Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1569,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("2240.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.17 | ||
Character | \(\chi\) | \(=\) | 2240.1569 |
Dual form | 2240.2.l.c.1569.18 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.29255 | 0.746254 | 0.373127 | − | 0.927780i | \(-0.378285\pi\) | ||||
0.373127 | + | 0.927780i | \(0.378285\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.437032 | + | 2.19294i | 0.195447 | + | 0.980714i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.32931 | −0.443104 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.711996i | − | 0.214675i | −0.994223 | − | 0.107337i | \(-0.965767\pi\) | ||
0.994223 | − | 0.107337i | \(-0.0342325\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.85608 | 0.514784 | 0.257392 | − | 0.966307i | \(-0.417137\pi\) | ||||
0.257392 | + | 0.966307i | \(0.417137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.564886 | + | 2.83449i | 0.145853 | + | 0.731862i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.75616i | − | 0.911004i | −0.890235 | − | 0.455502i | \(-0.849460\pi\) | ||
0.890235 | − | 0.455502i | \(-0.150540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.57843i | 1.73861i | 0.494274 | + | 0.869306i | \(0.335434\pi\) | ||||
−0.494274 | + | 0.869306i | \(0.664566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.29255i | − | 0.282058i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.45250i | 1.76247i | 0.472681 | + | 0.881234i | \(0.343286\pi\) | ||||
−0.472681 | + | 0.881234i | \(0.656714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61801 | + | 1.91677i | −0.923601 | + | 0.383355i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.59586 | −1.07692 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.24684i | 0.974314i | 0.873314 | + | 0.487157i | \(0.161966\pi\) | ||||
−0.873314 | + | 0.487157i | \(0.838034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.349014 | 0.0626847 | 0.0313424 | − | 0.999509i | \(-0.490022\pi\) | ||||
0.0313424 | + | 0.999509i | \(0.490022\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.920291i | − | 0.160202i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.19294 | − | 0.437032i | 0.370675 | − | 0.0738719i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.50603 | 1.23398 | 0.616992 | − | 0.786969i | \(-0.288351\pi\) | ||||
0.616992 | + | 0.786969i | \(0.288351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.39908 | 0.384160 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.74755 | 0.429095 | 0.214547 | − | 0.976714i | \(-0.431172\pi\) | ||||
0.214547 | + | 0.976714i | \(0.431172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.07092 | 0.315813 | 0.157906 | − | 0.987454i | \(-0.449526\pi\) | ||||
0.157906 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.580952 | − | 2.91511i | −0.0866032 | − | 0.434559i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.69919i | 0.685448i | 0.939436 | + | 0.342724i | \(0.111349\pi\) | ||||
−0.939436 | + | 0.342724i | \(0.888651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.85503i | − | 0.679841i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.81202 | 1.34778 | 0.673892 | − | 0.738830i | \(-0.264621\pi\) | ||||
0.673892 | + | 0.738830i | \(0.264621\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56137 | − | 0.311165i | 0.210535 | − | 0.0419575i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.79551i | 1.29745i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.54305i | − | 0.851832i | −0.904763 | − | 0.425916i | \(-0.859952\pi\) | ||
0.904763 | − | 0.425916i | \(-0.140048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50330i | 0.832663i | 0.909213 | + | 0.416331i | \(0.136684\pi\) | ||||
−0.909213 | + | 0.416331i | \(0.863316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32931i | 0.167478i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.811166 | + | 4.07028i | 0.100613 | + | 0.504856i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4937 | −1.28201 | −0.641004 | − | 0.767538i | \(-0.721482\pi\) | ||||
−0.641004 | + | 0.767538i | \(0.721482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.9253i | 1.31525i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.53965 | 0.657435 | 0.328718 | − | 0.944428i | \(-0.393384\pi\) | ||||
0.328718 | + | 0.944428i | \(0.393384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.10513i | 1.06567i | 0.846218 | + | 0.532837i | \(0.178874\pi\) | ||||
−0.846218 | + | 0.532837i | \(0.821126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.96901 | + | 2.47753i | −0.689242 | + | 0.286080i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.711996 | −0.0811395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.54792 | −0.511681 | −0.255841 | − | 0.966719i | \(-0.582352\pi\) | ||||
−0.255841 | + | 0.966719i | \(0.582352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.24499 | −0.360554 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.92352 | −0.540427 | −0.270213 | − | 0.962800i | \(-0.587094\pi\) | ||||
−0.270213 | + | 0.962800i | \(0.587094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.23706 | − | 1.64156i | 0.893434 | − | 0.178053i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.78181i | 0.727086i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.58518 | −0.592028 | −0.296014 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296014 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.85608i | − | 0.194570i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.451118 | 0.0467787 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.6191 | + | 3.31202i | −1.70508 | + | 0.339806i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1673i | 1.43847i | 0.694768 | + | 0.719234i | \(0.255507\pi\) | ||||
−0.694768 | + | 0.719234i | \(0.744493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.946466i | 0.0951234i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.69475i | 0.168634i | 0.996439 | + | 0.0843168i | \(0.0268708\pi\) | ||||
−0.996439 | + | 0.0843168i | \(0.973129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3218i | 1.11557i | 0.829984 | + | 0.557787i | \(0.188350\pi\) | ||||
−0.829984 | + | 0.557787i | \(0.811650\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.83449 | − | 0.564886i | 0.276618 | − | 0.0551272i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.25954 | 0.218438 | 0.109219 | − | 0.994018i | \(-0.465165\pi\) | ||||
0.109219 | + | 0.994018i | \(0.465165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.5031i | − | 1.77228i | −0.463422 | − | 0.886138i | \(-0.653379\pi\) | ||
0.463422 | − | 0.886138i | \(-0.346621\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.70193 | 0.920866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19.7639i | − | 1.85923i | −0.368535 | − | 0.929614i | \(-0.620140\pi\) | ||
0.368535 | − | 0.929614i | \(-0.379860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.5359 | + | 3.69401i | −1.72848 | + | 0.344468i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.46731 | −0.228103 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.75616 | −0.344327 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4931 | 0.953915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.55134 | 0.320214 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.22159 | − | 9.28934i | −0.556476 | − | 0.830864i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.43468i | 0.748456i | 0.927337 | + | 0.374228i | \(0.122092\pi\) | ||||
−0.927337 | + | 0.374228i | \(0.877908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.67677 | 0.235677 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.23358i | − | 0.107779i | −0.998547 | − | 0.0538894i | \(-0.982838\pi\) | ||
0.998547 | − | 0.0538894i | \(-0.0171618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.57843 | 0.657133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.44557 | − | 12.2714i | −0.210481 | − | 1.05615i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.5866i | 1.41709i | 0.705665 | + | 0.708546i | \(0.250648\pi\) | ||||
−0.705665 | + | 0.708546i | \(0.749352\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.3119i | − | 1.55319i | −0.629998 | − | 0.776597i | \(-0.716944\pi\) | ||
0.629998 | − | 0.776597i | \(-0.283056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.07394i | 0.511518i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.32152i | − | 0.110511i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.5060 | + | 2.29304i | −0.955524 | + | 0.190426i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.29255 | −0.106608 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.2743i | − | 0.923626i | −0.886977 | − | 0.461813i | \(-0.847199\pi\) | ||
0.886977 | − | 0.461813i | \(-0.152801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5681 | −1.18554 | −0.592769 | − | 0.805372i | \(-0.701965\pi\) | ||||
−0.592769 | + | 0.805372i | \(0.701965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.99312i | 0.403670i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.152530 | + | 0.765367i | 0.0122515 | + | 0.0614758i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1294 | 0.808415 | 0.404207 | − | 0.914667i | \(-0.367547\pi\) | ||||
0.404207 | + | 0.914667i | \(0.367547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.6825 | 1.00579 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.45250 | 0.666150 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.96429 | 0.545486 | 0.272743 | − | 0.962087i | \(-0.412069\pi\) | ||||
0.272743 | + | 0.962087i | \(0.412069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.01815 | − | 0.402197i | 0.157113 | − | 0.0313110i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.55615i | − | 0.352566i | −0.984340 | − | 0.176283i | \(-0.943593\pi\) | ||
0.984340 | − | 0.176283i | \(-0.0564074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.55497 | −0.734998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 10.0741i | − | 0.770386i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.1315 | 1.60660 | 0.803300 | − | 0.595574i | \(-0.203075\pi\) | ||||
0.803300 | + | 0.595574i | \(0.203075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.91677 | + | 4.61801i | 0.144894 | + | 0.349088i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.45722i | − | 0.635684i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.6347i | 1.61705i | 0.588458 | + | 0.808527i | \(0.299735\pi\) | ||||
−0.588458 | + | 0.808527i | \(0.700265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.01846i | 0.670337i | 0.942158 | + | 0.335168i | \(0.108793\pi\) | ||||
−0.942158 | + | 0.335168i | \(0.891207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.40585i | 0.621378i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.28038 | + | 16.4603i | 0.241178 | + | 1.21019i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.67438 | −0.195570 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.59586i | 0.407039i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1324 | −0.877872 | −0.438936 | − | 0.898518i | \(-0.644645\pi\) | ||||
−0.438936 | + | 0.898518i | \(0.644645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.9798i | − | 0.790342i | −0.918608 | − | 0.395171i | \(-0.870685\pi\) | ||
0.918608 | − | 0.395171i | \(-0.129315\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.04847 | + | 5.26104i | 0.0750828 | + | 0.376751i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.349165 | −0.0248770 | −0.0124385 | − | 0.999923i | \(-0.503959\pi\) | ||||
−0.0124385 | + | 0.999923i | \(0.503959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8923 | −1.55190 | −0.775951 | − | 0.630793i | \(-0.782730\pi\) | ||||
−0.775951 | + | 0.630793i | \(0.782730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5636 | −0.956704 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.24684 | 0.368256 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.20077 | + | 6.02521i | 0.0838651 | + | 0.420819i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 11.2360i | − | 0.780957i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.39582 | 0.373236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.6498i | − | 1.00853i | −0.863548 | − | 0.504267i | \(-0.831763\pi\) | ||
0.863548 | − | 0.504267i | \(-0.168237\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.16028 | 0.490614 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.905060 | + | 4.54142i | 0.0617246 | + | 0.309722i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.349014i | − | 0.0236926i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.7688i | 0.795265i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.97174i | − | 0.468970i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9248i | 1.26730i | 0.773619 | + | 0.633651i | \(0.218444\pi\) | ||||
−0.773619 | + | 0.633651i | \(0.781556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.13877 | − | 2.54799i | 0.409252 | − | 0.169866i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.2624 | 1.21212 | 0.606058 | − | 0.795420i | \(-0.292750\pi\) | ||||
0.606058 | + | 0.795420i | \(0.292750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 7.23742i | − | 0.478262i | −0.970987 | − | 0.239131i | \(-0.923137\pi\) | ||
0.970987 | − | 0.239131i | \(-0.0768626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.920291 | −0.0605507 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.6650i | − | 1.22278i | −0.791329 | − | 0.611391i | \(-0.790610\pi\) | ||
0.791329 | − | 0.611391i | \(-0.209390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3051 | + | 2.05370i | −0.672228 | + | 0.133968i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.87842 | −0.381845 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.993443 | 0.0642605 | 0.0321302 | − | 0.999484i | \(-0.489771\pi\) | ||||
0.0321302 | + | 0.999484i | \(0.489771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2196 | 1.36687 | 0.683436 | − | 0.730010i | \(-0.260485\pi\) | ||||
0.683436 | + | 0.730010i | \(0.260485\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.5933 | 0.807858 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.437032 | − | 2.19294i | −0.0279210 | − | 0.140102i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0662i | 0.895009i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.36390 | −0.403296 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.2669i | − | 0.963641i | −0.876270 | − | 0.481820i | \(-0.839976\pi\) | ||
0.876270 | − | 0.481820i | \(-0.160024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.01815 | 0.378358 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.6468 | − | 2.12181i | 0.666729 | − | 0.132873i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.5310i | − | 1.77971i | −0.456240 | − | 0.889857i | \(-0.650804\pi\) | ||
0.456240 | − | 0.889857i | \(-0.349196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.50603i | − | 0.466402i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.97469i | − | 0.431723i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.51697i | − | 0.340191i | −0.985428 | − | 0.170095i | \(-0.945592\pi\) | ||
0.985428 | − | 0.170095i | \(-0.0544076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.28817 | + | 21.5172i | 0.263420 | + | 1.32179i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.21912 | −0.441803 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.79256i | 0.536092i | 0.963406 | + | 0.268046i | \(0.0863779\pi\) | ||||
−0.963406 | + | 0.268046i | \(0.913622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.95225 | −0.118591 | −0.0592954 | − | 0.998240i | \(-0.518885\pi\) | ||||
−0.0592954 | + | 0.998240i | \(0.518885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.39908i | − | 0.145199i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.36474 | + | 3.28800i | 0.0822967 | + | 0.198274i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.1637 | −1.03127 | −0.515635 | − | 0.856808i | \(-0.672444\pi\) | ||||
−0.515635 | + | 0.856808i | \(0.672444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.463948 | −0.0277759 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2087 | 1.44417 | 0.722085 | − | 0.691805i | \(-0.243184\pi\) | ||||
0.722085 | + | 0.691805i | \(0.243184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8658 | 0.705350 | 0.352675 | − | 0.935746i | \(-0.385272\pi\) | ||||
0.352675 | + | 0.935746i | \(0.385272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.4810 | + | 4.28095i | −1.27242 | + | 0.253582i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.74755i | − | 0.162183i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.89123 | 0.170072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.3119i | 1.07346i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5627 | −0.675502 | −0.337751 | − | 0.941235i | \(-0.609666\pi\) | ||||
−0.337751 | + | 0.941235i | \(0.609666\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3485 | − | 2.85952i | 0.835404 | − | 0.166488i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.98423i | 0.231188i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.6885i | 0.907290i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.07092i | − | 0.119366i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.19055i | 0.125844i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.2614 | + | 2.84215i | −0.816604 | + | 0.162741i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.2849 | −1.72845 | −0.864225 | − | 0.503106i | \(-0.832191\pi\) | ||||
−0.864225 | + | 0.503106i | \(0.832191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6341i | 0.832503i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.8962 | 1.75196 | 0.875981 | − | 0.482346i | \(-0.160215\pi\) | ||||
0.875981 | + | 0.482346i | \(0.160215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.39647i | − | 0.418073i | −0.977908 | − | 0.209037i | \(-0.932967\pi\) | ||
0.977908 | − | 0.209037i | \(-0.0670328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.91511 | + | 0.580952i | −0.164248 | + | 0.0327330i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.4720 | 1.43065 | 0.715326 | − | 0.698791i | \(-0.246278\pi\) | ||||
0.715326 | + | 0.698791i | \(0.246278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.73573 | 0.209161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.92058 | 0.163011 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.4658 | 1.58388 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.57139 | + | 3.55768i | −0.475455 | + | 0.197345i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 23.9162i | − | 1.32257i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.69919 | 0.259075 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.33587i | 0.513146i | 0.966525 | + | 0.256573i | \(0.0825934\pi\) | ||||
−0.966525 | + | 0.256573i | \(0.917407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.97786 | −0.546784 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.58608 | − | 23.0121i | −0.250564 | − | 1.25728i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.92273i | 0.322632i | 0.986903 | + | 0.161316i | \(0.0515738\pi\) | ||||
−0.986903 | + | 0.161316i | \(0.948426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 25.5458i | − | 1.38746i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.248496i | − | 0.0134568i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.9585 | + | 4.77470i | −1.28988 | + | 0.257061i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.107524 | 0.00577220 | 0.00288610 | − | 0.999996i | \(-0.499081\pi\) | ||||
0.00288610 | + | 0.999996i | \(0.499081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.23635i | 0.226766i | 0.993551 | + | 0.113383i | \(0.0361688\pi\) | ||||
−0.993551 | + | 0.113383i | \(0.963831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3864 | −0.554383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.0592i | − | 1.22732i | −0.789571 | − | 0.613659i | \(-0.789697\pi\) | ||
0.789571 | − | 0.613659i | \(-0.210303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.42100 | + | 12.1481i | 0.128494 | + | 0.644756i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.85503 | −0.256956 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.94196 | 0.102493 | 0.0512464 | − | 0.998686i | \(-0.483681\pi\) | ||||
0.0512464 | + | 0.998686i | \(0.483681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −38.4326 | −2.02277 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.5628 | 0.711863 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.9670 | + | 3.97923i | −1.04512 | + | 0.208283i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.2406i | − | 0.847753i | −0.905720 | − | 0.423876i | \(-0.860669\pi\) | ||
0.905720 | − | 0.423876i | \(-0.139331\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.65235 | −0.190134 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.81202i | − | 0.509415i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.818104 | 0.0423598 | 0.0211799 | − | 0.999776i | \(-0.493258\pi\) | ||||
0.0211799 | + | 0.999776i | \(0.493258\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.04172 | − | 12.0069i | −0.415273 | − | 0.620036i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.73856i | 0.501561i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.90152i | 0.0976745i | 0.998807 | + | 0.0488373i | \(0.0155516\pi\) | ||||
−0.998807 | + | 0.0488373i | \(0.984448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9022i | 0.558539i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.24670i | − | 0.319191i | −0.987182 | − | 0.159596i | \(-0.948981\pi\) | ||
0.987182 | − | 0.159596i | \(-0.0510190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.311165 | − | 1.56137i | −0.0158584 | − | 0.0795747i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.75290 | −0.139938 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 18.6095i | − | 0.943537i | −0.881722 | − | 0.471769i | \(-0.843616\pi\) | ||
0.881722 | − | 0.471769i | \(-0.156384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.7490 | 1.60561 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.59447i | − | 0.0804304i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.98759 | − | 9.97334i | −0.100006 | − | 0.501813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.57650 | −0.179499 | −0.0897497 | − | 0.995964i | \(-0.528607\pi\) | ||||
−0.0897497 | + | 0.995964i | \(0.528607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.79551 | 0.490389 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.9125 | −1.29401 | −0.647004 | − | 0.762487i | \(-0.723978\pi\) | ||||
−0.647004 | + | 0.762487i | \(0.723978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.647797 | 0.0322691 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.41816 | − | 7.11608i | −0.0704692 | − | 0.353601i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.34427i | − | 0.264905i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1037 | 0.994062 | 0.497031 | − | 0.867733i | \(-0.334424\pi\) | ||||
0.497031 | + | 0.867733i | \(0.334424\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.4391i | 1.05751i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.54305 | −0.321962 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.15174 | − | 10.7970i | −0.105625 | − | 0.530004i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 23.6690i | − | 1.15908i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.413171i | 0.0201847i | 0.999949 | + | 0.0100924i | \(0.00321256\pi\) | ||||
−0.999949 | + | 0.0100924i | \(0.996787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 5.85147i | − | 0.285183i | −0.989782 | − | 0.142591i | \(-0.954456\pi\) | ||
0.989782 | − | 0.142591i | \(-0.0455435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.24670i | − | 0.303725i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.19972 | + | 17.3460i | 0.349238 | + | 0.841404i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.50330 | 0.314717 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.70813i | − | 0.0824695i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.55603 | 0.267625 | 0.133812 | − | 0.991007i | \(-0.457278\pi\) | ||||
0.133812 | + | 0.991007i | \(0.457278\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.1942i | − | 1.16270i | −0.813654 | − | 0.581350i | \(-0.802525\pi\) | ||
0.813654 | − | 0.581350i | \(-0.197475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.8721 | + | 2.96387i | −0.713064 | + | 0.142107i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −64.0567 | −3.06425 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.9665 | −1.33477 | −0.667385 | − | 0.744713i | \(-0.732586\pi\) | ||||
−0.667385 | + | 0.744713i | \(0.732586\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.32931 | 0.0633006 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5932 | 0.883391 | 0.441696 | − | 0.897165i | \(-0.354377\pi\) | ||||
0.441696 | + | 0.897165i | \(0.354377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.44090 | − | 12.2480i | −0.115710 | − | 0.580610i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.5726i | − | 0.689260i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.3079 | 1.09997 | 0.549985 | − | 0.835174i | \(-0.314633\pi\) | ||||
0.549985 | + | 0.835174i | \(0.314633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.95624i | − | 0.0921159i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.8301 | −0.884714 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.07028 | − | 0.811166i | 0.190818 | − | 0.0380281i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.1043i | 1.40822i | 0.710092 | + | 0.704109i | \(0.248653\pi\) | ||||
−0.710092 | + | 0.704109i | \(0.751347\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.0190i | 0.981081i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.9144i | 1.43983i | 0.694063 | + | 0.719914i | \(0.255819\pi\) | ||||
−0.694063 | + | 0.719914i | \(0.744181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.26313i | 0.244599i | 0.992493 | + | 0.122299i | \(0.0390268\pi\) | ||||
−0.992493 | + | 0.122299i | \(0.960973\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.197153 | + | 0.989276i | 0.00914275 | + | 0.0458766i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.20172 | −0.194433 | −0.0972163 | − | 0.995263i | \(-0.530994\pi\) | ||||
−0.0972163 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4937i | 0.484553i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.0928 | 0.603283 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.47449i | − | 0.0677971i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.5261 | − | 34.9972i | −0.666505 | − | 1.60578i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0432 | −0.597209 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.2017 | 1.28857 | 0.644283 | − | 0.764787i | \(-0.277156\pi\) | ||||
0.644283 | + | 0.764787i | \(0.277156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9318 | 0.635235 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.9253 | 0.497117 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.0680 | + | 6.19155i | −1.41073 | + | 0.281144i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.8032i | − | 0.534852i | −0.963578 | − | 0.267426i | \(-0.913827\pi\) | ||
0.963578 | − | 0.267426i | \(-0.0861731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00170 | 0.407071 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.305569i | − | 0.0137901i | −0.999976 | − | 0.00689507i | \(-0.997805\pi\) | ||
0.999976 | − | 0.00689507i | \(-0.00219479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.7080 | 0.887604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.07555 | + | 0.413636i | −0.0932889 | + | 0.0185916i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.53965i | − | 0.248487i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.15472i | − | 0.230757i | −0.993322 | − | 0.115378i | \(-0.963192\pi\) | ||
0.993322 | − | 0.115378i | \(-0.0368081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 5.88906i | − | 0.263104i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.5322i | − | 0.960076i | −0.877248 | − | 0.480038i | \(-0.840623\pi\) | ||
0.877248 | − | 0.480038i | \(-0.159377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.71649 | + | 0.740659i | −0.165381 | + | 0.0329589i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3503 | −0.548495 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.1494i | − | 0.715810i | −0.933758 | − | 0.357905i | \(-0.883491\pi\) | ||
0.933758 | − | 0.357905i | \(-0.116509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.10513 | 0.402787 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 42.4078i | − | 1.87235i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.8282 | + | 4.94801i | −1.09406 | + | 0.218035i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.34581 | 0.147148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.3136 | 1.19893 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.44181 | −0.326032 | −0.163016 | − | 0.986623i | \(-0.552122\pi\) | ||||
−0.163016 | + | 0.986623i | \(0.552122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1132 | 0.792036 | 0.396018 | − | 0.918243i | \(-0.370392\pi\) | ||||
0.396018 | + | 0.918243i | \(0.370392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.47753 | + | 5.96901i | 0.108128 | + | 0.260509i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.31095i | − | 0.0571060i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −48.4447 | −2.10629 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.69775i | 0.377450i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.09967 | 0.220891 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.987493 | + | 4.95505i | 0.0426931 | + | 0.214226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.9640i | 1.20673i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.711996i | 0.0306679i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.3864i | − | 0.962466i | −0.876593 | − | 0.481233i | \(-0.840189\pi\) | ||
0.876593 | − | 0.481233i | \(-0.159811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.6568i | 0.500242i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.5763 | − | 8.08645i | 1.73810 | − | 0.346385i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.7568 | 1.40058 | 0.700290 | − | 0.713858i | \(-0.253054\pi\) | ||||
0.700290 | + | 0.713858i | \(0.253054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 8.64492i | − | 0.368956i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.7628 | −1.69395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.54792i | 0.193397i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.24005 | + | 21.2758i | 0.179980 | + | 0.903107i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.01493 | 0.127747 | 0.0638734 | − | 0.997958i | \(-0.479655\pi\) | ||||
0.0638734 | + | 0.997958i | \(0.479655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.84380 | 0.162575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45677 | −0.145945 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.92403 | −0.123233 | −0.0616166 | − | 0.998100i | \(-0.519626\pi\) | ||||
−0.0616166 | + | 0.998100i | \(0.519626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.3410 | − | 8.63744i | 1.82337 | − | 0.363380i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.24499i | 0.136277i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.9064 | −0.960285 | −0.480143 | − | 0.877190i | \(-0.659415\pi\) | ||||
−0.480143 | + | 0.877190i | \(0.659415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.5106i | 1.65347i | 0.562593 | + | 0.826734i | \(0.309804\pi\) | ||||
−0.562593 | + | 0.826734i | \(0.690196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.6818 | −0.655116 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.2015 | − | 39.0337i | −0.675650 | − | 1.62782i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6976i | 0.820023i | 0.912080 | + | 0.410012i | \(0.134475\pi\) | ||||
−0.912080 | + | 0.410012i | \(0.865525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 14.1919i | − | 0.589796i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.92352i | 0.204262i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.98612i | − | 0.289336i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.07829 | − | 5.41067i | −0.0445820 | − | 0.223704i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.1220 | 1.28454 | 0.642270 | − | 0.766478i | \(-0.277993\pi\) | ||||
0.642270 | + | 0.766478i | \(0.277993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.64498i | 0.108984i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.451314 | −0.0185646 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.6520i | − | 1.29979i | −0.760023 | − | 0.649896i | \(-0.774812\pi\) | ||
0.760023 | − | 0.649896i | \(-0.225188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.64156 | − | 8.23706i | −0.0672976 | − | 0.337686i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.2969 | −1.15811 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.9208 | −1.91713 | −0.958566 | − | 0.284870i | \(-0.908050\pi\) | ||||
−0.958566 | + | 0.284870i | \(0.908050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7934 | 0.848179 | 0.424089 | − | 0.905620i | \(-0.360594\pi\) | ||||
0.424089 | + | 0.905620i | \(0.360594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.9494 | 0.568063 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.58580 | + | 23.0107i | 0.186439 | + | 0.935518i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.52360i | − | 0.102430i | −0.998688 | − | 0.0512148i | \(-0.983691\pi\) | ||
0.998688 | − | 0.0512148i | \(-0.0163093\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.78181 | 0.274813 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.72207i | 0.352857i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.0993 | 1.65999 | 0.829993 | − | 0.557774i | \(-0.188344\pi\) | ||||
0.829993 | + | 0.557774i | \(0.188344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.55205 | + | 7.78790i | 0.0625847 | + | 0.314038i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.4277i | − | 0.580839i | −0.956899 | − | 0.290420i | \(-0.906205\pi\) | ||
0.956899 | − | 0.290420i | \(-0.0937949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.03872i | − | 0.0417497i | −0.999782 | − | 0.0208749i | \(-0.993355\pi\) | ||
0.999782 | − | 0.0208749i | \(-0.00664516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 47.2990i | − | 1.89804i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.58518i | 0.223765i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6520 | − | 17.7033i | 0.706078 | − | 0.708134i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.97437 | 0.278529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 28.1939i | − | 1.12416i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.4094 | −0.931912 | −0.465956 | − | 0.884808i | \(-0.654290\pi\) | ||||
−0.465956 | + | 0.884808i | \(0.654290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 18.9356i | − | 0.752623i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.4968 | + | 3.68622i | −0.734022 | + | 0.146283i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85608 | −0.0735406 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.36392 | −0.291312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.1178 | −0.597115 | −0.298558 | − | 0.954392i | \(-0.596506\pi\) | ||||
−0.298558 | + | 0.954392i | \(0.596506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.9767 | 1.81314 | 0.906572 | − | 0.422051i | \(-0.138690\pi\) | ||||
0.906572 | + | 0.422051i | \(0.138690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.16984 | + | 5.87001i | 0.0460622 | + | 0.231132i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.0253i | − | 1.18042i | −0.807251 | − | 0.590208i | \(-0.799046\pi\) | ||
0.807251 | − | 0.590208i | \(-0.200954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.65863 | −0.182867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.451118i | − | 0.0176807i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.8944 | −0.974192 | −0.487096 | − | 0.873348i | \(-0.661944\pi\) | ||||
−0.487096 | + | 0.873348i | \(0.661944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.70518 | − | 0.539116i | 0.105700 | − | 0.0210650i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.1036i | − | 0.472205i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.8754i | − | 1.43646i | −0.695804 | − | 0.718231i | \(-0.744952\pi\) | ||
0.695804 | − | 0.718231i | \(-0.255048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5668i | 0.605477i | 0.953074 | + | 0.302739i | \(0.0979010\pi\) | ||||
−0.953074 | + | 0.302739i | \(0.902099\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 9.01133i | − | 0.349971i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.31202 | + | 16.6191i | 0.128435 | + | 0.644460i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.3489 | −1.71720 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.4613i | 0.945729i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.63033 | 0.178752 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.30821i | − | 0.320258i | −0.987096 | − | 0.160129i | \(-0.948809\pi\) | ||
0.987096 | − | 0.160129i | \(-0.0511910\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.8417 | − | 10.7260i | 0.994647 | − | 0.412844i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8042 | −0.914872 | −0.457436 | − | 0.889243i | \(-0.651232\pi\) | ||||
−0.457436 | + | 0.889243i | \(0.651232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1673 | 0.543690 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.6050 | 0.904547 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.33136 | 0.357055 | 0.178527 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178527 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.3735 | + | 7.24889i | −1.38976 | + | 0.276966i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.35473i | − | 0.356905i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.2119 | 0.693818 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.3925i | − | 0.813810i | −0.913471 | − | 0.406905i | \(-0.866608\pi\) | ||
0.913471 | − | 0.406905i | \(-0.133392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.946466 | 0.0359533 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.1569 | − | 8.00288i | 1.52324 | − | 0.303567i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.3202i | − | 0.390907i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 24.1254i | − | 0.912507i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 47.0880i | − | 1.77849i | −0.457431 | − | 0.889245i | \(-0.651230\pi\) | ||
0.457431 | − | 0.889245i | \(-0.348770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.8840i | 2.14542i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.3198 | + | 2.65451i | −0.501653 | + | 0.0999746i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.69475 | 0.0637375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.9549i | 1.27520i | 0.770366 | + | 0.637602i | \(0.220073\pi\) | ||||
−0.770366 | + | 0.637602i | \(0.779927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.04561 | 0.226728 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.95004i | 0.110480i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.89802 | − | 0.577548i | 0.108380 | − | 0.0215991i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.28407 | 0.0479547 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.89494 | 0.0706692 | 0.0353346 | − | 0.999376i | \(-0.488750\pi\) | ||||
0.0353346 | + | 0.999376i | \(0.488750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3218 | 0.421648 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.4274 | 1.02003 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0570 | − | 24.2300i | −0.373508 | − | 0.899878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9082i | 1.25759i | 0.777573 | + | 0.628793i | \(0.216451\pi\) | ||||
−0.777573 | + | 0.628793i | \(0.783549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0124 | 0.963422 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.77873i | − | 0.287707i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.2130 | 1.15288 | 0.576439 | − | 0.817140i | \(-0.304442\pi\) | ||||
0.576439 | + | 0.817140i | \(0.304442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.564886 | − | 2.83449i | −0.0208361 | − | 0.104552i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.47147i | 0.275215i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.8444i | 1.42891i | 0.699680 | + | 0.714456i | \(0.253326\pi\) | ||||
−0.699680 | + | 0.714456i | \(0.746674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.1812i | 0.667905i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.04781i | 0.185186i | 0.995704 | + | 0.0925931i | \(0.0295156\pi\) | ||||
−0.995704 | + | 0.0925931i | \(0.970484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.7239 | − | 4.92723i | 0.905813 | − | 0.180520i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.54490 | 0.239465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.25954i | − | 0.0825620i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.8436 | −1.85531 | −0.927655 | − | 0.373437i | \(-0.878179\pi\) | ||||
−0.927655 | + | 0.373437i | \(0.878179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.7333i | − | 0.719121i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.36675 | − | 31.9471i | −0.231710 | − | 1.16267i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8379 | 0.721021 | 0.360511 | − | 0.932755i | \(-0.382602\pi\) | ||||
0.360511 | + | 0.932755i | \(0.382602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.77876 | 0.282351 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7095 | −1.22197 | −0.610985 | − | 0.791642i | \(-0.709226\pi\) | ||||
−0.610985 | + | 0.791642i | \(0.709226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.5031 | −0.669857 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.9496 | + | 2.18215i | −0.395885 | + | 0.0788959i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.1444i | − | 0.438509i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.8641 | 1.25723 | 0.628616 | − | 0.777716i | \(-0.283622\pi\) | ||||
0.628616 | + | 0.777716i | \(0.283622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 36.8777i | − | 1.32812i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.74412 | −0.0627315 | −0.0313657 | − | 0.999508i | \(-0.509986\pi\) | ||||
−0.0313657 | + | 0.999508i | \(0.509986\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.61175 | + | 0.668980i | −0.0578957 | + | 0.0240305i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.70193i | − | 0.348055i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.8221i | 0.746029i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.94421i | − | 0.141135i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 29.3606i | − | 1.04926i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.42688 | + | 22.2132i | 0.158002 | + | 0.792824i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.1967 | −0.933810 | −0.466905 | − | 0.884308i | \(-0.654631\pi\) | ||||
−0.466905 | + | 0.884308i | \(0.654631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 7.13096i | − | 0.253869i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.7639 | −0.702722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0706i | 0.428641i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.54267 | + | 27.8121i | 0.196578 | + | 0.986393i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.7303 | 0.875992 | 0.437996 | − | 0.898977i | \(-0.355688\pi\) | ||||
0.437996 | + | 0.898977i | \(0.355688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6509 | 0.624445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.42445 | 0.262330 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.48282 | 0.228774 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.69401 | + | 18.5359i | 0.130197 | + | 0.653303i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.3648i | 0.400061i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.4914 | −1.45876 | −0.729379 | − | 0.684110i | \(-0.760191\pi\) | ||||
−0.729379 | + | 0.684110i | \(0.760191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.1293i | − | 0.425919i | −0.977061 | − | 0.212960i | \(-0.931690\pi\) | ||
0.977061 | − | 0.212960i | \(-0.0683103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.52338 | −0.0884988 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.04362 | + | 15.2723i | 0.106613 | + | 0.534966i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.6944i | 0.549076i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.46731i | 0.0862148i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.87577i | − | 0.239966i | −0.992776 | − | 0.119983i | \(-0.961716\pi\) | ||
0.992776 | − | 0.119983i | \(-0.0382840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0346i | 1.25609i | 0.778178 | + | 0.628044i | \(0.216144\pi\) | ||||
−0.778178 | + | 0.628044i | \(0.783856\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.76399 | + | 4.24991i | 0.0614143 | + | 0.147963i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.6307 | −0.647853 | −0.323927 | − | 0.946082i | \(-0.605003\pi\) | ||||
−0.323927 | + | 0.946082i | \(0.605003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.9525i | − | 0.519321i | −0.965700 | − | 0.259661i | \(-0.916389\pi\) | ||
0.965700 | − | 0.259661i | \(-0.0836107\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.1850 | −0.769590 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.75616i | 0.130143i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.99139 | − | 1.99119i | 0.345766 | − | 0.0689078i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.95303 | −0.0675066 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.4613 | 0.464734 | 0.232367 | − | 0.972628i | \(-0.425353\pi\) | ||||
0.232367 | + | 0.972628i | \(0.425353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.47064 | 0.0507119 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.2910 | 1.07772 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.17583 | − | 20.9535i | −0.143653 | − | 0.720823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.4931i | − | 0.360546i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3372 | 0.526371 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.4447i | 2.17486i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6691 | 1.66640 | 0.833200 | − | 0.552972i | \(-0.186507\pi\) | ||||
0.833200 | + | 0.552972i | \(0.186507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.0920 | − | 4.40271i | 0.755529 | − | 0.150569i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.947295i | − | 0.0323590i | −0.999869 | − | 0.0161795i | \(-0.994850\pi\) | ||
0.999869 | − | 0.0161795i | \(-0.00515032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.917522i | 0.0313055i | 0.999877 | + | 0.0156527i | \(0.00498262\pi\) | ||||
−0.999877 | + | 0.0156527i | \(0.995017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 3.55134i | − | 0.121029i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 20.8807i | − | 0.710789i | −0.934716 | − | 0.355394i | \(-0.884347\pi\) | ||
0.934716 | − | 0.355394i | \(-0.115653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.23516 | + | 46.3403i | 0.314005 | + | 1.57562i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.73706 | 0.126917 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.23811i | 0.109845i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.4771 | −0.659957 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 18.8327i | − | 0.637391i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.28934 | + | 6.22159i | −0.314037 | + | 0.210328i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.7337 | 1.64562 | 0.822810 | − | 0.568316i | \(-0.192405\pi\) | ||||
0.822810 | + | 0.568316i | \(0.192405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.9454 | −0.504097 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.1537 | −1.08329 | −0.541643 | − | 0.840609i | \(-0.682198\pi\) | ||||
−0.541643 | + | 0.840609i | \(0.682198\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.4051 | −1.72992 | −0.864959 | − | 0.501842i | \(-0.832656\pi\) | ||||
−0.864959 | + | 0.501842i | \(0.832656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.5462 | − | 3.69608i | 0.623424 | − | 0.124242i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 38.2250i | − | 1.28347i | −0.766926 | − | 0.641735i | \(-0.778215\pi\) | ||
0.766926 | − | 0.641735i | \(-0.221785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.43468 | 0.282890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.31042i | 0.0774020i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.6125 | −1.19173 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.4437 | + | 9.45507i | −1.58587 | + | 0.316048i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.2782i | 0.677069i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.83122i | 0.0610746i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 36.8556i | − | 1.22784i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.67677i | − | 0.0890774i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.7770 | + | 3.94135i | −0.657409 | + | 0.131015i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.6808 | −0.587081 | −0.293540 | − | 0.955947i | \(-0.594834\pi\) | ||||
−0.293540 | + | 0.955947i | \(0.594834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.25285i | − | 0.0747223i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.52564 | −0.0505467 | −0.0252733 | − | 0.999681i | \(-0.508046\pi\) | ||||
−0.0252733 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.50553i | 0.116016i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.4336 | + | 3.67362i | −0.609394 | + | 0.121446i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.23358 | −0.0407365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.3054 | 0.966697 | 0.483348 | − | 0.875428i | \(-0.339420\pi\) | ||||
0.483348 | + | 0.875428i | \(0.339420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.1447 | −1.28986 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2820 | 0.338437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.6629 | + | 14.3874i | −1.13971 | + | 0.473054i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 15.0503i | − | 0.494316i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.2981 | −0.961241 | −0.480620 | − | 0.876929i | \(-0.659588\pi\) | ||||
−0.480620 | + | 0.876929i | \(0.659588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.57843i | − | 0.248373i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.9349 | 1.30741 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.16879 | − | 5.86476i | −0.0382235 | − | 0.191798i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.4748i | 0.668884i | 0.942416 | + | 0.334442i | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334442i | \(0.891452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9.56031i | − | 0.311989i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.1365i | 1.47141i | 0.677303 | + | 0.735704i | \(0.263149\pi\) | ||||
−0.677303 | + | 0.735704i | \(0.736851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.2236i | 0.756265i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.2714 | + | 2.44557i | −0.399189 | + | 0.0795543i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −60.0236 | −1.95050 | −0.975252 | − | 0.221097i | \(-0.929036\pi\) | ||||
−0.975252 | + | 0.221097i | \(0.929036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8998i | 0.548592i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.9239 | 1.06763 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.6147i | 1.38043i | 0.723606 | + | 0.690213i | \(0.242483\pi\) | ||||
−0.723606 | + | 0.690213i | \(0.757517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.30226 | − | 26.6058i | −0.171577 | − | 0.860942i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.82862 | 0.156087 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.5866 | 0.535610 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8782 | −0.996071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.00364 | −0.0967910 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0780 | − | 4.79852i | 0.775100 | − | 0.154470i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3051i | 1.03886i | 0.854513 | + | 0.519431i | \(0.173856\pi\) | ||||
−0.854513 | + | 0.519431i | \(0.826144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.7935 | 1.18198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.5761i | 0.981235i | 0.871375 | + | 0.490617i | \(0.163229\pi\) | ||||
−0.871375 | + | 0.490617i | \(0.836771\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3119 | −0.587052 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.0790 | + | 4.59849i | −0.354810 | + | 0.147269i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 33.2108i | − | 1.06251i | −0.847212 | − | 0.531254i | \(-0.821721\pi\) | ||
0.847212 | − | 0.531254i | \(-0.178279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.97663i | 0.127094i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.5964i | 0.785303i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.5681i | 0.783601i | 0.920050 | + | 0.391800i | \(0.128148\pi\) | ||||
−0.920050 | + | 0.391800i | \(0.871852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.152596 | − | 0.765700i | −0.00486212 | − | 0.0243972i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.07394 | 0.193336 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.5045i | 0.556610i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.13397 | 0.226618 | 0.113309 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113309 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0671i | 0.382937i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.56763 | − | 48.0085i | −0.303314 | − | 1.52197i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.2715 | −0.420312 | −0.210156 | − | 0.977668i | \(-0.567397\pi\) | ||||
−0.210156 | + | 0.977668i | \(0.567397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −42.0027 | −1.32891 |
(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 | 2240.2.l.c.1569.17 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.l.c.1569.8 | yes | 24 | |
5.4 | even | 2 | 2240.2.l.d.1569.8 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.l.d.1569.18 | yes | 24 | ||
8.5 | even | 2 | 2240.2.l.d.1569.7 | yes | 24 | ||
20.19 | odd | 2 | 2240.2.l.d.1569.17 | yes | 24 | ||
40.19 | odd | 2 | inner | 2240.2.l.c.1569.7 | ✓ | 24 | |
40.29 | even | 2 | inner | 2240.2.l.c.1569.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.l.c.1569.7 | ✓ | 24 | 40.19 | odd | 2 | inner | |
2240.2.l.c.1569.8 | yes | 24 | 4.3 | odd | 2 | inner | |
2240.2.l.c.1569.17 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.l.c.1569.18 | yes | 24 | 40.29 | even | 2 | inner | |
2240.2.l.d.1569.7 | yes | 24 | 8.5 | even | 2 | ||
2240.2.l.d.1569.8 | yes | 24 | 5.4 | even | 2 | ||
2240.2.l.d.1569.17 | yes | 24 | 20.19 | odd | 2 | ||
2240.2.l.d.1569.18 | yes | 24 | 8.3 | odd | 2 |