Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (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: | \(3.92371580679\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.113 |
Dual form | 144.3.q.a.65.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | + | 1.73205i | 0.600000 | + | 0.346410i | 0.769042 | − | 0.639199i | \(-0.220734\pi\) |
−0.169042 | + | 0.985609i | \(0.554067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | 0.928571 | − | 0.371154i | \(-0.121038\pi\) |
−0.785714 | + | 0.618590i | \(0.787704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.136364 | − | 0.0787296i | −0.430266 | − | 0.902702i | \(-0.641580\pi\) |
0.566630 | + | 0.823972i | \(0.308247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.153846 | − | 0.266469i | −0.778792 | − | 0.627282i | \(-0.784167\pi\) |
0.932638 | + | 0.360813i | \(0.117501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.3923i | 0.692820i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.5885i | 0.916968i | 0.888703 | + | 0.458484i | \(0.151607\pi\) | ||||
−0.888703 | + | 0.458484i | \(0.848393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.0000 | −0.578947 | −0.289474 | − | 0.957186i | \(-0.593480\pi\) | ||||
−0.289474 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 5.19615i | −0.142857 | + | 0.247436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0000 | + | 13.8564i | 1.04348 | + | 0.602452i | 0.920817 | − | 0.389996i | \(-0.127524\pi\) |
0.122662 | + | 0.992449i | \(0.460857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.50000 | − | 11.2583i | −0.260000 | − | 0.450333i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.0000 | − | 22.5167i | 1.34483 | − | 0.776437i | 0.357316 | − | 0.933984i | \(-0.383692\pi\) |
0.987511 | + | 0.157547i | \(0.0503586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.0000 | − | 27.7128i | 0.516129 | − | 0.893962i | −0.483696 | − | 0.875236i | \(-0.660706\pi\) |
0.999825 | − | 0.0187254i | \(-0.00596084\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | + | 2.59808i | 0.136364 | + | 0.0787296i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.92820i | 0.197949i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.0000 | −0.918919 | −0.459459 | − | 0.888199i | \(-0.651957\pi\) | ||||
−0.459459 | + | 0.888199i | \(0.651957\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.0000 | 0.307692 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5000 | − | 6.06218i | −0.256098 | − | 0.147858i | 0.366456 | − | 0.930436i | \(-0.380571\pi\) |
−0.622553 | + | 0.782578i | \(0.713905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.5000 | − | 52.8275i | −0.709302 | − | 1.22855i | −0.965116 | − | 0.261822i | \(-0.915677\pi\) |
0.255814 | − | 0.966726i | \(-0.417657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.0000 | + | 15.5885i | −0.600000 | + | 0.346410i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.0000 | − | 24.2487i | 0.893617 | − | 0.515930i | 0.0184931 | − | 0.999829i | \(-0.494113\pi\) |
0.875124 | + | 0.483899i | \(0.160780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.5000 | − | 38.9711i | 0.459184 | − | 0.795329i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −40.5000 | + | 23.3827i | −0.794118 | + | 0.458484i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.109091 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5000 | − | 28.5788i | −0.289474 | − | 0.501383i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43.5000 | − | 25.1147i | −0.737288 | − | 0.425674i | 0.0837943 | − | 0.996483i | \(-0.473296\pi\) |
−0.821082 | + | 0.570810i | \(0.806629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.0000 | − | 48.4974i | −0.459016 | − | 0.795040i | 0.539893 | − | 0.841734i | \(-0.318465\pi\) |
−0.998909 | + | 0.0466940i | \(0.985131\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −18.0000 | −0.285714 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | − | 6.92820i | 0.184615 | − | 0.106588i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5000 | + | 26.8468i | −0.231343 | + | 0.400698i | −0.958204 | − | 0.286087i | \(-0.907645\pi\) |
0.726860 | + | 0.686785i | \(0.240979\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 83.1384i | 1.20490i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 31.1769i | 0.439111i | 0.975600 | + | 0.219556i | \(0.0704608\pi\) | ||||
−0.975600 | + | 0.219556i | \(0.929539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.0000 | 0.890411 | 0.445205 | − | 0.895428i | \(-0.353131\pi\) | ||||
0.445205 | + | 0.895428i | \(0.353131\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 19.5000 | − | 33.7750i | 0.260000 | − | 0.450333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | + | 1.73205i | 0.0389610 | + | 0.0224942i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.0000 | + | 32.9090i | 0.240506 | + | 0.416569i | 0.960859 | − | 0.277039i | \(-0.0893532\pi\) |
−0.720352 | + | 0.693608i | \(0.756020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42.0000 | − | 24.2487i | 0.506024 | − | 0.292153i | −0.225174 | − | 0.974319i | \(-0.572295\pi\) |
0.731198 | + | 0.682165i | \(0.238962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.0000 | + | 46.7654i | −0.317647 | + | 0.550181i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 117.000 | + | 67.5500i | 1.34483 | + | 0.776437i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 96.0000 | 1.03226 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −33.0000 | − | 19.0526i | −0.347368 | − | 0.200553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 57.5000 | + | 99.5929i | 0.592784 | + | 1.02673i | 0.993856 | + | 0.110685i | \(0.0353044\pi\) |
−0.401072 | + | 0.916047i | \(0.631362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5885i | 0.157459i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 39.0000 | − | 22.5167i | 0.386139 | − | 0.222937i | −0.294347 | − | 0.955699i | \(-0.595102\pi\) |
0.680486 | + | 0.732761i | \(0.261769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.0000 | + | 34.6410i | −0.194175 | + | 0.336321i | −0.946630 | − | 0.322323i | \(-0.895536\pi\) |
0.752455 | + | 0.658644i | \(0.228870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.0000 | + | 10.3923i | −0.171429 | + | 0.0989743i | ||||
\(106\) | 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 | ||||||||
\(111\) | −51.0000 | − | 88.3346i | −0.459459 | − | 0.795807i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −78.0000 | − | 45.0333i | −0.690265 | − | 0.398525i | 0.113446 | − | 0.993544i | \(-0.463811\pi\) |
−0.803711 | + | 0.595019i | \(0.797144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48.0000 | + | 83.1384i | 0.417391 | + | 0.722943i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0000 | + | 31.1769i | 0.153846 | + | 0.266469i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.0000 | + | 15.5885i | −0.226891 | + | 0.130995i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.0000 | + | 102.191i | −0.487603 | + | 0.844554i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 36.3731i | − | 0.295716i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 131.636i | − | 1.05309i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 0.125984 | 0.0629921 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629921 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 91.5000 | − | 158.483i | 0.709302 | − | 1.22855i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −138.000 | − | 79.6743i | −1.05344 | − | 0.608201i | −0.129826 | − | 0.991537i | \(-0.541442\pi\) |
−0.923609 | + | 0.383336i | \(0.874775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.0000 | − | 19.0526i | −0.0827068 | − | 0.143252i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −81.0000 | − | 46.7654i | −0.600000 | − | 0.346410i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −163.500 | + | 94.3968i | −1.19343 | + | 0.689028i | −0.959083 | − | 0.283125i | \(-0.908629\pi\) |
−0.234348 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | − | 4.33013i | 0.0179856 | − | 0.0311520i | −0.856893 | − | 0.515495i | \(-0.827608\pi\) |
0.874878 | + | 0.484343i | \(0.160941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 126.000 | + | 72.7461i | 0.893617 | + | 0.515930i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.92820i | − | 0.0484490i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 156.000 | 1.07586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 135.000 | 0.918367 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −132.000 | − | 76.2102i | −0.885906 | − | 0.511478i | −0.0133049 | − | 0.999911i | \(-0.504235\pi\) |
−0.872601 | + | 0.488433i | \(0.837569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | + | 17.3205i | 0.0662252 | + | 0.114705i | 0.897237 | − | 0.441550i | \(-0.145571\pi\) |
−0.831012 | + | 0.556255i | \(0.812238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −121.500 | − | 70.1481i | −0.794118 | − | 0.458484i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 96.0000 | − | 55.4256i | 0.619355 | − | 0.357585i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0000 | − | 34.6410i | 0.127389 | − | 0.220643i | −0.795276 | − | 0.606248i | \(-0.792674\pi\) |
0.922664 | + | 0.385605i | \(0.126007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 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 | \(0.394584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.00000 | + | 15.5885i | 0.0545455 | + | 0.0944755i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −165.000 | − | 95.2628i | −0.988024 | − | 0.570436i | −0.0833409 | − | 0.996521i | \(-0.526559\pi\) |
−0.904683 | + | 0.426085i | \(0.859892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 76.5000 | + | 132.502i | 0.452663 | + | 0.784035i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 49.5000 | − | 85.7365i | 0.289474 | − | 0.501383i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 201.000 | − | 116.047i | 1.16185 | − | 0.670794i | 0.210103 | − | 0.977679i | \(-0.432620\pi\) |
0.951747 | + | 0.306885i | \(0.0992867\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0000 | − | 22.5167i | 0.0742857 | − | 0.128667i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 150.688i | − | 0.851347i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 62.3538i | − | 0.348345i | −0.984715 | − | 0.174173i | \(-0.944275\pi\) | ||
0.984715 | − | 0.174173i | \(-0.0557251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −232.000 | −1.28177 | −0.640884 | − | 0.767638i | \(-0.721432\pi\) | ||||
−0.640884 | + | 0.767638i | \(0.721432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 84.0000 | − | 145.492i | 0.459016 | − | 0.795040i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −102.000 | − | 58.8897i | −0.551351 | − | 0.318323i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5000 | + | 23.3827i | 0.0721925 | + | 0.125041i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.0000 | − | 46.7654i | −0.142857 | − | 0.247436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −201.000 | + | 116.047i | −1.05236 | + | 0.607578i | −0.923308 | − | 0.384060i | \(-0.874525\pi\) |
−0.129048 | + | 0.991638i | \(0.541192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 132.500 | − | 229.497i | 0.686528 | − | 1.18910i | −0.286425 | − | 0.958103i | \(-0.592467\pi\) |
0.972954 | − | 0.231000i | \(-0.0741996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36.0000 | + | 20.7846i | 0.184615 | + | 0.106588i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 124.708i | 0.633034i | 0.948587 | + | 0.316517i | \(0.102513\pi\) | ||||
−0.948587 | + | 0.316517i | \(0.897487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −290.000 | −1.45729 | −0.728643 | − | 0.684893i | \(-0.759849\pi\) | ||||
−0.728643 | + | 0.684893i | \(0.759849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −93.0000 | −0.462687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78.0000 | + | 45.0333i | 0.384236 | + | 0.221839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.0000 | − | 36.3731i | −0.102439 | − | 0.177430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −216.000 | + | 124.708i | −1.04348 | + | 0.602452i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.5000 | + | 9.52628i | −0.0789474 | + | 0.0455803i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −47.0000 | + | 81.4064i | −0.222749 | + | 0.385812i | −0.955642 | − | 0.294532i | \(-0.904836\pi\) |
0.732893 | + | 0.680344i | \(0.238170\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −81.0000 | + | 46.7654i | −0.380282 | + | 0.219556i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 211.310i | − | 0.982838i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 64.0000 | 0.294931 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 97.5000 | + | 168.875i | 0.445205 | + | 0.771119i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 54.0000 | + | 31.1769i | 0.244344 | + | 0.141072i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0000 | − | 45.0333i | −0.116592 | − | 0.201943i | 0.801823 | − | 0.597562i | \(-0.203864\pi\) |
−0.918415 | + | 0.395618i | \(0.870530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 117.000 | 0.520000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 163.500 | − | 94.3968i | 0.720264 | − | 0.415845i | −0.0945856 | − | 0.995517i | \(-0.530153\pi\) |
0.814850 | + | 0.579672i | \(0.196819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −133.000 | + | 230.363i | −0.580786 | + | 1.00595i | 0.414600 | + | 0.910004i | \(0.363921\pi\) |
−0.995386 | + | 0.0959473i | \(0.969412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3923i | 0.0449883i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 202.650i | 0.869742i | 0.900493 | + | 0.434871i | \(0.143206\pi\) | ||||
−0.900493 | + | 0.434871i | \(0.856794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 168.000 | 0.714894 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −57.0000 | + | 98.7269i | −0.240506 | + | 0.416569i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 348.000 | + | 200.918i | 1.45607 | + | 0.840661i | 0.998815 | − | 0.0486764i | \(-0.0155003\pi\) |
0.457252 | + | 0.889337i | \(0.348834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −59.5000 | − | 103.057i | −0.246888 | − | 0.427623i | 0.715773 | − | 0.698333i | \(-0.246075\pi\) |
−0.962661 | + | 0.270711i | \(0.912741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 135.000 | − | 77.9423i | 0.551020 | − | 0.318132i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.0000 | + | 38.1051i | −0.0890688 | + | 0.154272i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 126.000 | + | 72.7461i | 0.506024 | + | 0.292153i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 389.711i | 1.55264i | 0.630342 | + | 0.776318i | \(0.282915\pi\) | ||||
−0.630342 | + | 0.776318i | \(0.717085\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.0000 | 0.189723 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −162.000 | −0.635294 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 151.500 | + | 87.4686i | 0.589494 | + | 0.340345i | 0.764897 | − | 0.644152i | \(-0.222790\pi\) |
−0.175403 | + | 0.984497i | \(0.556123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.0000 | − | 58.8897i | −0.131274 | − | 0.227373i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 405.300i | 1.55287i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −39.0000 | + | 22.5167i | −0.148289 | + | 0.0856147i | −0.572309 | − | 0.820038i | \(-0.693952\pi\) |
0.424020 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −324.000 | + | 187.061i | −1.21348 | + | 0.700605i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 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 | \(-0.335364\pi\) | ||||
0.494465 | + | 0.869198i | \(0.335364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | + | 20.7846i | 0.0439560 | + | 0.0761341i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.5000 | − | 11.2583i | −0.0709091 | − | 0.0409394i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.0000 | − | 48.4974i | −0.101083 | − | 0.175081i | 0.811048 | − | 0.584979i | \(-0.198897\pi\) |
−0.912131 | + | 0.409899i | \(0.865564\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 144.000 | + | 249.415i | 0.516129 | + | 0.893962i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −42.0000 | + | 24.2487i | −0.149466 | + | 0.0862943i | −0.572868 | − | 0.819648i | \(-0.694169\pi\) |
0.423402 | + | 0.905942i | \(0.360836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 187.000 | − | 323.894i | 0.660777 | − | 1.14450i | −0.319634 | − | 0.947541i | \(-0.603560\pi\) |
0.980412 | − | 0.196959i | \(-0.0631066\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 114.315i | − | 0.401107i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 24.2487i | − | 0.0844903i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.0000 | 0.159170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −172.500 | + | 298.779i | −0.592784 | + | 1.02673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 219.000 | + | 126.440i | 0.747440 | + | 0.431535i | 0.824768 | − | 0.565471i | \(-0.191306\pi\) |
−0.0773280 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87.0000 | − | 150.688i | −0.294915 | − | 0.510808i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −40.5000 | + | 23.3827i | −0.136364 | + | 0.0787296i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 96.0000 | − | 55.4256i | 0.321070 | − | 0.185370i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61.0000 | − | 105.655i | 0.202658 | − | 0.351014i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 117.000 | + | 67.5500i | 0.386139 | + | 0.222937i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 193.990i | − | 0.636032i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −533.000 | −1.73616 | −0.868078 | − | 0.496428i | \(-0.834645\pi\) | ||||
−0.868078 | + | 0.496428i | \(0.834645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −120.000 | −0.388350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 213.000 | + | 122.976i | 0.684887 | + | 0.395420i | 0.801694 | − | 0.597735i | \(-0.203932\pi\) |
−0.116806 | + | 0.993155i | \(0.537266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −77.5000 | − | 134.234i | −0.247604 | − | 0.428862i | 0.715257 | − | 0.698862i | \(-0.246310\pi\) |
−0.962860 | + | 0.269999i | \(0.912976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −54.0000 | − | 31.1769i | −0.171429 | − | 0.0989743i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −42.0000 | + | 24.2487i | −0.132492 | + | 0.0764944i | −0.564781 | − | 0.825241i | \(-0.691039\pi\) |
0.432289 | + | 0.901735i | \(0.357706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.0000 | − | 67.5500i | 0.122257 | − | 0.211755i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −364.500 | + | 210.444i | −1.13551 | + | 0.655589i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 171.473i | − | 0.530876i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −52.0000 | −0.160000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −78.0000 | − | 135.100i | −0.238532 | − | 0.413150i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 84.0000 | + | 48.4974i | 0.255319 | + | 0.147409i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | + | 1.73205i | 0.00302115 | + | 0.00523278i | 0.867532 | − | 0.497381i | \(-0.165705\pi\) |
−0.864511 | + | 0.502614i | \(0.832372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 153.000 | − | 265.004i | 0.459459 | − | 0.795807i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −93.0000 | + | 53.6936i | −0.277612 | + | 0.160279i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −38.5000 | + | 66.6840i | −0.114243 | + | 0.197875i | −0.917477 | − | 0.397789i | \(-0.869778\pi\) |
0.803234 | + | 0.595664i | \(0.203111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 270.200i | − | 0.797050i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 55.4256i | − | 0.162538i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 188.000 | 0.548105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −144.000 | + | 249.415i | −0.417391 | + | 0.722943i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −97.5000 | − | 56.2917i | −0.280980 | − | 0.162224i | 0.352887 | − | 0.935666i | \(-0.385200\pi\) |
−0.633867 | + | 0.773442i | \(0.718533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −208.000 | − | 360.267i | −0.595989 | − | 1.03228i | −0.993407 | − | 0.114645i | \(-0.963427\pi\) |
0.397418 | − | 0.917638i | \(-0.369906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.0000 | + | 93.5307i | −0.153846 | + | 0.266469i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 0.866025i | −0.00424929 | + | 0.00245333i | −0.502123 | − | 0.864796i | \(-0.667448\pi\) |
0.497874 | + | 0.867249i | \(0.334114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −54.0000 | + | 93.5307i | −0.152113 | + | 0.263467i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −81.0000 | − | 46.7654i | −0.226891 | − | 0.130995i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 592.361i | − | 1.65003i | −0.565110 | − | 0.825016i | \(-0.691166\pi\) | ||
0.565110 | − | 0.825016i | \(-0.308834\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.000 | −0.664820 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −354.000 | −0.975207 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 195.000 | + | 112.583i | 0.534247 | + | 0.308447i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −179.000 | − | 310.037i | −0.487738 | − | 0.844788i | 0.512162 | − | 0.858889i | \(-0.328845\pi\) |
−0.999901 | + | 0.0141011i | \(0.995511\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 94.5000 | − | 54.5596i | 0.256098 | − | 0.147858i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 290.000 | − | 502.295i | 0.777480 | − | 1.34663i | −0.155910 | − | 0.987771i | \(-0.549831\pi\) |
0.933390 | − | 0.358863i | \(-0.116836\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 342.000 | − | 197.454i | 0.912000 | − | 0.526543i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 180.133i | − | 0.477807i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −83.0000 | −0.218997 | −0.109499 | − | 0.993987i | \(-0.534925\pi\) | ||||
−0.109499 | + | 0.993987i | \(0.534925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0000 | + | 41.5692i | 0.0629921 | + | 0.109106i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 483.000 | + | 278.860i | 1.26110 | + | 0.728094i | 0.973287 | − | 0.229593i | \(-0.0737395\pi\) |
0.287810 | + | 0.957688i | \(0.407073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 10.3923i | 0.0155844 | + | 0.0269930i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 549.000 | 1.41860 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −447.000 | + | 258.076i | −1.14910 | + | 0.663433i | −0.948668 | − | 0.316274i | \(-0.897568\pi\) |
−0.200432 | + | 0.979708i | \(0.564235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −216.000 | + | 374.123i | −0.552430 | + | 0.956836i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 478.046i | − | 1.21640i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 131.636i | 0.333255i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 362.000 | 0.911839 | 0.455919 | − | 0.890021i | \(-0.349311\pi\) | ||||
0.455919 | + | 0.890021i | \(0.349311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.0000 | − | 57.1577i | 0.0827068 | − | 0.143252i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 340.500 | + | 196.588i | 0.849127 | + | 0.490244i | 0.860356 | − | 0.509693i | \(-0.170241\pi\) |
−0.0112291 | + | 0.999937i | \(0.503574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −64.0000 | − | 110.851i | −0.158809 | − | 0.275065i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 280.592i | − | 0.692820i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.0000 | + | 29.4449i | −0.125307 | + | 0.0723461i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −110.500 | + | 191.392i | −0.270171 | + | 0.467950i | −0.968905 | − | 0.247431i | \(-0.920414\pi\) |
0.698734 | + | 0.715381i | \(0.253747\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −490.500 | − | 283.190i | −1.19343 | − | 0.689028i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 100.459i | − | 0.243242i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 168.000 | 0.404819 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0000 | 0.0359712 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −678.000 | − | 391.443i | −1.61814 | − | 0.934233i | −0.987401 | − | 0.158236i | \(-0.949419\pi\) |
−0.630737 | − | 0.775997i | \(-0.717247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 341.000 | + | 590.629i | 0.809976 | + | 1.40292i | 0.912880 | + | 0.408229i | \(0.133853\pi\) |
−0.102903 | + | 0.994691i | \(0.532813\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 436.477i | 1.03186i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 175.500 | − | 101.325i | 0.412941 | − | 0.238412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.0000 | − | 96.9948i | 0.131148 | − | 0.227154i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.0000 | − | 10.3923i | 0.0419580 | − | 0.0242245i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 280.592i | 0.651026i | 0.945538 | + | 0.325513i | \(0.105537\pi\) | ||||
−0.945538 | + | 0.325513i | \(0.894463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −295.000 | −0.681293 | −0.340647 | − | 0.940191i | \(-0.610646\pi\) | ||||
−0.340647 | + | 0.940191i | \(0.610646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 234.000 | + | 405.300i | 0.537931 | + | 0.931724i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −264.000 | − | 152.420i | −0.604119 | − | 0.348788i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 406.000 | + | 703.213i | 0.924829 | + | 1.60185i | 0.791836 | + | 0.610734i | \(0.209126\pi\) |
0.132993 | + | 0.991117i | \(0.457541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 202.500 | + | 350.740i | 0.459184 | + | 0.795329i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −79.5000 | + | 45.8993i | −0.179458 | + | 0.103610i | −0.587038 | − | 0.809559i | \(-0.699706\pi\) |
0.407580 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −216.000 | + | 374.123i | −0.485393 | + | 0.840726i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 457.261i | − | 1.02296i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.0000 | + | 51.9615i | −0.0662252 | + | 0.114705i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | + | 13.8564i | 0.0527473 | + | 0.0304536i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.5000 | − | 56.2917i | −0.0711160 | − | 0.123176i | 0.828275 | − | 0.560322i | \(-0.189323\pi\) |
−0.899391 | + | 0.437146i | \(0.855989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 420.888i | − | 0.916968i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −690.000 | + | 398.372i | −1.49675 | + | 0.864147i | −0.999993 | − | 0.00374501i | \(-0.998808\pi\) |
−0.496753 | + | 0.867892i | \(0.665475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 367.000 | − | 635.663i | 0.792657 | − | 1.37292i | −0.131660 | − | 0.991295i | \(-0.542031\pi\) |
0.924317 | − | 0.381627i | \(-0.124636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 288.000 | + | 166.277i | 0.619355 | + | 0.357585i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||||||
\(471\) | 120.000 | 0.254777 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −91.5000 | − | 52.8275i | −0.193446 | − | 0.111686i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 71.5000 | + | 123.842i | 0.150526 | + | 0.260719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −525.000 | + | 303.109i | −1.09603 | + | 0.632795i | −0.935176 | − | 0.354183i | \(-0.884759\pi\) |
−0.160857 | + | 0.986978i | \(0.551426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −68.0000 | + | 117.779i | −0.141372 | + | 0.244864i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −144.000 | + | 83.1384i | −0.298137 | + | 0.172129i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 398.372i | 0.821385i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 106.000 | 0.217659 | 0.108830 | − | 0.994060i | \(-0.465290\pi\) | ||||
0.108830 | + | 0.994060i | \(0.465290\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 159.000 | + | 275.396i | 0.325153 | + | 0.563182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 199.500 | + | 115.181i | 0.406314 | + | 0.234585i | 0.689205 | − | 0.724567i | \(-0.257960\pi\) |
−0.282891 | + | 0.959152i | \(0.591293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 351.000 | + | 607.950i | 0.711968 | + | 1.23316i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.0000 | + | 46.7654i | −0.0545455 | + | 0.0944755i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −54.0000 | + | 31.1769i | −0.108652 | + | 0.0627302i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −393.500 | + | 681.562i | −0.788577 | + | 1.36586i | 0.138261 | + | 0.990396i | \(0.455849\pi\) |
−0.926839 | + | 0.375460i | \(0.877485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 571.577i | − | 1.14087i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 623.538i | − | 1.23964i | −0.784745 | − | 0.619819i | \(-0.787206\pi\) | ||
0.784745 | − | 0.619819i | \(-0.212794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 156.000 | 0.308911 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −229.500 | + | 397.506i | −0.452663 | + | 0.784035i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −186.000 | − | 107.387i | −0.365422 | − | 0.210977i | 0.306034 | − | 0.952020i | \(-0.400998\pi\) |
−0.671457 | + | 0.741044i | \(0.734331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65.0000 | + | 112.583i | 0.127202 | + | 0.220320i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 297.000 | 0.578947 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −120.000 | + | 69.2820i | −0.233010 | + | 0.134528i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.0000 | − | 72.7461i | 0.0812379 | − | 0.140708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 603.000 | + | 348.142i | 1.16185 | + | 0.670794i | ||||
\(520\) | 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 | \(0.423179\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 78.0000 | 0.148571 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 432.000 | + | 249.415i | 0.819734 | + | 0.473274i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 119.500 | + | 206.980i | 0.225898 | + | 0.391267i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 391.500 | − | 226.033i | 0.737288 | − | 0.425674i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.0000 | + | 24.2487i | −0.0787992 | + | 0.0454948i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −243.000 | + | 420.888i | −0.454206 | + | 0.786707i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 162.000 | − | 93.5307i | 0.301676 | − | 0.174173i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 77.9423i | − | 0.144605i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 650.000 | 1.20148 | 0.600739 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600739 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −348.000 | − | 602.754i | −0.640884 | − | 1.11004i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −156.000 | − | 90.0666i | −0.286239 | − | 0.165260i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 311.500 | + | 539.534i | 0.569470 | + | 0.986351i | 0.996618 | + | 0.0821692i | \(0.0261848\pi\) |
−0.427149 | + | 0.904181i | \(0.640482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 504.000 | 0.918033 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −429.000 | + | 247.683i | −0.778584 | + | 0.449516i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.0000 | + | 65.8179i | −0.0687161 | + | 0.119020i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 353.338i | − | 0.636646i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 530.008i | 0.951540i | 0.879570 | + | 0.475770i | \(0.157830\pi\) | ||||
−0.879570 | + | 0.475770i | \(0.842170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −244.000 | −0.436494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −40.5000 | + | 70.1481i | −0.0721925 | + | 0.125041i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −97.5000 | − | 56.2917i | −0.173179 | − | 0.0999852i | 0.410905 | − | 0.911678i | \(-0.365213\pi\) |
−0.584084 | + | 0.811693i | \(0.698546\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −156.000 | − | 270.200i | −0.276106 | − | 0.478230i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 81.0000 | − | 140.296i | 0.142857 | − | 0.247436i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 565.500 | − | 326.492i | 0.993849 | − | 0.573799i | 0.0874263 | − | 0.996171i | \(-0.472136\pi\) |
0.906423 | + | 0.422372i | \(0.138802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 272.500 | − | 471.984i | 0.477233 | − | 0.826592i | −0.522427 | − | 0.852684i | \(-0.674973\pi\) |
0.999660 | + | 0.0260926i | \(0.00830647\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −603.000 | − | 348.142i | −1.05236 | − | 0.607578i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 360.267i | − | 0.626551i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −871.000 | −1.50953 | −0.754766 | − | 0.655994i | \(-0.772250\pi\) | ||||
−0.754766 | + | 0.655994i | \(0.772250\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 795.000 | 1.37306 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 84.0000 | + | 48.4974i | 0.144578 | + | 0.0834723i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 124.708i | 0.213175i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50000 | − | 0.866025i | 0.00255537 | − | 0.00147534i | −0.498722 | − | 0.866762i | \(-0.666197\pi\) |
0.501277 | + | 0.865287i | \(0.332864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −176.000 | + | 304.841i | −0.298812 | + | 0.517557i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −324.000 | + | 187.061i | −0.548223 | + | 0.316517i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 187.061i | 0.315449i | 0.987483 | + | 0.157725i | \(0.0504159\pi\) | ||||
−0.987483 | + | 0.157725i | \(0.949584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −108.000 | −0.181513 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −435.000 | − | 753.442i | −0.728643 | − | 1.26205i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −489.000 | − | 282.324i | −0.816361 | − | 0.471326i | 0.0327992 | − | 0.999462i | \(-0.489558\pi\) |
−0.849160 | + | 0.528136i | \(0.822891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −230.500 | − | 399.238i | −0.383527 | − | 0.664289i | 0.608036 | − | 0.793909i | \(-0.291958\pi\) |
−0.991564 | + | 0.129620i | \(0.958624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −139.500 | − | 241.621i | −0.231343 | − | 0.400698i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −354.000 | + | 204.382i | −0.585124 | + | 0.337821i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −56.0000 | + | 96.9948i | −0.0922570 | + | 0.159794i | −0.908461 | − | 0.417971i | \(-0.862741\pi\) |
0.816204 | + | 0.577765i | \(0.196075\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 270.200i | 0.443678i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 193.990i | − | 0.317495i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 902.000 | 1.47145 | 0.735726 | − | 0.677279i | \(-0.236841\pi\) | ||||
0.735726 | + | 0.677279i | \(0.236841\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.0000 | − | 109.119i | 0.102439 | − | 0.177430i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −307.500 | − | 177.535i | −0.498379 | − | 0.287739i | 0.229665 | − | 0.973270i | \(-0.426237\pi\) |
−0.728044 | + | 0.685530i | \(0.759570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −399.500 | − | 691.954i | −0.645396 | − | 1.11786i | −0.984210 | − | 0.177005i | \(-0.943359\pi\) |
0.338814 | − | 0.940853i | \(-0.389974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −648.000 | − | 374.123i | −1.04348 | − | 0.602452i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −216.000 | + | 124.708i | −0.346709 | + | 0.200173i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 65.5000 | − | 113.449i | 0.104800 | − | 0.181519i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −49.5000 | − | 28.5788i | −0.0789474 | − | 0.0455803i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 530.008i | − | 0.842619i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −830.000 | −1.31537 | −0.657686 | − | 0.753292i | \(-0.728465\pi\) | ||||
−0.657686 | + | 0.753292i | \(0.728465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −282.000 | −0.445498 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 48.0000 | + | 27.7128i | 0.0755906 | + | 0.0436422i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −90.0000 | − | 155.885i | −0.141287 | − | 0.244717i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −243.000 | − | 140.296i | −0.380282 | − | 0.219556i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −325.500 | + | 187.928i | −0.507800 | + | 0.293179i | −0.731929 | − | 0.681381i | \(-0.761380\pi\) |
0.224129 | + | 0.974560i | \(0.428046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.50000 | + | 11.2583i | −0.0101089 | + | 0.0175091i | −0.871036 | − | 0.491220i | \(-0.836551\pi\) |
0.860927 | + | 0.508729i | \(0.169884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 549.000 | − | 316.965i | 0.851163 | − | 0.491419i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 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 | ||||||||
\(651\) | 96.0000 | + | 166.277i | 0.147465 | + | 0.255418i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 327.000 | + | 188.794i | 0.500766 | + | 0.289117i | 0.729030 | − | 0.684482i | \(-0.239972\pi\) |
−0.228264 | + | 0.973599i | \(0.573305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −276.000 | − | 478.046i | −0.421374 | − | 0.729841i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −292.500 | + | 506.625i | −0.445205 | + | 0.771119i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 852.000 | − | 491.902i | 1.29287 | − | 0.746438i | 0.313706 | − | 0.949520i | \(-0.398429\pi\) |
0.979162 | + | 0.203082i | \(0.0650959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 191.000 | − | 330.822i | 0.288956 | − | 0.500487i | −0.684605 | − | 0.728915i | \(-0.740025\pi\) |
0.973561 | + | 0.228428i | \(0.0733585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 187.061i | 0.282144i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 76.2102i | − | 0.114602i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1248.00 | 1.87106 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 78.0000 | − | 135.100i | 0.116592 | − | 0.201943i | ||||
\(670\) | 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 | \(-0.307949\pi\) |
−0.996822 | + | 0.0796633i | \(0.974615\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 175.500 | + | 303.975i | 0.260000 | + | 0.450333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 606.000 | − | 349.874i | 0.895126 | − | 0.516801i | 0.0195100 | − | 0.999810i | \(-0.493789\pi\) |
0.875616 | + | 0.483009i | \(0.160456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −115.000 | + | 199.186i | −0.169367 | + | 0.293352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 490.500 | + | 283.190i | 0.720264 | + | 0.415845i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1044.43i | 1.52918i | 0.644520 | + | 0.764588i | \(0.277057\pi\) | ||||
−0.644520 | + | 0.764588i | \(0.722943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −654.000 | −0.954745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −798.000 | −1.16157 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 91.0000 | + | 157.617i | 0.131693 | + | 0.228099i | 0.924329 | − | 0.381596i | \(-0.124625\pi\) |
−0.792636 | + | 0.609695i | \(0.791292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.0000 | + | 15.5885i | −0.0389610 | + | 0.0224942i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0000 | − | 8.66025i | 0.0215827 | − | 0.0124608i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 94.5000 | − | 163.679i | 0.135581 | − | 0.234833i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −526.500 | + | 303.975i | −0.753219 | + | 0.434871i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 374.000 | 0.532006 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 252.000 | + | 436.477i | 0.357447 | + | 0.619116i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 78.0000 | + | 45.0333i | 0.110325 | + | 0.0636964i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 350.000 | + | 606.218i | 0.493653 | + | 0.855032i | 0.999973 | − | 0.00731341i | \(-0.00232795\pi\) |
−0.506320 | + | 0.862346i | \(0.668995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −342.000 | −0.481013 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 768.000 | − | 443.405i | 1.07714 | − | 0.621886i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | − | 20.7846i | 0.0167832 | − | 0.0290694i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1205.51i | 1.68132i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 592.361i | 0.823868i | 0.911214 | + | 0.411934i | \(0.135147\pi\) | ||||
−0.911214 | + | 0.411934i | \(0.864853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.0000 | −0.110957 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 178.500 | − | 309.171i | 0.246888 | − | 0.427623i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −507.000 | − | 292.717i | −0.699310 | − | 0.403747i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −332.000 | − | 575.041i | −0.456671 | − | 0.790978i | 0.542111 | − | 0.840307i | \(-0.317625\pi\) |
−0.998783 | + | 0.0493289i | \(0.984292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 1.00000 | ||||||||
\(730\) | 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 | \(-0.682248\pi\) |
0.998802 | + | 0.0489306i | \(0.0155813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 405.000 | + | 233.827i | 0.551020 | + | 0.318132i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.6936i | 0.0728542i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −317.000 | −0.428958 | −0.214479 | − | 0.976729i | \(-0.568805\pi\) | ||||
−0.214479 | + | 0.976729i | \(0.568805\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −132.000 | −0.178138 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 537.000 | + | 310.037i | 0.722746 | + | 0.417277i | 0.815762 | − | 0.578387i | \(-0.196318\pi\) |
−0.0930168 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −264.000 | − | 457.261i | −0.354362 | − | 0.613774i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 436.477i | 0.584306i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −243.000 | + | 140.296i | −0.324433 | + | 0.187311i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 655.000 | − | 1134.49i | 0.872170 | − | 1.51064i | 0.0124237 | − | 0.999923i | \(-0.496045\pi\) |
0.859747 | − | 0.510721i | \(-0.170621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1012.50 | + | 584.567i | −1.34462 | + | 0.776318i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 69.2820i | 0.0917643i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 218.000 | 0.287979 | 0.143989 | − | 0.989579i | \(-0.454007\pi\) | ||||
0.143989 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 72.0000 | + | 124.708i | 0.0948617 | + | 0.164305i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 570.000 | + | 329.090i | 0.749014 | + | 0.432444i | 0.825338 | − | 0.564639i | \(-0.190985\pi\) |
−0.0763232 | + | 0.997083i | \(0.524318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.0000 | − | 90.0666i | −0.0681520 | − | 0.118043i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −243.000 | − | 420.888i | −0.317647 | − | 0.550181i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −174.000 | + | 100.459i | −0.226858 | + | 0.130976i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −511.000 | + | 885.078i | −0.664499 | + | 1.15095i | 0.314921 | + | 0.949118i | \(0.398022\pi\) |
−0.979421 | + | 0.201829i | \(0.935312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 524.811i | 0.680689i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1184.72i | 1.53263i | 0.642465 | + | 0.766315i | \(0.277912\pi\) | ||||
−0.642465 | + | 0.766315i | \(0.722088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −416.000 | −0.536774 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 102.000 | − | 176.669i | 0.131274 | − | 0.227373i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 115.500 | + | 66.6840i | 0.148267 | + | 0.0856020i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | + | 46.7654i | 0.0345711 | + | 0.0598788i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1053.00 | + | 607.950i | −1.34483 | + | 0.776437i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 120.000 | − | 69.2820i | 0.152866 | − | 0.0882574i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −65.0000 | + | 112.583i | −0.0825921 | + | 0.143054i | −0.904363 | − | 0.426765i | \(-0.859653\pi\) |
0.821771 | + | 0.569819i | \(0.192987\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −117.000 | − | 67.5500i | −0.148289 | − | 0.0856147i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 180.133i | − | 0.227729i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −224.000 | −0.282472 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 273.000 | + | 157.617i | 0.342535 | + | 0.197762i | 0.661392 | − | 0.750040i | \(-0.269966\pi\) |
−0.318858 | + | 0.947803i | \(0.603299\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 378.000 | + | 654.715i | 0.473091 | + | 0.819418i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −972.000 | − | 561.184i | −1.21348 | − | 0.700605i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 97.5000 | − | 56.2917i | 0.121420 | − | 0.0701017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −96.0000 | + | 166.277i | −0.119255 | + | 0.206555i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 486.000 | − | 280.592i | 0.602230 | − | 0.347698i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 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 | \(-0.559015\pi\) | ||||
−0.184340 | + | 0.982862i | \(0.559015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 402.000 | + | 696.284i | 0.494465 | + | 0.856438i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 318.000 | + | 183.597i | 0.390184 | + | 0.225273i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 335.500 | + | 581.103i | 0.410649 | + | 0.711264i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.0000 | + | 62.3538i | −0.0439560 | + | 0.0761341i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 525.000 | − | 303.109i | 0.639464 | − | 0.369195i | −0.144944 | − | 0.989440i | \(-0.546300\pi\) |
0.784408 | + | 0.620245i | \(0.212967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −407.000 | + | 704.945i | −0.494532 | + | 0.856555i | −0.999980 | − | 0.00630221i | \(-0.997994\pi\) |
0.505448 | + | 0.862857i | \(0.331327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 67.5500i | − | 0.0818788i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 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 | ||||||||
\(831\) | 84.0000 | − | 145.492i | 0.101083 | − | 0.175081i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 607.500 | + | 350.740i | 0.729292 | + | 0.421057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −330.000 | − | 571.577i | −0.395210 | − | 0.684523i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −432.000 | + | 748.246i | −0.516129 | + | 0.893962i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 690.000 | − | 398.372i | 0.822408 | − | 0.474817i | −0.0288384 | − | 0.999584i | \(-0.509181\pi\) |
0.851246 | + | 0.524767i | \(0.175847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 593.500 | − | 1027.97i | 0.705707 | − | 1.22232i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −126.000 | − | 72.7461i | −0.149466 | − | 0.0862943i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 530.008i | 0.627228i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −236.000 | −0.278630 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1122.00 | 1.32155 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −816.000 | − | 471.118i | −0.958872 | − | 0.553605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −712.000 | − | 1233.22i | −0.834701 | − | 1.44574i | −0.894274 | − | 0.447521i | \(-0.852307\pi\) |
0.0595725 | − | 0.998224i | \(-0.481026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 297.000 | − | 171.473i | 0.347368 | − | 0.200553i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 606.000 | − | 349.874i | 0.707118 | − | 0.408255i | −0.102875 | − | 0.994694i | \(-0.532804\pi\) |
0.809993 | + | 0.586440i | \(0.199471\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 155.500 | − | 269.334i | 0.181024 | − | 0.313544i | −0.761205 | − | 0.648511i | \(-0.775392\pi\) |
0.942230 | + | 0.334968i | \(0.108725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 63.0000 | − | 36.3731i | 0.0731707 | − | 0.0422451i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1028.84i | 1.19216i | 0.802923 | + | 0.596082i | \(0.203277\pi\) | ||||
−0.802923 | + | 0.596082i | \(0.796723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 804.000 | 0.929480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 69.0000 | + | 119.512i | 0.0795848 | + | 0.137845i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.0000 | + | 32.9090i | 0.0655926 | + | 0.0378699i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62.0000 | + | 107.387i | 0.0711825 | + | 0.123292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1035.00 | −1.18557 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 228.000 | − | 131.636i | 0.260571 | − | 0.150441i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.0000 | + | 90.0666i | −0.0592930 | + | 0.102699i | −0.894148 | − | 0.447771i | \(-0.852218\pi\) |
0.834855 | + | 0.550470i | \(0.185551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 758.638i | 0.863070i | ||||||||
\(880\) | 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 | \(0.521465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 261.000 | − | 452.065i | 0.294915 | − | 0.510808i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1029.00 | − | 594.093i | −1.16009 | − | 0.669778i | −0.208765 | − | 0.977966i | \(-0.566944\pi\) |
−0.951326 | + | 0.308188i | \(0.900278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 27.7128i | 0.0179978 | + | 0.0311730i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −121.500 | − | 70.1481i | −0.136364 | − | 0.0787296i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −462.000 | + | 266.736i | −0.517357 | + | 0.298696i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 108.000 | − | 187.061i | 0.120670 | − | 0.209007i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 288.000 | + | 166.277i | 0.321070 | + | 0.185370i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1441.07i | − | 1.60297i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 366.000 | 0.405316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −696.000 | − | 401.836i | −0.769061 | − | 0.444017i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 347.500 | + | 601.888i | 0.383131 | + | 0.663603i | 0.991508 | − | 0.130046i | \(-0.0415124\pi\) |
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 405.300i | 0.445874i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1500.00 | − | 866.025i | 1.64654 | − | 0.950632i | 0.668110 | − | 0.744062i | \(-0.267103\pi\) |
0.978432 | − | 0.206569i | \(-0.0662299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.0000 | − | 72.7461i | 0.0460022 | − | 0.0796781i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 504.000 | − | 290.985i | 0.550820 | − | 0.318016i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 318.697i | − | 0.347543i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.0000 | −0.0609358 | −0.0304679 | − | 0.999536i | \(-0.509700\pi\) | ||||
−0.0304679 | + | 0.999536i | \(0.509700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −799.500 | − | 1384.77i | −0.868078 | − | 1.50356i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 108.000 | + | 62.3538i | 0.117010 | + | 0.0675556i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 221.000 | + | 382.783i | 0.238919 | + | 0.413820i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −180.000 | − | 311.769i | −0.194175 | − | 0.336321i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −690.000 | + | 398.372i | −0.742734 | + | 0.428818i | −0.823063 | − | 0.567951i | \(-0.807736\pi\) |
0.0803285 | + | 0.996768i | \(0.474403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −247.500 | + | 428.683i | −0.265843 | + | 0.460454i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 737.854i | 0.790840i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 93.5307i | 0.100033i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 470.000 | 0.501601 | 0.250800 | − | 0.968039i | \(-0.419306\pi\) | ||||
0.250800 | + | 0.968039i | \(0.419306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 232.500 | − | 402.702i | 0.247604 | − | 0.428862i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −348.000 | − | 200.918i | −0.369819 | − | 0.213515i | 0.303560 | − | 0.952812i | \(-0.401825\pi\) |
−0.673380 | + | 0.739297i | \(0.735158\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −168.000 | − | 290.985i | −0.178155 | − | 0.308573i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 187.061i | − | 0.197949i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.50000 | − | 0.866025i | 0.00158395 | − | 0.000914494i | −0.499208 | − | 0.866482i | \(-0.666376\pi\) |
0.500792 | + | 0.865568i | \(0.333042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 130.000 | − | 225.167i | 0.136986 | − | 0.237267i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −126.000 | − | 72.7461i | −0.132492 | − | 0.0764944i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 826.188i | 0.866934i | 0.901169 | + | 0.433467i | \(0.142710\pi\) | ||||
−0.901169 | + | 0.433467i | \(0.857290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −804.000 | −0.841885 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 234.000 | 0.244514 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −327.000 | − | 188.794i | −0.340980 | − | 0.196865i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.5000 | − | 54.5596i | −0.0327784 | − | 0.0567738i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1093.50 | − | 631.333i | −1.13551 | − | 0.655589i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 795.000 | − | 458.993i | 0.823834 | − | 0.475641i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 601.000 | − | 1040.96i | 0.621510 | − | 1.07649i | −0.367695 | − | 0.929946i | \(-0.619853\pi\) |
0.989205 | − | 0.146540i | \(-0.0468137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 445.500 | − | 257.210i | 0.459752 | − | 0.265438i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 187.061i | 0.192648i | 0.995350 | + | 0.0963241i | \(0.0307085\pi\) | ||||
−0.995350 | + | 0.0963241i | \(0.969291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | 0.0102775 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −78.0000 | − | 135.100i | −0.0800000 | − | 0.138564i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −361.500 | − | 208.712i | −0.370010 | − | 0.213626i | 0.303453 | − | 0.952847i | \(-0.401861\pi\) |
−0.673463 | + | 0.739221i | \(0.735194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 108.000 | + | 187.061i | 0.110317 | + | 0.191074i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 234.000 | − | 405.300i | 0.238532 | − | 0.413150i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1011.00 | + | 583.701i | −1.02848 | + | 0.593796i | −0.916550 | − | 0.399920i | \(-0.869038\pi\) |
−0.111934 | + | 0.993716i | \(0.535705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −216.000 | + | 374.123i | −0.219289 | + | 0.379820i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 290.985i | 0.294817i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1690.48i | − | 1.70928i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1420.00 | 1.43290 | 0.716448 | − | 0.697640i | \(-0.245767\pi\) | ||||
0.716448 | + | 0.697640i | \(0.245767\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.00000 | + | 5.19615i | −0.00302115 | + | 0.00523278i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −870.000 | − | 502.295i | −0.874372 | − | 0.504819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −262.000 | − | 453.797i | −0.262788 | − | 0.455163i | 0.704193 | − | 0.710008i | \(-0.251309\pi\) |
−0.966982 | + | 0.254845i | \(0.917975\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 918.000 | 0.918919 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))