Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.2 | ||
Character | \(\chi\) | \(=\) | 1148.57 |
Dual form | 1148.2.n.d.141.2 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | −2.86083 | −1.65170 | −0.825849 | − | 0.563891i | \(-0.809304\pi\) | ||||
−0.825849 | + | 0.563891i | \(0.809304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.47370 | − | 2.52379i | −1.55349 | − | 1.12867i | −0.941107 | − | 0.338109i | \(-0.890213\pi\) |
−0.612379 | − | 0.790564i | \(-0.709787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.18432 | 1.72811 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.93088 | − | 1.40287i | 0.582184 | − | 0.422981i | −0.257327 | − | 0.966324i | \(-0.582842\pi\) |
0.839511 | + | 0.543343i | \(0.182842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.878790 | − | 2.70464i | 0.243733 | − | 0.750132i | −0.752110 | − | 0.659038i | \(-0.770964\pi\) |
0.995842 | − | 0.0910938i | \(-0.0290363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.93765 | + | 7.22013i | 2.56589 | + | 1.86423i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.32741 | − | 4.59714i | 1.53462 | − | 1.11497i | 0.581026 | − | 0.813885i | \(-0.302652\pi\) |
0.953598 | − | 0.301084i | \(-0.0973485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.619498 | − | 1.90662i | −0.142123 | − | 0.437409i | 0.854507 | − | 0.519440i | \(-0.173859\pi\) |
−0.996630 | + | 0.0820311i | \(0.973859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.884044 | − | 2.72081i | −0.192914 | − | 0.593729i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.422882 | − | 1.30150i | 0.0881770 | − | 0.271381i | −0.897239 | − | 0.441546i | \(-0.854430\pi\) |
0.985416 | + | 0.170165i | \(0.0544301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.15199 | + | 12.7785i | 0.830397 | + | 2.55570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.24897 | −1.20262 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.17810 | − | 2.30902i | −0.590158 | − | 0.428775i | 0.252214 | − | 0.967672i | \(-0.418841\pi\) |
−0.842372 | + | 0.538897i | \(0.818841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.30062 | + | 1.67150i | −0.413204 | + | 0.300210i | −0.774898 | − | 0.632087i | \(-0.782199\pi\) |
0.361694 | + | 0.932297i | \(0.382199\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.52393 | + | 4.01337i | −0.961592 | + | 0.698637i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.32684 | − | 4.08358i | 0.224276 | − | 0.690251i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.27040 | − | 6.73534i | −1.52404 | − | 1.10728i | −0.959437 | − | 0.281924i | \(-0.909028\pi\) |
−0.564608 | − | 0.825360i | \(-0.690972\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.51407 | + | 7.73750i | −0.402573 | + | 1.23899i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20070 | − | 6.28954i | 0.187519 | − | 0.982261i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.353583 | + | 1.08822i | −0.0539209 | + | 0.165951i | −0.974390 | − | 0.224863i | \(-0.927807\pi\) |
0.920470 | + | 0.390814i | \(0.127807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.0088 | − | 13.0842i | −2.68459 | − | 1.95047i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.654034 | − | 2.01291i | 0.0954007 | − | 0.293613i | −0.891957 | − | 0.452120i | \(-0.850668\pi\) |
0.987358 | + | 0.158507i | \(0.0506679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.1016 | + | 13.1516i | −2.53474 | + | 1.84159i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.40632 | + | 3.20138i | 0.605254 | + | 0.439743i | 0.847740 | − | 0.530412i | \(-0.177963\pi\) |
−0.242486 | + | 0.970155i | \(0.577963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.2479 | −1.38182 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.77228 | + | 5.45451i | 0.234744 | + | 0.722467i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.97301 | + | 9.14999i | −0.387053 | + | 1.19123i | 0.547927 | + | 0.836526i | \(0.315417\pi\) |
−0.934980 | + | 0.354700i | \(0.884583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65006 | − | 5.07837i | −0.211269 | − | 0.650219i | −0.999397 | − | 0.0347084i | \(-0.988950\pi\) |
0.788128 | − | 0.615511i | \(-0.211050\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.60204 | + | 4.93059i | 0.201839 | + | 0.621195i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.87860 | + | 7.17722i | −1.22529 | + | 0.890225i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.74042 | + | 6.35029i | 1.06781 | + | 0.775811i | 0.975518 | − | 0.219921i | \(-0.0705798\pi\) |
0.0922947 | + | 0.995732i | \(0.470580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.20979 | + | 3.72336i | −0.145642 | + | 0.448240i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.04660 | − | 3.66657i | 0.598921 | − | 0.435141i | −0.246575 | − | 0.969124i | \(-0.579305\pi\) |
0.845496 | + | 0.533982i | \(0.179305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.96989 | −1.16689 | −0.583444 | − | 0.812153i | \(-0.698295\pi\) | ||||
−0.583444 | + | 0.812153i | \(0.698295\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.8781 | − | 36.5571i | −1.37157 | − | 4.22125i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.93088 | + | 1.40287i | 0.220045 | + | 0.159872i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.99970 | 1.01255 | 0.506273 | − | 0.862373i | \(-0.331023\pi\) | ||||
0.506273 | + | 0.862373i | \(0.331023\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.32425 | 0.258250 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.51170 | −0.385459 | −0.192730 | − | 0.981252i | \(-0.561734\pi\) | ||||
−0.192730 | + | 0.981252i | \(0.561734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33.5817 | −3.64245 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.09199 | + | 6.60571i | 0.974763 | + | 0.708207i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60053 | + | 4.92592i | 0.169656 | + | 0.522146i | 0.999349 | − | 0.0360730i | \(-0.0114849\pi\) |
−0.829694 | + | 0.558219i | \(0.811485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.84383 | 0.298114 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.58168 | − | 4.78187i | 0.682488 | − | 0.495857i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.65996 | + | 8.18651i | −0.272906 | + | 0.839918i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6968 | − | 8.49821i | −1.18763 | − | 0.862862i | −0.194617 | − | 0.980879i | \(-0.562346\pi\) |
−0.993012 | + | 0.118017i | \(0.962346\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.0103 | − | 7.27293i | 1.00608 | − | 0.730957i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.90191 | + | 5.85346i | 0.189247 | + | 0.582441i | 0.999996 | − | 0.00295258i | \(-0.000939838\pi\) |
−0.810749 | + | 0.585394i | \(0.800940\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.43336 | − | 10.5668i | −0.338299 | − | 1.04118i | −0.965074 | − | 0.261978i | \(-0.915625\pi\) |
0.626775 | − | 0.779201i | \(-0.284375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.79585 | + | 11.6824i | −0.370437 | + | 1.14009i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.05459 | − | 12.4787i | −0.391972 | − | 1.20637i | −0.931295 | − | 0.364266i | \(-0.881320\pi\) |
0.539323 | − | 0.842099i | \(-0.318680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.78660 | −0.745821 | −0.372911 | − | 0.927867i | \(-0.621640\pi\) | ||||
−0.372911 | + | 0.927867i | \(0.621640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.5210 | + | 19.2686i | 2.51726 | + | 1.82890i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.32239 | − | 3.86694i | 0.500689 | − | 0.363772i | −0.308591 | − | 0.951195i | \(-0.599858\pi\) |
0.809280 | + | 0.587423i | \(0.199858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.75367 | + | 3.45375i | −0.443282 | + | 0.322063i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.55593 | − | 14.0217i | 0.421196 | − | 1.29631i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.32741 | + | 4.59714i | 0.580033 | + | 0.421419i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.63891 | + | 5.04406i | −0.148992 | + | 0.458551i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.43501 | + | 17.9933i | −0.309724 | + | 1.62240i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1933 | − | 34.4495i | 1.00116 | − | 3.08126i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.12801 | − | 5.17880i | −0.632508 | − | 0.459544i | 0.224760 | − | 0.974414i | \(-0.427840\pi\) |
−0.857268 | + | 0.514870i | \(0.827840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.01154 | − | 3.11320i | 0.0890611 | − | 0.274102i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.77066 | − | 3.46609i | 0.416815 | − | 0.302833i | −0.359540 | − | 0.933130i | \(-0.617066\pi\) |
0.776355 | + | 0.630296i | \(0.217066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62187 | − | 1.17836i | 0.140634 | − | 0.102176i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.7071 | + | 15.7711i | 1.86825 | + | 1.35736i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.7196 | −1.68476 | −0.842381 | − | 0.538882i | \(-0.818847\pi\) | ||||
−0.842381 | + | 0.538882i | \(0.818847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.12532 | + | 21.9295i | 0.604362 | + | 1.86003i | 0.501120 | + | 0.865378i | \(0.332922\pi\) |
0.103242 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.87108 | + | 5.75859i | −0.157573 | + | 0.484960i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.09741 | − | 6.45517i | −0.175394 | − | 0.539809i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.21227 | + | 16.0417i | 0.432855 | + | 1.33219i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.31446 | − | 1.68155i | 0.190893 | − | 0.138692i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.65346 | + | 4.10748i | 0.463149 | + | 0.336498i | 0.794765 | − | 0.606917i | \(-0.207594\pi\) |
−0.331616 | + | 0.943414i | \(0.607594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.94583 | − | 15.2217i | 0.402486 | − | 1.23872i | −0.520490 | − | 0.853868i | \(-0.674251\pi\) |
0.922976 | − | 0.384857i | \(-0.125749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 32.8034 | − | 23.8330i | 2.65200 | − | 1.92679i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2102 | 0.980745 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.59637 | − | 17.2239i | −0.446639 | − | 1.37461i | −0.880676 | − | 0.473719i | \(-0.842911\pi\) |
0.434037 | − | 0.900895i | \(-0.357089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.6057 | − | 9.15858i | −0.999697 | − | 0.726323i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.36848 | 0.107851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.57568 | 0.201743 | 0.100871 | − | 0.994899i | \(-0.467837\pi\) | ||||
0.100871 | + | 0.994899i | \(0.467837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29.3174 | 2.28235 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0198 | −1.47180 | −0.735900 | − | 0.677090i | \(-0.763241\pi\) | ||||
−0.735900 | + | 0.677090i | \(0.763241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.97442 | + | 2.88759i | 0.305725 | + | 0.222122i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.21168 | − | 9.88454i | −0.245603 | − | 0.755889i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1626 | 1.07676 | 0.538380 | − | 0.842702i | \(-0.319036\pi\) | ||||
0.538380 | + | 0.842702i | \(0.319036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.8700 | + | 7.89755i | −0.821698 | + | 0.596999i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.50527 | − | 26.1765i | 0.639295 | − | 1.96755i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.17454 | + | 5.93915i | 0.610994 | + | 0.443913i | 0.849764 | − | 0.527163i | \(-0.176744\pi\) |
−0.238770 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7295 | + | 9.97509i | −1.02051 | + | 0.741443i | −0.966387 | − | 0.257091i | \(-0.917236\pi\) |
−0.0541216 | + | 0.998534i | \(0.517236\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.72054 | + | 14.5283i | 0.348953 | + | 1.07397i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2040 | + | 46.7931i | 1.11782 | + | 3.44030i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.76832 | − | 17.7531i | 0.421822 | − | 1.29823i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.93104 | − | 5.94313i | −0.140462 | − | 0.432299i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.74500 | −0.632766 | −0.316383 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316383 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.55125 | − | 5.48630i | −0.543551 | − | 0.394913i | 0.281851 | − | 0.959458i | \(-0.409051\pi\) |
−0.825402 | + | 0.564545i | \(0.809051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.2609 | − | 20.5328i | 2.02381 | − | 1.47038i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.95819 | − | 7.23505i | 0.709492 | − | 0.515476i | −0.173518 | − | 0.984831i | \(-0.555513\pi\) |
0.883010 | + | 0.469355i | \(0.155513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.25698 | + | 19.2570i | −0.443546 | + | 1.36509i | 0.440525 | + | 0.897740i | \(0.354792\pi\) |
−0.884071 | + | 0.467353i | \(0.845208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.0048 | − | 18.1671i | −1.76370 | − | 1.28141i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.21393 | − | 3.73608i | 0.0852009 | − | 0.262221i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.0444 | + | 18.8176i | −1.39996 | + | 1.31428i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.19236 | − | 6.74738i | 0.152379 | − | 0.468976i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.87092 | − | 2.81239i | −0.267757 | − | 0.194537i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.73030 | + | 14.5584i | −0.325647 | + | 1.00224i | 0.645501 | + | 0.763760i | \(0.276649\pi\) |
−0.971148 | + | 0.238479i | \(0.923351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.4374 | + | 10.4894i | −0.989237 | + | 0.718723i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.97467 | − | 2.88777i | 0.271070 | − | 0.196944i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.30062 | − | 1.67150i | −0.156176 | − | 0.113469i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.5221 | 1.92735 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.87312 | − | 21.1533i | −0.462336 | − | 1.42292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.57042 | + | 26.3770i | −0.573918 | + | 1.76634i | 0.0659172 | + | 0.997825i | \(0.479003\pi\) |
−0.639835 | + | 0.768512i | \(0.720997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.5253 | + | 66.2479i | 1.43502 | + | 4.41653i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.55351 | + | 20.1696i | 0.434972 | + | 1.33871i | 0.893116 | + | 0.449827i | \(0.148514\pi\) |
−0.458144 | + | 0.888878i | \(0.651486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.9804 | + | 15.2431i | −1.38642 | + | 1.00729i | −0.390175 | + | 0.920741i | \(0.627585\pi\) |
−0.996247 | + | 0.0865540i | \(0.972415\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.52393 | − | 4.01337i | −0.363448 | − | 0.264060i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.35757 | − | 10.3336i | 0.219962 | − | 0.676974i | −0.778802 | − | 0.627270i | \(-0.784172\pi\) |
0.998764 | − | 0.0497036i | \(-0.0158277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.35208 | + | 5.34160i | −0.479597 | + | 0.348448i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.7466 | −1.67242 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.75412 | + | 5.39864i | 0.113465 | + | 0.349209i | 0.991624 | − | 0.129160i | \(-0.0412282\pi\) |
−0.878159 | + | 0.478369i | \(0.841228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0987 | + | 13.8760i | 1.23025 | + | 0.893831i | 0.996909 | − | 0.0785629i | \(-0.0250332\pi\) |
0.233344 | + | 0.972394i | \(0.425033\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.0976 | 0.776064 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29373 | 0.274316 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.70113 | −0.362754 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0464 | 0.636663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.7736 | − | 10.7337i | −0.932503 | − | 0.677503i | 0.0141011 | − | 0.999901i | \(-0.495511\pi\) |
−0.946604 | + | 0.322397i | \(0.895511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00929 | − | 3.10629i | −0.0634538 | − | 0.195291i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 96.0715 | 6.01623 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.2419 | + | 7.44120i | −0.638875 | + | 0.464170i | −0.859463 | − | 0.511197i | \(-0.829202\pi\) |
0.220589 | + | 0.975367i | \(0.429202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.54098 | − | 10.8980i | 0.220026 | − | 0.677169i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4763 | − | 11.9707i | −1.01986 | − | 0.740969i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.65956 | − | 6.29154i | 0.533972 | − | 0.387953i | −0.287870 | − | 0.957670i | \(-0.592947\pi\) |
0.821841 | + | 0.569717i | \(0.192947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.22662 | − | 22.2412i | −0.443928 | − | 1.36627i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.57883 | − | 14.0922i | −0.280220 | − | 0.862428i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.440874 | − | 1.35687i | 0.0268806 | − | 0.0827299i | −0.936716 | − | 0.350090i | \(-0.886151\pi\) |
0.963597 | + | 0.267360i | \(0.0861512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64011 | − | 11.2031i | −0.221121 | − | 0.680541i | −0.998662 | − | 0.0517087i | \(-0.983533\pi\) |
0.777541 | − | 0.628832i | \(-0.216467\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.13569 | −0.492394 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.9436 | + | 18.8491i | 1.56446 | + | 1.13664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.7737 | − | 12.9133i | 1.06792 | − | 0.775886i | 0.0923794 | − | 0.995724i | \(-0.470553\pi\) |
0.975536 | + | 0.219838i | \(0.0705528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.9272 | + | 8.66559i | −0.714061 | + | 0.518796i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.85782 | − | 5.71778i | 0.110828 | − | 0.341094i | −0.880226 | − | 0.474555i | \(-0.842609\pi\) |
0.991054 | + | 0.133461i | \(0.0426090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.53212 | + | 1.11315i | 0.0910751 | + | 0.0661699i | 0.632391 | − | 0.774649i | \(-0.282074\pi\) |
−0.541316 | + | 0.840819i | \(0.682074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.60968 | − | 23.4202i | 0.450758 | − | 1.38729i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.35275 | − | 0.801636i | 0.374991 | − | 0.0473191i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.6492 | − | 42.0080i | 0.802896 | − | 2.47106i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.4625 | + | 24.3119i | 1.96160 | + | 1.42519i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.46997 | + | 4.52410i | −0.0858766 | + | 0.264301i | −0.984769 | − | 0.173869i | \(-0.944373\pi\) |
0.898892 | + | 0.438170i | \(0.144373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.4200 | − | 24.2810i | 1.94579 | − | 1.41370i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.0660 | + | 8.76650i | −0.700143 | + | 0.508684i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.14845 | − | 2.28749i | −0.182080 | − | 0.132289i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.14422 | −0.0659516 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.44102 | − | 16.7457i | −0.312578 | − | 0.962018i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.08493 | + | 21.8052i | −0.405682 | + | 1.24856i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.32593 | − | 13.3138i | −0.246894 | − | 0.759861i | −0.995319 | − | 0.0966421i | \(-0.969190\pi\) |
0.748425 | − | 0.663219i | \(-0.230810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.82226 | + | 30.2298i | 0.558769 | + | 1.71971i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.99874 | + | 5.81142i | −0.453567 | + | 0.329535i | −0.791002 | − | 0.611813i | \(-0.790440\pi\) |
0.337436 | + | 0.941349i | \(0.390440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.94427 | + | 5.04531i | 0.392513 | + | 0.285178i | 0.766485 | − | 0.642263i | \(-0.222004\pi\) |
−0.373971 | + | 0.927440i | \(0.622004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.87875 | − | 21.1706i | 0.387573 | − | 1.19283i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.07374 | + | 2.95975i | −0.228804 | + | 0.166236i | −0.696281 | − | 0.717769i | \(-0.745163\pi\) |
0.467477 | + | 0.884005i | \(0.345163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.37580 | −0.524944 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.5995 | + | 35.6995i | 0.647419 | + | 1.99255i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.6848 | − | 9.21606i | −0.705802 | − | 0.512795i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.2100 | 2.11951 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.2761 | 1.23187 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.11650 | 0.116686 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.4824 | −1.73043 | −0.865216 | − | 0.501400i | \(-0.832819\pi\) | ||||
−0.865216 | + | 0.501400i | \(0.832819\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −48.0608 | − | 34.9182i | −2.63371 | − | 1.91350i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.3348 | − | 44.1180i | −0.783194 | − | 2.41042i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.15986 | −0.498970 | −0.249485 | − | 0.968379i | \(-0.580261\pi\) | ||||
−0.249485 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.2264 | + | 11.0627i | −0.826987 | + | 0.600841i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.09734 | + | 6.45494i | −0.113577 | + | 0.349555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5994 | − | 9.88056i | 0.732169 | − | 0.531952i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.34576 | − | 16.4526i | −0.286976 | − | 0.883220i | −0.985800 | − | 0.167926i | \(-0.946293\pi\) |
0.698824 | − | 0.715294i | \(-0.253707\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.160432 | + | 0.493758i | 0.00858771 | + | 0.0264303i | 0.955259 | − | 0.295772i | \(-0.0955769\pi\) |
−0.946671 | + | 0.322202i | \(0.895577\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.49154 | + | 16.9012i | −0.293117 | + | 0.902120i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.83645 | + | 5.65200i | 0.0977442 | + | 0.300826i | 0.987959 | − | 0.154715i | \(-0.0494460\pi\) |
−0.890215 | + | 0.455541i | \(0.849446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.7840 | −1.42155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.1016 | − | 13.1516i | −0.958040 | − | 0.696057i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.4848 | + | 21.4220i | −1.55615 | + | 1.13061i | −0.617072 | + | 0.786907i | \(0.711681\pi\) |
−0.939079 | + | 0.343702i | \(0.888319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1199 | − | 8.80562i | 0.637890 | − | 0.463454i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.68865 | − | 14.4302i | 0.246090 | − | 0.757388i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.6324 | + | 25.1619i | 1.81274 | + | 1.31704i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.95425 | − | 12.1699i | 0.206410 | − | 0.635265i | −0.793242 | − | 0.608906i | \(-0.791609\pi\) |
0.999653 | − | 0.0263590i | \(-0.00839130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.22484 | − | 32.6070i | 0.324052 | − | 1.69745i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68306 | + | 5.17993i | −0.0873803 | + | 0.268929i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.556622 | + | 0.404409i | 0.0288208 | + | 0.0209395i | 0.602102 | − | 0.798419i | \(-0.294330\pi\) |
−0.573282 | + | 0.819358i | \(0.694330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.0222 | + | 98.5541i | −1.65362 | + | 5.08931i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.03796 | + | 6.56646i | −0.465478 | + | 0.338190i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9355 | + | 15.9371i | −1.12675 | + | 0.818633i | −0.985219 | − | 0.171301i | \(-0.945203\pi\) |
−0.141533 | + | 0.989934i | \(0.545203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.3920 | + | 14.8156i | 1.04471 | + | 0.759029i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.1677 | −1.64369 | −0.821846 | − | 0.569709i | \(-0.807056\pi\) | ||||
−0.821846 | + | 0.569709i | \(0.807056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.16676 | − | 9.74630i | −0.161393 | − | 0.496717i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.83309 | + | 5.64167i | −0.0931811 | + | 0.286782i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.24481 | − | 19.2195i | −0.316624 | − | 0.974469i | −0.975081 | − | 0.221851i | \(-0.928790\pi\) |
0.658456 | − | 0.752619i | \(-0.271210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.30741 | − | 10.1792i | −0.167263 | − | 0.514782i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.6480 | + | 9.91587i | −0.688452 | + | 0.500190i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.2623 | − | 22.7134i | −1.57298 | − | 1.14283i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.81492 | − | 14.8188i | 0.241654 | − | 0.743734i | −0.754515 | − | 0.656283i | \(-0.772128\pi\) |
0.996169 | − | 0.0874511i | \(-0.0278722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.63988 | + | 3.37107i | −0.232285 | + | 0.168765i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.25948 | −0.412459 | −0.206229 | − | 0.978504i | \(-0.566119\pi\) | ||||
−0.206229 | + | 0.978504i | \(0.566119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.49904 | + | 7.69125i | 0.124486 | + | 0.383128i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.07374 | − | 5.86592i | −0.401187 | − | 0.291480i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.3489 | −1.35563 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2378 | 1.19848 | 0.599240 | − | 0.800569i | \(-0.295470\pi\) | ||||
0.599240 | + | 0.800569i | \(0.295470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.4144 | 2.78272 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.62086 | −0.473412 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.1986 | + | 8.86280i | 0.598806 | + | 0.435058i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.3843 | − | 62.7364i | −0.998223 | − | 3.07222i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.2743 | −0.843904 | −0.421952 | − | 0.906618i | \(-0.638655\pi\) | ||||
−0.421952 | + | 0.906618i | \(0.638655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.9576 | + | 11.5939i | −0.777727 | + | 0.565052i | −0.904296 | − | 0.426906i | \(-0.859603\pi\) |
0.126569 | + | 0.991958i | \(0.459603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.39073 | − | 10.4356i | 0.164863 | − | 0.507395i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 85.0159 | + | 61.7676i | 4.12387 | + | 2.99617i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.31992 | − | 3.13861i | 0.209056 | − | 0.151888i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00033 | + | 18.4671i | 0.289699 | + | 0.891601i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.42075 | − | 4.37263i | −0.0684353 | − | 0.210622i | 0.910990 | − | 0.412428i | \(-0.135319\pi\) |
−0.979426 | + | 0.201806i | \(0.935319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.792408 | − | 2.43878i | 0.0380807 | − | 0.117200i | −0.930209 | − | 0.367030i | \(-0.880375\pi\) |
0.968290 | + | 0.249830i | \(0.0803746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.9114 | − | 45.8925i | −0.714946 | − | 2.20038i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.74344 | −0.131236 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0515 | + | 9.48244i | 0.622912 | + | 0.452572i | 0.853937 | − | 0.520376i | \(-0.174208\pi\) |
−0.231025 | + | 0.972948i | \(0.574208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.19421 | + | 3.04727i | −0.199724 | + | 0.145108i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8166 | − | 19.4834i | 1.27410 | − | 0.925684i | 0.274737 | − | 0.961519i | \(-0.411409\pi\) |
0.999358 | + | 0.0358351i | \(0.0114091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.87223 | − | 21.1505i | 0.325775 | − | 1.00263i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.1736 | − | 11.7508i | −0.764983 | − | 0.555792i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.65246 | − | 14.3188i | 0.219563 | − | 0.675746i | −0.779235 | − | 0.626732i | \(-0.784392\pi\) |
0.998798 | − | 0.0490138i | \(-0.0156078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.50498 | − | 13.8288i | −0.306308 | − | 0.651173i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1492 | + | 43.5467i | −0.664786 | + | 2.04600i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.87860 | − | 7.17722i | −0.463116 | − | 0.336473i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.99588 | − | 24.6088i | 0.374032 | − | 1.15115i | −0.570098 | − | 0.821577i | \(-0.693095\pi\) |
0.944130 | − | 0.329574i | \(-0.106905\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.5398 | + | 28.7274i | −1.84556 | + | 1.34088i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6842 | − | 14.3014i | 0.916783 | − | 0.666082i | −0.0259378 | − | 0.999664i | \(-0.508257\pi\) |
0.942721 | + | 0.333581i | \(0.108257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.51693 | − | 3.28175i | −0.209920 | − | 0.152516i | 0.477858 | − | 0.878437i | \(-0.341413\pi\) |
−0.687777 | + | 0.725922i | \(0.741413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.9312 | −1.61990 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.645695 | + | 1.98725i | 0.0298792 | + | 0.0919588i | 0.964884 | − | 0.262676i | \(-0.0846051\pi\) |
−0.935005 | + | 0.354635i | \(0.884605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.33854 | + | 10.2750i | −0.154160 | + | 0.474455i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0103 | + | 49.2745i | 0.737713 | + | 2.27045i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.843898 | + | 2.59725i | 0.0388025 | + | 0.119422i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.7916 | − | 15.8325i | 0.999867 | − | 0.726446i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.8438 | + | 16.5970i | 1.04594 | + | 0.759923i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.79687 | − | 8.60787i | 0.127792 | − | 0.393304i | −0.866607 | − | 0.498991i | \(-0.833704\pi\) |
0.994399 | + | 0.105687i | \(0.0337042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.3634 | + | 19.1541i | −1.20207 | + | 0.873353i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.91497 | −0.178137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.1834 | + | 59.0405i | 0.871074 | + | 2.68089i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.76593 | − | 4.91574i | −0.306594 | − | 0.222753i | 0.423840 | − | 0.905737i | \(-0.360682\pi\) |
−0.730433 | + | 0.682984i | \(0.760682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.36857 | −0.333218 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5935 | −1.24528 | −0.622638 | − | 0.782510i | \(-0.713939\pi\) | ||||
−0.622638 | + | 0.782510i | \(0.713939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.7240 | −1.38374 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −53.1283 | −2.38794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.04660 | + | 3.66657i | 0.226371 | + | 0.164468i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.61824 | − | 17.2912i | −0.251507 | − | 0.774059i | −0.994498 | − | 0.104757i | \(-0.966593\pi\) |
0.742991 | − | 0.669302i | \(-0.233407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 54.4125 | 2.43097 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.91619 | − | 6.47799i | 0.397553 | − | 0.288839i | −0.370990 | − | 0.928637i | \(-0.620982\pi\) |
0.768544 | + | 0.639797i | \(0.220982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.16627 | − | 25.1332i | 0.363394 | − | 1.11841i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.3701 | − | 8.26089i | −0.504966 | − | 0.366879i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2038 | − | 14.6789i | 0.895519 | − | 0.650633i | −0.0417920 | − | 0.999126i | \(-0.513307\pi\) |
0.937311 | + | 0.348494i | \(0.113307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.08087 | − | 9.48193i | −0.136290 | − | 0.419456i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.87123 | + | 11.9144i | 0.170919 | + | 0.526034i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.7419 | + | 45.3710i | −0.649607 | + | 1.99929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.56099 | − | 4.80422i | −0.0686521 | − | 0.211290i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.5167 | −1.77848 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.14579 | − | 3.73863i | −0.225441 | − | 0.163792i | 0.469332 | − | 0.883022i | \(-0.344495\pi\) |
−0.694772 | + | 0.719230i | \(0.744495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.11940 | − | 0.813292i | 0.0489480 | − | 0.0355628i | −0.563042 | − | 0.826428i | \(-0.690369\pi\) |
0.611990 | + | 0.790865i | \(0.290369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 31.0973 | − | 22.5935i | 1.35720 | − | 0.986062i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.87288 | + | 21.1525i | −0.299387 | + | 0.921419i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0923 | + | 12.4183i | 0.743145 | + | 0.539926i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.4131 | + | 47.4365i | −0.668869 | + | 2.05857i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9558 | − | 8.77466i | −0.691121 | − | 0.380073i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.4093 | + | 53.5803i | −0.752670 | + | 2.31648i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.3859 | − | 16.9909i | −1.00918 | − | 0.733210i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.737532 | + | 2.26989i | −0.0317678 | + | 0.0977711i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6277 | + | 7.72150i | −0.456922 | + | 0.331973i | −0.792323 | − | 0.610102i | \(-0.791128\pi\) |
0.335401 | + | 0.942076i | \(0.391128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39.2778 | − | 28.5370i | 1.68557 | − | 1.22464i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.0483 | + | 19.6518i | 1.15862 | + | 0.841789i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3714 | 0.443448 | 0.221724 | − | 0.975109i | \(-0.428832\pi\) | ||||
0.221724 | + | 0.975109i | \(0.428832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.55447 | − | 26.3279i | −0.365096 | − | 1.12365i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.43360 | + | 7.48986i | −0.103675 | + | 0.319079i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.78106 | + | 8.55922i | 0.118263 | + | 0.363975i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −43.4960 | − | 133.867i | −1.84630 | − | 5.68233i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.3510 | − | 11.1531i | 0.650442 | − | 0.472574i | −0.212980 | − | 0.977057i | \(-0.568317\pi\) |
0.863422 | + | 0.504483i | \(0.168317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.63251 | + | 1.91263i | 0.111343 | + | 0.0808955i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5022 | + | 50.7885i | −0.696722 | + | 2.14429i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.262642 | − | 0.190821i | 0.0110690 | − | 0.00804213i | −0.582237 | − | 0.813019i | \(-0.697822\pi\) |
0.593306 | + | 0.804977i | \(0.297822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.2478 | −1.18839 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.718232 | + | 2.21049i | 0.0301629 | + | 0.0928319i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1732 | + | 10.2974i | 0.594172 | + | 0.431691i | 0.843805 | − | 0.536649i | \(-0.180310\pi\) |
−0.249634 | + | 0.968340i | \(0.580310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.9911 | −0.585507 | −0.292754 | − | 0.956188i | \(-0.594572\pi\) | ||||
−0.292754 | + | 0.956188i | \(0.594572\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.0179 | 1.04514 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.3870 | 0.766790 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.08012 | −0.128227 | −0.0641135 | − | 0.997943i | \(-0.520422\pi\) | ||||
−0.0641135 | + | 0.997943i | \(0.520422\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.6028 | + | 15.6954i | 0.897782 | + | 0.652277i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.08518 | − | 3.33983i | −0.0450207 | − | 0.138559i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9992 | 0.538372 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −51.2138 | + | 37.2090i | −2.11743 | + | 1.53840i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.06783 | − | 18.6748i | 0.250446 | − | 0.770793i | −0.744247 | − | 0.667905i | \(-0.767191\pi\) |
0.994693 | − | 0.102889i | \(-0.0328086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.61214 | + | 3.35092i | 0.190040 | + | 0.138072i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.4887 | + | 20.6982i | −1.17187 | + | 0.851411i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.53839 | + | 17.0454i | 0.227434 | + | 0.699971i | 0.998035 | + | 0.0626532i | \(0.0199562\pi\) |
−0.770601 | + | 0.637318i | \(0.780044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.3773 | − | 31.9381i | −0.425429 | − | 1.30934i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.9001 | − | 55.0910i | 0.732604 | − | 2.25472i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.96065 | − | 24.5004i | −0.325263 | − | 1.00106i | −0.971322 | − | 0.237769i | \(-0.923584\pi\) |
0.646058 | − | 0.763288i | \(-0.276416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.0305 | 1.34734 | 0.673671 | − | 0.739031i | \(-0.264717\pi\) | ||||
0.673671 | + | 0.739031i | \(0.264717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.3132 | + | 32.9220i | 1.84530 | + | 1.34069i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.4233 | − | 13.3853i | 0.749012 | − | 0.544189i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.6954 | + | 9.22372i | −0.515289 | + | 0.374379i | −0.814826 | − | 0.579705i | \(-0.803168\pi\) |
0.299537 | + | 0.954085i | \(0.403168\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.47283 | + | 10.6883i | −0.140726 | + | 0.433111i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.86944 | − | 3.53785i | −0.196996 | − | 0.143126i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.74475 | + | 14.6029i | −0.191639 | + | 0.589804i | 0.808361 | + | 0.588688i | \(0.200355\pi\) |
−0.999999 | + | 0.00111595i | \(0.999645\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 57.3435 | − | 53.8340i | 2.31231 | − | 2.17080i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.52826 | + | 7.78120i | −0.101784 | + | 0.313259i | −0.988962 | − | 0.148168i | \(-0.952662\pi\) |
0.887178 | + | 0.461427i | \(0.152662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.4340 | + | 26.4708i | 1.46441 | + | 1.06395i | 0.982188 | + | 0.187901i | \(0.0601685\pi\) |
0.482217 | + | 0.876052i | \(0.339832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.64258 | + | 8.13302i | −0.106043 | + | 0.326367i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.19023 | + | 3.04438i | −0.167878 | + | 0.121971i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −71.4755 | + | 51.9300i | −2.85902 | + | 2.07720i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0740 | + | 8.04575i | 0.442254 | + | 0.321316i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −89.6209 | −3.57342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.73932 | + | 14.5861i | 0.188669 | + | 0.580664i | 0.999992 | − | 0.00393404i | \(-0.00125225\pi\) |
−0.811323 | + | 0.584598i | \(0.801252\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5326 | − | 41.6489i | 0.537871 | − | 1.65540i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6904 | + | 35.9792i | 0.463917 | + | 1.42779i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.878790 | + | 2.70464i | 0.0348189 | + | 0.107162i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.1632 | − | 19.0087i | 1.03500 | − | 0.751972i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.9045 | − | 8.64910i | −0.470198 | − | 0.341619i | 0.327320 | − | 0.944913i | \(-0.393854\pi\) |
−0.797518 | + | 0.603295i | \(0.793854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.62551 | + | 14.2359i | −0.182412 | + | 0.561408i | −0.999894 | − | 0.0145468i | \(-0.995369\pi\) |
0.817482 | + | 0.575954i | \(0.195369\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.3708 | + | 8.26140i | −0.447726 | + | 0.325292i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0097 | 0.865291 | 0.432646 | − | 0.901564i | \(-0.357580\pi\) | ||||
0.432646 | + | 0.901564i | \(0.357580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.09570 | + | 21.8383i | 0.278531 | + | 0.857229i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.58168 | + | 4.78187i | 0.257956 | + | 0.187416i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.64792 | −0.221020 | −0.110510 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110510 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.3195 | −0.989316 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −51.6872 | −2.01651 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.5700 | 0.801295 | 0.400647 | − | 0.916232i | \(-0.368785\pi\) | ||||
0.400647 | + | 0.916232i | \(0.368785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5451 | − | 9.11458i | −0.487950 | − | 0.354516i | 0.316446 | − | 0.948611i | \(-0.397511\pi\) |
−0.804395 | + | 0.594094i | \(0.797511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.6628 | + | 60.5159i | 0.763640 | + | 2.35024i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.60781 | −0.333796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.34915 | + | 3.15984i | −0.168400 | + | 0.122350i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.5185 | − | 75.4601i | 0.947939 | − | 2.91746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.3104 | − | 7.49093i | −0.398028 | − | 0.289184i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.1078 | + | 17.5154i | −0.929288 | + | 0.675167i | −0.945818 | − | 0.324696i | \(-0.894738\pi\) |
0.0165303 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9457 | − | 79.8525i | −0.998649 | − | 3.07352i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.05408 | − | 21.7102i | −0.271110 | − | 0.834392i | −0.990222 | − | 0.139498i | \(-0.955451\pi\) |
0.719112 | − | 0.694894i | \(-0.244549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.46777 | − | 13.7504i | 0.171457 | − | 0.527692i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.7485 | − | 57.7018i | −0.718442 | − | 2.21114i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.00946 | −0.268210 | −0.134105 | − | 0.990967i | \(-0.542816\pi\) | ||||
−0.134105 | + | 0.990967i | \(0.542816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.5001 | + | 49.7682i | 2.61725 | + | 1.90155i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 60.0212 | − | 43.6080i | 2.28995 | − | 1.66375i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.5308 | − | 9.10415i | 0.477385 | − | 0.346841i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9075 | − | 39.7251i | 0.491023 | − | 1.51121i | −0.332041 | − | 0.943265i | \(-0.607737\pi\) |
0.823064 | − | 0.567949i | \(-0.192263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0103 | + | 7.27293i | 0.380261 | + | 0.276276i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.5942 | − | 94.1593i | 1.16050 | − | 3.57166i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.3165 | − | 45.3163i | −0.807420 | − | 1.71648i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.60544 | + | 29.5625i | −0.363311 | + | 1.11816i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.6561 | + | 30.2649i | 1.57333 | + | 1.14309i | 0.923878 | + | 0.382686i | \(0.125001\pi\) |
0.649450 | + | 0.760404i | \(0.274999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.09874 | + | 21.8477i | −0.267734 | + | 0.824000i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.0330 | − | 15.2814i | 0.792150 | − | 0.575531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.97925 | + | 3.61764i | −0.187264 | + | 0.136055i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.92265 | − | 4.30306i | −0.222430 | − | 0.161605i | 0.470990 | − | 0.882139i | \(-0.343897\pi\) |
−0.693420 | + | 0.720534i | \(0.743897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.6574 | 1.74979 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.20256 | + | 3.70110i | 0.0450362 | + | 0.138607i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.00572 | + | 27.7168i | −0.336795 | + | 1.03655i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.01824 | − | 15.4446i | −0.187410 | − | 0.576788i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.99380 | + | 15.3693i | 0.186237 | + | 0.573179i | 0.999967 | − | 0.00806352i | \(-0.00256672\pi\) |
−0.813730 | + | 0.581243i | \(0.802567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.98866 | − | 6.53065i | 0.334755 | − | 0.243214i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.6380 | − | 39.6968i | −2.03201 | − | 1.47634i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.3104 | − | 50.1984i | 0.605755 | − | 1.86432i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.25915 | + | 3.82099i | −0.195051 | + | 0.141713i | −0.681024 | − | 0.732261i | \(-0.738465\pi\) |
0.485973 | + | 0.873974i | \(0.338465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.5820 | −1.54007 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.76541 | + | 8.51106i | 0.102282 | + | 0.314793i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.34452 | − | 1.70339i | −0.0865967 | − | 0.0629162i | 0.543644 | − | 0.839316i | \(-0.317044\pi\) |
−0.630241 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.2836 | −0.453088 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7854 | 0.949817 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.9575 | −1.94807 | −0.974036 | − | 0.226393i | \(-0.927307\pi\) | ||||
−0.974036 | + | 0.226393i | \(0.927307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3099 | 0.599160 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.8527 | + | 28.2282i | 1.42537 | + | 1.03559i | 0.990856 | + | 0.134924i | \(0.0430792\pi\) |
0.434512 | + | 0.900666i | \(0.356921\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.27200 | − | 28.5363i | −0.339700 | − | 1.04549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.2058 | −0.666116 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.6151 | − | 7.71229i | 0.387865 | − | 0.281801i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.51458 | + | 29.2829i | −0.347192 | + | 1.06855i | 0.613208 | + | 0.789922i | \(0.289879\pi\) |
−0.960400 | + | 0.278626i | \(0.910121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.2648 | + | 30.7072i | 1.54021 | + | 1.11903i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.5967 | + | 40.3934i | −2.02337 | + | 1.47007i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5636 | + | 35.5892i | 0.420288 | + | 1.29351i | 0.907435 | + | 0.420193i | \(0.138037\pi\) |
−0.487147 | + | 0.873320i | \(0.661963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.88742 | + | 8.88655i | 0.104807 | + | 0.322562i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.37875 | − | 19.6318i | 0.231229 | − | 0.711651i | −0.766370 | − | 0.642400i | \(-0.777939\pi\) |
0.997599 | − | 0.0692513i | \(-0.0220610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.40619 | − | 7.40550i | −0.0871100 | − | 0.268097i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −174.099 | −6.29455 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.1347 | + | 16.0818i | 0.799239 | + | 0.580681i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3984 | − | 9.00796i | 0.447097 | − | 0.324835i | −0.341351 | − | 0.939936i | \(-0.610885\pi\) |
0.788449 | + | 0.615101i | \(0.210885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.3004 | − | 21.2880i | 1.05523 | − | 0.766668i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.2584 | + | 34.6497i | −0.404935 | + | 1.24626i | 0.516014 | + | 0.856580i | \(0.327415\pi\) |
−0.920949 | + | 0.389682i | \(0.872585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.9114 | − | 22.4585i | −1.11037 | − | 0.806731i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.1301 | + | 31.1773i | −0.363416 | + | 1.11848i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.7356 | + | 1.60707i | −0.456300 | + | 0.0575793i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.60068 | − | 14.1594i | 0.164625 | − | 0.506665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.8598 | + | 14.4290i | 0.709733 | + | 0.515651i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.0293 | + | 73.9546i | −0.857643 | + | 2.63955i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.25578 | + | 5.99818i | −0.294287 | + | 0.213812i | −0.725125 | − | 0.688617i | \(-0.758218\pi\) |
0.430838 | + | 0.902429i | \(0.358218\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.7735 | + | 17.9990i | −0.881960 | + | 0.640782i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.32239 | + | 3.86694i | 0.189243 | + | 0.137493i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.1852 | −0.539243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.6741 | + | 63.6283i | 0.733234 | + | 2.25666i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0070 | − | 36.9536i | 0.425308 | − | 1.30896i | −0.477390 | − | 0.878691i | \(-0.658417\pi\) |
0.902699 | − | 0.430273i | \(-0.141583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.11528 | − | 15.7432i | −0.180965 | − | 0.556955i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.29765 | + | 25.5375i | 0.293183 | + | 0.902325i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.2507 | + | 13.9865i | −0.679343 | + | 0.493572i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.75367 | − | 3.45375i | −0.167545 | − | 0.121729i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.26126 | + | 3.88177i | −0.0443986 | + | 0.136645i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0169 | − | 15.2696i | 0.738914 | − | 0.536852i | −0.153457 | − | 0.988155i | \(-0.549041\pi\) |
0.892371 | + | 0.451303i | \(0.149041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.0855 | 1.68851 | 0.844255 | − | 0.535941i | \(-0.180043\pi\) | ||||
0.844255 | + | 0.535941i | \(0.180043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.4137 | + | 32.0502i | 0.365225 | + | 1.12405i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.94714 | − | 6.50048i | −0.313405 | − | 0.227702i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.29386 | 0.0802520 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.7433 | 0.515173 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.9151 | 1.21854 | 0.609272 | − | 0.792961i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.8381 | 1.31895 | 0.659477 | − | 0.751725i | \(-0.270778\pi\) | ||||
0.659477 | + | 0.751725i | \(0.270778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −74.2201 | − | 53.9240i | −2.58401 | − | 1.87739i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7109 | + | 39.1200i | 0.442000 | + | 1.36033i | 0.885741 | + | 0.464180i | \(0.153651\pi\) |
−0.443741 | + | 0.896155i | \(0.646349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.5797 | −0.818958 | −0.409479 | − | 0.912319i | \(-0.634290\pi\) | ||||
−0.409479 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.8474 | + | 36.9428i | −1.76388 | + | 1.28153i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.41686 | + | 7.43832i | −0.0837391 | + | 0.257723i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.0692 | + | 48.0021i | 2.28642 | + | 1.66118i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.3765 | − | 10.4452i | 0.496925 | − | 0.361037i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.1004 | − | 31.0858i | −0.348704 | − | 1.07320i | −0.959571 | − | 0.281468i | \(-0.909179\pi\) |
0.610866 | − | 0.791734i | \(-0.290821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.19277 | − | 12.9040i | −0.144578 | − | 0.444967i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.31490 | + | 16.3576i | −0.183055 | + | 0.563385i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.51829 | − | 20.0612i | −0.224236 | − | 0.690127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.30364 | −0.182235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.38313 | − | 3.18453i | −0.150429 | − | 0.109293i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6863 | + | 9.21715i | −0.434881 | + | 0.315960i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.2640 | + | 16.1757i | −0.762304 | + | 0.553847i | −0.899616 | − | 0.436681i | \(-0.856154\pi\) |
0.137312 | + | 0.990528i | \(0.456154\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.7901 | + | 42.4415i | −0.471611 | + | 1.45147i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.5448 | − | 29.4575i | −1.38498 | − | 1.00625i | −0.996395 | − | 0.0848382i | \(-0.972963\pi\) |
−0.388589 | − | 0.921411i | \(-0.627037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7081 | − | 42.1892i | 0.467715 | − | 1.43948i | −0.387821 | − | 0.921735i | \(-0.626772\pi\) |
0.855536 | − | 0.517743i | \(-0.173228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.1741 | + | 2.29334i | −0.619372 | + | 0.0781569i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.1973 | − | 34.4617i | 0.381161 | − | 1.17309i | −0.558067 | − | 0.829796i | \(-0.688457\pi\) |
0.939227 | − | 0.343296i | \(-0.111543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.1965 | − | 35.7434i | −1.67273 | − | 1.21531i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.0481 | + | 120.178i | −1.32614 | + | 4.08144i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.3774 | − | 12.6254i | 0.589487 | − | 0.428288i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8562 | − | 18.0591i | 0.842221 | − | 0.611910i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −60.6399 | − | 44.0575i | −2.05235 | − | 1.49112i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.2224 | 1.22454 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.02942 | + | 27.7897i | 0.304902 | + | 0.938391i | 0.979714 | + | 0.200402i | \(0.0642247\pi\) |
−0.674812 | + | 0.737990i | \(0.735775\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.20533 | − | 12.9427i | 0.141842 | − | 0.436546i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.02940 | − | 21.6343i | −0.236826 | − | 0.728877i | −0.996874 | − | 0.0790092i | \(-0.974824\pi\) |
0.760047 | − | 0.649868i | \(-0.225176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.3418 | + | 37.9840i | 0.415333 | + | 1.27826i | 0.911953 | + | 0.410295i | \(0.134574\pi\) |
−0.496620 | + | 0.867968i | \(0.665426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −95.6088 | + | 69.4639i | −3.21385 | + | 2.33500i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.4032 | − | 27.1750i | −1.25588 | − | 0.912447i | −0.257328 | − | 0.966324i | \(-0.582842\pi\) |
−0.998548 | + | 0.0538768i | \(0.982842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.72266 | − | 8.37948i | 0.0913150 | − | 0.281039i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.48786 | − | 3.26062i | 0.150349 | − | 0.109235i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.24303 | −0.141988 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.4067 | − | 41.2616i | −0.448137 | − | 1.37922i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.00718 | + | 6.54410i | 0.300741 | + | 0.218501i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1711 | 0.372578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.5977 | 1.41914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.27341 | 0.108932 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 72.8674 | 2.42219 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.3969 | − | 7.55378i | −0.345223 | − | 0.250819i | 0.401639 | − | 0.915798i | \(-0.368441\pi\) |
−0.746862 | + | 0.664979i | \(0.768441\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.86010 | + | 30.3463i | 0.327039 | + | 1.00652i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5040 | −0.944379 | −0.472189 | − | 0.881497i | \(-0.656536\pi\) | ||||
−0.472189 | + | 0.881497i | \(0.656536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.78069 | + | 4.92646i | −0.224408 | + | 0.163042i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.2687 | − | 62.3808i | 0.670064 | − | 2.06224i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.77066 | + | 3.46609i | 0.157541 | + | 0.114460i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2573 | − | 24.1629i | 1.09706 | − | 0.797060i | 0.116481 | − | 0.993193i | \(-0.462838\pi\) |
0.980577 | + | 0.196133i | \(0.0628385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3757 | + | 38.0886i | 0.407794 | + | 1.25506i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.48184 | − | 16.8714i | −0.180437 | − | 0.555328i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.5770 | − | 146.427i | 1.56432 | − | 4.81449i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.7997 | − | 54.7818i | −0.584618 | − | 1.79927i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.28138 | 0.206085 | 0.103043 | − | 0.994677i | \(-0.467142\pi\) | ||||
0.103043 | + | 0.994677i | \(0.467142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.62187 | + | 1.17836i | 0.0531546 | + | 0.0386191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.8830 | − | 16.6255i | 0.749155 | − | 0.544293i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −64.8425 | + | 47.1108i | −2.12058 | + | 1.54069i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.27331 | + | 22.3849i | −0.237609 | + | 0.731284i | 0.759156 | + | 0.650909i | \(0.225612\pi\) |
−0.996765 | + | 0.0803754i | \(0.974388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8663 | − | 14.4337i | −0.648314 | − | 0.471027i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.06914 | − | 24.8342i | 0.263046 | − | 0.809573i | −0.729091 | − | 0.684417i | \(-0.760057\pi\) |
0.992137 | − | 0.125156i | \(-0.0399432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.67806 | − | 4.22245i | −0.250032 | − | 0.137502i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.29136 | + | 25.5182i | −0.269718 | + | 0.830106i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7226 | + | 7.79046i | 0.348439 | + | 0.253156i | 0.748214 | − | 0.663458i | \(-0.230912\pi\) |
−0.399775 | + | 0.916613i | \(0.630912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.76145 | + | 26.9650i | −0.284409 | + | 0.875320i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6543 | − | 8.46733i | 0.377916 | − | 0.274572i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.21435 | − | 5.24153i | 0.233696 | − | 0.169790i | −0.464774 | − | 0.885429i | \(-0.653865\pi\) |
0.698470 | + | 0.715639i | \(0.253865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.3775 | + | 22.0705i | 0.982993 | + | 0.714186i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.8225 | 0.867049 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.09370 | − | 18.7545i | −0.196776 | − | 0.605614i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.08058 | + | 21.7918i | −0.228406 | + | 0.702961i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.0203 | − | 64.6938i | −0.677370 | − | 2.08473i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.3845 | + | 38.1155i | 0.398671 | + | 1.22698i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.91111 | − | 7.20084i | 0.318720 | − | 0.231563i | −0.416909 | − | 0.908948i | \(-0.636887\pi\) |
0.735629 | + | 0.677385i | \(0.236887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.2890 | + | 26.3655i | 1.16577 | + | 0.846983i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.1604 | + | 46.6590i | −0.486521 | + | 1.49736i | 0.343244 | + | 0.939246i | \(0.388474\pi\) |
−0.829765 | + | 0.558113i | \(0.811526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.6543 | + | 13.5532i | −0.598030 | + | 0.434494i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −109.312 | −3.50079 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.59866 | − | 14.1532i | −0.147124 | − | 0.452802i | 0.850154 | − | 0.526534i | \(-0.176509\pi\) |
−0.997278 | + | 0.0737325i | \(0.976509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0009 | + | 7.26604i | 0.319629 | + | 0.232224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.3683 | −1.28886 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.5699 | −0.656077 | −0.328038 | − | 0.944664i | \(-0.606388\pi\) | ||||
−0.328038 | + | 0.944664i | \(0.606388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.8515 | −1.68399 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.05494 | −0.192731 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.26679 | + | 0.920374i | 0.0402815 | + | 0.0292662i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.89316 | − | 24.2927i | −0.250735 | − | 0.771682i | −0.994640 | − | 0.103397i | \(-0.967029\pi\) |
0.743906 | − | 0.668285i | \(-0.232971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 90.0658 | 2.85815 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 70.3355 | − | 51.1018i | 2.22979 | − | 1.62003i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.92214 | − | 18.2265i | 0.187556 | − | 0.577238i | −0.812427 | − | 0.583063i | \(-0.801854\pi\) |
0.999983 | + | 0.00582463i | \(0.00185405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57.9305 | + | 42.0890i | 1.83284 | + | 1.33164i |
(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 | 1148.2.n.d.57.2 | ✓ | 24 | |
41.18 | even | 5 | inner | 1148.2.n.d.141.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.d.57.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1148.2.n.d.141.2 | yes | 24 | 41.18 | even | 5 | inner |