Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,2,Mod(25,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.e (of order \(3\), 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: | \(1.00611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.25 |
Dual form | 126.2.e.a.121.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | −4.50000 | − | 2.59808i | −1.16190 | − | 0.670820i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | 4.50000 | − | 7.79423i | 0.938315 | − | 1.62521i | 0.169701 | − | 0.985496i | \(-0.445720\pi\) |
0.768613 | − | 0.639713i | \(-0.220947\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 4.50000 | + | 2.59808i | 0.821584 | + | 0.474342i | ||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | 1.50000 | − | 2.59808i | 0.257248 | − | 0.445566i | ||||
\(35\) | 7.50000 | − | 2.59808i | 1.26773 | − | 0.439155i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | −3.50000 | − | 6.06218i | −0.567775 | − | 0.983415i | ||||
\(39\) | −1.50000 | + | 0.866025i | −0.240192 | + | 0.138675i | ||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | −3.00000 | + | 3.46410i | −0.462910 | + | 0.534522i | ||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 4.50000 | − | 7.79423i | 0.670820 | − | 1.16190i | ||||
\(46\) | −4.50000 | + | 7.79423i | −0.663489 | + | 1.14920i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | −4.50000 | − | 2.59808i | −0.630126 | − | 0.363803i | ||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | −9.00000 | −1.21356 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | −10.5000 | + | 6.06218i | −1.39076 | + | 0.802955i | ||||
\(58\) | 1.50000 | − | 2.59808i | 0.196960 | − | 0.341144i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −4.50000 | − | 2.59808i | −0.580948 | − | 0.335410i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 4.50000 | − | 2.59808i | 0.553912 | − | 0.319801i | ||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | 13.5000 | + | 7.79423i | 1.62521 | + | 0.938315i | ||||
\(70\) | −7.50000 | + | 2.59808i | −0.896421 | + | 0.310530i | ||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −5.50000 | + | 9.52628i | −0.643726 | + | 1.11497i | 0.340868 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174855i | \(0.944054\pi\) | |||||||
\(74\) | −0.500000 | − | 0.866025i | −0.0581238 | − | 0.100673i | ||||
\(75\) | 6.00000 | − | 3.46410i | 0.692820 | − | 0.400000i | ||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | 1.50000 | − | 0.866025i | 0.169842 | − | 0.0980581i | ||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | −1.50000 | + | 2.59808i | −0.167705 | + | 0.290474i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | 3.00000 | − | 3.46410i | 0.327327 | − | 0.377964i | ||||
\(85\) | −4.50000 | − | 7.79423i | −0.488094 | − | 0.845403i | ||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | −4.50000 | − | 2.59808i | −0.482451 | − | 0.278543i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | −4.50000 | + | 7.79423i | −0.474342 | + | 0.821584i | ||||
\(91\) | 0.500000 | − | 2.59808i | 0.0524142 | − | 0.272352i | ||||
\(92\) | 4.50000 | − | 7.79423i | 0.469157 | − | 0.812605i | ||||
\(93\) | 13.8564i | 1.43684i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.0000 | −2.15455 | ||||||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 0.500000 | − | 0.866025i | 0.0507673 | − | 0.0879316i | −0.839525 | − | 0.543321i | \(-0.817167\pi\) |
0.890292 | + | 0.455389i | \(0.150500\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −4.50000 | − | 7.79423i | −0.452267 | − | 0.783349i | ||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 4.50000 | + | 2.59808i | 0.445566 | + | 0.257248i | ||||
\(103\) | 6.50000 | − | 11.2583i | 0.640464 | − | 1.10932i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | −0.500000 | − | 0.866025i | −0.0490290 | − | 0.0849208i | ||||
\(105\) | 4.50000 | + | 12.9904i | 0.439155 | + | 1.26773i | ||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −4.50000 | − | 7.79423i | −0.435031 | − | 0.753497i | 0.562267 | − | 0.826956i | \(-0.309929\pi\) |
−0.997298 | + | 0.0734594i | \(0.976596\pi\) | |||||||
\(108\) | − | 5.19615i | − | 0.500000i | ||||||
\(109\) | 6.50000 | − | 11.2583i | 0.622587 | − | 1.07835i | −0.366415 | − | 0.930451i | \(-0.619415\pi\) |
0.989002 | − | 0.147901i | \(-0.0472517\pi\) | |||||||
\(110\) | 9.00000 | 0.858116 | ||||||||
\(111\) | −1.50000 | + | 0.866025i | −0.142374 | + | 0.0821995i | ||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 10.5000 | − | 6.06218i | 0.983415 | − | 0.567775i | ||||
\(115\) | 13.5000 | + | 23.3827i | 1.25888 | + | 2.18045i | ||||
\(116\) | −1.50000 | + | 2.59808i | −0.139272 | + | 0.241225i | ||||
\(117\) | −1.50000 | − | 2.59808i | −0.138675 | − | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.50000 | − | 2.59808i | 0.687524 | − | 0.238165i | ||||
\(120\) | 4.50000 | + | 2.59808i | 0.410792 | + | 0.237171i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 4.50000 | − | 2.59808i | 0.405751 | − | 0.234261i | ||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | −6.00000 | − | 5.19615i | −0.534522 | − | 0.462910i | ||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | 3.00000 | 0.263117 | ||||||||
\(131\) | −7.50000 | + | 12.9904i | −0.655278 | + | 1.13497i | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | −4.50000 | + | 2.59808i | −0.391675 | + | 0.226134i | ||||
\(133\) | 3.50000 | − | 18.1865i | 0.303488 | − | 1.57697i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 13.5000 | + | 7.79423i | 1.16190 | + | 0.670820i | ||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | −13.5000 | − | 7.79423i | −1.14920 | − | 0.663489i | ||||
\(139\) | 3.50000 | + | 6.06218i | 0.296866 | + | 0.514187i | 0.975417 | − | 0.220366i | \(-0.0707252\pi\) |
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 7.50000 | − | 2.59808i | 0.633866 | − | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | −1.50000 | + | 2.59808i | −0.125436 | + | 0.217262i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −4.50000 | − | 7.79423i | −0.373705 | − | 0.647275i | ||||
\(146\) | 5.50000 | − | 9.52628i | 0.455183 | − | 0.788400i | ||||
\(147\) | −12.0000 | + | 1.73205i | −0.989743 | + | 0.142857i | ||||
\(148\) | 0.500000 | + | 0.866025i | 0.0410997 | + | 0.0711868i | ||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | −6.00000 | + | 3.46410i | −0.489898 | + | 0.282843i | ||||
\(151\) | 3.50000 | + | 6.06218i | 0.284826 | + | 0.493333i | 0.972567 | − | 0.232623i | \(-0.0747309\pi\) |
−0.687741 | + | 0.725956i | \(0.741398\pi\) | |||||||
\(152\) | −3.50000 | − | 6.06218i | −0.283887 | − | 0.491708i | ||||
\(153\) | 4.50000 | − | 7.79423i | 0.363803 | − | 0.630126i | ||||
\(154\) | −1.50000 | + | 7.79423i | −0.120873 | + | 0.628077i | ||||
\(155\) | −12.0000 | + | 20.7846i | −0.963863 | + | 1.66946i | ||||
\(156\) | −1.50000 | + | 0.866025i | −0.120096 | + | 0.0693375i | ||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 16.0000 | 1.27289 | ||||||||
\(159\) | −4.50000 | − | 2.59808i | −0.356873 | − | 0.206041i | ||||
\(160\) | 1.50000 | − | 2.59808i | 0.118585 | − | 0.205396i | ||||
\(161\) | −22.5000 | + | 7.79423i | −1.77325 | + | 0.614271i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | 9.50000 | + | 16.4545i | 0.744097 | + | 1.28881i | 0.950615 | + | 0.310372i | \(0.100454\pi\) |
−0.206518 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | − | 15.5885i | − | 1.21356i | ||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | 7.50000 | + | 12.9904i | 0.580367 | + | 1.00523i | 0.995436 | + | 0.0954356i | \(0.0304244\pi\) |
−0.415068 | + | 0.909790i | \(0.636242\pi\) | |||||||
\(168\) | −3.00000 | + | 3.46410i | −0.231455 | + | 0.267261i | ||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 4.50000 | + | 7.79423i | 0.345134 | + | 0.597790i | ||||
\(171\) | −10.5000 | − | 18.1865i | −0.802955 | − | 1.39076i | ||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 4.50000 | + | 2.59808i | 0.341144 | + | 0.196960i | ||||
\(175\) | −2.00000 | + | 10.3923i | −0.151186 | + | 0.785584i | ||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.50000 | + | 2.59808i | 0.112430 | + | 0.194734i | ||||
\(179\) | 10.5000 | − | 18.1865i | 0.784807 | − | 1.35933i | −0.144308 | − | 0.989533i | \(-0.546095\pi\) |
0.929114 | − | 0.369792i | \(-0.120571\pi\) | |||||||
\(180\) | 4.50000 | − | 7.79423i | 0.335410 | − | 0.580948i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −0.500000 | + | 2.59808i | −0.0370625 | + | 0.192582i | ||||
\(183\) | 3.46410i | 0.256074i | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | − | 13.8564i | − | 1.01600i | ||||||
\(187\) | −9.00000 | −0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 21.0000 | 1.52350 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 1.73205i | 0.125000i | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −0.500000 | + | 0.866025i | −0.0358979 | + | 0.0621770i | ||||
\(195\) | − | 5.19615i | − | 0.372104i | ||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 4.50000 | + | 7.79423i | 0.319801 | + | 0.553912i | ||||
\(199\) | 12.5000 | − | 21.6506i | 0.886102 | − | 1.53477i | 0.0416556 | − | 0.999132i | \(-0.486737\pi\) |
0.844446 | − | 0.535641i | \(-0.179930\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 1.50000 | + | 2.59808i | 0.105540 | + | 0.182800i | ||||
\(203\) | 7.50000 | − | 2.59808i | 0.526397 | − | 0.182349i | ||||
\(204\) | −4.50000 | − | 2.59808i | −0.315063 | − | 0.181902i | ||||
\(205\) | 9.00000 | 0.628587 | ||||||||
\(206\) | −6.50000 | + | 11.2583i | −0.452876 | + | 0.784405i | ||||
\(207\) | −13.5000 | + | 23.3827i | −0.938315 | + | 1.62521i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −10.5000 | + | 18.1865i | −0.726300 | + | 1.25799i | ||||
\(210\) | −4.50000 | − | 12.9904i | −0.310530 | − | 0.896421i | ||||
\(211\) | −2.50000 | − | 4.33013i | −0.172107 | − | 0.298098i | 0.767049 | − | 0.641588i | \(-0.221724\pi\) |
−0.939156 | + | 0.343490i | \(0.888391\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 20.7846i | 1.42414i | ||||||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 1.50000 | + | 2.59808i | 0.102299 | + | 0.177187i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −16.0000 | − | 13.8564i | −1.08615 | − | 0.940634i | ||||
\(218\) | −6.50000 | + | 11.2583i | −0.440236 | + | 0.762510i | ||||
\(219\) | −16.5000 | − | 9.52628i | −1.11497 | − | 0.643726i | ||||
\(220\) | −9.00000 | −0.606780 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 1.50000 | − | 0.866025i | 0.100673 | − | 0.0581238i | ||||
\(223\) | 0.500000 | − | 0.866025i | 0.0334825 | − | 0.0579934i | −0.848799 | − | 0.528716i | \(-0.822674\pi\) |
0.882281 | + | 0.470723i | \(0.156007\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 6.00000 | + | 10.3923i | 0.400000 | + | 0.692820i | ||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | −10.5000 | + | 6.06218i | −0.695379 | + | 0.401478i | ||||
\(229\) | 6.50000 | − | 11.2583i | 0.429532 | − | 0.743971i | −0.567300 | − | 0.823511i | \(-0.692012\pi\) |
0.996832 | + | 0.0795401i | \(0.0253452\pi\) | |||||||
\(230\) | −13.5000 | − | 23.3827i | −0.890164 | − | 1.54181i | ||||
\(231\) | 13.5000 | + | 2.59808i | 0.888235 | + | 0.170941i | ||||
\(232\) | 1.50000 | − | 2.59808i | 0.0984798 | − | 0.170572i | ||||
\(233\) | −1.50000 | − | 2.59808i | −0.0982683 | − | 0.170206i | 0.812700 | − | 0.582683i | \(-0.197997\pi\) |
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(234\) | 1.50000 | + | 2.59808i | 0.0980581 | + | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 27.7128i | − | 1.80014i | ||||||
\(238\) | −7.50000 | + | 2.59808i | −0.486153 | + | 0.168408i | ||||
\(239\) | 1.50000 | + | 2.59808i | 0.0970269 | + | 0.168056i | 0.910453 | − | 0.413613i | \(-0.135733\pi\) |
−0.813426 | + | 0.581669i | \(0.802400\pi\) | |||||||
\(240\) | −4.50000 | − | 2.59808i | −0.290474 | − | 0.167705i | ||||
\(241\) | 6.50000 | + | 11.2583i | 0.418702 | + | 0.725213i | 0.995809 | − | 0.0914555i | \(-0.0291519\pi\) |
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −19.5000 | − | 7.79423i | −1.24581 | − | 0.497955i | ||||
\(246\) | −4.50000 | + | 2.59808i | −0.286910 | + | 0.165647i | ||||
\(247\) | −3.50000 | + | 6.06218i | −0.222700 | + | 0.385727i | ||||
\(248\) | −8.00000 | −0.508001 | ||||||||
\(249\) | 13.5000 | + | 7.79423i | 0.855528 | + | 0.493939i | ||||
\(250\) | 3.00000 | 0.189737 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 6.00000 | + | 5.19615i | 0.377964 | + | 0.327327i | ||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | 13.5000 | − | 7.79423i | 0.845403 | − | 0.488094i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.5000 | − | 18.1865i | 0.654972 | − | 1.13444i | −0.326929 | − | 0.945049i | \(-0.606014\pi\) |
0.981901 | − | 0.189396i | \(-0.0606529\pi\) | |||||||
\(258\) | −1.50000 | − | 0.866025i | −0.0933859 | − | 0.0539164i | ||||
\(259\) | 0.500000 | − | 2.59808i | 0.0310685 | − | 0.161437i | ||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | 7.50000 | − | 12.9904i | 0.463352 | − | 0.802548i | ||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | 4.50000 | − | 2.59808i | 0.276956 | − | 0.159901i | ||||
\(265\) | −4.50000 | − | 7.79423i | −0.276433 | − | 0.478796i | ||||
\(266\) | −3.50000 | + | 18.1865i | −0.214599 | + | 1.11509i | ||||
\(267\) | 4.50000 | − | 2.59808i | 0.275396 | − | 0.159000i | ||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | −7.50000 | + | 12.9904i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486418i | \(-0.984511\pi\) |
0.541533 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(270\) | −13.5000 | − | 7.79423i | −0.821584 | − | 0.474342i | ||||
\(271\) | −2.50000 | − | 4.33013i | −0.151864 | − | 0.263036i | 0.780049 | − | 0.625719i | \(-0.215194\pi\) |
−0.931913 | + | 0.362682i | \(0.881861\pi\) | |||||||
\(272\) | −1.50000 | + | 2.59808i | −0.0909509 | + | 0.157532i | ||||
\(273\) | 4.50000 | + | 0.866025i | 0.272352 | + | 0.0524142i | ||||
\(274\) | −4.50000 | − | 7.79423i | −0.271855 | − | 0.470867i | ||||
\(275\) | 6.00000 | − | 10.3923i | 0.361814 | − | 0.626680i | ||||
\(276\) | 13.5000 | + | 7.79423i | 0.812605 | + | 0.469157i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | −3.50000 | − | 6.06218i | −0.209916 | − | 0.363585i | ||||
\(279\) | −24.0000 | −1.43684 | ||||||||
\(280\) | −7.50000 | + | 2.59808i | −0.448211 | + | 0.155265i | ||||
\(281\) | 10.5000 | − | 18.1865i | 0.626377 | − | 1.08492i | −0.361895 | − | 0.932219i | \(-0.617870\pi\) |
0.988273 | − | 0.152699i | \(-0.0487965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | − | 36.3731i | − | 2.15455i | ||||||
\(286\) | 1.50000 | − | 2.59808i | 0.0886969 | − | 0.153627i | ||||
\(287\) | −1.50000 | + | 7.79423i | −0.0885422 | + | 0.460079i | ||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 4.50000 | + | 7.79423i | 0.264249 | + | 0.457693i | ||||
\(291\) | 1.50000 | + | 0.866025i | 0.0879316 | + | 0.0507673i | ||||
\(292\) | −5.50000 | + | 9.52628i | −0.321863 | + | 0.557483i | ||||
\(293\) | 4.50000 | + | 7.79423i | 0.262893 | + | 0.455344i | 0.967009 | − | 0.254741i | \(-0.0819901\pi\) |
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(294\) | 12.0000 | − | 1.73205i | 0.699854 | − | 0.101015i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.500000 | − | 0.866025i | −0.0290619 | − | 0.0503367i | ||||
\(297\) | 13.5000 | − | 7.79423i | 0.783349 | − | 0.452267i | ||||
\(298\) | −4.50000 | + | 7.79423i | −0.260678 | + | 0.451508i | ||||
\(299\) | 9.00000 | 0.520483 | ||||||||
\(300\) | 6.00000 | − | 3.46410i | 0.346410 | − | 0.200000i | ||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | −3.50000 | − | 6.06218i | −0.201402 | − | 0.348839i | ||||
\(303\) | 4.50000 | − | 2.59808i | 0.258518 | − | 0.149256i | ||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | −3.00000 | + | 5.19615i | −0.171780 | + | 0.297531i | ||||
\(306\) | −4.50000 | + | 7.79423i | −0.257248 | + | 0.445566i | ||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 1.50000 | − | 7.79423i | 0.0854704 | − | 0.444117i | ||||
\(309\) | 19.5000 | + | 11.2583i | 1.10932 | + | 0.640464i | ||||
\(310\) | 12.0000 | − | 20.7846i | 0.681554 | − | 1.18049i | ||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 1.50000 | − | 0.866025i | 0.0849208 | − | 0.0490290i | ||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | −22.5000 | + | 7.79423i | −1.26773 | + | 0.439155i | ||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 4.50000 | + | 2.59808i | 0.252347 | + | 0.145693i | ||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | 13.5000 | − | 7.79423i | 0.753497 | − | 0.435031i | ||||
\(322\) | 22.5000 | − | 7.79423i | 1.25388 | − | 0.434355i | ||||
\(323\) | −21.0000 | −1.16847 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 2.00000 | − | 3.46410i | 0.110940 | − | 0.192154i | ||||
\(326\) | −9.50000 | − | 16.4545i | −0.526156 | − | 0.911330i | ||||
\(327\) | 19.5000 | + | 11.2583i | 1.07835 | + | 0.622587i | ||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 15.5885i | 0.858116i | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | −1.50000 | − | 2.59808i | −0.0821995 | − | 0.142374i | ||||
\(334\) | −7.50000 | − | 12.9904i | −0.410382 | − | 0.710802i | ||||
\(335\) | 6.00000 | − | 10.3923i | 0.327815 | − | 0.567792i | ||||
\(336\) | 3.00000 | − | 3.46410i | 0.163663 | − | 0.188982i | ||||
\(337\) | 6.50000 | + | 11.2583i | 0.354078 | + | 0.613280i | 0.986960 | − | 0.160968i | \(-0.0514616\pi\) |
−0.632882 | + | 0.774248i | \(0.718128\pi\) | |||||||
\(338\) | −6.00000 | + | 10.3923i | −0.326357 | + | 0.565267i | ||||
\(339\) | −13.5000 | + | 7.79423i | −0.733219 | + | 0.423324i | ||||
\(340\) | −4.50000 | − | 7.79423i | −0.244047 | − | 0.422701i | ||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 10.5000 | + | 18.1865i | 0.567775 | + | 0.983415i | ||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −0.500000 | + | 0.866025i | −0.0269582 | + | 0.0466930i | ||||
\(345\) | −40.5000 | + | 23.3827i | −2.18045 | + | 1.25888i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | −4.50000 | − | 2.59808i | −0.241225 | − | 0.139272i | ||||
\(349\) | −11.5000 | + | 19.9186i | −0.615581 | + | 1.06622i | 0.374701 | + | 0.927146i | \(0.377745\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 2.00000 | − | 10.3923i | 0.106904 | − | 0.555492i | ||||
\(351\) | 4.50000 | − | 2.59808i | 0.240192 | − | 0.138675i | ||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | −1.50000 | − | 2.59808i | −0.0798369 | − | 0.138282i | 0.823343 | − | 0.567545i | \(-0.192107\pi\) |
−0.903179 | + | 0.429263i | \(0.858773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | + | 31.1769i | −0.955341 | + | 1.65470i | ||||
\(356\) | −1.50000 | − | 2.59808i | −0.0794998 | − | 0.137698i | ||||
\(357\) | 4.50000 | + | 12.9904i | 0.238165 | + | 0.687524i | ||||
\(358\) | −10.5000 | + | 18.1865i | −0.554942 | + | 0.961188i | ||||
\(359\) | −4.50000 | − | 7.79423i | −0.237501 | − | 0.411364i | 0.722496 | − | 0.691375i | \(-0.242995\pi\) |
−0.959997 | + | 0.280012i | \(0.909662\pi\) | |||||||
\(360\) | −4.50000 | + | 7.79423i | −0.237171 | + | 0.410792i | ||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | −2.00000 | −0.105118 | ||||||||
\(363\) | 3.00000 | + | 1.73205i | 0.157459 | + | 0.0909091i | ||||
\(364\) | 0.500000 | − | 2.59808i | 0.0262071 | − | 0.136176i | ||||
\(365\) | −16.5000 | − | 28.5788i | −0.863649 | − | 1.49588i | ||||
\(366\) | − | 3.46410i | − | 0.181071i | ||||||
\(367\) | −8.50000 | − | 14.7224i | −0.443696 | − | 0.768505i | 0.554264 | − | 0.832341i | \(-0.313000\pi\) |
−0.997960 | + | 0.0638362i | \(0.979666\pi\) | |||||||
\(368\) | 4.50000 | − | 7.79423i | 0.234579 | − | 0.406302i | ||||
\(369\) | 4.50000 | + | 7.79423i | 0.234261 | + | 0.405751i | ||||
\(370\) | 3.00000 | 0.155963 | ||||||||
\(371\) | 7.50000 | − | 2.59808i | 0.389381 | − | 0.134885i | ||||
\(372\) | 13.8564i | 0.718421i | ||||||||
\(373\) | 6.50000 | − | 11.2583i | 0.336557 | − | 0.582934i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
0.983783 | + | 0.179364i | \(0.0574041\pi\) | |||||||
\(374\) | 9.00000 | 0.465379 | ||||||||
\(375\) | − | 5.19615i | − | 0.268328i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 9.00000 | − | 10.3923i | 0.462910 | − | 0.534522i | ||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | −21.0000 | −1.07728 | ||||||||
\(381\) | − | 6.92820i | − | 0.354943i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.50000 | + | 12.9904i | −0.383232 | + | 0.663777i | −0.991522 | − | 0.129937i | \(-0.958522\pi\) |
0.608290 | + | 0.793715i | \(0.291856\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 18.0000 | + | 15.5885i | 0.917365 | + | 0.794461i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | 0.500000 | − | 0.866025i | 0.0253837 | − | 0.0439658i | ||||
\(389\) | −13.5000 | − | 23.3827i | −0.684477 | − | 1.18555i | −0.973601 | − | 0.228257i | \(-0.926697\pi\) |
0.289124 | − | 0.957292i | \(-0.406636\pi\) | |||||||
\(390\) | 5.19615i | 0.263117i | ||||||||
\(391\) | 13.5000 | + | 23.3827i | 0.682724 | + | 1.18251i | ||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | −22.5000 | − | 12.9904i | −1.13497 | − | 0.655278i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 24.0000 | − | 41.5692i | 1.20757 | − | 2.09157i | ||||
\(396\) | −4.50000 | − | 7.79423i | −0.226134 | − | 0.391675i | ||||
\(397\) | 6.50000 | + | 11.2583i | 0.326226 | + | 0.565039i | 0.981760 | − | 0.190126i | \(-0.0608897\pi\) |
−0.655534 | + | 0.755166i | \(0.727556\pi\) | |||||||
\(398\) | −12.5000 | + | 21.6506i | −0.626568 | + | 1.08525i | ||||
\(399\) | 31.5000 | + | 6.06218i | 1.57697 | + | 0.303488i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 6.92820i | 0.345547i | ||||||||
\(403\) | 4.00000 | + | 6.92820i | 0.199254 | + | 0.345118i | ||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | −13.5000 | + | 23.3827i | −0.670820 | + | 1.16190i | ||||
\(406\) | −7.50000 | + | 2.59808i | −0.372219 | + | 0.128940i | ||||
\(407\) | −1.50000 | + | 2.59808i | −0.0743522 | + | 0.128782i | ||||
\(408\) | 4.50000 | + | 2.59808i | 0.222783 | + | 0.128624i | ||||
\(409\) | −34.0000 | −1.68119 | −0.840596 | − | 0.541663i | \(-0.817795\pi\) | ||||
−0.840596 | + | 0.541663i | \(0.817795\pi\) | |||||||
\(410\) | −9.00000 | −0.444478 | ||||||||
\(411\) | −13.5000 | + | 7.79423i | −0.665906 | + | 0.384461i | ||||
\(412\) | 6.50000 | − | 11.2583i | 0.320232 | − | 0.554658i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.5000 | − | 23.3827i | 0.663489 | − | 1.14920i | ||||
\(415\) | 13.5000 | + | 23.3827i | 0.662689 | + | 1.14781i | ||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | −10.5000 | + | 6.06218i | −0.514187 | + | 0.296866i | ||||
\(418\) | 10.5000 | − | 18.1865i | 0.513572 | − | 0.889532i | ||||
\(419\) | −4.50000 | − | 7.79423i | −0.219839 | − | 0.380773i | 0.734919 | − | 0.678155i | \(-0.237220\pi\) |
−0.954759 | + | 0.297382i | \(0.903887\pi\) | |||||||
\(420\) | 4.50000 | + | 12.9904i | 0.219578 | + | 0.633866i | ||||
\(421\) | −17.5000 | + | 30.3109i | −0.852898 | + | 1.47726i | 0.0256838 | + | 0.999670i | \(0.491824\pi\) |
−0.878582 | + | 0.477592i | \(0.841510\pi\) | |||||||
\(422\) | 2.50000 | + | 4.33013i | 0.121698 | + | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | − | 20.7846i | − | 1.00702i | ||||||
\(427\) | −4.00000 | − | 3.46410i | −0.193574 | − | 0.167640i | ||||
\(428\) | −4.50000 | − | 7.79423i | −0.217516 | − | 0.376748i | ||||
\(429\) | −4.50000 | − | 2.59808i | −0.217262 | − | 0.125436i | ||||
\(430\) | −1.50000 | − | 2.59808i | −0.0723364 | − | 0.125290i | ||||
\(431\) | −13.5000 | + | 23.3827i | −0.650272 | + | 1.12630i | 0.332785 | + | 0.943003i | \(0.392012\pi\) |
−0.983057 | + | 0.183301i | \(0.941322\pi\) | |||||||
\(432\) | − | 5.19615i | − | 0.250000i | ||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 16.0000 | + | 13.8564i | 0.768025 | + | 0.665129i | ||||
\(435\) | 13.5000 | − | 7.79423i | 0.647275 | − | 0.373705i | ||||
\(436\) | 6.50000 | − | 11.2583i | 0.311294 | − | 0.539176i | ||||
\(437\) | 63.0000 | 3.01370 | ||||||||
\(438\) | 16.5000 | + | 9.52628i | 0.788400 | + | 0.455183i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 3.00000 | 0.142695 | ||||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | −1.50000 | + | 0.866025i | −0.0711868 | + | 0.0410997i | ||||
\(445\) | 9.00000 | 0.426641 | ||||||||
\(446\) | −0.500000 | + | 0.866025i | −0.0236757 | + | 0.0410075i | ||||
\(447\) | 13.5000 | + | 7.79423i | 0.638528 | + | 0.368654i | ||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | −6.00000 | − | 10.3923i | −0.282843 | − | 0.489898i | ||||
\(451\) | 4.50000 | − | 7.79423i | 0.211897 | − | 0.367016i | ||||
\(452\) | 4.50000 | + | 7.79423i | 0.211662 | + | 0.366610i | ||||
\(453\) | −10.5000 | + | 6.06218i | −0.493333 | + | 0.284826i | ||||
\(454\) | −1.50000 | − | 2.59808i | −0.0703985 | − | 0.121934i | ||||
\(455\) | 6.00000 | + | 5.19615i | 0.281284 | + | 0.243599i | ||||
\(456\) | 10.5000 | − | 6.06218i | 0.491708 | − | 0.283887i | ||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | −6.50000 | + | 11.2583i | −0.303725 | + | 0.526067i | ||||
\(459\) | 13.5000 | + | 7.79423i | 0.630126 | + | 0.363803i | ||||
\(460\) | 13.5000 | + | 23.3827i | 0.629441 | + | 1.09022i | ||||
\(461\) | 4.50000 | − | 7.79423i | 0.209586 | − | 0.363013i | −0.741998 | − | 0.670402i | \(-0.766122\pi\) |
0.951584 | + | 0.307388i | \(0.0994551\pi\) | |||||||
\(462\) | −13.5000 | − | 2.59808i | −0.628077 | − | 0.120873i | ||||
\(463\) | −20.5000 | − | 35.5070i | −0.952716 | − | 1.65015i | −0.739511 | − | 0.673145i | \(-0.764943\pi\) |
−0.213205 | − | 0.977007i | \(-0.568390\pi\) | |||||||
\(464\) | −1.50000 | + | 2.59808i | −0.0696358 | + | 0.120613i | ||||
\(465\) | −36.0000 | − | 20.7846i | −1.66946 | − | 0.963863i | ||||
\(466\) | 1.50000 | + | 2.59808i | 0.0694862 | + | 0.120354i | ||||
\(467\) | 1.50000 | + | 2.59808i | 0.0694117 | + | 0.120225i | 0.898642 | − | 0.438682i | \(-0.144554\pi\) |
−0.829231 | + | 0.558906i | \(0.811221\pi\) | |||||||
\(468\) | −1.50000 | − | 2.59808i | −0.0693375 | − | 0.120096i | ||||
\(469\) | 8.00000 | + | 6.92820i | 0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 38.1051i | − | 1.75579i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | 0.137940 | ||||||||
\(474\) | 27.7128i | 1.27289i | ||||||||
\(475\) | 14.0000 | − | 24.2487i | 0.642364 | − | 1.11261i | ||||
\(476\) | 7.50000 | − | 2.59808i | 0.343762 | − | 0.119083i | ||||
\(477\) | 4.50000 | − | 7.79423i | 0.206041 | − | 0.356873i | ||||
\(478\) | −1.50000 | − | 2.59808i | −0.0686084 | − | 0.118833i | ||||
\(479\) | 1.50000 | + | 2.59808i | 0.0685367 | + | 0.118709i | 0.898257 | − | 0.439470i | \(-0.144834\pi\) |
−0.829721 | + | 0.558179i | \(0.811500\pi\) | |||||||
\(480\) | 4.50000 | + | 2.59808i | 0.205396 | + | 0.118585i | ||||
\(481\) | −0.500000 | + | 0.866025i | −0.0227980 | + | 0.0394874i | ||||
\(482\) | −6.50000 | − | 11.2583i | −0.296067 | − | 0.512803i | ||||
\(483\) | −13.5000 | − | 38.9711i | −0.614271 | − | 1.77325i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 1.50000 | + | 2.59808i | 0.0681115 | + | 0.117973i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 12.5000 | − | 21.6506i | 0.566429 | − | 0.981084i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.996915 | − | 0.0784867i | \(-0.0250088\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | −28.5000 | + | 16.4545i | −1.28881 | + | 0.744097i | ||||
\(490\) | 19.5000 | + | 7.79423i | 0.880920 | + | 0.352107i | ||||
\(491\) | −10.5000 | − | 18.1865i | −0.473858 | − | 0.820747i | 0.525694 | − | 0.850674i | \(-0.323806\pi\) |
−0.999552 | + | 0.0299272i | \(0.990472\pi\) | |||||||
\(492\) | 4.50000 | − | 2.59808i | 0.202876 | − | 0.117130i | ||||
\(493\) | −4.50000 | − | 7.79423i | −0.202670 | − | 0.351034i | ||||
\(494\) | 3.50000 | − | 6.06218i | 0.157472 | − | 0.272750i | ||||
\(495\) | 27.0000 | 1.21356 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −24.0000 | − | 20.7846i | −1.07655 | − | 0.932317i | ||||
\(498\) | −13.5000 | − | 7.79423i | −0.604949 | − | 0.349268i | ||||
\(499\) | 12.5000 | − | 21.6506i | 0.559577 | − | 0.969216i | −0.437955 | − | 0.898997i | \(-0.644297\pi\) |
0.997532 | − | 0.0702185i | \(-0.0223697\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | −22.5000 | + | 12.9904i | −1.00523 | + | 0.580367i | ||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −6.00000 | − | 5.19615i | −0.267261 | − | 0.231455i | ||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | −27.0000 | −1.20030 | ||||||||
\(507\) | 18.0000 | + | 10.3923i | 0.799408 | + | 0.461538i | ||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | −13.5000 | + | 7.79423i | −0.597790 | + | 0.345134i | ||||
\(511\) | 27.5000 | − | 9.52628i | 1.21653 | − | 0.421418i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 31.5000 | − | 18.1865i | 1.39076 | − | 0.802955i | ||||
\(514\) | −10.5000 | + | 18.1865i | −0.463135 | + | 0.802174i | ||||
\(515\) | 19.5000 | + | 33.7750i | 0.859273 | + | 1.48830i | ||||
\(516\) | 1.50000 | + | 0.866025i | 0.0660338 | + | 0.0381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.500000 | + | 2.59808i | −0.0219687 | + | 0.114153i | ||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | 3.00000 | 0.131559 | ||||||||
\(521\) | −1.50000 | + | 2.59808i | −0.0657162 | + | 0.113824i | −0.897011 | − | 0.442007i | \(-0.854267\pi\) |
0.831295 | + | 0.555831i | \(0.187600\pi\) | |||||||
\(522\) | −4.50000 | + | 7.79423i | −0.196960 | + | 0.341144i | ||||
\(523\) | 3.50000 | + | 6.06218i | 0.153044 | + | 0.265081i | 0.932345 | − | 0.361569i | \(-0.117759\pi\) |
−0.779301 | + | 0.626650i | \(0.784426\pi\) | |||||||
\(524\) | −7.50000 | + | 12.9904i | −0.327639 | + | 0.567487i | ||||
\(525\) | −18.0000 | − | 3.46410i | −0.785584 | − | 0.151186i | ||||
\(526\) | 4.50000 | + | 7.79423i | 0.196209 | + | 0.339845i | ||||
\(527\) | −12.0000 | + | 20.7846i | −0.522728 | + | 0.905392i | ||||
\(528\) | −4.50000 | + | 2.59808i | −0.195837 | + | 0.113067i | ||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.50000 | − | 18.1865i | 0.151744 | − | 0.788486i | ||||
\(533\) | 1.50000 | − | 2.59808i | 0.0649722 | − | 0.112535i | ||||
\(534\) | −4.50000 | + | 2.59808i | −0.194734 | + | 0.112430i | ||||
\(535\) | 27.0000 | 1.16731 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 31.5000 | + | 18.1865i | 1.35933 | + | 0.784807i | ||||
\(538\) | 7.50000 | − | 12.9904i | 0.323348 | − | 0.560055i | ||||
\(539\) | −16.5000 | + | 12.9904i | −0.710705 | + | 0.559535i | ||||
\(540\) | 13.5000 | + | 7.79423i | 0.580948 | + | 0.335410i | ||||
\(541\) | −5.50000 | − | 9.52628i | −0.236463 | − | 0.409567i | 0.723234 | − | 0.690604i | \(-0.242655\pi\) |
−0.959697 | + | 0.281037i | \(0.909322\pi\) | |||||||
\(542\) | 2.50000 | + | 4.33013i | 0.107384 | + | 0.185995i | ||||
\(543\) | 3.46410i | 0.148659i | ||||||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | 19.5000 | + | 33.7750i | 0.835288 | + | 1.44676i | ||||
\(546\) | −4.50000 | − | 0.866025i | −0.192582 | − | 0.0370625i | ||||
\(547\) | −5.50000 | + | 9.52628i | −0.235163 | + | 0.407314i | −0.959320 | − | 0.282321i | \(-0.908896\pi\) |
0.724157 | + | 0.689635i | \(0.242229\pi\) | |||||||
\(548\) | 4.50000 | + | 7.79423i | 0.192230 | + | 0.332953i | ||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | −6.00000 | + | 10.3923i | −0.255841 | + | 0.443129i | ||||
\(551\) | −21.0000 | −0.894630 | ||||||||
\(552\) | −13.5000 | − | 7.79423i | −0.574598 | − | 0.331744i | ||||
\(553\) | 32.0000 | + | 27.7128i | 1.36078 | + | 1.17847i | ||||
\(554\) | −0.500000 | − | 0.866025i | −0.0212430 | − | 0.0367939i | ||||
\(555\) | − | 5.19615i | − | 0.220564i | ||||||
\(556\) | 3.50000 | + | 6.06218i | 0.148433 | + | 0.257094i | ||||
\(557\) | 4.50000 | − | 7.79423i | 0.190671 | − | 0.330252i | −0.754802 | − | 0.655953i | \(-0.772267\pi\) |
0.945473 | + | 0.325701i | \(0.105600\pi\) | |||||||
\(558\) | 24.0000 | 1.01600 | ||||||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | 7.50000 | − | 2.59808i | 0.316933 | − | 0.109789i | ||||
\(561\) | − | 15.5885i | − | 0.658145i | ||||||
\(562\) | −10.5000 | + | 18.1865i | −0.442916 | + | 0.767153i | ||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | −1.13590 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | −18.0000 | − | 15.5885i | −0.755929 | − | 0.654654i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 36.3731i | 1.52350i | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | −1.50000 | + | 2.59808i | −0.0627182 | + | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.50000 | − | 7.79423i | 0.0626088 | − | 0.325325i | ||||
\(575\) | −36.0000 | −1.50130 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 12.5000 | − | 21.6506i | 0.520382 | − | 0.901328i | −0.479337 | − | 0.877631i | \(-0.659123\pi\) |
0.999719 | − | 0.0236970i | \(-0.00754370\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | −4.50000 | − | 7.79423i | −0.186852 | − | 0.323638i | ||||
\(581\) | −22.5000 | + | 7.79423i | −0.933457 | + | 0.323359i | ||||
\(582\) | −1.50000 | − | 0.866025i | −0.0621770 | − | 0.0358979i | ||||
\(583\) | −9.00000 | −0.372742 | ||||||||
\(584\) | 5.50000 | − | 9.52628i | 0.227592 | − | 0.394200i | ||||
\(585\) | 9.00000 | 0.372104 | ||||||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | −12.0000 | + | 1.73205i | −0.494872 | + | 0.0714286i | ||||
\(589\) | 28.0000 | + | 48.4974i | 1.15372 | + | 1.99830i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1769i | 1.28245i | ||||||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | −19.5000 | − | 33.7750i | −0.800769 | − | 1.38697i | −0.919111 | − | 0.394000i | \(-0.871091\pi\) |
0.118342 | − | 0.992973i | \(-0.462242\pi\) | |||||||
\(594\) | −13.5000 | + | 7.79423i | −0.553912 | + | 0.319801i | ||||
\(595\) | −4.50000 | + | 23.3827i | −0.184482 | + | 0.958597i | ||||
\(596\) | 4.50000 | − | 7.79423i | 0.184327 | − | 0.319264i | ||||
\(597\) | 37.5000 | + | 21.6506i | 1.53477 | + | 0.886102i | ||||
\(598\) | −9.00000 | −0.368037 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −6.00000 | + | 3.46410i | −0.244949 | + | 0.141421i | ||||
\(601\) | 12.5000 | − | 21.6506i | 0.509886 | − | 0.883148i | −0.490049 | − | 0.871695i | \(-0.663021\pi\) |
0.999934 | − | 0.0114528i | \(-0.00364562\pi\) | |||||||
\(602\) | 2.50000 | − | 0.866025i | 0.101892 | − | 0.0352966i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 3.50000 | + | 6.06218i | 0.142413 | + | 0.246667i | ||||
\(605\) | 3.00000 | + | 5.19615i | 0.121967 | + | 0.211254i | ||||
\(606\) | −4.50000 | + | 2.59808i | −0.182800 | + | 0.105540i | ||||
\(607\) | 6.50000 | − | 11.2583i | 0.263827 | − | 0.456962i | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | −3.50000 | − | 6.06218i | −0.141944 | − | 0.245854i | ||||
\(609\) | 4.50000 | + | 12.9904i | 0.182349 | + | 0.526397i | ||||
\(610\) | 3.00000 | − | 5.19615i | 0.121466 | − | 0.210386i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.50000 | − | 7.79423i | 0.181902 | − | 0.315063i | ||||
\(613\) | −11.5000 | + | 19.9186i | −0.464481 | + | 0.804504i | −0.999178 | − | 0.0405396i | \(-0.987092\pi\) |
0.534697 | + | 0.845044i | \(0.320426\pi\) | |||||||
\(614\) | 28.0000 | 1.12999 | ||||||||
\(615\) | 15.5885i | 0.628587i | ||||||||
\(616\) | −1.50000 | + | 7.79423i | −0.0604367 | + | 0.314038i | ||||
\(617\) | 22.5000 | + | 38.9711i | 0.905816 | + | 1.56892i | 0.819818 | + | 0.572624i | \(0.194074\pi\) |
0.0859976 | + | 0.996295i | \(0.472592\pi\) | |||||||
\(618\) | −19.5000 | − | 11.2583i | −0.784405 | − | 0.452876i | ||||
\(619\) | −8.50000 | − | 14.7224i | −0.341644 | − | 0.591744i | 0.643094 | − | 0.765787i | \(-0.277650\pi\) |
−0.984738 | + | 0.174042i | \(0.944317\pi\) | |||||||
\(620\) | −12.0000 | + | 20.7846i | −0.481932 | + | 0.834730i | ||||
\(621\) | −40.5000 | − | 23.3827i | −1.62521 | − | 0.938315i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | −1.50000 | + | 7.79423i | −0.0600962 | + | 0.312269i | ||||
\(624\) | −1.50000 | + | 0.866025i | −0.0600481 | + | 0.0346688i | ||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | −31.5000 | − | 18.1865i | −1.25799 | − | 0.726300i | ||||
\(628\) | −22.0000 | −0.877896 | ||||||||
\(629\) | −3.00000 | −0.119618 | ||||||||
\(630\) | 22.5000 | − | 7.79423i | 0.896421 | − | 0.310530i | ||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 16.0000 | 0.636446 | ||||||||
\(633\) | 7.50000 | − | 4.33013i | 0.298098 | − | 0.172107i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 6.00000 | − | 10.3923i | 0.238103 | − | 0.412406i | ||||
\(636\) | −4.50000 | − | 2.59808i | −0.178437 | − | 0.103020i | ||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | −36.0000 | −1.42414 | ||||||||
\(640\) | 1.50000 | − | 2.59808i | 0.0592927 | − | 0.102698i | ||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | −13.5000 | + | 7.79423i | −0.532803 | + | 0.307614i | ||||
\(643\) | −14.5000 | − | 25.1147i | −0.571824 | − | 0.990429i | −0.996379 | − | 0.0850262i | \(-0.972903\pi\) |
0.424555 | − | 0.905402i | \(-0.360431\pi\) | |||||||
\(644\) | −22.5000 | + | 7.79423i | −0.886624 | + | 0.307136i | ||||
\(645\) | −4.50000 | + | 2.59808i | −0.177187 | + | 0.102299i | ||||
\(646\) | 21.0000 | 0.826234 | ||||||||
\(647\) | 10.5000 | − | 18.1865i | 0.412798 | − | 0.714986i | −0.582397 | − | 0.812905i | \(-0.697885\pi\) |
0.995194 | + | 0.0979182i | \(0.0312184\pi\) | |||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.00000 | + | 3.46410i | −0.0784465 | + | 0.135873i | ||||
\(651\) | 24.0000 | − | 27.7128i | 0.940634 | − | 1.08615i | ||||
\(652\) | 9.50000 | + | 16.4545i | 0.372049 | + | 0.644407i | ||||
\(653\) | −7.50000 | + | 12.9904i | −0.293498 | + | 0.508353i | −0.974634 | − | 0.223803i | \(-0.928153\pi\) |
0.681137 | + | 0.732156i | \(0.261486\pi\) | |||||||
\(654\) | −19.5000 | − | 11.2583i | −0.762510 | − | 0.440236i | ||||
\(655\) | −22.5000 | − | 38.9711i | −0.879148 | − | 1.52273i | ||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 16.5000 | − | 28.5788i | 0.643726 | − | 1.11497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.50000 | + | 2.59808i | −0.0584317 | + | 0.101207i | −0.893762 | − | 0.448542i | \(-0.851943\pi\) |
0.835330 | + | 0.549749i | \(0.185277\pi\) | |||||||
\(660\) | − | 15.5885i | − | 0.606780i | ||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | − | 5.19615i | − | 0.201802i | ||||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | 42.0000 | + | 36.3731i | 1.62869 | + | 1.41049i | ||||
\(666\) | 1.50000 | + | 2.59808i | 0.0581238 | + | 0.100673i | ||||
\(667\) | 13.5000 | + | 23.3827i | 0.522722 | + | 0.905381i | ||||
\(668\) | 7.50000 | + | 12.9904i | 0.290184 | + | 0.502613i | ||||
\(669\) | 1.50000 | + | 0.866025i | 0.0579934 | + | 0.0334825i | ||||
\(670\) | −6.00000 | + | 10.3923i | −0.231800 | + | 0.401490i | ||||
\(671\) | 3.00000 | + | 5.19615i | 0.115814 | + | 0.200595i | ||||
\(672\) | −3.00000 | + | 3.46410i | −0.115728 | + | 0.133631i | ||||
\(673\) | −17.5000 | + | 30.3109i | −0.674575 | + | 1.16840i | 0.302017 | + | 0.953302i | \(0.402340\pi\) |
−0.976593 | + | 0.215096i | \(0.930993\pi\) | |||||||
\(674\) | −6.50000 | − | 11.2583i | −0.250371 | − | 0.433655i | ||||
\(675\) | −18.0000 | + | 10.3923i | −0.692820 | + | 0.400000i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | 13.5000 | − | 7.79423i | 0.518464 | − | 0.299336i | ||||
\(679\) | −2.50000 | + | 0.866025i | −0.0959412 | + | 0.0332350i | ||||
\(680\) | 4.50000 | + | 7.79423i | 0.172567 | + | 0.298895i | ||||
\(681\) | −4.50000 | + | 2.59808i | −0.172440 | + | 0.0995585i | ||||
\(682\) | −12.0000 | − | 20.7846i | −0.459504 | − | 0.795884i | ||||
\(683\) | 4.50000 | − | 7.79423i | 0.172188 | − | 0.298238i | −0.766997 | − | 0.641651i | \(-0.778250\pi\) |
0.939184 | + | 0.343413i | \(0.111583\pi\) | |||||||
\(684\) | −10.5000 | − | 18.1865i | −0.401478 | − | 0.695379i | ||||
\(685\) | −27.0000 | −1.03162 | ||||||||
\(686\) | −10.0000 | + | 15.5885i | −0.381802 | + | 0.595170i | ||||
\(687\) | 19.5000 | + | 11.2583i | 0.743971 | + | 0.429532i | ||||
\(688\) | 0.500000 | − | 0.866025i | 0.0190623 | − | 0.0330169i | ||||
\(689\) | −3.00000 | −0.114291 | ||||||||
\(690\) | 40.5000 | − | 23.3827i | 1.54181 | − | 0.890164i | ||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −4.50000 | + | 23.3827i | −0.170941 | + | 0.888235i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −21.0000 | −0.796575 | ||||||||
\(696\) | 4.50000 | + | 2.59808i | 0.170572 | + | 0.0984798i | ||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 11.5000 | − | 19.9186i | 0.435281 | − | 0.753930i | ||||
\(699\) | 4.50000 | − | 2.59808i | 0.170206 | − | 0.0982683i | ||||
\(700\) | −2.00000 | + | 10.3923i | −0.0755929 | + | 0.392792i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −4.50000 | + | 2.59808i | −0.169842 | + | 0.0980581i | ||||
\(703\) | −3.50000 | + | 6.06218i | −0.132005 | + | 0.228639i | ||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.50000 | + | 2.59808i | 0.0564532 | + | 0.0977799i | ||||
\(707\) | −1.50000 | + | 7.79423i | −0.0564133 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | 18.0000 | − | 31.1769i | 0.675528 | − | 1.17005i | ||||
\(711\) | 48.0000 | 1.80014 | ||||||||
\(712\) | 1.50000 | + | 2.59808i | 0.0562149 | + | 0.0973670i | ||||
\(713\) | 36.0000 | − | 62.3538i | 1.34821 | − | 2.33517i | ||||
\(714\) | −4.50000 | − | 12.9904i | −0.168408 | − | 0.486153i | ||||
\(715\) | −4.50000 | − | 7.79423i | −0.168290 | − | 0.291488i | ||||
\(716\) | 10.5000 | − | 18.1865i | 0.392403 | − | 0.679663i | ||||
\(717\) | −4.50000 | + | 2.59808i | −0.168056 | + | 0.0970269i | ||||
\(718\) | 4.50000 | + | 7.79423i | 0.167939 | + | 0.290878i | ||||
\(719\) | 7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 4.50000 | − | 7.79423i | 0.167705 | − | 0.290474i | ||||
\(721\) | −32.5000 | + | 11.2583i | −1.21036 | + | 0.419282i | ||||
\(722\) | 15.0000 | − | 25.9808i | 0.558242 | − | 0.966904i | ||||
\(723\) | −19.5000 | + | 11.2583i | −0.725213 | + | 0.418702i | ||||
\(724\) | 2.00000 | 0.0743294 | ||||||||
\(725\) | 12.0000 | 0.445669 | ||||||||
\(726\) | −3.00000 | − | 1.73205i | −0.111340 | − | 0.0642824i | ||||
\(727\) | 6.50000 | − | 11.2583i | 0.241072 | − | 0.417548i | −0.719948 | − | 0.694028i | \(-0.755834\pi\) |
0.961020 | + | 0.276479i | \(0.0891678\pi\) | |||||||
\(728\) | −0.500000 | + | 2.59808i | −0.0185312 | + | 0.0962911i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 16.5000 | + | 28.5788i | 0.610692 | + | 1.05775i | ||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 3.46410i | 0.128037i | ||||||||
\(733\) | 0.500000 | − | 0.866025i | 0.0184679 | − | 0.0319874i | −0.856644 | − | 0.515908i | \(-0.827454\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(734\) | 8.50000 | + | 14.7224i | 0.313741 | + | 0.543415i | ||||
\(735\) | 13.5000 | − | 33.7750i | 0.497955 | − | 1.24581i | ||||
\(736\) | −4.50000 | + | 7.79423i | −0.165872 | + | 0.287299i | ||||
\(737\) | −6.00000 | − | 10.3923i | −0.221013 | − | 0.382805i | ||||
\(738\) | −4.50000 | − | 7.79423i | −0.165647 | − | 0.286910i | ||||
\(739\) | −11.5000 | + | 19.9186i | −0.423034 | + | 0.732717i | −0.996235 | − | 0.0866983i | \(-0.972368\pi\) |
0.573200 | + | 0.819415i | \(0.305702\pi\) | |||||||
\(740\) | −3.00000 | −0.110282 | ||||||||
\(741\) | −10.5000 | − | 6.06218i | −0.385727 | − | 0.222700i | ||||
\(742\) | −7.50000 | + | 2.59808i | −0.275334 | + | 0.0953784i | ||||
\(743\) | −10.5000 | − | 18.1865i | −0.385208 | − | 0.667199i | 0.606590 | − | 0.795015i | \(-0.292537\pi\) |
−0.991798 | + | 0.127815i | \(0.959204\pi\) | |||||||
\(744\) | − | 13.8564i | − | 0.508001i | ||||||
\(745\) | 13.5000 | + | 23.3827i | 0.494602 | + | 0.856675i | ||||
\(746\) | −6.50000 | + | 11.2583i | −0.237982 | + | 0.412197i | ||||
\(747\) | −13.5000 | + | 23.3827i | −0.493939 | + | 0.855528i | ||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | −4.50000 | + | 23.3827i | −0.164426 | + | 0.854385i | ||||
\(750\) | 5.19615i | 0.189737i | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.7846i | 0.757433i | ||||||||
\(754\) | 3.00000 | 0.109254 | ||||||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | −9.00000 | + | 10.3923i | −0.327327 | + | 0.377964i | ||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 28.0000 | 1.01701 | ||||||||
\(759\) | 46.7654i | 1.69748i | ||||||||
\(760\) | 21.0000 | 0.761750 | ||||||||
\(761\) | 22.5000 | − | 38.9711i | 0.815624 | − | 1.41270i | −0.0932544 | − | 0.995642i | \(-0.529727\pi\) |
0.908879 | − | 0.417061i | \(-0.136940\pi\) | |||||||
\(762\) | 6.92820i | 0.250982i | ||||||||
\(763\) | −32.5000 | + | 11.2583i | −1.17658 | + | 0.407579i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.5000 | + | 23.3827i | 0.488094 | + | 0.845403i | ||||
\(766\) | 7.50000 | − | 12.9904i | 0.270986 | − | 0.469362i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.73205i | 0.0625000i | ||||||||
\(769\) | −11.5000 | − | 19.9186i | −0.414701 | − | 0.718283i | 0.580696 | − | 0.814120i | \(-0.302780\pi\) |
−0.995397 | + | 0.0958377i | \(0.969447\pi\) | |||||||
\(770\) | −18.0000 | − | 15.5885i | −0.648675 | − | 0.561769i | ||||
\(771\) | 31.5000 | + | 18.1865i | 1.13444 | + | 0.654972i | ||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | −13.5000 | + | 23.3827i | −0.485561 | + | 0.841017i | −0.999862 | − | 0.0165929i | \(-0.994718\pi\) |
0.514301 | + | 0.857610i | \(0.328051\pi\) | |||||||
\(774\) | 1.50000 | − | 2.59808i | 0.0539164 | − | 0.0933859i | ||||
\(775\) | −16.0000 | − | 27.7128i | −0.574737 | − | 0.995474i | ||||
\(776\) | −0.500000 | + | 0.866025i | −0.0179490 | + | 0.0310885i | ||||
\(777\) | 4.50000 | + | 0.866025i | 0.161437 | + | 0.0310685i | ||||
\(778\) | 13.5000 | + | 23.3827i | 0.483998 | + | 0.838310i | ||||
\(779\) | 10.5000 | − | 18.1865i | 0.376202 | − | 0.651600i | ||||
\(780\) | − | 5.19615i | − | 0.186052i | ||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | −13.5000 | − | 23.3827i | −0.482759 | − | 0.836163i | ||||
\(783\) | 13.5000 | + | 7.79423i | 0.482451 | + | 0.278543i | ||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 33.0000 | − | 57.1577i | 1.17782 | − | 2.04004i | ||||
\(786\) | 22.5000 | + | 12.9904i | 0.802548 | + | 0.463352i | ||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | 13.5000 | − | 7.79423i | 0.480613 | − | 0.277482i | ||||
\(790\) | −24.0000 | + | 41.5692i | −0.853882 | + | 1.47897i | ||||
\(791\) | 4.50000 | − | 23.3827i | 0.160002 | − | 0.831393i | ||||
\(792\) | 4.50000 | + | 7.79423i | 0.159901 | + | 0.276956i | ||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | −6.50000 | − | 11.2583i | −0.230676 | − | 0.399543i | ||||
\(795\) | 13.5000 | − | 7.79423i | 0.478796 | − | 0.276433i | ||||
\(796\) | 12.5000 | − | 21.6506i | 0.443051 | − | 0.767386i | ||||
\(797\) | 10.5000 | + | 18.1865i | 0.371929 | + | 0.644200i | 0.989862 | − | 0.142031i | \(-0.0453631\pi\) |
−0.617933 | + | 0.786231i | \(0.712030\pi\) | |||||||
\(798\) | −31.5000 | − | 6.06218i | −1.11509 | − | 0.214599i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.00000 | + | 3.46410i | 0.0707107 | + | 0.122474i | ||||
\(801\) | 4.50000 | + | 7.79423i | 0.159000 | + | 0.275396i | ||||
\(802\) | 13.5000 | − | 23.3827i | 0.476702 | − | 0.825671i | ||||
\(803\) | −33.0000 | −1.16454 | ||||||||
\(804\) | − | 6.92820i | − | 0.244339i | ||||||
\(805\) | 13.5000 | − | 70.1481i | 0.475812 | − | 2.47239i | ||||
\(806\) | −4.00000 | − | 6.92820i | −0.140894 | − | 0.244036i | ||||
\(807\) | −22.5000 | − | 12.9904i | −0.792038 | − | 0.457283i | ||||
\(808\) | 1.50000 | + | 2.59808i | 0.0527698 | + | 0.0914000i | ||||
\(809\) | 16.5000 | − | 28.5788i | 0.580109 | − | 1.00478i | −0.415357 | − | 0.909659i | \(-0.636343\pi\) |
0.995466 | − | 0.0951198i | \(-0.0303234\pi\) | |||||||
\(810\) | 13.5000 | − | 23.3827i | 0.474342 | − | 0.821584i | ||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 7.50000 | − | 2.59808i | 0.263198 | − | 0.0911746i | ||||
\(813\) | 7.50000 | − | 4.33013i | 0.263036 | − | 0.151864i | ||||
\(814\) | 1.50000 | − | 2.59808i | 0.0525750 | − | 0.0910625i | ||||
\(815\) | −57.0000 | −1.99662 | ||||||||
\(816\) | −4.50000 | − | 2.59808i | −0.157532 | − | 0.0909509i | ||||
\(817\) | 7.00000 | 0.244899 | ||||||||
\(818\) | 34.0000 | 1.18878 | ||||||||
\(819\) | −1.50000 | + | 7.79423i | −0.0524142 | + | 0.272352i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | 13.5000 | − | 7.79423i | 0.470867 | − | 0.271855i | ||||
\(823\) | −40.0000 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(824\) | −6.50000 | + | 11.2583i | −0.226438 | + | 0.392203i | ||||
\(825\) | 18.0000 | + | 10.3923i | 0.626680 | + | 0.361814i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | −13.5000 | + | 23.3827i | −0.469157 | + | 0.812605i | ||||
\(829\) | −5.50000 | + | 9.52628i | −0.191023 | + | 0.330861i | −0.945589 | − | 0.325362i | \(-0.894514\pi\) |
0.754567 | + | 0.656223i | \(0.227847\pi\) | |||||||
\(830\) | −13.5000 | − | 23.3827i | −0.468592 | − | 0.811625i | ||||
\(831\) | −1.50000 | + | 0.866025i | −0.0520344 | + | 0.0300421i | ||||
\(832\) | 0.500000 | + | 0.866025i | 0.0173344 | + | 0.0300240i | ||||
\(833\) | −19.5000 | − | 7.79423i | −0.675635 | − | 0.270054i | ||||
\(834\) | 10.5000 | − | 6.06218i | 0.363585 | − | 0.209916i | ||||
\(835\) | −45.0000 | −1.55729 | ||||||||
\(836\) | −10.5000 | + | 18.1865i | −0.363150 | + | 0.628994i | ||||
\(837\) | − | 41.5692i | − | 1.43684i | ||||||
\(838\) | 4.50000 | + | 7.79423i | 0.155450 | + | 0.269247i | ||||
\(839\) | −7.50000 | + | 12.9904i | −0.258929 | + | 0.448478i | −0.965955 | − | 0.258709i | \(-0.916703\pi\) |
0.707026 | + | 0.707187i | \(0.250036\pi\) | |||||||
\(840\) | −4.50000 | − | 12.9904i | −0.155265 | − | 0.448211i | ||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 17.5000 | − | 30.3109i | 0.603090 | − | 1.04458i | ||||
\(843\) | 31.5000 | + | 18.1865i | 1.08492 | + | 0.626377i | ||||
\(844\) | −2.50000 | − | 4.33013i | −0.0860535 | − | 0.149049i | ||||
\(845\) | 18.0000 | + | 31.1769i | 0.619219 | + | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | + | 1.73205i | −0.171802 | + | 0.0595140i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | − | 6.92820i | − | 0.237775i | ||||||
\(850\) | −12.0000 | −0.411597 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | 20.7846i | 0.712069i | ||||||||
\(853\) | 0.500000 | − | 0.866025i | 0.0171197 | − | 0.0296521i | −0.857339 | − | 0.514753i | \(-0.827884\pi\) |
0.874458 | + | 0.485101i | \(0.161217\pi\) | |||||||
\(854\) | 4.00000 | + | 3.46410i | 0.136877 | + | 0.118539i | ||||
\(855\) | 63.0000 | 2.15455 | ||||||||
\(856\) | 4.50000 | + | 7.79423i | 0.153807 | + | 0.266401i | ||||
\(857\) | −1.50000 | − | 2.59808i | −0.0512390 | − | 0.0887486i | 0.839268 | − | 0.543718i | \(-0.182984\pi\) |
−0.890507 | + | 0.454969i | \(0.849650\pi\) | |||||||
\(858\) | 4.50000 | + | 2.59808i | 0.153627 | + | 0.0886969i | ||||
\(859\) | 12.5000 | − | 21.6506i | 0.426494 | − | 0.738710i | −0.570064 | − | 0.821600i | \(-0.693082\pi\) |
0.996559 | + | 0.0828900i | \(0.0264150\pi\) | |||||||
\(860\) | 1.50000 | + | 2.59808i | 0.0511496 | + | 0.0885937i | ||||
\(861\) | −13.5000 | − | 2.59808i | −0.460079 | − | 0.0885422i | ||||
\(862\) | 13.5000 | − | 23.3827i | 0.459812 | − | 0.796417i | ||||
\(863\) | 25.5000 | + | 44.1673i | 0.868030 | + | 1.50347i | 0.864007 | + | 0.503480i | \(0.167947\pi\) |
0.00402340 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | −16.0000 | − | 13.8564i | −0.543075 | − | 0.470317i | ||||
\(869\) | −24.0000 | − | 41.5692i | −0.814144 | − | 1.41014i | ||||
\(870\) | −13.5000 | + | 7.79423i | −0.457693 | + | 0.264249i | ||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | −6.50000 | + | 11.2583i | −0.220118 | + | 0.381255i | ||||
\(873\) | −1.50000 | + | 2.59808i | −0.0507673 | + | 0.0879316i | ||||
\(874\) | −63.0000 | −2.13101 | ||||||||
\(875\) | 6.00000 | + | 5.19615i | 0.202837 | + | 0.175662i | ||||
\(876\) | −16.5000 | − | 9.52628i | −0.557483 | − | 0.321863i | ||||
\(877\) | −23.5000 | + | 40.7032i | −0.793539 | + | 1.37445i | 0.130224 | + | 0.991485i | \(0.458430\pi\) |
−0.923763 | + | 0.382965i | \(0.874903\pi\) | |||||||
\(878\) | −8.00000 | −0.269987 | ||||||||
\(879\) | −13.5000 | + | 7.79423i | −0.455344 | + | 0.262893i | ||||
\(880\) | −9.00000 | −0.303390 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 3.00000 | + | 20.7846i | 0.101015 | + | 0.699854i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | −3.00000 | −0.100901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −1.20944 | ||||||||
\(887\) | 16.5000 | − | 28.5788i | 0.554016 | − | 0.959583i | −0.443964 | − | 0.896045i | \(-0.646428\pi\) |
0.997979 | − | 0.0635387i | \(-0.0202386\pi\) | |||||||
\(888\) | 1.50000 | − | 0.866025i | 0.0503367 | − | 0.0290619i | ||||
\(889\) | 8.00000 | + | 6.92820i | 0.268311 | + | 0.232364i | ||||
\(890\) | −9.00000 | −0.301681 | ||||||||
\(891\) | 13.5000 | + | 23.3827i | 0.452267 | + | 0.783349i | ||||
\(892\) | 0.500000 | − | 0.866025i | 0.0167412 | − | 0.0289967i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −13.5000 | − | 7.79423i | −0.451508 | − | 0.260678i | ||||
\(895\) | 31.5000 | + | 54.5596i | 1.05293 | + | 1.82373i | ||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | 15.5885i | 0.520483i | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | 6.00000 | + | 10.3923i | 0.200000 | + | 0.346410i | ||||
\(901\) | −4.50000 | − | 7.79423i | −0.149917 | − | 0.259663i | ||||
\(902\) | −4.50000 | + | 7.79423i | −0.149834 | + | 0.259519i | ||||
\(903\) | −1.50000 | − | 4.33013i | −0.0499169 | − | 0.144098i | ||||
\(904\) | −4.50000 | − | 7.79423i | −0.149668 | − | 0.259232i | ||||
\(905\) | −3.00000 | + | 5.19615i | −0.0997234 | + | 0.172726i | ||||
\(906\) | 10.5000 | − | 6.06218i | 0.348839 | − | 0.201402i | ||||
\(907\) | 21.5000 | + | 37.2391i | 0.713896 | + | 1.23650i | 0.963384 | + | 0.268126i | \(0.0864043\pi\) |
−0.249488 | + | 0.968378i | \(0.580262\pi\) | |||||||
\(908\) | 1.50000 | + | 2.59808i | 0.0497792 | + | 0.0862202i | ||||
\(909\) | 4.50000 | + | 7.79423i | 0.149256 | + | 0.258518i | ||||
\(910\) | −6.00000 | − | 5.19615i | −0.198898 | − | 0.172251i | ||||
\(911\) | −19.5000 | + | 33.7750i | −0.646064 | + | 1.11902i | 0.337991 | + | 0.941149i | \(0.390253\pi\) |
−0.984055 | + | 0.177866i | \(0.943081\pi\) | |||||||
\(912\) | −10.5000 | + | 6.06218i | −0.347690 | + | 0.200739i | ||||
\(913\) | 27.0000 | 0.893570 | ||||||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | −9.00000 | − | 5.19615i | −0.297531 | − | 0.171780i | ||||
\(916\) | 6.50000 | − | 11.2583i | 0.214766 | − | 0.371986i | ||||
\(917\) | 37.5000 | − | 12.9904i | 1.23836 | − | 0.428980i | ||||
\(918\) | −13.5000 | − | 7.79423i | −0.445566 | − | 0.257248i | ||||
\(919\) | −26.5000 | − | 45.8993i | −0.874154 | − | 1.51408i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) |
−0.0164935 | − | 0.999864i | \(-0.505250\pi\) | |||||||
\(920\) | −13.5000 | − | 23.3827i | −0.445082 | − | 0.770904i | ||||
\(921\) | − | 48.4974i | − | 1.59804i | ||||||
\(922\) | −4.50000 | + | 7.79423i | −0.148200 | + | 0.256689i | ||||
\(923\) | 6.00000 | + | 10.3923i | 0.197492 | + | 0.342067i | ||||
\(924\) | 13.5000 | + | 2.59808i | 0.444117 | + | 0.0854704i | ||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 20.5000 | + | 35.5070i | 0.673672 | + | 1.16683i | ||||
\(927\) | −19.5000 | + | 33.7750i | −0.640464 | + | 1.10932i | ||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 36.0000 | + | 20.7846i | 1.18049 | + | 0.681554i | ||||
\(931\) | −38.5000 | + | 30.3109i | −1.26179 | + | 0.993399i | ||||
\(932\) | −1.50000 | − | 2.59808i | −0.0491341 | − | 0.0851028i | ||||
\(933\) | − | 41.5692i | − | 1.36092i | ||||||
\(934\) | −1.50000 | − | 2.59808i | −0.0490815 | − | 0.0850117i | ||||
\(935\) | 13.5000 | − | 23.3827i | 0.441497 | − | 0.764696i | ||||
\(936\) | 1.50000 | + | 2.59808i | 0.0490290 | + | 0.0849208i | ||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −8.00000 | − | 6.92820i | −0.261209 | − | 0.226214i | ||||
\(939\) | − | 17.3205i | − | 0.565233i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 38.1051i | 1.24153i | ||||||||
\(943\) | −27.0000 | −0.879241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.5000 | − | 38.9711i | −0.439155 | − | 1.26773i | ||||
\(946\) | −3.00000 | −0.0975384 | ||||||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | − | 27.7128i | − | 0.900070i | ||||||
\(949\) | −11.0000 | −0.357075 | ||||||||
\(950\) | −14.0000 | + | 24.2487i | −0.454220 | + | 0.786732i | ||||
\(951\) | 31.1769i | 1.01098i | ||||||||
\(952\) | −7.50000 | + | 2.59808i | −0.243076 | + | 0.0842041i | ||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | −4.50000 | + | 7.79423i | −0.145693 | + | 0.252347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.50000 | + | 2.59808i | 0.0485135 | + | 0.0840278i | ||||
\(957\) | − | 15.5885i | − | 0.503903i | ||||||
\(958\) | −1.50000 | − | 2.59808i | −0.0484628 | − | 0.0839400i | ||||
\(959\) | 4.50000 | − | 23.3827i | 0.145313 | − | 0.755066i | ||||
\(960\) | −4.50000 | − | 2.59808i | −0.145237 | − | 0.0838525i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0.500000 | − | 0.866025i | 0.0161206 | − | 0.0279218i | ||||
\(963\) | 13.5000 | + | 23.3827i | 0.435031 | + | 0.753497i | ||||
\(964\) | 6.50000 | + | 11.2583i | 0.209351 | + | 0.362606i | ||||
\(965\) | −21.0000 | + | 36.3731i | −0.676014 | + | 1.17089i | ||||
\(966\) | 13.5000 | + | 38.9711i | 0.434355 | + | 1.25388i | ||||
\(967\) | −20.5000 | − | 35.5070i | −0.659236 | − | 1.14183i | −0.980814 | − | 0.194946i | \(-0.937547\pi\) |
0.321578 | − | 0.946883i | \(-0.395787\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | − | 36.3731i | − | 1.16847i | ||||||
\(970\) | −1.50000 | − | 2.59808i | −0.0481621 | − | 0.0834192i | ||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 3.50000 | − | 18.1865i | 0.112205 | − | 0.583033i | ||||
\(974\) | −12.5000 | + | 21.6506i | −0.400526 | + | 0.693731i | ||||
\(975\) | 6.00000 | + | 3.46410i | 0.192154 | + | 0.110940i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 28.5000 | − | 16.4545i | 0.911330 | − | 0.526156i | ||||
\(979\) | 4.50000 | − | 7.79423i | 0.143821 | − | 0.249105i | ||||
\(980\) | −19.5000 | − | 7.79423i | −0.622905 | − | 0.248978i | ||||
\(981\) | −19.5000 | + | 33.7750i | −0.622587 | + | 1.07835i | ||||
\(982\) | 10.5000 | + | 18.1865i | 0.335068 | + | 0.580356i | ||||
\(983\) | 7.50000 | + | 12.9904i | 0.239213 | + | 0.414329i | 0.960489 | − | 0.278319i | \(-0.0897773\pi\) |
−0.721276 | + | 0.692648i | \(0.756444\pi\) | |||||||
\(984\) | −4.50000 | + | 2.59808i | −0.143455 | + | 0.0828236i | ||||
\(985\) | −27.0000 | + | 46.7654i | −0.860292 | + | 1.49007i | ||||
\(986\) | 4.50000 | + | 7.79423i | 0.143309 | + | 0.248219i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.50000 | + | 6.06218i | −0.111350 | + | 0.192864i | ||||
\(989\) | −4.50000 | − | 7.79423i | −0.143092 | − | 0.247842i | ||||
\(990\) | −27.0000 | −0.858116 | ||||||||
\(991\) | 12.5000 | − | 21.6506i | 0.397076 | − | 0.687755i | −0.596288 | − | 0.802771i | \(-0.703358\pi\) |
0.993364 | + | 0.115015i | \(0.0366917\pi\) | |||||||
\(992\) | −8.00000 | −0.254000 | ||||||||
\(993\) | 13.8564i | 0.439720i | ||||||||
\(994\) | 24.0000 | + | 20.7846i | 0.761234 | + | 0.659248i | ||||
\(995\) | 37.5000 | + | 64.9519i | 1.18883 | + | 2.05911i | ||||
\(996\) | 13.5000 | + | 7.79423i | 0.427764 | + | 0.246970i | ||||
\(997\) | 6.50000 | + | 11.2583i | 0.205857 | + | 0.356555i | 0.950405 | − | 0.311014i | \(-0.100668\pi\) |
−0.744548 | + | 0.667568i | \(0.767335\pi\) | |||||||
\(998\) | −12.5000 | + | 21.6506i | −0.395681 | + | 0.685339i | ||||
\(999\) | 4.50000 | − | 2.59808i | 0.142374 | − | 0.0821995i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))