Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | 1.41553 | 0.817259 | 0.408629 | − | 0.912700i | \(-0.366007\pi\) | ||||
0.408629 | + | 0.912700i | \(0.366007\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.642687 | 0.287418 | 0.143709 | − | 0.989620i | \(-0.454097\pi\) | ||||
0.143709 | + | 0.989620i | \(0.454097\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.33052 | 0.502890 | 0.251445 | − | 0.967872i | \(-0.419094\pi\) | ||||
0.251445 | + | 0.967872i | \(0.419094\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.996264 | −0.332088 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.93346 | 0.582960 | 0.291480 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291480 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.21530 | −1.44646 | −0.723232 | − | 0.690605i | \(-0.757344\pi\) | ||||
−0.723232 | + | 0.690605i | \(0.757344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.909745 | 0.234895 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.65264 | −0.400824 | −0.200412 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200412 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.88340 | 0.410991 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.45774 | 0.303960 | 0.151980 | − | 0.988384i | \(-0.451435\pi\) | ||||
0.151980 | + | 0.988384i | \(0.451435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58695 | −0.917391 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0964612 | −0.0179124 | −0.00895619 | − | 0.999960i | \(-0.502851\pi\) | ||||
−0.00895619 | + | 0.999960i | \(0.502851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.73913 | −1.03078 | −0.515389 | − | 0.856956i | \(-0.672353\pi\) | ||||
−0.515389 | + | 0.856956i | \(0.672353\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.73688 | 0.476430 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.855108 | 0.144540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.59822 | −1.24914 | −0.624570 | − | 0.780969i | \(-0.714726\pi\) | ||||
−0.624570 | + | 0.780969i | \(0.714726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.38243 | −1.18214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.41539 | 0.845741 | 0.422871 | − | 0.906190i | \(-0.361022\pi\) | ||||
0.422871 | + | 0.906190i | \(0.361022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.60481 | −1.00722 | −0.503612 | − | 0.863930i | \(-0.667996\pi\) | ||||
−0.503612 | + | 0.863930i | \(0.667996\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.640286 | −0.0954482 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50562 | 0.219617 | 0.109809 | − | 0.993953i | \(-0.464976\pi\) | ||||
0.109809 | + | 0.993953i | \(0.464976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.22971 | −0.747102 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.33937 | −0.327577 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0801188 | 0.0110052 | 0.00550258 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550258 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.24261 | 0.167554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41553 | 0.187492 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.20139 | −0.937540 | −0.468770 | − | 0.883320i | \(-0.655303\pi\) | ||||
−0.468770 | + | 0.883320i | \(0.655303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8769 | 1.39265 | 0.696324 | − | 0.717728i | \(-0.254818\pi\) | ||||
0.696324 | + | 0.717728i | \(0.254818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.32555 | −0.167004 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.35181 | −0.415740 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.7930 | −1.80726 | −0.903629 | − | 0.428315i | \(-0.859107\pi\) | ||||
−0.903629 | + | 0.428315i | \(0.859107\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.06348 | 0.248414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.01632 | −0.951362 | −0.475681 | − | 0.879618i | \(-0.657798\pi\) | ||||
−0.475681 | + | 0.879618i | \(0.657798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6504 | 1.24654 | 0.623268 | − | 0.782008i | \(-0.285804\pi\) | ||||
0.623268 | + | 0.782008i | \(0.285804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.49299 | −0.749746 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.57251 | 0.293165 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.01867 | −0.557630 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.39572 | 0.811785 | 0.405893 | − | 0.913921i | \(-0.366961\pi\) | ||||
0.405893 | + | 0.913921i | \(0.366961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.06213 | −0.115204 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.136544 | −0.0146391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.64376 | −0.492238 | −0.246119 | − | 0.969240i | \(-0.579155\pi\) | ||||
−0.246119 | + | 0.969240i | \(0.579155\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.93907 | −0.727412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.12394 | −0.842413 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.642687 | 0.0659383 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.13964 | −0.521851 | −0.260926 | − | 0.965359i | \(-0.584028\pi\) | ||||
−0.260926 | + | 0.965359i | \(0.584028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.92624 | −0.193594 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1457 | 1.10904 | 0.554520 | − | 0.832170i | \(-0.312902\pi\) | ||||
0.554520 | + | 0.832170i | \(0.312902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.15830 | −0.705329 | −0.352664 | − | 0.935750i | \(-0.614724\pi\) | ||||
−0.352664 | + | 0.935750i | \(0.614724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.21043 | 0.118126 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4227 | 1.29762 | 0.648809 | − | 0.760951i | \(-0.275267\pi\) | ||||
0.648809 | + | 0.760951i | \(0.275267\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.85953 | −0.848589 | −0.424294 | − | 0.905524i | \(-0.639478\pi\) | ||||
−0.424294 | + | 0.905524i | \(0.639478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.7555 | −1.02087 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2233 | 1.62024 | 0.810118 | − | 0.586267i | \(-0.199403\pi\) | ||||
0.810118 | + | 0.586267i | \(0.199403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.936872 | 0.0873638 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.19582 | 0.480353 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.19887 | −0.201570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.26173 | −0.660157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.66566 | 0.691190 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.16141 | −0.551093 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8815 | −1.05431 | −0.527157 | − | 0.849768i | \(-0.676742\pi\) | ||||
−0.527157 | + | 0.849768i | \(0.676742\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.34933 | −0.823163 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.7271 | −1.46145 | −0.730726 | − | 0.682671i | \(-0.760818\pi\) | ||||
−0.730726 | + | 0.682671i | \(0.760818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.33052 | 0.115371 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.63558 | −0.312901 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.3185 | −1.30875 | −0.654373 | − | 0.756172i | \(-0.727067\pi\) | ||||
−0.654373 | + | 0.756172i | \(0.727067\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.32048 | 0.620915 | 0.310457 | − | 0.950587i | \(-0.399518\pi\) | ||||
0.310457 | + | 0.950587i | \(0.399518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.13126 | 0.179484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0836 | −0.843231 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0619943 | −0.00514835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.40284 | −0.610576 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.4219 | 1.42726 | 0.713631 | − | 0.700522i | \(-0.247049\pi\) | ||||
0.713631 | + | 0.700522i | \(0.247049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.53489 | 0.694559 | 0.347280 | − | 0.937762i | \(-0.387105\pi\) | ||||
0.347280 | + | 0.937762i | \(0.387105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.64647 | 0.133109 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.68847 | −0.296265 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.6908 | 1.81093 | 0.905463 | − | 0.424425i | \(-0.139524\pi\) | ||||
0.905463 | + | 0.424425i | \(0.139524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.113411 | 0.00899407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.93956 | 0.152859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3631 | −1.28166 | −0.640828 | − | 0.767684i | \(-0.721409\pi\) | ||||
−0.640828 | + | 0.767684i | \(0.721409\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.75896 | 0.136935 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.4032 | −1.81099 | −0.905497 | − | 0.424353i | \(-0.860501\pi\) | ||||
−0.905497 | + | 0.424353i | \(0.860501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.1994 | 1.09226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.996264 | −0.0761862 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0490 | −1.67635 | −0.838175 | − | 0.545401i | \(-0.816377\pi\) | ||||
−0.838175 | + | 0.545401i | \(0.816377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.10304 | −0.461346 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1938 | −0.766213 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.45284 | 0.631795 | 0.315897 | − | 0.948793i | \(-0.397694\pi\) | ||||
0.315897 | + | 0.948793i | \(0.397694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2964 | −1.28563 | −0.642817 | − | 0.766020i | \(-0.722234\pi\) | ||||
−0.642817 | + | 0.766020i | \(0.722234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3967 | 1.13815 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.88328 | −0.359026 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.19532 | −0.233665 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.52655 | −0.547476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6517 | 0.843089 | 0.421544 | − | 0.906808i | \(-0.361488\pi\) | ||||
0.421544 | + | 0.906808i | \(0.361488\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3297 | 0.743547 | 0.371773 | − | 0.928324i | \(-0.378750\pi\) | ||||
0.371773 | + | 0.928324i | \(0.378750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.74459 | −0.339767 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.98534 | −0.426437 | −0.213219 | − | 0.977004i | \(-0.568395\pi\) | ||||
−0.213219 | + | 0.977004i | \(0.568395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.70869 | −0.333790 | −0.166895 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166895 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.9401 | −1.47700 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.128344 | −0.00900795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.48040 | 0.243082 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.45230 | −0.100942 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.93346 | 0.133740 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0324 | 1.17256 | 0.586278 | − | 0.810110i | \(-0.300593\pi\) | ||||
0.586278 | + | 0.810110i | \(0.300593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3474 | −0.777509 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.24483 | −0.289495 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.63603 | −0.518368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.0760 | 1.01874 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.61902 | 0.579778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4741 | 1.17015 | 0.585075 | − | 0.810979i | \(-0.301065\pi\) | ||||
0.585075 | + | 0.810979i | \(0.301065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.56982 | 0.304654 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.2456 | 1.34375 | 0.671874 | − | 0.740665i | \(-0.265489\pi\) | ||||
0.671874 | + | 0.740665i | \(0.265489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8439 | −1.04700 | −0.523499 | − | 0.852026i | \(-0.675373\pi\) | ||||
−0.523499 | + | 0.852026i | \(0.675373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.64147 | 0.239591 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.8263 | 1.69194 | 0.845969 | − | 0.533232i | \(-0.179023\pi\) | ||||
0.845969 | + | 0.533232i | \(0.179023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.967643 | 0.0631221 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.41553 | −0.0919488 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4909 | −0.807972 | −0.403986 | − | 0.914765i | \(-0.632376\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8050 | −0.824840 | −0.412420 | − | 0.910994i | \(-0.635316\pi\) | ||||
−0.412420 | + | 0.910994i | \(0.635316\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.86645 | 0.632933 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.36107 | −0.214731 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.21530 | −0.331842 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4689 | 0.663439 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.527481 | −0.0332943 | −0.0166472 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166472 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.81849 | 0.177197 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.50348 | −0.0941517 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.54045 | −0.220847 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1096 | −0.628179 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0961008 | 0.00594849 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.3694 | 1.13270 | 0.566352 | − | 0.824163i | \(-0.308354\pi\) | ||||
0.566352 | + | 0.824163i | \(0.308354\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0514913 | 0.00316309 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.57340 | −0.402286 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.8957 | −0.725295 | −0.362647 | − | 0.931926i | \(-0.618127\pi\) | ||||
−0.362647 | + | 0.931926i | \(0.618127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.58733 | −0.460898 | −0.230449 | − | 0.973084i | \(-0.574019\pi\) | ||||
−0.230449 | + | 0.973084i | \(0.574019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.82248 | −0.594484 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.86870 | −0.534802 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1353 | 0.909389 | 0.454695 | − | 0.890647i | \(-0.349748\pi\) | ||||
0.454695 | + | 0.890647i | \(0.349748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.71769 | 0.342309 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.86338 | −0.469090 | −0.234545 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234545 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3069 | 1.20712 | 0.603560 | − | 0.797318i | \(-0.293748\pi\) | ||||
0.603560 | + | 0.797318i | \(0.293748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.909745 | 0.0538887 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.20528 | 0.425314 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2688 | −0.839340 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.27533 | −0.426488 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2096 | −0.654873 | −0.327436 | − | 0.944873i | \(-0.606185\pi\) | ||||
−0.327436 | + | 0.944873i | \(0.606185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.62824 | −0.269466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9373 | −0.634646 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.60257 | −0.439668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.78784 | −0.506523 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.7771 | 0.906373 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.99046 | 0.400272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.11820 | 0.463330 | 0.231665 | − | 0.972796i | \(-0.425583\pi\) | ||||
0.231665 | + | 0.972796i | \(0.425583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1328 | −0.576436 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.83714 | −0.217584 | −0.108792 | − | 0.994065i | \(-0.534698\pi\) | ||||
−0.108792 | + | 0.994065i | \(0.534698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.88873 | −0.276327 | −0.138164 | − | 0.990409i | \(-0.544120\pi\) | ||||
−0.138164 | + | 0.990409i | \(0.544120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.851914 | −0.0479999 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.36341 | 0.525901 | 0.262951 | − | 0.964809i | \(-0.415304\pi\) | ||||
0.262951 | + | 0.964809i | \(0.415304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.186504 | −0.0104422 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.0002 | 1.06049 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.65264 | −0.0919554 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.9223 | 1.32697 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.5410 | −0.693517 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.00326 | 0.110443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.04474 | 0.0574239 | 0.0287120 | − | 0.999588i | \(-0.490859\pi\) | ||||
0.0287120 | + | 0.999588i | \(0.490859\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.56983 | 0.414824 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.50730 | −0.519439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1550 | 1.64265 | 0.821324 | − | 0.570462i | \(-0.193236\pi\) | ||||
0.821324 | + | 0.570462i | \(0.193236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.3802 | 1.32415 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0964 | −0.600903 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.2719 | −0.878599 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.32617 | 0.0713988 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7269 | −1.11268 | −0.556340 | − | 0.830955i | \(-0.687795\pi\) | ||||
−0.556340 | + | 0.830955i | \(0.687795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.1358 | −1.39902 | −0.699509 | − | 0.714624i | \(-0.746598\pi\) | ||||
−0.699509 | + | 0.714624i | \(0.746598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.5022 | 1.57471 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.10887 | 0.271918 | 0.135959 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135959 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.15198 | −0.273439 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.11258 | −0.164735 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.7863 | 0.622059 | 0.311029 | − | 0.950400i | \(-0.399326\pi\) | ||||
0.311029 | + | 0.950400i | \(0.399326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2792 | −0.539519 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.84488 | 0.358277 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5919 | −0.709494 | −0.354747 | − | 0.934962i | \(-0.615433\pi\) | ||||
−0.354747 | + | 0.934962i | \(0.615433\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.39515 | −0.280861 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.106600 | 0.00553438 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.174924 | 0.00905722 | 0.00452861 | − | 0.999990i | \(-0.498558\pi\) | ||||
0.00452861 | + | 0.999990i | \(0.498558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.72168 | −0.450386 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.503074 | 0.0259096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.78000 | 0.348265 | 0.174133 | − | 0.984722i | \(-0.444288\pi\) | ||||
0.174133 | + | 0.984722i | \(0.444288\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.8187 | −0.861647 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7147 | −0.598591 | −0.299296 | − | 0.954160i | \(-0.596752\pi\) | ||||
−0.299296 | + | 0.954160i | \(0.596752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.65332 | 0.0842609 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.58014 | 0.334487 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.3448 | 1.28503 | 0.642515 | − | 0.766273i | \(-0.277891\pi\) | ||||
0.642515 | + | 0.766273i | \(0.277891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.40913 | −0.121835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.6778 | −1.19438 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.642687 | −0.0323371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.5061 | −1.93257 | −0.966284 | − | 0.257480i | \(-0.917108\pi\) | ||||
−0.966284 | + | 0.257480i | \(0.917108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.88340 | 0.0942878 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.1188 | −1.70381 | −0.851905 | − | 0.523697i | \(-0.824552\pi\) | ||||
−0.851905 | + | 0.523697i | \(0.824552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.9313 | 1.49098 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.22543 | −0.160273 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6909 | −0.728199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6675 | 0.725260 | 0.362630 | − | 0.931933i | \(-0.381879\pi\) | ||||
0.362630 | + | 0.931933i | \(0.381879\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.6838 | −1.06958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.58159 | −0.471479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.75313 | 0.233322 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3624 | 0.507448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.1940 | −1.13310 | −0.566550 | − | 0.824027i | \(-0.691722\pi\) | ||||
−0.566550 | + | 0.824027i | \(0.691722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7906 | −0.769588 | −0.384794 | − | 0.923002i | \(-0.625728\pi\) | ||||
−0.384794 | + | 0.923002i | \(0.625728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.50000 | −0.0729323 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.58059 | 0.367713 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4720 | 0.700348 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.2736 | −0.689138 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.55450 | 0.171214 | 0.0856072 | − | 0.996329i | \(-0.472717\pi\) | ||||
0.0856072 | + | 0.996329i | \(0.472717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.44653 | 0.261743 | 0.130872 | − | 0.991399i | \(-0.458222\pi\) | ||||
0.130872 | + | 0.991399i | \(0.458222\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0877551 | −0.00420753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.45774 | 0.0697333 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1089 | 0.816565 | 0.408283 | − | 0.912856i | \(-0.366128\pi\) | ||||
0.408283 | + | 0.912856i | \(0.366128\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.21018 | 0.248104 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1017 | −0.622482 | −0.311241 | − | 0.950331i | \(-0.600745\pi\) | ||||
−0.311241 | + | 0.950331i | \(0.600745\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.98449 | −0.141478 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.6614 | 1.16644 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.0013 | −1.27427 | −0.637135 | − | 0.770752i | \(-0.719881\pi\) | ||||
−0.637135 | + | 0.770752i | \(0.719881\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4704 | 0.493034 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0814 | 0.567635 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.45965 | −0.209071 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2455 | 1.18093 | 0.590467 | − | 0.807062i | \(-0.298944\pi\) | ||||
0.590467 | + | 0.807062i | \(0.298944\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.34874 | 0.436362 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.3158 | −1.55167 | −0.775837 | − | 0.630934i | \(-0.782672\pi\) | ||||
−0.775837 | + | 0.630934i | \(0.782672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6210 | 0.772444 | 0.386222 | − | 0.922406i | \(-0.373780\pi\) | ||||
0.386222 | + | 0.922406i | \(0.373780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.22115 | −0.242125 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.87012 | 0.132813 | 0.0664067 | − | 0.997793i | \(-0.478847\pi\) | ||||
0.0664067 | + | 0.997793i | \(0.478847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6825 | −0.908852 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.1197 | 1.48000 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.7701 | −0.587172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.58695 | −0.210464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0798195 | −0.00365468 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.75270 | −0.0800828 | −0.0400414 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400414 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.6270 | 1.80684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.74551 | 0.124925 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.30318 | −0.149990 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.1357 | −0.640551 | −0.320276 | − | 0.947324i | \(-0.603776\pi\) | ||||
−0.320276 | + | 0.947324i | \(0.603776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.1625 | −1.04745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8121 | −0.939236 | −0.469618 | − | 0.882870i | \(-0.655608\pi\) | ||||
−0.469618 | + | 0.882870i | \(0.655608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.159416 | 0.00717972 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.23797 | −0.0556425 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6659 | −0.478430 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.2900 | 1.93793 | 0.968963 | − | 0.247205i | \(-0.0795121\pi\) | ||||
0.968963 | + | 0.247205i | \(0.0795121\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.1280 | −1.48005 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.5372 | 1.45076 | 0.725381 | − | 0.688348i | \(-0.241664\pi\) | ||||
0.725381 | + | 0.688348i | \(0.241664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.16321 | 0.318759 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0997 | 0.892658 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3895 | 0.637804 | 0.318902 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318902 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1706 | 0.626870 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.60055 | −0.202724 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.91106 | 0.128028 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.2110 | −1.37001 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0622 | −0.791319 | −0.395659 | − | 0.918397i | \(-0.629484\pi\) | ||||
−0.395659 | + | 0.918397i | \(0.629484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.9305 | −0.740319 | −0.370160 | − | 0.928968i | \(-0.620697\pi\) | ||||
−0.370160 | + | 0.928968i | \(0.620697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.63906 | −0.377039 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.48473 | 0.413161 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8750 | −0.907608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.17448 | 0.311346 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.2429 | −1.22333 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.62657 | 0.372959 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9653 | 0.516340 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1114 | −0.435531 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.7390 | −0.504700 | −0.252350 | − | 0.967636i | \(-0.581203\pi\) | ||||
−0.252350 | + | 0.967636i | \(0.581203\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.4837 | −1.05070 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.69390 | −0.243900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8322 | −0.634177 | −0.317089 | − | 0.948396i | \(-0.602705\pi\) | ||||
−0.317089 | + | 0.948396i | \(0.602705\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8363 | −0.462481 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0964612 | −0.00410938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.33052 | −0.0565795 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.91244 | −0.293417 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0955 | 1.65653 | 0.828264 | − | 0.560338i | \(-0.189329\pi\) | ||||
0.828264 | + | 0.560338i | \(0.189329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4461 | 1.45691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.52308 | −0.190965 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.43413 | −0.0604413 | −0.0302207 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302207 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0692 | 0.465685 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.67744 | −0.280426 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.7102 | −1.53897 | −0.769486 | − | 0.638664i | \(-0.779487\pi\) | ||||
−0.769486 | + | 0.638664i | \(0.779487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.6097 | −1.65762 | −0.828808 | − | 0.559534i | \(-0.810980\pi\) | ||||
−0.828808 | + | 0.559534i | \(0.810980\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4934 | 0.689022 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.68660 | −0.278850 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8492 | 0.576548 | 0.288274 | − | 0.957548i | \(-0.406919\pi\) | ||||
0.288274 | + | 0.957548i | \(0.406919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6220 | 0.607670 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.84015 | 0.408238 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.154907 | 0.00641557 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.33928 | 0.138062 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.1456 | 1.36806 | 0.684032 | − | 0.729452i | \(-0.260225\pi\) | ||||
0.684032 | + | 0.729452i | \(0.260225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.73913 | −0.236477 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.47244 | −0.348510 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.5972 | −0.969022 | −0.484511 | − | 0.874785i | \(-0.661002\pi\) | ||||
−0.484511 | + | 0.874785i | \(0.661002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.41319 | −0.0579350 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.66531 | −0.272793 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6611 | −1.70223 | −0.851114 | − | 0.524981i | \(-0.824072\pi\) | ||||
−0.851114 | + | 0.524981i | \(0.824072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.57740 | −0.268298 | −0.134149 | − | 0.990961i | \(-0.542830\pi\) | ||||
−0.134149 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.7378 | 0.600169 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.66702 | −0.189741 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3654 | 1.15132 | 0.575658 | − | 0.817690i | \(-0.304746\pi\) | ||||
0.575658 | + | 0.817690i | \(0.304746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.181675 | −0.00736183 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.85226 | −0.317669 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.06554 | 0.285374 | 0.142687 | − | 0.989768i | \(-0.454426\pi\) | ||||
0.142687 | + | 0.989768i | \(0.454426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.92662 | 0.198661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.3501 | 1.78547 | 0.892733 | − | 0.450586i | \(-0.148785\pi\) | ||||
0.892733 | + | 0.450586i | \(0.148785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5118 | 0.744050 | 0.372025 | − | 0.928223i | \(-0.378664\pi\) | ||||
0.372025 | + | 0.928223i | \(0.378664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.24623 | −0.330910 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.17862 | −0.247541 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9749 | 0.758996 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.73688 | 0.109300 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.5571 | 0.500686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6945 | 0.465550 | 0.232775 | − | 0.972531i | \(-0.425219\pi\) | ||||
0.232775 | + | 0.972531i | \(0.425219\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.1099 | 0.958282 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.63609 | −0.303029 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.2745 | 1.08066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.98637 | 0.315936 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.8803 | 1.33819 | 0.669095 | − | 0.743177i | \(-0.266682\pi\) | ||||
0.669095 | + | 0.743177i | \(0.266682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.1523 | 1.70176 | 0.850881 | − | 0.525359i | \(-0.176069\pi\) | ||||
0.850881 | + | 0.525359i | \(0.176069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00869 | −0.236592 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.4426 | −1.39339 | −0.696697 | − | 0.717366i | \(-0.745348\pi\) | ||||
−0.696697 | + | 0.717366i | \(0.745348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9236 | −0.546549 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.8091 | −0.423641 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0569 | 1.52841 | 0.764207 | − | 0.644971i | \(-0.223130\pi\) | ||||
0.764207 | + | 0.644971i | \(0.223130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7503 | −0.420048 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.6106 | −0.413960 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.2655 | 1.21793 | 0.608965 | − | 0.793197i | \(-0.291585\pi\) | ||||
0.608965 | + | 0.793197i | \(0.291585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8381 | 0.810510 | 0.405255 | − | 0.914204i | \(-0.367183\pi\) | ||||
0.405255 | + | 0.914204i | \(0.367183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.2005 | 0.473829 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.855108 | 0.0331597 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.140616 | −0.00544466 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.7351 | 0.956315 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0301 | 0.811858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.2747 | −1.51393 | −0.756964 | − | 0.653456i | \(-0.773318\pi\) | ||||
−0.756964 | + | 0.653456i | \(0.773318\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9477 | 0.998727 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.38317 | 0.130026 | 0.0650129 | − | 0.997884i | \(-0.479291\pi\) | ||||
0.0650129 | + | 0.997884i | \(0.479291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.83840 | −0.262434 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.6584 | 1.09819 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.2944 | 0.814809 | 0.407405 | − | 0.913248i | \(-0.366434\pi\) | ||||
0.407405 | + | 0.913248i | \(0.366434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.84499 | −0.376158 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.4276 | −0.855668 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.417844 | −0.0159186 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.0941 | −1.44917 | −0.724584 | − | 0.689187i | \(-0.757968\pi\) | ||||
−0.724584 | + | 0.689187i | \(0.757968\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.56290 | −0.0973565 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.70478 | 0.178462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.94969 | −0.338994 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.5580 | 1.38275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.91662 | −0.185698 | −0.0928490 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928490 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.59822 | −0.286572 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.36973 | 0.0515871 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8296 | 0.557725 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0735 | −0.979212 | −0.489606 | − | 0.871944i | \(-0.662859\pi\) | ||||
−0.489606 | + | 0.871944i | \(0.662859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.996264 | 0.0373628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.36618 | −0.313316 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.48059 | −0.242360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.6813 | −0.660322 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.73114 | 0.176442 | 0.0882209 | − | 0.996101i | \(-0.471882\pi\) | ||||
0.0882209 | + | 0.996101i | \(0.471882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.52427 | −0.354702 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.1259 | −0.674108 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.442463 | 0.0164327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.3031 | −1.68020 | −0.840099 | − | 0.542434i | \(-0.817503\pi\) | ||||
−0.840099 | + | 0.542434i | \(0.817503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0223 | 1.07490 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9154 | 0.403720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.7436 | −1.94813 | −0.974065 | − | 0.226268i | \(-0.927347\pi\) | ||||
−0.974065 | + | 0.226268i | \(0.927347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.75771 | −0.175491 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.6018 | −1.05356 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6112 | −0.684622 | −0.342311 | − | 0.939587i | \(-0.611210\pi\) | ||||
−0.342311 | + | 0.939587i | \(0.611210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.38243 | −0.271201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.405748 | 0.0148855 | 0.00744273 | − | 0.999972i | \(-0.497631\pi\) | ||||
0.00744273 | + | 0.999972i | \(0.497631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1969 | 0.410221 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.36808 | −0.269584 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.8591 | 0.652558 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4223 | 0.635749 | 0.317874 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317874 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.746668 | −0.0272101 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.48526 | 0.199629 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.1639 | −0.478450 | −0.239225 | − | 0.970964i | \(-0.576893\pi\) | ||||
−0.239225 | + | 0.970964i | \(0.576893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.98967 | 0.144816 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4807 | 1.03242 | 0.516212 | − | 0.856461i | \(-0.327342\pi\) | ||||
0.516212 | + | 0.856461i | \(0.327342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.7878 | −0.426747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.05816 | 0.0382580 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.5574 | 1.35612 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.7191 | 1.46837 | 0.734184 | − | 0.678951i | \(-0.237565\pi\) | ||||
0.734184 | + | 0.678951i | \(0.237565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.01163 | −0.180489 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.7812 | 0.927286 | 0.463643 | − | 0.886022i | \(-0.346542\pi\) | ||||
0.463643 | + | 0.886022i | \(0.346542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.3251 | 0.945627 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.3105 | −0.513385 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.41539 | 0.194026 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.4992 | −0.554606 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.545666 | 0.0195005 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.5831 | 0.520493 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.38688 | −0.192021 | −0.0960107 | − | 0.995380i | \(-0.530608\pi\) | ||||
−0.0960107 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.0025 | 0.925713 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.9160 | 0.814800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.7264 | −2.01441 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0728877 | 0.00258506 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.2002 | −0.715526 | −0.357763 | − | 0.933812i | \(-0.616460\pi\) | ||||
−0.357763 | + | 0.933812i | \(0.616460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.48825 | −0.0880280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.62641 | 0.163466 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.5922 | 0.726682 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.24653 | 0.0439343 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8388 | −0.592754 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.95846 | 0.209488 | 0.104744 | − | 0.994499i | \(-0.466598\pi\) | ||||
0.104744 | + | 0.994499i | \(0.466598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1558 | −0.532193 | −0.266096 | − | 0.963946i | \(-0.585734\pi\) | ||||
−0.266096 | + | 0.963946i | \(0.585734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.7401 | −0.376673 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5163 | −0.368372 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.60481 | −0.231073 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.91314 | 0.241565 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2340 | 0.357169 | 0.178584 | − | 0.983925i | \(-0.442848\pi\) | ||||
0.178584 | + | 0.983925i | \(0.442848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.1399 | −1.36433 | −0.682165 | − | 0.731199i | \(-0.738961\pi\) | ||||
−0.682165 | + | 0.731199i | \(0.738961\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5539 | −0.437072 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.1583 | −1.46599 | −0.732994 | − | 0.680235i | \(-0.761878\pi\) | ||||
−0.732994 | + | 0.680235i | \(0.761878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4950 | 1.30226 | 0.651128 | − | 0.758968i | \(-0.274296\pi\) | ||||
0.651128 | + | 0.758968i | \(0.274296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.4245 | 0.743207 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.64284 | 0.299457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0409 | −0.520513 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.4654 | 1.12217 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5279 | −0.674178 | −0.337089 | − | 0.941473i | \(-0.609442\pi\) | ||||
−0.337089 | + | 0.941473i | \(0.609442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9907 | −0.999679 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1309 | −0.383368 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.12574 | 0.313935 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.66188 | −0.331986 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.7451 | 0.986529 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0763 | −0.379689 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6923 | 1.05088 | 0.525442 | − | 0.850829i | \(-0.323900\pi\) | ||||
0.525442 | + | 0.850829i | \(0.323900\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.640286 | −0.0218973 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.2942 | −0.419960 | −0.209980 | − | 0.977706i | \(-0.567340\pi\) | ||||
−0.209980 | + | 0.977706i | \(0.567340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4783 | 0.835190 | 0.417595 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417595 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.1993 | 0.347592 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.1764 | −0.618731 | −0.309366 | − | 0.950943i | \(-0.600117\pi\) | ||||
−0.309366 | + | 0.950943i | \(0.600117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1706 | −0.481814 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.1979 | −0.685958 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.93346 | −0.0655882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77.1502 | 2.61413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.12044 | 0.173301 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.19788 | −0.277139 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.2526 | 1.08909 | 0.544547 | − | 0.838730i | \(-0.316702\pi\) | ||||
0.544547 | + | 0.838730i | \(0.316702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.8676 | −0.535201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.3656 | −1.52841 | −0.764204 | − | 0.644975i | \(-0.776868\pi\) | ||||
−0.764204 | + | 0.644975i | \(0.776868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.3669 | −0.685402 | −0.342701 | − | 0.939444i | \(-0.611342\pi\) | ||||
−0.342701 | + | 0.939444i | \(0.611342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.55142 | −0.220224 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.0111 | −1.81351 | −0.906757 | − | 0.421654i | \(-0.861450\pi\) | ||||
−0.906757 | + | 0.421654i | \(0.861450\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.8086 | −0.530203 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.70340 | −0.325076 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.50562 | 0.0503837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.43253 | 0.181589 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.7617 | −0.359322 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.553603 | 0.0184637 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.132408 | −0.00441114 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.4395 | −0.413960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1162 | −0.369515 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.58408 | 0.285030 | 0.142515 | − | 0.989793i | \(-0.454481\pi\) | ||||
0.142515 | + | 0.989793i | \(0.454481\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1041 | −0.368299 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.7805 | −1.84809 | −0.924045 | − | 0.382283i | \(-0.875138\pi\) | ||||
−0.924045 | + | 0.382283i | \(0.875138\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.2993 | 0.473239 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.89523 | 0.327126 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.2557 | −0.734949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2970 | 0.768497 | 0.384248 | − | 0.923230i | \(-0.374461\pi\) | ||||
0.384248 | + | 0.923230i | \(0.374461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.4916 | 0.378660 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.8075 | 1.37611 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.8527 | 1.14595 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.13156 | 0.234231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.7079 | 1.00749 | 0.503746 | − | 0.863852i | \(-0.331955\pi\) | ||||
0.503746 | + | 0.863852i | \(0.331955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.22971 | −0.171397 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.43161 | −0.177823 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.05359 | −0.0671596 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.54260 | 0.311743 | 0.155872 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155872 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.92017 | −0.225831 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.1446 | 0.558899 | 0.279450 | − | 0.960160i | \(-0.409848\pi\) | ||||
0.279450 | + | 0.960160i | \(0.409848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.89424 | 0.257072 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.83722 | −0.157355 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.6790 | 0.899446 | 0.449723 | − | 0.893168i | \(-0.351523\pi\) | ||||
0.449723 | + | 0.893168i | \(0.351523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.5451 | −1.80307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.2542 | 0.429798 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.7690 | 1.51500 | 0.757498 | − | 0.652837i | \(-0.226421\pi\) | ||||
0.757498 | + | 0.652837i | \(0.226421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.48841 | 0.242319 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.264003 | −0.00853399 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.3816 | −0.658155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.93764 | 0.0625045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.3725 | −0.430923 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.63875 | 0.213709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6617 | 0.793066 | 0.396533 | − | 0.918021i | \(-0.370213\pi\) | ||||
0.396533 | + | 0.918021i | \(0.370213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.33937 | −0.0751514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.9613 | −1.12196 | −0.560981 | − | 0.827828i | \(-0.689576\pi\) | ||||
−0.560981 | + | 0.827828i | \(0.689576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.74005 | 0.312252 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33.8629 | 1.08448 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.8874 | −1.27611 | −0.638056 | − | 0.769990i | \(-0.720261\pi\) | ||||
−0.638056 | + | 0.769990i | \(0.720261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.97854 | −0.286955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.82643 | 0.281806 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.4845 | 0.812831 | 0.406415 | − | 0.913688i | \(-0.366779\pi\) | ||||
0.406415 | + | 0.913688i | \(0.366779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.84670 | −0.122566 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.83568 | 0.0902607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.62812 | −0.306156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3321 | −0.328211 | −0.164106 | − | 0.986443i | \(-0.552474\pi\) | ||||
−0.164106 | + | 0.986443i | \(0.552474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.47886 | 0.0469302 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.02622 | −0.0959375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.1889 | −1.08277 | −0.541387 | − | 0.840774i | \(-0.682100\pi\) | ||||
−0.541387 | + | 0.840774i | \(0.682100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.9820 | 1.35989 |
(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 | 6004.2.a.g.1.21 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.21 | ✓ | 27 | 1.1 | even | 1 | trivial |