Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(113,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.m (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.20138089353117696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(-1.12465 - 0.857418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.337 |
Dual form | 448.2.m.d.113.4 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.416854 | − | 0.416854i | −0.240671 | − | 0.240671i | 0.576457 | − | 0.817128i | \(-0.304435\pi\) |
−0.817128 | + | 0.576457i | \(0.804435\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.13169 | + | 1.13169i | −0.506108 | + | 0.506108i | −0.913329 | − | 0.407222i | \(-0.866498\pi\) |
0.407222 | + | 0.913329i | \(0.366498\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.65247i | − | 0.884155i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.85718 | + | 3.85718i | −1.16298 | + | 1.16298i | −0.179163 | + | 0.983819i | \(0.557339\pi\) |
−0.983819 | + | 0.179163i | \(0.942661\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.66311 | + | 4.66311i | 1.29332 | + | 1.29332i | 0.932724 | + | 0.360591i | \(0.117425\pi\) |
0.360591 | + | 0.932724i | \(0.382575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.943500 | 0.243611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.33230 | −1.29327 | −0.646637 | − | 0.762798i | \(-0.723825\pi\) | ||||
−0.646637 | + | 0.762798i | \(0.723825\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.55919 | + | 2.55919i | 0.587119 | + | 0.587119i | 0.936850 | − | 0.349731i | \(-0.113727\pi\) |
−0.349731 | + | 0.936850i | \(0.613727\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.416854 | − | 0.416854i | 0.0909650 | − | 0.0909650i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.60484i | 0.543147i | 0.962418 | + | 0.271574i | \(0.0875441\pi\) | ||||
−0.962418 | + | 0.271574i | \(0.912456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.43855i | 0.487710i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.35625 | + | 2.35625i | −0.453461 | + | 0.453461i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.22279 | − | 1.22279i | −0.227067 | − | 0.227067i | 0.584399 | − | 0.811466i | \(-0.301330\pi\) |
−0.811466 | + | 0.584399i | \(0.801330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.833708 | 0.149738 | 0.0748692 | − | 0.997193i | \(-0.476146\pi\) | ||||
0.0748692 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.21576 | 0.559792 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.13169 | − | 1.13169i | −0.191291 | − | 0.191291i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.42967 | + | 4.42967i | −0.728234 | + | 0.728234i | −0.970268 | − | 0.242034i | \(-0.922185\pi\) |
0.242034 | + | 0.970268i | \(0.422185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.88768i | − | 0.622526i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.263382i | − | 0.0411333i | −0.999788 | − | 0.0205667i | \(-0.993453\pi\) | ||
0.999788 | − | 0.0205667i | \(-0.00654703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.25233 | + | 1.25233i | −0.190979 | + | 0.190979i | −0.796119 | − | 0.605140i | \(-0.793117\pi\) |
0.605140 | + | 0.796119i | \(0.293117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00177 | + | 3.00177i | 0.447478 | + | 0.447478i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.7559 | 1.56891 | 0.784455 | − | 0.620186i | \(-0.212943\pi\) | ||||
0.784455 | + | 0.620186i | \(0.212943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22279 | + | 2.22279i | 0.311253 | + | 0.311253i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0476221 | − | 0.0476221i | 0.00654139 | − | 0.00654139i | −0.703829 | − | 0.710370i | \(-0.748528\pi\) |
0.710370 | + | 0.703829i | \(0.248528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.73026i | − | 1.17719i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.13362i | − | 0.282605i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.60682 | − | 3.60682i | 0.469567 | − | 0.469567i | −0.432207 | − | 0.901774i | \(-0.642265\pi\) |
0.901774 | + | 0.432207i | \(0.142265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.46399 | + | 4.46399i | 0.571556 | + | 0.571556i | 0.932563 | − | 0.361007i | \(-0.117567\pi\) |
−0.361007 | + | 0.932563i | \(0.617567\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.65247 | 0.334179 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5544 | −1.30911 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.50964 | − | 9.50964i | −1.16179 | − | 1.16179i | −0.984084 | − | 0.177704i | \(-0.943133\pi\) |
−0.177704 | − | 0.984084i | \(-0.556867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08584 | − | 1.08584i | 0.130720 | − | 0.130720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.05301i | − | 0.243647i | −0.992552 | − | 0.121824i | \(-0.961126\pi\) | ||
0.992552 | − | 0.121824i | \(-0.0388743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.48268i | − | 0.641700i | −0.947130 | − | 0.320850i | \(-0.896032\pi\) | ||
0.947130 | − | 0.320850i | \(-0.103968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.01652 | − | 1.01652i | 0.117378 | − | 0.117378i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.85718 | − | 3.85718i | −0.439566 | − | 0.439566i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.21576 | −0.586819 | −0.293409 | − | 0.955987i | \(-0.594790\pi\) | ||||
−0.293409 | + | 0.955987i | \(0.594790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.99297 | −0.665885 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.84045 | − | 5.84045i | −0.641073 | − | 0.641073i | 0.309746 | − | 0.950819i | \(-0.399756\pi\) |
−0.950819 | + | 0.309746i | \(0.899756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.03452 | − | 6.03452i | 0.654535 | − | 0.654535i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.01945i | 0.109297i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.32651i | − | 0.670609i | −0.942110 | − | 0.335304i | \(-0.891161\pi\) | ||
0.942110 | − | 0.335304i | \(-0.108839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.66311 | + | 4.66311i | −0.488827 | + | 0.488827i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.347535 | − | 0.347535i | −0.0360377 | − | 0.0360377i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.79243 | −0.594291 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8089 | 1.90976 | 0.954878 | − | 0.296999i | \(-0.0959858\pi\) | ||||
0.954878 | + | 0.296999i | \(0.0959858\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.2310 | + | 10.2310i | 1.02826 | + | 1.02826i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.88523 | + | 2.88523i | −0.287091 | + | 0.287091i | −0.835929 | − | 0.548838i | \(-0.815070\pi\) |
0.548838 | + | 0.835929i | \(0.315070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74040i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.943500i | 0.0920762i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.33447 | − | 2.33447i | 0.225682 | − | 0.225682i | −0.585204 | − | 0.810886i | \(-0.698986\pi\) |
0.810886 | + | 0.585204i | \(0.198986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.92827 | − | 4.92827i | −0.472042 | − | 0.472042i | 0.430533 | − | 0.902575i | \(-0.358326\pi\) |
−0.902575 | + | 0.430533i | \(0.858326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.69306 | 0.350529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.24381 | 0.493296 | 0.246648 | − | 0.969105i | \(-0.420671\pi\) | ||||
0.246648 | + | 0.969105i | \(0.420671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.94788 | − | 2.94788i | −0.274891 | − | 0.274891i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.3687 | − | 12.3687i | 1.14349 | − | 1.14349i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.33230i | − | 0.488811i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 18.7556i | − | 1.70506i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.109792 | + | 0.109792i | −0.00989959 | + | 0.00989959i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.41814 | − | 8.41814i | −0.752941 | − | 0.752941i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6789 | 1.56875 | 0.784373 | − | 0.620290i | \(-0.212985\pi\) | ||||
0.784373 | + | 0.620290i | \(0.212985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.04408 | 0.0919262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.17911 | + | 2.17911i | 0.190390 | + | 0.190390i | 0.795865 | − | 0.605475i | \(-0.207017\pi\) |
−0.605475 | + | 0.795865i | \(0.707017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.55919 | + | 2.55919i | −0.221910 | + | 0.221910i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.33310i | − | 0.459000i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.54650i | 0.730177i | 0.930973 | + | 0.365088i | \(0.118961\pi\) | ||||
−0.930973 | + | 0.365088i | \(0.881039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.72549 | − | 5.72549i | 0.485629 | − | 0.485629i | −0.421295 | − | 0.906924i | \(-0.638424\pi\) |
0.906924 | + | 0.421295i | \(0.138424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.48364 | − | 4.48364i | −0.377591 | − | 0.377591i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35.9729 | −3.00821 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76764 | 0.229840 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.416854 | + | 0.416854i | 0.0343815 | + | 0.0343815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.395157 | − | 0.395157i | 0.0323725 | − | 0.0323725i | −0.690735 | − | 0.723108i | \(-0.742713\pi\) |
0.723108 | + | 0.690735i | \(0.242713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.71559i | 0.302371i | 0.988505 | + | 0.151185i | \(0.0483090\pi\) | ||||
−0.988505 | + | 0.151185i | \(0.951691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.1437i | 1.14345i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.943500 | + | 0.943500i | −0.0757837 | + | 0.0757837i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.99542 | + | 3.99542i | 0.318869 | + | 0.318869i | 0.848333 | − | 0.529464i | \(-0.177607\pi\) |
−0.529464 | + | 0.848333i | \(0.677607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0397029 | −0.00314864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.60484 | −0.205290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.37168 | − | 3.37168i | −0.264090 | − | 0.264090i | 0.562623 | − | 0.826713i | \(-0.309792\pi\) |
−0.826713 | + | 0.562623i | \(0.809792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.63925 | + | 3.63925i | −0.283315 | + | 0.283315i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4233i | 0.961345i | 0.876900 | + | 0.480673i | \(0.159607\pi\) | ||||
−0.876900 | + | 0.480673i | \(0.840393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.4893i | 2.34533i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.78817 | − | 6.78817i | 0.519105 | − | 0.519105i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.25908 | + | 9.25908i | 0.703955 | + | 0.703955i | 0.965257 | − | 0.261302i | \(-0.0841519\pi\) |
−0.261302 | + | 0.965257i | \(0.584152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.43855 | −0.184337 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00703 | −0.226022 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.95523 | + | 9.95523i | 0.744088 | + | 0.744088i | 0.973362 | − | 0.229274i | \(-0.0736350\pi\) |
−0.229274 | + | 0.973362i | \(0.573635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.08125 | + | 5.08125i | −0.377687 | + | 0.377687i | −0.870267 | − | 0.492580i | \(-0.836054\pi\) |
0.492580 | + | 0.870267i | \(0.336054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.72167i | − | 0.275114i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 10.0260i | − | 0.737129i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.5676 | − | 20.5676i | 1.50405 | − | 1.50405i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.35625 | − | 2.35625i | −0.171392 | − | 0.171392i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7927 | −1.50451 | −0.752254 | − | 0.658873i | \(-0.771033\pi\) | ||||
−0.752254 | + | 0.658873i | \(0.771033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3447 | 0.960574 | 0.480287 | − | 0.877111i | \(-0.340533\pi\) | ||||
0.480287 | + | 0.877111i | \(0.340533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.39965 | + | 4.39965i | 0.315065 | + | 0.315065i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.194462 | − | 0.194462i | 0.0138549 | − | 0.0138549i | −0.700145 | − | 0.714000i | \(-0.746882\pi\) |
0.714000 | + | 0.700145i | \(0.246882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.4003i | 1.02081i | 0.859935 | + | 0.510403i | \(0.170504\pi\) | ||||
−0.859935 | + | 0.510403i | \(0.829496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.92827i | 0.559217i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.22279 | − | 1.22279i | 0.0858232 | − | 0.0858232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.298067 | + | 0.298067i | 0.0208179 | + | 0.0208179i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.90926 | 0.480227 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.7425 | −1.36562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.72356 | − | 7.72356i | −0.531711 | − | 0.531711i | 0.389370 | − | 0.921081i | \(-0.372693\pi\) |
−0.921081 | + | 0.389370i | \(0.872693\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.855805 | + | 0.855805i | −0.0586388 | + | 0.0586388i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.83451i | − | 0.193312i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.833708i | 0.0565958i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.28548 | + | 2.28548i | −0.154438 | + | 0.154438i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.8651 | − | 24.8651i | −1.67261 | − | 1.67261i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.06285 | 0.472963 | 0.236482 | − | 0.971636i | \(-0.424006\pi\) | ||||
0.236482 | + | 0.971636i | \(0.424006\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.46817 | 0.431212 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8229 | + | 11.8229i | 0.784711 | + | 0.784711i | 0.980622 | − | 0.195911i | \(-0.0627664\pi\) |
−0.195911 | + | 0.980622i | \(0.562766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.37815 | + | 9.37815i | −0.619726 | + | 0.619726i | −0.945461 | − | 0.325735i | \(-0.894388\pi\) |
0.325735 | + | 0.945461i | \(0.394388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.21576i | 0.211581i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4385i | 1.60102i | 0.599318 | + | 0.800511i | \(0.295439\pi\) | ||||
−0.599318 | + | 0.800511i | \(0.704561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1724 | + | 12.1724i | −0.794037 | + | 0.794037i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.17421 | + | 2.17421i | 0.141230 | + | 0.141230i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.27660 | 0.406000 | 0.203000 | − | 0.979179i | \(-0.434931\pi\) | ||||
0.203000 | + | 0.979179i | \(0.434931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0124 | −0.967034 | −0.483517 | − | 0.875335i | \(-0.660641\pi\) | ||||
−0.483517 | + | 0.875335i | \(0.660641\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.56695 | + | 9.56695i | 0.613720 | + | 0.613720i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.13169 | − | 1.13169i | 0.0723011 | − | 0.0723011i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8676i | 1.51866i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.86923i | 0.308575i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7926 | + | 11.7926i | −0.744339 | + | 0.744339i | −0.973410 | − | 0.229071i | \(-0.926431\pi\) |
0.229071 | + | 0.973410i | \(0.426431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0473 | − | 10.0473i | −0.631671 | − | 0.631671i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.03103 | −0.315055 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.3977 | 1.27237 | 0.636186 | − | 0.771536i | \(-0.280511\pi\) | ||||
0.636186 | + | 0.771536i | \(0.280511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.42967 | − | 4.42967i | −0.275247 | − | 0.275247i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.24341 | + | 3.24341i | −0.200762 | + | 0.200762i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 23.3452i | − | 1.43953i | −0.694219 | − | 0.719764i | \(-0.744250\pi\) | ||
0.694219 | − | 0.719764i | \(-0.255750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.107787i | 0.00662130i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.63723 | + | 2.63723i | −0.161396 | + | 0.161396i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0705 | + | 22.0705i | 1.34566 | + | 1.34566i | 0.890312 | + | 0.455352i | \(0.150487\pi\) |
0.455352 | + | 0.890312i | \(0.349513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.46392 | −0.0889266 | −0.0444633 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444633 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.88768 | 0.235293 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.40592 | − | 9.40592i | −0.567199 | − | 0.567199i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.39234 | + | 1.39234i | −0.0836578 | + | 0.0836578i | −0.747697 | − | 0.664040i | \(-0.768841\pi\) |
0.664040 | + | 0.747697i | \(0.268841\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.21138i | − | 0.132392i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.66742i | − | 0.338090i | −0.985608 | − | 0.169045i | \(-0.945932\pi\) | ||
0.985608 | − | 0.169045i | \(-0.0540683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.6615 | − | 16.6615i | 0.990424 | − | 0.990424i | −0.00953050 | − | 0.999955i | \(-0.503034\pi\) |
0.999955 | + | 0.00953050i | \(0.00303370\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.41460 | + | 2.41460i | 0.143029 | + | 0.143029i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.263382 | 0.0155469 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4334 | 0.672555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.84057 | − | 7.84057i | −0.459622 | − | 0.459622i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1121 | − | 17.1121i | 0.999698 | − | 0.999698i | −0.000302098 | − | 1.00000i | \(-0.500096\pi\) |
1.00000 | 0.000302098i | \(9.61608e-5\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.16360i | 0.475303i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 18.1770i | − | 1.05473i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.1467 | + | 12.1467i | −0.702461 | + | 0.702461i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25233 | − | 1.25233i | −0.0721833 | − | 0.0721833i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.40544 | 0.138189 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1037 | −0.578537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.59837 | + | 9.59837i | 0.547808 | + | 0.547808i | 0.925806 | − | 0.377998i | \(-0.123388\pi\) |
−0.377998 | + | 0.925806i | \(0.623388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.22662 | − | 3.22662i | 0.183556 | − | 0.183556i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1866i | 1.08797i | 0.839094 | + | 0.543987i | \(0.183086\pi\) | ||||
−0.839094 | + | 0.543987i | \(0.816914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.03963i | − | 0.284857i | −0.989805 | − | 0.142428i | \(-0.954509\pi\) | ||
0.989805 | − | 0.142428i | \(-0.0454911\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00177 | + | 3.00177i | −0.169131 | + | 0.169131i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.52596 | + | 5.52596i | 0.310369 | + | 0.310369i | 0.845052 | − | 0.534683i | \(-0.179569\pi\) |
−0.534683 | + | 0.845052i | \(0.679569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.43305 | 0.528149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.94627 | −0.108630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6464 | − | 13.6464i | −0.759306 | − | 0.759306i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3712 | + | 11.3712i | −0.630763 | + | 0.630763i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.10874i | 0.227214i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.7559i | 0.592992i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7514 | − | 14.7514i | 0.810813 | − | 0.810813i | −0.173943 | − | 0.984756i | \(-0.555651\pi\) |
0.984756 | + | 0.173943i | \(0.0556509\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.7496 | + | 11.7496i | 0.643872 | + | 0.643872i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.5239 | 1.17598 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7111 | 0.910311 | 0.455156 | − | 0.890412i | \(-0.349584\pi\) | ||||
0.455156 | + | 0.890412i | \(0.349584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.18590 | − | 2.18590i | −0.118722 | − | 0.118722i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.21576 | + | 3.21576i | −0.174143 | + | 0.174143i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.45767i | 0.132316i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.57925 | + | 5.57925i | −0.299510 | + | 0.299510i | −0.840822 | − | 0.541312i | \(-0.817928\pi\) |
0.541312 | + | 0.840822i | \(0.317928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.9789 | − | 17.9789i | −0.962388 | − | 0.962388i | 0.0369299 | − | 0.999318i | \(-0.488242\pi\) |
−0.999318 | + | 0.0369299i | \(0.988242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.9750 | −1.17294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.0318 | −1.33231 | −0.666155 | − | 0.745814i | \(-0.732061\pi\) | ||||
−0.666155 | + | 0.745814i | \(0.732061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.32337 | + | 2.32337i | 0.123312 | + | 0.123312i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.22279 | + | 2.22279i | −0.117643 | + | 0.117643i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.9910i | − | 0.949526i | −0.880114 | − | 0.474763i | \(-0.842534\pi\) | ||
0.880114 | − | 0.474763i | \(-0.157466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 5.90105i | − | 0.310582i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.81836 | + | 7.81836i | −0.410357 | + | 0.410357i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.20470 | + | 6.20470i | 0.324769 | + | 0.324769i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3077 | −0.538060 | −0.269030 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269030 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.698611 | −0.0363682 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0476221 | + | 0.0476221i | 0.00247241 | + | 0.00247241i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0555 | − | 16.0555i | 0.831324 | − | 0.831324i | −0.156374 | − | 0.987698i | \(-0.549981\pi\) |
0.987698 | + | 0.156374i | \(0.0499805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.01827i | 0.362422i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.4040i | − | 0.587338i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7922 | + | 15.7922i | −0.811190 | + | 0.811190i | −0.984812 | − | 0.173622i | \(-0.944453\pi\) |
0.173622 | + | 0.984812i | \(0.444453\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.36951 | − | 7.36951i | −0.377551 | − | 0.377551i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.3633 | −0.938319 | −0.469160 | − | 0.883113i | \(-0.655443\pi\) | ||||
−0.469160 | + | 0.883113i | \(0.655443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.73026 | 0.444935 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.32177 | + | 3.32177i | 0.168855 | + | 0.168855i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9554 | − | 13.9554i | 0.707565 | − | 0.707565i | −0.258458 | − | 0.966023i | \(-0.583214\pi\) |
0.966023 | + | 0.258458i | \(0.0832143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.8898i | − | 0.702438i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.81674i | − | 0.0916426i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.90263 | − | 5.90263i | 0.296993 | − | 0.296993i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12815 | − | 1.12815i | −0.0566202 | − | 0.0566202i | 0.678230 | − | 0.734850i | \(-0.262747\pi\) |
−0.734850 | + | 0.678230i | \(0.762747\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.13362 | 0.106815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3470 | −0.716454 | −0.358227 | − | 0.933635i | \(-0.616619\pi\) | ||||
−0.358227 | + | 0.933635i | \(0.616619\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.88768 | + | 3.88768i | 0.193659 | + | 0.193659i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.78219 | − | 6.78219i | 0.337010 | − | 0.337010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 34.1721i | − | 1.69385i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 39.2518i | − | 1.94088i | −0.241350 | − | 0.970438i | \(-0.577590\pi\) | ||
0.241350 | − | 0.970438i | \(-0.422410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.56264 | − | 3.56264i | 0.175732 | − | 0.175732i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.60682 | + | 3.60682i | 0.177480 | + | 0.177480i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2192 | 0.648904 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.77338 | −0.233754 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.41473 | + | 4.41473i | 0.215673 | + | 0.215673i | 0.806672 | − | 0.590999i | \(-0.201266\pi\) |
−0.590999 | + | 0.806672i | \(0.701266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.57494 | + | 7.57494i | −0.369180 | + | 0.369180i | −0.867178 | − | 0.497998i | \(-0.834069\pi\) |
0.497998 | + | 0.867178i | \(0.334069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 28.5297i | − | 1.38716i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 13.0031i | − | 0.630743i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.46399 | + | 4.46399i | −0.216028 | + | 0.216028i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.9955 | + | 14.9955i | 0.723987 | + | 0.723987i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.5396 | 0.893020 | 0.446510 | − | 0.894779i | \(-0.352667\pi\) | ||||
0.446510 | + | 0.894779i | \(0.352667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.21190 | 0.346582 | 0.173291 | − | 0.984871i | \(-0.444560\pi\) | ||||
0.173291 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.15370 | − | 1.15370i | −0.0553159 | − | 0.0553159i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.66630 | + | 6.66630i | −0.318892 | + | 0.318892i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.1615i | − | 0.723617i | −0.932252 | − | 0.361809i | \(-0.882159\pi\) | ||
0.932252 | − | 0.361809i | \(-0.117841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.65247i | 0.126308i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.11746 | − | 2.11746i | 0.100603 | − | 0.100603i | −0.655014 | − | 0.755617i | \(-0.727337\pi\) |
0.755617 | + | 0.655014i | \(0.227337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.15965 | + | 7.15965i | 0.339400 | + | 0.339400i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.329445 | −0.0155822 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.29509 | 0.202698 | 0.101349 | − | 0.994851i | \(-0.467684\pi\) | ||||
0.101349 | + | 0.994851i | \(0.467684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01591 | + | 1.01591i | 0.0478373 | + | 0.0478373i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.54886 | − | 1.54886i | 0.0727718 | − | 0.0727718i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 10.5544i | − | 0.494798i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.7833i | − | 1.29965i | −0.760085 | − | 0.649823i | \(-0.774843\pi\) | ||
0.760085 | − | 0.649823i | \(-0.225157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.5643 | − | 12.5643i | 0.586449 | − | 0.586449i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.50912 | − | 6.50912i | −0.303160 | − | 0.303160i | 0.539089 | − | 0.842249i | \(-0.318769\pi\) |
−0.842249 | + | 0.539089i | \(0.818769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.1018 | 1.81722 | 0.908608 | − | 0.417650i | \(-0.137146\pi\) | ||||
0.908608 | + | 0.417650i | \(0.137146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.786604 | 0.0364779 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4618 | − | 16.4618i | −0.761762 | − | 0.761762i | 0.214879 | − | 0.976641i | \(-0.431064\pi\) |
−0.976641 | + | 0.214879i | \(0.931064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.50964 | − | 9.50964i | 0.439114 | − | 0.439114i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 3.33101i | − | 0.153485i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.66094i | − | 0.444210i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.24073 | + | 6.24073i | −0.286344 | + | 0.286344i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.126316 | − | 0.126316i | −0.00578361 | − | 0.00578361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.2565 | 1.70229 | 0.851145 | − | 0.524930i | \(-0.175908\pi\) | ||||
0.851145 | + | 0.524930i | \(0.175908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.3121 | −1.88367 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.08584 | + | 1.08584i | 0.0494074 | + | 0.0494074i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.2859 | + | 21.2859i | −0.966542 | + | 0.966542i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.4219i | 1.74106i | 0.492113 | + | 0.870531i | \(0.336225\pi\) | ||||
−0.492113 | + | 0.870531i | \(0.663775\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.81100i | 0.127118i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.52330 | + | 9.52330i | −0.429781 | + | 0.429781i | −0.888554 | − | 0.458773i | \(-0.848289\pi\) |
0.458773 | + | 0.888554i | \(0.348289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.52029 | + | 6.52029i | 0.293659 | + | 0.293659i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.1567 | −1.04082 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.05301 | 0.0920901 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.78190 | − | 9.78190i | −0.437898 | − | 0.437898i | 0.453406 | − | 0.891304i | \(-0.350209\pi\) |
−0.891304 | + | 0.453406i | \(0.850209\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.17871 | − | 5.17871i | 0.231368 | − | 0.231368i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0554i | 0.492938i | 0.969151 | + | 0.246469i | \(0.0792703\pi\) | ||||
−0.969151 | + | 0.246469i | \(0.920730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.53038i | − | 0.290598i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7096 | − | 12.7096i | 0.564452 | − | 0.564452i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.173240 | − | 0.173240i | −0.00767871 | − | 0.00767871i | 0.703257 | − | 0.710936i | \(-0.251728\pi\) |
−0.710936 | + | 0.703257i | \(0.751728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.48268 | 0.242540 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0602 | −0.532472 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.75973 | − | 8.75973i | −0.386000 | − | 0.386000i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.4874 | + | 41.4874i | −1.82461 | + | 1.82461i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.71937i | − | 0.338843i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9861i | 1.31371i | 0.754015 | + | 0.656857i | \(0.228115\pi\) | ||||
−0.754015 | + | 0.656857i | \(0.771885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.48931 | + | 1.48931i | −0.0651228 | + | 0.0651228i | −0.738918 | − | 0.673795i | \(-0.764663\pi\) |
0.673795 | + | 0.738918i | \(0.264663\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.01652 | + | 1.01652i | 0.0443646 | + | 0.0443646i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.44558 | −0.193653 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2148 | 0.704991 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.56695 | − | 9.56695i | −0.415170 | − | 0.415170i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.22818 | − | 1.22818i | 0.0531983 | − | 0.0531983i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.28380i | 0.228439i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.29975i | − | 0.358161i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.85718 | − | 3.85718i | 0.166140 | − | 0.166140i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0837 | + | 12.0837i | 0.519519 | + | 0.519519i | 0.917426 | − | 0.397907i | \(-0.130263\pi\) |
−0.397907 | + | 0.917426i | \(0.630263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.23628 | 0.181796 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1545 | 0.477808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2663 | − | 12.2663i | −0.524468 | − | 0.524468i | 0.394449 | − | 0.918918i | \(-0.370935\pi\) |
−0.918918 | + | 0.394449i | \(0.870935\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8406 | − | 11.8406i | 0.505344 | − | 0.505344i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.25872i | − | 0.266631i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.21576i | − | 0.221797i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.17940 | + | 4.17940i | −0.177406 | + | 0.177406i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.32720 | − | 2.32720i | −0.0986065 | − | 0.0986065i | 0.656083 | − | 0.754689i | \(-0.272212\pi\) |
−0.754689 | + | 0.656083i | \(0.772212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.6795 | −0.493992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.1474 | −0.723964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0571 | + | 12.0571i | 0.508146 | + | 0.508146i | 0.913957 | − | 0.405811i | \(-0.133011\pi\) |
−0.405811 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.93437 | + | 5.93437i | −0.249661 | + | 0.249661i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.99297i | − | 0.251681i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.99770i | − | 0.335281i | −0.985848 | − | 0.167641i | \(-0.946385\pi\) | ||
0.985848 | − | 0.167641i | \(-0.0536148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0516 | + | 22.0516i | −0.922832 | + | 0.922832i | −0.997229 | − | 0.0743968i | \(-0.976297\pi\) |
0.0743968 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.66753 | + | 8.66753i | 0.362091 | + | 0.362091i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.35204 | −0.264899 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.4199 | 1.80760 | 0.903798 | − | 0.427960i | \(-0.140768\pi\) | ||||
0.903798 | + | 0.427960i | \(0.140768\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.56280 | − | 5.56280i | −0.231182 | − | 0.231182i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.84045 | − | 5.84045i | 0.242303 | − | 0.242303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.367373i | 0.0152150i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.9952i | 1.15746i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.2274 | − | 18.2274i | 0.752326 | − | 0.752326i | −0.222587 | − | 0.974913i | \(-0.571450\pi\) |
0.974913 | + | 0.222587i | \(0.0714502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13362 | + | 2.13362i | 0.0879143 | + | 0.0879143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.162125 | −0.00666892 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7514 | −1.63239 | −0.816197 | − | 0.577773i | \(-0.803922\pi\) | ||||
−0.816197 | + | 0.577773i | \(0.803922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.03452 | + | 6.03452i | 0.247391 | + | 0.247391i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00280 | − | 6.00280i | 0.245678 | − | 0.245678i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 37.5296i | − | 1.53342i | −0.641996 | − | 0.766708i | \(-0.721893\pi\) | ||
0.641996 | − | 0.766708i | \(-0.278107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.99899i | 0.163122i | 0.996668 | + | 0.0815611i | \(0.0259906\pi\) | ||||
−0.996668 | + | 0.0815611i | \(0.974009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.2240 | + | 25.2240i | −1.02720 | + | 1.02720i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.2256 | + | 21.2256i | 0.862942 | + | 0.862942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3672 | 0.989035 | 0.494517 | − | 0.869168i | \(-0.335345\pi\) | ||||
0.494517 | + | 0.869168i | \(0.335345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01945 | −0.0413103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.1560 | + | 50.1560i | 2.02909 | + | 2.02909i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.7167 | + | 16.7167i | −0.675179 | + | 0.675179i | −0.958905 | − | 0.283726i | \(-0.908429\pi\) |
0.283726 | + | 0.958905i | \(0.408429\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.248501i | − | 0.0100205i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.64202i | 0.106364i | 0.998585 | + | 0.0531819i | \(0.0169363\pi\) | ||||
−0.998585 | + | 0.0531819i | \(0.983064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.9772 | + | 26.9772i | −1.08431 | + | 1.08431i | −0.0882048 | + | 0.996102i | \(0.528113\pi\) |
−0.996102 | + | 0.0882048i | \(0.971887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.13767 | − | 6.13767i | −0.246296 | − | 0.246296i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.32651 | 0.253466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.86071 | 0.274428 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.22975 | + | 8.22975i | 0.328665 | + | 0.328665i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.6204 | − | 23.6204i | 0.941805 | − | 0.941805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9710i | 0.755223i | 0.925964 | + | 0.377611i | \(0.123254\pi\) | ||||
−0.925964 | + | 0.377611i | \(0.876746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.43919i | 0.255935i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.0070 | + | 20.0070i | −0.793954 | + | 0.793954i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.66311 | − | 4.66311i | −0.184759 | − | 0.184759i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.44554 | −0.215422 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.3762 | 1.23929 | 0.619643 | − | 0.784884i | \(-0.287277\pi\) | ||||
0.619643 | + | 0.784884i | \(0.287277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5690 | − | 13.5690i | −0.535110 | − | 0.535110i | 0.386978 | − | 0.922089i | \(-0.373519\pi\) |
−0.922089 | + | 0.386978i | \(0.873519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.18158 | + | 1.18158i | −0.0465245 | + | 0.0465245i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.6587i | 1.55915i | 0.626312 | + | 0.779573i | \(0.284564\pi\) | ||||
−0.626312 | + | 0.779573i | \(0.715436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.8242i | 1.09220i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.347535 | − | 0.347535i | 0.0136210 | − | 0.0136210i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.96664 | + | 2.96664i | 0.116094 | + | 0.116094i | 0.762767 | − | 0.646673i | \(-0.223840\pi\) |
−0.646673 | + | 0.762767i | \(0.723840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.93216 | −0.192715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.5426 | −0.567362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.5078 | + | 19.5078i | 0.759915 | + | 0.759915i | 0.976307 | − | 0.216391i | \(-0.0694287\pi\) |
−0.216391 | + | 0.976307i | \(0.569429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9741 | − | 11.9741i | 0.465739 | − | 0.465739i | −0.434792 | − | 0.900531i | \(-0.643178\pi\) |
0.900531 | + | 0.434792i | \(0.143178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.7303i | 0.805097i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5.79243i | − | 0.224621i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.18518 | − | 3.18518i | 0.123331 | − | 0.123331i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.94418 | − | 2.94418i | −0.113828 | − | 0.113828i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.4368 | −1.32942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.9400 | −1.19265 | −0.596324 | − | 0.802744i | \(-0.703373\pi\) | ||||
−0.596324 | + | 0.802744i | \(0.703373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.74585 | − | 5.74585i | −0.221158 | − | 0.221158i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.0123354 | + | 0.0123354i | −0.000474089 | + | 0.000474089i | −0.707344 | − | 0.706870i | \(-0.750107\pi\) |
0.706870 | + | 0.707344i | \(0.250107\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8089i | 0.721820i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 9.85681i | − | 0.377714i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.1350 | − | 14.1350i | 0.540860 | − | 0.540860i | −0.382921 | − | 0.923781i | \(-0.625082\pi\) |
0.923781 | + | 0.382921i | \(0.125082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.67199 | − | 9.67199i | −0.369548 | − | 0.369548i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.81864 | 0.298300 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.444134 | 0.0169202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.5355 | − | 31.5355i | −1.19967 | − | 1.19967i | −0.974266 | − | 0.225402i | \(-0.927631\pi\) |
−0.225402 | − | 0.974266i | \(-0.572369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.2310 | + | 10.2310i | −0.388645 | + | 0.388645i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9590i | 0.491561i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.40443i | 0.0531966i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.1873 | − | 10.1873i | 0.385319 | − | 0.385319i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8654 | − | 16.8654i | −0.636998 | − | 0.636998i | 0.312816 | − | 0.949814i | \(-0.398728\pi\) |
−0.949814 | + | 0.312816i | \(0.898728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6728 | −0.855120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1482 | 0.382203 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.88523 | − | 2.88523i | −0.108510 | − | 0.108510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.6343 | − | 21.6343i | 0.812493 | − | 0.812493i | −0.172514 | − | 0.985007i | \(-0.555189\pi\) |
0.985007 | + | 0.172514i | \(0.0551890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8346i | 0.518839i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.17168i | 0.0813300i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.7102 | − | 40.7102i | 1.52248 | − | 1.52248i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.61643 | − | 2.61643i | −0.0977123 | − | 0.0977123i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.3698 | −1.50554 | −0.752769 | − | 0.658284i | \(-0.771283\pi\) | ||||
−0.752769 | + | 0.658284i | \(0.771283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.74040 | −0.288267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.25799 | + | 6.25799i | 0.232737 | + | 0.232737i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.98184 | − | 2.98184i | 0.110743 | − | 0.110743i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.43634i | 0.127447i | 0.997968 | + | 0.0637234i | \(0.0202976\pi\) | ||||
−0.997968 | + | 0.0637234i | \(0.979702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.0029i | 0.370476i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.67782 | − | 6.67782i | 0.246988 | − | 0.246988i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.3393 | − | 27.3393i | −1.00980 | − | 1.00980i | −0.999951 | − | 0.00984960i | \(-0.996865\pi\) |
−0.00984960 | − | 0.999951i | \(-0.503135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.943500 | −0.0348015 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 73.3607 | 2.70228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.3591 | + | 28.3591i | 1.04321 | + | 1.04321i | 0.999023 | + | 0.0441845i | \(0.0140690\pi\) |
0.0441845 | + | 0.999023i | \(0.485931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.94932 | − | 9.94932i | 0.365497 | − | 0.365497i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1733i | 1.25370i | 0.779141 | + | 0.626848i | \(0.215656\pi\) | ||||
−0.779141 | + | 0.626848i | \(0.784344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.894391i | 0.0327679i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.4916 | + | 15.4916i | −0.566808 | + | 0.566808i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.33447 | + | 2.33447i | 0.0852997 | + | 0.0852997i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.55791 | −0.312282 | −0.156141 | − | 0.987735i | \(-0.549905\pi\) | ||||
−0.156141 | + | 0.987735i | \(0.549905\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.83155 | 0.358281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.20490 | − | 4.20490i | −0.153032 | − | 0.153032i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0492 | + | 25.0492i | −0.910428 | + | 0.910428i | −0.996306 | − | 0.0858779i | \(-0.972631\pi\) |
0.0858779 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.37655i | 0.304050i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4224i | 1.03031i | 0.857097 | + | 0.515155i | \(0.172266\pi\) | ||||
−0.857097 | + | 0.515155i | \(0.827734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.92827 | − | 4.92827i | 0.178415 | − | 0.178415i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0063 | − | 16.0063i | −0.578711 | − | 0.578711i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6380 | 1.21460 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.0189 | −0.433413 | −0.216707 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216707 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.50286 | − | 8.50286i | −0.306223 | − | 0.306223i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.06913 | − | 5.06913i | 0.182324 | − | 0.182324i | −0.610044 | − | 0.792368i | \(-0.708848\pi\) |
0.792368 | + | 0.610044i | \(0.208848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.03304i | 0.0730290i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.69306i | 0.132488i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.674045 | − | 0.674045i | 0.0241502 | − | 0.0241502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.91882 | + | 7.91882i | 0.283358 | + | 0.283358i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.76241 | 0.205932 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.04315 | −0.322764 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.9635 | − | 16.9635i | −0.604684 | − | 0.604684i | 0.336868 | − | 0.941552i | \(-0.390632\pi\) |
−0.941552 | + | 0.336868i | \(0.890632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.73155 | + | 9.73155i | −0.346453 | + | 0.346453i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.24381i | 0.186448i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.6322i | 1.47840i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0449314 | − | 0.0449314i | 0.00159355 | − | 0.00159355i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.5609 | + | 35.5609i | 1.25963 | + | 1.25963i | 0.951268 | + | 0.308366i | \(0.0997820\pi\) |
0.308366 | + | 0.951268i | \(0.400218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.3537 | −2.02903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7808 | −0.592922 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.1477 | + | 21.1477i | 0.746285 | + | 0.746285i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.94788 | − | 2.94788i | 0.103899 | − | 0.103899i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.4004i | − | 0.647724i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.8621i | 0.417050i | 0.978017 | + | 0.208525i | \(0.0668663\pi\) | ||||
−0.978017 | + | 0.208525i | \(0.933134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.4859 | + | 20.4859i | −0.719357 | + | 0.719357i | −0.968473 | − | 0.249117i | \(-0.919860\pi\) |
0.249117 | + | 0.968473i | \(0.419860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.610240 | + | 0.610240i | 0.0214020 | + | 0.0214020i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.63140 | 0.267316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.40993 | −0.224255 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.3687 | + | 12.3687i | 0.432199 | + | 0.432199i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0707 | + | 29.0707i | −1.01458 | + | 1.01458i | −0.0146829 | + | 0.999892i | \(0.504674\pi\) |
−0.999892 | + | 0.0146829i | \(0.995326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.3595i | − | 1.79028i | −0.445785 | − | 0.895140i | \(-0.647075\pi\) | ||
0.445785 | − | 0.895140i | \(-0.352925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.84180i | 0.273016i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4414 | − | 24.4414i | 0.849912 | − | 0.849912i | −0.140210 | − | 0.990122i | \(-0.544778\pi\) |
0.990122 | + | 0.140210i | \(0.0447777\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3861 | − | 11.3861i | −0.395455 | − | 0.395455i | 0.481172 | − | 0.876626i | \(-0.340211\pi\) |
−0.876626 | + | 0.481172i | \(0.840211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.16081 | 0.0402680 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.33230 | 0.184753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0594 | − | 14.0594i | −0.486544 | − | 0.486544i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.96443 | + | 1.96443i | −0.0679006 | + | 0.0679006i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 35.2906i | − | 1.21837i | −0.793029 | − | 0.609184i | \(-0.791497\pi\) | ||
0.793029 | − | 0.609184i | \(-0.208503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 26.0096i | − | 0.896881i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.36249 | + | 2.36249i | −0.0813683 | + | 0.0813683i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.5044 | − | 34.5044i | −1.18699 | − | 1.18699i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.7556 | 0.644451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.8908 | −0.476732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.5386 | − | 11.5386i | −0.395538 | − | 0.395538i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.93449 | + | 6.93449i | −0.237432 | + | 0.237432i | −0.815786 | − | 0.578354i | \(-0.803695\pi\) |
0.578354 | + | 0.815786i | \(0.303695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3642i | 0.525445i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.1791i | 0.996737i | 0.866965 | + | 0.498369i | \(0.166067\pi\) | ||||
−0.866965 | + | 0.498369i | \(0.833933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.62614 | − | 1.62614i | 0.0554833 | − | 0.0554833i | −0.678821 | − | 0.734304i | \(-0.737509\pi\) |
0.734304 | + | 0.678821i | \(0.237509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.109792 | − | 0.109792i | −0.00374169 | − | 0.00374169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.7059 | 1.14736 | 0.573681 | − | 0.819079i | \(-0.305515\pi\) | ||||
0.573681 | + | 0.819079i | \(0.305515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9568 | −0.712554 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.76608 | − | 4.76608i | −0.161864 | − | 0.161864i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1181 | − | 20.1181i | 0.682460 | − | 0.682460i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 88.6891i | − | 3.00512i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 49.8900i | − | 1.68852i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.41814 | − | 8.41814i | 0.284585 | − | 0.284585i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.3846 | − | 25.3846i | −0.857178 | − | 0.857178i | 0.133827 | − | 0.991005i | \(-0.457273\pi\) |
−0.991005 | + | 0.133827i | \(0.957273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.2665 | −0.481196 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0482 | 0.439606 | 0.219803 | − | 0.975544i | \(-0.429459\pi\) | ||||
0.219803 | + | 0.975544i | \(0.429459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2895 | + | 24.2895i | 0.817407 | + | 0.817407i | 0.985732 | − | 0.168325i | \(-0.0538358\pi\) |
−0.168325 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.40303 | − | 3.40303i | 0.114392 | − | 0.114392i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.8489i | 0.666461i | 0.942845 | + | 0.333230i | \(0.108139\pi\) | ||||
−0.942845 | + | 0.333230i | \(0.891861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.6789i | 0.592930i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.1159 | − | 23.1159i | 0.774413 | − | 0.774413i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.5264 | + | 27.5264i | 0.921137 | + | 0.921137i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.5325 | −0.753178 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1268 | 0.338124 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.01945 | − | 1.01945i | −0.0340006 | − | 0.0340006i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.253935 | + | 0.253935i | −0.00845981 | + | 0.00845981i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.04408i | 0.0347448i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.5008i | − | 0.382300i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.6217 | − | 39.6217i | 1.31562 | − | 1.31562i | 0.398408 | − | 0.917208i | \(-0.369563\pi\) |
0.917208 | − | 0.398408i | \(-0.130437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.65297 | + | 7.65297i | 0.253833 | + | 0.253833i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6260 | −0.385188 | −0.192594 | − | 0.981279i | \(-0.561690\pi\) | ||||
−0.192594 | + | 0.981279i | \(0.561690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0553 | 1.49111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.21178 | + | 4.21178i | 0.139237 | + | 0.139237i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.17911 | + | 2.17911i | −0.0719606 | + | 0.0719606i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1056i | 1.38894i | 0.719523 | + | 0.694468i | \(0.244360\pi\) | ||||
−0.719523 | + | 0.694468i | \(0.755640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 8.00224i | − | 0.263683i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.57342 | − | 9.57342i | 0.315113 | − | 0.315113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8020 | − | 10.8020i | −0.355167 | − | 0.355167i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.5311 | 0.674331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.3239 | 0.994894 | 0.497447 | − | 0.867494i | \(-0.334271\pi\) | ||||
0.497447 | + | 0.867494i | \(0.334271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.55919 | − | 2.55919i | −0.0838742 | − | 0.0838742i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.99802 | − | 7.99802i | 0.261843 | − | 0.261843i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.5524i | 1.52243i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7772i | 0.580757i | 0.956912 | + | 0.290378i | \(0.0937812\pi\) | ||||
−0.956912 | + | 0.290378i | \(0.906219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.10079 | + | 2.10079i | −0.0685567 | + | 0.0685567i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1596 | − | 21.1596i | −0.689783 | − | 0.689783i | 0.272401 | − | 0.962184i | \(-0.412182\pi\) |
−0.962184 | + | 0.272401i | \(0.912182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.686068 | 0.0223415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.33310 | 0.173486 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.8498 | − | 11.8498i | −0.385066 | − | 0.385066i | 0.487857 | − | 0.872923i | \(-0.337779\pi\) |
−0.872923 | + | 0.487857i | \(0.837779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5664 | − | 25.5664i | 0.829920 | − | 0.829920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.60704i | − | 0.149394i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.1855i | − | 0.459513i | −0.973248 | − | 0.229757i | \(-0.926207\pi\) | ||
0.973248 | − | 0.229757i | \(-0.0737930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.5309 | − | 23.5309i | 0.761443 | − | 0.761443i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.93220 | − | 3.93220i | −0.127110 | − | 0.127110i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.54650 | −0.275981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3049 | −0.977578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.19211 | − | 6.19211i | −0.199538 | − | 0.199538i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.1021 | + | 15.1021i | −0.486154 | + | 0.486154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.54873i | − | 0.274909i | −0.990508 | − | 0.137454i | \(-0.956108\pi\) | ||
0.990508 | − | 0.137454i | \(-0.0438920\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3771i | 0.365485i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5089 | − | 25.5089i | 0.818619 | − | 0.818619i | −0.167289 | − | 0.985908i | \(-0.553501\pi\) |
0.985908 | + | 0.167289i | \(0.0535014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.72549 | + | 5.72549i | 0.183551 | + | 0.183551i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.48030 | 0.303613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2375 | 0.423506 | 0.211753 | − | 0.977323i | \(-0.432083\pi\) | ||||
0.211753 | + | 0.977323i | \(0.432083\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.4025 | + | 24.4025i | 0.779906 | + | 0.779906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0721 | + | 13.0721i | −0.417359 | + | 0.417359i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9233i | 0.635455i | 0.948182 | + | 0.317727i | \(0.102920\pi\) | ||||
−0.948182 | + | 0.317727i | \(0.897080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.440142i | 0.0140241i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.48364 | − | 4.48364i | 0.142716 | − | 0.142716i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.26213 | − | 3.26213i | −0.103730 | − | 0.103730i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.3594 | −1.72678 | −0.863392 | − | 0.504533i | \(-0.831665\pi\) | ||||
−0.863392 | + | 0.504533i | \(0.831665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.2984 | −0.390278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.2966 | − | 16.2966i | −0.516638 | − | 0.516638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.4032 | − | 14.4032i | 0.456153 | − | 0.456153i | −0.441237 | − | 0.897390i | \(-0.645460\pi\) |
0.897390 | + | 0.441237i | \(0.145460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 20.8749i | − | 0.660452i |
(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 | 448.2.m.d.337.4 | 12 | ||
4.3 | odd | 2 | 112.2.m.d.29.5 | ✓ | 12 | ||
8.3 | odd | 2 | 896.2.m.g.673.4 | 12 | |||
8.5 | even | 2 | 896.2.m.h.673.3 | 12 | |||
16.3 | odd | 4 | 896.2.m.g.225.4 | 12 | |||
16.5 | even | 4 | inner | 448.2.m.d.113.4 | 12 | ||
16.11 | odd | 4 | 112.2.m.d.85.5 | yes | 12 | ||
16.13 | even | 4 | 896.2.m.h.225.3 | 12 | |||
28.3 | even | 6 | 784.2.x.m.765.1 | 24 | |||
28.11 | odd | 6 | 784.2.x.l.765.1 | 24 | |||
28.19 | even | 6 | 784.2.x.m.557.4 | 24 | |||
28.23 | odd | 6 | 784.2.x.l.557.4 | 24 | |||
28.27 | even | 2 | 784.2.m.h.589.5 | 12 | |||
32.5 | even | 8 | 7168.2.a.bi.1.7 | 12 | |||
32.11 | odd | 8 | 7168.2.a.bj.1.7 | 12 | |||
32.21 | even | 8 | 7168.2.a.bi.1.6 | 12 | |||
32.27 | odd | 8 | 7168.2.a.bj.1.6 | 12 | |||
112.11 | odd | 12 | 784.2.x.l.373.4 | 24 | |||
112.27 | even | 4 | 784.2.m.h.197.5 | 12 | |||
112.59 | even | 12 | 784.2.x.m.373.4 | 24 | |||
112.75 | even | 12 | 784.2.x.m.165.1 | 24 | |||
112.107 | odd | 12 | 784.2.x.l.165.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.5 | ✓ | 12 | 4.3 | odd | 2 | ||
112.2.m.d.85.5 | yes | 12 | 16.11 | odd | 4 | ||
448.2.m.d.113.4 | 12 | 16.5 | even | 4 | inner | ||
448.2.m.d.337.4 | 12 | 1.1 | even | 1 | trivial | ||
784.2.m.h.197.5 | 12 | 112.27 | even | 4 | |||
784.2.m.h.589.5 | 12 | 28.27 | even | 2 | |||
784.2.x.l.165.1 | 24 | 112.107 | odd | 12 | |||
784.2.x.l.373.4 | 24 | 112.11 | odd | 12 | |||
784.2.x.l.557.4 | 24 | 28.23 | odd | 6 | |||
784.2.x.l.765.1 | 24 | 28.11 | odd | 6 | |||
784.2.x.m.165.1 | 24 | 112.75 | even | 12 | |||
784.2.x.m.373.4 | 24 | 112.59 | even | 12 | |||
784.2.x.m.557.4 | 24 | 28.19 | even | 6 | |||
784.2.x.m.765.1 | 24 | 28.3 | even | 6 | |||
896.2.m.g.225.4 | 12 | 16.3 | odd | 4 | |||
896.2.m.g.673.4 | 12 | 8.3 | odd | 2 | |||
896.2.m.h.225.3 | 12 | 16.13 | even | 4 | |||
896.2.m.h.673.3 | 12 | 8.5 | even | 2 | |||
7168.2.a.bi.1.6 | 12 | 32.21 | even | 8 | |||
7168.2.a.bi.1.7 | 12 | 32.5 | even | 8 | |||
7168.2.a.bj.1.6 | 12 | 32.27 | odd | 8 | |||
7168.2.a.bj.1.7 | 12 | 32.11 | odd | 8 |