Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(49,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bv (of order \(6\), degree \(2\), 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.433 |
Dual form | 624.2.bv.e.49.2 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.267949i | − | 0.119831i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) | ||
0.998203 | − | 0.0599153i | \(-0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.633975 | + | 0.366025i | −0.239620 | + | 0.138345i | −0.615002 | − | 0.788526i | \(-0.710845\pi\) |
0.375382 | + | 0.926870i | \(0.377511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.09808 | + | 2.36603i | 1.23562 | + | 0.713384i | 0.968195 | − | 0.250196i | \(-0.0804951\pi\) |
0.267421 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | − | 2.50000i | 0.720577 | − | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.232051 | − | 0.133975i | −0.0599153 | − | 0.0345921i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.13397 | − | 1.96410i | −0.275029 | − | 0.476365i | 0.695113 | − | 0.718900i | \(-0.255354\pi\) |
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09808 | − | 0.633975i | 0.251916 | − | 0.145444i | −0.368725 | − | 0.929538i | \(-0.620206\pi\) |
0.620641 | + | 0.784095i | \(0.286872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051i | 0.159747i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09808 | − | 5.36603i | 0.645994 | − | 1.11889i | −0.338078 | − | 0.941118i | \(-0.609777\pi\) |
0.984071 | − | 0.177775i | \(-0.0568901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.92820 | 0.985641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.23205 | + | 2.13397i | −0.228786 | + | 0.396269i | −0.957449 | − | 0.288604i | \(-0.906809\pi\) |
0.728663 | + | 0.684873i | \(0.240142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.46410i | − | 0.981382i | −0.871334 | − | 0.490691i | \(-0.836744\pi\) | ||
0.871334 | − | 0.490691i | \(-0.163256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.09808 | − | 2.36603i | 0.713384 | − | 0.411872i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0980762 | + | 0.169873i | 0.0165779 | + | 0.0287138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.06218 | − | 5.23205i | −1.48981 | − | 0.860144i | −0.489881 | − | 0.871789i | \(-0.662960\pi\) |
−0.999932 | + | 0.0116456i | \(0.996293\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.866025 | − | 3.50000i | −0.138675 | − | 0.560449i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.86603 | + | 5.69615i | 1.54081 | + | 0.889590i | 0.998788 | + | 0.0492283i | \(0.0156762\pi\) |
0.542027 | + | 0.840361i | \(0.317657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83013 | − | 6.63397i | −0.584089 | − | 1.01167i | −0.994988 | − | 0.0999910i | \(-0.968119\pi\) |
0.410899 | − | 0.911681i | \(-0.365215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.232051 | + | 0.133975i | −0.0345921 | + | 0.0199718i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.19615i | 1.19553i | 0.801671 | + | 0.597766i | \(0.203945\pi\) | ||||
−0.801671 | + | 0.597766i | \(0.796055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23205 | + | 5.59808i | −0.461722 | + | 0.799725i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.26795 | −0.317576 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.464102 | 0.0637493 | 0.0318746 | − | 0.999492i | \(-0.489852\pi\) | ||||
0.0318746 | + | 0.999492i | \(0.489852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.633975 | − | 1.09808i | 0.0854851 | − | 0.148065i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.26795i | − | 0.167944i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | + | 4.00000i | −0.901975 | + | 0.520756i | −0.877841 | − | 0.478953i | \(-0.841016\pi\) |
−0.0241347 | + | 0.999709i | \(0.507683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.598076 | − | 1.03590i | −0.0765758 | − | 0.132633i | 0.825195 | − | 0.564848i | \(-0.191065\pi\) |
−0.901770 | + | 0.432215i | \(0.857732\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.633975 | + | 0.366025i | 0.0798733 | + | 0.0461149i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.669873 | − | 0.696152i | −0.0830875 | − | 0.0863471i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.63397 | + | 5.56218i | 1.17698 | + | 0.679528i | 0.955313 | − | 0.295595i | \(-0.0955179\pi\) |
0.221664 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09808 | − | 5.36603i | −0.372965 | − | 0.645994i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.09808 | − | 0.633975i | 0.130318 | − | 0.0752389i | −0.433424 | − | 0.901190i | \(-0.642695\pi\) |
0.563742 | + | 0.825951i | \(0.309361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.73205i | − | 1.13905i | −0.821974 | − | 0.569525i | \(-0.807127\pi\) | ||
0.821974 | − | 0.569525i | \(-0.192873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.46410 | − | 4.26795i | 0.284530 | − | 0.492820i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | −0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.46410 | 1.06479 | 0.532397 | − | 0.846495i | \(-0.321291\pi\) | ||||
0.532397 | + | 0.846495i | \(0.321291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1962i | 1.11917i | 0.828772 | + | 0.559587i | \(0.189040\pi\) | ||||
−0.828772 | + | 0.559587i | \(0.810960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.526279 | + | 0.303848i | −0.0570830 | + | 0.0329569i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.23205 | + | 2.13397i | 0.132090 | + | 0.228786i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.19615 | + | 1.26795i | 0.232792 | + | 0.134402i | 0.611859 | − | 0.790967i | \(-0.290422\pi\) |
−0.379068 | + | 0.925369i | \(0.623755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.732051 | + | 2.53590i | −0.0767398 | + | 0.265834i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.73205 | − | 2.73205i | −0.490691 | − | 0.283300i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.169873 | − | 0.294229i | −0.0174286 | − | 0.0301872i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.19615 | − | 3.00000i | 0.527589 | − | 0.304604i | −0.212445 | − | 0.977173i | \(-0.568143\pi\) |
0.740034 | + | 0.672569i | \(0.234809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.73205i | − | 0.475589i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.96410 | + | 10.3301i | −0.593450 | + | 1.02789i | 0.400313 | + | 0.916378i | \(0.368901\pi\) |
−0.993764 | + | 0.111508i | \(0.964432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.7321 | −1.84572 | −0.922862 | − | 0.385131i | \(-0.874156\pi\) | ||||
−0.922862 | + | 0.385131i | \(0.874156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.196152 | 0.0191425 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0980762 | + | 0.169873i | −0.00948139 | + | 0.0164222i | −0.870727 | − | 0.491766i | \(-0.836351\pi\) |
0.861246 | + | 0.508189i | \(0.169685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.46410i | 0.523366i | 0.965154 | + | 0.261683i | \(0.0842775\pi\) | ||||
−0.965154 | + | 0.261683i | \(0.915723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.06218 | + | 5.23205i | −0.860144 | + | 0.496604i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.33013 | + | 16.1603i | 0.877705 | + | 1.52023i | 0.853854 | + | 0.520513i | \(0.174259\pi\) |
0.0238510 | + | 0.999716i | \(0.492407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.43782 | − | 0.830127i | −0.134078 | − | 0.0774097i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.46410 | − | 1.00000i | −0.320256 | − | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.43782 | + | 0.830127i | 0.131805 | + | 0.0760976i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.69615 | + | 9.86603i | 0.517832 | + | 0.896911i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.86603 | − | 5.69615i | 0.889590 | − | 0.513605i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.66025i | − | 0.237940i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.92820 | + | 15.4641i | −0.792250 | + | 1.37222i | 0.132321 | + | 0.991207i | \(0.457757\pi\) |
−0.924571 | + | 0.381010i | \(0.875576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.66025 | −0.674448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4641 | −1.17636 | −0.588182 | − | 0.808729i | \(-0.700156\pi\) | ||||
−0.588182 | + | 0.808729i | \(0.700156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.464102 | + | 0.803848i | −0.0402427 | + | 0.0697024i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.267949i | 0.0230614i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.66987 | + | 0.964102i | −0.142667 | + | 0.0823688i | −0.569634 | − | 0.821898i | \(-0.692915\pi\) |
0.426968 | + | 0.904267i | \(0.359582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.92820 | − | 8.53590i | −0.418005 | − | 0.724005i | 0.577734 | − | 0.816225i | \(-0.303937\pi\) |
−0.995739 | + | 0.0922197i | \(0.970604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.09808 | + | 4.09808i | 0.597766 | + | 0.345120i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.5622 | − | 4.09808i | 1.38500 | − | 0.342698i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.571797 | + | 0.330127i | 0.0474851 | + | 0.0274156i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.23205 | + | 5.59808i | 0.266575 | + | 0.461722i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.42820 | + | 1.40192i | −0.198926 | + | 0.114850i | −0.596154 | − | 0.802870i | \(-0.703305\pi\) |
0.397228 | + | 0.917720i | \(0.369972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.26795i | − | 0.265942i | −0.991120 | − | 0.132971i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132971i | \(-0.0424517\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.13397 | + | 1.96410i | −0.0916764 | + | 0.158788i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.5885 | −1.88256 | −0.941282 | − | 0.337622i | \(-0.890378\pi\) | ||||
−0.941282 | + | 0.337622i | \(0.890378\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.232051 | − | 0.401924i | 0.0184028 | − | 0.0318746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.53590i | 0.357479i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.66025 | − | 3.26795i | 0.443345 | − | 0.255966i | −0.261670 | − | 0.965157i | \(-0.584273\pi\) |
0.705016 | + | 0.709192i | \(0.250940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.633975 | − | 1.09808i | −0.0493549 | − | 0.0854851i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.19615 | − | 1.26795i | −0.169943 | − | 0.0981169i | 0.412616 | − | 0.910905i | \(-0.364615\pi\) |
−0.582559 | + | 0.812788i | \(0.697949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | − | 12.9904i | 0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.09808 | − | 0.633975i | −0.0839720 | − | 0.0484812i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.19615 | − | 14.1962i | −0.623142 | − | 1.07931i | −0.988897 | − | 0.148602i | \(-0.952523\pi\) |
0.365755 | − | 0.930711i | \(-0.380811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12436 | + | 1.80385i | −0.236179 | + | 0.136358i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000i | 0.601317i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0263 | + | 19.0981i | −0.824143 | + | 1.42746i | 0.0784298 | + | 0.996920i | \(0.475009\pi\) |
−0.902573 | + | 0.430538i | \(0.858324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.80385 | −0.654385 | −0.327192 | − | 0.944958i | \(-0.606103\pi\) | ||||
−0.327192 | + | 0.944958i | \(0.606103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.19615 | −0.0884221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.40192 | + | 2.42820i | −0.103071 | + | 0.178525i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.7321i | − | 0.784805i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.633975 | − | 0.366025i | 0.0461149 | − | 0.0266244i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.46410 | + | 6.00000i | 0.250654 | + | 0.434145i | 0.963706 | − | 0.266966i | \(-0.0860212\pi\) |
−0.713052 | + | 0.701111i | \(0.752688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.16025 | + | 4.13397i | 0.515406 | + | 0.297570i | 0.735053 | − | 0.678009i | \(-0.237157\pi\) |
−0.219647 | + | 0.975579i | \(0.570490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.937822 | + | 0.232051i | −0.0671588 | + | 0.0166175i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.53590 | + | 4.92820i | 0.608158 | + | 0.351120i | 0.772244 | − | 0.635326i | \(-0.219134\pi\) |
−0.164086 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90192 | + | 3.29423i | 0.134824 | + | 0.233522i | 0.925530 | − | 0.378674i | \(-0.123620\pi\) |
−0.790706 | + | 0.612196i | \(0.790286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.63397 | − | 5.56218i | 0.679528 | − | 0.392326i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.80385i | − | 0.126605i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52628 | − | 2.64359i | 0.106600 | − | 0.184637i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.19615 | −0.430662 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.19615 | + | 3.80385i | −0.151189 | + | 0.261868i | −0.931665 | − | 0.363319i | \(-0.881644\pi\) |
0.780476 | + | 0.625186i | \(0.214977\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.26795i | − | 0.0868784i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.77757 | + | 1.02628i | −0.121229 | + | 0.0699917i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | + | 3.46410i | 0.135769 | + | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.42820 | − | 4.86603i | −0.569525 | − | 0.328816i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.85641 | − | 2.26795i | −0.528479 | − | 0.152559i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3205 | + | 6.53590i | 0.758077 | + | 0.437676i | 0.828605 | − | 0.559834i | \(-0.189135\pi\) |
−0.0705277 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | − | 4.26795i | −0.164273 | − | 0.284530i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.56218 | + | 0.901924i | −0.103685 | + | 0.0598628i | −0.550946 | − | 0.834541i | \(-0.685733\pi\) |
0.447261 | + | 0.894404i | \(0.352400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8564i | 1.04782i | 0.851773 | + | 0.523910i | \(0.175527\pi\) | ||||
−0.851773 | + | 0.523910i | \(0.824473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.73205 | + | 3.00000i | −0.113961 | + | 0.197386i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8564 | −1.30084 | −0.650418 | − | 0.759576i | \(-0.725406\pi\) | ||||
−0.650418 | + | 0.759576i | \(0.725406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.19615 | 0.143261 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.73205 | − | 8.19615i | 0.307380 | − | 0.532397i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.66025i | − | 0.624870i | −0.949939 | − | 0.312435i | \(-0.898855\pi\) | ||
0.949939 | − | 0.312435i | \(-0.101145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2321 | + | 8.79423i | −0.981183 | + | 0.566486i | −0.902627 | − | 0.430424i | \(-0.858364\pi\) |
−0.0785557 | + | 0.996910i | \(0.525031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.50000 | + | 0.866025i | 0.0958315 | + | 0.0553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.26795 | − | 4.39230i | 0.0806777 | − | 0.279476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.83013 | + | 5.09808i | 0.559587 | + | 0.323077i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.26795 | − | 5.66025i | −0.206271 | − | 0.357272i | 0.744266 | − | 0.667883i | \(-0.232800\pi\) |
−0.950537 | + | 0.310611i | \(0.899466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.3923 | − | 14.6603i | 1.59640 | − | 0.921682i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.607695i | 0.0380553i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3301 | − | 23.0885i | 0.831510 | − | 1.44022i | −0.0653297 | − | 0.997864i | \(-0.520810\pi\) |
0.896840 | − | 0.442355i | \(-0.145857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.66025 | 0.475985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.46410 | 0.152524 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.0263 | − | 24.2942i | 0.864897 | − | 1.49805i | −0.00225153 | − | 0.999997i | \(-0.500717\pi\) |
0.867149 | − | 0.498049i | \(-0.165950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.124356i | − | 0.00763911i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19615 | − | 1.26795i | 0.134402 | − | 0.0775972i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.732051 | + | 1.26795i | 0.0446339 | + | 0.0773082i | 0.887479 | − | 0.460848i | \(-0.152455\pi\) |
−0.842845 | + | 0.538156i | \(0.819121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07180 | + | 2.92820i | 0.308090 | + | 0.177876i | 0.646071 | − | 0.763277i | \(-0.276411\pi\) |
−0.337982 | + | 0.941153i | \(0.609744\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.83013 | + | 1.90192i | 0.110764 | + | 0.115110i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.1962 | + | 11.6603i | 1.21787 | + | 0.703140i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.13397 | − | 1.96410i | −0.0681339 | − | 0.118011i | 0.829946 | − | 0.557844i | \(-0.188371\pi\) |
−0.898080 | + | 0.439832i | \(0.855038\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.73205 | + | 2.73205i | −0.283300 | + | 0.163564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.3205i | − | 1.33153i | −0.746162 | − | 0.665765i | \(-0.768105\pi\) | ||
0.746162 | − | 0.665765i | \(-0.231895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16987 | + | 7.22243i | −0.247873 | + | 0.429329i | −0.962936 | − | 0.269732i | \(-0.913065\pi\) |
0.715062 | + | 0.699061i | \(0.246398\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.339746 | −0.0201248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.33975 | −0.492280 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.92820 | − | 10.2679i | 0.348718 | − | 0.603997i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.00000i | − | 0.351726i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.5718 | + | 7.25833i | −0.734452 | + | 0.424036i | −0.820049 | − | 0.572294i | \(-0.806054\pi\) |
0.0855965 | + | 0.996330i | \(0.472720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.07180 | + | 1.85641i | 0.0624024 | + | 0.108084i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.09808 | − | 2.36603i | −0.237795 | − | 0.137291i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.36603 | − | 21.6865i | −0.310325 | − | 1.25416i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.85641 | + | 2.80385i | 0.279919 | + | 0.161611i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.96410 | + | 10.3301i | 0.342629 | + | 0.593450i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.277568 | + | 0.160254i | −0.0158935 | + | 0.00917612i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.58846i | − | 0.490169i | −0.969502 | − | 0.245085i | \(-0.921184\pi\) | ||
0.969502 | − | 0.245085i | \(-0.0788157\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.36603 | + | 16.2224i | −0.532815 | + | 0.922862i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6603 | 0.888012 | 0.444006 | − | 0.896024i | \(-0.353557\pi\) | ||||
0.444006 | + | 0.896024i | \(0.353557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4641 | 0.761036 | 0.380518 | − | 0.924774i | \(-0.375746\pi\) | ||||
0.380518 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0980762 | − | 0.169873i | 0.00552597 | − | 0.00957126i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.33975i | − | 0.187579i | −0.995592 | − | 0.0937894i | \(-0.970102\pi\) | ||
0.995592 | − | 0.0937894i | \(-0.0298980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0981 | + | 5.83013i | −0.565384 | + | 0.326424i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0980762 | + | 0.169873i | 0.00547408 | + | 0.00948139i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.49038 | − | 1.43782i | −0.138569 | − | 0.0800026i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8038 | − | 12.3205i | 0.710230 | − | 0.683419i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.73205 | + | 2.73205i | 0.261683 | + | 0.151083i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205 | − | 10.0000i | 0.952021 | − | 0.549650i | 0.0583130 | − | 0.998298i | \(-0.481428\pi\) |
0.893708 | + | 0.448649i | \(0.148095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.4641i | 0.573429i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.49038 | − | 2.58142i | 0.0814282 | − | 0.141038i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.85641 | −0.373492 | −0.186746 | − | 0.982408i | \(-0.559794\pi\) | ||||
−0.186746 | + | 0.982408i | \(0.559794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6603 | 1.01349 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9282 | − | 22.3923i | 0.700101 | − | 1.21261i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.85641i | − | 0.532196i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.43782 | + | 0.830127i | −0.0774097 | + | 0.0446925i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.43782 | + | 7.68653i | 0.238235 | + | 0.412635i | 0.960208 | − | 0.279286i | \(-0.0900979\pi\) |
−0.721973 | + | 0.691921i | \(0.756765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7321 | + | 9.66025i | 0.895646 | + | 0.517102i | 0.875785 | − | 0.482701i | \(-0.160344\pi\) |
0.0198610 | + | 0.999803i | \(0.493678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59808 | + | 2.50000i | −0.138675 | + | 0.133440i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.1340 | + | 9.89230i | 0.911949 | + | 0.526514i | 0.881058 | − | 0.473008i | \(-0.156832\pi\) |
0.0308916 | + | 0.999523i | \(0.490165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.169873 | − | 0.294229i | −0.00901592 | − | 0.0156160i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.43782 | − | 0.830127i | 0.0760976 | − | 0.0439350i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.1244i | − | 1.22046i | −0.792226 | − | 0.610228i | \(-0.791078\pi\) | ||
0.792226 | − | 0.610228i | \(-0.208922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.69615 | + | 15.0622i | −0.457692 | + | 0.792746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3923 | 0.597941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.60770 | −0.136493 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.36603 | + | 12.7583i | −0.384503 | + | 0.665979i | −0.991700 | − | 0.128572i | \(-0.958961\pi\) |
0.607197 | + | 0.794551i | \(0.292294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 11.3923i | − | 0.593060i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.294229 | + | 0.169873i | −0.0152756 | + | 0.00881937i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.13397 | + | 8.89230i | 0.265827 | + | 0.460426i | 0.967780 | − | 0.251797i | \(-0.0810216\pi\) |
−0.701953 | + | 0.712223i | \(0.747688\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.30385 | − | 1.33013i | −0.118970 | − | 0.0686875i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.13397 | + | 8.62436i | 0.109905 | + | 0.444177i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.26795 | − | 0.732051i | −0.0651302 | − | 0.0376029i | 0.467081 | − | 0.884214i | \(-0.345306\pi\) |
−0.532211 | + | 0.846611i | \(0.678639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.92820 | + | 15.4641i | 0.457406 | + | 0.792250i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.73205 | − | 2.73205i | 0.241797 | − | 0.139601i | −0.374206 | − | 0.927346i | \(-0.622085\pi\) |
0.616002 | + | 0.787744i | \(0.288751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.928203i | 0.0473056i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.83013 | + | 6.63397i | −0.194696 | + | 0.337224i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.7846 | 1.51014 | 0.755070 | − | 0.655644i | \(-0.227603\pi\) | ||||
0.755070 | + | 0.655644i | \(0.227603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0526 | −0.710668 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.73205 | + | 11.6603i | −0.339587 | + | 0.588182i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2.53590i | − | 0.127595i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.339746 | + | 0.196152i | −0.0170514 | + | 0.00984461i | −0.508501 | − | 0.861061i | \(-0.669800\pi\) |
0.491450 | + | 0.870906i | \(0.336467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.464102 | + | 0.803848i | 0.0232341 | + | 0.0402427i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.9904 | − | 10.9641i | −0.948334 | − | 0.547521i | −0.0557713 | − | 0.998444i | \(-0.517762\pi\) |
−0.892563 | + | 0.450922i | \(0.851095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6603 | − | 14.1962i | −0.680466 | − | 0.707161i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.232051 | + | 0.133975i | 0.0115307 | + | 0.00665725i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.7583 | − | 42.8827i | −1.22722 | − | 2.12562i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3564 | + | 7.13397i | −0.610985 | + | 0.352752i | −0.773351 | − | 0.633978i | \(-0.781421\pi\) |
0.162366 | + | 0.986731i | \(0.448088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.92820i | 0.0951113i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.92820 | − | 5.07180i | 0.144087 | − | 0.249567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.73205 | 0.134111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.85641 | −0.482670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.26795 | + | 9.12436i | −0.257356 | + | 0.445754i | −0.965533 | − | 0.260281i | \(-0.916185\pi\) |
0.708177 | + | 0.706035i | \(0.249518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.7128i | − | 1.59432i | −0.603765 | − | 0.797162i | \(-0.706333\pi\) | ||
0.603765 | − | 0.797162i | \(-0.293667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.09808 | − | 4.09808i | 0.345120 | − | 0.199255i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.58846 | − | 9.67949i | −0.271080 | − | 0.469524i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.758330 | + | 0.437822i | 0.0366982 | + | 0.0211877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.73205 | − | 16.3923i | 0.228466 | − | 0.791428i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.63397 | + | 5.56218i | 0.464052 | + | 0.267921i | 0.713747 | − | 0.700404i | \(-0.246997\pi\) |
−0.249694 | + | 0.968325i | \(0.580330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.42820 | − | 12.8660i | −0.356977 | − | 0.618302i | 0.630478 | − | 0.776208i | \(-0.282859\pi\) |
−0.987454 | + | 0.157906i | \(0.949526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.571797 | − | 0.330127i | 0.0274156 | − | 0.0158284i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7.85641i | − | 0.375823i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.83013 | − | 15.2942i | 0.421439 | − | 0.729954i | −0.574642 | − | 0.818405i | \(-0.694859\pi\) |
0.996080 | + | 0.0884515i | \(0.0281918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.46410 | 0.307814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.3923 | −1.72905 | −0.864525 | − | 0.502589i | \(-0.832381\pi\) | ||||
−0.864525 | + | 0.502589i | \(0.832381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.339746 | − | 0.588457i | 0.0161055 | − | 0.0278955i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.80385i | 0.132617i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.1962 | + | 11.6603i | −0.953115 | + | 0.550281i | −0.894047 | − | 0.447973i | \(-0.852146\pi\) |
−0.0590680 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.9545 | + | 46.6865i | 1.26924 | + | 2.19838i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.83013 | − | 1.63397i | −0.132971 | − | 0.0767708i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.679492 | + | 0.196152i | 0.0318551 | + | 0.00919577i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.1603 | + | 9.33013i | 0.755945 | + | 0.436445i | 0.827838 | − | 0.560967i | \(-0.189571\pi\) |
−0.0718931 | + | 0.997412i | \(0.522904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.13397 | + | 1.96410i | 0.0529294 | + | 0.0916764i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.2846 | + | 12.8660i | −1.03790 | + | 0.599231i | −0.919237 | − | 0.393704i | \(-0.871193\pi\) |
−0.118661 | + | 0.992935i | \(0.537860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0526i | 1.30371i | 0.758342 | + | 0.651856i | \(0.226010\pi\) | ||||
−0.758342 | + | 0.651856i | \(0.773990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.732051 | + | 1.26795i | −0.0339480 | + | 0.0587997i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.5885 | −0.582524 | −0.291262 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291262 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.14359 | −0.376036 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7942 | + | 20.4282i | −0.543449 | + | 0.941282i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 36.2487i | − | 1.66672i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.41154 | − | 3.12436i | 0.248299 | − | 0.143355i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.232051 | − | 0.401924i | −0.0106249 | − | 0.0184028i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9808 | + | 13.2679i | 1.05002 | + | 0.606228i | 0.922654 | − | 0.385628i | \(-0.126015\pi\) |
0.127363 | + | 0.991856i | \(0.459349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.6244 | + | 9.06218i | −1.66993 | + | 0.413200i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.92820 | + | 2.26795i | 0.178739 | + | 0.103195i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.803848 | − | 1.39230i | −0.0365008 | − | 0.0632213i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.2942 | − | 10.5622i | 0.828991 | − | 0.478618i | −0.0245163 | − | 0.999699i | \(-0.507805\pi\) |
0.853507 | + | 0.521081i | \(0.174471\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.53590i | − | 0.295564i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.63397 | + | 4.56218i | −0.118870 | + | 0.205888i | −0.919320 | − | 0.393511i | \(-0.871260\pi\) |
0.800450 | + | 0.599399i | \(0.204594\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.58846 | 0.251691 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26795 | −0.0569901 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.464102 | + | 0.803848i | −0.0208178 | + | 0.0360575i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000i | 1.43252i | 0.697835 | + | 0.716258i | \(0.254147\pi\) | ||||
−0.697835 | + | 0.716258i | \(0.745853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.19615 | + | 1.26795i | −0.0981169 | + | 0.0566478i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.49038 | − | 9.50962i | −0.244804 | − | 0.424013i | 0.717272 | − | 0.696793i | \(-0.245390\pi\) |
−0.962076 | + | 0.272780i | \(0.912057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.76795 | + | 1.59808i | 0.123172 | + | 0.0711135i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | − | 6.92820i | −0.488527 | − | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.89230 | + | 5.13397i | 0.394144 | + | 0.227559i | 0.683954 | − | 0.729525i | \(-0.260259\pi\) |
−0.289810 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.56218 | + | 6.16987i | 0.157581 | + | 0.272939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.09808 | + | 0.633975i | −0.0484812 | + | 0.0279907i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.01924i | 0.221174i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3923 | + | 33.5885i | −0.852873 | + | 1.47722i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4449 | −0.764273 | −0.382137 | − | 0.924106i | \(-0.624812\pi\) | ||||
−0.382137 | + | 0.924106i | \(0.624812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2224 | − | 31.5622i | 0.796811 | − | 1.38012i | −0.124871 | − | 0.992173i | \(-0.539852\pi\) |
0.921683 | − | 0.387945i | \(-0.126815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60770i | 0.157453i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.7321 | + | 6.19615i | −0.467495 | + | 0.269909i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.69615 | − | 13.3301i | −0.334615 | − | 0.579571i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.92820 | + | 4.00000i | 0.300658 | + | 0.173585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.8731 | − | 9.86603i | 1.72709 | − | 0.427345i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0455173 | + | 0.0262794i | 0.00196789 | + | 0.00113616i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.0263 | + | 19.0981i | 0.475819 | + | 0.824143i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.4904 | + | 15.2942i | −1.14102 | + | 0.658769i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3205i | 1.73351i | 0.498731 | + | 0.866757i | \(0.333800\pi\) | ||||
−0.498731 | + | 0.866757i | \(0.666200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.40192 | + | 7.62436i | −0.188905 | + | 0.327192i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.46410 | 0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.19615 | −0.264928 | −0.132464 | − | 0.991188i | \(-0.542289\pi\) | ||||
−0.132464 | + | 0.991188i | \(0.542289\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.598076 | + | 1.03590i | −0.0255253 | + | 0.0442111i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.12436i | 0.133102i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | + | 3.46410i | −0.255146 | + | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.40192 | + | 2.42820i | 0.0595084 | + | 0.103071i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3038 | + | 15.1865i | 1.11453 | + | 0.643474i | 0.939999 | − | 0.341178i | \(-0.110826\pi\) |
0.174531 | + | 0.984652i | \(0.444159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.5359 | − | 7.66025i | −1.12235 | − | 0.323994i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.29423 | − | 5.36603i | −0.392403 | − | 0.226554i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5359 | − | 18.2487i | −0.444035 | − | 0.769091i | 0.553949 | − | 0.832550i | \(-0.313120\pi\) |
−0.997984 | + | 0.0634589i | \(0.979787\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.33013 | − | 2.50000i | 0.182170 | − | 0.105176i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.732051i | − | 0.0307432i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.3205 | + | 33.4641i | −0.809958 | + | 1.40289i | 0.102935 | + | 0.994688i | \(0.467177\pi\) |
−0.912893 | + | 0.408200i | \(0.866157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0526 | −1.00657 | −0.503284 | − | 0.864121i | \(-0.667875\pi\) | ||||
−0.503284 | + | 0.864121i | \(0.667875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.92820 | 0.289430 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.2679 | − | 26.4449i | 0.636717 | − | 1.10283i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.267949i | − | 0.0111549i | −0.999984 | − | 0.00557744i | \(-0.998225\pi\) | ||
0.999984 | − | 0.00557744i | \(-0.00177536\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.16025 | − | 4.13397i | 0.297570 | − | 0.171802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.73205 | − | 6.46410i | −0.154832 | − | 0.268176i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.90192 | + | 1.09808i | 0.0787696 | + | 0.0454777i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.267949 | + | 0.928203i | −0.0110783 | + | 0.0383765i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8564 | − | 8.00000i | −0.571915 | − | 0.330195i | 0.185999 | − | 0.982550i | \(-0.440448\pi\) |
−0.757914 | + | 0.652355i | \(0.773781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.46410 | − | 6.00000i | −0.142736 | − | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.53590 | − | 4.92820i | 0.351120 | − | 0.202719i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 36.8564i | − | 1.51351i | −0.653698 | − | 0.756756i | \(-0.726783\pi\) | ||
0.653698 | − | 0.756756i | \(-0.273217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.222432 | − | 0.385263i | 0.00911882 | − | 0.0157943i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.80385 | 0.155681 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.46410 | 0.386693 | 0.193346 | − | 0.981131i | \(-0.438066\pi\) | ||||
0.193346 | + | 0.981131i | \(0.438066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.96410 | − | 5.13397i | 0.120908 | − | 0.209419i | −0.799218 | − | 0.601041i | \(-0.794753\pi\) |
0.920126 | + | 0.391622i | \(0.128086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11.1244i | − | 0.453019i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.64359 | − | 1.52628i | 0.107477 | − | 0.0620521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.392305 | + | 0.679492i | 0.0159232 | + | 0.0275797i | 0.873877 | − | 0.486147i | \(-0.161598\pi\) |
−0.857954 | + | 0.513726i | \(0.828265\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.56218 | − | 0.901924i | −0.0633026 | − | 0.0365478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.4904 | + | 21.2942i | 0.828952 | + | 0.861472i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.86603 | + | 5.69615i | 0.398485 | + | 0.230065i | 0.685830 | − | 0.727762i | \(-0.259439\pi\) |
−0.287345 | + | 0.957827i | \(0.592773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.52628 | − | 2.64359i | −0.0615455 | − | 0.106600i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.5263 | + | 17.6244i | −1.22894 | + | 0.709530i | −0.966809 | − | 0.255502i | \(-0.917759\pi\) |
−0.262133 | + | 0.965032i | \(0.584426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.5359i | − | 0.423474i | −0.977327 | − | 0.211737i | \(-0.932088\pi\) | ||
0.977327 | − | 0.211737i | \(-0.0679119\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.09808 | + | 5.36603i | −0.124322 | + | 0.215331i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.85641 | −0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.7321i | 0.946259i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.3205 | + | 23.8564i | −1.64494 | + | 0.949709i | −0.665904 | + | 0.746037i | \(0.731954\pi\) |
−0.979039 | + | 0.203671i | \(0.934713\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.19615 | + | 3.80385i | 0.0872892 | + | 0.151189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.14359 | + | 2.39230i | 0.164433 | + | 0.0949357i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.59808 | + | 22.6244i | 0.221804 | + | 0.896410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.09808 | − | 0.633975i | −0.0434392 | − | 0.0250796i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9904 | + | 22.5000i | 0.513089 | + | 0.888697i | 0.999885 | + | 0.0151806i | \(0.00483233\pi\) |
−0.486796 | + | 0.873516i | \(0.661834\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000 | − | 6.92820i | 0.473234 | − | 0.273222i | −0.244359 | − | 0.969685i | \(-0.578577\pi\) |
0.717592 | + | 0.696463i | \(0.245244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.05256i | 0.0808194i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.1244 | + | 22.7321i | −0.515972 | + | 0.893689i | 0.483856 | + | 0.875147i | \(0.339236\pi\) |
−0.999828 | + | 0.0185417i | \(0.994098\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.8564 | −1.48599 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.26795 | − | 9.12436i | 0.206151 | − | 0.357064i | −0.744348 | − | 0.667792i | \(-0.767240\pi\) |
0.950499 | + | 0.310728i | \(0.100573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.60770i | 0.140964i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.42820 | + | 4.86603i | −0.328816 | + | 0.189842i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1244 | + | 33.1244i | 0.744979 | + | 1.29034i | 0.950205 | + | 0.311627i | \(0.100874\pi\) |
−0.205225 | + | 0.978715i | \(0.565793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.13397 | + | 4.69615i | 0.316375 | + | 0.182659i | 0.649776 | − | 0.760126i | \(-0.274863\pi\) |
−0.333401 | + | 0.942785i | \(0.608196\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.89230 | + | 5.66987i | −0.228838 | + | 0.220200i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.215390 | + | 0.124356i | 0.00835248 | + | 0.00482231i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.63397 | + | 13.2224i | 0.295589 | + | 0.511975i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.3205 | − | 6.53590i | 0.437676 | − | 0.252692i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.66025i | − | 0.218512i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.03590 | − | 12.1865i | 0.271214 | − | 0.469756i | −0.697959 | − | 0.716138i | \(-0.745908\pi\) |
0.969173 | + | 0.246381i | \(0.0792416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.92820 | −0.189687 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.5359 | −1.48105 | −0.740527 | − | 0.672026i | \(-0.765424\pi\) | ||||
−0.740527 | + | 0.672026i | \(0.765424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.19615 | + | 3.80385i | −0.0842806 | + | 0.145978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.80385i | 0.0691236i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7846 | − | 18.9282i | 1.25447 | − | 0.724268i | 0.282475 | − | 0.959275i | \(-0.408845\pi\) |
0.971994 | + | 0.235007i | \(0.0755114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.258330 | + | 0.447441i | 0.00987029 | + | 0.0170958i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7321 | + | 7.92820i | 0.523910 | + | 0.302480i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.20577 | − | 1.16025i | 0.0459362 | − | 0.0442022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.8109 | − | 13.1699i | −0.867767 | − | 0.501006i | −0.00116153 | − | 0.999999i | \(-0.500370\pi\) |
−0.866606 | + | 0.498994i | \(0.833703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.73205 | + | 3.00000i | 0.0657952 | + | 0.113961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.28719 | + | 1.32051i | −0.0867580 | + | 0.0500897i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 25.8372i | − | 0.978653i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.92820 | + | 17.1962i | −0.375519 | + | 0.650418i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3205 | −1.18296 | −0.591480 | − | 0.806320i | \(-0.701456\pi\) | ||||
−0.591480 | + | 0.806320i | \(0.701456\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.2679 | −0.500410 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.09808 | − | 1.90192i | 0.0413559 | − | 0.0716306i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 8.73205i | − | 0.328403i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3827 | − | 20.4282i | 1.32882 | − | 0.767197i | 0.343707 | − | 0.939077i | \(-0.388317\pi\) |
0.985118 | + | 0.171880i | \(0.0549841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.73205 | − | 8.19615i | −0.177466 | − | 0.307380i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.3205 | − | 16.9282i | −1.09806 | − | 0.633966i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09808 | − | 4.43782i | −0.0410657 | − | 0.165965i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.36603 | − | 4.83013i | −0.312435 | − | 0.180384i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2679 | + | 19.5167i | 0.420224 | + | 0.727849i | 0.995961 | − | 0.0897860i | \(-0.0286183\pi\) |
−0.575737 | + | 0.817635i | \(0.695285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8756 | − | 6.85641i | 0.442272 | − | 0.255346i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.5885i | 0.654122i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.07180 | + | 10.5167i | −0.225501 | + | 0.390579i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.9808 | 0.778133 | 0.389067 | − | 0.921210i | \(-0.372798\pi\) | ||||
0.389067 | + | 0.921210i | \(0.372798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.68653 | + | 15.0455i | −0.321283 | + | 0.556479i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.0000i | − | 0.701781i | −0.936416 | − | 0.350891i | \(-0.885879\pi\) | ||
0.936416 | − | 0.350891i | \(-0.114121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.50000 | − | 0.866025i | 0.0553283 | − | 0.0319438i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.3205 | + | 45.5885i | 0.969528 | + | 1.67927i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.46410 | − | 5.46410i | −0.348143 | − | 0.201000i | 0.315724 | − | 0.948851i | \(-0.397753\pi\) |
−0.663867 | + | 0.747851i | \(0.731086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.16987 | − | 3.29423i | −0.116448 | − | 0.121017i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.9090 | + | 13.8038i | 0.877135 | + | 0.506414i | 0.869713 | − | 0.493558i | \(-0.164304\pi\) |
0.00742221 | + | 0.999972i | \(0.497637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.375644 | + | 0.650635i | 0.0137625 | + | 0.0238374i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.83013 | − | 5.09808i | 0.323077 | − | 0.186529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.143594i | − | 0.00524679i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.95448 | + | 13.7776i | −0.290263 | + | 0.502751i | −0.973872 | − | 0.227098i | \(-0.927076\pi\) |
0.683609 | + | 0.729849i | \(0.260410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.53590 | −0.238181 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.875644 | −0.0318680 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.53590 | + | 6.12436i | −0.128514 | + | 0.222593i | −0.923101 | − | 0.384557i | \(-0.874354\pi\) |
0.794587 | + | 0.607151i | \(0.207688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 29.3205i | − | 1.06427i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1962 | + | 11.6603i | −0.732110 | + | 0.422684i | −0.819194 | − | 0.573517i | \(-0.805579\pi\) |
0.0870836 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | − | 3.46410i | −0.0724049 | − | 0.125409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.526279 | + | 0.303848i | 0.0190277 | + | 0.0109856i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | + | 27.7128i | −0.288863 | + | 1.00065i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.9808 | − | 8.07180i | −0.504159 | − | 0.291076i | 0.226270 | − | 0.974065i | \(-0.427347\pi\) |
−0.730429 | + | 0.682988i | \(0.760680\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3301 | − | 23.0885i | −0.480073 | − | 0.831510i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3731 | − | 17.5359i | 1.09244 | − | 0.630722i | 0.158217 | − | 0.987404i | \(-0.449425\pi\) |
0.934226 | + | 0.356682i | \(0.116092\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.9282i | − | 0.967290i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.83013 | − | 6.63397i | 0.137405 | − | 0.237993i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.4449 | 0.517541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.23205 | − | 2.13397i | 0.0440299 | − | 0.0762620i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.32051i | 0.225589i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0526 | + | 19.6603i | −1.21384 | + | 0.700812i | −0.963594 | − | 0.267369i | \(-0.913846\pi\) |
−0.250248 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.0263 | − | 24.2942i | −0.499349 | − | 0.864897i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.8301 | − | 6.83013i | −0.420631 | − | 0.242851i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.14359 | − | 1.19615i | −0.147143 | − | 0.0424766i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.107695 | − | 0.0621778i | −0.00381955 | − | 0.00220522i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0000 | − | 29.4449i | −0.602171 | − | 1.04299i | −0.992492 | − | 0.122312i | \(-0.960969\pi\) |
0.390321 | − | 0.920679i | \(-0.372364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0981 | − | 9.29423i | 0.569509 | − | 0.328806i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.53590i | − | 0.0896016i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.0263 | − | 39.8827i | 0.812580 | − | 1.40743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.21539 | 0.0428369 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.46410 | 0.0515388 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.2058 | − | 19.4090i | 0.393974 | − | 0.682383i | −0.598996 | − | 0.800752i | \(-0.704433\pi\) |
0.992970 | + | 0.118369i | \(0.0377667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 45.1769i | − | 1.58638i | −0.608977 | − | 0.793188i | \(-0.708420\pi\) | ||
0.608977 | − | 0.793188i | \(-0.291580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.07180 | − | 2.92820i | 0.177876 | − | 0.102697i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.875644 | − | 1.51666i | −0.0306725 | − | 0.0531263i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.41154 | − | 4.85641i | −0.294283 | − | 0.169904i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56218 | − | 0.633975i | 0.0895297 | − | 0.0221529i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1962 | + | 6.46410i | 0.390748 | + | 0.225599i | 0.682484 | − | 0.730900i | \(-0.260900\pi\) |
−0.291736 | + | 0.956499i | \(0.594233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | + | 36.0000i | 0.724506 | + | 1.25488i | 0.959177 | + | 0.282806i | \(0.0912654\pi\) |
−0.234671 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.1962 | − | 11.6603i | 0.703140 | − | 0.405958i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 33.4641i | − | 1.16366i | −0.813310 | − | 0.581830i | \(-0.802337\pi\) | ||
0.813310 | − | 0.581830i | \(-0.197663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.06218 | − | 10.5000i | 0.210548 | − | 0.364680i | −0.741338 | − | 0.671132i | \(-0.765808\pi\) |
0.951886 | + | 0.306452i | \(0.0991418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.26795 | −0.0786743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6603 | 0.507948 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.339746 | + | 0.588457i | −0.0117574 | + | 0.0203644i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.46410i | 0.188867i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2487 | + | 7.07180i | −0.422872 | + | 0.244146i | −0.696306 | − | 0.717745i | \(-0.745174\pi\) |
0.273433 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4641 | + | 19.8564i | 0.395314 | + | 0.684704i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.3301 | − | 11.1603i | −0.665765 | − | 0.384380i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.48076 | − | 0.133975i | −0.119742 | − | 0.00460887i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.22243 | − | 4.16987i | −0.248166 | − | 0.143279i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.16987 | + | 7.22243i | 0.143110 | + | 0.247873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56.1506 | + | 32.4186i | −1.92482 | + | 1.11129i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.17691i | 0.279972i | 0.990153 | + | 0.139986i | \(0.0447058\pi\) | ||||
−0.990153 | + | 0.139986i | \(0.955294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.169873 | + | 0.294229i | −0.00580953 | + | 0.0100624i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.4449 | 0.664224 | 0.332112 | − | 0.943240i | \(-0.392239\pi\) | ||||
0.332112 | + | 0.943240i | \(0.392239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8756 | 0.780507 | 0.390253 | − | 0.920707i | \(-0.372387\pi\) | ||||
0.390253 | + | 0.920707i | \(0.372387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.16987 | + | 7.22243i | −0.142109 | + | 0.246140i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.12436i | 0.242516i | 0.992621 | + | 0.121258i | \(0.0386928\pi\) | ||||
−0.992621 | + | 0.121258i | \(0.961307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.80385 | + | 2.19615i | −0.129335 | + | 0.0746714i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.92820 | − | 10.2679i | −0.201332 | − | 0.348718i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.7846 | + | 22.3923i | 1.31568 | + | 0.759607i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.9352 | − | 9.63397i | 1.31927 | − | 0.326435i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.19615 | − | 3.00000i | −0.175863 | − | 0.101535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.973721 | + | 1.68653i | 0.0329178 | + | 0.0570152i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.72243 | + | 5.03590i | −0.294536 | + | 0.170050i | −0.639985 | − | 0.768387i | \(-0.721060\pi\) |
0.345450 | + | 0.938437i | \(0.387726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.5167i | 0.489635i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9186 | − | 44.8923i | 0.873219 | − | 1.51246i | 0.0145717 | − | 0.999894i | \(-0.495362\pi\) |
0.858648 | − | 0.512566i | \(-0.171305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0718 | 0.978344 | 0.489172 | − | 0.872187i | \(-0.337299\pi\) | ||||
0.489172 | + | 0.872187i | \(0.337299\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.14359 | 0.0720561 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.07180 | − | 8.78461i | 0.170294 | − | 0.294958i | −0.768228 | − | 0.640176i | \(-0.778862\pi\) |
0.938523 | + | 0.345217i | \(0.112195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.0718i | − | 0.438414i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.09808 | + | 2.36603i | −0.137291 | + | 0.0792648i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.19615 | + | 9.00000i | 0.173883 | + | 0.301174i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.11731 | + | 2.95448i | 0.171053 | + | 0.0987575i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4641 | − | 6.19615i | −0.716665 | − | 0.206884i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.6603 | + | 6.73205i | 0.388891 | + | 0.224526i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.526279 | − | 0.911543i | −0.0175329 | − | 0.0303679i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.85641 | − | 2.80385i | 0.161611 | − | 0.0933062i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.35898i | 0.0784153i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.80385 | + | 13.5167i | −0.259123 | + | 0.448813i | −0.966007 | − | 0.258516i | \(-0.916767\pi\) |
0.706885 | + | 0.707329i | \(0.250100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.9282 | 0.395634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.46410 | 0.313560 | 0.156780 | − | 0.987634i | \(-0.449889\pi\) | ||||
0.156780 | + | 0.987634i | \(0.449889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1244 | + | 41.7846i | −0.798400 | + | 1.38287i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.320508i | 0.0105957i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.53590 | − | 4.92820i | 0.281880 | − | 0.162744i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.9808 | − | 50.1962i | −0.955987 | − | 1.65582i | −0.732093 | − | 0.681205i | \(-0.761456\pi\) |
−0.223894 | − | 0.974613i | \(-0.571877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.43782 | − | 4.29423i | −0.245085 | − | 0.141500i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.26795 | − | 4.39230i | 0.0417351 | − | 0.144574i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.6603 | − | 25.7846i | −1.46842 | − | 0.847793i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.36603 | + | 16.2224i | 0.307621 | + | 0.532815i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.00962 | + | 4.62436i | −0.262787 | + | 0.151720i | −0.625605 | − | 0.780140i | \(-0.715148\pi\) |
0.362818 | + | 0.931860i | \(0.381815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.19615i | 0.268618i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.83013 | − | 13.5622i | 0.256347 | − | 0.444006i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.87564 | −0.0940436 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.2487 | 1.41287 | 0.706437 | − | 0.707776i | \(-0.250301\pi\) | ||||
0.706437 | + | 0.707776i | \(0.250301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.73205 | − | 11.6603i | 0.219692 | − | 0.380518i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.6410i | 1.84644i | 0.384267 | + | 0.923222i | \(0.374454\pi\) | ||||
−0.384267 | + | 0.923222i | \(0.625546\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.1314 | − | 35.2942i | 1.99071 | − | 1.14934i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.0980762 | − | 0.169873i | −0.00319042 | − | 0.00552597i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2487 | + | 17.4641i | 0.982951 | + | 0.567507i | 0.903160 | − | 0.429305i | \(-0.141241\pi\) |
0.0797913 | + | 0.996812i | \(0.474575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.3301 | − | 25.2846i | −0.789789 | − | 0.820773i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.89230 | − | 1.66987i | −0.0937894 | − | 0.0541493i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.7846 | − | 36.0000i | −0.673280 | − | 1.16615i | −0.976969 | − | 0.213383i | \(-0.931552\pi\) |
0.303689 | − | 0.952771i | \(-0.401782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.60770 | − | 0.928203i | 0.0520238 | − | 0.0300360i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.6603i | 0.376922i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.705771 | − | 1.22243i | 0.0227905 | − | 0.0394744i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.196152 | 0.00632092 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.10770 | − | 1.91858i | 0.0356580 | − | 0.0617614i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.8756i | − | 0.607000i | −0.952831 | − | 0.303500i | \(-0.901845\pi\) | ||
0.952831 | − | 0.303500i | \(-0.0981552\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.49038 | + | 1.43782i | −0.0800026 | + | 0.0461895i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.12436 | − | 15.8038i | −0.292815 | − | 0.507170i | 0.681660 | − | 0.731669i | \(-0.261259\pi\) |
−0.974474 | + | 0.224500i | \(0.927925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.24871 | + | 3.60770i | 0.200324 | + | 0.115657i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.26795 | − | 17.2487i | −0.136684 | − | 0.552401i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7750 | + | 16.0359i | 0.888601 | + | 0.513034i | 0.873485 | − | 0.486852i | \(-0.161855\pi\) |
0.0151161 | + | 0.999886i | \(0.495188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | + | 10.3923i | 0.191761 | + | 0.332140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.73205 | − | 2.73205i | 0.151083 | − | 0.0872277i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.7846i | 0.662926i | 0.943468 | + | 0.331463i | \(0.107542\pi\) | ||||
−0.943468 | + | 0.331463i | \(0.892458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.32051 | − | 2.28719i | 0.0420749 | − | 0.0728758i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.4641 | −1.50927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.29423 | + | 7.43782i | −0.136411 | + | 0.236270i | −0.926135 | − | 0.377191i | \(-0.876890\pi\) |
0.789725 | + | 0.613461i | \(0.210223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 20.0000i | − | 0.634681i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.882686 | − | 0.509619i | 0.0279830 | − | 0.0161560i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.3301 | − | 33.4808i | −0.612191 | − | 1.06035i | −0.990870 | − | 0.134818i | \(-0.956955\pi\) |
0.378679 | − | 0.925528i | \(-0.376378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.06218 | + | 5.23205i | 0.286715 | + | 0.165535i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))