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 | 49.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.49 |
Dual form | 624.2.bv.e.433.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | \(0.0190830\pi\) | ||||
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.633975 | − | 0.366025i | −0.239620 | − | 0.138345i | 0.375382 | − | 0.926870i | \(-0.377511\pi\) |
−0.615002 | + | 0.788526i | \(0.710845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.09808 | − | 2.36603i | 1.23562 | − | 0.713384i | 0.267421 | − | 0.963580i | \(-0.413828\pi\) |
0.968195 | + | 0.250196i | \(0.0804951\pi\) | |||||||
\(12\) | 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 | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09808 | + | 0.633975i | 0.251916 | + | 0.145444i | 0.620641 | − | 0.784095i | \(-0.286872\pi\) |
−0.368725 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.732051i | − | 0.159747i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09808 | + | 5.36603i | 0.645994 | + | 1.11889i | 0.984071 | + | 0.177775i | \(0.0568901\pi\) |
−0.338078 | + | 0.941118i | \(0.609777\pi\) | |||||||
\(24\) | 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 | 0.728663 | − | 0.684873i | \(-0.240142\pi\) |
−0.957449 | + | 0.288604i | \(0.906809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410i | 0.981382i | 0.871334 | + | 0.490691i | \(0.163256\pi\) | ||||
−0.871334 | + | 0.490691i | \(0.836744\pi\) | |||||||
\(32\) | 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 | −0.999932 | − | 0.0116456i | \(-0.996293\pi\) |
−0.489881 | + | 0.871789i | \(0.662960\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.866025 | + | 3.50000i | −0.138675 | + | 0.560449i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.86603 | − | 5.69615i | 1.54081 | − | 0.889590i | 0.542027 | − | 0.840361i | \(-0.317657\pi\) |
0.998788 | − | 0.0492283i | \(-0.0156762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83013 | + | 6.63397i | −0.584089 | + | 1.01167i | 0.410899 | + | 0.911681i | \(0.365215\pi\) |
−0.994988 | + | 0.0999910i | \(0.968119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.232051 | − | 0.133975i | −0.0345921 | − | 0.0199718i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.19615i | − | 1.19553i | −0.801671 | − | 0.597766i | \(-0.796055\pi\) | ||
0.801671 | − | 0.597766i | \(-0.203945\pi\) | |||||||
\(48\) | 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 | −0.0241347 | − | 0.999709i | \(-0.507683\pi\) |
−0.877841 | + | 0.478953i | \(0.841016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.598076 | + | 1.03590i | −0.0765758 | + | 0.132633i | −0.901770 | − | 0.432215i | \(-0.857732\pi\) |
0.825195 | + | 0.564848i | \(0.191065\pi\) | |||||||
\(62\) | 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 | 0.221664 | − | 0.975123i | \(-0.428851\pi\) |
0.955313 | + | 0.295595i | \(0.0955179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09808 | + | 5.36603i | −0.372965 | + | 0.645994i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.09808 | + | 0.633975i | 0.130318 | + | 0.0752389i | 0.563742 | − | 0.825951i | \(-0.309361\pi\) |
−0.433424 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.73205i | 1.13905i | 0.821974 | + | 0.569525i | \(0.192873\pi\) | ||||
−0.821974 | + | 0.569525i | \(0.807127\pi\) | |||||||
\(74\) | 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 | \(-0.810960\pi\) | ||
0.828772 | − | 0.559587i | \(-0.189040\pi\) | |||||||
\(84\) | 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 | −0.379068 | − | 0.925369i | \(-0.623755\pi\) |
0.611859 | + | 0.790967i | \(0.290422\pi\) | |||||||
\(90\) | 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 | 0.740034 | − | 0.672569i | \(-0.234809\pi\) |
−0.212445 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.73205i | 0.475589i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.96410 | − | 10.3301i | −0.593450 | − | 1.02789i | −0.993764 | − | 0.111508i | \(-0.964432\pi\) |
0.400313 | − | 0.916378i | \(-0.368901\pi\) | |||||||
\(102\) | 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 | 0.861246 | − | 0.508189i | \(-0.169685\pi\) |
−0.870727 | + | 0.491766i | \(0.836351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.46410i | − | 0.523366i | −0.965154 | − | 0.261683i | \(-0.915723\pi\) | ||
0.965154 | − | 0.261683i | \(-0.0842775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.06218 | − | 5.23205i | −0.860144 | − | 0.496604i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.33013 | − | 16.1603i | 0.877705 | − | 1.52023i | 0.0238510 | − | 0.999716i | \(-0.492407\pi\) |
0.853854 | − | 0.520513i | \(-0.174259\pi\) | |||||||
\(114\) | 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 | −0.924571 | − | 0.381010i | \(-0.875576\pi\) |
0.132321 | − | 0.991207i | \(-0.457757\pi\) | |||||||
\(128\) | 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 | 0.426968 | − | 0.904267i | \(-0.359582\pi\) |
−0.569634 | + | 0.821898i | \(0.692915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.92820 | + | 8.53590i | −0.418005 | + | 0.724005i | −0.995739 | − | 0.0922197i | \(-0.970604\pi\) |
0.577734 | + | 0.816225i | \(0.303937\pi\) | |||||||
\(140\) | 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 | 0.397228 | − | 0.917720i | \(-0.369972\pi\) |
−0.596154 | + | 0.802870i | \(0.703305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.26795i | 0.265942i | 0.991120 | + | 0.132971i | \(0.0424517\pi\) | ||||
−0.991120 | + | 0.132971i | \(0.957548\pi\) | |||||||
\(152\) | 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 | 0.705016 | − | 0.709192i | \(-0.250940\pi\) |
−0.261670 | + | 0.965157i | \(0.584273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.633975 | + | 1.09808i | −0.0493549 | + | 0.0854851i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.19615 | + | 1.26795i | −0.169943 | + | 0.0981169i | −0.582559 | − | 0.812788i | \(-0.697949\pi\) |
0.412616 | + | 0.910905i | \(0.364615\pi\) | |||||||
\(168\) | 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 | 0.365755 | + | 0.930711i | \(0.380811\pi\) |
−0.988897 | + | 0.148602i | \(0.952523\pi\) | |||||||
\(174\) | 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 | −0.902573 | − | 0.430538i | \(-0.858324\pi\) |
0.0784298 | − | 0.996920i | \(-0.475009\pi\) | |||||||
\(180\) | 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 | −0.713052 | − | 0.701111i | \(-0.752688\pi\) |
0.963706 | + | 0.266966i | \(0.0860212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.16025 | − | 4.13397i | 0.515406 | − | 0.297570i | −0.219647 | − | 0.975579i | \(-0.570490\pi\) |
0.735053 | + | 0.678009i | \(0.237157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.937822 | − | 0.232051i | −0.0671588 | − | 0.0166175i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.53590 | − | 4.92820i | 0.608158 | − | 0.351120i | −0.164086 | − | 0.986446i | \(-0.552468\pi\) |
0.772244 | + | 0.635326i | \(0.219134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90192 | − | 3.29423i | 0.134824 | − | 0.233522i | −0.790706 | − | 0.612196i | \(-0.790286\pi\) |
0.925530 | + | 0.378674i | \(0.123620\pi\) | |||||||
\(200\) | 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 | 0.780476 | − | 0.625186i | \(-0.214977\pi\) |
−0.931665 | + | 0.363319i | \(0.881644\pi\) | |||||||
\(212\) | 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 | −0.0705277 | − | 0.997510i | \(-0.522468\pi\) |
0.828605 | + | 0.559834i | \(0.189135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | + | 4.26795i | −0.164273 | + | 0.284530i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.56218 | − | 0.901924i | −0.103685 | − | 0.0598628i | 0.447261 | − | 0.894404i | \(-0.352400\pi\) |
−0.550946 | + | 0.834541i | \(0.685733\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.8564i | − | 1.04782i | −0.851773 | − | 0.523910i | \(-0.824473\pi\) | ||
0.851773 | − | 0.523910i | \(-0.175527\pi\) | |||||||
\(230\) | 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 | \(0.101145\pi\) | ||||
−0.949939 | + | 0.312435i | \(0.898855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2321 | − | 8.79423i | −0.981183 | − | 0.566486i | −0.0785557 | − | 0.996910i | \(-0.525031\pi\) |
−0.902627 | + | 0.430424i | \(0.858364\pi\) | |||||||
\(242\) | 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 | −0.950537 | − | 0.310611i | \(-0.899466\pi\) |
0.744266 | + | 0.667883i | \(0.232800\pi\) | |||||||
\(252\) | 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 | 0.896840 | + | 0.442355i | \(0.145857\pi\) |
−0.0653297 | + | 0.997864i | \(0.520810\pi\) | |||||||
\(258\) | 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 | 0.867149 | + | 0.498049i | \(0.165950\pi\) |
−0.00225153 | + | 0.999997i | \(0.500717\pi\) | |||||||
\(264\) | 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 | −0.842845 | − | 0.538156i | \(-0.819121\pi\) |
0.887479 | + | 0.460848i | \(0.152455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07180 | − | 2.92820i | 0.308090 | − | 0.177876i | −0.337982 | − | 0.941153i | \(-0.609744\pi\) |
0.646071 | + | 0.763277i | \(0.276411\pi\) | |||||||
\(272\) | 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 | −0.898080 | − | 0.439832i | \(-0.855038\pi\) |
0.829946 | + | 0.557844i | \(0.188371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.73205 | − | 2.73205i | −0.283300 | − | 0.163564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3205i | 1.33153i | 0.746162 | + | 0.665765i | \(0.231895\pi\) | ||||
−0.746162 | + | 0.665765i | \(0.768105\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16987 | − | 7.22243i | −0.247873 | − | 0.429329i | 0.715062 | − | 0.699061i | \(-0.246398\pi\) |
−0.962936 | + | 0.269732i | \(0.913065\pi\) | |||||||
\(284\) | 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 | 0.0855965 | − | 0.996330i | \(-0.472720\pi\) |
−0.820049 | + | 0.572294i | \(0.806054\pi\) | |||||||
\(294\) | 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 | \(0.0788157\pi\) | ||||
−0.969502 | + | 0.245085i | \(0.921184\pi\) | |||||||
\(308\) | 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 | \(0.0298980\pi\) | ||||
−0.995592 | + | 0.0937894i | \(0.970102\pi\) | |||||||
\(318\) | 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 | 0.893708 | − | 0.448649i | \(-0.148095\pi\) |
0.0583130 | + | 0.998298i | \(0.481428\pi\) | |||||||
\(332\) | 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 | −0.721973 | − | 0.691921i | \(-0.756765\pi\) |
0.960208 | + | 0.279286i | \(0.0900979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7321 | − | 9.66025i | 0.895646 | − | 0.517102i | 0.0198610 | − | 0.999803i | \(-0.493678\pi\) |
0.875785 | + | 0.482701i | \(0.160344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.59808 | − | 2.50000i | −0.138675 | − | 0.133440i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.1340 | − | 9.89230i | 0.911949 | − | 0.526514i | 0.0308916 | − | 0.999523i | \(-0.490165\pi\) |
0.881058 | + | 0.473008i | \(0.156832\pi\) | |||||||
\(354\) | 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 | \(0.208922\pi\) | ||||
−0.792226 | + | 0.610228i | \(0.791078\pi\) | |||||||
\(360\) | 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 | 0.607197 | − | 0.794551i | \(-0.292294\pi\) |
−0.991700 | + | 0.128572i | \(0.958961\pi\) | |||||||
\(368\) | 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 | −0.701953 | − | 0.712223i | \(-0.747688\pi\) |
0.967780 | + | 0.251797i | \(0.0810216\pi\) | |||||||
\(374\) | 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 | −0.532211 | − | 0.846611i | \(-0.678639\pi\) |
0.467081 | + | 0.884214i | \(0.345306\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.92820 | − | 15.4641i | 0.457406 | − | 0.792250i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.73205 | + | 2.73205i | 0.241797 | + | 0.139601i | 0.616002 | − | 0.787744i | \(-0.288751\pi\) |
−0.374206 | + | 0.927346i | \(0.622085\pi\) | |||||||
\(384\) | 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 | 0.491450 | − | 0.870906i | \(-0.336467\pi\) |
−0.508501 | + | 0.861061i | \(0.669800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.464102 | − | 0.803848i | 0.0232341 | − | 0.0402427i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.9904 | + | 10.9641i | −0.948334 | + | 0.547521i | −0.892563 | − | 0.450922i | \(-0.851095\pi\) |
−0.0557713 | + | 0.998444i | \(0.517762\pi\) | |||||||
\(402\) | 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 | 0.162366 | − | 0.986731i | \(-0.448088\pi\) |
−0.773351 | + | 0.633978i | \(0.781421\pi\) | |||||||
\(410\) | 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 | 0.708177 | − | 0.706035i | \(-0.249518\pi\) |
−0.965533 | + | 0.260281i | \(0.916185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7128i | 1.59432i | 0.603765 | + | 0.797162i | \(0.293667\pi\) | ||||
−0.603765 | + | 0.797162i | \(0.706333\pi\) | |||||||
\(422\) | 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 | −0.249694 | − | 0.968325i | \(-0.580330\pi\) |
0.713747 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.42820 | + | 12.8660i | −0.356977 | + | 0.618302i | −0.987454 | − | 0.157906i | \(-0.949526\pi\) |
0.630478 | + | 0.776208i | \(0.282859\pi\) | |||||||
\(434\) | 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 | 0.996080 | − | 0.0884515i | \(-0.0281918\pi\) |
−0.574642 | + | 0.818405i | \(0.694859\pi\) | |||||||
\(440\) | 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 | −0.0590680 | − | 0.998254i | \(-0.518813\pi\) |
−0.894047 | + | 0.447973i | \(0.852146\pi\) | |||||||
\(450\) | 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 | −0.0718931 | − | 0.997412i | \(-0.522904\pi\) |
0.827838 | + | 0.560967i | \(0.189571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.13397 | − | 1.96410i | 0.0529294 | − | 0.0916764i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.2846 | − | 12.8660i | −1.03790 | − | 0.599231i | −0.118661 | − | 0.992935i | \(-0.537860\pi\) |
−0.919237 | + | 0.393704i | \(0.871193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.0526i | − | 1.30371i | −0.758342 | − | 0.651856i | \(-0.773990\pi\) | ||
0.758342 | − | 0.651856i | \(-0.226010\pi\) | |||||||
\(464\) | 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 | 0.127363 | − | 0.991856i | \(-0.459349\pi\) |
0.922654 | + | 0.385628i | \(0.126015\pi\) | |||||||
\(480\) | 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 | 0.853507 | − | 0.521081i | \(-0.174471\pi\) |
−0.0245163 | + | 0.999699i | \(0.507805\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.53590i | 0.295564i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.63397 | − | 4.56218i | −0.118870 | − | 0.205888i | 0.800450 | − | 0.599399i | \(-0.204594\pi\) |
−0.919320 | + | 0.393511i | \(0.871260\pi\) | |||||||
\(492\) | 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 | \(-0.745853\pi\) | ||
0.697835 | − | 0.716258i | \(-0.254147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.19615 | − | 1.26795i | −0.0981169 | − | 0.0566478i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.49038 | + | 9.50962i | −0.244804 | + | 0.424013i | −0.962076 | − | 0.272780i | \(-0.912057\pi\) |
0.717272 | + | 0.696793i | \(0.245390\pi\) | |||||||
\(504\) | 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 | −0.289810 | − | 0.957084i | \(-0.593592\pi\) |
0.683954 | + | 0.729525i | \(0.260259\pi\) | |||||||
\(510\) | 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 | 0.921683 | + | 0.387945i | \(0.126815\pi\) |
−0.124871 | + | 0.992173i | \(0.539852\pi\) | |||||||
\(524\) | 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 | \(-0.666200\pi\) | ||
0.498731 | − | 0.866757i | \(-0.333800\pi\) | |||||||
\(542\) | 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 | 0.174531 | − | 0.984652i | \(-0.444159\pi\) |
0.939999 | + | 0.341178i | \(0.110826\pi\) | |||||||
\(558\) | 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 | −0.997984 | − | 0.0634589i | \(-0.979787\pi\) |
0.553949 | + | 0.832550i | \(0.313120\pi\) | |||||||
\(564\) | 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 | −0.912893 | − | 0.408200i | \(-0.866157\pi\) |
0.102935 | − | 0.994688i | \(-0.467177\pi\) | |||||||
\(570\) | 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 | \(0.00177536\pi\) | ||||
−0.999984 | + | 0.00557744i | \(0.998225\pi\) | |||||||
\(578\) | 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 | −0.757914 | − | 0.652355i | \(-0.773781\pi\) |
0.185999 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(588\) | 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 | \(0.273217\pi\) | ||||
−0.653698 | + | 0.756756i | \(0.726783\pi\) | |||||||
\(594\) | 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 | 0.920126 | − | 0.391622i | \(-0.128086\pi\) |
−0.799218 | + | 0.601041i | \(0.794753\pi\) | |||||||
\(602\) | 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 | −0.857954 | − | 0.513726i | \(-0.828265\pi\) |
0.873877 | + | 0.486147i | \(0.161598\pi\) | |||||||
\(608\) | 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 | −0.287345 | − | 0.957827i | \(-0.592773\pi\) |
0.685830 | + | 0.727762i | \(0.259439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.52628 | + | 2.64359i | −0.0615455 | + | 0.106600i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.5263 | − | 17.6244i | −1.22894 | − | 0.709530i | −0.262133 | − | 0.965032i | \(-0.584426\pi\) |
−0.966809 | + | 0.255502i | \(0.917759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.5359i | 0.423474i | 0.977327 | + | 0.211737i | \(0.0679119\pi\) | ||||
−0.977327 | + | 0.211737i | \(0.932088\pi\) | |||||||
\(620\) | 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 | −0.979039 | − | 0.203671i | \(-0.934713\pi\) |
−0.665904 | − | 0.746037i | \(-0.731954\pi\) | |||||||
\(632\) | 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 | −0.486796 | − | 0.873516i | \(-0.661834\pi\) |
0.999885 | − | 0.0151806i | \(-0.00483233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000 | + | 6.92820i | 0.473234 | + | 0.273222i | 0.717592 | − | 0.696463i | \(-0.245244\pi\) |
−0.244359 | + | 0.969685i | \(0.578577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.05256i | − | 0.0808194i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.1244 | − | 22.7321i | −0.515972 | − | 0.893689i | −0.999828 | − | 0.0185417i | \(-0.994098\pi\) |
0.483856 | − | 0.875147i | \(-0.339236\pi\) | |||||||
\(648\) | 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 | 0.950499 | − | 0.310728i | \(-0.100573\pi\) |
−0.744348 | + | 0.667792i | \(0.767240\pi\) | |||||||
\(654\) | 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 | −0.205225 | − | 0.978715i | \(-0.565793\pi\) |
0.950205 | − | 0.311627i | \(-0.100874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.13397 | − | 4.69615i | 0.316375 | − | 0.182659i | −0.333401 | − | 0.942785i | \(-0.608196\pi\) |
0.649776 | + | 0.760126i | \(0.274863\pi\) | |||||||
\(662\) | 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 | 0.969173 | − | 0.246381i | \(-0.0792416\pi\) |
−0.697959 | + | 0.716138i | \(0.745908\pi\) | |||||||
\(674\) | 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 | 0.971994 | − | 0.235007i | \(-0.0755114\pi\) |
0.282475 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(684\) | 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 | −0.866606 | − | 0.498994i | \(-0.833703\pi\) |
−0.00116153 | + | 0.999999i | \(0.500370\pi\) | |||||||
\(692\) | 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 | 0.985118 | − | 0.171880i | \(-0.0549841\pi\) |
0.343707 | + | 0.939077i | \(0.388317\pi\) | |||||||
\(710\) | 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 | −0.575737 | − | 0.817635i | \(-0.695285\pi\) |
0.995961 | + | 0.0897860i | \(0.0286183\pi\) | |||||||
\(720\) | 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 | \(0.114121\pi\) | ||||
−0.936416 | + | 0.350891i | \(0.885879\pi\) | |||||||
\(734\) | 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 | −0.663867 | − | 0.747851i | \(-0.731086\pi\) |
0.315724 | + | 0.948851i | \(0.397753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.16987 | + | 3.29423i | −0.116448 | + | 0.121017i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.9090 | − | 13.8038i | 0.877135 | − | 0.506414i | 0.00742221 | − | 0.999972i | \(-0.497637\pi\) |
0.869713 | + | 0.493558i | \(0.164304\pi\) | |||||||
\(744\) | 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 | 0.683609 | − | 0.729849i | \(-0.260410\pi\) |
−0.973872 | + | 0.227098i | \(0.927076\pi\) | |||||||
\(752\) | 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 | 0.794587 | − | 0.607151i | \(-0.207688\pi\) |
−0.923101 | + | 0.384557i | \(0.874354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.3205i | 1.06427i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1962 | − | 11.6603i | −0.732110 | − | 0.422684i | 0.0870836 | − | 0.996201i | \(-0.472245\pi\) |
−0.819194 | + | 0.573517i | \(0.805579\pi\) | |||||||
\(762\) | 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 | −0.730429 | − | 0.682988i | \(-0.760680\pi\) |
0.226270 | + | 0.974065i | \(0.427347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3301 | + | 23.0885i | −0.480073 | + | 0.831510i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3731 | + | 17.5359i | 1.09244 | + | 0.630722i | 0.934226 | − | 0.356682i | \(-0.116092\pi\) |
0.158217 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(774\) | 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 | −0.250248 | − | 0.968182i | \(-0.580512\pi\) |
−0.963594 | + | 0.267369i | \(0.913846\pi\) | |||||||
\(788\) | 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 | 0.390321 | + | 0.920679i | \(0.372364\pi\) |
−0.992492 | + | 0.122312i | \(0.960969\pi\) | |||||||
\(798\) | 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 | 0.992970 | − | 0.118369i | \(-0.0377667\pi\) |
−0.598996 | + | 0.800752i | \(0.704433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.1769i | 1.58638i | 0.608977 | + | 0.793188i | \(0.291580\pi\) | ||||
−0.608977 | + | 0.793188i | \(0.708420\pi\) | |||||||
\(812\) | 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 | −0.291736 | − | 0.956499i | \(-0.594233\pi\) |
0.682484 | + | 0.730900i | \(0.260900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | − | 36.0000i | 0.724506 | − | 1.25488i | −0.234671 | − | 0.972075i | \(-0.575401\pi\) |
0.959177 | − | 0.282806i | \(-0.0912654\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.1962 | + | 11.6603i | 0.703140 | + | 0.405958i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.4641i | 1.16366i | 0.813310 | + | 0.581830i | \(0.197663\pi\) | ||||
−0.813310 | + | 0.581830i | \(0.802337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.06218 | + | 10.5000i | 0.210548 | + | 0.364680i | 0.951886 | − | 0.306452i | \(-0.0991418\pi\) |
−0.741338 | + | 0.671132i | \(0.765808\pi\) | |||||||
\(830\) | 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 | 0.273433 | − | 0.961891i | \(-0.411841\pi\) |
−0.696306 | + | 0.717745i | \(0.745174\pi\) | |||||||
\(840\) | 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 | \(-0.955294\pi\) | ||
0.990153 | − | 0.139986i | \(-0.0447058\pi\) | |||||||
\(854\) | 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 | \(-0.961307\pi\) | ||
0.992621 | − | 0.121258i | \(-0.0386928\pi\) | |||||||
\(864\) | 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 | 0.345450 | − | 0.938437i | \(-0.387726\pi\) |
−0.639985 | + | 0.768387i | \(0.721060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 14.5167i | − | 0.489635i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9186 | + | 44.8923i | 0.873219 | + | 1.51246i | 0.858648 | + | 0.512566i | \(0.171305\pi\) |
0.0145717 | + | 0.999894i | \(0.495362\pi\) | |||||||
\(882\) | 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 | 0.938523 | − | 0.345217i | \(-0.112195\pi\) |
−0.768228 | + | 0.640176i | \(0.778862\pi\) | |||||||
\(888\) | 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 | 0.706885 | − | 0.707329i | \(-0.250100\pi\) |
−0.966007 | + | 0.258516i | \(0.916767\pi\) | |||||||
\(908\) | 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 | −0.223894 | + | 0.974613i | \(0.571877\pi\) |
−0.732093 | + | 0.681205i | \(0.761456\pi\) | |||||||
\(920\) | 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 | 0.362818 | − | 0.931860i | \(-0.381815\pi\) |
−0.625605 | + | 0.780140i | \(0.715148\pi\) | |||||||
\(930\) | 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 | \(-0.625546\pi\) | ||
0.384267 | − | 0.923222i | \(-0.374454\pi\) | |||||||
\(942\) | 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 | 0.0797913 | − | 0.996812i | \(-0.474575\pi\) |
0.903160 | + | 0.429305i | \(0.141241\pi\) | |||||||
\(948\) | 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 | 0.303689 | + | 0.952771i | \(0.401782\pi\) |
−0.976969 | + | 0.213383i | \(0.931552\pi\) | |||||||
\(954\) | 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 | \(0.0981552\pi\) | ||||
−0.952831 | + | 0.303500i | \(0.901845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.49038 | − | 1.43782i | −0.0800026 | − | 0.0461895i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.12436 | + | 15.8038i | −0.292815 | + | 0.507170i | −0.974474 | − | 0.224500i | \(-0.927925\pi\) |
0.681660 | + | 0.731669i | \(0.261259\pi\) | |||||||
\(972\) | 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 | 0.0151161 | − | 0.999886i | \(-0.495188\pi\) |
0.873485 | + | 0.486852i | \(0.161855\pi\) | |||||||
\(978\) | 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 | \(-0.892458\pi\) | ||
0.943468 | − | 0.331463i | \(-0.107542\pi\) | |||||||
\(984\) | 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 | 0.789725 | − | 0.613461i | \(-0.210223\pi\) |
−0.926135 | + | 0.377191i | \(0.876890\pi\) | |||||||
\(992\) | 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 | 0.378679 | + | 0.925528i | \(0.376378\pi\) |
−0.990870 | + | 0.134818i | \(0.956955\pi\) | |||||||
\(998\) | 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 \(a_p\))