Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 81.11 | ||
Character | \(\chi\) | \(=\) | 1148.81 |
Dual form | 1148.2.r.a.737.11 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.900937 | − | 0.520156i | −0.520156 | − | 0.300312i | 0.216842 | − | 0.976207i | \(-0.430424\pi\) |
−0.736999 | + | 0.675894i | \(0.763758\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.292521 | − | 0.506661i | −0.130819 | − | 0.226586i | 0.793173 | − | 0.608996i | \(-0.208427\pi\) |
−0.923993 | + | 0.382410i | \(0.875094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.31637 | − | 1.27845i | −0.875505 | − | 0.483208i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.958875 | − | 1.66082i | −0.319625 | − | 0.553607i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.20234 | + | 1.84887i | 0.965541 | + | 0.557456i | 0.897874 | − | 0.440252i | \(-0.145111\pi\) |
0.0676673 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.26808i | 1.46110i | 0.682858 | + | 0.730551i | \(0.260737\pi\) | ||||
−0.682858 | + | 0.730551i | \(0.739263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.608626i | 0.157147i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.11543 | − | 3.53075i | −1.48321 | − | 0.856332i | −0.483393 | − | 0.875404i | \(-0.660596\pi\) |
−0.999818 | + | 0.0190716i | \(0.993929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.31072 | + | 0.756747i | −0.300701 | + | 0.173610i | −0.642758 | − | 0.766070i | \(-0.722210\pi\) |
0.342057 | + | 0.939679i | \(0.388876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.42191 | + | 2.35668i | 0.310286 | + | 0.514269i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.874295 | − | 1.51432i | −0.182303 | − | 0.315758i | 0.760361 | − | 0.649500i | \(-0.225022\pi\) |
−0.942664 | + | 0.333742i | \(0.891689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32886 | − | 4.03371i | 0.465773 | − | 0.806742i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.11600i | 0.984574i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.75036i | 1.06781i | 0.845543 | + | 0.533907i | \(0.179277\pi\) | ||||
−0.845543 | + | 0.533907i | \(0.820723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.171926 | + | 0.297785i | −0.0308789 | + | 0.0534838i | −0.881052 | − | 0.473020i | \(-0.843164\pi\) |
0.850173 | + | 0.526503i | \(0.176497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.92340 | − | 3.33143i | −0.334821 | − | 0.579928i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0298462 | + | 1.54759i | 0.00504492 | + | 0.261590i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.45853 | + | 9.45446i | 0.897377 | + | 1.55430i | 0.830835 | + | 0.556520i | \(0.187864\pi\) |
0.0665428 | + | 0.997784i | \(0.478803\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.74022 | − | 4.74620i | 0.438787 | − | 0.760001i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.85299 | + | 2.59664i | 0.914083 | + | 0.405527i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.68054 | −1.01877 | −0.509386 | − | 0.860538i | \(-0.670128\pi\) | ||||
−0.509386 | + | 0.860538i | \(0.670128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.560982 | + | 0.971650i | −0.0836263 | + | 0.144845i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.16800 | + | 1.82904i | −0.462100 | + | 0.266793i | −0.712927 | − | 0.701238i | \(-0.752631\pi\) |
0.250827 | + | 0.968032i | \(0.419298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.73114 | + | 5.92272i | 0.533019 | + | 0.846103i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.67308 | + | 6.36196i | 0.514334 | + | 0.890853i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.70126 | + | 3.29163i | 0.783129 | + | 0.452140i | 0.837538 | − | 0.546379i | \(-0.183994\pi\) |
−0.0544092 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.16333i | − | 0.291704i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.57451 | 0.208549 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.32530 | + | 7.49164i | −0.563106 | + | 0.975329i | 0.434117 | + | 0.900857i | \(0.357061\pi\) |
−0.997223 | + | 0.0744722i | \(0.976273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89099 | + | 8.47144i | 0.626227 | + | 1.08466i | 0.988302 | + | 0.152508i | \(0.0487349\pi\) |
−0.362075 | + | 0.932149i | \(0.617932\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0978348 | + | 5.07295i | 0.0123260 | + | 0.639131i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.66913 | − | 1.54102i | 0.331065 | − | 0.191140i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.77152 | − | 3.33219i | −0.705103 | − | 0.407092i | 0.104142 | − | 0.994562i | \(-0.466790\pi\) |
−0.809245 | + | 0.587471i | \(0.800124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.81908i | 0.218991i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.578775i | − | 0.0686879i | −0.999410 | − | 0.0343440i | \(-0.989066\pi\) | ||
0.999410 | − | 0.0343440i | \(-0.0109342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.30933 | − | 2.26783i | 0.153246 | − | 0.265430i | −0.779173 | − | 0.626809i | \(-0.784361\pi\) |
0.932419 | + | 0.361379i | \(0.117694\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.19632 | + | 2.42274i | −0.484549 | + | 0.279754i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.05411 | − | 8.37670i | −0.575970 | − | 0.954613i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.98613 | + | 4.03344i | −0.786001 | + | 0.453798i | −0.838553 | − | 0.544821i | \(-0.816598\pi\) |
0.0525521 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.215510 | + | 0.373274i | −0.0239455 | + | 0.0414749i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5509 | −1.37764 | −0.688818 | − | 0.724934i | \(-0.741870\pi\) | ||||
−0.688818 | + | 0.724934i | \(0.741870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.13127i | 0.448099i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.99108 | − | 5.18071i | 0.320678 | − | 0.555430i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.86660 | + | 3.38708i | −0.621858 | + | 0.359030i | −0.777592 | − | 0.628769i | \(-0.783559\pi\) |
0.155734 | + | 0.987799i | \(0.450226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.73497 | − | 12.2028i | 0.706017 | − | 1.27920i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.309790 | − | 0.178857i | 0.0321237 | − | 0.0185466i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.766829 | + | 0.442729i | 0.0786750 | + | 0.0454230i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7925i | 1.40042i | 0.713937 | + | 0.700210i | \(0.246910\pi\) | ||||
−0.713937 | + | 0.700210i | \(0.753090\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 7.09135i | − | 0.712707i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.25226 | + | 4.18710i | 0.721627 | + | 0.416632i | 0.815351 | − | 0.578967i | \(-0.196544\pi\) |
−0.0937241 | + | 0.995598i | \(0.529877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.43768 | − | 5.95424i | −0.338725 | − | 0.586689i | 0.645468 | − | 0.763787i | \(-0.276662\pi\) |
−0.984193 | + | 0.177098i | \(0.943329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.778098 | − | 1.40980i | 0.0759345 | − | 0.137583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.90236 | − | 5.02704i | −0.280582 | − | 0.485982i | 0.690946 | − | 0.722906i | \(-0.257194\pi\) |
−0.971528 | + | 0.236924i | \(0.923861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.86552 | − | 4.54116i | −0.753380 | − | 0.434964i | 0.0735340 | − | 0.997293i | \(-0.476572\pi\) |
−0.826914 | + | 0.562329i | \(0.809906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.3572i | − | 1.07797i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.42377 | 0.322081 | 0.161041 | − | 0.986948i | \(-0.448515\pi\) | ||||
0.161041 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.511499 | + | 0.885943i | −0.0476976 | + | 0.0826146i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.74933 | − | 5.05143i | 0.808876 | − | 0.467005i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.65173 | + | 15.9968i | 0.884772 | + | 1.46642i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.33665 | + | 2.31514i | 0.121513 | + | 0.210467i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.92251 | − | 5.38388i | −0.353681 | − | 0.485448i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65017 | −0.505367 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.31448 | 0.649055 | 0.324527 | − | 0.945876i | \(-0.394795\pi\) | ||||
0.324527 | + | 0.945876i | \(0.394795\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.01874 | + | 3.47492i | 0.529921 | + | 0.305950i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.56165 | + | 16.5613i | 0.835406 | + | 1.44696i | 0.893700 | + | 0.448665i | \(0.148100\pi\) |
−0.0582943 | + | 0.998299i | \(0.518566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00359 | − | 0.0772115i | 0.347155 | − | 0.00669509i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59208 | − | 1.49654i | 0.223090 | − | 0.128801i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.23653 | − | 0.713909i | −0.105644 | − | 0.0609933i | 0.446247 | − | 0.894910i | \(-0.352760\pi\) |
−0.551891 | + | 0.833916i | \(0.686094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3168 | −1.04470 | −0.522348 | − | 0.852732i | \(-0.674944\pi\) | ||||
−0.522348 | + | 0.852732i | \(0.674944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.80555 | 0.320485 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.74000 | + | 16.8702i | −0.814499 | + | 1.41075i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.91348 | − | 1.68210i | 0.241952 | − | 0.139691i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.280778 | − | 7.27677i | −0.0231582 | − | 0.600178i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3161 | − | 8.26542i | 1.17282 | − | 0.677129i | 0.218479 | − | 0.975842i | \(-0.429890\pi\) |
0.954343 | + | 0.298712i | \(0.0965570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00794 | − | 1.15929i | −0.163404 | − | 0.0943414i | 0.416068 | − | 0.909334i | \(-0.363408\pi\) |
−0.579472 | + | 0.814992i | \(0.696741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.5422i | 1.09482i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.201168 | 0.0161582 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.76182 | + | 2.17189i | 0.300226 | + | 0.173335i | 0.642544 | − | 0.766249i | \(-0.277879\pi\) |
−0.342319 | + | 0.939584i | \(0.611212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.42432 | − | 5.93109i | −0.271566 | − | 0.470366i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0892051 | + | 4.62548i | 0.00703034 | + | 0.364539i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.99921 | + | 17.3191i | 0.783199 | + | 1.35654i | 0.930069 | + | 0.367385i | \(0.119747\pi\) |
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.12527 | + | 1.94903i | −0.0876023 | + | 0.151732i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 10.1008i | − | 0.781626i | −0.920470 | − | 0.390813i | \(-0.872194\pi\) | ||
0.920470 | − | 0.390813i | \(-0.127806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.7526 | −1.13482 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.51364 | + | 1.45125i | 0.192223 | + | 0.110980i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8888 | − | 20.5921i | −0.903891 | − | 1.56559i | −0.822399 | − | 0.568912i | \(-0.807365\pi\) |
−0.0814928 | − | 0.996674i | \(-0.525969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5514 | + | 6.36623i | −0.797611 | + | 0.481242i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.79365 | − | 4.49966i | 0.585806 | − | 0.338215i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.44227 | + | 0.832694i | 0.107800 | + | 0.0622385i | 0.552931 | − | 0.833227i | \(-0.313509\pi\) |
−0.445131 | + | 0.895466i | \(0.646843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.05454i | − | 0.227042i | −0.993536 | − | 0.113521i | \(-0.963787\pi\) | ||
0.993536 | − | 0.113521i | \(-0.0362129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.1763i | − | 0.752254i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.19347 | − | 5.53125i | 0.234789 | − | 0.406666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.0558 | − | 22.6133i | −0.954734 | − | 1.65365i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.54054 | − | 11.8505i | 0.475754 | − | 0.862000i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.6233 | − | 13.6389i | 1.70932 | − | 0.986876i | 0.773920 | − | 0.633283i | \(-0.218293\pi\) |
0.935399 | − | 0.353593i | \(-0.115040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3992 | − | 9.46809i | −1.18044 | − | 0.681528i | −0.224324 | − | 0.974515i | \(-0.572017\pi\) |
−0.956116 | + | 0.292987i | \(0.905351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.20629 | −0.229607 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.61440 | −0.613750 | −0.306875 | − | 0.951750i | \(-0.599283\pi\) | ||||
−0.306875 | + | 0.951750i | \(0.599283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9211 | − | 9.76942i | −1.19951 | − | 0.692536i | −0.239061 | − | 0.971004i | \(-0.576840\pi\) |
−0.960445 | + | 0.278469i | \(0.910173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.46652 | + | 6.00418i | 0.244509 | + | 0.423502i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.35154 | − | 13.3200i | 0.515977 | − | 0.934877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.396505 | − | 3.72505i | −0.0276931 | − | 0.260169i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.67668 | + | 2.90410i | −0.116537 | + | 0.201849i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.59651 | −0.387119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.936344i | − | 0.0644606i | −0.999480 | − | 0.0322303i | \(-0.989739\pi\) | ||
0.999480 | − | 0.0322303i | \(-0.0102610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.301053 | + | 0.521439i | −0.0206278 | + | 0.0357284i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95420 | + | 3.38477i | 0.133275 | + | 0.230839i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.778949 | − | 0.469982i | 0.0528785 | − | 0.0319044i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.35925 | + | 1.36212i | −0.159424 | + | 0.0920432i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6003 | − | 32.2166i | 1.25119 | − | 2.16712i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.5956 | −1.24526 | −0.622628 | − | 0.782518i | \(-0.713935\pi\) | ||||
−0.622628 | + | 0.782518i | \(0.713935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.93236 | −0.595490 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.12475 | − | 5.26818i | −0.605631 | − | 0.349661i | 0.165623 | − | 0.986189i | \(-0.447037\pi\) |
−0.771254 | + | 0.636528i | \(0.780370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.83362 | + | 3.36804i | −0.385496 | + | 0.222567i | −0.680207 | − | 0.733020i | \(-0.738110\pi\) |
0.294711 | + | 0.955587i | \(0.404777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.196246 | + | 10.1758i | 0.0129121 | + | 0.669518i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.97709 | + | 4.02822i | −0.457084 | + | 0.263898i | −0.710817 | − | 0.703376i | \(-0.751675\pi\) |
0.253733 | + | 0.967274i | \(0.418341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.85341 | + | 1.07007i | 0.120903 | + | 0.0698035i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.39208 | 0.545124 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.32187i | − | 0.538297i | −0.963099 | − | 0.269148i | \(-0.913258\pi\) | ||
0.963099 | − | 0.269148i | \(-0.0867422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.96507 | + | 5.13565i | −0.190997 | + | 0.330816i | −0.945581 | − | 0.325387i | \(-0.894505\pi\) |
0.754584 | + | 0.656203i | \(0.227839\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6801 | − | 7.89819i | 0.877577 | − | 0.506669i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.90938 | − | 3.62294i | 0.121986 | − | 0.231461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.98660 | − | 6.90500i | −0.253662 | − | 0.439355i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.3075 | + | 6.52841i | 0.716586 | + | 0.413721i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.32172 | −0.146545 | −0.0732727 | − | 0.997312i | \(-0.523344\pi\) | ||||
−0.0732727 | + | 0.997312i | \(0.523344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.46584i | − | 0.406504i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.14891 | − | 3.72201i | 0.134570 | − | 0.233082i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.45940 | − | 4.30669i | 0.465305 | − | 0.268644i | −0.248967 | − | 0.968512i | \(-0.580091\pi\) |
0.714272 | + | 0.699868i | \(0.246758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.556939 | − | 28.8785i | −0.0346065 | − | 1.79442i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.55031 | − | 5.51388i | 0.591150 | − | 0.341300i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.2714 | + | 11.1264i | 1.18833 | + | 0.686081i | 0.957926 | − | 0.287015i | \(-0.0926630\pi\) |
0.230401 | + | 0.973096i | \(0.425996\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.85148i | − | 0.236594i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.04724 | 0.431284 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.10793 | + | 5.38310i | −0.189494 | + | 0.328213i | −0.945082 | − | 0.326834i | \(-0.894018\pi\) |
0.755588 | + | 0.655048i | \(0.227351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.63733 | − | 6.30003i | −0.220952 | − | 0.382700i | 0.734145 | − | 0.678992i | \(-0.237583\pi\) |
−0.955097 | + | 0.296292i | \(0.904250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.4151 | + | 7.49073i | −0.751399 | + | 0.453360i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.9156 | − | 8.61153i | 0.899445 | − | 0.519295i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.27160 | + | 3.93452i | −0.136487 | + | 0.236403i | −0.926165 | − | 0.377120i | \(-0.876915\pi\) |
0.789677 | + | 0.613522i | \(0.210248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.659424 | 0.0394787 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.41305i | − | 0.501880i | −0.968003 | − | 0.250940i | \(-0.919260\pi\) | ||
0.968003 | − | 0.250940i | \(-0.0807398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3453 | + | 17.9186i | −0.614965 | + | 1.06515i | 0.375426 | + | 0.926853i | \(0.377497\pi\) |
−0.990391 | + | 0.138298i | \(0.955837\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.460576 | − | 0.797741i | −0.0272822 | − | 0.0472541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.2380 | − | 13.4975i | −0.604331 | − | 0.796734i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4324 | + | 28.4617i | 0.966609 | + | 1.67422i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.17427 | − | 12.4262i | 0.420563 | − | 0.728437i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.574132i | 0.0335411i | 0.999859 | + | 0.0167706i | \(0.00533849\pi\) | ||||
−0.999859 | + | 0.0167706i | \(0.994662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.06097 | 0.294661 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.45882 | + | 16.3832i | −0.548856 | + | 0.950647i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.97758 | − | 4.60586i | 0.461355 | − | 0.266363i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4746 | + | 8.54073i | 0.891941 | + | 0.492279i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.35589 | − | 7.54462i | −0.250239 | − | 0.433427i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.86143 | − | 4.95615i | 0.163845 | − | 0.283788i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.74527 | −0.327900 | −0.163950 | − | 0.986469i | \(-0.552424\pi\) | ||||
−0.163950 | + | 0.986469i | \(0.552424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.15253i | 0.406893i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.92886 | − | 4.57773i | −0.449604 | − | 0.259579i | 0.258059 | − | 0.966129i | \(-0.416917\pi\) |
−0.707663 | + | 0.706550i | \(0.750251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.03179 | − | 2.32776i | 0.227890 | − | 0.131573i | −0.381708 | − | 0.924283i | \(-0.624664\pi\) |
0.609598 | + | 0.792710i | \(0.291331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.54165 | − | 1.53351i | 0.143206 | − | 0.0864036i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0258 | − | 7.52048i | 0.731605 | − | 0.422392i | −0.0874044 | − | 0.996173i | \(-0.527857\pi\) |
0.819009 | + | 0.573781i | \(0.194524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6317 | + | 18.4146i | −0.595259 | + | 1.03102i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.03873i | 0.337049i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.6875 | 0.594670 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.2499 | + | 12.2686i | 1.17873 | + | 0.680541i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.72422 | + | 8.18259i | 0.261250 | + | 0.452498i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.67659 | − | 0.186619i | 0.533488 | − | 0.0102886i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.6856 | + | 12.5202i | −1.19195 | + | 0.688173i | −0.958748 | − | 0.284256i | \(-0.908254\pi\) |
−0.233202 | + | 0.972428i | \(0.574920\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.4681 | − | 18.1313i | 0.573649 | − | 0.993589i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.89894i | 0.213022i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.4017 | −1.32924 | −0.664622 | − | 0.747180i | \(-0.731407\pi\) | ||||
−0.664622 | + | 0.747180i | \(0.731407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.08460 | − | 1.78090i | −0.167533 | − | 0.0967250i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.10113 | + | 0.635740i | −0.0596297 | + | 0.0344272i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.07079 | − | 18.4893i | −0.0578174 | − | 0.998327i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.921657 | − | 0.532119i | 0.0496203 | − | 0.0286483i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.6563 | − | 14.2354i | −1.32362 | − | 0.764194i | −0.339318 | − | 0.940672i | \(-0.610196\pi\) |
−0.984305 | + | 0.176478i | \(0.943529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.7122 | −1.10870 | −0.554349 | − | 0.832284i | \(-0.687033\pi\) | ||||
−0.554349 | + | 0.832284i | \(0.687033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.9515 | −1.43856 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.20828 | − | 9.02101i | 0.277209 | − | 0.480140i | −0.693481 | − | 0.720475i | \(-0.743924\pi\) |
0.970690 | + | 0.240335i | \(0.0772573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.293243 | + | 0.169304i | −0.0155637 | + | 0.00898571i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.374767 | − | 19.4325i | −0.0198348 | − | 1.02848i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.194552 | − | 0.336974i | −0.0102681 | − | 0.0177848i | 0.860846 | − | 0.508866i | \(-0.169935\pi\) |
−0.871114 | + | 0.491081i | \(0.836602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.35467 | + | 14.4707i | −0.439719 | + | 0.761616i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.78106i | − | 0.145968i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.53203 | −0.0801901 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5896 | + | 23.5378i | −0.709370 | + | 1.22867i | 0.255721 | + | 0.966751i | \(0.417687\pi\) |
−0.965091 | + | 0.261915i | \(0.915646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.29973 | − | 12.2106i | −0.0676613 | − | 0.635659i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.99806 | − | 14.9134i | −0.467156 | − | 0.774265i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2112 | + | 19.4183i | 0.580491 | + | 1.00544i | 0.995421 | + | 0.0955871i | \(0.0304728\pi\) |
−0.414930 | + | 0.909853i | \(0.636194\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.09045 | + | 2.93897i | 0.262870 | + | 0.151768i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.2933 | −1.56019 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0751 | 1.64759 | 0.823793 | − | 0.566890i | \(-0.191854\pi\) | ||||
0.823793 | + | 0.566890i | \(0.191854\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.58988 | − | 3.80467i | −0.337610 | − | 0.194919i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0836 | − | 8.70853i | 0.770737 | − | 0.444985i | −0.0624006 | − | 0.998051i | \(-0.519876\pi\) |
0.833137 | + | 0.553066i | \(0.186542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.76571 | + | 5.01108i | −0.140954 | + | 0.255388i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.40580 | + | 11.0952i | 0.325625 | + | 0.563999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.13827 | − | 1.97154i | 0.0577124 | − | 0.0999609i | −0.835726 | − | 0.549147i | \(-0.814953\pi\) |
0.893438 | + | 0.449186i | \(0.148286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3477i | 0.624448i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.8942i | − | 1.00353i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.08718 | + | 2.35973i | 0.205648 | + | 0.118731i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1801 | + | 9.34156i | −0.812054 | + | 0.468840i | −0.847669 | − | 0.530526i | \(-0.821994\pi\) |
0.0356146 | + | 0.999366i | \(0.488661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.64714 | − | 2.01293i | −0.182585 | − | 0.100772i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5182 | + | 33.8065i | 0.974693 | + | 1.68822i | 0.680945 | + | 0.732334i | \(0.261569\pi\) |
0.293748 | + | 0.955883i | \(0.405097\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.56876 | − | 0.905722i | −0.0781453 | − | 0.0451172i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.252164 | 0.0125301 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.3685i | 2.00099i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3868 | − | 23.1865i | 0.661932 | − | 1.14650i | −0.318175 | − | 0.948032i | \(-0.603070\pi\) |
0.980107 | − | 0.198468i | \(-0.0635967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.742688 | + | 1.28637i | 0.0366341 | + | 0.0634521i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.5967 | − | 11.8237i | 0.964290 | − | 0.581808i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.67139 | + | 6.35904i | 0.180222 | + | 0.312153i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0966 | + | 6.40665i | 0.543405 | + | 0.313735i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1830 | 1.08371 | 0.541856 | − | 0.840471i | \(-0.317722\pi\) | ||||
0.541856 | + | 0.840471i | \(0.317722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.2304i | 1.57081i | 0.618981 | + | 0.785406i | \(0.287546\pi\) | ||||
−0.618981 | + | 0.785406i | \(0.712454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.07543 | + | 3.50765i | 0.295397 | + | 0.170548i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.4840 | + | 16.4453i | −1.38168 | + | 0.797712i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.499031 | − | 25.8759i | −0.0241498 | − | 1.25222i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.5502 | − | 10.1326i | 0.847334 | − | 0.489208i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1879 | − | 19.3781i | 0.538904 | − | 0.933409i | −0.460059 | − | 0.887888i | \(-0.652172\pi\) |
0.998963 | − | 0.0455210i | \(-0.0144948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1125 | 1.73546 | 0.867729 | − | 0.497038i | \(-0.165579\pi\) | ||||
0.867729 | + | 0.497038i | \(0.165579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.49982 | −0.167803 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.29192 | + | 1.32324i | 0.109637 | + | 0.0632992i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.80962 | − | 2.77684i | 0.229551 | − | 0.132531i | −0.380814 | − | 0.924652i | \(-0.624356\pi\) |
0.610365 | + | 0.792120i | \(0.291023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.25888 | − | 11.8759i | 0.298042 | − | 0.565519i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1112 | + | 29.6374i | 0.812977 | + | 1.40812i | 0.910772 | + | 0.412911i | \(0.135488\pi\) |
−0.0977946 | + | 0.995207i | \(0.531179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.43220 | + | 1.98158i | 0.162702 | + | 0.0939361i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.1972 | −0.813401 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.79859 | −0.273652 | −0.136826 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136826 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.9424 | + | 19.1367i | 0.656522 | + | 0.901114i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.20602 | + | 2.08889i | 0.0566638 | + | 0.0981445i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.15281 | + | 0.157232i | −0.382210 | + | 0.00737114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.2389 | + | 15.7264i | −1.27418 | + | 0.735650i | −0.975773 | − | 0.218787i | \(-0.929790\pi\) |
−0.298411 | + | 0.954438i | \(0.596457\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.0633 | − | 31.2865i | 0.843122 | − | 1.46033i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0603 | −1.02745 | −0.513726 | − | 0.857955i | \(-0.671735\pi\) | ||||
−0.513726 | + | 0.857955i | \(0.671735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.2913i | − | 0.850070i | −0.905177 | − | 0.425035i | \(-0.860262\pi\) | ||
0.905177 | − | 0.425035i | \(-0.139738\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.181240 | − | 0.104639i | −0.00840480 | − | 0.00485252i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.7429 | − | 28.9995i | −0.774768 | − | 1.34194i | −0.934925 | − | 0.354846i | \(-0.884533\pi\) |
0.160157 | − | 0.987092i | \(-0.448800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.10894 | + | 15.0972i | 0.420612 | + | 0.697123i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.25944 | − | 3.91347i | −0.104110 | − | 0.180323i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.3933 | − | 12.3515i | −0.983667 | − | 0.567920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.04944i | 0.323451i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.6250i | − | 0.578061i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.69684 | + | 0.979671i | 0.0775306 | + | 0.0447623i | 0.538264 | − | 0.842776i | \(-0.319080\pi\) |
−0.460734 | + | 0.887539i | \(0.652414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.8068 | + | 28.7560i | −2.27100 | + | 1.31116i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.32560 | − | 4.21366i | 0.105819 | − | 0.191728i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.98814 | − | 4.03460i | 0.317315 | − | 0.183202i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.91828 | + | 13.7149i | −0.358811 | + | 0.621480i | −0.987763 | − | 0.155965i | \(-0.950151\pi\) |
0.628951 | + | 0.777445i | \(0.283485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.8046i | − | 0.940817i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.42402 | −0.289912 | −0.144956 | − | 0.989438i | \(-0.546304\pi\) | ||||
−0.144956 | + | 0.989438i | \(0.546304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.3031 | − | 35.1659i | 0.914404 | − | 1.58379i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.59291 | + | 2.07437i | −0.161489 | + | 0.0932359i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.739934 | + | 1.34066i | −0.0331906 | + | 0.0601366i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.7146 | + | 21.1972i | −1.64357 | + | 0.948917i | −0.664023 | + | 0.747712i | \(0.731152\pi\) |
−0.979549 | + | 0.201205i | \(0.935514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.25401 | + | 9.10021i | −0.234732 | + | 0.406567i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2174i | 1.43650i | 0.695783 | + | 0.718252i | \(0.255058\pi\) | ||||
−0.695783 | + | 0.718252i | \(0.744942\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.89925i | − | 0.218014i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.2912 | + | 7.67368i | 0.590283 | + | 0.340800i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.01038 | + | 5.20215i | −0.399378 | + | 0.230581i | −0.686216 | − | 0.727398i | \(-0.740729\pi\) |
0.286837 | + | 0.957979i | \(0.407396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.93221 | + | 3.57922i | −0.262425 | + | 0.158335i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.87152 | − | 6.70566i | −0.170932 | − | 0.296062i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.01119 | + | 3.48348i | −0.0886236 | + | 0.153501i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5267 | −0.594902 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.7362i | 1.08580i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.8054 | + | 17.7855i | 1.34961 | + | 0.779196i | 0.988194 | − | 0.153209i | \(-0.0489608\pi\) |
0.361414 | + | 0.932405i | \(0.382294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.77765 | + | 4.81103i | 0.121458 | + | 0.210372i | 0.920343 | − | 0.391112i | \(-0.127910\pi\) |
−0.798885 | + | 0.601484i | \(0.794576\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.8176 | − | 0.247195i | 0.559405 | − | 0.0107885i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.10281 | − | 1.21406i | 0.0915999 | − | 0.0528852i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.97122 | − | 17.2707i | 0.433531 | − | 0.750898i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.5897 | 0.719932 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6793 | + | 30.8340i | −0.592516 | + | 1.33557i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.69800 | + | 2.94103i | −0.0734111 | + | 0.127152i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.866262 | − | 1.50041i | −0.0373820 | − | 0.0647475i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.998013 | + | 25.8649i | 0.0429875 | + | 1.11408i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2603 | − | 28.1638i | −0.699087 | − | 1.21085i | −0.968783 | − | 0.247909i | \(-0.920257\pi\) |
0.269696 | − | 0.962945i | \(-0.413077\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.58884 | + | 2.75194i | −0.0681835 | + | 0.118097i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.31354i | 0.227607i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.1614i | − | 0.605498i | −0.953070 | − | 0.302749i | \(-0.902096\pi\) | ||
0.953070 | − | 0.302749i | \(-0.0979044\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.37969 | − | 16.2461i | 0.400316 | − | 0.693367i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.35157 | − | 7.53714i | −0.185383 | − | 0.321093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.3390 | − | 0.411535i | 0.907426 | − | 0.0175003i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.75423 | + | 3.32221i | −0.244253 | + | 0.141020i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5490 | + | 7.82251i | 0.574089 | + | 0.331451i | 0.758781 | − | 0.651346i | \(-0.225795\pi\) |
−0.184692 | + | 0.982797i | \(0.559129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 35.1936i | − | 1.48853i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.1642i | 1.14687i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.19721 | − | 3.00061i | −0.219036 | − | 0.126461i | 0.386468 | − | 0.922303i | \(-0.373695\pi\) |
−0.605504 | + | 0.795842i | \(0.707028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.00153 | − | 1.73469i | −0.0421345 | − | 0.0729791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.976411 | − | 0.589122i | 0.0410054 | − | 0.0247408i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6124 | + | 35.7018i | 0.864119 | + | 1.49670i | 0.867920 | + | 0.496705i | \(0.165457\pi\) |
−0.00380101 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0634 | − | 16.2024i | −1.17442 | − | 0.678050i | −0.219701 | − | 0.975567i | \(-0.570508\pi\) |
−0.954717 | + | 0.297517i | \(0.903842\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.3774 | −1.18548 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.14446 | −0.339647 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8069 | − | 13.7449i | −0.991094 | − | 0.572209i | −0.0854930 | − | 0.996339i | \(-0.527247\pi\) |
−0.905601 | + | 0.424130i | \(0.860580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.84976 | + | 17.0603i | 0.409342 | + | 0.709002i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0724 | + | 16.0456i | 1.20613 | + | 0.665685i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.1716 | + | 21.0818i | 0.504096 | + | 0.873119i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.11873 | − | 2.95530i | −0.211633 | − | 0.122187i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7733i | 0.816131i | 0.912953 | + | 0.408065i | \(0.133796\pi\) | ||||
−0.912953 | + | 0.408065i | \(0.866204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.520420i | − | 0.0214435i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.76103 | + | 4.48083i | 0.319246 | + | 0.184317i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.04327 | − | 4.64378i | 0.330297 | − | 0.190697i | −0.325676 | − | 0.945482i | \(-0.605592\pi\) |
0.655973 | + | 0.754784i | \(0.272258\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28162 | − | 9.56955i | 0.216525 | − | 0.392313i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.1632 | + | 17.6033i | 0.415954 | + | 0.720453i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.34701 | + | 7.52925i | −0.177614 | + | 0.307637i | −0.941063 | − | 0.338232i | \(-0.890171\pi\) |
0.763449 | + | 0.645868i | \(0.223505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.12212i | 0.372099i | 0.982540 | + | 0.186050i | \(0.0595685\pi\) | ||||
−0.982540 | + | 0.186050i | \(0.940432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.7806i | 0.520467i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.781995 | − | 1.35446i | 0.0317926 | − | 0.0550664i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3288 | + | 19.6220i | 0.459821 | + | 0.796434i | 0.998951 | − | 0.0457886i | \(-0.0145801\pi\) |
−0.539130 | + | 0.842223i | \(0.681247\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.5517 | + | 8.17649i | −0.549144 | + | 0.331328i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.63555 | − | 16.6893i | −0.389812 | − | 0.675175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5566 | + | 25.2129i | −0.587937 | + | 1.01834i | 0.406565 | + | 0.913622i | \(0.366727\pi\) |
−0.994502 | + | 0.104716i | \(0.966607\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.58038 | + | 3.56228i | −0.0637272 | + | 0.143645i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.3830 | 1.06214 | 0.531070 | − | 0.847328i | \(-0.321790\pi\) | ||||
0.531070 | + | 0.847328i | \(0.321790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.18786 | − | 2.05743i | 0.0477440 | − | 0.0826950i | −0.841166 | − | 0.540777i | \(-0.818130\pi\) |
0.888910 | + | 0.458082i | \(0.151464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.74727 | − | 4.47289i | 0.310887 | − | 0.179491i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.9194 | − | 0.345587i | 0.717926 | − | 0.0138456i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.99152 | − | 17.3058i | −0.399661 | − | 0.692233i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.04210 | + | 2.91106i | 0.201362 | + | 0.116257i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 77.0908i | − | 3.07381i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2459 | 0.447692 | 0.223846 | − | 0.974625i | \(-0.428139\pi\) | ||||
0.223846 | + | 0.974625i | \(0.428139\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.487045 | + | 0.843587i | −0.0193583 | + | 0.0335296i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.13964 | − | 3.70596i | −0.0849089 | − | 0.147067i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.2014 | + | 19.6559i | −1.23624 | + | 0.778796i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.961241 | + | 0.554973i | −0.0380261 | + | 0.0219544i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.2431 | − | 9.95529i | −0.681060 | − | 0.393210i | 0.119194 | − | 0.992871i | \(-0.461969\pi\) |
−0.800254 | + | 0.599661i | \(0.795302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5171i | 1.12460i | 0.826932 | + | 0.562302i | \(0.190084\pi\) | ||||
−0.826932 | + | 0.562302i | \(0.809916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.06595i | − | 0.160097i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.4912 | + | 21.6353i | −0.491078 | + | 0.850572i | −0.999947 | − | 0.0102720i | \(-0.996730\pi\) |
0.508869 | + | 0.860844i | \(0.330064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.7022 | + | 15.9939i | −1.08741 | + | 0.627814i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.946247 | + | 0.0182489i | −0.0370864 | + | 0.000715233i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.6188 | + | 13.0590i | −0.885141 | + | 0.511037i | −0.872350 | − | 0.488882i | \(-0.837405\pi\) |
−0.0127912 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.59397 | − | 9.68904i | 0.218574 | − | 0.378582i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.02195 | −0.195925 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 14.3637i | − | 0.559530i | −0.960069 | − | 0.279765i | \(-0.909744\pi\) | ||
0.960069 | − | 0.279765i | \(-0.0902565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.48560 | − | 9.50134i | 0.213365 | − | 0.369559i | −0.739400 | − | 0.673266i | \(-0.764891\pi\) |
0.952766 | + | 0.303707i | \(0.0982243\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.5153 | + | 19.3501i | −1.30163 | + | 0.751494i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.21025 | − | 2.00588i | −0.0469316 | − | 0.0777845i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.70790 | − | 5.02751i | 0.337171 | − | 0.194666i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7535 | + | 9.67263i | 0.647727 | + | 0.373966i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.1712i | 1.39637i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 29.2345i | − | 1.12691i | −0.826148 | − | 0.563454i | \(-0.809472\pi\) | ||
0.826148 | − | 0.563454i | \(-0.190528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.6364 | + | 11.9145i | 0.794297 | + | 0.458588i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.00843068 | − | 0.0146024i | −0.000324017 | − | 0.000561215i | 0.865863 | − | 0.500281i | \(-0.166770\pi\) |
−0.866187 | + | 0.499719i | \(0.833436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.6331 | − | 31.9486i | 0.676694 | − | 1.22607i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.48055 | + | 9.49259i | 0.210015 | + | 0.363757i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.5896 | − | 15.9289i | −1.05569 | − | 0.609502i | −0.131452 | − | 0.991323i | \(-0.541964\pi\) |
−0.924236 | + | 0.381821i | \(0.875297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.835333i | 0.0319164i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00763 | 0.267358 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3405 | + | 30.0347i | −0.660622 | + | 1.14423i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9978 | − | 13.8551i | 0.912918 | − | 0.527073i | 0.0315489 | − | 0.999502i | \(-0.489956\pi\) |
0.881369 | + | 0.472429i | \(0.156623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.06593 | + | 16.4262i | −0.344386 | + | 0.623979i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.60292 | + | 6.24044i | 0.136667 | + | 0.236713i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.6255 | − | 36.5450i | −1.00851 | − | 1.38424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.38122 | 0.317007 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.43510 | −0.129742 | −0.0648710 | − | 0.997894i | \(-0.520664\pi\) | ||||
−0.0648710 | + | 0.997894i | \(0.520664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3093 | − | 8.26146i | −0.539684 | − | 0.311587i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.11320 | − | 1.92813i | −0.0419257 | − | 0.0726174i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4459 | − | 18.9705i | −0.430469 | − | 0.713460i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.6236 | − | 18.8352i | 1.22520 | − | 0.707372i | 0.259181 | − | 0.965829i | \(-0.416547\pi\) |
0.966023 | + | 0.258457i | \(0.0832140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3976 | + | 7.73513i | 0.502451 | + | 0.290090i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.601258 | 0.0225173 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3966 | 0.426209 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.32867 | + | 7.49748i | −0.161657 | + | 0.279998i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3528 | − | 6.55453i | 0.423387 | − | 0.244443i | −0.273138 | − | 0.961975i | \(-0.588062\pi\) |
0.696525 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.350750 | + | 18.1871i | 0.0130626 | + | 0.677324i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.34268 | − | 3.08460i | 0.198696 | − | 0.114717i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.1953 | + | 13.3918i | 0.861451 | + | 0.497359i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5578i | 1.39294i | 0.717586 | + | 0.696470i | \(0.245247\pi\) | ||||
−0.717586 | + | 0.696470i | \(0.754753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.1401 | −0.560745 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.8544 | + | 23.5873i | 1.51105 | + | 0.872407i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.71153 | + | 15.0888i | 0.321768 | + | 0.557318i | 0.980853 | − | 0.194750i | \(-0.0623897\pi\) |
−0.659085 | + | 0.752068i | \(0.729056\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.60472 | + | 2.27087i | −0.132962 | + | 0.0837622i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.3216 | − | 21.3416i | −0.453871 | − | 0.786128i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.8677 | − | 24.0195i | 0.510131 | − | 0.883572i | −0.489800 | − | 0.871835i | \(-0.662930\pi\) |
0.999931 | − | 0.0117377i | \(-0.00373630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.29462i | 0.304711i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1178 | 0.664676 | 0.332338 | − | 0.943160i | \(-0.392163\pi\) | ||||
0.332338 | + | 0.943160i | \(0.392163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.37553 | − | 4.83562i | −0.306856 | − | 0.177163i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0347 | + | 20.8447i | 0.440327 | + | 0.762669i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.296130 | + | 15.3550i | 0.0108204 | + | 0.561060i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2287 | − | 13.9884i | 0.884118 | − | 0.510446i | 0.0121037 | − | 0.999927i | \(-0.496147\pi\) |
0.872014 | + | 0.489481i | \(0.162814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.09172 | + | 1.20766i | 0.0762265 | + | 0.0440094i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.35646i | 0.0493667i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.89388i | 0.323254i | 0.986852 | + | 0.161627i | \(0.0516741\pi\) | ||||
−0.986852 | + | 0.161627i | \(0.948326\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.36324 | + | 5.82531i | −0.122078 | + | 0.211445i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.17287 | + | 2.03146i | 0.0425163 | + | 0.0736405i | 0.886500 | − | 0.462728i | \(-0.153129\pi\) |
−0.843984 | + | 0.536368i | \(0.819796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.4138 | + | 20.5747i | 0.449410 | + | 0.744853i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.86130 | − | 3.96137i | 0.248071 | − | 0.143224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.4666 | − | 22.7860i | −1.42505 | − | 0.822756i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.5978 | −1.21157 | −0.605783 | − | 0.795630i | \(-0.707140\pi\) | ||||
−0.605783 | + | 0.795630i | \(0.707140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.96060 | −0.322708 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.9753 | − | 11.5328i | −0.718463 | − | 0.414805i | 0.0957237 | − | 0.995408i | \(-0.469483\pi\) |
−0.814187 | + | 0.580603i | \(0.802817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.800786 | + | 1.38700i | 0.0287651 | + | 0.0498226i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.5195 | + | 26.3074i | −0.520886 | + | 0.943772i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.63666 | + | 1.02575i | −0.345269 | + | 0.0367514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07008 | − | 1.85343i | 0.0382905 | − | 0.0663210i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.4188 | −1.05134 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.54129i | − | 0.0907025i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.16267 | − | 5.47791i | 0.112737 | − | 0.195266i | −0.804136 | − | 0.594446i | \(-0.797372\pi\) |
0.916873 | + | 0.399179i | \(0.130705\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.5749 | − | 20.0483i | −0.412077 | − | 0.713738i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.93072 | − | 4.37712i | −0.281984 | − | 0.155632i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.6282 | + | 25.7661i | −1.58479 | + | 0.914981i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00337 | + | 3.46994i | −0.0710522 | + | 0.123066i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.0158 | 1.62996 | 0.814982 | − | 0.579487i | \(-0.196747\pi\) | ||||
0.814982 | + | 0.579487i | \(0.196747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.8316 | 0.913855 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.2507 | + | 6.49558i | 0.397523 | + | 0.229510i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.38586 | − | 4.84158i | 0.295930 | − | 0.170856i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31745 | − | 1.39825i | 0.0816795 | − | 0.0492817i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.60010 | − | 3.23322i | 0.197133 | − | 0.113815i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0256 | + | 6.36564i | 0.387640 | + | 0.223804i | 0.681137 | − | 0.732156i | \(-0.261486\pi\) |
−0.293497 | + | 0.955960i | \(0.594819\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.4308 | −0.998342 | −0.499171 | − | 0.866504i | \(-0.666362\pi\) | ||||
−0.499171 | + | 0.866504i | \(0.666362\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.56791i | 0.265418i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.84996 | − | 10.1324i | 0.204915 | − | 0.354923i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.75635 | − | 5.05548i | 0.306346 | − | 0.176869i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.7247 | + | 0.515402i | −0.933836 | + | 0.0180096i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1866 | + | 26.3039i | 0.530014 | + | 0.918012i | 0.999387 | + | 0.0350117i | \(0.0111468\pi\) |
−0.469372 | + | 0.883000i | \(0.655520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8687 | + | 20.1314i | 1.21545 | + | 0.701738i | 0.963941 | − | 0.266118i | \(-0.0857410\pi\) |
0.251505 | + | 0.967856i | \(0.419074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.9174 | −0.623803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0056i | 0.834756i | 0.908733 | + | 0.417378i | \(0.137051\pi\) | ||||
−0.908733 | + | 0.417378i | \(0.862949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.1467 | + | 45.2874i | −0.908112 | + | 1.57290i | −0.0914267 | + | 0.995812i | \(0.529143\pi\) |
−0.816685 | + | 0.577084i | \(0.804191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.09313 | − | 2.36317i | 0.141989 | − | 0.0819775i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.90588 | − | 49.3937i | −0.0660349 | − | 1.71139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.11770 | + | 2.95470i | −0.177105 | + | 0.102252i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.52347 | − | 0.879575i | −0.0526588 | − | 0.0304026i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.2679i | 0.423536i | 0.977320 | + | 0.211768i | \(0.0679221\pi\) | ||||
−0.977320 | + | 0.211768i | \(0.932078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.06661 | −0.140228 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.37610 | + | 7.57962i | −0.150721 | + | 0.261056i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.31546 | + | 7.47459i | 0.148456 | + | 0.257134i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.136379 | − | 7.07156i | −0.00468605 | − | 0.242982i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.6409 | − | 10.7624i | 0.639756 | − | 0.369363i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.54474 | − | 16.5320i | 0.327189 | − | 0.566709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.2232 | 1.51418 | 0.757088 | − | 0.653313i | \(-0.226622\pi\) | ||||
0.757088 | + | 0.653313i | \(0.226622\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.69809i | − | 0.0580734i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5558 | − | 18.2832i | 0.360579 | − | 0.624542i | −0.627477 | − | 0.778635i | \(-0.715912\pi\) |
0.988056 | + | 0.154093i | \(0.0492457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.85048 | + | 6.66923i | 0.131377 | + | 0.227551i | 0.924207 | − | 0.381891i | \(-0.124727\pi\) |
−0.792831 | + | 0.609442i | \(0.791394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.20298 | + | 17.4858i | 0.0750774 | + | 0.595914i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.2174 | − | 36.7495i | −0.722247 | − | 1.25097i | −0.960097 | − | 0.279667i | \(-0.909776\pi\) |
0.237850 | − | 0.971302i | \(-0.423557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.95547 | + | 12.0472i | −0.236493 | + | 0.409618i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 34.1896i | − | 1.16114i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.8293 | −1.01189 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5542 | − | 30.4048i | 0.594802 | − | 1.03023i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9069 | − | 13.2253i | 0.775282 | − | 0.447609i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.0879 | + | 7.22346i | 0.442451 | + | 0.244198i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.73195 | − | 15.1242i | −0.294857 | − | 0.510707i | 0.680095 | − | 0.733124i | \(-0.261939\pi\) |
−0.974952 | + | 0.222417i | \(0.928605\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.298638 | − | 0.517256i | 0.0100728 | − | 0.0174466i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.2007 | 1.21963 | 0.609816 | − | 0.792543i | \(-0.291244\pi\) | ||||
0.609816 | + | 0.792543i | \(0.291244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.5032i | 1.32939i | 0.747115 | + | 0.664695i | \(0.231439\pi\) | ||||
−0.747115 | + | 0.664695i | \(0.768561\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.55961 | − | 2.63249i | −0.153270 | − | 0.0884903i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.5877 | − | 27.4748i | 1.59784 | − | 0.922513i | 0.605937 | − | 0.795512i | \(-0.292798\pi\) |
0.991903 | − | 0.127001i | \(-0.0405351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9430 | − | 9.35118i | −0.568251 | − | 0.313629i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.38027 | + | 0.796899i | −0.0462408 | + | 0.0266971i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.76825 | − | 4.79475i | 0.0926359 | − | 0.160450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.974322i | − | 0.0325680i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.58305 | −0.319969 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.71237 | − | 0.988639i | −0.0571108 | − | 0.0329729i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.2438 | − | 40.2594i | −0.774363 | − | 1.34124i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.49912 | − | 15.7439i | −0.316111 | − | 0.523923i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.54761 | + | 0.893516i | −0.0514445 | + | 0.0297015i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2387 | + | 40.2506i | −0.771628 | + | 1.33650i | 0.165042 | + | 0.986286i | \(0.447224\pi\) |
−0.936670 | + | 0.350212i | \(0.886109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 16.0596i | − | 0.532664i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.0452 | 1.72433 | 0.862167 | − | 0.506625i | \(-0.169107\pi\) | ||||
0.862167 | + | 0.506625i | \(0.169107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.1921 | − | 23.2049i | −1.33017 | − | 0.767971i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.15594 | + | 2.97678i | −0.170450 | + | 0.0984094i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.975583 | − | 50.5861i | −0.0322166 | − | 1.67050i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2435 | + | 13.4196i | −0.766731 | + | 0.442672i | −0.831707 | − | 0.555214i | \(-0.812636\pi\) |
0.0649762 | + | 0.997887i | \(0.479303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.17612 | + | 2.98844i | 0.170559 | + | 0.0984723i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.04903 | 0.100360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.8487 | 1.67190 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.59262 | + | 11.4188i | −0.216530 | + | 0.375041i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.0869 | − | 22.5668i | 1.28240 | − | 0.740394i | 0.305113 | − | 0.952316i | \(-0.401306\pi\) |
0.977287 | + | 0.211922i | \(0.0679723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.37250 | − | 4.93953i | −0.307171 | − | 0.161887i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.76227 | + | 8.24849i | 0.155910 | + | 0.270043i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.63819 | + | 13.2297i | −0.249795 | + | 0.432658i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.4963i | − | 0.930933i | −0.885066 | − | 0.465466i | \(-0.845887\pi\) | ||
0.885066 | − | 0.465466i | \(-0.154113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.84319 | −0.158051 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.54446 | − | 11.3353i | 0.213343 | − | 0.369522i | −0.739415 | − | 0.673249i | \(-0.764898\pi\) |
0.952759 | + | 0.303728i | \(0.0982314\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.18509 | − | 11.1335i | −0.0385917 | − | 0.362558i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.91745 | + | 0.152693i | −0.257555 | + | 0.00496710i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.7983 | − | 18.7031i | −0.350896 | − | 0.607770i | 0.635510 | − | 0.772092i | \(-0.280790\pi\) |
−0.986407 | + | 0.164322i | \(0.947456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9471 | + | 6.89767i | 0.387820 | + | 0.223908i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.6473 | −0.507398 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.7433 | −1.38459 | −0.692295 | − | 0.721614i | \(-0.743400\pi\) | ||||
−0.692295 | + | 0.721614i | \(0.743400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8206 | − | 7.97933i | −0.447224 | − | 0.258205i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.1569 | − | 11.0603i | 0.619255 | − | 0.357527i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.95156 | + | 3.23451i | 0.0630190 | + | 0.104448i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4409 | + | 26.7444i | 0.498093 | + | 0.862722i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.56601 | + | 9.64061i | −0.179362 | + | 0.310664i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0785i | 0.356628i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.6835i | − | 1.17966i | −0.807526 | − | 0.589831i | \(-0.799194\pi\) | ||
0.807526 | − | 0.589831i | \(-0.200806\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.62879 | − | 5.55919i | −0.309321 | − | 0.178587i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.2893 | + | 24.4157i | −1.35713 | + | 0.783539i | −0.989236 | − | 0.146330i | \(-0.953254\pi\) |
−0.367893 | + | 0.929868i | \(0.619921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.5302 | + | 15.7464i | 0.914637 | + | 0.504806i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.7632 | − | 22.1065i | −0.408750 | − | 0.707975i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.6851 | − | 28.6857i | −1.58957 | − | 0.917736i | −0.993378 | − | 0.114891i | \(-0.963348\pi\) |
−0.596188 | − | 0.802845i | \(-0.703319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0491 | −0.800573 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4176i | 0.556102i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.20981 | − | 14.2198i | 0.261852 | − | 0.453541i | −0.704882 | − | 0.709325i | \(-0.749000\pi\) |
0.966734 | + | 0.255783i | \(0.0823334\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.51989 | + | 4.36458i | 0.0802904 | + | 0.139067i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.81507 | − | 4.86521i | −0.280587 | − | 0.154861i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.84076 | + | 10.1165i | 0.185725 | + | 0.321686i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.9544 | + | 23.6451i | 1.30096 | + | 0.751110i | 0.980569 | − | 0.196175i | \(-0.0628522\pi\) |
0.320391 | + | 0.947285i | \(0.396186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.0498 | 0.826667 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.4310i | 0.362388i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.9347 | − | 7.46785i | −0.409646 | − | 0.236509i | 0.280992 | − | 0.959710i | \(-0.409337\pi\) |
−0.690638 | + | 0.723201i | \(0.742670\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −48.3690 | + | 27.9258i | −1.53033 | + | 0.883534i |
(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.r.a.81.11 | ✓ | 56 | |
7.2 | even | 3 | inner | 1148.2.r.a.737.18 | yes | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.81.18 | yes | 56 | |
287.163 | even | 6 | inner | 1148.2.r.a.737.11 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.11 | ✓ | 56 | 1.1 | even | 1 | trivial | |
1148.2.r.a.81.18 | yes | 56 | 41.40 | even | 2 | inner | |
1148.2.r.a.737.11 | yes | 56 | 287.163 | even | 6 | inner | |
1148.2.r.a.737.18 | yes | 56 | 7.2 | even | 3 | inner |