Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2695680219\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} - 446 x^{10} - 12159 x^{9} + 4398 x^{8} + 17347 x^{7} - 7839 x^{6} - 12832 x^{5} + \cdots - 112 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(0.925440\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.925440 | 0.654385 | 0.327192 | − | 0.944958i | \(-0.393897\pi\) | ||||
0.327192 | + | 0.944958i | \(0.393897\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.14356 | −0.571780 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.925440 | 0.377809 | ||||||||
\(7\) | −0.122708 | −0.0463792 | −0.0231896 | − | 0.999731i | \(-0.507382\pi\) | ||||
−0.0231896 | + | 0.999731i | \(0.507382\pi\) | |||||||
\(8\) | −2.90918 | −1.02855 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.925440 | 0.292650 | ||||||||
\(11\) | −1.64812 | −0.496928 | −0.248464 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248464 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(12\) | −1.14356 | −0.330118 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.113559 | −0.0303498 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.405146 | −0.101287 | ||||||||
\(17\) | 1.77746 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(18\) | 0.925440 | 0.218128 | ||||||||
\(19\) | 7.23513 | 1.65985 | 0.829926 | − | 0.557873i | \(-0.188382\pi\) | ||||
0.829926 | + | 0.557873i | \(0.188382\pi\) | |||||||
\(20\) | −1.14356 | −0.255708 | ||||||||
\(21\) | −0.122708 | −0.0267770 | ||||||||
\(22\) | −1.52524 | −0.325182 | ||||||||
\(23\) | −9.25137 | −1.92904 | −0.964522 | − | 0.264003i | \(-0.914957\pi\) | ||||
−0.964522 | + | 0.264003i | \(0.914957\pi\) | |||||||
\(24\) | −2.90918 | −0.593833 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.925440 | −0.181494 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.140324 | 0.0265187 | ||||||||
\(29\) | 2.07063 | 0.384506 | 0.192253 | − | 0.981345i | \(-0.438421\pi\) | ||||
0.192253 | + | 0.981345i | \(0.438421\pi\) | |||||||
\(30\) | 0.925440 | 0.168961 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 5.44342 | 0.962269 | ||||||||
\(33\) | −1.64812 | −0.286902 | ||||||||
\(34\) | 1.64493 | 0.282104 | ||||||||
\(35\) | −0.122708 | −0.0207414 | ||||||||
\(36\) | −1.14356 | −0.190593 | ||||||||
\(37\) | −0.846152 | −0.139106 | −0.0695532 | − | 0.997578i | \(-0.522157\pi\) | ||||
−0.0695532 | + | 0.997578i | \(0.522157\pi\) | |||||||
\(38\) | 6.69568 | 1.08618 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.90918 | −0.459981 | ||||||||
\(41\) | 7.40266 | 1.15610 | 0.578050 | − | 0.816001i | \(-0.303814\pi\) | ||||
0.578050 | + | 0.816001i | \(0.303814\pi\) | |||||||
\(42\) | −0.113559 | −0.0175225 | ||||||||
\(43\) | 1.31837 | 0.201049 | 0.100524 | − | 0.994935i | \(-0.467948\pi\) | ||||
0.100524 | + | 0.994935i | \(0.467948\pi\) | |||||||
\(44\) | 1.88473 | 0.284134 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −8.56159 | −1.26234 | ||||||||
\(47\) | 3.41193 | 0.497681 | 0.248841 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248841 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(48\) | −0.405146 | −0.0584778 | ||||||||
\(49\) | −6.98494 | −0.997849 | ||||||||
\(50\) | 0.925440 | 0.130877 | ||||||||
\(51\) | 1.77746 | 0.248895 | ||||||||
\(52\) | 1.14356 | 0.158583 | ||||||||
\(53\) | 3.60465 | 0.495136 | 0.247568 | − | 0.968870i | \(-0.420369\pi\) | ||||
0.247568 | + | 0.968870i | \(0.420369\pi\) | |||||||
\(54\) | 0.925440 | 0.125936 | ||||||||
\(55\) | −1.64812 | −0.222233 | ||||||||
\(56\) | 0.356979 | 0.0477033 | ||||||||
\(57\) | 7.23513 | 0.958316 | ||||||||
\(58\) | 1.91624 | 0.251615 | ||||||||
\(59\) | 12.7031 | 1.65381 | 0.826904 | − | 0.562344i | \(-0.190100\pi\) | ||||
0.826904 | + | 0.562344i | \(0.190100\pi\) | |||||||
\(60\) | −1.14356 | −0.147633 | ||||||||
\(61\) | −2.15214 | −0.275553 | −0.137776 | − | 0.990463i | \(-0.543996\pi\) | ||||
−0.137776 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(62\) | 0.925440 | 0.117531 | ||||||||
\(63\) | −0.122708 | −0.0154597 | ||||||||
\(64\) | 5.84785 | 0.730981 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | −1.52524 | −0.187744 | ||||||||
\(67\) | −1.37225 | −0.167647 | −0.0838235 | − | 0.996481i | \(-0.526713\pi\) | ||||
−0.0838235 | + | 0.996481i | \(0.526713\pi\) | |||||||
\(68\) | −2.03264 | −0.246493 | ||||||||
\(69\) | −9.25137 | −1.11373 | ||||||||
\(70\) | −0.113559 | −0.0135729 | ||||||||
\(71\) | −1.00563 | −0.119346 | −0.0596729 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596729 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(72\) | −2.90918 | −0.342850 | ||||||||
\(73\) | 9.62315 | 1.12630 | 0.563152 | − | 0.826353i | \(-0.309588\pi\) | ||||
0.563152 | + | 0.826353i | \(0.309588\pi\) | |||||||
\(74\) | −0.783062 | −0.0910292 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −8.27381 | −0.949071 | ||||||||
\(77\) | 0.202238 | 0.0230471 | ||||||||
\(78\) | −0.925440 | −0.104785 | ||||||||
\(79\) | −1.33307 | −0.149982 | −0.0749909 | − | 0.997184i | \(-0.523893\pi\) | ||||
−0.0749909 | + | 0.997184i | \(0.523893\pi\) | |||||||
\(80\) | −0.405146 | −0.0452967 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.85072 | 0.756535 | ||||||||
\(83\) | 11.1226 | 1.22087 | 0.610434 | − | 0.792067i | \(-0.290995\pi\) | ||||
0.610434 | + | 0.792067i | \(0.290995\pi\) | |||||||
\(84\) | 0.140324 | 0.0153106 | ||||||||
\(85\) | 1.77746 | 0.192793 | ||||||||
\(86\) | 1.22007 | 0.131563 | ||||||||
\(87\) | 2.07063 | 0.221995 | ||||||||
\(88\) | 4.79468 | 0.511115 | ||||||||
\(89\) | −2.66859 | −0.282870 | −0.141435 | − | 0.989948i | \(-0.545172\pi\) | ||||
−0.141435 | + | 0.989948i | \(0.545172\pi\) | |||||||
\(90\) | 0.925440 | 0.0975499 | ||||||||
\(91\) | 0.122708 | 0.0128633 | ||||||||
\(92\) | 10.5795 | 1.10299 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 3.15754 | 0.325675 | ||||||||
\(95\) | 7.23513 | 0.742309 | ||||||||
\(96\) | 5.44342 | 0.555566 | ||||||||
\(97\) | 16.1017 | 1.63488 | 0.817438 | − | 0.576016i | \(-0.195394\pi\) | ||||
0.817438 | + | 0.576016i | \(0.195394\pi\) | |||||||
\(98\) | −6.46414 | −0.652977 | ||||||||
\(99\) | −1.64812 | −0.165643 | ||||||||
\(100\) | −1.14356 | −0.114356 | ||||||||
\(101\) | −8.59122 | −0.854858 | −0.427429 | − | 0.904049i | \(-0.640581\pi\) | ||||
−0.427429 | + | 0.904049i | \(0.640581\pi\) | |||||||
\(102\) | 1.64493 | 0.162873 | ||||||||
\(103\) | −3.26439 | −0.321650 | −0.160825 | − | 0.986983i | \(-0.551415\pi\) | ||||
−0.160825 | + | 0.986983i | \(0.551415\pi\) | |||||||
\(104\) | 2.90918 | 0.285268 | ||||||||
\(105\) | −0.122708 | −0.0119751 | ||||||||
\(106\) | 3.33588 | 0.324010 | ||||||||
\(107\) | 16.7289 | 1.61724 | 0.808620 | − | 0.588331i | \(-0.200215\pi\) | ||||
0.808620 | + | 0.588331i | \(0.200215\pi\) | |||||||
\(108\) | −1.14356 | −0.110039 | ||||||||
\(109\) | −6.39717 | −0.612737 | −0.306369 | − | 0.951913i | \(-0.599114\pi\) | ||||
−0.306369 | + | 0.951913i | \(0.599114\pi\) | |||||||
\(110\) | −1.52524 | −0.145426 | ||||||||
\(111\) | −0.846152 | −0.0803132 | ||||||||
\(112\) | 0.0497146 | 0.00469759 | ||||||||
\(113\) | 13.5830 | 1.27778 | 0.638892 | − | 0.769296i | \(-0.279393\pi\) | ||||
0.638892 | + | 0.769296i | \(0.279393\pi\) | |||||||
\(114\) | 6.69568 | 0.627108 | ||||||||
\(115\) | −9.25137 | −0.862695 | ||||||||
\(116\) | −2.36789 | −0.219853 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 11.7560 | 1.08223 | ||||||||
\(119\) | −0.218108 | −0.0199940 | ||||||||
\(120\) | −2.90918 | −0.265570 | ||||||||
\(121\) | −8.28369 | −0.753063 | ||||||||
\(122\) | −1.99167 | −0.180318 | ||||||||
\(123\) | 7.40266 | 0.667475 | ||||||||
\(124\) | −1.14356 | −0.102695 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.113559 | −0.0101166 | ||||||||
\(127\) | −18.0085 | −1.59800 | −0.798999 | − | 0.601332i | \(-0.794637\pi\) | ||||
−0.798999 | + | 0.601332i | \(0.794637\pi\) | |||||||
\(128\) | −5.47500 | −0.483926 | ||||||||
\(129\) | 1.31837 | 0.116076 | ||||||||
\(130\) | −0.925440 | −0.0811664 | ||||||||
\(131\) | −5.17806 | −0.452410 | −0.226205 | − | 0.974080i | \(-0.572632\pi\) | ||||
−0.226205 | + | 0.974080i | \(0.572632\pi\) | |||||||
\(132\) | 1.88473 | 0.164045 | ||||||||
\(133\) | −0.887807 | −0.0769826 | ||||||||
\(134\) | −1.26993 | −0.109706 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −5.17095 | −0.443406 | ||||||||
\(137\) | 5.27213 | 0.450428 | 0.225214 | − | 0.974309i | \(-0.427692\pi\) | ||||
0.225214 | + | 0.974309i | \(0.427692\pi\) | |||||||
\(138\) | −8.56159 | −0.728811 | ||||||||
\(139\) | 14.6523 | 1.24280 | 0.621398 | − | 0.783495i | \(-0.286565\pi\) | ||||
0.621398 | + | 0.783495i | \(0.286565\pi\) | |||||||
\(140\) | 0.140324 | 0.0118595 | ||||||||
\(141\) | 3.41193 | 0.287336 | ||||||||
\(142\) | −0.930646 | −0.0780981 | ||||||||
\(143\) | 1.64812 | 0.137823 | ||||||||
\(144\) | −0.405146 | −0.0337622 | ||||||||
\(145\) | 2.07063 | 0.171956 | ||||||||
\(146\) | 8.90565 | 0.737037 | ||||||||
\(147\) | −6.98494 | −0.576108 | ||||||||
\(148\) | 0.967626 | 0.0795384 | ||||||||
\(149\) | 13.7879 | 1.12955 | 0.564774 | − | 0.825246i | \(-0.308963\pi\) | ||||
0.564774 | + | 0.825246i | \(0.308963\pi\) | |||||||
\(150\) | 0.925440 | 0.0755619 | ||||||||
\(151\) | 11.0546 | 0.899611 | 0.449805 | − | 0.893127i | \(-0.351493\pi\) | ||||
0.449805 | + | 0.893127i | \(0.351493\pi\) | |||||||
\(152\) | −21.0483 | −1.70724 | ||||||||
\(153\) | 1.77746 | 0.143699 | ||||||||
\(154\) | 0.187159 | 0.0150817 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 1.14356 | 0.0915582 | ||||||||
\(157\) | 9.06646 | 0.723582 | 0.361791 | − | 0.932259i | \(-0.382165\pi\) | ||||
0.361791 | + | 0.932259i | \(0.382165\pi\) | |||||||
\(158\) | −1.23367 | −0.0981458 | ||||||||
\(159\) | 3.60465 | 0.285867 | ||||||||
\(160\) | 5.44342 | 0.430340 | ||||||||
\(161\) | 1.13521 | 0.0894675 | ||||||||
\(162\) | 0.925440 | 0.0727094 | ||||||||
\(163\) | 8.77132 | 0.687023 | 0.343511 | − | 0.939149i | \(-0.388384\pi\) | ||||
0.343511 | + | 0.939149i | \(0.388384\pi\) | |||||||
\(164\) | −8.46539 | −0.661036 | ||||||||
\(165\) | −1.64812 | −0.128306 | ||||||||
\(166\) | 10.2933 | 0.798918 | ||||||||
\(167\) | 2.78486 | 0.215499 | 0.107749 | − | 0.994178i | \(-0.465636\pi\) | ||||
0.107749 | + | 0.994178i | \(0.465636\pi\) | |||||||
\(168\) | 0.356979 | 0.0275415 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.64493 | 0.126161 | ||||||||
\(171\) | 7.23513 | 0.553284 | ||||||||
\(172\) | −1.50763 | −0.114956 | ||||||||
\(173\) | −11.1032 | −0.844163 | −0.422081 | − | 0.906558i | \(-0.638700\pi\) | ||||
−0.422081 | + | 0.906558i | \(0.638700\pi\) | |||||||
\(174\) | 1.91624 | 0.145270 | ||||||||
\(175\) | −0.122708 | −0.00927584 | ||||||||
\(176\) | 0.667731 | 0.0503321 | ||||||||
\(177\) | 12.7031 | 0.954826 | ||||||||
\(178\) | −2.46962 | −0.185106 | ||||||||
\(179\) | −9.88354 | −0.738731 | −0.369365 | − | 0.929284i | \(-0.620425\pi\) | ||||
−0.369365 | + | 0.929284i | \(0.620425\pi\) | |||||||
\(180\) | −1.14356 | −0.0852360 | ||||||||
\(181\) | −7.16446 | −0.532530 | −0.266265 | − | 0.963900i | \(-0.585790\pi\) | ||||
−0.266265 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(182\) | 0.113559 | 0.00841753 | ||||||||
\(183\) | −2.15214 | −0.159091 | ||||||||
\(184\) | 26.9139 | 1.98412 | ||||||||
\(185\) | −0.846152 | −0.0622103 | ||||||||
\(186\) | 0.925440 | 0.0678565 | ||||||||
\(187\) | −2.92948 | −0.214225 | ||||||||
\(188\) | −3.90175 | −0.284564 | ||||||||
\(189\) | −0.122708 | −0.00892568 | ||||||||
\(190\) | 6.69568 | 0.485756 | ||||||||
\(191\) | 11.0610 | 0.800347 | 0.400174 | − | 0.916439i | \(-0.368950\pi\) | ||||
0.400174 | + | 0.916439i | \(0.368950\pi\) | |||||||
\(192\) | 5.84785 | 0.422032 | ||||||||
\(193\) | 12.3088 | 0.886005 | 0.443002 | − | 0.896520i | \(-0.353913\pi\) | ||||
0.443002 | + | 0.896520i | \(0.353913\pi\) | |||||||
\(194\) | 14.9011 | 1.06984 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 7.98771 | 0.570551 | ||||||||
\(197\) | −1.76121 | −0.125481 | −0.0627405 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627405 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(198\) | −1.52524 | −0.108394 | ||||||||
\(199\) | 7.85890 | 0.557103 | 0.278551 | − | 0.960421i | \(-0.410146\pi\) | ||||
0.278551 | + | 0.960421i | \(0.410146\pi\) | |||||||
\(200\) | −2.90918 | −0.205710 | ||||||||
\(201\) | −1.37225 | −0.0967910 | ||||||||
\(202\) | −7.95066 | −0.559406 | ||||||||
\(203\) | −0.254082 | −0.0178331 | ||||||||
\(204\) | −2.03264 | −0.142313 | ||||||||
\(205\) | 7.40266 | 0.517024 | ||||||||
\(206\) | −3.02100 | −0.210483 | ||||||||
\(207\) | −9.25137 | −0.643015 | ||||||||
\(208\) | 0.405146 | 0.0280918 | ||||||||
\(209\) | −11.9244 | −0.824827 | ||||||||
\(210\) | −0.113559 | −0.00783629 | ||||||||
\(211\) | 15.9547 | 1.09836 | 0.549182 | − | 0.835703i | \(-0.314939\pi\) | ||||
0.549182 | + | 0.835703i | \(0.314939\pi\) | |||||||
\(212\) | −4.12213 | −0.283109 | ||||||||
\(213\) | −1.00563 | −0.0689043 | ||||||||
\(214\) | 15.4816 | 1.05830 | ||||||||
\(215\) | 1.31837 | 0.0899118 | ||||||||
\(216\) | −2.90918 | −0.197944 | ||||||||
\(217\) | −0.122708 | −0.00832995 | ||||||||
\(218\) | −5.92019 | −0.400966 | ||||||||
\(219\) | 9.62315 | 0.650272 | ||||||||
\(220\) | 1.88473 | 0.127068 | ||||||||
\(221\) | −1.77746 | −0.119565 | ||||||||
\(222\) | −0.783062 | −0.0525557 | ||||||||
\(223\) | 19.8537 | 1.32950 | 0.664750 | − | 0.747066i | \(-0.268538\pi\) | ||||
0.664750 | + | 0.747066i | \(0.268538\pi\) | |||||||
\(224\) | −0.667949 | −0.0446292 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 12.5703 | 0.836163 | ||||||||
\(227\) | 18.5763 | 1.23295 | 0.616475 | − | 0.787375i | \(-0.288560\pi\) | ||||
0.616475 | + | 0.787375i | \(0.288560\pi\) | |||||||
\(228\) | −8.27381 | −0.547947 | ||||||||
\(229\) | −9.67200 | −0.639144 | −0.319572 | − | 0.947562i | \(-0.603539\pi\) | ||||
−0.319572 | + | 0.947562i | \(0.603539\pi\) | |||||||
\(230\) | −8.56159 | −0.564534 | ||||||||
\(231\) | 0.202238 | 0.0133063 | ||||||||
\(232\) | −6.02383 | −0.395484 | ||||||||
\(233\) | 6.15546 | 0.403258 | 0.201629 | − | 0.979462i | \(-0.435377\pi\) | ||||
0.201629 | + | 0.979462i | \(0.435377\pi\) | |||||||
\(234\) | −0.925440 | −0.0604979 | ||||||||
\(235\) | 3.41193 | 0.222570 | ||||||||
\(236\) | −14.5268 | −0.945615 | ||||||||
\(237\) | −1.33307 | −0.0865920 | ||||||||
\(238\) | −0.201846 | −0.0130838 | ||||||||
\(239\) | 2.82872 | 0.182975 | 0.0914873 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914873 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(240\) | −0.405146 | −0.0261521 | ||||||||
\(241\) | −7.70559 | −0.496361 | −0.248180 | − | 0.968714i | \(-0.579833\pi\) | ||||
−0.248180 | + | 0.968714i | \(0.579833\pi\) | |||||||
\(242\) | −7.66606 | −0.492793 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.46110 | 0.157556 | ||||||||
\(245\) | −6.98494 | −0.446252 | ||||||||
\(246\) | 6.85072 | 0.436786 | ||||||||
\(247\) | −7.23513 | −0.460360 | ||||||||
\(248\) | −2.90918 | −0.184733 | ||||||||
\(249\) | 11.1226 | 0.704869 | ||||||||
\(250\) | 0.925440 | 0.0585300 | ||||||||
\(251\) | −22.1922 | −1.40076 | −0.700379 | − | 0.713771i | \(-0.746986\pi\) | ||||
−0.700379 | + | 0.713771i | \(0.746986\pi\) | |||||||
\(252\) | 0.140324 | 0.00883957 | ||||||||
\(253\) | 15.2474 | 0.958596 | ||||||||
\(254\) | −16.6658 | −1.04571 | ||||||||
\(255\) | 1.77746 | 0.111309 | ||||||||
\(256\) | −16.7625 | −1.04765 | ||||||||
\(257\) | 16.3216 | 1.01811 | 0.509056 | − | 0.860734i | \(-0.329995\pi\) | ||||
0.509056 | + | 0.860734i | \(0.329995\pi\) | |||||||
\(258\) | 1.22007 | 0.0759581 | ||||||||
\(259\) | 0.103829 | 0.00645164 | ||||||||
\(260\) | 1.14356 | 0.0709206 | ||||||||
\(261\) | 2.07063 | 0.128169 | ||||||||
\(262\) | −4.79199 | −0.296050 | ||||||||
\(263\) | 3.71964 | 0.229363 | 0.114681 | − | 0.993402i | \(-0.463415\pi\) | ||||
0.114681 | + | 0.993402i | \(0.463415\pi\) | |||||||
\(264\) | 4.79468 | 0.295092 | ||||||||
\(265\) | 3.60465 | 0.221432 | ||||||||
\(266\) | −0.821612 | −0.0503763 | ||||||||
\(267\) | −2.66859 | −0.163315 | ||||||||
\(268\) | 1.56925 | 0.0958573 | ||||||||
\(269\) | −23.2982 | −1.42052 | −0.710259 | − | 0.703941i | \(-0.751422\pi\) | ||||
−0.710259 | + | 0.703941i | \(0.751422\pi\) | |||||||
\(270\) | 0.925440 | 0.0563205 | ||||||||
\(271\) | −10.3204 | −0.626920 | −0.313460 | − | 0.949601i | \(-0.601488\pi\) | ||||
−0.313460 | + | 0.949601i | \(0.601488\pi\) | |||||||
\(272\) | −0.720132 | −0.0436644 | ||||||||
\(273\) | 0.122708 | 0.00742661 | ||||||||
\(274\) | 4.87904 | 0.294753 | ||||||||
\(275\) | −1.64812 | −0.0993856 | ||||||||
\(276\) | 10.5795 | 0.636811 | ||||||||
\(277\) | 10.0064 | 0.601225 | 0.300612 | − | 0.953746i | \(-0.402809\pi\) | ||||
0.300612 | + | 0.953746i | \(0.402809\pi\) | |||||||
\(278\) | 13.5599 | 0.813266 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0.356979 | 0.0213336 | ||||||||
\(281\) | −1.14620 | −0.0683768 | −0.0341884 | − | 0.999415i | \(-0.510885\pi\) | ||||
−0.0341884 | + | 0.999415i | \(0.510885\pi\) | |||||||
\(282\) | 3.15754 | 0.188029 | ||||||||
\(283\) | 17.3625 | 1.03209 | 0.516046 | − | 0.856561i | \(-0.327403\pi\) | ||||
0.516046 | + | 0.856561i | \(0.327403\pi\) | |||||||
\(284\) | 1.14999 | 0.0682396 | ||||||||
\(285\) | 7.23513 | 0.428572 | ||||||||
\(286\) | 1.52524 | 0.0901893 | ||||||||
\(287\) | −0.908364 | −0.0536190 | ||||||||
\(288\) | 5.44342 | 0.320756 | ||||||||
\(289\) | −13.8406 | −0.814155 | ||||||||
\(290\) | 1.91624 | 0.112526 | ||||||||
\(291\) | 16.1017 | 0.943896 | ||||||||
\(292\) | −11.0047 | −0.643999 | ||||||||
\(293\) | 16.9457 | 0.989980 | 0.494990 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494990 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(294\) | −6.46414 | −0.376997 | ||||||||
\(295\) | 12.7031 | 0.739605 | ||||||||
\(296\) | 2.46160 | 0.143078 | ||||||||
\(297\) | −1.64812 | −0.0956338 | ||||||||
\(298\) | 12.7599 | 0.739159 | ||||||||
\(299\) | 9.25137 | 0.535020 | ||||||||
\(300\) | −1.14356 | −0.0660235 | ||||||||
\(301\) | −0.161774 | −0.00932448 | ||||||||
\(302\) | 10.2304 | 0.588692 | ||||||||
\(303\) | −8.59122 | −0.493553 | ||||||||
\(304\) | −2.93129 | −0.168121 | ||||||||
\(305\) | −2.15214 | −0.123231 | ||||||||
\(306\) | 1.64493 | 0.0940347 | ||||||||
\(307\) | −24.8948 | −1.42082 | −0.710410 | − | 0.703788i | \(-0.751490\pi\) | ||||
−0.710410 | + | 0.703788i | \(0.751490\pi\) | |||||||
\(308\) | −0.231271 | −0.0131779 | ||||||||
\(309\) | −3.26439 | −0.185705 | ||||||||
\(310\) | 0.925440 | 0.0525615 | ||||||||
\(311\) | 21.5736 | 1.22333 | 0.611664 | − | 0.791118i | \(-0.290501\pi\) | ||||
0.611664 | + | 0.791118i | \(0.290501\pi\) | |||||||
\(312\) | 2.90918 | 0.164700 | ||||||||
\(313\) | −7.07729 | −0.400032 | −0.200016 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200016 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(314\) | 8.39046 | 0.473501 | ||||||||
\(315\) | −0.122708 | −0.00691380 | ||||||||
\(316\) | 1.52444 | 0.0857566 | ||||||||
\(317\) | −25.8494 | −1.45185 | −0.725925 | − | 0.687774i | \(-0.758588\pi\) | ||||
−0.725925 | + | 0.687774i | \(0.758588\pi\) | |||||||
\(318\) | 3.33588 | 0.187067 | ||||||||
\(319\) | −3.41265 | −0.191072 | ||||||||
\(320\) | 5.84785 | 0.326905 | ||||||||
\(321\) | 16.7289 | 0.933714 | ||||||||
\(322\) | 1.05057 | 0.0585461 | ||||||||
\(323\) | 12.8602 | 0.715559 | ||||||||
\(324\) | −1.14356 | −0.0635312 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 8.11733 | 0.449577 | ||||||||
\(327\) | −6.39717 | −0.353764 | ||||||||
\(328\) | −21.5356 | −1.18911 | ||||||||
\(329\) | −0.418670 | −0.0230820 | ||||||||
\(330\) | −1.52524 | −0.0839617 | ||||||||
\(331\) | −20.8358 | −1.14524 | −0.572621 | − | 0.819820i | \(-0.694073\pi\) | ||||
−0.572621 | + | 0.819820i | \(0.694073\pi\) | |||||||
\(332\) | −12.7194 | −0.698069 | ||||||||
\(333\) | −0.846152 | −0.0463688 | ||||||||
\(334\) | 2.57722 | 0.141019 | ||||||||
\(335\) | −1.37225 | −0.0749740 | ||||||||
\(336\) | 0.0497146 | 0.00271215 | ||||||||
\(337\) | −6.66018 | −0.362803 | −0.181401 | − | 0.983409i | \(-0.558063\pi\) | ||||
−0.181401 | + | 0.983409i | \(0.558063\pi\) | |||||||
\(338\) | 0.925440 | 0.0503373 | ||||||||
\(339\) | 13.5830 | 0.737729 | ||||||||
\(340\) | −2.03264 | −0.110235 | ||||||||
\(341\) | −1.64812 | −0.0892509 | ||||||||
\(342\) | 6.69568 | 0.362061 | ||||||||
\(343\) | 1.71606 | 0.0926586 | ||||||||
\(344\) | −3.83536 | −0.206789 | ||||||||
\(345\) | −9.25137 | −0.498077 | ||||||||
\(346\) | −10.2754 | −0.552407 | ||||||||
\(347\) | −8.94312 | −0.480092 | −0.240046 | − | 0.970762i | \(-0.577163\pi\) | ||||
−0.240046 | + | 0.970762i | \(0.577163\pi\) | |||||||
\(348\) | −2.36789 | −0.126932 | ||||||||
\(349\) | 3.26398 | 0.174717 | 0.0873584 | − | 0.996177i | \(-0.472157\pi\) | ||||
0.0873584 | + | 0.996177i | \(0.472157\pi\) | |||||||
\(350\) | −0.113559 | −0.00606997 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −8.97142 | −0.478178 | ||||||||
\(353\) | −2.31856 | −0.123405 | −0.0617024 | − | 0.998095i | \(-0.519653\pi\) | ||||
−0.0617024 | + | 0.998095i | \(0.519653\pi\) | |||||||
\(354\) | 11.7560 | 0.624824 | ||||||||
\(355\) | −1.00563 | −0.0533731 | ||||||||
\(356\) | 3.05169 | 0.161739 | ||||||||
\(357\) | −0.218108 | −0.0115435 | ||||||||
\(358\) | −9.14662 | −0.483414 | ||||||||
\(359\) | −9.13662 | −0.482212 | −0.241106 | − | 0.970499i | \(-0.577510\pi\) | ||||
−0.241106 | + | 0.970499i | \(0.577510\pi\) | |||||||
\(360\) | −2.90918 | −0.153327 | ||||||||
\(361\) | 33.3471 | 1.75511 | ||||||||
\(362\) | −6.63028 | −0.348480 | ||||||||
\(363\) | −8.28369 | −0.434781 | ||||||||
\(364\) | −0.140324 | −0.00735497 | ||||||||
\(365\) | 9.62315 | 0.503699 | ||||||||
\(366\) | −1.99167 | −0.104106 | ||||||||
\(367\) | −36.6342 | −1.91229 | −0.956145 | − | 0.292894i | \(-0.905382\pi\) | ||||
−0.956145 | + | 0.292894i | \(0.905382\pi\) | |||||||
\(368\) | 3.74816 | 0.195386 | ||||||||
\(369\) | 7.40266 | 0.385367 | ||||||||
\(370\) | −0.783062 | −0.0407095 | ||||||||
\(371\) | −0.442318 | −0.0229640 | ||||||||
\(372\) | −1.14356 | −0.0592909 | ||||||||
\(373\) | −4.57955 | −0.237120 | −0.118560 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118560 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(374\) | −2.71106 | −0.140185 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −9.92591 | −0.511890 | ||||||||
\(377\) | −2.07063 | −0.106643 | ||||||||
\(378\) | −0.113559 | −0.00584083 | ||||||||
\(379\) | 8.56969 | 0.440196 | 0.220098 | − | 0.975478i | \(-0.429362\pi\) | ||||
0.220098 | + | 0.975478i | \(0.429362\pi\) | |||||||
\(380\) | −8.27381 | −0.424438 | ||||||||
\(381\) | −18.0085 | −0.922605 | ||||||||
\(382\) | 10.2363 | 0.523735 | ||||||||
\(383\) | −3.49724 | −0.178701 | −0.0893503 | − | 0.996000i | \(-0.528479\pi\) | ||||
−0.0893503 | + | 0.996000i | \(0.528479\pi\) | |||||||
\(384\) | −5.47500 | −0.279395 | ||||||||
\(385\) | 0.202238 | 0.0103070 | ||||||||
\(386\) | 11.3910 | 0.579788 | ||||||||
\(387\) | 1.31837 | 0.0670163 | ||||||||
\(388\) | −18.4132 | −0.934790 | ||||||||
\(389\) | 5.50166 | 0.278945 | 0.139473 | − | 0.990226i | \(-0.455459\pi\) | ||||
0.139473 | + | 0.990226i | \(0.455459\pi\) | |||||||
\(390\) | −0.925440 | −0.0468615 | ||||||||
\(391\) | −16.4440 | −0.831607 | ||||||||
\(392\) | 20.3204 | 1.02634 | ||||||||
\(393\) | −5.17806 | −0.261199 | ||||||||
\(394\) | −1.62989 | −0.0821129 | ||||||||
\(395\) | −1.33307 | −0.0670739 | ||||||||
\(396\) | 1.88473 | 0.0947112 | ||||||||
\(397\) | −37.4412 | −1.87912 | −0.939560 | − | 0.342385i | \(-0.888765\pi\) | ||||
−0.939560 | + | 0.342385i | \(0.888765\pi\) | |||||||
\(398\) | 7.27294 | 0.364560 | ||||||||
\(399\) | −0.887807 | −0.0444459 | ||||||||
\(400\) | −0.405146 | −0.0202573 | ||||||||
\(401\) | −14.2887 | −0.713543 | −0.356772 | − | 0.934192i | \(-0.616123\pi\) | ||||
−0.356772 | + | 0.934192i | \(0.616123\pi\) | |||||||
\(402\) | −1.26993 | −0.0633386 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | 9.82459 | 0.488791 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −0.235138 | −0.0116697 | ||||||||
\(407\) | 1.39456 | 0.0691259 | ||||||||
\(408\) | −5.17095 | −0.256000 | ||||||||
\(409\) | −4.13702 | −0.204563 | −0.102281 | − | 0.994756i | \(-0.532614\pi\) | ||||
−0.102281 | + | 0.994756i | \(0.532614\pi\) | |||||||
\(410\) | 6.85072 | 0.338333 | ||||||||
\(411\) | 5.27213 | 0.260055 | ||||||||
\(412\) | 3.73303 | 0.183913 | ||||||||
\(413\) | −1.55877 | −0.0767022 | ||||||||
\(414\) | −8.56159 | −0.420779 | ||||||||
\(415\) | 11.1226 | 0.545989 | ||||||||
\(416\) | −5.44342 | −0.266885 | ||||||||
\(417\) | 14.6523 | 0.717528 | ||||||||
\(418\) | −11.0353 | −0.539755 | ||||||||
\(419\) | 7.81628 | 0.381850 | 0.190925 | − | 0.981605i | \(-0.438851\pi\) | ||||
0.190925 | + | 0.981605i | \(0.438851\pi\) | |||||||
\(420\) | 0.140324 | 0.00684710 | ||||||||
\(421\) | −25.4889 | −1.24225 | −0.621125 | − | 0.783711i | \(-0.713324\pi\) | ||||
−0.621125 | + | 0.783711i | \(0.713324\pi\) | |||||||
\(422\) | 14.7651 | 0.718753 | ||||||||
\(423\) | 3.41193 | 0.165894 | ||||||||
\(424\) | −10.4866 | −0.509272 | ||||||||
\(425\) | 1.77746 | 0.0862196 | ||||||||
\(426\) | −0.930646 | −0.0450899 | ||||||||
\(427\) | 0.264084 | 0.0127799 | ||||||||
\(428\) | −19.1305 | −0.924706 | ||||||||
\(429\) | 1.64812 | 0.0795722 | ||||||||
\(430\) | 1.22007 | 0.0588369 | ||||||||
\(431\) | −14.6779 | −0.707008 | −0.353504 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353504 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(432\) | −0.405146 | −0.0194926 | ||||||||
\(433\) | 2.22019 | 0.106695 | 0.0533476 | − | 0.998576i | \(-0.483011\pi\) | ||||
0.0533476 | + | 0.998576i | \(0.483011\pi\) | |||||||
\(434\) | −0.113559 | −0.00545099 | ||||||||
\(435\) | 2.07063 | 0.0992791 | ||||||||
\(436\) | 7.31555 | 0.350351 | ||||||||
\(437\) | −66.9349 | −3.20193 | ||||||||
\(438\) | 8.90565 | 0.425528 | ||||||||
\(439\) | 15.2422 | 0.727473 | 0.363736 | − | 0.931502i | \(-0.381501\pi\) | ||||
0.363736 | + | 0.931502i | \(0.381501\pi\) | |||||||
\(440\) | 4.79468 | 0.228578 | ||||||||
\(441\) | −6.98494 | −0.332616 | ||||||||
\(442\) | −1.64493 | −0.0782416 | ||||||||
\(443\) | 38.5482 | 1.83148 | 0.915740 | − | 0.401771i | \(-0.131605\pi\) | ||||
0.915740 | + | 0.401771i | \(0.131605\pi\) | |||||||
\(444\) | 0.967626 | 0.0459215 | ||||||||
\(445\) | −2.66859 | −0.126503 | ||||||||
\(446\) | 18.3734 | 0.870004 | ||||||||
\(447\) | 13.7879 | 0.652145 | ||||||||
\(448\) | −0.717576 | −0.0339023 | ||||||||
\(449\) | −2.78231 | −0.131305 | −0.0656526 | − | 0.997843i | \(-0.520913\pi\) | ||||
−0.0656526 | + | 0.997843i | \(0.520913\pi\) | |||||||
\(450\) | 0.925440 | 0.0436257 | ||||||||
\(451\) | −12.2005 | −0.574499 | ||||||||
\(452\) | −15.5330 | −0.730612 | ||||||||
\(453\) | 11.0546 | 0.519390 | ||||||||
\(454\) | 17.1912 | 0.806823 | ||||||||
\(455\) | 0.122708 | 0.00575263 | ||||||||
\(456\) | −21.0483 | −0.985676 | ||||||||
\(457\) | 38.8366 | 1.81670 | 0.908349 | − | 0.418212i | \(-0.137343\pi\) | ||||
0.908349 | + | 0.418212i | \(0.137343\pi\) | |||||||
\(458\) | −8.95086 | −0.418246 | ||||||||
\(459\) | 1.77746 | 0.0829648 | ||||||||
\(460\) | 10.5795 | 0.493272 | ||||||||
\(461\) | −8.98963 | −0.418689 | −0.209344 | − | 0.977842i | \(-0.567133\pi\) | ||||
−0.209344 | + | 0.977842i | \(0.567133\pi\) | |||||||
\(462\) | 0.187159 | 0.00870741 | ||||||||
\(463\) | 24.0697 | 1.11861 | 0.559307 | − | 0.828961i | \(-0.311067\pi\) | ||||
0.559307 | + | 0.828961i | \(0.311067\pi\) | |||||||
\(464\) | −0.838908 | −0.0389453 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 5.69651 | 0.263886 | ||||||||
\(467\) | 17.9629 | 0.831225 | 0.415612 | − | 0.909542i | \(-0.363567\pi\) | ||||
0.415612 | + | 0.909542i | \(0.363567\pi\) | |||||||
\(468\) | 1.14356 | 0.0528611 | ||||||||
\(469\) | 0.168386 | 0.00777533 | ||||||||
\(470\) | 3.15754 | 0.145646 | ||||||||
\(471\) | 9.06646 | 0.417760 | ||||||||
\(472\) | −36.9557 | −1.70102 | ||||||||
\(473\) | −2.17283 | −0.0999068 | ||||||||
\(474\) | −1.23367 | −0.0566645 | ||||||||
\(475\) | 7.23513 | 0.331971 | ||||||||
\(476\) | 0.249420 | 0.0114322 | ||||||||
\(477\) | 3.60465 | 0.165045 | ||||||||
\(478\) | 2.61781 | 0.119736 | ||||||||
\(479\) | 2.06291 | 0.0942568 | 0.0471284 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471284 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(480\) | 5.44342 | 0.248457 | ||||||||
\(481\) | 0.846152 | 0.0385812 | ||||||||
\(482\) | −7.13106 | −0.324811 | ||||||||
\(483\) | 1.13521 | 0.0516541 | ||||||||
\(484\) | 9.47290 | 0.430586 | ||||||||
\(485\) | 16.1017 | 0.731139 | ||||||||
\(486\) | 0.925440 | 0.0419788 | ||||||||
\(487\) | −21.6835 | −0.982572 | −0.491286 | − | 0.870998i | \(-0.663473\pi\) | ||||
−0.491286 | + | 0.870998i | \(0.663473\pi\) | |||||||
\(488\) | 6.26095 | 0.283420 | ||||||||
\(489\) | 8.77132 | 0.396653 | ||||||||
\(490\) | −6.46414 | −0.292020 | ||||||||
\(491\) | 17.3189 | 0.781590 | 0.390795 | − | 0.920478i | \(-0.372200\pi\) | ||||
0.390795 | + | 0.920478i | \(0.372200\pi\) | |||||||
\(492\) | −8.46539 | −0.381649 | ||||||||
\(493\) | 3.68047 | 0.165760 | ||||||||
\(494\) | −6.69568 | −0.301253 | ||||||||
\(495\) | −1.64812 | −0.0740777 | ||||||||
\(496\) | −0.405146 | −0.0181916 | ||||||||
\(497\) | 0.123398 | 0.00553516 | ||||||||
\(498\) | 10.2933 | 0.461256 | ||||||||
\(499\) | 10.4577 | 0.468152 | 0.234076 | − | 0.972218i | \(-0.424794\pi\) | ||||
0.234076 | + | 0.972218i | \(0.424794\pi\) | |||||||
\(500\) | −1.14356 | −0.0511416 | ||||||||
\(501\) | 2.78486 | 0.124418 | ||||||||
\(502\) | −20.5375 | −0.916635 | ||||||||
\(503\) | 25.9440 | 1.15679 | 0.578394 | − | 0.815758i | \(-0.303680\pi\) | ||||
0.578394 | + | 0.815758i | \(0.303680\pi\) | |||||||
\(504\) | 0.356979 | 0.0159011 | ||||||||
\(505\) | −8.59122 | −0.382304 | ||||||||
\(506\) | 14.1106 | 0.627291 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 20.5939 | 0.913704 | ||||||||
\(509\) | 25.0715 | 1.11128 | 0.555638 | − | 0.831424i | \(-0.312474\pi\) | ||||
0.555638 | + | 0.831424i | \(0.312474\pi\) | |||||||
\(510\) | 1.64493 | 0.0728389 | ||||||||
\(511\) | −1.18084 | −0.0522371 | ||||||||
\(512\) | −4.56266 | −0.201643 | ||||||||
\(513\) | 7.23513 | 0.319439 | ||||||||
\(514\) | 15.1046 | 0.666237 | ||||||||
\(515\) | −3.26439 | −0.143846 | ||||||||
\(516\) | −1.50763 | −0.0663698 | ||||||||
\(517\) | −5.62328 | −0.247312 | ||||||||
\(518\) | 0.0960878 | 0.00422186 | ||||||||
\(519\) | −11.1032 | −0.487378 | ||||||||
\(520\) | 2.90918 | 0.127576 | ||||||||
\(521\) | −18.3380 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(522\) | 1.91624 | 0.0838717 | ||||||||
\(523\) | −4.00266 | −0.175024 | −0.0875121 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875121 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(524\) | 5.92143 | 0.258679 | ||||||||
\(525\) | −0.122708 | −0.00535541 | ||||||||
\(526\) | 3.44230 | 0.150092 | ||||||||
\(527\) | 1.77746 | 0.0774275 | ||||||||
\(528\) | 0.667731 | 0.0290593 | ||||||||
\(529\) | 62.5878 | 2.72121 | ||||||||
\(530\) | 3.33588 | 0.144902 | ||||||||
\(531\) | 12.7031 | 0.551269 | ||||||||
\(532\) | 1.01526 | 0.0440172 | ||||||||
\(533\) | −7.40266 | −0.320645 | ||||||||
\(534\) | −2.46962 | −0.106871 | ||||||||
\(535\) | 16.7289 | 0.723252 | ||||||||
\(536\) | 3.99212 | 0.172433 | ||||||||
\(537\) | −9.88354 | −0.426506 | ||||||||
\(538\) | −21.5611 | −0.929565 | ||||||||
\(539\) | 11.5121 | 0.495859 | ||||||||
\(540\) | −1.14356 | −0.0492110 | ||||||||
\(541\) | −15.8853 | −0.682962 | −0.341481 | − | 0.939889i | \(-0.610928\pi\) | ||||
−0.341481 | + | 0.939889i | \(0.610928\pi\) | |||||||
\(542\) | −9.55091 | −0.410247 | ||||||||
\(543\) | −7.16446 | −0.307456 | ||||||||
\(544\) | 9.67547 | 0.414832 | ||||||||
\(545\) | −6.39717 | −0.274025 | ||||||||
\(546\) | 0.113559 | 0.00485986 | ||||||||
\(547\) | −3.75156 | −0.160405 | −0.0802026 | − | 0.996779i | \(-0.525557\pi\) | ||||
−0.0802026 | + | 0.996779i | \(0.525557\pi\) | |||||||
\(548\) | −6.02900 | −0.257546 | ||||||||
\(549\) | −2.15214 | −0.0918509 | ||||||||
\(550\) | −1.52524 | −0.0650364 | ||||||||
\(551\) | 14.9813 | 0.638224 | ||||||||
\(552\) | 26.9139 | 1.14553 | ||||||||
\(553\) | 0.163578 | 0.00695603 | ||||||||
\(554\) | 9.26030 | 0.393432 | ||||||||
\(555\) | −0.846152 | −0.0359171 | ||||||||
\(556\) | −16.7558 | −0.710606 | ||||||||
\(557\) | 40.5053 | 1.71626 | 0.858132 | − | 0.513430i | \(-0.171625\pi\) | ||||
0.858132 | + | 0.513430i | \(0.171625\pi\) | |||||||
\(558\) | 0.925440 | 0.0391770 | ||||||||
\(559\) | −1.31837 | −0.0557609 | ||||||||
\(560\) | 0.0497146 | 0.00210083 | ||||||||
\(561\) | −2.92948 | −0.123683 | ||||||||
\(562\) | −1.06074 | −0.0447448 | ||||||||
\(563\) | 11.3096 | 0.476641 | 0.238320 | − | 0.971187i | \(-0.423403\pi\) | ||||
0.238320 | + | 0.971187i | \(0.423403\pi\) | |||||||
\(564\) | −3.90175 | −0.164293 | ||||||||
\(565\) | 13.5830 | 0.571443 | ||||||||
\(566\) | 16.0679 | 0.675386 | ||||||||
\(567\) | −0.122708 | −0.00515324 | ||||||||
\(568\) | 2.92554 | 0.122753 | ||||||||
\(569\) | 17.3368 | 0.726798 | 0.363399 | − | 0.931634i | \(-0.381616\pi\) | ||||
0.363399 | + | 0.931634i | \(0.381616\pi\) | |||||||
\(570\) | 6.69568 | 0.280451 | ||||||||
\(571\) | −25.6460 | −1.07325 | −0.536627 | − | 0.843820i | \(-0.680302\pi\) | ||||
−0.536627 | + | 0.843820i | \(0.680302\pi\) | |||||||
\(572\) | −1.88473 | −0.0788045 | ||||||||
\(573\) | 11.0610 | 0.462081 | ||||||||
\(574\) | −0.840636 | −0.0350875 | ||||||||
\(575\) | −9.25137 | −0.385809 | ||||||||
\(576\) | 5.84785 | 0.243660 | ||||||||
\(577\) | 1.31756 | 0.0548509 | 0.0274255 | − | 0.999624i | \(-0.491269\pi\) | ||||
0.0274255 | + | 0.999624i | \(0.491269\pi\) | |||||||
\(578\) | −12.8087 | −0.532770 | ||||||||
\(579\) | 12.3088 | 0.511535 | ||||||||
\(580\) | −2.36789 | −0.0983213 | ||||||||
\(581\) | −1.36483 | −0.0566229 | ||||||||
\(582\) | 14.9011 | 0.617671 | ||||||||
\(583\) | −5.94090 | −0.246047 | ||||||||
\(584\) | −27.9954 | −1.15846 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 15.6822 | 0.647828 | ||||||||
\(587\) | −19.8016 | −0.817300 | −0.408650 | − | 0.912691i | \(-0.634000\pi\) | ||||
−0.408650 | + | 0.912691i | \(0.634000\pi\) | |||||||
\(588\) | 7.98771 | 0.329408 | ||||||||
\(589\) | 7.23513 | 0.298118 | ||||||||
\(590\) | 11.7560 | 0.483986 | ||||||||
\(591\) | −1.76121 | −0.0724465 | ||||||||
\(592\) | 0.342815 | 0.0140896 | ||||||||
\(593\) | −20.9097 | −0.858658 | −0.429329 | − | 0.903148i | \(-0.641250\pi\) | ||||
−0.429329 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(594\) | −1.52524 | −0.0625813 | ||||||||
\(595\) | −0.218108 | −0.00894157 | ||||||||
\(596\) | −15.7673 | −0.645854 | ||||||||
\(597\) | 7.85890 | 0.321644 | ||||||||
\(598\) | 8.56159 | 0.350109 | ||||||||
\(599\) | −2.12689 | −0.0869023 | −0.0434511 | − | 0.999056i | \(-0.513835\pi\) | ||||
−0.0434511 | + | 0.999056i | \(0.513835\pi\) | |||||||
\(600\) | −2.90918 | −0.118767 | ||||||||
\(601\) | −0.348888 | −0.0142314 | −0.00711571 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711571 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(602\) | −0.149712 | −0.00610180 | ||||||||
\(603\) | −1.37225 | −0.0558823 | ||||||||
\(604\) | −12.6416 | −0.514380 | ||||||||
\(605\) | −8.28369 | −0.336780 | ||||||||
\(606\) | −7.95066 | −0.322973 | ||||||||
\(607\) | −13.0912 | −0.531354 | −0.265677 | − | 0.964062i | \(-0.585596\pi\) | ||||
−0.265677 | + | 0.964062i | \(0.585596\pi\) | |||||||
\(608\) | 39.3838 | 1.59722 | ||||||||
\(609\) | −0.254082 | −0.0102959 | ||||||||
\(610\) | −1.99167 | −0.0806405 | ||||||||
\(611\) | −3.41193 | −0.138032 | ||||||||
\(612\) | −2.03264 | −0.0821645 | ||||||||
\(613\) | −4.28341 | −0.173005 | −0.0865026 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865026 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(614\) | −23.0386 | −0.929763 | ||||||||
\(615\) | 7.40266 | 0.298504 | ||||||||
\(616\) | −0.588345 | −0.0237051 | ||||||||
\(617\) | −18.6834 | −0.752167 | −0.376083 | − | 0.926586i | \(-0.622729\pi\) | ||||
−0.376083 | + | 0.926586i | \(0.622729\pi\) | |||||||
\(618\) | −3.02100 | −0.121522 | ||||||||
\(619\) | −25.3256 | −1.01792 | −0.508961 | − | 0.860790i | \(-0.669970\pi\) | ||||
−0.508961 | + | 0.860790i | \(0.669970\pi\) | |||||||
\(620\) | −1.14356 | −0.0459265 | ||||||||
\(621\) | −9.25137 | −0.371245 | ||||||||
\(622\) | 19.9651 | 0.800527 | ||||||||
\(623\) | 0.327456 | 0.0131193 | ||||||||
\(624\) | 0.405146 | 0.0162188 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.54961 | −0.261775 | ||||||||
\(627\) | −11.9244 | −0.476214 | ||||||||
\(628\) | −10.3680 | −0.413730 | ||||||||
\(629\) | −1.50400 | −0.0599685 | ||||||||
\(630\) | −0.113559 | −0.00452429 | ||||||||
\(631\) | −17.4282 | −0.693806 | −0.346903 | − | 0.937901i | \(-0.612767\pi\) | ||||
−0.346903 | + | 0.937901i | \(0.612767\pi\) | |||||||
\(632\) | 3.87813 | 0.154264 | ||||||||
\(633\) | 15.9547 | 0.634141 | ||||||||
\(634\) | −23.9221 | −0.950068 | ||||||||
\(635\) | −18.0085 | −0.714647 | ||||||||
\(636\) | −4.12213 | −0.163453 | ||||||||
\(637\) | 6.98494 | 0.276754 | ||||||||
\(638\) | −3.15821 | −0.125035 | ||||||||
\(639\) | −1.00563 | −0.0397819 | ||||||||
\(640\) | −5.47500 | −0.216418 | ||||||||
\(641\) | −5.63300 | −0.222490 | −0.111245 | − | 0.993793i | \(-0.535484\pi\) | ||||
−0.111245 | + | 0.993793i | \(0.535484\pi\) | |||||||
\(642\) | 15.4816 | 0.611008 | ||||||||
\(643\) | −5.93111 | −0.233900 | −0.116950 | − | 0.993138i | \(-0.537312\pi\) | ||||
−0.116950 | + | 0.993138i | \(0.537312\pi\) | |||||||
\(644\) | −1.29819 | −0.0511557 | ||||||||
\(645\) | 1.31837 | 0.0519106 | ||||||||
\(646\) | 11.9013 | 0.468251 | ||||||||
\(647\) | −12.1864 | −0.479096 | −0.239548 | − | 0.970885i | \(-0.576999\pi\) | ||||
−0.239548 | + | 0.970885i | \(0.576999\pi\) | |||||||
\(648\) | −2.90918 | −0.114283 | ||||||||
\(649\) | −20.9363 | −0.821823 | ||||||||
\(650\) | −0.925440 | −0.0362987 | ||||||||
\(651\) | −0.122708 | −0.00480930 | ||||||||
\(652\) | −10.0305 | −0.392826 | ||||||||
\(653\) | −32.9623 | −1.28991 | −0.644957 | − | 0.764219i | \(-0.723125\pi\) | ||||
−0.644957 | + | 0.764219i | \(0.723125\pi\) | |||||||
\(654\) | −5.92019 | −0.231498 | ||||||||
\(655\) | −5.17806 | −0.202324 | ||||||||
\(656\) | −2.99916 | −0.117097 | ||||||||
\(657\) | 9.62315 | 0.375435 | ||||||||
\(658\) | −0.387454 | −0.0151045 | ||||||||
\(659\) | −39.1020 | −1.52320 | −0.761599 | − | 0.648049i | \(-0.775585\pi\) | ||||
−0.761599 | + | 0.648049i | \(0.775585\pi\) | |||||||
\(660\) | 1.88473 | 0.0733630 | ||||||||
\(661\) | 24.3273 | 0.946221 | 0.473111 | − | 0.881003i | \(-0.343131\pi\) | ||||
0.473111 | + | 0.881003i | \(0.343131\pi\) | |||||||
\(662\) | −19.2823 | −0.749429 | ||||||||
\(663\) | −1.77746 | −0.0690309 | ||||||||
\(664\) | −32.3577 | −1.25572 | ||||||||
\(665\) | −0.887807 | −0.0344277 | ||||||||
\(666\) | −0.783062 | −0.0303431 | ||||||||
\(667\) | −19.1562 | −0.741729 | ||||||||
\(668\) | −3.18466 | −0.123218 | ||||||||
\(669\) | 19.8537 | 0.767587 | ||||||||
\(670\) | −1.26993 | −0.0490619 | ||||||||
\(671\) | 3.54699 | 0.136930 | ||||||||
\(672\) | −0.667949 | −0.0257667 | ||||||||
\(673\) | 34.5179 | 1.33057 | 0.665284 | − | 0.746591i | \(-0.268311\pi\) | ||||
0.665284 | + | 0.746591i | \(0.268311\pi\) | |||||||
\(674\) | −6.16359 | −0.237413 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −1.14356 | −0.0439831 | ||||||||
\(677\) | −27.3961 | −1.05292 | −0.526458 | − | 0.850201i | \(-0.676480\pi\) | ||||
−0.526458 | + | 0.850201i | \(0.676480\pi\) | |||||||
\(678\) | 12.5703 | 0.482759 | ||||||||
\(679\) | −1.97580 | −0.0758242 | ||||||||
\(680\) | −5.17095 | −0.198297 | ||||||||
\(681\) | 18.5763 | 0.711844 | ||||||||
\(682\) | −1.52524 | −0.0584044 | ||||||||
\(683\) | 29.1363 | 1.11487 | 0.557434 | − | 0.830221i | \(-0.311786\pi\) | ||||
0.557434 | + | 0.830221i | \(0.311786\pi\) | |||||||
\(684\) | −8.27381 | −0.316357 | ||||||||
\(685\) | 5.27213 | 0.201438 | ||||||||
\(686\) | 1.58811 | 0.0606344 | ||||||||
\(687\) | −9.67200 | −0.369010 | ||||||||
\(688\) | −0.534131 | −0.0203636 | ||||||||
\(689\) | −3.60465 | −0.137326 | ||||||||
\(690\) | −8.56159 | −0.325934 | ||||||||
\(691\) | −41.8367 | −1.59154 | −0.795771 | − | 0.605598i | \(-0.792934\pi\) | ||||
−0.795771 | + | 0.605598i | \(0.792934\pi\) | |||||||
\(692\) | 12.6972 | 0.482676 | ||||||||
\(693\) | 0.202238 | 0.00768237 | ||||||||
\(694\) | −8.27632 | −0.314165 | ||||||||
\(695\) | 14.6523 | 0.555795 | ||||||||
\(696\) | −6.02383 | −0.228333 | ||||||||
\(697\) | 13.1579 | 0.498393 | ||||||||
\(698\) | 3.02062 | 0.114332 | ||||||||
\(699\) | 6.15546 | 0.232821 | ||||||||
\(700\) | 0.140324 | 0.00530374 | ||||||||
\(701\) | −2.66627 | −0.100704 | −0.0503518 | − | 0.998732i | \(-0.516034\pi\) | ||||
−0.0503518 | + | 0.998732i | \(0.516034\pi\) | |||||||
\(702\) | −0.925440 | −0.0349285 | ||||||||
\(703\) | −6.12202 | −0.230896 | ||||||||
\(704\) | −9.63797 | −0.363245 | ||||||||
\(705\) | 3.41193 | 0.128501 | ||||||||
\(706\) | −2.14569 | −0.0807542 | ||||||||
\(707\) | 1.05421 | 0.0396476 | ||||||||
\(708\) | −14.5268 | −0.545951 | ||||||||
\(709\) | 32.1566 | 1.20767 | 0.603833 | − | 0.797111i | \(-0.293639\pi\) | ||||
0.603833 | + | 0.797111i | \(0.293639\pi\) | |||||||
\(710\) | −0.930646 | −0.0349265 | ||||||||
\(711\) | −1.33307 | −0.0499939 | ||||||||
\(712\) | 7.76339 | 0.290945 | ||||||||
\(713\) | −9.25137 | −0.346466 | ||||||||
\(714\) | −0.201846 | −0.00755391 | ||||||||
\(715\) | 1.64812 | 0.0616363 | ||||||||
\(716\) | 11.3024 | 0.422392 | ||||||||
\(717\) | 2.82872 | 0.105640 | ||||||||
\(718\) | −8.45539 | −0.315553 | ||||||||
\(719\) | 0.324398 | 0.0120980 | 0.00604901 | − | 0.999982i | \(-0.498075\pi\) | ||||
0.00604901 | + | 0.999982i | \(0.498075\pi\) | |||||||
\(720\) | −0.405146 | −0.0150989 | ||||||||
\(721\) | 0.400566 | 0.0149179 | ||||||||
\(722\) | 30.8608 | 1.14852 | ||||||||
\(723\) | −7.70559 | −0.286574 | ||||||||
\(724\) | 8.19300 | 0.304490 | ||||||||
\(725\) | 2.07063 | 0.0769012 | ||||||||
\(726\) | −7.66606 | −0.284514 | ||||||||
\(727\) | −7.11521 | −0.263888 | −0.131944 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131944 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(728\) | −0.356979 | −0.0132305 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.90565 | 0.329613 | ||||||||
\(731\) | 2.34335 | 0.0866718 | ||||||||
\(732\) | 2.46110 | 0.0909649 | ||||||||
\(733\) | −39.5190 | −1.45967 | −0.729835 | − | 0.683624i | \(-0.760403\pi\) | ||||
−0.729835 | + | 0.683624i | \(0.760403\pi\) | |||||||
\(734\) | −33.9028 | −1.25137 | ||||||||
\(735\) | −6.98494 | −0.257643 | ||||||||
\(736\) | −50.3590 | −1.85626 | ||||||||
\(737\) | 2.26164 | 0.0833085 | ||||||||
\(738\) | 6.85072 | 0.252178 | ||||||||
\(739\) | 10.8952 | 0.400788 | 0.200394 | − | 0.979715i | \(-0.435778\pi\) | ||||
0.200394 | + | 0.979715i | \(0.435778\pi\) | |||||||
\(740\) | 0.967626 | 0.0355706 | ||||||||
\(741\) | −7.23513 | −0.265789 | ||||||||
\(742\) | −0.409339 | −0.0150273 | ||||||||
\(743\) | 38.3859 | 1.40824 | 0.704121 | − | 0.710080i | \(-0.251341\pi\) | ||||
0.704121 | + | 0.710080i | \(0.251341\pi\) | |||||||
\(744\) | −2.90918 | −0.106656 | ||||||||
\(745\) | 13.7879 | 0.505149 | ||||||||
\(746\) | −4.23810 | −0.155168 | ||||||||
\(747\) | 11.1226 | 0.406956 | ||||||||
\(748\) | 3.35004 | 0.122489 | ||||||||
\(749\) | −2.05276 | −0.0750063 | ||||||||
\(750\) | 0.925440 | 0.0337923 | ||||||||
\(751\) | 12.9318 | 0.471888 | 0.235944 | − | 0.971767i | \(-0.424182\pi\) | ||||
0.235944 | + | 0.971767i | \(0.424182\pi\) | |||||||
\(752\) | −1.38233 | −0.0504084 | ||||||||
\(753\) | −22.1922 | −0.808728 | ||||||||
\(754\) | −1.91624 | −0.0697855 | ||||||||
\(755\) | 11.0546 | 0.402318 | ||||||||
\(756\) | 0.140324 | 0.00510353 | ||||||||
\(757\) | 41.3902 | 1.50435 | 0.752176 | − | 0.658962i | \(-0.229004\pi\) | ||||
0.752176 | + | 0.658962i | \(0.229004\pi\) | |||||||
\(758\) | 7.93074 | 0.288057 | ||||||||
\(759\) | 15.2474 | 0.553446 | ||||||||
\(760\) | −21.0483 | −0.763501 | ||||||||
\(761\) | 46.8386 | 1.69790 | 0.848948 | − | 0.528476i | \(-0.177236\pi\) | ||||
0.848948 | + | 0.528476i | \(0.177236\pi\) | |||||||
\(762\) | −16.6658 | −0.603739 | ||||||||
\(763\) | 0.784982 | 0.0284183 | ||||||||
\(764\) | −12.6490 | −0.457623 | ||||||||
\(765\) | 1.77746 | 0.0642643 | ||||||||
\(766\) | −3.23648 | −0.116939 | ||||||||
\(767\) | −12.7031 | −0.458684 | ||||||||
\(768\) | −16.7625 | −0.604864 | ||||||||
\(769\) | −52.8158 | −1.90459 | −0.952294 | − | 0.305183i | \(-0.901283\pi\) | ||||
−0.952294 | + | 0.305183i | \(0.901283\pi\) | |||||||
\(770\) | 0.187159 | 0.00674473 | ||||||||
\(771\) | 16.3216 | 0.587807 | ||||||||
\(772\) | −14.0758 | −0.506600 | ||||||||
\(773\) | −42.0977 | −1.51415 | −0.757075 | − | 0.653328i | \(-0.773372\pi\) | ||||
−0.757075 | + | 0.653328i | \(0.773372\pi\) | |||||||
\(774\) | 1.22007 | 0.0438545 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −46.8426 | −1.68155 | ||||||||
\(777\) | 0.103829 | 0.00372486 | ||||||||
\(778\) | 5.09145 | 0.182537 | ||||||||
\(779\) | 53.5592 | 1.91896 | ||||||||
\(780\) | 1.14356 | 0.0409461 | ||||||||
\(781\) | 1.65740 | 0.0593063 | ||||||||
\(782\) | −15.2179 | −0.544191 | ||||||||
\(783\) | 2.07063 | 0.0739983 | ||||||||
\(784\) | 2.82992 | 0.101069 | ||||||||
\(785\) | 9.06646 | 0.323596 | ||||||||
\(786\) | −4.79199 | −0.170925 | ||||||||
\(787\) | 20.8820 | 0.744361 | 0.372181 | − | 0.928160i | \(-0.378610\pi\) | ||||
0.372181 | + | 0.928160i | \(0.378610\pi\) | |||||||
\(788\) | 2.01405 | 0.0717476 | ||||||||
\(789\) | 3.71964 | 0.132423 | ||||||||
\(790\) | −1.23367 | −0.0438921 | ||||||||
\(791\) | −1.66674 | −0.0592626 | ||||||||
\(792\) | 4.79468 | 0.170372 | ||||||||
\(793\) | 2.15214 | 0.0764246 | ||||||||
\(794\) | −34.6496 | −1.22967 | ||||||||
\(795\) | 3.60465 | 0.127844 | ||||||||
\(796\) | −8.98714 | −0.318541 | ||||||||
\(797\) | −26.1259 | −0.925427 | −0.462714 | − | 0.886508i | \(-0.653124\pi\) | ||||
−0.462714 | + | 0.886508i | \(0.653124\pi\) | |||||||
\(798\) | −0.821612 | −0.0290847 | ||||||||
\(799\) | 6.06458 | 0.214549 | ||||||||
\(800\) | 5.44342 | 0.192454 | ||||||||
\(801\) | −2.66859 | −0.0942899 | ||||||||
\(802\) | −13.2233 | −0.466932 | ||||||||
\(803\) | −15.8601 | −0.559692 | ||||||||
\(804\) | 1.56925 | 0.0553432 | ||||||||
\(805\) | 1.13521 | 0.0400111 | ||||||||
\(806\) | −0.925440 | −0.0325972 | ||||||||
\(807\) | −23.2982 | −0.820136 | ||||||||
\(808\) | 24.9934 | 0.879264 | ||||||||
\(809\) | −18.2401 | −0.641286 | −0.320643 | − | 0.947200i | \(-0.603899\pi\) | ||||
−0.320643 | + | 0.947200i | \(0.603899\pi\) | |||||||
\(810\) | 0.925440 | 0.0325166 | ||||||||
\(811\) | −10.3561 | −0.363651 | −0.181826 | − | 0.983331i | \(-0.558201\pi\) | ||||
−0.181826 | + | 0.983331i | \(0.558201\pi\) | |||||||
\(812\) | 0.290559 | 0.0101966 | ||||||||
\(813\) | −10.3204 | −0.361952 | ||||||||
\(814\) | 1.29058 | 0.0452349 | ||||||||
\(815\) | 8.77132 | 0.307246 | ||||||||
\(816\) | −0.720132 | −0.0252097 | ||||||||
\(817\) | 9.53855 | 0.333712 | ||||||||
\(818\) | −3.82857 | −0.133863 | ||||||||
\(819\) | 0.122708 | 0.00428776 | ||||||||
\(820\) | −8.46539 | −0.295624 | ||||||||
\(821\) | −30.3405 | −1.05889 | −0.529445 | − | 0.848344i | \(-0.677600\pi\) | ||||
−0.529445 | + | 0.848344i | \(0.677600\pi\) | |||||||
\(822\) | 4.87904 | 0.170176 | ||||||||
\(823\) | −27.7806 | −0.968373 | −0.484186 | − | 0.874965i | \(-0.660884\pi\) | ||||
−0.484186 | + | 0.874965i | \(0.660884\pi\) | |||||||
\(824\) | 9.49669 | 0.330833 | ||||||||
\(825\) | −1.64812 | −0.0573803 | ||||||||
\(826\) | −1.44255 | −0.0501928 | ||||||||
\(827\) | −26.7571 | −0.930435 | −0.465218 | − | 0.885196i | \(-0.654024\pi\) | ||||
−0.465218 | + | 0.885196i | \(0.654024\pi\) | |||||||
\(828\) | 10.5795 | 0.367663 | ||||||||
\(829\) | 5.69140 | 0.197671 | 0.0988353 | − | 0.995104i | \(-0.468488\pi\) | ||||
0.0988353 | + | 0.995104i | \(0.468488\pi\) | |||||||
\(830\) | 10.2933 | 0.357287 | ||||||||
\(831\) | 10.0064 | 0.347117 | ||||||||
\(832\) | −5.84785 | −0.202738 | ||||||||
\(833\) | −12.4155 | −0.430171 | ||||||||
\(834\) | 13.5599 | 0.469540 | ||||||||
\(835\) | 2.78486 | 0.0963740 | ||||||||
\(836\) | 13.6363 | 0.471620 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 7.23350 | 0.249877 | ||||||||
\(839\) | 30.0221 | 1.03648 | 0.518240 | − | 0.855235i | \(-0.326588\pi\) | ||||
0.518240 | + | 0.855235i | \(0.326588\pi\) | |||||||
\(840\) | 0.356979 | 0.0123169 | ||||||||
\(841\) | −24.7125 | −0.852155 | ||||||||
\(842\) | −23.5884 | −0.812910 | ||||||||
\(843\) | −1.14620 | −0.0394774 | ||||||||
\(844\) | −18.2451 | −0.628023 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 3.15754 | 0.108558 | ||||||||
\(847\) | 1.01647 | 0.0349264 | ||||||||
\(848\) | −1.46041 | −0.0501506 | ||||||||
\(849\) | 17.3625 | 0.595879 | ||||||||
\(850\) | 1.64493 | 0.0564208 | ||||||||
\(851\) | 7.82806 | 0.268342 | ||||||||
\(852\) | 1.14999 | 0.0393982 | ||||||||
\(853\) | −51.3358 | −1.75770 | −0.878852 | − | 0.477095i | \(-0.841690\pi\) | ||||
−0.878852 | + | 0.477095i | \(0.841690\pi\) | |||||||
\(854\) | 0.244394 | 0.00836298 | ||||||||
\(855\) | 7.23513 | 0.247436 | ||||||||
\(856\) | −48.6672 | −1.66341 | ||||||||
\(857\) | 2.32929 | 0.0795670 | 0.0397835 | − | 0.999208i | \(-0.487333\pi\) | ||||
0.0397835 | + | 0.999208i | \(0.487333\pi\) | |||||||
\(858\) | 1.52524 | 0.0520708 | ||||||||
\(859\) | 2.01410 | 0.0687201 | 0.0343601 | − | 0.999410i | \(-0.489061\pi\) | ||||
0.0343601 | + | 0.999410i | \(0.489061\pi\) | |||||||
\(860\) | −1.50763 | −0.0514098 | ||||||||
\(861\) | −0.908364 | −0.0309569 | ||||||||
\(862\) | −13.5835 | −0.462656 | ||||||||
\(863\) | −22.5353 | −0.767112 | −0.383556 | − | 0.923518i | \(-0.625301\pi\) | ||||
−0.383556 | + | 0.923518i | \(0.625301\pi\) | |||||||
\(864\) | 5.44342 | 0.185189 | ||||||||
\(865\) | −11.1032 | −0.377521 | ||||||||
\(866\) | 2.05465 | 0.0698198 | ||||||||
\(867\) | −13.8406 | −0.470052 | ||||||||
\(868\) | 0.140324 | 0.00476290 | ||||||||
\(869\) | 2.19706 | 0.0745301 | ||||||||
\(870\) | 1.91624 | 0.0649667 | ||||||||
\(871\) | 1.37225 | 0.0464969 | ||||||||
\(872\) | 18.6105 | 0.630231 | ||||||||
\(873\) | 16.1017 | 0.544959 | ||||||||
\(874\) | −61.9442 | −2.09529 | ||||||||
\(875\) | −0.122708 | −0.00414828 | ||||||||
\(876\) | −11.0047 | −0.371813 | ||||||||
\(877\) | 22.1993 | 0.749617 | 0.374809 | − | 0.927102i | \(-0.377708\pi\) | ||||
0.374809 | + | 0.927102i | \(0.377708\pi\) | |||||||
\(878\) | 14.1058 | 0.476047 | ||||||||
\(879\) | 16.9457 | 0.571565 | ||||||||
\(880\) | 0.667731 | 0.0225092 | ||||||||
\(881\) | −8.42036 | −0.283689 | −0.141845 | − | 0.989889i | \(-0.545303\pi\) | ||||
−0.141845 | + | 0.989889i | \(0.545303\pi\) | |||||||
\(882\) | −6.46414 | −0.217659 | ||||||||
\(883\) | 4.60615 | 0.155009 | 0.0775046 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775046 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(884\) | 2.03264 | 0.0683650 | ||||||||
\(885\) | 12.7031 | 0.427011 | ||||||||
\(886\) | 35.6740 | 1.19849 | ||||||||
\(887\) | 41.3899 | 1.38974 | 0.694868 | − | 0.719137i | \(-0.255463\pi\) | ||||
0.694868 | + | 0.719137i | \(0.255463\pi\) | |||||||
\(888\) | 2.46160 | 0.0826060 | ||||||||
\(889\) | 2.20979 | 0.0741139 | ||||||||
\(890\) | −2.46962 | −0.0827818 | ||||||||
\(891\) | −1.64812 | −0.0552142 | ||||||||
\(892\) | −22.7039 | −0.760182 | ||||||||
\(893\) | 24.6858 | 0.826077 | ||||||||
\(894\) | 12.7599 | 0.426754 | ||||||||
\(895\) | −9.88354 | −0.330370 | ||||||||
\(896\) | 0.671825 | 0.0224441 | ||||||||
\(897\) | 9.25137 | 0.308894 | ||||||||
\(898\) | −2.57486 | −0.0859241 | ||||||||
\(899\) | 2.07063 | 0.0690594 | ||||||||
\(900\) | −1.14356 | −0.0381187 | ||||||||
\(901\) | 6.40712 | 0.213452 | ||||||||
\(902\) | −11.2908 | −0.375943 | ||||||||
\(903\) | −0.161774 | −0.00538349 | ||||||||
\(904\) | −39.5154 | −1.31426 | ||||||||
\(905\) | −7.16446 | −0.238155 | ||||||||
\(906\) | 10.2304 | 0.339881 | ||||||||
\(907\) | −35.2866 | −1.17167 | −0.585837 | − | 0.810429i | \(-0.699234\pi\) | ||||
−0.585837 | + | 0.810429i | \(0.699234\pi\) | |||||||
\(908\) | −21.2431 | −0.704976 | ||||||||
\(909\) | −8.59122 | −0.284953 | ||||||||
\(910\) | 0.113559 | 0.00376443 | ||||||||
\(911\) | −2.88455 | −0.0955696 | −0.0477848 | − | 0.998858i | \(-0.515216\pi\) | ||||
−0.0477848 | + | 0.998858i | \(0.515216\pi\) | |||||||
\(912\) | −2.93129 | −0.0970646 | ||||||||
\(913\) | −18.3315 | −0.606684 | ||||||||
\(914\) | 35.9409 | 1.18882 | ||||||||
\(915\) | −2.15214 | −0.0711474 | ||||||||
\(916\) | 11.0605 | 0.365450 | ||||||||
\(917\) | 0.635389 | 0.0209824 | ||||||||
\(918\) | 1.64493 | 0.0542909 | ||||||||
\(919\) | 33.1282 | 1.09280 | 0.546399 | − | 0.837525i | \(-0.315998\pi\) | ||||
0.546399 | + | 0.837525i | \(0.315998\pi\) | |||||||
\(920\) | 26.9139 | 0.887324 | ||||||||
\(921\) | −24.8948 | −0.820310 | ||||||||
\(922\) | −8.31936 | −0.273984 | ||||||||
\(923\) | 1.00563 | 0.0331006 | ||||||||
\(924\) | −0.231271 | −0.00760826 | ||||||||
\(925\) | −0.846152 | −0.0278213 | ||||||||
\(926\) | 22.2751 | 0.732004 | ||||||||
\(927\) | −3.26439 | −0.107217 | ||||||||
\(928\) | 11.2713 | 0.369998 | ||||||||
\(929\) | 50.1823 | 1.64643 | 0.823214 | − | 0.567731i | \(-0.192179\pi\) | ||||
0.823214 | + | 0.567731i | \(0.192179\pi\) | |||||||
\(930\) | 0.925440 | 0.0303464 | ||||||||
\(931\) | −50.5370 | −1.65628 | ||||||||
\(932\) | −7.03915 | −0.230575 | ||||||||
\(933\) | 21.5736 | 0.706289 | ||||||||
\(934\) | 16.6236 | 0.543941 | ||||||||
\(935\) | −2.92948 | −0.0958042 | ||||||||
\(936\) | 2.90918 | 0.0950894 | ||||||||
\(937\) | 13.2509 | 0.432888 | 0.216444 | − | 0.976295i | \(-0.430554\pi\) | ||||
0.216444 | + | 0.976295i | \(0.430554\pi\) | |||||||
\(938\) | 0.155831 | 0.00508806 | ||||||||
\(939\) | −7.07729 | −0.230959 | ||||||||
\(940\) | −3.90175 | −0.127261 | ||||||||
\(941\) | 17.3318 | 0.564999 | 0.282500 | − | 0.959267i | \(-0.408836\pi\) | ||||
0.282500 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(942\) | 8.39046 | 0.273376 | ||||||||
\(943\) | −68.4847 | −2.23017 | ||||||||
\(944\) | −5.14663 | −0.167508 | ||||||||
\(945\) | −0.122708 | −0.00399168 | ||||||||
\(946\) | −2.01082 | −0.0653775 | ||||||||
\(947\) | −10.5526 | −0.342913 | −0.171457 | − | 0.985192i | \(-0.554847\pi\) | ||||
−0.171457 | + | 0.985192i | \(0.554847\pi\) | |||||||
\(948\) | 1.52444 | 0.0495116 | ||||||||
\(949\) | −9.62315 | −0.312381 | ||||||||
\(950\) | 6.69568 | 0.217237 | ||||||||
\(951\) | −25.8494 | −0.838226 | ||||||||
\(952\) | 0.634516 | 0.0205648 | ||||||||
\(953\) | −37.9440 | −1.22913 | −0.614563 | − | 0.788868i | \(-0.710668\pi\) | ||||
−0.614563 | + | 0.788868i | \(0.710668\pi\) | |||||||
\(954\) | 3.33588 | 0.108003 | ||||||||
\(955\) | 11.0610 | 0.357926 | ||||||||
\(956\) | −3.23481 | −0.104621 | ||||||||
\(957\) | −3.41265 | −0.110315 | ||||||||
\(958\) | 1.90910 | 0.0616802 | ||||||||
\(959\) | −0.646931 | −0.0208905 | ||||||||
\(960\) | 5.84785 | 0.188738 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0.783062 | 0.0252469 | ||||||||
\(963\) | 16.7289 | 0.539080 | ||||||||
\(964\) | 8.81181 | 0.283809 | ||||||||
\(965\) | 12.3088 | 0.396233 | ||||||||
\(966\) | 1.05057 | 0.0338016 | ||||||||
\(967\) | −12.9381 | −0.416062 | −0.208031 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208031 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(968\) | 24.0987 | 0.774562 | ||||||||
\(969\) | 12.8602 | 0.413128 | ||||||||
\(970\) | 14.9011 | 0.478446 | ||||||||
\(971\) | −24.3054 | −0.779997 | −0.389998 | − | 0.920816i | \(-0.627524\pi\) | ||||
−0.389998 | + | 0.920816i | \(0.627524\pi\) | |||||||
\(972\) | −1.14356 | −0.0366797 | ||||||||
\(973\) | −1.79796 | −0.0576398 | ||||||||
\(974\) | −20.0668 | −0.642981 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0.871930 | 0.0279098 | ||||||||
\(977\) | −22.8576 | −0.731278 | −0.365639 | − | 0.930757i | \(-0.619150\pi\) | ||||
−0.365639 | + | 0.930757i | \(0.619150\pi\) | |||||||
\(978\) | 8.11733 | 0.259564 | ||||||||
\(979\) | 4.39816 | 0.140566 | ||||||||
\(980\) | 7.98771 | 0.255158 | ||||||||
\(981\) | −6.39717 | −0.204246 | ||||||||
\(982\) | 16.0276 | 0.511461 | ||||||||
\(983\) | 53.1225 | 1.69435 | 0.847173 | − | 0.531318i | \(-0.178303\pi\) | ||||
0.847173 | + | 0.531318i | \(0.178303\pi\) | |||||||
\(984\) | −21.5356 | −0.686531 | ||||||||
\(985\) | −1.76121 | −0.0561168 | ||||||||
\(986\) | 3.40605 | 0.108471 | ||||||||
\(987\) | −0.418670 | −0.0133264 | ||||||||
\(988\) | 8.27381 | 0.263225 | ||||||||
\(989\) | −12.1967 | −0.387832 | ||||||||
\(990\) | −1.52524 | −0.0484753 | ||||||||
\(991\) | −8.71986 | −0.276995 | −0.138498 | − | 0.990363i | \(-0.544227\pi\) | ||||
−0.138498 | + | 0.990363i | \(0.544227\pi\) | |||||||
\(992\) | 5.44342 | 0.172829 | ||||||||
\(993\) | −20.8358 | −0.661206 | ||||||||
\(994\) | 0.114197 | 0.00362212 | ||||||||
\(995\) | 7.85890 | 0.249144 | ||||||||
\(996\) | −12.7194 | −0.403030 | ||||||||
\(997\) | 39.7224 | 1.25802 | 0.629011 | − | 0.777396i | \(-0.283460\pi\) | ||||
0.629011 | + | 0.777396i | \(0.283460\pi\) | |||||||
\(998\) | 9.67799 | 0.306352 | ||||||||
\(999\) | −0.846152 | −0.0267711 |
(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 | 6045.2.a.bi.1.11 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.bi.1.11 | ✓ | 18 | 1.1 | even | 1 | trivial |