Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), 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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 264 x^{18} + 28274 x^{16} - 1545308 x^{14} + 45358441 x^{12} - 637328868 x^{10} + 1825819356 x^{8} + 32794262368 x^{6} + 135580415344 x^{4} + \cdots + 194396337216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.19 | ||
Root | \(8.89263 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.q.721.20 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.89263 | 1.77853 | 0.889263 | − | 0.457397i | \(-0.151218\pi\) | ||||
0.889263 | + | 0.457397i | \(0.151218\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.08883 | −0.584118 | −0.292059 | − | 0.956400i | \(-0.594340\pi\) | ||||
−0.292059 | + | 0.956400i | \(0.594340\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.37788 | −0.397989 | −0.198995 | − | 0.980001i | \(-0.563768\pi\) | ||||
−0.198995 | + | 0.980001i | \(0.563768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 13.7670i | − | 1.05900i | −0.848309 | − | 0.529502i | \(-0.822379\pi\) | ||
0.848309 | − | 0.529502i | \(-0.177621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.0927 | −0.828981 | −0.414490 | − | 0.910054i | \(-0.636040\pi\) | ||||
−0.414490 | + | 0.910054i | \(0.636040\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.6112 | + | 15.0393i | −0.611115 | + | 0.791542i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.99929 | −0.304317 | −0.152158 | − | 0.988356i | \(-0.548622\pi\) | ||||
−0.152158 | + | 0.988356i | \(0.548622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.0788 | 2.16315 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 31.8337i | − | 1.09771i | −0.835916 | − | 0.548857i | \(-0.815063\pi\) | ||
0.835916 | − | 0.548857i | \(-0.184937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.3543i | 0.398525i | 0.979946 | + | 0.199262i | \(0.0638546\pi\) | ||||
−0.979946 | + | 0.199262i | \(0.936145\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −36.3604 | −1.03887 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.89820i | − | 0.132384i | −0.997807 | − | 0.0661918i | \(-0.978915\pi\) | ||
0.997807 | − | 0.0661918i | \(-0.0210849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 73.1184i | − | 1.78337i | −0.452652 | − | 0.891687i | \(-0.649522\pi\) | ||
0.452652 | − | 0.891687i | \(-0.350478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.8862 | 0.555492 | 0.277746 | − | 0.960655i | \(-0.410413\pi\) | ||||
0.277746 | + | 0.960655i | \(0.410413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −43.3597 | −0.922547 | −0.461274 | − | 0.887258i | \(-0.652607\pi\) | ||||
−0.461274 | + | 0.887258i | \(0.652607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −32.2815 | −0.658806 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.4462i | 1.23483i | 0.786636 | + | 0.617417i | \(0.211821\pi\) | ||||
−0.786636 | + | 0.617417i | \(0.788179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −38.9309 | −0.707834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 62.3993i | − | 1.05761i | −0.848742 | − | 0.528807i | \(-0.822639\pi\) | ||
0.848742 | − | 0.528807i | \(-0.177361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −70.1235 | −1.14957 | −0.574783 | − | 0.818306i | \(-0.694914\pi\) | ||||
−0.574783 | + | 0.818306i | \(0.694914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 122.425i | − | 1.88346i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 126.526i | − | 1.88844i | −0.329311 | − | 0.944222i | \(-0.606816\pi\) | ||
0.329311 | − | 0.944222i | \(-0.393184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 44.9262i | − | 0.632763i | −0.948632 | − | 0.316382i | \(-0.897532\pi\) | ||
0.948632 | − | 0.316382i | \(-0.102468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.118545 | −0.00162390 | −0.000811950 | − | 1.00000i | \(-0.500258\pi\) | ||||
−0.000811950 | 1.00000i | \(0.500258\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.9004 | 0.232473 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.5093i | 0.246953i | 0.992347 | + | 0.123477i | \(0.0394044\pi\) | ||||
−0.992347 | + | 0.123477i | \(0.960596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −97.8163 | −1.17851 | −0.589255 | − | 0.807947i | \(-0.700579\pi\) | ||||
−0.589255 | + | 0.807947i | \(0.700579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −125.321 | −1.47436 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.6943i | − | 0.176340i | −0.996105 | − | 0.0881702i | \(-0.971898\pi\) | ||
0.996105 | − | 0.0881702i | \(-0.0281019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56.2911i | 0.618583i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −103.254 | + | 133.739i | −1.08688 | + | 1.40778i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.98703i | − | 0.0720312i | −0.999351 | − | 0.0360156i | \(-0.988533\pi\) | ||
0.999351 | − | 0.0360156i | \(-0.0114666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 75.8791 | 0.751279 | 0.375639 | − | 0.926766i | \(-0.377423\pi\) | ||||
0.375639 | + | 0.926766i | \(0.377423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 172.570i | − | 1.67544i | −0.546100 | − | 0.837720i | \(-0.683888\pi\) | ||
0.546100 | − | 0.837720i | \(-0.316112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 169.804i | 1.58695i | 0.608602 | + | 0.793475i | \(0.291730\pi\) | ||||
−0.608602 | + | 0.793475i | \(0.708270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23.5902i | 0.216423i | 0.994128 | + | 0.108212i | \(0.0345124\pi\) | ||||
−0.994128 | + | 0.108212i | \(0.965488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 68.2272i | − | 0.603781i | −0.953343 | − | 0.301890i | \(-0.902382\pi\) | ||
0.953343 | − | 0.301890i | \(-0.0976177\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −62.2421 | −0.541235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 57.6225 | 0.484223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −101.834 | −0.841605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 258.587 | 2.06870 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.69781i | − | 0.0369906i | −0.999829 | − | 0.0184953i | \(-0.994112\pi\) | ||
0.999829 | − | 0.0184953i | \(-0.00588758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −24.4766 | −0.186844 | −0.0934220 | − | 0.995627i | \(-0.529781\pi\) | ||||
−0.0934220 | + | 0.995627i | \(0.529781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.4761 | − | 61.4931i | 0.356963 | − | 0.462354i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −66.9886 | −0.488968 | −0.244484 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244484 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.137 | 1.31034 | 0.655169 | − | 0.755482i | \(-0.272597\pi\) | ||||
0.655169 | + | 0.755482i | \(0.272597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60.2705i | 0.421472i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 283.086i | − | 1.95231i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 203.480 | 1.36564 | 0.682818 | − | 0.730589i | \(-0.260754\pi\) | ||||
0.682818 | + | 0.730589i | \(0.260754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 225.098i | − | 1.49071i | −0.666666 | − | 0.745357i | \(-0.732279\pi\) | ||
0.666666 | − | 0.745357i | \(-0.267721\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 109.862i | 0.708786i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 72.8209 | 0.463827 | 0.231914 | − | 0.972736i | \(-0.425501\pi\) | ||||
0.231914 | + | 0.972736i | \(0.425501\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.6189 | 0.177757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −274.540 | −1.68430 | −0.842148 | − | 0.539246i | \(-0.818709\pi\) | ||||
−0.842148 | + | 0.539246i | \(0.818709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 162.610i | 0.973711i | 0.873483 | + | 0.486855i | \(0.161856\pi\) | ||||
−0.873483 | + | 0.486855i | \(0.838144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.5314 | −0.121488 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 180.593i | 1.04389i | 0.852979 | + | 0.521946i | \(0.174794\pi\) | ||||
−0.852979 | + | 0.521946i | \(0.825206\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −221.119 | −1.26354 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.9660i | 0.139475i | 0.997565 | + | 0.0697375i | \(0.0222162\pi\) | ||||
−0.997565 | + | 0.0697375i | \(0.977784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 73.8968i | 0.408269i | 0.978943 | + | 0.204135i | \(0.0654380\pi\) | ||||
−0.978943 | + | 0.204135i | \(0.934562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 43.5578i | − | 0.235448i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 61.6961 | 0.329925 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −199.072 | −1.04226 | −0.521130 | − | 0.853477i | \(-0.674489\pi\) | ||||
−0.521130 | + | 0.853477i | \(0.674489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 225.689i | − | 1.16937i | −0.811259 | − | 0.584687i | \(-0.801217\pi\) | ||
0.811259 | − | 0.584687i | \(-0.198783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 184.669 | 0.937405 | 0.468703 | − | 0.883356i | \(-0.344722\pi\) | ||||
0.468703 | + | 0.883356i | \(0.344722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −341.471 | −1.71594 | −0.857968 | − | 0.513703i | \(-0.828273\pi\) | ||||
−0.857968 | + | 0.513703i | \(0.828273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 130.163i | 0.641196i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 650.214i | − | 3.17178i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 50.8324 | − | 65.8403i | 0.243217 | − | 0.315025i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7087i | 0.0554916i | 0.999615 | + | 0.0277458i | \(0.00883290\pi\) | ||||
−0.999615 | + | 0.0277458i | \(0.991167\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 212.411 | 0.987957 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 50.5145i | − | 0.232786i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 194.014i | 0.877893i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 107.679i | − | 0.482866i | −0.970418 | − | 0.241433i | \(-0.922383\pi\) | ||
0.970418 | − | 0.241433i | \(-0.0776174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 231.845i | − | 1.02134i | −0.859776 | − | 0.510671i | \(-0.829397\pi\) | ||
0.859776 | − | 0.510671i | \(-0.170603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −94.0527 | −0.410710 | −0.205355 | − | 0.978688i | \(-0.565835\pi\) | ||||
−0.205355 | + | 0.978688i | \(0.565835\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 64.2586 | 0.275788 | 0.137894 | − | 0.990447i | \(-0.455967\pi\) | ||||
0.137894 | + | 0.990447i | \(0.455967\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −385.582 | −1.64077 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 254.410 | 1.06448 | 0.532239 | − | 0.846594i | \(-0.321351\pi\) | ||||
0.532239 | + | 0.846594i | \(0.321351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 360.169i | 1.49448i | 0.664557 | + | 0.747238i | \(0.268620\pi\) | ||||
−0.664557 | + | 0.747238i | \(0.731380\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −287.067 | −1.17170 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 207.047 | + | 159.852i | 0.838246 | + | 0.647172i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 190.633 | 0.759494 | 0.379747 | − | 0.925090i | \(-0.376011\pi\) | ||||
0.379747 | + | 0.925090i | \(0.376011\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.6421 | 0.121115 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26.0030i | − | 0.101179i | −0.998720 | − | 0.0505895i | \(-0.983890\pi\) | ||
0.998720 | − | 0.0505895i | \(-0.0161100\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0279i | 0.0773278i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −187.438 | −0.712693 | −0.356346 | − | 0.934354i | \(-0.615978\pi\) | ||||
−0.356346 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 581.989i | 2.19618i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 345.243i | 1.28343i | 0.766943 | + | 0.641715i | \(0.221777\pi\) | ||||
−0.766943 | + | 0.641715i | \(0.778223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 196.509 | 0.725124 | 0.362562 | − | 0.931960i | \(-0.381902\pi\) | ||||
0.362562 | + | 0.931960i | \(0.381902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −236.751 | −0.860911 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −501.779 | −1.81148 | −0.905738 | − | 0.423839i | \(-0.860682\pi\) | ||||
−0.905738 | + | 0.423839i | \(0.860682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 448.171i | − | 1.59492i | −0.603375 | − | 0.797458i | \(-0.706178\pi\) | ||
0.603375 | − | 0.797458i | \(-0.293822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 186.965 | 0.660655 | 0.330328 | − | 0.943866i | \(-0.392841\pi\) | ||||
0.330328 | + | 0.943866i | \(0.392841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 298.969i | 1.04170i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −90.3966 | −0.312791 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 152.099i | 0.519111i | 0.965728 | + | 0.259555i | \(0.0835760\pi\) | ||||
−0.965728 | + | 0.259555i | \(0.916424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 554.893i | − | 1.88099i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 96.3595i | 0.322273i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −97.6665 | −0.324473 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −623.582 | −2.04453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 223.721i | 0.728733i | 0.931256 | + | 0.364367i | \(0.118714\pi\) | ||||
−0.931256 | + | 0.364367i | \(0.881286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −107.817 | −0.346678 | −0.173339 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173339 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9501 | −0.0605435 | −0.0302718 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302718 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 316.377i | − | 0.998034i | −0.866592 | − | 0.499017i | \(-0.833694\pi\) | ||
0.866592 | − | 0.499017i | \(-0.166306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 139.364i | 0.436879i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 163.633 | − | 211.944i | 0.506602 | − | 0.656173i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 744.505i | − | 2.29079i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 177.291 | 0.538877 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 562.873i | − | 1.70052i | −0.526362 | − | 0.850261i | \(-0.676444\pi\) | ||
0.526362 | − | 0.850261i | \(-0.323556\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1125.15i | − | 3.35864i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 335.863i | 0.996628i | 0.866997 | + | 0.498314i | \(0.166047\pi\) | ||||
−0.866997 | + | 0.498314i | \(0.833953\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 54.0855i | − | 0.158609i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 332.346 | 0.968939 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 288.891 | 0.832538 | 0.416269 | − | 0.909241i | \(-0.363337\pi\) | ||||
0.416269 | + | 0.909241i | \(0.363337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −332.076 | −0.951508 | −0.475754 | − | 0.879578i | \(-0.657825\pi\) | ||||
−0.475754 | + | 0.879578i | \(0.657825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 100.942 | 0.285954 | 0.142977 | − | 0.989726i | \(-0.454333\pi\) | ||||
0.142977 | + | 0.989726i | \(0.454333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 399.512i | − | 1.12539i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −126.478 | −0.352306 | −0.176153 | − | 0.984363i | \(-0.556365\pi\) | ||||
−0.176153 | + | 0.984363i | \(0.556365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −91.3610 | − | 349.248i | −0.253078 | − | 0.967446i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05417 | −0.00288815 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −385.079 | −1.04926 | −0.524631 | − | 0.851330i | \(-0.675797\pi\) | ||||
−0.524631 | + | 0.851330i | \(0.675797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 267.598i | − | 0.721290i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 188.228i | − | 0.504632i | −0.967645 | − | 0.252316i | \(-0.918808\pi\) | ||
0.967645 | − | 0.252316i | \(-0.0811922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −438.256 | −1.16248 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 694.899i | − | 1.83351i | −0.399453 | − | 0.916754i | \(-0.630800\pi\) | ||
0.399453 | − | 0.916754i | \(-0.369200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 496.495i | − | 1.29633i | −0.761500 | − | 0.648165i | \(-0.775537\pi\) | ||
0.761500 | − | 0.648165i | \(-0.224463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 159.182 | 0.413459 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −454.909 | −1.16943 | −0.584715 | − | 0.811239i | \(-0.698794\pi\) | ||||
−0.584715 | + | 0.811239i | \(0.698794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 98.6387 | 0.252273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 173.489i | 0.439213i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 56.0875 | 0.141278 | 0.0706392 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706392 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.3922i | 0.0533470i | 0.999644 | + | 0.0266735i | \(0.00849145\pi\) | ||||
−0.999644 | + | 0.0266735i | \(0.991509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 170.082 | 0.422039 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.4437i | 0.0526873i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 259.092i | 0.633476i | 0.948513 | + | 0.316738i | \(0.102588\pi\) | ||||
−0.948513 | + | 0.316738i | \(0.897412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 255.140i | 0.617772i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −869.844 | −2.09601 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −822.708 | −1.96350 | −0.981752 | − | 0.190166i | \(-0.939097\pi\) | ||||
−0.981752 | + | 0.190166i | \(0.939097\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 512.963i | − | 1.21844i | −0.793002 | − | 0.609219i | \(-0.791483\pi\) | ||
0.793002 | − | 0.609219i | \(-0.208517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −762.115 | −1.79321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 286.723 | 0.671483 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 217.995i | − | 0.505789i | −0.967494 | − | 0.252894i | \(-0.918617\pi\) | ||
0.967494 | − | 0.252894i | \(-0.0813826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 474.721i | − | 1.09635i | −0.836363 | − | 0.548177i | \(-0.815322\pi\) | ||
0.836363 | − | 0.548177i | \(-0.184678\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 81.2700 | − | 105.264i | 0.185973 | − | 0.240880i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 610.886i | 1.39154i | 0.718264 | + | 0.695770i | \(0.244937\pi\) | ||||
−0.718264 | + | 0.695770i | \(0.755063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 743.578 | 1.67851 | 0.839253 | − | 0.543741i | \(-0.182992\pi\) | ||||
0.839253 | + | 0.543741i | \(0.182992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 139.564i | − | 0.313626i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 244.636i | 0.544846i | 0.962178 | + | 0.272423i | \(0.0878249\pi\) | ||||
−0.962178 | + | 0.272423i | \(0.912175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 320.104i | 0.709764i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 500.576i | 1.10017i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 456.513 | 0.998934 | 0.499467 | − | 0.866333i | \(-0.333529\pi\) | ||||
0.499467 | + | 0.866333i | \(0.333529\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −230.954 | −0.500986 | −0.250493 | − | 0.968118i | \(-0.580593\pi\) | ||||
−0.250493 | + | 0.968118i | \(0.580593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 438.242 | 0.946527 | 0.473264 | − | 0.880921i | \(-0.343076\pi\) | ||||
0.473264 | + | 0.880921i | \(0.343076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 443.535 | 0.949753 | 0.474877 | − | 0.880052i | \(-0.342493\pi\) | ||||
0.474877 | + | 0.880052i | \(0.342493\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 517.342i | 1.10307i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −104.571 | −0.221080 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −627.919 | + | 813.307i | −1.32193 | + | 1.71223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 263.159 | 0.549393 | 0.274696 | − | 0.961531i | \(-0.411423\pi\) | ||||
0.274696 | + | 0.961531i | \(0.411423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −67.4337 | −0.140195 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 62.1331i | − | 0.128109i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 270.643i | − | 0.555735i | −0.960619 | − | 0.277868i | \(-0.910372\pi\) | ||
0.960619 | − | 0.277868i | \(-0.0896276\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 331.509 | 0.675172 | 0.337586 | − | 0.941295i | \(-0.390390\pi\) | ||||
0.337586 | + | 0.941295i | \(0.390390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 448.622i | 0.909985i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 183.696i | 0.369609i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −846.591 | −1.69658 | −0.848288 | − | 0.529536i | \(-0.822366\pi\) | ||||
−0.848288 | + | 0.529536i | \(0.822366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 714.432 | 1.42034 | 0.710171 | − | 0.704030i | \(-0.248618\pi\) | ||||
0.710171 | + | 0.704030i | \(0.248618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 674.765 | 1.33617 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 171.981i | − | 0.337880i | −0.985626 | − | 0.168940i | \(-0.945966\pi\) | ||
0.985626 | − | 0.168940i | \(-0.0540345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.484709 | 0.000948550 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1534.60i | − | 2.97981i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 189.824 | 0.367164 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 624.308i | 1.19829i | 0.800641 | + | 0.599144i | \(0.204492\pi\) | ||||
−0.800641 | + | 0.599144i | \(0.795508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 874.036i | − | 1.67120i | −0.549340 | − | 0.835599i | \(-0.685121\pi\) | ||
0.549340 | − | 0.835599i | \(-0.314879\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 174.105i | − | 0.330369i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −480.010 | −0.907391 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1006.62 | −1.88860 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1510.00i | 2.82243i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 141.324 | 0.262198 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −382.026 | −0.706149 | −0.353074 | − | 0.935595i | \(-0.614864\pi\) | ||||
−0.353074 | + | 0.935595i | \(0.614864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 209.778i | 0.384915i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 494.309i | 0.903672i | 0.892101 | + | 0.451836i | \(0.149231\pi\) | ||||
−0.892101 | + | 0.451836i | \(0.850769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 478.757 | + | 369.627i | 0.868888 | + | 0.670830i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 79.7703i | − | 0.144250i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 987.867 | 1.77355 | 0.886775 | − | 0.462201i | \(-0.152940\pi\) | ||||
0.886775 | + | 0.462201i | \(0.152940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 328.842i | − | 0.588268i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 444.761i | 0.789984i | 0.918685 | + | 0.394992i | \(0.129253\pi\) | ||||
−0.918685 | + | 0.394992i | \(0.870747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 606.719i | − | 1.07384i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 760.247i | 1.33611i | 0.744111 | + | 0.668056i | \(0.232873\pi\) | ||||
−0.744111 | + | 0.668056i | \(0.767127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −587.441 | −1.02879 | −0.514397 | − | 0.857552i | \(-0.671984\pi\) | ||||
−0.514397 | + | 0.857552i | \(0.671984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −378.513 | −0.658284 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 470.148 | 0.814814 | 0.407407 | − | 0.913247i | \(-0.366433\pi\) | ||||
0.407407 | + | 0.913247i | \(0.366433\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 399.954 | 0.688389 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 286.516i | − | 0.491451i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −559.569 | −0.953269 | −0.476634 | − | 0.879102i | \(-0.658143\pi\) | ||||
−0.476634 | + | 0.879102i | \(0.658143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −185.799 | − | 143.448i | −0.315449 | − | 0.243544i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 923.095 | 1.55665 | 0.778326 | − | 0.627860i | \(-0.216069\pi\) | ||||
0.778326 | + | 0.627860i | \(0.216069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 512.416 | 0.861203 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 569.367i | 0.950529i | 0.879843 | + | 0.475264i | \(0.157648\pi\) | ||||
−0.879843 | + | 0.475264i | \(0.842352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 575.057i | 0.956833i | 0.878133 | + | 0.478417i | \(0.158789\pi\) | ||||
−0.878133 | + | 0.478417i | \(0.841211\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −905.573 | −1.49682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 941.747i | − | 1.55148i | −0.631054 | − | 0.775739i | \(-0.717377\pi\) | ||
0.631054 | − | 0.775739i | \(-0.282623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 596.935i | 0.976981i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −835.577 | −1.36309 | −0.681547 | − | 0.731774i | \(-0.738693\pi\) | ||||
−0.681547 | + | 0.731774i | \(0.738693\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 725.675 | 1.17613 | 0.588067 | − | 0.808812i | \(-0.299889\pi\) | ||||
0.588067 | + | 0.808812i | \(0.299889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 539.760 | 0.871988 | 0.435994 | − | 0.899950i | \(-0.356397\pi\) | ||||
0.435994 | + | 0.899950i | \(0.356397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 64.1713i | 0.103004i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 947.548 | 1.51608 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 69.0287i | 0.109744i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1166.75 | 1.84905 | 0.924524 | − | 0.381123i | \(-0.124463\pi\) | ||||
0.924524 | + | 0.381123i | \(0.124463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 41.7759i | − | 0.0657888i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 444.420i | 0.697677i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1000.68i | 1.56112i | 0.625083 | + | 0.780558i | \(0.285065\pi\) | ||||
−0.625083 | + | 0.780558i | \(0.714935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 857.488 | 1.33357 | 0.666787 | − | 0.745248i | \(-0.267669\pi\) | ||||
0.666787 | + | 0.745248i | \(0.267669\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −83.5434 | −0.129124 | −0.0645621 | − | 0.997914i | \(-0.520565\pi\) | ||||
−0.0645621 | + | 0.997914i | \(0.520565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 273.177i | 0.420919i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −482.731 | −0.739252 | −0.369626 | − | 0.929181i | \(-0.620514\pi\) | ||||
−0.369626 | + | 0.929181i | \(0.620514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −217.661 | −0.332307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 292.175i | 0.443360i | 0.975119 | + | 0.221680i | \(0.0711541\pi\) | ||||
−0.975119 | + | 0.221680i | \(0.928846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 524.668i | − | 0.793748i | −0.917873 | − | 0.396874i | \(-0.870095\pi\) | ||
0.917873 | − | 0.396874i | \(-0.129905\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 422.188 | − | 546.835i | 0.634868 | − | 0.822309i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 222.813i | 0.334053i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 306.992 | 0.457515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 933.628i | 1.38726i | 0.720330 | + | 0.693632i | \(0.243990\pi\) | ||||
−0.720330 | + | 0.693632i | \(0.756010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 221.809i | 0.327635i | 0.986491 | + | 0.163818i | \(0.0523809\pi\) | ||||
−0.986491 | + | 0.163818i | \(0.947619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.5688i | 0.0420748i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1042.38i | 1.52618i | 0.646293 | + | 0.763090i | \(0.276319\pi\) | ||||
−0.646293 | + | 0.763090i | \(0.723681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −595.705 | −0.869642 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 901.001 | 1.30769 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −296.453 | −0.429020 | −0.214510 | − | 0.976722i | \(-0.568815\pi\) | ||||
−0.214510 | + | 0.976722i | \(0.568815\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1619.68 | 2.33047 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1030.43i | 1.47838i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1000.32 | −1.42700 | −0.713499 | − | 0.700657i | \(-0.752890\pi\) | ||||
−0.713499 | + | 0.700657i | \(0.752890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 73.6654 | + | 56.8738i | 0.104787 | + | 0.0809016i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −310.257 | −0.438836 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −198.456 | −0.279909 | −0.139955 | − | 0.990158i | \(-0.544696\pi\) | ||||
−0.139955 | + | 0.990158i | \(0.544696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 86.4711i | − | 0.121278i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 535.963i | 0.749598i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −648.586 | −0.902067 | −0.451033 | − | 0.892507i | \(-0.648944\pi\) | ||||
−0.451033 | + | 0.892507i | \(0.648944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 705.611i | 0.978656i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1721.53i | − | 2.37452i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1282.65 | 1.76431 | 0.882155 | − | 0.470960i | \(-0.156092\pi\) | ||||
0.882155 | + | 0.470960i | \(0.156092\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −336.620 | −0.460492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 892.888 | 1.21813 | 0.609064 | − | 0.793121i | \(-0.291545\pi\) | ||||
0.609064 | + | 0.793121i | \(0.291545\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 553.915i | 0.751580i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1150.31 | 1.55658 | 0.778290 | − | 0.627905i | \(-0.216087\pi\) | ||||
0.778290 | + | 0.627905i | \(0.216087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 436.802i | 0.587889i | 0.955822 | + | 0.293945i | \(0.0949681\pi\) | ||||
−0.955822 | + | 0.293945i | \(0.905032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1809.47 | 2.42882 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 694.298i | − | 0.926967i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 491.952i | 0.655063i | 0.944840 | + | 0.327531i | \(0.106217\pi\) | ||||
−0.944840 | + | 0.327531i | \(0.893783\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2001.71i | − | 2.65127i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1120.04 | −1.47958 | −0.739789 | − | 0.672839i | \(-0.765075\pi\) | ||||
−0.739789 | + | 0.672839i | \(0.765075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 235.547 | 0.309523 | 0.154761 | − | 0.987952i | \(-0.450539\pi\) | ||||
0.154761 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 96.4561i | − | 0.126417i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −859.053 | −1.12002 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 558.287 | 0.725991 | 0.362996 | − | 0.931791i | \(-0.381754\pi\) | ||||
0.362996 | + | 0.931791i | \(0.381754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 964.213i | 1.24737i | 0.781678 | + | 0.623683i | \(0.214364\pi\) | ||||
−0.781678 | + | 0.623683i | \(0.785636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 668.104i | 0.862070i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1099.65 | + | 848.991i | 1.41162 | + | 1.08985i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 196.682i | 0.251833i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 647.569 | 0.824928 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 734.077i | 0.932754i | 0.884586 | + | 0.466377i | \(0.154441\pi\) | ||||
−0.884586 | + | 0.466377i | \(0.845559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 278.969i | 0.352680i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 965.393i | 1.21739i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1208.84i | − | 1.51673i | −0.651827 | − | 0.758367i | \(-0.725997\pi\) | ||
0.651827 | − | 0.758367i | \(-0.274003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 611.054 | 0.764774 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.518975 | 0.000646295 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 254.497 | 0.316146 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1294.97 | 1.60070 | 0.800349 | − | 0.599534i | \(-0.204647\pi\) | ||||
0.800349 | + | 0.599534i | \(0.204647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 698.570i | − | 0.861369i | −0.902503 | − | 0.430685i | \(-0.858272\pi\) | ||
0.902503 | − | 0.430685i | \(-0.141728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2441.38 | −2.99556 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −277.347 | + | 359.231i | −0.339470 | + | 0.439695i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 642.039 | 0.782021 | 0.391011 | − | 0.920386i | \(-0.372126\pi\) | ||||
0.391011 | + | 0.920386i | \(0.372126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −808.191 | −0.982006 | −0.491003 | − | 0.871158i | \(-0.663370\pi\) | ||||
−0.491003 | + | 0.871158i | \(0.663370\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1092.17i | 1.32064i | 0.750983 | + | 0.660321i | \(0.229580\pi\) | ||||
−0.750983 | + | 0.660321i | \(0.770420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 552.397i | − | 0.666341i | −0.942867 | − | 0.333170i | \(-0.891882\pi\) | ||
0.942867 | − | 0.333170i | \(-0.108118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 454.932 | 0.546137 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1446.03i | 1.73177i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 308.616i | 0.367838i | 0.982941 | + | 0.183919i | \(0.0588784\pi\) | ||||
−0.982941 | + | 0.183919i | \(0.941122\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −172.387 | −0.204978 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −182.578 | −0.216069 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 416.382 | 0.491597 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.2839i | 0.0402866i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 513.281 | 0.601737 | 0.300868 | − | 0.953666i | \(-0.402724\pi\) | ||||
0.300868 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 902.528i | 1.05312i | 0.850137 | + | 0.526562i | \(0.176519\pi\) | ||||
−0.850137 | + | 0.526562i | \(0.823481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −279.345 | −0.325197 | −0.162599 | − | 0.986692i | \(-0.551988\pi\) | ||||
−0.162599 | + | 0.986692i | \(0.551988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 974.538i | − | 1.12924i | −0.825349 | − | 0.564622i | \(-0.809022\pi\) | ||
0.825349 | − | 0.564622i | \(-0.190978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1605.95i | 1.85659i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 85.4095i | − | 0.0982848i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1741.88 | −1.99987 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1057.32 | −1.20836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1355.21i | − | 1.54527i | −0.634848 | − | 0.772637i | \(-0.718937\pi\) | ||
0.634848 | − | 0.772637i | \(-0.281063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1598.89 | −1.81486 | −0.907431 | − | 0.420200i | \(-0.861960\pi\) | ||||
−0.907431 | + | 0.420200i | \(0.861960\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 298.404 | 0.337944 | 0.168972 | − | 0.985621i | \(-0.445955\pi\) | ||||
0.168972 | + | 0.985621i | \(0.445955\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 277.416i | 0.312757i | 0.987697 | + | 0.156379i | \(0.0499820\pi\) | ||||
−0.987697 | + | 0.156379i | \(0.950018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2085i | 0.0216069i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 503.458 | − | 652.100i | 0.563782 | − | 0.730235i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 222.014i | 0.248060i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 393.282 | 0.437467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 922.312i | − | 1.02365i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 657.136i | 0.726117i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 588.225i | 0.648539i | 0.945965 | + | 0.324270i | \(0.105119\pi\) | ||||
−0.945965 | + | 0.324270i | \(0.894881\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 456.868i | − | 0.501502i | −0.968052 | − | 0.250751i | \(-0.919323\pi\) | ||
0.968052 | − | 0.250751i | \(-0.0806775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 428.228 | 0.469034 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 100.080 | 0.109139 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.98423 | 0.00433540 | 0.00216770 | − | 0.999998i | \(-0.499310\pi\) | ||||
0.00216770 | + | 0.999998i | \(0.499310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −618.501 | −0.670099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 264.889i | − | 0.286366i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −742.264 | −0.798993 | −0.399496 | − | 0.916735i | \(-0.630815\pi\) | ||||
−0.399496 | + | 0.916735i | \(0.630815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 374.826 | − | 485.491i | 0.402606 | − | 0.521472i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 548.640 | 0.586781 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 415.097 | 0.443006 | 0.221503 | − | 0.975160i | \(-0.428904\pi\) | ||||
0.221503 | + | 0.975160i | \(0.428904\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 883.401i | − | 0.938790i | −0.882988 | − | 0.469395i | \(-0.844472\pi\) | ||
0.882988 | − | 0.469395i | \(-0.155528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 511.777i | 0.542711i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 465.843 | 0.491915 | 0.245957 | − | 0.969281i | \(-0.420898\pi\) | ||||
0.245957 | + | 0.969281i | \(0.420898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.63201i | 0.00171972i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 479.320i | − | 0.502959i | −0.967863 | − | 0.251479i | \(-0.919083\pi\) | ||
0.967863 | − | 0.251479i | \(-0.0809171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1770.27 | −1.85369 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 273.905 | 0.285615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 808.372 | 0.841178 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2006.97i | − | 2.07976i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0426 | −0.0496821 | −0.0248411 | − | 0.999691i | \(-0.507908\pi\) | ||||
−0.0248411 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 954.276i | 0.982776i | 0.870941 | + | 0.491388i | \(0.163510\pi\) | ||||
−0.870941 | + | 0.491388i | \(0.836490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −744.727 | −0.765393 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 230.509i | 0.235935i | 0.993017 | + | 0.117968i | \(0.0376379\pi\) | ||||
−0.993017 | + | 0.117968i | \(0.962362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.7078i | 0.0701816i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 525.483i | 0.534571i | 0.963617 | + | 0.267285i | \(0.0861266\pi\) | ||||
−0.963617 | + | 0.267285i | \(0.913873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1642.19 | 1.66720 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −167.186 | −0.169046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 988.597i | − | 0.997575i | −0.866724 | − | 0.498787i | \(-0.833779\pi\) | ||
0.866724 | − | 0.498787i | \(-0.166221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3036.58 | −3.05184 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 307.985 | 0.308912 | 0.154456 | − | 0.988000i | \(-0.450638\pi\) | ||||
0.154456 | + | 0.988000i | \(0.450638\pi\) | |||||||
\(998\) | 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 | 2736.3.o.q.721.19 | 20 | ||
3.2 | odd | 2 | inner | 2736.3.o.q.721.1 | 20 | ||
4.3 | odd | 2 | 1368.3.o.d.721.19 | yes | 20 | ||
12.11 | even | 2 | 1368.3.o.d.721.1 | ✓ | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.q.721.20 | 20 | ||
57.56 | even | 2 | inner | 2736.3.o.q.721.2 | 20 | ||
76.75 | even | 2 | 1368.3.o.d.721.20 | yes | 20 | ||
228.227 | odd | 2 | 1368.3.o.d.721.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.3.o.d.721.1 | ✓ | 20 | 12.11 | even | 2 | ||
1368.3.o.d.721.2 | yes | 20 | 228.227 | odd | 2 | ||
1368.3.o.d.721.19 | yes | 20 | 4.3 | odd | 2 | ||
1368.3.o.d.721.20 | yes | 20 | 76.75 | even | 2 | ||
2736.3.o.q.721.1 | 20 | 3.2 | odd | 2 | inner | ||
2736.3.o.q.721.2 | 20 | 57.56 | even | 2 | inner | ||
2736.3.o.q.721.19 | 20 | 1.1 | even | 1 | trivial | ||
2736.3.o.q.721.20 | 20 | 19.18 | odd | 2 | inner |