Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,3,Mod(19,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.980928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.19 |
Dual form | 36.3.d.c.19.2 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | 2.00000 | 0.400000 | 0.200000 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.92820i | 0.989743i | 0.868966 | + | 0.494872i | \(0.164785\pi\) | ||||
−0.868966 | + | 0.494872i | \(0.835215\pi\) | |||||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(11\) | 6.92820i | 0.629837i | 0.949119 | + | 0.314918i | \(0.101977\pi\) | ||||
−0.949119 | + | 0.314918i | \(0.898023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.153846 | 0.0769231 | − | 0.997037i | \(-0.475490\pi\) | ||||
0.0769231 | + | 0.997037i | \(0.475490\pi\) | |||||||
\(14\) | 12.0000 | + | 6.92820i | 0.857143 | + | 0.494872i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | −10.0000 | −0.588235 | −0.294118 | − | 0.955769i | \(-0.595026\pi\) | ||||
−0.294118 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.7846i | − | 1.09393i | −0.837157 | − | 0.546963i | \(-0.815784\pi\) | ||
0.837157 | − | 0.546963i | \(-0.184216\pi\) | |||||||
\(20\) | −4.00000 | − | 6.92820i | −0.200000 | − | 0.346410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | + | 6.92820i | 0.545455 | + | 0.314918i | ||||
\(23\) | − | 27.7128i | − | 1.20490i | −0.798155 | − | 0.602452i | \(-0.794190\pi\) | ||
0.798155 | − | 0.602452i | \(-0.205810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.0000 | −0.840000 | ||||||||
\(26\) | 2.00000 | − | 3.46410i | 0.0769231 | − | 0.133235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24.0000 | − | 13.8564i | 0.857143 | − | 0.494872i | ||||
\(29\) | 26.0000 | 0.896552 | 0.448276 | − | 0.893895i | \(-0.352038\pi\) | ||||
0.448276 | + | 0.893895i | \(0.352038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.92820i | − | 0.223490i | −0.993737 | − | 0.111745i | \(-0.964356\pi\) | ||
0.993737 | − | 0.111745i | \(-0.0356441\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.0000 | + | 17.3205i | −0.294118 | + | 0.509427i | ||||
\(35\) | 13.8564i | 0.395897i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000 | 0.702703 | 0.351351 | − | 0.936244i | \(-0.385722\pi\) | ||||
0.351351 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(38\) | −36.0000 | − | 20.7846i | −0.947368 | − | 0.546963i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.0000 | −0.400000 | ||||||||
\(41\) | −58.0000 | −1.41463 | −0.707317 | − | 0.706896i | \(-0.750095\pi\) | ||||
−0.707317 | + | 0.706896i | \(0.750095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.4974i | 1.12785i | 0.825827 | + | 0.563924i | \(0.190709\pi\) | ||||
−0.825827 | + | 0.563924i | \(0.809291\pi\) | |||||||
\(44\) | 24.0000 | − | 13.8564i | 0.545455 | − | 0.314918i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.0000 | − | 27.7128i | −1.04348 | − | 0.602452i | ||||
\(47\) | 69.2820i | 1.47409i | 0.675846 | + | 0.737043i | \(0.263778\pi\) | ||||
−0.675846 | + | 0.737043i | \(0.736222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.0204082 | ||||||||
\(50\) | −21.0000 | + | 36.3731i | −0.420000 | + | 0.727461i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 6.92820i | −0.0769231 | − | 0.133235i | ||||
\(53\) | 74.0000 | 1.39623 | 0.698113 | − | 0.715987i | \(-0.254023\pi\) | ||||
0.698113 | + | 0.715987i | \(0.254023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8564i | 0.251935i | ||||||||
\(56\) | − | 55.4256i | − | 0.989743i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 26.0000 | − | 45.0333i | 0.448276 | − | 0.776437i | ||||
\(59\) | − | 90.0666i | − | 1.52655i | −0.646072 | − | 0.763277i | \(-0.723589\pi\) | ||
0.646072 | − | 0.763277i | \(-0.276411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.0000 | 0.426230 | 0.213115 | − | 0.977027i | \(-0.431639\pi\) | ||||
0.213115 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(62\) | −12.0000 | − | 6.92820i | −0.193548 | − | 0.111745i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 4.00000 | 0.0615385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.92820i | − | 0.103406i | −0.998663 | − | 0.0517030i | \(-0.983535\pi\) | ||
0.998663 | − | 0.0517030i | \(-0.0164649\pi\) | |||||||
\(68\) | 20.0000 | + | 34.6410i | 0.294118 | + | 0.509427i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.0000 | + | 13.8564i | 0.342857 | + | 0.197949i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −46.0000 | −0.630137 | −0.315068 | − | 0.949069i | \(-0.602027\pi\) | ||||
−0.315068 | + | 0.949069i | \(0.602027\pi\) | |||||||
\(74\) | 26.0000 | − | 45.0333i | 0.351351 | − | 0.608558i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −72.0000 | + | 41.5692i | −0.947368 | + | 0.546963i | ||||
\(77\) | −48.0000 | −0.623377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 117.779i | − | 1.49088i | −0.666573 | − | 0.745440i | \(-0.732240\pi\) | ||
0.666573 | − | 0.745440i | \(-0.267760\pi\) | |||||||
\(80\) | −16.0000 | + | 27.7128i | −0.200000 | + | 0.346410i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −58.0000 | + | 100.459i | −0.707317 | + | 1.22511i | ||||
\(83\) | 48.4974i | 0.584306i | 0.956372 | + | 0.292153i | \(0.0943717\pi\) | ||||
−0.956372 | + | 0.292153i | \(0.905628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.0000 | −0.235294 | ||||||||
\(86\) | 84.0000 | + | 48.4974i | 0.976744 | + | 0.563924i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 55.4256i | − | 0.629837i | ||||||
\(89\) | −82.0000 | −0.921348 | −0.460674 | − | 0.887569i | \(-0.652392\pi\) | ||||
−0.460674 | + | 0.887569i | \(0.652392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8564i | 0.152268i | ||||||||
\(92\) | −96.0000 | + | 55.4256i | −1.04348 | + | 0.602452i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 120.000 | + | 69.2820i | 1.27660 | + | 0.737043i | ||||
\(95\) | − | 41.5692i | − | 0.437571i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.0206186 | 0.0103093 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103093 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(98\) | 1.00000 | − | 1.73205i | 0.0102041 | − | 0.0176740i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 42.0000 | + | 72.7461i | 0.420000 | + | 0.727461i | ||||
\(101\) | 74.0000 | 0.732673 | 0.366337 | − | 0.930482i | \(-0.380612\pi\) | ||||
0.366337 | + | 0.930482i | \(0.380612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.2102i | 0.739905i | 0.929051 | + | 0.369953i | \(0.120626\pi\) | ||||
−0.929051 | + | 0.369953i | \(0.879374\pi\) | |||||||
\(104\) | −16.0000 | −0.153846 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 74.0000 | − | 128.172i | 0.698113 | − | 1.20917i | ||||
\(107\) | 20.7846i | 0.194249i | 0.995272 | + | 0.0971243i | \(0.0309645\pi\) | ||||
−0.995272 | + | 0.0971243i | \(0.969036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −46.0000 | −0.422018 | −0.211009 | − | 0.977484i | \(-0.567675\pi\) | ||||
−0.211009 | + | 0.977484i | \(0.567675\pi\) | |||||||
\(110\) | 24.0000 | + | 13.8564i | 0.218182 | + | 0.125967i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −96.0000 | − | 55.4256i | −0.857143 | − | 0.494872i | ||||
\(113\) | 110.000 | 0.973451 | 0.486726 | − | 0.873555i | \(-0.338191\pi\) | ||||
0.486726 | + | 0.873555i | \(0.338191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 55.4256i | − | 0.481962i | ||||||
\(116\) | −52.0000 | − | 90.0666i | −0.448276 | − | 0.776437i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −156.000 | − | 90.0666i | −1.32203 | − | 0.763277i | ||||
\(119\) | − | 69.2820i | − | 0.582202i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 73.0000 | 0.603306 | ||||||||
\(122\) | 26.0000 | − | 45.0333i | 0.213115 | − | 0.369126i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.0000 | + | 13.8564i | −0.193548 | + | 0.111745i | ||||
\(125\) | −92.0000 | −0.736000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.492i | 1.14561i | 0.819692 | + | 0.572804i | \(0.194144\pi\) | ||||
−0.819692 | + | 0.572804i | \(0.805856\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | − | 6.92820i | 0.0307692 | − | 0.0532939i | ||||
\(131\) | 117.779i | 0.899080i | 0.893260 | + | 0.449540i | \(0.148412\pi\) | ||||
−0.893260 | + | 0.449540i | \(0.851588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 144.000 | 1.08271 | ||||||||
\(134\) | −12.0000 | − | 6.92820i | −0.0895522 | − | 0.0517030i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 80.0000 | 0.588235 | ||||||||
\(137\) | −10.0000 | −0.0729927 | −0.0364964 | − | 0.999334i | \(-0.511620\pi\) | ||||
−0.0364964 | + | 0.999334i | \(0.511620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 48.4974i | − | 0.348902i | −0.984666 | − | 0.174451i | \(-0.944185\pi\) | ||
0.984666 | − | 0.174451i | \(-0.0558151\pi\) | |||||||
\(140\) | 48.0000 | − | 27.7128i | 0.342857 | − | 0.197949i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564i | 0.0968979i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 52.0000 | 0.358621 | ||||||||
\(146\) | −46.0000 | + | 79.6743i | −0.315068 | + | 0.545715i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −52.0000 | − | 90.0666i | −0.351351 | − | 0.608558i | ||||
\(149\) | 2.00000 | 0.0134228 | 0.00671141 | − | 0.999977i | \(-0.497864\pi\) | ||||
0.00671141 | + | 0.999977i | \(0.497864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 90.0666i | 0.596468i | 0.954493 | + | 0.298234i | \(0.0963975\pi\) | ||||
−0.954493 | + | 0.298234i | \(0.903602\pi\) | |||||||
\(152\) | 166.277i | 1.09393i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −48.0000 | + | 83.1384i | −0.311688 | + | 0.539860i | ||||
\(155\) | − | 13.8564i | − | 0.0893962i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −214.000 | −1.36306 | −0.681529 | − | 0.731791i | \(-0.738685\pi\) | ||||
−0.681529 | + | 0.731791i | \(0.738685\pi\) | |||||||
\(158\) | −204.000 | − | 117.779i | −1.29114 | − | 0.745440i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 32.0000 | + | 55.4256i | 0.200000 | + | 0.346410i | ||||
\(161\) | 192.000 | 1.19255 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.7846i | − | 0.127513i | −0.997965 | − | 0.0637565i | \(-0.979692\pi\) | ||
0.997965 | − | 0.0637565i | \(-0.0203081\pi\) | |||||||
\(164\) | 116.000 | + | 200.918i | 0.707317 | + | 1.22511i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 84.0000 | + | 48.4974i | 0.506024 | + | 0.292153i | ||||
\(167\) | 96.9948i | 0.580807i | 0.956904 | + | 0.290404i | \(0.0937896\pi\) | ||||
−0.956904 | + | 0.290404i | \(0.906210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −165.000 | −0.976331 | ||||||||
\(170\) | −20.0000 | + | 34.6410i | −0.117647 | + | 0.203771i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 168.000 | − | 96.9948i | 0.976744 | − | 0.563924i | ||||
\(173\) | −334.000 | −1.93064 | −0.965318 | − | 0.261077i | \(-0.915922\pi\) | ||||
−0.965318 | + | 0.261077i | \(0.915922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 145.492i | − | 0.831384i | ||||||
\(176\) | −96.0000 | − | 55.4256i | −0.545455 | − | 0.314918i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −82.0000 | + | 142.028i | −0.460674 | + | 0.797911i | ||||
\(179\) | − | 187.061i | − | 1.04504i | −0.852628 | − | 0.522518i | \(-0.824993\pi\) | ||
0.852628 | − | 0.522518i | \(-0.175007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.0110497 | 0.00552486 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552486 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | 24.0000 | + | 13.8564i | 0.131868 | + | 0.0761341i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 221.703i | 1.20490i | ||||||||
\(185\) | 52.0000 | 0.281081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 69.2820i | − | 0.370492i | ||||||
\(188\) | 240.000 | − | 138.564i | 1.27660 | − | 0.737043i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −72.0000 | − | 41.5692i | −0.378947 | − | 0.218785i | ||||
\(191\) | − | 221.703i | − | 1.16075i | −0.814351 | − | 0.580373i | \(-0.802907\pi\) | ||
0.814351 | − | 0.580373i | \(-0.197093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 290.000 | 1.50259 | 0.751295 | − | 0.659966i | \(-0.229429\pi\) | ||||
0.751295 | + | 0.659966i | \(0.229429\pi\) | |||||||
\(194\) | 2.00000 | − | 3.46410i | 0.0103093 | − | 0.0178562i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | − | 3.46410i | −0.0102041 | − | 0.0176740i | ||||
\(197\) | 26.0000 | 0.131980 | 0.0659898 | − | 0.997820i | \(-0.478980\pi\) | ||||
0.0659898 | + | 0.997820i | \(0.478980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 394.908i | − | 1.98446i | −0.124416 | − | 0.992230i | \(-0.539706\pi\) | ||
0.124416 | − | 0.992230i | \(-0.460294\pi\) | |||||||
\(200\) | 168.000 | 0.840000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 74.0000 | − | 128.172i | 0.366337 | − | 0.634514i | ||||
\(203\) | 180.133i | 0.887356i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −116.000 | −0.565854 | ||||||||
\(206\) | 132.000 | + | 76.2102i | 0.640777 | + | 0.369953i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.0000 | + | 27.7128i | −0.0769231 | + | 0.133235i | ||||
\(209\) | 144.000 | 0.688995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 242.487i | 1.14923i | 0.818425 | + | 0.574614i | \(0.194848\pi\) | ||||
−0.818425 | + | 0.574614i | \(0.805152\pi\) | |||||||
\(212\) | −148.000 | − | 256.344i | −0.698113 | − | 1.20917i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 36.0000 | + | 20.7846i | 0.168224 | + | 0.0971243i | ||||
\(215\) | 96.9948i | 0.451139i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48.0000 | 0.221198 | ||||||||
\(218\) | −46.0000 | + | 79.6743i | −0.211009 | + | 0.365479i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 48.0000 | − | 27.7128i | 0.218182 | − | 0.125967i | ||||
\(221\) | −20.0000 | −0.0904977 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 339.482i | 1.52234i | 0.648552 | + | 0.761170i | \(0.275375\pi\) | ||||
−0.648552 | + | 0.761170i | \(0.724625\pi\) | |||||||
\(224\) | −192.000 | + | 110.851i | −0.857143 | + | 0.494872i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 110.000 | − | 190.526i | 0.486726 | − | 0.843034i | ||||
\(227\) | − | 284.056i | − | 1.25135i | −0.780084 | − | 0.625675i | \(-0.784824\pi\) | ||
0.780084 | − | 0.625675i | \(-0.215176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −142.000 | −0.620087 | −0.310044 | − | 0.950722i | \(-0.600344\pi\) | ||||
−0.310044 | + | 0.950722i | \(0.600344\pi\) | |||||||
\(230\) | −96.0000 | − | 55.4256i | −0.417391 | − | 0.240981i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −208.000 | −0.896552 | ||||||||
\(233\) | −82.0000 | −0.351931 | −0.175966 | − | 0.984396i | \(-0.556305\pi\) | ||||
−0.175966 | + | 0.984396i | \(0.556305\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 138.564i | 0.589634i | ||||||||
\(236\) | −312.000 | + | 180.133i | −1.32203 | + | 0.763277i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −120.000 | − | 69.2820i | −0.504202 | − | 0.291101i | ||||
\(239\) | 387.979i | 1.62334i | 0.584113 | + | 0.811672i | \(0.301442\pi\) | ||||
−0.584113 | + | 0.811672i | \(0.698558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −46.0000 | −0.190871 | −0.0954357 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954357 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(242\) | 73.0000 | − | 126.440i | 0.301653 | − | 0.522478i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −52.0000 | − | 90.0666i | −0.213115 | − | 0.369126i | ||||
\(245\) | 2.00000 | 0.00816327 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 41.5692i | − | 0.168296i | ||||||
\(248\) | 55.4256i | 0.223490i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −92.0000 | + | 159.349i | −0.368000 | + | 0.637395i | ||||
\(251\) | 145.492i | 0.579650i | 0.957080 | + | 0.289825i | \(0.0935972\pi\) | ||||
−0.957080 | + | 0.289825i | \(0.906403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 192.000 | 0.758893 | ||||||||
\(254\) | 252.000 | + | 145.492i | 0.992126 | + | 0.572804i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | 254.000 | 0.988327 | 0.494163 | − | 0.869369i | \(-0.335474\pi\) | ||||
0.494163 | + | 0.869369i | \(0.335474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 180.133i | 0.695495i | ||||||||
\(260\) | −8.00000 | − | 13.8564i | −0.0307692 | − | 0.0532939i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 204.000 | + | 117.779i | 0.778626 | + | 0.449540i | ||||
\(263\) | 152.420i | 0.579546i | 0.957095 | + | 0.289773i | \(0.0935797\pi\) | ||||
−0.957095 | + | 0.289773i | \(0.906420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 148.000 | 0.558491 | ||||||||
\(266\) | 144.000 | − | 249.415i | 0.541353 | − | 0.937652i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −24.0000 | + | 13.8564i | −0.0895522 | + | 0.0517030i | ||||
\(269\) | −262.000 | −0.973978 | −0.486989 | − | 0.873408i | \(-0.661905\pi\) | ||||
−0.486989 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.7846i | − | 0.0766960i | −0.999264 | − | 0.0383480i | \(-0.987790\pi\) | ||
0.999264 | − | 0.0383480i | \(-0.0122095\pi\) | |||||||
\(272\) | 80.0000 | − | 138.564i | 0.294118 | − | 0.509427i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0000 | + | 17.3205i | −0.0364964 | + | 0.0632135i | ||||
\(275\) | − | 145.492i | − | 0.529063i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 290.000 | 1.04693 | 0.523466 | − | 0.852047i | \(-0.324639\pi\) | ||||
0.523466 | + | 0.852047i | \(0.324639\pi\) | |||||||
\(278\) | −84.0000 | − | 48.4974i | −0.302158 | − | 0.174451i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 110.851i | − | 0.395897i | ||||||
\(281\) | −226.000 | −0.804270 | −0.402135 | − | 0.915580i | \(-0.631732\pi\) | ||||
−0.402135 | + | 0.915580i | \(0.631732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 297.913i | − | 1.05270i | −0.850269 | − | 0.526348i | \(-0.823561\pi\) | ||
0.850269 | − | 0.526348i | \(-0.176439\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | + | 13.8564i | 0.0839161 | + | 0.0484490i | ||||
\(287\) | − | 401.836i | − | 1.40012i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −189.000 | −0.653979 | ||||||||
\(290\) | 52.0000 | − | 90.0666i | 0.179310 | − | 0.310575i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 92.0000 | + | 159.349i | 0.315068 | + | 0.545715i | ||||
\(293\) | 362.000 | 1.23549 | 0.617747 | − | 0.786377i | \(-0.288045\pi\) | ||||
0.617747 | + | 0.786377i | \(0.288045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 180.133i | − | 0.610621i | ||||||
\(296\) | −208.000 | −0.702703 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | − | 3.46410i | 0.00671141 | − | 0.0116245i | ||||
\(299\) | − | 55.4256i | − | 0.185370i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −336.000 | −1.11628 | ||||||||
\(302\) | 156.000 | + | 90.0666i | 0.516556 | + | 0.298234i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 288.000 | + | 166.277i | 0.947368 | + | 0.546963i | ||||
\(305\) | 52.0000 | 0.170492 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 145.492i | − | 0.473916i | −0.971520 | − | 0.236958i | \(-0.923850\pi\) | ||
0.971520 | − | 0.236958i | \(-0.0761504\pi\) | |||||||
\(308\) | 96.0000 | + | 166.277i | 0.311688 | + | 0.539860i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.0000 | − | 13.8564i | −0.0774194 | − | 0.0446981i | ||||
\(311\) | − | 235.559i | − | 0.757424i | −0.925515 | − | 0.378712i | \(-0.876367\pi\) | ||
0.925515 | − | 0.378712i | \(-0.123633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −478.000 | −1.52716 | −0.763578 | − | 0.645715i | \(-0.776559\pi\) | ||||
−0.763578 | + | 0.645715i | \(0.776559\pi\) | |||||||
\(314\) | −214.000 | + | 370.659i | −0.681529 | + | 1.18044i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −408.000 | + | 235.559i | −1.29114 | + | 0.745440i | ||||
\(317\) | 170.000 | 0.536278 | 0.268139 | − | 0.963380i | \(-0.413591\pi\) | ||||
0.268139 | + | 0.963380i | \(0.413591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 180.133i | 0.564681i | ||||||||
\(320\) | 128.000 | 0.400000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 192.000 | − | 332.554i | 0.596273 | − | 1.03278i | ||||
\(323\) | 207.846i | 0.643486i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.0000 | −0.129231 | ||||||||
\(326\) | −36.0000 | − | 20.7846i | −0.110429 | − | 0.0637565i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 464.000 | 1.41463 | ||||||||
\(329\) | −480.000 | −1.45897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 408.764i | − | 1.23494i | −0.786596 | − | 0.617468i | \(-0.788158\pi\) | ||
0.786596 | − | 0.617468i | \(-0.211842\pi\) | |||||||
\(332\) | 168.000 | − | 96.9948i | 0.506024 | − | 0.292153i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 168.000 | + | 96.9948i | 0.502994 | + | 0.290404i | ||||
\(335\) | − | 13.8564i | − | 0.0413624i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 338.000 | 1.00297 | 0.501484 | − | 0.865167i | \(-0.332788\pi\) | ||||
0.501484 | + | 0.865167i | \(0.332788\pi\) | |||||||
\(338\) | −165.000 | + | 285.788i | −0.488166 | + | 0.845528i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 40.0000 | + | 69.2820i | 0.117647 | + | 0.203771i | ||||
\(341\) | 48.0000 | 0.140762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 346.410i | 1.00994i | ||||||||
\(344\) | − | 387.979i | − | 1.12785i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −334.000 | + | 578.505i | −0.965318 | + | 1.67198i | ||||
\(347\) | 200.918i | 0.579014i | 0.957176 | + | 0.289507i | \(0.0934914\pi\) | ||||
−0.957176 | + | 0.289507i | \(0.906509\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 506.000 | 1.44986 | 0.724928 | − | 0.688824i | \(-0.241873\pi\) | ||||
0.724928 | + | 0.688824i | \(0.241873\pi\) | |||||||
\(350\) | −252.000 | − | 145.492i | −0.720000 | − | 0.415692i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −192.000 | + | 110.851i | −0.545455 | + | 0.314918i | ||||
\(353\) | −178.000 | −0.504249 | −0.252125 | − | 0.967695i | \(-0.581129\pi\) | ||||
−0.252125 | + | 0.967695i | \(0.581129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 164.000 | + | 284.056i | 0.460674 | + | 0.797911i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −324.000 | − | 187.061i | −0.905028 | − | 0.522518i | ||||
\(359\) | 166.277i | 0.463167i | 0.972815 | + | 0.231583i | \(0.0743906\pi\) | ||||
−0.972815 | + | 0.231583i | \(0.925609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −71.0000 | −0.196676 | ||||||||
\(362\) | 2.00000 | − | 3.46410i | 0.00552486 | − | 0.00956934i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 48.0000 | − | 27.7128i | 0.131868 | − | 0.0761341i | ||||
\(365\) | −92.0000 | −0.252055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 200.918i | − | 0.547460i | −0.961807 | − | 0.273730i | \(-0.911742\pi\) | ||
0.961807 | − | 0.273730i | \(-0.0882575\pi\) | |||||||
\(368\) | 384.000 | + | 221.703i | 1.04348 | + | 0.602452i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 52.0000 | − | 90.0666i | 0.140541 | − | 0.243423i | ||||
\(371\) | 512.687i | 1.38191i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −310.000 | −0.831099 | −0.415550 | − | 0.909571i | \(-0.636411\pi\) | ||||
−0.415550 | + | 0.909571i | \(0.636411\pi\) | |||||||
\(374\) | −120.000 | − | 69.2820i | −0.320856 | − | 0.185246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 554.256i | − | 1.47409i | ||||||
\(377\) | 52.0000 | 0.137931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 436.477i | 1.15165i | 0.817572 | + | 0.575827i | \(0.195320\pi\) | ||||
−0.817572 | + | 0.575827i | \(0.804680\pi\) | |||||||
\(380\) | −144.000 | + | 83.1384i | −0.378947 | + | 0.218785i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −384.000 | − | 221.703i | −1.00524 | − | 0.580373i | ||||
\(383\) | − | 609.682i | − | 1.59186i | −0.605390 | − | 0.795929i | \(-0.706983\pi\) | ||
0.605390 | − | 0.795929i | \(-0.293017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −96.0000 | −0.249351 | ||||||||
\(386\) | 290.000 | − | 502.295i | 0.751295 | − | 1.30128i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.00000 | − | 6.92820i | −0.0103093 | − | 0.0178562i | ||||
\(389\) | 578.000 | 1.48586 | 0.742931 | − | 0.669368i | \(-0.233435\pi\) | ||||
0.742931 | + | 0.669368i | \(0.233435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 277.128i | 0.708768i | ||||||||
\(392\) | −8.00000 | −0.0204082 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.0000 | − | 45.0333i | 0.0659898 | − | 0.114298i | ||||
\(395\) | − | 235.559i | − | 0.596352i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000 | 0.0654912 | 0.0327456 | − | 0.999464i | \(-0.489575\pi\) | ||||
0.0327456 | + | 0.999464i | \(0.489575\pi\) | |||||||
\(398\) | −684.000 | − | 394.908i | −1.71859 | − | 0.992230i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 168.000 | − | 290.985i | 0.420000 | − | 0.727461i | ||||
\(401\) | −250.000 | −0.623441 | −0.311721 | − | 0.950174i | \(-0.600905\pi\) | ||||
−0.311721 | + | 0.950174i | \(0.600905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.8564i | − | 0.0343831i | ||||||
\(404\) | −148.000 | − | 256.344i | −0.366337 | − | 0.634514i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 312.000 | + | 180.133i | 0.768473 | + | 0.443678i | ||||
\(407\) | 180.133i | 0.442588i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 290.000 | 0.709046 | 0.354523 | − | 0.935047i | \(-0.384643\pi\) | ||||
0.354523 | + | 0.935047i | \(0.384643\pi\) | |||||||
\(410\) | −116.000 | + | 200.918i | −0.282927 | + | 0.490044i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 264.000 | − | 152.420i | 0.640777 | − | 0.369953i | ||||
\(413\) | 624.000 | 1.51090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 96.9948i | 0.233723i | ||||||||
\(416\) | 32.0000 | + | 55.4256i | 0.0769231 | + | 0.133235i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 144.000 | − | 249.415i | 0.344498 | − | 0.596687i | ||||
\(419\) | − | 339.482i | − | 0.810219i | −0.914268 | − | 0.405110i | \(-0.867233\pi\) | ||
0.914268 | − | 0.405110i | \(-0.132767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 674.000 | 1.60095 | 0.800475 | − | 0.599366i | \(-0.204581\pi\) | ||||
0.800475 | + | 0.599366i | \(0.204581\pi\) | |||||||
\(422\) | 420.000 | + | 242.487i | 0.995261 | + | 0.574614i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −592.000 | −1.39623 | ||||||||
\(425\) | 210.000 | 0.494118 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 180.133i | 0.421858i | ||||||||
\(428\) | 72.0000 | − | 41.5692i | 0.168224 | − | 0.0971243i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 168.000 | + | 96.9948i | 0.390698 | + | 0.225569i | ||||
\(431\) | 540.400i | 1.25383i | 0.779088 | + | 0.626914i | \(0.215682\pi\) | ||||
−0.779088 | + | 0.626914i | \(0.784318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −334.000 | −0.771363 | −0.385681 | − | 0.922632i | \(-0.626034\pi\) | ||||
−0.385681 | + | 0.922632i | \(0.626034\pi\) | |||||||
\(434\) | 48.0000 | − | 83.1384i | 0.110599 | − | 0.191563i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 92.0000 | + | 159.349i | 0.211009 | + | 0.365479i | ||||
\(437\) | −576.000 | −1.31808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 117.779i | − | 0.268290i | −0.990962 | − | 0.134145i | \(-0.957171\pi\) | ||
0.990962 | − | 0.134145i | \(-0.0428288\pi\) | |||||||
\(440\) | − | 110.851i | − | 0.251935i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.0000 | + | 34.6410i | −0.0452489 | + | 0.0783733i | ||||
\(443\) | − | 76.2102i | − | 0.172032i | −0.996294 | − | 0.0860161i | \(-0.972586\pi\) | ||
0.996294 | − | 0.0860161i | \(-0.0274136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −164.000 | −0.368539 | ||||||||
\(446\) | 588.000 | + | 339.482i | 1.31839 | + | 0.761170i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 443.405i | 0.989743i | ||||||||
\(449\) | −394.000 | −0.877506 | −0.438753 | − | 0.898608i | \(-0.644580\pi\) | ||||
−0.438753 | + | 0.898608i | \(0.644580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 401.836i | − | 0.890988i | ||||||
\(452\) | −220.000 | − | 381.051i | −0.486726 | − | 0.843034i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −492.000 | − | 284.056i | −1.08370 | − | 0.625675i | ||||
\(455\) | 27.7128i | 0.0609073i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −478.000 | −1.04595 | −0.522976 | − | 0.852347i | \(-0.675178\pi\) | ||||
−0.522976 | + | 0.852347i | \(0.675178\pi\) | |||||||
\(458\) | −142.000 | + | 245.951i | −0.310044 | + | 0.537011i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −192.000 | + | 110.851i | −0.417391 | + | 0.240981i | ||||
\(461\) | −142.000 | −0.308026 | −0.154013 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154013 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 630.466i | − | 1.36170i | −0.732423 | − | 0.680849i | \(-0.761611\pi\) | ||
0.732423 | − | 0.680849i | \(-0.238389\pi\) | |||||||
\(464\) | −208.000 | + | 360.267i | −0.448276 | + | 0.776437i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −82.0000 | + | 142.028i | −0.175966 | + | 0.304781i | ||||
\(467\) | 20.7846i | 0.0445067i | 0.999752 | + | 0.0222533i | \(0.00708404\pi\) | ||||
−0.999752 | + | 0.0222533i | \(0.992916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0000 | 0.102345 | ||||||||
\(470\) | 240.000 | + | 138.564i | 0.510638 | + | 0.294817i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 720.533i | 1.52655i | ||||||||
\(473\) | −336.000 | −0.710359 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 436.477i | 0.918899i | ||||||||
\(476\) | −240.000 | + | 138.564i | −0.504202 | + | 0.291101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 672.000 | + | 387.979i | 1.40586 | + | 0.811672i | ||||
\(479\) | 734.390i | 1.53317i | 0.642141 | + | 0.766586i | \(0.278046\pi\) | ||||
−0.642141 | + | 0.766586i | \(0.721954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.0000 | 0.108108 | ||||||||
\(482\) | −46.0000 | + | 79.6743i | −0.0954357 | + | 0.165299i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −146.000 | − | 252.879i | −0.301653 | − | 0.522478i | ||||
\(485\) | 4.00000 | 0.00824742 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 103.923i | − | 0.213394i | −0.994292 | − | 0.106697i | \(-0.965972\pi\) | ||
0.994292 | − | 0.106697i | \(-0.0340275\pi\) | |||||||
\(488\) | −208.000 | −0.426230 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | − | 3.46410i | 0.00408163 | − | 0.00706960i | ||||
\(491\) | − | 921.451i | − | 1.87668i | −0.345711 | − | 0.938341i | \(-0.612362\pi\) | ||
0.345711 | − | 0.938341i | \(-0.387638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −260.000 | −0.527383 | ||||||||
\(494\) | −72.0000 | − | 41.5692i | −0.145749 | − | 0.0841482i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 96.0000 | + | 55.4256i | 0.193548 | + | 0.111745i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 76.2102i | 0.152726i | 0.997080 | + | 0.0763630i | \(0.0243308\pi\) | ||||
−0.997080 | + | 0.0763630i | \(0.975669\pi\) | |||||||
\(500\) | 184.000 | + | 318.697i | 0.368000 | + | 0.637395i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 252.000 | + | 145.492i | 0.501992 | + | 0.289825i | ||||
\(503\) | − | 581.969i | − | 1.15700i | −0.815684 | − | 0.578498i | \(-0.803639\pi\) | ||
0.815684 | − | 0.578498i | \(-0.196361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 148.000 | 0.293069 | ||||||||
\(506\) | 192.000 | − | 332.554i | 0.379447 | − | 0.657221i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 504.000 | − | 290.985i | 0.992126 | − | 0.572804i | ||||
\(509\) | 842.000 | 1.65422 | 0.827112 | − | 0.562037i | \(-0.189982\pi\) | ||||
0.827112 | + | 0.562037i | \(0.189982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 318.697i | − | 0.623674i | ||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 254.000 | − | 439.941i | 0.494163 | − | 0.855916i | ||||
\(515\) | 152.420i | 0.295962i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −480.000 | −0.928433 | ||||||||
\(518\) | 312.000 | + | 180.133i | 0.602317 | + | 0.347748i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.0000 | −0.0615385 | ||||||||
\(521\) | 326.000 | 0.625720 | 0.312860 | − | 0.949799i | \(-0.398713\pi\) | ||||
0.312860 | + | 0.949799i | \(0.398713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 311.769i | − | 0.596117i | −0.954548 | − | 0.298058i | \(-0.903661\pi\) | ||
0.954548 | − | 0.298058i | \(-0.0963390\pi\) | |||||||
\(524\) | 408.000 | − | 235.559i | 0.778626 | − | 0.449540i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 264.000 | + | 152.420i | 0.501901 | + | 0.289773i | ||||
\(527\) | 69.2820i | 0.131465i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −239.000 | −0.451796 | ||||||||
\(530\) | 148.000 | − | 256.344i | 0.279245 | − | 0.483667i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −288.000 | − | 498.831i | −0.541353 | − | 0.937652i | ||||
\(533\) | −116.000 | −0.217636 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.5692i | 0.0776995i | ||||||||
\(536\) | 55.4256i | 0.103406i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −262.000 | + | 453.797i | −0.486989 | + | 0.843489i | ||||
\(539\) | 6.92820i | 0.0128538i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 530.000 | 0.979667 | 0.489834 | − | 0.871816i | \(-0.337058\pi\) | ||||
0.489834 | + | 0.871816i | \(0.337058\pi\) | |||||||
\(542\) | −36.0000 | − | 20.7846i | −0.0664207 | − | 0.0383480i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −160.000 | − | 277.128i | −0.294118 | − | 0.509427i | ||||
\(545\) | −92.0000 | −0.168807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 339.482i | 0.620625i | 0.950635 | + | 0.310313i | \(0.100434\pi\) | ||||
−0.950635 | + | 0.310313i | \(0.899566\pi\) | |||||||
\(548\) | 20.0000 | + | 34.6410i | 0.0364964 | + | 0.0632135i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −252.000 | − | 145.492i | −0.458182 | − | 0.264531i | ||||
\(551\) | − | 540.400i | − | 0.980762i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 816.000 | 1.47559 | ||||||||
\(554\) | 290.000 | − | 502.295i | 0.523466 | − | 0.906669i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −168.000 | + | 96.9948i | −0.302158 | + | 0.174451i | ||||
\(557\) | −766.000 | −1.37522 | −0.687612 | − | 0.726078i | \(-0.741341\pi\) | ||||
−0.687612 | + | 0.726078i | \(0.741341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 96.9948i | 0.173515i | ||||||||
\(560\) | −192.000 | − | 110.851i | −0.342857 | − | 0.197949i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −226.000 | + | 391.443i | −0.402135 | + | 0.696519i | ||||
\(563\) | 491.902i | 0.873717i | 0.899530 | + | 0.436858i | \(0.143909\pi\) | ||||
−0.899530 | + | 0.436858i | \(0.856091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 220.000 | 0.389381 | ||||||||
\(566\) | −516.000 | − | 297.913i | −0.911661 | − | 0.526348i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 422.000 | 0.741652 | 0.370826 | − | 0.928702i | \(-0.379075\pi\) | ||||
0.370826 | + | 0.928702i | \(0.379075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.056i | 0.497472i | 0.968571 | + | 0.248736i | \(0.0800151\pi\) | ||||
−0.968571 | + | 0.248736i | \(0.919985\pi\) | |||||||
\(572\) | 48.0000 | − | 27.7128i | 0.0839161 | − | 0.0484490i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −696.000 | − | 401.836i | −1.21254 | − | 0.700062i | ||||
\(575\) | 581.969i | 1.01212i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.0000 | −0.0797227 | −0.0398614 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398614 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(578\) | −189.000 | + | 327.358i | −0.326990 | + | 0.566363i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −104.000 | − | 180.133i | −0.179310 | − | 0.310575i | ||||
\(581\) | −336.000 | −0.578313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 512.687i | 0.879395i | ||||||||
\(584\) | 368.000 | 0.630137 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 362.000 | − | 627.002i | 0.617747 | − | 1.06997i | ||||
\(587\) | 630.466i | 1.07405i | 0.843567 | + | 0.537024i | \(0.180452\pi\) | ||||
−0.843567 | + | 0.537024i | \(0.819548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −144.000 | −0.244482 | ||||||||
\(590\) | −312.000 | − | 180.133i | −0.528814 | − | 0.305311i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −208.000 | + | 360.267i | −0.351351 | + | 0.608558i | ||||
\(593\) | −82.0000 | −0.138280 | −0.0691400 | − | 0.997607i | \(-0.522026\pi\) | ||||
−0.0691400 | + | 0.997607i | \(0.522026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 138.564i | − | 0.232881i | ||||||
\(596\) | −4.00000 | − | 6.92820i | −0.00671141 | − | 0.0116245i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −96.0000 | − | 55.4256i | −0.160535 | − | 0.0926850i | ||||
\(599\) | 55.4256i | 0.0925303i | 0.998929 | + | 0.0462651i | \(0.0147319\pi\) | ||||
−0.998929 | + | 0.0462651i | \(0.985268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −334.000 | −0.555740 | −0.277870 | − | 0.960619i | \(-0.589629\pi\) | ||||
−0.277870 | + | 0.960619i | \(0.589629\pi\) | |||||||
\(602\) | −336.000 | + | 581.969i | −0.558140 | + | 0.966726i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 312.000 | − | 180.133i | 0.516556 | − | 0.298234i | ||||
\(605\) | 146.000 | 0.241322 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 367.195i | 0.604934i | 0.953160 | + | 0.302467i | \(0.0978102\pi\) | ||||
−0.953160 | + | 0.302467i | \(0.902190\pi\) | |||||||
\(608\) | 576.000 | − | 332.554i | 0.947368 | − | 0.546963i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 52.0000 | − | 90.0666i | 0.0852459 | − | 0.147650i | ||||
\(611\) | 138.564i | 0.226782i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −214.000 | −0.349103 | −0.174551 | − | 0.984648i | \(-0.555848\pi\) | ||||
−0.174551 | + | 0.984648i | \(0.555848\pi\) | |||||||
\(614\) | −252.000 | − | 145.492i | −0.410423 | − | 0.236958i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 384.000 | 0.623377 | ||||||||
\(617\) | 1118.00 | 1.81199 | 0.905997 | − | 0.423285i | \(-0.139123\pi\) | ||||
0.905997 | + | 0.423285i | \(0.139123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 672.036i | 1.08568i | 0.839836 | + | 0.542840i | \(0.182651\pi\) | ||||
−0.839836 | + | 0.542840i | \(0.817349\pi\) | |||||||
\(620\) | −48.0000 | + | 27.7128i | −0.0774194 | + | 0.0446981i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −408.000 | − | 235.559i | −0.655949 | − | 0.378712i | ||||
\(623\) | − | 568.113i | − | 0.911898i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 341.000 | 0.545600 | ||||||||
\(626\) | −478.000 | + | 827.920i | −0.763578 | + | 1.32256i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 428.000 | + | 741.318i | 0.681529 | + | 1.18044i | ||||
\(629\) | −260.000 | −0.413355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 145.492i | 0.230574i | 0.993332 | + | 0.115287i | \(0.0367788\pi\) | ||||
−0.993332 | + | 0.115287i | \(0.963221\pi\) | |||||||
\(632\) | 942.236i | 1.49088i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 170.000 | − | 294.449i | 0.268139 | − | 0.464430i | ||||
\(635\) | 290.985i | 0.458243i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.00313972 | ||||||||
\(638\) | 312.000 | + | 180.133i | 0.489028 | + | 0.282341i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 128.000 | − | 221.703i | 0.200000 | − | 0.346410i | ||||
\(641\) | −10.0000 | −0.0156006 | −0.00780031 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00780031 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1212.44i | − | 1.88559i | −0.333370 | − | 0.942796i | \(-0.608186\pi\) | ||
0.333370 | − | 0.942796i | \(-0.391814\pi\) | |||||||
\(644\) | −384.000 | − | 665.108i | −0.596273 | − | 1.03278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 360.000 | + | 207.846i | 0.557276 | + | 0.321743i | ||||
\(647\) | − | 332.554i | − | 0.513993i | −0.966412 | − | 0.256997i | \(-0.917267\pi\) | ||
0.966412 | − | 0.256997i | \(-0.0827330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 624.000 | 0.961479 | ||||||||
\(650\) | −42.0000 | + | 72.7461i | −0.0646154 | + | 0.111917i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −72.0000 | + | 41.5692i | −0.110429 | + | 0.0637565i | ||||
\(653\) | −670.000 | −1.02603 | −0.513017 | − | 0.858379i | \(-0.671472\pi\) | ||||
−0.513017 | + | 0.858379i | \(0.671472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 235.559i | 0.359632i | ||||||||
\(656\) | 464.000 | − | 803.672i | 0.707317 | − | 1.22511i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −480.000 | + | 831.384i | −0.729483 | + | 1.26350i | ||||
\(659\) | − | 824.456i | − | 1.25107i | −0.780195 | − | 0.625536i | \(-0.784880\pi\) | ||
0.780195 | − | 0.625536i | \(-0.215120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1222.00 | −1.84871 | −0.924357 | − | 0.381529i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381529i | \(0.875398\pi\) | |||||||
\(662\) | −708.000 | − | 408.764i | −1.06949 | − | 0.617468i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 387.979i | − | 0.584306i | ||||||
\(665\) | 288.000 | 0.433083 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 720.533i | − | 1.08026i | ||||||
\(668\) | 336.000 | − | 193.990i | 0.502994 | − | 0.290404i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.0000 | − | 13.8564i | −0.0358209 | − | 0.0206812i | ||||
\(671\) | 180.133i | 0.268455i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −334.000 | −0.496285 | −0.248143 | − | 0.968724i | \(-0.579820\pi\) | ||||
−0.248143 | + | 0.968724i | \(0.579820\pi\) | |||||||
\(674\) | 338.000 | − | 585.433i | 0.501484 | − | 0.868595i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 330.000 | + | 571.577i | 0.488166 | + | 0.845528i | ||||
\(677\) | −1006.00 | −1.48597 | −0.742984 | − | 0.669309i | \(-0.766590\pi\) | ||||
−0.742984 | + | 0.669309i | \(0.766590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8564i | 0.0204071i | ||||||||
\(680\) | 160.000 | 0.235294 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.0000 | − | 83.1384i | 0.0703812 | − | 0.121904i | ||||
\(683\) | − | 187.061i | − | 0.273882i | −0.990579 | − | 0.136941i | \(-0.956273\pi\) | ||
0.990579 | − | 0.136941i | \(-0.0437271\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0000 | −0.0291971 | ||||||||
\(686\) | 600.000 | + | 346.410i | 0.874636 | + | 0.504971i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −672.000 | − | 387.979i | −0.976744 | − | 0.563924i | ||||
\(689\) | 148.000 | 0.214804 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 990.733i | − | 1.43377i | −0.697193 | − | 0.716884i | \(-0.745568\pi\) | ||
0.697193 | − | 0.716884i | \(-0.254432\pi\) | |||||||
\(692\) | 668.000 | + | 1157.01i | 0.965318 | + | 1.67198i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 348.000 | + | 200.918i | 0.501441 | + | 0.289507i | ||||
\(695\) | − | 96.9948i | − | 0.139561i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 580.000 | 0.832138 | ||||||||
\(698\) | 506.000 | − | 876.418i | 0.724928 | − | 1.25561i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −504.000 | + | 290.985i | −0.720000 | + | 0.415692i | ||||
\(701\) | 1034.00 | 1.47504 | 0.737518 | − | 0.675328i | \(-0.235998\pi\) | ||||
0.737518 | + | 0.675328i | \(0.235998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 540.400i | − | 0.768705i | ||||||
\(704\) | 443.405i | 0.629837i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −178.000 | + | 308.305i | −0.252125 | + | 0.436693i | ||||
\(707\) | 512.687i | 0.725158i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 530.000 | 0.747532 | 0.373766 | − | 0.927523i | \(-0.378066\pi\) | ||||
0.373766 | + | 0.927523i | \(0.378066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 656.000 | 0.921348 | ||||||||
\(713\) | −192.000 | −0.269285 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.7128i | 0.0387592i | ||||||||
\(716\) | −648.000 | + | 374.123i | −0.905028 | + | 0.522518i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 288.000 | + | 166.277i | 0.401114 | + | 0.231583i | ||||
\(719\) | − | 706.677i | − | 0.982861i | −0.870917 | − | 0.491430i | \(-0.836474\pi\) | ||
0.870917 | − | 0.491430i | \(-0.163526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −528.000 | −0.732316 | ||||||||
\(722\) | −71.0000 | + | 122.976i | −0.0983380 | + | 0.170326i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.00000 | − | 6.92820i | −0.00552486 | − | 0.00956934i | ||||
\(725\) | −546.000 | −0.753103 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 242.487i | − | 0.333545i | −0.985995 | − | 0.166772i | \(-0.946665\pi\) | ||
0.985995 | − | 0.166772i | \(-0.0533345\pi\) | |||||||
\(728\) | − | 110.851i | − | 0.152268i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −92.0000 | + | 159.349i | −0.126027 | + | 0.218286i | ||||
\(731\) | − | 484.974i | − | 0.663439i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 194.000 | 0.264666 | 0.132333 | − | 0.991205i | \(-0.457753\pi\) | ||||
0.132333 | + | 0.991205i | \(0.457753\pi\) | |||||||
\(734\) | −348.000 | − | 200.918i | −0.474114 | − | 0.273730i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 768.000 | − | 443.405i | 1.04348 | − | 0.602452i | ||||
\(737\) | 48.0000 | 0.0651289 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1351.00i | 1.82815i | 0.405550 | + | 0.914073i | \(0.367080\pi\) | ||||
−0.405550 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(740\) | −104.000 | − | 180.133i | −0.140541 | − | 0.243423i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 888.000 | + | 512.687i | 1.19677 | + | 0.690953i | ||||
\(743\) | 678.964i | 0.913814i | 0.889514 | + | 0.456907i | \(0.151043\pi\) | ||||
−0.889514 | + | 0.456907i | \(0.848957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | 0.00536913 | ||||||||
\(746\) | −310.000 | + | 536.936i | −0.415550 | + | 0.719753i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −240.000 | + | 138.564i | −0.320856 | + | 0.185246i | ||||
\(749\) | −144.000 | −0.192256 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 658.179i | 0.876404i | 0.898877 | + | 0.438202i | \(0.144385\pi\) | ||||
−0.898877 | + | 0.438202i | \(0.855615\pi\) | |||||||
\(752\) | −960.000 | − | 554.256i | −1.27660 | − | 0.737043i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 52.0000 | − | 90.0666i | 0.0689655 | − | 0.119452i | ||||
\(755\) | 180.133i | 0.238587i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1006.00 | −1.32893 | −0.664465 | − | 0.747319i | \(-0.731341\pi\) | ||||
−0.664465 | + | 0.747319i | \(0.731341\pi\) | |||||||
\(758\) | 756.000 | + | 436.477i | 0.997361 | + | 0.575827i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 332.554i | 0.437571i | ||||||||
\(761\) | 758.000 | 0.996058 | 0.498029 | − | 0.867160i | \(-0.334057\pi\) | ||||
0.498029 | + | 0.867160i | \(0.334057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 318.697i | − | 0.417690i | ||||||
\(764\) | −768.000 | + | 443.405i | −1.00524 | + | 0.580373i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1056.00 | − | 609.682i | −1.37859 | − | 0.795929i | ||||
\(767\) | − | 180.133i | − | 0.234854i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.00260078 | 0.00130039 | − | 0.999999i | \(-0.499586\pi\) | ||||
0.00130039 | + | 0.999999i | \(0.499586\pi\) | |||||||
\(770\) | −96.0000 | + | 166.277i | −0.124675 | + | 0.215944i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −580.000 | − | 1004.59i | −0.751295 | − | 1.30128i | ||||
\(773\) | −262.000 | −0.338939 | −0.169470 | − | 0.985535i | \(-0.554205\pi\) | ||||
−0.169470 | + | 0.985535i | \(0.554205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 145.492i | 0.187732i | ||||||||
\(776\) | −16.0000 | −0.0206186 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 578.000 | − | 1001.13i | 0.742931 | − | 1.28679i | ||||
\(779\) | 1205.51i | 1.54751i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 480.000 | + | 277.128i | 0.613811 | + | 0.354384i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | + | 13.8564i | −0.0102041 | + | 0.0176740i | ||||
\(785\) | −428.000 | −0.545223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1447.99i | 1.83989i | 0.392046 | + | 0.919946i | \(0.371767\pi\) | ||||
−0.392046 | + | 0.919946i | \(0.628233\pi\) | |||||||
\(788\) | −52.0000 | − | 90.0666i | −0.0659898 | − | 0.114298i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −408.000 | − | 235.559i | −0.516456 | − | 0.298176i | ||||
\(791\) | 762.102i | 0.963467i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.0000 | 0.0655738 | ||||||||
\(794\) | 26.0000 | − | 45.0333i | 0.0327456 | − | 0.0567170i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1368.00 | + | 789.815i | −1.71859 | + | 0.992230i | ||||
\(797\) | 866.000 | 1.08657 | 0.543287 | − | 0.839547i | \(-0.317179\pi\) | ||||
0.543287 | + | 0.839547i | \(0.317179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 692.820i | − | 0.867109i | ||||||
\(800\) | −336.000 | − | 581.969i | −0.420000 | − | 0.727461i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −250.000 | + | 433.013i | −0.311721 | + | 0.539916i | ||||
\(803\) | − | 318.697i | − | 0.396883i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 384.000 | 0.477019 | ||||||||
\(806\) | −24.0000 | − | 13.8564i | −0.0297767 | − | 0.0171916i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −592.000 | −0.732673 | ||||||||
\(809\) | −10.0000 | −0.0123609 | −0.00618047 | − | 0.999981i | \(-0.501967\pi\) | ||||
−0.00618047 | + | 0.999981i | \(0.501967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 436.477i | 0.538196i | 0.963113 | + | 0.269098i | \(0.0867255\pi\) | ||||
−0.963113 | + | 0.269098i | \(0.913274\pi\) | |||||||
\(812\) | 624.000 | − | 360.267i | 0.768473 | − | 0.443678i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 312.000 | + | 180.133i | 0.383292 | + | 0.221294i | ||||
\(815\) | − | 41.5692i | − | 0.0510052i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1008.00 | 1.23378 | ||||||||
\(818\) | 290.000 | − | 502.295i | 0.354523 | − | 0.614052i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 232.000 | + | 401.836i | 0.282927 | + | 0.490044i | ||||
\(821\) | −838.000 | −1.02071 | −0.510353 | − | 0.859965i | \(-0.670485\pi\) | ||||
−0.510353 | + | 0.859965i | \(0.670485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 879.882i | − | 1.06912i | −0.845132 | − | 0.534558i | \(-0.820478\pi\) | ||
0.845132 | − | 0.534558i | \(-0.179522\pi\) | |||||||
\(824\) | − | 609.682i | − | 0.739905i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 624.000 | − | 1080.80i | 0.755448 | − | 1.30847i | ||||
\(827\) | − | 727.461i | − | 0.879639i | −0.898086 | − | 0.439819i | \(-0.855042\pi\) | ||
0.898086 | − | 0.439819i | \(-0.144958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1298.00 | 1.56574 | 0.782871 | − | 0.622184i | \(-0.213754\pi\) | ||||
0.782871 | + | 0.622184i | \(0.213754\pi\) | |||||||
\(830\) | 168.000 | + | 96.9948i | 0.202410 | + | 0.116861i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 128.000 | 0.153846 | ||||||||
\(833\) | −10.0000 | −0.0120048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 193.990i | 0.232323i | ||||||||
\(836\) | −288.000 | − | 498.831i | −0.344498 | − | 0.596687i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −588.000 | − | 339.482i | −0.701671 | − | 0.405110i | ||||
\(839\) | 193.990i | 0.231215i | 0.993295 | + | 0.115608i | \(0.0368815\pi\) | ||||
−0.993295 | + | 0.115608i | \(0.963118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −165.000 | −0.196195 | ||||||||
\(842\) | 674.000 | − | 1167.40i | 0.800475 | − | 1.38646i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 840.000 | − | 484.974i | 0.995261 | − | 0.574614i | ||||
\(845\) | −330.000 | −0.390533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 505.759i | 0.597118i | ||||||||
\(848\) | −592.000 | + | 1025.37i | −0.698113 | + | 1.20917i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 210.000 | − | 363.731i | 0.247059 | − | 0.427918i | ||||
\(851\) | − | 720.533i | − | 0.846690i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 506.000 | 0.593200 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(854\) | 312.000 | + | 180.133i | 0.365340 | + | 0.210929i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 166.277i | − | 0.194249i | ||||||
\(857\) | 998.000 | 1.16453 | 0.582264 | − | 0.813000i | \(-0.302167\pi\) | ||||
0.582264 | + | 0.813000i | \(0.302167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 505.759i | − | 0.588776i | −0.955686 | − | 0.294388i | \(-0.904884\pi\) | ||
0.955686 | − | 0.294388i | \(-0.0951158\pi\) | |||||||
\(860\) | 336.000 | − | 193.990i | 0.390698 | − | 0.225569i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 936.000 | + | 540.400i | 1.08585 | + | 0.626914i | ||||
\(863\) | 166.277i | 0.192673i | 0.995349 | + | 0.0963365i | \(0.0307125\pi\) | ||||
−0.995349 | + | 0.0963365i | \(0.969287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −668.000 | −0.772254 | ||||||||
\(866\) | −334.000 | + | 578.505i | −0.385681 | + | 0.668020i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −96.0000 | − | 166.277i | −0.110599 | − | 0.191563i | ||||
\(869\) | 816.000 | 0.939010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.8564i | − | 0.0159086i | ||||||
\(872\) | 368.000 | 0.422018 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −576.000 | + | 997.661i | −0.659039 | + | 1.14149i | ||||
\(875\) | − | 637.395i | − | 0.728451i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −646.000 | −0.736602 | −0.368301 | − | 0.929707i | \(-0.620060\pi\) | ||||
−0.368301 | + | 0.929707i | \(0.620060\pi\) | |||||||
\(878\) | −204.000 | − | 117.779i | −0.232346 | − | 0.134145i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −192.000 | − | 110.851i | −0.218182 | − | 0.125967i | ||||
\(881\) | −898.000 | −1.01930 | −0.509648 | − | 0.860383i | \(-0.670224\pi\) | ||||
−0.509648 | + | 0.860383i | \(0.670224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 727.461i | 0.823852i | 0.911217 | + | 0.411926i | \(0.135144\pi\) | ||||
−0.911217 | + | 0.411926i | \(0.864856\pi\) | |||||||
\(884\) | 40.0000 | + | 69.2820i | 0.0452489 | + | 0.0783733i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −132.000 | − | 76.2102i | −0.148984 | − | 0.0860161i | ||||
\(887\) | 845.241i | 0.952921i | 0.879196 | + | 0.476460i | \(0.158080\pi\) | ||||
−0.879196 | + | 0.476460i | \(0.841920\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1008.00 | −1.13386 | ||||||||
\(890\) | −164.000 | + | 284.056i | −0.184270 | + | 0.319164i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1176.00 | − | 678.964i | 1.31839 | − | 0.761170i | ||||
\(893\) | 1440.00 | 1.61254 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 374.123i | − | 0.418014i | ||||||
\(896\) | 768.000 | + | 443.405i | 0.857143 | + | 0.494872i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −394.000 | + | 682.428i | −0.438753 | + | 0.759942i | ||||
\(899\) | − | 180.133i | − | 0.200371i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −740.000 | −0.821310 | ||||||||
\(902\) | −696.000 | − | 401.836i | −0.771619 | − | 0.445494i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −880.000 | −0.973451 | ||||||||
\(905\) | 4.00000 | 0.00441989 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1364.86i | − | 1.50480i | −0.658705 | − | 0.752401i | \(-0.728895\pi\) | ||
0.658705 | − | 0.752401i | \(-0.271105\pi\) | |||||||
\(908\) | −984.000 | + | 568.113i | −1.08370 | + | 0.625675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 48.0000 | + | 27.7128i | 0.0527473 | + | 0.0304536i | ||||
\(911\) | − | 387.979i | − | 0.425883i | −0.977065 | − | 0.212941i | \(-0.931696\pi\) | ||
0.977065 | − | 0.212941i | \(-0.0683044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −336.000 | −0.368018 | ||||||||
\(914\) | −478.000 | + | 827.920i | −0.522976 | + | 0.905821i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 284.000 | + | 491.902i | 0.310044 | + | 0.537011i | ||||
\(917\) | −816.000 | −0.889858 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 602.754i | − | 0.655880i | −0.944699 | − | 0.327940i | \(-0.893646\pi\) | ||
0.944699 | − | 0.327940i | \(-0.106354\pi\) | |||||||
\(920\) | 443.405i | 0.481962i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −142.000 | + | 245.951i | −0.154013 | + | 0.266758i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −546.000 | −0.590270 | ||||||||
\(926\) | −1092.00 | − | 630.466i | −1.17927 | − | 0.680849i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 416.000 | + | 720.533i | 0.448276 | + | 0.776437i | ||||
\(929\) | −1594.00 | −1.71582 | −0.857912 | − | 0.513797i | \(-0.828238\pi\) | ||||
−0.857912 | + | 0.513797i | \(0.828238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20.7846i | − | 0.0223250i | ||||||
\(932\) | 164.000 | + | 284.056i | 0.175966 | + | 0.304781i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.0000 | + | 20.7846i | 0.0385439 | + | 0.0222533i | ||||
\(935\) | − | 138.564i | − | 0.148197i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 674.000 | 0.719317 | 0.359658 | − | 0.933084i | \(-0.382893\pi\) | ||||
0.359658 | + | 0.933084i | \(0.382893\pi\) | |||||||
\(938\) | 48.0000 | − | 83.1384i | 0.0511727 | − | 0.0886337i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 480.000 | − | 277.128i | 0.510638 | − | 0.294817i | ||||
\(941\) | −430.000 | −0.456961 | −0.228480 | − | 0.973549i | \(-0.573376\pi\) | ||||
−0.228480 | + | 0.973549i | \(0.573376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1607.34i | 1.70450i | ||||||||
\(944\) | 1248.00 | + | 720.533i | 1.32203 | + | 0.763277i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −336.000 | + | 581.969i | −0.355180 | + | 0.615189i | ||||
\(947\) | − | 76.2102i | − | 0.0804754i | −0.999190 | − | 0.0402377i | \(-0.987188\pi\) | ||
0.999190 | − | 0.0402377i | \(-0.0128115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −92.0000 | −0.0969442 | ||||||||
\(950\) | 756.000 | + | 436.477i | 0.795789 | + | 0.459449i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 554.256i | 0.582202i | ||||||||
\(953\) | −730.000 | −0.766002 | −0.383001 | − | 0.923748i | \(-0.625109\pi\) | ||||
−0.383001 | + | 0.923748i | \(0.625109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 443.405i | − | 0.464298i | ||||||
\(956\) | 1344.00 | − | 775.959i | 1.40586 | − | 0.811672i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1272.00 | + | 734.390i | 1.32777 | + | 0.766586i | ||||
\(959\) | − | 69.2820i | − | 0.0722440i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 913.000 | 0.950052 | ||||||||
\(962\) | 52.0000 | − | 90.0666i | 0.0540541 | − | 0.0936244i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 92.0000 | + | 159.349i | 0.0954357 | + | 0.165299i | ||||
\(965\) | 580.000 | 0.601036 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 921.451i | − | 0.952897i | −0.879202 | − | 0.476448i | \(-0.841924\pi\) | ||
0.879202 | − | 0.476448i | \(-0.158076\pi\) | |||||||
\(968\) | −584.000 | −0.603306 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.00000 | − | 6.92820i | 0.00412371 | − | 0.00714248i | ||||
\(971\) | 1475.71i | 1.51978i | 0.650051 | + | 0.759890i | \(0.274747\pi\) | ||||
−0.650051 | + | 0.759890i | \(0.725253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 336.000 | 0.345324 | ||||||||
\(974\) | −180.000 | − | 103.923i | −0.184805 | − | 0.106697i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −208.000 | + | 360.267i | −0.213115 | + | 0.369126i | ||||
\(977\) | −346.000 | −0.354145 | −0.177073 | − | 0.984198i | \(-0.556663\pi\) | ||||
−0.177073 | + | 0.984198i | \(0.556663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 568.113i | − | 0.580299i | ||||||
\(980\) | −4.00000 | − | 6.92820i | −0.00408163 | − | 0.00706960i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1596.00 | − | 921.451i | −1.62525 | − | 0.938341i | ||||
\(983\) | 734.390i | 0.747090i | 0.927612 | + | 0.373545i | \(0.121858\pi\) | ||||
−0.927612 | + | 0.373545i | \(0.878142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.0000 | 0.0527919 | ||||||||
\(986\) | −260.000 | + | 450.333i | −0.263692 | + | 0.456727i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −144.000 | + | 83.1384i | −0.145749 | + | 0.0841482i | ||||
\(989\) | 1344.00 | 1.35895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 976.877i | − | 0.985748i | −0.870101 | − | 0.492874i | \(-0.835946\pi\) | ||
0.870101 | − | 0.492874i | \(-0.164054\pi\) | |||||||
\(992\) | 192.000 | − | 110.851i | 0.193548 | − | 0.111745i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 789.815i | − | 0.793784i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 458.000 | 0.459378 | 0.229689 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229689 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(998\) | 132.000 | + | 76.2102i | 0.132265 | + | 0.0763630i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))