Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.a (trivial) |
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: | yes |
Analytic conductor: | \(59.8878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 11 x^{10} + 94 x^{9} + 27 x^{8} - 460 x^{7} + 55 x^{6} + 812 x^{5} - 127 x^{4} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 5^{3} \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(3.89742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7500.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.78808 | 1.43176 | 0.715880 | − | 0.698223i | \(-0.246026\pi\) | ||||
0.715880 | + | 0.698223i | \(0.246026\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.807679 | −0.243524 | −0.121762 | − | 0.992559i | \(-0.538855\pi\) | ||||
−0.121762 | + | 0.992559i | \(0.538855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74950 | 1.31727 | 0.658637 | − | 0.752461i | \(-0.271133\pi\) | ||||
0.658637 | + | 0.752461i | \(0.271133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.14884 | −0.278636 | −0.139318 | − | 0.990248i | \(-0.544491\pi\) | ||||
−0.139318 | + | 0.990248i | \(0.544491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0150112 | 0.00344380 | 0.00172190 | − | 0.999999i | \(-0.499452\pi\) | ||||
0.00172190 | + | 0.999999i | \(0.499452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.78808 | 0.826627 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.26797 | −1.30696 | −0.653481 | − | 0.756943i | \(-0.726692\pi\) | ||||
−0.653481 | + | 0.756943i | \(0.726692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70092 | 0.687243 | 0.343621 | − | 0.939108i | \(-0.388346\pi\) | ||||
0.343621 | + | 0.939108i | \(0.388346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.58209 | −0.284152 | −0.142076 | − | 0.989856i | \(-0.545378\pi\) | ||||
−0.142076 | + | 0.989856i | \(0.545378\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.807679 | −0.140599 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.54179 | −1.40426 | −0.702131 | − | 0.712048i | \(-0.747768\pi\) | ||||
−0.702131 | + | 0.712048i | \(0.747768\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.74950 | 0.760528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4989 | 1.79582 | 0.897912 | − | 0.440176i | \(-0.145084\pi\) | ||||
0.897912 | + | 0.440176i | \(0.145084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2458 | 1.56247 | 0.781234 | − | 0.624238i | \(-0.214591\pi\) | ||||
0.781234 | + | 0.624238i | \(0.214591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.526282 | −0.0767662 | −0.0383831 | − | 0.999263i | \(-0.512221\pi\) | ||||
−0.0383831 | + | 0.999263i | \(0.512221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.34957 | 1.04994 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.14884 | −0.160870 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.94976 | −0.405181 | −0.202591 | − | 0.979264i | \(-0.564936\pi\) | ||||
−0.202591 | + | 0.979264i | \(0.564936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0150112 | 0.00198828 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4436 | 1.48982 | 0.744912 | − | 0.667163i | \(-0.232492\pi\) | ||||
0.744912 | + | 0.667163i | \(0.232492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.14212 | 0.402307 | 0.201154 | − | 0.979560i | \(-0.435531\pi\) | ||||
0.201154 | + | 0.979560i | \(0.435531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.78808 | 0.477254 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2812 | 1.62256 | 0.811278 | − | 0.584660i | \(-0.198772\pi\) | ||||
0.811278 | + | 0.584660i | \(0.198772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.26797 | −0.754574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.91318 | −0.583088 | −0.291544 | − | 0.956557i | \(-0.594169\pi\) | ||||
−0.291544 | + | 0.956557i | \(0.594169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.67860 | −0.547589 | −0.273795 | − | 0.961788i | \(-0.588279\pi\) | ||||
−0.273795 | + | 0.961788i | \(0.588279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.05955 | −0.348668 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.27155 | 1.04313 | 0.521565 | − | 0.853211i | \(-0.325348\pi\) | ||||
0.521565 | + | 0.853211i | \(0.325348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.42370 | 0.156271 | 0.0781355 | − | 0.996943i | \(-0.475103\pi\) | ||||
0.0781355 | + | 0.996943i | \(0.475103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.70092 | 0.396780 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1067 | −1.70731 | −0.853655 | − | 0.520839i | \(-0.825619\pi\) | ||||
−0.853655 | + | 0.520839i | \(0.825619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.9915 | 1.88602 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.58209 | −0.164055 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.06203 | 0.818575 | 0.409287 | − | 0.912406i | \(-0.365777\pi\) | ||||
0.409287 | + | 0.912406i | \(0.365777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.807679 | −0.0811748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6496 | 1.15918 | 0.579590 | − | 0.814908i | \(-0.303213\pi\) | ||||
0.579590 | + | 0.814908i | \(0.303213\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.8439 | 1.85674 | 0.928370 | − | 0.371657i | \(-0.121210\pi\) | ||||
0.928370 | + | 0.371657i | \(0.121210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3957 | −1.39168 | −0.695842 | − | 0.718195i | \(-0.744969\pi\) | ||||
−0.695842 | + | 0.718195i | \(0.744969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.76186 | −0.551886 | −0.275943 | − | 0.961174i | \(-0.588990\pi\) | ||||
−0.275943 | + | 0.961174i | \(0.588990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.54179 | −0.810751 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9263 | 1.68637 | 0.843184 | − | 0.537624i | \(-0.180678\pi\) | ||||
0.843184 | + | 0.537624i | \(0.180678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.74950 | 0.439091 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.35192 | −0.398940 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3477 | −0.940696 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4989 | 1.03682 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.28981 | −0.203188 | −0.101594 | − | 0.994826i | \(-0.532394\pi\) | ||||
−0.101594 | + | 0.994826i | \(0.532394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.2458 | 0.902091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.04946 | −0.615914 | −0.307957 | − | 0.951400i | \(-0.599645\pi\) | ||||
−0.307957 | + | 0.951400i | \(0.599645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0568635 | 0.00493069 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.9329 | −1.87385 | −0.936927 | − | 0.349525i | \(-0.886343\pi\) | ||||
−0.936927 | + | 0.349525i | \(0.886343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.71761 | 0.824237 | 0.412118 | − | 0.911130i | \(-0.364789\pi\) | ||||
0.412118 | + | 0.911130i | \(0.364789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.526282 | −0.0443210 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.83607 | −0.320788 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.34957 | 0.606182 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9712 | −1.14457 | −0.572284 | − | 0.820056i | \(-0.693942\pi\) | ||||
−0.572284 | + | 0.820056i | \(0.693942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1871 | −1.64280 | −0.821400 | − | 0.570352i | \(-0.806807\pi\) | ||||
−0.821400 | + | 0.570352i | \(0.806807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.14884 | −0.0928786 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.76546 | 0.619751 | 0.309876 | − | 0.950777i | \(-0.399713\pi\) | ||||
0.309876 | + | 0.950777i | \(0.399713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.94976 | −0.233932 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.7436 | −1.87126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8908 | −1.08801 | −0.544006 | − | 0.839082i | \(-0.683093\pi\) | ||||
−0.544006 | + | 0.839082i | \(0.683093\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.89787 | −0.224244 | −0.112122 | − | 0.993694i | \(-0.535765\pi\) | ||||
−0.112122 | + | 0.993694i | \(0.535765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.55771 | 0.735209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0150112 | 0.00114793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.2338 | 1.15821 | 0.579104 | − | 0.815254i | \(-0.303403\pi\) | ||||
0.579104 | + | 0.815254i | \(0.303403\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.4436 | 0.860150 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.3056 | −1.74194 | −0.870971 | − | 0.491335i | \(-0.836509\pi\) | ||||
−0.870971 | + | 0.491335i | \(0.836509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6985 | 1.31552 | 0.657758 | − | 0.753229i | \(-0.271505\pi\) | ||||
0.657758 | + | 0.753229i | \(0.271505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.14212 | 0.232272 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.927897 | 0.0678546 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.78808 | 0.275542 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.36414 | 0.677566 | 0.338783 | − | 0.940865i | \(-0.389985\pi\) | ||||
0.338783 | + | 0.940865i | \(0.389985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9309 | 1.36268 | 0.681338 | − | 0.731969i | \(-0.261398\pi\) | ||||
0.681338 | + | 0.731969i | \(0.261398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.54357 | −0.537457 | −0.268729 | − | 0.963216i | \(-0.586603\pi\) | ||||
−0.268729 | + | 0.963216i | \(0.586603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.58560 | 0.254176 | 0.127088 | − | 0.991891i | \(-0.459437\pi\) | ||||
0.127088 | + | 0.991891i | \(0.459437\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2812 | 0.936783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0194 | 0.983967 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.26797 | −0.435654 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0121242 | −0.000838648 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.08493 | 0.143532 | 0.0717662 | − | 0.997421i | \(-0.477136\pi\) | ||||
0.0717662 | + | 0.997421i | \(0.477136\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.91318 | −0.336646 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.99309 | −0.406838 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.67860 | −0.316151 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.45643 | −0.367039 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0373 | 0.940007 | 0.470003 | − | 0.882665i | \(-0.344253\pi\) | ||||
0.470003 | + | 0.882665i | \(0.344253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.53486 | −0.168244 | −0.0841221 | − | 0.996455i | \(-0.526809\pi\) | ||||
−0.0841221 | + | 0.996455i | \(0.526809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5262 | −1.09208 | −0.546041 | − | 0.837759i | \(-0.683866\pi\) | ||||
−0.546041 | + | 0.837759i | \(0.683866\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.05955 | −0.201304 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.5208 | 1.73744 | 0.868719 | − | 0.495305i | \(-0.164944\pi\) | ||||
0.868719 | + | 0.495305i | \(0.164944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.27155 | 0.602252 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.46385 | −0.482797 | −0.241398 | − | 0.970426i | \(-0.577606\pi\) | ||||
−0.241398 | + | 0.970426i | \(0.577606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2978 | 0.663337 | 0.331669 | − | 0.943396i | \(-0.392388\pi\) | ||||
0.331669 | + | 0.943396i | \(0.392388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0712954 | 0.00453642 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.42370 | 0.0902231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5809 | 1.23593 | 0.617967 | − | 0.786204i | \(-0.287956\pi\) | ||||
0.617967 | + | 0.786204i | \(0.287956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.06250 | 0.318277 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.98030 | −0.373041 | −0.186520 | − | 0.982451i | \(-0.559721\pi\) | ||||
−0.186520 | + | 0.982451i | \(0.559721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.3570 | −2.01057 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.70092 | 0.229081 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.07038 | 0.374315 | 0.187158 | − | 0.982330i | \(-0.440072\pi\) | ||||
0.187158 | + | 0.982330i | \(0.440072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.1067 | −0.985716 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.61605 | 0.586301 | 0.293150 | − | 0.956066i | \(-0.405296\pi\) | ||||
0.293150 | + | 0.956066i | \(0.405296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.4276 | −1.84834 | −0.924171 | − | 0.381979i | \(-0.875243\pi\) | ||||
−0.924171 | + | 0.381979i | \(0.875243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.9915 | 1.08889 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.20393 | −0.432842 | −0.216421 | − | 0.976300i | \(-0.569438\pi\) | ||||
−0.216421 | + | 0.976300i | \(0.569438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.58209 | −0.0947173 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.7964 | 1.77750 | 0.888751 | − | 0.458390i | \(-0.151574\pi\) | ||||
0.888751 | + | 0.458390i | \(0.151574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.82402 | 0.524534 | 0.262267 | − | 0.964995i | \(-0.415530\pi\) | ||||
0.262267 | + | 0.964995i | \(0.415530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 43.5587 | 2.57119 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6802 | −0.922362 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.06203 | 0.472604 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.20743 | −0.245800 | −0.122900 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122900 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.807679 | −0.0468663 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.7697 | −1.72163 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.8119 | 2.23708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.6496 | 0.669253 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.41109 | 0.251754 | 0.125877 | − | 0.992046i | \(-0.459825\pi\) | ||||
0.125877 | + | 0.992046i | \(0.459825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.8439 | 1.07199 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.32058 | −0.358407 | −0.179204 | − | 0.983812i | \(-0.557352\pi\) | ||||
−0.179204 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3245 | −0.866193 | −0.433097 | − | 0.901347i | \(-0.642579\pi\) | ||||
−0.433097 | + | 0.901347i | \(0.642579\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.3155 | −1.19720 | −0.598600 | − | 0.801048i | \(-0.704276\pi\) | ||||
−0.598600 | + | 0.801048i | \(0.704276\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.98915 | −0.167360 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.3957 | −0.803489 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0172455 | −0.000959564 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.76186 | −0.318631 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99360 | −0.109911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8124 | 1.08899 | 0.544494 | − | 0.838764i | \(-0.316722\pi\) | ||||
0.544494 | + | 0.838764i | \(0.316722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.54179 | −0.468087 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0339 | −0.546583 | −0.273292 | − | 0.961931i | \(-0.588112\pi\) | ||||
−0.273292 | + | 0.961931i | \(0.588112\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.9263 | 0.973626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.27782 | 0.0691979 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.32419 | 0.0714997 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.8672 | 0.744429 | 0.372214 | − | 0.928147i | \(-0.378599\pi\) | ||||
0.372214 | + | 0.928147i | \(0.378599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2533 | 1.45883 | 0.729417 | − | 0.684069i | \(-0.239791\pi\) | ||||
0.729417 | + | 0.684069i | \(0.239791\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.74950 | 0.253509 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4138 | −0.660722 | −0.330361 | − | 0.943855i | \(-0.607170\pi\) | ||||
−0.330361 | + | 0.943855i | \(0.607170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.35192 | −0.230328 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.0244 | −1.00407 | −0.502034 | − | 0.864848i | \(-0.667415\pi\) | ||||
−0.502034 | + | 0.864848i | \(0.667415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9998 | −0.999988 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3477 | −0.543111 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.975194 | 0.0509047 | 0.0254524 | − | 0.999676i | \(-0.491897\pi\) | ||||
0.0254524 | + | 0.999676i | \(0.491897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4989 | 0.598608 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1740 | −0.580123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.7723 | 0.971994 | 0.485997 | − | 0.873960i | \(-0.338457\pi\) | ||||
0.485997 | + | 0.873960i | \(0.338457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.5775 | 0.905287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.44756 | −0.177089 | −0.0885447 | − | 0.996072i | \(-0.528222\pi\) | ||||
−0.0885447 | + | 0.996072i | \(0.528222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.28981 | −0.117311 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3045 | 1.39519 | 0.697597 | − | 0.716490i | \(-0.254253\pi\) | ||||
0.697597 | + | 0.716490i | \(0.254253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2458 | 0.520823 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.81725 | 0.497754 | 0.248877 | − | 0.968535i | \(-0.419938\pi\) | ||||
0.248877 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.20092 | 0.364166 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.04946 | −0.355598 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.6131 | −0.582846 | −0.291423 | − | 0.956594i | \(-0.594129\pi\) | ||||
−0.291423 | + | 0.956594i | \(0.594129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0568635 | 0.00284674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4145 | −1.26914 | −0.634570 | − | 0.772865i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772865i | \(0.718823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.51414 | −0.374306 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.89902 | 0.341972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.2515 | 0.853032 | 0.426516 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426516 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.9329 | −1.08187 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 43.3491 | 2.13307 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.71761 | 0.475873 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.4505 | −0.999074 | −0.499537 | − | 0.866293i | \(-0.666497\pi\) | ||||
−0.499537 | + | 0.866293i | \(0.666497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9082 | −1.01901 | −0.509503 | − | 0.860469i | \(-0.670171\pi\) | ||||
−0.509503 | + | 0.860469i | \(0.670171\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.526282 | −0.0255887 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9026 | 0.576008 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.83607 | −0.185207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.25191 | −0.445649 | −0.222824 | − | 0.974859i | \(-0.571528\pi\) | ||||
−0.222824 | + | 0.974859i | \(0.571528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.235240 | −0.0113049 | −0.00565246 | − | 0.999984i | \(-0.501799\pi\) | ||||
−0.00565246 | + | 0.999984i | \(0.501799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0940894 | −0.00450091 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.2013 | 1.48916 | 0.744578 | − | 0.667536i | \(-0.232651\pi\) | ||||
0.744578 | + | 0.667536i | \(0.232651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.34957 | 0.349979 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3862 | 1.15862 | 0.579311 | − | 0.815106i | \(-0.303322\pi\) | ||||
0.579311 | + | 0.815106i | \(0.303322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.9712 | −0.660816 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.9483 | 1.13019 | 0.565096 | − | 0.825025i | \(-0.308839\pi\) | ||||
0.565096 | + | 0.825025i | \(0.308839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.28740 | −0.437327 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.1871 | −0.948471 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.91244 | 0.183016 | 0.0915082 | − | 0.995804i | \(-0.470831\pi\) | ||||
0.0915082 | + | 0.995804i | \(0.470831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.14884 | −0.0536235 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58548 | −0.120418 | −0.0602090 | − | 0.998186i | \(-0.519177\pi\) | ||||
−0.0602090 | + | 0.998186i | \(0.519177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9089 | 1.01819 | 0.509096 | − | 0.860710i | \(-0.329980\pi\) | ||||
0.509096 | + | 0.860710i | \(0.329980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.19679 | 0.379302 | 0.189651 | − | 0.981852i | \(-0.439264\pi\) | ||||
0.189651 | + | 0.981852i | \(0.439264\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.3103 | 2.32311 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.76546 | 0.357814 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.27531 | −0.380499 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.94976 | −0.135060 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.15176 | −0.281081 | −0.140540 | − | 0.990075i | \(-0.544884\pi\) | ||||
−0.140540 | + | 0.990075i | \(0.544884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.5692 | −1.84980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.7436 | −1.08037 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.28171 | 0.284651 | 0.142326 | − | 0.989820i | \(-0.454542\pi\) | ||||
0.142326 | + | 0.989820i | \(0.454542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8908 | −0.628163 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.75137 | −0.124168 | −0.0620839 | − | 0.998071i | \(-0.519775\pi\) | ||||
−0.0620839 | + | 0.998071i | \(0.519775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.25178 | −0.191490 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.6115 | −0.834842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4263 | −0.735341 | −0.367670 | − | 0.929956i | \(-0.619844\pi\) | ||||
−0.367670 | + | 0.929956i | \(0.619844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.89787 | −0.129467 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.2874 | −0.547868 | −0.273934 | − | 0.961749i | \(-0.588325\pi\) | ||||
−0.273934 | + | 0.961749i | \(0.588325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.55771 | 0.424473 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5100 | −0.465848 | −0.232924 | − | 0.972495i | \(-0.574829\pi\) | ||||
−0.232924 | + | 0.972495i | \(0.574829\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7229 | −0.784017 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0150112 | 0.000662759 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.425067 | 0.0186944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.2338 | 0.668691 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.82409 | −0.342780 | −0.171390 | − | 0.985203i | \(-0.554826\pi\) | ||||
−0.171390 | + | 0.985203i | \(0.554826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0475 | 0.964068 | 0.482034 | − | 0.876153i | \(-0.339898\pi\) | ||||
0.482034 | + | 0.876153i | \(0.339898\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.81758 | 0.0791749 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2874 | 0.708148 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4436 | 0.496608 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.6139 | 2.36559 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.3056 | −1.00571 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.93609 | −0.255685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4670 | 0.535998 | 0.267999 | − | 0.963419i | \(-0.413638\pi\) | ||||
0.267999 | + | 0.963419i | \(0.413638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6985 | 0.759514 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.51606 | 0.107579 | 0.0537895 | − | 0.998552i | \(-0.482870\pi\) | ||||
0.0537895 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.14212 | 0.134102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0555550 | 0.00236672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.1214 | 1.49351 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.262544 | −0.0111244 | −0.00556218 | − | 0.999985i | \(-0.501771\pi\) | ||||
−0.00556218 | + | 0.999985i | \(0.501771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.6623 | 2.05820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.927897 | 0.0391759 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4826 | 1.36898 | 0.684489 | − | 0.729023i | \(-0.260025\pi\) | ||||
0.684489 | + | 0.729023i | \(0.260025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.78808 | 0.159085 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.7980 | −1.62650 | −0.813248 | − | 0.581917i | \(-0.802303\pi\) | ||||
−0.813248 | + | 0.581917i | \(0.802303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.6801 | −1.49317 | −0.746583 | − | 0.665292i | \(-0.768307\pi\) | ||||
−0.746583 | + | 0.665292i | \(0.768307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.36414 | 0.391193 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.3430 | −1.05504 | −0.527522 | − | 0.849542i | \(-0.676879\pi\) | ||||
−0.527522 | + | 0.849542i | \(0.676879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.9309 | 0.786741 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.39308 | 0.223743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.38246 | 0.0986715 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.515670 | 0.0212840 | 0.0106420 | − | 0.999943i | \(-0.496612\pi\) | ||||
0.0106420 | + | 0.999943i | \(0.496612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0237490 | −0.000978561 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.54357 | −0.310301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.14389 | 0.293364 | 0.146682 | − | 0.989184i | \(-0.453141\pi\) | ||||
0.146682 | + | 0.989184i | \(0.453141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.58560 | 0.146749 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.6627 | 0.966833 | 0.483417 | − | 0.875390i | \(-0.339396\pi\) | ||||
0.483417 | + | 0.875390i | \(0.339396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98023 | −0.325520 | −0.162760 | − | 0.986666i | \(-0.552040\pi\) | ||||
−0.162760 | + | 0.986666i | \(0.552040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.2812 | 0.540852 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2004 | −0.698144 | −0.349072 | − | 0.937096i | \(-0.613503\pi\) | ||||
−0.349072 | + | 0.937096i | \(0.613503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.0194 | 0.568094 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.49958 | −0.101122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7641 | 0.596315 | 0.298158 | − | 0.954517i | \(-0.403628\pi\) | ||||
0.298158 | + | 0.954517i | \(0.403628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4714 | 0.622854 | 0.311427 | − | 0.950270i | \(-0.399193\pi\) | ||||
0.311427 | + | 0.950270i | \(0.399193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.4710 | −1.50608 | −0.753042 | − | 0.657972i | \(-0.771414\pi\) | ||||
−0.753042 | + | 0.657972i | \(0.771414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.26797 | −0.251525 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −61.0136 | −2.44446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0121242 | −0.000484194 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.81319 | 0.391277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51672 | −0.0603796 | −0.0301898 | − | 0.999544i | \(-0.509611\pi\) | ||||
−0.0301898 | + | 0.999544i | \(0.509611\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.08493 | 0.0828685 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.9067 | 1.38306 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.91318 | −0.194363 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.86770 | −0.152765 | −0.0763825 | − | 0.997079i | \(-0.524337\pi\) | ||||
−0.0763825 | + | 0.997079i | \(0.524337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2212 | 0.915756 | 0.457878 | − | 0.889015i | \(-0.348610\pi\) | ||||
0.457878 | + | 0.889015i | \(0.348610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.1598 | 1.02845 | 0.514225 | − | 0.857655i | \(-0.328080\pi\) | ||||
0.514225 | + | 0.857655i | \(0.328080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.24271 | −0.362808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.99309 | −0.234888 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.55471 | −0.334772 | −0.167386 | − | 0.985891i | \(-0.553533\pi\) | ||||
−0.167386 | + | 0.985891i | \(0.553533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.67860 | −0.182530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.9383 | −1.63368 | −0.816841 | − | 0.576862i | \(-0.804277\pi\) | ||||
−0.816841 | + | 0.576862i | \(0.804277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5167 | −0.681322 | −0.340661 | − | 0.940186i | \(-0.610651\pi\) | ||||
−0.340661 | + | 0.940186i | \(0.610651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.45643 | −0.211910 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.1972 | −0.898200 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.0373 | 0.542713 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.53782 | −0.0979716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0952 | −1.12154 | −0.560769 | − | 0.827972i | \(-0.689494\pi\) | ||||
−0.560769 | + | 0.827972i | \(0.689494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.8863 | −1.14862 | −0.574311 | − | 0.818637i | \(-0.694730\pi\) | ||||
−0.574311 | + | 0.818637i | \(0.694730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.5396 | 1.17200 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.53486 | −0.0971359 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.2200 | −1.42419 | −0.712093 | − | 0.702086i | \(-0.752252\pi\) | ||||
−0.712093 | + | 0.702086i | \(0.752252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.5262 | −0.630514 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.0099 | −0.533734 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8596 | 0.641368 | 0.320684 | − | 0.947186i | \(-0.396087\pi\) | ||||
0.320684 | + | 0.947186i | \(0.396087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.05955 | −0.116223 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.2104 | −0.500380 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.5208 | 1.00311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3495 | −0.881898 | −0.440949 | − | 0.897532i | \(-0.645358\pi\) | ||||
−0.440949 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.128222 | −0.00483599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.1297 | 1.65967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0378 | 0.714978 | 0.357489 | − | 0.933917i | \(-0.383633\pi\) | ||||
0.357489 | + | 0.933917i | \(0.383633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.27155 | 0.347710 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.91650 | 0.371376 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.46385 | −0.278743 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.7399 | −0.549706 | −0.274853 | − | 0.961486i | \(-0.588629\pi\) | ||||
−0.274853 | + | 0.961486i | \(0.588629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 71.3821 | 2.65841 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.2978 | 0.382978 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.0617 | 1.11492 | 0.557462 | − | 0.830202i | \(-0.311775\pi\) | ||||
0.557462 | + | 0.830202i | \(0.311775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.7708 | −0.435359 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.6438 | −0.836368 | −0.418184 | − | 0.908362i | \(-0.637333\pi\) | ||||
−0.418184 | + | 0.908362i | \(0.637333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.7269 | −0.395132 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6810 | −0.944692 | −0.472346 | − | 0.881413i | \(-0.656593\pi\) | ||||
−0.472346 | + | 0.881413i | \(0.656593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0712954 | 0.00261910 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.9796 | −0.916411 | −0.458205 | − | 0.888846i | \(-0.651508\pi\) | ||||
−0.458205 | + | 0.888846i | \(0.651508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.42370 | 0.0520904 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.5321 | −1.99256 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9383 | 0.654580 | 0.327290 | − | 0.944924i | \(-0.393865\pi\) | ||||
0.327290 | + | 0.944924i | \(0.393865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.5809 | 0.713567 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.91474 | −0.360357 | −0.180179 | − | 0.983634i | \(-0.557668\pi\) | ||||
−0.180179 | + | 0.983634i | \(0.557668\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.06250 | 0.183757 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.6527 | −1.14741 | −0.573705 | − | 0.819062i | \(-0.694494\pi\) | ||||
−0.573705 | + | 0.819062i | \(0.694494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.8264 | −0.790168 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.3511 | 1.96250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3751 | 0.806868 | 0.403434 | − | 0.915009i | \(-0.367816\pi\) | ||||
0.403434 | + | 0.915009i | \(0.367816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.98030 | −0.215375 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.8317 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.3570 | −1.16080 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.172611 | 0.00618445 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.96827 | 0.141996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.70092 | 0.132260 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.5675 | −0.982677 | −0.491338 | − | 0.870969i | \(-0.663492\pi\) | ||||
−0.491338 | + | 0.870969i | \(0.663492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.07038 | 0.216111 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 67.9065 | 2.41448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9235 | 0.529948 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.1019 | −0.818311 | −0.409155 | − | 0.912465i | \(-0.634177\pi\) | ||||
−0.409155 | + | 0.912465i | \(0.634177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.604617 | 0.0213898 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.1067 | −0.569103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.77881 | 0.133351 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.61605 | 0.338501 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.69292 | −0.0595198 | −0.0297599 | − | 0.999557i | \(-0.509474\pi\) | ||||
−0.0297599 | + | 0.999557i | \(0.509474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5726 | 0.722400 | 0.361200 | − | 0.932488i | \(-0.382367\pi\) | ||||
0.361200 | + | 0.932488i | \(0.382367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.4276 | −1.06714 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.153801 | 0.00538082 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.9915 | 0.628673 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.0282 | −1.60639 | −0.803197 | − | 0.595713i | \(-0.796869\pi\) | ||||
−0.803197 | + | 0.595713i | \(0.796869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.9867 | 1.95157 | 0.975787 | − | 0.218721i | \(-0.0701884\pi\) | ||||
0.975787 | + | 0.218721i | \(0.0701884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6399 | 0.717721 | 0.358860 | − | 0.933391i | \(-0.383165\pi\) | ||||
0.358860 | + | 0.933391i | \(0.383165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.93898 | −0.0673437 | −0.0336718 | − | 0.999433i | \(-0.510720\pi\) | ||||
−0.0336718 | + | 0.999433i | \(0.510720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.20393 | −0.249901 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.44351 | −0.292550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.58209 | −0.0546851 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.2589 | 1.80418 | 0.902089 | − | 0.431551i | \(-0.142034\pi\) | ||||
0.902089 | + | 0.431551i | \(0.142034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3032 | −0.527697 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.7964 | 1.02624 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.1978 | −1.34685 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.82402 | 0.302840 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.5397 | 1.83532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5605 | −0.601260 | −0.300630 | − | 0.953741i | \(-0.597197\pi\) | ||||
−0.300630 | + | 0.953741i | \(0.597197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.9890 | 1.74175 | 0.870876 | − | 0.491503i | \(-0.163552\pi\) | ||||
0.870876 | + | 0.491503i | \(0.163552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.6336 | 0.635770 | 0.317885 | − | 0.948129i | \(-0.397027\pi\) | ||||
0.317885 | + | 0.948129i | \(0.397027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.5587 | 1.48448 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.292141 | 0.00994461 | 0.00497230 | − | 0.999988i | \(-0.498417\pi\) | ||||
0.00497230 | + | 0.999988i | \(0.498417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6802 | −0.532526 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.48843 | −0.254028 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.0790 | 2.13735 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.06203 | 0.272858 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.9604 | −1.28183 | −0.640916 | − | 0.767611i | \(-0.721445\pi\) | ||||
−0.640916 | + | 0.767611i | \(0.721445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.20743 | −0.141913 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6899 | −1.23612 | −0.618058 | − | 0.786133i | \(-0.712080\pi\) | ||||
−0.618058 | + | 0.786133i | \(0.712080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.6199 | −0.761220 | −0.380610 | − | 0.924736i | \(-0.624286\pi\) | ||||
−0.380610 | + | 0.924736i | \(0.624286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.4380 | −0.820548 | −0.410274 | − | 0.911962i | \(-0.634567\pi\) | ||||
−0.410274 | + | 0.911962i | \(0.634567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.67399 | −0.290916 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.807679 | −0.0270583 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.00790011 | −0.000264367 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.7697 | −0.993981 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.85519 | −0.195281 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.38882 | 0.112898 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.8119 | 1.29158 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.7792 | 1.08842 | 0.544208 | − | 0.838950i | \(-0.316830\pi\) | ||||
0.544208 | + | 0.838950i | \(0.316830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.6496 | 0.386393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.2897 | 0.904146 | 0.452073 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452073 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.14989 | −0.0380558 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.7039 | −0.881842 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.7202 | −1.37622 | −0.688112 | − | 0.725604i | \(-0.741560\pi\) | ||||
−0.688112 | + | 0.725604i | \(0.741560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.41109 | 0.145350 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.3351 | −0.768086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.8439 | 0.618913 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.7038 | −1.10579 | −0.552893 | − | 0.833252i | \(-0.686476\pi\) | ||||
−0.552893 | + | 0.833252i | \(0.686476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.110326 | 0.00361577 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.32058 | −0.206927 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.04606 | −0.0341732 | −0.0170866 | − | 0.999854i | \(-0.505439\pi\) | ||||
−0.0170866 | + | 0.999854i | \(0.505439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.3245 | −0.500097 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.72210 | 0.186535 | 0.0932676 | − | 0.995641i | \(-0.470269\pi\) | ||||
0.0932676 | + | 0.995641i | \(0.470269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −72.0746 | −2.34707 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5948 | 0.409275 | 0.204637 | − | 0.978838i | \(-0.434398\pi\) | ||||
0.204637 | + | 0.978838i | \(0.434398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.2210 | −0.721325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.3155 | −0.691204 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.3902 | 1.85905 | 0.929526 | − | 0.368757i | \(-0.120217\pi\) | ||||
0.929526 | + | 0.368757i | \(0.120217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.98915 | −0.0966255 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −83.0836 | −2.68291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4970 | −0.919258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3957 | −0.463895 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.84212 | 0.284343 | 0.142172 | − | 0.989842i | \(-0.454591\pi\) | ||||
0.142172 | + | 0.989842i | \(0.454591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0172455 | −0.000554005 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.9365 | 1.66672 | 0.833361 | − | 0.552730i | \(-0.186414\pi\) | ||||
0.833361 | + | 0.552730i | \(0.186414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.8111 | 1.18011 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.2345 | 1.19124 | 0.595619 | − | 0.803267i | \(-0.296907\pi\) | ||||
0.595619 | + | 0.803267i | \(0.296907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0091 | 0.415772 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.76186 | −0.183962 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.7610 | 1.14060 | 0.570299 | − | 0.821437i | \(-0.306827\pi\) | ||||
0.570299 | + | 0.821437i | \(0.306827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.99360 | −0.0634570 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.2203 | −2.04209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.8192 | −1.39196 | −0.695981 | − | 0.718060i | \(-0.745030\pi\) | ||||
−0.695981 | + | 0.718060i | \(0.745030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.8124 | 0.628728 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.5083 | 1.25124 | 0.625620 | − | 0.780128i | \(-0.284846\pi\) | ||||
0.625620 | + | 0.780128i | \(0.284846\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.54179 | −0.270250 |
(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 | 7500.2.a.n.1.9 | 12 | ||
5.2 | odd | 4 | 7500.2.d.g.1249.9 | 24 | |||
5.3 | odd | 4 | 7500.2.d.g.1249.16 | 24 | |||
5.4 | even | 2 | 7500.2.a.m.1.4 | 12 | |||
25.3 | odd | 20 | 1500.2.o.c.49.1 | 24 | |||
25.4 | even | 10 | 1500.2.m.d.1201.2 | 24 | |||
25.6 | even | 5 | 1500.2.m.c.301.5 | 24 | |||
25.8 | odd | 20 | 300.2.o.a.289.5 | yes | 24 | ||
25.17 | odd | 20 | 1500.2.o.c.949.1 | 24 | |||
25.19 | even | 10 | 1500.2.m.d.301.2 | 24 | |||
25.21 | even | 5 | 1500.2.m.c.1201.5 | 24 | |||
25.22 | odd | 20 | 300.2.o.a.109.5 | ✓ | 24 | ||
75.8 | even | 20 | 900.2.w.c.289.4 | 24 | |||
75.47 | even | 20 | 900.2.w.c.109.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.5 | ✓ | 24 | 25.22 | odd | 20 | ||
300.2.o.a.289.5 | yes | 24 | 25.8 | odd | 20 | ||
900.2.w.c.109.4 | 24 | 75.47 | even | 20 | |||
900.2.w.c.289.4 | 24 | 75.8 | even | 20 | |||
1500.2.m.c.301.5 | 24 | 25.6 | even | 5 | |||
1500.2.m.c.1201.5 | 24 | 25.21 | even | 5 | |||
1500.2.m.d.301.2 | 24 | 25.19 | even | 10 | |||
1500.2.m.d.1201.2 | 24 | 25.4 | even | 10 | |||
1500.2.o.c.49.1 | 24 | 25.3 | odd | 20 | |||
1500.2.o.c.949.1 | 24 | 25.17 | odd | 20 | |||
7500.2.a.m.1.4 | 12 | 5.4 | even | 2 | |||
7500.2.a.n.1.9 | 12 | 1.1 | even | 1 | trivial | ||
7500.2.d.g.1249.9 | 24 | 5.2 | odd | 4 | |||
7500.2.d.g.1249.16 | 24 | 5.3 | odd | 4 |