Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(67,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.x (of order \(12\), degree \(4\), not minimal) |
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: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 263.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.263 |
Dual form | 980.2.x.c.667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −0.133975 | − | 2.23205i | −0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.866025 | − | 0.500000i | ||||
\(10\) | 0.633975 | − | 3.09808i | 0.200480 | − | 0.979698i | ||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −1.09808 | − | 4.09808i | −0.266323 | − | 0.993929i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.695113 | − | 0.718900i | \(-0.255354\pi\) | |||||||
\(18\) | 4.09808 | − | 1.09808i | 0.965926 | − | 0.258819i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 2.00000 | − | 4.00000i | 0.447214 | − | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | 1.00000 | + | 1.73205i | 0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 9.56218 | + | 2.56218i | 1.57201 | + | 0.421219i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.19615 | − | 4.73205i | 0.663470 | − | 0.748203i | ||||
\(41\) | 8.00000 | 1.24939 | 0.624695 | − | 0.780869i | \(-0.285223\pi\) | ||||
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.69615 | − | 5.59808i | −0.550990 | − | 0.834512i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.00000 | − | 1.00000i | −0.989949 | − | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.732051 | + | 2.73205i | 0.101517 | + | 0.378867i | ||||
\(53\) | −12.2942 | + | 3.29423i | −1.68874 | + | 0.452497i | −0.970065 | − | 0.242846i | \(-0.921919\pi\) |
−0.718677 | + | 0.695344i | \(0.755252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.46410 | − | 5.46410i | 0.192246 | − | 0.717472i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 2.09808 | − | 2.36603i | 0.260234 | − | 0.293469i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(68\) | 2.19615 | − | 8.19615i | 0.266323 | − | 0.993929i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 8.19615 | + | 2.19615i | 0.965926 | + | 0.258819i | ||||
\(73\) | −15.0263 | + | 4.02628i | −1.75869 | + | 0.471240i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
−0.772246 | + | 0.635323i | \(0.780867\pi\) | |||||||
\(74\) | 12.1244 | + | 7.00000i | 1.40943 | + | 0.813733i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 7.46410 | − | 4.92820i | 0.834512 | − | 0.550990i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 10.9282 | + | 2.92820i | 1.20682 | + | 0.323366i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | + | 3.00000i | −0.976187 | + | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8564 | + | 8.00000i | −1.46878 | + | 0.847998i | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | −3.00000 | − | 9.00000i | −0.316228 | − | 0.948683i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0000 | + | 13.0000i | −1.31995 | + | 1.31995i | −0.406138 | + | 0.913812i | \(0.633125\pi\) |
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.19615 | − | 3.92820i | −0.919615 | − | 0.392820i | ||||
\(101\) | 1.00000 | − | 1.73205i | 0.0995037 | − | 0.172345i | −0.811976 | − | 0.583691i | \(-0.801608\pi\) |
0.911479 | + | 0.411346i | \(0.134941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(104\) | 4.00000i | 0.392232i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.0000 | −1.74831 | ||||||||
\(107\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.19615 | − | 3.00000i | −0.497701 | − | 0.287348i | 0.230063 | − | 0.973176i | \(-0.426107\pi\) |
−0.727764 | + | 0.685828i | \(0.759440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.00000 | − | 1.00000i | −0.0940721 | − | 0.0940721i | 0.658505 | − | 0.752577i | \(-0.271189\pi\) |
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.00000 | − | 6.92820i | 0.371391 | − | 0.643268i | ||||
\(117\) | 4.09808 | + | 1.09808i | 0.378867 | + | 0.101517i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | − | 9.52628i | −0.500000 | − | 0.866025i | ||||
\(122\) | 4.39230 | + | 16.3923i | 0.397661 | + | 1.48409i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.73205 | − | 2.46410i | 0.327323 | − | 0.216116i | ||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | − | 10.3923i | 0.514496 | − | 0.891133i | ||||
\(137\) | −2.56218 | − | 9.56218i | −0.218902 | − | 0.816952i | −0.984757 | − | 0.173939i | \(-0.944351\pi\) |
0.765855 | − | 0.643013i | \(-0.222316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.3923 | + | 6.00000i | 0.866025 | + | 0.500000i | ||||
\(145\) | −8.92820 | + | 0.535898i | −0.741447 | + | 0.0445039i | ||||
\(146\) | −22.0000 | −1.82073 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0000 | + | 14.0000i | 1.15079 | + | 1.15079i | ||||
\(149\) | −12.1244 | + | 7.00000i | −0.993266 | + | 0.573462i | −0.906249 | − | 0.422744i | \(-0.861067\pi\) |
−0.0870170 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.00000 | − | 9.00000i | −0.727607 | − | 0.727607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.22243 | + | 23.2224i | 0.496604 | + | 1.85335i | 0.520854 | + | 0.853646i | \(0.325614\pi\) |
−0.0242497 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.0000 | − | 4.00000i | 0.948683 | − | 0.316228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(164\) | 13.8564 | + | 8.00000i | 1.08200 | + | 0.624695i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | −13.3923 | + | 0.803848i | −1.02714 | + | 0.0616523i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.02628 | − | 15.0263i | 0.306112 | − | 1.14243i | −0.625871 | − | 0.779926i | \(-0.715256\pi\) |
0.931984 | − | 0.362500i | \(-0.118077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.8564 | + | 5.85641i | −1.63821 | + | 0.438956i | ||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | −0.803848 | − | 13.3923i | −0.0599153 | − | 0.998203i | ||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.43782 | − | 21.6865i | 0.326275 | − | 1.59443i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.9545 | + | 6.95448i | −1.86824 | + | 0.500595i | −0.868255 | + | 0.496119i | \(0.834758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | −22.5167 | + | 13.0000i | −1.61660 | + | 0.933346i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0000 | − | 13.0000i | 0.926212 | − | 0.926212i | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) |
0.997459 | + | 0.0712470i | \(0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | −11.1244 | − | 8.73205i | −0.786611 | − | 0.617449i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.00000 | − | 2.00000i | 0.140720 | − | 0.140720i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07180 | − | 17.8564i | −0.0748575 | − | 1.24715i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.46410 | + | 5.46410i | −0.101517 | + | 0.378867i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | −24.5885 | − | 6.58846i | −1.68874 | − | 0.452497i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | − | 6.00000i | −0.406371 | − | 0.406371i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | + | 9.00000i | −0.800000 | + | 0.600000i | ||||
\(226\) | −1.00000 | − | 1.73205i | −0.0665190 | − | 0.115214i | ||||
\(227\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46410 | − | 2.00000i | 0.228914 | − | 0.132164i | −0.381157 | − | 0.924510i | \(-0.624474\pi\) |
0.610071 | + | 0.792347i | \(0.291141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | − | 8.00000i | 0.525226 | − | 0.525226i | ||||
\(233\) | −7.68653 | + | 28.6865i | −0.503562 | + | 1.87932i | −0.0280525 | + | 0.999606i | \(0.508931\pi\) |
−0.475509 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(234\) | 5.19615 | + | 3.00000i | 0.339683 | + | 0.196116i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | + | 6.92820i | −0.257663 | + | 0.446285i | −0.965615 | − | 0.259975i | \(-0.916286\pi\) |
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(242\) | −4.02628 | − | 15.0263i | −0.258819 | − | 0.965926i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.0000i | 1.53644i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.29423 | + | 15.7583i | −0.0818542 | + | 0.996644i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −23.2224 | − | 6.22243i | −1.44858 | − | 0.388145i | −0.553047 | − | 0.833150i | \(-0.686535\pi\) |
−0.895528 | + | 0.445005i | \(0.853202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | − | 2.00000i | 0.372104 | − | 0.124035i | ||||
\(261\) | −6.00000 | − | 10.3923i | −0.371391 | − | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | + | 27.0000i | 0.552866 | + | 1.65860i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.5167 | + | 13.0000i | 1.37287 | + | 0.792624i | 0.991288 | − | 0.131713i | \(-0.0420477\pi\) |
0.381577 | + | 0.924337i | \(0.375381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | 12.0000 | − | 12.0000i | 0.727607 | − | 0.727607i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 14.0000i | − | 0.845771i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.41858 | + | 31.4186i | 0.505824 | + | 1.88776i | 0.458103 | + | 0.888899i | \(0.348529\pi\) |
0.0477206 | + | 0.998861i | \(0.484804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.0000 | 1.90896 | 0.954480 | − | 0.298275i | \(-0.0964112\pi\) | ||||
0.954480 | + | 0.298275i | \(0.0964112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.707107 | + | 0.707107i | ||||
\(289\) | −0.866025 | + | 0.500000i | −0.0509427 | + | 0.0294118i | ||||
\(290\) | −12.3923 | − | 2.53590i | −0.727701 | − | 0.148913i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −30.0526 | − | 8.05256i | −1.75869 | − | 0.471240i | ||||
\(293\) | −19.0000 | − | 19.0000i | −1.10999 | − | 1.10999i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) |
−0.116841 | − | 0.993151i | \(-0.537277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 14.0000 | + | 24.2487i | 0.813733 | + | 1.40943i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1244 | + | 5.12436i | −1.10784 | + | 0.296846i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.3923 | − | 14.7846i | 1.28218 | − | 0.846564i | ||||
\(306\) | −9.00000 | − | 15.5885i | −0.514496 | − | 0.891133i | ||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.366025 | − | 1.36603i | 0.0206890 | − | 0.0772123i | −0.954810 | − | 0.297218i | \(-0.903941\pi\) |
0.975499 | + | 0.220006i | \(0.0706077\pi\) | |||||||
\(314\) | 34.0000i | 1.91873i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.09808 | − | 1.09808i | −0.230171 | − | 0.0616741i | 0.141890 | − | 0.989882i | \(-0.454682\pi\) |
−0.372061 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.8564 | − | 1.07180i | 0.998203 | − | 0.0599153i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.5885 | − | 9.00000i | 0.866025 | − | 0.500000i | ||||
\(325\) | −5.56218 | − | 4.36603i | −0.308534 | − | 0.242184i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.0000 | + | 16.0000i | 0.883452 | + | 0.883452i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.6865 | − | 7.68653i | 1.57201 | − | 0.421219i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | + | 7.00000i | −0.381314 | + | 0.381314i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) |
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 4.02628 | − | 15.0263i | 0.219001 | − | 0.817322i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.5885 | − | 3.80385i | −1.00810 | − | 0.206293i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0000 | − | 19.0526i | 0.591364 | − | 1.02427i | ||||
\(347\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 36.0000i | − | 1.92704i | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||
0.267644 | − | 0.963518i | \(-0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2942 | − | 3.29423i | 0.654356 | − | 0.175334i | 0.0836583 | − | 0.996495i | \(-0.473340\pi\) |
0.570697 | + | 0.821160i | \(0.306673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −32.0000 | −1.69600 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 3.80385 | − | 18.5885i | 0.200480 | − | 0.979698i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 24.5885 | + | 6.58846i | 1.29234 | + | 0.346282i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.0000 | + | 33.0000i | 0.575766 | + | 1.72730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.7846 | − | 12.0000i | 1.08200 | − | 0.624695i | ||||
\(370\) | 14.0000 | − | 28.0000i | 0.727825 | − | 1.45565i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.02628 | + | 15.0263i | −0.208473 | + | 0.778031i | 0.779890 | + | 0.625917i | \(0.215275\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | − | 4.00000i | 0.206010 | − | 0.206010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −38.0000 | −1.93415 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −35.5167 | + | 9.51666i | −1.80309 | + | 0.483135i | ||||
\(389\) | 29.4449 | + | 17.0000i | 1.49291 | + | 0.861934i | 0.999967 | − | 0.00812520i | \(-0.00258636\pi\) |
0.492947 | + | 0.870059i | \(0.335920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.5167 | − | 13.0000i | 1.13437 | − | 0.654931i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7583 | + | 4.75833i | 0.891265 | + | 0.238814i | 0.675261 | − | 0.737579i | \(-0.264031\pi\) |
0.216004 | + | 0.976392i | \(0.430698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | −1.00000 | − | 1.73205i | −0.0499376 | − | 0.0864945i | 0.839976 | − | 0.542623i | \(-0.182569\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.46410 | − | 2.00000i | 0.172345 | − | 0.0995037i | ||||
\(405\) | −18.0000 | − | 9.00000i | −0.894427 | − | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.19615 | + | 3.00000i | 0.256933 | + | 0.148340i | 0.622935 | − | 0.782274i | \(-0.285940\pi\) |
−0.366002 | + | 0.930614i | \(0.619274\pi\) | |||||||
\(410\) | 5.07180 | − | 24.7846i | 0.250478 | − | 1.22402i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.00000 | + | 6.92820i | −0.196116 | + | 0.339683i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −31.1769 | − | 18.0000i | −1.51408 | − | 0.874157i | ||||
\(425\) | 7.90192 | + | 19.6865i | 0.383300 | + | 0.954937i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.0000 | − | 29.0000i | −1.39365 | − | 1.39365i | −0.816968 | − | 0.576683i | \(-0.804347\pi\) |
−0.576683 | − | 0.816968i | \(-0.695653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | − | 10.3923i | −0.287348 | − | 0.497701i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.7128 | + | 29.8564i | 0.934477 | + | 1.41533i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.0000i | − | 0.660701i | −0.943858 | − | 0.330350i | \(-0.892833\pi\) | ||
0.943858 | − | 0.330350i | \(-0.107167\pi\) | |||||||
\(450\) | −19.6865 | + | 7.90192i | −0.928032 | + | 0.372500i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.732051 | − | 2.73205i | −0.0344328 | − | 0.128505i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2224 | + | 6.22243i | 1.08630 | + | 0.291073i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
0.329125 | + | 0.944286i | \(0.393246\pi\) | |||||||
\(458\) | 5.46410 | − | 1.46410i | 0.255321 | − | 0.0684130i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.0000 | 1.76984 | 0.884918 | − | 0.465746i | \(-0.154214\pi\) | ||||
0.884918 | + | 0.465746i | \(0.154214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 13.8564 | − | 8.00000i | 0.643268 | − | 0.371391i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.0000 | + | 36.3731i | −0.972806 | + | 1.68495i | ||||
\(467\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(468\) | 6.00000 | + | 6.00000i | 0.277350 | + | 0.277350i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.0000 | + | 27.0000i | −1.23625 | + | 1.23625i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.00000 | + | 12.1244i | 0.319173 | + | 0.552823i | ||||
\(482\) | −8.00000 | + | 8.00000i | −0.364390 | + | 0.364390i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 22.0000i | − | 1.00000i | ||||||
\(485\) | 30.7583 | + | 27.2750i | 1.39666 | + | 1.23849i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(488\) | −8.78461 | + | 32.7846i | −0.397661 | + | 1.48409i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.3923 | + | 4.39230i | −0.738272 | + | 0.197819i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(500\) | −7.53590 | + | 21.0526i | −0.337016 | + | 0.941499i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | − | 2.00000i | −0.177998 | − | 0.0889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.1051 | − | 22.0000i | 1.68898 | − | 0.975133i | 0.733679 | − | 0.679496i | \(-0.237801\pi\) |
0.955300 | − | 0.295637i | \(-0.0955319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.4449 | − | 17.0000i | −1.29876 | − | 0.749838i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.92820 | − | 0.535898i | 0.391528 | − | 0.0235007i | ||||
\(521\) | 11.0000 | − | 19.0526i | 0.481919 | − | 0.834708i | −0.517866 | − | 0.855462i | \(-0.673273\pi\) |
0.999785 | + | 0.0207541i | \(0.00660670\pi\) | |||||||
\(522\) | −4.39230 | − | 16.3923i | −0.192246 | − | 0.717472i | ||||
\(523\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9186 | − | 11.5000i | −0.866025 | − | 0.500000i | ||||
\(530\) | 2.41154 | + | 40.1769i | 0.104751 | + | 1.74517i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | + | 8.00000i | 0.346518 | + | 0.346518i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.0000 | + | 26.0000i | 1.12094 | + | 1.12094i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0000 | − | 36.3731i | −0.902861 | − | 1.56380i | −0.823764 | − | 0.566933i | \(-0.808130\pi\) |
−0.0790969 | − | 0.996867i | \(-0.525204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.7846 | − | 12.0000i | 0.891133 | − | 0.514496i | ||||
\(545\) | −6.00000 | + | 12.0000i | −0.257012 | + | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 5.12436 | − | 19.1244i | 0.218902 | − | 0.816952i | ||||
\(549\) | 31.1769 | + | 18.0000i | 1.33060 | + | 0.768221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 46.0000i | 1.95435i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.0788 | + | 45.0788i | 0.511797 | + | 1.91005i | 0.400599 | + | 0.916253i | \(0.368802\pi\) |
0.111198 | + | 0.993798i | \(0.464531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 43.7128 | + | 11.7128i | 1.84391 | + | 0.494075i | ||||
\(563\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.09808 | + | 2.36603i | −0.0882667 | + | 0.0995394i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.5167 | − | 13.0000i | 0.943948 | − | 0.544988i | 0.0527519 | − | 0.998608i | \(-0.483201\pi\) |
0.891196 | + | 0.453619i | \(0.149867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | −8.41858 | − | 31.4186i | −0.350470 | − | 1.30797i | −0.886090 | − | 0.463513i | \(-0.846589\pi\) |
0.535620 | − | 0.844459i | \(-0.320078\pi\) | |||||||
\(578\) | −1.36603 | + | 0.366025i | −0.0568192 | + | 0.0152246i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.0000 | − | 8.00000i | −0.664364 | − | 0.332182i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −38.1051 | − | 22.0000i | −1.57680 | − | 0.910366i | ||||
\(585\) | 1.90192 | − | 9.29423i | 0.0786349 | − | 0.384269i | ||||
\(586\) | −19.0000 | − | 32.9090i | −0.784883 | − | 1.35946i | ||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.2487 | + | 38.2487i | 0.421219 | + | 1.57201i | ||||
\(593\) | 11.3468 | − | 42.3468i | 0.465957 | − | 1.73897i | −0.187741 | − | 0.982219i | \(-0.560117\pi\) |
0.653698 | − | 0.756756i | \(-0.273217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.0000 | −1.14692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 48.0000 | 1.95796 | 0.978980 | − | 0.203954i | \(-0.0653794\pi\) | ||||
0.978980 | + | 0.203954i | \(0.0653794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.5263 | + | 13.5526i | −0.834512 | + | 0.550990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.0000 | − | 12.0000i | 1.45760 | − | 0.485866i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.58846 | − | 24.5885i | −0.266323 | − | 0.993929i | ||||
\(613\) | 1.36603 | − | 0.366025i | 0.0551732 | − | 0.0147836i | −0.231127 | − | 0.972924i | \(-0.574241\pi\) |
0.286300 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.00000 | − | 3.00000i | 0.120775 | − | 0.120775i | −0.644136 | − | 0.764911i | \(-0.722783\pi\) |
0.764911 | + | 0.644136i | \(0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | 1.00000 | − | 1.73205i | 0.0399680 | − | 0.0692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.4449 | + | 46.4449i | −0.496604 | + | 1.85335i | ||||
\(629\) | − | 42.0000i | − | 1.67465i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.19615 | − | 3.00000i | −0.206366 | − | 0.119145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.7846 | + | 5.07180i | 0.979698 | + | 0.200480i | ||||
\(641\) | 4.00000 | − | 6.92820i | 0.157991 | − | 0.273648i | −0.776153 | − | 0.630544i | \(-0.782832\pi\) |
0.934144 | + | 0.356897i | \(0.116165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(648\) | 24.5885 | − | 6.58846i | 0.965926 | − | 0.258819i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.00000 | − | 8.00000i | −0.235339 | − | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.29423 | − | 12.2942i | 0.128913 | − | 0.481110i | −0.871036 | − | 0.491220i | \(-0.836551\pi\) |
0.999949 | + | 0.0101092i | \(0.00321793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16.0000 | + | 27.7128i | 0.624695 | + | 1.08200i | ||||
\(657\) | −33.0000 | + | 33.0000i | −1.28745 | + | 1.28745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | − | 10.3923i | 0.233373 | − | 0.404214i | −0.725426 | − | 0.688301i | \(-0.758357\pi\) |
0.958799 | + | 0.284087i | \(0.0916904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 42.0000 | 1.62747 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | − | 11.0000i | −0.424019 | − | 0.424019i | 0.462566 | − | 0.886585i | \(-0.346929\pi\) |
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | −12.1244 | + | 7.00000i | −0.467013 | + | 0.269630i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | − | 19.0526i | 0.423077 | − | 0.732791i | ||||
\(677\) | −36.8827 | − | 9.88269i | −1.41752 | − | 0.379822i | −0.532915 | − | 0.846169i | \(-0.678903\pi\) |
−0.884602 | + | 0.466347i | \(0.845570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.0000 | − | 12.0000i | −0.920358 | − | 0.460179i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.0000 | + | 7.00000i | −0.802369 | + | 0.267456i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.5885 | − | 9.00000i | −0.593873 | − | 0.342873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 22.0000 | − | 22.0000i | 0.836315 | − | 0.836315i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.78461 | − | 32.7846i | −0.332741 | − | 1.24181i | ||||
\(698\) | 13.1769 | − | 49.1769i | 0.498754 | − | 1.86137i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.0000 | 1.96401 | 0.982006 | − | 0.188847i | \(-0.0604752\pi\) | ||||
0.982006 | + | 0.188847i | \(0.0604752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.1051 | + | 22.0000i | −1.43107 | + | 0.826227i | −0.997202 | − | 0.0747503i | \(-0.976184\pi\) |
−0.433865 | + | 0.900978i | \(0.642851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −43.7128 | − | 11.7128i | −1.63821 | − | 0.438956i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 12.0000 | − | 24.0000i | 0.447214 | − | 0.894427i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.0000 | − | 19.0000i | 0.707107 | − | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31.1769 | + | 18.0000i | 1.15868 | + | 0.668965i | ||||
\(725\) | 2.39230 | + | 19.8564i | 0.0888480 | + | 0.737448i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 2.94744 | + | 49.1051i | 0.109090 | + | 1.81746i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6147 | + | 39.6147i | −0.392064 | + | 1.46320i | 0.434659 | + | 0.900595i | \(0.356869\pi\) |
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 32.7846 | − | 8.78461i | 1.20682 | − | 0.323366i | ||||
\(739\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(740\) | 29.3731 | − | 33.1244i | 1.07978 | − | 1.21768i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.2487 | + | 26.1244i | 0.631944 | + | 0.957122i | ||||
\(746\) | −11.0000 | + | 19.0526i | −0.402739 | + | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.92820 | − | 4.00000i | 0.252310 | − | 0.145671i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0000 | + | 17.0000i | −0.617876 | + | 0.617876i | −0.944986 | − | 0.327111i | \(-0.893925\pi\) |
0.327111 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0000 | − | 32.9090i | −0.688749 | − | 1.19295i | −0.972243 | − | 0.233975i | \(-0.924827\pi\) |
0.283493 | − | 0.958974i | \(-0.408507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.8827 | + | 21.2942i | −0.682705 | + | 0.769894i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0000i | 0.865462i | 0.901523 | + | 0.432731i | \(0.142450\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −51.9090 | − | 13.9090i | −1.86824 | − | 0.500595i | ||||
\(773\) | 53.2750 | − | 14.2750i | 1.91617 | − | 0.513436i | 0.925172 | − | 0.379549i | \(-0.123921\pi\) |
0.990997 | − | 0.133887i | \(-0.0427458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −52.0000 | −1.86669 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.0000 | + | 34.0000i | 1.21896 | + | 1.21896i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.0000 | − | 17.0000i | 1.82027 | − | 0.606756i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(788\) | 35.5167 | − | 9.51666i | 1.26523 | − | 0.339017i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.39230 | + | 16.3923i | −0.155975 | + | 0.582108i | ||||
\(794\) | 22.5167 | + | 13.0000i | 0.799086 | + | 0.461353i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.0000 | − | 37.0000i | 1.31061 | − | 1.31061i | 0.389640 | − | 0.920967i | \(-0.372599\pi\) |
0.920967 | − | 0.389640i | \(-0.127401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −10.5359 | − | 26.2487i | −0.372500 | − | 0.928032i | ||||
\(801\) | −24.0000 | + | 41.5692i | −0.847998 | + | 1.46878i | ||||
\(802\) | −0.732051 | − | 2.73205i | −0.0258496 | − | 0.0964721i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.46410 | − | 1.46410i | 0.192226 | − | 0.0515069i | ||||
\(809\) | −48.4974 | − | 28.0000i | −1.70508 | − | 0.984428i | −0.940435 | − | 0.339975i | \(-0.889582\pi\) |
−0.764644 | − | 0.644453i | \(-0.777085\pi\) | |||||||
\(810\) | −21.2942 | − | 18.8827i | −0.748203 | − | 0.663470i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.00000 | + | 6.00000i | 0.209785 | + | 0.209785i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.0000 | − | 32.0000i | 0.558744 | − | 1.11749i | ||||
\(821\) | 14.0000 | + | 24.2487i | 0.488603 | + | 0.846286i | 0.999914 | − | 0.0131101i | \(-0.00417319\pi\) |
−0.511311 | + | 0.859396i | \(0.670840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.7654 | − | 27.0000i | −1.62423 | − | 0.937749i | −0.985771 | − | 0.168091i | \(-0.946240\pi\) |
−0.638457 | − | 0.769657i | \(-0.720427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.00000 | + | 8.00000i | −0.277350 | + | 0.277350i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | −38.2487 | − | 10.2487i | −1.31814 | − | 0.353194i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.5526 | + | 1.47372i | −0.844634 | + | 0.0506975i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −36.0000 | − | 36.0000i | −1.23625 | − | 1.23625i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.58846 | + | 29.7846i | 0.123083 | + | 1.02160i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.0000 | + | 41.0000i | 1.40381 | + | 1.40381i | 0.787505 | + | 0.616308i | \(0.211372\pi\) |
0.616308 | + | 0.787505i | \(0.288628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0788 | − | 45.0788i | −0.412605 | − | 1.53986i | −0.789584 | − | 0.613642i | \(-0.789704\pi\) |
0.376979 | − | 0.926222i | \(-0.376963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.0788 | − | 6.97372i | −1.15872 | − | 0.237114i | ||||
\(866\) | −29.0000 | − | 50.2295i | −0.985460 | − | 1.70687i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.39230 | − | 16.3923i | −0.148742 | − | 0.555113i | ||||
\(873\) | −14.2750 | + | 53.2750i | −0.483135 | + | 1.80309i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.4186 | − | 8.41858i | −1.06093 | − | 0.284275i | −0.314169 | − | 0.949367i | \(-0.601726\pi\) |
−0.746762 | + | 0.665092i | \(0.768392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.0000 | −1.07811 | −0.539054 | − | 0.842271i | \(-0.681218\pi\) | ||||
−0.539054 | + | 0.842271i | \(0.681218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 10.3923 | − | 6.00000i | 0.349531 | − | 0.201802i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.0000 | + | 48.0000i | 0.536321 | + | 1.60896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.12436 | − | 19.1244i | 0.171002 | − | 0.638188i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −29.7846 | + | 3.58846i | −0.992820 | + | 0.119615i | ||||
\(901\) | 27.0000 | + | 46.7654i | 0.899500 | + | 1.55798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.00000i | − | 0.133038i | ||||||
\(905\) | −2.41154 | − | 40.1769i | −0.0801624 | − | 1.33553i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6.00000i | − | 0.199007i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 29.4449 | + | 17.0000i | 0.973950 | + | 0.562310i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51.9090 | + | 13.9090i | 1.70953 | + | 0.458067i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.0000 | − | 7.00000i | −1.61111 | − | 0.230159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21.8564 | − | 5.85641i | 0.717472 | − | 0.192246i | ||||
\(929\) | −39.8372 | + | 23.0000i | −1.30702 | + | 0.754606i | −0.981597 | − | 0.190965i | \(-0.938838\pi\) |
−0.325418 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −42.0000 | + | 42.0000i | −1.37576 | + | 1.37576i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | + | 10.3923i | 0.196116 | + | 0.339683i | ||||
\(937\) | −43.0000 | + | 43.0000i | −1.40475 | + | 1.40475i | −0.620703 | + | 0.784046i | \(0.713153\pi\) |
−0.784046 | + | 0.620703i | \(0.786847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.0000 | + | 50.2295i | −0.945373 | + | 1.63743i | −0.190370 | + | 0.981712i | \(0.560969\pi\) |
−0.755003 | + | 0.655722i | \(0.772364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.0526 | − | 11.0000i | −0.618472 | − | 0.357075i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.0000 | − | 41.0000i | −1.32812 | − | 1.32812i | −0.907009 | − | 0.421111i | \(-0.861640\pi\) |
−0.421111 | − | 0.907009i | \(-0.638360\pi\) | |||||||
\(954\) | −46.7654 | + | 27.0000i | −1.51408 | + | 0.874157i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | − | 26.8468i | −0.500000 | − | 0.866025i | ||||
\(962\) | 5.12436 | + | 19.1244i | 0.165216 | + | 0.616594i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.8564 | + | 8.00000i | −0.446285 | + | 0.257663i | ||||
\(965\) | 19.0000 | + | 57.0000i | 0.611632 | + | 1.83489i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 8.05256 | − | 30.0526i | 0.258819 | − | 0.965926i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.0333 | + | 48.5167i | 1.02853 | + | 1.55778i | ||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0000 | + | 41.5692i | −0.768221 | + | 1.33060i | ||||
\(977\) | −9.88269 | − | 36.8827i | −0.316175 | − | 1.17998i | −0.922890 | − | 0.385063i | \(-0.874180\pi\) |
0.606715 | − | 0.794919i | \(-0.292487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.7583 | − | 27.2750i | −0.980042 | − | 0.869053i | ||||
\(986\) | −24.0000 | −0.764316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5429 | + | 50.5429i | 0.428909 | + | 1.60071i | 0.755235 | + | 0.655454i | \(0.227523\pi\) |
−0.326326 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))