Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (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: | \(1.34947179416\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.22 |
Dual form | 169.2.c.a.146.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 1.50000i | −0.612372 | + | 1.06066i | 0.378467 | + | 0.925615i | \(0.376451\pi\) |
−0.990839 | + | 0.135045i | \(0.956882\pi\) | |||||||
\(3\) | −1.00000 | + | 1.73205i | −0.577350 | + | 1.00000i | 0.418432 | + | 0.908248i | \(0.362580\pi\) |
−0.995782 | + | 0.0917517i | \(0.970753\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | −1.73205 | − | 3.00000i | −0.707107 | − | 1.22474i | ||||
\(7\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205 | − | 3.00000i | 0.447214 | − | 0.774597i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 1.73205 | 0.408248 | ||||||||
\(19\) | 1.73205 | + | 3.00000i | 0.397360 | + | 0.688247i | 0.993399 | − | 0.114708i | \(-0.0365932\pi\) |
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0.866025 | + | 1.50000i | 0.193649 | + | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 1.73205 | − | 3.00000i | 0.353553 | − | 0.612372i | ||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 3.00000 | + | 5.19615i | 0.547723 | + | 0.948683i | ||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 2.59808 | + | 4.50000i | 0.459279 | + | 0.795495i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.19615 | 0.891133 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −4.33013 | + | 7.50000i | −0.711868 | + | 1.23299i | 0.252286 | + | 0.967653i | \(0.418817\pi\) |
−0.964155 | + | 0.265340i | \(0.914516\pi\) | |||||||
\(38\) | −6.00000 | −0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −2.59808 | + | 4.50000i | −0.405751 | + | 0.702782i | −0.994409 | − | 0.105601i | \(-0.966323\pi\) |
0.588657 | + | 0.808383i | \(0.299657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.866025 | + | 1.50000i | 0.129099 | + | 0.223607i | ||||
\(46\) | −5.19615 | − | 9.00000i | −0.766131 | − | 1.32698i | ||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 5.00000 | + | 8.66025i | 0.721688 | + | 1.25000i | ||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | 1.73205 | − | 3.00000i | 0.244949 | − | 0.424264i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 3.46410 | − | 6.00000i | 0.471405 | − | 0.816497i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.92820 | −0.917663 | ||||||||
\(58\) | −2.59808 | − | 4.50000i | −0.341144 | − | 0.590879i | ||||
\(59\) | 3.46410 | + | 6.00000i | 0.450988 | + | 0.781133i | 0.998448 | − | 0.0556984i | \(-0.0177385\pi\) |
−0.547460 | + | 0.836832i | \(0.684405\pi\) | |||||||
\(60\) | −3.46410 | −0.447214 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | −3.00000 | + | 5.19615i | −0.381000 | + | 0.659912i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73205 | − | 3.00000i | 0.211604 | − | 0.366508i | −0.740613 | − | 0.671932i | \(-0.765465\pi\) |
0.952217 | + | 0.305424i | \(0.0987981\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | −6.00000 | − | 10.3923i | −0.722315 | − | 1.25109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.73205 | − | 3.00000i | −0.205557 | − | 0.356034i | 0.744753 | − | 0.667340i | \(-0.232567\pi\) |
−0.950310 | + | 0.311305i | \(0.899234\pi\) | |||||||
\(72\) | 0.866025 | + | 1.50000i | 0.102062 | + | 0.176777i | ||||
\(73\) | −1.73205 | −0.202721 | −0.101361 | − | 0.994850i | \(-0.532320\pi\) | ||||
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | −7.50000 | − | 12.9904i | −0.871857 | − | 1.51010i | ||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | 1.73205 | − | 3.00000i | 0.198680 | − | 0.344124i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −4.33013 | + | 7.50000i | −0.484123 | + | 0.838525i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | −4.50000 | − | 7.79423i | −0.496942 | − | 0.860729i | ||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.59808 | + | 4.50000i | 0.281801 | + | 0.488094i | ||||
\(86\) | −13.8564 | −1.49417 | ||||||||
\(87\) | −3.00000 | − | 5.19615i | −0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410 | − | 6.00000i | 0.367194 | − | 0.635999i | −0.621932 | − | 0.783072i | \(-0.713652\pi\) |
0.989126 | + | 0.147073i | \(0.0469852\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −3.46410 | + | 6.00000i | −0.359211 | + | 0.622171i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | −10.3923 | −1.06066 | ||||||||
\(97\) | −3.46410 | − | 6.00000i | −0.351726 | − | 0.609208i | 0.634826 | − | 0.772655i | \(-0.281072\pi\) |
−0.986552 | + | 0.163448i | \(0.947739\pi\) | |||||||
\(98\) | 6.06218 | + | 10.5000i | 0.612372 | + | 1.06066i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | −5.19615 | + | 9.00000i | −0.514496 | + | 0.891133i | ||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.59808 | − | 4.50000i | 0.252347 | − | 0.437079i | ||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | −13.8564 | −1.32720 | −0.663602 | − | 0.748086i | \(-0.730973\pi\) | ||||
−0.663602 | + | 0.748086i | \(0.730973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.66025 | − | 15.0000i | −0.821995 | − | 1.42374i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.50000 | + | 12.9904i | 0.705541 | + | 1.22203i | 0.966496 | + | 0.256681i | \(0.0826291\pi\) |
−0.260955 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(114\) | 6.00000 | − | 10.3923i | 0.561951 | − | 0.973329i | ||||
\(115\) | 5.19615 | − | 9.00000i | 0.484544 | − | 0.839254i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 1.73205 | 0.156813 | ||||||||
\(123\) | −5.19615 | − | 9.00000i | −0.468521 | − | 0.811503i | ||||
\(124\) | −1.73205 | − | 3.00000i | −0.155543 | − | 0.269408i | ||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | + | 1.73205i | −0.0887357 | + | 0.153695i | −0.906977 | − | 0.421180i | \(-0.861616\pi\) |
0.818241 | + | 0.574875i | \(0.194949\pi\) | |||||||
\(128\) | −6.06218 | + | 10.5000i | −0.535826 | + | 0.928078i | ||||
\(129\) | −16.0000 | −1.40872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000 | 1.57267 | 0.786334 | − | 0.617802i | \(-0.211977\pi\) | ||||
0.786334 | + | 0.617802i | \(0.211977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.00000 | + | 5.19615i | 0.259161 | + | 0.448879i | ||||
\(135\) | 6.92820 | 0.596285 | ||||||||
\(136\) | 2.59808 | + | 4.50000i | 0.222783 | + | 0.385872i | ||||
\(137\) | −7.79423 | − | 13.5000i | −0.665906 | − | 1.15338i | −0.979039 | − | 0.203674i | \(-0.934712\pi\) |
0.313133 | − | 0.949709i | \(-0.398621\pi\) | |||||||
\(138\) | 20.7846 | 1.76930 | ||||||||
\(139\) | 2.00000 | + | 3.46410i | 0.169638 | + | 0.293821i | 0.938293 | − | 0.345843i | \(-0.112407\pi\) |
−0.768655 | + | 0.639664i | \(0.779074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.46410 | + | 6.00000i | −0.291730 | + | 0.505291i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 2.59808 | − | 4.50000i | 0.215758 | − | 0.373705i | ||||
\(146\) | 1.50000 | − | 2.59808i | 0.124141 | − | 0.215018i | ||||
\(147\) | 7.00000 | + | 12.1244i | 0.577350 | + | 1.00000i | ||||
\(148\) | 8.66025 | 0.711868 | ||||||||
\(149\) | 9.52628 | + | 16.5000i | 0.780423 | + | 1.35173i | 0.931695 | + | 0.363241i | \(0.118330\pi\) |
−0.151272 | + | 0.988492i | \(0.548337\pi\) | |||||||
\(150\) | 3.46410 | + | 6.00000i | 0.282843 | + | 0.489898i | ||||
\(151\) | −17.3205 | −1.40952 | −0.704761 | − | 0.709444i | \(-0.748946\pi\) | ||||
−0.704761 | + | 0.709444i | \(0.748946\pi\) | |||||||
\(152\) | −3.00000 | − | 5.19615i | −0.243332 | − | 0.421464i | ||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | −3.46410 | + | 6.00000i | −0.275589 | + | 0.477334i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | −4.50000 | − | 7.79423i | −0.355756 | − | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.52628 | + | 16.5000i | 0.748455 | + | 1.29636i | ||||
\(163\) | 10.3923 | + | 18.0000i | 0.813988 | + | 1.40987i | 0.910052 | + | 0.414494i | \(0.136041\pi\) |
−0.0960641 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(164\) | 5.19615 | 0.405751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | + | 20.7846i | −0.931381 | + | 1.61320i | ||||
\(167\) | 6.92820 | − | 12.0000i | 0.536120 | − | 0.928588i | −0.462988 | − | 0.886365i | \(-0.653223\pi\) |
0.999108 | − | 0.0422232i | \(-0.0134441\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | 1.73205 | − | 3.00000i | 0.132453 | − | 0.229416i | ||||
\(172\) | 4.00000 | − | 6.92820i | 0.304997 | − | 0.528271i | ||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 10.3923 | 0.787839 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.8564 | −1.04151 | ||||||||
\(178\) | 6.00000 | + | 10.3923i | 0.449719 | + | 0.778936i | ||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0.866025 | − | 1.50000i | 0.0645497 | − | 0.111803i | ||||
\(181\) | −11.0000 | −0.817624 | −0.408812 | − | 0.912619i | \(-0.634057\pi\) | ||||
−0.408812 | + | 0.912619i | \(0.634057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 5.19615 | − | 9.00000i | 0.383065 | − | 0.663489i | ||||
\(185\) | 7.50000 | − | 12.9904i | 0.551411 | − | 0.955072i | ||||
\(186\) | −6.00000 | − | 10.3923i | −0.439941 | − | 0.762001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.73205 | − | 3.00000i | −0.126323 | − | 0.218797i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.3923 | 0.753937 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | −1.00000 | + | 1.73205i | −0.0721688 | + | 0.125000i | ||||
\(193\) | 2.59808 | − | 4.50000i | 0.187014 | − | 0.323917i | −0.757240 | − | 0.653137i | \(-0.773452\pi\) |
0.944253 | + | 0.329220i | \(0.106786\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 6.92820 | − | 12.0000i | 0.493614 | − | 0.854965i | −0.506359 | − | 0.862323i | \(-0.669009\pi\) |
0.999973 | + | 0.00735824i | \(0.00234222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | − | 1.73205i | −0.0708881 | − | 0.122782i | 0.828403 | − | 0.560133i | \(-0.189250\pi\) |
−0.899291 | + | 0.437351i | \(0.855917\pi\) | |||||||
\(200\) | 3.46410 | 0.244949 | ||||||||
\(201\) | 3.46410 | + | 6.00000i | 0.244339 | + | 0.423207i | ||||
\(202\) | −2.59808 | − | 4.50000i | −0.182800 | − | 0.316619i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | −8.66025 | + | 15.0000i | −0.603388 | + | 1.04510i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | + | 8.66025i | −0.344214 | + | 0.596196i | −0.985211 | − | 0.171347i | \(-0.945188\pi\) |
0.640996 | + | 0.767544i | \(0.278521\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | 6.92820 | 0.474713 | ||||||||
\(214\) | −5.19615 | − | 9.00000i | −0.355202 | − | 0.615227i | ||||
\(215\) | −6.92820 | − | 12.0000i | −0.472500 | − | 0.818393i | ||||
\(216\) | 6.92820 | 0.471405 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.0000 | − | 20.7846i | 0.812743 | − | 1.40771i | ||||
\(219\) | 1.73205 | − | 3.00000i | 0.117041 | − | 0.202721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 30.0000 | 2.01347 | ||||||||
\(223\) | −5.19615 | + | 9.00000i | −0.347960 | + | 0.602685i | −0.985887 | − | 0.167412i | \(-0.946459\pi\) |
0.637927 | + | 0.770097i | \(0.279792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 1.73205i | 0.0666667 | + | 0.115470i | ||||
\(226\) | −25.9808 | −1.72821 | ||||||||
\(227\) | −12.1244 | − | 21.0000i | −0.804722 | − | 1.39382i | −0.916479 | − | 0.400083i | \(-0.868981\pi\) |
0.111757 | − | 0.993736i | \(-0.464352\pi\) | |||||||
\(228\) | 3.46410 | + | 6.00000i | 0.229416 | + | 0.397360i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 9.00000 | + | 15.5885i | 0.593442 | + | 1.02787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.59808 | − | 4.50000i | 0.170572 | − | 0.295439i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 3.46410 | − | 6.00000i | 0.225494 | − | 0.390567i | ||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | −8.66025 | − | 15.0000i | −0.559017 | − | 0.968246i | ||||
\(241\) | −0.866025 | − | 1.50000i | −0.0557856 | − | 0.0966235i | 0.836784 | − | 0.547533i | \(-0.184433\pi\) |
−0.892570 | + | 0.450910i | \(0.851100\pi\) | |||||||
\(242\) | −19.0526 | −1.22474 | ||||||||
\(243\) | 5.00000 | + | 8.66025i | 0.320750 | + | 0.555556i | ||||
\(244\) | −0.500000 | + | 0.866025i | −0.0320092 | + | 0.0554416i | ||||
\(245\) | −6.06218 | + | 10.5000i | −0.387298 | + | 0.670820i | ||||
\(246\) | 18.0000 | 1.14764 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | −13.8564 | + | 24.0000i | −0.878114 | + | 1.52094i | ||||
\(250\) | −10.5000 | + | 18.1865i | −0.664078 | + | 1.15022i | ||||
\(251\) | −9.00000 | − | 15.5885i | −0.568075 | − | 0.983935i | −0.996756 | − | 0.0804789i | \(-0.974355\pi\) |
0.428681 | − | 0.903456i | \(-0.358978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.73205 | − | 3.00000i | −0.108679 | − | 0.188237i | ||||
\(255\) | −10.3923 | −0.650791 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 13.8564 | − | 24.0000i | 0.862662 | − | 1.49417i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | −15.5885 | + | 27.0000i | −0.963058 | + | 1.66807i | ||||
\(263\) | −6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | \(-0.953967\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615 | 0.319197 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.92820 | + | 12.0000i | 0.423999 | + | 0.734388i | ||||
\(268\) | −3.46410 | −0.211604 | ||||||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | −6.00000 | + | 10.3923i | −0.365148 | + | 0.632456i | ||||
\(271\) | −10.3923 | + | 18.0000i | −0.631288 | + | 1.09342i | 0.356001 | + | 0.934485i | \(0.384140\pi\) |
−0.987289 | + | 0.158937i | \(0.949193\pi\) | |||||||
\(272\) | −15.0000 | −0.909509 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.0000 | 1.63113 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | −3.50000 | − | 6.06218i | −0.210295 | − | 0.364241i | 0.741512 | − | 0.670940i | \(-0.234109\pi\) |
−0.951807 | + | 0.306699i | \(0.900776\pi\) | |||||||
\(278\) | −6.92820 | −0.415526 | ||||||||
\(279\) | −1.73205 | − | 3.00000i | −0.103695 | − | 0.179605i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5167 | 1.34323 | 0.671616 | − | 0.740900i | \(-0.265601\pi\) | ||||
0.671616 | + | 0.740900i | \(0.265601\pi\) | |||||||
\(282\) | −6.00000 | − | 10.3923i | −0.357295 | − | 0.618853i | ||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | −1.73205 | + | 3.00000i | −0.102778 | + | 0.178017i | ||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.59808 | − | 4.50000i | 0.153093 | − | 0.265165i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 4.50000 | + | 7.79423i | 0.264249 | + | 0.457693i | ||||
\(291\) | 13.8564 | 0.812277 | ||||||||
\(292\) | 0.866025 | + | 1.50000i | 0.0506803 | + | 0.0877809i | ||||
\(293\) | 2.59808 | + | 4.50000i | 0.151781 | + | 0.262893i | 0.931882 | − | 0.362761i | \(-0.118166\pi\) |
−0.780101 | + | 0.625653i | \(0.784832\pi\) | |||||||
\(294\) | −24.2487 | −1.41421 | ||||||||
\(295\) | −6.00000 | − | 10.3923i | −0.349334 | − | 0.605063i | ||||
\(296\) | 7.50000 | − | 12.9904i | 0.435929 | − | 0.755051i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.0000 | −1.91164 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.0000 | − | 25.9808i | 0.863153 | − | 1.49502i | ||||
\(303\) | −3.00000 | − | 5.19615i | −0.172345 | − | 0.298511i | ||||
\(304\) | 17.3205 | 0.993399 | ||||||||
\(305\) | 0.866025 | + | 1.50000i | 0.0495885 | + | 0.0858898i | ||||
\(306\) | −2.59808 | − | 4.50000i | −0.148522 | − | 0.257248i | ||||
\(307\) | 17.3205 | 0.988534 | 0.494267 | − | 0.869310i | \(-0.335437\pi\) | ||||
0.494267 | + | 0.869310i | \(0.335437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0000 | + | 17.3205i | −0.568880 | + | 0.985329i | ||||
\(310\) | 5.19615 | − | 9.00000i | 0.295122 | − | 0.511166i | ||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 11.2583 | − | 19.5000i | 0.635344 | − | 1.10045i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | − | 3.46410i | −0.112509 | − | 0.194871i | ||||
\(317\) | −5.19615 | −0.291845 | −0.145922 | − | 0.989296i | \(-0.546615\pi\) | ||||
−0.145922 | + | 0.989296i | \(0.546615\pi\) | |||||||
\(318\) | 5.19615 | + | 9.00000i | 0.291386 | + | 0.504695i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.73205 | −0.0968246 | ||||||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.19615 | − | 9.00000i | 0.289122 | − | 0.500773i | ||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.0000 | −1.99386 | ||||||||
\(327\) | 13.8564 | − | 24.0000i | 0.766261 | − | 1.32720i | ||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8564 | + | 24.0000i | 0.761617 | + | 1.31916i | 0.942017 | + | 0.335566i | \(0.108928\pi\) |
−0.180400 | + | 0.983593i | \(0.557739\pi\) | |||||||
\(332\) | −6.92820 | − | 12.0000i | −0.380235 | − | 0.658586i | ||||
\(333\) | 8.66025 | 0.474579 | ||||||||
\(334\) | 12.0000 | + | 20.7846i | 0.656611 | + | 1.13728i | ||||
\(335\) | −3.00000 | + | 5.19615i | −0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.0000 | −1.62938 | ||||||||
\(340\) | 2.59808 | − | 4.50000i | 0.140900 | − | 0.244047i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.00000 | + | 5.19615i | 0.162221 | + | 0.280976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.92820 | − | 12.0000i | −0.373544 | − | 0.646997i | ||||
\(345\) | 10.3923 | + | 18.0000i | 0.559503 | + | 0.969087i | ||||
\(346\) | −10.3923 | −0.558694 | ||||||||
\(347\) | 15.0000 | + | 25.9808i | 0.805242 | + | 1.39472i | 0.916127 | + | 0.400887i | \(0.131298\pi\) |
−0.110885 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(348\) | −3.00000 | + | 5.19615i | −0.160817 | + | 0.278543i | ||||
\(349\) | −6.92820 | + | 12.0000i | −0.370858 | + | 0.642345i | −0.989698 | − | 0.143172i | \(-0.954270\pi\) |
0.618840 | + | 0.785517i | \(0.287603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.4545 | − | 28.5000i | 0.875784 | − | 1.51690i | 0.0198582 | − | 0.999803i | \(-0.493679\pi\) |
0.855926 | − | 0.517099i | \(-0.172988\pi\) | |||||||
\(354\) | 12.0000 | − | 20.7846i | 0.637793 | − | 1.10469i | ||||
\(355\) | 3.00000 | + | 5.19615i | 0.159223 | + | 0.275783i | ||||
\(356\) | −6.92820 | −0.367194 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92820 | 0.365657 | 0.182828 | − | 0.983145i | \(-0.441475\pi\) | ||||
0.182828 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(360\) | −1.50000 | − | 2.59808i | −0.0790569 | − | 0.136931i | ||||
\(361\) | 3.50000 | − | 6.06218i | 0.184211 | − | 0.319062i | ||||
\(362\) | 9.52628 | − | 16.5000i | 0.500690 | − | 0.867221i | ||||
\(363\) | −22.0000 | −1.15470 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | 0.157027 | ||||||||
\(366\) | −1.73205 | + | 3.00000i | −0.0905357 | + | 0.156813i | ||||
\(367\) | 11.0000 | − | 19.0526i | 0.574195 | − | 0.994535i | −0.421933 | − | 0.906627i | \(-0.638648\pi\) |
0.996129 | − | 0.0879086i | \(-0.0280183\pi\) | |||||||
\(368\) | 15.0000 | + | 25.9808i | 0.781929 | + | 1.35434i | ||||
\(369\) | 5.19615 | 0.270501 | ||||||||
\(370\) | 12.9904 | + | 22.5000i | 0.675338 | + | 1.16972i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.92820 | 0.359211 | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1244 | + | 21.0000i | −0.626099 | + | 1.08444i | ||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1244 | + | 21.0000i | −0.622786 | + | 1.07870i | 0.366178 | + | 0.930545i | \(0.380666\pi\) |
−0.988964 | + | 0.148153i | \(0.952667\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | −2.00000 | − | 3.46410i | −0.102463 | − | 0.177471i | ||||
\(382\) | 31.1769 | 1.59515 | ||||||||
\(383\) | 10.3923 | + | 18.0000i | 0.531022 | + | 0.919757i | 0.999345 | + | 0.0361995i | \(0.0115252\pi\) |
−0.468323 | + | 0.883558i | \(0.655141\pi\) | |||||||
\(384\) | −12.1244 | − | 21.0000i | −0.618718 | − | 1.07165i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.50000 | + | 7.79423i | 0.229044 | + | 0.396716i | ||||
\(387\) | 4.00000 | − | 6.92820i | 0.203331 | − | 0.352180i | ||||
\(388\) | −3.46410 | + | 6.00000i | −0.175863 | + | 0.304604i | ||||
\(389\) | 9.00000 | 0.456318 | 0.228159 | − | 0.973624i | \(-0.426729\pi\) | ||||
0.228159 | + | 0.973624i | \(0.426729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | −6.06218 | + | 10.5000i | −0.306186 | + | 0.530330i | ||||
\(393\) | −18.0000 | + | 31.1769i | −0.907980 | + | 1.57267i | ||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | −6.92820 | −0.348596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.92820 | − | 12.0000i | −0.347717 | − | 0.602263i | 0.638127 | − | 0.769931i | \(-0.279710\pi\) |
−0.985843 | + | 0.167668i | \(0.946376\pi\) | |||||||
\(398\) | 3.46410 | 0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | + | 8.66025i | −0.250000 | + | 0.433013i | ||||
\(401\) | 0.866025 | − | 1.50000i | 0.0432472 | − | 0.0749064i | −0.843592 | − | 0.536985i | \(-0.819563\pi\) |
0.886839 | + | 0.462079i | \(0.152896\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.00000 | 0.149256 | ||||||||
\(405\) | −9.52628 | + | 16.5000i | −0.473365 | + | 0.819892i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −10.3923 | −0.514496 | ||||||||
\(409\) | −7.79423 | − | 13.5000i | −0.385400 | − | 0.667532i | 0.606425 | − | 0.795141i | \(-0.292603\pi\) |
−0.991825 | + | 0.127609i | \(0.959270\pi\) | |||||||
\(410\) | 7.79423 | + | 13.5000i | 0.384930 | + | 0.666717i | ||||
\(411\) | 31.1769 | 1.53784 | ||||||||
\(412\) | −5.00000 | − | 8.66025i | −0.246332 | − | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.19615 | + | 9.00000i | −0.255377 | + | 0.442326i | ||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.00000 | + | 15.5885i | −0.439679 | + | 0.761546i | −0.997665 | − | 0.0683046i | \(-0.978241\pi\) |
0.557986 | + | 0.829851i | \(0.311574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5885 | 0.759735 | 0.379867 | − | 0.925041i | \(-0.375970\pi\) | ||||
0.379867 | + | 0.925041i | \(0.375970\pi\) | |||||||
\(422\) | −8.66025 | − | 15.0000i | −0.421575 | − | 0.730189i | ||||
\(423\) | −1.73205 | − | 3.00000i | −0.0842152 | − | 0.145865i | ||||
\(424\) | 5.19615 | 0.252347 | ||||||||
\(425\) | 3.00000 | + | 5.19615i | 0.145521 | + | 0.252050i | ||||
\(426\) | −6.00000 | + | 10.3923i | −0.290701 | + | 0.503509i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.0000 | 1.15738 | ||||||||
\(431\) | −3.46410 | + | 6.00000i | −0.166860 | + | 0.289010i | −0.937314 | − | 0.348485i | \(-0.886696\pi\) |
0.770454 | + | 0.637495i | \(0.220029\pi\) | |||||||
\(432\) | −10.0000 | + | 17.3205i | −0.481125 | + | 0.833333i | ||||
\(433\) | −8.50000 | − | 14.7224i | −0.408484 | − | 0.707515i | 0.586236 | − | 0.810140i | \(-0.300609\pi\) |
−0.994720 | + | 0.102625i | \(0.967276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.19615 | + | 9.00000i | 0.249136 | + | 0.431517i | ||||
\(436\) | 6.92820 | + | 12.0000i | 0.331801 | + | 0.574696i | ||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 3.00000 | + | 5.19615i | 0.143346 | + | 0.248282i | ||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | −8.66025 | + | 15.0000i | −0.410997 | + | 0.711868i | ||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | −9.00000 | − | 15.5885i | −0.426162 | − | 0.738135i | ||||
\(447\) | −38.1051 | −1.80231 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.46410 | − | 6.00000i | −0.163481 | − | 0.283158i | 0.772634 | − | 0.634852i | \(-0.218939\pi\) |
−0.936115 | + | 0.351694i | \(0.885606\pi\) | |||||||
\(450\) | −3.46410 | −0.163299 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.50000 | − | 12.9904i | 0.352770 | − | 0.611016i | ||||
\(453\) | 17.3205 | − | 30.0000i | 0.813788 | − | 1.40952i | ||||
\(454\) | 42.0000 | 1.97116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | 0.866025 | − | 1.50000i | 0.0405110 | − | 0.0701670i | −0.845059 | − | 0.534673i | \(-0.820435\pi\) |
0.885570 | + | 0.464506i | \(0.153768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.00000 | + | 10.3923i | 0.280056 | + | 0.485071i | ||||
\(460\) | −10.3923 | −0.484544 | ||||||||
\(461\) | −11.2583 | − | 19.5000i | −0.524353 | − | 0.908206i | −0.999598 | − | 0.0283522i | \(-0.990974\pi\) |
0.475245 | − | 0.879853i | \(-0.342359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8564 | −0.643962 | −0.321981 | − | 0.946746i | \(-0.604349\pi\) | ||||
−0.321981 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(464\) | 7.50000 | + | 12.9904i | 0.348179 | + | 0.603063i | ||||
\(465\) | 6.00000 | − | 10.3923i | 0.278243 | − | 0.481932i | ||||
\(466\) | 5.19615 | − | 9.00000i | 0.240707 | − | 0.416917i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.19615 | − | 9.00000i | 0.239681 | − | 0.415139i | ||||
\(471\) | 13.0000 | − | 22.5167i | 0.599008 | − | 1.03751i | ||||
\(472\) | −6.00000 | − | 10.3923i | −0.276172 | − | 0.478345i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.92820 | − | 12.0000i | −0.318223 | − | 0.551178i | ||||
\(475\) | −3.46410 | − | 6.00000i | −0.158944 | − | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.50000 | + | 2.59808i | 0.0686803 | + | 0.118958i | ||||
\(478\) | 18.0000 | − | 31.1769i | 0.823301 | − | 1.42600i | ||||
\(479\) | −12.1244 | + | 21.0000i | −0.553976 | + | 0.959514i | 0.444006 | + | 0.896024i | \(0.353557\pi\) |
−0.997982 | + | 0.0634909i | \(0.979777\pi\) | |||||||
\(480\) | 18.0000 | 0.821584 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.00000 | 0.136646 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50000 | − | 9.52628i | 0.250000 | − | 0.433013i | ||||
\(485\) | 6.00000 | + | 10.3923i | 0.272446 | + | 0.471890i | ||||
\(486\) | −17.3205 | −0.785674 | ||||||||
\(487\) | 3.46410 | + | 6.00000i | 0.156973 | + | 0.271886i | 0.933776 | − | 0.357858i | \(-0.116493\pi\) |
−0.776802 | + | 0.629744i | \(0.783160\pi\) | |||||||
\(488\) | 0.866025 | + | 1.50000i | 0.0392031 | + | 0.0679018i | ||||
\(489\) | −41.5692 | −1.87983 | ||||||||
\(490\) | −10.5000 | − | 18.1865i | −0.474342 | − | 0.821584i | ||||
\(491\) | 6.00000 | − | 10.3923i | 0.270776 | − | 0.468998i | −0.698285 | − | 0.715820i | \(-0.746053\pi\) |
0.969061 | + | 0.246822i | \(0.0793863\pi\) | |||||||
\(492\) | −5.19615 | + | 9.00000i | −0.234261 | + | 0.405751i | ||||
\(493\) | 9.00000 | 0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.66025 | − | 15.0000i | 0.388857 | − | 0.673520i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.0000 | − | 41.5692i | −1.07547 | − | 1.86276i | ||||
\(499\) | 31.1769 | 1.39567 | 0.697835 | − | 0.716258i | \(-0.254147\pi\) | ||||
0.697835 | + | 0.716258i | \(0.254147\pi\) | |||||||
\(500\) | −6.06218 | − | 10.5000i | −0.271109 | − | 0.469574i | ||||
\(501\) | 13.8564 | + | 24.0000i | 0.619059 | + | 1.07224i | ||||
\(502\) | 31.1769 | 1.39149 | ||||||||
\(503\) | −18.0000 | − | 31.1769i | −0.802580 | − | 1.39011i | −0.917912 | − | 0.396783i | \(-0.870127\pi\) |
0.115332 | − | 0.993327i | \(-0.463207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59808 | − | 4.50000i | 0.115613 | − | 0.200247i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | 9.52628 | − | 16.5000i | 0.422245 | − | 0.731350i | −0.573914 | − | 0.818916i | \(-0.694576\pi\) |
0.996159 | + | 0.0875661i | \(0.0279089\pi\) | |||||||
\(510\) | 9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | −6.92820 | − | 12.0000i | −0.305888 | − | 0.529813i | ||||
\(514\) | 2.59808 | + | 4.50000i | 0.114596 | + | 0.198486i | ||||
\(515\) | −17.3205 | −0.763233 | ||||||||
\(516\) | 8.00000 | + | 13.8564i | 0.352180 | + | 0.609994i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | 0.394297 | 0.197149 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197149 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(522\) | −2.59808 | + | 4.50000i | −0.113715 | + | 0.196960i | ||||
\(523\) | 8.00000 | − | 13.8564i | 0.349816 | − | 0.605898i | −0.636401 | − | 0.771358i | \(-0.719578\pi\) |
0.986216 | + | 0.165460i | \(0.0529109\pi\) | |||||||
\(524\) | −9.00000 | − | 15.5885i | −0.393167 | − | 0.680985i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.3923 | − | 18.0000i | −0.453126 | − | 0.784837i | ||||
\(527\) | −5.19615 | − | 9.00000i | −0.226348 | − | 0.392046i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −4.50000 | + | 7.79423i | −0.195468 | + | 0.338560i | ||||
\(531\) | 3.46410 | − | 6.00000i | 0.150329 | − | 0.260378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −24.0000 | −1.03858 | ||||||||
\(535\) | 5.19615 | − | 9.00000i | 0.224649 | − | 0.389104i | ||||
\(536\) | −3.00000 | + | 5.19615i | −0.129580 | + | 0.224440i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.3923 | −0.448044 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.46410 | − | 6.00000i | −0.149071 | − | 0.258199i | ||||
\(541\) | −29.4449 | −1.26593 | −0.632967 | − | 0.774179i | \(-0.718163\pi\) | ||||
−0.632967 | + | 0.774179i | \(0.718163\pi\) | |||||||
\(542\) | −18.0000 | − | 31.1769i | −0.773166 | − | 1.33916i | ||||
\(543\) | 11.0000 | − | 19.0526i | 0.472055 | − | 0.817624i | ||||
\(544\) | 7.79423 | − | 13.5000i | 0.334175 | − | 0.578808i | ||||
\(545\) | 24.0000 | 1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0000 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(548\) | −7.79423 | + | 13.5000i | −0.332953 | + | 0.576691i | ||||
\(549\) | −0.500000 | + | 0.866025i | −0.0213395 | + | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3923 | −0.442727 | ||||||||
\(552\) | 10.3923 | + | 18.0000i | 0.442326 | + | 0.766131i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.1244 | 0.515115 | ||||||||
\(555\) | 15.0000 | + | 25.9808i | 0.636715 | + | 1.10282i | ||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | 7.79423 | − | 13.5000i | 0.330252 | − | 0.572013i | −0.652309 | − | 0.757953i | \(-0.726200\pi\) |
0.982561 | + | 0.185940i | \(0.0595329\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5000 | + | 33.7750i | −0.822558 | + | 1.42471i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 6.92820 | 0.291730 | ||||||||
\(565\) | −12.9904 | − | 22.5000i | −0.546509 | − | 0.946582i | ||||
\(566\) | 3.46410 | + | 6.00000i | 0.145607 | + | 0.252199i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | −21.0000 | + | 36.3731i | −0.880366 | + | 1.52484i | −0.0294311 | + | 0.999567i | \(0.509370\pi\) |
−0.850935 | + | 0.525271i | \(0.823964\pi\) | |||||||
\(570\) | −10.3923 | + | 18.0000i | −0.435286 | + | 0.753937i | ||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.0000 | 1.50392 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | − | 10.3923i | 0.250217 | − | 0.433389i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −19.0526 | −0.793168 | −0.396584 | − | 0.917998i | \(-0.629805\pi\) | ||||
−0.396584 | + | 0.917998i | \(0.629805\pi\) | |||||||
\(578\) | 6.92820 | + | 12.0000i | 0.288175 | + | 0.499134i | ||||
\(579\) | 5.19615 | + | 9.00000i | 0.215945 | + | 0.374027i | ||||
\(580\) | −5.19615 | −0.215758 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.0000 | + | 20.7846i | −0.497416 | + | 0.861550i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.00000 | 0.124141 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.00000 | −0.371787 | ||||||||
\(587\) | −10.3923 | + | 18.0000i | −0.428936 | + | 0.742940i | −0.996779 | − | 0.0801976i | \(-0.974445\pi\) |
0.567843 | + | 0.823137i | \(0.307778\pi\) | |||||||
\(588\) | 7.00000 | − | 12.1244i | 0.288675 | − | 0.500000i | ||||
\(589\) | 6.00000 | + | 10.3923i | 0.247226 | + | 0.428207i | ||||
\(590\) | 20.7846 | 0.855689 | ||||||||
\(591\) | 13.8564 | + | 24.0000i | 0.569976 | + | 0.987228i | ||||
\(592\) | 21.6506 | + | 37.5000i | 0.889836 | + | 1.54124i | ||||
\(593\) | 25.9808 | 1.06690 | 0.533451 | − | 0.845831i | \(-0.320895\pi\) | ||||
0.533451 | + | 0.845831i | \(0.320895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.52628 | − | 16.5000i | 0.390212 | − | 0.675866i | ||||
\(597\) | 4.00000 | 0.163709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | −3.46410 | + | 6.00000i | −0.141421 | + | 0.244949i | ||||
\(601\) | −12.5000 | + | 21.6506i | −0.509886 | + | 0.883148i | 0.490049 | + | 0.871695i | \(0.336979\pi\) |
−0.999934 | + | 0.0114528i | \(0.996354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.46410 | −0.141069 | ||||||||
\(604\) | 8.66025 | + | 15.0000i | 0.352381 | + | 0.610341i | ||||
\(605\) | −9.52628 | − | 16.5000i | −0.387298 | − | 0.670820i | ||||
\(606\) | 10.3923 | 0.422159 | ||||||||
\(607\) | 17.0000 | + | 29.4449i | 0.690009 | + | 1.19513i | 0.971834 | + | 0.235665i | \(0.0757267\pi\) |
−0.281826 | + | 0.959466i | \(0.590940\pi\) | |||||||
\(608\) | −9.00000 | + | 15.5885i | −0.364998 | + | 0.632195i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.00000 | 0.121268 | ||||||||
\(613\) | −6.06218 | + | 10.5000i | −0.244849 | + | 0.424091i | −0.962089 | − | 0.272735i | \(-0.912072\pi\) |
0.717240 | + | 0.696826i | \(0.245405\pi\) | |||||||
\(614\) | −15.0000 | + | 25.9808i | −0.605351 | + | 1.04850i | ||||
\(615\) | 9.00000 | + | 15.5885i | 0.362915 | + | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.2583 | + | 19.5000i | 0.453243 | + | 0.785040i | 0.998585 | − | 0.0531732i | \(-0.0169335\pi\) |
−0.545342 | + | 0.838214i | \(0.683600\pi\) | |||||||
\(618\) | −17.3205 | − | 30.0000i | −0.696733 | − | 1.20678i | ||||
\(619\) | 20.7846 | 0.835404 | 0.417702 | − | 0.908584i | \(-0.362836\pi\) | ||||
0.417702 | + | 0.908584i | \(0.362836\pi\) | |||||||
\(620\) | 3.00000 | + | 5.19615i | 0.120483 | + | 0.208683i | ||||
\(621\) | 12.0000 | − | 20.7846i | 0.481543 | − | 0.834058i | ||||
\(622\) | −25.9808 | + | 45.0000i | −1.04173 | + | 1.80434i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −8.66025 | + | 15.0000i | −0.346133 | + | 0.599521i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.50000 | + | 11.2583i | 0.259378 | + | 0.449256i | ||||
\(629\) | 25.9808 | 1.03592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.2487 | − | 42.0000i | −0.965326 | − | 1.67199i | −0.708737 | − | 0.705473i | \(-0.750735\pi\) |
−0.256589 | − | 0.966521i | \(-0.582599\pi\) | |||||||
\(632\) | −6.92820 | −0.275589 | ||||||||
\(633\) | −10.0000 | − | 17.3205i | −0.397464 | − | 0.688428i | ||||
\(634\) | 4.50000 | − | 7.79423i | 0.178718 | − | 0.309548i | ||||
\(635\) | 1.73205 | − | 3.00000i | 0.0687343 | − | 0.119051i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.73205 | + | 3.00000i | −0.0685189 | + | 0.118678i | ||||
\(640\) | 10.5000 | − | 18.1865i | 0.415049 | − | 0.718886i | ||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 20.7846 | 0.820303 | ||||||||
\(643\) | −6.92820 | − | 12.0000i | −0.273222 | − | 0.473234i | 0.696463 | − | 0.717592i | \(-0.254756\pi\) |
−0.969685 | + | 0.244359i | \(0.921423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.7128 | 1.09119 | ||||||||
\(646\) | 9.00000 | + | 15.5885i | 0.354100 | + | 0.613320i | ||||
\(647\) | 9.00000 | − | 15.5885i | 0.353827 | − | 0.612845i | −0.633090 | − | 0.774078i | \(-0.718214\pi\) |
0.986916 | + | 0.161233i | \(0.0515470\pi\) | |||||||
\(648\) | −9.52628 | + | 16.5000i | −0.374228 | + | 0.648181i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.3923 | − | 18.0000i | 0.406994 | − | 0.704934i | ||||
\(653\) | 15.0000 | − | 25.9808i | 0.586995 | − | 1.01671i | −0.407628 | − | 0.913148i | \(-0.633644\pi\) |
0.994623 | − | 0.103558i | \(-0.0330227\pi\) | |||||||
\(654\) | 24.0000 | + | 41.5692i | 0.938474 | + | 1.62549i | ||||
\(655\) | −31.1769 | −1.21818 | ||||||||
\(656\) | 12.9904 | + | 22.5000i | 0.507189 | + | 0.878477i | ||||
\(657\) | 0.866025 | + | 1.50000i | 0.0337869 | + | 0.0585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3827 | − | 40.5000i | 0.909481 | − | 1.57527i | 0.0946945 | − | 0.995506i | \(-0.469813\pi\) |
0.814787 | − | 0.579761i | \(-0.196854\pi\) | |||||||
\(662\) | −48.0000 | −1.86557 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0000 | −0.931381 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.50000 | + | 12.9904i | −0.290619 | + | 0.503367i | ||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | −13.8564 | −0.536120 | ||||||||
\(669\) | −10.3923 | − | 18.0000i | −0.401790 | − | 0.695920i | ||||
\(670\) | −5.19615 | − | 9.00000i | −0.200745 | − | 0.347700i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | + | 16.4545i | −0.366198 | + | 0.634274i | −0.988968 | − | 0.148132i | \(-0.952674\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(674\) | −19.9186 | + | 34.5000i | −0.767235 | + | 1.32889i | ||||
\(675\) | 8.00000 | 0.307920 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 25.9808 | − | 45.0000i | 0.997785 | − | 1.72821i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | 48.4974 | 1.85843 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1244 | + | 21.0000i | 0.463926 | + | 0.803543i | 0.999152 | − | 0.0411658i | \(-0.0131072\pi\) |
−0.535227 | + | 0.844708i | \(0.679774\pi\) | |||||||
\(684\) | −3.46410 | −0.132453 | ||||||||
\(685\) | 13.5000 | + | 23.3827i | 0.515808 | + | 0.893407i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 40.0000 | 1.52499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −36.0000 | −1.37050 | ||||||||
\(691\) | 6.92820 | − | 12.0000i | 0.263561 | − | 0.456502i | −0.703624 | − | 0.710572i | \(-0.748436\pi\) |
0.967186 | + | 0.254071i | \(0.0817696\pi\) | |||||||
\(692\) | 3.00000 | − | 5.19615i | 0.114043 | − | 0.197528i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −51.9615 | −1.97243 | ||||||||
\(695\) | −3.46410 | − | 6.00000i | −0.131401 | − | 0.227593i | ||||
\(696\) | 5.19615 | + | 9.00000i | 0.196960 | + | 0.341144i | ||||
\(697\) | 15.5885 | 0.590455 | ||||||||
\(698\) | −12.0000 | − | 20.7846i | −0.454207 | − | 0.786709i | ||||
\(699\) | 6.00000 | − | 10.3923i | 0.226941 | − | 0.393073i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.0000 | −1.13147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00000 | − | 10.3923i | 0.225973 | − | 0.391397i | ||||
\(706\) | 28.5000 | + | 49.3634i | 1.07261 | + | 1.85782i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.92820 | + | 12.0000i | 0.260378 | + | 0.450988i | ||||
\(709\) | −2.59808 | − | 4.50000i | −0.0975728 | − | 0.169001i | 0.813107 | − | 0.582115i | \(-0.197775\pi\) |
−0.910679 | + | 0.413114i | \(0.864441\pi\) | |||||||
\(710\) | −10.3923 | −0.390016 | ||||||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | −6.00000 | + | 10.3923i | −0.224860 | + | 0.389468i | ||||
\(713\) | −10.3923 | + | 18.0000i | −0.389195 | + | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7846 | − | 36.0000i | 0.776215 | − | 1.34444i | ||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | −24.0000 | − | 41.5692i | −0.895049 | − | 1.55027i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
−0.0613050 | − | 0.998119i | \(-0.519526\pi\) | |||||||
\(720\) | 8.66025 | 0.322749 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.06218 | + | 10.5000i | 0.225611 | + | 0.390770i | ||||
\(723\) | 3.46410 | 0.128831 | ||||||||
\(724\) | 5.50000 | + | 9.52628i | 0.204406 | + | 0.354041i | ||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 19.0526 | − | 33.0000i | 0.707107 | − | 1.22474i | ||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.59808 | + | 4.50000i | −0.0961591 | + | 0.166552i | ||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | −1.00000 | − | 1.73205i | −0.0369611 | − | 0.0640184i | ||||
\(733\) | 12.1244 | 0.447823 | 0.223912 | − | 0.974609i | \(-0.428117\pi\) | ||||
0.223912 | + | 0.974609i | \(0.428117\pi\) | |||||||
\(734\) | 19.0526 | + | 33.0000i | 0.703243 | + | 1.21805i | ||||
\(735\) | −12.1244 | − | 21.0000i | −0.447214 | − | 0.774597i | ||||
\(736\) | −31.1769 | −1.14920 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.50000 | + | 7.79423i | −0.165647 | + | 0.286910i | ||||
\(739\) | 10.3923 | − | 18.0000i | 0.382287 | − | 0.662141i | −0.609102 | − | 0.793092i | \(-0.708470\pi\) |
0.991389 | + | 0.130951i | \(0.0418032\pi\) | |||||||
\(740\) | −15.0000 | −0.551411 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.3205 | + | 30.0000i | −0.635428 | + | 1.10059i | 0.350997 | + | 0.936377i | \(0.385843\pi\) |
−0.986424 | + | 0.164216i | \(0.947490\pi\) | |||||||
\(744\) | 6.00000 | − | 10.3923i | 0.219971 | − | 0.381000i | ||||
\(745\) | −16.5000 | − | 28.5788i | −0.604513 | − | 1.04705i | ||||
\(746\) | 32.9090 | 1.20488 | ||||||||
\(747\) | −6.92820 | − | 12.0000i | −0.253490 | − | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21.0000 | − | 36.3731i | −0.766812 | − | 1.32816i | ||||
\(751\) | −8.00000 | + | 13.8564i | −0.291924 | + | 0.505627i | −0.974265 | − | 0.225407i | \(-0.927629\pi\) |
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(752\) | 8.66025 | − | 15.0000i | 0.315807 | − | 0.546994i | ||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0000 | − | 22.5167i | 0.472493 | − | 0.818382i | −0.527011 | − | 0.849858i | \(-0.676688\pi\) |
0.999505 | + | 0.0314762i | \(0.0100208\pi\) | |||||||
\(758\) | −21.0000 | − | 36.3731i | −0.762754 | − | 1.32113i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.19615 | + | 9.00000i | 0.188484 | + | 0.326464i | ||||
\(761\) | 17.3205 | + | 30.0000i | 0.627868 | + | 1.08750i | 0.987979 | + | 0.154590i | \(0.0494055\pi\) |
−0.360111 | + | 0.932910i | \(0.617261\pi\) | |||||||
\(762\) | 6.92820 | 0.250982 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.00000 | + | 15.5885i | −0.325609 | + | 0.563971i | ||||
\(765\) | 2.59808 | − | 4.50000i | 0.0939336 | − | 0.162698i | ||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38.0000 | 1.37121 | ||||||||
\(769\) | 3.46410 | − | 6.00000i | 0.124919 | − | 0.216366i | −0.796782 | − | 0.604266i | \(-0.793466\pi\) |
0.921701 | + | 0.387901i | \(0.126800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | + | 5.19615i | 0.108042 | + | 0.187135i | ||||
\(772\) | −5.19615 | −0.187014 | ||||||||
\(773\) | 17.3205 | + | 30.0000i | 0.622975 | + | 1.07903i | 0.988929 | + | 0.148392i | \(0.0474097\pi\) |
−0.365953 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(774\) | 6.92820 | + | 12.0000i | 0.249029 | + | 0.431331i | ||||
\(775\) | −6.92820 | −0.248868 | ||||||||
\(776\) | 6.00000 | + | 10.3923i | 0.215387 | + | 0.373062i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.79423 | + | 13.5000i | −0.279437 | + | 0.483998i | ||||
\(779\) | −18.0000 | −0.644917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −15.5885 | + | 27.0000i | −0.557442 | + | 0.965518i | ||||
\(783\) | 6.00000 | − | 10.3923i | 0.214423 | − | 0.371391i | ||||
\(784\) | −17.5000 | − | 30.3109i | −0.625000 | − | 1.08253i | ||||
\(785\) | 22.5167 | 0.803654 | ||||||||
\(786\) | −31.1769 | − | 54.0000i | −1.11204 | − | 1.92612i | ||||
\(787\) | 19.0526 | + | 33.0000i | 0.679150 | + | 1.17632i | 0.975237 | + | 0.221162i | \(0.0709849\pi\) |
−0.296087 | + | 0.955161i | \(0.595682\pi\) | |||||||
\(788\) | −13.8564 | −0.493614 | ||||||||
\(789\) | −12.0000 | − | 20.7846i | −0.427211 | − | 0.739952i | ||||
\(790\) | 6.00000 | − | 10.3923i | 0.213470 | − | 0.369742i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 24.0000 | 0.851728 | ||||||||
\(795\) | −5.19615 | + | 9.00000i | −0.184289 | + | 0.319197i | ||||
\(796\) | −1.00000 | + | 1.73205i | −0.0354441 | + | 0.0613909i | ||||
\(797\) | 21.0000 | + | 36.3731i | 0.743858 | + | 1.28840i | 0.950726 | + | 0.310031i | \(0.100340\pi\) |
−0.206868 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.19615 | − | 9.00000i | −0.183827 | − | 0.318397i | ||||
\(800\) | −5.19615 | − | 9.00000i | −0.183712 | − | 0.318198i | ||||
\(801\) | −6.92820 | −0.244796 | ||||||||
\(802\) | 1.50000 | + | 2.59808i | 0.0529668 | + | 0.0917413i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.46410 | − | 6.00000i | 0.122169 | − | 0.211604i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | 2.59808 | − | 4.50000i | 0.0914000 | − | 0.158309i | ||||
\(809\) | −16.5000 | + | 28.5788i | −0.580109 | + | 1.00478i | 0.415357 | + | 0.909659i | \(0.363657\pi\) |
−0.995466 | + | 0.0951198i | \(0.969677\pi\) | |||||||
\(810\) | −16.5000 | − | 28.5788i | −0.579751 | − | 1.00416i | ||||
\(811\) | −38.1051 | −1.33805 | −0.669026 | − | 0.743239i | \(-0.733288\pi\) | ||||
−0.669026 | + | 0.743239i | \(0.733288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.7846 | − | 36.0000i | −0.728948 | − | 1.26258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0000 | − | 31.1769i | −0.630512 | − | 1.09208i | ||||
\(816\) | 15.0000 | − | 25.9808i | 0.525105 | − | 0.909509i | ||||
\(817\) | −13.8564 | + | 24.0000i | −0.484774 | + | 0.839654i | ||||
\(818\) | 27.0000 | 0.944033 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −20.7846 | + | 36.0000i | −0.725388 | + | 1.25641i | 0.233426 | + | 0.972375i | \(0.425006\pi\) |
−0.958814 | + | 0.284034i | \(0.908327\pi\) | |||||||
\(822\) | −27.0000 | + | 46.7654i | −0.941733 | + | 1.63113i | ||||
\(823\) | −2.00000 | − | 3.46410i | −0.0697156 | − | 0.120751i | 0.829060 | − | 0.559159i | \(-0.188876\pi\) |
−0.898776 | + | 0.438408i | \(0.855543\pi\) | |||||||
\(824\) | −17.3205 | −0.603388 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.7846 | −0.722752 | −0.361376 | − | 0.932420i | \(-0.617693\pi\) | ||||
−0.361376 | + | 0.932420i | \(0.617693\pi\) | |||||||
\(828\) | −3.00000 | − | 5.19615i | −0.104257 | − | 0.180579i | ||||
\(829\) | 12.5000 | − | 21.6506i | 0.434143 | − | 0.751958i | −0.563082 | − | 0.826401i | \(-0.690385\pi\) |
0.997225 | + | 0.0744432i | \(0.0237179\pi\) | |||||||
\(830\) | 20.7846 | − | 36.0000i | 0.721444 | − | 1.24958i | ||||
\(831\) | 14.0000 | 0.485655 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.0000 | −0.727607 | ||||||||
\(834\) | 6.92820 | − | 12.0000i | 0.239904 | − | 0.415526i | ||||
\(835\) | −12.0000 | + | 20.7846i | −0.415277 | + | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.8564 | −0.478947 | ||||||||
\(838\) | −15.5885 | − | 27.0000i | −0.538494 | − | 0.932700i | ||||
\(839\) | 22.5167 | + | 39.0000i | 0.777361 | + | 1.34643i | 0.933458 | + | 0.358688i | \(0.116776\pi\) |
−0.156096 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | −13.5000 | + | 23.3827i | −0.465241 | + | 0.805821i | ||||
\(843\) | −22.5167 | + | 39.0000i | −0.775515 | + | 1.34323i | ||||
\(844\) | 10.0000 | 0.344214 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.50000 | + | 12.9904i | −0.257551 | + | 0.446092i | ||||
\(849\) | 4.00000 | + | 6.92820i | 0.137280 | + | 0.237775i | ||||
\(850\) | −10.3923 | −0.356453 | ||||||||
\(851\) | −25.9808 | − | 45.0000i | −0.890609 | − | 1.54258i | ||||
\(852\) | −3.46410 | − | 6.00000i | −0.118678 | − | 0.205557i | ||||
\(853\) | −25.9808 | −0.889564 | −0.444782 | − | 0.895639i | \(-0.646719\pi\) | ||||
−0.444782 | + | 0.895639i | \(0.646719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | ||||
\(856\) | 5.19615 | − | 9.00000i | 0.177601 | − | 0.307614i | ||||
\(857\) | −3.00000 | −0.102478 | −0.0512390 | − | 0.998686i | \(-0.516317\pi\) | ||||
−0.0512390 | + | 0.998686i | \(0.516317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | −0.477674 | −0.238837 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | −6.92820 | + | 12.0000i | −0.236250 | + | 0.409197i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | − | 10.3923i | −0.204361 | − | 0.353963i | ||||
\(863\) | −27.7128 | −0.943355 | −0.471678 | − | 0.881771i | \(-0.656351\pi\) | ||||
−0.471678 | + | 0.881771i | \(0.656351\pi\) | |||||||
\(864\) | −10.3923 | − | 18.0000i | −0.353553 | − | 0.612372i | ||||
\(865\) | −5.19615 | − | 9.00000i | −0.176674 | − | 0.306009i | ||||
\(866\) | 29.4449 | 1.00058 | ||||||||
\(867\) | 8.00000 | + | 13.8564i | 0.271694 | + | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −18.0000 | −0.610257 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 24.0000 | 0.812743 | ||||||||
\(873\) | −3.46410 | + | 6.00000i | −0.117242 | + | 0.203069i | ||||
\(874\) | 18.0000 | − | 31.1769i | 0.608859 | − | 1.05457i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.46410 | −0.117041 | ||||||||
\(877\) | −6.06218 | − | 10.5000i | −0.204705 | − | 0.354560i | 0.745334 | − | 0.666692i | \(-0.232290\pi\) |
−0.950039 | + | 0.312132i | \(0.898957\pi\) | |||||||
\(878\) | −24.2487 | − | 42.0000i | −0.818354 | − | 1.41743i | ||||
\(879\) | −10.3923 | −0.350524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.5000 | − | 23.3827i | 0.454827 | − | 0.787783i | −0.543852 | − | 0.839181i | \(-0.683035\pi\) |
0.998678 | + | 0.0513987i | \(0.0163679\pi\) | |||||||
\(882\) | 6.06218 | − | 10.5000i | 0.204124 | − | 0.353553i | ||||
\(883\) | −10.0000 | −0.336527 | −0.168263 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168263 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 10.3923 | − | 18.0000i | 0.349136 | − | 0.604722i | ||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | 15.0000 | + | 25.9808i | 0.503367 | + | 0.871857i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.3923 | − | 18.0000i | −0.348351 | − | 0.603361i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3923 | 0.347960 | ||||||||
\(893\) | 6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | ||||
\(894\) | 33.0000 | − | 57.1577i | 1.10369 | − | 1.91164i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0000 | 0.400445 | ||||||||
\(899\) | −5.19615 | + | 9.00000i | −0.173301 | + | 0.300167i | ||||
\(900\) | 1.00000 | − | 1.73205i | 0.0333333 | − | 0.0577350i | ||||
\(901\) | 4.50000 | + | 7.79423i | 0.149917 | + | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.9904 | − | 22.5000i | −0.432054 | − | 0.748339i | ||||
\(905\) | 19.0526 | 0.633328 | ||||||||
\(906\) | 30.0000 | + | 51.9615i | 0.996683 | + | 1.72631i | ||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | −12.1244 | + | 21.0000i | −0.402361 | + | 0.696909i | ||||
\(909\) | 3.00000 | 0.0995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | −17.3205 | + | 30.0000i | −0.573539 | + | 0.993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.50000 | + | 2.59808i | 0.0496156 | + | 0.0859367i | ||||
\(915\) | −3.46410 | −0.114520 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −20.7846 | −0.685994 | ||||||||
\(919\) | −11.0000 | − | 19.0526i | −0.362857 | − | 0.628486i | 0.625573 | − | 0.780165i | \(-0.284865\pi\) |
−0.988430 | + | 0.151680i | \(0.951532\pi\) | |||||||
\(920\) | −9.00000 | + | 15.5885i | −0.296721 | + | 0.513936i | ||||
\(921\) | −17.3205 | + | 30.0000i | −0.570730 | + | 0.988534i | ||||
\(922\) | 39.0000 | 1.28440 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.66025 | − | 15.0000i | 0.284747 | − | 0.493197i | ||||
\(926\) | 12.0000 | − | 20.7846i | 0.394344 | − | 0.683025i | ||||
\(927\) | −5.00000 | − | 8.66025i | −0.164222 | − | 0.284440i | ||||
\(928\) | −15.5885 | −0.511716 | ||||||||
\(929\) | 23.3827 | + | 40.5000i | 0.767161 | + | 1.32876i | 0.939096 | + | 0.343654i | \(0.111665\pi\) |
−0.171935 | + | 0.985108i | \(0.555002\pi\) | |||||||
\(930\) | 10.3923 | + | 18.0000i | 0.340777 | + | 0.590243i | ||||
\(931\) | 24.2487 | 0.794719 | ||||||||
\(932\) | 3.00000 | + | 5.19615i | 0.0982683 | + | 0.170206i | ||||
\(933\) | −30.0000 | + | 51.9615i | −0.982156 | + | 1.70114i | ||||
\(934\) | 10.3923 | − | 18.0000i | 0.340047 | − | 0.588978i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | 0.228680 | 0.114340 | − | 0.993442i | \(-0.463525\pi\) | ||||
0.114340 | + | 0.993442i | \(0.463525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0000 | + | 17.3205i | −0.326338 | + | 0.565233i | ||||
\(940\) | 3.00000 | + | 5.19615i | 0.0978492 | + | 0.169480i | ||||
\(941\) | 20.7846 | 0.677559 | 0.338779 | − | 0.940866i | \(-0.389986\pi\) | ||||
0.338779 | + | 0.940866i | \(0.389986\pi\) | |||||||
\(942\) | 22.5167 | + | 39.0000i | 0.733632 | + | 1.27069i | ||||
\(943\) | −15.5885 | − | 27.0000i | −0.507630 | − | 0.879241i | ||||
\(944\) | 34.6410 | 1.12747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.66025 | − | 15.0000i | 0.281420 | − | 0.487435i | −0.690314 | − | 0.723510i | \(-0.742528\pi\) |
0.971735 | + | 0.236075i | \(0.0758611\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12.0000 | 0.389331 | ||||||||
\(951\) | 5.19615 | − | 9.00000i | 0.168497 | − | 0.291845i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | \(-0.197649\pi\) |
−0.910516 | + | 0.413473i | \(0.864315\pi\) | |||||||
\(954\) | −5.19615 | −0.168232 | ||||||||
\(955\) | 15.5885 | + | 27.0000i | 0.504431 | + | 0.873699i | ||||
\(956\) | 10.3923 | + | 18.0000i | 0.336111 | + | 0.582162i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0000 | − | 36.3731i | −0.678479 | − | 1.17516i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.73205 | − | 3.00000i | 0.0559017 | − | 0.0968246i | ||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | −0.866025 | + | 1.50000i | −0.0278928 | + | 0.0483117i | ||||
\(965\) | −4.50000 | + | 7.79423i | −0.144860 | + | 0.250905i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.8897 | 1.89377 | 0.946883 | − | 0.321578i | \(-0.104213\pi\) | ||||
0.946883 | + | 0.321578i | \(0.104213\pi\) | |||||||
\(968\) | −9.52628 | − | 16.5000i | −0.306186 | − | 0.530330i | ||||
\(969\) | 10.3923 | + | 18.0000i | 0.333849 | + | 0.578243i | ||||
\(970\) | −20.7846 | −0.667354 | ||||||||
\(971\) | −3.00000 | − | 5.19615i | −0.0962746 | − | 0.166752i | 0.813865 | − | 0.581054i | \(-0.197359\pi\) |
−0.910140 | + | 0.414301i | \(0.864026\pi\) | |||||||
\(972\) | 5.00000 | − | 8.66025i | 0.160375 | − | 0.277778i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | −0.160046 | ||||||||
\(977\) | 21.6506 | − | 37.5000i | 0.692665 | − | 1.19973i | −0.278296 | − | 0.960495i | \(-0.589770\pi\) |
0.970961 | − | 0.239236i | \(-0.0768970\pi\) | |||||||
\(978\) | 36.0000 | − | 62.3538i | 1.15115 | − | 1.99386i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 12.1244 | 0.387298 | ||||||||
\(981\) | 6.92820 | + | 12.0000i | 0.221201 | + | 0.383131i | ||||
\(982\) | 10.3923 | + | 18.0000i | 0.331632 | + | 0.574403i | ||||
\(983\) | −51.9615 | −1.65732 | −0.828658 | − | 0.559756i | \(-0.810895\pi\) | ||||
−0.828658 | + | 0.559756i | \(0.810895\pi\) | |||||||
\(984\) | 9.00000 | + | 15.5885i | 0.286910 | + | 0.496942i | ||||
\(985\) | −12.0000 | + | 20.7846i | −0.382352 | + | 0.662253i | ||||
\(986\) | −7.79423 | + | 13.5000i | −0.248219 | + | 0.429928i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.0000 | −1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | + | 1.73205i | −0.0317660 | + | 0.0550204i | −0.881471 | − | 0.472237i | \(-0.843446\pi\) |
0.849705 | + | 0.527258i | \(0.176780\pi\) | |||||||
\(992\) | 9.00000 | + | 15.5885i | 0.285750 | + | 0.494934i | ||||
\(993\) | −55.4256 | −1.75888 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.73205 | + | 3.00000i | 0.0549097 | + | 0.0951064i | ||||
\(996\) | 27.7128 | 0.878114 | ||||||||
\(997\) | −8.50000 | − | 14.7224i | −0.269198 | − | 0.466264i | 0.699457 | − | 0.714675i | \(-0.253425\pi\) |
−0.968655 | + | 0.248410i | \(0.920092\pi\) | |||||||
\(998\) | −27.0000 | + | 46.7654i | −0.854670 | + | 1.48033i | ||||
\(999\) | 17.3205 | − | 30.0000i | 0.547997 | − | 0.949158i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))