Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3311,1,Mod(62,3311)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3311, base_ring=CyclotomicField(210))
chi = DirichletCharacter(H, H._module([105, 147, 95]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3311.62");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3311 = 7 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3311.gb (of order \(210\), degree \(48\), 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: | \(1.65240425683\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Coefficient field: | \(\Q(\zeta_{210})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{210}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{210} - \cdots)\) |
Embedding invariants
Embedding label | 1448.1 | ||
Root | \(-0.575617 + 0.817719i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3311.1448 |
Dual form | 3311.1.gb.a.734.1 |
$q$-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 \(\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times\).
\(n\) | \(904\) | \(1893\) | \(2927\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(e\left(\frac{41}{42}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71874 | − | 0.311906i | −1.71874 | − | 0.311906i | −0.772417 | − | 0.635116i | \(-0.780952\pi\) |
−0.946327 | + | 0.323210i | \(0.895238\pi\) | |||||||
\(3\) | 0 | 0 | 0.237080 | − | 0.971490i | \(-0.423810\pi\) | ||||
−0.237080 | + | 0.971490i | \(0.576190\pi\) | |||||||
\(4\) | 1.92056 | + | 0.720799i | 1.92056 | + | 0.720799i | ||||
\(5\) | 0 | 0 | −0.800134 | − | 0.599822i | \(-0.795238\pi\) | ||||
0.800134 | + | 0.599822i | \(0.204762\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(8\) | −1.57658 | − | 0.941963i | −1.57658 | − | 0.941963i | ||||
\(9\) | −0.887586 | − | 0.460642i | −0.887586 | − | 0.460642i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.753071 | − | 0.657939i | −0.753071 | − | 0.657939i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.981148 | − | 0.193256i | \(-0.0619048\pi\) | ||||
−0.981148 | + | 0.193256i | \(0.938095\pi\) | |||||||
\(14\) | 1.61634 | + | 0.662437i | 1.61634 | + | 0.662437i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.871109 | + | 0.761065i | 0.871109 | + | 0.761065i | ||||
\(17\) | 0 | 0 | −0.323210 | − | 0.946327i | \(-0.604762\pi\) | ||||
0.323210 | + | 0.946327i | \(0.395238\pi\) | |||||||
\(18\) | 1.38186 | + | 1.06857i | 1.38186 | + | 1.06857i | ||||
\(19\) | 0 | 0 | 0.447313 | − | 0.894377i | \(-0.352381\pi\) | ||||
−0.447313 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.08912 | + | 1.36572i | 1.08912 | + | 1.36572i | ||||
\(23\) | −0.420593 | + | 1.07165i | −0.420593 | + | 1.07165i | 0.550897 | + | 0.834573i | \(0.314286\pi\) |
−0.971490 | + | 0.237080i | \(0.923810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.280427 | + | 0.959875i | 0.280427 | + | 0.959875i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.72873 | − | 1.10435i | −1.72873 | − | 1.10435i | ||||
\(29\) | −1.38413 | + | 0.337781i | −1.38413 | + | 0.337781i | −0.858449 | − | 0.512899i | \(-0.828571\pi\) |
−0.525684 | + | 0.850680i | \(0.676190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.337330 | − | 0.941386i | \(-0.609524\pi\) | ||||
0.337330 | + | 0.941386i | \(0.390476\pi\) | |||||||
\(32\) | −0.114765 | − | 0.143911i | −0.114765 | − | 0.143911i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.37263 | − | 1.52446i | −1.37263 | − | 1.52446i | ||||
\(37\) | 0.133230 | + | 0.119961i | 0.133230 | + | 0.119961i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.990950 | − | 0.134233i | \(-0.0428571\pi\) | ||||
−0.990950 | + | 0.134233i | \(0.957143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.842721 | + | 0.538351i | 0.842721 | + | 0.538351i | ||||
\(44\) | −0.972079 | − | 1.80643i | −0.972079 | − | 1.80643i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05715 | − | 1.71071i | 1.05715 | − | 1.71071i | ||||
\(47\) | 0 | 0 | −0.550897 | − | 0.834573i | \(-0.685714\pi\) | ||||
0.550897 | + | 0.834573i | \(0.314286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(50\) | −0.182592 | − | 1.73725i | −0.182592 | − | 1.73725i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.49537 | − | 0.179825i | 1.49537 | − | 0.179825i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.34628 | + | 1.24917i | 1.34628 | + | 1.24917i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.48433 | − | 0.148839i | 2.48433 | − | 0.148839i | ||||
\(59\) | 0 | 0 | 0.858449 | − | 0.512899i | \(-0.171429\pi\) | ||||
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.337330 | − | 0.941386i | \(-0.390476\pi\) | ||||
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.772417 | + | 0.635116i | 0.772417 | + | 0.635116i | ||||
\(64\) | −0.395779 | − | 0.735480i | −0.395779 | − | 0.735480i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.97678 | + | 0.297951i | 1.97678 | + | 0.297951i | 0.992847 | + | 0.119394i | \(0.0380952\pi\) |
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.07080 | − | 1.67621i | 1.07080 | − | 1.67621i | 0.447313 | − | 0.894377i | \(-0.352381\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(72\) | 0.965442 | + | 1.56231i | 0.965442 | + | 1.56231i | ||||
\(73\) | 0 | 0 | 0.420357 | − | 0.907359i | \(-0.361905\pi\) | ||||
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(74\) | −0.191572 | − | 0.247737i | −0.191572 | − | 0.247737i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.599822 | + | 0.800134i | 0.599822 | + | 0.800134i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.437934 | − | 0.983616i | −0.437934 | − | 0.983616i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.550897 | − | 0.834573i | \(-0.314286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.575617 | + | 0.817719i | 0.575617 | + | 0.817719i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.762830 | − | 0.646600i | \(-0.223810\pi\) | ||||
−0.762830 | + | 0.646600i | \(0.776190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.28051 | − | 1.18814i | −1.28051 | − | 1.18814i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.567524 | + | 1.74666i | 0.567524 | + | 1.74666i | ||||
\(89\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.58022 | + | 1.75501i | −1.58022 | + | 1.75501i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) | ||||
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(98\) | −1.44329 | − | 0.984017i | −1.44329 | − | 0.984017i | ||||
\(99\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(100\) | −0.153299 | + | 2.04563i | −0.153299 | + | 2.04563i | ||||
\(101\) | 0 | 0 | −0.967835 | − | 0.251587i | \(-0.919048\pi\) | ||||
0.967835 | + | 0.251587i | \(0.0809524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.0149594 | − | 0.999888i | \(-0.504762\pi\) | ||||
0.0149594 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.62625 | − | 0.157342i | −2.62625 | − | 0.157342i | ||||
\(107\) | −1.20645 | − | 1.15348i | −1.20645 | − | 1.15348i | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.38355 | + | 0.543003i | 1.38355 | + | 0.543003i | 0.936235 | − | 0.351375i | \(-0.114286\pi\) |
0.447313 | + | 0.894377i | \(0.352381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.693839 | − | 0.925547i | −0.693839 | − | 0.925547i | ||||
\(113\) | −0.168770 | + | 1.87519i | −0.168770 | + | 1.87519i | 0.251587 | + | 0.967835i | \(0.419048\pi\) |
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.90178 | − | 0.348952i | −2.90178 | − | 0.348952i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.134233 | + | 0.990950i | 0.134233 | + | 0.990950i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.12949 | − | 1.33252i | −1.12949 | − | 1.33252i | ||||
\(127\) | 0.366172 | + | 0.197046i | 0.366172 | + | 0.197046i | 0.646600 | − | 0.762830i | \(-0.276190\pi\) |
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(128\) | 0.507722 | + | 1.56261i | 0.507722 | + | 1.56261i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.30464 | − | 1.12867i | −3.30464 | − | 1.12867i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.697417 | − | 0.298090i | 0.697417 | − | 0.298090i | −0.0149594 | − | 0.999888i | \(-0.504762\pi\) |
0.712376 | + | 0.701798i | \(0.247619\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.486989 | − | 0.873408i | \(-0.338095\pi\) | ||||
−0.486989 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.36326 | + | 2.54698i | −2.36326 | + | 2.54698i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.422605 | − | 1.07678i | −0.422605 | − | 1.07678i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.169409 | + | 0.326424i | 0.169409 | + | 0.326424i | ||||
\(149\) | −0.183830 | − | 0.707179i | −0.183830 | − | 0.707179i | −0.992847 | − | 0.119394i | \(-0.961905\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.27889 | − | 1.33761i | 1.27889 | − | 1.33761i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.781374 | − | 1.56231i | −0.781374 | − | 1.56231i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.0598042 | − | 0.998210i | \(-0.519048\pi\) | ||||
0.0598042 | + | 0.998210i | \(0.480952\pi\) | |||||||
\(158\) | 0.445901 | + | 1.82718i | 0.445901 | + | 1.82718i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.634211 | − | 0.960789i | 0.634211 | − | 0.960789i | ||||
\(162\) | −0.734287 | − | 1.58499i | −0.734287 | − | 1.58499i | ||||
\(163\) | −0.884319 | + | 1.70394i | −0.884319 | + | 1.70394i | −0.193256 | + | 0.981148i | \(0.561905\pi\) |
−0.691063 | + | 0.722795i | \(0.742857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.323210 | − | 0.946327i | \(-0.395238\pi\) | ||||
−0.323210 | + | 0.946327i | \(0.604762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.925304 | − | 0.379225i | 0.925304 | − | 0.379225i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.23046 | + | 1.64137i | 1.23046 | + | 1.64137i | ||||
\(173\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(176\) | −0.155273 | − | 1.14627i | −0.155273 | − | 1.14627i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.48612 | + | 1.33811i | −1.48612 | + | 1.33811i | −0.733052 | + | 0.680173i | \(0.761905\pi\) |
−0.753071 | + | 0.657939i | \(0.771429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.712376 | − | 0.701798i | \(-0.247619\pi\) | ||||
−0.712376 | + | 0.701798i | \(0.752381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.67256 | − | 1.29337i | 1.67256 | − | 1.29337i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.352289 | + | 0.0585016i | −0.352289 | + | 0.0585016i | −0.337330 | − | 0.941386i | \(-0.609524\pi\) |
−0.0149594 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.345627 | + | 1.90456i | 0.345627 | + | 1.90456i | 0.420357 | + | 0.907359i | \(0.361905\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.46135 | + | 1.43965i | 1.46135 | + | 1.43965i | ||||
\(197\) | 0.689193 | + | 1.01086i | 0.689193 | + | 1.01086i | 0.998210 | + | 0.0598042i | \(0.0190476\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(198\) | −0.337583 | − | 1.71389i | −0.337583 | − | 1.71389i | ||||
\(199\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(200\) | 0.462051 | − | 1.77747i | 0.462051 | − | 1.77747i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.42411 | − | 0.0426221i | 1.42411 | − | 0.0426221i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.866962 | − | 0.757442i | 0.866962 | − | 0.757442i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.48916 | + | 0.410983i | −1.48916 | + | 0.410983i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.575617 | + | 0.817719i | \(0.695238\pi\) | |||||||
\(212\) | 3.00157 | + | 0.732496i | 3.00157 | + | 0.732496i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.71380 | + | 2.35884i | 1.71380 | + | 2.35884i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.20860 | − | 1.36482i | −2.20860 | − | 1.36482i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.512899 | − | 0.858449i | \(-0.328571\pi\) | ||||
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(224\) | 0.0823363 | + | 0.164627i | 0.0823363 | + | 0.164627i | ||||
\(225\) | 0.193256 | − | 0.981148i | 0.193256 | − | 0.981148i | ||||
\(226\) | 0.874958 | − | 3.17034i | 0.874958 | − | 3.17034i | ||||
\(227\) | 0 | 0 | 0.280427 | − | 0.959875i | \(-0.409524\pi\) | ||||
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.646600 | − | 0.762830i | \(-0.276190\pi\) | ||||
−0.646600 | + | 0.762830i | \(0.723810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.50037 | + | 0.771263i | 2.50037 | + | 0.771263i | ||||
\(233\) | 0.999552 | + | 0.0299155i | 0.999552 | + | 0.0299155i | 0.525684 | − | 0.850680i | \(-0.323810\pi\) |
0.473869 | + | 0.880596i | \(0.342857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.75503 | + | 0.877761i | 1.75503 | + | 0.877761i | 0.963963 | + | 0.266037i | \(0.0857143\pi\) |
0.791071 | + | 0.611724i | \(0.209524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(242\) | 0.0783706 | − | 1.74506i | 0.0783706 | − | 1.74506i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(252\) | 1.02568 | + | 1.77654i | 1.02568 | + | 1.77654i | ||||
\(253\) | 1.02182 | − | 0.530307i | 1.02182 | − | 0.530307i | ||||
\(254\) | −0.567897 | − | 0.452882i | −0.567897 | − | 0.452882i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.273145 | − | 2.01644i | −0.273145 | − | 2.01644i | ||||
\(257\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.105377 | − | 0.145039i | −0.105377 | − | 0.145039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.38413 | + | 0.337781i | 1.38413 | + | 0.337781i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.480819 | + | 0.148313i | −0.480819 | + | 0.148313i | −0.525684 | − | 0.850680i | \(-0.676190\pi\) |
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.58176 | + | 1.99709i | 3.58176 | + | 1.99709i | ||||
\(269\) | 0 | 0 | −0.963963 | − | 0.266037i | \(-0.914286\pi\) | ||||
0.963963 | + | 0.266037i | \(0.0857143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.907359 | − | 0.420357i | \(-0.861905\pi\) | ||||
0.907359 | + | 0.420357i | \(0.138095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.29166 | + | 0.294812i | −1.29166 | + | 0.294812i | ||||
\(275\) | 0.420357 | − | 0.907359i | 0.420357 | − | 0.907359i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.953345 | + | 0.939189i | 0.953345 | + | 0.939189i | 0.998210 | − | 0.0598042i | \(-0.0190476\pi\) |
−0.0448648 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.891652 | + | 0.231783i | −0.891652 | + | 0.231783i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.959875 | − | 0.280427i | \(-0.0904762\pi\) | ||||
−0.959875 | + | 0.280427i | \(0.909524\pi\) | |||||||
\(284\) | 3.26475 | − | 2.44743i | 3.26475 | − | 2.44743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0355723 | + | 0.180599i | 0.0355723 | + | 0.180599i | ||||
\(289\) | −0.791071 | + | 0.611724i | −0.791071 | + | 0.611724i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.0896393 | − | 0.995974i | \(-0.528571\pi\) | ||||
0.0896393 | + | 0.995974i | \(0.471429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0970492 | − | 0.314626i | −0.0970492 | − | 0.314626i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0953831 | + | 1.27280i | 0.0953831 | + | 1.27280i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.712376 | − | 0.701798i | −0.712376 | − | 0.701798i | ||||
\(302\) | −2.61529 | + | 1.90012i | −2.61529 | + | 1.90012i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(308\) | 0.575260 | + | 1.96906i | 0.575260 | + | 1.96906i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.420357 | − | 0.907359i | \(-0.638095\pi\) | ||||
0.420357 | + | 0.907359i | \(0.361905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.0299155 | − | 0.999552i | \(-0.509524\pi\) | ||||
0.0299155 | + | 0.999552i | \(0.490476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.132090 | − | 2.20476i | −0.132090 | − | 2.20476i | ||||
\(317\) | 0.662421 | − | 1.54981i | 0.662421 | − | 1.54981i | −0.163818 | − | 0.986491i | \(-0.552381\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.26459 | + | 0.656301i | 1.26459 | + | 0.656301i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.38972 | + | 1.45354i | −1.38972 | + | 1.45354i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.516097 | + | 1.98538i | 0.516097 | + | 1.98538i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.05139 | − | 2.65282i | 2.05139 | − | 2.65282i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.34803 | − | 1.45284i | 1.34803 | − | 1.45284i | 0.575617 | − | 0.817719i | \(-0.304762\pi\) |
0.772417 | − | 0.635116i | \(-0.219048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0629940 | − | 0.167847i | −0.0629940 | − | 0.167847i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.202501 | + | 0.952694i | −0.202501 | + | 0.952694i | 0.753071 | + | 0.657939i | \(0.228571\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(338\) | −1.70864 | + | 0.363184i | −1.70864 | + | 0.363184i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(344\) | −0.821511 | − | 1.64257i | −0.821511 | − | 1.64257i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.836182 | − | 0.986491i | −0.836182 | − | 0.986491i | 0.163818 | − | 0.986491i | \(-0.447619\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.0149594 | − | 0.999888i | \(-0.495238\pi\) | ||||
−0.0149594 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(350\) | −0.182592 | + | 1.73725i | −0.182592 | + | 1.73725i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.00825820 | + | 0.183883i | −0.00825820 | + | 0.183883i | ||||
\(353\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.97163 | − | 1.83634i | 2.97163 | − | 1.83634i | ||||
\(359\) | 0.651501 | + | 0.792344i | 0.651501 | + | 0.792344i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.599822 | − | 0.800134i | −0.599822 | − | 0.800134i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.998210 | − | 0.0598042i | \(-0.980952\pi\) | ||||
0.998210 | + | 0.0598042i | \(0.0190476\pi\) | |||||||
\(368\) | −1.18198 | + | 0.613428i | −1.18198 | + | 0.613428i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.50008 | − | 0.135010i | −1.50008 | − | 0.135010i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.142820 | + | 1.90580i | −0.142820 | + | 1.90580i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.330422 | + | 0.773060i | 0.330422 | + | 0.773060i | 0.999552 | + | 0.0299155i | \(0.00952381\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.623742 | + | 0.00933186i | 0.623742 | + | 0.00933186i | ||||
\(383\) | 0 | 0 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.38126i | − | 3.38126i | ||||||
\(387\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.342721 | + | 0.327675i | −0.342721 | + | 0.327675i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.05715 | − | 1.50178i | −1.05715 | − | 1.50178i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.869253 | − | 1.95237i | −0.869253 | − | 1.95237i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0306872 | + | 2.05114i | 0.0306872 | + | 2.05114i | ||||
\(397\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.486245 | + | 1.04958i | −0.486245 | + | 1.04958i | ||||
\(401\) | 0.831706 | + | 1.34590i | 0.831706 | + | 1.34590i | 0.936235 | + | 0.351375i | \(0.114286\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.46098 | − | 0.370933i | −2.46098 | − | 0.370933i | ||||
\(407\) | −0.0214048 | − | 0.177996i | −0.0214048 | − | 0.177996i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.473869 | − | 0.880596i | \(-0.657143\pi\) | ||||
0.473869 | + | 0.880596i | \(0.342857\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.72634 | + | 1.03144i | −1.72634 | + | 1.03144i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.693256 | − | 0.115123i | −0.693256 | − | 0.115123i | −0.193256 | − | 0.981148i | \(-0.561905\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | 2.68768 | − | 0.241895i | 2.68768 | − | 0.241895i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.52696 | − | 1.12507i | −2.52696 | − | 1.12507i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.48563 | − | 3.08495i | −1.48563 | − | 3.08495i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.05140 | + | 1.44713i | −1.05140 | + | 1.44713i | −0.163818 | + | 0.986491i | \(0.552381\pi\) |
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.379225 | − | 0.925304i | \(-0.623810\pi\) | ||||
0.379225 | + | 0.925304i | \(0.376190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.26579 | + | 2.04013i | 2.26579 | + | 2.04013i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.59580 | − | 0.889773i | 1.59580 | − | 0.889773i | 0.599822 | − | 0.800134i | \(-0.295238\pi\) |
0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.234215 | + | 0.801695i | 0.234215 | + | 0.801695i | ||||
\(449\) | −0.891446 | + | 0.904883i | −0.891446 | + | 0.904883i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(450\) | −0.638184 | + | 1.62607i | −0.638184 | + | 1.62607i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.67577 | + | 3.47978i | −1.67577 | + | 3.47978i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.829730 | + | 0.724913i | 0.829730 | + | 0.724913i | 0.963963 | − | 0.266037i | \(-0.0857143\pi\) |
−0.134233 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.563320 | − | 0.826239i | \(-0.309524\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.954688 | − | 1.02891i | −0.954688 | − | 1.02891i | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) |
0.0448648 | − | 0.998993i | \(-0.485714\pi\) | |||||||
\(464\) | −1.46280 | − | 0.759171i | −1.46280 | − | 0.759171i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.70864 | − | 0.363184i | −1.70864 | − | 0.363184i | ||||
\(467\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.87163 | − | 0.702435i | −1.87163 | − | 0.702435i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.280427 | − | 0.959875i | −0.280427 | − | 0.959875i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41010 | − | 0.529221i | −1.41010 | − | 0.529221i | ||||
\(478\) | −2.74268 | − | 2.05605i | −2.74268 | − | 2.05605i | ||||
\(479\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.456472 | + | 1.99994i | −0.456472 | + | 1.99994i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.64257 | − | 0.673190i | −1.64257 | − | 0.673190i | −0.646600 | − | 0.762830i | \(-0.723810\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.56447 | + | 1.20978i | 1.56447 | + | 1.20978i | 0.873408 | + | 0.486989i | \(0.161905\pi\) |
0.691063 | + | 0.722795i | \(0.257143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.39591 | + | 1.41695i | −1.39591 | + | 1.41695i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.99776 | + | 0.0298887i | −1.99776 | + | 0.0298887i | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) |
−0.998210 | + | 0.0598042i | \(0.980952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.873408 | − | 0.486989i | \(-0.161905\pi\) | ||||
−0.873408 | + | 0.486989i | \(0.838095\pi\) | |||||||
\(504\) | −0.619522 | − | 1.72890i | −0.619522 | − | 1.72890i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.92165 | + | 0.592751i | −1.92165 | + | 0.592751i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.561226 | + | 0.642375i | 0.561226 | + | 0.642375i | ||||
\(509\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.0857586 | + | 1.90956i | −0.0857586 | + | 1.90956i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.135878 | + | 0.282154i | 0.135878 | + | 0.282154i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.817719 | − | 0.575617i | \(-0.195238\pi\) | ||||
−0.817719 | + | 0.575617i | \(0.804762\pi\) | |||||||
\(522\) | −2.27361 | − | 1.01228i | −2.27361 | − | 1.01228i | ||||
\(523\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.872665 | − | 0.104942i | 0.872665 | − | 0.104942i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.238491 | − | 0.221287i | −0.238491 | − | 0.221287i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.83589 | − | 2.33179i | −2.83589 | − | 2.33179i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.420357 | − | 0.907359i | −0.420357 | − | 0.907359i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0210231 | − | 0.702435i | 0.0210231 | − | 0.702435i | −0.925304 | − | 0.379225i | \(-0.876190\pi\) |
0.946327 | − | 0.323210i | \(-0.104762\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.832156 | + | 1.07613i | 0.832156 | + | 1.07613i | 0.995974 | + | 0.0896393i | \(0.0285714\pi\) |
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(548\) | 1.55429 | − | 0.0698035i | 1.55429 | − | 0.0698035i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.00550 | + | 1.42841i | −1.00550 | + | 1.42841i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.223859 | + | 1.05317i | 0.223859 | + | 1.05317i | ||||
\(554\) | −1.34562 | − | 1.91158i | −1.34562 | − | 1.91158i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.384580 | − | 0.367696i | 0.384580 | − | 0.367696i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.60482 | − | 0.120264i | 1.60482 | − | 0.120264i | ||||
\(563\) | 0 | 0 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.393025 | − | 0.919528i | −0.393025 | − | 0.919528i | ||||
\(568\) | −3.26713 | + | 1.63402i | −3.26713 | + | 1.63402i | ||||
\(569\) | 0.534897 | − | 0.247805i | 0.534897 | − | 0.247805i | −0.134233 | − | 0.990950i | \(-0.542857\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.54711 | − | 1.05480i | −1.54711 | − | 1.05480i | −0.971490 | − | 0.237080i | \(-0.923810\pi\) |
−0.575617 | − | 0.817719i | \(-0.695238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.14660 | − | 0.103196i | −1.14660 | − | 0.103196i | ||||
\(576\) | 0.0124942 | + | 0.835114i | 0.0124942 | + | 0.835114i | ||||
\(577\) | 0 | 0 | −0.941386 | − | 0.337330i | \(-0.890476\pi\) | ||||
0.941386 | + | 0.337330i | \(0.109524\pi\) | |||||||
\(578\) | 1.55045 | − | 0.804658i | 1.55045 | − | 0.804658i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.24443 | − | 0.848441i | −1.24443 | − | 0.848441i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.635116 | − | 0.772417i | \(-0.719048\pi\) | ||||
0.635116 | + | 0.772417i | \(0.280952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0247599 | + | 0.205896i | 0.0247599 | + | 0.205896i | ||||
\(593\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.156677 | − | 1.49069i | 0.156677 | − | 1.49069i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21074 | + | 1.42838i | 1.21074 | + | 1.42838i | 0.873408 | + | 0.486989i | \(0.161905\pi\) |
0.337330 | + | 0.941386i | \(0.390476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(602\) | 1.00550 | + | 1.42841i | 1.00550 | + | 1.42841i | ||||
\(603\) | −1.61731 | − | 1.17504i | −1.61731 | − | 1.17504i | ||||
\(604\) | 3.42033 | − | 1.64714i | 3.42033 | − | 1.64714i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.946327 | − | 0.323210i | \(-0.895238\pi\) | ||||
0.946327 | + | 0.323210i | \(0.104762\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.562294 | − | 1.49823i | −0.562294 | − | 1.49823i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) |
0.280427 | − | 0.959875i | \(-0.409524\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.191971 | − | 1.82649i | −0.191971 | − | 1.82649i | ||||
\(617\) | 0.141209 | + | 0.359794i | 0.141209 | + | 0.359794i | 0.983930 | − | 0.178557i | \(-0.0571429\pi\) |
−0.842721 | + | 0.538351i | \(0.819048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.575617 | − | 0.817719i | \(-0.304762\pi\) | ||||
−0.575617 | + | 0.817719i | \(0.695238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.842721 | + | 0.538351i | −0.842721 | + | 0.538351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.243197 | − | 0.996553i | −0.243197 | − | 0.996553i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.712376 | − | 0.701798i | \(-0.247619\pi\) | |||||||
\(632\) | −0.236092 | + | 1.96327i | −0.236092 | + | 1.96327i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.62193 | + | 2.45712i | −1.62193 | + | 2.45712i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.96880 | − | 1.52245i | −1.96880 | − | 1.52245i | ||||
\(639\) | −1.72256 | + | 0.994522i | −1.72256 | + | 0.994522i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.444054 | − | 0.293118i | 0.444054 | − | 0.293118i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.753071 | + | 0.657939i | \(0.228571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.473869 | − | 0.880596i | \(-0.342857\pi\) | ||||
−0.473869 | + | 0.880596i | \(0.657143\pi\) | |||||||
\(644\) | 1.91058 | − | 1.38812i | 1.91058 | − | 1.38812i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.178557 | − | 0.983930i | \(-0.442857\pi\) | ||||
−0.178557 | + | 0.983930i | \(0.557143\pi\) | |||||||
\(648\) | −0.137245 | − | 1.83141i | −0.137245 | − | 1.83141i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.92659 | + | 2.63511i | −2.92659 | + | 2.63511i | ||||
\(653\) | 0.146600 | + | 1.62885i | 0.146600 | + | 1.62885i | 0.646600 | + | 0.762830i | \(0.276190\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.85654 | + | 0.139129i | 1.85654 | + | 0.139129i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(662\) | −2.77007 | + | 2.07659i | −2.77007 | + | 2.07659i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0559181 | + | 0.308134i | 0.0559181 | + | 0.308134i | ||||
\(667\) | 0.220173 | − | 1.62538i | 0.220173 | − | 1.62538i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.238438 | − | 0.917253i | 0.238438 | − | 0.917253i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.971490 | − | 0.237080i | \(-0.0761905\pi\) | |||||||
\(674\) | 0.645199 | − | 1.57428i | 0.645199 | − | 1.57428i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.05045 | − | 0.0613676i | 2.05045 | − | 0.0613676i | ||||
\(677\) | 0 | 0 | −0.963963 | − | 0.266037i | \(-0.914286\pi\) | ||||
0.963963 | + | 0.266037i | \(0.0857143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.86938 | + | 0.576628i | −1.86938 | + | 0.576628i | −0.873408 | + | 0.486989i | \(0.838095\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.20716 | + | 1.26259i | 1.20716 | + | 1.26259i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.324382 | + | 1.11033i | 0.324382 | + | 1.11033i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.850680 | − | 0.525684i | \(-0.823810\pi\) | ||||
0.850680 | + | 0.525684i | \(0.176190\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.163818 | − | 0.986491i | −0.163818 | − | 0.986491i | ||||
\(694\) | 1.12949 | + | 1.95634i | 1.12949 | + | 1.95634i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.575260 | − | 1.96906i | 0.575260 | − | 1.96906i | ||||
\(701\) | −0.0582479 | − | 0.104467i | −0.0582479 | − | 0.104467i | 0.842721 | − | 0.538351i | \(-0.180952\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.185851 | + | 0.814267i | −0.185851 | + | 0.814267i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.86224 | − | 0.337947i | 1.86224 | − | 0.337947i | 0.873408 | − | 0.486989i | \(-0.161905\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0643912 | + | 1.07477i | −0.0643912 | + | 1.07477i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.81870 | + | 1.49873i | −3.81870 | + | 1.49873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.872626 | − | 1.56504i | −0.872626 | − | 1.56504i | ||||
\(719\) | 0 | 0 | 0.280427 | − | 0.959875i | \(-0.409524\pi\) | ||||
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.781374 | + | 1.56231i | 0.781374 | + | 1.56231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.712376 | − | 1.23387i | −0.712376 | − | 1.23387i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.134233 | − | 0.990950i | −0.134233 | − | 0.990950i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.691063 | − | 0.722795i | \(-0.742857\pi\) | ||||
0.691063 | + | 0.722795i | \(0.257143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.202492 | − | 0.0624604i | 0.202492 | − | 0.0624604i | ||||
\(737\) | −1.29262 | − | 1.52498i | −1.29262 | − | 1.52498i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.591952 | + | 0.517173i | −0.591952 | + | 0.517173i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.53614 | + | 0.699931i | 2.53614 | + | 0.699931i | ||||
\(743\) | 1.19911 | − | 0.0358879i | 1.19911 | − | 0.0358879i | 0.575617 | − | 0.817719i | \(-0.304762\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.839902 | − | 3.23104i | 0.839902 | − | 3.23104i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.940264 | + | 1.37911i | 0.940264 | + | 1.37911i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.25307 | − | 1.52396i | 1.25307 | − | 1.52396i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.753071 | − | 0.657939i | \(-0.228571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.650887 | + | 0.487939i | −0.650887 | + | 0.487939i | −0.873408 | − | 0.486989i | \(-0.838095\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(758\) | −0.326788 | − | 1.43175i | −0.326788 | − | 1.43175i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.193256 | − | 0.981148i | \(-0.561905\pi\) | ||||
0.193256 | + | 0.981148i | \(0.438095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.24042 | − | 0.818792i | −1.24042 | − | 0.818792i | ||||
\(764\) | −0.718761 | − | 0.141574i | −0.718761 | − | 0.141574i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||||
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.709008 | + | 3.90696i | −0.709008 | + | 3.90696i | ||||
\(773\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(774\) | 0.589254 | + | 1.64443i | 0.589254 | + | 1.64443i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.691253 | − | 0.456292i | 0.691253 | − | 0.456292i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.90923 | + | 0.557782i | −1.90923 | + | 0.557782i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.486245 | + | 1.04958i | 0.486245 | + | 1.04958i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.119394 | − | 0.992847i | \(-0.461905\pi\) | ||||
−0.119394 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(788\) | 0.595011 | + | 2.43819i | 0.595011 | + | 2.43819i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.554957 | − | 1.79913i | 0.554957 | − | 1.79913i | ||||
\(792\) | 0.300859 | − | 1.81174i | 0.300859 | − | 1.81174i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.251587 | − | 0.967835i | \(-0.580952\pi\) | ||||
0.251587 | + | 0.967835i | \(0.419048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.105953 | − | 0.150516i | 0.105953 | − | 0.150516i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.00970 | − | 2.57267i | −1.00970 | − | 2.57267i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.436004 | + | 0.186357i | −0.436004 | + | 0.186357i | −0.599822 | − | 0.800134i | \(-0.704762\pi\) |
0.163818 | + | 0.986491i | \(0.447619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(812\) | 2.76582 | + | 0.944642i | 2.76582 | + | 0.944642i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0187287 | + | 0.312606i | −0.0187287 | + | 0.312606i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.104739 | − | 0.279077i | 0.104739 | − | 0.279077i | −0.873408 | − | 0.486989i | \(-0.838095\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.135176 | + | 1.28611i | −0.135176 | + | 1.28611i | 0.691063 | + | 0.722795i | \(0.257143\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.238121 | + | 1.98014i | 0.238121 | + | 1.98014i | 0.193256 | + | 0.981148i | \(0.438095\pi\) |
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(828\) | 2.21102 | − | 0.829808i | 2.21102 | − | 0.829808i | ||||
\(829\) | 0 | 0 | −0.959875 | − | 0.280427i | \(-0.909524\pi\) | ||||
0.959875 | + | 0.280427i | \(0.0904762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.722795 | − | 0.691063i | \(-0.757143\pi\) | ||||
0.722795 | + | 0.691063i | \(0.242857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.914141 | − | 0.474424i | 0.914141 | − | 0.474424i | ||||
\(842\) | 1.15562 | + | 0.414098i | 1.15562 | + | 0.414098i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.15626 | − | 0.284069i | −3.15626 | − | 0.284069i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(848\) | 1.43949 | + | 0.981426i | 1.43949 | + | 0.981426i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.184592 | + | 0.0923217i | −0.184592 | + | 0.0923217i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.815526 | + | 2.95499i | 0.815526 | + | 2.95499i | ||||
\(857\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.25846 | − | 2.15931i | 2.25846 | − | 2.15931i | ||||
\(863\) | −1.42020 | + | 1.20381i | −1.42020 | + | 1.20381i | −0.473869 | + | 0.880596i | \(0.657143\pi\) |
−0.946327 | + | 0.323210i | \(0.895238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.317363 | + | 1.02887i | −0.317363 | + | 1.02887i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.66979 | − | 2.15934i | −1.66979 | − | 2.15934i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.39124 | + | 0.979332i | 1.39124 | + | 0.979332i | 0.998210 | + | 0.0598042i | \(0.0190476\pi\) |
0.393025 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(882\) | 0.827762 | + | 1.53824i | 0.827762 | + | 1.53824i | ||||
\(883\) | 0.343758 | + | 0.282653i | 0.343758 | + | 0.282653i | 0.791071 | − | 0.611724i | \(-0.209524\pi\) |
−0.447313 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.02029 | + | 1.03155i | −3.02029 | + | 1.03155i | ||||
\(887\) | 0 | 0 | 0.858449 | − | 0.512899i | \(-0.171429\pi\) | ||||
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.317202 | − | 0.268871i | −0.317202 | − | 0.268871i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.171743 | − | 1.63402i | −0.171743 | − | 1.63402i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.81441 | − | 1.27721i | 1.81441 | − | 1.27721i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.07837 | − | 1.74506i | 1.07837 | − | 1.74506i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.03244 | − | 2.79742i | 2.03244 | − | 2.79742i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0225748 | − | 0.502667i | 0.0225748 | − | 0.502667i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.741260 | + | 0.848441i | 0.741260 | + | 0.848441i | 0.992847 | − | 0.119394i | \(-0.0380952\pi\) |
−0.251587 | + | 0.967835i | \(0.580952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.19999 | − | 1.50474i | −1.19999 | − | 1.50474i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0393651 | + | 0.0450570i | −0.0393651 | + | 0.0450570i | −0.772417 | − | 0.635116i | \(-0.780952\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0777861 | + | 0.161524i | −0.0777861 | + | 0.161524i | ||||
\(926\) | 1.31994 | + | 2.06620i | 1.31994 | + | 2.06620i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.207460 | + | 0.160426i | 0.207460 | + | 0.160426i | ||||
\(929\) | 0 | 0 | −0.323210 | − | 0.946327i | \(-0.604762\pi\) | ||||
0.323210 | + | 0.946327i | \(0.395238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.89814 | + | 0.777931i | 1.89814 | + | 0.777931i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.887586 | − | 0.460642i | \(-0.847619\pi\) | ||||
0.887586 | + | 0.460642i | \(0.152381\pi\) | |||||||
\(938\) | 2.99776 | + | 1.79108i | 2.99776 | + | 1.79108i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.800134 | − | 0.599822i | \(-0.795238\pi\) | ||||
0.800134 | + | 0.599822i | \(0.204762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.182592 | + | 1.73725i | 0.182592 | + | 1.73725i | ||||
\(947\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.262600 | + | 0.0558173i | 0.262600 | + | 0.0558173i | 0.337330 | − | 0.941386i | \(-0.390476\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(954\) | 2.25854 | + | 1.34942i | 2.25854 | + | 1.34942i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.73796 | + | 2.95082i | 2.73796 | + | 2.95082i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.744153 | + | 0.146575i | −0.744153 | + | 0.146575i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.772417 | + | 0.635116i | −0.772417 | + | 0.635116i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.539484 | + | 1.57956i | 0.539484 | + | 1.57956i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.787376 | − | 1.63500i | 0.787376 | − | 1.63500i | 0.0149594 | − | 0.999888i | \(-0.495238\pi\) |
0.772417 | − | 0.635116i | \(-0.219048\pi\) | |||||||
\(968\) | 0.721809 | − | 1.68876i | 0.721809 | − | 1.68876i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.280427 | − | 0.959875i | \(-0.590476\pi\) | ||||
0.280427 | + | 0.959875i | \(0.409524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.61319 | + | 1.66937i | 2.61319 | + | 1.66937i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.579161 | − | 1.61626i | −0.579161 | − | 1.61626i | −0.772417 | − | 0.635116i | \(-0.780952\pi\) |
0.193256 | − | 0.981148i | \(-0.438095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.977888 | − | 1.11928i | −0.977888 | − | 1.11928i | ||||
\(982\) | −2.31159 | − | 2.56728i | −2.31159 | − | 2.56728i | ||||
\(983\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.931368 | + | 0.676678i | −0.931368 | + | 0.676678i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.678448 | − | 1.40881i | −0.678448 | − | 1.40881i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.222521 | − | 0.974928i | \(-0.428571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.84116 | − | 1.99998i | 2.84116 | − | 1.99998i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | ||||
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(998\) | 3.44297 | + | 0.571743i | 3.44297 | + | 0.571743i | ||||
\(999\) | 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 | 3311.1.gb.a.1448.1 | yes | 48 | |
7.6 | odd | 2 | CM | 3311.1.gb.a.1448.1 | yes | 48 | |
11.8 | odd | 10 | 3311.1.gb.b.2351.1 | yes | 48 | ||
43.3 | odd | 42 | 3311.1.gb.b.3142.1 | yes | 48 | ||
77.41 | even | 10 | 3311.1.gb.b.2351.1 | yes | 48 | ||
301.132 | even | 42 | 3311.1.gb.b.3142.1 | yes | 48 | ||
473.261 | even | 210 | inner | 3311.1.gb.a.734.1 | ✓ | 48 | |
3311.734 | odd | 210 | inner | 3311.1.gb.a.734.1 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3311.1.gb.a.734.1 | ✓ | 48 | 473.261 | even | 210 | inner | |
3311.1.gb.a.734.1 | ✓ | 48 | 3311.734 | odd | 210 | inner | |
3311.1.gb.a.1448.1 | yes | 48 | 1.1 | even | 1 | trivial | |
3311.1.gb.a.1448.1 | yes | 48 | 7.6 | odd | 2 | CM | |
3311.1.gb.b.2351.1 | yes | 48 | 11.8 | odd | 10 | ||
3311.1.gb.b.2351.1 | yes | 48 | 77.41 | even | 10 | ||
3311.1.gb.b.3142.1 | yes | 48 | 43.3 | odd | 42 | ||
3311.1.gb.b.3142.1 | yes | 48 | 301.132 | even | 42 |