Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1057,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.t (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1333.15 | ||
Character | \(\chi\) | \(=\) | 1380.1333 |
Dual form | 1380.2.t.a.1057.15 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23126 | − | 0.146576i | −0.997849 | − | 0.0655508i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93317 | + | 2.93317i | 1.10863 | + | 1.10863i | 0.993330 | + | 0.115304i | \(0.0367843\pi\) |
0.115304 | + | 0.993330i | \(0.463216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.31685i | − | 1.90460i | −0.305162 | − | 0.952300i | \(-0.598711\pi\) | ||
0.305162 | − | 0.952300i | \(-0.401289\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.106466 | + | 0.106466i | 0.0295283 | + | 0.0295283i | 0.721717 | − | 0.692189i | \(-0.243353\pi\) |
−0.692189 | + | 0.721717i | \(0.743353\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.47409 | − | 1.68138i | −0.380609 | − | 0.434131i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.74862 | − | 2.74862i | −0.666639 | − | 0.666639i | 0.290298 | − | 0.956936i | \(-0.406246\pi\) |
−0.956936 | + | 0.290298i | \(0.906246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.24616 | 1.66238 | 0.831191 | − | 0.555986i | \(-0.187659\pi\) | ||||
0.831191 | + | 0.555986i | \(0.187659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.14813i | 0.905196i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.53063 | − | 1.57269i | 0.944702 | − | 0.327929i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.95703 | + | 0.654098i | 0.991406 | + | 0.130820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.94170i | 1.84613i | 0.384647 | + | 0.923064i | \(0.374323\pi\) | ||||
−0.384647 | + | 0.923064i | \(0.625677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.76853 | 1.21566 | 0.607832 | − | 0.794066i | \(-0.292040\pi\) | ||||
0.607832 | + | 0.794066i | \(0.292040\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.46668 | − | 4.46668i | 0.777550 | − | 0.777550i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.11473 | − | 6.97460i | −1.03358 | − | 1.17892i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.65576 | − | 1.65576i | −0.272205 | − | 0.272205i | 0.557782 | − | 0.829987i | \(-0.311652\pi\) |
−0.829987 | + | 0.557782i | \(0.811652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.150565i | 0.0241097i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.29087 | 1.29482 | 0.647409 | − | 0.762143i | \(-0.275853\pi\) | ||||
0.647409 | + | 0.762143i | \(0.275853\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.22159 | + | 5.22159i | −0.796285 | + | 0.796285i | −0.982508 | − | 0.186223i | \(-0.940375\pi\) |
0.186223 | + | 0.982508i | \(0.440375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.146576 | − | 2.23126i | 0.0218503 | − | 0.332616i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00474 | + | 3.00474i | −0.438286 | + | 0.438286i | −0.891435 | − | 0.453149i | \(-0.850301\pi\) |
0.453149 | + | 0.891435i | \(0.350301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.2070i | 1.45814i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.88714i | − | 0.544308i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.34794 | + | 8.34794i | −1.14668 | + | 1.14668i | −0.159475 | + | 0.987202i | \(0.550980\pi\) |
−0.987202 | + | 0.159475i | \(0.949020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.925898 | + | 14.0945i | −0.124848 | + | 1.90050i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12381 | + | 5.12381i | 0.678665 | + | 0.678665i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.05589i | − | 0.137465i | −0.997635 | − | 0.0687324i | \(-0.978105\pi\) | ||
0.997635 | − | 0.0687324i | \(-0.0218955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.36075i | 0.174226i | 0.996198 | + | 0.0871128i | \(0.0277640\pi\) | ||||
−0.996198 | + | 0.0871128i | \(0.972236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.93317 | + | 2.93317i | −0.369545 | + | 0.369545i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.221947 | − | 0.253158i | −0.0275291 | − | 0.0314003i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.30746 | − | 4.30746i | −0.526240 | − | 0.526240i | 0.393209 | − | 0.919449i | \(-0.371365\pi\) |
−0.919449 | + | 0.393209i | \(0.871365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.31570 | + | 2.09158i | 0.519550 | + | 0.251796i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7517 | 1.27599 | 0.637994 | − | 0.770041i | \(-0.279764\pi\) | ||||
0.637994 | + | 0.770041i | \(0.279764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.69127 | − | 5.69127i | −0.666112 | − | 0.666112i | 0.290701 | − | 0.956814i | \(-0.406111\pi\) |
−0.956814 | + | 0.290701i | \(0.906111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.04263 | + | 3.96767i | 0.351333 | + | 0.458147i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.5284 | − | 18.5284i | 2.11151 | − | 2.11151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.92020 | 0.666075 | 0.333038 | − | 0.942914i | \(-0.391926\pi\) | ||||
0.333038 | + | 0.942914i | \(0.391926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.73628 | − | 4.73628i | 0.519874 | − | 0.519874i | −0.397659 | − | 0.917533i | \(-0.630177\pi\) |
0.917533 | + | 0.397659i | \(0.130177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.73000 | + | 6.53577i | 0.621506 | + | 0.708903i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.02985 | + | 7.02985i | −0.753679 | + | 0.753679i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3203 | 1.62395 | 0.811973 | − | 0.583695i | \(-0.198394\pi\) | ||||
0.811973 | + | 0.583695i | \(0.198394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.624564i | 0.0654721i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.78607 | + | 4.78607i | 0.496292 | + | 0.496292i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.1681 | − | 1.06211i | −1.65881 | − | 0.108970i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.23025 | + | 3.23025i | 0.327982 | + | 0.327982i | 0.851819 | − | 0.523836i | \(-0.175500\pi\) |
−0.523836 | + | 0.851819i | \(0.675500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.31685 | 0.634867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.13229 | −0.411178 | −0.205589 | − | 0.978638i | \(-0.565911\pi\) | ||||
−0.205589 | + | 0.978638i | \(0.565911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0148961 | + | 0.0148961i | −0.00146776 | + | 0.00146776i | −0.707840 | − | 0.706373i | \(-0.750330\pi\) |
0.706373 | + | 0.707840i | \(0.250330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.608016 | − | 9.25555i | 0.0593363 | − | 0.903249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.78001 | + | 8.78001i | 0.848795 | + | 0.848795i | 0.989983 | − | 0.141187i | \(-0.0450920\pi\) |
−0.141187 | + | 0.989983i | \(0.545092\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.07610 | 0.773550 | 0.386775 | − | 0.922174i | \(-0.373589\pi\) | ||||
0.386775 | + | 0.922174i | \(0.373589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.34160i | − | 0.222254i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.67779 | − | 3.67779i | 0.345978 | − | 0.345978i | −0.512631 | − | 0.858609i | \(-0.671329\pi\) |
0.858609 | + | 0.512631i | \(0.171329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3395 | + | 2.84501i | −0.964166 | + | 0.265298i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.106466 | + | 0.106466i | −0.00984275 | + | 0.00984275i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.1244i | − | 1.47812i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28.9025 | −2.62750 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.86253 | + | 5.86253i | 0.528607 | + | 0.528607i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9645 | − | 2.18604i | −0.980699 | − | 0.195526i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8751 | − | 10.8751i | 0.965008 | − | 0.965008i | −0.0343998 | − | 0.999408i | \(-0.510952\pi\) |
0.999408 | + | 0.0343998i | \(0.0109520\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.38444 | −0.650164 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.40858 | −0.559920 | −0.279960 | − | 0.960012i | \(-0.590321\pi\) | ||||
−0.279960 | + | 0.960012i | \(0.590321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.2542 | + | 21.2542i | 1.84298 | + | 1.84298i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.68138 | − | 1.47409i | 0.144710 | − | 0.126870i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.578043 | + | 0.578043i | 0.0493855 | + | 0.0493855i | 0.731368 | − | 0.681983i | \(-0.238882\pi\) |
−0.681983 | + | 0.731368i | \(0.738882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.06060i | − | 0.429235i | −0.976698 | − | 0.214617i | \(-0.931150\pi\) | ||
0.976698 | − | 0.214617i | \(-0.0688504\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.24934 | −0.357859 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.672527 | − | 0.672527i | 0.0562395 | − | 0.0562395i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.45721 | − | 22.1825i | 0.121015 | − | 1.84216i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.21743 | + | 7.21743i | −0.595284 | + | 0.595284i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7441 | −1.04403 | −0.522017 | − | 0.852935i | \(-0.674820\pi\) | ||||
−0.522017 | + | 0.852935i | \(0.674820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.76352 | −0.306271 | −0.153135 | − | 0.988205i | \(-0.548937\pi\) | ||||
−0.153135 | + | 0.988205i | \(0.548937\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.74862 | − | 2.74862i | 0.222213 | − | 0.222213i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.1023 | − | 0.992103i | −1.21305 | − | 0.0796877i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2000 | − | 15.2000i | −1.21310 | − | 1.21310i | −0.970003 | − | 0.243092i | \(-0.921838\pi\) |
−0.243092 | − | 0.970003i | \(-0.578162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.8058 | −0.936258 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.9021 | + | 8.67614i | 1.41088 | + | 0.683776i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.10629 | + | 1.10629i | 0.0866513 | + | 0.0866513i | 0.749104 | − | 0.662453i | \(-0.230484\pi\) |
−0.662453 | + | 0.749104i | \(0.730484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6210 | + | 9.31162i | −0.826847 | + | 0.724909i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.17558 | + | 6.17558i | −0.477881 | + | 0.477881i | −0.904453 | − | 0.426573i | \(-0.859721\pi\) |
0.426573 | + | 0.904453i | \(0.359721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9773i | − | 0.998256i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.24616i | 0.554128i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.66960 | + | 1.66960i | 0.126937 | + | 0.126937i | 0.767721 | − | 0.640784i | \(-0.221391\pi\) |
−0.640784 | + | 0.767721i | \(0.721391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.6212 | + | 16.4584i | 0.954076 | + | 1.24414i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.746625 | − | 0.746625i | 0.0561197 | − | 0.0561197i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.183978i | 0.0137512i | 0.999976 | + | 0.00687558i | \(0.00218858\pi\) | ||||
−0.999976 | + | 0.00687558i | \(0.997811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.17646i | − | 0.459092i | −0.973298 | − | 0.229546i | \(-0.926276\pi\) | ||
0.973298 | − | 0.229546i | \(-0.0737242\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.962192 | + | 0.962192i | −0.0711273 | + | 0.0711273i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.45173 | + | 3.93712i | 0.253776 | + | 0.289463i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3626 | + | 17.3626i | −1.26968 | + | 1.26968i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.14813 | −0.301732 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.64744i | 0.263919i | 0.991255 | + | 0.131960i | \(0.0421269\pi\) | ||||
−0.991255 | + | 0.131960i | \(0.957873\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0597192 | − | 0.0597192i | −0.00429868 | − | 0.00429868i | 0.704954 | − | 0.709253i | \(-0.250968\pi\) |
−0.709253 | + | 0.704954i | \(0.750968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0220692 | − | 0.335950i | 0.00158041 | − | 0.0240579i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.46537 | − | 7.46537i | 0.531886 | − | 0.531886i | −0.389248 | − | 0.921133i | \(-0.627265\pi\) |
0.921133 | + | 0.389248i | \(0.127265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.48802 | 0.247259 | 0.123630 | − | 0.992328i | \(-0.460547\pi\) | ||||
0.123630 | + | 0.992328i | \(0.460547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.09167i | − | 0.429673i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.1607 | + | 29.1607i | −2.04668 | + | 2.04668i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.4991 | − | 1.21524i | −1.29203 | − | 0.0848763i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.57269 | + | 4.53063i | 0.109310 | + | 0.314901i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 45.7729i | − | 3.16618i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5777 | −1.00357 | −0.501787 | − | 0.864991i | \(-0.667324\pi\) | ||||
−0.501787 | + | 0.864991i | \(0.667324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.60258 | + | 7.60258i | 0.520920 | + | 0.520920i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.4161 | − | 10.8854i | 0.846769 | − | 0.742375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8532 | + | 19.8532i | 1.34773 | + | 1.34773i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 8.04867i | − | 0.543879i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.585267i | − | 0.0393693i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.74761 | + | 9.74761i | 0.652748 | + | 0.652748i | 0.953654 | − | 0.300906i | \(-0.0972889\pi\) |
−0.300906 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.654098 | + | 4.95703i | −0.0436065 | + | 0.330469i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6157 | − | 12.6157i | −0.837330 | − | 0.837330i | 0.151176 | − | 0.988507i | \(-0.451694\pi\) |
−0.988507 | + | 0.151176i | \(0.951694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.80818 | 0.449897 | 0.224949 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224949 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.2031 | 1.72404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.92399 | − | 7.92399i | −0.519118 | − | 0.519118i | 0.398187 | − | 0.917304i | \(-0.369640\pi\) |
−0.917304 | + | 0.398187i | \(0.869640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.14477 | − | 6.26392i | 0.466073 | − | 0.408613i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.18622 | + | 4.18622i | 0.271924 | + | 0.271924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.60910i | − | 0.168768i | −0.996433 | − | 0.0843842i | \(-0.973108\pi\) | ||
0.996433 | − | 0.0843842i | \(-0.0268923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.5739i | − | 0.681123i | −0.940222 | − | 0.340562i | \(-0.889383\pi\) | ||
0.940222 | − | 0.340562i | \(-0.110617\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.49610 | − | 22.7744i | 0.0955823 | − | 1.45501i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.771467 | + | 0.771467i | 0.0490873 | + | 0.0490873i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.69811 | 0.424475 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.1440i | 1.20836i | 0.796849 | + | 0.604178i | \(0.206498\pi\) | ||||
−0.796849 | + | 0.604178i | \(0.793502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.93447 | − | 28.6193i | −0.624575 | − | 1.79928i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.569761 | + | 8.67321i | −0.0356798 | + | 0.543137i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1968 | + | 14.1968i | −0.885570 | + | 0.885570i | −0.994094 | − | 0.108524i | \(-0.965387\pi\) |
0.108524 | + | 0.994094i | \(0.465387\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.71324i | − | 0.603552i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.94170 | −0.615376 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.96207 | + | 6.96207i | −0.429299 | + | 0.429299i | −0.888390 | − | 0.459090i | \(-0.848175\pi\) |
0.459090 | + | 0.888390i | \(0.348175\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.8500 | − | 17.4028i | 1.21938 | − | 1.06905i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8331 | + | 10.8331i | 0.662973 | + | 0.662973i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7.98055i | − | 0.486583i | −0.969953 | − | 0.243291i | \(-0.921773\pi\) | ||
0.969953 | − | 0.243291i | \(-0.0782271\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.22574 | −0.499678 | −0.249839 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249839 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.441633 | + | 0.441633i | −0.0267289 | + | 0.0267289i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.13184 | − | 31.3128i | 0.249159 | − | 1.88823i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.4074 | − | 21.4074i | 1.28625 | − | 1.28625i | 0.349200 | − | 0.937048i | \(-0.386453\pi\) |
0.937048 | − | 0.349200i | \(-0.113547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.76853i | 0.405221i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.1447i | − | 0.963114i | −0.876415 | − | 0.481557i | \(-0.840071\pi\) | ||
0.876415 | − | 0.481557i | \(-0.159929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.4428 | + | 18.4428i | −1.09631 | + | 1.09631i | −0.101470 | + | 0.994839i | \(0.532355\pi\) |
−0.994839 | + | 0.101470i | \(0.967645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.6815 | − | 12.1836i | −0.632718 | − | 0.721692i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.3186 | + | 24.3186i | 1.43548 | + | 1.43548i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.89017i | − | 0.111186i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.56827i | 0.267797i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.405108 | + | 0.405108i | −0.0236667 | + | 0.0236667i | −0.718841 | − | 0.695174i | \(-0.755327\pi\) |
0.695174 | + | 0.718841i | \(0.255327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.154768 | + | 2.35596i | −0.00901092 | + | 0.137169i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.46668 | + | 4.46668i | 0.259183 | + | 0.259183i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.649795 | + | 0.314919i | 0.0375786 | + | 0.0182122i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.6316 | −1.76558 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.92197 | − | 2.92197i | −0.167863 | − | 0.167863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.199453 | − | 3.03617i | 0.0114206 | − | 0.173851i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0982 | + | 10.0982i | −0.576335 | + | 0.576335i | −0.933891 | − | 0.357557i | \(-0.883610\pi\) |
0.357557 | + | 0.933891i | \(0.383610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0210663 | −0.00119842 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.6681 | −1.51221 | −0.756105 | − | 0.654451i | \(-0.772900\pi\) | ||||
−0.756105 | + | 0.654451i | \(0.772900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3355 | + | 20.3355i | −1.14943 | + | 1.14943i | −0.162764 | + | 0.986665i | \(0.552041\pi\) |
−0.986665 | + | 0.162764i | \(0.947959\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.97460 | − | 6.11473i | 0.392974 | − | 0.344526i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.6180 | − | 17.6180i | 0.989527 | − | 0.989527i | −0.0104187 | − | 0.999946i | \(-0.503316\pi\) |
0.999946 | + | 0.0104187i | \(0.00331643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 62.8002 | 3.51614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4168i | 0.693039i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.9169 | − | 19.9169i | −1.10821 | − | 1.10821i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.458114 | + | 0.597392i | 0.0254116 | + | 0.0331374i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.71067 | + | 5.71067i | 0.315801 | + | 0.315801i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.6268 | −0.971798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.3715 | 1.55944 | 0.779719 | − | 0.626130i | \(-0.215362\pi\) | ||||
0.779719 | + | 0.626130i | \(0.215362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65576 | − | 1.65576i | 0.0907350 | − | 0.0907350i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.97969 | + | 10.2424i | 0.490613 | + | 0.559604i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2664 | + | 10.2664i | 0.559247 | + | 0.559247i | 0.929093 | − | 0.369846i | \(-0.120589\pi\) |
−0.369846 | + | 0.929093i | \(0.620589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.20119 | 0.282490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 42.7557i | − | 2.31535i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.40665 | + | 9.40665i | −0.507911 | + | 0.507911i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.32288 | − | 5.29943i | −0.501927 | − | 0.285312i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0938 | − | 10.0938i | 0.541864 | − | 0.541864i | −0.382211 | − | 0.924075i | \(-0.624837\pi\) |
0.924075 | + | 0.382211i | \(0.124837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8622i | 1.06320i | 0.846996 | + | 0.531600i | \(0.178409\pi\) | ||||
−0.846996 | + | 0.531600i | \(0.821591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.150565 | −0.00803657 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.91280 | − | 6.91280i | −0.367931 | − | 0.367931i | 0.498791 | − | 0.866722i | \(-0.333777\pi\) |
−0.866722 | + | 0.498791i | \(0.833777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.9898 | − | 1.57594i | −1.27324 | − | 0.0836420i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.4016 | − | 11.4016i | 0.603439 | − | 0.603439i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.15659 | 0.0610427 | 0.0305213 | − | 0.999534i | \(-0.490283\pi\) | ||||
0.0305213 | + | 0.999534i | \(0.490283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.5068 | 1.76352 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.4372 | − | 20.4372i | −1.07267 | − | 1.07267i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.8645 | + | 13.5329i | 0.621016 | + | 0.708344i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0789 | − | 22.0789i | −1.15251 | − | 1.15251i | −0.986048 | − | 0.166460i | \(-0.946766\pi\) |
−0.166460 | − | 0.986048i | \(-0.553234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.29087i | 0.431606i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.9719 | −2.54249 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1301 | + | 19.1301i | −0.990520 | + | 0.990520i | −0.999955 | − | 0.00943553i | \(-0.996997\pi\) |
0.00943553 | + | 0.999955i | \(0.496997\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.20734 | − | 9.29887i | −0.320545 | − | 0.480192i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.05845 | + | 1.05845i | −0.0545129 | + | 0.0545129i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.43150 | −0.176264 | −0.0881321 | − | 0.996109i | \(-0.528090\pi\) | ||||
−0.0881321 | + | 0.996109i | \(0.528090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3797 | 0.787926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.46410 | + | 7.46410i | −0.381398 | + | 0.381398i | −0.871606 | − | 0.490208i | \(-0.836921\pi\) |
0.490208 | + | 0.871606i | \(0.336921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −44.0575 | + | 38.6258i | −2.24538 | + | 1.96855i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.22159 | − | 5.22159i | −0.265428 | − | 0.265428i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7776 | −1.20557 | −0.602786 | − | 0.797903i | \(-0.705943\pi\) | ||||
−0.602786 | + | 0.797903i | \(0.705943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7757 | − | 8.13025i | −0.848385 | − | 0.411165i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.53155 | − | 4.53155i | −0.228587 | − | 0.228587i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.2095 | − | 0.867760i | −0.664643 | − | 0.0436617i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5571 | + | 11.5571i | −0.580033 | + | 0.580033i | −0.934912 | − | 0.354880i | \(-0.884522\pi\) |
0.354880 | + | 0.934912i | \(0.384522\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0580i | 1.50478i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.76249i | − | 0.487516i | −0.969836 | − | 0.243758i | \(-0.921620\pi\) | ||
0.969836 | − | 0.243758i | \(-0.0783802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.720615 | + | 0.720615i | 0.0358964 | + | 0.0358964i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.23126 | + | 0.146576i | 0.110872 | + | 0.00728342i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4592 | + | 10.4592i | −0.518442 | + | 0.518442i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.98559i | 0.147628i | 0.997272 | + | 0.0738139i | \(0.0235171\pi\) | ||||
−0.997272 | + | 0.0738139i | \(0.976483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.817476i | 0.0403231i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.09710 | − | 3.09710i | 0.152398 | − | 0.152398i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.2621 | + | 9.87364i | −0.552834 | + | 0.484678i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.57839 | − | 3.57839i | 0.175234 | − | 0.175234i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.6516 | −1.79055 | −0.895275 | − | 0.445515i | \(-0.853021\pi\) | ||||
−0.895275 | + | 0.445515i | \(0.853021\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4164i | 1.28745i | 0.765255 | + | 0.643727i | \(0.222613\pi\) | ||||
−0.765255 | + | 0.643727i | \(0.777387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00474 | − | 3.00474i | −0.146095 | − | 0.146095i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8271 | − | 15.4229i | −0.573700 | − | 0.748119i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.99130 | + | 3.99130i | −0.193152 | + | 0.193152i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.951097 | 0.0459194 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.35855i | 0.113607i | 0.998385 | + | 0.0568037i | \(0.0180909\pi\) | ||||
−0.998385 | + | 0.0568037i | \(0.981909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.8910 | + | 18.8910i | −0.907845 | + | 0.907845i | −0.996098 | − | 0.0882534i | \(-0.971871\pi\) |
0.0882534 | + | 0.996098i | \(0.471871\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.7158 | − | 14.6550i | 0.801462 | − | 0.702653i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.8297 | − | 11.3960i | 1.57046 | − | 0.545144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9535i | 0.713692i | 0.934163 | + | 0.356846i | \(0.116148\pi\) | ||||
−0.934163 | + | 0.356846i | \(0.883852\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.2070 | −0.486047 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.13367 | + | 6.13367i | 0.291419 | + | 0.291419i | 0.837641 | − | 0.546221i | \(-0.183934\pi\) |
−0.546221 | + | 0.837641i | \(0.683934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.1835 | − | 2.24558i | −1.62045 | − | 0.106451i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.01141 | − | 9.01141i | −0.426225 | − | 0.426225i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.6266i | 1.06782i | 0.845543 | + | 0.533908i | \(0.179277\pi\) | ||||
−0.845543 | + | 0.533908i | \(0.820723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 52.3722i | − | 2.46611i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.66121 | − | 2.66121i | −0.125034 | − | 0.125034i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0915461 | − | 1.39356i | 0.00429175 | − | 0.0653313i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7282 | − | 13.7282i | −0.642178 | − | 0.642178i | 0.308912 | − | 0.951091i | \(-0.400035\pi\) |
−0.951091 | + | 0.308912i | \(0.900035\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.88714 | 0.181436 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.9835 | 1.07045 | 0.535224 | − | 0.844710i | \(-0.320227\pi\) | ||||
0.535224 | + | 0.844710i | \(0.320227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.97713 | − | 6.97713i | −0.324255 | − | 0.324255i | 0.526142 | − | 0.850397i | \(-0.323638\pi\) |
−0.850397 | + | 0.526142i | \(0.823638\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.97744 | − | 11.3805i | −0.462693 | − | 0.527757i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.22506 | − | 3.22506i | −0.149238 | − | 0.149238i | 0.628540 | − | 0.777778i | \(-0.283653\pi\) |
−0.777778 | + | 0.628540i | \(0.783653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 25.2690i | − | 1.16682i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.4961i | − | 0.990488i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.9840 | + | 32.9840i | 1.51660 | + | 1.51660i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.9194 | + | 4.73970i | 1.64810 | + | 0.217472i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.34794 | − | 8.34794i | −0.382226 | − | 0.382226i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7869 | 0.858394 | 0.429197 | − | 0.903211i | \(-0.358797\pi\) | ||||
0.429197 | + | 0.903211i | \(0.358797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.352563i | − | 0.0160755i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.52374 | + | 18.7937i | 0.296840 | + | 0.855141i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.73405 | − | 7.68101i | −0.305778 | − | 0.348777i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.126953 | − | 0.126953i | 0.00575279 | − | 0.00575279i | −0.704225 | − | 0.709977i | \(-0.748705\pi\) |
0.709977 | + | 0.704225i | \(0.248705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.56453i | 0.0707505i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3584 | −0.647987 | −0.323993 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323993 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.3260 | − | 27.3260i | 1.23070 | − | 1.23070i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.0945 | − | 0.925898i | −0.633501 | − | 0.0416160i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.5365 | + | 31.5365i | 1.41460 | + | 1.41460i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.7714i | − | 1.46705i | −0.679663 | − | 0.733525i | \(-0.737874\pi\) | ||
0.679663 | − | 0.733525i | \(-0.262126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.73359 | −0.390188 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.77769 | + | 1.77769i | −0.0792632 | + | 0.0792632i | −0.745627 | − | 0.666364i | \(-0.767850\pi\) |
0.666364 | + | 0.745627i | \(0.267850\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.22021 | + | 0.605695i | 0.410294 | + | 0.0269531i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.17636 | − | 9.17636i | 0.407536 | − | 0.407536i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.6802i | − | 0.783660i | −0.920038 | − | 0.391830i | \(-0.871842\pi\) | ||
0.920038 | − | 0.391830i | \(-0.128158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 33.3869i | − | 1.47695i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.12381 | + | 5.12381i | −0.226222 | + | 0.226222i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0354206 | − | 0.0310537i | 0.00156082 | − | 0.00136839i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.9805 | + | 18.9805i | 0.834760 | + | 0.834760i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.36117i | 0.103644i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.3631i | 0.892125i | 0.895002 | + | 0.446063i | \(0.147174\pi\) | ||||
−0.895002 | + | 0.446063i | \(0.852826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.12123 | + | 7.12123i | −0.311390 | + | 0.311390i | −0.845448 | − | 0.534058i | \(-0.820666\pi\) |
0.534058 | + | 0.845448i | \(0.320666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.71328 | + | 20.5624i | −0.118417 | + | 0.897417i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.6041 | − | 18.6041i | −0.810408 | − | 0.810408i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.0533 | − | 14.2506i | 0.784925 | − | 0.619591i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.05589 | 0.0458216 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.882693 | + | 0.882693i | 0.0382337 | + | 0.0382337i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.3035 | − | 20.8774i | −0.791331 | − | 0.902609i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.130092 | + | 0.130092i | −0.00561389 | + | 0.00561389i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 64.4760 | 2.77718 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.5846 | 1.52990 | 0.764950 | − | 0.644090i | \(-0.222764\pi\) | ||||
0.764950 | + | 0.644090i | \(0.222764\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.36742 | − | 4.36742i | 0.187424 | − | 0.187424i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0199 | − | 1.18376i | −0.771887 | − | 0.0507068i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8186 | − | 24.8186i | 1.06117 | − | 1.06117i | 0.0631656 | − | 0.998003i | \(-0.479880\pi\) |
0.998003 | − | 0.0631656i | \(-0.0201196\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.36075 | −0.0580752 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 72.0392i | 3.06897i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.3650 | + | 17.3650i | 0.738434 | + | 0.738434i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.343222 | + | 5.22471i | −0.0145690 | + | 0.221776i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.04871 | + | 4.04871i | 0.171549 | + | 0.171549i | 0.787660 | − | 0.616110i | \(-0.211292\pi\) |
−0.616110 | + | 0.787660i | \(0.711292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.11184 | −0.0470258 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.5544 | −1.03669 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.2808 | − | 13.2808i | 0.559718 | − | 0.559718i | −0.369509 | − | 0.929227i | \(-0.620474\pi\) |
0.929227 | + | 0.369509i | \(0.120474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.74519 | + | 7.66703i | −0.367913 | + | 0.322554i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.93317 | − | 2.93317i | −0.123182 | − | 0.123182i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.5541 | −1.07129 | −0.535643 | − | 0.844445i | \(-0.679931\pi\) | ||||
−0.535643 | + | 0.844445i | \(0.679931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.55410i | 0.106886i | 0.998571 | + | 0.0534428i | \(0.0170195\pi\) | ||||
−0.998571 | + | 0.0534428i | \(0.982981\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.57913 | + | 2.57913i | −0.107745 | + | 0.107745i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.4872 | − | 4.83242i | 0.979483 | − | 0.201526i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6735 | + | 23.6735i | −0.985542 | + | 0.985542i | −0.999897 | − | 0.0143549i | \(-0.995431\pi\) |
0.0143549 | + | 0.999897i | \(0.495431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 0.0844557i | − | 0.00350986i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.7846 | 1.15270 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.7326 | + | 52.7326i | 2.18396 | + | 2.18396i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.253158 | − | 0.221947i | 0.0104668 | − | 0.00917638i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.3244 | + | 30.3244i | −1.25162 | + | 1.25162i | −0.296632 | + | 0.954992i | \(0.595863\pi\) |
−0.954992 | + | 0.296632i | \(0.904137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.0458 | 2.02090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.5576 | 0.434283 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.87145 | − | 2.87145i | −0.117916 | − | 0.117916i | 0.645686 | − | 0.763603i | \(-0.276571\pi\) |
−0.763603 | + | 0.645686i | \(0.776571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.36344 | + | 35.9776i | −0.0968917 | + | 1.47494i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.46640 | + | 2.46640i | 0.100943 | + | 0.100943i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.4702i | 1.32670i | 0.748311 | + | 0.663348i | \(0.230865\pi\) | ||||
−0.748311 | + | 0.663348i | \(0.769135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.4240 | 0.710738 | 0.355369 | − | 0.934726i | \(-0.384355\pi\) | ||||
0.355369 | + | 0.934726i | \(0.384355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.30746 | − | 4.30746i | 0.175413 | − | 0.175413i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.4891 | + | 4.23642i | 2.62185 | + | 0.172235i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5614 | − | 11.5614i | 0.469264 | − | 0.469264i | −0.432412 | − | 0.901676i | \(-0.642337\pi\) |
0.901676 | + | 0.432412i | \(0.142337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −41.2395 | −1.67111 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.639802 | −0.0258836 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.08084 | − | 1.08084i | 0.0436548 | − | 0.0436548i | −0.684942 | − | 0.728597i | \(-0.740173\pi\) |
0.728597 | + | 0.684942i | \(0.240173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.2215 | − | 13.9401i | −0.492819 | − | 0.562121i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.85476 | − | 1.85476i | −0.0746698 | − | 0.0746698i | 0.668786 | − | 0.743455i | \(-0.266814\pi\) |
−0.743455 | + | 0.668786i | \(0.766814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3231 | −1.25898 | −0.629492 | − | 0.777007i | \(-0.716737\pi\) | ||||
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.09158 | + | 4.31570i | −0.0839322 | + | 0.173183i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.9370 | + | 44.9370i | 1.80036 | + | 1.80036i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1443 | + | 6.48477i | 0.965772 | + | 0.259391i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.3663 | − | 32.3663i | 1.29259 | − | 1.29259i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.10210i | 0.362925i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.5906i | − | 1.21779i | −0.793250 | − | 0.608896i | \(-0.791613\pi\) | ||
0.793250 | − | 0.608896i | \(-0.208387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3080 | − | 10.3080i | −0.409707 | − | 0.409707i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.8592 | + | 22.6711i | −1.02619 | + | 0.899676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.08669 | + | 1.08669i | −0.0430564 | + | 0.0430564i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.7517i | 0.425329i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 16.7055i | − | 0.659828i | −0.944011 | − | 0.329914i | \(-0.892980\pi\) | ||
0.944011 | − | 0.329914i | \(-0.107020\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0718 | + | 13.0718i | −0.515501 | + | 0.515501i | −0.916207 | − | 0.400706i | \(-0.868765\pi\) |
0.400706 | + | 0.916207i | \(0.368765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.4766 | + | 1.08238i | 0.648765 | + | 0.0426187i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7003 | − | 31.7003i | 1.24627 | − | 1.24627i | 0.288912 | − | 0.957356i | \(-0.406706\pi\) |
0.957356 | − | 0.288912i | \(-0.0932936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.66987 | −0.261815 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.0767i | 1.10041i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.2125 | + | 15.2125i | 0.595311 | + | 0.595311i | 0.939061 | − | 0.343750i | \(-0.111697\pi\) |
−0.343750 | + | 0.939061i | \(0.611697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2992 | + | 0.939344i | 0.558716 | + | 0.0367032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.69127 | − | 5.69127i | 0.222037 | − | 0.222037i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.36828 | 0.364936 | 0.182468 | − | 0.983212i | \(-0.441591\pi\) | ||||
0.182468 | + | 0.983212i | \(0.441591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 41.9718i | − | 1.63251i | −0.577689 | − | 0.816257i | \(-0.696045\pi\) | ||
0.577689 | − | 0.816257i | \(-0.303955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.413846 | − | 0.413846i | 0.0160725 | − | 0.0160725i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −44.3083 | − | 50.5390i | −1.71820 | − | 1.95982i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6353 | + | 45.0422i | 0.605400 | + | 1.74404i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.7852i | 0.532967i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.59562 | 0.331830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.5699 | − | 26.5699i | −1.02419 | − | 1.02419i | −0.999700 | − | 0.0244944i | \(-0.992202\pi\) |
−0.0244944 | − | 0.999700i | \(-0.507798\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.96767 | + | 3.04263i | −0.152716 | + | 0.117111i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5890 | + | 28.5890i | 1.09877 | + | 1.09877i | 0.994555 | + | 0.104210i | \(0.0332314\pi\) |
0.104210 | + | 0.994555i | \(0.466769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.9498i | 0.727225i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.8412i | − | 0.683677i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.7372 | − | 27.7372i | −1.06134 | − | 1.06134i | −0.997992 | − | 0.0633437i | \(-0.979824\pi\) |
−0.0633437 | − | 0.997992i | \(-0.520176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.20504 | − | 1.37449i | −0.0460421 | − | 0.0525166i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.81411 | + | 4.81411i | 0.183670 | + | 0.183670i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.77754 | −0.0677188 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0366 | −0.876355 | −0.438178 | − | 0.898888i | \(-0.644376\pi\) | ||||
−0.438178 | + | 0.898888i | \(0.644376\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.5284 | + | 18.5284i | 0.703835 | + | 0.703835i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.741763 | + | 11.2915i | −0.0281367 | + | 0.428311i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.7885 | − | 22.7885i | −0.863175 | − | 0.863175i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 11.2062i | − | 0.423858i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.7206i | − | 1.27361i | −0.771024 | − | 0.636806i | \(-0.780255\pi\) | ||
0.771024 | − | 0.636806i | \(-0.219745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9979 | − | 11.9979i | −0.452509 | − | 0.452509i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.48137 | + | 0.622851i | 0.357089 | + | 0.0234579i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1207 | − | 12.1207i | −0.455847 | − | 0.455847i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.943683 | −0.0354408 | −0.0177204 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177204 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.92020i | 0.222025i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.6657 | − | 10.6448i | 1.14844 | − | 0.398652i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.59916 | + | 1.40201i | −0.0598051 | + | 0.0524320i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.84491 | − | 1.84491i | 0.0688994 | − | 0.0688994i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.9715i | 0.558343i | 0.960241 | + | 0.279171i | \(0.0900597\pi\) | ||||
−0.960241 | + | 0.279171i | \(0.909940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0873859 | −0.00325442 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.47686 | − | 7.47686i | 0.278067 | − | 0.278067i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.50285 | + | 49.2813i | −0.241510 | + | 1.83026i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.05219 | − | 8.05219i | −0.298639 | − | 0.298639i | 0.541841 | − | 0.840481i | \(-0.317727\pi\) |
−0.840481 | + | 0.541841i | \(0.817727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.7043 | 1.06167 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.80288 | − | 7.80288i | 0.288206 | − | 0.288206i | −0.548165 | − | 0.836370i | \(-0.684673\pi\) |
0.836370 | + | 0.548165i | \(0.184673\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.1619 | − | 15.0461i | 0.633025 | − | 0.554982i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.2096 | + | 27.2096i | −1.00228 | + | 1.00228i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 33.5645i | − | 1.23469i | −0.786693 | − | 0.617344i | \(-0.788208\pi\) | ||
0.786693 | − | 0.617344i | \(-0.211792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.09102i | 0.0400796i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5754 | − | 14.5754i | 0.534721 | − | 0.534721i | −0.387252 | − | 0.921974i | \(-0.626576\pi\) |
0.921974 | + | 0.387252i | \(0.126576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.4353 | + | 1.86797i | 1.04179 | + | 0.0684372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.73628 | + | 4.73628i | 0.173291 | + | 0.173291i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.5065i | 1.88201i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.4139i | 1.54770i | 0.633366 | + | 0.773852i | \(0.281673\pi\) | ||||
−0.633366 | + | 0.773852i | \(0.718327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.5368 | + | 13.5368i | −0.493309 | + | 0.493309i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.39738 | + | 0.551641i | 0.305612 | + | 0.0200763i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.60003 | + | 2.60003i | 0.0944998 | + | 0.0944998i | 0.752776 | − | 0.658276i | \(-0.228714\pi\) |
−0.658276 | + | 0.752776i | \(0.728714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.2122 | − | 27.2616i | 0.479572 | − | 0.989535i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.88477 | −0.358323 | −0.179161 | − | 0.983820i | \(-0.557338\pi\) | ||||
−0.179161 | + | 0.983820i | \(0.557338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6886 | + | 23.6886i | 0.857585 | + | 0.857585i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.53577 | + | 5.73000i | −0.236301 | + | 0.207169i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.112416 | − | 0.112416i | 0.00405909 | − | 0.00405909i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.4565 | −1.27859 | −0.639297 | − | 0.768960i | \(-0.720775\pi\) | ||||
−0.639297 | + | 0.768960i | \(0.720775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0773 | −0.723065 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.54553 | − | 6.54553i | 0.235426 | − | 0.235426i | −0.579527 | − | 0.814953i | \(-0.696763\pi\) |
0.814953 | + | 0.579527i | \(0.196763\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.5518 | + | 4.42728i | 1.20522 | + | 0.159033i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.86830 | − | 6.86830i | 0.246399 | − | 0.246399i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 60.0770 | 2.15248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 67.9166i | − | 2.43025i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.02985 | − | 7.02985i | −0.251226 | − | 0.251226i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.6873 | + | 36.1432i | 1.13097 | + | 1.29001i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9311 | − | 11.9311i | −0.425296 | − | 0.425296i | 0.461726 | − | 0.887022i | \(-0.347230\pi\) |
−0.887022 | + | 0.461726i | \(0.847230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.84585 | −0.350522 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.5752 | 0.767126 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.144873 | + | 0.144873i | −0.00514458 | + | 0.00514458i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.3417 | + | 1.73044i | 0.934244 | + | 0.0613724i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.02206 | + | 3.02206i | 0.107047 | + | 0.107047i | 0.758602 | − | 0.651555i | \(-0.225883\pi\) |
−0.651555 | + | 0.758602i | \(0.725883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.5178 | 0.584356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3203i | 0.541315i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.9509 | + | 35.9509i | −1.26868 | + | 1.26868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.6725 | − | 21.9827i | −1.36303 | − | 0.774790i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.64310 | − | 5.64310i | 0.198646 | − | 0.198646i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6163i | 1.11157i | 0.831326 | + | 0.555785i | \(0.187582\pi\) | ||||
−0.831326 | + | 0.555785i | \(0.812418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.8020 | 1.85413 | 0.927064 | − | 0.374902i | \(-0.122324\pi\) | ||||
0.927064 | + | 0.374902i | \(0.122324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.81647 | − | 5.81647i | −0.203993 | − | 0.203993i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.30626 | − | 2.63057i | −0.0807849 | − | 0.0921450i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.8364 | + | 37.8364i | −1.32373 | + | 1.32373i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.624564 | −0.0218240 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0997 | −1.05049 | −0.525244 | − | 0.850952i | \(-0.676026\pi\) | ||||
−0.525244 | + | 0.850952i | \(0.676026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.1196 | + | 20.1196i | 0.701326 | + | 0.701326i | 0.964695 | − | 0.263369i | \(-0.0848337\pi\) |
−0.263369 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.0631 | − | 19.2198i | 0.872587 | − | 0.669149i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.4610 | − | 19.4610i | −0.676725 | − | 0.676725i | 0.282532 | − | 0.959258i | \(-0.408826\pi\) |
−0.959258 | + | 0.282532i | \(0.908826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.60357i | − | 0.229352i | −0.993403 | − | 0.114676i | \(-0.963417\pi\) | ||
0.993403 | − | 0.114676i | \(-0.0365829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.2747 | 1.05022 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.0551 | − | 28.0551i | 0.972053 | − | 0.972053i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.6845 | − | 12.8741i | 0.508178 | − | 0.445527i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.78607 | + | 4.78607i | −0.165431 | + | 0.165431i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.7680 | −1.51104 | −0.755520 | − | 0.655125i | \(-0.772616\pi\) | ||||
−0.755520 | + | 0.655125i | \(0.772616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −69.8374 | −2.40819 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.4160 | − | 11.4160i | 0.393190 | − | 0.393190i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.90217 | + | 28.9558i | −0.0654365 | + | 0.996109i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −84.7761 | − | 84.7761i | −2.91294 | − | 2.91294i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.0820 | −0.895133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1056 | − | 4.89763i | −0.346417 | − | 0.167889i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.3300 | − | 25.3300i | −0.867282 | − | 0.867282i | 0.124889 | − | 0.992171i | \(-0.460143\pi\) |
−0.992171 | + | 0.124889i | \(0.960143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.06211 | − | 16.1681i | 0.0363235 | − | 0.552936i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7542 | − | 13.7542i | 0.469834 | − | 0.469834i | −0.432027 | − | 0.901861i | \(-0.642201\pi\) |
0.901861 | + | 0.432027i | \(0.142201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5835i | 0.463464i | 0.972780 | + | 0.231732i | \(0.0744393\pi\) | ||||
−0.972780 | + | 0.231732i | \(0.925561\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.3916i | 1.17206i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.9035 | − | 16.9035i | −0.575404 | − | 0.575404i | 0.358230 | − | 0.933633i | \(-0.383380\pi\) |
−0.933633 | + | 0.358230i | \(0.883380\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.48059 | − | 3.97003i | −0.118343 | − | 0.134985i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.33655 | − | 1.33655i | 0.0453916 | − | 0.0453916i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 37.3970i | − | 1.26861i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.917193i | − | 0.0310779i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.23025 | + | 3.23025i | −0.109327 | + | 0.109327i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.7488 | − | 38.5729i | −0.870470 | − | 1.30400i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1266 | + | 24.1266i | −0.814697 | + | 0.814697i | −0.985334 | − | 0.170637i | \(-0.945418\pi\) |
0.170637 | + | 0.985334i | \(0.445418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.572910 | −0.0193238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.45862i | 0.284978i | 0.989796 | + | 0.142489i | \(0.0455106\pi\) | ||||
−0.989796 | + | 0.142489i | \(0.954489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9736 | + | 28.9736i | 0.975038 | + | 0.975038i | 0.999696 | − | 0.0246583i | \(-0.00784979\pi\) |
−0.0246583 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.77535 | + | 1.55648i | −0.0596777 | + | 0.0523204i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.8411 | + | 34.8411i | −1.16985 | + | 1.16985i | −0.187606 | + | 0.982244i | \(0.560073\pi\) |
−0.982244 | + | 0.187606i | \(0.939927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.7970 | 2.13968 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.31685i | 0.211622i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.7728 | + | 21.7728i | −0.728599 | + | 0.728599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0269668 | − | 0.410503i | 0.000901400 | − | 0.0137216i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.236793 | + | 0.682155i | 0.00790628 | + | 0.0227765i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.2907i | 2.24427i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.8906 | 1.52884 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.6598 | − | 21.6598i | −0.720794 | − | 0.720794i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.905320 | + | 13.7813i | −0.0300939 | + | 0.458105i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3992 | + | 12.3992i | 0.411708 | + | 0.411708i | 0.882333 | − | 0.470625i | \(-0.155972\pi\) |
−0.470625 | + | 0.882333i | \(0.655972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 4.13229i | − | 0.137059i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2952i | 0.374228i | 0.982338 | + | 0.187114i | \(0.0599134\pi\) | ||||
−0.982338 | + | 0.187114i | \(0.940087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.9183 | − | 29.9183i | −0.990153 | − | 0.990153i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.28793 | − | 2.00587i | 0.0756368 | − | 0.0663119i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.7975 | − | 18.7975i | −0.620747 | − | 0.620747i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.9795 | −1.08789 | −0.543946 | − | 0.839120i | \(-0.683070\pi\) | ||||
−0.543946 | + | 0.839120i | \(0.683070\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.2810 | −0.470575 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.14468 | + | 1.14468i | 0.0376777 | + | 0.0376777i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12462 | − | 9.29067i | −0.234256 | − | 0.305475i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0148961 | − | 0.0148961i | −0.000489254 | − | 0.000489254i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.3308i | 1.45445i | 0.686401 | + | 0.727224i | \(0.259190\pi\) | ||||
−0.686401 | + | 0.727224i | \(0.740810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 73.9615i | 2.42399i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8572 | − | 18.8572i | −0.617357 | − | 0.617357i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.2854 | − | 36.1955i | 1.35018 | − | 1.18372i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.5012 | + | 31.5012i | 1.02910 | + | 1.02910i | 0.999564 | + | 0.0295365i | \(0.00940311\pi\) |
0.0295365 | + | 0.999564i | \(0.490597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.7587 | −0.938505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2358i | 1.50724i | 0.657308 | + | 0.753622i | \(0.271695\pi\) | ||||
−0.657308 | + | 0.753622i | \(0.728305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.5629 | − | 13.0390i | 1.22322 | − | 0.424609i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.25555 | + | 0.608016i | 0.301083 | + | 0.0197788i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.5069 | − | 37.5069i | 1.21881 | − | 1.21881i | 0.250761 | − | 0.968049i | \(-0.419319\pi\) |
0.968049 | − | 0.250761i | \(-0.0806808\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.21185i | − | 0.0393383i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.9157 | 0.807945 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.45623 | − | 7.45623i | 0.241531 | − | 0.241531i | −0.575952 | − | 0.817483i | \(-0.695369\pi\) |
0.817483 | + | 0.575952i | \(0.195369\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.534627 | − | 8.13838i | 0.0173001 | − | 0.263352i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 44.4065 | + | 44.4065i | 1.43546 | + | 1.43546i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.39100i | 0.109501i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8129 | 0.477837 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.78001 | + | 8.78001i | −0.282932 | + | 0.282932i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.124496 | + | 0.142002i | 0.00400766 | + | 0.00457122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.7966 | + | 23.7966i | −0.765245 | + | 0.765245i | −0.977265 | − | 0.212020i | \(-0.931996\pi\) |
0.212020 | + | 0.977265i | \(0.431996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 28.1668i | − | 0.904848i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.0517i | − | 0.643489i | −0.946827 | − | 0.321744i | \(-0.895731\pi\) | ||
0.946827 | − | 0.321744i | \(-0.104269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8436 | − | 14.8436i | 0.475864 | − | 0.475864i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0984843 | + | 0.746356i | −0.00315402 | + | 0.0239025i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.1637 | + | 38.1637i | 1.22096 | + | 1.22096i | 0.967290 | + | 0.253673i | \(0.0816389\pi\) |
0.253673 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 96.7758i | − | 3.09297i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.07610i | 0.257850i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.33397 | − | 8.33397i | 0.265812 | − | 0.265812i | −0.561598 | − | 0.827410i | \(-0.689813\pi\) |
0.827410 | + | 0.561598i | \(0.189813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.7514 | + | 15.5629i | −0.565607 | + | 0.495876i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.4640 | − | 12.4640i | −0.396735 | − | 0.396735i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.4451 | + | 31.8691i | −0.491127 | + | 1.01338i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7694 | −0.850359 | −0.425179 | − | 0.905109i | \(-0.639789\pi\) | ||||
−0.425179 | + | 0.905109i | \(0.639789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0617 | + | 20.0617i | 0.636638 | + | 0.636638i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.78268 | − | 0.511260i | −0.246727 | − | 0.0162080i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5895 | − | 14.5895i | 0.462054 | − | 0.462054i | −0.437274 | − | 0.899328i | \(-0.644056\pi\) |
0.899328 | + | 0.437274i | \(0.144056\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.34160 | 0.0740848 |
(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 | 1380.2.t.a.1333.15 | yes | 48 | |
5.2 | odd | 4 | inner | 1380.2.t.a.1057.16 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1333.16 | yes | 48 | |
115.22 | even | 4 | inner | 1380.2.t.a.1057.15 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.15 | ✓ | 48 | 115.22 | even | 4 | inner | |
1380.2.t.a.1057.16 | yes | 48 | 5.2 | odd | 4 | inner | |
1380.2.t.a.1333.15 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1333.16 | yes | 48 | 23.22 | odd | 2 | inner |