Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6024,2,Mod(1,6024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6024 = 2^{3} \cdot 3 \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6024.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: | \(48.1018821776\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 9 x^{19} - 31 x^{18} + 471 x^{17} - 82 x^{16} - 9476 x^{15} + 12881 x^{14} + 94079 x^{13} + \cdots + 24832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(3.18186\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6024.1 |
$q$-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 | ||||||||
\(5\) | 3.18186 | 1.42297 | 0.711486 | − | 0.702701i | \(-0.248023\pi\) | ||||
0.711486 | + | 0.702701i | \(0.248023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54652 | 0.962495 | 0.481248 | − | 0.876585i | \(-0.340184\pi\) | ||||
0.481248 | + | 0.876585i | \(0.340184\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.62213 | −0.489090 | −0.244545 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244545 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.61755 | 1.28068 | 0.640339 | − | 0.768092i | \(-0.278794\pi\) | ||||
0.640339 | + | 0.768092i | \(0.278794\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.18186 | 0.821553 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.01883 | 0.247101 | 0.123551 | − | 0.992338i | \(-0.460572\pi\) | ||||
0.123551 | + | 0.992338i | \(0.460572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.19172 | −0.732230 | −0.366115 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366115 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.54652 | 0.555697 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.05733 | −1.68007 | −0.840035 | − | 0.542532i | \(-0.817466\pi\) | ||||
−0.840035 | + | 0.542532i | \(0.817466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.12424 | 1.02485 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.44948 | 1.19764 | 0.598819 | − | 0.800884i | \(-0.295637\pi\) | ||||
0.598819 | + | 0.800884i | \(0.295637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.09823 | −0.556459 | −0.278229 | − | 0.960515i | \(-0.589748\pi\) | ||||
−0.278229 | + | 0.960515i | \(0.589748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.62213 | −0.282376 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.10268 | 1.36960 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9412 | 1.79873 | 0.899365 | − | 0.437198i | \(-0.144029\pi\) | ||||
0.899365 | + | 0.437198i | \(0.144029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.61755 | 0.739400 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.892781 | 0.139429 | 0.0697145 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697145 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.16844 | 0.635680 | 0.317840 | − | 0.948144i | \(-0.397042\pi\) | ||||
0.317840 | + | 0.948144i | \(0.397042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18186 | 0.474324 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.40522 | −1.22603 | −0.613014 | − | 0.790072i | \(-0.710043\pi\) | ||||
−0.613014 | + | 0.790072i | \(0.710043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.515219 | −0.0736027 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.01883 | 0.142664 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.66438 | −0.365981 | −0.182990 | − | 0.983115i | \(-0.558578\pi\) | ||||
−0.182990 | + | 0.983115i | \(0.558578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.16139 | −0.695962 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.19172 | −0.422753 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.88643 | 1.15691 | 0.578457 | − | 0.815713i | \(-0.303655\pi\) | ||||
0.578457 | + | 0.815713i | \(0.303655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.85906 | 1.26232 | 0.631162 | − | 0.775651i | \(-0.282578\pi\) | ||||
0.631162 | + | 0.775651i | \(0.282578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.54652 | 0.320832 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.6924 | 1.82237 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.55934 | 0.434842 | 0.217421 | − | 0.976078i | \(-0.430236\pi\) | ||||
0.217421 | + | 0.976078i | \(0.430236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.05733 | −0.969989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2193 | −1.21281 | −0.606403 | − | 0.795158i | \(-0.707388\pi\) | ||||
−0.606403 | + | 0.795158i | \(0.707388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.54079 | −0.297377 | −0.148688 | − | 0.988884i | \(-0.547505\pi\) | ||||
−0.148688 | + | 0.988884i | \(0.547505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.12424 | 0.591696 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.13079 | −0.470747 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.05853 | 1.01916 | 0.509582 | − | 0.860422i | \(-0.329800\pi\) | ||||
0.509582 | + | 0.860422i | \(0.329800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.8724 | 1.96175 | 0.980877 | − | 0.194627i | \(-0.0623497\pi\) | ||||
0.980877 | + | 0.194627i | \(0.0623497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.24176 | 0.351618 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.44948 | 0.691457 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.63901 | −1.02173 | −0.510866 | − | 0.859660i | \(-0.670675\pi\) | ||||
−0.510866 | + | 0.859660i | \(0.670675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.7587 | 1.23265 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.09823 | −0.321272 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1556 | −1.04194 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.93524 | −0.298029 | −0.149014 | − | 0.988835i | \(-0.547610\pi\) | ||||
−0.149014 | + | 0.988835i | \(0.547610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.62213 | −0.163030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.3984 | 1.63170 | 0.815852 | − | 0.578261i | \(-0.196268\pi\) | ||||
0.815852 | + | 0.578261i | \(0.196268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9427 | 1.27528 | 0.637639 | − | 0.770335i | \(-0.279911\pi\) | ||||
0.637639 | + | 0.770335i | \(0.279911\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.10268 | 0.790741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.440004 | 0.0425368 | 0.0212684 | − | 0.999774i | \(-0.493230\pi\) | ||||
0.0212684 | + | 0.999774i | \(0.493230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.580594 | 0.0556108 | 0.0278054 | − | 0.999613i | \(-0.491148\pi\) | ||||
0.0278054 | + | 0.999613i | \(0.491148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.9412 | 1.03850 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.67348 | −0.439644 | −0.219822 | − | 0.975540i | \(-0.570548\pi\) | ||||
−0.219822 | + | 0.975540i | \(0.570548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.6373 | −2.39069 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.61755 | 0.426893 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.59446 | 0.237834 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.36870 | −0.760791 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.892781 | 0.0804994 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.395304 | 0.0353571 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9773 | −0.974080 | −0.487040 | − | 0.873380i | \(-0.661923\pi\) | ||||
−0.487040 | + | 0.873380i | \(0.661923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.16844 | 0.367010 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.204993 | −0.0179103 | −0.00895514 | − | 0.999960i | \(-0.502851\pi\) | ||||
−0.00895514 | + | 0.999960i | \(0.502851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.12778 | −0.704768 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.18186 | 0.273851 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5791 | 0.903832 | 0.451916 | − | 0.892060i | \(-0.350741\pi\) | ||||
0.451916 | + | 0.892060i | \(0.350741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.38787 | −0.456993 | −0.228496 | − | 0.973545i | \(-0.573381\pi\) | ||||
−0.228496 | + | 0.973545i | \(0.573381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.40522 | −0.707847 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.49027 | −0.626367 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.5213 | 1.70421 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.515219 | −0.0424945 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.16765 | −0.0956576 | −0.0478288 | − | 0.998856i | \(-0.515230\pi\) | ||||
−0.0478288 | + | 0.998856i | \(0.515230\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7530 | 1.03782 | 0.518912 | − | 0.854828i | \(-0.326337\pi\) | ||||
0.518912 | + | 0.854828i | \(0.326337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.01883 | 0.0823672 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.85814 | −0.791825 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.86775 | −0.548106 | −0.274053 | − | 0.961715i | \(-0.588364\pi\) | ||||
−0.274053 | + | 0.961715i | \(0.588364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.66438 | −0.211299 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.5182 | −1.61706 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.15118 | 0.325145 | 0.162573 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162573 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.16139 | −0.401814 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.3817 | −1.26765 | −0.633827 | − | 0.773475i | \(-0.718517\pi\) | ||||
−0.633827 | + | 0.773475i | \(0.718517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.32179 | 0.640137 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.19172 | −0.244077 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.5984 | −1.26196 | −0.630978 | − | 0.775801i | \(-0.717346\pi\) | ||||
−0.630978 | + | 0.775801i | \(0.717346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0490 | 0.986411 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.88643 | 0.667945 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.9511 | −1.04276 | −0.521378 | − | 0.853326i | \(-0.674582\pi\) | ||||
−0.521378 | + | 0.853326i | \(0.674582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.9274 | −1.40686 | −0.703432 | − | 0.710762i | \(-0.748350\pi\) | ||||
−0.703432 | + | 0.710762i | \(0.748350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.85906 | 0.728803 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 34.8135 | 2.55954 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.65267 | −0.120855 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.54652 | 0.185232 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.81038 | −0.709854 | −0.354927 | − | 0.934894i | \(-0.615494\pi\) | ||||
−0.354927 | + | 0.934894i | \(0.615494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.85083 | −0.205207 | −0.102603 | − | 0.994722i | \(-0.532717\pi\) | ||||
−0.102603 | + | 0.994722i | \(0.532717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.6924 | 1.05215 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.00576 | −0.641634 | −0.320817 | − | 0.947141i | \(-0.603957\pi\) | ||||
−0.320817 | + | 0.947141i | \(0.603957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8945 | −0.914068 | −0.457034 | − | 0.889449i | \(-0.651088\pi\) | ||||
−0.457034 | + | 0.889449i | \(0.651088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.55934 | 0.251056 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.4238 | 1.15272 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.84071 | 0.198403 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.05733 | −0.560023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.17738 | 0.358127 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.9805 | 1.92626 | 0.963128 | − | 0.269042i | \(-0.0867071\pi\) | ||||
0.963128 | + | 0.269042i | \(0.0867071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2193 | −0.700214 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.2634 | 0.904555 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.88972 | −0.535589 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.54079 | −0.171691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.70448 | 0.316458 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.9010 | −1.19874 | −0.599371 | − | 0.800471i | \(-0.704583\pi\) | ||||
−0.599371 | + | 0.800471i | \(0.704583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.12424 | 0.341616 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0625 | 1.26523 | 0.632613 | − | 0.774468i | \(-0.281983\pi\) | ||||
0.632613 | + | 0.774468i | \(0.281983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.8183 | −1.57395 | −0.786977 | − | 0.616982i | \(-0.788355\pi\) | ||||
−0.786977 | + | 0.616982i | \(0.788355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.13079 | −0.271786 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.0140 | 1.31116 | 0.655580 | − | 0.755126i | \(-0.272424\pi\) | ||||
0.655580 | + | 0.755126i | \(0.272424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.7442 | −1.74460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.05853 | 0.588415 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.1391 | 0.785212 | 0.392606 | − | 0.919707i | \(-0.371574\pi\) | ||||
0.392606 | + | 0.919707i | \(0.371574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.19115 | 0.527639 | 0.263819 | − | 0.964572i | \(-0.415018\pi\) | ||||
0.263819 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.63935 | −0.104735 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.7379 | −0.937751 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.8724 | 1.13262 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0700 | 0.821706 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.24176 | 0.203007 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.2209 | 1.94751 | 0.973753 | − | 0.227608i | \(-0.0730904\pi\) | ||||
0.973753 | + | 0.227608i | \(0.0730904\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.8621 | 1.73127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.44948 | 0.399213 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6076 | −1.82568 | −0.912842 | − | 0.408314i | \(-0.866117\pi\) | ||||
−0.912842 | + | 0.408314i | \(0.866117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47769 | −0.520780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.63901 | −0.589898 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.09323 | 0.310539 | 0.155270 | − | 0.987872i | \(-0.450375\pi\) | ||||
0.155270 | + | 0.987872i | \(0.450375\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.24681 | 0.197230 | 0.0986149 | − | 0.995126i | \(-0.468559\pi\) | ||||
0.0986149 | + | 0.995126i | \(0.468559\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.7587 | 0.711669 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.31217 | −0.501243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.54366 | 0.333087 | 0.166543 | − | 0.986034i | \(-0.446739\pi\) | ||||
0.166543 | + | 0.986034i | \(0.446739\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.09823 | −0.185486 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.6076 | −1.82589 | −0.912947 | − | 0.408078i | \(-0.866199\pi\) | ||||
−0.912947 | + | 0.408078i | \(0.866199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2155 | 0.785578 | 0.392789 | − | 0.919629i | \(-0.371510\pi\) | ||||
0.392789 | + | 0.919629i | \(0.371510\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.1556 | −0.601566 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.27349 | 0.134200 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9620 | −0.938941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.93524 | −0.172067 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.3977 | 1.30849 | 0.654244 | − | 0.756283i | \(-0.272987\pi\) | ||||
0.654244 | + | 0.756283i | \(0.272987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2754 | 1.64626 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.62213 | −0.0941255 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.2052 | −2.15163 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.6150 | 0.611839 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.3984 | 0.942065 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.3702 | 1.79625 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.4179 | −1.22238 | −0.611192 | − | 0.791482i | \(-0.709310\pi\) | ||||
−0.611192 | + | 0.791482i | \(0.709310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9427 | 0.736282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.68607 | −0.549246 | −0.274623 | − | 0.961552i | \(-0.588553\pi\) | ||||
−0.274623 | + | 0.961552i | \(0.588553\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.2893 | 1.42944 | 0.714719 | − | 0.699412i | \(-0.246555\pi\) | ||||
0.714719 | + | 0.699412i | \(0.246555\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.10268 | 0.456534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.9181 | −1.39954 | −0.699769 | − | 0.714369i | \(-0.746714\pi\) | ||||
−0.699769 | + | 0.714369i | \(0.746714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4619 | −0.585753 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.440004 | 0.0245586 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.25180 | −0.180935 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.6614 | 1.31250 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.580594 | 0.0321069 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.4041 | −1.18005 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.5728 | 0.636099 | 0.318050 | − | 0.948074i | \(-0.396972\pi\) | ||||
0.318050 | + | 0.948074i | \(0.396972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.9412 | 0.599577 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3253 | 0.618768 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.177114 | −0.00964802 | −0.00482401 | − | 0.999988i | \(-0.501536\pi\) | ||||
−0.00482401 | + | 0.999988i | \(0.501536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.67348 | −0.253829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02573 | 0.272159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1377 | −1.03334 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.6373 | −1.38027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.6159 | −0.838308 | −0.419154 | − | 0.907915i | \(-0.637673\pi\) | ||||
−0.419154 | + | 0.907915i | \(0.637673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.5794 | 1.36923 | 0.684617 | − | 0.728903i | \(-0.259969\pi\) | ||||
0.684617 | + | 0.728903i | \(0.259969\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.61755 | 0.246467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.0040 | −1.38405 | −0.692025 | − | 0.721873i | \(-0.743281\pi\) | ||||
−0.692025 | + | 0.721873i | \(0.743281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.5163 | −1.72579 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.59446 | 0.137314 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.4722 | −0.605478 | −0.302739 | − | 0.953074i | \(-0.597901\pi\) | ||||
−0.302739 | + | 0.953074i | \(0.597901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.81295 | −0.463839 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.36870 | −0.439243 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.08444 | −0.423159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.02999 | −0.366962 | −0.183481 | − | 0.983023i | \(-0.558737\pi\) | ||||
−0.183481 | + | 0.983023i | \(0.558737\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.892781 | 0.0464763 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.78491 | −0.352255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.9323 | −1.34273 | −0.671363 | − | 0.741129i | \(-0.734291\pi\) | ||||
−0.671363 | + | 0.741129i | \(0.734291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.395304 | 0.0204134 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.7808 | 1.53379 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1083 | −0.570595 | −0.285298 | − | 0.958439i | \(-0.592092\pi\) | ||||
−0.285298 | + | 0.958439i | \(0.592092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9773 | −0.562385 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.6807 | 0.596854 | 0.298427 | − | 0.954432i | \(-0.403538\pi\) | ||||
0.298427 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1436 | −0.669860 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.16844 | 0.211893 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.32296 | 0.371289 | 0.185644 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185644 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.20902 | −0.415148 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.204993 | −0.0103405 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.8230 | 1.45024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.9337 | −1.70308 | −0.851541 | − | 0.524288i | \(-0.824331\pi\) | ||||
−0.851541 | + | 0.524288i | \(0.824331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.12778 | −0.406898 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.6825 | −1.68202 | −0.841012 | − | 0.541016i | \(-0.818040\pi\) | ||||
−0.841012 | + | 0.541016i | \(0.818040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3062 | −0.712645 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.18186 | 0.158108 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.7481 | −0.879742 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.209950 | 0.0103814 | 0.00519069 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00519069 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5791 | 0.521828 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.6295 | 1.11353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 56.8676 | 2.79152 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.38787 | −0.263845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.3446 | −1.14046 | −0.570230 | − | 0.821485i | \(-0.693146\pi\) | ||||
−0.570230 | + | 0.821485i | \(0.693146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.58174 | −0.272037 | −0.136019 | − | 0.990706i | \(-0.543431\pi\) | ||||
−0.136019 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.40522 | −0.408676 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.22070 | 0.253241 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.1063 | 1.21498 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.49027 | −0.361633 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.3722 | 1.55932 | 0.779658 | − | 0.626206i | \(-0.215393\pi\) | ||||
0.779658 | + | 0.626206i | \(0.215393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3860 | 1.21998 | 0.609988 | − | 0.792411i | \(-0.291174\pi\) | ||||
0.609988 | + | 0.792411i | \(0.291174\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.5213 | 0.983923 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.7167 | 1.23020 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3593 | −0.589878 | −0.294939 | − | 0.955516i | \(-0.595299\pi\) | ||||
−0.294939 | + | 0.955516i | \(0.595299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.515219 | −0.0245342 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5409 | 1.49855 | 0.749277 | − | 0.662256i | \(-0.230401\pi\) | ||||
0.749277 | + | 0.662256i | \(0.230401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.6700 | −1.45390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.16765 | −0.0552279 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.54571 | −0.214525 | −0.107263 | − | 0.994231i | \(-0.534209\pi\) | ||||
−0.107263 | + | 0.994231i | \(0.534209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.44821 | −0.0681934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7530 | 0.599188 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.4146 | 1.75402 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4704 | −0.489782 | −0.244891 | − | 0.969551i | \(-0.578752\pi\) | ||||
−0.244891 | + | 0.969551i | \(0.578752\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.01883 | 0.0475547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.6733 | 1.19573 | 0.597863 | − | 0.801598i | \(-0.296017\pi\) | ||||
0.597863 | + | 0.801598i | \(0.296017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.74247 | 0.220401 | 0.110201 | − | 0.993909i | \(-0.464851\pi\) | ||||
0.110201 | + | 0.993909i | \(0.464851\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.85814 | −0.457160 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.6202 | −1.32439 | −0.662193 | − | 0.749333i | \(-0.730374\pi\) | ||||
−0.662193 | + | 0.749333i | \(0.730374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.06393 | 0.418534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.86775 | −0.316449 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.76174 | −0.310905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.3551 | −0.750424 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.66438 | −0.121994 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.60861 | −0.210573 | −0.105286 | − | 0.994442i | \(-0.533576\pi\) | ||||
−0.105286 | + | 0.994442i | \(0.533576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.5218 | 2.30360 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.5182 | −0.933610 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.33953 | −0.424086 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2111 | 0.779910 | 0.389955 | − | 0.920834i | \(-0.372491\pi\) | ||||
0.389955 | + | 0.920834i | \(0.372491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.15118 | 0.187723 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1783 | −0.730115 | −0.365057 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365057 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.57090 | 0.295938 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.16139 | −0.231987 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.0236 | −1.16732 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.16541 | 0.186469 | 0.0932346 | − | 0.995644i | \(-0.470279\pi\) | ||||
0.0932346 | + | 0.995644i | \(0.470279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.3817 | −0.731880 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.6308 | 0.964470 | 0.482235 | − | 0.876042i | \(-0.339825\pi\) | ||||
0.482235 | + | 0.876042i | \(0.339825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.1775 | 2.32187 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.32179 | 0.369583 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8268 | −0.657185 | −0.328592 | − | 0.944472i | \(-0.606574\pi\) | ||||
−0.328592 | + | 0.944472i | \(0.606574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.47018 | −0.286224 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.19172 | −0.140918 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 41.1817 | 1.81468 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6344 | 0.599638 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.5984 | −0.728590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.1515 | −0.532366 | −0.266183 | − | 0.963923i | \(-0.585763\pi\) | ||||
−0.266183 | + | 0.963923i | \(0.585763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00258 | −0.131294 | −0.0656469 | − | 0.997843i | \(-0.520911\pi\) | ||||
−0.0656469 | + | 0.997843i | \(0.520911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.0490 | 0.569505 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.15656 | −0.137502 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.9206 | 1.82264 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.88643 | 0.385638 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.12246 | 0.178564 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.40003 | 0.0605286 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.9511 | −0.602035 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.835752 | 0.0359984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7626 | 0.505715 | 0.252857 | − | 0.967504i | \(-0.418630\pi\) | ||||
0.252857 | + | 0.967504i | \(0.418630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9274 | −0.812254 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.84737 | 0.0791326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2984 | 0.525840 | 0.262920 | − | 0.964818i | \(-0.415315\pi\) | ||||
0.262920 | + | 0.964818i | \(0.415315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.85906 | 0.420774 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.5849 | −0.876947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.0678 | 0.980941 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.8135 | 1.47775 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.54560 | 0.234975 | 0.117487 | − | 0.993074i | \(-0.462516\pi\) | ||||
0.117487 | + | 0.993074i | \(0.462516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.2480 | 0.814102 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65267 | −0.0697756 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.3567 | −1.15295 | −0.576474 | − | 0.817115i | \(-0.695572\pi\) | ||||
−0.576474 | + | 0.817115i | \(0.695572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8704 | −0.625601 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.54652 | 0.106944 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3712 | −0.518627 | −0.259313 | − | 0.965793i | \(-0.583496\pi\) | ||||
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.892374 | −0.0373447 | −0.0186723 | − | 0.999826i | \(-0.505944\pi\) | ||||
−0.0186723 | + | 0.999826i | \(0.505944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.81038 | −0.409835 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.2877 | −1.72182 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.69701 | −0.320431 | −0.160215 | − | 0.987082i | \(-0.551219\pi\) | ||||
−0.160215 | + | 0.987082i | \(0.551219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.85083 | −0.118476 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.5126 | 1.88818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.32197 | 0.178998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.6924 | 0.607456 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.6475 | 1.67770 | 0.838851 | − | 0.544361i | \(-0.183228\pi\) | ||||
0.838851 | + | 0.544361i | \(0.183228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.88867 | 0.407456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00576 | −0.370447 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.7480 | −1.46799 | −0.733997 | − | 0.679153i | \(-0.762347\pi\) | ||||
−0.733997 | + | 0.679153i | \(0.762347\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.25522 | 0.338431 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.8945 | −0.527737 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.1766 | −0.865251 | −0.432626 | − | 0.901574i | \(-0.642413\pi\) | ||||
−0.432626 | + | 0.901574i | \(0.642413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.3403 | −0.748117 | −0.374058 | − | 0.927405i | \(-0.622034\pi\) | ||||
−0.374058 | + | 0.927405i | \(0.622034\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.55934 | 0.144947 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.6280 | −1.08258 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.8694 | 1.74002 | 0.870009 | − | 0.493037i | \(-0.164113\pi\) | ||||
0.870009 | + | 0.493037i | \(0.164113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.4238 | 0.665524 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.8115 | −1.57015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9476 | 0.765288 | 0.382644 | − | 0.923896i | \(-0.375014\pi\) | ||||
0.382644 | + | 0.923896i | \(0.375014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.84071 | 0.114548 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.1414 | 1.73681 | 0.868404 | − | 0.495857i | \(-0.165146\pi\) | ||||
0.868404 | + | 0.495857i | \(0.165146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6131 | 0.506963 | 0.253481 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253481 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.05733 | −0.323330 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.5460 | −0.983413 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3634 | −0.974535 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.17738 | 0.206764 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1472 | 0.444469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.5826 | 0.739763 | 0.369881 | − | 0.929079i | \(-0.379398\pi\) | ||||
0.369881 | + | 0.929079i | \(0.379398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.9805 | 1.11212 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.9283 | −1.38609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.37905 | −0.0942614 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.2193 | −0.404269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.4755 | −0.927226 | −0.463613 | − | 0.886038i | \(-0.653447\pi\) | ||||
−0.463613 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3178 | 0.801254 | 0.400627 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400627 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.2634 | 0.522245 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.9646 | 1.02078 | 0.510388 | − | 0.859944i | \(-0.329502\pi\) | ||||
0.510388 | + | 0.859944i | \(0.329502\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.4149 | −0.565836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.88972 | −0.309222 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.9130 | 1.17058 | 0.585292 | − | 0.810822i | \(-0.300980\pi\) | ||||
0.585292 | + | 0.810822i | \(0.300980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.652258 | −0.0254858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.54079 | −0.0991256 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1774 | −1.40927 | −0.704635 | − | 0.709570i | \(-0.748889\pi\) | ||||
−0.704635 | + | 0.709570i | \(0.748889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0345 | 1.24600 | 0.622998 | − | 0.782223i | \(-0.285914\pi\) | ||||
0.622998 | + | 0.782223i | \(0.285914\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.70448 | 0.182707 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.8615 | −1.00286 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.9656 | −2.01212 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.9010 | −0.692094 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.9927 | −0.617390 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5447 | −0.445016 | −0.222508 | − | 0.974931i | \(-0.571424\pi\) | ||||
−0.222508 | + | 0.974931i | \(0.571424\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.12424 | 0.197232 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.9909 | 0.768314 | 0.384157 | − | 0.923268i | \(-0.374492\pi\) | ||||
0.384157 | + | 0.923268i | \(0.374492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.47466 | −0.286851 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0625 | 0.730478 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.2003 | 0.543361 | 0.271681 | − | 0.962387i | \(-0.412421\pi\) | ||||
0.271681 | + | 0.962387i | \(0.412421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.6612 | 1.28613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.8183 | −0.908723 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.3029 | −0.468704 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.9475 | 1.40555 | 0.702774 | − | 0.711413i | \(-0.251944\pi\) | ||||
0.702774 | + | 0.711413i | \(0.251944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.13079 | −0.156916 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.1434 | −0.650288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.909588 | 0.0344531 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.0140 | 0.756998 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.68012 | −0.252305 | −0.126152 | − | 0.992011i | \(-0.540263\pi\) | ||||
−0.126152 | + | 0.992011i | \(0.540263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.9214 | −1.31708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.7442 | −1.00725 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.7590 | 1.57051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.84256 | −0.332089 | −0.166045 | − | 0.986118i | \(-0.553100\pi\) | ||||
−0.166045 | + | 0.986118i | \(0.553100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.05853 | 0.339721 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9635 | 0.934890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.8330 | −0.891303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.1391 | 0.453342 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.1888 | 0.529153 | 0.264576 | − | 0.964365i | \(-0.414768\pi\) | ||||
0.264576 | + | 0.964365i | \(0.414768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.9588 | 1.22745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.19115 | 0.304632 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.0487 | 1.22740 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3785 | 0.570357 | 0.285179 | − | 0.958474i | \(-0.407947\pi\) | ||||
0.285179 | + | 0.958474i | \(0.407947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.24691 | 0.157078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1056 | 0.631809 | 0.315905 | − | 0.948791i | \(-0.397692\pi\) | ||||
0.315905 | + | 0.948791i | \(0.397692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.63935 | −0.0604685 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.77370 | −0.212677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.04399 | 0.185546 | 0.0927731 | − | 0.995687i | \(-0.470427\pi\) | ||||
0.0927731 | + | 0.995687i | \(0.470427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.7379 | −0.541411 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4802 | −0.898092 | −0.449046 | − | 0.893509i | \(-0.648236\pi\) | ||||
−0.449046 | + | 0.893509i | \(0.648236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.71530 | −0.136118 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.8724 | 0.653918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12048 | 0.0409415 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.6809 | −0.572206 | −0.286103 | − | 0.958199i | \(-0.592360\pi\) | ||||
−0.286103 | + | 0.958199i | \(0.592360\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00000 | −0.0364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.5782 | 1.47679 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0970 | 1.49370 | 0.746848 | − | 0.664995i | \(-0.231566\pi\) | ||||
0.746848 | + | 0.664995i | \(0.231566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.0700 | 0.474412 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.2573 | −1.71307 | −0.856537 | − | 0.516085i | \(-0.827389\pi\) | ||||
−0.856537 | + | 0.516085i | \(0.827389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.47850 | 0.0535251 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.24176 | 0.117206 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.0336 | 1.48164 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.5359 | 1.20934 | 0.604668 | − | 0.796477i | \(-0.293306\pi\) | ||||
0.604668 | + | 0.796477i | \(0.293306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2209 | 1.12439 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.4683 | −1.38361 | −0.691804 | − | 0.722085i | \(-0.743184\pi\) | ||||
−0.691804 | + | 0.722085i | \(0.743184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.8761 | −0.570285 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.8621 | 0.999549 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.84950 | −0.102094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.5770 | 0.593172 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.44948 | 0.230486 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8522 | −0.779939 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3174 | −0.510361 | −0.255180 | − | 0.966893i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966893i | \(0.582135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.6076 | −1.05406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9011 | −0.423156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.5247 | 1.61663 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.47769 | −0.300673 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.4897 | −0.796627 | −0.398313 | − | 0.917249i | \(-0.630404\pi\) | ||||
−0.398313 | + | 0.917249i | \(0.630404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.56345 | −0.302953 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.63901 | −0.340578 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.12149 | 0.145444 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −65.2860 | −2.30103 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.09323 | 0.179290 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.5024 | 0.931773 | 0.465887 | − | 0.884844i | \(-0.345735\pi\) | ||||
0.465887 | + | 0.884844i | \(0.345735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.247194 | 0.00868016 | 0.00434008 | − | 0.999991i | \(-0.498619\pi\) | ||||
0.00434008 | + | 0.999991i | \(0.498619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24681 | 0.113871 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.2085 | 0.462673 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.3045 | −0.465464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.7587 | 0.410882 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.39546 | −0.118502 | −0.0592512 | − | 0.998243i | \(-0.518871\pi\) | ||||
−0.0592512 | + | 0.998243i | \(0.518871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.53601 | −0.158115 | −0.0790577 | − | 0.996870i | \(-0.525191\pi\) | ||||
−0.0790577 | + | 0.996870i | \(0.525191\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.31217 | −0.289393 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0363 | −1.14879 | −0.574393 | − | 0.818580i | \(-0.694762\pi\) | ||||
−0.574393 | + | 0.818580i | \(0.694762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.1442 | 0.977489 | 0.488745 | − | 0.872427i | \(-0.337455\pi\) | ||||
0.488745 | + | 0.872427i | \(0.337455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.54366 | 0.192308 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.524918 | −0.0181873 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.1243 | −1.80383 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.09823 | −0.107091 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.8869 | −0.997288 | −0.498644 | − | 0.866807i | \(-0.666168\pi\) | ||||
−0.498644 | + | 0.866807i | \(0.666168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5958 | 0.434338 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.6076 | −1.05418 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.4788 | 0.910897 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.3111 | −0.732257 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2155 | 0.453554 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −88.1573 | −3.02199 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.99486 | −0.102542 | −0.0512711 | − | 0.998685i | \(-0.516327\pi\) | ||||
−0.0512711 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.1556 | −0.347314 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.0681 | −0.856311 | −0.428156 | − | 0.903705i | \(-0.640837\pi\) | ||||
−0.428156 | + | 0.903705i | \(0.640837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.3838 | −1.95791 | −0.978955 | − | 0.204075i | \(-0.934581\pi\) | ||||
−0.978955 | + | 0.204075i | \(0.934581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.27349 | 0.0774803 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.2953 | −1.20147 | −0.600733 | − | 0.799450i | \(-0.705124\pi\) | ||||
−0.600733 | + | 0.799450i | \(0.705124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.8139 | −1.79573 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.9620 | −0.542098 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.6941 | −0.498463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.4354 | 0.556893 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.93524 | −0.0993429 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00665 | 0.0340310 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.6134 | 1.10128 | 0.550638 | − | 0.834744i | \(-0.314384\pi\) | ||||
0.550638 | + | 0.834744i | \(0.314384\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.3977 | 0.755456 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0953 | −0.946556 | −0.473278 | − | 0.880913i | \(-0.656929\pi\) | ||||
−0.473278 | + | 0.880913i | \(0.656929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.7008 | −1.90813 | −0.954067 | − | 0.299594i | \(-0.903149\pi\) | ||||
−0.954067 | + | 0.299594i | \(0.903149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.2754 | 0.950467 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.86724 | 0.163426 | 0.0817130 | − | 0.996656i | \(-0.473961\pi\) | ||||
0.0817130 | + | 0.996656i | \(0.473961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.9540 | −0.937547 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.62213 | −0.0543434 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.8271 | 0.897734 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.3905 | −1.48381 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.2052 | −1.24224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.9820 | −0.666436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.71454 | −0.0904344 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.6150 | 0.353246 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −60.2244 | −2.00193 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.2178 | 1.53464 | 0.767319 | − | 0.641266i | \(-0.221590\pi\) | ||||
0.767319 | + | 0.641266i | \(0.221590\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.3984 | 0.543901 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.0739 | −1.09579 | −0.547894 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547894 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.9914 | −0.959475 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.3702 | 1.03707 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.522018 | −0.0172386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.55287 | 0.282133 | 0.141067 | − | 0.990000i | \(-0.454947\pi\) | ||||
0.141067 | + | 0.990000i | \(0.454947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.4179 | −0.705744 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47.1881 | −1.55321 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56.0656 | 1.84342 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9427 | 0.425093 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.5574 | −1.23222 | −0.616109 | − | 0.787661i | \(-0.711292\pi\) | ||||
−0.616109 | + | 0.787661i | \(0.711292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.64443 | 0.0538941 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.68607 | −0.317108 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.25855 | −0.171973 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.5161 | 1.78096 | 0.890482 | − | 0.455018i | \(-0.150367\pi\) | ||||
0.890482 | + | 0.455018i | \(0.150367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.2893 | 0.825286 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.30412 | 0.172909 | 0.0864546 | − | 0.996256i | \(-0.472446\pi\) | ||||
0.0864546 | + | 0.996256i | \(0.472446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.19344 | −0.234251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.10268 | 0.263580 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.7266 | −1.45342 | −0.726709 | − | 0.686945i | \(-0.758951\pi\) | ||||
−0.726709 | + | 0.686945i | \(0.758951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.7322 | −0.380844 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9181 | −0.808024 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.44990 | 0.144147 | 0.0720733 | − | 0.997399i | \(-0.477038\pi\) | ||||
0.0720733 | + | 0.997399i | \(0.477038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.2153 | −1.01010 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.4619 | −0.338185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.9399 | 0.869935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4010 | −0.690354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.440004 | 0.0141789 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.07093 | −0.292004 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.5929 | 1.91638 | 0.958189 | − | 0.286135i | \(-0.0923706\pi\) | ||||
0.958189 | + | 0.286135i | \(0.0923706\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.25180 | −0.104463 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.5141 | 0.882970 | 0.441485 | − | 0.897269i | \(-0.354452\pi\) | ||||
0.441485 | + | 0.897269i | \(0.354452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7203 | −0.439854 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.6614 | 0.757772 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2616 | 0.424277 | 0.212139 | − | 0.977240i | \(-0.431957\pi\) | ||||
0.212139 | + | 0.977240i | \(0.431957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6357 | 0.499720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.580594 | 0.0185369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.3890 | −0.618412 | −0.309206 | − | 0.950995i | \(-0.600063\pi\) | ||||
−0.309206 | + | 0.950995i | \(0.600063\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.6551 | −0.913026 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.4041 | −0.681300 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.5865 | −1.06799 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9938 | −0.380997 | −0.190498 | − | 0.981688i | \(-0.561010\pi\) | ||||
−0.190498 | + | 0.981688i | \(0.561010\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.5728 | 0.367252 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.0285 | −1.30069 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.7712 | −1.29124 | −0.645619 | − | 0.763660i | \(-0.723401\pi\) | ||||
−0.645619 | + | 0.763660i | \(0.723401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.9412 | 0.346166 |
(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 | 6024.2.a.r.1.17 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6024.2.a.r.1.17 | ✓ | 20 | 1.1 | even | 1 | trivial |