Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 251.2 | ||
Root | \(-0.570223 - 1.63550i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.251 |
Dual form | 363.3.h.f.269.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(3\) | −1.04781 | + | 2.81107i | −0.349270 | + | 0.937022i | ||||
\(4\) | −3.23607 | − | 2.35114i | −0.809017 | − | 0.587785i | ||||
\(5\) | −9.46289 | + | 3.07468i | −1.89258 | + | 0.614936i | −0.915388 | + | 0.402574i | \(0.868116\pi\) |
−0.977191 | + | 0.212362i | \(0.931884\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.80418 | − | 5.89093i | −0.756021 | − | 0.654548i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 10.0000 | − | 6.63325i | 0.833333 | − | 0.552771i | ||||
\(13\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27219 | − | 29.8225i | 0.0848129 | − | 1.98817i | ||||
\(16\) | 4.94427 | + | 15.2169i | 0.309017 | + | 0.951057i | ||||
\(17\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | 37.8516 | + | 12.2987i | 1.89258 | + | 0.614936i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.8496i | 1.29781i | 0.760870 | + | 0.648905i | \(0.224773\pi\) | ||||
−0.760870 | + | 0.648905i | \(0.775227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 59.8673 | − | 43.4961i | 2.39469 | − | 1.73984i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 23.6893 | − | 12.9544i | 0.877381 | − | 0.479794i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.4336 | − | 35.1891i | 0.368827 | − | 1.13513i | −0.578723 | − | 0.815524i | \(-0.696449\pi\) |
0.947550 | − | 0.319608i | \(-0.103551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.16839 | + | 35.0611i | 0.226900 | + | 0.973918i | ||||
\(37\) | −20.2254 | − | 14.6946i | −0.546633 | − | 0.397152i | 0.279909 | − | 0.960026i | \(-0.409696\pi\) |
−0.826543 | + | 0.562874i | \(0.809696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 82.5000 | + | 34.8246i | 1.83333 | + | 0.773879i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.7871 | + | 64.3969i | 0.995471 | + | 1.37015i | 0.928063 | + | 0.372422i | \(0.121473\pi\) |
0.0674071 | + | 0.997726i | \(0.478527\pi\) | |||||||
\(48\) | −47.9564 | − | 2.04576i | −0.999091 | − | 0.0426201i | ||||
\(49\) | −15.1418 | − | 46.6018i | −0.309017 | − | 0.951057i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −75.7031 | − | 24.5974i | −1.42836 | − | 0.464103i | −0.510113 | − | 0.860108i | \(-0.670396\pi\) |
−0.918248 | + | 0.396005i | \(0.870396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 29.2419 | − | 40.2481i | 0.495626 | − | 0.682171i | −0.485787 | − | 0.874077i | \(-0.661467\pi\) |
0.981413 | + | 0.191906i | \(0.0614669\pi\) | |||||||
\(60\) | −74.2338 | + | 93.5165i | −1.23723 | + | 1.55861i | ||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19.7771 | − | 60.8676i | 0.309017 | − | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −35.0000 | −0.522388 | −0.261194 | − | 0.965286i | \(-0.584116\pi\) | ||||
−0.261194 | + | 0.965286i | \(0.584116\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −83.9093 | − | 31.2768i | −1.21608 | − | 0.453286i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 47.3145 | − | 15.3734i | 0.666401 | − | 0.216527i | 0.0437690 | − | 0.999042i | \(-0.486063\pi\) |
0.622632 | + | 0.782515i | \(0.286063\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 59.5409 | + | 213.867i | 0.793878 | + | 2.85155i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | −93.5742 | − | 128.794i | −1.16968 | − | 1.60992i | ||||
\(81\) | 11.5939 | + | 80.1660i | 0.143134 | + | 0.989703i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 149.248i | − | 1.67695i | −0.544944 | − | 0.838473i | \(-0.683449\pi\) | ||
0.544944 | − | 0.838473i | \(-0.316551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 70.1807 | − | 96.5954i | 0.762833 | − | 1.04995i | ||||
\(93\) | 86.9386 | + | 69.0122i | 0.934823 | + | 0.742067i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29.3566 | − | 90.3504i | 0.302646 | − | 0.931447i | −0.677900 | − | 0.735154i | \(-0.737110\pi\) |
0.980545 | − | 0.196293i | \(-0.0628903\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −296.000 | −2.96000 | ||||||||
\(101\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 153.713 | + | 111.679i | 1.49236 | + | 1.08426i | 0.973303 | + | 0.229526i | \(0.0737174\pi\) |
0.519059 | + | 0.854739i | \(0.326283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(108\) | −107.118 | − | 13.7755i | −0.991832 | − | 0.127551i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 62.5000 | − | 41.4578i | 0.563063 | − | 0.373494i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 40.9387 | + | 56.3473i | 0.362290 | + | 0.498649i | 0.950785 | − | 0.309852i | \(-0.100279\pi\) |
−0.588495 | + | 0.808501i | \(0.700279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −91.7780 | − | 282.464i | −0.798070 | − | 2.45621i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −119.735 | + | 86.9922i | −0.965601 | + | 0.701550i | ||||
\(125\) | −286.571 | + | 394.431i | −2.29257 | + | 3.15545i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −184.339 | + | 195.423i | −1.36547 | + | 1.44758i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −66.2402 | + | 21.5228i | −0.483505 | + | 0.157100i | −0.540620 | − | 0.841267i | \(-0.681810\pi\) |
0.0571141 | + | 0.998368i | \(0.481810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −230.048 | + | 64.0459i | −1.63155 | + | 0.454226i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 56.0000 | − | 132.665i | 0.388889 | − | 0.921285i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 146.866 | + | 6.26515i | 0.999091 | + | 0.0426201i | ||||
\(148\) | 30.9017 | + | 95.1057i | 0.208795 | + | 0.642606i | ||||
\(149\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 368.145i | 2.37513i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 173.939 | − | 126.374i | 1.10789 | − | 0.804929i | 0.125560 | − | 0.992086i | \(-0.459927\pi\) |
0.982330 | + | 0.187157i | \(0.0599274\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 148.468 | − | 187.033i | 0.933759 | − | 1.17631i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.6312 | + | 66.5740i | −0.132707 | + | 0.408429i | −0.995226 | − | 0.0975945i | \(-0.968885\pi\) |
0.862520 | + | 0.506024i | \(0.168885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 136.724 | + | 99.3357i | 0.809017 | + | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 82.5000 | + | 124.373i | 0.466102 | + | 0.702675i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −204.694 | − | 281.737i | −1.14354 | − | 1.57395i | −0.759335 | − | 0.650700i | \(-0.774476\pi\) |
−0.384205 | − | 0.923248i | \(-0.625524\pi\) | |||||||
\(180\) | −185.098 | − | 306.664i | −1.02832 | − | 1.70369i | ||||
\(181\) | 81.2715 | + | 250.128i | 0.449014 | + | 1.38192i | 0.878022 | + | 0.478621i | \(0.158863\pi\) |
−0.429008 | + | 0.903301i | \(0.641137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 236.572 | + | 76.8670i | 1.27877 | + | 0.415497i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 318.396i | − | 1.69360i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 204.694 | − | 281.737i | 1.07169 | − | 1.47506i | 0.203345 | − | 0.979107i | \(-0.434819\pi\) |
0.868349 | − | 0.495954i | \(-0.165181\pi\) | |||||||
\(192\) | 150.380 | + | 119.372i | 0.783230 | + | 0.621732i | ||||
\(193\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −60.5673 | + | 186.407i | −0.309017 | + | 0.951057i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.0100503 | −0.00502513 | − | 0.999987i | \(-0.501600\pi\) | ||||
−0.00502513 | + | 0.999987i | \(0.501600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.6734 | − | 98.3873i | 0.182455 | − | 0.489489i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 175.842 | − | 203.102i | 0.849479 | − | 0.981171i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(212\) | 187.148 | + | 257.588i | 0.882776 | + | 1.21504i | ||||
\(213\) | −6.36097 | + | 149.113i | −0.0298637 | + | 0.700059i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 360.013 | − | 261.564i | 1.61441 | − | 1.17293i | 0.767864 | − | 0.640613i | \(-0.221320\pi\) |
0.846542 | − | 0.532322i | \(-0.178680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −663.580 | − | 56.7184i | −2.94925 | − | 0.252082i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 133.804 | − | 411.807i | 0.584299 | − | 1.79829i | −0.0177708 | − | 0.999842i | \(-0.505657\pi\) |
0.602069 | − | 0.798444i | \(-0.294343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −640.741 | − | 465.526i | −2.72656 | − | 1.98096i | ||||
\(236\) | −189.258 | + | 61.4936i | −0.801940 | + | 0.260566i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(240\) | 460.096 | − | 128.092i | 1.91707 | − | 0.533715i | ||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −237.500 | − | 51.4077i | −0.977366 | − | 0.211554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 286.571 | + | 394.431i | 1.16968 | + | 1.60992i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −425.830 | − | 138.361i | −1.69653 | − | 0.551237i | −0.708533 | − | 0.705678i | \(-0.750642\pi\) |
−0.988002 | + | 0.154441i | \(0.950642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −207.108 | + | 150.473i | −0.809017 | + | 0.587785i | ||||
\(257\) | 280.723 | − | 386.382i | 1.09231 | − | 1.50343i | 0.247100 | − | 0.968990i | \(-0.420522\pi\) |
0.845206 | − | 0.534441i | \(-0.179478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 792.000 | 2.98868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 419.546 | + | 156.384i | 1.57133 | + | 0.585707i | ||||
\(268\) | 113.262 | + | 82.2899i | 0.422621 | + | 0.307052i | ||||
\(269\) | 378.516 | − | 122.987i | 1.40712 | − | 0.457202i | 0.495635 | − | 0.868531i | \(-0.334935\pi\) |
0.911487 | + | 0.411329i | \(0.134935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 198.000 | + | 298.496i | 0.717391 | + | 1.08151i | ||||
\(277\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −285.093 | + | 172.078i | −1.02184 | + | 0.616768i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | −189.258 | − | 61.4936i | −0.666401 | − | 0.216527i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −233.806 | + | 169.870i | −0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 223.221 | + | 177.193i | 0.767081 | + | 0.608912i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −152.963 | + | 470.773i | −0.518520 | + | 1.59584i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 310.152 | − | 832.076i | 1.03384 | − | 2.77359i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −475.000 | + | 315.079i | −1.53722 | + | 1.01967i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −233.936 | − | 321.985i | −0.752204 | − | 1.03532i | −0.997823 | − | 0.0659539i | \(-0.978991\pi\) |
0.245618 | − | 0.969367i | \(-0.421009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 81.8895 | + | 252.030i | 0.261628 | + | 0.805208i | 0.992451 | + | 0.122641i | \(0.0391363\pi\) |
−0.730823 | + | 0.682567i | \(0.760864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 596.162 | + | 193.705i | 1.88064 | + | 0.611056i | 0.986623 | + | 0.163020i | \(0.0521234\pi\) |
0.894015 | + | 0.448037i | \(0.147877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 636.792i | 1.98997i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 150.963 | − | 286.681i | 0.465935 | − | 0.884819i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 563.000 | 1.70091 | 0.850453 | − | 0.526051i | \(-0.176328\pi\) | ||||
0.850453 | + | 0.526051i | \(0.176328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51.0525 | + | 219.132i | 0.153311 | + | 0.658053i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 331.201 | − | 107.614i | 0.988660 | − | 0.321235i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −201.292 | + | 56.0401i | −0.593782 | + | 0.165310i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 890.190 | + | 37.9745i | 2.58026 | + | 0.110071i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | − | 328.346i | − | 0.930158i | −0.885269 | − | 0.465079i | \(-0.846026\pi\) | ||
0.885269 | − | 0.465079i | \(-0.153974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −400.463 | + | 290.954i | −1.12807 | + | 0.819588i | ||||
\(356\) | −350.903 | + | 482.977i | −0.985684 | + | 1.35668i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −111.555 | + | 343.331i | −0.309017 | + | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −513.726 | − | 373.244i | −1.39980 | − | 1.01701i | −0.994709 | − | 0.102735i | \(-0.967241\pi\) |
−0.405089 | − | 0.914277i | \(-0.632759\pi\) | |||||||
\(368\) | −454.219 | + | 147.585i | −1.23429 | + | 0.401045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −119.082 | − | 427.733i | −0.320112 | − | 1.14982i | ||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −808.500 | − | 1218.86i | −2.15600 | − | 3.25029i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −41.0993 | − | 126.491i | −0.108441 | − | 0.333748i | 0.882081 | − | 0.471097i | \(-0.156142\pi\) |
−0.990523 | + | 0.137349i | \(0.956142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −123.018 | − | 39.9708i | −0.321195 | − | 0.104363i | 0.143982 | − | 0.989580i | \(-0.454009\pi\) |
−0.465177 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −307.426 | + | 223.358i | −0.792336 | + | 0.575666i | ||||
\(389\) | −321.661 | + | 442.729i | −0.826893 | + | 1.13812i | 0.161600 | + | 0.986856i | \(0.448334\pi\) |
−0.988493 | + | 0.151264i | \(0.951666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −790.000 | −1.98992 | −0.994962 | − | 0.100251i | \(-0.968036\pi\) | ||||
−0.994962 | + | 0.100251i | \(0.968036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 957.876 | + | 695.938i | 2.39469 | + | 1.73984i | ||||
\(401\) | −757.031 | + | 245.974i | −1.88786 | + | 0.613403i | −0.906169 | + | 0.422915i | \(0.861007\pi\) |
−0.981690 | + | 0.190487i | \(0.938993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −356.196 | − | 722.955i | −0.879497 | − | 1.78507i | ||||
\(406\) | 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 | ||||||||
\(411\) | 8.90535 | − | 208.758i | 0.0216675 | − | 0.507926i | ||||
\(412\) | −234.853 | − | 722.803i | −0.570031 | − | 1.75438i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 795.990i | − | 1.89974i | −0.312649 | − | 0.949869i | \(-0.601216\pi\) | ||
0.312649 | − | 0.949869i | \(-0.398784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −600.291 | + | 436.137i | −1.42587 | + | 1.03595i | −0.435101 | + | 0.900382i | \(0.643287\pi\) |
−0.990767 | + | 0.135572i | \(0.956713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 61.0098 | − | 713.788i | 0.144231 | − | 1.68744i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(432\) | 314.253 | + | 296.428i | 0.727437 | + | 0.686175i | ||||
\(433\) | 20.2254 | + | 14.6946i | 0.0467100 | + | 0.0339368i | 0.610895 | − | 0.791711i | \(-0.290810\pi\) |
−0.564185 | + | 0.825648i | \(0.690810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.500 | + | 406.287i | −0.388889 | + | 0.921285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −450.326 | − | 619.821i | −1.01654 | − | 1.39914i | −0.914603 | − | 0.404352i | \(-0.867497\pi\) |
−0.101934 | − | 0.994791i | \(-0.532503\pi\) | |||||||
\(444\) | −299.727 | − | 12.7860i | −0.675062 | − | 0.0287973i | ||||
\(445\) | 458.890 | + | 1412.32i | 1.03121 | + | 3.17375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 615.088 | + | 199.854i | 1.36991 | + | 0.445110i | 0.899338 | − | 0.437254i | \(-0.144049\pi\) |
0.470568 | + | 0.882364i | \(0.344049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 278.596i | − | 0.616364i | ||||||
\(453\) | 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 | ||||||||
\(460\) | −367.112 | + | 1129.86i | −0.798070 | + | 2.45621i | ||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.0000 | 0.0755940 | 0.0377970 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377970 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1034.88 | − | 385.747i | −2.22555 | − | 0.829563i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −123.018 | + | 39.9708i | −0.263421 | + | 0.0855907i | −0.437750 | − | 0.899097i | \(-0.644224\pi\) |
0.174329 | + | 0.984687i | \(0.444224\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 172.990 | + | 621.369i | 0.367283 | + | 1.31925i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 370.196 | + | 613.328i | 0.776093 | + | 1.28580i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 945.238i | 1.94894i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 707.890 | − | 514.312i | 1.45357 | − | 1.05608i | 0.468593 | − | 0.883414i | \(-0.344761\pi\) |
0.984980 | − | 0.172668i | \(-0.0552387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −164.478 | − | 130.564i | −0.336357 | − | 0.267001i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 592.000 | 1.19355 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 487.028 | + | 353.847i | 0.976008 | + | 0.709112i | 0.956813 | − | 0.290704i | \(-0.0938895\pi\) |
0.0191955 | + | 0.999816i | \(0.493890\pi\) | |||||||
\(500\) | 1854.73 | − | 602.637i | 3.70945 | − | 1.20527i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −422.500 | + | 280.255i | −0.833333 | + | 0.552771i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −87.7258 | − | 120.744i | −0.172349 | − | 0.237219i | 0.714100 | − | 0.700043i | \(-0.246836\pi\) |
−0.886450 | + | 0.462825i | \(0.846836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1797.95 | − | 584.189i | −3.49116 | − | 1.13435i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 380.145 | − | 523.225i | 0.729646 | − | 1.00427i | −0.269502 | − | 0.963000i | \(-0.586859\pi\) |
0.999148 | − | 0.0412712i | \(-0.0131408\pi\) | |||||||
\(522\) | 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 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −362.000 | −0.684310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −436.066 | + | 101.593i | −0.821217 | + | 0.191324i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1006.46 | − | 280.201i | 1.87423 | − | 0.521789i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1056.00 | − | 198.997i | 1.95556 | − | 0.368514i | ||||
\(541\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −788.283 | − | 33.6272i | −1.45172 | − | 0.0619286i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(548\) | 264.961 | + | 86.0910i | 0.483505 | + | 0.157100i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −463.961 | + | 584.478i | −0.835966 | + | 1.05311i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(564\) | 895.032 | + | 333.619i | 1.58694 | + | 0.591523i | ||||
\(565\) | −560.649 | − | 407.335i | −0.992299 | − | 0.720947i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 577.500 | + | 870.614i | 1.00785 | + | 1.51940i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1298.34 | + | 1787.02i | 2.25799 | + | 3.10785i | ||||
\(576\) | −493.134 | + | 297.649i | −0.856135 | + | 0.516752i | ||||
\(577\) | −326.013 | − | 1003.36i | −0.565014 | − | 1.73893i | −0.667911 | − | 0.744241i | \(-0.732811\pi\) |
0.102897 | − | 0.994692i | \(-0.467189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −187.148 | + | 257.588i | −0.318822 | + | 0.438821i | −0.938107 | − | 0.346345i | \(-0.887423\pi\) |
0.619285 | + | 0.785166i | \(0.287423\pi\) | |||||||
\(588\) | −460.539 | − | 365.578i | −0.783230 | − | 0.621732i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 123.607 | − | 380.423i | 0.208795 | − | 0.642606i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.09562 | − | 5.62213i | 0.00351025 | − | 0.00941731i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1135.55 | + | 368.962i | −1.89574 | + | 0.615963i | −0.922591 | + | 0.385781i | \(0.873932\pi\) |
−0.973148 | + | 0.230182i | \(0.926068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 238.146 | + | 206.183i | 0.394936 | + | 0.341928i | ||||
\(604\) | 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 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1114.39i | − | 1.80614i | −0.429498 | − | 0.903068i | \(-0.641309\pi\) | ||
0.429498 | − | 0.903068i | \(-0.358691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1000.75 | − | 727.090i | 1.61673 | − | 1.17462i | 0.784743 | − | 0.619821i | \(-0.212795\pi\) |
0.831984 | − | 0.554800i | \(-0.187205\pi\) | |||||||
\(620\) | 865.562 | − | 1191.34i | 1.39607 | − | 1.92152i | ||||
\(621\) | 386.685 | + | 707.117i | 0.622681 | + | 1.13867i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 927.360 | − | 2854.12i | 1.48378 | − | 4.56659i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −860.000 | −1.36943 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −981.338 | − | 712.984i | −1.55521 | − | 1.12993i | −0.939803 | − | 0.341717i | \(-0.888992\pi\) |
−0.615407 | − | 0.788209i | \(-0.711008\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −920.192 | + | 256.183i | −1.44684 | + | 0.402804i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −412.500 | − | 174.123i | −0.645540 | − | 0.272493i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −614.081 | − | 845.210i | −0.958005 | − | 1.31858i | −0.947879 | − | 0.318631i | \(-0.896777\pi\) |
−0.0101258 | − | 0.999949i | \(-0.503223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 122.062 | + | 375.667i | 0.189832 | + | 0.584242i | 0.999998 | − | 0.00195828i | \(-0.000623341\pi\) |
−0.810166 | + | 0.586200i | \(0.800623\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1107.16 | + | 359.738i | 1.71122 | + | 0.556009i | 0.990536 | − | 0.137256i | \(-0.0438283\pi\) |
0.720683 | + | 0.693265i | \(0.243828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 226.525 | − | 164.580i | 0.347431 | − | 0.252423i | ||||
\(653\) | −99.4226 | + | 136.843i | −0.152255 | + | 0.209561i | −0.878330 | − | 0.478054i | \(-0.841342\pi\) |
0.726075 | + | 0.687615i | \(0.241342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1153.00 | 1.74433 | 0.872163 | − | 0.489215i | \(-0.162717\pi\) | ||||
0.872163 | + | 0.489215i | \(0.162717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 358.050 | + | 1286.09i | 0.535202 | + | 1.92241i | ||||
\(670\) | 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 | ||||||||
\(675\) | 854.746 | − | 1805.94i | 1.26629 | − | 2.67546i | ||||
\(676\) | −208.895 | − | 642.914i | −0.309017 | − | 0.951057i | ||||
\(677\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1114.39i | 1.63160i | 0.578331 | + | 0.815802i | \(0.303704\pi\) | ||||
−0.578331 | + | 0.815802i | \(0.696296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 560.649 | − | 407.335i | 0.818465 | − | 0.594650i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1017.42 | + | 807.629i | 1.48096 | + | 1.17559i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.756 | + | 1039.50i | −0.488792 | + | 1.50435i | 0.337620 | + | 0.941283i | \(0.390378\pi\) |
−0.826412 | + | 0.563066i | \(0.809622\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1980.00 | − | 1313.38i | 2.80851 | − | 1.86296i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 25.4439 | − | 596.450i | 0.0359377 | − | 0.842444i | ||||
\(709\) | 326.631 | + | 1005.27i | 0.460692 | + | 1.41787i | 0.864320 | + | 0.502942i | \(0.167749\pi\) |
−0.403628 | + | 0.914923i | \(0.632251\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1050.38 | + | 341.290i | 1.47319 | + | 0.478667i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1392.98i | 1.94551i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 497.113 | − | 684.217i | 0.691395 | − | 0.951624i | −0.308605 | − | 0.951190i | \(-0.599862\pi\) |
1.00000 | 0.000433404i | \(-0.000137957\pi\) | ||||||||
\(720\) | −122.020 | + | 1427.58i | −0.169472 | + | 1.98275i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 325.086 | − | 1000.51i | 0.449014 | − | 1.38192i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1355.00 | −1.86382 | −0.931912 | − | 0.362685i | \(-0.881860\pi\) | ||||
−0.931912 | + | 0.362685i | \(0.881860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 393.365 | − | 613.763i | 0.539596 | − | 0.841924i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1409.04 | + | 392.281i | −1.91707 | + | 0.533715i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(740\) | −584.839 | − | 804.962i | −0.790323 | − | 1.08779i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −787.174 | + | 571.915i | −1.04817 | + | 0.761538i | −0.971863 | − | 0.235547i | \(-0.924312\pi\) |
−0.0763041 | + | 0.997085i | \(0.524312\pi\) | |||||||
\(752\) | −748.594 | + | 1030.35i | −0.995471 | + | 1.37015i | ||||
\(753\) | 835.130 | − | 1052.06i | 1.10907 | − | 1.39716i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.6312 | − | 66.5740i | 0.0285749 | − | 0.0879445i | −0.935752 | − | 0.352659i | \(-0.885278\pi\) |
0.964327 | + | 0.264714i | \(0.0852776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1324.80 | + | 430.455i | −1.73404 | + | 0.563423i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −205.979 | − | 739.863i | −0.268202 | − | 0.963363i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 792.000 | + | 1193.98i | 1.02724 | + | 1.54862i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 421.084 | + | 579.572i | 0.544740 | + | 0.749770i | 0.989287 | − | 0.145985i | \(-0.0466352\pi\) |
−0.444547 | + | 0.895756i | \(0.646635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −846.089 | − | 2603.99i | −1.09173 | − | 3.35999i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 634.269 | − | 460.824i | 0.809017 | − | 0.587785i | ||||
\(785\) | −1257.40 | + | 1730.67i | −1.60179 | + | 2.20467i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −829.866 | + | 2226.36i | −1.04386 | + | 2.80046i | ||||
\(796\) | 6.47214 | + | 4.70228i | 0.00813082 | + | 0.00590739i | ||||
\(797\) | 160.869 | − | 52.2696i | 0.201843 | − | 0.0655829i | −0.206351 | − | 0.978478i | \(-0.566159\pi\) |
0.408194 | + | 0.912895i | \(0.366159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −879.210 | + | 1015.51i | −1.09764 | + | 1.26780i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −350.000 | + | 232.164i | −0.435323 | + | 0.288761i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −50.8877 | + | 1192.90i | −0.0630579 | + | 1.47819i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | − | 696.491i | − | 0.854590i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 233.308 | − | 718.048i | 0.283485 | − | 0.872476i | −0.703364 | − | 0.710830i | \(-0.748320\pi\) |
0.986849 | − | 0.161646i | \(-0.0516803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(828\) | −1046.56 | + | 243.823i | −1.26396 | + | 0.294473i | ||||
\(829\) | 660.967 | + | 480.221i | 0.797306 | + | 0.579277i | 0.910123 | − | 0.414339i | \(-0.135987\pi\) |
−0.112816 | + | 0.993616i | \(0.535987\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −185.000 | − | 981.721i | −0.221027 | − | 1.17290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 964.984 | + | 1328.19i | 1.15016 | + | 1.58306i | 0.742380 | + | 0.669979i | \(0.233697\pi\) |
0.407780 | + | 0.913080i | \(0.366303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 259.883 | + | 799.839i | 0.309017 | + | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1599.23 | − | 519.621i | −1.89258 | − | 0.614936i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1273.58i | − | 1.50187i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 438.629 | − | 603.721i | 0.515428 | − | 0.709426i | ||||
\(852\) | 371.169 | − | 467.583i | 0.435644 | − | 0.548806i | ||||
\(853\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −757.000 | −0.881257 | −0.440629 | − | 0.897689i | \(-0.645244\pi\) | ||||
−0.440629 | + | 0.897689i | \(0.645244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1589.77 | − | 516.546i | 1.84214 | − | 0.598547i | 0.844084 | − | 0.536211i | \(-0.180145\pi\) |
0.998055 | − | 0.0623360i | \(-0.0198550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −232.531 | − | 835.235i | −0.268202 | − | 0.963363i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −731.996 | + | 441.823i | −0.838483 | + | 0.506097i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 945.238i | 1.07291i | 0.843927 | + | 0.536457i | \(0.180238\pi\) | ||||
−0.843927 | + | 0.536457i | \(0.819762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1108.35 | − | 805.266i | 1.25521 | − | 0.911966i | 0.256701 | − | 0.966491i | \(-0.417364\pi\) |
0.998512 | + | 0.0545251i | \(0.0173645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1163.10 | − | 923.271i | −1.31423 | − | 1.04324i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1780.00 | −1.99552 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2803.24 | + | 2036.68i | 3.13212 | + | 2.27562i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2014.04 | + | 1743.72i | 2.23782 | + | 1.93746i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1538.13 | − | 2117.05i | −1.69959 | − | 2.33928i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −540.780 | − | 1664.35i | −0.596229 | − | 1.83500i | −0.548511 | − | 0.836143i | \(-0.684805\pi\) |
−0.0477182 | − | 0.998861i | \(-0.515195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −378.516 | − | 122.987i | −0.415495 | − | 0.135002i | 0.0938071 | − | 0.995590i | \(-0.470096\pi\) |
−0.509302 | + | 0.860588i | \(0.670096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1401.22 | + | 1018.04i | −1.52971 | + | 1.11140i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1850.00 | −2.00000 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −387.999 | − | 1665.40i | −0.418553 | − | 1.79655i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1514.06 | − | 491.949i | 1.62978 | − | 0.529547i | 0.655557 | − | 0.755146i | \(-0.272434\pi\) |
0.974220 | + | 0.225599i | \(0.0724340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1150.24 | − | 320.229i | 1.23284 | − | 0.343225i | ||||
\(934\) | 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 | ||||||||
\(939\) | −794.278 | − | 33.8830i | −0.845876 | − | 0.0360841i | ||||
\(940\) | 978.966 | + | 3012.95i | 1.04145 | + | 3.20526i | ||||
\(941\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 757.031 | + | 245.974i | 0.801940 | + | 0.260566i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1323.33i | − | 1.39740i | −0.715417 | − | 0.698698i | \(-0.753763\pi\) | ||
0.715417 | − | 0.698698i | \(-0.246237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1169.18 | + | 1472.89i | −1.22942 | + | 1.54878i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1070.74 | + | 3295.41i | −1.12120 | + | 3.45069i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1790.06 | − | 667.238i | −1.86465 | − | 0.695039i | ||||
\(961\) | −330.079 | − | 239.816i | −0.343474 | − | 0.249549i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1140.44 | − | 1569.68i | −1.17450 | − | 1.61656i | −0.621825 | − | 0.783156i | \(-0.713609\pi\) |
−0.552671 | − | 0.833399i | \(-0.686391\pi\) | |||||||
\(972\) | 647.699 | + | 724.755i | 0.666357 | + | 0.745632i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1447.82 | − | 470.426i | −1.48191 | − | 0.481501i | −0.547225 | − | 0.836986i | \(-0.684316\pi\) |
−0.934682 | + | 0.355485i | \(0.884316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 1950.18i | − | 1.98997i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1093.65 | − | 1505.28i | 1.11256 | − | 1.53131i | 0.294976 | − | 0.955505i | \(-0.404688\pi\) |
0.817586 | − | 0.575806i | \(-0.195312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1582.00 | 1.59637 | 0.798184 | − | 0.602414i | \(-0.205794\pi\) | ||||
0.798184 | + | 0.602414i | \(0.205794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −589.918 | + | 1582.63i | −0.594076 | + | 1.59379i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.9258 | − | 6.14936i | 0.0190209 | − | 0.00618026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −669.487 | − | 86.0966i | −0.670157 | − | 0.0861828i |
(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 | 363.3.h.f.251.2 | 8 | ||
3.2 | odd | 2 | inner | 363.3.h.f.251.1 | 8 | ||
11.2 | odd | 10 | inner | 363.3.h.f.245.2 | 8 | ||
11.3 | even | 5 | inner | 363.3.h.f.323.1 | 8 | ||
11.4 | even | 5 | 363.3.b.c.122.1 | ✓ | 2 | ||
11.5 | even | 5 | inner | 363.3.h.f.269.1 | 8 | ||
11.6 | odd | 10 | inner | 363.3.h.f.269.1 | 8 | ||
11.7 | odd | 10 | 363.3.b.c.122.1 | ✓ | 2 | ||
11.8 | odd | 10 | inner | 363.3.h.f.323.1 | 8 | ||
11.9 | even | 5 | inner | 363.3.h.f.245.2 | 8 | ||
11.10 | odd | 2 | CM | 363.3.h.f.251.2 | 8 | ||
33.2 | even | 10 | inner | 363.3.h.f.245.1 | 8 | ||
33.5 | odd | 10 | inner | 363.3.h.f.269.2 | 8 | ||
33.8 | even | 10 | inner | 363.3.h.f.323.2 | 8 | ||
33.14 | odd | 10 | inner | 363.3.h.f.323.2 | 8 | ||
33.17 | even | 10 | inner | 363.3.h.f.269.2 | 8 | ||
33.20 | odd | 10 | inner | 363.3.h.f.245.1 | 8 | ||
33.26 | odd | 10 | 363.3.b.c.122.2 | yes | 2 | ||
33.29 | even | 10 | 363.3.b.c.122.2 | yes | 2 | ||
33.32 | even | 2 | inner | 363.3.h.f.251.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.c.122.1 | ✓ | 2 | 11.4 | even | 5 | ||
363.3.b.c.122.1 | ✓ | 2 | 11.7 | odd | 10 | ||
363.3.b.c.122.2 | yes | 2 | 33.26 | odd | 10 | ||
363.3.b.c.122.2 | yes | 2 | 33.29 | even | 10 | ||
363.3.h.f.245.1 | 8 | 33.2 | even | 10 | inner | ||
363.3.h.f.245.1 | 8 | 33.20 | odd | 10 | inner | ||
363.3.h.f.245.2 | 8 | 11.2 | odd | 10 | inner | ||
363.3.h.f.245.2 | 8 | 11.9 | even | 5 | inner | ||
363.3.h.f.251.1 | 8 | 3.2 | odd | 2 | inner | ||
363.3.h.f.251.1 | 8 | 33.32 | even | 2 | inner | ||
363.3.h.f.251.2 | 8 | 1.1 | even | 1 | trivial | ||
363.3.h.f.251.2 | 8 | 11.10 | odd | 2 | CM | ||
363.3.h.f.269.1 | 8 | 11.5 | even | 5 | inner | ||
363.3.h.f.269.1 | 8 | 11.6 | odd | 10 | inner | ||
363.3.h.f.269.2 | 8 | 33.5 | odd | 10 | inner | ||
363.3.h.f.269.2 | 8 | 33.17 | even | 10 | inner | ||
363.3.h.f.323.1 | 8 | 11.3 | even | 5 | inner | ||
363.3.h.f.323.1 | 8 | 11.8 | odd | 10 | inner | ||
363.3.h.f.323.2 | 8 | 33.8 | even | 10 | inner | ||
363.3.h.f.323.2 | 8 | 33.14 | odd | 10 | inner |