Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.a.529.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.50000 | − | 2.59808i | 1.16190 | − | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | − | 7.79423i | −0.938315 | − | 1.62521i | −0.768613 | − | 0.639713i | \(-0.779053\pi\) |
−0.169701 | − | 0.985496i | \(-0.554280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | − | 2.59808i | −0.278543 | − | 0.482451i | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.50000 | − | 2.59808i | −1.26773 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | + | 0.866025i | 0.240192 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.50000 | + | 7.79423i | 0.670820 | + | 1.16190i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | − | 2.59808i | 0.630126 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.5000 | − | 6.06218i | −1.39076 | − | 0.802955i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | + | 5.19615i | −0.755929 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5000 | − | 7.79423i | 1.62521 | − | 0.938315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.00000 | − | 3.46410i | −0.692820 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | + | 7.79423i | 0.170941 | + | 0.888235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000 | 1.80014 | 0.900070 | − | 0.435745i | \(-0.143515\pi\) | ||||
0.900070 | + | 0.435745i | \(0.143515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50000 | − | 7.79423i | −0.493939 | − | 0.855528i | 0.506036 | − | 0.862512i | \(-0.331110\pi\) |
−0.999976 | + | 0.00698436i | \(0.997777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.50000 | − | 2.59808i | 0.482451 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.500000 | − | 2.59808i | −0.0524142 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 13.8564i | − | 1.43684i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.0000 | 2.15455 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.50000 | − | 7.79423i | 0.452267 | − | 0.783349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.50000 | − | 11.2583i | −0.640464 | − | 1.10932i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.344865 | − | 0.938652i | \(-0.387925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.50000 | − | 12.9904i | 0.439155 | − | 1.26773i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50000 | − | 7.79423i | 0.435031 | − | 0.753497i | −0.562267 | − | 0.826956i | \(-0.690071\pi\) |
0.997298 | + | 0.0734594i | \(0.0234039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.50000 | + | 11.2583i | 0.622587 | + | 1.07835i | 0.989002 | + | 0.147901i | \(0.0472517\pi\) |
−0.366415 | + | 0.930451i | \(0.619415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.50000 | + | 0.866025i | 0.142374 | + | 0.0821995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | − | 7.79423i | 0.423324 | − | 0.733219i | −0.572938 | − | 0.819599i | \(-0.694196\pi\) |
0.996262 | + | 0.0863794i | \(0.0275297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5000 | + | 23.3827i | −1.25888 | + | 2.18045i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | + | 2.59808i | −0.138675 | + | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.50000 | − | 2.59808i | −0.687524 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.50000 | − | 2.59808i | −0.405751 | − | 0.234261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | − | 0.866025i | 0.132068 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.50000 | + | 12.9904i | 0.655278 | + | 1.13497i | 0.981824 | + | 0.189794i | \(0.0607819\pi\) |
−0.326546 | + | 0.945181i | \(0.605885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | + | 18.1865i | 0.303488 | + | 1.57697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.5000 | + | 7.79423i | −1.16190 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50000 | + | 6.06218i | −0.296866 | + | 0.514187i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50000 | + | 2.59808i | 0.125436 | + | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0000 | + | 1.73205i | 0.989743 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | + | 7.79423i | 0.368654 | + | 0.638528i | 0.989355 | − | 0.145519i | \(-0.0464853\pi\) |
−0.620701 | + | 0.784047i | \(0.713152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | + | 6.06218i | −0.284826 | + | 0.493333i | −0.972567 | − | 0.232623i | \(-0.925269\pi\) |
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | + | 20.7846i | 0.963863 | + | 1.66946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | − | 2.59808i | 0.356873 | − | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.5000 | − | 7.79423i | −1.77325 | − | 0.614271i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50000 | + | 16.4545i | −0.744097 | + | 1.28881i | 0.206518 | + | 0.978443i | \(0.433787\pi\) |
−0.950615 | + | 0.310372i | \(0.899546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.5885i | 1.21356i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.50000 | + | 12.9904i | −0.580367 | + | 1.00523i | 0.415068 | + | 0.909790i | \(0.363758\pi\) |
−0.995436 | + | 0.0954356i | \(0.969576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5000 | − | 18.1865i | 0.802955 | − | 1.39076i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 10.3923i | 0.151186 | + | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | − | 18.1865i | −0.784807 | − | 1.35933i | −0.929114 | − | 0.369792i | \(-0.879429\pi\) |
0.144308 | − | 0.989533i | \(-0.453905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.46410i | 0.256074i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | 0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | − | 10.3923i | −0.654654 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 5.19615i | − | 0.372104i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5000 | − | 21.6506i | −0.886102 | − | 1.53477i | −0.844446 | − | 0.535641i | \(-0.820070\pi\) |
−0.0416556 | − | 0.999132i | \(-0.513263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.92820i | 0.488678i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.50000 | − | 2.59808i | −0.526397 | − | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | 0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.5000 | + | 23.3827i | 0.938315 | + | 1.62521i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5000 | − | 18.1865i | −0.726300 | − | 1.25799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 20.7846i | − | 1.42414i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.50000 | + | 2.59808i | −0.102299 | + | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | + | 13.8564i | −1.08615 | + | 0.940634i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5000 | − | 9.52628i | 1.11497 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.500000 | − | 0.866025i | −0.0334825 | − | 0.0579934i | 0.848799 | − | 0.528716i | \(-0.177326\pi\) |
−0.882281 | + | 0.470723i | \(0.843993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | − | 10.3923i | 0.400000 | − | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.50000 | + | 11.2583i | 0.429532 | + | 0.743971i | 0.996832 | − | 0.0795401i | \(-0.0253452\pi\) |
−0.567300 | + | 0.823511i | \(0.692012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.5000 | + | 2.59808i | −0.888235 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.50000 | + | 2.59808i | −0.0982683 | + | 0.170206i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.7128i | 1.80014i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50000 | + | 2.59808i | −0.0970269 | + | 0.168056i | −0.910453 | − | 0.413613i | \(-0.864267\pi\) |
0.813426 | + | 0.581669i | \(0.197600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | − | 11.2583i | 0.418702 | − | 0.725213i | −0.577107 | − | 0.816668i | \(-0.695819\pi\) |
0.995809 | + | 0.0914555i | \(0.0291519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.5000 | + | 7.79423i | −1.24581 | + | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.50000 | + | 6.06218i | 0.222700 | + | 0.385727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5000 | − | 7.79423i | 0.855528 | − | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.5000 | − | 7.79423i | −0.845403 | − | 0.488094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5000 | + | 18.1865i | 0.654972 | + | 1.13444i | 0.981901 | + | 0.189396i | \(0.0606529\pi\) |
−0.326929 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.500000 | − | 2.59808i | −0.0310685 | − | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | − | 7.79423i | 0.277482 | − | 0.480613i | −0.693276 | − | 0.720672i | \(-0.743833\pi\) |
0.970758 | + | 0.240059i | \(0.0771668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.50000 | − | 2.59808i | −0.275396 | − | 0.159000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.50000 | − | 12.9904i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840679i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.50000 | − | 4.33013i | 0.151864 | − | 0.263036i | −0.780049 | − | 0.625719i | \(-0.784806\pi\) |
0.931913 | + | 0.362682i | \(0.118139\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.50000 | − | 0.866025i | 0.272352 | − | 0.0524142i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | − | 10.3923i | −0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.0000 | 1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5000 | + | 18.1865i | 0.626377 | + | 1.08492i | 0.988273 | + | 0.152699i | \(0.0487965\pi\) |
−0.361895 | + | 0.932219i | \(0.617870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 36.3731i | 2.15455i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50000 | + | 7.79423i | 0.0885422 | + | 0.460079i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50000 | + | 0.866025i | −0.0879316 | + | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.00000 | −0.520483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | − | 0.866025i | −0.144098 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.50000 | − | 2.59808i | −0.258518 | − | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.5000 | − | 11.2583i | 1.10932 | − | 0.640464i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.5000 | + | 7.79423i | 1.26773 | + | 0.439155i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | 0.503903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | + | 7.79423i | 0.753497 | + | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0000 | 1.16847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.5000 | + | 11.2583i | −1.07835 | + | 0.622587i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.50000 | + | 2.59808i | −0.0821995 | + | 0.142374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | − | 10.3923i | −0.327815 | − | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.50000 | − | 11.2583i | 0.354078 | − | 0.613280i | −0.632882 | − | 0.774248i | \(-0.718128\pi\) |
0.986960 | + | 0.160968i | \(0.0514616\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5000 | + | 7.79423i | 0.733219 | + | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | − | 20.7846i | 0.649836 | − | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −40.5000 | − | 23.3827i | −2.18045 | − | 1.25888i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5000 | − | 19.9186i | −0.615581 | − | 1.06622i | −0.990282 | − | 0.139072i | \(-0.955588\pi\) |
0.374701 | − | 0.927146i | \(-0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.50000 | − | 2.59808i | −0.240192 | − | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | + | 31.1769i | 0.955341 | + | 1.65470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.50000 | − | 12.9904i | 0.238165 | − | 0.687524i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.50000 | − | 7.79423i | 0.237501 | − | 0.411364i | −0.722496 | − | 0.691375i | \(-0.757005\pi\) |
0.959997 | + | 0.280012i | \(0.0903384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | + | 1.73205i | −0.157459 | + | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.5000 | + | 28.5788i | −0.863649 | + | 1.49588i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | − | 14.7224i | 0.443696 | − | 0.768505i | −0.554264 | − | 0.832341i | \(-0.687000\pi\) |
0.997960 | + | 0.0638362i | \(0.0203335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.50000 | − | 2.59808i | −0.389381 | − | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50000 | + | 11.2583i | 0.336557 | + | 0.582934i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 5.19615i | − | 0.268328i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.92820i | 0.354943i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.50000 | + | 12.9904i | 0.383232 | + | 0.663777i | 0.991522 | − | 0.129937i | \(-0.0414776\pi\) |
−0.608290 | + | 0.793715i | \(0.708144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | − | 15.5885i | 0.917365 | − | 0.794461i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.50000 | + | 2.59808i | 0.0762493 | + | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.5000 | + | 23.3827i | −0.684477 | + | 1.18555i | 0.289124 | + | 0.957292i | \(0.406636\pi\) |
−0.973601 | + | 0.228257i | \(0.926697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5000 | + | 23.3827i | −0.682724 | + | 1.18251i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.5000 | + | 12.9904i | −1.13497 | + | 0.655278i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.0000 | − | 41.5692i | −1.20757 | − | 2.09157i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −31.5000 | + | 6.06218i | −1.57697 | + | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | − | 23.3827i | −0.674158 | − | 1.16768i | −0.976714 | − | 0.214544i | \(-0.931173\pi\) |
0.302556 | − | 0.953131i | \(-0.402160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 6.92820i | −0.199254 | + | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.5000 | − | 23.3827i | −0.670820 | − | 1.16190i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.50000 | + | 2.59808i | 0.0743522 | + | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0000 | −1.68119 | −0.840596 | − | 0.541663i | \(-0.817795\pi\) | ||||
−0.840596 | + | 0.541663i | \(0.817795\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | + | 7.79423i | 0.665906 | + | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5000 | + | 23.3827i | −0.662689 | + | 1.14781i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.5000 | − | 6.06218i | −0.514187 | − | 0.296866i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5000 | − | 30.3109i | −0.852898 | − | 1.47726i | −0.878582 | − | 0.477592i | \(-0.841510\pi\) |
0.0256838 | − | 0.999670i | \(-0.491824\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000 | − | 3.46410i | 0.193574 | − | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.50000 | + | 2.59808i | −0.217262 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5000 | + | 23.3827i | 0.650272 | + | 1.12630i | 0.983057 | + | 0.183301i | \(0.0586785\pi\) |
−0.332785 | + | 0.943003i | \(0.607988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.5000 | − | 7.79423i | −0.647275 | − | 0.373705i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 63.0000 | 3.01370 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.0000 | −1.71041 | −0.855206 | − | 0.518289i | \(-0.826569\pi\) | ||||
−0.855206 | + | 0.518289i | \(0.826569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | 0.426641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5000 | + | 7.79423i | −0.638528 | + | 0.368654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5000 | − | 6.06218i | −0.493333 | − | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.00000 | + | 5.19615i | −0.281284 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.5000 | + | 7.79423i | −0.630126 | + | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50000 | + | 7.79423i | 0.209586 | + | 0.363013i | 0.951584 | − | 0.307388i | \(-0.0994551\pi\) |
−0.741998 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5000 | − | 35.5070i | 0.952716 | − | 1.65015i | 0.213205 | − | 0.977007i | \(-0.431610\pi\) |
0.739511 | − | 0.673145i | \(-0.235057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −36.0000 | + | 20.7846i | −1.66946 | + | 0.963863i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.50000 | + | 2.59808i | −0.0694117 | + | 0.120225i | −0.898642 | − | 0.438682i | \(-0.855446\pi\) |
0.829231 | + | 0.558906i | \(0.188779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | − | 6.92820i | 0.369406 | − | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 38.1051i | − | 1.75579i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | 0.137940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | − | 24.2487i | −0.642364 | − | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.50000 | + | 7.79423i | 0.206041 | + | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.50000 | + | 2.59808i | −0.0685367 | + | 0.118709i | −0.898257 | − | 0.439470i | \(-0.855166\pi\) |
0.829721 | + | 0.558179i | \(0.188500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.500000 | − | 0.866025i | −0.0227980 | − | 0.0394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.5000 | − | 38.9711i | 0.614271 | − | 1.77325i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.50000 | − | 2.59808i | 0.0681115 | − | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5000 | − | 21.6506i | −0.566429 | − | 0.981084i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
0.430486 | − | 0.902597i | \(-0.358342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.5000 | − | 16.4545i | −1.28881 | − | 0.744097i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5000 | − | 18.1865i | 0.473858 | − | 0.820747i | −0.525694 | − | 0.850674i | \(-0.676194\pi\) |
0.999552 | + | 0.0299272i | \(0.00952753\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.50000 | + | 7.79423i | −0.202670 | + | 0.351034i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.0000 | −1.21356 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | + | 20.7846i | −1.07655 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | − | 21.6506i | −0.559577 | − | 0.969216i | −0.997532 | − | 0.0702185i | \(-0.977630\pi\) |
0.437955 | − | 0.898997i | \(-0.355703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.5000 | − | 12.9904i | −1.00523 | − | 0.580367i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.0000 | + | 10.3923i | −0.799408 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50000 | + | 7.79423i | 0.199459 | + | 0.345473i | 0.948353 | − | 0.317217i | \(-0.102748\pi\) |
−0.748894 | + | 0.662690i | \(0.769415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5000 | − | 9.52628i | −1.21653 | − | 0.421418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.5000 | + | 18.1865i | 1.39076 | + | 0.802955i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.5000 | + | 33.7750i | −0.859273 | + | 1.48830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.50000 | − | 2.59808i | −0.0657162 | − | 0.113824i | 0.831295 | − | 0.555831i | \(-0.187600\pi\) |
−0.897011 | + | 0.442007i | \(0.854267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.50000 | + | 6.06218i | −0.153044 | + | 0.265081i | −0.932345 | − | 0.361569i | \(-0.882241\pi\) |
0.779301 | + | 0.626650i | \(0.215574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.0000 | + | 3.46410i | −0.785584 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | + | 50.2295i | −1.26087 | + | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.50000 | + | 2.59808i | 0.0649722 | + | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.0000 | −1.16731 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.5000 | − | 18.1865i | 1.35933 | − | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | + | 12.9904i | 0.710705 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50000 | + | 9.52628i | −0.236463 | + | 0.409567i | −0.959697 | − | 0.281037i | \(-0.909322\pi\) |
0.723234 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.46410i | 0.148659i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5000 | − | 33.7750i | 0.835288 | − | 1.44676i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.50000 | + | 9.52628i | 0.235163 | + | 0.407314i | 0.959320 | − | 0.282321i | \(-0.0911043\pi\) |
−0.724157 | + | 0.689635i | \(0.757771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000 | 0.894630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000 | − | 27.7128i | 1.36078 | − | 1.17847i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 5.19615i | − | 0.220564i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50000 | + | 7.79423i | 0.190671 | + | 0.330252i | 0.945473 | − | 0.325701i | \(-0.105600\pi\) |
−0.754802 | + | 0.655953i | \(0.772267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5885i | 0.658145i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | −1.13590 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.0000 | 1.50130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5000 | + | 21.6506i | 0.520382 | + | 0.901328i | 0.999719 | + | 0.0236970i | \(0.00754370\pi\) |
−0.479337 | + | 0.877631i | \(0.659123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.5000 | − | 7.79423i | −0.933457 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | 0.372742 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | 0.372104 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50000 | + | 2.59808i | 0.0619116 | + | 0.107234i | 0.895320 | − | 0.445424i | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | − | 48.4974i | 1.15372 | − | 1.99830i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1769i | 1.28245i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5000 | + | 33.7750i | −0.800769 | + | 1.38697i | 0.118342 | + | 0.992973i | \(0.462242\pi\) |
−0.919111 | + | 0.394000i | \(0.871091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | + | 23.3827i | 0.184482 | + | 0.958597i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.5000 | − | 21.6506i | 1.53477 | − | 0.886102i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | + | 21.6506i | 0.509886 | + | 0.883148i | 0.999934 | + | 0.0114528i | \(0.00364562\pi\) |
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | − | 5.19615i | 0.121967 | − | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | − | 11.2583i | −0.263827 | − | 0.456962i | 0.703429 | − | 0.710766i | \(-0.251651\pi\) |
−0.967256 | + | 0.253804i | \(0.918318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.50000 | − | 12.9904i | 0.182349 | − | 0.526397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5000 | − | 19.9186i | −0.464481 | − | 0.804504i | 0.534697 | − | 0.845044i | \(-0.320426\pi\) |
−0.999178 | + | 0.0405396i | \(0.987092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.5885i | 0.628587i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5000 | − | 38.9711i | 0.905816 | − | 1.56892i | 0.0859976 | − | 0.996295i | \(-0.472592\pi\) |
0.819818 | − | 0.572624i | \(-0.194074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.50000 | − | 14.7224i | 0.341644 | − | 0.591744i | −0.643094 | − | 0.765787i | \(-0.722350\pi\) |
0.984738 | + | 0.174042i | \(0.0556830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.5000 | + | 23.3827i | −1.62521 | + | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.50000 | + | 7.79423i | 0.0600962 | + | 0.312269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.5000 | − | 18.1865i | 1.25799 | − | 0.726300i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.00000 | −0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.50000 | + | 4.33013i | 0.298098 | + | 0.172107i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | − | 10.3923i | −0.238103 | − | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | − | 4.33013i | −0.217918 | − | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.0000 | 1.42414 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5000 | − | 25.1147i | 0.571824 | − | 0.990429i | −0.424555 | − | 0.905402i | \(-0.639569\pi\) |
0.996379 | − | 0.0850262i | \(-0.0270974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.50000 | − | 2.59808i | −0.177187 | − | 0.102299i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.5000 | − | 18.1865i | −0.412798 | − | 0.714986i | 0.582397 | − | 0.812905i | \(-0.302115\pi\) |
−0.995194 | + | 0.0979182i | \(0.968782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.0000 | − | 27.7128i | −0.940634 | − | 1.08615i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.50000 | − | 12.9904i | −0.293498 | − | 0.508353i | 0.681137 | − | 0.732156i | \(-0.261486\pi\) |
−0.974634 | + | 0.223803i | \(0.928153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5000 | − | 38.9711i | 0.879148 | − | 1.52273i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5000 | + | 28.5788i | 0.643726 | + | 1.11497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.50000 | + | 2.59808i | 0.0584317 | + | 0.101207i | 0.893762 | − | 0.448542i | \(-0.148057\pi\) |
−0.835330 | + | 0.549749i | \(0.814723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5.19615i | − | 0.201802i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 42.0000 | − | 36.3731i | 1.62869 | − | 1.41049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.5000 | + | 23.3827i | −0.522722 | + | 0.905381i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.50000 | − | 0.866025i | 0.0579934 | − | 0.0334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | + | 5.19615i | −0.115814 | + | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5000 | − | 30.3109i | −0.674575 | − | 1.16840i | −0.976593 | − | 0.215096i | \(-0.930993\pi\) |
0.302017 | − | 0.953302i | \(-0.402340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0000 | + | 10.3923i | 0.692820 | + | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.50000 | + | 0.866025i | 0.0959412 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.50000 | − | 7.79423i | −0.172188 | − | 0.298238i | 0.766997 | − | 0.641651i | \(-0.221750\pi\) |
−0.939184 | + | 0.343413i | \(0.888417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.0000 | −1.03162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.5000 | + | 11.2583i | −0.743971 | + | 0.429532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | −0.114291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.0000 | −1.67384 | −0.836919 | − | 0.547326i | \(-0.815646\pi\) | ||||
−0.836919 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.50000 | − | 23.3827i | −0.170941 | − | 0.888235i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0000 | 0.796575 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50000 | − | 2.59808i | −0.170206 | − | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.50000 | + | 6.06218i | 0.132005 | + | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 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 | \(0.337644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.0000 | −1.80014 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.0000 | + | 62.3538i | 1.34821 | + | 2.33517i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.50000 | − | 7.79423i | 0.168290 | − | 0.291488i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.50000 | − | 2.59808i | −0.168056 | − | 0.0970269i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50000 | + | 12.9904i | −0.279703 | + | 0.484459i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.5000 | − | 11.2583i | −1.21036 | − | 0.419282i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.5000 | + | 11.2583i | 0.725213 | + | 0.418702i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0000 | 0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.50000 | − | 11.2583i | −0.241072 | − | 0.417548i | 0.719948 | − | 0.694028i | \(-0.244166\pi\) |
−0.961020 | + | 0.276479i | \(0.910832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.500000 | + | 0.866025i | 0.0184679 | + | 0.0319874i | 0.875112 | − | 0.483921i | \(-0.160788\pi\) |
−0.856644 | + | 0.515908i | \(0.827454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5000 | − | 33.7750i | −0.497955 | − | 1.24581i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5000 | + | 19.9186i | 0.423034 | + | 0.732717i | 0.996235 | − | 0.0866983i | \(-0.0276316\pi\) |
−0.573200 | + | 0.819415i | \(0.694298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5000 | + | 6.06218i | −0.385727 | + | 0.222700i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5000 | − | 18.1865i | 0.385208 | − | 0.667199i | −0.606590 | − | 0.795015i | \(-0.707463\pi\) |
0.991798 | + | 0.127815i | \(0.0407965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | − | 23.3827i | 0.494602 | − | 0.856675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5000 | + | 23.3827i | 0.493939 | + | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.50000 | − | 23.3827i | −0.164426 | − | 0.854385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | − | 11.2583i | −0.237188 | − | 0.410822i | 0.722718 | − | 0.691143i | \(-0.242893\pi\) |
−0.959906 | + | 0.280321i | \(0.909559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 20.7846i | − | 0.757433i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.0000 | 0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.7654i | 1.69748i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5000 | + | 38.9711i | 0.815624 | + | 1.41270i | 0.908879 | + | 0.417061i | \(0.136940\pi\) |
−0.0932544 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5000 | + | 11.2583i | 1.17658 | + | 0.407579i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.5000 | − | 23.3827i | 0.488094 | − | 0.845403i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5000 | + | 19.9186i | −0.414701 | + | 0.718283i | −0.995397 | − | 0.0958377i | \(-0.969447\pi\) |
0.580696 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.5000 | + | 18.1865i | −1.13444 | + | 0.654972i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5000 | − | 23.3827i | −0.485561 | − | 0.841017i | 0.514301 | − | 0.857610i | \(-0.328051\pi\) |
−0.999862 | + | 0.0165929i | \(0.994718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0000 | − | 27.7128i | 0.574737 | − | 0.995474i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.50000 | − | 0.866025i | 0.161437 | − | 0.0310685i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5000 | − | 18.1865i | −0.376202 | − | 0.651600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.5000 | + | 7.79423i | −0.482451 | + | 0.278543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.0000 | + | 57.1577i | 1.17782 | + | 2.04004i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000 | 0.998092 | 0.499046 | − | 0.866575i | \(-0.333684\pi\) | ||||
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.5000 | + | 7.79423i | 0.480613 | + | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.50000 | − | 23.3827i | −0.160002 | − | 0.831393i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5000 | − | 18.1865i | 0.371929 | − | 0.644200i | −0.617933 | − | 0.786231i | \(-0.712030\pi\) |
0.989862 | + | 0.142031i | \(0.0453631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.50000 | − | 7.79423i | 0.159000 | − | 0.275396i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.0000 | 1.16454 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.5000 | + | 70.1481i | 0.475812 | + | 2.47239i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.5000 | − | 12.9904i | 0.792038 | − | 0.457283i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5000 | + | 28.5788i | 0.580109 | + | 1.00478i | 0.995466 | + | 0.0951198i | \(0.0303234\pi\) |
−0.415357 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.50000 | + | 4.33013i | 0.263036 | + | 0.151864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 57.0000 | 1.99662 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | 0.244899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.50000 | + | 7.79423i | 0.0524142 | + | 0.272352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0000 | 1.39431 | 0.697156 | − | 0.716919i | \(-0.254448\pi\) | ||||
0.697156 | + | 0.716919i | \(0.254448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.0000 | − | 10.3923i | 0.626680 | − | 0.361814i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.50000 | + | 0.866025i | 0.0520344 | + | 0.0300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.5000 | + | 7.79423i | −0.675635 | + | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.0000 | 1.55729 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.5692i | 1.43684i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.50000 | + | 12.9904i | 0.258929 | + | 0.448478i | 0.965955 | − | 0.258709i | \(-0.0832972\pi\) |
−0.707026 | + | 0.707187i | \(0.749964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.5000 | + | 18.1865i | −1.08492 | + | 0.626377i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0000 | − | 31.1769i | 0.619219 | − | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00000 | + | 1.73205i | 0.171802 | + | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.92820i | 0.237775i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00000 | −0.308516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.500000 | + | 0.866025i | 0.0171197 | + | 0.0296521i | 0.874458 | − | 0.485101i | \(-0.161217\pi\) |
−0.857339 | + | 0.514753i | \(0.827884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −63.0000 | −2.15455 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.50000 | + | 2.59808i | −0.0512390 | + | 0.0887486i | −0.890507 | − | 0.454969i | \(-0.849650\pi\) |
0.839268 | + | 0.543718i | \(0.182984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5000 | − | 21.6506i | −0.426494 | − | 0.738710i | 0.570064 | − | 0.821600i | \(-0.306918\pi\) |
−0.996559 | + | 0.0828900i | \(0.973585\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.5000 | + | 2.59808i | −0.460079 | + | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5000 | + | 44.1673i | −0.868030 | + | 1.50347i | −0.00402340 | + | 0.999992i | \(0.501281\pi\) |
−0.864007 | + | 0.503480i | \(0.832053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0000 | + | 6.92820i | 0.407541 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | + | 41.5692i | −0.814144 | + | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 3.46410i | 0.0677674 | − | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.50000 | − | 2.59808i | −0.0507673 | − | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | + | 5.19615i | −0.202837 | + | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5000 | − | 40.7032i | −0.793539 | − | 1.37445i | −0.923763 | − | 0.382965i | \(-0.874903\pi\) |
0.130224 | − | 0.991485i | \(-0.458430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.5000 | + | 7.79423i | 0.455344 | + | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.5000 | − | 28.5788i | −0.554016 | − | 0.959583i | −0.997979 | − | 0.0635387i | \(-0.979761\pi\) |
0.443964 | − | 0.896045i | \(-0.353572\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 6.92820i | 0.268311 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5000 | + | 54.5596i | −1.05293 | + | 1.82373i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 15.5885i | − | 0.520483i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.50000 | + | 7.79423i | −0.149917 | + | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.50000 | − | 4.33013i | 0.0499169 | − | 0.144098i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.00000 | − | 5.19615i | −0.0997234 | − | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.5000 | + | 37.2391i | −0.713896 | + | 1.23650i | 0.249488 | + | 0.968378i | \(0.419738\pi\) |
−0.963384 | + | 0.268126i | \(0.913596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.50000 | − | 7.79423i | 0.149256 | − | 0.258518i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.5000 | + | 33.7750i | 0.646064 | + | 1.11902i | 0.984055 | + | 0.177866i | \(0.0569194\pi\) |
−0.337991 | + | 0.941149i | \(0.609747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0000 | 0.893570 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.00000 | − | 5.19615i | 0.297531 | − | 0.171780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.5000 | + | 12.9904i | 1.23836 | + | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5000 | − | 45.8993i | 0.874154 | − | 1.51408i | 0.0164935 | − | 0.999864i | \(-0.494750\pi\) |
0.857661 | − | 0.514216i | \(-0.171917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.4974i | 1.59804i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | + | 10.3923i | −0.197492 | + | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.5000 | + | 33.7750i | 0.640464 | + | 1.10932i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.5000 | + | 30.3109i | 1.26179 | + | 0.993399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.5692i | 1.36092i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.5000 | − | 23.3827i | −0.441497 | − | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 17.3205i | − | 0.565233i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0000 | 0.879241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.5000 | + | 38.9711i | −0.439155 | + | 1.26773i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0000 | −0.357075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.1769i | 1.01098i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.5885i | 0.503903i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.50000 | − | 23.3827i | −0.145313 | − | 0.755066i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5000 | + | 23.3827i | −0.435031 | + | 0.753497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0000 | − | 36.3731i | −0.676014 | − | 1.17089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.5000 | − | 35.5070i | 0.659236 | − | 1.14183i | −0.321578 | − | 0.946883i | \(-0.604213\pi\) |
0.980814 | − | 0.194946i | \(-0.0624533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.3731i | 1.16847i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5000 | − | 28.5788i | 0.529510 | − | 0.917139i | −0.469897 | − | 0.882721i | \(-0.655709\pi\) |
0.999408 | − | 0.0344175i | \(-0.0109576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.50000 | + | 18.1865i | 0.112205 | + | 0.583033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 3.46410i | −0.192154 | + | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.50000 | − | 7.79423i | −0.143821 | − | 0.249105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.5000 | − | 33.7750i | −0.622587 | − | 1.07835i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.50000 | + | 12.9904i | −0.239213 | + | 0.414329i | −0.960489 | − | 0.278319i | \(-0.910223\pi\) |
0.721276 | + | 0.692648i | \(0.243556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | − | 46.7654i | −0.860292 | − | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50000 | + | 7.79423i | −0.143092 | + | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5000 | − | 21.6506i | −0.397076 | − | 0.687755i | 0.596288 | − | 0.802771i | \(-0.296642\pi\) |
−0.993364 | + | 0.115015i | \(0.963308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.5000 | + | 64.9519i | −1.18883 | + | 2.05911i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.50000 | − | 11.2583i | 0.205857 | − | 0.356555i | −0.744548 | − | 0.667568i | \(-0.767335\pi\) |
0.950405 | + | 0.311014i | \(0.100668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 \(a_p\))