Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.4 | ||
Root | \(0.456937 - 0.263813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.4.c.i.1727.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − 13.1987i | − 1.18052i | −0.807212 | − | 0.590262i | \(-0.799024\pi\) | ||||
0.807212 | − | 0.590262i | \(-0.200976\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.49091i | 0.242486i | 0.992623 | + | 0.121243i | \(0.0386881\pi\) | ||||
−0.992623 | + | 0.121243i | \(0.961312\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.3519 | 0.612669 | 0.306335 | − | 0.951924i | \(-0.400897\pi\) | ||||
0.306335 | + | 0.951924i | \(0.400897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 73.5402 | 1.56895 | 0.784476 | − | 0.620159i | \(-0.212932\pi\) | ||||
0.784476 | + | 0.620159i | \(0.212932\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.6199i | 0.608050i | 0.952664 | + | 0.304025i | \(0.0983307\pi\) | ||||
−0.952664 | + | 0.304025i | \(0.901669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 122.563i | 1.47989i | 0.672669 | + | 0.739943i | \(0.265148\pi\) | ||||
−0.672669 | + | 0.739943i | \(0.734852\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −197.965 | −1.79472 | −0.897360 | − | 0.441299i | \(-0.854518\pi\) | ||||
−0.897360 | + | 0.441299i | \(0.854518\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49.2047 | −0.393638 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.6816i | 0.0940102i | 0.998895 | + | 0.0470051i | \(0.0149677\pi\) | ||||
−0.998895 | + | 0.0470051i | \(0.985032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.133i | 0.852448i | 0.904618 | + | 0.426224i | \(0.140156\pi\) | ||||
−0.904618 | + | 0.426224i | \(0.859844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.2740 | 0.286261 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −234.154 | −1.04040 | −0.520199 | − | 0.854045i | \(-0.674142\pi\) | ||||
−0.520199 | + | 0.854045i | \(0.674142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 396.340i | 1.50970i | 0.655895 | + | 0.754852i | \(0.272292\pi\) | ||||
−0.655895 | + | 0.754852i | \(0.727708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 280.764i | − 0.995725i | −0.867256 | − | 0.497863i | \(-0.834118\pi\) | ||||
0.867256 | − | 0.497863i | \(-0.165882\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −534.237 | −1.65801 | −0.829006 | − | 0.559240i | \(-0.811093\pi\) | ||||
−0.829006 | + | 0.559240i | \(0.811093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 322.832 | 0.941200 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 337.497i | − 0.874695i | −0.899293 | − | 0.437347i | \(-0.855918\pi\) | ||||
0.899293 | − | 0.437347i | \(-0.144082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 295.016i | − 0.723271i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −672.928 | −1.48488 | −0.742439 | − | 0.669914i | \(-0.766331\pi\) | ||||
−0.742439 | + | 0.669914i | \(0.766331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 80.8693 | 0.169742 | 0.0848709 | − | 0.996392i | \(-0.472952\pi\) | ||||
0.0848709 | + | 0.996392i | \(0.472952\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 970.632i | − 1.85219i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 251.791i | 0.459121i | 0.973294 | + | 0.229560i | \(0.0737289\pi\) | ||||
−0.973294 | + | 0.229560i | \(0.926271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 95.8124 | 0.160153 | 0.0800763 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800763 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −251.422 | −0.403106 | −0.201553 | − | 0.979478i | \(-0.564599\pi\) | ||||
−0.201553 | + | 0.979478i | \(0.564599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 100.381i | 0.148564i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 499.839i | 0.711852i | 0.934514 | + | 0.355926i | \(0.115835\pi\) | ||||
−0.934514 | + | 0.355926i | \(0.884165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.1731 | 0.0213882 | 0.0106941 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106941 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 562.526 | 0.717818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 321.011i | − 0.382327i | −0.981558 | − | 0.191164i | \(-0.938774\pi\) | ||||
0.981558 | − | 0.191164i | \(-0.0612261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 330.263i | 0.380450i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1617.67 | 1.74704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −210.036 | −0.219855 | −0.109928 | − | 0.993940i | \(-0.535062\pi\) | ||||
−0.109928 | + | 0.993940i | \(0.535062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1568.74i | 1.54550i | 0.634713 | + | 0.772748i | \(0.281118\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 544.057i | 0.520462i | 0.965546 | + | 0.260231i | \(0.0837987\pi\) | ||||
−0.965546 | + | 0.260231i | \(0.916201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1105.78 | −0.999064 | −0.499532 | − | 0.866295i | \(-0.666495\pi\) | ||||
−0.499532 | + | 0.866295i | \(0.666495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6601 | −0.0155186 | −0.00775932 | − | 0.999970i | \(-0.502470\pi\) | ||||
−0.00775932 | + | 0.999970i | \(0.502470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1603.29i | 1.33473i | 0.744729 | + | 0.667367i | \(0.232579\pi\) | ||||
−0.744729 | + | 0.667367i | \(0.767421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2612.87i | 2.11871i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −191.402 | −0.147444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −831.391 | −0.624636 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1000.40i | − 0.715825i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2080.04i | 1.45334i | 0.686988 | + | 0.726669i | \(0.258932\pi\) | ||||
−0.686988 | + | 0.726669i | \(0.741068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1093.35 | 0.729213 | 0.364606 | − | 0.931162i | \(-0.381204\pi\) | ||||
0.364606 | + | 0.931162i | \(0.381204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −550.419 | −0.358853 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1344.61i | − 0.838522i | −0.907866 | − | 0.419261i | \(-0.862289\pi\) | ||||
0.907866 | − | 0.419261i | \(-0.137711\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 805.378i | 0.491448i | 0.969340 | + | 0.245724i | \(0.0790257\pi\) | ||||
−0.969340 | + | 0.245724i | \(0.920974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1643.77 | 0.961249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 193.777 | 0.110981 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 879.365i | 0.483493i | 0.970339 | + | 0.241746i | \(0.0777202\pi\) | ||||
−0.970339 | + | 0.241746i | \(0.922280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1826.20i | 0.984197i | 0.870540 | + | 0.492098i | \(0.163770\pi\) | ||||
−0.870540 | + | 0.492098i | \(0.836230\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1941.96 | 1.00634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3417.81 | −1.73740 | −0.868698 | − | 0.495342i | \(-0.835043\pi\) | ||||
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 889.044i | − 0.435195i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1190.78i | − 0.572204i | −0.958199 | − | 0.286102i | \(-0.907640\pi\) | ||||
0.958199 | − | 0.286102i | \(-0.0923596\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2123.75 | −0.984077 | −0.492039 | − | 0.870573i | \(-0.663748\pi\) | ||||
−0.492039 | + | 0.870573i | \(0.663748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3211.16 | 1.46161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1769.12i | − 0.777477i | −0.921348 | − | 0.388738i | \(-0.872911\pi\) | ||||
0.921348 | − | 0.388738i | \(-0.127089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 220.974i | − 0.0954519i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3685.89 | 1.53909 | 0.769543 | − | 0.638595i | \(-0.220484\pi\) | ||||
0.769543 | + | 0.638595i | \(0.220484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2425.51 | 0.996059 | 0.498030 | − | 0.867160i | \(-0.334057\pi\) | ||||
0.498030 | + | 0.867160i | \(0.334057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3090.52i | 1.22822i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 952.638i | 0.372534i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1367.60 | 0.518096 | 0.259048 | − | 0.965865i | \(-0.416591\pi\) | ||||
0.259048 | + | 0.965865i | \(0.416591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1240.32 | −0.462591 | −0.231296 | − | 0.972883i | \(-0.574296\pi\) | ||||
−0.231296 | + | 0.972883i | \(0.574296\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2889.56i | − 1.04504i | −0.852628 | − | 0.522519i | \(-0.824992\pi\) | ||||
0.852628 | − | 0.522519i | \(-0.175008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1851.53i | 0.659555i | 0.944059 | + | 0.329777i | \(0.106974\pi\) | ||||
−0.944059 | + | 0.329777i | \(0.893026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −65.9336 | −0.0227962 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5231.16 | 1.78224 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2739.52i | 0.906681i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4177.37i | 1.36295i | 0.731843 | + | 0.681474i | \(0.238661\pi\) | ||||
−0.731843 | + | 0.681474i | \(0.761339\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3705.72 | −1.17548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −660.762 | −0.206707 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3134.28i | 0.954002i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1155.67i | − 0.347039i | −0.984830 | − | 0.173519i | \(-0.944486\pi\) | ||||
0.984830 | − | 0.173519i | \(-0.0555139\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1499.50 | 0.438437 | 0.219218 | − | 0.975676i | \(-0.429649\pi\) | ||||
0.219218 | + | 0.975676i | \(0.429649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 320.011 | 0.0923445 | 0.0461723 | − | 0.998933i | \(-0.485298\pi\) | ||||
0.0461723 | + | 0.998933i | \(0.485298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1446.64i | − 0.406749i | −0.979101 | − | 0.203374i | \(-0.934809\pi\) | ||||
0.979101 | − | 0.203374i | \(-0.0651909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7051.22i | 1.95732i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1432.06 | 0.387582 | 0.193791 | − | 0.981043i | \(-0.437922\pi\) | ||||
0.193791 | + | 0.981043i | \(0.437922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1148.97 | −0.307102 | −0.153551 | − | 0.988141i | \(-0.549071\pi\) | ||||
−0.153551 | + | 0.988141i | \(0.549071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4260.95i | − 1.11111i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9013.30i | 2.32187i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3652.62 | −0.918531 | −0.459266 | − | 0.888299i | \(-0.651887\pi\) | ||||
−0.459266 | + | 0.888299i | \(0.651887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4424.90 | −1.09957 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5362.37i | − 1.30154i | −0.759275 | − | 0.650770i | \(-0.774446\pi\) | ||||
0.759275 | − | 0.650770i | \(-0.225554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1051.57i | − 0.252283i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1096.98 | 0.257196 | 0.128598 | − | 0.991697i | \(-0.458952\pi\) | ||||
0.128598 | + | 0.991697i | \(0.458952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4454.51 | −1.03260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5602.35i | 1.26982i | 0.772586 | + | 0.634910i | \(0.218963\pi\) | ||||
−0.772586 | + | 0.634910i | \(0.781037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1051.62i | 0.235725i | 0.993030 | + | 0.117862i | \(0.0376041\pi\) | ||||
−0.993030 | + | 0.117862i | \(0.962396\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1099.82 | −0.241170 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2739.10 | −0.594139 | −0.297069 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297069 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 423.244i | − 0.0898528i | −0.998990 | − | 0.0449264i | \(-0.985695\pi\) | ||||
0.998990 | − | 0.0449264i | \(-0.0143053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1630.51i | 0.342486i | 0.985229 | + | 0.171243i | \(0.0547783\pi\) | ||||
−0.985229 | + | 0.171243i | \(0.945222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1779.93 | −0.366083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3096.54 | 0.630275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2352.75i | 0.469109i | 0.972103 | + | 0.234554i | \(0.0753631\pi\) | ||||
−0.972103 | + | 0.234554i | \(0.924637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8881.76i | 1.75293i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14558.4 | −2.81583 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1260.89 | 0.241450 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1067.37i | − 0.200384i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10088.6i | 1.87554i | 0.347263 | + | 0.937768i | \(0.387111\pi\) | ||||
−0.347263 | + | 0.937768i | \(0.612889\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3970.97 | −0.724029 | −0.362015 | − | 0.932172i | \(-0.617911\pi\) | ||||
−0.362015 | + | 0.932172i | \(0.617911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4539.33 | 0.819738 | 0.409869 | − | 0.912144i | \(-0.365574\pi\) | ||||
0.409869 | + | 0.912144i | \(0.365574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4211.47i | − 0.746181i | −0.927795 | − | 0.373091i | \(-0.878298\pi\) | ||||
0.927795 | − | 0.373091i | \(-0.121702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 328.161i | 0.0575972i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5223.62 | −0.899846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3618.52 | −0.617599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2399.21i | − 0.402045i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3143.43i | 0.521990i | 0.965340 | + | 0.260995i | \(0.0840506\pi\) | ||||
−0.965340 | + | 0.260995i | \(0.915949\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3323.30 | 0.542004 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7102.24 | 1.14802 | 0.574012 | − | 0.818847i | \(-0.305386\pi\) | ||||
0.574012 | + | 0.818847i | \(0.305386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3288.71i | 0.522269i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2990.19i | 0.470715i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4871.70 | 0.753678 | 0.376839 | − | 0.926279i | \(-0.377011\pi\) | ||||
0.376839 | + | 0.926279i | \(0.377011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7245.91 | 1.11136 | 0.555680 | − | 0.831396i | \(-0.312458\pi\) | ||||
0.555680 | + | 0.831396i | \(0.312458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9352.32i | 1.41012i | 0.709146 | + | 0.705062i | \(0.249081\pi\) | ||||
−0.709146 | + | 0.705062i | \(0.750919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1264.60i | − 0.189064i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5162.08 | 0.758898 | 0.379449 | − | 0.925213i | \(-0.376114\pi\) | ||||
0.379449 | + | 0.925213i | \(0.376114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8162.66 | −1.19006 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3318.44i | 0.475877i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3138.93i | 0.446460i | 0.974766 | + | 0.223230i | \(0.0716600\pi\) | ||||
−0.974766 | + | 0.223230i | \(0.928340\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1515.67 | 0.212102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3085.24 | −0.428278 | −0.214139 | − | 0.976803i | \(-0.568695\pi\) | ||||
−0.214139 | + | 0.976803i | \(0.568695\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1079.68i | 0.147498i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 13468.6i | − 1.82542i | −0.408611 | − | 0.912709i | \(-0.633987\pi\) | ||||
0.408611 | − | 0.912709i | \(-0.366013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1100.69 | −0.146847 | −0.0734235 | − | 0.997301i | \(-0.523392\pi\) | ||||
−0.0734235 | + | 0.997301i | \(0.523392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1324.89 | 0.175383 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10089.1i | 1.31501i | 0.753452 | + | 0.657503i | \(0.228387\pi\) | ||||
−0.753452 | + | 0.657503i | \(0.771613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 8437.26i | − 1.09128i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6597.21 | 0.840359 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1596.47 | −0.201825 | −0.100912 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100912 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 4818.54i | − 0.600066i | −0.953929 | − | 0.300033i | \(-0.903002\pi\) | ||||
0.953929 | − | 0.300033i | \(-0.0969977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10820.2i | 1.33745i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5233.80 | −0.637420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4223.57 | −0.510617 | −0.255308 | − | 0.966860i | \(-0.582177\pi\) | ||||
−0.255308 | + | 0.966860i | \(0.582177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3022.06i | − 0.360063i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 213.463i | − 0.0252493i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1165.75 | −0.135921 | −0.0679604 | − | 0.997688i | \(-0.521649\pi\) | ||||
−0.0679604 | + | 0.997688i | \(0.521649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9114.56 | 1.05515 | 0.527573 | − | 0.849510i | \(-0.323102\pi\) | ||||
0.527573 | + | 0.849510i | \(0.323102\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 2097.10i | − 0.239352i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 363.177i | 0.0411601i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6631.38 | −0.741120 | −0.370560 | − | 0.928809i | \(-0.620834\pi\) | ||||
−0.370560 | + | 0.928809i | \(0.620834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15681.8 | −1.74046 | −0.870230 | − | 0.492646i | \(-0.836030\pi\) | ||||
−0.870230 | + | 0.492646i | \(0.836030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 24263.2i | − 2.65598i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 7923.17i | − 0.861395i | −0.902496 | − | 0.430697i | \(-0.858268\pi\) | ||||
0.902496 | − | 0.430697i | \(-0.141732\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14013.0 | 1.50289 | 0.751445 | − | 0.659796i | \(-0.229357\pi\) | ||||
0.751445 | + | 0.659796i | \(0.229357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4236.92 | −0.451346 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5967.60i | 0.627235i | 0.949549 | + | 0.313617i | \(0.101541\pi\) | ||||
−0.949549 | + | 0.313617i | \(0.898459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8858.96i | 0.924950i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4359.02 | 0.449130 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12901.4 | 1.32057 | 0.660285 | − | 0.751015i | \(-0.270435\pi\) | ||||
0.660285 | + | 0.751015i | \(0.270435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9801.20i | − 0.990212i | −0.868833 | − | 0.495106i | \(-0.835129\pi\) | ||||
0.868833 | − | 0.495106i | \(-0.164871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3427.68i | 0.344056i | 0.985092 | + | 0.172028i | \(0.0550320\pi\) | ||||
−0.985092 | + | 0.172028i | \(0.944968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13777.2 | 1.36517 | 0.682583 | − | 0.730808i | \(-0.260856\pi\) | ||||
0.682583 | + | 0.730808i | \(0.260856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1130.77 | −0.111331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6275.63i | − 0.610050i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6030.67i | − 0.582539i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2793.91 | −0.266507 | −0.133254 | − | 0.991082i | \(-0.542542\pi\) | ||||
−0.133254 | + | 0.991082i | \(0.542542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17219.8 | −1.63234 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2772.20i | 0.259545i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17643.8i | 1.64172i | 0.571131 | + | 0.820859i | \(0.306505\pi\) | ||||
−0.571131 | + | 0.820859i | \(0.693495\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4816.53 | −0.442703 | −0.221351 | − | 0.975194i | \(-0.571047\pi\) | ||||
−0.221351 | + | 0.975194i | \(0.571047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −625.727 | −0.0571629 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 430.285i | 0.0388349i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9504.01i | 0.852621i | 0.904577 | + | 0.426311i | \(0.140187\pi\) | ||||
−0.904577 | + | 0.426311i | \(0.859813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13840.8 | 1.22690 | 0.613452 | − | 0.789732i | \(-0.289780\pi\) | ||||
0.613452 | + | 0.789732i | \(0.289780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20705.2 | 1.82450 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8144.19i | − 0.709204i | −0.935017 | − | 0.354602i | \(-0.884616\pi\) | ||||
0.935017 | − | 0.354602i | \(-0.115384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1129.12i | − 0.0977478i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7180.83 | 0.614418 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11941.2 | −1.01581 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21121.1i | 1.77607i | 0.459779 | + | 0.888034i | \(0.347929\pi\) | ||||
−0.459779 | + | 0.888034i | \(0.652071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15414.6i | − 1.28878i | −0.764696 | − | 0.644391i | \(-0.777111\pi\) | ||||
0.764696 | − | 0.644391i | \(-0.222889\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6270.81 | −0.518331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27023.2 | 2.22102 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29146.9i | 2.36865i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14594.8i | 1.17942i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7215.91 | 0.576644 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3269.66 | 0.259840 | 0.129920 | − | 0.991524i | \(-0.458528\pi\) | ||||
0.129920 | + | 0.991524i | \(0.458528\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 233.090i | 0.0183201i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2028.46i | 0.158557i | 0.996853 | + | 0.0792784i | \(0.0252616\pi\) | ||||
−0.996853 | + | 0.0792784i | \(0.974738\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1799.41 | −0.139124 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2244.74 | −0.172615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5968.99i | 0.454065i | 0.973887 | + | 0.227032i | \(0.0729023\pi\) | ||||
−0.973887 | + | 0.227032i | \(0.927098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 20647.5i | − 1.56225i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13107.0 | −0.981161 | −0.490581 | − | 0.871396i | \(-0.663215\pi\) | ||||
−0.490581 | + | 0.871396i | \(0.663215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21161.3 | 1.57569 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 20162.7i | − 1.48553i | −0.669553 | − | 0.742764i | \(-0.733514\pi\) | ||||
0.669553 | − | 0.742764i | \(-0.266486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 9396.23i | − 0.688652i | −0.938850 | − | 0.344326i | \(-0.888108\pi\) | ||||
0.938850 | − | 0.344326i | \(-0.111892\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9740.82 | 0.706470 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3349.25 | −0.241648 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 72.6318i | 0.00518636i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7543.72i | − 0.535899i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5156.24 | 0.362557 | 0.181278 | − | 0.983432i | \(-0.441977\pi\) | ||||
0.181278 | + | 0.983432i | \(0.441977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18033.1 | −1.26153 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 19449.0i | − 1.34684i | −0.739261 | − | 0.673419i | \(-0.764825\pi\) | ||||
0.739261 | − | 0.673419i | \(-0.235175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2526.26i | 0.174061i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25726.7 | 1.75486 | 0.877432 | − | 0.479701i | \(-0.159255\pi\) | ||||
0.877432 | + | 0.479701i | \(0.159255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11668.4 | −0.791952 | −0.395976 | − | 0.918261i | \(-0.629594\pi\) | ||||
−0.395976 | + | 0.918261i | \(0.629594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10973.3i | 0.737399i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 26441.9i | − 1.76811i | −0.467382 | − | 0.884055i | \(-0.654803\pi\) | ||||
0.467382 | − | 0.884055i | \(-0.345197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39287.9 | −2.60134 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4001.56 | 0.263656 | 0.131828 | − | 0.991273i | \(-0.457915\pi\) | ||||
0.131828 | + | 0.991273i | \(0.457915\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25511.2i | 1.66457i | 0.554347 | + | 0.832286i | \(0.312968\pi\) | ||||
−0.554347 | + | 0.832286i | \(0.687032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 25105.1i | − 1.63014i | −0.579361 | − | 0.815071i | \(-0.696698\pi\) | ||||
0.579361 | − | 0.815071i | \(-0.303302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1441.63 | 0.0927091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19354.5 | −1.23869 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 9979.65i | − 0.632614i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 10090.6i | − 0.636612i | −0.947988 | − | 0.318306i | \(-0.896886\pi\) | ||||
0.947988 | − | 0.318306i | \(-0.103114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27453.8 | 1.71570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23741.1 | 1.47670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 155.209i | − 0.00956376i | −0.999989 | − | 0.00478188i | \(-0.998478\pi\) | ||||
0.999989 | − | 0.00478188i | \(-0.00152213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8048.26i | − 0.493612i | −0.969065 | − | 0.246806i | \(-0.920619\pi\) | ||||
0.969065 | − | 0.246806i | \(-0.0793810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17128.5 | −1.04079 | −0.520394 | − | 0.853926i | \(-0.674215\pi\) | ||||
−0.520394 | + | 0.853926i | \(0.674215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15041.2 | −0.909739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5854.10i | 0.350825i | 0.984495 | + | 0.175412i | \(0.0561259\pi\) | ||||
−0.984495 | + | 0.175412i | \(0.943874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 14430.8i | − 0.860853i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22130.6 | −1.30817 | −0.654086 | − | 0.756420i | \(-0.726947\pi\) | ||||
−0.654086 | + | 0.756420i | \(0.726947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19160.0 | −1.12744 | −0.563721 | − | 0.825965i | \(-0.690631\pi\) | ||||
−0.563721 | + | 0.825965i | \(0.690631\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7264.80i | 0.423634i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2906.44i | − 0.168722i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1807.58 | 0.103996 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24302.6 | 1.39197 | 0.695984 | − | 0.718057i | \(-0.254968\pi\) | ||||
0.695984 | + | 0.718057i | \(0.254968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 16656.4i | − 0.945581i | −0.881175 | − | 0.472791i | \(-0.843247\pi\) | ||||
0.881175 | − | 0.472791i | \(-0.156753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 943.255i | − 0.0533120i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24952.6 | −1.39793 | −0.698964 | − | 0.715157i | \(-0.746355\pi\) | ||||
−0.698964 | + | 0.715157i | \(0.746355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17747.0 | −0.989895 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 24819.6i | − 1.37235i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 15536.7i | − 0.855346i | −0.903934 | − | 0.427673i | \(-0.859334\pi\) | ||||
0.903934 | − | 0.427673i | \(-0.140666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10629.9 | 0.580166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16892.0 | −0.917976 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9683.38i | 0.521735i | 0.965375 | + | 0.260868i | \(0.0840086\pi\) | ||||
−0.965375 | + | 0.260868i | \(0.915991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 28698.6i | − 1.53967i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7045.06 | −0.374762 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15665.5 | 0.829801 | 0.414901 | − | 0.909867i | \(-0.363816\pi\) | ||||
0.414901 | + | 0.909867i | \(0.363816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 29127.2i | − 1.52991i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 21695.5i | − 1.13478i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15944.3 | −0.827015 | −0.413507 | − | 0.910501i | \(-0.635696\pi\) | ||||
−0.413507 | + | 0.910501i | \(0.635696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2443.31 | −0.126205 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 722.402i | − 0.0370060i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23773.6i | 1.21281i | 0.795156 | + | 0.606405i | \(0.207389\pi\) | ||||
−0.795156 | + | 0.606405i | \(0.792611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11966.2 | 0.605451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16190.1 | 0.815818 | 0.407909 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407909 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5628.00i | 0.281289i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3013.13i | 0.149986i | 0.997184 | + | 0.0749930i | \(0.0238934\pi\) | ||||
−0.997184 | + | 0.0749930i | \(0.976107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14363.7 | −0.709225 | −0.354613 | − | 0.935013i | \(-0.615387\pi\) | ||||
−0.354613 | + | 0.935013i | \(0.615387\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11606.4 | 0.570775 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4965.96i | − 0.242260i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 21754.9i | − 1.05705i | −0.848917 | − | 0.528526i | \(-0.822745\pi\) | ||||
0.848917 | − | 0.528526i | \(-0.177255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24103.3 | 1.16187 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25070.4 | −1.20370 | −0.601848 | − | 0.798611i | \(-0.705569\pi\) | ||||
−0.601848 | + | 0.798611i | \(0.705569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20326.9i | 0.968263i | 0.874995 | + | 0.484132i | \(0.160864\pi\) | ||||
−0.874995 | + | 0.484132i | \(0.839136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 79.3101i | − 0.00376306i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −49487.3 | −2.32970 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4680.89 | −0.219502 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2385.68i | − 0.111005i | −0.998459 | − | 0.0555025i | \(-0.982324\pi\) | ||||
0.998459 | − | 0.0555025i | \(-0.0176761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 7239.65i | − 0.335556i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48576.6 | −2.23419 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2141.59 | 0.0981206 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45110.6i | 2.05104i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8714.78i | − 0.394725i | −0.980331 | − | 0.197362i | \(-0.936762\pi\) | ||||
0.980331 | − | 0.197362i | \(-0.0632375\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7200.24 | −0.323655 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5947.14 | 0.266317 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15364.9i | 0.682876i | 0.939904 | + | 0.341438i | \(0.110914\pi\) | ||||
−0.939904 | + | 0.341438i | \(0.889086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 22769.2i | − 1.00815i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5619.77 | −0.246971 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11734.2 | −0.513759 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 25153.9i | − 1.09316i | −0.837408 | − | 0.546578i | \(-0.815930\pi\) | ||||
0.837408 | − | 0.546578i | \(-0.184070\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20366.0i | − 0.881807i | −0.897554 | − | 0.440904i | \(-0.854658\pi\) | ||||
0.897554 | − | 0.440904i | \(-0.145342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15716.7 | −0.675501 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34411.3 | 1.47356 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 781.431i | − 0.0332182i | −0.999862 | − | 0.0166091i | \(-0.994713\pi\) | ||||
0.999862 | − | 0.0166091i | \(-0.00528708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32821.3i | 1.39013i | 0.718945 | + | 0.695067i | \(0.244625\pi\) | ||||
−0.718945 | + | 0.695067i | \(0.755375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43717.4 | 1.83821 | 0.919106 | − | 0.394010i | \(-0.128913\pi\) | ||||
0.919106 | + | 0.394010i | \(0.128913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13211.9 | −0.553521 | −0.276761 | − | 0.960939i | \(-0.589261\pi\) | ||||
−0.276761 | + | 0.960939i | \(0.589261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13759.1i | 0.572297i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28030.7i | 1.16173i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33876.0 | 1.39396 | 0.696978 | − | 0.717092i | \(-0.254527\pi\) | ||||
0.696978 | + | 0.717092i | \(0.254527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24173.5 | 0.991162 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 42383.0i | − 1.72547i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3733.70i | − 0.151466i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46354.4 | 1.86722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14748.5 | 0.592005 | 0.296002 | − | 0.955187i | \(-0.404346\pi\) | ||||
0.296002 | + | 0.955187i | \(0.404346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24382.3i | 0.971859i | 0.873998 | + | 0.485929i | \(0.161519\pi\) | ||||
−0.873998 | + | 0.485929i | \(0.838481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21247.2i | − 0.843942i | −0.906609 | − | 0.421971i | \(-0.861338\pi\) | ||||
0.906609 | − | 0.421971i | \(-0.138662\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4434.51 | 0.174916 | 0.0874581 | − | 0.996168i | \(-0.472126\pi\) | ||||
0.0874581 | + | 0.996168i | \(0.472126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23350.0 | −0.917830 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11172.4i | 0.436130i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18516.7i | 0.720339i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4492.69 | 0.173578 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13985.9 | 0.538507 | 0.269253 | − | 0.963069i | \(-0.413223\pi\) | ||||
0.269253 | + | 0.963069i | \(0.413223\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 4428.74i | − 0.169362i | −0.996408 | − | 0.0846812i | \(-0.973013\pi\) | ||||
0.996408 | − | 0.0846812i | \(-0.0269872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 40519.1i | − 1.54426i | −0.635467 | − | 0.772128i | \(-0.719192\pi\) | ||||
0.635467 | − | 0.772128i | \(-0.280808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31161.7 | −1.17960 | −0.589802 | − | 0.807548i | \(-0.700794\pi\) | ||||
−0.589802 | + | 0.807548i | \(0.700794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9341.29 | −0.352415 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 65477.7i | − 2.45367i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 48648.9i | − 1.81693i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2160.14 | −0.0801388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14384.1 | 0.531858 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 32013.5i | − 1.17587i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24021.4i | − 0.879402i | −0.898144 | − | 0.439701i | \(-0.855084\pi\) | ||||
0.898144 | − | 0.439701i | \(-0.144916\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33057.5 | 1.20225 | 0.601123 | − | 0.799157i | \(-0.294720\pi\) | ||||
0.601123 | + | 0.799157i | \(0.294720\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 361.499 | 0.0131039 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4910.16i | 0.176824i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10303.3i | 0.369831i | 0.982754 | + | 0.184915i | \(0.0592011\pi\) | ||||
−0.982754 | + | 0.184915i | \(0.940799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7046.06 | 0.251272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11521.5 | 0.409540 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 7704.91i | − 0.272110i | −0.990701 | − | 0.136055i | \(-0.956558\pi\) | ||||
0.990701 | − | 0.136055i | \(-0.0434424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39567.2i | 1.39287i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12573.5 | 0.439785 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44189.8 | −1.54068 | −0.770340 | − | 0.637633i | \(-0.779914\pi\) | ||||
−0.770340 | + | 0.637633i | \(0.779914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51448.1i | 1.78232i | 0.453691 | + | 0.891159i | \(0.350107\pi\) | ||||
−0.453691 | + | 0.891159i | \(0.649893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 78461.5i | − 2.70950i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17691.3 | −0.607066 | −0.303533 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303533 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18489.6 | −0.632454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 27331.2i | − 0.929007i | −0.885571 | − | 0.464504i | \(-0.846233\pi\) | ||||
0.885571 | − | 0.464504i | \(-0.153767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18050.5i | − 0.611624i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6038.51 | 0.203330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8142.84 | 0.273332 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16370.6i | 0.546101i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 48045.3i | − 1.59776i | −0.601492 | − | 0.798879i | \(-0.705427\pi\) | ||||
0.601492 | − | 0.798879i | \(-0.294573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6999.70 | −0.231340 | −0.115670 | − | 0.993288i | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3616.88 | −0.119169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42914.1i | 1.40527i | 0.711552 | + | 0.702633i | \(0.247992\pi\) | ||||
−0.711552 | + | 0.702633i | \(0.752008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7175.22i | − 0.234240i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1615.78 | −0.0524266 | −0.0262133 | − | 0.999656i | \(-0.508345\pi\) | ||||
−0.0262133 | + | 0.999656i | \(0.508345\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38138.3 | −1.23369 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55581.6i | 1.78705i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15725.6i | 0.504076i | 0.967717 | + | 0.252038i | \(0.0811008\pi\) | ||||
−0.967717 | + | 0.252038i | \(0.918899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24437.7 | 0.778620 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22555.5 | 0.716489 | 0.358244 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358244 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(998\) | 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 | 1728.4.c.i.1727.4 | 12 | ||
3.2 | odd | 2 | inner | 1728.4.c.i.1727.10 | 12 | ||
4.3 | odd | 2 | inner | 1728.4.c.i.1727.3 | 12 | ||
8.3 | odd | 2 | 108.4.b.a.107.10 | yes | 12 | ||
8.5 | even | 2 | 108.4.b.a.107.4 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.4.c.i.1727.9 | 12 | ||
24.5 | odd | 2 | 108.4.b.a.107.9 | yes | 12 | ||
24.11 | even | 2 | 108.4.b.a.107.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.a.107.3 | ✓ | 12 | 24.11 | even | 2 | ||
108.4.b.a.107.4 | yes | 12 | 8.5 | even | 2 | ||
108.4.b.a.107.9 | yes | 12 | 24.5 | odd | 2 | ||
108.4.b.a.107.10 | yes | 12 | 8.3 | odd | 2 | ||
1728.4.c.i.1727.3 | 12 | 4.3 | odd | 2 | inner | ||
1728.4.c.i.1727.4 | 12 | 1.1 | even | 1 | trivial | ||
1728.4.c.i.1727.9 | 12 | 12.11 | even | 2 | inner | ||
1728.4.c.i.1727.10 | 12 | 3.2 | odd | 2 | inner |