Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.95007\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.950069 | −0.548523 | −0.274261 | − | 0.961655i | \(-0.588433\pi\) | ||||
−0.274261 | + | 0.961655i | \(0.588433\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.28693 | −1.02275 | −0.511374 | − | 0.859358i | \(-0.670863\pi\) | ||||
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.71022 | −1.02437 | −0.512184 | − | 0.858876i | \(-0.671163\pi\) | ||||
−0.512184 | + | 0.858876i | \(0.671163\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.09737 | −0.699123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36880 | −0.412710 | −0.206355 | − | 0.978477i | \(-0.566160\pi\) | ||||
−0.206355 | + | 0.978477i | \(0.566160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93079 | −0.812856 | −0.406428 | − | 0.913683i | \(-0.633226\pi\) | ||||
−0.406428 | + | 0.913683i | \(0.633226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.17275 | 0.561001 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.61287 | −0.633715 | −0.316857 | − | 0.948473i | \(-0.602628\pi\) | ||||
−0.316857 | + | 0.948473i | \(0.602628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.79104 | 1.78739 | 0.893694 | − | 0.448677i | \(-0.148105\pi\) | ||||
0.893694 | + | 0.448677i | \(0.148105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.57490 | 0.561888 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.61064 | 0.544356 | 0.272178 | − | 0.962247i | \(-0.412256\pi\) | ||||
0.272178 | + | 0.962247i | \(0.412256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.230071 | 0.0460143 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.84285 | 0.932007 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.314480 | −0.0583974 | −0.0291987 | − | 0.999574i | \(-0.509296\pi\) | ||||
−0.0291987 | + | 0.999574i | \(0.509296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.95126 | 1.42809 | 0.714044 | − | 0.700101i | \(-0.246862\pi\) | ||||
0.714044 | + | 0.700101i | \(0.246862\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.30046 | 0.226381 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.19810 | 1.04767 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.17299 | −0.686035 | −0.343017 | − | 0.939329i | \(-0.611449\pi\) | ||||
−0.343017 | + | 0.939329i | \(0.611449\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.78446 | 0.445870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.16482 | 0.962783 | 0.481391 | − | 0.876506i | \(-0.340132\pi\) | ||||
0.481391 | + | 0.876506i | \(0.340132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.457851 | −0.0698216 | −0.0349108 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349108 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.79655 | 0.715027 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.67118 | −1.11896 | −0.559478 | − | 0.828845i | \(-0.688998\pi\) | ||||
−0.559478 | + | 0.828845i | \(0.688998\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.345296 | 0.0493279 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.48241 | 0.347607 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26306 | 0.997658 | 0.498829 | − | 0.866700i | \(-0.333763\pi\) | ||||
0.498829 | + | 0.866700i | \(0.333763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.13037 | 0.422099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.40203 | −0.980423 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.217166 | −0.0282726 | −0.0141363 | − | 0.999900i | \(-0.504500\pi\) | ||||
−0.0141363 | + | 0.999900i | \(0.504500\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.26694 | 0.930436 | 0.465218 | − | 0.885196i | \(-0.345976\pi\) | ||||
0.465218 | + | 0.885196i | \(0.345976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.68433 | 0.716159 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.70253 | 0.831347 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1022 | −1.23418 | −0.617091 | − | 0.786892i | \(-0.711689\pi\) | ||||
−0.617091 | + | 0.786892i | \(0.711689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.48029 | −0.298592 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.5088 | 1.95924 | 0.979619 | − | 0.200863i | \(-0.0643746\pi\) | ||||
0.979619 | + | 0.200863i | \(0.0643746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86838 | 0.335718 | 0.167859 | − | 0.985811i | \(-0.446315\pi\) | ||||
0.167859 | + | 0.985811i | \(0.446315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.218584 | −0.0252399 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.70976 | 0.422767 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0222 | 1.80264 | 0.901320 | − | 0.433153i | \(-0.142599\pi\) | ||||
0.901320 | + | 0.433153i | \(0.142599\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.69106 | 0.187896 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5312 | −1.37548 | −0.687741 | − | 0.725956i | \(-0.741398\pi\) | ||||
−0.687741 | + | 0.725956i | \(0.741398\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.97547 | 0.648131 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.298777 | 0.0320323 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.0952234 | −0.0100937 | −0.00504683 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504683 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.94310 | 0.832663 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.55424 | −0.783339 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.8176 | −1.82805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.27640 | −0.941875 | −0.470938 | − | 0.882167i | \(-0.656084\pi\) | ||||
−0.470938 | + | 0.882167i | \(0.656084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.87089 | 0.288535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.77727 | 0.873371 | 0.436686 | − | 0.899614i | \(-0.356152\pi\) | ||||
0.436686 | + | 0.899614i | \(0.356152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.52475 | −0.150238 | −0.0751189 | − | 0.997175i | \(-0.523934\pi\) | ||||
−0.0751189 | + | 0.997175i | \(0.523934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.88862 | −0.574670 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.6358 | 1.70492 | 0.852460 | − | 0.522792i | \(-0.175110\pi\) | ||||
0.852460 | + | 0.522792i | \(0.175110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.91427 | −0.470702 | −0.235351 | − | 0.971910i | \(-0.575624\pi\) | ||||
−0.235351 | + | 0.971910i | \(0.575624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.96462 | 0.376305 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.102880 | 0.00967811 | 0.00483905 | − | 0.999988i | \(-0.498460\pi\) | ||||
0.00483905 | + | 0.999988i | \(0.498460\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.97037 | −0.556740 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.14696 | 0.568286 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.08146 | 0.649157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.12637 | −0.829670 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.85700 | −0.528108 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9085 | 0.975687 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7682 | −1.31046 | −0.655232 | − | 0.755428i | \(-0.727429\pi\) | ||||
−0.655232 | + | 0.755428i | \(0.727429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.434990 | 0.0382987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.01646 | −0.263549 | −0.131775 | − | 0.991280i | \(-0.542068\pi\) | ||||
−0.131775 | + | 0.991280i | \(0.542068\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.1154 | −1.83094 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.0753 | −0.953209 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.370190 | 0.0316275 | 0.0158137 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158137 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0944 | −1.11065 | −0.555324 | − | 0.831634i | \(-0.687406\pi\) | ||||
−0.555324 | + | 0.831634i | \(0.687406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.28815 | 0.613773 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.01168 | 0.335474 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.719195 | 0.0597259 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.328055 | −0.0270575 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.61923 | −0.460345 | −0.230173 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230173 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.99662 | 0.569377 | 0.284689 | − | 0.958620i | \(-0.408110\pi\) | ||||
0.284689 | + | 0.958620i | \(0.408110\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.48016 | 0.443045 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.1840 | −1.46058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5849 | 0.844764 | 0.422382 | − | 0.906418i | \(-0.361194\pi\) | ||||
0.422382 | + | 0.906418i | \(0.361194\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.90041 | −0.547238 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.07541 | −0.557621 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.74396 | 0.371576 | 0.185788 | − | 0.982590i | \(-0.440516\pi\) | ||||
0.185788 | + | 0.982590i | \(0.440516\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.97406 | −0.231531 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.4650 | −1.19672 | −0.598360 | − | 0.801227i | \(-0.704181\pi\) | ||||
−0.598360 | + | 0.801227i | \(0.704181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41045 | −0.339265 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.3407 | −1.24960 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0030 | −1.36874 | −0.684372 | − | 0.729133i | \(-0.739924\pi\) | ||||
−0.684372 | + | 0.729133i | \(0.739924\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.623544 | −0.0471355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.206322 | 0.0155081 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.6390 | −1.69212 | −0.846058 | − | 0.533092i | \(-0.821030\pi\) | ||||
−0.846058 | + | 0.533092i | \(0.821030\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.97984 | 0.221490 | 0.110745 | − | 0.993849i | \(-0.464676\pi\) | ||||
0.110745 | + | 0.993849i | \(0.464676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.90409 | −0.510365 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.54335 | 0.701641 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.57651 | 0.261541 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.1252 | −0.954718 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.09564 | −0.296350 | −0.148175 | − | 0.988961i | \(-0.547340\pi\) | ||||
−0.148175 | + | 0.988961i | \(0.547340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1708 | −1.52391 | −0.761955 | − | 0.647630i | \(-0.775760\pi\) | ||||
−0.761955 | + | 0.647630i | \(0.775760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.36787 | −0.456013 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5139 | 1.31906 | 0.659531 | − | 0.751677i | \(-0.270755\pi\) | ||||
0.659531 | + | 0.751677i | \(0.270755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.56711 | 0.111089 | 0.0555447 | − | 0.998456i | \(-0.482310\pi\) | ||||
0.0555447 | + | 0.998456i | \(0.482310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.59779 | 0.676976 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.852309 | 0.0598204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0985 | −0.984685 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.47548 | −0.380572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.6644 | −0.737673 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.8488 | 1.57298 | 0.786489 | − | 0.617604i | \(-0.211897\pi\) | ||||
0.786489 | + | 0.617604i | \(0.211897\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.6845 | −1.07469 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.04708 | 0.0714100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.5497 | −1.46289 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.72516 | −0.184149 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.65779 | 0.515119 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.75557 | −0.318457 | −0.159228 | − | 0.987242i | \(-0.550901\pi\) | ||||
−0.159228 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.482545 | −0.0321696 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.4709 | 1.82331 | 0.911655 | − | 0.410956i | \(-0.134805\pi\) | ||||
0.911655 | + | 0.410956i | \(0.134805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.52436 | −0.298978 | −0.149489 | − | 0.988763i | \(-0.547763\pi\) | ||||
−0.149489 | + | 0.988763i | \(0.547763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.52453 | −0.231897 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5567 | −0.691594 | −0.345797 | − | 0.938309i | \(-0.612391\pi\) | ||||
−0.345797 | + | 0.938309i | \(0.612391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.5435 | 1.14441 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.2222 | −0.988789 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.3072 | 1.83104 | 0.915522 | − | 0.402269i | \(-0.131778\pi\) | ||||
0.915522 | + | 0.402269i | \(0.131778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6922 | −0.688748 | −0.344374 | − | 0.938833i | \(-0.611909\pi\) | ||||
−0.344374 | + | 0.938833i | \(0.611909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1352 | −1.03507 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.789669 | −0.0504501 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.8339 | −1.45289 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.9055 | 0.754483 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.42359 | 0.216095 | 0.108048 | − | 0.994146i | \(-0.465540\pi\) | ||||
0.108048 | + | 0.994146i | \(0.465540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.57346 | −0.224661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.67711 | −0.355514 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2524 | −0.701906 | −0.350953 | − | 0.936393i | \(-0.614142\pi\) | ||||
−0.350953 | + | 0.936393i | \(0.614142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3097 | 0.702751 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.659580 | 0.0408270 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.429180 | −0.0264643 | −0.0132322 | − | 0.999912i | \(-0.504212\pi\) | ||||
−0.0132322 | + | 0.999912i | \(0.504212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.6102 | −1.02035 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0904688 | 0.00553660 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.2320 | 0.928712 | 0.464356 | − | 0.885649i | \(-0.346286\pi\) | ||||
0.464356 | + | 0.885649i | \(0.346286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7850 | −1.08036 | −0.540182 | − | 0.841548i | \(-0.681645\pi\) | ||||
−0.540182 | + | 0.841548i | \(0.681645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.54649 | −0.456734 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.314923 | −0.0189906 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1882 | 0.912570 | 0.456285 | − | 0.889834i | \(-0.349180\pi\) | ||||
0.456285 | + | 0.889834i | \(0.349180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.6767 | −0.998409 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0885 | 1.19838 | 0.599191 | − | 0.800606i | \(-0.295489\pi\) | ||||
0.599191 | + | 0.800606i | \(0.295489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.63497 | 0.0971889 | 0.0485945 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485945 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.9280 | 1.00273 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.7080 | −0.986243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1729 | −0.598405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.81321 | 0.516640 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.1892 | −0.595262 | −0.297631 | − | 0.954681i | \(-0.596196\pi\) | ||||
−0.297631 | + | 0.954681i | \(0.596196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.496644 | 0.0289157 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.62892 | −0.384649 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.65125 | −0.442483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.24088 | 0.0715230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.33901 | −0.479064 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.6190 | −0.951602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3682 | 0.934184 | 0.467092 | − | 0.884209i | \(-0.345302\pi\) | ||||
0.467092 | + | 0.884209i | \(0.345302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.44861 | 0.0824088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.98922 | −0.396322 | −0.198161 | − | 0.980169i | \(-0.563497\pi\) | ||||
−0.198161 | + | 0.980169i | \(0.563497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.22444 | 0.125733 | 0.0628665 | − | 0.998022i | \(-0.479976\pi\) | ||||
0.0628665 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.9997 | −0.732450 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.49687 | 0.196404 | 0.0982019 | − | 0.995167i | \(-0.468691\pi\) | ||||
0.0982019 | + | 0.995167i | \(0.468691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.430461 | 0.0241012 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.7553 | −0.935187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.3570 | −1.13269 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.674292 | −0.0374030 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.66889 | 0.258190 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.7906 | 1.14622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8654 | 0.762112 | 0.381056 | − | 0.924552i | \(-0.375561\pi\) | ||||
0.381056 | + | 0.924552i | \(0.375561\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.75229 | 0.479623 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.1031 | 1.26226 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0259 | −1.79903 | −0.899517 | − | 0.436885i | \(-0.856082\pi\) | ||||
−0.899517 | + | 0.436885i | \(0.856082\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0977428 | −0.00530866 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.8837 | −0.589387 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0357 | 0.973837 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.67226 | 0.305384 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.417829 | 0.0224302 | 0.0112151 | − | 0.999937i | \(-0.496430\pi\) | ||||
0.0112151 | + | 0.999937i | \(0.496430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.68607 | −0.464955 | −0.232477 | − | 0.972602i | \(-0.574683\pi\) | ||||
−0.232477 | + | 0.972602i | \(0.574683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.1934 | −0.757588 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.09582 | −0.484122 | −0.242061 | − | 0.970261i | \(-0.577823\pi\) | ||||
−0.242061 | + | 0.970261i | \(0.577823\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.7546 | −2.00381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.72788 | −0.356077 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.51998 | −0.291333 | −0.145667 | − | 0.989334i | \(-0.546533\pi\) | ||||
−0.145667 | + | 0.989334i | \(0.546533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.7004 | 2.19476 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.67068 | 0.455093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.55979 | −0.343355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3639 | −0.854188 | −0.427094 | − | 0.904207i | \(-0.640463\pi\) | ||||
−0.427094 | + | 0.904207i | \(0.640463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.9299 | −0.673104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.6845 | −1.02197 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.5721 | −1.22051 | −0.610257 | − | 0.792203i | \(-0.708934\pi\) | ||||
−0.610257 | + | 0.792203i | \(0.708934\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.3638 | −0.535186 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.921675 | 0.0474687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8307 | 1.17273 | 0.586367 | − | 0.810045i | \(-0.300558\pi\) | ||||
0.586367 | + | 0.810045i | \(0.300558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0308 | 0.718819 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.8257 | −1.11524 | −0.557622 | − | 0.830095i | \(-0.688286\pi\) | ||||
−0.557622 | + | 0.830095i | \(0.688286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.48399 | −0.432384 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.960283 | 0.0488139 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.7462 | 1.50819 | 0.754097 | − | 0.656763i | \(-0.228075\pi\) | ||||
0.754097 | + | 0.656763i | \(0.228075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.82127 | −0.344967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.86584 | 0.144563 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.6418 | −1.84365 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.5561 | 1.43319 | 0.716595 | − | 0.697489i | \(-0.245700\pi\) | ||||
0.716595 | + | 0.697489i | \(0.245700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.0611 | 1.00431 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9970 | 0.698975 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.3035 | −1.16083 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.86735 | −0.192170 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.71200 | 0.283133 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.2429 | −0.902055 | −0.451028 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451028 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.351706 | −0.0173484 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.588567 | 0.0289615 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.6581 | 1.40677 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4405 | 0.609216 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.78645 | −0.478099 | −0.239050 | − | 0.971007i | \(-0.576836\pi\) | ||||
−0.239050 | + | 0.971007i | \(0.576836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.26639 | 0.110457 | 0.0552286 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552286 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.0893 | 0.782288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.601147 | −0.0291599 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.6950 | −0.953109 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.81138 | −0.184015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.29790 | −0.207023 | −0.103511 | − | 0.994628i | \(-0.533008\pi\) | ||||
−0.103511 | + | 0.994628i | \(0.533008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6114 | −0.798292 | −0.399146 | − | 0.916887i | \(-0.630693\pi\) | ||||
−0.399146 | + | 0.916887i | \(0.630693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.683284 | −0.0327610 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3396 | 0.972976 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4863 | 1.02548 | 0.512742 | − | 0.858542i | \(-0.328630\pi\) | ||||
0.512742 | + | 0.858542i | \(0.328630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.724212 | −0.0344863 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6047 | 0.931447 | 0.465724 | − | 0.884930i | \(-0.345794\pi\) | ||||
0.465724 | + | 0.884930i | \(0.345794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.217770 | 0.0103233 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.33866 | 0.252510 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.1455 | −1.65862 | −0.829310 | − | 0.558789i | \(-0.811266\pi\) | ||||
−0.829310 | + | 0.558789i | \(0.811266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.43843 | −0.397350 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.64728 | −0.312316 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.1653 | −0.851605 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8432 | −0.554002 | −0.277001 | − | 0.960870i | \(-0.589341\pi\) | ||||
−0.277001 | + | 0.960870i | \(0.589341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6538 | −0.590627 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1286 | 0.797756 | 0.398878 | − | 0.917004i | \(-0.369400\pi\) | ||||
0.398878 | + | 0.917004i | \(0.369400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.92218 | 0.321701 | 0.160850 | − | 0.986979i | \(-0.448576\pi\) | ||||
0.160850 | + | 0.986979i | \(0.448576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.2761 | 0.801158 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.6395 | 1.51038 | 0.755188 | − | 0.655508i | \(-0.227545\pi\) | ||||
0.755188 | + | 0.655508i | \(0.227545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.3792 | 1.26425 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0563 | −0.463372 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.626709 | 0.0288161 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.79250 | 0.0822454 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.2333 | −0.697486 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.78005 | −0.401171 | −0.200585 | − | 0.979676i | \(-0.564284\pi\) | ||||
−0.200585 | + | 0.979676i | \(0.564284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.2302 | 0.557647 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.72213 | 0.305868 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.2145 | 0.963301 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1617 | 1.04956 | 0.524779 | − | 0.851238i | \(-0.324148\pi\) | ||||
0.524779 | + | 0.851238i | \(0.324148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.50709 | −0.203818 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.15363 | −0.367968 | −0.183984 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183984 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.821696 | 0.0370073 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.56554 | −0.295099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.7426 | −2.00698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.6993 | −1.37429 | −0.687144 | − | 0.726521i | \(-0.741136\pi\) | ||||
−0.687144 | + | 0.726521i | \(0.741136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6929 | 0.656428 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0731 | −0.893239 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.19023 | 0.186095 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.39080 | −0.283267 | −0.141634 | − | 0.989919i | \(-0.545235\pi\) | ||||
−0.141634 | + | 0.989919i | \(0.545235\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.77394 | −0.343899 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.7309 | 1.66586 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.48700 | 0.153655 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5003 | 0.461805 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1041 | 0.750787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2745 | −0.493944 | −0.246972 | − | 0.969023i | \(-0.579436\pi\) | ||||
−0.246972 | + | 0.969023i | \(0.579436\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6154 | −0.813993 | −0.406996 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.592410 | 0.0258549 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7756 | −0.905001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1846 | −0.703676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.455477 | 0.0197660 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0678 | −0.782604 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.3320 | −1.74370 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.5086 | 0.928163 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.472642 | −0.0203581 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.6446 | −1.57547 | −0.787736 | − | 0.616013i | \(-0.788747\pi\) | ||||
−0.787736 | + | 0.616013i | \(0.788747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.83105 | −0.121492 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2386 | 0.481409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4186 | −0.830280 | −0.415140 | − | 0.909758i | \(-0.636267\pi\) | ||||
−0.415140 | + | 0.909758i | \(0.636267\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.2415 | −0.650490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.45013 | −0.104379 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.4238 | −1.84657 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.06684 | −0.384866 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.6561 | −1.51080 | −0.755398 | − | 0.655266i | \(-0.772556\pi\) | ||||
−0.755398 | + | 0.655266i | \(0.772556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.34187 | 0.0567549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.39793 | −0.143461 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.0879 | 1.43663 | 0.718316 | − | 0.695717i | \(-0.244913\pi\) | ||||
0.718316 | + | 0.695717i | \(0.244913\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.235279 | −0.00989827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.58316 | −0.192475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0323 | 0.546342 | 0.273171 | − | 0.961965i | \(-0.411927\pi\) | ||||
0.273171 | + | 0.961965i | \(0.411927\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5710 | −1.19566 | −0.597829 | − | 0.801624i | \(-0.703970\pi\) | ||||
−0.597829 | + | 0.801624i | \(0.703970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.89114 | 0.162555 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.600634 | 0.0250482 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.1508 | 1.67150 | 0.835750 | − | 0.549110i | \(-0.185033\pi\) | ||||
0.835750 | + | 0.549110i | \(0.185033\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.1137 | 0.835899 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9624 | 1.40900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.94172 | −0.411744 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.0577 | −0.581214 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.26390 | 0.0521666 | 0.0260833 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260833 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.9486 | 2.55255 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5895 | −0.723535 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.473003 | 0.0194239 | 0.00971196 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971196 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1948 | −0.663924 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.48886 | −0.0609350 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.8689 | −1.17955 | −0.589775 | − | 0.807568i | \(-0.700783\pi\) | ||||
−0.589775 | + | 0.807568i | \(0.700783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.88531 | 0.362439 | 0.181220 | − | 0.983443i | \(-0.441996\pi\) | ||||
0.181220 | + | 0.983443i | \(0.441996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.1881 | 0.862845 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.8714 | 0.848544 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.6612 | −1.16332 | −0.581662 | − | 0.813431i | \(-0.697597\pi\) | ||||
−0.581662 | + | 0.813431i | \(0.697597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.809753 | −0.0328128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.4826 | 0.909550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.9961 | 1.89815 | 0.949077 | − | 0.315043i | \(-0.102019\pi\) | ||||
0.949077 | + | 0.315043i | \(0.102019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.3946 | 0.540122 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.3030 | −0.978401 | −0.489201 | − | 0.872171i | \(-0.662711\pi\) | ||||
−0.489201 | + | 0.872171i | \(0.662711\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.4552 | −1.58584 | −0.792920 | − | 0.609326i | \(-0.791440\pi\) | ||||
−0.792920 | + | 0.609326i | \(0.791440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.6429 | 0.507344 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.258077 | 0.0103396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.0974 | −1.04390 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.1319 | 0.404630 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.9035 | 0.434750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.7457 | −1.38320 | −0.691602 | − | 0.722279i | \(-0.743095\pi\) | ||||
−0.691602 | + | 0.722279i | \(0.743095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.7080 | −0.862814 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.7738 | 1.34027 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.01199 | −0.0400965 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.6251 | −1.36975 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.3173 | −1.67143 | −0.835716 | − | 0.549163i | \(-0.814947\pi\) | ||||
−0.835716 | + | 0.549163i | \(0.814947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.5672 | 1.24489 | 0.622444 | − | 0.782664i | \(-0.286140\pi\) | ||||
0.622444 | + | 0.782664i | \(0.286140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.994794 | −0.0391700 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6664 | 1.79533 | 0.897667 | − | 0.440675i | \(-0.145261\pi\) | ||||
0.897667 | + | 0.440675i | \(0.145261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.297258 | 0.0116684 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.4737 | 0.802426 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.15705 | 0.280077 | 0.140039 | − | 0.990146i | \(-0.455277\pi\) | ||||
0.140039 | + | 0.990146i | \(0.455277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.89844 | 0.269545 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.01605 | −0.234708 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1603 | −0.473696 | −0.236848 | − | 0.971547i | \(-0.576114\pi\) | ||||
−0.236848 | + | 0.971547i | \(0.576114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.2194 | −0.591968 | −0.295984 | − | 0.955193i | \(-0.595647\pi\) | ||||
−0.295984 | + | 0.955193i | \(0.595647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.27543 | −0.282554 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.2896 | 1.87259 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.820994 | −0.0317890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.51812 | 0.174681 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.94702 | −0.384001 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.9359 | 1.34668 | 0.673340 | − | 0.739333i | \(-0.264859\pi\) | ||||
0.673340 | + | 0.739333i | \(0.264859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.11420 | 0.0428856 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.6078 | −0.676721 | −0.338361 | − | 0.941016i | \(-0.609872\pi\) | ||||
−0.338361 | + | 0.941016i | \(0.609872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.1411 | 0.964826 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0993 | −1.00013 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.5075 | 1.66477 | 0.832385 | − | 0.554198i | \(-0.186975\pi\) | ||||
0.832385 | + | 0.554198i | \(0.186975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.846600 | −0.0323469 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.29846 | 0.163996 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.2865 | −0.810953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.05256 | 0.0780829 | 0.0390415 | − | 0.999238i | \(-0.487570\pi\) | ||||
0.0390415 | + | 0.999238i | \(0.487570\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.78074 | −0.295566 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.9459 | 1.13591 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.1079 | −0.610130 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0296 | 0.379355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.44349 | −0.356676 | −0.178338 | − | 0.983969i | \(-0.557072\pi\) | ||||
−0.178338 | + | 0.983969i | \(0.557072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.5119 | −1.22621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.6675 | −0.627735 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.7883 | −0.894653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.9123 | 0.597598 | 0.298799 | − | 0.954316i | \(-0.403414\pi\) | ||||
0.298799 | + | 0.954316i | \(0.403414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.6045 | −1.26027 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7579 | 0.777389 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.17446 | −0.343105 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.8938 | −1.00437 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.9061 | −0.928842 | −0.464421 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464421 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.13240 | 0.153899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.1584 | 0.377794 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0723528 | −0.00268712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5573 | −0.428636 | −0.214318 | − | 0.976764i | \(-0.568753\pi\) | ||||
−0.214318 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.2563 | 0.379865 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.19631 | 0.0442470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.9918 | 0.442926 | 0.221463 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221463 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.750240 | 0.0276730 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8280 | 0.509359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.3255 | −1.77768 | −0.888840 | − | 0.458217i | \(-0.848488\pi\) | ||||
−0.888840 | + | 0.458217i | \(0.848488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.6938 | 0.796942 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.3146 | −1.47900 | −0.739499 | − | 0.673158i | \(-0.764937\pi\) | ||||
−0.739499 | + | 0.673158i | \(0.764937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.8508 | 0.470817 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.2826 | 0.961632 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.7970 | −1.74646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.6091 | 1.77377 | 0.886885 | − | 0.461990i | \(-0.152864\pi\) | ||||
0.886885 | + | 0.461990i | \(0.152864\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.25265 | −0.118533 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0008 | −0.582330 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.8319 | −1.62944 | −0.814721 | − | 0.579853i | \(-0.803110\pi\) | ||||
−0.814721 | + | 0.579853i | \(0.803110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.39503 | 0.123232 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.4812 | −1.14119 | −0.570596 | − | 0.821231i | \(-0.693288\pi\) | ||||
−0.570596 | + | 0.821231i | \(0.693288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3188 | 0.482171 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.5328 | −0.453123 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.636468 | 0.0229815 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.6134 | 1.10395 | 0.551974 | − | 0.833861i | \(-0.313875\pi\) | ||||
0.551974 | + | 0.833861i | \(0.313875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6906 | 0.385011 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.8605 | 0.930136 | 0.465068 | − | 0.885275i | \(-0.346030\pi\) | ||||
0.465068 | + | 0.885275i | \(0.346030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.82936 | 0.0657125 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.7450 | −0.385475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.0304 | 1.72087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.5974 | −0.808598 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.52298 | −0.0544268 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.2069 | −0.863981 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.7233 | −1.13081 | −0.565406 | − | 0.824813i | \(-0.691281\pi\) | ||||
−0.565406 | + | 0.824813i | \(0.691281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.407750 | 0.0145163 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.278827 | −0.00991394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.2979 | −0.756311 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.7808 | 0.559687 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −55.1753 | −1.95441 | −0.977205 | − | 0.212296i | \(-0.931906\pi\) | ||||
−0.977205 | + | 0.212296i | \(0.931906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0438 | 0.709099 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.199719 | 0.00705671 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.92625 | −0.138554 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.1810 | 0.570306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4715 | −0.509420 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.04923 | −0.212680 | −0.106340 | − | 0.994330i | \(-0.533913\pi\) | ||||
−0.106340 | + | 0.994330i | \(0.533913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.97693 | 0.139649 | 0.0698244 | − | 0.997559i | \(-0.477756\pi\) | ||||
0.0698244 | + | 0.997559i | \(0.477756\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.8970 | 0.592604 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.8491 | −0.380029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.56714 | −0.124798 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.6596 | −0.582134 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5562 | 0.577815 | 0.288907 | − | 0.957357i | \(-0.406708\pi\) | ||||
0.288907 | + | 0.957357i | \(0.406708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9588 | 1.04430 | 0.522150 | − | 0.852854i | \(-0.325130\pi\) | ||||
0.522150 | + | 0.852854i | \(0.325130\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.299198 | 0.0104168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.4061 | 1.37029 | 0.685143 | − | 0.728409i | \(-0.259740\pi\) | ||||
0.685143 | + | 0.728409i | \(0.259740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.63817 | 0.230553 | 0.115277 | − | 0.993333i | \(-0.463225\pi\) | ||||
0.115277 | + | 0.993333i | \(0.463225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.4298 | −0.500565 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.902214 | −0.0312599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.3675 | 1.22394 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.5068 | 1.33099 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.4839 | 1.91552 | 0.957759 | − | 0.287574i | \(-0.0928486\pi\) | ||||
0.957759 | + | 0.287574i | \(0.0928486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9011 | −0.996590 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.0855 | −0.657340 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0864 | 0.346983 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.7345 | 0.849887 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.55334 | −0.0533103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8942 | −0.373447 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.3264 | −0.798680 | −0.399340 | − | 0.916803i | \(-0.630761\pi\) | ||||
−0.399340 | + | 0.916803i | \(0.630761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.3701 | 1.27803 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5822 | 0.703075 | 0.351537 | − | 0.936174i | \(-0.385659\pi\) | ||||
0.351537 | + | 0.936174i | \(0.385659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.7526 | 1.56106 | 0.780529 | − | 0.625120i | \(-0.214950\pi\) | ||||
0.780529 | + | 0.625120i | \(0.214950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.8738 | 0.540977 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.0848 | −0.343290 | −0.171645 | − | 0.985159i | \(-0.554908\pi\) | ||||
−0.171645 | + | 0.985159i | \(0.554908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.1717 | 1.39988 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.66495 | 0.328239 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.9313 | −0.743968 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.6075 | 1.00321 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.4560 | 0.658487 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.5645 | −0.999462 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.30564 | 0.111624 | 0.0558118 | − | 0.998441i | \(-0.482225\pi\) | ||||
0.0558118 | + | 0.998441i | \(0.482225\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.68048 | 0.326515 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.30907 | 0.279940 | 0.139970 | − | 0.990156i | \(-0.455299\pi\) | ||||
0.139970 | + | 0.990156i | \(0.455299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.65895 | −0.0894807 | −0.0447403 | − | 0.998999i | \(-0.514246\pi\) | ||||
−0.0447403 | + | 0.998999i | \(0.514246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.471846 | −0.0158609 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.5846 | 0.724740 | 0.362370 | − | 0.932034i | \(-0.381968\pi\) | ||||
0.362370 | + | 0.932034i | \(0.381968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.0250 | 1.34240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.31474 | −0.0775466 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −59.7665 | −2.00001 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.7738 | 1.73061 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.26921 | 0.242712 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.50051 | −0.0833967 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.9775 | −0.632231 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.17892 | −0.0392320 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.81470 | −0.226528 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.95616 | 0.197771 | 0.0988855 | − | 0.995099i | \(-0.468472\pi\) | ||||
0.0988855 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.4092 | −0.610594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.9730 | −0.496079 | −0.248040 | − | 0.968750i | \(-0.579786\pi\) | ||||
−0.248040 | + | 0.968750i | \(0.579786\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1528 | 0.567676 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.7892 | 0.521975 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.17527 | 0.269971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.4164 | 0.706463 | 0.353232 | − | 0.935536i | \(-0.385083\pi\) | ||||
0.353232 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.5509 | −0.512421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.3840 | −1.59258 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.960085 | −0.0315674 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.19796 | 0.105035 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.4153 | −1.68688 | −0.843441 | − | 0.537221i | \(-0.819474\pi\) | ||||
−0.843441 | + | 0.537221i | \(0.819474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69021 | 0.0881682 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.64024 | 0.217392 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.17925 | −0.267490 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.9350 | −1.36996 | −0.684979 | − | 0.728563i | \(-0.740188\pi\) | ||||
−0.684979 | + | 0.728563i | \(0.740188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.11337 | −0.0689674 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.8467 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705065\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0941 | 0.524097 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.0165 | 0.976436 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.12177 | −0.0689481 | −0.0344741 | − | 0.999406i | \(-0.510976\pi\) | ||||
−0.0344741 | + | 0.999406i | \(0.510976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.40663 | −0.272891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.32227 | −0.107732 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.5643 | 0.439391 | 0.219695 | − | 0.975569i | \(-0.429494\pi\) | ||||
0.219695 | + | 0.975569i | \(0.429494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.36645 | 0.303091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.408968 | −0.0132201 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00330 | −0.0323981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.2225 | 1.03944 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.9889 | −1.19195 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.4163 | 1.55858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.95719 | −0.191570 | −0.0957851 | − | 0.995402i | \(-0.530536\pi\) | ||||
−0.0957851 | + | 0.995402i | \(0.530536\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.3406 | 0.621308 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1772 | −0.390785 | −0.195392 | − | 0.980725i | \(-0.562598\pi\) | ||||
−0.195392 | + | 0.980725i | \(0.562598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.4886 | 1.13771 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.640624 | 0.0205164 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.69439 | 0.246165 | 0.123083 | − | 0.992396i | \(-0.460722\pi\) | ||||
0.123083 | + | 0.992396i | \(0.460722\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.130342 | 0.00416576 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3070 | 0.329078 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.2144 | 0.389578 | 0.194789 | − | 0.980845i | \(-0.437598\pi\) | ||||
0.194789 | + | 0.980845i | \(0.437598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.3401 | −1.34907 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.7525 | −0.628729 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.19529 | −0.0380079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.35228 | −0.0747227 | −0.0373613 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373613 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.1731 | −0.418036 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.58387 | −0.113616 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2415 | 0.609384 | 0.304692 | − | 0.952451i | \(-0.401446\pi\) | ||||
0.304692 | + | 0.952451i | \(0.401446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.2092 | −0.639389 |
(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 | 8048.2.a.p.1.2 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.6 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.6 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.5 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.2 | 10 | 1.1 | even | 1 | trivial |