Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.361 |
Dual form | 2646.2.h.d.667.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | + | 2.59808i | −0.474342 | + | 0.821584i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | −0.926995 | − | 0.375073i | \(-0.877618\pi\) |
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 9.00000 | 1.87663 | 0.938315 | − | 0.345782i | \(-0.112386\pi\) | ||||
0.938315 | + | 0.345782i | \(0.112386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 7.00000 | 1.13555 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −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 | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50000 | + | 7.79423i | −0.663489 | + | 1.14920i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.50000 | + | 2.59808i | −0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.50000 | + | 6.06218i | −0.401478 | + | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | − | 13.8564i | 0.900070 | − | 1.55897i | 0.0726692 | − | 0.997356i | \(-0.476848\pi\) |
0.827401 | − | 0.561611i | \(-0.189818\pi\) | |||||||
\(80\) | −1.50000 | + | 2.59808i | −0.167705 | + | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.50000 | − | 2.59808i | −0.165647 | − | 0.286910i | ||||
\(83\) | 4.50000 | + | 7.79423i | 0.493939 | + | 0.855528i | 0.999976 | − | 0.00698436i | \(-0.00222321\pi\) |
−0.506036 | + | 0.862512i | \(0.668890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.50000 | − | 7.79423i | −0.469157 | − | 0.812605i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5000 | − | 18.1865i | −1.07728 | − | 1.86590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 3.00000 | 0.298511 | 0.149256 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149256 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0000 | 1.28093 | 0.640464 | − | 0.767988i | \(-0.278742\pi\) | ||||
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −0.500000 | + | 0.866025i | −0.0490290 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.50000 | + | 2.59808i | 0.145693 | + | 0.252347i | ||||
\(107\) | 4.50000 | + | 7.79423i | 0.435031 | + | 0.753497i | 0.997298 | − | 0.0734594i | \(-0.0234039\pi\) |
−0.562267 | + | 0.826956i | \(0.690071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.50000 | − | 11.2583i | 0.622587 | − | 1.07835i | −0.366415 | − | 0.930451i | \(-0.619415\pi\) |
0.989002 | − | 0.147901i | \(-0.0472517\pi\) | |||||||
\(110\) | −4.50000 | + | 7.79423i | −0.429058 | + | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.50000 | + | 7.79423i | −0.423324 | + | 0.733219i | −0.996262 | − | 0.0863794i | \(-0.972470\pi\) |
0.572938 | + | 0.819599i | \(0.305804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.0000 | 2.51776 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 1.00000 | + | 1.73205i | 0.0905357 | + | 0.156813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | − | 6.92820i | 0.359211 | − | 0.622171i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.50000 | − | 2.59808i | −0.131559 | − | 0.227866i | ||||
\(131\) | 15.0000 | 1.31056 | 0.655278 | − | 0.755388i | \(-0.272551\pi\) | ||||
0.655278 | + | 0.755388i | \(0.272551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | 9.00000 | 0.768922 | 0.384461 | − | 0.923141i | \(-0.374387\pi\) | ||||
0.384461 | + | 0.923141i | \(0.374387\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 6.00000 | − | 10.3923i | 0.503509 | − | 0.872103i | ||||
\(143\) | −1.50000 | + | 2.59808i | −0.125436 | + | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | + | 7.79423i | 0.373705 | + | 0.647275i | ||||
\(146\) | 5.50000 | + | 9.52628i | 0.455183 | + | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.500000 | − | 0.866025i | 0.0410997 | − | 0.0711868i | ||||
\(149\) | 9.00000 | 0.737309 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.00000 | −0.569652 | −0.284826 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284826 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(152\) | −3.50000 | − | 6.06218i | −0.283887 | − | 0.491708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | + | 20.7846i | 0.963863 | + | 1.66946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0000 | − | 19.0526i | −0.877896 | − | 1.52056i | −0.853646 | − | 0.520854i | \(-0.825614\pi\) |
−0.0242497 | − | 0.999706i | \(-0.507720\pi\) | |||||||
\(158\) | 8.00000 | + | 13.8564i | 0.636446 | + | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | − | 2.59808i | −0.118585 | − | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.50000 | + | 16.4545i | 0.744097 | + | 1.28881i | 0.950615 | + | 0.310372i | \(0.100454\pi\) |
−0.206518 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | −0.698535 | ||||||||
\(167\) | 7.50000 | − | 12.9904i | 0.580367 | − | 1.00523i | −0.415068 | − | 0.909790i | \(-0.636242\pi\) |
0.995436 | − | 0.0954356i | \(-0.0304244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | −4.50000 | − | 7.79423i | −0.345134 | − | 0.597790i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | 0.224860 | ||||||||
\(179\) | −10.5000 | + | 18.1865i | −0.784807 | + | 1.35933i | 0.144308 | + | 0.989533i | \(0.453905\pi\) |
−0.929114 | + | 0.369792i | \(0.879429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.00000 | 0.663489 | ||||||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.0000 | 1.52350 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | − | 12.1244i | −0.503871 | − | 0.872730i | −0.999990 | − | 0.00447566i | \(-0.998575\pi\) |
0.496119 | − | 0.868255i | \(-0.334758\pi\) | |||||||
\(194\) | 1.00000 | 0.0717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5000 | + | 21.6506i | −0.886102 | + | 1.53477i | −0.0416556 | + | 0.999132i | \(0.513263\pi\) |
−0.844446 | + | 0.535641i | \(0.820070\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.50000 | + | 2.59808i | −0.105540 | + | 0.182800i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | −6.50000 | + | 11.2583i | −0.452876 | + | 0.784405i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | −10.5000 | − | 18.1865i | −0.726300 | − | 1.25799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.50000 | + | 4.33013i | −0.172107 | + | 0.298098i | −0.939156 | − | 0.343490i | \(-0.888391\pi\) |
0.767049 | + | 0.641588i | \(0.221724\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.00000 | −0.615227 | ||||||||
\(215\) | 1.50000 | + | 2.59808i | 0.102299 | + | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.50000 | + | 11.2583i | 0.440236 | + | 0.762510i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.50000 | − | 7.79423i | −0.303390 | − | 0.525487i | ||||
\(221\) | −1.50000 | − | 2.59808i | −0.100901 | − | 0.174766i | ||||
\(222\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | −3.00000 | −0.199117 | −0.0995585 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995585 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | −13.5000 | + | 23.3827i | −0.890164 | + | 1.54181i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | + | 2.59808i | 0.0984798 | + | 0.170572i | ||||
\(233\) | 1.50000 | + | 2.59808i | 0.0982683 | + | 0.170206i | 0.910968 | − | 0.412477i | \(-0.135336\pi\) |
−0.812700 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(241\) | 13.0000 | 0.837404 | 0.418702 | − | 0.908124i | \(-0.362485\pi\) | ||||
0.418702 | + | 0.908124i | \(0.362485\pi\) | |||||||
\(242\) | 1.00000 | − | 1.73205i | 0.0642824 | − | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | 0.445399 | ||||||||
\(248\) | 4.00000 | + | 6.92820i | 0.254000 | + | 0.439941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | − | 2.59808i | 0.0948683 | − | 0.164317i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 2.00000 | − | 3.46410i | 0.125491 | − | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −21.0000 | −1.30994 | −0.654972 | − | 0.755653i | \(-0.727320\pi\) | ||||
−0.654972 | + | 0.755653i | \(0.727320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.00000 | 0.186052 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.50000 | + | 12.9904i | −0.463352 | + | 0.802548i | ||||
\(263\) | −9.00000 | −0.554964 | −0.277482 | − | 0.960731i | \(-0.589500\pi\) | ||||
−0.277482 | + | 0.960731i | \(0.589500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.50000 | − | 7.79423i | 0.276433 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | −7.50000 | + | 12.9904i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486418i | \(-0.984511\pi\) |
0.541533 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.50000 | + | 4.33013i | 0.151864 | + | 0.263036i | 0.931913 | − | 0.362682i | \(-0.118139\pi\) |
−0.780049 | + | 0.625719i | \(0.784806\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.50000 | + | 7.79423i | −0.271855 | + | 0.470867i | ||||
\(275\) | 12.0000 | 0.723627 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | −0.0600842 | −0.0300421 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300421 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(278\) | −3.50000 | − | 6.06218i | −0.209916 | − | 0.363585i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5000 | − | 18.1865i | −0.626377 | − | 1.08492i | −0.988273 | − | 0.152699i | \(-0.951204\pi\) |
0.361895 | − | 0.932219i | \(-0.382130\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 6.00000 | + | 10.3923i | 0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.50000 | − | 2.59808i | −0.0886969 | − | 0.153627i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.0000 | −0.643726 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 0.500000 | + | 0.866025i | 0.0290619 | + | 0.0503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.50000 | + | 7.79423i | −0.260678 | + | 0.451508i | ||||
\(299\) | −4.50000 | + | 7.79423i | −0.260242 | + | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.50000 | − | 6.06218i | 0.201402 | − | 0.348839i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.00000 | 0.401478 | ||||||||
\(305\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.0000 | −1.36311 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | + | 8.66025i | −0.282617 | + | 0.489506i | −0.972028 | − | 0.234863i | \(-0.924536\pi\) |
0.689412 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | + | 7.79423i | 0.251952 | + | 0.436393i | ||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0000 | 1.16847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | + | 3.46410i | −0.110940 | + | 0.192154i | ||||
\(326\) | −19.0000 | −1.05231 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.50000 | + | 2.59808i | −0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | + | 6.92820i | −0.219860 | + | 0.380808i | −0.954765 | − | 0.297361i | \(-0.903893\pi\) |
0.734905 | + | 0.678170i | \(0.237227\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.50000 | + | 12.9904i | 0.410382 | + | 0.710802i | ||||
\(335\) | 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 | \(0.0514616\pi\) | |||||||
\(338\) | −12.0000 | −0.652714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | 0.488094 | ||||||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5000 | + | 19.9186i | 0.615581 | + | 1.06622i | 0.990282 | + | 0.139072i | \(0.0444119\pi\) |
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | 3.00000 | 0.159674 | 0.0798369 | − | 0.996808i | \(-0.474560\pi\) | ||||
0.0798369 | + | 0.996808i | \(0.474560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.0000 | −1.91068 | ||||||||
\(356\) | −1.50000 | + | 2.59808i | −0.0794998 | + | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.5000 | − | 18.1865i | −0.554942 | − | 0.961188i | ||||
\(359\) | 4.50000 | + | 7.79423i | 0.237501 | + | 0.411364i | 0.959997 | − | 0.280012i | \(-0.0903384\pi\) |
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 1.00000 | − | 1.73205i | 0.0525588 | − | 0.0910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.5000 | − | 28.5788i | 0.863649 | − | 1.49588i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0000 | −0.887393 | −0.443696 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443696 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(368\) | −4.50000 | + | 7.79423i | −0.234579 | + | 0.406302i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.00000 | −0.155963 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | −0.673114 | −0.336557 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | −4.50000 | − | 7.79423i | −0.232689 | − | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | −10.5000 | + | 18.1865i | −0.538639 | + | 0.932949i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0000 | 0.766464 | 0.383232 | − | 0.923652i | \(-0.374811\pi\) | ||||
0.383232 | + | 0.923652i | \(0.374811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.500000 | + | 0.866025i | −0.0253837 | + | 0.0439658i | ||||
\(389\) | −27.0000 | −1.36895 | −0.684477 | − | 0.729034i | \(-0.739969\pi\) | ||||
−0.684477 | + | 0.729034i | \(0.739969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5000 | + | 23.3827i | −0.682724 | + | 1.18251i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | − | 15.5885i | 0.453413 | − | 0.785335i | ||||
\(395\) | 24.0000 | − | 41.5692i | 1.20757 | − | 2.09157i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.50000 | − | 11.2583i | −0.326226 | − | 0.565039i | 0.655534 | − | 0.755166i | \(-0.272444\pi\) |
−0.981760 | + | 0.190126i | \(0.939110\pi\) | |||||||
\(398\) | −12.5000 | − | 21.6506i | −0.626568 | − | 1.08525i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −27.0000 | −1.34832 | −0.674158 | − | 0.738587i | \(-0.735493\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.50000 | + | 2.59808i | 0.0743522 | + | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0000 | − | 29.4449i | −0.840596 | − | 1.45595i | −0.889392 | − | 0.457146i | \(-0.848872\pi\) |
0.0487958 | − | 0.998809i | \(-0.484462\pi\) | |||||||
\(410\) | −4.50000 | − | 7.79423i | −0.222239 | − | 0.384930i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.50000 | − | 11.2583i | −0.320232 | − | 0.554658i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5000 | + | 23.3827i | 0.662689 | + | 1.14781i | ||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.0000 | 1.02714 | ||||||||
\(419\) | −4.50000 | + | 7.79423i | −0.219839 | + | 0.380773i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5000 | − | 30.3109i | −0.852898 | − | 1.47726i | −0.878582 | − | 0.477592i | \(-0.841510\pi\) |
0.0256838 | − | 0.999670i | \(-0.491824\pi\) | |||||||
\(422\) | −2.50000 | − | 4.33013i | −0.121698 | − | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.50000 | − | 7.79423i | 0.217516 | − | 0.376748i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | −0.144673 | ||||||||
\(431\) | 13.5000 | − | 23.3827i | 0.650272 | − | 1.12630i | −0.332785 | − | 0.943003i | \(-0.607988\pi\) |
0.983057 | − | 0.183301i | \(-0.0586785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.0000 | −0.622587 | ||||||||
\(437\) | −31.5000 | − | 54.5596i | −1.50685 | − | 2.60994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.00000 | 0.142695 | ||||||||
\(443\) | 18.0000 | − | 31.1769i | 0.855206 | − | 1.48126i | −0.0212481 | − | 0.999774i | \(-0.506764\pi\) |
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | − | 7.79423i | −0.213320 | − | 0.369482i | ||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 9.00000 | 0.423324 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.50000 | − | 2.59808i | 0.0703985 | − | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | −6.50000 | + | 11.2583i | −0.303725 | + | 0.526067i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.5000 | − | 23.3827i | −0.629441 | − | 1.09022i | ||||
\(461\) | 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 | \(0.568390\pi\) |
−0.739511 | + | 0.673145i | \(0.764943\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | −0.138972 | ||||||||
\(467\) | 1.50000 | + | 2.59808i | 0.0694117 | + | 0.120225i | 0.898642 | − | 0.438682i | \(-0.144554\pi\) |
−0.829231 | + | 0.558906i | \(0.811221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.50000 | + | 2.59808i | 0.0689701 | + | 0.119460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | − | 24.2487i | −0.642364 | − | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.50000 | − | 2.59808i | −0.0686084 | − | 0.118833i | ||||
\(479\) | −3.00000 | −0.137073 | −0.0685367 | − | 0.997649i | \(-0.521833\pi\) | ||||
−0.0685367 | + | 0.997649i | \(0.521833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | −0.0455961 | ||||||||
\(482\) | −6.50000 | + | 11.2583i | −0.296067 | + | 0.512803i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −1.50000 | − | 2.59808i | −0.0681115 | − | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5000 | − | 21.6506i | 0.566429 | − | 0.981084i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.996915 | − | 0.0784867i | \(-0.0250088\pi\) | |||||||
\(488\) | 1.00000 | − | 1.73205i | 0.0452679 | − | 0.0784063i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | −3.50000 | + | 6.06218i | −0.157472 | + | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0000 | −1.11915 | −0.559577 | − | 0.828778i | \(-0.689036\pi\) | ||||
−0.559577 | + | 0.828778i | \(0.689036\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.00000 | + | 10.3923i | −0.267793 | + | 0.463831i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | −13.5000 | + | 23.3827i | −0.600148 | + | 1.03949i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | + | 3.46410i | 0.0887357 | + | 0.153695i | ||||
\(509\) | −9.00000 | −0.398918 | −0.199459 | − | 0.979906i | \(-0.563918\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.5000 | − | 18.1865i | 0.463135 | − | 0.802174i | ||||
\(515\) | 39.0000 | 1.71855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50000 | + | 2.59808i | −0.0657794 | + | 0.113933i | ||||
\(521\) | −1.50000 | + | 2.59808i | −0.0657162 | + | 0.113824i | −0.897011 | − | 0.442007i | \(-0.854267\pi\) |
0.831295 | + | 0.555831i | \(0.187600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.50000 | − | 6.06218i | −0.153044 | − | 0.265081i | 0.779301 | − | 0.626650i | \(-0.215574\pi\) |
−0.932345 | + | 0.361569i | \(0.882241\pi\) | |||||||
\(524\) | −7.50000 | − | 12.9904i | −0.327639 | − | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.50000 | − | 7.79423i | 0.196209 | − | 0.339845i | ||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 58.0000 | 2.52174 | ||||||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.50000 | − | 2.59808i | −0.0649722 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5000 | + | 23.3827i | 0.583656 | + | 1.01092i | ||||
\(536\) | 2.00000 | + | 3.46410i | 0.0863868 | + | 0.149626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.50000 | − | 12.9904i | −0.323348 | − | 0.560055i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50000 | − | 9.52628i | −0.236463 | − | 0.409567i | 0.723234 | − | 0.690604i | \(-0.242655\pi\) |
−0.959697 | + | 0.281037i | \(0.909322\pi\) | |||||||
\(542\) | −5.00000 | −0.214768 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 19.5000 | − | 33.7750i | 0.835288 | − | 1.44676i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.50000 | − | 9.52628i | −0.235163 | − | 0.407314i | 0.724157 | − | 0.689635i | \(-0.242229\pi\) |
−0.959320 | + | 0.282321i | \(0.908896\pi\) | |||||||
\(548\) | −4.50000 | − | 7.79423i | −0.192230 | − | 0.332953i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | + | 10.3923i | −0.255841 | + | 0.443129i | ||||
\(551\) | 10.5000 | − | 18.1865i | 0.447315 | − | 0.774772i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.500000 | − | 0.866025i | 0.0212430 | − | 0.0367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | 0.296866 | ||||||||
\(557\) | −4.50000 | + | 7.79423i | −0.190671 | + | 0.330252i | −0.945473 | − | 0.325701i | \(-0.894400\pi\) |
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.0000 | 0.885832 | ||||||||
\(563\) | −6.00000 | − | 10.3923i | −0.252870 | − | 0.437983i | 0.711445 | − | 0.702742i | \(-0.248041\pi\) |
−0.964315 | + | 0.264758i | \(0.914708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5000 | + | 23.3827i | −0.567949 | + | 0.983717i | ||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 3.00000 | 0.125436 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.0000 | 1.50130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5000 | + | 21.6506i | −0.520382 | + | 0.901328i | 0.479337 | + | 0.877631i | \(0.340877\pi\) |
−0.999719 | + | 0.0236970i | \(0.992456\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.50000 | − | 7.79423i | 0.186852 | − | 0.323638i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 5.50000 | − | 9.52628i | 0.227592 | − | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | −1.50000 | − | 2.59808i | −0.0619116 | − | 0.107234i | 0.833408 | − | 0.552658i | \(-0.186386\pi\) |
−0.895320 | + | 0.445424i | \(0.853053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | − | 48.4974i | 1.15372 | − | 1.99830i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | −19.5000 | − | 33.7750i | −0.800769 | − | 1.38697i | −0.919111 | − | 0.394000i | \(-0.871091\pi\) |
0.118342 | − | 0.992973i | \(-0.462242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.50000 | − | 7.79423i | −0.184327 | − | 0.319264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.50000 | − | 7.79423i | −0.184019 | − | 0.318730i | ||||
\(599\) | −12.0000 | − | 20.7846i | −0.490307 | − | 0.849236i | 0.509631 | − | 0.860393i | \(-0.329782\pi\) |
−0.999938 | + | 0.0111569i | \(0.996449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5000 | − | 21.6506i | −0.509886 | − | 0.883148i | −0.999934 | − | 0.0114528i | \(-0.996354\pi\) |
0.490049 | − | 0.871695i | \(-0.336979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.50000 | + | 6.06218i | 0.142413 | + | 0.246667i | ||||
\(605\) | −6.00000 | −0.243935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0000 | 0.527654 | 0.263827 | − | 0.964570i | \(-0.415015\pi\) | ||||
0.263827 | + | 0.964570i | \(0.415015\pi\) | |||||||
\(608\) | −3.50000 | + | 6.06218i | −0.141944 | + | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.00000 | + | 5.19615i | 0.121466 | + | 0.210386i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5000 | + | 19.9186i | −0.464481 | + | 0.804504i | −0.999178 | − | 0.0405396i | \(-0.987092\pi\) |
0.534697 | + | 0.845044i | \(0.320426\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.5000 | + | 38.9711i | −0.905816 | + | 1.56892i | −0.0859976 | + | 0.996295i | \(0.527408\pi\) |
−0.819818 | + | 0.572624i | \(0.805926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.0000 | −0.683288 | −0.341644 | − | 0.939829i | \(-0.610984\pi\) | ||||
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | 12.0000 | − | 20.7846i | 0.481932 | − | 0.834730i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0000 | + | 19.0526i | −0.438948 | + | 0.760280i | ||||
\(629\) | −3.00000 | −0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 8.00000 | − | 13.8564i | 0.318223 | − | 0.551178i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | −12.0000 | −0.476205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.50000 | + | 2.59808i | −0.0592927 | + | 0.102698i | ||||
\(641\) | 33.0000 | 1.30342 | 0.651711 | − | 0.758468i | \(-0.274052\pi\) | ||||
0.651711 | + | 0.758468i | \(0.274052\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5000 | + | 18.1865i | −0.413117 | + | 0.715540i | ||||
\(647\) | 10.5000 | − | 18.1865i | 0.412798 | − | 0.714986i | −0.582397 | − | 0.812905i | \(-0.697885\pi\) |
0.995194 | + | 0.0979182i | \(0.0312184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.00000 | − | 3.46410i | −0.0784465 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.50000 | − | 16.4545i | 0.372049 | − | 0.644407i | ||||
\(653\) | −15.0000 | −0.586995 | −0.293498 | − | 0.955960i | \(-0.594819\pi\) | ||||
−0.293498 | + | 0.955960i | \(0.594819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.0000 | 1.75830 | ||||||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | ||||||||
\(661\) | −11.0000 | − | 19.0526i | −0.427850 | − | 0.741059i | 0.568831 | − | 0.822454i | \(-0.307396\pi\) |
−0.996682 | + | 0.0813955i | \(0.974062\pi\) | |||||||
\(662\) | −4.00000 | − | 6.92820i | −0.155464 | − | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.50000 | + | 7.79423i | 0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5000 | + | 23.3827i | 0.522722 | + | 0.905381i | ||||
\(668\) | −15.0000 | −0.580367 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0000 | −0.463600 | ||||||||
\(671\) | 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 | \(-0.402340\pi\) | |||||||
\(674\) | 6.50000 | + | 11.2583i | 0.250371 | + | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 15.0000 | − | 25.9808i | 0.576497 | − | 0.998522i | −0.419380 | − | 0.907811i | \(-0.637753\pi\) |
0.995877 | − | 0.0907112i | \(-0.0289140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.50000 | + | 7.79423i | −0.172567 | + | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.0000 | −0.919007 | ||||||||
\(683\) | −4.50000 | + | 7.79423i | −0.172188 | + | 0.298238i | −0.939184 | − | 0.343413i | \(-0.888417\pi\) |
0.766997 | + | 0.641651i | \(0.221750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.0000 | 1.03162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | 1.50000 | + | 2.59808i | 0.0571454 | + | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0000 | − | 38.1051i | 0.836919 | − | 1.44959i | −0.0555386 | − | 0.998457i | \(-0.517688\pi\) |
0.892458 | − | 0.451130i | \(-0.148979\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −10.5000 | + | 18.1865i | −0.398288 | + | 0.689855i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.50000 | − | 7.79423i | −0.170450 | − | 0.295227i | ||||
\(698\) | −23.0000 | −0.870563 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.50000 | − | 6.06218i | 0.132005 | − | 0.228639i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.50000 | + | 2.59808i | −0.0564532 | + | 0.0977799i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 18.0000 | − | 31.1769i | 0.675528 | − | 1.17005i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.50000 | − | 2.59808i | −0.0562149 | − | 0.0973670i | ||||
\(713\) | 36.0000 | + | 62.3538i | 1.34821 | + | 2.33517i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.50000 | + | 7.79423i | −0.168290 | + | 0.291488i | ||||
\(716\) | 21.0000 | 0.784807 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.00000 | −0.335877 | ||||||||
\(719\) | 7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | − | 25.9808i | −0.558242 | − | 0.966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.00000 | + | 1.73205i | 0.0371647 | + | 0.0643712i | ||||
\(725\) | 6.00000 | + | 10.3923i | 0.222834 | + | 0.385961i | ||||
\(726\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.5000 | + | 28.5788i | 0.610692 | + | 1.05775i | ||||
\(731\) | −3.00000 | −0.110959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | 0.0369358 | 0.0184679 | − | 0.999829i | \(-0.494121\pi\) | ||||
0.0184679 | + | 0.999829i | \(0.494121\pi\) | |||||||
\(734\) | 8.50000 | − | 14.7224i | 0.313741 | − | 0.543415i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.50000 | − | 7.79423i | −0.165872 | − | 0.287299i | ||||
\(737\) | 6.00000 | + | 10.3923i | 0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5000 | + | 19.9186i | −0.423034 | + | 0.732717i | −0.996235 | − | 0.0866983i | \(-0.972368\pi\) |
0.573200 | + | 0.819415i | \(0.305702\pi\) | |||||||
\(740\) | 1.50000 | − | 2.59808i | 0.0551411 | − | 0.0955072i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(745\) | 27.0000 | 0.989203 | ||||||||
\(746\) | 6.50000 | − | 11.2583i | 0.237982 | − | 0.412197i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.00000 | 0.329073 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | −0.474377 | −0.237188 | − | 0.971464i | \(-0.576226\pi\) | ||||
−0.237188 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.50000 | − | 2.59808i | 0.0546268 | − | 0.0946164i | ||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 14.0000 | − | 24.2487i | 0.508503 | − | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.5000 | − | 18.1865i | −0.380875 | − | 0.659695i | ||||
\(761\) | −45.0000 | −1.63125 | −0.815624 | − | 0.578582i | \(-0.803606\pi\) | ||||
−0.815624 | + | 0.578582i | \(0.803606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5000 | − | 19.9186i | 0.414701 | − | 0.718283i | −0.580696 | − | 0.814120i | \(-0.697220\pi\) |
0.995397 | + | 0.0958377i | \(0.0305530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | + | 12.1244i | −0.251936 | + | 0.436365i | ||||
\(773\) | −13.5000 | + | 23.3827i | −0.485561 | + | 0.841017i | −0.999862 | − | 0.0165929i | \(-0.994718\pi\) |
0.514301 | + | 0.857610i | \(0.328051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0000 | + | 27.7128i | 0.574737 | + | 0.995474i | ||||
\(776\) | −0.500000 | − | 0.866025i | −0.0179490 | − | 0.0310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.5000 | − | 23.3827i | 0.483998 | − | 0.838310i | ||||
\(779\) | 21.0000 | 0.752403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | −13.5000 | − | 23.3827i | −0.482759 | − | 0.836163i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.0000 | − | 57.1577i | −1.17782 | − | 2.04004i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | − | 24.2487i | −0.499046 | − | 0.864373i | 0.500953 | − | 0.865474i | \(-0.332983\pi\) |
−0.999999 | + | 0.00110111i | \(0.999650\pi\) | |||||||
\(788\) | 9.00000 | + | 15.5885i | 0.320612 | + | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.0000 | + | 41.5692i | 0.853882 | + | 1.47897i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 13.0000 | 0.461353 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.0000 | 0.886102 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.5000 | − | 23.3827i | 0.476702 | − | 0.825671i | ||||
\(803\) | 16.5000 | − | 28.5788i | 0.582272 | − | 1.00853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | − | 6.92820i | 0.140894 | − | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.00000 | 0.105540 | ||||||||
\(809\) | −16.5000 | + | 28.5788i | −0.580109 | + | 1.00478i | 0.415357 | + | 0.909659i | \(0.363657\pi\) |
−0.995466 | + | 0.0951198i | \(0.969677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | −0.105150 | ||||||||
\(815\) | 28.5000 | + | 49.3634i | 0.998311 | + | 1.72913i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50000 | − | 6.06218i | 0.122449 | − | 0.212089i | ||||
\(818\) | 34.0000 | 1.18878 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 13.0000 | 0.452876 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | −27.0000 | −0.937184 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.500000 | + | 0.866025i | −0.0173344 | + | 0.0300240i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.5000 | − | 38.9711i | 0.778645 | − | 1.34865i | ||||
\(836\) | −10.5000 | + | 18.1865i | −0.363150 | + | 0.628994i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.50000 | − | 7.79423i | −0.155450 | − | 0.269247i | ||||
\(839\) | −7.50000 | − | 12.9904i | −0.258929 | − | 0.448478i | 0.707026 | − | 0.707187i | \(-0.250036\pi\) |
−0.965955 | + | 0.258709i | \(0.916703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 35.0000 | 1.20618 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.00000 | 0.172107 | ||||||||
\(845\) | 18.0000 | + | 31.1769i | 0.619219 | + | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.50000 | + | 2.59808i | 0.0515102 | + | 0.0892183i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | − | 10.3923i | −0.205798 | − | 0.356453i | ||||
\(851\) | 4.50000 | + | 7.79423i | 0.154258 | + | 0.267183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.500000 | − | 0.866025i | −0.0171197 | − | 0.0296521i | 0.857339 | − | 0.514753i | \(-0.172116\pi\) |
−0.874458 | + | 0.485101i | \(0.838783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.50000 | + | 7.79423i | 0.153807 | + | 0.266401i | ||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0000 | 0.852989 | 0.426494 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426494 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(860\) | 1.50000 | − | 2.59808i | 0.0511496 | − | 0.0885937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.5000 | + | 23.3827i | 0.459812 | + | 0.796417i | ||||
\(863\) | −25.5000 | − | 44.1673i | −0.868030 | − | 1.50347i | −0.864007 | − | 0.503480i | \(-0.832053\pi\) |
−0.00402340 | − | 0.999992i | \(-0.501281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | 1.00000 | − | 1.73205i | 0.0339814 | − | 0.0588575i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | − | 41.5692i | 0.814144 | − | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | −0.135535 | ||||||||
\(872\) | 6.50000 | − | 11.2583i | 0.220118 | − | 0.381255i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 63.0000 | 2.13101 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.0000 | 1.58708 | 0.793539 | − | 0.608520i | \(-0.208236\pi\) | ||||
0.793539 | + | 0.608520i | \(0.208236\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.50000 | + | 7.79423i | −0.151695 | + | 0.262743i | ||||
\(881\) | −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 | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | −1.50000 | + | 2.59808i | −0.0504505 | + | 0.0873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | −33.0000 | −1.10803 | −0.554016 | − | 0.832506i | \(-0.686905\pi\) | ||||
−0.554016 | + | 0.832506i | \(0.686905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.500000 | + | 0.866025i | −0.0167412 | + | 0.0289967i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5000 | + | 54.5596i | −1.05293 | + | 1.82373i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | − | 5.19615i | 0.100111 | − | 0.173398i | ||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.50000 | + | 7.79423i | 0.149917 | + | 0.259663i | ||||
\(902\) | −4.50000 | − | 7.79423i | −0.149834 | − | 0.259519i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.50000 | + | 7.79423i | −0.149668 | + | 0.259232i | ||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.0000 | −1.42779 | −0.713896 | − | 0.700252i | \(-0.753071\pi\) | ||||
−0.713896 | + | 0.700252i | \(0.753071\pi\) | |||||||
\(908\) | 1.50000 | + | 2.59808i | 0.0497792 | + | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(913\) | 13.5000 | + | 23.3827i | 0.446785 | + | 0.773854i | ||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.50000 | − | 11.2583i | −0.214766 | − | 0.371986i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5000 | − | 45.8993i | −0.874154 | − | 1.51408i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) |
−0.0164935 | − | 0.999864i | \(-0.505250\pi\) | |||||||
\(920\) | 27.0000 | 0.890164 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.00000 | −0.296399 | ||||||||
\(923\) | 6.00000 | − | 10.3923i | 0.197492 | − | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | −20.5000 | − | 35.5070i | −0.673672 | − | 1.16683i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | − | 2.59808i | 0.0491341 | − | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.00000 | −0.0981630 | ||||||||
\(935\) | −13.5000 | + | 23.3827i | −0.441497 | + | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.5000 | + | 23.3827i | −0.439620 | + | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.00000 | −0.0975384 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | + | 9.52628i | 0.178538 | + | 0.309236i | ||||
\(950\) | 28.0000 | 0.908440 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | 0.0970269 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.50000 | − | 2.59808i | 0.0484628 | − | 0.0839400i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0.500000 | − | 0.866025i | 0.0161206 | − | 0.0279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.50000 | − | 11.2583i | −0.209351 | − | 0.362606i | ||||
\(965\) | −21.0000 | − | 36.3731i | −0.676014 | − | 1.17089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5000 | + | 35.5070i | −0.659236 | + | 1.14183i | 0.321578 | + | 0.946883i | \(0.395787\pi\) |
−0.980814 | + | 0.194946i | \(0.937547\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.00000 | 0.0963242 | ||||||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.5000 | + | 21.6506i | 0.400526 | + | 0.693731i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | −15.0000 | − | 25.9808i | −0.479893 | − | 0.831198i | 0.519841 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230645i | \(0.992658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.50000 | − | 7.79423i | −0.143821 | − | 0.249105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.5000 | + | 18.1865i | 0.335068 | + | 0.580356i | ||||
\(983\) | −15.0000 | −0.478426 | −0.239213 | − | 0.970967i | \(-0.576889\pi\) | ||||
−0.239213 | + | 0.970967i | \(0.576889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.0000 | −1.72058 | ||||||||
\(986\) | 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 | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5000 | − | 21.6506i | 0.397076 | − | 0.687755i | −0.596288 | − | 0.802771i | \(-0.703358\pi\) |
0.993364 | + | 0.115015i | \(0.0366917\pi\) | |||||||
\(992\) | 4.00000 | − | 6.92820i | 0.127000 | − | 0.219971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.5000 | + | 64.9519i | −1.18883 | + | 2.05911i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | 0.411714 | 0.205857 | − | 0.978582i | \(-0.434002\pi\) | ||||
0.205857 | + | 0.978582i | \(0.434002\pi\) | |||||||
\(998\) | 12.5000 | − | 21.6506i | 0.395681 | − | 0.685339i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))