Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,2,Mod(29,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.29");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.279476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.29 |
Dual form | 35.2.b.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | −0.957427 | − | 0.288675i | \(-0.906785\pi\) | ||
0.957427 | − | 0.288675i | \(-0.0932147\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 2.00000 | − | 4.00000i | 0.632456 | − | 1.26491i | ||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −1.00000 | + | 2.00000i | −0.258199 | + | 0.516398i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 7.00000i | 1.69775i | 0.528594 | + | 0.848875i | \(0.322719\pi\) | ||||
−0.528594 | + | 0.848875i | \(0.677281\pi\) | |||||||
\(18\) | 4.00000i | 0.942809i | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 4.00000 | + | 2.00000i | 0.894427 | + | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | −4.00000 | − | 2.00000i | −0.730297 | − | 0.365148i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | − | 8.00000i | − | 1.41421i | ||||||
\(33\) | 3.00000i | 0.522233i | ||||||||
\(34\) | −14.0000 | −2.40098 | ||||||||
\(35\) | −1.00000 | + | 2.00000i | −0.169031 | + | 0.338062i | ||||
\(36\) | −4.00000 | −0.666667 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | − | 2.00000i | − | 0.308607i | ||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | −4.00000 | − | 2.00000i | −0.596285 | − | 0.298142i | ||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −8.00000 | + | 6.00000i | −1.13137 | + | 0.848528i | ||||
\(51\) | 7.00000 | 0.980196 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 10.0000 | 1.36083 | ||||||||
\(55\) | 6.00000 | + | 3.00000i | 0.809040 | + | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000i | 1.31306i | ||||||||
\(59\) | −10.0000 | −1.30189 | −0.650945 | − | 0.759125i | \(-0.725627\pi\) | ||||
−0.650945 | + | 0.759125i | \(0.725627\pi\) | |||||||
\(60\) | 2.00000 | − | 4.00000i | 0.258199 | − | 0.516398i | ||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | − | 2.00000i | − | 0.251976i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −1.00000 | + | 2.00000i | −0.124035 | + | 0.248069i | ||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | − | 14.0000i | − | 1.69775i | ||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | −4.00000 | − | 2.00000i | −0.478091 | − | 0.239046i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 4.00000 | − | 3.00000i | 0.461880 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000i | 0.341882i | ||||||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | 8.00000 | + | 4.00000i | 0.894427 | + | 0.447214i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.00000i | 0.441726i | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | 7.00000 | − | 14.0000i | 0.759257 | − | 1.51851i | ||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | − | 5.00000i | − | 0.536056i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 4.00000 | − | 8.00000i | 0.421637 | − | 0.843274i | ||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 12.0000i | 1.25109i | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.00000 | −0.816497 | ||||||||
\(97\) | 7.00000i | 0.710742i | 0.934725 | + | 0.355371i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | − | 2.00000i | − | 0.202031i | ||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −6.00000 | − | 8.00000i | −0.600000 | − | 0.800000i | ||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 14.0000i | 1.38621i | ||||||||
\(103\) | 19.0000i | 1.87213i | 0.351833 | + | 0.936063i | \(0.385559\pi\) | ||||
−0.351833 | + | 0.936063i | \(0.614441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | + | 1.00000i | 0.195180 | + | 0.0975900i | ||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | − | 8.00000i | − | 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 10.0000i | 0.962250i | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | −6.00000 | + | 12.0000i | −0.572078 | + | 1.14416i | ||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | + | 12.0000i | −0.559503 | + | 1.11901i | ||||
\(116\) | −10.0000 | −0.928477 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | − | 20.0000i | − | 1.84115i | ||||||
\(119\) | 7.00000 | 0.641689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 16.0000i | − | 1.44857i | ||||||
\(123\) | − | 2.00000i | − | 0.180334i | ||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | −4.00000 | − | 2.00000i | −0.350823 | − | 0.175412i | ||||
\(131\) | 22.0000 | 1.92215 | 0.961074 | − | 0.276289i | \(-0.0891049\pi\) | ||||
0.961074 | + | 0.276289i | \(0.0891049\pi\) | |||||||
\(132\) | − | 6.00000i | − | 0.522233i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −5.00000 | + | 10.0000i | −0.430331 | + | 0.860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | − | 12.0000i | − | 1.02151i | ||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 2.00000 | − | 4.00000i | 0.169031 | − | 0.338062i | ||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | − | 16.0000i | − | 1.34269i | ||||||
\(143\) | 3.00000i | 0.250873i | ||||||||
\(144\) | −8.00000 | −0.666667 | ||||||||
\(145\) | −10.0000 | − | 5.00000i | −0.830455 | − | 0.415227i | ||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 6.00000 | + | 8.00000i | 0.489898 | + | 0.653197i | ||||
\(151\) | −13.0000 | −1.05792 | −0.528962 | − | 0.848645i | \(-0.677419\pi\) | ||||
−0.528962 | + | 0.848645i | \(0.677419\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0000i | 1.13183i | ||||||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | −4.00000 | − | 2.00000i | −0.321288 | − | 0.160644i | ||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | − | 18.0000i | − | 1.43656i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) | ||
0.695756 | − | 0.718278i | \(-0.255069\pi\) | |||||||
\(158\) | 10.0000i | 0.795557i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −8.00000 | + | 16.0000i | −0.632456 | + | 1.26491i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 2.00000i | 0.157135i | ||||||||
\(163\) | 14.0000i | 1.09656i | 0.836293 | + | 0.548282i | \(0.184718\pi\) | ||||
−0.836293 | + | 0.548282i | \(0.815282\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | 3.00000 | − | 6.00000i | 0.233550 | − | 0.467099i | ||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | − | 3.00000i | − | 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 28.0000 | + | 14.0000i | 2.14750 | + | 1.07375i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 9.00000i | 0.684257i | 0.939653 | + | 0.342129i | \(0.111148\pi\) | ||||
−0.939653 | + | 0.342129i | \(0.888852\pi\) | |||||||
\(174\) | 10.0000 | 0.758098 | ||||||||
\(175\) | 4.00000 | − | 3.00000i | 0.302372 | − | 0.226779i | ||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | 10.0000i | 0.751646i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0000 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(180\) | 8.00000 | + | 4.00000i | 0.596285 | + | 0.298142i | ||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | − | 2.00000i | − | 0.148250i | ||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 4.00000i | 0.147043 | − | 0.294086i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | − | 21.0000i | − | 1.53567i | ||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | − | 8.00000i | − | 0.577350i | ||||||
\(193\) | − | 16.0000i | − | 1.15171i | −0.817554 | − | 0.575853i | \(-0.804670\pi\) | ||
0.817554 | − | 0.575853i | \(-0.195330\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 2.00000 | + | 1.00000i | 0.143223 | + | 0.0716115i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | − | 12.0000i | − | 0.852803i | ||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | 24.0000i | 1.68863i | ||||||||
\(203\) | − | 5.00000i | − | 0.350931i | ||||||
\(204\) | −14.0000 | −0.980196 | ||||||||
\(205\) | −4.00000 | − | 2.00000i | −0.279372 | − | 0.139686i | ||||
\(206\) | −38.0000 | −2.64759 | ||||||||
\(207\) | − | 12.0000i | − | 0.834058i | ||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.00000 | + | 4.00000i | −0.138013 | + | 0.276026i | ||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 12.0000i | 0.824163i | ||||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | 16.0000 | 1.09374 | ||||||||
\(215\) | 4.00000 | − | 8.00000i | 0.272798 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | − | 10.0000i | − | 0.677285i | ||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | −12.0000 | − | 6.00000i | −0.809040 | − | 0.404520i | ||||
\(221\) | 7.00000 | 0.470871 | ||||||||
\(222\) | 4.00000i | 0.268462i | ||||||||
\(223\) | − | 21.0000i | − | 1.40626i | −0.711059 | − | 0.703132i | \(-0.751784\pi\) | ||
0.711059 | − | 0.703132i | \(-0.248216\pi\) | |||||||
\(224\) | −8.00000 | −0.534522 | ||||||||
\(225\) | 6.00000 | + | 8.00000i | 0.400000 | + | 0.533333i | ||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 17.0000i | 1.12833i | 0.825662 | + | 0.564165i | \(0.190802\pi\) | ||||
−0.825662 | + | 0.564165i | \(0.809198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −24.0000 | − | 12.0000i | −1.58251 | − | 0.791257i | ||||
\(231\) | 3.00000 | 0.197386 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0000i | − | 1.04819i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||
0.851658 | − | 0.524097i | \(-0.175597\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | −3.00000 | + | 6.00000i | −0.195698 | + | 0.391397i | ||||
\(236\) | 20.0000 | 1.30189 | ||||||||
\(237\) | − | 5.00000i | − | 0.324785i | ||||||
\(238\) | 14.0000i | 0.907485i | ||||||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 4.00000 | − | 8.00000i | 0.258199 | − | 0.516398i | ||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | − | 4.00000i | − | 0.257130i | ||||||
\(243\) | − | 16.0000i | − | 1.02640i | ||||||
\(244\) | 16.0000 | 1.02430 | ||||||||
\(245\) | 2.00000 | + | 1.00000i | 0.127775 | + | 0.0638877i | ||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 22.0000 | − | 4.00000i | 1.39140 | − | 0.252982i | ||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | −14.0000 | − | 7.00000i | −0.876714 | − | 0.438357i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 22.0000i | 1.37232i | 0.727450 | + | 0.686161i | \(0.240706\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 2.00000 | − | 4.00000i | 0.124035 | − | 0.248069i | ||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 44.0000i | 2.71833i | ||||||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 12.0000i | −0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | −20.0000 | − | 10.0000i | −1.21716 | − | 0.608581i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | − | 28.0000i | − | 1.69775i | ||||||
\(273\) | 1.00000i | 0.0605228i | ||||||||
\(274\) | −24.0000 | −1.44989 | ||||||||
\(275\) | −9.00000 | − | 12.0000i | −0.542720 | − | 0.723627i | ||||
\(276\) | 12.0000 | 0.722315 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 20.0000i | 1.19952i | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | − | 6.00000i | − | 0.357295i | ||||||
\(283\) | − | 11.0000i | − | 0.653882i | −0.945045 | − | 0.326941i | \(-0.893982\pi\) | ||
0.945045 | − | 0.326941i | \(-0.106018\pi\) | |||||||
\(284\) | 16.0000 | 0.949425 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | − | 2.00000i | − | 0.118056i | ||||||
\(288\) | − | 16.0000i | − | 0.942809i | ||||||
\(289\) | −32.0000 | −1.88235 | ||||||||
\(290\) | 10.0000 | − | 20.0000i | 0.587220 | − | 1.17444i | ||||
\(291\) | 7.00000 | 0.410347 | ||||||||
\(292\) | 12.0000i | 0.702247i | ||||||||
\(293\) | 9.00000i | 0.525786i | 0.964825 | + | 0.262893i | \(0.0846766\pi\) | ||||
−0.964825 | + | 0.262893i | \(0.915323\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 20.0000 | + | 10.0000i | 1.16445 | + | 0.582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0000i | 0.870388i | ||||||||
\(298\) | − | 20.0000i | − | 1.15857i | ||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | −8.00000 | + | 6.00000i | −0.461880 | + | 0.346410i | ||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | − | 26.0000i | − | 1.49613i | ||||||
\(303\) | − | 12.0000i | − | 0.689382i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.0000 | + | 8.00000i | 0.916157 | + | 0.458079i | ||||
\(306\) | −28.0000 | −1.60065 | ||||||||
\(307\) | 7.00000i | 0.399511i | 0.979846 | + | 0.199756i | \(0.0640148\pi\) | ||||
−0.979846 | + | 0.199756i | \(0.935985\pi\) | |||||||
\(308\) | − | 6.00000i | − | 0.341882i | ||||||
\(309\) | 19.0000 | 1.08087 | ||||||||
\(310\) | 4.00000 | − | 8.00000i | 0.227185 | − | 0.454369i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.0000i | − | 1.18699i | −0.804838 | − | 0.593495i | \(-0.797748\pi\) | ||
0.804838 | − | 0.593495i | \(-0.202252\pi\) | |||||||
\(314\) | 36.0000 | 2.03160 | ||||||||
\(315\) | −2.00000 | + | 4.00000i | −0.112687 | + | 0.225374i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 12.0000i | 0.673987i | 0.941507 | + | 0.336994i | \(0.109410\pi\) | ||||
−0.941507 | + | 0.336994i | \(0.890590\pi\) | |||||||
\(318\) | − | 12.0000i | − | 0.672927i | ||||||
\(319\) | −15.0000 | −0.839839 | ||||||||
\(320\) | −16.0000 | − | 8.00000i | −0.894427 | − | 0.447214i | ||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | − | 12.0000i | − | 0.668734i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 4.00000 | − | 3.00000i | 0.221880 | − | 0.166410i | ||||
\(326\) | −28.0000 | −1.55078 | ||||||||
\(327\) | 5.00000i | 0.276501i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | −0.165395 | ||||||||
\(330\) | 12.0000 | + | 6.00000i | 0.660578 | + | 0.330289i | ||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | − | 8.00000i | − | 0.439057i | ||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | 2.00000 | − | 4.00000i | 0.109272 | − | 0.218543i | ||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | 24.0000i | 1.30543i | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | −14.0000 | + | 28.0000i | −0.759257 | + | 1.51851i | ||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 6.00000i | 0.646058 | + | 0.323029i | ||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | − | 18.0000i | − | 0.966291i | −0.875540 | − | 0.483145i | \(-0.839494\pi\) | ||
0.875540 | − | 0.483145i | \(-0.160506\pi\) | |||||||
\(348\) | 10.0000i | 0.536056i | ||||||||
\(349\) | 20.0000 | 1.07058 | 0.535288 | − | 0.844670i | \(-0.320203\pi\) | ||||
0.535288 | + | 0.844670i | \(0.320203\pi\) | |||||||
\(350\) | 6.00000 | + | 8.00000i | 0.320713 | + | 0.427618i | ||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 24.0000i | 1.27920i | ||||||||
\(353\) | − | 11.0000i | − | 0.585471i | −0.956193 | − | 0.292735i | \(-0.905434\pi\) | ||
0.956193 | − | 0.292735i | \(-0.0945655\pi\) | |||||||
\(354\) | −20.0000 | −1.06299 | ||||||||
\(355\) | 16.0000 | + | 8.00000i | 0.849192 | + | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 7.00000i | − | 0.370479i | ||||||
\(358\) | 40.0000i | 2.11407i | ||||||||
\(359\) | 20.0000 | 1.05556 | 0.527780 | − | 0.849381i | \(-0.323025\pi\) | ||||
0.527780 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − | 36.0000i | − | 1.89212i | ||||||
\(363\) | 2.00000i | 0.104973i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −6.00000 | + | 12.0000i | −0.314054 | + | 0.628109i | ||||
\(366\) | −16.0000 | −0.836333 | ||||||||
\(367\) | − | 3.00000i | − | 0.156599i | −0.996930 | − | 0.0782994i | \(-0.975051\pi\) | ||
0.996930 | − | 0.0782994i | \(-0.0249490\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 8.00000 | + | 4.00000i | 0.415900 | + | 0.207950i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | 24.0000i | 1.24267i | 0.783544 | + | 0.621336i | \(0.213410\pi\) | ||||
−0.783544 | + | 0.621336i | \(0.786590\pi\) | |||||||
\(374\) | 42.0000 | 2.17177 | ||||||||
\(375\) | −11.0000 | + | 2.00000i | −0.568038 | + | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.00000i | − | 0.257513i | ||||||
\(378\) | − | 10.0000i | − | 0.514344i | ||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | − | 16.0000i | − | 0.817562i | −0.912633 | − | 0.408781i | \(-0.865954\pi\) | ||
0.912633 | − | 0.408781i | \(-0.134046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | − | 6.00000i | 0.152894 | − | 0.305788i | ||||
\(386\) | 32.0000 | 1.62876 | ||||||||
\(387\) | 8.00000i | 0.406663i | ||||||||
\(388\) | − | 14.0000i | − | 0.710742i | ||||||
\(389\) | −5.00000 | −0.253510 | −0.126755 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126755 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(390\) | −2.00000 | + | 4.00000i | −0.101274 | + | 0.202548i | ||||
\(391\) | 42.0000 | 2.12403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 22.0000i | − | 1.10975i | ||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | −10.0000 | − | 5.00000i | −0.503155 | − | 0.251577i | ||||
\(396\) | 12.0000 | 0.603023 | ||||||||
\(397\) | 7.00000i | 0.351320i | 0.984451 | + | 0.175660i | \(0.0562059\pi\) | ||||
−0.984451 | + | 0.175660i | \(0.943794\pi\) | |||||||
\(398\) | 20.0000i | 1.00251i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | −3.00000 | −0.149813 | −0.0749064 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749064 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(402\) | 4.00000i | 0.199502i | ||||||||
\(403\) | − | 2.00000i | − | 0.0996271i | ||||||
\(404\) | −24.0000 | −1.19404 | ||||||||
\(405\) | −2.00000 | − | 1.00000i | −0.0993808 | − | 0.0496904i | ||||
\(406\) | 10.0000 | 0.496292 | ||||||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0000 | −0.988936 | −0.494468 | − | 0.869196i | \(-0.664637\pi\) | ||||
−0.494468 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(410\) | 4.00000 | − | 8.00000i | 0.197546 | − | 0.395092i | ||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | − | 38.0000i | − | 1.87213i | ||||||
\(413\) | 10.0000i | 0.492068i | ||||||||
\(414\) | 24.0000 | 1.17954 | ||||||||
\(415\) | 4.00000 | − | 8.00000i | 0.196352 | − | 0.392705i | ||||
\(416\) | −8.00000 | −0.392232 | ||||||||
\(417\) | − | 10.0000i | − | 0.489702i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | −4.00000 | − | 2.00000i | −0.195180 | − | 0.0975900i | ||||
\(421\) | −3.00000 | −0.146211 | −0.0731055 | − | 0.997324i | \(-0.523291\pi\) | ||||
−0.0731055 | + | 0.997324i | \(0.523291\pi\) | |||||||
\(422\) | − | 26.0000i | − | 1.26566i | ||||||
\(423\) | − | 6.00000i | − | 0.291730i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.0000 | + | 21.0000i | −1.35820 | + | 1.01865i | ||||
\(426\) | −16.0000 | −0.775203 | ||||||||
\(427\) | 8.00000i | 0.387147i | ||||||||
\(428\) | 16.0000i | 0.773389i | ||||||||
\(429\) | 3.00000 | 0.144841 | ||||||||
\(430\) | 16.0000 | + | 8.00000i | 0.771589 | + | 0.385794i | ||||
\(431\) | −23.0000 | −1.10787 | −0.553936 | − | 0.832560i | \(-0.686875\pi\) | ||||
−0.553936 | + | 0.832560i | \(0.686875\pi\) | |||||||
\(432\) | 20.0000i | 0.962250i | ||||||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | 4.00000 | 0.192006 | ||||||||
\(435\) | −5.00000 | + | 10.0000i | −0.239732 | + | 0.479463i | ||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 12.0000i | − | 0.573382i | ||||||
\(439\) | −30.0000 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 14.0000i | 0.665912i | ||||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 42.0000 | 1.98876 | ||||||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | 5.00000 | 0.235965 | 0.117982 | − | 0.993016i | \(-0.462357\pi\) | ||||
0.117982 | + | 0.993016i | \(0.462357\pi\) | |||||||
\(450\) | −16.0000 | + | 12.0000i | −0.754247 | + | 0.565685i | ||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | 13.0000i | 0.610793i | ||||||||
\(454\) | −34.0000 | −1.59570 | ||||||||
\(455\) | 2.00000 | + | 1.00000i | 0.0937614 | + | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 38.0000i | − | 1.77757i | −0.458329 | − | 0.888783i | \(-0.651552\pi\) | ||
0.458329 | − | 0.888783i | \(-0.348448\pi\) | |||||||
\(458\) | 20.0000i | 0.934539i | ||||||||
\(459\) | 35.0000 | 1.63366 | ||||||||
\(460\) | 12.0000 | − | 24.0000i | 0.559503 | − | 1.11901i | ||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 6.00000i | 0.279145i | ||||||||
\(463\) | − | 36.0000i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(464\) | −20.0000 | −0.928477 | ||||||||
\(465\) | −2.00000 | + | 4.00000i | −0.0927478 | + | 0.185496i | ||||
\(466\) | 32.0000 | 1.48237 | ||||||||
\(467\) | 27.0000i | 1.24941i | 0.780860 | + | 0.624705i | \(0.214781\pi\) | ||||
−0.780860 | + | 0.624705i | \(0.785219\pi\) | |||||||
\(468\) | 4.00000i | 0.184900i | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | −12.0000 | − | 6.00000i | −0.553519 | − | 0.276759i | ||||
\(471\) | −18.0000 | −0.829396 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.0000i | − | 0.551761i | ||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.0000 | −0.641689 | ||||||||
\(477\) | − | 12.0000i | − | 0.549442i | ||||||
\(478\) | − | 30.0000i | − | 1.37217i | ||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 16.0000 | + | 8.00000i | 0.730297 | + | 0.365148i | ||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 44.0000i | 2.00415i | ||||||||
\(483\) | 6.00000i | 0.273009i | ||||||||
\(484\) | 4.00000 | 0.181818 | ||||||||
\(485\) | 7.00000 | − | 14.0000i | 0.317854 | − | 0.635707i | ||||
\(486\) | 32.0000 | 1.45155 | ||||||||
\(487\) | 42.0000i | 1.90320i | 0.307337 | + | 0.951601i | \(0.400562\pi\) | ||||
−0.307337 | + | 0.951601i | \(0.599438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0000 | 0.633102 | ||||||||
\(490\) | −2.00000 | + | 4.00000i | −0.0903508 | + | 0.180702i | ||||
\(491\) | 7.00000 | 0.315906 | 0.157953 | − | 0.987447i | \(-0.449511\pi\) | ||||
0.157953 | + | 0.987447i | \(0.449511\pi\) | |||||||
\(492\) | 4.00000i | 0.180334i | ||||||||
\(493\) | 35.0000i | 1.57632i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | + | 6.00000i | 0.539360 | + | 0.269680i | ||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 8.00000i | 0.358489i | ||||||||
\(499\) | 35.0000 | 1.56682 | 0.783408 | − | 0.621508i | \(-0.213480\pi\) | ||||
0.783408 | + | 0.621508i | \(0.213480\pi\) | |||||||
\(500\) | 4.00000 | + | 22.0000i | 0.178885 | + | 0.983870i | ||||
\(501\) | −3.00000 | −0.134030 | ||||||||
\(502\) | − | 36.0000i | − | 1.60676i | ||||||
\(503\) | 9.00000i | 0.401290i | 0.979664 | + | 0.200645i | \(0.0643038\pi\) | ||||
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | − | 12.0000i | −1.06799 | − | 0.533993i | ||||
\(506\) | −36.0000 | −1.60040 | ||||||||
\(507\) | − | 12.0000i | − | 0.532939i | ||||||
\(508\) | − | 4.00000i | − | 0.177471i | ||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 14.0000 | − | 28.0000i | 0.619930 | − | 1.23986i | ||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −44.0000 | −1.94076 | ||||||||
\(515\) | 19.0000 | − | 38.0000i | 0.837240 | − | 1.67448i | ||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | 9.00000i | 0.395820i | ||||||||
\(518\) | 4.00000i | 0.175750i | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | 20.0000i | 0.875376i | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | −44.0000 | −1.92215 | ||||||||
\(525\) | −3.00000 | − | 4.00000i | −0.130931 | − | 0.174574i | ||||
\(526\) | −48.0000 | −2.09290 | ||||||||
\(527\) | 14.0000i | 0.609850i | ||||||||
\(528\) | − | 12.0000i | − | 0.522233i | ||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −24.0000 | − | 12.0000i | −1.04249 | − | 0.521247i | ||||
\(531\) | −20.0000 | −0.867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.00000i | − | 0.0866296i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | + | 16.0000i | −0.345870 | + | 0.691740i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 20.0000i | − | 0.863064i | ||||||
\(538\) | − | 20.0000i | − | 0.862261i | ||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 10.0000 | − | 20.0000i | 0.430331 | − | 0.860663i | ||||
\(541\) | 27.0000 | 1.16082 | 0.580410 | − | 0.814324i | \(-0.302892\pi\) | ||||
0.580410 | + | 0.814324i | \(0.302892\pi\) | |||||||
\(542\) | − | 16.0000i | − | 0.687259i | ||||||
\(543\) | 18.0000i | 0.772454i | ||||||||
\(544\) | 56.0000 | 2.40098 | ||||||||
\(545\) | 10.0000 | + | 5.00000i | 0.428353 | + | 0.214176i | ||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | 32.0000i | 1.36822i | 0.729378 | + | 0.684111i | \(0.239809\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760191\pi\) | |||||||
\(548\) | − | 24.0000i | − | 1.02523i | ||||||
\(549\) | −16.0000 | −0.682863 | ||||||||
\(550\) | 24.0000 | − | 18.0000i | 1.02336 | − | 0.767523i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.00000i | − | 0.212622i | ||||||
\(554\) | −4.00000 | −0.169944 | ||||||||
\(555\) | −4.00000 | − | 2.00000i | −0.169791 | − | 0.0848953i | ||||
\(556\) | −20.0000 | −0.848189 | ||||||||
\(557\) | − | 28.0000i | − | 1.18640i | −0.805056 | − | 0.593199i | \(-0.797865\pi\) | ||
0.805056 | − | 0.593199i | \(-0.202135\pi\) | |||||||
\(558\) | 8.00000i | 0.338667i | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 4.00000 | − | 8.00000i | 0.169031 | − | 0.338062i | ||||
\(561\) | −21.0000 | −0.886621 | ||||||||
\(562\) | 14.0000i | 0.590554i | ||||||||
\(563\) | 24.0000i | 1.01148i | 0.862686 | + | 0.505740i | \(0.168780\pi\) | ||||
−0.862686 | + | 0.505740i | \(0.831220\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | −6.00000 | + | 12.0000i | −0.252422 | + | 0.504844i | ||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | − | 6.00000i | − | 0.250873i | ||||||
\(573\) | 3.00000i | 0.125327i | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | 16.0000 | 0.666667 | ||||||||
\(577\) | − | 43.0000i | − | 1.79011i | −0.445952 | − | 0.895057i | \(-0.647135\pi\) | ||
0.445952 | − | 0.895057i | \(-0.352865\pi\) | |||||||
\(578\) | − | 64.0000i | − | 2.66205i | ||||||
\(579\) | −16.0000 | −0.664937 | ||||||||
\(580\) | 20.0000 | + | 10.0000i | 0.830455 | + | 0.415227i | ||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | 14.0000i | 0.580319i | ||||||||
\(583\) | 18.0000i | 0.745484i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | + | 4.00000i | −0.0826898 | + | 0.165380i | ||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | − | 2.00000i | − | 0.0824786i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −20.0000 | + | 40.0000i | −0.823387 | + | 1.64677i | ||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | − | 8.00000i | − | 0.328798i | ||||||
\(593\) | − | 41.0000i | − | 1.68367i | −0.539736 | − | 0.841834i | \(-0.681476\pi\) | ||
0.539736 | − | 0.841834i | \(-0.318524\pi\) | |||||||
\(594\) | −30.0000 | −1.23091 | ||||||||
\(595\) | −14.0000 | − | 7.00000i | −0.573944 | − | 0.286972i | ||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | − | 10.0000i | − | 0.409273i | ||||||
\(598\) | − | 12.0000i | − | 0.490716i | ||||||
\(599\) | −25.0000 | −1.02147 | −0.510736 | − | 0.859738i | \(-0.670627\pi\) | ||||
−0.510736 | + | 0.859738i | \(0.670627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 26.0000 | 1.05792 | ||||||||
\(605\) | 4.00000 | + | 2.00000i | 0.162623 | + | 0.0813116i | ||||
\(606\) | 24.0000 | 0.974933 | ||||||||
\(607\) | 27.0000i | 1.09590i | 0.836512 | + | 0.547948i | \(0.184591\pi\) | ||||
−0.836512 | + | 0.547948i | \(0.815409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | −0.202610 | ||||||||
\(610\) | −16.0000 | + | 32.0000i | −0.647821 | + | 1.29564i | ||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | − | 28.0000i | − | 1.13183i | ||||||
\(613\) | 44.0000i | 1.77714i | 0.458738 | + | 0.888572i | \(0.348302\pi\) | ||||
−0.458738 | + | 0.888572i | \(0.651698\pi\) | |||||||
\(614\) | −14.0000 | −0.564994 | ||||||||
\(615\) | −2.00000 | + | 4.00000i | −0.0806478 | + | 0.161296i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000i | 0.885687i | 0.896599 | + | 0.442843i | \(0.146030\pi\) | ||||
−0.896599 | + | 0.442843i | \(0.853970\pi\) | |||||||
\(618\) | 38.0000i | 1.52858i | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 8.00000 | + | 4.00000i | 0.321288 | + | 0.160644i | ||||
\(621\) | −30.0000 | −1.20386 | ||||||||
\(622\) | 24.0000i | 0.962312i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 42.0000 | 1.67866 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.0000i | 1.43656i | ||||||||
\(629\) | −14.0000 | −0.558217 | ||||||||
\(630\) | −8.00000 | − | 4.00000i | −0.318728 | − | 0.159364i | ||||
\(631\) | 37.0000 | 1.47295 | 0.736473 | − | 0.676467i | \(-0.236490\pi\) | ||||
0.736473 | + | 0.676467i | \(0.236490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0000i | 0.516704i | ||||||||
\(634\) | −24.0000 | −0.953162 | ||||||||
\(635\) | 2.00000 | − | 4.00000i | 0.0793676 | − | 0.158735i | ||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | − | 30.0000i | − | 1.18771i | ||||||
\(639\) | −16.0000 | −0.632950 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.0000 | 0.868948 | 0.434474 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434474 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(642\) | − | 16.0000i | − | 0.631470i | ||||||
\(643\) | − | 1.00000i | − | 0.0394362i | −0.999806 | − | 0.0197181i | \(-0.993723\pi\) | ||
0.999806 | − | 0.0197181i | \(-0.00627687\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | −8.00000 | − | 4.00000i | −0.315000 | − | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8.00000i | − | 0.314512i | −0.987558 | − | 0.157256i | \(-0.949735\pi\) | ||
0.987558 | − | 0.157256i | \(-0.0502649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.0000 | 1.17760 | ||||||||
\(650\) | 6.00000 | + | 8.00000i | 0.235339 | + | 0.313786i | ||||
\(651\) | −2.00000 | −0.0783862 | ||||||||
\(652\) | − | 28.0000i | − | 1.09656i | ||||||
\(653\) | 4.00000i | 0.156532i | 0.996933 | + | 0.0782660i | \(0.0249384\pi\) | ||||
−0.996933 | + | 0.0782660i | \(0.975062\pi\) | |||||||
\(654\) | −10.0000 | −0.391031 | ||||||||
\(655\) | −44.0000 | − | 22.0000i | −1.71922 | − | 0.859611i | ||||
\(656\) | −8.00000 | −0.312348 | ||||||||
\(657\) | − | 12.0000i | − | 0.468165i | ||||||
\(658\) | − | 6.00000i | − | 0.233904i | ||||||
\(659\) | 15.0000 | 0.584317 | 0.292159 | − | 0.956370i | \(-0.405627\pi\) | ||||
0.292159 | + | 0.956370i | \(0.405627\pi\) | |||||||
\(660\) | −6.00000 | + | 12.0000i | −0.233550 | + | 0.467099i | ||||
\(661\) | 12.0000 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 24.0000i | 0.932786i | ||||||||
\(663\) | − | 7.00000i | − | 0.271857i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | − | 30.0000i | − | 1.16160i | ||||||
\(668\) | 6.00000i | 0.232147i | ||||||||
\(669\) | −21.0000 | −0.811907 | ||||||||
\(670\) | 8.00000 | + | 4.00000i | 0.309067 | + | 0.154533i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 8.00000i | 0.308607i | ||||||||
\(673\) | 24.0000i | 0.925132i | 0.886585 | + | 0.462566i | \(0.153071\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | 36.0000 | 1.38667 | ||||||||
\(675\) | 20.0000 | − | 15.0000i | 0.769800 | − | 0.577350i | ||||
\(676\) | −24.0000 | −0.923077 | ||||||||
\(677\) | − | 43.0000i | − | 1.65262i | −0.563212 | − | 0.826312i | \(-0.690435\pi\) | ||
0.563212 | − | 0.826312i | \(-0.309565\pi\) | |||||||
\(678\) | − | 12.0000i | − | 0.460857i | ||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.0000 | 0.651441 | ||||||||
\(682\) | − | 12.0000i | − | 0.459504i | ||||||
\(683\) | − | 16.0000i | − | 0.612223i | −0.951996 | − | 0.306111i | \(-0.900972\pi\) | ||
0.951996 | − | 0.306111i | \(-0.0990280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | − | 24.0000i | 0.458496 | − | 0.916993i | ||||
\(686\) | −2.00000 | −0.0763604 | ||||||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | − | 16.0000i | − | 0.609994i | ||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | −12.0000 | + | 24.0000i | −0.456832 | + | 0.913664i | ||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 6.00000i | 0.227921i | ||||||||
\(694\) | 36.0000 | 1.36654 | ||||||||
\(695\) | −20.0000 | − | 10.0000i | −0.758643 | − | 0.379322i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0000i | 0.530288i | ||||||||
\(698\) | 40.0000i | 1.51402i | ||||||||
\(699\) | −16.0000 | −0.605176 | ||||||||
\(700\) | −8.00000 | + | 6.00000i | −0.302372 | + | 0.226779i | ||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | − | 10.0000i | − | 0.377426i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −24.0000 | −0.904534 | ||||||||
\(705\) | 6.00000 | + | 3.00000i | 0.225973 | + | 0.112987i | ||||
\(706\) | 22.0000 | 0.827981 | ||||||||
\(707\) | − | 12.0000i | − | 0.451306i | ||||||
\(708\) | − | 20.0000i | − | 0.751646i | ||||||
\(709\) | −35.0000 | −1.31445 | −0.657226 | − | 0.753693i | \(-0.728270\pi\) | ||||
−0.657226 | + | 0.753693i | \(0.728270\pi\) | |||||||
\(710\) | −16.0000 | + | 32.0000i | −0.600469 | + | 1.20094i | ||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 14.0000 | 0.523937 | ||||||||
\(715\) | 3.00000 | − | 6.00000i | 0.112194 | − | 0.224387i | ||||
\(716\) | −40.0000 | −1.49487 | ||||||||
\(717\) | 15.0000i | 0.560185i | ||||||||
\(718\) | 40.0000i | 1.49279i | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 16.0000 | + | 8.00000i | 0.596285 | + | 0.298142i | ||||
\(721\) | 19.0000 | 0.707597 | ||||||||
\(722\) | − | 38.0000i | − | 1.41421i | ||||||
\(723\) | − | 22.0000i | − | 0.818189i | ||||||
\(724\) | 36.0000 | 1.33793 | ||||||||
\(725\) | 15.0000 | + | 20.0000i | 0.557086 | + | 0.742781i | ||||
\(726\) | −4.00000 | −0.148454 | ||||||||
\(727\) | − | 28.0000i | − | 1.03846i | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||
0.854634 | − | 0.519231i | \(-0.173782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −24.0000 | − | 12.0000i | −0.888280 | − | 0.444140i | ||||
\(731\) | −28.0000 | −1.03562 | ||||||||
\(732\) | − | 16.0000i | − | 0.591377i | ||||||
\(733\) | − | 1.00000i | − | 0.0369358i | −0.999829 | − | 0.0184679i | \(-0.994121\pi\) | ||
0.999829 | − | 0.0184679i | \(-0.00587886\pi\) | |||||||
\(734\) | 6.00000 | 0.221464 | ||||||||
\(735\) | 1.00000 | − | 2.00000i | 0.0368856 | − | 0.0737711i | ||||
\(736\) | −48.0000 | −1.76930 | ||||||||
\(737\) | − | 6.00000i | − | 0.221013i | ||||||
\(738\) | 8.00000i | 0.294484i | ||||||||
\(739\) | 35.0000 | 1.28750 | 0.643748 | − | 0.765238i | \(-0.277379\pi\) | ||||
0.643748 | + | 0.765238i | \(0.277379\pi\) | |||||||
\(740\) | −4.00000 | + | 8.00000i | −0.147043 | + | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 12.0000i | − | 0.440534i | ||||||
\(743\) | 14.0000i | 0.513610i | 0.966463 | + | 0.256805i | \(0.0826698\pi\) | ||||
−0.966463 | + | 0.256805i | \(0.917330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0000 | + | 10.0000i | 0.732743 | + | 0.366372i | ||||
\(746\) | −48.0000 | −1.75740 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | 42.0000i | 1.53567i | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | −4.00000 | − | 22.0000i | −0.146059 | − | 0.803326i | ||||
\(751\) | −33.0000 | −1.20419 | −0.602094 | − | 0.798426i | \(-0.705667\pi\) | ||||
−0.602094 | + | 0.798426i | \(0.705667\pi\) | |||||||
\(752\) | 12.0000i | 0.437595i | ||||||||
\(753\) | 18.0000i | 0.655956i | ||||||||
\(754\) | 10.0000 | 0.364179 | ||||||||
\(755\) | 26.0000 | + | 13.0000i | 0.946237 | + | 0.473118i | ||||
\(756\) | 10.0000 | 0.363696 | ||||||||
\(757\) | 32.0000i | 1.16306i | 0.813525 | + | 0.581530i | \(0.197546\pi\) | ||||
−0.813525 | + | 0.581530i | \(0.802454\pi\) | |||||||
\(758\) | − | 40.0000i | − | 1.45287i | ||||||
\(759\) | 18.0000 | 0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.00000 | 0.0724999 | 0.0362500 | − | 0.999343i | \(-0.488459\pi\) | ||||
0.0362500 | + | 0.999343i | \(0.488459\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | 5.00000i | 0.181012i | ||||||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 14.0000 | − | 28.0000i | 0.506171 | − | 1.01234i | ||||
\(766\) | 32.0000 | 1.15621 | ||||||||
\(767\) | 10.0000i | 0.361079i | ||||||||
\(768\) | − | 16.0000i | − | 0.577350i | ||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 12.0000 | + | 6.00000i | 0.432450 | + | 0.216225i | ||||
\(771\) | 22.0000 | 0.792311 | ||||||||
\(772\) | 32.0000i | 1.15171i | ||||||||
\(773\) | − | 21.0000i | − | 0.755318i | −0.925945 | − | 0.377659i | \(-0.876729\pi\) | ||
0.925945 | − | 0.377659i | \(-0.123271\pi\) | |||||||
\(774\) | −16.0000 | −0.575108 | ||||||||
\(775\) | 6.00000 | + | 8.00000i | 0.215526 | + | 0.287368i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.00000i | − | 0.0717496i | ||||||
\(778\) | − | 10.0000i | − | 0.358517i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −4.00000 | − | 2.00000i | −0.143223 | − | 0.0716115i | ||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 84.0000i | 3.00383i | ||||||||
\(783\) | − | 25.0000i | − | 0.893427i | ||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −18.0000 | + | 36.0000i | −0.642448 | + | 1.28490i | ||||
\(786\) | 44.0000 | 1.56943 | ||||||||
\(787\) | 17.0000i | 0.605985i | 0.952993 | + | 0.302992i | \(0.0979856\pi\) | ||||
−0.952993 | + | 0.302992i | \(0.902014\pi\) | |||||||
\(788\) | − | 4.00000i | − | 0.142494i | ||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | 10.0000 | − | 20.0000i | 0.355784 | − | 0.711568i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000i | 0.284088i | ||||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 12.0000 | + | 6.00000i | 0.425596 | + | 0.212798i | ||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | − | 13.0000i | − | 0.460484i | −0.973133 | − | 0.230242i | \(-0.926048\pi\) | ||
0.973133 | − | 0.230242i | \(-0.0739517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000 | 0.742927 | ||||||||
\(800\) | 32.0000 | − | 24.0000i | 1.13137 | − | 0.848528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 6.00000i | − | 0.211867i | ||||||
\(803\) | 18.0000i | 0.635206i | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 12.0000 | + | 6.00000i | 0.422944 | + | 0.211472i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 10.0000i | 0.352017i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 2.00000 | − | 4.00000i | 0.0702728 | − | 0.140546i | ||||
\(811\) | −38.0000 | −1.33436 | −0.667180 | − | 0.744896i | \(-0.732499\pi\) | ||||
−0.667180 | + | 0.744896i | \(0.732499\pi\) | |||||||
\(812\) | 10.0000i | 0.350931i | ||||||||
\(813\) | 8.00000i | 0.280572i | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 14.0000 | − | 28.0000i | 0.490399 | − | 0.980797i | ||||
\(816\) | −28.0000 | −0.980196 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 40.0000i | − | 1.39857i | ||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 8.00000 | + | 4.00000i | 0.279372 | + | 0.139686i | ||||
\(821\) | −23.0000 | −0.802706 | −0.401353 | − | 0.915924i | \(-0.631460\pi\) | ||||
−0.401353 | + | 0.915924i | \(0.631460\pi\) | |||||||
\(822\) | 24.0000i | 0.837096i | ||||||||
\(823\) | − | 26.0000i | − | 0.906303i | −0.891434 | − | 0.453152i | \(-0.850300\pi\) | ||
0.891434 | − | 0.453152i | \(-0.149700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 9.00000i | −0.417786 | + | 0.313340i | ||||
\(826\) | −20.0000 | −0.695889 | ||||||||
\(827\) | − | 18.0000i | − | 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | 24.0000i | 0.834058i | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 16.0000 | + | 8.00000i | 0.555368 | + | 0.277684i | ||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | − | 8.00000i | − | 0.277350i | ||||||
\(833\) | − | 7.00000i | − | 0.242536i | ||||||
\(834\) | 20.0000 | 0.692543 | ||||||||
\(835\) | −3.00000 | + | 6.00000i | −0.103819 | + | 0.207639i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.0000i | − | 0.345651i | ||||||
\(838\) | − | 60.0000i | − | 2.07267i | ||||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | − | 6.00000i | − | 0.206774i | ||||||
\(843\) | − | 7.00000i | − | 0.241093i | ||||||
\(844\) | 26.0000 | 0.894957 | ||||||||
\(845\) | −24.0000 | − | 12.0000i | −0.825625 | − | 0.412813i | ||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | 24.0000i | 0.824163i | ||||||||
\(849\) | −11.0000 | −0.377519 | ||||||||
\(850\) | −42.0000 | − | 56.0000i | −1.44059 | − | 1.92078i | ||||
\(851\) | 12.0000 | 0.411355 | ||||||||
\(852\) | − | 16.0000i | − | 0.548151i | ||||||
\(853\) | 54.0000i | 1.84892i | 0.381273 | + | 0.924462i | \(0.375486\pi\) | ||||
−0.381273 | + | 0.924462i | \(0.624514\pi\) | |||||||
\(854\) | −16.0000 | −0.547509 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | 6.00000i | 0.204837i | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | −8.00000 | + | 16.0000i | −0.272798 | + | 0.545595i | ||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | − | 46.0000i | − | 1.56677i | ||||||
\(863\) | 54.0000i | 1.83818i | 0.394046 | + | 0.919091i | \(0.371075\pi\) | ||||
−0.394046 | + | 0.919091i | \(0.628925\pi\) | |||||||
\(864\) | −40.0000 | −1.36083 | ||||||||
\(865\) | 9.00000 | − | 18.0000i | 0.306009 | − | 0.612018i | ||||
\(866\) | 52.0000 | 1.76703 | ||||||||
\(867\) | 32.0000i | 1.08678i | ||||||||
\(868\) | 4.00000i | 0.135769i | ||||||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | −20.0000 | − | 10.0000i | −0.678064 | − | 0.339032i | ||||
\(871\) | 2.00000 | 0.0677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.0000i | 0.473828i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0000 | + | 2.00000i | −0.371868 | + | 0.0676123i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 32.0000i | 1.08056i | 0.841484 | + | 0.540282i | \(0.181682\pi\) | ||||
−0.841484 | + | 0.540282i | \(0.818318\pi\) | |||||||
\(878\) | − | 60.0000i | − | 2.02490i | ||||||
\(879\) | 9.00000 | 0.303562 | ||||||||
\(880\) | −24.0000 | − | 12.0000i | −0.809040 | − | 0.404520i | ||||
\(881\) | 32.0000 | 1.07811 | 0.539054 | − | 0.842271i | \(-0.318782\pi\) | ||||
0.539054 | + | 0.842271i | \(0.318782\pi\) | |||||||
\(882\) | − | 4.00000i | − | 0.134687i | ||||||
\(883\) | − | 36.0000i | − | 1.21150i | −0.795656 | − | 0.605748i | \(-0.792874\pi\) | ||
0.795656 | − | 0.605748i | \(-0.207126\pi\) | |||||||
\(884\) | −14.0000 | −0.470871 | ||||||||
\(885\) | 10.0000 | − | 20.0000i | 0.336146 | − | 0.672293i | ||||
\(886\) | −8.00000 | −0.268765 | ||||||||
\(887\) | − | 28.0000i | − | 0.940148i | −0.882627 | − | 0.470074i | \(-0.844227\pi\) | ||
0.882627 | − | 0.470074i | \(-0.155773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | 42.0000i | 1.40626i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −20.0000 | −0.668900 | ||||||||
\(895\) | −40.0000 | − | 20.0000i | −1.33705 | − | 0.668526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | 10.0000i | 0.333704i | ||||||||
\(899\) | 10.0000 | 0.333519 | ||||||||
\(900\) | −12.0000 | − | 16.0000i | −0.400000 | − | 0.533333i | ||||
\(901\) | 42.0000 | 1.39922 | ||||||||
\(902\) | − | 12.0000i | − | 0.399556i | ||||||
\(903\) | − | 4.00000i | − | 0.133112i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.0000 | + | 18.0000i | 1.19668 | + | 0.598340i | ||||
\(906\) | −26.0000 | −0.863792 | ||||||||
\(907\) | − | 38.0000i | − | 1.26177i | −0.775877 | − | 0.630885i | \(-0.782692\pi\) | ||
0.775877 | − | 0.630885i | \(-0.217308\pi\) | |||||||
\(908\) | − | 34.0000i | − | 1.12833i | ||||||
\(909\) | 24.0000 | 0.796030 | ||||||||
\(910\) | −2.00000 | + | 4.00000i | −0.0662994 | + | 0.132599i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | 76.0000 | 2.51386 | ||||||||
\(915\) | 8.00000 | − | 16.0000i | 0.264472 | − | 0.528944i | ||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | − | 22.0000i | − | 0.726504i | ||||||
\(918\) | 70.0000i | 2.31034i | ||||||||
\(919\) | 5.00000 | 0.164935 | 0.0824674 | − | 0.996594i | \(-0.473720\pi\) | ||||
0.0824674 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.00000 | 0.230658 | ||||||||
\(922\) | 24.0000i | 0.790398i | ||||||||
\(923\) | 8.00000i | 0.263323i | ||||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | −8.00000 | + | 6.00000i | −0.263038 | + | 0.197279i | ||||
\(926\) | 72.0000 | 2.36607 | ||||||||
\(927\) | 38.0000i | 1.24808i | ||||||||
\(928\) | − | 40.0000i | − | 1.31306i | ||||||
\(929\) | 50.0000 | 1.64045 | 0.820223 | − | 0.572043i | \(-0.193849\pi\) | ||||
0.820223 | + | 0.572043i | \(0.193849\pi\) | |||||||
\(930\) | −8.00000 | − | 4.00000i | −0.262330 | − | 0.131165i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.0000i | 1.04819i | ||||||||
\(933\) | − | 12.0000i | − | 0.392862i | ||||||
\(934\) | −54.0000 | −1.76693 | ||||||||
\(935\) | −21.0000 | + | 42.0000i | −0.686773 | + | 1.37355i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.0000i | − | 0.424691i | −0.977195 | − | 0.212346i | \(-0.931890\pi\) | ||
0.977195 | − | 0.212346i | \(-0.0681103\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | −21.0000 | −0.685309 | ||||||||
\(940\) | 6.00000 | − | 12.0000i | 0.195698 | − | 0.391397i | ||||
\(941\) | −48.0000 | −1.56476 | −0.782378 | − | 0.622804i | \(-0.785993\pi\) | ||||
−0.782378 | + | 0.622804i | \(0.785993\pi\) | |||||||
\(942\) | − | 36.0000i | − | 1.17294i | ||||||
\(943\) | − | 12.0000i | − | 0.390774i | ||||||
\(944\) | 40.0000 | 1.30189 | ||||||||
\(945\) | 10.0000 | + | 5.00000i | 0.325300 | + | 0.162650i | ||||
\(946\) | 24.0000 | 0.780307 | ||||||||
\(947\) | 42.0000i | 1.36482i | 0.730971 | + | 0.682408i | \(0.239067\pi\) | ||||
−0.730971 | + | 0.682408i | \(0.760933\pi\) | |||||||
\(948\) | 10.0000i | 0.324785i | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 24.0000 | 0.777029 | ||||||||
\(955\) | 6.00000 | + | 3.00000i | 0.194155 | + | 0.0970777i | ||||
\(956\) | 30.0000 | 0.970269 | ||||||||
\(957\) | 15.0000i | 0.484881i | ||||||||
\(958\) | 60.0000i | 1.93851i | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | −8.00000 | + | 16.0000i | −0.258199 | + | 0.516398i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 4.00000i | 0.128965i | ||||||||
\(963\) | − | 16.0000i | − | 0.515593i | ||||||
\(964\) | −44.0000 | −1.41714 | ||||||||
\(965\) | −16.0000 | + | 32.0000i | −0.515058 | + | 1.03012i | ||||
\(966\) | −12.0000 | −0.386094 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.0000 | + | 14.0000i | 0.899026 | + | 0.449513i | ||||
\(971\) | 22.0000 | 0.706014 | 0.353007 | − | 0.935621i | \(-0.385159\pi\) | ||||
0.353007 | + | 0.935621i | \(0.385159\pi\) | |||||||
\(972\) | 32.0000i | 1.02640i | ||||||||
\(973\) | − | 10.0000i | − | 0.320585i | ||||||
\(974\) | −84.0000 | −2.69153 | ||||||||
\(975\) | −3.00000 | − | 4.00000i | −0.0960769 | − | 0.128103i | ||||
\(976\) | 32.0000 | 1.02430 | ||||||||
\(977\) | 12.0000i | 0.383914i | 0.981403 | + | 0.191957i | \(0.0614834\pi\) | ||||
−0.981403 | + | 0.191957i | \(0.938517\pi\) | |||||||
\(978\) | 28.0000i | 0.895341i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.00000 | − | 2.00000i | −0.127775 | − | 0.0638877i | ||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 14.0000i | 0.446758i | ||||||||
\(983\) | − | 51.0000i | − | 1.62665i | −0.581811 | − | 0.813324i | \(-0.697656\pi\) | ||
0.581811 | − | 0.813324i | \(-0.302344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00000 | − | 4.00000i | 0.0637253 | − | 0.127451i | ||||
\(986\) | −70.0000 | −2.22925 | ||||||||
\(987\) | 3.00000i | 0.0954911i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | −12.0000 | + | 24.0000i | −0.381385 | + | 0.762770i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | − | 16.0000i | − | 0.508001i | ||||||
\(993\) | − | 12.0000i | − | 0.380808i | ||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | −20.0000 | − | 10.0000i | −0.634043 | − | 0.317021i | ||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | − | 13.0000i | − | 0.411714i | −0.978582 | − | 0.205857i | \(-0.934002\pi\) | ||
0.978582 | − | 0.205857i | \(-0.0659982\pi\) | |||||||
\(998\) | 70.0000i | 2.21581i | ||||||||
\(999\) | 10.0000 | 0.316386 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))