Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6300,2,Mod(3401,6300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("6300.3401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6300.d (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: | \(50.3057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.101415451701035401216.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 1260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3401.16 | ||
Root | \(0.752908 - 0.137538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6300.3401 |
Dual form | 6300.2.d.f.3401.13 |
$q$-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 \(\left(\mathbb{Z}/6300\mathbb{Z}\right)^\times\).
\(n\) | \(2801\) | \(3151\) | \(3277\) | \(3601\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.57794 | + | 0.595188i | 0.974368 | + | 0.224960i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.74166i | 1.12815i | 0.825723 | + | 0.564076i | \(0.190768\pi\) | ||||
−0.825723 | + | 0.564076i | \(0.809232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.36028i | − | 0.931975i | −0.884791 | − | 0.465987i | \(-0.845699\pi\) | ||
0.884791 | − | 0.465987i | \(-0.154301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.841723 | 0.204148 | 0.102074 | − | 0.994777i | \(-0.467452\pi\) | ||||
0.102074 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.59388i | 1.28332i | 0.766987 | + | 0.641662i | \(0.221755\pi\) | ||||
−0.766987 | + | 0.641662i | \(0.778245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.35425i | − | 0.490895i | −0.969410 | − | 0.245447i | \(-0.921065\pi\) | ||
0.969410 | − | 0.245447i | \(-0.0789349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.66259i | − | 1.55585i | −0.628359 | − | 0.777924i | \(-0.716273\pi\) | ||
0.628359 | − | 0.777924i | \(-0.283727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.15587 | 0.847620 | 0.423810 | − | 0.905751i | \(-0.360692\pi\) | ||||
0.423810 | + | 0.905751i | \(0.360692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74103 | −0.896599 | −0.448300 | − | 0.893883i | \(-0.647970\pi\) | ||||
−0.448300 | + | 0.893883i | \(0.647970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.32941 | 0.507730 | 0.253865 | − | 0.967240i | \(-0.418298\pi\) | ||||
0.253865 | + | 0.967240i | \(0.418298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.43560 | 0.938729 | 0.469365 | − | 0.883004i | \(-0.344483\pi\) | ||||
0.469365 | + | 0.883004i | \(0.344483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.29150 | + | 3.06871i | 0.898786 | + | 0.438387i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.64575i | 1.32495i | 0.749086 | + | 0.662473i | \(0.230493\pi\) | ||||
−0.749086 | + | 0.662473i | \(0.769507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2508 | 1.59491 | 0.797456 | − | 0.603377i | \(-0.206178\pi\) | ||||
0.797456 | + | 0.603377i | \(0.206178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.82646 | 0.223138 | 0.111569 | − | 0.993757i | \(-0.464412\pi\) | ||||
0.111569 | + | 0.993757i | \(0.464412\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.74166i | 0.444053i | 0.975041 | + | 0.222027i | \(0.0712672\pi\) | ||||
−0.975041 | + | 0.222027i | \(0.928733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.979531i | 0.114645i | 0.998356 | + | 0.0573227i | \(0.0182564\pi\) | ||||
−0.998356 | + | 0.0573227i | \(0.981744\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.22699 | + | 9.64575i | −0.253789 | + | 1.09924i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.58301 | 0.740646 | 0.370323 | − | 0.928903i | \(-0.379247\pi\) | ||||
0.370323 | + | 0.928903i | \(0.379247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5730 | −1.38007 | −0.690035 | − | 0.723776i | \(-0.742405\pi\) | ||||
−0.690035 | + | 0.723776i | \(0.742405\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.16991 | −0.230010 | −0.115005 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115005 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 8.66259i | 0.209657 | − | 0.908086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0399i | 1.22247i | 0.791450 | + | 0.611234i | \(0.209327\pi\) | ||||
−0.791450 | + | 0.611234i | \(0.790673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.74103 | 0.571254 | 0.285627 | − | 0.958341i | \(-0.407798\pi\) | ||||
0.285627 | + | 0.958341i | \(0.407798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.4411i | − | 1.32439i | −0.749330 | − | 0.662197i | \(-0.769624\pi\) | ||
0.749330 | − | 0.662197i | \(-0.230376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9373i | 1.63739i | 0.574231 | + | 0.818693i | \(0.305301\pi\) | ||||
−0.574231 | + | 0.818693i | \(0.694699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8745 | −1.71207 | −0.856034 | − | 0.516920i | \(-0.827078\pi\) | ||||
−0.856034 | + | 0.516920i | \(0.827078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.93725i | 0.464458i | 0.972661 | + | 0.232229i | \(0.0746018\pi\) | ||||
−0.972661 | + | 0.232229i | \(0.925398\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.16991 | + | 0.500983i | 0.198915 | + | 0.0459251i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3117 | 0.915019 | 0.457510 | − | 0.889205i | \(-0.348742\pi\) | ||||
0.457510 | + | 0.889205i | \(0.348742\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.91094 | −0.691182 | −0.345591 | − | 0.938385i | \(-0.612322\pi\) | ||||
−0.345591 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.32941 | + | 14.4207i | −0.288696 | + | 1.25043i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.2288i | 1.04477i | 0.852709 | + | 0.522387i | \(0.174958\pi\) | ||||
−0.852709 | + | 0.522387i | \(0.825042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.61226i | − | 0.306388i | −0.988196 | − | 0.153194i | \(-0.951044\pi\) | ||
0.988196 | − | 0.153194i | \(-0.0489559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5730 | 1.05141 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.3828i | − | 1.42406i | −0.702151 | − | 0.712028i | \(-0.747777\pi\) | ||
0.702151 | − | 0.712028i | \(-0.252223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.29150 | −0.430616 | −0.215308 | − | 0.976546i | \(-0.569076\pi\) | ||||
−0.215308 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.3725i | − | 1.62591i | −0.582329 | − | 0.812953i | \(-0.697859\pi\) | ||
0.582329 | − | 0.812953i | \(-0.302141\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.40122 | − | 6.06910i | 0.110432 | − | 0.478312i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.6921 | 1.60120 | 0.800601 | − | 0.599198i | \(-0.204514\pi\) | ||||
0.800601 | + | 0.599198i | \(0.204514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.70850 | 0.131423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.4651 | 1.40387 | 0.701937 | − | 0.712239i | \(-0.252319\pi\) | ||||
0.701937 | + | 0.712239i | \(0.252319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.39655i | 0.627587i | 0.949491 | + | 0.313794i | \(0.101600\pi\) | ||||
−0.949491 | + | 0.313794i | \(0.898400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.5313i | 1.97206i | 0.166575 | + | 0.986029i | \(0.446729\pi\) | ||||
−0.166575 | + | 0.986029i | \(0.553271\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.14944i | 0.230310i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.8818i | − | 1.22153i | −0.791813 | − | 0.610763i | \(-0.790863\pi\) | ||
0.791813 | − | 0.610763i | \(-0.209137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4676 | 1.11338 | 0.556692 | − | 0.830719i | \(-0.312071\pi\) | ||||
0.556692 | + | 0.830719i | \(0.312071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.8118i | 1.91026i | 0.296189 | + | 0.955129i | \(0.404284\pi\) | ||||
−0.296189 | + | 0.955129i | \(0.595716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.68097i | 0.473601i | 0.971558 | + | 0.236801i | \(0.0760988\pi\) | ||||
−0.971558 | + | 0.236801i | \(0.923901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.841723 | + | 3.64575i | −0.0590774 | + | 0.255882i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.9304 | −1.44779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.29150 | −0.364282 | −0.182141 | − | 0.983272i | \(-0.558303\pi\) | ||||
−0.182141 | + | 0.983272i | \(0.558303\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.15587 | − | 22.3316i | 0.350003 | − | 1.51597i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.82843i | − | 0.190261i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.2098i | − | 0.951560i | −0.879564 | − | 0.475780i | \(-0.842166\pi\) | ||
0.879564 | − | 0.475780i | \(-0.157834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.0270 | −1.13012 | −0.565061 | − | 0.825049i | \(-0.691147\pi\) | ||||
−0.565061 | + | 0.825049i | \(0.691147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.4442i | − | 1.68140i | −0.541499 | − | 0.840701i | \(-0.682143\pi\) | ||
0.541499 | − | 0.840701i | \(-0.317857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.6458i | 1.41806i | 0.705178 | + | 0.709030i | \(0.250867\pi\) | ||||
−0.705178 | + | 0.709030i | \(0.749133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0554i | 0.973851i | 0.873444 | + | 0.486925i | \(0.161882\pi\) | ||||
−0.873444 | + | 0.486925i | \(0.838118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11905i | 0.522994i | 0.965204 | + | 0.261497i | \(0.0842161\pi\) | ||||
−0.965204 | + | 0.261497i | \(0.915784\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.7970 | 1.19603 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5906 | 1.04719 | 0.523594 | − | 0.851968i | \(-0.324591\pi\) | ||||
0.523594 | + | 0.851968i | \(0.324591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.80879 | 0.553804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.89206 | 0.367537 | 0.183768 | − | 0.982970i | \(-0.441170\pi\) | ||||
0.183768 | + | 0.982970i | \(0.441170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.2915 | + | 3.06871i | 0.825894 | + | 0.190681i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.64575i | − | 0.594783i | −0.954756 | − | 0.297391i | \(-0.903883\pi\) | ||
0.954756 | − | 0.297391i | \(-0.0961166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.9027 | −1.57932 | −0.789659 | − | 0.613546i | \(-0.789742\pi\) | ||||
−0.789659 | + | 0.613546i | \(0.789742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8000i | 0.899037i | 0.893271 | + | 0.449519i | \(0.148404\pi\) | ||||
−0.893271 | + | 0.449519i | \(0.851596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.4558 | 1.52949 | 0.764747 | − | 0.644331i | \(-0.222864\pi\) | ||||
0.764747 | + | 0.644331i | \(0.222864\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.06713i | − | 0.302280i | −0.988512 | − | 0.151140i | \(-0.951706\pi\) | ||
0.988512 | − | 0.151140i | \(-0.0482944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.6510i | 1.64368i | 0.569719 | + | 0.821839i | \(0.307052\pi\) | ||||
−0.569719 | + | 0.821839i | \(0.692948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.8000 | − | 3.41699i | −0.873617 | − | 0.201699i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2915 | −0.958324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.2540 | −1.12483 | −0.562415 | − | 0.826855i | \(-0.690128\pi\) | ||||
−0.562415 | + | 0.826855i | \(0.690128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.91094 | −0.457502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.58301 | + | 1.98162i | 0.494716 | + | 0.114219i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5496i | 1.05868i | 0.848409 | + | 0.529342i | \(0.177561\pi\) | ||||
−0.848409 | + | 0.529342i | \(0.822439\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9304 | −1.18685 | −0.593427 | − | 0.804888i | \(-0.702225\pi\) | ||||
−0.593427 | + | 0.804888i | \(0.702225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.55066i | 0.257218i | 0.991695 | + | 0.128609i | \(0.0410513\pi\) | ||||
−0.991695 | + | 0.128609i | \(0.958949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8118i | 0.831911i | 0.909385 | + | 0.415956i | \(0.136553\pi\) | ||||
−0.909385 | + | 0.415956i | \(0.863447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.29150 | −0.296267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.70850i | 0.261988i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5906 | + | 3.83039i | 0.914668 | + | 0.211176i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.8745 | 0.652682 | 0.326341 | − | 0.945252i | \(-0.394184\pi\) | ||||
0.326341 | + | 0.945252i | \(0.394184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9529 | 1.30480 | 0.652399 | − | 0.757876i | \(-0.273763\pi\) | ||||
0.652399 | + | 0.757876i | \(0.273763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.4125 | 1.75523 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.3926 | + | 11.6556i | 0.777129 | + | 0.629342i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.9373i | 1.55343i | 0.629850 | + | 0.776717i | \(0.283116\pi\) | ||||
−0.629850 | + | 0.776717i | \(0.716884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.6000i | − | 1.58445i | −0.610227 | − | 0.792227i | \(-0.708922\pi\) | ||
0.610227 | − | 0.792227i | \(-0.291078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4651 | 0.982797 | 0.491399 | − | 0.870935i | \(-0.336486\pi\) | ||||
0.491399 | + | 0.870935i | \(0.336486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 29.1975i | − | 1.54099i | −0.637449 | − | 0.770493i | \(-0.720010\pi\) | ||
0.637449 | − | 0.770493i | \(-0.279990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2915 | −0.646921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.6510i | − | 1.44337i | −0.692223 | − | 0.721684i | \(-0.743368\pi\) | ||
0.692223 | − | 0.721684i | \(-0.256632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.74103 | + | 24.8661i | −0.298060 | + | 1.29098i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.9352 | 1.60177 | 0.800883 | − | 0.598821i | \(-0.204364\pi\) | ||||
0.800883 | + | 0.598821i | \(0.204364\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.75216 | 0.244749 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.70850 | 0.139126 | 0.0695631 | − | 0.997578i | \(-0.477839\pi\) | ||||
0.0695631 | + | 0.997578i | \(0.477839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.6921 | −1.05732 | −0.528658 | − | 0.848835i | \(-0.677305\pi\) | ||||
−0.528658 | + | 0.848835i | \(0.677305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.06713i | 0.256914i | 0.991715 | + | 0.128457i | \(0.0410024\pi\) | ||||
−0.991715 | + | 0.128457i | \(0.958998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.98162i | − | 0.100215i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.0327i | − | 0.804660i | −0.915495 | − | 0.402330i | \(-0.868201\pi\) | ||
0.915495 | − | 0.402330i | \(-0.131799\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.5504i | 0.626740i | 0.949631 | + | 0.313370i | \(0.101458\pi\) | ||||
−0.949631 | + | 0.313370i | \(0.898542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.1088 | −1.45001 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.2915i | 0.956244i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.2565i | 0.704937i | 0.935824 | + | 0.352469i | \(0.114658\pi\) | ||||
−0.935824 | + | 0.352469i | \(0.885342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.5817 | + | 7.29150i | 1.55403 | + | 0.358791i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.14226 | 0.348922 | 0.174461 | − | 0.984664i | \(-0.444182\pi\) | ||||
0.174461 | + | 0.984664i | \(0.444182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8745 | 1.16357 | 0.581786 | − | 0.813342i | \(-0.302354\pi\) | ||||
0.581786 | + | 0.813342i | \(0.302354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.39655i | − | 0.404447i | −0.979339 | − | 0.202224i | \(-0.935183\pi\) | ||
0.979339 | − | 0.202224i | \(-0.0648168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.7727i | − | 1.71913i | −0.511028 | − | 0.859564i | \(-0.670735\pi\) | ||
0.511028 | − | 0.859564i | \(-0.329265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1694 | 0.629977 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.50679i | 0.215098i | 0.994200 | + | 0.107549i | \(0.0343002\pi\) | ||||
−0.994200 | + | 0.107549i | \(0.965700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.64575i | − | 0.458283i | −0.973393 | − | 0.229142i | \(-0.926408\pi\) | ||
0.973393 | − | 0.229142i | \(-0.0735919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.6965i | 1.35427i | 0.735858 | + | 0.677136i | \(0.236779\pi\) | ||||
−0.735858 | + | 0.677136i | \(0.763221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 21.4810i | − | 1.01150i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.98823 | −0.467230 | −0.233615 | − | 0.972329i | \(-0.575055\pi\) | ||||
−0.233615 | + | 0.972329i | \(0.575055\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0112 | 1.44434 | 0.722169 | − | 0.691717i | \(-0.243145\pi\) | ||||
0.722169 | + | 0.691717i | \(0.243145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9706 | −0.788689 | −0.394344 | − | 0.918963i | \(-0.629028\pi\) | ||||
−0.394344 | + | 0.918963i | \(0.629028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7105 | 0.865816 | 0.432908 | − | 0.901438i | \(-0.357487\pi\) | ||||
0.432908 | + | 0.901438i | \(0.357487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.70850 | + | 1.08709i | 0.217418 | + | 0.0501970i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4575i | 0.572797i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.9304 | 0.956334 | 0.478167 | − | 0.878269i | \(-0.341301\pi\) | ||||
0.478167 | + | 0.878269i | \(0.341301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 17.3252i | − | 0.789960i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.98233 | 0.316400 | 0.158200 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158200 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1916i | 1.18201i | 0.806668 | + | 0.591005i | \(0.201269\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19038i | 0.0536118i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.22699 | + | 9.64575i | −0.0998941 | + | 0.432671i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7085 | −0.837507 | −0.418754 | − | 0.908100i | \(-0.637533\pi\) | ||||
−0.418754 | + | 0.908100i | \(0.637533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.82087 | 0.348715 | 0.174358 | − | 0.984682i | \(-0.444215\pi\) | ||||
0.174358 | + | 0.984682i | \(0.444215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.2425 | 1.34048 | 0.670239 | − | 0.742146i | \(-0.266192\pi\) | ||||
0.670239 | + | 0.742146i | \(0.266192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.583005 | + | 2.52517i | −0.0257906 | + | 0.111707i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0798i | 1.05903i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2231 | −0.754558 | −0.377279 | − | 0.926100i | \(-0.623140\pi\) | ||||
−0.377279 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.4411i | − | 0.587740i | −0.955845 | − | 0.293870i | \(-0.905057\pi\) | ||
0.955845 | − | 0.293870i | \(-0.0949432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.29150i | − | 0.317623i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.4575 | 0.759022 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.2915i | 0.835608i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.4821 | + | 23.5406i | −0.494568 | + | 1.01397i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.8745 | −0.854472 | −0.427236 | − | 0.904140i | \(-0.640513\pi\) | ||||
−0.427236 | + | 0.904140i | \(0.640513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.4558 | −1.08841 | −0.544207 | − | 0.838951i | \(-0.683169\pi\) | ||||
−0.544207 | + | 0.838951i | \(0.683169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.91094 | −0.337017 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.9706 | + | 3.91813i | 0.721662 | + | 0.166616i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.5203i | 0.827100i | 0.910481 | + | 0.413550i | \(0.135711\pi\) | ||||
−0.910481 | + | 0.413550i | \(0.864289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11.1878i | − | 0.473192i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.27980 | −0.0960823 | −0.0480411 | − | 0.998845i | \(-0.515298\pi\) | ||||
−0.0480411 | + | 0.998845i | \(0.515298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.2152i | − | 0.931308i | −0.884967 | − | 0.465654i | \(-0.845819\pi\) | ||
0.884967 | − | 0.465654i | \(-0.154181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5830 | 0.945069 | 0.472535 | − | 0.881312i | \(-0.343339\pi\) | ||||
0.472535 | + | 0.881312i | \(0.343339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0931i | 1.12790i | 0.825809 | + | 0.563950i | \(0.190719\pi\) | ||||
−0.825809 | + | 0.563950i | \(0.809281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.4125 | − | 7.48331i | −1.34470 | − | 0.310460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0911 | −1.49474 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.9669 | 1.36069 | 0.680345 | − | 0.732892i | \(-0.261830\pi\) | ||||
0.680345 | + | 0.732892i | \(0.261830\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.4575 | 1.99666 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.3730 | −1.12408 | −0.562038 | − | 0.827111i | \(-0.689983\pi\) | ||||
−0.562038 | + | 0.827111i | \(0.689983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26.1916i | − | 1.07016i | −0.844801 | − | 0.535080i | \(-0.820281\pi\) | ||
0.844801 | − | 0.535080i | \(-0.179719\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.4259i | − | 1.11872i | −0.828923 | − | 0.559362i | \(-0.811046\pi\) | ||
0.828923 | − | 0.559362i | \(-0.188954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.3715i | 1.39510i | 0.716538 | + | 0.697548i | \(0.245726\pi\) | ||||
−0.716538 | + | 0.697548i | \(0.754274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 21.6255i | − | 0.874872i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.2823 | 1.10192 | 0.550961 | − | 0.834531i | \(-0.314261\pi\) | ||||
0.550961 | + | 0.834531i | \(0.314261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.52026i | − | 0.302754i | −0.988476 | − | 0.151377i | \(-0.951629\pi\) | ||
0.988476 | − | 0.151377i | \(-0.0483708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.9374i | 0.841547i | 0.907166 | + | 0.420773i | \(0.138241\pi\) | ||||
−0.907166 | + | 0.420773i | \(0.861759\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.59388 | − | 1.29150i | −0.224114 | − | 0.0517430i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.33981 | 0.173040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1660 | −0.842606 | −0.421303 | − | 0.906920i | \(-0.638427\pi\) | ||||
−0.421303 | + | 0.906920i | \(0.638427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.3117 | − | 21.1412i | 0.408566 | − | 0.837646i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.23871i | 0.0884236i | 0.999022 | + | 0.0442118i | \(0.0140776\pi\) | ||||
−0.999022 | + | 0.0442118i | \(0.985922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.0317i | − | 1.18433i | −0.805815 | − | 0.592167i | \(-0.798272\pi\) | ||
0.805815 | − | 0.592167i | \(-0.201728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1461 | −0.988593 | −0.494297 | − | 0.869293i | \(-0.664574\pi\) | ||||
−0.494297 | + | 0.869293i | \(0.664574\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.8381i | 1.79930i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1033i | 0.864968i | 0.901642 | + | 0.432484i | \(0.142363\pi\) | ||||
−0.901642 | + | 0.432484i | \(0.857637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09070i | 0.0424878i | 0.999774 | + | 0.0212439i | \(0.00676264\pi\) | ||||
−0.999774 | + | 0.0212439i | \(0.993237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.13742i | 0.238718i | 0.992851 | + | 0.119359i | \(0.0380840\pi\) | ||||
−0.992851 | + | 0.119359i | \(0.961916\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.32941 | 0.128915 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.16177 | 0.314613 | 0.157307 | − | 0.987550i | \(-0.449719\pi\) | ||||
0.157307 | + | 0.987550i | \(0.449719\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8086 | −1.29937 | −0.649686 | − | 0.760203i | \(-0.725100\pi\) | ||||
−0.649686 | + | 0.760203i | \(0.725100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.16601 | + | 31.0381i | −0.275006 | + | 1.19113i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.5203i | − | 0.746922i | −0.927646 | − | 0.373461i | \(-0.878171\pi\) | ||
0.927646 | − | 0.373461i | \(-0.121829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.4125 | 1.23482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.52517i | − | 0.0960619i | −0.998846 | − | 0.0480310i | \(-0.984705\pi\) | ||
0.998846 | − | 0.0480310i | \(-0.0152946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.83236 | −0.183039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.7299i | 0.518571i | 0.965801 | + | 0.259285i | \(0.0834870\pi\) | ||||
−0.965801 | + | 0.259285i | \(0.916513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.8413i | 1.08777i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8000 | + | 3.41699i | 0.556612 | + | 0.128509i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.1660 | −1.84647 | −0.923234 | − | 0.384238i | \(-0.874464\pi\) | ||||
−0.923234 | + | 0.384238i | \(0.874464\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.3939 | −0.763757 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.2896 | −1.42796 | −0.713981 | − | 0.700165i | \(-0.753110\pi\) | ||||
−0.713981 | + | 0.700165i | \(0.753110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | − | 34.6504i | 0.297936 | − | 1.29045i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.91813i | − | 0.145315i | −0.997357 | − | 0.0726576i | \(-0.976852\pi\) | ||
0.997357 | − | 0.0726576i | \(-0.0231480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.80244 | 0.103652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.9990i | 0.517064i | 0.966003 | + | 0.258532i | \(0.0832387\pi\) | ||||
−0.966003 | + | 0.258532i | \(0.916761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.83399i | 0.251733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.16601 | 0.337177 | 0.168589 | − | 0.985687i | \(-0.446079\pi\) | ||||
0.168589 | + | 0.985687i | \(0.446079\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.9373i | − | 1.06160i | −0.847496 | − | 0.530802i | \(-0.821891\pi\) | ||
0.847496 | − | 0.530802i | \(-0.178109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.0808 | + | 43.6631i | −0.368346 | + | 1.59542i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.2915 | −1.06886 | −0.534431 | − | 0.845212i | \(-0.679474\pi\) | ||||
−0.534431 | + | 0.845212i | \(0.679474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6412 | 0.495796 | 0.247898 | − | 0.968786i | \(-0.420260\pi\) | ||||
0.247898 | + | 0.968786i | \(0.420260\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.1729 | −1.85502 | −0.927509 | − | 0.373802i | \(-0.878054\pi\) | ||||
−0.927509 | + | 0.373802i | \(0.878054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.0793 | − | 10.6387i | −1.66818 | − | 0.385146i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 41.1660i | − | 1.48642i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.4259i | 0.989002i | 0.869177 | + | 0.494501i | \(0.164649\pi\) | ||||
−0.869177 | + | 0.494501i | \(0.835351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1349 | −0.400496 | −0.200248 | − | 0.979745i | \(-0.564175\pi\) | ||||
−0.200248 | + | 0.979745i | \(0.564175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 32.1147i | − | 1.15063i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | −0.500959 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.0798i | − | 0.858353i | −0.903221 | − | 0.429177i | \(-0.858804\pi\) | ||
0.903221 | − | 0.429177i | \(-0.141196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.93859 | + | 12.7279i | −0.104484 | + | 0.452553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2860 | 0.931096 | 0.465548 | − | 0.885023i | \(-0.345857\pi\) | ||||
0.465548 | + | 0.885023i | \(0.345857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.41699 | 0.191639 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.66507 | −0.129338 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 50.1445i | − | 1.76299i | −0.472197 | − | 0.881493i | \(-0.656539\pi\) | ||
0.472197 | − | 0.881493i | \(-0.343461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8000i | 0.519699i | 0.965649 | + | 0.259849i | \(0.0836729\pi\) | ||||
−0.965649 | + | 0.259849i | \(0.916327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.6243i | 0.651583i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.89949i | − | 0.345495i | −0.984966 | − | 0.172747i | \(-0.944736\pi\) | ||
0.984966 | − | 0.172747i | \(-0.0552644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2823 | 0.951001 | 0.475501 | − | 0.879715i | \(-0.342267\pi\) | ||||
0.475501 | + | 0.879715i | \(0.342267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 52.9373i | − | 1.84081i | −0.390968 | − | 0.920404i | \(-0.627860\pi\) | ||
0.390968 | − | 0.920404i | \(-0.372140\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.3436i | − | 0.532904i | −0.963848 | − | 0.266452i | \(-0.914149\pi\) | ||
0.963848 | − | 0.266452i | \(-0.0858514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.29570 | + | 2.58301i | 0.183485 | + | 0.0894958i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.33981 | −0.149827 | −0.0749135 | − | 0.997190i | \(-0.523868\pi\) | ||||
−0.0749135 | + | 0.997190i | \(0.523868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.73381 | − | 1.78556i | −0.265737 | − | 0.0613527i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12.1382i | − | 0.416092i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.210845i | 0.00721918i | 0.999993 | + | 0.00360959i | \(0.00114897\pi\) | ||||
−0.999993 | + | 0.00360959i | \(0.998851\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1853 | 0.552879 | 0.276439 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276439 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39.1572i | − | 1.33603i | −0.744150 | − | 0.668013i | \(-0.767145\pi\) | ||
0.744150 | − | 0.668013i | \(-0.232855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 48.6863i | − | 1.65730i | −0.559767 | − | 0.828650i | \(-0.689109\pi\) | ||
0.559767 | − | 0.828650i | \(-0.310891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.6314i | 0.835561i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.13742i | − | 0.207959i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.9706 | 0.573055 | 0.286528 | − | 0.958072i | \(-0.407499\pi\) | ||||
0.286528 | + | 0.958072i | \(0.407499\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1894 | −0.511742 | −0.255871 | − | 0.966711i | \(-0.582362\pi\) | ||||
−0.255871 | + | 0.966711i | \(0.582362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.50295 | 0.0505783 | 0.0252891 | − | 0.999680i | \(-0.491949\pi\) | ||||
0.0252891 | + | 0.999680i | \(0.491949\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.66507 | −0.123061 | −0.0615305 | − | 0.998105i | \(-0.519598\pi\) | ||||
−0.0615305 | + | 0.998105i | \(0.519598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.5830 | + | 6.13742i | 0.891565 | + | 0.205843i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0000i | 1.20469i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.2508 | 0.408586 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.11905i | 0.270485i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.4323 | −0.977283 | −0.488641 | − | 0.872485i | \(-0.662507\pi\) | ||||
−0.488641 | + | 0.872485i | \(0.662507\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49.6435i | − | 1.64476i | −0.568936 | − | 0.822381i | \(-0.692645\pi\) | ||
0.568936 | − | 0.822381i | \(-0.307355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 47.0440i | − | 1.55693i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.3939 | − | 4.70850i | −0.673466 | − | 0.155488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.8745 | −1.57923 | −0.789617 | − | 0.613600i | \(-0.789721\pi\) | ||||
−0.789617 | + | 0.613600i | \(0.789721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.5730 | 0.413846 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.70728 | 0.121632 | 0.0608160 | − | 0.998149i | \(-0.480630\pi\) | ||||
0.0608160 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1660 | + | 35.1939i | −0.562593 | + | 1.15343i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.7533i | 0.743318i | 0.928369 | + | 0.371659i | \(0.121211\pi\) | ||||
−0.928369 | + | 0.371659i | \(0.878789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.50972 | 0.212211 | 0.106105 | − | 0.994355i | \(-0.466162\pi\) | ||||
0.106105 | + | 0.994355i | \(0.466162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5158i | 0.440136i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28.9373i | − | 0.940334i | −0.882577 | − | 0.470167i | \(-0.844194\pi\) | ||
0.882577 | − | 0.470167i | \(-0.155806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.29150 | 0.106847 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.81176i | 0.0910819i | 0.998962 | + | 0.0455409i | \(0.0145011\pi\) | ||||
−0.998962 | + | 0.0455409i | \(0.985499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.27841 | + | 31.5249i | −0.235032 | + | 1.01799i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.0405 | −1.42066 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.47938 | −0.176205 | −0.0881025 | − | 0.996111i | \(-0.528080\pi\) | ||||
−0.0881025 | + | 0.996111i | \(0.528080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.8608 | 1.34338 | 0.671688 | − | 0.740834i | \(-0.265570\pi\) | ||||
0.671688 | + | 0.740834i | \(0.265570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.14997 | − | 9.31216i | 0.0689249 | − | 0.298534i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60.6863i | − | 1.94153i | −0.240040 | − | 0.970763i | \(-0.577161\pi\) | ||
0.240040 | − | 0.970763i | \(-0.422839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.11905i | − | 0.259486i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.9767 | 0.381996 | 0.190998 | − | 0.981590i | \(-0.438828\pi\) | ||||
0.190998 | + | 0.981590i | \(0.438828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 7.83826i | − | 0.249242i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4575 | 0.459258 | 0.229629 | − | 0.973278i | \(-0.426249\pi\) | ||||
0.229629 | + | 0.973278i | \(0.426249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.46878i | 0.268209i | 0.990967 | + | 0.134105i | \(0.0428158\pi\) | ||||
−0.990967 | + | 0.134105i | \(0.957184\pi\) | |||||||
\(998\) | 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 | 6300.2.d.f.3401.16 | 16 | ||
3.2 | odd | 2 | inner | 6300.2.d.f.3401.15 | 16 | ||
5.2 | odd | 4 | 1260.2.f.a.629.4 | yes | 8 | ||
5.3 | odd | 4 | 1260.2.f.b.629.3 | yes | 8 | ||
5.4 | even | 2 | inner | 6300.2.d.f.3401.2 | 16 | ||
7.6 | odd | 2 | inner | 6300.2.d.f.3401.14 | 16 | ||
15.2 | even | 4 | 1260.2.f.b.629.5 | yes | 8 | ||
15.8 | even | 4 | 1260.2.f.a.629.6 | yes | 8 | ||
15.14 | odd | 2 | inner | 6300.2.d.f.3401.1 | 16 | ||
20.3 | even | 4 | 5040.2.k.e.1889.3 | 8 | |||
20.7 | even | 4 | 5040.2.k.f.1889.4 | 8 | |||
21.20 | even | 2 | inner | 6300.2.d.f.3401.13 | 16 | ||
35.13 | even | 4 | 1260.2.f.b.629.6 | yes | 8 | ||
35.27 | even | 4 | 1260.2.f.a.629.5 | yes | 8 | ||
35.34 | odd | 2 | inner | 6300.2.d.f.3401.4 | 16 | ||
60.23 | odd | 4 | 5040.2.k.f.1889.6 | 8 | |||
60.47 | odd | 4 | 5040.2.k.e.1889.5 | 8 | |||
105.62 | odd | 4 | 1260.2.f.b.629.4 | yes | 8 | ||
105.83 | odd | 4 | 1260.2.f.a.629.3 | ✓ | 8 | ||
105.104 | even | 2 | inner | 6300.2.d.f.3401.3 | 16 | ||
140.27 | odd | 4 | 5040.2.k.f.1889.5 | 8 | |||
140.83 | odd | 4 | 5040.2.k.e.1889.6 | 8 | |||
420.83 | even | 4 | 5040.2.k.f.1889.3 | 8 | |||
420.167 | even | 4 | 5040.2.k.e.1889.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.f.a.629.3 | ✓ | 8 | 105.83 | odd | 4 | ||
1260.2.f.a.629.4 | yes | 8 | 5.2 | odd | 4 | ||
1260.2.f.a.629.5 | yes | 8 | 35.27 | even | 4 | ||
1260.2.f.a.629.6 | yes | 8 | 15.8 | even | 4 | ||
1260.2.f.b.629.3 | yes | 8 | 5.3 | odd | 4 | ||
1260.2.f.b.629.4 | yes | 8 | 105.62 | odd | 4 | ||
1260.2.f.b.629.5 | yes | 8 | 15.2 | even | 4 | ||
1260.2.f.b.629.6 | yes | 8 | 35.13 | even | 4 | ||
5040.2.k.e.1889.3 | 8 | 20.3 | even | 4 | |||
5040.2.k.e.1889.4 | 8 | 420.167 | even | 4 | |||
5040.2.k.e.1889.5 | 8 | 60.47 | odd | 4 | |||
5040.2.k.e.1889.6 | 8 | 140.83 | odd | 4 | |||
5040.2.k.f.1889.3 | 8 | 420.83 | even | 4 | |||
5040.2.k.f.1889.4 | 8 | 20.7 | even | 4 | |||
5040.2.k.f.1889.5 | 8 | 140.27 | odd | 4 | |||
5040.2.k.f.1889.6 | 8 | 60.23 | odd | 4 | |||
6300.2.d.f.3401.1 | 16 | 15.14 | odd | 2 | inner | ||
6300.2.d.f.3401.2 | 16 | 5.4 | even | 2 | inner | ||
6300.2.d.f.3401.3 | 16 | 105.104 | even | 2 | inner | ||
6300.2.d.f.3401.4 | 16 | 35.34 | odd | 2 | inner | ||
6300.2.d.f.3401.13 | 16 | 21.20 | even | 2 | inner | ||
6300.2.d.f.3401.14 | 16 | 7.6 | odd | 2 | inner | ||
6300.2.d.f.3401.15 | 16 | 3.2 | odd | 2 | inner | ||
6300.2.d.f.3401.16 | 16 | 1.1 | even | 1 | trivial |