Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
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: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.239575536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.54431\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.54431 | −1.46896 | −0.734478 | − | 0.678633i | \(-0.762573\pi\) | ||||
−0.734478 | + | 0.678633i | \(0.762573\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.47349 | 1.15783 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.91228 | −1.17960 | −0.589799 | − | 0.807550i | \(-0.700793\pi\) | ||||
−0.589799 | + | 0.807550i | \(0.700793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47349 | 0.963373 | 0.481687 | − | 0.876344i | \(-0.340024\pi\) | ||||
0.481687 | + | 0.876344i | \(0.340024\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.08262 | −1.23272 | −0.616358 | − | 0.787466i | \(-0.711393\pi\) | ||||
−0.616358 | + | 0.787466i | \(0.711393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.25188 | −1.20486 | −0.602432 | − | 0.798170i | \(-0.705802\pi\) | ||||
−0.602432 | + | 0.798170i | \(0.705802\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.01780 | −1.25480 | −0.627399 | − | 0.778698i | \(-0.715880\pi\) | ||||
−0.627399 | + | 0.778698i | \(0.715880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.20471 | −0.231846 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2660 | −1.90635 | −0.953175 | − | 0.302419i | \(-0.902206\pi\) | ||||
−0.953175 | + | 0.302419i | \(0.902206\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04350 | 0.367024 | 0.183512 | − | 0.983017i | \(-0.441253\pi\) | ||||
0.183512 | + | 0.983017i | \(0.441253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.95405 | 1.73278 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.405001 | 0.0665818 | 0.0332909 | − | 0.999446i | \(-0.489401\pi\) | ||||
0.0332909 | + | 0.999446i | \(0.489401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.83763 | −1.41515 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.57534 | −0.402200 | −0.201100 | − | 0.979571i | \(-0.564452\pi\) | ||||
−0.201100 | + | 0.979571i | \(0.564452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.15769 | −0.939038 | −0.469519 | − | 0.882922i | \(-0.655573\pi\) | ||||
−0.469519 | + | 0.882922i | \(0.655573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.480556 | −0.0700963 | −0.0350481 | − | 0.999386i | \(-0.511158\pi\) | ||||
−0.0350481 | + | 0.999386i | \(0.511158\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9317 | 1.81081 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.466428 | 0.0640688 | 0.0320344 | − | 0.999487i | \(-0.489801\pi\) | ||||
0.0320344 | + | 0.999487i | \(0.489801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.3624 | 1.76989 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3113 | −1.34242 | −0.671208 | − | 0.741269i | \(-0.734224\pi\) | ||||
−0.671208 | + | 0.741269i | \(0.734224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.08088 | 1.03465 | 0.517325 | − | 0.855789i | \(-0.326928\pi\) | ||||
0.517325 | + | 0.855789i | \(0.326928\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.15169 | 0.507210 | 0.253605 | − | 0.967308i | \(-0.418384\pi\) | ||||
0.253605 | + | 0.967308i | \(0.418384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.3111 | 1.84324 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.28658 | −0.508724 | −0.254362 | − | 0.967109i | \(-0.581865\pi\) | ||||
−0.254362 | + | 0.967109i | \(0.581865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.81483 | 0.563533 | 0.281767 | − | 0.959483i | \(-0.409080\pi\) | ||||
0.281767 | + | 0.959483i | \(0.409080\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6639 | −1.42481 | −0.712403 | − | 0.701771i | \(-0.752393\pi\) | ||||
−0.712403 | + | 0.701771i | \(0.752393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.35533 | −0.817259 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.42280 | 0.924522 | 0.462261 | − | 0.886744i | \(-0.347038\pi\) | ||||
0.462261 | + | 0.886744i | \(0.347038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.1199 | 2.80034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.38595 | 0.252910 | 0.126455 | − | 0.991972i | \(-0.459640\pi\) | ||||
0.126455 | + | 0.991972i | \(0.459640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19930 | −0.539142 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.32080 | 0.134107 | 0.0670537 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670537 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5893 | −1.36577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.75166 | 0.771319 | 0.385660 | − | 0.922641i | \(-0.373974\pi\) | ||||
0.385660 | + | 0.922641i | \(0.373974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.20364 | 0.217131 | 0.108565 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108565 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8235 | −1.04635 | −0.523176 | − | 0.852225i | \(-0.675253\pi\) | ||||
−0.523176 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0433 | −1.05776 | −0.528880 | − | 0.848697i | \(-0.677388\pi\) | ||||
−0.528880 | + | 0.848697i | \(0.677388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03045 | −0.0978057 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.29167 | 0.685942 | 0.342971 | − | 0.939346i | \(-0.388567\pi\) | ||||
0.342971 | + | 0.939346i | \(0.388567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0651 | 1.11542 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.30597 | 0.391452 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.55244 | 0.590814 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.66305 | 0.679986 | 0.339993 | − | 0.940428i | \(-0.389575\pi\) | ||||
0.339993 | + | 0.940428i | \(0.389575\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.6670 | 1.37941 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.2119 | −1.50381 | −0.751906 | − | 0.659270i | \(-0.770865\pi\) | ||||
−0.751906 | + | 0.659270i | \(0.770865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.26072 | −0.449454 | −0.224727 | − | 0.974422i | \(-0.572149\pi\) | ||||
−0.224727 | + | 0.974422i | \(0.572149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2148 | −1.29050 | −0.645250 | − | 0.763971i | \(-0.723247\pi\) | ||||
−0.645250 | + | 0.763971i | \(0.723247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22268 | 0.102968 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.5893 | −1.13639 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.01721 | −0.0833335 | −0.0416667 | − | 0.999132i | \(-0.513267\pi\) | ||||
−0.0416667 | + | 0.999132i | \(0.513267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2583 | 1.07894 | 0.539472 | − | 0.842004i | \(-0.318624\pi\) | ||||
0.539472 | + | 0.842004i | \(0.318624\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.6544 | −1.42728 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.7722 | 1.41838 | 0.709189 | − | 0.705019i | \(-0.249061\pi\) | ||||
0.709189 | + | 0.705019i | \(0.249061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.18674 | −0.0941143 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.91952 | 0.228675 | 0.114337 | − | 0.993442i | \(-0.463526\pi\) | ||||
0.114337 | + | 0.993442i | \(0.463526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.21710 | −0.713240 | −0.356620 | − | 0.934249i | \(-0.616071\pi\) | ||||
−0.356620 | + | 0.934249i | \(0.616071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.934854 | −0.0719118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2424 | −1.39503 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.6803 | −1.64832 | −0.824162 | − | 0.566354i | \(-0.808353\pi\) | ||||
−0.824162 | + | 0.566354i | \(0.808353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.2351 | 1.97195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.9965 | −1.86833 | −0.934164 | − | 0.356843i | \(-0.883853\pi\) | ||||
−0.934164 | + | 0.356843i | \(0.883853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.17900 | −0.310623 | −0.155311 | − | 0.987866i | \(-0.549638\pi\) | ||||
−0.155311 | + | 0.987866i | \(0.549638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5602 | −1.51986 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.8846 | 1.45411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.97169 | −0.649169 | −0.324585 | − | 0.945857i | \(-0.605224\pi\) | ||||
−0.324585 | + | 0.945857i | \(0.605224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.2218 | −1.31164 | −0.655818 | − | 0.754919i | \(-0.727676\pi\) | ||||
−0.655818 | + | 0.754919i | \(0.727676\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.5632 | 1.67881 | 0.839403 | − | 0.543509i | \(-0.182905\pi\) | ||||
0.839403 | + | 0.543509i | \(0.182905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7163 | 1.46854 | 0.734271 | − | 0.678856i | \(-0.237524\pi\) | ||||
0.734271 | + | 0.678856i | \(0.237524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5632 | −0.745069 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.9028 | −1.45284 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.5469 | 1.42126 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.69865 | 0.529997 | 0.264998 | − | 0.964249i | \(-0.414629\pi\) | ||||
0.264998 | + | 0.964249i | \(0.414629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.9064 | 0.747292 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.2504 | −0.827805 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.6544 | −1.18757 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7136 | 0.851366 | 0.425683 | − | 0.904872i | \(-0.360034\pi\) | ||||
0.425683 | + | 0.904872i | \(0.360034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7229 | −0.711706 | −0.355853 | − | 0.934542i | \(-0.615810\pi\) | ||||
−0.355853 | + | 0.934542i | \(0.615810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.7892 | −1.63812 | −0.819059 | − | 0.573709i | \(-0.805504\pi\) | ||||
−0.819059 | + | 0.573709i | \(0.805504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.7544 | 1.49069 | 0.745345 | − | 0.666679i | \(-0.232285\pi\) | ||||
0.745345 | + | 0.666679i | \(0.232285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.2210 | 2.09298 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.49071 | −0.0964258 | −0.0482129 | − | 0.998837i | \(-0.515353\pi\) | ||||
−0.0482129 | + | 0.998837i | \(0.515353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.1677 | 1.68561 | 0.842806 | − | 0.538217i | \(-0.180902\pi\) | ||||
0.842806 | + | 0.538217i | \(0.180902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3283 | 1.43236 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2424 | −1.16073 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.4302 | −1.35808 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.90277 | 0.309460 | 0.154730 | − | 0.987957i | \(-0.450549\pi\) | ||||
0.154730 | + | 0.987957i | \(0.450549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.5433 | 1.48016 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3399 | 0.769739 | 0.384870 | − | 0.922971i | \(-0.374246\pi\) | ||||
0.384870 | + | 0.922971i | \(0.374246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −35.6589 | −2.20723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.1247 | −1.24094 | −0.620471 | − | 0.784229i | \(-0.713059\pi\) | ||||
−0.620471 | + | 0.784229i | \(0.713059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.07059 | −0.371514 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.9394 | −0.910874 | −0.455437 | − | 0.890268i | \(-0.650517\pi\) | ||||
−0.455437 | + | 0.890268i | \(0.650517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.80932 | −0.352891 | −0.176446 | − | 0.984310i | \(-0.556460\pi\) | ||||
−0.176446 | + | 0.984310i | \(0.556460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.9390 | −1.55853 | −0.779263 | − | 0.626697i | \(-0.784406\pi\) | ||||
−0.779263 | + | 0.626697i | \(0.784406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.09809 | 0.424952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8840 | −0.887904 | −0.443952 | − | 0.896051i | \(-0.646424\pi\) | ||||
−0.443952 | + | 0.896051i | \(0.646424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.71540 | 0.577520 | 0.288760 | − | 0.957401i | \(-0.406757\pi\) | ||||
0.288760 | + | 0.957401i | \(0.406757\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.83301 | 0.519589 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.36053 | −0.196998 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.08596 | −0.472387 | −0.236194 | − | 0.971706i | \(-0.575900\pi\) | ||||
−0.236194 | + | 0.971706i | \(0.575900\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.71316 | 0.273485 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.9028 | −1.20884 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.7226 | −1.13303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.81809 | 0.503275 | 0.251637 | − | 0.967822i | \(-0.419031\pi\) | ||||
0.251637 | + | 0.967822i | \(0.419031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.60673 | −0.318956 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.66439 | 0.548017 | 0.274009 | − | 0.961727i | \(-0.411650\pi\) | ||||
0.274009 | + | 0.961727i | \(0.411650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.1864 | 1.53667 | 0.768334 | − | 0.640049i | \(-0.221086\pi\) | ||||
0.768334 | + | 0.640049i | \(0.221086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1583 | −0.682876 | −0.341438 | − | 0.939904i | \(-0.610914\pi\) | ||||
−0.341438 | + | 0.939904i | \(0.610914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.1635 | 2.24873 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.5384 | 1.53704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.6933 | 1.48526 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.0976 | 1.55380 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42945 | −0.188500 | −0.0942499 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942499 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.40677 | 0.0770904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.39770 | 0.0761375 | 0.0380687 | − | 0.999275i | \(-0.487879\pi\) | ||||
0.0380687 | + | 0.999275i | \(0.487879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.5522 | −1.00762 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.99477 | −0.432941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.46302 | −0.185904 | −0.0929522 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929522 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2360 | −1.02968 | −0.514838 | − | 0.857287i | \(-0.672148\pi\) | ||||
−0.514838 | + | 0.857287i | \(0.672148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.18454 | −0.223354 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.2651 | 0.918931 | 0.459465 | − | 0.888196i | \(-0.348041\pi\) | ||||
0.459465 | + | 0.888196i | \(0.348041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.867633 | 0.0457919 | 0.0228960 | − | 0.999738i | \(-0.492711\pi\) | ||||
0.0228960 | + | 0.999738i | \(0.492711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.58226 | 0.451698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9557 | −0.575025 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4984 | −0.861210 | −0.430605 | − | 0.902541i | \(-0.641700\pi\) | ||||
−0.430605 | + | 0.902541i | \(0.641700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.94541 | −0.465679 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3871 | −1.05560 | −0.527801 | − | 0.849368i | \(-0.676983\pi\) | ||||
−0.527801 | + | 0.849368i | \(0.676983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −35.6589 | −1.83653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1652 | 0.676251 | 0.338126 | − | 0.941101i | \(-0.390207\pi\) | ||||
0.338126 | + | 0.941101i | \(0.390207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4971 | −0.998869 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.19162 | 0.265280 | 0.132640 | − | 0.991164i | \(-0.457655\pi\) | ||||
0.132640 | + | 0.991164i | \(0.457655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.3887 | −1.08725 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.1419 | 1.57896 | 0.789478 | − | 0.613779i | \(-0.210351\pi\) | ||||
0.789478 | + | 0.613779i | \(0.210351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.5862 | 1.54681 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 43.7924 | 2.20903 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1065 | −0.758174 | −0.379087 | − | 0.925361i | \(-0.623762\pi\) | ||||
−0.379087 | + | 0.925361i | \(0.623762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2471 | 0.811340 | 0.405670 | − | 0.914020i | \(-0.367038\pi\) | ||||
0.405670 | + | 0.914020i | \(0.367038\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.09809 | 0.353581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.58448 | −0.0785397 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3206 | 1.64760 | 0.823798 | − | 0.566883i | \(-0.191851\pi\) | ||||
0.823798 | + | 0.566883i | \(0.191851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3849 | 0.660228 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.7110 | 1.89569 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3290 | 0.553457 | 0.276729 | − | 0.960948i | \(-0.410750\pi\) | ||||
0.276729 | + | 0.960948i | \(0.410750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5047 | 0.609440 | 0.304720 | − | 0.952442i | \(-0.401437\pi\) | ||||
0.304720 | + | 0.952442i | \(0.401437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.66921 | −0.0811596 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.5753 | 1.66931 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.14713 | −0.247928 | −0.123964 | − | 0.992287i | \(-0.539561\pi\) | ||||
−0.123964 | + | 0.992287i | \(0.539561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.88420 | 0.0905491 | 0.0452745 | − | 0.998975i | \(-0.485584\pi\) | ||||
0.0452745 | + | 0.998975i | \(0.485584\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.6048 | 1.51186 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5904 | 0.505454 | 0.252727 | − | 0.967538i | \(-0.418673\pi\) | ||||
0.252727 | + | 0.967538i | \(0.418673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3510 | 1.15695 | 0.578476 | − | 0.815700i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815700i | \(0.303648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.58811 | 0.122413 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.2506 | 0.955684 | 0.477842 | − | 0.878446i | \(-0.341419\pi\) | ||||
0.477842 | + | 0.878446i | \(0.341419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0754 | 0.474434 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.7331 | −1.58492 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.1864 | −0.897503 | −0.448752 | − | 0.893657i | \(-0.648131\pi\) | ||||
−0.448752 | + | 0.893657i | \(0.648131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.12307 | 0.285801 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.4096 | −0.624548 | −0.312274 | − | 0.949992i | \(-0.601091\pi\) | ||||
−0.312274 | + | 0.949992i | \(0.601091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7864 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2100 | 0.703835 | 0.351918 | − | 0.936031i | \(-0.385530\pi\) | ||||
0.351918 | + | 0.936031i | \(0.385530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −45.2180 | −2.08353 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0906 | 1.10769 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.62013 | 0.0741809 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5684 | −0.574266 | −0.287133 | − | 0.957891i | \(-0.592702\pi\) | ||||
−0.287133 | + | 0.957891i | \(0.592702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.40677 | 0.0641431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7901 | 0.624888 | 0.312444 | − | 0.949936i | \(-0.398852\pi\) | ||||
0.312444 | + | 0.949936i | \(0.398852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.42816 | −0.335913 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4423 | 1.23845 | 0.619226 | − | 0.785213i | \(-0.287447\pi\) | ||||
0.619226 | + | 0.785213i | \(0.287447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.1782 | 2.34999 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7379 | −0.883590 | −0.441795 | − | 0.897116i | \(-0.645658\pi\) | ||||
−0.441795 | + | 0.897116i | \(0.645658\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.4511 | 1.04772 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.00417 | 0.223125 | 0.111562 | − | 0.993757i | \(-0.464415\pi\) | ||||
0.111562 | + | 0.993757i | \(0.464415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.37855 | 0.105635 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.7592 | 1.00878 | 0.504392 | − | 0.863475i | \(-0.331717\pi\) | ||||
0.504392 | + | 0.863475i | \(0.331717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.32699 | 0.279343 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.88007 | 0.0826854 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.1614 | 2.42131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5371 | −0.768315 | −0.384158 | − | 0.923267i | \(-0.625508\pi\) | ||||
−0.384158 | + | 0.923267i | \(0.625508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7901 | −0.602998 | −0.301499 | − | 0.953467i | \(-0.597487\pi\) | ||||
−0.301499 | + | 0.953467i | \(0.597487\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3863 | −0.452436 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.2139 | 0.574517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.8162 | −1.55429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.94541 | −0.387469 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 63.5988 | 2.74449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 46.0001 | 1.97770 | 0.988849 | − | 0.148922i | \(-0.0475805\pi\) | ||||
0.988849 | + | 0.148922i | \(0.0475805\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.6327 | 0.456291 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4411 | 1.13054 | 0.565270 | − | 0.824906i | \(-0.308772\pi\) | ||||
0.565270 | + | 0.824906i | \(0.308772\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 28.0689 | 1.19795 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.9159 | 2.29689 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.7219 | −1.34410 | −0.672050 | − | 0.740506i | \(-0.734586\pi\) | ||||
−0.672050 | + | 0.740506i | \(0.734586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.3887 | −0.904644 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.5926 | −2.13602 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7249 | −0.873448 | −0.436724 | − | 0.899595i | \(-0.643861\pi\) | ||||
−0.436724 | + | 0.899595i | \(0.643861\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.5454 | 1.78360 | 0.891799 | − | 0.452432i | \(-0.149444\pi\) | ||||
0.891799 | + | 0.452432i | \(0.149444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1062 | 1.25990 | 0.629952 | − | 0.776634i | \(-0.283074\pi\) | ||||
0.629952 | + | 0.776634i | \(0.283074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8267 | 0.953601 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2683 | −0.427473 | −0.213736 | − | 0.976891i | \(-0.568563\pi\) | ||||
−0.213736 | + | 0.976891i | \(0.568563\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.3619 | 1.92674 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.82480 | −0.0755755 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.5546 | 1.71514 | 0.857570 | − | 0.514367i | \(-0.171973\pi\) | ||||
0.857570 | + | 0.514367i | \(0.171973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7322 | −0.442214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −59.9519 | −2.46609 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.9303 | 0.982698 | 0.491349 | − | 0.870963i | \(-0.336504\pi\) | ||||
0.491349 | + | 0.870963i | \(0.336504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −52.7087 | −2.15722 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.08267 | 0.371108 | 0.185554 | − | 0.982634i | \(-0.440592\pi\) | ||||
0.185554 | + | 0.982634i | \(0.440592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8162 | −1.21623 | −0.608114 | − | 0.793850i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793850i | \(0.708074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4209 | 0.587263 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5480 | 0.590486 | 0.295243 | − | 0.955422i | \(-0.404599\pi\) | ||||
0.295243 | + | 0.955422i | \(0.404599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.66921 | −0.0675289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3228 | 0.416934 | 0.208467 | − | 0.978029i | \(-0.433153\pi\) | ||||
0.208467 | + | 0.978029i | \(0.433153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0906 | 0.527008 | 0.263504 | − | 0.964658i | \(-0.415122\pi\) | ||||
0.263504 | + | 0.964658i | \(0.415122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5588 | −1.30865 | −0.654325 | − | 0.756213i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756213i | \(0.727047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.24969 | 0.290920 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −52.2775 | −2.08776 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.05847 | −0.0820764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2537 | −0.527620 | −0.263810 | − | 0.964575i | \(-0.584979\pi\) | ||||
−0.263810 | + | 0.964575i | \(0.584979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.5877 | −0.778542 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.8894 | −0.589016 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.703073 | 0.0277697 | 0.0138848 | − | 0.999904i | \(-0.495580\pi\) | ||||
0.0138848 | + | 0.999904i | \(0.495580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.64163 | 0.183048 | 0.0915240 | − | 0.995803i | \(-0.470826\pi\) | ||||
0.0915240 | + | 0.995803i | \(0.470826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0354 | 0.473161 | 0.236580 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236580 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.3407 | 1.58351 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2464 | 0.714036 | 0.357018 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357018 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.7243 | 0.652476 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.4231 | 1.14616 | 0.573081 | − | 0.819499i | \(-0.305748\pi\) | ||||
0.573081 | + | 0.819499i | \(0.305748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2957 | −0.672723 | −0.336361 | − | 0.941733i | \(-0.609196\pi\) | ||||
−0.336361 | + | 0.941733i | \(0.609196\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.9183 | 1.74448 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 61.7788 | 2.39208 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.3473 | −1.25062 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.6147 | −1.22047 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.7525 | −1.10833 | −0.554164 | − | 0.832407i | \(-0.686962\pi\) | ||||
−0.554164 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.48594 | −0.210842 | −0.105421 | − | 0.994428i | \(-0.533619\pi\) | ||||
−0.105421 | + | 0.994428i | \(0.533619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2824 | 1.04546 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.3768 | −0.435319 | −0.217660 | − | 0.976025i | \(-0.569842\pi\) | ||||
−0.217660 | + | 0.976025i | \(0.569842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 63.0714 | 2.40632 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.62013 | 0.0617222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.3261 | −1.72429 | −0.862144 | − | 0.506664i | \(-0.830879\pi\) | ||||
−0.862144 | + | 0.506664i | \(0.830879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0894 | 0.495798 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −57.8941 | −2.18976 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.87634 | 0.184177 | 0.0920884 | − | 0.995751i | \(-0.470646\pi\) | ||||
0.0920884 | + | 0.995751i | \(0.470646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.12702 | −0.0802220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.8887 | −0.934713 | −0.467357 | − | 0.884069i | \(-0.654794\pi\) | ||||
−0.467357 | + | 0.884069i | \(0.654794\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.9881 | −1.64968 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.2974 | −0.460541 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.79281 | 0.141645 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.43573 | −0.202719 | −0.101359 | − | 0.994850i | \(-0.532319\pi\) | ||||
−0.101359 | + | 0.994850i | \(0.532319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −66.5787 | −2.47609 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.1112 | 0.634621 | 0.317310 | − | 0.948322i | \(-0.397220\pi\) | ||||
0.317310 | + | 0.948322i | \(0.397220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.7441 | −1.28682 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.2972 | 1.15757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.85744 | 0.290221 | 0.145111 | − | 0.989415i | \(-0.453646\pi\) | ||||
0.145111 | + | 0.989415i | \(0.453646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.2426 | −0.598304 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.0109 | 1.87647 | 0.938234 | − | 0.346002i | \(-0.112461\pi\) | ||||
0.938234 | + | 0.346002i | \(0.112461\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 46.4142 | 1.70507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.82733 | 0.250470 | 0.125235 | − | 0.992127i | \(-0.460031\pi\) | ||||
0.125235 | + | 0.992127i | \(0.460031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29.2565 | 1.07044 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.3570 | 1.18072 | 0.590361 | − | 0.807139i | \(-0.298985\pi\) | ||||
0.590361 | + | 0.807139i | \(0.298985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.4742 | −0.454583 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1180 | −1.05831 | −0.529156 | − | 0.848524i | \(-0.677491\pi\) | ||||
−0.529156 | + | 0.848524i | \(0.677491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −59.9014 | −2.17428 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.1730 | 1.02127 | 0.510636 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510636 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.8162 | −1.29325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.5017 | 0.595065 | 0.297532 | − | 0.954712i | \(-0.403836\pi\) | ||||
0.297532 | + | 0.954712i | \(0.403836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3964 | −1.13071 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.4891 | −0.665005 | −0.332503 | − | 0.943102i | \(-0.607893\pi\) | ||||
−0.332503 | + | 0.943102i | \(0.607893\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.5254 | 0.484596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7703 | 0.600089 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.3675 | 0.441980 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7443 | 0.561224 | 0.280612 | − | 0.959821i | \(-0.409463\pi\) | ||||
0.280612 | + | 0.959821i | \(0.409463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.2034 | 1.82289 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.0689 | 0.996755 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.9307 | −1.06020 | −0.530100 | − | 0.847935i | \(-0.677846\pi\) | ||||
−0.530100 | + | 0.847935i | \(0.677846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.44248 | 0.0864088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.28758 | 0.292827 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.8370 | −0.664743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.0105 | 1.33803 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.16658 | 0.181647 | 0.0908236 | − | 0.995867i | \(-0.471050\pi\) | ||||
0.0908236 | + | 0.995867i | \(0.471050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.4698 | −1.35086 | −0.675430 | − | 0.737425i | \(-0.736042\pi\) | ||||
−0.675430 | + | 0.737425i | \(0.736042\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7807 | 0.518381 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.3394 | 1.13141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.69551 | −0.128974 | −0.0644872 | − | 0.997919i | \(-0.520541\pi\) | ||||
−0.0644872 | + | 0.997919i | \(0.520541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.4030 | −1.47807 | −0.739037 | − | 0.673665i | \(-0.764719\pi\) | ||||
−0.739037 | + | 0.673665i | \(0.764719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.0950 | −1.39424 | −0.697120 | − | 0.716954i | \(-0.745536\pi\) | ||||
−0.697120 | + | 0.716954i | \(0.745536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.8264 | 1.86947 | 0.934734 | − | 0.355347i | \(-0.115637\pi\) | ||||
0.934734 | + | 0.355347i | \(0.115637\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 65.9968 | 2.28941 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.46183 | −0.0850931 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1002 | −0.866556 | −0.433278 | − | 0.901260i | \(-0.642643\pi\) | ||||
−0.433278 | + | 0.901260i | \(0.642643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.3910 | 2.63417 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.8694 | 1.30429 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.7189 | −0.848352 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.43721 | −0.0835466 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7320 | 0.915286 | 0.457643 | − | 0.889136i | \(-0.348694\pi\) | ||||
0.457643 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.5891 | 1.59145 | 0.795726 | − | 0.605657i | \(-0.207089\pi\) | ||||
0.795726 | + | 0.605657i | \(0.207089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6535 | −0.636448 | −0.318224 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318224 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.8239 | −0.606733 | −0.303367 | − | 0.952874i | \(-0.598111\pi\) | ||||
−0.303367 | + | 0.952874i | \(0.598111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.4739 | −0.763253 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.5450 | 1.68070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.4209 | 0.488633 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.58781 | 0.155274 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7793 | 0.904273 | 0.452136 | − | 0.891949i | \(-0.350662\pi\) | ||||
0.452136 | + | 0.891949i | \(0.350662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.5732 | 0.693916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5843 | 0.592429 | 0.296215 | − | 0.955121i | \(-0.404276\pi\) | ||||
0.296215 | + | 0.955121i | \(0.404276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.9638 | −0.638182 | −0.319091 | − | 0.947724i | \(-0.603378\pi\) | ||||
−0.319091 | + | 0.947724i | \(0.603378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.1654 | −0.374897 | −0.187448 | − | 0.982274i | \(-0.560022\pi\) | ||||
−0.187448 | + | 0.982274i | \(0.560022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.7761 | 0.964037 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.52382 | 0.0844565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 53.1830 | 1.77573 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.9786 | −0.699676 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.37068 | −0.0789787 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1647 | 1.26724 | 0.633619 | − | 0.773645i | \(-0.281569\pi\) | ||||
0.633619 | + | 0.773645i | \(0.281569\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.9253 | 0.893057 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0251 | 1.55801 | 0.779006 | − | 0.627016i | \(-0.215724\pi\) | ||||
0.779006 | + | 0.627016i | \(0.215724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.9524 | −1.09056 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3879 | 0.837469 | 0.418734 | − | 0.908109i | \(-0.362474\pi\) | ||||
0.418734 | + | 0.908109i | \(0.362474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.4359 | −0.739288 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.8894 | −0.490091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.65432 | 0.251401 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.64709 | 0.250893 | 0.125446 | − | 0.992100i | \(-0.459964\pi\) | ||||
0.125446 | + | 0.992100i | \(0.459964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.5892 | −0.805013 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.40923 | 0.0460375 | 0.0230188 | − | 0.999735i | \(-0.492672\pi\) | ||||
0.0230188 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −69.1706 | −2.25730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.4101 | 1.70852 | 0.854260 | − | 0.519845i | \(-0.174010\pi\) | ||||
0.854260 | + | 0.519845i | \(0.174010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.4978 | 0.504679 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.7229 | −1.06335 | −0.531675 | − | 0.846948i | \(-0.678437\pi\) | ||||
−0.531675 | + | 0.846948i | \(0.678437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.7243 | 0.542893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.9344 | 1.00312 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7747 | −1.35322 | −0.676608 | − | 0.736344i | \(-0.736551\pi\) | ||||
−0.676608 | + | 0.736344i | \(0.736551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −102.188 | −3.30328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8241 | −0.865293 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.5955 | −1.21150 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.47375 | −0.208182 | −0.104091 | − | 0.994568i | \(-0.533193\pi\) | ||||
−0.104091 | + | 0.994568i | \(0.533193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −67.9159 | −2.18177 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.1743 | −1.06462 | −0.532308 | − | 0.846551i | \(-0.678675\pi\) | ||||
−0.532308 | + | 0.846551i | \(0.678675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.0711 | 1.28199 | 0.640994 | − | 0.767546i | \(-0.278522\pi\) | ||||
0.640994 | + | 0.767546i | \(0.278522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.33452 | −0.298333 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.3589 | −1.22471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.852116 | 0.0271783 | 0.0135891 | − | 0.999908i | \(-0.495674\pi\) | ||||
0.0135891 | + | 0.999908i | \(0.495674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.0557 | 1.17830 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.02760 | −0.159707 | −0.0798535 | − | 0.996807i | \(-0.525445\pi\) | ||||
−0.0798535 | + | 0.996807i | \(0.525445\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.72558 | 0.276898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.0291 | 0.856021 | 0.428011 | − | 0.903774i | \(-0.359215\pi\) | ||||
0.428011 | + | 0.903774i | \(0.359215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.487908 | −0.0154367 |
(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 | 9800.2.a.cx.1.1 | 6 | ||
5.2 | odd | 4 | 1960.2.g.f.1569.11 | 12 | |||
5.3 | odd | 4 | 1960.2.g.f.1569.2 | 12 | |||
5.4 | even | 2 | 9800.2.a.cv.1.6 | 6 | |||
7.2 | even | 3 | 1400.2.q.n.1201.6 | 12 | |||
7.4 | even | 3 | 1400.2.q.n.401.6 | 12 | |||
7.6 | odd | 2 | 9800.2.a.cw.1.6 | 6 | |||
35.2 | odd | 12 | 280.2.bg.a.249.2 | yes | 24 | ||
35.4 | even | 6 | 1400.2.q.o.401.1 | 12 | |||
35.9 | even | 6 | 1400.2.q.o.1201.1 | 12 | |||
35.13 | even | 4 | 1960.2.g.e.1569.11 | 12 | |||
35.18 | odd | 12 | 280.2.bg.a.9.2 | ✓ | 24 | ||
35.23 | odd | 12 | 280.2.bg.a.249.11 | yes | 24 | ||
35.27 | even | 4 | 1960.2.g.e.1569.2 | 12 | |||
35.32 | odd | 12 | 280.2.bg.a.9.11 | yes | 24 | ||
35.34 | odd | 2 | 9800.2.a.cy.1.1 | 6 | |||
140.23 | even | 12 | 560.2.bw.f.529.2 | 24 | |||
140.67 | even | 12 | 560.2.bw.f.289.2 | 24 | |||
140.107 | even | 12 | 560.2.bw.f.529.11 | 24 | |||
140.123 | even | 12 | 560.2.bw.f.289.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.2 | ✓ | 24 | 35.18 | odd | 12 | ||
280.2.bg.a.9.11 | yes | 24 | 35.32 | odd | 12 | ||
280.2.bg.a.249.2 | yes | 24 | 35.2 | odd | 12 | ||
280.2.bg.a.249.11 | yes | 24 | 35.23 | odd | 12 | ||
560.2.bw.f.289.2 | 24 | 140.67 | even | 12 | |||
560.2.bw.f.289.11 | 24 | 140.123 | even | 12 | |||
560.2.bw.f.529.2 | 24 | 140.23 | even | 12 | |||
560.2.bw.f.529.11 | 24 | 140.107 | even | 12 | |||
1400.2.q.n.401.6 | 12 | 7.4 | even | 3 | |||
1400.2.q.n.1201.6 | 12 | 7.2 | even | 3 | |||
1400.2.q.o.401.1 | 12 | 35.4 | even | 6 | |||
1400.2.q.o.1201.1 | 12 | 35.9 | even | 6 | |||
1960.2.g.e.1569.2 | 12 | 35.27 | even | 4 | |||
1960.2.g.e.1569.11 | 12 | 35.13 | even | 4 | |||
1960.2.g.f.1569.2 | 12 | 5.3 | odd | 4 | |||
1960.2.g.f.1569.11 | 12 | 5.2 | odd | 4 | |||
9800.2.a.cv.1.6 | 6 | 5.4 | even | 2 | |||
9800.2.a.cw.1.6 | 6 | 7.6 | odd | 2 | |||
9800.2.a.cx.1.1 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cy.1.1 | 6 | 35.34 | odd | 2 |