Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (of order \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{12} + 424x^{8} - 159x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1793.3 | ||
Root | \(0.660512 + 0.0465948i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1793 |
Dual form | 2100.2.s.a.1457.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.541157 | + | 1.64534i | −0.312437 | + | 0.949938i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.41430 | − | 1.78078i | −0.804766 | − | 0.593592i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09218i | 0.932326i | 0.884699 | + | 0.466163i | \(0.154364\pi\) | ||||
−0.884699 | + | 0.466163i | \(0.845636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.310029 | + | 0.310029i | 0.0859866 | + | 0.0859866i | 0.748792 | − | 0.662805i | \(-0.230634\pi\) |
−0.662805 | + | 0.748792i | \(0.730634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.41433 | + | 3.41433i | 0.828097 | + | 0.828097i | 0.987253 | − | 0.159156i | \(-0.0508773\pi\) |
−0.159156 | + | 0.987253i | \(0.550877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.12311i | − | 0.257658i | −0.991667 | − | 0.128829i | \(-0.958878\pi\) | ||
0.991667 | − | 0.128829i | \(-0.0411218\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.780776 | + | 1.54609i | 0.170379 | + | 0.337384i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.22783 | + | 1.22783i | −0.256021 | + | 0.256021i | −0.823434 | − | 0.567413i | \(-0.807945\pi\) |
0.567413 | + | 0.823434i | \(0.307945\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.23650 | − | 3.00867i | 0.815315 | − | 0.579018i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35576 | −0.251758 | −0.125879 | − | 0.992046i | \(-0.540175\pi\) | ||||
−0.125879 | + | 0.992046i | \(0.540175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.24621 | −1.48106 | −0.740532 | − | 0.672022i | \(-0.765426\pi\) | ||||
−0.740532 | + | 0.672022i | \(0.765426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.08769 | − | 1.67335i | −0.885652 | − | 0.291293i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.20837 | − | 2.20837i | 0.363054 | − | 0.363054i | −0.501882 | − | 0.864936i | \(-0.667359\pi\) |
0.864936 | + | 0.501882i | \(0.167359\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.677878 | + | 0.342329i | −0.108547 | + | 0.0548165i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.18435i | 0.965834i | 0.875666 | + | 0.482917i | \(0.160423\pi\) | ||||
−0.875666 | + | 0.482917i | \(0.839577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24517 | + | 7.24517i | 1.10488 | + | 1.10488i | 0.993813 | + | 0.111064i | \(0.0354259\pi\) |
0.111064 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.18650 | + | 2.18650i | 0.318934 | + | 0.318934i | 0.848357 | − | 0.529424i | \(-0.177592\pi\) |
−0.529424 | + | 0.848357i | \(0.677592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.46543 | + | 3.77005i | −1.04537 | + | 0.527913i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.22783 | − | 1.22783i | 0.168656 | − | 0.168656i | −0.617732 | − | 0.786388i | \(-0.711948\pi\) |
0.786388 | + | 0.617732i | \(0.211948\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.84789 | + | 0.607777i | 0.244759 | + | 0.0805020i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.65719 | −1.25726 | −0.628630 | − | 0.777705i | \(-0.716384\pi\) | ||||
−0.628630 | + | 0.777705i | \(0.716384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.12311 | −0.655946 | −0.327973 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327973 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.96637 | + | 0.447967i | −0.373727 | + | 0.0564386i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.86522 | + | 7.86522i | −0.960890 | + | 0.960890i | −0.999263 | − | 0.0383735i | \(-0.987782\pi\) |
0.0383735 | + | 0.999263i | \(0.487782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.35576 | − | 2.68466i | −0.163214 | − | 0.323195i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1051i | 1.67397i | 0.547226 | + | 0.836985i | \(0.315684\pi\) | ||||
−0.547226 | + | 0.836985i | \(0.684316\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24264 | + | 4.24264i | 0.496564 | + | 0.496564i | 0.910366 | − | 0.413803i | \(-0.135800\pi\) |
−0.413803 | + | 0.910366i | \(0.635800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.18650 | + | 2.18650i | 0.249175 | + | 0.249175i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.56155i | 0.625724i | 0.949799 | + | 0.312862i | \(0.101288\pi\) | ||||
−0.949799 | + | 0.312862i | \(0.898712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.65767 | + | 8.59865i | 0.295297 | + | 0.955406i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.22783 | + | 1.22783i | −0.134772 | + | 0.134772i | −0.771275 | − | 0.636502i | \(-0.780381\pi\) |
0.636502 | + | 0.771275i | \(0.280381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.733677 | − | 2.23068i | 0.0786584 | − | 0.239154i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3687 | −1.31108 | −0.655540 | − | 0.755160i | \(-0.727559\pi\) | ||||
−0.655540 | + | 0.755160i | \(0.727559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.438447 | 0.0459618 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.46250 | − | 13.5678i | 0.462739 | − | 1.40692i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.51840 | − | 2.51840i | 0.255705 | − | 0.255705i | −0.567600 | − | 0.823305i | \(-0.692128\pi\) |
0.823305 | + | 0.567600i | \(0.192128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.50647 | − | 7.46543i | 0.553421 | − | 0.750304i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.47284i | − | 0.345561i | −0.984960 | − | 0.172780i | \(-0.944725\pi\) | ||
0.984960 | − | 0.172780i | \(-0.0552751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.69250 | − | 2.69250i | −0.265299 | − | 0.265299i | 0.561903 | − | 0.827203i | \(-0.310069\pi\) |
−0.827203 | + | 0.561903i | \(0.810069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3468 | − | 14.3468i | −1.38696 | − | 1.38696i | −0.831630 | − | 0.555330i | \(-0.812592\pi\) |
−0.555330 | − | 0.831630i | \(-0.687408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.9309i | − | 1.23855i | −0.785173 | − | 0.619276i | \(-0.787426\pi\) | ||
0.785173 | − | 0.619276i | \(-0.212574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.43845 | + | 4.82860i | 0.231447 | + | 0.458310i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.22783 | − | 1.22783i | 0.115505 | − | 0.115505i | −0.646992 | − | 0.762497i | \(-0.723973\pi\) |
0.762497 | + | 0.646992i | \(0.223973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.196410 | − | 1.30059i | −0.0181581 | − | 0.120240i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.82860 | 0.442637 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.43845 | 0.130768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.1754 | − | 3.34671i | −0.917482 | − | 0.301762i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.27691 | + | 6.27691i | −0.556986 | + | 0.556986i | −0.928448 | − | 0.371462i | \(-0.878857\pi\) |
0.371462 | + | 0.928448i | \(0.378857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.8415 | + | 8.00000i | −1.39477 | + | 0.704361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5531i | 1.62099i | 0.585747 | + | 0.810494i | \(0.300801\pi\) | ||||
−0.585747 | + | 0.810494i | \(0.699199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.794156 | − | 0.794156i | −0.0688620 | − | 0.0688620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.14516 | + | 3.14516i | 0.268709 | + | 0.268709i | 0.828580 | − | 0.559871i | \(-0.189149\pi\) |
−0.559871 | + | 0.828580i | \(0.689149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.0000i | − | 0.848189i | −0.905618 | − | 0.424094i | \(-0.860592\pi\) | ||
0.905618 | − | 0.424094i | \(-0.139408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.78078 | + | 2.41430i | −0.402614 | + | 0.203321i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.958664 | + | 0.958664i | −0.0801675 | + | 0.0801675i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.64534 | + | 0.541157i | 0.135705 | + | 0.0446339i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8415 | −1.29779 | −0.648895 | − | 0.760878i | \(-0.724769\pi\) | ||||
−0.648895 | + | 0.760878i | \(0.724769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.56155 | −0.452593 | −0.226296 | − | 0.974058i | \(-0.572662\pi\) | ||||
−0.226296 | + | 0.974058i | \(0.572662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.16305 | − | 14.3234i | −0.174873 | − | 1.15798i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4878 | + | 11.4878i | −0.916827 | + | 0.916827i | −0.996797 | − | 0.0799705i | \(-0.974517\pi\) |
0.0799705 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.35576 | + | 2.68466i | 0.107518 | + | 0.212907i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.73642i | 0.136849i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6937 | + | 10.6937i | 0.837591 | + | 0.837591i | 0.988541 | − | 0.150950i | \(-0.0482333\pi\) |
−0.150950 | + | 0.988541i | \(0.548233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.3882 | − | 13.3882i | −1.03601 | − | 1.03601i | −0.999327 | − | 0.0366800i | \(-0.988322\pi\) |
−0.0366800 | − | 0.999327i | \(-0.511678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.8078i | − | 0.985213i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 2.71151i | −0.152944 | + | 0.207354i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.958664 | + | 0.958664i | −0.0728859 | + | 0.0728859i | −0.742610 | − | 0.669724i | \(-0.766412\pi\) |
0.669724 | + | 0.742610i | \(0.266412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.22606 | − | 15.8894i | 0.392815 | − | 1.19432i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5780 | 1.31384 | 0.656919 | − | 0.753961i | \(-0.271859\pi\) | ||||
0.656919 | + | 0.753961i | \(0.271859\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2462 | −0.910254 | −0.455127 | − | 0.890427i | \(-0.650406\pi\) | ||||
−0.455127 | + | 0.890427i | \(0.650406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.77240 | − | 8.42926i | 0.204942 | − | 0.623109i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5577 | + | 10.5577i | −0.772057 | + | 0.772057i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.868210 | − | 5.12311i | 0.0631530 | − | 0.372651i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.56502i | − | 0.475028i | −0.971384 | − | 0.237514i | \(-0.923667\pi\) | ||
0.971384 | − | 0.237514i | \(-0.0763325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528 | + | 8.48528i | 0.610784 | + | 0.610784i | 0.943150 | − | 0.332366i | \(-0.107847\pi\) |
−0.332366 | + | 0.943150i | \(0.607847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.97383 | − | 9.97383i | −0.710606 | − | 0.710606i | 0.256056 | − | 0.966662i | \(-0.417577\pi\) |
−0.966662 | + | 0.256056i | \(0.917577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4924i | 1.59445i | 0.603685 | + | 0.797223i | \(0.293698\pi\) | ||||
−0.603685 | + | 0.797223i | \(0.706302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68466 | − | 17.1973i | −0.612569 | − | 1.21300i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.958664 | + | 0.958664i | −0.0672850 | + | 0.0672850i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.15086 | − | 0.777860i | 0.358009 | − | 0.0540650i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.47284 | 0.240221 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31534 | 0.503609 | 0.251804 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251804 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.2077 | − | 7.63309i | −1.59017 | − | 0.523011i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.83095 | + | 5.83095i | −0.395831 | + | 0.395831i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.27653 | + | 4.68466i | −0.626850 | + | 0.316560i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.11708i | 0.142411i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0062 | + | 14.0062i | 0.937925 | + | 0.937925i | 0.998183 | − | 0.0602580i | \(-0.0191924\pi\) |
−0.0602580 | + | 0.998183i | \(0.519192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3055 | + | 15.3055i | 1.01586 | + | 1.01586i | 0.999872 | + | 0.0159889i | \(0.00508965\pi\) |
0.0159889 | + | 0.999872i | \(0.494910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.24621i | 0.544925i | 0.962166 | + | 0.272462i | \(0.0878381\pi\) | ||||
−0.962166 | + | 0.272462i | \(0.912162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.78078 | + | 2.41430i | −0.314552 | + | 0.158849i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8912 | − | 11.8912i | 0.779016 | − | 0.779016i | −0.200648 | − | 0.979663i | \(-0.564305\pi\) |
0.979663 | + | 0.200648i | \(0.0643047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.15065 | − | 3.00967i | −0.594399 | − | 0.195499i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9337 | 1.22472 | 0.612360 | − | 0.790579i | \(-0.290220\pi\) | ||||
0.612360 | + | 0.790579i | \(0.290220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.246211 | 0.0158599 | 0.00792993 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792993 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5859 | − | 0.280444i | −0.999838 | − | 0.0179905i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.348195 | − | 0.348195i | 0.0221551 | − | 0.0221551i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.35576 | − | 2.68466i | −0.0859175 | − | 0.170133i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.65719i | 0.609557i | 0.952423 | + | 0.304778i | \(0.0985824\pi\) | ||||
−0.952423 | + | 0.304778i | \(0.901418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.79668 | − | 3.79668i | −0.238695 | − | 0.238695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.9477 | + | 19.9477i | 1.24430 | + | 1.24430i | 0.958199 | + | 0.286101i | \(0.0923594\pi\) |
0.286101 | + | 0.958199i | \(0.407641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.12311i | − | 0.194060i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.27320 | + | 2.41430i | 0.202606 | + | 0.149441i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.60083 | + | 5.60083i | −0.345362 | + | 0.345362i | −0.858379 | − | 0.513017i | \(-0.828528\pi\) |
0.513017 | + | 0.858379i | \(0.328528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.69341 | − | 20.3507i | 0.409630 | − | 1.24545i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.4987 | −1.55469 | −0.777343 | − | 0.629077i | \(-0.783433\pi\) | ||||
−0.777343 | + | 0.629077i | \(0.783433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1231 | 1.04015 | 0.520077 | − | 0.854119i | \(-0.325903\pi\) | ||||
0.520077 | + | 0.854119i | \(0.325903\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.237269 | + | 0.721395i | −0.0143602 | + | 0.0436608i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6937 | − | 10.6937i | 0.642519 | − | 0.642519i | −0.308655 | − | 0.951174i | \(-0.599879\pi\) |
0.951174 | + | 0.308655i | \(0.0998788\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.9088 | + | 14.6847i | 1.19191 | + | 0.879148i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.54011i | − | 0.449805i | −0.974381 | − | 0.224903i | \(-0.927794\pi\) | ||
0.974381 | − | 0.224903i | \(-0.0722064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.31255 | − | 3.31255i | −0.196911 | − | 0.196911i | 0.601763 | − | 0.798674i | \(-0.294465\pi\) |
−0.798674 | + | 0.601763i | \(0.794465\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.37300 | + | 4.37300i | 0.258130 | + | 0.258130i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31534i | 0.371491i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.78078 | + | 5.50647i | 0.163012 | + | 0.322795i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1603 | − | 12.1603i | 0.710414 | − | 0.710414i | −0.256208 | − | 0.966622i | \(-0.582473\pi\) |
0.966622 | + | 0.256208i | \(0.0824731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.30332 | + | 13.1000i | 0.539834 | + | 0.760139i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.761329 | −0.0440288 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2462 | 0.590582 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.71401 | + | 1.87935i | 0.328261 | + | 0.107966i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.58442 | + | 3.58442i | −0.204573 | + | 0.204573i | −0.801956 | − | 0.597383i | \(-0.796207\pi\) |
0.597383 | + | 0.801956i | \(0.296207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.88714 | − | 2.97301i | 0.334908 | − | 0.169129i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.2102i | − | 1.59966i | −0.600229 | − | 0.799828i | \(-0.704924\pi\) | ||
0.600229 | − | 0.799828i | \(-0.295076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9057 | + | 23.9057i | 1.35123 | + | 1.35123i | 0.884288 | + | 0.466942i | \(0.154644\pi\) |
0.466942 | + | 0.884288i | \(0.345356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.6372 | − | 20.6372i | −1.15910 | − | 1.15910i | −0.984670 | − | 0.174428i | \(-0.944192\pi\) |
−0.174428 | − | 0.984670i | \(-0.555808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.19224i | − | 0.234720i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.3693 | − | 15.8415i | 1.75086 | − | 0.884189i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.83466 | − | 3.83466i | 0.213366 | − | 0.213366i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.2757 | + | 6.99763i | 1.17655 | + | 0.386970i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.09218 | 0.170477 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.24621 | −0.343323 | −0.171661 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171661 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.26427 | + | 1.39905i | −0.507679 | + | 0.0766675i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.21342 | − | 8.21342i | 0.447413 | − | 0.447413i | −0.447080 | − | 0.894494i | \(-0.647536\pi\) |
0.894494 | + | 0.447080i | \(0.147536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.35576 | + | 2.68466i | 0.0736346 | + | 0.145811i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 25.4987i | − | 1.38083i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.6312 | + | 23.6312i | 1.26859 | + | 1.26859i | 0.946818 | + | 0.321769i | \(0.104277\pi\) |
0.321769 | + | 0.946818i | \(0.395723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.3693i | − | 1.03682i | −0.855133 | − | 0.518408i | \(-0.826525\pi\) | ||
0.855133 | − | 0.518408i | \(-0.173475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.24621 | + | 0.380664i | 0.119894 | + | 0.0203184i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5333 | + | 16.5333i | −0.879980 | + | 0.879980i | −0.993532 | − | 0.113552i | \(-0.963777\pi\) |
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.61303 | + | 7.94469i | −0.138296 | + | 0.420478i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0010 | 1.21395 | 0.606973 | − | 0.794723i | \(-0.292384\pi\) | ||||
0.606973 | + | 0.794723i | \(0.292384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7386 | 0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.778426 | + | 2.36674i | −0.0408568 | + | 0.124221i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.34935 | + | 8.34935i | −0.435833 | + | 0.435833i | −0.890607 | − | 0.454774i | \(-0.849720\pi\) |
0.454774 | + | 0.890607i | \(0.349720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0129 | − | 14.9309i | 0.573311 | − | 0.777270i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.73642i | − | 0.0901504i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3238 | + | 23.3238i | 1.20766 | + | 1.20766i | 0.971783 | + | 0.235878i | \(0.0757967\pi\) |
0.235878 | + | 0.971783i | \(0.424203\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.420324 | − | 0.420324i | −0.0216478 | − | 0.0216478i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4924i | 0.847159i | 0.905859 | + | 0.423579i | \(0.139227\pi\) | ||||
−0.905859 | + | 0.423579i | \(0.860773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.93087 | − | 13.7245i | −0.355079 | − | 0.703125i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.7198 | + | 18.7198i | −0.956538 | + | 0.956538i | −0.999094 | − | 0.0425558i | \(-0.986450\pi\) |
0.0425558 | + | 0.999094i | \(0.486450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.58997 | − | 30.3940i | −0.233321 | − | 1.54501i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.35576 | −0.0687396 | −0.0343698 | − | 0.999409i | \(-0.510942\pi\) | ||||
−0.0343698 | + | 0.999409i | \(0.510942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.38447 | −0.424021 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −30.5261 | − | 10.0401i | −1.53984 | − | 0.506457i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.52345 | + | 8.52345i | −0.427780 | + | 0.427780i | −0.887871 | − | 0.460092i | \(-0.847816\pi\) |
0.460092 | + | 0.887871i | \(0.347816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.73642 | − | 0.876894i | 0.0869297 | − | 0.0438996i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.9088i | − | 0.994199i | −0.867694 | − | 0.497099i | \(-0.834398\pi\) | ||
0.867694 | − | 0.497099i | \(-0.165602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.55656 | − | 2.55656i | −0.127352 | − | 0.127352i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.82867 | + | 6.82867i | 0.338484 | + | 0.338484i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.12311i | − | 0.253321i | −0.991946 | − | 0.126661i | \(-0.959574\pi\) | ||
0.991946 | − | 0.126661i | \(-0.0404259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.87689 | + | 3.47284i | −0.339212 | + | 0.171303i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.82867 | + | 6.82867i | −0.336017 | + | 0.336017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.4534 | + | 5.41157i | 0.805727 | + | 0.265006i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.65719 | 0.471785 | 0.235892 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235892 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1771 | 1.12958 | 0.564791 | − | 0.825234i | \(-0.308957\pi\) | ||||
0.564791 | + | 0.825234i | \(0.308957\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.38519 | − | 9.17252i | −0.0673505 | − | 0.445983i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.62258 | + | 3.62258i | −0.175309 | + | 0.175309i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.05854 | − | 2.09612i | −0.0511069 | − | 0.101202i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.9337i | − | 0.912005i | −0.889978 | − | 0.456003i | \(-0.849281\pi\) | ||
0.889978 | − | 0.456003i | \(-0.150719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3162 | + | 14.3162i | 0.687994 | + | 0.687994i | 0.961788 | − | 0.273794i | \(-0.0882787\pi\) |
−0.273794 | + | 0.961788i | \(0.588279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.37899 | + | 1.37899i | 0.0659659 | + | 0.0659659i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4924i | 1.07350i | 0.843740 | + | 0.536752i | \(0.180349\pi\) | ||||
−0.843740 | + | 0.536752i | \(0.819651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.78078 | + | 2.41430i | −0.0847989 | + | 0.114967i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0042 | − | 28.0042i | 1.33052 | − | 1.33052i | 0.425612 | − | 0.904906i | \(-0.360059\pi\) |
0.904906 | − | 0.425612i | \(-0.139941\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.57276 | − | 26.0648i | 0.405478 | − | 1.23282i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.82860 | 0.227876 | 0.113938 | − | 0.993488i | \(-0.463654\pi\) | ||||
0.113938 | + | 0.993488i | \(0.463654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1231 | −0.900472 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.00967 | − | 9.15065i | 0.141407 | − | 0.429935i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7723 | − | 26.7723i | 1.25236 | − | 1.25236i | 0.297694 | − | 0.954661i | \(-0.403783\pi\) |
0.954661 | − | 0.297694i | \(-0.0962174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.7374 | + | 4.19224i | 1.15464 | + | 0.195677i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.7374i | − | 1.15214i | −0.817402 | − | 0.576068i | \(-0.804586\pi\) | ||
0.817402 | − | 0.576068i | \(-0.195414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.58831 | + | 1.58831i | 0.0738151 | + | 0.0738151i | 0.743050 | − | 0.669235i | \(-0.233378\pi\) |
−0.669235 | + | 0.743050i | \(0.733378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.64816 | + | 1.64816i | 0.0762677 | + | 0.0762677i | 0.744212 | − | 0.667944i | \(-0.232825\pi\) |
−0.667944 | + | 0.744212i | \(0.732825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1231i | 0.513617i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6847 | − | 25.1181i | −0.584478 | − | 1.15738i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.4033 | + | 22.4033i | −1.03011 | + | 1.03011i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.15086 | + | 0.777860i | −0.235842 | + | 0.0356158i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.9218 | 1.41285 | 0.706426 | − | 0.707787i | \(-0.250306\pi\) | ||||
0.706426 | + | 0.707787i | \(0.250306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36932 | 0.0624355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.85700 | − | 0.939676i | −0.129998 | − | 0.0427567i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.1840 | + | 25.1840i | −1.14120 | + | 1.14120i | −0.152963 | + | 0.988232i | \(0.548882\pi\) |
−0.988232 | + | 0.152963i | \(0.951118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.3817 | + | 11.8078i | −1.05735 | + | 0.533966i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.27653i | 0.418644i | 0.977847 | + | 0.209322i | \(0.0671257\pi\) | ||||
−0.977847 | + | 0.209322i | \(0.932874\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.62900 | − | 4.62900i | −0.208480 | − | 0.208480i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.97383 | + | 9.97383i | 0.447387 | + | 0.447387i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0540i | 0.629142i | 0.949234 | + | 0.314571i | \(0.101861\pi\) | ||||
−0.949234 | + | 0.314571i | \(0.898139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.2732 | − | 14.7830i | 1.30783 | − | 0.660456i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.4708 | − | 11.4708i | 0.511459 | − | 0.511459i | −0.403514 | − | 0.914973i | \(-0.632211\pi\) |
0.914973 | + | 0.403514i | \(0.132211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0731 | + | 6.93101i | 0.935891 | + | 0.307817i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1300 | 0.581978 | 0.290989 | − | 0.956726i | \(-0.406016\pi\) | ||||
0.290989 | + | 0.956726i | \(0.406016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.37905 | − | 4.75804i | −0.149189 | − | 0.210072i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.76104 | + | 6.76104i | −0.297350 | + | 0.297350i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.05854 | − | 2.09612i | −0.0464648 | − | 0.0920094i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.89586i | − | 0.389735i | −0.980830 | − | 0.194867i | \(-0.937572\pi\) | ||
0.980830 | − | 0.194867i | \(-0.0624277\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3188 | − | 17.3188i | −0.757296 | − | 0.757296i | 0.218533 | − | 0.975830i | \(-0.429873\pi\) |
−0.975830 | + | 0.218533i | \(0.929873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.1553 | − | 28.1553i | −1.22646 | − | 1.22646i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9848i | 0.868906i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.3153 | + | 17.1973i | 1.01180 | + | 0.746299i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.91733 | + | 1.91733i | −0.0830487 | + | 0.0830487i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.51244 | + | 28.9218i | −0.410492 | + | 1.24807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.09218 | 0.133189 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6847 | 1.49121 | 0.745605 | − | 0.666388i | \(-0.232161\pi\) | ||||
0.745605 | + | 0.666388i | \(0.232161\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.62712 | − | 20.1492i | 0.284397 | − | 0.864685i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.89697 | − | 6.89697i | 0.294893 | − | 0.294893i | −0.544117 | − | 0.839010i | \(-0.683135\pi\) |
0.839010 | + | 0.544117i | \(0.183135\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3687 | + | 9.12311i | 0.527883 | + | 0.389365i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.52266i | 0.0648674i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.93261 | + | 3.93261i | 0.167232 | + | 0.167232i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.5122 | − | 10.5122i | −0.445415 | − | 0.445415i | 0.448412 | − | 0.893827i | \(-0.351990\pi\) |
−0.893827 | + | 0.448412i | \(0.851990\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.49242i | 0.190009i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.6577 | − | 23.0844i | −0.492187 | − | 0.974626i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.97383 | + | 9.97383i | −0.420347 | + | 0.420347i | −0.885323 | − | 0.464976i | \(-0.846063\pi\) |
0.464976 | + | 0.885323i | \(0.346063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.95942 | + | 4.20091i | 0.334264 | + | 0.176422i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3687 | −0.518523 | −0.259262 | − | 0.965807i | \(-0.583479\pi\) | ||||
−0.259262 | + | 0.965807i | \(0.583479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.7386 | −1.11898 | −0.559488 | − | 0.828838i | \(-0.689002\pi\) | ||||
−0.559488 | + | 0.828838i | \(0.689002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8017 | + | 3.55270i | 0.451247 | + | 0.148416i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.07496 | + | 5.07496i | −0.211273 | + | 0.211273i | −0.804808 | − | 0.593535i | \(-0.797732\pi\) |
0.593535 | + | 0.804808i | \(0.297732\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.5531 | + | 9.36932i | −0.771039 | + | 0.389376i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73642i | 0.0720388i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.79668 | + | 3.79668i | 0.157242 | + | 0.157242i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.7198 | − | 18.7198i | −0.772650 | − | 0.772650i | 0.205919 | − | 0.978569i | \(-0.433982\pi\) |
−0.978569 | + | 0.205919i | \(0.933982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.26137i | 0.381608i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.8078 | − | 11.0129i | 0.897052 | − | 0.453012i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.78733 | + | 7.78733i | −0.319787 | + | 0.319787i | −0.848685 | − | 0.528898i | \(-0.822605\pi\) |
0.528898 | + | 0.848685i | \(0.322605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.0077 | − | 12.1719i | −1.51463 | − | 0.498164i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.9880 | 0.489818 | 0.244909 | − | 0.969546i | \(-0.421242\pi\) | ||||
0.244909 | + | 0.969546i | \(0.421242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6307 | −0.841543 | −0.420772 | − | 0.907167i | \(-0.638241\pi\) | ||||
−0.420772 | + | 0.907167i | \(0.638241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.9952 | − | 4.98279i | 1.34367 | − | 0.202915i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.4864 | + | 16.4864i | −0.669164 | + | 0.669164i | −0.957522 | − | 0.288359i | \(-0.906890\pi\) |
0.288359 | + | 0.957522i | \(0.406890\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.05854 | − | 2.09612i | −0.0428943 | − | 0.0849390i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.35576i | 0.0548480i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.06854 | − | 4.06854i | −0.164327 | − | 0.164327i | 0.620154 | − | 0.784480i | \(-0.287070\pi\) |
−0.784480 | + | 0.620154i | \(0.787070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.4658 | − | 27.4658i | −1.10573 | − | 1.10573i | −0.993705 | − | 0.112027i | \(-0.964266\pi\) |
−0.112027 | − | 0.993705i | \(-0.535734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.4924i | − | 0.743273i | −0.928378 | − | 0.371637i | \(-0.878797\pi\) | ||
0.928378 | − | 0.371637i | \(-0.121203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50758 | + | 8.89586i | −0.0604970 | + | 0.356979i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.74599 | + | 8.74599i | −0.350401 | + | 0.350401i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.87935 | + | 5.71401i | −0.0750541 | + | 0.228196i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0802 | 0.601288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0540 | 1.03719 | 0.518596 | − | 0.855019i | \(-0.326455\pi\) | ||||
0.518596 | + | 0.855019i | \(0.326455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.95875 | + | 12.0362i | −0.157346 | + | 0.478397i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.310029 | − | 0.310029i | 0.0122838 | − | 0.0122838i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.1181 | − | 34.0540i | 0.993656 | − | 1.34715i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3687i | 0.488534i | 0.969708 | + | 0.244267i | \(0.0785474\pi\) | ||||
−0.969708 | + | 0.244267i | \(0.921453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8664 | − | 15.8664i | −0.625709 | − | 0.625709i | 0.321277 | − | 0.946985i | \(-0.395888\pi\) |
−0.946985 | + | 0.321277i | \(0.895888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.9215 | + | 29.9215i | 1.17634 | + | 1.17634i | 0.980671 | + | 0.195664i | \(0.0626862\pi\) |
0.195664 | + | 0.980671i | \(0.437314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.8617i | − | 1.17218i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.43845 | − | 12.7494i | −0.252343 | − | 0.499687i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.2945 | − | 34.2945i | 1.34205 | − | 1.34205i | 0.448027 | − | 0.894020i | \(-0.352127\pi\) |
0.894020 | − | 0.448027i | \(-0.147873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.68780 | − | 17.7982i | −0.104861 | − | 0.694374i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2222 | −0.631928 | −0.315964 | − | 0.948771i | \(-0.602328\pi\) | ||||
−0.315964 | + | 0.948771i | \(0.602328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3693 | 0.753379 | 0.376690 | − | 0.926340i | \(-0.377062\pi\) | ||||
0.376690 | + | 0.926340i | \(0.377062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.48333 | − | 1.14568i | −0.135281 | − | 0.0444943i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.66464 | − | 1.66464i | 0.0644553 | − | 0.0644553i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.6245 | + | 15.4654i | −1.18401 | + | 0.597928i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.8415i | − | 0.611556i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6274 | + | 22.6274i | 0.872223 | + | 0.872223i | 0.992714 | − | 0.120492i | \(-0.0384471\pi\) |
−0.120492 | + | 0.992714i | \(0.538447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0777 | + | 14.0777i | 0.541048 | + | 0.541048i | 0.923836 | − | 0.382788i | \(-0.125036\pi\) |
−0.382788 | + | 0.923836i | \(0.625036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.56155i | − | 0.136680i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.4654 | + | 16.9001i | −1.28240 | + | 0.647613i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5122 | − | 10.5122i | 0.402237 | − | 0.402237i | −0.476784 | − | 0.879021i | \(-0.658197\pi\) |
0.879021 | + | 0.476784i | \(0.158197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.5678 | − | 4.46250i | −0.517645 | − | 0.170255i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.761329 | 0.0290043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6307 | 0.480494 | 0.240247 | − | 0.970712i | \(-0.422772\pi\) | ||||
0.240247 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.38519 | − | 9.17252i | −0.0526192 | − | 0.348435i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.1154 | + | 21.1154i | −0.799804 | + | 0.799804i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1300 | + | 26.0000i | 0.496623 | + | 0.983410i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.0388i | − | 1.24786i | −0.781480 | − | 0.623930i | \(-0.785535\pi\) | ||
0.781480 | − | 0.623930i | \(-0.214465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.48023 | − | 2.48023i | −0.0935437 | − | 0.0935437i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.45567 | − | 2.45567i | −0.0923549 | − | 0.0923549i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.8078i | 0.668785i | 0.942434 | + | 0.334392i | \(0.108531\pi\) | ||||
−0.942434 | + | 0.334392i | \(0.891469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.90388 | − | 13.4272i | 0.371425 | − | 0.503561i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1250 | − | 10.1250i | 0.379184 | − | 0.379184i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.2461 | + | 31.1524i | −0.382648 | + | 1.16341i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.65719 | 0.360153 | 0.180076 | − | 0.983653i | \(-0.442366\pi\) | ||||
0.180076 | + | 0.983653i | \(0.442366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.80776 | −0.141809 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.133239 | + | 0.405102i | −0.00495521 | + | 0.0150659i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.2208 | − | 30.2208i | 1.12083 | − | 1.12083i | 0.129209 | − | 0.991617i | \(-0.458756\pi\) |
0.991617 | − | 0.129209i | \(-0.0412439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.89586 | − | 25.4924i | 0.329476 | − | 0.944164i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.4748i | 1.82989i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.1141 | − | 26.1141i | −0.964545 | − | 0.964545i | 0.0348475 | − | 0.999393i | \(-0.488905\pi\) |
−0.999393 | + | 0.0348475i | \(0.988905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3207 | − | 24.3207i | −0.895863 | − | 0.895863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.1771i | − | 1.36758i | −0.729678 | − | 0.683791i | \(-0.760330\pi\) | ||
0.729678 | − | 0.683791i | \(-0.239670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.384472 | + | 0.761329i | 0.0141239 | + | 0.0279681i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.3772 | − | 32.3772i | 1.18780 | − | 1.18780i | 0.210129 | − | 0.977674i | \(-0.432612\pi\) |
0.977674 | − | 0.210129i | \(-0.0673884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.15086 | − | 0.777860i | 0.188460 | − | 0.0284604i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.2895 | −0.741361 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.4233 | 1.43858 | 0.719288 | − | 0.694712i | \(-0.244468\pi\) | ||||
0.719288 | + | 0.694712i | \(0.244468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.8894 | − | 5.22606i | −0.579041 | − | 0.190448i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.06854 | − | 4.06854i | 0.147874 | − | 0.147874i | −0.629294 | − | 0.777168i | \(-0.716656\pi\) |
0.777168 | + | 0.629294i | \(0.216656\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.30144 | − | 4.19224i | 0.301323 | − | 0.152169i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.3403i | − | 1.49858i | −0.662240 | − | 0.749292i | \(-0.730394\pi\) | ||
0.662240 | − | 0.749292i | \(-0.269606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.14351 | − | 9.14351i | −0.331017 | − | 0.331017i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.99401 | − | 2.99401i | −0.108107 | − | 0.108107i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.1231i | − | 0.617475i | −0.951147 | − | 0.308737i | \(-0.900094\pi\) | ||
0.951147 | − | 0.308737i | \(-0.0999065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.6155 | + | 22.0259i | −1.57077 | + | 0.793243i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.2793 | + | 25.2793i | −0.909234 | + | 0.909234i | −0.996210 | − | 0.0869764i | \(-0.972280\pi\) |
0.0869764 | + | 0.996210i | \(0.472280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.13858 | + | 1.69009i | 0.184345 | + | 0.0606317i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.94568 | 0.248855 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.6155 | −1.56069 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.74366 | + | 4.07902i | −0.205262 | + | 0.145772i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2196 | + | 22.2196i | −0.792044 | + | 0.792044i | −0.981826 | − | 0.189782i | \(-0.939222\pi\) |
0.189782 | + | 0.981826i | \(0.439222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.18435 | − | 12.2462i | −0.220169 | − | 0.435977i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.73642i | − | 0.0617400i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.58831 | − | 1.58831i | −0.0564026 | − | 0.0564026i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.6987 | − | 12.6987i | −0.449810 | − | 0.449810i | 0.445481 | − | 0.895291i | \(-0.353033\pi\) |
−0.895291 | + | 0.445481i | \(0.853033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.9309i | 0.528216i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.8617 | + | 22.0259i | 1.05511 | + | 0.778247i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1190 | + | 13.1190i | −0.462959 | + | 0.462959i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.7988 | − | 41.9541i | 0.485742 | − | 1.47686i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.8002 | −1.18835 | −0.594175 | − | 0.804335i | \(-0.702522\pi\) | ||||
−0.594175 | + | 0.804335i | \(0.702522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7386 | −1.43053 | −0.715263 | − | 0.698855i | \(-0.753693\pi\) | ||||
−0.715263 | + | 0.698855i | \(0.753693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.26629 | + | 28.1734i | −0.324983 | + | 0.988083i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.13709 | − | 8.13709i | 0.284681 | − | 0.284681i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.05854 | − | 0.780776i | −0.0369885 | − | 0.0272825i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.4075i | 1.58473i | 0.610044 | + | 0.792367i | \(0.291152\pi\) | ||||
−0.610044 | + | 0.792367i | \(0.708848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3505 | − | 16.3505i | −0.569943 | − | 0.569943i | 0.362169 | − | 0.932112i | \(-0.382036\pi\) |
−0.932112 | + | 0.362169i | \(0.882036\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.1755 | + | 21.1755i | 0.736344 | + | 0.736344i | 0.971868 | − | 0.235524i | \(-0.0756808\pi\) |
−0.235524 | + | 0.971868i | \(0.575681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 19.7538i | − | 0.686077i | −0.939321 | − | 0.343039i | \(-0.888544\pi\) | ||
0.939321 | − | 0.343039i | \(-0.111456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.8078 | + | 23.3817i | 0.409607 | + | 0.811101i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.41433 | − | 3.41433i | 0.118300 | − | 0.118300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.9351 | + | 24.8101i | −1.20753 | + | 0.857562i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.8131 | −1.54712 | −0.773560 | − | 0.633723i | \(-0.781526\pi\) | ||||
−0.773560 | + | 0.633723i | \(0.781526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1619 | −0.936618 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4061 | + | 4.08038i | 0.427287 | + | 0.140536i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.01714 | − | 1.01714i | 0.0349492 | − | 0.0349492i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.24289 | − | 3.65767i | 0.248575 | − | 0.125531i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.42302i | 0.185899i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6644 | + | 14.6644i | 0.502100 | + | 0.502100i | 0.912090 | − | 0.409990i | \(-0.134468\pi\) |
−0.409990 | + | 0.912090i | \(0.634468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.6573 | + | 13.6573i | 0.466526 | + | 0.466526i | 0.900787 | − | 0.434261i | \(-0.142991\pi\) |
−0.434261 | + | 0.900787i | \(0.642991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3693i | 1.20679i | 0.797444 | + | 0.603393i | \(0.206185\pi\) | ||||
−0.797444 | + | 0.603393i | \(0.793815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.56155 | + | 4.82860i | −0.325857 | + | 0.164558i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.06249 | − | 5.06249i | 0.172329 | − | 0.172329i | −0.615673 | − | 0.788002i | \(-0.711116\pi\) |
0.788002 | + | 0.615673i | \(0.211116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.3909 | − | 3.41759i | −0.352893 | − | 0.116067i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1973 | −0.583378 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.87689 | −0.165247 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.5649 | + | 1.59546i | −0.357567 | + | 0.0539981i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.6619 | − | 11.6619i | 0.393795 | − | 0.393795i | −0.482243 | − | 0.876037i | \(-0.660178\pi\) |
0.876037 | + | 0.482243i | \(0.160178\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.4272 | + | 26.5885i | 0.452890 | + | 0.896809i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7917i | 0.599419i | 0.954031 | + | 0.299709i | \(0.0968897\pi\) | ||||
−0.954031 | + | 0.299709i | \(0.903110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0101 | + | 12.0101i | 0.404172 | + | 0.404172i | 0.879700 | − | 0.475528i | \(-0.157743\pi\) |
−0.475528 | + | 0.879700i | \(0.657743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.4295 | + | 12.4295i | 0.417342 | + | 0.417342i | 0.884286 | − | 0.466945i | \(-0.154645\pi\) |
−0.466945 | + | 0.884286i | \(0.654645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.87689i | 0.297721i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.5885 | + | 8.21799i | −0.890750 | + | 0.275313i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.45567 | − | 2.45567i | 0.0821758 | − | 0.0821758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.411998 | − | 1.25265i | 0.0137562 | − | 0.0418246i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1798 | 0.372869 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.38447 | 0.279327 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.54481 | + | 16.8585i | −0.184520 | + | 0.561016i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.5221 | − | 13.5221i | 0.448993 | − | 0.448993i | −0.446027 | − | 0.895020i | \(-0.647161\pi\) |
0.895020 | + | 0.446027i | \(0.147161\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.18435 | + | 8.38447i | −0.205122 | + | 0.278095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.5281i | − | 0.646996i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.79668 | − | 3.79668i | −0.125652 | − | 0.125652i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1190 | + | 13.1190i | 0.433227 | + | 0.433227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.17708i | − | 0.0388283i | −0.999812 | − | 0.0194142i | \(-0.993820\pi\) | ||
0.999812 | − | 0.0194142i | \(-0.00618011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.95786 | − | 7.83732i | −0.130416 | − | 0.258249i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.37300 | + | 4.37300i | −0.143939 | + | 0.143939i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.70575 | + | 11.2952i | 0.0560243 | + | 0.370984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.3946 | 1.12845 | 0.564225 | − | 0.825621i | \(-0.309175\pi\) | ||||
0.564225 | + | 0.825621i | \(0.309175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12311 | −0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46.4155 | + | 15.2662i | 1.51958 | + | 0.499792i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.2589 | − | 30.2589i | 0.988517 | − | 0.988517i | −0.0114182 | − | 0.999935i | \(-0.503635\pi\) |
0.999935 | + | 0.0114182i | \(0.00363460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.2698 | + | 26.3963i | −1.70576 | + | 0.861411i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.9975i | 1.66247i | 0.555921 | + | 0.831235i | \(0.312366\pi\) | ||||
−0.555921 | + | 0.831235i | \(0.687634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.59336 | − | 7.59336i | −0.247274 | − | 0.247274i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.0101 | − | 25.0101i | −0.812721 | − | 0.812721i | 0.172320 | − | 0.985041i | \(-0.444874\pi\) |
−0.985041 | + | 0.172320i | \(0.944874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.63068i | 0.0853956i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.1231 | − | 22.7872i | 1.46322 | − | 0.738926i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.4658 | + | 27.4658i | −0.889705 | + | 0.889705i | −0.994494 | − | 0.104789i | \(-0.966583\pi\) |
0.104789 | + | 0.994494i | \(0.466583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.89766 | + | 2.26866i | 0.222970 | + | 0.0733353i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.44793 | 0.143631 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.0000 | 1.19355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.08903 | + | 60.1860i | 0.292890 | + | 1.93947i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2208 | + | 30.2208i | −0.971835 | + | 0.971835i | −0.999614 | − | 0.0277794i | \(-0.991156\pi\) |
0.0277794 | + | 0.999614i | \(0.491156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.23417 | + | 8.38447i | 0.136021 | + | 0.269348i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.2361i | 1.61215i | 0.591810 | + | 0.806077i | \(0.298413\pi\) | ||||
−0.591810 | + | 0.806077i | \(0.701587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.07107 | − | 7.07107i | −0.226688 | − | 0.226688i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.6615 | + | 41.6615i | 1.33287 | + | 1.33287i | 0.902792 | + | 0.430077i | \(0.141514\pi\) |
0.430077 | + | 0.902792i | \(0.358486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 38.2462i | − | 1.22235i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.0270 | + | 31.2190i | −0.735195 | + | 0.996745i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.10383 | − | 4.10383i | 0.130892 | − | 0.130892i | −0.638626 | − | 0.769517i | \(-0.720497\pi\) |
0.769517 | + | 0.638626i | \(0.220497\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.67335 | + | 5.08769i | −0.0532634 | + | 0.161943i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.7917 | −0.565744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.7538 | −0.691032 | −0.345516 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345516 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.38018 | − | 10.2772i | 0.107267 | − | 0.326136i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.7047 | − | 43.7047i | 1.38414 | − | 1.38414i | 0.547025 | − | 0.837116i | \(-0.315760\pi\) |
0.837116 | − | 0.547025i | \(-0.184240\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.71151 | − | 16.0000i | 0.0857884 | − | 0.506218i |
(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 | 2100.2.s.a.1793.3 | yes | 16 | |
3.2 | odd | 2 | inner | 2100.2.s.a.1793.7 | yes | 16 | |
5.2 | odd | 4 | inner | 2100.2.s.a.1457.7 | yes | 16 | |
5.3 | odd | 4 | inner | 2100.2.s.a.1457.2 | ✓ | 16 | |
5.4 | even | 2 | inner | 2100.2.s.a.1793.6 | yes | 16 | |
15.2 | even | 4 | inner | 2100.2.s.a.1457.3 | yes | 16 | |
15.8 | even | 4 | inner | 2100.2.s.a.1457.6 | yes | 16 | |
15.14 | odd | 2 | inner | 2100.2.s.a.1793.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.s.a.1457.2 | ✓ | 16 | 5.3 | odd | 4 | inner | |
2100.2.s.a.1457.3 | yes | 16 | 15.2 | even | 4 | inner | |
2100.2.s.a.1457.6 | yes | 16 | 15.8 | even | 4 | inner | |
2100.2.s.a.1457.7 | yes | 16 | 5.2 | odd | 4 | inner | |
2100.2.s.a.1793.2 | yes | 16 | 15.14 | odd | 2 | inner | |
2100.2.s.a.1793.3 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.s.a.1793.6 | yes | 16 | 5.4 | even | 2 | inner | |
2100.2.s.a.1793.7 | yes | 16 | 3.2 | odd | 2 | inner |