Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.381966 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.23607 | −1.60108 | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(8\) | 1.47214 | 0.520479 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −0.472136 | −0.149302 | ||||||||
\(11\) | −3.61803 | −1.09088 | −0.545439 | − | 0.838150i | \(-0.683637\pi\) | ||||
−0.545439 | + | 0.838150i | \(0.683637\pi\) | |||||||
\(12\) | 4.85410 | 1.40126 | ||||||||
\(13\) | 1.38197 | 0.383288 | 0.191644 | − | 0.981464i | \(-0.438618\pi\) | ||||
0.191644 | + | 0.981464i | \(0.438618\pi\) | |||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | −3.23607 | −0.835549 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | 6.09017 | 1.47708 | 0.738542 | − | 0.674208i | \(-0.235515\pi\) | ||||
0.738542 | + | 0.674208i | \(0.235515\pi\) | |||||||
\(18\) | −1.47214 | −0.346986 | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | −2.29180 | −0.512461 | ||||||||
\(21\) | 11.0902 | 2.42007 | ||||||||
\(22\) | 1.38197 | 0.294636 | ||||||||
\(23\) | 4.38197 | 0.913703 | 0.456852 | − | 0.889543i | \(-0.348977\pi\) | ||||
0.456852 | + | 0.889543i | \(0.348977\pi\) | |||||||
\(24\) | −3.85410 | −0.786715 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | −0.527864 | −0.103523 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 7.85410 | 1.48429 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 1.23607 | 0.225674 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | 9.47214 | 1.64889 | ||||||||
\(34\) | −2.32624 | −0.398947 | ||||||||
\(35\) | −5.23607 | −0.885057 | ||||||||
\(36\) | −7.14590 | −1.19098 | ||||||||
\(37\) | −4.85410 | −0.798009 | −0.399005 | − | 0.916949i | \(-0.630644\pi\) | ||||
−0.399005 | + | 0.916949i | \(0.630644\pi\) | |||||||
\(38\) | 0.472136 | 0.0765906 | ||||||||
\(39\) | −3.61803 | −0.579349 | ||||||||
\(40\) | 1.81966 | 0.287714 | ||||||||
\(41\) | 9.47214 | 1.47930 | 0.739650 | − | 0.672992i | \(-0.234991\pi\) | ||||
0.739650 | + | 0.672992i | \(0.234991\pi\) | |||||||
\(42\) | −4.23607 | −0.653639 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 6.70820 | 1.01130 | ||||||||
\(45\) | 4.76393 | 0.710165 | ||||||||
\(46\) | −1.67376 | −0.246783 | ||||||||
\(47\) | 1.14590 | 0.167146 | 0.0835732 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835732 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(48\) | −8.23607 | −1.18877 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 1.32624 | 0.187558 | ||||||||
\(51\) | −15.9443 | −2.23264 | ||||||||
\(52\) | −2.56231 | −0.355328 | ||||||||
\(53\) | −1.38197 | −0.189828 | −0.0949138 | − | 0.995485i | \(-0.530258\pi\) | ||||
−0.0949138 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(54\) | 0.854102 | 0.116229 | ||||||||
\(55\) | −4.47214 | −0.603023 | ||||||||
\(56\) | −6.23607 | −0.833330 | ||||||||
\(57\) | 3.23607 | 0.428628 | ||||||||
\(58\) | −1.14590 | −0.150464 | ||||||||
\(59\) | 5.09017 | 0.662684 | 0.331342 | − | 0.943511i | \(-0.392499\pi\) | ||||
0.331342 | + | 0.943511i | \(0.392499\pi\) | |||||||
\(60\) | 6.00000 | 0.774597 | ||||||||
\(61\) | 2.85410 | 0.365430 | 0.182715 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182715 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.3262 | −2.05691 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 1.70820 | 0.211877 | ||||||||
\(66\) | −3.61803 | −0.445349 | ||||||||
\(67\) | −3.85410 | −0.470853 | −0.235427 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235427 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(68\) | −11.2918 | −1.36933 | ||||||||
\(69\) | −11.4721 | −1.38108 | ||||||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | −10.7984 | −1.28153 | −0.640766 | − | 0.767737i | \(-0.721383\pi\) | ||||
−0.640766 | + | 0.767737i | \(0.721383\pi\) | |||||||
\(72\) | 5.67376 | 0.668659 | ||||||||
\(73\) | 1.85410 | 0.217006 | 0.108503 | − | 0.994096i | \(-0.465394\pi\) | ||||
0.108503 | + | 0.994096i | \(0.465394\pi\) | |||||||
\(74\) | 1.85410 | 0.215535 | ||||||||
\(75\) | 9.09017 | 1.04964 | ||||||||
\(76\) | 2.29180 | 0.262887 | ||||||||
\(77\) | 15.3262 | 1.74659 | ||||||||
\(78\) | 1.38197 | 0.156477 | ||||||||
\(79\) | −1.38197 | −0.155483 | −0.0777417 | − | 0.996974i | \(-0.524771\pi\) | ||||
−0.0777417 | + | 0.996974i | \(0.524771\pi\) | |||||||
\(80\) | 3.88854 | 0.434752 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −3.61803 | −0.399545 | ||||||||
\(83\) | 16.0344 | 1.76001 | 0.880004 | − | 0.474966i | \(-0.157540\pi\) | ||||
0.880004 | + | 0.474966i | \(0.157540\pi\) | |||||||
\(84\) | −20.5623 | −2.24353 | ||||||||
\(85\) | 7.52786 | 0.816511 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.85410 | −0.842048 | ||||||||
\(88\) | −5.32624 | −0.567779 | ||||||||
\(89\) | −1.85410 | −0.196534 | −0.0982672 | − | 0.995160i | \(-0.531330\pi\) | ||||
−0.0982672 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(90\) | −1.81966 | −0.191809 | ||||||||
\(91\) | −5.85410 | −0.613677 | ||||||||
\(92\) | −8.12461 | −0.847049 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.437694 | −0.0451447 | ||||||||
\(95\) | −1.52786 | −0.156756 | ||||||||
\(96\) | 10.8541 | 1.10779 | ||||||||
\(97\) | −9.23607 | −0.937781 | −0.468890 | − | 0.883256i | \(-0.655346\pi\) | ||||
−0.468890 | + | 0.883256i | \(0.655346\pi\) | |||||||
\(98\) | −4.18034 | −0.422278 | ||||||||
\(99\) | −13.9443 | −1.40145 | ||||||||
\(100\) | 6.43769 | 0.643769 | ||||||||
\(101\) | 3.76393 | 0.374525 | 0.187263 | − | 0.982310i | \(-0.440038\pi\) | ||||
0.187263 | + | 0.982310i | \(0.440038\pi\) | |||||||
\(102\) | 6.09017 | 0.603017 | ||||||||
\(103\) | −16.4164 | −1.61756 | −0.808778 | − | 0.588114i | \(-0.799871\pi\) | ||||
−0.808778 | + | 0.588114i | \(0.799871\pi\) | |||||||
\(104\) | 2.03444 | 0.199493 | ||||||||
\(105\) | 13.7082 | 1.33778 | ||||||||
\(106\) | 0.527864 | 0.0512707 | ||||||||
\(107\) | 7.52786 | 0.727746 | 0.363873 | − | 0.931449i | \(-0.381454\pi\) | ||||
0.363873 | + | 0.931449i | \(0.381454\pi\) | |||||||
\(108\) | 4.14590 | 0.398939 | ||||||||
\(109\) | −13.8541 | −1.32698 | −0.663491 | − | 0.748184i | \(-0.730926\pi\) | ||||
−0.663491 | + | 0.748184i | \(0.730926\pi\) | |||||||
\(110\) | 1.70820 | 0.162871 | ||||||||
\(111\) | 12.7082 | 1.20621 | ||||||||
\(112\) | −13.3262 | −1.25921 | ||||||||
\(113\) | −15.6180 | −1.46922 | −0.734611 | − | 0.678489i | \(-0.762635\pi\) | ||||
−0.734611 | + | 0.678489i | \(0.762635\pi\) | |||||||
\(114\) | −1.23607 | −0.115768 | ||||||||
\(115\) | 5.41641 | 0.505083 | ||||||||
\(116\) | −5.56231 | −0.516447 | ||||||||
\(117\) | 5.32624 | 0.492411 | ||||||||
\(118\) | −1.94427 | −0.178985 | ||||||||
\(119\) | −25.7984 | −2.36493 | ||||||||
\(120\) | −4.76393 | −0.434886 | ||||||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | −1.09017 | −0.0986993 | ||||||||
\(123\) | −24.7984 | −2.23599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 6.23607 | 0.555553 | ||||||||
\(127\) | −14.6525 | −1.30020 | −0.650098 | − | 0.759850i | \(-0.725272\pi\) | ||||
−0.650098 | + | 0.759850i | \(0.725272\pi\) | |||||||
\(128\) | 10.0902 | 0.891853 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.652476 | −0.0572259 | ||||||||
\(131\) | 9.94427 | 0.868835 | 0.434418 | − | 0.900712i | \(-0.356954\pi\) | ||||
0.434418 | + | 0.900712i | \(0.356954\pi\) | |||||||
\(132\) | −17.5623 | −1.52860 | ||||||||
\(133\) | 5.23607 | 0.454025 | ||||||||
\(134\) | 1.47214 | 0.127173 | ||||||||
\(135\) | −2.76393 | −0.237881 | ||||||||
\(136\) | 8.96556 | 0.768790 | ||||||||
\(137\) | 3.70820 | 0.316813 | 0.158407 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158407 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(138\) | 4.38197 | 0.373018 | ||||||||
\(139\) | −5.29180 | −0.448844 | −0.224422 | − | 0.974492i | \(-0.572049\pi\) | ||||
−0.224422 | + | 0.974492i | \(0.572049\pi\) | |||||||
\(140\) | 9.70820 | 0.820493 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 4.12461 | 0.346130 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | 12.1246 | 1.01038 | ||||||||
\(145\) | 3.70820 | 0.307950 | ||||||||
\(146\) | −0.708204 | −0.0586114 | ||||||||
\(147\) | −28.6525 | −2.36322 | ||||||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | 9.00000 | 0.737309 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(150\) | −3.47214 | −0.283499 | ||||||||
\(151\) | −8.85410 | −0.720537 | −0.360268 | − | 0.932849i | \(-0.617315\pi\) | ||||
−0.360268 | + | 0.932849i | \(0.617315\pi\) | |||||||
\(152\) | −1.81966 | −0.147594 | ||||||||
\(153\) | 23.4721 | 1.89761 | ||||||||
\(154\) | −5.85410 | −0.471737 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.70820 | 0.537086 | ||||||||
\(157\) | −5.14590 | −0.410687 | −0.205344 | − | 0.978690i | \(-0.565831\pi\) | ||||
−0.205344 | + | 0.978690i | \(0.565831\pi\) | |||||||
\(158\) | 0.527864 | 0.0419946 | ||||||||
\(159\) | 3.61803 | 0.286929 | ||||||||
\(160\) | −5.12461 | −0.405136 | ||||||||
\(161\) | −18.5623 | −1.46291 | ||||||||
\(162\) | 2.18034 | 0.171304 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | −17.5623 | −1.37139 | ||||||||
\(165\) | 11.7082 | 0.911482 | ||||||||
\(166\) | −6.12461 | −0.475362 | ||||||||
\(167\) | 14.2361 | 1.10162 | 0.550810 | − | 0.834631i | \(-0.314319\pi\) | ||||
0.550810 | + | 0.834631i | \(0.314319\pi\) | |||||||
\(168\) | 16.3262 | 1.25960 | ||||||||
\(169\) | −11.0902 | −0.853090 | ||||||||
\(170\) | −2.87539 | −0.220532 | ||||||||
\(171\) | −4.76393 | −0.364307 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.76393 | −0.286166 | −0.143083 | − | 0.989711i | \(-0.545702\pi\) | ||||
−0.143083 | + | 0.989711i | \(0.545702\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 14.7082 | 1.11184 | ||||||||
\(176\) | −11.3820 | −0.857948 | ||||||||
\(177\) | −13.3262 | −1.00166 | ||||||||
\(178\) | 0.708204 | 0.0530821 | ||||||||
\(179\) | 9.65248 | 0.721460 | 0.360730 | − | 0.932670i | \(-0.382528\pi\) | ||||
0.360730 | + | 0.932670i | \(0.382528\pi\) | |||||||
\(180\) | −8.83282 | −0.658359 | ||||||||
\(181\) | −19.3820 | −1.44065 | −0.720325 | − | 0.693637i | \(-0.756007\pi\) | ||||
−0.720325 | + | 0.693637i | \(0.756007\pi\) | |||||||
\(182\) | 2.23607 | 0.165748 | ||||||||
\(183\) | −7.47214 | −0.552356 | ||||||||
\(184\) | 6.45085 | 0.475563 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.0344 | −1.61132 | ||||||||
\(188\) | −2.12461 | −0.154953 | ||||||||
\(189\) | 9.47214 | 0.688997 | ||||||||
\(190\) | 0.583592 | 0.0423382 | ||||||||
\(191\) | −14.5279 | −1.05120 | −0.525600 | − | 0.850732i | \(-0.676159\pi\) | ||||
−0.525600 | + | 0.850732i | \(0.676159\pi\) | |||||||
\(192\) | 12.3262 | 0.889570 | ||||||||
\(193\) | 2.70820 | 0.194941 | 0.0974704 | − | 0.995238i | \(-0.468925\pi\) | ||||
0.0974704 | + | 0.995238i | \(0.468925\pi\) | |||||||
\(194\) | 3.52786 | 0.253286 | ||||||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | −20.2918 | −1.44941 | ||||||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 5.32624 | 0.378519 | ||||||||
\(199\) | 1.94427 | 0.137826 | 0.0689129 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689129 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(200\) | −5.11146 | −0.361435 | ||||||||
\(201\) | 10.0902 | 0.711706 | ||||||||
\(202\) | −1.43769 | −0.101156 | ||||||||
\(203\) | −12.7082 | −0.891941 | ||||||||
\(204\) | 29.5623 | 2.06978 | ||||||||
\(205\) | 11.7082 | 0.817736 | ||||||||
\(206\) | 6.27051 | 0.436887 | ||||||||
\(207\) | 16.8885 | 1.17383 | ||||||||
\(208\) | 4.34752 | 0.301447 | ||||||||
\(209\) | 4.47214 | 0.309344 | ||||||||
\(210\) | −5.23607 | −0.361323 | ||||||||
\(211\) | −9.23607 | −0.635837 | −0.317919 | − | 0.948118i | \(-0.602984\pi\) | ||||
−0.317919 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(212\) | 2.56231 | 0.175980 | ||||||||
\(213\) | 28.2705 | 1.93706 | ||||||||
\(214\) | −2.87539 | −0.196557 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.29180 | −0.223978 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.29180 | 0.358406 | ||||||||
\(219\) | −4.85410 | −0.328010 | ||||||||
\(220\) | 8.29180 | 0.559033 | ||||||||
\(221\) | 8.41641 | 0.566149 | ||||||||
\(222\) | −4.85410 | −0.325786 | ||||||||
\(223\) | 2.76393 | 0.185087 | 0.0925433 | − | 0.995709i | \(-0.470500\pi\) | ||||
0.0925433 | + | 0.995709i | \(0.470500\pi\) | |||||||
\(224\) | 17.5623 | 1.17343 | ||||||||
\(225\) | −13.3820 | −0.892131 | ||||||||
\(226\) | 5.96556 | 0.396823 | ||||||||
\(227\) | −1.47214 | −0.0977091 | −0.0488545 | − | 0.998806i | \(-0.515557\pi\) | ||||
−0.0488545 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(228\) | −6.00000 | −0.397360 | ||||||||
\(229\) | −2.29180 | −0.151446 | −0.0757231 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757231 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(230\) | −2.06888 | −0.136418 | ||||||||
\(231\) | −40.1246 | −2.64001 | ||||||||
\(232\) | 4.41641 | 0.289951 | ||||||||
\(233\) | 18.0344 | 1.18148 | 0.590738 | − | 0.806864i | \(-0.298837\pi\) | ||||
0.590738 | + | 0.806864i | \(0.298837\pi\) | |||||||
\(234\) | −2.03444 | −0.132996 | ||||||||
\(235\) | 1.41641 | 0.0923963 | ||||||||
\(236\) | −9.43769 | −0.614342 | ||||||||
\(237\) | 3.61803 | 0.235017 | ||||||||
\(238\) | 9.85410 | 0.638747 | ||||||||
\(239\) | −8.29180 | −0.536352 | −0.268176 | − | 0.963370i | \(-0.586421\pi\) | ||||
−0.268176 | + | 0.963370i | \(0.586421\pi\) | |||||||
\(240\) | −10.1803 | −0.657138 | ||||||||
\(241\) | 4.27051 | 0.275088 | 0.137544 | − | 0.990496i | \(-0.456079\pi\) | ||||
0.137544 | + | 0.990496i | \(0.456079\pi\) | |||||||
\(242\) | −0.798374 | −0.0513214 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | −5.29180 | −0.338773 | ||||||||
\(245\) | 13.5279 | 0.864264 | ||||||||
\(246\) | 9.47214 | 0.603921 | ||||||||
\(247\) | −1.70820 | −0.108690 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −41.9787 | −2.66029 | ||||||||
\(250\) | 4.00000 | 0.252982 | ||||||||
\(251\) | −29.1803 | −1.84185 | −0.920923 | − | 0.389744i | \(-0.872564\pi\) | ||||
−0.920923 | + | 0.389744i | \(0.872564\pi\) | |||||||
\(252\) | 30.2705 | 1.90686 | ||||||||
\(253\) | −15.8541 | −0.996739 | ||||||||
\(254\) | 5.59675 | 0.351171 | ||||||||
\(255\) | −19.7082 | −1.23418 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 3.43769 | 0.214437 | 0.107219 | − | 0.994235i | \(-0.465805\pi\) | ||||
0.107219 | + | 0.994235i | \(0.465805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5623 | 1.27768 | ||||||||
\(260\) | −3.16718 | −0.196420 | ||||||||
\(261\) | 11.5623 | 0.715689 | ||||||||
\(262\) | −3.79837 | −0.234664 | ||||||||
\(263\) | 27.5066 | 1.69613 | 0.848064 | − | 0.529894i | \(-0.177768\pi\) | ||||
0.848064 | + | 0.529894i | \(0.177768\pi\) | |||||||
\(264\) | 13.9443 | 0.858211 | ||||||||
\(265\) | −1.70820 | −0.104934 | ||||||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | 4.85410 | 0.297066 | ||||||||
\(268\) | 7.14590 | 0.436505 | ||||||||
\(269\) | 11.5623 | 0.704966 | 0.352483 | − | 0.935818i | \(-0.385337\pi\) | ||||
0.352483 | + | 0.935818i | \(0.385337\pi\) | |||||||
\(270\) | 1.05573 | 0.0642496 | ||||||||
\(271\) | 13.8541 | 0.841577 | 0.420788 | − | 0.907159i | \(-0.361753\pi\) | ||||
0.420788 | + | 0.907159i | \(0.361753\pi\) | |||||||
\(272\) | 19.1591 | 1.16169 | ||||||||
\(273\) | 15.3262 | 0.927586 | ||||||||
\(274\) | −1.41641 | −0.0855683 | ||||||||
\(275\) | 12.5623 | 0.757536 | ||||||||
\(276\) | 21.2705 | 1.28033 | ||||||||
\(277\) | −12.4721 | −0.749378 | −0.374689 | − | 0.927151i | \(-0.622251\pi\) | ||||
−0.374689 | + | 0.927151i | \(0.622251\pi\) | |||||||
\(278\) | 2.02129 | 0.121229 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.70820 | −0.460653 | ||||||||
\(281\) | 7.47214 | 0.445750 | 0.222875 | − | 0.974847i | \(-0.428456\pi\) | ||||
0.222875 | + | 0.974847i | \(0.428456\pi\) | |||||||
\(282\) | 1.14590 | 0.0682372 | ||||||||
\(283\) | 10.7639 | 0.639849 | 0.319925 | − | 0.947443i | \(-0.396342\pi\) | ||||
0.319925 | + | 0.947443i | \(0.396342\pi\) | |||||||
\(284\) | 20.0213 | 1.18804 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 1.90983 | 0.112931 | ||||||||
\(287\) | −40.1246 | −2.36848 | ||||||||
\(288\) | −15.9787 | −0.941555 | ||||||||
\(289\) | 20.0902 | 1.18177 | ||||||||
\(290\) | −1.41641 | −0.0831743 | ||||||||
\(291\) | 24.1803 | 1.41748 | ||||||||
\(292\) | −3.43769 | −0.201176 | ||||||||
\(293\) | −12.0902 | −0.706315 | −0.353158 | − | 0.935564i | \(-0.614892\pi\) | ||||
−0.353158 | + | 0.935564i | \(0.614892\pi\) | |||||||
\(294\) | 10.9443 | 0.638283 | ||||||||
\(295\) | 6.29180 | 0.366323 | ||||||||
\(296\) | −7.14590 | −0.415347 | ||||||||
\(297\) | 8.09017 | 0.469439 | ||||||||
\(298\) | −3.43769 | −0.199140 | ||||||||
\(299\) | 6.05573 | 0.350212 | ||||||||
\(300\) | −16.8541 | −0.973072 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.38197 | 0.194610 | ||||||||
\(303\) | −9.85410 | −0.566103 | ||||||||
\(304\) | −3.88854 | −0.223023 | ||||||||
\(305\) | 3.52786 | 0.202005 | ||||||||
\(306\) | −8.96556 | −0.512527 | ||||||||
\(307\) | −23.2148 | −1.32494 | −0.662469 | − | 0.749090i | \(-0.730491\pi\) | ||||
−0.662469 | + | 0.749090i | \(0.730491\pi\) | |||||||
\(308\) | −28.4164 | −1.61918 | ||||||||
\(309\) | 42.9787 | 2.44497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.8328 | −1.69166 | −0.845832 | − | 0.533450i | \(-0.820895\pi\) | ||||
−0.845832 | + | 0.533450i | \(0.820895\pi\) | |||||||
\(312\) | −5.32624 | −0.301539 | ||||||||
\(313\) | 13.1246 | 0.741847 | 0.370923 | − | 0.928663i | \(-0.379041\pi\) | ||||
0.370923 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(314\) | 1.96556 | 0.110923 | ||||||||
\(315\) | −20.1803 | −1.13703 | ||||||||
\(316\) | 2.56231 | 0.144141 | ||||||||
\(317\) | 33.3050 | 1.87059 | 0.935296 | − | 0.353866i | \(-0.115133\pi\) | ||||
0.935296 | + | 0.353866i | \(0.115133\pi\) | |||||||
\(318\) | −1.38197 | −0.0774968 | ||||||||
\(319\) | −10.8541 | −0.607713 | ||||||||
\(320\) | −5.81966 | −0.325329 | ||||||||
\(321\) | −19.7082 | −1.10000 | ||||||||
\(322\) | 7.09017 | 0.395120 | ||||||||
\(323\) | −7.52786 | −0.418862 | ||||||||
\(324\) | 10.5836 | 0.587977 | ||||||||
\(325\) | −4.79837 | −0.266166 | ||||||||
\(326\) | −5.34752 | −0.296172 | ||||||||
\(327\) | 36.2705 | 2.00576 | ||||||||
\(328\) | 13.9443 | 0.769944 | ||||||||
\(329\) | −4.85410 | −0.267615 | ||||||||
\(330\) | −4.47214 | −0.246183 | ||||||||
\(331\) | −5.47214 | −0.300776 | −0.150388 | − | 0.988627i | \(-0.548052\pi\) | ||||
−0.150388 | + | 0.988627i | \(0.548052\pi\) | |||||||
\(332\) | −29.7295 | −1.63162 | ||||||||
\(333\) | −18.7082 | −1.02520 | ||||||||
\(334\) | −5.43769 | −0.297537 | ||||||||
\(335\) | −4.76393 | −0.260281 | ||||||||
\(336\) | 34.8885 | 1.90333 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 4.23607 | 0.230412 | ||||||||
\(339\) | 40.8885 | 2.22076 | ||||||||
\(340\) | −13.9574 | −0.756948 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.81966 | 0.0983959 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.1803 | −0.763444 | ||||||||
\(346\) | 1.43769 | 0.0772909 | ||||||||
\(347\) | 10.0902 | 0.541669 | 0.270834 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270834 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(348\) | 14.5623 | 0.780622 | ||||||||
\(349\) | 20.7082 | 1.10848 | 0.554242 | − | 0.832355i | \(-0.313008\pi\) | ||||
0.554242 | + | 0.832355i | \(0.313008\pi\) | |||||||
\(350\) | −5.61803 | −0.300297 | ||||||||
\(351\) | −3.09017 | −0.164941 | ||||||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | −17.2361 | −0.917383 | −0.458692 | − | 0.888595i | \(-0.651682\pi\) | ||||
−0.458692 | + | 0.888595i | \(0.651682\pi\) | |||||||
\(354\) | 5.09017 | 0.270539 | ||||||||
\(355\) | −13.3475 | −0.708413 | ||||||||
\(356\) | 3.43769 | 0.182197 | ||||||||
\(357\) | 67.5410 | 3.57465 | ||||||||
\(358\) | −3.68692 | −0.194860 | ||||||||
\(359\) | −5.34752 | −0.282232 | −0.141116 | − | 0.989993i | \(-0.545069\pi\) | ||||
−0.141116 | + | 0.989993i | \(0.545069\pi\) | |||||||
\(360\) | 7.01316 | 0.369626 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 7.40325 | 0.389106 | ||||||||
\(363\) | −5.47214 | −0.287213 | ||||||||
\(364\) | 10.8541 | 0.568910 | ||||||||
\(365\) | 2.29180 | 0.119958 | ||||||||
\(366\) | 2.85410 | 0.149186 | ||||||||
\(367\) | 19.1803 | 1.00121 | 0.500603 | − | 0.865677i | \(-0.333112\pi\) | ||||
0.500603 | + | 0.865677i | \(0.333112\pi\) | |||||||
\(368\) | 13.7852 | 0.718604 | ||||||||
\(369\) | 36.5066 | 1.90046 | ||||||||
\(370\) | 2.29180 | 0.119145 | ||||||||
\(371\) | 5.85410 | 0.303930 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 8.41641 | 0.435202 | ||||||||
\(375\) | 27.4164 | 1.41578 | ||||||||
\(376\) | 1.68692 | 0.0869961 | ||||||||
\(377\) | 4.14590 | 0.213525 | ||||||||
\(378\) | −3.61803 | −0.186092 | ||||||||
\(379\) | −27.3607 | −1.40542 | −0.702712 | − | 0.711475i | \(-0.748028\pi\) | ||||
−0.702712 | + | 0.711475i | \(0.748028\pi\) | |||||||
\(380\) | 2.83282 | 0.145320 | ||||||||
\(381\) | 38.3607 | 1.96528 | ||||||||
\(382\) | 5.54915 | 0.283919 | ||||||||
\(383\) | 38.1246 | 1.94808 | 0.974038 | − | 0.226383i | \(-0.0726901\pi\) | ||||
0.974038 | + | 0.226383i | \(0.0726901\pi\) | |||||||
\(384\) | −26.4164 | −1.34806 | ||||||||
\(385\) | 18.9443 | 0.965489 | ||||||||
\(386\) | −1.03444 | −0.0526517 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.1246 | 0.869370 | ||||||||
\(389\) | −35.0689 | −1.77806 | −0.889031 | − | 0.457846i | \(-0.848621\pi\) | ||||
−0.889031 | + | 0.457846i | \(0.848621\pi\) | |||||||
\(390\) | 1.70820 | 0.0864983 | ||||||||
\(391\) | 26.6869 | 1.34962 | ||||||||
\(392\) | 16.1115 | 0.813751 | ||||||||
\(393\) | −26.0344 | −1.31326 | ||||||||
\(394\) | 1.12461 | 0.0566571 | ||||||||
\(395\) | −1.70820 | −0.0859491 | ||||||||
\(396\) | 25.8541 | 1.29922 | ||||||||
\(397\) | 32.4164 | 1.62693 | 0.813466 | − | 0.581612i | \(-0.197578\pi\) | ||||
0.813466 | + | 0.581612i | \(0.197578\pi\) | |||||||
\(398\) | −0.742646 | −0.0372255 | ||||||||
\(399\) | −13.7082 | −0.686269 | ||||||||
\(400\) | −10.9230 | −0.546149 | ||||||||
\(401\) | −25.4164 | −1.26923 | −0.634617 | − | 0.772826i | \(-0.718842\pi\) | ||||
−0.634617 | + | 0.772826i | \(0.718842\pi\) | |||||||
\(402\) | −3.85410 | −0.192225 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.97871 | −0.347204 | ||||||||
\(405\) | −7.05573 | −0.350602 | ||||||||
\(406\) | 4.85410 | 0.240905 | ||||||||
\(407\) | 17.5623 | 0.870531 | ||||||||
\(408\) | −23.4721 | −1.16204 | ||||||||
\(409\) | 8.90983 | 0.440563 | 0.220281 | − | 0.975436i | \(-0.429302\pi\) | ||||
0.220281 | + | 0.975436i | \(0.429302\pi\) | |||||||
\(410\) | −4.47214 | −0.220863 | ||||||||
\(411\) | −9.70820 | −0.478870 | ||||||||
\(412\) | 30.4377 | 1.49956 | ||||||||
\(413\) | −21.5623 | −1.06101 | ||||||||
\(414\) | −6.45085 | −0.317042 | ||||||||
\(415\) | 19.8197 | 0.972909 | ||||||||
\(416\) | −5.72949 | −0.280911 | ||||||||
\(417\) | 13.8541 | 0.678438 | ||||||||
\(418\) | −1.70820 | −0.0835510 | ||||||||
\(419\) | −10.2361 | −0.500065 | −0.250032 | − | 0.968237i | \(-0.580441\pi\) | ||||
−0.250032 | + | 0.968237i | \(0.580441\pi\) | |||||||
\(420\) | −25.4164 | −1.24019 | ||||||||
\(421\) | −7.65248 | −0.372959 | −0.186479 | − | 0.982459i | \(-0.559708\pi\) | ||||
−0.186479 | + | 0.982459i | \(0.559708\pi\) | |||||||
\(422\) | 3.52786 | 0.171734 | ||||||||
\(423\) | 4.41641 | 0.214733 | ||||||||
\(424\) | −2.03444 | −0.0988012 | ||||||||
\(425\) | −21.1459 | −1.02573 | ||||||||
\(426\) | −10.7984 | −0.523183 | ||||||||
\(427\) | −12.0902 | −0.585084 | ||||||||
\(428\) | −13.9574 | −0.674658 | ||||||||
\(429\) | 13.0902 | 0.631999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7984 | −1.19450 | −0.597248 | − | 0.802057i | \(-0.703739\pi\) | ||||
−0.597248 | + | 0.802057i | \(0.703739\pi\) | |||||||
\(432\) | −7.03444 | −0.338445 | ||||||||
\(433\) | −34.7082 | −1.66797 | −0.833985 | − | 0.551787i | \(-0.813946\pi\) | ||||
−0.833985 | + | 0.551787i | \(0.813946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.70820 | −0.465473 | ||||||||
\(436\) | 25.6869 | 1.23018 | ||||||||
\(437\) | −5.41641 | −0.259102 | ||||||||
\(438\) | 1.85410 | 0.0885924 | ||||||||
\(439\) | 1.14590 | 0.0546907 | 0.0273454 | − | 0.999626i | \(-0.491295\pi\) | ||||
0.0273454 | + | 0.999626i | \(0.491295\pi\) | |||||||
\(440\) | −6.58359 | −0.313860 | ||||||||
\(441\) | 42.1803 | 2.00859 | ||||||||
\(442\) | −3.21478 | −0.152912 | ||||||||
\(443\) | 2.47214 | 0.117455 | 0.0587274 | − | 0.998274i | \(-0.481296\pi\) | ||||
0.0587274 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(444\) | −23.5623 | −1.11822 | ||||||||
\(445\) | −2.29180 | −0.108642 | ||||||||
\(446\) | −1.05573 | −0.0499902 | ||||||||
\(447\) | −23.5623 | −1.11446 | ||||||||
\(448\) | 19.9443 | 0.942278 | ||||||||
\(449\) | −32.8328 | −1.54948 | −0.774738 | − | 0.632282i | \(-0.782118\pi\) | ||||
−0.774738 | + | 0.632282i | \(0.782118\pi\) | |||||||
\(450\) | 5.11146 | 0.240956 | ||||||||
\(451\) | −34.2705 | −1.61374 | ||||||||
\(452\) | 28.9574 | 1.36204 | ||||||||
\(453\) | 23.1803 | 1.08911 | ||||||||
\(454\) | 0.562306 | 0.0263903 | ||||||||
\(455\) | −7.23607 | −0.339232 | ||||||||
\(456\) | 4.76393 | 0.223092 | ||||||||
\(457\) | −15.7082 | −0.734799 | −0.367399 | − | 0.930063i | \(-0.619752\pi\) | ||||
−0.367399 | + | 0.930063i | \(0.619752\pi\) | |||||||
\(458\) | 0.875388 | 0.0409042 | ||||||||
\(459\) | −13.6180 | −0.635635 | ||||||||
\(460\) | −10.0426 | −0.468237 | ||||||||
\(461\) | −31.5967 | −1.47161 | −0.735804 | − | 0.677195i | \(-0.763195\pi\) | ||||
−0.735804 | + | 0.677195i | \(0.763195\pi\) | |||||||
\(462\) | 15.3262 | 0.713041 | ||||||||
\(463\) | −29.8328 | −1.38645 | −0.693224 | − | 0.720722i | \(-0.743810\pi\) | ||||
−0.693224 | + | 0.720722i | \(0.743810\pi\) | |||||||
\(464\) | 9.43769 | 0.438134 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.88854 | −0.319106 | ||||||||
\(467\) | −15.0557 | −0.696696 | −0.348348 | − | 0.937365i | \(-0.613257\pi\) | ||||
−0.348348 | + | 0.937365i | \(0.613257\pi\) | |||||||
\(468\) | −9.87539 | −0.456490 | ||||||||
\(469\) | 16.3262 | 0.753876 | ||||||||
\(470\) | −0.541020 | −0.0249554 | ||||||||
\(471\) | 13.4721 | 0.620763 | ||||||||
\(472\) | 7.49342 | 0.344913 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.38197 | −0.0634758 | ||||||||
\(475\) | 4.29180 | 0.196921 | ||||||||
\(476\) | 47.8328 | 2.19241 | ||||||||
\(477\) | −5.32624 | −0.243872 | ||||||||
\(478\) | 3.16718 | 0.144864 | ||||||||
\(479\) | −13.8197 | −0.631436 | −0.315718 | − | 0.948853i | \(-0.602245\pi\) | ||||
−0.315718 | + | 0.948853i | \(0.602245\pi\) | |||||||
\(480\) | 13.4164 | 0.612372 | ||||||||
\(481\) | −6.70820 | −0.305868 | ||||||||
\(482\) | −1.63119 | −0.0742987 | ||||||||
\(483\) | 48.5967 | 2.21123 | ||||||||
\(484\) | −3.87539 | −0.176154 | ||||||||
\(485\) | −11.4164 | −0.518392 | ||||||||
\(486\) | −8.27051 | −0.375158 | ||||||||
\(487\) | 1.32624 | 0.0600976 | 0.0300488 | − | 0.999548i | \(-0.490434\pi\) | ||||
0.0300488 | + | 0.999548i | \(0.490434\pi\) | |||||||
\(488\) | 4.20163 | 0.190199 | ||||||||
\(489\) | −36.6525 | −1.65748 | ||||||||
\(490\) | −5.16718 | −0.233430 | ||||||||
\(491\) | 21.6525 | 0.977163 | 0.488581 | − | 0.872518i | \(-0.337515\pi\) | ||||
0.488581 | + | 0.872518i | \(0.337515\pi\) | |||||||
\(492\) | 45.9787 | 2.07288 | ||||||||
\(493\) | 18.2705 | 0.822862 | ||||||||
\(494\) | 0.652476 | 0.0293563 | ||||||||
\(495\) | −17.2361 | −0.774704 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 45.7426 | 2.05184 | ||||||||
\(498\) | 16.0344 | 0.718521 | ||||||||
\(499\) | 13.8541 | 0.620195 | 0.310097 | − | 0.950705i | \(-0.399638\pi\) | ||||
0.310097 | + | 0.950705i | \(0.399638\pi\) | |||||||
\(500\) | 19.4164 | 0.868328 | ||||||||
\(501\) | −37.2705 | −1.66512 | ||||||||
\(502\) | 11.1459 | 0.497466 | ||||||||
\(503\) | −13.4721 | −0.600693 | −0.300346 | − | 0.953830i | \(-0.597102\pi\) | ||||
−0.300346 | + | 0.953830i | \(0.597102\pi\) | |||||||
\(504\) | −24.0344 | −1.07058 | ||||||||
\(505\) | 4.65248 | 0.207032 | ||||||||
\(506\) | 6.05573 | 0.269210 | ||||||||
\(507\) | 29.0344 | 1.28946 | ||||||||
\(508\) | 27.1672 | 1.20535 | ||||||||
\(509\) | 18.7082 | 0.829227 | 0.414613 | − | 0.909998i | \(-0.363917\pi\) | ||||
0.414613 | + | 0.909998i | \(0.363917\pi\) | |||||||
\(510\) | 7.52786 | 0.333339 | ||||||||
\(511\) | −7.85410 | −0.347445 | ||||||||
\(512\) | −22.3050 | −0.985749 | ||||||||
\(513\) | 2.76393 | 0.122031 | ||||||||
\(514\) | −1.31308 | −0.0579176 | ||||||||
\(515\) | −20.2918 | −0.894163 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.14590 | −0.182336 | ||||||||
\(518\) | −7.85410 | −0.345089 | ||||||||
\(519\) | 9.85410 | 0.432547 | ||||||||
\(520\) | 2.51471 | 0.110277 | ||||||||
\(521\) | −22.0344 | −0.965346 | −0.482673 | − | 0.875801i | \(-0.660334\pi\) | ||||
−0.482673 | + | 0.875801i | \(0.660334\pi\) | |||||||
\(522\) | −4.41641 | −0.193301 | ||||||||
\(523\) | 35.8328 | 1.56686 | 0.783430 | − | 0.621480i | \(-0.213468\pi\) | ||||
0.783430 | + | 0.621480i | \(0.213468\pi\) | |||||||
\(524\) | −18.4377 | −0.805454 | ||||||||
\(525\) | −38.5066 | −1.68056 | ||||||||
\(526\) | −10.5066 | −0.458109 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 29.7984 | 1.29681 | ||||||||
\(529\) | −3.79837 | −0.165147 | ||||||||
\(530\) | 0.652476 | 0.0283417 | ||||||||
\(531\) | 19.6180 | 0.851350 | ||||||||
\(532\) | −9.70820 | −0.420904 | ||||||||
\(533\) | 13.0902 | 0.566998 | ||||||||
\(534\) | −1.85410 | −0.0802348 | ||||||||
\(535\) | 9.30495 | 0.402288 | ||||||||
\(536\) | −5.67376 | −0.245069 | ||||||||
\(537\) | −25.2705 | −1.09050 | ||||||||
\(538\) | −4.41641 | −0.190405 | ||||||||
\(539\) | −39.5967 | −1.70555 | ||||||||
\(540\) | 5.12461 | 0.220528 | ||||||||
\(541\) | −37.9443 | −1.63135 | −0.815676 | − | 0.578509i | \(-0.803635\pi\) | ||||
−0.815676 | + | 0.578509i | \(0.803635\pi\) | |||||||
\(542\) | −5.29180 | −0.227302 | ||||||||
\(543\) | 50.7426 | 2.17758 | ||||||||
\(544\) | −25.2492 | −1.08255 | ||||||||
\(545\) | −17.1246 | −0.733538 | ||||||||
\(546\) | −5.85410 | −0.250532 | ||||||||
\(547\) | 21.0000 | 0.897895 | 0.448948 | − | 0.893558i | \(-0.351799\pi\) | ||||
0.448948 | + | 0.893558i | \(0.351799\pi\) | |||||||
\(548\) | −6.87539 | −0.293702 | ||||||||
\(549\) | 11.0000 | 0.469469 | ||||||||
\(550\) | −4.79837 | −0.204603 | ||||||||
\(551\) | −3.70820 | −0.157975 | ||||||||
\(552\) | −16.8885 | −0.718824 | ||||||||
\(553\) | 5.85410 | 0.248942 | ||||||||
\(554\) | 4.76393 | 0.202400 | ||||||||
\(555\) | 15.7082 | 0.666776 | ||||||||
\(556\) | 9.81153 | 0.416102 | ||||||||
\(557\) | −38.5623 | −1.63394 | −0.816969 | − | 0.576682i | \(-0.804347\pi\) | ||||
−0.816969 | + | 0.576682i | \(0.804347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −16.4721 | −0.696075 | ||||||||
\(561\) | 57.6869 | 2.43554 | ||||||||
\(562\) | −2.85410 | −0.120393 | ||||||||
\(563\) | −1.32624 | −0.0558943 | −0.0279471 | − | 0.999609i | \(-0.508897\pi\) | ||||
−0.0279471 | + | 0.999609i | \(0.508897\pi\) | |||||||
\(564\) | 5.56231 | 0.234215 | ||||||||
\(565\) | −19.3050 | −0.812165 | ||||||||
\(566\) | −4.11146 | −0.172817 | ||||||||
\(567\) | 24.1803 | 1.01548 | ||||||||
\(568\) | −15.8967 | −0.667010 | ||||||||
\(569\) | −25.9443 | −1.08764 | −0.543820 | − | 0.839202i | \(-0.683023\pi\) | ||||
−0.543820 | + | 0.839202i | \(0.683023\pi\) | |||||||
\(570\) | −1.52786 | −0.0639952 | ||||||||
\(571\) | −43.1803 | −1.80704 | −0.903520 | − | 0.428545i | \(-0.859026\pi\) | ||||
−0.903520 | + | 0.428545i | \(0.859026\pi\) | |||||||
\(572\) | 9.27051 | 0.387619 | ||||||||
\(573\) | 38.0344 | 1.58891 | ||||||||
\(574\) | 15.3262 | 0.639705 | ||||||||
\(575\) | −15.2148 | −0.634500 | ||||||||
\(576\) | −18.1459 | −0.756079 | ||||||||
\(577\) | −28.2148 | −1.17460 | −0.587298 | − | 0.809371i | \(-0.699808\pi\) | ||||
−0.587298 | + | 0.809371i | \(0.699808\pi\) | |||||||
\(578\) | −7.67376 | −0.319186 | ||||||||
\(579\) | −7.09017 | −0.294657 | ||||||||
\(580\) | −6.87539 | −0.285485 | ||||||||
\(581\) | −67.9230 | −2.81792 | ||||||||
\(582\) | −9.23607 | −0.382847 | ||||||||
\(583\) | 5.00000 | 0.207079 | ||||||||
\(584\) | 2.72949 | 0.112947 | ||||||||
\(585\) | 6.58359 | 0.272198 | ||||||||
\(586\) | 4.61803 | 0.190769 | ||||||||
\(587\) | 15.7426 | 0.649769 | 0.324884 | − | 0.945754i | \(-0.394675\pi\) | ||||
0.324884 | + | 0.945754i | \(0.394675\pi\) | |||||||
\(588\) | 53.1246 | 2.19082 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.40325 | −0.0989403 | ||||||||
\(591\) | 7.70820 | 0.317073 | ||||||||
\(592\) | −15.2705 | −0.627614 | ||||||||
\(593\) | −30.4721 | −1.25134 | −0.625670 | − | 0.780088i | \(-0.715174\pi\) | ||||
−0.625670 | + | 0.780088i | \(0.715174\pi\) | |||||||
\(594\) | −3.09017 | −0.126791 | ||||||||
\(595\) | −31.8885 | −1.30730 | ||||||||
\(596\) | −16.6869 | −0.683523 | ||||||||
\(597\) | −5.09017 | −0.208327 | ||||||||
\(598\) | −2.31308 | −0.0945890 | ||||||||
\(599\) | 36.2361 | 1.48057 | 0.740283 | − | 0.672296i | \(-0.234692\pi\) | ||||
0.740283 | + | 0.672296i | \(0.234692\pi\) | |||||||
\(600\) | 13.3820 | 0.546316 | ||||||||
\(601\) | 29.4164 | 1.19992 | 0.599960 | − | 0.800030i | \(-0.295183\pi\) | ||||
0.599960 | + | 0.800030i | \(0.295183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8541 | −0.604906 | ||||||||
\(604\) | 16.4164 | 0.667974 | ||||||||
\(605\) | 2.58359 | 0.105038 | ||||||||
\(606\) | 3.76393 | 0.152899 | ||||||||
\(607\) | −23.8541 | −0.968208 | −0.484104 | − | 0.875010i | \(-0.660854\pi\) | ||||
−0.484104 | + | 0.875010i | \(0.660854\pi\) | |||||||
\(608\) | 5.12461 | 0.207830 | ||||||||
\(609\) | 33.2705 | 1.34819 | ||||||||
\(610\) | −1.34752 | −0.0545597 | ||||||||
\(611\) | 1.58359 | 0.0640653 | ||||||||
\(612\) | −43.5197 | −1.75918 | ||||||||
\(613\) | 5.20163 | 0.210092 | 0.105046 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105046 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(614\) | 8.86726 | 0.357853 | ||||||||
\(615\) | −30.6525 | −1.23603 | ||||||||
\(616\) | 22.5623 | 0.909061 | ||||||||
\(617\) | 9.70820 | 0.390838 | 0.195419 | − | 0.980720i | \(-0.437393\pi\) | ||||
0.195419 | + | 0.980720i | \(0.437393\pi\) | |||||||
\(618\) | −16.4164 | −0.660365 | ||||||||
\(619\) | −30.2705 | −1.21667 | −0.608337 | − | 0.793679i | \(-0.708163\pi\) | ||||
−0.608337 | + | 0.793679i | \(0.708163\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.79837 | −0.393195 | ||||||||
\(622\) | 11.3951 | 0.456903 | ||||||||
\(623\) | 7.85410 | 0.314668 | ||||||||
\(624\) | −11.3820 | −0.455643 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | −5.01316 | −0.200366 | ||||||||
\(627\) | −11.7082 | −0.467581 | ||||||||
\(628\) | 9.54102 | 0.380728 | ||||||||
\(629\) | −29.5623 | −1.17873 | ||||||||
\(630\) | 7.70820 | 0.307102 | ||||||||
\(631\) | −27.0902 | −1.07844 | −0.539221 | − | 0.842164i | \(-0.681281\pi\) | ||||
−0.539221 | + | 0.842164i | \(0.681281\pi\) | |||||||
\(632\) | −2.03444 | −0.0809258 | ||||||||
\(633\) | 24.1803 | 0.961082 | ||||||||
\(634\) | −12.7214 | −0.505230 | ||||||||
\(635\) | −18.1115 | −0.718731 | ||||||||
\(636\) | −6.70820 | −0.265998 | ||||||||
\(637\) | 15.1246 | 0.599259 | ||||||||
\(638\) | 4.14590 | 0.164138 | ||||||||
\(639\) | −41.6180 | −1.64638 | ||||||||
\(640\) | 12.4721 | 0.493004 | ||||||||
\(641\) | 10.8197 | 0.427351 | 0.213675 | − | 0.976905i | \(-0.431457\pi\) | ||||
0.213675 | + | 0.976905i | \(0.431457\pi\) | |||||||
\(642\) | 7.52786 | 0.297101 | ||||||||
\(643\) | 9.43769 | 0.372186 | 0.186093 | − | 0.982532i | \(-0.440417\pi\) | ||||
0.186093 | + | 0.982532i | \(0.440417\pi\) | |||||||
\(644\) | 34.4164 | 1.35620 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.87539 | 0.113131 | ||||||||
\(647\) | −21.6738 | −0.852084 | −0.426042 | − | 0.904703i | \(-0.640092\pi\) | ||||
−0.426042 | + | 0.904703i | \(0.640092\pi\) | |||||||
\(648\) | −8.40325 | −0.330111 | ||||||||
\(649\) | −18.4164 | −0.722907 | ||||||||
\(650\) | 1.83282 | 0.0718889 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.9574 | −1.01657 | ||||||||
\(653\) | −32.8885 | −1.28703 | −0.643514 | − | 0.765434i | \(-0.722524\pi\) | ||||
−0.643514 | + | 0.765434i | \(0.722524\pi\) | |||||||
\(654\) | −13.8541 | −0.541738 | ||||||||
\(655\) | 12.2918 | 0.480280 | ||||||||
\(656\) | 29.7984 | 1.16343 | ||||||||
\(657\) | 7.14590 | 0.278788 | ||||||||
\(658\) | 1.85410 | 0.0722804 | ||||||||
\(659\) | −29.3607 | −1.14373 | −0.571865 | − | 0.820348i | \(-0.693780\pi\) | ||||
−0.571865 | + | 0.820348i | \(0.693780\pi\) | |||||||
\(660\) | −21.7082 | −0.844991 | ||||||||
\(661\) | −43.3951 | −1.68787 | −0.843937 | − | 0.536442i | \(-0.819768\pi\) | ||||
−0.843937 | + | 0.536442i | \(0.819768\pi\) | |||||||
\(662\) | 2.09017 | 0.0812368 | ||||||||
\(663\) | −22.0344 | −0.855747 | ||||||||
\(664\) | 23.6049 | 0.916047 | ||||||||
\(665\) | 6.47214 | 0.250979 | ||||||||
\(666\) | 7.14590 | 0.276898 | ||||||||
\(667\) | 13.1459 | 0.509011 | ||||||||
\(668\) | −26.3951 | −1.02126 | ||||||||
\(669\) | −7.23607 | −0.279763 | ||||||||
\(670\) | 1.81966 | 0.0702996 | ||||||||
\(671\) | −10.3262 | −0.398640 | ||||||||
\(672\) | −45.9787 | −1.77367 | ||||||||
\(673\) | 13.8328 | 0.533216 | 0.266608 | − | 0.963805i | \(-0.414097\pi\) | ||||
0.266608 | + | 0.963805i | \(0.414097\pi\) | |||||||
\(674\) | −10.6950 | −0.411958 | ||||||||
\(675\) | 7.76393 | 0.298834 | ||||||||
\(676\) | 20.5623 | 0.790858 | ||||||||
\(677\) | −31.7639 | −1.22079 | −0.610394 | − | 0.792098i | \(-0.708989\pi\) | ||||
−0.610394 | + | 0.792098i | \(0.708989\pi\) | |||||||
\(678\) | −15.6180 | −0.599807 | ||||||||
\(679\) | 39.1246 | 1.50146 | ||||||||
\(680\) | 11.0820 | 0.424977 | ||||||||
\(681\) | 3.85410 | 0.147690 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.1246 | −0.425671 | −0.212836 | − | 0.977088i | \(-0.568270\pi\) | ||||
−0.212836 | + | 0.977088i | \(0.568270\pi\) | |||||||
\(684\) | 8.83282 | 0.337731 | ||||||||
\(685\) | 4.58359 | 0.175130 | ||||||||
\(686\) | 6.38197 | 0.243665 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.90983 | −0.0727587 | ||||||||
\(690\) | 5.41641 | 0.206199 | ||||||||
\(691\) | 15.7295 | 0.598378 | 0.299189 | − | 0.954194i | \(-0.403284\pi\) | ||||
0.299189 | + | 0.954194i | \(0.403284\pi\) | |||||||
\(692\) | 6.97871 | 0.265291 | ||||||||
\(693\) | 59.0689 | 2.24384 | ||||||||
\(694\) | −3.85410 | −0.146300 | ||||||||
\(695\) | −6.54102 | −0.248115 | ||||||||
\(696\) | −11.5623 | −0.438268 | ||||||||
\(697\) | 57.6869 | 2.18505 | ||||||||
\(698\) | −7.90983 | −0.299391 | ||||||||
\(699\) | −47.2148 | −1.78583 | ||||||||
\(700\) | −27.2705 | −1.03073 | ||||||||
\(701\) | −14.5066 | −0.547906 | −0.273953 | − | 0.961743i | \(-0.588331\pi\) | ||||
−0.273953 | + | 0.961743i | \(0.588331\pi\) | |||||||
\(702\) | 1.18034 | 0.0445491 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 17.0344 | 0.642010 | ||||||||
\(705\) | −3.70820 | −0.139659 | ||||||||
\(706\) | 6.58359 | 0.247777 | ||||||||
\(707\) | −15.9443 | −0.599646 | ||||||||
\(708\) | 24.7082 | 0.928591 | ||||||||
\(709\) | 28.8885 | 1.08493 | 0.542466 | − | 0.840078i | \(-0.317491\pi\) | ||||
0.542466 | + | 0.840078i | \(0.317491\pi\) | |||||||
\(710\) | 5.09830 | 0.191336 | ||||||||
\(711\) | −5.32624 | −0.199750 | ||||||||
\(712\) | −2.72949 | −0.102292 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −25.7984 | −0.965480 | ||||||||
\(715\) | −6.18034 | −0.231132 | ||||||||
\(716\) | −17.8967 | −0.668830 | ||||||||
\(717\) | 21.7082 | 0.810708 | ||||||||
\(718\) | 2.04257 | 0.0762281 | ||||||||
\(719\) | −10.7984 | −0.402711 | −0.201356 | − | 0.979518i | \(-0.564535\pi\) | ||||
−0.201356 | + | 0.979518i | \(0.564535\pi\) | |||||||
\(720\) | 14.9868 | 0.558527 | ||||||||
\(721\) | 69.5410 | 2.58984 | ||||||||
\(722\) | 6.67376 | 0.248372 | ||||||||
\(723\) | −11.1803 | −0.415801 | ||||||||
\(724\) | 35.9361 | 1.33556 | ||||||||
\(725\) | −10.4164 | −0.386856 | ||||||||
\(726\) | 2.09017 | 0.0775735 | ||||||||
\(727\) | −17.9787 | −0.666794 | −0.333397 | − | 0.942787i | \(-0.608195\pi\) | ||||
−0.333397 | + | 0.942787i | \(0.608195\pi\) | |||||||
\(728\) | −8.61803 | −0.319406 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −0.875388 | −0.0323996 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 13.8541 | 0.512062 | ||||||||
\(733\) | 24.5410 | 0.906443 | 0.453222 | − | 0.891398i | \(-0.350275\pi\) | ||||
0.453222 | + | 0.891398i | \(0.350275\pi\) | |||||||
\(734\) | −7.32624 | −0.270416 | ||||||||
\(735\) | −35.4164 | −1.30635 | ||||||||
\(736\) | −18.1672 | −0.669651 | ||||||||
\(737\) | 13.9443 | 0.513644 | ||||||||
\(738\) | −13.9443 | −0.513296 | ||||||||
\(739\) | 49.5410 | 1.82240 | 0.911198 | − | 0.411969i | \(-0.135159\pi\) | ||||
0.911198 | + | 0.411969i | \(0.135159\pi\) | |||||||
\(740\) | 11.1246 | 0.408949 | ||||||||
\(741\) | 4.47214 | 0.164288 | ||||||||
\(742\) | −2.23607 | −0.0820886 | ||||||||
\(743\) | 33.3607 | 1.22388 | 0.611942 | − | 0.790902i | \(-0.290388\pi\) | ||||
0.611942 | + | 0.790902i | \(0.290388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1246 | 0.407574 | ||||||||
\(746\) | −2.29180 | −0.0839086 | ||||||||
\(747\) | 61.7984 | 2.26108 | ||||||||
\(748\) | 40.8541 | 1.49377 | ||||||||
\(749\) | −31.8885 | −1.16518 | ||||||||
\(750\) | −10.4721 | −0.382388 | ||||||||
\(751\) | −37.9787 | −1.38586 | −0.692931 | − | 0.721003i | \(-0.743681\pi\) | ||||
−0.692931 | + | 0.721003i | \(0.743681\pi\) | |||||||
\(752\) | 3.60488 | 0.131456 | ||||||||
\(753\) | 76.3951 | 2.78399 | ||||||||
\(754\) | −1.58359 | −0.0576710 | ||||||||
\(755\) | −10.9443 | −0.398303 | ||||||||
\(756\) | −17.5623 | −0.638735 | ||||||||
\(757\) | −30.9787 | −1.12594 | −0.562970 | − | 0.826477i | \(-0.690341\pi\) | ||||
−0.562970 | + | 0.826477i | \(0.690341\pi\) | |||||||
\(758\) | 10.4508 | 0.379592 | ||||||||
\(759\) | 41.5066 | 1.50659 | ||||||||
\(760\) | −2.24922 | −0.0815879 | ||||||||
\(761\) | 1.09017 | 0.0395186 | 0.0197593 | − | 0.999805i | \(-0.493710\pi\) | ||||
0.0197593 | + | 0.999805i | \(0.493710\pi\) | |||||||
\(762\) | −14.6525 | −0.530803 | ||||||||
\(763\) | 58.6869 | 2.12461 | ||||||||
\(764\) | 26.9361 | 0.974515 | ||||||||
\(765\) | 29.0132 | 1.04897 | ||||||||
\(766\) | −14.5623 | −0.526157 | ||||||||
\(767\) | 7.03444 | 0.253999 | ||||||||
\(768\) | −14.5623 | −0.525472 | ||||||||
\(769\) | 19.8885 | 0.717199 | 0.358600 | − | 0.933491i | \(-0.383254\pi\) | ||||
0.358600 | + | 0.933491i | \(0.383254\pi\) | |||||||
\(770\) | −7.23607 | −0.260770 | ||||||||
\(771\) | −9.00000 | −0.324127 | ||||||||
\(772\) | −5.02129 | −0.180720 | ||||||||
\(773\) | 15.5967 | 0.560976 | 0.280488 | − | 0.959858i | \(-0.409504\pi\) | ||||
0.280488 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.5967 | −0.488095 | ||||||||
\(777\) | −53.8328 | −1.93124 | ||||||||
\(778\) | 13.3951 | 0.480238 | ||||||||
\(779\) | −11.7082 | −0.419490 | ||||||||
\(780\) | 8.29180 | 0.296894 | ||||||||
\(781\) | 39.0689 | 1.39799 | ||||||||
\(782\) | −10.1935 | −0.364519 | ||||||||
\(783\) | −6.70820 | −0.239732 | ||||||||
\(784\) | 34.4296 | 1.22963 | ||||||||
\(785\) | −6.36068 | −0.227022 | ||||||||
\(786\) | 9.94427 | 0.354700 | ||||||||
\(787\) | 10.4508 | 0.372533 | 0.186266 | − | 0.982499i | \(-0.440361\pi\) | ||||
0.186266 | + | 0.982499i | \(0.440361\pi\) | |||||||
\(788\) | 5.45898 | 0.194468 | ||||||||
\(789\) | −72.0132 | −2.56374 | ||||||||
\(790\) | 0.652476 | 0.0232140 | ||||||||
\(791\) | 66.1591 | 2.35235 | ||||||||
\(792\) | −20.5279 | −0.729426 | ||||||||
\(793\) | 3.94427 | 0.140065 | ||||||||
\(794\) | −12.3820 | −0.439420 | ||||||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | −3.60488 | −0.127772 | ||||||||
\(797\) | −8.23607 | −0.291736 | −0.145868 | − | 0.989304i | \(-0.546598\pi\) | ||||
−0.145868 | + | 0.989304i | \(0.546598\pi\) | |||||||
\(798\) | 5.23607 | 0.185355 | ||||||||
\(799\) | 6.97871 | 0.246889 | ||||||||
\(800\) | 14.3951 | 0.508944 | ||||||||
\(801\) | −7.14590 | −0.252488 | ||||||||
\(802\) | 9.70820 | 0.342809 | ||||||||
\(803\) | −6.70820 | −0.236727 | ||||||||
\(804\) | −18.7082 | −0.659787 | ||||||||
\(805\) | −22.9443 | −0.808679 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.2705 | −1.06557 | ||||||||
\(808\) | 5.54102 | 0.194932 | ||||||||
\(809\) | 4.74265 | 0.166743 | 0.0833713 | − | 0.996519i | \(-0.473431\pi\) | ||||
0.0833713 | + | 0.996519i | \(0.473431\pi\) | |||||||
\(810\) | 2.69505 | 0.0946943 | ||||||||
\(811\) | 47.3951 | 1.66427 | 0.832134 | − | 0.554575i | \(-0.187119\pi\) | ||||
0.832134 | + | 0.554575i | \(0.187119\pi\) | |||||||
\(812\) | 23.5623 | 0.826875 | ||||||||
\(813\) | −36.2705 | −1.27206 | ||||||||
\(814\) | −6.70820 | −0.235122 | ||||||||
\(815\) | 17.3050 | 0.606166 | ||||||||
\(816\) | −50.1591 | −1.75592 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.40325 | −0.118992 | ||||||||
\(819\) | −22.5623 | −0.788391 | ||||||||
\(820\) | −21.7082 | −0.758083 | ||||||||
\(821\) | 0.326238 | 0.0113858 | 0.00569289 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569289 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(822\) | 3.70820 | 0.129338 | ||||||||
\(823\) | 52.0132 | 1.81306 | 0.906532 | − | 0.422136i | \(-0.138720\pi\) | ||||
0.906532 | + | 0.422136i | \(0.138720\pi\) | |||||||
\(824\) | −24.1672 | −0.841904 | ||||||||
\(825\) | −32.8885 | −1.14503 | ||||||||
\(826\) | 8.23607 | 0.286569 | ||||||||
\(827\) | 9.18034 | 0.319232 | 0.159616 | − | 0.987179i | \(-0.448974\pi\) | ||||
0.159616 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(828\) | −31.3131 | −1.08820 | ||||||||
\(829\) | 28.1591 | 0.978004 | 0.489002 | − | 0.872283i | \(-0.337361\pi\) | ||||
0.489002 | + | 0.872283i | \(0.337361\pi\) | |||||||
\(830\) | −7.57044 | −0.262774 | ||||||||
\(831\) | 32.6525 | 1.13270 | ||||||||
\(832\) | −6.50658 | −0.225575 | ||||||||
\(833\) | 66.6525 | 2.30937 | ||||||||
\(834\) | −5.29180 | −0.183240 | ||||||||
\(835\) | 17.5967 | 0.608961 | ||||||||
\(836\) | −8.29180 | −0.286778 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.90983 | 0.135063 | ||||||||
\(839\) | 25.8885 | 0.893772 | 0.446886 | − | 0.894591i | \(-0.352533\pi\) | ||||
0.446886 | + | 0.894591i | \(0.352533\pi\) | |||||||
\(840\) | 20.1803 | 0.696288 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 2.92299 | 0.100733 | ||||||||
\(843\) | −19.5623 | −0.673762 | ||||||||
\(844\) | 17.1246 | 0.589453 | ||||||||
\(845\) | −13.7082 | −0.471577 | ||||||||
\(846\) | −1.68692 | −0.0579974 | ||||||||
\(847\) | −8.85410 | −0.304231 | ||||||||
\(848\) | −4.34752 | −0.149295 | ||||||||
\(849\) | −28.1803 | −0.967147 | ||||||||
\(850\) | 8.07701 | 0.277039 | ||||||||
\(851\) | −21.2705 | −0.729144 | ||||||||
\(852\) | −52.4164 | −1.79576 | ||||||||
\(853\) | 11.2574 | 0.385444 | 0.192722 | − | 0.981253i | \(-0.438268\pi\) | ||||
0.192722 | + | 0.981253i | \(0.438268\pi\) | |||||||
\(854\) | 4.61803 | 0.158026 | ||||||||
\(855\) | −5.88854 | −0.201384 | ||||||||
\(856\) | 11.0820 | 0.378776 | ||||||||
\(857\) | −36.1803 | −1.23590 | −0.617948 | − | 0.786219i | \(-0.712036\pi\) | ||||
−0.617948 | + | 0.786219i | \(0.712036\pi\) | |||||||
\(858\) | −5.00000 | −0.170697 | ||||||||
\(859\) | −49.4164 | −1.68607 | −0.843033 | − | 0.537862i | \(-0.819232\pi\) | ||||
−0.843033 | + | 0.537862i | \(0.819232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 105.048 | 3.58001 | ||||||||
\(862\) | 9.47214 | 0.322622 | ||||||||
\(863\) | 9.50658 | 0.323608 | 0.161804 | − | 0.986823i | \(-0.448269\pi\) | ||||
0.161804 | + | 0.986823i | \(0.448269\pi\) | |||||||
\(864\) | 9.27051 | 0.315389 | ||||||||
\(865\) | −4.65248 | −0.158189 | ||||||||
\(866\) | 13.2574 | 0.450503 | ||||||||
\(867\) | −52.5967 | −1.78628 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | 0.169613 | ||||||||
\(870\) | 3.70820 | 0.125720 | ||||||||
\(871\) | −5.32624 | −0.180473 | ||||||||
\(872\) | −20.3951 | −0.690666 | ||||||||
\(873\) | −35.5967 | −1.20477 | ||||||||
\(874\) | 2.06888 | 0.0699810 | ||||||||
\(875\) | 44.3607 | 1.49966 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | −7.65248 | −0.258406 | −0.129203 | − | 0.991618i | \(-0.541242\pi\) | ||||
−0.129203 | + | 0.991618i | \(0.541242\pi\) | |||||||
\(878\) | −0.437694 | −0.0147715 | ||||||||
\(879\) | 31.6525 | 1.06761 | ||||||||
\(880\) | −14.0689 | −0.474262 | ||||||||
\(881\) | 33.7639 | 1.13754 | 0.568768 | − | 0.822498i | \(-0.307420\pi\) | ||||
0.568768 | + | 0.822498i | \(0.307420\pi\) | |||||||
\(882\) | −16.1115 | −0.542501 | ||||||||
\(883\) | 13.1246 | 0.441678 | 0.220839 | − | 0.975310i | \(-0.429120\pi\) | ||||
0.220839 | + | 0.975310i | \(0.429120\pi\) | |||||||
\(884\) | −15.6049 | −0.524849 | ||||||||
\(885\) | −16.4721 | −0.553705 | ||||||||
\(886\) | −0.944272 | −0.0317234 | ||||||||
\(887\) | −52.9574 | −1.77814 | −0.889068 | − | 0.457775i | \(-0.848647\pi\) | ||||
−0.889068 | + | 0.457775i | \(0.848647\pi\) | |||||||
\(888\) | 18.7082 | 0.627806 | ||||||||
\(889\) | 62.0689 | 2.08172 | ||||||||
\(890\) | 0.875388 | 0.0293431 | ||||||||
\(891\) | 20.6525 | 0.691884 | ||||||||
\(892\) | −5.12461 | −0.171585 | ||||||||
\(893\) | −1.41641 | −0.0473983 | ||||||||
\(894\) | 9.00000 | 0.301005 | ||||||||
\(895\) | 11.9311 | 0.398813 | ||||||||
\(896\) | −42.7426 | −1.42793 | ||||||||
\(897\) | −15.8541 | −0.529353 | ||||||||
\(898\) | 12.5410 | 0.418499 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 24.8115 | 0.827051 | ||||||||
\(901\) | −8.41641 | −0.280391 | ||||||||
\(902\) | 13.0902 | 0.435855 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.9919 | −0.764698 | ||||||||
\(905\) | −23.9574 | −0.796372 | ||||||||
\(906\) | −8.85410 | −0.294158 | ||||||||
\(907\) | −21.7082 | −0.720809 | −0.360405 | − | 0.932796i | \(-0.617361\pi\) | ||||
−0.360405 | + | 0.932796i | \(0.617361\pi\) | |||||||
\(908\) | 2.72949 | 0.0905813 | ||||||||
\(909\) | 14.5066 | 0.481153 | ||||||||
\(910\) | 2.76393 | 0.0916235 | ||||||||
\(911\) | −42.9787 | −1.42395 | −0.711974 | − | 0.702206i | \(-0.752199\pi\) | ||||
−0.711974 | + | 0.702206i | \(0.752199\pi\) | |||||||
\(912\) | 10.1803 | 0.337105 | ||||||||
\(913\) | −58.0132 | −1.91996 | ||||||||
\(914\) | 6.00000 | 0.198462 | ||||||||
\(915\) | −9.23607 | −0.305335 | ||||||||
\(916\) | 4.24922 | 0.140398 | ||||||||
\(917\) | −42.1246 | −1.39108 | ||||||||
\(918\) | 5.20163 | 0.171679 | ||||||||
\(919\) | 29.3951 | 0.969656 | 0.484828 | − | 0.874610i | \(-0.338882\pi\) | ||||
0.484828 | + | 0.874610i | \(0.338882\pi\) | |||||||
\(920\) | 7.97369 | 0.262885 | ||||||||
\(921\) | 60.7771 | 2.00267 | ||||||||
\(922\) | 12.0689 | 0.397468 | ||||||||
\(923\) | −14.9230 | −0.491196 | ||||||||
\(924\) | 74.3951 | 2.44742 | ||||||||
\(925\) | 16.8541 | 0.554159 | ||||||||
\(926\) | 11.3951 | 0.374467 | ||||||||
\(927\) | −63.2705 | −2.07808 | ||||||||
\(928\) | −12.4377 | −0.408287 | ||||||||
\(929\) | 35.2361 | 1.15606 | 0.578029 | − | 0.816016i | \(-0.303822\pi\) | ||||
0.578029 | + | 0.816016i | \(0.303822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.5279 | −0.443358 | ||||||||
\(932\) | −33.4377 | −1.09529 | ||||||||
\(933\) | 78.1033 | 2.55699 | ||||||||
\(934\) | 5.75078 | 0.188171 | ||||||||
\(935\) | −27.2361 | −0.890715 | ||||||||
\(936\) | 7.84095 | 0.256289 | ||||||||
\(937\) | −55.3262 | −1.80743 | −0.903715 | − | 0.428135i | \(-0.859171\pi\) | ||||
−0.903715 | + | 0.428135i | \(0.859171\pi\) | |||||||
\(938\) | −6.23607 | −0.203615 | ||||||||
\(939\) | −34.3607 | −1.12132 | ||||||||
\(940\) | −2.62616 | −0.0856560 | ||||||||
\(941\) | −26.2361 | −0.855271 | −0.427636 | − | 0.903951i | \(-0.640653\pi\) | ||||
−0.427636 | + | 0.903951i | \(0.640653\pi\) | |||||||
\(942\) | −5.14590 | −0.167662 | ||||||||
\(943\) | 41.5066 | 1.35164 | ||||||||
\(944\) | 16.0132 | 0.521184 | ||||||||
\(945\) | 11.7082 | 0.380868 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3607 | 0.824111 | 0.412056 | − | 0.911159i | \(-0.364811\pi\) | ||||
0.412056 | + | 0.911159i | \(0.364811\pi\) | |||||||
\(948\) | −6.70820 | −0.217872 | ||||||||
\(949\) | 2.56231 | 0.0831760 | ||||||||
\(950\) | −1.63932 | −0.0531866 | ||||||||
\(951\) | −87.1935 | −2.82744 | ||||||||
\(952\) | −37.9787 | −1.23090 | ||||||||
\(953\) | −38.8885 | −1.25972 | −0.629862 | − | 0.776707i | \(-0.716888\pi\) | ||||
−0.629862 | + | 0.776707i | \(0.716888\pi\) | |||||||
\(954\) | 2.03444 | 0.0658675 | ||||||||
\(955\) | −17.9574 | −0.581089 | ||||||||
\(956\) | 15.3738 | 0.497225 | ||||||||
\(957\) | 28.4164 | 0.918572 | ||||||||
\(958\) | 5.27864 | 0.170545 | ||||||||
\(959\) | −15.7082 | −0.507244 | ||||||||
\(960\) | 15.2361 | 0.491742 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 2.56231 | 0.0826121 | ||||||||
\(963\) | 29.0132 | 0.934936 | ||||||||
\(964\) | −7.91796 | −0.255020 | ||||||||
\(965\) | 3.34752 | 0.107761 | ||||||||
\(966\) | −18.5623 | −0.597232 | ||||||||
\(967\) | 38.1033 | 1.22532 | 0.612660 | − | 0.790346i | \(-0.290099\pi\) | ||||
0.612660 | + | 0.790346i | \(0.290099\pi\) | |||||||
\(968\) | 3.07701 | 0.0988990 | ||||||||
\(969\) | 19.7082 | 0.633119 | ||||||||
\(970\) | 4.36068 | 0.140013 | ||||||||
\(971\) | −17.3607 | −0.557131 | −0.278565 | − | 0.960417i | \(-0.589859\pi\) | ||||
−0.278565 | + | 0.960417i | \(0.589859\pi\) | |||||||
\(972\) | −40.1459 | −1.28768 | ||||||||
\(973\) | 22.4164 | 0.718637 | ||||||||
\(974\) | −0.506578 | −0.0162318 | ||||||||
\(975\) | 12.5623 | 0.402316 | ||||||||
\(976\) | 8.97871 | 0.287402 | ||||||||
\(977\) | 41.2361 | 1.31926 | 0.659629 | − | 0.751591i | \(-0.270713\pi\) | ||||
0.659629 | + | 0.751591i | \(0.270713\pi\) | |||||||
\(978\) | 14.0000 | 0.447671 | ||||||||
\(979\) | 6.70820 | 0.214395 | ||||||||
\(980\) | −25.0820 | −0.801216 | ||||||||
\(981\) | −53.3951 | −1.70478 | ||||||||
\(982\) | −8.27051 | −0.263923 | ||||||||
\(983\) | −10.4721 | −0.334009 | −0.167005 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(984\) | −36.5066 | −1.16379 | ||||||||
\(985\) | −3.63932 | −0.115958 | ||||||||
\(986\) | −6.97871 | −0.222248 | ||||||||
\(987\) | 12.7082 | 0.404507 | ||||||||
\(988\) | 3.16718 | 0.100762 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.58359 | 0.209240 | ||||||||
\(991\) | −10.8197 | −0.343698 | −0.171849 | − | 0.985123i | \(-0.554974\pi\) | ||||
−0.171849 | + | 0.985123i | \(0.554974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.3262 | 0.454629 | ||||||||
\(994\) | −17.4721 | −0.554183 | ||||||||
\(995\) | 2.40325 | 0.0761882 | ||||||||
\(996\) | 77.8328 | 2.46623 | ||||||||
\(997\) | −19.4508 | −0.616015 | −0.308007 | − | 0.951384i | \(-0.599662\pi\) | ||||
−0.308007 | + | 0.951384i | \(0.599662\pi\) | |||||||
\(998\) | −5.29180 | −0.167509 | ||||||||
\(999\) | 10.8541 | 0.343409 |
(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 | 1849.2.a.e.1.2 | 2 | ||
43.6 | even | 3 | 43.2.c.b.36.2 | yes | 4 | ||
43.36 | even | 3 | 43.2.c.b.6.2 | ✓ | 4 | ||
43.42 | odd | 2 | 1849.2.a.h.1.1 | 2 | |||
129.92 | odd | 6 | 387.2.h.d.208.1 | 4 | |||
129.122 | odd | 6 | 387.2.h.d.307.1 | 4 | |||
172.79 | odd | 6 | 688.2.i.e.49.1 | 4 | |||
172.135 | odd | 6 | 688.2.i.e.337.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.c.b.6.2 | ✓ | 4 | 43.36 | even | 3 | ||
43.2.c.b.36.2 | yes | 4 | 43.6 | even | 3 | ||
387.2.h.d.208.1 | 4 | 129.92 | odd | 6 | |||
387.2.h.d.307.1 | 4 | 129.122 | odd | 6 | |||
688.2.i.e.49.1 | 4 | 172.79 | odd | 6 | |||
688.2.i.e.337.1 | 4 | 172.135 | odd | 6 | |||
1849.2.a.e.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1849.2.a.h.1.1 | 2 | 43.42 | odd | 2 |