Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 214.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.214 |
Dual form | 441.2.h.a.373.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | −2.50000 | − | 4.33013i | −0.693375 | − | 1.20096i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.277350 | − | 0.960769i | \(-0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.50000 | − | 4.33013i | −0.533002 | − | 0.923186i | ||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 5.19615i | 1.06066i | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | −2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 1.50000 | + | 0.866025i | 0.273861 | + | 0.158114i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | −7.50000 | + | 4.33013i | −1.30558 | + | 0.753778i | ||||
\(34\) | 1.50000 | − | 2.59808i | 0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | −7.50000 | + | 4.33013i | −1.20096 | + | 0.693375i | ||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 2.50000 | + | 4.33013i | 0.376889 | + | 0.652791i | ||||
\(45\) | 1.50000 | − | 2.59808i | 0.223607 | − | 0.387298i | ||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | −4.50000 | − | 2.59808i | −0.630126 | − | 0.363803i | ||||
\(52\) | 2.50000 | + | 4.33013i | 0.346688 | + | 0.600481i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50000 | − | 0.866025i | 0.198680 | − | 0.114708i | ||||
\(58\) | 0.500000 | − | 0.866025i | 0.0656532 | − | 0.113715i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −1.50000 | − | 0.866025i | −0.193649 | − | 0.111803i | ||||
\(61\) | 14.0000 | 1.79252 | 0.896258 | − | 0.443533i | \(-0.146275\pi\) | ||||
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | −7.50000 | + | 4.33013i | −0.923186 | + | 0.533002i | ||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | 4.50000 | + | 2.59808i | 0.541736 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 9.00000 | 1.06066 | ||||||||
\(73\) | 1.50000 | − | 2.59808i | 0.175562 | − | 0.304082i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | −1.50000 | − | 2.59808i | −0.174371 | − | 0.302020i | ||||
\(75\) | 6.00000 | − | 3.46410i | 0.692820 | − | 0.400000i | ||||
\(76\) | −0.500000 | − | 0.866025i | −0.0573539 | − | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.50000 | + | 4.33013i | −0.849208 | + | 0.490290i | ||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −2.50000 | − | 4.33013i | −0.276079 | − | 0.478183i | ||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | + | 2.59808i | 0.162698 | + | 0.281801i | ||||
\(86\) | 0.500000 | − | 0.866025i | 0.0539164 | − | 0.0933859i | ||||
\(87\) | −1.50000 | − | 0.866025i | −0.160817 | − | 0.0928477i | ||||
\(88\) | 7.50000 | + | 12.9904i | 0.799503 | + | 1.38478i | ||||
\(89\) | −6.50000 | − | 11.2583i | −0.688999 | − | 1.19338i | −0.972162 | − | 0.234309i | \(-0.924717\pi\) |
0.283164 | − | 0.959072i | \(-0.408616\pi\) | |||||||
\(90\) | 1.50000 | − | 2.59808i | 0.158114 | − | 0.273861i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.50000 | − | 2.59808i | 0.156386 | − | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | − | 8.66025i | − | 0.883883i | ||||||
\(97\) | −4.50000 | + | 7.79423i | −0.456906 | + | 0.791384i | −0.998796 | − | 0.0490655i | \(-0.984376\pi\) |
0.541890 | + | 0.840450i | \(0.317709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.50000 | + | 12.9904i | 0.753778 | + | 1.30558i | ||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | −8.50000 | − | 14.7224i | −0.845782 | − | 1.46494i | −0.884941 | − | 0.465704i | \(-0.845801\pi\) |
0.0391591 | − | 0.999233i | \(-0.487532\pi\) | |||||||
\(102\) | −4.50000 | − | 2.59808i | −0.445566 | − | 0.257248i | ||||
\(103\) | −0.500000 | + | 0.866025i | −0.0492665 | + | 0.0853320i | −0.889607 | − | 0.456727i | \(-0.849022\pi\) |
0.840341 | + | 0.542059i | \(0.182355\pi\) | |||||||
\(104\) | 7.50000 | + | 12.9904i | 0.735436 | + | 1.27381i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.50000 | − | 7.79423i | 0.437079 | − | 0.757042i | ||||
\(107\) | −8.50000 | − | 14.7224i | −0.821726 | − | 1.42327i | −0.904396 | − | 0.426694i | \(-0.859678\pi\) |
0.0826699 | − | 0.996577i | \(-0.473655\pi\) | |||||||
\(108\) | − | 5.19615i | − | 0.500000i | ||||||
\(109\) | 4.50000 | − | 7.79423i | 0.431022 | − | 0.746552i | −0.565940 | − | 0.824447i | \(-0.691487\pi\) |
0.996962 | + | 0.0778949i | \(0.0248199\pi\) | |||||||
\(110\) | 5.00000 | 0.476731 | ||||||||
\(111\) | −4.50000 | + | 2.59808i | −0.427121 | + | 0.246598i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | + | 0.866025i | 0.0470360 | + | 0.0814688i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | 1.50000 | − | 0.866025i | 0.140488 | − | 0.0811107i | ||||
\(115\) | −1.50000 | − | 2.59808i | −0.139876 | − | 0.242272i | ||||
\(116\) | −0.500000 | + | 0.866025i | −0.0464238 | + | 0.0804084i | ||||
\(117\) | 7.50000 | + | 12.9904i | 0.693375 | + | 1.20096i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.50000 | − | 2.59808i | −0.410792 | − | 0.237171i | ||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 14.0000 | 1.26750 | ||||||||
\(123\) | −7.50000 | + | 4.33013i | −0.676252 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | −1.50000 | − | 0.866025i | −0.132068 | − | 0.0762493i | ||||
\(130\) | 5.00000 | 0.438529 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | 7.50000 | − | 4.33013i | 0.652791 | − | 0.376889i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | −4.50000 | − | 2.59808i | −0.387298 | − | 0.223607i | ||||
\(136\) | −4.50000 | + | 7.79423i | −0.385872 | + | 0.668350i | ||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 4.50000 | + | 2.59808i | 0.383065 | + | 0.221163i | ||||
\(139\) | 4.50000 | + | 7.79423i | 0.381685 | + | 0.661098i | 0.991303 | − | 0.131597i | \(-0.0420106\pi\) |
−0.609618 | + | 0.792695i | \(0.708677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | −12.5000 | + | 21.6506i | −1.04530 | + | 1.81052i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0.500000 | + | 0.866025i | 0.0415227 | + | 0.0719195i | ||||
\(146\) | 1.50000 | − | 2.59808i | 0.124141 | − | 0.215018i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.50000 | + | 2.59808i | 0.123299 | + | 0.213561i | ||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | 6.00000 | − | 3.46410i | 0.489898 | − | 0.282843i | ||||
\(151\) | −2.50000 | − | 4.33013i | −0.203447 | − | 0.352381i | 0.746190 | − | 0.665733i | \(-0.231881\pi\) |
−0.949637 | + | 0.313353i | \(0.898548\pi\) | |||||||
\(152\) | −1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | ||||
\(153\) | −4.50000 | + | 7.79423i | −0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.50000 | − | 4.33013i | 0.600481 | − | 0.346688i | ||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | −13.5000 | − | 7.79423i | −1.07062 | − | 0.618123i | ||||
\(160\) | −2.50000 | + | 4.33013i | −0.197642 | + | 0.342327i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 5.50000 | + | 9.52628i | 0.430793 | + | 0.746156i | 0.996942 | − | 0.0781474i | \(-0.0249005\pi\) |
−0.566149 | + | 0.824303i | \(0.691567\pi\) | |||||||
\(164\) | 2.50000 | + | 4.33013i | 0.195217 | + | 0.338126i | ||||
\(165\) | − | 8.66025i | − | 0.674200i | ||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | −9.50000 | − | 16.4545i | −0.735132 | − | 1.27329i | −0.954665 | − | 0.297681i | \(-0.903787\pi\) |
0.219533 | − | 0.975605i | \(-0.429547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | + | 10.3923i | −0.461538 | + | 0.799408i | ||||
\(170\) | 1.50000 | + | 2.59808i | 0.115045 | + | 0.199263i | ||||
\(171\) | −1.50000 | − | 2.59808i | −0.114708 | − | 0.198680i | ||||
\(172\) | −0.500000 | + | 0.866025i | −0.0381246 | + | 0.0660338i | ||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | −1.50000 | − | 0.866025i | −0.113715 | − | 0.0656532i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.50000 | + | 4.33013i | 0.188445 | + | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.50000 | − | 11.2583i | −0.487196 | − | 0.843848i | ||||
\(179\) | −9.50000 | + | 16.4545i | −0.710063 | + | 1.22987i | 0.254770 | + | 0.967002i | \(0.418000\pi\) |
−0.964833 | + | 0.262864i | \(0.915333\pi\) | |||||||
\(180\) | −1.50000 | + | 2.59808i | −0.111803 | + | 0.193649i | ||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 24.2487i | − | 1.79252i | ||||||
\(184\) | 4.50000 | − | 7.79423i | 0.331744 | − | 0.574598i | ||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000 | −0.0725476 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | − | 12.1244i | − | 0.875000i | ||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | −4.50000 | + | 7.79423i | −0.323081 | + | 0.559593i | ||||
\(195\) | − | 8.66025i | − | 0.620174i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 7.50000 | + | 12.9904i | 0.533002 | + | 0.923186i | ||||
\(199\) | 1.50000 | − | 2.59808i | 0.106332 | − | 0.184173i | −0.807950 | − | 0.589252i | \(-0.799423\pi\) |
0.914282 | + | 0.405079i | \(0.132756\pi\) | |||||||
\(200\) | −6.00000 | − | 10.3923i | −0.424264 | − | 0.734847i | ||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | −8.50000 | − | 14.7224i | −0.598058 | − | 1.03587i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.50000 | + | 2.59808i | 0.315063 | + | 0.181902i | ||||
\(205\) | 5.00000 | 0.349215 | ||||||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 4.50000 | − | 7.79423i | 0.312772 | − | 0.541736i | ||||
\(208\) | 2.50000 | + | 4.33013i | 0.173344 | + | 0.300240i | ||||
\(209\) | 2.50000 | − | 4.33013i | 0.172929 | − | 0.299521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | −4.50000 | + | 7.79423i | −0.309061 | + | 0.535310i | ||||
\(213\) | 20.7846i | 1.42414i | ||||||||
\(214\) | −8.50000 | − | 14.7224i | −0.581048 | − | 1.00640i | ||||
\(215\) | 0.500000 | + | 0.866025i | 0.0340997 | + | 0.0590624i | ||||
\(216\) | − | 15.5885i | − | 1.06066i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.50000 | − | 7.79423i | 0.304778 | − | 0.527892i | ||||
\(219\) | −4.50000 | − | 2.59808i | −0.304082 | − | 0.175562i | ||||
\(220\) | −5.00000 | −0.337100 | ||||||||
\(221\) | −15.0000 | −1.00901 | ||||||||
\(222\) | −4.50000 | + | 2.59808i | −0.302020 | + | 0.174371i | ||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | − | 10.3923i | −0.400000 | − | 0.692820i | ||||
\(226\) | 0.500000 | + | 0.866025i | 0.0332595 | + | 0.0576072i | ||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | −1.50000 | + | 0.866025i | −0.0993399 | + | 0.0573539i | ||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | −1.50000 | − | 2.59808i | −0.0989071 | − | 0.171312i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50000 | + | 2.59808i | −0.0984798 | + | 0.170572i | ||||
\(233\) | −1.50000 | − | 2.59808i | −0.0982683 | − | 0.170206i | 0.812700 | − | 0.582683i | \(-0.197997\pi\) |
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(234\) | 7.50000 | + | 12.9904i | 0.490290 | + | 0.849208i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | −1.50000 | − | 0.866025i | −0.0968246 | − | 0.0559017i | ||||
\(241\) | 5.50000 | + | 9.52628i | 0.354286 | + | 0.613642i | 0.986996 | − | 0.160748i | \(-0.0513906\pi\) |
−0.632709 | + | 0.774389i | \(0.718057\pi\) | |||||||
\(242\) | −7.00000 | + | 12.1244i | −0.449977 | + | 0.779383i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | −14.0000 | −0.896258 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.50000 | + | 4.33013i | −0.478183 | + | 0.276079i | ||||
\(247\) | 2.50000 | − | 4.33013i | 0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5000 | + | 7.79423i | 0.855528 | + | 0.493939i | ||||
\(250\) | −9.00000 | −0.569210 | ||||||||
\(251\) | 28.0000 | 1.76734 | 0.883672 | − | 0.468106i | \(-0.155064\pi\) | ||||
0.883672 | + | 0.468106i | \(0.155064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 4.50000 | − | 2.59808i | 0.281801 | − | 0.162698i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −14.5000 | + | 25.1147i | −0.904485 | + | 1.56661i | −0.0828783 | + | 0.996560i | \(0.526411\pi\) |
−0.821607 | + | 0.570055i | \(0.806922\pi\) | |||||||
\(258\) | −1.50000 | − | 0.866025i | −0.0933859 | − | 0.0539164i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | −0.500000 | + | 0.866025i | −0.0308901 | + | 0.0535032i | ||||
\(263\) | −2.50000 | − | 4.33013i | −0.154157 | − | 0.267007i | 0.778595 | − | 0.627527i | \(-0.215933\pi\) |
−0.932752 | + | 0.360520i | \(0.882599\pi\) | |||||||
\(264\) | 22.5000 | − | 12.9904i | 1.38478 | − | 0.799503i | ||||
\(265\) | 4.50000 | + | 7.79423i | 0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.5000 | + | 11.2583i | −1.19338 | + | 0.688999i | ||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | −4.50000 | − | 2.59808i | −0.273861 | − | 0.158114i | ||||
\(271\) | 0.500000 | + | 0.866025i | 0.0303728 | + | 0.0526073i | 0.880812 | − | 0.473466i | \(-0.156997\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | −1.50000 | + | 2.59808i | −0.0909509 | + | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.50000 | + | 7.79423i | 0.271855 | + | 0.470867i | ||||
\(275\) | 10.0000 | − | 17.3205i | 0.603023 | − | 1.04447i | ||||
\(276\) | −4.50000 | − | 2.59808i | −0.270868 | − | 0.156386i | ||||
\(277\) | −9.50000 | − | 16.4545i | −0.570800 | − | 0.988654i | −0.996484 | − | 0.0837823i | \(-0.973300\pi\) |
0.425684 | − | 0.904872i | \(-0.360033\pi\) | |||||||
\(278\) | 4.50000 | + | 7.79423i | 0.269892 | + | 0.467467i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5000 | − | 25.1147i | 0.864997 | − | 1.49822i | −0.00205220 | − | 0.999998i | \(-0.500653\pi\) |
0.867050 | − | 0.498222i | \(-0.166013\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0000 | −1.66443 | −0.832214 | − | 0.554455i | \(-0.812927\pi\) | ||||
−0.832214 | + | 0.554455i | \(0.812927\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 1.73205i | 0.102598i | ||||||||
\(286\) | −12.5000 | + | 21.6506i | −0.739140 | + | 1.28023i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −15.0000 | −0.883883 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0.500000 | + | 0.866025i | 0.0293610 | + | 0.0508548i | ||||
\(291\) | 13.5000 | + | 7.79423i | 0.791384 | + | 0.456906i | ||||
\(292\) | −1.50000 | + | 2.59808i | −0.0877809 | + | 0.152041i | ||||
\(293\) | −2.50000 | − | 4.33013i | −0.146052 | − | 0.252969i | 0.783713 | − | 0.621123i | \(-0.213323\pi\) |
−0.929765 | + | 0.368154i | \(0.879990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.50000 | + | 7.79423i | 0.261557 | + | 0.453030i | ||||
\(297\) | 22.5000 | − | 12.9904i | 1.30558 | − | 0.753778i | ||||
\(298\) | −1.50000 | + | 2.59808i | −0.0868927 | + | 0.150503i | ||||
\(299\) | 15.0000 | 0.867472 | ||||||||
\(300\) | −6.00000 | + | 3.46410i | −0.346410 | + | 0.200000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.50000 | − | 4.33013i | −0.143859 | − | 0.249171i | ||||
\(303\) | −25.5000 | + | 14.7224i | −1.46494 | + | 0.845782i | ||||
\(304\) | −0.500000 | − | 0.866025i | −0.0286770 | − | 0.0496700i | ||||
\(305\) | −7.00000 | + | 12.1244i | −0.400819 | + | 0.694239i | ||||
\(306\) | −4.50000 | + | 7.79423i | −0.257248 | + | 0.445566i | ||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50000 | + | 0.866025i | 0.0853320 | + | 0.0492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 22.5000 | − | 12.9904i | 1.27381 | − | 0.735436i | ||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | −13.5000 | − | 7.79423i | −0.757042 | − | 0.437079i | ||||
\(319\) | −5.00000 | −0.279946 | ||||||||
\(320\) | −3.50000 | + | 6.06218i | −0.195656 | + | 0.338886i | ||||
\(321\) | −25.5000 | + | 14.7224i | −1.42327 | + | 0.821726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 10.0000 | − | 17.3205i | 0.554700 | − | 0.960769i | ||||
\(326\) | 5.50000 | + | 9.52628i | 0.304617 | + | 0.527612i | ||||
\(327\) | −13.5000 | − | 7.79423i | −0.746552 | − | 0.431022i | ||||
\(328\) | 7.50000 | + | 12.9904i | 0.414118 | + | 0.717274i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 8.66025i | − | 0.476731i | ||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | 4.50000 | + | 7.79423i | 0.246598 | + | 0.427121i | ||||
\(334\) | −9.50000 | − | 16.4545i | −0.519817 | − | 0.900349i | ||||
\(335\) | −2.00000 | + | 3.46410i | −0.109272 | + | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5000 | + | 25.1147i | 0.789865 | + | 1.36809i | 0.926049 | + | 0.377403i | \(0.123183\pi\) |
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | −6.00000 | + | 10.3923i | −0.326357 | + | 0.565267i | ||||
\(339\) | 1.50000 | − | 0.866025i | 0.0814688 | − | 0.0470360i | ||||
\(340\) | −1.50000 | − | 2.59808i | −0.0813489 | − | 0.140900i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.50000 | − | 2.59808i | −0.0811107 | − | 0.140488i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.50000 | + | 2.59808i | −0.0808746 | + | 0.140079i | ||||
\(345\) | −4.50000 | + | 2.59808i | −0.242272 | + | 0.139876i | ||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | 4.00000 | 0.214731 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 1.50000 | + | 0.866025i | 0.0804084 | + | 0.0464238i | ||||
\(349\) | 9.50000 | − | 16.4545i | 0.508523 | − | 0.880788i | −0.491428 | − | 0.870918i | \(-0.663525\pi\) |
0.999951 | − | 0.00987003i | \(-0.00314178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.5000 | − | 12.9904i | 1.20096 | − | 0.693375i | ||||
\(352\) | −12.5000 | − | 21.6506i | −0.666252 | − | 1.15398i | ||||
\(353\) | 5.50000 | + | 9.52628i | 0.292735 | + | 0.507033i | 0.974456 | − | 0.224580i | \(-0.0721011\pi\) |
−0.681720 | + | 0.731613i | \(0.738768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 10.3923i | 0.318447 | − | 0.551566i | ||||
\(356\) | 6.50000 | + | 11.2583i | 0.344499 | + | 0.596690i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.50000 | + | 16.4545i | −0.502091 | + | 0.869646i | ||||
\(359\) | 5.50000 | + | 9.52628i | 0.290279 | + | 0.502778i | 0.973876 | − | 0.227082i | \(-0.0729186\pi\) |
−0.683597 | + | 0.729860i | \(0.739585\pi\) | |||||||
\(360\) | −4.50000 | + | 7.79423i | −0.237171 | + | 0.410792i | ||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 14.0000 | 0.735824 | ||||||||
\(363\) | 21.0000 | + | 12.1244i | 1.10221 | + | 0.636364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.50000 | + | 2.59808i | 0.0785136 | + | 0.135990i | ||||
\(366\) | − | 24.2487i | − | 1.26750i | ||||||
\(367\) | −1.50000 | − | 2.59808i | −0.0782994 | − | 0.135618i | 0.824217 | − | 0.566274i | \(-0.191616\pi\) |
−0.902516 | + | 0.430656i | \(0.858282\pi\) | |||||||
\(368\) | 1.50000 | − | 2.59808i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 7.50000 | + | 12.9904i | 0.390434 | + | 0.676252i | ||||
\(370\) | 3.00000 | 0.155963 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | − | 21.6506i | 0.647225 | − | 1.12103i | −0.336557 | − | 0.941663i | \(-0.609263\pi\) |
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | −15.0000 | −0.775632 | ||||||||
\(375\) | 15.5885i | 0.804984i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 1.00000 | 0.0512989 | ||||||||
\(381\) | 20.7846i | 1.06483i | ||||||||
\(382\) | 8.00000 | 0.409316 | ||||||||
\(383\) | 13.5000 | − | 23.3827i | 0.689818 | − | 1.19480i | −0.282079 | − | 0.959391i | \(-0.591024\pi\) |
0.971897 | − | 0.235408i | \(-0.0756427\pi\) | |||||||
\(384\) | 5.19615i | 0.265165i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | 4.50000 | − | 7.79423i | 0.228453 | − | 0.395692i | ||||
\(389\) | 4.50000 | + | 7.79423i | 0.228159 | + | 0.395183i | 0.957263 | − | 0.289220i | \(-0.0933960\pi\) |
−0.729103 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(390\) | − | 8.66025i | − | 0.438529i | ||||||
\(391\) | 4.50000 | + | 7.79423i | 0.227575 | + | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.50000 | + | 0.866025i | 0.0756650 | + | 0.0436852i | ||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | −7.50000 | − | 12.9904i | −0.376889 | − | 0.652791i | ||||
\(397\) | 7.50000 | + | 12.9904i | 0.376414 | + | 0.651969i | 0.990538 | − | 0.137241i | \(-0.0438236\pi\) |
−0.614123 | + | 0.789210i | \(0.710490\pi\) | |||||||
\(398\) | 1.50000 | − | 2.59808i | 0.0751882 | − | 0.130230i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | − | 6.92820i | − | 0.345547i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.50000 | + | 14.7224i | 0.422891 | + | 0.732468i | ||||
\(405\) | −4.50000 | + | 7.79423i | −0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.50000 | + | 12.9904i | −0.371761 | + | 0.643909i | ||||
\(408\) | 13.5000 | + | 7.79423i | 0.668350 | + | 0.385872i | ||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 5.00000 | 0.246932 | ||||||||
\(411\) | 13.5000 | − | 7.79423i | 0.665906 | − | 0.384461i | ||||
\(412\) | 0.500000 | − | 0.866025i | 0.0246332 | − | 0.0426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.50000 | − | 7.79423i | 0.221163 | − | 0.383065i | ||||
\(415\) | −4.50000 | − | 7.79423i | −0.220896 | − | 0.382604i | ||||
\(416\) | −12.5000 | − | 21.6506i | −0.612863 | − | 1.06151i | ||||
\(417\) | 13.5000 | − | 7.79423i | 0.661098 | − | 0.381685i | ||||
\(418\) | 2.50000 | − | 4.33013i | 0.122279 | − | 0.211793i | ||||
\(419\) | 4.50000 | + | 7.79423i | 0.219839 | + | 0.380773i | 0.954759 | − | 0.297382i | \(-0.0961133\pi\) |
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | − | 0.866025i | 0.0243685 | − | 0.0422075i | −0.853584 | − | 0.520955i | \(-0.825576\pi\) |
0.877952 | + | 0.478748i | \(0.158909\pi\) | |||||||
\(422\) | −6.50000 | − | 11.2583i | −0.316415 | − | 0.548047i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.5000 | + | 23.3827i | −0.655618 | + | 1.13556i | ||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 20.7846i | 1.00702i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.50000 | + | 14.7224i | 0.410863 | + | 0.711636i | ||||
\(429\) | 37.5000 | + | 21.6506i | 1.81052 | + | 1.04530i | ||||
\(430\) | 0.500000 | + | 0.866025i | 0.0241121 | + | 0.0417635i | ||||
\(431\) | 4.50000 | − | 7.79423i | 0.216757 | − | 0.375435i | −0.737057 | − | 0.675830i | \(-0.763785\pi\) |
0.953815 | + | 0.300395i | \(0.0971186\pi\) | |||||||
\(432\) | − | 5.19615i | − | 0.250000i | ||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.50000 | − | 0.866025i | 0.0719195 | − | 0.0415227i | ||||
\(436\) | −4.50000 | + | 7.79423i | −0.215511 | + | 0.373276i | ||||
\(437\) | −3.00000 | −0.143509 | ||||||||
\(438\) | −4.50000 | − | 2.59808i | −0.215018 | − | 0.124141i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −15.0000 | −0.715097 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.0000 | −0.713477 | ||||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | 4.50000 | − | 2.59808i | 0.213561 | − | 0.123299i | ||||
\(445\) | 13.0000 | 0.616259 | ||||||||
\(446\) | 9.50000 | − | 16.4545i | 0.449838 | − | 0.779142i | ||||
\(447\) | 4.50000 | + | 2.59808i | 0.212843 | + | 0.122885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −6.00000 | − | 10.3923i | −0.282843 | − | 0.489898i | ||||
\(451\) | −12.5000 | + | 21.6506i | −0.588602 | + | 1.01949i | ||||
\(452\) | −0.500000 | − | 0.866025i | −0.0235180 | − | 0.0407344i | ||||
\(453\) | −7.50000 | + | 4.33013i | −0.352381 | + | 0.203447i | ||||
\(454\) | −1.50000 | − | 2.59808i | −0.0703985 | − | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.50000 | + | 2.59808i | −0.210732 | + | 0.121666i | ||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | −0.500000 | + | 0.866025i | −0.0233635 | + | 0.0404667i | ||||
\(459\) | 13.5000 | + | 7.79423i | 0.630126 | + | 0.363803i | ||||
\(460\) | 1.50000 | + | 2.59808i | 0.0699379 | + | 0.121136i | ||||
\(461\) | 9.50000 | − | 16.4545i | 0.442459 | − | 0.766362i | −0.555412 | − | 0.831575i | \(-0.687440\pi\) |
0.997871 | + | 0.0652135i | \(0.0207728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.50000 | − | 11.2583i | −0.302081 | − | 0.523219i | 0.674526 | − | 0.738251i | \(-0.264348\pi\) |
−0.976607 | + | 0.215032i | \(0.931015\pi\) | |||||||
\(464\) | −0.500000 | + | 0.866025i | −0.0232119 | + | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50000 | − | 2.59808i | −0.0694862 | − | 0.120354i | ||||
\(467\) | −13.5000 | − | 23.3827i | −0.624705 | − | 1.08202i | −0.988598 | − | 0.150581i | \(-0.951886\pi\) |
0.363892 | − | 0.931441i | \(-0.381448\pi\) | |||||||
\(468\) | −7.50000 | − | 12.9904i | −0.346688 | − | 0.600481i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 24.2487i | − | 1.11732i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | −0.229900 | ||||||||
\(474\) | − | 13.8564i | − | 0.636446i | ||||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.5000 | + | 23.3827i | −0.618123 | + | 1.07062i | ||||
\(478\) | 7.50000 | + | 12.9904i | 0.343042 | + | 0.594166i | ||||
\(479\) | 12.5000 | + | 21.6506i | 0.571140 | + | 0.989243i | 0.996449 | + | 0.0841949i | \(0.0268318\pi\) |
−0.425310 | + | 0.905048i | \(0.639835\pi\) | |||||||
\(480\) | 7.50000 | + | 4.33013i | 0.342327 | + | 0.197642i | ||||
\(481\) | −7.50000 | + | 12.9904i | −0.341971 | + | 0.592310i | ||||
\(482\) | 5.50000 | + | 9.52628i | 0.250518 | + | 0.433910i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | − | 12.1244i | 0.318182 | − | 0.551107i | ||||
\(485\) | −4.50000 | − | 7.79423i | −0.204334 | − | 0.353918i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | −9.50000 | + | 16.4545i | −0.430486 | + | 0.745624i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
0.566429 | + | 0.824110i | \(0.308325\pi\) | |||||||
\(488\) | −42.0000 | −1.90125 | ||||||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.50000 | − | 11.2583i | −0.293341 | − | 0.508081i | 0.681257 | − | 0.732045i | \(-0.261434\pi\) |
−0.974598 | + | 0.223963i | \(0.928100\pi\) | |||||||
\(492\) | 7.50000 | − | 4.33013i | 0.338126 | − | 0.195217i | ||||
\(493\) | −1.50000 | − | 2.59808i | −0.0675566 | − | 0.117011i | ||||
\(494\) | 2.50000 | − | 4.33013i | 0.112480 | − | 0.194822i | ||||
\(495\) | −15.0000 | −0.674200 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.5000 | + | 7.79423i | 0.604949 | + | 0.349268i | ||||
\(499\) | −15.5000 | + | 26.8468i | −0.693875 | + | 1.20183i | 0.276683 | + | 0.960961i | \(0.410765\pi\) |
−0.970558 | + | 0.240866i | \(0.922569\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | −28.5000 | + | 16.4545i | −1.27329 | + | 0.735132i | ||||
\(502\) | 28.0000 | 1.24970 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 15.0000 | 0.666831 | ||||||||
\(507\) | 18.0000 | + | 10.3923i | 0.799408 | + | 0.461538i | ||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | −14.5000 | + | 25.1147i | −0.642701 | + | 1.11319i | 0.342126 | + | 0.939654i | \(0.388853\pi\) |
−0.984827 | + | 0.173537i | \(0.944480\pi\) | |||||||
\(510\) | 4.50000 | − | 2.59808i | 0.199263 | − | 0.115045i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −4.50000 | + | 2.59808i | −0.198680 | + | 0.114708i | ||||
\(514\) | −14.5000 | + | 25.1147i | −0.639568 | + | 1.10776i | ||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | 1.50000 | + | 0.866025i | 0.0660338 | + | 0.0381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.2487i | − | 1.06440i | ||||||
\(520\) | −15.0000 | −0.657794 | ||||||||
\(521\) | 1.50000 | − | 2.59808i | 0.0657162 | − | 0.113824i | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | −1.50000 | + | 2.59808i | −0.0656532 | + | 0.113715i | ||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 0.500000 | − | 0.866025i | 0.0218426 | − | 0.0378325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.50000 | − | 4.33013i | −0.109005 | − | 0.188803i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 7.50000 | − | 4.33013i | 0.326396 | − | 0.188445i | ||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.5000 | + | 21.6506i | −0.541435 | + | 0.937793i | ||||
\(534\) | −19.5000 | + | 11.2583i | −0.843848 | + | 0.487196i | ||||
\(535\) | 17.0000 | 0.734974 | ||||||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | 28.5000 | + | 16.4545i | 1.22987 | + | 0.710063i | ||||
\(538\) | 1.50000 | − | 2.59808i | 0.0646696 | − | 0.112011i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.50000 | + | 2.59808i | 0.193649 | + | 0.111803i | ||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | 0.500000 | + | 0.866025i | 0.0214768 | + | 0.0371990i | ||||
\(543\) | − | 24.2487i | − | 1.04061i | ||||||
\(544\) | 7.50000 | − | 12.9904i | 0.321560 | − | 0.556958i | ||||
\(545\) | 4.50000 | + | 7.79423i | 0.192759 | + | 0.333868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5000 | − | 25.1147i | 0.619975 | − | 1.07383i | −0.369514 | − | 0.929225i | \(-0.620476\pi\) |
0.989490 | − | 0.144604i | \(-0.0461907\pi\) | |||||||
\(548\) | −4.50000 | − | 7.79423i | −0.192230 | − | 0.332953i | ||||
\(549\) | −42.0000 | −1.79252 | ||||||||
\(550\) | 10.0000 | − | 17.3205i | 0.426401 | − | 0.738549i | ||||
\(551\) | 1.00000 | 0.0426014 | ||||||||
\(552\) | −13.5000 | − | 7.79423i | −0.574598 | − | 0.331744i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.50000 | − | 16.4545i | −0.403616 | − | 0.699084i | ||||
\(555\) | − | 5.19615i | − | 0.220564i | ||||||
\(556\) | −4.50000 | − | 7.79423i | −0.190843 | − | 0.330549i | ||||
\(557\) | 18.5000 | − | 32.0429i | 0.783870 | − | 1.35770i | −0.145802 | − | 0.989314i | \(-0.546576\pi\) |
0.929672 | − | 0.368389i | \(-0.120091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.9808i | 1.09691i | ||||||||
\(562\) | 14.5000 | − | 25.1147i | 0.611646 | − | 1.05940i | ||||
\(563\) | 28.0000 | 1.18006 | 0.590030 | − | 0.807382i | \(-0.299116\pi\) | ||||
0.590030 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.00000 | −0.0420703 | ||||||||
\(566\) | −28.0000 | −1.17693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.0000 | 1.51053 | ||||||||
\(569\) | −34.0000 | −1.42535 | −0.712677 | − | 0.701492i | \(-0.752517\pi\) | ||||
−0.712677 | + | 0.701492i | \(0.752517\pi\) | |||||||
\(570\) | 1.73205i | 0.0725476i | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 12.5000 | − | 21.6506i | 0.522651 | − | 0.905259i | ||||
\(573\) | − | 13.8564i | − | 0.578860i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | −21.0000 | −0.875000 | ||||||||
\(577\) | 15.5000 | − | 26.8468i | 0.645273 | − | 1.11765i | −0.338965 | − | 0.940799i | \(-0.610077\pi\) |
0.984238 | − | 0.176847i | \(-0.0565899\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 17.3205i | 0.719816i | ||||||||
\(580\) | −0.500000 | − | 0.866025i | −0.0207614 | − | 0.0359597i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.5000 | + | 7.79423i | 0.559593 | + | 0.323081i | ||||
\(583\) | −45.0000 | −1.86371 | ||||||||
\(584\) | −4.50000 | + | 7.79423i | −0.186211 | + | 0.322527i | ||||
\(585\) | −15.0000 | −0.620174 | ||||||||
\(586\) | −2.50000 | − | 4.33013i | −0.103274 | − | 0.178876i | ||||
\(587\) | −18.5000 | + | 32.0429i | −0.763577 | + | 1.32255i | 0.177419 | + | 0.984135i | \(0.443225\pi\) |
−0.940996 | + | 0.338418i | \(0.890108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.46410i | − | 0.142494i | ||||||
\(592\) | 1.50000 | + | 2.59808i | 0.0616496 | + | 0.106780i | ||||
\(593\) | 7.50000 | + | 12.9904i | 0.307988 | + | 0.533451i | 0.977922 | − | 0.208970i | \(-0.0670110\pi\) |
−0.669934 | + | 0.742421i | \(0.733678\pi\) | |||||||
\(594\) | 22.5000 | − | 12.9904i | 0.923186 | − | 0.533002i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.50000 | − | 2.59808i | 0.0614424 | − | 0.106421i | ||||
\(597\) | −4.50000 | − | 2.59808i | −0.184173 | − | 0.106332i | ||||
\(598\) | 15.0000 | 0.613396 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −18.0000 | + | 10.3923i | −0.734847 | + | 0.424264i | ||||
\(601\) | −4.50000 | + | 7.79423i | −0.183559 | + | 0.317933i | −0.943090 | − | 0.332538i | \(-0.892095\pi\) |
0.759531 | + | 0.650471i | \(0.225428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | −7.00000 | − | 12.1244i | −0.284590 | − | 0.492925i | ||||
\(606\) | −25.5000 | + | 14.7224i | −1.03587 | + | 0.598058i | ||||
\(607\) | −0.500000 | + | 0.866025i | −0.0202944 | + | 0.0351509i | −0.875994 | − | 0.482322i | \(-0.839794\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.00000 | + | 12.1244i | −0.283422 | + | 0.490901i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.50000 | − | 7.79423i | 0.181902 | − | 0.315063i | ||||
\(613\) | −9.50000 | + | 16.4545i | −0.383701 | + | 0.664590i | −0.991588 | − | 0.129433i | \(-0.958684\pi\) |
0.607887 | + | 0.794024i | \(0.292017\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | − | 8.66025i | − | 0.349215i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | 1.50000 | + | 0.866025i | 0.0603388 | + | 0.0348367i | ||||
\(619\) | 12.5000 | + | 21.6506i | 0.502417 | + | 0.870212i | 0.999996 | + | 0.00279365i | \(0.000889247\pi\) |
−0.497579 | + | 0.867419i | \(0.665777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.50000 | − | 4.33013i | 0.300240 | − | 0.173344i | ||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | −14.0000 | −0.559553 | ||||||||
\(627\) | −7.50000 | − | 4.33013i | −0.299521 | − | 0.172929i | ||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | −9.00000 | −0.358854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | −24.0000 | −0.954669 | ||||||||
\(633\) | −19.5000 | + | 11.2583i | −0.775055 | + | 0.447478i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 6.00000 | − | 10.3923i | 0.238103 | − | 0.412406i | ||||
\(636\) | 13.5000 | + | 7.79423i | 0.535310 | + | 0.309061i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.00000 | −0.197952 | ||||||||
\(639\) | 36.0000 | 1.42414 | ||||||||
\(640\) | 1.50000 | − | 2.59808i | 0.0592927 | − | 0.102698i | ||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | −25.5000 | + | 14.7224i | −1.00640 | + | 0.581048i | ||||
\(643\) | −9.50000 | − | 16.4545i | −0.374643 | − | 0.648901i | 0.615630 | − | 0.788035i | \(-0.288902\pi\) |
−0.990274 | + | 0.139134i | \(0.955568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.50000 | − | 0.866025i | 0.0590624 | − | 0.0340997i | ||||
\(646\) | 3.00000 | 0.118033 | ||||||||
\(647\) | 15.5000 | − | 26.8468i | 0.609368 | − | 1.05546i | −0.381977 | − | 0.924172i | \(-0.624757\pi\) |
0.991345 | − | 0.131284i | \(-0.0419101\pi\) | |||||||
\(648\) | −27.0000 | −1.06066 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.0000 | − | 17.3205i | 0.392232 | − | 0.679366i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.50000 | − | 9.52628i | −0.215397 | − | 0.373078i | ||||
\(653\) | −1.50000 | + | 2.59808i | −0.0586995 | + | 0.101671i | −0.893882 | − | 0.448303i | \(-0.852029\pi\) |
0.835182 | + | 0.549973i | \(0.185362\pi\) | |||||||
\(654\) | −13.5000 | − | 7.79423i | −0.527892 | − | 0.304778i | ||||
\(655\) | −0.500000 | − | 0.866025i | −0.0195366 | − | 0.0338384i | ||||
\(656\) | 2.50000 | + | 4.33013i | 0.0976086 | + | 0.169063i | ||||
\(657\) | −4.50000 | + | 7.79423i | −0.175562 | + | 0.304082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5000 | + | 23.3827i | −0.525885 | + | 0.910860i | 0.473660 | + | 0.880708i | \(0.342933\pi\) |
−0.999545 | + | 0.0301523i | \(0.990401\pi\) | |||||||
\(660\) | 8.66025i | 0.337100i | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 8.00000 | 0.310929 | ||||||||
\(663\) | 25.9808i | 1.00901i | ||||||||
\(664\) | 13.5000 | − | 23.3827i | 0.523902 | − | 0.907424i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.50000 | + | 7.79423i | 0.174371 | + | 0.302020i | ||||
\(667\) | 1.50000 | + | 2.59808i | 0.0580802 | + | 0.100598i | ||||
\(668\) | 9.50000 | + | 16.4545i | 0.367566 | + | 0.636643i | ||||
\(669\) | −28.5000 | − | 16.4545i | −1.10187 | − | 0.636167i | ||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | −35.0000 | − | 60.6218i | −1.35116 | − | 2.34028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | − | 25.1147i | 0.558934 | − | 0.968102i | −0.438652 | − | 0.898657i | \(-0.644544\pi\) |
0.997586 | − | 0.0694449i | \(-0.0221228\pi\) | |||||||
\(674\) | 14.5000 | + | 25.1147i | 0.558519 | + | 0.967384i | ||||
\(675\) | −18.0000 | + | 10.3923i | −0.692820 | + | 0.400000i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 1.50000 | − | 0.866025i | 0.0576072 | − | 0.0332595i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | −4.50000 | + | 2.59808i | −0.172440 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50000 | − | 7.79423i | 0.172188 | − | 0.298238i | −0.766997 | − | 0.641651i | \(-0.778250\pi\) |
0.939184 | + | 0.343413i | \(0.111583\pi\) | |||||||
\(684\) | 1.50000 | + | 2.59808i | 0.0573539 | + | 0.0993399i | ||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.50000 | + | 0.866025i | 0.0572286 | + | 0.0330409i | ||||
\(688\) | −0.500000 | + | 0.866025i | −0.0190623 | + | 0.0330169i | ||||
\(689\) | −45.0000 | −1.71436 | ||||||||
\(690\) | −4.50000 | + | 2.59808i | −0.171312 | + | 0.0989071i | ||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | −14.0000 | −0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | −9.00000 | −0.341389 | ||||||||
\(696\) | 4.50000 | + | 2.59808i | 0.170572 | + | 0.0984798i | ||||
\(697\) | −15.0000 | −0.568166 | ||||||||
\(698\) | 9.50000 | − | 16.4545i | 0.359580 | − | 0.622811i | ||||
\(699\) | −4.50000 | + | 2.59808i | −0.170206 | + | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 22.5000 | − | 12.9904i | 0.849208 | − | 0.490290i | ||||
\(703\) | 1.50000 | − | 2.59808i | 0.0565736 | − | 0.0979883i | ||||
\(704\) | −17.5000 | − | 30.3109i | −0.659556 | − | 1.14238i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.50000 | + | 9.52628i | 0.206995 | + | 0.358526i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.00000 | −0.225335 | −0.112667 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112667 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(710\) | 6.00000 | − | 10.3923i | 0.225176 | − | 0.390016i | ||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | 19.5000 | + | 33.7750i | 0.730793 | + | 1.26577i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5000 | − | 21.6506i | −0.467473 | − | 0.809688i | ||||
\(716\) | 9.50000 | − | 16.4545i | 0.355032 | − | 0.614933i | ||||
\(717\) | 22.5000 | − | 12.9904i | 0.840278 | − | 0.485135i | ||||
\(718\) | 5.50000 | + | 9.52628i | 0.205258 | + | 0.355518i | ||||
\(719\) | −13.5000 | − | 23.3827i | −0.503465 | − | 0.872027i | −0.999992 | − | 0.00400572i | \(-0.998725\pi\) |
0.496527 | − | 0.868021i | \(-0.334608\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.00000 | − | 15.5885i | 0.334945 | − | 0.580142i | ||||
\(723\) | 16.5000 | − | 9.52628i | 0.613642 | − | 0.354286i | ||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 21.0000 | + | 12.1244i | 0.779383 | + | 0.449977i | ||||
\(727\) | 23.5000 | − | 40.7032i | 0.871567 | − | 1.50960i | 0.0111912 | − | 0.999937i | \(-0.496438\pi\) |
0.860376 | − | 0.509661i | \(-0.170229\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 1.50000 | + | 2.59808i | 0.0555175 | + | 0.0961591i | ||||
\(731\) | −1.50000 | − | 2.59808i | −0.0554795 | − | 0.0960933i | ||||
\(732\) | 24.2487i | 0.896258i | ||||||||
\(733\) | 13.5000 | − | 23.3827i | 0.498634 | − | 0.863659i | −0.501365 | − | 0.865236i | \(-0.667169\pi\) |
0.999999 | + | 0.00157675i | \(0.000501894\pi\) | |||||||
\(734\) | −1.50000 | − | 2.59808i | −0.0553660 | − | 0.0958967i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.50000 | + | 12.9904i | −0.276454 | + | 0.478832i | ||||
\(737\) | −10.0000 | − | 17.3205i | −0.368355 | − | 0.638009i | ||||
\(738\) | 7.50000 | + | 12.9904i | 0.276079 | + | 0.478183i | ||||
\(739\) | 4.50000 | − | 7.79423i | 0.165535 | − | 0.286715i | −0.771310 | − | 0.636460i | \(-0.780398\pi\) |
0.936845 | + | 0.349744i | \(0.113732\pi\) | |||||||
\(740\) | −3.00000 | −0.110282 | ||||||||
\(741\) | −7.50000 | − | 4.33013i | −0.275519 | − | 0.159071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.50000 | + | 12.9904i | 0.275148 | + | 0.476571i | 0.970173 | − | 0.242415i | \(-0.0779397\pi\) |
−0.695024 | + | 0.718986i | \(0.744606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50000 | − | 2.59808i | −0.0549557 | − | 0.0951861i | ||||
\(746\) | 12.5000 | − | 21.6506i | 0.457658 | − | 0.792686i | ||||
\(747\) | 13.5000 | − | 23.3827i | 0.493939 | − | 0.855528i | ||||
\(748\) | 15.0000 | 0.548454 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.5885i | 0.569210i | ||||||||
\(751\) | −15.5000 | + | 26.8468i | −0.565603 | + | 0.979653i | 0.431390 | + | 0.902165i | \(0.358023\pi\) |
−0.996993 | + | 0.0774878i | \(0.975310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 48.4974i | − | 1.76734i | ||||||
\(754\) | −5.00000 | −0.182089 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −12.0000 | −0.435860 | ||||||||
\(759\) | − | 25.9808i | − | 0.943042i | ||||||
\(760\) | 3.00000 | 0.108821 | ||||||||
\(761\) | 13.5000 | − | 23.3827i | 0.489375 | − | 0.847622i | −0.510551 | − | 0.859848i | \(-0.670558\pi\) |
0.999925 | + | 0.0122260i | \(0.00389175\pi\) | |||||||
\(762\) | 20.7846i | 0.752947i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | −4.50000 | − | 7.79423i | −0.162698 | − | 0.281801i | ||||
\(766\) | 13.5000 | − | 23.3827i | 0.487775 | − | 0.844851i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 29.4449i | 1.06250i | ||||||||
\(769\) | 11.5000 | + | 19.9186i | 0.414701 | + | 0.718283i | 0.995397 | − | 0.0958377i | \(-0.0305530\pi\) |
−0.580696 | + | 0.814120i | \(0.697220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.5000 | + | 25.1147i | 1.56661 | + | 0.904485i | ||||
\(772\) | 10.0000 | 0.359908 | ||||||||
\(773\) | 15.5000 | − | 26.8468i | 0.557496 | − | 0.965612i | −0.440208 | − | 0.897896i | \(-0.645095\pi\) |
0.997705 | − | 0.0677162i | \(-0.0215712\pi\) | |||||||
\(774\) | −1.50000 | + | 2.59808i | −0.0539164 | + | 0.0933859i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.5000 | − | 23.3827i | 0.484622 | − | 0.839390i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | + | 7.79423i | 0.161333 | + | 0.279437i | ||||
\(779\) | 2.50000 | − | 4.33013i | 0.0895718 | − | 0.155143i | ||||
\(780\) | 8.66025i | 0.310087i | ||||||||
\(781\) | 30.0000 | + | 51.9615i | 1.07348 | + | 1.85933i | ||||
\(782\) | 4.50000 | + | 7.79423i | 0.160920 | + | 0.278721i | ||||
\(783\) | 4.50000 | + | 2.59808i | 0.160817 | + | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.00000 | + | 12.1244i | −0.249841 | + | 0.432737i | ||||
\(786\) | 1.50000 | + | 0.866025i | 0.0535032 | + | 0.0308901i | ||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | −2.00000 | −0.0712470 | ||||||||
\(789\) | −7.50000 | + | 4.33013i | −0.267007 | + | 0.154157i | ||||
\(790\) | −4.00000 | + | 6.92820i | −0.142314 | + | 0.246494i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −22.5000 | − | 38.9711i | −0.799503 | − | 1.38478i | ||||
\(793\) | −35.0000 | − | 60.6218i | −1.24289 | − | 2.15274i | ||||
\(794\) | 7.50000 | + | 12.9904i | 0.266165 | + | 0.461011i | ||||
\(795\) | 13.5000 | − | 7.79423i | 0.478796 | − | 0.276433i | ||||
\(796\) | −1.50000 | + | 2.59808i | −0.0531661 | + | 0.0920864i | ||||
\(797\) | 11.5000 | + | 19.9186i | 0.407351 | + | 0.705552i | 0.994592 | − | 0.103860i | \(-0.0331193\pi\) |
−0.587241 | + | 0.809412i | \(0.699786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 10.0000 | + | 17.3205i | 0.353553 | + | 0.612372i | ||||
\(801\) | 19.5000 | + | 33.7750i | 0.688999 | + | 1.19338i | ||||
\(802\) | −1.50000 | + | 2.59808i | −0.0529668 | + | 0.0917413i | ||||
\(803\) | −15.0000 | −0.529339 | ||||||||
\(804\) | 6.92820i | 0.244339i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.50000 | − | 2.59808i | −0.158408 | − | 0.0914566i | ||||
\(808\) | 25.5000 | + | 44.1673i | 0.897087 | + | 1.55380i | ||||
\(809\) | 4.50000 | − | 7.79423i | 0.158212 | − | 0.274030i | −0.776012 | − | 0.630718i | \(-0.782761\pi\) |
0.934224 | + | 0.356687i | \(0.116094\pi\) | |||||||
\(810\) | −4.50000 | + | 7.79423i | −0.158114 | + | 0.273861i | ||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.50000 | − | 0.866025i | 0.0526073 | − | 0.0303728i | ||||
\(814\) | −7.50000 | + | 12.9904i | −0.262875 | + | 0.455313i | ||||
\(815\) | −11.0000 | −0.385313 | ||||||||
\(816\) | 4.50000 | + | 2.59808i | 0.157532 | + | 0.0909509i | ||||
\(817\) | 1.00000 | 0.0349856 | ||||||||
\(818\) | −14.0000 | −0.489499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.00000 | −0.174608 | ||||||||
\(821\) | 22.0000 | 0.767805 | 0.383903 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383903 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(822\) | 13.5000 | − | 7.79423i | 0.470867 | − | 0.271855i | ||||
\(823\) | −24.0000 | −0.836587 | −0.418294 | − | 0.908312i | \(-0.637372\pi\) | ||||
−0.418294 | + | 0.908312i | \(0.637372\pi\) | |||||||
\(824\) | 1.50000 | − | 2.59808i | 0.0522550 | − | 0.0905083i | ||||
\(825\) | −30.0000 | − | 17.3205i | −1.04447 | − | 0.603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | −4.50000 | + | 7.79423i | −0.156386 | + | 0.270868i | ||||
\(829\) | −12.5000 | + | 21.6506i | −0.434143 | + | 0.751958i | −0.997225 | − | 0.0744432i | \(-0.976282\pi\) |
0.563082 | + | 0.826401i | \(0.309615\pi\) | |||||||
\(830\) | −4.50000 | − | 7.79423i | −0.156197 | − | 0.270542i | ||||
\(831\) | −28.5000 | + | 16.4545i | −0.988654 | + | 0.570800i | ||||
\(832\) | −17.5000 | − | 30.3109i | −0.606703 | − | 1.05084i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.5000 | − | 7.79423i | 0.467467 | − | 0.269892i | ||||
\(835\) | 19.0000 | 0.657522 | ||||||||
\(836\) | −2.50000 | + | 4.33013i | −0.0864643 | + | 0.149761i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.50000 | + | 7.79423i | 0.155450 | + | 0.269247i | ||||
\(839\) | −18.5000 | + | 32.0429i | −0.638691 | + | 1.10625i | 0.347029 | + | 0.937854i | \(0.387190\pi\) |
−0.985720 | + | 0.168391i | \(0.946143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0.500000 | − | 0.866025i | 0.0172311 | − | 0.0298452i | ||||
\(843\) | −43.5000 | − | 25.1147i | −1.49822 | − | 0.864997i | ||||
\(844\) | 6.50000 | + | 11.2583i | 0.223739 | + | 0.387528i | ||||
\(845\) | −6.00000 | − | 10.3923i | −0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.50000 | + | 7.79423i | −0.154531 | + | 0.267655i | ||||
\(849\) | 48.4974i | 1.66443i | ||||||||
\(850\) | 12.0000 | 0.411597 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | − | 20.7846i | − | 0.712069i | ||||||
\(853\) | −18.5000 | + | 32.0429i | −0.633428 | + | 1.09713i | 0.353418 | + | 0.935466i | \(0.385019\pi\) |
−0.986846 | + | 0.161664i | \(0.948314\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | 0.102598 | ||||||||
\(856\) | 25.5000 | + | 44.1673i | 0.871572 | + | 1.50961i | ||||
\(857\) | 5.50000 | + | 9.52628i | 0.187876 | + | 0.325412i | 0.944542 | − | 0.328391i | \(-0.106506\pi\) |
−0.756666 | + | 0.653802i | \(0.773173\pi\) | |||||||
\(858\) | 37.5000 | + | 21.6506i | 1.28023 | + | 0.739140i | ||||
\(859\) | −0.500000 | + | 0.866025i | −0.0170598 | + | 0.0295484i | −0.874429 | − | 0.485153i | \(-0.838764\pi\) |
0.857369 | + | 0.514701i | \(0.172097\pi\) | |||||||
\(860\) | −0.500000 | − | 0.866025i | −0.0170499 | − | 0.0295312i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.50000 | − | 7.79423i | 0.153271 | − | 0.265472i | ||||
\(863\) | 19.5000 | + | 33.7750i | 0.663788 | + | 1.14971i | 0.979612 | + | 0.200897i | \(0.0643855\pi\) |
−0.315825 | + | 0.948818i | \(0.602281\pi\) | |||||||
\(864\) | 25.9808i | 0.883883i | ||||||||
\(865\) | −7.00000 | + | 12.1244i | −0.238007 | + | 0.412240i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | 12.0000 | − | 6.92820i | 0.407541 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0000 | − | 34.6410i | −0.678454 | − | 1.17512i | ||||
\(870\) | 1.50000 | − | 0.866025i | 0.0508548 | − | 0.0293610i | ||||
\(871\) | −10.0000 | − | 17.3205i | −0.338837 | − | 0.586883i | ||||
\(872\) | −13.5000 | + | 23.3827i | −0.457168 | + | 0.791838i | ||||
\(873\) | 13.5000 | − | 23.3827i | 0.456906 | − | 0.791384i | ||||
\(874\) | −3.00000 | −0.101477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.50000 | + | 2.59808i | 0.152041 | + | 0.0877809i | ||||
\(877\) | 26.5000 | − | 45.8993i | 0.894841 | − | 1.54991i | 0.0608407 | − | 0.998147i | \(-0.480622\pi\) |
0.834001 | − | 0.551763i | \(-0.186045\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.50000 | + | 4.33013i | −0.252969 | + | 0.146052i | ||||
\(880\) | −5.00000 | −0.168550 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 15.0000 | 0.504505 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 1.20944 | ||||||||
\(887\) | −14.5000 | + | 25.1147i | −0.486862 | + | 0.843270i | −0.999886 | − | 0.0151042i | \(-0.995192\pi\) |
0.513024 | + | 0.858375i | \(0.328525\pi\) | |||||||
\(888\) | 13.5000 | − | 7.79423i | 0.453030 | − | 0.261557i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.0000 | 0.435761 | ||||||||
\(891\) | −22.5000 | − | 38.9711i | −0.753778 | − | 1.30558i | ||||
\(892\) | −9.50000 | + | 16.4545i | −0.318084 | + | 0.550937i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 4.50000 | + | 2.59808i | 0.150503 | + | 0.0868927i | ||||
\(895\) | −9.50000 | − | 16.4545i | −0.317550 | − | 0.550013i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 25.9808i | − | 0.867472i | ||||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 6.00000 | + | 10.3923i | 0.200000 | + | 0.346410i | ||||
\(901\) | −13.5000 | − | 23.3827i | −0.449750 | − | 0.778990i | ||||
\(902\) | −12.5000 | + | 21.6506i | −0.416204 | + | 0.720887i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.50000 | − | 2.59808i | −0.0498893 | − | 0.0864107i | ||||
\(905\) | −7.00000 | + | 12.1244i | −0.232688 | + | 0.403027i | ||||
\(906\) | −7.50000 | + | 4.33013i | −0.249171 | + | 0.143859i | ||||
\(907\) | −2.50000 | − | 4.33013i | −0.0830111 | − | 0.143780i | 0.821531 | − | 0.570164i | \(-0.193120\pi\) |
−0.904542 | + | 0.426385i | \(0.859787\pi\) | |||||||
\(908\) | 1.50000 | + | 2.59808i | 0.0497792 | + | 0.0862202i | ||||
\(909\) | 25.5000 | + | 44.1673i | 0.845782 | + | 1.46494i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5000 | + | 23.3827i | −0.447275 | + | 0.774703i | −0.998208 | − | 0.0598468i | \(-0.980939\pi\) |
0.550933 | + | 0.834550i | \(0.314272\pi\) | |||||||
\(912\) | −1.50000 | + | 0.866025i | −0.0496700 | + | 0.0286770i | ||||
\(913\) | 45.0000 | 1.48928 | ||||||||
\(914\) | 22.0000 | 0.727695 | ||||||||
\(915\) | 21.0000 | + | 12.1244i | 0.694239 | + | 0.400819i | ||||
\(916\) | 0.500000 | − | 0.866025i | 0.0165205 | − | 0.0286143i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.5000 | + | 7.79423i | 0.445566 | + | 0.257248i | ||||
\(919\) | −8.50000 | − | 14.7224i | −0.280389 | − | 0.485648i | 0.691091 | − | 0.722767i | \(-0.257130\pi\) |
−0.971481 | + | 0.237119i | \(0.923797\pi\) | |||||||
\(920\) | 4.50000 | + | 7.79423i | 0.148361 | + | 0.256968i | ||||
\(921\) | 48.4974i | 1.59804i | ||||||||
\(922\) | 9.50000 | − | 16.4545i | 0.312866 | − | 0.541900i | ||||
\(923\) | 30.0000 | + | 51.9615i | 0.987462 | + | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | − | 10.3923i | 0.197279 | − | 0.341697i | ||||
\(926\) | −6.50000 | − | 11.2583i | −0.213603 | − | 0.369972i | ||||
\(927\) | 1.50000 | − | 2.59808i | 0.0492665 | − | 0.0853320i | ||||
\(928\) | 2.50000 | − | 4.33013i | 0.0820665 | − | 0.142143i | ||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | + | 2.59808i | 0.0491341 | + | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.5000 | − | 23.3827i | −0.441733 | − | 0.765105i | ||||
\(935\) | 7.50000 | − | 12.9904i | 0.245276 | − | 0.424831i | ||||
\(936\) | −22.5000 | − | 38.9711i | −0.735436 | − | 1.27381i | ||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2487i | 0.791327i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | − | 24.2487i | − | 0.790066i | ||||||
\(943\) | 15.0000 | 0.488467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.00000 | −0.162564 | ||||||||
\(947\) | −20.0000 | −0.649913 | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 13.8564i | 0.450035i | ||||||||
\(949\) | −15.0000 | −0.486921 | ||||||||
\(950\) | −2.00000 | + | 3.46410i | −0.0648886 | + | 0.112390i | ||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | −13.5000 | + | 23.3827i | −0.437079 | + | 0.757042i | ||||
\(955\) | −4.00000 | + | 6.92820i | −0.129437 | + | 0.224191i | ||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 8.66025i | 0.279946i | ||||||||
\(958\) | 12.5000 | + | 21.6506i | 0.403857 | + | 0.699500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.5000 | + | 6.06218i | 0.338886 | + | 0.195656i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −7.50000 | + | 12.9904i | −0.241810 | + | 0.418827i | ||||
\(963\) | 25.5000 | + | 44.1673i | 0.821726 | + | 1.42327i | ||||
\(964\) | −5.50000 | − | 9.52628i | −0.177143 | − | 0.306821i | ||||
\(965\) | 5.00000 | − | 8.66025i | 0.160956 | − | 0.278783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.50000 | − | 11.2583i | −0.209026 | − | 0.362043i | 0.742382 | − | 0.669977i | \(-0.233696\pi\) |
−0.951408 | + | 0.307933i | \(0.900363\pi\) | |||||||
\(968\) | 21.0000 | − | 36.3731i | 0.674966 | − | 1.16907i | ||||
\(969\) | − | 5.19615i | − | 0.166924i | ||||||
\(970\) | −4.50000 | − | 7.79423i | −0.144486 | − | 0.250258i | ||||
\(971\) | 28.5000 | + | 49.3634i | 0.914609 | + | 1.58415i | 0.807473 | + | 0.589904i | \(0.200834\pi\) |
0.107135 | + | 0.994244i | \(0.465832\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.50000 | + | 16.4545i | −0.304400 | + | 0.527236i | ||||
\(975\) | −30.0000 | − | 17.3205i | −0.960769 | − | 0.554700i | ||||
\(976\) | −14.0000 | −0.448129 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 16.5000 | − | 9.52628i | 0.527612 | − | 0.304617i | ||||
\(979\) | −32.5000 | + | 56.2917i | −1.03870 | + | 1.79909i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5000 | + | 23.3827i | −0.431022 | + | 0.746552i | ||||
\(982\) | −6.50000 | − | 11.2583i | −0.207423 | − | 0.359268i | ||||
\(983\) | −1.50000 | − | 2.59808i | −0.0478426 | − | 0.0828658i | 0.841112 | − | 0.540860i | \(-0.181901\pi\) |
−0.888955 | + | 0.457995i | \(0.848568\pi\) | |||||||
\(984\) | 22.5000 | − | 12.9904i | 0.717274 | − | 0.414118i | ||||
\(985\) | −1.00000 | + | 1.73205i | −0.0318626 | + | 0.0551877i | ||||
\(986\) | −1.50000 | − | 2.59808i | −0.0477697 | − | 0.0827396i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.50000 | + | 4.33013i | −0.0795356 | + | 0.137760i | ||||
\(989\) | 1.50000 | + | 2.59808i | 0.0476972 | + | 0.0826140i | ||||
\(990\) | −15.0000 | −0.476731 | ||||||||
\(991\) | 18.5000 | − | 32.0429i | 0.587672 | − | 1.01788i | −0.406865 | − | 0.913488i | \(-0.633378\pi\) |
0.994537 | − | 0.104389i | \(-0.0332887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.50000 | + | 2.59808i | 0.0475532 | + | 0.0823646i | ||||
\(996\) | −13.5000 | − | 7.79423i | −0.427764 | − | 0.246970i | ||||
\(997\) | −8.50000 | − | 14.7224i | −0.269198 | − | 0.466264i | 0.699457 | − | 0.714675i | \(-0.253425\pi\) |
−0.968655 | + | 0.248410i | \(0.920092\pi\) | |||||||
\(998\) | −15.5000 | + | 26.8468i | −0.490644 | + | 0.849820i | ||||
\(999\) | 13.5000 | − | 7.79423i | 0.427121 | − | 0.246598i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))