\) | 42.9124 | 1.73322 | 0.866608 | − | 0.498989i | \(-0.166295\pi\) | ||||
0.866608 | + | 0.498989i | \(0.166295\pi\) | |||||||
\(614\) | 10.4427 | 0.421433 | ||||||||
\(615\) | −9.74250 | −0.392855 | ||||||||
\(616\) | −158.332 | −6.37936 | ||||||||
\(617\) | −28.5801 | −1.15059 | −0.575295 | − | 0.817946i | \(-0.695113\pi\) | ||||
−0.575295 | + | 0.817946i | \(0.695113\pi\) | |||||||
\(618\) | 16.6339 | 0.669114 | ||||||||
\(619\) | 45.8167 | 1.84153 | 0.920764 | − | 0.390120i | \(-0.127567\pi\) | ||||
0.920764 | + | 0.390120i | \(0.127567\pi\) | |||||||
\(620\) | −14.1936 | −0.570030 | ||||||||
\(621\) | −21.0641 | −0.845273 | ||||||||
\(622\) | 41.8306 | 1.67725 | ||||||||
\(623\) | 12.4378 | 0.498310 | ||||||||
\(624\) | 39.4831 | 1.58059 | ||||||||
\(625\) | −14.5702 | −0.582809 | ||||||||
\(626\) | 29.5243 | 1.18003 | ||||||||
\(627\) | 8.92046 | 0.356249 | ||||||||
\(628\) | −59.6127 | −2.37881 | ||||||||
\(629\) | −2.36367 | −0.0942459 | ||||||||
\(630\) | −58.2702 | −2.32154 | ||||||||
\(631\) | −24.9912 | −0.994883 | −0.497441 | − | 0.867498i | \(-0.665727\pi\) | ||||
−0.497441 | + | 0.867498i | \(0.665727\pi\) | |||||||
\(632\) | 112.184 | 4.46242 | ||||||||
\(633\) | 12.4117 | 0.493319 | ||||||||
\(634\) | 55.8416 | 2.21775 | ||||||||
\(635\) | 8.35628 | 0.331609 | ||||||||
\(636\) | −10.0146 | −0.397106 | ||||||||
\(637\) | 110.085 | 4.36174 | ||||||||
\(638\) | 74.2085 | 2.93794 | ||||||||
\(639\) | 14.3521 | 0.567760 | ||||||||
\(640\) | 9.44828 | 0.373476 | ||||||||
\(641\) | −13.6363 | −0.538600 | −0.269300 | − | 0.963056i | \(-0.586792\pi\) | ||||
−0.269300 | + | 0.963056i | \(0.586792\pi\) | |||||||
\(642\) | −5.74702 | −0.226817 | ||||||||
\(643\) | 19.4148 | 0.765646 | 0.382823 | − | 0.923822i | \(-0.374952\pi\) | ||||
0.382823 | + | 0.923822i | \(0.374952\pi\) | |||||||
\(644\) | −120.425 | −4.74542 | ||||||||
\(645\) | −4.29163 | −0.168983 | ||||||||
\(646\) | 39.8488 | 1.56783 | ||||||||
\(647\) | −33.1636 | −1.30380 | −0.651898 | − | 0.758307i | \(-0.726027\pi\) | ||||
−0.651898 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(648\) | −28.3269 | −1.11279 | ||||||||
\(649\) | 21.1764 | 0.831245 | ||||||||
\(650\) | 24.3942 | 0.956820 | ||||||||
\(651\) | 6.32760 | 0.247998 | ||||||||
\(652\) | 55.7083 | 2.18171 | ||||||||
\(653\) | 32.6631 | 1.27821 | 0.639104 | − | 0.769120i | \(-0.279305\pi\) | ||||
0.639104 | + | 0.769120i | \(0.279305\pi\) | |||||||
\(654\) | −16.8849 | −0.660251 | ||||||||
\(655\) | 10.1982 | 0.398475 | ||||||||
\(656\) | −59.5683 | −2.32575 | ||||||||
\(657\) | 12.9498 | 0.505219 | ||||||||
\(658\) | 23.6470 | 0.921855 | ||||||||
\(659\) | 29.2818 | 1.14066 | 0.570329 | − | 0.821417i | \(-0.306816\pi\) | ||||
0.570329 | + | 0.821417i | \(0.306816\pi\) | |||||||
\(660\) | −29.8914 | −1.16352 | ||||||||
\(661\) | −12.1162 | −0.471264 | −0.235632 | − | 0.971842i | \(-0.575716\pi\) | ||||
−0.235632 | + | 0.971842i | \(0.575716\pi\) | |||||||
\(662\) | −50.2274 | −1.95214 | ||||||||
\(663\) | 27.1128 | 1.05297 | ||||||||
\(664\) | 0.179301 | 0.00695822 | ||||||||
\(665\) | 24.1717 | 0.937337 | ||||||||
\(666\) | −2.48207 | −0.0961784 | ||||||||
\(667\) | 32.4026 | 1.25463 | ||||||||
\(668\) | −112.861 | −4.36673 | ||||||||
\(669\) | −18.0162 | −0.696547 | ||||||||
\(670\) | −56.6577 | −2.18888 | ||||||||
\(671\) | −50.3838 | −1.94505 | ||||||||
\(672\) | 32.7095 | 1.26180 | ||||||||
\(673\) | −19.7654 | −0.761901 | −0.380950 | − | 0.924596i | \(-0.624403\pi\) | ||||
−0.380950 | + | 0.924596i | \(0.624403\pi\) | |||||||
\(674\) | −38.8088 | −1.49486 | ||||||||
\(675\) | 6.56997 | 0.252878 | ||||||||
\(676\) | 105.266 | 4.04870 | ||||||||
\(677\) | −5.95906 | −0.229025 | −0.114513 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114513 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(678\) | 40.2680 | 1.54648 | ||||||||
\(679\) | −59.5421 | −2.28501 | ||||||||
\(680\) | −76.6566 | −2.93964 | ||||||||
\(681\) | −7.33313 | −0.281006 | ||||||||
\(682\) | −19.0225 | −0.728409 | ||||||||
\(683\) | −29.3246 | −1.12208 | −0.561038 | − | 0.827790i | \(-0.689598\pi\) | ||||
−0.561038 | + | 0.827790i | \(0.689598\pi\) | |||||||
\(684\) | 29.3460 | 1.12207 | ||||||||
\(685\) | −4.89556 | −0.187050 | ||||||||
\(686\) | 150.235 | 5.73599 | ||||||||
\(687\) | 7.59437 | 0.289743 | ||||||||
\(688\) | −26.2402 | −1.00040 | ||||||||
\(689\) | −16.5647 | −0.631064 | ||||||||
\(690\) | −18.6108 | −0.708502 | ||||||||
\(691\) | 14.6338 | 0.556697 | 0.278349 | − | 0.960480i | \(-0.410213\pi\) | ||||
0.278349 | + | 0.960480i | \(0.410213\pi\) | |||||||
\(692\) | −49.2808 | −1.87337 | ||||||||
\(693\) | −54.7679 | −2.08046 | ||||||||
\(694\) | 54.8495 | 2.08206 | ||||||||
\(695\) | 26.7375 | 1.01421 | ||||||||
\(696\) | −34.1001 | −1.29256 | ||||||||
\(697\) | −40.9052 | −1.54939 | ||||||||
\(698\) | 61.2958 | 2.32008 | ||||||||
\(699\) | 4.89922 | 0.185305 | ||||||||
\(700\) | 37.5611 | 1.41968 | ||||||||
\(701\) | 31.4420 | 1.18755 | 0.593773 | − | 0.804632i | \(-0.297638\pi\) | ||||
0.593773 | + | 0.804632i | \(0.297638\pi\) | |||||||
\(702\) | 63.8691 | 2.41059 | ||||||||
\(703\) | 1.02961 | 0.0388327 | ||||||||
\(704\) | −20.4915 | −0.772302 | ||||||||
\(705\) | 2.56289 | 0.0965239 | ||||||||
\(706\) | 29.8010 | 1.12158 | ||||||||
\(707\) | −51.9565 | −1.95402 | ||||||||
\(708\) | −16.9503 | −0.637031 | ||||||||
\(709\) | −15.3996 | −0.578345 | −0.289172 | − | 0.957277i | \(-0.593380\pi\) | ||||
−0.289172 | + | 0.957277i | \(0.593380\pi\) | |||||||
\(710\) | 28.4464 | 1.06758 | ||||||||
\(711\) | 38.8050 | 1.45530 | ||||||||
\(712\) | 17.1820 | 0.643923 | ||||||||
\(713\) | −8.30603 | −0.311063 | ||||||||
\(714\) | 59.5277 | 2.22777 | ||||||||
\(715\) | −49.4418 | −1.84902 | ||||||||
\(716\) | −46.7269 | −1.74627 | ||||||||
\(717\) | −14.8590 | −0.554918 | ||||||||
\(718\) | 21.0581 | 0.785882 | ||||||||
\(719\) | −20.4106 | −0.761186 | −0.380593 | − | 0.924743i | \(-0.624280\pi\) | ||||
−0.380593 | + | 0.924743i | \(0.624280\pi\) | |||||||
\(720\) | −38.6141 | −1.43906 | ||||||||
\(721\) | 42.3637 | 1.57771 | ||||||||
\(722\) | 31.8066 | 1.18372 | ||||||||
\(723\) | −8.10768 | −0.301528 | ||||||||
\(724\) | −108.373 | −4.02767 | ||||||||
\(725\) | −10.1065 | −0.375345 | ||||||||
\(726\) | −18.2513 | −0.677370 | ||||||||
\(727\) | −43.4520 | −1.61154 | −0.805772 | − | 0.592226i | \(-0.798249\pi\) | ||||
−0.805772 | + | 0.592226i | \(0.798249\pi\) | |||||||
\(728\) | 209.624 | 7.76919 | ||||||||
\(729\) | −0.264847 | −0.00980915 | ||||||||
\(730\) | 25.6670 | 0.949978 | ||||||||
\(731\) | −18.0190 | −0.666456 | ||||||||
\(732\) | 40.3290 | 1.49060 | ||||||||
\(733\) | −22.9809 | −0.848818 | −0.424409 | − | 0.905471i | \(-0.639518\pi\) | ||||
−0.424409 | + | 0.905471i | \(0.639518\pi\) | |||||||
\(734\) | 8.49812 | 0.313671 | ||||||||
\(735\) | 26.1956 | 0.966240 | ||||||||
\(736\) | −42.9366 | −1.58267 | ||||||||
\(737\) | −53.2523 | −1.96157 | ||||||||
\(738\) | −42.9541 | −1.58116 | ||||||||
\(739\) | −14.9032 | −0.548224 | −0.274112 | − | 0.961698i | \(-0.588384\pi\) | ||||
−0.274112 | + | 0.961698i | \(0.588384\pi\) | |||||||
\(740\) | −3.45011 | −0.126829 | ||||||||
\(741\) | −11.8103 | −0.433863 | ||||||||
\(742\) | −36.3687 | −1.33514 | ||||||||
\(743\) | 4.41987 | 0.162149 | 0.0810747 | − | 0.996708i | \(-0.474165\pi\) | ||||
0.0810747 | + | 0.996708i | \(0.474165\pi\) | |||||||
\(744\) | 8.74116 | 0.320466 | ||||||||
\(745\) | −5.45762 | −0.199952 | ||||||||
\(746\) | −53.5865 | −1.96194 | ||||||||
\(747\) | 0.0620213 | 0.00226924 | ||||||||
\(748\) | −125.503 | −4.58884 | ||||||||
\(749\) | −14.6367 | −0.534812 | ||||||||
\(750\) | 24.1269 | 0.880991 | ||||||||
\(751\) | 15.2773 | 0.557478 | 0.278739 | − | 0.960367i | \(-0.410084\pi\) | ||||
0.278739 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(752\) | 15.6702 | 0.571434 | ||||||||
\(753\) | −12.8841 | −0.469521 | ||||||||
\(754\) | −98.2489 | −3.57801 | ||||||||
\(755\) | 6.16841 | 0.224491 | ||||||||
\(756\) | 98.3427 | 3.57669 | ||||||||
\(757\) | 17.8436 | 0.648538 | 0.324269 | − | 0.945965i | \(-0.394882\pi\) | ||||
0.324269 | + | 0.945965i | \(0.394882\pi\) | |||||||
\(758\) | 15.7379 | 0.571628 | ||||||||
\(759\) | −17.4922 | −0.634928 | ||||||||
\(760\) | 33.3915 | 1.21124 | ||||||||
\(761\) | 36.3083 | 1.31617 | 0.658087 | − | 0.752942i | \(-0.271366\pi\) | ||||
0.658087 | + | 0.752942i | \(0.271366\pi\) | |||||||
\(762\) | −8.96422 | −0.324739 | ||||||||
\(763\) | −43.0028 | −1.55681 | ||||||||
\(764\) | 111.895 | 4.04822 | ||||||||
\(765\) | −26.5160 | −0.958688 | ||||||||
\(766\) | 80.5633 | 2.91087 | ||||||||
\(767\) | −28.0366 | −1.01234 | ||||||||
\(768\) | −17.1216 | −0.617822 | ||||||||
\(769\) | −11.8439 | −0.427101 | −0.213551 | − | 0.976932i | \(-0.568503\pi\) | ||||
−0.213551 | + | 0.976932i | \(0.568503\pi\) | |||||||
\(770\) | −108.552 | −3.91195 | ||||||||
\(771\) | −6.47008 | −0.233014 | ||||||||
\(772\) | −90.1920 | −3.24608 | ||||||||
\(773\) | −40.8618 | −1.46970 | −0.734849 | − | 0.678231i | \(-0.762747\pi\) | ||||
−0.734849 | + | 0.678231i | \(0.762747\pi\) | |||||||
\(774\) | −18.9216 | −0.680122 | ||||||||
\(775\) | 2.59068 | 0.0930599 | ||||||||
\(776\) | −82.2534 | −2.95272 | ||||||||
\(777\) | 1.53808 | 0.0551783 | ||||||||
\(778\) | −35.4233 | −1.26999 | ||||||||
\(779\) | 17.8183 | 0.638405 | ||||||||
\(780\) | 39.5749 | 1.41701 | ||||||||
\(781\) | 26.7367 | 0.956715 | ||||||||
\(782\) | −78.1400 | −2.79428 | ||||||||
\(783\) | −26.4609 | −0.945634 | ||||||||
\(784\) | 160.167 | 5.72026 | ||||||||
\(785\) | −23.4631 | −0.837435 | ||||||||
\(786\) | −10.9401 | −0.390221 | ||||||||
\(787\) | 50.9887 | 1.81755 | 0.908776 | − | 0.417284i | \(-0.137018\pi\) | ||||
0.908776 | + | 0.417284i | \(0.137018\pi\) | |||||||
\(788\) | −33.3509 | −1.18808 | ||||||||
\(789\) | 3.48786 | 0.124171 | ||||||||
\(790\) | 76.9131 | 2.73645 | ||||||||
\(791\) | 102.556 | 3.64646 | ||||||||
\(792\) | −75.6582 | −2.68840 | ||||||||
\(793\) | 66.7061 | 2.36880 | ||||||||
\(794\) | −33.2964 | −1.18164 | ||||||||
\(795\) | −3.94169 | −0.139797 | ||||||||
\(796\) | 62.2280 | 2.20561 | ||||||||
\(797\) | 1.67963 | 0.0594955 | 0.0297477 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297477 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(798\) | −25.9302 | −0.917920 | ||||||||
\(799\) | 10.7606 | 0.380683 | ||||||||
\(800\) | 13.3921 | 0.473482 | ||||||||
\(801\) | 5.94337 | 0.209999 | ||||||||
\(802\) | 59.2627 | 2.09264 | ||||||||
\(803\) | 24.1243 | 0.851328 | ||||||||
\(804\) | 42.6250 | 1.50327 | ||||||||
\(805\) | −47.3985 | −1.67058 | ||||||||
\(806\) | 25.1850 | 0.887103 | ||||||||
\(807\) | −24.5130 | −0.862897 | ||||||||
\(808\) | −71.7744 | −2.52501 | ||||||||
\(809\) | −36.7198 | −1.29100 | −0.645500 | − | 0.763760i | \(-0.723351\pi\) | ||||
−0.645500 | + | 0.763760i | \(0.723351\pi\) | |||||||
\(810\) | −19.4210 | −0.682383 | ||||||||
\(811\) | 43.2016 | 1.51701 | 0.758507 | − | 0.651665i | \(-0.225929\pi\) | ||||
0.758507 | + | 0.651665i | \(0.225929\pi\) | |||||||
\(812\) | −151.279 | −5.30885 | ||||||||
\(813\) | −14.6796 | −0.514837 | ||||||||
\(814\) | −4.62389 | −0.162067 | ||||||||
\(815\) | 21.9264 | 0.768047 | ||||||||
\(816\) | 39.4474 | 1.38094 | ||||||||
\(817\) | 7.84906 | 0.274604 | ||||||||
\(818\) | −12.2755 | −0.429202 | ||||||||
\(819\) | 72.5104 | 2.53372 | ||||||||
\(820\) | −59.7068 | −2.08505 | ||||||||
\(821\) | 6.10920 | 0.213212 | 0.106606 | − | 0.994301i | \(-0.466002\pi\) | ||||
0.106606 | + | 0.994301i | \(0.466002\pi\) | |||||||
\(822\) | 5.25172 | 0.183175 | ||||||||
\(823\) | −3.82763 | −0.133423 | −0.0667113 | − | 0.997772i | \(-0.521251\pi\) | ||||
−0.0667113 | + | 0.997772i | \(0.521251\pi\) | |||||||
\(824\) | 58.5226 | 2.03873 | ||||||||
\(825\) | 5.45589 | 0.189950 | ||||||||
\(826\) | −61.5560 | −2.14181 | ||||||||
\(827\) | −5.27275 | −0.183352 | −0.0916758 | − | 0.995789i | \(-0.529222\pi\) | ||||
−0.0916758 | + | 0.995789i | \(0.529222\pi\) | |||||||
\(828\) | −57.5449 | −1.99982 | ||||||||
\(829\) | −22.5151 | −0.781982 | −0.390991 | − | 0.920395i | \(-0.627868\pi\) | ||||
−0.390991 | + | 0.920395i | \(0.627868\pi\) | |||||||
\(830\) | 0.122929 | 0.00426692 | ||||||||
\(831\) | −3.82175 | −0.132575 | ||||||||
\(832\) | 27.1299 | 0.940558 | ||||||||
\(833\) | 109.986 | 3.81078 | ||||||||
\(834\) | −28.6827 | −0.993201 | ||||||||
\(835\) | −44.4214 | −1.53726 | ||||||||
\(836\) | 54.6690 | 1.89077 | ||||||||
\(837\) | 6.78293 | 0.234452 | ||||||||
\(838\) | 38.0471 | 1.31432 | ||||||||
\(839\) | −34.3175 | −1.18477 | −0.592386 | − | 0.805654i | \(-0.701814\pi\) | ||||
−0.592386 | + | 0.805654i | \(0.701814\pi\) | |||||||
\(840\) | 49.8816 | 1.72108 | ||||||||
\(841\) | 11.7043 | 0.403598 | ||||||||
\(842\) | 63.4485 | 2.18658 | ||||||||
\(843\) | 18.6384 | 0.641942 | ||||||||
\(844\) | 76.0647 | 2.61825 | ||||||||
\(845\) | 41.4320 | 1.42530 | ||||||||
\(846\) | 11.2996 | 0.388489 | ||||||||
\(847\) | −46.4829 | −1.59717 | ||||||||
\(848\) | −24.1006 | −0.827617 | ||||||||
\(849\) | 0.574858 | 0.0197291 | ||||||||
\(850\) | 24.3721 | 0.835957 | ||||||||
\(851\) | −2.01898 | −0.0692099 | ||||||||
\(852\) | −21.4010 | −0.733186 | ||||||||
\(853\) | −17.1442 | −0.587008 | −0.293504 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293504 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(854\) | 146.457 | 5.01166 | ||||||||
\(855\) | 11.5504 | 0.395014 | ||||||||
\(856\) | −20.2196 | −0.691091 | ||||||||
\(857\) | 18.4468 | 0.630130 | 0.315065 | − | 0.949070i | \(-0.397974\pi\) | ||||
0.315065 | + | 0.949070i | \(0.397974\pi\) | |||||||
\(858\) | 53.0388 | 1.81072 | ||||||||
\(859\) | 22.8708 | 0.780341 | 0.390171 | − | 0.920743i | \(-0.372416\pi\) | ||||
0.390171 | + | 0.920743i | \(0.372416\pi\) | |||||||
\(860\) | −26.3012 | −0.896864 | ||||||||
\(861\) | 26.6176 | 0.907126 | ||||||||
\(862\) | −68.4470 | −2.33131 | ||||||||
\(863\) | 29.9703 | 1.02020 | 0.510101 | − | 0.860115i | \(-0.329608\pi\) | ||||
0.510101 | + | 0.860115i | \(0.329608\pi\) | |||||||
\(864\) | 35.0633 | 1.19288 | ||||||||
\(865\) | −19.3965 | −0.659502 | ||||||||
\(866\) | 58.3494 | 1.98279 | ||||||||
\(867\) | 14.0625 | 0.477588 | ||||||||
\(868\) | 38.7786 | 1.31623 | ||||||||
\(869\) | 72.2904 | 2.45228 | ||||||||
\(870\) | −23.3790 | −0.792624 | ||||||||
\(871\) | 70.5038 | 2.38893 | ||||||||
\(872\) | −59.4055 | −2.01172 | ||||||||
\(873\) | −28.4520 | −0.962954 | ||||||||
\(874\) | 34.0377 | 1.15134 | ||||||||
\(875\) | 61.4471 | 2.07729 | ||||||||
\(876\) | −19.3099 | −0.652422 | ||||||||
\(877\) | −1.15505 | −0.0390031 | −0.0195016 | − | 0.999810i | \(-0.506208\pi\) | ||||
−0.0195016 | + | 0.999810i | \(0.506208\pi\) | |||||||
\(878\) | 61.0828 | 2.06144 | ||||||||
\(879\) | 10.6726 | 0.359979 | ||||||||
\(880\) | −71.9346 | −2.42492 | ||||||||
\(881\) | −34.2596 | −1.15424 | −0.577118 | − | 0.816661i | \(-0.695823\pi\) | ||||
−0.577118 | + | 0.816661i | \(0.695823\pi\) | |||||||
\(882\) | 115.495 | 3.88892 | ||||||||
\(883\) | 50.3106 | 1.69309 | 0.846543 | − | 0.532320i | \(-0.178680\pi\) | ||||
0.846543 | + | 0.532320i | \(0.178680\pi\) | |||||||
\(884\) | 166.160 | 5.58858 | ||||||||
\(885\) | −6.67151 | −0.224260 | ||||||||
\(886\) | 87.8332 | 2.95081 | ||||||||
\(887\) | 51.3685 | 1.72478 | 0.862392 | − | 0.506240i | \(-0.168965\pi\) | ||||
0.862392 | + | 0.506240i | \(0.168965\pi\) | |||||||
\(888\) | 2.12475 | 0.0713021 | ||||||||
\(889\) | −22.8303 | −0.765704 | ||||||||
\(890\) | 11.7800 | 0.394866 | ||||||||
\(891\) | −18.2537 | −0.611522 | ||||||||
\(892\) | −110.412 | −3.69687 | ||||||||
\(893\) | −4.68732 | −0.156855 | ||||||||
\(894\) | 5.85468 | 0.195810 | ||||||||
\(895\) | −18.3914 | −0.614755 | ||||||||
\(896\) | −25.8138 | −0.862378 | ||||||||
\(897\) | 23.1590 | 0.773256 | ||||||||
\(898\) | −39.8492 | −1.32979 | ||||||||
\(899\) | −10.4341 | −0.347996 | ||||||||
\(900\) | 17.9484 | 0.598281 | ||||||||
\(901\) | −16.5497 | −0.551350 | ||||||||
\(902\) | −80.0198 | −2.66437 | ||||||||
\(903\) | 11.7252 | 0.390191 | ||||||||
\(904\) | 141.674 | 4.71200 | ||||||||
\(905\) | −42.6550 | −1.41790 | ||||||||
\(906\) | −6.61718 | −0.219841 | ||||||||
\(907\) | −16.7231 | −0.555282 | −0.277641 | − | 0.960685i | \(-0.589553\pi\) | ||||
−0.277641 | + | 0.960685i | \(0.589553\pi\) | |||||||
\(908\) | −44.9410 | −1.49142 | ||||||||
\(909\) | −24.8272 | −0.823468 | ||||||||
\(910\) | 143.719 | 4.76422 | ||||||||
\(911\) | 37.5732 | 1.24486 | 0.622428 | − | 0.782677i | \(-0.286146\pi\) | ||||
0.622428 | + | 0.782677i | \(0.286146\pi\) | |||||||
\(912\) | −17.1833 | −0.568994 | ||||||||
\(913\) | 0.115540 | 0.00382383 | ||||||||
\(914\) | 10.3356 | 0.341871 | ||||||||
\(915\) | 15.8732 | 0.524751 | ||||||||
\(916\) | 46.5420 | 1.53779 | ||||||||
\(917\) | −27.8625 | −0.920102 | ||||||||
\(918\) | 63.8113 | 2.10609 | ||||||||
\(919\) | 49.0002 | 1.61637 | 0.808184 | − | 0.588931i | \(-0.200451\pi\) | ||||
0.808184 | + | 0.588931i | \(0.200451\pi\) | |||||||
\(920\) | −65.4779 | −2.15874 | ||||||||
\(921\) | −3.09219 | −0.101891 | ||||||||
\(922\) | 75.9374 | 2.50087 | ||||||||
\(923\) | −35.3983 | −1.16515 | ||||||||
\(924\) | 81.6667 | 2.68664 | ||||||||
\(925\) | 0.629728 | 0.0207053 | ||||||||
\(926\) | −109.063 | −3.58405 | ||||||||
\(927\) | 20.2433 | 0.664879 | ||||||||
\(928\) | −53.9373 | −1.77058 | ||||||||
\(929\) | −19.4990 | −0.639741 | −0.319870 | − | 0.947461i | \(-0.603639\pi\) | ||||
−0.319870 | + | 0.947461i | \(0.603639\pi\) | |||||||
\(930\) | 5.99294 | 0.196516 | ||||||||
\(931\) | −47.9097 | −1.57018 | ||||||||
\(932\) | 30.0248 | 0.983495 | ||||||||
\(933\) | −12.3864 | −0.405514 | ||||||||
\(934\) | 89.8602 | 2.94031 | ||||||||
\(935\) | −49.3970 | −1.61546 | ||||||||
\(936\) | 100.168 | 3.27410 | ||||||||
\(937\) | −56.5182 | −1.84637 | −0.923185 | − | 0.384355i | \(-0.874424\pi\) | ||||
−0.923185 | + | 0.384355i | \(0.874424\pi\) | |||||||
\(938\) | 154.795 | 5.05424 | ||||||||
\(939\) | −8.74243 | −0.285298 | ||||||||
\(940\) | 15.7066 | 0.512294 | ||||||||
\(941\) | 30.8643 | 1.00615 | 0.503074 | − | 0.864243i | \(-0.332202\pi\) | ||||
0.503074 | + | 0.864243i | \(0.332202\pi\) | |||||||
\(942\) | 25.1701 | 0.820087 | ||||||||
\(943\) | −34.9400 | −1.13780 | ||||||||
\(944\) | −40.7915 | −1.32765 | ||||||||
\(945\) | 38.7070 | 1.25914 | ||||||||
\(946\) | −35.2492 | −1.14605 | ||||||||
\(947\) | −14.2544 | −0.463205 | −0.231602 | − | 0.972811i | \(-0.574397\pi\) | ||||
−0.231602 | + | 0.972811i | \(0.574397\pi\) | |||||||
\(948\) | −57.8637 | −1.87933 | ||||||||
\(949\) | −31.9396 | −1.03680 | ||||||||
\(950\) | −10.6165 | −0.344444 | ||||||||
\(951\) | −16.5353 | −0.536192 | ||||||||
\(952\) | 209.434 | 6.78781 | ||||||||
\(953\) | 2.97643 | 0.0964159 | 0.0482079 | − | 0.998837i | \(-0.484649\pi\) | ||||
0.0482079 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(954\) | −17.3787 | −0.562655 | ||||||||
\(955\) | 44.0411 | 1.42514 | ||||||||
\(956\) | −91.0630 | −2.94519 | ||||||||
\(957\) | −21.9739 | −0.710314 | ||||||||
\(958\) | 4.29986 | 0.138922 | ||||||||
\(959\) | 13.3752 | 0.431909 | ||||||||
\(960\) | 6.45574 | 0.208358 | ||||||||
\(961\) | −28.3253 | −0.913721 | ||||||||
\(962\) | 6.12183 | 0.197376 | ||||||||
\(963\) | −6.99408 | −0.225381 | ||||||||
\(964\) | −49.6878 | −1.60034 | ||||||||
\(965\) | −35.4989 | −1.14275 | ||||||||
\(966\) | 50.8469 | 1.63597 | ||||||||
\(967\) | 16.6289 | 0.534751 | 0.267375 | − | 0.963592i | \(-0.413844\pi\) | ||||
0.267375 | + | 0.963592i | \(0.413844\pi\) | |||||||
\(968\) | −64.2130 | −2.06388 | ||||||||
\(969\) | −11.7996 | −0.379058 | ||||||||
\(970\) | −56.3930 | −1.81067 | ||||||||
\(971\) | −58.6271 | −1.88143 | −0.940717 | − | 0.339193i | \(-0.889846\pi\) | ||||
−0.940717 | + | 0.339193i | \(0.889846\pi\) | |||||||
\(972\) | 73.0376 | 2.34268 | ||||||||
\(973\) | −73.0498 | −2.34187 | ||||||||
\(974\) | 17.1751 | 0.550327 | ||||||||
\(975\) | −7.22337 | −0.231333 | ||||||||
\(976\) | 97.0531 | 3.10659 | ||||||||
\(977\) | −8.58363 | −0.274615 | −0.137307 | − | 0.990528i | \(-0.543845\pi\) | ||||
−0.137307 | + | 0.990528i | \(0.543845\pi\) | |||||||
\(978\) | −23.5216 | −0.752137 | ||||||||
\(979\) | 11.0720 | 0.353862 | ||||||||
\(980\) | 160.539 | 5.12825 | ||||||||
\(981\) | −20.5488 | −0.656071 | ||||||||
\(982\) | 45.9701 | 1.46697 | ||||||||
\(983\) | −48.9536 | −1.56138 | −0.780689 | − | 0.624919i | \(-0.785132\pi\) | ||||
−0.780689 | + | 0.624919i | \(0.785132\pi\) | |||||||
\(984\) | 36.7705 | 1.17220 | ||||||||
\(985\) | −13.1267 | −0.418250 | ||||||||
\(986\) | −98.1600 | −3.12605 | ||||||||
\(987\) | −7.00210 | −0.222879 | ||||||||
\(988\) | −72.3794 | −2.30269 | ||||||||
\(989\) | −15.3913 | −0.489415 | ||||||||
\(990\) | −51.8714 | −1.64858 | ||||||||
\(991\) | 16.9560 | 0.538625 | 0.269313 | − | 0.963053i | \(-0.413203\pi\) | ||||
0.269313 | + | 0.963053i | \(0.413203\pi\) | |||||||
\(992\) | 13.8262 | 0.438982 | ||||||||
\(993\) | 14.8728 | 0.471975 | ||||||||
\(994\) | −77.7189 | −2.46509 | ||||||||
\(995\) | 24.4925 | 0.776464 | ||||||||
\(996\) | −0.0924824 | −0.00293042 | ||||||||
\(997\) | 28.6720 | 0.908052 | 0.454026 | − | 0.890988i | \(-0.349987\pi\) | ||||
0.454026 | + | 0.890988i | \(0.349987\pi\) | |||||||
\(998\) | 34.0306 | 1.07722 | ||||||||
\(999\) | 1.64876 | 0.0521644 |
(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 | 5077.2.a.b.1.15 | ✓ | 205 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.b.1.15 | ✓ | 205 | 1.1 | even | 1 | trivial |