Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,4,Mod(145,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.145");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.i (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: | \(25.4888251225\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.289 |
Dual form | 432.4.i.a.145.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.50000 | − | 7.79423i | −0.402492 | − | 0.697137i | 0.591534 | − | 0.806280i | \(-0.298523\pi\) |
−0.994026 | + | 0.109143i | \(0.965189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.5000 | + | 26.8468i | −0.836921 | + | 1.44959i | 0.0555351 | + | 0.998457i | \(0.482314\pi\) |
−0.892456 | + | 0.451134i | \(0.851020\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.50000 | − | 12.9904i | 0.205576 | − | 0.356068i | −0.744740 | − | 0.667355i | \(-0.767427\pi\) |
0.950316 | + | 0.311287i | \(0.100760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5000 | + | 32.0429i | 0.394691 | + | 0.683624i | 0.993062 | − | 0.117595i | \(-0.0375185\pi\) |
−0.598371 | + | 0.801219i | \(0.704185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.0000 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.0000 | 0.338086 | 0.169043 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169043 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −97.5000 | − | 168.875i | −0.883920 | − | 1.53099i | −0.846947 | − | 0.531678i | \(-0.821562\pi\) |
−0.0369731 | − | 0.999316i | \(-0.511772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | − | 38.1051i | 0.176000 | − | 0.304841i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 55.5000 | − | 96.1288i | 0.355382 | − | 0.615540i | −0.631801 | − | 0.775131i | \(-0.717684\pi\) |
0.987183 | + | 0.159590i | \(0.0510173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −102.500 | − | 177.535i | −0.593856 | − | 1.02859i | −0.993707 | − | 0.112009i | \(-0.964271\pi\) |
0.399851 | − | 0.916580i | \(-0.369062\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 279.000 | 1.34742 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −166.000 | −0.737574 | −0.368787 | − | 0.929514i | \(-0.620227\pi\) | ||||
−0.368787 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −130.500 | − | 226.033i | −0.497090 | − | 0.860985i | 0.502905 | − | 0.864342i | \(-0.332265\pi\) |
−0.999994 | + | 0.00335732i | \(0.998931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.5000 | + | 37.2391i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −88.5000 | + | 153.286i | −0.274661 | + | 0.475726i | −0.970049 | − | 0.242907i | \(-0.921899\pi\) |
0.695389 | + | 0.718634i | \(0.255232\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −309.000 | − | 535.204i | −0.900875 | − | 1.56036i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −114.000 | −0.295455 | −0.147727 | − | 0.989028i | \(-0.547196\pi\) | ||||
−0.147727 | + | 0.989028i | \(0.547196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −79.5000 | − | 137.698i | −0.175424 | − | 0.303843i | 0.764884 | − | 0.644168i | \(-0.222796\pi\) |
−0.940308 | + | 0.340325i | \(0.889463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.5000 | + | 165.411i | −0.200451 | + | 0.347192i | −0.948674 | − | 0.316256i | \(-0.897574\pi\) |
0.748223 | + | 0.663448i | \(0.230907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 166.500 | − | 288.386i | 0.317720 | − | 0.550307i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −210.500 | − | 364.597i | −0.383831 | − | 0.664815i | 0.607775 | − | 0.794109i | \(-0.292062\pi\) |
−0.991606 | + | 0.129294i | \(0.958729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 156.000 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 182.000 | 0.291801 | 0.145901 | − | 0.989299i | \(-0.453392\pi\) | ||||
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 232.500 | + | 402.702i | 0.344102 | + | 0.596002i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 566.500 | − | 981.207i | 0.806788 | − | 1.39740i | −0.108290 | − | 0.994119i | \(-0.534537\pi\) |
0.915078 | − | 0.403278i | \(-0.132129\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 541.500 | − | 937.906i | 0.716113 | − | 1.24034i | −0.246416 | − | 0.969164i | \(-0.579253\pi\) |
0.962529 | − | 0.271179i | \(-0.0874136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −189.000 | − | 327.358i | −0.241176 | − | 0.417728i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1050.00 | 1.25056 | 0.625280 | − | 0.780401i | \(-0.284985\pi\) | ||||
0.625280 | + | 0.780401i | \(0.284985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1147.00 | −1.32130 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −126.000 | − | 218.238i | −0.136077 | − | 0.235693i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 450.500 | − | 780.289i | 0.471560 | − | 0.816766i | −0.527910 | − | 0.849300i | \(-0.677024\pi\) |
0.999471 | + | 0.0325338i | \(0.0103576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 193.500 | − | 335.152i | 0.190633 | − | 0.330187i | −0.754827 | − | 0.655924i | \(-0.772279\pi\) |
0.945460 | + | 0.325737i | \(0.105613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 275.500 | + | 477.180i | 0.263552 | + | 0.456485i | 0.967183 | − | 0.254080i | \(-0.0817727\pi\) |
−0.703631 | + | 0.710565i | \(0.748439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −0.0108419 | −0.00542095 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542095 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −502.000 | −0.441127 | −0.220564 | − | 0.975373i | \(-0.570790\pi\) | ||||
−0.220564 | + | 0.975373i | \(0.570790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −700.500 | − | 1213.30i | −0.583164 | − | 1.01007i | −0.995102 | − | 0.0988572i | \(-0.968481\pi\) |
0.411938 | − | 0.911212i | \(-0.364852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −877.500 | + | 1519.87i | −0.711542 | + | 1.23243i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −651.000 | + | 1127.57i | −0.501488 | + | 0.868603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 553.000 | + | 957.824i | 0.415477 | + | 0.719627i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 880.000 | 0.614861 | 0.307431 | − | 0.951571i | \(-0.400531\pi\) | ||||
0.307431 | + | 0.951571i | \(0.400531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −751.500 | − | 1301.64i | −0.501213 | − | 0.868126i | −0.999999 | − | 0.00140084i | \(-0.999554\pi\) |
0.498786 | − | 0.866725i | \(-0.333779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −434.000 | + | 751.710i | −0.282952 | + | 0.490087i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1330.50 | + | 2304.49i | −0.829725 | + | 1.43713i | 0.0685295 | + | 0.997649i | \(0.478169\pi\) |
−0.898254 | + | 0.439476i | \(0.855164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −60.5000 | − | 104.789i | −0.0369176 | − | 0.0639431i | 0.846976 | − | 0.531631i | \(-0.178421\pi\) |
−0.883894 | + | 0.467688i | \(0.845087\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 555.000 | 0.324555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −999.000 | −0.572155 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1414.50 | − | 2449.99i | −0.777721 | − | 1.34705i | −0.933253 | − | 0.359221i | \(-0.883043\pi\) |
0.155532 | − | 0.987831i | \(-0.450291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 230.500 | − | 399.238i | 0.124224 | − | 0.215162i | −0.797205 | − | 0.603708i | \(-0.793689\pi\) |
0.921429 | + | 0.388546i | \(0.127023\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −922.500 | + | 1597.82i | −0.478045 | + | 0.827998i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1488.50 | + | 2578.16i | 0.756658 | + | 1.31057i | 0.944546 | + | 0.328379i | \(0.106502\pi\) |
−0.187889 | + | 0.982190i | \(0.560164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6045.00 | 2.95909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3316.00 | 1.59343 | 0.796715 | − | 0.604355i | \(-0.206569\pi\) | ||||
0.796715 | + | 0.604355i | \(0.206569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 340.500 | + | 589.763i | 0.157777 | + | 0.273277i | 0.934067 | − | 0.357099i | \(-0.116234\pi\) |
−0.776290 | + | 0.630376i | \(0.782901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 414.000 | − | 717.069i | 0.188439 | − | 0.326386i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1990.50 | + | 3447.65i | −0.874768 | + | 1.51514i | −0.0177589 | + | 0.999842i | \(0.505653\pi\) |
−0.857009 | + | 0.515301i | \(0.827680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 682.000 | + | 1181.26i | 0.294596 | + | 0.510256i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2004.00 | 0.836793 | 0.418397 | − | 0.908264i | \(-0.362592\pi\) | ||||
0.418397 | + | 0.908264i | \(0.362592\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1274.00 | 0.523181 | 0.261590 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261590 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 747.000 | + | 1293.84i | 0.296868 | + | 0.514190i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 315.000 | − | 545.596i | 0.123182 | − | 0.213358i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −580.500 | + | 1005.46i | −0.219914 | + | 0.380902i | −0.954781 | − | 0.297309i | \(-0.903911\pi\) |
0.734868 | + | 0.678210i | \(0.237244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1805.50 | − | 3127.22i | −0.673382 | − | 1.16633i | −0.976939 | − | 0.213519i | \(-0.931508\pi\) |
0.303557 | − | 0.952813i | \(-0.401826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2046.00 | −0.739957 | −0.369978 | − | 0.929040i | \(-0.620635\pi\) | ||||
−0.369978 | + | 0.929040i | \(0.620635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2996.00 | −1.06724 | −0.533620 | − | 0.845724i | \(-0.679169\pi\) | ||||
−0.533620 | + | 0.845724i | \(0.679169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1720.50 | + | 2979.99i | 0.594854 | + | 1.03032i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1174.50 | + | 2034.29i | −0.400149 | + | 0.693079i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 210.000 | − | 363.731i | 0.0695024 | − | 0.120382i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 377.500 | + | 653.849i | 0.123167 | + | 0.213331i | 0.921015 | − | 0.389528i | \(-0.127362\pi\) |
−0.797848 | + | 0.602858i | \(0.794028\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 387.000 | 0.122759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6355.00 | 1.98804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 777.000 | + | 1345.80i | 0.236501 | + | 0.409631i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1731.50 | + | 2999.05i | −0.519954 | + | 0.900587i | 0.479777 | + | 0.877391i | \(0.340718\pi\) |
−0.999731 | + | 0.0231966i | \(0.992616\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3112.50 | + | 5391.01i | −0.910061 | + | 1.57627i | −0.0960856 | + | 0.995373i | \(0.530632\pi\) |
−0.813976 | + | 0.580899i | \(0.802701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 732.500 | + | 1268.73i | 0.211375 | + | 0.366113i | 0.952145 | − | 0.305646i | \(-0.0988724\pi\) |
−0.740770 | + | 0.671759i | \(0.765539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2634.00 | −0.740597 | −0.370298 | − | 0.928913i | \(-0.620745\pi\) | ||||
−0.370298 | + | 0.928913i | \(0.620745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1593.00 | 0.442195 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3457.50 | − | 5988.57i | −0.935762 | − | 1.62079i | −0.773270 | − | 0.634077i | \(-0.781380\pi\) |
−0.162492 | − | 0.986710i | \(-0.551953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 744.500 | − | 1289.51i | 0.198994 | − | 0.344667i | −0.749209 | − | 0.662334i | \(-0.769566\pi\) |
0.948202 | + | 0.317667i | \(0.102899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2781.00 | + | 4816.83i | −0.725190 | + | 1.25607i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 518.000 | + | 897.202i | 0.133439 | + | 0.231124i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4620.00 | −1.16180 | −0.580900 | − | 0.813975i | \(-0.697299\pi\) | ||||
−0.580900 | + | 0.813975i | \(0.697299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2925.00 | −0.726850 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1675.50 | + | 2902.05i | 0.406672 | + | 0.704377i | 0.994515 | − | 0.104598i | \(-0.0333557\pi\) |
−0.587842 | + | 0.808976i | \(0.700022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2573.00 | − | 4456.57i | 0.617291 | − | 1.06918i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 301.500 | − | 522.213i | 0.0706893 | − | 0.122437i | −0.828514 | − | 0.559968i | \(-0.810813\pi\) |
0.899204 | + | 0.437530i | \(0.144147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 513.000 | + | 888.542i | 0.118918 | + | 0.205972i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1470.00 | 0.333188 | 0.166594 | − | 0.986026i | \(-0.446723\pi\) | ||||
0.166594 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2072.00 | −0.464447 | −0.232223 | − | 0.972662i | \(-0.574600\pi\) | ||||
−0.232223 | + | 0.972662i | \(0.574600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −330.000 | − | 571.577i | −0.0723627 | − | 0.125336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3569.50 | + | 6182.56i | −0.774262 | + | 1.34106i | 0.160947 | + | 0.986963i | \(0.448545\pi\) |
−0.935209 | + | 0.354097i | \(0.884788\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4213.50 | − | 7298.00i | 0.894507 | − | 1.54933i | 0.0600924 | − | 0.998193i | \(-0.480860\pi\) |
0.834414 | − | 0.551138i | \(-0.185806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −228.500 | − | 395.774i | −0.0479962 | − | 0.0831318i | 0.841029 | − | 0.540990i | \(-0.181950\pi\) |
−0.889025 | + | 0.457858i | \(0.848617\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8091.00 | 1.66410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2944.50 | − | 5100.02i | −0.587097 | − | 1.01688i | −0.994610 | − | 0.103683i | \(-0.966937\pi\) |
0.407513 | − | 0.913199i | \(-0.366396\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −715.500 | + | 1239.28i | −0.141214 | + | 0.244589i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3607.50 | − | 6248.37i | 0.697750 | − | 1.20854i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −666.500 | − | 1154.41i | −0.127629 | − | 0.221060i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1719.00 | 0.322720 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1204.00 | 0.223830 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1642.50 | + | 2844.89i | 0.299478 | + | 0.518711i | 0.976017 | − | 0.217696i | \(-0.0698542\pi\) |
−0.676539 | + | 0.736407i | \(0.736521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5028.50 | − | 8709.62i | 0.908075 | − | 1.57283i | 0.0913406 | − | 0.995820i | \(-0.470885\pi\) |
0.816735 | − | 0.577013i | \(-0.195782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1147.50 | − | 1987.53i | 0.203312 | − | 0.352147i | −0.746281 | − | 0.665631i | \(-0.768163\pi\) |
0.949594 | + | 0.313483i | \(0.101496\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −832.500 | − | 1441.93i | −0.146116 | − | 0.253081i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1176.00 | 0.202583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1628.00 | 0.277862 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2743.50 | − | 4751.88i | −0.459739 | − | 0.796291i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3339.50 | + | 5784.18i | −0.554548 | + | 0.960506i | 0.443390 | + | 0.896329i | \(0.353776\pi\) |
−0.997939 | + | 0.0641773i | \(0.979558\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1894.50 | + | 3281.37i | −0.308978 | + | 0.535165i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1091.50 | − | 1890.53i | −0.176433 | − | 0.305590i | 0.764224 | − | 0.644951i | \(-0.223122\pi\) |
−0.940656 | + | 0.339361i | \(0.889789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3075.00 | −0.488330 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8525.00 | 1.34200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1945.50 | − | 3369.70i | −0.300980 | − | 0.521312i | 0.675379 | − | 0.737471i | \(-0.263980\pi\) |
−0.976358 | + | 0.216159i | \(0.930647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1397.50 | + | 2420.54i | −0.214345 | + | 0.371257i | −0.953070 | − | 0.302751i | \(-0.902095\pi\) |
0.738725 | + | 0.674007i | \(0.235428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2377.50 | − | 4117.95i | 0.358475 | − | 0.620896i | −0.629232 | − | 0.777218i | \(-0.716630\pi\) |
0.987706 | + | 0.156322i | \(0.0499636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −702.000 | − | 1215.90i | −0.104953 | − | 0.181784i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4608.00 | 0.677440 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −819.000 | − | 1418.55i | −0.117448 | − | 0.203425i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1922.50 | − | 3329.87i | 0.273443 | − | 0.473618i | −0.696298 | − | 0.717753i | \(-0.745171\pi\) |
0.969741 | + | 0.244135i | \(0.0785041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1767.00 | − | 3060.53i | 0.247272 | − | 0.428288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4158.50 | + | 7202.73i | 0.577263 | + | 0.999848i | 0.995792 | + | 0.0916449i | \(0.0292125\pi\) |
−0.418529 | + | 0.908203i | \(0.637454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4107.00 | 0.561064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12560.0 | −1.70228 | −0.851140 | − | 0.524939i | \(-0.824088\pi\) | ||||
−0.851140 | + | 0.524939i | \(0.824088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6043.50 | − | 10467.6i | −0.806288 | − | 1.39653i | −0.915418 | − | 0.402505i | \(-0.868140\pi\) |
0.109130 | − | 0.994028i | \(-0.465194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2092.50 | − | 3624.32i | 0.276997 | − | 0.479772i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4270.50 | + | 7396.72i | −0.556614 | + | 0.964084i | 0.441162 | + | 0.897428i | \(0.354567\pi\) |
−0.997776 | + | 0.0666565i | \(0.978767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4095.00 | − | 7092.75i | −0.529650 | − | 0.917380i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10197.0 | −1.29890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13174.0 | −1.66545 | −0.832726 | − | 0.553686i | \(-0.813221\pi\) | ||||
−0.832726 | + | 0.553686i | \(0.813221\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4801.50 | + | 8316.44i | 0.597944 | + | 1.03567i | 0.993124 | + | 0.117066i | \(0.0373488\pi\) |
−0.395180 | + | 0.918604i | \(0.629318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3792.50 | − | 6568.80i | 0.468779 | − | 0.811949i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1245.00 | + | 2156.40i | −0.151627 | + | 0.262626i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5735.50 | − | 9934.18i | −0.693404 | − | 1.20101i | −0.970716 | − | 0.240231i | \(-0.922777\pi\) |
0.277312 | − | 0.960780i | \(-0.410557\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4929.00 | 0.587264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9747.00 | −1.15292 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2986.50 | + | 5172.77i | 0.348210 | + | 0.603118i | 0.985932 | − | 0.167149i | \(-0.0534562\pi\) |
−0.637721 | + | 0.770267i | \(0.720123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4452.50 | − | 7711.96i | 0.515443 | − | 0.892774i | −0.484396 | − | 0.874849i | \(-0.660961\pi\) |
0.999839 | − | 0.0179250i | \(-0.00570601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 924.000 | − | 1600.41i | 0.105460 | − | 0.182662i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2960.50 | − | 5127.74i | −0.335524 | − | 0.581144i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1416.00 | 0.158251 | 0.0791257 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791257 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10766.0 | 1.19488 | 0.597438 | − | 0.801915i | \(-0.296186\pi\) | ||||
0.597438 | + | 0.801915i | \(0.296186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2730.00 | − | 4728.50i | −0.298841 | − | 0.517608i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2174.50 | − | 3766.34i | 0.236408 | − | 0.409471i | −0.723273 | − | 0.690562i | \(-0.757363\pi\) |
0.959681 | + | 0.281091i | \(0.0906964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7273.50 | − | 12598.1i | 0.780078 | − | 1.35113i | −0.151818 | − | 0.988408i | \(-0.548513\pi\) |
0.931896 | − | 0.362726i | \(-0.118154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4725.00 | − | 8183.94i | −0.503340 | − | 0.871811i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3330.00 | 0.350005 | 0.175003 | − | 0.984568i | \(-0.444007\pi\) | ||||
0.175003 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3915.00 | −0.408759 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5161.50 | + | 8939.98i | 0.531813 | + | 0.921127i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4073.50 | + | 7055.51i | −0.416959 | + | 0.722194i | −0.995632 | − | 0.0933655i | \(-0.970237\pi\) |
0.578673 | + | 0.815560i | \(0.303571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4015.50 | − | 6955.05i | 0.405684 | − | 0.702666i | −0.588717 | − | 0.808340i | \(-0.700367\pi\) |
0.994401 | + | 0.105674i | \(0.0336999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2141.50 | + | 3709.19i | 0.214955 | + | 0.372312i | 0.953259 | − | 0.302156i | \(-0.0977063\pi\) |
−0.738304 | + | 0.674468i | \(0.764373\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5460.00 | 0.541025 | 0.270512 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270512 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13051.0 | 1.28494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 322.500 | + | 558.586i | 0.0313500 | + | 0.0542999i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 616.000 | − | 1066.94i | 0.0595032 | − | 0.103063i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −214.500 | + | 371.525i | −0.0204609 | + | 0.0354393i | −0.876075 | − | 0.482176i | \(-0.839847\pi\) |
0.855614 | + | 0.517615i | \(0.173180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3071.00 | − | 5319.13i | −0.291113 | − | 0.504223i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8109.00 | −0.759197 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11296.0 | 1.05107 | 0.525535 | − | 0.850772i | \(-0.323865\pi\) | ||||
0.525535 | + | 0.850772i | \(0.323865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7336.50 | + | 12707.2i | 0.674321 | + | 1.16796i | 0.976667 | + | 0.214760i | \(0.0688969\pi\) |
−0.302346 | + | 0.953198i | \(0.597770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2331.00 | − | 4037.41i | 0.212947 | − | 0.368835i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2418.00 | + | 4188.10i | −0.218234 | + | 0.377992i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6719.50 | + | 11638.5i | 0.602818 | + | 1.04411i | 0.992392 | + | 0.123116i | \(0.0392888\pi\) |
−0.389574 | + | 0.920995i | \(0.627378\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17388.0 | −1.54134 | −0.770669 | − | 0.637236i | \(-0.780078\pi\) | ||||
−0.770669 | + | 0.637236i | \(0.780078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3483.00 | −0.306914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1894.50 | − | 3281.37i | −0.164975 | − | 0.285745i | 0.771671 | − | 0.636021i | \(-0.219421\pi\) |
−0.936646 | + | 0.350276i | \(0.886088\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2821.00 | + | 4886.12i | −0.244215 | + | 0.422992i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2479.50 | − | 4294.62i | 0.212155 | − | 0.367463i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1327.50 | + | 2299.30i | 0.112927 | + | 0.195596i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9786.00 | −0.822903 | −0.411451 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411451 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8008.00 | 0.669532 | 0.334766 | − | 0.942301i | \(-0.391343\pi\) | ||||
0.334766 | + | 0.942301i | \(0.391343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4305.00 | − | 7456.48i | −0.355842 | − | 0.616336i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12929.0 | + | 22393.7i | −1.06263 | + | 1.84053i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4828.50 | − | 8363.21i | 0.392393 | − | 0.679645i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.0000 | + | 93.5307i | 0.00436378 | + | 0.00755829i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9270.00 | −0.740793 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2938.00 | −0.233483 | −0.116742 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116742 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2259.00 | + | 3912.70i | 0.177550 | + | 0.307526i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5187.50 | + | 8985.01i | −0.405487 | + | 0.702324i | −0.994378 | − | 0.105888i | \(-0.966231\pi\) |
0.588891 | + | 0.808213i | \(0.299565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1554.00 | − | 2691.61i | 0.120150 | − | 0.208106i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17561.5 | + | 30417.4i | 1.35044 | + | 2.33902i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3306.00 | −0.251490 | −0.125745 | − | 0.992063i | \(-0.540132\pi\) | ||||
−0.125745 | + | 0.992063i | \(0.540132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1591.00 | −0.120379 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10546.5 | + | 18267.1i | 0.789488 | + | 1.36743i | 0.926281 | + | 0.376834i | \(0.122987\pi\) |
−0.136792 | + | 0.990600i | \(0.543679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6304.50 | + | 10919.7i | −0.469438 | + | 0.813090i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 643.500 | − | 1114.57i | 0.0474111 | − | 0.0821185i | −0.841346 | − | 0.540497i | \(-0.818236\pi\) |
0.888757 | + | 0.458379i | \(0.151570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7517.50 | + | 13020.7i | 0.550959 | + | 0.954289i | 0.998206 | + | 0.0598783i | \(0.0190713\pi\) |
−0.447247 | + | 0.894411i | \(0.647595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8580.00 | −0.622280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1190.00 | 0.0858585 | 0.0429292 | − | 0.999078i | \(-0.486331\pi\) | ||||
0.0429292 | + | 0.999078i | \(0.486331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16786.5 | + | 29075.1i | 1.19866 | + | 2.07614i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −855.000 | + | 1480.90i | −0.0607384 | + | 0.105202i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8941.50 | − | 15487.1i | 0.628714 | − | 1.08896i | −0.359096 | − | 0.933301i | \(-0.616915\pi\) |
0.987810 | − | 0.155664i | \(-0.0497518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2870.00 | − | 4970.99i | −0.200775 | − | 0.347752i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20118.0 | −1.39317 | −0.696583 | − | 0.717476i | \(-0.745297\pi\) | ||||
−0.696583 | + | 0.717476i | \(0.745297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11718.0 | 0.807380 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 532.500 | + | 922.317i | 0.0363228 | + | 0.0629129i | 0.883615 | − | 0.468214i | \(-0.155102\pi\) |
−0.847293 | + | 0.531127i | \(0.821769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10362.5 | − | 17948.4i | 0.703320 | − | 1.21819i | −0.263975 | − | 0.964530i | \(-0.585034\pi\) |
0.967294 | − | 0.253656i | \(-0.0816331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4977.00 | − | 8620.42i | 0.334453 | − | 0.579289i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7872.50 | − | 13635.6i | −0.526417 | − | 0.911780i | −0.999526 | − | 0.0307768i | \(-0.990202\pi\) |
0.473110 | − | 0.881004i | \(-0.343131\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6549.00 | −0.433624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5042.00 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5026.50 | − | 8706.15i | −0.327973 | − | 0.568066i | 0.654137 | − | 0.756376i | \(-0.273032\pi\) |
−0.982110 | + | 0.188311i | \(0.939699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2991.50 | + | 5181.43i | −0.194246 | + | 0.336445i | −0.946653 | − | 0.322254i | \(-0.895559\pi\) |
0.752407 | + | 0.658699i | \(0.228893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16275.0 | + | 28189.1i | −1.04662 | + | 1.81280i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4094.50 | + | 7091.88i | 0.262048 | + | 0.453880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6972.00 | −0.441958 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19696.0 | 1.24261 | 0.621304 | − | 0.783570i | \(-0.286603\pi\) | ||||
0.621304 | + | 0.783570i | \(0.286603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3960.00 | − | 6858.92i | −0.247477 | − | 0.428642i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11433.0 | − | 19802.5i | 0.711133 | − | 1.23172i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5488.50 | + | 9506.36i | −0.338195 | + | 0.585770i | −0.984093 | − | 0.177653i | \(-0.943150\pi\) |
0.645899 | + | 0.763423i | \(0.276483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7914.50 | − | 13708.3i | −0.485408 | − | 0.840752i | 0.514451 | − | 0.857520i | \(-0.327996\pi\) |
−0.999859 | + | 0.0167681i | \(0.994662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28224.0 | 1.71499 | 0.857496 | − | 0.514490i | \(-0.172019\pi\) | ||||
0.857496 | + | 0.514490i | \(0.172019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2385.00 | −0.144252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14083.5 | + | 24393.3i | 0.843997 | + | 1.46185i | 0.886490 | + | 0.462749i | \(0.153137\pi\) |
−0.0424927 | + | 0.999097i | \(0.513530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6763.50 | + | 11714.7i | −0.403468 | + | 0.698828i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5368.50 | + | 9298.51i | −0.317340 | + | 0.549649i | −0.979932 | − | 0.199331i | \(-0.936123\pi\) |
0.662592 | + | 0.748980i | \(0.269456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5063.50 | − | 8770.24i | −0.297954 | − | 0.516071i | 0.677714 | − | 0.735326i | \(-0.262971\pi\) |
−0.975668 | + | 0.219255i | \(0.929637\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7812.00 | 0.455543 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21645.0 | −1.25652 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1432.50 | + | 2481.16i | 0.0824159 | + | 0.142748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −125.500 | + | 217.372i | −0.00718822 | + | 0.0124504i | −0.869597 | − | 0.493762i | \(-0.835621\pi\) |
0.862409 | + | 0.506212i | \(0.168955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4225.50 | − | 7318.78i | 0.239881 | − | 0.415485i | −0.720799 | − | 0.693144i | \(-0.756225\pi\) |
0.960680 | + | 0.277659i | \(0.0895584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13965.5 | + | 24189.0i | 0.789318 | + | 1.36714i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25884.0 | −1.45011 | −0.725054 | − | 0.688692i | \(-0.758185\pi\) | ||||
−0.725054 | + | 0.688692i | \(0.758185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23949.0 | 1.33583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2109.00 | − | 3652.90i | −0.116613 | − | 0.201980i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3182.50 | − | 5512.25i | 0.175207 | − | 0.303467i | −0.765026 | − | 0.643999i | \(-0.777274\pi\) |
0.940233 | + | 0.340532i | \(0.110607\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −544.500 | + | 943.102i | −0.0297181 | + | 0.0514732i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5481.00 | − | 9493.37i | −0.297859 | − | 0.515907i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1122.00 | −0.0604527 | −0.0302264 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302264 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4648.00 | −0.249364 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5998.50 | + | 10389.7i | 0.319090 | + | 0.552681i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2141.50 | + | 3709.19i | −0.113435 | + | 0.196476i | −0.917153 | − | 0.398535i | \(-0.869519\pi\) |
0.803718 | + | 0.595011i | \(0.202852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19987.5 | + | 34619.4i | −1.04984 | + | 1.81838i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2497.50 | − | 4325.80i | −0.130631 | − | 0.226260i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4032.00 | 0.209135 | 0.104568 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104568 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17081.0 | −0.882288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2442.00 | − | 4229.67i | −0.125095 | − | 0.216670i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12002.5 | − | 20788.9i | 0.612308 | − | 1.06055i | −0.378542 | − | 0.925584i | \(-0.623574\pi\) |
0.990850 | − | 0.134965i | \(-0.0430922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −903.000 | + | 1564.04i | −0.0456890 | + | 0.0791357i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18750.5 | + | 32476.8i | 0.944837 | + | 1.63651i | 0.756077 | + | 0.654482i | \(0.227113\pi\) |
0.188760 | + | 0.982023i | \(0.439553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6315.00 | −0.315626 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 880.000 | 0.0438042 | 0.0219021 | − | 0.999760i | \(-0.493028\pi\) | ||||
0.0219021 | + | 0.999760i | \(0.493028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −811.500 | − | 1405.56i | −0.0400687 | − | 0.0694010i | 0.845296 | − | 0.534299i | \(-0.179424\pi\) |
−0.885364 | + | 0.464898i | \(0.846091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12730.5 | + | 22049.9i | −0.626053 | + | 1.08436i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 186.000 | − | 322.161i | 0.00907382 | − | 0.0157163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3444.50 | − | 5966.05i | −0.167366 | − | 0.289886i | 0.770127 | − | 0.637890i | \(-0.220193\pi\) |
−0.937493 | + | 0.348005i | \(0.886859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4149.00 | −0.199997 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12850.0 | −0.616963 | −0.308482 | − | 0.951230i | \(-0.599821\pi\) | ||||
−0.308482 | + | 0.951230i | \(0.599821\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2305.50 | + | 3993.24i | 0.109822 | + | 0.190217i | 0.915698 | − | 0.401867i | \(-0.131639\pi\) |
−0.805876 | + | 0.592084i | \(0.798305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7781.00 | − | 13477.1i | 0.369189 | − | 0.639454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2941.50 | − | 5094.83i | 0.138476 | − | 0.239848i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1152.50 | + | 1996.19i | 0.0540445 | + | 0.0936078i | 0.891782 | − | 0.452465i | \(-0.149455\pi\) |
−0.837737 | + | 0.546073i | \(0.816122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34902.0 | 1.62398 | 0.811991 | − | 0.583670i | \(-0.198384\pi\) | ||||
0.811991 | + | 0.583670i | \(0.198384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9020.00 | −0.418075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3654.00 | − | 6328.91i | −0.168059 | − | 0.291087i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1170.00 | − | 2026.50i | 0.0536055 | − | 0.0928474i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13396.5 | − | 23203.4i | 0.609098 | − | 1.05499i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13127.5 | + | 22737.5i | 0.594593 | + | 1.02987i | 0.993604 | + | 0.112919i | \(0.0360202\pi\) |
−0.399011 | + | 0.916946i | \(0.630646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43431.0 | 1.95225 | ||||||||
\(792\) | 0 | 0 |