Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88550 | −1.33325 | −0.666626 | − | 0.745392i | \(-0.732262\pi\) | ||||
−0.666626 | + | 0.745392i | \(0.732262\pi\) | |||||||
\(3\) | 3.14155 | 1.81378 | 0.906888 | − | 0.421371i | \(-0.138451\pi\) | ||||
0.906888 | + | 0.421371i | \(0.138451\pi\) | |||||||
\(4\) | 1.55513 | 0.777563 | ||||||||
\(5\) | −2.47668 | −1.10761 | −0.553803 | − | 0.832648i | \(-0.686824\pi\) | ||||
−0.553803 | + | 0.832648i | \(0.686824\pi\) | |||||||
\(6\) | −5.92341 | −2.41822 | ||||||||
\(7\) | 4.66231 | 1.76219 | 0.881094 | − | 0.472941i | \(-0.156808\pi\) | ||||
0.881094 | + | 0.472941i | \(0.156808\pi\) | |||||||
\(8\) | 0.838810 | 0.296564 | ||||||||
\(9\) | 6.86935 | 2.28978 | ||||||||
\(10\) | 4.66980 | 1.47672 | ||||||||
\(11\) | −0.962397 | −0.290174 | −0.145087 | − | 0.989419i | \(-0.546346\pi\) | ||||
−0.145087 | + | 0.989419i | \(0.546346\pi\) | |||||||
\(12\) | 4.88551 | 1.41033 | ||||||||
\(13\) | −3.22360 | −0.894064 | −0.447032 | − | 0.894518i | \(-0.647519\pi\) | ||||
−0.447032 | + | 0.894518i | \(0.647519\pi\) | |||||||
\(14\) | −8.79081 | −2.34944 | ||||||||
\(15\) | −7.78063 | −2.00895 | ||||||||
\(16\) | −4.69183 | −1.17296 | ||||||||
\(17\) | −0.966111 | −0.234316 | −0.117158 | − | 0.993113i | \(-0.537378\pi\) | ||||
−0.117158 | + | 0.993113i | \(0.537378\pi\) | |||||||
\(18\) | −12.9522 | −3.05286 | ||||||||
\(19\) | −7.38402 | −1.69401 | −0.847005 | − | 0.531585i | \(-0.821597\pi\) | ||||
−0.847005 | + | 0.531585i | \(0.821597\pi\) | |||||||
\(20\) | −3.85156 | −0.861234 | ||||||||
\(21\) | 14.6469 | 3.19621 | ||||||||
\(22\) | 1.81460 | 0.386875 | ||||||||
\(23\) | 8.81219 | 1.83747 | 0.918734 | − | 0.394877i | \(-0.129213\pi\) | ||||
0.918734 | + | 0.394877i | \(0.129213\pi\) | |||||||
\(24\) | 2.63517 | 0.537901 | ||||||||
\(25\) | 1.13396 | 0.226792 | ||||||||
\(26\) | 6.07810 | 1.19201 | ||||||||
\(27\) | 12.1558 | 2.33938 | ||||||||
\(28\) | 7.25049 | 1.37021 | ||||||||
\(29\) | −7.87334 | −1.46204 | −0.731021 | − | 0.682355i | \(-0.760956\pi\) | ||||
−0.731021 | + | 0.682355i | \(0.760956\pi\) | |||||||
\(30\) | 14.6704 | 2.67844 | ||||||||
\(31\) | −6.88170 | −1.23599 | −0.617995 | − | 0.786182i | \(-0.712055\pi\) | ||||
−0.617995 | + | 0.786182i | \(0.712055\pi\) | |||||||
\(32\) | 7.16885 | 1.26729 | ||||||||
\(33\) | −3.02342 | −0.526310 | ||||||||
\(34\) | 1.82161 | 0.312403 | ||||||||
\(35\) | −11.5471 | −1.95181 | ||||||||
\(36\) | 10.6827 | 1.78045 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 13.9226 | 2.25854 | ||||||||
\(39\) | −10.1271 | −1.62163 | ||||||||
\(40\) | −2.07747 | −0.328476 | ||||||||
\(41\) | 10.1834 | 1.59037 | 0.795187 | − | 0.606364i | \(-0.207372\pi\) | ||||
0.795187 | + | 0.606364i | \(0.207372\pi\) | |||||||
\(42\) | −27.6168 | −4.26136 | ||||||||
\(43\) | 12.1719 | 1.85620 | 0.928099 | − | 0.372334i | \(-0.121442\pi\) | ||||
0.928099 | + | 0.372334i | \(0.121442\pi\) | |||||||
\(44\) | −1.49665 | −0.225628 | ||||||||
\(45\) | −17.0132 | −2.53618 | ||||||||
\(46\) | −16.6154 | −2.44981 | ||||||||
\(47\) | 9.31410 | 1.35860 | 0.679301 | − | 0.733860i | \(-0.262283\pi\) | ||||
0.679301 | + | 0.733860i | \(0.262283\pi\) | |||||||
\(48\) | −14.7396 | −2.12748 | ||||||||
\(49\) | 14.7371 | 2.10531 | ||||||||
\(50\) | −2.13809 | −0.302372 | ||||||||
\(51\) | −3.03509 | −0.424997 | ||||||||
\(52\) | −5.01310 | −0.695192 | ||||||||
\(53\) | 7.66767 | 1.05324 | 0.526618 | − | 0.850102i | \(-0.323460\pi\) | ||||
0.526618 | + | 0.850102i | \(0.323460\pi\) | |||||||
\(54\) | −22.9198 | −3.11899 | ||||||||
\(55\) | 2.38355 | 0.321398 | ||||||||
\(56\) | 3.91079 | 0.522602 | ||||||||
\(57\) | −23.1973 | −3.07255 | ||||||||
\(58\) | 14.8452 | 1.94927 | ||||||||
\(59\) | 9.29419 | 1.21000 | 0.605000 | − | 0.796225i | \(-0.293173\pi\) | ||||
0.605000 | + | 0.796225i | \(0.293173\pi\) | |||||||
\(60\) | −12.0999 | −1.56209 | ||||||||
\(61\) | 6.99911 | 0.896145 | 0.448072 | − | 0.893997i | \(-0.352111\pi\) | ||||
0.448072 | + | 0.893997i | \(0.352111\pi\) | |||||||
\(62\) | 12.9755 | 1.64789 | ||||||||
\(63\) | 32.0271 | 4.03503 | ||||||||
\(64\) | −4.13324 | −0.516655 | ||||||||
\(65\) | 7.98383 | 0.990272 | ||||||||
\(66\) | 5.70068 | 0.701705 | ||||||||
\(67\) | 2.99266 | 0.365612 | 0.182806 | − | 0.983149i | \(-0.441482\pi\) | ||||
0.182806 | + | 0.983149i | \(0.441482\pi\) | |||||||
\(68\) | −1.50243 | −0.182196 | ||||||||
\(69\) | 27.6839 | 3.33276 | ||||||||
\(70\) | 21.7721 | 2.60226 | ||||||||
\(71\) | 9.33956 | 1.10840 | 0.554201 | − | 0.832383i | \(-0.313024\pi\) | ||||
0.554201 | + | 0.832383i | \(0.313024\pi\) | |||||||
\(72\) | 5.76208 | 0.679068 | ||||||||
\(73\) | −3.36832 | −0.394232 | −0.197116 | − | 0.980380i | \(-0.563158\pi\) | ||||
−0.197116 | + | 0.980380i | \(0.563158\pi\) | |||||||
\(74\) | −1.88550 | −0.219185 | ||||||||
\(75\) | 3.56240 | 0.411351 | ||||||||
\(76\) | −11.4831 | −1.31720 | ||||||||
\(77\) | −4.48700 | −0.511341 | ||||||||
\(78\) | 19.0947 | 2.16205 | ||||||||
\(79\) | 4.28866 | 0.482512 | 0.241256 | − | 0.970462i | \(-0.422441\pi\) | ||||
0.241256 | + | 0.970462i | \(0.422441\pi\) | |||||||
\(80\) | 11.6202 | 1.29918 | ||||||||
\(81\) | 17.5799 | 1.95333 | ||||||||
\(82\) | −19.2008 | −2.12037 | ||||||||
\(83\) | −13.4224 | −1.47330 | −0.736650 | − | 0.676274i | \(-0.763593\pi\) | ||||
−0.736650 | + | 0.676274i | \(0.763593\pi\) | |||||||
\(84\) | 22.7778 | 2.48526 | ||||||||
\(85\) | 2.39275 | 0.259530 | ||||||||
\(86\) | −22.9502 | −2.47478 | ||||||||
\(87\) | −24.7345 | −2.65182 | ||||||||
\(88\) | −0.807269 | −0.0860551 | ||||||||
\(89\) | 17.4343 | 1.84803 | 0.924015 | − | 0.382356i | \(-0.124887\pi\) | ||||
0.924015 | + | 0.382356i | \(0.124887\pi\) | |||||||
\(90\) | 32.0785 | 3.38137 | ||||||||
\(91\) | −15.0294 | −1.57551 | ||||||||
\(92\) | 13.7041 | 1.42875 | ||||||||
\(93\) | −21.6192 | −2.24181 | ||||||||
\(94\) | −17.5618 | −1.81136 | ||||||||
\(95\) | 18.2879 | 1.87630 | ||||||||
\(96\) | 22.5213 | 2.29857 | ||||||||
\(97\) | 3.21593 | 0.326528 | 0.163264 | − | 0.986582i | \(-0.447798\pi\) | ||||
0.163264 | + | 0.986582i | \(0.447798\pi\) | |||||||
\(98\) | −27.7870 | −2.80691 | ||||||||
\(99\) | −6.61105 | −0.664435 | ||||||||
\(100\) | 1.76345 | 0.176345 | ||||||||
\(101\) | −1.54359 | −0.153593 | −0.0767965 | − | 0.997047i | \(-0.524469\pi\) | ||||
−0.0767965 | + | 0.997047i | \(0.524469\pi\) | |||||||
\(102\) | 5.72267 | 0.566629 | ||||||||
\(103\) | 11.8362 | 1.16626 | 0.583130 | − | 0.812379i | \(-0.301828\pi\) | ||||
0.583130 | + | 0.812379i | \(0.301828\pi\) | |||||||
\(104\) | −2.70398 | −0.265147 | ||||||||
\(105\) | −36.2757 | −3.54015 | ||||||||
\(106\) | −14.4574 | −1.40423 | ||||||||
\(107\) | 4.99090 | 0.482489 | 0.241244 | − | 0.970464i | \(-0.422444\pi\) | ||||
0.241244 | + | 0.970464i | \(0.422444\pi\) | |||||||
\(108\) | 18.9038 | 1.81902 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −4.49420 | −0.428505 | ||||||||
\(111\) | 3.14155 | 0.298183 | ||||||||
\(112\) | −21.8748 | −2.06697 | ||||||||
\(113\) | −10.2072 | −0.960211 | −0.480105 | − | 0.877211i | \(-0.659402\pi\) | ||||
−0.480105 | + | 0.877211i | \(0.659402\pi\) | |||||||
\(114\) | 43.7386 | 4.09649 | ||||||||
\(115\) | −21.8250 | −2.03519 | ||||||||
\(116\) | −12.2440 | −1.13683 | ||||||||
\(117\) | −22.1440 | −2.04721 | ||||||||
\(118\) | −17.5242 | −1.61324 | ||||||||
\(119\) | −4.50431 | −0.412909 | ||||||||
\(120\) | −6.52647 | −0.595783 | ||||||||
\(121\) | −10.0738 | −0.915799 | ||||||||
\(122\) | −13.1969 | −1.19479 | ||||||||
\(123\) | 31.9916 | 2.88458 | ||||||||
\(124\) | −10.7019 | −0.961061 | ||||||||
\(125\) | 9.57495 | 0.856410 | ||||||||
\(126\) | −60.3872 | −5.37972 | ||||||||
\(127\) | −3.55746 | −0.315673 | −0.157837 | − | 0.987465i | \(-0.550452\pi\) | ||||
−0.157837 | + | 0.987465i | \(0.550452\pi\) | |||||||
\(128\) | −6.54447 | −0.578455 | ||||||||
\(129\) | 38.2387 | 3.36673 | ||||||||
\(130\) | −15.0535 | −1.32028 | ||||||||
\(131\) | −1.35242 | −0.118162 | −0.0590808 | − | 0.998253i | \(-0.518817\pi\) | ||||
−0.0590808 | + | 0.998253i | \(0.518817\pi\) | |||||||
\(132\) | −4.70180 | −0.409240 | ||||||||
\(133\) | −34.4266 | −2.98516 | ||||||||
\(134\) | −5.64268 | −0.487453 | ||||||||
\(135\) | −30.1060 | −2.59111 | ||||||||
\(136\) | −0.810384 | −0.0694898 | ||||||||
\(137\) | −4.97282 | −0.424857 | −0.212428 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212428 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(138\) | −52.1982 | −4.44341 | ||||||||
\(139\) | 5.83934 | 0.495287 | 0.247643 | − | 0.968851i | \(-0.420344\pi\) | ||||
0.247643 | + | 0.968851i | \(0.420344\pi\) | |||||||
\(140\) | −17.9572 | −1.51766 | ||||||||
\(141\) | 29.2607 | 2.46420 | ||||||||
\(142\) | −17.6098 | −1.47778 | ||||||||
\(143\) | 3.10238 | 0.259434 | ||||||||
\(144\) | −32.2299 | −2.68582 | ||||||||
\(145\) | 19.4998 | 1.61937 | ||||||||
\(146\) | 6.35099 | 0.525612 | ||||||||
\(147\) | 46.2975 | 3.81855 | ||||||||
\(148\) | 1.55513 | 0.127831 | ||||||||
\(149\) | −19.3627 | −1.58625 | −0.793126 | − | 0.609058i | \(-0.791548\pi\) | ||||
−0.793126 | + | 0.609058i | \(0.791548\pi\) | |||||||
\(150\) | −6.71692 | −0.548434 | ||||||||
\(151\) | 3.83050 | 0.311722 | 0.155861 | − | 0.987779i | \(-0.450185\pi\) | ||||
0.155861 | + | 0.987779i | \(0.450185\pi\) | |||||||
\(152\) | −6.19379 | −0.502383 | ||||||||
\(153\) | −6.63656 | −0.536534 | ||||||||
\(154\) | 8.46025 | 0.681746 | ||||||||
\(155\) | 17.0438 | 1.36899 | ||||||||
\(156\) | −15.7489 | −1.26092 | ||||||||
\(157\) | −0.535485 | −0.0427364 | −0.0213682 | − | 0.999772i | \(-0.506802\pi\) | ||||
−0.0213682 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(158\) | −8.08629 | −0.643310 | ||||||||
\(159\) | 24.0884 | 1.91033 | ||||||||
\(160\) | −17.7550 | −1.40365 | ||||||||
\(161\) | 41.0852 | 3.23796 | ||||||||
\(162\) | −33.1471 | −2.60428 | ||||||||
\(163\) | −12.5476 | −0.982805 | −0.491403 | − | 0.870933i | \(-0.663516\pi\) | ||||
−0.491403 | + | 0.870933i | \(0.663516\pi\) | |||||||
\(164\) | 15.8364 | 1.23662 | ||||||||
\(165\) | 7.48806 | 0.582945 | ||||||||
\(166\) | 25.3080 | 1.96428 | ||||||||
\(167\) | 3.36955 | 0.260744 | 0.130372 | − | 0.991465i | \(-0.458383\pi\) | ||||
0.130372 | + | 0.991465i | \(0.458383\pi\) | |||||||
\(168\) | 12.2860 | 0.947883 | ||||||||
\(169\) | −2.60843 | −0.200649 | ||||||||
\(170\) | −4.51154 | −0.346020 | ||||||||
\(171\) | −50.7234 | −3.87892 | ||||||||
\(172\) | 18.9289 | 1.44331 | ||||||||
\(173\) | 6.39975 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(174\) | 46.6370 | 3.53554 | ||||||||
\(175\) | 5.28688 | 0.399651 | ||||||||
\(176\) | 4.51541 | 0.340362 | ||||||||
\(177\) | 29.1982 | 2.19467 | ||||||||
\(178\) | −32.8724 | −2.46389 | ||||||||
\(179\) | 16.6011 | 1.24083 | 0.620413 | − | 0.784275i | \(-0.286965\pi\) | ||||
0.620413 | + | 0.784275i | \(0.286965\pi\) | |||||||
\(180\) | −26.4577 | −1.97204 | ||||||||
\(181\) | −7.44531 | −0.553405 | −0.276703 | − | 0.960956i | \(-0.589242\pi\) | ||||
−0.276703 | + | 0.960956i | \(0.589242\pi\) | |||||||
\(182\) | 28.3380 | 2.10055 | ||||||||
\(183\) | 21.9881 | 1.62541 | ||||||||
\(184\) | 7.39175 | 0.544927 | ||||||||
\(185\) | −2.47668 | −0.182089 | ||||||||
\(186\) | 40.7632 | 2.98890 | ||||||||
\(187\) | 0.929783 | 0.0679924 | ||||||||
\(188\) | 14.4846 | 1.05640 | ||||||||
\(189\) | 56.6740 | 4.12243 | ||||||||
\(190\) | −34.4819 | −2.50158 | ||||||||
\(191\) | 4.04583 | 0.292746 | 0.146373 | − | 0.989229i | \(-0.453240\pi\) | ||||
0.146373 | + | 0.989229i | \(0.453240\pi\) | |||||||
\(192\) | −12.9848 | −0.937096 | ||||||||
\(193\) | 15.0082 | 1.08031 | 0.540156 | − | 0.841565i | \(-0.318365\pi\) | ||||
0.540156 | + | 0.841565i | \(0.318365\pi\) | |||||||
\(194\) | −6.06365 | −0.435345 | ||||||||
\(195\) | 25.0816 | 1.79613 | ||||||||
\(196\) | 22.9181 | 1.63701 | ||||||||
\(197\) | 12.7603 | 0.909136 | 0.454568 | − | 0.890712i | \(-0.349794\pi\) | ||||
0.454568 | + | 0.890712i | \(0.349794\pi\) | |||||||
\(198\) | 12.4652 | 0.885860 | ||||||||
\(199\) | 9.39122 | 0.665726 | 0.332863 | − | 0.942975i | \(-0.391985\pi\) | ||||
0.332863 | + | 0.942975i | \(0.391985\pi\) | |||||||
\(200\) | 0.951179 | 0.0672585 | ||||||||
\(201\) | 9.40161 | 0.663138 | ||||||||
\(202\) | 2.91045 | 0.204778 | ||||||||
\(203\) | −36.7079 | −2.57639 | ||||||||
\(204\) | −4.71995 | −0.330462 | ||||||||
\(205\) | −25.2210 | −1.76151 | ||||||||
\(206\) | −22.3173 | −1.55492 | ||||||||
\(207\) | 60.5340 | 4.20741 | ||||||||
\(208\) | 15.1246 | 1.04870 | ||||||||
\(209\) | 7.10636 | 0.491557 | ||||||||
\(210\) | 68.3980 | 4.71991 | ||||||||
\(211\) | −1.81639 | −0.125045 | −0.0625227 | − | 0.998044i | \(-0.519915\pi\) | ||||
−0.0625227 | + | 0.998044i | \(0.519915\pi\) | |||||||
\(212\) | 11.9242 | 0.818957 | ||||||||
\(213\) | 29.3407 | 2.01039 | ||||||||
\(214\) | −9.41037 | −0.643280 | ||||||||
\(215\) | −30.1460 | −2.05594 | ||||||||
\(216\) | 10.1964 | 0.693776 | ||||||||
\(217\) | −32.0846 | −2.17805 | ||||||||
\(218\) | 1.88550 | 0.127702 | ||||||||
\(219\) | −10.5818 | −0.715050 | ||||||||
\(220\) | 3.70673 | 0.249908 | ||||||||
\(221\) | 3.11435 | 0.209494 | ||||||||
\(222\) | −5.92341 | −0.397553 | ||||||||
\(223\) | 3.18174 | 0.213065 | 0.106532 | − | 0.994309i | \(-0.466025\pi\) | ||||
0.106532 | + | 0.994309i | \(0.466025\pi\) | |||||||
\(224\) | 33.4234 | 2.23320 | ||||||||
\(225\) | 7.78958 | 0.519306 | ||||||||
\(226\) | 19.2457 | 1.28020 | ||||||||
\(227\) | −2.08476 | −0.138370 | −0.0691852 | − | 0.997604i | \(-0.522040\pi\) | ||||
−0.0691852 | + | 0.997604i | \(0.522040\pi\) | |||||||
\(228\) | −36.0747 | −2.38911 | ||||||||
\(229\) | −26.9614 | −1.78166 | −0.890831 | − | 0.454335i | \(-0.849877\pi\) | ||||
−0.890831 | + | 0.454335i | \(0.849877\pi\) | |||||||
\(230\) | 41.1511 | 2.71343 | ||||||||
\(231\) | −14.0961 | −0.927457 | ||||||||
\(232\) | −6.60423 | −0.433589 | ||||||||
\(233\) | −15.1250 | −0.990870 | −0.495435 | − | 0.868645i | \(-0.664991\pi\) | ||||
−0.495435 | + | 0.868645i | \(0.664991\pi\) | |||||||
\(234\) | 41.7526 | 2.72946 | ||||||||
\(235\) | −23.0681 | −1.50480 | ||||||||
\(236\) | 14.4536 | 0.940852 | ||||||||
\(237\) | 13.4731 | 0.875169 | ||||||||
\(238\) | 8.49290 | 0.550513 | ||||||||
\(239\) | −11.0264 | −0.713239 | −0.356620 | − | 0.934250i | \(-0.616071\pi\) | ||||
−0.356620 | + | 0.934250i | \(0.616071\pi\) | |||||||
\(240\) | 36.5054 | 2.35642 | ||||||||
\(241\) | −8.84780 | −0.569937 | −0.284969 | − | 0.958537i | \(-0.591983\pi\) | ||||
−0.284969 | + | 0.958537i | \(0.591983\pi\) | |||||||
\(242\) | 18.9942 | 1.22099 | ||||||||
\(243\) | 18.7610 | 1.20352 | ||||||||
\(244\) | 10.8845 | 0.696809 | ||||||||
\(245\) | −36.4992 | −2.33185 | ||||||||
\(246\) | −60.3203 | −3.84588 | ||||||||
\(247\) | 23.8031 | 1.51455 | ||||||||
\(248\) | −5.77244 | −0.366551 | ||||||||
\(249\) | −42.1672 | −2.67224 | ||||||||
\(250\) | −18.0536 | −1.14181 | ||||||||
\(251\) | 30.9323 | 1.95243 | 0.976215 | − | 0.216804i | \(-0.0695632\pi\) | ||||
0.976215 | + | 0.216804i | \(0.0695632\pi\) | |||||||
\(252\) | 49.8061 | 3.13749 | ||||||||
\(253\) | −8.48083 | −0.533185 | ||||||||
\(254\) | 6.70760 | 0.420872 | ||||||||
\(255\) | 7.51695 | 0.470730 | ||||||||
\(256\) | 20.6061 | 1.28788 | ||||||||
\(257\) | 3.76602 | 0.234918 | 0.117459 | − | 0.993078i | \(-0.462525\pi\) | ||||
0.117459 | + | 0.993078i | \(0.462525\pi\) | |||||||
\(258\) | −72.0992 | −4.48870 | ||||||||
\(259\) | 4.66231 | 0.289702 | ||||||||
\(260\) | 12.4159 | 0.769999 | ||||||||
\(261\) | −54.0847 | −3.34776 | ||||||||
\(262\) | 2.54999 | 0.157539 | ||||||||
\(263\) | 21.7434 | 1.34075 | 0.670377 | − | 0.742021i | \(-0.266132\pi\) | ||||
0.670377 | + | 0.742021i | \(0.266132\pi\) | |||||||
\(264\) | −2.53608 | −0.156085 | ||||||||
\(265\) | −18.9904 | −1.16657 | ||||||||
\(266\) | 64.9115 | 3.97998 | ||||||||
\(267\) | 54.7707 | 3.35191 | ||||||||
\(268\) | 4.65397 | 0.284287 | ||||||||
\(269\) | 21.9524 | 1.33846 | 0.669231 | − | 0.743054i | \(-0.266624\pi\) | ||||
0.669231 | + | 0.743054i | \(0.266624\pi\) | |||||||
\(270\) | 56.7650 | 3.45461 | ||||||||
\(271\) | 25.0407 | 1.52112 | 0.760558 | − | 0.649270i | \(-0.224925\pi\) | ||||
0.760558 | + | 0.649270i | \(0.224925\pi\) | |||||||
\(272\) | 4.53283 | 0.274843 | ||||||||
\(273\) | −47.2157 | −2.85762 | ||||||||
\(274\) | 9.37627 | 0.566441 | ||||||||
\(275\) | −1.09132 | −0.0658092 | ||||||||
\(276\) | 43.0521 | 2.59143 | ||||||||
\(277\) | −1.11436 | −0.0669556 | −0.0334778 | − | 0.999439i | \(-0.510658\pi\) | ||||
−0.0334778 | + | 0.999439i | \(0.510658\pi\) | |||||||
\(278\) | −11.0101 | −0.660343 | ||||||||
\(279\) | −47.2729 | −2.83015 | ||||||||
\(280\) | −9.68580 | −0.578837 | ||||||||
\(281\) | 6.28813 | 0.375119 | 0.187559 | − | 0.982253i | \(-0.439942\pi\) | ||||
0.187559 | + | 0.982253i | \(0.439942\pi\) | |||||||
\(282\) | −55.1713 | −3.28540 | ||||||||
\(283\) | −19.4081 | −1.15369 | −0.576845 | − | 0.816854i | \(-0.695716\pi\) | ||||
−0.576845 | + | 0.816854i | \(0.695716\pi\) | |||||||
\(284\) | 14.5242 | 0.861853 | ||||||||
\(285\) | 57.4523 | 3.40318 | ||||||||
\(286\) | −5.84955 | −0.345891 | ||||||||
\(287\) | 47.4780 | 2.80254 | ||||||||
\(288\) | 49.2454 | 2.90181 | ||||||||
\(289\) | −16.0666 | −0.945096 | ||||||||
\(290\) | −36.7669 | −2.15903 | ||||||||
\(291\) | 10.1030 | 0.592249 | ||||||||
\(292\) | −5.23817 | −0.306541 | ||||||||
\(293\) | 4.23655 | 0.247502 | 0.123751 | − | 0.992313i | \(-0.460508\pi\) | ||||
0.123751 | + | 0.992313i | \(0.460508\pi\) | |||||||
\(294\) | −87.2942 | −5.09110 | ||||||||
\(295\) | −23.0188 | −1.34020 | ||||||||
\(296\) | 0.838810 | 0.0487549 | ||||||||
\(297\) | −11.6987 | −0.678827 | ||||||||
\(298\) | 36.5084 | 2.11488 | ||||||||
\(299\) | −28.4069 | −1.64281 | ||||||||
\(300\) | 5.53999 | 0.319851 | ||||||||
\(301\) | 56.7492 | 3.27097 | ||||||||
\(302\) | −7.22243 | −0.415604 | ||||||||
\(303\) | −4.84927 | −0.278583 | ||||||||
\(304\) | 34.6446 | 1.98700 | ||||||||
\(305\) | −17.3346 | −0.992576 | ||||||||
\(306\) | 12.5133 | 0.715335 | ||||||||
\(307\) | −23.3781 | −1.33426 | −0.667130 | − | 0.744941i | \(-0.732478\pi\) | ||||
−0.667130 | + | 0.744941i | \(0.732478\pi\) | |||||||
\(308\) | −6.97785 | −0.397600 | ||||||||
\(309\) | 37.1842 | 2.11533 | ||||||||
\(310\) | −32.1362 | −1.82521 | ||||||||
\(311\) | 16.6144 | 0.942119 | 0.471059 | − | 0.882101i | \(-0.343872\pi\) | ||||
0.471059 | + | 0.882101i | \(0.343872\pi\) | |||||||
\(312\) | −8.49471 | −0.480918 | ||||||||
\(313\) | 6.00130 | 0.339214 | 0.169607 | − | 0.985512i | \(-0.445750\pi\) | ||||
0.169607 | + | 0.985512i | \(0.445750\pi\) | |||||||
\(314\) | 1.00966 | 0.0569784 | ||||||||
\(315\) | −79.3209 | −4.46923 | ||||||||
\(316\) | 6.66941 | 0.375184 | ||||||||
\(317\) | −16.3912 | −0.920622 | −0.460311 | − | 0.887758i | \(-0.652262\pi\) | ||||
−0.460311 | + | 0.887758i | \(0.652262\pi\) | |||||||
\(318\) | −45.4188 | −2.54696 | ||||||||
\(319\) | 7.57728 | 0.424246 | ||||||||
\(320\) | 10.2367 | 0.572250 | ||||||||
\(321\) | 15.6792 | 0.875127 | ||||||||
\(322\) | −77.4662 | −4.31703 | ||||||||
\(323\) | 7.13378 | 0.396934 | ||||||||
\(324\) | 27.3391 | 1.51884 | ||||||||
\(325\) | −3.65543 | −0.202767 | ||||||||
\(326\) | 23.6586 | 1.31033 | ||||||||
\(327\) | −3.14155 | −0.173728 | ||||||||
\(328\) | 8.54191 | 0.471648 | ||||||||
\(329\) | 43.4252 | 2.39411 | ||||||||
\(330\) | −14.1188 | −0.777213 | ||||||||
\(331\) | −16.2096 | −0.890961 | −0.445480 | − | 0.895292i | \(-0.646967\pi\) | ||||
−0.445480 | + | 0.895292i | \(0.646967\pi\) | |||||||
\(332\) | −20.8735 | −1.14558 | ||||||||
\(333\) | 6.86935 | 0.376438 | ||||||||
\(334\) | −6.35330 | −0.347637 | ||||||||
\(335\) | −7.41188 | −0.404954 | ||||||||
\(336\) | −68.7208 | −3.74903 | ||||||||
\(337\) | −22.1472 | −1.20643 | −0.603216 | − | 0.797578i | \(-0.706114\pi\) | ||||
−0.603216 | + | 0.797578i | \(0.706114\pi\) | |||||||
\(338\) | 4.91821 | 0.267516 | ||||||||
\(339\) | −32.0664 | −1.74161 | ||||||||
\(340\) | 3.72103 | 0.201801 | ||||||||
\(341\) | 6.62293 | 0.358652 | ||||||||
\(342\) | 95.6392 | 5.17158 | ||||||||
\(343\) | 36.0730 | 1.94776 | ||||||||
\(344\) | 10.2099 | 0.550482 | ||||||||
\(345\) | −68.5644 | −3.69138 | ||||||||
\(346\) | −12.0668 | −0.648713 | ||||||||
\(347\) | −3.61850 | −0.194251 | −0.0971256 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971256 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(348\) | −38.4653 | −2.06196 | ||||||||
\(349\) | −1.51397 | −0.0810408 | −0.0405204 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405204 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(350\) | −9.96844 | −0.532836 | ||||||||
\(351\) | −39.1853 | −2.09156 | ||||||||
\(352\) | −6.89929 | −0.367733 | ||||||||
\(353\) | −12.0128 | −0.639374 | −0.319687 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319687 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(354\) | −55.0533 | −2.92605 | ||||||||
\(355\) | −23.1311 | −1.22767 | ||||||||
\(356\) | 27.1125 | 1.43696 | ||||||||
\(357\) | −14.1505 | −0.748925 | ||||||||
\(358\) | −31.3015 | −1.65434 | ||||||||
\(359\) | −34.6875 | −1.83074 | −0.915368 | − | 0.402619i | \(-0.868100\pi\) | ||||
−0.915368 | + | 0.402619i | \(0.868100\pi\) | |||||||
\(360\) | −14.2709 | −0.752140 | ||||||||
\(361\) | 35.5237 | 1.86967 | ||||||||
\(362\) | 14.0382 | 0.737829 | ||||||||
\(363\) | −31.6473 | −1.66105 | ||||||||
\(364\) | −23.3726 | −1.22506 | ||||||||
\(365\) | 8.34227 | 0.436654 | ||||||||
\(366\) | −41.4586 | −2.16708 | ||||||||
\(367\) | −22.2414 | −1.16099 | −0.580497 | − | 0.814262i | \(-0.697142\pi\) | ||||
−0.580497 | + | 0.814262i | \(0.697142\pi\) | |||||||
\(368\) | −41.3453 | −2.15527 | ||||||||
\(369\) | 69.9531 | 3.64161 | ||||||||
\(370\) | 4.66980 | 0.242771 | ||||||||
\(371\) | 35.7491 | 1.85600 | ||||||||
\(372\) | −33.6207 | −1.74315 | ||||||||
\(373\) | 3.86313 | 0.200025 | 0.100013 | − | 0.994986i | \(-0.468112\pi\) | ||||
0.100013 | + | 0.994986i | \(0.468112\pi\) | |||||||
\(374\) | −1.75311 | −0.0906511 | ||||||||
\(375\) | 30.0802 | 1.55334 | ||||||||
\(376\) | 7.81276 | 0.402913 | ||||||||
\(377\) | 25.3804 | 1.30716 | ||||||||
\(378\) | −106.859 | −5.49624 | ||||||||
\(379\) | −26.8479 | −1.37908 | −0.689542 | − | 0.724245i | \(-0.742188\pi\) | ||||
−0.689542 | + | 0.724245i | \(0.742188\pi\) | |||||||
\(380\) | 28.4400 | 1.45894 | ||||||||
\(381\) | −11.1759 | −0.572560 | ||||||||
\(382\) | −7.62844 | −0.390305 | ||||||||
\(383\) | −8.62786 | −0.440863 | −0.220432 | − | 0.975402i | \(-0.570747\pi\) | ||||
−0.220432 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(384\) | −20.5598 | −1.04919 | ||||||||
\(385\) | 11.1129 | 0.566364 | ||||||||
\(386\) | −28.2980 | −1.44033 | ||||||||
\(387\) | 83.6131 | 4.25029 | ||||||||
\(388\) | 5.00118 | 0.253896 | ||||||||
\(389\) | 10.6546 | 0.540209 | 0.270104 | − | 0.962831i | \(-0.412942\pi\) | ||||
0.270104 | + | 0.962831i | \(0.412942\pi\) | |||||||
\(390\) | −47.2915 | −2.39470 | ||||||||
\(391\) | −8.51355 | −0.430549 | ||||||||
\(392\) | 12.3617 | 0.624358 | ||||||||
\(393\) | −4.24870 | −0.214319 | ||||||||
\(394\) | −24.0597 | −1.21211 | ||||||||
\(395\) | −10.6217 | −0.534433 | ||||||||
\(396\) | −10.2810 | −0.516641 | ||||||||
\(397\) | 3.77458 | 0.189441 | 0.0947205 | − | 0.995504i | \(-0.469804\pi\) | ||||
0.0947205 | + | 0.995504i | \(0.469804\pi\) | |||||||
\(398\) | −17.7072 | −0.887581 | ||||||||
\(399\) | −108.153 | −5.41442 | ||||||||
\(400\) | −5.32036 | −0.266018 | ||||||||
\(401\) | −5.88149 | −0.293708 | −0.146854 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146854 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(402\) | −17.7268 | −0.884131 | ||||||||
\(403\) | 22.1838 | 1.10506 | ||||||||
\(404\) | −2.40048 | −0.119428 | ||||||||
\(405\) | −43.5400 | −2.16352 | ||||||||
\(406\) | 69.2130 | 3.43498 | ||||||||
\(407\) | −0.962397 | −0.0477043 | ||||||||
\(408\) | −2.54586 | −0.126039 | ||||||||
\(409\) | −24.8526 | −1.22888 | −0.614442 | − | 0.788962i | \(-0.710619\pi\) | ||||
−0.614442 | + | 0.788962i | \(0.710619\pi\) | |||||||
\(410\) | 47.5543 | 2.34854 | ||||||||
\(411\) | −15.6224 | −0.770595 | ||||||||
\(412\) | 18.4069 | 0.906841 | ||||||||
\(413\) | 43.3324 | 2.13225 | ||||||||
\(414\) | −114.137 | −5.60954 | ||||||||
\(415\) | 33.2430 | 1.63184 | ||||||||
\(416\) | −23.1095 | −1.13304 | ||||||||
\(417\) | 18.3446 | 0.898339 | ||||||||
\(418\) | −13.3991 | −0.655370 | ||||||||
\(419\) | 26.6992 | 1.30434 | 0.652171 | − | 0.758072i | \(-0.273858\pi\) | ||||
0.652171 | + | 0.758072i | \(0.273858\pi\) | |||||||
\(420\) | −56.4134 | −2.75269 | ||||||||
\(421\) | −15.8071 | −0.770389 | −0.385195 | − | 0.922835i | \(-0.625866\pi\) | ||||
−0.385195 | + | 0.922835i | \(0.625866\pi\) | |||||||
\(422\) | 3.42481 | 0.166717 | ||||||||
\(423\) | 63.9819 | 3.11090 | ||||||||
\(424\) | 6.43172 | 0.312352 | ||||||||
\(425\) | −1.09553 | −0.0531411 | ||||||||
\(426\) | −55.3221 | −2.68036 | ||||||||
\(427\) | 32.6321 | 1.57918 | ||||||||
\(428\) | 7.76149 | 0.375166 | ||||||||
\(429\) | 9.74629 | 0.470555 | ||||||||
\(430\) | 56.8403 | 2.74108 | ||||||||
\(431\) | −13.6763 | −0.658766 | −0.329383 | − | 0.944196i | \(-0.606841\pi\) | ||||
−0.329383 | + | 0.944196i | \(0.606841\pi\) | |||||||
\(432\) | −57.0329 | −2.74400 | ||||||||
\(433\) | 1.31622 | 0.0632534 | 0.0316267 | − | 0.999500i | \(-0.489931\pi\) | ||||
0.0316267 | + | 0.999500i | \(0.489931\pi\) | |||||||
\(434\) | 60.4957 | 2.90389 | ||||||||
\(435\) | 61.2595 | 2.93717 | ||||||||
\(436\) | −1.55513 | −0.0744771 | ||||||||
\(437\) | −65.0693 | −3.11269 | ||||||||
\(438\) | 19.9520 | 0.953342 | ||||||||
\(439\) | −29.2462 | −1.39585 | −0.697923 | − | 0.716173i | \(-0.745892\pi\) | ||||
−0.697923 | + | 0.716173i | \(0.745892\pi\) | |||||||
\(440\) | 1.99935 | 0.0953152 | ||||||||
\(441\) | 101.235 | 4.82070 | ||||||||
\(442\) | −5.87212 | −0.279308 | ||||||||
\(443\) | −34.6794 | −1.64767 | −0.823833 | − | 0.566832i | \(-0.808169\pi\) | ||||
−0.823833 | + | 0.566832i | \(0.808169\pi\) | |||||||
\(444\) | 4.88551 | 0.231856 | ||||||||
\(445\) | −43.1792 | −2.04689 | ||||||||
\(446\) | −5.99918 | −0.284069 | ||||||||
\(447\) | −60.8289 | −2.87711 | ||||||||
\(448\) | −19.2704 | −0.910443 | ||||||||
\(449\) | 7.40171 | 0.349308 | 0.174654 | − | 0.984630i | \(-0.444119\pi\) | ||||
0.174654 | + | 0.984630i | \(0.444119\pi\) | |||||||
\(450\) | −14.6873 | −0.692366 | ||||||||
\(451\) | −9.80044 | −0.461485 | ||||||||
\(452\) | −15.8735 | −0.746625 | ||||||||
\(453\) | 12.0337 | 0.565394 | ||||||||
\(454\) | 3.93082 | 0.184483 | ||||||||
\(455\) | 37.2231 | 1.74504 | ||||||||
\(456\) | −19.4581 | −0.911210 | ||||||||
\(457\) | 26.1181 | 1.22175 | 0.610876 | − | 0.791726i | \(-0.290817\pi\) | ||||
0.610876 | + | 0.791726i | \(0.290817\pi\) | |||||||
\(458\) | 50.8359 | 2.37541 | ||||||||
\(459\) | −11.7438 | −0.548155 | ||||||||
\(460\) | −33.9406 | −1.58249 | ||||||||
\(461\) | 2.67482 | 0.124579 | 0.0622893 | − | 0.998058i | \(-0.480160\pi\) | ||||
0.0622893 | + | 0.998058i | \(0.480160\pi\) | |||||||
\(462\) | 26.5783 | 1.23654 | ||||||||
\(463\) | −10.6459 | −0.494759 | −0.247380 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247380 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(464\) | 36.9404 | 1.71491 | ||||||||
\(465\) | 53.5440 | 2.48304 | ||||||||
\(466\) | 28.5182 | 1.32108 | ||||||||
\(467\) | −15.2321 | −0.704859 | −0.352430 | − | 0.935838i | \(-0.614644\pi\) | ||||
−0.352430 | + | 0.935838i | \(0.614644\pi\) | |||||||
\(468\) | −34.4367 | −1.59184 | ||||||||
\(469\) | 13.9527 | 0.644277 | ||||||||
\(470\) | 43.4950 | 2.00627 | ||||||||
\(471\) | −1.68226 | −0.0775142 | ||||||||
\(472\) | 7.79606 | 0.358843 | ||||||||
\(473\) | −11.7142 | −0.538620 | ||||||||
\(474\) | −25.4035 | −1.16682 | ||||||||
\(475\) | −8.37319 | −0.384188 | ||||||||
\(476\) | −7.00477 | −0.321063 | ||||||||
\(477\) | 52.6719 | 2.41168 | ||||||||
\(478\) | 20.7903 | 0.950928 | ||||||||
\(479\) | 21.8413 | 0.997956 | 0.498978 | − | 0.866615i | \(-0.333709\pi\) | ||||
0.498978 | + | 0.866615i | \(0.333709\pi\) | |||||||
\(480\) | −55.7782 | −2.54592 | ||||||||
\(481\) | −3.22360 | −0.146983 | ||||||||
\(482\) | 16.6826 | 0.759870 | ||||||||
\(483\) | 129.071 | 5.87294 | ||||||||
\(484\) | −15.6660 | −0.712092 | ||||||||
\(485\) | −7.96484 | −0.361665 | ||||||||
\(486\) | −35.3740 | −1.60460 | ||||||||
\(487\) | 2.58327 | 0.117059 | 0.0585296 | − | 0.998286i | \(-0.481359\pi\) | ||||
0.0585296 | + | 0.998286i | \(0.481359\pi\) | |||||||
\(488\) | 5.87093 | 0.265764 | ||||||||
\(489\) | −39.4190 | −1.78259 | ||||||||
\(490\) | 68.8195 | 3.10895 | ||||||||
\(491\) | 21.0707 | 0.950909 | 0.475454 | − | 0.879740i | \(-0.342284\pi\) | ||||
0.475454 | + | 0.879740i | \(0.342284\pi\) | |||||||
\(492\) | 49.7510 | 2.24295 | ||||||||
\(493\) | 7.60652 | 0.342580 | ||||||||
\(494\) | −44.8808 | −2.01928 | ||||||||
\(495\) | 16.3735 | 0.735933 | ||||||||
\(496\) | 32.2878 | 1.44977 | ||||||||
\(497\) | 43.5439 | 1.95321 | ||||||||
\(498\) | 79.5064 | 3.56277 | ||||||||
\(499\) | −11.9247 | −0.533823 | −0.266912 | − | 0.963721i | \(-0.586003\pi\) | ||||
−0.266912 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(500\) | 14.8903 | 0.665913 | ||||||||
\(501\) | 10.5856 | 0.472931 | ||||||||
\(502\) | −58.3230 | −2.60308 | ||||||||
\(503\) | −8.05541 | −0.359173 | −0.179586 | − | 0.983742i | \(-0.557476\pi\) | ||||
−0.179586 | + | 0.983742i | \(0.557476\pi\) | |||||||
\(504\) | 26.8646 | 1.19665 | ||||||||
\(505\) | 3.82298 | 0.170121 | ||||||||
\(506\) | 15.9906 | 0.710870 | ||||||||
\(507\) | −8.19453 | −0.363932 | ||||||||
\(508\) | −5.53230 | −0.245456 | ||||||||
\(509\) | −27.2131 | −1.20620 | −0.603099 | − | 0.797666i | \(-0.706068\pi\) | ||||
−0.603099 | + | 0.797666i | \(0.706068\pi\) | |||||||
\(510\) | −14.1732 | −0.627602 | ||||||||
\(511\) | −15.7042 | −0.694712 | ||||||||
\(512\) | −25.7640 | −1.13862 | ||||||||
\(513\) | −89.7584 | −3.96293 | ||||||||
\(514\) | −7.10085 | −0.313205 | ||||||||
\(515\) | −29.3146 | −1.29176 | ||||||||
\(516\) | 59.4660 | 2.61784 | ||||||||
\(517\) | −8.96387 | −0.394230 | ||||||||
\(518\) | −8.79081 | −0.386246 | ||||||||
\(519\) | 20.1051 | 0.882518 | ||||||||
\(520\) | 6.69691 | 0.293679 | ||||||||
\(521\) | −27.2910 | −1.19564 | −0.597821 | − | 0.801630i | \(-0.703966\pi\) | ||||
−0.597821 | + | 0.801630i | \(0.703966\pi\) | |||||||
\(522\) | 101.977 | 4.46341 | ||||||||
\(523\) | −12.4316 | −0.543597 | −0.271798 | − | 0.962354i | \(-0.587618\pi\) | ||||
−0.271798 | + | 0.962354i | \(0.587618\pi\) | |||||||
\(524\) | −2.10319 | −0.0918781 | ||||||||
\(525\) | 16.6090 | 0.724877 | ||||||||
\(526\) | −40.9972 | −1.78756 | ||||||||
\(527\) | 6.64849 | 0.289613 | ||||||||
\(528\) | 14.1854 | 0.617340 | ||||||||
\(529\) | 54.6546 | 2.37629 | ||||||||
\(530\) | 35.8065 | 1.55533 | ||||||||
\(531\) | 63.8451 | 2.77064 | ||||||||
\(532\) | −53.5377 | −2.32115 | ||||||||
\(533\) | −32.8271 | −1.42190 | ||||||||
\(534\) | −103.270 | −4.46895 | ||||||||
\(535\) | −12.3609 | −0.534408 | ||||||||
\(536\) | 2.51028 | 0.108427 | ||||||||
\(537\) | 52.1533 | 2.25058 | ||||||||
\(538\) | −41.3914 | −1.78451 | ||||||||
\(539\) | −14.1830 | −0.610905 | ||||||||
\(540\) | −46.8187 | −2.01475 | ||||||||
\(541\) | 43.7701 | 1.88182 | 0.940911 | − | 0.338654i | \(-0.109972\pi\) | ||||
0.940911 | + | 0.338654i | \(0.109972\pi\) | |||||||
\(542\) | −47.2144 | −2.02803 | ||||||||
\(543\) | −23.3898 | −1.00375 | ||||||||
\(544\) | −6.92591 | −0.296946 | ||||||||
\(545\) | 2.47668 | 0.106089 | ||||||||
\(546\) | 89.0253 | 3.80993 | ||||||||
\(547\) | 4.55584 | 0.194794 | 0.0973968 | − | 0.995246i | \(-0.468948\pi\) | ||||
0.0973968 | + | 0.995246i | \(0.468948\pi\) | |||||||
\(548\) | −7.73337 | −0.330353 | ||||||||
\(549\) | 48.0794 | 2.05198 | ||||||||
\(550\) | 2.05769 | 0.0877403 | ||||||||
\(551\) | 58.1368 | 2.47671 | ||||||||
\(552\) | 23.2216 | 0.988376 | ||||||||
\(553\) | 19.9951 | 0.850277 | ||||||||
\(554\) | 2.10114 | 0.0892687 | ||||||||
\(555\) | −7.78063 | −0.330269 | ||||||||
\(556\) | 9.08092 | 0.385117 | ||||||||
\(557\) | −39.6417 | −1.67967 | −0.839836 | − | 0.542840i | \(-0.817349\pi\) | ||||
−0.839836 | + | 0.542840i | \(0.817349\pi\) | |||||||
\(558\) | 89.1332 | 3.77331 | ||||||||
\(559\) | −39.2373 | −1.65956 | ||||||||
\(560\) | 54.1769 | 2.28939 | ||||||||
\(561\) | 2.92096 | 0.123323 | ||||||||
\(562\) | −11.8563 | −0.500128 | ||||||||
\(563\) | 7.45319 | 0.314114 | 0.157057 | − | 0.987590i | \(-0.449799\pi\) | ||||
0.157057 | + | 0.987590i | \(0.449799\pi\) | |||||||
\(564\) | 45.5042 | 1.91607 | ||||||||
\(565\) | 25.2800 | 1.06354 | ||||||||
\(566\) | 36.5940 | 1.53816 | ||||||||
\(567\) | 81.9632 | 3.44213 | ||||||||
\(568\) | 7.83412 | 0.328712 | ||||||||
\(569\) | −9.77723 | −0.409883 | −0.204941 | − | 0.978774i | \(-0.565700\pi\) | ||||
−0.204941 | + | 0.978774i | \(0.565700\pi\) | |||||||
\(570\) | −108.327 | −4.53730 | ||||||||
\(571\) | −29.2452 | −1.22387 | −0.611936 | − | 0.790907i | \(-0.709609\pi\) | ||||
−0.611936 | + | 0.790907i | \(0.709609\pi\) | |||||||
\(572\) | 4.82459 | 0.201726 | ||||||||
\(573\) | 12.7102 | 0.530976 | ||||||||
\(574\) | −89.5200 | −3.73649 | ||||||||
\(575\) | 9.99268 | 0.416724 | ||||||||
\(576\) | −28.3927 | −1.18303 | ||||||||
\(577\) | 18.4699 | 0.768913 | 0.384457 | − | 0.923143i | \(-0.374389\pi\) | ||||
0.384457 | + | 0.923143i | \(0.374389\pi\) | |||||||
\(578\) | 30.2937 | 1.26005 | ||||||||
\(579\) | 47.1490 | 1.95944 | ||||||||
\(580\) | 30.3246 | 1.25916 | ||||||||
\(581\) | −62.5794 | −2.59623 | ||||||||
\(582\) | −19.0493 | −0.789618 | ||||||||
\(583\) | −7.37935 | −0.305621 | ||||||||
\(584\) | −2.82538 | −0.116915 | ||||||||
\(585\) | 54.8437 | 2.26751 | ||||||||
\(586\) | −7.98804 | −0.329983 | ||||||||
\(587\) | 31.7415 | 1.31011 | 0.655056 | − | 0.755580i | \(-0.272645\pi\) | ||||
0.655056 | + | 0.755580i | \(0.272645\pi\) | |||||||
\(588\) | 71.9985 | 2.96917 | ||||||||
\(589\) | 50.8146 | 2.09378 | ||||||||
\(590\) | 43.4020 | 1.78683 | ||||||||
\(591\) | 40.0872 | 1.64897 | ||||||||
\(592\) | −4.69183 | −0.192833 | ||||||||
\(593\) | −23.5019 | −0.965107 | −0.482553 | − | 0.875867i | \(-0.660291\pi\) | ||||
−0.482553 | + | 0.875867i | \(0.660291\pi\) | |||||||
\(594\) | 22.0579 | 0.905048 | ||||||||
\(595\) | 11.1557 | 0.457341 | ||||||||
\(596\) | −30.1114 | −1.23341 | ||||||||
\(597\) | 29.5030 | 1.20748 | ||||||||
\(598\) | 53.5614 | 2.19029 | ||||||||
\(599\) | −17.5921 | −0.718793 | −0.359396 | − | 0.933185i | \(-0.617017\pi\) | ||||
−0.359396 | + | 0.933185i | \(0.617017\pi\) | |||||||
\(600\) | 2.98818 | 0.121992 | ||||||||
\(601\) | 39.9434 | 1.62932 | 0.814662 | − | 0.579936i | \(-0.196922\pi\) | ||||
0.814662 | + | 0.579936i | \(0.196922\pi\) | |||||||
\(602\) | −107.001 | −4.36103 | ||||||||
\(603\) | 20.5577 | 0.837173 | ||||||||
\(604\) | 5.95692 | 0.242384 | ||||||||
\(605\) | 24.9496 | 1.01435 | ||||||||
\(606\) | 9.14332 | 0.371422 | ||||||||
\(607\) | −17.4151 | −0.706855 | −0.353428 | − | 0.935462i | \(-0.614984\pi\) | ||||
−0.353428 | + | 0.935462i | \(0.614984\pi\) | |||||||
\(608\) | −52.9349 | −2.14680 | ||||||||
\(609\) | −115.320 | −4.67300 | ||||||||
\(610\) | 32.6845 | 1.32335 | ||||||||
\(611\) | −30.0249 | −1.21468 | ||||||||
\(612\) | −10.3207 | −0.417189 | ||||||||
\(613\) | 23.6579 | 0.955533 | 0.477767 | − | 0.878487i | \(-0.341446\pi\) | ||||
0.477767 | + | 0.878487i | \(0.341446\pi\) | |||||||
\(614\) | 44.0796 | 1.77891 | ||||||||
\(615\) | −79.2330 | −3.19498 | ||||||||
\(616\) | −3.76374 | −0.151645 | ||||||||
\(617\) | −15.5629 | −0.626537 | −0.313269 | − | 0.949665i | \(-0.601424\pi\) | ||||
−0.313269 | + | 0.949665i | \(0.601424\pi\) | |||||||
\(618\) | −70.1109 | −2.82027 | ||||||||
\(619\) | 31.0690 | 1.24877 | 0.624385 | − | 0.781117i | \(-0.285350\pi\) | ||||
0.624385 | + | 0.781117i | \(0.285350\pi\) | |||||||
\(620\) | 26.5053 | 1.06448 | ||||||||
\(621\) | 107.119 | 4.29854 | ||||||||
\(622\) | −31.3266 | −1.25608 | ||||||||
\(623\) | 81.2840 | 3.25658 | ||||||||
\(624\) | 47.5146 | 1.90211 | ||||||||
\(625\) | −29.3839 | −1.17536 | ||||||||
\(626\) | −11.3155 | −0.452257 | ||||||||
\(627\) | 22.3250 | 0.891575 | ||||||||
\(628\) | −0.832748 | −0.0332302 | ||||||||
\(629\) | −0.966111 | −0.0385214 | ||||||||
\(630\) | 149.560 | 5.95861 | ||||||||
\(631\) | −7.19600 | −0.286468 | −0.143234 | − | 0.989689i | \(-0.545750\pi\) | ||||
−0.143234 | + | 0.989689i | \(0.545750\pi\) | |||||||
\(632\) | 3.59737 | 0.143096 | ||||||||
\(633\) | −5.70628 | −0.226804 | ||||||||
\(634\) | 30.9057 | 1.22742 | ||||||||
\(635\) | 8.81069 | 0.349642 | ||||||||
\(636\) | 37.4605 | 1.48541 | ||||||||
\(637\) | −47.5066 | −1.88228 | ||||||||
\(638\) | −14.2870 | −0.565627 | ||||||||
\(639\) | 64.1567 | 2.53800 | ||||||||
\(640\) | 16.2086 | 0.640701 | ||||||||
\(641\) | 4.86319 | 0.192085 | 0.0960423 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960423 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(642\) | −29.5632 | −1.16677 | ||||||||
\(643\) | −11.6229 | −0.458363 | −0.229182 | − | 0.973384i | \(-0.573605\pi\) | ||||
−0.229182 | + | 0.973384i | \(0.573605\pi\) | |||||||
\(644\) | 63.8926 | 2.51772 | ||||||||
\(645\) | −94.7051 | −3.72901 | ||||||||
\(646\) | −13.4508 | −0.529214 | ||||||||
\(647\) | −19.8855 | −0.781781 | −0.390890 | − | 0.920437i | \(-0.627833\pi\) | ||||
−0.390890 | + | 0.920437i | \(0.627833\pi\) | |||||||
\(648\) | 14.7462 | 0.579287 | ||||||||
\(649\) | −8.94471 | −0.351110 | ||||||||
\(650\) | 6.89234 | 0.270340 | ||||||||
\(651\) | −100.796 | −3.95049 | ||||||||
\(652\) | −19.5131 | −0.764194 | ||||||||
\(653\) | 7.28945 | 0.285258 | 0.142629 | − | 0.989776i | \(-0.454444\pi\) | ||||
0.142629 | + | 0.989776i | \(0.454444\pi\) | |||||||
\(654\) | 5.92341 | 0.231624 | ||||||||
\(655\) | 3.34952 | 0.130876 | ||||||||
\(656\) | −47.7787 | −1.86544 | ||||||||
\(657\) | −23.1382 | −0.902707 | ||||||||
\(658\) | −81.8785 | −3.19196 | ||||||||
\(659\) | −22.5229 | −0.877368 | −0.438684 | − | 0.898641i | \(-0.644555\pi\) | ||||
−0.438684 | + | 0.898641i | \(0.644555\pi\) | |||||||
\(660\) | 11.6449 | 0.453276 | ||||||||
\(661\) | −4.84123 | −0.188302 | −0.0941510 | − | 0.995558i | \(-0.530014\pi\) | ||||
−0.0941510 | + | 0.995558i | \(0.530014\pi\) | |||||||
\(662\) | 30.5633 | 1.18788 | ||||||||
\(663\) | 9.78390 | 0.379975 | ||||||||
\(664\) | −11.2588 | −0.436928 | ||||||||
\(665\) | 85.2638 | 3.30639 | ||||||||
\(666\) | −12.9522 | −0.501887 | ||||||||
\(667\) | −69.3813 | −2.68646 | ||||||||
\(668\) | 5.24008 | 0.202745 | ||||||||
\(669\) | 9.99559 | 0.386452 | ||||||||
\(670\) | 13.9751 | 0.539906 | ||||||||
\(671\) | −6.73593 | −0.260038 | ||||||||
\(672\) | 105.001 | 4.05052 | ||||||||
\(673\) | 11.9610 | 0.461062 | 0.230531 | − | 0.973065i | \(-0.425954\pi\) | ||||
0.230531 | + | 0.973065i | \(0.425954\pi\) | |||||||
\(674\) | 41.7586 | 1.60848 | ||||||||
\(675\) | 13.7842 | 0.530554 | ||||||||
\(676\) | −4.05645 | −0.156017 | ||||||||
\(677\) | 46.9617 | 1.80489 | 0.902443 | − | 0.430809i | \(-0.141772\pi\) | ||||
0.902443 | + | 0.430809i | \(0.141772\pi\) | |||||||
\(678\) | 60.4613 | 2.32200 | ||||||||
\(679\) | 14.9937 | 0.575404 | ||||||||
\(680\) | 2.00706 | 0.0769674 | ||||||||
\(681\) | −6.54938 | −0.250973 | ||||||||
\(682\) | −12.4876 | −0.478174 | ||||||||
\(683\) | −25.5505 | −0.977663 | −0.488832 | − | 0.872378i | \(-0.662577\pi\) | ||||
−0.488832 | + | 0.872378i | \(0.662577\pi\) | |||||||
\(684\) | −78.8813 | −3.01610 | ||||||||
\(685\) | 12.3161 | 0.470574 | ||||||||
\(686\) | −68.0158 | −2.59685 | ||||||||
\(687\) | −84.7008 | −3.23154 | ||||||||
\(688\) | −57.1086 | −2.17724 | ||||||||
\(689\) | −24.7175 | −0.941660 | ||||||||
\(690\) | 129.278 | 4.92155 | ||||||||
\(691\) | −26.3063 | −1.00074 | −0.500370 | − | 0.865812i | \(-0.666803\pi\) | ||||
−0.500370 | + | 0.865812i | \(0.666803\pi\) | |||||||
\(692\) | 9.95242 | 0.378334 | ||||||||
\(693\) | −30.8228 | −1.17086 | ||||||||
\(694\) | 6.82270 | 0.258986 | ||||||||
\(695\) | −14.4622 | −0.548583 | ||||||||
\(696\) | −20.7476 | −0.786434 | ||||||||
\(697\) | −9.83826 | −0.372651 | ||||||||
\(698\) | 2.85459 | 0.108048 | ||||||||
\(699\) | −47.5159 | −1.79722 | ||||||||
\(700\) | 8.22177 | 0.310754 | ||||||||
\(701\) | −1.94129 | −0.0733214 | −0.0366607 | − | 0.999328i | \(-0.511672\pi\) | ||||
−0.0366607 | + | 0.999328i | \(0.511672\pi\) | |||||||
\(702\) | 73.8841 | 2.78857 | ||||||||
\(703\) | −7.38402 | −0.278493 | ||||||||
\(704\) | 3.97782 | 0.149920 | ||||||||
\(705\) | −72.4696 | −2.72936 | ||||||||
\(706\) | 22.6501 | 0.852448 | ||||||||
\(707\) | −7.19670 | −0.270660 | ||||||||
\(708\) | 45.4069 | 1.70650 | ||||||||
\(709\) | −11.6460 | −0.437374 | −0.218687 | − | 0.975795i | \(-0.570177\pi\) | ||||
−0.218687 | + | 0.975795i | \(0.570177\pi\) | |||||||
\(710\) | 43.6139 | 1.63680 | ||||||||
\(711\) | 29.4603 | 1.10485 | ||||||||
\(712\) | 14.6241 | 0.548060 | ||||||||
\(713\) | −60.6429 | −2.27109 | ||||||||
\(714\) | 26.6809 | 0.998507 | ||||||||
\(715\) | −7.68361 | −0.287351 | ||||||||
\(716\) | 25.8169 | 0.964821 | ||||||||
\(717\) | −34.6400 | −1.29366 | ||||||||
\(718\) | 65.4034 | 2.44083 | ||||||||
\(719\) | −43.2884 | −1.61439 | −0.807193 | − | 0.590288i | \(-0.799014\pi\) | ||||
−0.807193 | + | 0.590288i | \(0.799014\pi\) | |||||||
\(720\) | 79.8232 | 2.97483 | ||||||||
\(721\) | 55.1842 | 2.05517 | ||||||||
\(722\) | −66.9801 | −2.49274 | ||||||||
\(723\) | −27.7958 | −1.03374 | ||||||||
\(724\) | −11.5784 | −0.430308 | ||||||||
\(725\) | −8.92806 | −0.331580 | ||||||||
\(726\) | 59.6712 | 2.21461 | ||||||||
\(727\) | −5.14695 | −0.190890 | −0.0954450 | − | 0.995435i | \(-0.530427\pi\) | ||||
−0.0954450 | + | 0.995435i | \(0.530427\pi\) | |||||||
\(728\) | −12.6068 | −0.467240 | ||||||||
\(729\) | 6.19885 | 0.229587 | ||||||||
\(730\) | −15.7294 | −0.582171 | ||||||||
\(731\) | −11.7594 | −0.434937 | ||||||||
\(732\) | 34.1943 | 1.26386 | ||||||||
\(733\) | 17.4741 | 0.645419 | 0.322710 | − | 0.946498i | \(-0.395406\pi\) | ||||
0.322710 | + | 0.946498i | \(0.395406\pi\) | |||||||
\(734\) | 41.9363 | 1.54790 | ||||||||
\(735\) | −114.664 | −4.22946 | ||||||||
\(736\) | 63.1733 | 2.32860 | ||||||||
\(737\) | −2.88013 | −0.106091 | ||||||||
\(738\) | −131.897 | −4.85519 | ||||||||
\(739\) | −6.52220 | −0.239923 | −0.119962 | − | 0.992779i | \(-0.538277\pi\) | ||||
−0.119962 | + | 0.992779i | \(0.538277\pi\) | |||||||
\(740\) | −3.85156 | −0.141586 | ||||||||
\(741\) | 74.7786 | 2.74706 | ||||||||
\(742\) | −67.4050 | −2.47452 | ||||||||
\(743\) | −2.65513 | −0.0974072 | −0.0487036 | − | 0.998813i | \(-0.515509\pi\) | ||||
−0.0487036 | + | 0.998813i | \(0.515509\pi\) | |||||||
\(744\) | −18.1344 | −0.664841 | ||||||||
\(745\) | 47.9552 | 1.75694 | ||||||||
\(746\) | −7.28396 | −0.266685 | ||||||||
\(747\) | −92.2032 | −3.37354 | ||||||||
\(748\) | 1.44593 | 0.0528684 | ||||||||
\(749\) | 23.2691 | 0.850236 | ||||||||
\(750\) | −56.7164 | −2.07099 | ||||||||
\(751\) | −0.572086 | −0.0208757 | −0.0104379 | − | 0.999946i | \(-0.503323\pi\) | ||||
−0.0104379 | + | 0.999946i | \(0.503323\pi\) | |||||||
\(752\) | −43.7002 | −1.59358 | ||||||||
\(753\) | 97.1755 | 3.54127 | ||||||||
\(754\) | −47.8549 | −1.74277 | ||||||||
\(755\) | −9.48695 | −0.345265 | ||||||||
\(756\) | 88.1353 | 3.20545 | ||||||||
\(757\) | 40.1993 | 1.46107 | 0.730535 | − | 0.682875i | \(-0.239271\pi\) | ||||
0.730535 | + | 0.682875i | \(0.239271\pi\) | |||||||
\(758\) | 50.6219 | 1.83867 | ||||||||
\(759\) | −26.6430 | −0.967078 | ||||||||
\(760\) | 15.3401 | 0.556442 | ||||||||
\(761\) | 24.4453 | 0.886141 | 0.443070 | − | 0.896487i | \(-0.353889\pi\) | ||||
0.443070 | + | 0.896487i | \(0.353889\pi\) | |||||||
\(762\) | 21.0723 | 0.763368 | ||||||||
\(763\) | −4.66231 | −0.168787 | ||||||||
\(764\) | 6.29179 | 0.227629 | ||||||||
\(765\) | 16.4367 | 0.594268 | ||||||||
\(766\) | 16.2679 | 0.587782 | ||||||||
\(767\) | −29.9607 | −1.08182 | ||||||||
\(768\) | 64.7352 | 2.33593 | ||||||||
\(769\) | −12.5550 | −0.452745 | −0.226373 | − | 0.974041i | \(-0.572687\pi\) | ||||
−0.226373 | + | 0.974041i | \(0.572687\pi\) | |||||||
\(770\) | −20.9534 | −0.755107 | ||||||||
\(771\) | 11.8312 | 0.426089 | ||||||||
\(772\) | 23.3396 | 0.840011 | ||||||||
\(773\) | −3.94708 | −0.141967 | −0.0709833 | − | 0.997478i | \(-0.522614\pi\) | ||||
−0.0709833 | + | 0.997478i | \(0.522614\pi\) | |||||||
\(774\) | −157.653 | −5.66672 | ||||||||
\(775\) | −7.80359 | −0.280313 | ||||||||
\(776\) | 2.69755 | 0.0968366 | ||||||||
\(777\) | 14.6469 | 0.525454 | ||||||||
\(778\) | −20.0893 | −0.720235 | ||||||||
\(779\) | −75.1941 | −2.69411 | ||||||||
\(780\) | 39.0051 | 1.39661 | ||||||||
\(781\) | −8.98837 | −0.321629 | ||||||||
\(782\) | 16.0523 | 0.574030 | ||||||||
\(783\) | −95.7065 | −3.42027 | ||||||||
\(784\) | −69.1442 | −2.46944 | ||||||||
\(785\) | 1.32623 | 0.0473351 | ||||||||
\(786\) | 8.01094 | 0.285741 | ||||||||
\(787\) | 24.0639 | 0.857785 | 0.428892 | − | 0.903356i | \(-0.358904\pi\) | ||||
0.428892 | + | 0.903356i | \(0.358904\pi\) | |||||||
\(788\) | 19.8439 | 0.706911 | ||||||||
\(789\) | 68.3080 | 2.43183 | ||||||||
\(790\) | 20.0272 | 0.712535 | ||||||||
\(791\) | −47.5891 | −1.69207 | ||||||||
\(792\) | −5.54541 | −0.197048 | ||||||||
\(793\) | −22.5623 | −0.801211 | ||||||||
\(794\) | −7.11700 | −0.252573 | ||||||||
\(795\) | −59.6593 | −2.11590 | ||||||||
\(796\) | 14.6045 | 0.517644 | ||||||||
\(797\) | −33.6271 | −1.19113 | −0.595566 | − | 0.803307i | \(-0.703072\pi\) | ||||
−0.595566 | + | 0.803307i | \(0.703072\pi\) | |||||||
\(798\) | 203.923 | 7.21879 | ||||||||
\(799\) | −8.99846 | −0.318343 | ||||||||
\(800\) | 8.12921 | 0.287411 | ||||||||
\(801\) | 119.762 | 4.23159 | ||||||||
\(802\) | 11.0896 | 0.391586 | ||||||||
\(803\) | 3.24167 | 0.114396 | ||||||||
\(804\) | 14.6207 | 0.515632 | ||||||||
\(805\) | −101.755 | −3.58639 | ||||||||
\(806\) | −41.8277 | −1.47332 | ||||||||
\(807\) | 68.9647 | 2.42767 | ||||||||
\(808\) | −1.29478 | −0.0455502 | ||||||||
\(809\) | 37.7478 | 1.32714 | 0.663572 | − | 0.748113i | \(-0.269040\pi\) | ||||
0.663572 | + | 0.748113i | \(0.269040\pi\) | |||||||
\(810\) | 82.0948 | 2.88452 | ||||||||
\(811\) | −25.2396 | −0.886284 | −0.443142 | − | 0.896451i | \(-0.646136\pi\) | ||||
−0.443142 | + | 0.896451i | \(0.646136\pi\) | |||||||
\(812\) | −57.0855 | −2.00331 | ||||||||
\(813\) | 78.6668 | 2.75896 | ||||||||
\(814\) | 1.81460 | 0.0636019 | ||||||||
\(815\) | 31.0765 | 1.08856 | ||||||||
\(816\) | 14.2401 | 0.498504 | ||||||||
\(817\) | −89.8775 | −3.14442 | ||||||||
\(818\) | 46.8598 | 1.63841 | ||||||||
\(819\) | −103.242 | −3.60758 | ||||||||
\(820\) | −39.2218 | −1.36969 | ||||||||
\(821\) | 46.7434 | 1.63136 | 0.815678 | − | 0.578507i | \(-0.196364\pi\) | ||||
0.815678 | + | 0.578507i | \(0.196364\pi\) | |||||||
\(822\) | 29.4561 | 1.02740 | ||||||||
\(823\) | 26.2895 | 0.916393 | 0.458197 | − | 0.888851i | \(-0.348496\pi\) | ||||
0.458197 | + | 0.888851i | \(0.348496\pi\) | |||||||
\(824\) | 9.92836 | 0.345871 | ||||||||
\(825\) | −3.42844 | −0.119363 | ||||||||
\(826\) | −81.7035 | −2.84283 | ||||||||
\(827\) | −7.00302 | −0.243519 | −0.121759 | − | 0.992560i | \(-0.538854\pi\) | ||||
−0.121759 | + | 0.992560i | \(0.538854\pi\) | |||||||
\(828\) | 94.1381 | 3.27152 | ||||||||
\(829\) | −2.22179 | −0.0771659 | −0.0385829 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385829 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(830\) | −62.6799 | −2.17565 | ||||||||
\(831\) | −3.50083 | −0.121442 | ||||||||
\(832\) | 13.3239 | 0.461923 | ||||||||
\(833\) | −14.2377 | −0.493308 | ||||||||
\(834\) | −34.5888 | −1.19771 | ||||||||
\(835\) | −8.34531 | −0.288801 | ||||||||
\(836\) | 11.0513 | 0.382217 | ||||||||
\(837\) | −83.6525 | −2.89145 | ||||||||
\(838\) | −50.3415 | −1.73902 | ||||||||
\(839\) | 6.64832 | 0.229525 | 0.114763 | − | 0.993393i | \(-0.463389\pi\) | ||||
0.114763 | + | 0.993393i | \(0.463389\pi\) | |||||||
\(840\) | −30.4284 | −1.04988 | ||||||||
\(841\) | 32.9894 | 1.13757 | ||||||||
\(842\) | 29.8043 | 1.02712 | ||||||||
\(843\) | 19.7545 | 0.680381 | ||||||||
\(844\) | −2.82472 | −0.0972308 | ||||||||
\(845\) | 6.46027 | 0.222240 | ||||||||
\(846\) | −120.638 | −4.14762 | ||||||||
\(847\) | −46.9671 | −1.61381 | ||||||||
\(848\) | −35.9754 | −1.23540 | ||||||||
\(849\) | −60.9715 | −2.09254 | ||||||||
\(850\) | 2.06563 | 0.0708506 | ||||||||
\(851\) | 8.81219 | 0.302078 | ||||||||
\(852\) | 45.6286 | 1.56321 | ||||||||
\(853\) | 2.71839 | 0.0930760 | 0.0465380 | − | 0.998917i | \(-0.485181\pi\) | ||||
0.0465380 | + | 0.998917i | \(0.485181\pi\) | |||||||
\(854\) | −61.5279 | −2.10544 | ||||||||
\(855\) | 125.626 | 4.29631 | ||||||||
\(856\) | 4.18642 | 0.143089 | ||||||||
\(857\) | −3.14670 | −0.107489 | −0.0537445 | − | 0.998555i | \(-0.517116\pi\) | ||||
−0.0537445 | + | 0.998555i | \(0.517116\pi\) | |||||||
\(858\) | −18.3767 | −0.627369 | ||||||||
\(859\) | 42.8976 | 1.46365 | 0.731824 | − | 0.681493i | \(-0.238669\pi\) | ||||
0.731824 | + | 0.681493i | \(0.238669\pi\) | |||||||
\(860\) | −46.8808 | −1.59862 | ||||||||
\(861\) | 149.155 | 5.08318 | ||||||||
\(862\) | 25.7868 | 0.878301 | ||||||||
\(863\) | 14.5518 | 0.495349 | 0.247674 | − | 0.968843i | \(-0.420334\pi\) | ||||
0.247674 | + | 0.968843i | \(0.420334\pi\) | |||||||
\(864\) | 87.1430 | 2.96466 | ||||||||
\(865\) | −15.8502 | −0.538921 | ||||||||
\(866\) | −2.48173 | −0.0843327 | ||||||||
\(867\) | −50.4742 | −1.71419 | ||||||||
\(868\) | −49.8957 | −1.69357 | ||||||||
\(869\) | −4.12740 | −0.140012 | ||||||||
\(870\) | −115.505 | −3.91599 | ||||||||
\(871\) | −9.64713 | −0.326881 | ||||||||
\(872\) | −0.838810 | −0.0284057 | ||||||||
\(873\) | 22.0914 | 0.747679 | ||||||||
\(874\) | 122.689 | 4.15000 | ||||||||
\(875\) | 44.6414 | 1.50916 | ||||||||
\(876\) | −16.4560 | −0.555996 | ||||||||
\(877\) | 36.1123 | 1.21942 | 0.609712 | − | 0.792623i | \(-0.291285\pi\) | ||||
0.609712 | + | 0.792623i | \(0.291285\pi\) | |||||||
\(878\) | 55.1439 | 1.86102 | ||||||||
\(879\) | 13.3093 | 0.448913 | ||||||||
\(880\) | −11.1832 | −0.376987 | ||||||||
\(881\) | −10.0254 | −0.337765 | −0.168883 | − | 0.985636i | \(-0.554016\pi\) | ||||
−0.168883 | + | 0.985636i | \(0.554016\pi\) | |||||||
\(882\) | −190.878 | −6.42721 | ||||||||
\(883\) | −22.5904 | −0.760229 | −0.380114 | − | 0.924939i | \(-0.624115\pi\) | ||||
−0.380114 | + | 0.924939i | \(0.624115\pi\) | |||||||
\(884\) | 4.84321 | 0.162895 | ||||||||
\(885\) | −72.3147 | −2.43083 | ||||||||
\(886\) | 65.3881 | 2.19676 | ||||||||
\(887\) | −13.7256 | −0.460861 | −0.230430 | − | 0.973089i | \(-0.574013\pi\) | ||||
−0.230430 | + | 0.973089i | \(0.574013\pi\) | |||||||
\(888\) | 2.63517 | 0.0884304 | ||||||||
\(889\) | −16.5860 | −0.556275 | ||||||||
\(890\) | 81.4146 | 2.72902 | ||||||||
\(891\) | −16.9189 | −0.566804 | ||||||||
\(892\) | 4.94800 | 0.165671 | ||||||||
\(893\) | −68.7755 | −2.30148 | ||||||||
\(894\) | 114.693 | 3.83591 | ||||||||
\(895\) | −41.1157 | −1.37435 | ||||||||
\(896\) | −30.5124 | −1.01935 | ||||||||
\(897\) | −89.2418 | −2.97970 | ||||||||
\(898\) | −13.9559 | −0.465716 | ||||||||
\(899\) | 54.1820 | 1.80707 | ||||||||
\(900\) | 12.1138 | 0.403793 | ||||||||
\(901\) | −7.40782 | −0.246790 | ||||||||
\(902\) | 18.4788 | 0.615276 | ||||||||
\(903\) | 178.281 | 5.93281 | ||||||||
\(904\) | −8.56189 | −0.284764 | ||||||||
\(905\) | 18.4397 | 0.612955 | ||||||||
\(906\) | −22.6896 | −0.753813 | ||||||||
\(907\) | 6.39168 | 0.212232 | 0.106116 | − | 0.994354i | \(-0.466158\pi\) | ||||
0.106116 | + | 0.994354i | \(0.466158\pi\) | |||||||
\(908\) | −3.24207 | −0.107592 | ||||||||
\(909\) | −10.6035 | −0.351695 | ||||||||
\(910\) | −70.1843 | −2.32659 | ||||||||
\(911\) | −0.258998 | −0.00858098 | −0.00429049 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429049 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(912\) | 108.838 | 3.60398 | ||||||||
\(913\) | 12.9177 | 0.427513 | ||||||||
\(914\) | −49.2457 | −1.62890 | ||||||||
\(915\) | −54.4575 | −1.80031 | ||||||||
\(916\) | −41.9285 | −1.38536 | ||||||||
\(917\) | −6.30541 | −0.208223 | ||||||||
\(918\) | 22.1430 | 0.730829 | ||||||||
\(919\) | 26.3692 | 0.869838 | 0.434919 | − | 0.900470i | \(-0.356777\pi\) | ||||
0.434919 | + | 0.900470i | \(0.356777\pi\) | |||||||
\(920\) | −18.3070 | −0.603565 | ||||||||
\(921\) | −73.4436 | −2.42005 | ||||||||
\(922\) | −5.04338 | −0.166095 | ||||||||
\(923\) | −30.1070 | −0.990983 | ||||||||
\(924\) | −21.9213 | −0.721157 | ||||||||
\(925\) | 1.13396 | 0.0372844 | ||||||||
\(926\) | 20.0730 | 0.659639 | ||||||||
\(927\) | 81.3073 | 2.67048 | ||||||||
\(928\) | −56.4428 | −1.85283 | ||||||||
\(929\) | 44.7404 | 1.46788 | 0.733942 | − | 0.679212i | \(-0.237678\pi\) | ||||
0.733942 | + | 0.679212i | \(0.237678\pi\) | |||||||
\(930\) | −100.957 | −3.31053 | ||||||||
\(931\) | −108.819 | −3.56641 | ||||||||
\(932\) | −23.5212 | −0.770464 | ||||||||
\(933\) | 52.1952 | 1.70879 | ||||||||
\(934\) | 28.7203 | 0.939756 | ||||||||
\(935\) | −2.30278 | −0.0753089 | ||||||||
\(936\) | −18.5746 | −0.607131 | ||||||||
\(937\) | −28.1796 | −0.920588 | −0.460294 | − | 0.887766i | \(-0.652256\pi\) | ||||
−0.460294 | + | 0.887766i | \(0.652256\pi\) | |||||||
\(938\) | −26.3079 | −0.858984 | ||||||||
\(939\) | 18.8534 | 0.615257 | ||||||||
\(940\) | −35.8738 | −1.17007 | ||||||||
\(941\) | −21.5781 | −0.703427 | −0.351713 | − | 0.936108i | \(-0.614401\pi\) | ||||
−0.351713 | + | 0.936108i | \(0.614401\pi\) | |||||||
\(942\) | 3.17190 | 0.103346 | ||||||||
\(943\) | 89.7377 | 2.92226 | ||||||||
\(944\) | −43.6068 | −1.41928 | ||||||||
\(945\) | −140.364 | −4.56603 | ||||||||
\(946\) | 22.0872 | 0.718117 | ||||||||
\(947\) | −52.6534 | −1.71101 | −0.855503 | − | 0.517798i | \(-0.826752\pi\) | ||||
−0.855503 | + | 0.517798i | \(0.826752\pi\) | |||||||
\(948\) | 20.9523 | 0.680499 | ||||||||
\(949\) | 10.8581 | 0.352469 | ||||||||
\(950\) | 15.7877 | 0.512220 | ||||||||
\(951\) | −51.4938 | −1.66980 | ||||||||
\(952\) | −3.77826 | −0.122454 | ||||||||
\(953\) | 19.6542 | 0.636662 | 0.318331 | − | 0.947980i | \(-0.396878\pi\) | ||||
0.318331 | + | 0.947980i | \(0.396878\pi\) | |||||||
\(954\) | −99.3132 | −3.21538 | ||||||||
\(955\) | −10.0203 | −0.324248 | ||||||||
\(956\) | −17.1475 | −0.554589 | ||||||||
\(957\) | 23.8044 | 0.769488 | ||||||||
\(958\) | −41.1819 | −1.33053 | ||||||||
\(959\) | −23.1848 | −0.748677 | ||||||||
\(960\) | 32.1592 | 1.03793 | ||||||||
\(961\) | 16.3579 | 0.527673 | ||||||||
\(962\) | 6.07810 | 0.195966 | ||||||||
\(963\) | 34.2843 | 1.10480 | ||||||||
\(964\) | −13.7595 | −0.443162 | ||||||||
\(965\) | −37.1705 | −1.19656 | ||||||||
\(966\) | −243.364 | −7.83012 | ||||||||
\(967\) | 0.886849 | 0.0285192 | 0.0142596 | − | 0.999898i | \(-0.495461\pi\) | ||||
0.0142596 | + | 0.999898i | \(0.495461\pi\) | |||||||
\(968\) | −8.45000 | −0.271593 | ||||||||
\(969\) | 22.4111 | 0.719950 | ||||||||
\(970\) | 15.0177 | 0.482191 | ||||||||
\(971\) | −15.1111 | −0.484939 | −0.242470 | − | 0.970159i | \(-0.577957\pi\) | ||||
−0.242470 | + | 0.970159i | \(0.577957\pi\) | |||||||
\(972\) | 29.1757 | 0.935813 | ||||||||
\(973\) | 27.2248 | 0.872788 | ||||||||
\(974\) | −4.87077 | −0.156070 | ||||||||
\(975\) | −11.4837 | −0.367774 | ||||||||
\(976\) | −32.8387 | −1.05114 | ||||||||
\(977\) | −30.6129 | −0.979392 | −0.489696 | − | 0.871893i | \(-0.662892\pi\) | ||||
−0.489696 | + | 0.871893i | \(0.662892\pi\) | |||||||
\(978\) | 74.3247 | 2.37664 | ||||||||
\(979\) | −16.7787 | −0.536250 | ||||||||
\(980\) | −56.7610 | −1.81316 | ||||||||
\(981\) | −6.86935 | −0.219322 | ||||||||
\(982\) | −39.7290 | −1.26780 | ||||||||
\(983\) | −15.6440 | −0.498967 | −0.249484 | − | 0.968379i | \(-0.580261\pi\) | ||||
−0.249484 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(984\) | 26.8349 | 0.855464 | ||||||||
\(985\) | −31.6033 | −1.00696 | ||||||||
\(986\) | −14.3421 | −0.456746 | ||||||||
\(987\) | 136.423 | 4.34238 | ||||||||
\(988\) | 37.0168 | 1.17766 | ||||||||
\(989\) | 107.261 | 3.41070 | ||||||||
\(990\) | −30.8723 | −0.981185 | ||||||||
\(991\) | 32.6209 | 1.03624 | 0.518119 | − | 0.855309i | \(-0.326632\pi\) | ||||
0.518119 | + | 0.855309i | \(0.326632\pi\) | |||||||
\(992\) | −49.3339 | −1.56635 | ||||||||
\(993\) | −50.9233 | −1.61600 | ||||||||
\(994\) | −82.1023 | −2.60413 | ||||||||
\(995\) | −23.2591 | −0.737363 | ||||||||
\(996\) | −65.5753 | −2.07783 | ||||||||
\(997\) | −7.69707 | −0.243769 | −0.121884 | − | 0.992544i | \(-0.538894\pi\) | ||||
−0.121884 | + | 0.992544i | \(0.538894\pi\) | |||||||
\(998\) | 22.4841 | 0.711721 | ||||||||
\(999\) | 12.1558 | 0.384592 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4033.2.a.f.1.17 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.17 | ✓ | 85 | 1.1 | even | 1 | trivial |