Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.5 | ||
Root | \(-0.312316 - 1.97546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.161 |
Dual form | 384.3.i.c.353.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.18505 | + | 2.75602i | −0.395015 | + | 0.918675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.00985921 | + | 0.00985921i | 0.00197184 | + | 0.00197184i | 0.708092 | − | 0.706120i | \(-0.249556\pi\) |
−0.706120 | + | 0.708092i | \(0.749556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.42277i | − | 0.917538i | −0.888556 | − | 0.458769i | \(-0.848291\pi\) | ||
0.888556 | − | 0.458769i | \(-0.151709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.19134 | − | 6.53203i | −0.687926 | − | 0.725781i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.07186 | + | 9.07186i | 0.824715 | + | 0.824715i | 0.986780 | − | 0.162065i | \(-0.0518155\pi\) |
−0.162065 | + | 0.986780i | \(0.551815\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.6098 | − | 12.6098i | −0.969987 | − | 0.969987i | 0.0295753 | − | 0.999563i | \(-0.490585\pi\) |
−0.999563 | + | 0.0295753i | \(0.990585\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0388558 | + | 0.0154886i | −0.00259039 | + | 0.00103257i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 19.0155i | − | 1.11856i | −0.828978 | − | 0.559281i | \(-0.811077\pi\) | ||
0.828978 | − | 0.559281i | \(-0.188923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.07165 | − | 2.07165i | −0.109034 | − | 0.109034i | 0.650485 | − | 0.759519i | \(-0.274566\pi\) |
−0.759519 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.7013 | + | 7.61127i | 0.842919 | + | 0.362441i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.5712 | −0.850923 | −0.425461 | − | 0.904977i | \(-0.639888\pi\) | ||||
−0.425461 | + | 0.904977i | \(0.639888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 24.9998i | − | 0.999992i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.3394 | − | 9.32272i | 0.938497 | − | 0.345286i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.1742 | − | 11.1742i | 0.385319 | − | 0.385319i | −0.487695 | − | 0.873014i | \(-0.662162\pi\) |
0.873014 | + | 0.487695i | \(0.162162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.9385 | 1.93350 | 0.966750 | − | 0.255725i | \(-0.0823142\pi\) | ||||
0.966750 | + | 0.255725i | \(0.0823142\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −35.7528 | + | 14.2517i | −1.08342 | + | 0.431870i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0633234 | − | 0.0633234i | 0.00180924 | − | 0.00180924i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.32707 | + | 9.32707i | −0.252083 | + | 0.252083i | −0.821824 | − | 0.569741i | \(-0.807043\pi\) |
0.569741 | + | 0.821824i | \(0.307043\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 49.6962 | − | 19.8098i | 1.27426 | − | 0.507943i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 47.2639 | 1.15278 | 0.576389 | − | 0.817176i | \(-0.304461\pi\) | ||||
0.576389 | + | 0.817176i | \(0.304461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.1220 | − | 24.1220i | 0.560978 | − | 0.560978i | −0.368607 | − | 0.929585i | \(-0.620165\pi\) |
0.929585 | + | 0.368607i | \(0.120165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.00335893 | − | 0.125442i | 7.46430e−5 | − | 0.00278761i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.29702i | 0.133979i | 0.997754 | + | 0.0669896i | \(0.0213394\pi\) | ||||
−0.997754 | + | 0.0669896i | \(0.978661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.74808 | 0.158124 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.4073 | + | 22.5343i | 1.02759 | + | 0.441849i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20.6409 | − | 20.6409i | −0.389450 | − | 0.389450i | 0.485041 | − | 0.874491i | \(-0.338805\pi\) |
−0.874491 | + | 0.485041i | \(0.838805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.178883i | 0.00325242i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.16452 | − | 3.25452i | 0.143237 | − | 0.0570968i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.3533 | − | 60.3533i | −1.02294 | − | 1.02294i | −0.999731 | − | 0.0232062i | \(-0.992613\pi\) |
−0.0232062 | − | 0.999731i | \(-0.507387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.0230 | − | 48.0230i | −0.787262 | − | 0.787262i | 0.193782 | − | 0.981045i | \(-0.437924\pi\) |
−0.981045 | + | 0.193782i | \(0.937924\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.9537 | + | 39.7655i | −0.665931 | + | 0.631198i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.248646i | − | 0.00382532i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23.7768 | − | 23.7768i | −0.354878 | − | 0.354878i | 0.507043 | − | 0.861921i | \(-0.330738\pi\) |
−0.861921 | + | 0.507043i | \(0.830738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.1928 | − | 53.9388i | 0.336127 | − | 0.781721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5743 | −0.191188 | −0.0955938 | − | 0.995420i | \(-0.530475\pi\) | ||||
−0.0955938 | + | 0.995420i | \(0.530475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31.4516i | 0.430844i | 0.976521 | + | 0.215422i | \(0.0691127\pi\) | ||||
−0.976521 | + | 0.215422i | \(0.930887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 68.9001 | + | 29.6259i | 0.918668 | + | 0.395012i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 58.2665 | − | 58.2665i | 0.756707 | − | 0.756707i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −47.4718 | −0.600909 | −0.300455 | − | 0.953796i | \(-0.597138\pi\) | ||||
−0.300455 | + | 0.953796i | \(0.597138\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.33472 | + | 80.8839i | −0.0535151 | + | 0.998567i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −70.3318 | + | 70.3318i | −0.847372 | + | 0.847372i | −0.989804 | − | 0.142433i | \(-0.954507\pi\) |
0.142433 | + | 0.989804i | \(0.454507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.187478 | − | 0.187478i | 0.00220563 | − | 0.00220563i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.5545 | + | 44.0385i | 0.201776 | + | 0.506189i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −95.1729 | −1.06936 | −0.534679 | − | 0.845055i | \(-0.679568\pi\) | ||||
−0.534679 | + | 0.845055i | \(0.679568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.9900 | + | 80.9900i | −0.890000 | + | 0.890000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −71.0298 | + | 165.192i | −0.763761 | + | 1.77626i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.0408497i | − | 0.000429997i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61.6218 | 0.635276 | 0.317638 | − | 0.948212i | \(-0.397110\pi\) | ||||
0.317638 | + | 0.948212i | \(0.397110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.09069 | − | 115.425i | 0.0312191 | − | 1.16591i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −48.1867 | − | 48.1867i | −0.477096 | − | 0.477096i | 0.427106 | − | 0.904202i | \(-0.359533\pi\) |
−0.904202 | + | 0.427106i | \(0.859533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.73669i | 0.0459873i | 0.999736 | + | 0.0229936i | \(0.00731975\pi\) | ||||
−0.999736 | + | 0.0229936i | \(0.992680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0994797 | + | 0.249562i | 0.000947426 | + | 0.00237678i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −40.9462 | − | 40.9462i | −0.382674 | − | 0.382674i | 0.489390 | − | 0.872065i | \(-0.337219\pi\) |
−0.872065 | + | 0.489390i | \(0.837219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 120.437 | + | 120.437i | 1.10493 | + | 1.10493i | 0.993807 | + | 0.111123i | \(0.0354447\pi\) |
0.111123 | + | 0.993807i | \(0.464555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6526 | − | 36.7586i | −0.132006 | − | 0.331159i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 205.193i | − | 1.81587i | −0.419110 | − | 0.907936i | \(-0.637658\pi\) | ||
0.419110 | − | 0.907936i | \(-0.362342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.192957 | − | 0.192957i | −0.00167789 | − | 0.00167789i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.29604 | + | 160.439i | −0.0367183 | + | 1.37128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −122.132 | −1.02632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43.5974i | 0.360309i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −56.0098 | + | 130.260i | −0.455365 | + | 1.05903i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.492959 | − | 0.492959i | 0.00394367 | − | 0.00394367i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −54.1458 | −0.426345 | −0.213173 | − | 0.977015i | \(-0.568380\pi\) | ||||
−0.213173 | + | 0.977015i | \(0.568380\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 37.8952 | + | 95.0666i | 0.293761 | + | 0.736951i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31.2584 | − | 31.2584i | 0.238614 | − | 0.238614i | −0.577662 | − | 0.816276i | \(-0.696035\pi\) |
0.816276 | + | 0.577662i | \(0.196035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.3057 | + | 13.3057i | −0.100043 | + | 0.100043i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.341742 | + | 0.157912i | 0.00253142 | + | 0.00116972i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 42.9176 | 0.313267 | 0.156633 | − | 0.987657i | \(-0.449936\pi\) | ||||
0.156633 | + | 0.987657i | \(0.449936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −47.0945 | + | 47.0945i | −0.338809 | + | 0.338809i | −0.855919 | − | 0.517110i | \(-0.827008\pi\) |
0.517110 | + | 0.855919i | \(0.327008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.3547 | − | 7.46225i | −0.123083 | − | 0.0529238i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 228.789i | − | 1.59993i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.220339 | 0.00151958 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.18183 | + | 21.3539i | −0.0624614 | + | 0.145265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.532 | + | 131.532i | 0.882766 | + | 0.882766i | 0.993815 | − | 0.111049i | \(-0.0354210\pi\) |
−0.111049 | + | 0.993815i | \(0.535421\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 145.908i | 0.966281i | 0.875543 | + | 0.483140i | \(0.160504\pi\) | ||||
−0.875543 | + | 0.483140i | \(0.839496\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −124.210 | + | 117.732i | −0.811830 | + | 0.769488i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.590946 | + | 0.590946i | 0.00381256 | + | 0.00381256i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 55.2586 | + | 55.2586i | 0.351966 | + | 0.351966i | 0.860840 | − | 0.508875i | \(-0.169938\pi\) |
−0.508875 | + | 0.860840i | \(0.669938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 81.3470 | − | 32.4263i | 0.511617 | − | 0.203939i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 125.701i | 0.780754i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 70.6156 | + | 70.6156i | 0.433225 | + | 0.433225i | 0.889724 | − | 0.456499i | \(-0.150897\pi\) |
−0.456499 | + | 0.889724i | \(0.650897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.493006 | − | 0.211984i | −0.00298791 | − | 0.00128475i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −86.2013 | −0.516176 | −0.258088 | − | 0.966121i | \(-0.583092\pi\) | ||||
−0.258088 | + | 0.966121i | \(0.583092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 149.016i | 0.881751i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.705790 | + | 26.3584i | −0.00412743 | + | 0.154142i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 58.2425 | − | 58.2425i | 0.336662 | − | 0.336662i | −0.518448 | − | 0.855109i | \(-0.673490\pi\) |
0.855109 | + | 0.518448i | \(0.173490\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −160.568 | −0.917531 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 237.856 | − | 94.8137i | 1.34382 | − | 0.535671i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9272 | − | 18.9272i | 0.105738 | − | 0.105738i | −0.652258 | − | 0.757997i | \(-0.726178\pi\) |
0.757997 | + | 0.652258i | \(0.226178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.5109 | + | 24.5109i | −0.135420 | + | 0.135420i | −0.771567 | − | 0.636148i | \(-0.780527\pi\) |
0.636148 | + | 0.771567i | \(0.280527\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 189.262 | − | 75.4431i | 1.03422 | − | 0.412257i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.183915 | −0.000994136 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 172.506 | − | 172.506i | 0.922494 | − | 0.922494i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59.8777 | − | 162.749i | −0.316813 | − | 0.861107i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 156.422i | 0.818962i | 0.912319 | + | 0.409481i | \(0.134290\pi\) | ||||
−0.912319 | + | 0.409481i | \(0.865710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −217.972 | −1.12939 | −0.564695 | − | 0.825299i | \(-0.691006\pi\) | ||||
−0.564695 | + | 0.825299i | \(0.691006\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.685275 | + | 0.294657i | 0.00351423 | + | 0.00151106i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −245.945 | − | 245.945i | −1.24845 | − | 1.24845i | −0.956403 | − | 0.292050i | \(-0.905663\pi\) |
−0.292050 | − | 0.956403i | \(-0.594337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 233.190i | − | 1.17181i | −0.810379 | − | 0.585905i | \(-0.800739\pi\) | ||
0.810379 | − | 0.585905i | \(-0.199261\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 93.7060 | − | 37.3528i | 0.466199 | − | 0.185835i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −71.7695 | − | 71.7695i | −0.353545 | − | 0.353545i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.465985 | + | 0.465985i | 0.00227310 | + | 0.00227310i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 121.172 | + | 127.840i | 0.585372 | + | 0.617583i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 37.5875i | − | 0.179844i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.49504 | − | 8.49504i | −0.0402609 | − | 0.0402609i | 0.686690 | − | 0.726951i | \(-0.259063\pi\) |
−0.726951 | + | 0.686690i | \(0.759063\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0862 | − | 37.4111i | 0.0755220 | − | 0.175639i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.475649 | 0.00221232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 384.971i | − | 1.77406i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −86.6814 | − | 37.2716i | −0.395806 | − | 0.170190i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −239.783 | + | 239.783i | −1.08499 | + | 1.08499i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9290 | 0.0490090 | 0.0245045 | − | 0.999700i | \(-0.492199\pi\) | ||||
0.0245045 | + | 0.999700i | \(0.492199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −163.299 | + | 154.782i | −0.725775 | + | 0.687921i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −99.9027 | + | 99.9027i | −0.440100 | + | 0.440100i | −0.892045 | − | 0.451946i | \(-0.850730\pi\) |
0.451946 | + | 0.892045i | \(0.350730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 231.857 | − | 231.857i | 1.01248 | − | 1.01248i | 0.0125555 | − | 0.999921i | \(-0.496003\pi\) |
0.999921 | − | 0.0125555i | \(-0.00399663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 91.5354 | + | 229.632i | 0.396257 | + | 0.994079i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 316.641 | 1.35897 | 0.679486 | − | 0.733688i | \(-0.262203\pi\) | ||||
0.679486 | + | 0.733688i | \(0.262203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0620836 | + | 0.0620836i | −0.000264186 | + | 0.000264186i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 56.2562 | − | 130.833i | 0.237368 | − | 0.552040i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 382.691i | 1.60122i | 0.599187 | + | 0.800609i | \(0.295491\pi\) | ||||
−0.599187 | + | 0.800609i | \(0.704509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −91.3157 | −0.378903 | −0.189452 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189452 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −217.781 | − | 107.798i | −0.896219 | − | 0.443612i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0763900 | + | 0.0763900i | 0.000311796 | + | 0.000311796i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 52.2463i | 0.211524i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −110.490 | − | 277.183i | −0.443734 | − | 1.11318i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 128.768 | + | 128.768i | 0.513021 | + | 0.513021i | 0.915451 | − | 0.402430i | \(-0.131834\pi\) |
−0.402430 | + | 0.915451i | \(0.631834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −177.547 | − | 177.547i | −0.701769 | − | 0.701769i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.294524 | + | 0.738865i | 0.00115500 | + | 0.00289751i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 123.915i | 0.482159i | 0.970505 | + | 0.241079i | \(0.0775014\pi\) | ||||
−0.970505 | + | 0.241079i | \(0.922499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 59.9056 | + | 59.9056i | 0.231296 | + | 0.231296i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −142.174 | − | 3.80695i | −0.544728 | − | 0.0145860i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 194.379 | 0.739085 | 0.369542 | − | 0.929214i | \(-0.379514\pi\) | ||||
0.369542 | + | 0.929214i | \(0.379514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.407005i | − | 0.00153587i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 112.784 | − | 262.299i | 0.422413 | − | 0.982393i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 296.636 | − | 296.636i | 1.10274 | − | 1.10274i | 0.108658 | − | 0.994079i | \(-0.465345\pi\) |
0.994079 | − | 0.108658i | \(-0.0346555\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 278.227 | 1.02667 | 0.513334 | − | 0.858189i | \(-0.328410\pi\) | ||||
0.513334 | + | 0.858189i | \(0.328410\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −127.234 | − | 319.187i | −0.466057 | − | 1.16918i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 226.795 | − | 226.795i | 0.824709 | − | 0.824709i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 60.1513 | − | 60.1513i | 0.217153 | − | 0.217153i | −0.590145 | − | 0.807297i | \(-0.700929\pi\) |
0.807297 | + | 0.590145i | \(0.200929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −371.099 | − | 391.520i | −1.33010 | − | 1.40330i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −313.645 | −1.11617 | −0.558087 | − | 0.829782i | \(-0.688465\pi\) | ||||
−0.558087 | + | 0.829782i | \(0.688465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 286.980 | − | 286.980i | 1.01406 | − | 1.01406i | 0.0141627 | − | 0.999900i | \(-0.495492\pi\) |
0.999900 | − | 0.0141627i | \(-0.00450829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.112583 | + | 0.0484087i | 0.000395027 | + | 0.000169855i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 303.565i | − | 1.05772i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −72.5910 | −0.251180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −73.0246 | + | 169.831i | −0.250944 | + | 0.583612i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 176.501 | + | 176.501i | 0.602394 | + | 0.602394i | 0.940947 | − | 0.338553i | \(-0.109938\pi\) |
−0.338553 | + | 0.940947i | \(0.609938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.19007i | − | 0.00403414i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 314.450 | + | 145.301i | 1.05876 | + | 0.489230i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 246.790 | + | 246.790i | 0.825384 | + | 0.825384i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −154.930 | − | 154.930i | −0.514718 | − | 0.514718i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 189.907 | − | 75.7002i | 0.626756 | − | 0.249836i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.946938i | − | 0.00310471i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 63.9904 | + | 63.9904i | 0.208438 | + | 0.208438i | 0.803603 | − | 0.595165i | \(-0.202913\pi\) |
−0.595165 | + | 0.803603i | \(0.702913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0544 | − | 5.61319i | −0.0422473 | − | 0.0181657i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 532.288 | 1.71154 | 0.855769 | − | 0.517359i | \(-0.173085\pi\) | ||||
0.855769 | + | 0.517359i | \(0.173085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 185.676i | 0.593215i | 0.954999 | + | 0.296607i | \(0.0958553\pi\) | ||||
−0.954999 | + | 0.296607i | \(0.904145\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.805687 | − | 0.0215736i | −0.00255774 | − | 6.84878e-5i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −168.127 | + | 168.127i | −0.530370 | + | 0.530370i | −0.920683 | − | 0.390312i | \(-0.872367\pi\) |
0.390312 | + | 0.920683i | \(0.372367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 202.742 | 0.635556 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 161.372 | − | 64.3256i | 0.502715 | − | 0.200391i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.3936 | + | 39.3936i | −0.121962 | + | 0.121962i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −315.243 | + | 315.243i | −0.969980 | + | 0.969980i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −474.652 | + | 189.204i | −1.45153 | + | 0.578607i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.4443 | 0.122931 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −241.678 | + | 241.678i | −0.730144 | + | 0.730144i | −0.970648 | − | 0.240504i | \(-0.922687\pi\) |
0.240504 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 118.672 | + | 3.17764i | 0.356371 | + | 0.00954245i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 0.468841i | − | 0.00139953i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 396.856 | 1.17762 | 0.588808 | − | 0.808273i | \(-0.299598\pi\) | ||||
0.588808 | + | 0.808273i | \(0.299598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 565.518 | + | 243.163i | 1.66819 | + | 0.717296i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 543.754 | + | 543.754i | 1.59459 | + | 1.59459i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 364.480i | − | 1.06262i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.760456 | − | 0.303131i | 0.00220422 | − | 0.000878641i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 38.5699 | + | 38.5699i | 0.111153 | + | 0.111153i | 0.760496 | − | 0.649343i | \(-0.224956\pi\) |
−0.649343 | + | 0.760496i | \(0.724956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4065 | − | 10.4065i | −0.0298180 | − | 0.0298180i | 0.692041 | − | 0.721859i | \(-0.256712\pi\) |
−0.721859 | + | 0.692041i | \(0.756712\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −437.084 | − | 201.968i | −1.24525 | − | 0.575408i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 209.294i | 0.592900i | 0.955048 | + | 0.296450i | \(0.0958028\pi\) | ||||
−0.955048 | + | 0.296450i | \(0.904197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.133832 | − | 0.133832i | −0.000376992 | − | 0.000376992i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 144.732 | − | 336.600i | 0.405413 | − | 0.942857i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −42.6682 | −0.118853 | −0.0594264 | − | 0.998233i | \(-0.518927\pi\) | ||||
−0.0594264 | + | 0.998233i | \(0.518927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 352.417i | − | 0.976223i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −120.156 | − | 51.6649i | −0.331007 | − | 0.142328i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.310088 | + | 0.310088i | −0.000849557 | + | 0.000849557i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2444 | 0.0442627 | 0.0221313 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221313 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −292.627 | − | 308.729i | −0.793026 | − | 0.836664i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −132.571 | + | 132.571i | −0.357335 | + | 0.357335i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −351.379 | + | 351.379i | −0.942035 | + | 0.942035i | −0.998410 | − | 0.0563743i | \(-0.982046\pi\) |
0.0563743 | + | 0.998410i | \(0.482046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.774428 | + | 1.94278i | 0.00206514 | + | 0.00518076i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −281.811 | −0.747509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −170.505 | + | 170.505i | −0.449880 | + | 0.449880i | −0.895315 | − | 0.445435i | \(-0.853049\pi\) |
0.445435 | + | 0.895315i | \(0.353049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 64.1653 | − | 149.227i | 0.168413 | − | 0.391673i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 256.234i | − | 0.669017i | −0.942393 | − | 0.334509i | \(-0.891430\pi\) | ||
0.942393 | − | 0.334509i | \(-0.108570\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.14892 | 0.00298422 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −306.913 | − | 8.21813i | −0.793058 | − | 0.0212355i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −376.214 | − | 376.214i | −0.967130 | − | 0.967130i | 0.0323468 | − | 0.999477i | \(-0.489702\pi\) |
−0.999477 | + | 0.0323468i | \(0.989702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 372.158i | 0.951810i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.1063 | + | 123.192i | 0.124953 | + | 0.313465i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.468035 | − | 0.468035i | −0.00118490 | − | 0.00118490i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 312.905 | + | 312.905i | 0.788174 | + | 0.788174i | 0.981195 | − | 0.193021i | \(-0.0618284\pi\) |
−0.193021 | + | 0.981195i | \(0.561828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.9030 | − | 52.4388i | −0.0523885 | − | 0.131426i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.22373i | 0.0230018i | 0.999934 | + | 0.0115009i | \(0.00366093\pi\) | ||||
−0.999934 | + | 0.0115009i | \(0.996339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −755.814 | − | 755.814i | −1.87547 | − | 1.87547i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.840189 | + | 0.754715i | −0.00207454 | + | 0.00186349i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −169.228 | −0.415793 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 322.436i | 0.788352i | 0.919035 | + | 0.394176i | \(0.128970\pi\) | ||||
−0.919035 | + | 0.394176i | \(0.871030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −50.8592 | + | 118.282i | −0.123745 | + | 0.287790i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −387.635 | + | 387.635i | −0.938583 | + | 0.938583i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38683 | −0.00334177 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −73.9845 | − | 185.603i | −0.177421 | − | 0.445090i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 226.569 | − | 226.569i | 0.540738 | − | 0.540738i | −0.383007 | − | 0.923745i | \(-0.625112\pi\) |
0.923745 | + | 0.383007i | \(0.125112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 498.861 | − | 498.861i | 1.18494 | − | 1.18494i | 0.206495 | − | 0.978448i | \(-0.433794\pi\) |
0.978448 | − | 0.206495i | \(-0.0662058\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 41.1323 | − | 38.9870i | 0.0972394 | − | 0.0921677i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −475.385 | −1.11855 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −308.440 | + | 308.440i | −0.722343 | + | 0.722343i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 630.549 | + | 271.126i | 1.46981 | + | 0.631995i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 452.283i | 1.04938i | 0.851293 | + | 0.524690i | \(0.175819\pi\) | ||||
−0.851293 | + | 0.524690i | \(0.824181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 379.557 | 0.876574 | 0.438287 | − | 0.898835i | \(-0.355585\pi\) | ||||
0.438287 | + | 0.898835i | \(0.355585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.261111 | + | 0.607258i | −0.000600255 | + | 0.00139600i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.5447 | + | 40.5447i | 0.0927797 | + | 0.0927797i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 689.509i | 1.57063i | 0.619094 | + | 0.785317i | \(0.287500\pi\) | ||||
−0.619094 | + | 0.785317i | \(0.712500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −47.9710 | − | 50.6107i | −0.108778 | − | 0.114763i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 97.5600 | + | 97.5600i | 0.220226 | + | 0.220226i | 0.808593 | − | 0.588368i | \(-0.200229\pi\) |
−0.588368 | + | 0.808593i | \(0.700229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.938330 | − | 0.938330i | −0.00210861 | − | 0.00210861i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −518.377 | + | 206.634i | −1.15968 | + | 0.462269i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 718.711i | 1.60069i | 0.599538 | + | 0.800347i | \(0.295351\pi\) | ||||
−0.599538 | + | 0.800347i | \(0.704649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 428.772 | + | 428.772i | 0.950713 | + | 0.950713i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −402.127 | − | 172.908i | −0.887698 | − | 0.381695i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.59700 | −0.00350988 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 489.021i | 1.07007i | 0.844830 | + | 0.535034i | \(0.179701\pi\) | ||||
−0.844830 | + | 0.535034i | \(0.820299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −177.277 | − | 481.843i | −0.386224 | − | 1.04977i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −459.082 | + | 459.082i | −0.995840 | + | 0.995840i | −0.999991 | − | 0.00415179i | \(-0.998678\pi\) |
0.00415179 | + | 0.999991i | \(0.498678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −587.611 | −1.26914 | −0.634569 | − | 0.772866i | \(-0.718822\pi\) | ||||
−0.634569 | + | 0.772866i | \(0.718822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.32896 | + | 0.928364i | −0.00500852 | + | 0.00199648i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 89.5077 | − | 89.5077i | 0.191665 | − | 0.191665i | −0.604750 | − | 0.796415i | \(-0.706727\pi\) |
0.796415 | + | 0.604750i | \(0.206727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −152.713 | + | 152.713i | −0.325614 | + | 0.325614i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −217.778 | + | 86.8101i | −0.462374 | + | 0.184310i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 437.664 | 0.925293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51.7909 | + | 51.7909i | −0.109033 | + | 0.109033i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.03213 | + | 262.621i | −0.0147424 | + | 0.550568i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 439.291i | 0.917101i | 0.888668 | + | 0.458550i | \(0.151631\pi\) | ||||
−0.888668 | + | 0.458550i | \(0.848369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 235.226 | 0.489034 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −346.436 | − | 148.962i | −0.717259 | − | 0.308410i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.607542 | + | 0.607542i | 0.00125266 | + | 0.00125266i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 499.716i | − | 1.02611i | −0.858355 | − | 0.513056i | \(-0.828513\pi\) | ||
0.858355 | − | 0.513056i | \(-0.171487\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −278.301 | + | 110.936i | −0.569123 | + | 0.226862i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −359.246 | − | 359.246i | −0.731663 | − | 0.731663i | 0.239286 | − | 0.970949i | \(-0.423087\pi\) |
−0.970949 | + | 0.239286i | \(0.923087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −212.484 | − | 212.484i | −0.431003 | − | 0.431003i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.16847 | − | 1.10752i | 0.00236054 | − | 0.00223742i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 87.1846i | 0.175422i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −64.4682 | − | 64.4682i | −0.129195 | − | 0.129195i | 0.639553 | − | 0.768747i | \(-0.279120\pi\) |
−0.768747 | + | 0.639553i | \(0.779120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 102.152 | − | 237.573i | 0.203897 | − | 0.474197i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 597.277 | 1.18743 | 0.593714 | − | 0.804676i | \(-0.297661\pi\) | ||||
0.593714 | + | 0.804676i | \(0.297661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.950165i | − | 0.00188151i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −410.691 | − | 176.591i | −0.810042 | − | 0.348305i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 359.574 | − | 359.574i | 0.706433 | − | 0.706433i | −0.259350 | − | 0.965783i | \(-0.583508\pi\) |
0.965783 | + | 0.259350i | \(0.0835084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 202.006 | 0.395316 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −71.8079 | − | 33.1810i | −0.139976 | − | 0.0646804i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0467000 | + | 0.0467000i | −9.06796e−5 | + | 9.06796e-5i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.1257 | + | 57.1257i | −0.110495 | + | 0.110495i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 91.4977 | + | 229.538i | 0.176296 | + | 0.442269i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 862.399 | 1.65528 | 0.827639 | − | 0.561261i | \(-0.189684\pi\) | ||||
0.827639 | + | 0.561261i | \(0.189684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −256.574 | + | 256.574i | −0.490581 | + | 0.490581i | −0.908489 | − | 0.417908i | \(-0.862763\pi\) |
0.417908 | + | 0.908489i | \(0.362763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 190.280 | − | 442.529i | 0.362438 | − | 0.842912i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1139.76i | − | 2.16274i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −145.967 | −0.275930 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.5617 | + | 767.897i | −0.0387227 | + | 1.44613i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −595.990 | − | 595.990i | −1.11818 | − | 1.11818i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.807394i | − | 0.00150915i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.7342 | + | 74.5933i | 0.0553709 | + | 0.138907i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 70.2895 | + | 70.2895i | 0.130407 | + | 0.130407i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431.469 | + | 431.469i | 0.797540 | + | 0.797540i | 0.982707 | − | 0.185167i | \(-0.0592826\pi\) |
−0.185167 | + | 0.982707i | \(0.559283\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.5062 | − | 96.5993i | −0.0709137 | − | 0.177899i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.37483i | 0.00435749i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 335.381 | + | 335.381i | 0.613127 | + | 0.613127i | 0.943760 | − | 0.330632i | \(-0.107262\pi\) |
−0.330632 | + | 0.943760i | \(0.607262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.3609 | + | 611.014i | −0.0298014 | + | 1.11296i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.2983 | −0.0840259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 304.900i | 0.551357i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.217948 | − | 0.506874i | 0.000392699 | − | 0.000913287i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 118.642 | − | 118.642i | 0.213001 | − | 0.213001i | −0.592540 | − | 0.805541i | \(-0.701875\pi\) |
0.805541 | + | 0.592540i | \(0.201875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −608.350 | −1.08828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 271.004 | + | 679.860i | 0.483073 | + | 1.21187i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 290.766 | − | 290.766i | 0.516459 | − | 0.516459i | −0.400039 | − | 0.916498i | \(-0.631003\pi\) |
0.916498 | + | 0.400039i | \(0.131003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.02305 | − | 2.02305i | 0.00358061 | − | 0.00358061i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 519.499 | + | 27.8409i | 0.916223 | + | 0.0491021i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −669.398 | −1.17645 | −0.588223 | − | 0.808699i | \(-0.700172\pi\) | ||||
−0.588223 | + | 0.808699i | \(0.700172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 454.971 | − | 454.971i | 0.796798 | − | 0.796798i | −0.185792 | − | 0.982589i | \(-0.559485\pi\) |
0.982589 | + | 0.185792i | \(0.0594849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −431.102 | − | 185.367i | −0.752359 | − | 0.323502i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 489.277i | 0.850916i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −288.393 | −0.499814 | −0.249907 | − | 0.968270i | \(-0.580400\pi\) | ||||
−0.249907 | + | 0.968270i | \(0.580400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 258.307 | − | 600.737i | 0.446126 | − | 1.03754i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 451.725 | + | 451.725i | 0.777496 | + | 0.777496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 374.502i | − | 0.642371i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.62416 | + | 1.53945i | −0.00277635 | + | 0.00263154i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 393.610 | + | 393.610i | 0.670545 | + | 0.670545i | 0.957842 | − | 0.287297i | \(-0.0927566\pi\) |
−0.287297 | + | 0.957842i | \(0.592757\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −124.172 | − | 124.172i | −0.210818 | − | 0.210818i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 969.287 | − | 386.375i | 1.64008 | − | 0.653764i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 707.638i | − | 1.19332i | −0.802495 | − | 0.596659i | \(-0.796494\pi\) | ||
0.802495 | − | 0.596659i | \(-0.203506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.20413 | − | 1.20413i | −0.00202375 | − | 0.00202375i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 642.678 | + | 276.341i | 1.07651 | + | 0.462883i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −996.581 | −1.66374 | −0.831870 | − | 0.554970i | \(-0.812730\pi\) | ||||
−0.831870 | + | 0.554970i | \(0.812730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 214.386i | − | 0.356716i | −0.983966 | − | 0.178358i | \(-0.942921\pi\) | ||
0.983966 | − | 0.178358i | \(-0.0570785\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.10051 | + | 302.521i | −0.0134337 | + | 0.501693i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.429836 | + | 0.429836i | −0.000710474 | + | 0.000710474i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 989.981 | 1.63094 | 0.815470 | − | 0.578799i | \(-0.196478\pi\) | ||||
0.815470 | + | 0.578799i | \(0.196478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 282.849 | − | 112.748i | 0.464448 | − | 0.185137i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 79.4044 | − | 79.4044i | 0.129958 | − | 0.129958i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −277.427 | + | 277.427i | −0.452572 | + | 0.452572i | −0.896207 | − | 0.443636i | \(-0.853688\pi\) |
0.443636 | + | 0.896207i | \(0.353688\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.83648 | + | 0.732052i | −0.00298614 | + | 0.00119033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 294.951 | 0.478040 | 0.239020 | − | 0.971015i | \(-0.423174\pi\) | ||||
0.239020 | + | 0.971015i | \(0.423174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 717.374 | − | 717.374i | 1.15892 | − | 1.15892i | 0.174218 | − | 0.984707i | \(-0.444260\pi\) |
0.984707 | − | 0.174218i | \(-0.0557396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −495.924 | + | 182.457i | −0.798589 | + | 0.293812i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 611.273i | 0.981177i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −624.985 | −0.999977 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 103.592 | + | 44.5428i | 0.165218 | + | 0.0710412i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 177.359 | + | 177.359i | 0.281970 | + | 0.281970i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 526.114i | 0.833779i | 0.908957 | + | 0.416889i | \(0.136880\pi\) | ||||
−0.908957 | + | 0.416889i | \(0.863120\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.4795 | − | 13.3455i | 0.0528903 | − | 0.0210830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.533835 | − | 0.533835i | −0.000840686 | − | 0.000840686i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −97.7020 | − | 97.7020i | −0.153378 | − | 0.153378i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 84.0431 | + | 88.6678i | 0.131523 | + | 0.138760i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1025.84i | − | 1.60037i | −0.599754 | − | 0.800184i | \(-0.704735\pi\) | ||
0.599754 | − | 0.800184i | \(-0.295265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −366.197 | − | 366.197i | −0.569514 | − | 0.569514i | 0.362479 | − | 0.931992i | \(-0.381931\pi\) |
−0.931992 | + | 0.362479i | \(0.881931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.563665 | + | 1.31090i | −0.000873900 | + | 0.00203240i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −90.9084 | −0.140508 | −0.0702538 | − | 0.997529i | \(-0.522381\pi\) | ||||
−0.0702538 | + | 0.997529i | \(0.522381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1095.03i | − | 1.68726i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1060.99 | + | 456.208i | 1.62978 | + | 0.700780i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 291.274 | − | 291.274i | 0.446056 | − | 0.446056i | −0.447985 | − | 0.894041i | \(-0.647858\pi\) |
0.894041 | + | 0.447985i | \(0.147858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.616367 | 0.000941019 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 205.443 | − | 194.728i | 0.312698 | − | 0.296389i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −817.853 | + | 817.853i | −1.24105 | + | 1.24105i | −0.281486 | + | 0.959565i | \(0.590827\pi\) |
−0.959565 | + | 0.281486i | \(0.909173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 673.995 | − | 673.995i | 1.01966 | − | 1.01966i | 0.0198568 | − | 0.999803i | \(-0.493679\pi\) |
0.999803 | − | 0.0198568i | \(-0.00632103\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −376.694 | − | 945.001i | −0.568166 | − | 1.42534i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.262368 | −0.000394538 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −218.694 | + | 218.694i | −0.327877 | + | 0.327877i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9514 | + | 30.1206i | −0.0193593 | + | 0.0450233i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 871.316i | − | 1.29853i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −526.059 | −0.781662 | −0.390831 | − | 0.920462i | \(-0.627812\pi\) | ||||
−0.390831 | + | 0.920462i | \(0.627812\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −233.066 | − | 633.481i | −0.345283 | − | 0.938490i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 143.663 | + | 143.663i | 0.212205 | + | 0.212205i | 0.805204 | − | 0.592998i | \(-0.202056\pi\) |
−0.592998 | + | 0.805204i | \(0.702056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 395.782i | − | 0.582890i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −156.945 | − | 393.723i | −0.230462 | − | 0.578155i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −50.6262 | − | 50.6262i | −0.0741232 | − | 0.0741232i | 0.669073 | − | 0.743196i | \(-0.266691\pi\) |
−0.743196 | + | 0.669073i | \(0.766691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.423133 | + | 0.423133i | 0.000617713 | + | 0.000617713i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 364.243 | + | 913.765i | 0.530193 | + | 1.33008i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 520.556i | 0.755523i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 396.186 | + | 396.186i | 0.573351 | + | 0.573351i | 0.933063 | − | 0.359712i | \(-0.117125\pi\) |
−0.359712 | + | 0.933063i | \(0.617125\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −741.345 | − | 19.8508i | −1.06976 | − | 0.0286447i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.928629 | −0.00133616 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 898.749i | − | 1.28945i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −375.233 | + | 872.669i | −0.536815 | + | 1.24845i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 525.886 | − | 525.886i | 0.750195 | − | 0.750195i | −0.224321 | − | 0.974515i | \(-0.572016\pi\) |
0.974515 | + | 0.224321i | \(0.0720164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.6449 | 0.0549713 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0975321 | − | 0.244676i | −0.000138343 | − | 0.000347058i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −309.492 | + | 309.492i | −0.437753 | + | 0.437753i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 99.4062 | − | 99.4062i | 0.140206 | − | 0.140206i | −0.633520 | − | 0.773726i | \(-0.718391\pi\) |
0.773726 | + | 0.633520i | \(0.218391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 293.914 | + | 310.087i | 0.413381 | + | 0.436128i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1173.07 | −1.64526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.25568 | − | 2.25568i | 0.00315480 | − | 0.00315480i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1054.71 | − | 453.506i | −1.47100 | − | 0.632505i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 551.765i | − | 0.767406i | −0.923456 | − | 0.383703i | \(-0.874649\pi\) | ||
0.923456 | − | 0.383703i | \(-0.125351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.4226 | 0.0421951 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 108.213 | − | 251.668i | 0.149673 | − | 0.348089i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −279.354 | − | 279.354i | −0.385316 | − | 0.385316i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 75.0947i | 0.103294i | 0.998665 | + | 0.0516470i | \(0.0164471\pi\) | ||||
−0.998665 | + | 0.0516470i | \(0.983553\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 555.174 | − | 472.465i | 0.761555 | − | 0.648100i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −458.694 | − | 458.694i | −0.627488 | − | 0.627488i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −442.709 | − | 442.709i | −0.603968 | − | 0.603968i | 0.337395 | − | 0.941363i | \(-0.390454\pi\) |
−0.941363 | + | 0.337395i | \(0.890454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.301058 | + | 0.120007i | −0.000409603 | + | 0.000163275i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 431.400i | − | 0.585346i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 283.395 | + | 283.395i | 0.383485 | + | 0.383485i | 0.872356 | − | 0.488871i | \(-0.162591\pi\) |
−0.488871 | + | 0.872356i | \(0.662591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −143.992 | − | 61.9143i | −0.194321 | − | 0.0835550i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 835.949 | 1.12510 | 0.562550 | − | 0.826763i | \(-0.309820\pi\) | ||||
0.562550 | + | 0.826763i | \(0.309820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.59361i | 0.00348135i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 894.857 | + | 23.9613i | 1.19794 | + | 0.0320768i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −262.988 | + | 262.988i | −0.351118 | + | 0.351118i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −753.712 | −1.00361 | −0.501806 | − | 0.864980i | \(-0.667331\pi\) | ||||
−0.501806 | + | 0.864980i | \(0.667331\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −507.485 | + | 202.292i | −0.673951 | + | 0.268648i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.43854 | + | 1.43854i | −0.00190535 | + | 0.00190535i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 335.789 | − | 335.789i | 0.443578 | − | 0.443578i | −0.449634 | − | 0.893213i | \(-0.648446\pi\) |
0.893213 | + | 0.449634i | \(0.148446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 699.727 | − | 278.923i | 0.921906 | − | 0.367488i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1094.53 | 1.43828 | 0.719138 | − | 0.694868i | \(-0.244537\pi\) | ||||
0.719138 | + | 0.694868i | \(0.244537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 773.541 | − | 773.541i | 1.01381 | − | 1.01381i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.38535 | − | 0.0638720i | −0.00311811 | − | 8.34928e-5i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1522.09i | 1.98447i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 290.367 | 0.377590 | 0.188795 | − | 0.982016i | \(-0.439542\pi\) | ||||
0.188795 | + | 0.982016i | \(0.439542\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −341.512 | − | 146.845i | −0.442947 | − | 0.190460i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 193.239 | + | 193.239i | 0.249986 | + | 0.249986i | 0.820965 | − | 0.570979i | \(-0.193436\pi\) |
−0.570979 | + | 0.820965i | \(0.693436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1498.45i | − | 1.93348i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −236.092 | + | 94.1104i | −0.303851 | + | 0.121120i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −97.9143 | − | 97.9143i | −0.125692 | − | 0.125692i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −123.144 | − | 123.144i | −0.157675 | − | 0.157675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 178.975 | − | 387.323i | 0.228575 | − | 0.494666i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.08961i | 0.00138804i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 483.899 | + | 483.899i | 0.614865 | + | 0.614865i | 0.944210 | − | 0.329345i | \(-0.106828\pi\) |
−0.329345 | + | 0.944210i | \(0.606828\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −230.348 | + | 535.714i | −0.291950 | + | 0.678979i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1317.91 | −1.66613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1211.12i | 1.52727i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.12172 | + | 0.482320i | 0.00141096 | + | 0.000606691i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 872.325 | − | 872.325i | 1.09451 | − | 1.09451i | 0.0994694 | − | 0.995041i | \(-0.468285\pi\) |
0.995041 | − | 0.0994694i | \(-0.0317145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 119.741 | 0.149864 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 589.248 | + | 621.672i | 0.735640 | + | 0.776120i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −285.325 | + | 285.325i | −0.355324 | + | 0.355324i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.23932 | + | 1.23932i | −0.00153952 | + | 0.00153952i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 466.009 | + | 1169.06i | 0.577459 | + | 1.44865i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −146.162 | −0.180670 | −0.0903349 | − | 0.995911i | \(-0.528794\pi\) | ||||
−0.0903349 | + | 0.995911i | \(0.528794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −375.179 | + | 375.179i | −0.462613 | + | 0.462613i | −0.899511 | − | 0.436898i | \(-0.856077\pi\) |
0.436898 | + | 0.899511i | \(0.356077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −329.711 | + | 766.800i | −0.405549 | + | 0.943173i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.39243i | 0.00170850i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −99.9449 | −0.122332 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1030.47 | + | 27.5925i | 1.25820 | + | 0.0336904i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −671.154 | − | 671.154i | −0.817484 | − | 0.817484i | 0.168259 | − | 0.985743i | \(-0.446186\pi\) |
−0.985743 | + | 0.168259i | \(0.946186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 675.121i | 0.820317i | 0.912014 | + | 0.410159i | \(0.134527\pi\) | ||||
−0.912014 | + | 0.410159i | \(0.865473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 356.290 | + | 893.814i | 0.431867 | + | 1.08341i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1052.16 | − | 1052.16i | −1.27226 | − | 1.27226i | −0.944901 | − | 0.327355i | \(-0.893843\pi\) |
−0.327355 | − | 0.944901i | \(-0.606157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 95.3529 | + | 95.3529i | 0.115022 | + | 0.115022i | 0.762275 | − | 0.647253i | \(-0.224082\pi\) |
−0.647253 | + | 0.762275i | \(0.724082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 94.4964 | + | 237.060i | 0.113714 | + | 0.285271i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 147.334i | − | 0.176872i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.849877 | − | 0.849877i | −0.00101782 | − | 0.00101782i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1518.81 | − | 558.790i | 1.81458 | − | 0.667610i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −581.969 | −0.693646 | −0.346823 | − | 0.937931i | \(-0.612740\pi\) | ||||
−0.346823 | + | 0.937931i | \(0.612740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 591.273i | 0.703059i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 371.684 | − | 864.413i | 0.440906 | − | 1.02540i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.46918 | + | 1.46918i | −0.00173867 | + | 0.00173867i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 280.016 | 0.330598 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 450.839 | + | 1131.01i | 0.531024 | + | 1.33216i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 182.542 | − | 182.542i | 0.214503 | − | 0.214503i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −595.516 | + | 595.516i | −0.698143 | + | 0.698143i | −0.964010 | − | 0.265866i | \(-0.914342\pi\) |
0.265866 | + | 0.964010i | \(0.414342\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.266831 | + | 0.252914i | −0.000312083 | + | 0.000295806i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 731.802 | 0.853912 | 0.426956 | − | 0.904273i | \(-0.359586\pi\) | ||||
0.426956 | + | 0.904273i | \(0.359586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 303.614 | − | 303.614i | 0.353451 | − | 0.353451i | −0.507941 | − | 0.861392i | \(-0.669593\pi\) |
0.861392 | + | 0.507941i | \(0.169593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 836.632 | + | 359.738i | 0.971698 | + | 0.417814i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1423.90i | − | 1.64995i | −0.565173 | − | 0.824973i | \(-0.691190\pi\) | ||
0.565173 | − | 0.824973i | \(-0.308810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.14845 | 0.00132769 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 86.0236 | − | 200.062i | 0.0992198 | − | 0.230753i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −430.658 | − | 430.658i | −0.495579 | − | 0.495579i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 599.643i | 0.688453i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −381.521 | − | 402.515i | −0.437023 | − | 0.461071i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.16616 | − | 3.16616i | −0.00361847 | − | 0.00361847i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 524.721 | + | 524.721i | 0.598314 | + | 0.598314i | 0.939864 | − | 0.341550i | \(-0.110952\pi\) |
−0.341550 | + | 0.939864i | \(0.610952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −695.604 | + | 277.280i | −0.791358 | + | 0.315449i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.0313i | − | 0.0579243i | −0.999581 | − | 0.0289622i | \(-0.990780\pi\) | ||
0.999581 | − | 0.0289622i | \(-0.00922023\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −935.183 | − | 935.183i | −1.05910 | − | 1.05910i | −0.998140 | − | 0.0609574i | \(-0.980585\pi\) |
−0.0609574 | − | 0.998140i | \(-0.519415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.27987 | + | 1.41029i | 0.00370606 | + | 0.00159355i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1077.88 | 1.21520 | 0.607598 | − | 0.794245i | \(-0.292133\pi\) | ||||
0.607598 | + | 0.794245i | \(0.292133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 347.766i | 0.391188i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −773.092 | + | 694.444i | −0.867668 | + | 0.779398i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0452 | − | 13.0452i | 0.0146083 | − | 0.0146083i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.373214 | 0.000416999 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −972.616 | + | 387.702i | −1.08430 | + | 0.432220i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 669.767 | − | 669.767i | 0.745013 | − | 0.745013i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −392.497 | + | 392.497i | −0.435624 | + | 0.435624i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 610.591 | − | 243.392i | 0.676180 | − | 0.269537i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.483317 | −0.000534052 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1091.36 | + | 1091.36i | −1.20327 | + | 1.20327i | −0.230101 | + | 0.973167i | \(0.573906\pi\) |
−0.973167 | + | 0.230101i | \(0.926094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.4167 | + | 613.096i | −0.0180602 | + | 0.674473i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 599.270i | 0.657816i | 0.944362 | + | 0.328908i | \(0.106681\pi\) | ||||
−0.944362 | + | 0.328908i | \(0.893319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1276.08 | −1.39768 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.60978 | + | 1.12216i | 0.00285222 | + | 0.00122641i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −200.766 | − | 200.766i | −0.218937 | − | 0.218937i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1271.46i | 1.38353i | 0.722123 | + | 0.691765i | \(0.243166\pi\) | ||||
−0.722123 | + | 0.691765i | \(0.756834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −252.190 | + | 100.528i | −0.273822 | + | 0.109150i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 171.170 | + | 171.170i | 0.185449 | + | 0.185449i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 233.175 | + | 233.175i | 0.252081 | + | 0.252081i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.9402 | − | 29.3264i | 0.0333767 | − | 0.0316358i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1274.81i | − | 1.37224i | −0.727488 | − | 0.686120i | \(-0.759312\pi\) | ||
0.727488 | − | 0.686120i | \(-0.240688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.0513 | − | 16.0513i | −0.0172409 | − | 0.0172409i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −630.785 | + | 1467.00i | −0.676083 | + | 1.57235i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.40156 | 0.00363803 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 416.118i | − | 0.444096i | −0.975036 | − | 0.222048i | \(-0.928726\pi\) | ||
0.975036 | − | 0.222048i | \(-0.0712742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −511.728 | − | 220.035i | −0.544971 | − | 0.234329i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.8023 | + | 59.8023i | −0.0635518 | + | 0.0635518i | −0.738168 | − | 0.674617i | \(-0.764309\pi\) |
0.674617 | + | 0.738168i | \(0.264309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −925.012 | −0.980925 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.01423 | − | 2.19493i | 0.00107326 | − | 0.00232267i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −438.459 | + | 438.459i | −0.462998 | + | 0.462998i | −0.899637 | − | 0.436639i | \(-0.856169\pi\) |
0.436639 | + | 0.899637i | \(0.356169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 396.600 | − | 396.600i | 0.417913 | − | 0.417913i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −264.125 | − | 662.602i | −0.277733 | − | 0.696742i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 874.202 | 0.917316 | 0.458658 | − | 0.888613i | \(-0.348330\pi\) | ||||
0.458658 | + | 0.888613i | \(0.348330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.54219 | + | 1.54219i | −0.00161486 | + | 0.00161486i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −240.259 | + | 558.763i | −0.251054 | + | 0.583869i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 275.649i | − | 0.287434i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2631.62 | 2.73842 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.9499 | + | 520.973i | −0.0144859 | + | 0.540989i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.14904 | − | 2.14904i | −0.00222698 | − | 0.00222698i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 78.0123i | − | 0.0806746i | −0.999186 | − | 0.0403373i | \(-0.987157\pi\) | ||
0.999186 | − | 0.0403373i | \(-0.0128432\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −61.8865 | − | 155.253i | −0.0638663 | − | 0.160220i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −545.451 | − | 545.451i | −0.561742 | − | 0.561742i | 0.368060 | − | 0.929802i | \(-0.380022\pi\) |
−0.929802 | + | 0.368060i | \(0.880022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 302.477 | + | 302.477i | 0.310870 | + | 0.310870i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −495.241 | − | 1242.40i | −0.507939 | − | 1.27425i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1711.35i | 1.75164i | 0.482640 | + | 0.875819i | \(0.339678\pi\) | ||||
−0.482640 | + | 0.875819i | \(0.660322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −863.396 | − | 863.396i | −0.881916 | − | 0.881916i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.0318 | − | 1532.37i | 0.0418265 | − | 1.56205i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1349.18 | −1.37252 | −0.686259 | − | 0.727358i | \(-0.740748\pi\) | ||||
−0.686259 | + | 0.727358i | \(0.740748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.84965i | − | 0.00492351i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.9283 | + | 111.465i | −0.0485596 | + | 0.112934i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −472.098 | + | 472.098i | −0.477349 | + | 0.477349i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 923.093 | 0.931476 | 0.465738 | − | 0.884923i | \(-0.345789\pi\) | ||||
0.465738 | + | 0.884923i | \(0.345789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −379.671 | − | 952.469i | −0.382347 | − | 0.959183i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.29907 | − | 2.29907i | 0.00231063 | − | 0.00231063i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −371.389 | + | 371.389i | −0.372507 | + | 0.372507i | −0.868390 | − | 0.495883i | \(-0.834845\pi\) |
0.495883 | + | 0.868390i | \(0.334845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −149.389 | + | 323.296i | −0.149538 | + | 0.323620i |
(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 | 384.3.i.c.161.5 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.c.161.9 | 20 | ||
4.3 | odd | 2 | 384.3.i.d.161.6 | 20 | |||
8.3 | odd | 2 | 48.3.i.b.29.5 | yes | 20 | ||
8.5 | even | 2 | 192.3.i.b.17.6 | 20 | |||
12.11 | even | 2 | 384.3.i.d.161.2 | 20 | |||
16.3 | odd | 4 | 48.3.i.b.5.6 | yes | 20 | ||
16.5 | even | 4 | inner | 384.3.i.c.353.9 | 20 | ||
16.11 | odd | 4 | 384.3.i.d.353.2 | 20 | |||
16.13 | even | 4 | 192.3.i.b.113.2 | 20 | |||
24.5 | odd | 2 | 192.3.i.b.17.2 | 20 | |||
24.11 | even | 2 | 48.3.i.b.29.6 | yes | 20 | ||
48.5 | odd | 4 | inner | 384.3.i.c.353.5 | 20 | ||
48.11 | even | 4 | 384.3.i.d.353.6 | 20 | |||
48.29 | odd | 4 | 192.3.i.b.113.6 | 20 | |||
48.35 | even | 4 | 48.3.i.b.5.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.5 | ✓ | 20 | 48.35 | even | 4 | ||
48.3.i.b.5.6 | yes | 20 | 16.3 | odd | 4 | ||
48.3.i.b.29.5 | yes | 20 | 8.3 | odd | 2 | ||
48.3.i.b.29.6 | yes | 20 | 24.11 | even | 2 | ||
192.3.i.b.17.2 | 20 | 24.5 | odd | 2 | |||
192.3.i.b.17.6 | 20 | 8.5 | even | 2 | |||
192.3.i.b.113.2 | 20 | 16.13 | even | 4 | |||
192.3.i.b.113.6 | 20 | 48.29 | odd | 4 | |||
384.3.i.c.161.5 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.c.161.9 | 20 | 3.2 | odd | 2 | inner | ||
384.3.i.c.353.5 | 20 | 48.5 | odd | 4 | inner | ||
384.3.i.c.353.9 | 20 | 16.5 | even | 4 | inner | ||
384.3.i.d.161.2 | 20 | 12.11 | even | 2 | |||
384.3.i.d.161.6 | 20 | 4.3 | odd | 2 | |||
384.3.i.d.353.2 | 20 | 16.11 | odd | 4 | |||
384.3.i.d.353.6 | 20 | 48.11 | even | 4 |