Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,2,Mod(129,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("130.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.c (of order \(2\), degree \(1\), 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: | \(1.03805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.129 |
Dual form | 130.2.c.a.129.4 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | − | 2.52434i | − | 1.45743i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) | ||
0.684819 | − | 0.728714i | \(-0.259881\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.18614 | − | 0.469882i | 0.977672 | − | 0.210138i | ||||
\(6\) | 2.52434i | 1.03056i | ||||||||
\(7\) | −2.37228 | −0.896638 | −0.448319 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448319 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.37228 | −1.12409 | ||||||||
\(10\) | −2.18614 | + | 0.469882i | −0.691318 | + | 0.148590i | ||||
\(11\) | − | 1.58457i | − | 0.477767i | −0.971048 | − | 0.238884i | \(-0.923219\pi\) | ||
0.971048 | − | 0.238884i | \(-0.0767814\pi\) | |||||||
\(12\) | − | 2.52434i | − | 0.728714i | ||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 2.37228 | 0.634019 | ||||||||
\(15\) | −1.18614 | − | 5.51856i | −0.306260 | − | 1.42489i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.98844i | 1.45241i | 0.687478 | + | 0.726205i | \(0.258718\pi\) | ||||
−0.687478 | + | 0.726205i | \(0.741282\pi\) | |||||||
\(18\) | 3.37228 | 0.794854 | ||||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 2.18614 | − | 0.469882i | 0.488836 | − | 0.105069i | ||||
\(21\) | 5.98844i | 1.30678i | ||||||||
\(22\) | 1.58457i | 0.337832i | ||||||||
\(23\) | 6.63325i | 1.38313i | 0.722315 | + | 0.691564i | \(0.243078\pi\) | ||||
−0.722315 | + | 0.691564i | \(0.756922\pi\) | |||||||
\(24\) | 2.52434i | 0.515278i | ||||||||
\(25\) | 4.55842 | − | 2.05446i | 0.911684 | − | 0.410891i | ||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | 0.939764i | 0.180858i | ||||||||
\(28\) | −2.37228 | −0.448319 | ||||||||
\(29\) | 2.74456 | 0.509652 | 0.254826 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254826 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(30\) | 1.18614 | + | 5.51856i | 0.216559 | + | 1.00755i | ||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | − | 5.98844i | − | 1.02701i | ||||||
\(35\) | −5.18614 | + | 1.11469i | −0.876618 | + | 0.188417i | ||||
\(36\) | −3.37228 | −0.562047 | ||||||||
\(37\) | 9.11684 | 1.49880 | 0.749400 | − | 0.662118i | \(-0.230342\pi\) | ||||
0.749400 | + | 0.662118i | \(0.230342\pi\) | |||||||
\(38\) | 3.46410i | 0.561951i | ||||||||
\(39\) | −8.74456 | − | 2.52434i | −1.40025 | − | 0.404218i | ||||
\(40\) | −2.18614 | + | 0.469882i | −0.345659 | + | 0.0742949i | ||||
\(41\) | 10.0974i | 1.57694i | 0.615072 | + | 0.788471i | \(0.289127\pi\) | ||||
−0.615072 | + | 0.788471i | \(0.710873\pi\) | |||||||
\(42\) | − | 5.98844i | − | 0.924036i | ||||||
\(43\) | − | 0.644810i | − | 0.0983326i | −0.998791 | − | 0.0491663i | \(-0.984344\pi\) | ||
0.998791 | − | 0.0491663i | \(-0.0156564\pi\) | |||||||
\(44\) | − | 1.58457i | − | 0.238884i | ||||||
\(45\) | −7.37228 | + | 1.58457i | −1.09899 | + | 0.236214i | ||||
\(46\) | − | 6.63325i | − | 0.978019i | ||||||
\(47\) | 10.3723 | 1.51295 | 0.756476 | − | 0.654021i | \(-0.226919\pi\) | ||||
0.756476 | + | 0.654021i | \(0.226919\pi\) | |||||||
\(48\) | − | 2.52434i | − | 0.364357i | ||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | −4.55842 | + | 2.05446i | −0.644658 | + | 0.290544i | ||||
\(51\) | 15.1168 | 2.11678 | ||||||||
\(52\) | 1.00000 | − | 3.46410i | 0.138675 | − | 0.480384i | ||||
\(53\) | − | 5.04868i | − | 0.693489i | −0.937960 | − | 0.346744i | \(-0.887287\pi\) | ||
0.937960 | − | 0.346744i | \(-0.112713\pi\) | |||||||
\(54\) | − | 0.939764i | − | 0.127886i | ||||||
\(55\) | −0.744563 | − | 3.46410i | −0.100397 | − | 0.467099i | ||||
\(56\) | 2.37228 | 0.317009 | ||||||||
\(57\) | −8.74456 | −1.15825 | ||||||||
\(58\) | −2.74456 | −0.360379 | ||||||||
\(59\) | 6.63325i | 0.863576i | 0.901975 | + | 0.431788i | \(0.142117\pi\) | ||||
−0.901975 | + | 0.431788i | \(0.857883\pi\) | |||||||
\(60\) | −1.18614 | − | 5.51856i | −0.153130 | − | 0.712443i | ||||
\(61\) | −6.74456 | −0.863553 | −0.431776 | − | 0.901981i | \(-0.642113\pi\) | ||||
−0.431776 | + | 0.901981i | \(0.642113\pi\) | |||||||
\(62\) | − | 3.46410i | − | 0.439941i | ||||||
\(63\) | 8.00000 | 1.00791 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.558422 | − | 8.04290i | 0.0692637 | − | 0.997598i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 5.98844i | 0.726205i | ||||||||
\(69\) | 16.7446 | 2.01581 | ||||||||
\(70\) | 5.18614 | − | 1.11469i | 0.619862 | − | 0.133231i | ||||
\(71\) | − | 12.6217i | − | 1.49792i | −0.662616 | − | 0.748959i | \(-0.730554\pi\) | ||
0.662616 | − | 0.748959i | \(-0.269446\pi\) | |||||||
\(72\) | 3.37228 | 0.397427 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −9.11684 | −1.05981 | ||||||||
\(75\) | −5.18614 | − | 11.5070i | −0.598844 | − | 1.32871i | ||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | 3.75906i | 0.428384i | ||||||||
\(78\) | 8.74456 | + | 2.52434i | 0.990127 | + | 0.285825i | ||||
\(79\) | 4.74456 | 0.533805 | 0.266903 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266903 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(80\) | 2.18614 | − | 0.469882i | 0.244418 | − | 0.0525344i | ||||
\(81\) | −7.74456 | −0.860507 | ||||||||
\(82\) | − | 10.0974i | − | 1.11507i | ||||||
\(83\) | −8.74456 | −0.959840 | −0.479920 | − | 0.877312i | \(-0.659334\pi\) | ||||
−0.479920 | + | 0.877312i | \(0.659334\pi\) | |||||||
\(84\) | 5.98844i | 0.653392i | ||||||||
\(85\) | 2.81386 | + | 13.0916i | 0.305206 | + | 1.41998i | ||||
\(86\) | 0.644810i | 0.0695317i | ||||||||
\(87\) | − | 6.92820i | − | 0.742781i | ||||||
\(88\) | 1.58457i | 0.168916i | ||||||||
\(89\) | 1.87953i | 0.199230i | 0.995026 | + | 0.0996148i | \(0.0317610\pi\) | ||||
−0.995026 | + | 0.0996148i | \(0.968239\pi\) | |||||||
\(90\) | 7.37228 | − | 1.58457i | 0.777107 | − | 0.167029i | ||||
\(91\) | −2.37228 | + | 8.21782i | −0.248683 | + | 0.861462i | ||||
\(92\) | 6.63325i | 0.691564i | ||||||||
\(93\) | 8.74456 | 0.906769 | ||||||||
\(94\) | −10.3723 | −1.06982 | ||||||||
\(95\) | −1.62772 | − | 7.57301i | −0.167000 | − | 0.776975i | ||||
\(96\) | 2.52434i | 0.257639i | ||||||||
\(97\) | −6.74456 | −0.684807 | −0.342403 | − | 0.939553i | \(-0.611241\pi\) | ||||
−0.342403 | + | 0.939553i | \(0.611241\pi\) | |||||||
\(98\) | 1.37228 | 0.138621 | ||||||||
\(99\) | 5.34363i | 0.537055i | ||||||||
\(100\) | 4.55842 | − | 2.05446i | 0.455842 | − | 0.205446i | ||||
\(101\) | −14.7446 | −1.46714 | −0.733569 | − | 0.679615i | \(-0.762147\pi\) | ||||
−0.733569 | + | 0.679615i | \(0.762147\pi\) | |||||||
\(102\) | −15.1168 | −1.49679 | ||||||||
\(103\) | 10.3923i | 1.02398i | 0.858990 | + | 0.511992i | \(0.171092\pi\) | ||||
−0.858990 | + | 0.511992i | \(0.828908\pi\) | |||||||
\(104\) | −1.00000 | + | 3.46410i | −0.0980581 | + | 0.339683i | ||||
\(105\) | 2.81386 | + | 13.0916i | 0.274605 | + | 1.27761i | ||||
\(106\) | 5.04868i | 0.490371i | ||||||||
\(107\) | 13.5615i | 1.31104i | 0.755180 | + | 0.655518i | \(0.227549\pi\) | ||||
−0.755180 | + | 0.655518i | \(0.772451\pi\) | |||||||
\(108\) | 0.939764i | 0.0904288i | ||||||||
\(109\) | − | 2.81929i | − | 0.270039i | −0.990843 | − | 0.135020i | \(-0.956890\pi\) | ||
0.990843 | − | 0.135020i | \(-0.0431097\pi\) | |||||||
\(110\) | 0.744563 | + | 3.46410i | 0.0709913 | + | 0.330289i | ||||
\(111\) | − | 23.0140i | − | 2.18439i | ||||||
\(112\) | −2.37228 | −0.224160 | ||||||||
\(113\) | − | 3.75906i | − | 0.353622i | −0.984245 | − | 0.176811i | \(-0.943422\pi\) | ||
0.984245 | − | 0.176811i | \(-0.0565782\pi\) | |||||||
\(114\) | 8.74456 | 0.819003 | ||||||||
\(115\) | 3.11684 | + | 14.5012i | 0.290647 | + | 1.35225i | ||||
\(116\) | 2.74456 | 0.254826 | ||||||||
\(117\) | −3.37228 | + | 11.6819i | −0.311768 | + | 1.07999i | ||||
\(118\) | − | 6.63325i | − | 0.610640i | ||||||
\(119\) | − | 14.2063i | − | 1.30229i | ||||||
\(120\) | 1.18614 | + | 5.51856i | 0.108279 | + | 0.503773i | ||||
\(121\) | 8.48913 | 0.771739 | ||||||||
\(122\) | 6.74456 | 0.610624 | ||||||||
\(123\) | 25.4891 | 2.29828 | ||||||||
\(124\) | 3.46410i | 0.311086i | ||||||||
\(125\) | 9.00000 | − | 6.63325i | 0.804984 | − | 0.593296i | ||||
\(126\) | −8.00000 | −0.712697 | ||||||||
\(127\) | − | 3.46410i | − | 0.307389i | −0.988118 | − | 0.153695i | \(-0.950883\pi\) | ||
0.988118 | − | 0.153695i | \(-0.0491172\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.62772 | −0.143313 | ||||||||
\(130\) | −0.558422 | + | 8.04290i | −0.0489768 | + | 0.705409i | ||||
\(131\) | −1.62772 | −0.142214 | −0.0711072 | − | 0.997469i | \(-0.522653\pi\) | ||||
−0.0711072 | + | 0.997469i | \(0.522653\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | 8.21782i | 0.712576i | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0.441578 | + | 2.05446i | 0.0380050 | + | 0.176819i | ||||
\(136\) | − | 5.98844i | − | 0.513504i | ||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | −16.7446 | −1.42539 | ||||||||
\(139\) | 6.37228 | 0.540490 | 0.270245 | − | 0.962792i | \(-0.412895\pi\) | ||||
0.270245 | + | 0.962792i | \(0.412895\pi\) | |||||||
\(140\) | −5.18614 | + | 1.11469i | −0.438309 | + | 0.0942087i | ||||
\(141\) | − | 26.1831i | − | 2.20502i | ||||||
\(142\) | 12.6217i | 1.05919i | ||||||||
\(143\) | −5.48913 | − | 1.58457i | −0.459024 | − | 0.132509i | ||||
\(144\) | −3.37228 | −0.281023 | ||||||||
\(145\) | 6.00000 | − | 1.28962i | 0.498273 | − | 0.107097i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 3.46410i | 0.285714i | ||||||||
\(148\) | 9.11684 | 0.749400 | ||||||||
\(149\) | 17.0256i | 1.39479i | 0.716688 | + | 0.697394i | \(0.245657\pi\) | ||||
−0.716688 | + | 0.697394i | \(0.754343\pi\) | |||||||
\(150\) | 5.18614 | + | 11.5070i | 0.423447 | + | 0.939542i | ||||
\(151\) | 7.57301i | 0.616283i | 0.951341 | + | 0.308142i | \(0.0997070\pi\) | ||||
−0.951341 | + | 0.308142i | \(0.900293\pi\) | |||||||
\(152\) | 3.46410i | 0.280976i | ||||||||
\(153\) | − | 20.1947i | − | 1.63264i | ||||||
\(154\) | − | 3.75906i | − | 0.302913i | ||||||
\(155\) | 1.62772 | + | 7.57301i | 0.130742 | + | 0.608279i | ||||
\(156\) | −8.74456 | − | 2.52434i | −0.700125 | − | 0.202109i | ||||
\(157\) | − | 15.1460i | − | 1.20878i | −0.796687 | − | 0.604392i | \(-0.793416\pi\) | ||
0.796687 | − | 0.604392i | \(-0.206584\pi\) | |||||||
\(158\) | −4.74456 | −0.377457 | ||||||||
\(159\) | −12.7446 | −1.01071 | ||||||||
\(160\) | −2.18614 | + | 0.469882i | −0.172830 | + | 0.0371474i | ||||
\(161\) | − | 15.7359i | − | 1.24017i | ||||||
\(162\) | 7.74456 | 0.608470 | ||||||||
\(163\) | −24.7446 | −1.93814 | −0.969072 | − | 0.246779i | \(-0.920628\pi\) | ||||
−0.969072 | + | 0.246779i | \(0.920628\pi\) | |||||||
\(164\) | 10.0974i | 0.788471i | ||||||||
\(165\) | −8.74456 | + | 1.87953i | −0.680763 | + | 0.146321i | ||||
\(166\) | 8.74456 | 0.678710 | ||||||||
\(167\) | −17.4891 | −1.35335 | −0.676675 | − | 0.736282i | \(-0.736580\pi\) | ||||
−0.676675 | + | 0.736282i | \(0.736580\pi\) | |||||||
\(168\) | − | 5.98844i | − | 0.462018i | ||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | −2.81386 | − | 13.0916i | −0.215813 | − | 1.00408i | ||||
\(171\) | 11.6819i | 0.893339i | ||||||||
\(172\) | − | 0.644810i | − | 0.0491663i | ||||||
\(173\) | − | 18.9051i | − | 1.43733i | −0.695358 | − | 0.718663i | \(-0.744754\pi\) | ||
0.695358 | − | 0.718663i | \(-0.255246\pi\) | |||||||
\(174\) | 6.92820i | 0.525226i | ||||||||
\(175\) | −10.8139 | + | 4.87375i | −0.817451 | + | 0.368421i | ||||
\(176\) | − | 1.58457i | − | 0.119442i | ||||||
\(177\) | 16.7446 | 1.25860 | ||||||||
\(178\) | − | 1.87953i | − | 0.140877i | ||||||
\(179\) | 4.88316 | 0.364984 | 0.182492 | − | 0.983207i | \(-0.441584\pi\) | ||||
0.182492 | + | 0.983207i | \(0.441584\pi\) | |||||||
\(180\) | −7.37228 | + | 1.58457i | −0.549497 | + | 0.118107i | ||||
\(181\) | −3.48913 | −0.259345 | −0.129672 | − | 0.991557i | \(-0.541393\pi\) | ||||
−0.129672 | + | 0.991557i | \(0.541393\pi\) | |||||||
\(182\) | 2.37228 | − | 8.21782i | 0.175845 | − | 0.609146i | ||||
\(183\) | 17.0256i | 1.25857i | ||||||||
\(184\) | − | 6.63325i | − | 0.489010i | ||||||
\(185\) | 19.9307 | − | 4.28384i | 1.46533 | − | 0.314954i | ||||
\(186\) | −8.74456 | −0.641182 | ||||||||
\(187\) | 9.48913 | 0.693914 | ||||||||
\(188\) | 10.3723 | 0.756476 | ||||||||
\(189\) | − | 2.22938i | − | 0.162164i | ||||||
\(190\) | 1.62772 | + | 7.57301i | 0.118087 | + | 0.549404i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | − | 2.52434i | − | 0.182178i | ||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 6.74456 | 0.484231 | ||||||||
\(195\) | −20.3030 | − | 1.40965i | −1.45393 | − | 0.100947i | ||||
\(196\) | −1.37228 | −0.0980201 | ||||||||
\(197\) | 4.37228 | 0.311512 | 0.155756 | − | 0.987796i | \(-0.450219\pi\) | ||||
0.155756 | + | 0.987796i | \(0.450219\pi\) | |||||||
\(198\) | − | 5.34363i | − | 0.379755i | ||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | −4.55842 | + | 2.05446i | −0.322329 | + | 0.145272i | ||||
\(201\) | 10.0974i | 0.712212i | ||||||||
\(202\) | 14.7446 | 1.03742 | ||||||||
\(203\) | −6.51087 | −0.456974 | ||||||||
\(204\) | 15.1168 | 1.05839 | ||||||||
\(205\) | 4.74456 | + | 22.0742i | 0.331375 | + | 1.54173i | ||||
\(206\) | − | 10.3923i | − | 0.724066i | ||||||
\(207\) | − | 22.3692i | − | 1.55477i | ||||||
\(208\) | 1.00000 | − | 3.46410i | 0.0693375 | − | 0.240192i | ||||
\(209\) | −5.48913 | −0.379691 | ||||||||
\(210\) | −2.81386 | − | 13.0916i | −0.194175 | − | 0.903404i | ||||
\(211\) | 3.11684 | 0.214572 | 0.107286 | − | 0.994228i | \(-0.465784\pi\) | ||||
0.107286 | + | 0.994228i | \(0.465784\pi\) | |||||||
\(212\) | − | 5.04868i | − | 0.346744i | ||||||
\(213\) | −31.8614 | −2.18311 | ||||||||
\(214\) | − | 13.5615i | − | 0.927042i | ||||||
\(215\) | −0.302985 | − | 1.40965i | −0.0206634 | − | 0.0961370i | ||||
\(216\) | − | 0.939764i | − | 0.0639428i | ||||||
\(217\) | − | 8.21782i | − | 0.557862i | ||||||
\(218\) | 2.81929i | 0.190947i | ||||||||
\(219\) | 25.2434i | 1.70579i | ||||||||
\(220\) | −0.744563 | − | 3.46410i | −0.0501984 | − | 0.233550i | ||||
\(221\) | 20.7446 | + | 5.98844i | 1.39543 | + | 0.402826i | ||||
\(222\) | 23.0140i | 1.54460i | ||||||||
\(223\) | 15.1168 | 1.01230 | 0.506149 | − | 0.862446i | \(-0.331068\pi\) | ||||
0.506149 | + | 0.862446i | \(0.331068\pi\) | |||||||
\(224\) | 2.37228 | 0.158505 | ||||||||
\(225\) | −15.3723 | + | 6.92820i | −1.02482 | + | 0.461880i | ||||
\(226\) | 3.75906i | 0.250049i | ||||||||
\(227\) | 5.48913 | 0.364326 | 0.182163 | − | 0.983268i | \(-0.441690\pi\) | ||||
0.182163 | + | 0.983268i | \(0.441690\pi\) | |||||||
\(228\) | −8.74456 | −0.579123 | ||||||||
\(229\) | − | 24.8935i | − | 1.64501i | −0.568758 | − | 0.822505i | \(-0.692576\pi\) | ||
0.568758 | − | 0.822505i | \(-0.307424\pi\) | |||||||
\(230\) | −3.11684 | − | 14.5012i | −0.205519 | − | 0.956182i | ||||
\(231\) | 9.48913 | 0.624339 | ||||||||
\(232\) | −2.74456 | −0.180189 | ||||||||
\(233\) | − | 7.86797i | − | 0.515448i | −0.966219 | − | 0.257724i | \(-0.917028\pi\) | ||
0.966219 | − | 0.257724i | \(-0.0829725\pi\) | |||||||
\(234\) | 3.37228 | − | 11.6819i | 0.220453 | − | 0.763671i | ||||
\(235\) | 22.6753 | − | 4.87375i | 1.47917 | − | 0.317928i | ||||
\(236\) | 6.63325i | 0.431788i | ||||||||
\(237\) | − | 11.9769i | − | 0.777982i | ||||||
\(238\) | 14.2063i | 0.920855i | ||||||||
\(239\) | 9.45254i | 0.611434i | 0.952122 | + | 0.305717i | \(0.0988962\pi\) | ||||
−0.952122 | + | 0.305717i | \(0.901104\pi\) | |||||||
\(240\) | −1.18614 | − | 5.51856i | −0.0765651 | − | 0.356221i | ||||
\(241\) | − | 8.21782i | − | 0.529357i | −0.964337 | − | 0.264678i | \(-0.914734\pi\) | ||
0.964337 | − | 0.264678i | \(-0.0852658\pi\) | |||||||
\(242\) | −8.48913 | −0.545702 | ||||||||
\(243\) | 22.3692i | 1.43498i | ||||||||
\(244\) | −6.74456 | −0.431776 | ||||||||
\(245\) | −3.00000 | + | 0.644810i | −0.191663 | + | 0.0411954i | ||||
\(246\) | −25.4891 | −1.62513 | ||||||||
\(247\) | −12.0000 | − | 3.46410i | −0.763542 | − | 0.220416i | ||||
\(248\) | − | 3.46410i | − | 0.219971i | ||||||
\(249\) | 22.0742i | 1.39890i | ||||||||
\(250\) | −9.00000 | + | 6.63325i | −0.569210 | + | 0.419524i | ||||
\(251\) | −22.9783 | −1.45037 | −0.725187 | − | 0.688552i | \(-0.758247\pi\) | ||||
−0.725187 | + | 0.688552i | \(0.758247\pi\) | |||||||
\(252\) | 8.00000 | 0.503953 | ||||||||
\(253\) | 10.5109 | 0.660813 | ||||||||
\(254\) | 3.46410i | 0.217357i | ||||||||
\(255\) | 33.0475 | − | 7.10313i | 2.06952 | − | 0.444815i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.2063i | 0.886162i | 0.896481 | + | 0.443081i | \(0.146115\pi\) | ||||
−0.896481 | + | 0.443081i | \(0.853885\pi\) | |||||||
\(258\) | 1.62772 | 0.101337 | ||||||||
\(259\) | −21.6277 | −1.34388 | ||||||||
\(260\) | 0.558422 | − | 8.04290i | 0.0346319 | − | 0.498799i | ||||
\(261\) | −9.25544 | −0.572897 | ||||||||
\(262\) | 1.62772 | 0.100561 | ||||||||
\(263\) | − | 18.0202i | − | 1.11117i | −0.831458 | − | 0.555587i | \(-0.812493\pi\) | ||
0.831458 | − | 0.555587i | \(-0.187507\pi\) | |||||||
\(264\) | 4.00000 | 0.246183 | ||||||||
\(265\) | −2.37228 | − | 11.0371i | −0.145728 | − | 0.678005i | ||||
\(266\) | − | 8.21782i | − | 0.503867i | ||||||
\(267\) | 4.74456 | 0.290363 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 2.74456 | 0.167339 | 0.0836695 | − | 0.996494i | \(-0.473336\pi\) | ||||
0.0836695 | + | 0.996494i | \(0.473336\pi\) | |||||||
\(270\) | −0.441578 | − | 2.05446i | −0.0268736 | − | 0.125030i | ||||
\(271\) | 21.4294i | 1.30174i | 0.759187 | + | 0.650872i | \(0.225597\pi\) | ||||
−0.759187 | + | 0.650872i | \(0.774403\pi\) | |||||||
\(272\) | 5.98844i | 0.363102i | ||||||||
\(273\) | 20.7446 | + | 5.98844i | 1.25552 | + | 0.362437i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −3.25544 | − | 7.22316i | −0.196310 | − | 0.435573i | ||||
\(276\) | 16.7446 | 1.00790 | ||||||||
\(277\) | 23.3639i | 1.40380i | 0.712277 | + | 0.701899i | \(0.247664\pi\) | ||||
−0.712277 | + | 0.701899i | \(0.752336\pi\) | |||||||
\(278\) | −6.37228 | −0.382184 | ||||||||
\(279\) | − | 11.6819i | − | 0.699379i | ||||||
\(280\) | 5.18614 | − | 1.11469i | 0.309931 | − | 0.0666156i | ||||
\(281\) | 1.87953i | 0.112123i | 0.998427 | + | 0.0560616i | \(0.0178543\pi\) | ||||
−0.998427 | + | 0.0560616i | \(0.982146\pi\) | |||||||
\(282\) | 26.1831i | 1.55918i | ||||||||
\(283\) | 17.3205i | 1.02960i | 0.857311 | + | 0.514799i | \(0.172133\pi\) | ||||
−0.857311 | + | 0.514799i | \(0.827867\pi\) | |||||||
\(284\) | − | 12.6217i | − | 0.748959i | ||||||
\(285\) | −19.1168 | + | 4.10891i | −1.13238 | + | 0.243391i | ||||
\(286\) | 5.48913 | + | 1.58457i | 0.324579 | + | 0.0936978i | ||||
\(287\) | − | 23.9538i | − | 1.41395i | ||||||
\(288\) | 3.37228 | 0.198714 | ||||||||
\(289\) | −18.8614 | −1.10949 | ||||||||
\(290\) | −6.00000 | + | 1.28962i | −0.352332 | + | 0.0757291i | ||||
\(291\) | 17.0256i | 0.998056i | ||||||||
\(292\) | −10.0000 | −0.585206 | ||||||||
\(293\) | −2.13859 | −0.124938 | −0.0624690 | − | 0.998047i | \(-0.519897\pi\) | ||||
−0.0624690 | + | 0.998047i | \(0.519897\pi\) | |||||||
\(294\) | − | 3.46410i | − | 0.202031i | ||||||
\(295\) | 3.11684 | + | 14.5012i | 0.181470 | + | 0.844293i | ||||
\(296\) | −9.11684 | −0.529906 | ||||||||
\(297\) | 1.48913 | 0.0864078 | ||||||||
\(298\) | − | 17.0256i | − | 0.986264i | ||||||
\(299\) | 22.9783 | + | 6.63325i | 1.32887 | + | 0.383611i | ||||
\(300\) | −5.18614 | − | 11.5070i | −0.299422 | − | 0.664357i | ||||
\(301\) | 1.52967i | 0.0881688i | ||||||||
\(302\) | − | 7.57301i | − | 0.435778i | ||||||
\(303\) | 37.2203i | 2.13825i | ||||||||
\(304\) | − | 3.46410i | − | 0.198680i | ||||||
\(305\) | −14.7446 | + | 3.16915i | −0.844271 | + | 0.181465i | ||||
\(306\) | 20.1947i | 1.15445i | ||||||||
\(307\) | −18.2337 | −1.04065 | −0.520326 | − | 0.853968i | \(-0.674189\pi\) | ||||
−0.520326 | + | 0.853968i | \(0.674189\pi\) | |||||||
\(308\) | 3.75906i | 0.214192i | ||||||||
\(309\) | 26.2337 | 1.49238 | ||||||||
\(310\) | −1.62772 | − | 7.57301i | −0.0924482 | − | 0.430118i | ||||
\(311\) | 3.25544 | 0.184599 | 0.0922995 | − | 0.995731i | \(-0.470578\pi\) | ||||
0.0922995 | + | 0.995731i | \(0.470578\pi\) | |||||||
\(312\) | 8.74456 | + | 2.52434i | 0.495063 | + | 0.142912i | ||||
\(313\) | 12.3267i | 0.696748i | 0.937356 | + | 0.348374i | \(0.113266\pi\) | ||||
−0.937356 | + | 0.348374i | \(0.886734\pi\) | |||||||
\(314\) | 15.1460i | 0.854740i | ||||||||
\(315\) | 17.4891 | − | 3.75906i | 0.985401 | − | 0.211799i | ||||
\(316\) | 4.74456 | 0.266903 | ||||||||
\(317\) | −16.9783 | −0.953594 | −0.476797 | − | 0.879014i | \(-0.658202\pi\) | ||||
−0.476797 | + | 0.879014i | \(0.658202\pi\) | |||||||
\(318\) | 12.7446 | 0.714680 | ||||||||
\(319\) | − | 4.34896i | − | 0.243495i | ||||||
\(320\) | 2.18614 | − | 0.469882i | 0.122209 | − | 0.0262672i | ||||
\(321\) | 34.2337 | 1.91074 | ||||||||
\(322\) | 15.7359i | 0.876929i | ||||||||
\(323\) | 20.7446 | 1.15426 | ||||||||
\(324\) | −7.74456 | −0.430253 | ||||||||
\(325\) | −2.55842 | − | 17.8453i | −0.141916 | − | 0.989879i | ||||
\(326\) | 24.7446 | 1.37047 | ||||||||
\(327\) | −7.11684 | −0.393562 | ||||||||
\(328\) | − | 10.0974i | − | 0.557533i | ||||||
\(329\) | −24.6060 | −1.35657 | ||||||||
\(330\) | 8.74456 | − | 1.87953i | 0.481372 | − | 0.103465i | ||||
\(331\) | 10.3923i | 0.571213i | 0.958347 | + | 0.285606i | \(0.0921950\pi\) | ||||
−0.958347 | + | 0.285606i | \(0.907805\pi\) | |||||||
\(332\) | −8.74456 | −0.479920 | ||||||||
\(333\) | −30.7446 | −1.68479 | ||||||||
\(334\) | 17.4891 | 0.956962 | ||||||||
\(335\) | −8.74456 | + | 1.87953i | −0.477766 | + | 0.102690i | ||||
\(336\) | 5.98844i | 0.326696i | ||||||||
\(337\) | − | 1.52967i | − | 0.0833265i | −0.999132 | − | 0.0416632i | \(-0.986734\pi\) | ||
0.999132 | − | 0.0416632i | \(-0.0132657\pi\) | |||||||
\(338\) | 11.0000 | + | 6.92820i | 0.598321 | + | 0.376845i | ||||
\(339\) | −9.48913 | −0.515379 | ||||||||
\(340\) | 2.81386 | + | 13.0916i | 0.152603 | + | 0.709990i | ||||
\(341\) | 5.48913 | 0.297253 | ||||||||
\(342\) | − | 11.6819i | − | 0.631686i | ||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 0.644810i | 0.0347658i | ||||||||
\(345\) | 36.6060 | − | 7.86797i | 1.97080 | − | 0.423597i | ||||
\(346\) | 18.9051i | 1.01634i | ||||||||
\(347\) | − | 20.8395i | − | 1.11872i | −0.828924 | − | 0.559362i | \(-0.811046\pi\) | ||
0.828924 | − | 0.559362i | \(-0.188954\pi\) | |||||||
\(348\) | − | 6.92820i | − | 0.371391i | ||||||
\(349\) | − | 27.4728i | − | 1.47058i | −0.677751 | − | 0.735292i | \(-0.737045\pi\) | ||
0.677751 | − | 0.735292i | \(-0.262955\pi\) | |||||||
\(350\) | 10.8139 | − | 4.87375i | 0.578025 | − | 0.260513i | ||||
\(351\) | 3.25544 | + | 0.939764i | 0.173762 | + | 0.0501609i | ||||
\(352\) | 1.58457i | 0.0844581i | ||||||||
\(353\) | −11.4891 | −0.611504 | −0.305752 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305752 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(354\) | −16.7446 | −0.889963 | ||||||||
\(355\) | −5.93070 | − | 27.5928i | −0.314769 | − | 1.46447i | ||||
\(356\) | 1.87953i | 0.0996148i | ||||||||
\(357\) | −35.8614 | −1.89799 | ||||||||
\(358\) | −4.88316 | −0.258083 | ||||||||
\(359\) | − | 2.87419i | − | 0.151694i | −0.997119 | − | 0.0758471i | \(-0.975834\pi\) | ||
0.997119 | − | 0.0758471i | \(-0.0241661\pi\) | |||||||
\(360\) | 7.37228 | − | 1.58457i | 0.388553 | − | 0.0835144i | ||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 3.48913 | 0.183384 | ||||||||
\(363\) | − | 21.4294i | − | 1.12475i | ||||||
\(364\) | −2.37228 | + | 8.21782i | −0.124341 | + | 0.430731i | ||||
\(365\) | −21.8614 | + | 4.69882i | −1.14428 | + | 0.245947i | ||||
\(366\) | − | 17.0256i | − | 0.889940i | ||||||
\(367\) | 4.75372i | 0.248142i | 0.992273 | + | 0.124071i | \(0.0395951\pi\) | ||||
−0.992273 | + | 0.124071i | \(0.960405\pi\) | |||||||
\(368\) | 6.63325i | 0.345782i | ||||||||
\(369\) | − | 34.0511i | − | 1.77263i | ||||||
\(370\) | −19.9307 | + | 4.28384i | −1.03615 | + | 0.222706i | ||||
\(371\) | 11.9769i | 0.621809i | ||||||||
\(372\) | 8.74456 | 0.453384 | ||||||||
\(373\) | − | 9.50744i | − | 0.492277i | −0.969235 | − | 0.246138i | \(-0.920838\pi\) | ||
0.969235 | − | 0.246138i | \(-0.0791618\pi\) | |||||||
\(374\) | −9.48913 | −0.490671 | ||||||||
\(375\) | −16.7446 | − | 22.7190i | −0.864685 | − | 1.17321i | ||||
\(376\) | −10.3723 | −0.534910 | ||||||||
\(377\) | 2.74456 | − | 9.50744i | 0.141352 | − | 0.489658i | ||||
\(378\) | 2.22938i | 0.114667i | ||||||||
\(379\) | − | 17.3205i | − | 0.889695i | −0.895606 | − | 0.444847i | \(-0.853258\pi\) | ||
0.895606 | − | 0.444847i | \(-0.146742\pi\) | |||||||
\(380\) | −1.62772 | − | 7.57301i | −0.0835002 | − | 0.388487i | ||||
\(381\) | −8.74456 | −0.447998 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.8832 | 0.862689 | 0.431344 | − | 0.902187i | \(-0.358039\pi\) | ||||
0.431344 | + | 0.902187i | \(0.358039\pi\) | |||||||
\(384\) | 2.52434i | 0.128820i | ||||||||
\(385\) | 1.76631 | + | 8.21782i | 0.0900196 | + | 0.418819i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 2.17448i | 0.110535i | ||||||||
\(388\) | −6.74456 | −0.342403 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 20.3030 | + | 1.40965i | 1.02808 | + | 0.0713802i | ||||
\(391\) | −39.7228 | −2.00887 | ||||||||
\(392\) | 1.37228 | 0.0693107 | ||||||||
\(393\) | 4.10891i | 0.207267i | ||||||||
\(394\) | −4.37228 | −0.220272 | ||||||||
\(395\) | 10.3723 | − | 2.22938i | 0.521886 | − | 0.112172i | ||||
\(396\) | 5.34363i | 0.268527i | ||||||||
\(397\) | 8.51087 | 0.427149 | 0.213574 | − | 0.976927i | \(-0.431489\pi\) | ||||
0.213574 | + | 0.976927i | \(0.431489\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 20.7446 | 1.03853 | ||||||||
\(400\) | 4.55842 | − | 2.05446i | 0.227921 | − | 0.102723i | ||||
\(401\) | 32.1716i | 1.60657i | 0.595593 | + | 0.803286i | \(0.296917\pi\) | ||||
−0.595593 | + | 0.803286i | \(0.703083\pi\) | |||||||
\(402\) | − | 10.0974i | − | 0.503610i | ||||||
\(403\) | 12.0000 | + | 3.46410i | 0.597763 | + | 0.172559i | ||||
\(404\) | −14.7446 | −0.733569 | ||||||||
\(405\) | −16.9307 | + | 3.63903i | −0.841293 | + | 0.180825i | ||||
\(406\) | 6.51087 | 0.323129 | ||||||||
\(407\) | − | 14.4463i | − | 0.716077i | ||||||
\(408\) | −15.1168 | −0.748395 | ||||||||
\(409\) | − | 5.63858i | − | 0.278810i | −0.990235 | − | 0.139405i | \(-0.955481\pi\) | ||
0.990235 | − | 0.139405i | \(-0.0445190\pi\) | |||||||
\(410\) | −4.74456 | − | 22.0742i | −0.234317 | − | 1.09017i | ||||
\(411\) | − | 15.1460i | − | 0.747098i | ||||||
\(412\) | 10.3923i | 0.511992i | ||||||||
\(413\) | − | 15.7359i | − | 0.774315i | ||||||
\(414\) | 22.3692i | 1.09939i | ||||||||
\(415\) | −19.1168 | + | 4.10891i | −0.938409 | + | 0.201699i | ||||
\(416\) | −1.00000 | + | 3.46410i | −0.0490290 | + | 0.169842i | ||||
\(417\) | − | 16.0858i | − | 0.787725i | ||||||
\(418\) | 5.48913 | 0.268482 | ||||||||
\(419\) | 19.1168 | 0.933919 | 0.466959 | − | 0.884279i | \(-0.345349\pi\) | ||||
0.466959 | + | 0.884279i | \(0.345349\pi\) | |||||||
\(420\) | 2.81386 | + | 13.0916i | 0.137302 | + | 0.638803i | ||||
\(421\) | 11.0371i | 0.537916i | 0.963152 | + | 0.268958i | \(0.0866793\pi\) | ||||
−0.963152 | + | 0.268958i | \(0.913321\pi\) | |||||||
\(422\) | −3.11684 | −0.151726 | ||||||||
\(423\) | −34.9783 | −1.70070 | ||||||||
\(424\) | 5.04868i | 0.245185i | ||||||||
\(425\) | 12.3030 | + | 27.2978i | 0.596782 | + | 1.32414i | ||||
\(426\) | 31.8614 | 1.54369 | ||||||||
\(427\) | 16.0000 | 0.774294 | ||||||||
\(428\) | 13.5615i | 0.655518i | ||||||||
\(429\) | −4.00000 | + | 13.8564i | −0.193122 | + | 0.668994i | ||||
\(430\) | 0.302985 | + | 1.40965i | 0.0146112 | + | 0.0679792i | ||||
\(431\) | − | 26.4781i | − | 1.27540i | −0.770283 | − | 0.637702i | \(-0.779885\pi\) | ||
0.770283 | − | 0.637702i | \(-0.220115\pi\) | |||||||
\(432\) | 0.939764i | 0.0452144i | ||||||||
\(433\) | − | 34.4010i | − | 1.65320i | −0.562786 | − | 0.826602i | \(-0.690271\pi\) | ||
0.562786 | − | 0.826602i | \(-0.309729\pi\) | |||||||
\(434\) | 8.21782i | 0.394468i | ||||||||
\(435\) | −3.25544 | − | 15.1460i | −0.156086 | − | 0.726196i | ||||
\(436\) | − | 2.81929i | − | 0.135020i | ||||||
\(437\) | 22.9783 | 1.09920 | ||||||||
\(438\) | − | 25.2434i | − | 1.20618i | ||||||
\(439\) | 22.2337 | 1.06116 | 0.530578 | − | 0.847636i | \(-0.321975\pi\) | ||||
0.530578 | + | 0.847636i | \(0.321975\pi\) | |||||||
\(440\) | 0.744563 | + | 3.46410i | 0.0354956 | + | 0.165145i | ||||
\(441\) | 4.62772 | 0.220368 | ||||||||
\(442\) | −20.7446 | − | 5.98844i | −0.986718 | − | 0.284841i | ||||
\(443\) | − | 4.40387i | − | 0.209234i | −0.994513 | − | 0.104617i | \(-0.966638\pi\) | ||
0.994513 | − | 0.104617i | \(-0.0333617\pi\) | |||||||
\(444\) | − | 23.0140i | − | 1.09220i | ||||||
\(445\) | 0.883156 | + | 4.10891i | 0.0418656 | + | 0.194781i | ||||
\(446\) | −15.1168 | −0.715803 | ||||||||
\(447\) | 42.9783 | 2.03280 | ||||||||
\(448\) | −2.37228 | −0.112080 | ||||||||
\(449\) | 7.51811i | 0.354802i | 0.984139 | + | 0.177401i | \(0.0567689\pi\) | ||||
−0.984139 | + | 0.177401i | \(0.943231\pi\) | |||||||
\(450\) | 15.3723 | − | 6.92820i | 0.724656 | − | 0.326599i | ||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | − | 3.75906i | − | 0.176811i | ||||||
\(453\) | 19.1168 | 0.898188 | ||||||||
\(454\) | −5.48913 | −0.257617 | ||||||||
\(455\) | −1.32473 | + | 19.0800i | −0.0621045 | + | 0.894485i | ||||
\(456\) | 8.74456 | 0.409502 | ||||||||
\(457\) | 24.9783 | 1.16843 | 0.584217 | − | 0.811598i | \(-0.301402\pi\) | ||||
0.584217 | + | 0.811598i | \(0.301402\pi\) | |||||||
\(458\) | 24.8935i | 1.16320i | ||||||||
\(459\) | −5.62772 | −0.262679 | ||||||||
\(460\) | 3.11684 | + | 14.5012i | 0.145324 | + | 0.676123i | ||||
\(461\) | 1.63948i | 0.0763580i | 0.999271 | + | 0.0381790i | \(0.0121557\pi\) | ||||
−0.999271 | + | 0.0381790i | \(0.987844\pi\) | |||||||
\(462\) | −9.48913 | −0.441474 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 2.74456 | 0.127413 | ||||||||
\(465\) | 19.1168 | − | 4.10891i | 0.886522 | − | 0.190546i | ||||
\(466\) | 7.86797i | 0.364477i | ||||||||
\(467\) | 27.4179i | 1.26875i | 0.773027 | + | 0.634374i | \(0.218742\pi\) | ||||
−0.773027 | + | 0.634374i | \(0.781258\pi\) | |||||||
\(468\) | −3.37228 | + | 11.6819i | −0.155884 | + | 0.539997i | ||||
\(469\) | 9.48913 | 0.438167 | ||||||||
\(470\) | −22.6753 | + | 4.87375i | −1.04593 | + | 0.224809i | ||||
\(471\) | −38.2337 | −1.76172 | ||||||||
\(472\) | − | 6.63325i | − | 0.305320i | ||||||
\(473\) | −1.02175 | −0.0469801 | ||||||||
\(474\) | 11.9769i | 0.550116i | ||||||||
\(475\) | −7.11684 | − | 15.7908i | −0.326543 | − | 0.724533i | ||||
\(476\) | − | 14.2063i | − | 0.651143i | ||||||
\(477\) | 17.0256i | 0.779547i | ||||||||
\(478\) | − | 9.45254i | − | 0.432349i | ||||||
\(479\) | − | 18.2603i | − | 0.834333i | −0.908830 | − | 0.417167i | \(-0.863023\pi\) | ||
0.908830 | − | 0.417167i | \(-0.136977\pi\) | |||||||
\(480\) | 1.18614 | + | 5.51856i | 0.0541397 | + | 0.251887i | ||||
\(481\) | 9.11684 | − | 31.5817i | 0.415692 | − | 1.44000i | ||||
\(482\) | 8.21782i | 0.374312i | ||||||||
\(483\) | −39.7228 | −1.80745 | ||||||||
\(484\) | 8.48913 | 0.385869 | ||||||||
\(485\) | −14.7446 | + | 3.16915i | −0.669516 | + | 0.143904i | ||||
\(486\) | − | 22.3692i | − | 1.01469i | ||||||
\(487\) | 1.48913 | 0.0674787 | 0.0337394 | − | 0.999431i | \(-0.489258\pi\) | ||||
0.0337394 | + | 0.999431i | \(0.489258\pi\) | |||||||
\(488\) | 6.74456 | 0.305312 | ||||||||
\(489\) | 62.4636i | 2.82470i | ||||||||
\(490\) | 3.00000 | − | 0.644810i | 0.135526 | − | 0.0291296i | ||||
\(491\) | −25.6277 | −1.15656 | −0.578281 | − | 0.815837i | \(-0.696276\pi\) | ||||
−0.578281 | + | 0.815837i | \(0.696276\pi\) | |||||||
\(492\) | 25.4891 | 1.14914 | ||||||||
\(493\) | 16.4356i | 0.740224i | ||||||||
\(494\) | 12.0000 | + | 3.46410i | 0.539906 | + | 0.155857i | ||||
\(495\) | 2.51087 | + | 11.6819i | 0.112855 | + | 0.525063i | ||||
\(496\) | 3.46410i | 0.155543i | ||||||||
\(497\) | 29.9422i | 1.34309i | ||||||||
\(498\) | − | 22.0742i | − | 0.989170i | ||||||
\(499\) | 16.0309i | 0.717641i | 0.933407 | + | 0.358821i | \(0.116821\pi\) | ||||
−0.933407 | + | 0.358821i | \(0.883179\pi\) | |||||||
\(500\) | 9.00000 | − | 6.63325i | 0.402492 | − | 0.296648i | ||||
\(501\) | 44.1485i | 1.97241i | ||||||||
\(502\) | 22.9783 | 1.02557 | ||||||||
\(503\) | 6.63325i | 0.295762i | 0.989005 | + | 0.147881i | \(0.0472453\pi\) | ||||
−0.989005 | + | 0.147881i | \(0.952755\pi\) | |||||||
\(504\) | −8.00000 | −0.356348 | ||||||||
\(505\) | −32.2337 | + | 6.92820i | −1.43438 | + | 0.308301i | ||||
\(506\) | −10.5109 | −0.467265 | ||||||||
\(507\) | −17.4891 | + | 27.7677i | −0.776719 | + | 1.23321i | ||||
\(508\) | − | 3.46410i | − | 0.153695i | ||||||
\(509\) | 3.16915i | 0.140470i | 0.997530 | + | 0.0702350i | \(0.0223749\pi\) | ||||
−0.997530 | + | 0.0702350i | \(0.977625\pi\) | |||||||
\(510\) | −33.0475 | + | 7.10313i | −1.46337 | + | 0.314532i | ||||
\(511\) | 23.7228 | 1.04944 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.25544 | 0.143731 | ||||||||
\(514\) | − | 14.2063i | − | 0.626611i | ||||||
\(515\) | 4.88316 | + | 22.7190i | 0.215178 | + | 1.00112i | ||||
\(516\) | −1.62772 | −0.0716563 | ||||||||
\(517\) | − | 16.4356i | − | 0.722839i | ||||||
\(518\) | 21.6277 | 0.950267 | ||||||||
\(519\) | −47.7228 | −2.09480 | ||||||||
\(520\) | −0.558422 | + | 8.04290i | −0.0244884 | + | 0.352704i | ||||
\(521\) | 18.6060 | 0.815142 | 0.407571 | − | 0.913173i | \(-0.366376\pi\) | ||||
0.407571 | + | 0.913173i | \(0.366376\pi\) | |||||||
\(522\) | 9.25544 | 0.405099 | ||||||||
\(523\) | − | 10.3923i | − | 0.454424i | −0.973845 | − | 0.227212i | \(-0.927039\pi\) | ||
0.973845 | − | 0.227212i | \(-0.0729610\pi\) | |||||||
\(524\) | −1.62772 | −0.0711072 | ||||||||
\(525\) | 12.3030 | + | 27.2978i | 0.536946 | + | 1.19138i | ||||
\(526\) | 18.0202i | 0.785719i | ||||||||
\(527\) | −20.7446 | −0.903647 | ||||||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | 2.37228 | + | 11.0371i | 0.103045 | + | 0.479422i | ||||
\(531\) | − | 22.3692i | − | 0.970740i | ||||||
\(532\) | 8.21782i | 0.356288i | ||||||||
\(533\) | 34.9783 | + | 10.0974i | 1.51508 | + | 0.437365i | ||||
\(534\) | −4.74456 | −0.205317 | ||||||||
\(535\) | 6.37228 | + | 29.6472i | 0.275498 | + | 1.28176i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | − | 12.3267i | − | 0.531938i | ||||||
\(538\) | −2.74456 | −0.118326 | ||||||||
\(539\) | 2.17448i | 0.0936615i | ||||||||
\(540\) | 0.441578 | + | 2.05446i | 0.0190025 | + | 0.0884097i | ||||
\(541\) | − | 30.5321i | − | 1.31268i | −0.754466 | − | 0.656339i | \(-0.772104\pi\) | ||
0.754466 | − | 0.656339i | \(-0.227896\pi\) | |||||||
\(542\) | − | 21.4294i | − | 0.920472i | ||||||
\(543\) | 8.80773i | 0.377976i | ||||||||
\(544\) | − | 5.98844i | − | 0.256752i | ||||||
\(545\) | −1.32473 | − | 6.16337i | −0.0567454 | − | 0.264010i | ||||
\(546\) | −20.7446 | − | 5.98844i | −0.887785 | − | 0.256282i | ||||
\(547\) | 21.4294i | 0.916256i | 0.888886 | + | 0.458128i | \(0.151480\pi\) | ||||
−0.888886 | + | 0.458128i | \(0.848520\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | 22.7446 | 0.970714 | ||||||||
\(550\) | 3.25544 | + | 7.22316i | 0.138812 | + | 0.307996i | ||||
\(551\) | − | 9.50744i | − | 0.405031i | ||||||
\(552\) | −16.7446 | −0.712696 | ||||||||
\(553\) | −11.2554 | −0.478630 | ||||||||
\(554\) | − | 23.3639i | − | 0.992635i | ||||||
\(555\) | −10.8139 | − | 50.3118i | −0.459023 | − | 2.13562i | ||||
\(556\) | 6.37228 | 0.270245 | ||||||||
\(557\) | 1.11684 | 0.0473222 | 0.0236611 | − | 0.999720i | \(-0.492468\pi\) | ||||
0.0236611 | + | 0.999720i | \(0.492468\pi\) | |||||||
\(558\) | 11.6819i | 0.494535i | ||||||||
\(559\) | −2.23369 | − | 0.644810i | −0.0944749 | − | 0.0272726i | ||||
\(560\) | −5.18614 | + | 1.11469i | −0.219154 | + | 0.0471043i | ||||
\(561\) | − | 23.9538i | − | 1.01133i | ||||||
\(562\) | − | 1.87953i | − | 0.0792831i | ||||||
\(563\) | − | 1.82462i | − | 0.0768988i | −0.999261 | − | 0.0384494i | \(-0.987758\pi\) | ||
0.999261 | − | 0.0384494i | \(-0.0122418\pi\) | |||||||
\(564\) | − | 26.1831i | − | 1.10251i | ||||||
\(565\) | −1.76631 | − | 8.21782i | −0.0743093 | − | 0.345726i | ||||
\(566\) | − | 17.3205i | − | 0.728035i | ||||||
\(567\) | 18.3723 | 0.771563 | ||||||||
\(568\) | 12.6217i | 0.529594i | ||||||||
\(569\) | −16.3723 | −0.686362 | −0.343181 | − | 0.939269i | \(-0.611504\pi\) | ||||
−0.343181 | + | 0.939269i | \(0.611504\pi\) | |||||||
\(570\) | 19.1168 | − | 4.10891i | 0.800716 | − | 0.172103i | ||||
\(571\) | 12.8832 | 0.539143 | 0.269572 | − | 0.962980i | \(-0.413118\pi\) | ||||
0.269572 | + | 0.962980i | \(0.413118\pi\) | |||||||
\(572\) | −5.48913 | − | 1.58457i | −0.229512 | − | 0.0662544i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 23.9538i | 0.999811i | ||||||||
\(575\) | 13.6277 | + | 30.2372i | 0.568315 | + | 1.26098i | ||||
\(576\) | −3.37228 | −0.140512 | ||||||||
\(577\) | −20.9783 | −0.873336 | −0.436668 | − | 0.899623i | \(-0.643842\pi\) | ||||
−0.436668 | + | 0.899623i | \(0.643842\pi\) | |||||||
\(578\) | 18.8614 | 0.784531 | ||||||||
\(579\) | − | 35.3407i | − | 1.46871i | ||||||
\(580\) | 6.00000 | − | 1.28962i | 0.249136 | − | 0.0535486i | ||||
\(581\) | 20.7446 | 0.860629 | ||||||||
\(582\) | − | 17.0256i | − | 0.705732i | ||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | −1.88316 | + | 27.1229i | −0.0778589 | + | 1.12139i | ||||
\(586\) | 2.13859 | 0.0883445 | ||||||||
\(587\) | −19.7228 | −0.814048 | −0.407024 | − | 0.913418i | \(-0.633433\pi\) | ||||
−0.407024 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(588\) | 3.46410i | 0.142857i | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | −3.11684 | − | 14.5012i | −0.128318 | − | 0.597006i | ||||
\(591\) | − | 11.0371i | − | 0.454006i | ||||||
\(592\) | 9.11684 | 0.374700 | ||||||||
\(593\) | −32.2337 | −1.32368 | −0.661839 | − | 0.749646i | \(-0.730224\pi\) | ||||
−0.661839 | + | 0.749646i | \(0.730224\pi\) | |||||||
\(594\) | −1.48913 | −0.0610996 | ||||||||
\(595\) | −6.67527 | − | 31.0569i | −0.273659 | − | 1.27321i | ||||
\(596\) | 17.0256i | 0.697394i | ||||||||
\(597\) | − | 20.1947i | − | 0.826514i | ||||||
\(598\) | −22.9783 | − | 6.63325i | −0.939651 | − | 0.271254i | ||||
\(599\) | 31.7228 | 1.29616 | 0.648080 | − | 0.761573i | \(-0.275572\pi\) | ||||
0.648080 | + | 0.761573i | \(0.275572\pi\) | |||||||
\(600\) | 5.18614 | + | 11.5070i | 0.211723 | + | 0.469771i | ||||
\(601\) | −32.3723 | −1.32049 | −0.660246 | − | 0.751049i | \(-0.729548\pi\) | ||||
−0.660246 | + | 0.751049i | \(0.729548\pi\) | |||||||
\(602\) | − | 1.52967i | − | 0.0623447i | ||||||
\(603\) | 13.4891 | 0.549320 | ||||||||
\(604\) | 7.57301i | 0.308142i | ||||||||
\(605\) | 18.5584 | − | 3.98889i | 0.754507 | − | 0.162171i | ||||
\(606\) | − | 37.2203i | − | 1.51197i | ||||||
\(607\) | − | 3.46410i | − | 0.140604i | −0.997526 | − | 0.0703018i | \(-0.977604\pi\) | ||
0.997526 | − | 0.0703018i | \(-0.0223962\pi\) | |||||||
\(608\) | 3.46410i | 0.140488i | ||||||||
\(609\) | 16.4356i | 0.666006i | ||||||||
\(610\) | 14.7446 | − | 3.16915i | 0.596990 | − | 0.128315i | ||||
\(611\) | 10.3723 | − | 35.9306i | 0.419618 | − | 1.45360i | ||||
\(612\) | − | 20.1947i | − | 0.816322i | ||||||
\(613\) | 19.4891 | 0.787158 | 0.393579 | − | 0.919291i | \(-0.371237\pi\) | ||||
0.393579 | + | 0.919291i | \(0.371237\pi\) | |||||||
\(614\) | 18.2337 | 0.735852 | ||||||||
\(615\) | 55.7228 | − | 11.9769i | 2.24696 | − | 0.482954i | ||||
\(616\) | − | 3.75906i | − | 0.151457i | ||||||
\(617\) | −14.7446 | −0.593594 | −0.296797 | − | 0.954941i | \(-0.595918\pi\) | ||||
−0.296797 | + | 0.954941i | \(0.595918\pi\) | |||||||
\(618\) | −26.2337 | −1.05527 | ||||||||
\(619\) | − | 9.10268i | − | 0.365868i | −0.983125 | − | 0.182934i | \(-0.941441\pi\) | ||
0.983125 | − | 0.182934i | \(-0.0585594\pi\) | |||||||
\(620\) | 1.62772 | + | 7.57301i | 0.0653708 | + | 0.304140i | ||||
\(621\) | −6.23369 | −0.250149 | ||||||||
\(622\) | −3.25544 | −0.130531 | ||||||||
\(623\) | − | 4.45877i | − | 0.178637i | ||||||
\(624\) | −8.74456 | − | 2.52434i | −0.350063 | − | 0.101054i | ||||
\(625\) | 16.5584 | − | 18.7302i | 0.662337 | − | 0.749206i | ||||
\(626\) | − | 12.3267i | − | 0.492675i | ||||||
\(627\) | 13.8564i | 0.553372i | ||||||||
\(628\) | − | 15.1460i | − | 0.604392i | ||||||
\(629\) | 54.5957i | 2.17687i | ||||||||
\(630\) | −17.4891 | + | 3.75906i | −0.696783 | + | 0.149764i | ||||
\(631\) | 40.4443i | 1.61006i | 0.593232 | + | 0.805031i | \(0.297852\pi\) | ||||
−0.593232 | + | 0.805031i | \(0.702148\pi\) | |||||||
\(632\) | −4.74456 | −0.188729 | ||||||||
\(633\) | − | 7.86797i | − | 0.312724i | ||||||
\(634\) | 16.9783 | 0.674292 | ||||||||
\(635\) | −1.62772 | − | 7.57301i | −0.0645940 | − | 0.300526i | ||||
\(636\) | −12.7446 | −0.505355 | ||||||||
\(637\) | −1.37228 | + | 4.75372i | −0.0543718 | + | 0.188349i | ||||
\(638\) | 4.34896i | 0.172177i | ||||||||
\(639\) | 42.5639i | 1.68380i | ||||||||
\(640\) | −2.18614 | + | 0.469882i | −0.0864148 | + | 0.0185737i | ||||
\(641\) | −16.9783 | −0.670601 | −0.335300 | − | 0.942111i | \(-0.608838\pi\) | ||||
−0.335300 | + | 0.942111i | \(0.608838\pi\) | |||||||
\(642\) | −34.2337 | −1.35110 | ||||||||
\(643\) | 37.4891 | 1.47843 | 0.739213 | − | 0.673471i | \(-0.235197\pi\) | ||||
0.739213 | + | 0.673471i | \(0.235197\pi\) | |||||||
\(644\) | − | 15.7359i | − | 0.620083i | ||||||
\(645\) | −3.55842 | + | 0.764836i | −0.140113 | + | 0.0301154i | ||||
\(646\) | −20.7446 | −0.816184 | ||||||||
\(647\) | − | 21.0796i | − | 0.828723i | −0.910112 | − | 0.414362i | \(-0.864005\pi\) | ||
0.910112 | − | 0.414362i | \(-0.135995\pi\) | |||||||
\(648\) | 7.74456 | 0.304235 | ||||||||
\(649\) | 10.5109 | 0.412588 | ||||||||
\(650\) | 2.55842 | + | 17.8453i | 0.100350 | + | 0.699950i | ||||
\(651\) | −20.7446 | −0.813044 | ||||||||
\(652\) | −24.7446 | −0.969072 | ||||||||
\(653\) | 17.0256i | 0.666261i | 0.942881 | + | 0.333131i | \(0.108105\pi\) | ||||
−0.942881 | + | 0.333131i | \(0.891895\pi\) | |||||||
\(654\) | 7.11684 | 0.278291 | ||||||||
\(655\) | −3.55842 | + | 0.764836i | −0.139039 | + | 0.0298846i | ||||
\(656\) | 10.0974i | 0.394235i | ||||||||
\(657\) | 33.7228 | 1.31565 | ||||||||
\(658\) | 24.6060 | 0.959241 | ||||||||
\(659\) | −40.4674 | −1.57639 | −0.788193 | − | 0.615429i | \(-0.788983\pi\) | ||||
−0.788193 | + | 0.615429i | \(0.788983\pi\) | |||||||
\(660\) | −8.74456 | + | 1.87953i | −0.340382 | + | 0.0731605i | ||||
\(661\) | 9.50744i | 0.369797i | 0.982758 | + | 0.184898i | \(0.0591956\pi\) | ||||
−0.982758 | + | 0.184898i | \(0.940804\pi\) | |||||||
\(662\) | − | 10.3923i | − | 0.403908i | ||||||
\(663\) | 15.1168 | − | 52.3663i | 0.587090 | − | 2.03374i | ||||
\(664\) | 8.74456 | 0.339355 | ||||||||
\(665\) | 3.86141 | + | 17.9653i | 0.149739 | + | 0.696665i | ||||
\(666\) | 30.7446 | 1.19133 | ||||||||
\(667\) | 18.2054i | 0.704915i | ||||||||
\(668\) | −17.4891 | −0.676675 | ||||||||
\(669\) | − | 38.1600i | − | 1.47535i | ||||||
\(670\) | 8.74456 | − | 1.87953i | 0.337832 | − | 0.0726125i | ||||
\(671\) | 10.6873i | 0.412577i | ||||||||
\(672\) | − | 5.98844i | − | 0.231009i | ||||||
\(673\) | 9.74749i | 0.375738i | 0.982194 | + | 0.187869i | \(0.0601581\pi\) | ||||
−0.982194 | + | 0.187869i | \(0.939842\pi\) | |||||||
\(674\) | 1.52967i | 0.0589207i | ||||||||
\(675\) | 1.93070 | + | 4.28384i | 0.0743128 | + | 0.164885i | ||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 39.0998i | 1.50273i | 0.659889 | + | 0.751363i | \(0.270603\pi\) | ||||
−0.659889 | + | 0.751363i | \(0.729397\pi\) | |||||||
\(678\) | 9.48913 | 0.364428 | ||||||||
\(679\) | 16.0000 | 0.614024 | ||||||||
\(680\) | −2.81386 | − | 13.0916i | −0.107907 | − | 0.502039i | ||||
\(681\) | − | 13.8564i | − | 0.530979i | ||||||
\(682\) | −5.48913 | −0.210189 | ||||||||
\(683\) | 8.74456 | 0.334601 | 0.167301 | − | 0.985906i | \(-0.446495\pi\) | ||||
0.167301 | + | 0.985906i | \(0.446495\pi\) | |||||||
\(684\) | 11.6819i | 0.446670i | ||||||||
\(685\) | 13.1168 | − | 2.81929i | 0.501169 | − | 0.107720i | ||||
\(686\) | −19.8614 | −0.758312 | ||||||||
\(687\) | −62.8397 | −2.39748 | ||||||||
\(688\) | − | 0.644810i | − | 0.0245832i | ||||||
\(689\) | −17.4891 | − | 5.04868i | −0.666283 | − | 0.192339i | ||||
\(690\) | −36.6060 | + | 7.86797i | −1.39357 | + | 0.299528i | ||||
\(691\) | − | 39.3947i | − | 1.49865i | −0.662204 | − | 0.749323i | \(-0.730379\pi\) | ||
0.662204 | − | 0.749323i | \(-0.269621\pi\) | |||||||
\(692\) | − | 18.9051i | − | 0.718663i | ||||||
\(693\) | − | 12.6766i | − | 0.481544i | ||||||
\(694\) | 20.8395i | 0.791057i | ||||||||
\(695\) | 13.9307 | − | 2.99422i | 0.528422 | − | 0.113577i | ||||
\(696\) | 6.92820i | 0.262613i | ||||||||
\(697\) | −60.4674 | −2.29037 | ||||||||
\(698\) | 27.4728i | 1.03986i | ||||||||
\(699\) | −19.8614 | −0.751227 | ||||||||
\(700\) | −10.8139 | + | 4.87375i | −0.408725 | + | 0.184210i | ||||
\(701\) | 16.9783 | 0.641260 | 0.320630 | − | 0.947205i | \(-0.396105\pi\) | ||||
0.320630 | + | 0.947205i | \(0.396105\pi\) | |||||||
\(702\) | −3.25544 | − | 0.939764i | −0.122869 | − | 0.0354691i | ||||
\(703\) | − | 31.5817i | − | 1.19113i | ||||||
\(704\) | − | 1.58457i | − | 0.0597209i | ||||||
\(705\) | −12.3030 | − | 57.2400i | −0.463357 | − | 2.15578i | ||||
\(706\) | 11.4891 | 0.432399 | ||||||||
\(707\) | 34.9783 | 1.31549 | ||||||||
\(708\) | 16.7446 | 0.629299 | ||||||||
\(709\) | 20.7846i | 0.780582i | 0.920691 | + | 0.390291i | \(0.127626\pi\) | ||||
−0.920691 | + | 0.390291i | \(0.872374\pi\) | |||||||
\(710\) | 5.93070 | + | 27.5928i | 0.222575 | + | 1.03554i | ||||
\(711\) | −16.0000 | −0.600047 | ||||||||
\(712\) | − | 1.87953i | − | 0.0704383i | ||||||
\(713\) | −22.9783 | −0.860542 | ||||||||
\(714\) | 35.8614 | 1.34208 | ||||||||
\(715\) | −12.7446 | − | 0.884861i | −0.476620 | − | 0.0330919i | ||||
\(716\) | 4.88316 | 0.182492 | ||||||||
\(717\) | 23.8614 | 0.891121 | ||||||||
\(718\) | 2.87419i | 0.107264i | ||||||||
\(719\) | −48.0000 | −1.79010 | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | −7.37228 | + | 1.58457i | −0.274749 | + | 0.0590536i | ||||
\(721\) | − | 24.6535i | − | 0.918143i | ||||||
\(722\) | −7.00000 | −0.260513 | ||||||||
\(723\) | −20.7446 | −0.771499 | ||||||||
\(724\) | −3.48913 | −0.129672 | ||||||||
\(725\) | 12.5109 | − | 5.63858i | 0.464642 | − | 0.209412i | ||||
\(726\) | 21.4294i | 0.795320i | ||||||||
\(727\) | 2.17448i | 0.0806470i | 0.999187 | + | 0.0403235i | \(0.0128389\pi\) | ||||
−0.999187 | + | 0.0403235i | \(0.987161\pi\) | |||||||
\(728\) | 2.37228 | − | 8.21782i | 0.0879226 | − | 0.304573i | ||||
\(729\) | 33.2337 | 1.23088 | ||||||||
\(730\) | 21.8614 | − | 4.69882i | 0.809127 | − | 0.173911i | ||||
\(731\) | 3.86141 | 0.142819 | ||||||||
\(732\) | 17.0256i | 0.629283i | ||||||||
\(733\) | −16.0951 | −0.594486 | −0.297243 | − | 0.954802i | \(-0.596067\pi\) | ||||
−0.297243 | + | 0.954802i | \(0.596067\pi\) | |||||||
\(734\) | − | 4.75372i | − | 0.175463i | ||||||
\(735\) | 1.62772 | + | 7.57301i | 0.0600393 | + | 0.279335i | ||||
\(736\) | − | 6.63325i | − | 0.244505i | ||||||
\(737\) | 6.33830i | 0.233474i | ||||||||
\(738\) | 34.0511i | 1.25344i | ||||||||
\(739\) | − | 28.1176i | − | 1.03432i | −0.855888 | − | 0.517161i | \(-0.826989\pi\) | ||
0.855888 | − | 0.517161i | \(-0.173011\pi\) | |||||||
\(740\) | 19.9307 | − | 4.28384i | 0.732667 | − | 0.157477i | ||||
\(741\) | −8.74456 | + | 30.2921i | −0.321240 | + | 1.11281i | ||||
\(742\) | − | 11.9769i | − | 0.439685i | ||||||
\(743\) | 7.11684 | 0.261092 | 0.130546 | − | 0.991442i | \(-0.458327\pi\) | ||||
0.130546 | + | 0.991442i | \(0.458327\pi\) | |||||||
\(744\) | −8.74456 | −0.320591 | ||||||||
\(745\) | 8.00000 | + | 37.2203i | 0.293097 | + | 1.36364i | ||||
\(746\) | 9.50744i | 0.348092i | ||||||||
\(747\) | 29.4891 | 1.07895 | ||||||||
\(748\) | 9.48913 | 0.346957 | ||||||||
\(749\) | − | 32.1716i | − | 1.17552i | ||||||
\(750\) | 16.7446 | + | 22.7190i | 0.611425 | + | 0.829582i | ||||
\(751\) | 25.4891 | 0.930111 | 0.465056 | − | 0.885281i | \(-0.346034\pi\) | ||||
0.465056 | + | 0.885281i | \(0.346034\pi\) | |||||||
\(752\) | 10.3723 | 0.378238 | ||||||||
\(753\) | 58.0049i | 2.11381i | ||||||||
\(754\) | −2.74456 | + | 9.50744i | −0.0999511 | + | 0.346241i | ||||
\(755\) | 3.55842 | + | 16.5557i | 0.129504 | + | 0.602523i | ||||
\(756\) | − | 2.22938i | − | 0.0810819i | ||||||
\(757\) | − | 45.4381i | − | 1.65148i | −0.564055 | − | 0.825738i | \(-0.690759\pi\) | ||
0.564055 | − | 0.825738i | \(-0.309241\pi\) | |||||||
\(758\) | 17.3205i | 0.629109i | ||||||||
\(759\) | − | 26.5330i | − | 0.963087i | ||||||
\(760\) | 1.62772 | + | 7.57301i | 0.0590436 | + | 0.274702i | ||||
\(761\) | 1.87953i | 0.0681328i | 0.999420 | + | 0.0340664i | \(0.0108458\pi\) | ||||
−0.999420 | + | 0.0340664i | \(0.989154\pi\) | |||||||
\(762\) | 8.74456 | 0.316782 | ||||||||
\(763\) | 6.68815i | 0.242127i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.48913 | − | 44.1485i | −0.343080 | − | 1.59619i | ||||
\(766\) | −16.8832 | −0.610013 | ||||||||
\(767\) | 22.9783 | + | 6.63325i | 0.829697 | + | 0.239513i | ||||
\(768\) | − | 2.52434i | − | 0.0910892i | ||||||
\(769\) | − | 16.4356i | − | 0.592685i | −0.955082 | − | 0.296342i | \(-0.904233\pi\) | ||
0.955082 | − | 0.296342i | \(-0.0957669\pi\) | |||||||
\(770\) | −1.76631 | − | 8.21782i | −0.0636535 | − | 0.296150i | ||||
\(771\) | 35.8614 | 1.29152 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | −30.6060 | −1.10082 | −0.550410 | − | 0.834894i | \(-0.685529\pi\) | ||||
−0.550410 | + | 0.834894i | \(0.685529\pi\) | |||||||
\(774\) | − | 2.17448i | − | 0.0781601i | ||||||
\(775\) | 7.11684 | + | 15.7908i | 0.255645 | + | 0.567224i | ||||
\(776\) | 6.74456 | 0.242116 | ||||||||
\(777\) | 54.5957i | 1.95861i | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 34.9783 | 1.25323 | ||||||||
\(780\) | −20.3030 | − | 1.40965i | −0.726963 | − | 0.0504734i | ||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 39.7228 | 1.42048 | ||||||||
\(783\) | 2.57924i | 0.0921745i | ||||||||
\(784\) | −1.37228 | −0.0490100 | ||||||||
\(785\) | −7.11684 | − | 33.1113i | −0.254011 | − | 1.18179i | ||||
\(786\) | − | 4.10891i | − | 0.146560i | ||||||
\(787\) | 44.0000 | 1.56843 | 0.784215 | − | 0.620489i | \(-0.213066\pi\) | ||||
0.784215 | + | 0.620489i | \(0.213066\pi\) | |||||||
\(788\) | 4.37228 | 0.155756 | ||||||||
\(789\) | −45.4891 | −1.61946 | ||||||||
\(790\) | −10.3723 | + | 2.22938i | −0.369029 | + | 0.0793179i | ||||
\(791\) | 8.91754i | 0.317071i | ||||||||
\(792\) | − | 5.34363i | − | 0.189878i | ||||||
\(793\) | −6.74456 | + | 23.3639i | −0.239506 | + | 0.829675i | ||||
\(794\) | −8.51087 | −0.302040 | ||||||||
\(795\) | −27.8614 | + | 5.98844i | −0.988142 | + | 0.212388i | ||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | 25.2434i | 0.894166i | 0.894492 | + | 0.447083i | \(0.147537\pi\) | ||||
−0.894492 | + | 0.447083i | \(0.852463\pi\) | |||||||
\(798\) | −20.7446 | −0.734350 | ||||||||
\(799\) | 62.1138i | 2.19743i | ||||||||
\(800\) | −4.55842 | + | 2.05446i | −0.161165 | + | 0.0726360i | ||||
\(801\) | − | 6.33830i | − | 0.223953i | ||||||
\(802\) | − | 32.1716i | − | 1.13602i | ||||||
\(803\) | 15.8457i | 0.559184i | ||||||||
\(804\) | 10.0974i | 0.356106i | ||||||||
\(805\) | −7.39403 | − | 34.4010i | −0.260605 | − | 1.21247i | ||||
\(806\) | −12.0000 | − | 3.46410i | −0.422682 | − | 0.122018i | ||||
\(807\) | − | 6.92820i | − | 0.243884i | ||||||
\(808\) | 14.7446 | 0.518712 | ||||||||
\(809\) | 39.3505 | 1.38349 | 0.691746 | − | 0.722141i | \(-0.256842\pi\) | ||||
0.691746 | + | 0.722141i | \(0.256842\pi\) | |||||||
\(810\) | 16.9307 | − | 3.63903i | 0.594884 | − | 0.127862i | ||||
\(811\) | − | 41.9740i | − | 1.47391i | −0.675944 | − | 0.736953i | \(-0.736264\pi\) | ||
0.675944 | − | 0.736953i | \(-0.263736\pi\) | |||||||
\(812\) | −6.51087 | −0.228487 | ||||||||
\(813\) | 54.0951 | 1.89720 | ||||||||
\(814\) | 14.4463i | 0.506343i | ||||||||
\(815\) | −54.0951 | + | 11.6270i | −1.89487 | + | 0.407277i | ||||
\(816\) | 15.1168 | 0.529195 | ||||||||
\(817\) | −2.23369 | −0.0781468 | ||||||||
\(818\) | 5.63858i | 0.197148i | ||||||||
\(819\) | 8.00000 | − | 27.7128i | 0.279543 | − | 0.968364i | ||||
\(820\) | 4.74456 | + | 22.0742i | 0.165687 | + | 0.770866i | ||||
\(821\) | − | 25.5932i | − | 0.893210i | −0.894731 | − | 0.446605i | \(-0.852633\pi\) | ||
0.894731 | − | 0.446605i | \(-0.147367\pi\) | |||||||
\(822\) | 15.1460i | 0.528278i | ||||||||
\(823\) | 54.5408i | 1.90117i | 0.310462 | + | 0.950586i | \(0.399516\pi\) | ||||
−0.310462 | + | 0.950586i | \(0.600484\pi\) | |||||||
\(824\) | − | 10.3923i | − | 0.362033i | ||||||
\(825\) | −18.2337 | + | 8.21782i | −0.634816 | + | 0.286108i | ||||
\(826\) | 15.7359i | 0.547523i | ||||||||
\(827\) | 15.2554 | 0.530484 | 0.265242 | − | 0.964182i | \(-0.414548\pi\) | ||||
0.265242 | + | 0.964182i | \(0.414548\pi\) | |||||||
\(828\) | − | 22.3692i | − | 0.777383i | ||||||
\(829\) | −48.2337 | −1.67523 | −0.837613 | − | 0.546265i | \(-0.816049\pi\) | ||||
−0.837613 | + | 0.546265i | \(0.816049\pi\) | |||||||
\(830\) | 19.1168 | − | 4.10891i | 0.663555 | − | 0.142622i | ||||
\(831\) | 58.9783 | 2.04593 | ||||||||
\(832\) | 1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | ||||
\(833\) | − | 8.21782i | − | 0.284731i | ||||||
\(834\) | 16.0858i | 0.557005i | ||||||||
\(835\) | −38.2337 | + | 8.21782i | −1.32313 | + | 0.284390i | ||||
\(836\) | −5.48913 | −0.189845 | ||||||||
\(837\) | −3.25544 | −0.112524 | ||||||||
\(838\) | −19.1168 | −0.660380 | ||||||||
\(839\) | 13.5615i | 0.468193i | 0.972213 | + | 0.234097i | \(0.0752132\pi\) | ||||
−0.972213 | + | 0.234097i | \(0.924787\pi\) | |||||||
\(840\) | −2.81386 | − | 13.0916i | −0.0970874 | − | 0.451702i | ||||
\(841\) | −21.4674 | −0.740254 | ||||||||
\(842\) | − | 11.0371i | − | 0.380364i | ||||||
\(843\) | 4.74456 | 0.163411 | ||||||||
\(844\) | 3.11684 | 0.107286 | ||||||||
\(845\) | −27.3030 | − | 9.97733i | −0.939251 | − | 0.343230i | ||||
\(846\) | 34.9783 | 1.20258 | ||||||||
\(847\) | −20.1386 | −0.691970 | ||||||||
\(848\) | − | 5.04868i | − | 0.173372i | ||||||
\(849\) | 43.7228 | 1.50056 | ||||||||
\(850\) | −12.3030 | − | 27.2978i | −0.421989 | − | 0.936308i | ||||
\(851\) | 60.4743i | 2.07303i | ||||||||
\(852\) | −31.8614 | −1.09155 | ||||||||
\(853\) | −5.11684 | −0.175197 | −0.0875987 | − | 0.996156i | \(-0.527919\pi\) | ||||
−0.0875987 | + | 0.996156i | \(0.527919\pi\) | |||||||
\(854\) | −16.0000 | −0.547509 | ||||||||
\(855\) | 5.48913 | + | 25.5383i | 0.187724 | + | 0.873393i | ||||
\(856\) | − | 13.5615i | − | 0.463521i | ||||||
\(857\) | − | 22.7739i | − | 0.777943i | −0.921250 | − | 0.388972i | \(-0.872830\pi\) | ||
0.921250 | − | 0.388972i | \(-0.127170\pi\) | |||||||
\(858\) | 4.00000 | − | 13.8564i | 0.136558 | − | 0.473050i | ||||
\(859\) | −32.4674 | −1.10777 | −0.553886 | − | 0.832592i | \(-0.686856\pi\) | ||||
−0.553886 | + | 0.832592i | \(0.686856\pi\) | |||||||
\(860\) | −0.302985 | − | 1.40965i | −0.0103317 | − | 0.0480685i | ||||
\(861\) | −60.4674 | −2.06072 | ||||||||
\(862\) | 26.4781i | 0.901848i | ||||||||
\(863\) | 3.86141 | 0.131444 | 0.0657219 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657219 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(864\) | − | 0.939764i | − | 0.0319714i | ||||||
\(865\) | −8.88316 | − | 41.3292i | −0.302036 | − | 1.40523i | ||||
\(866\) | 34.4010i | 1.16899i | ||||||||
\(867\) | 47.6126i | 1.61701i | ||||||||
\(868\) | − | 8.21782i | − | 0.278931i | ||||||
\(869\) | − | 7.51811i | − | 0.255034i | ||||||
\(870\) | 3.25544 | + | 15.1460i | 0.110370 | + | 0.513498i | ||||
\(871\) | −4.00000 | + | 13.8564i | −0.135535 | + | 0.469506i | ||||
\(872\) | 2.81929i | 0.0954733i | ||||||||
\(873\) | 22.7446 | 0.769787 | ||||||||
\(874\) | −22.9783 | −0.777251 | ||||||||
\(875\) | −21.3505 | + | 15.7359i | −0.721780 | + | 0.531972i | ||||
\(876\) | 25.2434i | 0.852895i | ||||||||
\(877\) | 47.3505 | 1.59891 | 0.799457 | − | 0.600723i | \(-0.205121\pi\) | ||||
0.799457 | + | 0.600723i | \(0.205121\pi\) | |||||||
\(878\) | −22.2337 | −0.750351 | ||||||||
\(879\) | 5.39853i | 0.182088i | ||||||||
\(880\) | −0.744563 | − | 3.46410i | −0.0250992 | − | 0.116775i | ||||
\(881\) | −54.6060 | −1.83972 | −0.919861 | − | 0.392245i | \(-0.871699\pi\) | ||||
−0.919861 | + | 0.392245i | \(0.871699\pi\) | |||||||
\(882\) | −4.62772 | −0.155823 | ||||||||
\(883\) | − | 58.6497i | − | 1.97372i | −0.161581 | − | 0.986859i | \(-0.551659\pi\) | ||
0.161581 | − | 0.986859i | \(-0.448341\pi\) | |||||||
\(884\) | 20.7446 | + | 5.98844i | 0.697715 | + | 0.201413i | ||||
\(885\) | 36.6060 | − | 7.86797i | 1.23050 | − | 0.264479i | ||||
\(886\) | 4.40387i | 0.147951i | ||||||||
\(887\) | − | 45.7330i | − | 1.53556i | −0.640711 | − | 0.767782i | \(-0.721360\pi\) | ||
0.640711 | − | 0.767782i | \(-0.278640\pi\) | |||||||
\(888\) | 23.0140i | 0.772299i | ||||||||
\(889\) | 8.21782i | 0.275617i | ||||||||
\(890\) | −0.883156 | − | 4.10891i | −0.0296035 | − | 0.137731i | ||||
\(891\) | 12.2718i | 0.411122i | ||||||||
\(892\) | 15.1168 | 0.506149 | ||||||||
\(893\) | − | 35.9306i | − | 1.20237i | ||||||
\(894\) | −42.9783 | −1.43741 | ||||||||
\(895\) | 10.6753 | − | 2.29451i | 0.356835 | − | 0.0766969i | ||||
\(896\) | 2.37228 | 0.0792524 | ||||||||
\(897\) | 16.7446 | − | 58.0049i | 0.559085 | − | 1.93673i | ||||
\(898\) | − | 7.51811i | − | 0.250883i | ||||||
\(899\) | 9.50744i | 0.317091i | ||||||||
\(900\) | −15.3723 | + | 6.92820i | −0.512409 | + | 0.230940i | ||||
\(901\) | 30.2337 | 1.00723 | ||||||||
\(902\) | −16.0000 | −0.532742 | ||||||||
\(903\) | 3.86141 | 0.128500 | ||||||||
\(904\) | 3.75906i | 0.125024i | ||||||||
\(905\) | −7.62772 | + | 1.63948i | −0.253554 | + | 0.0544981i | ||||
\(906\) | −19.1168 | −0.635115 | ||||||||
\(907\) | − | 0.644810i | − | 0.0214106i | −0.999943 | − | 0.0107053i | \(-0.996592\pi\) | ||
0.999943 | − | 0.0107053i | \(-0.00340766\pi\) | |||||||
\(908\) | 5.48913 | 0.182163 | ||||||||
\(909\) | 49.7228 | 1.64920 | ||||||||
\(910\) | 1.32473 | − | 19.0800i | 0.0439145 | − | 0.632496i | ||||
\(911\) | 34.9783 | 1.15888 | 0.579441 | − | 0.815014i | \(-0.303271\pi\) | ||||
0.579441 | + | 0.815014i | \(0.303271\pi\) | |||||||
\(912\) | −8.74456 | −0.289561 | ||||||||
\(913\) | 13.8564i | 0.458580i | ||||||||
\(914\) | −24.9783 | −0.826207 | ||||||||
\(915\) | 8.00000 | + | 37.2203i | 0.264472 | + | 1.23046i | ||||
\(916\) | − | 24.8935i | − | 0.822505i | ||||||
\(917\) | 3.86141 | 0.127515 | ||||||||
\(918\) | 5.62772 | 0.185742 | ||||||||
\(919\) | 42.9783 | 1.41772 | 0.708861 | − | 0.705348i | \(-0.249209\pi\) | ||||
0.708861 | + | 0.705348i | \(0.249209\pi\) | |||||||
\(920\) | −3.11684 | − | 14.5012i | −0.102759 | − | 0.478091i | ||||
\(921\) | 46.0280i | 1.51667i | ||||||||
\(922\) | − | 1.63948i | − | 0.0539933i | ||||||
\(923\) | −43.7228 | − | 12.6217i | −1.43915 | − | 0.415448i | ||||
\(924\) | 9.48913 | 0.312169 | ||||||||
\(925\) | 41.5584 | − | 18.7302i | 1.36643 | − | 0.615844i | ||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | − | 35.0458i | − | 1.15105i | ||||||
\(928\) | −2.74456 | −0.0900947 | ||||||||
\(929\) | − | 47.9075i | − | 1.57179i | −0.618357 | − | 0.785897i | \(-0.712201\pi\) | ||
0.618357 | − | 0.785897i | \(-0.287799\pi\) | |||||||
\(930\) | −19.1168 | + | 4.10891i | −0.626866 | + | 0.134737i | ||||
\(931\) | 4.75372i | 0.155797i | ||||||||
\(932\) | − | 7.86797i | − | 0.257724i | ||||||
\(933\) | − | 8.21782i | − | 0.269039i | ||||||
\(934\) | − | 27.4179i | − | 0.897140i | ||||||
\(935\) | 20.7446 | − | 4.45877i | 0.678420 | − | 0.145817i | ||||
\(936\) | 3.37228 | − | 11.6819i | 0.110226 | − | 0.381836i | ||||
\(937\) | 30.2921i | 0.989598i | 0.869007 | + | 0.494799i | \(0.164758\pi\) | ||||
−0.869007 | + | 0.494799i | \(0.835242\pi\) | |||||||
\(938\) | −9.48913 | −0.309831 | ||||||||
\(939\) | 31.1168 | 1.01546 | ||||||||
\(940\) | 22.6753 | − | 4.87375i | 0.739586 | − | 0.158964i | ||||
\(941\) | 40.6295i | 1.32448i | 0.749291 | + | 0.662241i | \(0.230395\pi\) | ||||
−0.749291 | + | 0.662241i | \(0.769605\pi\) | |||||||
\(942\) | 38.2337 | 1.24572 | ||||||||
\(943\) | −66.9783 | −2.18111 | ||||||||
\(944\) | 6.63325i | 0.215894i | ||||||||
\(945\) | −1.04755 | − | 4.87375i | −0.0340767 | − | 0.158543i | ||||
\(946\) | 1.02175 | 0.0332199 | ||||||||
\(947\) | −29.4891 | −0.958268 | −0.479134 | − | 0.877742i | \(-0.659049\pi\) | ||||
−0.479134 | + | 0.877742i | \(0.659049\pi\) | |||||||
\(948\) | − | 11.9769i | − | 0.388991i | ||||||
\(949\) | −10.0000 | + | 34.6410i | −0.324614 | + | 1.12449i | ||||
\(950\) | 7.11684 | + | 15.7908i | 0.230901 | + | 0.512322i | ||||
\(951\) | 42.8588i | 1.38979i | ||||||||
\(952\) | 14.2063i | 0.460428i | ||||||||
\(953\) | − | 16.0858i | − | 0.521070i | −0.965464 | − | 0.260535i | \(-0.916101\pi\) | ||
0.965464 | − | 0.260535i | \(-0.0838989\pi\) | |||||||
\(954\) | − | 17.0256i | − | 0.551223i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.45254i | 0.305717i | ||||||||
\(957\) | −10.9783 | −0.354876 | ||||||||
\(958\) | 18.2603i | 0.589963i | ||||||||
\(959\) | −14.2337 | −0.459630 | ||||||||
\(960\) | −1.18614 | − | 5.51856i | −0.0382825 | − | 0.178111i | ||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −9.11684 | + | 31.5817i | −0.293939 | + | 1.01823i | ||||
\(963\) | − | 45.7330i | − | 1.47373i | ||||||
\(964\) | − | 8.21782i | − | 0.264678i | ||||||
\(965\) | 30.6060 | − | 6.57835i | 0.985241 | − | 0.211764i | ||||
\(966\) | 39.7228 | 1.27806 | ||||||||
\(967\) | 5.35053 | 0.172062 | 0.0860308 | − | 0.996292i | \(-0.472582\pi\) | ||||
0.0860308 | + | 0.996292i | \(0.472582\pi\) | |||||||
\(968\) | −8.48913 | −0.272851 | ||||||||
\(969\) | − | 52.3663i | − | 1.68225i | ||||||
\(970\) | 14.7446 | − | 3.16915i | 0.473419 | − | 0.101755i | ||||
\(971\) | −12.6060 | −0.404545 | −0.202272 | − | 0.979329i | \(-0.564833\pi\) | ||||
−0.202272 | + | 0.979329i | \(0.564833\pi\) | |||||||
\(972\) | 22.3692i | 0.717492i | ||||||||
\(973\) | −15.1168 | −0.484624 | ||||||||
\(974\) | −1.48913 | −0.0477147 | ||||||||
\(975\) | −45.0475 | + | 6.45832i | −1.44268 | + | 0.206832i | ||||
\(976\) | −6.74456 | −0.215888 | ||||||||
\(977\) | −25.7228 | −0.822946 | −0.411473 | − | 0.911422i | \(-0.634986\pi\) | ||||
−0.411473 | + | 0.911422i | \(0.634986\pi\) | |||||||
\(978\) | − | 62.4636i | − | 1.99737i | ||||||
\(979\) | 2.97825 | 0.0951853 | ||||||||
\(980\) | −3.00000 | + | 0.644810i | −0.0958315 | + | 0.0205977i | ||||
\(981\) | 9.50744i | 0.303549i | ||||||||
\(982\) | 25.6277 | 0.817813 | ||||||||
\(983\) | 42.0951 | 1.34263 | 0.671313 | − | 0.741174i | \(-0.265731\pi\) | ||||
0.671313 | + | 0.741174i | \(0.265731\pi\) | |||||||
\(984\) | −25.4891 | −0.812564 | ||||||||
\(985\) | 9.55842 | − | 2.05446i | 0.304557 | − | 0.0654604i | ||||
\(986\) | − | 16.4356i | − | 0.523418i | ||||||
\(987\) | 62.1138i | 1.97710i | ||||||||
\(988\) | −12.0000 | − | 3.46410i | −0.381771 | − | 0.110208i | ||||
\(989\) | 4.27719 | 0.136007 | ||||||||
\(990\) | −2.51087 | − | 11.6819i | −0.0798008 | − | 0.371276i | ||||
\(991\) | −1.76631 | −0.0561088 | −0.0280544 | − | 0.999606i | \(-0.508931\pi\) | ||||
−0.0280544 | + | 0.999606i | \(0.508931\pi\) | |||||||
\(992\) | − | 3.46410i | − | 0.109985i | ||||||
\(993\) | 26.2337 | 0.832501 | ||||||||
\(994\) | − | 29.9422i | − | 0.949709i | ||||||
\(995\) | 17.4891 | − | 3.75906i | 0.554443 | − | 0.119170i | ||||
\(996\) | 22.0742i | 0.699449i | ||||||||
\(997\) | − | 4.34896i | − | 0.137733i | −0.997626 | − | 0.0688665i | \(-0.978062\pi\) | ||
0.997626 | − | 0.0688665i | \(-0.0219383\pi\) | |||||||
\(998\) | − | 16.0309i | − | 0.507449i | ||||||
\(999\) | 8.56768i | 0.271069i |
(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 | 130.2.c.a.129.1 | ✓ | 4 | |
3.2 | odd | 2 | 1170.2.f.b.649.2 | 4 | |||
4.3 | odd | 2 | 1040.2.f.d.129.4 | 4 | |||
5.2 | odd | 4 | 650.2.d.e.51.1 | 8 | |||
5.3 | odd | 4 | 650.2.d.e.51.8 | 8 | |||
5.4 | even | 2 | 130.2.c.b.129.4 | yes | 4 | ||
13.5 | odd | 4 | 1690.2.b.d.339.5 | 8 | |||
13.8 | odd | 4 | 1690.2.b.d.339.1 | 8 | |||
13.12 | even | 2 | 130.2.c.b.129.1 | yes | 4 | ||
15.14 | odd | 2 | 1170.2.f.a.649.4 | 4 | |||
20.19 | odd | 2 | 1040.2.f.c.129.1 | 4 | |||
39.38 | odd | 2 | 1170.2.f.a.649.3 | 4 | |||
52.51 | odd | 2 | 1040.2.f.c.129.4 | 4 | |||
65.8 | even | 4 | 8450.2.a.cj.1.4 | 4 | |||
65.12 | odd | 4 | 650.2.d.e.51.5 | 8 | |||
65.18 | even | 4 | 8450.2.a.cn.1.4 | 4 | |||
65.34 | odd | 4 | 1690.2.b.d.339.8 | 8 | |||
65.38 | odd | 4 | 650.2.d.e.51.4 | 8 | |||
65.44 | odd | 4 | 1690.2.b.d.339.4 | 8 | |||
65.47 | even | 4 | 8450.2.a.cn.1.1 | 4 | |||
65.57 | even | 4 | 8450.2.a.cj.1.1 | 4 | |||
65.64 | even | 2 | inner | 130.2.c.a.129.4 | yes | 4 | |
195.194 | odd | 2 | 1170.2.f.b.649.1 | 4 | |||
260.259 | odd | 2 | 1040.2.f.d.129.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.c.a.129.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
130.2.c.a.129.4 | yes | 4 | 65.64 | even | 2 | inner | |
130.2.c.b.129.1 | yes | 4 | 13.12 | even | 2 | ||
130.2.c.b.129.4 | yes | 4 | 5.4 | even | 2 | ||
650.2.d.e.51.1 | 8 | 5.2 | odd | 4 | |||
650.2.d.e.51.4 | 8 | 65.38 | odd | 4 | |||
650.2.d.e.51.5 | 8 | 65.12 | odd | 4 | |||
650.2.d.e.51.8 | 8 | 5.3 | odd | 4 | |||
1040.2.f.c.129.1 | 4 | 20.19 | odd | 2 | |||
1040.2.f.c.129.4 | 4 | 52.51 | odd | 2 | |||
1040.2.f.d.129.1 | 4 | 260.259 | odd | 2 | |||
1040.2.f.d.129.4 | 4 | 4.3 | odd | 2 | |||
1170.2.f.a.649.3 | 4 | 39.38 | odd | 2 | |||
1170.2.f.a.649.4 | 4 | 15.14 | odd | 2 | |||
1170.2.f.b.649.1 | 4 | 195.194 | odd | 2 | |||
1170.2.f.b.649.2 | 4 | 3.2 | odd | 2 | |||
1690.2.b.d.339.1 | 8 | 13.8 | odd | 4 | |||
1690.2.b.d.339.4 | 8 | 65.44 | odd | 4 | |||
1690.2.b.d.339.5 | 8 | 13.5 | odd | 4 | |||
1690.2.b.d.339.8 | 8 | 65.34 | odd | 4 | |||
8450.2.a.cj.1.1 | 4 | 65.57 | even | 4 | |||
8450.2.a.cj.1.4 | 4 | 65.8 | even | 4 | |||
8450.2.a.cn.1.1 | 4 | 65.47 | even | 4 | |||
8450.2.a.cn.1.4 | 4 | 65.18 | even | 4 |