Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 230x^{12} - 96x^{10} + 25551x^{8} - 7776x^{6} - 1509030x^{4} + 1062882x^{2} + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.10 | ||
Root | \(-2.87096 - 0.870383i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.b.809.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.25978 | + | 2.61807i | −0.851956 | + | 0.523614i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.80818i | − | 0.686882i | −0.939174 | − | 0.343441i | \(-0.888407\pi\) | ||
0.939174 | − | 0.343441i | \(-0.111593\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.02424 | + | 3.70251i | −0.602424 | + | 0.370251i | ||||
\(11\) | 4.90332i | 0.445757i | 0.974846 | + | 0.222878i | \(0.0715453\pi\) | ||||
−0.974846 | + | 0.222878i | \(0.928455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.9323i | 1.14864i | 0.818632 | + | 0.574318i | \(0.194733\pi\) | ||||
−0.818632 | + | 0.574318i | \(0.805267\pi\) | |||||||
\(14\) | − | 6.79979i | − | 0.485699i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −6.09874 | −0.358750 | −0.179375 | − | 0.983781i | \(-0.557407\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.5280 | 0.764630 | 0.382315 | − | 0.924032i | \(-0.375127\pi\) | ||||
0.382315 | + | 0.924032i | \(0.375127\pi\) | |||||||
\(20\) | −8.51956 | + | 5.23614i | −0.425978 | + | 0.261807i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.93435i | 0.315198i | ||||||||
\(23\) | −42.3965 | −1.84332 | −0.921662 | − | 0.387993i | \(-0.873169\pi\) | ||||
−0.921662 | + | 0.387993i | \(0.873169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.2914 | − | 22.3048i | 0.451657 | − | 0.892192i | ||||
\(26\) | 21.1174i | 0.812209i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 9.61635i | − | 0.343441i | ||||||
\(29\) | 40.0051i | 1.37949i | 0.724054 | + | 0.689743i | \(0.242276\pi\) | ||||
−0.724054 | + | 0.689743i | \(0.757724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.1593 | −1.39224 | −0.696118 | − | 0.717928i | \(-0.745091\pi\) | ||||
−0.696118 | + | 0.717928i | \(0.745091\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.62493 | −0.253674 | ||||||||
\(35\) | 12.5881 | + | 20.4818i | 0.359661 | + | 0.585193i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49.3976i | 1.33507i | 0.744578 | + | 0.667535i | \(0.232651\pi\) | ||||
−0.744578 | + | 0.667535i | \(0.767349\pi\) | |||||||
\(38\) | 20.5457 | 0.540675 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.0485 | + | 7.40502i | −0.301212 | + | 0.185125i | ||||
\(41\) | 32.8725i | 0.801768i | 0.916129 | + | 0.400884i | \(0.131297\pi\) | ||||
−0.916129 | + | 0.400884i | \(0.868703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.5395i | 0.733477i | 0.930324 | + | 0.366739i | \(0.119526\pi\) | ||||
−0.930324 | + | 0.366739i | \(0.880474\pi\) | |||||||
\(44\) | 9.80665i | 0.222878i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −59.9577 | −1.30343 | ||||||||
\(47\) | 4.72351 | 0.100500 | 0.0502501 | − | 0.998737i | \(-0.483998\pi\) | ||||
0.0502501 | + | 0.998737i | \(0.483998\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.8814 | 0.528192 | ||||||||
\(50\) | 15.9685 | − | 31.5437i | 0.319370 | − | 0.630875i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29.8645i | 0.574318i | ||||||||
\(53\) | −19.9361 | −0.376153 | −0.188076 | − | 0.982154i | \(-0.560225\pi\) | ||||
−0.188076 | + | 0.982154i | \(0.560225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.8372 | − | 20.8871i | −0.233404 | − | 0.379765i | ||||
\(56\) | − | 13.5996i | − | 0.242850i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 56.5757i | 0.975444i | ||||||||
\(59\) | 75.5886i | 1.28116i | 0.767890 | + | 0.640582i | \(0.221307\pi\) | ||||
−0.767890 | + | 0.640582i | \(0.778693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.65935 | −0.0599893 | −0.0299946 | − | 0.999550i | \(-0.509549\pi\) | ||||
−0.0299946 | + | 0.999550i | \(0.509549\pi\) | |||||||
\(62\) | −61.0365 | −0.984459 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −39.0937 | − | 63.6082i | −0.601442 | − | 0.978587i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 59.3429i | − | 0.885715i | −0.896592 | − | 0.442858i | \(-0.853965\pi\) | ||
0.896592 | − | 0.442858i | \(-0.146035\pi\) | |||||||
\(68\) | −12.1975 | −0.179375 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.8023 | + | 28.9656i | 0.254319 | + | 0.413794i | ||||
\(71\) | 73.3308i | 1.03283i | 0.856339 | + | 0.516414i | \(0.172734\pi\) | ||||
−0.856339 | + | 0.516414i | \(0.827266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 45.6159i | − | 0.624876i | −0.949938 | − | 0.312438i | \(-0.898854\pi\) | ||
0.949938 | − | 0.312438i | \(-0.101146\pi\) | |||||||
\(74\) | 69.8588i | 0.944037i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 29.0560 | 0.382315 | ||||||||
\(77\) | 23.5761 | 0.306182 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −124.381 | −1.57445 | −0.787224 | − | 0.616667i | \(-0.788482\pi\) | ||||
−0.787224 | + | 0.616667i | \(0.788482\pi\) | |||||||
\(80\) | −17.0391 | + | 10.4723i | −0.212989 | + | 0.130903i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 46.4887i | 0.566935i | ||||||||
\(83\) | −83.6935 | −1.00835 | −0.504177 | − | 0.863600i | \(-0.668204\pi\) | ||||
−0.504177 | + | 0.863600i | \(0.668204\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.9793 | − | 15.9669i | 0.305639 | − | 0.187846i | ||||
\(86\) | 44.6036i | 0.518647i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.8687i | 0.157599i | ||||||||
\(89\) | − | 138.123i | − | 1.55195i | −0.630765 | − | 0.775974i | \(-0.717259\pi\) | ||
0.630765 | − | 0.775974i | \(-0.282741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 71.7970 | 0.788978 | ||||||||
\(92\) | −84.7929 | −0.921662 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.68005 | 0.0710644 | ||||||||
\(95\) | −61.8860 | + | 38.0353i | −0.651431 | + | 0.400371i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0793i | 0.103910i | 0.998649 | + | 0.0519549i | \(0.0165452\pi\) | ||||
−0.998649 | + | 0.0519549i | \(0.983455\pi\) | |||||||
\(98\) | 36.6019 | 0.373488 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22.5829 | − | 44.6096i | 0.225829 | − | 0.446096i | ||||
\(101\) | 155.933i | 1.54389i | 0.635691 | + | 0.771943i | \(0.280715\pi\) | ||||
−0.635691 | + | 0.771943i | \(0.719285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 159.388i | − | 1.54746i | −0.633518 | − | 0.773728i | \(-0.718390\pi\) | ||
0.633518 | − | 0.773728i | \(-0.281610\pi\) | |||||||
\(104\) | 42.2348i | 0.406104i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.1939 | −0.265980 | ||||||||
\(107\) | −55.2076 | −0.515959 | −0.257979 | − | 0.966150i | \(-0.583057\pi\) | ||||
−0.257979 | + | 0.966150i | \(0.583057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 101.451 | 0.930743 | 0.465371 | − | 0.885115i | \(-0.345921\pi\) | ||||
0.465371 | + | 0.885115i | \(0.345921\pi\) | |||||||
\(110\) | −18.1546 | − | 29.5388i | −0.165042 | − | 0.268534i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 19.2327i | − | 0.171721i | ||||||
\(113\) | 155.980 | 1.38035 | 0.690176 | − | 0.723641i | \(-0.257533\pi\) | ||||
0.690176 | + | 0.723641i | \(0.257533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 180.600 | − | 110.997i | 1.57043 | − | 0.965191i | ||||
\(116\) | 80.0102i | 0.689743i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 106.898i | 0.905919i | ||||||||
\(119\) | 29.3238i | 0.246419i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 96.9574 | 0.801301 | ||||||||
\(122\) | −5.17510 | −0.0424188 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −86.3186 | −0.696118 | ||||||||
\(125\) | 10.2965 | + | 124.575i | 0.0823722 | + | 0.996602i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 115.909i | − | 0.912668i | −0.889809 | − | 0.456334i | \(-0.849162\pi\) | ||
0.889809 | − | 0.456334i | \(-0.150838\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −55.2869 | − | 89.9556i | −0.425284 | − | 0.691966i | ||||
\(131\) | 66.7763i | 0.509743i | 0.966975 | + | 0.254872i | \(0.0820332\pi\) | ||||
−0.966975 | + | 0.254872i | \(0.917967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 69.8531i | − | 0.525211i | ||||||
\(134\) | − | 83.9235i | − | 0.626295i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.2499 | −0.126837 | ||||||||
\(137\) | 71.6499 | 0.522992 | 0.261496 | − | 0.965205i | \(-0.415784\pi\) | ||||
0.261496 | + | 0.965205i | \(0.415784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 115.435 | 0.830465 | 0.415233 | − | 0.909715i | \(-0.363700\pi\) | ||||
0.415233 | + | 0.909715i | \(0.363700\pi\) | |||||||
\(140\) | 25.1763 | + | 40.9635i | 0.179831 | + | 0.292597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 103.705i | 0.730320i | ||||||||
\(143\) | −73.2178 | −0.512012 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −104.736 | − | 170.413i | −0.722318 | − | 1.17526i | ||||
\(146\) | − | 64.5107i | − | 0.441854i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 98.7952i | 0.667535i | ||||||||
\(149\) | − | 178.379i | − | 1.19717i | −0.801058 | − | 0.598587i | \(-0.795729\pi\) | ||
0.801058 | − | 0.598587i | \(-0.204271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 268.628 | 1.77899 | 0.889497 | − | 0.456941i | \(-0.151055\pi\) | ||||
0.889497 | + | 0.456941i | \(0.151055\pi\) | |||||||
\(152\) | 41.0913 | 0.270338 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 33.3416 | 0.216504 | ||||||||
\(155\) | 183.849 | − | 112.994i | 1.18612 | − | 0.728994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 259.211i | 1.65102i | 0.564385 | + | 0.825512i | \(0.309113\pi\) | ||||
−0.564385 | + | 0.825512i | \(0.690887\pi\) | |||||||
\(158\) | −175.902 | −1.11330 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −24.0969 | + | 14.8100i | −0.150606 | + | 0.0925627i | ||||
\(161\) | 203.850i | 1.26615i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.67785i | 0.0102936i | 0.999987 | + | 0.00514679i | \(0.00163828\pi\) | ||||
−0.999987 | + | 0.00514679i | \(0.998362\pi\) | |||||||
\(164\) | 65.7450i | 0.400884i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −118.360 | −0.713015 | ||||||||
\(167\) | −180.166 | −1.07884 | −0.539420 | − | 0.842037i | \(-0.681356\pi\) | ||||
−0.539420 | + | 0.842037i | \(0.681356\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −53.9728 | −0.319366 | ||||||||
\(170\) | 36.7403 | − | 22.5807i | 0.216119 | − | 0.132827i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 63.0791i | 0.366739i | ||||||||
\(173\) | −83.6891 | −0.483752 | −0.241876 | − | 0.970307i | \(-0.577763\pi\) | ||||
−0.241876 | + | 0.970307i | \(0.577763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −107.245 | − | 54.2912i | −0.612831 | − | 0.310235i | ||||
\(176\) | 19.6133i | 0.111439i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 195.336i | − | 1.09739i | ||||||
\(179\) | − | 50.5590i | − | 0.282453i | −0.989977 | − | 0.141226i | \(-0.954895\pi\) | ||
0.989977 | − | 0.141226i | \(-0.0451045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −191.874 | −1.06008 | −0.530038 | − | 0.847974i | \(-0.677822\pi\) | ||||
−0.530038 | + | 0.847974i | \(0.677822\pi\) | |||||||
\(182\) | 101.536 | 0.557892 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −119.915 | −0.651714 | ||||||||
\(185\) | −129.326 | − | 210.423i | −0.699061 | − | 1.13742i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 29.9041i | − | 0.159915i | ||||||
\(188\) | 9.44702 | 0.0502501 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −87.5200 | + | 53.7900i | −0.460631 | + | 0.283105i | ||||
\(191\) | − | 113.164i | − | 0.592481i | −0.955113 | − | 0.296241i | \(-0.904267\pi\) | ||
0.955113 | − | 0.296241i | \(-0.0957331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 118.486i | − | 0.613918i | −0.951723 | − | 0.306959i | \(-0.900688\pi\) | ||
0.951723 | − | 0.306959i | \(-0.0993115\pi\) | |||||||
\(194\) | 14.2542i | 0.0734754i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 51.7629 | 0.264096 | ||||||||
\(197\) | 247.866 | 1.25820 | 0.629102 | − | 0.777323i | \(-0.283423\pi\) | ||||
0.629102 | + | 0.777323i | \(0.283423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 83.8620 | 0.421417 | 0.210708 | − | 0.977549i | \(-0.432423\pi\) | ||||
0.210708 | + | 0.977549i | \(0.432423\pi\) | |||||||
\(200\) | 31.9370 | − | 63.0875i | 0.159685 | − | 0.315437i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 220.522i | 1.09169i | ||||||||
\(203\) | 192.352 | 0.947545 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −86.0624 | − | 140.029i | −0.419817 | − | 0.683071i | ||||
\(206\) | − | 225.409i | − | 1.09422i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 59.7291i | 0.287159i | ||||||||
\(209\) | 71.2354i | 0.340839i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −80.5908 | −0.381947 | −0.190973 | − | 0.981595i | \(-0.561164\pi\) | ||||
−0.190973 | + | 0.981595i | \(0.561164\pi\) | |||||||
\(212\) | −39.8722 | −0.188076 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −78.0753 | −0.364838 | ||||||||
\(215\) | −82.5727 | − | 134.351i | −0.384059 | − | 0.624890i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 207.518i | 0.956302i | ||||||||
\(218\) | 143.473 | 0.658135 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −25.6745 | − | 41.7741i | −0.116702 | − | 0.189882i | ||||
\(221\) | − | 91.0681i | − | 0.412073i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 32.8692i | 0.147396i | 0.997281 | + | 0.0736979i | \(0.0234800\pi\) | ||||
−0.997281 | + | 0.0736979i | \(0.976520\pi\) | |||||||
\(224\) | − | 27.1992i | − | 0.121425i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 220.589 | 0.976056 | ||||||||
\(227\) | −91.6646 | −0.403809 | −0.201904 | − | 0.979405i | \(-0.564713\pi\) | ||||
−0.201904 | + | 0.979405i | \(0.564713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73.6946 | 0.321811 | 0.160905 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160905 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(230\) | 255.406 | − | 156.973i | 1.11046 | − | 0.682493i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 113.151i | 0.487722i | ||||||||
\(233\) | 13.3749 | 0.0574029 | 0.0287014 | − | 0.999588i | \(-0.490863\pi\) | ||||
0.0287014 | + | 0.999588i | \(0.490863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.1211 | + | 12.3665i | −0.0856217 | + | 0.0526233i | ||||
\(236\) | 151.177i | 0.640582i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 41.4702i | 0.174244i | ||||||||
\(239\) | − | 223.710i | − | 0.936026i | −0.883722 | − | 0.468013i | \(-0.844970\pi\) | ||
0.883722 | − | 0.468013i | \(-0.155030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −215.351 | −0.893571 | −0.446786 | − | 0.894641i | \(-0.647431\pi\) | ||||
−0.446786 | + | 0.894641i | \(0.647431\pi\) | |||||||
\(242\) | 137.118 | 0.566605 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.31869 | −0.0299946 | ||||||||
\(245\) | −110.249 | + | 67.7594i | −0.449997 | + | 0.276569i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 216.936i | 0.878282i | ||||||||
\(248\) | −122.073 | −0.492230 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.5615 | + | 176.176i | 0.0582459 | + | 0.704704i | ||||
\(251\) | − | 5.69286i | − | 0.0226807i | −0.999936 | − | 0.0113404i | \(-0.996390\pi\) | ||
0.999936 | − | 0.0113404i | \(-0.00360982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 207.884i | − | 0.821675i | ||||||
\(254\) | − | 163.920i | − | 0.645354i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 96.4638 | 0.375346 | 0.187673 | − | 0.982232i | \(-0.439906\pi\) | ||||
0.187673 | + | 0.982232i | \(0.439906\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 237.512 | 0.917036 | ||||||||
\(260\) | −78.1875 | − | 127.216i | −0.300721 | − | 0.489294i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 94.4360i | 0.360443i | ||||||||
\(263\) | 233.601 | 0.888218 | 0.444109 | − | 0.895973i | \(-0.353520\pi\) | ||||
0.444109 | + | 0.895973i | \(0.353520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 84.9233 | − | 52.1941i | 0.320465 | − | 0.196959i | ||||
\(266\) | − | 98.7872i | − | 0.371380i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 118.686i | − | 0.442858i | ||||||
\(269\) | − | 492.222i | − | 1.82982i | −0.403655 | − | 0.914911i | \(-0.632260\pi\) | ||
0.403655 | − | 0.914911i | \(-0.367740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 183.942 | 0.678752 | 0.339376 | − | 0.940651i | \(-0.389784\pi\) | ||||
0.339376 | + | 0.940651i | \(0.389784\pi\) | |||||||
\(272\) | −24.3950 | −0.0896874 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 101.328 | 0.369811 | ||||||||
\(275\) | 109.368 | + | 55.3655i | 0.397700 | + | 0.201329i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 226.087i | 0.816199i | 0.912937 | + | 0.408100i | \(0.133808\pi\) | ||||
−0.912937 | + | 0.408100i | \(0.866192\pi\) | |||||||
\(278\) | 163.249 | 0.587228 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 35.6046 | + | 57.9312i | 0.127159 | + | 0.206897i | ||||
\(281\) | − | 150.264i | − | 0.534749i | −0.963593 | − | 0.267374i | \(-0.913844\pi\) | ||
0.963593 | − | 0.267374i | \(-0.0861560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 316.153i | − | 1.11715i | −0.829455 | − | 0.558574i | \(-0.811349\pi\) | ||
0.829455 | − | 0.558574i | \(-0.188651\pi\) | |||||||
\(284\) | 146.662i | 0.516414i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −103.546 | −0.362047 | ||||||||
\(287\) | 158.057 | 0.550720 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −251.805 | −0.871299 | ||||||||
\(290\) | −148.119 | − | 241.000i | −0.510756 | − | 0.831035i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 91.2319i | − | 0.312438i | ||||||
\(293\) | 171.722 | 0.586081 | 0.293041 | − | 0.956100i | \(-0.405333\pi\) | ||||
0.293041 | + | 0.956100i | \(0.405333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −197.896 | − | 321.991i | −0.670835 | − | 1.09149i | ||||
\(296\) | 139.718i | 0.472019i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 252.266i | − | 0.846530i | ||||||
\(299\) | − | 633.076i | − | 2.11731i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 151.648 | 0.503813 | ||||||||
\(302\) | 379.898 | 1.25794 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 58.1119 | 0.191158 | ||||||||
\(305\) | 15.5880 | − | 9.58042i | 0.0511082 | − | 0.0314112i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 226.678i | 0.738365i | 0.929357 | + | 0.369182i | \(0.120362\pi\) | ||||
−0.929357 | + | 0.369182i | \(0.879638\pi\) | |||||||
\(308\) | 47.1521 | 0.153091 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 260.002 | − | 159.798i | 0.838716 | − | 0.515477i | ||||
\(311\) | 348.817i | 1.12160i | 0.827952 | + | 0.560800i | \(0.189506\pi\) | ||||
−0.827952 | + | 0.560800i | \(0.810494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 510.550i | 1.63115i | 0.578652 | + | 0.815574i | \(0.303579\pi\) | ||||
−0.578652 | + | 0.815574i | \(0.696421\pi\) | |||||||
\(314\) | 366.579i | 1.16745i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −248.763 | −0.787224 | ||||||||
\(317\) | 200.685 | 0.633077 | 0.316538 | − | 0.948580i | \(-0.397479\pi\) | ||||
0.316538 | + | 0.948580i | \(0.397479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −196.158 | −0.614915 | ||||||||
\(320\) | −34.0782 | + | 20.9446i | −0.106494 | + | 0.0654517i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 288.287i | 0.895302i | ||||||||
\(323\) | −88.6024 | −0.274311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 333.061 | + | 168.607i | 1.02480 | + | 0.518790i | ||||
\(326\) | 2.37284i | 0.00727866i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 92.9774i | 0.283468i | ||||||||
\(329\) | − | 22.7115i | − | 0.0690318i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3687 | −0.0706002 | −0.0353001 | − | 0.999377i | \(-0.511239\pi\) | ||||
−0.0353001 | + | 0.999377i | \(0.511239\pi\) | |||||||
\(332\) | −167.387 | −0.504177 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −254.794 | −0.762855 | ||||||||
\(335\) | 155.364 | + | 252.788i | 0.463773 | + | 0.754590i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 413.512i | 1.22704i | 0.789680 | + | 0.613519i | \(0.210247\pi\) | ||||
−0.789680 | + | 0.613519i | \(0.789753\pi\) | |||||||
\(338\) | −76.3291 | −0.225826 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 51.9586 | − | 31.9339i | 0.152819 | − | 0.0939231i | ||||
\(341\) | − | 211.624i | − | 0.620598i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 360.043i | − | 1.04969i | ||||||
\(344\) | 89.2072i | 0.259323i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −118.354 | −0.342064 | ||||||||
\(347\) | 145.826 | 0.420248 | 0.210124 | − | 0.977675i | \(-0.432613\pi\) | ||||
0.210124 | + | 0.977675i | \(0.432613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −75.1353 | −0.215287 | −0.107644 | − | 0.994190i | \(-0.534331\pi\) | ||||
−0.107644 | + | 0.994190i | \(0.534331\pi\) | |||||||
\(350\) | −151.668 | − | 76.7793i | −0.433337 | − | 0.219369i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.7374i | 0.0787994i | ||||||||
\(353\) | −218.797 | −0.619822 | −0.309911 | − | 0.950766i | \(-0.600299\pi\) | ||||
−0.309911 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −191.985 | − | 312.373i | −0.540803 | − | 0.879924i | ||||
\(356\) | − | 276.247i | − | 0.775974i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 71.5013i | − | 0.199724i | ||||||
\(359\) | 371.972i | 1.03613i | 0.855340 | + | 0.518067i | \(0.173348\pi\) | ||||
−0.855340 | + | 0.518067i | \(0.826652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −149.938 | −0.415340 | ||||||||
\(362\) | −271.350 | −0.749587 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 143.594 | 0.394489 | ||||||||
\(365\) | 119.426 | + | 194.314i | 0.327194 | + | 0.532366i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 614.883i | 1.67543i | 0.546107 | + | 0.837715i | \(0.316109\pi\) | ||||
−0.546107 | + | 0.837715i | \(0.683891\pi\) | |||||||
\(368\) | −169.586 | −0.460831 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −182.895 | − | 297.583i | −0.494311 | − | 0.804278i | ||||
\(371\) | 95.8563i | 0.258373i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 147.562i | − | 0.395609i | −0.980242 | − | 0.197804i | \(-0.936619\pi\) | ||
0.980242 | − | 0.197804i | \(-0.0633811\pi\) | |||||||
\(374\) | − | 42.2908i | − | 0.113077i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.3601 | 0.0355322 | ||||||||
\(377\) | −597.367 | −1.58453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 145.687 | 0.384398 | 0.192199 | − | 0.981356i | \(-0.438438\pi\) | ||||
0.192199 | + | 0.981356i | \(0.438438\pi\) | |||||||
\(380\) | −123.772 | + | 76.0705i | −0.325716 | + | 0.200186i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 160.038i | − | 0.418948i | ||||||
\(383\) | −94.6363 | −0.247092 | −0.123546 | − | 0.992339i | \(-0.539427\pi\) | ||||
−0.123546 | + | 0.992339i | \(0.539427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −100.429 | + | 61.7237i | −0.260854 | + | 0.160321i | ||||
\(386\) | − | 167.565i | − | 0.434106i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.1585i | 0.0519549i | ||||||||
\(389\) | − | 137.838i | − | 0.354338i | −0.984180 | − | 0.177169i | \(-0.943306\pi\) | ||
0.984180 | − | 0.177169i | \(-0.0566940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 258.565 | 0.661292 | ||||||||
\(392\) | 73.2037 | 0.186744 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 350.536 | 0.889685 | ||||||||
\(395\) | 529.837 | − | 325.639i | 1.34136 | − | 0.824403i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 735.633i | 1.85298i | 0.376320 | + | 0.926490i | \(0.377189\pi\) | ||||
−0.376320 | + | 0.926490i | \(0.622811\pi\) | |||||||
\(398\) | 118.599 | 0.297987 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 45.1657 | − | 89.2192i | 0.112914 | − | 0.223048i | ||||
\(401\) | 99.1697i | 0.247306i | 0.992326 | + | 0.123653i | \(0.0394610\pi\) | ||||
−0.992326 | + | 0.123653i | \(0.960539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 644.467i | − | 1.59917i | ||||||
\(404\) | 311.865i | 0.771943i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 272.026 | 0.670015 | ||||||||
\(407\) | −242.212 | −0.595117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −816.046 | −1.99522 | −0.997611 | − | 0.0690850i | \(-0.977992\pi\) | ||||
−0.997611 | + | 0.0690850i | \(0.977992\pi\) | |||||||
\(410\) | −121.711 | − | 198.032i | −0.296855 | − | 0.483004i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 318.776i | − | 0.773728i | ||||||
\(413\) | 363.443 | 0.880008 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 356.516 | − | 219.115i | 0.859074 | − | 0.527989i | ||||
\(416\) | 84.4697i | 0.203052i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 100.742i | 0.241010i | ||||||||
\(419\) | − | 180.693i | − | 0.431249i | −0.976476 | − | 0.215624i | \(-0.930821\pi\) | ||
0.976476 | − | 0.215624i | \(-0.0691786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −414.762 | −0.985183 | −0.492592 | − | 0.870261i | \(-0.663950\pi\) | ||||
−0.492592 | + | 0.870261i | \(0.663950\pi\) | |||||||
\(422\) | −113.973 | −0.270077 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −56.3878 | −0.132990 | ||||||||
\(425\) | −68.8635 | + | 136.031i | −0.162032 | + | 0.320073i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5948i | 0.0412056i | ||||||||
\(428\) | −110.415 | −0.257979 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −116.775 | − | 190.002i | −0.271571 | − | 0.441864i | ||||
\(431\) | − | 440.794i | − | 1.02272i | −0.859366 | − | 0.511362i | \(-0.829141\pi\) | ||
0.859366 | − | 0.511362i | \(-0.170859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 357.721i | 0.826147i | 0.910698 | + | 0.413073i | \(0.135545\pi\) | ||||
−0.910698 | + | 0.413073i | \(0.864455\pi\) | |||||||
\(434\) | 293.474i | 0.676208i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 202.902 | 0.465371 | ||||||||
\(437\) | −615.935 | −1.40946 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 193.113 | 0.439893 | 0.219947 | − | 0.975512i | \(-0.429412\pi\) | ||||
0.219947 | + | 0.975512i | \(0.429412\pi\) | |||||||
\(440\) | −36.3092 | − | 59.0776i | −0.0825209 | − | 0.134267i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 128.790i | − | 0.291380i | ||||||
\(443\) | 58.2692 | 0.131533 | 0.0657665 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657665 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 361.616 | + | 588.375i | 0.812621 | + | 1.32219i | ||||
\(446\) | 46.4841i | 0.104225i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 38.4654i | − | 0.0858603i | ||||||
\(449\) | 594.072i | 1.32310i | 0.749901 | + | 0.661550i | \(0.230101\pi\) | ||||
−0.749901 | + | 0.661550i | \(0.769899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −161.184 | −0.357393 | ||||||||
\(452\) | 311.960 | 0.690176 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −129.633 | −0.285536 | ||||||||
\(455\) | −305.839 | + | 187.970i | −0.672175 | + | 0.413120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 304.884i | − | 0.667143i | −0.942725 | − | 0.333571i | \(-0.891746\pi\) | ||
0.942725 | − | 0.333571i | \(-0.108254\pi\) | |||||||
\(458\) | 104.220 | 0.227554 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 361.199 | − | 221.994i | 0.785216 | − | 0.482595i | ||||
\(461\) | 419.206i | 0.909340i | 0.890660 | + | 0.454670i | \(0.150243\pi\) | ||||
−0.890660 | + | 0.454670i | \(0.849757\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 101.562i | − | 0.219357i | −0.993967 | − | 0.109679i | \(-0.965018\pi\) | ||
0.993967 | − | 0.109679i | \(-0.0349822\pi\) | |||||||
\(464\) | 160.020i | 0.344871i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.9149 | 0.0405899 | ||||||||
\(467\) | 446.284 | 0.955640 | 0.477820 | − | 0.878458i | \(-0.341427\pi\) | ||||
0.477820 | + | 0.878458i | \(0.341427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −285.331 | −0.608382 | ||||||||
\(470\) | −28.4555 | + | 17.4888i | −0.0605437 | + | 0.0372103i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 213.797i | 0.452960i | ||||||||
\(473\) | −154.649 | −0.326952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 164.042 | − | 324.044i | 0.345351 | − | 0.682197i | ||||
\(476\) | 58.6477i | 0.123209i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 316.374i | − | 0.661871i | ||||||
\(479\) | − | 214.839i | − | 0.448515i | −0.974530 | − | 0.224258i | \(-0.928004\pi\) | ||
0.974530 | − | 0.224258i | \(-0.0719957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −737.618 | −1.53351 | ||||||||
\(482\) | −304.552 | −0.631850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 193.915 | 0.400650 | ||||||||
\(485\) | −26.3882 | − | 42.9354i | −0.0544087 | − | 0.0885266i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 151.238i | 0.310551i | 0.987871 | + | 0.155276i | \(0.0496265\pi\) | ||||
−0.987871 | + | 0.155276i | \(0.950373\pi\) | |||||||
\(488\) | −10.3502 | −0.0212094 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −155.916 | + | 95.8262i | −0.318196 | + | 0.195564i | ||||
\(491\) | − | 507.056i | − | 1.03270i | −0.856378 | − | 0.516350i | \(-0.827290\pi\) | ||
0.856378 | − | 0.516350i | \(-0.172710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 243.981i | − | 0.494890i | ||||||
\(494\) | 306.794i | 0.621039i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −172.637 | −0.348059 | ||||||||
\(497\) | 352.588 | 0.709432 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 933.476 | 1.87069 | 0.935346 | − | 0.353733i | \(-0.115088\pi\) | ||||
0.935346 | + | 0.353733i | \(0.115088\pi\) | |||||||
\(500\) | 20.5930 | + | 249.150i | 0.0411861 | + | 0.498301i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 8.05091i | − | 0.0160377i | ||||||
\(503\) | −271.226 | −0.539217 | −0.269608 | − | 0.962970i | \(-0.586894\pi\) | ||||
−0.269608 | + | 0.962970i | \(0.586894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −408.242 | − | 664.238i | −0.808401 | − | 1.31532i | ||||
\(506\) | − | 293.992i | − | 0.581012i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 231.818i | − | 0.456334i | ||||||
\(509\) | 361.501i | 0.710219i | 0.934825 | + | 0.355109i | \(0.115556\pi\) | ||||
−0.934825 | + | 0.355109i | \(0.884444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −219.329 | −0.429216 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 136.420 | 0.265409 | ||||||||
\(515\) | 417.289 | + | 678.957i | 0.810269 | + | 1.31836i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.1609i | 0.0447986i | ||||||||
\(518\) | 335.893 | 0.648443 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −110.574 | − | 179.911i | −0.212642 | − | 0.345983i | ||||
\(521\) | 673.089i | 1.29192i | 0.763373 | + | 0.645958i | \(0.223542\pi\) | ||||
−0.763373 | + | 0.645958i | \(0.776458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 150.339i | − | 0.287455i | −0.989617 | − | 0.143728i | \(-0.954091\pi\) | ||
0.989617 | − | 0.143728i | \(-0.0459089\pi\) | |||||||
\(524\) | 133.553i | 0.254872i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 330.362 | 0.628065 | ||||||||
\(527\) | 263.217 | 0.499464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1268.46 | 2.39785 | ||||||||
\(530\) | 120.100 | − | 73.8136i | 0.226603 | − | 0.139271i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 139.706i | − | 0.262606i | ||||||
\(533\) | −490.861 | −0.920940 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 235.172 | − | 144.537i | 0.439574 | − | 0.270163i | ||||
\(536\) | − | 167.847i | − | 0.313148i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 696.107i | − | 1.29388i | ||||||
\(539\) | 126.905i | 0.235445i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 713.274 | 1.31844 | 0.659218 | − | 0.751952i | \(-0.270888\pi\) | ||||
0.659218 | + | 0.751952i | \(0.270888\pi\) | |||||||
\(542\) | 260.133 | 0.479950 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.4997 | −0.0634186 | ||||||||
\(545\) | −432.159 | + | 265.606i | −0.792952 | + | 0.487350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 579.412i | 1.05925i | 0.848231 | + | 0.529627i | \(0.177668\pi\) | ||||
−0.848231 | + | 0.529627i | \(0.822332\pi\) | |||||||
\(548\) | 143.300 | 0.261496 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 154.669 | + | 78.2987i | 0.281217 | + | 0.142361i | ||||
\(551\) | 581.193i | 1.05480i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 598.048i | 1.08146i | ||||||||
\(554\) | 319.736i | 0.577140i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 230.869 | 0.415233 | ||||||||
\(557\) | −727.043 | −1.30528 | −0.652642 | − | 0.757667i | \(-0.726339\pi\) | ||||
−0.652642 | + | 0.757667i | \(0.726339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −470.957 | −0.842499 | ||||||||
\(560\) | 50.3526 | + | 81.9271i | 0.0899153 | + | 0.146298i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 212.506i | − | 0.378124i | ||||||
\(563\) | −239.775 | −0.425888 | −0.212944 | − | 0.977064i | \(-0.568305\pi\) | ||||
−0.212944 | + | 0.977064i | \(0.568305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −664.439 | + | 408.366i | −1.17600 | + | 0.722772i | ||||
\(566\) | − | 447.108i | − | 0.789943i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 207.411i | 0.365160i | ||||||||
\(569\) | − | 564.169i | − | 0.991509i | −0.868463 | − | 0.495755i | \(-0.834892\pi\) | ||
0.868463 | − | 0.495755i | \(-0.165108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 55.4054 | 0.0970322 | 0.0485161 | − | 0.998822i | \(-0.484551\pi\) | ||||
0.0485161 | + | 0.998822i | \(0.484551\pi\) | |||||||
\(572\) | −146.436 | −0.256006 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 223.526 | 0.389418 | ||||||||
\(575\) | −478.717 | + | 945.645i | −0.832551 | + | 1.64460i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 616.099i | 1.06776i | 0.845559 | + | 0.533881i | \(0.179267\pi\) | ||||
−0.845559 | + | 0.533881i | \(0.820733\pi\) | |||||||
\(578\) | −356.107 | −0.616101 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −209.472 | − | 340.826i | −0.361159 | − | 0.587630i | ||||
\(581\) | 402.413i | 0.692621i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 97.7531i | − | 0.167673i | ||||||
\(584\) | − | 129.021i | − | 0.220927i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 242.851 | 0.414422 | ||||||||
\(587\) | −252.812 | −0.430685 | −0.215343 | − | 0.976539i | \(-0.569087\pi\) | ||||
−0.215343 | + | 0.976539i | \(0.569087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −627.017 | −1.06455 | ||||||||
\(590\) | −279.868 | − | 455.364i | −0.474352 | − | 0.771803i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 197.590i | 0.333768i | ||||||||
\(593\) | −431.589 | −0.727805 | −0.363903 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363903 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −76.7718 | − | 124.913i | −0.129028 | − | 0.209938i | ||||
\(596\) | − | 356.758i | − | 0.598587i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 895.304i | − | 1.49716i | ||||||
\(599\) | − | 559.986i | − | 0.934868i | −0.884028 | − | 0.467434i | \(-0.845179\pi\) | ||
0.884028 | − | 0.467434i | \(-0.154821\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 537.374 | 0.894132 | 0.447066 | − | 0.894501i | \(-0.352469\pi\) | ||||
0.447066 | + | 0.894501i | \(0.352469\pi\) | |||||||
\(602\) | 214.462 | 0.356249 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 537.256 | 0.889497 | ||||||||
\(605\) | −413.017 | + | 253.841i | −0.682673 | + | 0.419572i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 482.841i | 0.795454i | 0.917504 | + | 0.397727i | \(0.130201\pi\) | ||||
−0.917504 | + | 0.397727i | \(0.869799\pi\) | |||||||
\(608\) | 82.1827 | 0.135169 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.0448 | − | 13.5488i | 0.0361390 | − | 0.0222111i | ||||
\(611\) | 70.5327i | 0.115438i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 259.741i | 0.423721i | 0.977300 | + | 0.211860i | \(0.0679522\pi\) | ||||
−0.977300 | + | 0.211860i | \(0.932048\pi\) | |||||||
\(614\) | 320.571i | 0.522103i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 66.6831 | 0.108252 | ||||||||
\(617\) | 157.281 | 0.254912 | 0.127456 | − | 0.991844i | \(-0.459319\pi\) | ||||
0.127456 | + | 0.991844i | \(0.459319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −710.098 | −1.14717 | −0.573585 | − | 0.819146i | \(-0.694448\pi\) | ||||
−0.573585 | + | 0.819146i | \(0.694448\pi\) | |||||||
\(620\) | 367.698 | − | 225.988i | 0.593062 | − | 0.364497i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 493.302i | 0.793090i | ||||||||
\(623\) | −664.121 | −1.06601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −370.007 | − | 503.706i | −0.592012 | − | 0.805929i | ||||
\(626\) | 722.026i | 1.15340i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 518.421i | 0.825512i | ||||||||
\(629\) | − | 301.263i | − | 0.478956i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −165.617 | −0.262467 | −0.131234 | − | 0.991351i | \(-0.541894\pi\) | ||||
−0.131234 | + | 0.991351i | \(0.541894\pi\) | |||||||
\(632\) | −351.804 | −0.556651 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 283.812 | 0.447653 | ||||||||
\(635\) | 303.457 | + | 493.746i | 0.477886 | + | 0.777553i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 386.469i | 0.606701i | ||||||||
\(638\) | −277.409 | −0.434811 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −48.1939 | + | 29.6201i | −0.0753030 | + | 0.0462814i | ||||
\(641\) | − | 299.414i | − | 0.467104i | −0.972344 | − | 0.233552i | \(-0.924965\pi\) | ||
0.972344 | − | 0.233552i | \(-0.0750349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 53.5070i | 0.0832146i | 0.999134 | + | 0.0416073i | \(0.0132478\pi\) | ||||
−0.999134 | + | 0.0416073i | \(0.986752\pi\) | |||||||
\(644\) | 407.700i | 0.633074i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −125.303 | −0.193967 | ||||||||
\(647\) | −145.933 | −0.225553 | −0.112776 | − | 0.993620i | \(-0.535974\pi\) | ||||
−0.112776 | + | 0.993620i | \(0.535974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −370.635 | −0.571087 | ||||||||
\(650\) | 471.020 | + | 238.446i | 0.724646 | + | 0.366840i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.35571i | 0.00514679i | ||||||||
\(653\) | 275.649 | 0.422127 | 0.211064 | − | 0.977472i | \(-0.432307\pi\) | ||||
0.211064 | + | 0.977472i | \(0.432307\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −174.825 | − | 284.452i | −0.266909 | − | 0.434279i | ||||
\(656\) | 131.490i | 0.200442i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 32.1189i | − | 0.0488129i | ||||||
\(659\) | 334.958i | 0.508282i | 0.967167 | + | 0.254141i | \(0.0817927\pi\) | ||||
−0.967167 | + | 0.254141i | \(0.918207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 155.582 | 0.235374 | 0.117687 | − | 0.993051i | \(-0.462452\pi\) | ||||
0.117687 | + | 0.993051i | \(0.462452\pi\) | |||||||
\(662\) | −33.0483 | −0.0499219 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −236.721 | −0.356507 | ||||||||
\(665\) | 182.880 | + | 297.559i | 0.275008 | + | 0.447457i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1696.07i | − | 2.54284i | ||||||
\(668\) | −360.333 | −0.539420 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 219.718 | + | 357.496i | 0.327937 | + | 0.533576i | ||||
\(671\) | − | 17.9430i | − | 0.0267406i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1338.17i | 1.98837i | 0.107672 | + | 0.994186i | \(0.465660\pi\) | ||||
−0.107672 | + | 0.994186i | \(0.534340\pi\) | |||||||
\(674\) | 584.794i | 0.867647i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −107.946 | −0.159683 | ||||||||
\(677\) | −178.334 | −0.263418 | −0.131709 | − | 0.991288i | \(-0.542046\pi\) | ||||
−0.131709 | + | 0.991288i | \(0.542046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.4629 | 0.0713739 | ||||||||
\(680\) | 73.4805 | − | 45.1613i | 0.108060 | − | 0.0664137i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 299.282i | − | 0.438829i | ||||||
\(683\) | −219.879 | −0.321931 | −0.160966 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160966 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −305.213 | + | 187.584i | −0.445566 | + | 0.273846i | ||||
\(686\) | − | 509.178i | − | 0.742242i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 126.158i | 0.183369i | ||||||||
\(689\) | − | 297.691i | − | 0.432063i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −90.0762 | −0.130356 | −0.0651782 | − | 0.997874i | \(-0.520762\pi\) | ||||
−0.0651782 | + | 0.997874i | \(0.520762\pi\) | |||||||
\(692\) | −167.378 | −0.241876 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 206.229 | 0.297160 | ||||||||
\(695\) | −491.726 | + | 302.216i | −0.707520 | + | 0.434843i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 200.481i | − | 0.287634i | ||||||
\(698\) | −106.257 | −0.152231 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −214.491 | − | 108.582i | −0.306415 | − | 0.155118i | ||||
\(701\) | − | 239.302i | − | 0.341373i | −0.985325 | − | 0.170686i | \(-0.945401\pi\) | ||
0.985325 | − | 0.170686i | \(-0.0545985\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 717.647i | 1.02084i | ||||||||
\(704\) | 39.2266i | 0.0557196i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −309.426 | −0.438280 | ||||||||
\(707\) | 749.751 | 1.06047 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1227.43 | −1.73122 | −0.865609 | − | 0.500720i | \(-0.833069\pi\) | ||||
−0.865609 | + | 0.500720i | \(0.833069\pi\) | |||||||
\(710\) | −271.508 | − | 441.762i | −0.382406 | − | 0.622200i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 390.672i | − | 0.548696i | ||||||
\(713\) | 1829.80 | 2.56634 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 311.892 | − | 191.689i | 0.436212 | − | 0.268097i | ||||
\(716\) | − | 101.118i | − | 0.141226i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 526.048i | 0.732658i | ||||||||
\(719\) | − | 177.318i | − | 0.246617i | −0.992368 | − | 0.123309i | \(-0.960649\pi\) | ||
0.992368 | − | 0.123309i | \(-0.0393505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −766.365 | −1.06292 | ||||||||
\(722\) | −212.044 | −0.293690 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −383.747 | −0.530038 | ||||||||
\(725\) | 892.305 | + | 451.714i | 1.23077 | + | 0.623054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 52.1000i | − | 0.0716644i | −0.999358 | − | 0.0358322i | \(-0.988592\pi\) | ||
0.999358 | − | 0.0358322i | \(-0.0114082\pi\) | |||||||
\(728\) | 203.073 | 0.278946 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 168.893 | + | 274.801i | 0.231361 | + | 0.376440i | ||||
\(731\) | − | 192.351i | − | 0.263135i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 771.432i | 1.05243i | 0.850351 | + | 0.526216i | \(0.176389\pi\) | ||||
−0.850351 | + | 0.526216i | \(0.823611\pi\) | |||||||
\(734\) | 869.576i | 1.18471i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −239.831 | −0.325857 | ||||||||
\(737\) | 290.977 | 0.394813 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −250.154 | −0.338504 | −0.169252 | − | 0.985573i | \(-0.554135\pi\) | ||||
−0.169252 | + | 0.985573i | \(0.554135\pi\) | |||||||
\(740\) | −258.653 | − | 420.846i | −0.349531 | − | 0.568710i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 135.561i | 0.182697i | ||||||||
\(743\) | −404.762 | −0.544768 | −0.272384 | − | 0.962189i | \(-0.587812\pi\) | ||||
−0.272384 | + | 0.962189i | \(0.587812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 467.008 | + | 759.855i | 0.626857 | + | 1.01994i | ||||
\(746\) | − | 208.684i | − | 0.279738i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 59.8082i | − | 0.0799575i | ||||||
\(749\) | 265.448i | 0.354403i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 477.233 | 0.635464 | 0.317732 | − | 0.948181i | \(-0.397079\pi\) | ||||
0.317732 | + | 0.948181i | \(0.397079\pi\) | |||||||
\(752\) | 18.8940 | 0.0251251 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −844.804 | −1.12043 | ||||||||
\(755\) | −1144.30 | + | 703.287i | −1.51562 | + | 0.931506i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1011.95i | 1.33679i | 0.743806 | + | 0.668396i | \(0.233019\pi\) | ||||
−0.743806 | + | 0.668396i | \(0.766981\pi\) | |||||||
\(758\) | 206.033 | 0.271811 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −175.040 | + | 107.580i | −0.230316 | + | 0.141553i | ||||
\(761\) | 71.1576i | 0.0935054i | 0.998906 | + | 0.0467527i | \(0.0148873\pi\) | ||||
−0.998906 | + | 0.0467527i | \(0.985113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 487.794i | − | 0.639311i | ||||||
\(764\) | − | 226.328i | − | 0.296241i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −133.836 | −0.174720 | ||||||||
\(767\) | −1128.71 | −1.47159 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 960.734 | 1.24933 | 0.624664 | − | 0.780893i | \(-0.285236\pi\) | ||||
0.624664 | + | 0.780893i | \(0.285236\pi\) | |||||||
\(770\) | −142.028 | + | 87.2906i | −0.184452 | + | 0.113364i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 236.973i | − | 0.306959i | ||||||
\(773\) | 1055.23 | 1.36511 | 0.682554 | − | 0.730835i | \(-0.260869\pi\) | ||||
0.682554 | + | 0.730835i | \(0.260869\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −487.330 | + | 962.659i | −0.628813 | + | 1.24214i | ||||
\(776\) | 28.5084i | 0.0367377i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 194.932i | − | 0.250555i | ||||||
\(779\) | 477.571i | 0.613056i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −359.565 | −0.460390 | ||||||||
\(782\) | 365.666 | 0.467604 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 103.526 | 0.132048 | ||||||||
\(785\) | −678.632 | − | 1104.18i | −0.864499 | − | 1.40660i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3469i | 0.0144179i | 0.999974 | + | 0.00720893i | \(0.00229469\pi\) | ||||
−0.999974 | + | 0.00720893i | \(0.997705\pi\) | |||||||
\(788\) | 495.732 | 0.629102 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 749.303 | − | 460.523i | 0.948485 | − | 0.582941i | ||||
\(791\) | − | 749.979i | − | 0.948140i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.6424i | − | 0.0689059i | ||||||
\(794\) | 1040.34i | 1.31025i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 167.724 | 0.210708 | ||||||||
\(797\) | −1004.53 | −1.26038 | −0.630192 | − | 0.776440i | \(-0.717024\pi\) | ||||
−0.630192 | + | 0.776440i | \(0.717024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.8075 | −0.0360544 | ||||||||
\(800\) | 63.8739 | − | 126.175i | 0.0798424 | − | 0.157719i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 140.247i | 0.174872i | ||||||||
\(803\) | 223.670 | 0.278543 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −533.693 | − | 868.355i | −0.662972 | − | 1.07870i | ||||
\(806\) | − | 911.413i | − | 1.13079i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 441.044i | 0.545846i | ||||||||
\(809\) | − | 634.764i | − | 0.784628i | −0.919831 | − | 0.392314i | \(-0.871675\pi\) | ||
0.919831 | − | 0.392314i | \(-0.128325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1007.27 | 1.24201 | 0.621007 | − | 0.783805i | \(-0.286724\pi\) | ||||
0.621007 | + | 0.783805i | \(0.286724\pi\) | |||||||
\(812\) | 384.703 | 0.473772 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −342.540 | −0.420811 | ||||||||
\(815\) | −4.39274 | − | 7.14729i | −0.00538986 | − | 0.00876968i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 458.206i | 0.560839i | ||||||||
\(818\) | −1154.06 | −1.41083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −172.125 | − | 280.059i | −0.209908 | − | 0.341535i | ||||
\(821\) | − | 312.574i | − | 0.380724i | −0.981714 | − | 0.190362i | \(-0.939034\pi\) | ||
0.981714 | − | 0.190362i | \(-0.0609661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 547.719i | 0.665515i | 0.943012 | + | 0.332758i | \(0.107979\pi\) | ||||
−0.943012 | + | 0.332758i | \(0.892021\pi\) | |||||||
\(824\) | − | 450.817i | − | 0.547108i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 513.987 | 0.622260 | ||||||||
\(827\) | 1258.40 | 1.52164 | 0.760820 | − | 0.648963i | \(-0.224797\pi\) | ||||
0.760820 | + | 0.648963i | \(0.224797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1126.79 | 1.35922 | 0.679608 | − | 0.733576i | \(-0.262150\pi\) | ||||
0.679608 | + | 0.733576i | \(0.262150\pi\) | |||||||
\(830\) | 504.189 | − | 309.876i | 0.607457 | − | 0.373344i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 119.458i | 0.143580i | ||||||||
\(833\) | −157.844 | −0.189489 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 767.469 | − | 471.688i | 0.919124 | − | 0.564896i | ||||
\(836\) | 142.471i | 0.170420i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 255.539i | − | 0.304939i | ||||||
\(839\) | 615.550i | 0.733671i | 0.930286 | + | 0.366836i | \(0.119559\pi\) | ||||
−0.930286 | + | 0.366836i | \(0.880441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −759.407 | −0.902981 | ||||||||
\(842\) | −586.562 | −0.696630 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −161.182 | −0.190973 | ||||||||
\(845\) | 229.912 | − | 141.305i | 0.272085 | − | 0.167224i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 466.188i | − | 0.550400i | ||||||
\(848\) | −79.7444 | −0.0940382 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −97.3877 | + | 192.377i | −0.114574 | + | 0.226326i | ||||
\(851\) | − | 2094.28i | − | 2.46097i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 623.863i | − | 0.731375i | −0.930738 | − | 0.365688i | \(-0.880834\pi\) | ||
0.930738 | − | 0.365688i | \(-0.119166\pi\) | |||||||
\(854\) | 24.8828i | 0.0291368i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −156.151 | −0.182419 | ||||||||
\(857\) | 1672.77 | 1.95189 | 0.975943 | − | 0.218025i | \(-0.0699615\pi\) | ||||
0.975943 | + | 0.218025i | \(0.0699615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1005.64 | −1.17071 | −0.585353 | − | 0.810779i | \(-0.699044\pi\) | ||||
−0.585353 | + | 0.810779i | \(0.699044\pi\) | |||||||
\(860\) | −165.145 | − | 268.703i | −0.192029 | − | 0.312445i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 623.377i | − | 0.723175i | ||||||
\(863\) | 669.746 | 0.776068 | 0.388034 | − | 0.921645i | \(-0.373154\pi\) | ||||
0.388034 | + | 0.921645i | \(0.373154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 356.497 | − | 219.104i | 0.412135 | − | 0.253299i | ||||
\(866\) | 505.895i | 0.584174i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 415.035i | 0.478151i | ||||||||
\(869\) | − | 609.882i | − | 0.701821i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 886.125 | 1.01736 | ||||||||
\(872\) | 286.947 | 0.329067 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −871.064 | −0.996640 | ||||||||
\(875\) | 598.980 | − | 49.5075i | 0.684548 | − | 0.0565800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 241.526i | 0.275400i | 0.990474 | + | 0.137700i | \(0.0439710\pi\) | ||||
−0.990474 | + | 0.137700i | \(0.956029\pi\) | |||||||
\(878\) | 273.103 | 0.311052 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −51.3490 | − | 83.5483i | −0.0583511 | − | 0.0949412i | ||||
\(881\) | 557.597i | 0.632913i | 0.948607 | + | 0.316457i | \(0.102493\pi\) | ||||
−0.948607 | + | 0.316457i | \(0.897507\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 996.485i | − | 1.12852i | −0.825596 | − | 0.564261i | \(-0.809161\pi\) | ||
0.825596 | − | 0.564261i | \(-0.190839\pi\) | |||||||
\(884\) | − | 182.136i | − | 0.206036i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 82.4050 | 0.0930079 | ||||||||
\(887\) | 939.799 | 1.05953 | 0.529763 | − | 0.848146i | \(-0.322281\pi\) | ||||
0.529763 | + | 0.848146i | \(0.322281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −557.310 | −0.626896 | ||||||||
\(890\) | 511.403 | + | 832.088i | 0.574610 | + | 0.934930i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 65.7385i | 0.0736979i | ||||||||
\(893\) | 68.6231 | 0.0768455 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 132.367 | + | 215.370i | 0.147896 | + | 0.240637i | ||||
\(896\) | − | 54.3983i | − | 0.0607124i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 840.145i | 0.935573i | ||||||||
\(899\) | − | 1726.59i | − | 1.92057i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 121.585 | 0.134945 | ||||||||
\(902\) | −227.949 | −0.252715 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 441.177 | 0.488028 | ||||||||
\(905\) | 817.339 | − | 502.339i | 0.903137 | − | 0.555070i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1335.88i | − | 1.47286i | −0.676514 | − | 0.736430i | \(-0.736510\pi\) | ||
0.676514 | − | 0.736430i | \(-0.263490\pi\) | |||||||
\(908\) | −183.329 | −0.201904 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −432.522 | + | 265.829i | −0.475299 | + | 0.292120i | ||||
\(911\) | − | 1418.35i | − | 1.55692i | −0.627695 | − | 0.778459i | \(-0.716001\pi\) | ||
0.627695 | − | 0.778459i | \(-0.283999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 410.376i | − | 0.449481i | ||||||
\(914\) | − | 431.171i | − | 0.471741i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 147.389 | 0.160905 | ||||||||
\(917\) | 321.073 | 0.350134 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1152.91 | 1.25452 | 0.627262 | − | 0.778808i | \(-0.284176\pi\) | ||||
0.627262 | + | 0.778808i | \(0.284176\pi\) | |||||||
\(920\) | 510.813 | − | 313.947i | 0.555231 | − | 0.341246i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 592.846i | 0.643000i | ||||||||
\(923\) | −1095.00 | −1.18634 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1101.80 | + | 557.769i | 1.19114 | + | 0.602994i | ||||
\(926\) | − | 143.631i | − | 0.155109i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 226.303i | 0.243861i | ||||||||
\(929\) | − | 1316.30i | − | 1.41690i | −0.705762 | − | 0.708449i | \(-0.749395\pi\) | ||
0.705762 | − | 0.708449i | \(-0.250605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 376.005 | 0.403872 | ||||||||
\(932\) | 26.7497 | 0.0287014 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 631.141 | 0.675740 | ||||||||
\(935\) | 78.2910 | + | 127.385i | 0.0837337 | + | 0.136241i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.3567i | 0.0622804i | 0.999515 | + | 0.0311402i | \(0.00991384\pi\) | ||||
−0.999515 | + | 0.0311402i | \(0.990086\pi\) | |||||||
\(938\) | −403.519 | −0.430191 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −40.2422 | + | 24.7330i | −0.0428109 | + | 0.0263117i | ||||
\(941\) | 411.509i | 0.437310i | 0.975802 | + | 0.218655i | \(0.0701670\pi\) | ||||
−0.975802 | + | 0.218655i | \(0.929833\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1393.68i | − | 1.47792i | ||||||
\(944\) | 302.354i | 0.320291i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −218.706 | −0.231190 | ||||||||
\(947\) | −35.2946 | −0.0372699 | −0.0186350 | − | 0.999826i | \(-0.505932\pi\) | ||||
−0.0186350 | + | 0.999826i | \(0.505932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 681.150 | 0.717755 | ||||||||
\(950\) | 231.990 | − | 458.267i | 0.244200 | − | 0.482386i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 82.9403i | 0.0871222i | ||||||||
\(953\) | −118.637 | −0.124488 | −0.0622440 | − | 0.998061i | \(-0.519826\pi\) | ||||
−0.0622440 | + | 0.998061i | \(0.519826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 296.271 | + | 482.053i | 0.310231 | + | 0.504768i | ||||
\(956\) | − | 447.421i | − | 0.468013i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 303.828i | − | 0.317148i | ||||||
\(959\) | − | 344.505i | − | 0.359234i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 901.725 | 0.938320 | ||||||||
\(962\) | −1043.15 | −1.08436 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −430.701 | −0.446786 | ||||||||
\(965\) | 310.205 | + | 504.725i | 0.321456 | + | 0.523031i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1055.06i | − | 1.09107i | −0.838089 | − | 0.545533i | \(-0.816327\pi\) | ||
0.838089 | − | 0.545533i | \(-0.183673\pi\) | |||||||
\(968\) | 274.237 | 0.283303 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −37.3185 | − | 60.7198i | −0.0384727 | − | 0.0625978i | ||||
\(971\) | 313.380i | 0.322739i | 0.986894 | + | 0.161370i | \(0.0515912\pi\) | ||||
−0.986894 | + | 0.161370i | \(0.948409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 555.030i | − | 0.570432i | ||||||
\(974\) | 213.883i | 0.219593i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.6374 | −0.0149973 | ||||||||
\(977\) | −295.679 | −0.302639 | −0.151320 | − | 0.988485i | \(-0.548352\pi\) | ||||
−0.151320 | + | 0.988485i | \(0.548352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 677.263 | 0.691791 | ||||||||
\(980\) | −220.498 | + | 135.519i | −0.224998 | + | 0.138284i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 717.085i | − | 0.730229i | ||||||
\(983\) | 1828.74 | 1.86037 | 0.930185 | − | 0.367092i | \(-0.119646\pi\) | ||||
0.930185 | + | 0.367092i | \(0.119646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1055.86 | + | 648.931i | −1.07193 | + | 0.658813i | ||||
\(986\) | − | 345.041i | − | 0.349940i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 433.872i | 0.439141i | ||||||||
\(989\) | − | 1337.16i | − | 1.35204i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1935.94 | −1.95352 | −0.976760 | − | 0.214338i | \(-0.931241\pi\) | ||||
−0.976760 | + | 0.214338i | \(0.931241\pi\) | |||||||
\(992\) | −244.146 | −0.246115 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 498.634 | 0.501644 | ||||||||
\(995\) | −357.233 | + | 219.556i | −0.359029 | + | 0.220660i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1689.33i | − | 1.69441i | −0.531263 | − | 0.847207i | \(-0.678282\pi\) | ||
0.531263 | − | 0.847207i | \(-0.321718\pi\) | |||||||
\(998\) | 1320.13 | 1.32278 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 810.3.b.b.809.10 | 16 | ||
3.2 | odd | 2 | inner | 810.3.b.b.809.7 | 16 | ||
5.4 | even | 2 | inner | 810.3.b.b.809.8 | 16 | ||
9.2 | odd | 6 | 270.3.j.b.179.8 | 16 | |||
9.4 | even | 3 | 270.3.j.b.89.4 | 16 | |||
9.5 | odd | 6 | 90.3.j.b.29.7 | yes | 16 | ||
9.7 | even | 3 | 90.3.j.b.59.2 | yes | 16 | ||
15.14 | odd | 2 | inner | 810.3.b.b.809.9 | 16 | ||
45.2 | even | 12 | 1350.3.i.e.1151.2 | 16 | |||
45.4 | even | 6 | 270.3.j.b.89.8 | 16 | |||
45.7 | odd | 12 | 450.3.i.e.401.5 | 16 | |||
45.13 | odd | 12 | 1350.3.i.e.251.7 | 16 | |||
45.14 | odd | 6 | 90.3.j.b.29.2 | ✓ | 16 | ||
45.22 | odd | 12 | 1350.3.i.e.251.2 | 16 | |||
45.23 | even | 12 | 450.3.i.e.101.4 | 16 | |||
45.29 | odd | 6 | 270.3.j.b.179.4 | 16 | |||
45.32 | even | 12 | 450.3.i.e.101.5 | 16 | |||
45.34 | even | 6 | 90.3.j.b.59.7 | yes | 16 | ||
45.38 | even | 12 | 1350.3.i.e.1151.7 | 16 | |||
45.43 | odd | 12 | 450.3.i.e.401.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.j.b.29.2 | ✓ | 16 | 45.14 | odd | 6 | ||
90.3.j.b.29.7 | yes | 16 | 9.5 | odd | 6 | ||
90.3.j.b.59.2 | yes | 16 | 9.7 | even | 3 | ||
90.3.j.b.59.7 | yes | 16 | 45.34 | even | 6 | ||
270.3.j.b.89.4 | 16 | 9.4 | even | 3 | |||
270.3.j.b.89.8 | 16 | 45.4 | even | 6 | |||
270.3.j.b.179.4 | 16 | 45.29 | odd | 6 | |||
270.3.j.b.179.8 | 16 | 9.2 | odd | 6 | |||
450.3.i.e.101.4 | 16 | 45.23 | even | 12 | |||
450.3.i.e.101.5 | 16 | 45.32 | even | 12 | |||
450.3.i.e.401.4 | 16 | 45.43 | odd | 12 | |||
450.3.i.e.401.5 | 16 | 45.7 | odd | 12 | |||
810.3.b.b.809.7 | 16 | 3.2 | odd | 2 | inner | ||
810.3.b.b.809.8 | 16 | 5.4 | even | 2 | inner | ||
810.3.b.b.809.9 | 16 | 15.14 | odd | 2 | inner | ||
810.3.b.b.809.10 | 16 | 1.1 | even | 1 | trivial | ||
1350.3.i.e.251.2 | 16 | 45.22 | odd | 12 | |||
1350.3.i.e.251.7 | 16 | 45.13 | odd | 12 | |||
1350.3.i.e.1151.2 | 16 | 45.2 | even | 12 | |||
1350.3.i.e.1151.7 | 16 | 45.38 | even | 12 |