Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1672,2,Mod(1,1672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1672, 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("1672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1672 = 2^{3} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1672.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: | \(13.3509872180\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13676.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.42957\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1672.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.42957 | −0.825361 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.22628 | −1.44284 | −0.721419 | − | 0.692499i | \(-0.756510\pi\) | ||||
−0.721419 | + | 0.692499i | \(0.756510\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.429567 | 0.162361 | 0.0811805 | − | 0.996699i | \(-0.474131\pi\) | ||||
0.0811805 | + | 0.996699i | \(0.474131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.956338 | −0.318779 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.88213 | 1.35406 | 0.677030 | − | 0.735955i | \(-0.263267\pi\) | ||||
0.677030 | + | 0.735955i | \(0.263267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.61219 | 1.19086 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.70939 | 0.899660 | 0.449830 | − | 0.893114i | \(-0.351485\pi\) | ||||
0.449830 | + | 0.893114i | \(0.351485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.614095 | −0.134006 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.32349 | −0.692995 | −0.346498 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346498 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.40890 | 1.08178 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65585 | 1.08847 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.75305 | −0.511229 | −0.255615 | − | 0.966779i | \(-0.582278\pi\) | ||||
−0.255615 | + | 0.966779i | \(0.582278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.699512 | 0.125636 | 0.0628181 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628181 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.42957 | −0.248856 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.38591 | −0.234261 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.61409 | −0.265356 | −0.132678 | − | 0.991159i | \(-0.542358\pi\) | ||||
−0.132678 | + | 0.991159i | \(0.542358\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.97934 | −1.11759 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.99809 | −1.40527 | −0.702633 | − | 0.711552i | \(-0.747992\pi\) | ||||
−0.702633 | + | 0.711552i | \(0.747992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40890 | 1.12985 | 0.564924 | − | 0.825143i | \(-0.308906\pi\) | ||||
0.564924 | + | 0.825143i | \(0.308906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.08542 | 0.459947 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9051 | −1.59068 | −0.795339 | − | 0.606165i | \(-0.792707\pi\) | ||||
−0.795339 | + | 0.606165i | \(0.792707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.81547 | −0.973639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.30283 | −0.742544 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.452567 | 0.0621648 | 0.0310824 | − | 0.999517i | \(-0.490105\pi\) | ||||
0.0310824 | + | 0.999517i | \(0.490105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.22628 | −0.435032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.42957 | −0.189351 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.38591 | 0.310618 | 0.155309 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155309 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.62207 | −0.975906 | −0.487953 | − | 0.872870i | \(-0.662256\pi\) | ||||
−0.487953 | + | 0.872870i | \(0.662256\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.410811 | −0.0517574 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.7511 | −1.95369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.47132 | 0.912767 | 0.456384 | − | 0.889783i | \(-0.349144\pi\) | ||||
0.456384 | + | 0.889783i | \(0.349144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.75115 | 0.571971 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.32248 | −0.156950 | −0.0784749 | − | 0.996916i | \(-0.525005\pi\) | ||||
−0.0784749 | + | 0.996916i | \(0.525005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7643 | −1.61099 | −0.805493 | − | 0.592605i | \(-0.798099\pi\) | ||||
−0.805493 | + | 0.592605i | \(0.798099\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.73239 | −0.892860 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.429567 | 0.0489537 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.11596 | −0.238064 | −0.119032 | − | 0.992890i | \(-0.537979\pi\) | ||||
−0.119032 | + | 0.992890i | \(0.537979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.21640 | −0.579600 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.64597 | −0.949019 | −0.474509 | − | 0.880251i | \(-0.657374\pi\) | ||||
−0.474509 | + | 0.880251i | \(0.657374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.9676 | −1.29806 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.93568 | 0.421949 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.89201 | 0.412553 | 0.206276 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206276 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09720 | 0.219847 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.22628 | −0.331010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9793 | −1.41939 | −0.709693 | − | 0.704511i | \(-0.751167\pi\) | ||||
−0.709693 | + | 0.704511i | \(0.751167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.956338 | −0.0961156 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.65585 | 0.662282 | 0.331141 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331141 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4014 | 1.61607 | 0.808037 | − | 0.589132i | \(-0.200530\pi\) | ||||
0.808037 | + | 0.589132i | \(0.200530\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.98124 | 0.193350 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.01222 | 0.871244 | 0.435622 | − | 0.900130i | \(-0.356528\pi\) | ||||
0.435622 | + | 0.900130i | \(0.356528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.71827 | −0.739276 | −0.369638 | − | 0.929176i | \(-0.620518\pi\) | ||||
−0.369638 | + | 0.929176i | \(0.620518\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.30746 | 0.219014 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.7511 | −1.76396 | −0.881980 | − | 0.471287i | \(-0.843790\pi\) | ||||
−0.881980 | + | 0.471287i | \(0.843790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7225 | 0.999879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.66897 | −0.431646 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.59343 | 0.146070 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8634 | 1.15985 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.31924 | −0.117997 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.762934 | 0.0676995 | 0.0338497 | − | 0.999427i | \(-0.489223\pi\) | ||||
0.0338497 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5915 | −0.932532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9568 | −1.48152 | −0.740760 | − | 0.671770i | \(-0.765534\pi\) | ||||
−0.740760 | + | 0.671770i | \(0.765534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.429567 | 0.0372482 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.2474 | −1.57048 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.9075 | 1.44450 | 0.722251 | − | 0.691631i | \(-0.243107\pi\) | ||||
0.722251 | + | 0.691631i | \(0.243107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9577 | 1.52315 | 0.761575 | − | 0.648077i | \(-0.224426\pi\) | ||||
0.761575 | + | 0.648077i | \(0.224426\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5896 | 1.31288 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.88213 | 0.408265 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.88213 | 0.737621 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.74317 | 0.803603 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.1633 | −1.56992 | −0.784959 | − | 0.619548i | \(-0.787316\pi\) | ||||
−0.784959 | + | 0.619548i | \(0.787316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.02997 | −0.734848 | −0.367424 | − | 0.930053i | \(-0.619760\pi\) | ||||
−0.367424 | + | 0.930053i | \(0.619760\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.54743 | −0.286793 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.25683 | −0.181273 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.47423 | −0.516700 | −0.258350 | − | 0.966051i | \(-0.583179\pi\) | ||||
−0.258350 | + | 0.966051i | \(0.583179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.646975 | −0.0513084 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.42766 | −0.112515 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9962 | −1.25292 | −0.626459 | − | 0.779454i | \(-0.715496\pi\) | ||||
−0.626459 | + | 0.779454i | \(0.715496\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.61219 | 0.359058 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.85026 | 0.220560 | 0.110280 | − | 0.993901i | \(-0.464825\pi\) | ||||
0.110280 | + | 0.993901i | \(0.464825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8352 | 0.833479 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.956338 | −0.0731330 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.7991 | −1.58132 | −0.790661 | − | 0.612254i | \(-0.790263\pi\) | ||||
−0.790661 | + | 0.612254i | \(0.790263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.32349 | 0.175639 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.41081 | −0.256372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.84038 | 0.137556 | 0.0687782 | − | 0.997632i | \(-0.478090\pi\) | ||||
0.0687782 | + | 0.997632i | \(0.478090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.94556 | −0.218941 | −0.109471 | − | 0.993990i | \(-0.534916\pi\) | ||||
−0.109471 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8963 | 0.805475 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.20753 | 0.382865 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.70939 | 0.271258 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.42957 | 0.176725 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3732 | −1.04001 | −0.520005 | − | 0.854163i | \(-0.674070\pi\) | ||||
−0.520005 | + | 0.854163i | \(0.674070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.62106 | −0.692539 | −0.346270 | − | 0.938135i | \(-0.612552\pi\) | ||||
−0.346270 | + | 0.938135i | \(0.612552\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.5173 | 1.61250 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.0671 | −1.50097 | −0.750484 | − | 0.660888i | \(-0.770180\pi\) | ||||
−0.750484 | + | 0.660888i | \(0.770180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0911 | 1.06978 | 0.534888 | − | 0.844923i | \(-0.320354\pi\) | ||||
0.534888 | + | 0.844923i | \(0.320354\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6808 | −0.753362 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.18262 | −0.0830038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.0304 | 2.02757 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.17838 | 0.220912 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.272856 | 0.0187842 | 0.00939209 | − | 0.999956i | \(-0.497010\pi\) | ||||
0.00939209 | + | 0.999956i | \(0.497010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.89058 | 0.129540 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.9032 | −1.63019 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.300488 | 0.0203984 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.6769 | 1.32964 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1098 | 1.21819 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8760 | −0.862240 | −0.431120 | − | 0.902295i | \(-0.641881\pi\) | ||||
−0.431120 | + | 0.902295i | \(0.641881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.17274 | −0.344849 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.1046 | 1.53351 | 0.766753 | − | 0.641942i | \(-0.221871\pi\) | ||||
0.766753 | + | 0.641942i | \(0.221871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9187 | 1.25019 | 0.625093 | − | 0.780550i | \(-0.285061\pi\) | ||||
0.625093 | + | 0.780550i | \(0.285061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.614095 | −0.0404045 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8802 | 1.04035 | 0.520174 | − | 0.854060i | \(-0.325867\pi\) | ||||
0.520174 | + | 0.854060i | \(0.325867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.1831 | 2.29509 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.02491 | 0.196489 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6793 | −1.72574 | −0.862870 | − | 0.505427i | \(-0.831335\pi\) | ||||
−0.862870 | + | 0.505427i | \(0.831335\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.78550 | −0.179430 | −0.0897150 | − | 0.995967i | \(-0.528596\pi\) | ||||
−0.0897150 | + | 0.995967i | \(0.528596\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.51035 | −0.610089 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.9886 | 1.40480 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.88213 | 0.310643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.3600 | 0.783283 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6014 | 0.732274 | 0.366137 | − | 0.930561i | \(-0.380680\pi\) | ||||
0.366137 | + | 0.930561i | \(0.380680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.32349 | −0.208946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.1084 | 1.07137 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.04600 | −0.127626 | −0.0638130 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638130 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.693362 | −0.0430834 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.63285 | 0.162969 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.1807 | −1.61437 | −0.807186 | − | 0.590297i | \(-0.799011\pi\) | ||||
−0.807186 | + | 0.590297i | \(0.799011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.46011 | −0.0896938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.56389 | −0.340505 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.2864 | 0.871058 | 0.435529 | − | 0.900175i | \(-0.356561\pi\) | ||||
0.435529 | + | 0.900175i | \(0.356561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4920 | 0.698088 | 0.349044 | − | 0.937106i | \(-0.386506\pi\) | ||||
0.349044 | + | 0.937106i | \(0.386506\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.99809 | −0.181453 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.40890 | 0.326169 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.6057 | −1.23807 | −0.619037 | − | 0.785362i | \(-0.712477\pi\) | ||||
−0.619037 | + | 0.785362i | \(0.712477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.668970 | −0.0400502 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4051 | 1.03830 | 0.519150 | − | 0.854683i | \(-0.326248\pi\) | ||||
0.519150 | + | 0.854683i | \(0.326248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.92813 | −0.174059 | −0.0870297 | − | 0.996206i | \(-0.527738\pi\) | ||||
−0.0870297 | + | 0.996206i | \(0.527738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.61219 | 0.273202 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.86528 | −0.228161 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.24041 | −0.190612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.9844 | 1.17151 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.97319 | 0.582640 | 0.291320 | − | 0.956626i | \(-0.405906\pi\) | ||||
0.291320 | + | 0.956626i | \(0.405906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.69761 | −0.448172 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65585 | 0.328186 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2257 | −0.938357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.18262 | 0.183443 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.51498 | −0.546622 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5910 | 1.40807 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9140 | −0.622895 | −0.311448 | − | 0.950263i | \(-0.600814\pi\) | ||||
−0.311448 | + | 0.950263i | \(0.600814\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.4468 | −1.33384 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.14087 | −0.518331 | −0.259165 | − | 0.965833i | \(-0.583448\pi\) | ||||
−0.259165 | + | 0.965833i | \(0.583448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9193 | 0.786763 | 0.393381 | − | 0.919375i | \(-0.371305\pi\) | ||||
0.393381 | + | 0.919375i | \(0.371305\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.32539 | 0.0746775 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.2159 | −1.58476 | −0.792382 | − | 0.610025i | \(-0.791159\pi\) | ||||
−0.792382 | + | 0.610025i | \(0.791159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.75305 | −0.154141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8836 | −0.719091 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.70939 | 0.206396 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.4070 | 1.46480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.0338 | 0.610170 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.68449 | −0.258264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.29338 | −0.345915 | −0.172958 | − | 0.984929i | \(-0.555332\pi\) | ||||
−0.172958 | + | 0.984929i | \(0.555332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.54362 | 0.0845899 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.1046 | −1.31698 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.57043 | 0.521335 | 0.260667 | − | 0.965429i | \(-0.416057\pi\) | ||||
0.260667 | + | 0.965429i | \(0.416057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.8060 | 1.45590 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.699512 | 0.0378807 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.93467 | −0.320442 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.3286 | −0.825261 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.46144 | 0.239503 | 0.119751 | − | 0.992804i | \(-0.461790\pi\) | ||||
0.119751 | + | 0.992804i | \(0.461790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1320 | 0.702939 | 0.351470 | − | 0.936199i | \(-0.385682\pi\) | ||||
0.351470 | + | 0.936199i | \(0.385682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.6126 | 1.47385 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1140 | −1.12378 | −0.561892 | − | 0.827210i | \(-0.689926\pi\) | ||||
−0.561892 | + | 0.827210i | \(0.689926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.26671 | 0.226453 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.27792 | −0.120560 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.78593 | −0.463704 | −0.231852 | − | 0.972751i | \(-0.574478\pi\) | ||||
−0.231852 | + | 0.972751i | \(0.574478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.42957 | −0.0750328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.4074 | 2.32439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.68672 | 0.401244 | 0.200622 | − | 0.979669i | \(-0.435704\pi\) | ||||
0.200622 | + | 0.979669i | \(0.435704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.60522 | 0.447970 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.194408 | 0.0100932 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.71040 | 0.0885610 | 0.0442805 | − | 0.999019i | \(-0.485900\pi\) | ||||
0.0442805 | + | 0.999019i | \(0.485900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.88595 | 0.0973899 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.4408 | −0.692235 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7417 | −0.654497 | −0.327249 | − | 0.944938i | \(-0.606121\pi\) | ||||
−0.327249 | + | 0.944938i | \(0.606121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.09067 | −0.0558765 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.9652 | −1.32676 | −0.663380 | − | 0.748282i | \(-0.730879\pi\) | ||||
−0.663380 | + | 0.748282i | \(0.730879\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.38591 | −0.0706323 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.08542 | −0.360172 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.83747 | −0.143865 | −0.0719327 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719327 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3281 | −0.623460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.2408 | 1.22279 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.82669 | 0.343488 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.44226 | 0.122573 | 0.0612866 | − | 0.998120i | \(-0.480480\pi\) | ||||
0.0612866 | + | 0.998120i | \(0.480480\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.614095 | −0.0307432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2666 | 1.16188 | 0.580938 | − | 0.813948i | \(-0.302686\pi\) | ||||
0.580938 | + | 0.813948i | \(0.302686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.41511 | 0.170119 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.8296 | 0.836269 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.61409 | −0.0800077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6910 | 0.578084 | 0.289042 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289042 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.1704 | −1.19224 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.02491 | 0.0504323 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.8944 | 1.36928 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.6717 | −1.25715 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.5285 | 1.63798 | 0.818988 | − | 0.573811i | \(-0.194535\pi\) | ||||
0.818988 | + | 0.573811i | \(0.194535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.60098 | −0.321712 | −0.160856 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160856 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.4290 | 0.507075 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.0638 | 0.973235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27419 | −0.158449 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.97934 | −0.336966 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.24041 | −0.300590 | −0.150295 | − | 0.988641i | \(-0.548022\pi\) | ||||
−0.150295 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.2610 | −1.21397 | −0.606983 | − | 0.794715i | \(-0.707620\pi\) | ||||
−0.606983 | + | 0.794715i | \(0.707620\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6976 | −0.608804 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.32349 | −0.158984 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.948854 | −0.0452863 | −0.0226432 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226432 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.51790 | 0.310376 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1713 | 0.720809 | 0.360404 | − | 0.932796i | \(-0.382639\pi\) | ||||
0.360404 | + | 0.932796i | \(0.382639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.5567 | −0.595247 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.3952 | 1.29575 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.6787 | −1.68378 | −0.841891 | − | 0.539647i | \(-0.818558\pi\) | ||||
−0.841891 | + | 0.539647i | \(0.818558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.99809 | −0.423704 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9089 | 0.606515 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.76617 | −0.317203 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.8904 | 1.07077 | 0.535385 | − | 0.844608i | \(-0.320167\pi\) | ||||
0.535385 | + | 0.844608i | \(0.320167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.9798 | 0.979252 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.7980 | −1.24811 | −0.624055 | − | 0.781381i | \(-0.714516\pi\) | ||||
−0.624055 | + | 0.781381i | \(0.714516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6314 | 0.679978 | 0.339989 | − | 0.940429i | \(-0.389577\pi\) | ||||
0.339989 | + | 0.940429i | \(0.389577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.22628 | 0.149615 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.7460 | 0.728638 | 0.364319 | − | 0.931274i | \(-0.381302\pi\) | ||||
0.364319 | + | 0.931274i | \(0.381302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.20943 | 0.148198 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.25535 | 0.426464 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.40890 | 0.340662 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.40890 | 0.248178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.432807 | −0.0198169 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.90571 | −0.406912 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.88023 | −0.359307 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.04094 | 0.0928658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 45.1013 | 2.04794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.35073 | 0.151836 | 0.0759181 | − | 0.997114i | \(-0.475811\pi\) | ||||
0.0759181 | + | 0.997114i | \(0.475811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.8676 | 1.03411 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1601 | −0.864681 | −0.432341 | − | 0.901710i | \(-0.642312\pi\) | ||||
−0.432341 | + | 0.901710i | \(0.642312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2122 | −0.459933 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.08542 | 0.138679 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.568095 | −0.0254826 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.4665 | 1.27434 | 0.637168 | − | 0.770725i | \(-0.280106\pi\) | ||||
0.637168 | + | 0.770725i | \(0.280106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.07464 | −0.182041 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2407 | 1.03625 | 0.518127 | − | 0.855304i | \(-0.326630\pi\) | ||||
0.518127 | + | 0.855304i | \(0.326630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4737 | −0.955565 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.4897 | −0.687921 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.3295 | 0.901089 | 0.450545 | − | 0.892754i | \(-0.351230\pi\) | ||||
0.450545 | + | 0.892754i | \(0.351230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.91268 | −0.261561 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.65585 | 0.249712 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −52.9154 | −2.33173 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.9051 | −0.479607 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.7336 | 1.30516 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.68539 | 0.292892 | 0.146446 | − | 0.989219i | \(-0.453217\pi\) | ||||
0.146446 | + | 0.989219i | \(0.453217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.3463 | −1.15205 | −0.576023 | − | 0.817434i | \(-0.695396\pi\) | ||||
−0.576023 | + | 0.817434i | \(0.695396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.32158 | −0.144966 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.59477 | 0.113030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.9544 | −0.519758 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.28173 | −0.0990187 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.9299 | −1.90282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.0760 | −1.25706 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.63094 | −0.113534 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.81547 | −0.293563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.65958 | 0.157338 | 0.0786688 | − | 0.996901i | \(-0.474933\pi\) | ||||
0.0786688 | + | 0.996901i | \(0.474933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.21087 | 0.180706 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.9013 | 1.06666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7064 | −1.44118 | −0.720592 | − | 0.693360i | \(-0.756130\pi\) | ||||
−0.720592 | + | 0.693360i | \(0.756130\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.28927 | 0.311099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.75305 | −0.117284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.908947 | −0.0386523 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.44451 | −0.316002 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3897 | 1.11817 | 0.559083 | − | 0.829112i | \(-0.311153\pi\) | ||||
0.559083 | + | 0.829112i | \(0.311153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.1713 | 1.52988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.30283 | −0.223885 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.209105 | 0.00881272 | 0.00440636 | − | 0.999990i | \(-0.498597\pi\) | ||||
0.00440636 | + | 0.999990i | \(0.498597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 60.4965 | 2.54511 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.24080 | −0.0941045 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.3233 | −1.77429 | −0.887143 | − | 0.461494i | \(-0.847314\pi\) | ||||
−0.887143 | + | 0.461494i | \(0.847314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.5628 | 1.40456 | 0.702280 | − | 0.711901i | \(-0.252166\pi\) | ||||
0.702280 | + | 0.711901i | \(0.252166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.5475 | 0.858383 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.9764 | −0.749669 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4287 | 0.434151 | 0.217076 | − | 0.976155i | \(-0.430348\pi\) | ||||
0.217076 | + | 0.976155i | \(0.430348\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.7540 | 0.571595 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.71402 | −0.154084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.452567 | 0.0187434 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0634 | 0.622796 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.5023 | 1.54789 | 0.773943 | − | 0.633256i | \(-0.218282\pi\) | ||||
0.773943 | + | 0.633256i | \(0.218282\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.699512 | 0.0288229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.1168 | 1.23884 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.8262 | 0.978425 | 0.489213 | − | 0.872165i | \(-0.337284\pi\) | ||||
0.489213 | + | 0.872165i | \(0.337284\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.14087 | −0.210755 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.5737 | −0.882952 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.89144 | −0.118141 | −0.0590705 | − | 0.998254i | \(-0.518814\pi\) | ||||
−0.0590705 | + | 0.998254i | \(0.518814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3469 | 1.23788 | 0.618938 | − | 0.785440i | \(-0.287563\pi\) | ||||
0.618938 | + | 0.785440i | \(0.287563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.14511 | −0.290971 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.22628 | −0.131167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2851 | −0.863934 | −0.431967 | − | 0.901889i | \(-0.642180\pi\) | ||||
−0.431967 | + | 0.901889i | \(0.642180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.69064 | 0.0685081 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.2403 | −2.15387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.1384 | −1.29806 | −0.649029 | − | 0.760764i | \(-0.724824\pi\) | ||||
−0.649029 | + | 0.760764i | \(0.724824\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.5009 | −1.67348 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4507 | −0.541503 | −0.270752 | − | 0.962649i | \(-0.587272\pi\) | ||||
−0.270752 | + | 0.962649i | \(0.587272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.6849 | 0.630430 | 0.315215 | − | 0.949020i | \(-0.397923\pi\) | ||||
0.315215 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.7971 | −0.754304 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.67188 | 0.0669825 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.7883 | −0.911531 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.42957 | −0.0570914 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.98731 | −0.238730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0557776 | −0.00222047 | −0.00111024 | − | 0.999999i | \(-0.500353\pi\) | ||||
−0.00111024 | + | 0.999999i | \(0.500353\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.390066 | −0.0155037 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.46144 | −0.0976794 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.2740 | −1.31837 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.26474 | 0.0500324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3071 | −0.723086 | −0.361543 | − | 0.932355i | \(-0.617750\pi\) | ||||
−0.361543 | + | 0.932355i | \(0.617750\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −48.8246 | −1.92546 | −0.962728 | − | 0.270472i | \(-0.912820\pi\) | ||||
−0.962728 | + | 0.270472i | \(0.912820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34.1713 | 1.34549 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3919 | 0.683747 | 0.341873 | − | 0.939746i | \(-0.388939\pi\) | ||||
0.341873 | + | 0.939746i | \(0.388939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.38591 | 0.0936550 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.429567 | −0.0168361 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.1216 | −1.06135 | −0.530676 | − | 0.847575i | \(-0.678062\pi\) | ||||
−0.530676 | + | 0.847575i | \(0.678062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.7073 | 2.13759 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1633 | 0.513549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0696 | −0.625982 | −0.312991 | − | 0.949756i | \(-0.601331\pi\) | ||||
−0.312991 | + | 0.949756i | \(0.601331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.36233 | 0.0918841 | 0.0459420 | − | 0.998944i | \(-0.485371\pi\) | ||||
0.0459420 | + | 0.998944i | \(0.485371\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.8891 | −1.00545 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.38591 | −0.0537431 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.14974 | 0.354279 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4071 | 0.711659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.62207 | −0.294247 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1474 | −0.391155 | −0.195578 | − | 0.980688i | \(-0.562658\pi\) | ||||
−0.195578 | + | 0.980688i | \(0.562658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 30.5920 | 1.17749 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.8623 | −1.37830 | −0.689151 | − | 0.724618i | \(-0.742016\pi\) | ||||
−0.689151 | + | 0.724618i | \(0.742016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00506 | −0.230453 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.0296 | −1.26570 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.5108 | 0.440448 | 0.220224 | − | 0.975449i | \(-0.429321\pi\) | ||||
0.220224 | + | 0.975449i | \(0.429321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.5483 | −2.08418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.0456 | −1.03185 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.20949 | 0.0841750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.57517 | −0.288173 | −0.144086 | − | 0.989565i | \(-0.546024\pi\) | ||||
−0.144086 | + | 0.989565i | \(0.546024\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.410811 | −0.0156054 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −57.9365 | −2.19766 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.3775 | −1.26426 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.7019 | −0.858663 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9211 | 1.24341 | 0.621706 | − | 0.783251i | \(-0.286440\pi\) | ||||
0.621706 | + | 0.783251i | \(0.286440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.61409 | −0.0608767 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −50.2965 | −1.89428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.85913 | 0.107529 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.2867 | −1.43789 | −0.718944 | − | 0.695068i | \(-0.755374\pi\) | ||||
−0.718944 | + | 0.695068i | \(0.755374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.02357 | 0.0758899 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.32482 | −0.0870652 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.7511 | −0.589060 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.1398 | 1.42436 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.2146 | 1.01493 | 0.507467 | − | 0.861671i | \(-0.330582\pi\) | ||||
0.507467 | + | 0.861671i | \(0.330582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.04549 | 0.262388 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.98206 | 0.148095 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.8910 | −0.553038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.44078 | 0.0905235 | 0.0452618 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452618 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2449 | 1.08314 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.4825 | 1.01648 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.3825 | −1.15914 | −0.579570 | − | 0.814922i | \(-0.696779\pi\) | ||||
−0.579570 | + | 0.814922i | \(0.696779\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.4342 | −1.15947 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.47132 | 0.275210 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9277 | 0.549124 | 0.274562 | − | 0.961569i | \(-0.411467\pi\) | ||||
0.274562 | + | 0.961569i | \(0.411467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.97934 | −0.256392 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.2868 | −1.69810 | −0.849049 | − | 0.528314i | \(-0.822824\pi\) | ||||
−0.849049 | + | 0.528314i | \(0.822824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 61.8262 | 2.26514 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.26847 | 0.302528 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.87135 | 0.141456 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2102 | 0.555028 | 0.277514 | − | 0.960722i | \(-0.410490\pi\) | ||||
0.277514 | + | 0.960722i | \(0.410490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5850 | −0.604391 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.1332 | 1.06027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6145 | 1.29443 | 0.647215 | − | 0.762308i | \(-0.275934\pi\) | ||||
0.647215 | + | 0.762308i | \(0.275934\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.75115 | 0.172456 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.0701 | 1.34379 | 0.671896 | − | 0.740646i | \(-0.265480\pi\) | ||||
0.671896 | + | 0.740646i | \(0.265480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.31551 | −0.120030 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.4450 | 0.413796 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.6483 | 0.420596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.21311 | 0.260111 | 0.130056 | − | 0.991507i | \(-0.458484\pi\) | ||||
0.130056 | + | 0.991507i | \(0.458484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.92489 | 0.105337 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.8299 | −1.90016 | −0.950081 | − | 0.312005i | \(-0.898999\pi\) | ||||
−0.950081 | + | 0.312005i | \(0.898999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.78360 | 0.135911 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.991207 | 0.0355594 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.99809 | −0.322390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.32248 | −0.0473222 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.5709 | −0.556457 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.8877 | 0.745514 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.5012 | 1.55065 | 0.775324 | − | 0.631563i | \(-0.217586\pi\) | ||||
0.775324 | + | 0.631563i | \(0.217586\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.4271 | 1.33244 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.05488 | −0.286398 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.2120 | −1.32144 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.08732 | 0.0740298 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.5718 | −0.728691 | −0.364346 | − | 0.931264i | \(-0.618707\pi\) | ||||
−0.364346 | + | 0.931264i | \(0.618707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.4514 | −1.43107 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.72208 | −0.131513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7643 | −0.485730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.60604 | 0.162342 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.4234 | −0.718937 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.2365 | 1.66075 | 0.830374 | − | 0.557207i | \(-0.188127\pi\) | ||||
0.830374 | + | 0.557207i | \(0.188127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.86621 | −0.100646 | −0.0503230 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503230 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.4286 | −0.576175 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.6082 | 1.80776 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.40890 | 0.259205 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00564 | −0.0700826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3986 | −0.362912 | −0.181456 | − | 0.983399i | \(-0.558081\pi\) | ||||
−0.181456 | + | 0.983399i | \(0.558081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.6014 | −1.93814 | −0.969072 | − | 0.246780i | \(-0.920628\pi\) | ||||
−0.969072 | + | 0.246780i | \(0.920628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.73239 | −0.269207 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2728 | −0.878820 | −0.439410 | − | 0.898287i | \(-0.644813\pi\) | ||||
−0.439410 | + | 0.898287i | \(0.644813\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.8845 | −0.586422 | −0.293211 | − | 0.956048i | \(-0.594724\pi\) | ||||
−0.293211 | + | 0.956048i | \(0.594724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4572 | 1.02186 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.2813 | −0.875944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.19574 | −0.318232 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.95634 | 0.136751 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.6042 | −1.22919 | −0.614597 | − | 0.788841i | \(-0.710681\pi\) | ||||
−0.614597 | + | 0.788841i | \(0.710681\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4207 | −0.738645 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.8817 | −0.856973 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.9575 | −1.20258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.429567 | 0.0147601 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.18596 | 0.143662 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.36442 | 0.183890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.6592 | 1.28943 | 0.644713 | − | 0.764425i | \(-0.276977\pi\) | ||||
0.644713 | + | 0.764425i | \(0.276977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.08542 | 0.105519 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.25693 | −0.145414 | −0.0727069 | − | 0.997353i | \(-0.523164\pi\) | ||||
−0.0727069 | + | 0.997353i | \(0.523164\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.4679 | −1.58546 | −0.792732 | − | 0.609571i | \(-0.791342\pi\) | ||||
−0.792732 | + | 0.609571i | \(0.791342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.52568 | 0.188315 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.8291 | −1.83236 | −0.916181 | − | 0.400764i | \(-0.868745\pi\) | ||||
−0.916181 | + | 0.400764i | \(0.868745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 67.1036 | 2.28159 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.63238 | 0.157324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.11596 | −0.0717790 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.4760 | 1.23594 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.3690 | 0.452471 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.566703 | −0.0191581 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8239 | 0.770708 | 0.385354 | − | 0.922769i | \(-0.374079\pi\) | ||||
0.385354 | + | 0.922769i | \(0.374079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.2573 | −0.480888 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.0631 | 1.48452 | 0.742262 | − | 0.670109i | \(-0.233753\pi\) | ||||
0.742262 | + | 0.670109i | \(0.233753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8215 | −0.397826 | −0.198913 | − | 0.980017i | \(-0.563741\pi\) | ||||
−0.198913 | + | 0.980017i | \(0.563741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0042 | 0.369904 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.1079 | 0.809466 | 0.404733 | − | 0.914435i | \(-0.367365\pi\) | ||||
0.404733 | + | 0.914435i | \(0.367365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.327731 | 0.0109918 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.21640 | −0.174756 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.9051 | −0.364926 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.93758 | −0.198471 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.1957 | 0.774483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.92580 | −0.0642289 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67875 | 0.0559272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.54977 | −0.151407 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.50320 | 0.315897 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1371 | 0.569027 | 0.284513 | − | 0.958672i | \(-0.408168\pi\) | ||||
0.284513 | + | 0.958672i | \(0.408168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.36524 | −0.211122 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.22446 | −0.0736997 | −0.0368498 | − | 0.999321i | \(-0.511732\pi\) | ||||
−0.0368498 | + | 0.999321i | \(0.511732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.64597 | −0.286140 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −35.1544 | −1.16217 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.28407 | −0.240541 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.86662 | −0.292483 | −0.146241 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146241 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.6023 | 0.514114 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.45654 | −0.212520 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.73049 | −0.287057 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.6852 | −0.515171 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8252 | 0.912914 | 0.456457 | − | 0.889745i | \(-0.349118\pi\) | ||||
0.456457 | + | 0.889745i | \(0.349118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.81547 | −0.223368 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.0675 | 0.427810 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.9676 | −0.391381 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.45009 | −0.178047 | −0.0890233 | − | 0.996030i | \(-0.528375\pi\) | ||||
−0.0890233 | + | 0.996030i | \(0.528375\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8985 | −0.649363 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.858747 | −0.0279943 | −0.0139972 | − | 0.999902i | \(-0.504456\pi\) | ||||
−0.0139972 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.9051 | 0.973842 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.83847 | −0.254986 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.6323 | 1.15789 | 0.578947 | − | 0.815365i | \(-0.303464\pi\) | ||||
0.578947 | + | 0.815365i | \(0.303464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67.1990 | −2.18137 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.3366 | 1.30800 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.2728 | −0.365161 | −0.182580 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182580 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.3721 | 1.50056 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.93568 | 0.127222 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.26289 | 0.234531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5107 | −0.984216 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.61873 | −0.277735 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.0403 | 0.999222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.59850 | 0.308667 | 0.154333 | − | 0.988019i | \(-0.450677\pi\) | ||||
0.154333 | + | 0.988019i | \(0.450677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.30283 | −0.170351 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8632 | 0.829991 | 0.414995 | − | 0.909824i | \(-0.363783\pi\) | ||||
0.414995 | + | 0.909824i | \(0.363783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.71402 | 0.247300 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.7506 | −1.20899 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.3510 | 0.427136 | 0.213568 | − | 0.976928i | \(-0.431492\pi\) | ||||
0.213568 | + | 0.976928i | \(0.431492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.89201 | 0.124389 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.38127 | 0.235666 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.6233 | −1.51895 | −0.759473 | − | 0.650539i | \(-0.774543\pi\) | ||||
−0.759473 | + | 0.650539i | \(0.774543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 67.9684 | 2.16565 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.69679 | 0.213161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.6234 | −0.782979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.5586 | −1.51075 | −0.755374 | − | 0.655293i | \(-0.772545\pi\) | ||||
−0.755374 | + | 0.655293i | \(0.772545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.99680 | 0.285505 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.6880 | −1.54351 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7152 | 0.561046 | 0.280523 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280523 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.12908 | −0.288831 |
(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 | 1672.2.a.f.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 3344.2.a.s.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.f.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3344.2.a.s.1.3 | 4 | 4.3 | odd | 2 |