Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.8 | ||
Root | \(-0.957636 - 1.04064i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.f.199.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.169449 | + | 1.99281i | −0.0847243 | + | 0.996404i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.94257 | − | 0.675358i | −0.985644 | − | 0.168839i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.3959 | 1.77084 | 0.885422 | − | 0.464789i | \(-0.153870\pi\) | ||||
0.885422 | + | 0.464789i | \(0.153870\pi\) | |||||||
\(8\) | 2.01392 | − | 7.74236i | 0.251740 | − | 0.967795i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0403i | 1.00366i | 0.864965 | + | 0.501832i | \(0.167341\pi\) | ||||
−0.864965 | + | 0.501832i | \(0.832659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.82009i | − | 0.216930i | −0.994100 | − | 0.108465i | \(-0.965407\pi\) | ||
0.994100 | − | 0.108465i | \(-0.0345935\pi\) | |||||||
\(14\) | −2.10047 | + | 24.7027i | −0.150034 | + | 1.76448i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.0878 | + | 5.32529i | 0.942987 | + | 0.332831i | ||||
\(17\) | − | 6.52606i | − | 0.383886i | −0.981406 | − | 0.191943i | \(-0.938521\pi\) | ||
0.981406 | − | 0.191943i | \(-0.0614789\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 27.9928i | − | 1.47330i | −0.676273 | − | 0.736651i | \(-0.736406\pi\) | ||
0.676273 | − | 0.736651i | \(-0.263594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0012 | − | 1.87077i | −1.00006 | − | 0.0850348i | ||||
\(23\) | −7.90421 | −0.343661 | −0.171831 | − | 0.985126i | \(-0.554968\pi\) | ||||
−0.171831 | + | 0.985126i | \(0.554968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.61989 | + | 0.477860i | 0.216150 | + | 0.0183792i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −48.8718 | − | 8.37167i | −1.74542 | − | 0.298988i | ||||
\(29\) | 50.7169 | 1.74886 | 0.874429 | − | 0.485153i | \(-0.161236\pi\) | ||||
0.874429 | + | 0.485153i | \(0.161236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 36.3467i | − | 1.17247i | −0.810140 | − | 0.586236i | \(-0.800609\pi\) | ||
0.810140 | − | 0.586236i | \(-0.199391\pi\) | |||||||
\(32\) | −13.1689 | + | 29.1647i | −0.411528 | + | 0.911397i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.0052 | + | 1.10583i | 0.382506 | + | 0.0325245i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 18.9279i | − | 0.511566i | −0.966734 | − | 0.255783i | \(-0.917667\pi\) | ||
0.966734 | − | 0.255783i | \(-0.0823332\pi\) | |||||||
\(38\) | 55.7842 | + | 4.74333i | 1.46801 | + | 0.124825i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.30410 | −0.129368 | −0.0646842 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646842 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.5870 | 1.06016 | 0.530081 | − | 0.847947i | \(-0.322162\pi\) | ||||
0.530081 | + | 0.847947i | \(0.322162\pi\) | |||||||
\(44\) | 7.45616 | − | 43.5273i | 0.169458 | − | 0.989256i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.33936 | − | 15.7516i | 0.0291165 | − | 0.342426i | ||||
\(47\) | −11.7246 | −0.249460 | −0.124730 | − | 0.992191i | \(-0.539806\pi\) | ||||
−0.124730 | + | 0.992191i | \(0.539806\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 104.658 | 2.13589 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.90457 | + | 11.1184i | −0.0366263 | + | 0.213815i | ||||
\(53\) | 41.1680i | 0.776755i | 0.921500 | + | 0.388378i | \(0.126964\pi\) | ||||
−0.921500 | + | 0.388378i | \(0.873036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 24.9644 | − | 95.9735i | 0.445793 | − | 1.71381i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.59391 | + | 101.069i | −0.148171 | + | 1.74257i | ||||
\(59\) | − | 10.7008i | − | 0.181370i | −0.995880 | − | 0.0906848i | \(-0.971094\pi\) | ||
0.995880 | − | 0.0906848i | \(-0.0289056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 56.1297 | 0.920159 | 0.460080 | − | 0.887878i | \(-0.347821\pi\) | ||||
0.460080 | + | 0.887878i | \(0.347821\pi\) | |||||||
\(62\) | 72.4319 | + | 6.15889i | 1.16826 | + | 0.0993370i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −55.8882 | − | 31.1850i | −0.873254 | − | 0.487266i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.1709 | −0.241357 | −0.120679 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120679 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(68\) | −4.40743 | + | 25.7295i | −0.0648151 | + | 0.378375i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 66.1617i | 0.931855i | 0.884823 | + | 0.465928i | \(0.154279\pi\) | ||||
−0.884823 | + | 0.465928i | \(0.845721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.6330i | − | 0.214150i | −0.994251 | − | 0.107075i | \(-0.965851\pi\) | ||
0.994251 | − | 0.107075i | \(-0.0341485\pi\) | |||||||
\(74\) | 37.7198 | + | 3.20731i | 0.509727 | + | 0.0433421i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.9051 | + | 110.363i | −0.248752 | + | 1.45215i | ||||
\(77\) | 136.855i | 1.77733i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 123.057i | 1.55768i | 0.627223 | + | 0.778840i | \(0.284191\pi\) | ||||
−0.627223 | + | 0.778840i | \(0.715809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.898773 | − | 10.5701i | 0.0109606 | − | 0.128903i | ||||
\(83\) | −99.6700 | −1.20084 | −0.600422 | − | 0.799684i | \(-0.705001\pi\) | ||||
−0.600422 | + | 0.799684i | \(0.705001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.72465 | + | 90.8461i | −0.0898215 | + | 1.05635i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 85.4781 | + | 22.2343i | 0.971342 | + | 0.252663i | ||||
\(89\) | 101.083 | 1.13576 | 0.567881 | − | 0.823110i | \(-0.307763\pi\) | ||||
0.567881 | + | 0.823110i | \(0.307763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 34.9575i | − | 0.384148i | ||||||
\(92\) | 31.1629 | + | 5.33817i | 0.338728 | + | 0.0580236i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.98672 | − | 23.3649i | 0.0211353 | − | 0.248563i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 127.293i | 1.31230i | 0.754630 | + | 0.656151i | \(0.227817\pi\) | ||||
−0.754630 | + | 0.656151i | \(0.772183\pi\) | |||||||
\(98\) | −17.7342 | + | 208.564i | −0.180962 | + | 2.12821i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 94.3535 | 0.934193 | 0.467096 | − | 0.884206i | \(-0.345300\pi\) | ||||
0.467096 | + | 0.884206i | \(0.345300\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 31.8455 | 0.309180 | 0.154590 | − | 0.987979i | \(-0.450594\pi\) | ||||
0.154590 | + | 0.987979i | \(0.450594\pi\) | |||||||
\(104\) | −21.8341 | − | 5.67943i | −0.209943 | − | 0.0546099i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −82.0400 | − | 6.97587i | −0.773962 | − | 0.0658101i | ||||
\(107\) | −33.7912 | −0.315805 | −0.157903 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157903 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 83.4266 | 0.765382 | 0.382691 | − | 0.923876i | \(-0.374997\pi\) | ||||
0.382691 | + | 0.923876i | \(0.374997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 187.027 | + | 66.0118i | 1.66988 | + | 0.589391i | ||||
\(113\) | − | 111.796i | − | 0.989342i | −0.869080 | − | 0.494671i | \(-0.835289\pi\) | ||
0.869080 | − | 0.494671i | \(-0.164711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −199.955 | − | 34.2520i | −1.72375 | − | 0.295276i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21.3247 | + | 1.81324i | 0.180717 | + | 0.0153664i | ||||
\(119\) | − | 80.8964i | − | 0.679802i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | −9.51110 | + | 111.856i | −0.0779599 | + | 0.916851i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.5470 | + | 143.299i | −0.197960 | + | 1.15564i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6855 | 0.131382 | 0.0656909 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656909 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(128\) | 71.6160 | − | 106.090i | 0.559500 | − | 0.828831i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 196.418i | − | 1.49937i | −0.661794 | − | 0.749686i | \(-0.730204\pi\) | ||
0.661794 | − | 0.749686i | \(-0.269796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 346.995i | − | 2.60899i | ||||||
\(134\) | 2.74015 | − | 32.2256i | 0.0204488 | − | 0.240490i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −50.5271 | − | 13.1430i | −0.371523 | − | 0.0966396i | ||||
\(137\) | 117.127i | 0.854942i | 0.904029 | + | 0.427471i | \(0.140595\pi\) | ||||
−0.904029 | + | 0.427471i | \(0.859405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 187.238i | − | 1.34704i | −0.739170 | − | 0.673519i | \(-0.764782\pi\) | ||
0.739170 | − | 0.673519i | \(-0.235218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −131.848 | − | 11.2110i | −0.928505 | − | 0.0789508i | ||||
\(143\) | 31.1346 | 0.217725 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 31.1535 | + | 2.64899i | 0.213380 | + | 0.0181437i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.7831 | + | 74.6248i | −0.0863725 | + | 0.504222i | ||||
\(149\) | −50.2274 | −0.337096 | −0.168548 | − | 0.985693i | \(-0.553908\pi\) | ||||
−0.168548 | + | 0.985693i | \(0.553908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 213.160i | 1.41166i | 0.708382 | + | 0.705829i | \(0.249425\pi\) | ||||
−0.708382 | + | 0.705829i | \(0.750575\pi\) | |||||||
\(152\) | −216.730 | − | 56.3752i | −1.42585 | − | 0.370890i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −272.725 | − | 23.1898i | −1.77094 | − | 0.150583i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 203.918i | 1.29884i | 0.760431 | + | 0.649419i | \(0.224988\pi\) | ||||
−0.760431 | + | 0.649419i | \(0.775012\pi\) | |||||||
\(158\) | −245.228 | − | 20.8518i | −1.55208 | − | 0.131973i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −97.9798 | −0.608570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −215.898 | −1.32452 | −0.662262 | − | 0.749272i | \(-0.730404\pi\) | ||||
−0.662262 | + | 0.749272i | \(0.730404\pi\) | |||||||
\(164\) | 20.9118 | + | 3.58216i | 0.127511 | + | 0.0218425i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.8889 | − | 198.623i | 0.101741 | − | 1.19653i | ||||
\(167\) | 255.029 | 1.52712 | 0.763560 | − | 0.645737i | \(-0.223450\pi\) | ||||
0.763560 | + | 0.645737i | \(0.223450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 161.047 | 0.952942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −179.730 | − | 30.7875i | −1.04494 | − | 0.178997i | ||||
\(173\) | − | 235.426i | − | 1.36084i | −0.732822 | − | 0.680421i | \(-0.761797\pi\) | ||
0.732822 | − | 0.680421i | \(-0.238203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −58.7929 | + | 166.574i | −0.334051 | + | 0.946443i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.1284 | + | 201.439i | −0.0962267 | + | 1.13168i | ||||
\(179\) | 102.669i | 0.573572i | 0.957995 | + | 0.286786i | \(0.0925869\pi\) | ||||
−0.957995 | + | 0.286786i | \(0.907413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56.8222 | −0.313935 | −0.156967 | − | 0.987604i | \(-0.550172\pi\) | ||||
−0.156967 | + | 0.987604i | \(0.550172\pi\) | |||||||
\(182\) | 69.6636 | + | 5.92350i | 0.382767 | + | 0.0325467i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.9185 | + | 61.1972i | −0.0865134 | + | 0.332594i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.0498 | 0.385293 | ||||||||
\(188\) | 46.2251 | + | 7.91830i | 0.245878 | + | 0.0421186i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 158.493i | 0.829808i | 0.909865 | + | 0.414904i | \(0.136185\pi\) | ||||
−0.909865 | + | 0.414904i | \(0.863815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 156.732i | 0.812084i | 0.913854 | + | 0.406042i | \(0.133091\pi\) | ||||
−0.913854 | + | 0.406042i | \(0.866909\pi\) | |||||||
\(194\) | −253.671 | − | 21.5697i | −1.30758 | − | 0.111184i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −412.624 | − | 70.6819i | −2.10522 | − | 0.360622i | ||||
\(197\) | − | 260.127i | − | 1.32044i | −0.751072 | − | 0.660221i | \(-0.770463\pi\) | ||
0.751072 | − | 0.660221i | \(-0.229537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.0326i | − | 0.0705157i | −0.999378 | − | 0.0352579i | \(-0.988775\pi\) | ||
0.999378 | − | 0.0352579i | \(-0.0112253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.9881 | + | 188.028i | −0.0791489 | + | 0.930834i | ||||
\(203\) | 628.682 | 3.09696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.39618 | + | 63.4620i | −0.0261950 | + | 0.308068i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.0178 | − | 42.5488i | 0.0722009 | − | 0.204562i | ||||
\(209\) | 309.049 | 1.47870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 74.4941i | − | 0.353052i | −0.984296 | − | 0.176526i | \(-0.943514\pi\) | ||
0.984296 | − | 0.176526i | \(-0.0564860\pi\) | |||||||
\(212\) | 27.8031 | − | 162.308i | 0.131147 | − | 0.765604i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.72587 | − | 67.3393i | 0.0267564 | − | 0.314670i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 450.550i | − | 2.07627i | ||||||
\(218\) | −14.1365 | + | 166.253i | −0.0648465 | + | 0.762630i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4041 | −0.0832763 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −159.996 | −0.717471 | −0.358736 | − | 0.933439i | \(-0.616792\pi\) | ||||
−0.358736 | + | 0.933439i | \(0.616792\pi\) | |||||||
\(224\) | −163.240 | + | 361.523i | −0.728752 | + | 1.61394i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 222.787 | + | 18.9436i | 0.985784 | + | 0.0838213i | ||||
\(227\) | −175.978 | −0.775236 | −0.387618 | − | 0.921820i | \(-0.626702\pi\) | ||||
−0.387618 | + | 0.921820i | \(0.626702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 114.170 | 0.498560 | 0.249280 | − | 0.968431i | \(-0.419806\pi\) | ||||
0.249280 | + | 0.968431i | \(0.419806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 102.140 | − | 392.668i | 0.440258 | − | 1.69254i | ||||
\(233\) | 260.062i | 1.11615i | 0.829792 | + | 0.558073i | \(0.188459\pi\) | ||||
−0.829792 | + | 0.558073i | \(0.811541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.22687 | + | 42.1887i | −0.0306223 | + | 0.178766i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 161.211 | + | 13.7078i | 0.677358 | + | 0.0575958i | ||||
\(239\) | 140.089i | 0.586147i | 0.956090 | + | 0.293073i | \(0.0946780\pi\) | ||||
−0.956090 | + | 0.293073i | \(0.905322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 105.920 | 0.439503 | 0.219752 | − | 0.975556i | \(-0.429475\pi\) | ||||
0.219752 | + | 0.975556i | \(0.429475\pi\) | |||||||
\(242\) | 0.150563 | − | 1.77070i | 0.000622159 | − | 0.00731693i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −221.296 | − | 37.9076i | −0.906949 | − | 0.155359i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −78.9419 | −0.319603 | ||||||||
\(248\) | −281.409 | − | 73.1993i | −1.13471 | − | 0.295159i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 167.879i | − | 0.668839i | −0.942424 | − | 0.334420i | \(-0.891460\pi\) | ||
0.942424 | − | 0.334420i | \(-0.108540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 87.2650i | − | 0.344921i | ||||||
\(254\) | −2.82733 | + | 33.2510i | −0.0111312 | + | 0.130909i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 199.282 | + | 160.694i | 0.778447 | + | 0.627710i | ||||
\(257\) | − | 198.849i | − | 0.773732i | −0.922136 | − | 0.386866i | \(-0.873558\pi\) | ||
0.922136 | − | 0.386866i | \(-0.126442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 234.629i | − | 0.905903i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 391.423 | + | 33.2827i | 1.49398 | + | 0.127033i | ||||
\(263\) | −480.528 | −1.82710 | −0.913552 | − | 0.406722i | \(-0.866672\pi\) | ||||
−0.913552 | + | 0.406722i | \(0.866672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 691.496 | + | 58.7979i | 2.59961 | + | 0.221045i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 63.7552 | + | 10.9212i | 0.237892 | + | 0.0407506i | ||||
\(269\) | −291.496 | −1.08363 | −0.541815 | − | 0.840498i | \(-0.682263\pi\) | ||||
−0.541815 | + | 0.840498i | \(0.682263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 174.063i | 0.642299i | 0.947029 | + | 0.321150i | \(0.104069\pi\) | ||||
−0.947029 | + | 0.321150i | \(0.895931\pi\) | |||||||
\(272\) | 34.7532 | − | 98.4638i | 0.127769 | − | 0.361999i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −233.412 | − | 19.8470i | −0.851868 | − | 0.0724344i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 50.5203i | − | 0.182384i | −0.995833 | − | 0.0911918i | \(-0.970932\pi\) | ||
0.995833 | − | 0.0911918i | \(-0.0290676\pi\) | |||||||
\(278\) | 373.130 | + | 31.7273i | 1.34219 | + | 0.114127i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 66.0514 | 0.235058 | 0.117529 | − | 0.993069i | \(-0.462503\pi\) | ||||
0.117529 | + | 0.993069i | \(0.462503\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −116.934 | −0.413196 | −0.206598 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206598 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(284\) | 44.6828 | − | 260.848i | 0.157334 | − | 0.918477i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.27572 | + | 62.0454i | −0.0184466 | + | 0.216942i | ||||
\(287\) | −65.7491 | −0.229091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 246.411 | 0.852631 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.5578 | + | 61.6341i | −0.0361570 | + | 0.211076i | ||||
\(293\) | − | 68.3732i | − | 0.233356i | −0.993170 | − | 0.116678i | \(-0.962776\pi\) | ||
0.993170 | − | 0.116678i | \(-0.0372245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −146.547 | − | 38.1194i | −0.495091 | − | 0.128782i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.51096 | − | 100.094i | 0.0285603 | − | 0.335884i | ||||
\(299\) | 22.2905i | 0.0745503i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 565.092 | 1.87738 | ||||||||
\(302\) | −424.788 | − | 36.1197i | −1.40658 | − | 0.119602i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 149.070 | − | 422.349i | 0.490361 | − | 1.38930i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −369.497 | −1.20357 | −0.601786 | − | 0.798657i | \(-0.705544\pi\) | ||||
−0.601786 | + | 0.798657i | \(0.705544\pi\) | |||||||
\(308\) | 92.4258 | − | 539.560i | 0.300084 | − | 1.75182i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 303.446i | − | 0.975712i | −0.872924 | − | 0.487856i | \(-0.837779\pi\) | ||
0.872924 | − | 0.487856i | \(-0.162221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 297.693i | − | 0.951097i | −0.879689 | − | 0.475549i | \(-0.842250\pi\) | ||
0.879689 | − | 0.475549i | \(-0.157750\pi\) | |||||||
\(314\) | −406.369 | − | 34.5536i | −1.29417 | − | 0.110043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 83.1072 | − | 485.160i | 0.262998 | − | 1.53532i | ||||
\(317\) | − | 264.678i | − | 0.834948i | −0.908689 | − | 0.417474i | \(-0.862916\pi\) | ||
0.908689 | − | 0.417474i | \(-0.137084\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 559.931i | 1.75527i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.6026 | − | 195.255i | 0.0515607 | − | 0.606382i | ||||
\(323\) | −182.682 | −0.565580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 36.5835 | − | 430.243i | 0.112219 | − | 1.31976i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6820 | + | 41.0663i | −0.0325672 | + | 0.125202i | ||||
\(329\) | −145.337 | −0.441754 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 473.426i | − | 1.43029i | −0.698976 | − | 0.715145i | \(-0.746361\pi\) | ||
0.698976 | − | 0.715145i | \(-0.253639\pi\) | |||||||
\(332\) | 392.956 | + | 67.3129i | 1.18360 | + | 0.202750i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −43.2143 | + | 508.224i | −0.129384 | + | 1.52163i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.7588i | 0.0883051i | 0.999025 | + | 0.0441526i | \(0.0140588\pi\) | ||||
−0.999025 | + | 0.0441526i | \(0.985941\pi\) | |||||||
\(338\) | −27.2892 | + | 320.936i | −0.0807373 | + | 0.949515i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 401.278 | 1.17677 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 689.937 | 2.01148 | ||||||||
\(344\) | 91.8086 | − | 352.951i | 0.266885 | − | 1.02602i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 469.158 | + | 39.8925i | 1.35595 | + | 0.115296i | ||||
\(347\) | −306.190 | −0.882391 | −0.441195 | − | 0.897411i | \(-0.645445\pi\) | ||||
−0.441195 | + | 0.897411i | \(0.645445\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −649.149 | −1.86002 | −0.930012 | − | 0.367528i | \(-0.880204\pi\) | ||||
−0.930012 | + | 0.367528i | \(0.880204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −321.988 | − | 145.389i | −0.914737 | − | 0.413036i | ||||
\(353\) | − | 275.547i | − | 0.780587i | −0.920691 | − | 0.390293i | \(-0.872374\pi\) | ||
0.920691 | − | 0.390293i | \(-0.127626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −398.527 | − | 68.2671i | −1.11946 | − | 0.191761i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −204.600 | − | 17.3972i | −0.571510 | − | 0.0485955i | ||||
\(359\) | − | 507.672i | − | 1.41413i | −0.707149 | − | 0.707065i | \(-0.750019\pi\) | ||
0.707149 | − | 0.707065i | \(-0.249981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −422.594 | −1.17062 | ||||||||
\(362\) | 9.62845 | − | 113.236i | 0.0265979 | − | 0.312806i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.6088 | + | 137.823i | −0.0648594 | + | 0.378633i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −62.7671 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(368\) | −119.257 | − | 42.0923i | −0.324068 | − | 0.114381i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 510.315i | 1.37551i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 272.776i | 0.731302i | 0.930752 | + | 0.365651i | \(0.119154\pi\) | ||||
−0.930752 | + | 0.365651i | \(0.880846\pi\) | |||||||
\(374\) | −12.2087 | + | 143.581i | −0.0326437 | + | 0.383908i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.6124 | + | 90.7761i | −0.0627990 | + | 0.241426i | ||||
\(377\) | − | 143.026i | − | 0.379379i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 376.828i | 0.994270i | 0.867673 | + | 0.497135i | \(0.165615\pi\) | ||||
−0.867673 | + | 0.497135i | \(0.834385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −315.847 | − | 26.8565i | −0.826825 | − | 0.0703049i | ||||
\(383\) | −412.206 | −1.07625 | −0.538127 | − | 0.842864i | \(-0.680868\pi\) | ||||
−0.538127 | + | 0.842864i | \(0.680868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −312.337 | − | 26.5581i | −0.809164 | − | 0.0688032i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 85.9685 | − | 501.863i | 0.221568 | − | 1.29346i | ||||
\(389\) | −161.289 | −0.414623 | −0.207312 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207312 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.5834i | 0.131927i | ||||||||
\(392\) | 210.774 | − | 810.303i | 0.537689 | − | 2.06710i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 518.383 | + | 44.0782i | 1.31569 | + | 0.111874i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 186.505i | − | 0.469785i | −0.972021 | − | 0.234893i | \(-0.924526\pi\) | ||
0.972021 | − | 0.234893i | \(-0.0754738\pi\) | |||||||
\(398\) | 27.9643 | + | 2.37781i | 0.0702622 | + | 0.00597440i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −239.061 | −0.596162 | −0.298081 | − | 0.954541i | \(-0.596347\pi\) | ||||
−0.298081 | + | 0.954541i | \(0.596347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −102.501 | −0.254344 | ||||||||
\(404\) | −371.996 | − | 63.7223i | −0.920781 | − | 0.157729i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −106.529 | + | 1252.84i | −0.262387 | + | 3.08582i | ||||
\(407\) | 208.970 | 0.513441 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −47.8016 | −0.116874 | −0.0584372 | − | 0.998291i | \(-0.518612\pi\) | ||||
−0.0584372 | + | 0.998291i | \(0.518612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −125.553 | − | 21.5071i | −0.304741 | − | 0.0522017i | ||||
\(413\) | − | 132.646i | − | 0.321177i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 82.2470 | + | 37.1374i | 0.197709 | + | 0.0892726i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −52.3679 | + | 615.875i | −0.125282 | + | 1.47339i | ||||
\(419\) | 239.009i | 0.570428i | 0.958464 | + | 0.285214i | \(0.0920647\pi\) | ||||
−0.958464 | + | 0.285214i | \(0.907935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −257.592 | −0.611857 | −0.305929 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305929 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(422\) | 148.452 | + | 12.6229i | 0.351783 | + | 0.0299121i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 318.738 | + | 82.9092i | 0.751740 | + | 0.195541i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 695.779 | 1.62946 | ||||||||
\(428\) | 133.224 | + | 22.8211i | 0.311271 | + | 0.0533204i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 343.164i | 0.796205i | 0.917341 | + | 0.398103i | \(0.130331\pi\) | ||||
−0.917341 | + | 0.398103i | \(0.869669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 234.760i | 0.542171i | 0.962555 | + | 0.271085i | \(0.0873826\pi\) | ||||
−0.962555 | + | 0.271085i | \(0.912617\pi\) | |||||||
\(434\) | 897.859 | + | 76.3450i | 2.06880 | + | 0.175910i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −328.916 | − | 56.3428i | −0.754394 | − | 0.129227i | ||||
\(437\) | 221.261i | 0.506317i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 374.473i | − | 0.853013i | −0.904484 | − | 0.426507i | \(-0.859744\pi\) | ||
0.904484 | − | 0.426507i | \(-0.140256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.11854 | − | 36.6758i | 0.00705553 | − | 0.0829768i | ||||
\(443\) | 108.557 | 0.245050 | 0.122525 | − | 0.992465i | \(-0.460901\pi\) | ||||
0.122525 | + | 0.992465i | \(0.460901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.1111 | − | 318.842i | 0.0607873 | − | 0.714891i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −692.785 | − | 386.566i | −1.54640 | − | 0.862872i | ||||
\(449\) | −431.511 | −0.961050 | −0.480525 | − | 0.876981i | \(-0.659554\pi\) | ||||
−0.480525 | + | 0.876981i | \(0.659554\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 58.5589i | − | 0.129842i | ||||||
\(452\) | −75.5020 | + | 440.762i | −0.167040 | + | 0.975138i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.8193 | − | 350.692i | 0.0656813 | − | 0.772448i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 219.747i | 0.480847i | 0.970668 | + | 0.240424i | \(0.0772864\pi\) | ||||
−0.970668 | + | 0.240424i | \(0.922714\pi\) | |||||||
\(458\) | −19.3460 | + | 227.520i | −0.0422402 | + | 0.496768i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −223.434 | −0.484673 | −0.242337 | − | 0.970192i | \(-0.577914\pi\) | ||||
−0.242337 | + | 0.970192i | \(0.577914\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 740.855 | 1.60012 | 0.800059 | − | 0.599921i | \(-0.204802\pi\) | ||||
0.800059 | + | 0.599921i | \(0.204802\pi\) | |||||||
\(464\) | 765.206 | + | 270.082i | 1.64915 | + | 0.582074i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −518.254 | − | 44.0672i | −1.11213 | − | 0.0945648i | ||||
\(467\) | 249.381 | 0.534007 | 0.267004 | − | 0.963696i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963696i | \(0.413966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −200.454 | −0.427406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −82.8495 | − | 21.5506i | −0.175529 | − | 0.0456580i | ||||
\(473\) | 503.294i | 1.06405i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −54.6340 | + | 318.940i | −0.114777 | + | 0.670043i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −279.171 | − | 23.7379i | −0.584039 | − | 0.0496609i | ||||
\(479\) | − | 210.915i | − | 0.440324i | −0.975463 | − | 0.220162i | \(-0.929341\pi\) | ||
0.975463 | − | 0.220162i | \(-0.0706587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −53.3784 | −0.110974 | ||||||||
\(482\) | −17.9480 | + | 211.079i | −0.0372366 | + | 0.437923i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50315 | + | 0.600085i | 0.00723791 | + | 0.00123984i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 710.541 | 1.45902 | 0.729508 | − | 0.683972i | \(-0.239749\pi\) | ||||
0.729508 | + | 0.683972i | \(0.239749\pi\) | |||||||
\(488\) | 113.041 | − | 434.576i | 0.231641 | − | 0.890525i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 697.876i | 1.42134i | 0.703528 | + | 0.710668i | \(0.251607\pi\) | ||||
−0.703528 | + | 0.710668i | \(0.748393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 330.982i | − | 0.671363i | ||||||
\(494\) | 13.3766 | − | 157.316i | 0.0270781 | − | 0.318454i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 193.557 | − | 548.390i | 0.390235 | − | 1.10563i | ||||
\(497\) | 820.135i | 1.65017i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 875.602i | − | 1.75471i | −0.479838 | − | 0.877357i | \(-0.659305\pi\) | ||
0.479838 | − | 0.877357i | \(-0.340695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 334.550 | + | 28.4468i | 0.666434 | + | 0.0566670i | ||||
\(503\) | 142.849 | 0.283995 | 0.141997 | − | 0.989867i | \(-0.454648\pi\) | ||||
0.141997 | + | 0.989867i | \(0.454648\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 173.902 | + | 14.7869i | 0.343681 | + | 0.0292232i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −65.7837 | − | 11.2687i | −0.129496 | − | 0.0221824i | ||||
\(509\) | −147.662 | −0.290102 | −0.145051 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145051 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 193.785i | − | 0.379227i | ||||||
\(512\) | −354.000 | + | 369.903i | −0.691407 | + | 0.722466i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 396.268 | + | 33.6947i | 0.770950 | + | 0.0655539i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 129.443i | − | 0.250374i | ||||||
\(518\) | 467.571 | + | 39.7576i | 0.902646 | + | 0.0767520i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 348.592 | 0.669082 | 0.334541 | − | 0.942381i | \(-0.391419\pi\) | ||||
0.334541 | + | 0.942381i | \(0.391419\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −370.317 | −0.708063 | −0.354032 | − | 0.935233i | \(-0.615189\pi\) | ||||
−0.354032 | + | 0.935233i | \(0.615189\pi\) | |||||||
\(524\) | −132.652 | + | 774.392i | −0.253153 | + | 1.47785i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 81.4249 | − | 957.601i | 0.154800 | − | 1.82053i | ||||
\(527\) | −237.201 | −0.450096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −466.523 | −0.881897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −234.346 | + | 1368.06i | −0.440500 | + | 2.57153i | ||||
\(533\) | 14.9580i | 0.0280638i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −32.5670 | + | 125.201i | −0.0607594 | + | 0.233584i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 49.3937 | − | 580.897i | 0.0918098 | − | 1.07973i | ||||
\(539\) | 1155.46i | 2.14371i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −279.719 | −0.517041 | −0.258520 | − | 0.966006i | \(-0.583235\pi\) | ||||
−0.258520 | + | 0.966006i | \(0.583235\pi\) | |||||||
\(542\) | −346.874 | − | 29.4947i | −0.639990 | − | 0.0544183i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 190.331 | + | 85.9411i | 0.349873 | + | 0.157980i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −387.716 | −0.708804 | −0.354402 | − | 0.935093i | \(-0.615315\pi\) | ||||
−0.354402 | + | 0.935093i | \(0.615315\pi\) | |||||||
\(548\) | 79.1026 | − | 461.782i | 0.144348 | − | 0.842668i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1419.71i | − | 2.57660i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1525.40i | 2.75841i | ||||||||
\(554\) | 100.677 | + | 8.56059i | 0.181728 | + | 0.0154523i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −126.453 | + | 738.201i | −0.227433 | + | 1.32770i | ||||
\(557\) | − | 43.5564i | − | 0.0781983i | −0.999235 | − | 0.0390991i | \(-0.987551\pi\) | ||
0.999235 | − | 0.0390991i | \(-0.0124488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 128.559i | − | 0.229981i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.1923 | + | 131.628i | −0.0199152 | + | 0.234213i | ||||
\(563\) | −361.646 | −0.642355 | −0.321178 | − | 0.947019i | \(-0.604079\pi\) | ||||
−0.321178 | + | 0.947019i | \(0.604079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.8144 | − | 233.028i | 0.0350078 | − | 0.411710i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 512.248 | + | 133.245i | 0.901845 | + | 0.234586i | ||||
\(569\) | 888.559 | 1.56161 | 0.780807 | − | 0.624772i | \(-0.214808\pi\) | ||||
0.780807 | + | 0.624772i | \(0.214808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 447.745i | 0.784142i | 0.919935 | + | 0.392071i | \(0.128241\pi\) | ||||
−0.919935 | + | 0.392071i | \(0.871759\pi\) | |||||||
\(572\) | −122.751 | − | 21.0270i | −0.214599 | − | 0.0367605i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.1411 | − | 131.025i | 0.0194096 | − | 0.228267i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1069.90i | 1.85425i | 0.374756 | + | 0.927124i | \(0.377727\pi\) | ||||
−0.374756 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(578\) | −41.7539 | + | 491.049i | −0.0722386 | + | 0.849566i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1235.50 | −2.12651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −454.508 | −0.779602 | ||||||||
\(584\) | −121.036 | − | 31.4836i | −0.207253 | − | 0.0539102i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 136.255 | + | 11.5857i | 0.232517 | + | 0.0197709i | ||||
\(587\) | 129.637 | 0.220847 | 0.110424 | − | 0.993885i | \(-0.464779\pi\) | ||||
0.110424 | + | 0.993885i | \(0.464779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1017.44 | −1.72741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 100.797 | − | 285.581i | 0.170265 | − | 0.482400i | ||||
\(593\) | 892.757i | 1.50549i | 0.658311 | + | 0.752746i | \(0.271271\pi\) | ||||
−0.658311 | + | 0.752746i | \(0.728729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 198.025 | + | 33.9214i | 0.332257 | + | 0.0569151i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −44.4208 | − | 3.77710i | −0.0742823 | − | 0.00631623i | ||||
\(599\) | − | 1030.62i | − | 1.72057i | −0.509816 | − | 0.860284i | \(-0.670286\pi\) | ||
0.509816 | − | 0.860284i | \(-0.329714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −815.961 | −1.35767 | −0.678836 | − | 0.734289i | \(-0.737515\pi\) | ||||
−0.678836 | + | 0.734289i | \(0.737515\pi\) | |||||||
\(602\) | −95.7540 | + | 1126.12i | −0.159060 | + | 1.87063i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 143.959 | − | 840.401i | 0.238343 | − | 1.39139i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −842.678 | −1.38827 | −0.694133 | − | 0.719847i | \(-0.744212\pi\) | ||||
−0.694133 | + | 0.719847i | \(0.744212\pi\) | |||||||
\(608\) | 816.400 | + | 368.634i | 1.34276 | + | 0.606305i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.0644i | 0.0541152i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 731.088i | 1.19264i | 0.802747 | + | 0.596320i | \(0.203371\pi\) | ||||
−0.802747 | + | 0.596320i | \(0.796629\pi\) | |||||||
\(614\) | 62.6107 | − | 736.336i | 0.101972 | − | 1.19924i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1059.58 | + | 275.615i | 1.72009 | + | 0.447426i | ||||
\(617\) | 919.609i | 1.49045i | 0.666812 | + | 0.745226i | \(0.267658\pi\) | ||||
−0.666812 | + | 0.745226i | \(0.732342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 688.974i | 1.11304i | 0.830833 | + | 0.556522i | \(0.187865\pi\) | ||||
−0.830833 | + | 0.556522i | \(0.812135\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 604.711 | + | 51.4186i | 0.972203 | + | 0.0826665i | ||||
\(623\) | 1253.01 | 2.01126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 593.246 | + | 50.4438i | 0.947678 | + | 0.0805811i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 137.717 | − | 803.960i | 0.219295 | − | 1.28019i | ||||
\(629\) | −123.525 | −0.196383 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 418.968i | − | 0.663975i | −0.943284 | − | 0.331987i | \(-0.892281\pi\) | ||
0.943284 | − | 0.331987i | \(-0.107719\pi\) | |||||||
\(632\) | 952.749 | + | 247.827i | 1.50751 | + | 0.392131i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 527.454 | + | 44.8494i | 0.831946 | + | 0.0707404i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 295.146i | − | 0.463337i | ||||||
\(638\) | −1115.83 | − | 94.8795i | −1.74896 | − | 0.148714i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.2426 | 0.0737014 | 0.0368507 | − | 0.999321i | \(-0.488267\pi\) | ||||
0.0368507 | + | 0.999321i | \(0.488267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −710.880 | −1.10557 | −0.552784 | − | 0.833325i | \(-0.686435\pi\) | ||||
−0.552784 | + | 0.833325i | \(0.686435\pi\) | |||||||
\(644\) | 386.293 | + | 66.1714i | 0.599834 | + | 0.102751i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.9553 | − | 364.051i | 0.0479184 | − | 0.563547i | ||||
\(647\) | −468.195 | −0.723641 | −0.361820 | − | 0.932248i | \(-0.617845\pi\) | ||||
−0.361820 | + | 0.932248i | \(0.617845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 118.140 | 0.182034 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 851.192 | + | 145.808i | 1.30551 | + | 0.223632i | ||||
\(653\) | 551.066i | 0.843900i | 0.906619 | + | 0.421950i | \(0.138654\pi\) | ||||
−0.906619 | + | 0.421950i | \(0.861346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −80.0271 | − | 28.2459i | −0.121993 | − | 0.0430578i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.6272 | − | 289.629i | 0.0374273 | − | 0.440165i | ||||
\(659\) | 158.259i | 0.240151i | 0.992765 | + | 0.120075i | \(0.0383136\pi\) | ||||
−0.992765 | + | 0.120075i | \(0.961686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 92.4953 | 0.139932 | 0.0699662 | − | 0.997549i | \(-0.477711\pi\) | ||||
0.0699662 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(662\) | 943.447 | + | 80.2214i | 1.42515 | + | 0.121180i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −200.728 | + | 771.681i | −0.302301 | + | 1.16217i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −400.877 | −0.601015 | ||||||||
\(668\) | −1005.47 | − | 172.236i | −1.50520 | − | 0.257838i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 619.690i | 0.923532i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 956.062i | − | 1.42060i | −0.703900 | − | 0.710299i | \(-0.748560\pi\) | ||
0.703900 | − | 0.710299i | \(-0.251440\pi\) | |||||||
\(674\) | −59.3037 | − | 5.04259i | −0.0879876 | − | 0.00748159i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −634.940 | − | 108.764i | −0.939261 | − | 0.160894i | ||||
\(677\) | − | 1116.67i | − | 1.64944i | −0.565543 | − | 0.824719i | \(-0.691333\pi\) | ||
0.565543 | − | 0.824719i | \(-0.308667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1577.92i | 2.32388i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −67.9961 | + | 799.671i | −0.0997010 | + | 1.17254i | ||||
\(683\) | 826.776 | 1.21051 | 0.605254 | − | 0.796033i | \(-0.293072\pi\) | ||||
0.605254 | + | 0.796033i | \(0.293072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −116.909 | + | 1374.91i | −0.170421 | + | 2.00424i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 687.806 | + | 242.764i | 0.999718 | + | 0.352855i | ||||
\(689\) | 116.097 | 0.168501 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 965.432i | 1.39715i | 0.715536 | + | 0.698576i | \(0.246182\pi\) | ||||
−0.715536 | + | 0.698576i | \(0.753818\pi\) | |||||||
\(692\) | −158.996 | + | 928.183i | −0.229764 | + | 1.34130i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 51.8834 | − | 610.177i | 0.0747600 | − | 0.879218i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6149i | 0.0496627i | ||||||||
\(698\) | 109.997 | − | 1293.63i | 0.157589 | − | 1.85334i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1109.94 | 1.58337 | 0.791686 | − | 0.610928i | \(-0.209203\pi\) | ||||
0.791686 | + | 0.610928i | \(0.209203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −529.845 | −0.753691 | ||||||||
\(704\) | 344.292 | − | 617.024i | 0.489052 | − | 0.876454i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 549.113 | + | 46.6911i | 0.777780 | + | 0.0661347i | ||||
\(707\) | 1169.60 | 1.65431 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 964.244 | 1.36001 | 0.680003 | − | 0.733210i | \(-0.261979\pi\) | ||||
0.680003 | + | 0.733210i | \(0.261979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 203.573 | − | 782.620i | 0.285917 | − | 1.09919i | ||||
\(713\) | 287.292i | 0.402934i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 69.3385 | − | 404.782i | 0.0968415 | − | 0.565338i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1011.69 | + | 86.0244i | 1.40904 | + | 0.119811i | ||||
\(719\) | 190.820i | 0.265396i | 0.991157 | + | 0.132698i | \(0.0423641\pi\) | ||||
−0.991157 | + | 0.132698i | \(0.957636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 394.754 | 0.547509 | ||||||||
\(722\) | 71.6080 | − | 842.149i | 0.0991801 | − | 1.16641i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 224.026 | + | 38.3753i | 0.309428 | + | 0.0530046i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −202.134 | −0.278039 | −0.139019 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139019 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(728\) | −270.654 | − | 70.4017i | −0.371777 | − | 0.0967056i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 297.503i | − | 0.406981i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 962.435i | 1.31301i | 0.754322 | + | 0.656504i | \(0.227966\pi\) | ||||
−0.754322 | + | 0.656504i | \(0.772034\pi\) | |||||||
\(734\) | 10.6358 | − | 125.083i | 0.0144902 | − | 0.170413i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 104.090 | − | 230.524i | 0.141426 | − | 0.313212i | ||||
\(737\) | − | 178.532i | − | 0.242242i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 932.112i | − | 1.26132i | −0.776061 | − | 0.630658i | \(-0.782785\pi\) | ||
0.776061 | − | 0.630658i | \(-0.217215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1016.96 | − | 86.4722i | −1.37057 | − | 0.116539i | ||||
\(743\) | −1153.70 | −1.55276 | −0.776379 | − | 0.630266i | \(-0.782946\pi\) | ||||
−0.776379 | + | 0.630266i | \(0.782946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −543.590 | − | 46.2215i | −0.728672 | − | 0.0619591i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −284.062 | − | 48.6594i | −0.379762 | − | 0.0650526i | ||||
\(749\) | −418.872 | −0.559242 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 204.359i | 0.272116i | 0.990701 | + | 0.136058i | \(0.0434434\pi\) | ||||
−0.990701 | + | 0.136058i | \(0.956557\pi\) | |||||||
\(752\) | −176.898 | − | 62.4369i | −0.235237 | − | 0.0830279i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 285.023 | + | 24.2356i | 0.378015 | + | 0.0321427i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 216.739i | − | 0.286314i | −0.989700 | − | 0.143157i | \(-0.954275\pi\) | ||
0.989700 | − | 0.143157i | \(-0.0457253\pi\) | |||||||
\(758\) | −750.947 | − | 63.8530i | −0.990695 | − | 0.0842388i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1324.78 | −1.74085 | −0.870424 | − | 0.492303i | \(-0.836155\pi\) | ||||
−0.870424 | + | 0.492303i | \(0.836155\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1034.15 | 1.35537 | ||||||||
\(764\) | 107.040 | − | 624.872i | 0.140104 | − | 0.817895i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 69.8477 | − | 821.447i | 0.0911849 | − | 1.07238i | ||||
\(767\) | −30.1772 | −0.0393444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −444.088 | −0.577488 | −0.288744 | − | 0.957406i | \(-0.593238\pi\) | ||||
−0.288744 | + | 0.957406i | \(0.593238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 105.850 | − | 617.928i | 0.137112 | − | 0.800425i | ||||
\(773\) | − | 751.987i | − | 0.972817i | −0.873732 | − | 0.486408i | \(-0.838307\pi\) | ||
0.873732 | − | 0.486408i | \(-0.161693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 985.550 | + | 256.359i | 1.27004 | + | 0.330359i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.3301 | − | 321.417i | 0.0351287 | − | 0.413133i | ||||
\(779\) | 148.476i | 0.190599i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −730.446 | −0.935271 | ||||||||
\(782\) | −102.796 | − | 8.74073i | −0.131452 | − | 0.0111774i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1579.06 | + | 557.337i | 2.01411 | + | 0.710889i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 442.296 | 0.562002 | 0.281001 | − | 0.959707i | \(-0.409334\pi\) | ||||
0.281001 | + | 0.959707i | \(0.409334\pi\) | |||||||
\(788\) | −175.679 | + | 1025.57i | −0.222943 | + | 1.30148i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1385.81i | − | 1.75197i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 158.291i | − | 0.199610i | ||||||
\(794\) | 371.668 | + | 31.6030i | 0.468096 | + | 0.0398022i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.47704 | + | 55.3247i | −0.0119058 | + | 0.0695034i | ||||
\(797\) | 56.2072i | 0.0705235i | 0.999378 | + | 0.0352618i | \(0.0112265\pi\) | ||||
−0.999378 | + | 0.0352618i | \(0.988774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.5155i | 0.0957641i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.5086 | − | 476.403i | 0.0505094 | − | 0.594019i | ||||
\(803\) | 172.593 | 0.214935 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.3686 | − | 204.264i | 0.0215491 | − | 0.253430i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 190.021 | − | 730.518i | 0.235174 | − | 0.904107i | ||||
\(809\) | 1522.16 | 1.88153 | 0.940765 | − | 0.339060i | \(-0.110109\pi\) | ||||
0.940765 | + | 0.339060i | \(0.110109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 930.734i | 1.14764i | 0.818982 | + | 0.573819i | \(0.194539\pi\) | ||||
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(812\) | −2478.63 | − | 424.585i | −3.05249 | − | 0.522888i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.4098 | + | 416.438i | −0.0435009 | + | 0.511595i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1276.10i | − | 1.56194i | ||||||
\(818\) | 8.09992 | − | 95.2595i | 0.00990210 | − | 0.116454i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −349.814 | −0.426083 | −0.213041 | − | 0.977043i | \(-0.568337\pi\) | ||||
−0.213041 | + | 0.977043i | \(0.568337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 61.2187 | 0.0743849 | 0.0371924 | − | 0.999308i | \(-0.488159\pi\) | ||||
0.0371924 | + | 0.999308i | \(0.488159\pi\) | |||||||
\(824\) | 64.1344 | − | 246.559i | 0.0778330 | − | 0.299222i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 264.338 | + | 22.4767i | 0.320022 | + | 0.0272115i | ||||
\(827\) | 46.2063 | 0.0558721 | 0.0279361 | − | 0.999610i | \(-0.491107\pi\) | ||||
0.0279361 | + | 0.999610i | \(0.491107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −223.832 | −0.270002 | −0.135001 | − | 0.990845i | \(-0.543104\pi\) | ||||
−0.135001 | + | 0.990845i | \(0.543104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −87.9444 | + | 157.610i | −0.105702 | + | 0.189435i | ||||
\(833\) | − | 683.007i | − | 0.819937i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1218.45 | − | 208.718i | −1.45747 | − | 0.249663i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −476.300 | − | 40.4998i | −0.568377 | − | 0.0483291i | ||||
\(839\) | − | 361.794i | − | 0.431220i | −0.976480 | − | 0.215610i | \(-0.930826\pi\) | ||
0.976480 | − | 0.215610i | \(-0.0691740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1731.20 | 2.05851 | ||||||||
\(842\) | 43.6486 | − | 513.332i | 0.0518392 | − | 0.609657i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −50.3101 | + | 293.698i | −0.0596092 | + | 0.347984i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0143 | −0.0130039 | ||||||||
\(848\) | −219.232 | + | 621.134i | −0.258528 | + | 0.732470i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 149.610i | 0.175805i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 844.503i | 0.990039i | 0.868882 | + | 0.495019i | \(0.164839\pi\) | ||||
−0.868882 | + | 0.495019i | \(0.835161\pi\) | |||||||
\(854\) | −117.899 | + | 1386.55i | −0.138055 | + | 1.62360i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −68.0528 | + | 261.623i | −0.0795009 | + | 0.305635i | ||||
\(857\) | 1389.51i | 1.62137i | 0.585482 | + | 0.810685i | \(0.300905\pi\) | ||||
−0.585482 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1205.45i | − | 1.40332i | −0.712512 | − | 0.701660i | \(-0.752442\pi\) | ||
0.712512 | − | 0.701660i | \(-0.247558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −683.861 | − | 58.1487i | −0.793342 | − | 0.0674579i | ||||
\(863\) | −258.868 | −0.299963 | −0.149981 | − | 0.988689i | \(-0.547921\pi\) | ||||
−0.149981 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −467.832 | − | 39.7798i | −0.540222 | − | 0.0459351i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −304.282 | + | 1776.33i | −0.350555 | + | 2.04646i | ||||
\(869\) | −1358.58 | −1.56339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.6035i | 0.0523576i | ||||||||
\(872\) | 168.015 | − | 645.919i | 0.192677 | − | 0.740732i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −440.930 | − | 37.4923i | −0.504497 | − | 0.0428974i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 156.268i | − | 0.178185i | −0.996023 | − | 0.0890926i | \(-0.971603\pi\) | ||
0.996023 | − | 0.0890926i | \(-0.0283967\pi\) | |||||||
\(878\) | 746.253 | + | 63.4539i | 0.849946 | + | 0.0722710i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1343.58 | 1.52507 | 0.762533 | − | 0.646950i | \(-0.223956\pi\) | ||||
0.762533 | + | 0.646950i | \(0.223956\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 149.478 | 0.169284 | 0.0846420 | − | 0.996411i | \(-0.473025\pi\) | ||||
0.0846420 | + | 0.996411i | \(0.473025\pi\) | |||||||
\(884\) | 72.5594 | + | 12.4293i | 0.0820807 | + | 0.0140603i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.3949 | + | 216.334i | −0.0207617 | + | 0.244169i | ||||
\(887\) | −1532.07 | −1.72725 | −0.863626 | − | 0.504134i | \(-0.831812\pi\) | ||||
−0.863626 | + | 0.504134i | \(0.831812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 206.832 | 0.232656 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 630.796 | + | 108.055i | 0.707171 | + | 0.121137i | ||||
\(893\) | 328.204i | 0.367529i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 887.745 | − | 1315.09i | 0.990786 | − | 1.46773i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 73.1190 | − | 859.919i | 0.0814243 | − | 0.957594i | ||||
\(899\) | − | 1843.39i | − | 2.05049i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 268.665 | 0.298186 | ||||||||
\(902\) | 116.697 | + | 9.92273i | 0.129376 | + | 0.0110008i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −865.562 | − | 225.148i | −0.957480 | − | 0.249057i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1245.02 | 1.37268 | 0.686341 | − | 0.727280i | \(-0.259216\pi\) | ||||
0.686341 | + | 0.727280i | \(0.259216\pi\) | |||||||
\(908\) | 693.808 | + | 118.848i | 0.764106 | + | 0.130890i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 173.681i | 0.190649i | 0.995446 | + | 0.0953245i | \(0.0303889\pi\) | ||||
−0.995446 | + | 0.0953245i | \(0.969611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1100.39i | − | 1.20524i | ||||||
\(914\) | −437.914 | − | 37.2359i | −0.479118 | − | 0.0407395i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −450.125 | − | 77.1058i | −0.491403 | − | 0.0841766i | ||||
\(917\) | − | 2434.78i | − | 2.65515i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 874.426i | − | 0.951498i | −0.879581 | − | 0.475749i | \(-0.842177\pi\) | ||
0.879581 | − | 0.475749i | \(-0.157823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37.8607 | − | 445.262i | 0.0410636 | − | 0.482931i | ||||
\(923\) | 186.582 | 0.202147 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −125.537 | + | 1476.38i | −0.135569 | + | 1.59436i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −667.886 | + | 1479.14i | −0.719705 | + | 1.59390i | ||||
\(929\) | −1564.05 | −1.68358 | −0.841792 | − | 0.539803i | \(-0.818499\pi\) | ||||
−0.841792 | + | 0.539803i | \(0.818499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2929.68i | − | 3.14681i | ||||||
\(932\) | 175.635 | − | 1025.31i | 0.188450 | − | 1.10012i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −42.2573 | + | 496.970i | −0.0452434 | + | 0.532087i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 958.621i | 1.02308i | 0.859261 | + | 0.511538i | \(0.170924\pi\) | ||||
−0.859261 | + | 0.511538i | \(0.829076\pi\) | |||||||
\(938\) | 33.9666 | − | 399.466i | 0.0362117 | − | 0.425869i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 752.357 | 0.799529 | 0.399765 | − | 0.916618i | \(-0.369092\pi\) | ||||
0.399765 | + | 0.916618i | \(0.369092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.9247 | 0.0444589 | ||||||||
\(944\) | 56.9849 | − | 161.451i | 0.0603654 | − | 0.171029i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1002.97 | − | 85.2825i | −1.06022 | − | 0.0901507i | ||||
\(947\) | 1013.16 | 1.06986 | 0.534932 | − | 0.844895i | \(-0.320337\pi\) | ||||
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.0863 | −0.0464555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −626.329 | − | 162.919i | −0.657909 | − | 0.171134i | ||||
\(953\) | − | 21.5482i | − | 0.0226109i | −0.999936 | − | 0.0113054i | \(-0.996401\pi\) | ||
0.999936 | − | 0.0113054i | \(-0.00359871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 94.6102 | − | 552.312i | 0.0989646 | − | 0.577732i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 420.314 | + | 35.7393i | 0.438741 | + | 0.0373062i | ||||
\(959\) | 1451.90i | 1.51397i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −360.079 | −0.374692 | ||||||||
\(962\) | 9.04490 | − | 106.373i | 0.00940218 | − | 0.110575i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −417.599 | − | 71.5340i | −0.433193 | − | 0.0742054i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −303.965 | −0.314338 | −0.157169 | − | 0.987572i | \(-0.550237\pi\) | ||||
−0.157169 | + | 0.987572i | \(0.550237\pi\) | |||||||
\(968\) | −1.78946 | + | 6.87942i | −0.00184861 | + | 0.00710684i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 356.162i | 0.366799i | 0.983038 | + | 0.183399i | \(0.0587101\pi\) | ||||
−0.983038 | + | 0.183399i | \(0.941290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2320.99i | − | 2.38539i | ||||||
\(974\) | −120.400 | + | 1415.97i | −0.123614 | + | 1.45377i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 846.873 | + | 298.907i | 0.867698 | + | 0.306257i | ||||
\(977\) | 1845.09i | 1.88852i | 0.329194 | + | 0.944262i | \(0.393223\pi\) | ||||
−0.329194 | + | 0.944262i | \(0.606777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1115.99i | 1.13993i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1390.73 | − | 118.254i | −1.41623 | − | 0.120422i | ||||
\(983\) | 289.444 | 0.294449 | 0.147225 | − | 0.989103i | \(-0.452966\pi\) | ||||
0.147225 | + | 0.989103i | \(0.452966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 659.583 | + | 56.0844i | 0.668949 | + | 0.0568807i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 311.234 | + | 53.3140i | 0.315015 | + | 0.0539616i | ||||
\(989\) | −360.329 | −0.364337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 441.980i | − | 0.445994i | −0.974819 | − | 0.222997i | \(-0.928416\pi\) | ||
0.974819 | − | 0.222997i | \(-0.0715840\pi\) | |||||||
\(992\) | 1060.04 | + | 478.645i | 1.06859 | + | 0.482505i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1634.37 | − | 138.971i | −1.64424 | − | 0.139810i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1045.42i | − | 1.04856i | −0.851545 | − | 0.524282i | \(-0.824334\pi\) | ||
0.851545 | − | 0.524282i | \(-0.175666\pi\) | |||||||
\(998\) | 1744.91 | + | 148.370i | 1.74841 | + | 0.148667i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.3.f.f.199.8 | 16 | ||
3.2 | odd | 2 | 300.3.f.b.199.9 | 16 | |||
4.3 | odd | 2 | inner | 900.3.f.f.199.10 | 16 | ||
5.2 | odd | 4 | 900.3.c.u.451.1 | 8 | |||
5.3 | odd | 4 | 180.3.c.b.91.8 | 8 | |||
5.4 | even | 2 | inner | 900.3.f.f.199.9 | 16 | ||
12.11 | even | 2 | 300.3.f.b.199.7 | 16 | |||
15.2 | even | 4 | 300.3.c.d.151.8 | 8 | |||
15.8 | even | 4 | 60.3.c.a.31.1 | ✓ | 8 | ||
15.14 | odd | 2 | 300.3.f.b.199.8 | 16 | |||
20.3 | even | 4 | 180.3.c.b.91.7 | 8 | |||
20.7 | even | 4 | 900.3.c.u.451.2 | 8 | |||
20.19 | odd | 2 | inner | 900.3.f.f.199.7 | 16 | ||
40.3 | even | 4 | 2880.3.e.j.2431.4 | 8 | |||
40.13 | odd | 4 | 2880.3.e.j.2431.1 | 8 | |||
60.23 | odd | 4 | 60.3.c.a.31.2 | yes | 8 | ||
60.47 | odd | 4 | 300.3.c.d.151.7 | 8 | |||
60.59 | even | 2 | 300.3.f.b.199.10 | 16 | |||
120.53 | even | 4 | 960.3.e.c.511.7 | 8 | |||
120.83 | odd | 4 | 960.3.e.c.511.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.1 | ✓ | 8 | 15.8 | even | 4 | ||
60.3.c.a.31.2 | yes | 8 | 60.23 | odd | 4 | ||
180.3.c.b.91.7 | 8 | 20.3 | even | 4 | |||
180.3.c.b.91.8 | 8 | 5.3 | odd | 4 | |||
300.3.c.d.151.7 | 8 | 60.47 | odd | 4 | |||
300.3.c.d.151.8 | 8 | 15.2 | even | 4 | |||
300.3.f.b.199.7 | 16 | 12.11 | even | 2 | |||
300.3.f.b.199.8 | 16 | 15.14 | odd | 2 | |||
300.3.f.b.199.9 | 16 | 3.2 | odd | 2 | |||
300.3.f.b.199.10 | 16 | 60.59 | even | 2 | |||
900.3.c.u.451.1 | 8 | 5.2 | odd | 4 | |||
900.3.c.u.451.2 | 8 | 20.7 | even | 4 | |||
900.3.f.f.199.7 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.f.199.8 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.f.199.9 | 16 | 5.4 | even | 2 | inner | ||
900.3.f.f.199.10 | 16 | 4.3 | odd | 2 | inner | ||
960.3.e.c.511.4 | 8 | 120.83 | odd | 4 | |||
960.3.e.c.511.7 | 8 | 120.53 | even | 4 | |||
2880.3.e.j.2431.1 | 8 | 40.13 | odd | 4 | |||
2880.3.e.j.2431.4 | 8 | 40.3 | even | 4 |