Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [473,2,Mod(85,473)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(473, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("473.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 473 = 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 473.k (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.77692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.53418765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 10x^{6} + 21x^{5} + 89x^{4} + 231x^{3} - 1210x^{2} - 1331x + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 343.2 | ||
Root | \(-3.27276 + 0.537652i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 473.343 |
Dual form | 473.2.k.a.171.1 |
$q$-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 \(\left(\mathbb{Z}/473\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(3\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(4\) | 1.61803 | + | 1.17557i | 0.809017 | + | 0.587785i | ||||
\(5\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.927051 | − | 2.85317i | 0.309017 | − | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 3.27872i | 0.150756 | + | 0.988571i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.786343 | + | 0.255498i | 0.218092 | + | 0.0708625i | 0.416025 | − | 0.909353i | \(-0.363423\pi\) |
−0.197933 | + | 0.980216i | \(0.563423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | + | 3.80423i | 0.309017 | + | 0.951057i | ||||
\(17\) | 7.84052 | − | 2.54754i | 1.90160 | − | 0.617869i | 0.943655 | − | 0.330930i | \(-0.107363\pi\) |
0.957949 | − | 0.286938i | \(-0.0926374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.07338 | −0.849358 | −0.424679 | − | 0.905344i | \(-0.639613\pi\) | ||||
−0.424679 | + | 0.905344i | \(0.639613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.05894 | + | 3.25907i | −0.190190 | + | 0.585346i | −0.999999 | − | 0.00134811i | \(-0.999571\pi\) |
0.809809 | + | 0.586694i | \(0.199571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | − | 3.52671i | 0.809017 | − | 0.587785i | ||||
\(37\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85437 | + | 5.30508i | 0.601951 | + | 0.828514i | 0.995885 | − | 0.0906244i | \(-0.0288863\pi\) |
−0.393934 | + | 0.919139i | \(0.628886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.55744i | 1.00000i | ||||||||
\(44\) | −3.04535 | + | 5.89286i | −0.459104 | + | 0.888383i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.85453 | − | 6.43319i | 1.29157 | − | 0.938377i | 0.291730 | − | 0.956501i | \(-0.405769\pi\) |
0.999836 | + | 0.0181233i | \(0.00576913\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16312 | − | 6.65740i | −0.309017 | − | 0.951057i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.971973 | + | 1.33781i | 0.134788 | + | 0.185520i | ||||
\(53\) | 4.44106 | − | 13.6682i | 0.610027 | − | 1.87747i | 0.152420 | − | 0.988316i | \(-0.451293\pi\) |
0.457607 | − | 0.889155i | \(-0.348707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0909 | − | 8.78452i | −1.57410 | − | 1.14365i | −0.923096 | − | 0.384570i | \(-0.874350\pi\) |
−0.651000 | − | 0.759078i | \(-0.725650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.47214 | + | 7.60845i | −0.309017 | + | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8717 | −1.32820 | −0.664098 | − | 0.747646i | \(-0.731184\pi\) | ||||
−0.664098 | + | 0.747646i | \(0.731184\pi\) | |||||||
\(68\) | 15.6810 | + | 5.09508i | 1.90160 | + | 0.617869i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.38266 | + | 1.09909i | 0.380579 | + | 0.123657i | 0.493058 | − | 0.869997i | \(-0.335879\pi\) |
−0.112479 | + | 0.993654i | \(0.535879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.45786 | + | 1.44845i | −0.489314 | + | 0.158988i | −0.543274 | − | 0.839555i | \(-0.682816\pi\) |
0.0539604 | + | 0.998543i | \(0.482816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.59086 | − | 4.78854i | −0.687145 | − | 0.499240i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.87704 | + | 18.0877i | −0.596723 | + | 1.83652i | −0.0507673 | + | 0.998711i | \(0.516167\pi\) |
−0.545956 | + | 0.837814i | \(0.683833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.81827 | + | 1.61296i | 0.986773 | + | 0.162108i | ||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | −19.1128 | − | 6.21014i | −1.90180 | − | 0.617932i | −0.956514 | − | 0.291687i | \(-0.905783\pi\) |
−0.945285 | − | 0.326245i | \(-0.894217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.08220 | − | 4.41898i | −0.599297 | − | 0.435415i | 0.246332 | − | 0.969185i | \(-0.420775\pi\) |
−0.845629 | + | 0.533771i | \(0.820775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3264 | − | 15.5895i | −1.09496 | − | 1.50709i | −0.841895 | − | 0.539641i | \(-0.818560\pi\) |
−0.253069 | − | 0.967448i | \(-0.581440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.8007i | − | 1.13031i | −0.824986 | − | 0.565153i | \(-0.808817\pi\) | ||
0.824986 | − | 0.565153i | \(-0.191183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.45796 | − | 2.00671i | 0.134788 | − | 0.185520i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5000 | + | 3.27872i | −0.954545 | + | 0.298065i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.54466 | + | 4.02843i | −0.497925 | + | 0.361764i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.7095 | − | 6.07908i | 1.66020 | − | 0.539431i | 0.679285 | − | 0.733875i | \(-0.262290\pi\) |
0.980914 | + | 0.194444i | \(0.0622902\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8404 | + | 14.9206i | −0.919472 | + | 1.26554i | 0.0443550 | + | 0.999016i | \(0.485877\pi\) |
−0.963827 | + | 0.266529i | \(0.914123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.444536 | + | 2.70595i | −0.0371739 | + | 0.226283i | ||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 24.7320i | − | 1.99947i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(164\) | 13.1149i | 1.02410i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.6855 | + | 6.72114i | 1.60069 | + | 0.520097i | 0.967279 | − | 0.253715i | \(-0.0816525\pi\) |
0.633415 | + | 0.773812i | \(0.281653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.96417 | − | 7.23939i | −0.766474 | − | 0.556876i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.70873 | + | 10.6102i | −0.587785 | + | 0.809017i | ||||
\(173\) | 11.7820 | + | 16.2165i | 0.895769 | + | 1.23292i | 0.971798 | + | 0.235815i | \(0.0757760\pi\) |
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.8550 | + | 5.95483i | −0.893601 | + | 0.448862i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.13578 | − | 21.9617i | −0.530399 | − | 1.63240i | −0.753387 | − | 0.657578i | \(-0.771581\pi\) |
0.222988 | − | 0.974821i | \(-0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.2729 | + | 24.4331i | 0.897485 | + | 1.78672i | ||||
\(188\) | 21.8896 | 1.59646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1389 | − | 6.54352i | 1.44963 | − | 0.471013i | 0.524744 | − | 0.851260i | \(-0.324161\pi\) |
0.924885 | + | 0.380247i | \(0.124161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.32624 | − | 13.3148i | 0.309017 | − | 0.951057i | ||||
\(197\) | − | 17.6160i | − | 1.25509i | −0.778581 | − | 0.627544i | \(-0.784060\pi\) | ||
0.778581 | − | 0.627544i | \(-0.215940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.77623 | + | 11.6220i | −0.262466 | + | 0.807787i | ||||
\(208\) | 3.30724i | 0.229316i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(212\) | 23.2537 | − | 16.8948i | 1.59707 | − | 1.16034i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.81622 | 0.458509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.63525 | + | 14.2658i | 0.309017 | + | 0.951057i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.97785 | + | 24.5533i | −0.527191 | + | 1.62253i | 0.232750 | + | 0.972537i | \(0.425228\pi\) |
−0.759941 | + | 0.649992i | \(0.774772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.23660 | − | 28.4273i | −0.601251 | − | 1.85046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2703 | + | 18.2651i | 0.858387 | + | 1.18147i | 0.981952 | + | 0.189132i | \(0.0605675\pi\) |
−0.123564 | + | 0.992337i | \(0.539432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.55894 | + | 20.1863i | −0.413996 | + | 1.27415i | 0.499149 | + | 0.866516i | \(0.333646\pi\) |
−0.913146 | + | 0.407634i | \(0.866354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.03669 | − | 13.3555i | −0.128045 | − | 0.839650i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | + | 9.40456i | −0.809017 | + | 0.587785i | ||||
\(257\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.5909 | − | 12.7805i | −1.07453 | − | 0.780694i | ||||
\(269\) | 5.70532 | + | 17.5592i | 0.347860 | + | 1.07060i | 0.960035 | + | 0.279880i | \(0.0902946\pi\) |
−0.612175 | + | 0.790722i | \(0.709705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6277 | + | 22.8861i | −1.01006 | + | 1.39023i | −0.0911185 | + | 0.995840i | \(0.529044\pi\) |
−0.918943 | + | 0.394390i | \(0.870956\pi\) | |||||||
\(272\) | 19.3828 | + | 26.6782i | 1.17526 | + | 1.61760i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.6585 | − | 11.7932i | −0.703031 | − | 0.711159i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.31699 | + | 6.04265i | 0.497925 | + | 0.361764i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9675 | − | 5.18815i | 0.952540 | − | 0.309499i | 0.208792 | − | 0.977960i | \(-0.433047\pi\) |
0.743747 | + | 0.668461i | \(0.233047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.85437 | + | 5.30508i | 0.229118 | + | 0.315354i | 0.908062 | − | 0.418836i | \(-0.137562\pi\) |
−0.678944 | + | 0.734191i | \(0.737562\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.2304 | − | 29.9557i | 2.42532 | − | 1.76210i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.4175 | + | 21.2203i | −0.900698 | + | 1.23970i | 0.0695472 | + | 0.997579i | \(0.477845\pi\) |
−0.970245 | + | 0.242125i | \(0.922155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.20307 | − | 1.04074i | −0.185238 | − | 0.0601876i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13053i | 0.0645230i | 0.999479 | + | 0.0322615i | \(0.0102709\pi\) | ||||
−0.999479 | + | 0.0322615i | \(0.989729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9772 | − | 15.9673i | 1.24621 | − | 0.905424i | 0.248214 | − | 0.968705i | \(-0.420156\pi\) |
0.997996 | + | 0.0632807i | \(0.0201563\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.18119 | + | 5.75492i | 0.235210 | + | 0.323739i | ||||
\(317\) | 9.94106 | − | 30.5955i | 0.558346 | − | 1.71841i | −0.128594 | − | 0.991697i | \(-0.541046\pi\) |
0.686940 | − | 0.726714i | \(-0.258954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.56231 | − | 17.1190i | −0.309017 | − | 0.951057i | ||||
\(325\) | −3.93171 | + | 1.27749i | −0.218092 | + | 0.0708625i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | −8.91572 | − | 2.89689i | −0.489314 | − | 0.158988i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7563 | − | 18.9340i | 0.749355 | − | 1.03140i | −0.248670 | − | 0.968588i | \(-0.579994\pi\) |
0.998025 | − | 0.0628108i | \(-0.0200065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2150 | − | 1.84242i | −0.607328 | − | 0.0997725i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.6701 | −0.940486 | −0.470243 | − | 0.882537i | \(-0.655834\pi\) | ||||
−0.470243 | + | 0.882537i | \(0.655834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.02690 | + | 12.4245i | −0.476421 | + | 0.655738i | −0.977812 | − | 0.209483i | \(-0.932822\pi\) |
0.501391 | + | 0.865221i | \(0.332822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.87132 | + | 18.0701i | −0.309017 | + | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.09086 | − | 0.792556i | −0.0569424 | − | 0.0413711i | 0.558950 | − | 0.829201i | \(-0.311204\pi\) |
−0.615892 | + | 0.787830i | \(0.711204\pi\) | |||||||
\(368\) | −5.03497 | − | 15.4960i | −0.262466 | − | 0.807787i | ||||
\(369\) | 18.7095 | − | 6.07908i | 0.973977 | − | 0.316464i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2053 | + | 34.4864i | 0.575579 | + | 1.77145i | 0.634200 | + | 0.773169i | \(0.281330\pi\) |
−0.0586213 | + | 0.998280i | \(0.518670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.7095 | + | 6.07908i | 0.951057 | + | 0.309017i | ||||
\(388\) | −30.7726 | + | 22.3576i | −1.56224 | + | 1.13503i | ||||
\(389\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.9374 | + | 10.3771i | −1.61514 | + | 0.524791i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 13.9901 | + | 14.1519i | 0.703031 | + | 0.711159i | ||||
\(397\) | 39.6880 | 1.99188 | 0.995941 | − | 0.0900071i | \(-0.0286890\pi\) | ||||
0.995941 | + | 0.0900071i | \(0.0286890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.1803 | − | 11.7557i | −0.809017 | − | 0.587785i | ||||
\(401\) | 0.205322 | + | 0.631918i | 0.0102533 | + | 0.0315565i | 0.956052 | − | 0.293196i | \(-0.0947189\pi\) |
−0.945799 | + | 0.324753i | \(0.894719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.66537 | + | 2.29219i | −0.0829581 | + | 0.114182i | ||||
\(404\) | −23.6248 | − | 32.5167i | −1.17538 | − | 1.61777i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.64639 | − | 14.3001i | −0.228911 | − | 0.704516i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.1464 | − | 31.2274i | −0.493334 | − | 1.51833i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.2285 | + | 33.3477i | −1.17526 | + | 1.61760i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 38.5392i | − | 1.86286i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.0120 | − | 12.6758i | −1.87914 | − | 0.610571i | −0.987450 | − | 0.157930i | \(-0.949518\pi\) |
−0.891693 | − | 0.452640i | \(-0.850482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.8726 | − | 19.0940i | 0.664377 | − | 0.914437i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 37.6633i | − | 1.79757i | −0.438389 | − | 0.898785i | \(-0.644451\pi\) | ||
0.438389 | − | 0.898785i | \(-0.355549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.9438 | + | 14.4901i | −0.947561 | + | 0.688443i | −0.950229 | − | 0.311553i | \(-0.899151\pi\) |
0.00266799 | + | 0.999996i | \(0.499151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.4667 | + | 15.2899i | −0.728298 | + | 0.719974i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2305i | 1.12853i | 0.825595 | + | 0.564263i | \(0.190840\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(468\) | 4.71806 | − | 1.53299i | 0.218092 | − | 0.0708625i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.5000 | + | 3.27872i | −0.988571 | + | 0.150756i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.8806 | − | 25.3422i | −1.59707 | − | 1.16034i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.8667 | − | 11.6538i | 1.63879 | − | 0.532475i | 0.662522 | − | 0.749043i | \(-0.269486\pi\) |
0.976268 | + | 0.216568i | \(0.0694862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.8437 | − | 7.03841i | −0.947442 | − | 0.319928i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.2726 | + | 18.3616i | −1.14521 | + | 0.832044i | −0.987837 | − | 0.155495i | \(-0.950303\pi\) |
−0.157373 | + | 0.987539i | \(0.550303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.7071 | −0.615469 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.4190 | + | 12.1582i | 1.66020 | + | 0.539431i | ||||
\(509\) | 32.9772 | − | 23.9593i | 1.46169 | − | 1.06198i | 0.478767 | − | 0.877942i | \(-0.341084\pi\) |
0.982920 | − | 0.184035i | \(-0.0589161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.5199 | + | 25.8149i | 1.12236 | + | 1.13534i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.2505i | 1.23061i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.40761 | −0.278592 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.2726 | + | 26.3536i | −1.57410 | + | 1.14365i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.67541 | + | 5.15639i | 0.0725702 | + | 0.223348i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7462 | − | 10.4210i | 0.893601 | − | 0.448862i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.1825 | − | 10.1318i | −1.34064 | − | 0.435600i | −0.451106 | − | 0.892470i | \(-0.648970\pi\) |
−0.889533 | + | 0.456870i | \(0.848970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.7183 | − | 25.7635i | −0.800337 | − | 1.10157i | −0.992743 | − | 0.120254i | \(-0.961629\pi\) |
0.192406 | − | 0.981315i | \(-0.438371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −35.0803 | + | 11.3983i | −1.48774 | + | 0.483395i | ||||
\(557\) | 26.9806 | − | 37.1356i | 1.14320 | − | 1.57348i | 0.383066 | − | 0.923721i | \(-0.374868\pi\) |
0.760137 | − | 0.649763i | \(-0.225132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.67541 | + | 5.15639i | −0.0708625 | + | 0.218092i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.5847 | + | 13.1868i | 1.71044 | + | 0.555756i | 0.990407 | − | 0.138182i | \(-0.0441257\pi\) |
0.720035 | + | 0.693938i | \(0.244126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.3191 | − | 36.2252i | −1.10335 | − | 1.51864i | −0.830861 | − | 0.556480i | \(-0.812151\pi\) |
−0.272494 | − | 0.962157i | \(-0.587849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −3.90030 | + | 3.85573i | −0.163080 | + | 0.161216i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4772 | − | 11.9714i | 0.687145 | − | 0.499240i | ||||
\(576\) | 19.4164 | + | 14.1068i | 0.809017 | + | 0.587785i | ||||
\(577\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.0347 | + | 7.72691i | 1.94798 | + | 0.320016i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.1136 | + | 46.5150i | 0.617526 | + | 1.90055i | 0.347301 | + | 0.937754i | \(0.387098\pi\) |
0.270226 | + | 0.962797i | \(0.412902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0787 | + | 31.0189i | −0.410435 | + | 1.26319i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.60636 | − | 2.79638i | 0.348176 | − | 0.113129i | ||||
\(612\) | 29.0742 | − | 40.0172i | 1.17526 | − | 1.61760i | ||||
\(613\) | 26.9836 | + | 37.1398i | 1.08986 | + | 1.50006i | 0.848182 | + | 0.529705i | \(0.177697\pi\) |
0.241677 | + | 0.970357i | \(0.422303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6092 | −0.467370 | −0.233685 | − | 0.972312i | \(-0.575078\pi\) | ||||
−0.233685 | + | 0.972312i | \(0.575078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.6529 | − | 27.3564i | 1.51340 | − | 1.09955i | 0.548756 | − | 0.835982i | \(-0.315101\pi\) |
0.964641 | − | 0.263566i | \(-0.0848986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.78767i | − | 0.229316i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.853613 | + | 2.62715i | 0.0336632 | + | 0.103605i | 0.966476 | − | 0.256756i | \(-0.0826536\pi\) |
−0.932813 | + | 0.360361i | \(0.882654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7566 | − | 44.0348i | 0.893273 | − | 1.72852i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.4175 | + | 21.2203i | −0.601951 | + | 0.828514i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0588i | 1.40465i | 0.711855 | + | 0.702326i | \(0.247855\pi\) | ||||
−0.711855 | + | 0.702326i | \(0.752145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.52337 | 0.370416 | 0.185208 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185208 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 25.5687 | + | 35.1923i | 0.989284 | + | 1.36163i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.61195 | − | 23.4272i | −0.292767 | − | 0.901045i | ||||
\(677\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.2060 | −1.80629 | −0.903143 | − | 0.429339i | \(-0.858747\pi\) | ||||
−0.903143 | + | 0.429339i | \(0.858747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.9460 | + | 8.10544i | −0.951057 | + | 0.309017i | ||||
\(689\) | 6.98440 | − | 9.61320i | 0.266084 | − | 0.366234i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 40.0895i | 1.52397i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.7351 | + | 31.7754i | 1.65659 | + | 1.20358i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.41962 | − | 4.70670i | −0.129157 | − | 0.177770i | 0.739541 | − | 0.673112i | \(-0.235043\pi\) |
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −26.1820 | − | 4.30121i | −0.986773 | − | 0.162108i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.9120 | + | 33.5837i | 0.409809 | + | 1.26126i | 0.916812 | + | 0.399319i | \(0.130753\pi\) |
−0.507003 | + | 0.861944i | \(0.669247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.27179 | − | 8.63238i | 0.235210 | − | 0.323739i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.31344 | − | 13.2754i | 0.161540 | − | 0.497168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.0909 | − | 16.7765i | −0.861144 | − | 0.625658i | 0.0670521 | − | 0.997749i | \(-0.478641\pi\) |
−0.928196 | + | 0.372092i | \(0.878641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.2716 | − | 43.9234i | 0.530399 | − | 1.63240i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | + | 15.8702i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.7053 | + | 51.4137i | 0.617869 | + | 1.90160i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.43587 | − | 35.6454i | −0.200233 | − | 1.31302i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.0618i | 0.514495i | ||||||||
\(748\) | −8.86481 | + | 53.9612i | −0.324129 | + | 1.97302i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(752\) | 35.4181 | + | 25.7328i | 1.29157 | + | 0.938377i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.26313 | − | 9.99684i | −0.262256 | − | 0.360965i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.0208i | 1.91198i | 0.293403 | + | 0.955989i | \(0.405212\pi\) | ||||
−0.293403 | + | 0.955989i | \(0.594788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40.2778 | + | 13.0870i | 1.44963 | + | 0.471013i | ||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.29468 | − | 16.2953i | −0.190190 | − | 0.585346i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.6525 | − | 16.4580i | 0.809017 | − | 0.587785i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.6172 | − | 7.99863i | 0.877510 | − | 0.285120i | 0.164587 | − | 0.986363i | \(-0.447371\pi\) |
0.712923 | + | 0.701242i | \(0.247371\pi\) | |||||||
\(788\) | 20.7089 | − | 28.5033i | 0.737722 | − | 1.01539i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.93416 | − | 9.03040i | −0.103933 | − | 0.319873i | 0.885545 | − | 0.464553i | \(-0.153785\pi\) |
−0.989479 | + | 0.144679i | \(0.953785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.0353 | − | 72.9968i | 1.87625 | − | 2.58244i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.8920 | + | 16.2109i | −1.75411 | + | 0.569944i | −0.996563 | − | 0.0828389i | \(-0.973601\pi\) |
−0.757545 | + | 0.652783i | \(0.773601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.8293 | + | 43.8093i | −1.11085 | + | 1.52896i | −0.290696 | + | 0.956816i | \(0.593887\pi\) |
−0.820156 | + | 0.572140i | \(0.806113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4411 | − | 47.5227i | 0.538242 | − | 1.65654i | −0.198297 | − | 0.980142i | \(-0.563541\pi\) |
0.736539 | − | 0.676396i | \(-0.236459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.2141 | − | 6.89288i | −0.737686 | − | 0.239689i | −0.0840119 | − | 0.996465i | \(-0.526773\pi\) |
−0.653674 | + | 0.756776i | \(0.726773\pi\) | |||||||
\(828\) | −19.7726 | + | 14.3656i | −0.687145 | + | 0.499240i | ||||
\(829\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.88789 | + | 5.35122i | −0.134788 | + | 0.185520i | ||||
\(833\) | −33.9199 | − | 46.6868i | −1.17526 | − | 1.61760i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | − | 27.5806i | −0.309017 | − | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 57.4863 | 1.97409 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7095 | − | 6.07908i | 0.640601 | − | 0.208144i | 0.0293354 | − | 0.999570i | \(-0.490661\pi\) |
0.611265 | + | 0.791426i | \(0.290661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.1582i | 0.927707i | 0.885912 | + | 0.463854i | \(0.153534\pi\) | ||||
−0.885912 | + | 0.463854i | \(0.846466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.91228 | + | 11.6403i | −0.0648698 | + | 0.394871i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.54892 | − | 2.77771i | −0.289669 | − | 0.0941192i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.1589 | + | 33.5364i | 1.56224 | + | 1.13503i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.92450 | + | 10.9071i | 0.267591 | + | 0.368308i | 0.921575 | − | 0.388201i | \(-0.126903\pi\) |
−0.653983 | + | 0.756509i | \(0.726903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4685 | −0.824365 | −0.412182 | − | 0.911101i | \(-0.635233\pi\) | ||||
−0.412182 | + | 0.911101i | \(0.635233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.6458 | + | 23.7186i | −1.09862 | + | 0.798193i | −0.980834 | − | 0.194846i | \(-0.937579\pi\) |
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 11.0289 | + | 8.01295i | 0.370941 | + | 0.269505i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.7041 | − | 26.5179i | 0.459104 | − | 0.888383i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −9.27051 | + | 28.5317i | −0.309017 | + | 0.951057i | ||||
\(901\) | − | 118.479i | − | 3.94712i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2144 | + | 52.9806i | 0.571596 | + | 1.75919i | 0.647487 | + | 0.762077i | \(0.275820\pi\) |
−0.0758905 | + | 0.997116i | \(0.524180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.4372 | + | 48.7751i | −1.17538 | + | 1.61777i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.97798 | − | 13.8918i | −0.230937 | − | 0.459753i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.7726 | + | 30.3496i | −1.38020 | + | 1.00278i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.7658 | − | 18.1194i | 1.83955 | − | 0.597705i | 0.841167 | − | 0.540775i | \(-0.181869\pi\) |
0.998378 | − | 0.0569297i | \(-0.0181311\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.2466 | + | 13.2569i | −0.599297 | + | 0.435415i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.0546 | + | 9.44041i | −0.947153 | + | 0.307749i | −0.741558 | − | 0.670888i | \(-0.765913\pi\) |
−0.205595 | + | 0.978637i | \(0.565913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.7003 | − | 21.6096i | −0.511271 | − | 0.703705i | ||||
\(944\) | 18.4732 | − | 56.8546i | 0.601251 | − | 1.85046i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.18914 | 0.201120 | 0.100560 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100560 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 45.1537i | 1.46038i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5793 | + | 11.3191i | 0.502560 | + | 0.365131i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.9795 | + | 17.8639i | −1.77169 | + | 0.575657i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.5946i | − | 1.62701i | −0.581557 | − | 0.813506i | \(-0.697556\pi\) | ||
0.581557 | − | 0.813506i | \(-0.302444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.4772 | − | 27.9553i | 1.23479 | − | 0.897128i | 0.237551 | − | 0.971375i | \(-0.423655\pi\) |
0.997240 | + | 0.0742473i | \(0.0236554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.1708 | − | 37.4577i | 0.389377 | − | 1.19838i | −0.543878 | − | 0.839164i | \(-0.683045\pi\) |
0.933255 | − | 0.359215i | \(-0.116955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.6695 | − | 10.9399i | −1.07498 | − | 0.349284i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 26.7109i | − | 0.849358i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 473.2.k.a.343.2 | yes | 8 | |
11.6 | odd | 10 | inner | 473.2.k.a.171.1 | ✓ | 8 | |
43.42 | odd | 2 | CM | 473.2.k.a.343.2 | yes | 8 | |
473.171 | even | 10 | inner | 473.2.k.a.171.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
473.2.k.a.171.1 | ✓ | 8 | 11.6 | odd | 10 | inner | |
473.2.k.a.171.1 | ✓ | 8 | 473.171 | even | 10 | inner | |
473.2.k.a.343.2 | yes | 8 | 1.1 | even | 1 | trivial | |
473.2.k.a.343.2 | yes | 8 | 43.42 | odd | 2 | CM |