Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(521,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.521");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.t (of order \(6\), degree \(2\), 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: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.14 | ||
Character | \(\chi\) | \(=\) | 1764.521 |
Dual form | 1764.4.t.c.1097.14 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.582251 | + | 1.00849i | 0.0520781 | + | 0.0902020i | 0.890889 | − | 0.454221i | \(-0.150082\pi\) |
−0.838811 | + | 0.544422i | \(0.816749\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.8211 | + | 32.8057i | 1.55747 | + | 0.899208i | 0.997498 | + | 0.0706989i | \(0.0225230\pi\) |
0.559976 | + | 0.828509i | \(0.310810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 57.5711i | − | 1.22826i | −0.789206 | − | 0.614129i | \(-0.789507\pi\) | ||
0.789206 | − | 0.614129i | \(-0.210493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.6457 | − | 47.8837i | 0.394415 | − | 0.683147i | −0.598611 | − | 0.801040i | \(-0.704281\pi\) |
0.993026 | + | 0.117893i | \(0.0376139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −106.374 | + | 61.4153i | −1.28442 | + | 0.741559i | −0.977653 | − | 0.210226i | \(-0.932580\pi\) |
−0.306766 | + | 0.951785i | \(0.599247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 47.1869 | − | 27.2434i | 0.427789 | − | 0.246984i | −0.270615 | − | 0.962688i | \(-0.587227\pi\) |
0.698404 | + | 0.715703i | \(0.253894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.8220 | − | 107.079i | 0.494576 | − | 0.856630i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 105.124i | − | 0.673138i | −0.941659 | − | 0.336569i | \(-0.890733\pi\) | ||
0.941659 | − | 0.336569i | \(-0.109267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −84.6938 | − | 48.8980i | −0.490692 | − | 0.283301i | 0.234170 | − | 0.972196i | \(-0.424763\pi\) |
−0.724861 | + | 0.688895i | \(0.758096\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 65.0046 | + | 112.591i | 0.288829 | + | 0.500267i | 0.973531 | − | 0.228557i | \(-0.0734006\pi\) |
−0.684701 | + | 0.728824i | \(0.740067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.2322 | 0.263713 | 0.131857 | − | 0.991269i | \(-0.457906\pi\) | ||||
0.131857 | + | 0.991269i | \(0.457906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −87.1042 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −118.347 | − | 204.983i | −0.367291 | − | 0.636166i | 0.621850 | − | 0.783136i | \(-0.286381\pi\) |
−0.989141 | + | 0.146970i | \(0.953048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −357.505 | − | 206.406i | −0.926549 | − | 0.534943i | −0.0408306 | − | 0.999166i | \(-0.513000\pi\) |
−0.885719 | + | 0.464223i | \(0.846334\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 76.4046i | 0.187316i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −21.1051 | + | 36.5551i | −0.0465703 | + | 0.0806622i | −0.888371 | − | 0.459126i | \(-0.848162\pi\) |
0.841801 | + | 0.539789i | \(0.181496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 731.273 | − | 422.201i | 1.53492 | − | 0.886185i | 0.535792 | − | 0.844350i | \(-0.320013\pi\) |
0.999125 | − | 0.0418348i | \(-0.0133203\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.0598 | − | 33.5208i | 0.110791 | − | 0.0639654i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −321.867 | + | 557.490i | −0.586900 | + | 1.01654i | 0.407735 | + | 0.913100i | \(0.366319\pi\) |
−0.994636 | + | 0.103441i | \(0.967015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 749.296i | 1.25247i | 0.779636 | + | 0.626233i | \(0.215404\pi\) | ||||
−0.779636 | + | 0.626233i | \(0.784596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 691.161 | + | 399.042i | 1.10814 | + | 0.639786i | 0.938347 | − | 0.345694i | \(-0.112356\pi\) |
0.169794 | + | 0.985480i | \(0.445690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −179.996 | − | 311.762i | −0.256343 | − | 0.443999i | 0.708916 | − | 0.705292i | \(-0.249184\pi\) |
−0.965259 | + | 0.261293i | \(0.915851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1304.90 | −1.72568 | −0.862840 | − | 0.505477i | \(-0.831317\pi\) | ||||
−0.862840 | + | 0.505477i | \(0.831317\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 64.3869 | 0.0821616 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 54.8745 | + | 95.0454i | 0.0653560 | + | 0.113200i | 0.896852 | − | 0.442331i | \(-0.145848\pi\) |
−0.831496 | + | 0.555531i | \(0.812515\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −123.873 | − | 71.5182i | −0.133780 | − | 0.0772380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 781.538i | − | 0.818074i | −0.912518 | − | 0.409037i | \(-0.865865\pi\) | ||
0.912518 | − | 0.409037i | \(-0.134135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62.2697 | − | 107.854i | 0.0613472 | − | 0.106257i | −0.833721 | − | 0.552187i | \(-0.813794\pi\) |
0.895068 | + | 0.445930i | \(0.147127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −369.676 | + | 213.433i | −0.353644 | + | 0.204176i | −0.666289 | − | 0.745694i | \(-0.732118\pi\) |
0.312645 | + | 0.949870i | \(0.398785\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1743.21 | − | 1006.45i | 1.57498 | − | 0.909316i | 0.579437 | − | 0.815017i | \(-0.303273\pi\) |
0.995544 | − | 0.0942984i | \(-0.0300608\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 502.580 | − | 870.495i | 0.441637 | − | 0.764938i | −0.556174 | − | 0.831066i | \(-0.687731\pi\) |
0.997811 | + | 0.0661278i | \(0.0210645\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1151.55i | − | 0.958660i | −0.877635 | − | 0.479330i | \(-0.840880\pi\) | ||
0.877635 | − | 0.479330i | \(-0.159120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 54.9492 | + | 31.7250i | 0.0445569 | + | 0.0257249i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1486.93 | + | 2575.43i | 1.11715 | + | 1.93496i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 289.546 | 0.207183 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 66.4170 | 0.0464060 | 0.0232030 | − | 0.999731i | \(-0.492614\pi\) | ||||
0.0232030 | + | 0.999731i | \(0.492614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −928.121 | − | 1607.55i | −0.619010 | − | 1.07216i | −0.989667 | − | 0.143387i | \(-0.954201\pi\) |
0.370657 | − | 0.928770i | \(-0.379133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 688.705 | + | 397.624i | 0.429489 | + | 0.247966i | 0.699129 | − | 0.714995i | \(-0.253571\pi\) |
−0.269640 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1076.39i | − | 0.656820i | −0.944535 | − | 0.328410i | \(-0.893487\pi\) | ||
0.944535 | − | 0.328410i | \(-0.106513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1888.66 | − | 3271.25i | 1.10446 | − | 1.91298i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 106.016 | − | 61.2085i | 0.0607184 | − | 0.0350558i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1384.55 | − | 799.372i | 0.761255 | − | 0.439511i | −0.0684912 | − | 0.997652i | \(-0.521819\pi\) |
0.829746 | + | 0.558141i | \(0.188485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1130.03 | − | 1957.27i | 0.609011 | − | 1.05484i | −0.382393 | − | 0.924000i | \(-0.624900\pi\) |
0.991404 | − | 0.130838i | \(-0.0417667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 113.884i | − | 0.0590152i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1162.64 | − | 671.251i | −0.591011 | − | 0.341221i | 0.174486 | − | 0.984660i | \(-0.444174\pi\) |
−0.765497 | + | 0.643439i | \(0.777507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 522.209 | + | 904.492i | 0.250936 | + | 0.434634i | 0.963784 | − | 0.266685i | \(-0.0859284\pi\) |
−0.712848 | + | 0.701319i | \(0.752595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2538.50 | −1.17626 | −0.588129 | − | 0.808767i | \(-0.700135\pi\) | ||||
−0.588129 | + | 0.808767i | \(0.700135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1117.43 | −0.508618 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1962.35 | − | 3398.89i | −0.862396 | − | 1.49371i | −0.869610 | − | 0.493740i | \(-0.835630\pi\) |
0.00721379 | − | 0.999974i | \(-0.497704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1697.65 | − | 980.141i | −0.708875 | − | 0.409269i | 0.101770 | − | 0.994808i | \(-0.467550\pi\) |
−0.810644 | + | 0.585539i | \(0.800883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2865.74i | − | 1.17685i | −0.808553 | − | 0.588423i | \(-0.799749\pi\) | ||
0.808553 | − | 0.588423i | \(-0.200251\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −75.6980 | + | 131.113i | −0.0300834 | + | 0.0521060i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3141.71 | − | 1813.87i | 1.22858 | − | 0.709322i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1747.94 | − | 1009.17i | 0.662181 | − | 0.382311i | −0.130926 | − | 0.991392i | \(-0.541795\pi\) |
0.793108 | + | 0.609082i | \(0.208462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −735.941 | + | 1274.69i | −0.274478 | + | 0.475409i | −0.970003 | − | 0.243092i | \(-0.921838\pi\) |
0.695526 | + | 0.718501i | \(0.255172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5503.83i | 1.99051i | 0.0972758 | + | 0.995257i | \(0.468987\pi\) | ||||
−0.0972758 | + | 0.995257i | \(0.531013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4060.62 | + | 2344.40i | 1.44648 | + | 0.835126i | 0.998270 | − | 0.0588015i | \(-0.0187279\pi\) |
0.448211 | + | 0.893928i | \(0.352061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.3105 | + | 69.8198i | 0.0137337 | + | 0.0237875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8059.08 | −2.66726 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1542.29 | −0.503202 | −0.251601 | − | 0.967831i | \(-0.580957\pi\) | ||||
−0.251601 | + | 0.967831i | \(0.580957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −50.7165 | − | 87.8436i | −0.0160876 | − | 0.0278646i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2756.72 | − | 1591.59i | −0.839081 | − | 0.484444i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 544.576i | − | 0.163531i | −0.996652 | − | 0.0817657i | \(-0.973944\pi\) | ||
0.996652 | − | 0.0817657i | \(-0.0260559\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −837.169 | + | 1450.02i | −0.244779 | + | 0.423970i | −0.962070 | − | 0.272804i | \(-0.912049\pi\) |
0.717290 | + | 0.696774i | \(0.245382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4036.07 | − | 2330.22i | 1.16468 | − | 0.672426i | 0.212255 | − | 0.977214i | \(-0.431919\pi\) |
0.952420 | + | 0.304788i | \(0.0985858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5615.51 | − | 3242.12i | 1.57890 | − | 0.911580i | 0.583889 | − | 0.811833i | \(-0.301530\pi\) |
0.995013 | − | 0.0997461i | \(-0.0318030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 137.815 | − | 238.703i | 0.0382556 | − | 0.0662607i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 890.490i | − | 0.241008i | −0.992713 | − | 0.120504i | \(-0.961549\pi\) | ||
0.992713 | − | 0.120504i | \(-0.0384511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4304.74 | + | 2485.34i | 1.15059 | + | 0.664294i | 0.949031 | − | 0.315182i | \(-0.102066\pi\) |
0.201560 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3535.75 | + | 6124.09i | 0.910826 | + | 1.57760i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2469.89 | 0.621107 | 0.310554 | − | 0.950556i | \(-0.399486\pi\) | ||||
0.310554 | + | 0.950556i | \(0.399486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3574.95 | 0.888360 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1756.91 | − | 3043.06i | −0.426432 | − | 0.738602i | 0.570121 | − | 0.821561i | \(-0.306896\pi\) |
−0.996553 | + | 0.0829590i | \(0.973563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2447.74 | − | 1413.20i | −0.573895 | − | 0.331338i | 0.184809 | − | 0.982775i | \(-0.440833\pi\) |
−0.758703 | + | 0.651436i | \(0.774167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 480.720i | − | 0.111435i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4004.09 | − | 6935.28i | 0.907560 | − | 1.57194i | 0.0901161 | − | 0.995931i | \(-0.471276\pi\) |
0.817444 | − | 0.576008i | \(-0.195390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2734.34 | − | 1578.67i | 0.612912 | − | 0.353865i | −0.161192 | − | 0.986923i | \(-0.551534\pi\) |
0.774104 | + | 0.633058i | \(0.218201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7025.59 | − | 4056.22i | 1.54058 | − | 0.889453i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1127.81 | + | 1953.42i | −0.244633 | + | 0.423717i | −0.962028 | − | 0.272949i | \(-0.912001\pi\) |
0.717395 | + | 0.696666i | \(0.245334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7277.95i | − | 1.54507i | −0.634970 | − | 0.772537i | \(-0.718987\pi\) | ||
0.634970 | − | 0.772537i | \(-0.281013\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9560 | − | 7.48013i | −0.00272139 | − | 0.00157119i | 0.498639 | − | 0.866810i | \(-0.333833\pi\) |
−0.501360 | + | 0.865239i | \(0.667167\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 927.935 | + | 1607.23i | 0.188873 | + | 0.327138i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8446.59 | −1.68415 | −0.842074 | − | 0.539362i | \(-0.818665\pi\) | ||||
−0.842074 | + | 0.539362i | \(0.818665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.1539 | −0.00970118 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1568.43 | − | 2716.60i | −0.303360 | − | 0.525435i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 851.569 | + | 491.654i | 0.159871 | + | 0.0923017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7870.82i | − | 1.46323i | −0.681719 | − | 0.731615i | \(-0.738767\pi\) | ||
0.681719 | − | 0.731615i | \(-0.261233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3030.67 | − | 5249.27i | 0.552584 | − | 0.957103i | −0.445504 | − | 0.895280i | \(-0.646975\pi\) |
0.998087 | − | 0.0618227i | \(-0.0196913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4885.90 | + | 2820.87i | −0.882323 | + | 0.509410i | −0.871424 | − | 0.490531i | \(-0.836803\pi\) |
−0.0108997 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3888.70 | − | 2245.14i | 0.688994 | − | 0.397791i | −0.114241 | − | 0.993453i | \(-0.536444\pi\) |
0.803235 | + | 0.595662i | \(0.203110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3448.66 | − | 5973.25i | 0.605291 | − | 1.04839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6791.46i | 1.16993i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6164.65 | − | 3559.16i | −1.05216 | − | 0.607467i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5457.22 | + | 9452.19i | 0.906212 | + | 1.56961i | 0.819282 | + | 0.573391i | \(0.194372\pi\) |
0.0869300 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −749.630 | −0.122259 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6590.94 | −1.06537 | −0.532687 | − | 0.846312i | \(-0.678818\pi\) | ||||
−0.532687 | + | 0.846312i | \(0.678818\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3208.26 | − | 5556.87i | −0.509493 | − | 0.882468i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4612.55 | + | 2663.05i | 0.713586 | + | 0.411989i | 0.812388 | − | 0.583118i | \(-0.198167\pi\) |
−0.0988012 | + | 0.995107i | \(0.531501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8102.39i | − | 1.24272i | −0.783523 | − | 0.621362i | \(-0.786580\pi\) | ||
0.783523 | − | 0.621362i | \(-0.213420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 277.427 | − | 480.519i | 0.0418300 | − | 0.0724516i | −0.844352 | − | 0.535788i | \(-0.820015\pi\) |
0.886182 | + | 0.463337i | \(0.153348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −755.657 | + | 436.279i | −0.112975 | + | 0.0652261i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −349.424 | + | 201.740i | −0.0513702 | + | 0.0296586i | −0.525465 | − | 0.850815i | \(-0.676109\pi\) |
0.474095 | + | 0.880474i | \(0.342775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4114.17 | − | 7125.95i | 0.599821 | − | 1.03892i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 929.371i | 0.133275i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5617.83 | + | 3243.45i | 0.799041 | + | 0.461327i | 0.843136 | − | 0.537701i | \(-0.180707\pi\) |
−0.0440946 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3622.90 | − | 6275.05i | −0.502914 | − | 0.871072i | −0.999994 | − | 0.00336765i | \(-0.998928\pi\) |
0.497081 | − | 0.867704i | \(-0.334405\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6052.09 | −0.826787 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8439.30 | −1.14379 | −0.571897 | − | 0.820326i | \(-0.693792\pi\) | ||||
−0.571897 | + | 0.820326i | \(0.693792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3154.57 | − | 5463.87i | −0.420864 | − | 0.728957i | 0.575160 | − | 0.818041i | \(-0.304940\pi\) |
−0.996024 | + | 0.0890832i | \(0.971606\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2981.67 | − | 1721.47i | −0.388630 | − | 0.224375i | 0.292937 | − | 0.956132i | \(-0.405368\pi\) |
−0.681566 | + | 0.731756i | \(0.738701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3012.64i | − | 0.389657i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 209.605 | − | 363.047i | 0.0266997 | − | 0.0462453i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8919.34 | − | 5149.58i | 1.12758 | − | 0.651008i | 0.184254 | − | 0.982879i | \(-0.441013\pi\) |
0.943325 | + | 0.331871i | \(0.107680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 120.856 | − | 69.7764i | 0.0150506 | − | 0.00868944i | −0.492456 | − | 0.870337i | \(-0.663901\pi\) |
0.507506 | + | 0.861648i | \(0.330567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2815.11 | + | 4875.91i | −0.347967 | + | 0.602696i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8530.08i | 1.03887i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4385.88 | + | 2532.19i | 0.530239 | + | 0.306134i | 0.741114 | − | 0.671379i | \(-0.234298\pi\) |
−0.210874 | + | 0.977513i | \(0.567631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −759.780 | − | 1315.98i | −0.0898702 | − | 0.155660i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1888.80 | −0.220224 | −0.110112 | − | 0.993919i | \(-0.535121\pi\) | ||||
−0.110112 | + | 0.993919i | \(0.535121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12973.6 | 1.50188 | 0.750941 | − | 0.660369i | \(-0.229600\pi\) | ||||
0.750941 | + | 0.660369i | \(0.229600\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3418.22 | − | 5920.53i | −0.390136 | − | 0.675736i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7994.07 | − | 4615.38i | −0.893413 | − | 0.515812i | −0.0183555 | − | 0.999832i | \(-0.505843\pi\) |
−0.875057 | + | 0.484019i | \(0.839176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9931.42i | 1.10225i | 0.834423 | + | 0.551124i | \(0.185801\pi\) | ||||
−0.834423 | + | 0.551124i | \(0.814199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3346.32 | + | 5795.99i | −0.366307 | + | 0.634462i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5684.09 | − | 3281.71i | 0.617966 | − | 0.356783i | −0.158111 | − | 0.987421i | \(-0.550540\pi\) |
0.776077 | + | 0.630639i | \(0.217207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7539.39 | − | 4352.87i | 0.808595 | − | 0.466842i | −0.0378730 | − | 0.999283i | \(-0.512058\pi\) |
0.846468 | + | 0.532440i | \(0.178725\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −63.9014 | + | 110.681i | −0.00680723 | + | 0.0117905i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 11408.9i | − | 1.19915i | −0.800317 | − | 0.599577i | \(-0.795335\pi\) | ||
0.800317 | − | 0.599577i | \(-0.204665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3933.85 | + | 2271.21i | 0.410727 | + | 0.237133i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4340.84 | + | 7518.55i | 0.444323 | + | 0.769591i | 0.998005 | − | 0.0631379i | \(-0.0201108\pi\) |
−0.553681 | + | 0.832729i | \(0.686777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10427.6 | 1.05349 | 0.526746 | − | 0.850023i | \(-0.323412\pi\) | ||||
0.526746 | + | 0.850023i | \(0.323412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4918.91 | 0.493738 | 0.246869 | − | 0.969049i | \(-0.420598\pi\) | ||||
0.246869 | + | 0.969049i | \(0.420598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5656.62 | + | 9797.55i | 0.560508 | + | 0.970828i | 0.997452 | + | 0.0713395i | \(0.0227274\pi\) |
−0.436944 | + | 0.899489i | \(0.643939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4949.36 | − | 2857.51i | −0.481124 | − | 0.277777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15187.3i | 1.46703i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5574.32 | − | 9655.01i | 0.531727 | − | 0.920978i | −0.467587 | − | 0.883947i | \(-0.654877\pi\) |
0.999314 | − | 0.0370311i | \(-0.0117901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6482.00 | − | 3742.39i | 0.614457 | − | 0.354757i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 788.172 | − | 455.051i | 0.0737918 | − | 0.0426037i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6733.48 | + | 11662.7i | −0.626536 | + | 1.08519i | 0.361705 | + | 0.932293i | \(0.382195\pi\) |
−0.988242 | + | 0.152900i | \(0.951139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5130.89i | 0.471597i | 0.971802 | + | 0.235798i | \(0.0757705\pi\) | ||||
−0.971802 | + | 0.235798i | \(0.924229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5033.72 | − | 2906.22i | −0.459852 | − | 0.265496i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3968.71 | − | 6874.01i | −0.356040 | − | 0.616679i | 0.631256 | − | 0.775575i | \(-0.282540\pi\) |
−0.987295 | + | 0.158896i | \(0.949207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14153.2 | −1.25459 | −0.627294 | − | 0.778782i | \(-0.715838\pi\) | ||||
−0.627294 | + | 0.778782i | \(0.715838\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 145.027 | 0.0127794 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8850.32 | + | 15329.2i | 0.770694 | + | 1.33488i | 0.937183 | + | 0.348838i | \(0.113424\pi\) |
−0.166489 | + | 0.986043i | \(0.553243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −430.489 | − | 248.543i | −0.0368342 | − | 0.0212662i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15529.8i | − | 1.32108i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11420.4 | + | 19780.7i | −0.960339 | + | 1.66336i | −0.238690 | + | 0.971096i | \(0.576718\pi\) |
−0.721648 | + | 0.692260i | \(0.756615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17908.1 | + | 10339.2i | −1.49726 | + | 0.864443i | −0.999995 | − | 0.00315640i | \(-0.998995\pi\) |
−0.497264 | + | 0.867599i | \(0.665662\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4682.83 | + | 2703.63i | −0.387073 | + | 0.223476i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4599.10 | + | 7965.87i | −0.377998 | + | 0.654711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3985.77i | − | 0.323908i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2029.98 | + | 1172.01i | 0.164044 | + | 0.0947109i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8996.90 | + | 15583.1i | 0.714985 | + | 1.23839i | 0.962965 | + | 0.269625i | \(0.0868998\pi\) |
−0.247980 | + | 0.968765i | \(0.579767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1170.51 | 0.0919986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11216.0 | −0.876712 | −0.438356 | − | 0.898801i | \(-0.644439\pi\) | ||||
−0.438356 | + | 0.898801i | \(0.644439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6456.21 | + | 11182.5i | 0.499172 | + | 0.864591i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18757.9 | + | 10829.9i | 1.42692 | + | 0.823834i | 0.996877 | − | 0.0789726i | \(-0.0251639\pi\) |
0.430046 | + | 0.902807i | \(0.358497\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5014.68i | 0.379425i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9238.84 | − | 16002.1i | 0.691600 | − | 1.19789i | −0.279714 | − | 0.960083i | \(-0.590240\pi\) |
0.971314 | − | 0.237802i | \(-0.0764270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1161.32 | − | 670.491i | 0.0864730 | − | 0.0499252i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14511.3 | + | 8378.12i | −1.06915 | + | 0.617274i | −0.927949 | − | 0.372707i | \(-0.878430\pi\) |
−0.141201 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10045.3 | − | 17399.0i | 0.736224 | − | 1.27518i | −0.217961 | − | 0.975958i | \(-0.569941\pi\) |
0.954184 | − | 0.299219i | \(-0.0967262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6736.95i | − | 0.488609i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7839.05 | − | 4525.88i | −0.565587 | − | 0.326542i | 0.189798 | − | 0.981823i | \(-0.439217\pi\) |
−0.755385 | + | 0.655281i | \(0.772550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13542.6 | − | 23456.4i | −0.962051 | − | 1.66632i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15886.2 | 1.11703 | 0.558513 | − | 0.829496i | \(-0.311372\pi\) | ||||
0.558513 | + | 0.829496i | \(0.311372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12012.3 | 0.840338 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12975.8 | − | 22474.7i | −0.898570 | − | 1.55637i | −0.829324 | − | 0.558769i | \(-0.811274\pi\) |
−0.0692459 | − | 0.997600i | \(-0.522059\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13787.3 | + | 7960.08i | 0.940455 | + | 0.542972i | 0.890103 | − | 0.455760i | \(-0.150632\pi\) |
0.0503519 | + | 0.998732i | \(0.483966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5872.84i | − | 0.398599i | −0.979939 | − | 0.199300i | \(-0.936133\pi\) | ||
0.979939 | − | 0.199300i | \(-0.0638667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1731.53 | + | 2999.10i | −0.116358 | + | 0.201538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23980.6 | + | 13845.2i | −1.60353 | + | 0.925799i | −0.612758 | + | 0.790271i | \(0.709940\pi\) |
−0.990774 | + | 0.135528i | \(0.956727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11801.1 | + | 6813.36i | −0.781376 | + | 0.451128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4006.36 | − | 6939.22i | 0.263973 | − | 0.457214i | −0.703321 | − | 0.710872i | \(-0.748300\pi\) |
0.967294 | + | 0.253658i | \(0.0816338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1546.21i | − | 0.100888i | −0.998727 | − | 0.0504442i | \(-0.983936\pi\) | ||
0.998727 | − | 0.0504442i | \(-0.0160637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9942.26 | − | 5740.16i | −0.645578 | − | 0.372725i | 0.141182 | − | 0.989984i | \(-0.454910\pi\) |
−0.786760 | + | 0.617259i | \(0.788243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7559.16 | − | 13092.8i | −0.483786 | − | 0.837942i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7188.38 | 0.455675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12482.7 | −0.787524 | −0.393762 | − | 0.919212i | \(-0.628827\pi\) | ||||
−0.393762 | + | 0.919212i | \(0.628827\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.6714 | + | 66.9808i | 0.00241674 | + | 0.00418591i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3612.00 | + | 2085.39i | 0.222567 | + | 0.128499i | 0.607138 | − | 0.794596i | \(-0.292317\pi\) |
−0.384571 | + | 0.923095i | \(0.625651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18330.0i | 1.12421i | 0.827066 | + | 0.562105i | \(0.190008\pi\) | ||||
−0.827066 | + | 0.562105i | \(0.809992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5049.66 | + | 8746.26i | −0.306835 | + | 0.531455i | −0.977668 | − | 0.210154i | \(-0.932603\pi\) |
0.670833 | + | 0.741609i | \(0.265937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2398.43 | + | 1384.73i | −0.145064 | + | 0.0837528i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12968.1 | + | 7487.16i | −0.777155 | + | 0.448691i | −0.835421 | − | 0.549610i | \(-0.814776\pi\) |
0.0582660 | + | 0.998301i | \(0.481443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1080.80 | − | 1872.00i | 0.0644738 | − | 0.111672i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25422.5i | 1.50276i | 0.659870 | + | 0.751380i | \(0.270611\pi\) | ||||
−0.659870 | + | 0.751380i | \(0.729389\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5789.29 | − | 3342.45i | −0.340661 | − | 0.196681i | 0.319903 | − | 0.947450i | \(-0.396350\pi\) |
−0.660564 | + | 0.750769i | \(0.729683\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2863.93 | − | 4960.47i | −0.166254 | − | 0.287961i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55402.3 | 3.18746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4182.44 | 0.239556 | 0.119778 | − | 0.992801i | \(-0.461782\pi\) | ||||
0.119778 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6115.84 | + | 10593.0i | 0.347195 | + | 0.601359i | 0.985750 | − | 0.168217i | \(-0.0538009\pi\) |
−0.638555 | + | 0.769576i | \(0.720468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14005.9 | − | 8086.33i | −0.784659 | − | 0.453023i | 0.0534198 | − | 0.998572i | \(-0.482988\pi\) |
−0.838079 | + | 0.545549i | \(0.816321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 926.068i | 0.0516544i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11883.0 | + | 20582.0i | −0.657049 | + | 1.13804i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18032.3 | − | 10410.9i | 0.992734 | − | 0.573155i | 0.0866437 | − | 0.996239i | \(-0.472386\pi\) |
0.906090 | + | 0.423084i | \(0.139053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1085.52 | − | 626.727i | 0.0592464 | − | 0.0342059i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1913.97 | − | 3315.09i | 0.104013 | − | 0.180155i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35212.3i | − | 1.89722i | −0.316451 | − | 0.948609i | \(-0.602491\pi\) | ||
0.316451 | − | 0.948609i | \(-0.397509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13829.6 | − | 7984.55i | −0.741956 | − | 0.428368i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10423.6 | − | 18054.2i | −0.552138 | − | 0.956331i | −0.998120 | − | 0.0612888i | \(-0.980479\pi\) |
0.445982 | − | 0.895042i | \(-0.352854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5328.58 | −0.279883 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4398.70 | 0.230073 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5446.98 | + | 9434.44i | 0.282528 | + | 0.489354i | 0.972007 | − | 0.234953i | \(-0.0754935\pi\) |
−0.689478 | + | 0.724306i | \(0.742160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11256.5 | − | 6498.96i | −0.576630 | − | 0.332918i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31196.0i | 1.59147i | 0.605646 | + | 0.795734i | \(0.292915\pi\) | ||||
−0.605646 | + | 0.795734i | \(0.707085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2408.05 | + | 4170.87i | −0.121840 | + | 0.211033i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15525.3 | + | 8963.52i | −0.782318 | + | 0.451672i | −0.837251 | − | 0.546818i | \(-0.815839\pi\) |
0.0549330 | + | 0.998490i | \(0.482505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36577.7 | + | 21118.1i | −1.82816 | + | 1.05549i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7530.33 | + | 13042.9i | −0.374841 | + | 0.649244i | −0.990303 | − | 0.138922i | \(-0.955636\pi\) |
0.615462 | + | 0.788167i | \(0.288969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8750.44i | 0.432062i | 0.976386 | + | 0.216031i | \(0.0693113\pi\) | ||||
−0.976386 | + | 0.216031i | \(0.930689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1612.31 | + | 930.870i | 0.0792895 | + | 0.0457778i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11415.7 | + | 19772.5i | 0.554678 | + | 0.960730i | 0.997929 | + | 0.0643326i | \(0.0204918\pi\) |
−0.443251 | + | 0.896398i | \(0.646175\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2631.85 | 0.126865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12087.5 | 0.580353 | 0.290176 | − | 0.956973i | \(-0.406286\pi\) | ||||
0.290176 | + | 0.956973i | \(0.406286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18359.5 | + | 31799.5i | 0.874547 | + | 1.51476i | 0.857244 | + | 0.514910i | \(0.172175\pi\) |
0.0173026 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2104.52 | + | 1215.04i | 0.0990739 | + | 0.0572004i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2652.68i | 0.124393i | 0.998064 | + | 0.0621964i | \(0.0198105\pi\) | ||||
−0.998064 | + | 0.0621964i | \(0.980189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12335.0 | + | 21364.8i | −0.573944 | + | 0.994100i | 0.422211 | + | 0.906497i | \(0.361254\pi\) |
−0.996155 | + | 0.0876029i | \(0.972079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10471.9 | + | 6045.94i | −0.485369 | + | 0.280228i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7364.53 | + | 4251.91i | −0.338718 | + | 0.195559i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24581.2 | + | 42575.8i | −1.12623 | + | 1.95068i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1563.35i | − | 0.0710805i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14812.4 | + | 8551.94i | 0.670909 | + | 0.387349i | 0.796421 | − | 0.604743i | \(-0.206724\pi\) |
−0.125512 | + | 0.992092i | \(0.540057\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24306.6 | − | 42100.2i | −1.08846 | − | 1.88527i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26143.0 | −1.16190 | −0.580948 | − | 0.813940i | \(-0.697318\pi\) | ||||
−0.580948 | + | 0.813940i | \(0.697318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13087.1 | −0.579460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26181.7 | + | 45348.0i | 1.15060 | + | 1.99290i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21245.1 | + | 12265.8i | 0.923283 | + | 0.533058i | 0.884681 | − | 0.466197i | \(-0.154376\pi\) |
0.0386023 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8145.19i | 0.352671i | 0.984330 | + | 0.176336i | \(0.0564244\pi\) | ||||
−0.984330 | + | 0.176336i | \(0.943576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −608.113 | + | 1053.28i | −0.0261365 | + | 0.0452698i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9265.65 | − | 5349.53i | 0.396774 | − | 0.229077i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20871.3 | + | 12050.0i | −0.887225 | + | 0.512240i | −0.873034 | − | 0.487660i | \(-0.837851\pi\) |
−0.0141913 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16435.8 | + | 28467.6i | −0.696131 | + | 1.20573i | 0.273667 | + | 0.961824i | \(0.411763\pi\) |
−0.969798 | + | 0.243909i | \(0.921570\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5891.21i | − | 0.247712i | −0.992300 | − | 0.123856i | \(-0.960474\pi\) | ||
0.992300 | − | 0.123856i | \(-0.0395260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9443.28 | − | 5452.08i | −0.395632 | − | 0.228418i | 0.288966 | − | 0.957339i | \(-0.406689\pi\) |
−0.684597 | + | 0.728921i | \(0.740022\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1478.05 | − | 2560.05i | −0.0612574 | − | 0.106101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38021.0 | 1.56452 | 0.782259 | − | 0.622953i | \(-0.214067\pi\) | ||||
0.782259 | + | 0.622953i | \(0.214067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13338.0 | 0.546885 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −650.627 | − | 1126.92i | −0.0264879 | − | 0.0458783i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6134.73 | + | 3541.89i | 0.247116 | + | 0.142673i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30803.2i | 1.23644i | 0.786006 | + | 0.618218i | \(0.212145\pi\) | ||||
−0.786006 | + | 0.618218i | \(0.787855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2623.05 | − | 4543.25i | 0.104553 | − | 0.181090i | −0.809003 | − | 0.587805i | \(-0.799992\pi\) |
0.913555 | + | 0.406714i | \(0.133326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26498.6 | + | 15299.0i | −1.05253 | + | 0.607677i | −0.923356 | − | 0.383946i | \(-0.874565\pi\) |
−0.129171 | + | 0.991622i | \(0.541232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2009.18 | − | 1160.00i | 0.0792507 | − | 0.0457554i | −0.459851 | − | 0.887996i | \(-0.652097\pi\) |
0.539102 | + | 0.842241i | \(0.318764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2285.16 | − | 3958.01i | 0.0898239 | − | 0.155580i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 23619.5i | − | 0.922022i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32095.3 | + | 18530.3i | 1.24858 | + | 0.720865i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14115.0 | − | 24447.9i | −0.543477 | − | 0.941329i | −0.998701 | − | 0.0509526i | \(-0.983774\pi\) |
0.455224 | − | 0.890377i | \(-0.349559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16404.3 | 0.627325 | 0.313663 | − | 0.949535i | \(-0.398444\pi\) | ||||
0.313663 | + | 0.949535i | \(0.398444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12816.6 | 0.488463 | 0.244232 | − | 0.969717i | \(-0.421464\pi\) | ||||
0.244232 | + | 0.969717i | \(0.421464\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2424.10 | + | 4198.67i | 0.0917625 | + | 0.158937i | 0.908253 | − | 0.418422i | \(-0.137417\pi\) |
−0.816490 | + | 0.577359i | \(0.804083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25178.1 | + | 14536.6i | 0.943510 | + | 0.544736i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2282.75i | − | 0.0852558i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5140.34 | + | 8903.33i | −0.190701 | + | 0.330303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19766.9 | + | 11412.4i | −0.730890 | + | 0.421980i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2890.07 | − | 1668.58i | 0.106154 | − | 0.0612879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17965.6 | − | 31117.4i | 0.657706 | − | 1.13918i | −0.323503 | − | 0.946227i | \(-0.604860\pi\) |
0.981208 | − | 0.192952i | \(-0.0618062\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26942.0i | 0.979834i | 0.871769 | + | 0.489917i | \(0.162973\pi\) | ||||
−0.871769 | + | 0.489917i | \(0.837027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74145.9 | − | 42808.2i | −2.68770 | − | 1.55175i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9048.97 | + | 15673.3i | 0.324807 | + | 0.562583i | 0.981473 | − | 0.191599i | \(-0.0613672\pi\) |
−0.656666 | + | 0.754181i | \(0.728034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43137.8 | 1.53835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16074.8 | 0.571392 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13518.0 | − | 23413.9i | −0.477407 | − | 0.826894i | 0.522257 | − | 0.852788i | \(-0.325090\pi\) |
−0.999665 | + | 0.0258940i | \(0.991757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3658.53 | + | 2112.26i | 0.127965 | + | 0.0738804i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22915.3i | − | 0.798942i | −0.916746 | − | 0.399471i | \(-0.869194\pi\) | ||
0.916746 | − | 0.399471i | \(-0.130806\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14988.4 | + | 25960.7i | −0.519244 | + | 0.899356i | 0.480506 | + | 0.876991i | \(0.340453\pi\) |
−0.999750 | + | 0.0223651i | \(0.992880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3266.85 | − | 1886.12i | 0.112814 | − | 0.0651330i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42391.6 | + | 24474.8i | −1.45464 | + | 0.839835i | −0.998739 | − | 0.0501965i | \(-0.984015\pi\) |
−0.455898 | + | 0.890032i | \(0.650682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22973.3 | − | 39790.9i | 0.785822 | − | 1.36108i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10983.8i | − | 0.373349i | −0.982422 | − | 0.186674i | \(-0.940229\pi\) | ||
0.982422 | − | 0.186674i | \(-0.0597709\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2035.48 | + | 1175.19i | 0.0689703 | + | 0.0398200i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10113.5 | − | 17517.1i | −0.339481 | − | 0.587998i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1714.01 | −0.0571771 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45637.1 | −1.51767 | −0.758836 | − | 0.651281i | \(-0.774232\pi\) | ||||
−0.758836 | + | 0.651281i | \(0.774232\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14777.0 | + | 25594.5i | 0.488380 | + | 0.845899i | 0.999911 | − | 0.0133661i | \(-0.00425469\pi\) |
−0.511531 | + | 0.859265i | \(0.670921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17536.4 | − | 10124.6i | −0.574246 | − | 0.331541i | 0.184597 | − | 0.982814i | \(-0.440902\pi\) |
−0.758844 | + | 0.651273i | \(0.774235\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7200.78i | 0.235074i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −110.819 | + | 191.945i | −0.00359571 | + | 0.00622796i | −0.867818 | − | 0.496883i | \(-0.834478\pi\) |
0.864222 | + | 0.503111i | \(0.167811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5550.55 | + | 3204.61i | −0.179548 | + | 0.103662i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4110.18 | + | 2373.01i | −0.132150 | + | 0.0762966i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23116.6 | − | 40039.1i | 0.740991 | − | 1.28343i | −0.211054 | − | 0.977474i | \(-0.567690\pi\) |
0.952045 | − | 0.305959i | \(-0.0989770\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5460.12i | 0.173967i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −756.084 | − | 436.525i | −0.0240175 | − | 0.0138665i | 0.487943 | − | 0.872875i | \(-0.337747\pi\) |
−0.511961 | + | 0.859009i | \(0.671081\pi\) | |||||||
\(998\) | 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 | 1764.4.t.c.521.14 | 48 | ||
3.2 | odd | 2 | inner | 1764.4.t.c.521.11 | 48 | ||
7.2 | even | 3 | inner | 1764.4.t.c.1097.13 | 48 | ||
7.3 | odd | 6 | 1764.4.f.b.881.14 | yes | 24 | ||
7.4 | even | 3 | 1764.4.f.b.881.12 | yes | 24 | ||
7.5 | odd | 6 | inner | 1764.4.t.c.1097.11 | 48 | ||
7.6 | odd | 2 | inner | 1764.4.t.c.521.12 | 48 | ||
21.2 | odd | 6 | inner | 1764.4.t.c.1097.12 | 48 | ||
21.5 | even | 6 | inner | 1764.4.t.c.1097.14 | 48 | ||
21.11 | odd | 6 | 1764.4.f.b.881.13 | yes | 24 | ||
21.17 | even | 6 | 1764.4.f.b.881.11 | ✓ | 24 | ||
21.20 | even | 2 | inner | 1764.4.t.c.521.13 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.4.f.b.881.11 | ✓ | 24 | 21.17 | even | 6 | ||
1764.4.f.b.881.12 | yes | 24 | 7.4 | even | 3 | ||
1764.4.f.b.881.13 | yes | 24 | 21.11 | odd | 6 | ||
1764.4.f.b.881.14 | yes | 24 | 7.3 | odd | 6 | ||
1764.4.t.c.521.11 | 48 | 3.2 | odd | 2 | inner | ||
1764.4.t.c.521.12 | 48 | 7.6 | odd | 2 | inner | ||
1764.4.t.c.521.13 | 48 | 21.20 | even | 2 | inner | ||
1764.4.t.c.521.14 | 48 | 1.1 | even | 1 | trivial | ||
1764.4.t.c.1097.11 | 48 | 7.5 | odd | 6 | inner | ||
1764.4.t.c.1097.12 | 48 | 21.2 | odd | 6 | inner | ||
1764.4.t.c.1097.13 | 48 | 7.2 | even | 3 | inner | ||
1764.4.t.c.1097.14 | 48 | 21.5 | even | 6 | inner |