Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(428,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.428");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.e (of order \(2\), degree \(1\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 53x^{10} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 428.12 | ||
Root | \(-1.41171 - 0.0841020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.428 |
Dual form | 429.2.e.d.428.9 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.168204i | 0.118938i | 0.998230 | + | 0.0594691i | \(0.0189408\pi\) | ||||
−0.998230 | + | 0.0594691i | \(0.981059\pi\) | |||||||
\(3\) | 1.20277 | + | 1.24634i | 0.694417 | + | 0.719573i | ||||
\(4\) | 1.97171 | 0.985854 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −0.209639 | + | 0.202310i | −0.0855847 | + | 0.0825927i | ||||
\(7\) | 2.38069 | 0.899815 | 0.449908 | − | 0.893075i | \(-0.351457\pi\) | ||||
0.449908 | + | 0.893075i | \(0.351457\pi\) | |||||||
\(8\) | 0.668057i | 0.236194i | ||||||||
\(9\) | −0.106712 | + | 2.99810i | −0.0355708 | + | 0.999367i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.31662i | − | 1.00000i | ||||||
\(12\) | 2.37150 | + | 2.45741i | 0.684593 | + | 0.709394i | ||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | 0.400441i | 0.107022i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.83105 | 0.957761 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −0.504293 | − | 0.0179494i | −0.118863 | − | 0.00423072i | ||||
\(19\) | −2.62042 | −0.601166 | −0.300583 | − | 0.953756i | \(-0.597181\pi\) | ||||
−0.300583 | + | 0.953756i | \(0.597181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.86341 | + | 2.96714i | 0.624847 | + | 0.647483i | ||||
\(22\) | 0.557869 | 0.118938 | ||||||||
\(23\) | − | 5.04638i | − | 1.05224i | −0.850409 | − | 0.526122i | \(-0.823646\pi\) | ||
0.850409 | − | 0.526122i | \(-0.176354\pi\) | |||||||
\(24\) | −0.832624 | + | 0.803516i | −0.169959 | + | 0.164017i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | − | 0.606468i | − | 0.118938i | ||||||
\(27\) | −3.86500 | + | 3.47301i | −0.743819 | + | 0.668381i | ||||
\(28\) | 4.69402 | 0.887086 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 1.98051i | 0.350108i | ||||||||
\(33\) | 4.13363 | − | 3.98912i | 0.719573 | − | 0.694417i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.210406 | + | 5.91138i | −0.0350676 | + | 0.985230i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | − | 0.440765i | − | 0.0715016i | ||||||
\(39\) | −4.33663 | − | 4.49373i | −0.694417 | − | 0.719573i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1682i | 1.90035i | 0.311712 | + | 0.950177i | \(0.399098\pi\) | ||||
−0.311712 | + | 0.950177i | \(0.600902\pi\) | |||||||
\(42\) | −0.499084 | + | 0.481636i | −0.0770104 | + | 0.0743181i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | − | 6.53941i | − | 0.985854i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.848821 | 0.125152 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 4.60785 | + | 4.77477i | 0.665085 | + | 0.689179i | ||||
\(49\) | −1.33233 | −0.190333 | ||||||||
\(50\) | − | 0.841020i | − | 0.118938i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.10909 | −0.985854 | ||||||||
\(53\) | − | 6.26509i | − | 0.860576i | −0.902692 | − | 0.430288i | \(-0.858412\pi\) | ||
0.902692 | − | 0.430288i | \(-0.141588\pi\) | |||||||
\(54\) | −0.584174 | − | 0.650108i | −0.0794961 | − | 0.0884684i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.59043i | 0.212531i | ||||||||
\(57\) | −3.15175 | − | 3.26593i | −0.417460 | − | 0.432583i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.254049 | + | 7.13754i | −0.0320071 | + | 0.899246i | ||||
\(64\) | 7.32896 | 0.916120 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.670986 | + | 0.695293i | 0.0825927 | + | 0.0855847i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.28949 | − | 6.06961i | 0.757166 | − | 0.730695i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −2.00290 | − | 0.0712899i | −0.236044 | − | 0.00840160i | ||||
\(73\) | 14.3201 | 1.67604 | 0.838021 | − | 0.545638i | \(-0.183713\pi\) | ||||
0.838021 | + | 0.545638i | \(0.183713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.01383 | − | 6.23169i | −0.694417 | − | 0.719573i | ||||
\(76\) | −5.16671 | −0.592662 | ||||||||
\(77\) | − | 7.89585i | − | 0.899815i | ||||||
\(78\) | 0.755864 | − | 0.729439i | 0.0855847 | − | 0.0825927i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.97722 | − | 0.639869i | −0.997469 | − | 0.0710966i | ||||
\(82\) | −2.04674 | −0.226025 | ||||||||
\(83\) | − | 10.1593i | − | 1.11512i | −0.830135 | − | 0.557562i | \(-0.811737\pi\) | ||
0.830135 | − | 0.557562i | \(-0.188263\pi\) | |||||||
\(84\) | 5.64580 | + | 5.85033i | 0.616007 | + | 0.638323i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.21569 | 0.236194 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.58369 | −0.899815 | ||||||||
\(92\) | − | 9.94999i | − | 1.03736i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.46838 | + | 2.38209i | −0.251928 | + | 0.243121i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 0.224103i | − | 0.0226378i | ||||||
\(99\) | 9.94358 | + | 0.353925i | 0.999367 | + | 0.0355708i | ||||
\(100\) | −9.85854 | −0.985854 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.30314 | −0.719600 | −0.359800 | − | 0.933029i | \(-0.617155\pi\) | ||||
−0.359800 | + | 0.933029i | \(0.617155\pi\) | |||||||
\(104\) | − | 2.40871i | − | 0.236194i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.05381 | 0.102355 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −7.62064 | + | 6.84776i | −0.733296 | + | 0.658926i | ||||
\(109\) | −19.5610 | −1.87360 | −0.936800 | − | 0.349866i | \(-0.886227\pi\) | ||||
−0.936800 | + | 0.349866i | \(0.886227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.12052 | 0.861808 | ||||||||
\(113\) | − | 21.2211i | − | 1.99632i | −0.0606667 | − | 0.998158i | \(-0.519323\pi\) | ||
0.0606667 | − | 0.998158i | \(-0.480677\pi\) | |||||||
\(114\) | 0.549342 | − | 0.530137i | 0.0514506 | − | 0.0496519i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.384757 | − | 10.8098i | 0.0355708 | − | 0.999367i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.1657 | + | 14.6355i | −1.36744 | + | 1.31964i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.20056 | − | 0.0427320i | −0.106955 | − | 0.00380687i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 5.19378i | 0.459070i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 8.15031 | − | 7.86538i | 0.709394 | − | 0.684593i | ||||
\(133\) | −6.23841 | −0.540938 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 1.02093 | + | 1.05792i | 0.0869076 | + | 0.0900559i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9583i | 1.00000i | ||||||||
\(144\) | −0.408820 | + | 11.4859i | −0.0340683 | + | 0.957155i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.40870i | 0.199345i | ||||||||
\(147\) | −1.60248 | − | 1.66053i | −0.132170 | − | 0.136958i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 16.1861i | − | 1.32601i | −0.748613 | − | 0.663007i | \(-0.769280\pi\) | ||
0.748613 | − | 0.663007i | \(-0.230720\pi\) | |||||||
\(150\) | 1.04819 | − | 1.01155i | 0.0855847 | − | 0.0825927i | ||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | − | 1.75059i | − | 0.141992i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.32811 | 0.107022 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.55057 | − | 8.86033i | −0.684593 | − | 0.709394i | ||||
\(157\) | 15.2466 | 1.21681 | 0.608404 | − | 0.793628i | \(-0.291810\pi\) | ||||
0.608404 | + | 0.793628i | \(0.291810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.80841 | − | 7.53543i | 0.619247 | − | 0.597598i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.0139i | − | 0.946824i | ||||||
\(162\) | 0.107629 | − | 1.51000i | 0.00845609 | − | 0.118637i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 23.9921i | 1.87347i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.70883 | 0.132631 | ||||||||
\(167\) | 25.6168i | 1.98228i | 0.132804 | + | 0.991142i | \(0.457602\pi\) | ||||
−0.132804 | + | 0.991142i | \(0.542398\pi\) | |||||||
\(168\) | −1.98222 | + | 1.91292i | −0.152931 | + | 0.147585i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.279632 | − | 7.85629i | 0.0213840 | − | 0.600786i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9034 | −0.899815 | ||||||||
\(176\) | − | 12.7061i | − | 0.957761i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.9165i | 1.78760i | 0.448461 | + | 0.893802i | \(0.351972\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.10085 | 0.453473 | 0.226736 | − | 0.973956i | \(-0.427194\pi\) | ||||
0.226736 | + | 0.973956i | \(0.427194\pi\) | |||||||
\(182\) | − | 1.44381i | − | 0.107022i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.37127 | 0.248533 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.20134 | + | 8.26815i | −0.669299 | + | 0.601420i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0082i | 1.44774i | 0.689935 | + | 0.723871i | \(0.257639\pi\) | ||||
−0.689935 | + | 0.723871i | \(0.742361\pi\) | |||||||
\(192\) | 8.81502 | + | 9.13436i | 0.636169 | + | 0.659215i | ||||
\(193\) | 21.4983 | 1.54748 | 0.773742 | − | 0.633501i | \(-0.218383\pi\) | ||||
0.773742 | + | 0.633501i | \(0.218383\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.62696 | −0.187640 | ||||||||
\(197\) | 24.6075i | 1.75321i | 0.481207 | + | 0.876607i | \(0.340199\pi\) | ||||
−0.481207 | + | 0.876607i | \(0.659801\pi\) | |||||||
\(198\) | −0.0595316 | + | 1.67255i | −0.00423072 | + | 0.118863i | ||||
\(199\) | 23.8812 | 1.69290 | 0.846448 | − | 0.532471i | \(-0.178736\pi\) | ||||
0.846448 | + | 0.532471i | \(0.178736\pi\) | |||||||
\(200\) | − | 3.34028i | − | 0.236194i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 1.22842i | − | 0.0855879i | ||||||
\(207\) | 15.1296 | + | 0.538511i | 1.05158 | + | 0.0374291i | ||||
\(208\) | −13.8130 | −0.957761 | ||||||||
\(209\) | 8.69096i | 0.601166i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | − | 12.3529i | − | 0.848402i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.32017 | − | 2.58204i | −0.157868 | − | 0.175685i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 3.29023i | − | 0.222842i | ||||||
\(219\) | 17.2237 | + | 17.8477i | 1.16387 | + | 1.20603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 4.71498i | 0.315033i | ||||||||
\(225\) | 0.533562 | − | 14.9905i | 0.0355708 | − | 0.999367i | ||||
\(226\) | 3.56948 | 0.237438 | ||||||||
\(227\) | − | 26.2896i | − | 1.74490i | −0.488703 | − | 0.872450i | \(-0.662530\pi\) | ||
0.488703 | − | 0.872450i | \(-0.337470\pi\) | |||||||
\(228\) | −6.21433 | − | 6.43946i | −0.411554 | − | 0.426464i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.84089 | − | 9.49685i | 0.647483 | − | 0.624847i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 1.81825 | + | 0.0647176i | 0.118863 | + | 0.00423072i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.2711i | − | 1.56997i | −0.619515 | − | 0.784984i | \(-0.712671\pi\) | ||
0.619515 | − | 0.784984i | \(-0.287329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −31.0211 | −1.99824 | −0.999122 | − | 0.0419050i | \(-0.986657\pi\) | ||||
−0.999122 | + | 0.0419050i | \(0.986657\pi\) | |||||||
\(242\) | − | 1.85024i | − | 0.118938i | ||||||
\(243\) | −10.0000 | − | 11.9583i | −0.641500 | − | 0.767123i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.46175 | − | 2.55093i | −0.156955 | − | 0.162641i | ||||
\(247\) | 9.44807 | 0.601166 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6619 | − | 12.2192i | 0.802414 | − | 0.774361i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.9308i | 1.95234i | 0.217014 | + | 0.976169i | \(0.430368\pi\) | ||||
−0.217014 | + | 0.976169i | \(0.569632\pi\) | |||||||
\(252\) | −0.500910 | + | 14.0731i | −0.0315544 | + | 0.886525i | ||||
\(253\) | −16.7370 | −1.05224 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7843 | 0.861519 | ||||||||
\(257\) | − | 2.19692i | − | 0.137040i | −0.997650 | − | 0.0685200i | \(-0.978172\pi\) | ||
0.997650 | − | 0.0685200i | \(-0.0218277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 2.66496 | + | 2.76150i | 0.164017 | + | 0.169959i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 1.04932i | − | 0.0643382i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.0814i | 1.71215i | 0.516850 | + | 0.856076i | \(0.327104\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.2606 | 1.89895 | 0.949474 | − | 0.313845i | \(-0.101617\pi\) | ||||
0.949474 | + | 0.313845i | \(0.101617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3242 | − | 10.6982i | −0.624847 | − | 0.647483i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5831i | 1.00000i | ||||||||
\(276\) | 12.4010 | − | 11.9675i | 0.746455 | − | 0.720359i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6260i | 1.58837i | 0.607674 | + | 0.794187i | \(0.292103\pi\) | ||||
−0.607674 | + | 0.794187i | \(0.707897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.01143 | −0.118938 | ||||||||
\(287\) | 28.9687i | 1.70997i | ||||||||
\(288\) | −5.93777 | − | 0.211345i | −0.349887 | − | 0.0124536i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28.2351 | 1.65233 | ||||||||
\(293\) | − | 26.5330i | − | 1.55007i | −0.631916 | − | 0.775037i | \(-0.717731\pi\) | ||
0.631916 | − | 0.775037i | \(-0.282269\pi\) | |||||||
\(294\) | 0.279308 | − | 0.269543i | 0.0162896 | − | 0.0157201i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.5187 | + | 12.8187i | 0.668381 | + | 0.743819i | ||||
\(298\) | 2.72256 | 0.157714 | ||||||||
\(299\) | 18.1950i | 1.05224i | ||||||||
\(300\) | −11.8575 | − | 12.2871i | −0.684593 | − | 0.709394i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.42587i | 0.139593i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.0390 | −0.575774 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.8444 | −1.64624 | −0.823119 | − | 0.567869i | \(-0.807768\pi\) | ||||
−0.823119 | + | 0.567869i | \(0.807768\pi\) | |||||||
\(308\) | − | 15.5683i | − | 0.887086i | ||||||
\(309\) | −8.78396 | − | 9.10218i | −0.499702 | − | 0.517805i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.9642i | 1.98264i | 0.131470 | + | 0.991320i | \(0.458030\pi\) | ||||
−0.131470 | + | 0.991320i | \(0.541970\pi\) | |||||||
\(312\) | 3.00207 | − | 2.89712i | 0.169959 | − | 0.164017i | ||||
\(313\) | −32.4139 | −1.83214 | −0.916072 | − | 0.401014i | \(-0.868658\pi\) | ||||
−0.916072 | + | 0.401014i | \(0.868658\pi\) | |||||||
\(314\) | 2.56453i | 0.144725i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 1.26749 | + | 1.31341i | 0.0710772 | + | 0.0736521i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.02078 | 0.112614 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −17.7005 | − | 1.26163i | −0.983359 | − | 0.0700908i | ||||
\(325\) | 18.0278 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.5272 | − | 24.3795i | −1.30106 | − | 1.34819i | ||||
\(328\) | −8.12905 | −0.448852 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | − | 20.0311i | − | 1.09935i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.30884 | −0.235769 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.9698 | + | 11.3672i | 0.598454 | + | 0.620134i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 2.18665i | 0.118938i | ||||||||
\(339\) | 26.4487 | − | 25.5240i | 1.43650 | − | 1.38628i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.32146 | + | 0.0470351i | 0.0714564 | + | 0.00254337i | ||||
\(343\) | −19.8367 | −1.07108 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.7825 | 1.91539 | 0.957695 | − | 0.287784i | \(-0.0929185\pi\) | ||||
0.957695 | + | 0.287784i | \(0.0929185\pi\) | |||||||
\(350\) | − | 2.00221i | − | 0.107022i | ||||||
\(351\) | 13.9354 | − | 12.5221i | 0.743819 | − | 0.668381i | ||||
\(352\) | 6.56861 | 0.350108 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.02285 | −0.212614 | ||||||||
\(359\) | 6.14141i | 0.324131i | 0.986780 | + | 0.162066i | \(0.0518156\pi\) | ||||
−0.986780 | + | 0.162066i | \(0.948184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1334 | −0.638599 | ||||||||
\(362\) | 1.02619i | 0.0539352i | ||||||||
\(363\) | −13.2304 | − | 13.7097i | −0.694417 | − | 0.719573i | ||||
\(364\) | −16.9245 | −0.887086 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 38.3144 | 2.00000 | 0.999998 | − | 0.00174352i | \(-0.000554980\pi\) | ||||
0.999998 | + | 0.00174352i | \(0.000554980\pi\) | |||||||
\(368\) | − | 19.3329i | − | 1.00780i | ||||||
\(369\) | −36.4815 | − | 1.29850i | −1.89915 | − | 0.0675971i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 14.9152i | − | 0.774359i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.39074 | − | 1.54770i | −0.0715318 | − | 0.0796052i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.36546 | −0.172192 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −6.47320 | + | 6.24690i | −0.330334 | + | 0.318786i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.61610i | 0.184055i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 36.1772i | − | 1.83426i | −0.398593 | − | 0.917128i | \(-0.630501\pi\) | ||
0.398593 | − | 0.917128i | \(-0.369499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 0.890072i | − | 0.0449554i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.13909 | −0.208524 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 19.6058 | + | 0.697836i | 0.985230 | + | 0.0350676i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 4.01692i | 0.201350i | ||||||||
\(399\) | −7.50334 | − | 7.77516i | −0.375637 | − | 0.389245i | ||||
\(400\) | −19.1552 | −0.957761 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.21110 | −0.356566 | −0.178283 | − | 0.983979i | \(-0.557054\pi\) | ||||
−0.178283 | + | 0.983979i | \(0.557054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.3997 | −0.709420 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0905798 | + | 2.54485i | −0.00445175 | + | 0.125073i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 7.14083i | − | 0.350108i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.46185 | −0.0715016 | ||||||||
\(419\) | − | 10.7453i | − | 0.524943i | −0.964940 | − | 0.262471i | \(-0.915462\pi\) | ||
0.964940 | − | 0.262471i | \(-0.0845375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.18543 | 0.203263 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.9040 | + | 14.3830i | −0.719573 | + | 0.694417i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.4957i | 1.66160i | 0.556573 | + | 0.830799i | \(0.312116\pi\) | ||||
−0.556573 | + | 0.830799i | \(0.687884\pi\) | |||||||
\(432\) | −14.8070 | + | 13.3053i | −0.712401 | + | 0.640150i | ||||
\(433\) | −37.1987 | −1.78766 | −0.893828 | − | 0.448411i | \(-0.851990\pi\) | ||||
−0.893828 | + | 0.448411i | \(0.851990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.5685 | −1.84709 | ||||||||
\(437\) | 13.2237i | 0.632573i | ||||||||
\(438\) | −3.00205 | + | 2.89710i | −0.143444 | + | 0.138429i | ||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.142176 | − | 3.99446i | 0.00677029 | − | 0.190212i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 41.0236i | − | 1.94909i | −0.224192 | − | 0.974545i | \(-0.571974\pi\) | ||
0.224192 | − | 0.974545i | \(-0.428026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.1733 | − | 19.4680i | 0.954164 | − | 0.920806i | ||||
\(448\) | 17.4480 | 0.824339 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 2.52146 | + | 0.0897472i | 0.118863 | + | 0.00423072i | ||||
\(451\) | 40.3573 | 1.90035 | ||||||||
\(452\) | − | 41.8419i | − | 1.96808i | ||||||
\(453\) | 17.3465 | + | 17.9749i | 0.815011 | + | 0.844536i | ||||
\(454\) | 4.42201 | 0.207535 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.18183 | − | 2.10555i | 0.102173 | − | 0.0986014i | ||||
\(457\) | −3.83841 | −0.179553 | −0.0897767 | − | 0.995962i | \(-0.528615\pi\) | ||||
−0.0897767 | + | 0.995962i | \(0.528615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 23.2619i | − | 1.08342i | −0.840567 | − | 0.541708i | \(-0.817778\pi\) | ||
0.840567 | − | 0.541708i | \(-0.182222\pi\) | |||||||
\(462\) | 1.59741 | + | 1.65528i | 0.0743181 | + | 0.0770104i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.9165i | 1.10672i | 0.832941 | + | 0.553362i | \(0.186655\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0.758628 | − | 21.3138i | 0.0350676 | − | 0.985230i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3380 | + | 19.0023i | 0.844972 | + | 0.875582i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1021 | 0.601166 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.7834 | + | 0.668562i | 0.860031 | + | 0.0306114i | ||||
\(478\) | 4.08250 | 0.186729 | ||||||||
\(479\) | − | 6.63325i | − | 0.303081i | −0.988451 | − | 0.151540i | \(-0.951577\pi\) | ||
0.988451 | − | 0.151540i | \(-0.0484234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 5.21787i | − | 0.237667i | ||||||
\(483\) | 14.9733 | − | 14.4498i | 0.681309 | − | 0.657491i | ||||
\(484\) | −21.6888 | −0.985854 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.01143 | − | 1.68204i | 0.0912402 | − | 0.0762989i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −29.9023 | + | 28.8569i | −1.34810 | + | 1.30097i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.58920i | 0.0715016i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.05532 | + | 2.12978i | 0.0921011 | + | 0.0954376i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.9271 | + | 30.8109i | −1.42640 | + | 1.37653i | ||||
\(502\) | −5.20269 | −0.232207 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −4.76828 | − | 0.169719i | −0.212396 | − | 0.00755989i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.81522i | − | 0.125152i | ||||||
\(507\) | 15.6359 | + | 16.2024i | 0.694417 | + | 0.719573i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.0917 | 1.50813 | ||||||||
\(512\) | 12.7061i | 0.561537i | ||||||||
\(513\) | 10.1279 | − | 9.10076i | 0.447159 | − | 0.401808i | ||||
\(514\) | 0.369530 | 0.0162993 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.7803i | 1.47994i | 0.672639 | + | 0.739971i | \(0.265161\pi\) | ||||
−0.672639 | + | 0.739971i | \(0.734839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.3170 | − | 14.8357i | −0.624847 | − | 0.647483i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 15.8361 | − | 15.2825i | 0.689179 | − | 0.665085i | ||||
\(529\) | −2.46597 | −0.107216 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3003 | −0.533286 | ||||||||
\(533\) | − | 43.8731i | − | 1.90035i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.8080 | + | 28.7660i | −1.28631 | + | 1.24134i | ||||
\(538\) | −4.72340 | −0.203640 | ||||||||
\(539\) | 4.41884i | 0.190333i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.21421 | 0.310163 | 0.155081 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155081 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(542\) | 5.25816i | 0.225857i | ||||||||
\(543\) | 7.33789 | + | 7.60372i | 0.314899 | + | 0.326307i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.79947 | − | 1.73656i | 0.0770104 | − | 0.0743181i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.78935 | −0.118938 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.05485 | + | 4.20174i | 0.172586 | + | 0.178838i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 32.4867i | − | 1.37651i | −0.725470 | − | 0.688254i | \(-0.758378\pi\) | ||
0.725470 | − | 0.688254i | \(-0.241622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.47860 | −0.188918 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.3720 | − | 1.52333i | −0.897538 | − | 0.0639738i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 23.5782i | 0.985854i | ||||||||
\(573\) | −24.9370 | + | 24.0652i | −1.04176 | + | 1.00534i | ||||
\(574\) | −4.87265 | −0.203380 | ||||||||
\(575\) | 25.2319i | 1.05224i | ||||||||
\(576\) | −0.782091 | + | 21.9730i | −0.0325871 | + | 0.915540i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | − | 2.85947i | − | 0.118938i | ||||||
\(579\) | 25.8574 | + | 26.7942i | 1.07460 | + | 1.11353i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 24.1860i | − | 1.00341i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.7789 | −0.860576 | ||||||||
\(584\) | 9.56665i | 0.395871i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.46296 | 0.184363 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −3.15962 | − | 3.27408i | −0.130301 | − | 0.135021i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.6693 | + | 29.5971i | −1.26157 | + | 1.21746i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.13248i | − | 0.169701i | −0.996394 | − | 0.0848503i | \(-0.972959\pi\) | ||
0.996394 | − | 0.0848503i | \(-0.0270412\pi\) | |||||||
\(594\) | −2.15616 | + | 1.93749i | −0.0884684 | + | 0.0794961i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 31.9142i | − | 1.30726i | ||||||
\(597\) | 28.7235 | + | 29.7641i | 1.17558 | + | 1.21816i | ||||
\(598\) | −3.06047 | −0.125152 | ||||||||
\(599\) | − | 9.90389i | − | 0.404662i | −0.979317 | − | 0.202331i | \(-0.935148\pi\) | ||
0.979317 | − | 0.202331i | \(-0.0648517\pi\) | |||||||
\(600\) | 4.16312 | − | 4.01758i | 0.169959 | − | 0.164017i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.4364 | 1.15706 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | − | 5.18978i | − | 0.210473i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.2012 | 1.94683 | 0.973413 | − | 0.229056i | \(-0.0735639\pi\) | ||||
0.973413 | + | 0.229056i | \(0.0735639\pi\) | |||||||
\(614\) | − | 4.85174i | − | 0.195800i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.27487 | 0.212531 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 1.53102 | − | 1.47750i | 0.0615867 | − | 0.0594337i | ||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.5261 | + | 19.5042i | 0.703300 | + | 0.782678i | ||||
\(622\) | −5.88112 | −0.235812 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.6138 | − | 17.2157i | −0.665085 | − | 0.689179i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | − | 5.45215i | − | 0.217912i | ||||||
\(627\) | −10.8319 | + | 10.4532i | −0.432583 | + | 0.417460i | ||||
\(628\) | 30.0617 | 1.19959 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.3959 | − | 14.8577i | 0.610487 | − | 0.589144i | ||||
\(637\) | 4.80378 | 0.190333 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 38.1741i | − | 1.50779i | −0.656996 | − | 0.753894i | \(-0.728173\pi\) | ||
0.656996 | − | 0.753894i | \(-0.271827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | − | 23.6878i | − | 0.933430i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.9203i | 1.96257i | 0.192564 | + | 0.981284i | \(0.438320\pi\) | ||||
−0.192564 | + | 0.981284i | \(0.561680\pi\) | |||||||
\(648\) | 0.427469 | − | 5.99730i | 0.0167926 | − | 0.235596i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.03234i | 0.118938i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.8330i | − | 1.87185i | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||
0.352197 | − | 0.935926i | \(-0.385435\pi\) | |||||||
\(654\) | 4.10074 | − | 3.95737i | 0.160351 | − | 0.154746i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 46.6169i | 1.82008i | ||||||||
\(657\) | −1.52813 | + | 42.9331i | −0.0596181 | + | 1.67498i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.78697 | 0.263386 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 50.5088i | 1.95424i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.87645 | + | 5.67101i | −0.226689 | + | 0.218764i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.3250 | − | 17.3651i | 0.743819 | − | 0.668381i | ||||
\(676\) | 25.6322 | 0.985854 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 4.29324 | + | 4.44877i | 0.164881 | + | 0.170854i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32.7657 | − | 31.6202i | 1.25558 | − | 1.21169i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0.551352 | − | 15.4903i | 0.0210815 | − | 0.592287i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 3.33661i | − | 0.127392i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.5891i | 0.860576i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.6725 | + | 0.842584i | 0.899246 | + | 0.0320071i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.01875i | 0.227813i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.4701 | −0.887086 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 2.10627 | + | 2.34400i | 0.0794961 | + | 0.0884684i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 24.3074i | − | 0.916120i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 47.1564i | 1.76232i | ||||||||
\(717\) | 30.2500 | − | 29.1925i | 1.12971 | − | 1.09021i | ||||
\(718\) | −1.03301 | −0.0385516 | ||||||||
\(719\) | 23.9165i | 0.891936i | 0.895049 | + | 0.445968i | \(0.147140\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.3865 | −0.647507 | ||||||||
\(722\) | − | 2.04088i | − | 0.0759538i | ||||||
\(723\) | −37.3111 | − | 38.6627i | −1.38761 | − | 1.43788i | ||||
\(724\) | 12.0291 | 0.447058 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.30603 | − | 2.22541i | 0.0855847 | − | 0.0825927i | ||||
\(727\) | −9.86424 | −0.365844 | −0.182922 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182922 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(728\) | − | 5.73439i | − | 0.212531i | ||||||
\(729\) | 2.87637 | − | 26.8463i | 0.106532 | − | 0.994309i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.3052 | −1.67339 | −0.836693 | − | 0.547672i | \(-0.815514\pi\) | ||||
−0.836693 | + | 0.547672i | \(0.815514\pi\) | |||||||
\(734\) | 6.44464i | 0.237876i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.99441 | 0.368399 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.218412 | − | 6.13633i | 0.00803987 | − | 0.225882i | ||||
\(739\) | −50.1387 | −1.84438 | −0.922191 | − | 0.386734i | \(-0.873603\pi\) | ||||
−0.922191 | + | 0.386734i | \(0.873603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3638 | + | 11.7755i | 0.417460 | + | 0.432583i | ||||
\(742\) | 2.50880 | 0.0921009 | ||||||||
\(743\) | 33.1662i | 1.21675i | 0.793649 | + | 0.608376i | \(0.208179\pi\) | ||||
−0.793649 | + | 0.608376i | \(0.791821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.4585 | + | 1.08412i | 1.11442 | + | 0.0396659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.7476 | 1.92479 | 0.962394 | − | 0.271658i | \(-0.0875720\pi\) | ||||
0.962394 | + | 0.271658i | \(0.0875720\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38.5502 | + | 37.2025i | −1.40485 | + | 1.35574i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.1424 | + | 16.3024i | −0.659831 | + | 0.592912i | ||||
\(757\) | 17.8077 | 0.647230 | 0.323615 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323615 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.1306 | − | 20.8599i | −0.730695 | − | 0.757166i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 44.5403i | − | 1.61459i | −0.590151 | − | 0.807293i | \(-0.700932\pi\) | ||
0.590151 | − | 0.807293i | \(-0.299068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.5685 | −1.68589 | ||||||||
\(764\) | 39.4503i | 1.42726i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 16.5793 | + | 17.1799i | 0.598253 | + | 0.619926i | ||||
\(769\) | −2.45283 | −0.0884514 | −0.0442257 | − | 0.999022i | \(-0.514082\pi\) | ||||
−0.0442257 | + | 0.999022i | \(0.514082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.73810 | − | 2.64238i | 0.0986103 | − | 0.0951628i | ||||
\(772\) | 42.3884 | 1.52559 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.08514 | 0.218163 | ||||||||
\(779\) | − | 31.8858i | − | 1.14243i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.10421 | −0.182293 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.9001 | 1.95698 | 0.978488 | − | 0.206302i | \(-0.0661428\pi\) | ||||
0.978488 | + | 0.206302i | \(0.0661428\pi\) | |||||||
\(788\) | 48.5189i | 1.72841i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 50.5209i | − | 1.79632i | ||||||
\(792\) | −0.236442 | + | 6.64288i | −0.00840160 | + | 0.236044i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 47.0868 | 1.66895 | ||||||||
\(797\) | − | 47.8330i | − | 1.69433i | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||
0.531327 | − | 0.847167i | \(-0.321693\pi\) | |||||||
\(798\) | 1.30781 | − | 1.26209i | 0.0462961 | − | 0.0446775i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 9.90255i | − | 0.350108i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 47.4944i | − | 1.67604i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.9989 | + | 33.7753i | −1.23202 | + | 1.18895i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6160 | 1.42622 | 0.713110 | − | 0.701052i | \(-0.247286\pi\) | ||||
0.713110 | + | 0.701052i | \(0.247286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.5992 | + | 38.9613i | 1.31866 | + | 1.36643i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 1.21294i | − | 0.0424093i | ||||||
\(819\) | 0.915986 | − | 25.7348i | 0.0320071 | − | 0.899246i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.0660i | 1.85202i | 0.377504 | + | 0.926008i | \(0.376783\pi\) | ||||
−0.377504 | + | 0.926008i | \(0.623217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −56.2442 | −1.96055 | −0.980274 | − | 0.197641i | \(-0.936672\pi\) | ||||
−0.980274 | + | 0.197641i | \(0.936672\pi\) | |||||||
\(824\) | − | 4.87891i | − | 0.169965i | ||||||
\(825\) | −20.6682 | + | 19.9456i | −0.719573 | + | 0.694417i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.2527i | − | 0.773802i | −0.922121 | − | 0.386901i | \(-0.873546\pi\) | ||
0.922121 | − | 0.386901i | \(-0.126454\pi\) | |||||||
\(828\) | 29.8311 | + | 1.06179i | 1.03670 | + | 0.0368996i | ||||
\(829\) | 13.9660 | 0.485059 | 0.242530 | − | 0.970144i | \(-0.422023\pi\) | ||||
0.242530 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.4249 | −0.916120 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.1360i | 0.592662i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.80740 | 0.0624357 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.1850 | + | 32.0248i | −1.14295 | + | 1.10299i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.1876 | −0.899815 | ||||||||
\(848\) | − | 24.0018i | − | 0.824226i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7195 | −1.29149 | −0.645745 | − | 0.763553i | \(-0.723453\pi\) | ||||
−0.645745 | + | 0.763553i | \(0.723453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | −2.41927 | − | 2.50692i | −0.0825927 | − | 0.0855847i | ||||
\(859\) | −26.1127 | −0.890955 | −0.445477 | − | 0.895293i | \(-0.646966\pi\) | ||||
−0.445477 | + | 0.895293i | \(0.646966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.1047 | + | 34.8425i | −1.23045 | + | 1.18743i | ||||
\(862\) | −5.80231 | −0.197627 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −6.87834 | − | 7.65466i | −0.234006 | − | 0.260417i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 6.25697i | − | 0.212620i | ||||||
\(867\) | −20.4470 | − | 21.1877i | −0.694417 | − | 0.719573i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 13.0678i | − | 0.442533i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.22427 | −0.0752371 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.9601 | + | 35.1904i | 1.14741 | + | 1.18897i | ||||
\(877\) | −1.40243 | −0.0473567 | −0.0236784 | − | 0.999720i | \(-0.507538\pi\) | ||||
−0.0236784 | + | 0.999720i | \(0.507538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.0691 | − | 31.9130i | 1.11539 | − | 1.07640i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.1332i | − | 1.72272i | −0.507993 | − | 0.861361i | \(-0.669613\pi\) | ||
0.507993 | − | 0.861361i | \(-0.330387\pi\) | |||||||
\(882\) | 0.671884 | + | 0.0239146i | 0.0226235 | + | 0.000805246i | ||||
\(883\) | −54.9791 | −1.85019 | −0.925097 | − | 0.379731i | \(-0.876016\pi\) | ||||
−0.925097 | + | 0.379731i | \(0.876016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.90033 | 0.231821 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12221 | + | 29.7741i | −0.0710966 | + | 0.997469i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.27460 | + | 3.39323i | 0.109519 | + | 0.113486i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.3648i | 0.413078i | ||||||||
\(897\) | −22.6771 | + | 21.8843i | −0.757166 | + | 0.730695i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.05203 | − | 29.5569i | 0.0350676 | − | 0.985230i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.78827i | 0.226025i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.1769 | 0.471518 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.02345 | + | 2.91775i | −0.100448 | + | 0.0969359i | ||||
\(907\) | −54.9636 | −1.82504 | −0.912519 | − | 0.409035i | \(-0.865865\pi\) | ||||
−0.912519 | + | 0.409035i | \(0.865865\pi\) | |||||||
\(908\) | − | 51.8354i | − | 1.72022i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 46.7225i | − | 1.54799i | −0.633194 | − | 0.773993i | \(-0.718256\pi\) | ||
0.633194 | − | 0.773993i | \(-0.281744\pi\) | |||||||
\(912\) | −12.0745 | − | 12.5119i | −0.399827 | − | 0.414311i | ||||
\(913\) | −33.6945 | −1.11512 | ||||||||
\(914\) | − | 0.645636i | − | 0.0213558i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.6930 | − | 35.9499i | −1.14317 | − | 1.18459i | ||||
\(922\) | 3.91275 | 0.128859 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 19.4033 | − | 18.7250i | 0.638323 | − | 0.616007i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.779335 | − | 21.8956i | 0.0255967 | − | 0.719144i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49127 | 0.114422 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43.5772 | + | 42.0538i | −1.42665 | + | 1.37678i | ||||
\(934\) | −4.02285 | −0.131632 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.22157 | + | 0.257040i | 0.236044 | + | 0.00840160i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.9863 | − | 40.3987i | −1.27227 | − | 1.31836i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6444i | 0.933782i | 0.884315 | + | 0.466891i | \(0.154626\pi\) | ||||
−0.884315 | + | 0.466891i | \(0.845374\pi\) | |||||||
\(942\) | −3.19627 | + | 3.08453i | −0.104140 | + | 0.100499i | ||||
\(943\) | 61.4054 | 1.99963 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.6319 | −1.67604 | ||||||||
\(950\) | 2.20383i | 0.0715016i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | −0.112455 | + | 3.15944i | −0.00364086 | + | 0.102291i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 47.8556i | − | 1.54776i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.11574 | 0.0360479 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −61.1645 | −1.96998 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.43052 | + | 2.51857i | 0.0782007 | + | 0.0810337i | ||||
\(967\) | 15.5381 | 0.499671 | 0.249836 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249836 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(968\) | − | 7.34863i | − | 0.236194i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17.5823i | − | 0.564244i | −0.959379 | − | 0.282122i | \(-0.908962\pi\) | ||
0.959379 | − | 0.282122i | \(-0.0910382\pi\) | |||||||
\(972\) | −19.7171 | − | 23.5782i | −0.632425 | − | 0.756271i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.6832 | + | 22.4687i | 0.694417 | + | 0.719573i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.08740 | − | 58.6457i | 0.0666454 | − | 1.87241i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −9.77734 | − | 10.1315i | −0.311690 | − | 0.322982i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.6288 | 0.592662 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4183 | −0.616842 | −0.308421 | − | 0.951250i | \(-0.599801\pi\) | ||||
−0.308421 | + | 0.951250i | \(0.599801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 24.9655 | − | 24.0927i | 0.791062 | − | 0.763407i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 429.2.e.d.428.12 | yes | 20 | |
3.2 | odd | 2 | inner | 429.2.e.d.428.9 | ✓ | 20 | |
11.10 | odd | 2 | inner | 429.2.e.d.428.10 | yes | 20 | |
13.12 | even | 2 | inner | 429.2.e.d.428.10 | yes | 20 | |
33.32 | even | 2 | inner | 429.2.e.d.428.11 | yes | 20 | |
39.38 | odd | 2 | inner | 429.2.e.d.428.11 | yes | 20 | |
143.142 | odd | 2 | CM | 429.2.e.d.428.12 | yes | 20 | |
429.428 | even | 2 | inner | 429.2.e.d.428.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.e.d.428.9 | ✓ | 20 | 3.2 | odd | 2 | inner | |
429.2.e.d.428.9 | ✓ | 20 | 429.428 | even | 2 | inner | |
429.2.e.d.428.10 | yes | 20 | 11.10 | odd | 2 | inner | |
429.2.e.d.428.10 | yes | 20 | 13.12 | even | 2 | inner | |
429.2.e.d.428.11 | yes | 20 | 33.32 | even | 2 | inner | |
429.2.e.d.428.11 | yes | 20 | 39.38 | odd | 2 | inner | |
429.2.e.d.428.12 | yes | 20 | 1.1 | even | 1 | trivial | |
429.2.e.d.428.12 | yes | 20 | 143.142 | odd | 2 | CM |