Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.91539\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91539 | −1.35439 | −0.677193 | − | 0.735805i | \(-0.736804\pi\) | ||||
−0.677193 | + | 0.735805i | \(0.736804\pi\) | |||||||
\(3\) | 1.67190 | 0.965274 | 0.482637 | − | 0.875821i | \(-0.339679\pi\) | ||||
0.482637 | + | 0.875821i | \(0.339679\pi\) | |||||||
\(4\) | 1.66872 | 0.834361 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.20235 | −1.30735 | ||||||||
\(7\) | −4.22760 | −1.59788 | −0.798942 | − | 0.601408i | \(-0.794607\pi\) | ||||
−0.798942 | + | 0.601408i | \(0.794607\pi\) | |||||||
\(8\) | 0.634526 | 0.224339 | ||||||||
\(9\) | −0.204741 | −0.0682469 | ||||||||
\(10\) | −1.91539 | −0.605700 | ||||||||
\(11\) | 2.92847 | 0.882967 | 0.441484 | − | 0.897269i | \(-0.354452\pi\) | ||||
0.441484 | + | 0.897269i | \(0.354452\pi\) | |||||||
\(12\) | 2.78994 | 0.805387 | ||||||||
\(13\) | −2.06406 | −0.572468 | −0.286234 | − | 0.958160i | \(-0.592403\pi\) | ||||
−0.286234 | + | 0.958160i | \(0.592403\pi\) | |||||||
\(14\) | 8.09751 | 2.16415 | ||||||||
\(15\) | 1.67190 | 0.431683 | ||||||||
\(16\) | −4.55281 | −1.13820 | ||||||||
\(17\) | 3.59719 | 0.872448 | 0.436224 | − | 0.899838i | \(-0.356316\pi\) | ||||
0.436224 | + | 0.899838i | \(0.356316\pi\) | |||||||
\(18\) | 0.392159 | 0.0924327 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.66872 | 0.373138 | ||||||||
\(21\) | −7.06814 | −1.54240 | ||||||||
\(22\) | −5.60917 | −1.19588 | ||||||||
\(23\) | 8.02202 | 1.67271 | 0.836354 | − | 0.548190i | \(-0.184683\pi\) | ||||
0.836354 | + | 0.548190i | \(0.184683\pi\) | |||||||
\(24\) | 1.06087 | 0.216548 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.95348 | 0.775342 | ||||||||
\(27\) | −5.35802 | −1.03115 | ||||||||
\(28\) | −7.05470 | −1.33321 | ||||||||
\(29\) | −2.00502 | −0.372322 | −0.186161 | − | 0.982519i | \(-0.559605\pi\) | ||||
−0.186161 | + | 0.982519i | \(0.559605\pi\) | |||||||
\(30\) | −3.20235 | −0.584666 | ||||||||
\(31\) | −8.46117 | −1.51967 | −0.759836 | − | 0.650115i | \(-0.774721\pi\) | ||||
−0.759836 | + | 0.650115i | \(0.774721\pi\) | |||||||
\(32\) | 7.45136 | 1.31723 | ||||||||
\(33\) | 4.89612 | 0.852305 | ||||||||
\(34\) | −6.89003 | −1.18163 | ||||||||
\(35\) | −4.22760 | −0.714595 | ||||||||
\(36\) | −0.341655 | −0.0569426 | ||||||||
\(37\) | −2.20105 | −0.361851 | −0.180925 | − | 0.983497i | \(-0.557909\pi\) | ||||
−0.180925 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.45091 | −0.552588 | ||||||||
\(40\) | 0.634526 | 0.100327 | ||||||||
\(41\) | 9.76141 | 1.52448 | 0.762238 | − | 0.647297i | \(-0.224101\pi\) | ||||
0.762238 | + | 0.647297i | \(0.224101\pi\) | |||||||
\(42\) | 13.5383 | 2.08900 | ||||||||
\(43\) | 10.5308 | 1.60593 | 0.802967 | − | 0.596024i | \(-0.203254\pi\) | ||||
0.802967 | + | 0.596024i | \(0.203254\pi\) | |||||||
\(44\) | 4.88681 | 0.736714 | ||||||||
\(45\) | −0.204741 | −0.0305209 | ||||||||
\(46\) | −15.3653 | −2.26549 | ||||||||
\(47\) | 3.58295 | 0.522628 | 0.261314 | − | 0.965254i | \(-0.415844\pi\) | ||||
0.261314 | + | 0.965254i | \(0.415844\pi\) | |||||||
\(48\) | −7.61186 | −1.09868 | ||||||||
\(49\) | 10.8726 | 1.55323 | ||||||||
\(50\) | −1.91539 | −0.270877 | ||||||||
\(51\) | 6.01416 | 0.842151 | ||||||||
\(52\) | −3.44435 | −0.477645 | ||||||||
\(53\) | 3.24204 | 0.445328 | 0.222664 | − | 0.974895i | \(-0.428525\pi\) | ||||
0.222664 | + | 0.974895i | \(0.428525\pi\) | |||||||
\(54\) | 10.2627 | 1.39658 | ||||||||
\(55\) | 2.92847 | 0.394875 | ||||||||
\(56\) | −2.68252 | −0.358467 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.84039 | 0.504268 | ||||||||
\(59\) | −2.08653 | −0.271643 | −0.135822 | − | 0.990733i | \(-0.543367\pi\) | ||||
−0.135822 | + | 0.990733i | \(0.543367\pi\) | |||||||
\(60\) | 2.78994 | 0.360180 | ||||||||
\(61\) | −4.93614 | −0.632008 | −0.316004 | − | 0.948758i | \(-0.602341\pi\) | ||||
−0.316004 | + | 0.948758i | \(0.602341\pi\) | |||||||
\(62\) | 16.2065 | 2.05822 | ||||||||
\(63\) | 0.865563 | 0.109051 | ||||||||
\(64\) | −5.16665 | −0.645831 | ||||||||
\(65\) | −2.06406 | −0.256015 | ||||||||
\(66\) | −9.37798 | −1.15435 | ||||||||
\(67\) | 10.1043 | 1.23444 | 0.617218 | − | 0.786792i | \(-0.288260\pi\) | ||||
0.617218 | + | 0.786792i | \(0.288260\pi\) | |||||||
\(68\) | 6.00272 | 0.727937 | ||||||||
\(69\) | 13.4120 | 1.61462 | ||||||||
\(70\) | 8.09751 | 0.967838 | ||||||||
\(71\) | −2.85201 | −0.338471 | −0.169235 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169235 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(72\) | −0.129913 | −0.0153104 | ||||||||
\(73\) | 1.82820 | 0.213975 | 0.106987 | − | 0.994260i | \(-0.465880\pi\) | ||||
0.106987 | + | 0.994260i | \(0.465880\pi\) | |||||||
\(74\) | 4.21588 | 0.490086 | ||||||||
\(75\) | 1.67190 | 0.193055 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.3804 | −1.41088 | ||||||||
\(78\) | 6.60984 | 0.748417 | ||||||||
\(79\) | 12.7131 | 1.43033 | 0.715167 | − | 0.698954i | \(-0.246351\pi\) | ||||
0.715167 | + | 0.698954i | \(0.246351\pi\) | |||||||
\(80\) | −4.55281 | −0.509020 | ||||||||
\(81\) | −8.34386 | −0.927095 | ||||||||
\(82\) | −18.6969 | −2.06473 | ||||||||
\(83\) | 17.2197 | 1.89010 | 0.945051 | − | 0.326922i | \(-0.106012\pi\) | ||||
0.945051 | + | 0.326922i | \(0.106012\pi\) | |||||||
\(84\) | −11.7948 | −1.28691 | ||||||||
\(85\) | 3.59719 | 0.390170 | ||||||||
\(86\) | −20.1706 | −2.17505 | ||||||||
\(87\) | −3.35219 | −0.359393 | ||||||||
\(88\) | 1.85819 | 0.198084 | ||||||||
\(89\) | −2.46468 | −0.261256 | −0.130628 | − | 0.991431i | \(-0.541699\pi\) | ||||
−0.130628 | + | 0.991431i | \(0.541699\pi\) | |||||||
\(90\) | 0.392159 | 0.0413371 | ||||||||
\(91\) | 8.72603 | 0.914737 | ||||||||
\(92\) | 13.3865 | 1.39564 | ||||||||
\(93\) | −14.1463 | −1.46690 | ||||||||
\(94\) | −6.86276 | −0.707840 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 12.4579 | 1.27148 | ||||||||
\(97\) | 18.0240 | 1.83006 | 0.915029 | − | 0.403389i | \(-0.132168\pi\) | ||||
0.915029 | + | 0.403389i | \(0.132168\pi\) | |||||||
\(98\) | −20.8253 | −2.10368 | ||||||||
\(99\) | −0.599577 | −0.0602598 | ||||||||
\(100\) | 1.66872 | 0.166872 | ||||||||
\(101\) | 8.95602 | 0.891157 | 0.445579 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(102\) | −11.5195 | −1.14060 | ||||||||
\(103\) | −11.7838 | −1.16110 | −0.580548 | − | 0.814226i | \(-0.697162\pi\) | ||||
−0.580548 | + | 0.814226i | \(0.697162\pi\) | |||||||
\(104\) | −1.30970 | −0.128427 | ||||||||
\(105\) | −7.06814 | −0.689780 | ||||||||
\(106\) | −6.20976 | −0.603146 | ||||||||
\(107\) | −13.4561 | −1.30085 | −0.650426 | − | 0.759569i | \(-0.725410\pi\) | ||||
−0.650426 | + | 0.759569i | \(0.725410\pi\) | |||||||
\(108\) | −8.94104 | −0.860352 | ||||||||
\(109\) | 7.93487 | 0.760023 | 0.380012 | − | 0.924982i | \(-0.375920\pi\) | ||||
0.380012 | + | 0.924982i | \(0.375920\pi\) | |||||||
\(110\) | −5.60917 | −0.534813 | ||||||||
\(111\) | −3.67995 | −0.349285 | ||||||||
\(112\) | 19.2475 | 1.81872 | ||||||||
\(113\) | −8.25147 | −0.776233 | −0.388117 | − | 0.921610i | \(-0.626874\pi\) | ||||
−0.388117 | + | 0.921610i | \(0.626874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.02202 | 0.748058 | ||||||||
\(116\) | −3.34582 | −0.310651 | ||||||||
\(117\) | 0.422597 | 0.0390691 | ||||||||
\(118\) | 3.99653 | 0.367910 | ||||||||
\(119\) | −15.2075 | −1.39407 | ||||||||
\(120\) | 1.06087 | 0.0968433 | ||||||||
\(121\) | −2.42406 | −0.220369 | ||||||||
\(122\) | 9.45464 | 0.855983 | ||||||||
\(123\) | 16.3201 | 1.47154 | ||||||||
\(124\) | −14.1193 | −1.26796 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.65789 | −0.147697 | ||||||||
\(127\) | −2.06393 | −0.183144 | −0.0915721 | − | 0.995798i | \(-0.529189\pi\) | ||||
−0.0915721 | + | 0.995798i | \(0.529189\pi\) | |||||||
\(128\) | −5.00657 | −0.442523 | ||||||||
\(129\) | 17.6065 | 1.55017 | ||||||||
\(130\) | 3.95348 | 0.346744 | ||||||||
\(131\) | −0.968020 | −0.0845763 | −0.0422881 | − | 0.999105i | \(-0.513465\pi\) | ||||
−0.0422881 | + | 0.999105i | \(0.513465\pi\) | |||||||
\(132\) | 8.17026 | 0.711130 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.3537 | −1.67190 | ||||||||
\(135\) | −5.35802 | −0.461145 | ||||||||
\(136\) | 2.28251 | 0.195724 | ||||||||
\(137\) | 19.4256 | 1.65964 | 0.829819 | − | 0.558033i | \(-0.188444\pi\) | ||||
0.829819 | + | 0.558033i | \(0.188444\pi\) | |||||||
\(138\) | −25.6893 | −2.18682 | ||||||||
\(139\) | −10.2777 | −0.871746 | −0.435873 | − | 0.900008i | \(-0.643560\pi\) | ||||
−0.435873 | + | 0.900008i | \(0.643560\pi\) | |||||||
\(140\) | −7.05470 | −0.596231 | ||||||||
\(141\) | 5.99035 | 0.504479 | ||||||||
\(142\) | 5.46271 | 0.458420 | ||||||||
\(143\) | −6.04454 | −0.505470 | ||||||||
\(144\) | 0.932146 | 0.0776788 | ||||||||
\(145\) | −2.00502 | −0.166508 | ||||||||
\(146\) | −3.50172 | −0.289804 | ||||||||
\(147\) | 18.1780 | 1.49930 | ||||||||
\(148\) | −3.67295 | −0.301914 | ||||||||
\(149\) | 10.1694 | 0.833114 | 0.416557 | − | 0.909110i | \(-0.363237\pi\) | ||||
0.416557 | + | 0.909110i | \(0.363237\pi\) | |||||||
\(150\) | −3.20235 | −0.261471 | ||||||||
\(151\) | −2.79628 | −0.227558 | −0.113779 | − | 0.993506i | \(-0.536296\pi\) | ||||
−0.113779 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.736492 | −0.0595419 | ||||||||
\(154\) | 23.7133 | 1.91088 | ||||||||
\(155\) | −8.46117 | −0.679618 | ||||||||
\(156\) | −5.75861 | −0.461058 | ||||||||
\(157\) | −15.8271 | −1.26314 | −0.631569 | − | 0.775320i | \(-0.717589\pi\) | ||||
−0.631569 | + | 0.775320i | \(0.717589\pi\) | |||||||
\(158\) | −24.3505 | −1.93722 | ||||||||
\(159\) | 5.42037 | 0.429863 | ||||||||
\(160\) | 7.45136 | 0.589082 | ||||||||
\(161\) | −33.9139 | −2.67279 | ||||||||
\(162\) | 15.9818 | 1.25565 | ||||||||
\(163\) | 18.3145 | 1.43450 | 0.717251 | − | 0.696815i | \(-0.245400\pi\) | ||||
0.717251 | + | 0.696815i | \(0.245400\pi\) | |||||||
\(164\) | 16.2891 | 1.27196 | ||||||||
\(165\) | 4.89612 | 0.381162 | ||||||||
\(166\) | −32.9824 | −2.55993 | ||||||||
\(167\) | −5.46238 | −0.422692 | −0.211346 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211346 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(168\) | −4.48492 | −0.346019 | ||||||||
\(169\) | −8.73965 | −0.672281 | ||||||||
\(170\) | −6.89003 | −0.528441 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.5730 | 1.33993 | ||||||||
\(173\) | 7.69398 | 0.584962 | 0.292481 | − | 0.956271i | \(-0.405519\pi\) | ||||
0.292481 | + | 0.956271i | \(0.405519\pi\) | |||||||
\(174\) | 6.42076 | 0.486756 | ||||||||
\(175\) | −4.22760 | −0.319577 | ||||||||
\(176\) | −13.3328 | −1.00500 | ||||||||
\(177\) | −3.48848 | −0.262210 | ||||||||
\(178\) | 4.72082 | 0.353841 | ||||||||
\(179\) | 21.3618 | 1.59666 | 0.798328 | − | 0.602223i | \(-0.205718\pi\) | ||||
0.798328 | + | 0.602223i | \(0.205718\pi\) | |||||||
\(180\) | −0.341655 | −0.0254655 | ||||||||
\(181\) | 2.16604 | 0.161000 | 0.0805002 | − | 0.996755i | \(-0.474348\pi\) | ||||
0.0805002 | + | 0.996755i | \(0.474348\pi\) | |||||||
\(182\) | −16.7138 | −1.23891 | ||||||||
\(183\) | −8.25275 | −0.610061 | ||||||||
\(184\) | 5.09018 | 0.375253 | ||||||||
\(185\) | −2.20105 | −0.161825 | ||||||||
\(186\) | 27.0956 | 1.98675 | ||||||||
\(187\) | 10.5343 | 0.770343 | ||||||||
\(188\) | 5.97896 | 0.436060 | ||||||||
\(189\) | 22.6516 | 1.64766 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.80930 | 0.709776 | 0.354888 | − | 0.934909i | \(-0.384519\pi\) | ||||
0.354888 | + | 0.934909i | \(0.384519\pi\) | |||||||
\(192\) | −8.63813 | −0.623403 | ||||||||
\(193\) | 3.82213 | 0.275123 | 0.137561 | − | 0.990493i | \(-0.456074\pi\) | ||||
0.137561 | + | 0.990493i | \(0.456074\pi\) | |||||||
\(194\) | −34.5230 | −2.47860 | ||||||||
\(195\) | −3.45091 | −0.247125 | ||||||||
\(196\) | 18.1434 | 1.29596 | ||||||||
\(197\) | 10.7279 | 0.764329 | 0.382165 | − | 0.924094i | \(-0.375179\pi\) | ||||
0.382165 | + | 0.924094i | \(0.375179\pi\) | |||||||
\(198\) | 1.14842 | 0.0816150 | ||||||||
\(199\) | 23.6191 | 1.67432 | 0.837159 | − | 0.546960i | \(-0.184215\pi\) | ||||
0.837159 | + | 0.546960i | \(0.184215\pi\) | |||||||
\(200\) | 0.634526 | 0.0448678 | ||||||||
\(201\) | 16.8934 | 1.19157 | ||||||||
\(202\) | −17.1543 | −1.20697 | ||||||||
\(203\) | 8.47641 | 0.594928 | ||||||||
\(204\) | 10.0360 | 0.702658 | ||||||||
\(205\) | 9.76141 | 0.681766 | ||||||||
\(206\) | 22.5707 | 1.57257 | ||||||||
\(207\) | −1.64243 | −0.114157 | ||||||||
\(208\) | 9.39728 | 0.651584 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 13.5383 | 0.934229 | ||||||||
\(211\) | −14.6711 | −1.01000 | −0.505001 | − | 0.863119i | \(-0.668508\pi\) | ||||
−0.505001 | + | 0.863119i | \(0.668508\pi\) | |||||||
\(212\) | 5.41006 | 0.371564 | ||||||||
\(213\) | −4.76828 | −0.326717 | ||||||||
\(214\) | 25.7737 | 1.76186 | ||||||||
\(215\) | 10.5308 | 0.718195 | ||||||||
\(216\) | −3.39980 | −0.231327 | ||||||||
\(217\) | 35.7705 | 2.42826 | ||||||||
\(218\) | −15.1984 | −1.02936 | ||||||||
\(219\) | 3.05657 | 0.206544 | ||||||||
\(220\) | 4.88681 | 0.329468 | ||||||||
\(221\) | −7.42483 | −0.499448 | ||||||||
\(222\) | 7.04854 | 0.473067 | ||||||||
\(223\) | −3.94457 | −0.264148 | −0.132074 | − | 0.991240i | \(-0.542164\pi\) | ||||
−0.132074 | + | 0.991240i | \(0.542164\pi\) | |||||||
\(224\) | −31.5014 | −2.10478 | ||||||||
\(225\) | −0.204741 | −0.0136494 | ||||||||
\(226\) | 15.8048 | 1.05132 | ||||||||
\(227\) | 27.9711 | 1.85651 | 0.928254 | − | 0.371948i | \(-0.121310\pi\) | ||||
0.928254 | + | 0.371948i | \(0.121310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.40408 | −0.423193 | −0.211597 | − | 0.977357i | \(-0.567866\pi\) | ||||
−0.211597 | + | 0.977357i | \(0.567866\pi\) | |||||||
\(230\) | −15.3653 | −1.01316 | ||||||||
\(231\) | −20.6989 | −1.36188 | ||||||||
\(232\) | −1.27223 | −0.0835263 | ||||||||
\(233\) | 16.6633 | 1.09165 | 0.545824 | − | 0.837900i | \(-0.316217\pi\) | ||||
0.545824 | + | 0.837900i | \(0.316217\pi\) | |||||||
\(234\) | −0.809439 | −0.0529147 | ||||||||
\(235\) | 3.58295 | 0.233726 | ||||||||
\(236\) | −3.48184 | −0.226649 | ||||||||
\(237\) | 21.2550 | 1.38066 | ||||||||
\(238\) | 29.1283 | 1.88811 | ||||||||
\(239\) | −8.53879 | −0.552328 | −0.276164 | − | 0.961110i | \(-0.589063\pi\) | ||||
−0.276164 | + | 0.961110i | \(0.589063\pi\) | |||||||
\(240\) | −7.61186 | −0.491343 | ||||||||
\(241\) | −5.34514 | −0.344311 | −0.172155 | − | 0.985070i | \(-0.555073\pi\) | ||||
−0.172155 | + | 0.985070i | \(0.555073\pi\) | |||||||
\(242\) | 4.64302 | 0.298464 | ||||||||
\(243\) | 2.12392 | 0.136250 | ||||||||
\(244\) | −8.23705 | −0.527323 | ||||||||
\(245\) | 10.8726 | 0.694627 | ||||||||
\(246\) | −31.2594 | −1.99303 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.36883 | −0.340921 | ||||||||
\(249\) | 28.7896 | 1.82447 | ||||||||
\(250\) | −1.91539 | −0.121140 | ||||||||
\(251\) | −9.73324 | −0.614357 | −0.307178 | − | 0.951652i | \(-0.599385\pi\) | ||||
−0.307178 | + | 0.951652i | \(0.599385\pi\) | |||||||
\(252\) | 1.44438 | 0.0909876 | ||||||||
\(253\) | 23.4923 | 1.47695 | ||||||||
\(254\) | 3.95323 | 0.248048 | ||||||||
\(255\) | 6.01416 | 0.376621 | ||||||||
\(256\) | 19.9228 | 1.24518 | ||||||||
\(257\) | −6.34018 | −0.395490 | −0.197745 | − | 0.980254i | \(-0.563362\pi\) | ||||
−0.197745 | + | 0.980254i | \(0.563362\pi\) | |||||||
\(258\) | −33.7233 | −2.09952 | ||||||||
\(259\) | 9.30518 | 0.578196 | ||||||||
\(260\) | −3.44435 | −0.213609 | ||||||||
\(261\) | 0.410508 | 0.0254098 | ||||||||
\(262\) | 1.85414 | 0.114549 | ||||||||
\(263\) | 13.5339 | 0.834533 | 0.417267 | − | 0.908784i | \(-0.362988\pi\) | ||||
0.417267 | + | 0.908784i | \(0.362988\pi\) | |||||||
\(264\) | 3.10671 | 0.191205 | ||||||||
\(265\) | 3.24204 | 0.199157 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.12070 | −0.252183 | ||||||||
\(268\) | 16.8613 | 1.02997 | ||||||||
\(269\) | −13.5665 | −0.827164 | −0.413582 | − | 0.910467i | \(-0.635722\pi\) | ||||
−0.413582 | + | 0.910467i | \(0.635722\pi\) | |||||||
\(270\) | 10.2627 | 0.624568 | ||||||||
\(271\) | 1.81018 | 0.109960 | 0.0549802 | − | 0.998487i | \(-0.482490\pi\) | ||||
0.0549802 | + | 0.998487i | \(0.482490\pi\) | |||||||
\(272\) | −16.3773 | −0.993022 | ||||||||
\(273\) | 14.5891 | 0.882971 | ||||||||
\(274\) | −37.2075 | −2.24779 | ||||||||
\(275\) | 2.92847 | 0.176593 | ||||||||
\(276\) | 22.3810 | 1.34718 | ||||||||
\(277\) | −1.28308 | −0.0770929 | −0.0385465 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385465 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(278\) | 19.6859 | 1.18068 | ||||||||
\(279\) | 1.73235 | 0.103713 | ||||||||
\(280\) | −2.68252 | −0.160311 | ||||||||
\(281\) | −9.73693 | −0.580856 | −0.290428 | − | 0.956897i | \(-0.593798\pi\) | ||||
−0.290428 | + | 0.956897i | \(0.593798\pi\) | |||||||
\(282\) | −11.4739 | −0.683259 | ||||||||
\(283\) | 7.58068 | 0.450625 | 0.225312 | − | 0.974287i | \(-0.427660\pi\) | ||||
0.225312 | + | 0.974287i | \(0.427660\pi\) | |||||||
\(284\) | −4.75921 | −0.282407 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5777 | 0.684602 | ||||||||
\(287\) | −41.2674 | −2.43594 | ||||||||
\(288\) | −1.52560 | −0.0898967 | ||||||||
\(289\) | −4.06020 | −0.238835 | ||||||||
\(290\) | 3.84039 | 0.225515 | ||||||||
\(291\) | 30.1343 | 1.76651 | ||||||||
\(292\) | 3.05076 | 0.178532 | ||||||||
\(293\) | 1.18387 | 0.0691625 | 0.0345813 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345813 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(294\) | −34.8180 | −2.03062 | ||||||||
\(295\) | −2.08653 | −0.121483 | ||||||||
\(296\) | −1.39663 | −0.0811772 | ||||||||
\(297\) | −15.6908 | −0.910472 | ||||||||
\(298\) | −19.4785 | −1.12836 | ||||||||
\(299\) | −16.5579 | −0.957571 | ||||||||
\(300\) | 2.78994 | 0.161077 | ||||||||
\(301\) | −44.5201 | −2.56610 | ||||||||
\(302\) | 5.35597 | 0.308201 | ||||||||
\(303\) | 14.9736 | 0.860211 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.93614 | −0.282643 | ||||||||
\(306\) | 1.41067 | 0.0806426 | ||||||||
\(307\) | 13.4937 | 0.770126 | 0.385063 | − | 0.922890i | \(-0.374180\pi\) | ||||
0.385063 | + | 0.922890i | \(0.374180\pi\) | |||||||
\(308\) | −20.6595 | −1.17718 | ||||||||
\(309\) | −19.7014 | −1.12078 | ||||||||
\(310\) | 16.2065 | 0.920465 | ||||||||
\(311\) | 14.2694 | 0.809143 | 0.404571 | − | 0.914506i | \(-0.367421\pi\) | ||||
0.404571 | + | 0.914506i | \(0.367421\pi\) | |||||||
\(312\) | −2.18969 | −0.123967 | ||||||||
\(313\) | −28.9109 | −1.63414 | −0.817071 | − | 0.576537i | \(-0.804404\pi\) | ||||
−0.817071 | + | 0.576537i | \(0.804404\pi\) | |||||||
\(314\) | 30.3150 | 1.71078 | ||||||||
\(315\) | 0.865563 | 0.0487689 | ||||||||
\(316\) | 21.2146 | 1.19341 | ||||||||
\(317\) | −14.9871 | −0.841758 | −0.420879 | − | 0.907117i | \(-0.638278\pi\) | ||||
−0.420879 | + | 0.907117i | \(0.638278\pi\) | |||||||
\(318\) | −10.3821 | −0.582201 | ||||||||
\(319\) | −5.87163 | −0.328748 | ||||||||
\(320\) | −5.16665 | −0.288824 | ||||||||
\(321\) | −22.4973 | −1.25568 | ||||||||
\(322\) | 64.9584 | 3.61999 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −13.9236 | −0.773533 | ||||||||
\(325\) | −2.06406 | −0.114494 | ||||||||
\(326\) | −35.0794 | −1.94287 | ||||||||
\(327\) | 13.2663 | 0.733630 | ||||||||
\(328\) | 6.19386 | 0.341999 | ||||||||
\(329\) | −15.1473 | −0.835098 | ||||||||
\(330\) | −9.37798 | −0.516241 | ||||||||
\(331\) | 15.2205 | 0.836594 | 0.418297 | − | 0.908310i | \(-0.362627\pi\) | ||||
0.418297 | + | 0.908310i | \(0.362627\pi\) | |||||||
\(332\) | 28.7348 | 1.57703 | ||||||||
\(333\) | 0.450645 | 0.0246952 | ||||||||
\(334\) | 10.4626 | 0.572488 | ||||||||
\(335\) | 10.1043 | 0.552056 | ||||||||
\(336\) | 32.1799 | 1.75556 | ||||||||
\(337\) | 6.15921 | 0.335513 | 0.167757 | − | 0.985828i | \(-0.446348\pi\) | ||||
0.167757 | + | 0.985828i | \(0.446348\pi\) | |||||||
\(338\) | 16.7398 | 0.910528 | ||||||||
\(339\) | −13.7957 | −0.749277 | ||||||||
\(340\) | 6.00272 | 0.325543 | ||||||||
\(341\) | −24.7783 | −1.34182 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3720 | −0.884003 | ||||||||
\(344\) | 6.68207 | 0.360273 | ||||||||
\(345\) | 13.4120 | 0.722080 | ||||||||
\(346\) | −14.7370 | −0.792265 | ||||||||
\(347\) | 8.18354 | 0.439315 | 0.219658 | − | 0.975577i | \(-0.429506\pi\) | ||||
0.219658 | + | 0.975577i | \(0.429506\pi\) | |||||||
\(348\) | −5.59388 | −0.299863 | ||||||||
\(349\) | −10.7999 | −0.578104 | −0.289052 | − | 0.957313i | \(-0.593340\pi\) | ||||
−0.289052 | + | 0.957313i | \(0.593340\pi\) | |||||||
\(350\) | 8.09751 | 0.432830 | ||||||||
\(351\) | 11.0593 | 0.590300 | ||||||||
\(352\) | 21.8211 | 1.16307 | ||||||||
\(353\) | −8.84321 | −0.470677 | −0.235338 | − | 0.971914i | \(-0.575620\pi\) | ||||
−0.235338 | + | 0.971914i | \(0.575620\pi\) | |||||||
\(354\) | 6.68180 | 0.355134 | ||||||||
\(355\) | −2.85201 | −0.151369 | ||||||||
\(356\) | −4.11287 | −0.217981 | ||||||||
\(357\) | −25.4255 | −1.34566 | ||||||||
\(358\) | −40.9162 | −2.16249 | ||||||||
\(359\) | −3.39178 | −0.179011 | −0.0895055 | − | 0.995986i | \(-0.528529\pi\) | ||||
−0.0895055 | + | 0.995986i | \(0.528529\pi\) | |||||||
\(360\) | −0.129913 | −0.00684703 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −4.14881 | −0.218057 | ||||||||
\(363\) | −4.05279 | −0.212716 | ||||||||
\(364\) | 14.5613 | 0.763221 | ||||||||
\(365\) | 1.82820 | 0.0956923 | ||||||||
\(366\) | 15.8072 | 0.826258 | ||||||||
\(367\) | −12.2285 | −0.638323 | −0.319161 | − | 0.947700i | \(-0.603401\pi\) | ||||
−0.319161 | + | 0.947700i | \(0.603401\pi\) | |||||||
\(368\) | −36.5227 | −1.90388 | ||||||||
\(369\) | −1.99856 | −0.104041 | ||||||||
\(370\) | 4.21588 | 0.219173 | ||||||||
\(371\) | −13.7060 | −0.711582 | ||||||||
\(372\) | −23.6062 | −1.22392 | ||||||||
\(373\) | 13.7436 | 0.711619 | 0.355810 | − | 0.934558i | \(-0.384205\pi\) | ||||
0.355810 | + | 0.934558i | \(0.384205\pi\) | |||||||
\(374\) | −20.1773 | −1.04334 | ||||||||
\(375\) | 1.67190 | 0.0863367 | ||||||||
\(376\) | 2.27348 | 0.117246 | ||||||||
\(377\) | 4.13848 | 0.213142 | ||||||||
\(378\) | −43.3866 | −2.23157 | ||||||||
\(379\) | −22.5080 | −1.15616 | −0.578080 | − | 0.815980i | \(-0.696198\pi\) | ||||
−0.578080 | + | 0.815980i | \(0.696198\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.45069 | −0.176784 | ||||||||
\(382\) | −18.7886 | −0.961311 | ||||||||
\(383\) | 30.7611 | 1.57182 | 0.785909 | − | 0.618342i | \(-0.212195\pi\) | ||||
0.785909 | + | 0.618342i | \(0.212195\pi\) | |||||||
\(384\) | −8.37050 | −0.427155 | ||||||||
\(385\) | −12.3804 | −0.630964 | ||||||||
\(386\) | −7.32087 | −0.372622 | ||||||||
\(387\) | −2.15609 | −0.109600 | ||||||||
\(388\) | 30.0770 | 1.52693 | ||||||||
\(389\) | −21.0616 | −1.06786 | −0.533932 | − | 0.845528i | \(-0.679286\pi\) | ||||
−0.533932 | + | 0.845528i | \(0.679286\pi\) | |||||||
\(390\) | 6.60984 | 0.334702 | ||||||||
\(391\) | 28.8568 | 1.45935 | ||||||||
\(392\) | 6.89897 | 0.348450 | ||||||||
\(393\) | −1.61844 | −0.0816393 | ||||||||
\(394\) | −20.5481 | −1.03520 | ||||||||
\(395\) | 12.7131 | 0.639665 | ||||||||
\(396\) | −1.00053 | −0.0502784 | ||||||||
\(397\) | −22.0757 | −1.10795 | −0.553974 | − | 0.832534i | \(-0.686889\pi\) | ||||
−0.553974 | + | 0.832534i | \(0.686889\pi\) | |||||||
\(398\) | −45.2399 | −2.26767 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.55281 | −0.227641 | ||||||||
\(401\) | −28.7899 | −1.43770 | −0.718850 | − | 0.695165i | \(-0.755331\pi\) | ||||
−0.718850 | + | 0.695165i | \(0.755331\pi\) | |||||||
\(402\) | −32.3575 | −1.61384 | ||||||||
\(403\) | 17.4644 | 0.869963 | ||||||||
\(404\) | 14.9451 | 0.743547 | ||||||||
\(405\) | −8.34386 | −0.414610 | ||||||||
\(406\) | −16.2356 | −0.805761 | ||||||||
\(407\) | −6.44572 | −0.319503 | ||||||||
\(408\) | 3.81614 | 0.188927 | ||||||||
\(409\) | −18.3912 | −0.909385 | −0.454693 | − | 0.890648i | \(-0.650251\pi\) | ||||
−0.454693 | + | 0.890648i | \(0.650251\pi\) | |||||||
\(410\) | −18.6969 | −0.923375 | ||||||||
\(411\) | 32.4776 | 1.60200 | ||||||||
\(412\) | −19.6640 | −0.968774 | ||||||||
\(413\) | 8.82104 | 0.434055 | ||||||||
\(414\) | 3.14590 | 0.154613 | ||||||||
\(415\) | 17.2197 | 0.845279 | ||||||||
\(416\) | −15.3801 | −0.754070 | ||||||||
\(417\) | −17.1834 | −0.841473 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.2339 | −1.08619 | −0.543097 | − | 0.839670i | \(-0.682749\pi\) | ||||
−0.543097 | + | 0.839670i | \(0.682749\pi\) | |||||||
\(420\) | −11.7948 | −0.575526 | ||||||||
\(421\) | 26.7601 | 1.30421 | 0.652103 | − | 0.758130i | \(-0.273887\pi\) | ||||
0.652103 | + | 0.758130i | \(0.273887\pi\) | |||||||
\(422\) | 28.1009 | 1.36793 | ||||||||
\(423\) | −0.733577 | −0.0356677 | ||||||||
\(424\) | 2.05715 | 0.0999043 | ||||||||
\(425\) | 3.59719 | 0.174490 | ||||||||
\(426\) | 9.13311 | 0.442501 | ||||||||
\(427\) | 20.8681 | 1.00988 | ||||||||
\(428\) | −22.4545 | −1.08538 | ||||||||
\(429\) | −10.1059 | −0.487917 | ||||||||
\(430\) | −20.1706 | −0.972714 | ||||||||
\(431\) | −3.80319 | −0.183193 | −0.0915966 | − | 0.995796i | \(-0.529197\pi\) | ||||
−0.0915966 | + | 0.995796i | \(0.529197\pi\) | |||||||
\(432\) | 24.3940 | 1.17366 | ||||||||
\(433\) | −31.2833 | −1.50338 | −0.751691 | − | 0.659516i | \(-0.770761\pi\) | ||||
−0.751691 | + | 0.659516i | \(0.770761\pi\) | |||||||
\(434\) | −68.5145 | −3.28880 | ||||||||
\(435\) | −3.35219 | −0.160725 | ||||||||
\(436\) | 13.2411 | 0.634134 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.85453 | −0.279740 | ||||||||
\(439\) | 4.16432 | 0.198752 | 0.0993760 | − | 0.995050i | \(-0.468315\pi\) | ||||
0.0993760 | + | 0.995050i | \(0.468315\pi\) | |||||||
\(440\) | 1.85819 | 0.0885858 | ||||||||
\(441\) | −2.22607 | −0.106003 | ||||||||
\(442\) | 14.2214 | 0.676445 | ||||||||
\(443\) | −6.61530 | −0.314302 | −0.157151 | − | 0.987575i | \(-0.550231\pi\) | ||||
−0.157151 | + | 0.987575i | \(0.550231\pi\) | |||||||
\(444\) | −6.14081 | −0.291430 | ||||||||
\(445\) | −2.46468 | −0.116837 | ||||||||
\(446\) | 7.55539 | 0.357758 | ||||||||
\(447\) | 17.0023 | 0.804183 | ||||||||
\(448\) | 21.8425 | 1.03196 | ||||||||
\(449\) | −5.49993 | −0.259558 | −0.129779 | − | 0.991543i | \(-0.541427\pi\) | ||||
−0.129779 | + | 0.991543i | \(0.541427\pi\) | |||||||
\(450\) | 0.392159 | 0.0184865 | ||||||||
\(451\) | 28.5860 | 1.34606 | ||||||||
\(452\) | −13.7694 | −0.647659 | ||||||||
\(453\) | −4.67511 | −0.219656 | ||||||||
\(454\) | −53.5756 | −2.51443 | ||||||||
\(455\) | 8.72603 | 0.409083 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2315 | 1.64806 | 0.824029 | − | 0.566547i | \(-0.191721\pi\) | ||||
0.824029 | + | 0.566547i | \(0.191721\pi\) | |||||||
\(458\) | 12.2663 | 0.573167 | ||||||||
\(459\) | −19.2738 | −0.899625 | ||||||||
\(460\) | 13.3865 | 0.624150 | ||||||||
\(461\) | 5.62840 | 0.262141 | 0.131070 | − | 0.991373i | \(-0.458159\pi\) | ||||
0.131070 | + | 0.991373i | \(0.458159\pi\) | |||||||
\(462\) | 39.6464 | 1.84452 | ||||||||
\(463\) | −20.6970 | −0.961869 | −0.480935 | − | 0.876756i | \(-0.659703\pi\) | ||||
−0.480935 | + | 0.876756i | \(0.659703\pi\) | |||||||
\(464\) | 9.12846 | 0.423778 | ||||||||
\(465\) | −14.1463 | −0.656017 | ||||||||
\(466\) | −31.9167 | −1.47851 | ||||||||
\(467\) | −18.4881 | −0.855527 | −0.427764 | − | 0.903891i | \(-0.640698\pi\) | ||||
−0.427764 | + | 0.903891i | \(0.640698\pi\) | |||||||
\(468\) | 0.705198 | 0.0325978 | ||||||||
\(469\) | −42.7169 | −1.97249 | ||||||||
\(470\) | −6.86276 | −0.316555 | ||||||||
\(471\) | −26.4613 | −1.21927 | ||||||||
\(472\) | −1.32396 | −0.0609402 | ||||||||
\(473\) | 30.8392 | 1.41799 | ||||||||
\(474\) | −40.7117 | −1.86995 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.3771 | −1.16316 | ||||||||
\(477\) | −0.663777 | −0.0303922 | ||||||||
\(478\) | 16.3551 | 0.748066 | ||||||||
\(479\) | −32.0991 | −1.46664 | −0.733322 | − | 0.679881i | \(-0.762031\pi\) | ||||
−0.733322 | + | 0.679881i | \(0.762031\pi\) | |||||||
\(480\) | 12.4579 | 0.568625 | ||||||||
\(481\) | 4.54311 | 0.207148 | ||||||||
\(482\) | 10.2380 | 0.466329 | ||||||||
\(483\) | −56.7008 | −2.57998 | ||||||||
\(484\) | −4.04508 | −0.183867 | ||||||||
\(485\) | 18.0240 | 0.818426 | ||||||||
\(486\) | −4.06814 | −0.184535 | ||||||||
\(487\) | 3.54350 | 0.160571 | 0.0802856 | − | 0.996772i | \(-0.474417\pi\) | ||||
0.0802856 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(488\) | −3.13211 | −0.141784 | ||||||||
\(489\) | 30.6201 | 1.38469 | ||||||||
\(490\) | −20.8253 | −0.940793 | ||||||||
\(491\) | −19.7922 | −0.893207 | −0.446604 | − | 0.894732i | \(-0.647367\pi\) | ||||
−0.446604 | + | 0.894732i | \(0.647367\pi\) | |||||||
\(492\) | 27.2338 | 1.22779 | ||||||||
\(493\) | −7.21243 | −0.324832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.599577 | −0.0269490 | ||||||||
\(496\) | 38.5221 | 1.72969 | ||||||||
\(497\) | 12.0571 | 0.540837 | ||||||||
\(498\) | −55.1433 | −2.47103 | ||||||||
\(499\) | −29.4530 | −1.31850 | −0.659249 | − | 0.751925i | \(-0.729126\pi\) | ||||
−0.659249 | + | 0.751925i | \(0.729126\pi\) | |||||||
\(500\) | 1.66872 | 0.0746275 | ||||||||
\(501\) | −9.13257 | −0.408013 | ||||||||
\(502\) | 18.6430 | 0.832076 | ||||||||
\(503\) | 2.94849 | 0.131467 | 0.0657333 | − | 0.997837i | \(-0.479061\pi\) | ||||
0.0657333 | + | 0.997837i | \(0.479061\pi\) | |||||||
\(504\) | 0.549222 | 0.0244643 | ||||||||
\(505\) | 8.95602 | 0.398538 | ||||||||
\(506\) | −44.9969 | −2.00035 | ||||||||
\(507\) | −14.6118 | −0.648935 | ||||||||
\(508\) | −3.44413 | −0.152808 | ||||||||
\(509\) | 1.57700 | 0.0698995 | 0.0349497 | − | 0.999389i | \(-0.488873\pi\) | ||||
0.0349497 | + | 0.999389i | \(0.488873\pi\) | |||||||
\(510\) | −11.5195 | −0.510090 | ||||||||
\(511\) | −7.72890 | −0.341907 | ||||||||
\(512\) | −28.1469 | −1.24393 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.1439 | 0.535646 | ||||||||
\(515\) | −11.7838 | −0.519258 | ||||||||
\(516\) | 29.3803 | 1.29340 | ||||||||
\(517\) | 10.4926 | 0.461463 | ||||||||
\(518\) | −17.8231 | −0.783100 | ||||||||
\(519\) | 12.8636 | 0.564649 | ||||||||
\(520\) | −1.30970 | −0.0574342 | ||||||||
\(521\) | 0.569552 | 0.0249525 | 0.0124763 | − | 0.999922i | \(-0.496029\pi\) | ||||
0.0124763 | + | 0.999922i | \(0.496029\pi\) | |||||||
\(522\) | −0.786284 | −0.0344147 | ||||||||
\(523\) | 22.8370 | 0.998593 | 0.499296 | − | 0.866431i | \(-0.333592\pi\) | ||||
0.499296 | + | 0.866431i | \(0.333592\pi\) | |||||||
\(524\) | −1.61536 | −0.0705672 | ||||||||
\(525\) | −7.06814 | −0.308479 | ||||||||
\(526\) | −25.9226 | −1.13028 | ||||||||
\(527\) | −30.4365 | −1.32583 | ||||||||
\(528\) | −22.2911 | −0.970096 | ||||||||
\(529\) | 41.3529 | 1.79795 | ||||||||
\(530\) | −6.20976 | −0.269735 | ||||||||
\(531\) | 0.427198 | 0.0185388 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.1481 | −0.872713 | ||||||||
\(534\) | 7.89276 | 0.341553 | ||||||||
\(535\) | −13.4561 | −0.581759 | ||||||||
\(536\) | 6.41143 | 0.276932 | ||||||||
\(537\) | 35.7149 | 1.54121 | ||||||||
\(538\) | 25.9851 | 1.12030 | ||||||||
\(539\) | 31.8402 | 1.37145 | ||||||||
\(540\) | −8.94104 | −0.384761 | ||||||||
\(541\) | −14.2449 | −0.612434 | −0.306217 | − | 0.951962i | \(-0.599063\pi\) | ||||
−0.306217 | + | 0.951962i | \(0.599063\pi\) | |||||||
\(542\) | −3.46720 | −0.148929 | ||||||||
\(543\) | 3.62141 | 0.155409 | ||||||||
\(544\) | 26.8040 | 1.14921 | ||||||||
\(545\) | 7.93487 | 0.339893 | ||||||||
\(546\) | −27.9438 | −1.19588 | ||||||||
\(547\) | 2.72363 | 0.116454 | 0.0582270 | − | 0.998303i | \(-0.481455\pi\) | ||||
0.0582270 | + | 0.998303i | \(0.481455\pi\) | |||||||
\(548\) | 32.4159 | 1.38474 | ||||||||
\(549\) | 1.01063 | 0.0431326 | ||||||||
\(550\) | −5.60917 | −0.239176 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.51029 | 0.362222 | ||||||||
\(553\) | −53.7459 | −2.28551 | ||||||||
\(554\) | 2.45760 | 0.104414 | ||||||||
\(555\) | −3.67995 | −0.156205 | ||||||||
\(556\) | −17.1507 | −0.727351 | ||||||||
\(557\) | 27.7979 | 1.17784 | 0.588918 | − | 0.808193i | \(-0.299554\pi\) | ||||
0.588918 | + | 0.808193i | \(0.299554\pi\) | |||||||
\(558\) | −3.31812 | −0.140467 | ||||||||
\(559\) | −21.7362 | −0.919345 | ||||||||
\(560\) | 19.2475 | 0.813354 | ||||||||
\(561\) | 17.6123 | 0.743591 | ||||||||
\(562\) | 18.6500 | 0.786704 | ||||||||
\(563\) | −7.95268 | −0.335165 | −0.167583 | − | 0.985858i | \(-0.553596\pi\) | ||||
−0.167583 | + | 0.985858i | \(0.553596\pi\) | |||||||
\(564\) | 9.99624 | 0.420917 | ||||||||
\(565\) | −8.25147 | −0.347142 | ||||||||
\(566\) | −14.5200 | −0.610320 | ||||||||
\(567\) | 35.2745 | 1.48139 | ||||||||
\(568\) | −1.80967 | −0.0759321 | ||||||||
\(569\) | −6.92573 | −0.290342 | −0.145171 | − | 0.989407i | \(-0.546373\pi\) | ||||
−0.145171 | + | 0.989407i | \(0.546373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.9111 | 0.665857 | 0.332929 | − | 0.942952i | \(-0.391963\pi\) | ||||
0.332929 | + | 0.942952i | \(0.391963\pi\) | |||||||
\(572\) | −10.0867 | −0.421745 | ||||||||
\(573\) | 16.4002 | 0.685128 | ||||||||
\(574\) | 79.0431 | 3.29920 | ||||||||
\(575\) | 8.02202 | 0.334541 | ||||||||
\(576\) | 1.05782 | 0.0440760 | ||||||||
\(577\) | −29.5901 | −1.23185 | −0.615925 | − | 0.787805i | \(-0.711218\pi\) | ||||
−0.615925 | + | 0.787805i | \(0.711218\pi\) | |||||||
\(578\) | 7.77687 | 0.323475 | ||||||||
\(579\) | 6.39023 | 0.265569 | ||||||||
\(580\) | −3.34582 | −0.138927 | ||||||||
\(581\) | −72.7979 | −3.02016 | ||||||||
\(582\) | −57.7190 | −2.39253 | ||||||||
\(583\) | 9.49421 | 0.393210 | ||||||||
\(584\) | 1.16004 | 0.0480028 | ||||||||
\(585\) | 0.422597 | 0.0174723 | ||||||||
\(586\) | −2.26758 | −0.0936727 | ||||||||
\(587\) | −9.03206 | −0.372793 | −0.186397 | − | 0.982475i | \(-0.559681\pi\) | ||||
−0.186397 | + | 0.982475i | \(0.559681\pi\) | |||||||
\(588\) | 30.3340 | 1.25095 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.99653 | 0.164534 | ||||||||
\(591\) | 17.9360 | 0.737787 | ||||||||
\(592\) | 10.0210 | 0.411860 | ||||||||
\(593\) | 22.6342 | 0.929474 | 0.464737 | − | 0.885449i | \(-0.346149\pi\) | ||||
0.464737 | + | 0.885449i | \(0.346149\pi\) | |||||||
\(594\) | 30.0540 | 1.23313 | ||||||||
\(595\) | −15.2075 | −0.623447 | ||||||||
\(596\) | 16.9700 | 0.695118 | ||||||||
\(597\) | 39.4889 | 1.61617 | ||||||||
\(598\) | 31.7149 | 1.29692 | ||||||||
\(599\) | 5.73330 | 0.234256 | 0.117128 | − | 0.993117i | \(-0.462631\pi\) | ||||
0.117128 | + | 0.993117i | \(0.462631\pi\) | |||||||
\(600\) | 1.06087 | 0.0433097 | ||||||||
\(601\) | 2.62512 | 0.107081 | 0.0535404 | − | 0.998566i | \(-0.482949\pi\) | ||||
0.0535404 | + | 0.998566i | \(0.482949\pi\) | |||||||
\(602\) | 85.2734 | 3.47548 | ||||||||
\(603\) | −2.06876 | −0.0842464 | ||||||||
\(604\) | −4.66622 | −0.189866 | ||||||||
\(605\) | −2.42406 | −0.0985519 | ||||||||
\(606\) | −28.6803 | −1.16506 | ||||||||
\(607\) | −26.1933 | −1.06315 | −0.531577 | − | 0.847010i | \(-0.678401\pi\) | ||||
−0.531577 | + | 0.847010i | \(0.678401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.1717 | 0.574268 | ||||||||
\(610\) | 9.45464 | 0.382807 | ||||||||
\(611\) | −7.39544 | −0.299187 | ||||||||
\(612\) | −1.22900 | −0.0496794 | ||||||||
\(613\) | −22.4575 | −0.907048 | −0.453524 | − | 0.891244i | \(-0.649833\pi\) | ||||
−0.453524 | + | 0.891244i | \(0.649833\pi\) | |||||||
\(614\) | −25.8457 | −1.04305 | ||||||||
\(615\) | 16.3201 | 0.658091 | ||||||||
\(616\) | −7.85569 | −0.316515 | ||||||||
\(617\) | 2.85697 | 0.115017 | 0.0575086 | − | 0.998345i | \(-0.481684\pi\) | ||||
0.0575086 | + | 0.998345i | \(0.481684\pi\) | |||||||
\(618\) | 37.7360 | 1.51796 | ||||||||
\(619\) | 9.16843 | 0.368510 | 0.184255 | − | 0.982878i | \(-0.441013\pi\) | ||||
0.184255 | + | 0.982878i | \(0.441013\pi\) | |||||||
\(620\) | −14.1193 | −0.567047 | ||||||||
\(621\) | −42.9821 | −1.72481 | ||||||||
\(622\) | −27.3315 | −1.09589 | ||||||||
\(623\) | 10.4197 | 0.417456 | ||||||||
\(624\) | 15.7113 | 0.628957 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 55.3757 | 2.21326 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.4110 | −1.05391 | ||||||||
\(629\) | −7.91761 | −0.315696 | ||||||||
\(630\) | −1.65789 | −0.0660520 | ||||||||
\(631\) | 15.8291 | 0.630148 | 0.315074 | − | 0.949067i | \(-0.397971\pi\) | ||||
0.315074 | + | 0.949067i | \(0.397971\pi\) | |||||||
\(632\) | 8.06678 | 0.320879 | ||||||||
\(633\) | −24.5287 | −0.974927 | ||||||||
\(634\) | 28.7061 | 1.14007 | ||||||||
\(635\) | −2.06393 | −0.0819046 | ||||||||
\(636\) | 9.04509 | 0.358661 | ||||||||
\(637\) | −22.4418 | −0.889176 | ||||||||
\(638\) | 11.2465 | 0.445252 | ||||||||
\(639\) | 0.583922 | 0.0230996 | ||||||||
\(640\) | −5.00657 | −0.197902 | ||||||||
\(641\) | 26.7996 | 1.05852 | 0.529260 | − | 0.848460i | \(-0.322470\pi\) | ||||
0.529260 | + | 0.848460i | \(0.322470\pi\) | |||||||
\(642\) | 43.0912 | 1.70067 | ||||||||
\(643\) | 9.64700 | 0.380440 | 0.190220 | − | 0.981741i | \(-0.439080\pi\) | ||||
0.190220 | + | 0.981741i | \(0.439080\pi\) | |||||||
\(644\) | −56.5929 | −2.23007 | ||||||||
\(645\) | 17.6065 | 0.693255 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.93652 | −0.312017 | −0.156008 | − | 0.987756i | \(-0.549863\pi\) | ||||
−0.156008 | + | 0.987756i | \(0.549863\pi\) | |||||||
\(648\) | −5.29439 | −0.207983 | ||||||||
\(649\) | −6.11035 | −0.239852 | ||||||||
\(650\) | 3.95348 | 0.155068 | ||||||||
\(651\) | 59.8048 | 2.34393 | ||||||||
\(652\) | 30.5618 | 1.19689 | ||||||||
\(653\) | −12.3813 | −0.484517 | −0.242258 | − | 0.970212i | \(-0.577888\pi\) | ||||
−0.242258 | + | 0.970212i | \(0.577888\pi\) | |||||||
\(654\) | −25.4102 | −0.993618 | ||||||||
\(655\) | −0.968020 | −0.0378237 | ||||||||
\(656\) | −44.4418 | −1.73516 | ||||||||
\(657\) | −0.374307 | −0.0146031 | ||||||||
\(658\) | 29.0130 | 1.13105 | ||||||||
\(659\) | −20.5666 | −0.801162 | −0.400581 | − | 0.916261i | \(-0.631192\pi\) | ||||
−0.400581 | + | 0.916261i | \(0.631192\pi\) | |||||||
\(660\) | 8.17026 | 0.318027 | ||||||||
\(661\) | −14.8343 | −0.576989 | −0.288495 | − | 0.957482i | \(-0.593155\pi\) | ||||
−0.288495 | + | 0.957482i | \(0.593155\pi\) | |||||||
\(662\) | −29.1532 | −1.13307 | ||||||||
\(663\) | −12.4136 | −0.482104 | ||||||||
\(664\) | 10.9263 | 0.424023 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.863162 | −0.0334468 | ||||||||
\(667\) | −16.0843 | −0.622786 | ||||||||
\(668\) | −9.11520 | −0.352678 | ||||||||
\(669\) | −6.59494 | −0.254975 | ||||||||
\(670\) | −19.3537 | −0.747697 | ||||||||
\(671\) | −14.4554 | −0.558043 | ||||||||
\(672\) | −52.6673 | −2.03168 | ||||||||
\(673\) | −21.7573 | −0.838683 | −0.419342 | − | 0.907828i | \(-0.637739\pi\) | ||||
−0.419342 | + | 0.907828i | \(0.637739\pi\) | |||||||
\(674\) | −11.7973 | −0.454415 | ||||||||
\(675\) | −5.35802 | −0.206230 | ||||||||
\(676\) | −14.5841 | −0.560925 | ||||||||
\(677\) | 10.5635 | 0.405989 | 0.202995 | − | 0.979180i | \(-0.434933\pi\) | ||||
0.202995 | + | 0.979180i | \(0.434933\pi\) | |||||||
\(678\) | 26.4241 | 1.01481 | ||||||||
\(679\) | −76.1982 | −2.92422 | ||||||||
\(680\) | 2.28251 | 0.0875304 | ||||||||
\(681\) | 46.7650 | 1.79204 | ||||||||
\(682\) | 47.4601 | 1.81734 | ||||||||
\(683\) | −35.8085 | −1.37018 | −0.685088 | − | 0.728461i | \(-0.740236\pi\) | ||||
−0.685088 | + | 0.728461i | \(0.740236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.4256 | 0.742212 | ||||||||
\(686\) | 31.3587 | 1.19728 | ||||||||
\(687\) | −10.7070 | −0.408498 | ||||||||
\(688\) | −47.9448 | −1.82788 | ||||||||
\(689\) | −6.69176 | −0.254936 | ||||||||
\(690\) | −25.6893 | −0.977975 | ||||||||
\(691\) | 20.4006 | 0.776075 | 0.388038 | − | 0.921644i | \(-0.373153\pi\) | ||||
0.388038 | + | 0.921644i | \(0.373153\pi\) | |||||||
\(692\) | 12.8391 | 0.488070 | ||||||||
\(693\) | 2.53478 | 0.0962882 | ||||||||
\(694\) | −15.6747 | −0.595002 | ||||||||
\(695\) | −10.2777 | −0.389857 | ||||||||
\(696\) | −2.12705 | −0.0806257 | ||||||||
\(697\) | 35.1137 | 1.33003 | ||||||||
\(698\) | 20.6860 | 0.782976 | ||||||||
\(699\) | 27.8594 | 1.05374 | ||||||||
\(700\) | −7.05470 | −0.266643 | ||||||||
\(701\) | 47.5390 | 1.79552 | 0.897761 | − | 0.440483i | \(-0.145193\pi\) | ||||
0.897761 | + | 0.440483i | \(0.145193\pi\) | |||||||
\(702\) | −21.1828 | −0.799494 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −15.1304 | −0.570248 | ||||||||
\(705\) | 5.99035 | 0.225610 | ||||||||
\(706\) | 16.9382 | 0.637478 | ||||||||
\(707\) | −37.8625 | −1.42397 | ||||||||
\(708\) | −5.82131 | −0.218778 | ||||||||
\(709\) | 26.0530 | 0.978440 | 0.489220 | − | 0.872160i | \(-0.337282\pi\) | ||||
0.489220 | + | 0.872160i | \(0.337282\pi\) | |||||||
\(710\) | 5.46271 | 0.205012 | ||||||||
\(711\) | −2.60289 | −0.0976158 | ||||||||
\(712\) | −1.56390 | −0.0586097 | ||||||||
\(713\) | −67.8757 | −2.54197 | ||||||||
\(714\) | 48.6997 | 1.82254 | ||||||||
\(715\) | −6.04454 | −0.226053 | ||||||||
\(716\) | 35.6469 | 1.33219 | ||||||||
\(717\) | −14.2760 | −0.533148 | ||||||||
\(718\) | 6.49658 | 0.242450 | ||||||||
\(719\) | 9.90811 | 0.369510 | 0.184755 | − | 0.982785i | \(-0.440851\pi\) | ||||
0.184755 | + | 0.982785i | \(0.440851\pi\) | |||||||
\(720\) | 0.932146 | 0.0347390 | ||||||||
\(721\) | 49.8174 | 1.85530 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.93655 | −0.332354 | ||||||||
\(724\) | 3.61452 | 0.134333 | ||||||||
\(725\) | −2.00502 | −0.0744644 | ||||||||
\(726\) | 7.76267 | 0.288100 | ||||||||
\(727\) | −19.2073 | −0.712358 | −0.356179 | − | 0.934418i | \(-0.615921\pi\) | ||||
−0.356179 | + | 0.934418i | \(0.615921\pi\) | |||||||
\(728\) | 5.53689 | 0.205211 | ||||||||
\(729\) | 28.5826 | 1.05861 | ||||||||
\(730\) | −3.50172 | −0.129604 | ||||||||
\(731\) | 37.8814 | 1.40109 | ||||||||
\(732\) | −13.7716 | −0.509011 | ||||||||
\(733\) | 20.2835 | 0.749189 | 0.374595 | − | 0.927189i | \(-0.377782\pi\) | ||||
0.374595 | + | 0.927189i | \(0.377782\pi\) | |||||||
\(734\) | 23.4224 | 0.864535 | ||||||||
\(735\) | 18.1780 | 0.670505 | ||||||||
\(736\) | 59.7750 | 2.20334 | ||||||||
\(737\) | 29.5901 | 1.08997 | ||||||||
\(738\) | 3.82802 | 0.140911 | ||||||||
\(739\) | 52.0382 | 1.91425 | 0.957127 | − | 0.289668i | \(-0.0935449\pi\) | ||||
0.957127 | + | 0.289668i | \(0.0935449\pi\) | |||||||
\(740\) | −3.67295 | −0.135020 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.2524 | 0.963757 | ||||||||
\(743\) | 10.4897 | 0.384831 | 0.192416 | − | 0.981314i | \(-0.438368\pi\) | ||||
0.192416 | + | 0.981314i | \(0.438368\pi\) | |||||||
\(744\) | −8.97617 | −0.329082 | ||||||||
\(745\) | 10.1694 | 0.372580 | ||||||||
\(746\) | −26.3245 | −0.963807 | ||||||||
\(747\) | −3.52556 | −0.128994 | ||||||||
\(748\) | 17.5788 | 0.642744 | ||||||||
\(749\) | 56.8872 | 2.07861 | ||||||||
\(750\) | −3.20235 | −0.116933 | ||||||||
\(751\) | 45.0715 | 1.64468 | 0.822341 | − | 0.568996i | \(-0.192668\pi\) | ||||
0.822341 | + | 0.568996i | \(0.192668\pi\) | |||||||
\(752\) | −16.3125 | −0.594856 | ||||||||
\(753\) | −16.2730 | −0.593022 | ||||||||
\(754\) | −7.92680 | −0.288677 | ||||||||
\(755\) | −2.79628 | −0.101767 | ||||||||
\(756\) | 37.7992 | 1.37474 | ||||||||
\(757\) | −46.0535 | −1.67384 | −0.836922 | − | 0.547322i | \(-0.815647\pi\) | ||||
−0.836922 | + | 0.547322i | \(0.815647\pi\) | |||||||
\(758\) | 43.1117 | 1.56589 | ||||||||
\(759\) | 39.2768 | 1.42566 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.48523 | −0.307589 | −0.153795 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153795 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(762\) | 6.60942 | 0.239434 | ||||||||
\(763\) | −33.5455 | −1.21443 | ||||||||
\(764\) | 16.3690 | 0.592210 | ||||||||
\(765\) | −0.736492 | −0.0266279 | ||||||||
\(766\) | −58.9195 | −2.12885 | ||||||||
\(767\) | 4.30673 | 0.155507 | ||||||||
\(768\) | 33.3090 | 1.20194 | ||||||||
\(769\) | −3.92677 | −0.141603 | −0.0708015 | − | 0.997490i | \(-0.522556\pi\) | ||||
−0.0708015 | + | 0.997490i | \(0.522556\pi\) | |||||||
\(770\) | 23.7133 | 0.854569 | ||||||||
\(771\) | −10.6002 | −0.381756 | ||||||||
\(772\) | 6.37807 | 0.229552 | ||||||||
\(773\) | −31.1834 | −1.12159 | −0.560795 | − | 0.827955i | \(-0.689504\pi\) | ||||
−0.560795 | + | 0.827955i | \(0.689504\pi\) | |||||||
\(774\) | 4.12975 | 0.148441 | ||||||||
\(775\) | −8.46117 | −0.303934 | ||||||||
\(776\) | 11.4367 | 0.410553 | ||||||||
\(777\) | 15.5574 | 0.558117 | ||||||||
\(778\) | 40.3411 | 1.44630 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.75861 | −0.206191 | ||||||||
\(781\) | −8.35202 | −0.298859 | ||||||||
\(782\) | −55.2720 | −1.97652 | ||||||||
\(783\) | 10.7429 | 0.383920 | ||||||||
\(784\) | −49.5010 | −1.76789 | ||||||||
\(785\) | −15.8271 | −0.564892 | ||||||||
\(786\) | 3.09994 | 0.110571 | ||||||||
\(787\) | −18.7949 | −0.669966 | −0.334983 | − | 0.942224i | \(-0.608731\pi\) | ||||
−0.334983 | + | 0.942224i | \(0.608731\pi\) | |||||||
\(788\) | 17.9018 | 0.637727 | ||||||||
\(789\) | 22.6273 | 0.805553 | ||||||||
\(790\) | −24.3505 | −0.866353 | ||||||||
\(791\) | 34.8840 | 1.24033 | ||||||||
\(792\) | −0.380447 | −0.0135186 | ||||||||
\(793\) | 10.1885 | 0.361804 | ||||||||
\(794\) | 42.2836 | 1.50059 | ||||||||
\(795\) | 5.42037 | 0.192241 | ||||||||
\(796\) | 39.4138 | 1.39699 | ||||||||
\(797\) | 7.77327 | 0.275344 | 0.137672 | − | 0.990478i | \(-0.456038\pi\) | ||||
0.137672 | + | 0.990478i | \(0.456038\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.8886 | 0.455965 | ||||||||
\(800\) | 7.45136 | 0.263445 | ||||||||
\(801\) | 0.504620 | 0.0178299 | ||||||||
\(802\) | 55.1439 | 1.94720 | ||||||||
\(803\) | 5.35383 | 0.188933 | ||||||||
\(804\) | 28.1904 | 0.994198 | ||||||||
\(805\) | −33.9139 | −1.19531 | ||||||||
\(806\) | −33.4511 | −1.17827 | ||||||||
\(807\) | −22.6819 | −0.798439 | ||||||||
\(808\) | 5.68283 | 0.199921 | ||||||||
\(809\) | 23.0942 | 0.811950 | 0.405975 | − | 0.913884i | \(-0.366932\pi\) | ||||
0.405975 | + | 0.913884i | \(0.366932\pi\) | |||||||
\(810\) | 15.9818 | 0.561542 | ||||||||
\(811\) | −9.79395 | −0.343912 | −0.171956 | − | 0.985105i | \(-0.555009\pi\) | ||||
−0.171956 | + | 0.985105i | \(0.555009\pi\) | |||||||
\(812\) | 14.1448 | 0.496384 | ||||||||
\(813\) | 3.02644 | 0.106142 | ||||||||
\(814\) | 12.3461 | 0.432730 | ||||||||
\(815\) | 18.3145 | 0.641529 | ||||||||
\(816\) | −27.3813 | −0.958538 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 35.2263 | 1.23166 | ||||||||
\(819\) | −1.78657 | −0.0624280 | ||||||||
\(820\) | 16.2891 | 0.568839 | ||||||||
\(821\) | −30.3878 | −1.06054 | −0.530270 | − | 0.847829i | \(-0.677910\pi\) | ||||
−0.530270 | + | 0.847829i | \(0.677910\pi\) | |||||||
\(822\) | −62.2074 | −2.16973 | ||||||||
\(823\) | 24.7436 | 0.862507 | 0.431254 | − | 0.902231i | \(-0.358071\pi\) | ||||
0.431254 | + | 0.902231i | \(0.358071\pi\) | |||||||
\(824\) | −7.47715 | −0.260479 | ||||||||
\(825\) | 4.89612 | 0.170461 | ||||||||
\(826\) | −16.8957 | −0.587878 | ||||||||
\(827\) | −17.3269 | −0.602514 | −0.301257 | − | 0.953543i | \(-0.597406\pi\) | ||||
−0.301257 | + | 0.953543i | \(0.597406\pi\) | |||||||
\(828\) | −2.74077 | −0.0952483 | ||||||||
\(829\) | −45.9820 | −1.59702 | −0.798510 | − | 0.601981i | \(-0.794378\pi\) | ||||
−0.798510 | + | 0.601981i | \(0.794378\pi\) | |||||||
\(830\) | −32.9824 | −1.14483 | ||||||||
\(831\) | −2.14519 | −0.0744158 | ||||||||
\(832\) | 10.6643 | 0.369717 | ||||||||
\(833\) | 39.1110 | 1.35511 | ||||||||
\(834\) | 32.9129 | 1.13968 | ||||||||
\(835\) | −5.46238 | −0.189034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.3351 | 1.56701 | ||||||||
\(838\) | 42.5865 | 1.47113 | ||||||||
\(839\) | −11.6248 | −0.401334 | −0.200667 | − | 0.979660i | \(-0.564311\pi\) | ||||
−0.200667 | + | 0.979660i | \(0.564311\pi\) | |||||||
\(840\) | −4.48492 | −0.154744 | ||||||||
\(841\) | −24.9799 | −0.861376 | ||||||||
\(842\) | −51.2560 | −1.76640 | ||||||||
\(843\) | −16.2792 | −0.560685 | ||||||||
\(844\) | −24.4820 | −0.842706 | ||||||||
\(845\) | −8.73965 | −0.300653 | ||||||||
\(846\) | 1.40509 | 0.0483079 | ||||||||
\(847\) | 10.2480 | 0.352124 | ||||||||
\(848\) | −14.7604 | −0.506873 | ||||||||
\(849\) | 12.6742 | 0.434976 | ||||||||
\(850\) | −6.89003 | −0.236326 | ||||||||
\(851\) | −17.6569 | −0.605271 | ||||||||
\(852\) | −7.95693 | −0.272600 | ||||||||
\(853\) | −8.52849 | −0.292010 | −0.146005 | − | 0.989284i | \(-0.546642\pi\) | ||||
−0.146005 | + | 0.989284i | \(0.546642\pi\) | |||||||
\(854\) | −39.9705 | −1.36776 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.53826 | −0.291832 | ||||||||
\(857\) | 27.9866 | 0.956005 | 0.478002 | − | 0.878359i | \(-0.341361\pi\) | ||||
0.478002 | + | 0.878359i | \(0.341361\pi\) | |||||||
\(858\) | 19.3567 | 0.660828 | ||||||||
\(859\) | −43.4377 | −1.48208 | −0.741038 | − | 0.671464i | \(-0.765666\pi\) | ||||
−0.741038 | + | 0.671464i | \(0.765666\pi\) | |||||||
\(860\) | 17.5730 | 0.599234 | ||||||||
\(861\) | −68.9950 | −2.35134 | ||||||||
\(862\) | 7.28460 | 0.248114 | ||||||||
\(863\) | −24.1508 | −0.822101 | −0.411051 | − | 0.911613i | \(-0.634838\pi\) | ||||
−0.411051 | + | 0.911613i | \(0.634838\pi\) | |||||||
\(864\) | −39.9245 | −1.35826 | ||||||||
\(865\) | 7.69398 | 0.261603 | ||||||||
\(866\) | 59.9198 | 2.03616 | ||||||||
\(867\) | −6.78826 | −0.230541 | ||||||||
\(868\) | 59.6910 | 2.02605 | ||||||||
\(869\) | 37.2299 | 1.26294 | ||||||||
\(870\) | 6.42076 | 0.217684 | ||||||||
\(871\) | −20.8559 | −0.706674 | ||||||||
\(872\) | 5.03488 | 0.170503 | ||||||||
\(873\) | −3.69024 | −0.124896 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.22760 | −0.142919 | ||||||||
\(876\) | 5.10057 | 0.172332 | ||||||||
\(877\) | −45.4037 | −1.53317 | −0.766586 | − | 0.642141i | \(-0.778046\pi\) | ||||
−0.766586 | + | 0.642141i | \(0.778046\pi\) | |||||||
\(878\) | −7.97630 | −0.269187 | ||||||||
\(879\) | 1.97932 | 0.0667607 | ||||||||
\(880\) | −13.3328 | −0.449448 | ||||||||
\(881\) | −31.7657 | −1.07021 | −0.535107 | − | 0.844784i | \(-0.679729\pi\) | ||||
−0.535107 | + | 0.844784i | \(0.679729\pi\) | |||||||
\(882\) | 4.26380 | 0.143569 | ||||||||
\(883\) | −29.5408 | −0.994126 | −0.497063 | − | 0.867715i | \(-0.665588\pi\) | ||||
−0.497063 | + | 0.867715i | \(0.665588\pi\) | |||||||
\(884\) | −12.3900 | −0.416720 | ||||||||
\(885\) | −3.48848 | −0.117264 | ||||||||
\(886\) | 12.6709 | 0.425687 | ||||||||
\(887\) | −4.82481 | −0.162001 | −0.0810006 | − | 0.996714i | \(-0.525812\pi\) | ||||
−0.0810006 | + | 0.996714i | \(0.525812\pi\) | |||||||
\(888\) | −2.33502 | −0.0783582 | ||||||||
\(889\) | 8.72548 | 0.292643 | ||||||||
\(890\) | 4.72082 | 0.158242 | ||||||||
\(891\) | −24.4348 | −0.818595 | ||||||||
\(892\) | −6.58239 | −0.220395 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −32.5661 | −1.08917 | ||||||||
\(895\) | 21.3618 | 0.714046 | ||||||||
\(896\) | 21.1658 | 0.707100 | ||||||||
\(897\) | −27.6833 | −0.924318 | ||||||||
\(898\) | 10.5345 | 0.351542 | ||||||||
\(899\) | 16.9648 | 0.565807 | ||||||||
\(900\) | −0.341655 | −0.0113885 | ||||||||
\(901\) | 11.6622 | 0.388525 | ||||||||
\(902\) | −54.7534 | −1.82309 | ||||||||
\(903\) | −74.4333 | −2.47698 | ||||||||
\(904\) | −5.23577 | −0.174139 | ||||||||
\(905\) | 2.16604 | 0.0720016 | ||||||||
\(906\) | 8.95466 | 0.297499 | ||||||||
\(907\) | −34.7324 | −1.15327 | −0.576635 | − | 0.817002i | \(-0.695634\pi\) | ||||
−0.576635 | + | 0.817002i | \(0.695634\pi\) | |||||||
\(908\) | 46.6760 | 1.54900 | ||||||||
\(909\) | −1.83366 | −0.0608187 | ||||||||
\(910\) | −16.7138 | −0.554056 | ||||||||
\(911\) | 49.1485 | 1.62836 | 0.814181 | − | 0.580611i | \(-0.197186\pi\) | ||||
0.814181 | + | 0.580611i | \(0.197186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.4273 | 1.66890 | ||||||||
\(914\) | −67.4820 | −2.23211 | ||||||||
\(915\) | −8.25275 | −0.272828 | ||||||||
\(916\) | −10.6866 | −0.353096 | ||||||||
\(917\) | 4.09240 | 0.135143 | ||||||||
\(918\) | 36.9169 | 1.21844 | ||||||||
\(919\) | 38.1829 | 1.25954 | 0.629769 | − | 0.776783i | \(-0.283150\pi\) | ||||
0.629769 | + | 0.776783i | \(0.283150\pi\) | |||||||
\(920\) | 5.09018 | 0.167818 | ||||||||
\(921\) | 22.5602 | 0.743383 | ||||||||
\(922\) | −10.7806 | −0.355040 | ||||||||
\(923\) | 5.88671 | 0.193764 | ||||||||
\(924\) | −34.5406 | −1.13630 | ||||||||
\(925\) | −2.20105 | −0.0723702 | ||||||||
\(926\) | 39.6428 | 1.30274 | ||||||||
\(927\) | 2.41263 | 0.0792412 | ||||||||
\(928\) | −14.9401 | −0.490433 | ||||||||
\(929\) | −41.9415 | −1.37606 | −0.688028 | − | 0.725684i | \(-0.741524\pi\) | ||||
−0.688028 | + | 0.725684i | \(0.741524\pi\) | |||||||
\(930\) | 27.0956 | 0.888500 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.8064 | 0.910829 | ||||||||
\(933\) | 23.8570 | 0.781044 | ||||||||
\(934\) | 35.4119 | 1.15871 | ||||||||
\(935\) | 10.5343 | 0.344508 | ||||||||
\(936\) | 0.268149 | 0.00876472 | ||||||||
\(937\) | −27.1660 | −0.887473 | −0.443737 | − | 0.896157i | \(-0.646347\pi\) | ||||
−0.443737 | + | 0.896157i | \(0.646347\pi\) | |||||||
\(938\) | 81.8196 | 2.67151 | ||||||||
\(939\) | −48.3363 | −1.57739 | ||||||||
\(940\) | 5.97896 | 0.195012 | ||||||||
\(941\) | 41.4889 | 1.35250 | 0.676250 | − | 0.736672i | \(-0.263604\pi\) | ||||
0.676250 | + | 0.736672i | \(0.263604\pi\) | |||||||
\(942\) | 50.6838 | 1.65137 | ||||||||
\(943\) | 78.3062 | 2.55000 | ||||||||
\(944\) | 9.49959 | 0.309185 | ||||||||
\(945\) | 22.6516 | 0.736855 | ||||||||
\(946\) | −59.0691 | −1.92050 | ||||||||
\(947\) | 42.0065 | 1.36503 | 0.682513 | − | 0.730873i | \(-0.260887\pi\) | ||||
0.682513 | + | 0.730873i | \(0.260887\pi\) | |||||||
\(948\) | 35.4688 | 1.15197 | ||||||||
\(949\) | −3.77352 | −0.122494 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.0569 | −0.812527 | ||||||||
\(952\) | −9.64956 | −0.312744 | ||||||||
\(953\) | 24.2497 | 0.785525 | 0.392762 | − | 0.919640i | \(-0.371519\pi\) | ||||
0.392762 | + | 0.919640i | \(0.371519\pi\) | |||||||
\(954\) | 1.27139 | 0.0411628 | ||||||||
\(955\) | 9.80930 | 0.317422 | ||||||||
\(956\) | −14.2489 | −0.460841 | ||||||||
\(957\) | −9.81680 | −0.317332 | ||||||||
\(958\) | 61.4823 | 1.98640 | ||||||||
\(959\) | −82.1235 | −2.65191 | ||||||||
\(960\) | −8.63813 | −0.278795 | ||||||||
\(961\) | 40.5914 | 1.30940 | ||||||||
\(962\) | −8.70183 | −0.280558 | ||||||||
\(963\) | 2.75502 | 0.0887792 | ||||||||
\(964\) | −8.91955 | −0.287279 | ||||||||
\(965\) | 3.82213 | 0.123039 | ||||||||
\(966\) | 108.604 | 3.49428 | ||||||||
\(967\) | −7.93704 | −0.255238 | −0.127619 | − | 0.991823i | \(-0.540733\pi\) | ||||
−0.127619 | + | 0.991823i | \(0.540733\pi\) | |||||||
\(968\) | −1.53813 | −0.0494373 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.5230 | −1.10847 | ||||||||
\(971\) | 43.3213 | 1.39025 | 0.695123 | − | 0.718891i | \(-0.255350\pi\) | ||||
0.695123 | + | 0.718891i | \(0.255350\pi\) | |||||||
\(972\) | 3.54424 | 0.113682 | ||||||||
\(973\) | 43.4502 | 1.39295 | ||||||||
\(974\) | −6.78719 | −0.217475 | ||||||||
\(975\) | −3.45091 | −0.110518 | ||||||||
\(976\) | 22.4733 | 0.719353 | ||||||||
\(977\) | −37.7002 | −1.20614 | −0.603068 | − | 0.797690i | \(-0.706055\pi\) | ||||
−0.603068 | + | 0.797690i | \(0.706055\pi\) | |||||||
\(978\) | −58.6494 | −1.87540 | ||||||||
\(979\) | −7.21774 | −0.230680 | ||||||||
\(980\) | 18.1434 | 0.579570 | ||||||||
\(981\) | −1.62459 | −0.0518692 | ||||||||
\(982\) | 37.9097 | 1.20975 | ||||||||
\(983\) | 49.0724 | 1.56517 | 0.782584 | − | 0.622545i | \(-0.213901\pi\) | ||||
0.782584 | + | 0.622545i | \(0.213901\pi\) | |||||||
\(984\) | 10.3555 | 0.330123 | ||||||||
\(985\) | 10.7279 | 0.341818 | ||||||||
\(986\) | 13.8146 | 0.439947 | ||||||||
\(987\) | −25.3248 | −0.806098 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 84.4784 | 2.68626 | ||||||||
\(990\) | 1.14842 | 0.0364993 | ||||||||
\(991\) | −48.5874 | −1.54343 | −0.771715 | − | 0.635969i | \(-0.780601\pi\) | ||||
−0.771715 | + | 0.635969i | \(0.780601\pi\) | |||||||
\(992\) | −63.0472 | −2.00175 | ||||||||
\(993\) | 25.4472 | 0.807542 | ||||||||
\(994\) | −23.0942 | −0.732502 | ||||||||
\(995\) | 23.6191 | 0.748777 | ||||||||
\(996\) | 48.0418 | 1.52226 | ||||||||
\(997\) | −21.7606 | −0.689165 | −0.344582 | − | 0.938756i | \(-0.611979\pi\) | ||||
−0.344582 | + | 0.938756i | \(0.611979\pi\) | |||||||
\(998\) | 56.4140 | 1.78576 | ||||||||
\(999\) | 11.7933 | 0.373123 |
(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 | 1805.2.a.w.1.5 | ✓ | 16 | |
5.4 | even | 2 | 9025.2.a.cm.1.12 | 16 | |||
19.18 | odd | 2 | inner | 1805.2.a.w.1.12 | yes | 16 | |
95.94 | odd | 2 | 9025.2.a.cm.1.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.w.1.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1805.2.a.w.1.12 | yes | 16 | 19.18 | odd | 2 | inner | |
9025.2.a.cm.1.5 | 16 | 95.94 | odd | 2 | |||
9025.2.a.cm.1.12 | 16 | 5.4 | even | 2 |