Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,3,Mod(251,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.251");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.j (of order \(6\), 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: | \(18.3924178443\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.251 |
Dual form | 675.3.j.a.476.1 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −0.750000 | − | 0.433013i | 0.0756939 | − | 0.997131i | \(-0.475883\pi\) |
−0.825694 | + | 0.564118i | \(0.809216\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.73205i | 0.142857 | − | 0.247436i | −0.785714 | − | 0.618590i | \(-0.787704\pi\) |
0.928571 | + | 0.371154i | \(0.121038\pi\) | |||||||
\(8\) | 8.66025i | 1.08253i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 0.866025i | 0.136364 | + | 0.0787296i | 0.566630 | − | 0.823972i | \(-0.308247\pi\) |
−0.430266 | + | 0.902702i | \(0.641580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 3.46410i | −0.153846 | − | 0.266469i | 0.778792 | − | 0.627282i | \(-0.215833\pi\) |
−0.932638 | + | 0.360813i | \(0.882499\pi\) | |||||||
\(14\) | −3.00000 | + | 1.73205i | −0.214286 | + | 0.123718i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.50000 | − | 9.52628i | 0.343750 | − | 0.595392i | ||||
\(17\) | − | 15.5885i | − | 0.916968i | −0.888703 | − | 0.458484i | \(-0.848393\pi\) | ||
0.888703 | − | 0.458484i | \(-0.151607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.0000 | 0.578947 | 0.289474 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289474 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.0681818 | − | 0.118094i | ||||
\(23\) | −24.0000 | + | 13.8564i | −1.04348 | + | 0.602452i | −0.920817 | − | 0.389996i | \(-0.872476\pi\) |
−0.122662 | + | 0.992449i | \(0.539143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.92820i | 0.266469i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.0714286 | ||||||||
\(29\) | −39.0000 | − | 22.5167i | −1.34483 | − | 0.776437i | −0.357316 | − | 0.933984i | \(-0.616308\pi\) |
−0.987511 | + | 0.157547i | \(0.949641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0000 | − | 27.7128i | −0.516129 | − | 0.893962i | −0.999825 | − | 0.0187254i | \(-0.994039\pi\) |
0.483696 | − | 0.875236i | \(-0.339294\pi\) | |||||||
\(32\) | 13.5000 | − | 7.79423i | 0.421875 | − | 0.243570i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.5000 | + | 23.3827i | −0.397059 | + | 0.687726i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.0000 | 0.918919 | 0.459459 | − | 0.888199i | \(-0.348043\pi\) | ||||
0.459459 | + | 0.888199i | \(0.348043\pi\) | |||||||
\(38\) | −16.5000 | − | 9.52628i | −0.434211 | − | 0.250692i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5000 | − | 6.06218i | 0.256098 | − | 0.147858i | −0.366456 | − | 0.930436i | \(-0.619429\pi\) |
0.622553 | + | 0.782578i | \(0.286095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.5000 | + | 52.8275i | −0.709302 | + | 1.22855i | 0.255814 | + | 0.966726i | \(0.417657\pi\) |
−0.965116 | + | 0.261822i | \(0.915677\pi\) | |||||||
\(44\) | − | 1.73205i | − | 0.0393648i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 48.0000 | 1.04348 | ||||||||
\(47\) | −42.0000 | − | 24.2487i | −0.893617 | − | 0.515930i | −0.0184931 | − | 0.999829i | \(-0.505887\pi\) |
−0.875124 | + | 0.483899i | \(0.839220\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.5000 | + | 38.9711i | 0.459184 | + | 0.795329i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | + | 3.46410i | −0.0384615 | + | 0.0666173i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 15.0000 | + | 8.66025i | 0.267857 | + | 0.154647i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 39.0000 | + | 67.5500i | 0.672414 | + | 1.16465i | ||||
\(59\) | −43.5000 | + | 25.1147i | −0.737288 | + | 0.425674i | −0.821082 | − | 0.570810i | \(-0.806629\pi\) |
0.0837943 | + | 0.996483i | \(0.473296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.0000 | + | 48.4974i | −0.459016 | + | 0.795040i | −0.998909 | − | 0.0466940i | \(-0.985131\pi\) |
0.539893 | + | 0.841734i | \(0.318465\pi\) | |||||||
\(62\) | 55.4256i | 0.893962i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −71.0000 | −1.10938 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5000 | − | 26.8468i | −0.231343 | − | 0.400698i | 0.726860 | − | 0.686785i | \(-0.240979\pi\) |
−0.958204 | + | 0.286087i | \(0.907645\pi\) | |||||||
\(68\) | −13.5000 | + | 7.79423i | −0.198529 | + | 0.114621i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 31.1769i | − | 0.439111i | −0.975600 | − | 0.219556i | \(-0.929539\pi\) | ||
0.975600 | − | 0.219556i | \(-0.0704608\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65.0000 | −0.890411 | −0.445205 | − | 0.895428i | \(-0.646869\pi\) | ||||
−0.445205 | + | 0.895428i | \(0.646869\pi\) | |||||||
\(74\) | −51.0000 | − | 29.4449i | −0.689189 | − | 0.397904i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.50000 | − | 9.52628i | −0.0723684 | − | 0.125346i | ||||
\(77\) | 3.00000 | − | 1.73205i | 0.0389610 | − | 0.0224942i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.0000 | + | 32.9090i | −0.240506 | + | 0.416569i | −0.960859 | − | 0.277039i | \(-0.910647\pi\) |
0.720352 | + | 0.693608i | \(0.243980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21.0000 | −0.256098 | ||||||||
\(83\) | −42.0000 | − | 24.2487i | −0.506024 | − | 0.292153i | 0.225174 | − | 0.974319i | \(-0.427705\pi\) |
−0.731198 | + | 0.682165i | \(0.761038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 91.5000 | − | 52.8275i | 1.06395 | − | 0.614274i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.50000 | + | 12.9904i | −0.0852273 | + | 0.147618i | ||||
\(89\) | 124.708i | 1.40121i | 0.713549 | + | 0.700605i | \(0.247086\pi\) | ||||
−0.713549 | + | 0.700605i | \(0.752914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.0879121 | ||||||||
\(92\) | 24.0000 | + | 13.8564i | 0.260870 | + | 0.150613i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 42.0000 | + | 72.7461i | 0.446809 | + | 0.773895i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −57.5000 | + | 99.5929i | −0.592784 | + | 1.02673i | 0.401072 | + | 0.916047i | \(0.368638\pi\) |
−0.993856 | + | 0.110685i | \(0.964696\pi\) | |||||||
\(98\) | − | 77.9423i | − | 0.795329i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −39.0000 | − | 22.5167i | −0.386139 | − | 0.222937i | 0.294347 | − | 0.955699i | \(-0.404898\pi\) |
−0.680486 | + | 0.732761i | \(0.738231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.0000 | − | 34.6410i | −0.194175 | − | 0.336321i | 0.752455 | − | 0.658644i | \(-0.228870\pi\) |
−0.946630 | + | 0.322323i | \(0.895536\pi\) | |||||||
\(104\) | 30.0000 | − | 17.3205i | 0.288462 | − | 0.166543i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 140.296i | 1.31118i | 0.755118 | + | 0.655589i | \(0.227580\pi\) | ||||
−0.755118 | + | 0.655589i | \(0.772420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −52.0000 | −0.477064 | −0.238532 | − | 0.971135i | \(-0.576666\pi\) | ||||
−0.238532 | + | 0.971135i | \(0.576666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.0000 | − | 19.0526i | −0.0982143 | − | 0.170112i | ||||
\(113\) | −78.0000 | + | 45.0333i | −0.690265 | + | 0.398525i | −0.803711 | − | 0.595019i | \(-0.797144\pi\) |
0.113446 | + | 0.993544i | \(0.463811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 45.0333i | 0.388218i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 87.0000 | 0.737288 | ||||||||
\(119\) | −27.0000 | − | 15.5885i | −0.226891 | − | 0.130995i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.0000 | − | 102.191i | −0.487603 | − | 0.844554i | ||||
\(122\) | 84.0000 | − | 48.4974i | 0.688525 | − | 0.397520i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.0000 | + | 27.7128i | −0.129032 | + | 0.223490i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 0.125984 | 0.0629921 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629921 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(128\) | 52.5000 | + | 30.3109i | 0.410156 | + | 0.236804i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −138.000 | + | 79.6743i | −1.05344 | + | 0.608201i | −0.923609 | − | 0.383336i | \(-0.874775\pi\) |
−0.129826 | + | 0.991537i | \(0.541442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.0000 | − | 19.0526i | 0.0827068 | − | 0.143252i | ||||
\(134\) | 53.6936i | 0.400698i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 135.000 | 0.992647 | ||||||||
\(137\) | −163.500 | − | 94.3968i | −1.19343 | − | 0.689028i | −0.234348 | − | 0.972153i | \(-0.575295\pi\) |
−0.959083 | + | 0.283125i | \(0.908629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | − | 4.33013i | −0.0179856 | − | 0.0311520i | 0.856893 | − | 0.515495i | \(-0.172392\pi\) |
−0.874878 | + | 0.484343i | \(0.839059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −27.0000 | + | 46.7654i | −0.190141 | + | 0.329334i | ||||
\(143\) | − | 6.92820i | − | 0.0484490i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 97.5000 | + | 56.2917i | 0.667808 | + | 0.385559i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.0000 | − | 29.4449i | −0.114865 | − | 0.198952i | ||||
\(149\) | 132.000 | − | 76.2102i | 0.885906 | − | 0.511478i | 0.0133049 | − | 0.999911i | \(-0.495765\pi\) |
0.872601 | + | 0.488433i | \(0.162431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | + | 17.3205i | −0.0662252 | + | 0.114705i | −0.897237 | − | 0.441550i | \(-0.854429\pi\) |
0.831012 | + | 0.556255i | \(0.187762\pi\) | |||||||
\(152\) | 95.2628i | 0.626729i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | −0.0389610 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | − | 34.6410i | −0.127389 | − | 0.220643i | 0.795276 | − | 0.606248i | \(-0.207326\pi\) |
−0.922664 | + | 0.385605i | \(0.873993\pi\) | |||||||
\(158\) | 57.0000 | − | 32.9090i | 0.360759 | − | 0.208285i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 55.4256i | 0.344259i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 106.000 | 0.650307 | 0.325153 | − | 0.945661i | \(-0.394584\pi\) | ||||
0.325153 | + | 0.945661i | \(0.394584\pi\) | |||||||
\(164\) | −10.5000 | − | 6.06218i | −0.0640244 | − | 0.0369645i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 42.0000 | + | 72.7461i | 0.253012 | + | 0.438230i | ||||
\(167\) | 165.000 | − | 95.2628i | 0.988024 | − | 0.570436i | 0.0833409 | − | 0.996521i | \(-0.473441\pi\) |
0.904683 | + | 0.426085i | \(0.140108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 76.5000 | − | 132.502i | 0.452663 | − | 0.784035i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 61.0000 | 0.354651 | ||||||||
\(173\) | 201.000 | + | 116.047i | 1.16185 | + | 0.670794i | 0.951747 | − | 0.306885i | \(-0.0992867\pi\) |
0.210103 | + | 0.977679i | \(0.432620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.5000 | − | 9.52628i | 0.0937500 | − | 0.0541266i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 108.000 | − | 187.061i | 0.606742 | − | 1.05091i | ||||
\(179\) | 62.3538i | 0.348345i | 0.984715 | + | 0.174173i | \(0.0557251\pi\) | ||||
−0.984715 | + | 0.174173i | \(0.944275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −232.000 | −1.28177 | −0.640884 | − | 0.767638i | \(-0.721432\pi\) | ||||
−0.640884 | + | 0.767638i | \(0.721432\pi\) | |||||||
\(182\) | 12.0000 | + | 6.92820i | 0.0659341 | + | 0.0380671i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −120.000 | − | 207.846i | −0.652174 | − | 1.12960i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5000 | − | 23.3827i | 0.0721925 | − | 0.125041i | ||||
\(188\) | 48.4974i | 0.257965i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −201.000 | − | 116.047i | −1.05236 | − | 0.607578i | −0.129048 | − | 0.991638i | \(-0.541192\pi\) |
−0.923308 | + | 0.384060i | \(0.874525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −132.500 | − | 229.497i | −0.686528 | − | 1.18910i | −0.972954 | − | 0.231000i | \(-0.925800\pi\) |
0.286425 | − | 0.958103i | \(-0.407533\pi\) | |||||||
\(194\) | 172.500 | − | 99.5929i | 0.889175 | − | 0.513366i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.5000 | − | 38.9711i | 0.114796 | − | 0.198832i | ||||
\(197\) | − | 124.708i | − | 0.633034i | −0.948587 | − | 0.316517i | \(-0.897487\pi\) | ||
0.948587 | − | 0.316517i | \(-0.102513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 290.000 | 1.45729 | 0.728643 | − | 0.684893i | \(-0.240151\pi\) | ||||
0.728643 | + | 0.684893i | \(0.240151\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.0000 | + | 67.5500i | 0.193069 | + | 0.334406i | ||||
\(203\) | −78.0000 | + | 45.0333i | −0.384236 | + | 0.221839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 69.2820i | 0.336321i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −44.0000 | −0.211538 | ||||||||
\(209\) | 16.5000 | + | 9.52628i | 0.0789474 | + | 0.0455803i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 47.0000 | + | 81.4064i | 0.222749 | + | 0.385812i | 0.955642 | − | 0.294532i | \(-0.0951637\pi\) |
−0.732893 | + | 0.680344i | \(0.761830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 121.500 | − | 210.444i | 0.567757 | − | 0.983384i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −64.0000 | −0.294931 | ||||||||
\(218\) | 78.0000 | + | 45.0333i | 0.357798 | + | 0.206575i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −54.0000 | + | 31.1769i | −0.244344 | + | 0.141072i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0000 | + | 45.0333i | −0.116592 | + | 0.201943i | −0.918415 | − | 0.395618i | \(-0.870530\pi\) |
0.801823 | + | 0.597562i | \(0.203864\pi\) | |||||||
\(224\) | − | 31.1769i | − | 0.139183i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 156.000 | 0.690265 | ||||||||
\(227\) | −163.500 | − | 94.3968i | −0.720264 | − | 0.415845i | 0.0945856 | − | 0.995517i | \(-0.469847\pi\) |
−0.814850 | + | 0.579672i | \(0.803181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −133.000 | − | 230.363i | −0.580786 | − | 1.00595i | −0.995386 | − | 0.0959473i | \(-0.969412\pi\) |
0.414600 | − | 0.910004i | \(-0.363921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 195.000 | − | 337.750i | 0.840517 | − | 1.45582i | ||||
\(233\) | − | 202.650i | − | 0.869742i | −0.900493 | − | 0.434871i | \(-0.856794\pi\) | ||
0.900493 | − | 0.434871i | \(-0.143206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.5000 | + | 25.1147i | 0.184322 | + | 0.106418i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 27.0000 | + | 46.7654i | 0.113445 | + | 0.196493i | ||||
\(239\) | 348.000 | − | 200.918i | 1.45607 | − | 0.840661i | 0.457252 | − | 0.889337i | \(-0.348834\pi\) |
0.998815 | + | 0.0486764i | \(0.0155003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −59.5000 | + | 103.057i | −0.246888 | + | 0.427623i | −0.962661 | − | 0.270711i | \(-0.912741\pi\) |
0.715773 | + | 0.698333i | \(0.246075\pi\) | |||||||
\(242\) | 204.382i | 0.844554i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 56.0000 | 0.229508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.0000 | − | 38.1051i | −0.0890688 | − | 0.154272i | ||||
\(248\) | 240.000 | − | 138.564i | 0.967742 | − | 0.558726i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 389.711i | − | 1.55264i | −0.630342 | − | 0.776318i | \(-0.717085\pi\) | ||
0.630342 | − | 0.776318i | \(-0.282915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −48.0000 | −0.189723 | ||||||||
\(254\) | −24.0000 | − | 13.8564i | −0.0944882 | − | 0.0545528i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 89.5000 | + | 155.019i | 0.349609 | + | 0.605541i | ||||
\(257\) | 151.500 | − | 87.4686i | 0.589494 | − | 0.340345i | −0.175403 | − | 0.984497i | \(-0.556123\pi\) |
0.764897 | + | 0.644152i | \(0.222790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.0000 | − | 58.8897i | 0.131274 | − | 0.227373i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 276.000 | 1.05344 | ||||||||
\(263\) | 39.0000 | + | 22.5167i | 0.148289 | + | 0.0856147i | 0.572309 | − | 0.820038i | \(-0.306048\pi\) |
−0.424020 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −33.0000 | + | 19.0526i | −0.124060 | + | 0.0716262i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.5000 | + | 26.8468i | −0.0578358 | + | 0.100175i | ||||
\(269\) | − | 187.061i | − | 0.695396i | −0.937607 | − | 0.347698i | \(-0.886963\pi\) | ||
0.937607 | − | 0.347698i | \(-0.113037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −268.000 | −0.988930 | −0.494465 | − | 0.869198i | \(-0.664636\pi\) | ||||
−0.494465 | + | 0.869198i | \(0.664636\pi\) | |||||||
\(272\) | −148.500 | − | 85.7365i | −0.545956 | − | 0.315208i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 163.500 | + | 283.190i | 0.596715 | + | 1.03354i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0000 | − | 48.4974i | 0.101083 | − | 0.175081i | −0.811048 | − | 0.584979i | \(-0.801103\pi\) |
0.912131 | + | 0.409899i | \(0.134436\pi\) | |||||||
\(278\) | 8.66025i | 0.0311520i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 42.0000 | + | 24.2487i | 0.149466 | + | 0.0862943i | 0.572868 | − | 0.819648i | \(-0.305831\pi\) |
−0.423402 | + | 0.905942i | \(0.639164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 187.000 | + | 323.894i | 0.660777 | + | 1.14450i | 0.980412 | + | 0.196959i | \(0.0631066\pi\) |
−0.319634 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(284\) | −27.0000 | + | 15.5885i | −0.0950704 | + | 0.0548889i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | + | 10.3923i | −0.0209790 | + | 0.0363367i | ||||
\(287\) | − | 24.2487i | − | 0.0844903i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.0000 | 0.159170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32.5000 | + | 56.2917i | 0.111301 | + | 0.192780i | ||||
\(293\) | 219.000 | − | 126.440i | 0.747440 | − | 0.431535i | −0.0773280 | − | 0.997006i | \(-0.524639\pi\) |
0.824768 | + | 0.565471i | \(0.191306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 294.449i | 0.994759i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −264.000 | −0.885906 | ||||||||
\(299\) | 96.0000 | + | 55.4256i | 0.321070 | + | 0.185370i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61.0000 | + | 105.655i | 0.202658 | + | 0.351014i | ||||
\(302\) | 30.0000 | − | 17.3205i | 0.0993377 | − | 0.0573527i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 60.5000 | − | 104.789i | 0.199013 | − | 0.344701i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −533.000 | −1.73616 | −0.868078 | − | 0.496428i | \(-0.834645\pi\) | ||||
−0.868078 | + | 0.496428i | \(0.834645\pi\) | |||||||
\(308\) | −3.00000 | − | 1.73205i | −0.00974026 | − | 0.00562354i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 213.000 | − | 122.976i | 0.684887 | − | 0.395420i | −0.116806 | − | 0.993155i | \(-0.537266\pi\) |
0.801694 | + | 0.597735i | \(0.203932\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 77.5000 | − | 134.234i | 0.247604 | − | 0.428862i | −0.715257 | − | 0.698862i | \(-0.753690\pi\) |
0.962860 | + | 0.269999i | \(0.0870235\pi\) | |||||||
\(314\) | 69.2820i | 0.220643i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.0000 | 0.120253 | ||||||||
\(317\) | −42.0000 | − | 24.2487i | −0.132492 | − | 0.0764944i | 0.432289 | − | 0.901735i | \(-0.357706\pi\) |
−0.564781 | + | 0.825241i | \(0.691039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.0000 | − | 67.5500i | −0.122257 | − | 0.211755i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 48.0000 | − | 83.1384i | 0.149068 | − | 0.258194i | ||||
\(323\) | − | 171.473i | − | 0.530876i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −159.000 | − | 91.7987i | −0.487730 | − | 0.281591i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 52.5000 | + | 90.9327i | 0.160061 | + | 0.277234i | ||||
\(329\) | −84.0000 | + | 48.4974i | −0.255319 | + | 0.147409i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | + | 1.73205i | −0.00302115 | + | 0.00523278i | −0.867532 | − | 0.497381i | \(-0.834295\pi\) |
0.864511 | + | 0.502614i | \(0.167628\pi\) | |||||||
\(332\) | 48.4974i | 0.146077i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −330.000 | −0.988024 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 38.5000 | + | 66.6840i | 0.114243 | + | 0.197875i | 0.917477 | − | 0.397789i | \(-0.130222\pi\) |
−0.803234 | + | 0.595664i | \(0.796889\pi\) | |||||||
\(338\) | −229.500 | + | 132.502i | −0.678994 | + | 0.392017i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 55.4256i | − | 0.162538i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 188.000 | 0.548105 | ||||||||
\(344\) | −457.500 | − | 264.138i | −1.32994 | − | 0.767842i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −201.000 | − | 348.142i | −0.580925 | − | 1.00619i | ||||
\(347\) | 97.5000 | − | 56.2917i | 0.280980 | − | 0.162224i | −0.352887 | − | 0.935666i | \(-0.614800\pi\) |
0.633867 | + | 0.773442i | \(0.281467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −208.000 | + | 360.267i | −0.595989 | + | 1.03228i | 0.397418 | + | 0.917638i | \(0.369906\pi\) |
−0.993407 | + | 0.114645i | \(0.963427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.0000 | 0.0767045 | ||||||||
\(353\) | −1.50000 | − | 0.866025i | −0.00424929 | − | 0.00245333i | 0.497874 | − | 0.867249i | \(-0.334114\pi\) |
−0.502123 | + | 0.864796i | \(0.667448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 108.000 | − | 62.3538i | 0.303371 | − | 0.175151i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 54.0000 | − | 93.5307i | 0.150838 | − | 0.261259i | ||||
\(359\) | 592.361i | 1.65003i | 0.565110 | + | 0.825016i | \(0.308834\pi\) | ||||
−0.565110 | + | 0.825016i | \(0.691166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.000 | −0.664820 | ||||||||
\(362\) | 348.000 | + | 200.918i | 0.961326 | + | 0.555022i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | + | 6.92820i | 0.0109890 | + | 0.0190335i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −179.000 | + | 310.037i | −0.487738 | + | 0.844788i | −0.999901 | − | 0.0141011i | \(-0.995511\pi\) |
0.512162 | + | 0.858889i | \(0.328845\pi\) | |||||||
\(368\) | 304.841i | 0.828372i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −290.000 | − | 502.295i | −0.777480 | − | 1.34663i | −0.933390 | − | 0.358863i | \(-0.883164\pi\) |
0.155910 | − | 0.987771i | \(-0.450169\pi\) | |||||||
\(374\) | −40.5000 | + | 23.3827i | −0.108289 | + | 0.0625206i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 210.000 | − | 363.731i | 0.558511 | − | 0.967369i | ||||
\(377\) | 180.133i | 0.477807i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 83.0000 | 0.218997 | 0.109499 | − | 0.993987i | \(-0.465075\pi\) | ||||
0.109499 | + | 0.993987i | \(0.465075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 201.000 | + | 348.142i | 0.526178 | + | 0.911367i | ||||
\(383\) | −483.000 | + | 278.860i | −1.26110 | + | 0.728094i | −0.973287 | − | 0.229593i | \(-0.926260\pi\) |
−0.287810 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 458.993i | 1.18910i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 115.000 | 0.296392 | ||||||||
\(389\) | 447.000 | + | 258.076i | 1.14910 | + | 0.663433i | 0.948668 | − | 0.316274i | \(-0.102432\pi\) |
0.200432 | + | 0.979708i | \(0.435765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.000 | + | 374.123i | 0.552430 | + | 0.956836i | ||||
\(392\) | −337.500 | + | 194.856i | −0.860969 | + | 0.497081i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −108.000 | + | 187.061i | −0.274112 | + | 0.474775i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −362.000 | −0.911839 | −0.455919 | − | 0.890021i | \(-0.650689\pi\) | ||||
−0.455919 | + | 0.890021i | \(0.650689\pi\) | |||||||
\(398\) | −435.000 | − | 251.147i | −1.09296 | − | 0.631024i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −340.500 | + | 196.588i | −0.849127 | + | 0.490244i | −0.860356 | − | 0.509693i | \(-0.829759\pi\) |
0.0112291 | + | 0.999937i | \(0.496426\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −64.0000 | + | 110.851i | −0.158809 | + | 0.275065i | ||||
\(404\) | 45.0333i | 0.111469i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 156.000 | 0.384236 | ||||||||
\(407\) | 51.0000 | + | 29.4449i | 0.125307 | + | 0.0723461i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −110.500 | − | 191.392i | −0.270171 | − | 0.467950i | 0.698734 | − | 0.715381i | \(-0.253747\pi\) |
−0.968905 | + | 0.247431i | \(0.920414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.0000 | + | 34.6410i | −0.0485437 | + | 0.0840801i | ||||
\(413\) | 100.459i | 0.243242i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −54.0000 | − | 31.1769i | −0.129808 | − | 0.0749445i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.5000 | − | 28.5788i | −0.0394737 | − | 0.0683704i | ||||
\(419\) | −678.000 | + | 391.443i | −1.61814 | + | 0.934233i | −0.630737 | + | 0.775997i | \(0.717247\pi\) |
−0.987401 | + | 0.158236i | \(0.949419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 341.000 | − | 590.629i | 0.809976 | − | 1.40292i | −0.102903 | − | 0.994691i | \(-0.532813\pi\) |
0.912880 | − | 0.408229i | \(-0.133853\pi\) | |||||||
\(422\) | − | 162.813i | − | 0.385812i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.0000 | + | 96.9948i | 0.131148 | + | 0.227154i | ||||
\(428\) | 121.500 | − | 70.1481i | 0.283879 | − | 0.163897i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 280.592i | − | 0.651026i | −0.945538 | − | 0.325513i | \(-0.894463\pi\) | ||
0.945538 | − | 0.325513i | \(-0.105537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 295.000 | 0.681293 | 0.340647 | − | 0.940191i | \(-0.389354\pi\) | ||||
0.340647 | + | 0.940191i | \(0.389354\pi\) | |||||||
\(434\) | 96.0000 | + | 55.4256i | 0.221198 | + | 0.127709i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.0000 | + | 45.0333i | 0.0596330 | + | 0.103287i | ||||
\(437\) | −264.000 | + | 152.420i | −0.604119 | + | 0.348788i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −406.000 | + | 703.213i | −0.924829 | + | 1.60185i | −0.132993 | + | 0.991117i | \(0.542459\pi\) |
−0.791836 | + | 0.610734i | \(0.790874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 108.000 | 0.244344 | ||||||||
\(443\) | 79.5000 | + | 45.8993i | 0.179458 | + | 0.103610i | 0.587038 | − | 0.809559i | \(-0.300294\pi\) |
−0.407580 | + | 0.913170i | \(0.633627\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 78.0000 | − | 45.0333i | 0.174888 | − | 0.100972i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −71.0000 | + | 122.976i | −0.158482 | + | 0.274499i | ||||
\(449\) | − | 639.127i | − | 1.42344i | −0.702461 | − | 0.711722i | \(-0.747915\pi\) | ||
0.702461 | − | 0.711722i | \(-0.252085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0000 | 0.0465632 | ||||||||
\(452\) | 78.0000 | + | 45.0333i | 0.172566 | + | 0.0996312i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 163.500 | + | 283.190i | 0.360132 | + | 0.623767i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.5000 | − | 56.2917i | 0.0711160 | − | 0.123176i | −0.828275 | − | 0.560322i | \(-0.810677\pi\) |
0.899391 | + | 0.437146i | \(0.144011\pi\) | |||||||
\(458\) | 460.726i | 1.00595i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 690.000 | + | 398.372i | 1.49675 | + | 0.864147i | 0.999993 | − | 0.00374501i | \(-0.00119208\pi\) |
0.496753 | + | 0.867892i | \(0.334525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 367.000 | + | 635.663i | 0.792657 | + | 1.37292i | 0.924317 | + | 0.381627i | \(0.124636\pi\) |
−0.131660 | + | 0.991295i | \(0.542031\pi\) | |||||||
\(464\) | −429.000 | + | 247.683i | −0.924569 | + | 0.533800i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −175.500 | + | 303.975i | −0.376609 | + | 0.652307i | ||||
\(467\) | 202.650i | 0.433940i | 0.976178 | + | 0.216970i | \(0.0696174\pi\) | ||||
−0.976178 | + | 0.216970i | \(0.930383\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −62.0000 | −0.132196 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −217.500 | − | 376.721i | −0.460805 | − | 0.798138i | ||||
\(473\) | −91.5000 | + | 52.8275i | −0.193446 | + | 0.111686i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 31.1769i | 0.0654977i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −696.000 | −1.45607 | ||||||||
\(479\) | −525.000 | − | 303.109i | −1.09603 | − | 0.632795i | −0.160857 | − | 0.986978i | \(-0.551426\pi\) |
−0.935176 | + | 0.354183i | \(0.884759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −68.0000 | − | 117.779i | −0.141372 | − | 0.244864i | ||||
\(482\) | 178.500 | − | 103.057i | 0.370332 | − | 0.213811i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −59.0000 | + | 102.191i | −0.121901 | + | 0.211138i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 106.000 | 0.217659 | 0.108830 | − | 0.994060i | \(-0.465290\pi\) | ||||
0.108830 | + | 0.994060i | \(0.465290\pi\) | |||||||
\(488\) | −420.000 | − | 242.487i | −0.860656 | − | 0.496900i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 199.500 | − | 115.181i | 0.406314 | − | 0.234585i | −0.282891 | − | 0.959152i | \(-0.591293\pi\) |
0.689205 | + | 0.724567i | \(0.257960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −351.000 | + | 607.950i | −0.711968 | + | 1.23316i | ||||
\(494\) | 76.2102i | 0.154272i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −352.000 | −0.709677 | ||||||||
\(497\) | −54.0000 | − | 31.1769i | −0.108652 | − | 0.0627302i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 393.500 | + | 681.562i | 0.788577 | + | 1.36586i | 0.926839 | + | 0.375460i | \(0.122515\pi\) |
−0.138261 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −337.500 | + | 584.567i | −0.672311 | + | 1.16448i | ||||
\(503\) | − | 623.538i | − | 1.23964i | −0.784745 | − | 0.619819i | \(-0.787206\pi\) | ||
0.784745 | − | 0.619819i | \(-0.212794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 72.0000 | + | 41.5692i | 0.142292 | + | 0.0821526i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | − | 13.8564i | −0.0157480 | − | 0.0272764i | ||||
\(509\) | 186.000 | − | 107.387i | 0.365422 | − | 0.210977i | −0.306034 | − | 0.952020i | \(-0.599002\pi\) |
0.671457 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −65.0000 | + | 112.583i | −0.127202 | + | 0.220320i | ||||
\(512\) | − | 552.524i | − | 1.07915i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −303.000 | −0.589494 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.0000 | − | 72.7461i | −0.0812379 | − | 0.140708i | ||||
\(518\) | −102.000 | + | 58.8897i | −0.196911 | + | 0.113687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 202.650i | − | 0.388963i | −0.980906 | − | 0.194482i | \(-0.937698\pi\) | ||
0.980906 | − | 0.194482i | \(-0.0623025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 250.000 | 0.478011 | 0.239006 | − | 0.971018i | \(-0.423179\pi\) | ||||
0.239006 | + | 0.971018i | \(0.423179\pi\) | |||||||
\(524\) | 138.000 | + | 79.6743i | 0.263359 | + | 0.152050i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.0000 | − | 67.5500i | −0.0741445 | − | 0.128422i | ||||
\(527\) | −432.000 | + | 249.415i | −0.819734 | + | 0.473274i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 119.500 | − | 206.980i | 0.225898 | − | 0.391267i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.0000 | −0.0413534 | ||||||||
\(533\) | −42.0000 | − | 24.2487i | −0.0787992 | − | 0.0454948i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 232.500 | − | 134.234i | 0.433769 | − | 0.250436i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −162.000 | + | 280.592i | −0.301115 | + | 0.521547i | ||||
\(539\) | 77.9423i | 0.144605i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 650.000 | 1.20148 | 0.600739 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600739 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(542\) | 402.000 | + | 232.095i | 0.741697 | + | 0.428219i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −121.500 | − | 210.444i | −0.223346 | − | 0.386846i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 311.500 | − | 539.534i | 0.569470 | − | 0.986351i | −0.427149 | − | 0.904181i | \(-0.640482\pi\) |
0.996618 | − | 0.0821692i | \(-0.0261848\pi\) | |||||||
\(548\) | 188.794i | 0.344514i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −429.000 | − | 247.683i | −0.778584 | − | 0.449516i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.0000 | + | 65.8179i | 0.0687161 | + | 0.119020i | ||||
\(554\) | −84.0000 | + | 48.4974i | −0.151625 | + | 0.0875405i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | + | 4.33013i | −0.00449640 | + | 0.00778800i | ||||
\(557\) | − | 530.008i | − | 0.951540i | −0.879570 | − | 0.475770i | \(-0.842170\pi\) | ||
0.879570 | − | 0.475770i | \(-0.157830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 244.000 | 0.436494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −42.0000 | − | 72.7461i | −0.0747331 | − | 0.129442i | ||||
\(563\) | 97.5000 | − | 56.2917i | 0.173179 | − | 0.0999852i | −0.410905 | − | 0.911678i | \(-0.634787\pi\) |
0.584084 | + | 0.811693i | \(0.301454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 647.787i | − | 1.14450i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 270.000 | 0.475352 | ||||||||
\(569\) | −565.500 | − | 326.492i | −0.993849 | − | 0.573799i | −0.0874263 | − | 0.996171i | \(-0.527864\pi\) |
−0.906423 | + | 0.422372i | \(0.861198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −272.500 | − | 471.984i | −0.477233 | − | 0.826592i | 0.522427 | − | 0.852684i | \(-0.325027\pi\) |
−0.999660 | + | 0.0260926i | \(0.991694\pi\) | |||||||
\(572\) | −6.00000 | + | 3.46410i | −0.0104895 | + | 0.00605612i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.0000 | + | 36.3731i | −0.0365854 | + | 0.0633677i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 871.000 | 1.50953 | 0.754766 | − | 0.655994i | \(-0.227750\pi\) | ||||
0.754766 | + | 0.655994i | \(0.227750\pi\) | |||||||
\(578\) | −69.0000 | − | 39.8372i | −0.119377 | − | 0.0689224i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −84.0000 | + | 48.4974i | −0.144578 | + | 0.0834723i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 562.917i | − | 0.963898i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −438.000 | −0.747440 | ||||||||
\(587\) | −1.50000 | − | 0.866025i | −0.00255537 | − | 0.00147534i | 0.498722 | − | 0.866762i | \(-0.333803\pi\) |
−0.501277 | + | 0.865287i | \(0.667136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −176.000 | − | 304.841i | −0.298812 | − | 0.517557i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 187.000 | − | 323.894i | 0.315878 | − | 0.547117i | ||||
\(593\) | − | 187.061i | − | 0.315449i | −0.987483 | − | 0.157725i | \(-0.949584\pi\) | ||
0.987483 | − | 0.157725i | \(-0.0504159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −132.000 | − | 76.2102i | −0.221477 | − | 0.127870i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −96.0000 | − | 166.277i | −0.160535 | − | 0.278055i | ||||
\(599\) | −489.000 | + | 282.324i | −0.816361 | + | 0.471326i | −0.849160 | − | 0.528136i | \(-0.822891\pi\) |
0.0327992 | + | 0.999462i | \(0.489558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −230.500 | + | 399.238i | −0.383527 | + | 0.664289i | −0.991564 | − | 0.129620i | \(-0.958624\pi\) |
0.608036 | + | 0.793909i | \(0.291958\pi\) | |||||||
\(602\) | − | 211.310i | − | 0.351014i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.0331126 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −56.0000 | − | 96.9948i | −0.0922570 | − | 0.159794i | 0.816204 | − | 0.577765i | \(-0.196075\pi\) |
−0.908461 | + | 0.417971i | \(0.862741\pi\) | |||||||
\(608\) | 148.500 | − | 85.7365i | 0.244243 | − | 0.141014i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 193.990i | 0.317495i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −902.000 | −1.47145 | −0.735726 | − | 0.677279i | \(-0.763159\pi\) | ||||
−0.735726 | + | 0.677279i | \(0.763159\pi\) | |||||||
\(614\) | 799.500 | + | 461.592i | 1.30212 | + | 0.751778i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.0000 | + | 25.9808i | 0.0243506 | + | 0.0421766i | ||||
\(617\) | −307.500 | + | 177.535i | −0.498379 | + | 0.287739i | −0.728044 | − | 0.685530i | \(-0.759570\pi\) |
0.229665 | + | 0.973270i | \(0.426237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 399.500 | − | 691.954i | 0.645396 | − | 1.11786i | −0.338814 | − | 0.940853i | \(-0.610026\pi\) |
0.984210 | − | 0.177005i | \(-0.0566409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −426.000 | −0.684887 | ||||||||
\(623\) | 216.000 | + | 124.708i | 0.346709 | + | 0.200173i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −232.500 | + | 134.234i | −0.371406 | + | 0.214431i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.0000 | + | 34.6410i | −0.0318471 | + | 0.0551609i | ||||
\(629\) | − | 530.008i | − | 0.842619i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 830.000 | 1.31537 | 0.657686 | − | 0.753292i | \(-0.271535\pi\) | ||||
0.657686 | + | 0.753292i | \(0.271535\pi\) | |||||||
\(632\) | −285.000 | − | 164.545i | −0.450949 | − | 0.260356i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 42.0000 | + | 72.7461i | 0.0662461 | + | 0.114742i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 90.0000 | − | 155.885i | 0.141287 | − | 0.244717i | ||||
\(638\) | 135.100i | 0.211755i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 325.500 | + | 187.928i | 0.507800 | + | 0.293179i | 0.731929 | − | 0.681381i | \(-0.238620\pi\) |
−0.224129 | + | 0.974560i | \(0.571954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.50000 | − | 11.2583i | −0.0101089 | − | 0.0175091i | 0.860927 | − | 0.508729i | \(-0.169884\pi\) |
−0.871036 | + | 0.491220i | \(0.836551\pi\) | |||||||
\(644\) | 48.0000 | − | 27.7128i | 0.0745342 | − | 0.0430323i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −148.500 | + | 257.210i | −0.229876 | + | 0.398157i | ||||
\(647\) | − | 467.654i | − | 0.722803i | −0.932410 | − | 0.361402i | \(-0.882298\pi\) | ||
0.932410 | − | 0.361402i | \(-0.117702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −87.0000 | −0.134052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −53.0000 | − | 91.7987i | −0.0812883 | − | 0.140796i | ||||
\(653\) | 327.000 | − | 188.794i | 0.500766 | − | 0.289117i | −0.228264 | − | 0.973599i | \(-0.573305\pi\) |
0.729030 | + | 0.684482i | \(0.239972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 133.368i | − | 0.203305i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 168.000 | 0.255319 | ||||||||
\(659\) | 852.000 | + | 491.902i | 1.29287 | + | 0.746438i | 0.979162 | − | 0.203082i | \(-0.0650959\pi\) |
0.313706 | + | 0.949520i | \(0.398429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 191.000 | + | 330.822i | 0.288956 | + | 0.500487i | 0.973561 | − | 0.228428i | \(-0.0733585\pi\) |
−0.684605 | + | 0.728915i | \(0.740025\pi\) | |||||||
\(662\) | 3.00000 | − | 1.73205i | 0.00453172 | − | 0.00261639i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 210.000 | − | 363.731i | 0.316265 | − | 0.547787i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1248.00 | 1.87106 | ||||||||
\(668\) | −165.000 | − | 95.2628i | −0.247006 | − | 0.142609i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −84.0000 | + | 48.4974i | −0.125186 | + | 0.0722763i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 289.000 | − | 500.563i | 0.429421 | − | 0.743778i | −0.567401 | − | 0.823441i | \(-0.692051\pi\) |
0.996822 | + | 0.0796633i | \(0.0253845\pi\) | |||||||
\(674\) | − | 133.368i | − | 0.197875i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −153.000 | −0.226331 | ||||||||
\(677\) | 606.000 | + | 349.874i | 0.895126 | + | 0.516801i | 0.875616 | − | 0.483009i | \(-0.160456\pi\) |
0.0195100 | + | 0.999810i | \(0.493789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 115.000 | + | 199.186i | 0.169367 | + | 0.293352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −48.0000 | + | 83.1384i | −0.0703812 | + | 0.121904i | ||||
\(683\) | 1044.43i | 1.52918i | 0.644520 | + | 0.764588i | \(0.277057\pi\) | ||||
−0.644520 | + | 0.764588i | \(0.722943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −282.000 | − | 162.813i | −0.411079 | − | 0.237336i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 335.500 | + | 581.103i | 0.487645 | + | 0.844627i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −91.0000 | + | 157.617i | −0.131693 | + | 0.228099i | −0.924329 | − | 0.381596i | \(-0.875375\pi\) |
0.792636 | + | 0.609695i | \(0.208708\pi\) | |||||||
\(692\) | − | 232.095i | − | 0.335397i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −195.000 | −0.280980 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −94.5000 | − | 163.679i | −0.135581 | − | 0.234833i | ||||
\(698\) | 624.000 | − | 360.267i | 0.893983 | − | 0.516141i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 374.000 | 0.532006 | ||||||||
\(704\) | −106.500 | − | 61.4878i | −0.151278 | − | 0.0873406i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.50000 | + | 2.59808i | 0.00212465 | + | 0.00367999i | ||||
\(707\) | −78.0000 | + | 45.0333i | −0.110325 | + | 0.0636964i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 350.000 | − | 606.218i | 0.493653 | − | 0.855032i | −0.506320 | − | 0.862346i | \(-0.668995\pi\) |
0.999973 | + | 0.00731341i | \(0.00232795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1080.00 | −1.51685 | ||||||||
\(713\) | 768.000 | + | 443.405i | 1.07714 | + | 0.621886i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 54.0000 | − | 31.1769i | 0.0754190 | − | 0.0435432i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 513.000 | − | 888.542i | 0.714485 | − | 1.23752i | ||||
\(719\) | − | 592.361i | − | 0.823868i | −0.911214 | − | 0.411934i | \(-0.864853\pi\) | ||
0.911214 | − | 0.411934i | \(-0.135147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.0000 | −0.110957 | ||||||||
\(722\) | 360.000 | + | 207.846i | 0.498615 | + | 0.287875i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 116.000 | + | 200.918i | 0.160221 | + | 0.277511i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −332.000 | + | 575.041i | −0.456671 | + | 0.790978i | −0.998783 | − | 0.0493289i | \(-0.984292\pi\) |
0.542111 | + | 0.840307i | \(0.317625\pi\) | |||||||
\(728\) | − | 69.2820i | − | 0.0951676i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 823.500 | + | 475.448i | 1.12654 | + | 0.650408i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −335.000 | − | 580.237i | −0.457026 | − | 0.791592i | 0.541776 | − | 0.840523i | \(-0.317752\pi\) |
−0.998802 | + | 0.0489306i | \(0.984419\pi\) | |||||||
\(734\) | 537.000 | − | 310.037i | 0.731608 | − | 0.422394i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −216.000 | + | 374.123i | −0.293478 | + | 0.508319i | ||||
\(737\) | − | 53.6936i | − | 0.0728542i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 317.000 | 0.428958 | 0.214479 | − | 0.976729i | \(-0.431195\pi\) | ||||
0.214479 | + | 0.976729i | \(0.431195\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −537.000 | + | 310.037i | −0.722746 | + | 0.417277i | −0.815762 | − | 0.578387i | \(-0.803682\pi\) |
0.0930168 | + | 0.995665i | \(0.470349\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1004.59i | 1.34663i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.0000 | −0.0360963 | ||||||||
\(749\) | 243.000 | + | 140.296i | 0.324433 | + | 0.187311i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −655.000 | − | 1134.49i | −0.872170 | − | 1.51064i | −0.859747 | − | 0.510721i | \(-0.829379\pi\) |
−0.0124237 | − | 0.999923i | \(-0.503955\pi\) | |||||||
\(752\) | −462.000 | + | 266.736i | −0.614362 | + | 0.354702i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 156.000 | − | 270.200i | 0.206897 | − | 0.358355i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −218.000 | −0.287979 | −0.143989 | − | 0.989579i | \(-0.545993\pi\) | ||||
−0.143989 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(758\) | −124.500 | − | 71.8801i | −0.164248 | − | 0.0948286i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −570.000 | + | 329.090i | −0.749014 | + | 0.432444i | −0.825338 | − | 0.564639i | \(-0.809015\pi\) |
0.0763232 | + | 0.997083i | \(0.475682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.0000 | + | 90.0666i | −0.0681520 | + | 0.118043i | ||||
\(764\) | 232.095i | 0.303789i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 966.000 | 1.26110 | ||||||||
\(767\) | 174.000 | + | 100.459i | 0.226858 | + | 0.130976i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −511.000 | − | 885.078i | −0.664499 | − | 1.15095i | −0.979421 | − | 0.201829i | \(-0.935312\pi\) |
0.314921 | − | 0.949118i | \(-0.398022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −132.500 | + | 229.497i | −0.171632 | + | 0.297276i | ||||
\(773\) | − | 1184.72i | − | 1.53263i | −0.642465 | − | 0.766315i | \(-0.722088\pi\) | ||
0.642465 | − | 0.766315i | \(-0.277912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −862.500 | − | 497.965i | −1.11147 | − | 0.641707i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −447.000 | − | 774.227i | −0.574550 | − | 0.995150i | ||||
\(779\) | 115.500 | − | 66.6840i | 0.148267 | − | 0.0856020i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.0345711 | − | 0.0598788i | ||||
\(782\) | − | 748.246i | − | 0.956836i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 495.000 | 0.631378 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −65.0000 | − | 112.583i | −0.0825921 | − | 0.143054i | 0.821771 | − | 0.569819i | \(-0.192987\pi\) |
−0.904363 | + | 0.426765i | \(0.859653\pi\) | |||||||
\(788\) | −108.000 | + | 62.3538i | −0.137056 | + | 0.0791292i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 180.133i | 0.227729i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 224.000 | 0.282472 | ||||||||
\(794\) | 543.000 | + | 313.501i | 0.683879 | + | 0.394838i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −145.000 | − | 251.147i | −0.182161 | − | 0.315512i | ||||
\(797\) | 273.000 | − | 157.617i | 0.342535 | − | 0.197762i | −0.318858 | − | 0.947803i | \(-0.603299\pi\) |
0.661392 | + | 0.750040i | \(0.269966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −378.000 | + | 654.715i | −0.473091 | + | 0.819418i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 681.000 | 0.849127 | ||||||||
\(803\) | −97.5000 | − | 56.2917i | −0.121420 | − | 0.0701017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 192.000 | − | 110.851i | 0.238213 | − | 0.137533i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 195.000 | − | 337.750i | 0.241337 | − | 0.418007i | ||||
\(809\) | − | 140.296i | − | 0.173419i | −0.996234 | − | 0.0867096i | \(-0.972365\pi\) | ||
0.996234 | − | 0.0867096i | \(-0.0276352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 299.000 | 0.368681 | 0.184340 | − | 0.982862i | \(-0.440985\pi\) | ||||
0.184340 | + | 0.982862i | \(0.440985\pi\) | |||||||
\(812\) | 78.0000 | + | 45.0333i | 0.0960591 | + | 0.0554598i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −51.0000 | − | 88.3346i | −0.0626536 | − | 0.108519i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −335.500 | + | 581.103i | −0.410649 | + | 0.711264i | ||||
\(818\) | 382.783i | 0.467950i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −525.000 | − | 303.109i | −0.639464 | − | 0.369195i | 0.144944 | − | 0.989440i | \(-0.453700\pi\) |
−0.784408 | + | 0.620245i | \(0.787033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −407.000 | − | 704.945i | −0.494532 | − | 0.856555i | 0.505448 | − | 0.862857i | \(-0.331327\pi\) |
−0.999980 | + | 0.00630221i | \(0.997994\pi\) | |||||||
\(824\) | 300.000 | − | 173.205i | 0.364078 | − | 0.210200i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 87.0000 | − | 150.688i | 0.105327 | − | 0.182432i | ||||
\(827\) | 1434.14i | 1.73415i | 0.498182 | + | 0.867073i | \(0.334001\pi\) | ||||
−0.498182 | + | 0.867073i | \(0.665999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −718.000 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 142.000 | + | 245.951i | 0.170673 | + | 0.295614i | ||||
\(833\) | 607.500 | − | 350.740i | 0.729292 | − | 0.421057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 19.0526i | − | 0.0227901i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1356.00 | 1.61814 | ||||||||
\(839\) | 690.000 | + | 398.372i | 0.822408 | + | 0.474817i | 0.851246 | − | 0.524767i | \(-0.175847\pi\) |
−0.0288384 | + | 0.999584i | \(0.509181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 593.500 | + | 1027.97i | 0.705707 | + | 1.22232i | ||||
\(842\) | −1023.00 | + | 590.629i | −1.21496 | + | 0.701460i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.0000 | − | 81.4064i | 0.0556872 | − | 0.0964531i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −236.000 | −0.278630 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −816.000 | + | 471.118i | −0.958872 | + | 0.553605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 712.000 | − | 1233.22i | 0.834701 | − | 1.44574i | −0.0595725 | − | 0.998224i | \(-0.518974\pi\) |
0.894274 | − | 0.447521i | \(-0.147693\pi\) | |||||||
\(854\) | − | 193.990i | − | 0.227154i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1215.00 | −1.41939 | ||||||||
\(857\) | 606.000 | + | 349.874i | 0.707118 | + | 0.408255i | 0.809993 | − | 0.586440i | \(-0.199471\pi\) |
−0.102875 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −155.500 | − | 269.334i | −0.181024 | − | 0.313544i | 0.761205 | − | 0.648511i | \(-0.224608\pi\) |
−0.942230 | + | 0.334968i | \(0.891275\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −243.000 | + | 420.888i | −0.281903 | + | 0.488270i | ||||
\(863\) | 1028.84i | 1.19216i | 0.802923 | + | 0.596082i | \(0.203277\pi\) | ||||
−0.802923 | + | 0.596082i | \(0.796723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −442.500 | − | 255.477i | −0.510970 | − | 0.295009i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.0000 | + | 55.4256i | 0.0368664 | + | 0.0638544i | ||||
\(869\) | −57.0000 | + | 32.9090i | −0.0655926 | + | 0.0378699i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.0000 | + | 107.387i | −0.0711825 | + | 0.123292i | ||||
\(872\) | − | 450.333i | − | 0.516437i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 528.000 | 0.604119 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0000 | + | 90.0666i | 0.0592930 | + | 0.102699i | 0.894148 | − | 0.447771i | \(-0.147782\pi\) |
−0.834855 | + | 0.550470i | \(0.814449\pi\) | |||||||
\(878\) | 1218.00 | − | 703.213i | 1.38724 | − | 0.800926i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 62.3538i | 0.0707762i | 0.999374 | + | 0.0353881i | \(0.0112667\pi\) | ||||
−0.999374 | + | 0.0353881i | \(0.988733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −119.000 | −0.134768 | −0.0673839 | − | 0.997727i | \(-0.521465\pi\) | ||||
−0.0673839 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(884\) | 54.0000 | + | 31.1769i | 0.0610860 | + | 0.0352680i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −79.5000 | − | 137.698i | −0.0897291 | − | 0.155415i | ||||
\(887\) | 1029.00 | − | 594.093i | 1.16009 | − | 0.669778i | 0.208765 | − | 0.977966i | \(-0.433056\pi\) |
0.951326 | + | 0.308188i | \(0.0997224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | − | 27.7128i | 0.0179978 | − | 0.0311730i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 52.0000 | 0.0582960 | ||||||||
\(893\) | −462.000 | − | 266.736i | −0.517357 | − | 0.298696i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 105.000 | − | 60.6218i | 0.117188 | − | 0.0676582i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −553.500 | + | 958.690i | −0.616370 | + | 1.06758i | ||||
\(899\) | 1441.07i | 1.60297i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −31.5000 | − | 18.1865i | −0.0349224 | − | 0.0201625i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −390.000 | − | 675.500i | −0.431416 | − | 0.747234i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 347.500 | − | 601.888i | 0.383131 | − | 0.663603i | −0.608377 | − | 0.793648i | \(-0.708179\pi\) |
0.991508 | + | 0.130046i | \(0.0415124\pi\) | |||||||
\(908\) | 188.794i | 0.207922i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1500.00 | + | 866.025i | 1.64654 | + | 0.950632i | 0.978432 | + | 0.206569i | \(0.0662299\pi\) |
0.668110 | + | 0.744062i | \(0.267103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.0000 | − | 72.7461i | −0.0460022 | − | 0.0796781i | ||||
\(914\) | −97.5000 | + | 56.2917i | −0.106674 | + | 0.0615882i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −133.000 | + | 230.363i | −0.145197 | + | 0.251488i | ||||
\(917\) | 318.697i | 0.347543i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0000 | 0.0609358 | 0.0304679 | − | 0.999536i | \(-0.490300\pi\) | ||||
0.0304679 | + | 0.999536i | \(0.490300\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −690.000 | − | 1195.12i | −0.748373 | − | 1.29622i | ||||
\(923\) | −108.000 | + | 62.3538i | −0.117010 | + | 0.0675556i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1271.33i | − | 1.37292i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −702.000 | −0.756466 | ||||||||
\(929\) | 690.000 | + | 398.372i | 0.742734 | + | 0.428818i | 0.823063 | − | 0.567951i | \(-0.192264\pi\) |
−0.0803285 | + | 0.996768i | \(0.525597\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 247.500 | + | 428.683i | 0.265843 | + | 0.460454i | ||||
\(932\) | −175.500 | + | 101.325i | −0.188305 | + | 0.108718i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 175.500 | − | 303.975i | 0.187901 | − | 0.325455i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −470.000 | −0.501601 | −0.250800 | − | 0.968039i | \(-0.580694\pi\) | ||||
−0.250800 | + | 0.968039i | \(0.580694\pi\) | |||||||
\(938\) | 93.0000 | + | 53.6936i | 0.0991471 | + | 0.0572426i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 348.000 | − | 200.918i | 0.369819 | − | 0.213515i | −0.303560 | − | 0.952812i | \(-0.598175\pi\) |
0.673380 | + | 0.739297i | \(0.264842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −168.000 | + | 290.985i | −0.178155 | + | 0.308573i | ||||
\(944\) | 552.524i | 0.585301i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 183.000 | 0.193446 | ||||||||
\(947\) | −1.50000 | − | 0.866025i | −0.00158395 | − | 0.000914494i | 0.499208 | − | 0.866482i | \(-0.333624\pi\) |
−0.500792 | + | 0.865568i | \(0.666958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 130.000 | + | 225.167i | 0.136986 | + | 0.237267i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 135.000 | − | 233.827i | 0.141807 | − | 0.245616i | ||||
\(953\) | − | 826.188i | − | 0.866934i | −0.901169 | − | 0.433467i | \(-0.857290\pi\) | ||
0.901169 | − | 0.433467i | \(-0.142710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −348.000 | − | 200.918i | −0.364017 | − | 0.210165i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 525.000 | + | 909.327i | 0.548017 | + | 0.949193i | ||||
\(959\) | −327.000 | + | 188.794i | −0.340980 | + | 0.196865i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.5000 | + | 54.5596i | −0.0327784 | + | 0.0567738i | ||||
\(962\) | 235.559i | 0.244864i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 119.000 | 0.123444 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 601.000 | + | 1040.96i | 0.621510 | + | 1.07649i | 0.989205 | + | 0.146540i | \(0.0468137\pi\) |
−0.367695 | + | 0.929946i | \(0.619853\pi\) | |||||||
\(968\) | 885.000 | − | 510.955i | 0.914256 | − | 0.527846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 187.061i | − | 0.192648i | −0.995350 | − | 0.0963241i | \(-0.969291\pi\) | ||
0.995350 | − | 0.0963241i | \(-0.0307085\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | −0.0102775 | ||||||||
\(974\) | −159.000 | − | 91.7987i | −0.163244 | − | 0.0942492i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 308.000 | + | 533.472i | 0.315574 | + | 0.546590i | ||||
\(977\) | −361.500 | + | 208.712i | −0.370010 | + | 0.213626i | −0.673463 | − | 0.739221i | \(-0.735194\pi\) |
0.303453 | + | 0.952847i | \(0.401861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −108.000 | + | 187.061i | −0.110317 | + | 0.191074i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −399.000 | −0.406314 | ||||||||
\(983\) | 1011.00 | + | 583.701i | 1.02848 | + | 0.593796i | 0.916550 | − | 0.399920i | \(-0.130962\pi\) |
0.111934 | + | 0.993716i | \(0.464295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1053.00 | − | 607.950i | 1.06795 | − | 0.616582i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.0000 | + | 38.1051i | −0.0222672 | + | 0.0385679i | ||||
\(989\) | − | 1690.48i | − | 1.70928i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1420.00 | −1.43290 | −0.716448 | − | 0.697640i | \(-0.754233\pi\) | ||||
−0.716448 | + | 0.697640i | \(0.754233\pi\) | |||||||
\(992\) | −432.000 | − | 249.415i | −0.435484 | − | 0.251427i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 54.0000 | + | 93.5307i | 0.0543260 | + | 0.0940953i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 262.000 | − | 453.797i | 0.262788 | − | 0.455163i | −0.704193 | − | 0.710008i | \(-0.748691\pi\) |
0.966982 | + | 0.254845i | \(0.0820246\pi\) | |||||||
\(998\) | − | 1363.12i | − | 1.36586i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))