Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.f.22.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 1.50000i | −0.327327 | + | 0.566947i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205 | + | 3.00000i | 0.522233 | + | 0.904534i | 0.999665 | + | 0.0258656i | \(0.00823419\pi\) |
−0.477432 | + | 0.878668i | \(0.658432\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205 | + | 3.00000i | 0.447214 | + | 0.774597i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | + | 3.00000i | −0.397360 | + | 0.688247i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) |
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(20\) | 3.46410 | − | 6.00000i | 0.774597 | − | 1.34164i | ||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.73205 | + | 3.00000i | 0.327327 | + | 0.566947i | ||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205 | 0.311086 | 0.155543 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73205 | + | 3.00000i | −0.301511 | + | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | + | 5.19615i | −0.507093 | + | 0.878310i | ||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.46410 | − | 6.00000i | −0.541002 | − | 0.937043i | −0.998847 | − | 0.0480106i | \(-0.984712\pi\) |
0.457845 | − | 0.889032i | \(-0.348621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 6.92820 | 1.04447 | ||||||||
\(45\) | −1.73205 | + | 3.00000i | −0.258199 | + | 0.447214i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | 2.00000 | − | 3.46410i | 0.288675 | − | 0.500000i | ||||
\(49\) | 2.00000 | + | 3.46410i | 0.285714 | + | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 10.3923i | 0.809040 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.73205 | + | 3.00000i | −0.225494 | + | 0.390567i | −0.956467 | − | 0.291839i | \(-0.905733\pi\) |
0.730974 | + | 0.682406i | \(0.239066\pi\) | |||||||
\(60\) | 6.92820 | 0.894427 | ||||||||
\(61\) | −0.500000 | + | 0.866025i | −0.0640184 | + | 0.110883i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.866025 | − | 1.50000i | −0.109109 | − | 0.188982i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | + | 7.50000i | 0.529009 | + | 0.916271i | 0.999428 | + | 0.0338274i | \(0.0107696\pi\) |
−0.470418 | + | 0.882443i | \(0.655897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.19615 | − | 9.00000i | 0.616670 | − | 1.06810i | −0.373419 | − | 0.927663i | \(-0.621815\pi\) |
0.990089 | − | 0.140441i | \(-0.0448520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.73205 | −0.202721 | −0.101361 | − | 0.994850i | \(-0.532320\pi\) | ||||
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.50000 | + | 6.06218i | 0.404145 | + | 0.700000i | ||||
\(76\) | 3.46410 | + | 6.00000i | 0.397360 | + | 0.688247i | ||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0000 | −1.23760 | −0.618798 | − | 0.785550i | \(-0.712380\pi\) | ||||
−0.618798 | + | 0.785550i | \(0.712380\pi\) | |||||||
\(80\) | −6.92820 | − | 12.0000i | −0.774597 | − | 1.34164i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8564 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(84\) | −1.73205 | + | 3.00000i | −0.188982 | + | 0.327327i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | − | 5.19615i | 0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | − | 6.00000i | −0.367194 | − | 0.635999i | 0.621932 | − | 0.783072i | \(-0.286348\pi\) |
−0.989126 | + | 0.147073i | \(0.953015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.0000 | −1.25109 | ||||||||
\(93\) | 0.866025 | + | 1.50000i | 0.0898027 | + | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | + | 10.3923i | −0.615587 | + | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.59808 | − | 4.50000i | 0.263795 | − | 0.456906i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) |
0.967247 | + | 0.253837i | \(0.0816925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46410 | −0.348155 | ||||||||
\(100\) | 7.00000 | − | 12.1244i | 0.700000 | − | 1.21244i | ||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | 0.0985329 | 0.0492665 | − | 0.998786i | \(-0.484312\pi\) | ||||
0.0492665 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | −0.585540 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | −1.00000 | + | 1.73205i | −0.0962250 | + | 0.166667i | ||||
\(109\) | −15.5885 | −1.49310 | −0.746552 | − | 0.665327i | \(-0.768292\pi\) | ||||
−0.746552 | + | 0.665327i | \(0.768292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.92820 | 0.654654 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3923 | − | 18.0000i | −0.969087 | − | 1.67851i | ||||
\(116\) | −12.0000 | −1.11417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.46410 | − | 6.00000i | 0.312348 | − | 0.541002i | ||||
\(124\) | 1.73205 | − | 3.00000i | 0.155543 | − | 0.269408i | ||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.50000 | + | 11.2583i | 0.576782 | + | 0.999015i | 0.995846 | + | 0.0910585i | \(0.0290250\pi\) |
−0.419064 | + | 0.907957i | \(0.637642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 3.46410 | + | 6.00000i | 0.301511 | + | 0.522233i | ||||
\(133\) | −3.00000 | − | 5.19615i | −0.260133 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.46410 | −0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 6.00000 | + | 10.3923i | 0.507093 | + | 0.878310i | ||||
\(141\) | −1.73205 | − | 3.00000i | −0.145865 | − | 0.252646i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −10.3923 | − | 18.0000i | −0.863034 | − | 1.49482i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | + | 3.46410i | −0.164957 | + | 0.285714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.46410 | − | 6.00000i | 0.283790 | − | 0.491539i | −0.688525 | − | 0.725213i | \(-0.741741\pi\) |
0.972315 | + | 0.233674i | \(0.0750747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410 | 0.281905 | 0.140952 | − | 0.990016i | \(-0.454984\pi\) | ||||
0.140952 | + | 0.990016i | \(0.454984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | 0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.52628 | + | 16.5000i | −0.746156 | + | 1.29238i | 0.203497 | + | 0.979076i | \(0.434769\pi\) |
−0.949653 | + | 0.313304i | \(0.898564\pi\) | |||||||
\(164\) | −13.8564 | −1.08200 | ||||||||
\(165\) | −6.00000 | + | 10.3923i | −0.467099 | + | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.46410 | + | 6.00000i | 0.268060 | + | 0.464294i | 0.968361 | − | 0.249554i | \(-0.0802840\pi\) |
−0.700301 | + | 0.713848i | \(0.746951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.73205 | − | 3.00000i | −0.132453 | − | 0.229416i | ||||
\(172\) | 1.00000 | + | 1.73205i | 0.0762493 | + | 0.132068i | ||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.06218 | + | 10.5000i | −0.458258 | + | 0.793725i | ||||
\(176\) | 6.92820 | − | 12.0000i | 0.522233 | − | 0.904534i | ||||
\(177\) | −3.46410 | −0.260378 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 3.46410 | + | 6.00000i | 0.258199 | + | 0.447214i | ||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.46410 | + | 6.00000i | −0.252646 | + | 0.437595i | ||||
\(189\) | 0.866025 | − | 1.50000i | 0.0629941 | − | 0.109109i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | −4.00000 | − | 6.92820i | −0.288675 | − | 0.500000i | ||||
\(193\) | 7.79423 | + | 13.5000i | 0.561041 | + | 0.971751i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) |
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.00000 | 0.571429 | ||||||||
\(197\) | 6.92820 | + | 12.0000i | 0.493614 | + | 0.854965i | 0.999973 | − | 0.00735824i | \(-0.00234222\pi\) |
−0.506359 | + | 0.862323i | \(0.669009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.33013 | + | 7.50000i | −0.305424 | + | 0.529009i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | 0.729397 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | − | 20.7846i | −0.838116 | − | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 12.0000 | − | 20.7846i | 0.824163 | − | 1.42749i | ||||
\(213\) | 10.3923 | 0.712069 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.73205 | + | 3.00000i | −0.118125 | + | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | + | 2.59808i | −0.101827 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.866025 | − | 1.50000i | −0.0585206 | − | 0.101361i | ||||
\(220\) | 24.0000 | 1.61808 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.66025 | + | 15.0000i | 0.579934 | + | 1.00447i | 0.995486 | + | 0.0949052i | \(0.0302548\pi\) |
−0.415553 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.50000 | + | 6.06218i | −0.233333 | + | 0.404145i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3923 | + | 18.0000i | −0.689761 | + | 1.19470i | 0.282153 | + | 0.959369i | \(0.408951\pi\) |
−0.971915 | + | 0.235333i | \(0.924382\pi\) | |||||||
\(228\) | −3.46410 | + | 6.00000i | −0.229416 | + | 0.397360i | ||||
\(229\) | −27.7128 | −1.83131 | −0.915657 | − | 0.401960i | \(-0.868329\pi\) | ||||
−0.915657 | + | 0.401960i | \(0.868329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 3.46410 | + | 6.00000i | 0.225494 | + | 0.390567i | ||||
\(237\) | −5.50000 | − | 9.52628i | −0.357263 | − | 0.618798i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 6.92820 | − | 12.0000i | 0.447214 | − | 0.774597i | ||||
\(241\) | 10.3923 | − | 18.0000i | 0.669427 | − | 1.15948i | −0.308637 | − | 0.951180i | \(-0.599873\pi\) |
0.978065 | − | 0.208302i | \(-0.0667937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 1.00000 | + | 1.73205i | 0.0640184 | + | 0.110883i | ||||
\(245\) | 6.92820 | + | 12.0000i | 0.442627 | + | 0.766652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.92820 | − | 12.0000i | −0.439057 | − | 0.760469i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | 10.3923 | − | 18.0000i | 0.653359 | − | 1.13165i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.5692 | 2.55358 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.46410 | − | 6.00000i | 0.212000 | − | 0.367194i | ||||
\(268\) | 17.3205 | 1.05802 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.59808 | + | 4.50000i | 0.157822 | + | 0.273356i | 0.934083 | − | 0.357056i | \(-0.116219\pi\) |
−0.776261 | + | 0.630412i | \(0.782886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.1244 | + | 21.0000i | 0.731126 | + | 1.26635i | ||||
\(276\) | −6.00000 | − | 10.3923i | −0.361158 | − | 0.625543i | ||||
\(277\) | −5.00000 | + | 8.66025i | −0.300421 | + | 0.520344i | −0.976231 | − | 0.216731i | \(-0.930460\pi\) |
0.675810 | + | 0.737075i | \(0.263794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.866025 | + | 1.50000i | −0.0518476 | + | 0.0898027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2487 | 1.44656 | 0.723278 | − | 0.690557i | \(-0.242634\pi\) | ||||
0.723278 | + | 0.690557i | \(0.242634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.50000 | − | 9.52628i | −0.326941 | − | 0.566279i | 0.654962 | − | 0.755662i | \(-0.272685\pi\) |
−0.981903 | + | 0.189383i | \(0.939351\pi\) | |||||||
\(284\) | −10.3923 | − | 18.0000i | −0.616670 | − | 1.06810i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.19615 | 0.304604 | ||||||||
\(292\) | −1.73205 | + | 3.00000i | −0.101361 | + | 0.175562i | ||||
\(293\) | −8.66025 | + | 15.0000i | −0.505937 | + | 0.876309i | 0.494039 | + | 0.869440i | \(0.335520\pi\) |
−0.999976 | + | 0.00686959i | \(0.997813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.73205 | − | 3.00000i | −0.100504 | − | 0.174078i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14.0000 | 0.808290 | ||||||||
\(301\) | −0.866025 | − | 1.50000i | −0.0499169 | − | 0.0864586i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 13.8564 | 0.794719 | ||||||||
\(305\) | −1.73205 | + | 3.00000i | −0.0991769 | + | 0.171780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.73205 | 0.0988534 | 0.0494267 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494267 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(308\) | −6.00000 | + | 10.3923i | −0.341882 | + | 0.592157i | ||||
\(309\) | 0.500000 | + | 0.866025i | 0.0284440 | + | 0.0492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0000 | 0.734803 | 0.367402 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00000 | − | 5.19615i | −0.169031 | − | 0.292770i | ||||
\(316\) | −11.0000 | + | 19.0526i | −0.618798 | + | 1.07179i | ||||
\(317\) | 6.92820 | 0.389127 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.3923 | − | 18.0000i | 0.581857 | − | 1.00781i | ||||
\(320\) | −27.7128 | −1.54919 | ||||||||
\(321\) | −3.00000 | + | 5.19615i | −0.167444 | + | 0.290021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.79423 | − | 13.5000i | −0.431022 | − | 0.746552i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.00000 | − | 5.19615i | 0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.59808 | + | 4.50000i | −0.142803 | + | 0.247342i | −0.928551 | − | 0.371204i | \(-0.878945\pi\) |
0.785748 | + | 0.618547i | \(0.212278\pi\) | |||||||
\(332\) | −13.8564 | + | 24.0000i | −0.760469 | + | 1.31717i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0000 | + | 25.9808i | 0.819538 | + | 1.41948i | ||||
\(336\) | 3.46410 | + | 6.00000i | 0.188982 | + | 0.327327i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0526 | −1.02874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.3923 | − | 18.0000i | 0.559503 | − | 0.969087i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | − | 20.7846i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | −6.00000 | − | 10.3923i | −0.321634 | − | 0.557086i | ||||
\(349\) | 9.52628 | + | 16.5000i | 0.509930 | + | 0.883225i | 0.999934 | + | 0.0115044i | \(0.00366206\pi\) |
−0.490004 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.19615 | + | 9.00000i | 0.276563 | + | 0.479022i | 0.970528 | − | 0.240987i | \(-0.0774711\pi\) |
−0.693965 | + | 0.720009i | \(0.744138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 31.1769i | 0.955341 | − | 1.65470i | ||||
\(356\) | −13.8564 | −0.734388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.92820 | −0.365657 | −0.182828 | − | 0.983145i | \(-0.558525\pi\) | ||||
−0.182828 | + | 0.983145i | \(0.558525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.50000 | + | 6.06218i | 0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.50000 | − | 14.7224i | −0.443696 | − | 0.768505i | 0.554264 | − | 0.832341i | \(-0.313000\pi\) |
−0.997960 | + | 0.0638362i | \(0.979666\pi\) | |||||||
\(368\) | −12.0000 | + | 20.7846i | −0.625543 | + | 1.08347i | ||||
\(369\) | 6.92820 | 0.360668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3923 | + | 18.0000i | −0.539542 | + | 0.934513i | ||||
\(372\) | 3.46410 | 0.179605 | ||||||||
\(373\) | 5.50000 | − | 9.52628i | 0.284779 | − | 0.493252i | −0.687776 | − | 0.725923i | \(-0.741413\pi\) |
0.972556 | + | 0.232671i | \(0.0747464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.46410 | + | 6.00000i | 0.178885 | + | 0.309839i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2583 | − | 19.5000i | −0.578302 | − | 1.00165i | −0.995674 | − | 0.0929123i | \(-0.970382\pi\) |
0.417373 | − | 0.908735i | \(-0.362951\pi\) | |||||||
\(380\) | 12.0000 | + | 20.7846i | 0.615587 | + | 1.06623i | ||||
\(381\) | −6.50000 | + | 11.2583i | −0.333005 | + | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8564 | + | 24.0000i | −0.708029 | + | 1.22634i | 0.257558 | + | 0.966263i | \(0.417082\pi\) |
−0.965587 | + | 0.260080i | \(0.916251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.7846 | −1.05928 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.500000 | − | 0.866025i | −0.0254164 | − | 0.0440225i | ||||
\(388\) | −5.19615 | − | 9.00000i | −0.263795 | − | 0.456906i | ||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | + | 5.19615i | 0.151330 | + | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.1051 | −1.91728 | ||||||||
\(396\) | −3.46410 | + | 6.00000i | −0.174078 | + | 0.301511i | ||||
\(397\) | 7.79423 | − | 13.5000i | 0.391181 | − | 0.677546i | −0.601424 | − | 0.798930i | \(-0.705400\pi\) |
0.992606 | + | 0.121384i | \(0.0387333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.00000 | − | 5.19615i | 0.150188 | − | 0.260133i | ||||
\(400\) | −14.0000 | − | 24.2487i | −0.700000 | − | 1.21244i | ||||
\(401\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −36.0000 | −1.79107 | ||||||||
\(405\) | −1.73205 | − | 3.00000i | −0.0860663 | − | 0.149071i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.33013 | + | 7.50000i | −0.214111 | + | 0.370851i | −0.952997 | − | 0.302979i | \(-0.902019\pi\) |
0.738886 | + | 0.673830i | \(0.235352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.00000 | − | 1.73205i | 0.0492665 | − | 0.0853320i | ||||
\(413\) | −3.00000 | − | 5.19615i | −0.147620 | − | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −48.0000 | −2.35623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | −0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | −6.00000 | + | 10.3923i | −0.292770 | + | 0.507093i | ||||
\(421\) | −12.1244 | −0.590905 | −0.295452 | − | 0.955357i | \(-0.595470\pi\) | ||||
−0.295452 | + | 0.955357i | \(0.595470\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.73205 | − | 3.00000i | 0.0842152 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.866025 | − | 1.50000i | −0.0419099 | − | 0.0725901i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3923 | + | 18.0000i | 0.500580 | + | 0.867029i | 1.00000 | 0.000669521i | \(0.000213115\pi\) | |
−0.499420 | + | 0.866360i | \(0.666454\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | −11.5000 | + | 19.9186i | −0.552655 | + | 0.957226i | 0.445427 | + | 0.895318i | \(0.353052\pi\) |
−0.998082 | + | 0.0619079i | \(0.980282\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3923 | − | 18.0000i | 0.498273 | − | 0.863034i | ||||
\(436\) | −15.5885 | + | 27.0000i | −0.746552 | + | 1.29307i | ||||
\(437\) | 20.7846 | 0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5000 | + | 30.3109i | 0.835229 | + | 1.44666i | 0.893843 | + | 0.448379i | \(0.147999\pi\) |
−0.0586141 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.00000 | −0.190476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | − | 20.7846i | −0.568855 | − | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.92820 | 0.327693 | ||||||||
\(448\) | 6.92820 | − | 12.0000i | 0.327327 | − | 0.566947i | ||||
\(449\) | 19.0526 | − | 33.0000i | 0.899146 | − | 1.55737i | 0.0705577 | − | 0.997508i | \(-0.477522\pi\) |
0.828588 | − | 0.559859i | \(-0.189145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | 1.73205 | + | 3.00000i | 0.0813788 | + | 0.140952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.1865 | − | 31.5000i | −0.850730 | − | 1.47351i | −0.880550 | − | 0.473953i | \(-0.842827\pi\) |
0.0298202 | − | 0.999555i | \(-0.490507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −41.5692 | −1.93817 | ||||||||
\(461\) | 20.7846 | − | 36.0000i | 0.968036 | − | 1.67669i | 0.266808 | − | 0.963750i | \(-0.414031\pi\) |
0.701228 | − | 0.712938i | \(-0.252636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.3731 | 1.69040 | 0.845200 | − | 0.534450i | \(-0.179481\pi\) | ||||
0.845200 | + | 0.534450i | \(0.179481\pi\) | |||||||
\(464\) | −12.0000 | + | 20.7846i | −0.557086 | + | 0.964901i | ||||
\(465\) | 3.00000 | + | 5.19615i | 0.139122 | + | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.50000 | + | 9.52628i | 0.253427 | + | 0.438948i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.46410 | −0.159280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.1244 | + | 21.0000i | −0.556304 | + | 0.963546i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3205 | − | 30.0000i | −0.791394 | − | 1.37073i | −0.925104 | − | 0.379714i | \(-0.876022\pi\) |
0.133710 | − | 0.991021i | \(-0.457311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.19615 | + | 9.00000i | 0.236433 | + | 0.409514i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 9.00000 | − | 15.5885i | 0.408669 | − | 0.707835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1244 | − | 21.0000i | 0.549407 | − | 0.951601i | −0.448908 | − | 0.893578i | \(-0.648187\pi\) |
0.998315 | − | 0.0580230i | \(-0.0184797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.0526 | −0.861586 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | + | 5.19615i | 0.135388 | + | 0.234499i | 0.925746 | − | 0.378147i | \(-0.123439\pi\) |
−0.790358 | + | 0.612646i | \(0.790105\pi\) | |||||||
\(492\) | −6.92820 | − | 12.0000i | −0.312348 | − | 0.541002i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0000 | −0.539360 | ||||||||
\(496\) | −3.46410 | − | 6.00000i | −0.155543 | − | 0.269408i | ||||
\(497\) | 9.00000 | + | 15.5885i | 0.403705 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.1769 | 1.39567 | 0.697835 | − | 0.716258i | \(-0.254147\pi\) | ||||
0.697835 | + | 0.716258i | \(0.254147\pi\) | |||||||
\(500\) | 6.92820 | − | 12.0000i | 0.309839 | − | 0.536656i | ||||
\(501\) | −3.46410 | + | 6.00000i | −0.154765 | + | 0.268060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0000 | − | 25.9808i | 0.668817 | − | 1.15842i | −0.309418 | − | 0.950926i | \(-0.600134\pi\) |
0.978235 | − | 0.207499i | \(-0.0665323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.1769 | − | 54.0000i | −1.38735 | − | 2.40297i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.0000 | 1.15356 | ||||||||
\(509\) | −8.66025 | − | 15.0000i | −0.383859 | − | 0.664863i | 0.607751 | − | 0.794128i | \(-0.292072\pi\) |
−0.991610 | + | 0.129264i | \(0.958738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50000 | − | 2.59808i | 0.0663561 | − | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.73205 | − | 3.00000i | 0.0764719 | − | 0.132453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.46410 | 0.152647 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | + | 24.2487i | 0.612177 | + | 1.06032i | 0.990873 | + | 0.134801i | \(0.0430394\pi\) |
−0.378695 | + | 0.925521i | \(0.623627\pi\) | |||||||
\(524\) | 6.00000 | − | 10.3923i | 0.262111 | − | 0.453990i | ||||
\(525\) | −12.1244 | −0.529150 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 13.8564 | 0.603023 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.73205 | − | 3.00000i | −0.0751646 | − | 0.130189i | ||||
\(532\) | −12.0000 | −0.520266 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.3923 | + | 18.0000i | 0.449299 | + | 0.778208i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.92820 | + | 12.0000i | −0.298419 | + | 0.516877i | ||||
\(540\) | −3.46410 | + | 6.00000i | −0.149071 | + | 0.258199i | ||||
\(541\) | 29.4449 | 1.26593 | 0.632967 | − | 0.774179i | \(-0.281837\pi\) | ||||
0.632967 | + | 0.774179i | \(0.281837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00000 | − | 12.1244i | −0.300399 | − | 0.520306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −54.0000 | −2.31311 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0000 | −0.812381 | −0.406191 | − | 0.913788i | \(-0.633143\pi\) | ||||
−0.406191 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.500000 | − | 0.866025i | −0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7846 | 0.885454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.52628 | − | 16.5000i | 0.405099 | − | 0.701651i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00000 | + | 8.66025i | 0.212047 | + | 0.367277i | ||||
\(557\) | 13.8564 | + | 24.0000i | 0.587115 | + | 1.01691i | 0.994608 | + | 0.103704i | \(0.0330696\pi\) |
−0.407493 | + | 0.913208i | \(0.633597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24.0000 | 1.01419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0000 | + | 36.3731i | −0.885044 | + | 1.53294i | −0.0393818 | + | 0.999224i | \(0.512539\pi\) |
−0.845663 | + | 0.533718i | \(0.820794\pi\) | |||||||
\(564\) | −6.92820 | −0.291730 | ||||||||
\(565\) | −10.3923 | + | 18.0000i | −0.437208 | + | 0.757266i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.73205 | 0.0727393 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.0000 | − | 36.3731i | −0.875761 | − | 1.51686i | ||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | −34.6410 | −1.44212 | −0.721062 | − | 0.692870i | \(-0.756346\pi\) | ||||
−0.721062 | + | 0.692870i | \(0.756346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.79423 | + | 13.5000i | −0.323917 | + | 0.561041i | ||||
\(580\) | −41.5692 | −1.72607 | ||||||||
\(581\) | 12.0000 | − | 20.7846i | 0.497844 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7846 | + | 36.0000i | 0.860811 | + | 1.49097i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5885 | − | 27.0000i | −0.643404 | − | 1.11441i | −0.984668 | − | 0.174441i | \(-0.944188\pi\) |
0.341263 | − | 0.939968i | \(-0.389145\pi\) | |||||||
\(588\) | 4.00000 | + | 6.92820i | 0.164957 | + | 0.285714i | ||||
\(589\) | −3.00000 | + | 5.19615i | −0.123613 | + | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.92820 | + | 12.0000i | −0.284988 | + | 0.493614i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46410 | −0.142254 | −0.0711268 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711268 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.92820 | − | 12.0000i | −0.283790 | − | 0.491539i | ||||
\(597\) | 7.00000 | 0.286491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | + | 22.5167i | 0.530281 | + | 0.918474i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.66025 | −0.352673 | ||||||||
\(604\) | 3.46410 | − | 6.00000i | 0.140952 | − | 0.244137i | ||||
\(605\) | −1.73205 | + | 3.00000i | −0.0704179 | + | 0.121967i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.19615 | + | 9.00000i | 0.210559 | + | 0.364698i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.33013 | + | 7.50000i | 0.174892 | + | 0.302922i | 0.940124 | − | 0.340833i | \(-0.110709\pi\) |
−0.765232 | + | 0.643755i | \(0.777376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | − | 20.7846i | 0.483887 | − | 0.838116i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.19615 | − | 9.00000i | 0.209189 | − | 0.362326i | −0.742270 | − | 0.670101i | \(-0.766251\pi\) |
0.951459 | + | 0.307774i | \(0.0995842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9808 | −1.04425 | −0.522127 | − | 0.852867i | \(-0.674861\pi\) | ||||
−0.522127 | + | 0.852867i | \(0.674861\pi\) | |||||||
\(620\) | 6.00000 | − | 10.3923i | 0.240966 | − | 0.417365i | ||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | − | 10.3923i | −0.239617 | − | 0.415029i | ||||
\(628\) | 11.0000 | − | 19.0526i | 0.438948 | − | 0.760280i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.866025 | − | 1.50000i | 0.0344759 | − | 0.0597141i | −0.848273 | − | 0.529560i | \(-0.822357\pi\) |
0.882749 | + | 0.469846i | \(0.155690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.50000 | − | 11.2583i | 0.258352 | − | 0.447478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.5167 | + | 39.0000i | 0.893546 | + | 1.54767i | ||||
\(636\) | 24.0000 | 0.951662 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.19615 | + | 9.00000i | 0.205557 | + | 0.356034i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.52628 | + | 16.5000i | −0.375680 | + | 0.650696i | −0.990429 | − | 0.138027i | \(-0.955924\pi\) |
0.614749 | + | 0.788723i | \(0.289257\pi\) | |||||||
\(644\) | 10.3923 | − | 18.0000i | 0.409514 | − | 0.709299i | ||||
\(645\) | −3.46410 | −0.136399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00000 | − | 15.5885i | −0.353827 | − | 0.612845i | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.00000 | −0.117579 | ||||||||
\(652\) | 19.0526 | + | 33.0000i | 0.746156 | + | 1.29238i | ||||
\(653\) | −18.0000 | − | 31.1769i | −0.704394 | − | 1.22005i | −0.966910 | − | 0.255119i | \(-0.917885\pi\) |
0.262515 | − | 0.964928i | \(-0.415448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.7846 | 0.812122 | ||||||||
\(656\) | −13.8564 | + | 24.0000i | −0.541002 | + | 0.937043i | ||||
\(657\) | 0.866025 | − | 1.50000i | 0.0337869 | − | 0.0585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0000 | + | 41.5692i | −0.934907 | + | 1.61931i | −0.160108 | + | 0.987099i | \(0.551184\pi\) |
−0.774799 | + | 0.632207i | \(0.782149\pi\) | |||||||
\(660\) | 12.0000 | + | 20.7846i | 0.467099 | + | 0.809040i | ||||
\(661\) | 12.9904 | + | 22.5000i | 0.505267 | + | 0.875149i | 0.999981 | + | 0.00609283i | \(0.00193942\pi\) |
−0.494714 | + | 0.869056i | \(0.664727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.3923 | − | 18.0000i | −0.402996 | − | 0.698010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | + | 31.1769i | −0.696963 | + | 1.20717i | ||||
\(668\) | 13.8564 | 0.536120 | ||||||||
\(669\) | −8.66025 | + | 15.0000i | −0.334825 | + | 0.579934i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.46410 | −0.133730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.500000 | − | 0.866025i | −0.0192736 | − | 0.0333828i | 0.856228 | − | 0.516599i | \(-0.172802\pi\) |
−0.875501 | + | 0.483216i | \(0.839469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.0000 | 1.84479 | 0.922395 | − | 0.386248i | \(-0.126229\pi\) | ||||
0.922395 | + | 0.386248i | \(0.126229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50000 | + | 7.79423i | 0.172694 | + | 0.299115i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.7846 | −0.796468 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1244 | − | 21.0000i | 0.463926 | − | 0.803543i | −0.535227 | − | 0.844708i | \(-0.679774\pi\) |
0.999152 | + | 0.0411658i | \(0.0131072\pi\) | |||||||
\(684\) | −6.92820 | −0.264906 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8564 | − | 24.0000i | −0.528655 | − | 0.915657i | ||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6506 | + | 37.5000i | 0.823629 | + | 1.42657i | 0.902963 | + | 0.429719i | \(0.141387\pi\) |
−0.0793336 | + | 0.996848i | \(0.525279\pi\) | |||||||
\(692\) | 6.00000 | + | 10.3923i | 0.228086 | + | 0.395056i | ||||
\(693\) | 3.00000 | − | 5.19615i | 0.113961 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.66025 | + | 15.0000i | −0.328502 | + | 0.568982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | + | 15.5885i | 0.340411 | + | 0.589610i | ||||
\(700\) | 12.1244 | + | 21.0000i | 0.458258 | + | 0.793725i | ||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −13.8564 | − | 24.0000i | −0.522233 | − | 0.904534i | ||||
\(705\) | −6.00000 | − | 10.3923i | −0.225973 | − | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1769 | 1.17253 | ||||||||
\(708\) | −3.46410 | + | 6.00000i | −0.130189 | + | 0.225494i | ||||
\(709\) | −9.52628 | + | 16.5000i | −0.357767 | + | 0.619671i | −0.987587 | − | 0.157070i | \(-0.949795\pi\) |
0.629821 | + | 0.776741i | \(0.283128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.50000 | − | 9.52628i | 0.206266 | − | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.19615 | − | 9.00000i | −0.194597 | − | 0.337053i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 13.8564 | 0.516398 | ||||||||
\(721\) | −0.866025 | + | 1.50000i | −0.0322525 | + | 0.0558629i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.7846 | 0.772988 | ||||||||
\(724\) | −14.0000 | + | 24.2487i | −0.520306 | + | 0.901196i | ||||
\(725\) | −21.0000 | − | 36.3731i | −0.779920 | − | 1.35086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0000 | 1.29808 | 0.649039 | − | 0.760755i | \(-0.275171\pi\) | ||||
0.649039 | + | 0.760755i | \(0.275171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.00000 | + | 1.73205i | −0.0369611 | + | 0.0640184i | ||||
\(733\) | 39.8372 | 1.47142 | 0.735710 | − | 0.677297i | \(-0.236849\pi\) | ||||
0.735710 | + | 0.677297i | \(0.236849\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.92820 | + | 12.0000i | −0.255551 | + | 0.442627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.0000 | + | 25.9808i | −0.552532 | + | 0.957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.5167 | − | 39.0000i | −0.828289 | − | 1.43464i | −0.899380 | − | 0.437168i | \(-0.855981\pi\) |
0.0710909 | − | 0.997470i | \(-0.477352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.19615 | − | 9.00000i | −0.190628 | − | 0.330178i | 0.754830 | − | 0.655920i | \(-0.227719\pi\) |
−0.945459 | + | 0.325742i | \(0.894386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | − | 20.7846i | 0.439646 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.92820 | − | 12.0000i | 0.253490 | − | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3923 | −0.379727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 6.92820 | + | 12.0000i | 0.252646 | + | 0.437595i | ||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | −1.73205 | − | 3.00000i | −0.0629941 | − | 0.109109i | ||||
\(757\) | −17.0000 | − | 29.4449i | −0.617876 | − | 1.07019i | −0.989873 | − | 0.141958i | \(-0.954660\pi\) |
0.371997 | − | 0.928234i | \(-0.378673\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3923 | + | 18.0000i | −0.376721 | + | 0.652499i | −0.990583 | − | 0.136914i | \(-0.956282\pi\) |
0.613862 | + | 0.789413i | \(0.289615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5000 | − | 23.3827i | 0.488733 | − | 0.846510i | ||||
\(764\) | −18.0000 | − | 31.1769i | −0.651217 | − | 1.12794i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.0000 | −0.577350 | ||||||||
\(769\) | −3.46410 | − | 6.00000i | −0.124919 | − | 0.216366i | 0.796782 | − | 0.604266i | \(-0.206534\pi\) |
−0.921701 | + | 0.387901i | \(0.873200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.1769 | 1.12208 | ||||||||
\(773\) | 25.9808 | − | 45.0000i | 0.934463 | − | 1.61854i | 0.158874 | − | 0.987299i | \(-0.449213\pi\) |
0.775589 | − | 0.631239i | \(-0.217453\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1244 | 0.435520 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | + | 5.19615i | 0.107211 | + | 0.185695i | ||||
\(784\) | 8.00000 | − | 13.8564i | 0.285714 | − | 0.494872i | ||||
\(785\) | 38.1051 | 1.36003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4545 | − | 28.5000i | 0.586539 | − | 1.01592i | −0.408143 | − | 0.912918i | \(-0.633823\pi\) |
0.994682 | − | 0.102997i | \(-0.0328433\pi\) | |||||||
\(788\) | 27.7128 | 0.987228 | ||||||||
\(789\) | 6.00000 | − | 10.3923i | 0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.19615 | − | 9.00000i | −0.184754 | − | 0.320003i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.7846 | + | 36.0000i | 0.737154 | + | 1.27679i | ||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | 6.00000 | − | 10.3923i | 0.212531 | − | 0.368114i | −0.739975 | − | 0.672634i | \(-0.765163\pi\) |
0.952506 | + | 0.304520i | \(0.0984960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.92820 | 0.244796 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 8.66025 | + | 15.0000i | 0.305424 | + | 0.529009i | ||||
\(805\) | 36.0000 | 1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | − | 10.3923i | −0.210949 | − | 0.365374i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.9808 | −0.912308 | −0.456154 | − | 0.889901i | \(-0.650773\pi\) | ||||
−0.456154 | + | 0.889901i | \(0.650773\pi\) | |||||||
\(812\) | 10.3923 | − | 18.0000i | 0.364698 | − | 0.631676i | ||||
\(813\) | −2.59808 | + | 4.50000i | −0.0911185 | + | 0.157822i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0000 | + | 57.1577i | −1.15594 | + | 2.00215i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.73205 | − | 3.00000i | −0.0605968 | − | 0.104957i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.0000 | −1.67623 | ||||||||
\(821\) | 12.1244 | + | 21.0000i | 0.423143 | + | 0.732905i | 0.996245 | − | 0.0865789i | \(-0.0275935\pi\) |
−0.573102 | + | 0.819484i | \(0.694260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.1244 | + | 21.0000i | −0.422116 | + | 0.731126i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.4974 | −1.68642 | −0.843210 | − | 0.537584i | \(-0.819337\pi\) | ||||
−0.843210 | + | 0.537584i | \(0.819337\pi\) | |||||||
\(828\) | 6.00000 | − | 10.3923i | 0.208514 | − | 0.361158i | ||||
\(829\) | 15.5000 | + | 26.8468i | 0.538337 | + | 0.932427i | 0.998994 | + | 0.0448490i | \(0.0142807\pi\) |
−0.460657 | + | 0.887578i | \(0.652386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 20.7846i | 0.415277 | + | 0.719281i | ||||
\(836\) | −12.0000 | + | 20.7846i | −0.415029 | + | 0.718851i | ||||
\(837\) | −1.73205 | −0.0598684 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.5885 | − | 27.0000i | 0.538173 | − | 0.932144i | −0.460829 | − | 0.887489i | \(-0.652448\pi\) |
0.999002 | − | 0.0446547i | \(-0.0142187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.1244 | + | 21.0000i | 0.417585 | + | 0.723278i | ||||
\(844\) | −26.0000 | −0.894957 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.866025 | − | 1.50000i | −0.0297570 | − | 0.0515406i | ||||
\(848\) | −24.0000 | − | 41.5692i | −0.824163 | − | 1.42749i | ||||
\(849\) | 5.50000 | − | 9.52628i | 0.188760 | − | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 10.3923 | − | 18.0000i | 0.356034 | − | 0.616670i | ||||
\(853\) | 25.9808 | 0.889564 | 0.444782 | − | 0.895639i | \(-0.353281\pi\) | ||||
0.444782 | + | 0.895639i | \(0.353281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | − | 10.3923i | −0.205196 | − | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 3.46410 | + | 6.00000i | 0.118125 | + | 0.204598i | ||||
\(861\) | 6.00000 | + | 10.3923i | 0.204479 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.3205 | −0.589597 | −0.294798 | − | 0.955559i | \(-0.595253\pi\) | ||||
−0.294798 | + | 0.955559i | \(0.595253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.3923 | + | 18.0000i | −0.353349 | + | 0.612018i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.50000 | + | 14.7224i | −0.288675 | + | 0.500000i | ||||
\(868\) | 3.00000 | + | 5.19615i | 0.101827 | + | 0.176369i | ||||
\(869\) | −19.0526 | − | 33.0000i | −0.646314 | − | 1.11945i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.59808 | + | 4.50000i | 0.0879316 | + | 0.152302i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | + | 10.3923i | −0.202837 | + | 0.351324i | ||||
\(876\) | −3.46410 | −0.117041 | ||||||||
\(877\) | −20.7846 | + | 36.0000i | −0.701846 | + | 1.21563i | 0.265971 | + | 0.963981i | \(0.414307\pi\) |
−0.967818 | + | 0.251653i | \(0.919026\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.3205 | −0.584206 | ||||||||
\(880\) | 24.0000 | − | 41.5692i | 0.809040 | − | 1.40130i | ||||
\(881\) | −6.00000 | − | 10.3923i | −0.202145 | − | 0.350126i | 0.747074 | − | 0.664741i | \(-0.231458\pi\) |
−0.949219 | + | 0.314615i | \(0.898125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00000 | 0.168263 | 0.0841317 | − | 0.996455i | \(-0.473188\pi\) | ||||
0.0841317 | + | 0.996455i | \(0.473188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | −0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0000 | + | 36.3731i | 0.705111 | + | 1.22129i | 0.966651 | + | 0.256096i | \(0.0824362\pi\) |
−0.261540 | + | 0.965193i | \(0.584230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5167 | −0.755185 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73205 | − | 3.00000i | 0.0580259 | − | 0.100504i | ||||
\(892\) | 34.6410 | 1.15987 | ||||||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.7846 | + | 36.0000i | 0.694753 | + | 1.20335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.19615 | − | 9.00000i | −0.173301 | − | 0.300167i | ||||
\(900\) | 7.00000 | + | 12.1244i | 0.233333 | + | 0.404145i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.866025 | − | 1.50000i | 0.0288195 | − | 0.0499169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.4974 | −1.61211 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 20.7846 | + | 36.0000i | 0.689761 | + | 1.19470i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 6.92820 | + | 12.0000i | 0.229416 | + | 0.397360i | ||||
\(913\) | −24.0000 | − | 41.5692i | −0.794284 | − | 1.37574i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.46410 | −0.114520 | ||||||||
\(916\) | −27.7128 | + | 48.0000i | −0.915657 | + | 1.58596i | ||||
\(917\) | −5.19615 | + | 9.00000i | −0.171592 | + | 0.297206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | − | 27.7128i | 0.527791 | − | 0.914161i | −0.471684 | − | 0.881768i | \(-0.656354\pi\) |
0.999475 | − | 0.0323936i | \(-0.0103130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.866025 | + | 1.50000i | 0.0285365 | + | 0.0494267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.0000 | −0.394771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.500000 | + | 0.866025i | −0.0164222 | + | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.3923 | − | 18.0000i | 0.340960 | − | 0.590561i | −0.643651 | − | 0.765319i | \(-0.722581\pi\) |
0.984611 | + | 0.174758i | \(0.0559144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8564 | −0.454125 | ||||||||
\(932\) | 18.0000 | − | 31.1769i | 0.589610 | − | 1.02123i | ||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.50000 | + | 11.2583i | 0.212119 | + | 0.367402i | ||||
\(940\) | −12.0000 | + | 20.7846i | −0.391397 | + | 0.677919i | ||||
\(941\) | −10.3923 | −0.338779 | −0.169390 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169390 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | + | 36.0000i | −0.676840 | + | 1.17232i | ||||
\(944\) | 13.8564 | 0.450988 | ||||||||
\(945\) | 3.00000 | − | 5.19615i | 0.0975900 | − | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487 | + | 42.0000i | 0.787977 | + | 1.36482i | 0.927204 | + | 0.374556i | \(0.122205\pi\) |
−0.139227 | + | 0.990260i | \(0.544462\pi\) | |||||||
\(948\) | −22.0000 | −0.714527 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.46410 | + | 6.00000i | 0.112331 | + | 0.194563i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00000 | − | 5.19615i | 0.0971795 | − | 0.168320i | −0.813337 | − | 0.581793i | \(-0.802351\pi\) |
0.910516 | + | 0.413473i | \(0.135685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.1769 | − | 54.0000i | 1.00886 | − | 1.74740i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7846 | 0.671871 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.8564 | − | 24.0000i | −0.447214 | − | 0.774597i | ||||
\(961\) | −28.0000 | −0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −20.7846 | − | 36.0000i | −0.669427 | − | 1.15948i | ||||
\(965\) | 27.0000 | + | 46.7654i | 0.869161 | + | 1.50543i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.2487 | −0.779786 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | −1.00000 | − | 1.73205i | −0.0320750 | − | 0.0555556i | ||||
\(973\) | −4.33013 | − | 7.50000i | −0.138817 | − | 0.240439i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | 0.128037 | ||||||||
\(977\) | −13.8564 | − | 24.0000i | −0.443306 | − | 0.767828i | 0.554627 | − | 0.832099i | \(-0.312861\pi\) |
−0.997932 | + | 0.0642712i | \(0.979528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | − | 20.7846i | 0.383522 | − | 0.664279i | ||||
\(980\) | 27.7128 | 0.885253 | ||||||||
\(981\) | 7.79423 | − | 13.5000i | 0.248851 | − | 0.431022i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.3923 | 0.331463 | 0.165732 | − | 0.986171i | \(-0.447001\pi\) | ||||
0.165732 | + | 0.986171i | \(0.447001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | + | 41.5692i | 0.764704 | + | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | + | 13.8564i | 0.254128 | + | 0.440163i | 0.964658 | − | 0.263504i | \(-0.0848781\pi\) |
−0.710530 | + | 0.703667i | \(0.751545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.19615 | −0.164895 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.1244 | − | 21.0000i | 0.384368 | − | 0.665745i | ||||
\(996\) | −27.7128 | −0.878114 | ||||||||
\(997\) | −17.5000 | + | 30.3109i | −0.554231 | + | 0.959955i | 0.443732 | + | 0.896159i | \(0.353654\pi\) |
−0.997963 | + | 0.0637961i | \(0.979679\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))