Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5472,2,Mod(2431,5472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5472, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5472.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5472.k (of order \(2\), degree \(1\), 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: | \(43.6941399860\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 52 x^{18} + 986 x^{16} + 8824 x^{14} + 42757 x^{12} + 118964 x^{10} + 190576 x^{8} + 166880 x^{6} + \cdots + 784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{27} \) |
Twist minimal: | no (minimal twist has level 1824) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.13 | ||
Root | \(1.52988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5472.2431 |
Dual form | 5472.2.k.a.2431.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5472\mathbb{Z}\right)^\times\).
\(n\) | \(1217\) | \(2053\) | \(3745\) | \(4447\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.49782 | 0.669844 | 0.334922 | − | 0.942246i | \(-0.391290\pi\) | ||||
0.334922 | + | 0.942246i | \(0.391290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.665758i | − | 0.251633i | −0.992054 | − | 0.125816i | \(-0.959845\pi\) | ||
0.992054 | − | 0.125816i | \(-0.0401550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.592107i | − | 0.178527i | −0.996008 | − | 0.0892635i | \(-0.971549\pi\) | ||
0.996008 | − | 0.0892635i | \(-0.0284513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37538i | 0.381461i | 0.981642 | + | 0.190730i | \(0.0610856\pi\) | ||||
−0.981642 | + | 0.190730i | \(0.938914\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.18220 | 0.771796 | 0.385898 | − | 0.922541i | \(-0.373892\pi\) | ||||
0.385898 | + | 0.922541i | \(0.373892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.33389 | + | 0.466292i | 0.994262 | + | 0.106975i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.03453i | 1.67532i | 0.546195 | + | 0.837658i | \(0.316076\pi\) | ||||
−0.546195 | + | 0.837658i | \(0.683924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.75654 | −0.551309 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.06928i | − | 0.569952i | −0.958535 | − | 0.284976i | \(-0.908014\pi\) | ||
0.958535 | − | 0.284976i | \(-0.0919856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0945089 | 0.0169743 | 0.00848715 | − | 0.999964i | \(-0.497298\pi\) | ||||
0.00848715 | + | 0.999964i | \(0.497298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.997183i | − | 0.168555i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.62946i | 0.596679i | 0.954460 | + | 0.298339i | \(0.0964327\pi\) | ||||
−0.954460 | + | 0.298339i | \(0.903567\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.18397i | − | 0.653426i | −0.945124 | − | 0.326713i | \(-0.894059\pi\) | ||
0.945124 | − | 0.326713i | \(-0.105941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7263i | 1.63574i | 0.575401 | + | 0.817872i | \(0.304846\pi\) | ||||
−0.575401 | + | 0.817872i | \(0.695154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.22510i | 0.908024i | 0.890996 | + | 0.454012i | \(0.150008\pi\) | ||||
−0.890996 | + | 0.454012i | \(0.849992\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55677 | 0.936681 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.18397i | − | 0.574712i | −0.957824 | − | 0.287356i | \(-0.907224\pi\) | ||
0.957824 | − | 0.287356i | \(-0.0927763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.886868i | − | 0.119585i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.83326 | −1.01980 | −0.509902 | − | 0.860233i | \(-0.670318\pi\) | ||||
−0.509902 | + | 0.860233i | \(0.670318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.17521 | 0.534581 | 0.267290 | − | 0.963616i | \(-0.413872\pi\) | ||||
0.267290 | + | 0.963616i | \(0.413872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.06006i | 0.255519i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.03026 | 0.370205 | 0.185102 | − | 0.982719i | \(-0.440738\pi\) | ||||
0.185102 | + | 0.982719i | \(0.440738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4897 | −1.36358 | −0.681789 | − | 0.731549i | \(-0.738798\pi\) | ||||
−0.681789 | + | 0.731549i | \(0.738798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.21010 | 0.141631 | 0.0708155 | − | 0.997489i | \(-0.477440\pi\) | ||||
0.0708155 | + | 0.997489i | \(0.477440\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.394200 | −0.0449233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6176 | 1.19457 | 0.597286 | − | 0.802028i | \(-0.296246\pi\) | ||||
0.597286 | + | 0.802028i | \(0.296246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.84334i | 0.202333i | 0.994870 | + | 0.101167i | \(0.0322575\pi\) | ||||
−0.994870 | + | 0.101167i | \(0.967743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.76635 | 0.516983 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.73140i | − | 0.713527i | −0.934195 | − | 0.356764i | \(-0.883880\pi\) | ||
0.934195 | − | 0.356764i | \(-0.116120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.915667 | 0.0959880 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.49137 | + | 0.698421i | 0.666000 | + | 0.0716564i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7628i | 1.29587i | 0.761697 | + | 0.647933i | \(0.224366\pi\) | ||||
−0.761697 | + | 0.647933i | \(0.775634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.66838 | 0.962040 | 0.481020 | − | 0.876710i | \(-0.340266\pi\) | ||||
0.481020 | + | 0.876710i | \(0.340266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.35468 | 0.429079 | 0.214539 | − | 0.976715i | \(-0.431175\pi\) | ||||
0.214539 | + | 0.976715i | \(0.431175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.6610 | −1.03064 | −0.515320 | − | 0.856998i | \(-0.672327\pi\) | ||||
−0.515320 | + | 0.856998i | \(0.672327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7354i | 1.02827i | 0.857711 | + | 0.514133i | \(0.171886\pi\) | ||||
−0.857711 | + | 0.514133i | \(0.828114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.4769i | − | 1.07966i | −0.841776 | − | 0.539828i | \(-0.818489\pi\) | ||
0.841776 | − | 0.539828i | \(-0.181511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0343i | 1.12220i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.11857i | − | 0.194209i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6494 | 0.968128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6179 | −1.03914 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.18341 | −0.548689 | −0.274344 | − | 0.961631i | \(-0.588461\pi\) | ||||
−0.274344 | + | 0.961631i | \(0.588461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.71162i | − | 0.586397i | −0.956052 | − | 0.293198i | \(-0.905280\pi\) | ||
0.956052 | − | 0.293198i | \(-0.0947197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.310438 | − | 2.88532i | 0.0269184 | − | 0.250189i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.72463 | 0.489088 | 0.244544 | − | 0.969638i | \(-0.421362\pi\) | ||||
0.244544 | + | 0.969638i | \(0.421362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.12405i | 0.349797i | 0.984586 | + | 0.174899i | \(0.0559598\pi\) | ||||
−0.984586 | + | 0.174899i | \(0.944040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.814370 | 0.0681010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.59723i | − | 0.381779i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.71640 | 0.795999 | 0.397999 | − | 0.917386i | \(-0.369705\pi\) | ||||
0.397999 | + | 0.917386i | \(0.369705\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.39047 | 0.764185 | 0.382093 | − | 0.924124i | \(-0.375204\pi\) | ||||
0.382093 | + | 0.924124i | \(0.375204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.141557 | 0.0113701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.4441 | 1.79124 | 0.895619 | − | 0.444823i | \(-0.146733\pi\) | ||||
0.895619 | + | 0.444823i | \(0.146733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.34905 | 0.421564 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5987i | 1.14346i | 0.820442 | + | 0.571729i | \(0.193727\pi\) | ||||
−0.820442 | + | 0.571729i | \(0.806273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.68237 | 0.207568 | 0.103784 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103784 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1083 | 0.854488 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6910i | 0.964876i | 0.875930 | + | 0.482438i | \(0.160249\pi\) | ||||
−0.875930 | + | 0.482438i | \(0.839751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.83519i | 0.138727i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0063 | 0.972135 | 0.486067 | − | 0.873921i | \(-0.338431\pi\) | ||||
0.486067 | + | 0.873921i | \(0.338431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.88661i | − | 0.586207i | −0.956081 | − | 0.293103i | \(-0.905312\pi\) | ||
0.956081 | − | 0.293103i | \(-0.0946880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.43626i | 0.399682i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.88420i | − | 0.137786i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.06106i | 0.293848i | 0.989148 | + | 0.146924i | \(0.0469373\pi\) | ||||
−0.989148 | + | 0.146924i | \(0.953063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.77237i | 0.127578i | 0.997963 | + | 0.0637888i | \(0.0203184\pi\) | ||||
−0.997963 | + | 0.0637888i | \(0.979682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.851084 | 0.0606372 | 0.0303186 | − | 0.999540i | \(-0.490348\pi\) | ||||
0.0303186 | + | 0.999540i | \(0.490348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.78610i | − | 0.126613i | −0.997994 | − | 0.0633067i | \(-0.979835\pi\) | ||
0.997994 | − | 0.0633067i | \(-0.0201646\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.04340 | −0.143419 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 6.26681i | − | 0.437693i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.276095 | − | 2.56613i | 0.0190979 | − | 0.177503i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.23063 | 0.360091 | 0.180046 | − | 0.983658i | \(-0.442375\pi\) | ||||
0.180046 | + | 0.983658i | \(0.442375\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.0660i | 1.09569i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.0629201i | − | 0.00427129i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.37672i | 0.294410i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6398 | −1.24821 | −0.624106 | − | 0.781340i | \(-0.714536\pi\) | ||||
−0.624106 | + | 0.781340i | \(0.714536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.12713 | 0.605789 | 0.302894 | − | 0.953024i | \(-0.402047\pi\) | ||||
0.302894 | + | 0.953024i | \(0.402047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.58646 | −0.369164 | −0.184582 | − | 0.982817i | \(-0.559093\pi\) | ||||
−0.184582 | + | 0.982817i | \(0.559093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.1728 | −1.71464 | −0.857318 | − | 0.514787i | \(-0.827871\pi\) | ||||
−0.857318 | + | 0.514787i | \(0.827871\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.32406i | 0.608235i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.84844i | 0.248935i | 0.992224 | + | 0.124467i | \(0.0397222\pi\) | ||||
−0.992224 | + | 0.124467i | \(0.960278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.1576i | − | 1.04080i | −0.853922 | − | 0.520400i | \(-0.825783\pi\) | ||
0.853922 | − | 0.520400i | \(-0.174217\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.82084 | 0.627430 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.641327 | + | 5.96072i | −0.0408067 | + | 0.379272i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.9799i | − | 0.756166i | −0.925772 | − | 0.378083i | \(-0.876583\pi\) | ||
0.925772 | − | 0.378083i | \(-0.123417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.75730 | 0.299089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.9312i | − | 1.36803i | −0.729468 | − | 0.684015i | \(-0.760232\pi\) | ||
0.729468 | − | 0.684015i | \(-0.239768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.41634 | 0.150144 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.6496i | 1.33497i | 0.744623 | + | 0.667485i | \(0.232629\pi\) | ||||
−0.744623 | + | 0.667485i | \(0.767371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.26681i | − | 0.384967i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.05506i | 0.491126i | 0.969381 | + | 0.245563i | \(0.0789728\pi\) | ||||
−0.969381 | + | 0.245563i | \(0.921027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.68805i | 0.345524i | 0.984964 | + | 0.172762i | \(0.0552692\pi\) | ||||
−0.984964 | + | 0.172762i | \(0.944731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.63217i | 0.0984235i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2360 | −0.735190 | −0.367595 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367595 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.66307i | − | 0.576451i | −0.957563 | − | 0.288225i | \(-0.906935\pi\) | ||
0.957563 | − | 0.288225i | \(-0.0930652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2714i | 0.729456i | 0.931114 | + | 0.364728i | \(0.118838\pi\) | ||||
−0.931114 | + | 0.364728i | \(0.881162\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.78551 | −0.164423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.87362 | −0.404330 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.9593i | 1.92550i | 0.270386 | + | 0.962752i | \(0.412849\pi\) | ||||
−0.270386 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7328 | −0.683109 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0505 | −0.639067 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.14111 | 0.411607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.25370 | 0.358086 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.55235 | 0.373962 | 0.186981 | − | 0.982363i | \(-0.440130\pi\) | ||||
0.186981 | + | 0.982363i | \(0.440130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.9039i | − | 1.18535i | −0.805442 | − | 0.592674i | \(-0.798072\pi\) | ||
0.805442 | − | 0.592674i | \(-0.201928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.35540 | −0.246182 | −0.123091 | − | 0.992395i | \(-0.539281\pi\) | ||||
−0.123091 | + | 0.992395i | \(0.539281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.3719i | 0.863375i | 0.902023 | + | 0.431687i | \(0.142082\pi\) | ||||
−0.902023 | + | 0.431687i | \(0.857918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.81735 | −0.101752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.7913 | + | 1.48383i | 0.767368 | + | 0.0825628i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.79128i | − | 0.210303i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.14441 | 0.228489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6836 | −0.642188 | −0.321094 | − | 0.947047i | \(-0.604050\pi\) | ||||
−0.321094 | + | 0.947047i | \(0.604050\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.53877 | 0.247980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.1137i | − | 0.986714i | −0.869827 | − | 0.493357i | \(-0.835770\pi\) | ||
0.869827 | − | 0.493357i | \(-0.164230\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.0559594i | − | 0.00303037i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.02552i | − | 0.487332i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 14.5013i | − | 0.778469i | −0.921139 | − | 0.389234i | \(-0.872740\pi\) | ||
0.921139 | − | 0.389234i | \(-0.127260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7298 | 1.27023 | 0.635115 | − | 0.772418i | \(-0.280953\pi\) | ||||
0.635115 | + | 0.772418i | \(0.280953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9203 | 1.37960 | 0.689799 | − | 0.724001i | \(-0.257699\pi\) | ||||
0.689799 | + | 0.724001i | \(0.257699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.2095 | −0.913385 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2720i | 0.594913i | 0.954735 | + | 0.297457i | \(0.0961383\pi\) | ||||
−0.954735 | + | 0.297457i | \(0.903862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5651 | + | 4.04172i | 0.977113 | + | 0.212722i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.81250 | 0.0948707 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 22.0342i | − | 1.15018i | −0.818091 | − | 0.575089i | \(-0.804967\pi\) | ||
0.818091 | − | 0.575089i | \(-0.195033\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.78551 | −0.144616 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1677i | 1.56203i | 0.624514 | + | 0.781013i | \(0.285297\pi\) | ||||
−0.624514 | + | 0.781013i | \(0.714703\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.22142 | 0.217414 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.03179 | −0.104366 | −0.0521831 | − | 0.998638i | \(-0.516618\pi\) | ||||
−0.0521831 | + | 0.998638i | \(0.516618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7769 | 0.908355 | 0.454178 | − | 0.890911i | \(-0.349933\pi\) | ||||
0.454178 | + | 0.890911i | \(0.349933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.590439 | −0.0300916 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.2699 | 0.875620 | 0.437810 | − | 0.899068i | \(-0.355754\pi\) | ||||
0.437810 | + | 0.899068i | \(0.355754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.5675i | 1.29300i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.9032 | 0.800177 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0904 | −0.707178 | −0.353589 | − | 0.935401i | \(-0.615039\pi\) | ||||
−0.353589 | + | 0.935401i | \(0.615039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 34.9525i | − | 1.74544i | −0.488218 | − | 0.872722i | \(-0.662353\pi\) | ||
0.488218 | − | 0.872722i | \(-0.337647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.129985i | 0.00647503i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.14903 | 0.106523 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 24.5798i | − | 1.21539i | −0.794169 | − | 0.607696i | \(-0.792094\pi\) | ||
0.794169 | − | 0.607696i | \(-0.207906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.21505i | 0.256616i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.76099i | 0.135532i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.26287i | 0.354814i | 0.984138 | + | 0.177407i | \(0.0567710\pi\) | ||||
−0.984138 | + | 0.177407i | \(0.943229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5379i | 1.14717i | 0.819147 | + | 0.573583i | \(0.194447\pi\) | ||||
−0.819147 | + | 0.573583i | \(0.805553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.77187 | −0.425498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.77968i | − | 0.134518i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5328 | 0.603685 | 0.301842 | − | 0.953358i | \(-0.402398\pi\) | ||||
0.301842 | + | 0.953358i | \(0.402398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.4897i | − | 1.46524i | −0.680637 | − | 0.732621i | \(-0.738297\pi\) | ||
0.680637 | − | 0.732621i | \(-0.261703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.74644 | + | 34.8207i | −0.179217 | + | 1.66570i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.93198 | 0.187663 | 0.0938315 | − | 0.995588i | \(-0.470089\pi\) | ||||
0.0938315 | + | 0.995588i | \(0.470089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.2210i | 0.628150i | 0.949398 | + | 0.314075i | \(0.101694\pi\) | ||||
−0.949398 | + | 0.314075i | \(0.898306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 10.0824i | − | 0.477952i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5602i | 0.734332i | 0.930155 | + | 0.367166i | \(0.119672\pi\) | ||||
−0.930155 | + | 0.367166i | \(0.880328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.47736 | −0.116654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.37150 | 0.0642970 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1845 | 1.22486 | 0.612430 | − | 0.790525i | \(-0.290192\pi\) | ||||
0.612430 | + | 0.790525i | \(0.290192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3583 | −0.575585 | −0.287792 | − | 0.957693i | \(-0.592921\pi\) | ||||
−0.287792 | + | 0.957693i | \(0.592921\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7355i | 1.66077i | 0.557190 | + | 0.830385i | \(0.311879\pi\) | ||||
−0.557190 | + | 0.830385i | \(0.688121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 0.827129i | − | 0.0382750i | −0.999817 | − | 0.0191375i | \(-0.993908\pi\) | ||
0.999817 | − | 0.0191375i | \(-0.00609202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.01742i | − | 0.0931557i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.35111 | 0.292024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.9466 | − | 1.28536i | −0.548145 | − | 0.0589762i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3306i | 0.746164i | 0.927798 | + | 0.373082i | \(0.121699\pi\) | ||||
−0.927798 | + | 0.373082i | \(0.878301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.99187 | −0.227610 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.1163i | 0.868028i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.6701 | 0.800707 | 0.400354 | − | 0.916361i | \(-0.368887\pi\) | ||||
0.400354 | + | 0.916361i | \(0.368887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.9356i | 1.35098i | 0.737371 | + | 0.675488i | \(0.236067\pi\) | ||||
−0.737371 | + | 0.675488i | \(0.763933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.76707i | − | 0.439887i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.64937i | 0.343121i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.5155i | 1.50036i | 0.661233 | + | 0.750181i | \(0.270033\pi\) | ||||
−0.661233 | + | 0.750181i | \(0.729967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.57287i | − | 0.159307i | −0.996823 | − | 0.0796533i | \(-0.974619\pi\) | ||
0.996823 | − | 0.0796533i | \(-0.0253813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4815 | 0.644417 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 0.547009i | − | 0.0242457i | −0.999927 | − | 0.0121229i | \(-0.996141\pi\) | ||
0.999927 | − | 0.0121229i | \(-0.00385892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.805631i | − | 0.0356390i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.52251 | 0.287416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.68593 | 0.162107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.45971i | − | 0.151573i | −0.997124 | − | 0.0757863i | \(-0.975853\pi\) | ||
0.997124 | − | 0.0757863i | \(-0.0241467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7456 | −1.08205 | −0.541025 | − | 0.841006i | \(-0.681964\pi\) | ||||
−0.541025 | + | 0.841006i | \(0.681964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.300746 | 0.0131007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.5537 | −1.80668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.75453 | 0.249256 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.9683 | −0.690368 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.88231i | − | 0.167223i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0020 | 0.473014 | 0.236507 | − | 0.971630i | \(-0.423997\pi\) | ||||
0.236507 | + | 0.971630i | \(0.423997\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.0797i | 0.688777i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.5573 | 1.00724 | 0.503619 | − | 0.863926i | \(-0.332002\pi\) | ||||
0.503619 | + | 0.863926i | \(0.332002\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.43118 | − | 13.3019i | 0.0609705 | − | 0.566681i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.06874i | − | 0.300593i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.31667 | 0.394760 | 0.197380 | − | 0.980327i | \(-0.436757\pi\) | ||||
0.197380 | + | 0.980327i | \(0.436757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.7527 | −0.623972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7074 | 1.33631 | 0.668154 | − | 0.744023i | \(-0.267085\pi\) | ||||
0.668154 | + | 0.744023i | \(0.267085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.1903i | − | 0.723201i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 19.2592i | − | 0.807387i | −0.914894 | − | 0.403694i | \(-0.867726\pi\) | ||
0.914894 | − | 0.403694i | \(-0.132274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5757i | 0.819217i | 0.912261 | + | 0.409609i | \(0.134335\pi\) | ||||
−0.912261 | + | 0.409609i | \(0.865665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 22.1475i | − | 0.923617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.06979 | 0.169428 | 0.0847138 | − | 0.996405i | \(-0.473002\pi\) | ||||
0.0847138 | + | 0.996405i | \(0.473002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.22722 | 0.0509136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.47736 | −0.102602 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.6158i | 1.09855i | 0.835642 | + | 0.549275i | \(0.185096\pi\) | ||||
−0.835642 | + | 0.549275i | \(0.814904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.409591 | + | 0.0440688i | 0.0168769 | + | 0.00181582i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.23541 | −0.214993 | −0.107496 | − | 0.994205i | \(-0.534283\pi\) | ||||
−0.107496 | + | 0.994205i | \(0.534283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.17323i | − | 0.130090i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7600 | −0.848230 | −0.424115 | − | 0.905608i | \(-0.639415\pi\) | ||||
−0.424115 | + | 0.905608i | \(0.639415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.0547i | − | 0.450931i | −0.974251 | − | 0.225465i | \(-0.927610\pi\) | ||
0.974251 | − | 0.225465i | \(-0.0723902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.9509 | 0.648495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8896 | −0.482584 | −0.241292 | − | 0.970453i | \(-0.577571\pi\) | ||||
−0.241292 | + | 0.970453i | \(0.577571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.56185 | −0.346375 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.8139 | 1.20417 | 0.602085 | − | 0.798432i | \(-0.294337\pi\) | ||||
0.602085 | + | 0.798432i | \(0.294337\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8426 | −0.476765 | −0.238382 | − | 0.971171i | \(-0.576617\pi\) | ||||
−0.238382 | + | 0.971171i | \(0.576617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 43.5947i | − | 1.75222i | −0.482112 | − | 0.876110i | \(-0.660130\pi\) | ||
0.482112 | − | 0.876110i | \(-0.339870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.48148 | −0.179547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.61874 | −0.144750 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.5496i | 0.460515i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8947i | 0.911422i | 0.890128 | + | 0.455711i | \(0.150615\pi\) | ||||
−0.890128 | + | 0.455711i | \(0.849385\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.26162 | −0.367536 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.01802i | 0.357307i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 29.8752i | − | 1.18000i | −0.807404 | − | 0.589999i | \(-0.799128\pi\) | ||
0.807404 | − | 0.589999i | \(-0.200872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.5576i | − | 1.40226i | −0.713035 | − | 0.701128i | \(-0.752680\pi\) | ||
0.713035 | − | 0.701128i | \(-0.247320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 47.4811i | − | 1.86668i | −0.358999 | − | 0.933338i | \(-0.616882\pi\) | ||
0.358999 | − | 0.933338i | \(-0.383118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.63813i | 0.182062i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.1893 | −0.711802 | −0.355901 | − | 0.934524i | \(-0.615826\pi\) | ||||
−0.355901 | + | 0.934524i | \(0.615826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10.0528i | − | 0.392795i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.48997 | 0.213859 | 0.106929 | − | 0.994267i | \(-0.465898\pi\) | ||||
0.106929 | + | 0.994267i | \(0.465898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.0068i | 1.67277i | 0.548142 | + | 0.836385i | \(0.315335\pi\) | ||||
−0.548142 | + | 0.836385i | \(0.684665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.464979 | − | 4.32168i | 0.0180311 | − | 0.167588i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.6603 | 0.954849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.47217i | − | 0.0954371i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.4270i | − | 0.440478i | −0.975446 | − | 0.220239i | \(-0.929316\pi\) | ||
0.975446 | − | 0.220239i | \(-0.0706838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 22.3404i | − | 0.858612i | −0.903159 | − | 0.429306i | \(-0.858758\pi\) | ||
0.903159 | − | 0.429306i | \(-0.141242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.49694 | 0.326082 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.3763 | −1.46843 | −0.734214 | − | 0.678918i | \(-0.762449\pi\) | ||||
−0.734214 | + | 0.678918i | \(0.762449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.57445 | 0.327613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.75453 | 0.219230 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.7524i | − | 0.713376i | −0.934224 | − | 0.356688i | \(-0.883906\pi\) | ||
0.934224 | − | 0.356688i | \(-0.116094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.17707i | 0.234310i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 13.3142i | − | 0.504312i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.1772 | −0.422158 | −0.211079 | − | 0.977469i | \(-0.567698\pi\) | ||||
−0.211079 | + | 0.977469i | \(0.567698\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.69239 | + | 15.7296i | −0.0638296 | + | 0.593255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 6.43680i | − | 0.242081i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7173 | −1.11606 | −0.558029 | − | 0.829822i | \(-0.688442\pi\) | ||||
−0.558029 | + | 0.829822i | \(0.688442\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.759335i | 0.0284373i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.21978 | 0.0456171 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 25.0957i | − | 0.935912i | −0.883752 | − | 0.467956i | \(-0.844991\pi\) | ||
0.883752 | − | 0.467956i | \(-0.155009\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.89916i | − | 0.107970i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.46062i | 0.314220i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.58125i | 0.169909i | 0.996385 | + | 0.0849546i | \(0.0270745\pi\) | ||||
−0.996385 | + | 0.0849546i | \(0.972925\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.1332i | 1.26246i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.4938 | 0.387596 | 0.193798 | − | 0.981041i | \(-0.437919\pi\) | ||||
0.193798 | + | 0.981041i | \(0.437919\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.79424i | − | 0.0660916i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.0976i | − | 1.43823i | −0.694891 | − | 0.719115i | \(-0.744547\pi\) | ||
0.694891 | − | 0.719115i | \(-0.255453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0470 | −0.441960 | −0.220980 | − | 0.975278i | \(-0.570926\pi\) | ||||
−0.220980 | + | 0.975278i | \(0.570926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5534 | 0.533195 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.09766i | 0.259343i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0097 | 1.27752 | 0.638760 | − | 0.769406i | \(-0.279448\pi\) | ||||
0.638760 | + | 0.769406i | \(0.279448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0652 | 0.511885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.5970 | −1.80263 | −0.901316 | − | 0.433162i | \(-0.857398\pi\) | ||||
−0.901316 | + | 0.433162i | \(0.857398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2017 | −0.877312 | −0.438656 | − | 0.898655i | \(-0.644545\pi\) | ||||
−0.438656 | + | 0.898655i | \(0.644545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.14718 | 0.258745 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.7737i | − | 0.389015i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.7205 | −1.14387 | −0.571935 | − | 0.820299i | \(-0.693807\pi\) | ||||
−0.571935 | + | 0.820299i | \(0.693807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40.0757i | − | 1.44142i | −0.693236 | − | 0.720711i | \(-0.743816\pi\) | ||
0.693236 | − | 0.720711i | \(-0.256184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.260518 | −0.00935809 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.95095 | − | 18.1328i | 0.0699001 | − | 0.649676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.80314i | 0.243436i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.6172 | 1.19985 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.7243 | 0.524865 | 0.262433 | − | 0.964950i | \(-0.415475\pi\) | ||||
0.262433 | + | 0.964950i | \(0.415475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.64083 | −0.271677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.74248i | 0.203922i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.06094i | − | 0.0375805i | −0.999823 | − | 0.0187903i | \(-0.994019\pi\) | ||
0.999823 | − | 0.0187903i | \(-0.00598147\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.8095i | 0.700810i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 0.716506i | − | 0.0252850i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.01190 | 0.282382 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.9029 | −1.57870 | −0.789350 | − | 0.613943i | \(-0.789583\pi\) | ||||
−0.789350 | + | 0.613943i | \(0.789583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3679 | −0.469409 | −0.234704 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234704 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8662i | 0.765939i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00159 | + | 46.4865i | −0.174983 | + | 1.62636i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.80262 | 0.167613 | 0.0838063 | − | 0.996482i | \(-0.473292\pi\) | ||||
0.0838063 | + | 0.996482i | \(0.473292\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.0542i | − | 0.629329i | −0.949203 | − | 0.314664i | \(-0.898108\pi\) | ||
0.949203 | − | 0.314664i | \(-0.101892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.70731 | −0.163689 | −0.0818445 | − | 0.996645i | \(-0.526081\pi\) | ||||
−0.0818445 | + | 0.996645i | \(0.526081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.7736i | 1.10354i | 0.833996 | + | 0.551771i | \(0.186048\pi\) | ||||
−0.833996 | + | 0.551771i | \(0.813952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.8649 | 0.722927 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.01770 | 0.139038 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9648 | 0.413070 | 0.206535 | − | 0.978439i | \(-0.433781\pi\) | ||||
0.206535 | + | 0.978439i | \(0.433781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.5795 | 0.675155 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.6383 | 0.572374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.08993i | − | 0.243613i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.1610 | −0.999626 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1716 | −1.03306 | −0.516528 | − | 0.856270i | \(-0.672776\pi\) | ||||
−0.516528 | + | 0.856270i | \(0.672776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 45.5018i | − | 1.55431i | −0.629309 | − | 0.777156i | \(-0.716662\pi\) | ||
0.629309 | − | 0.777156i | \(-0.283338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 28.7358i | − | 0.980453i | −0.871595 | − | 0.490226i | \(-0.836914\pi\) | ||
0.871595 | − | 0.490226i | \(-0.163086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.0133 | 1.49823 | 0.749115 | − | 0.662440i | \(-0.230479\pi\) | ||||
0.749115 | + | 0.662440i | \(0.230479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.0087i | 0.646316i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.28675i | − | 0.213263i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.16774i | 0.141219i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.73470i | 0.261480i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.3517i | 1.49765i | 0.662767 | + | 0.748826i | \(0.269382\pi\) | ||||
−0.662767 | + | 0.748826i | \(0.730618\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.1569 | −1.31923 | −0.659615 | − | 0.751604i | \(-0.729281\pi\) | ||||
−0.659615 | + | 0.751604i | \(0.729281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.1304i | − | 1.31684i | −0.752650 | − | 0.658421i | \(-0.771225\pi\) | ||
0.752650 | − | 0.658421i | \(-0.228775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.4504 | −1.42535 | −0.712673 | − | 0.701496i | \(-0.752516\pi\) | ||||
−0.712673 | + | 0.701496i | \(0.752516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.11665i | 0.138068i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.90272 | + | 26.9789i | −0.0971357 | + | 0.902814i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.4810 | 0.651179 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.290075i | − | 0.00967454i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 13.3142i | − | 0.443561i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.8127i | − | 0.392667i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4407 | −0.512698 | −0.256349 | − | 0.966584i | \(-0.582520\pi\) | ||||
−0.256349 | + | 0.966584i | \(0.582520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.5096 | −1.57406 | −0.787032 | − | 0.616913i | \(-0.788383\pi\) | ||||
−0.787032 | + | 0.616913i | \(0.788383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.09146 | 0.0361219 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.46831 | −0.147557 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.62653i | − | 0.119628i | −0.998210 | − | 0.0598141i | \(-0.980949\pi\) | ||
0.998210 | − | 0.0598141i | \(-0.0190508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 15.8027i | − | 0.520151i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.0048i | − | 0.328954i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.4344 | 0.932903 | 0.466452 | − | 0.884547i | \(-0.345532\pi\) | ||||
0.466452 | + | 0.884547i | \(0.345532\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.4163 | + | 3.05737i | 0.931306 | + | 0.100201i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.82219i | − | 0.0922955i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.5453 | −0.867197 | −0.433598 | − | 0.901106i | \(-0.642756\pi\) | ||||
−0.433598 | + | 0.901106i | \(0.642756\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.39450i | 0.273653i | 0.990595 | + | 0.136826i | \(0.0436903\pi\) | ||||
−0.990595 | + | 0.136826i | \(0.956310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.6162 | 1.09469 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.9126i | 1.13451i | 0.823543 | + | 0.567254i | \(0.191994\pi\) | ||||
−0.823543 | + | 0.567254i | \(0.808006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.66434i | 0.0540266i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.2442i | 1.07689i | 0.842662 | + | 0.538443i | \(0.180987\pi\) | ||||
−0.842662 | + | 0.538443i | \(0.819013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.08273i | 0.196832i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 3.81122i | − | 0.123071i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9911 | −0.999712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.65468i | 0.0854571i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.6769i | − | 1.66182i | −0.556409 | − | 0.830908i | \(-0.687821\pi\) | ||
0.556409 | − | 0.830908i | \(-0.312179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.2613 | −1.58087 | −0.790436 | − | 0.612545i | \(-0.790146\pi\) | ||||
−0.790436 | + | 0.612545i | \(0.790146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.74562 | 0.0880205 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 49.1842i | − | 1.57354i | −0.617245 | − | 0.786771i | \(-0.711751\pi\) | ||
0.617245 | − | 0.786771i | \(-0.288249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.98571 | −0.127384 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.54411 | −0.144934 | −0.0724672 | − | 0.997371i | \(-0.523087\pi\) | ||||
−0.0724672 | + | 0.997371i | \(0.523087\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.27477 | 0.0406175 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −86.1807 | −2.74039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.1756 | 1.62565 | 0.812823 | − | 0.582511i | \(-0.197930\pi\) | ||||
0.812823 | + | 0.582511i | \(0.197930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.67525i | − | 0.0848112i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.6620 | −0.401008 | −0.200504 | − | 0.979693i | \(-0.564258\pi\) | ||||
−0.200504 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(998\) | 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 | 5472.2.k.a.2431.13 | 20 | ||
3.2 | odd | 2 | 1824.2.k.a.607.7 | ✓ | 20 | ||
4.3 | odd | 2 | 5472.2.k.b.2431.14 | 20 | |||
12.11 | even | 2 | 1824.2.k.b.607.8 | yes | 20 | ||
19.18 | odd | 2 | 5472.2.k.b.2431.13 | 20 | |||
24.5 | odd | 2 | 3648.2.k.l.2431.13 | 20 | |||
24.11 | even | 2 | 3648.2.k.k.2431.14 | 20 | |||
57.56 | even | 2 | 1824.2.k.b.607.7 | yes | 20 | ||
76.75 | even | 2 | inner | 5472.2.k.a.2431.14 | 20 | ||
228.227 | odd | 2 | 1824.2.k.a.607.8 | yes | 20 | ||
456.227 | odd | 2 | 3648.2.k.l.2431.14 | 20 | |||
456.341 | even | 2 | 3648.2.k.k.2431.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1824.2.k.a.607.7 | ✓ | 20 | 3.2 | odd | 2 | ||
1824.2.k.a.607.8 | yes | 20 | 228.227 | odd | 2 | ||
1824.2.k.b.607.7 | yes | 20 | 57.56 | even | 2 | ||
1824.2.k.b.607.8 | yes | 20 | 12.11 | even | 2 | ||
3648.2.k.k.2431.13 | 20 | 456.341 | even | 2 | |||
3648.2.k.k.2431.14 | 20 | 24.11 | even | 2 | |||
3648.2.k.l.2431.13 | 20 | 24.5 | odd | 2 | |||
3648.2.k.l.2431.14 | 20 | 456.227 | odd | 2 | |||
5472.2.k.a.2431.13 | 20 | 1.1 | even | 1 | trivial | ||
5472.2.k.a.2431.14 | 20 | 76.75 | even | 2 | inner | ||
5472.2.k.b.2431.13 | 20 | 19.18 | odd | 2 | |||
5472.2.k.b.2431.14 | 20 | 4.3 | odd | 2 |