Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 11 x^{10} + 60 x^{9} - 120 x^{8} - 342 x^{7} + 2709 x^{6} - 3078 x^{5} - 9720 x^{4} + 43740 x^{3} - 72171 x^{2} - 118098 x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.4 | ||
Root | \(0.459278 + 2.96464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.c.101.4 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.459278 | − | 2.96464i | −0.153093 | − | 0.988212i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.13490 | − | 7.16186i | −0.590700 | − | 1.02312i | −0.994138 | − | 0.108115i | \(-0.965518\pi\) |
0.403438 | − | 0.915007i | \(-0.367815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.57813 | + | 2.72318i | −0.953125 | + | 0.302576i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.29604 | − | 1.90297i | 0.299640 | − | 0.172997i | −0.342641 | − | 0.939466i | \(-0.611321\pi\) |
0.642281 | + | 0.766469i | \(0.277988\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.65850 | − | 16.7290i | 0.742962 | − | 1.28685i | −0.208179 | − | 0.978091i | \(-0.566754\pi\) |
0.951141 | − | 0.308757i | \(-0.0999129\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.87471i | − | 0.463218i | −0.972809 | − | 0.231609i | \(-0.925601\pi\) | ||
0.972809 | − | 0.231609i | \(-0.0743990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.3401 | −0.649478 | −0.324739 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324739 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.3332 | + | 15.5478i | −0.920630 | + | 0.740369i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.04738 | − | 0.604705i | −0.0455383 | − | 0.0262915i | 0.477058 | − | 0.878872i | \(-0.341703\pi\) |
−0.522596 | + | 0.852580i | \(0.675036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.0130 | + | 24.1803i | 0.444925 | + | 0.895568i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.7443 | − | 6.20324i | 0.370494 | − | 0.213905i | −0.303180 | − | 0.952933i | \(-0.598048\pi\) |
0.673674 | + | 0.739028i | \(0.264715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.65731 | + | 8.06669i | −0.150236 | + | 0.260216i | −0.931314 | − | 0.364217i | \(-0.881337\pi\) |
0.781078 | + | 0.624433i | \(0.214670\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.15541 | − | 8.89757i | −0.216831 | − | 0.269623i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −37.0571 | −1.00154 | −0.500772 | − | 0.865579i | \(-0.666950\pi\) | ||||
−0.500772 | + | 0.865579i | \(0.666950\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −54.0314 | − | 20.9507i | −1.38542 | − | 0.537197i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.1391 | + | 23.1743i | 0.979002 | + | 0.565227i | 0.901969 | − | 0.431802i | \(-0.142122\pi\) |
0.0770331 | + | 0.997029i | \(0.475455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.7083 | − | 53.1884i | −0.714148 | − | 1.23694i | −0.963287 | − | 0.268472i | \(-0.913481\pi\) |
0.249140 | − | 0.968468i | \(-0.419852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −79.7091 | + | 46.0201i | −1.69594 | + | 0.979151i | −0.746402 | + | 0.665496i | \(0.768220\pi\) |
−0.949537 | + | 0.313655i | \(0.898446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.69479 | + | 16.7919i | −0.197853 | + | 0.342691i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23.3456 | + | 3.61668i | −0.457758 | + | 0.0709152i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 52.1540i | 0.984038i | 0.870584 | + | 0.492019i | \(0.163741\pi\) | ||||
−0.870584 | + | 0.492019i | \(0.836259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.66752 | + | 36.5838i | 0.0994303 | + | 0.641822i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −54.4701 | − | 31.4484i | −0.923223 | − | 0.533023i | −0.0385610 | − | 0.999256i | \(-0.512277\pi\) |
−0.884662 | + | 0.466233i | \(0.845611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6631 | + | 20.2011i | 0.191199 | + | 0.331166i | 0.945648 | − | 0.325193i | \(-0.105429\pi\) |
−0.754449 | + | 0.656359i | \(0.772096\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 54.9727 | + | 50.1752i | 0.872583 | + | 0.796432i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.1692 | + | 93.8237i | −0.808495 | + | 1.40035i | 0.105411 | + | 0.994429i | \(0.466384\pi\) |
−0.913906 | + | 0.405926i | \(0.866949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.31169 | + | 3.38283i | −0.0190100 | + | 0.0490265i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 134.509i | − | 1.89449i | −0.320510 | − | 0.947245i | \(-0.603854\pi\) | ||
0.320510 | − | 0.947245i | \(-0.396146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.7798 | 0.914792 | 0.457396 | − | 0.889263i | \(-0.348782\pi\) | ||||
0.457396 | + | 0.889263i | \(0.348782\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.2576 | − | 15.7372i | −0.353995 | − | 0.204379i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62.2089 | + | 107.749i | 0.787455 | + | 1.36391i | 0.927521 | + | 0.373770i | \(0.121935\pi\) |
−0.140066 | + | 0.990142i | \(0.544732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 66.1686 | − | 46.7196i | 0.816896 | − | 0.576785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69.8921 | − | 40.3522i | 0.842074 | − | 0.486172i | −0.0158947 | − | 0.999874i | \(-0.505060\pi\) |
0.857969 | + | 0.513702i | \(0.171726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.3250 | − | 29.0040i | −0.268103 | − | 0.333380i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 176.513i | 1.98330i | 0.128976 | + | 0.991648i | \(0.458831\pi\) | ||||
−0.128976 | + | 0.991648i | \(0.541169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −159.748 | −1.75547 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.0538 | + | 10.1024i | 0.280148 | + | 0.108628i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −45.9441 | − | 79.5774i | −0.473650 | − | 0.820386i | 0.525895 | − | 0.850550i | \(-0.323731\pi\) |
−0.999545 | + | 0.0301635i | \(0.990397\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.0917 | + | 25.2997i | −0.233250 | + | 0.255552i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 35.2716 | − | 20.3641i | 0.349223 | − | 0.201624i | −0.315120 | − | 0.949052i | \(-0.602045\pi\) |
0.664343 | + | 0.747428i | \(0.268711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51.6856 | + | 89.5221i | −0.501802 | + | 0.869147i | 0.498196 | + | 0.867065i | \(0.333996\pi\) |
−0.999998 | + | 0.00208213i | \(0.999337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 21.9162i | − | 0.204824i | −0.994742 | − | 0.102412i | \(-0.967344\pi\) | ||
0.994742 | − | 0.102412i | \(-0.0326560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −80.9662 | −0.742810 | −0.371405 | − | 0.928471i | \(-0.621124\pi\) | ||||
−0.371405 | + | 0.928471i | \(0.621124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.0195 | + | 109.861i | 0.153329 | + | 0.989737i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −103.180 | − | 59.5708i | −0.913094 | − | 0.527175i | −0.0316683 | − | 0.999498i | \(-0.510082\pi\) |
−0.881425 | + | 0.472324i | \(0.843415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.2957 | + | 169.805i | −0.318767 | + | 1.45133i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −56.3975 | + | 32.5611i | −0.473929 | + | 0.273623i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.2574 | + | 92.2445i | −0.440144 | + | 0.762351i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 50.2684 | − | 129.641i | 0.408686 | − | 1.05399i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −136.157 | −1.07211 | −0.536053 | − | 0.844185i | \(-0.680085\pi\) | ||||
−0.536053 | + | 0.844185i | \(0.680085\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −143.581 | + | 115.467i | −1.11303 | + | 0.895095i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −162.827 | − | 94.0080i | −1.24295 | − | 0.717618i | −0.273257 | − | 0.961941i | \(-0.588101\pi\) |
−0.969694 | + | 0.244323i | \(0.921434\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51.0250 | + | 88.3779i | 0.383647 | + | 0.664495i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 226.868 | − | 130.982i | 1.65597 | − | 0.956075i | 0.681424 | − | 0.731889i | \(-0.261361\pi\) |
0.974546 | − | 0.224186i | \(-0.0719722\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 41.3482 | − | 71.6171i | 0.297469 | − | 0.515231i | −0.678087 | − | 0.734981i | \(-0.737191\pi\) |
0.975556 | + | 0.219750i | \(0.0705243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 173.041 | + | 215.172i | 1.22724 | + | 1.52605i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 73.5194i | − | 0.514122i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.2344 | + | 21.0294i | 0.368941 | + | 0.143057i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.5623 | − | 10.1396i | −0.117868 | − | 0.0680510i | 0.439907 | − | 0.898043i | \(-0.355011\pi\) |
−0.557775 | + | 0.829992i | \(0.688345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.31435 | − | 16.1329i | −0.0616844 | − | 0.106841i | 0.833534 | − | 0.552468i | \(-0.186314\pi\) |
−0.895218 | + | 0.445628i | \(0.852981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.4443 | + | 67.5502i | 0.140159 | + | 0.441505i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −89.4268 | + | 154.892i | −0.569598 | + | 0.986572i | 0.427008 | + | 0.904248i | \(0.359568\pi\) |
−0.996606 | + | 0.0823242i | \(0.973766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 154.618 | − | 23.9532i | 0.972438 | − | 0.150649i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0016i | 0.0621216i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.42383 | −0.0271401 | −0.0135700 | − | 0.999908i | \(-0.504320\pi\) | ||||
−0.0135700 | + | 0.999908i | \(0.504320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9679 | − | 8.06435i | −0.0836399 | − | 0.0482895i | 0.457597 | − | 0.889160i | \(-0.348710\pi\) |
−0.541237 | + | 0.840870i | \(0.682044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −102.073 | − | 176.796i | −0.603984 | − | 1.04613i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 105.855 | − | 33.6043i | 0.619034 | − | 0.196516i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 180.607 | − | 104.274i | 1.04397 | − | 0.602738i | 0.123017 | − | 0.992405i | \(-0.460743\pi\) |
0.920956 | + | 0.389666i | \(0.127410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −68.2160 | + | 175.928i | −0.385401 | + | 0.993942i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0917i | 0.0843110i | 0.999111 | + | 0.0421555i | \(0.0134225\pi\) | ||||
−0.999111 | + | 0.0421555i | \(0.986578\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −334.817 | −1.84982 | −0.924910 | − | 0.380187i | \(-0.875860\pi\) | ||||
−0.924910 | + | 0.380187i | \(0.875860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 54.5323 | − | 43.8548i | 0.297991 | − | 0.239644i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.9853 | − | 25.9554i | −0.0801355 | − | 0.138799i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 123.504 | − | 186.018i | 0.653458 | − | 0.984225i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 262.232 | − | 151.399i | 1.37294 | − | 0.792667i | 0.381643 | − | 0.924310i | \(-0.375358\pi\) |
0.991297 | + | 0.131642i | \(0.0420251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −84.4137 | + | 146.209i | −0.437377 | + | 0.757559i | −0.997486 | − | 0.0708599i | \(-0.977426\pi\) |
0.560110 | + | 0.828418i | \(0.310759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 327.080i | − | 1.66030i | −0.557537 | − | 0.830152i | \(-0.688254\pi\) | ||
0.557537 | − | 0.830152i | \(-0.311746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 165.715 | 0.832736 | 0.416368 | − | 0.909196i | \(-0.363303\pi\) | ||||
0.416368 | + | 0.909196i | \(0.363303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 303.032 | + | 117.501i | 1.50762 | + | 0.584580i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −88.8535 | − | 51.2996i | −0.437702 | − | 0.252707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.6313 | + | 2.33503i | 0.0513589 | + | 0.0112803i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.6734 | + | 23.4828i | −0.194610 | + | 0.112358i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 94.4460 | − | 163.585i | 0.447611 | − | 0.775285i | −0.550619 | − | 0.834757i | \(-0.685608\pi\) |
0.998230 | + | 0.0594715i | \(0.0189415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −398.770 | + | 61.7769i | −1.87216 | + | 0.290032i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 77.0300 | 0.354977 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.6705 | − | 197.978i | −0.140048 | − | 0.904009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −131.736 | − | 76.0579i | −0.596091 | − | 0.344153i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −143.892 | − | 249.229i | −0.645256 | − | 1.11762i | −0.984242 | − | 0.176825i | \(-0.943417\pi\) |
0.338986 | − | 0.940792i | \(-0.389916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 171.961 | − | 99.2817i | 0.757537 | − | 0.437364i | −0.0708736 | − | 0.997485i | \(-0.522579\pi\) |
0.828411 | + | 0.560121i | \(0.189245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 191.729 | − | 332.085i | 0.837245 | − | 1.45015i | −0.0549441 | − | 0.998489i | \(-0.517498\pi\) |
0.892189 | − | 0.451662i | \(-0.149169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −34.1362 | + | 88.0366i | −0.147776 | + | 0.381111i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 240.304i | 1.03135i | 0.856784 | + | 0.515675i | \(0.172459\pi\) | ||||
−0.856784 | + | 0.515675i | \(0.827541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 290.865 | − | 233.914i | 1.22728 | − | 0.986977i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −62.2301 | − | 35.9285i | −0.260377 | − | 0.150329i | 0.364130 | − | 0.931348i | \(-0.381367\pi\) |
−0.624506 | + | 0.781020i | \(0.714700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −85.1369 | − | 147.461i | −0.353265 | − | 0.611873i | 0.633554 | − | 0.773698i | \(-0.281595\pi\) |
−0.986819 | + | 0.161825i | \(0.948262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −168.896 | − | 174.708i | −0.695047 | − | 0.718965i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −119.187 | + | 206.437i | −0.482537 | + | 0.835779i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −151.730 | − | 188.672i | −0.609356 | − | 0.757718i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 78.9688i | − | 0.314617i | −0.987550 | − | 0.157308i | \(-0.949718\pi\) | ||
0.987550 | − | 0.157308i | \(-0.0502817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.60295 | −0.0181935 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −46.4932 | − | 26.8428i | −0.180907 | − | 0.104447i | 0.406812 | − | 0.913512i | \(-0.366641\pi\) |
−0.587719 | + | 0.809065i | \(0.699974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 153.227 | + | 265.398i | 0.591612 | + | 1.02470i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −75.2737 | + | 82.4710i | −0.288405 | + | 0.315981i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.94989 | − | 5.16722i | 0.0340300 | − | 0.0196472i | −0.482888 | − | 0.875682i | \(-0.660412\pi\) |
0.516918 | + | 0.856035i | \(0.327079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 523.298 | − | 81.0686i | 1.95992 | − | 0.303628i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.2492i | 0.112451i | 0.998418 | + | 0.0562254i | \(0.0179065\pi\) | ||||
−0.998418 | + | 0.0562254i | \(0.982093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −139.993 | −0.516579 | −0.258290 | − | 0.966068i | \(-0.583159\pi\) | ||||
−0.258290 | + | 0.966068i | \(0.583159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.3686 | + | 473.594i | 0.268749 | + | 1.73478i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.4980 | − | 47.6279i | −0.0992708 | − | 0.171942i | 0.812112 | − | 0.583501i | \(-0.198318\pi\) |
−0.911383 | + | 0.411559i | \(0.864984\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.9839 | − | 81.8798i | 0.0644584 | − | 0.293476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 427.134 | − | 246.606i | 1.52005 | − | 0.877600i | 0.520328 | − | 0.853967i | \(-0.325810\pi\) |
0.999721 | − | 0.0236336i | \(-0.00752352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 121.143 | − | 209.825i | 0.428066 | − | 0.741433i | −0.568635 | − | 0.822590i | \(-0.692528\pi\) |
0.996701 | + | 0.0811572i | \(0.0258616\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 383.294i | − | 1.33552i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 226.989 | 0.785429 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −214.817 | + | 172.756i | −0.738203 | + | 0.593662i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 112.750 | + | 65.0963i | 0.384812 | + | 0.222172i | 0.679910 | − | 0.733296i | \(-0.262019\pi\) |
−0.295098 | + | 0.955467i | \(0.595352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 85.6098 | + | 56.8390i | 0.288248 | + | 0.191377i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.2322 | + | 11.6811i | −0.0676664 | + | 0.0390672i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −253.952 | + | 439.857i | −0.843694 | + | 1.46132i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −76.5714 | − | 95.2146i | −0.252711 | − | 0.314240i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −117.072 | −0.381341 | −0.190670 | − | 0.981654i | \(-0.561066\pi\) | ||||
−0.190670 | + | 0.981654i | \(0.561066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 289.138 | + | 112.113i | 0.935723 | + | 0.362827i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.4771 | + | 9.51306i | 0.0529810 | + | 0.0305886i | 0.526257 | − | 0.850326i | \(-0.323595\pi\) |
−0.473276 | + | 0.880914i | \(0.656928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 83.5346 | + | 144.686i | 0.266884 | + | 0.462256i | 0.968055 | − | 0.250736i | \(-0.0806727\pi\) |
−0.701172 | + | 0.712992i | \(0.747339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 169.663 | − | 97.9549i | 0.535214 | − | 0.309006i | −0.207923 | − | 0.978145i | \(-0.566670\pi\) |
0.743137 | + | 0.669139i | \(0.233337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.6092 | − | 40.8923i | 0.0740100 | − | 0.128189i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −64.9735 | + | 10.0656i | −0.202410 | + | 0.0313571i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 97.1745i | 0.300850i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.1860 | + | 240.035i | 0.113719 | + | 0.734053i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 659.178 | + | 380.577i | 2.00358 | + | 1.15677i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 40.9636 | + | 70.9510i | 0.123757 | + | 0.214353i | 0.921246 | − | 0.388980i | \(-0.127172\pi\) |
−0.797489 | + | 0.603333i | \(0.793839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 317.881 | − | 100.913i | 0.954596 | − | 0.303043i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 263.107 | − | 455.714i | 0.780732 | − | 1.35227i | −0.150784 | − | 0.988567i | \(-0.548180\pi\) |
0.931516 | − | 0.363700i | \(-0.118487\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −129.217 | + | 333.249i | −0.381173 | + | 0.983036i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.4509i | 0.103962i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −244.872 | −0.713913 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 393.556 | + | 227.219i | 1.13417 | + | 0.654811i | 0.944979 | − | 0.327130i | \(-0.106082\pi\) |
0.189186 | + | 0.981941i | \(0.439415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 102.845 | + | 178.134i | 0.294686 | + | 0.510411i | 0.974912 | − | 0.222591i | \(-0.0714516\pi\) |
−0.680226 | + | 0.733003i | \(0.738118\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 520.541 | + | 32.5803i | 1.48302 | + | 0.0928213i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −87.3821 | + | 50.4501i | −0.247541 | + | 0.142918i | −0.618638 | − | 0.785676i | \(-0.712315\pi\) |
0.371097 | + | 0.928594i | \(0.378982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 122.434 | + | 152.243i | 0.342952 | + | 0.426452i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 430.783i | − | 1.19995i | −0.800018 | − | 0.599977i | \(-0.795177\pi\) | ||
0.800018 | − | 0.599977i | \(-0.204823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −208.722 | −0.578178 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 297.931 | + | 115.523i | 0.820748 | + | 0.318245i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −162.310 | − | 281.129i | −0.442261 | − | 0.766018i | 0.555596 | − | 0.831452i | \(-0.312490\pi\) |
−0.997857 | + | 0.0654344i | \(0.979157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −407.426 | − | 89.4861i | −1.10414 | − | 0.242510i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 373.520 | − | 215.652i | 1.00679 | − | 0.581271i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 68.2485 | − | 118.210i | 0.182972 | − | 0.316917i | −0.759919 | − | 0.650017i | \(-0.774762\pi\) |
0.942891 | + | 0.333101i | \(0.108095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 239.656i | − | 0.635693i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.1240 | −0.0689286 | −0.0344643 | − | 0.999406i | \(-0.510973\pi\) | ||||
−0.0344643 | + | 0.999406i | \(0.510973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 62.5341 | + | 403.657i | 0.164131 | + | 1.05947i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −421.006 | − | 243.068i | −1.09923 | − | 0.634642i | −0.163213 | − | 0.986591i | \(-0.552186\pi\) |
−0.936019 | + | 0.351948i | \(0.885519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 408.262 | + | 372.633i | 1.05494 | + | 0.962875i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 188.122 | − | 108.612i | 0.483605 | − | 0.279209i | −0.238313 | − | 0.971188i | \(-0.576594\pi\) |
0.721918 | + | 0.691979i | \(0.243261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76188 | + | 8.24781i | −0.0121787 | + | 0.0210941i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −203.917 | + | 525.897i | −0.518872 | + | 1.33816i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −506.995 | −1.27707 | −0.638533 | − | 0.769595i | \(-0.720458\pi\) | ||||
−0.638533 | + | 0.769595i | \(0.720458\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 238.574 | − | 191.861i | 0.597929 | − | 0.480853i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −433.469 | − | 250.263i | −1.08097 | − | 0.624098i | −0.149812 | − | 0.988715i | \(-0.547867\pi\) |
−0.931158 | + | 0.364616i | \(0.881200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 89.9652 | + | 155.824i | 0.223239 | + | 0.386661i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −122.142 | + | 70.5186i | −0.300103 | + | 0.173264i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −221.644 | + | 383.899i | −0.541917 | + | 0.938628i | 0.456877 | + | 0.889530i | \(0.348968\pi\) |
−0.998794 | + | 0.0490978i | \(0.984365\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −492.510 | − | 612.423i | −1.19832 | − | 1.49008i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 520.143i | 1.25943i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −231.309 | − | 89.6901i | −0.554698 | − | 0.215084i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −79.3438 | − | 45.8092i | −0.189365 | − | 0.109330i | 0.402320 | − | 0.915499i | \(-0.368204\pi\) |
−0.591685 | + | 0.806169i | \(0.701537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.07420 | + | 1.86057i | 0.00255155 | + | 0.00441941i | 0.867298 | − | 0.497789i | \(-0.165854\pi\) |
−0.864747 | + | 0.502208i | \(0.832521\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 558.434 | − | 611.829i | 1.32017 | − | 1.44640i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 96.4516 | − | 167.059i | 0.225882 | − | 0.391239i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −217.958 | + | 33.7658i | −0.508061 | + | 0.0787082i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 770.877i | − | 1.78858i | −0.447491 | − | 0.894289i | \(-0.647682\pi\) | ||
0.447491 | − | 0.894289i | \(-0.352318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −304.898 | −0.704153 | −0.352076 | − | 0.935971i | \(-0.614524\pi\) | ||||
−0.352076 | + | 0.935971i | \(0.614524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9248 | + | 7.46211i | 0.0295761 | + | 0.0170758i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −183.954 | − | 318.618i | −0.419031 | − | 0.725782i | 0.576812 | − | 0.816877i | \(-0.304297\pi\) |
−0.995842 | + | 0.0910950i | \(0.970963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.4358 | − | 170.443i | 0.0848885 | − | 0.386493i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −156.585 | + | 90.4041i | −0.353464 | + | 0.204073i | −0.666210 | − | 0.745764i | \(-0.732085\pi\) |
0.312746 | + | 0.949837i | \(0.398751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.9942 | + | 56.7227i | −0.0492041 | + | 0.126896i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 284.309i | 0.633205i | 0.948558 | + | 0.316603i | \(0.102542\pi\) | ||||
−0.948558 | + | 0.316603i | \(0.897458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 176.400 | 0.391131 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −43.5504 | + | 35.0232i | −0.0961377 | + | 0.0773138i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 119.510 | + | 206.998i | 0.261510 | + | 0.452949i | 0.966643 | − | 0.256126i | \(-0.0824461\pi\) |
−0.705133 | + | 0.709075i | \(0.749113\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 190.413 | − | 94.5987i | 0.414843 | − | 0.206097i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.0175 | + | 20.2174i | −0.0759599 | + | 0.0438555i | −0.537499 | − | 0.843264i | \(-0.680631\pi\) |
0.461539 | + | 0.887120i | \(0.347297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −317.928 | + | 550.667i | −0.686669 | + | 1.18935i | 0.286240 | + | 0.958158i | \(0.407595\pi\) |
−0.972909 | + | 0.231188i | \(0.925739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 34.8159i | − | 0.0745522i | −0.999305 | − | 0.0372761i | \(-0.988132\pi\) | ||
0.999305 | − | 0.0372761i | \(-0.0118681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 895.936 | 1.91031 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 500.270 | + | 193.980i | 1.06214 | + | 0.411846i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −202.432 | − | 116.874i | −0.427975 | − | 0.247091i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −142.025 | − | 447.384i | −0.297746 | − | 0.937912i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.1869 | + | 13.9643i | −0.0504945 | + | 0.0291530i | −0.525035 | − | 0.851081i | \(-0.675948\pi\) |
0.474540 | + | 0.880234i | \(0.342614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −357.916 | + | 619.929i | −0.744108 | + | 1.28883i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.6510 | − | 4.59350i | 0.0613893 | − | 0.00951036i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 236.451 | 0.485527 | 0.242763 | − | 0.970086i | \(-0.421946\pi\) | ||||
0.242763 | + | 0.970086i | \(0.421946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.03177 | + | 13.1150i | 0.00415494 | + | 0.0268201i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 59.4344 | + | 34.3145i | 0.121048 | + | 0.0698869i | 0.559301 | − | 0.828964i | \(-0.311070\pi\) |
−0.438254 | + | 0.898851i | \(0.644403\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.8487 | − | 84.6085i | −0.0990846 | − | 0.171620i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −963.333 | + | 556.180i | −1.93829 | + | 1.11908i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −148.403 | + | 257.042i | −0.297402 | + | 0.515115i | −0.975541 | − | 0.219819i | \(-0.929453\pi\) |
0.678139 | + | 0.734934i | \(0.262787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.4927 | + | 45.1134i | −0.0349156 | + | 0.0900467i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 854.175i | − | 1.69816i | −0.528263 | − | 0.849081i | \(-0.677157\pi\) | ||
0.528263 | − | 0.849081i | \(-0.322843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −477.256 | + | 383.809i | −0.941334 | + | 0.757019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −567.421 | − | 327.601i | −1.11478 | − | 0.643616i | −0.174714 | − | 0.984619i | \(-0.555900\pi\) |
−0.940062 | + | 0.341003i | \(0.889233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −276.128 | − | 478.268i | −0.540368 | − | 0.935944i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −148.241 | − | 298.387i | −0.288969 | − | 0.581651i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −175.150 | + | 303.368i | −0.338781 | + | 0.586786i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −392.083 | − | 487.545i | −0.755458 | − | 0.939392i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 886.683i | 1.70189i | 0.525258 | + | 0.850943i | \(0.323969\pi\) | ||||
−0.525258 | + | 0.850943i | \(0.676031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 416.390 | 0.796158 | 0.398079 | − | 0.917351i | \(-0.369677\pi\) | ||||
0.398079 | + | 0.917351i | \(0.369677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 63.5229 | + | 36.6749i | 0.120537 | + | 0.0695919i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −263.769 | − | 456.861i | −0.498618 | − | 0.863631i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 552.891 | + | 121.436i | 1.04123 | + | 0.228693i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 775.367 | − | 447.658i | 1.45472 | − | 0.839884i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.7413 | − | 6.93127i | 0.0833172 | − | 0.0129074i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73.7956i | 0.136912i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 932.175 | 1.72306 | 0.861529 | − | 0.507708i | \(-0.169507\pi\) | ||||
0.861529 | + | 0.507708i | \(0.169507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 153.774 | + | 992.611i | 0.283194 | + | 1.82801i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 320.108 | + | 554.443i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −155.059 | − | 141.527i | −0.282439 | − | 0.257790i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −132.586 | + | 76.5485i | −0.240628 | + | 0.138927i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 514.455 | − | 891.063i | 0.930299 | − | 1.61133i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 255.289i | 0.458328i | 0.973388 | + | 0.229164i | \(0.0735992\pi\) | ||||
−0.973388 | + | 0.229164i | \(0.926401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1186.39 | −2.12234 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −70.0658 | + | 56.3468i | −0.124894 | + | 0.100440i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −453.510 | − | 261.834i | −0.805525 | − | 0.465070i | 0.0398747 | − | 0.999205i | \(-0.487304\pi\) |
−0.845399 | + | 0.534135i | \(0.820637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −608.199 | − | 280.709i | −1.07266 | − | 0.495077i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −714.948 | + | 412.775i | −1.25650 | + | 0.725440i | −0.972392 | − | 0.233353i | \(-0.925030\pi\) |
−0.284107 | + | 0.958793i | \(0.591697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 72.0237 | − | 124.749i | 0.126136 | − | 0.218474i | −0.796040 | − | 0.605244i | \(-0.793076\pi\) |
0.922176 | + | 0.386769i | \(0.126409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −569.281 | − | 707.887i | −0.993510 | − | 1.23540i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −444.934 | −0.771116 | −0.385558 | − | 0.922684i | \(-0.625991\pi\) | ||||
−0.385558 | + | 0.922684i | \(0.625991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 472.225 | + | 183.105i | 0.815587 | + | 0.316244i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −577.994 | − | 333.705i | −0.994826 | − | 0.574363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 99.2476 | + | 171.902i | 0.170236 | + | 0.294857i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 62.3769 | − | 36.0133i | 0.106264 | − | 0.0613515i | −0.445926 | − | 0.895070i | \(-0.647126\pi\) |
0.552190 | + | 0.833718i | \(0.313792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.4716 | − | 99.5437i | 0.0975748 | − | 0.169005i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −969.673 | + | 150.221i | −1.64073 | + | 0.254180i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1018.32i | 1.71724i | 0.512614 | + | 0.858619i | \(0.328677\pi\) | ||||
−0.512614 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −76.1090 | − | 491.283i | −0.127486 | − | 0.822920i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −728.467 | − | 420.580i | −1.21614 | − | 0.702138i | −0.252048 | − | 0.967715i | \(-0.581104\pi\) |
−0.964090 | + | 0.265577i | \(0.914438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 288.843 | + | 500.290i | 0.480603 | + | 0.832429i | 0.999752 | − | 0.0222543i | \(-0.00708436\pi\) |
−0.519149 | + | 0.854684i | \(0.673751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 209.171 | − | 952.344i | 0.346884 | − | 1.57934i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −142.103 | + | 246.130i | −0.234108 | + | 0.405486i | −0.959013 | − | 0.283362i | \(-0.908550\pi\) |
0.724905 | + | 0.688848i | \(0.241883\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −111.276 | + | 286.979i | −0.182719 | + | 0.471230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1777.94i | 2.90989i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −272.783 | −0.444996 | −0.222498 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222498 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −68.4752 | − | 39.5342i | −0.110981 | − | 0.0640748i | 0.443482 | − | 0.896283i | \(-0.353743\pi\) |
−0.554463 | + | 0.832208i | \(0.687076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 171.368 | + | 296.818i | 0.276847 | + | 0.479513i | 0.970599 | − | 0.240701i | \(-0.0773772\pi\) |
−0.693753 | + | 0.720213i | \(0.744044\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.03981 | − | 32.5903i | 0.00328471 | − | 0.0524804i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1264.16 | − | 729.865i | 2.02915 | − | 1.17153i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 88.2984 | + | 109.797i | 0.140827 | + | 0.175114i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 291.814i | 0.463933i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −608.714 | −0.964681 | −0.482341 | − | 0.875984i | \(-0.660213\pi\) | ||||
−0.482341 | + | 0.875984i | \(0.660213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −528.347 | − | 204.867i | −0.834672 | − | 0.323644i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 187.274 | + | 324.368i | 0.293994 | + | 0.509213i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 366.292 | + | 1153.83i | 0.573227 | + | 1.80569i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 145.345 | − | 83.9152i | 0.226748 | − | 0.130913i | −0.382323 | − | 0.924029i | \(-0.624876\pi\) |
0.609071 | + | 0.793116i | \(0.291542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −106.469 | + | 184.409i | −0.165581 | + | 0.286795i | −0.936862 | − | 0.349700i | \(-0.886283\pi\) |
0.771280 | + | 0.636496i | \(0.219617\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 242.229i | 0.374388i | 0.982323 | + | 0.187194i | \(0.0599393\pi\) | ||||
−0.982323 | + | 0.187194i | \(0.940061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −239.381 | −0.368846 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.3782 | − | 228.366i | −0.0543443 | − | 0.350792i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 278.702 | + | 160.909i | 0.426802 | + | 0.246414i | 0.697983 | − | 0.716114i | \(-0.254081\pi\) |
−0.271181 | + | 0.962528i | \(0.587414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −572.846 | + | 181.854i | −0.871912 | + | 0.276794i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 411.471 | − | 237.563i | 0.624387 | − | 0.360490i | −0.154188 | − | 0.988042i | \(-0.549276\pi\) |
0.778575 | + | 0.627551i | \(0.215943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 579.528 | − | 1003.77i | 0.876745 | − | 1.51857i | 0.0218529 | − | 0.999761i | \(-0.493043\pi\) |
0.854892 | − | 0.518806i | \(-0.173623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −164.980 | + | 425.481i | −0.248839 | + | 0.641751i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0045 | −0.0224956 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −672.785 | + | 541.053i | −1.00566 | + | 0.808749i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 76.8842 | + | 44.3891i | 0.114582 | + | 0.0661537i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 72.8616 | + | 126.200i | 0.108264 | + | 0.187518i | 0.915067 | − | 0.403302i | \(-0.132138\pi\) |
−0.806803 | + | 0.590820i | \(0.798804\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 341.713 | − | 197.288i | 0.504745 | − | 0.291415i | −0.225926 | − | 0.974145i | \(-0.572541\pi\) |
0.730671 | + | 0.682730i | \(0.239207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −379.948 | + | 658.089i | −0.559570 | + | 0.969204i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −373.312 | − | 464.204i | −0.548182 | − | 0.681650i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 510.506i | 0.747447i | 0.927540 | + | 0.373723i | \(0.121919\pi\) | ||||
−0.927540 | + | 0.373723i | \(0.878081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1072.57 | − | 415.888i | −1.56123 | − | 0.605368i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 872.486 | + | 503.730i | 1.26631 | + | 0.731103i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −420.136 | − | 727.697i | −0.608011 | − | 1.05311i | −0.991568 | − | 0.129589i | \(-0.958634\pi\) |
0.383556 | − | 0.923517i | \(-0.374699\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 276.674 | + | 60.7682i | 0.399242 | + | 0.0876886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 182.491 | − | 316.083i | 0.261823 | − | 0.453491i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 712.415 | − | 110.366i | 1.01919 | − | 0.157892i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 596.790i | 0.851340i | 0.904878 | + | 0.425670i | \(0.139962\pi\) | ||||
−0.904878 | + | 0.425670i | \(0.860038\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 457.288 | 0.650480 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −291.689 | − | 168.407i | −0.412573 | − | 0.238199i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −660.644 | − | 1144.27i | −0.931797 | − | 1.61392i | −0.780248 | − | 0.625470i | \(-0.784907\pi\) |
−0.151549 | − | 0.988450i | \(-0.548426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −827.057 | − | 754.879i | −1.16323 | − | 1.06171i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.75594 | − | 5.63260i | 0.0136830 | − | 0.00789986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −77.9342 | + | 200.991i | −0.108695 | + | 0.280322i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 833.256i | 1.15891i | 0.815004 | + | 0.579455i | \(0.196734\pi\) | ||||
−0.815004 | + | 0.579455i | \(0.803266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 854.859 | 1.18566 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −398.068 | + | 320.126i | −0.550578 | + | 0.442774i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −136.886 | − | 237.094i | −0.188289 | − | 0.326126i | 0.756391 | − | 0.654120i | \(-0.226961\pi\) |
−0.944680 | + | 0.327994i | \(0.893628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −440.376 | + | 580.956i | −0.604083 | + | 0.796922i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −418.843 | + | 241.819i | −0.572973 | + | 0.330806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 269.002 | − | 465.925i | 0.366988 | − | 0.635642i | −0.622105 | − | 0.782934i | \(-0.713722\pi\) |
0.989093 | + | 0.147292i | \(0.0470557\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 412.329i | 0.559470i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.4149 | −0.0695736 | −0.0347868 | − | 0.999395i | \(-0.511075\pi\) | ||||
−0.0347868 | + | 0.999395i | \(0.511075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 666.752 | + | 258.533i | 0.899800 | + | 0.348897i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −722.188 | − | 416.955i | −0.971989 | − | 0.561178i | −0.0721467 | − | 0.997394i | \(-0.522985\pi\) |
−0.899842 | + | 0.436216i | \(0.856318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −489.657 | + | 536.476i | −0.655498 | + | 0.718174i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −156.961 | + | 90.6212i | −0.209560 | + | 0.120990i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 492.855 | − | 853.650i | 0.656265 | − | 1.13668i | −0.325310 | − | 0.945607i | \(-0.605469\pi\) |
0.981575 | − | 0.191077i | \(-0.0611979\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −234.114 | + | 36.2686i | −0.310908 | + | 0.0481655i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 414.403 | 0.547428 | 0.273714 | − | 0.961811i | \(-0.411748\pi\) | ||||
0.273714 | + | 0.961811i | \(0.411748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.11403 | + | 13.6461i | 0.00278528 | + | 0.0179790i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −401.140 | − | 231.598i | −0.527122 | − | 0.304334i | 0.212721 | − | 0.977113i | \(-0.431767\pi\) |
−0.739844 | + | 0.672779i | \(0.765101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 334.787 | + | 579.869i | 0.438778 | + | 0.759985i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1052.20 | + | 607.488i | −1.37184 | + | 0.792031i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 105.504 | − | 182.738i | 0.137196 | − | 0.237630i | −0.789238 | − | 0.614087i | \(-0.789524\pi\) |
0.926434 | + | 0.376457i | \(0.122858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.2260 | + | 150.164i | −0.0755201 | + | 0.194765i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1401.96i | 1.81367i | 0.421490 | + | 0.906833i | \(0.361507\pi\) | ||||
−0.421490 | + | 0.906833i | \(0.638493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 716.433 | − | 576.155i | 0.922051 | − | 0.741512i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −495.319 | − | 285.973i | −0.635840 | − | 0.367102i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −255.966 | − | 443.347i | −0.327742 | − | 0.567665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 279.068 | + | 185.282i | 0.356409 | + | 0.236631i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −196.231 | + | 339.881i | −0.249340 | + | 0.431870i | −0.963343 | − | 0.268273i | \(-0.913547\pi\) |
0.714003 | + | 0.700143i | \(0.246880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.4294 | − | 24.1600i | −0.0246254 | − | 0.0306210i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 985.276i | 1.24561i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 450.593 | 0.568213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 938.996 | + | 542.129i | 1.17816 | + | 0.680213i | 0.955589 | − | 0.294703i | \(-0.0952208\pi\) |
0.222574 | + | 0.974916i | \(0.428554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 362.395 | + | 627.686i | 0.453560 | + | 0.785589i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −480.678 | − | 1514.15i | −0.600097 | − | 1.89033i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 220.109 | − | 127.080i | 0.274109 | − | 0.158257i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 89.6780 | − | 13.8928i | 0.111125 | − | 0.0172154i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1256.56i | − | 1.55323i | −0.629975 | − | 0.776616i | \(-0.716935\pi\) | ||
0.629975 | − | 0.776616i | \(-0.283065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1478.32 | 1.82284 | 0.911418 | − | 0.411482i | \(-0.134989\pi\) | ||||
0.911418 | + | 0.411482i | \(0.134989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.2957 | + | 415.028i | 0.0790845 | + | 0.510490i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 378.943 | + | 656.349i | 0.463823 | + | 0.803365i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1370.34 | − | 435.022i | 1.67318 | − | 0.531163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 757.934 | − | 437.593i | 0.923184 | − | 0.533001i | 0.0385346 | − | 0.999257i | \(-0.487731\pi\) |
0.884649 | + | 0.466257i | \(0.154398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −242.040 | + | 419.225i | −0.294095 | + | 0.509387i | −0.974774 | − | 0.223195i | \(-0.928351\pi\) |
0.680679 | + | 0.732582i | \(0.261685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 262.221i | 0.317075i | 0.987353 | + | 0.158537i | \(0.0506778\pi\) | ||||
−0.987353 | + | 0.158537i | \(0.949322\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 441.413 | 0.532465 | 0.266232 | − | 0.963909i | \(-0.414221\pi\) | ||||
0.266232 | + | 0.963909i | \(0.414221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −128.570 | + | 103.396i | −0.154718 | + | 0.124424i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 132.231 | + | 76.3436i | 0.158741 | + | 0.0916490i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −251.003 | − | 15.7101i | −0.299885 | − | 0.0187696i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 632.454 | − | 365.147i | 0.753818 | − | 0.435217i | −0.0732535 | − | 0.997313i | \(-0.523338\pi\) |
0.827072 | + | 0.562096i | \(0.190005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −343.540 | + | 595.028i | −0.408489 | + | 0.707524i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −927.269 | − | 1153.03i | −1.09996 | − | 1.36778i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 880.856 | 1.03997 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −677.694 | − | 262.776i | −0.798226 | − | 0.309512i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.8129 | + | 22.4086i | 0.0456086 | + | 0.0263321i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −296.660 | − | 513.830i | −0.347784 | − | 0.602380i | 0.638071 | − | 0.769977i | \(-0.279733\pi\) |
−0.985856 | + | 0.167597i | \(0.946399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1223.11 | + | 706.162i | −1.42720 | + | 0.823993i | −0.996899 | − | 0.0786932i | \(-0.974925\pi\) |
−0.430299 | + | 0.902686i | \(0.641592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −350.028 | + | 606.266i | −0.407483 | + | 0.705781i | −0.994607 | − | 0.103716i | \(-0.966927\pi\) |
0.587124 | + | 0.809497i | \(0.300260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1136.33 | + | 176.038i | −1.31977 | + | 0.204458i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1185.65i | 1.37387i | 0.726719 | + | 0.686935i | \(0.241044\pi\) | ||||
−0.726719 | + | 0.686935i | \(0.758956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −104.251 | − | 672.940i | −0.120243 | − | 0.776170i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 410.087 | + | 236.764i | 0.471906 | + | 0.272455i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1046.39 | + | 1812.39i | 1.20136 | + | 2.08082i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 610.818 | + | 557.511i | 0.699677 | + | 0.638616i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 747.001 | − | 1293.84i | 0.851769 | − | 1.47531i | −0.0278418 | − | 0.999612i | \(-0.508863\pi\) |
0.879611 | − | 0.475694i | \(-0.157803\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 141.203 | − | 364.160i | 0.160641 | − | 0.414289i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 89.7969i | − | 0.101926i | −0.998701 | − | 0.0509630i | \(-0.983771\pi\) | ||
0.998701 | − | 0.0509630i | \(-0.0162291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −709.600 | −0.803624 | −0.401812 | − | 0.915722i | \(-0.631620\pi\) | ||||
−0.401812 | + | 0.915722i | \(0.631620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −588.161 | − | 339.575i | −0.663090 | − | 0.382835i | 0.130363 | − | 0.991466i | \(-0.458386\pi\) |
−0.793453 | + | 0.608631i | \(0.791719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 562.997 | + | 975.140i | 0.633293 | + | 1.09689i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 129.188 | − | 279.907i | 0.144992 | − | 0.314149i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 983.617 | − | 567.892i | 1.10147 | − | 0.635937i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.9224 | + | 54.6164i | 0.0489659 | + | 0.0608878i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 115.562i | 0.128545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 410.698 | 0.455824 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1420.65 | + | 550.858i | 1.57326 | + | 0.610031i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −125.977 | − | 218.198i | −0.138894 | − | 0.240571i | 0.788184 | − | 0.615439i | \(-0.211021\pi\) |
−0.927078 | + | 0.374868i | \(0.877688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −247.109 | + | 270.736i | −0.271847 | + | 0.297840i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −815.790 | + | 470.997i | −0.895488 | + | 0.517011i | −0.875734 | − | 0.482794i | \(-0.839622\pi\) |
−0.0197547 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 153.578 | − | 266.005i | 0.168213 | − | 0.291353i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1554.85i | 1.69559i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −795.449 | −0.865560 | −0.432780 | − | 0.901500i | \(-0.642467\pi\) | ||||
−0.432780 | + | 0.901500i | \(0.642467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.7684 | + | 347.075i | 0.0583805 | + | 0.376846i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2250.20 | − | 1299.15i | −2.43792 | − | 1.40753i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 199.581 | − | 908.681i | 0.215298 | − | 0.980239i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1414.36 | − | 816.581i | 1.52245 | − | 0.878989i | 0.522806 | − | 0.852452i | \(-0.324885\pi\) |
0.999648 | − | 0.0265372i | \(-0.00844804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 119.634 | − | 207.213i | 0.128501 | − | 0.222570i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.6352 | − | 53.2177i | 0.0221170 | − | 0.0570394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1336.80 | 1.42668 | 0.713341 | − | 0.700817i | \(-0.247181\pi\) | ||||
0.713341 | + | 0.700817i | \(0.247181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 390.576 | − | 314.101i | 0.415949 | − | 0.334506i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −702.449 | − | 405.559i | −0.746492 | − | 0.430987i | 0.0779329 | − | 0.996959i | \(-0.475168\pi\) |
−0.824425 | + | 0.565971i | \(0.808501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0272 | − | 48.5446i | −0.0297214 | − | 0.0514789i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 453.592 | − | 261.881i | 0.478978 | − | 0.276538i | −0.241013 | − | 0.970522i | \(-0.577480\pi\) |
0.719990 | + | 0.693984i | \(0.244146\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 644.993 | − | 1117.16i | 0.679656 | − | 1.17720i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −368.323 | − | 458.000i | −0.387301 | − | 0.481598i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 784.182i | − | 0.822856i | −0.911442 | − | 0.411428i | \(-0.865030\pi\) | ||
0.911442 | − | 0.411428i | \(-0.134970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −132.074 | − | 51.2117i | −0.138008 | − | 0.0535128i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1876.15 | − | 1083.20i | −1.95636 | − | 1.12951i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 437.119 | + | 757.112i | 0.454858 | + | 0.787838i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 59.6818 | + | 188.000i | 0.0619748 | + | 0.195223i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 557.120 | − | 964.960i | 0.576132 | − | 0.997890i | −0.419785 | − | 0.907623i | \(-0.637895\pi\) |
0.995918 | − | 0.0902669i | \(-0.0287720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 288.087 | − | 44.6301i | 0.297303 | − | 0.0460579i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1241.22i | 1.27829i | 0.769088 | + | 0.639143i | \(0.220711\pi\) | ||||
−0.769088 | + | 0.639143i | \(0.779289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −683.882 | −0.702859 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 825.547 | + | 476.629i | 0.844981 | + | 0.487850i | 0.858954 | − | 0.512052i | \(-0.171115\pi\) |
−0.0139732 | + | 0.999902i | \(0.504448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 335.900 | + | 581.795i | 0.343105 | + | 0.594275i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 694.539 | − | 220.486i | 0.707991 | − | 0.224756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −741.717 | + | 428.230i | −0.754544 | + | 0.435636i | −0.827333 | − | 0.561711i | \(-0.810143\pi\) |
0.0727894 | + | 0.997347i | \(0.476810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 825.526 | − | 2129.01i | 0.836399 | − | 2.15706i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 74.2780i | 0.0751041i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −995.644 | −1.00469 | −0.502343 | − | 0.864668i | \(-0.667529\pi\) | ||||
−0.502343 | + | 0.864668i | \(0.667529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 191.530 | − | 154.028i | 0.192880 | − | 0.155114i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −692.421 | − | 1199.31i | −0.694504 | − | 1.20292i | −0.970348 | − | 0.241714i | \(-0.922290\pi\) |
0.275843 | − | 0.961203i | \(-0.411043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −445.166 | − | 896.053i | −0.445612 | − | 0.896950i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.3.p.c.401.4 | 12 | ||
3.2 | odd | 2 | 2700.3.p.c.2501.1 | 12 | |||
5.2 | odd | 4 | 900.3.u.c.149.1 | 24 | |||
5.3 | odd | 4 | 900.3.u.c.149.12 | 24 | |||
5.4 | even | 2 | 180.3.o.b.41.3 | ✓ | 12 | ||
9.2 | odd | 6 | inner | 900.3.p.c.101.4 | 12 | ||
9.7 | even | 3 | 2700.3.p.c.1601.1 | 12 | |||
15.2 | even | 4 | 2700.3.u.c.449.11 | 24 | |||
15.8 | even | 4 | 2700.3.u.c.449.2 | 24 | |||
15.14 | odd | 2 | 540.3.o.b.341.6 | 12 | |||
20.19 | odd | 2 | 720.3.bs.b.401.4 | 12 | |||
45.2 | even | 12 | 900.3.u.c.749.12 | 24 | |||
45.4 | even | 6 | 1620.3.g.b.161.7 | 12 | |||
45.7 | odd | 12 | 2700.3.u.c.2249.2 | 24 | |||
45.14 | odd | 6 | 1620.3.g.b.161.1 | 12 | |||
45.29 | odd | 6 | 180.3.o.b.101.3 | yes | 12 | ||
45.34 | even | 6 | 540.3.o.b.521.6 | 12 | |||
45.38 | even | 12 | 900.3.u.c.749.1 | 24 | |||
45.43 | odd | 12 | 2700.3.u.c.2249.11 | 24 | |||
60.59 | even | 2 | 2160.3.bs.b.881.4 | 12 | |||
180.79 | odd | 6 | 2160.3.bs.b.1601.4 | 12 | |||
180.119 | even | 6 | 720.3.bs.b.641.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.b.41.3 | ✓ | 12 | 5.4 | even | 2 | ||
180.3.o.b.101.3 | yes | 12 | 45.29 | odd | 6 | ||
540.3.o.b.341.6 | 12 | 15.14 | odd | 2 | |||
540.3.o.b.521.6 | 12 | 45.34 | even | 6 | |||
720.3.bs.b.401.4 | 12 | 20.19 | odd | 2 | |||
720.3.bs.b.641.4 | 12 | 180.119 | even | 6 | |||
900.3.p.c.101.4 | 12 | 9.2 | odd | 6 | inner | ||
900.3.p.c.401.4 | 12 | 1.1 | even | 1 | trivial | ||
900.3.u.c.149.1 | 24 | 5.2 | odd | 4 | |||
900.3.u.c.149.12 | 24 | 5.3 | odd | 4 | |||
900.3.u.c.749.1 | 24 | 45.38 | even | 12 | |||
900.3.u.c.749.12 | 24 | 45.2 | even | 12 | |||
1620.3.g.b.161.1 | 12 | 45.14 | odd | 6 | |||
1620.3.g.b.161.7 | 12 | 45.4 | even | 6 | |||
2160.3.bs.b.881.4 | 12 | 60.59 | even | 2 | |||
2160.3.bs.b.1601.4 | 12 | 180.79 | odd | 6 | |||
2700.3.p.c.1601.1 | 12 | 9.7 | even | 3 | |||
2700.3.p.c.2501.1 | 12 | 3.2 | odd | 2 | |||
2700.3.u.c.449.2 | 24 | 15.8 | even | 4 | |||
2700.3.u.c.449.11 | 24 | 15.2 | even | 4 | |||
2700.3.u.c.2249.2 | 24 | 45.7 | odd | 12 | |||
2700.3.u.c.2249.11 | 24 | 45.43 | odd | 12 |