Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −2.91827 | −1.68486 | −0.842432 | − | 0.538803i | \(-0.818877\pi\) | ||||
−0.842432 | + | 0.538803i | \(0.818877\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.31238 | −1.62993 | −0.814963 | − | 0.579513i | \(-0.803243\pi\) | ||||
−0.814963 | + | 0.579513i | \(0.803243\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.51629 | 1.83876 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.32037 | 1.00113 | 0.500564 | − | 0.865699i | \(-0.333126\pi\) | ||||
0.500564 | + | 0.865699i | \(0.333126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.27795 | 1.46384 | 0.731920 | − | 0.681391i | \(-0.238625\pi\) | ||||
0.731920 | + | 0.681391i | \(0.238625\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.91827 | 0.753494 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.57087 | 1.35113 | 0.675567 | − | 0.737298i | \(-0.263899\pi\) | ||||
0.675567 | + | 0.737298i | \(0.263899\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.74798 | 0.630429 | 0.315214 | − | 0.949020i | \(-0.397924\pi\) | ||||
0.315214 | + | 0.949020i | \(0.397924\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.5847 | 2.74620 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.03475 | 0.215760 | 0.107880 | − | 0.994164i | \(-0.465594\pi\) | ||||
0.107880 | + | 0.994164i | \(0.465594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.34323 | −1.41320 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.925860 | −0.171928 | −0.0859639 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859639 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.47043 | 1.52133 | 0.760667 | − | 0.649142i | \(-0.224872\pi\) | ||||
0.760667 | + | 0.649142i | \(0.224872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.68973 | −1.68677 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.31238 | 0.728925 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.78281 | 0.293093 | 0.146546 | − | 0.989204i | \(-0.453184\pi\) | ||||
0.146546 | + | 0.989204i | \(0.453184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4025 | −2.46637 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.98377 | 1.55920 | 0.779601 | − | 0.626276i | \(-0.215422\pi\) | ||||
0.779601 | + | 0.626276i | \(0.215422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.674120 | 0.102802 | 0.0514011 | − | 0.998678i | \(-0.483631\pi\) | ||||
0.0514011 | + | 0.998678i | \(0.483631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.51629 | −0.822321 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41456 | 0.206335 | 0.103167 | − | 0.994664i | \(-0.467102\pi\) | ||||
0.103167 | + | 0.994664i | \(0.467102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.5966 | 1.65666 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.2573 | −2.27648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.67960 | 0.368071 | 0.184036 | − | 0.982920i | \(-0.441084\pi\) | ||||
0.184036 | + | 0.982920i | \(0.441084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.32037 | −0.447718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.01933 | −1.06219 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9693 | 1.68846 | 0.844232 | − | 0.535977i | \(-0.180057\pi\) | ||||
0.844232 | + | 0.535977i | \(0.180057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.37423 | 0.688100 | 0.344050 | − | 0.938951i | \(-0.388201\pi\) | ||||
0.344050 | + | 0.938951i | \(0.388201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −23.7884 | −2.99705 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.27795 | −0.654649 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.52502 | 1.16367 | 0.581833 | − | 0.813308i | \(-0.302336\pi\) | ||||
0.581833 | + | 0.813308i | \(0.302336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.01968 | −0.363526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.09924 | −0.367812 | −0.183906 | − | 0.982944i | \(-0.558874\pi\) | ||||
−0.183906 | + | 0.982944i | \(0.558874\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.83066 | −0.682427 | −0.341214 | − | 0.939986i | \(-0.610838\pi\) | ||||
−0.341214 | + | 0.939986i | \(0.610838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.91827 | −0.336973 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.3187 | −1.63177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9855 | −1.46098 | −0.730490 | − | 0.682923i | \(-0.760708\pi\) | ||||
−0.730490 | + | 0.682923i | \(0.760708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.88062 | 0.542292 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.48897 | −1.04155 | −0.520775 | − | 0.853694i | \(-0.674357\pi\) | ||||
−0.520775 | + | 0.853694i | \(0.674357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.57087 | −0.604246 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.70191 | 0.289675 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6686 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.7605 | −2.38595 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.7190 | −2.56324 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.74798 | −0.281936 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.14852 | −0.116614 | −0.0583072 | − | 0.998299i | \(-0.518570\pi\) | ||||
−0.0583072 | + | 0.998299i | \(0.518570\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.3161 | 1.84084 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4855 | 1.24235 | 0.621177 | − | 0.783670i | \(-0.286655\pi\) | ||||
0.621177 | + | 0.783670i | \(0.286655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.16985 | 0.509400 | 0.254700 | − | 0.967020i | \(-0.418023\pi\) | ||||
0.254700 | + | 0.967020i | \(0.418023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.5847 | −1.22814 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9665 | −1.25352 | −0.626758 | − | 0.779214i | \(-0.715618\pi\) | ||||
−0.626758 | + | 0.779214i | \(0.715618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7096 | 1.02579 | 0.512896 | − | 0.858451i | \(-0.328573\pi\) | ||||
0.512896 | + | 0.858451i | \(0.328573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.20273 | −0.493821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4369 | −1.64033 | −0.820163 | − | 0.572130i | \(-0.806117\pi\) | ||||
−0.820163 | + | 0.572130i | \(0.806117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.03475 | −0.0964909 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 29.1147 | 2.69166 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.0237 | −2.20225 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0248507 | 0.00225915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.1353 | −2.62704 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8509 | 1.67275 | 0.836373 | − | 0.548161i | \(-0.184672\pi\) | ||||
0.836373 | + | 0.548161i | \(0.184672\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.96726 | −0.173208 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.1817 | −1.50118 | −0.750588 | − | 0.660770i | \(-0.770230\pi\) | ||||
−0.750588 | + | 0.660770i | \(0.770230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.8503 | −1.02755 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.34323 | 0.632004 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.91551 | 0.334524 | 0.167262 | − | 0.985912i | \(-0.446507\pi\) | ||||
0.167262 | + | 0.985912i | \(0.446507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.6985 | −1.92527 | −0.962633 | − | 0.270810i | \(-0.912709\pi\) | ||||
−0.962633 | + | 0.270810i | \(0.912709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.12806 | −0.347645 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.5247 | 1.46549 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.925860 | 0.0768885 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33.8420 | −2.79124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.04715 | 0.0857862 | 0.0428931 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428931 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.12153 | 0.416784 | 0.208392 | − | 0.978045i | \(-0.433177\pi\) | ||||
0.208392 | + | 0.978045i | \(0.433177\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 30.7306 | 2.48442 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.47043 | −0.680362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.28082 | −0.261838 | −0.130919 | − | 0.991393i | \(-0.541793\pi\) | ||||
−0.130919 | + | 0.991393i | \(0.541793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.81979 | −0.620150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.46223 | −0.351673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6811 | −0.993262 | −0.496631 | − | 0.867962i | \(-0.665430\pi\) | ||||
−0.496631 | + | 0.867962i | \(0.665430\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.68973 | 0.754345 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.21551 | −0.713118 | −0.356559 | − | 0.934273i | \(-0.616050\pi\) | ||||
−0.356559 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8567 | 1.14283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.1586 | 1.15921 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6937 | 0.813027 | 0.406514 | − | 0.913645i | \(-0.366744\pi\) | ||||
0.406514 | + | 0.913645i | \(0.366744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.31238 | −0.325985 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −37.8480 | −2.84483 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.412909 | −0.0308623 | −0.0154311 | − | 0.999881i | \(-0.504912\pi\) | ||||
−0.0154311 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.46717 | 0.629360 | 0.314680 | − | 0.949198i | \(-0.398103\pi\) | ||||
0.314680 | + | 0.949198i | \(0.398103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.6835 | −1.15935 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.78281 | −0.131075 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.4973 | 1.35266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 31.6668 | 2.30342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.9445 | 0.791917 | 0.395958 | − | 0.918269i | \(-0.370412\pi\) | ||||
0.395958 | + | 0.918269i | \(0.370412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1178 | 0.872260 | 0.436130 | − | 0.899884i | \(-0.356349\pi\) | ||||
0.436130 | + | 0.899884i | \(0.356349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.4025 | 1.10299 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.82132 | −0.201010 | −0.100505 | − | 0.994937i | \(-0.532046\pi\) | ||||
−0.100505 | + | 0.994937i | \(0.532046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.85412 | −0.485875 | −0.242938 | − | 0.970042i | \(-0.578111\pi\) | ||||
−0.242938 | + | 0.970042i | \(0.578111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.7966 | −1.96062 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.99266 | 0.280230 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.98377 | −0.697297 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.70798 | 0.396732 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.12429 | 0.631140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.5752 | 1.76067 | 0.880336 | − | 0.474350i | \(-0.157317\pi\) | ||||
0.880336 | + | 0.474350i | \(0.157317\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.04442 | 0.619714 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.674120 | −0.0459746 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.5277 | −2.47966 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.0154 | 1.14980 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.4028 | 1.97784 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.59665 | 0.173885 | 0.0869424 | − | 0.996213i | \(-0.472290\pi\) | ||||
0.0869424 | + | 0.996213i | \(0.472290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.51629 | 0.367753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8232 | 0.718360 | 0.359180 | − | 0.933268i | \(-0.383056\pi\) | ||||
0.359180 | + | 0.933268i | \(0.383056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9657 | 0.988962 | 0.494481 | − | 0.869188i | \(-0.335358\pi\) | ||||
0.494481 | + | 0.869188i | \(0.335358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.7858 | 2.74930 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.54068 | −0.362982 | −0.181491 | − | 0.983393i | \(-0.558092\pi\) | ||||
−0.181491 | + | 0.983393i | \(0.558092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41456 | −0.0922756 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.8951 | 2.46155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.12190 | −0.395993 | −0.197996 | − | 0.980203i | \(-0.563443\pi\) | ||||
−0.197996 | + | 0.980203i | \(0.563443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6578 | −1.07303 | −0.536513 | − | 0.843892i | \(-0.680259\pi\) | ||||
−0.536513 | + | 0.843892i | \(0.680259\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.78670 | 0.499517 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.5966 | −0.740880 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.5037 | 0.922847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.6914 | 1.75487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.31022 | −0.145820 | −0.0729098 | − | 0.997339i | \(-0.523229\pi\) | ||||
−0.0729098 | + | 0.997339i | \(0.523229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.43575 | 0.216004 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.2573 | 1.01807 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.78628 | 0.236182 | 0.118091 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118091 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.68816 | −0.477719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.10732 | −0.316135 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.183960 | 0.0113434 | 0.00567172 | − | 0.999984i | \(-0.498195\pi\) | ||||
0.00567172 | + | 0.999984i | \(0.498195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.67960 | −0.164606 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −42.8070 | −2.61975 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.72726 | −0.593081 | −0.296541 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296541 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.31224 | −0.383441 | −0.191721 | − | 0.981450i | \(-0.561407\pi\) | ||||
−0.191721 | + | 0.981450i | \(0.561407\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66.4213 | 4.02000 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.32037 | 0.200226 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.3757 | 0.803666 | 0.401833 | − | 0.915713i | \(-0.368373\pi\) | ||||
0.401833 | + | 0.915713i | \(0.368373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46.7254 | 2.79738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.0312 | 1.73186 | 0.865928 | − | 0.500168i | \(-0.166729\pi\) | ||||
0.865928 | + | 0.500168i | \(0.166729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.3119 | 0.791308 | 0.395654 | − | 0.918400i | \(-0.370518\pi\) | ||||
0.395654 | + | 0.918400i | \(0.370518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.01933 | 0.475024 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −43.0538 | −2.54139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0346 | 0.825564 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.35168 | 0.196479 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.298727 | −0.0174518 | −0.00872591 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872591 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9693 | −0.755104 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.3822 | −1.41480 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.46135 | 0.315838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.90706 | −0.167560 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −36.4360 | −2.09320 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.37423 | −0.307728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9705 | −1.02563 | −0.512814 | − | 0.858500i | \(-0.671397\pi\) | ||||
−0.512814 | + | 0.858500i | \(0.671397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0870 | −0.858270 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.09599 | −0.459081 | −0.229541 | − | 0.973299i | \(-0.573722\pi\) | ||||
−0.229541 | + | 0.973299i | \(0.573722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0964 | 0.796773 | 0.398386 | − | 0.917218i | \(-0.369570\pi\) | ||||
0.398386 | + | 0.917218i | \(0.369570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.7884 | 1.34032 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.7475 | 1.89545 | 0.947723 | − | 0.319093i | \(-0.103378\pi\) | ||||
0.947723 | + | 0.319093i | \(0.103378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.07420 | −0.172122 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 37.8396 | 2.11200 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3086 | 0.851794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.27795 | 0.292768 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.2534 | −1.72832 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.10011 | −0.336310 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5670 | 1.79005 | 0.895023 | − | 0.446021i | \(-0.147159\pi\) | ||||
0.895023 | + | 0.446021i | \(0.147159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.83452 | 0.538928 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.52502 | −0.520408 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2884 | −1.10518 | −0.552591 | − | 0.833453i | \(-0.686361\pi\) | ||||
−0.552591 | + | 0.833453i | \(0.686361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 50.8856 | 2.76372 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.1250 | 1.52305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8223 | −1.07030 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.01968 | 0.162574 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.5164 | −0.618234 | −0.309117 | − | 0.951024i | \(-0.600033\pi\) | ||||
−0.309117 | + | 0.951024i | \(0.600033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0146 | −0.589599 | −0.294800 | − | 0.955559i | \(-0.595253\pi\) | ||||
−0.294800 | + | 0.955559i | \(0.595253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −38.7572 | −2.06870 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.1217 | −0.751624 | −0.375812 | − | 0.926696i | \(-0.622636\pi\) | ||||
−0.375812 | + | 0.926696i | \(0.622636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.09924 | 0.164491 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 70.1076 | 3.71049 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.6604 | 1.61819 | 0.809096 | − | 0.587676i | \(-0.199957\pi\) | ||||
0.809096 | + | 0.587676i | \(0.199957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4486 | −0.602560 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0725209 | −0.00380636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.83066 | 0.305191 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.65178 | −0.451619 | −0.225810 | − | 0.974171i | \(-0.572503\pi\) | ||||
−0.225810 | + | 0.974171i | \(0.572503\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 55.0734 | 2.86701 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5554 | −0.599929 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6273 | −0.653818 | −0.326909 | − | 0.945056i | \(-0.606007\pi\) | ||||
−0.326909 | + | 0.945056i | \(0.606007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.91827 | 0.150699 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.88664 | −0.251675 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4358 | −0.844252 | −0.422126 | − | 0.906537i | \(-0.638716\pi\) | ||||
−0.422126 | + | 0.906537i | \(0.638716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −55.0120 | −2.81835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2167 | −0.930832 | −0.465416 | − | 0.885092i | \(-0.654095\pi\) | ||||
−0.465416 | + | 0.885092i | \(0.654095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.3187 | 0.729748 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.71864 | 0.189029 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.38413 | 0.0701784 | 0.0350892 | − | 0.999384i | \(-0.488828\pi\) | ||||
0.0350892 | + | 0.999384i | \(0.488828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.76445 | 0.291521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 50.1410 | 2.52928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9855 | 0.653370 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.235691 | 0.0118290 | 0.00591450 | − | 0.999983i | \(-0.498117\pi\) | ||||
0.00591450 | + | 0.999983i | \(0.498117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 34.5824 | 1.73129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.7065 | 2.22699 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.88062 | −0.242520 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.91959 | 0.293423 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.86214 | −0.190970 | −0.0954852 | − | 0.995431i | \(-0.530440\pi\) | ||||
−0.0954852 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4265 | −0.563628 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −55.9287 | −2.75207 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.48897 | 0.465795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 66.2405 | 3.24381 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.9451 | −1.26750 | −0.633751 | − | 0.773537i | \(-0.718486\pi\) | ||||
−0.633751 | + | 0.773537i | \(0.718486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.5329 | 1.58556 | 0.792778 | − | 0.609510i | \(-0.208634\pi\) | ||||
0.792778 | + | 0.609510i | \(0.208634\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.80312 | 0.379401 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.57087 | 0.270227 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.1757 | −1.12155 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −51.1419 | −2.46915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.18644 | −0.442495 | −0.221248 | − | 0.975218i | \(-0.571013\pi\) | ||||
−0.221248 | + | 0.975218i | \(0.571013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7717 | −1.14239 | −0.571197 | − | 0.820813i | \(-0.693521\pi\) | ||||
−0.571197 | + | 0.820813i | \(0.693521\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.70191 | −0.129547 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.84347 | 0.136021 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.2561 | 1.15768 | 0.578840 | − | 0.815441i | \(-0.303506\pi\) | ||||
0.578840 | + | 0.815441i | \(0.303506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63.9703 | 3.04621 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.10423 | 0.385044 | 0.192522 | − | 0.981293i | \(-0.438333\pi\) | ||||
0.192522 | + | 0.981293i | \(0.438333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6686 | −0.695360 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.05588 | −0.144538 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0286 | −0.803629 | −0.401814 | − | 0.915721i | \(-0.631620\pi\) | ||||
−0.401814 | + | 0.915721i | \(0.631620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.1498 | 1.56096 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.9460 | −0.702225 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.7605 | 1.06703 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9279 | −0.885412 | −0.442706 | − | 0.896667i | \(-0.645981\pi\) | ||||
−0.442706 | + | 0.896667i | \(0.645981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −40.9081 | −1.90943 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.2886 | −1.73671 | −0.868353 | − | 0.495947i | \(-0.834821\pi\) | ||||
−0.868353 | + | 0.495947i | \(0.834821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0510 | 1.44306 | 0.721531 | − | 0.692382i | \(-0.243439\pi\) | ||||
0.721531 | + | 0.692382i | \(0.243439\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.7190 | 1.14632 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.65892 | −0.123040 | −0.0615201 | − | 0.998106i | \(-0.519595\pi\) | ||||
−0.0615201 | + | 0.998106i | \(0.519595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −41.0755 | −1.89669 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.57433 | 0.441162 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.23833 | 0.102918 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.74798 | 0.126086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.7815 | 0.676796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3789 | 1.20528 | 0.602642 | − | 0.798012i | \(-0.294115\pi\) | ||||
0.602642 | + | 0.798012i | \(0.294115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.40959 | 0.429040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.0220 | 0.592521 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.14852 | 0.0521515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2087 | 0.462600 | 0.231300 | − | 0.972882i | \(-0.425702\pi\) | ||||
0.231300 | + | 0.972882i | \(0.425702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.0069 | 1.67351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.9047 | −1.75574 | −0.877872 | − | 0.478896i | \(-0.841037\pi\) | ||||
−0.877872 | + | 0.478896i | \(0.841037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.15784 | −0.232298 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.3161 | −0.823249 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3651 | 0.599507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7854 | −1.10955 | −0.554774 | − | 0.832001i | \(-0.687195\pi\) | ||||
−0.554774 | + | 0.832001i | \(0.687195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.8934 | 1.20151 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.3530 | 1.39796 | 0.698982 | − | 0.715140i | \(-0.253637\pi\) | ||||
0.698982 | + | 0.715140i | \(0.253637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4855 | −0.555597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43.3560 | −1.92551 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.4976 | −1.92800 | −0.963999 | − | 0.265905i | \(-0.914329\pi\) | ||||
−0.963999 | + | 0.265905i | \(0.914329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.1440 | 1.11231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.1790 | −0.890925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.16985 | −0.227811 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.69686 | 0.206567 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.2071 | −1.36984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5220 | 0.811462 | 0.405731 | − | 0.913993i | \(-0.367017\pi\) | ||||
0.405731 | + | 0.913993i | \(0.367017\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6845 | −0.817017 | −0.408509 | − | 0.912754i | \(-0.633951\pi\) | ||||
−0.408509 | + | 0.912754i | \(0.633951\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5847 | 0.549241 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.1877 | 2.05553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9293 | −0.953448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 71.5427 | 3.10469 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.6938 | 2.28242 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.9665 | 0.560589 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.20498 | 0.0519988 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 38.5050 | 1.65853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9363 | 0.900123 | 0.450062 | − | 0.892997i | \(-0.351402\pi\) | ||||
0.450062 | + | 0.892997i | \(0.351402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.7095 | −1.06039 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.7096 | −0.458748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.8226 | −0.975825 | −0.487912 | − | 0.872893i | \(-0.662241\pi\) | ||||
−0.487912 | + | 0.872893i | \(0.662241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.6458 | 1.26525 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.54424 | −0.108388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.9983 | 2.38129 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.20273 | 0.220843 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.8697 | −1.56222 | −0.781111 | − | 0.624393i | \(-0.785346\pi\) | ||||
−0.781111 | + | 0.624393i | \(0.785346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.55797 | 0.150486 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53.9802 | −2.27905 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.1487 | −1.35490 | −0.677452 | − | 0.735567i | \(-0.736916\pi\) | ||||
−0.677452 | + | 0.735567i | \(0.736916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.4369 | 0.733576 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.0471 | −0.883895 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.8745 | 0.833184 | 0.416592 | − | 0.909094i | \(-0.363224\pi\) | ||||
0.416592 | + | 0.909094i | \(0.363224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0334 | 1.42425 | 0.712126 | − | 0.702051i | \(-0.247732\pi\) | ||||
0.712126 | + | 0.702051i | \(0.247732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.9390 | −1.33427 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03475 | 0.0431520 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.1983 | −1.88163 | −0.940815 | − | 0.338921i | \(-0.889938\pi\) | ||||
−0.940815 | + | 0.338921i | \(0.889938\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.3631 | −1.46964 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.9200 | 1.69765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.89726 | 0.368487 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −29.1147 | −1.20375 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.16135 | −0.254306 | −0.127153 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127153 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.2765 | 0.959093 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.23336 | 0.338675 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.4969 | 0.431055 | 0.215527 | − | 0.976498i | \(-0.430853\pi\) | ||||
0.215527 | + | 0.976498i | \(0.430853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0237 | 0.984876 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.0022 | 0.818634 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.53354 | 0.307812 | 0.153906 | − | 0.988085i | \(-0.450815\pi\) | ||||
0.153906 | + | 0.988085i | \(0.450815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.4629 | 1.56893 | 0.784466 | − | 0.620171i | \(-0.212937\pi\) | ||||
0.784466 | + | 0.620171i | \(0.212937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.5428 | 2.13971 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0248507 | −0.00101032 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.3296 | 1.06869 | 0.534343 | − | 0.845268i | \(-0.320559\pi\) | ||||
0.534343 | + | 0.845268i | \(0.320559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.6517 | −0.472149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.46597 | 0.302041 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.3413 | −0.942746 | −0.471373 | − | 0.881934i | \(-0.656241\pi\) | ||||
−0.471373 | + | 0.881934i | \(0.656241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.1353 | 1.17485 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.6407 | 1.19329 | 0.596646 | − | 0.802505i | \(-0.296500\pi\) | ||||
0.596646 | + | 0.802505i | \(0.296500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.2273 | −1.77764 | −0.888822 | − | 0.458253i | \(-0.848476\pi\) | ||||
−0.888822 | + | 0.458253i | \(0.848476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.59840 | −0.304913 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −63.2567 | −2.53433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −26.6271 | −1.06339 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.93181 | 0.396007 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7717 | 0.946336 | 0.473168 | − | 0.880972i | \(-0.343110\pi\) | ||||
0.473168 | + | 0.880972i | \(0.343110\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −74.6355 | −2.96649 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.8509 | −0.748075 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 61.2063 | 2.42508 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.0963 | −0.676321 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.2078 | −0.679666 | −0.339833 | − | 0.940486i | \(-0.610371\pi\) | ||||
−0.339833 | + | 0.940486i | \(0.610371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.9441 | −1.69355 | −0.846776 | − | 0.531950i | \(-0.821459\pi\) | ||||
−0.846776 | + | 0.531950i | \(0.821459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.96726 | 0.0774609 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.04996 | −0.198535 | −0.0992673 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992673 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.0630 | 1.69037 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 106.598 | 4.17789 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.9871 | 1.64308 | 0.821542 | − | 0.570149i | \(-0.193114\pi\) | ||||
0.821542 | + | 0.570149i | \(0.193114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1817 | 0.671346 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.1636 | −1.25482 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.6790 | 1.74045 | 0.870223 | − | 0.492658i | \(-0.163975\pi\) | ||||
0.870223 | + | 0.492658i | \(0.163975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.7989 | 1.31463 | 0.657313 | − | 0.753618i | \(-0.271693\pi\) | ||||
0.657313 | + | 0.753618i | \(0.271693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −85.8052 | −3.33240 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.8503 | 0.459535 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.958033 | −0.0370952 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.57773 | −0.292972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8444 | 0.688877 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0709 | −0.619489 | −0.309745 | − | 0.950820i | \(-0.600244\pi\) | ||||
−0.309745 | + | 0.950820i | \(0.600244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.34323 | −0.282641 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4968 | 0.480289 | 0.240145 | − | 0.970737i | \(-0.422805\pi\) | ||||
0.240145 | + | 0.970737i | \(0.422805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.95284 | 0.190073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.5849 | −1.21034 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1924 | −0.696112 | −0.348056 | − | 0.937474i | \(-0.613158\pi\) | ||||
−0.348056 | + | 0.937474i | \(0.613158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.91551 | −0.149604 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.6740 | −1.66627 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1428 | 0.538797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4643 | 0.968706 | 0.484353 | − | 0.874873i | \(-0.339055\pi\) | ||||
0.484353 | + | 0.874873i | \(0.339055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −78.9861 | −3.00043 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6985 | 0.861005 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.6183 | 2.10669 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.1692 | 0.611576 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.6968 | −1.19717 | −0.598586 | − | 0.801058i | \(-0.704271\pi\) | ||||
−0.598586 | + | 0.801058i | \(0.704271\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89912 | 0.184774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.12806 | 0.155472 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −53.8422 | −2.02494 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2265 | −1.06007 | −0.530034 | − | 0.847976i | \(-0.677821\pi\) | ||||
−0.530034 | + | 0.847976i | \(0.677821\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −71.6317 | −2.68640 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.76478 | 0.328243 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.5247 | −0.655388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.8654 | 0.667194 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.4890 | −1.88292 | −0.941461 | − | 0.337122i | \(-0.890546\pi\) | ||||
−0.941461 | + | 0.337122i | \(0.890546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.2943 | −0.830285 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.6121 | 1.80790 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.925860 | −0.0343856 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.2197 | 1.41749 | 0.708744 | − | 0.705465i | \(-0.249262\pi\) | ||||
0.708744 | + | 0.705465i | \(0.249262\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.3656 | −1.38391 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.75543 | 0.138900 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3158 | −1.23055 | −0.615273 | − | 0.788314i | \(-0.710954\pi\) | ||||
−0.615273 | + | 0.788314i | \(0.710954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.8420 | 1.24828 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.6266 | 1.16498 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5781 | 0.609834 | 0.304917 | − | 0.952379i | \(-0.401371\pi\) | ||||
0.304917 | + | 0.952379i | \(0.401371\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.3256 | −1.55487 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.7424 | 0.760966 | 0.380483 | − | 0.924788i | \(-0.375758\pi\) | ||||
0.380483 | + | 0.924788i | \(0.375758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.04715 | −0.0383648 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.3440 | −1.91517 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 55.9163 | 2.04314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.9330 | 1.16525 | 0.582625 | − | 0.812741i | \(-0.302026\pi\) | ||||
0.582625 | + | 0.812741i | \(0.302026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.74183 | 0.245686 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.12153 | −0.186392 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.7381 | −1.29892 | −0.649461 | − | 0.760395i | \(-0.725005\pi\) | ||||
−0.649461 | + | 0.760395i | \(0.725005\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0264 | −0.363937 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.3465 | −0.628809 | −0.314405 | − | 0.949289i | \(-0.601805\pi\) | ||||
−0.314405 | + | 0.949289i | \(0.601805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.1838 | −1.67196 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.7306 | −1.11107 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.4515 | 2.47164 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0004 | 0.360625 | 0.180312 | − | 0.983609i | \(-0.442289\pi\) | ||||
0.180312 | + | 0.983609i | \(0.442289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0494 | −0.397934 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.54683 | 0.127571 | 0.0637853 | − | 0.997964i | \(-0.479683\pi\) | ||||
0.0637853 | + | 0.997964i | \(0.479683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.47043 | 0.304267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.4361 | 0.804891 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4351 | 0.982966 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2906 | −0.368228 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.79880 | 0.242969 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.28082 | 0.117098 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.52935 | −0.304039 | −0.152019 | − | 0.988378i | \(-0.548578\pi\) | ||||
−0.152019 | + | 0.988378i | \(0.548578\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.536844 | −0.0191122 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 75.1945 | 2.67361 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.3649 | 1.00727 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.81979 | 0.277339 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.0007 | −1.23979 | −0.619894 | − | 0.784686i | \(-0.712824\pi\) | ||||
−0.619894 | + | 0.784686i | \(0.712824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.88032 | 0.278786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.9165 | 2.85905 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3599 | −0.683198 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.46223 | 0.157273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.3868 | 0.999261 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.25919 | −0.255220 | −0.127610 | − | 0.991824i | \(-0.540731\pi\) | ||||
−0.127610 | + | 0.991824i | \(0.540731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.6997 | −1.39404 | −0.697022 | − | 0.717050i | \(-0.745492\pi\) | ||||
−0.697022 | + | 0.717050i | \(0.745492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.4208 | 0.646046 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6811 | 0.444200 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.85246 | 0.0648095 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −125.554 | −4.38720 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.50403 | 0.296793 | 0.148396 | − | 0.988928i | \(-0.452589\pi\) | ||||
0.148396 | + | 0.988928i | \(0.452589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.7797 | −0.863765 | −0.431882 | − | 0.901930i | \(-0.642150\pi\) | ||||
−0.431882 | + | 0.901930i | \(0.642150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.68973 | −0.337353 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.9822 | 1.14690 | 0.573451 | − | 0.819240i | \(-0.305604\pi\) | ||||
0.573451 | + | 0.819240i | \(0.305604\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4214 | −0.500876 | −0.250438 | − | 0.968133i | \(-0.580575\pi\) | ||||
−0.250438 | + | 0.968133i | \(0.580575\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.0338 | −1.35407 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 64.6032 | 2.23837 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.21551 | 0.318916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.2003 | −2.14996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3853 | −0.496637 | −0.248319 | − | 0.968678i | \(-0.579878\pi\) | ||||
−0.248319 | + | 0.968678i | \(0.579878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1428 | −0.970441 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −84.7209 | −2.91794 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.8567 | −0.511088 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.107165 | −0.00368225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.8476 | −1.33325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.84476 | 0.0632377 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.8523 | −0.405815 | −0.202908 | − | 0.979198i | \(-0.565039\pi\) | ||||
−0.202908 | + | 0.979198i | \(0.565039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.1586 | −0.518415 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.6244 | 0.670357 | 0.335178 | − | 0.942155i | \(-0.391203\pi\) | ||||
0.335178 | + | 0.942155i | \(0.391203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.6781 | −0.807887 | −0.403943 | − | 0.914784i | \(-0.632361\pi\) | ||||
−0.403943 | + | 0.914784i | \(0.632361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 125.643 | 4.28189 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.5258 | −0.936989 | −0.468494 | − | 0.883467i | \(-0.655203\pi\) | ||||
−0.468494 | + | 0.883467i | \(0.655203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.6937 | −0.363597 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.9567 | −1.39096 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.1166 | −1.46263 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.2726 | 1.70342 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.33556 | −0.214426 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.31238 | 0.145785 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.1666 | 1.42387 | 0.711933 | − | 0.702247i | \(-0.247820\pi\) | ||||
0.711933 | + | 0.702247i | \(0.247820\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.871766 | 0.0294039 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.1450 | −1.01561 | −0.507805 | − | 0.861472i | \(-0.669543\pi\) | ||||
−0.507805 | + | 0.861472i | \(0.669543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.5409 | −1.63353 | −0.816765 | − | 0.576970i | \(-0.804235\pi\) | ||||
−0.816765 | + | 0.576970i | \(0.804235\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.8480 | 1.27225 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.8258 | −0.632107 | −0.316054 | − | 0.948741i | \(-0.602358\pi\) | ||||
−0.316054 | + | 0.948741i | \(0.602358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −81.2922 | −2.72645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.2055 | 0.542904 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.88717 | 0.130079 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.412909 | 0.0138020 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.9377 | −0.532144 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.84244 | −0.261560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9277 | 0.497314 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48358 | 0.282316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.46717 | −0.281458 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.7334 | −1.35253 | −0.676266 | − | 0.736658i | \(-0.736403\pi\) | ||||
−0.676266 | + | 0.736658i | \(0.736403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 68.8737 | 2.28440 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.1347 | 1.39598 | 0.697992 | − | 0.716106i | \(-0.254077\pi\) | ||||
0.697992 | + | 0.716106i | \(0.254077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.5069 | −1.04273 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.6835 | 0.518479 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74.0942 | 2.44681 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.2283 | 1.26104 | 0.630518 | − | 0.776175i | \(-0.282842\pi\) | ||||
0.630518 | + | 0.776175i | \(0.282842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 52.4426 | 1.72804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.3576 | −0.538418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.78281 | 0.0586185 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.5184 | 0.936667 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.1946 | −0.892226 | −0.446113 | − | 0.894977i | \(-0.647192\pi\) | ||||
−0.446113 | + | 0.894977i | \(0.647192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.8672 | 1.04441 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.6263 | 0.773489 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.4973 | −0.604928 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2139 | −0.431678 | −0.215839 | − | 0.976429i | \(-0.569249\pi\) | ||||
−0.215839 | + | 0.976429i | \(0.569249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.1370 | −1.34245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.66673 | 0.249928 | 0.124964 | − | 0.992161i | \(-0.460118\pi\) | ||||
0.124964 | + | 0.992161i | \(0.460118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3307 | 0.336414 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31.6668 | −1.03012 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.8576 | 1.16522 | 0.582608 | − | 0.812753i | \(-0.302032\pi\) | ||||
0.582608 | + | 0.812753i | \(0.302032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.7739 | −0.998964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −98.4842 | −3.19357 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.7551 | 1.02865 | 0.514324 | − | 0.857596i | \(-0.328043\pi\) | ||||
0.514324 | + | 0.857596i | \(0.328043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.9445 | −0.354156 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.97133 | 0.290002 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.8851 | −0.545250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7483 | 1.31446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −71.5268 | −2.30492 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.1178 | −0.390087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.74949 | 0.120576 | 0.0602878 | − | 0.998181i | \(-0.480798\pi\) | ||||
0.0602878 | + | 0.998181i | \(0.480798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.6746 | −1.43516 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.4254 | −0.751755 | −0.375878 | − | 0.926669i | \(-0.622659\pi\) | ||||
−0.375878 | + | 0.926669i | \(0.622659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 97.8847 | 3.13804 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4025 | −0.493274 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.6290 | 0.404038 | 0.202019 | − | 0.979382i | \(-0.435250\pi\) | ||||
0.202019 | + | 0.979382i | \(0.435250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.7053 | 1.55663 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 59.0772 | 1.88619 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3313 | 1.31826 | 0.659131 | − | 0.752028i | \(-0.270924\pi\) | ||||
0.659131 | + | 0.752028i | \(0.270924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.82132 | 0.0898946 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.8018 | 0.566636 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.697545 | 0.0221806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.6134 | −0.527742 | −0.263871 | − | 0.964558i | \(-0.584999\pi\) | ||||
−0.263871 | + | 0.964558i | \(0.584999\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −95.0393 | −3.01598 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.85412 | 0.217290 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0754 | −0.952496 | −0.476248 | − | 0.879311i | \(-0.658004\pi\) | ||||
−0.476248 | + | 0.879311i | \(0.658004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.0916 | −0.414200 |
(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 | 8020.2.a.e.1.5 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.e.1.5 | ✓ | 35 | 1.1 | even | 1 | trivial |