Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.a.1151.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 1.50000i | −0.783349 | + | 0.452267i | −0.837616 | − | 0.546259i | \(-0.816051\pi\) |
0.0542666 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 2.44949 | + | 1.00000i | 0.654654 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.95680 | + | 5.12132i | 0.717128 | + | 1.24210i | 0.962133 | + | 0.272581i | \(0.0878772\pi\) |
−0.245005 | + | 0.969522i | \(0.578789\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.12132 | − | 2.95680i | −1.17491 | − | 0.678335i | −0.220080 | − | 0.975482i | \(-0.570632\pi\) |
−0.954832 | + | 0.297146i | \(0.903965\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | −3.67423 | − | 2.12132i | −0.766131 | − | 0.442326i | 0.0653618 | − | 0.997862i | \(-0.479180\pi\) |
−0.831493 | + | 0.555536i | \(0.812513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.22474 | − | 2.12132i | 0.240192 | − | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.62132 | − | 2.09077i | −0.306401 | − | 0.395118i | ||||
\(29\) | − | 7.24264i | − | 1.34492i | −0.740131 | − | 0.672462i | \(-0.765237\pi\) | ||
0.740131 | − | 0.672462i | \(-0.234763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.86396 | + | 4.54026i | −1.41241 | + | 0.815455i | −0.995615 | − | 0.0935461i | \(-0.970180\pi\) |
−0.416794 | + | 0.909001i | \(0.636846\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.91359i | − | 1.01417i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.121320 | + | 0.210133i | −0.0199449 | + | 0.0345457i | −0.875826 | − | 0.482628i | \(-0.839682\pi\) |
0.855881 | + | 0.517173i | \(0.173016\pi\) | |||||||
\(38\) | 2.95680 | + | 5.12132i | 0.479656 | + | 0.830788i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8272 | 1.84710 | 0.923548 | − | 0.383483i | \(-0.125276\pi\) | ||||
0.923548 | + | 0.383483i | \(0.125276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.242641 | 0.0370024 | 0.0185012 | − | 0.999829i | \(-0.494111\pi\) | ||||
0.0185012 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(44\) | −2.59808 | − | 1.50000i | −0.391675 | − | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.12132 | + | 3.67423i | 0.312772 | + | 0.541736i | ||||
\(47\) | 2.95680 | − | 5.12132i | 0.431293 | − | 0.747021i | −0.565692 | − | 0.824617i | \(-0.691391\pi\) |
0.996985 | + | 0.0775953i | \(0.0247242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.12132 | + | 1.22474i | −0.294174 | + | 0.169842i | ||||
\(53\) | 6.27231 | − | 3.62132i | 0.861568 | − | 0.497427i | −0.00296896 | − | 0.999996i | \(-0.500945\pi\) |
0.864537 | + | 0.502569i | \(0.167612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.358719 | + | 2.62132i | 0.0479359 | + | 0.350289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.62132 | + | 6.27231i | −0.475503 | + | 0.823595i | ||||
\(59\) | 4.03295 | + | 6.98528i | 0.525046 | + | 0.909406i | 0.999575 | + | 0.0291661i | \(0.00928518\pi\) |
−0.474529 | + | 0.880240i | \(0.657381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.878680 | + | 0.507306i | 0.112503 | + | 0.0649539i | 0.555196 | − | 0.831720i | \(-0.312643\pi\) |
−0.442692 | + | 0.896674i | \(0.645977\pi\) | |||||||
\(62\) | 9.08052 | 1.15323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | −2.95680 | + | 5.12132i | −0.358564 | + | 0.621051i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.75736i | 0.208560i | 0.994548 | + | 0.104280i | \(0.0332538\pi\) | ||||
−0.994548 | + | 0.104280i | \(0.966746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.24264 | − | 0.717439i | 0.145440 | − | 0.0839699i | −0.425514 | − | 0.904952i | \(-0.639907\pi\) |
0.570954 | + | 0.820982i | \(0.306573\pi\) | |||||||
\(74\) | 0.210133 | − | 0.121320i | 0.0244275 | − | 0.0141032i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.91359i | − | 0.678335i | ||||||
\(77\) | 6.27231 | − | 4.86396i | 0.714796 | − | 0.554300i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.37868 | − | 2.38794i | 0.155114 | − | 0.268665i | −0.777987 | − | 0.628281i | \(-0.783759\pi\) |
0.933100 | + | 0.359616i | \(0.117092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.2426 | − | 5.91359i | −1.13111 | − | 0.653047i | ||||
\(83\) | −6.63103 | −0.727850 | −0.363925 | − | 0.931428i | \(-0.618564\pi\) | ||||
−0.363925 | + | 0.931428i | \(0.618564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.210133 | − | 0.121320i | −0.0226592 | − | 0.0130823i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | 5.19615 | − | 9.00000i | 0.550791 | − | 0.953998i | −0.447427 | − | 0.894321i | \(-0.647659\pi\) |
0.998218 | − | 0.0596775i | \(-0.0190072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.878680 | − | 6.42090i | −0.0921107 | − | 0.673093i | ||||
\(92\) | − | 4.24264i | − | 0.442326i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.12132 | + | 2.95680i | −0.528224 | + | 0.304970i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.5592i | − | 1.37673i | −0.725364 | − | 0.688366i | \(-0.758328\pi\) | ||
0.725364 | − | 0.688366i | \(-0.241672\pi\) | |||||||
\(98\) | −6.77962 | − | 1.74264i | −0.684845 | − | 0.176033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.75736 | + | 2.74666i | 0.468757 | + | 0.270637i | 0.715719 | − | 0.698388i | \(-0.246099\pi\) |
−0.246963 | + | 0.969025i | \(0.579432\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.24264 | −0.703467 | ||||||||
\(107\) | 9.94655 | + | 5.74264i | 0.961569 | + | 0.555162i | 0.896656 | − | 0.442729i | \(-0.145990\pi\) |
0.0649133 | + | 0.997891i | \(0.479323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.24264 | − | 16.0087i | −0.885284 | − | 1.53336i | −0.845387 | − | 0.534154i | \(-0.820630\pi\) |
−0.0398971 | − | 0.999204i | \(-0.512703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | − | 2.44949i | 0.0944911 | − | 0.231455i | ||||
\(113\) | 8.48528i | 0.798228i | 0.916901 | + | 0.399114i | \(0.130682\pi\) | ||||
−0.916901 | + | 0.399114i | \(0.869318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.27231 | − | 3.62132i | 0.582369 | − | 0.336231i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.06591i | − | 0.742527i | ||||||
\(119\) | −9.58783 | − | 12.3640i | −0.878915 | − | 1.13340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | −0.507306 | − | 0.878680i | −0.0459293 | − | 0.0795519i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.86396 | − | 4.54026i | −0.706205 | − | 0.407727i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.24264 | −0.287738 | −0.143869 | − | 0.989597i | \(-0.545954\pi\) | ||||
−0.143869 | + | 0.989597i | \(0.545954\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | + | 4.50000i | −0.226995 | + | 0.393167i | −0.956916 | − | 0.290365i | \(-0.906223\pi\) |
0.729921 | + | 0.683531i | \(0.239557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4853 | + | 5.91359i | 1.25603 | + | 0.512773i | ||||
\(134\) | 10.0000i | 0.863868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.12132 | − | 2.95680i | 0.439150 | − | 0.253543i | ||||
\(137\) | 2.15232 | − | 1.24264i | 0.183885 | − | 0.106166i | −0.405232 | − | 0.914214i | \(-0.632809\pi\) |
0.589117 | + | 0.808048i | \(0.299476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.594346i | − | 0.0504118i | −0.999682 | − | 0.0252059i | \(-0.991976\pi\) | ||
0.999682 | − | 0.0252059i | \(-0.00802413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.878680 | − | 1.52192i | 0.0737372 | − | 0.127717i | ||||
\(143\) | −3.67423 | − | 6.36396i | −0.307255 | − | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.43488 | −0.118751 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.242641 | −0.0199449 | ||||||||
\(149\) | −3.04384 | − | 1.75736i | −0.249361 | − | 0.143968i | 0.370111 | − | 0.928988i | \(-0.379320\pi\) |
−0.619472 | + | 0.785019i | \(0.712653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.62132 | − | 4.54026i | −0.213320 | − | 0.369481i | 0.739432 | − | 0.673232i | \(-0.235094\pi\) |
−0.952752 | + | 0.303751i | \(0.901761\pi\) | |||||||
\(152\) | −2.95680 | + | 5.12132i | −0.239828 | + | 0.415394i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.86396 | + | 1.07616i | −0.633696 | + | 0.0867193i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7279 | + | 7.34847i | −1.01580 | + | 0.586472i | −0.912884 | − | 0.408219i | \(-0.866150\pi\) |
−0.102915 | + | 0.994690i | \(0.532817\pi\) | |||||||
\(158\) | −2.38794 | + | 1.37868i | −0.189975 | + | 0.109682i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | + | 4.24264i | 0.819028 | + | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.12132 | + | 1.94218i | −0.0878286 | + | 0.152124i | −0.906593 | − | 0.422006i | \(-0.861326\pi\) |
0.818764 | + | 0.574130i | \(0.194659\pi\) | |||||||
\(164\) | 5.91359 | + | 10.2426i | 0.461774 | + | 0.799816i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.74264 | + | 3.31552i | 0.445715 | + | 0.257334i | ||||
\(167\) | 16.1318 | 1.24832 | 0.624159 | − | 0.781298i | \(-0.285442\pi\) | ||||
0.624159 | + | 0.781298i | \(0.285442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.121320 | + | 0.210133i | 0.00925059 | + | 0.0160225i | ||||
\(173\) | 10.3923 | − | 18.0000i | 0.790112 | − | 1.36851i | −0.135785 | − | 0.990738i | \(-0.543356\pi\) |
0.925897 | − | 0.377776i | \(-0.123311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | + | 5.19615i | −0.674579 | + | 0.389468i | ||||
\(179\) | 22.9369 | − | 13.2426i | 1.71439 | − | 0.989801i | 0.785966 | − | 0.618269i | \(-0.212166\pi\) |
0.928420 | − | 0.371532i | \(-0.121167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8272i | 0.879108i | 0.898216 | + | 0.439554i | \(0.144863\pi\) | ||||
−0.898216 | + | 0.439554i | \(0.855137\pi\) | |||||||
\(182\) | −2.44949 | + | 6.00000i | −0.181568 | + | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.12132 | + | 3.67423i | −0.156386 | + | 0.270868i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3640 | − | 8.87039i | −1.12352 | − | 0.648667i | ||||
\(188\) | 5.91359 | 0.431293 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.34847 | + | 4.24264i | 0.531717 | + | 0.306987i | 0.741715 | − | 0.670715i | \(-0.234013\pi\) |
−0.209999 | + | 0.977702i | \(0.567346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.74264 | + | 8.21449i | 0.341383 | + | 0.591292i | 0.984690 | − | 0.174316i | \(-0.0557714\pi\) |
−0.643307 | + | 0.765608i | \(0.722438\pi\) | |||||||
\(194\) | −6.77962 | + | 11.7426i | −0.486748 | + | 0.843072i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | + | 4.89898i | 0.357143 | + | 0.349927i | ||||
\(197\) | − | 26.4853i | − | 1.88700i | −0.331375 | − | 0.943499i | \(-0.607513\pi\) | ||
0.331375 | − | 0.943499i | \(-0.392487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9706 | − | 11.5300i | 1.41568 | − | 0.817341i | 0.419761 | − | 0.907635i | \(-0.362114\pi\) |
0.995915 | + | 0.0902942i | \(0.0287807\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | + | 18.9853i | 0.182349 | + | 1.33251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.74666 | − | 4.75736i | −0.191369 | − | 0.331461i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12132 | − | 1.22474i | −0.147087 | − | 0.0849208i | ||||
\(209\) | 17.7408 | 1.22716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.242641 | −0.0167041 | −0.00835204 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835204 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(212\) | 6.27231 | + | 3.62132i | 0.430784 | + | 0.248713i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.74264 | − | 9.94655i | −0.392559 | − | 0.679932i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9853 | − | 14.7224i | 1.28880 | − | 0.999424i | ||||
\(218\) | 18.4853i | 1.25198i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.5446 | + | 7.24264i | −0.843843 | + | 0.487193i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.15232i | − | 0.144130i | −0.997400 | − | 0.0720649i | \(-0.977041\pi\) | ||
0.997400 | − | 0.0720649i | \(-0.0229589\pi\) | |||||||
\(224\) | −2.09077 | + | 1.62132i | −0.139695 | + | 0.108329i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.24264 | − | 7.34847i | 0.282216 | − | 0.488813i | ||||
\(227\) | −7.79423 | − | 13.5000i | −0.517321 | − | 0.896026i | −0.999798 | − | 0.0201176i | \(-0.993596\pi\) |
0.482476 | − | 0.875909i | \(-0.339737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | − | 6.92820i | −0.792982 | − | 0.457829i | 0.0480291 | − | 0.998846i | \(-0.484706\pi\) |
−0.841011 | + | 0.541017i | \(0.818039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.24264 | −0.475503 | ||||||||
\(233\) | −16.2189 | − | 9.36396i | −1.06253 | − | 0.613453i | −0.136401 | − | 0.990654i | \(-0.543554\pi\) |
−0.926132 | + | 0.377200i | \(0.876887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.03295 | + | 6.98528i | −0.262523 | + | 0.454703i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.12132 | + | 15.5014i | 0.137505 | + | 1.00481i | ||||
\(239\) | − | 12.7279i | − | 0.823301i | −0.911342 | − | 0.411650i | \(-0.864952\pi\) | ||
0.911342 | − | 0.411650i | \(-0.135048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.25736 | − | 3.61269i | 0.403072 | − | 0.232714i | −0.284737 | − | 0.958606i | \(-0.591906\pi\) |
0.687809 | + | 0.725892i | \(0.258573\pi\) | |||||||
\(242\) | 1.73205 | − | 1.00000i | 0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.01461i | 0.0649539i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.24264 | − | 12.5446i | 0.460838 | − | 0.798195i | ||||
\(248\) | 4.54026 | + | 7.86396i | 0.288307 | + | 0.499362i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4156 | −1.73046 | −0.865230 | − | 0.501375i | \(-0.832828\pi\) | ||||
−0.865230 | + | 0.501375i | \(0.832828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7279 | 0.800198 | ||||||||
\(254\) | 2.80821 | + | 1.62132i | 0.176203 | + | 0.101731i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.15232 | + | 3.72792i | −0.134258 | + | 0.232541i | −0.925314 | − | 0.379203i | \(-0.876198\pi\) |
0.791056 | + | 0.611744i | \(0.209532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.242641 | − | 0.594346i | 0.0150770 | − | 0.0369309i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.50000 | − | 2.59808i | 0.278011 | − | 0.160510i | ||||
\(263\) | −13.1750 | + | 7.60660i | −0.812407 | + | 0.469043i | −0.847791 | − | 0.530331i | \(-0.822068\pi\) |
0.0353843 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.58783 | − | 12.3640i | −0.587867 | − | 0.758083i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00000 | − | 8.66025i | 0.305424 | − | 0.529009i | ||||
\(269\) | −6.98975 | − | 12.1066i | −0.426173 | − | 0.738153i | 0.570357 | − | 0.821397i | \(-0.306805\pi\) |
−0.996529 | + | 0.0832447i | \(0.973472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.37868 | − | 3.10538i | −0.326732 | − | 0.188639i | 0.327658 | − | 0.944797i | \(-0.393741\pi\) |
−0.654389 | + | 0.756158i | \(0.727074\pi\) | |||||||
\(272\) | −5.91359 | −0.358564 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.48528 | −0.150141 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.48528 | + | 11.2328i | 0.389663 | + | 0.674916i | 0.992404 | − | 0.123021i | \(-0.0392582\pi\) |
−0.602741 | + | 0.797937i | \(0.705925\pi\) | |||||||
\(278\) | −0.297173 | + | 0.514719i | −0.0178232 | + | 0.0308708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3640 | − | 10.6024i | 1.09162 | − | 0.630250i | 0.157616 | − | 0.987501i | \(-0.449619\pi\) |
0.934008 | + | 0.357251i | \(0.116286\pi\) | |||||||
\(284\) | −1.52192 | + | 0.878680i | −0.0903092 | + | 0.0521400i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.34847i | 0.434524i | ||||||||
\(287\) | −31.0028 | + | 4.24264i | −1.83004 | + | 0.250435i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.98528 | + | 15.5630i | −0.528546 | + | 0.915468i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.24264 | + | 0.717439i | 0.0727200 | + | 0.0419849i | ||||
\(293\) | 0.717439 | 0.0419132 | 0.0209566 | − | 0.999780i | \(-0.493329\pi\) | ||||
0.0209566 | + | 0.999780i | \(0.493329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.210133 | + | 0.121320i | 0.0122137 | + | 0.00705160i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.75736 | + | 3.04384i | 0.101801 | + | 0.176325i | ||||
\(299\) | 5.19615 | − | 9.00000i | 0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.636039 | + | 0.0870399i | −0.0366607 | + | 0.00501690i | ||||
\(302\) | 5.24264i | 0.301680i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.12132 | − | 2.95680i | 0.293728 | − | 0.169584i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.97204i | 0.569134i | 0.958656 | + | 0.284567i | \(0.0918499\pi\) | ||||
−0.958656 | + | 0.284567i | \(0.908150\pi\) | |||||||
\(308\) | 7.34847 | + | 3.00000i | 0.418718 | + | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.47871 | − | 7.75736i | −0.253965 | − | 0.439879i | 0.710649 | − | 0.703547i | \(-0.248401\pi\) |
−0.964614 | + | 0.263667i | \(0.915068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9853 | − | 9.22911i | −0.903542 | − | 0.521660i | −0.0251940 | − | 0.999683i | \(-0.508020\pi\) |
−0.878348 | + | 0.478023i | \(0.841354\pi\) | |||||||
\(314\) | 14.6969 | 0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.75736 | 0.155114 | ||||||||
\(317\) | −1.07616 | − | 0.621320i | −0.0604431 | − | 0.0348968i | 0.469474 | − | 0.882946i | \(-0.344444\pi\) |
−0.529917 | + | 0.848050i | \(0.677777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8640 | + | 18.8169i | 0.608265 | + | 1.05355i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.87868 | − | 8.87039i | −0.383334 | − | 0.494327i | ||||
\(323\) | − | 34.9706i | − | 1.94581i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.94218 | − | 1.12132i | 0.107568 | − | 0.0621042i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 11.8272i | − | 0.653047i | ||||||
\(329\) | −5.91359 | + | 14.4853i | −0.326027 | + | 0.798599i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.7279 | − | 28.9736i | 0.919450 | − | 1.59253i | 0.119197 | − | 0.992871i | \(-0.461968\pi\) |
0.800253 | − | 0.599663i | \(-0.204699\pi\) | |||||||
\(332\) | −3.31552 | − | 5.74264i | −0.181963 | − | 0.315168i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.9706 | − | 8.06591i | −0.764435 | − | 0.441347i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | −6.06218 | − | 3.50000i | −0.329739 | − | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.6208 | − | 23.5919i | 0.737607 | − | 1.27757i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | − | 0.242641i | − | 0.0130823i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | + | 10.3923i | −0.967686 | + | 0.558694i | ||||
\(347\) | −2.15232 | + | 1.24264i | −0.115542 | + | 0.0667084i | −0.556657 | − | 0.830742i | \(-0.687916\pi\) |
0.441115 | + | 0.897451i | \(0.354583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.27541i | − | 0.121800i | −0.998144 | − | 0.0608999i | \(-0.980603\pi\) | ||
0.998144 | − | 0.0608999i | \(-0.0193971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | 4.47871 | + | 7.75736i | 0.238378 | + | 0.412883i | 0.960249 | − | 0.279145i | \(-0.0900510\pi\) |
−0.721871 | + | 0.692028i | \(0.756718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.4853 | −1.39979 | ||||||||
\(359\) | −15.5885 | − | 9.00000i | −0.822727 | − | 0.475002i | 0.0286287 | − | 0.999590i | \(-0.490886\pi\) |
−0.851356 | + | 0.524588i | \(0.824219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.98528 | + | 13.8309i | 0.420278 | + | 0.727943i | ||||
\(362\) | 5.91359 | − | 10.2426i | 0.310811 | − | 0.538341i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.12132 | − | 3.97141i | 0.268430 | − | 0.208158i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3492 | − | 7.70719i | 0.696825 | − | 0.402312i | −0.109339 | − | 0.994005i | \(-0.534873\pi\) |
0.806164 | + | 0.591693i | \(0.201540\pi\) | |||||||
\(368\) | 3.67423 | − | 2.12132i | 0.191533 | − | 0.110581i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.1427 | + | 11.7426i | −0.786170 | + | 0.609648i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7279 | + | 25.5095i | −0.762583 | + | 1.32083i | 0.178932 | + | 0.983861i | \(0.442736\pi\) |
−0.941515 | + | 0.336971i | \(0.890598\pi\) | |||||||
\(374\) | 8.87039 | + | 15.3640i | 0.458677 | + | 0.794452i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.12132 | − | 2.95680i | −0.264112 | − | 0.152485i | ||||
\(377\) | 17.7408 | 0.913696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4853 | 0.641326 | 0.320663 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320663 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.24264 | − | 7.34847i | −0.217072 | − | 0.375980i | ||||
\(383\) | 11.1097 | − | 19.2426i | 0.567681 | − | 0.983253i | −0.429113 | − | 0.903251i | \(-0.641174\pi\) |
0.996795 | − | 0.0800023i | \(-0.0254928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.48528i | − | 0.482788i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.7426 | − | 6.77962i | 0.596142 | − | 0.344183i | ||||
\(389\) | −27.2416 | + | 15.7279i | −1.38120 | + | 0.797437i | −0.992302 | − | 0.123843i | \(-0.960478\pi\) |
−0.388900 | + | 0.921280i | \(0.627145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.0892i | − | 1.26882i | ||||||
\(392\) | −1.88064 | − | 6.74264i | −0.0949865 | − | 0.340555i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.2426 | + | 22.9369i | −0.667155 | + | 1.15555i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0000 | − | 6.92820i | −0.602263 | − | 0.347717i | 0.167668 | − | 0.985843i | \(-0.446376\pi\) |
−0.769931 | + | 0.638127i | \(0.779710\pi\) | |||||||
\(398\) | −23.0600 | −1.15589 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.1213 | − | 19.2627i | −0.553992 | − | 0.959543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.24264 | − | 17.7408i | 0.359446 | − | 0.880460i | ||||
\(407\) | − | 0.727922i | − | 0.0360818i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9853 | − | 7.49706i | 0.642081 | − | 0.370706i | −0.143335 | − | 0.989674i | \(-0.545783\pi\) |
0.785416 | + | 0.618969i | \(0.212449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.49333i | 0.270637i | ||||||||
\(413\) | −13.0774 | − | 16.8640i | −0.643498 | − | 0.829821i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.22474 | + | 2.12132i | 0.0600481 | + | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.3640 | − | 8.87039i | −0.751476 | − | 0.433865i | ||||
\(419\) | 23.6544 | 1.15559 | 0.577796 | − | 0.816181i | \(-0.303913\pi\) | ||||
0.577796 | + | 0.816181i | \(0.303913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2426 | −0.694144 | −0.347072 | − | 0.937839i | \(-0.612824\pi\) | ||||
−0.347072 | + | 0.937839i | \(0.612824\pi\) | |||||||
\(422\) | 0.210133 | + | 0.121320i | 0.0102291 | + | 0.00590578i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.62132 | − | 6.27231i | −0.175867 | − | 0.304610i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.48528 | − | 1.01461i | −0.120271 | − | 0.0491005i | ||||
\(428\) | 11.4853i | 0.555162i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.04384 | + | 1.75736i | −0.146616 | + | 0.0846490i | −0.571514 | − | 0.820593i | \(-0.693644\pi\) |
0.424897 | + | 0.905242i | \(0.360310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46410i | 0.166474i | 0.996530 | + | 0.0832370i | \(0.0265259\pi\) | ||||
−0.996530 | + | 0.0832370i | \(0.973474\pi\) | |||||||
\(434\) | −23.8030 | + | 3.25736i | −1.14258 | + | 0.156358i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.24264 | − | 16.0087i | 0.442642 | − | 0.766679i | ||||
\(437\) | 12.5446 | + | 21.7279i | 0.600091 | + | 1.03939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.5919 | − | 8.42463i | −0.696433 | − | 0.402086i | 0.109585 | − | 0.993977i | \(-0.465048\pi\) |
−0.806017 | + | 0.591892i | \(0.798381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.4853 | 0.688995 | ||||||||
\(443\) | 14.2512 | + | 8.22792i | 0.677094 | + | 0.390920i | 0.798759 | − | 0.601651i | \(-0.205490\pi\) |
−0.121665 | + | 0.992571i | \(0.538823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.07616 | + | 1.86396i | −0.0509576 | + | 0.0882611i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.62132 | − | 0.358719i | 0.123846 | − | 0.0169479i | ||||
\(449\) | 1.75736i | 0.0829349i | 0.999140 | + | 0.0414675i | \(0.0132033\pi\) | ||||
−0.999140 | + | 0.0414675i | \(0.986797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.7279 | + | 17.7408i | −1.44692 | + | 0.835380i | ||||
\(452\) | −7.34847 | + | 4.24264i | −0.345643 | + | 0.199557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.5885i | 0.731603i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | + | 19.9186i | −0.537947 | + | 0.931752i | 0.461067 | + | 0.887365i | \(0.347467\pi\) |
−0.999014 | + | 0.0443868i | \(0.985867\pi\) | |||||||
\(458\) | 6.92820 | + | 12.0000i | 0.323734 | + | 0.560723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.6118 | 1.51888 | 0.759441 | − | 0.650576i | \(-0.225472\pi\) | ||||
0.759441 | + | 0.650576i | \(0.225472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4558 | 1.36893 | 0.684465 | − | 0.729046i | \(-0.260036\pi\) | ||||
0.684465 | + | 0.729046i | \(0.260036\pi\) | |||||||
\(464\) | 6.27231 | + | 3.62132i | 0.291185 | + | 0.168116i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.36396 | + | 16.2189i | 0.433777 | + | 0.751324i | ||||
\(467\) | −19.8931 | + | 34.4558i | −0.920542 | + | 1.59443i | −0.121965 | + | 0.992534i | \(0.538920\pi\) |
−0.798578 | + | 0.601892i | \(0.794414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2132 | + | 20.9077i | 0.748656 | + | 0.965428i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.98528 | − | 4.03295i | 0.321524 | − | 0.185632i | ||||
\(473\) | −0.630399 | + | 0.363961i | −0.0289858 | + | 0.0167349i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.91359 | − | 14.4853i | 0.271049 | − | 0.663932i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.36396 | + | 11.0227i | −0.291081 | + | 0.504167i | ||||
\(479\) | 6.00063 | + | 10.3934i | 0.274176 | + | 0.474886i | 0.969927 | − | 0.243397i | \(-0.0782616\pi\) |
−0.695751 | + | 0.718283i | \(0.744928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.514719 | − | 0.297173i | −0.0234691 | − | 0.0135499i | ||||
\(482\) | −7.22538 | −0.329107 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.10660 | − | 12.3090i | −0.322031 | − | 0.557774i | 0.658876 | − | 0.752251i | \(-0.271032\pi\) |
−0.980907 | + | 0.194478i | \(0.937699\pi\) | |||||||
\(488\) | 0.507306 | − | 0.878680i | 0.0229647 | − | 0.0397760i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9706i | 0.630483i | 0.949012 | + | 0.315241i | \(0.102085\pi\) | ||||
−0.949012 | + | 0.315241i | \(0.897915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.0919 | − | 21.4150i | 1.67053 | − | 0.964483i | ||||
\(494\) | −12.5446 | + | 7.24264i | −0.564409 | + | 0.325862i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.08052i | − | 0.407727i | ||||||
\(497\) | −0.630399 | − | 4.60660i | −0.0282773 | − | 0.206634i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.9706 | + | 27.6618i | −0.714941 | + | 1.23831i | 0.248042 | + | 0.968749i | \(0.420213\pi\) |
−0.962982 | + | 0.269564i | \(0.913120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.7426 | + | 13.7078i | 1.05969 | + | 0.611810i | ||||
\(503\) | 31.0028 | 1.38235 | 0.691174 | − | 0.722688i | \(-0.257094\pi\) | ||||
0.691174 | + | 0.722688i | \(0.257094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.0227 | − | 6.36396i | −0.490019 | − | 0.282913i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.62132 | − | 2.80821i | −0.0719345 | − | 0.124594i | ||||
\(509\) | 8.59871 | − | 14.8934i | 0.381131 | − | 0.660138i | −0.610093 | − | 0.792330i | \(-0.708868\pi\) |
0.991224 | + | 0.132191i | \(0.0422013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 2.32640i | −0.132712 | + | 0.102914i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.72792 | − | 2.15232i | 0.164432 | − | 0.0949346i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.7408i | 0.780238i | ||||||||
\(518\) | −0.507306 | + | 0.393398i | −0.0222897 | + | 0.0172849i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.9363 | − | 29.3345i | −0.741993 | − | 1.28517i | −0.951587 | − | 0.307380i | \(-0.900548\pi\) |
0.209594 | − | 0.977788i | \(-0.432786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.84924 | − | 3.37706i | −0.255770 | − | 0.147669i | 0.366634 | − | 0.930365i | \(-0.380510\pi\) |
−0.622403 | + | 0.782697i | \(0.713844\pi\) | |||||||
\(524\) | −5.19615 | −0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.2132 | 0.663327 | ||||||||
\(527\) | −46.5043 | − | 26.8492i | −2.02576 | − | 1.16957i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | − | 4.33013i | −0.108696 | − | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.12132 | + | 15.5014i | 0.0919709 | + | 0.672072i | ||||
\(533\) | 28.9706i | 1.25485i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.66025 | + | 5.00000i | −0.374066 | + | 0.215967i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.9795i | 0.602699i | ||||||||
\(539\) | −14.6969 | + | 15.0000i | −0.633042 | + | 0.646096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.36396 | + | 12.7548i | −0.316601 | + | 0.548370i | −0.979777 | − | 0.200094i | \(-0.935875\pi\) |
0.663175 | + | 0.748464i | \(0.269208\pi\) | |||||||
\(542\) | 3.10538 | + | 5.37868i | 0.133388 | + | 0.231034i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.12132 | + | 2.95680i | 0.219575 | + | 0.126772i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.6985 | 1.69738 | 0.848692 | − | 0.528887i | \(-0.177390\pi\) | ||||
0.848692 | + | 0.528887i | \(0.177390\pi\) | |||||||
\(548\) | 2.15232 | + | 1.24264i | 0.0919424 | + | 0.0530830i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.4150 | + | 37.0919i | −0.912310 | + | 1.58017i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.75736 | + | 6.75412i | −0.117255 | + | 0.287215i | ||||
\(554\) | − | 12.9706i | − | 0.551066i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.514719 | − | 0.297173i | 0.0218289 | − | 0.0126029i | ||||
\(557\) | −8.42463 | + | 4.86396i | −0.356963 | + | 0.206093i | −0.667748 | − | 0.744388i | \(-0.732741\pi\) |
0.310785 | + | 0.950480i | \(0.399408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.594346i | 0.0251382i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | + | 5.19615i | −0.126547 | + | 0.219186i | ||||
\(563\) | −17.2950 | − | 29.9558i | −0.728898 | − | 1.26249i | −0.957349 | − | 0.288933i | \(-0.906700\pi\) |
0.228451 | − | 0.973555i | \(-0.426634\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.2049 | −0.891307 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.75736 | 0.0737372 | ||||||||
\(569\) | −8.87039 | − | 5.12132i | −0.371866 | − | 0.214697i | 0.302407 | − | 0.953179i | \(-0.402210\pi\) |
−0.674273 | + | 0.738482i | \(0.735543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.36396 | − | 7.55860i | −0.182626 | − | 0.316318i | 0.760148 | − | 0.649750i | \(-0.225126\pi\) |
−0.942774 | + | 0.333432i | \(0.891793\pi\) | |||||||
\(572\) | 3.67423 | − | 6.36396i | 0.153627 | − | 0.266091i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 28.9706 | + | 11.8272i | 1.20921 | + | 0.493657i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.25736 | + | 5.34474i | −0.385389 | + | 0.222504i | −0.680160 | − | 0.733063i | \(-0.738090\pi\) |
0.294771 | + | 0.955568i | \(0.404757\pi\) | |||||||
\(578\) | 15.5630 | − | 8.98528i | 0.647334 | − | 0.373738i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3821 | − | 2.37868i | 0.721129 | − | 0.0986843i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8640 | + | 18.8169i | −0.449939 | + | 0.779318i | ||||
\(584\) | −0.717439 | − | 1.24264i | −0.0296878 | − | 0.0514208i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.621320 | − | 0.358719i | −0.0256665 | − | 0.0148186i | ||||
\(587\) | −5.19615 | −0.214468 | −0.107234 | − | 0.994234i | \(-0.534199\pi\) | ||||
−0.107234 | + | 0.994234i | \(0.534199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.6985 | 2.21261 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.121320 | − | 0.210133i | −0.00498624 | − | 0.00863641i | ||||
\(593\) | 11.7401 | − | 20.3345i | 0.482110 | − | 0.835039i | −0.517679 | − | 0.855575i | \(-0.673204\pi\) |
0.999789 | + | 0.0205360i | \(0.00653726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.51472i | − | 0.143968i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.00000 | + | 5.19615i | −0.368037 | + | 0.212486i | ||||
\(599\) | −6.45695 | + | 3.72792i | −0.263824 | + | 0.152319i | −0.626078 | − | 0.779761i | \(-0.715341\pi\) |
0.362254 | + | 0.932079i | \(0.382007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3572i | 0.952760i | 0.879240 | + | 0.476380i | \(0.158051\pi\) | ||||
−0.879240 | + | 0.476380i | \(0.841949\pi\) | |||||||
\(602\) | 0.594346 | + | 0.242641i | 0.0242237 | + | 0.00988930i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.62132 | − | 4.54026i | 0.106660 | − | 0.184741i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3787 | + | 10.0336i | 0.705379 | + | 0.407251i | 0.809348 | − | 0.587330i | \(-0.199821\pi\) |
−0.103969 | + | 0.994581i | \(0.533154\pi\) | |||||||
\(608\) | −5.91359 | −0.239828 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5446 | + | 7.24264i | 0.507501 | + | 0.293006i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.6066 | − | 32.2276i | −0.751514 | − | 1.30166i | −0.947089 | − | 0.320971i | \(-0.895991\pi\) |
0.195575 | − | 0.980689i | \(-0.437343\pi\) | |||||||
\(614\) | 4.98602 | − | 8.63604i | 0.201219 | − | 0.348522i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.86396 | − | 6.27231i | −0.195975 | − | 0.252719i | ||||
\(617\) | − | 17.6985i | − | 0.712514i | −0.934388 | − | 0.356257i | \(-0.884053\pi\) | ||
0.934388 | − | 0.356257i | \(-0.115947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.33452 | − | 3.07989i | 0.214413 | − | 0.123791i | −0.388948 | − | 0.921260i | \(-0.627161\pi\) |
0.603360 | + | 0.797469i | \(0.293828\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.95743i | 0.359160i | ||||||||
\(623\) | −10.3923 | + | 25.4558i | −0.416359 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.22911 | + | 15.9853i | 0.368869 | + | 0.638900i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.7279 | − | 7.34847i | −0.507899 | − | 0.293236i | ||||
\(629\) | −1.43488 | −0.0572123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.7574 | 0.985575 | 0.492787 | − | 0.870150i | \(-0.335978\pi\) | ||||
0.492787 | + | 0.870150i | \(0.335978\pi\) | |||||||
\(632\) | −2.38794 | − | 1.37868i | −0.0949873 | − | 0.0548409i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.621320 | + | 1.07616i | 0.0246758 | + | 0.0427397i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.60660 | + | 16.5160i | 0.182520 | + | 0.654389i | ||||
\(638\) | − | 21.7279i | − | 0.860217i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.3273 | + | 8.84924i | −0.605393 | + | 0.349524i | −0.771160 | − | 0.636641i | \(-0.780323\pi\) |
0.165767 | + | 0.986165i | \(0.446990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 32.0174i | − | 1.26264i | −0.775520 | − | 0.631322i | \(-0.782512\pi\) | ||
0.775520 | − | 0.631322i | \(-0.217488\pi\) | |||||||
\(644\) | 1.52192 | + | 11.1213i | 0.0599720 | + | 0.438241i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.4853 | + | 30.2854i | −0.687949 | + | 1.19156i | ||||
\(647\) | 16.2189 | + | 28.0919i | 0.637629 | + | 1.10441i | 0.985952 | + | 0.167031i | \(0.0534180\pi\) |
−0.348323 | + | 0.937375i | \(0.613249\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.9558 | − | 12.0989i | −0.822589 | − | 0.474922i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.24264 | −0.0878286 | ||||||||
\(653\) | −16.6646 | − | 9.62132i | −0.652137 | − | 0.376511i | 0.137138 | − | 0.990552i | \(-0.456210\pi\) |
−0.789274 | + | 0.614041i | \(0.789543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.91359 | + | 10.2426i | −0.230887 | + | 0.399908i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.3640 | − | 9.58783i | 0.481997 | − | 0.373772i | ||||
\(659\) | − | 6.00000i | − | 0.233727i | −0.993148 | − | 0.116863i | \(-0.962716\pi\) | ||
0.993148 | − | 0.116863i | \(-0.0372840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.8787 | − | 17.8278i | 1.20104 | − | 0.693422i | 0.240255 | − | 0.970710i | \(-0.422769\pi\) |
0.960787 | + | 0.277288i | \(0.0894357\pi\) | |||||||
\(662\) | −28.9736 | + | 16.7279i | −1.12609 | + | 0.650149i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.63103i | 0.257334i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3640 | + | 26.6112i | −0.594895 | + | 1.03039i | ||||
\(668\) | 8.06591 | + | 13.9706i | 0.312079 | + | 0.540537i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.04384 | −0.117506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9706 | −0.692714 | −0.346357 | − | 0.938103i | \(-0.612581\pi\) | ||||
−0.346357 | + | 0.938103i | \(0.612581\pi\) | |||||||
\(674\) | −4.33013 | − | 2.50000i | −0.166790 | − | 0.0962964i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | −1.07616 | + | 1.86396i | −0.0413601 | + | 0.0716378i | −0.885964 | − | 0.463753i | \(-0.846502\pi\) |
0.844604 | + | 0.535391i | \(0.179836\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.86396 | + | 35.5431i | 0.186662 | + | 1.36402i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −23.5919 | + | 13.6208i | −0.903380 | + | 0.521567i | ||||
\(683\) | 6.90271 | − | 3.98528i | 0.264125 | − | 0.152493i | −0.362090 | − | 0.932143i | \(-0.617937\pi\) |
0.626215 | + | 0.779651i | \(0.284603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.3967 | + | 2.13604i | 0.702388 | + | 0.0815543i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.121320 | + | 0.210133i | −0.00462529 | + | 0.00801125i | ||||
\(689\) | 8.87039 | + | 15.3640i | 0.337935 | + | 0.585320i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7279 | + | 14.2767i | 0.940694 | + | 0.543110i | 0.890178 | − | 0.455613i | \(-0.150580\pi\) |
0.0505165 | + | 0.998723i | \(0.483913\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.48528 | 0.0943400 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.9706 | + | 60.5708i | 1.32460 | + | 2.29428i | ||||
\(698\) | −1.13770 | + | 1.97056i | −0.0430628 | + | 0.0745869i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.6985i | − | 0.781771i | −0.920439 | − | 0.390885i | \(-0.872169\pi\) | ||
0.920439 | − | 0.390885i | \(-0.127831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.24264 | − | 0.717439i | 0.0468671 | − | 0.0270587i | ||||
\(704\) | 2.59808 | − | 1.50000i | 0.0979187 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 8.95743i | − | 0.337117i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4853 | + | 23.3572i | −0.506450 | + | 0.877198i | 0.493522 | + | 0.869733i | \(0.335709\pi\) |
−0.999972 | + | 0.00746433i | \(0.997624\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | − | 5.19615i | −0.337289 | − | 0.194734i | ||||
\(713\) | 38.5254 | 1.44279 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.9369 | + | 13.2426i | 0.857193 | + | 0.494901i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | + | 15.5885i | 0.335877 | + | 0.581756i | ||||
\(719\) | −8.06591 | + | 13.9706i | −0.300808 | + | 0.521014i | −0.976319 | − | 0.216335i | \(-0.930590\pi\) |
0.675511 | + | 0.737349i | \(0.263923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4558 | − | 5.49333i | −0.501122 | − | 0.204582i | ||||
\(722\) | − | 15.9706i | − | 0.594363i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.2426 | + | 5.91359i | −0.380665 | + | 0.219777i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7041i | 0.434081i | 0.976163 | + | 0.217040i | \(0.0696403\pi\) | ||||
−0.976163 | + | 0.217040i | \(0.930360\pi\) | |||||||
\(728\) | −6.42090 | + | 0.878680i | −0.237974 | + | 0.0325660i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.717439 | + | 1.24264i | 0.0265354 | + | 0.0459607i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.09188 | − | 2.36245i | −0.151137 | − | 0.0872591i | 0.422524 | − | 0.906352i | \(-0.361144\pi\) |
−0.573661 | + | 0.819093i | \(0.694477\pi\) | |||||||
\(734\) | −15.4144 | −0.568955 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.24264 | −0.156386 | ||||||||
\(737\) | 25.9808 | + | 15.0000i | 0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.72792 | − | 13.3852i | −0.284276 | − | 0.492381i | 0.688157 | − | 0.725562i | \(-0.258420\pi\) |
−0.972433 | + | 0.233181i | \(0.925087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.9853 | − | 2.59808i | 0.696972 | − | 0.0953784i | ||||
\(743\) | 38.4853i | 1.41189i | 0.708268 | + | 0.705944i | \(0.249477\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.5095 | − | 14.7279i | 0.933969 | − | 0.539228i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 17.7408i | − | 0.648667i | ||||||
\(749\) | −28.1331 | − | 11.4853i | −1.02796 | − | 0.419663i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6213 | + | 30.5210i | −0.643011 | + | 1.11373i | 0.341746 | + | 0.939792i | \(0.388982\pi\) |
−0.984757 | + | 0.173936i | \(0.944352\pi\) | |||||||
\(752\) | 2.95680 | + | 5.12132i | 0.107823 | + | 0.186755i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.3640 | − | 8.87039i | −0.559522 | − | 0.323040i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.7574 | 1.22693 | 0.613466 | − | 0.789721i | \(-0.289775\pi\) | ||||
0.613466 | + | 0.789721i | \(0.289775\pi\) | |||||||
\(758\) | −10.8126 | − | 6.24264i | −0.392730 | − | 0.226743i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.7840 | + | 25.6066i | −0.535919 | + | 0.928239i | 0.463199 | + | 0.886254i | \(0.346701\pi\) |
−0.999118 | + | 0.0419845i | \(0.986632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.9706 | + | 38.6485i | 1.08501 | + | 1.39917i | ||||
\(764\) | 8.48528i | 0.306987i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.2426 | + | 11.1097i | −0.695265 | + | 0.401411i | ||||
\(767\) | −17.1104 | + | 9.87868i | −0.617820 | + | 0.356698i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.84895i | 0.355162i | 0.984106 | + | 0.177581i | \(0.0568272\pi\) | ||||
−0.984106 | + | 0.177581i | \(0.943173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.74264 | + | 8.21449i | −0.170691 | + | 0.295646i | ||||
\(773\) | −8.06591 | − | 13.9706i | −0.290111 | − | 0.502486i | 0.683725 | − | 0.729740i | \(-0.260359\pi\) |
−0.973836 | + | 0.227253i | \(0.927025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.5592 | −0.486748 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.4558 | 1.12775 | ||||||||
\(779\) | −60.5708 | − | 34.9706i | −2.17017 | − | 1.25295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.63604 | − | 4.56575i | −0.0943249 | − | 0.163376i | ||||
\(782\) | −12.5446 | + | 21.7279i | −0.448595 | + | 0.776989i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74264 | + | 6.77962i | −0.0622372 | + | 0.242129i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.8787 | + | 16.0958i | −0.993768 | + | 0.573752i | −0.906398 | − | 0.422424i | \(-0.861179\pi\) |
−0.0873693 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(788\) | 22.9369 | − | 13.2426i | 0.817094 | − | 0.471750i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.04384 | − | 22.2426i | −0.108226 | − | 0.790857i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.24264 | + | 2.15232i | −0.0441275 | + | 0.0764310i | ||||
\(794\) | 6.92820 | + | 12.0000i | 0.245873 | + | 0.425864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.9706 | + | 11.5300i | 0.707838 | + | 0.408670i | ||||
\(797\) | −6.45695 | −0.228717 | −0.114358 | − | 0.993440i | \(-0.536481\pi\) | ||||
−0.114358 | + | 0.993440i | \(0.536481\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.9706 | 1.23717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.15232 | + | 3.72792i | −0.0759536 | + | 0.131556i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.2426i | 0.783464i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.08767 | + | 3.51472i | −0.214031 | + | 0.123571i | −0.603183 | − | 0.797602i | \(-0.706101\pi\) |
0.389152 | + | 0.921173i | \(0.372768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | −15.1427 | + | 11.7426i | −0.531405 | + | 0.412086i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.363961 | + | 0.630399i | −0.0127568 | + | 0.0220955i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.24264 | − | 0.717439i | −0.0434745 | − | 0.0251000i | ||||
\(818\) | −14.9941 | −0.524257 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.2969 | + | 20.3787i | 1.23187 | + | 0.711221i | 0.967420 | − | 0.253178i | \(-0.0814759\pi\) |
0.264451 | + | 0.964399i | \(0.414809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.9706 | + | 25.9298i | 0.521841 | + | 0.903855i | 0.999677 | + | 0.0254062i | \(0.00808791\pi\) |
−0.477836 | + | 0.878449i | \(0.658579\pi\) | |||||||
\(824\) | 2.74666 | − | 4.75736i | 0.0956845 | − | 0.165730i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.89340 | + | 21.1433i | 0.100674 | + | 0.735671i | ||||
\(827\) | 37.9706i | 1.32037i | 0.751105 | + | 0.660183i | \(0.229521\pi\) | ||||
−0.751105 | + | 0.660183i | \(0.770479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3345 | − | 6.54399i | 0.393664 | − | 0.227282i | −0.290082 | − | 0.957002i | \(-0.593683\pi\) |
0.683747 | + | 0.729720i | \(0.260349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | 29.5680 | + | 28.9706i | 1.02447 | + | 1.00377i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.87039 | + | 15.3640i | 0.306789 | + | 0.531374i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.4853 | − | 11.8272i | −0.707652 | − | 0.408563i | ||||
\(839\) | 10.2182 | 0.352772 | 0.176386 | − | 0.984321i | \(-0.443559\pi\) | ||||
0.176386 | + | 0.984321i | \(0.443559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4558 | −0.808822 | ||||||||
\(842\) | 12.3345 | + | 7.12132i | 0.425075 | + | 0.245417i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.121320 | − | 0.210133i | −0.00417602 | − | 0.00723308i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | − | 4.89898i | 0.0687208 | − | 0.168331i | ||||
\(848\) | 7.24264i | 0.248713i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.891519 | − | 0.514719i | 0.0305609 | − | 0.0176443i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.9164i | − | 1.26399i | −0.774971 | − | 0.631997i | \(-0.782235\pi\) | ||
0.774971 | − | 0.631997i | \(-0.217765\pi\) | |||||||
\(854\) | 1.64501 | + | 2.12132i | 0.0562911 | + | 0.0725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.74264 | − | 9.94655i | 0.196279 | − | 0.339966i | ||||
\(857\) | −16.9363 | − | 29.3345i | −0.578533 | − | 1.00205i | −0.995648 | − | 0.0931946i | \(-0.970292\pi\) |
0.417115 | − | 0.908854i | \(-0.363041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.12132 | + | 4.68885i | 0.277096 | + | 0.159981i | 0.632108 | − | 0.774880i | \(-0.282190\pi\) |
−0.355012 | + | 0.934862i | \(0.615523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.51472 | 0.119712 | ||||||||
\(863\) | −29.0246 | − | 16.7574i | −0.988009 | − | 0.570427i | −0.0833303 | − | 0.996522i | \(-0.526556\pi\) |
−0.904679 | + | 0.426095i | \(0.859889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.73205 | − | 3.00000i | 0.0588575 | − | 0.101944i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.2426 | + | 9.08052i | 0.754964 | + | 0.308213i | ||||
\(869\) | 8.27208i | 0.280611i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2132 | − | 12.2474i | 0.718782 | − | 0.414989i | ||||
\(872\) | −16.0087 | + | 9.24264i | −0.542124 | + | 0.312995i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 25.0892i | − | 0.848656i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.24264 | − | 3.88437i | 0.0757286 | − | 0.131166i | −0.825674 | − | 0.564147i | \(-0.809205\pi\) |
0.901403 | + | 0.432981i | \(0.142538\pi\) | |||||||
\(878\) | 8.42463 | + | 14.5919i | 0.284317 | + | 0.492452i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.0016 | 0.640179 | 0.320090 | − | 0.947387i | \(-0.396287\pi\) | ||||
0.320090 | + | 0.947387i | \(0.396287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.4558 | −1.39510 | −0.697550 | − | 0.716536i | \(-0.745727\pi\) | ||||
−0.697550 | + | 0.716536i | \(0.745727\pi\) | |||||||
\(884\) | −12.5446 | − | 7.24264i | −0.421921 | − | 0.243596i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.22792 | − | 14.2512i | −0.276422 | − | 0.478778i | ||||
\(887\) | −5.28319 | + | 9.15076i | −0.177392 | + | 0.307252i | −0.940987 | − | 0.338444i | \(-0.890099\pi\) |
0.763594 | + | 0.645696i | \(0.223433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.50000 | − | 1.16320i | 0.285081 | − | 0.0390124i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.86396 | − | 1.07616i | 0.0624100 | − | 0.0360324i | ||||
\(893\) | −30.2854 | + | 17.4853i | −1.01346 | + | 0.585123i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.44949 | − | 1.00000i | −0.0818317 | − | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.878680 | − | 1.52192i | 0.0293219 | − | 0.0507871i | ||||
\(899\) | 32.8835 | + | 56.9558i | 1.09673 | + | 1.89958i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.0919 | + | 21.4150i | 1.23571 | + | 0.713437i | ||||
\(902\) | 35.4815 | 1.18141 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.48528 | 0.282216 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.8492 | − | 27.4517i | −0.526265 | − | 0.911519i | −0.999532 | − | 0.0305991i | \(-0.990258\pi\) |
0.473266 | − | 0.880919i | \(-0.343075\pi\) | |||||||
\(908\) | 7.79423 | − | 13.5000i | 0.258661 | − | 0.448013i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.72792i | 0.222906i | 0.993770 | + | 0.111453i | \(0.0355505\pi\) | ||||
−0.993770 | + | 0.111453i | \(0.964450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.2279 | − | 9.94655i | 0.570161 | − | 0.329183i | ||||
\(914\) | 19.9186 | − | 11.5000i | 0.658848 | − | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 5.19615 | − | 12.7279i | 0.171592 | − | 0.420313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2426 | + | 31.5972i | −0.601769 | + | 1.04229i | 0.390784 | + | 0.920482i | \(0.372204\pi\) |
−0.992553 | + | 0.121812i | \(0.961129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.2426 | − | 16.3059i | −0.930122 | − | 0.537006i | ||||
\(923\) | −4.30463 | −0.141689 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −25.5095 | − | 14.7279i | −0.838294 | − | 0.483990i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.62132 | − | 6.27231i | −0.118876 | − | 0.205899i | ||||
\(929\) | −15.5014 | + | 26.8492i | −0.508585 | + | 0.880895i | 0.491366 | + | 0.870953i | \(0.336498\pi\) |
−0.999951 | + | 0.00994164i | \(0.996835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.0919 | − | 10.3053i | −1.31396 | − | 0.337741i | ||||
\(932\) | − | 18.7279i | − | 0.613453i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.4558 | − | 19.8931i | 1.12743 | − | 0.650922i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.1844i | 1.14942i | 0.818356 | + | 0.574712i | \(0.194886\pi\) | ||||
−0.818356 | + | 0.574712i | \(0.805114\pi\) | |||||||
\(938\) | −3.58719 | − | 26.2132i | −0.117126 | − | 0.855891i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.7949 | + | 23.8934i | 0.449700 | + | 0.778903i | 0.998366 | − | 0.0571387i | \(-0.0181977\pi\) |
−0.548667 | + | 0.836041i | \(0.684864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.4558 | − | 25.0892i | −1.41512 | − | 0.817018i | ||||
\(944\) | −8.06591 | −0.262523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.727922 | 0.0236668 | ||||||||
\(947\) | 9.50079 | + | 5.48528i | 0.308734 | + | 0.178248i | 0.646360 | − | 0.763033i | \(-0.276291\pi\) |
−0.337626 | + | 0.941280i | \(0.609624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.75736 | + | 3.04384i | 0.0570463 | + | 0.0988071i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.3640 | + | 9.58783i | −0.400718 | + | 0.310743i | ||||
\(953\) | − | 17.6985i | − | 0.573310i | −0.958034 | − | 0.286655i | \(-0.907457\pi\) | ||
0.958034 | − | 0.286655i | \(-0.0925434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.0227 | − | 6.36396i | 0.356500 | − | 0.205825i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 12.0013i | − | 0.387743i | ||||||
\(959\) | −5.19615 | + | 4.02944i | −0.167793 | + | 0.130117i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.7279 | − | 44.5621i | 0.829933 | − | 1.43749i | ||||
\(962\) | 0.297173 | + | 0.514719i | 0.00958124 | + | 0.0165952i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.25736 | + | 3.61269i | 0.201536 | + | 0.116357i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.7279 | −1.53483 | −0.767413 | − | 0.641153i | \(-0.778456\pi\) | ||||
−0.767413 | + | 0.641153i | \(0.778456\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5337 | − | 23.4411i | 0.434318 | − | 0.752262i | −0.562921 | − | 0.826510i | \(-0.690323\pi\) |
0.997240 | + | 0.0742490i | \(0.0236559\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.213203 | + | 1.55797i | 0.00683499 | + | 0.0499463i | ||||
\(974\) | 14.2132i | 0.455420i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.878680 | + | 0.507306i | −0.0281259 | + | 0.0162385i | ||||
\(977\) | 34.8511 | − | 20.1213i | 1.11499 | − | 0.643738i | 0.174871 | − | 0.984591i | \(-0.444049\pi\) |
0.940116 | + | 0.340853i | \(0.110716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1769i | 0.996419i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.98528 | − | 12.0989i | 0.222909 | − | 0.386090i | ||||
\(983\) | 23.6544 | + | 40.9706i | 0.754457 | + | 1.30676i | 0.945644 | + | 0.325204i | \(0.105433\pi\) |
−0.191187 | + | 0.981554i | \(0.561234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −42.8300 | −1.36399 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.4853 | 0.460838 | ||||||||
\(989\) | −0.891519 | − | 0.514719i | −0.0283486 | − | 0.0163671i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1066 | − | 45.2180i | −0.829304 | − | 1.43640i | −0.898585 | − | 0.438799i | \(-0.855404\pi\) |
0.0692818 | − | 0.997597i | \(-0.477929\pi\) | |||||||
\(992\) | −4.54026 | + | 7.86396i | −0.144153 | + | 0.249681i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.75736 | + | 4.30463i | −0.0557401 | + | 0.136535i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.7279 | − | 19.4728i | 1.06817 | − | 0.616711i | 0.140492 | − | 0.990082i | \(-0.455132\pi\) |
0.927682 | + | 0.373371i | \(0.121798\pi\) | |||||||
\(998\) | 27.6618 | − | 15.9706i | 0.875620 | − | 0.505539i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))