Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.77 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.43355 | 1.98236 | 0.991180 | − | 0.132521i | \(-0.0423074\pi\) | ||||
0.991180 | + | 0.132521i | \(0.0423074\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.08896 | 0.934210 | 0.467105 | − | 0.884202i | \(-0.345297\pi\) | ||||
0.467105 | + | 0.884202i | \(0.345297\pi\) | |||||||
\(6\) | −3.43355 | −1.40174 | ||||||||
\(7\) | 2.40538 | 0.909147 | 0.454574 | − | 0.890709i | \(-0.349792\pi\) | ||||
0.454574 | + | 0.890709i | \(0.349792\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.78926 | 2.92975 | ||||||||
\(10\) | −2.08896 | −0.660586 | ||||||||
\(11\) | 4.45759 | 1.34401 | 0.672007 | − | 0.740545i | \(-0.265433\pi\) | ||||
0.672007 | + | 0.740545i | \(0.265433\pi\) | |||||||
\(12\) | 3.43355 | 0.991180 | ||||||||
\(13\) | −0.0803882 | −0.0222957 | −0.0111478 | − | 0.999938i | \(-0.503549\pi\) | ||||
−0.0111478 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(14\) | −2.40538 | −0.642864 | ||||||||
\(15\) | 7.17254 | 1.85194 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.60116 | 0.873410 | 0.436705 | − | 0.899605i | \(-0.356145\pi\) | ||||
0.436705 | + | 0.899605i | \(0.356145\pi\) | |||||||
\(18\) | −8.78926 | −2.07165 | ||||||||
\(19\) | −3.47507 | −0.797237 | −0.398618 | − | 0.917117i | \(-0.630510\pi\) | ||||
−0.398618 | + | 0.917117i | \(0.630510\pi\) | |||||||
\(20\) | 2.08896 | 0.467105 | ||||||||
\(21\) | 8.25898 | 1.80226 | ||||||||
\(22\) | −4.45759 | −0.950361 | ||||||||
\(23\) | −6.45531 | −1.34603 | −0.673013 | − | 0.739631i | \(-0.735000\pi\) | ||||
−0.673013 | + | 0.739631i | \(0.735000\pi\) | |||||||
\(24\) | −3.43355 | −0.700870 | ||||||||
\(25\) | −0.636259 | −0.127252 | ||||||||
\(26\) | 0.0803882 | 0.0157654 | ||||||||
\(27\) | 19.8777 | 3.82546 | ||||||||
\(28\) | 2.40538 | 0.454574 | ||||||||
\(29\) | −0.536723 | −0.0996669 | −0.0498334 | − | 0.998758i | \(-0.515869\pi\) | ||||
−0.0498334 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(30\) | −7.17254 | −1.30952 | ||||||||
\(31\) | −5.71930 | −1.02722 | −0.513608 | − | 0.858025i | \(-0.671691\pi\) | ||||
−0.513608 | + | 0.858025i | \(0.671691\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 15.3054 | 2.66432 | ||||||||
\(34\) | −3.60116 | −0.617594 | ||||||||
\(35\) | 5.02473 | 0.849334 | ||||||||
\(36\) | 8.78926 | 1.46488 | ||||||||
\(37\) | 10.2724 | 1.68877 | 0.844383 | − | 0.535741i | \(-0.179968\pi\) | ||||
0.844383 | + | 0.535741i | \(0.179968\pi\) | |||||||
\(38\) | 3.47507 | 0.563732 | ||||||||
\(39\) | −0.276017 | −0.0441980 | ||||||||
\(40\) | −2.08896 | −0.330293 | ||||||||
\(41\) | 7.44082 | 1.16206 | 0.581031 | − | 0.813882i | \(-0.302650\pi\) | ||||
0.581031 | + | 0.813882i | \(0.302650\pi\) | |||||||
\(42\) | −8.25898 | −1.27439 | ||||||||
\(43\) | −12.7213 | −1.93998 | −0.969988 | − | 0.243151i | \(-0.921819\pi\) | ||||
−0.969988 | + | 0.243151i | \(0.921819\pi\) | |||||||
\(44\) | 4.45759 | 0.672007 | ||||||||
\(45\) | 18.3604 | 2.73700 | ||||||||
\(46\) | 6.45531 | 0.951784 | ||||||||
\(47\) | −7.24592 | −1.05693 | −0.528463 | − | 0.848956i | \(-0.677232\pi\) | ||||
−0.528463 | + | 0.848956i | \(0.677232\pi\) | |||||||
\(48\) | 3.43355 | 0.495590 | ||||||||
\(49\) | −1.21416 | −0.173452 | ||||||||
\(50\) | 0.636259 | 0.0899806 | ||||||||
\(51\) | 12.3648 | 1.73141 | ||||||||
\(52\) | −0.0803882 | −0.0111478 | ||||||||
\(53\) | −4.43522 | −0.609225 | −0.304612 | − | 0.952476i | \(-0.598527\pi\) | ||||
−0.304612 | + | 0.952476i | \(0.598527\pi\) | |||||||
\(54\) | −19.8777 | −2.70501 | ||||||||
\(55\) | 9.31171 | 1.25559 | ||||||||
\(56\) | −2.40538 | −0.321432 | ||||||||
\(57\) | −11.9318 | −1.58041 | ||||||||
\(58\) | 0.536723 | 0.0704751 | ||||||||
\(59\) | −11.4846 | −1.49516 | −0.747581 | − | 0.664170i | \(-0.768785\pi\) | ||||
−0.747581 | + | 0.664170i | \(0.768785\pi\) | |||||||
\(60\) | 7.17254 | 0.925970 | ||||||||
\(61\) | −5.67707 | −0.726875 | −0.363437 | − | 0.931619i | \(-0.618397\pi\) | ||||
−0.363437 | + | 0.931619i | \(0.618397\pi\) | |||||||
\(62\) | 5.71930 | 0.726351 | ||||||||
\(63\) | 21.1415 | 2.66358 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.167927 | −0.0208288 | ||||||||
\(66\) | −15.3054 | −1.88396 | ||||||||
\(67\) | 12.8745 | 1.57287 | 0.786437 | − | 0.617671i | \(-0.211924\pi\) | ||||
0.786437 | + | 0.617671i | \(0.211924\pi\) | |||||||
\(68\) | 3.60116 | 0.436705 | ||||||||
\(69\) | −22.1646 | −2.66831 | ||||||||
\(70\) | −5.02473 | −0.600570 | ||||||||
\(71\) | 3.84772 | 0.456641 | 0.228320 | − | 0.973586i | \(-0.426677\pi\) | ||||
0.228320 | + | 0.973586i | \(0.426677\pi\) | |||||||
\(72\) | −8.78926 | −1.03582 | ||||||||
\(73\) | 4.11923 | 0.482119 | 0.241060 | − | 0.970510i | \(-0.422505\pi\) | ||||
0.241060 | + | 0.970510i | \(0.422505\pi\) | |||||||
\(74\) | −10.2724 | −1.19414 | ||||||||
\(75\) | −2.18463 | −0.252259 | ||||||||
\(76\) | −3.47507 | −0.398618 | ||||||||
\(77\) | 10.7222 | 1.22191 | ||||||||
\(78\) | 0.276017 | 0.0312527 | ||||||||
\(79\) | 14.8916 | 1.67544 | 0.837720 | − | 0.546100i | \(-0.183888\pi\) | ||||
0.837720 | + | 0.546100i | \(0.183888\pi\) | |||||||
\(80\) | 2.08896 | 0.233552 | ||||||||
\(81\) | 41.8833 | 4.65370 | ||||||||
\(82\) | −7.44082 | −0.821701 | ||||||||
\(83\) | −7.72704 | −0.848152 | −0.424076 | − | 0.905627i | \(-0.639401\pi\) | ||||
−0.424076 | + | 0.905627i | \(0.639401\pi\) | |||||||
\(84\) | 8.25898 | 0.901128 | ||||||||
\(85\) | 7.52268 | 0.815949 | ||||||||
\(86\) | 12.7213 | 1.37177 | ||||||||
\(87\) | −1.84286 | −0.197576 | ||||||||
\(88\) | −4.45759 | −0.475181 | ||||||||
\(89\) | −14.9446 | −1.58413 | −0.792064 | − | 0.610438i | \(-0.790994\pi\) | ||||
−0.792064 | + | 0.610438i | \(0.790994\pi\) | |||||||
\(90\) | −18.3604 | −1.93535 | ||||||||
\(91\) | −0.193364 | −0.0202700 | ||||||||
\(92\) | −6.45531 | −0.673013 | ||||||||
\(93\) | −19.6375 | −2.03631 | ||||||||
\(94\) | 7.24592 | 0.747360 | ||||||||
\(95\) | −7.25928 | −0.744787 | ||||||||
\(96\) | −3.43355 | −0.350435 | ||||||||
\(97\) | −11.6638 | −1.18427 | −0.592137 | − | 0.805837i | \(-0.701716\pi\) | ||||
−0.592137 | + | 0.805837i | \(0.701716\pi\) | |||||||
\(98\) | 1.21416 | 0.122649 | ||||||||
\(99\) | 39.1789 | 3.93763 | ||||||||
\(100\) | −0.636259 | −0.0636259 | ||||||||
\(101\) | 7.02329 | 0.698844 | 0.349422 | − | 0.936966i | \(-0.386378\pi\) | ||||
0.349422 | + | 0.936966i | \(0.386378\pi\) | |||||||
\(102\) | −12.3648 | −1.22429 | ||||||||
\(103\) | 15.1392 | 1.49171 | 0.745856 | − | 0.666107i | \(-0.232040\pi\) | ||||
0.745856 | + | 0.666107i | \(0.232040\pi\) | |||||||
\(104\) | 0.0803882 | 0.00788271 | ||||||||
\(105\) | 17.2527 | 1.68369 | ||||||||
\(106\) | 4.43522 | 0.430787 | ||||||||
\(107\) | 12.3144 | 1.19047 | 0.595237 | − | 0.803550i | \(-0.297058\pi\) | ||||
0.595237 | + | 0.803550i | \(0.297058\pi\) | |||||||
\(108\) | 19.8777 | 1.91273 | ||||||||
\(109\) | −0.398614 | −0.0381803 | −0.0190901 | − | 0.999818i | \(-0.506077\pi\) | ||||
−0.0190901 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(110\) | −9.31171 | −0.887837 | ||||||||
\(111\) | 35.2706 | 3.34774 | ||||||||
\(112\) | 2.40538 | 0.227287 | ||||||||
\(113\) | −4.90227 | −0.461167 | −0.230584 | − | 0.973053i | \(-0.574064\pi\) | ||||
−0.230584 | + | 0.973053i | \(0.574064\pi\) | |||||||
\(114\) | 11.9318 | 1.11752 | ||||||||
\(115\) | −13.4849 | −1.25747 | ||||||||
\(116\) | −0.536723 | −0.0498334 | ||||||||
\(117\) | −0.706552 | −0.0653208 | ||||||||
\(118\) | 11.4846 | 1.05724 | ||||||||
\(119\) | 8.66216 | 0.794058 | ||||||||
\(120\) | −7.17254 | −0.654760 | ||||||||
\(121\) | 8.87010 | 0.806373 | ||||||||
\(122\) | 5.67707 | 0.513978 | ||||||||
\(123\) | 25.5484 | 2.30362 | ||||||||
\(124\) | −5.71930 | −0.513608 | ||||||||
\(125\) | −11.7739 | −1.05309 | ||||||||
\(126\) | −21.1415 | −1.88343 | ||||||||
\(127\) | 3.29909 | 0.292747 | 0.146373 | − | 0.989229i | \(-0.453240\pi\) | ||||
0.146373 | + | 0.989229i | \(0.453240\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −43.6791 | −3.84573 | ||||||||
\(130\) | 0.167927 | 0.0147282 | ||||||||
\(131\) | −11.5779 | −1.01157 | −0.505784 | − | 0.862660i | \(-0.668797\pi\) | ||||
−0.505784 | + | 0.862660i | \(0.668797\pi\) | |||||||
\(132\) | 15.3054 | 1.33216 | ||||||||
\(133\) | −8.35886 | −0.724805 | ||||||||
\(134\) | −12.8745 | −1.11219 | ||||||||
\(135\) | 41.5236 | 3.57379 | ||||||||
\(136\) | −3.60116 | −0.308797 | ||||||||
\(137\) | 6.14494 | 0.524997 | 0.262499 | − | 0.964932i | \(-0.415453\pi\) | ||||
0.262499 | + | 0.964932i | \(0.415453\pi\) | |||||||
\(138\) | 22.1646 | 1.88678 | ||||||||
\(139\) | −10.3964 | −0.881815 | −0.440907 | − | 0.897553i | \(-0.645343\pi\) | ||||
−0.440907 | + | 0.897553i | \(0.645343\pi\) | |||||||
\(140\) | 5.02473 | 0.424667 | ||||||||
\(141\) | −24.8792 | −2.09521 | ||||||||
\(142\) | −3.84772 | −0.322894 | ||||||||
\(143\) | −0.358337 | −0.0299657 | ||||||||
\(144\) | 8.78926 | 0.732438 | ||||||||
\(145\) | −1.12119 | −0.0931098 | ||||||||
\(146\) | −4.11923 | −0.340910 | ||||||||
\(147\) | −4.16888 | −0.343844 | ||||||||
\(148\) | 10.2724 | 0.844383 | ||||||||
\(149\) | −13.7946 | −1.13010 | −0.565049 | − | 0.825058i | \(-0.691143\pi\) | ||||
−0.565049 | + | 0.825058i | \(0.691143\pi\) | |||||||
\(150\) | 2.18463 | 0.178374 | ||||||||
\(151\) | 18.2701 | 1.48680 | 0.743399 | − | 0.668848i | \(-0.233212\pi\) | ||||
0.743399 | + | 0.668848i | \(0.233212\pi\) | |||||||
\(152\) | 3.47507 | 0.281866 | ||||||||
\(153\) | 31.6515 | 2.55888 | ||||||||
\(154\) | −10.7222 | −0.864018 | ||||||||
\(155\) | −11.9474 | −0.959636 | ||||||||
\(156\) | −0.276017 | −0.0220990 | ||||||||
\(157\) | −3.86962 | −0.308830 | −0.154415 | − | 0.988006i | \(-0.549349\pi\) | ||||
−0.154415 | + | 0.988006i | \(0.549349\pi\) | |||||||
\(158\) | −14.8916 | −1.18472 | ||||||||
\(159\) | −15.2286 | −1.20770 | ||||||||
\(160\) | −2.08896 | −0.165147 | ||||||||
\(161\) | −15.5275 | −1.22374 | ||||||||
\(162\) | −41.8833 | −3.29066 | ||||||||
\(163\) | −10.8307 | −0.848328 | −0.424164 | − | 0.905585i | \(-0.639432\pi\) | ||||
−0.424164 | + | 0.905585i | \(0.639432\pi\) | |||||||
\(164\) | 7.44082 | 0.581031 | ||||||||
\(165\) | 31.9722 | 2.48903 | ||||||||
\(166\) | 7.72704 | 0.599734 | ||||||||
\(167\) | 12.7546 | 0.986980 | 0.493490 | − | 0.869751i | \(-0.335721\pi\) | ||||
0.493490 | + | 0.869751i | \(0.335721\pi\) | |||||||
\(168\) | −8.25898 | −0.637194 | ||||||||
\(169\) | −12.9935 | −0.999503 | ||||||||
\(170\) | −7.52268 | −0.576963 | ||||||||
\(171\) | −30.5433 | −2.33571 | ||||||||
\(172\) | −12.7213 | −0.969988 | ||||||||
\(173\) | −21.7963 | −1.65714 | −0.828570 | − | 0.559886i | \(-0.810845\pi\) | ||||
−0.828570 | + | 0.559886i | \(0.810845\pi\) | |||||||
\(174\) | 1.84286 | 0.139707 | ||||||||
\(175\) | −1.53044 | −0.115691 | ||||||||
\(176\) | 4.45759 | 0.336003 | ||||||||
\(177\) | −39.4328 | −2.96395 | ||||||||
\(178\) | 14.9446 | 1.12015 | ||||||||
\(179\) | −9.63144 | −0.719887 | −0.359944 | − | 0.932974i | \(-0.617204\pi\) | ||||
−0.359944 | + | 0.932974i | \(0.617204\pi\) | |||||||
\(180\) | 18.3604 | 1.36850 | ||||||||
\(181\) | 15.6087 | 1.16018 | 0.580092 | − | 0.814551i | \(-0.303016\pi\) | ||||
0.580092 | + | 0.814551i | \(0.303016\pi\) | |||||||
\(182\) | 0.193364 | 0.0143331 | ||||||||
\(183\) | −19.4925 | −1.44093 | ||||||||
\(184\) | 6.45531 | 0.475892 | ||||||||
\(185\) | 21.4585 | 1.57766 | ||||||||
\(186\) | 19.6375 | 1.43989 | ||||||||
\(187\) | 16.0525 | 1.17388 | ||||||||
\(188\) | −7.24592 | −0.528463 | ||||||||
\(189\) | 47.8133 | 3.47791 | ||||||||
\(190\) | 7.25928 | 0.526644 | ||||||||
\(191\) | 11.6148 | 0.840419 | 0.420210 | − | 0.907427i | \(-0.361957\pi\) | ||||
0.420210 | + | 0.907427i | \(0.361957\pi\) | |||||||
\(192\) | 3.43355 | 0.247795 | ||||||||
\(193\) | −25.3588 | −1.82537 | −0.912683 | − | 0.408669i | \(-0.865993\pi\) | ||||
−0.912683 | + | 0.408669i | \(0.865993\pi\) | |||||||
\(194\) | 11.6638 | 0.837409 | ||||||||
\(195\) | −0.576587 | −0.0412903 | ||||||||
\(196\) | −1.21416 | −0.0867258 | ||||||||
\(197\) | −8.48353 | −0.604427 | −0.302213 | − | 0.953240i | \(-0.597725\pi\) | ||||
−0.302213 | + | 0.953240i | \(0.597725\pi\) | |||||||
\(198\) | −39.1789 | −2.78432 | ||||||||
\(199\) | 11.5177 | 0.816465 | 0.408232 | − | 0.912878i | \(-0.366145\pi\) | ||||
0.408232 | + | 0.912878i | \(0.366145\pi\) | |||||||
\(200\) | 0.636259 | 0.0449903 | ||||||||
\(201\) | 44.2053 | 3.11800 | ||||||||
\(202\) | −7.02329 | −0.494157 | ||||||||
\(203\) | −1.29102 | −0.0906118 | ||||||||
\(204\) | 12.3648 | 0.865707 | ||||||||
\(205\) | 15.5436 | 1.08561 | ||||||||
\(206\) | −15.1392 | −1.05480 | ||||||||
\(207\) | −56.7374 | −3.94352 | ||||||||
\(208\) | −0.0803882 | −0.00557392 | ||||||||
\(209\) | −15.4905 | −1.07150 | ||||||||
\(210\) | −17.2527 | −1.19055 | ||||||||
\(211\) | −13.1396 | −0.904565 | −0.452283 | − | 0.891875i | \(-0.649390\pi\) | ||||
−0.452283 | + | 0.891875i | \(0.649390\pi\) | |||||||
\(212\) | −4.43522 | −0.304612 | ||||||||
\(213\) | 13.2113 | 0.905226 | ||||||||
\(214\) | −12.3144 | −0.841792 | ||||||||
\(215\) | −26.5742 | −1.81235 | ||||||||
\(216\) | −19.8777 | −1.35251 | ||||||||
\(217\) | −13.7571 | −0.933890 | ||||||||
\(218\) | 0.398614 | 0.0269975 | ||||||||
\(219\) | 14.1436 | 0.955734 | ||||||||
\(220\) | 9.31171 | 0.627796 | ||||||||
\(221\) | −0.289491 | −0.0194733 | ||||||||
\(222\) | −35.2706 | −2.36721 | ||||||||
\(223\) | −11.4947 | −0.769739 | −0.384870 | − | 0.922971i | \(-0.625754\pi\) | ||||
−0.384870 | + | 0.922971i | \(0.625754\pi\) | |||||||
\(224\) | −2.40538 | −0.160716 | ||||||||
\(225\) | −5.59224 | −0.372816 | ||||||||
\(226\) | 4.90227 | 0.326094 | ||||||||
\(227\) | −6.20823 | −0.412055 | −0.206027 | − | 0.978546i | \(-0.566054\pi\) | ||||
−0.206027 | + | 0.978546i | \(0.566054\pi\) | |||||||
\(228\) | −11.9318 | −0.790205 | ||||||||
\(229\) | −17.0912 | −1.12942 | −0.564708 | − | 0.825291i | \(-0.691011\pi\) | ||||
−0.564708 | + | 0.825291i | \(0.691011\pi\) | |||||||
\(230\) | 13.4849 | 0.889166 | ||||||||
\(231\) | 36.8151 | 2.42226 | ||||||||
\(232\) | 0.536723 | 0.0352376 | ||||||||
\(233\) | 6.33038 | 0.414717 | 0.207358 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207358 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(234\) | 0.706552 | 0.0461888 | ||||||||
\(235\) | −15.1364 | −0.987391 | ||||||||
\(236\) | −11.4846 | −0.747581 | ||||||||
\(237\) | 51.1312 | 3.32133 | ||||||||
\(238\) | −8.66216 | −0.561484 | ||||||||
\(239\) | 22.2594 | 1.43984 | 0.719920 | − | 0.694057i | \(-0.244178\pi\) | ||||
0.719920 | + | 0.694057i | \(0.244178\pi\) | |||||||
\(240\) | 7.17254 | 0.462985 | ||||||||
\(241\) | 23.3716 | 1.50550 | 0.752748 | − | 0.658309i | \(-0.228728\pi\) | ||||
0.752748 | + | 0.658309i | \(0.228728\pi\) | |||||||
\(242\) | −8.87010 | −0.570192 | ||||||||
\(243\) | 84.1751 | 5.39984 | ||||||||
\(244\) | −5.67707 | −0.363437 | ||||||||
\(245\) | −2.53633 | −0.162040 | ||||||||
\(246\) | −25.5484 | −1.62891 | ||||||||
\(247\) | 0.279355 | 0.0177749 | ||||||||
\(248\) | 5.71930 | 0.363176 | ||||||||
\(249\) | −26.5312 | −1.68134 | ||||||||
\(250\) | 11.7739 | 0.744647 | ||||||||
\(251\) | 13.5974 | 0.858262 | 0.429131 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429131 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(252\) | 21.1415 | 1.33179 | ||||||||
\(253\) | −28.7751 | −1.80908 | ||||||||
\(254\) | −3.29909 | −0.207003 | ||||||||
\(255\) | 25.8295 | 1.61750 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.5031 | −1.71560 | −0.857799 | − | 0.513985i | \(-0.828169\pi\) | ||||
−0.857799 | + | 0.513985i | \(0.828169\pi\) | |||||||
\(258\) | 43.6791 | 2.71934 | ||||||||
\(259\) | 24.7089 | 1.53534 | ||||||||
\(260\) | −0.167927 | −0.0104144 | ||||||||
\(261\) | −4.71739 | −0.291999 | ||||||||
\(262\) | 11.5779 | 0.715286 | ||||||||
\(263\) | 23.7210 | 1.46270 | 0.731350 | − | 0.682002i | \(-0.238891\pi\) | ||||
0.731350 | + | 0.682002i | \(0.238891\pi\) | |||||||
\(264\) | −15.3054 | −0.941979 | ||||||||
\(265\) | −9.26499 | −0.569144 | ||||||||
\(266\) | 8.35886 | 0.512515 | ||||||||
\(267\) | −51.3132 | −3.14031 | ||||||||
\(268\) | 12.8745 | 0.786437 | ||||||||
\(269\) | −5.48744 | −0.334575 | −0.167288 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167288 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(270\) | −41.5236 | −2.52705 | ||||||||
\(271\) | −24.2332 | −1.47206 | −0.736031 | − | 0.676948i | \(-0.763302\pi\) | ||||
−0.736031 | + | 0.676948i | \(0.763302\pi\) | |||||||
\(272\) | 3.60116 | 0.218353 | ||||||||
\(273\) | −0.663924 | −0.0401825 | ||||||||
\(274\) | −6.14494 | −0.371229 | ||||||||
\(275\) | −2.83618 | −0.171028 | ||||||||
\(276\) | −22.1646 | −1.33415 | ||||||||
\(277\) | −9.51697 | −0.571819 | −0.285910 | − | 0.958257i | \(-0.592296\pi\) | ||||
−0.285910 | + | 0.958257i | \(0.592296\pi\) | |||||||
\(278\) | 10.3964 | 0.623537 | ||||||||
\(279\) | −50.2684 | −3.00949 | ||||||||
\(280\) | −5.02473 | −0.300285 | ||||||||
\(281\) | 29.8158 | 1.77866 | 0.889332 | − | 0.457262i | \(-0.151170\pi\) | ||||
0.889332 | + | 0.457262i | \(0.151170\pi\) | |||||||
\(282\) | 24.8792 | 1.48154 | ||||||||
\(283\) | −11.8968 | −0.707193 | −0.353596 | − | 0.935398i | \(-0.615041\pi\) | ||||
−0.353596 | + | 0.935398i | \(0.615041\pi\) | |||||||
\(284\) | 3.84772 | 0.228320 | ||||||||
\(285\) | −24.9251 | −1.47644 | ||||||||
\(286\) | 0.358337 | 0.0211889 | ||||||||
\(287\) | 17.8980 | 1.05648 | ||||||||
\(288\) | −8.78926 | −0.517912 | ||||||||
\(289\) | −4.03162 | −0.237154 | ||||||||
\(290\) | 1.12119 | 0.0658386 | ||||||||
\(291\) | −40.0481 | −2.34766 | ||||||||
\(292\) | 4.11923 | 0.241060 | ||||||||
\(293\) | 22.3570 | 1.30611 | 0.653055 | − | 0.757311i | \(-0.273487\pi\) | ||||
0.653055 | + | 0.757311i | \(0.273487\pi\) | |||||||
\(294\) | 4.16888 | 0.243134 | ||||||||
\(295\) | −23.9908 | −1.39680 | ||||||||
\(296\) | −10.2724 | −0.597069 | ||||||||
\(297\) | 88.6066 | 5.14148 | ||||||||
\(298\) | 13.7946 | 0.799099 | ||||||||
\(299\) | 0.518931 | 0.0300105 | ||||||||
\(300\) | −2.18463 | −0.126129 | ||||||||
\(301\) | −30.5995 | −1.76372 | ||||||||
\(302\) | −18.2701 | −1.05133 | ||||||||
\(303\) | 24.1148 | 1.38536 | ||||||||
\(304\) | −3.47507 | −0.199309 | ||||||||
\(305\) | −11.8592 | −0.679053 | ||||||||
\(306\) | −31.6515 | −1.80940 | ||||||||
\(307\) | −12.4569 | −0.710952 | −0.355476 | − | 0.934685i | \(-0.615681\pi\) | ||||
−0.355476 | + | 0.934685i | \(0.615681\pi\) | |||||||
\(308\) | 10.7222 | 0.610953 | ||||||||
\(309\) | 51.9813 | 2.95711 | ||||||||
\(310\) | 11.9474 | 0.678565 | ||||||||
\(311\) | −9.15293 | −0.519015 | −0.259508 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259508 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(312\) | 0.276017 | 0.0156264 | ||||||||
\(313\) | 13.0712 | 0.738829 | 0.369414 | − | 0.929265i | \(-0.379558\pi\) | ||||
0.369414 | + | 0.929265i | \(0.379558\pi\) | |||||||
\(314\) | 3.86962 | 0.218376 | ||||||||
\(315\) | 44.1636 | 2.48834 | ||||||||
\(316\) | 14.8916 | 0.837720 | ||||||||
\(317\) | −0.588556 | −0.0330566 | −0.0165283 | − | 0.999863i | \(-0.505261\pi\) | ||||
−0.0165283 | + | 0.999863i | \(0.505261\pi\) | |||||||
\(318\) | 15.2286 | 0.853975 | ||||||||
\(319\) | −2.39249 | −0.133954 | ||||||||
\(320\) | 2.08896 | 0.116776 | ||||||||
\(321\) | 42.2819 | 2.35995 | ||||||||
\(322\) | 15.5275 | 0.865312 | ||||||||
\(323\) | −12.5143 | −0.696315 | ||||||||
\(324\) | 41.8833 | 2.32685 | ||||||||
\(325\) | 0.0511477 | 0.00283716 | ||||||||
\(326\) | 10.8307 | 0.599858 | ||||||||
\(327\) | −1.36866 | −0.0756871 | ||||||||
\(328\) | −7.44082 | −0.410851 | ||||||||
\(329\) | −17.4292 | −0.960902 | ||||||||
\(330\) | −31.9722 | −1.76001 | ||||||||
\(331\) | 9.55008 | 0.524920 | 0.262460 | − | 0.964943i | \(-0.415466\pi\) | ||||
0.262460 | + | 0.964943i | \(0.415466\pi\) | |||||||
\(332\) | −7.72704 | −0.424076 | ||||||||
\(333\) | 90.2864 | 4.94766 | ||||||||
\(334\) | −12.7546 | −0.697900 | ||||||||
\(335\) | 26.8943 | 1.46939 | ||||||||
\(336\) | 8.25898 | 0.450564 | ||||||||
\(337\) | 22.0093 | 1.19893 | 0.599463 | − | 0.800403i | \(-0.295381\pi\) | ||||
0.599463 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(338\) | 12.9935 | 0.706755 | ||||||||
\(339\) | −16.8322 | −0.914200 | ||||||||
\(340\) | 7.52268 | 0.407974 | ||||||||
\(341\) | −25.4943 | −1.38059 | ||||||||
\(342\) | 30.5433 | 1.65159 | ||||||||
\(343\) | −19.7582 | −1.06684 | ||||||||
\(344\) | 12.7213 | 0.685885 | ||||||||
\(345\) | −46.3010 | −2.49276 | ||||||||
\(346\) | 21.7963 | 1.17177 | ||||||||
\(347\) | −14.4373 | −0.775035 | −0.387518 | − | 0.921862i | \(-0.626667\pi\) | ||||
−0.387518 | + | 0.921862i | \(0.626667\pi\) | |||||||
\(348\) | −1.84286 | −0.0987878 | ||||||||
\(349\) | 14.2407 | 0.762285 | 0.381143 | − | 0.924516i | \(-0.375531\pi\) | ||||
0.381143 | + | 0.924516i | \(0.375531\pi\) | |||||||
\(350\) | 1.53044 | 0.0818056 | ||||||||
\(351\) | −1.59793 | −0.0852913 | ||||||||
\(352\) | −4.45759 | −0.237590 | ||||||||
\(353\) | −0.617420 | −0.0328620 | −0.0164310 | − | 0.999865i | \(-0.505230\pi\) | ||||
−0.0164310 | + | 0.999865i | \(0.505230\pi\) | |||||||
\(354\) | 39.4328 | 2.09583 | ||||||||
\(355\) | 8.03773 | 0.426598 | ||||||||
\(356\) | −14.9446 | −0.792064 | ||||||||
\(357\) | 29.7419 | 1.57411 | ||||||||
\(358\) | 9.63144 | 0.509037 | ||||||||
\(359\) | 0.756867 | 0.0399459 | 0.0199729 | − | 0.999801i | \(-0.493642\pi\) | ||||
0.0199729 | + | 0.999801i | \(0.493642\pi\) | |||||||
\(360\) | −18.3604 | −0.967677 | ||||||||
\(361\) | −6.92386 | −0.364414 | ||||||||
\(362\) | −15.6087 | −0.820375 | ||||||||
\(363\) | 30.4559 | 1.59852 | ||||||||
\(364\) | −0.193364 | −0.0101350 | ||||||||
\(365\) | 8.60489 | 0.450401 | ||||||||
\(366\) | 19.4925 | 1.01889 | ||||||||
\(367\) | 23.5275 | 1.22813 | 0.614063 | − | 0.789257i | \(-0.289534\pi\) | ||||
0.614063 | + | 0.789257i | \(0.289534\pi\) | |||||||
\(368\) | −6.45531 | −0.336506 | ||||||||
\(369\) | 65.3993 | 3.40455 | ||||||||
\(370\) | −21.4585 | −1.11558 | ||||||||
\(371\) | −10.6684 | −0.553875 | ||||||||
\(372\) | −19.6375 | −1.01816 | ||||||||
\(373\) | −9.93608 | −0.514471 | −0.257235 | − | 0.966349i | \(-0.582812\pi\) | ||||
−0.257235 | + | 0.966349i | \(0.582812\pi\) | |||||||
\(374\) | −16.0525 | −0.830055 | ||||||||
\(375\) | −40.4263 | −2.08760 | ||||||||
\(376\) | 7.24592 | 0.373680 | ||||||||
\(377\) | 0.0431461 | 0.00222214 | ||||||||
\(378\) | −47.8133 | −2.45925 | ||||||||
\(379\) | −24.2797 | −1.24716 | −0.623581 | − | 0.781758i | \(-0.714323\pi\) | ||||
−0.623581 | + | 0.781758i | \(0.714323\pi\) | |||||||
\(380\) | −7.25928 | −0.372393 | ||||||||
\(381\) | 11.3276 | 0.580330 | ||||||||
\(382\) | −11.6148 | −0.594266 | ||||||||
\(383\) | 26.3998 | 1.34897 | 0.674483 | − | 0.738290i | \(-0.264367\pi\) | ||||
0.674483 | + | 0.738290i | \(0.264367\pi\) | |||||||
\(384\) | −3.43355 | −0.175218 | ||||||||
\(385\) | 22.3982 | 1.14152 | ||||||||
\(386\) | 25.3588 | 1.29073 | ||||||||
\(387\) | −111.811 | −5.68365 | ||||||||
\(388\) | −11.6638 | −0.592137 | ||||||||
\(389\) | −20.8011 | −1.05466 | −0.527328 | − | 0.849661i | \(-0.676806\pi\) | ||||
−0.527328 | + | 0.849661i | \(0.676806\pi\) | |||||||
\(390\) | 0.576587 | 0.0291966 | ||||||||
\(391\) | −23.2466 | −1.17563 | ||||||||
\(392\) | 1.21416 | 0.0613244 | ||||||||
\(393\) | −39.7534 | −2.00529 | ||||||||
\(394\) | 8.48353 | 0.427394 | ||||||||
\(395\) | 31.1080 | 1.56521 | ||||||||
\(396\) | 39.1789 | 1.96881 | ||||||||
\(397\) | 17.9867 | 0.902729 | 0.451364 | − | 0.892340i | \(-0.350937\pi\) | ||||
0.451364 | + | 0.892340i | \(0.350937\pi\) | |||||||
\(398\) | −11.5177 | −0.577328 | ||||||||
\(399\) | −28.7006 | −1.43683 | ||||||||
\(400\) | −0.636259 | −0.0318129 | ||||||||
\(401\) | −26.1569 | −1.30622 | −0.653108 | − | 0.757265i | \(-0.726535\pi\) | ||||
−0.653108 | + | 0.757265i | \(0.726535\pi\) | |||||||
\(402\) | −44.2053 | −2.20476 | ||||||||
\(403\) | 0.459764 | 0.0229025 | ||||||||
\(404\) | 7.02329 | 0.349422 | ||||||||
\(405\) | 87.4923 | 4.34753 | ||||||||
\(406\) | 1.29102 | 0.0640723 | ||||||||
\(407\) | 45.7900 | 2.26972 | ||||||||
\(408\) | −12.3648 | −0.612147 | ||||||||
\(409\) | −28.2204 | −1.39541 | −0.697704 | − | 0.716386i | \(-0.745795\pi\) | ||||
−0.697704 | + | 0.716386i | \(0.745795\pi\) | |||||||
\(410\) | −15.5436 | −0.767642 | ||||||||
\(411\) | 21.0989 | 1.04073 | ||||||||
\(412\) | 15.1392 | 0.745856 | ||||||||
\(413\) | −27.6247 | −1.35932 | ||||||||
\(414\) | 56.7374 | 2.78849 | ||||||||
\(415\) | −16.1414 | −0.792352 | ||||||||
\(416\) | 0.0803882 | 0.00394135 | ||||||||
\(417\) | −35.6967 | −1.74807 | ||||||||
\(418\) | 15.4905 | 0.757663 | ||||||||
\(419\) | −0.106804 | −0.00521771 | −0.00260885 | − | 0.999997i | \(-0.500830\pi\) | ||||
−0.00260885 | + | 0.999997i | \(0.500830\pi\) | |||||||
\(420\) | 17.2527 | 0.841843 | ||||||||
\(421\) | 14.1587 | 0.690053 | 0.345026 | − | 0.938593i | \(-0.387870\pi\) | ||||
0.345026 | + | 0.938593i | \(0.387870\pi\) | |||||||
\(422\) | 13.1396 | 0.639624 | ||||||||
\(423\) | −63.6863 | −3.09653 | ||||||||
\(424\) | 4.43522 | 0.215393 | ||||||||
\(425\) | −2.29127 | −0.111143 | ||||||||
\(426\) | −13.2113 | −0.640092 | ||||||||
\(427\) | −13.6555 | −0.660836 | ||||||||
\(428\) | 12.3144 | 0.595237 | ||||||||
\(429\) | −1.23037 | −0.0594028 | ||||||||
\(430\) | 26.5742 | 1.28152 | ||||||||
\(431\) | 3.51166 | 0.169151 | 0.0845755 | − | 0.996417i | \(-0.473047\pi\) | ||||
0.0845755 | + | 0.996417i | \(0.473047\pi\) | |||||||
\(432\) | 19.8777 | 0.956366 | ||||||||
\(433\) | −24.8991 | −1.19657 | −0.598286 | − | 0.801282i | \(-0.704151\pi\) | ||||
−0.598286 | + | 0.801282i | \(0.704151\pi\) | |||||||
\(434\) | 13.7571 | 0.660360 | ||||||||
\(435\) | −3.84966 | −0.184577 | ||||||||
\(436\) | −0.398614 | −0.0190901 | ||||||||
\(437\) | 22.4327 | 1.07310 | ||||||||
\(438\) | −14.1436 | −0.675806 | ||||||||
\(439\) | 36.4703 | 1.74063 | 0.870316 | − | 0.492494i | \(-0.163915\pi\) | ||||
0.870316 | + | 0.492494i | \(0.163915\pi\) | |||||||
\(440\) | −9.31171 | −0.443918 | ||||||||
\(441\) | −10.6716 | −0.508170 | ||||||||
\(442\) | 0.289491 | 0.0137697 | ||||||||
\(443\) | −3.54480 | −0.168419 | −0.0842094 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842094 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(444\) | 35.2706 | 1.67387 | ||||||||
\(445\) | −31.2187 | −1.47991 | ||||||||
\(446\) | 11.4947 | 0.544288 | ||||||||
\(447\) | −47.3644 | −2.24026 | ||||||||
\(448\) | 2.40538 | 0.113643 | ||||||||
\(449\) | −14.2267 | −0.671401 | −0.335701 | − | 0.941969i | \(-0.608973\pi\) | ||||
−0.335701 | + | 0.941969i | \(0.608973\pi\) | |||||||
\(450\) | 5.59224 | 0.263621 | ||||||||
\(451\) | 33.1681 | 1.56183 | ||||||||
\(452\) | −4.90227 | −0.230584 | ||||||||
\(453\) | 62.7312 | 2.94737 | ||||||||
\(454\) | 6.20823 | 0.291367 | ||||||||
\(455\) | −0.403929 | −0.0189365 | ||||||||
\(456\) | 11.9318 | 0.558759 | ||||||||
\(457\) | 5.83438 | 0.272921 | 0.136460 | − | 0.990646i | \(-0.456427\pi\) | ||||
0.136460 | + | 0.990646i | \(0.456427\pi\) | |||||||
\(458\) | 17.0912 | 0.798618 | ||||||||
\(459\) | 71.5828 | 3.34120 | ||||||||
\(460\) | −13.4849 | −0.628735 | ||||||||
\(461\) | 16.8067 | 0.782767 | 0.391384 | − | 0.920228i | \(-0.371997\pi\) | ||||
0.391384 | + | 0.920228i | \(0.371997\pi\) | |||||||
\(462\) | −36.8151 | −1.71280 | ||||||||
\(463\) | −12.2503 | −0.569318 | −0.284659 | − | 0.958629i | \(-0.591880\pi\) | ||||
−0.284659 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(464\) | −0.536723 | −0.0249167 | ||||||||
\(465\) | −41.0219 | −1.90234 | ||||||||
\(466\) | −6.33038 | −0.293249 | ||||||||
\(467\) | 34.7821 | 1.60953 | 0.804763 | − | 0.593597i | \(-0.202293\pi\) | ||||
0.804763 | + | 0.593597i | \(0.202293\pi\) | |||||||
\(468\) | −0.706552 | −0.0326604 | ||||||||
\(469\) | 30.9681 | 1.42997 | ||||||||
\(470\) | 15.1364 | 0.698191 | ||||||||
\(471\) | −13.2865 | −0.612212 | ||||||||
\(472\) | 11.4846 | 0.528620 | ||||||||
\(473\) | −56.7062 | −2.60736 | ||||||||
\(474\) | −51.1312 | −2.34853 | ||||||||
\(475\) | 2.21105 | 0.101450 | ||||||||
\(476\) | 8.66216 | 0.397029 | ||||||||
\(477\) | −38.9823 | −1.78488 | ||||||||
\(478\) | −22.2594 | −1.01812 | ||||||||
\(479\) | 13.3228 | 0.608736 | 0.304368 | − | 0.952555i | \(-0.401555\pi\) | ||||
0.304368 | + | 0.952555i | \(0.401555\pi\) | |||||||
\(480\) | −7.17254 | −0.327380 | ||||||||
\(481\) | −0.825776 | −0.0376521 | ||||||||
\(482\) | −23.3716 | −1.06455 | ||||||||
\(483\) | −53.3143 | −2.42588 | ||||||||
\(484\) | 8.87010 | 0.403187 | ||||||||
\(485\) | −24.3651 | −1.10636 | ||||||||
\(486\) | −84.1751 | −3.81826 | ||||||||
\(487\) | −4.86783 | −0.220583 | −0.110291 | − | 0.993899i | \(-0.535178\pi\) | ||||
−0.110291 | + | 0.993899i | \(0.535178\pi\) | |||||||
\(488\) | 5.67707 | 0.256989 | ||||||||
\(489\) | −37.1878 | −1.68169 | ||||||||
\(490\) | 2.53633 | 0.114580 | ||||||||
\(491\) | 34.9278 | 1.57627 | 0.788135 | − | 0.615503i | \(-0.211047\pi\) | ||||
0.788135 | + | 0.615503i | \(0.211047\pi\) | |||||||
\(492\) | 25.5484 | 1.15181 | ||||||||
\(493\) | −1.93283 | −0.0870501 | ||||||||
\(494\) | −0.279355 | −0.0125688 | ||||||||
\(495\) | 81.8430 | 3.67857 | ||||||||
\(496\) | −5.71930 | −0.256804 | ||||||||
\(497\) | 9.25522 | 0.415154 | ||||||||
\(498\) | 26.5312 | 1.18889 | ||||||||
\(499\) | 10.7868 | 0.482881 | 0.241441 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241441 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(500\) | −11.7739 | −0.526545 | ||||||||
\(501\) | 43.7935 | 1.95655 | ||||||||
\(502\) | −13.5974 | −0.606883 | ||||||||
\(503\) | 20.8016 | 0.927496 | 0.463748 | − | 0.885967i | \(-0.346504\pi\) | ||||
0.463748 | + | 0.885967i | \(0.346504\pi\) | |||||||
\(504\) | −21.1415 | −0.941716 | ||||||||
\(505\) | 14.6714 | 0.652867 | ||||||||
\(506\) | 28.7751 | 1.27921 | ||||||||
\(507\) | −44.6139 | −1.98137 | ||||||||
\(508\) | 3.29909 | 0.146373 | ||||||||
\(509\) | 29.1530 | 1.29218 | 0.646092 | − | 0.763259i | \(-0.276402\pi\) | ||||
0.646092 | + | 0.763259i | \(0.276402\pi\) | |||||||
\(510\) | −25.8295 | −1.14375 | ||||||||
\(511\) | 9.90830 | 0.438317 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −69.0765 | −3.04980 | ||||||||
\(514\) | 27.5031 | 1.21311 | ||||||||
\(515\) | 31.6252 | 1.39357 | ||||||||
\(516\) | −43.6791 | −1.92287 | ||||||||
\(517\) | −32.2994 | −1.42052 | ||||||||
\(518\) | −24.7089 | −1.08565 | ||||||||
\(519\) | −74.8386 | −3.28505 | ||||||||
\(520\) | 0.167927 | 0.00736410 | ||||||||
\(521\) | 22.3117 | 0.977492 | 0.488746 | − | 0.872426i | \(-0.337454\pi\) | ||||
0.488746 | + | 0.872426i | \(0.337454\pi\) | |||||||
\(522\) | 4.71739 | 0.206475 | ||||||||
\(523\) | −30.9247 | −1.35224 | −0.676122 | − | 0.736790i | \(-0.736341\pi\) | ||||
−0.676122 | + | 0.736790i | \(0.736341\pi\) | |||||||
\(524\) | −11.5779 | −0.505784 | ||||||||
\(525\) | −5.25485 | −0.229340 | ||||||||
\(526\) | −23.7210 | −1.03429 | ||||||||
\(527\) | −20.5961 | −0.897181 | ||||||||
\(528\) | 15.3054 | 0.666080 | ||||||||
\(529\) | 18.6711 | 0.811786 | ||||||||
\(530\) | 9.26499 | 0.402445 | ||||||||
\(531\) | −100.941 | −4.38046 | ||||||||
\(532\) | −8.35886 | −0.362403 | ||||||||
\(533\) | −0.598154 | −0.0259089 | ||||||||
\(534\) | 51.3132 | 2.22054 | ||||||||
\(535\) | 25.7242 | 1.11215 | ||||||||
\(536\) | −12.8745 | −0.556095 | ||||||||
\(537\) | −33.0700 | −1.42708 | ||||||||
\(538\) | 5.48744 | 0.236580 | ||||||||
\(539\) | −5.41223 | −0.233121 | ||||||||
\(540\) | 41.5236 | 1.78689 | ||||||||
\(541\) | −21.8348 | −0.938752 | −0.469376 | − | 0.882998i | \(-0.655521\pi\) | ||||
−0.469376 | + | 0.882998i | \(0.655521\pi\) | |||||||
\(542\) | 24.2332 | 1.04090 | ||||||||
\(543\) | 53.5932 | 2.29990 | ||||||||
\(544\) | −3.60116 | −0.154399 | ||||||||
\(545\) | −0.832687 | −0.0356684 | ||||||||
\(546\) | 0.663924 | 0.0284133 | ||||||||
\(547\) | −10.0395 | −0.429259 | −0.214630 | − | 0.976696i | \(-0.568854\pi\) | ||||
−0.214630 | + | 0.976696i | \(0.568854\pi\) | |||||||
\(548\) | 6.14494 | 0.262499 | ||||||||
\(549\) | −49.8972 | −2.12956 | ||||||||
\(550\) | 2.83618 | 0.120935 | ||||||||
\(551\) | 1.86515 | 0.0794581 | ||||||||
\(552\) | 22.1646 | 0.943389 | ||||||||
\(553\) | 35.8200 | 1.52322 | ||||||||
\(554\) | 9.51697 | 0.404337 | ||||||||
\(555\) | 73.6789 | 3.12749 | ||||||||
\(556\) | −10.3964 | −0.440907 | ||||||||
\(557\) | 33.3109 | 1.41143 | 0.705714 | − | 0.708497i | \(-0.250626\pi\) | ||||
0.705714 | + | 0.708497i | \(0.250626\pi\) | |||||||
\(558\) | 50.2684 | 2.12803 | ||||||||
\(559\) | 1.02264 | 0.0432531 | ||||||||
\(560\) | 5.02473 | 0.212334 | ||||||||
\(561\) | 55.1171 | 2.32704 | ||||||||
\(562\) | −29.8158 | −1.25771 | ||||||||
\(563\) | 23.4519 | 0.988380 | 0.494190 | − | 0.869354i | \(-0.335465\pi\) | ||||
0.494190 | + | 0.869354i | \(0.335465\pi\) | |||||||
\(564\) | −24.8792 | −1.04760 | ||||||||
\(565\) | −10.2406 | −0.430827 | ||||||||
\(566\) | 11.8968 | 0.500061 | ||||||||
\(567\) | 100.745 | 4.23089 | ||||||||
\(568\) | −3.84772 | −0.161447 | ||||||||
\(569\) | −18.7244 | −0.784968 | −0.392484 | − | 0.919759i | \(-0.628384\pi\) | ||||
−0.392484 | + | 0.919759i | \(0.628384\pi\) | |||||||
\(570\) | 24.9251 | 1.04400 | ||||||||
\(571\) | −39.5840 | −1.65654 | −0.828269 | − | 0.560330i | \(-0.810674\pi\) | ||||
−0.828269 | + | 0.560330i | \(0.810674\pi\) | |||||||
\(572\) | −0.358337 | −0.0149828 | ||||||||
\(573\) | 39.8801 | 1.66601 | ||||||||
\(574\) | −17.8980 | −0.747047 | ||||||||
\(575\) | 4.10725 | 0.171284 | ||||||||
\(576\) | 8.78926 | 0.366219 | ||||||||
\(577\) | −44.0722 | −1.83475 | −0.917375 | − | 0.398024i | \(-0.869696\pi\) | ||||
−0.917375 | + | 0.398024i | \(0.869696\pi\) | |||||||
\(578\) | 4.03162 | 0.167693 | ||||||||
\(579\) | −87.0706 | −3.61853 | ||||||||
\(580\) | −1.12119 | −0.0465549 | ||||||||
\(581\) | −18.5864 | −0.771095 | ||||||||
\(582\) | 40.0481 | 1.66005 | ||||||||
\(583\) | −19.7704 | −0.818807 | ||||||||
\(584\) | −4.11923 | −0.170455 | ||||||||
\(585\) | −1.47596 | −0.0610233 | ||||||||
\(586\) | −22.3570 | −0.923559 | ||||||||
\(587\) | −25.3849 | −1.04775 | −0.523873 | − | 0.851797i | \(-0.675513\pi\) | ||||
−0.523873 | + | 0.851797i | \(0.675513\pi\) | |||||||
\(588\) | −4.16888 | −0.171922 | ||||||||
\(589\) | 19.8750 | 0.818934 | ||||||||
\(590\) | 23.9908 | 0.987684 | ||||||||
\(591\) | −29.1286 | −1.19819 | ||||||||
\(592\) | 10.2724 | 0.422191 | ||||||||
\(593\) | 37.5655 | 1.54263 | 0.771315 | − | 0.636454i | \(-0.219599\pi\) | ||||
0.771315 | + | 0.636454i | \(0.219599\pi\) | |||||||
\(594\) | −88.6066 | −3.63557 | ||||||||
\(595\) | 18.0949 | 0.741817 | ||||||||
\(596\) | −13.7946 | −0.565049 | ||||||||
\(597\) | 39.5464 | 1.61853 | ||||||||
\(598\) | −0.518931 | −0.0212207 | ||||||||
\(599\) | −1.42028 | −0.0580310 | −0.0290155 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290155 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(600\) | 2.18463 | 0.0891870 | ||||||||
\(601\) | −9.00275 | −0.367230 | −0.183615 | − | 0.982998i | \(-0.558780\pi\) | ||||
−0.183615 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(602\) | 30.5995 | 1.24714 | ||||||||
\(603\) | 113.158 | 4.60813 | ||||||||
\(604\) | 18.2701 | 0.743399 | ||||||||
\(605\) | 18.5293 | 0.753322 | ||||||||
\(606\) | −24.1148 | −0.979597 | ||||||||
\(607\) | 35.0380 | 1.42215 | 0.711074 | − | 0.703118i | \(-0.248209\pi\) | ||||
0.711074 | + | 0.703118i | \(0.248209\pi\) | |||||||
\(608\) | 3.47507 | 0.140933 | ||||||||
\(609\) | −4.43278 | −0.179625 | ||||||||
\(610\) | 11.8592 | 0.480163 | ||||||||
\(611\) | 0.582487 | 0.0235649 | ||||||||
\(612\) | 31.6515 | 1.27944 | ||||||||
\(613\) | −19.0816 | −0.770700 | −0.385350 | − | 0.922770i | \(-0.625919\pi\) | ||||
−0.385350 | + | 0.922770i | \(0.625919\pi\) | |||||||
\(614\) | 12.4569 | 0.502719 | ||||||||
\(615\) | 53.3696 | 2.15207 | ||||||||
\(616\) | −10.7222 | −0.432009 | ||||||||
\(617\) | −19.1883 | −0.772491 | −0.386246 | − | 0.922396i | \(-0.626228\pi\) | ||||
−0.386246 | + | 0.922396i | \(0.626228\pi\) | |||||||
\(618\) | −51.9813 | −2.09099 | ||||||||
\(619\) | 8.15411 | 0.327741 | 0.163871 | − | 0.986482i | \(-0.447602\pi\) | ||||
0.163871 | + | 0.986482i | \(0.447602\pi\) | |||||||
\(620\) | −11.9474 | −0.479818 | ||||||||
\(621\) | −128.317 | −5.14917 | ||||||||
\(622\) | 9.15293 | 0.366999 | ||||||||
\(623\) | −35.9475 | −1.44021 | ||||||||
\(624\) | −0.276017 | −0.0110495 | ||||||||
\(625\) | −21.4139 | −0.856555 | ||||||||
\(626\) | −13.0712 | −0.522431 | ||||||||
\(627\) | −53.1872 | −2.12409 | ||||||||
\(628\) | −3.86962 | −0.154415 | ||||||||
\(629\) | 36.9924 | 1.47499 | ||||||||
\(630\) | −44.1636 | −1.75952 | ||||||||
\(631\) | −26.7250 | −1.06391 | −0.531954 | − | 0.846774i | \(-0.678542\pi\) | ||||
−0.531954 | + | 0.846774i | \(0.678542\pi\) | |||||||
\(632\) | −14.8916 | −0.592358 | ||||||||
\(633\) | −45.1153 | −1.79317 | ||||||||
\(634\) | 0.588556 | 0.0233745 | ||||||||
\(635\) | 6.89166 | 0.273487 | ||||||||
\(636\) | −15.2286 | −0.603852 | ||||||||
\(637\) | 0.0976042 | 0.00386722 | ||||||||
\(638\) | 2.39249 | 0.0947195 | ||||||||
\(639\) | 33.8186 | 1.33784 | ||||||||
\(640\) | −2.08896 | −0.0825733 | ||||||||
\(641\) | 31.7244 | 1.25304 | 0.626519 | − | 0.779406i | \(-0.284479\pi\) | ||||
0.626519 | + | 0.779406i | \(0.284479\pi\) | |||||||
\(642\) | −42.2819 | −1.66873 | ||||||||
\(643\) | 16.0940 | 0.634684 | 0.317342 | − | 0.948311i | \(-0.397210\pi\) | ||||
0.317342 | + | 0.948311i | \(0.397210\pi\) | |||||||
\(644\) | −15.5275 | −0.611868 | ||||||||
\(645\) | −91.2438 | −3.59272 | ||||||||
\(646\) | 12.5143 | 0.492369 | ||||||||
\(647\) | −48.3086 | −1.89921 | −0.949603 | − | 0.313455i | \(-0.898513\pi\) | ||||
−0.949603 | + | 0.313455i | \(0.898513\pi\) | |||||||
\(648\) | −41.8833 | −1.64533 | ||||||||
\(649\) | −51.1935 | −2.00952 | ||||||||
\(650\) | −0.0511477 | −0.00200618 | ||||||||
\(651\) | −47.2356 | −1.85131 | ||||||||
\(652\) | −10.8307 | −0.424164 | ||||||||
\(653\) | 27.3298 | 1.06950 | 0.534749 | − | 0.845011i | \(-0.320406\pi\) | ||||
0.534749 | + | 0.845011i | \(0.320406\pi\) | |||||||
\(654\) | 1.36866 | 0.0535189 | ||||||||
\(655\) | −24.1858 | −0.945017 | ||||||||
\(656\) | 7.44082 | 0.290515 | ||||||||
\(657\) | 36.2050 | 1.41249 | ||||||||
\(658\) | 17.4292 | 0.679460 | ||||||||
\(659\) | 15.3807 | 0.599148 | 0.299574 | − | 0.954073i | \(-0.403155\pi\) | ||||
0.299574 | + | 0.954073i | \(0.403155\pi\) | |||||||
\(660\) | 31.9722 | 1.24452 | ||||||||
\(661\) | 0.864894 | 0.0336405 | 0.0168202 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168202 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(662\) | −9.55008 | −0.371175 | ||||||||
\(663\) | −0.993981 | −0.0386030 | ||||||||
\(664\) | 7.72704 | 0.299867 | ||||||||
\(665\) | −17.4613 | −0.677120 | ||||||||
\(666\) | −90.2864 | −3.49853 | ||||||||
\(667\) | 3.46471 | 0.134154 | ||||||||
\(668\) | 12.7546 | 0.493490 | ||||||||
\(669\) | −39.4675 | −1.52590 | ||||||||
\(670\) | −26.8943 | −1.03902 | ||||||||
\(671\) | −25.3061 | −0.976929 | ||||||||
\(672\) | −8.25898 | −0.318597 | ||||||||
\(673\) | −13.3815 | −0.515818 | −0.257909 | − | 0.966169i | \(-0.583034\pi\) | ||||
−0.257909 | + | 0.966169i | \(0.583034\pi\) | |||||||
\(674\) | −22.0093 | −0.847768 | ||||||||
\(675\) | −12.6474 | −0.486797 | ||||||||
\(676\) | −12.9935 | −0.499751 | ||||||||
\(677\) | −8.27187 | −0.317914 | −0.158957 | − | 0.987286i | \(-0.550813\pi\) | ||||
−0.158957 | + | 0.987286i | \(0.550813\pi\) | |||||||
\(678\) | 16.8322 | 0.646437 | ||||||||
\(679\) | −28.0557 | −1.07668 | ||||||||
\(680\) | −7.52268 | −0.288481 | ||||||||
\(681\) | −21.3163 | −0.816840 | ||||||||
\(682\) | 25.4943 | 0.976226 | ||||||||
\(683\) | −7.26621 | −0.278034 | −0.139017 | − | 0.990290i | \(-0.544394\pi\) | ||||
−0.139017 | + | 0.990290i | \(0.544394\pi\) | |||||||
\(684\) | −30.5433 | −1.16785 | ||||||||
\(685\) | 12.8365 | 0.490458 | ||||||||
\(686\) | 19.7582 | 0.754370 | ||||||||
\(687\) | −58.6834 | −2.23891 | ||||||||
\(688\) | −12.7213 | −0.484994 | ||||||||
\(689\) | 0.356539 | 0.0135831 | ||||||||
\(690\) | 46.3010 | 1.76265 | ||||||||
\(691\) | −12.0324 | −0.457733 | −0.228866 | − | 0.973458i | \(-0.573502\pi\) | ||||
−0.228866 | + | 0.973458i | \(0.573502\pi\) | |||||||
\(692\) | −21.7963 | −0.828570 | ||||||||
\(693\) | 94.2400 | 3.57988 | ||||||||
\(694\) | 14.4373 | 0.548033 | ||||||||
\(695\) | −21.7177 | −0.823800 | ||||||||
\(696\) | 1.84286 | 0.0698535 | ||||||||
\(697\) | 26.7956 | 1.01496 | ||||||||
\(698\) | −14.2407 | −0.539017 | ||||||||
\(699\) | 21.7357 | 0.822118 | ||||||||
\(700\) | −1.53044 | −0.0578453 | ||||||||
\(701\) | 0.556650 | 0.0210244 | 0.0105122 | − | 0.999945i | \(-0.496654\pi\) | ||||
0.0105122 | + | 0.999945i | \(0.496654\pi\) | |||||||
\(702\) | 1.59793 | 0.0603100 | ||||||||
\(703\) | −35.6972 | −1.34635 | ||||||||
\(704\) | 4.45759 | 0.168002 | ||||||||
\(705\) | −51.9717 | −1.95737 | ||||||||
\(706\) | 0.617420 | 0.0232369 | ||||||||
\(707\) | 16.8937 | 0.635352 | ||||||||
\(708\) | −39.4328 | −1.48198 | ||||||||
\(709\) | −13.4741 | −0.506030 | −0.253015 | − | 0.967462i | \(-0.581422\pi\) | ||||
−0.253015 | + | 0.967462i | \(0.581422\pi\) | |||||||
\(710\) | −8.03773 | −0.301651 | ||||||||
\(711\) | 130.886 | 4.90862 | ||||||||
\(712\) | 14.9446 | 0.560074 | ||||||||
\(713\) | 36.9199 | 1.38266 | ||||||||
\(714\) | −29.7419 | −1.11306 | ||||||||
\(715\) | −0.748552 | −0.0279942 | ||||||||
\(716\) | −9.63144 | −0.359944 | ||||||||
\(717\) | 76.4287 | 2.85428 | ||||||||
\(718\) | −0.756867 | −0.0282460 | ||||||||
\(719\) | 11.9621 | 0.446110 | 0.223055 | − | 0.974806i | \(-0.428397\pi\) | ||||
0.223055 | + | 0.974806i | \(0.428397\pi\) | |||||||
\(720\) | 18.3604 | 0.684251 | ||||||||
\(721\) | 36.4156 | 1.35619 | ||||||||
\(722\) | 6.92386 | 0.257679 | ||||||||
\(723\) | 80.2475 | 2.98444 | ||||||||
\(724\) | 15.6087 | 0.580092 | ||||||||
\(725\) | 0.341495 | 0.0126828 | ||||||||
\(726\) | −30.4559 | −1.13033 | ||||||||
\(727\) | −20.3032 | −0.753003 | −0.376501 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376501 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(728\) | 0.193364 | 0.00716654 | ||||||||
\(729\) | 163.370 | 6.05073 | ||||||||
\(730\) | −8.60489 | −0.318481 | ||||||||
\(731\) | −45.8114 | −1.69440 | ||||||||
\(732\) | −19.4925 | −0.720464 | ||||||||
\(733\) | −5.44730 | −0.201201 | −0.100600 | − | 0.994927i | \(-0.532076\pi\) | ||||
−0.100600 | + | 0.994927i | \(0.532076\pi\) | |||||||
\(734\) | −23.5275 | −0.868417 | ||||||||
\(735\) | −8.70862 | −0.321222 | ||||||||
\(736\) | 6.45531 | 0.237946 | ||||||||
\(737\) | 57.3893 | 2.11396 | ||||||||
\(738\) | −65.3993 | −2.40738 | ||||||||
\(739\) | 43.5350 | 1.60146 | 0.800730 | − | 0.599025i | \(-0.204445\pi\) | ||||
0.800730 | + | 0.599025i | \(0.204445\pi\) | |||||||
\(740\) | 21.4585 | 0.788831 | ||||||||
\(741\) | 0.959179 | 0.0352363 | ||||||||
\(742\) | 10.6684 | 0.391649 | ||||||||
\(743\) | 22.6640 | 0.831461 | 0.415730 | − | 0.909488i | \(-0.363526\pi\) | ||||
0.415730 | + | 0.909488i | \(0.363526\pi\) | |||||||
\(744\) | 19.6375 | 0.719945 | ||||||||
\(745\) | −28.8163 | −1.05575 | ||||||||
\(746\) | 9.93608 | 0.363786 | ||||||||
\(747\) | −67.9149 | −2.48488 | ||||||||
\(748\) | 16.0525 | 0.586938 | ||||||||
\(749\) | 29.6207 | 1.08232 | ||||||||
\(750\) | 40.4263 | 1.47616 | ||||||||
\(751\) | 11.7707 | 0.429519 | 0.214760 | − | 0.976667i | \(-0.431103\pi\) | ||||
0.214760 | + | 0.976667i | \(0.431103\pi\) | |||||||
\(752\) | −7.24592 | −0.264232 | ||||||||
\(753\) | 46.6874 | 1.70138 | ||||||||
\(754\) | −0.0431461 | −0.00157129 | ||||||||
\(755\) | 38.1654 | 1.38898 | ||||||||
\(756\) | 47.8133 | 1.73895 | ||||||||
\(757\) | 26.0857 | 0.948102 | 0.474051 | − | 0.880497i | \(-0.342791\pi\) | ||||
0.474051 | + | 0.880497i | \(0.342791\pi\) | |||||||
\(758\) | 24.2797 | 0.881877 | ||||||||
\(759\) | −98.8008 | −3.58624 | ||||||||
\(760\) | 7.25928 | 0.263322 | ||||||||
\(761\) | 17.2991 | 0.627090 | 0.313545 | − | 0.949573i | \(-0.398483\pi\) | ||||
0.313545 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(762\) | −11.3276 | −0.410355 | ||||||||
\(763\) | −0.958817 | −0.0347115 | ||||||||
\(764\) | 11.6148 | 0.420210 | ||||||||
\(765\) | 66.1187 | 2.39053 | ||||||||
\(766\) | −26.3998 | −0.953863 | ||||||||
\(767\) | 0.923223 | 0.0333356 | ||||||||
\(768\) | 3.43355 | 0.123898 | ||||||||
\(769\) | −18.7925 | −0.677676 | −0.338838 | − | 0.940845i | \(-0.610034\pi\) | ||||
−0.338838 | + | 0.940845i | \(0.610034\pi\) | |||||||
\(770\) | −22.3982 | −0.807174 | ||||||||
\(771\) | −94.4333 | −3.40093 | ||||||||
\(772\) | −25.3588 | −0.912683 | ||||||||
\(773\) | 23.2957 | 0.837886 | 0.418943 | − | 0.908012i | \(-0.362401\pi\) | ||||
0.418943 | + | 0.908012i | \(0.362401\pi\) | |||||||
\(774\) | 111.811 | 4.01895 | ||||||||
\(775\) | 3.63895 | 0.130715 | ||||||||
\(776\) | 11.6638 | 0.418704 | ||||||||
\(777\) | 84.8392 | 3.04359 | ||||||||
\(778\) | 20.8011 | 0.745755 | ||||||||
\(779\) | −25.8574 | −0.926438 | ||||||||
\(780\) | −0.576587 | −0.0206451 | ||||||||
\(781\) | 17.1516 | 0.613731 | ||||||||
\(782\) | 23.2466 | 0.831298 | ||||||||
\(783\) | −10.6688 | −0.381272 | ||||||||
\(784\) | −1.21416 | −0.0433629 | ||||||||
\(785\) | −8.08348 | −0.288512 | ||||||||
\(786\) | 39.7534 | 1.41796 | ||||||||
\(787\) | 41.8803 | 1.49287 | 0.746436 | − | 0.665457i | \(-0.231763\pi\) | ||||
0.746436 | + | 0.665457i | \(0.231763\pi\) | |||||||
\(788\) | −8.48353 | −0.302213 | ||||||||
\(789\) | 81.4472 | 2.89960 | ||||||||
\(790\) | −31.1080 | −1.10677 | ||||||||
\(791\) | −11.7918 | −0.419269 | ||||||||
\(792\) | −39.1789 | −1.39216 | ||||||||
\(793\) | 0.456369 | 0.0162062 | ||||||||
\(794\) | −17.9867 | −0.638326 | ||||||||
\(795\) | −31.8118 | −1.12825 | ||||||||
\(796\) | 11.5177 | 0.408232 | ||||||||
\(797\) | −0.265984 | −0.00942165 | −0.00471083 | − | 0.999989i | \(-0.501500\pi\) | ||||
−0.00471083 | + | 0.999989i | \(0.501500\pi\) | |||||||
\(798\) | 28.7006 | 1.01599 | ||||||||
\(799\) | −26.0938 | −0.923131 | ||||||||
\(800\) | 0.636259 | 0.0224951 | ||||||||
\(801\) | −131.352 | −4.64110 | ||||||||
\(802\) | 26.1569 | 0.923634 | ||||||||
\(803\) | 18.3618 | 0.647975 | ||||||||
\(804\) | 44.2053 | 1.55900 | ||||||||
\(805\) | −32.4362 | −1.14323 | ||||||||
\(806\) | −0.459764 | −0.0161945 | ||||||||
\(807\) | −18.8414 | −0.663248 | ||||||||
\(808\) | −7.02329 | −0.247079 | ||||||||
\(809\) | −32.6344 | −1.14736 | −0.573682 | − | 0.819078i | \(-0.694485\pi\) | ||||
−0.573682 | + | 0.819078i | \(0.694485\pi\) | |||||||
\(810\) | −87.4923 | −3.07417 | ||||||||
\(811\) | 7.64978 | 0.268620 | 0.134310 | − | 0.990939i | \(-0.457118\pi\) | ||||
0.134310 | + | 0.990939i | \(0.457118\pi\) | |||||||
\(812\) | −1.29102 | −0.0453059 | ||||||||
\(813\) | −83.2058 | −2.91816 | ||||||||
\(814\) | −45.7900 | −1.60494 | ||||||||
\(815\) | −22.6249 | −0.792516 | ||||||||
\(816\) | 12.3648 | 0.432854 | ||||||||
\(817\) | 44.2074 | 1.54662 | ||||||||
\(818\) | 28.2204 | 0.986702 | ||||||||
\(819\) | −1.69952 | −0.0593862 | ||||||||
\(820\) | 15.5436 | 0.542805 | ||||||||
\(821\) | −39.1225 | −1.36538 | −0.682692 | − | 0.730706i | \(-0.739191\pi\) | ||||
−0.682692 | + | 0.730706i | \(0.739191\pi\) | |||||||
\(822\) | −21.0989 | −0.735910 | ||||||||
\(823\) | 21.9452 | 0.764963 | 0.382481 | − | 0.923963i | \(-0.375070\pi\) | ||||
0.382481 | + | 0.923963i | \(0.375070\pi\) | |||||||
\(824\) | −15.1392 | −0.527400 | ||||||||
\(825\) | −9.73817 | −0.339039 | ||||||||
\(826\) | 27.6247 | 0.961186 | ||||||||
\(827\) | 42.5631 | 1.48007 | 0.740033 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(828\) | −56.7374 | −1.97176 | ||||||||
\(829\) | −22.3044 | −0.774663 | −0.387331 | − | 0.921941i | \(-0.626603\pi\) | ||||
−0.387331 | + | 0.921941i | \(0.626603\pi\) | |||||||
\(830\) | 16.1414 | 0.560278 | ||||||||
\(831\) | −32.6770 | −1.13355 | ||||||||
\(832\) | −0.0803882 | −0.00278696 | ||||||||
\(833\) | −4.37239 | −0.151494 | ||||||||
\(834\) | 35.6967 | 1.23608 | ||||||||
\(835\) | 26.6438 | 0.922047 | ||||||||
\(836\) | −15.4905 | −0.535749 | ||||||||
\(837\) | −113.686 | −3.92958 | ||||||||
\(838\) | 0.106804 | 0.00368947 | ||||||||
\(839\) | 26.4596 | 0.913486 | 0.456743 | − | 0.889599i | \(-0.349016\pi\) | ||||
0.456743 | + | 0.889599i | \(0.349016\pi\) | |||||||
\(840\) | −17.2527 | −0.595273 | ||||||||
\(841\) | −28.7119 | −0.990067 | ||||||||
\(842\) | −14.1587 | −0.487941 | ||||||||
\(843\) | 102.374 | 3.52595 | ||||||||
\(844\) | −13.1396 | −0.452283 | ||||||||
\(845\) | −27.1429 | −0.933746 | ||||||||
\(846\) | 63.6863 | 2.18958 | ||||||||
\(847\) | 21.3359 | 0.733112 | ||||||||
\(848\) | −4.43522 | −0.152306 | ||||||||
\(849\) | −40.8483 | −1.40191 | ||||||||
\(850\) | 2.29127 | 0.0785900 | ||||||||
\(851\) | −66.3113 | −2.27312 | ||||||||
\(852\) | 13.2113 | 0.452613 | ||||||||
\(853\) | 41.5777 | 1.42359 | 0.711796 | − | 0.702386i | \(-0.247882\pi\) | ||||
0.711796 | + | 0.702386i | \(0.247882\pi\) | |||||||
\(854\) | 13.6555 | 0.467282 | ||||||||
\(855\) | −63.8037 | −2.18204 | ||||||||
\(856\) | −12.3144 | −0.420896 | ||||||||
\(857\) | 12.6766 | 0.433025 | 0.216513 | − | 0.976280i | \(-0.430532\pi\) | ||||
0.216513 | + | 0.976280i | \(0.430532\pi\) | |||||||
\(858\) | 1.23037 | 0.0420041 | ||||||||
\(859\) | −16.3223 | −0.556909 | −0.278454 | − | 0.960449i | \(-0.589822\pi\) | ||||
−0.278454 | + | 0.960449i | \(0.589822\pi\) | |||||||
\(860\) | −26.5742 | −0.906173 | ||||||||
\(861\) | 61.4536 | 2.09433 | ||||||||
\(862\) | −3.51166 | −0.119608 | ||||||||
\(863\) | −50.4171 | −1.71622 | −0.858109 | − | 0.513468i | \(-0.828361\pi\) | ||||
−0.858109 | + | 0.513468i | \(0.828361\pi\) | |||||||
\(864\) | −19.8777 | −0.676253 | ||||||||
\(865\) | −45.5315 | −1.54812 | ||||||||
\(866\) | 24.8991 | 0.846105 | ||||||||
\(867\) | −13.8428 | −0.470125 | ||||||||
\(868\) | −13.7571 | −0.466945 | ||||||||
\(869\) | 66.3808 | 2.25181 | ||||||||
\(870\) | 3.84966 | 0.130516 | ||||||||
\(871\) | −1.03496 | −0.0350683 | ||||||||
\(872\) | 0.398614 | 0.0134988 | ||||||||
\(873\) | −102.516 | −3.46963 | ||||||||
\(874\) | −22.4327 | −0.758797 | ||||||||
\(875\) | −28.3207 | −0.957413 | ||||||||
\(876\) | 14.1436 | 0.477867 | ||||||||
\(877\) | −21.3978 | −0.722554 | −0.361277 | − | 0.932459i | \(-0.617659\pi\) | ||||
−0.361277 | + | 0.932459i | \(0.617659\pi\) | |||||||
\(878\) | −36.4703 | −1.23081 | ||||||||
\(879\) | 76.7638 | 2.58918 | ||||||||
\(880\) | 9.31171 | 0.313898 | ||||||||
\(881\) | 12.7457 | 0.429412 | 0.214706 | − | 0.976679i | \(-0.431121\pi\) | ||||
0.214706 | + | 0.976679i | \(0.431121\pi\) | |||||||
\(882\) | 10.6716 | 0.359331 | ||||||||
\(883\) | 56.5758 | 1.90393 | 0.951964 | − | 0.306211i | \(-0.0990614\pi\) | ||||
0.951964 | + | 0.306211i | \(0.0990614\pi\) | |||||||
\(884\) | −0.289491 | −0.00973663 | ||||||||
\(885\) | −82.3734 | −2.76895 | ||||||||
\(886\) | 3.54480 | 0.119090 | ||||||||
\(887\) | 18.1010 | 0.607771 | 0.303886 | − | 0.952708i | \(-0.401716\pi\) | ||||
0.303886 | + | 0.952708i | \(0.401716\pi\) | |||||||
\(888\) | −35.2706 | −1.18361 | ||||||||
\(889\) | 7.93555 | 0.266150 | ||||||||
\(890\) | 31.2187 | 1.04645 | ||||||||
\(891\) | 186.698 | 6.25463 | ||||||||
\(892\) | −11.4947 | −0.384870 | ||||||||
\(893\) | 25.1801 | 0.842621 | ||||||||
\(894\) | 47.3644 | 1.58410 | ||||||||
\(895\) | −20.1197 | −0.672526 | ||||||||
\(896\) | −2.40538 | −0.0803580 | ||||||||
\(897\) | 1.78177 | 0.0594917 | ||||||||
\(898\) | 14.2267 | 0.474752 | ||||||||
\(899\) | 3.06968 | 0.102379 | ||||||||
\(900\) | −5.59224 | −0.186408 | ||||||||
\(901\) | −15.9720 | −0.532103 | ||||||||
\(902\) | −33.1681 | −1.10438 | ||||||||
\(903\) | −105.065 | −3.49634 | ||||||||
\(904\) | 4.90227 | 0.163047 | ||||||||
\(905\) | 32.6059 | 1.08386 | ||||||||
\(906\) | −62.7312 | −2.08411 | ||||||||
\(907\) | −11.8053 | −0.391988 | −0.195994 | − | 0.980605i | \(-0.562793\pi\) | ||||
−0.195994 | + | 0.980605i | \(0.562793\pi\) | |||||||
\(908\) | −6.20823 | −0.206027 | ||||||||
\(909\) | 61.7295 | 2.04744 | ||||||||
\(910\) | 0.403929 | 0.0133901 | ||||||||
\(911\) | −0.323842 | −0.0107294 | −0.00536468 | − | 0.999986i | \(-0.501708\pi\) | ||||
−0.00536468 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(912\) | −11.9318 | −0.395103 | ||||||||
\(913\) | −34.4440 | −1.13993 | ||||||||
\(914\) | −5.83438 | −0.192984 | ||||||||
\(915\) | −40.7190 | −1.34613 | ||||||||
\(916\) | −17.0912 | −0.564708 | ||||||||
\(917\) | −27.8493 | −0.919664 | ||||||||
\(918\) | −71.5828 | −2.36259 | ||||||||
\(919\) | 1.21792 | 0.0401754 | 0.0200877 | − | 0.999798i | \(-0.493605\pi\) | ||||
0.0200877 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(920\) | 13.4849 | 0.444583 | ||||||||
\(921\) | −42.7713 | −1.40936 | ||||||||
\(922\) | −16.8067 | −0.553500 | ||||||||
\(923\) | −0.309311 | −0.0101811 | ||||||||
\(924\) | 36.8151 | 1.21113 | ||||||||
\(925\) | −6.53588 | −0.214898 | ||||||||
\(926\) | 12.2503 | 0.402568 | ||||||||
\(927\) | 133.063 | 4.37035 | ||||||||
\(928\) | 0.536723 | 0.0176188 | ||||||||
\(929\) | −19.7982 | −0.649556 | −0.324778 | − | 0.945790i | \(-0.605290\pi\) | ||||
−0.324778 | + | 0.945790i | \(0.605290\pi\) | |||||||
\(930\) | 41.0219 | 1.34516 | ||||||||
\(931\) | 4.21930 | 0.138282 | ||||||||
\(932\) | 6.33038 | 0.207358 | ||||||||
\(933\) | −31.4270 | −1.02887 | ||||||||
\(934\) | −34.7821 | −1.13811 | ||||||||
\(935\) | 33.5330 | 1.09665 | ||||||||
\(936\) | 0.706552 | 0.0230944 | ||||||||
\(937\) | 50.9316 | 1.66386 | 0.831932 | − | 0.554878i | \(-0.187235\pi\) | ||||
0.831932 | + | 0.554878i | \(0.187235\pi\) | |||||||
\(938\) | −30.9681 | −1.01114 | ||||||||
\(939\) | 44.8806 | 1.46462 | ||||||||
\(940\) | −15.1364 | −0.493696 | ||||||||
\(941\) | −4.03548 | −0.131553 | −0.0657764 | − | 0.997834i | \(-0.520952\pi\) | ||||
−0.0657764 | + | 0.997834i | \(0.520952\pi\) | |||||||
\(942\) | 13.2865 | 0.432899 | ||||||||
\(943\) | −48.0328 | −1.56416 | ||||||||
\(944\) | −11.4846 | −0.373791 | ||||||||
\(945\) | 99.8800 | 3.24910 | ||||||||
\(946\) | 56.7062 | 1.84368 | ||||||||
\(947\) | −27.2389 | −0.885146 | −0.442573 | − | 0.896732i | \(-0.645934\pi\) | ||||
−0.442573 | + | 0.896732i | \(0.645934\pi\) | |||||||
\(948\) | 51.1312 | 1.66066 | ||||||||
\(949\) | −0.331137 | −0.0107492 | ||||||||
\(950\) | −2.21105 | −0.0717358 | ||||||||
\(951\) | −2.02083 | −0.0655301 | ||||||||
\(952\) | −8.66216 | −0.280742 | ||||||||
\(953\) | −41.4605 | −1.34304 | −0.671519 | − | 0.740987i | \(-0.734358\pi\) | ||||
−0.671519 | + | 0.740987i | \(0.734358\pi\) | |||||||
\(954\) | 38.9823 | 1.26210 | ||||||||
\(955\) | 24.2629 | 0.785128 | ||||||||
\(956\) | 22.2594 | 0.719920 | ||||||||
\(957\) | −8.21473 | −0.265544 | ||||||||
\(958\) | −13.3228 | −0.430441 | ||||||||
\(959\) | 14.7809 | 0.477300 | ||||||||
\(960\) | 7.17254 | 0.231493 | ||||||||
\(961\) | 1.71036 | 0.0551729 | ||||||||
\(962\) | 0.825776 | 0.0266241 | ||||||||
\(963\) | 108.234 | 3.48779 | ||||||||
\(964\) | 23.3716 | 0.752748 | ||||||||
\(965\) | −52.9734 | −1.70527 | ||||||||
\(966\) | 53.3143 | 1.71536 | ||||||||
\(967\) | 35.7484 | 1.14959 | 0.574795 | − | 0.818298i | \(-0.305082\pi\) | ||||
0.574795 | + | 0.818298i | \(0.305082\pi\) | |||||||
\(968\) | −8.87010 | −0.285096 | ||||||||
\(969\) | −42.9685 | −1.38035 | ||||||||
\(970\) | 24.3651 | 0.782316 | ||||||||
\(971\) | −7.78210 | −0.249739 | −0.124870 | − | 0.992173i | \(-0.539851\pi\) | ||||
−0.124870 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(972\) | 84.1751 | 2.69992 | ||||||||
\(973\) | −25.0074 | −0.801699 | ||||||||
\(974\) | 4.86783 | 0.155975 | ||||||||
\(975\) | 0.175618 | 0.00562428 | ||||||||
\(976\) | −5.67707 | −0.181719 | ||||||||
\(977\) | −25.5927 | −0.818784 | −0.409392 | − | 0.912359i | \(-0.634259\pi\) | ||||
−0.409392 | + | 0.912359i | \(0.634259\pi\) | |||||||
\(978\) | 37.1878 | 1.18914 | ||||||||
\(979\) | −66.6171 | −2.12909 | ||||||||
\(980\) | −2.53633 | −0.0810201 | ||||||||
\(981\) | −3.50352 | −0.111859 | ||||||||
\(982\) | −34.9278 | −1.11459 | ||||||||
\(983\) | 25.8265 | 0.823738 | 0.411869 | − | 0.911243i | \(-0.364876\pi\) | ||||
0.411869 | + | 0.911243i | \(0.364876\pi\) | |||||||
\(984\) | −25.5484 | −0.814454 | ||||||||
\(985\) | −17.7217 | −0.564661 | ||||||||
\(986\) | 1.93283 | 0.0615537 | ||||||||
\(987\) | −59.8439 | −1.90485 | ||||||||
\(988\) | 0.279355 | 0.00888746 | ||||||||
\(989\) | 82.1198 | 2.61126 | ||||||||
\(990\) | −81.8430 | −2.60114 | ||||||||
\(991\) | 46.1516 | 1.46605 | 0.733027 | − | 0.680200i | \(-0.238107\pi\) | ||||
0.733027 | + | 0.680200i | \(0.238107\pi\) | |||||||
\(992\) | 5.71930 | 0.181588 | ||||||||
\(993\) | 32.7907 | 1.04058 | ||||||||
\(994\) | −9.25522 | −0.293558 | ||||||||
\(995\) | 24.0599 | 0.762750 | ||||||||
\(996\) | −26.5312 | −0.840672 | ||||||||
\(997\) | −13.3430 | −0.422578 | −0.211289 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211289 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(998\) | −10.7868 | −0.341449 | ||||||||
\(999\) | 204.191 | 6.46031 |
(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 | 8002.2.a.e.1.77 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.77 | ✓ | 77 | 1.1 | even | 1 | trivial |