Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(37,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("108.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.6831243.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 13x^{4} + 49x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(-1.23396i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.73 |
Dual form | 108.4.e.a.37.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.92194 | − | 11.9892i | −0.619117 | − | 1.07234i | −0.989647 | − | 0.143522i | \(-0.954157\pi\) |
0.370530 | − | 0.928821i | \(-0.379176\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.3540 | + | 26.5939i | −0.829038 | + | 1.43594i | 0.0697558 | + | 0.997564i | \(0.477778\pi\) |
−0.898794 | + | 0.438372i | \(0.855555\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.9523 | + | 38.0225i | −0.601715 | + | 1.04220i | 0.390846 | + | 0.920456i | \(0.372182\pi\) |
−0.992561 | + | 0.121745i | \(0.961151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.11853 | + | 10.5976i | 0.130536 | + | 0.226096i | 0.923883 | − | 0.382674i | \(-0.124997\pi\) |
−0.793347 | + | 0.608770i | \(0.791663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −76.0286 | −1.08468 | −0.542342 | − | 0.840158i | \(-0.682462\pi\) | ||||
−0.542342 | + | 0.840158i | \(0.682462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.1789 | −0.533439 | −0.266720 | − | 0.963774i | \(-0.585940\pi\) | ||||
−0.266720 | + | 0.963774i | \(0.585940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.3135 | − | 68.0930i | −0.356410 | − | 0.617321i | 0.630948 | − | 0.775825i | \(-0.282666\pi\) |
−0.987358 | + | 0.158504i | \(0.949333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33.3265 | + | 57.7232i | −0.266612 | + | 0.461786i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −46.3903 | + | 80.3504i | −0.297050 | + | 0.514506i | −0.975460 | − | 0.220178i | \(-0.929336\pi\) |
0.678409 | + | 0.734684i | \(0.262670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 71.5329 | + | 123.899i | 0.414442 | + | 0.717834i | 0.995370 | − | 0.0961208i | \(-0.0306435\pi\) |
−0.580928 | + | 0.813955i | \(0.697310\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 425.118 | 2.05309 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.4741 | −0.144289 | −0.0721447 | − | 0.997394i | \(-0.522984\pi\) | ||||
−0.0721447 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −167.778 | − | 290.599i | −0.639084 | − | 1.10693i | −0.985634 | − | 0.168895i | \(-0.945980\pi\) |
0.346550 | − | 0.938031i | \(-0.387353\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 249.166 | − | 431.567i | 0.883660 | − | 1.53054i | 0.0364186 | − | 0.999337i | \(-0.488405\pi\) |
0.847242 | − | 0.531208i | \(-0.178262\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −140.882 | + | 244.016i | −0.437230 | + | 0.757305i | −0.997475 | − | 0.0710223i | \(-0.977374\pi\) |
0.560244 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −299.990 | − | 519.599i | −0.874608 | − | 1.51487i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 628.565 | 1.62906 | 0.814529 | − | 0.580123i | \(-0.196995\pi\) | ||||
0.814529 | + | 0.580123i | \(0.196995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 607.810 | 1.49013 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 252.327 | + | 437.043i | 0.556782 | + | 0.964375i | 0.997762 | + | 0.0668584i | \(0.0212976\pi\) |
−0.440980 | + | 0.897517i | \(0.645369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.951 | + | 322.076i | −0.390304 | + | 0.676026i | −0.992489 | − | 0.122330i | \(-0.960963\pi\) |
0.602186 | + | 0.798356i | \(0.294297\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 84.7041 | − | 146.712i | 0.161635 | − | 0.279960i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 81.3304 | + | 140.868i | 0.148300 | + | 0.256863i | 0.930599 | − | 0.366040i | \(-0.119287\pi\) |
−0.782299 | + | 0.622903i | \(0.785953\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −433.512 | −0.724626 | −0.362313 | − | 0.932056i | \(-0.618013\pi\) | ||||
−0.362313 | + | 0.932056i | \(0.618013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −629.645 | −1.00951 | −0.504756 | − | 0.863262i | \(-0.668418\pi\) | ||||
−0.504756 | + | 0.863262i | \(0.668418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −674.111 | − | 1167.59i | −0.997689 | − | 1.72805i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −86.3649 | + | 149.588i | −0.122998 | + | 0.213038i | −0.920948 | − | 0.389684i | \(-0.872584\pi\) |
0.797951 | + | 0.602723i | \(0.205917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −87.4288 | + | 151.431i | −0.115621 | + | 0.200262i | −0.918028 | − | 0.396516i | \(-0.870219\pi\) |
0.802407 | + | 0.596778i | \(0.203553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 526.265 | + | 911.518i | 0.671547 | + | 1.16315i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −336.716 | −0.401032 | −0.200516 | − | 0.979690i | \(-0.564262\pi\) | ||||
−0.200516 | + | 0.979690i | \(0.564262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −375.775 | −0.432879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 305.804 | + | 529.668i | 0.330261 | + | 0.572029i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −42.1594 | + | 73.0222i | −0.0441303 | + | 0.0764358i | −0.887247 | − | 0.461295i | \(-0.847385\pi\) |
0.843117 | + | 0.537731i | \(0.180718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −874.902 | + | 1515.38i | −0.861941 | + | 1.49293i | 0.00811161 | + | 0.999967i | \(0.497418\pi\) |
−0.870053 | + | 0.492959i | \(0.835915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −55.6978 | − | 96.4714i | −0.0532822 | − | 0.0922875i | 0.838154 | − | 0.545433i | \(-0.183635\pi\) |
−0.891436 | + | 0.453146i | \(0.850302\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −895.520 | −0.809095 | −0.404548 | − | 0.914517i | \(-0.632571\pi\) | ||||
−0.404548 | + | 0.914517i | \(0.632571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −716.957 | −0.630019 | −0.315009 | − | 0.949089i | \(-0.602008\pi\) | ||||
−0.315009 | + | 0.949089i | \(0.602008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 115.526 | + | 200.096i | 0.0961746 | + | 0.166579i | 0.910098 | − | 0.414393i | \(-0.136006\pi\) |
−0.813924 | + | 0.580972i | \(0.802673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −544.252 | + | 942.672i | −0.441320 | + | 0.764388i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1167.34 | − | 2021.90i | 0.899245 | − | 1.55754i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −298.306 | − | 516.681i | −0.224122 | − | 0.388190i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −807.748 | −0.577978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1715.22 | 1.19843 | 0.599217 | − | 0.800586i | \(-0.295478\pi\) | ||||
0.599217 | + | 0.800586i | \(0.295478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 666.435 | + | 1154.30i | 0.444479 | + | 0.769859i | 0.998016 | − | 0.0629650i | \(-0.0200557\pi\) |
−0.553537 | + | 0.832824i | \(0.686722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 678.323 | − | 1174.89i | 0.442241 | − | 0.765984i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1259.49 | − | 2181.50i | 0.785443 | − | 1.36043i | −0.143292 | − | 0.989680i | \(-0.545769\pi\) |
0.928734 | − | 0.370746i | \(-0.120898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −311.442 | − | 539.433i | −0.190044 | − | 0.329166i | 0.755220 | − | 0.655471i | \(-0.227530\pi\) |
−0.945265 | + | 0.326305i | \(0.894196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −537.263 | −0.314183 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1284.44 | 0.735636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1204.47 | + | 2086.21i | 0.662243 | + | 1.14704i | 0.980025 | + | 0.198875i | \(0.0637289\pi\) |
−0.317781 | + | 0.948164i | \(0.602938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −33.8218 | + | 58.5810i | −0.0182277 | + | 0.0315712i | −0.874995 | − | 0.484131i | \(-0.839136\pi\) |
0.856768 | + | 0.515703i | \(0.172469\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 990.293 | − | 1715.24i | 0.513176 | − | 0.888847i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.19676 | + | 3.80490i | 0.00111669 | + | 0.00193417i | 0.866583 | − | 0.499033i | \(-0.166311\pi\) |
−0.865467 | + | 0.500967i | \(0.832978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2414.48 | 1.18191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2863.88 | −1.37617 | −0.688087 | − | 0.725628i | \(-0.741549\pi\) | ||||
−0.688087 | + | 0.725628i | \(0.741549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 214.757 | + | 371.970i | 0.0995114 | + | 0.172359i | 0.911483 | − | 0.411339i | \(-0.134939\pi\) |
−0.811971 | + | 0.583698i | \(0.801605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1023.63 | − | 1772.97i | 0.465920 | − | 0.806998i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1287.14 | + | 2229.40i | −0.565663 | + | 0.979756i | 0.431325 | + | 0.902197i | \(0.358046\pi\) |
−0.996988 | + | 0.0775599i | \(0.975287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1023.39 | − | 1772.56i | −0.442063 | − | 0.765676i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −807.448 | −0.337159 | −0.168580 | − | 0.985688i | \(-0.553918\pi\) | ||||
−0.168580 | + | 0.985688i | \(0.553918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4296.57 | 1.76443 | 0.882215 | − | 0.470847i | \(-0.156052\pi\) | ||||
0.882215 | + | 0.470847i | \(0.156052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 224.784 | + | 389.337i | 0.0893321 | + | 0.154728i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1669.00 | − | 2890.79i | 0.652671 | − | 1.13046i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −153.147 | + | 265.259i | −0.0580176 | + | 0.100489i | −0.893575 | − | 0.448913i | \(-0.851811\pi\) |
0.835558 | + | 0.549402i | \(0.185145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 856.177 | + | 1482.94i | 0.319321 | + | 0.553080i | 0.980347 | − | 0.197283i | \(-0.0632119\pi\) |
−0.661026 | + | 0.750363i | \(0.729879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 263.636 | 0.0953466 | 0.0476733 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476733 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3835.87 | −1.36642 | −0.683211 | − | 0.730221i | \(-0.739417\pi\) | ||||
−0.683211 | + | 0.730221i | \(0.739417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1424.55 | − | 2467.40i | −0.492532 | − | 0.853091i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2322.69 | + | 4023.02i | −0.791336 | + | 1.37063i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 969.829 | − | 1679.79i | 0.320978 | − | 0.555951i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2034.66 | + | 3524.14i | 0.663848 | + | 1.14982i | 0.979596 | + | 0.200976i | \(0.0644112\pi\) |
−0.315748 | + | 0.948843i | \(0.602255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6898.84 | −2.18836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4393.27 | −1.37435 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −465.183 | − | 805.720i | −0.141591 | − | 0.245243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3078.07 | + | 5331.38i | −0.924318 | + | 1.60097i | −0.131664 | + | 0.991294i | \(0.542032\pi\) |
−0.792654 | + | 0.609672i | \(0.791301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1307 | − | 21.0110i | 0.00354689 | − | 0.00614339i | −0.864247 | − | 0.503069i | \(-0.832204\pi\) |
0.867793 | + | 0.496925i | \(0.165538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 316.209 | + | 547.691i | 0.0912476 | + | 0.158045i | 0.908036 | − | 0.418891i | \(-0.137581\pi\) |
−0.816789 | + | 0.576937i | \(0.804248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3163.59 | 0.889502 | 0.444751 | − | 0.895654i | \(-0.353292\pi\) | ||||
0.444751 | + | 0.895654i | \(0.353292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3900.72 | 1.08279 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1110.57 | + | 1923.57i | 0.300573 | + | 0.520608i | 0.976266 | − | 0.216575i | \(-0.0694887\pi\) |
−0.675693 | + | 0.737183i | \(0.736155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 300.730 | − | 520.879i | 0.0803805 | − | 0.139223i | −0.823033 | − | 0.567994i | \(-0.807720\pi\) |
0.903413 | + | 0.428771i | \(0.141053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4153.03 | + | 7193.26i | −1.08297 | + | 1.87576i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −270.310 | − | 468.191i | −0.0696332 | − | 0.120608i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1350.71 | −0.339665 | −0.169833 | − | 0.985473i | \(-0.554323\pi\) | ||||
−0.169833 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3452.09 | 0.857830 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3521.95 | − | 6100.20i | −0.854838 | − | 1.48062i | −0.876795 | − | 0.480865i | \(-0.840323\pi\) |
0.0219564 | − | 0.999759i | \(-0.493010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 498.607 | − | 863.613i | 0.119621 | − | 0.207190i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1162.13 | − | 2012.87i | 0.272472 | − | 0.471935i | −0.697022 | − | 0.717050i | \(-0.745492\pi\) |
0.969494 | + | 0.245114i | \(0.0788255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4350.89 | − | 7535.97i | −1.00858 | − | 1.74691i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3675.87 | 0.833167 | 0.416584 | − | 0.909097i | \(-0.363227\pi\) | ||||
0.416584 | + | 0.909097i | \(0.363227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1881.48 | −0.421741 | −0.210871 | − | 0.977514i | \(-0.567630\pi\) | ||||
−0.210871 | + | 0.977514i | \(0.567630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1463.19 | − | 2534.31i | −0.320849 | − | 0.555727i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −732.008 | + | 1267.87i | −0.158780 | + | 0.275015i | −0.934429 | − | 0.356149i | \(-0.884089\pi\) |
0.775649 | + | 0.631165i | \(0.217423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4116.28 | + | 7129.61i | −0.873867 | + | 1.51358i | −0.0159023 | + | 0.999874i | \(0.505062\pi\) |
−0.857965 | + | 0.513709i | \(0.828271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −844.364 | − | 1462.48i | −0.177358 | − | 0.307192i | 0.763617 | − | 0.645669i | \(-0.223422\pi\) |
−0.940975 | + | 0.338477i | \(0.890088\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10304.2 | 2.11930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 867.343 | 0.176540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 255.866 | + | 443.173i | 0.0510166 | + | 0.0883633i | 0.890406 | − | 0.455167i | \(-0.150421\pi\) |
−0.839389 | + | 0.543531i | \(0.817087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3493.18 | − | 6050.37i | 0.689427 | − | 1.19412i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 481.082 | − | 833.258i | 0.0930491 | − | 0.161166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7651.37 | + | 13252.6i | 1.46518 | + | 2.53776i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5148.55 | 0.966575 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3171.98 | −0.589690 | −0.294845 | − | 0.955545i | \(-0.595268\pi\) | ||||
−0.294845 | + | 0.955545i | \(0.595268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2530.39 | + | 4382.76i | 0.461367 | + | 0.799112i | 0.999029 | − | 0.0440487i | \(-0.0140257\pi\) |
−0.537662 | + | 0.843160i | \(0.680692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4732.92 | − | 8197.66i | 0.854698 | − | 1.48038i | −0.0222263 | − | 0.999753i | \(-0.507075\pi\) |
0.876925 | − | 0.480628i | \(-0.159591\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3208.57 | − | 5557.40i | 0.568489 | − | 0.984652i | −0.428226 | − | 0.903671i | \(-0.640861\pi\) |
0.996716 | − | 0.0809808i | \(-0.0258052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2036.75 | − | 3527.75i | −0.357479 | − | 0.619172i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3358.86 | 0.578613 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −815.637 | −0.139210 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4326.22 | − | 7493.23i | −0.724961 | − | 1.25567i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3332.37 | + | 5771.83i | −0.553364 | + | 0.958455i | 0.444665 | + | 0.895697i | \(0.353323\pi\) |
−0.998029 | + | 0.0627575i | \(0.980011\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1125.93 | − | 1950.17i | 0.183630 | − | 0.318056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5244.05 | − | 9082.95i | −0.847660 | − | 1.46819i | −0.883291 | − | 0.468825i | \(-0.844678\pi\) |
0.0356314 | − | 0.999365i | \(-0.488656\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6281.25 | −0.997503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7891.37 | 1.24226 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1074.48 | + | 1861.05i | 0.166228 | + | 0.287915i | 0.937091 | − | 0.349086i | \(-0.113508\pi\) |
−0.770863 | + | 0.637001i | \(0.780175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1388.53 | − | 2405.00i | 0.212969 | − | 0.368874i | −0.739673 | − | 0.672966i | \(-0.765020\pi\) |
0.952642 | + | 0.304093i | \(0.0983532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3898.72 | − | 6752.78i | 0.587841 | − | 1.01817i | −0.406673 | − | 0.913574i | \(-0.633311\pi\) |
0.994515 | − | 0.104597i | \(-0.0333554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3000.75 | + | 5197.45i | 0.448629 | + | 0.777047i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2309.31 | −0.339500 | −0.169750 | − | 0.985487i | \(-0.554296\pi\) | ||||
−0.169750 | + | 0.985487i | \(0.554296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4907.22 | −0.715443 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4358.36 | + | 7548.91i | 0.625006 | + | 1.08254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3105.66 | − | 5379.16i | 0.441728 | − | 0.765095i | −0.556090 | − | 0.831122i | \(-0.687699\pi\) |
0.997818 | + | 0.0660271i | \(0.0210324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9650.99 | + | 16716.0i | −1.35055 | + | 2.33922i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4349.61 | − | 7533.75i | −0.603792 | − | 1.04580i | −0.992241 | − | 0.124328i | \(-0.960323\pi\) |
0.388450 | − | 0.921470i | \(-0.373011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1135.36 | −0.155104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5954.77 | 0.807061 | 0.403531 | − | 0.914966i | \(-0.367783\pi\) | ||||
0.403531 | + | 0.914966i | \(0.367783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2128.35 | + | 3686.41i | 0.283952 | + | 0.491819i | 0.972354 | − | 0.233510i | \(-0.0750211\pi\) |
−0.688403 | + | 0.725329i | \(0.741688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9332.31 | + | 16164.0i | −1.23537 | + | 2.13973i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 801.019 | − | 1387.41i | 0.104404 | − | 0.180834i | −0.809090 | − | 0.587684i | \(-0.800040\pi\) |
0.913495 | + | 0.406851i | \(0.133373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2988.95 | + | 5177.02i | 0.386593 | + | 0.669598i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2391.25 | 0.304600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7987.87 | −1.00982 | −0.504912 | − | 0.863171i | \(-0.668475\pi\) | ||||
−0.504912 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3534.75 | − | 6122.36i | −0.440191 | − | 0.762434i | 0.557512 | − | 0.830169i | \(-0.311756\pi\) |
−0.997703 | + | 0.0677350i | \(0.978423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −875.352 | + | 1516.15i | −0.108200 | + | 0.187407i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 712.881 | − | 1234.75i | 0.0868211 | − | 0.150379i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5932.38 | + | 10275.2i | 0.717207 | + | 1.24224i | 0.962102 | + | 0.272689i | \(0.0879129\pi\) |
−0.244896 | + | 0.969549i | \(0.578754\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15496.9 | −1.84637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2420.71 | 0.286332 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6171.30 | − | 10689.0i | −0.719541 | − | 1.24628i | −0.961182 | − | 0.275916i | \(-0.911019\pi\) |
0.241641 | − | 0.970366i | \(-0.422314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2732.93 | + | 4733.58i | −0.316377 | + | 0.547982i | −0.979729 | − | 0.200326i | \(-0.935800\pi\) |
0.663352 | + | 0.748308i | \(0.269133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2533.77 | − | 4388.61i | 0.289190 | − | 0.500892i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5710.17 | − | 9890.30i | −0.647153 | − | 1.12090i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8997.67 | −1.00557 | −0.502787 | − | 0.864410i | \(-0.667692\pi\) | ||||
−0.502787 | + | 0.864410i | \(0.667692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10967.4 | −1.21723 | −0.608615 | − | 0.793466i | \(-0.708275\pi\) | ||||
−0.608615 | + | 0.793466i | \(0.708275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1736.83 | + | 3008.28i | 0.190123 | + | 0.329303i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3563.51 | + | 6172.18i | −0.387419 | + | 0.671029i | −0.992102 | − | 0.125437i | \(-0.959967\pi\) |
0.604683 | + | 0.796467i | \(0.293300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4434.28 | − | 7680.39i | 0.475573 | − | 0.823716i | −0.524036 | − | 0.851696i | \(-0.675574\pi\) |
0.999608 | + | 0.0279799i | \(0.00890744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2330.73 | + | 4036.94i | 0.248286 | + | 0.430043i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9835.05 | −1.03373 | −0.516865 | − | 0.856067i | \(-0.672901\pi\) | ||||
−0.516865 | + | 0.856067i | \(0.672901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14732.4 | 1.53819 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2601.09 | + | 4505.23i | 0.268003 | + | 0.464194i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4443.25 | − | 7695.93i | 0.454806 | − | 0.787747i | −0.543871 | − | 0.839169i | \(-0.683042\pi\) |
0.998677 | + | 0.0514218i | \(0.0163753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 932.894 | − | 1615.82i | 0.0942499 | − | 0.163246i | −0.815045 | − | 0.579397i | \(-0.803288\pi\) |
0.909295 | + | 0.416151i | \(0.136621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6811.70 | + | 11798.2i | 0.683729 | + | 1.18425i | 0.973834 | + | 0.227259i | \(0.0729763\pi\) |
−0.290105 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9328.97 | 0.924397 | 0.462199 | − | 0.886776i | \(-0.347061\pi\) | ||||
0.462199 | + | 0.886776i | \(0.347061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4994.99 | −0.491785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10939.5 | + | 18947.8i | 1.06342 | + | 1.84190i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1472.33 | − | 2550.15i | 0.142221 | − | 0.246335i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1330.15 | − | 2303.89i | 0.126881 | − | 0.219765i | −0.795586 | − | 0.605841i | \(-0.792837\pi\) |
0.922467 | + | 0.386077i | \(0.126170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −198.694 | − | 344.147i | −0.0188350 | − | 0.0326232i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1167.30 | 0.109287 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20450.7 | −1.90289 | −0.951447 | − | 0.307813i | \(-0.900403\pi\) | ||||
−0.951447 | + | 0.307813i | \(0.900403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10327.4 | + | 17887.7i | 0.949228 | + | 1.64411i | 0.747055 | + | 0.664762i | \(0.231467\pi\) |
0.202173 | + | 0.979350i | \(0.435200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3526.99 | − | 6108.92i | 0.322206 | − | 0.558077i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6656.15 | − | 11528.8i | 0.600743 | − | 1.04052i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8733.31 | − | 15126.5i | −0.783480 | − | 1.35703i | −0.929903 | − | 0.367805i | \(-0.880109\pi\) |
0.146423 | − | 0.989222i | \(-0.453224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19951.2 | −1.76855 | −0.884275 | − | 0.466966i | \(-0.845347\pi\) | ||||
−0.884275 | + | 0.466966i | \(0.845347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24224.1 | 2.13457 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3638.88 | − | 6302.73i | −0.316878 | − | 0.548848i | 0.662957 | − | 0.748657i | \(-0.269301\pi\) |
−0.979835 | + | 0.199809i | \(0.935968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9667.57 | − | 16744.7i | 0.836924 | − | 1.44959i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −771.074 | + | 1335.54i | −0.0659759 | + | 0.114274i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6185.39 | − | 10713.4i | −0.526176 | − | 0.911364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11664.5 | 0.980866 | 0.490433 | − | 0.871479i | \(-0.336839\pi\) | ||||
0.490433 | + | 0.871479i | \(0.336839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8925.51 | −0.746243 | −0.373122 | − | 0.927782i | \(-0.621713\pi\) | ||||
−0.373122 | + | 0.927782i | \(0.621713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5438.55 | − | 9419.84i | −0.449539 | − | 0.778624i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2992.39 | − | 5182.98i | 0.245943 | − | 0.425986i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2053.10 | − | 3556.08i | 0.166848 | − | 0.288988i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6198.74 | + | 10736.5i | 0.500925 | + | 0.867627i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26341.9 | 2.10506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12334.1 | 0.980193 | 0.490097 | − | 0.871668i | \(-0.336962\pi\) | ||||
0.490097 | + | 0.871668i | \(0.336962\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4962.74 | + | 8595.71i | 0.390056 | + | 0.675596i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2284.81 | + | 3957.41i | −0.178595 | + | 0.309336i | −0.941400 | − | 0.337293i | \(-0.890489\pi\) |
0.762804 | + | 0.646629i | \(0.223822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2049.47 | − | 3549.79i | 0.158458 | − | 0.274458i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2652.09 | − | 4593.56i | −0.203939 | − | 0.353233i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8154.40 | 0.620310 | 0.310155 | − | 0.950686i | \(-0.399619\pi\) | ||||
0.310155 | + | 0.950686i | \(0.399619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6098.10 | 0.461399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8086.82 | − | 14006.8i | −0.605362 | − | 1.04852i | −0.991994 | − | 0.126284i | \(-0.959695\pi\) |
0.386632 | − | 0.922234i | \(-0.373638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1599.32 | − | 2770.11i | 0.119087 | − | 0.206264i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4548.76 | + | 7878.69i | −0.335139 | + | 0.580478i | −0.983512 | − | 0.180845i | \(-0.942117\pi\) |
0.648372 | + | 0.761323i | \(0.275450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1647.54 | + | 2853.63i | 0.120749 | + | 0.209143i | 0.920063 | − | 0.391770i | \(-0.128137\pi\) |
−0.799314 | + | 0.600913i | \(0.794804\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5240.73 | 0.380093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15544.7 | 1.12155 | 0.560775 | − | 0.827968i | \(-0.310503\pi\) | ||||
0.560775 | + | 0.827968i | \(0.310503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2684.76 | − | 4650.14i | −0.191709 | − | 0.332049i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13798.4 | + | 23899.6i | −0.980229 | + | 1.69781i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2344.33 | + | 4060.50i | −0.164840 | + | 0.285511i | −0.936598 | − | 0.350405i | \(-0.886044\pi\) |
0.771759 | + | 0.635916i | \(0.219377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3160.25 | − | 5473.71i | −0.221079 | − | 0.382921i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16637.6 | −1.15215 | −0.576075 | − | 0.817397i | \(-0.695416\pi\) | ||||
−0.576075 | + | 0.817397i | \(0.695416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32321.1 | −2.22695 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2933.73 | − | 5081.37i | −0.200115 | − | 0.346610i | 0.748450 | − | 0.663191i | \(-0.230798\pi\) |
−0.948565 | + | 0.316581i | \(0.897465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10337.9 | + | 17905.8i | −0.701649 | + | 1.21529i | 0.266238 | + | 0.963907i | \(0.414219\pi\) |
−0.967887 | + | 0.251385i | \(0.919114\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4129.71 | + | 7152.87i | −0.277515 | + | 0.480671i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6303.86 | − | 10918.6i | −0.421525 | − | 0.730103i | 0.574564 | − | 0.818460i | \(-0.305172\pi\) |
−0.996089 | + | 0.0883567i | \(0.971838\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3447.97 | −0.228298 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12469.7 | 0.821608 | 0.410804 | − | 0.911724i | \(-0.365248\pi\) | ||||
0.410804 | + | 0.911724i | \(0.365248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9293.48 | + | 16096.8i | 0.606388 | + | 1.05030i | 0.991830 | + | 0.127563i | \(0.0407156\pi\) |
−0.385442 | + | 0.922732i | \(0.625951\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5972.96 | − | 10345.5i | 0.387841 | − | 0.671761i | −0.604318 | − | 0.796743i | \(-0.706554\pi\) |
0.992159 | + | 0.124983i | \(0.0398876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5169.94 | − | 8954.60i | 0.332471 | − | 0.575856i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9757.00 | + | 16899.6i | 0.624448 | + | 1.08158i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2468.96 | 0.156509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4285.35 | 0.270360 | 0.135180 | − | 0.990821i | \(-0.456839\pi\) | ||||
0.135180 | + | 0.990821i | \(0.456839\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11872.7 | − | 20564.0i | −0.741972 | − | 1.28513i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3671.00 | − | 6358.36i | 0.228336 | − | 0.395490i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10879.1 | + | 18843.2i | −0.670357 | + | 1.16109i | 0.307446 | + | 0.951566i | \(0.400526\pi\) |
−0.977803 | + | 0.209527i | \(0.932808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3671.54 | + | 6359.30i | 0.225181 | + | 0.390025i | 0.956374 | − | 0.292146i | \(-0.0943692\pi\) |
−0.731193 | + | 0.682171i | \(0.761036\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9483.24 | −0.576236 | −0.288118 | − | 0.957595i | \(-0.593030\pi\) | ||||
−0.288118 | + | 0.957595i | \(0.593030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22156.6 | −1.34010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2392.09 | + | 4143.23i | 0.143353 | + | 0.248295i | 0.928757 | − | 0.370688i | \(-0.120878\pi\) |
−0.785404 | + | 0.618984i | \(0.787545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9226.05 | − | 15980.0i | 0.550369 | − | 0.953266i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16034.0 | + | 27771.6i | −0.947791 | + | 1.64162i | −0.197727 | + | 0.980257i | \(0.563356\pi\) |
−0.750064 | + | 0.661365i | \(0.769977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3762.64 | + | 6517.09i | 0.221407 | + | 0.383488i | 0.955235 | − | 0.295847i | \(-0.0956019\pi\) |
−0.733829 | + | 0.679335i | \(0.762269\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18781.3 | −1.09520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7295.07 | 0.423487 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8164.08 | − | 14140.6i | −0.469703 | − | 0.813550i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3670.98 | − | 6358.32i | 0.210261 | − | 0.364183i | −0.741535 | − | 0.670914i | \(-0.765902\pi\) |
0.951796 | + | 0.306731i | \(0.0992352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4760.52 | − | 8245.45i | 0.270253 | − | 0.468092i | −0.698673 | − | 0.715441i | \(-0.746226\pi\) |
0.968927 | + | 0.247348i | \(0.0795592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1294.63 | − | 2242.36i | −0.0731713 | − | 0.126736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1475.06 | 0.0826377 | 0.0413188 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413188 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34872.5 | −1.94512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3845.89 | + | 6661.28i | 0.212651 | + | 0.368323i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17080.4 | + | 29584.0i | −0.940329 | + | 1.62870i | −0.175484 | + | 0.984482i | \(0.556149\pi\) |
−0.764844 | + | 0.644215i | \(0.777184\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4311.56 | + | 7467.84i | −0.235319 | + | 0.407585i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12755.9 | + | 22093.8i | 0.693205 | + | 1.20067i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29427.2 | 1.58552 | 0.792759 | − | 0.609535i | \(-0.208644\pi\) | ||||
0.792759 | + | 0.609535i | \(0.208644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1434.67 | 0.0769696 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26866.5 | − | 46534.1i | −1.42916 | − | 2.47538i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9846.43 | + | 17054.5i | −0.521566 | + | 0.903379i | 0.478119 | + | 0.878295i | \(0.341319\pi\) |
−0.999685 | + | 0.0250840i | \(0.992015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5624.42 | − | 9741.79i | 0.295423 | − | 0.511687i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3718.90 | + | 6441.32i | 0.194516 | + | 0.336912i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33746.9 | 1.75041 | 0.875206 | − | 0.483751i | \(-0.160726\pi\) | ||||
0.875206 | + | 0.483751i | \(0.160726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3420.74 | 0.176692 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3092.05 | − | 5355.60i | −0.158395 | − | 0.274347i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10380.4 | + | 17979.4i | −0.529558 | + | 0.917221i | 0.469848 | + | 0.882748i | \(0.344309\pi\) |
−0.999406 | + | 0.0344737i | \(0.989025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18943.7 | + | 32811.4i | −0.958492 | + | 1.66016i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7122.02 | − | 12335.7i | −0.358878 | − | 0.621596i | 0.628895 | − | 0.777490i | \(-0.283507\pi\) |
−0.987774 | + | 0.155894i | \(0.950174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7141.55 | −0.356937 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27490.2 | 1.36839 | 0.684196 | − | 0.729298i | \(-0.260153\pi\) | ||||
0.684196 | + | 0.729298i | \(0.260153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18234.0 | + | 31582.3i | 0.900326 | + | 1.55941i | 0.827072 | + | 0.562096i | \(0.190005\pi\) |
0.0732537 | + | 0.997313i | \(0.476662\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16674.6 | − | 28881.2i | 0.820013 | − | 1.42030i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13749.8 | − | 23815.4i | 0.670771 | − | 1.16181i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19341.5 | − | 33500.5i | −0.939791 | − | 1.62777i | −0.765860 | − | 0.643007i | \(-0.777686\pi\) |
−0.173931 | − | 0.984758i | \(-0.555647\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 936.449 | 0.0451402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37768.4 | 1.81337 | 0.906683 | − | 0.421813i | \(-0.138606\pi\) | ||||
0.906683 | + | 0.421813i | \(0.138606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10406.6 | − | 18024.7i | −0.495714 | − | 0.858603i | 0.504273 | − | 0.863544i | \(-0.331760\pi\) |
−0.999988 | + | 0.00494154i | \(0.998427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11008.2 | − | 19066.7i | 0.522310 | − | 0.904667i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3087.74 | + | 5348.12i | −0.145361 | + | 0.251772i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3060.85 | − | 5301.55i | −0.143533 | − | 0.248607i | 0.785291 | − | 0.619126i | \(-0.212513\pi\) |
−0.928825 | + | 0.370519i | \(0.879180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34251.2 | 1.59370 | 0.796850 | − | 0.604177i | \(-0.206498\pi\) | ||||
0.796850 | + | 0.604177i | \(0.206498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9535.78 | −0.441981 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7412.23 | + | 12838.4i | 0.340912 | + | 0.590478i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9516.59 | − | 16483.2i | 0.436018 | − | 0.755206i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.4117 | − | 52.6746i | 0.00138273 | − | 0.00239495i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4561.34 | + | 7900.47i | 0.206600 | + | 0.357842i | 0.950641 | − | 0.310292i | \(-0.100427\pi\) |
−0.744041 | + | 0.668134i | \(0.767093\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7095.12 | −0.318930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4550.97 | −0.203795 | ||||||||
\(794\) | 0 | 0 | ||||||||