Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(883,2646)]
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([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.f (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: | \(1\) |
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 | 1765.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1765 |
Dual form | 2646.2.f.d.883.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 1.50000 | + | 2.59808i | 0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | −4.50000 | + | 7.79423i | −0.938315 | + | 1.62521i | −0.169701 | + | 0.985496i | \(0.554280\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 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 | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −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 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 3.50000 | + | 6.06218i | 0.567775 | + | 0.983415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.00000 | 1.32698 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.00000 | −1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.50000 | − | 2.59808i | 0.196960 | − | 0.341144i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 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 | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 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 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 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 | 0.827401 | + | 0.561611i | \(0.189818\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | −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 | ||||
\(86\) | 0.500000 | − | 0.866025i | 0.0539164 | − | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 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 | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.50000 | − | 11.2583i | 0.640464 | − | 1.10932i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 0.500000 | − | 0.866025i | 0.0490290 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.50000 | + | 2.59808i | 0.145693 | + | 0.252347i | ||||
\(107\) | −9.00000 | −0.870063 | −0.435031 | − | 0.900415i | \(-0.643263\pi\) | ||||
−0.435031 | + | 0.900415i | \(0.643263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0000 | −1.24517 | −0.622587 | − | 0.782551i | \(-0.713918\pi\) | ||||
−0.622587 | + | 0.782551i | \(0.713918\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 13.5000 | + | 23.3827i | 1.25888 | + | 2.18045i | ||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −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 | ||||
\(131\) | 7.50000 | − | 12.9904i | 0.655278 | − | 1.13497i | −0.326546 | − | 0.945181i | \(-0.605885\pi\) |
0.981824 | − | 0.189794i | \(-0.0607819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | − | 6.06218i | 0.296866 | − | 0.514187i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.975417 | + | 0.220366i | \(0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | −3.00000 | −0.250873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | −5.50000 | − | 9.52628i | −0.455183 | − | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.500000 | − | 0.866025i | 0.0410997 | − | 0.0711868i | ||||
\(149\) | −4.50000 | + | 7.79423i | −0.368654 | + | 0.638528i | −0.989355 | − | 0.145519i | \(-0.953515\pi\) |
0.620701 | + | 0.784047i | \(0.286848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50000 | + | 6.06218i | 0.284826 | + | 0.493333i | 0.972567 | − | 0.232623i | \(-0.0747309\pi\) |
−0.687741 | + | 0.725956i | \(0.741398\pi\) | |||||||
\(152\) | −7.00000 | −0.567775 | ||||||||
\(153\) | 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 | 0.0242497 | − | 0.999706i | \(-0.492280\pi\) |
0.853646 | − | 0.520854i | \(-0.174386\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −19.0000 | −1.48819 | −0.744097 | − | 0.668071i | \(-0.767120\pi\) | ||||
−0.744097 | + | 0.668071i | \(0.767120\pi\) | |||||||
\(164\) | 1.50000 | + | 2.59808i | 0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | −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 | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.50000 | + | 2.59808i | 0.112430 | + | 0.194734i | ||||
\(179\) | 21.0000 | 1.56961 | 0.784807 | − | 0.619740i | \(-0.212762\pi\) | ||||
0.784807 | + | 0.619740i | \(0.212762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | −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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 0.500000 | − | 0.866025i | 0.0358979 | − | 0.0621770i | ||||
\(195\) | 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 | ||||||||
\(199\) | −25.0000 | −1.77220 | −0.886102 | − | 0.463491i | \(-0.846597\pi\) | ||||
−0.886102 | + | 0.463491i | \(0.846597\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 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 | ||||
\(206\) | −13.0000 | −0.905753 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 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 | \(0.221724\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 3.00000 | 0.204598 | ||||||||
\(216\) | 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 | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | 0.598671 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.50000 | − | 11.2583i | 0.429532 | − | 0.743971i | −0.567300 | − | 0.823511i | \(-0.692012\pi\) |
0.996832 | + | 0.0795401i | \(0.0253452\pi\) | |||||||
\(230\) | 13.5000 | − | 23.3827i | 0.890164 | − | 1.54181i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | + | 2.59808i | 0.0984798 | + | 0.170572i | ||||
\(233\) | −3.00000 | −0.196537 | −0.0982683 | − | 0.995160i | \(-0.531330\pi\) | ||||
−0.0982683 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(234\) | 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 | ||||||||
\(241\) | 6.50000 | + | 11.2583i | 0.418702 | + | 0.725213i | 0.995809 | − | 0.0914555i | \(-0.0291519\pi\) |
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50000 | + | 6.06218i | −0.222700 | + | 0.385727i | ||||
\(248\) | −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 | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.00000 | 0.186052 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.0000 | −0.926703 | ||||||||
\(263\) | 4.50000 | + | 7.79423i | 0.277482 | + | 0.480613i | 0.970758 | − | 0.240059i | \(-0.0771668\pi\) |
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(264\) | 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 | ||||
\(269\) | −15.0000 | −0.914566 | −0.457283 | − | 0.889321i | \(-0.651177\pi\) | ||||
−0.457283 | + | 0.889321i | \(0.651177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.00000 | 0.303728 | 0.151864 | − | 0.988401i | \(-0.451472\pi\) | ||||
0.151864 | + | 0.988401i | \(0.451472\pi\) | |||||||
\(272\) | 1.50000 | + | 2.59808i | 0.0909509 | + | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.50000 | + | 7.79423i | −0.271855 | + | 0.470867i | ||||
\(275\) | −6.00000 | + | 10.3923i | −0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | 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 | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 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 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −4.50000 | − | 7.79423i | −0.264249 | − | 0.457693i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.50000 | + | 9.52628i | −0.321863 | + | 0.557483i | ||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.00000 | 0.521356 | ||||||||
\(299\) | 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 | ||||||||
\(304\) | 3.50000 | + | 6.06218i | 0.200739 | + | 0.347690i | ||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0000 | − | 20.7846i | 0.681554 | − | 1.18049i | ||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 1.50000 | − | 2.59808i | 0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0000 | 1.16847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 9.50000 | + | 16.4545i | 0.526156 | + | 0.911330i | ||||
\(327\) | 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 | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 9.00000 | 0.493939 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.0000 | 0.820763 | ||||||||
\(335\) | −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 | \(0.0514616\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.50000 | − | 7.79423i | −0.244047 | − | 0.422701i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 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 | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 1.50000 | + | 2.59808i | 0.0798369 | + | 0.138282i | 0.903179 | − | 0.429263i | \(-0.141227\pi\) |
−0.823343 | + | 0.567545i | \(0.807893\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | + | 31.1769i | −0.955341 | + | 1.65470i | ||||
\(356\) | 1.50000 | − | 2.59808i | 0.0794998 | − | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.5000 | − | 18.1865i | −0.554942 | − | 0.961188i | ||||
\(359\) | −9.00000 | −0.475002 | −0.237501 | − | 0.971387i | \(-0.576328\pi\) | ||||
−0.237501 | + | 0.971387i | \(0.576328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −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 | ||||||||
\(367\) | −8.50000 | − | 14.7224i | −0.443696 | − | 0.768505i | 0.554264 | − | 0.832341i | \(-0.313000\pi\) |
−0.997960 | + | 0.0638362i | \(0.979666\pi\) | |||||||
\(368\) | 9.00000 | 0.469157 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.00000 | 0.155963 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50000 | − | 11.2583i | 0.336557 | − | 0.582934i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
0.983783 | + | 0.179364i | \(0.0574041\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | 7.50000 | − | 12.9904i | 0.383232 | − | 0.663777i | −0.608290 | − | 0.793715i | \(-0.708144\pi\) |
0.991522 | + | 0.129937i | \(0.0414776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 13.5000 | + | 23.3827i | 0.684477 | + | 1.18555i | 0.973601 | + | 0.228257i | \(0.0733028\pi\) |
−0.289124 | + | 0.957292i | \(0.593364\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | 48.0000 | 2.41514 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | −0.652451 | −0.326226 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326226 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(398\) | 12.5000 | + | 21.6506i | 0.626568 | + | 1.08525i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 6.92820i | 0.199254 | + | 0.345118i | ||||
\(404\) | −3.00000 | −0.149256 | ||||||||
\(405\) | 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 | −0.0487958 | − | 0.998809i | \(-0.515538\pi\) |
0.889392 | − | 0.457146i | \(-0.151128\pi\) | |||||||
\(410\) | −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 | ||||||||
\(415\) | −27.0000 | −1.32538 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.5000 | − | 18.1865i | 0.513572 | − | 0.889532i | ||||
\(419\) | 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 | \(-0.491824\pi\) | |||||||
\(422\) | 5.00000 | 0.243396 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 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 | ||||||||
\(430\) | −1.50000 | − | 2.59808i | −0.0723364 | − | 0.125290i | ||||
\(431\) | −27.0000 | −1.30054 | −0.650272 | − | 0.759701i | \(-0.725345\pi\) | ||||
−0.650272 | + | 0.759701i | \(0.725345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.50000 | − | 11.2583i | 0.311294 | − | 0.539176i | ||||
\(437\) | 31.5000 | − | 54.5596i | 1.50685 | − | 2.60994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | −9.00000 | −0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.00000 | 0.142695 | ||||||||
\(443\) | 18.0000 | + | 31.1769i | 0.855206 | + | 1.48126i | 0.876454 | + | 0.481486i | \(0.159903\pi\) |
−0.0212481 | + | 0.999774i | \(0.506764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | + | 7.79423i | −0.213320 | + | 0.369482i | ||||
\(446\) | 0.500000 | − | 0.866025i | 0.0236757 | − | 0.0410075i | ||||
\(447\) | 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 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | −4.50000 | − | 7.79423i | −0.211662 | − | 0.366610i | ||||
\(453\) | 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 | 0.958950 | − | 0.283577i | \(-0.0915211\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | −13.0000 | −0.607450 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −27.0000 | −1.25888 | ||||||||
\(461\) | −4.50000 | − | 7.79423i | −0.209586 | − | 0.363013i | 0.741998 | − | 0.670402i | \(-0.233878\pi\) |
−0.951584 | + | 0.307388i | \(0.900545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5000 | + | 35.5070i | −0.952716 | + | 1.65015i | −0.213205 | + | 0.977007i | \(0.568390\pi\) |
−0.739511 | + | 0.673145i | \(0.764943\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50000 | + | 2.59808i | 0.0694862 | + | 0.120354i | ||||
\(467\) | 3.00000 | 0.138823 | 0.0694117 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | 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 | ||||||||
\(478\) | 3.00000 | 0.137217 | ||||||||
\(479\) | −1.50000 | − | 2.59808i | −0.0685367 | − | 0.118709i | 0.829721 | − | 0.558179i | \(-0.188500\pi\) |
−0.898257 | + | 0.439470i | \(0.855166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.500000 | + | 0.866025i | −0.0227980 | + | 0.0394874i | ||||
\(482\) | 6.50000 | − | 11.2583i | 0.296067 | − | 0.512803i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 3.00000 | 0.136223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0000 | −1.13286 | −0.566429 | − | 0.824110i | \(-0.691675\pi\) | ||||
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | −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 | ||||||||
\(493\) | −4.50000 | − | 7.79423i | −0.202670 | − | 0.351034i | ||||
\(494\) | 7.00000 | 0.314945 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | − | 21.6506i | 0.559577 | − | 0.969216i | −0.437955 | − | 0.898997i | \(-0.644297\pi\) |
0.997532 | − | 0.0702185i | \(-0.0223697\pi\) | |||||||
\(500\) | −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 | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 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 | ||||
\(509\) | −4.50000 | + | 7.79423i | −0.199459 | + | 0.345473i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.0000 | 0.926270 | ||||||||
\(515\) | −19.5000 | − | 33.7750i | −0.859273 | − | 1.48830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50000 | − | 2.59808i | −0.0657794 | − | 0.113933i | ||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | −0.306089 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(524\) | 7.50000 | + | 12.9904i | 0.327639 | + | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.50000 | − | 7.79423i | 0.196209 | − | 0.339845i | ||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 9.00000 | 0.390935 | ||||||||
\(531\) | 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 | ||||||||
\(541\) | 11.0000 | 0.472927 | 0.236463 | − | 0.971640i | \(-0.424012\pi\) | ||||
0.236463 | + | 0.971640i | \(0.424012\pi\) | |||||||
\(542\) | −2.50000 | − | 4.33013i | −0.107384 | − | 0.185995i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | −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 | \(0.908896\pi\) | |||||||
\(548\) | 9.00000 | 0.384461 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.0000 | 0.511682 | ||||||||
\(551\) | −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 | ||||||||
\(556\) | 3.50000 | + | 6.06218i | 0.148433 | + | 0.257094i | ||||
\(557\) | 9.00000 | 0.381342 | 0.190671 | − | 0.981654i | \(-0.438934\pi\) | ||||
0.190671 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5000 | + | 18.1865i | −0.442916 | + | 0.767153i | ||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | 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 | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 1.50000 | − | 2.59808i | 0.0627182 | − | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.0000 | 1.50130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0000 | −1.04076 | −0.520382 | − | 0.853934i | \(-0.674210\pi\) | ||||
−0.520382 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 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 | ||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | 0.371787 | ||||||||
\(587\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | −39.0000 | −1.60154 | −0.800769 | − | 0.598973i | \(-0.795576\pi\) | ||||
−0.800769 | + | 0.598973i | \(0.795576\pi\) | |||||||
\(594\) | 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 | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.00000 | −0.284826 | ||||||||
\(605\) | −3.00000 | − | 5.19615i | −0.121967 | − | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | − | 11.2583i | 0.263827 | − | 0.456962i | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 23.0000 | 0.928961 | 0.464481 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464481 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −8.50000 | − | 14.7224i | −0.341644 | − | 0.591744i | 0.643094 | − | 0.765787i | \(-0.277650\pi\) |
−0.984738 | + | 0.174042i | \(0.944317\pi\) | |||||||
\(620\) | −24.0000 | −0.963863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 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 | ||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5000 | + | 25.1147i | −0.571824 | + | 0.990429i | 0.424555 | + | 0.905402i | \(0.360431\pi\) |
−0.996379 | + | 0.0850262i | \(0.972903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5000 | − | 18.1865i | −0.413117 | − | 0.715540i | ||||
\(647\) | 21.0000 | 0.825595 | 0.412798 | − | 0.910823i | \(-0.364552\pi\) | ||||
0.412798 | + | 0.910823i | \(0.364552\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | 7.50000 | − | 12.9904i | 0.293498 | − | 0.508353i | −0.681137 | − | 0.732156i | \(-0.738514\pi\) |
0.974634 | + | 0.223803i | \(0.0718474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.5000 | − | 38.9711i | −0.879148 | − | 1.52273i | ||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | 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 | \(-0.692604\pi\) |
0.996682 | + | 0.0813955i | \(0.0259377\pi\) | |||||||
\(662\) | −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 | ||||||||
\(667\) | −27.0000 | −1.04544 | ||||||||
\(668\) | −7.50000 | − | 12.9904i | −0.290184 | − | 0.502613i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | + | 10.3923i | −0.231800 | + | 0.401490i | ||||
\(671\) | −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 | \(-0.402340\pi\) | |||||||
\(674\) | −13.0000 | −0.500741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −15.0000 | − | 25.9808i | −0.576497 | − | 0.998522i | −0.995877 | − | 0.0907112i | \(-0.971086\pi\) |
0.419380 | − | 0.907811i | \(-0.362247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.50000 | + | 7.79423i | −0.172567 | + | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | − | 20.7846i | −0.459504 | − | 0.795884i | ||||
\(683\) | 9.00000 | 0.344375 | 0.172188 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172188 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.0000 | −1.03162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.500000 | − | 0.866025i | 0.0190623 | − | 0.0330169i | ||||
\(689\) | −1.50000 | + | 2.59808i | −0.0571454 | + | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −11.5000 | + | 19.9186i | −0.435281 | + | 0.753930i | ||||
\(699\) | 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 | ||||||||
\(703\) | 7.00000 | 0.264010 | ||||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 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 | 0.511683 | − | 0.859174i | \(-0.329022\pi\) |
−0.999908 | + | 0.0135434i | \(0.995689\pi\) | |||||||
\(710\) | 36.0000 | 1.35106 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | −0.112430 | ||||||||
\(713\) | −36.0000 | − | 62.3538i | −1.34821 | − | 2.33517i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.50000 | + | 7.79423i | −0.168290 | + | 0.291488i | ||||
\(716\) | −10.5000 | + | 18.1865i | −0.392403 | + | 0.679663i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.50000 | + | 7.79423i | 0.167939 | + | 0.290878i | ||||
\(719\) | 15.0000 | 0.559406 | 0.279703 | − | 0.960087i | \(-0.409764\pi\) | ||||
0.279703 | + | 0.960087i | \(0.409764\pi\) | |||||||
\(720\) | 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 | 0.961020 | − | 0.276479i | \(-0.0891678\pi\) |
−0.719948 | + | 0.694028i | \(0.755834\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33.0000 | −1.22138 | ||||||||
\(731\) | −1.50000 | − | 2.59808i | −0.0554795 | − | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.500000 | − | 0.866025i | 0.0184679 | − | 0.0319874i | −0.856644 | − | 0.515908i | \(-0.827454\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(734\) | −8.50000 | + | 14.7224i | −0.313741 | + | 0.543415i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.50000 | − | 7.79423i | −0.165872 | − | 0.287299i | ||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0000 | 0.846069 | 0.423034 | − | 0.906114i | \(-0.360965\pi\) | ||||
0.423034 | + | 0.906114i | \(0.360965\pi\) | |||||||
\(740\) | −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 | ||||||||
\(745\) | 13.5000 | + | 23.3827i | 0.494602 | + | 0.856675i | ||||
\(746\) | −13.0000 | −0.475964 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 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 | ||||
\(761\) | −22.5000 | + | 38.9711i | −0.815624 | + | 1.41270i | 0.0932544 | + | 0.995642i | \(0.470273\pi\) |
−0.908879 | + | 0.417061i | \(0.863060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.0000 | −0.541972 | ||||||||
\(767\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | − | 12.1244i | −0.251936 | − | 0.436365i | ||||
\(773\) | −27.0000 | −0.971123 | −0.485561 | − | 0.874203i | \(-0.661385\pi\) | ||||
−0.485561 | + | 0.874203i | \(0.661385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | 1.14947 | ||||||||
\(776\) | 0.500000 | + | 0.866025i | 0.0179490 | + | 0.0310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.5000 | − | 23.3827i | 0.483998 | − | 0.838310i | ||||
\(779\) | −10.5000 | + | 18.1865i | −0.376202 | + | 0.651600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | −27.0000 | −0.965518 | ||||||||
\(783\) | 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 | \(-0.667017\pi\) |
0.999999 | + | 0.00110111i | \(0.000350496\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | 6.50000 | + | 11.2583i | 0.230676 | + | 0.399543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.5000 | − | 21.6506i | 0.443051 | − | 0.767386i | ||||
\(797\) | −10.5000 | + | 18.1865i | −0.371929 | + | 0.644200i | −0.989862 | − | 0.142031i | \(-0.954637\pi\) |
0.617933 | + | 0.786231i | \(0.287970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.0000 | −0.953403 | ||||||||
\(803\) | −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 | ||||||||
\(808\) | 1.50000 | + | 2.59808i | 0.0527698 | + | 0.0914000i | ||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.50000 | − | 2.59808i | 0.0525750 | − | 0.0910625i | ||||
\(815\) | −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 | −0.955636 | − | 0.294549i | \(-0.904831\pi\) |
0.222731 | − | 0.974880i | \(-0.428503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 6.50000 | − | 11.2583i | 0.226438 | − | 0.392203i | ||||
\(825\) | 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 | ||||||||
\(829\) | 11.0000 | 0.382046 | 0.191023 | − | 0.981586i | \(-0.438820\pi\) | ||||
0.191023 | + | 0.981586i | \(0.438820\pi\) | |||||||
\(830\) | 13.5000 | + | 23.3827i | 0.468592 | + | 0.811625i | ||||
\(831\) | 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 | ||||
\(836\) | −21.0000 | −0.726300 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.00000 | −0.310900 | ||||||||
\(839\) | 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 | ||||
\(842\) | −17.5000 | + | 30.3109i | −0.603090 | + | 1.04458i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.50000 | − | 4.33013i | −0.0860535 | − | 0.149049i | ||||
\(845\) | 36.0000 | 1.23844 | ||||||||
\(846\) | 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 | 0.874458 | − | 0.485101i | \(-0.161217\pi\) |
−0.857339 | + | 0.514753i | \(0.827884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | 1.50000 | + | 2.59808i | 0.0512390 | + | 0.0887486i | 0.890507 | − | 0.454969i | \(-0.150350\pi\) |
−0.839268 | + | 0.543718i | \(0.817016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5000 | − | 21.6506i | 0.426494 | − | 0.738710i | −0.570064 | − | 0.821600i | \(-0.693082\pi\) |
0.996559 | + | 0.0828900i | \(0.0264150\pi\) | |||||||
\(860\) | −1.50000 | + | 2.59808i | −0.0511496 | + | 0.0885937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.5000 | + | 23.3827i | 0.459812 | + | 0.796417i | ||||
\(863\) | 51.0000 | 1.73606 | 0.868030 | − | 0.496512i | \(-0.165386\pi\) | ||||
0.868030 | + | 0.496512i | \(0.165386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | −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 | ||||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | −13.0000 | −0.440236 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −63.0000 | −2.13101 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5000 | + | 40.7032i | −0.793539 | + | 1.37445i | 0.130224 | + | 0.991485i | \(0.458430\pi\) |
−0.923763 | + | 0.382965i | \(0.874903\pi\) | |||||||
\(878\) | −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 | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 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 | ||||
\(887\) | −16.5000 | + | 28.5788i | −0.554016 | + | 0.959583i | 0.443964 | + | 0.896045i | \(0.353572\pi\) |
−0.997979 | + | 0.0635387i | \(0.979761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 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 | ||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 4.50000 | + | 7.79423i | 0.149834 | + | 0.259519i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.50000 | + | 7.79423i | −0.149668 | + | 0.259232i | ||||
\(905\) | 3.00000 | − | 5.19615i | 0.0997234 | − | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5000 | + | 37.2391i | 0.713896 | + | 1.23650i | 0.963384 | + | 0.268126i | \(0.0864043\pi\) |
−0.249488 | + | 0.968378i | \(0.580262\pi\) | |||||||
\(908\) | 3.00000 | 0.0995585 | ||||||||
\(909\) | 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 | ||||||||
\(919\) | 53.0000 | 1.74831 | 0.874154 | − | 0.485648i | \(-0.161416\pi\) | ||||
0.874154 | + | 0.485648i | \(0.161416\pi\) | |||||||
\(920\) | 13.5000 | + | 23.3827i | 0.445082 | + | 0.770904i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.50000 | + | 7.79423i | −0.148200 | + | 0.256689i | ||||
\(923\) | −6.00000 | + | 10.3923i | −0.197492 | + | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 41.0000 | 1.34734 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.00000 | −0.0984798 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | − | 2.59808i | 0.0491341 | − | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.50000 | − | 2.59808i | −0.0490815 | − | 0.0850117i | ||||
\(935\) | 27.0000 | 0.882994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 5.19615i | −0.0977972 | + | 0.169390i | −0.910773 | − | 0.412908i | \(-0.864513\pi\) |
0.812975 | + | 0.582298i | \(0.197846\pi\) | |||||||
\(942\) | 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 | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | − | 9.52628i | 0.178538 | − | 0.309236i | ||||
\(950\) | 14.0000 | − | 24.2487i | 0.454220 | − | 0.786732i | ||||
\(951\) | 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 | ||||||||
\(956\) | −1.50000 | − | 2.59808i | −0.0485135 | − | 0.0840278i | ||||
\(957\) | 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 | ||||
\(962\) | 1.00000 | 0.0322413 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.0000 | −0.418702 | ||||||||
\(965\) | 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 | \(0.937547\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.50000 | − | 2.59808i | −0.0481621 | − | 0.0834192i | ||||
\(971\) | −33.0000 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(972\) | 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 | −0.999734 | − | 0.0230645i | \(-0.992658\pi\) |
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.50000 | + | 7.79423i | 0.143821 | + | 0.249105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.0000 | −0.670137 | ||||||||
\(983\) | −7.50000 | − | 12.9904i | −0.239213 | − | 0.414329i | 0.721276 | − | 0.692648i | \(-0.243556\pi\) |
−0.960489 | + | 0.278319i | \(0.910223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | + | 46.7654i | −0.860292 | + | 1.49007i | ||||
\(986\) | −4.50000 | + | 7.79423i | −0.143309 | + | 0.248219i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.50000 | − | 6.06218i | −0.111350 | − | 0.192864i | ||||
\(989\) | −9.00000 | −0.286183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0000 | −0.794151 | −0.397076 | − | 0.917786i | \(-0.629975\pi\) | ||||
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(992\) | −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 | ||||||||
\(997\) | 6.50000 | + | 11.2583i | 0.205857 | + | 0.356555i | 0.950405 | − | 0.311014i | \(-0.100668\pi\) |
−0.744548 | + | 0.667568i | \(0.767335\pi\) | |||||||
\(998\) | −25.0000 | −0.791361 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))