Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.74043072.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 21x^{2} - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.924607\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.924607 | 0.653796 | 0.326898 | − | 0.945060i | \(-0.393997\pi\) | ||||
0.326898 | + | 0.945060i | \(0.393997\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.14510 | −0.572551 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.64003 | −1.75377 | −0.876884 | − | 0.480702i | \(-0.840382\pi\) | ||||
−0.876884 | + | 0.480702i | \(0.840382\pi\) | |||||||
\(8\) | −2.90798 | −1.02813 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.924607 | 0.292386 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −4.29021 | −1.14661 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.398534 | −0.0996336 | ||||||||
\(17\) | −6.37208 | −1.54546 | −0.772729 | − | 0.634736i | \(-0.781109\pi\) | ||||
−0.772729 | + | 0.634736i | \(0.781109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.64003 | −1.06450 | −0.532248 | − | 0.846588i | \(-0.678653\pi\) | ||||
−0.532248 | + | 0.846588i | \(0.678653\pi\) | |||||||
\(20\) | −1.14510 | −0.256053 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.74657 | 1.40676 | 0.703378 | − | 0.710816i | \(-0.251674\pi\) | ||||
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.31331 | 1.00412 | ||||||||
\(29\) | −3.46410 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.20293 | −0.395658 | −0.197829 | − | 0.980237i | \(-0.563389\pi\) | ||||
−0.197829 | + | 0.980237i | \(0.563389\pi\) | |||||||
\(32\) | 5.44748 | 0.962987 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.89167 | −1.01041 | ||||||||
\(35\) | −4.64003 | −0.784309 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.45636 | 0.568223 | 0.284111 | − | 0.958791i | \(-0.408301\pi\) | ||||
0.284111 | + | 0.958791i | \(0.408301\pi\) | |||||||
\(38\) | −4.29021 | −0.695963 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.90798 | −0.459792 | ||||||||
\(41\) | −5.81597 | −0.908301 | −0.454151 | − | 0.890925i | \(-0.650057\pi\) | ||||
−0.454151 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.234325 | 0.0357342 | 0.0178671 | − | 0.999840i | \(-0.494312\pi\) | ||||
0.0178671 | + | 0.999840i | \(0.494312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.23792 | 0.919731 | ||||||||
\(47\) | −9.32698 | −1.36048 | −0.680240 | − | 0.732990i | \(-0.738124\pi\) | ||||
−0.680240 | + | 0.732990i | \(0.738124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5299 | 2.07570 | ||||||||
\(50\) | 0.924607 | 0.130759 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.54364 | 0.486756 | 0.243378 | − | 0.969932i | \(-0.421744\pi\) | ||||
0.243378 | + | 0.969932i | \(0.421744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.4931 | 1.80310 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.20293 | −0.420565 | ||||||||
\(59\) | 14.5804 | 1.89821 | 0.949104 | − | 0.314963i | \(-0.101992\pi\) | ||||
0.949104 | + | 0.314963i | \(0.101992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.96638 | 0.251769 | 0.125884 | − | 0.992045i | \(-0.459823\pi\) | ||||
0.125884 | + | 0.992045i | \(0.459823\pi\) | |||||||
\(62\) | −2.03684 | −0.258680 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.83384 | 0.729230 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45636 | −0.177923 | −0.0889615 | − | 0.996035i | \(-0.528355\pi\) | ||||
−0.0889615 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(68\) | 7.29669 | 0.884854 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.29021 | −0.512778 | ||||||||
\(71\) | −2.58041 | −0.306238 | −0.153119 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153119 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6858 | 1.60180 | 0.800899 | − | 0.598799i | \(-0.204355\pi\) | ||||
0.800899 | + | 0.598799i | \(0.204355\pi\) | |||||||
\(74\) | 3.19578 | 0.371501 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.31331 | 0.609479 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.58126 | 0.402924 | 0.201462 | − | 0.979496i | \(-0.435431\pi\) | ||||
0.201462 | + | 0.979496i | \(0.435431\pi\) | |||||||
\(80\) | −0.398534 | −0.0445575 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.37748 | −0.593843 | ||||||||
\(83\) | −7.16253 | −0.786190 | −0.393095 | − | 0.919498i | \(-0.628596\pi\) | ||||
−0.393095 | + | 0.919498i | \(0.628596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.37208 | −0.691150 | ||||||||
\(86\) | 0.216658 | 0.0233628 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.98627 | −0.952543 | −0.476272 | − | 0.879298i | \(-0.658012\pi\) | ||||
−0.476272 | + | 0.879298i | \(0.658012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.72551 | −0.805440 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.62379 | −0.889476 | ||||||||
\(95\) | −4.64003 | −0.476057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4426 | −1.26336 | −0.631679 | − | 0.775230i | \(-0.717634\pi\) | ||||
−0.631679 | + | 0.775230i | \(0.717634\pi\) | |||||||
\(98\) | 13.4345 | 1.35708 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.14510 | −0.114510 | ||||||||
\(101\) | −15.0960 | −1.50211 | −0.751056 | − | 0.660239i | \(-0.770455\pi\) | ||||
−0.751056 | + | 0.660239i | \(0.770455\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.0230 | 1.87440 | 0.937198 | − | 0.348797i | \(-0.113410\pi\) | ||||
0.937198 | + | 0.348797i | \(0.113410\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.27647 | 0.318239 | ||||||||
\(107\) | 17.2670 | 1.66927 | 0.834634 | − | 0.550805i | \(-0.185679\pi\) | ||||
0.834634 | + | 0.550805i | \(0.185679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1544 | 1.35575 | 0.677874 | − | 0.735178i | \(-0.262901\pi\) | ||||
0.677874 | + | 0.735178i | \(0.262901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.84921 | 0.174734 | ||||||||
\(113\) | −3.94950 | −0.371538 | −0.185769 | − | 0.982593i | \(-0.559478\pi\) | ||||
−0.185769 | + | 0.982593i | \(0.559478\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.74657 | 0.629121 | ||||||||
\(116\) | 3.96675 | 0.368304 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.4811 | 1.24104 | ||||||||
\(119\) | 29.5667 | 2.71037 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.81812 | 0.164605 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.52258 | 0.226535 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5063 | 1.46470 | 0.732348 | − | 0.680930i | \(-0.238424\pi\) | ||||
0.732348 | + | 0.680930i | \(0.238424\pi\) | |||||||
\(128\) | −5.50095 | −0.486220 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9739 | 1.39565 | 0.697825 | − | 0.716268i | \(-0.254151\pi\) | ||||
0.697825 | + | 0.716268i | \(0.254151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.5299 | 1.86688 | ||||||||
\(134\) | −1.34656 | −0.116325 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.5299 | 1.58893 | ||||||||
\(137\) | 5.03677 | 0.430321 | 0.215160 | − | 0.976579i | \(-0.430973\pi\) | ||||
0.215160 | + | 0.976579i | \(0.430973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.8479 | −1.59866 | −0.799330 | − | 0.600892i | \(-0.794812\pi\) | ||||
−0.799330 | + | 0.600892i | \(0.794812\pi\) | |||||||
\(140\) | 5.31331 | 0.449057 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.38586 | −0.200217 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.46410 | −0.287678 | ||||||||
\(146\) | 12.6540 | 1.04725 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.95789 | −0.325337 | ||||||||
\(149\) | 9.74872 | 0.798646 | 0.399323 | − | 0.916810i | \(-0.369245\pi\) | ||||
0.399323 | + | 0.916810i | \(0.369245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2670 | 1.40517 | 0.702586 | − | 0.711599i | \(-0.252029\pi\) | ||||
0.702586 | + | 0.711599i | \(0.252029\pi\) | |||||||
\(152\) | 13.4931 | 1.09444 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.20293 | −0.176944 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.61718 | −0.528109 | −0.264054 | − | 0.964508i | \(-0.585060\pi\) | ||||
−0.264054 | + | 0.964508i | \(0.585060\pi\) | |||||||
\(158\) | 3.31126 | 0.263430 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.44748 | 0.430661 | ||||||||
\(161\) | −31.3043 | −2.46712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4426 | −0.974582 | −0.487291 | − | 0.873240i | \(-0.662015\pi\) | ||||
−0.487291 | + | 0.873240i | \(0.662015\pi\) | |||||||
\(164\) | 6.65988 | 0.520049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.62252 | −0.514007 | ||||||||
\(167\) | −2.17101 | −0.167998 | −0.0839988 | − | 0.996466i | \(-0.526769\pi\) | ||||
−0.0839988 | + | 0.996466i | \(0.526769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −5.89167 | −0.451871 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.268326 | −0.0204597 | ||||||||
\(173\) | 8.81142 | 0.669920 | 0.334960 | − | 0.942232i | \(-0.391277\pi\) | ||||
0.334960 | + | 0.942232i | \(0.391277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.64003 | −0.350754 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.30877 | −0.622768 | ||||||||
\(179\) | 13.8990 | 1.03886 | 0.519430 | − | 0.854513i | \(-0.326144\pi\) | ||||
0.519430 | + | 0.854513i | \(0.326144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.6172 | −1.53246 | −0.766232 | − | 0.642564i | \(-0.777870\pi\) | ||||
−0.766232 | + | 0.642564i | \(0.777870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.6189 | −1.44632 | ||||||||
\(185\) | 3.45636 | 0.254117 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.6803 | 0.778944 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.29021 | −0.311244 | ||||||||
\(191\) | 13.4931 | 0.976329 | 0.488165 | − | 0.872752i | \(-0.337667\pi\) | ||||
0.488165 | + | 0.872752i | \(0.337667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7308 | 1.34827 | 0.674135 | − | 0.738608i | \(-0.264517\pi\) | ||||
0.674135 | + | 0.738608i | \(0.264517\pi\) | |||||||
\(194\) | −11.5045 | −0.825978 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.6382 | −1.18845 | ||||||||
\(197\) | 13.8564 | 0.987228 | 0.493614 | − | 0.869681i | \(-0.335676\pi\) | ||||
0.493614 | + | 0.869681i | \(0.335676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3638 | −1.37266 | −0.686330 | − | 0.727290i | \(-0.740779\pi\) | ||||
−0.686330 | + | 0.727290i | \(0.740779\pi\) | |||||||
\(200\) | −2.90798 | −0.205625 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.9579 | −0.982074 | ||||||||
\(203\) | 16.0735 | 1.12814 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.81597 | −0.406205 | ||||||||
\(206\) | 17.5888 | 1.22547 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.351487 | −0.0241974 | −0.0120987 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120987 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(212\) | −4.05783 | −0.278693 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.9652 | 1.09136 | ||||||||
\(215\) | 0.234325 | 0.0159808 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.2217 | 0.693892 | ||||||||
\(218\) | 13.0873 | 0.886382 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.94950 | 0.197513 | 0.0987565 | − | 0.995112i | \(-0.468513\pi\) | ||||
0.0987565 | + | 0.995112i | \(0.468513\pi\) | |||||||
\(224\) | −25.2765 | −1.68886 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.65173 | −0.242910 | ||||||||
\(227\) | 10.5732 | 0.701765 | 0.350883 | − | 0.936419i | \(-0.385882\pi\) | ||||
0.350883 | + | 0.936419i | \(0.385882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9495 | −0.789645 | −0.394823 | − | 0.918757i | \(-0.629194\pi\) | ||||
−0.394823 | + | 0.918757i | \(0.629194\pi\) | |||||||
\(230\) | 6.23792 | 0.411316 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0735 | 0.661361 | ||||||||
\(233\) | −7.48432 | −0.490314 | −0.245157 | − | 0.969483i | \(-0.578840\pi\) | ||||
−0.245157 | + | 0.969483i | \(0.578840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.32698 | −0.608425 | ||||||||
\(236\) | −16.6961 | −1.08682 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 27.3376 | 1.77203 | ||||||||
\(239\) | 28.3088 | 1.83115 | 0.915574 | − | 0.402150i | \(-0.131737\pi\) | ||||
0.915574 | + | 0.402150i | \(0.131737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.13776 | −0.395368 | −0.197684 | − | 0.980266i | \(-0.563342\pi\) | ||||
−0.197684 | + | 0.980266i | \(0.563342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.25170 | −0.144150 | ||||||||
\(245\) | 14.5299 | 0.928282 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.40609 | 0.406787 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.924607 | 0.0584773 | ||||||||
\(251\) | −2.98627 | −0.188492 | −0.0942459 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942459 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.2618 | 0.957612 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.7539 | −1.04712 | ||||||||
\(257\) | 24.1240 | 1.50482 | 0.752408 | − | 0.658697i | \(-0.228892\pi\) | ||||
0.752408 | + | 0.658697i | \(0.228892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0376 | −0.996530 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.7696 | 0.912470 | ||||||||
\(263\) | −9.46092 | −0.583386 | −0.291693 | − | 0.956512i | \(-0.594218\pi\) | ||||
−0.291693 | + | 0.956512i | \(0.594218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.54364 | 0.217684 | ||||||||
\(266\) | 19.9067 | 1.22056 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.66769 | 0.101870 | ||||||||
\(269\) | 1.08727 | 0.0662923 | 0.0331461 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331461 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.10376 | −0.370777 | −0.185388 | − | 0.982665i | \(-0.559354\pi\) | ||||
−0.185388 | + | 0.982665i | \(0.559354\pi\) | |||||||
\(272\) | 2.53950 | 0.153980 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.65703 | 0.281342 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4299 | 1.58802 | 0.794011 | − | 0.607904i | \(-0.207989\pi\) | ||||
0.794011 | + | 0.607904i | \(0.207989\pi\) | |||||||
\(278\) | −17.4269 | −1.04520 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.4931 | 0.806369 | ||||||||
\(281\) | −30.5333 | −1.82147 | −0.910733 | − | 0.412996i | \(-0.864482\pi\) | ||||
−0.910733 | + | 0.412996i | \(0.864482\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.28817 | 0.136018 | 0.0680088 | − | 0.997685i | \(-0.478335\pi\) | ||||
0.0680088 | + | 0.997685i | \(0.478335\pi\) | |||||||
\(284\) | 2.95484 | 0.175337 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.9863 | 1.59295 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.6035 | 1.38844 | ||||||||
\(290\) | −3.20293 | −0.188083 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.6716 | −0.917112 | ||||||||
\(293\) | −21.2338 | −1.24049 | −0.620246 | − | 0.784408i | \(-0.712967\pi\) | ||||
−0.620246 | + | 0.784408i | \(0.712967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5804 | 0.848904 | ||||||||
\(296\) | −10.0510 | −0.584205 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.01373 | 0.522151 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.08727 | −0.0626694 | ||||||||
\(302\) | 15.9652 | 0.918695 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.84921 | 0.106060 | ||||||||
\(305\) | 1.96638 | 0.112594 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5682 | 0.660234 | 0.330117 | − | 0.943940i | \(-0.392912\pi\) | ||||
0.330117 | + | 0.943940i | \(0.392912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.03684 | −0.115685 | ||||||||
\(311\) | −13.8990 | −0.788140 | −0.394070 | − | 0.919080i | \(-0.628933\pi\) | ||||
−0.394070 | + | 0.919080i | \(0.628933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1745 | 0.688146 | 0.344073 | − | 0.938943i | \(-0.388193\pi\) | ||||
0.344073 | + | 0.938943i | \(0.388193\pi\) | |||||||
\(314\) | −6.11829 | −0.345275 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.10091 | −0.230694 | ||||||||
\(317\) | 26.7045 | 1.49987 | 0.749936 | − | 0.661510i | \(-0.230084\pi\) | ||||
0.749936 | + | 0.661510i | \(0.230084\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.83384 | 0.326122 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.9442 | −1.61300 | ||||||||
\(323\) | 29.5667 | 1.64513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.5045 | −0.637178 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.9127 | 0.933849 | ||||||||
\(329\) | 43.2775 | 2.38597 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4648 | −1.06988 | −0.534940 | − | 0.844890i | \(-0.679666\pi\) | ||||
−0.534940 | + | 0.844890i | \(0.679666\pi\) | |||||||
\(332\) | 8.20183 | 0.450134 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.00733 | −0.109836 | ||||||||
\(335\) | −1.45636 | −0.0795696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.5063 | −0.899155 | −0.449577 | − | 0.893241i | \(-0.648425\pi\) | ||||
−0.449577 | + | 0.893241i | \(0.648425\pi\) | |||||||
\(338\) | −12.0199 | −0.653796 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.29669 | 0.395719 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −34.9390 | −1.88653 | ||||||||
\(344\) | −0.681412 | −0.0367393 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.14709 | 0.437991 | ||||||||
\(347\) | 1.05877 | 0.0568377 | 0.0284189 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284189 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5983 | −0.727901 | −0.363950 | − | 0.931418i | \(-0.618572\pi\) | ||||
−0.363950 | + | 0.931418i | \(0.618572\pi\) | |||||||
\(350\) | −4.29021 | −0.229321 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.0093 | 1.54401 | 0.772005 | − | 0.635616i | \(-0.219254\pi\) | ||||
0.772005 | + | 0.635616i | \(0.219254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.58041 | −0.136954 | ||||||||
\(356\) | 10.2902 | 0.545380 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.8511 | 0.679202 | ||||||||
\(359\) | 14.0907 | 0.743680 | 0.371840 | − | 0.928297i | \(-0.378727\pi\) | ||||
0.371840 | + | 0.928297i | \(0.378727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.52991 | 0.133153 | ||||||||
\(362\) | −19.0628 | −1.00192 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.6858 | 0.716346 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.01373 | 0.261714 | 0.130857 | − | 0.991401i | \(-0.458227\pi\) | ||||
0.130857 | + | 0.991401i | \(0.458227\pi\) | |||||||
\(368\) | −2.68874 | −0.140160 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.19578 | 0.166140 | ||||||||
\(371\) | −16.4426 | −0.853657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.91935 | −0.513604 | −0.256802 | − | 0.966464i | \(-0.582669\pi\) | ||||
−0.256802 | + | 0.966464i | \(0.582669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.1227 | 1.39875 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.92112 | 0.252781 | 0.126390 | − | 0.991981i | \(-0.459661\pi\) | ||||
0.126390 | + | 0.991981i | \(0.459661\pi\) | |||||||
\(380\) | 5.31331 | 0.272567 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.4758 | 0.638320 | ||||||||
\(383\) | −17.9725 | −0.918354 | −0.459177 | − | 0.888345i | \(-0.651856\pi\) | ||||
−0.459177 | + | 0.888345i | \(0.651856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3186 | 0.881493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.2481 | 0.723337 | ||||||||
\(389\) | −13.0598 | −0.662159 | −0.331080 | − | 0.943603i | \(-0.607413\pi\) | ||||
−0.331080 | + | 0.943603i | \(0.607413\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.9897 | −2.17408 | ||||||||
\(392\) | −42.2527 | −2.13408 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.8117 | 0.645445 | ||||||||
\(395\) | 3.58126 | 0.180193 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.7045 | −1.39045 | −0.695223 | − | 0.718794i | \(-0.744695\pi\) | ||||
−0.695223 | + | 0.718794i | \(0.744695\pi\) | |||||||
\(398\) | −17.9039 | −0.897439 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.398534 | −0.0199267 | ||||||||
\(401\) | 31.0598 | 1.55105 | 0.775527 | − | 0.631315i | \(-0.217484\pi\) | ||||
0.775527 | + | 0.631315i | \(0.217484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17.2865 | 0.860036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.8617 | 0.737574 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.8058 | −1.27602 | −0.638008 | − | 0.770030i | \(-0.720241\pi\) | ||||
−0.638008 | + | 0.770030i | \(0.720241\pi\) | |||||||
\(410\) | −5.37748 | −0.265575 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.7833 | −1.07319 | ||||||||
\(413\) | −67.6536 | −3.32902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.16253 | −0.351595 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2618 | 0.745589 | 0.372794 | − | 0.927914i | \(-0.378400\pi\) | ||||
0.372794 | + | 0.927914i | \(0.378400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.9220 | 1.84821 | 0.924104 | − | 0.382142i | \(-0.124813\pi\) | ||||
0.924104 | + | 0.382142i | \(0.124813\pi\) | |||||||
\(422\) | −0.324987 | −0.0158201 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.3048 | −0.500447 | ||||||||
\(425\) | −6.37208 | −0.309091 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.12405 | −0.441544 | ||||||||
\(428\) | −19.7725 | −0.955741 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.216658 | 0.0104482 | ||||||||
\(431\) | −18.6671 | −0.899161 | −0.449581 | − | 0.893240i | \(-0.648427\pi\) | ||||
−0.449581 | + | 0.893240i | \(0.648427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4426 | −0.886297 | −0.443148 | − | 0.896448i | \(-0.646138\pi\) | ||||
−0.443148 | + | 0.896448i | \(0.646138\pi\) | |||||||
\(434\) | 9.45103 | 0.453664 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.2083 | −0.776235 | ||||||||
\(437\) | −31.3043 | −1.49749 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.46373 | −0.0698598 | −0.0349299 | − | 0.999390i | \(-0.511121\pi\) | ||||
−0.0349299 | + | 0.999390i | \(0.511121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.8853 | −0.802243 | −0.401122 | − | 0.916025i | \(-0.631380\pi\) | ||||
−0.401122 | + | 0.916025i | \(0.631380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.98627 | −0.425990 | ||||||||
\(446\) | 2.72713 | 0.129133 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −27.0692 | −1.27890 | ||||||||
\(449\) | −15.2618 | −0.720250 | −0.360125 | − | 0.932904i | \(-0.617266\pi\) | ||||
−0.360125 | + | 0.932904i | \(0.617266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.52258 | 0.212724 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.77601 | 0.458811 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.58089 | −0.0739508 | −0.0369754 | − | 0.999316i | \(-0.511772\pi\) | ||||
−0.0369754 | + | 0.999316i | \(0.511772\pi\) | |||||||
\(458\) | −11.0486 | −0.516267 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.72551 | −0.360204 | ||||||||
\(461\) | −7.86550 | −0.366333 | −0.183166 | − | 0.983082i | \(-0.558635\pi\) | ||||
−0.183166 | + | 0.983082i | \(0.558635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.6677 | 1.65762 | 0.828809 | − | 0.559532i | \(-0.189019\pi\) | ||||
0.828809 | + | 0.559532i | \(0.189019\pi\) | |||||||
\(464\) | 1.38056 | 0.0640911 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.92005 | −0.320565 | ||||||||
\(467\) | −20.8937 | −0.966843 | −0.483422 | − | 0.875388i | \(-0.660606\pi\) | ||||
−0.483422 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.75757 | 0.312036 | ||||||||
\(470\) | −8.62379 | −0.397786 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −42.3996 | −1.95160 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.64003 | −0.212899 | ||||||||
\(476\) | −33.8569 | −1.55183 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.1745 | 1.19720 | ||||||||
\(479\) | 10.2174 | 0.466843 | 0.233422 | − | 0.972376i | \(-0.425008\pi\) | ||||
0.233422 | + | 0.972376i | \(0.425008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.67501 | −0.258490 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.4426 | −0.564991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3186 | 0.694151 | 0.347076 | − | 0.937837i | \(-0.387175\pi\) | ||||
0.347076 | + | 0.937837i | \(0.387175\pi\) | |||||||
\(488\) | −5.71819 | −0.258850 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.4345 | 0.606907 | ||||||||
\(491\) | 34.5341 | 1.55850 | 0.779251 | − | 0.626712i | \(-0.215600\pi\) | ||||
0.779251 | + | 0.626712i | \(0.215600\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0735 | 0.994143 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.877944 | 0.0394208 | ||||||||
\(497\) | 11.9732 | 0.537071 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.6035 | 1.32523 | 0.662616 | − | 0.748959i | \(-0.269446\pi\) | ||||
0.662616 | + | 0.748959i | \(0.269446\pi\) | |||||||
\(500\) | −1.14510 | −0.0512105 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.76113 | −0.123235 | ||||||||
\(503\) | 3.81990 | 0.170321 | 0.0851604 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851604 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.0960 | −0.671765 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.9014 | −0.838614 | ||||||||
\(509\) | 33.7980 | 1.49807 | 0.749035 | − | 0.662530i | \(-0.230517\pi\) | ||||
0.749035 | + | 0.662530i | \(0.230517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −63.5025 | −2.80918 | ||||||||
\(512\) | −4.48887 | −0.198382 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.3053 | 0.983843 | ||||||||
\(515\) | 19.0230 | 0.838256 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −14.8285 | −0.651527 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.26182 | −0.142903 | −0.0714515 | − | 0.997444i | \(-0.522763\pi\) | ||||
−0.0714515 | + | 0.997444i | \(0.522763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8653 | 0.475105 | 0.237552 | − | 0.971375i | \(-0.423655\pi\) | ||||
0.237552 | + | 0.971375i | \(0.423655\pi\) | |||||||
\(524\) | −18.2918 | −0.799081 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.74763 | −0.381415 | ||||||||
\(527\) | 14.0373 | 0.611473 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5162 | 0.978964 | ||||||||
\(530\) | 3.27647 | 0.142321 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.6540 | −1.06888 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.2670 | 0.746519 | ||||||||
\(536\) | 4.23508 | 0.182928 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.00530 | 0.0433416 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.3160 | 0.873451 | 0.436726 | − | 0.899595i | \(-0.356138\pi\) | ||||
0.436726 | + | 0.899595i | \(0.356138\pi\) | |||||||
\(542\) | −5.64358 | −0.242412 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.7118 | −1.48826 | ||||||||
\(545\) | 14.1544 | 0.606309 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1365 | −0.989244 | −0.494622 | − | 0.869108i | \(-0.664694\pi\) | ||||
−0.494622 | + | 0.869108i | \(0.664694\pi\) | |||||||
\(548\) | −5.76762 | −0.246381 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0735 | 0.684756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.6172 | −0.706635 | ||||||||
\(554\) | 24.4373 | 1.03824 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.5828 | 0.915315 | ||||||||
\(557\) | −0.449182 | −0.0190324 | −0.00951622 | − | 0.999955i | \(-0.503029\pi\) | ||||
−0.00951622 | + | 0.999955i | \(0.503029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.84921 | 0.0781435 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.2313 | −1.19087 | ||||||||
\(563\) | 16.4426 | 0.692973 | 0.346486 | − | 0.938055i | \(-0.387375\pi\) | ||||
0.346486 | + | 0.938055i | \(0.387375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.94950 | −0.166157 | ||||||||
\(566\) | 2.11566 | 0.0889277 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.50379 | 0.314852 | ||||||||
\(569\) | 8.97774 | 0.376366 | 0.188183 | − | 0.982134i | \(-0.439740\pi\) | ||||
0.188183 | + | 0.982134i | \(0.439740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7321 | −0.909461 | −0.454731 | − | 0.890629i | \(-0.650265\pi\) | ||||
−0.454731 | + | 0.890629i | \(0.650265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.9517 | 1.04146 | ||||||||
\(575\) | 6.74657 | 0.281351 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4426 | −0.684516 | −0.342258 | − | 0.939606i | \(-0.611192\pi\) | ||||
−0.342258 | + | 0.939606i | \(0.611192\pi\) | |||||||
\(578\) | 21.8239 | 0.907755 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.96675 | 0.164710 | ||||||||
\(581\) | 33.2344 | 1.37879 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −39.7980 | −1.64685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.6329 | −0.811028 | ||||||||
\(587\) | 13.8338 | 0.570984 | 0.285492 | − | 0.958381i | \(-0.407843\pi\) | ||||
0.285492 | + | 0.958381i | \(0.407843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2217 | 0.421177 | ||||||||
\(590\) | 13.4811 | 0.555010 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.37748 | −0.0566141 | ||||||||
\(593\) | 18.0915 | 0.742928 | 0.371464 | − | 0.928447i | \(-0.378856\pi\) | ||||
0.371464 | + | 0.928447i | \(0.378856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.5667 | 1.21212 | ||||||||
\(596\) | −11.1633 | −0.457266 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.7138 | −1.54094 | −0.770472 | − | 0.637474i | \(-0.779979\pi\) | ||||
−0.770472 | + | 0.637474i | \(0.779979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.98205 | −0.366385 | −0.183193 | − | 0.983077i | \(-0.558643\pi\) | ||||
−0.183193 | + | 0.983077i | \(0.558643\pi\) | |||||||
\(602\) | −1.00530 | −0.0409730 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.7725 | −0.804533 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.34277 | 0.338623 | 0.169311 | − | 0.985563i | \(-0.445846\pi\) | ||||
0.169311 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(608\) | −25.2765 | −1.02510 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.81812 | 0.0736137 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5872 | −1.31618 | −0.658092 | − | 0.752938i | \(-0.728636\pi\) | ||||
−0.658092 | + | 0.752938i | \(0.728636\pi\) | |||||||
\(614\) | 10.6961 | 0.431658 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.1745 | −0.812197 | −0.406098 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406098 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.3354 | −1.42025 | −0.710124 | − | 0.704076i | \(-0.751361\pi\) | ||||
−0.710124 | + | 0.704076i | \(0.751361\pi\) | |||||||
\(620\) | 2.52258 | 0.101309 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.8511 | −0.515282 | ||||||||
\(623\) | 41.6966 | 1.67054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.2567 | 0.449907 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.57736 | 0.302369 | ||||||||
\(629\) | −22.0242 | −0.878164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.6456 | −0.423793 | −0.211897 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211897 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(632\) | −10.4143 | −0.414257 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.6911 | 0.980610 | ||||||||
\(635\) | 16.5063 | 0.655032 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.50095 | −0.217444 | ||||||||
\(641\) | 4.94018 | 0.195125 | 0.0975627 | − | 0.995229i | \(-0.468895\pi\) | ||||
0.0975627 | + | 0.995229i | \(0.468895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.1240 | 1.62177 | 0.810887 | − | 0.585203i | \(-0.198985\pi\) | ||||
0.810887 | + | 0.585203i | \(0.198985\pi\) | |||||||
\(644\) | 35.8466 | 1.41256 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.3376 | 1.07558 | ||||||||
\(647\) | −37.4005 | −1.47037 | −0.735183 | − | 0.677868i | \(-0.762904\pi\) | ||||
−0.735183 | + | 0.677868i | \(0.762904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.2481 | 0.557998 | ||||||||
\(653\) | −15.2344 | −0.596167 | −0.298083 | − | 0.954540i | \(-0.596347\pi\) | ||||
−0.298083 | + | 0.954540i | \(0.596347\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.9739 | 0.624154 | ||||||||
\(656\) | 2.31786 | 0.0904973 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 40.0147 | 1.55993 | ||||||||
\(659\) | 3.05484 | 0.119000 | 0.0594998 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0594998 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.4426 | −1.33966 | −0.669832 | − | 0.742513i | \(-0.733634\pi\) | ||||
−0.669832 | + | 0.742513i | \(0.733634\pi\) | |||||||
\(662\) | −17.9972 | −0.699483 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.8285 | 0.808303 | ||||||||
\(665\) | 21.5299 | 0.834894 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3708 | −0.904921 | ||||||||
\(668\) | 2.48603 | 0.0961873 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.34656 | −0.0520223 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.9345 | −1.46227 | −0.731134 | − | 0.682234i | \(-0.761008\pi\) | ||||
−0.731134 | + | 0.682234i | \(0.761008\pi\) | |||||||
\(674\) | −15.2618 | −0.587863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.8863 | 0.572551 | ||||||||
\(677\) | −9.15268 | −0.351766 | −0.175883 | − | 0.984411i | \(-0.556278\pi\) | ||||
−0.175883 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 57.7342 | 2.21564 | ||||||||
\(680\) | 18.5299 | 0.710590 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.7980 | 1.06366 | 0.531830 | − | 0.846851i | \(-0.321504\pi\) | ||||
0.531830 | + | 0.846851i | \(0.321504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.03677 | 0.192445 | ||||||||
\(686\) | −32.3049 | −1.23341 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0933864 | −0.00356033 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.4373 | 1.11985 | 0.559924 | − | 0.828544i | \(-0.310830\pi\) | ||||
0.559924 | + | 0.828544i | \(0.310830\pi\) | |||||||
\(692\) | −10.0900 | −0.383563 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.978945 | 0.0371603 | ||||||||
\(695\) | −18.8479 | −0.714943 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.0598 | 1.40374 | ||||||||
\(698\) | −12.5731 | −0.475898 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.31331 | 0.200824 | ||||||||
\(701\) | 6.92820 | 0.261675 | 0.130837 | − | 0.991404i | \(-0.458233\pi\) | ||||
0.130837 | + | 0.991404i | \(0.458233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0376 | −0.604871 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.8222 | 1.00947 | ||||||||
\(707\) | 70.0461 | 2.63435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.9956 | −1.95274 | −0.976368 | − | 0.216116i | \(-0.930661\pi\) | ||||
−0.976368 | + | 0.216116i | \(0.930661\pi\) | |||||||
\(710\) | −2.38586 | −0.0895399 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 26.1319 | 0.979335 | ||||||||
\(713\) | −14.8622 | −0.556595 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.9158 | −0.594801 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.0284 | 0.486215 | ||||||||
\(719\) | −27.3921 | −1.02155 | −0.510777 | − | 0.859713i | \(-0.670642\pi\) | ||||
−0.510777 | + | 0.859713i | \(0.670642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −88.2676 | −3.28726 | ||||||||
\(722\) | 2.33917 | 0.0870549 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.6088 | 0.877414 | ||||||||
\(725\) | −3.46410 | −0.128654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9588 | 1.81578 | 0.907891 | − | 0.419206i | \(-0.137692\pi\) | ||||
0.907891 | + | 0.419206i | \(0.137692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.6540 | 0.468344 | ||||||||
\(731\) | −1.49314 | −0.0552256 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5510 | 0.906813 | 0.453407 | − | 0.891304i | \(-0.350209\pi\) | ||||
0.453407 | + | 0.891304i | \(0.350209\pi\) | |||||||
\(734\) | 4.63572 | 0.171108 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.7518 | 1.35469 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5605 | 0.756331 | 0.378165 | − | 0.925738i | \(-0.376555\pi\) | ||||
0.378165 | + | 0.925738i | \(0.376555\pi\) | |||||||
\(740\) | −3.95789 | −0.145495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.2029 | −0.558117 | ||||||||
\(743\) | 29.3082 | 1.07521 | 0.537607 | − | 0.843195i | \(-0.319328\pi\) | ||||
0.537607 | + | 0.843195i | \(0.319328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.74872 | 0.357165 | ||||||||
\(746\) | −9.17149 | −0.335792 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −80.1196 | −2.92751 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.95789 | 0.107935 | 0.0539675 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539675 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(752\) | 3.71712 | 0.135550 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.2670 | 0.628412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.36909 | 0.0861060 | 0.0430530 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430530 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(758\) | 4.55010 | 0.165267 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.4931 | 0.489448 | ||||||||
\(761\) | 52.8599 | 1.91617 | 0.958085 | − | 0.286485i | \(-0.0924869\pi\) | ||||
0.958085 | + | 0.286485i | \(0.0924869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −65.6770 | −2.37767 | ||||||||
\(764\) | −15.4510 | −0.558999 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6175 | −0.600416 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.48531 | −0.305988 | −0.152994 | − | 0.988227i | \(-0.548892\pi\) | ||||
−0.152994 | + | 0.988227i | \(0.548892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.4486 | −0.771954 | ||||||||
\(773\) | 39.7917 | 1.43121 | 0.715605 | − | 0.698506i | \(-0.246151\pi\) | ||||
0.715605 | + | 0.698506i | \(0.246151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.20293 | −0.0791316 | ||||||||
\(776\) | 36.1830 | 1.29889 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.0752 | −0.432917 | ||||||||
\(779\) | 26.9863 | 0.966884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −39.7486 | −1.42141 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.79067 | −0.206810 | ||||||||
\(785\) | −6.61718 | −0.236177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0907 | 0.502280 | 0.251140 | − | 0.967951i | \(-0.419194\pi\) | ||||
0.251140 | + | 0.967951i | \(0.419194\pi\) | |||||||
\(788\) | −15.8670 | −0.565239 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.31126 | 0.117809 | ||||||||
\(791\) | 18.3258 | 0.651591 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25.6157 | −0.909068 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.1735 | 0.785918 | ||||||||
\(797\) | −37.0598 | −1.31273 | −0.656363 | − | 0.754445i | \(-0.727906\pi\) | ||||
−0.656363 | + | 0.754445i | \(0.727906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.4323 | 2.10256 | ||||||||
\(800\) | 5.44748 | 0.192597 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.7181 | 1.01407 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.3043 | −1.10333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 43.8990 | 1.54436 | ||||||||
\(809\) | 7.52424 | 0.264538 | 0.132269 | − | 0.991214i | \(-0.457774\pi\) | ||||
0.132269 | + | 0.991214i | \(0.457774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0579 | −1.40662 | −0.703312 | − | 0.710881i | \(-0.748296\pi\) | ||||
−0.703312 | + | 0.710881i | \(0.748296\pi\) | |||||||
\(812\) | −18.4059 | −0.645919 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.4426 | −0.435847 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.08727 | −0.0380389 | ||||||||
\(818\) | −23.8602 | −0.834253 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.65988 | 0.232573 | ||||||||
\(821\) | 42.4676 | 1.48213 | 0.741064 | − | 0.671434i | \(-0.234321\pi\) | ||||
0.741064 | + | 0.671434i | \(0.234321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5299 | 0.611054 | 0.305527 | − | 0.952183i | \(-0.401167\pi\) | ||||
0.305527 | + | 0.952183i | \(0.401167\pi\) | |||||||
\(824\) | −55.3187 | −1.92712 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −62.5530 | −2.17650 | ||||||||
\(827\) | −24.7854 | −0.861872 | −0.430936 | − | 0.902383i | \(-0.641816\pi\) | ||||
−0.430936 | + | 0.902383i | \(0.641816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.66769 | 0.301041 | 0.150521 | − | 0.988607i | \(-0.451905\pi\) | ||||
0.150521 | + | 0.988607i | \(0.451905\pi\) | |||||||
\(830\) | −6.62252 | −0.229871 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −92.5858 | −3.20791 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.17101 | −0.0751308 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.1112 | 0.487463 | ||||||||
\(839\) | 43.4657 | 1.50060 | 0.750301 | − | 0.661096i | \(-0.229909\pi\) | ||||
0.750301 | + | 0.661096i | \(0.229909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 35.0630 | 1.20835 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.402489 | 0.0138542 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.41226 | −0.0484973 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.89167 | −0.202083 | ||||||||
\(851\) | 23.3186 | 0.799351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7262 | 0.743891 | 0.371946 | − | 0.928254i | \(-0.378691\pi\) | ||||
0.371946 | + | 0.928254i | \(0.378691\pi\) | |||||||
\(854\) | −8.43615 | −0.288679 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −50.2123 | −1.71622 | ||||||||
\(857\) | 32.7977 | 1.12035 | 0.560174 | − | 0.828375i | \(-0.310734\pi\) | ||||
0.560174 | + | 0.828375i | \(0.310734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.442636 | −0.0151025 | −0.00755127 | − | 0.999971i | \(-0.502404\pi\) | ||||
−0.00755127 | + | 0.999971i | \(0.502404\pi\) | |||||||
\(860\) | −0.268326 | −0.00914983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.2597 | −0.587868 | ||||||||
\(863\) | 19.9265 | 0.678304 | 0.339152 | − | 0.940732i | \(-0.389860\pi\) | ||||
0.339152 | + | 0.940732i | \(0.389860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.81142 | 0.299597 | ||||||||
\(866\) | −17.0522 | −0.579457 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.7049 | −0.397289 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −41.1608 | −1.39388 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.9442 | −0.979051 | ||||||||
\(875\) | −4.64003 | −0.156862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6590 | −0.866442 | −0.433221 | − | 0.901288i | \(-0.642623\pi\) | ||||
−0.433221 | + | 0.901288i | \(0.642623\pi\) | |||||||
\(878\) | −1.35337 | −0.0456740 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.9863 | −1.11134 | −0.555668 | − | 0.831404i | \(-0.687537\pi\) | ||||
−0.555668 | + | 0.831404i | \(0.687537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5897 | 1.50056 | 0.750282 | − | 0.661118i | \(-0.229918\pi\) | ||||
0.750282 | + | 0.661118i | \(0.229918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6122 | −0.524503 | ||||||||
\(887\) | 25.5953 | 0.859405 | 0.429703 | − | 0.902970i | \(-0.358618\pi\) | ||||
0.429703 | + | 0.902970i | \(0.358618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −76.5897 | −2.56874 | ||||||||
\(890\) | −8.30877 | −0.278511 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.37748 | −0.113086 | ||||||||
\(893\) | 43.2775 | 1.44823 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8990 | 0.464592 | ||||||||
\(896\) | 25.5246 | 0.852716 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.1112 | −0.470896 | ||||||||
\(899\) | 7.63118 | 0.254514 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.5804 | −0.752261 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.4851 | 0.381988 | ||||||||
\(905\) | −20.6172 | −0.685338 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.29554 | −0.142631 | −0.0713156 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713156 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(908\) | −12.1074 | −0.401797 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.6814 | −0.420154 | −0.210077 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210077 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.46170 | −0.0483487 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.6834 | 0.452112 | ||||||||
\(917\) | −74.1196 | −2.44765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6238 | 0.614343 | 0.307172 | − | 0.951654i | \(-0.400617\pi\) | ||||
0.307172 | + | 0.951654i | \(0.400617\pi\) | |||||||
\(920\) | −19.6189 | −0.646816 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.27249 | −0.239507 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.45636 | 0.113645 | ||||||||
\(926\) | 32.9786 | 1.08374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.8706 | −0.619458 | ||||||||
\(929\) | 42.2206 | 1.38521 | 0.692607 | − | 0.721315i | \(-0.256462\pi\) | ||||
0.692607 | + | 0.721315i | \(0.256462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67.4193 | −2.20958 | ||||||||
\(932\) | 8.57032 | 0.280730 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.3184 | −0.632118 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0270 | 0.458243 | 0.229122 | − | 0.973398i | \(-0.426415\pi\) | ||||
0.229122 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(938\) | 6.24810 | 0.204008 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6803 | 0.348355 | ||||||||
\(941\) | −44.0485 | −1.43594 | −0.717970 | − | 0.696075i | \(-0.754928\pi\) | ||||
−0.717970 | + | 0.696075i | \(0.754928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.2378 | −1.27776 | ||||||||
\(944\) | −5.81080 | −0.189125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.7191 | 0.998237 | 0.499119 | − | 0.866534i | \(-0.333657\pi\) | ||||
0.499119 | + | 0.866534i | \(0.333657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.29021 | −0.139193 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −85.9794 | −2.78661 | ||||||||
\(953\) | 31.9479 | 1.03489 | 0.517447 | − | 0.855715i | \(-0.326883\pi\) | ||||
0.517447 | + | 0.855715i | \(0.326883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.4931 | 0.436628 | ||||||||
\(956\) | −32.4165 | −1.04843 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.44704 | 0.305220 | ||||||||
\(959\) | −23.3708 | −0.754682 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1471 | −0.843455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.02836 | 0.226368 | ||||||||
\(965\) | 18.7308 | 0.602965 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5978 | 1.11259 | 0.556295 | − | 0.830985i | \(-0.312223\pi\) | ||||
0.556295 | + | 0.830985i | \(0.312223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.5045 | −0.369389 | ||||||||
\(971\) | −32.9588 | −1.05770 | −0.528849 | − | 0.848716i | \(-0.677376\pi\) | ||||
−0.528849 | + | 0.848716i | \(0.677376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 87.4550 | 2.80368 | ||||||||
\(974\) | 14.1637 | 0.453833 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.783668 | −0.0250846 | ||||||||
\(977\) | −39.3584 | −1.25919 | −0.629594 | − | 0.776925i | \(-0.716779\pi\) | ||||
−0.629594 | + | 0.776925i | \(0.716779\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −16.6382 | −0.531489 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.9304 | 1.01894 | ||||||||
\(983\) | 40.3868 | 1.28814 | 0.644069 | − | 0.764967i | \(-0.277245\pi\) | ||||
0.644069 | + | 0.764967i | \(0.277245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8564 | 0.441502 | ||||||||
\(986\) | 20.4093 | 0.649966 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.58089 | 0.0502693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.67302 | −0.148443 | −0.0742217 | − | 0.997242i | \(-0.523647\pi\) | ||||
−0.0742217 | + | 0.997242i | \(0.523647\pi\) | |||||||
\(992\) | −12.0004 | −0.381014 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.0705 | 0.351135 | ||||||||
\(995\) | −19.3638 | −0.613872 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.6544 | −0.907495 | −0.453747 | − | 0.891130i | \(-0.649913\pi\) | ||||
−0.453747 | + | 0.891130i | \(0.649913\pi\) | |||||||
\(998\) | 27.3716 | 0.866431 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.by.1.4 | yes | 6 | |
3.2 | odd | 2 | 5445.2.a.bw.1.3 | ✓ | 6 | ||
11.10 | odd | 2 | inner | 5445.2.a.by.1.3 | yes | 6 | |
33.32 | even | 2 | 5445.2.a.bw.1.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5445.2.a.bw.1.3 | ✓ | 6 | 3.2 | odd | 2 | ||
5445.2.a.bw.1.4 | yes | 6 | 33.32 | even | 2 | ||
5445.2.a.by.1.3 | yes | 6 | 11.10 | odd | 2 | inner | |
5445.2.a.by.1.4 | yes | 6 | 1.1 | even | 1 | trivial |