Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.195727752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} - 25x^{3} - 3x^{2} + 9x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.457832\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59172 | −0.979577 | −0.489788 | − | 0.871841i | \(-0.662926\pi\) | ||||
−0.489788 | + | 0.871841i | \(0.662926\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.555013 | 0.167343 | 0.0836713 | − | 0.996493i | \(-0.473335\pi\) | ||||
0.0836713 | + | 0.996493i | \(0.473335\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55262 | 1.54002 | 0.770009 | − | 0.638033i | \(-0.220252\pi\) | ||||
0.770009 | + | 0.638033i | \(0.220252\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.185828 | −0.0450700 | −0.0225350 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225350 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.29081 | −0.525547 | −0.262773 | − | 0.964858i | \(-0.584637\pi\) | ||||
−0.262773 | + | 0.964858i | \(0.584637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.59172 | −0.565559 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.888313 | −0.185226 | −0.0926130 | − | 0.995702i | \(-0.529522\pi\) | ||||
−0.0926130 | + | 0.995702i | \(0.529522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.39504 | −0.259052 | −0.129526 | − | 0.991576i | \(-0.541346\pi\) | ||||
−0.129526 | + | 0.991576i | \(0.541346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.32155 | −0.596568 | −0.298284 | − | 0.954477i | \(-0.596414\pi\) | ||||
−0.298284 | + | 0.954477i | \(0.596414\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.555013 | 0.0966153 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.59172 | 0.438080 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.98676 | 1.31301 | 0.656507 | − | 0.754320i | \(-0.272033\pi\) | ||||
0.656507 | + | 0.754320i | \(0.272033\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.55262 | 0.889130 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.86462 | 0.915900 | 0.457950 | − | 0.888978i | \(-0.348584\pi\) | ||||
0.457950 | + | 0.888978i | \(0.348584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7310 | −1.78896 | −0.894480 | − | 0.447108i | \(-0.852454\pi\) | ||||
−0.894480 | + | 0.447108i | \(0.852454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6969 | 1.70616 | 0.853081 | − | 0.521779i | \(-0.174732\pi\) | ||||
0.853081 | + | 0.521779i | \(0.174732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.283009 | −0.0404298 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.185828 | −0.0260212 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.91980 | 0.401066 | 0.200533 | − | 0.979687i | \(-0.435733\pi\) | ||||
0.200533 | + | 0.979687i | \(0.435733\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.555013 | −0.0748379 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.29081 | −0.303425 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.00861 | 1.17282 | 0.586410 | − | 0.810014i | \(-0.300541\pi\) | ||||
0.586410 | + | 0.810014i | \(0.300541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.74680 | 0.735802 | 0.367901 | − | 0.929865i | \(-0.380077\pi\) | ||||
0.367901 | + | 0.929865i | \(0.380077\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.59172 | −0.326526 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.55262 | −0.688717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.888313 | −0.106940 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6850 | −1.38675 | −0.693377 | − | 0.720575i | \(-0.743878\pi\) | ||||
−0.693377 | + | 0.720575i | \(0.743878\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.45020 | 0.403815 | 0.201908 | − | 0.979405i | \(-0.435286\pi\) | ||||
0.201908 | + | 0.979405i | \(0.435286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.43844 | −0.163925 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73304 | 0.194983 | 0.0974913 | − | 0.995236i | \(-0.468918\pi\) | ||||
0.0974913 | + | 0.995236i | \(0.468918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.853271 | 0.0936587 | 0.0468293 | − | 0.998903i | \(-0.485088\pi\) | ||||
0.0468293 | + | 0.998903i | \(0.485088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.185828 | 0.0201559 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.39504 | −0.149564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5911 | 1.54666 | 0.773329 | − | 0.634005i | \(-0.218590\pi\) | ||||
0.773329 | + | 0.634005i | \(0.218590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3908 | −1.50857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.32155 | −0.344429 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.29081 | 0.235032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.48187 | 0.556599 | 0.278300 | − | 0.960494i | \(-0.410229\pi\) | ||||
0.278300 | + | 0.960494i | \(0.410229\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.555013 | 0.0557809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9657 | −1.09113 | −0.545565 | − | 0.838069i | \(-0.683685\pi\) | ||||
−0.545565 | + | 0.838069i | \(0.683685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1870 | −1.10229 | −0.551143 | − | 0.834411i | \(-0.685808\pi\) | ||||
−0.551143 | + | 0.834411i | \(0.685808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.59172 | 0.252926 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6031 | 1.50841 | 0.754203 | − | 0.656642i | \(-0.228024\pi\) | ||||
0.754203 | + | 0.656642i | \(0.228024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.3247 | 1.65941 | 0.829703 | − | 0.558205i | \(-0.188510\pi\) | ||||
0.829703 | + | 0.558205i | \(0.188510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.98676 | 0.758069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2366 | 1.05705 | 0.528526 | − | 0.848917i | \(-0.322745\pi\) | ||||
0.528526 | + | 0.848917i | \(0.322745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.888313 | 0.0828356 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.55262 | 0.513340 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.481614 | 0.0441495 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6920 | −0.971996 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.86462 | 0.528795 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.11359 | 0.808700 | 0.404350 | − | 0.914604i | \(-0.367498\pi\) | ||||
0.404350 | + | 0.914604i | \(0.367498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7310 | −1.03286 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.31390 | −0.376907 | −0.188454 | − | 0.982082i | \(-0.560348\pi\) | ||||
−0.188454 | + | 0.982082i | \(0.560348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.93712 | 0.514813 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.22792 | −0.532087 | −0.266044 | − | 0.963961i | \(-0.585717\pi\) | ||||
−0.266044 | + | 0.963961i | \(0.585717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1346 | 1.70780 | 0.853899 | − | 0.520439i | \(-0.174232\pi\) | ||||
0.853899 | + | 0.520439i | \(0.174232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6969 | 0.985053 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.08177 | 0.257711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.39504 | 0.115852 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.283009 | −0.0233422 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0754 | 1.23503 | 0.617513 | − | 0.786561i | \(-0.288140\pi\) | ||||
0.617513 | + | 0.786561i | \(0.288140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.6332 | 1.92324 | 0.961622 | − | 0.274378i | \(-0.0884719\pi\) | ||||
0.961622 | + | 0.274378i | \(0.0884719\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.185828 | −0.0150233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.32155 | 0.266793 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.16618 | 0.571924 | 0.285962 | − | 0.958241i | \(-0.407687\pi\) | ||||
0.285962 | + | 0.958241i | \(0.407687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.91980 | 0.231555 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.30225 | 0.181443 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4483 | −1.52331 | −0.761655 | − | 0.647982i | \(-0.775613\pi\) | ||||
−0.761655 | + | 0.647982i | \(0.775613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.555013 | −0.0432077 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.64067 | −0.436488 | −0.218244 | − | 0.975894i | \(-0.570033\pi\) | ||||
−0.218244 | + | 0.975894i | \(0.570033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.8315 | 1.37166 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.29081 | −0.175182 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4733 | −1.02436 | −0.512178 | − | 0.858879i | \(-0.671161\pi\) | ||||
−0.512178 | + | 0.858879i | \(0.671161\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.59172 | −0.195915 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00861 | 0.677128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.6586 | 1.31987 | 0.659933 | − | 0.751325i | \(-0.270585\pi\) | ||||
0.659933 | + | 0.751325i | \(0.270585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4214 | 0.774615 | 0.387308 | − | 0.921951i | \(-0.373405\pi\) | ||||
0.387308 | + | 0.921951i | \(0.373405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.74680 | 0.424816 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.98676 | −0.587198 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.103137 | −0.00754214 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.59172 | −0.188520 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8649 | 1.43738 | 0.718688 | − | 0.695332i | \(-0.244743\pi\) | ||||
0.718688 | + | 0.695332i | \(0.244743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.23272 | −0.304678 | −0.152339 | − | 0.988328i | \(-0.548680\pi\) | ||||
−0.152339 | + | 0.988328i | \(0.548680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.55262 | −0.397631 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9353 | 1.20659 | 0.603294 | − | 0.797519i | \(-0.293855\pi\) | ||||
0.603294 | + | 0.797519i | \(0.293855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.84324 | −0.272440 | −0.136220 | − | 0.990679i | \(-0.543495\pi\) | ||||
−0.136220 | + | 0.990679i | \(0.543495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.61555 | 0.253762 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.86462 | −0.409603 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.888313 | −0.0617420 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.27143 | −0.0879464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.2584 | 1.87655 | 0.938274 | − | 0.345893i | \(-0.112424\pi\) | ||||
0.938274 | + | 0.345893i | \(0.112424\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6850 | −0.800643 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7310 | 0.800047 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.60852 | 0.584384 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.45020 | 0.233143 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.03183 | −0.0694087 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.84326 | −0.190399 | −0.0951995 | − | 0.995458i | \(-0.530349\pi\) | ||||
−0.0951995 | + | 0.995458i | \(0.530349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.7298 | −1.70774 | −0.853872 | − | 0.520483i | \(-0.825752\pi\) | ||||
−0.853872 | + | 0.520483i | \(0.825752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5116 | −1.35544 | −0.677722 | − | 0.735318i | \(-0.737033\pi\) | ||||
−0.677722 | + | 0.735318i | \(0.737033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.43844 | −0.0946421 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.93481 | 0.454315 | 0.227157 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227157 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6969 | −0.763018 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73304 | 0.112573 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.64142 | −0.235544 | −0.117772 | − | 0.993041i | \(-0.537575\pi\) | ||||
−0.117772 | + | 0.993041i | \(0.537575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5267 | −1.45108 | −0.725538 | − | 0.688183i | \(-0.758409\pi\) | ||||
−0.725538 | + | 0.688183i | \(0.758409\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.283009 | 0.0180808 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7200 | −0.809352 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.853271 | 0.0540739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6475 | 1.24014 | 0.620068 | − | 0.784548i | \(-0.287105\pi\) | ||||
0.620068 | + | 0.784548i | \(0.287105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.493025 | −0.0309962 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.185828 | 0.0116370 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.60737 | 0.599291 | 0.299646 | − | 0.954051i | \(-0.403132\pi\) | ||||
0.299646 | + | 0.954051i | \(0.403132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.6994 | −1.28620 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.39504 | −0.0863508 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.6492 | 1.02663 | 0.513317 | − | 0.858199i | \(-0.328416\pi\) | ||||
0.513317 | + | 0.858199i | \(0.328416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.91980 | −0.179362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5911 | 0.892963 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.9576 | 0.790038 | 0.395019 | − | 0.918673i | \(-0.370738\pi\) | ||||
0.395019 | + | 0.918673i | \(0.370738\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.4319 | −1.78786 | −0.893930 | − | 0.448207i | \(-0.852063\pi\) | ||||
−0.893930 | + | 0.448207i | \(0.852063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.3908 | −0.870971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.555013 | 0.0334685 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6288 | 0.818873 | 0.409436 | − | 0.912339i | \(-0.365725\pi\) | ||||
0.409436 | + | 0.912339i | \(0.365725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.32155 | −0.198856 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7784 | 1.06057 | 0.530285 | − | 0.847819i | \(-0.322085\pi\) | ||||
0.530285 | + | 0.847819i | \(0.322085\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4991 | −0.624109 | −0.312055 | − | 0.950064i | \(-0.601017\pi\) | ||||
−0.312055 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.29081 | 0.135696 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.1994 | −0.897194 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9655 | −0.997969 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.48187 | 0.321353 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.7883 | 0.863943 | 0.431972 | − | 0.901887i | \(-0.357818\pi\) | ||||
0.431972 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00861 | −0.524501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.555013 | 0.0322051 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.93246 | −0.285252 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.4034 | 1.75242 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.9657 | −0.629964 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.74680 | −0.329061 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8573 | −1.47575 | −0.737876 | − | 0.674936i | \(-0.764171\pi\) | ||||
−0.737876 | + | 0.674936i | \(0.764171\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.1870 | −0.636405 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7273 | −1.28875 | −0.644375 | − | 0.764710i | \(-0.722882\pi\) | ||||
−0.644375 | + | 0.764710i | \(0.722882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.3090 | −1.43055 | −0.715275 | − | 0.698844i | \(-0.753698\pi\) | ||||
−0.715275 | + | 0.698844i | \(0.753698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.59172 | 0.146027 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.1284 | −1.41135 | −0.705677 | − | 0.708534i | \(-0.749357\pi\) | ||||
−0.705677 | + | 0.708534i | \(0.749357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.774265 | −0.0433505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.6031 | 0.870878 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.425697 | 0.0236864 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.55262 | 0.308004 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3247 | 0.958059 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.3149 | −1.67132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7348 | 1.02976 | 0.514879 | − | 0.857263i | \(-0.327837\pi\) | ||||
0.514879 | + | 0.857263i | \(0.327837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.98676 | 0.437672 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5676 | −1.55618 | −0.778089 | − | 0.628155i | \(-0.783811\pi\) | ||||
−0.778089 | + | 0.628155i | \(0.783811\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2366 | 0.610290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.84350 | −0.0998313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8755 | 1.01918 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.888313 | 0.0478252 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.33485 | 0.393755 | 0.196878 | − | 0.980428i | \(-0.436920\pi\) | ||||
0.196878 | + | 0.980428i | \(0.436920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.490240 | −0.0262420 | −0.0131210 | − | 0.999914i | \(-0.504177\pi\) | ||||
−0.0131210 | + | 0.999914i | \(0.504177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.55262 | 0.296377 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.9530 | −1.48779 | −0.743895 | − | 0.668297i | \(-0.767024\pi\) | ||||
−0.743895 | + | 0.668297i | \(0.767024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.6850 | 0.620176 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.481614 | 0.0254897 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9750 | 1.15979 | 0.579897 | − | 0.814690i | \(-0.303093\pi\) | ||||
0.579897 | + | 0.814690i | \(0.303093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7522 | −0.723800 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.6920 | −0.561182 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.45020 | −0.180592 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4768 | 0.755684 | 0.377842 | − | 0.925870i | \(-0.376666\pi\) | ||||
0.377842 | + | 0.925870i | \(0.376666\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.86462 | 0.305300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.56730 | −0.392875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7751 | 0.557915 | 0.278958 | − | 0.960303i | \(-0.410011\pi\) | ||||
0.278958 | + | 0.960303i | \(0.410011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.74612 | −0.398946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.9005 | −1.17632 | −0.588160 | − | 0.808745i | \(-0.700147\pi\) | ||||
−0.588160 | + | 0.808745i | \(0.700147\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.11359 | 0.466903 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.6968 | 1.82402 | 0.912010 | − | 0.410167i | \(-0.134530\pi\) | ||||
0.912010 | + | 0.410167i | \(0.134530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.43844 | 0.0733095 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.7310 | −0.596320 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.6775 | 1.60611 | 0.803056 | − | 0.595904i | \(-0.203206\pi\) | ||||
0.803056 | + | 0.595904i | \(0.203206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.165074 | 0.00834814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.31390 | −0.217608 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.73304 | −0.0871989 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3673 | 0.921829 | 0.460914 | − | 0.887445i | \(-0.347522\pi\) | ||||
0.460914 | + | 0.887445i | \(0.347522\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.93712 | 0.297228 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.5580 | −1.27631 | −0.638153 | − | 0.769909i | \(-0.720301\pi\) | ||||
−0.638153 | + | 0.769909i | \(0.720301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.4433 | −0.918726 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.43275 | 0.219723 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02869 | −0.0508657 | −0.0254328 | − | 0.999677i | \(-0.508096\pi\) | ||||
−0.0254328 | + | 0.999677i | \(0.508096\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.22792 | −0.307201 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.3478 | −1.14887 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.853271 | −0.0418854 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.1346 | 0.985998 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1306 | −0.641470 | −0.320735 | − | 0.947169i | \(-0.603930\pi\) | ||||
−0.320735 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3744 | −1.18794 | −0.593968 | − | 0.804488i | \(-0.702440\pi\) | ||||
−0.593968 | + | 0.804488i | \(0.702440\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.6969 | 0.568720 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.185828 | −0.00901400 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.8941 | −0.720774 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.08177 | 0.148789 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.81841 | −0.376600 | −0.188300 | − | 0.982112i | \(-0.560298\pi\) | ||||
−0.188300 | + | 0.982112i | \(0.560298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.5024 | −1.46585 | −0.732927 | − | 0.680308i | \(-0.761846\pi\) | ||||
−0.732927 | + | 0.680308i | \(0.761846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.39504 | 0.0668871 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.03495 | 0.0973450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0100 | −1.19366 | −0.596830 | − | 0.802368i | \(-0.703573\pi\) | ||||
−0.596830 | + | 0.802368i | \(0.703573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.283009 | −0.0134766 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.0228 | −1.37892 | −0.689458 | − | 0.724326i | \(-0.742151\pi\) | ||||
−0.689458 | + | 0.724326i | \(0.742151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5911 | −0.691686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.0754 | 0.713042 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1375 | 0.855962 | 0.427981 | − | 0.903788i | \(-0.359225\pi\) | ||||
0.427981 | + | 0.903788i | \(0.359225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.25494 | 0.153269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.6332 | 1.11039 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.3908 | 0.674651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2384 | 0.712821 | 0.356411 | − | 0.934329i | \(-0.384000\pi\) | ||||
0.356411 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.185828 | −0.00867373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.56516 | 0.166046 | 0.0830230 | − | 0.996548i | \(-0.473542\pi\) | ||||
0.0830230 | + | 0.996548i | \(0.473542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2852 | −1.36100 | −0.680499 | − | 0.732749i | \(-0.738237\pi\) | ||||
−0.680499 | + | 0.732749i | \(0.738237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.32155 | 0.154033 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3770 | 0.942934 | 0.471467 | − | 0.881884i | \(-0.343725\pi\) | ||||
0.471467 | + | 0.881884i | \(0.343725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.59172 | −0.119674 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.16618 | 0.330200 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.51085 | −0.299369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.29081 | −0.105109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.91980 | 0.133689 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.0674 | 1.14536 | 0.572680 | − | 0.819779i | \(-0.305904\pi\) | ||||
0.572680 | + | 0.819779i | \(0.305904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.3474 | 2.02207 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.30225 | 0.104756 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.48187 | −0.248919 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7106 | 1.02911 | 0.514557 | − | 0.857456i | \(-0.327956\pi\) | ||||
0.514557 | + | 0.857456i | \(0.327956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4483 | −0.879484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.14000 | −0.322224 | −0.161112 | − | 0.986936i | \(-0.551508\pi\) | ||||
−0.161112 | + | 0.986936i | \(0.551508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.259238 | 0.0116755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.555013 | −0.0249460 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.2842 | 1.35843 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.97471 | −0.177932 | −0.0889662 | − | 0.996035i | \(-0.528356\pi\) | ||||
−0.0889662 | + | 0.996035i | \(0.528356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.64067 | −0.252007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.21243 | 0.276999 | 0.138499 | − | 0.990363i | \(-0.455772\pi\) | ||||
0.138499 | + | 0.990363i | \(0.455772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9657 | 0.487968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8315 | 0.791927 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.8268 | 1.80961 | 0.904807 | − | 0.425822i | \(-0.140015\pi\) | ||||
0.904807 | + | 0.425822i | \(0.140015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.94194 | −0.395568 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.29081 | −0.101142 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.1870 | 0.492957 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.49190 | 0.285514 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.4733 | −0.591412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.6283 | 1.47328 | 0.736642 | − | 0.676283i | \(-0.236410\pi\) | ||||
0.736642 | + | 0.676283i | \(0.236410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.6068 | 1.03225 | 0.516127 | − | 0.856512i | \(-0.327373\pi\) | ||||
0.516127 | + | 0.856512i | \(0.327373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.59172 | −0.113112 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.617239 | 0.0268873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2109 | −0.965691 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.00861 | 0.390940 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.5640 | 1.41050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.6031 | −0.674579 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.6586 | 0.762024 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.157073 | −0.00676563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2952 | −0.657594 | −0.328797 | − | 0.944401i | \(-0.606643\pi\) | ||||
−0.328797 | + | 0.944401i | \(0.606643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.4214 | 0.447224 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.3247 | −0.742109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.3464 | −1.46855 | −0.734273 | − | 0.678854i | \(-0.762477\pi\) | ||||
−0.734273 | + | 0.678854i | \(0.762477\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.74680 | 0.245267 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.19577 | 0.136144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.49156 | −0.191000 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.98676 | −0.339019 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.83573 | 0.0777825 | 0.0388912 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388912 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −65.1377 | −2.75503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.103137 | −0.00435445 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.97854 | −0.420545 | −0.210273 | − | 0.977643i | \(-0.567435\pi\) | ||||
−0.210273 | + | 0.977643i | \(0.567435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2366 | −0.472728 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.59172 | −0.108842 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1749 | 0.552321 | 0.276160 | − | 0.961112i | \(-0.410938\pi\) | ||||
0.276160 | + | 0.961112i | \(0.410938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5420 | −0.524868 | −0.262434 | − | 0.964950i | \(-0.584525\pi\) | ||||
−0.262434 | + | 0.964950i | \(0.584525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.8649 | 0.829870 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.888313 | −0.0370452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.54978 | 0.0645182 | 0.0322591 | − | 0.999480i | \(-0.489730\pi\) | ||||
0.0322591 | + | 0.999480i | \(0.489730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.23272 | −0.175906 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.21144 | −0.0917459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.62053 | 0.0671154 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.55262 | −0.229572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.3396 | −1.83009 | −0.915045 | − | 0.403351i | \(-0.867845\pi\) | ||||
−0.915045 | + | 0.403351i | \(0.867845\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.60903 | 0.313525 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.9353 | 0.696624 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.8725 | −1.76056 | −0.880281 | − | 0.474453i | \(-0.842646\pi\) | ||||
−0.880281 | + | 0.474453i | \(0.842646\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.481614 | −0.0197443 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.84324 | −0.157293 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.26522 | 0.378567 | 0.189283 | − | 0.981923i | \(-0.439384\pi\) | ||||
0.189283 | + | 0.981923i | \(0.439384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.9859 | 1.18236 | 0.591180 | − | 0.806539i | \(-0.298662\pi\) | ||||
0.591180 | + | 0.806539i | \(0.298662\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6920 | 0.434690 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.04351 | −0.0423549 | −0.0211774 | − | 0.999776i | \(-0.506741\pi\) | ||||
−0.0211774 | + | 0.999776i | \(0.506741\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.61555 | 0.146509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.9481 | 2.62752 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.41274 | −0.299398 | −0.149699 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149699 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.86462 | −0.236484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.44106 | 0.0982735 | 0.0491367 | − | 0.998792i | \(-0.484353\pi\) | ||||
0.0491367 | + | 0.998792i | \(0.484353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.07274 | 0.163697 | 0.0818487 | − | 0.996645i | \(-0.473918\pi\) | ||||
0.0818487 | + | 0.996645i | \(0.473918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.888313 | −0.0356468 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.8161 | −1.51507 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.27143 | −0.0507759 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.48417 | −0.0591776 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7734 | −1.22507 | −0.612535 | − | 0.790444i | \(-0.709850\pi\) | ||||
−0.612535 | + | 0.790444i | \(0.709850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.2584 | 1.08343 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.11359 | −0.361662 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.57144 | −0.0622627 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.6850 | −0.462252 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.7423 | −0.503290 | −0.251645 | − | 0.967820i | \(-0.580972\pi\) | ||||
−0.251645 | + | 0.967820i | \(0.580972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.93195 | 0.273369 | 0.136685 | − | 0.990615i | \(-0.456355\pi\) | ||||
0.136685 | + | 0.990615i | \(0.456355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.7310 | 0.461907 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.7455 | 0.579704 | 0.289852 | − | 0.957071i | \(-0.406394\pi\) | ||||
0.289852 | + | 0.957071i | \(0.406394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.99989 | 0.196263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.60852 | 0.337394 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.7761 | −0.930432 | −0.465216 | − | 0.885197i | \(-0.654023\pi\) | ||||
−0.465216 | + | 0.885197i | \(0.654023\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.31390 | 0.168558 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.45020 | 0.134605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.8307 | −1.43472 | −0.717360 | − | 0.696703i | \(-0.754650\pi\) | ||||
−0.717360 | + | 0.696703i | \(0.754650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1029 | −0.392957 | −0.196478 | − | 0.980508i | \(-0.562951\pi\) | ||||
−0.196478 | + | 0.980508i | \(0.562951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.03183 | −0.0400731 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.93712 | −0.230232 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.23923 | 0.0479833 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.84326 | −0.109927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18955 | 0.123131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7292 | −0.991788 | −0.495894 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.4420 | −0.708785 | −0.354392 | − | 0.935097i | \(-0.615312\pi\) | ||||
−0.354392 | + | 0.935097i | \(0.615312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2074 | −0.545232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.7298 | −0.985966 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.2539 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.22792 | 0.237957 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.5116 | −0.782566 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.2125 | 0.617649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.56495 | −0.249742 | −0.124871 | − | 0.992173i | \(-0.539852\pi\) | ||||
−0.124871 | + | 0.992173i | \(0.539852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.43844 | −0.0546416 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.1346 | −0.763750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08981 | −0.0412796 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.93481 | 0.262299 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.4783 | 1.11338 | 0.556691 | − | 0.830720i | \(-0.312071\pi\) | ||||
0.556691 | + | 0.830720i | \(0.312071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2961 | −0.690051 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.6969 | −0.440529 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.4200 | 1.06884 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6530 | 1.45164 | 0.725822 | − | 0.687883i | \(-0.241460\pi\) | ||||
0.725822 | + | 0.687883i | \(0.241460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.73304 | 0.0649942 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.95058 | 0.110500 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.08177 | −0.115252 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.64142 | −0.135991 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.6110 | −1.02972 | −0.514858 | − | 0.857275i | \(-0.672155\pi\) | ||||
−0.514858 | + | 0.857275i | \(0.672155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.9935 | 1.07977 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.5267 | −0.837779 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.39504 | −0.0518105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.2682 | 1.12259 | 0.561293 | − | 0.827617i | \(-0.310304\pi\) | ||||
0.561293 | + | 0.827617i | \(0.310304\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.17995 | 0.0806284 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.0158 | 1.73657 | 0.868284 | − | 0.496068i | \(-0.165223\pi\) | ||||
0.868284 | + | 0.496068i | \(0.165223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.283009 | 0.0104389 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.555013 | 0.0204442 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2046 | −0.669669 | −0.334834 | − | 0.942277i | \(-0.608680\pi\) | ||||
−0.334834 | + | 0.942277i | \(0.608680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.7200 | −0.467280 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7706 | −0.982118 | −0.491059 | − | 0.871126i | \(-0.663390\pi\) | ||||
−0.491059 | + | 0.871126i | \(0.663390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0754 | −0.552320 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.853271 | 0.0312196 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.4387 | −1.47760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7310 | −0.537543 | −0.268771 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268771 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.6475 | 0.715993 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.6332 | −0.860101 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9109 | 0.469254 | 0.234627 | − | 0.972085i | \(-0.424613\pi\) | ||||
0.234627 | + | 0.972085i | \(0.424613\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.493025 | −0.0178957 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.2743 | 1.13369 | 0.566846 | − | 0.823824i | \(-0.308164\pi\) | ||||
0.566846 | + | 0.823824i | \(0.308164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.9007 | −1.62552 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.185828 | 0.00671864 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.0213 | 1.80617 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.6774 | 0.385036 | 0.192518 | − | 0.981293i | \(-0.438335\pi\) | ||||
0.192518 | + | 0.981293i | \(0.438335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.60737 | 0.346001 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7619 | 0.638851 | 0.319426 | − | 0.947611i | \(-0.396510\pi\) | ||||
0.319426 | + | 0.947611i | \(0.396510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.32155 | −0.119314 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.6994 | −0.742587 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.4347 | −0.481348 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.48533 | −0.232063 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.39504 | −0.0498547 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.16618 | −0.255772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.76761 | −0.241239 | −0.120620 | − | 0.992699i | \(-0.538488\pi\) | ||||
−0.120620 | + | 0.992699i | \(0.538488\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.6492 | 0.592728 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.1221 | −1.03546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.9098 | 1.13315 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.91980 | −0.103555 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.8700 | −1.55396 | −0.776978 | − | 0.629528i | \(-0.783248\pi\) | ||||
−0.776978 | + | 0.629528i | \(0.783248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.17361 | −0.0768967 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.5911 | 0.515553 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.91491 | 0.0675756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.30225 | −0.0811438 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.9576 | 0.456128 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.2929 | 1.17052 | 0.585258 | − | 0.810847i | \(-0.300993\pi\) | ||||
0.585258 | + | 0.810847i | \(0.300993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8674 | −0.522064 | −0.261032 | − | 0.965330i | \(-0.584063\pi\) | ||||
−0.261032 | + | 0.965330i | \(0.584063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.4319 | −1.03222 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.4483 | 0.681245 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8734 | 0.940182 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.3908 | −0.502855 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.469447 | 0.0163838 | 0.00819190 | − | 0.999966i | \(-0.497392\pi\) | ||||
0.00819190 | + | 0.999966i | \(0.497392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2132 | 0.565155 | 0.282578 | − | 0.959244i | \(-0.408811\pi\) | ||||
0.282578 | + | 0.959244i | \(0.408811\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.555013 | 0.0193231 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.4593 | 1.75464 | 0.877321 | − | 0.479904i | \(-0.159328\pi\) | ||||
0.877321 | + | 0.479904i | \(0.159328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.90119 | −0.135494 | −0.0677470 | − | 0.997703i | \(-0.521581\pi\) | ||||
−0.0677470 | + | 0.997703i | \(0.521581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6288 | 0.472776 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0525911 | 0.00182217 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.64067 | 0.195203 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.32155 | −0.114810 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5448 | −0.364048 | −0.182024 | − | 0.983294i | \(-0.558265\pi\) | ||||
−0.182024 | + | 0.983294i | \(0.558265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0539 | −0.932892 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.7784 | 0.612320 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.8315 | −0.613424 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7105 | 0.952145 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.4991 | −0.360330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.09474 | −0.243205 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.4265 | 0.733630 | 0.366815 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366815 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.29081 | 0.0783439 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.8336 | −0.711663 | −0.355832 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355832 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3190 | 0.522677 | 0.261339 | − | 0.965247i | \(-0.415836\pi\) | ||||
0.261339 | + | 0.965247i | \(0.415836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.1994 | −0.517995 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.5886 | −1.07529 | −0.537645 | − | 0.843171i | \(-0.680686\pi\) | ||||
−0.537645 | + | 0.843171i | \(0.680686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.4733 | 0.458106 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9655 | −0.576177 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.961862 | 0.0326289 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.55262 | 0.188143 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.48187 | 0.185533 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.59172 | 0.0876160 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.82660 | −0.0616800 | −0.0308400 | − | 0.999524i | \(-0.509818\pi\) | ||||
−0.0308400 | + | 0.999524i | \(0.509818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.7883 | 0.498798 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.30232 | 0.111258 | 0.0556289 | − | 0.998452i | \(-0.482284\pi\) | ||||
0.0556289 | + | 0.998452i | \(0.482284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.5403 | −1.36429 | −0.682146 | − | 0.731216i | \(-0.738953\pi\) | ||||
−0.682146 | + | 0.731216i | \(0.738953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.00861 | −0.302821 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3321 | −0.346917 | −0.173458 | − | 0.984841i | \(-0.555494\pi\) | ||||
−0.173458 | + | 0.984841i | \(0.555494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.6198 | −0.792183 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.555013 | 0.0185936 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.7952 | −0.896668 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.6586 | −0.590262 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.93246 | −0.164690 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.63370 | 0.154543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.542582 | −0.0180760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.4034 | 1.01176 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.4214 | −0.346419 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.11151 | −0.0369071 | −0.0184536 | − | 0.999830i | \(-0.505874\pi\) | ||||
−0.0184536 | + | 0.999830i | \(0.505874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9657 | −0.363710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.8583 | 1.28743 | 0.643716 | − | 0.765265i | \(-0.277392\pi\) | ||||
0.643716 | + | 0.765265i | \(0.277392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.473576 | 0.0156731 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.74680 | −0.189983 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.1804 | 0.369210 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.43530 | −0.146307 | −0.0731536 | − | 0.997321i | \(-0.523306\pi\) | ||||
−0.0731536 | + | 0.997321i | \(0.523306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.8573 | −0.852026 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −64.8823 | −2.13563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.98676 | 0.262603 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.1870 | −0.367429 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.3768 | 1.39034 | 0.695168 | − | 0.718847i | \(-0.255330\pi\) | ||||
0.695168 | + | 0.718847i | \(0.255330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.648318 | 0.0212478 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.7273 | −0.744060 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.103137 | 0.00337295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.3496 | −0.632122 | −0.316061 | − | 0.948739i | \(-0.602360\pi\) | ||||
−0.316061 | + | 0.948739i | \(0.602360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3090 | −0.825928 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.5229 | 1.48400 | 0.742002 | − | 0.670397i | \(-0.233876\pi\) | ||||
0.742002 | + | 0.670397i | \(0.233876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.20962 | −0.169649 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.59172 | 0.0843085 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −60.2821 | −1.95891 | −0.979453 | − | 0.201671i | \(-0.935363\pi\) | ||||
−0.979453 | + | 0.201671i | \(0.935363\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.1576 | 0.621883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.1284 | −0.814845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.20417 | −0.168579 | −0.0842897 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842897 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.8649 | −0.642814 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.774265 | −0.0250284 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.1410 | 0.521220 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9673 | −0.644106 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.6031 | 0.502802 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.23272 | 0.136256 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.1822 | −1.16354 | −0.581770 | − | 0.813353i | \(-0.697640\pi\) | ||||
−0.581770 | + | 0.813353i | \(0.697640\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.425697 | 0.0136754 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7045 | −0.503983 | −0.251991 | − | 0.967729i | \(-0.581085\pi\) | ||||
−0.251991 | + | 0.967729i | \(0.581085\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.1833 | −1.67292 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.55262 | 0.177826 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.3486 | 1.13090 | 0.565452 | − | 0.824781i | \(-0.308702\pi\) | ||||
0.565452 | + | 0.824781i | \(0.308702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.09827 | 0.258822 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3247 | 0.553136 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.788593 | 0.0251522 | 0.0125761 | − | 0.999921i | \(-0.495997\pi\) | ||||
0.0125761 | + | 0.999921i | \(0.495997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.9353 | −0.539602 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.3149 | −0.964934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.4208 | 0.331362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.0610 | 1.62201 | 0.811003 | − | 0.585042i | \(-0.198922\pi\) | ||||
0.811003 | + | 0.585042i | \(0.198922\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7348 | 0.594531 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.84324 | 0.121839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.1766 | 0.924034 | 0.462017 | − | 0.886871i | \(-0.347126\pi\) | ||||
0.462017 | + | 0.886871i | \(0.347126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.98676 | 0.252690 |
(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 | 4020.2.a.g.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.g.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |