Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, 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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.37108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.48604\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | −2.18039 | −1.25885 | −0.629425 | − | 0.777061i | \(-0.716709\pi\) | ||||
−0.629425 | + | 0.777061i | \(0.716709\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.18039 | 0.975101 | 0.487550 | − | 0.873095i | \(-0.337891\pi\) | ||||
0.487550 | + | 0.873095i | \(0.337891\pi\) | |||||||
\(6\) | 2.18039 | 0.890141 | ||||||||
\(7\) | 4.66643 | 1.76375 | 0.881873 | − | 0.471488i | \(-0.156283\pi\) | ||||
0.881873 | + | 0.471488i | \(0.156283\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.75411 | 0.584703 | ||||||||
\(10\) | −2.18039 | −0.689500 | ||||||||
\(11\) | −2.48604 | −0.749569 | −0.374785 | − | 0.927112i | \(-0.622283\pi\) | ||||
−0.374785 | + | 0.927112i | \(0.622283\pi\) | |||||||
\(12\) | −2.18039 | −0.629425 | ||||||||
\(13\) | −4.48604 | −1.24420 | −0.622102 | − | 0.782936i | \(-0.713721\pi\) | ||||
−0.622102 | + | 0.782936i | \(0.713721\pi\) | |||||||
\(14\) | −4.66643 | −1.24716 | ||||||||
\(15\) | −4.75411 | −1.22751 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.62885 | −0.637591 | −0.318795 | − | 0.947824i | \(-0.603278\pi\) | ||||
−0.318795 | + | 0.947824i | \(0.603278\pi\) | |||||||
\(18\) | −1.75411 | −0.413447 | ||||||||
\(19\) | −2.93450 | −0.673221 | −0.336610 | − | 0.941644i | \(-0.609281\pi\) | ||||
−0.336610 | + | 0.941644i | \(0.609281\pi\) | |||||||
\(20\) | 2.18039 | 0.487550 | ||||||||
\(21\) | −10.1746 | −2.22029 | ||||||||
\(22\) | 2.48604 | 0.530025 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.18039 | 0.445071 | ||||||||
\(25\) | −0.245891 | −0.0491782 | ||||||||
\(26\) | 4.48604 | 0.879785 | ||||||||
\(27\) | 2.71653 | 0.522797 | ||||||||
\(28\) | 4.66643 | 0.881873 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 4.75411 | 0.867978 | ||||||||
\(31\) | −10.4860 | −1.88335 | −0.941674 | − | 0.336526i | \(-0.890748\pi\) | ||||
−0.941674 | + | 0.336526i | \(0.890748\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.42054 | 0.943595 | ||||||||
\(34\) | 2.62885 | 0.450845 | ||||||||
\(35\) | 10.1746 | 1.71983 | ||||||||
\(36\) | 1.75411 | 0.292351 | ||||||||
\(37\) | −7.27773 | −1.19645 | −0.598225 | − | 0.801328i | \(-0.704127\pi\) | ||||
−0.598225 | + | 0.801328i | \(0.704127\pi\) | |||||||
\(38\) | 2.93450 | 0.476039 | ||||||||
\(39\) | 9.78132 | 1.56627 | ||||||||
\(40\) | −2.18039 | −0.344750 | ||||||||
\(41\) | 7.63851 | 1.19293 | 0.596467 | − | 0.802637i | \(-0.296570\pi\) | ||||
0.596467 | + | 0.802637i | \(0.296570\pi\) | |||||||
\(42\) | 10.1746 | 1.56998 | ||||||||
\(43\) | −8.35504 | −1.27413 | −0.637066 | − | 0.770809i | \(-0.719852\pi\) | ||||
−0.637066 | + | 0.770809i | \(0.719852\pi\) | |||||||
\(44\) | −2.48604 | −0.374785 | ||||||||
\(45\) | 3.82464 | 0.570144 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 12.7158 | 1.85479 | 0.927397 | − | 0.374079i | \(-0.122041\pi\) | ||||
0.927397 | + | 0.374079i | \(0.122041\pi\) | |||||||
\(48\) | −2.18039 | −0.314712 | ||||||||
\(49\) | 14.7756 | 2.11080 | ||||||||
\(50\) | 0.245891 | 0.0347743 | ||||||||
\(51\) | 5.73193 | 0.802631 | ||||||||
\(52\) | −4.48604 | −0.622102 | ||||||||
\(53\) | −13.6328 | −1.87260 | −0.936302 | − | 0.351195i | \(-0.885775\pi\) | ||||
−0.936302 | + | 0.351195i | \(0.885775\pi\) | |||||||
\(54\) | −2.71653 | −0.369673 | ||||||||
\(55\) | −5.42054 | −0.730905 | ||||||||
\(56\) | −4.66643 | −0.623578 | ||||||||
\(57\) | 6.39836 | 0.847484 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 4.97208 | 0.647310 | 0.323655 | − | 0.946175i | \(-0.395088\pi\) | ||||
0.323655 | + | 0.946175i | \(0.395088\pi\) | |||||||
\(60\) | −4.75411 | −0.613753 | ||||||||
\(61\) | −1.33357 | −0.170746 | −0.0853730 | − | 0.996349i | \(-0.527208\pi\) | ||||
−0.0853730 | + | 0.996349i | \(0.527208\pi\) | |||||||
\(62\) | 10.4860 | 1.33173 | ||||||||
\(63\) | 8.18543 | 1.03127 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.78132 | −1.21322 | ||||||||
\(66\) | −5.42054 | −0.667222 | ||||||||
\(67\) | 0.628853 | 0.0768267 | 0.0384133 | − | 0.999262i | \(-0.487770\pi\) | ||||
0.0384133 | + | 0.999262i | \(0.487770\pi\) | |||||||
\(68\) | −2.62885 | −0.318795 | ||||||||
\(69\) | 2.18039 | 0.262488 | ||||||||
\(70\) | −10.1746 | −1.21610 | ||||||||
\(71\) | 1.50822 | 0.178993 | 0.0894963 | − | 0.995987i | \(-0.471474\pi\) | ||||
0.0894963 | + | 0.995987i | \(0.471474\pi\) | |||||||
\(72\) | −1.75411 | −0.206724 | ||||||||
\(73\) | 3.63851 | 0.425855 | 0.212928 | − | 0.977068i | \(-0.431700\pi\) | ||||
0.212928 | + | 0.977068i | \(0.431700\pi\) | |||||||
\(74\) | 7.27773 | 0.846018 | ||||||||
\(75\) | 0.536139 | 0.0619080 | ||||||||
\(76\) | −2.93450 | −0.336610 | ||||||||
\(77\) | −11.6009 | −1.32205 | ||||||||
\(78\) | −9.78132 | −1.10752 | ||||||||
\(79\) | −9.68861 | −1.09005 | −0.545027 | − | 0.838419i | \(-0.683481\pi\) | ||||
−0.545027 | + | 0.838419i | \(0.683481\pi\) | |||||||
\(80\) | 2.18039 | 0.243775 | ||||||||
\(81\) | −11.1854 | −1.24283 | ||||||||
\(82\) | −7.63851 | −0.843532 | ||||||||
\(83\) | 7.86900 | 0.863735 | 0.431868 | − | 0.901937i | \(-0.357855\pi\) | ||||
0.431868 | + | 0.901937i | \(0.357855\pi\) | |||||||
\(84\) | −10.1746 | −1.11015 | ||||||||
\(85\) | −5.73193 | −0.621715 | ||||||||
\(86\) | 8.35504 | 0.900947 | ||||||||
\(87\) | 2.18039 | 0.233763 | ||||||||
\(88\) | 2.48604 | 0.265013 | ||||||||
\(89\) | −12.4979 | −1.32477 | −0.662385 | − | 0.749164i | \(-0.730456\pi\) | ||||
−0.662385 | + | 0.749164i | \(0.730456\pi\) | |||||||
\(90\) | −3.82464 | −0.403153 | ||||||||
\(91\) | −20.9338 | −2.19446 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 22.8637 | 2.37085 | ||||||||
\(94\) | −12.7158 | −1.31154 | ||||||||
\(95\) | −6.39836 | −0.656458 | ||||||||
\(96\) | 2.18039 | 0.222535 | ||||||||
\(97\) | −8.72157 | −0.885541 | −0.442771 | − | 0.896635i | \(-0.646004\pi\) | ||||
−0.442771 | + | 0.896635i | \(0.646004\pi\) | |||||||
\(98\) | −14.7756 | −1.49256 | ||||||||
\(99\) | −4.36078 | −0.438275 | ||||||||
\(100\) | −0.245891 | −0.0245891 | ||||||||
\(101\) | −8.37834 | −0.833676 | −0.416838 | − | 0.908981i | \(-0.636862\pi\) | ||||
−0.416838 | + | 0.908981i | \(0.636862\pi\) | |||||||
\(102\) | −5.73193 | −0.567546 | ||||||||
\(103\) | −17.4080 | −1.71526 | −0.857632 | − | 0.514265i | \(-0.828065\pi\) | ||||
−0.857632 | + | 0.514265i | \(0.828065\pi\) | |||||||
\(104\) | 4.48604 | 0.439892 | ||||||||
\(105\) | −22.1847 | −2.16501 | ||||||||
\(106\) | 13.6328 | 1.32413 | ||||||||
\(107\) | 11.8690 | 1.14742 | 0.573710 | − | 0.819059i | \(-0.305504\pi\) | ||||
0.573710 | + | 0.819059i | \(0.305504\pi\) | |||||||
\(108\) | 2.71653 | 0.261398 | ||||||||
\(109\) | −11.9675 | −1.14627 | −0.573137 | − | 0.819459i | \(-0.694274\pi\) | ||||
−0.573137 | + | 0.819459i | \(0.694274\pi\) | |||||||
\(110\) | 5.42054 | 0.516828 | ||||||||
\(111\) | 15.8683 | 1.50615 | ||||||||
\(112\) | 4.66643 | 0.440936 | ||||||||
\(113\) | 8.97208 | 0.844022 | 0.422011 | − | 0.906591i | \(-0.361324\pi\) | ||||
0.422011 | + | 0.906591i | \(0.361324\pi\) | |||||||
\(114\) | −6.39836 | −0.599261 | ||||||||
\(115\) | −2.18039 | −0.203323 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −7.86900 | −0.727489 | ||||||||
\(118\) | −4.97208 | −0.457717 | ||||||||
\(119\) | −12.2674 | −1.12455 | ||||||||
\(120\) | 4.75411 | 0.433989 | ||||||||
\(121\) | −4.81961 | −0.438146 | ||||||||
\(122\) | 1.33357 | 0.120736 | ||||||||
\(123\) | −16.6549 | −1.50173 | ||||||||
\(124\) | −10.4860 | −0.941674 | ||||||||
\(125\) | −11.4381 | −1.02305 | ||||||||
\(126\) | −8.18543 | −0.729216 | ||||||||
\(127\) | 21.0357 | 1.86662 | 0.933310 | − | 0.359070i | \(-0.116906\pi\) | ||||
0.933310 | + | 0.359070i | \(0.116906\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 18.2173 | 1.60394 | ||||||||
\(130\) | 9.78132 | 0.857879 | ||||||||
\(131\) | −2.57372 | −0.224867 | −0.112433 | − | 0.993659i | \(-0.535864\pi\) | ||||
−0.112433 | + | 0.993659i | \(0.535864\pi\) | |||||||
\(132\) | 5.42054 | 0.471797 | ||||||||
\(133\) | −13.6936 | −1.18739 | ||||||||
\(134\) | −0.628853 | −0.0543247 | ||||||||
\(135\) | 5.92310 | 0.509779 | ||||||||
\(136\) | 2.62885 | 0.225422 | ||||||||
\(137\) | 4.74837 | 0.405680 | 0.202840 | − | 0.979212i | \(-0.434983\pi\) | ||||
0.202840 | + | 0.979212i | \(0.434983\pi\) | |||||||
\(138\) | −2.18039 | −0.185607 | ||||||||
\(139\) | 15.8683 | 1.34593 | 0.672966 | − | 0.739674i | \(-0.265020\pi\) | ||||
0.672966 | + | 0.739674i | \(0.265020\pi\) | |||||||
\(140\) | 10.1746 | 0.859915 | ||||||||
\(141\) | −27.7255 | −2.33491 | ||||||||
\(142\) | −1.50822 | −0.126567 | ||||||||
\(143\) | 11.1525 | 0.932616 | ||||||||
\(144\) | 1.75411 | 0.146176 | ||||||||
\(145\) | −2.18039 | −0.181072 | ||||||||
\(146\) | −3.63851 | −0.301125 | ||||||||
\(147\) | −32.2166 | −2.65718 | ||||||||
\(148\) | −7.27773 | −0.598225 | ||||||||
\(149\) | −0.311390 | −0.0255101 | −0.0127550 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127550 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(150\) | −0.536139 | −0.0437756 | ||||||||
\(151\) | −11.7380 | −0.955225 | −0.477613 | − | 0.878571i | \(-0.658498\pi\) | ||||
−0.477613 | + | 0.878571i | \(0.658498\pi\) | |||||||
\(152\) | 2.93450 | 0.238019 | ||||||||
\(153\) | −4.61129 | −0.372801 | ||||||||
\(154\) | 11.6009 | 0.934830 | ||||||||
\(155\) | −22.8637 | −1.83645 | ||||||||
\(156\) | 9.78132 | 0.783133 | ||||||||
\(157\) | −14.9521 | −1.19330 | −0.596652 | − | 0.802500i | \(-0.703503\pi\) | ||||
−0.596652 | + | 0.802500i | \(0.703503\pi\) | |||||||
\(158\) | 9.68861 | 0.770784 | ||||||||
\(159\) | 29.7248 | 2.35733 | ||||||||
\(160\) | −2.18039 | −0.172375 | ||||||||
\(161\) | −4.66643 | −0.367766 | ||||||||
\(162\) | 11.1854 | 0.878810 | ||||||||
\(163\) | 20.8461 | 1.63279 | 0.816397 | − | 0.577491i | \(-0.195968\pi\) | ||||
0.816397 | + | 0.577491i | \(0.195968\pi\) | |||||||
\(164\) | 7.63851 | 0.596467 | ||||||||
\(165\) | 11.8189 | 0.920100 | ||||||||
\(166\) | −7.86900 | −0.610753 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 10.1746 | 0.784991 | ||||||||
\(169\) | 7.12455 | 0.548042 | ||||||||
\(170\) | 5.73193 | 0.439619 | ||||||||
\(171\) | −5.14743 | −0.393634 | ||||||||
\(172\) | −8.35504 | −0.637066 | ||||||||
\(173\) | −16.6657 | −1.26707 | −0.633536 | − | 0.773713i | \(-0.718397\pi\) | ||||
−0.633536 | + | 0.773713i | \(0.718397\pi\) | |||||||
\(174\) | −2.18039 | −0.165295 | ||||||||
\(175\) | −1.14743 | −0.0867379 | ||||||||
\(176\) | −2.48604 | −0.187392 | ||||||||
\(177\) | −10.8411 | −0.814866 | ||||||||
\(178\) | 12.4979 | 0.936754 | ||||||||
\(179\) | 3.08306 | 0.230439 | 0.115219 | − | 0.993340i | \(-0.463243\pi\) | ||||
0.115219 | + | 0.993340i | \(0.463243\pi\) | |||||||
\(180\) | 3.82464 | 0.285072 | ||||||||
\(181\) | 7.52003 | 0.558960 | 0.279480 | − | 0.960152i | \(-0.409838\pi\) | ||||
0.279480 | + | 0.960152i | \(0.409838\pi\) | |||||||
\(182\) | 20.9338 | 1.55172 | ||||||||
\(183\) | 2.90770 | 0.214944 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −15.8683 | −1.16666 | ||||||||
\(186\) | −22.8637 | −1.67645 | ||||||||
\(187\) | 6.53543 | 0.477918 | ||||||||
\(188\) | 12.7158 | 0.927397 | ||||||||
\(189\) | 12.6765 | 0.922080 | ||||||||
\(190\) | 6.39836 | 0.464186 | ||||||||
\(191\) | −2.97208 | −0.215052 | −0.107526 | − | 0.994202i | \(-0.534293\pi\) | ||||
−0.107526 | + | 0.994202i | \(0.534293\pi\) | |||||||
\(192\) | −2.18039 | −0.157356 | ||||||||
\(193\) | 22.7101 | 1.63471 | 0.817354 | − | 0.576136i | \(-0.195440\pi\) | ||||
0.817354 | + | 0.576136i | \(0.195440\pi\) | |||||||
\(194\) | 8.72157 | 0.626172 | ||||||||
\(195\) | 21.3271 | 1.52727 | ||||||||
\(196\) | 14.7756 | 1.05540 | ||||||||
\(197\) | −6.72157 | −0.478892 | −0.239446 | − | 0.970910i | \(-0.576966\pi\) | ||||
−0.239446 | + | 0.970910i | \(0.576966\pi\) | |||||||
\(198\) | 4.36078 | 0.309907 | ||||||||
\(199\) | 12.9721 | 0.919566 | 0.459783 | − | 0.888031i | \(-0.347927\pi\) | ||||
0.459783 | + | 0.888031i | \(0.347927\pi\) | |||||||
\(200\) | 0.245891 | 0.0173871 | ||||||||
\(201\) | −1.37115 | −0.0967132 | ||||||||
\(202\) | 8.37834 | 0.589498 | ||||||||
\(203\) | −4.66643 | −0.327519 | ||||||||
\(204\) | 5.73193 | 0.401315 | ||||||||
\(205\) | 16.6549 | 1.16323 | ||||||||
\(206\) | 17.4080 | 1.21287 | ||||||||
\(207\) | −1.75411 | −0.121919 | ||||||||
\(208\) | −4.48604 | −0.311051 | ||||||||
\(209\) | 7.29528 | 0.504625 | ||||||||
\(210\) | 22.1847 | 1.53089 | ||||||||
\(211\) | −11.0773 | −0.762594 | −0.381297 | − | 0.924453i | \(-0.624522\pi\) | ||||
−0.381297 | + | 0.924453i | \(0.624522\pi\) | |||||||
\(212\) | −13.6328 | −0.936302 | ||||||||
\(213\) | −3.28851 | −0.225325 | ||||||||
\(214\) | −11.8690 | −0.811348 | ||||||||
\(215\) | −18.2173 | −1.24241 | ||||||||
\(216\) | −2.71653 | −0.184837 | ||||||||
\(217\) | −48.9324 | −3.32175 | ||||||||
\(218\) | 11.9675 | 0.810539 | ||||||||
\(219\) | −7.93338 | −0.536088 | ||||||||
\(220\) | −5.42054 | −0.365453 | ||||||||
\(221\) | 11.7931 | 0.793292 | ||||||||
\(222\) | −15.8683 | −1.06501 | ||||||||
\(223\) | 16.7216 | 1.11976 | 0.559879 | − | 0.828574i | \(-0.310847\pi\) | ||||
0.559879 | + | 0.828574i | \(0.310847\pi\) | |||||||
\(224\) | −4.66643 | −0.311789 | ||||||||
\(225\) | −0.431320 | −0.0287547 | ||||||||
\(226\) | −8.97208 | −0.596814 | ||||||||
\(227\) | −21.1285 | −1.40235 | −0.701173 | − | 0.712991i | \(-0.747340\pi\) | ||||
−0.701173 | + | 0.712991i | \(0.747340\pi\) | |||||||
\(228\) | 6.39836 | 0.423742 | ||||||||
\(229\) | 7.31284 | 0.483246 | 0.241623 | − | 0.970370i | \(-0.422320\pi\) | ||||
0.241623 | + | 0.970370i | \(0.422320\pi\) | |||||||
\(230\) | 2.18039 | 0.143771 | ||||||||
\(231\) | 25.2946 | 1.66426 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 4.38408 | 0.287211 | 0.143605 | − | 0.989635i | \(-0.454130\pi\) | ||||
0.143605 | + | 0.989635i | \(0.454130\pi\) | |||||||
\(234\) | 7.86900 | 0.514413 | ||||||||
\(235\) | 27.7255 | 1.80861 | ||||||||
\(236\) | 4.97208 | 0.323655 | ||||||||
\(237\) | 21.1250 | 1.37221 | ||||||||
\(238\) | 12.2674 | 0.795175 | ||||||||
\(239\) | 2.55370 | 0.165185 | 0.0825925 | − | 0.996583i | \(-0.473680\pi\) | ||||
0.0825925 | + | 0.996583i | \(0.473680\pi\) | |||||||
\(240\) | −4.75411 | −0.306876 | ||||||||
\(241\) | −30.4538 | −1.96170 | −0.980852 | − | 0.194756i | \(-0.937609\pi\) | ||||
−0.980852 | + | 0.194756i | \(0.937609\pi\) | |||||||
\(242\) | 4.81961 | 0.309816 | ||||||||
\(243\) | 16.2390 | 1.04173 | ||||||||
\(244\) | −1.33357 | −0.0853730 | ||||||||
\(245\) | 32.2166 | 2.05824 | ||||||||
\(246\) | 16.6549 | 1.06188 | ||||||||
\(247\) | 13.1643 | 0.837623 | ||||||||
\(248\) | 10.4860 | 0.665864 | ||||||||
\(249\) | −17.1575 | −1.08731 | ||||||||
\(250\) | 11.4381 | 0.723409 | ||||||||
\(251\) | −10.5497 | −0.665892 | −0.332946 | − | 0.942946i | \(-0.608043\pi\) | ||||
−0.332946 | + | 0.942946i | \(0.608043\pi\) | |||||||
\(252\) | 8.18543 | 0.515634 | ||||||||
\(253\) | 2.48604 | 0.156296 | ||||||||
\(254\) | −21.0357 | −1.31990 | ||||||||
\(255\) | 12.4979 | 0.782646 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.3192 | 1.26748 | 0.633739 | − | 0.773547i | \(-0.281519\pi\) | ||||
0.633739 | + | 0.773547i | \(0.281519\pi\) | |||||||
\(258\) | −18.2173 | −1.13416 | ||||||||
\(259\) | −33.9610 | −2.11023 | ||||||||
\(260\) | −9.78132 | −0.606612 | ||||||||
\(261\) | −1.75411 | −0.108577 | ||||||||
\(262\) | 2.57372 | 0.159005 | ||||||||
\(263\) | −10.6958 | −0.659532 | −0.329766 | − | 0.944063i | \(-0.606970\pi\) | ||||
−0.329766 | + | 0.944063i | \(0.606970\pi\) | |||||||
\(264\) | −5.42054 | −0.333611 | ||||||||
\(265\) | −29.7248 | −1.82598 | ||||||||
\(266\) | 13.6936 | 0.839611 | ||||||||
\(267\) | 27.2502 | 1.66769 | ||||||||
\(268\) | 0.628853 | 0.0384133 | ||||||||
\(269\) | −18.8472 | −1.14913 | −0.574566 | − | 0.818459i | \(-0.694829\pi\) | ||||
−0.574566 | + | 0.818459i | \(0.694829\pi\) | |||||||
\(270\) | −5.92310 | −0.360469 | ||||||||
\(271\) | −23.3064 | −1.41576 | −0.707881 | − | 0.706331i | \(-0.750349\pi\) | ||||
−0.707881 | + | 0.706331i | \(0.750349\pi\) | |||||||
\(272\) | −2.62885 | −0.159398 | ||||||||
\(273\) | 45.6439 | 2.76249 | ||||||||
\(274\) | −4.74837 | −0.286859 | ||||||||
\(275\) | 0.611295 | 0.0368625 | ||||||||
\(276\) | 2.18039 | 0.131244 | ||||||||
\(277\) | 30.9889 | 1.86194 | 0.930972 | − | 0.365090i | \(-0.118962\pi\) | ||||
0.930972 | + | 0.365090i | \(0.118962\pi\) | |||||||
\(278\) | −15.8683 | −0.951717 | ||||||||
\(279\) | −18.3937 | −1.10120 | ||||||||
\(280\) | −10.1746 | −0.608052 | ||||||||
\(281\) | −9.81890 | −0.585747 | −0.292873 | − | 0.956151i | \(-0.594611\pi\) | ||||
−0.292873 | + | 0.956151i | \(0.594611\pi\) | |||||||
\(282\) | 27.7255 | 1.65103 | ||||||||
\(283\) | −24.6160 | −1.46327 | −0.731633 | − | 0.681698i | \(-0.761242\pi\) | ||||
−0.731633 | + | 0.681698i | \(0.761242\pi\) | |||||||
\(284\) | 1.50822 | 0.0894963 | ||||||||
\(285\) | 13.9509 | 0.826382 | ||||||||
\(286\) | −11.1525 | −0.659459 | ||||||||
\(287\) | 35.6446 | 2.10403 | ||||||||
\(288\) | −1.75411 | −0.103362 | ||||||||
\(289\) | −10.0891 | −0.593478 | ||||||||
\(290\) | 2.18039 | 0.128037 | ||||||||
\(291\) | 19.0164 | 1.11476 | ||||||||
\(292\) | 3.63851 | 0.212928 | ||||||||
\(293\) | 2.95206 | 0.172461 | 0.0862306 | − | 0.996275i | \(-0.472518\pi\) | ||||
0.0862306 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(294\) | 32.2166 | 1.87891 | ||||||||
\(295\) | 10.8411 | 0.631192 | ||||||||
\(296\) | 7.27773 | 0.423009 | ||||||||
\(297\) | −6.75340 | −0.391872 | ||||||||
\(298\) | 0.311390 | 0.0180384 | ||||||||
\(299\) | 4.48604 | 0.259434 | ||||||||
\(300\) | 0.536139 | 0.0309540 | ||||||||
\(301\) | −38.9882 | −2.24724 | ||||||||
\(302\) | 11.7380 | 0.675446 | ||||||||
\(303\) | 18.2681 | 1.04947 | ||||||||
\(304\) | −2.93450 | −0.168305 | ||||||||
\(305\) | −2.90770 | −0.166495 | ||||||||
\(306\) | 4.61129 | 0.263610 | ||||||||
\(307\) | 24.0129 | 1.37049 | 0.685243 | − | 0.728314i | \(-0.259696\pi\) | ||||
0.685243 | + | 0.728314i | \(0.259696\pi\) | |||||||
\(308\) | −11.6009 | −0.661024 | ||||||||
\(309\) | 37.9563 | 2.15926 | ||||||||
\(310\) | 22.8637 | 1.29857 | ||||||||
\(311\) | 9.59486 | 0.544075 | 0.272037 | − | 0.962287i | \(-0.412303\pi\) | ||||
0.272037 | + | 0.962287i | \(0.412303\pi\) | |||||||
\(312\) | −9.78132 | −0.553758 | ||||||||
\(313\) | −33.0093 | −1.86579 | −0.932897 | − | 0.360142i | \(-0.882728\pi\) | ||||
−0.932897 | + | 0.360142i | \(0.882728\pi\) | |||||||
\(314\) | 14.9521 | 0.843794 | ||||||||
\(315\) | 17.8474 | 1.00559 | ||||||||
\(316\) | −9.68861 | −0.545027 | ||||||||
\(317\) | −2.47422 | −0.138966 | −0.0694831 | − | 0.997583i | \(-0.522135\pi\) | ||||
−0.0694831 | + | 0.997583i | \(0.522135\pi\) | |||||||
\(318\) | −29.7248 | −1.66688 | ||||||||
\(319\) | 2.48604 | 0.139191 | ||||||||
\(320\) | 2.18039 | 0.121888 | ||||||||
\(321\) | −25.8791 | −1.44443 | ||||||||
\(322\) | 4.66643 | 0.260050 | ||||||||
\(323\) | 7.71437 | 0.429239 | ||||||||
\(324\) | −11.1854 | −0.621413 | ||||||||
\(325\) | 1.10308 | 0.0611877 | ||||||||
\(326\) | −20.8461 | −1.15456 | ||||||||
\(327\) | 26.0938 | 1.44299 | ||||||||
\(328\) | −7.63851 | −0.421766 | ||||||||
\(329\) | 59.3375 | 3.27138 | ||||||||
\(330\) | −11.8189 | −0.650609 | ||||||||
\(331\) | −7.24589 | −0.398270 | −0.199135 | − | 0.979972i | \(-0.563813\pi\) | ||||
−0.199135 | + | 0.979972i | \(0.563813\pi\) | |||||||
\(332\) | 7.86900 | 0.431868 | ||||||||
\(333\) | −12.7659 | −0.699568 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 1.37115 | 0.0749137 | ||||||||
\(336\) | −10.1746 | −0.555073 | ||||||||
\(337\) | −9.58337 | −0.522040 | −0.261020 | − | 0.965333i | \(-0.584059\pi\) | ||||
−0.261020 | + | 0.965333i | \(0.584059\pi\) | |||||||
\(338\) | −7.12455 | −0.387524 | ||||||||
\(339\) | −19.5626 | −1.06250 | ||||||||
\(340\) | −5.73193 | −0.310858 | ||||||||
\(341\) | 26.0687 | 1.41170 | ||||||||
\(342\) | 5.14743 | 0.278341 | ||||||||
\(343\) | 36.2842 | 1.95916 | ||||||||
\(344\) | 8.35504 | 0.450474 | ||||||||
\(345\) | 4.75411 | 0.255953 | ||||||||
\(346\) | 16.6657 | 0.895955 | ||||||||
\(347\) | 3.20186 | 0.171885 | 0.0859425 | − | 0.996300i | \(-0.472610\pi\) | ||||
0.0859425 | + | 0.996300i | \(0.472610\pi\) | |||||||
\(348\) | 2.18039 | 0.116881 | ||||||||
\(349\) | −10.1865 | −0.545269 | −0.272634 | − | 0.962118i | \(-0.587895\pi\) | ||||
−0.272634 | + | 0.962118i | \(0.587895\pi\) | |||||||
\(350\) | 1.14743 | 0.0613329 | ||||||||
\(351\) | −12.1865 | −0.650465 | ||||||||
\(352\) | 2.48604 | 0.132506 | ||||||||
\(353\) | 17.9817 | 0.957071 | 0.478536 | − | 0.878068i | \(-0.341168\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341168\pi\) | |||||||
\(354\) | 10.8411 | 0.576197 | ||||||||
\(355\) | 3.28851 | 0.174536 | ||||||||
\(356\) | −12.4979 | −0.662385 | ||||||||
\(357\) | 26.7477 | 1.41564 | ||||||||
\(358\) | −3.08306 | −0.162945 | ||||||||
\(359\) | 4.19724 | 0.221522 | 0.110761 | − | 0.993847i | \(-0.464671\pi\) | ||||
0.110761 | + | 0.993847i | \(0.464671\pi\) | |||||||
\(360\) | −3.82464 | −0.201576 | ||||||||
\(361\) | −10.3887 | −0.546774 | ||||||||
\(362\) | −7.52003 | −0.395244 | ||||||||
\(363\) | 10.5086 | 0.551560 | ||||||||
\(364\) | −20.9338 | −1.09723 | ||||||||
\(365\) | 7.93338 | 0.415252 | ||||||||
\(366\) | −2.90770 | −0.151988 | ||||||||
\(367\) | 3.95094 | 0.206237 | 0.103119 | − | 0.994669i | \(-0.467118\pi\) | ||||
0.103119 | + | 0.994669i | \(0.467118\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 13.3988 | 0.697513 | ||||||||
\(370\) | 15.8683 | 0.824953 | ||||||||
\(371\) | −63.6164 | −3.30280 | ||||||||
\(372\) | 22.8637 | 1.18543 | ||||||||
\(373\) | −6.18039 | −0.320009 | −0.160004 | − | 0.987116i | \(-0.551151\pi\) | ||||
−0.160004 | + | 0.987116i | \(0.551151\pi\) | |||||||
\(374\) | −6.53543 | −0.337939 | ||||||||
\(375\) | 24.9395 | 1.28787 | ||||||||
\(376\) | −12.7158 | −0.655769 | ||||||||
\(377\) | 4.48604 | 0.231043 | ||||||||
\(378\) | −12.6765 | −0.652009 | ||||||||
\(379\) | −4.37227 | −0.224588 | −0.112294 | − | 0.993675i | \(-0.535820\pi\) | ||||
−0.112294 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(380\) | −6.39836 | −0.328229 | ||||||||
\(381\) | −45.8662 | −2.34980 | ||||||||
\(382\) | 2.97208 | 0.152065 | ||||||||
\(383\) | 0.317133 | 0.0162047 | 0.00810237 | − | 0.999967i | \(-0.497421\pi\) | ||||
0.00810237 | + | 0.999967i | \(0.497421\pi\) | |||||||
\(384\) | 2.18039 | 0.111268 | ||||||||
\(385\) | −25.2946 | −1.28913 | ||||||||
\(386\) | −22.7101 | −1.15591 | ||||||||
\(387\) | −14.6557 | −0.744989 | ||||||||
\(388\) | −8.72157 | −0.442771 | ||||||||
\(389\) | −30.1625 | −1.52930 | −0.764649 | − | 0.644447i | \(-0.777087\pi\) | ||||
−0.764649 | + | 0.644447i | \(0.777087\pi\) | |||||||
\(390\) | −21.3271 | −1.07994 | ||||||||
\(391\) | 2.62885 | 0.132947 | ||||||||
\(392\) | −14.7756 | −0.746280 | ||||||||
\(393\) | 5.61171 | 0.283073 | ||||||||
\(394\) | 6.72157 | 0.338628 | ||||||||
\(395\) | −21.1250 | −1.06291 | ||||||||
\(396\) | −4.36078 | −0.219138 | ||||||||
\(397\) | −16.2187 | −0.813992 | −0.406996 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(398\) | −12.9721 | −0.650232 | ||||||||
\(399\) | 29.8575 | 1.49475 | ||||||||
\(400\) | −0.245891 | −0.0122946 | ||||||||
\(401\) | 28.4678 | 1.42161 | 0.710806 | − | 0.703388i | \(-0.248330\pi\) | ||||
0.710806 | + | 0.703388i | \(0.248330\pi\) | |||||||
\(402\) | 1.37115 | 0.0683866 | ||||||||
\(403\) | 47.0408 | 2.34327 | ||||||||
\(404\) | −8.37834 | −0.416838 | ||||||||
\(405\) | −24.3886 | −1.21188 | ||||||||
\(406\) | 4.66643 | 0.231591 | ||||||||
\(407\) | 18.0927 | 0.896823 | ||||||||
\(408\) | −5.73193 | −0.283773 | ||||||||
\(409\) | −6.48100 | −0.320465 | −0.160232 | − | 0.987079i | \(-0.551224\pi\) | ||||
−0.160232 | + | 0.987079i | \(0.551224\pi\) | |||||||
\(410\) | −16.6549 | −0.822529 | ||||||||
\(411\) | −10.3533 | −0.510691 | ||||||||
\(412\) | −17.4080 | −0.857632 | ||||||||
\(413\) | 23.2019 | 1.14169 | ||||||||
\(414\) | 1.75411 | 0.0862097 | ||||||||
\(415\) | 17.1575 | 0.842229 | ||||||||
\(416\) | 4.48604 | 0.219946 | ||||||||
\(417\) | −34.5991 | −1.69433 | ||||||||
\(418\) | −7.29528 | −0.356824 | ||||||||
\(419\) | −16.7913 | −0.820309 | −0.410155 | − | 0.912016i | \(-0.634525\pi\) | ||||
−0.410155 | + | 0.912016i | \(0.634525\pi\) | |||||||
\(420\) | −22.1847 | −1.08250 | ||||||||
\(421\) | 9.95996 | 0.485419 | 0.242709 | − | 0.970099i | \(-0.421964\pi\) | ||||
0.242709 | + | 0.970099i | \(0.421964\pi\) | |||||||
\(422\) | 11.0773 | 0.539235 | ||||||||
\(423\) | 22.3049 | 1.08450 | ||||||||
\(424\) | 13.6328 | 0.662066 | ||||||||
\(425\) | 0.646412 | 0.0313556 | ||||||||
\(426\) | 3.28851 | 0.159329 | ||||||||
\(427\) | −6.22301 | −0.301152 | ||||||||
\(428\) | 11.8690 | 0.573710 | ||||||||
\(429\) | −24.3168 | −1.17402 | ||||||||
\(430\) | 18.2173 | 0.878514 | ||||||||
\(431\) | 23.2770 | 1.12121 | 0.560607 | − | 0.828082i | \(-0.310568\pi\) | ||||
0.560607 | + | 0.828082i | \(0.310568\pi\) | |||||||
\(432\) | 2.71653 | 0.130699 | ||||||||
\(433\) | 26.8665 | 1.29112 | 0.645560 | − | 0.763710i | \(-0.276624\pi\) | ||||
0.645560 | + | 0.763710i | \(0.276624\pi\) | |||||||
\(434\) | 48.9324 | 2.34883 | ||||||||
\(435\) | 4.75411 | 0.227942 | ||||||||
\(436\) | −11.9675 | −0.573137 | ||||||||
\(437\) | 2.93450 | 0.140376 | ||||||||
\(438\) | 7.93338 | 0.379071 | ||||||||
\(439\) | 0.759852 | 0.0362657 | 0.0181329 | − | 0.999836i | \(-0.494228\pi\) | ||||
0.0181329 | + | 0.999836i | \(0.494228\pi\) | |||||||
\(440\) | 5.42054 | 0.258414 | ||||||||
\(441\) | 25.9180 | 1.23419 | ||||||||
\(442\) | −11.7931 | −0.560942 | ||||||||
\(443\) | 11.6324 | 0.552674 | 0.276337 | − | 0.961061i | \(-0.410879\pi\) | ||||
0.276337 | + | 0.961061i | \(0.410879\pi\) | |||||||
\(444\) | 15.8683 | 0.753076 | ||||||||
\(445\) | −27.2502 | −1.29178 | ||||||||
\(446\) | −16.7216 | −0.791789 | ||||||||
\(447\) | 0.678953 | 0.0321134 | ||||||||
\(448\) | 4.66643 | 0.220468 | ||||||||
\(449\) | 10.3293 | 0.487469 | 0.243734 | − | 0.969842i | \(-0.421627\pi\) | ||||
0.243734 | + | 0.969842i | \(0.421627\pi\) | |||||||
\(450\) | 0.431320 | 0.0203326 | ||||||||
\(451\) | −18.9896 | −0.894187 | ||||||||
\(452\) | 8.97208 | 0.422011 | ||||||||
\(453\) | 25.5934 | 1.20249 | ||||||||
\(454\) | 21.1285 | 0.991608 | ||||||||
\(455\) | −45.6439 | −2.13982 | ||||||||
\(456\) | −6.39836 | −0.299631 | ||||||||
\(457\) | 33.6844 | 1.57569 | 0.787845 | − | 0.615874i | \(-0.211197\pi\) | ||||
0.787845 | + | 0.615874i | \(0.211197\pi\) | |||||||
\(458\) | −7.31284 | −0.341707 | ||||||||
\(459\) | −7.14136 | −0.333330 | ||||||||
\(460\) | −2.18039 | −0.101661 | ||||||||
\(461\) | 9.27526 | 0.431992 | 0.215996 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215996 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(462\) | −25.2946 | −1.17681 | ||||||||
\(463\) | −20.6464 | −0.959520 | −0.479760 | − | 0.877400i | \(-0.659276\pi\) | ||||
−0.479760 | + | 0.877400i | \(0.659276\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 49.8518 | 2.31182 | ||||||||
\(466\) | −4.38408 | −0.203089 | ||||||||
\(467\) | 25.1700 | 1.16473 | 0.582365 | − | 0.812927i | \(-0.302127\pi\) | ||||
0.582365 | + | 0.812927i | \(0.302127\pi\) | |||||||
\(468\) | −7.86900 | −0.363745 | ||||||||
\(469\) | 2.93450 | 0.135503 | ||||||||
\(470\) | −27.7255 | −1.27888 | ||||||||
\(471\) | 32.6013 | 1.50219 | ||||||||
\(472\) | −4.97208 | −0.228858 | ||||||||
\(473\) | 20.7710 | 0.955050 | ||||||||
\(474\) | −21.1250 | −0.970302 | ||||||||
\(475\) | 0.721568 | 0.0331078 | ||||||||
\(476\) | −12.2674 | −0.562274 | ||||||||
\(477\) | −23.9134 | −1.09492 | ||||||||
\(478\) | −2.55370 | −0.116803 | ||||||||
\(479\) | −28.1553 | −1.28645 | −0.643225 | − | 0.765677i | \(-0.722404\pi\) | ||||
−0.643225 | + | 0.765677i | \(0.722404\pi\) | |||||||
\(480\) | 4.75411 | 0.216994 | ||||||||
\(481\) | 32.6482 | 1.48863 | ||||||||
\(482\) | 30.4538 | 1.38713 | ||||||||
\(483\) | 10.1746 | 0.462963 | ||||||||
\(484\) | −4.81961 | −0.219073 | ||||||||
\(485\) | −19.0164 | −0.863492 | ||||||||
\(486\) | −16.2390 | −0.736617 | ||||||||
\(487\) | −11.3855 | −0.515928 | −0.257964 | − | 0.966155i | \(-0.583052\pi\) | ||||
−0.257964 | + | 0.966155i | \(0.583052\pi\) | |||||||
\(488\) | 1.33357 | 0.0603678 | ||||||||
\(489\) | −45.4527 | −2.05544 | ||||||||
\(490\) | −32.2166 | −1.45540 | ||||||||
\(491\) | −31.9728 | −1.44291 | −0.721457 | − | 0.692460i | \(-0.756527\pi\) | ||||
−0.721457 | + | 0.692460i | \(0.756527\pi\) | |||||||
\(492\) | −16.6549 | −0.750863 | ||||||||
\(493\) | 2.62885 | 0.118398 | ||||||||
\(494\) | −13.1643 | −0.592289 | ||||||||
\(495\) | −9.50822 | −0.427363 | ||||||||
\(496\) | −10.4860 | −0.470837 | ||||||||
\(497\) | 7.03799 | 0.315697 | ||||||||
\(498\) | 17.1575 | 0.768846 | ||||||||
\(499\) | 23.9248 | 1.07102 | 0.535512 | − | 0.844528i | \(-0.320119\pi\) | ||||
0.535512 | + | 0.844528i | \(0.320119\pi\) | |||||||
\(500\) | −11.4381 | −0.511527 | ||||||||
\(501\) | −17.4431 | −0.779302 | ||||||||
\(502\) | 10.5497 | 0.470857 | ||||||||
\(503\) | 17.3096 | 0.771795 | 0.385898 | − | 0.922542i | \(-0.373892\pi\) | ||||
0.385898 | + | 0.922542i | \(0.373892\pi\) | |||||||
\(504\) | −8.18543 | −0.364608 | ||||||||
\(505\) | −18.2681 | −0.812918 | ||||||||
\(506\) | −2.48604 | −0.110518 | ||||||||
\(507\) | −15.5343 | −0.689903 | ||||||||
\(508\) | 21.0357 | 0.933310 | ||||||||
\(509\) | 5.48175 | 0.242974 | 0.121487 | − | 0.992593i | \(-0.461234\pi\) | ||||
0.121487 | + | 0.992593i | \(0.461234\pi\) | |||||||
\(510\) | −12.4979 | −0.553414 | ||||||||
\(511\) | 16.9789 | 0.751100 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.97166 | −0.351957 | ||||||||
\(514\) | −20.3192 | −0.896242 | ||||||||
\(515\) | −37.9563 | −1.67255 | ||||||||
\(516\) | 18.2173 | 0.801970 | ||||||||
\(517\) | −31.6120 | −1.39030 | ||||||||
\(518\) | 33.9610 | 1.49216 | ||||||||
\(519\) | 36.3378 | 1.59505 | ||||||||
\(520\) | 9.78132 | 0.428939 | ||||||||
\(521\) | 12.2126 | 0.535042 | 0.267521 | − | 0.963552i | \(-0.413796\pi\) | ||||
0.267521 | + | 0.963552i | \(0.413796\pi\) | |||||||
\(522\) | 1.75411 | 0.0767753 | ||||||||
\(523\) | −39.8276 | −1.74154 | −0.870769 | − | 0.491693i | \(-0.836378\pi\) | ||||
−0.870769 | + | 0.491693i | \(0.836378\pi\) | |||||||
\(524\) | −2.57372 | −0.112433 | ||||||||
\(525\) | 2.50186 | 0.109190 | ||||||||
\(526\) | 10.6958 | 0.466359 | ||||||||
\(527\) | 27.5663 | 1.20081 | ||||||||
\(528\) | 5.42054 | 0.235899 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 29.7248 | 1.29116 | ||||||||
\(531\) | 8.72157 | 0.378484 | ||||||||
\(532\) | −13.6936 | −0.593695 | ||||||||
\(533\) | −34.2667 | −1.48425 | ||||||||
\(534\) | −27.2502 | −1.17923 | ||||||||
\(535\) | 25.8791 | 1.11885 | ||||||||
\(536\) | −0.628853 | −0.0271623 | ||||||||
\(537\) | −6.72227 | −0.290088 | ||||||||
\(538\) | 18.8472 | 0.812558 | ||||||||
\(539\) | −36.7327 | −1.58219 | ||||||||
\(540\) | 5.92310 | 0.254890 | ||||||||
\(541\) | 9.78777 | 0.420809 | 0.210405 | − | 0.977614i | \(-0.432522\pi\) | ||||
0.210405 | + | 0.977614i | \(0.432522\pi\) | |||||||
\(542\) | 23.3064 | 1.00110 | ||||||||
\(543\) | −16.3966 | −0.703646 | ||||||||
\(544\) | 2.62885 | 0.112711 | ||||||||
\(545\) | −26.0938 | −1.11773 | ||||||||
\(546\) | −45.6439 | −1.95338 | ||||||||
\(547\) | 9.19108 | 0.392982 | 0.196491 | − | 0.980506i | \(-0.437045\pi\) | ||||
0.196491 | + | 0.980506i | \(0.437045\pi\) | |||||||
\(548\) | 4.74837 | 0.202840 | ||||||||
\(549\) | −2.33922 | −0.0998357 | ||||||||
\(550\) | −0.611295 | −0.0260657 | ||||||||
\(551\) | 2.93450 | 0.125014 | ||||||||
\(552\) | −2.18039 | −0.0928036 | ||||||||
\(553\) | −45.2112 | −1.92258 | ||||||||
\(554\) | −30.9889 | −1.31659 | ||||||||
\(555\) | 34.5991 | 1.46865 | ||||||||
\(556\) | 15.8683 | 0.672966 | ||||||||
\(557\) | −3.81994 | −0.161856 | −0.0809280 | − | 0.996720i | \(-0.525788\pi\) | ||||
−0.0809280 | + | 0.996720i | \(0.525788\pi\) | |||||||
\(558\) | 18.3937 | 0.778666 | ||||||||
\(559\) | 37.4810 | 1.58528 | ||||||||
\(560\) | 10.1746 | 0.429957 | ||||||||
\(561\) | −14.2498 | −0.601627 | ||||||||
\(562\) | 9.81890 | 0.414185 | ||||||||
\(563\) | 38.6586 | 1.62926 | 0.814632 | − | 0.579978i | \(-0.196939\pi\) | ||||
0.814632 | + | 0.579978i | \(0.196939\pi\) | |||||||
\(564\) | −27.7255 | −1.16745 | ||||||||
\(565\) | 19.5626 | 0.823007 | ||||||||
\(566\) | 24.6160 | 1.03469 | ||||||||
\(567\) | −52.1960 | −2.19203 | ||||||||
\(568\) | −1.50822 | −0.0632834 | ||||||||
\(569\) | 6.26490 | 0.262638 | 0.131319 | − | 0.991340i | \(-0.458079\pi\) | ||||
0.131319 | + | 0.991340i | \(0.458079\pi\) | |||||||
\(570\) | −13.9509 | −0.584340 | ||||||||
\(571\) | −11.2341 | −0.470131 | −0.235066 | − | 0.971979i | \(-0.575531\pi\) | ||||
−0.235066 | + | 0.971979i | \(0.575531\pi\) | |||||||
\(572\) | 11.1525 | 0.466308 | ||||||||
\(573\) | 6.48030 | 0.270718 | ||||||||
\(574\) | −35.6446 | −1.48778 | ||||||||
\(575\) | 0.245891 | 0.0102544 | ||||||||
\(576\) | 1.75411 | 0.0730879 | ||||||||
\(577\) | −6.11881 | −0.254729 | −0.127365 | − | 0.991856i | \(-0.540652\pi\) | ||||
−0.127365 | + | 0.991856i | \(0.540652\pi\) | |||||||
\(578\) | 10.0891 | 0.419652 | ||||||||
\(579\) | −49.5169 | −2.05785 | ||||||||
\(580\) | −2.18039 | −0.0905358 | ||||||||
\(581\) | 36.7202 | 1.52341 | ||||||||
\(582\) | −19.0164 | −0.788257 | ||||||||
\(583\) | 33.8916 | 1.40365 | ||||||||
\(584\) | −3.63851 | −0.150563 | ||||||||
\(585\) | −17.1575 | −0.709376 | ||||||||
\(586\) | −2.95206 | −0.121948 | ||||||||
\(587\) | 22.4166 | 0.925233 | 0.462617 | − | 0.886558i | \(-0.346911\pi\) | ||||
0.462617 | + | 0.886558i | \(0.346911\pi\) | |||||||
\(588\) | −32.2166 | −1.32859 | ||||||||
\(589\) | 30.7713 | 1.26791 | ||||||||
\(590\) | −10.8411 | −0.446320 | ||||||||
\(591\) | 14.6557 | 0.602853 | ||||||||
\(592\) | −7.27773 | −0.299113 | ||||||||
\(593\) | −13.0408 | −0.535521 | −0.267760 | − | 0.963486i | \(-0.586284\pi\) | ||||
−0.267760 | + | 0.963486i | \(0.586284\pi\) | |||||||
\(594\) | 6.75340 | 0.277095 | ||||||||
\(595\) | −26.7477 | −1.09655 | ||||||||
\(596\) | −0.311390 | −0.0127550 | ||||||||
\(597\) | −28.2842 | −1.15760 | ||||||||
\(598\) | −4.48604 | −0.183448 | ||||||||
\(599\) | 38.3329 | 1.56624 | 0.783120 | − | 0.621871i | \(-0.213627\pi\) | ||||
0.783120 | + | 0.621871i | \(0.213627\pi\) | |||||||
\(600\) | −0.536139 | −0.0218878 | ||||||||
\(601\) | 38.2261 | 1.55928 | 0.779638 | − | 0.626230i | \(-0.215403\pi\) | ||||
0.779638 | + | 0.626230i | \(0.215403\pi\) | |||||||
\(602\) | 38.9882 | 1.58904 | ||||||||
\(603\) | 1.10308 | 0.0449208 | ||||||||
\(604\) | −11.7380 | −0.477613 | ||||||||
\(605\) | −10.5086 | −0.427237 | ||||||||
\(606\) | −18.2681 | −0.742090 | ||||||||
\(607\) | −36.8729 | −1.49663 | −0.748313 | − | 0.663346i | \(-0.769136\pi\) | ||||
−0.748313 | + | 0.663346i | \(0.769136\pi\) | |||||||
\(608\) | 2.93450 | 0.119010 | ||||||||
\(609\) | 10.1746 | 0.412298 | ||||||||
\(610\) | 2.90770 | 0.117729 | ||||||||
\(611\) | −57.0437 | −2.30774 | ||||||||
\(612\) | −4.61129 | −0.186401 | ||||||||
\(613\) | 39.3798 | 1.59053 | 0.795267 | − | 0.606259i | \(-0.207330\pi\) | ||||
0.795267 | + | 0.606259i | \(0.207330\pi\) | |||||||
\(614\) | −24.0129 | −0.969080 | ||||||||
\(615\) | −36.3143 | −1.46433 | ||||||||
\(616\) | 11.6009 | 0.467415 | ||||||||
\(617\) | −19.8132 | −0.797648 | −0.398824 | − | 0.917028i | \(-0.630582\pi\) | ||||
−0.398824 | + | 0.917028i | \(0.630582\pi\) | |||||||
\(618\) | −37.9563 | −1.52683 | ||||||||
\(619\) | 0.820731 | 0.0329880 | 0.0164940 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164940 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(620\) | −22.8637 | −0.918227 | ||||||||
\(621\) | −2.71653 | −0.109011 | ||||||||
\(622\) | −9.59486 | −0.384719 | ||||||||
\(623\) | −58.3204 | −2.33656 | ||||||||
\(624\) | 9.78132 | 0.391566 | ||||||||
\(625\) | −23.7101 | −0.948403 | ||||||||
\(626\) | 33.0093 | 1.31932 | ||||||||
\(627\) | −15.9066 | −0.635248 | ||||||||
\(628\) | −14.9521 | −0.596652 | ||||||||
\(629\) | 19.1321 | 0.762846 | ||||||||
\(630\) | −17.8474 | −0.711059 | ||||||||
\(631\) | 2.92772 | 0.116551 | 0.0582754 | − | 0.998301i | \(-0.481440\pi\) | ||||
0.0582754 | + | 0.998301i | \(0.481440\pi\) | |||||||
\(632\) | 9.68861 | 0.385392 | ||||||||
\(633\) | 24.1529 | 0.959991 | ||||||||
\(634\) | 2.47422 | 0.0982640 | ||||||||
\(635\) | 45.8662 | 1.82014 | ||||||||
\(636\) | 29.7248 | 1.17866 | ||||||||
\(637\) | −66.2838 | −2.62626 | ||||||||
\(638\) | −2.48604 | −0.0984232 | ||||||||
\(639\) | 2.64558 | 0.104657 | ||||||||
\(640\) | −2.18039 | −0.0861876 | ||||||||
\(641\) | 0.0765681 | 0.00302426 | 0.00151213 | − | 0.999999i | \(-0.499519\pi\) | ||||
0.00151213 | + | 0.999999i | \(0.499519\pi\) | |||||||
\(642\) | 25.8791 | 1.02137 | ||||||||
\(643\) | 0.144239 | 0.00568824 | 0.00284412 | − | 0.999996i | \(-0.499095\pi\) | ||||
0.00284412 | + | 0.999996i | \(0.499095\pi\) | |||||||
\(644\) | −4.66643 | −0.183883 | ||||||||
\(645\) | 39.7208 | 1.56400 | ||||||||
\(646\) | −7.71437 | −0.303518 | ||||||||
\(647\) | 12.3110 | 0.483996 | 0.241998 | − | 0.970277i | \(-0.422197\pi\) | ||||
0.241998 | + | 0.970277i | \(0.422197\pi\) | |||||||
\(648\) | 11.1854 | 0.439405 | ||||||||
\(649\) | −12.3608 | −0.485203 | ||||||||
\(650\) | −1.10308 | −0.0432662 | ||||||||
\(651\) | 106.692 | 4.18158 | ||||||||
\(652\) | 20.8461 | 0.816397 | ||||||||
\(653\) | 23.7573 | 0.929696 | 0.464848 | − | 0.885391i | \(-0.346109\pi\) | ||||
0.464848 | + | 0.885391i | \(0.346109\pi\) | |||||||
\(654\) | −26.0938 | −1.02035 | ||||||||
\(655\) | −5.61171 | −0.219268 | ||||||||
\(656\) | 7.63851 | 0.298234 | ||||||||
\(657\) | 6.38234 | 0.248999 | ||||||||
\(658\) | −59.3375 | −2.31322 | ||||||||
\(659\) | 19.7140 | 0.767948 | 0.383974 | − | 0.923344i | \(-0.374555\pi\) | ||||
0.383974 | + | 0.923344i | \(0.374555\pi\) | |||||||
\(660\) | 11.8189 | 0.460050 | ||||||||
\(661\) | 35.9105 | 1.39676 | 0.698379 | − | 0.715728i | \(-0.253905\pi\) | ||||
0.698379 | + | 0.715728i | \(0.253905\pi\) | |||||||
\(662\) | 7.24589 | 0.281620 | ||||||||
\(663\) | −25.7137 | −0.998636 | ||||||||
\(664\) | −7.86900 | −0.305376 | ||||||||
\(665\) | −29.8575 | −1.15782 | ||||||||
\(666\) | 12.7659 | 0.494670 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | −36.4596 | −1.40961 | ||||||||
\(670\) | −1.37115 | −0.0529720 | ||||||||
\(671\) | 3.31530 | 0.127986 | ||||||||
\(672\) | 10.1746 | 0.392496 | ||||||||
\(673\) | 30.7777 | 1.18639 | 0.593197 | − | 0.805057i | \(-0.297865\pi\) | ||||
0.593197 | + | 0.805057i | \(0.297865\pi\) | |||||||
\(674\) | 9.58337 | 0.369138 | ||||||||
\(675\) | −0.667971 | −0.0257102 | ||||||||
\(676\) | 7.12455 | 0.274021 | ||||||||
\(677\) | 32.1732 | 1.23652 | 0.618259 | − | 0.785974i | \(-0.287838\pi\) | ||||
0.618259 | + | 0.785974i | \(0.287838\pi\) | |||||||
\(678\) | 19.5626 | 0.751299 | ||||||||
\(679\) | −40.6986 | −1.56187 | ||||||||
\(680\) | 5.73193 | 0.219810 | ||||||||
\(681\) | 46.0683 | 1.76534 | ||||||||
\(682\) | −26.0687 | −0.998222 | ||||||||
\(683\) | −2.50327 | −0.0957849 | −0.0478924 | − | 0.998852i | \(-0.515250\pi\) | ||||
−0.0478924 | + | 0.998852i | \(0.515250\pi\) | |||||||
\(684\) | −5.14743 | −0.196817 | ||||||||
\(685\) | 10.3533 | 0.395579 | ||||||||
\(686\) | −36.2842 | −1.38534 | ||||||||
\(687\) | −15.9449 | −0.608334 | ||||||||
\(688\) | −8.35504 | −0.318533 | ||||||||
\(689\) | 61.1571 | 2.32990 | ||||||||
\(690\) | −4.75411 | −0.180986 | ||||||||
\(691\) | −5.35288 | −0.203633 | −0.101817 | − | 0.994803i | \(-0.532465\pi\) | ||||
−0.101817 | + | 0.994803i | \(0.532465\pi\) | |||||||
\(692\) | −16.6657 | −0.633536 | ||||||||
\(693\) | −20.3493 | −0.773006 | ||||||||
\(694\) | −3.20186 | −0.121541 | ||||||||
\(695\) | 34.5991 | 1.31242 | ||||||||
\(696\) | −2.18039 | −0.0826475 | ||||||||
\(697\) | −20.0805 | −0.760604 | ||||||||
\(698\) | 10.1865 | 0.385563 | ||||||||
\(699\) | −9.55902 | −0.361555 | ||||||||
\(700\) | −1.14743 | −0.0433689 | ||||||||
\(701\) | 4.08265 | 0.154200 | 0.0770999 | − | 0.997023i | \(-0.475434\pi\) | ||||
0.0770999 | + | 0.997023i | \(0.475434\pi\) | |||||||
\(702\) | 12.1865 | 0.459948 | ||||||||
\(703\) | 21.3565 | 0.805475 | ||||||||
\(704\) | −2.48604 | −0.0936961 | ||||||||
\(705\) | −60.4524 | −2.27677 | ||||||||
\(706\) | −17.9817 | −0.676752 | ||||||||
\(707\) | −39.0970 | −1.47039 | ||||||||
\(708\) | −10.8411 | −0.407433 | ||||||||
\(709\) | −6.03359 | −0.226596 | −0.113298 | − | 0.993561i | \(-0.536142\pi\) | ||||
−0.113298 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(710\) | −3.28851 | −0.123415 | ||||||||
\(711\) | −16.9949 | −0.637358 | ||||||||
\(712\) | 12.4979 | 0.468377 | ||||||||
\(713\) | 10.4860 | 0.392705 | ||||||||
\(714\) | −26.7477 | −1.00101 | ||||||||
\(715\) | 24.3168 | 0.909395 | ||||||||
\(716\) | 3.08306 | 0.115219 | ||||||||
\(717\) | −5.56806 | −0.207943 | ||||||||
\(718\) | −4.19724 | −0.156640 | ||||||||
\(719\) | −38.9865 | −1.45395 | −0.726975 | − | 0.686664i | \(-0.759074\pi\) | ||||
−0.726975 | + | 0.686664i | \(0.759074\pi\) | |||||||
\(720\) | 3.82464 | 0.142536 | ||||||||
\(721\) | −81.2333 | −3.02529 | ||||||||
\(722\) | 10.3887 | 0.386628 | ||||||||
\(723\) | 66.4013 | 2.46949 | ||||||||
\(724\) | 7.52003 | 0.279480 | ||||||||
\(725\) | 0.245891 | 0.00913217 | ||||||||
\(726\) | −10.5086 | −0.390012 | ||||||||
\(727\) | −34.3776 | −1.27500 | −0.637498 | − | 0.770452i | \(-0.720031\pi\) | ||||
−0.637498 | + | 0.770452i | \(0.720031\pi\) | |||||||
\(728\) | 20.9338 | 0.775858 | ||||||||
\(729\) | −1.85115 | −0.0685613 | ||||||||
\(730\) | −7.93338 | −0.293627 | ||||||||
\(731\) | 21.9642 | 0.812374 | ||||||||
\(732\) | 2.90770 | 0.107472 | ||||||||
\(733\) | 24.1096 | 0.890507 | 0.445254 | − | 0.895405i | \(-0.353114\pi\) | ||||
0.445254 | + | 0.895405i | \(0.353114\pi\) | |||||||
\(734\) | −3.95094 | −0.145832 | ||||||||
\(735\) | −70.2447 | −2.59102 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −1.56335 | −0.0575869 | ||||||||
\(738\) | −13.3988 | −0.493216 | ||||||||
\(739\) | −18.5344 | −0.681799 | −0.340899 | − | 0.940100i | \(-0.610732\pi\) | ||||
−0.340899 | + | 0.940100i | \(0.610732\pi\) | |||||||
\(740\) | −15.8683 | −0.583330 | ||||||||
\(741\) | −28.7033 | −1.05444 | ||||||||
\(742\) | 63.6164 | 2.33543 | ||||||||
\(743\) | −11.0776 | −0.406399 | −0.203200 | − | 0.979137i | \(-0.565134\pi\) | ||||
−0.203200 | + | 0.979137i | \(0.565134\pi\) | |||||||
\(744\) | −22.8637 | −0.838223 | ||||||||
\(745\) | −0.678953 | −0.0248749 | ||||||||
\(746\) | 6.18039 | 0.226280 | ||||||||
\(747\) | 13.8031 | 0.505028 | ||||||||
\(748\) | 6.53543 | 0.238959 | ||||||||
\(749\) | 55.3859 | 2.02376 | ||||||||
\(750\) | −24.9395 | −0.910663 | ||||||||
\(751\) | 27.9556 | 1.02012 | 0.510058 | − | 0.860140i | \(-0.329624\pi\) | ||||
0.510058 | + | 0.860140i | \(0.329624\pi\) | |||||||
\(752\) | 12.7158 | 0.463698 | ||||||||
\(753\) | 23.0025 | 0.838258 | ||||||||
\(754\) | −4.48604 | −0.163372 | ||||||||
\(755\) | −25.5934 | −0.931441 | ||||||||
\(756\) | 12.6765 | 0.461040 | ||||||||
\(757\) | 45.9356 | 1.66956 | 0.834778 | − | 0.550586i | \(-0.185596\pi\) | ||||
0.834778 | + | 0.550586i | \(0.185596\pi\) | |||||||
\(758\) | 4.37227 | 0.158808 | ||||||||
\(759\) | −5.42054 | −0.196753 | ||||||||
\(760\) | 6.39836 | 0.232093 | ||||||||
\(761\) | 15.5766 | 0.564651 | 0.282326 | − | 0.959319i | \(-0.408894\pi\) | ||||
0.282326 | + | 0.959319i | \(0.408894\pi\) | |||||||
\(762\) | 45.8662 | 1.66156 | ||||||||
\(763\) | −55.8453 | −2.02174 | ||||||||
\(764\) | −2.97208 | −0.107526 | ||||||||
\(765\) | −10.0544 | −0.363519 | ||||||||
\(766\) | −0.317133 | −0.0114585 | ||||||||
\(767\) | −22.3049 | −0.805385 | ||||||||
\(768\) | −2.18039 | −0.0786781 | ||||||||
\(769\) | −20.0115 | −0.721633 | −0.360816 | − | 0.932637i | \(-0.617502\pi\) | ||||
−0.360816 | + | 0.932637i | \(0.617502\pi\) | |||||||
\(770\) | 25.2946 | 0.911553 | ||||||||
\(771\) | −44.3039 | −1.59556 | ||||||||
\(772\) | 22.7101 | 0.817354 | ||||||||
\(773\) | −20.1280 | −0.723956 | −0.361978 | − | 0.932187i | \(-0.617898\pi\) | ||||
−0.361978 | + | 0.932187i | \(0.617898\pi\) | |||||||
\(774\) | 14.6557 | 0.526787 | ||||||||
\(775\) | 2.57842 | 0.0926197 | ||||||||
\(776\) | 8.72157 | 0.313086 | ||||||||
\(777\) | 74.0483 | 2.65647 | ||||||||
\(778\) | 30.1625 | 1.08138 | ||||||||
\(779\) | −22.4152 | −0.803108 | ||||||||
\(780\) | 21.3271 | 0.763633 | ||||||||
\(781\) | −3.74949 | −0.134167 | ||||||||
\(782\) | −2.62885 | −0.0940076 | ||||||||
\(783\) | −2.71653 | −0.0970809 | ||||||||
\(784\) | 14.7756 | 0.527699 | ||||||||
\(785\) | −32.6013 | −1.16359 | ||||||||
\(786\) | −5.61171 | −0.200163 | ||||||||
\(787\) | −34.3211 | −1.22341 | −0.611707 | − | 0.791084i | \(-0.709517\pi\) | ||||
−0.611707 | + | 0.791084i | \(0.709517\pi\) | |||||||
\(788\) | −6.72157 | −0.239446 | ||||||||
\(789\) | 23.3210 | 0.830251 | ||||||||
\(790\) | 21.1250 | 0.751593 | ||||||||
\(791\) | 41.8676 | 1.48864 | ||||||||
\(792\) | 4.36078 | 0.154954 | ||||||||
\(793\) | 5.98244 | 0.212443 | ||||||||
\(794\) | 16.2187 | 0.575579 | ||||||||
\(795\) | 64.8117 | 2.29863 | ||||||||
\(796\) | 12.9721 | 0.459783 | ||||||||
\(797\) | −44.2935 | −1.56895 | −0.784477 | − | 0.620157i | \(-0.787069\pi\) | ||||
−0.784477 | + | 0.620157i | \(0.787069\pi\) | |||||||
\(798\) | −29.8575 | −1.05694 | ||||||||
\(799\) | −33.4280 | −1.18260 | ||||||||
\(800\) | 0.245891 | 0.00869356 | ||||||||
\(801\) | −21.9226 | −0.774597 | ||||||||
\(802\) | −28.4678 | −1.00523 | ||||||||
\(803\) | −9.04548 | −0.319208 | ||||||||
\(804\) | −1.37115 | −0.0483566 | ||||||||
\(805\) | −10.1746 | −0.358609 | ||||||||
\(806\) | −47.0408 | −1.65694 | ||||||||
\(807\) | 41.0942 | 1.44658 | ||||||||
\(808\) | 8.37834 | 0.294749 | ||||||||
\(809\) | −53.9069 | −1.89527 | −0.947633 | − | 0.319361i | \(-0.896532\pi\) | ||||
−0.947633 | + | 0.319361i | \(0.896532\pi\) | |||||||
\(810\) | 24.3886 | 0.856929 | ||||||||
\(811\) | −26.4667 | −0.929373 | −0.464686 | − | 0.885475i | \(-0.653833\pi\) | ||||
−0.464686 | + | 0.885475i | \(0.653833\pi\) | |||||||
\(812\) | −4.66643 | −0.163760 | ||||||||
\(813\) | 50.8171 | 1.78223 | ||||||||
\(814\) | −18.0927 | −0.634149 | ||||||||
\(815\) | 45.4527 | 1.59214 | ||||||||
\(816\) | 5.73193 | 0.200658 | ||||||||
\(817\) | 24.5179 | 0.857772 | ||||||||
\(818\) | 6.48100 | 0.226603 | ||||||||
\(819\) | −36.7202 | −1.28311 | ||||||||
\(820\) | 16.6549 | 0.581616 | ||||||||
\(821\) | 50.6812 | 1.76878 | 0.884392 | − | 0.466745i | \(-0.154573\pi\) | ||||
0.884392 | + | 0.466745i | \(0.154573\pi\) | |||||||
\(822\) | 10.3533 | 0.361113 | ||||||||
\(823\) | −1.60023 | −0.0557804 | −0.0278902 | − | 0.999611i | \(-0.508879\pi\) | ||||
−0.0278902 | + | 0.999611i | \(0.508879\pi\) | |||||||
\(824\) | 17.4080 | 0.606437 | ||||||||
\(825\) | −1.33286 | −0.0464043 | ||||||||
\(826\) | −23.2019 | −0.807296 | ||||||||
\(827\) | −32.8078 | −1.14084 | −0.570420 | − | 0.821353i | \(-0.693220\pi\) | ||||
−0.570420 | + | 0.821353i | \(0.693220\pi\) | |||||||
\(828\) | −1.75411 | −0.0609595 | ||||||||
\(829\) | −2.07516 | −0.0720731 | −0.0360366 | − | 0.999350i | \(-0.511473\pi\) | ||||
−0.0360366 | + | 0.999350i | \(0.511473\pi\) | |||||||
\(830\) | −17.1575 | −0.595546 | ||||||||
\(831\) | −67.5680 | −2.34391 | ||||||||
\(832\) | −4.48604 | −0.155525 | ||||||||
\(833\) | −38.8428 | −1.34582 | ||||||||
\(834\) | 34.5991 | 1.19807 | ||||||||
\(835\) | 17.4431 | 0.603645 | ||||||||
\(836\) | 7.29528 | 0.252313 | ||||||||
\(837\) | −28.4856 | −0.984608 | ||||||||
\(838\) | 16.7913 | 0.580046 | ||||||||
\(839\) | −14.7724 | −0.509999 | −0.254999 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254999 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(840\) | 22.1847 | 0.765446 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −9.95996 | −0.343243 | ||||||||
\(843\) | 21.4091 | 0.737367 | ||||||||
\(844\) | −11.0773 | −0.381297 | ||||||||
\(845\) | 15.5343 | 0.534397 | ||||||||
\(846\) | −22.3049 | −0.766860 | ||||||||
\(847\) | −22.4904 | −0.772778 | ||||||||
\(848\) | −13.6328 | −0.468151 | ||||||||
\(849\) | 53.6724 | 1.84203 | ||||||||
\(850\) | −0.646412 | −0.0221717 | ||||||||
\(851\) | 7.27773 | 0.249477 | ||||||||
\(852\) | −3.28851 | −0.112662 | ||||||||
\(853\) | 24.9148 | 0.853067 | 0.426534 | − | 0.904472i | \(-0.359735\pi\) | ||||
0.426534 | + | 0.904472i | \(0.359735\pi\) | |||||||
\(854\) | 6.22301 | 0.212947 | ||||||||
\(855\) | −11.2234 | −0.383833 | ||||||||
\(856\) | −11.8690 | −0.405674 | ||||||||
\(857\) | 30.4671 | 1.04074 | 0.520368 | − | 0.853942i | \(-0.325795\pi\) | ||||
0.520368 | + | 0.853942i | \(0.325795\pi\) | |||||||
\(858\) | 24.3168 | 0.830160 | ||||||||
\(859\) | 16.9632 | 0.578776 | 0.289388 | − | 0.957212i | \(-0.406548\pi\) | ||||
0.289388 | + | 0.957212i | \(0.406548\pi\) | |||||||
\(860\) | −18.2173 | −0.621204 | ||||||||
\(861\) | −77.7192 | −2.64866 | ||||||||
\(862\) | −23.2770 | −0.792818 | ||||||||
\(863\) | 34.6640 | 1.17998 | 0.589988 | − | 0.807412i | \(-0.299133\pi\) | ||||
0.589988 | + | 0.807412i | \(0.299133\pi\) | |||||||
\(864\) | −2.71653 | −0.0924183 | ||||||||
\(865\) | −36.3378 | −1.23552 | ||||||||
\(866\) | −26.8665 | −0.912960 | ||||||||
\(867\) | 21.9983 | 0.747100 | ||||||||
\(868\) | −48.9324 | −1.66087 | ||||||||
\(869\) | 24.0863 | 0.817071 | ||||||||
\(870\) | −4.75411 | −0.161179 | ||||||||
\(871\) | −2.82106 | −0.0955880 | ||||||||
\(872\) | 11.9675 | 0.405269 | ||||||||
\(873\) | −15.2986 | −0.517778 | ||||||||
\(874\) | −2.93450 | −0.0992610 | ||||||||
\(875\) | −53.3751 | −1.80441 | ||||||||
\(876\) | −7.93338 | −0.268044 | ||||||||
\(877\) | −45.7889 | −1.54618 | −0.773091 | − | 0.634295i | \(-0.781291\pi\) | ||||
−0.773091 | + | 0.634295i | \(0.781291\pi\) | |||||||
\(878\) | −0.759852 | −0.0256438 | ||||||||
\(879\) | −6.43665 | −0.217103 | ||||||||
\(880\) | −5.42054 | −0.182726 | ||||||||
\(881\) | 14.3769 | 0.484371 | 0.242186 | − | 0.970230i | \(-0.422136\pi\) | ||||
0.242186 | + | 0.970230i | \(0.422136\pi\) | |||||||
\(882\) | −25.9180 | −0.872704 | ||||||||
\(883\) | −20.2025 | −0.679868 | −0.339934 | − | 0.940449i | \(-0.610405\pi\) | ||||
−0.339934 | + | 0.940449i | \(0.610405\pi\) | |||||||
\(884\) | 11.7931 | 0.396646 | ||||||||
\(885\) | −23.6378 | −0.794576 | ||||||||
\(886\) | −11.6324 | −0.390799 | ||||||||
\(887\) | −28.8614 | −0.969072 | −0.484536 | − | 0.874771i | \(-0.661012\pi\) | ||||
−0.484536 | + | 0.874771i | \(0.661012\pi\) | |||||||
\(888\) | −15.8683 | −0.532505 | ||||||||
\(889\) | 98.1619 | 3.29224 | ||||||||
\(890\) | 27.2502 | 0.913430 | ||||||||
\(891\) | 27.8074 | 0.931584 | ||||||||
\(892\) | 16.7216 | 0.559879 | ||||||||
\(893\) | −37.3146 | −1.24869 | ||||||||
\(894\) | −0.678953 | −0.0227076 | ||||||||
\(895\) | 6.72227 | 0.224701 | ||||||||
\(896\) | −4.66643 | −0.155895 | ||||||||
\(897\) | −9.78132 | −0.326589 | ||||||||
\(898\) | −10.3293 | −0.344692 | ||||||||
\(899\) | 10.4860 | 0.349729 | ||||||||
\(900\) | −0.431320 | −0.0143773 | ||||||||
\(901\) | 35.8385 | 1.19396 | ||||||||
\(902\) | 18.9896 | 0.632286 | ||||||||
\(903\) | 85.0096 | 2.82894 | ||||||||
\(904\) | −8.97208 | −0.298407 | ||||||||
\(905\) | 16.3966 | 0.545042 | ||||||||
\(906\) | −25.5934 | −0.850285 | ||||||||
\(907\) | 16.3844 | 0.544036 | 0.272018 | − | 0.962292i | \(-0.412309\pi\) | ||||
0.272018 | + | 0.962292i | \(0.412309\pi\) | |||||||
\(908\) | −21.1285 | −0.701173 | ||||||||
\(909\) | −14.6965 | −0.487453 | ||||||||
\(910\) | 45.6439 | 1.51308 | ||||||||
\(911\) | −55.0018 | −1.82229 | −0.911145 | − | 0.412085i | \(-0.864801\pi\) | ||||
−0.911145 | + | 0.412085i | \(0.864801\pi\) | |||||||
\(912\) | 6.39836 | 0.211871 | ||||||||
\(913\) | −19.5626 | −0.647429 | ||||||||
\(914\) | −33.6844 | −1.11418 | ||||||||
\(915\) | 6.33993 | 0.209592 | ||||||||
\(916\) | 7.31284 | 0.241623 | ||||||||
\(917\) | −12.0101 | −0.396608 | ||||||||
\(918\) | 7.14136 | 0.235700 | ||||||||
\(919\) | −30.3952 | −1.00264 | −0.501322 | − | 0.865261i | \(-0.667153\pi\) | ||||
−0.501322 | + | 0.865261i | \(0.667153\pi\) | |||||||
\(920\) | 2.18039 | 0.0718854 | ||||||||
\(921\) | −52.3575 | −1.72524 | ||||||||
\(922\) | −9.27526 | −0.305465 | ||||||||
\(923\) | −6.76592 | −0.222703 | ||||||||
\(924\) | 25.2946 | 0.832131 | ||||||||
\(925\) | 1.78953 | 0.0588393 | ||||||||
\(926\) | 20.6464 | 0.678483 | ||||||||
\(927\) | −30.5356 | −1.00292 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 47.6288 | 1.56265 | 0.781325 | − | 0.624125i | \(-0.214544\pi\) | ||||
0.781325 | + | 0.624125i | \(0.214544\pi\) | |||||||
\(930\) | −49.8518 | −1.63470 | ||||||||
\(931\) | −43.3590 | −1.42103 | ||||||||
\(932\) | 4.38408 | 0.143605 | ||||||||
\(933\) | −20.9206 | −0.684908 | ||||||||
\(934\) | −25.1700 | −0.823589 | ||||||||
\(935\) | 14.2498 | 0.466018 | ||||||||
\(936\) | 7.86900 | 0.257206 | ||||||||
\(937\) | −24.0945 | −0.787132 | −0.393566 | − | 0.919296i | \(-0.628759\pi\) | ||||
−0.393566 | + | 0.919296i | \(0.628759\pi\) | |||||||
\(938\) | −2.93450 | −0.0958148 | ||||||||
\(939\) | 71.9732 | 2.34876 | ||||||||
\(940\) | 27.7255 | 0.904306 | ||||||||
\(941\) | −24.4284 | −0.796344 | −0.398172 | − | 0.917311i | \(-0.630355\pi\) | ||||
−0.398172 | + | 0.917311i | \(0.630355\pi\) | |||||||
\(942\) | −32.6013 | −1.06221 | ||||||||
\(943\) | −7.63851 | −0.248744 | ||||||||
\(944\) | 4.97208 | 0.161827 | ||||||||
\(945\) | 27.6397 | 0.899121 | ||||||||
\(946\) | −20.7710 | −0.675322 | ||||||||
\(947\) | 7.12413 | 0.231503 | 0.115752 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115752 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(948\) | 21.1250 | 0.686107 | ||||||||
\(949\) | −16.3225 | −0.529851 | ||||||||
\(950\) | −0.721568 | −0.0234107 | ||||||||
\(951\) | 5.39478 | 0.174938 | ||||||||
\(952\) | 12.2674 | 0.397588 | ||||||||
\(953\) | −49.1013 | −1.59055 | −0.795273 | − | 0.606251i | \(-0.792673\pi\) | ||||
−0.795273 | + | 0.606251i | \(0.792673\pi\) | |||||||
\(954\) | 23.9134 | 0.774224 | ||||||||
\(955\) | −6.48030 | −0.209697 | ||||||||
\(956\) | 2.55370 | 0.0825925 | ||||||||
\(957\) | −5.42054 | −0.175221 | ||||||||
\(958\) | 28.1553 | 0.909658 | ||||||||
\(959\) | 22.1579 | 0.715517 | ||||||||
\(960\) | −4.75411 | −0.153438 | ||||||||
\(961\) | 78.9570 | 2.54700 | ||||||||
\(962\) | −32.6482 | −1.05262 | ||||||||
\(963\) | 20.8195 | 0.670900 | ||||||||
\(964\) | −30.4538 | −0.980852 | ||||||||
\(965\) | 49.5169 | 1.59400 | ||||||||
\(966\) | −10.1746 | −0.327364 | ||||||||
\(967\) | 8.94807 | 0.287751 | 0.143875 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143875 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(968\) | 4.81961 | 0.154908 | ||||||||
\(969\) | −16.8204 | −0.540348 | ||||||||
\(970\) | 19.0164 | 0.610581 | ||||||||
\(971\) | −16.9606 | −0.544291 | −0.272146 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272146 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(972\) | 16.2390 | 0.520867 | ||||||||
\(973\) | 74.0483 | 2.37388 | ||||||||
\(974\) | 11.3855 | 0.364816 | ||||||||
\(975\) | −2.40514 | −0.0770261 | ||||||||
\(976\) | −1.33357 | −0.0426865 | ||||||||
\(977\) | −3.42666 | −0.109629 | −0.0548143 | − | 0.998497i | \(-0.517457\pi\) | ||||
−0.0548143 | + | 0.998497i | \(0.517457\pi\) | |||||||
\(978\) | 45.4527 | 1.45342 | ||||||||
\(979\) | 31.0702 | 0.993007 | ||||||||
\(980\) | 32.2166 | 1.02912 | ||||||||
\(981\) | −20.9922 | −0.670230 | ||||||||
\(982\) | 31.9728 | 1.02029 | ||||||||
\(983\) | −14.9517 | −0.476885 | −0.238442 | − | 0.971157i | \(-0.576637\pi\) | ||||
−0.238442 | + | 0.971157i | \(0.576637\pi\) | |||||||
\(984\) | 16.6549 | 0.530940 | ||||||||
\(985\) | −14.6557 | −0.466968 | ||||||||
\(986\) | −2.62885 | −0.0837197 | ||||||||
\(987\) | −129.379 | −4.11818 | ||||||||
\(988\) | 13.1643 | 0.418812 | ||||||||
\(989\) | 8.35504 | 0.265675 | ||||||||
\(990\) | 9.50822 | 0.302191 | ||||||||
\(991\) | −4.21223 | −0.133806 | −0.0669029 | − | 0.997759i | \(-0.521312\pi\) | ||||
−0.0669029 | + | 0.997759i | \(0.521312\pi\) | |||||||
\(992\) | 10.4860 | 0.332932 | ||||||||
\(993\) | 15.7989 | 0.501362 | ||||||||
\(994\) | −7.03799 | −0.223232 | ||||||||
\(995\) | 28.2842 | 0.896670 | ||||||||
\(996\) | −17.1575 | −0.543656 | ||||||||
\(997\) | −6.43418 | −0.203773 | −0.101886 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101886 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(998\) | −23.9248 | −0.757328 | ||||||||
\(999\) | −19.7702 | −0.625500 |
(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 | 1334.2.a.d.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |