Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [140,2,Mod(111,140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("140.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.11790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 140.111 |
Dual form | 140.2.g.b.111.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.258819 | − | 0.965926i | ||||
\(3\) | 1.73205 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.633975 | − | 2.36603i | 0.258819 | − | 0.965926i | ||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.36603 | + | 0.366025i | 0.431975 | + | 0.115747i | ||||
\(11\) | − | 0.267949i | − | 0.0807897i | −0.999184 | − | 0.0403949i | \(-0.987138\pi\) | ||
0.999184 | − | 0.0403949i | \(-0.0128616\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.866025 | − | 0.500000i | ||||
\(13\) | 0.464102i | 0.128719i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) | ||||
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | −2.09808 | − | 3.09808i | −0.560734 | − | 0.827996i | ||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 6.46410i | 1.56777i | 0.620903 | + | 0.783887i | \(0.286766\pi\) | ||||
−0.620903 | + | 0.783887i | \(0.713234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | −0.366025 | − | 0.0980762i | −0.0780369 | − | 0.0209099i | ||||
\(23\) | − | 1.46410i | − | 0.305286i | −0.988281 | − | 0.152643i | \(-0.951221\pi\) | ||
0.988281 | − | 0.152643i | \(-0.0487785\pi\) | |||||||
\(24\) | −3.46410 | + | 3.46410i | −0.707107 | + | 0.707107i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.633975 | + | 0.169873i | 0.124333 | + | 0.0333148i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −5.00000 | + | 1.73205i | −0.944911 | + | 0.327327i | ||||
\(29\) | 7.92820 | 1.47223 | 0.736115 | − | 0.676856i | \(-0.236658\pi\) | ||||
0.736115 | + | 0.676856i | \(0.236658\pi\) | |||||||
\(30\) | 2.36603 | + | 0.633975i | 0.431975 | + | 0.115747i | ||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.965926 | − | 0.258819i | ||||
\(33\) | − | 0.464102i | − | 0.0807897i | ||||||
\(34\) | 8.83013 | + | 2.36603i | 1.51435 | + | 0.405770i | ||||
\(35\) | 2.00000 | + | 1.73205i | 0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.46410 | −1.55589 | −0.777944 | − | 0.628333i | \(-0.783737\pi\) | ||||
−0.777944 | + | 0.628333i | \(0.783737\pi\) | |||||||
\(38\) | −2.19615 | + | 8.19615i | −0.356263 | + | 1.32959i | ||||
\(39\) | 0.803848i | 0.128719i | ||||||||
\(40\) | −2.00000 | − | 2.00000i | −0.316228 | − | 0.316228i | ||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | −3.63397 | − | 5.36603i | −0.560734 | − | 0.827996i | ||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −0.267949 | + | 0.464102i | −0.0403949 | + | 0.0699660i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | − | 0.535898i | −0.294884 | − | 0.0790139i | ||||
\(47\) | −1.73205 | −0.252646 | −0.126323 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126323 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(48\) | 3.46410 | + | 6.00000i | 0.500000 | + | 0.866025i | ||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | −0.366025 | + | 1.36603i | −0.0517638 | + | 0.193185i | ||||
\(51\) | 11.1962i | 1.56777i | ||||||||
\(52\) | 0.464102 | − | 0.803848i | 0.0643593 | − | 0.111474i | ||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | −1.90192 | + | 7.09808i | −0.258819 | + | 0.965926i | ||||
\(55\) | 0.267949 | 0.0361303 | ||||||||
\(56\) | 0.535898 | + | 7.46410i | 0.0716124 | + | 0.997433i | ||||
\(57\) | −10.3923 | −1.37649 | ||||||||
\(58\) | 2.90192 | − | 10.8301i | 0.381041 | − | 1.42207i | ||||
\(59\) | 3.46410 | 0.450988 | 0.225494 | − | 0.974245i | \(-0.427600\pi\) | ||||
0.225494 | + | 0.974245i | \(0.427600\pi\) | |||||||
\(60\) | 1.73205 | − | 3.00000i | 0.223607 | − | 0.387298i | ||||
\(61\) | − | 9.46410i | − | 1.21175i | −0.795558 | − | 0.605877i | \(-0.792822\pi\) | ||
0.795558 | − | 0.605877i | \(-0.207178\pi\) | |||||||
\(62\) | 2.19615 | − | 8.19615i | 0.278912 | − | 1.04091i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −0.464102 | −0.0575647 | ||||||||
\(66\) | −0.633975 | − | 0.169873i | −0.0780369 | − | 0.0209099i | ||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 6.46410 | − | 11.1962i | 0.783887 | − | 1.35773i | ||||
\(69\) | − | 2.53590i | − | 0.305286i | ||||||
\(70\) | 3.09808 | − | 2.09808i | 0.370291 | − | 0.250768i | ||||
\(71\) | − | 7.46410i | − | 0.885826i | −0.896565 | − | 0.442913i | \(-0.853945\pi\) | ||
0.896565 | − | 0.442913i | \(-0.146055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.9282i | − | 1.51313i | −0.653917 | − | 0.756566i | \(-0.726876\pi\) | ||
0.653917 | − | 0.756566i | \(-0.273124\pi\) | |||||||
\(74\) | −3.46410 | + | 12.9282i | −0.402694 | + | 1.50287i | ||||
\(75\) | −1.73205 | −0.200000 | ||||||||
\(76\) | 10.3923 | + | 6.00000i | 1.19208 | + | 0.688247i | ||||
\(77\) | −0.535898 | − | 0.464102i | −0.0610713 | − | 0.0528893i | ||||
\(78\) | 1.09808 | + | 0.294229i | 0.124333 | + | 0.0333148i | ||||
\(79\) | − | 14.6603i | − | 1.64941i | −0.565565 | − | 0.824704i | \(-0.691342\pi\) | ||
0.565565 | − | 0.824704i | \(-0.308658\pi\) | |||||||
\(80\) | −3.46410 | + | 2.00000i | −0.387298 | + | 0.223607i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 4.73205 | + | 1.26795i | 0.522568 | + | 0.140022i | ||||
\(83\) | −15.4641 | −1.69741 | −0.848703 | − | 0.528870i | \(-0.822616\pi\) | ||||
−0.848703 | + | 0.528870i | \(0.822616\pi\) | |||||||
\(84\) | −8.66025 | + | 3.00000i | −0.944911 | + | 0.327327i | ||||
\(85\) | −6.46410 | −0.701130 | ||||||||
\(86\) | −2.73205 | − | 0.732051i | −0.294605 | − | 0.0789391i | ||||
\(87\) | 13.7321 | 1.47223 | ||||||||
\(88\) | 0.535898 | + | 0.535898i | 0.0571270 | + | 0.0571270i | ||||
\(89\) | − | 2.53590i | − | 0.268805i | −0.990927 | − | 0.134402i | \(-0.957089\pi\) | ||
0.990927 | − | 0.134402i | \(-0.0429115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.928203 | + | 0.803848i | 0.0973021 | + | 0.0842661i | ||||
\(92\) | −1.46410 | + | 2.53590i | −0.152643 | + | 0.264386i | ||||
\(93\) | 10.3923 | 1.07763 | ||||||||
\(94\) | −0.633975 | + | 2.36603i | −0.0653895 | + | 0.244037i | ||||
\(95\) | − | 6.00000i | − | 0.615587i | ||||||
\(96\) | 9.46410 | − | 2.53590i | 0.965926 | − | 0.258819i | ||||
\(97\) | 13.3923i | 1.35978i | 0.733313 | + | 0.679891i | \(0.237973\pi\) | ||||
−0.733313 | + | 0.679891i | \(0.762027\pi\) | |||||||
\(98\) | −9.83013 | − | 1.16987i | −0.992993 | − | 0.118175i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | + | 1.00000i | 0.173205 | + | 0.100000i | ||||
\(101\) | 15.4641i | 1.53874i | 0.638806 | + | 0.769368i | \(0.279429\pi\) | ||||
−0.638806 | + | 0.769368i | \(0.720571\pi\) | |||||||
\(102\) | 15.2942 | + | 4.09808i | 1.51435 | + | 0.405770i | ||||
\(103\) | 6.80385 | 0.670403 | 0.335202 | − | 0.942146i | \(-0.391196\pi\) | ||||
0.335202 | + | 0.942146i | \(0.391196\pi\) | |||||||
\(104\) | −0.928203 | − | 0.928203i | −0.0910178 | − | 0.0910178i | ||||
\(105\) | 3.46410 | + | 3.00000i | 0.338062 | + | 0.292770i | ||||
\(106\) | 0.732051 | − | 2.73205i | 0.0711031 | − | 0.265360i | ||||
\(107\) | 2.39230i | 0.231273i | 0.993292 | + | 0.115636i | \(0.0368907\pi\) | ||||
−0.993292 | + | 0.115636i | \(0.963109\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | 2.07180 | 0.198442 | 0.0992211 | − | 0.995065i | \(-0.468365\pi\) | ||||
0.0992211 | + | 0.995065i | \(0.468365\pi\) | |||||||
\(110\) | 0.0980762 | − | 0.366025i | 0.00935120 | − | 0.0348992i | ||||
\(111\) | −16.3923 | −1.55589 | ||||||||
\(112\) | 10.3923 | + | 2.00000i | 0.981981 | + | 0.188982i | ||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | −3.80385 | + | 14.1962i | −0.356263 | + | 1.32959i | ||||
\(115\) | 1.46410 | 0.136528 | ||||||||
\(116\) | −13.7321 | − | 7.92820i | −1.27499 | − | 0.736115i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.26795 | − | 4.73205i | 0.116724 | − | 0.435621i | ||||
\(119\) | 12.9282 | + | 11.1962i | 1.18513 | + | 1.02635i | ||||
\(120\) | −3.46410 | − | 3.46410i | −0.316228 | − | 0.316228i | ||||
\(121\) | 10.9282 | 0.993473 | ||||||||
\(122\) | −12.9282 | − | 3.46410i | −1.17046 | − | 0.313625i | ||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | −10.3923 | − | 6.00000i | −0.933257 | − | 0.538816i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4641i | 1.37222i | 0.727499 | + | 0.686109i | \(0.240683\pi\) | ||||
−0.727499 | + | 0.686109i | \(0.759317\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.965926 | − | 0.258819i | ||||
\(129\) | − | 3.46410i | − | 0.304997i | ||||||
\(130\) | −0.169873 | + | 0.633975i | −0.0148988 | + | 0.0556033i | ||||
\(131\) | −2.53590 | −0.221562 | −0.110781 | − | 0.993845i | \(-0.535335\pi\) | ||||
−0.110781 | + | 0.993845i | \(0.535335\pi\) | |||||||
\(132\) | −0.464102 | + | 0.803848i | −0.0403949 | + | 0.0699660i | ||||
\(133\) | −10.3923 | + | 12.0000i | −0.901127 | + | 1.04053i | ||||
\(134\) | 4.73205 | + | 1.26795i | 0.408787 | + | 0.109534i | ||||
\(135\) | − | 5.19615i | − | 0.447214i | ||||||
\(136\) | −12.9282 | − | 12.9282i | −1.10858 | − | 1.10858i | ||||
\(137\) | 20.3923 | 1.74223 | 0.871116 | − | 0.491077i | \(-0.163397\pi\) | ||||
0.871116 | + | 0.491077i | \(0.163397\pi\) | |||||||
\(138\) | −3.46410 | − | 0.928203i | −0.294884 | − | 0.0790139i | ||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | −1.73205 | − | 5.00000i | −0.146385 | − | 0.422577i | ||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | −10.1962 | − | 2.73205i | −0.855642 | − | 0.229269i | ||||
\(143\) | 0.124356 | 0.0103991 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.92820i | 0.658401i | ||||||||
\(146\) | −17.6603 | − | 4.73205i | −1.46157 | − | 0.391627i | ||||
\(147\) | −1.73205 | − | 12.0000i | −0.142857 | − | 0.989743i | ||||
\(148\) | 16.3923 | + | 9.46410i | 1.34744 | + | 0.777944i | ||||
\(149\) | 3.07180 | 0.251651 | 0.125826 | − | 0.992052i | \(-0.459842\pi\) | ||||
0.125826 | + | 0.992052i | \(0.459842\pi\) | |||||||
\(150\) | −0.633975 | + | 2.36603i | −0.0517638 | + | 0.193185i | ||||
\(151\) | − | 15.1962i | − | 1.23665i | −0.785924 | − | 0.618323i | \(-0.787812\pi\) | ||
0.785924 | − | 0.618323i | \(-0.212188\pi\) | |||||||
\(152\) | 12.0000 | − | 12.0000i | 0.973329 | − | 0.973329i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.830127 | + | 0.562178i | −0.0668935 | + | 0.0453016i | ||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 0.803848 | − | 1.39230i | 0.0643593 | − | 0.111474i | ||||
\(157\) | − | 7.85641i | − | 0.627009i | −0.949587 | − | 0.313505i | \(-0.898497\pi\) | ||
0.949587 | − | 0.313505i | \(-0.101503\pi\) | |||||||
\(158\) | −20.0263 | − | 5.36603i | −1.59321 | − | 0.426898i | ||||
\(159\) | 3.46410 | 0.274721 | ||||||||
\(160\) | 1.46410 | + | 5.46410i | 0.115747 | + | 0.431975i | ||||
\(161\) | −2.92820 | − | 2.53590i | −0.230775 | − | 0.199857i | ||||
\(162\) | −3.29423 | + | 12.2942i | −0.258819 | + | 0.965926i | ||||
\(163\) | 20.7846i | 1.62798i | 0.580881 | + | 0.813988i | \(0.302708\pi\) | ||||
−0.580881 | + | 0.813988i | \(0.697292\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | 0.464102 | 0.0361303 | ||||||||
\(166\) | −5.66025 | + | 21.1244i | −0.439321 | + | 1.63957i | ||||
\(167\) | 5.19615 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(168\) | 0.928203 | + | 12.9282i | 0.0716124 | + | 0.997433i | ||||
\(169\) | 12.7846 | 0.983432 | ||||||||
\(170\) | −2.36603 | + | 8.83013i | −0.181466 | + | 0.677240i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 14.3205i | 1.08877i | 0.838836 | + | 0.544384i | \(0.183237\pi\) | ||||
−0.838836 | + | 0.544384i | \(0.816763\pi\) | |||||||
\(174\) | 5.02628 | − | 18.7583i | 0.381041 | − | 1.42207i | ||||
\(175\) | −1.73205 | + | 2.00000i | −0.130931 | + | 0.151186i | ||||
\(176\) | 0.928203 | − | 0.535898i | 0.0699660 | − | 0.0403949i | ||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | −3.46410 | − | 0.928203i | −0.259645 | − | 0.0695718i | ||||
\(179\) | 6.39230i | 0.477783i | 0.971046 | + | 0.238892i | \(0.0767841\pi\) | ||||
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.928203i | 0.0689928i | 0.999405 | + | 0.0344964i | \(0.0109827\pi\) | ||||
−0.999405 | + | 0.0344964i | \(0.989017\pi\) | |||||||
\(182\) | 1.43782 | − | 0.973721i | 0.106578 | − | 0.0721770i | ||||
\(183\) | − | 16.3923i | − | 1.21175i | ||||||
\(184\) | 2.92820 | + | 2.92820i | 0.215870 | + | 0.215870i | ||||
\(185\) | − | 9.46410i | − | 0.695815i | ||||||
\(186\) | 3.80385 | − | 14.1962i | 0.278912 | − | 1.04091i | ||||
\(187\) | 1.73205 | 0.126660 | ||||||||
\(188\) | 3.00000 | + | 1.73205i | 0.218797 | + | 0.126323i | ||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | −8.19615 | − | 2.19615i | −0.594611 | − | 0.159326i | ||||
\(191\) | − | 7.19615i | − | 0.520695i | −0.965515 | − | 0.260348i | \(-0.916163\pi\) | ||
0.965515 | − | 0.260348i | \(-0.0838372\pi\) | |||||||
\(192\) | − | 13.8564i | − | 1.00000i | ||||||
\(193\) | −9.46410 | −0.681241 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(194\) | 18.2942 | + | 4.90192i | 1.31345 | + | 0.351938i | ||||
\(195\) | −0.803848 | −0.0575647 | ||||||||
\(196\) | −5.19615 | + | 13.0000i | −0.371154 | + | 0.928571i | ||||
\(197\) | −13.3205 | −0.949047 | −0.474523 | − | 0.880243i | \(-0.657380\pi\) | ||||
−0.474523 | + | 0.880243i | \(0.657380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.46410 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 2.00000 | − | 2.00000i | 0.141421 | − | 0.141421i | ||||
\(201\) | 6.00000i | 0.423207i | ||||||||
\(202\) | 21.1244 | + | 5.66025i | 1.48630 | + | 0.398254i | ||||
\(203\) | 13.7321 | − | 15.8564i | 0.963801 | − | 1.11290i | ||||
\(204\) | 11.1962 | − | 19.3923i | 0.783887 | − | 1.35773i | ||||
\(205\) | −3.46410 | −0.241943 | ||||||||
\(206\) | 2.49038 | − | 9.29423i | 0.173513 | − | 0.647560i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.60770 | + | 0.928203i | −0.111474 | + | 0.0643593i | ||||
\(209\) | 1.60770i | 0.111207i | ||||||||
\(210\) | 5.36603 | − | 3.63397i | 0.370291 | − | 0.250768i | ||||
\(211\) | − | 3.19615i | − | 0.220032i | −0.993930 | − | 0.110016i | \(-0.964910\pi\) | ||
0.993930 | − | 0.110016i | \(-0.0350902\pi\) | |||||||
\(212\) | −3.46410 | − | 2.00000i | −0.237915 | − | 0.137361i | ||||
\(213\) | − | 12.9282i | − | 0.885826i | ||||||
\(214\) | 3.26795 | + | 0.875644i | 0.223392 | + | 0.0598578i | ||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | 10.3923 | − | 12.0000i | 0.705476 | − | 0.814613i | ||||
\(218\) | 0.758330 | − | 2.83013i | 0.0513606 | − | 0.191680i | ||||
\(219\) | − | 22.3923i | − | 1.51313i | ||||||
\(220\) | −0.464102 | − | 0.267949i | −0.0312897 | − | 0.0180651i | ||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | −6.00000 | + | 22.3923i | −0.402694 | + | 1.50287i | ||||
\(223\) | 13.7321 | 0.919566 | 0.459783 | − | 0.888031i | \(-0.347927\pi\) | ||||
0.459783 | + | 0.888031i | \(0.347927\pi\) | |||||||
\(224\) | 6.53590 | − | 13.4641i | 0.436698 | − | 0.899608i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | − | 7.46410i | 0.133038 | − | 0.496505i | ||||
\(227\) | −20.6603 | −1.37127 | −0.685635 | − | 0.727946i | \(-0.740475\pi\) | ||||
−0.685635 | + | 0.727946i | \(0.740475\pi\) | |||||||
\(228\) | 18.0000 | + | 10.3923i | 1.19208 | + | 0.688247i | ||||
\(229\) | 8.53590i | 0.564068i | 0.959404 | + | 0.282034i | \(0.0910091\pi\) | ||||
−0.959404 | + | 0.282034i | \(0.908991\pi\) | |||||||
\(230\) | 0.535898 | − | 2.00000i | 0.0353361 | − | 0.131876i | ||||
\(231\) | −0.928203 | − | 0.803848i | −0.0610713 | − | 0.0528893i | ||||
\(232\) | −15.8564 | + | 15.8564i | −1.04102 | + | 1.04102i | ||||
\(233\) | −9.07180 | −0.594313 | −0.297157 | − | 0.954829i | \(-0.596038\pi\) | ||||
−0.297157 | + | 0.954829i | \(0.596038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.73205i | − | 0.112987i | ||||||
\(236\) | −6.00000 | − | 3.46410i | −0.390567 | − | 0.225494i | ||||
\(237\) | − | 25.3923i | − | 1.64941i | ||||||
\(238\) | 20.0263 | − | 13.5622i | 1.29811 | − | 0.879105i | ||||
\(239\) | 23.9808i | 1.55119i | 0.631233 | + | 0.775593i | \(0.282549\pi\) | ||||
−0.631233 | + | 0.775593i | \(0.717451\pi\) | |||||||
\(240\) | −6.00000 | + | 3.46410i | −0.387298 | + | 0.223607i | ||||
\(241\) | − | 16.3923i | − | 1.05592i | −0.849269 | − | 0.527961i | \(-0.822957\pi\) | ||
0.849269 | − | 0.527961i | \(-0.177043\pi\) | |||||||
\(242\) | 4.00000 | − | 14.9282i | 0.257130 | − | 0.959621i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.46410 | + | 16.3923i | −0.605877 | + | 1.04941i | ||||
\(245\) | 6.92820 | − | 1.00000i | 0.442627 | − | 0.0638877i | ||||
\(246\) | 8.19615 | + | 2.19615i | 0.522568 | + | 0.140022i | ||||
\(247\) | − | 2.78461i | − | 0.177180i | ||||||
\(248\) | −12.0000 | + | 12.0000i | −0.762001 | + | 0.762001i | ||||
\(249\) | −26.7846 | −1.69741 | ||||||||
\(250\) | −1.36603 | − | 0.366025i | −0.0863950 | − | 0.0231495i | ||||
\(251\) | 25.8564 | 1.63204 | 0.816021 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816021 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.392305 | −0.0246640 | ||||||||
\(254\) | 21.1244 | + | 5.66025i | 1.32546 | + | 0.355156i | ||||
\(255\) | −11.1962 | −0.701130 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | − | 6.00000i | − | 0.374270i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) | ||
0.982334 | − | 0.187135i | \(-0.0599201\pi\) | |||||||
\(258\) | −4.73205 | − | 1.26795i | −0.294605 | − | 0.0789391i | ||||
\(259\) | −16.3923 | + | 18.9282i | −1.01857 | + | 1.17614i | ||||
\(260\) | 0.803848 | + | 0.464102i | 0.0498525 | + | 0.0287824i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.928203 | + | 3.46410i | −0.0573446 | + | 0.214013i | ||||
\(263\) | 11.4641i | 0.706907i | 0.935452 | + | 0.353453i | \(0.114993\pi\) | ||||
−0.935452 | + | 0.353453i | \(0.885007\pi\) | |||||||
\(264\) | 0.928203 | + | 0.928203i | 0.0571270 | + | 0.0571270i | ||||
\(265\) | 2.00000i | 0.122859i | ||||||||
\(266\) | 12.5885 | + | 18.5885i | 0.771848 | + | 1.13973i | ||||
\(267\) | − | 4.39230i | − | 0.268805i | ||||||
\(268\) | 3.46410 | − | 6.00000i | 0.211604 | − | 0.366508i | ||||
\(269\) | 12.0000i | 0.731653i | 0.930683 | + | 0.365826i | \(0.119214\pi\) | ||||
−0.930683 | + | 0.365826i | \(0.880786\pi\) | |||||||
\(270\) | −7.09808 | − | 1.90192i | −0.431975 | − | 0.115747i | ||||
\(271\) | −9.46410 | −0.574903 | −0.287452 | − | 0.957795i | \(-0.592808\pi\) | ||||
−0.287452 | + | 0.957795i | \(0.592808\pi\) | |||||||
\(272\) | −22.3923 | + | 12.9282i | −1.35773 | + | 0.783887i | ||||
\(273\) | 1.60770 | + | 1.39230i | 0.0973021 | + | 0.0842661i | ||||
\(274\) | 7.46410 | − | 27.8564i | 0.450923 | − | 1.68287i | ||||
\(275\) | 0.267949i | 0.0161579i | ||||||||
\(276\) | −2.53590 | + | 4.39230i | −0.152643 | + | 0.264386i | ||||
\(277\) | 16.7846 | 1.00849 | 0.504245 | − | 0.863561i | \(-0.331771\pi\) | ||||
0.504245 | + | 0.863561i | \(0.331771\pi\) | |||||||
\(278\) | −2.53590 | + | 9.46410i | −0.152093 | + | 0.567619i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.46410 | + | 0.535898i | −0.446065 | + | 0.0320261i | ||||
\(281\) | −7.92820 | −0.472957 | −0.236478 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236478 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(282\) | −1.09808 | + | 4.09808i | −0.0653895 | + | 0.244037i | ||||
\(283\) | −12.1244 | −0.720718 | −0.360359 | − | 0.932814i | \(-0.617346\pi\) | ||||
−0.360359 | + | 0.932814i | \(0.617346\pi\) | |||||||
\(284\) | −7.46410 | + | 12.9282i | −0.442913 | + | 0.767148i | ||||
\(285\) | − | 10.3923i | − | 0.615587i | ||||||
\(286\) | 0.0455173 | − | 0.169873i | 0.00269150 | − | 0.0100448i | ||||
\(287\) | 6.92820 | + | 6.00000i | 0.408959 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.7846 | −1.45792 | ||||||||
\(290\) | 10.8301 | + | 2.90192i | 0.635967 | + | 0.170407i | ||||
\(291\) | 23.1962i | 1.35978i | ||||||||
\(292\) | −12.9282 | + | 22.3923i | −0.756566 | + | 1.31041i | ||||
\(293\) | − | 20.3205i | − | 1.18714i | −0.804784 | − | 0.593568i | \(-0.797719\pi\) | ||
0.804784 | − | 0.593568i | \(-0.202281\pi\) | |||||||
\(294\) | −17.0263 | − | 2.02628i | −0.992993 | − | 0.118175i | ||||
\(295\) | 3.46410i | 0.201688i | ||||||||
\(296\) | 18.9282 | − | 18.9282i | 1.10018 | − | 1.10018i | ||||
\(297\) | 1.39230i | 0.0807897i | ||||||||
\(298\) | 1.12436 | − | 4.19615i | 0.0651322 | − | 0.243077i | ||||
\(299\) | 0.679492 | 0.0392960 | ||||||||
\(300\) | 3.00000 | + | 1.73205i | 0.173205 | + | 0.100000i | ||||
\(301\) | −4.00000 | − | 3.46410i | −0.230556 | − | 0.199667i | ||||
\(302\) | −20.7583 | − | 5.56218i | −1.19451 | − | 0.320067i | ||||
\(303\) | 26.7846i | 1.53874i | ||||||||
\(304\) | −12.0000 | − | 20.7846i | −0.688247 | − | 1.19208i | ||||
\(305\) | 9.46410 | 0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | −0.0988534 | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 0.464102 | + | 1.33975i | 0.0264446 | + | 0.0763391i | ||||
\(309\) | 11.7846 | 0.670403 | ||||||||
\(310\) | 8.19615 | + | 2.19615i | 0.465510 | + | 0.124733i | ||||
\(311\) | −7.85641 | −0.445496 | −0.222748 | − | 0.974876i | \(-0.571503\pi\) | ||||
−0.222748 | + | 0.974876i | \(0.571503\pi\) | |||||||
\(312\) | −1.60770 | − | 1.60770i | −0.0910178 | − | 0.0910178i | ||||
\(313\) | 17.5359i | 0.991188i | 0.868554 | + | 0.495594i | \(0.165050\pi\) | ||||
−0.868554 | + | 0.495594i | \(0.834950\pi\) | |||||||
\(314\) | −10.7321 | − | 2.87564i | −0.605645 | − | 0.162282i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.6603 | + | 25.3923i | −0.824704 | + | 1.42843i | ||||
\(317\) | −3.07180 | −0.172529 | −0.0862646 | − | 0.996272i | \(-0.527493\pi\) | ||||
−0.0862646 | + | 0.996272i | \(0.527493\pi\) | |||||||
\(318\) | 1.26795 | − | 4.73205i | 0.0711031 | − | 0.265360i | ||||
\(319\) | − | 2.12436i | − | 0.118941i | ||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | 4.14359i | 0.231273i | ||||||||
\(322\) | −4.53590 | + | 3.07180i | −0.252776 | + | 0.171185i | ||||
\(323\) | − | 38.7846i | − | 2.15803i | ||||||
\(324\) | 15.5885 | + | 9.00000i | 0.866025 | + | 0.500000i | ||||
\(325\) | − | 0.464102i | − | 0.0257437i | ||||||
\(326\) | 28.3923 | + | 7.60770i | 1.57250 | + | 0.421351i | ||||
\(327\) | 3.58846 | 0.198442 | ||||||||
\(328\) | −6.92820 | − | 6.92820i | −0.382546 | − | 0.382546i | ||||
\(329\) | −3.00000 | + | 3.46410i | −0.165395 | + | 0.190982i | ||||
\(330\) | 0.169873 | − | 0.633975i | 0.00935120 | − | 0.0348992i | ||||
\(331\) | 26.3923i | 1.45065i | 0.688405 | + | 0.725326i | \(0.258311\pi\) | ||||
−0.688405 | + | 0.725326i | \(0.741689\pi\) | |||||||
\(332\) | 26.7846 | + | 15.4641i | 1.47000 | + | 0.848703i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.90192 | − | 7.09808i | 0.104069 | − | 0.388389i | ||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 18.0000 | + | 3.46410i | 0.981981 | + | 0.188982i | ||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 4.67949 | − | 17.4641i | 0.254531 | − | 0.949922i | ||||
\(339\) | 9.46410 | 0.514019 | ||||||||
\(340\) | 11.1962 | + | 6.46410i | 0.607197 | + | 0.350565i | ||||
\(341\) | − | 1.60770i | − | 0.0870616i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 4.00000 | + | 4.00000i | 0.215666 | + | 0.215666i | ||||
\(345\) | 2.53590 | 0.136528 | ||||||||
\(346\) | 19.5622 | + | 5.24167i | 1.05167 | + | 0.281794i | ||||
\(347\) | − | 34.2487i | − | 1.83857i | −0.393596 | − | 0.919284i | \(-0.628769\pi\) | ||
0.393596 | − | 0.919284i | \(-0.371231\pi\) | |||||||
\(348\) | −23.7846 | − | 13.7321i | −1.27499 | − | 0.736115i | ||||
\(349\) | 5.32051i | 0.284800i | 0.989809 | + | 0.142400i | \(0.0454820\pi\) | ||||
−0.989809 | + | 0.142400i | \(0.954518\pi\) | |||||||
\(350\) | 2.09808 | + | 3.09808i | 0.112147 | + | 0.165599i | ||||
\(351\) | − | 2.41154i | − | 0.128719i | ||||||
\(352\) | −0.392305 | − | 1.46410i | −0.0209099 | − | 0.0780369i | ||||
\(353\) | 7.39230i | 0.393453i | 0.980458 | + | 0.196726i | \(0.0630311\pi\) | ||||
−0.980458 | + | 0.196726i | \(0.936969\pi\) | |||||||
\(354\) | 2.19615 | − | 8.19615i | 0.116724 | − | 0.435621i | ||||
\(355\) | 7.46410 | 0.396153 | ||||||||
\(356\) | −2.53590 | + | 4.39230i | −0.134402 | + | 0.232792i | ||||
\(357\) | 22.3923 | + | 19.3923i | 1.18513 | + | 1.02635i | ||||
\(358\) | 8.73205 | + | 2.33975i | 0.461503 | + | 0.123659i | ||||
\(359\) | − | 25.3205i | − | 1.33637i | −0.743997 | − | 0.668183i | \(-0.767072\pi\) | ||
0.743997 | − | 0.668183i | \(-0.232928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 1.26795 | + | 0.339746i | 0.0666419 | + | 0.0178567i | ||||
\(363\) | 18.9282 | 0.993473 | ||||||||
\(364\) | −0.803848 | − | 2.32051i | −0.0421331 | − | 0.121628i | ||||
\(365\) | 12.9282 | 0.676693 | ||||||||
\(366\) | −22.3923 | − | 6.00000i | −1.17046 | − | 0.313625i | ||||
\(367\) | −11.8756 | −0.619904 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(368\) | 5.07180 | − | 2.92820i | 0.264386 | − | 0.152643i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.9282 | − | 3.46410i | −0.672105 | − | 0.180090i | ||||
\(371\) | 3.46410 | − | 4.00000i | 0.179847 | − | 0.207670i | ||||
\(372\) | −18.0000 | − | 10.3923i | −0.933257 | − | 0.538816i | ||||
\(373\) | −3.60770 | −0.186799 | −0.0933997 | − | 0.995629i | \(-0.529773\pi\) | ||||
−0.0933997 | + | 0.995629i | \(0.529773\pi\) | |||||||
\(374\) | 0.633975 | − | 2.36603i | 0.0327820 | − | 0.122344i | ||||
\(375\) | − | 1.73205i | − | 0.0894427i | ||||||
\(376\) | 3.46410 | − | 3.46410i | 0.178647 | − | 0.178647i | ||||
\(377\) | 3.67949i | 0.189503i | ||||||||
\(378\) | 10.9019 | + | 16.0981i | 0.560734 | + | 0.827996i | ||||
\(379\) | − | 5.60770i | − | 0.288048i | −0.989574 | − | 0.144024i | \(-0.953996\pi\) | ||
0.989574 | − | 0.144024i | \(-0.0460042\pi\) | |||||||
\(380\) | −6.00000 | + | 10.3923i | −0.307794 | + | 0.533114i | ||||
\(381\) | 26.7846i | 1.37222i | ||||||||
\(382\) | −9.83013 | − | 2.63397i | −0.502953 | − | 0.134766i | ||||
\(383\) | −27.4641 | −1.40335 | −0.701675 | − | 0.712497i | \(-0.747564\pi\) | ||||
−0.701675 | + | 0.712497i | \(0.747564\pi\) | |||||||
\(384\) | −18.9282 | − | 5.07180i | −0.965926 | − | 0.258819i | ||||
\(385\) | 0.464102 | − | 0.535898i | 0.0236528 | − | 0.0273119i | ||||
\(386\) | −3.46410 | + | 12.9282i | −0.176318 | + | 0.658028i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.3923 | − | 23.1962i | 0.679891 | − | 1.17761i | ||||
\(389\) | −20.8564 | −1.05746 | −0.528731 | − | 0.848790i | \(-0.677332\pi\) | ||||
−0.528731 | + | 0.848790i | \(0.677332\pi\) | |||||||
\(390\) | −0.294229 | + | 1.09808i | −0.0148988 | + | 0.0556033i | ||||
\(391\) | 9.46410 | 0.478620 | ||||||||
\(392\) | 15.8564 | + | 11.8564i | 0.800869 | + | 0.598839i | ||||
\(393\) | −4.39230 | −0.221562 | ||||||||
\(394\) | −4.87564 | + | 18.1962i | −0.245631 | + | 0.916709i | ||||
\(395\) | 14.6603 | 0.737637 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.4641i | − | 0.625555i | −0.949826 | − | 0.312778i | \(-0.898741\pi\) | ||
0.949826 | − | 0.312778i | \(-0.101259\pi\) | |||||||
\(398\) | −1.26795 | + | 4.73205i | −0.0635566 | + | 0.237196i | ||||
\(399\) | −18.0000 | + | 20.7846i | −0.901127 | + | 1.04053i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −10.0718 | −0.502962 | −0.251481 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251481 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(402\) | 8.19615 | + | 2.19615i | 0.408787 | + | 0.109534i | ||||
\(403\) | 2.78461i | 0.138711i | ||||||||
\(404\) | 15.4641 | − | 26.7846i | 0.769368 | − | 1.33258i | ||||
\(405\) | − | 9.00000i | − | 0.447214i | ||||||
\(406\) | −16.6340 | − | 24.5622i | −0.825530 | − | 1.21900i | ||||
\(407\) | 2.53590i | 0.125700i | ||||||||
\(408\) | −22.3923 | − | 22.3923i | −1.10858 | − | 1.10858i | ||||
\(409\) | − | 4.14359i | − | 0.204888i | −0.994739 | − | 0.102444i | \(-0.967334\pi\) | ||
0.994739 | − | 0.102444i | \(-0.0326662\pi\) | |||||||
\(410\) | −1.26795 | + | 4.73205i | −0.0626195 | + | 0.233699i | ||||
\(411\) | 35.3205 | 1.74223 | ||||||||
\(412\) | −11.7846 | − | 6.80385i | −0.580586 | − | 0.335202i | ||||
\(413\) | 6.00000 | − | 6.92820i | 0.295241 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.4641i | − | 0.759103i | ||||||
\(416\) | 0.679492 | + | 2.53590i | 0.0333148 | + | 0.124333i | ||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 2.19615 | + | 0.588457i | 0.107417 | + | 0.0287824i | ||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | −3.00000 | − | 8.66025i | −0.146385 | − | 0.422577i | ||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | −4.36603 | − | 1.16987i | −0.212535 | − | 0.0569485i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.00000 | + | 4.00000i | −0.194257 | + | 0.194257i | ||||
\(425\) | − | 6.46410i | − | 0.313555i | ||||||
\(426\) | −17.6603 | − | 4.73205i | −0.855642 | − | 0.229269i | ||||
\(427\) | −18.9282 | − | 16.3923i | −0.916000 | − | 0.793279i | ||||
\(428\) | 2.39230 | − | 4.14359i | 0.115636 | − | 0.200288i | ||||
\(429\) | 0.215390 | 0.0103991 | ||||||||
\(430\) | 0.732051 | − | 2.73205i | 0.0353026 | − | 0.131751i | ||||
\(431\) | 13.5885i | 0.654533i | 0.944932 | + | 0.327266i | \(0.106127\pi\) | ||||
−0.944932 | + | 0.327266i | \(0.893873\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.500000 | − | 0.866025i | ||||
\(433\) | 31.8564i | 1.53092i | 0.643483 | + | 0.765461i | \(0.277489\pi\) | ||||
−0.643483 | + | 0.765461i | \(0.722511\pi\) | |||||||
\(434\) | −12.5885 | − | 18.5885i | −0.604265 | − | 0.892275i | ||||
\(435\) | 13.7321i | 0.658401i | ||||||||
\(436\) | −3.58846 | − | 2.07180i | −0.171856 | − | 0.0992211i | ||||
\(437\) | 8.78461i | 0.420225i | ||||||||
\(438\) | −30.5885 | − | 8.19615i | −1.46157 | − | 0.391627i | ||||
\(439\) | 39.7128 | 1.89539 | 0.947695 | − | 0.319179i | \(-0.103407\pi\) | ||||
0.947695 | + | 0.319179i | \(0.103407\pi\) | |||||||
\(440\) | −0.535898 | + | 0.535898i | −0.0255480 | + | 0.0255480i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.09808 | + | 4.09808i | −0.0522302 | + | 0.194926i | ||||
\(443\) | 26.0000i | 1.23530i | 0.786454 | + | 0.617649i | \(0.211915\pi\) | ||||
−0.786454 | + | 0.617649i | \(0.788085\pi\) | |||||||
\(444\) | 28.3923 | + | 16.3923i | 1.34744 | + | 0.777944i | ||||
\(445\) | 2.53590 | 0.120213 | ||||||||
\(446\) | 5.02628 | − | 18.7583i | 0.238001 | − | 0.888233i | ||||
\(447\) | 5.32051 | 0.251651 | ||||||||
\(448\) | −16.0000 | − | 13.8564i | −0.755929 | − | 0.654654i | ||||
\(449\) | 11.9282 | 0.562927 | 0.281463 | − | 0.959572i | \(-0.409180\pi\) | ||||
0.281463 | + | 0.959572i | \(0.409180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.928203 | 0.0437074 | ||||||||
\(452\) | −9.46410 | − | 5.46410i | −0.445154 | − | 0.257010i | ||||
\(453\) | − | 26.3205i | − | 1.23665i | ||||||
\(454\) | −7.56218 | + | 28.2224i | −0.354911 | + | 1.32454i | ||||
\(455\) | −0.803848 | + | 0.928203i | −0.0376850 | + | 0.0435148i | ||||
\(456\) | 20.7846 | − | 20.7846i | 0.973329 | − | 0.973329i | ||||
\(457\) | 20.5359 | 0.960629 | 0.480314 | − | 0.877096i | \(-0.340523\pi\) | ||||
0.480314 | + | 0.877096i | \(0.340523\pi\) | |||||||
\(458\) | 11.6603 | + | 3.12436i | 0.544848 | + | 0.145992i | ||||
\(459\) | − | 33.5885i | − | 1.56777i | ||||||
\(460\) | −2.53590 | − | 1.46410i | −0.118237 | − | 0.0682641i | ||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | −1.43782 | + | 0.973721i | −0.0668935 | + | 0.0453016i | ||||
\(463\) | 16.3923i | 0.761815i | 0.924613 | + | 0.380908i | \(0.124388\pi\) | ||||
−0.924613 | + | 0.380908i | \(0.875612\pi\) | |||||||
\(464\) | 15.8564 | + | 27.4641i | 0.736115 | + | 1.27499i | ||||
\(465\) | 10.3923i | 0.481932i | ||||||||
\(466\) | −3.32051 | + | 12.3923i | −0.153820 | + | 0.574062i | ||||
\(467\) | −22.5167 | −1.04195 | −0.520973 | − | 0.853573i | \(-0.674431\pi\) | ||||
−0.520973 | + | 0.853573i | \(0.674431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.92820 | + | 6.00000i | 0.319915 | + | 0.277054i | ||||
\(470\) | −2.36603 | − | 0.633975i | −0.109137 | − | 0.0292431i | ||||
\(471\) | − | 13.6077i | − | 0.627009i | ||||||
\(472\) | −6.92820 | + | 6.92820i | −0.318896 | + | 0.318896i | ||||
\(473\) | −0.535898 | −0.0246406 | ||||||||
\(474\) | −34.6865 | − | 9.29423i | −1.59321 | − | 0.426898i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | −11.1962 | − | 32.3205i | −0.513175 | − | 1.48141i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.7583 | + | 8.77757i | 1.49833 | + | 0.401477i | ||||
\(479\) | −25.1769 | −1.15036 | −0.575181 | − | 0.818026i | \(-0.695068\pi\) | ||||
−0.575181 | + | 0.818026i | \(0.695068\pi\) | |||||||
\(480\) | 2.53590 | + | 9.46410i | 0.115747 | + | 0.431975i | ||||
\(481\) | − | 4.39230i | − | 0.200272i | ||||||
\(482\) | −22.3923 | − | 6.00000i | −1.01994 | − | 0.273293i | ||||
\(483\) | −5.07180 | − | 4.39230i | −0.230775 | − | 0.199857i | ||||
\(484\) | −18.9282 | − | 10.9282i | −0.860373 | − | 0.496737i | ||||
\(485\) | −13.3923 | −0.608113 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7846i | 0.579326i | 0.957129 | + | 0.289663i | \(0.0935432\pi\) | ||||
−0.957129 | + | 0.289663i | \(0.906457\pi\) | |||||||
\(488\) | 18.9282 | + | 18.9282i | 0.856840 | + | 0.856840i | ||||
\(489\) | 36.0000i | 1.62798i | ||||||||
\(490\) | 1.16987 | − | 9.83013i | 0.0528495 | − | 0.444080i | ||||
\(491\) | 9.87564i | 0.445682i | 0.974855 | + | 0.222841i | \(0.0715330\pi\) | ||||
−0.974855 | + | 0.222841i | \(0.928467\pi\) | |||||||
\(492\) | 6.00000 | − | 10.3923i | 0.270501 | − | 0.468521i | ||||
\(493\) | 51.2487i | 2.30813i | ||||||||
\(494\) | −3.80385 | − | 1.01924i | −0.171143 | − | 0.0458577i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000 | + | 20.7846i | 0.538816 | + | 0.933257i | ||||
\(497\) | −14.9282 | − | 12.9282i | −0.669621 | − | 0.579909i | ||||
\(498\) | −9.80385 | + | 36.5885i | −0.439321 | + | 1.63957i | ||||
\(499\) | − | 25.5885i | − | 1.14550i | −0.819731 | − | 0.572748i | \(-0.805877\pi\) | ||
0.819731 | − | 0.572748i | \(-0.194123\pi\) | |||||||
\(500\) | −1.00000 | + | 1.73205i | −0.0447214 | + | 0.0774597i | ||||
\(501\) | 9.00000 | 0.402090 | ||||||||
\(502\) | 9.46410 | − | 35.3205i | 0.422404 | − | 1.57643i | ||||
\(503\) | 15.5885 | 0.695055 | 0.347527 | − | 0.937670i | \(-0.387021\pi\) | ||||
0.347527 | + | 0.937670i | \(0.387021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4641 | −0.688143 | ||||||||
\(506\) | −0.143594 | + | 0.535898i | −0.00638351 | + | 0.0238236i | ||||
\(507\) | 22.1436 | 0.983432 | ||||||||
\(508\) | 15.4641 | − | 26.7846i | 0.686109 | − | 1.18837i | ||||
\(509\) | − | 25.8564i | − | 1.14607i | −0.819533 | − | 0.573033i | \(-0.805767\pi\) | ||
0.819533 | − | 0.573033i | \(-0.194233\pi\) | |||||||
\(510\) | −4.09808 | + | 15.2942i | −0.181466 | + | 0.677240i | ||||
\(511\) | −25.8564 | − | 22.3923i | −1.14382 | − | 0.990577i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 31.1769 | 1.37649 | ||||||||
\(514\) | −8.19615 | − | 2.19615i | −0.361517 | − | 0.0968681i | ||||
\(515\) | 6.80385i | 0.299813i | ||||||||
\(516\) | −3.46410 | + | 6.00000i | −0.152499 | + | 0.264135i | ||||
\(517\) | 0.464102i | 0.0204112i | ||||||||
\(518\) | 19.8564 | + | 29.3205i | 0.872440 | + | 1.28827i | ||||
\(519\) | 24.8038i | 1.08877i | ||||||||
\(520\) | 0.928203 | − | 0.928203i | 0.0407044 | − | 0.0407044i | ||||
\(521\) | − | 13.6077i | − | 0.596164i | −0.954540 | − | 0.298082i | \(-0.903653\pi\) | ||
0.954540 | − | 0.298082i | \(-0.0963469\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.2487 | 1.06032 | 0.530161 | − | 0.847897i | \(-0.322131\pi\) | ||||
0.530161 | + | 0.847897i | \(0.322131\pi\) | |||||||
\(524\) | 4.39230 | + | 2.53590i | 0.191879 | + | 0.110781i | ||||
\(525\) | −3.00000 | + | 3.46410i | −0.130931 | + | 0.151186i | ||||
\(526\) | 15.6603 | + | 4.19615i | 0.682820 | + | 0.182961i | ||||
\(527\) | 38.7846i | 1.68948i | ||||||||
\(528\) | 1.60770 | − | 0.928203i | 0.0699660 | − | 0.0403949i | ||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 2.73205 | + | 0.732051i | 0.118673 | + | 0.0317983i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30.0000 | − | 10.3923i | 1.30066 | − | 0.450564i | ||||
\(533\) | −1.60770 | −0.0696370 | ||||||||
\(534\) | −6.00000 | − | 1.60770i | −0.259645 | − | 0.0695718i | ||||
\(535\) | −2.39230 | −0.103428 | ||||||||
\(536\) | −6.92820 | − | 6.92820i | −0.299253 | − | 0.299253i | ||||
\(537\) | 11.0718i | 0.477783i | ||||||||
\(538\) | 16.3923 | + | 4.39230i | 0.706722 | + | 0.189366i | ||||
\(539\) | −1.85641 | + | 0.267949i | −0.0799611 | + | 0.0115414i | ||||
\(540\) | −5.19615 | + | 9.00000i | −0.223607 | + | 0.387298i | ||||
\(541\) | 7.78461 | 0.334687 | 0.167343 | − | 0.985899i | \(-0.446481\pi\) | ||||
0.167343 | + | 0.985899i | \(0.446481\pi\) | |||||||
\(542\) | −3.46410 | + | 12.9282i | −0.148796 | + | 0.555314i | ||||
\(543\) | 1.60770i | 0.0689928i | ||||||||
\(544\) | 9.46410 | + | 35.3205i | 0.405770 | + | 1.51435i | ||||
\(545\) | 2.07180i | 0.0887460i | ||||||||
\(546\) | 2.49038 | − | 1.68653i | 0.106578 | − | 0.0721770i | ||||
\(547\) | − | 21.4641i | − | 0.917739i | −0.888504 | − | 0.458869i | \(-0.848255\pi\) | ||
0.888504 | − | 0.458869i | \(-0.151745\pi\) | |||||||
\(548\) | −35.3205 | − | 20.3923i | −1.50882 | − | 0.871116i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.366025 | + | 0.0980762i | 0.0156074 | + | 0.00418198i | ||||
\(551\) | −47.5692 | −2.02652 | ||||||||
\(552\) | 5.07180 | + | 5.07180i | 0.215870 | + | 0.215870i | ||||
\(553\) | −29.3205 | − | 25.3923i | −1.24683 | − | 1.07979i | ||||
\(554\) | 6.14359 | − | 22.9282i | 0.261016 | − | 0.974126i | ||||
\(555\) | − | 16.3923i | − | 0.695815i | ||||||
\(556\) | 12.0000 | + | 6.92820i | 0.508913 | + | 0.293821i | ||||
\(557\) | −21.8564 | −0.926086 | −0.463043 | − | 0.886336i | \(-0.653242\pi\) | ||||
−0.463043 | + | 0.886336i | \(0.653242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.928203 | 0.0392588 | ||||||||
\(560\) | −2.00000 | + | 10.3923i | −0.0845154 | + | 0.439155i | ||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | −2.90192 | + | 10.8301i | −0.122410 | + | 0.456841i | ||||
\(563\) | −19.1769 | −0.808211 | −0.404105 | − | 0.914712i | \(-0.632417\pi\) | ||||
−0.404105 | + | 0.914712i | \(0.632417\pi\) | |||||||
\(564\) | 5.19615 | + | 3.00000i | 0.218797 | + | 0.126323i | ||||
\(565\) | 5.46410i | 0.229876i | ||||||||
\(566\) | −4.43782 | + | 16.5622i | −0.186536 | + | 0.696160i | ||||
\(567\) | −15.5885 | + | 18.0000i | −0.654654 | + | 0.755929i | ||||
\(568\) | 14.9282 | + | 14.9282i | 0.626373 | + | 0.626373i | ||||
\(569\) | 7.07180 | 0.296465 | 0.148233 | − | 0.988953i | \(-0.452642\pi\) | ||||
0.148233 | + | 0.988953i | \(0.452642\pi\) | |||||||
\(570\) | −14.1962 | − | 3.80385i | −0.594611 | − | 0.159326i | ||||
\(571\) | 6.67949i | 0.279528i | 0.990185 | + | 0.139764i | \(0.0446344\pi\) | ||||
−0.990185 | + | 0.139764i | \(0.955366\pi\) | |||||||
\(572\) | −0.215390 | − | 0.124356i | −0.00900592 | − | 0.00519957i | ||||
\(573\) | − | 12.4641i | − | 0.520695i | ||||||
\(574\) | 10.7321 | − | 7.26795i | 0.447947 | − | 0.303358i | ||||
\(575\) | 1.46410i | 0.0610573i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.3923i | − | 0.807312i | −0.914911 | − | 0.403656i | \(-0.867739\pi\) | ||
0.914911 | − | 0.403656i | \(-0.132261\pi\) | |||||||
\(578\) | −9.07180 | + | 33.8564i | −0.377337 | + | 1.40824i | ||||
\(579\) | −16.3923 | −0.681241 | ||||||||
\(580\) | 7.92820 | − | 13.7321i | 0.329201 | − | 0.570192i | ||||
\(581\) | −26.7846 | + | 30.9282i | −1.11121 | + | 1.28312i | ||||
\(582\) | 31.6865 | + | 8.49038i | 1.31345 | + | 0.351938i | ||||
\(583\) | − | 0.535898i | − | 0.0221946i | ||||||
\(584\) | 25.8564 | + | 25.8564i | 1.06995 | + | 1.06995i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.7583 | − | 7.43782i | −1.14669 | − | 0.307254i | ||||
\(587\) | 20.5359 | 0.847607 | 0.423804 | − | 0.905754i | \(-0.360695\pi\) | ||||
0.423804 | + | 0.905754i | \(0.360695\pi\) | |||||||
\(588\) | −9.00000 | + | 22.5167i | −0.371154 | + | 0.928571i | ||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 4.73205 | + | 1.26795i | 0.194815 | + | 0.0522006i | ||||
\(591\) | −23.0718 | −0.949047 | ||||||||
\(592\) | −18.9282 | − | 32.7846i | −0.777944 | − | 1.34744i | ||||
\(593\) | − | 30.4641i | − | 1.25101i | −0.780220 | − | 0.625505i | \(-0.784893\pi\) | ||
0.780220 | − | 0.625505i | \(-0.215107\pi\) | |||||||
\(594\) | 1.90192 | + | 0.509619i | 0.0780369 | + | 0.0209099i | ||||
\(595\) | −11.1962 | + | 12.9282i | −0.458997 | + | 0.530005i | ||||
\(596\) | −5.32051 | − | 3.07180i | −0.217937 | − | 0.125826i | ||||
\(597\) | −6.00000 | −0.245564 | ||||||||
\(598\) | 0.248711 | − | 0.928203i | 0.0101706 | − | 0.0379571i | ||||
\(599\) | 10.1244i | 0.413670i | 0.978376 | + | 0.206835i | \(0.0663163\pi\) | ||||
−0.978376 | + | 0.206835i | \(0.933684\pi\) | |||||||
\(600\) | 3.46410 | − | 3.46410i | 0.141421 | − | 0.141421i | ||||
\(601\) | 14.7846i | 0.603077i | 0.953454 | + | 0.301538i | \(0.0975001\pi\) | ||||
−0.953454 | + | 0.301538i | \(0.902500\pi\) | |||||||
\(602\) | −6.19615 | + | 4.19615i | −0.252536 | + | 0.171022i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.1962 | + | 26.3205i | −0.618323 | + | 1.07097i | ||||
\(605\) | 10.9282i | 0.444295i | ||||||||
\(606\) | 36.5885 | + | 9.80385i | 1.48630 | + | 0.398254i | ||||
\(607\) | 29.1962 | 1.18504 | 0.592518 | − | 0.805557i | \(-0.298134\pi\) | ||||
0.592518 | + | 0.805557i | \(0.298134\pi\) | |||||||
\(608\) | −32.7846 | + | 8.78461i | −1.32959 | + | 0.356263i | ||||
\(609\) | 23.7846 | − | 27.4641i | 0.963801 | − | 1.11290i | ||||
\(610\) | 3.46410 | − | 12.9282i | 0.140257 | − | 0.523448i | ||||
\(611\) | − | 0.803848i | − | 0.0325202i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0000 | −0.403896 | −0.201948 | − | 0.979396i | \(-0.564727\pi\) | ||||
−0.201948 | + | 0.979396i | \(0.564727\pi\) | |||||||
\(614\) | −0.633975 | + | 2.36603i | −0.0255851 | + | 0.0954850i | ||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 2.00000 | − | 0.143594i | 0.0805823 | − | 0.00578555i | ||||
\(617\) | −22.9282 | −0.923055 | −0.461527 | − | 0.887126i | \(-0.652698\pi\) | ||||
−0.461527 | + | 0.887126i | \(0.652698\pi\) | |||||||
\(618\) | 4.31347 | − | 16.0981i | 0.173513 | − | 0.647560i | ||||
\(619\) | −0.679492 | −0.0273111 | −0.0136555 | − | 0.999907i | \(-0.504347\pi\) | ||||
−0.0136555 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(620\) | 6.00000 | − | 10.3923i | 0.240966 | − | 0.417365i | ||||
\(621\) | 7.60770i | 0.305286i | ||||||||
\(622\) | −2.87564 | + | 10.7321i | −0.115303 | + | 0.430316i | ||||
\(623\) | −5.07180 | − | 4.39230i | −0.203197 | − | 0.175974i | ||||
\(624\) | −2.78461 | + | 1.60770i | −0.111474 | + | 0.0643593i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.9545 | + | 6.41858i | 0.957414 | + | 0.256538i | ||||
\(627\) | 2.78461i | 0.111207i | ||||||||
\(628\) | −7.85641 | + | 13.6077i | −0.313505 | + | 0.543006i | ||||
\(629\) | − | 61.1769i | − | 2.43928i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.9090i | − | 1.54894i | −0.632610 | − | 0.774471i | \(-0.718016\pi\) | ||
0.632610 | − | 0.774471i | \(-0.281984\pi\) | |||||||
\(632\) | 29.3205 | + | 29.3205i | 1.16631 | + | 1.16631i | ||||
\(633\) | − | 5.53590i | − | 0.220032i | ||||||
\(634\) | −1.12436 | + | 4.19615i | −0.0446539 | + | 0.166651i | ||||
\(635\) | −15.4641 | −0.613674 | ||||||||
\(636\) | −6.00000 | − | 3.46410i | −0.237915 | − | 0.137361i | ||||
\(637\) | 3.21539 | − | 0.464102i | 0.127398 | − | 0.0183884i | ||||
\(638\) | −2.90192 | − | 0.777568i | −0.114888 | − | 0.0307842i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.92820 | − | 10.9282i | 0.115747 | − | 0.431975i | ||||
\(641\) | 8.92820 | 0.352643 | 0.176321 | − | 0.984333i | \(-0.443580\pi\) | ||||
0.176321 | + | 0.984333i | \(0.443580\pi\) | |||||||
\(642\) | 5.66025 | + | 1.51666i | 0.223392 | + | 0.0598578i | ||||
\(643\) | −7.05256 | −0.278126 | −0.139063 | − | 0.990284i | \(-0.544409\pi\) | ||||
−0.139063 | + | 0.990284i | \(0.544409\pi\) | |||||||
\(644\) | 2.53590 | + | 7.32051i | 0.0999284 | + | 0.288468i | ||||
\(645\) | 3.46410 | 0.136399 | ||||||||
\(646\) | −52.9808 | − | 14.1962i | −2.08450 | − | 0.558540i | ||||
\(647\) | 10.3923 | 0.408564 | 0.204282 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.707107 | − | 0.707107i | ||||
\(649\) | − | 0.928203i | − | 0.0364352i | ||||||
\(650\) | −0.633975 | − | 0.169873i | −0.0248665 | − | 0.00666297i | ||||
\(651\) | 18.0000 | − | 20.7846i | 0.705476 | − | 0.814613i | ||||
\(652\) | 20.7846 | − | 36.0000i | 0.813988 | − | 1.40987i | ||||
\(653\) | 17.6077 | 0.689042 | 0.344521 | − | 0.938779i | \(-0.388041\pi\) | ||||
0.344521 | + | 0.938779i | \(0.388041\pi\) | |||||||
\(654\) | 1.31347 | − | 4.90192i | 0.0513606 | − | 0.191680i | ||||
\(655\) | − | 2.53590i | − | 0.0990857i | ||||||
\(656\) | −12.0000 | + | 6.92820i | −0.468521 | + | 0.270501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.63397 | + | 5.36603i | 0.141667 | + | 0.209189i | ||||
\(659\) | 31.1962i | 1.21523i | 0.794232 | + | 0.607615i | \(0.207874\pi\) | ||||
−0.794232 | + | 0.607615i | \(0.792126\pi\) | |||||||
\(660\) | −0.803848 | − | 0.464102i | −0.0312897 | − | 0.0180651i | ||||
\(661\) | − | 39.7128i | − | 1.54465i | −0.635228 | − | 0.772325i | \(-0.719094\pi\) | ||
0.635228 | − | 0.772325i | \(-0.280906\pi\) | |||||||
\(662\) | 36.0526 | + | 9.66025i | 1.40122 | + | 0.375456i | ||||
\(663\) | −5.19615 | −0.201802 | ||||||||
\(664\) | 30.9282 | − | 30.9282i | 1.20025 | − | 1.20025i | ||||
\(665\) | −12.0000 | − | 10.3923i | −0.465340 | − | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.6077i | − | 0.449452i | ||||||
\(668\) | −9.00000 | − | 5.19615i | −0.348220 | − | 0.201045i | ||||
\(669\) | 23.7846 | 0.919566 | ||||||||
\(670\) | −1.26795 | + | 4.73205i | −0.0489852 | + | 0.182815i | ||||
\(671\) | −2.53590 | −0.0978973 | ||||||||
\(672\) | 11.3205 | − | 23.3205i | 0.436698 | − | 0.899608i | ||||
\(673\) | −13.1769 | −0.507933 | −0.253966 | − | 0.967213i | \(-0.581735\pi\) | ||||
−0.253966 | + | 0.967213i | \(0.581735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.19615 | 0.200000 | ||||||||
\(676\) | −22.1436 | − | 12.7846i | −0.851677 | − | 0.491716i | ||||
\(677\) | 25.3923i | 0.975906i | 0.872870 | + | 0.487953i | \(0.162256\pi\) | ||||
−0.872870 | + | 0.487953i | \(0.837744\pi\) | |||||||
\(678\) | 3.46410 | − | 12.9282i | 0.133038 | − | 0.496505i | ||||
\(679\) | 26.7846 | + | 23.1962i | 1.02790 | + | 0.890187i | ||||
\(680\) | 12.9282 | − | 12.9282i | 0.495774 | − | 0.495774i | ||||
\(681\) | −35.7846 | −1.37127 | ||||||||
\(682\) | −2.19615 | − | 0.588457i | −0.0840950 | − | 0.0225332i | ||||
\(683\) | − | 7.32051i | − | 0.280111i | −0.990144 | − | 0.140056i | \(-0.955272\pi\) | ||
0.990144 | − | 0.140056i | \(-0.0447282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3923i | 0.779150i | ||||||||
\(686\) | −19.3660 | + | 17.6340i | −0.739398 | + | 0.673268i | ||||
\(687\) | 14.7846i | 0.564068i | ||||||||
\(688\) | 6.92820 | − | 4.00000i | 0.264135 | − | 0.152499i | ||||
\(689\) | 0.928203i | 0.0353617i | ||||||||
\(690\) | 0.928203 | − | 3.46410i | 0.0353361 | − | 0.131876i | ||||
\(691\) | 22.6410 | 0.861305 | 0.430652 | − | 0.902518i | \(-0.358283\pi\) | ||||
0.430652 | + | 0.902518i | \(0.358283\pi\) | |||||||
\(692\) | 14.3205 | − | 24.8038i | 0.544384 | − | 0.942901i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −46.7846 | − | 12.5359i | −1.77592 | − | 0.475856i | ||||
\(695\) | − | 6.92820i | − | 0.262802i | ||||||
\(696\) | −27.4641 | + | 27.4641i | −1.04102 | + | 1.04102i | ||||
\(697\) | −22.3923 | −0.848169 | ||||||||
\(698\) | 7.26795 | + | 1.94744i | 0.275096 | + | 0.0737117i | ||||
\(699\) | −15.7128 | −0.594313 | ||||||||
\(700\) | 5.00000 | − | 1.73205i | 0.188982 | − | 0.0654654i | ||||
\(701\) | −37.7846 | −1.42711 | −0.713553 | − | 0.700602i | \(-0.752915\pi\) | ||||
−0.713553 | + | 0.700602i | \(0.752915\pi\) | |||||||
\(702\) | −3.29423 | − | 0.882686i | −0.124333 | − | 0.0333148i | ||||
\(703\) | 56.7846 | 2.14167 | ||||||||
\(704\) | −2.14359 | −0.0807897 | ||||||||
\(705\) | − | 3.00000i | − | 0.112987i | ||||||
\(706\) | 10.0981 | + | 2.70577i | 0.380046 | + | 0.101833i | ||||
\(707\) | 30.9282 | + | 26.7846i | 1.16317 | + | 1.00734i | ||||
\(708\) | −10.3923 | − | 6.00000i | −0.390567 | − | 0.225494i | ||||
\(709\) | 21.0000 | 0.788672 | 0.394336 | − | 0.918966i | \(-0.370975\pi\) | ||||
0.394336 | + | 0.918966i | \(0.370975\pi\) | |||||||
\(710\) | 2.73205 | − | 10.1962i | 0.102532 | − | 0.382655i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.07180 | + | 5.07180i | 0.190074 | + | 0.190074i | ||||
\(713\) | − | 8.78461i | − | 0.328986i | ||||||
\(714\) | 34.6865 | − | 23.4904i | 1.29811 | − | 0.879105i | ||||
\(715\) | 0.124356i | 0.00465064i | ||||||||
\(716\) | 6.39230 | − | 11.0718i | 0.238892 | − | 0.413772i | ||||
\(717\) | 41.5359i | 1.55119i | ||||||||
\(718\) | −34.5885 | − | 9.26795i | −1.29083 | − | 0.345877i | ||||
\(719\) | −38.5359 | −1.43715 | −0.718573 | − | 0.695451i | \(-0.755205\pi\) | ||||
−0.718573 | + | 0.695451i | \(0.755205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7846 | − | 13.6077i | 0.438882 | − | 0.506777i | ||||
\(722\) | 6.22243 | − | 23.2224i | 0.231575 | − | 0.864249i | ||||
\(723\) | − | 28.3923i | − | 1.05592i | ||||||
\(724\) | 0.928203 | − | 1.60770i | 0.0344964 | − | 0.0597495i | ||||
\(725\) | −7.92820 | −0.294446 | ||||||||
\(726\) | 6.92820 | − | 25.8564i | 0.257130 | − | 0.959621i | ||||
\(727\) | 13.6077 | 0.504681 | 0.252341 | − | 0.967638i | \(-0.418800\pi\) | ||||
0.252341 | + | 0.967638i | \(0.418800\pi\) | |||||||
\(728\) | −3.46410 | + | 0.248711i | −0.128388 | + | 0.00921785i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 4.73205 | − | 17.6603i | 0.175141 | − | 0.653635i | ||||
\(731\) | 12.9282 | 0.478167 | ||||||||
\(732\) | −16.3923 | + | 28.3923i | −0.605877 | + | 1.04941i | ||||
\(733\) | − | 11.5359i | − | 0.426088i | −0.977043 | − | 0.213044i | \(-0.931662\pi\) | ||
0.977043 | − | 0.213044i | \(-0.0683378\pi\) | |||||||
\(734\) | −4.34679 | + | 16.2224i | −0.160443 | + | 0.598781i | ||||
\(735\) | 12.0000 | − | 1.73205i | 0.442627 | − | 0.0638877i | ||||
\(736\) | −2.14359 | − | 8.00000i | −0.0790139 | − | 0.294884i | ||||
\(737\) | 0.928203 | 0.0341908 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.26795i | 0.156999i | 0.996914 | + | 0.0784995i | \(0.0250129\pi\) | ||||
−0.996914 | + | 0.0784995i | \(0.974987\pi\) | |||||||
\(740\) | −9.46410 | + | 16.3923i | −0.347907 | + | 0.602593i | ||||
\(741\) | − | 4.82309i | − | 0.177180i | ||||||
\(742\) | −4.19615 | − | 6.19615i | −0.154046 | − | 0.227468i | ||||
\(743\) | − | 30.3923i | − | 1.11499i | −0.830182 | − | 0.557493i | \(-0.811763\pi\) | ||
0.830182 | − | 0.557493i | \(-0.188237\pi\) | |||||||
\(744\) | −20.7846 | + | 20.7846i | −0.762001 | + | 0.762001i | ||||
\(745\) | 3.07180i | 0.112542i | ||||||||
\(746\) | −1.32051 | + | 4.92820i | −0.0483472 | + | 0.180434i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.00000 | − | 1.73205i | −0.109691 | − | 0.0633300i | ||||
\(749\) | 4.78461 | + | 4.14359i | 0.174826 | + | 0.151404i | ||||
\(750\) | −2.36603 | − | 0.633975i | −0.0863950 | − | 0.0231495i | ||||
\(751\) | 25.5885i | 0.933736i | 0.884327 | + | 0.466868i | \(0.154618\pi\) | ||||
−0.884327 | + | 0.466868i | \(0.845382\pi\) | |||||||
\(752\) | −3.46410 | − | 6.00000i | −0.126323 | − | 0.218797i | ||||
\(753\) | 44.7846 | 1.63204 | ||||||||
\(754\) | 5.02628 | + | 1.34679i | 0.183046 | + | 0.0490471i | ||||
\(755\) | 15.1962 | 0.553045 | ||||||||
\(756\) | 25.9808 | − | 9.00000i | 0.944911 | − | 0.327327i | ||||
\(757\) | 37.8564 | 1.37591 | 0.687957 | − | 0.725751i | \(-0.258508\pi\) | ||||
0.687957 | + | 0.725751i | \(0.258508\pi\) | |||||||
\(758\) | −7.66025 | − | 2.05256i | −0.278233 | − | 0.0745523i | ||||
\(759\) | −0.679492 | −0.0246640 | ||||||||
\(760\) | 12.0000 | + | 12.0000i | 0.435286 | + | 0.435286i | ||||
\(761\) | 42.2487i | 1.53151i | 0.643130 | + | 0.765757i | \(0.277636\pi\) | ||||
−0.643130 | + | 0.765757i | \(0.722364\pi\) | |||||||
\(762\) | 36.5885 | + | 9.80385i | 1.32546 | + | 0.355156i | ||||
\(763\) | 3.58846 | − | 4.14359i | 0.129911 | − | 0.150008i | ||||
\(764\) | −7.19615 | + | 12.4641i | −0.260348 | + | 0.450935i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.0526 | + | 37.5167i | −0.363214 | + | 1.35553i | ||||
\(767\) | 1.60770i | 0.0580505i | ||||||||
\(768\) | −13.8564 | + | 24.0000i | −0.500000 | + | 0.866025i | ||||
\(769\) | − | 18.0000i | − | 0.649097i | −0.945869 | − | 0.324548i | \(-0.894788\pi\) | ||
0.945869 | − | 0.324548i | \(-0.105212\pi\) | |||||||
\(770\) | −0.562178 | − | 0.830127i | −0.0202595 | − | 0.0299157i | ||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | 16.3923 | + | 9.46410i | 0.589972 | + | 0.340620i | ||||
\(773\) | 5.53590i | 0.199112i | 0.995032 | + | 0.0995562i | \(0.0317423\pi\) | ||||
−0.995032 | + | 0.0995562i | \(0.968258\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | −26.7846 | − | 26.7846i | −0.961511 | − | 0.961511i | ||||
\(777\) | −28.3923 | + | 32.7846i | −1.01857 | + | 1.17614i | ||||
\(778\) | −7.63397 | + | 28.4904i | −0.273691 | + | 1.02143i | ||||
\(779\) | − | 20.7846i | − | 0.744686i | ||||||
\(780\) | 1.39230 | + | 0.803848i | 0.0498525 | + | 0.0287824i | ||||
\(781\) | −2.00000 | −0.0715656 | ||||||||
\(782\) | 3.46410 | − | 12.9282i | 0.123876 | − | 0.462312i | ||||
\(783\) | −41.1962 | −1.47223 | ||||||||
\(784\) | 22.0000 | − | 17.3205i | 0.785714 | − | 0.618590i | ||||
\(785\) | 7.85641 | 0.280407 | ||||||||
\(786\) | −1.60770 | + | 6.00000i | −0.0573446 | + | 0.214013i | ||||
\(787\) | −32.6603 | −1.16421 | −0.582106 | − | 0.813113i | \(-0.697771\pi\) | ||||
−0.582106 | + | 0.813113i | \(0.697771\pi\) | |||||||
\(788\) | 23.0718 | + | 13.3205i | 0.821899 | + | 0.474523i | ||||
\(789\) | 19.8564i | 0.706907i | ||||||||
\(790\) | 5.36603 | − | 20.0263i | 0.190915 | − | 0.712503i | ||||
\(791\) | 9.46410 | − | 10.9282i | 0.336505 | − | 0.388562i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.39230 | 0.155975 | ||||||||
\(794\) | −17.0263 | − | 4.56218i | −0.604240 | − | 0.161906i | ||||
\(795\) | 3.46410i | 0.122859i | ||||||||
\(796\) | 6.00000 | + | 3.46410i | 0.212664 | + | 0.122782i | ||||
\(797\) | 22.1769i | 0.785547i | 0.919635 | + | 0.392773i | \(0.128484\pi\) | ||||
−0.919635 | + | 0.392773i | \(0.871516\pi\) | |||||||
\(798\) | 21.8038 | + | 32.1962i | 0.771848 | + | 1.13973i | ||||
\(799\) | − | 11.1962i | − | 0.396091i | ||||||
\(800\) | −5.46410 | + | 1.46410i | −0.193185 | + | 0.0517638i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.68653 | + | 13.7583i | −0.130176 | + | 0.485824i | ||||
\(803\) | −3.46410 | −0.122245 | ||||||||
\(804\) | 6.00000 | − | 10.3923i | 0.211604 | − | 0.366508i | ||||
\(805\) | 2.53590 | − | 2.92820i | 0.0893787 | − | 0.103206i | ||||
\(806\) | 3.80385 | + | 1.01924i | 0.133985 | + | 0.0359011i | ||||
\(807\) | 20.7846i | 0.731653i | ||||||||
\(808\) | −30.9282 | − | 30.9282i | −1.08805 | − | 1.08805i | ||||
\(809\) | 7.92820 | 0.278741 | 0.139370 | − | 0.990240i | \(-0.455492\pi\) | ||||
0.139370 | + | 0.990240i | \(0.455492\pi\) | |||||||
\(810\) | −12.2942 | − | 3.29423i | −0.431975 | − | 0.115747i | ||||
\(811\) | −29.0718 | −1.02085 | −0.510424 | − | 0.859923i | \(-0.670512\pi\) | ||||
−0.510424 | + | 0.859923i | \(0.670512\pi\) | |||||||
\(812\) | −39.6410 | + | 13.7321i | −1.39113 | + | 0.481901i | ||||
\(813\) | −16.3923 | −0.574903 | ||||||||
\(814\) | 3.46410 | + | 0.928203i | 0.121417 | + | 0.0325335i | ||||
\(815\) | −20.7846 | −0.728053 | ||||||||
\(816\) | −38.7846 | + | 22.3923i | −1.35773 | + | 0.783887i | ||||
\(817\) | 12.0000i | 0.419827i | ||||||||
\(818\) | −5.66025 | − | 1.51666i | −0.197906 | − | 0.0530288i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | + | 3.46410i | 0.209529 | + | 0.120972i | ||||
\(821\) | 27.7846 | 0.969690 | 0.484845 | − | 0.874600i | \(-0.338876\pi\) | ||||
0.484845 | + | 0.874600i | \(0.338876\pi\) | |||||||
\(822\) | 12.9282 | − | 48.2487i | 0.450923 | − | 1.68287i | ||||
\(823\) | − | 11.0718i | − | 0.385939i | −0.981205 | − | 0.192969i | \(-0.938188\pi\) | ||
0.981205 | − | 0.192969i | \(-0.0618118\pi\) | |||||||
\(824\) | −13.6077 | + | 13.6077i | −0.474047 | + | 0.474047i | ||||
\(825\) | 0.464102i | 0.0161579i | ||||||||
\(826\) | −7.26795 | − | 10.7321i | −0.252884 | − | 0.373416i | ||||
\(827\) | − | 14.1436i | − | 0.491821i | −0.969293 | − | 0.245910i | \(-0.920913\pi\) | ||
0.969293 | − | 0.245910i | \(-0.0790869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.248711i | − | 0.00863810i | −0.999991 | − | 0.00431905i | \(-0.998625\pi\) | ||
0.999991 | − | 0.00431905i | \(-0.00137480\pi\) | |||||||
\(830\) | −21.1244 | − | 5.66025i | −0.733237 | − | 0.196470i | ||||
\(831\) | 29.0718 | 1.00849 | ||||||||
\(832\) | 3.71281 | 0.128719 | ||||||||
\(833\) | 44.7846 | − | 6.46410i | 1.55169 | − | 0.223968i | ||||
\(834\) | −4.39230 | + | 16.3923i | −0.152093 | + | 0.567619i | ||||
\(835\) | 5.19615i | 0.179820i | ||||||||
\(836\) | 1.60770 | − | 2.78461i | 0.0556033 | − | 0.0963077i | ||||
\(837\) | −31.1769 | −1.07763 | ||||||||
\(838\) | 8.87564 | − | 33.1244i | 0.306604 | − | 1.14426i | ||||
\(839\) | −4.39230 | −0.151639 | −0.0758196 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758196 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(840\) | −12.9282 | + | 0.928203i | −0.446065 | + | 0.0320261i | ||||
\(841\) | 33.8564 | 1.16746 | ||||||||
\(842\) | 6.95448 | − | 25.9545i | 0.239667 | − | 0.894451i | ||||
\(843\) | −13.7321 | −0.472957 | ||||||||
\(844\) | −3.19615 | + | 5.53590i | −0.110016 | + | 0.190553i | ||||
\(845\) | 12.7846i | 0.439804i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9282 | − | 21.8564i | 0.650381 | − | 0.750995i | ||||
\(848\) | 4.00000 | + | 6.92820i | 0.137361 | + | 0.237915i | ||||
\(849\) | −21.0000 | −0.720718 | ||||||||
\(850\) | −8.83013 | − | 2.36603i | −0.302871 | − | 0.0811540i | ||||
\(851\) | 13.8564i | 0.474991i | ||||||||
\(852\) | −12.9282 | + | 22.3923i | −0.442913 | + | 0.767148i | ||||
\(853\) | 2.78461i | 0.0953432i | 0.998863 | + | 0.0476716i | \(0.0151801\pi\) | ||||
−0.998863 | + | 0.0476716i | \(0.984820\pi\) | |||||||
\(854\) | −29.3205 | + | 19.8564i | −1.00333 | + | 0.679472i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.78461 | − | 4.78461i | −0.163535 | − | 0.163535i | ||||
\(857\) | − | 57.7128i | − | 1.97143i | −0.168416 | − | 0.985716i | \(-0.553865\pi\) | ||
0.168416 | − | 0.985716i | \(-0.446135\pi\) | |||||||
\(858\) | 0.0788383 | − | 0.294229i | 0.00269150 | − | 0.0100448i | ||||
\(859\) | −39.7128 | −1.35498 | −0.677492 | − | 0.735530i | \(-0.736933\pi\) | ||||
−0.677492 | + | 0.735530i | \(0.736933\pi\) | |||||||
\(860\) | −3.46410 | − | 2.00000i | −0.118125 | − | 0.0681994i | ||||
\(861\) | 12.0000 | + | 10.3923i | 0.408959 | + | 0.354169i | ||||
\(862\) | 18.5622 | + | 4.97372i | 0.632230 | + | 0.169406i | ||||
\(863\) | 39.8564i | 1.35673i | 0.734726 | + | 0.678364i | \(0.237311\pi\) | ||||
−0.734726 | + | 0.678364i | \(0.762689\pi\) | |||||||
\(864\) | −28.3923 | + | 7.60770i | −0.965926 | + | 0.258819i | ||||
\(865\) | −14.3205 | −0.486912 | ||||||||
\(866\) | 43.5167 | + | 11.6603i | 1.47876 | + | 0.396232i | ||||
\(867\) | −42.9282 | −1.45792 | ||||||||
\(868\) | −30.0000 | + | 10.3923i | −1.01827 | + | 0.352738i | ||||
\(869\) | −3.92820 | −0.133255 | ||||||||
\(870\) | 18.7583 | + | 5.02628i | 0.635967 | + | 0.170407i | ||||
\(871\) | −1.60770 | −0.0544747 | ||||||||
\(872\) | −4.14359 | + | 4.14359i | −0.140320 | + | 0.140320i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | + | 3.21539i | 0.405906 | + | 0.108762i | ||||
\(875\) | −2.00000 | − | 1.73205i | −0.0676123 | − | 0.0585540i | ||||
\(876\) | −22.3923 | + | 38.7846i | −0.756566 | + | 1.31041i | ||||
\(877\) | −18.3923 | −0.621064 | −0.310532 | − | 0.950563i | \(-0.600507\pi\) | ||||
−0.310532 | + | 0.950563i | \(0.600507\pi\) | |||||||
\(878\) | 14.5359 | − | 54.2487i | 0.490563 | − | 1.83081i | ||||
\(879\) | − | 35.1962i | − | 1.18714i | ||||||
\(880\) | 0.535898 | + | 0.928203i | 0.0180651 | + | 0.0312897i | ||||
\(881\) | 29.0718i | 0.979454i | 0.871876 | + | 0.489727i | \(0.162904\pi\) | ||||
−0.871876 | + | 0.489727i | \(0.837096\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.6077i | 0.794462i | 0.917719 | + | 0.397231i | \(0.130029\pi\) | ||||
−0.917719 | + | 0.397231i | \(0.869971\pi\) | |||||||
\(884\) | 5.19615 | + | 3.00000i | 0.174766 | + | 0.100901i | ||||
\(885\) | 6.00000i | 0.201688i | ||||||||
\(886\) | 35.5167 | + | 9.51666i | 1.19321 | + | 0.319718i | ||||
\(887\) | 8.53590 | 0.286607 | 0.143304 | − | 0.989679i | \(-0.454227\pi\) | ||||
0.143304 | + | 0.989679i | \(0.454227\pi\) | |||||||
\(888\) | 32.7846 | − | 32.7846i | 1.10018 | − | 1.10018i | ||||
\(889\) | 30.9282 | + | 26.7846i | 1.03730 | + | 0.898327i | ||||
\(890\) | 0.928203 | − | 3.46410i | 0.0311134 | − | 0.116117i | ||||
\(891\) | 2.41154i | 0.0807897i | ||||||||
\(892\) | −23.7846 | − | 13.7321i | −0.796368 | − | 0.459783i | ||||
\(893\) | 10.3923 | 0.347765 | ||||||||
\(894\) | 1.94744 | − | 7.26795i | 0.0651322 | − | 0.243077i | ||||
\(895\) | −6.39230 | −0.213671 | ||||||||
\(896\) | −24.7846 | + | 16.7846i | −0.827996 | + | 0.560734i | ||||
\(897\) | 1.17691 | 0.0392960 | ||||||||
\(898\) | 4.36603 | − | 16.2942i | 0.145696 | − | 0.543745i | ||||
\(899\) | 47.5692 | 1.58652 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9282i | 0.430701i | ||||||||
\(902\) | 0.339746 | − | 1.26795i | 0.0113123 | − | 0.0422181i | ||||
\(903\) | −6.92820 | − | 6.00000i | −0.230556 | − | 0.199667i | ||||
\(904\) | −10.9282 | + | 10.9282i | −0.363467 | + | 0.363467i | ||||
\(905\) | −0.928203 | −0.0308545 | ||||||||
\(906\) | −35.9545 | − | 9.63397i | −1.19451 | − | 0.320067i | ||||
\(907\) | 32.3923i | 1.07557i | 0.843082 | + | 0.537784i | \(0.180739\pi\) | ||||
−0.843082 | + | 0.537784i | \(0.819261\pi\) | |||||||
\(908\) | 35.7846 | + | 20.6603i | 1.18755 | + | 0.685635i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.973721 | + | 1.43782i | 0.0322785 | + | 0.0476633i | ||||
\(911\) | 20.2487i | 0.670870i | 0.942063 | + | 0.335435i | \(0.108883\pi\) | ||||
−0.942063 | + | 0.335435i | \(0.891117\pi\) | |||||||
\(912\) | −20.7846 | − | 36.0000i | −0.688247 | − | 1.19208i | ||||
\(913\) | 4.14359i | 0.137133i | ||||||||
\(914\) | 7.51666 | − | 28.0526i | 0.248629 | − | 0.927896i | ||||
\(915\) | 16.3923 | 0.541913 | ||||||||
\(916\) | 8.53590 | − | 14.7846i | 0.282034 | − | 0.488497i | ||||
\(917\) | −4.39230 | + | 5.07180i | −0.145047 | + | 0.167485i | ||||
\(918\) | −45.8827 | − | 12.2942i | −1.51435 | − | 0.405770i | ||||
\(919\) | 6.41154i | 0.211497i | 0.994393 | + | 0.105749i | \(0.0337239\pi\) | ||||
−0.994393 | + | 0.105749i | \(0.966276\pi\) | |||||||
\(920\) | −2.92820 | + | 2.92820i | −0.0965400 | + | 0.0965400i | ||||
\(921\) | −3.00000 | −0.0988534 | ||||||||
\(922\) | −37.8564 | − | 10.1436i | −1.24673 | − | 0.334061i | ||||
\(923\) | 3.46410 | 0.114022 | ||||||||
\(924\) | 0.803848 | + | 2.32051i | 0.0264446 | + | 0.0763391i | ||||
\(925\) | 9.46410 | 0.311178 | ||||||||
\(926\) | 22.3923 | + | 6.00000i | 0.735857 | + | 0.197172i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 43.3205 | − | 11.6077i | 1.42207 | − | 0.381041i | ||||
\(929\) | 54.4974i | 1.78800i | 0.448065 | + | 0.894001i | \(0.352113\pi\) | ||||
−0.448065 | + | 0.894001i | \(0.647887\pi\) | |||||||
\(930\) | 14.1962 | + | 3.80385i | 0.465510 | + | 0.124733i | ||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | 15.7128 | + | 9.07180i | 0.514690 | + | 0.297157i | ||||
\(933\) | −13.6077 | −0.445496 | ||||||||
\(934\) | −8.24167 | + | 30.7583i | −0.269676 | + | 1.00644i | ||||
\(935\) | 1.73205i | 0.0566441i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3923i | 0.829530i | 0.909928 | + | 0.414765i | \(0.136136\pi\) | ||||
−0.909928 | + | 0.414765i | \(0.863864\pi\) | |||||||
\(938\) | 10.7321 | − | 7.26795i | 0.350414 | − | 0.237307i | ||||
\(939\) | 30.3731i | 0.991188i | ||||||||
\(940\) | −1.73205 | + | 3.00000i | −0.0564933 | + | 0.0978492i | ||||
\(941\) | − | 39.0333i | − | 1.27245i | −0.771504 | − | 0.636225i | \(-0.780495\pi\) | ||
0.771504 | − | 0.636225i | \(-0.219505\pi\) | |||||||
\(942\) | −18.5885 | − | 4.98076i | −0.605645 | − | 0.162282i | ||||
\(943\) | 5.07180 | 0.165160 | ||||||||
\(944\) | 6.92820 | + | 12.0000i | 0.225494 | + | 0.390567i | ||||
\(945\) | −10.3923 | − | 9.00000i | −0.338062 | − | 0.292770i | ||||
\(946\) | −0.196152 | + | 0.732051i | −0.00637747 | + | 0.0238010i | ||||
\(947\) | − | 22.7846i | − | 0.740400i | −0.928952 | − | 0.370200i | \(-0.879289\pi\) | ||
0.928952 | − | 0.370200i | \(-0.120711\pi\) | |||||||
\(948\) | −25.3923 | + | 43.9808i | −0.824704 | + | 1.42843i | ||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 2.19615 | − | 8.19615i | 0.0712526 | − | 0.265918i | ||||
\(951\) | −5.32051 | −0.172529 | ||||||||
\(952\) | −48.2487 | + | 3.46410i | −1.56375 | + | 0.112272i | ||||
\(953\) | 21.3205 | 0.690639 | 0.345320 | − | 0.938485i | \(-0.387771\pi\) | ||||
0.345320 | + | 0.938485i | \(0.387771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.19615 | 0.232862 | ||||||||
\(956\) | 23.9808 | − | 41.5359i | 0.775593 | − | 1.34337i | ||||
\(957\) | − | 3.67949i | − | 0.118941i | ||||||
\(958\) | −9.21539 | + | 34.3923i | −0.297736 | + | 1.11116i | ||||
\(959\) | 35.3205 | − | 40.7846i | 1.14056 | − | 1.31700i | ||||
\(960\) | 13.8564 | 0.447214 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −6.00000 | − | 1.60770i | −0.193448 | − | 0.0518342i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.3923 | + | 28.3923i | −0.527961 | + | 0.914455i | ||||
\(965\) | − | 9.46410i | − | 0.304660i | ||||||
\(966\) | −7.85641 | + | 5.32051i | −0.252776 | + | 0.171185i | ||||
\(967\) | − | 31.1769i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(968\) | −21.8564 | + | 21.8564i | −0.702492 | + | 0.702492i | ||||
\(969\) | − | 67.1769i | − | 2.15803i | ||||||
\(970\) | −4.90192 | + | 18.2942i | −0.157391 | + | 0.587392i | ||||
\(971\) | −14.7846 | −0.474461 | −0.237230 | − | 0.971453i | \(-0.576240\pi\) | ||||
−0.237230 | + | 0.971453i | \(0.576240\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 13.8564i | −0.384702 | + | 0.444216i | ||||
\(974\) | 17.4641 | + | 4.67949i | 0.559586 | + | 0.149941i | ||||
\(975\) | − | 0.803848i | − | 0.0257437i | ||||||
\(976\) | 32.7846 | − | 18.9282i | 1.04941 | − | 0.605877i | ||||
\(977\) | −4.24871 | −0.135928 | −0.0679642 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679642 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(978\) | 49.1769 | + | 13.1769i | 1.57250 | + | 0.421351i | ||||
\(979\) | −0.679492 | −0.0217167 | ||||||||
\(980\) | −13.0000 | − | 5.19615i | −0.415270 | − | 0.165985i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.4904 | + | 3.61474i | 0.430495 | + | 0.115351i | ||||
\(983\) | 27.5885 | 0.879935 | 0.439968 | − | 0.898014i | \(-0.354990\pi\) | ||||
0.439968 | + | 0.898014i | \(0.354990\pi\) | |||||||
\(984\) | −12.0000 | − | 12.0000i | −0.382546 | − | 0.382546i | ||||
\(985\) | − | 13.3205i | − | 0.424427i | ||||||
\(986\) | 70.0070 | + | 18.7583i | 2.22948 | + | 0.597387i | ||||
\(987\) | −5.19615 | + | 6.00000i | −0.165395 | + | 0.190982i | ||||
\(988\) | −2.78461 | + | 4.82309i | −0.0885902 | + | 0.153443i | ||||
\(989\) | −2.92820 | −0.0931114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.1769i | − | 1.49862i | −0.662217 | − | 0.749312i | \(-0.730384\pi\) | ||
0.662217 | − | 0.749312i | \(-0.269616\pi\) | |||||||
\(992\) | 32.7846 | − | 8.78461i | 1.04091 | − | 0.278912i | ||||
\(993\) | 45.7128i | 1.45065i | ||||||||
\(994\) | −23.1244 | + | 15.6603i | −0.733460 | + | 0.496713i | ||||
\(995\) | − | 3.46410i | − | 0.109819i | ||||||
\(996\) | 46.3923 | + | 26.7846i | 1.47000 | + | 0.848703i | ||||
\(997\) | − | 5.53590i | − | 0.175324i | −0.996150 | − | 0.0876618i | \(-0.972061\pi\) | ||
0.996150 | − | 0.0876618i | \(-0.0279395\pi\) | |||||||
\(998\) | −34.9545 | − | 9.36603i | −1.10646 | − | 0.296476i | ||||
\(999\) | 49.1769 | 1.55589 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))