Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [578,2,Mod(251,578)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(578, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("578.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 578 = 2 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 578.c (of order \(4\), 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: | \(4.61535323683\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 34) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 327.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 578.327 |
Dual form | 578.2.c.e.251.1 |
$q$-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 \(\left(\mathbb{Z}/578\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.41421 | + | 1.41421i | −0.816497 | + | 0.816497i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(6\) | −1.41421 | − | 1.41421i | −0.577350 | − | 0.577350i | ||||
\(7\) | 2.82843 | + | 2.82843i | 1.06904 | + | 1.06904i | 0.997433 | + | 0.0716124i | \(0.0228145\pi\) |
0.0716124 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264 | + | 4.24264i | 1.27920 | + | 1.27920i | 0.941113 | + | 0.338091i | \(0.109781\pi\) |
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | 1.41421 | − | 1.41421i | 0.408248 | − | 0.408248i | ||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | −2.82843 | + | 2.82843i | −0.755929 | + | 0.755929i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.00000 | −1.74574 | ||||||||
\(22\) | −4.24264 | + | 4.24264i | −0.904534 | + | 0.904534i | ||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | 1.41421 | + | 1.41421i | 0.288675 | + | 0.288675i | ||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | − | 2.00000i | − | 0.392232i | ||||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | −2.82843 | − | 2.82843i | −0.534522 | − | 0.534522i | ||||
\(29\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | + | 2.82843i | −0.508001 | + | 0.508001i | −0.913912 | − | 0.405912i | \(-0.866954\pi\) |
0.405912 | + | 0.913912i | \(0.366954\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −12.0000 | −2.08893 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −2.82843 | + | 2.82843i | −0.464991 | + | 0.464991i | −0.900287 | − | 0.435297i | \(-0.856644\pi\) |
0.435297 | + | 0.900287i | \(0.356644\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 2.82843 | − | 2.82843i | 0.452911 | − | 0.452911i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24264 | − | 4.24264i | −0.662589 | − | 0.662589i | 0.293400 | − | 0.955990i | \(-0.405213\pi\) |
−0.955990 | + | 0.293400i | \(0.905213\pi\) | |||||||
\(42\) | − | 8.00000i | − | 1.23443i | ||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −4.24264 | − | 4.24264i | −0.639602 | − | 0.639602i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −1.41421 | + | 1.41421i | −0.204124 | + | 0.204124i | ||||
\(49\) | 9.00000i | 1.28571i | ||||||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 2.82843 | − | 2.82843i | 0.384900 | − | 0.384900i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82843 | − | 2.82843i | 0.377964 | − | 0.377964i | ||||
\(57\) | 5.65685 | + | 5.65685i | 0.749269 | + | 0.749269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | + | 2.82843i | 0.362143 | + | 0.362143i | 0.864601 | − | 0.502458i | \(-0.167571\pi\) |
−0.502458 | + | 0.864601i | \(0.667571\pi\) | |||||||
\(62\) | −2.82843 | − | 2.82843i | −0.359211 | − | 0.359211i | ||||
\(63\) | 2.82843 | − | 2.82843i | 0.356348 | − | 0.356348i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 12.0000i | − | 1.47710i | ||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.41421 | + | 1.41421i | −0.165521 | + | 0.165521i | −0.785007 | − | 0.619486i | \(-0.787341\pi\) |
0.619486 | + | 0.785007i | \(0.287341\pi\) | |||||||
\(74\) | −2.82843 | − | 2.82843i | −0.328798 | − | 0.328798i | ||||
\(75\) | −7.07107 | − | 7.07107i | −0.816497 | − | 0.816497i | ||||
\(76\) | 4.00000i | 0.458831i | ||||||||
\(77\) | 24.0000i | 2.73505i | ||||||||
\(78\) | 2.82843 | + | 2.82843i | 0.320256 | + | 0.320256i | ||||
\(79\) | 5.65685 | + | 5.65685i | 0.636446 | + | 0.636446i | 0.949677 | − | 0.313231i | \(-0.101411\pi\) |
−0.313231 | + | 0.949677i | \(0.601411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 4.24264 | − | 4.24264i | 0.468521 | − | 0.468521i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 8.00000 | 0.872872 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | − | 4.24264i | 0.452267 | − | 0.452267i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.65685 | − | 5.65685i | −0.592999 | − | 0.592999i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.41421 | − | 1.41421i | −0.144338 | − | 0.144338i | ||||
\(97\) | −9.89949 | + | 9.89949i | −1.00514 | + | 1.00514i | −0.00515471 | + | 0.999987i | \(0.501641\pi\) |
−0.999987 | + | 0.00515471i | \(0.998359\pi\) | |||||||
\(98\) | −9.00000 | −0.909137 | ||||||||
\(99\) | 4.24264 | − | 4.24264i | 0.426401 | − | 0.426401i | ||||
\(100\) | − | 5.00000i | − | 0.500000i | ||||||
\(101\) | 18.0000 | 1.79107 | 0.895533 | − | 0.444994i | \(-0.146794\pi\) | ||||
0.895533 | + | 0.444994i | \(0.146794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 2.00000i | 0.196116i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 4.24264 | − | 4.24264i | 0.410152 | − | 0.410152i | −0.471640 | − | 0.881791i | \(-0.656338\pi\) |
0.881791 | + | 0.471640i | \(0.156338\pi\) | |||||||
\(108\) | 2.82843 | + | 2.82843i | 0.272166 | + | 0.272166i | ||||
\(109\) | 11.3137 | + | 11.3137i | 1.08366 | + | 1.08366i | 0.996165 | + | 0.0874915i | \(0.0278851\pi\) |
0.0874915 | + | 0.996165i | \(0.472115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.00000i | − | 0.759326i | ||||||
\(112\) | 2.82843 | + | 2.82843i | 0.267261 | + | 0.267261i | ||||
\(113\) | −4.24264 | − | 4.24264i | −0.399114 | − | 0.399114i | 0.478806 | − | 0.877920i | \(-0.341070\pi\) |
−0.877920 | + | 0.478806i | \(0.841070\pi\) | |||||||
\(114\) | −5.65685 | + | 5.65685i | −0.529813 | + | 0.529813i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0000i | 2.27273i | ||||||||
\(122\) | −2.82843 | + | 2.82843i | −0.256074 | + | 0.256074i | ||||
\(123\) | 12.0000 | 1.08200 | ||||||||
\(124\) | 2.82843 | − | 2.82843i | 0.254000 | − | 0.254000i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.82843 | + | 2.82843i | 0.251976 | + | 0.251976i | ||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 11.3137 | + | 11.3137i | 0.996116 | + | 0.996116i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.24264 | − | 4.24264i | 0.370681 | − | 0.370681i | −0.497044 | − | 0.867725i | \(-0.665581\pi\) |
0.867725 | + | 0.497044i | \(0.165581\pi\) | |||||||
\(132\) | 12.0000 | 1.04447 | ||||||||
\(133\) | 11.3137 | − | 11.3137i | 0.981023 | − | 0.981023i | ||||
\(134\) | 8.00000i | 0.691095i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41421 | − | 1.41421i | 0.119952 | − | 0.119952i | −0.644583 | − | 0.764535i | \(-0.722969\pi\) |
0.764535 | + | 0.644583i | \(0.222969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.48528 | − | 8.48528i | −0.709575 | − | 0.709575i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.41421 | − | 1.41421i | −0.117041 | − | 0.117041i | ||||
\(147\) | −12.7279 | − | 12.7279i | −1.04978 | − | 1.04978i | ||||
\(148\) | 2.82843 | − | 2.82843i | 0.232495 | − | 0.232495i | ||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 7.07107 | − | 7.07107i | 0.577350 | − | 0.577350i | ||||
\(151\) | − | 16.0000i | − | 1.30206i | −0.759051 | − | 0.651031i | \(-0.774337\pi\) | ||
0.759051 | − | 0.651031i | \(-0.225663\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.0000 | −1.93398 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.82843 | + | 2.82843i | −0.226455 | + | 0.226455i | ||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −5.65685 | + | 5.65685i | −0.450035 | + | 0.450035i | ||||
\(159\) | 8.48528 | + | 8.48528i | 0.672927 | + | 0.672927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.0000i | 0.864242i | ||||||||
\(163\) | −1.41421 | − | 1.41421i | −0.110770 | − | 0.110770i | 0.649550 | − | 0.760319i | \(-0.274958\pi\) |
−0.760319 | + | 0.649550i | \(0.774958\pi\) | |||||||
\(164\) | 4.24264 | + | 4.24264i | 0.331295 | + | 0.331295i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.48528 | − | 8.48528i | 0.656611 | − | 0.656611i | −0.297966 | − | 0.954577i | \(-0.596308\pi\) |
0.954577 | + | 0.297966i | \(0.0963081\pi\) | |||||||
\(168\) | 8.00000i | 0.617213i | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | 16.9706 | − | 16.9706i | 1.29025 | − | 1.29025i | 0.355616 | − | 0.934632i | \(-0.384271\pi\) |
0.934632 | − | 0.355616i | \(-0.115729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.1421 | + | 14.1421i | −1.06904 | + | 1.06904i | ||||
\(176\) | 4.24264 | + | 4.24264i | 0.319801 | + | 0.319801i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.82843 | − | 2.82843i | −0.210235 | − | 0.210235i | 0.594132 | − | 0.804367i | \(-0.297496\pi\) |
−0.804367 | + | 0.594132i | \(0.797496\pi\) | |||||||
\(182\) | 5.65685 | − | 5.65685i | 0.419314 | − | 0.419314i | ||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 16.0000i | − | 1.16383i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | 1.41421 | − | 1.41421i | 0.102062 | − | 0.102062i | ||||
\(193\) | −7.07107 | − | 7.07107i | −0.508987 | − | 0.508987i | 0.405229 | − | 0.914215i | \(-0.367192\pi\) |
−0.914215 | + | 0.405229i | \(0.867192\pi\) | |||||||
\(194\) | −9.89949 | − | 9.89949i | −0.710742 | − | 0.710742i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 9.00000i | − | 0.642857i | ||||||
\(197\) | 8.48528 | + | 8.48528i | 0.604551 | + | 0.604551i | 0.941517 | − | 0.336966i | \(-0.109401\pi\) |
−0.336966 | + | 0.941517i | \(0.609401\pi\) | |||||||
\(198\) | 4.24264 | + | 4.24264i | 0.301511 | + | 0.301511i | ||||
\(199\) | 11.3137 | − | 11.3137i | 0.802008 | − | 0.802008i | −0.181402 | − | 0.983409i | \(-0.558063\pi\) |
0.983409 | + | 0.181402i | \(0.0580634\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | −11.3137 | + | 11.3137i | −0.798007 | + | 0.798007i | ||||
\(202\) | 18.0000i | 1.26648i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 16.0000i | − | 1.11477i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 16.9706 | − | 16.9706i | 1.17388 | − | 1.17388i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.07107 | + | 7.07107i | 0.486792 | + | 0.486792i | 0.907292 | − | 0.420500i | \(-0.138145\pi\) |
−0.420500 | + | 0.907292i | \(0.638145\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.24264 | + | 4.24264i | 0.290021 | + | 0.290021i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.82843 | + | 2.82843i | −0.192450 | + | 0.192450i | ||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | −11.3137 | + | 11.3137i | −0.766261 | + | 0.766261i | ||||
\(219\) | − | 4.00000i | − | 0.270295i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.00000 | 0.536925 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | −2.82843 | + | 2.82843i | −0.188982 | + | 0.188982i | ||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 4.24264 | − | 4.24264i | 0.282216 | − | 0.282216i | ||||
\(227\) | −4.24264 | − | 4.24264i | −0.281594 | − | 0.281594i | 0.552151 | − | 0.833744i | \(-0.313807\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(228\) | −5.65685 | − | 5.65685i | −0.374634 | − | 0.374634i | ||||
\(229\) | − | 14.0000i | − | 0.925146i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) | ||
0.886581 | − | 0.462573i | \(-0.153074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −33.9411 | − | 33.9411i | −2.23316 | − | 2.23316i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7279 | + | 12.7279i | −0.833834 | + | 0.833834i | −0.988039 | − | 0.154205i | \(-0.950718\pi\) |
0.154205 | + | 0.988039i | \(0.450718\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.07107 | + | 7.07107i | −0.455488 | + | 0.455488i | −0.897171 | − | 0.441683i | \(-0.854381\pi\) |
0.441683 | + | 0.897171i | \(0.354381\pi\) | |||||||
\(242\) | −25.0000 | −1.60706 | ||||||||
\(243\) | −7.07107 | + | 7.07107i | −0.453609 | + | 0.453609i | ||||
\(244\) | −2.82843 | − | 2.82843i | −0.181071 | − | 0.181071i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000i | 0.765092i | ||||||||
\(247\) | 8.00000i | 0.509028i | ||||||||
\(248\) | 2.82843 | + | 2.82843i | 0.179605 | + | 0.179605i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | −2.82843 | + | 2.82843i | −0.178174 | + | 0.178174i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | −11.3137 | + | 11.3137i | −0.704361 | + | 0.704361i | ||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.24264 | + | 4.24264i | 0.262111 | + | 0.262111i | ||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 12.0000i | 0.738549i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.3137 | + | 11.3137i | 0.693688 | + | 0.693688i | ||||
\(267\) | −8.48528 | + | 8.48528i | −0.519291 | + | 0.519291i | ||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | −16.9706 | + | 16.9706i | −1.03471 | + | 1.03471i | −0.0353381 | + | 0.999375i | \(0.511251\pi\) |
−0.999375 | + | 0.0353381i | \(0.988749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | −21.2132 | + | 21.2132i | −1.27920 | + | 1.27920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.65685 | + | 5.65685i | −0.339887 | + | 0.339887i | −0.856325 | − | 0.516437i | \(-0.827258\pi\) |
0.516437 | + | 0.856325i | \(0.327258\pi\) | |||||||
\(278\) | 1.41421 | + | 1.41421i | 0.0848189 | + | 0.0848189i | ||||
\(279\) | 2.82843 | + | 2.82843i | 0.169334 | + | 0.169334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.89949 | + | 9.89949i | 0.588464 | + | 0.588464i | 0.937215 | − | 0.348751i | \(-0.113394\pi\) |
−0.348751 | + | 0.937215i | \(0.613394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.48528 | − | 8.48528i | 0.501745 | − | 0.501745i | ||||
\(287\) | − | 24.0000i | − | 1.41668i | ||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 28.0000i | − | 1.64139i | ||||||
\(292\) | 1.41421 | − | 1.41421i | 0.0827606 | − | 0.0827606i | ||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 12.7279 | − | 12.7279i | 0.742307 | − | 0.742307i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.82843 | + | 2.82843i | 0.164399 | + | 0.164399i | ||||
\(297\) | − | 24.0000i | − | 1.39262i | ||||||
\(298\) | − | 6.00000i | − | 0.347571i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.07107 | + | 7.07107i | 0.408248 | + | 0.408248i | ||||
\(301\) | 22.6274 | − | 22.6274i | 1.30422 | − | 1.30422i | ||||
\(302\) | 16.0000 | 0.920697 | ||||||||
\(303\) | −25.4558 | + | 25.4558i | −1.46240 | + | 1.46240i | ||||
\(304\) | − | 4.00000i | − | 0.229416i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | − | 24.0000i | − | 1.36753i | ||||||
\(309\) | 22.6274 | − | 22.6274i | 1.28723 | − | 1.28723i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.48528 | + | 8.48528i | −0.481156 | + | 0.481156i | −0.905501 | − | 0.424345i | \(-0.860505\pi\) |
0.424345 | + | 0.905501i | \(0.360505\pi\) | |||||||
\(312\) | −2.82843 | − | 2.82843i | −0.160128 | − | 0.160128i | ||||
\(313\) | 24.0416 | + | 24.0416i | 1.35891 | + | 1.35891i | 0.875259 | + | 0.483654i | \(0.160691\pi\) |
0.483654 | + | 0.875259i | \(0.339309\pi\) | |||||||
\(314\) | − | 14.0000i | − | 0.790066i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65685 | − | 5.65685i | −0.318223 | − | 0.318223i | ||||
\(317\) | −8.48528 | − | 8.48528i | −0.476581 | − | 0.476581i | 0.427456 | − | 0.904036i | \(-0.359410\pi\) |
−0.904036 | + | 0.427456i | \(0.859410\pi\) | |||||||
\(318\) | −8.48528 | + | 8.48528i | −0.475831 | + | 0.475831i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000i | 0.669775i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | − | 10.0000i | − | 0.554700i | ||||||
\(326\) | 1.41421 | − | 1.41421i | 0.0783260 | − | 0.0783260i | ||||
\(327\) | −32.0000 | −1.76960 | ||||||||
\(328\) | −4.24264 | + | 4.24264i | −0.234261 | + | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0000i | 0.879440i | 0.898135 | + | 0.439720i | \(0.144922\pi\) | ||||
−0.898135 | + | 0.439720i | \(0.855078\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.82843 | + | 2.82843i | 0.154997 | + | 0.154997i | ||||
\(334\) | 8.48528 | + | 8.48528i | 0.464294 | + | 0.464294i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.00000 | −0.436436 | ||||||||
\(337\) | −15.5563 | + | 15.5563i | −0.847408 | + | 0.847408i | −0.989809 | − | 0.142401i | \(-0.954518\pi\) |
0.142401 | + | 0.989809i | \(0.454518\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | − | 4.00000i | − | 0.216295i | ||||||
\(343\) | −5.65685 | + | 5.65685i | −0.305441 | + | 0.305441i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.9706 | + | 16.9706i | 0.912343 | + | 0.912343i | ||||
\(347\) | −12.7279 | − | 12.7279i | −0.683271 | − | 0.683271i | 0.277465 | − | 0.960736i | \(-0.410506\pi\) |
−0.960736 | + | 0.277465i | \(0.910506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.0000i | − | 1.39175i | −0.718164 | − | 0.695874i | \(-0.755017\pi\) | ||
0.718164 | − | 0.695874i | \(-0.244983\pi\) | |||||||
\(350\) | −14.1421 | − | 14.1421i | −0.755929 | − | 0.755929i | ||||
\(351\) | 5.65685 | + | 5.65685i | 0.301941 | + | 0.301941i | ||||
\(352\) | −4.24264 | + | 4.24264i | −0.226134 | + | 0.226134i | ||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 24.0000i | 1.26667i | 0.773877 | + | 0.633336i | \(0.218315\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 2.82843 | − | 2.82843i | 0.148659 | − | 0.148659i | ||||
\(363\) | −35.3553 | − | 35.3553i | −1.85567 | − | 1.85567i | ||||
\(364\) | 5.65685 | + | 5.65685i | 0.296500 | + | 0.296500i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 8.00000i | − | 0.418167i | ||||||
\(367\) | 11.3137 | + | 11.3137i | 0.590571 | + | 0.590571i | 0.937786 | − | 0.347215i | \(-0.112873\pi\) |
−0.347215 | + | 0.937786i | \(0.612873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.24264 | + | 4.24264i | −0.220863 | + | 0.220863i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9706 | − | 16.9706i | 0.881068 | − | 0.881068i | ||||
\(372\) | 8.00000i | 0.414781i | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 16.0000 | 0.822951 | ||||||||
\(379\) | −9.89949 | + | 9.89949i | −0.508503 | + | 0.508503i | −0.914067 | − | 0.405564i | \(-0.867075\pi\) |
0.405564 | + | 0.914067i | \(0.367075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.6274 | − | 22.6274i | −1.15924 | − | 1.15924i | ||||
\(382\) | 24.0000i | 1.22795i | ||||||||
\(383\) | 24.0000i | 1.22634i | 0.789950 | + | 0.613171i | \(0.210106\pi\) | ||||
−0.789950 | + | 0.613171i | \(0.789894\pi\) | |||||||
\(384\) | 1.41421 | + | 1.41421i | 0.0721688 | + | 0.0721688i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.07107 | − | 7.07107i | 0.359908 | − | 0.359908i | ||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 9.89949 | − | 9.89949i | 0.502571 | − | 0.502571i | ||||
\(389\) | 30.0000i | 1.52106i | 0.649303 | + | 0.760530i | \(0.275061\pi\) | ||||
−0.649303 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 9.00000 | 0.454569 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | −8.48528 | + | 8.48528i | −0.427482 | + | 0.427482i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.24264 | + | 4.24264i | −0.213201 | + | 0.213201i | ||||
\(397\) | 14.1421 | + | 14.1421i | 0.709773 | + | 0.709773i | 0.966487 | − | 0.256714i | \(-0.0826398\pi\) |
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(398\) | 11.3137 | + | 11.3137i | 0.567105 | + | 0.567105i | ||||
\(399\) | 32.0000i | 1.60200i | ||||||||
\(400\) | 5.00000i | 0.250000i | ||||||||
\(401\) | −21.2132 | − | 21.2132i | −1.05934 | − | 1.05934i | −0.998125 | − | 0.0612120i | \(-0.980503\pi\) |
−0.0612120 | − | 0.998125i | \(-0.519497\pi\) | |||||||
\(402\) | −11.3137 | − | 11.3137i | −0.564276 | − | 0.564276i | ||||
\(403\) | 5.65685 | − | 5.65685i | 0.281788 | − | 0.281788i | ||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.48528 | + | 8.48528i | −0.418548 | + | 0.418548i | ||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2.00000i | − | 0.0980581i | ||||||
\(417\) | 4.00000i | 0.195881i | ||||||||
\(418\) | 16.9706 | + | 16.9706i | 0.830057 | + | 0.830057i | ||||
\(419\) | −21.2132 | − | 21.2132i | −1.03633 | − | 1.03633i | −0.999315 | − | 0.0370182i | \(-0.988214\pi\) |
−0.0370182 | − | 0.999315i | \(-0.511786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | −7.07107 | + | 7.07107i | −0.344214 | + | 0.344214i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0000i | 0.774294i | ||||||||
\(428\) | −4.24264 | + | 4.24264i | −0.205076 | + | 0.205076i | ||||
\(429\) | 24.0000 | 1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9706 | + | 16.9706i | 0.817443 | + | 0.817443i | 0.985737 | − | 0.168294i | \(-0.0538257\pi\) |
−0.168294 | + | 0.985737i | \(0.553826\pi\) | |||||||
\(432\) | −2.82843 | − | 2.82843i | −0.136083 | − | 0.136083i | ||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | − | 16.0000i | − | 0.768025i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3137 | − | 11.3137i | −0.541828 | − | 0.541828i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | 5.65685 | − | 5.65685i | 0.269987 | − | 0.269987i | −0.559108 | − | 0.829095i | \(-0.688856\pi\) |
0.829095 | + | 0.559108i | \(0.188856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | 8.00000i | 0.379663i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | 8.48528 | − | 8.48528i | 0.401340 | − | 0.401340i | ||||
\(448\) | −2.82843 | − | 2.82843i | −0.133631 | − | 0.133631i | ||||
\(449\) | 12.7279 | + | 12.7279i | 0.600668 | + | 0.600668i | 0.940490 | − | 0.339822i | \(-0.110367\pi\) |
−0.339822 | + | 0.940490i | \(0.610367\pi\) | |||||||
\(450\) | 5.00000i | 0.235702i | ||||||||
\(451\) | − | 36.0000i | − | 1.69517i | ||||||
\(452\) | 4.24264 | + | 4.24264i | 0.199557 | + | 0.199557i | ||||
\(453\) | 22.6274 | + | 22.6274i | 1.06313 | + | 1.06313i | ||||
\(454\) | 4.24264 | − | 4.24264i | 0.199117 | − | 0.199117i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.65685 | − | 5.65685i | 0.264906 | − | 0.264906i | ||||
\(457\) | 26.0000i | 1.21623i | 0.793849 | + | 0.608114i | \(0.208074\pi\) | ||||
−0.793849 | + | 0.608114i | \(0.791926\pi\) | |||||||
\(458\) | 14.0000 | 0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.00000i | − | 0.279448i | −0.990190 | − | 0.139724i | \(-0.955378\pi\) | ||
0.990190 | − | 0.139724i | \(-0.0446215\pi\) | |||||||
\(462\) | 33.9411 | − | 33.9411i | 1.57908 | − | 1.57908i | ||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.7279 | − | 12.7279i | −0.589610 | − | 0.589610i | ||||
\(467\) | − | 12.0000i | − | 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | 22.6274 | + | 22.6274i | 1.04484 | + | 1.04484i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7990 | − | 19.7990i | 0.912289 | − | 0.912289i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.9411 | − | 33.9411i | 1.56061 | − | 1.56061i | ||||
\(474\) | − | 16.0000i | − | 0.734904i | ||||||
\(475\) | 20.0000 | 0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 24.0000i | 1.09773i | ||||||||
\(479\) | 16.9706 | − | 16.9706i | 0.775405 | − | 0.775405i | −0.203641 | − | 0.979046i | \(-0.565277\pi\) |
0.979046 | + | 0.203641i | \(0.0652775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65685 | − | 5.65685i | 0.257930 | − | 0.257930i | ||||
\(482\) | −7.07107 | − | 7.07107i | −0.322078 | − | 0.322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 25.0000i | − | 1.13636i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.07107 | − | 7.07107i | −0.320750 | − | 0.320750i | ||||
\(487\) | 5.65685 | + | 5.65685i | 0.256337 | + | 0.256337i | 0.823562 | − | 0.567226i | \(-0.191983\pi\) |
−0.567226 | + | 0.823562i | \(0.691983\pi\) | |||||||
\(488\) | 2.82843 | − | 2.82843i | 0.128037 | − | 0.128037i | ||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.0000i | − | 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | −12.0000 | −0.541002 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.82843 | + | 2.82843i | −0.127000 | + | 0.127000i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.89949 | + | 9.89949i | 0.443162 | + | 0.443162i | 0.893073 | − | 0.449911i | \(-0.148544\pi\) |
−0.449911 | + | 0.893073i | \(0.648544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000i | 1.07224i | ||||||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | 16.9706 | + | 16.9706i | 0.756680 | + | 0.756680i | 0.975717 | − | 0.219037i | \(-0.0702914\pi\) |
−0.219037 | + | 0.975717i | \(0.570291\pi\) | |||||||
\(504\) | −2.82843 | − | 2.82843i | −0.125988 | − | 0.125988i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7279 | − | 12.7279i | 0.565267 | − | 0.565267i | ||||
\(508\) | − | 16.0000i | − | 0.709885i | ||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −11.3137 | + | 11.3137i | −0.499512 | + | 0.499512i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.3137 | − | 11.3137i | −0.498058 | − | 0.498058i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 16.0000i | − | 0.703000i | ||||||
\(519\) | 48.0000i | 2.10697i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.7279 | − | 12.7279i | −0.557620 | − | 0.557620i | 0.371009 | − | 0.928629i | \(-0.379012\pi\) |
−0.928629 | + | 0.371009i | \(0.879012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | −4.24264 | + | 4.24264i | −0.185341 | + | 0.185341i | ||||
\(525\) | − | 40.0000i | − | 1.74574i | ||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | − | 23.0000i | − | 1.00000i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.3137 | + | 11.3137i | −0.490511 | + | 0.490511i | ||||
\(533\) | 8.48528 | + | 8.48528i | 0.367538 | + | 0.367538i | ||||
\(534\) | −8.48528 | − | 8.48528i | −0.367194 | − | 0.367194i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.00000i | − | 0.345547i | ||||||
\(537\) | 16.9706 | + | 16.9706i | 0.732334 | + | 0.732334i | ||||
\(538\) | −16.9706 | − | 16.9706i | −0.731653 | − | 0.731653i | ||||
\(539\) | −38.1838 | + | 38.1838i | −1.64469 | + | 1.64469i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1421 | − | 14.1421i | 0.608018 | − | 0.608018i | −0.334410 | − | 0.942428i | \(-0.608537\pi\) |
0.942428 | + | 0.334410i | \(0.108537\pi\) | |||||||
\(542\) | 8.00000i | 0.343629i | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.0000i | 0.684737i | ||||||||
\(547\) | 1.41421 | − | 1.41421i | 0.0604674 | − | 0.0604674i | −0.676226 | − | 0.736694i | \(-0.736386\pi\) |
0.736694 | + | 0.676226i | \(0.236386\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 2.82843 | − | 2.82843i | 0.120714 | − | 0.120714i | ||||
\(550\) | −21.2132 | − | 21.2132i | −0.904534 | − | 0.904534i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000i | 1.36078i | ||||||||
\(554\) | −5.65685 | − | 5.65685i | −0.240337 | − | 0.240337i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.41421 | + | 1.41421i | −0.0599760 | + | 0.0599760i | ||||
\(557\) | 30.0000 | 1.27114 | 0.635570 | − | 0.772043i | \(-0.280765\pi\) | ||||
0.635570 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(558\) | −2.82843 | + | 2.82843i | −0.119737 | + | 0.119737i | ||||
\(559\) | 16.0000i | 0.676728i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | − | 24.0000i | − | 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.89949 | + | 9.89949i | −0.416107 | + | 0.416107i | ||||
\(567\) | 31.1127 | + | 31.1127i | 1.30661 | + | 1.30661i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0000i | 1.25767i | 0.777541 | + | 0.628833i | \(0.216467\pi\) | ||||
−0.777541 | + | 0.628833i | \(0.783533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3848 | − | 18.3848i | −0.769379 | − | 0.769379i | 0.208618 | − | 0.977997i | \(-0.433103\pi\) |
−0.977997 | + | 0.208618i | \(0.933103\pi\) | |||||||
\(572\) | 8.48528 | + | 8.48528i | 0.354787 | + | 0.354787i | ||||
\(573\) | −33.9411 | + | 33.9411i | −1.41791 | + | 1.41791i | ||||
\(574\) | 24.0000 | 1.00174 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.0000 | 0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 28.0000 | 1.16064 | ||||||||
\(583\) | 25.4558 | − | 25.4558i | 1.05427 | − | 1.05427i | ||||
\(584\) | 1.41421 | + | 1.41421i | 0.0585206 | + | 0.0585206i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 6.00000i | − | 0.247858i | ||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 12.7279 | + | 12.7279i | 0.524891 | + | 0.524891i | ||||
\(589\) | 11.3137 | + | 11.3137i | 0.466173 | + | 0.466173i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0000 | −0.987228 | ||||||||
\(592\) | −2.82843 | + | 2.82843i | −0.116248 | + | 0.116248i | ||||
\(593\) | − | 30.0000i | − | 1.23195i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) | ||
0.787765 | − | 0.615976i | \(-0.211238\pi\) | |||||||
\(594\) | 24.0000 | 0.984732 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 32.0000i | 1.30967i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | −7.07107 | + | 7.07107i | −0.288675 | + | 0.288675i | ||||
\(601\) | −32.5269 | − | 32.5269i | −1.32680 | − | 1.32680i | −0.908145 | − | 0.418655i | \(-0.862502\pi\) |
−0.418655 | − | 0.908145i | \(-0.637498\pi\) | |||||||
\(602\) | 22.6274 | + | 22.6274i | 0.922225 | + | 0.922225i | ||||
\(603\) | − | 8.00000i | − | 0.325785i | ||||||
\(604\) | 16.0000i | 0.651031i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −25.4558 | − | 25.4558i | −1.03407 | − | 1.03407i | ||||
\(607\) | −14.1421 | + | 14.1421i | −0.574012 | + | 0.574012i | −0.933247 | − | 0.359235i | \(-0.883038\pi\) |
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 20.0000i | 0.807134i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | 0.966988 | ||||||||
\(617\) | 21.2132 | − | 21.2132i | 0.854011 | − | 0.854011i | −0.136613 | − | 0.990624i | \(-0.543622\pi\) |
0.990624 | + | 0.136613i | \(0.0436217\pi\) | |||||||
\(618\) | 22.6274 | + | 22.6274i | 0.910208 | + | 0.910208i | ||||
\(619\) | −18.3848 | − | 18.3848i | −0.738947 | − | 0.738947i | 0.233428 | − | 0.972374i | \(-0.425006\pi\) |
−0.972374 | + | 0.233428i | \(0.925006\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.48528 | − | 8.48528i | −0.340229 | − | 0.340229i | ||||
\(623\) | 16.9706 | + | 16.9706i | 0.679911 | + | 0.679911i | ||||
\(624\) | 2.82843 | − | 2.82843i | 0.113228 | − | 0.113228i | ||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | −24.0416 | + | 24.0416i | −0.960897 | + | 0.960897i | ||||
\(627\) | 48.0000i | 1.91694i | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000i | 0.318475i | 0.987240 | + | 0.159237i | \(0.0509036\pi\) | ||||
−0.987240 | + | 0.159237i | \(0.949096\pi\) | |||||||
\(632\) | 5.65685 | − | 5.65685i | 0.225018 | − | 0.225018i | ||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 8.48528 | − | 8.48528i | 0.336994 | − | 0.336994i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.48528 | − | 8.48528i | −0.336463 | − | 0.336463i | ||||
\(637\) | − | 18.0000i | − | 0.713186i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7279 | − | 12.7279i | 0.502723 | − | 0.502723i | −0.409560 | − | 0.912283i | \(-0.634318\pi\) |
0.912283 | + | 0.409560i | \(0.134318\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | 9.89949 | − | 9.89949i | 0.390398 | − | 0.390398i | −0.484431 | − | 0.874829i | \(-0.660973\pi\) |
0.874829 | + | 0.484431i | \(0.160973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.0000 | −1.88707 | −0.943537 | − | 0.331266i | \(-0.892524\pi\) | ||||
−0.943537 | + | 0.331266i | \(0.892524\pi\) | |||||||
\(648\) | − | 11.0000i | − | 0.432121i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.0000 | 0.392232 | ||||||||
\(651\) | 22.6274 | − | 22.6274i | 0.886838 | − | 0.886838i | ||||
\(652\) | 1.41421 | + | 1.41421i | 0.0553849 | + | 0.0553849i | ||||
\(653\) | −16.9706 | − | 16.9706i | −0.664109 | − | 0.664109i | 0.292237 | − | 0.956346i | \(-0.405601\pi\) |
−0.956346 | + | 0.292237i | \(0.905601\pi\) | |||||||
\(654\) | − | 32.0000i | − | 1.25130i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.24264 | − | 4.24264i | −0.165647 | − | 0.165647i | ||||
\(657\) | 1.41421 | + | 1.41421i | 0.0551737 | + | 0.0551737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 46.0000i | − | 1.78919i | −0.446875 | − | 0.894596i | \(-0.647463\pi\) | ||
0.446875 | − | 0.894596i | \(-0.352537\pi\) | |||||||
\(662\) | −16.0000 | −0.621858 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.82843 | + | 2.82843i | −0.109599 | + | 0.109599i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −8.48528 | + | 8.48528i | −0.328305 | + | 0.328305i | ||||
\(669\) | −11.3137 | − | 11.3137i | −0.437413 | − | 0.437413i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000i | 0.926510i | ||||||||
\(672\) | − | 8.00000i | − | 0.308607i | ||||||
\(673\) | −26.8701 | − | 26.8701i | −1.03576 | − | 1.03576i | −0.999336 | − | 0.0364283i | \(-0.988402\pi\) |
−0.0364283 | − | 0.999336i | \(-0.511598\pi\) | |||||||
\(674\) | −15.5563 | − | 15.5563i | −0.599208 | − | 0.599208i | ||||
\(675\) | 14.1421 | − | 14.1421i | 0.544331 | − | 0.544331i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −8.48528 | + | 8.48528i | −0.326116 | + | 0.326116i | −0.851107 | − | 0.524992i | \(-0.824068\pi\) |
0.524992 | + | 0.851107i | \(0.324068\pi\) | |||||||
\(678\) | 12.0000i | 0.460857i | ||||||||
\(679\) | −56.0000 | −2.14908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | − | 24.0000i | − | 0.919007i | ||||||
\(683\) | 21.2132 | − | 21.2132i | 0.811701 | − | 0.811701i | −0.173188 | − | 0.984889i | \(-0.555407\pi\) |
0.984889 | + | 0.173188i | \(0.0554069\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.65685 | − | 5.65685i | −0.215980 | − | 0.215980i | ||||
\(687\) | 19.7990 | + | 19.7990i | 0.755379 | + | 0.755379i | ||||
\(688\) | − | 8.00000i | − | 0.304997i | ||||||
\(689\) | 12.0000i | 0.457164i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.07107 | − | 7.07107i | −0.268996 | − | 0.268996i | 0.559700 | − | 0.828696i | \(-0.310917\pi\) |
−0.828696 | + | 0.559700i | \(0.810917\pi\) | |||||||
\(692\) | −16.9706 | + | 16.9706i | −0.645124 | + | 0.645124i | ||||
\(693\) | 24.0000 | 0.911685 | ||||||||
\(694\) | 12.7279 | − | 12.7279i | 0.483145 | − | 0.483145i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 26.0000 | 0.984115 | ||||||||
\(699\) | − | 36.0000i | − | 1.36165i | ||||||
\(700\) | 14.1421 | − | 14.1421i | 0.534522 | − | 0.534522i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −5.65685 | + | 5.65685i | −0.213504 | + | 0.213504i | ||||
\(703\) | 11.3137 | + | 11.3137i | 0.426705 | + | 0.426705i | ||||
\(704\) | −4.24264 | − | 4.24264i | −0.159901 | − | 0.159901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.00000i | − | 0.225813i | ||||||
\(707\) | 50.9117 | + | 50.9117i | 1.91473 | + | 1.91473i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.3137 | − | 11.3137i | 0.424895 | − | 0.424895i | −0.461990 | − | 0.886885i | \(-0.652864\pi\) |
0.886885 | + | 0.461990i | \(0.152864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.65685 | − | 5.65685i | 0.212149 | − | 0.212149i | ||||
\(712\) | − | 6.00000i | − | 0.224860i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000i | 0.448461i | ||||||||
\(717\) | −33.9411 | + | 33.9411i | −1.26755 | + | 1.26755i | ||||
\(718\) | −24.0000 | −0.895672 | ||||||||
\(719\) | −33.9411 | + | 33.9411i | −1.26579 | + | 1.26579i | −0.317548 | + | 0.948242i | \(0.602860\pi\) |
−0.948242 | + | 0.317548i | \(0.897140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.2548 | − | 45.2548i | −1.68538 | − | 1.68538i | ||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | − | 20.0000i | − | 0.743808i | ||||||
\(724\) | 2.82843 | + | 2.82843i | 0.105118 | + | 0.105118i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 35.3553 | − | 35.3553i | 1.31216 | − | 1.31216i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | −5.65685 | + | 5.65685i | −0.209657 | + | 0.209657i | ||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 8.00000 | 0.295689 | ||||||||
\(733\) | − | 22.0000i | − | 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | −11.3137 | + | 11.3137i | −0.417597 | + | 0.417597i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9411 | + | 33.9411i | 1.25024 | + | 1.25024i | ||||
\(738\) | −4.24264 | − | 4.24264i | −0.156174 | − | 0.156174i | ||||
\(739\) | − | 20.0000i | − | 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.3137 | − | 11.3137i | −0.415619 | − | 0.415619i | ||||
\(742\) | 16.9706 | + | 16.9706i | 0.623009 | + | 0.623009i | ||||
\(743\) | 25.4558 | − | 25.4558i | 0.933884 | − | 0.933884i | −0.0640616 | − | 0.997946i | \(-0.520405\pi\) |
0.997946 | + | 0.0640616i | \(0.0204054\pi\) | |||||||
\(744\) | −8.00000 | −0.293294 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 22.0000i | − | 0.805477i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000 | 0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.65685 | − | 5.65685i | 0.206422 | − | 0.206422i | −0.596323 | − | 0.802745i | \(-0.703372\pi\) |
0.802745 | + | 0.596323i | \(0.203372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.9411 | + | 33.9411i | −1.23688 | + | 1.23688i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 16.0000i | 0.581914i | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | −9.89949 | − | 9.89949i | −0.359566 | − | 0.359566i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 22.6274 | − | 22.6274i | 0.819705 | − | 0.819705i | ||||
\(763\) | 64.0000i | 2.31696i | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.41421 | + | 1.41421i | −0.0510310 | + | 0.0510310i | ||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.48528 | − | 8.48528i | −0.305590 | − | 0.305590i | ||||
\(772\) | 7.07107 | + | 7.07107i | 0.254493 | + | 0.254493i | ||||
\(773\) | 42.0000i | 1.51064i | 0.655359 | + | 0.755318i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755318i | \(0.727483\pi\) | |||||||
\(774\) | − | 8.00000i | − | 0.287554i | ||||||
\(775\) | −14.1421 | − | 14.1421i | −0.508001 | − | 0.508001i | ||||
\(776\) | 9.89949 | + | 9.89949i | 0.355371 | + | 0.355371i | ||||
\(777\) | 22.6274 | − | 22.6274i | 0.811754 | − | 0.811754i | ||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | −16.9706 | + | 16.9706i | −0.608034 | + | 0.608034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00000i | 0.321429i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | 32.5269 | − | 32.5269i | 1.15946 | − | 1.15946i | 0.174867 | − | 0.984592i | \(-0.444050\pi\) |
0.984592 | − | 0.174867i | \(-0.0559496\pi\) | |||||||
\(788\) | −8.48528 | − | 8.48528i | −0.302276 | − | 0.302276i | ||||
\(789\) | 33.9411 | + | 33.9411i | 1.20834 | + | 1.20834i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.0000i | − | 0.853342i | ||||||
\(792\) | −4.24264 | − | 4.24264i | −0.150756 | − | 0.150756i | ||||
\(793\) | −5.65685 | − | 5.65685i | −0.200881 | − | 0.200881i | ||||
\(794\) | −14.1421 | + | 14.1421i | −0.501886 | + | 0.501886i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.3137 | + | 11.3137i | −0.401004 | + | 0.401004i | ||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | −32.0000 | −1.13279 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | − | 6.00000i | − | 0.212000i | ||||||
\(802\) | 21.2132 | − | 21.2132i | 0.749064 | − | 0.749064i | ||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 11.3137 | − | 11.3137i | 0.399004 | − | 0.399004i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.65685 | + | 5.65685i | 0.199254 | + | 0.199254i | ||||
\(807\) | − | 48.0000i | − | 1.68968i | ||||||
\(808\) | − | 18.0000i | − | 0.633238i | ||||||
\(809\) | −21.2132 | − | 21.2132i | −0.745817 | − | 0.745817i | 0.227874 | − | 0.973691i | \(-0.426823\pi\) |
−0.973691 | + | 0.227874i | \(0.926823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.8701 | + | 26.8701i | −0.943535 | + | 0.943535i | −0.998489 | − | 0.0549536i | \(-0.982499\pi\) |
0.0549536 | + | 0.998489i | \(0.482499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3137 | + | 11.3137i | −0.396789 | + | 0.396789i | ||||
\(814\) | − | 24.0000i | − | 0.841200i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | −5.65685 | + | 5.65685i | −0.197666 | + | 0.197666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.4558 | + | 25.4558i | −0.888415 | + | 0.888415i | −0.994371 | − | 0.105956i | \(-0.966210\pi\) |
0.105956 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(822\) | −8.48528 | − | 8.48528i | −0.295958 | − | 0.295958i | ||||
\(823\) | 11.3137 | + | 11.3137i | 0.394371 | + | 0.394371i | 0.876242 | − | 0.481871i | \(-0.160043\pi\) |
−0.481871 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(824\) | 16.0000i | 0.557386i | ||||||||
\(825\) | − | 60.0000i | − | 2.08893i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.24264 | + | 4.24264i | 0.147531 | + | 0.147531i | 0.777014 | − | 0.629483i | \(-0.216733\pi\) |
−0.629483 | + | 0.777014i | \(0.716733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 16.0000i | − | 0.555034i | ||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.9706 | + | 16.9706i | −0.586939 | + | 0.586939i | ||||
\(837\) | 16.0000 | 0.553041 | ||||||||
\(838\) | 21.2132 | − | 21.2132i | 0.732798 | − | 0.732798i | ||||
\(839\) | −25.4558 | − | 25.4558i | −0.878833 | − | 0.878833i | 0.114581 | − | 0.993414i | \(-0.463448\pi\) |
−0.993414 | + | 0.114581i | \(0.963448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000i | 1.00000i | ||||||||
\(842\) | − | 2.00000i | − | 0.0689246i | ||||||
\(843\) | 8.48528 | + | 8.48528i | 0.292249 | + | 0.292249i | ||||
\(844\) | −7.07107 | − | 7.07107i | −0.243396 | − | 0.243396i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −70.7107 | + | 70.7107i | −2.42965 | + | 2.42965i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −28.0000 | −0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2843 | + | 28.2843i | −0.968435 | + | 0.968435i | −0.999517 | − | 0.0310818i | \(-0.990105\pi\) |
0.0310818 | + | 0.999517i | \(0.490105\pi\) | |||||||
\(854\) | −16.0000 | −0.547509 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.24264 | − | 4.24264i | −0.145010 | − | 0.145010i | ||||
\(857\) | 12.7279 | + | 12.7279i | 0.434778 | + | 0.434778i | 0.890250 | − | 0.455472i | \(-0.150530\pi\) |
−0.455472 | + | 0.890250i | \(0.650530\pi\) | |||||||
\(858\) | 24.0000i | 0.819346i | ||||||||
\(859\) | 16.0000i | 0.545913i | 0.962026 | + | 0.272956i | \(0.0880015\pi\) | ||||
−0.962026 | + | 0.272956i | \(0.911998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.9411 | + | 33.9411i | 1.15671 | + | 1.15671i | ||||
\(862\) | −16.9706 | + | 16.9706i | −0.578020 | + | 0.578020i | ||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | 2.82843 | − | 2.82843i | 0.0962250 | − | 0.0962250i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | 48.0000i | 1.62829i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 11.3137 | − | 11.3137i | 0.383131 | − | 0.383131i | ||||
\(873\) | 9.89949 | + | 9.89949i | 0.335047 | + | 0.335047i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000i | 0.135147i | ||||||||
\(877\) | −22.6274 | − | 22.6274i | −0.764074 | − | 0.764074i | 0.212982 | − | 0.977056i | \(-0.431682\pi\) |
−0.977056 | + | 0.212982i | \(0.931682\pi\) | |||||||
\(878\) | 5.65685 | + | 5.65685i | 0.190910 | + | 0.190910i | ||||
\(879\) | 8.48528 | − | 8.48528i | 0.286201 | − | 0.286201i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7279 | − | 12.7279i | 0.428815 | − | 0.428815i | −0.459410 | − | 0.888224i | \(-0.651939\pi\) |
0.888224 | + | 0.459410i | \(0.151939\pi\) | |||||||
\(882\) | 9.00000i | 0.303046i | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 24.0000i | − | 0.806296i | ||||||
\(887\) | 16.9706 | − | 16.9706i | 0.569816 | − | 0.569816i | −0.362261 | − | 0.932077i | \(-0.617995\pi\) |
0.932077 | + | 0.362261i | \(0.117995\pi\) | |||||||
\(888\) | −8.00000 | −0.268462 | ||||||||
\(889\) | −45.2548 | + | 45.2548i | −1.51780 | + | 1.51780i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.6690 | + | 46.6690i | 1.56347 | + | 1.56347i | ||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.48528 | + | 8.48528i | 0.283790 | + | 0.283790i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.82843 | − | 2.82843i | 0.0944911 | − | 0.0944911i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.7279 | + | 12.7279i | −0.424736 | + | 0.424736i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 36.0000 | 1.19867 | ||||||||
\(903\) | 64.0000i | 2.12979i | ||||||||
\(904\) | −4.24264 | + | 4.24264i | −0.141108 | + | 0.141108i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22.6274 | + | 22.6274i | −0.751746 | + | 0.751746i | ||||
\(907\) | −41.0122 | − | 41.0122i | −1.36179 | − | 1.36179i | −0.871639 | − | 0.490149i | \(-0.836942\pi\) |
−0.490149 | − | 0.871639i | \(-0.663058\pi\) | |||||||
\(908\) | 4.24264 | + | 4.24264i | 0.140797 | + | 0.140797i | ||||
\(909\) | − | 18.0000i | − | 0.597022i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.48528 | − | 8.48528i | −0.281130 | − | 0.281130i | 0.552430 | − | 0.833560i | \(-0.313701\pi\) |
−0.833560 | + | 0.552430i | \(0.813701\pi\) | |||||||
\(912\) | 5.65685 | + | 5.65685i | 0.187317 | + | 0.187317i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.0000 | −0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000i | 0.462573i | ||||||||
\(917\) | 24.0000 | 0.792550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0000 | 1.84727 | 0.923635 | − | 0.383274i | \(-0.125203\pi\) | ||||
0.923635 | + | 0.383274i | \(0.125203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2843 | + | 28.2843i | −0.931998 | + | 0.931998i | ||||
\(922\) | 6.00000 | 0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 33.9411 | + | 33.9411i | 1.11658 | + | 1.11658i | ||||
\(925\) | −14.1421 | − | 14.1421i | −0.464991 | − | 0.464991i | ||||
\(926\) | 16.0000i | 0.525793i | ||||||||
\(927\) | 16.0000i | 0.525509i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.7279 | − | 12.7279i | −0.417590 | − | 0.417590i | 0.466783 | − | 0.884372i | \(-0.345413\pi\) |
−0.884372 | + | 0.466783i | \(0.845413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0000 | 1.17985 | ||||||||
\(932\) | 12.7279 | − | 12.7279i | 0.416917 | − | 0.416917i | ||||
\(933\) | − | 24.0000i | − | 0.785725i | ||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | − | 58.0000i | − | 1.89478i | −0.320085 | − | 0.947389i | \(-0.603712\pi\) | ||
0.320085 | − | 0.947389i | \(-0.396288\pi\) | |||||||
\(938\) | −22.6274 | + | 22.6274i | −0.738811 | + | 0.738811i | ||||
\(939\) | −68.0000 | −2.21910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.4558 | − | 25.4558i | −0.829837 | − | 0.829837i | 0.157657 | − | 0.987494i | \(-0.449606\pi\) |
−0.987494 | + | 0.157657i | \(0.949606\pi\) | |||||||
\(942\) | 19.7990 | + | 19.7990i | 0.645086 | + | 0.645086i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.9411 | + | 33.9411i | 1.10352 | + | 1.10352i | ||||
\(947\) | −12.7279 | + | 12.7279i | −0.413602 | + | 0.413602i | −0.882991 | − | 0.469389i | \(-0.844474\pi\) |
0.469389 | + | 0.882991i | \(0.344474\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | 2.82843 | − | 2.82843i | 0.0918146 | − | 0.0918146i | ||||
\(950\) | 20.0000i | 0.648886i | ||||||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0000 | −0.971795 | −0.485898 | − | 0.874016i | \(-0.661507\pi\) | ||||
−0.485898 | + | 0.874016i | \(0.661507\pi\) | |||||||
\(954\) | − | 6.00000i | − | 0.194257i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.0000 | −0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.9706 | + | 16.9706i | 0.548294 | + | 0.548294i | ||||
\(959\) | 16.9706 | + | 16.9706i | 0.548008 | + | 0.548008i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000i | 0.483871i | ||||||||
\(962\) | 5.65685 | + | 5.65685i | 0.182384 | + | 0.182384i | ||||
\(963\) | −4.24264 | − | 4.24264i | −0.136717 | − | 0.136717i | ||||
\(964\) | 7.07107 | − | 7.07107i | 0.227744 | − | 0.227744i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0000i | − | 1.28631i | −0.765735 | − | 0.643157i | \(-0.777624\pi\) | ||
0.765735 | − | 0.643157i | \(-0.222376\pi\) | |||||||
\(968\) | 25.0000 | 0.803530 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.0000i | − | 0.770197i | −0.922876 | − | 0.385098i | \(-0.874168\pi\) | ||
0.922876 | − | 0.385098i | \(-0.125832\pi\) | |||||||
\(972\) | 7.07107 | − | 7.07107i | 0.226805 | − | 0.226805i | ||||
\(973\) | 8.00000 | 0.256468 | ||||||||
\(974\) | −5.65685 | + | 5.65685i | −0.181257 | + | 0.181257i | ||||
\(975\) | 14.1421 | + | 14.1421i | 0.452911 | + | 0.452911i | ||||
\(976\) | 2.82843 | + | 2.82843i | 0.0905357 | + | 0.0905357i | ||||
\(977\) | − | 42.0000i | − | 1.34370i | −0.740688 | − | 0.671850i | \(-0.765500\pi\) | ||
0.740688 | − | 0.671850i | \(-0.234500\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | 25.4558 | + | 25.4558i | 0.813572 | + | 0.813572i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3137 | − | 11.3137i | 0.361219 | − | 0.361219i | ||||
\(982\) | 12.0000 | 0.382935 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | − | 12.0000i | − | 0.382546i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.00000i | − | 0.254514i | ||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3137 | − | 11.3137i | 0.359392 | − | 0.359392i | −0.504197 | − | 0.863589i | \(-0.668211\pi\) |
0.863589 | + | 0.504197i | \(0.168211\pi\) | |||||||
\(992\) | −2.82843 | − | 2.82843i | −0.0898027 | − | 0.0898027i | ||||
\(993\) | −22.6274 | − | 22.6274i | −0.718059 | − | 0.718059i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7990 | − | 19.7990i | −0.627040 | − | 0.627040i | 0.320282 | − | 0.947322i | \(-0.396222\pi\) |
−0.947322 | + | 0.320282i | \(0.896222\pi\) | |||||||
\(998\) | −9.89949 | + | 9.89949i | −0.313363 | + | 0.313363i | ||||
\(999\) | 16.0000 | 0.506218 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))