Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(5\) | −2.57233 | −1.15038 | −0.575191 | − | 0.818019i | \(-0.695072\pi\) | ||||
−0.575191 | + | 0.818019i | \(0.695072\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.722776 | −0.273184 | −0.136592 | − | 0.990627i | \(-0.543615\pi\) | ||||
−0.136592 | + | 0.990627i | \(0.543615\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16379 | −0.350897 | −0.175449 | − | 0.984489i | \(-0.556138\pi\) | ||||
−0.175449 | + | 0.984489i | \(0.556138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.87974 | 0.798695 | 0.399347 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399347 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.57233 | 0.664173 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.88201 | 1.66913 | 0.834566 | − | 0.550908i | \(-0.185718\pi\) | ||||
0.834566 | + | 0.550908i | \(0.185718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0742278 | 0.0170290 | 0.00851451 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851451 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.722776 | 0.157723 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.64876 | 1.38636 | 0.693181 | − | 0.720763i | \(-0.256208\pi\) | ||||
0.693181 | + | 0.720763i | \(0.256208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.61688 | 0.323377 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.36633 | −1.55359 | −0.776794 | − | 0.629755i | \(-0.783155\pi\) | ||||
−0.776794 | + | 0.629755i | \(0.783155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.34718 | −1.13999 | −0.569993 | − | 0.821649i | \(-0.693054\pi\) | ||||
−0.569993 | + | 0.821649i | \(0.693054\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.16379 | 0.202591 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85922 | 0.314265 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.23390 | −0.696049 | −0.348024 | − | 0.937486i | \(-0.613147\pi\) | ||||
−0.348024 | + | 0.937486i | \(0.613147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.87974 | −0.461127 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08057 | 0.168757 | 0.0843785 | − | 0.996434i | \(-0.473110\pi\) | ||||
0.0843785 | + | 0.996434i | \(0.473110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.62336 | 0.552557 | 0.276278 | − | 0.961078i | \(-0.410899\pi\) | ||||
0.276278 | + | 0.961078i | \(0.410899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.57233 | −0.383460 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46403 | −0.213550 | −0.106775 | − | 0.994283i | \(-0.534052\pi\) | ||||
−0.106775 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47759 | −0.925371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.88201 | −0.963674 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.12358 | 1.25322 | 0.626610 | − | 0.779333i | \(-0.284442\pi\) | ||||
0.626610 | + | 0.779333i | \(0.284442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.99366 | 0.403666 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0742278 | −0.00983171 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.35277 | −0.566682 | −0.283341 | − | 0.959019i | \(-0.591443\pi\) | ||||
−0.283341 | + | 0.959019i | \(0.591443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.87947 | 0.752789 | 0.376395 | − | 0.926459i | \(-0.377164\pi\) | ||||
0.376395 | + | 0.926459i | \(0.377164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.722776 | −0.0910613 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.40763 | −0.918804 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.793907 | 0.0969912 | 0.0484956 | − | 0.998823i | \(-0.484557\pi\) | ||||
0.0484956 | + | 0.998823i | \(0.484557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.64876 | −0.800417 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3782 | −1.35035 | −0.675174 | − | 0.737658i | \(-0.735932\pi\) | ||||
−0.675174 | + | 0.737658i | \(0.735932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.16804 | 1.07304 | 0.536519 | − | 0.843888i | \(-0.319739\pi\) | ||||
0.536519 | + | 0.843888i | \(0.319739\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.61688 | −0.186702 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.841163 | 0.0958594 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.61559 | −0.744313 | −0.372156 | − | 0.928170i | \(-0.621381\pi\) | ||||
−0.372156 | + | 0.928170i | \(0.621381\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.56912 | −1.05035 | −0.525174 | − | 0.850995i | \(-0.676000\pi\) | ||||
−0.525174 | + | 0.850995i | \(0.676000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.7028 | −1.92014 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.36633 | 0.896965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.56938 | −1.01435 | −0.507176 | − | 0.861842i | \(-0.669311\pi\) | ||||
−0.507176 | + | 0.861842i | \(0.669311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.08140 | −0.218190 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.34718 | 0.658172 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.190938 | −0.0195899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.48629 | 0.150910 | 0.0754550 | − | 0.997149i | \(-0.475959\pi\) | ||||
0.0754550 | + | 0.997149i | \(0.475959\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16379 | −0.116966 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12534 | −0.708998 | −0.354499 | − | 0.935056i | \(-0.615349\pi\) | ||||
−0.354499 | + | 0.935056i | \(0.615349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8664 | 1.56336 | 0.781681 | − | 0.623678i | \(-0.214363\pi\) | ||||
0.781681 | + | 0.623678i | \(0.214363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.85922 | −0.181441 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.7466 | −1.13559 | −0.567793 | − | 0.823171i | \(-0.692203\pi\) | ||||
−0.567793 | + | 0.823171i | \(0.692203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.74173 | 0.645741 | 0.322870 | − | 0.946443i | \(-0.395352\pi\) | ||||
0.322870 | + | 0.946443i | \(0.395352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.23390 | 0.401864 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6407 | 1.00099 | 0.500494 | − | 0.865740i | \(-0.333152\pi\) | ||||
0.500494 | + | 0.865740i | \(0.333152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.1028 | −1.59485 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.87974 | 0.266232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.97415 | −0.455980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.64558 | −0.876871 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.08057 | −0.0974319 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.70249 | 0.778374 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9124 | 1.32326 | 0.661631 | − | 0.749830i | \(-0.269865\pi\) | ||||
0.661631 | + | 0.749830i | \(0.269865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.62336 | −0.319019 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8252 | −1.29528 | −0.647640 | − | 0.761947i | \(-0.724244\pi\) | ||||
−0.647640 | + | 0.761947i | \(0.724244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0536501 | −0.00465205 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.57233 | 0.221391 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.36156 | 0.628941 | 0.314470 | − | 0.949267i | \(-0.398173\pi\) | ||||
0.314470 | + | 0.949267i | \(0.398173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7613 | 0.912760 | 0.456380 | − | 0.889785i | \(-0.349146\pi\) | ||||
0.456380 | + | 0.889785i | \(0.349146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.46403 | 0.123293 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.35142 | −0.280260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.5210 | 1.78722 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.47759 | 0.534263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.55528 | 0.373183 | 0.186592 | − | 0.982438i | \(-0.440256\pi\) | ||||
0.186592 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8097 | 1.36796 | 0.683978 | − | 0.729503i | \(-0.260248\pi\) | ||||
0.683978 | + | 0.729503i | \(0.260248\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.88201 | 0.556377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.3270 | 1.31142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.8841 | 1.66673 | 0.833365 | − | 0.552724i | \(-0.186412\pi\) | ||||
0.833365 | + | 0.552724i | \(0.186412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.12358 | −0.723547 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.80557 | −0.378732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1953 | 1.11186 | 0.555931 | − | 0.831229i | \(-0.312362\pi\) | ||||
0.555931 | + | 0.831229i | \(0.312362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.99366 | −0.233056 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.19459 | −0.634116 | −0.317058 | − | 0.948406i | \(-0.602695\pi\) | ||||
−0.317058 | + | 0.948406i | \(0.602695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.70712 | −0.362086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0742278 | 0.00567634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.82182 | −0.746739 | −0.373370 | − | 0.927683i | \(-0.621798\pi\) | ||||
−0.373370 | + | 0.927683i | \(0.621798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.16865 | −0.0883413 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.35277 | 0.327174 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.55904 | 0.191271 | 0.0956357 | − | 0.995416i | \(-0.469512\pi\) | ||||
0.0956357 | + | 0.995416i | \(0.469512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.1502 | 1.79507 | 0.897535 | − | 0.440944i | \(-0.145356\pi\) | ||||
0.897535 | + | 0.440944i | \(0.145356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.87947 | −0.434623 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8910 | 0.800721 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00924 | −0.585694 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.722776 | 0.0525742 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3924 | 1.83733 | 0.918663 | − | 0.395042i | \(-0.129270\pi\) | ||||
0.918663 | + | 0.395042i | \(0.129270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8275 | 1.06731 | 0.533655 | − | 0.845702i | \(-0.320818\pi\) | ||||
0.533655 | + | 0.845702i | \(0.320818\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.40763 | 0.530472 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6035 | 0.826716 | 0.413358 | − | 0.910569i | \(-0.364356\pi\) | ||||
0.413358 | + | 0.910569i | \(0.364356\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2671 | 1.36581 | 0.682904 | − | 0.730508i | \(-0.260717\pi\) | ||||
0.682904 | + | 0.730508i | \(0.260717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.793907 | −0.0559979 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.04698 | 0.424415 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.77959 | −0.194135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.64876 | 0.462121 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0863859 | −0.00597544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.79962 | −0.330420 | −0.165210 | − | 0.986258i | \(-0.552830\pi\) | ||||
−0.165210 | + | 0.986258i | \(0.552830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3782 | 0.779624 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.32047 | −0.635651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.58759 | 0.311426 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.16804 | −0.619519 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8184 | 1.33313 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7175 | 1.38735 | 0.693674 | − | 0.720289i | \(-0.255991\pi\) | ||||
0.693674 | + | 0.720289i | \(0.255991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.61688 | 0.107792 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.6740 | −1.83679 | −0.918393 | − | 0.395670i | \(-0.870512\pi\) | ||||
−0.918393 | + | 0.395670i | \(0.870512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7378 | −1.43648 | −0.718238 | − | 0.695798i | \(-0.755051\pi\) | ||||
−0.718238 | + | 0.695798i | \(0.755051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.841163 | −0.0553445 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.46491 | 0.0959695 | 0.0479847 | − | 0.998848i | \(-0.484720\pi\) | ||||
0.0479847 | + | 0.998848i | \(0.484720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.76596 | 0.245664 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.61559 | 0.429729 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.03018 | −0.131321 | −0.0656606 | − | 0.997842i | \(-0.520915\pi\) | ||||
−0.0656606 | + | 0.997842i | \(0.520915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.739602 | −0.0476419 | −0.0238210 | − | 0.999716i | \(-0.507583\pi\) | ||||
−0.0238210 | + | 0.999716i | \(0.507583\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.6625 | 1.06453 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.213756 | 0.0136010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.56912 | 0.606419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6351 | −0.986880 | −0.493440 | − | 0.869780i | \(-0.664261\pi\) | ||||
−0.493440 | + | 0.869780i | \(0.664261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.73779 | −0.486471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.7028 | 1.10859 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.67976 | 0.104781 | 0.0523904 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523904 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.06016 | 0.190149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.36633 | −0.517863 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.85110 | −0.114144 | −0.0570719 | − | 0.998370i | \(-0.518176\pi\) | ||||
−0.0570719 | + | 0.998370i | \(0.518176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.4689 | −1.44168 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.56938 | 0.585637 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.43192 | −0.453132 | −0.226566 | − | 0.973996i | \(-0.572750\pi\) | ||||
−0.226566 | + | 0.973996i | \(0.572750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.02618 | 0.123082 | 0.0615408 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615408 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.08140 | 0.125972 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.88172 | −0.113472 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.59687 | −0.336283 | −0.168142 | − | 0.985763i | \(-0.553777\pi\) | ||||
−0.168142 | + | 0.985763i | \(0.553777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.34718 | −0.379996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9685 | 0.654328 | 0.327164 | − | 0.944968i | \(-0.393907\pi\) | ||||
0.327164 | + | 0.944968i | \(0.393907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8585 | 0.645471 | 0.322736 | − | 0.946489i | \(-0.395398\pi\) | ||||
0.322736 | + | 0.946489i | \(0.395398\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.190938 | 0.0113102 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.781012 | −0.0461017 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.3620 | 1.78600 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.48629 | −0.0871280 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.01975 | −0.293257 | −0.146628 | − | 0.989192i | \(-0.546842\pi\) | ||||
−0.146628 | + | 0.989192i | \(0.546842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1968 | 0.651901 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.16379 | 0.0675302 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.1467 | 1.10728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61888 | −0.150949 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.12534 | 0.409340 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1239 | −0.865995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.19596 | −0.524841 | −0.262421 | − | 0.964954i | \(-0.584521\pi\) | ||||
−0.262421 | + | 0.964954i | \(0.584521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.8664 | −0.902607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4505 | 0.649298 | 0.324649 | − | 0.945835i | \(-0.394754\pi\) | ||||
0.324649 | + | 0.945835i | \(0.394754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0645 | 0.568879 | 0.284440 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284440 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.85922 | 0.104755 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0774 | 1.29616 | 0.648078 | − | 0.761574i | \(-0.275573\pi\) | ||||
0.648078 | + | 0.761574i | \(0.275573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.73669 | 0.545150 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.7466 | 0.655631 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.510836 | 0.0284237 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.65620 | 0.258279 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.74173 | −0.372819 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.05816 | 0.0583384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4192 | −1.06737 | −0.533687 | − | 0.845682i | \(-0.679194\pi\) | ||||
−0.533687 | + | 0.845682i | \(0.679194\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.23390 | −0.232016 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.04219 | −0.111577 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5655 | 0.684486 | 0.342243 | − | 0.939611i | \(-0.388813\pi\) | ||||
0.342243 | + | 0.939611i | \(0.388813\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6407 | −0.577921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.38681 | 0.400018 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.74129 | 0.525980 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.1028 | 0.920785 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4344 | −0.721194 | −0.360597 | − | 0.932722i | \(-0.617427\pi\) | ||||
−0.360597 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.55386 | 0.457878 | 0.228939 | − | 0.973441i | \(-0.426474\pi\) | ||||
0.228939 | + | 0.973441i | \(0.426474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.87974 | −0.153709 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1849 | −1.71303 | −0.856514 | − | 0.516123i | \(-0.827375\pi\) | ||||
−0.856514 | + | 0.516123i | \(0.827375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.2686 | 1.55342 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.97415 | 0.263260 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.1313 | −1.22082 | −0.610411 | − | 0.792085i | \(-0.708996\pi\) | ||||
−0.610411 | + | 0.792085i | \(0.708996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9945 | −0.999710 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.64558 | 0.506262 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.5832 | −1.23440 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3085 | −0.694697 | −0.347348 | − | 0.937736i | \(-0.612918\pi\) | ||||
−0.347348 | + | 0.937736i | \(0.612918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.08057 | 0.0562523 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.59431 | −0.342360 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.53899 | −0.442132 | −0.221066 | − | 0.975259i | \(-0.570954\pi\) | ||||
−0.221066 | + | 0.975259i | \(0.570954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.70249 | −0.449395 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0928 | −1.24084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.68583 | −0.0865955 | −0.0432977 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432977 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.9124 | −0.763986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.9264 | 0.915998 | 0.457999 | − | 0.888953i | \(-0.348566\pi\) | ||||
0.457999 | + | 0.888953i | \(0.348566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.16375 | −0.110275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.62336 | 0.184186 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.27069 | 0.368639 | 0.184319 | − | 0.982866i | \(-0.440992\pi\) | ||||
0.184319 | + | 0.982866i | \(0.440992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.7568 | 2.31402 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.8252 | 0.747830 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.0175 | 0.856243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.88145 | 0.144616 | 0.0723079 | − | 0.997382i | \(-0.476964\pi\) | ||||
0.0723079 | + | 0.997382i | \(0.476964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0536501 | 0.00268586 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.4803 | 0.922863 | 0.461432 | − | 0.887176i | \(-0.347336\pi\) | ||||
0.461432 | + | 0.887176i | \(0.347336\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.2782 | −0.910502 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.57233 | −0.127820 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.92739 | 0.244242 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.522001 | −0.0258113 | −0.0129056 | − | 0.999917i | \(-0.504108\pi\) | ||||
−0.0129056 | + | 0.999917i | \(0.504108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.36156 | −0.363119 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.14608 | 0.154808 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.6149 | 1.20830 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.7613 | −0.526982 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7685 | 1.30773 | 0.653864 | − | 0.756612i | \(-0.273147\pi\) | ||||
0.653864 | + | 0.756612i | \(0.273147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.27029 | 0.256858 | 0.128429 | − | 0.991719i | \(-0.459006\pi\) | ||||
0.128429 | + | 0.991719i | \(0.459006\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.46403 | −0.0711834 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1274 | 0.539759 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.24954 | −0.205650 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.35142 | 0.161808 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.0709 | 1.20762 | 0.603812 | − | 0.797127i | \(-0.293648\pi\) | ||||
0.603812 | + | 0.797127i | \(0.293648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0380 | 1.15519 | 0.577597 | − | 0.816322i | \(-0.303990\pi\) | ||||
0.577597 | + | 0.816322i | \(0.303990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.5210 | −1.03185 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.493523 | 0.0236084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.24906 | 0.441434 | 0.220717 | − | 0.975338i | \(-0.429160\pi\) | ||||
0.220717 | + | 0.975338i | \(0.429160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47759 | −0.308457 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2431 | 0.486662 | 0.243331 | − | 0.969943i | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.6156 | 1.16689 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.55528 | −0.215457 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.5705 | 1.82025 | 0.910127 | − | 0.414330i | \(-0.135984\pi\) | ||||
0.910127 | + | 0.414330i | \(0.135984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.25756 | −0.0592164 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.8097 | −0.789790 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.35406 | 0.251002 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7459 | 1.53179 | 0.765893 | − | 0.642968i | \(-0.222297\pi\) | ||||
0.765893 | + | 0.642968i | \(0.222297\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.88201 | −0.321225 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.7574 | −1.71196 | −0.855982 | − | 0.517005i | \(-0.827047\pi\) | ||||
−0.855982 | + | 0.517005i | \(0.827047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.80280 | 0.223205 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.3270 | −0.757148 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.4603 | 0.807968 | 0.403984 | − | 0.914766i | \(-0.367625\pi\) | ||||
0.403984 | + | 0.914766i | \(0.367625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.573817 | −0.0264964 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.8841 | −0.962287 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.21684 | −0.193891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.120018 | 0.00550679 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.12358 | 0.417740 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0184 | 0.594825 | 0.297412 | − | 0.954749i | \(-0.403876\pi\) | ||||
0.297412 | + | 0.954749i | \(0.403876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1925 | −0.555931 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.80557 | 0.218661 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.82323 | −0.173604 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.20441 | −0.0998913 | −0.0499456 | − | 0.998752i | \(-0.515905\pi\) | ||||
−0.0499456 | + | 0.998752i | \(0.515905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.1953 | −0.641934 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6437 | 0.570601 | 0.285300 | − | 0.958438i | \(-0.407907\pi\) | ||||
0.285300 | + | 0.958438i | \(0.407907\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −57.5771 | −2.59314 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.99366 | 0.134555 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.22392 | 0.368893 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.7988 | −1.28921 | −0.644605 | − | 0.764516i | \(-0.722978\pi\) | ||||
−0.644605 | + | 0.764516i | \(0.722978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.19459 | 0.366107 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3287 | 0.815618 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.70712 | 0.209051 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4826 | 0.553282 | 0.276641 | − | 0.960973i | \(-0.410779\pi\) | ||||
0.276641 | + | 0.960973i | \(0.410779\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.62644 | −0.293137 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0742278 | −0.00327724 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.8136 | −1.79846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.70383 | 0.0749342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.82182 | 0.431130 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7837 | 1.17342 | 0.586708 | − | 0.809798i | \(-0.300424\pi\) | ||||
0.586708 | + | 0.809798i | \(0.300424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9616 | 0.523042 | 0.261521 | − | 0.965198i | \(-0.415776\pi\) | ||||
0.261521 | + | 0.965198i | \(0.415776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.16865 | 0.0510039 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −43.6813 | −1.90279 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2060 | 0.922002 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.35277 | −0.188894 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.11176 | 0.134785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.2161 | 1.30636 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.55904 | −0.110431 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.53859 | 0.324710 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1088 | 0.606587 | 0.303293 | − | 0.952897i | \(-0.401914\pi\) | ||||
0.303293 | + | 0.952897i | \(0.401914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.1502 | −1.03638 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.3420 | −0.742848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.99094 | −0.170640 | −0.0853201 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853201 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.87947 | 0.250930 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.621014 | −0.0264561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.78159 | 0.203334 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.8910 | −0.462297 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.4985 | 1.80072 | 0.900360 | − | 0.435146i | \(-0.143303\pi\) | ||||
0.900360 | + | 0.435146i | \(0.143303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4343 | 0.441324 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00924 | 0.338151 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.9247 | −1.26118 | −0.630588 | − | 0.776118i | \(-0.717186\pi\) | ||||
−0.630588 | + | 0.776118i | \(0.717186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.3713 | −1.15152 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.722776 | −0.0303538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.6732 | 1.62126 | 0.810632 | − | 0.585556i | \(-0.199124\pi\) | ||||
0.810632 | + | 0.585556i | \(0.199124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.92014 | −0.289599 | −0.144799 | − | 0.989461i | \(-0.546254\pi\) | ||||
−0.144799 | + | 0.989461i | \(0.546254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.3924 | −1.06078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.7503 | 0.448318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4161 | 0.891566 | 0.445783 | − | 0.895141i | \(-0.352925\pi\) | ||||
0.445783 | + | 0.895141i | \(0.352925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.8275 | −0.616212 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.91633 | 0.286938 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.6180 | −0.439752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.40763 | −0.306268 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.34161 | −0.0553743 | −0.0276872 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276872 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.471137 | −0.0194129 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6035 | −0.477305 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.7837 | 0.771353 | 0.385676 | − | 0.922634i | \(-0.373968\pi\) | ||||
0.385676 | + | 0.922634i | \(0.373968\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.7952 | 0.524551 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.2671 | −0.788550 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.7971 | −1.01318 | −0.506591 | − | 0.862186i | \(-0.669095\pi\) | ||||
−0.506591 | + | 0.862186i | \(0.669095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.99006 | 0.121967 | 0.0609836 | − | 0.998139i | \(-0.480576\pi\) | ||||
0.0609836 | + | 0.998139i | \(0.480576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.793907 | 0.0323304 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.8116 | 1.00874 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9071 | 0.808005 | 0.404002 | − | 0.914758i | \(-0.367619\pi\) | ||||
0.404002 | + | 0.914758i | \(0.367619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.04698 | −0.245036 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.21601 | −0.170561 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0313 | 0.768667 | 0.384333 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384333 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.77959 | 0.112084 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.2349 | −1.13670 | −0.568348 | − | 0.822788i | \(-0.692417\pi\) | ||||
−0.568348 | + | 0.822788i | \(0.692417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0463 | −1.12727 | −0.563637 | − | 0.826022i | \(-0.690598\pi\) | ||||
−0.563637 | + | 0.826022i | \(0.690598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.64876 | −0.266806 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.91652 | 0.277105 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4701 | −1.21880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0863859 | 0.00344992 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.1377 | −1.16180 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.7128 | −1.93923 | −0.969613 | − | 0.244645i | \(-0.921329\pi\) | ||||
−0.969613 | + | 0.244645i | \(0.921329\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.79962 | 0.190768 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.3596 | −1.52226 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6538 | −0.739089 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3782 | −0.450116 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.3127 | −0.525822 | −0.262911 | − | 0.964820i | \(-0.584682\pi\) | ||||
−0.262911 | + | 0.964820i | \(0.584682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.14076 | 0.123859 | 0.0619297 | − | 0.998081i | \(-0.480275\pi\) | ||||
0.0619297 | + | 0.998081i | \(0.480275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.32047 | 0.366993 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.4882 | 0.412333 | 0.206166 | − | 0.978517i | \(-0.433901\pi\) | ||||
0.206166 | + | 0.978517i | \(0.433901\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.06573 | 0.198847 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.58759 | −0.179802 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.9881 | −1.01699 | −0.508497 | − | 0.861064i | \(-0.669799\pi\) | ||||
−0.508497 | + | 0.861064i | \(0.669799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.1352 | 1.49007 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.16804 | 0.357679 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8964 | 1.43728 | 0.718641 | − | 0.695382i | \(-0.244765\pi\) | ||||
0.718641 | + | 0.695382i | \(0.244765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.26856 | 0.0493414 | 0.0246707 | − | 0.999696i | \(-0.492146\pi\) | ||||
0.0246707 | + | 0.999696i | \(0.492146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.8184 | −0.769681 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.138006 | 0.00535163 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −55.6257 | −2.15384 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7175 | −0.800986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.84250 | −0.264152 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3186 | 0.436299 | 0.218150 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218150 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.61688 | −0.0622339 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.2752 | 1.70163 | 0.850816 | − | 0.525463i | \(-0.176108\pi\) | ||||
0.850816 | + | 0.525463i | \(0.176108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.07426 | −0.0412262 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.6740 | 1.06047 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.88334 | 0.148592 | 0.0742960 | − | 0.997236i | \(-0.476329\pi\) | ||||
0.0742960 | + | 0.997236i | \(0.476329\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.9364 | −0.723522 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.7378 | 0.829350 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.2735 | 1.00094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.4599 | 1.38700 | 0.693499 | − | 0.720458i | \(-0.256068\pi\) | ||||
0.693499 | + | 0.720458i | \(0.256068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.841163 | 0.0319531 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.6816 | −1.05002 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.43650 | 0.281678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.46491 | −0.0554080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.20540 | −0.121066 | −0.0605331 | − | 0.998166i | \(-0.519280\pi\) | ||||
−0.0605331 | + | 0.998166i | \(0.519280\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.314273 | −0.0118530 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.76596 | −0.141834 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.15003 | 0.193687 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.29626 | 0.0862377 | 0.0431189 | − | 0.999070i | \(-0.486271\pi\) | ||||
0.0431189 | + | 0.999070i | \(0.486271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.61559 | −0.248104 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.2009 | −1.58044 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.62096 | 0.322406 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.03018 | 0.0758183 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.65049 | −0.0988466 | −0.0494233 | − | 0.998778i | \(-0.515738\pi\) | ||||
−0.0494233 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4679 | −0.427085 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.739602 | 0.0275061 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.5274 | −0.502395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.4593 | 1.24094 | 0.620468 | − | 0.784232i | \(-0.286943\pi\) | ||||
0.620468 | + | 0.784232i | \(0.286943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.9360 | 0.922290 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.6822 | 1.17021 | 0.585104 | − | 0.810958i | \(-0.301054\pi\) | ||||
0.585104 | + | 0.810958i | \(0.301054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.6625 | −0.614606 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.923945 | −0.0340339 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9975 | −0.882763 | −0.441381 | − | 0.897320i | \(-0.645511\pi\) | ||||
−0.441381 | + | 0.897320i | \(0.645511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.213756 | −0.00785254 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.2534 | −1.29332 | −0.646662 | − | 0.762777i | \(-0.723835\pi\) | ||||
−0.646662 | + | 0.762777i | \(0.723835\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7177 | −0.429303 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.56912 | −0.350116 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.49017 | 0.310224 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.7924 | −1.26959 | −0.634796 | − | 0.772680i | \(-0.718916\pi\) | ||||
−0.634796 | + | 0.772680i | \(0.718916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.6351 | 0.569775 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.2402 | −1.57367 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4069 | −0.741701 | −0.370850 | − | 0.928693i | \(-0.620934\pi\) | ||||
−0.370850 | + | 0.928693i | \(0.620934\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.73779 | 0.280864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.2926 | 1.35186 | 0.675929 | − | 0.736967i | \(-0.263743\pi\) | ||||
0.675929 | + | 0.736967i | \(0.263743\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.87276 | −0.176406 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.7028 | −0.640046 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.5348 | −0.452606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5785 | 0.814203 | 0.407101 | − | 0.913383i | \(-0.366540\pi\) | ||||
0.407101 | + | 0.913383i | \(0.366540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.67976 | −0.0604952 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.5941 | 1.49604 | 0.748019 | − | 0.663678i | \(-0.231005\pi\) | ||||
0.748019 | + | 0.663678i | \(0.231005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.2627 | −0.368645 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.06016 | −0.109783 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0802084 | 0.00287377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.2419 | 0.473834 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.36633 | 0.298988 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −53.7207 | −1.91737 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.1243 | 1.46592 | 0.732961 | − | 0.680271i | \(-0.238138\pi\) | ||||
0.732961 | + | 0.680271i | \(0.238138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.85110 | 0.0659009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.69081 | −0.273454 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.9313 | 0.601249 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4689 | 0.832355 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.3180 | 1.39271 | 0.696357 | − | 0.717695i | \(-0.254803\pi\) | ||||
0.696357 | + | 0.717695i | \(0.254803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0754 | −0.356444 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.56938 | −0.338117 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6697 | −0.376526 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.3615 | 0.435686 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.43192 | 0.261616 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.1504 | −0.532661 | −0.266330 | − | 0.963882i | \(-0.585811\pi\) | ||||
−0.266330 | + | 0.963882i | \(0.585811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.1738 | −1.27023 | −0.635117 | − | 0.772416i | \(-0.719048\pi\) | ||||
−0.635117 | + | 0.772416i | \(0.719048\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.02618 | −0.0710612 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.5150 | −1.27906 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.268954 | 0.00940950 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.08140 | −0.0727302 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0699 | 0.456144 | 0.228072 | − | 0.973644i | \(-0.426758\pi\) | ||||
0.228072 | + | 0.973644i | \(0.426758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.77380 | 0.201262 | 0.100631 | − | 0.994924i | \(-0.467914\pi\) | ||||
0.100631 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.88172 | 0.0655131 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0476 | 0.558031 | 0.279016 | − | 0.960287i | \(-0.409992\pi\) | ||||
0.279016 | + | 0.960287i | \(0.409992\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.9625 | 0.866983 | 0.433492 | − | 0.901158i | \(-0.357281\pi\) | ||||
0.433492 | + | 0.901158i | \(0.357281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.59687 | 0.194153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.5789 | −1.54457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.0792 | 0.729475 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.34718 | 0.219391 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9000 | 0.548929 | 0.274464 | − | 0.961597i | \(-0.411499\pi\) | ||||
0.274464 | + | 0.961597i | \(0.411499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.9955 | 1.41364 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.9685 | −0.377776 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1083 | 0.416537 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.97160 | 0.239547 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.8585 | −0.372663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.1502 | −0.964976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.4168 | −1.48656 | −0.743282 | − | 0.668978i | \(-0.766732\pi\) | ||||
−0.743282 | + | 0.668978i | \(0.766732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.190938 | −0.00652995 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.8811 | −0.542487 | −0.271243 | − | 0.962511i | \(-0.587435\pi\) | ||||
−0.271243 | + | 0.962511i | \(0.587435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.8203 | 0.983335 | 0.491668 | − | 0.870783i | \(-0.336388\pi\) | ||||
0.491668 | + | 0.870783i | \(0.336388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.781012 | 0.0266168 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6253 | −1.14462 | −0.572309 | − | 0.820038i | \(-0.693952\pi\) | ||||
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.2650 | 0.859035 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.3620 | −1.03115 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.69919 | 0.261177 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.28624 | 0.0774664 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.48629 | 0.0503034 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.28995 | −0.212639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.13685 | 0.0721561 | 0.0360781 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360781 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.01975 | 0.169312 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.2878 | −1.66055 | −0.830274 | − | 0.557355i | \(-0.811816\pi\) | ||||
−0.830274 | + | 0.557355i | \(0.811816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8136 | 0.936004 | 0.468002 | − | 0.883727i | \(-0.344974\pi\) | ||||
0.468002 | + | 0.883727i | \(0.344974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.1968 | −0.376375 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.295664 | 0.00992743 | 0.00496371 | − | 0.999988i | \(-0.498420\pi\) | ||||
0.00496371 | + | 0.999988i | \(0.498420\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.7783 | −0.361494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16379 | −0.0389886 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.108671 | −0.00363655 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.58269 | −0.220035 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.1467 | −0.639289 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.1026 | 1.77107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.7886 | 2.09179 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.61888 | 0.0871507 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −62.1223 | −2.06501 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.2844 | −1.43723 | −0.718617 | − | 0.695406i | \(-0.755225\pi\) | ||||
−0.718617 | + | 0.695406i | \(0.755225\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.12534 | −0.236333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.0762 | −1.16213 | −0.581063 | − | 0.813858i | \(-0.697363\pi\) | ||||
−0.581063 | + | 0.813858i | \(0.697363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1365 | 0.368564 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.1239 | 0.499982 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7153 | 0.353849 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.22975 | −0.172513 | −0.0862567 | − | 0.996273i | \(-0.527491\pi\) | ||||
−0.0862567 | + | 0.996273i | \(0.527491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.19596 | 0.303017 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.7663 | −1.07852 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.84573 | −0.225086 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.8664 | 0.521121 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.3894 | −1.35794 | −0.678971 | − | 0.734165i | \(-0.737574\pi\) | ||||
−0.678971 | + | 0.734165i | \(0.737574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.480817 | −0.0157582 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.4505 | −0.374872 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.6024 | 0.673771 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4145 | 0.993599 | 0.496799 | − | 0.867865i | \(-0.334509\pi\) | ||||
0.496799 | + | 0.867865i | \(0.334509\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0645 | −0.328442 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.0814 | 1.14362 | 0.571810 | − | 0.820386i | \(-0.306241\pi\) | ||||
0.571810 | + | 0.820386i | \(0.306241\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.18446 | 0.233958 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.85922 | −0.0604804 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.0852 | −1.75753 | −0.878766 | − | 0.477253i | \(-0.841633\pi\) | ||||
−0.878766 | + | 0.477253i | \(0.841633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.4015 | 0.857030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0774 | −0.748336 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.7409 | −0.704256 | −0.352128 | − | 0.935952i | \(-0.614542\pi\) | ||||
−0.352128 | + | 0.935952i | \(0.614542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65.3175 | −2.11363 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.73669 | −0.314742 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.32076 | −0.171816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.28667 | 0.299570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.7466 | −0.378529 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.1413 | −1.22781 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.2475 | −1.48722 | −0.743610 | − | 0.668614i | \(-0.766888\pi\) | ||||
−0.743610 | + | 0.668614i | \(0.766888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.510836 | −0.0164104 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.3342 | 1.13393 | 0.566965 | − | 0.823742i | \(-0.308118\pi\) | ||||
0.566965 | + | 0.823742i | \(0.308118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.77800 | −0.249351 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.65620 | −0.149118 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9307 | 0.605645 | 0.302823 | − | 0.953047i | \(-0.402071\pi\) | ||||
0.302823 | + | 0.953047i | \(0.402071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1368 | 0.355934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.74173 | 0.215247 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.2239 | −0.740727 | −0.370363 | − | 0.928887i | \(-0.620767\pi\) | ||||
−0.370363 | + | 0.928887i | \(0.620767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.8481 | −0.951039 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.05816 | −0.0336817 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0908 | 0.766044 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.8566 | −1.52022 | −0.760108 | − | 0.649797i | \(-0.774854\pi\) | ||||
−0.760108 | + | 0.649797i | \(0.774854\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.4192 | 0.616248 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.5613 | −1.57120 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.4541 | −0.489437 | −0.244719 | − | 0.969594i | \(-0.578696\pi\) | ||||
−0.244719 | + | 0.969594i | \(0.578696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.23390 | 0.133955 |
(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 | 6036.2.a.i.1.6 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.6 | ✓ | 26 | 1.1 | even | 1 | trivial |