Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1053,2,Mod(352,1053)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1053, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1053.352");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1053 = 3^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1053.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.40824733284\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 352.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1053.352 |
Dual form | 1053.2.e.b.703.1 |
$q$-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 \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(730\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0.633316 | − | 0.773893i | \(-0.281693\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | −2.00000 | − | 3.46410i | −0.603023 | − | 1.04447i | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | ||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | + | 3.46410i | −0.426401 | + | 0.738549i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 5.00000 | + | 8.66025i | 0.928477 | + | 1.60817i | 0.785872 | + | 0.618389i | \(0.212214\pi\) |
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | −2.50000 | + | 4.33013i | −0.441942 | + | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | − | 1.73205i | −0.171499 | − | 0.297044i | ||||
\(35\) | −8.00000 | −1.35225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | − | 5.19615i | 0.474342 | − | 0.821584i | ||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 10.3923i | 0.914991 | + | 1.58481i | 0.806914 | + | 0.590669i | \(0.201136\pi\) |
0.108078 | + | 0.994142i | \(0.465531\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | −6.00000 | − | 10.3923i | −0.801784 | − | 1.38873i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.00000 | − | 8.66025i | 0.656532 | − | 1.13715i | ||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | − | 6.92820i | 0.488678 | − | 0.846415i | −0.511237 | − | 0.859440i | \(-0.670813\pi\) |
0.999915 | + | 0.0130248i | \(0.00414604\pi\) | |||||||
\(68\) | 1.00000 | − | 1.73205i | 0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.00000 | + | 6.92820i | 0.478091 | + | 0.828079i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | − | 13.8564i | 0.911685 | − | 1.57908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | −2.00000 | − | 3.46410i | −0.219529 | − | 0.380235i | 0.735135 | − | 0.677920i | \(-0.237119\pi\) |
−0.954664 | + | 0.297686i | \(0.903785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | + | 3.46410i | −0.216930 | + | 0.375735i | ||||
\(86\) | 6.00000 | − | 10.3923i | 0.646997 | − | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | + | 10.3923i | 0.639602 | + | 1.10782i | ||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | − | 8.66025i | −0.507673 | − | 0.879316i | −0.999961 | − | 0.00888289i | \(-0.997172\pi\) |
0.492287 | − | 0.870433i | \(-0.336161\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 1.50000 | − | 2.59808i | 0.147087 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −4.00000 | − | 6.92820i | −0.381385 | − | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | + | 3.46410i | −0.188982 | + | 0.327327i | ||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.0000 | 0.928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 4.00000 | + | 6.92820i | 0.366679 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 1.00000 | − | 1.73205i | 0.0905357 | − | 0.156813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 1.50000 | + | 2.59808i | 0.132583 | + | 0.229640i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | −2.00000 | + | 3.46410i | −0.174741 | + | 0.302660i | −0.940072 | − | 0.340977i | \(-0.889242\pi\) |
0.765331 | + | 0.643637i | \(0.222575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | + | 10.3923i | −0.508913 | + | 0.881464i | 0.491033 | + | 0.871141i | \(0.336619\pi\) |
−0.999947 | + | 0.0103230i | \(0.996714\pi\) | |||||||
\(140\) | −4.00000 | + | 6.92820i | −0.338062 | + | 0.585540i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.0000 | −1.66091 | ||||||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.0000 | −1.28932 | ||||||||
\(155\) | −4.00000 | − | 6.92820i | −0.321288 | − | 0.556487i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | − | 15.5885i | 0.718278 | − | 1.24409i | −0.243403 | − | 0.969925i | \(-0.578264\pi\) |
0.961681 | − | 0.274169i | \(-0.0884028\pi\) | |||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.00000 | − | 8.66025i | −0.395285 | − | 0.684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | 4.00000 | − | 6.92820i | 0.309529 | − | 0.536120i | −0.668730 | − | 0.743505i | \(-0.733162\pi\) |
0.978259 | + | 0.207385i | \(0.0664952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0000 | 0.914991 | ||||||||
\(173\) | −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 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | + | 1.73205i | 0.0749532 | + | 0.129823i | ||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 2.00000 | + | 3.46410i | 0.148250 | + | 0.256776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | − | 6.92820i | −0.289430 | − | 0.501307i | 0.684244 | − | 0.729253i | \(-0.260132\pi\) |
−0.973674 | + | 0.227946i | \(0.926799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.00000 | + | 15.5885i | −0.647834 | + | 1.12208i | 0.335805 | + | 0.941932i | \(0.390992\pi\) |
−0.983639 | + | 0.180150i | \(0.942342\pi\) | |||||||
\(194\) | −5.00000 | + | 8.66025i | −0.358979 | + | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.50000 | + | 7.79423i | 0.321429 | + | 0.556731i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | −1.50000 | − | 2.59808i | −0.106066 | − | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.00000 | − | 15.5885i | 0.633238 | − | 1.09680i | ||||
\(203\) | −20.0000 | + | 34.6410i | −1.40372 | + | 2.43132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −24.0000 | −1.63679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 1.00000 | + | 1.73205i | 0.0677285 | + | 0.117309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.00000 | − | 6.92820i | 0.269680 | − | 0.467099i | ||||
\(221\) | −1.00000 | + | 1.73205i | −0.0672673 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | − | 3.46410i | −0.133930 | − | 0.231973i | 0.791258 | − | 0.611482i | \(-0.209426\pi\) |
−0.925188 | + | 0.379509i | \(0.876093\pi\) | |||||||
\(224\) | −20.0000 | −1.33631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.0000 | − | 25.9808i | −0.984798 | − | 1.70572i | ||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | + | 10.3923i | 0.390567 | + | 0.676481i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | − | 6.92820i | 0.259281 | − | 0.449089i | ||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −9.00000 | − | 15.5885i | −0.574989 | − | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.00000 | − | 10.3923i | 0.381000 | − | 0.659912i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | −13.0000 | + | 22.5167i | −0.810918 | + | 1.40455i | 0.101305 | + | 0.994855i | \(0.467698\pi\) |
−0.912222 | + | 0.409695i | \(0.865635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 6.92820i | −0.248548 | − | 0.430498i | ||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 10.3923i | −0.368577 | + | 0.638394i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | 22.0000 | 1.34136 | 0.670682 | − | 0.741745i | \(-0.266002\pi\) | ||||
0.670682 | + | 0.741745i | \(0.266002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 1.00000 | + | 1.73205i | 0.0606339 | + | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | + | 5.19615i | −0.181237 | + | 0.313911i | ||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 12.0000 | 0.719712 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 24.0000 | 1.43427 | ||||||||
\(281\) | 5.00000 | + | 8.66025i | 0.298275 | + | 0.516627i | 0.975741 | − | 0.218926i | \(-0.0702554\pi\) |
−0.677466 | + | 0.735554i | \(0.736922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | + | 10.3923i | −0.356663 | + | 0.617758i | −0.987401 | − | 0.158237i | \(-0.949419\pi\) |
0.630738 | + | 0.775996i | \(0.282752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | − | 3.46410i | −0.118262 | − | 0.204837i | ||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 10.0000 | + | 17.3205i | 0.587220 | + | 1.01710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | − | 1.73205i | 0.0585206 | − | 0.101361i | ||||
\(293\) | 3.00000 | − | 5.19615i | 0.175262 | − | 0.303562i | −0.764990 | − | 0.644042i | \(-0.777256\pi\) |
0.940252 | + | 0.340480i | \(0.110589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | − | 20.7846i | −0.698667 | − | 1.21013i | ||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.0000 | + | 41.5692i | −1.38334 | + | 2.39601i | ||||
\(302\) | −2.00000 | + | 3.46410i | −0.115087 | + | 0.199337i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −8.00000 | − | 13.8564i | −0.455842 | − | 0.789542i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.00000 | + | 6.92820i | −0.227185 | + | 0.393496i | ||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | + | 5.19615i | 0.169570 | + | 0.293704i | 0.938269 | − | 0.345907i | \(-0.112429\pi\) |
−0.768699 | + | 0.639611i | \(0.779095\pi\) | |||||||
\(314\) | −18.0000 | −1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −13.0000 | − | 22.5167i | −0.730153 | − | 1.26466i | −0.956818 | − | 0.290689i | \(-0.906116\pi\) |
0.226665 | − | 0.973973i | \(-0.427218\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0000 | − | 34.6410i | 1.11979 | − | 1.93952i | ||||
\(320\) | −7.00000 | + | 12.1244i | −0.391312 | + | 0.677772i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.00000 | − | 15.5885i | 0.496942 | − | 0.860729i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | + | 13.8564i | 0.439720 | + | 0.761617i | 0.997668 | − | 0.0682590i | \(-0.0217444\pi\) |
−0.557948 | + | 0.829876i | \(0.688411\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 8.00000 | + | 13.8564i | 0.437087 | + | 0.757056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00000 | + | 15.5885i | −0.490261 | + | 0.849157i | −0.999937 | − | 0.0112091i | \(-0.996432\pi\) |
0.509676 | + | 0.860366i | \(0.329765\pi\) | |||||||
\(338\) | −0.500000 | + | 0.866025i | −0.0271964 | + | 0.0471056i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −18.0000 | − | 31.1769i | −0.970495 | − | 1.68095i | ||||
\(345\) | 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 | ||||||||
\(349\) | 13.0000 | + | 22.5167i | 0.695874 | + | 1.20529i | 0.969885 | + | 0.243563i | \(0.0783162\pi\) |
−0.274011 | + | 0.961727i | \(0.588351\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.0000 | 1.06600 | ||||||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | + | 1.73205i | −0.0529999 | + | 0.0917985i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | − | 3.46410i | −0.105703 | − | 0.183083i | ||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | + | 3.46410i | −0.104828 | + | 0.181568i | ||||
\(365\) | −2.00000 | + | 3.46410i | −0.104685 | + | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | − | 13.8564i | −0.417597 | − | 0.723299i | 0.578101 | − | 0.815966i | \(-0.303794\pi\) |
−0.995697 | + | 0.0926670i | \(0.970461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 12.0000 | + | 20.7846i | 0.623009 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0000 | −0.515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | + | 6.92820i | −0.204658 | + | 0.354478i | ||||
\(383\) | 8.00000 | − | 13.8564i | 0.408781 | − | 0.708029i | −0.585973 | − | 0.810331i | \(-0.699287\pi\) |
0.994753 | + | 0.102302i | \(0.0326207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | + | 27.7128i | 0.815436 | + | 1.41238i | ||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −11.0000 | − | 19.0526i | −0.557722 | − | 0.966003i | −0.997686 | − | 0.0679877i | \(-0.978342\pi\) |
0.439964 | − | 0.898015i | \(-0.354991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 13.5000 | − | 23.3827i | 0.681853 | − | 1.18100i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.0000 | 1.90717 | 0.953583 | − | 0.301131i | \(-0.0973643\pi\) | ||||
0.953583 | + | 0.301131i | \(0.0973643\pi\) | |||||||
\(398\) | −4.00000 | − | 6.92820i | −0.200502 | − | 0.347279i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −11.0000 | + | 19.0526i | −0.549314 | + | 0.951439i | 0.449008 | + | 0.893528i | \(0.351777\pi\) |
−0.998322 | + | 0.0579116i | \(0.981556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.0000 | 1.98517 | ||||||||
\(407\) | 4.00000 | + | 6.92820i | 0.198273 | + | 0.343418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0000 | + | 29.4449i | −0.840596 | + | 1.45595i | 0.0487958 | + | 0.998809i | \(0.484462\pi\) |
−0.889392 | + | 0.457146i | \(0.848872\pi\) | |||||||
\(410\) | −6.00000 | + | 10.3923i | −0.296319 | + | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −48.0000 | −2.36193 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | −2.50000 | − | 4.33013i | −0.122573 | − | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.00000 | + | 3.46410i | −0.0977064 | + | 0.169232i | −0.910735 | − | 0.412991i | \(-0.864484\pi\) |
0.813029 | + | 0.582224i | \(0.197817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | −20.0000 | −0.973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | −0.874157 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 6.92820i | −0.193574 | + | 0.335279i | ||||
\(428\) | 6.00000 | − | 10.3923i | 0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | + | 20.7846i | 0.578691 | + | 1.00232i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 8.00000 | + | 13.8564i | 0.384012 | + | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | −24.0000 | −1.14416 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 2.00000 | + | 3.46410i | 0.0950229 | + | 0.164584i | 0.909618 | − | 0.415445i | \(-0.136374\pi\) |
−0.814595 | + | 0.580030i | \(0.803041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | −2.00000 | + | 3.46410i | −0.0947027 | + | 0.164030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.0000 | + | 24.2487i | 0.661438 | + | 1.14564i | ||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000 | 1.13012 | ||||||||
\(452\) | −3.00000 | − | 5.19615i | −0.141108 | − | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.0000 | − | 17.3205i | 0.469323 | − | 0.812892i | ||||
\(455\) | 4.00000 | − | 6.92820i | 0.187523 | − | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.73205i | −0.0467780 | − | 0.0810219i | 0.841688 | − | 0.539964i | \(-0.181562\pi\) |
−0.888466 | + | 0.458942i | \(0.848229\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0000 | + | 32.9090i | 0.884918 | + | 1.53272i | 0.845807 | + | 0.533488i | \(0.179119\pi\) |
0.0391109 | + | 0.999235i | \(0.487547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | + | 3.46410i | −0.0929479 | + | 0.160990i | −0.908750 | − | 0.417340i | \(-0.862962\pi\) |
0.815802 | + | 0.578331i | \(0.196296\pi\) | |||||||
\(464\) | −5.00000 | + | 8.66025i | −0.232119 | + | 0.402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.00000 | + | 12.1244i | 0.324269 | + | 0.561650i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.0000 | − | 31.1769i | 0.828517 | − | 1.43503i | ||||
\(473\) | 24.0000 | − | 41.5692i | 1.10352 | − | 1.91135i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.00000 | 0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.0000 | −1.09773 | ||||||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00000 | − | 1.73205i | 0.0455961 | − | 0.0789747i | ||||
\(482\) | −5.00000 | + | 8.66025i | −0.227744 | + | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.50000 | + | 4.33013i | 0.113636 | + | 0.196824i | ||||
\(485\) | 20.0000 | 0.908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | −3.00000 | − | 5.19615i | −0.135804 | − | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.00000 | + | 15.5885i | −0.406579 | + | 0.704215i | ||||
\(491\) | 6.00000 | − | 10.3923i | 0.270776 | − | 0.468998i | −0.698285 | − | 0.715820i | \(-0.746053\pi\) |
0.969061 | + | 0.246822i | \(0.0793863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | + | 17.3205i | 0.450377 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0000 | − | 20.7846i | 0.537194 | − | 0.930447i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) |
0.999054 | − | 0.0434940i | \(-0.0138489\pi\) | |||||||
\(500\) | −6.00000 | + | 10.3923i | −0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −8.00000 | −0.356702 | −0.178351 | − | 0.983967i | \(-0.557076\pi\) | ||||
−0.178351 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | + | 13.8564i | −0.354943 | + | 0.614779i | ||||
\(509\) | −5.00000 | + | 8.66025i | −0.221621 | + | 0.383859i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733679 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.0000 | 1.14681 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.00000 | + | 6.92820i | −0.175750 | + | 0.304408i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | + | 5.19615i | 0.131559 | + | 0.227866i | ||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000 | 1.92399 | 0.961993 | − | 0.273075i | \(-0.0880406\pi\) | ||||
0.961993 | + | 0.273075i | \(0.0880406\pi\) | |||||||
\(524\) | 2.00000 | + | 3.46410i | 0.0873704 | + | 0.151330i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | −4.00000 | + | 6.92820i | −0.174243 | + | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 12.0000 | 0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.00000 | − | 5.19615i | −0.129944 | − | 0.225070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | + | 20.7846i | −0.518805 | + | 0.898597i | ||||
\(536\) | −12.0000 | + | 20.7846i | −0.518321 | + | 0.897758i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.0000 | − | 19.0526i | −0.474244 | − | 0.821414i | ||||
\(539\) | 36.0000 | 1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 6.00000 | + | 10.3923i | 0.257722 | + | 0.446388i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.00000 | + | 8.66025i | −0.214373 | + | 0.371305i | ||||
\(545\) | 2.00000 | − | 3.46410i | 0.0856706 | − | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00000 | − | 3.46410i | −0.0855138 | − | 0.148114i | 0.820096 | − | 0.572226i | \(-0.193920\pi\) |
−0.905610 | + | 0.424111i | \(0.860587\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | − | 27.7128i | 0.680389 | − | 1.17847i | ||||
\(554\) | 5.00000 | − | 8.66025i | 0.212430 | − | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | + | 10.3923i | 0.254457 | + | 0.440732i | ||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | −4.00000 | − | 6.92820i | −0.169031 | − | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | − | 8.66025i | 0.210912 | − | 0.365311i | ||||
\(563\) | 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 | ||||||||
\(565\) | 6.00000 | + | 10.3923i | 0.252422 | + | 0.437208i | ||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.0000 | − | 29.4449i | −0.712677 | − | 1.23439i | −0.963849 | − | 0.266450i | \(-0.914149\pi\) |
0.251172 | − | 0.967943i | \(-0.419184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | + | 20.7846i | 0.500870 | + | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.0000 | −1.91501 | −0.957503 | − | 0.288425i | \(-0.906868\pi\) | ||||
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 6.50000 | + | 11.2583i | 0.270364 | + | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.0000 | + | 17.3205i | −0.415227 | + | 0.719195i | ||||
\(581\) | 8.00000 | − | 13.8564i | 0.331896 | − | 0.574861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −14.0000 | − | 24.2487i | −0.577842 | − | 1.00085i | −0.995726 | − | 0.0923513i | \(-0.970562\pi\) |
0.417885 | − | 0.908500i | \(-0.362772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −12.0000 | + | 20.7846i | −0.494032 | + | 0.855689i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.0000 | − | 34.6410i | 0.817178 | − | 1.41539i | −0.0905757 | − | 0.995890i | \(-0.528871\pi\) |
0.907754 | − | 0.419504i | \(-0.137796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | + | 32.9090i | 0.775026 | + | 1.34238i | 0.934780 | + | 0.355228i | \(0.115597\pi\) |
−0.159754 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(602\) | 48.0000 | 1.95633 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | −0.162758 | ||||||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | + | 3.46410i | 0.0809776 | + | 0.140257i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 8.00000 | + | 13.8564i | 0.322854 | + | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −24.0000 | + | 41.5692i | −0.966988 | + | 1.67487i | ||||
\(617\) | −11.0000 | + | 19.0526i | −0.442843 | + | 0.767027i | −0.997899 | − | 0.0647859i | \(-0.979364\pi\) |
0.555056 | + | 0.831813i | \(0.312697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | − | 20.7846i | −0.482321 | − | 0.835404i | 0.517473 | − | 0.855699i | \(-0.326873\pi\) |
−0.999794 | + | 0.0202954i | \(0.993539\pi\) | |||||||
\(620\) | −8.00000 | −0.321288 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.00000 | − | 6.92820i | −0.160257 | − | 0.277573i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 3.00000 | − | 5.19615i | 0.119904 | − | 0.207680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | − | 15.5885i | −0.359139 | − | 0.622047i | ||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 12.0000 | + | 20.7846i | 0.477334 | + | 0.826767i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.0000 | + | 22.5167i | −0.516296 | + | 0.894251i | ||||
\(635\) | 16.0000 | − | 27.7128i | 0.634941 | − | 1.09975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50000 | − | 7.79423i | −0.178296 | − | 0.308819i | ||||
\(638\) | −40.0000 | −1.58362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.00000 | −0.237171 | ||||||||
\(641\) | −1.00000 | − | 1.73205i | −0.0394976 | − | 0.0684119i | 0.845601 | − | 0.533816i | \(-0.179242\pi\) |
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | − | 34.6410i | 0.788723 | − | 1.36611i | −0.138027 | − | 0.990429i | \(-0.544076\pi\) |
0.926750 | − | 0.375680i | \(-0.122591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.00000 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0000 | 1.88416 | ||||||||
\(650\) | 0.500000 | + | 0.866025i | 0.0196116 | + | 0.0339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.00000 | − | 6.92820i | 0.156652 | − | 0.271329i | ||||
\(653\) | −3.00000 | + | 5.19615i | −0.117399 | + | 0.203341i | −0.918736 | − | 0.394872i | \(-0.870789\pi\) |
0.801337 | + | 0.598213i | \(0.204122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | − | 6.92820i | −0.156293 | − | 0.270707i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | − | 24.2487i | −0.545363 | − | 0.944596i | −0.998584 | − | 0.0531977i | \(-0.983059\pi\) |
0.453221 | − | 0.891398i | \(-0.350275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0000 | + | 25.9808i | −0.583432 | + | 1.01053i | 0.411636 | + | 0.911348i | \(0.364957\pi\) |
−0.995069 | + | 0.0991864i | \(0.968376\pi\) | |||||||
\(662\) | 8.00000 | − | 13.8564i | 0.310929 | − | 0.538545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.00000 | − | 6.92820i | −0.154765 | − | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000 | − | 13.8564i | 0.309067 | − | 0.535320i | ||||
\(671\) | 4.00000 | − | 6.92820i | 0.154418 | − | 0.267460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.00000 | + | 12.1244i | 0.269830 | + | 0.467360i | 0.968818 | − | 0.247774i | \(-0.0796991\pi\) |
−0.698988 | + | 0.715134i | \(0.746366\pi\) | |||||||
\(674\) | 18.0000 | 0.693334 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | −11.0000 | − | 19.0526i | −0.422764 | − | 0.732249i | 0.573444 | − | 0.819244i | \(-0.305607\pi\) |
−0.996209 | + | 0.0869952i | \(0.972274\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0000 | − | 34.6410i | 0.767530 | − | 1.32940i | ||||
\(680\) | 6.00000 | − | 10.3923i | 0.230089 | − | 0.398527i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.00000 | − | 13.8564i | −0.306336 | − | 0.530589i | ||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 4.00000 | + | 6.92820i | 0.152721 | + | 0.264520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.00000 | + | 10.3923i | −0.228748 | + | 0.396203i | ||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | + | 20.7846i | 0.456502 | + | 0.790684i | 0.998773 | − | 0.0495194i | \(-0.0157690\pi\) |
−0.542272 | + | 0.840203i | \(0.682436\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −12.0000 | − | 20.7846i | −0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | + | 10.3923i | −0.227266 | + | 0.393637i | ||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | + | 3.46410i | 0.0755929 | + | 0.130931i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −14.0000 | − | 24.2487i | −0.527645 | − | 0.913908i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.00000 | − | 1.73205i | 0.0376355 | − | 0.0651866i | ||||
\(707\) | −36.0000 | + | 62.3538i | −1.35392 | + | 2.34506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | + | 22.5167i | 0.488225 | + | 0.845631i | 0.999908 | − | 0.0135434i | \(-0.00431112\pi\) |
−0.511683 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | + | 6.92820i | −0.149592 | + | 0.259100i | ||||
\(716\) | 2.00000 | − | 3.46410i | 0.0747435 | − | 0.129460i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.0000 | − | 20.7846i | −0.447836 | − | 0.775675i | ||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.50000 | + | 16.4545i | 0.353553 | + | 0.612372i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | −5.00000 | + | 8.66025i | −0.185695 | + | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 12.0000 | 0.444750 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.00000 | 0.148047 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | + | 25.9808i | −0.554038 | + | 0.959621i | 0.443940 | + | 0.896056i | \(0.353580\pi\) |
−0.997978 | + | 0.0635649i | \(0.979753\pi\) | |||||||
\(734\) | −8.00000 | + | 13.8564i | −0.295285 | + | 0.511449i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.0000 | −1.17874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0000 | 1.17714 | 0.588570 | − | 0.808447i | \(-0.299691\pi\) | ||||
0.588570 | + | 0.808447i | \(0.299691\pi\) | |||||||
\(740\) | −2.00000 | − | 3.46410i | −0.0735215 | − | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | − | 20.7846i | 0.440534 | − | 0.763027i | ||||
\(743\) | −24.0000 | + | 41.5692i | −0.880475 | + | 1.52503i | −0.0296605 | + | 0.999560i | \(0.509443\pi\) |
−0.850814 | + | 0.525467i | \(0.823891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | + | 10.3923i | 0.219823 | + | 0.380745i | ||||
\(746\) | −26.0000 | −0.951928 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | 24.0000 | + | 41.5692i | 0.876941 | + | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | + | 6.92820i | −0.145962 | + | 0.252814i | −0.929731 | − | 0.368238i | \(-0.879961\pi\) |
0.783769 | + | 0.621052i | \(0.213294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.00000 | + | 8.66025i | 0.182089 | + | 0.315388i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 12.0000 | + | 20.7846i | 0.435860 | + | 0.754931i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.00000 | − | 8.66025i | 0.181250 | − | 0.313934i | −0.761057 | − | 0.648686i | \(-0.775319\pi\) |
0.942306 | + | 0.334752i | \(0.108652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | − | 6.92820i | −0.144810 | − | 0.250818i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | −6.00000 | − | 10.3923i | −0.216647 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0000 | − | 25.9808i | 0.540914 | − | 0.936890i | −0.457938 | − | 0.888984i | \(-0.651412\pi\) |
0.998852 | − | 0.0479061i | \(-0.0152548\pi\) | |||||||
\(770\) | 16.0000 | − | 27.7128i | 0.576600 | − | 0.998700i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.00000 | + | 15.5885i | 0.323917 | + | 0.561041i | ||||
\(773\) | 10.0000 | 0.359675 | 0.179838 | − | 0.983696i | \(-0.442443\pi\) | ||||
0.179838 | + | 0.983696i | \(0.442443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 15.0000 | + | 25.9808i | 0.538469 | + | 0.932655i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.0000 | + | 19.0526i | −0.394369 | + | 0.683067i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 18.0000 | + | 31.1769i | 0.642448 | + | 1.11275i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | − | 27.7128i | 0.570338 | − | 0.987855i | −0.426193 | − | 0.904632i | \(-0.640145\pi\) |
0.996531 | − | 0.0832226i | \(-0.0265213\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | − | 13.8564i | −0.284627 | − | 0.492989i | ||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | −19.0000 | − | 32.9090i | −0.674285 | − | 1.16790i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | − | 6.92820i | 0.141776 | − | 0.245564i | ||||
\(797\) | −23.0000 | + | 39.8372i | −0.814702 | + | 1.41110i | 0.0948400 | + | 0.995493i | \(0.469766\pi\) |
−0.909542 | + | 0.415612i | \(0.863567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.0000 | 0.776847 | ||||||||
\(803\) | −4.00000 | − | 6.92820i | −0.141157 | − | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | + | 3.46410i | −0.0704470 | + | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.0000 | − | 46.7654i | −0.949857 | − | 1.64520i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 20.0000 | + | 34.6410i | 0.701862 | + | 1.21566i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | − | 6.92820i | 0.140200 | − | 0.242833i | ||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 34.0000 | 1.18878 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | 11.0000 | + | 19.0526i | 0.383903 | + | 0.664939i | 0.991616 | − | 0.129217i | \(-0.0412465\pi\) |
−0.607714 | + | 0.794156i | \(0.707913\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | + | 41.5692i | 0.835067 | + | 1.44638i | ||||
\(827\) | 4.00000 | 0.139094 | 0.0695468 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695468 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −4.00000 | − | 6.92820i | −0.138842 | − | 0.240481i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.50000 | + | 6.06218i | −0.121341 | + | 0.210168i | ||||
\(833\) | −9.00000 | + | 15.5885i | −0.311832 | + | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | + | 13.8564i | 0.276851 | + | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.00000 | 0.138178 | ||||||||
\(839\) | −24.0000 | − | 41.5692i | −0.828572 | − | 1.43513i | −0.899158 | − | 0.437623i | \(-0.855820\pi\) |
0.0705865 | − | 0.997506i | \(-0.477513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.5000 | + | 61.4878i | −1.22414 | + | 2.12027i | ||||
\(842\) | 5.00000 | − | 8.66025i | 0.172311 | − | 0.298452i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 17.3205i | −0.344214 | − | 0.596196i | ||||
\(845\) | 2.00000 | 0.0688021 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | −0.687208 | ||||||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000 | − | 1.73205i | 0.0342997 | − | 0.0594089i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | − | 25.9808i | −0.513590 | − | 0.889564i | −0.999876 | − | 0.0157644i | \(-0.994982\pi\) |
0.486286 | − | 0.873800i | \(-0.338351\pi\) | |||||||
\(854\) | 8.00000 | 0.273754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.0000 | −1.23045 | ||||||||
\(857\) | 23.0000 | + | 39.8372i | 0.785665 | + | 1.36081i | 0.928601 | + | 0.371080i | \(0.121012\pi\) |
−0.142936 | + | 0.989732i | \(0.545654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | − | 38.1051i | 0.750630 | − | 1.30013i | −0.196887 | − | 0.980426i | \(-0.563083\pi\) |
0.947518 | − | 0.319704i | \(-0.103583\pi\) | |||||||
\(860\) | −12.0000 | + | 20.7846i | −0.409197 | + | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0000 | 0.544646 | 0.272323 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272323 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | −17.0000 | − | 29.4449i | −0.577684 | − | 1.00058i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.00000 | + | 13.8564i | −0.271538 | + | 0.470317i | ||||
\(869\) | −16.0000 | + | 27.7128i | −0.542763 | + | 0.940093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | + | 6.92820i | 0.135535 | + | 0.234753i | ||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | − | 41.5692i | −0.811348 | − | 1.40530i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.00000 | − | 8.66025i | 0.168838 | − | 0.292436i | −0.769174 | − | 0.639040i | \(-0.779332\pi\) |
0.938012 | + | 0.346604i | \(0.112665\pi\) | |||||||
\(878\) | −16.0000 | + | 27.7128i | −0.539974 | + | 0.935262i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.00000 | + | 6.92820i | 0.134840 | + | 0.233550i | ||||
\(881\) | 58.0000 | 1.95407 | 0.977035 | − | 0.213080i | \(-0.0683494\pi\) | ||||
0.977035 | + | 0.213080i | \(0.0683494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 1.00000 | + | 1.73205i | 0.0336336 | + | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.00000 | − | 3.46410i | 0.0671913 | − | 0.116379i | ||||
\(887\) | 24.0000 | − | 41.5692i | 0.805841 | − | 1.39576i | −0.109881 | − | 0.993945i | \(-0.535047\pi\) |
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | − | 55.4256i | −1.07325 | − | 1.85892i | ||||
\(890\) | −4.00000 | −0.134080 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | + | 6.92820i | −0.133705 | + | 0.231584i | ||||
\(896\) | −6.00000 | + | 10.3923i | −0.200446 | + | 0.347183i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0000 | − | 19.0526i | −0.367075 | − | 0.635792i | ||||
\(899\) | −40.0000 | −1.33407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −12.0000 | − | 20.7846i | −0.399556 | − | 0.692052i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.00000 | + | 15.5885i | −0.299336 | + | 0.518464i | ||||
\(905\) | 10.0000 | − | 17.3205i | 0.332411 | − | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | 20.0000 | 0.663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00000 | −0.265197 | ||||||||
\(911\) | 20.0000 | + | 34.6410i | 0.662630 | + | 1.14771i | 0.979922 | + | 0.199380i | \(0.0638929\pi\) |
−0.317293 | + | 0.948328i | \(0.602774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | −1.00000 | + | 1.73205i | −0.0330771 | + | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.00000 | − | 8.66025i | −0.165205 | − | 0.286143i | ||||
\(917\) | −16.0000 | −0.528367 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0000 | −1.58337 | −0.791687 | − | 0.610927i | \(-0.790797\pi\) | ||||
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.0000 | − | 32.9090i | 0.625732 | − | 1.08380i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | − | 1.73205i | −0.0328798 | − | 0.0569495i | ||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −50.0000 | −1.64133 | ||||||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.00000 | + | 12.1244i | −0.229293 | + | 0.397146i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 16.0000 | 0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −16.0000 | − | 27.7128i | −0.522419 | − | 0.904855i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.00000 | − | 12.1244i | 0.228193 | − | 0.395243i | −0.729079 | − | 0.684429i | \(-0.760051\pi\) |
0.957273 | + | 0.289187i | \(0.0933848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.0000 | −1.56061 | ||||||||
\(947\) | 30.0000 | + | 51.9615i | 0.974869 | + | 1.68852i | 0.680367 | + | 0.732872i | \(0.261821\pi\) |
0.294502 | + | 0.955651i | \(0.404846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | + | 1.73205i | −0.0324614 | + | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | − | 20.7846i | −0.388922 | − | 0.673633i | ||||
\(953\) | −30.0000 | −0.971795 | −0.485898 | − | 0.874016i | \(-0.661507\pi\) | ||||
−0.485898 | + | 0.874016i | \(0.661507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0000 | 0.517748 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | − | 20.7846i | 0.387702 | − | 0.671520i | ||||
\(959\) | 12.0000 | − | 20.7846i | 0.387500 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | −2.00000 | −0.0644826 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | −18.0000 | − | 31.1769i | −0.579441 | − | 1.00362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0000 | − | 45.0333i | 0.836104 | − | 1.44817i | −0.0570251 | − | 0.998373i | \(-0.518161\pi\) |
0.893129 | − | 0.449801i | \(-0.148505\pi\) | |||||||
\(968\) | 7.50000 | − | 12.9904i | 0.241059 | − | 0.417527i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.0000 | − | 17.3205i | −0.321081 | − | 0.556128i | ||||
\(971\) | −60.0000 | −1.92549 | −0.962746 | − | 0.270408i | \(-0.912841\pi\) | ||||
−0.962746 | + | 0.270408i | \(0.912841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.0000 | −1.53881 | ||||||||
\(974\) | −6.00000 | − | 10.3923i | −0.192252 | − | 0.332991i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | + | 1.73205i | −0.0320092 | + | 0.0554416i | ||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | + | 6.92820i | 0.127841 | + | 0.221426i | ||||
\(980\) | −18.0000 | −0.574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.0000 | −0.382935 | ||||||||
\(983\) | −8.00000 | − | 13.8564i | −0.255160 | − | 0.441951i | 0.709779 | − | 0.704425i | \(-0.248795\pi\) |
−0.964939 | + | 0.262474i | \(0.915462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0000 | + | 31.1769i | −0.573528 | + | 0.993379i | ||||
\(986\) | 10.0000 | − | 17.3205i | 0.318465 | − | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | −10.0000 | − | 17.3205i | −0.317500 | − | 0.549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | + | 13.8564i | −0.253617 | + | 0.439278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | −24.0000 | −0.759707 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))