Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(3.85677441763\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −2.61803 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.23607 | −1.33956 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | −6.85410 | −1.90099 | −0.950493 | − | 0.310746i | \(-0.899421\pi\) | ||||
−0.950493 | + | 0.310746i | \(0.899421\pi\) | |||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | 2.61803 | 0.675973 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 3.47214 | 0.842117 | 0.421058 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421058 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(18\) | 1.61803 | 0.381374 | ||||||||
\(19\) | −3.76393 | −0.863505 | −0.431753 | − | 0.901992i | \(-0.642105\pi\) | ||||
−0.431753 | + | 0.901992i | \(0.642105\pi\) | |||||||
\(20\) | −1.61803 | −0.361803 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.61803 | −0.771367 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | −11.0902 | −2.17496 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.618034 | 0.116797 | ||||||||
\(29\) | 10.7082 | 1.98846 | 0.994232 | − | 0.107253i | \(-0.0342054\pi\) | ||||
0.994232 | + | 0.107253i | \(0.0342054\pi\) | |||||||
\(30\) | 4.23607 | 0.773397 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 5.61803 | 0.963485 | ||||||||
\(35\) | −2.61803 | −0.442529 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −9.47214 | −1.55721 | −0.778605 | − | 0.627515i | \(-0.784072\pi\) | ||||
−0.778605 | + | 0.627515i | \(0.784072\pi\) | |||||||
\(38\) | −6.09017 | −0.987956 | ||||||||
\(39\) | 6.85410 | 1.09753 | ||||||||
\(40\) | 5.85410 | 0.925615 | ||||||||
\(41\) | −4.70820 | −0.735298 | −0.367649 | − | 0.929965i | \(-0.619837\pi\) | ||||
−0.367649 | + | 0.929965i | \(0.619837\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | 7.32624 | 1.11724 | 0.558620 | − | 0.829423i | \(-0.311331\pi\) | ||||
0.558620 | + | 0.829423i | \(0.311331\pi\) | |||||||
\(44\) | −1.38197 | −0.208339 | ||||||||
\(45\) | −2.61803 | −0.390273 | ||||||||
\(46\) | 1.61803 | 0.238566 | ||||||||
\(47\) | 0.763932 | 0.111431 | 0.0557155 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557155 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(48\) | 4.85410 | 0.700629 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | −3.47214 | −0.486196 | ||||||||
\(52\) | −4.23607 | −0.587437 | ||||||||
\(53\) | −1.38197 | −0.189828 | −0.0949138 | − | 0.995485i | \(-0.530258\pi\) | ||||
−0.0949138 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 5.85410 | 0.789367 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 3.76393 | 0.498545 | ||||||||
\(58\) | 17.3262 | 2.27505 | ||||||||
\(59\) | 1.85410 | 0.241384 | 0.120692 | − | 0.992690i | \(-0.461489\pi\) | ||||
0.120692 | + | 0.992690i | \(0.461489\pi\) | |||||||
\(60\) | 1.61803 | 0.208887 | ||||||||
\(61\) | 2.09017 | 0.267619 | 0.133809 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133809 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(62\) | −8.09017 | −1.02745 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 17.9443 | 2.22571 | ||||||||
\(66\) | 3.61803 | 0.445349 | ||||||||
\(67\) | −0.145898 | −0.0178243 | −0.00891214 | − | 0.999960i | \(-0.502837\pi\) | ||||
−0.00891214 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(68\) | 2.14590 | 0.260228 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −4.23607 | −0.506307 | ||||||||
\(71\) | 11.6180 | 1.37881 | 0.689403 | − | 0.724378i | \(-0.257873\pi\) | ||||
0.689403 | + | 0.724378i | \(0.257873\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | 5.47214 | 0.640465 | 0.320233 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320233 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(74\) | −15.3262 | −1.78164 | ||||||||
\(75\) | −1.85410 | −0.214093 | ||||||||
\(76\) | −2.32624 | −0.266838 | ||||||||
\(77\) | −2.23607 | −0.254824 | ||||||||
\(78\) | 11.0902 | 1.25571 | ||||||||
\(79\) | −11.9443 | −1.34384 | −0.671918 | − | 0.740626i | \(-0.734529\pi\) | ||||
−0.671918 | + | 0.740626i | \(0.734529\pi\) | |||||||
\(80\) | 12.7082 | 1.42082 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.61803 | −0.841271 | ||||||||
\(83\) | −9.94427 | −1.09153 | −0.545763 | − | 0.837940i | \(-0.683760\pi\) | ||||
−0.545763 | + | 0.837940i | \(0.683760\pi\) | |||||||
\(84\) | −0.618034 | −0.0674330 | ||||||||
\(85\) | −9.09017 | −0.985967 | ||||||||
\(86\) | 11.8541 | 1.27826 | ||||||||
\(87\) | −10.7082 | −1.14804 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | −0.673762 | −0.0714186 | −0.0357093 | − | 0.999362i | \(-0.511369\pi\) | ||||
−0.0357093 | + | 0.999362i | \(0.511369\pi\) | |||||||
\(90\) | −4.23607 | −0.446521 | ||||||||
\(91\) | −6.85410 | −0.718505 | ||||||||
\(92\) | 0.618034 | 0.0644345 | ||||||||
\(93\) | 5.00000 | 0.518476 | ||||||||
\(94\) | 1.23607 | 0.127491 | ||||||||
\(95\) | 9.85410 | 1.01101 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | 5.18034 | 0.525984 | 0.262992 | − | 0.964798i | \(-0.415291\pi\) | ||||
0.262992 | + | 0.964798i | \(0.415291\pi\) | |||||||
\(98\) | 1.61803 | 0.163446 | ||||||||
\(99\) | −2.23607 | −0.224733 | ||||||||
\(100\) | 1.14590 | 0.114590 | ||||||||
\(101\) | −4.90983 | −0.488546 | −0.244273 | − | 0.969706i | \(-0.578549\pi\) | ||||
−0.244273 | + | 0.969706i | \(0.578549\pi\) | |||||||
\(102\) | −5.61803 | −0.556268 | ||||||||
\(103\) | −6.47214 | −0.637719 | −0.318859 | − | 0.947802i | \(-0.603300\pi\) | ||||
−0.318859 | + | 0.947802i | \(0.603300\pi\) | |||||||
\(104\) | 15.3262 | 1.50286 | ||||||||
\(105\) | 2.61803 | 0.255494 | ||||||||
\(106\) | −2.23607 | −0.217186 | ||||||||
\(107\) | −0.854102 | −0.0825692 | −0.0412846 | − | 0.999147i | \(-0.513145\pi\) | ||||
−0.0412846 | + | 0.999147i | \(0.513145\pi\) | |||||||
\(108\) | −0.618034 | −0.0594703 | ||||||||
\(109\) | −14.0344 | −1.34426 | −0.672128 | − | 0.740435i | \(-0.734619\pi\) | ||||
−0.672128 | + | 0.740435i | \(0.734619\pi\) | |||||||
\(110\) | 9.47214 | 0.903133 | ||||||||
\(111\) | 9.47214 | 0.899055 | ||||||||
\(112\) | −4.85410 | −0.458670 | ||||||||
\(113\) | −7.09017 | −0.666987 | −0.333494 | − | 0.942752i | \(-0.608228\pi\) | ||||
−0.333494 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(114\) | 6.09017 | 0.570397 | ||||||||
\(115\) | −2.61803 | −0.244133 | ||||||||
\(116\) | 6.61803 | 0.614469 | ||||||||
\(117\) | −6.85410 | −0.633662 | ||||||||
\(118\) | 3.00000 | 0.276172 | ||||||||
\(119\) | 3.47214 | 0.318290 | ||||||||
\(120\) | −5.85410 | −0.534404 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 3.38197 | 0.306189 | ||||||||
\(123\) | 4.70820 | 0.424524 | ||||||||
\(124\) | −3.09017 | −0.277505 | ||||||||
\(125\) | 8.23607 | 0.736656 | ||||||||
\(126\) | 1.61803 | 0.144146 | ||||||||
\(127\) | −2.67376 | −0.237258 | −0.118629 | − | 0.992939i | \(-0.537850\pi\) | ||||
−0.118629 | + | 0.992939i | \(0.537850\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | −7.32624 | −0.645039 | ||||||||
\(130\) | 29.0344 | 2.54649 | ||||||||
\(131\) | −12.4164 | −1.08483 | −0.542413 | − | 0.840112i | \(-0.682489\pi\) | ||||
−0.542413 | + | 0.840112i | \(0.682489\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | −3.76393 | −0.326374 | ||||||||
\(134\) | −0.236068 | −0.0203932 | ||||||||
\(135\) | 2.61803 | 0.225324 | ||||||||
\(136\) | −7.76393 | −0.665752 | ||||||||
\(137\) | −19.9443 | −1.70395 | −0.851977 | − | 0.523579i | \(-0.824596\pi\) | ||||
−0.851977 | + | 0.523579i | \(0.824596\pi\) | |||||||
\(138\) | −1.61803 | −0.137736 | ||||||||
\(139\) | 19.8541 | 1.68400 | 0.842001 | − | 0.539475i | \(-0.181377\pi\) | ||||
0.842001 | + | 0.539475i | \(0.181377\pi\) | |||||||
\(140\) | −1.61803 | −0.136749 | ||||||||
\(141\) | −0.763932 | −0.0643347 | ||||||||
\(142\) | 18.7984 | 1.57752 | ||||||||
\(143\) | 15.3262 | 1.28164 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | −28.0344 | −2.32813 | ||||||||
\(146\) | 8.85410 | 0.732771 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −5.85410 | −0.481204 | ||||||||
\(149\) | −14.6525 | −1.20038 | −0.600189 | − | 0.799858i | \(-0.704908\pi\) | ||||
−0.600189 | + | 0.799858i | \(0.704908\pi\) | |||||||
\(150\) | −3.00000 | −0.244949 | ||||||||
\(151\) | −1.70820 | −0.139012 | −0.0695058 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695058 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(152\) | 8.41641 | 0.682661 | ||||||||
\(153\) | 3.47214 | 0.280706 | ||||||||
\(154\) | −3.61803 | −0.291549 | ||||||||
\(155\) | 13.0902 | 1.05143 | ||||||||
\(156\) | 4.23607 | 0.339157 | ||||||||
\(157\) | −14.1803 | −1.13171 | −0.565857 | − | 0.824503i | \(-0.691455\pi\) | ||||
−0.565857 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(158\) | −19.3262 | −1.53751 | ||||||||
\(159\) | 1.38197 | 0.109597 | ||||||||
\(160\) | 8.85410 | 0.699978 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 1.61803 | 0.127125 | ||||||||
\(163\) | −22.5066 | −1.76285 | −0.881426 | − | 0.472323i | \(-0.843416\pi\) | ||||
−0.881426 | + | 0.472323i | \(0.843416\pi\) | |||||||
\(164\) | −2.90983 | −0.227220 | ||||||||
\(165\) | −5.85410 | −0.455741 | ||||||||
\(166\) | −16.0902 | −1.24884 | ||||||||
\(167\) | 11.4721 | 0.887741 | 0.443870 | − | 0.896091i | \(-0.353605\pi\) | ||||
0.443870 | + | 0.896091i | \(0.353605\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | 33.9787 | 2.61375 | ||||||||
\(170\) | −14.7082 | −1.12807 | ||||||||
\(171\) | −3.76393 | −0.287835 | ||||||||
\(172\) | 4.52786 | 0.345246 | ||||||||
\(173\) | −11.2918 | −0.858499 | −0.429250 | − | 0.903186i | \(-0.641222\pi\) | ||||
−0.429250 | + | 0.903186i | \(0.641222\pi\) | |||||||
\(174\) | −17.3262 | −1.31350 | ||||||||
\(175\) | 1.85410 | 0.140157 | ||||||||
\(176\) | 10.8541 | 0.818159 | ||||||||
\(177\) | −1.85410 | −0.139363 | ||||||||
\(178\) | −1.09017 | −0.0817117 | ||||||||
\(179\) | 20.0344 | 1.49744 | 0.748722 | − | 0.662884i | \(-0.230668\pi\) | ||||
0.748722 | + | 0.662884i | \(0.230668\pi\) | |||||||
\(180\) | −1.61803 | −0.120601 | ||||||||
\(181\) | −15.1803 | −1.12835 | −0.564173 | − | 0.825657i | \(-0.690805\pi\) | ||||
−0.564173 | + | 0.825657i | \(0.690805\pi\) | |||||||
\(182\) | −11.0902 | −0.822058 | ||||||||
\(183\) | −2.09017 | −0.154510 | ||||||||
\(184\) | −2.23607 | −0.164845 | ||||||||
\(185\) | 24.7984 | 1.82321 | ||||||||
\(186\) | 8.09017 | 0.593200 | ||||||||
\(187\) | −7.76393 | −0.567755 | ||||||||
\(188\) | 0.472136 | 0.0344341 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 15.9443 | 1.15672 | ||||||||
\(191\) | 21.7082 | 1.57075 | 0.785375 | − | 0.619020i | \(-0.212470\pi\) | ||||
0.785375 | + | 0.619020i | \(0.212470\pi\) | |||||||
\(192\) | −4.23607 | −0.305712 | ||||||||
\(193\) | −18.1803 | −1.30865 | −0.654325 | − | 0.756214i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756214i | \(0.727047\pi\) | |||||||
\(194\) | 8.38197 | 0.601790 | ||||||||
\(195\) | −17.9443 | −1.28502 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | −25.3262 | −1.80442 | −0.902210 | − | 0.431297i | \(-0.858056\pi\) | ||||
−0.902210 | + | 0.431297i | \(0.858056\pi\) | |||||||
\(198\) | −3.61803 | −0.257122 | ||||||||
\(199\) | −9.56231 | −0.677854 | −0.338927 | − | 0.940813i | \(-0.610064\pi\) | ||||
−0.338927 | + | 0.940813i | \(0.610064\pi\) | |||||||
\(200\) | −4.14590 | −0.293159 | ||||||||
\(201\) | 0.145898 | 0.0102909 | ||||||||
\(202\) | −7.94427 | −0.558957 | ||||||||
\(203\) | 10.7082 | 0.751569 | ||||||||
\(204\) | −2.14590 | −0.150243 | ||||||||
\(205\) | 12.3262 | 0.860902 | ||||||||
\(206\) | −10.4721 | −0.729628 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 33.2705 | 2.30689 | ||||||||
\(209\) | 8.41641 | 0.582175 | ||||||||
\(210\) | 4.23607 | 0.292316 | ||||||||
\(211\) | 15.0000 | 1.03264 | 0.516321 | − | 0.856395i | \(-0.327301\pi\) | ||||
0.516321 | + | 0.856395i | \(0.327301\pi\) | |||||||
\(212\) | −0.854102 | −0.0586600 | ||||||||
\(213\) | −11.6180 | −0.796055 | ||||||||
\(214\) | −1.38197 | −0.0944693 | ||||||||
\(215\) | −19.1803 | −1.30809 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −5.00000 | −0.339422 | ||||||||
\(218\) | −22.7082 | −1.53799 | ||||||||
\(219\) | −5.47214 | −0.369773 | ||||||||
\(220\) | 3.61803 | 0.243928 | ||||||||
\(221\) | −23.7984 | −1.60085 | ||||||||
\(222\) | 15.3262 | 1.02863 | ||||||||
\(223\) | 18.3262 | 1.22722 | 0.613608 | − | 0.789611i | \(-0.289718\pi\) | ||||
0.613608 | + | 0.789611i | \(0.289718\pi\) | |||||||
\(224\) | −3.38197 | −0.225967 | ||||||||
\(225\) | 1.85410 | 0.123607 | ||||||||
\(226\) | −11.4721 | −0.763115 | ||||||||
\(227\) | 15.2705 | 1.01354 | 0.506770 | − | 0.862081i | \(-0.330839\pi\) | ||||
0.506770 | + | 0.862081i | \(0.330839\pi\) | |||||||
\(228\) | 2.32624 | 0.154059 | ||||||||
\(229\) | −5.67376 | −0.374933 | −0.187466 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187466 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(230\) | −4.23607 | −0.279318 | ||||||||
\(231\) | 2.23607 | 0.147122 | ||||||||
\(232\) | −23.9443 | −1.57202 | ||||||||
\(233\) | 7.09017 | 0.464492 | 0.232246 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232246 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(234\) | −11.0902 | −0.724987 | ||||||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 1.14590 | 0.0745916 | ||||||||
\(237\) | 11.9443 | 0.775864 | ||||||||
\(238\) | 5.61803 | 0.364163 | ||||||||
\(239\) | −6.61803 | −0.428085 | −0.214043 | − | 0.976824i | \(-0.568663\pi\) | ||||
−0.214043 | + | 0.976824i | \(0.568663\pi\) | |||||||
\(240\) | −12.7082 | −0.820311 | ||||||||
\(241\) | 28.7082 | 1.84926 | 0.924629 | − | 0.380869i | \(-0.124375\pi\) | ||||
0.924629 | + | 0.380869i | \(0.124375\pi\) | |||||||
\(242\) | −9.70820 | −0.624067 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.29180 | 0.0826988 | ||||||||
\(245\) | −2.61803 | −0.167260 | ||||||||
\(246\) | 7.61803 | 0.485708 | ||||||||
\(247\) | 25.7984 | 1.64151 | ||||||||
\(248\) | 11.1803 | 0.709952 | ||||||||
\(249\) | 9.94427 | 0.630193 | ||||||||
\(250\) | 13.3262 | 0.842825 | ||||||||
\(251\) | −12.2918 | −0.775851 | −0.387926 | − | 0.921691i | \(-0.626808\pi\) | ||||
−0.387926 | + | 0.921691i | \(0.626808\pi\) | |||||||
\(252\) | 0.618034 | 0.0389325 | ||||||||
\(253\) | −2.23607 | −0.140580 | ||||||||
\(254\) | −4.32624 | −0.271452 | ||||||||
\(255\) | 9.09017 | 0.569249 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 29.7082 | 1.85315 | 0.926573 | − | 0.376114i | \(-0.122740\pi\) | ||||
0.926573 | + | 0.376114i | \(0.122740\pi\) | |||||||
\(258\) | −11.8541 | −0.738004 | ||||||||
\(259\) | −9.47214 | −0.588570 | ||||||||
\(260\) | 11.0902 | 0.687783 | ||||||||
\(261\) | 10.7082 | 0.662821 | ||||||||
\(262\) | −20.0902 | −1.24117 | ||||||||
\(263\) | 5.00000 | 0.308313 | 0.154157 | − | 0.988046i | \(-0.450734\pi\) | ||||
0.154157 | + | 0.988046i | \(0.450734\pi\) | |||||||
\(264\) | −5.00000 | −0.307729 | ||||||||
\(265\) | 3.61803 | 0.222254 | ||||||||
\(266\) | −6.09017 | −0.373412 | ||||||||
\(267\) | 0.673762 | 0.0412336 | ||||||||
\(268\) | −0.0901699 | −0.00550801 | ||||||||
\(269\) | −2.85410 | −0.174018 | −0.0870088 | − | 0.996208i | \(-0.527731\pi\) | ||||
−0.0870088 | + | 0.996208i | \(0.527731\pi\) | |||||||
\(270\) | 4.23607 | 0.257799 | ||||||||
\(271\) | −17.1803 | −1.04363 | −0.521816 | − | 0.853058i | \(-0.674745\pi\) | ||||
−0.521816 | + | 0.853058i | \(0.674745\pi\) | |||||||
\(272\) | −16.8541 | −1.02193 | ||||||||
\(273\) | 6.85410 | 0.414829 | ||||||||
\(274\) | −32.2705 | −1.94953 | ||||||||
\(275\) | −4.14590 | −0.250007 | ||||||||
\(276\) | −0.618034 | −0.0372013 | ||||||||
\(277\) | 21.2148 | 1.27467 | 0.637336 | − | 0.770586i | \(-0.280036\pi\) | ||||
0.637336 | + | 0.770586i | \(0.280036\pi\) | |||||||
\(278\) | 32.1246 | 1.92671 | ||||||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 5.85410 | 0.349850 | ||||||||
\(281\) | −21.5967 | −1.28835 | −0.644177 | − | 0.764876i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764876i | \(0.722800\pi\) | |||||||
\(282\) | −1.23607 | −0.0736068 | ||||||||
\(283\) | 14.3262 | 0.851606 | 0.425803 | − | 0.904816i | \(-0.359992\pi\) | ||||
0.425803 | + | 0.904816i | \(0.359992\pi\) | |||||||
\(284\) | 7.18034 | 0.426075 | ||||||||
\(285\) | −9.85410 | −0.583707 | ||||||||
\(286\) | 24.7984 | 1.46636 | ||||||||
\(287\) | −4.70820 | −0.277916 | ||||||||
\(288\) | −3.38197 | −0.199284 | ||||||||
\(289\) | −4.94427 | −0.290840 | ||||||||
\(290\) | −45.3607 | −2.66367 | ||||||||
\(291\) | −5.18034 | −0.303677 | ||||||||
\(292\) | 3.38197 | 0.197915 | ||||||||
\(293\) | −9.52786 | −0.556624 | −0.278312 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278312 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(294\) | −1.61803 | −0.0943657 | ||||||||
\(295\) | −4.85410 | −0.282617 | ||||||||
\(296\) | 21.1803 | 1.23108 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | −23.7082 | −1.37338 | ||||||||
\(299\) | −6.85410 | −0.396383 | ||||||||
\(300\) | −1.14590 | −0.0661585 | ||||||||
\(301\) | 7.32624 | 0.422277 | ||||||||
\(302\) | −2.76393 | −0.159046 | ||||||||
\(303\) | 4.90983 | 0.282062 | ||||||||
\(304\) | 18.2705 | 1.04789 | ||||||||
\(305\) | −5.47214 | −0.313334 | ||||||||
\(306\) | 5.61803 | 0.321162 | ||||||||
\(307\) | 25.9443 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(308\) | −1.38197 | −0.0787448 | ||||||||
\(309\) | 6.47214 | 0.368187 | ||||||||
\(310\) | 21.1803 | 1.20296 | ||||||||
\(311\) | 7.61803 | 0.431979 | 0.215990 | − | 0.976396i | \(-0.430702\pi\) | ||||
0.215990 | + | 0.976396i | \(0.430702\pi\) | |||||||
\(312\) | −15.3262 | −0.867677 | ||||||||
\(313\) | −1.52786 | −0.0863600 | −0.0431800 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431800 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(314\) | −22.9443 | −1.29482 | ||||||||
\(315\) | −2.61803 | −0.147510 | ||||||||
\(316\) | −7.38197 | −0.415268 | ||||||||
\(317\) | −22.1459 | −1.24384 | −0.621919 | − | 0.783082i | \(-0.713647\pi\) | ||||
−0.621919 | + | 0.783082i | \(0.713647\pi\) | |||||||
\(318\) | 2.23607 | 0.125392 | ||||||||
\(319\) | −23.9443 | −1.34062 | ||||||||
\(320\) | −11.0902 | −0.619959 | ||||||||
\(321\) | 0.854102 | 0.0476713 | ||||||||
\(322\) | 1.61803 | 0.0901695 | ||||||||
\(323\) | −13.0689 | −0.727172 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | −12.7082 | −0.704924 | ||||||||
\(326\) | −36.4164 | −2.01692 | ||||||||
\(327\) | 14.0344 | 0.776106 | ||||||||
\(328\) | 10.5279 | 0.581304 | ||||||||
\(329\) | 0.763932 | 0.0421169 | ||||||||
\(330\) | −9.47214 | −0.521424 | ||||||||
\(331\) | 10.9443 | 0.601552 | 0.300776 | − | 0.953695i | \(-0.402754\pi\) | ||||
0.300776 | + | 0.953695i | \(0.402754\pi\) | |||||||
\(332\) | −6.14590 | −0.337300 | ||||||||
\(333\) | −9.47214 | −0.519070 | ||||||||
\(334\) | 18.5623 | 1.01568 | ||||||||
\(335\) | 0.381966 | 0.0208690 | ||||||||
\(336\) | 4.85410 | 0.264813 | ||||||||
\(337\) | −18.5623 | −1.01115 | −0.505577 | − | 0.862782i | \(-0.668720\pi\) | ||||
−0.505577 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(338\) | 54.9787 | 2.99045 | ||||||||
\(339\) | 7.09017 | 0.385085 | ||||||||
\(340\) | −5.61803 | −0.304681 | ||||||||
\(341\) | 11.1803 | 0.605449 | ||||||||
\(342\) | −6.09017 | −0.329319 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −16.3820 | −0.883256 | ||||||||
\(345\) | 2.61803 | 0.140950 | ||||||||
\(346\) | −18.2705 | −0.982229 | ||||||||
\(347\) | −3.65248 | −0.196075 | −0.0980376 | − | 0.995183i | \(-0.531257\pi\) | ||||
−0.0980376 | + | 0.995183i | \(0.531257\pi\) | |||||||
\(348\) | −6.61803 | −0.354764 | ||||||||
\(349\) | −6.50658 | −0.348289 | −0.174145 | − | 0.984720i | \(-0.555716\pi\) | ||||
−0.174145 | + | 0.984720i | \(0.555716\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 6.85410 | 0.365845 | ||||||||
\(352\) | 7.56231 | 0.403072 | ||||||||
\(353\) | −26.5967 | −1.41560 | −0.707801 | − | 0.706412i | \(-0.750313\pi\) | ||||
−0.707801 | + | 0.706412i | \(0.750313\pi\) | |||||||
\(354\) | −3.00000 | −0.159448 | ||||||||
\(355\) | −30.4164 | −1.61434 | ||||||||
\(356\) | −0.416408 | −0.0220696 | ||||||||
\(357\) | −3.47214 | −0.183765 | ||||||||
\(358\) | 32.4164 | 1.71326 | ||||||||
\(359\) | 22.7984 | 1.20325 | 0.601626 | − | 0.798778i | \(-0.294520\pi\) | ||||
0.601626 | + | 0.798778i | \(0.294520\pi\) | |||||||
\(360\) | 5.85410 | 0.308538 | ||||||||
\(361\) | −4.83282 | −0.254359 | ||||||||
\(362\) | −24.5623 | −1.29097 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | −4.23607 | −0.222030 | ||||||||
\(365\) | −14.3262 | −0.749870 | ||||||||
\(366\) | −3.38197 | −0.176778 | ||||||||
\(367\) | −32.4508 | −1.69392 | −0.846960 | − | 0.531656i | \(-0.821570\pi\) | ||||
−0.846960 | + | 0.531656i | \(0.821570\pi\) | |||||||
\(368\) | −4.85410 | −0.253038 | ||||||||
\(369\) | −4.70820 | −0.245099 | ||||||||
\(370\) | 40.1246 | 2.08598 | ||||||||
\(371\) | −1.38197 | −0.0717481 | ||||||||
\(372\) | 3.09017 | 0.160218 | ||||||||
\(373\) | 2.88854 | 0.149563 | 0.0747816 | − | 0.997200i | \(-0.476174\pi\) | ||||
0.0747816 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(374\) | −12.5623 | −0.649581 | ||||||||
\(375\) | −8.23607 | −0.425309 | ||||||||
\(376\) | −1.70820 | −0.0880939 | ||||||||
\(377\) | −73.3951 | −3.78004 | ||||||||
\(378\) | −1.61803 | −0.0832227 | ||||||||
\(379\) | −20.9443 | −1.07583 | −0.537917 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537917 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(380\) | 6.09017 | 0.312419 | ||||||||
\(381\) | 2.67376 | 0.136981 | ||||||||
\(382\) | 35.1246 | 1.79713 | ||||||||
\(383\) | −4.52786 | −0.231363 | −0.115682 | − | 0.993286i | \(-0.536905\pi\) | ||||
−0.115682 | + | 0.993286i | \(0.536905\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 5.85410 | 0.298353 | ||||||||
\(386\) | −29.4164 | −1.49726 | ||||||||
\(387\) | 7.32624 | 0.372414 | ||||||||
\(388\) | 3.20163 | 0.162538 | ||||||||
\(389\) | 22.1246 | 1.12176 | 0.560881 | − | 0.827896i | \(-0.310462\pi\) | ||||
0.560881 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(390\) | −29.0344 | −1.47022 | ||||||||
\(391\) | 3.47214 | 0.175593 | ||||||||
\(392\) | −2.23607 | −0.112938 | ||||||||
\(393\) | 12.4164 | 0.626325 | ||||||||
\(394\) | −40.9787 | −2.06448 | ||||||||
\(395\) | 31.2705 | 1.57339 | ||||||||
\(396\) | −1.38197 | −0.0694464 | ||||||||
\(397\) | 15.2361 | 0.764676 | 0.382338 | − | 0.924022i | \(-0.375119\pi\) | ||||
0.382338 | + | 0.924022i | \(0.375119\pi\) | |||||||
\(398\) | −15.4721 | −0.775548 | ||||||||
\(399\) | 3.76393 | 0.188432 | ||||||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | 6.81966 | 0.340558 | 0.170279 | − | 0.985396i | \(-0.445533\pi\) | ||||
0.170279 | + | 0.985396i | \(0.445533\pi\) | |||||||
\(402\) | 0.236068 | 0.0117740 | ||||||||
\(403\) | 34.2705 | 1.70714 | ||||||||
\(404\) | −3.03444 | −0.150969 | ||||||||
\(405\) | −2.61803 | −0.130091 | ||||||||
\(406\) | 17.3262 | 0.859887 | ||||||||
\(407\) | 21.1803 | 1.04987 | ||||||||
\(408\) | 7.76393 | 0.384372 | ||||||||
\(409\) | 23.6525 | 1.16954 | 0.584770 | − | 0.811199i | \(-0.301185\pi\) | ||||
0.584770 | + | 0.811199i | \(0.301185\pi\) | |||||||
\(410\) | 19.9443 | 0.984977 | ||||||||
\(411\) | 19.9443 | 0.983778 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 1.85410 | 0.0912344 | ||||||||
\(414\) | 1.61803 | 0.0795220 | ||||||||
\(415\) | 26.0344 | 1.27798 | ||||||||
\(416\) | 23.1803 | 1.13651 | ||||||||
\(417\) | −19.8541 | −0.972260 | ||||||||
\(418\) | 13.6180 | 0.666080 | ||||||||
\(419\) | 19.5623 | 0.955681 | 0.477841 | − | 0.878447i | \(-0.341420\pi\) | ||||
0.477841 | + | 0.878447i | \(0.341420\pi\) | |||||||
\(420\) | 1.61803 | 0.0789520 | ||||||||
\(421\) | 10.6738 | 0.520207 | 0.260104 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(422\) | 24.2705 | 1.18147 | ||||||||
\(423\) | 0.763932 | 0.0371436 | ||||||||
\(424\) | 3.09017 | 0.150072 | ||||||||
\(425\) | 6.43769 | 0.312274 | ||||||||
\(426\) | −18.7984 | −0.910784 | ||||||||
\(427\) | 2.09017 | 0.101150 | ||||||||
\(428\) | −0.527864 | −0.0255153 | ||||||||
\(429\) | −15.3262 | −0.739958 | ||||||||
\(430\) | −31.0344 | −1.49661 | ||||||||
\(431\) | 19.9098 | 0.959023 | 0.479511 | − | 0.877536i | \(-0.340814\pi\) | ||||
0.479511 | + | 0.877536i | \(0.340814\pi\) | |||||||
\(432\) | 4.85410 | 0.233543 | ||||||||
\(433\) | 23.1246 | 1.11130 | 0.555649 | − | 0.831417i | \(-0.312470\pi\) | ||||
0.555649 | + | 0.831417i | \(0.312470\pi\) | |||||||
\(434\) | −8.09017 | −0.388341 | ||||||||
\(435\) | 28.0344 | 1.34415 | ||||||||
\(436\) | −8.67376 | −0.415398 | ||||||||
\(437\) | −3.76393 | −0.180053 | ||||||||
\(438\) | −8.85410 | −0.423065 | ||||||||
\(439\) | −17.9443 | −0.856433 | −0.428217 | − | 0.903676i | \(-0.640858\pi\) | ||||
−0.428217 | + | 0.903676i | \(0.640858\pi\) | |||||||
\(440\) | −13.0902 | −0.624049 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −38.5066 | −1.83157 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 5.85410 | 0.277823 | ||||||||
\(445\) | 1.76393 | 0.0836184 | ||||||||
\(446\) | 29.6525 | 1.40409 | ||||||||
\(447\) | 14.6525 | 0.693038 | ||||||||
\(448\) | 4.23607 | 0.200135 | ||||||||
\(449\) | 12.9098 | 0.609253 | 0.304626 | − | 0.952472i | \(-0.401468\pi\) | ||||
0.304626 | + | 0.952472i | \(0.401468\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | 10.5279 | 0.495738 | ||||||||
\(452\) | −4.38197 | −0.206110 | ||||||||
\(453\) | 1.70820 | 0.0802584 | ||||||||
\(454\) | 24.7082 | 1.15961 | ||||||||
\(455\) | 17.9443 | 0.841240 | ||||||||
\(456\) | −8.41641 | −0.394134 | ||||||||
\(457\) | −32.7984 | −1.53424 | −0.767122 | − | 0.641502i | \(-0.778312\pi\) | ||||
−0.767122 | + | 0.641502i | \(0.778312\pi\) | |||||||
\(458\) | −9.18034 | −0.428969 | ||||||||
\(459\) | −3.47214 | −0.162065 | ||||||||
\(460\) | −1.61803 | −0.0754412 | ||||||||
\(461\) | 6.14590 | 0.286243 | 0.143122 | − | 0.989705i | \(-0.454286\pi\) | ||||
0.143122 | + | 0.989705i | \(0.454286\pi\) | |||||||
\(462\) | 3.61803 | 0.168326 | ||||||||
\(463\) | 14.5967 | 0.678368 | 0.339184 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339184 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(464\) | −51.9787 | −2.41305 | ||||||||
\(465\) | −13.0902 | −0.607042 | ||||||||
\(466\) | 11.4721 | 0.531436 | ||||||||
\(467\) | 18.8885 | 0.874058 | 0.437029 | − | 0.899448i | \(-0.356031\pi\) | ||||
0.437029 | + | 0.899448i | \(0.356031\pi\) | |||||||
\(468\) | −4.23607 | −0.195812 | ||||||||
\(469\) | −0.145898 | −0.00673695 | ||||||||
\(470\) | −3.23607 | −0.149269 | ||||||||
\(471\) | 14.1803 | 0.653396 | ||||||||
\(472\) | −4.14590 | −0.190830 | ||||||||
\(473\) | −16.3820 | −0.753244 | ||||||||
\(474\) | 19.3262 | 0.887684 | ||||||||
\(475\) | −6.97871 | −0.320205 | ||||||||
\(476\) | 2.14590 | 0.0983571 | ||||||||
\(477\) | −1.38197 | −0.0632759 | ||||||||
\(478\) | −10.7082 | −0.489782 | ||||||||
\(479\) | −5.65248 | −0.258268 | −0.129134 | − | 0.991627i | \(-0.541220\pi\) | ||||
−0.129134 | + | 0.991627i | \(0.541220\pi\) | |||||||
\(480\) | −8.85410 | −0.404133 | ||||||||
\(481\) | 64.9230 | 2.96023 | ||||||||
\(482\) | 46.4508 | 2.11578 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −3.70820 | −0.168555 | ||||||||
\(485\) | −13.5623 | −0.615833 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | 17.7639 | 0.804961 | 0.402480 | − | 0.915429i | \(-0.368148\pi\) | ||||
0.402480 | + | 0.915429i | \(0.368148\pi\) | |||||||
\(488\) | −4.67376 | −0.211571 | ||||||||
\(489\) | 22.5066 | 1.01778 | ||||||||
\(490\) | −4.23607 | −0.191366 | ||||||||
\(491\) | 28.0902 | 1.26769 | 0.633846 | − | 0.773459i | \(-0.281475\pi\) | ||||
0.633846 | + | 0.773459i | \(0.281475\pi\) | |||||||
\(492\) | 2.90983 | 0.131185 | ||||||||
\(493\) | 37.1803 | 1.67452 | ||||||||
\(494\) | 41.7426 | 1.87809 | ||||||||
\(495\) | 5.85410 | 0.263122 | ||||||||
\(496\) | 24.2705 | 1.08978 | ||||||||
\(497\) | 11.6180 | 0.521140 | ||||||||
\(498\) | 16.0902 | 0.721018 | ||||||||
\(499\) | 12.7984 | 0.572934 | 0.286467 | − | 0.958090i | \(-0.407519\pi\) | ||||
0.286467 | + | 0.958090i | \(0.407519\pi\) | |||||||
\(500\) | 5.09017 | 0.227639 | ||||||||
\(501\) | −11.4721 | −0.512537 | ||||||||
\(502\) | −19.8885 | −0.887669 | ||||||||
\(503\) | −21.0902 | −0.940364 | −0.470182 | − | 0.882569i | \(-0.655812\pi\) | ||||
−0.470182 | + | 0.882569i | \(0.655812\pi\) | |||||||
\(504\) | −2.23607 | −0.0996024 | ||||||||
\(505\) | 12.8541 | 0.572000 | ||||||||
\(506\) | −3.61803 | −0.160841 | ||||||||
\(507\) | −33.9787 | −1.50905 | ||||||||
\(508\) | −1.65248 | −0.0733168 | ||||||||
\(509\) | 25.7082 | 1.13950 | 0.569748 | − | 0.821819i | \(-0.307041\pi\) | ||||
0.569748 | + | 0.821819i | \(0.307041\pi\) | |||||||
\(510\) | 14.7082 | 0.651290 | ||||||||
\(511\) | 5.47214 | 0.242073 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 3.76393 | 0.166182 | ||||||||
\(514\) | 48.0689 | 2.12023 | ||||||||
\(515\) | 16.9443 | 0.746654 | ||||||||
\(516\) | −4.52786 | −0.199328 | ||||||||
\(517\) | −1.70820 | −0.0751267 | ||||||||
\(518\) | −15.3262 | −0.673396 | ||||||||
\(519\) | 11.2918 | 0.495655 | ||||||||
\(520\) | −40.1246 | −1.75958 | ||||||||
\(521\) | −3.52786 | −0.154559 | −0.0772793 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772793 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(522\) | 17.3262 | 0.758349 | ||||||||
\(523\) | 32.8328 | 1.43568 | 0.717839 | − | 0.696209i | \(-0.245131\pi\) | ||||
0.717839 | + | 0.696209i | \(0.245131\pi\) | |||||||
\(524\) | −7.67376 | −0.335230 | ||||||||
\(525\) | −1.85410 | −0.0809196 | ||||||||
\(526\) | 8.09017 | 0.352748 | ||||||||
\(527\) | −17.3607 | −0.756243 | ||||||||
\(528\) | −10.8541 | −0.472364 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.85410 | 0.254286 | ||||||||
\(531\) | 1.85410 | 0.0804612 | ||||||||
\(532\) | −2.32624 | −0.100855 | ||||||||
\(533\) | 32.2705 | 1.39779 | ||||||||
\(534\) | 1.09017 | 0.0471763 | ||||||||
\(535\) | 2.23607 | 0.0966736 | ||||||||
\(536\) | 0.326238 | 0.0140913 | ||||||||
\(537\) | −20.0344 | −0.864550 | ||||||||
\(538\) | −4.61803 | −0.199098 | ||||||||
\(539\) | −2.23607 | −0.0963143 | ||||||||
\(540\) | 1.61803 | 0.0696291 | ||||||||
\(541\) | −23.2361 | −0.998997 | −0.499498 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499498 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(542\) | −27.7984 | −1.19404 | ||||||||
\(543\) | 15.1803 | 0.651451 | ||||||||
\(544\) | −11.7426 | −0.503462 | ||||||||
\(545\) | 36.7426 | 1.57388 | ||||||||
\(546\) | 11.0902 | 0.474615 | ||||||||
\(547\) | −26.6180 | −1.13810 | −0.569052 | − | 0.822301i | \(-0.692690\pi\) | ||||
−0.569052 | + | 0.822301i | \(0.692690\pi\) | |||||||
\(548\) | −12.3262 | −0.526551 | ||||||||
\(549\) | 2.09017 | 0.0892063 | ||||||||
\(550\) | −6.70820 | −0.286039 | ||||||||
\(551\) | −40.3050 | −1.71705 | ||||||||
\(552\) | 2.23607 | 0.0951734 | ||||||||
\(553\) | −11.9443 | −0.507922 | ||||||||
\(554\) | 34.3262 | 1.45838 | ||||||||
\(555\) | −24.7984 | −1.05263 | ||||||||
\(556\) | 12.2705 | 0.520386 | ||||||||
\(557\) | −17.2361 | −0.730316 | −0.365158 | − | 0.930946i | \(-0.618985\pi\) | ||||
−0.365158 | + | 0.930946i | \(0.618985\pi\) | |||||||
\(558\) | −8.09017 | −0.342484 | ||||||||
\(559\) | −50.2148 | −2.12386 | ||||||||
\(560\) | 12.7082 | 0.537020 | ||||||||
\(561\) | 7.76393 | 0.327793 | ||||||||
\(562\) | −34.9443 | −1.47404 | ||||||||
\(563\) | 8.56231 | 0.360858 | 0.180429 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180429 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(564\) | −0.472136 | −0.0198805 | ||||||||
\(565\) | 18.5623 | 0.780922 | ||||||||
\(566\) | 23.1803 | 0.974342 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −25.9787 | −1.09004 | ||||||||
\(569\) | 27.7771 | 1.16448 | 0.582238 | − | 0.813018i | \(-0.302177\pi\) | ||||
0.582238 | + | 0.813018i | \(0.302177\pi\) | |||||||
\(570\) | −15.9443 | −0.667832 | ||||||||
\(571\) | −44.7771 | −1.87386 | −0.936931 | − | 0.349513i | \(-0.886347\pi\) | ||||
−0.936931 | + | 0.349513i | \(0.886347\pi\) | |||||||
\(572\) | 9.47214 | 0.396050 | ||||||||
\(573\) | −21.7082 | −0.906873 | ||||||||
\(574\) | −7.61803 | −0.317971 | ||||||||
\(575\) | 1.85410 | 0.0773214 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −17.4164 | −0.725055 | −0.362527 | − | 0.931973i | \(-0.618086\pi\) | ||||
−0.362527 | + | 0.931973i | \(0.618086\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 18.1803 | 0.755549 | ||||||||
\(580\) | −17.3262 | −0.719433 | ||||||||
\(581\) | −9.94427 | −0.412558 | ||||||||
\(582\) | −8.38197 | −0.347444 | ||||||||
\(583\) | 3.09017 | 0.127982 | ||||||||
\(584\) | −12.2361 | −0.506332 | ||||||||
\(585\) | 17.9443 | 0.741904 | ||||||||
\(586\) | −15.4164 | −0.636846 | ||||||||
\(587\) | 2.56231 | 0.105758 | 0.0528788 | − | 0.998601i | \(-0.483160\pi\) | ||||
0.0528788 | + | 0.998601i | \(0.483160\pi\) | |||||||
\(588\) | −0.618034 | −0.0254873 | ||||||||
\(589\) | 18.8197 | 0.775451 | ||||||||
\(590\) | −7.85410 | −0.323348 | ||||||||
\(591\) | 25.3262 | 1.04178 | ||||||||
\(592\) | 45.9787 | 1.88971 | ||||||||
\(593\) | −24.2918 | −0.997545 | −0.498772 | − | 0.866733i | \(-0.666216\pi\) | ||||
−0.498772 | + | 0.866733i | \(0.666216\pi\) | |||||||
\(594\) | 3.61803 | 0.148450 | ||||||||
\(595\) | −9.09017 | −0.372661 | ||||||||
\(596\) | −9.05573 | −0.370937 | ||||||||
\(597\) | 9.56231 | 0.391359 | ||||||||
\(598\) | −11.0902 | −0.453511 | ||||||||
\(599\) | 7.72949 | 0.315818 | 0.157909 | − | 0.987454i | \(-0.449525\pi\) | ||||
0.157909 | + | 0.987454i | \(0.449525\pi\) | |||||||
\(600\) | 4.14590 | 0.169256 | ||||||||
\(601\) | 12.5066 | 0.510154 | 0.255077 | − | 0.966921i | \(-0.417899\pi\) | ||||
0.255077 | + | 0.966921i | \(0.417899\pi\) | |||||||
\(602\) | 11.8541 | 0.483137 | ||||||||
\(603\) | −0.145898 | −0.00594143 | ||||||||
\(604\) | −1.05573 | −0.0429570 | ||||||||
\(605\) | 15.7082 | 0.638629 | ||||||||
\(606\) | 7.94427 | 0.322714 | ||||||||
\(607\) | −8.38197 | −0.340214 | −0.170107 | − | 0.985426i | \(-0.554411\pi\) | ||||
−0.170107 | + | 0.985426i | \(0.554411\pi\) | |||||||
\(608\) | 12.7295 | 0.516249 | ||||||||
\(609\) | −10.7082 | −0.433918 | ||||||||
\(610\) | −8.85410 | −0.358492 | ||||||||
\(611\) | −5.23607 | −0.211829 | ||||||||
\(612\) | 2.14590 | 0.0867428 | ||||||||
\(613\) | −6.34752 | −0.256374 | −0.128187 | − | 0.991750i | \(-0.540916\pi\) | ||||
−0.128187 | + | 0.991750i | \(0.540916\pi\) | |||||||
\(614\) | 41.9787 | 1.69412 | ||||||||
\(615\) | −12.3262 | −0.497042 | ||||||||
\(616\) | 5.00000 | 0.201456 | ||||||||
\(617\) | −4.74265 | −0.190932 | −0.0954659 | − | 0.995433i | \(-0.530434\pi\) | ||||
−0.0954659 | + | 0.995433i | \(0.530434\pi\) | |||||||
\(618\) | 10.4721 | 0.421251 | ||||||||
\(619\) | 0.270510 | 0.0108727 | 0.00543635 | − | 0.999985i | \(-0.498270\pi\) | ||||
0.00543635 | + | 0.999985i | \(0.498270\pi\) | |||||||
\(620\) | 8.09017 | 0.324909 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 12.3262 | 0.494237 | ||||||||
\(623\) | −0.673762 | −0.0269937 | ||||||||
\(624\) | −33.2705 | −1.33189 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | −2.47214 | −0.0988064 | ||||||||
\(627\) | −8.41641 | −0.336119 | ||||||||
\(628\) | −8.76393 | −0.349719 | ||||||||
\(629\) | −32.8885 | −1.31135 | ||||||||
\(630\) | −4.23607 | −0.168769 | ||||||||
\(631\) | −33.7639 | −1.34412 | −0.672060 | − | 0.740496i | \(-0.734591\pi\) | ||||
−0.672060 | + | 0.740496i | \(0.734591\pi\) | |||||||
\(632\) | 26.7082 | 1.06240 | ||||||||
\(633\) | −15.0000 | −0.596196 | ||||||||
\(634\) | −35.8328 | −1.42310 | ||||||||
\(635\) | 7.00000 | 0.277787 | ||||||||
\(636\) | 0.854102 | 0.0338673 | ||||||||
\(637\) | −6.85410 | −0.271569 | ||||||||
\(638\) | −38.7426 | −1.53384 | ||||||||
\(639\) | 11.6180 | 0.459602 | ||||||||
\(640\) | −35.6525 | −1.40929 | ||||||||
\(641\) | −26.3820 | −1.04203 | −0.521013 | − | 0.853549i | \(-0.674446\pi\) | ||||
−0.521013 | + | 0.853549i | \(0.674446\pi\) | |||||||
\(642\) | 1.38197 | 0.0545418 | ||||||||
\(643\) | −35.5066 | −1.40024 | −0.700121 | − | 0.714024i | \(-0.746871\pi\) | ||||
−0.700121 | + | 0.714024i | \(0.746871\pi\) | |||||||
\(644\) | 0.618034 | 0.0243540 | ||||||||
\(645\) | 19.1803 | 0.755225 | ||||||||
\(646\) | −21.1459 | −0.831974 | ||||||||
\(647\) | −9.09017 | −0.357371 | −0.178686 | − | 0.983906i | \(-0.557185\pi\) | ||||
−0.178686 | + | 0.983906i | \(0.557185\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | −4.14590 | −0.162741 | ||||||||
\(650\) | −20.5623 | −0.806520 | ||||||||
\(651\) | 5.00000 | 0.195965 | ||||||||
\(652\) | −13.9098 | −0.544751 | ||||||||
\(653\) | −20.9098 | −0.818265 | −0.409132 | − | 0.912475i | \(-0.634169\pi\) | ||||
−0.409132 | + | 0.912475i | \(0.634169\pi\) | |||||||
\(654\) | 22.7082 | 0.887961 | ||||||||
\(655\) | 32.5066 | 1.27014 | ||||||||
\(656\) | 22.8541 | 0.892303 | ||||||||
\(657\) | 5.47214 | 0.213488 | ||||||||
\(658\) | 1.23607 | 0.0481869 | ||||||||
\(659\) | 20.5967 | 0.802335 | 0.401168 | − | 0.916005i | \(-0.368604\pi\) | ||||
0.401168 | + | 0.916005i | \(0.368604\pi\) | |||||||
\(660\) | −3.61803 | −0.140832 | ||||||||
\(661\) | 29.1803 | 1.13498 | 0.567492 | − | 0.823379i | \(-0.307914\pi\) | ||||
0.567492 | + | 0.823379i | \(0.307914\pi\) | |||||||
\(662\) | 17.7082 | 0.688249 | ||||||||
\(663\) | 23.7984 | 0.924252 | ||||||||
\(664\) | 22.2361 | 0.862927 | ||||||||
\(665\) | 9.85410 | 0.382126 | ||||||||
\(666\) | −15.3262 | −0.593880 | ||||||||
\(667\) | 10.7082 | 0.414623 | ||||||||
\(668\) | 7.09017 | 0.274327 | ||||||||
\(669\) | −18.3262 | −0.708533 | ||||||||
\(670\) | 0.618034 | 0.0238767 | ||||||||
\(671\) | −4.67376 | −0.180429 | ||||||||
\(672\) | 3.38197 | 0.130462 | ||||||||
\(673\) | 4.05573 | 0.156337 | 0.0781684 | − | 0.996940i | \(-0.475093\pi\) | ||||
0.0781684 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(674\) | −30.0344 | −1.15688 | ||||||||
\(675\) | −1.85410 | −0.0713644 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | −23.7984 | −0.914646 | −0.457323 | − | 0.889301i | \(-0.651192\pi\) | ||||
−0.457323 | + | 0.889301i | \(0.651192\pi\) | |||||||
\(678\) | 11.4721 | 0.440585 | ||||||||
\(679\) | 5.18034 | 0.198803 | ||||||||
\(680\) | 20.3262 | 0.779476 | ||||||||
\(681\) | −15.2705 | −0.585167 | ||||||||
\(682\) | 18.0902 | 0.692708 | ||||||||
\(683\) | 27.2918 | 1.04429 | 0.522146 | − | 0.852856i | \(-0.325132\pi\) | ||||
0.522146 | + | 0.852856i | \(0.325132\pi\) | |||||||
\(684\) | −2.32624 | −0.0889459 | ||||||||
\(685\) | 52.2148 | 1.99502 | ||||||||
\(686\) | 1.61803 | 0.0617768 | ||||||||
\(687\) | 5.67376 | 0.216468 | ||||||||
\(688\) | −35.5623 | −1.35580 | ||||||||
\(689\) | 9.47214 | 0.360860 | ||||||||
\(690\) | 4.23607 | 0.161264 | ||||||||
\(691\) | 3.79837 | 0.144497 | 0.0722485 | − | 0.997387i | \(-0.476983\pi\) | ||||
0.0722485 | + | 0.997387i | \(0.476983\pi\) | |||||||
\(692\) | −6.97871 | −0.265291 | ||||||||
\(693\) | −2.23607 | −0.0849412 | ||||||||
\(694\) | −5.90983 | −0.224334 | ||||||||
\(695\) | −51.9787 | −1.97166 | ||||||||
\(696\) | 23.9443 | 0.907605 | ||||||||
\(697\) | −16.3475 | −0.619207 | ||||||||
\(698\) | −10.5279 | −0.398486 | ||||||||
\(699\) | −7.09017 | −0.268175 | ||||||||
\(700\) | 1.14590 | 0.0433109 | ||||||||
\(701\) | −7.20163 | −0.272002 | −0.136001 | − | 0.990709i | \(-0.543425\pi\) | ||||
−0.136001 | + | 0.990709i | \(0.543425\pi\) | |||||||
\(702\) | 11.0902 | 0.418571 | ||||||||
\(703\) | 35.6525 | 1.34466 | ||||||||
\(704\) | −9.47214 | −0.356995 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | −43.0344 | −1.61962 | ||||||||
\(707\) | −4.90983 | −0.184653 | ||||||||
\(708\) | −1.14590 | −0.0430655 | ||||||||
\(709\) | 3.32624 | 0.124919 | 0.0624597 | − | 0.998047i | \(-0.480105\pi\) | ||||
0.0624597 | + | 0.998047i | \(0.480105\pi\) | |||||||
\(710\) | −49.2148 | −1.84700 | ||||||||
\(711\) | −11.9443 | −0.447945 | ||||||||
\(712\) | 1.50658 | 0.0564614 | ||||||||
\(713\) | −5.00000 | −0.187251 | ||||||||
\(714\) | −5.61803 | −0.210250 | ||||||||
\(715\) | −40.1246 | −1.50058 | ||||||||
\(716\) | 12.3820 | 0.462736 | ||||||||
\(717\) | 6.61803 | 0.247155 | ||||||||
\(718\) | 36.8885 | 1.37667 | ||||||||
\(719\) | 22.7082 | 0.846873 | 0.423437 | − | 0.905926i | \(-0.360824\pi\) | ||||
0.423437 | + | 0.905926i | \(0.360824\pi\) | |||||||
\(720\) | 12.7082 | 0.473607 | ||||||||
\(721\) | −6.47214 | −0.241035 | ||||||||
\(722\) | −7.81966 | −0.291018 | ||||||||
\(723\) | −28.7082 | −1.06767 | ||||||||
\(724\) | −9.38197 | −0.348678 | ||||||||
\(725\) | 19.8541 | 0.737363 | ||||||||
\(726\) | 9.70820 | 0.360305 | ||||||||
\(727\) | −25.7639 | −0.955531 | −0.477766 | − | 0.878487i | \(-0.658553\pi\) | ||||
−0.477766 | + | 0.878487i | \(0.658553\pi\) | |||||||
\(728\) | 15.3262 | 0.568028 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.1803 | −0.857943 | ||||||||
\(731\) | 25.4377 | 0.940847 | ||||||||
\(732\) | −1.29180 | −0.0477462 | ||||||||
\(733\) | −38.5410 | −1.42355 | −0.711773 | − | 0.702410i | \(-0.752107\pi\) | ||||
−0.711773 | + | 0.702410i | \(0.752107\pi\) | |||||||
\(734\) | −52.5066 | −1.93805 | ||||||||
\(735\) | 2.61803 | 0.0965676 | ||||||||
\(736\) | −3.38197 | −0.124661 | ||||||||
\(737\) | 0.326238 | 0.0120171 | ||||||||
\(738\) | −7.61803 | −0.280424 | ||||||||
\(739\) | −13.5836 | −0.499681 | −0.249840 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249840 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(740\) | 15.3262 | 0.563404 | ||||||||
\(741\) | −25.7984 | −0.947727 | ||||||||
\(742\) | −2.23607 | −0.0820886 | ||||||||
\(743\) | −48.3951 | −1.77544 | −0.887722 | − | 0.460379i | \(-0.847713\pi\) | ||||
−0.887722 | + | 0.460379i | \(0.847713\pi\) | |||||||
\(744\) | −11.1803 | −0.409891 | ||||||||
\(745\) | 38.3607 | 1.40543 | ||||||||
\(746\) | 4.67376 | 0.171119 | ||||||||
\(747\) | −9.94427 | −0.363842 | ||||||||
\(748\) | −4.79837 | −0.175446 | ||||||||
\(749\) | −0.854102 | −0.0312082 | ||||||||
\(750\) | −13.3262 | −0.486605 | ||||||||
\(751\) | −20.9098 | −0.763011 | −0.381505 | − | 0.924367i | \(-0.624594\pi\) | ||||
−0.381505 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(752\) | −3.70820 | −0.135224 | ||||||||
\(753\) | 12.2918 | 0.447938 | ||||||||
\(754\) | −118.756 | −4.32483 | ||||||||
\(755\) | 4.47214 | 0.162758 | ||||||||
\(756\) | −0.618034 | −0.0224777 | ||||||||
\(757\) | −5.58359 | −0.202939 | −0.101470 | − | 0.994839i | \(-0.532354\pi\) | ||||
−0.101470 | + | 0.994839i | \(0.532354\pi\) | |||||||
\(758\) | −33.8885 | −1.23089 | ||||||||
\(759\) | 2.23607 | 0.0811641 | ||||||||
\(760\) | −22.0344 | −0.799273 | ||||||||
\(761\) | 18.1115 | 0.656540 | 0.328270 | − | 0.944584i | \(-0.393534\pi\) | ||||
0.328270 | + | 0.944584i | \(0.393534\pi\) | |||||||
\(762\) | 4.32624 | 0.156723 | ||||||||
\(763\) | −14.0344 | −0.508081 | ||||||||
\(764\) | 13.4164 | 0.485389 | ||||||||
\(765\) | −9.09017 | −0.328656 | ||||||||
\(766\) | −7.32624 | −0.264708 | ||||||||
\(767\) | −12.7082 | −0.458867 | ||||||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −45.9574 | −1.65727 | −0.828634 | − | 0.559791i | \(-0.810881\pi\) | ||||
−0.828634 | + | 0.559791i | \(0.810881\pi\) | |||||||
\(770\) | 9.47214 | 0.341352 | ||||||||
\(771\) | −29.7082 | −1.06991 | ||||||||
\(772\) | −11.2361 | −0.404395 | ||||||||
\(773\) | 40.0132 | 1.43917 | 0.719587 | − | 0.694403i | \(-0.244331\pi\) | ||||
0.719587 | + | 0.694403i | \(0.244331\pi\) | |||||||
\(774\) | 11.8541 | 0.426087 | ||||||||
\(775\) | −9.27051 | −0.333007 | ||||||||
\(776\) | −11.5836 | −0.415827 | ||||||||
\(777\) | 9.47214 | 0.339811 | ||||||||
\(778\) | 35.7984 | 1.28343 | ||||||||
\(779\) | 17.7214 | 0.634934 | ||||||||
\(780\) | −11.0902 | −0.397092 | ||||||||
\(781\) | −25.9787 | −0.929591 | ||||||||
\(782\) | 5.61803 | 0.200900 | ||||||||
\(783\) | −10.7082 | −0.382680 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 37.1246 | 1.32503 | ||||||||
\(786\) | 20.0902 | 0.716593 | ||||||||
\(787\) | 22.7984 | 0.812674 | 0.406337 | − | 0.913723i | \(-0.366806\pi\) | ||||
0.406337 | + | 0.913723i | \(0.366806\pi\) | |||||||
\(788\) | −15.6525 | −0.557596 | ||||||||
\(789\) | −5.00000 | −0.178005 | ||||||||
\(790\) | 50.5967 | 1.80015 | ||||||||
\(791\) | −7.09017 | −0.252097 | ||||||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | −14.3262 | −0.508740 | ||||||||
\(794\) | 24.6525 | 0.874884 | ||||||||
\(795\) | −3.61803 | −0.128318 | ||||||||
\(796\) | −5.90983 | −0.209468 | ||||||||
\(797\) | 9.70820 | 0.343882 | 0.171941 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171941 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(798\) | 6.09017 | 0.215590 | ||||||||
\(799\) | 2.65248 | 0.0938378 | ||||||||
\(800\) | −6.27051 | −0.221696 | ||||||||
\(801\) | −0.673762 | −0.0238062 | ||||||||
\(802\) | 11.0344 | 0.389640 | ||||||||
\(803\) | −12.2361 | −0.431801 | ||||||||
\(804\) | 0.0901699 | 0.00318005 | ||||||||
\(805\) | −2.61803 | −0.0922736 | ||||||||
\(806\) | 55.4508 | 1.95317 | ||||||||
\(807\) | 2.85410 | 0.100469 | ||||||||
\(808\) | 10.9787 | 0.386230 | ||||||||
\(809\) | −22.5623 | −0.793248 | −0.396624 | − | 0.917981i | \(-0.629818\pi\) | ||||
−0.396624 | + | 0.917981i | \(0.629818\pi\) | |||||||
\(810\) | −4.23607 | −0.148840 | ||||||||
\(811\) | 41.5410 | 1.45870 | 0.729351 | − | 0.684139i | \(-0.239822\pi\) | ||||
0.729351 | + | 0.684139i | \(0.239822\pi\) | |||||||
\(812\) | 6.61803 | 0.232247 | ||||||||
\(813\) | 17.1803 | 0.602541 | ||||||||
\(814\) | 34.2705 | 1.20118 | ||||||||
\(815\) | 58.9230 | 2.06398 | ||||||||
\(816\) | 16.8541 | 0.590012 | ||||||||
\(817\) | −27.5755 | −0.964743 | ||||||||
\(818\) | 38.2705 | 1.33810 | ||||||||
\(819\) | −6.85410 | −0.239502 | ||||||||
\(820\) | 7.61803 | 0.266033 | ||||||||
\(821\) | 25.7082 | 0.897223 | 0.448611 | − | 0.893727i | \(-0.351919\pi\) | ||||
0.448611 | + | 0.893727i | \(0.351919\pi\) | |||||||
\(822\) | 32.2705 | 1.12556 | ||||||||
\(823\) | 54.9787 | 1.91644 | 0.958219 | − | 0.286036i | \(-0.0923378\pi\) | ||||
0.958219 | + | 0.286036i | \(0.0923378\pi\) | |||||||
\(824\) | 14.4721 | 0.504161 | ||||||||
\(825\) | 4.14590 | 0.144342 | ||||||||
\(826\) | 3.00000 | 0.104383 | ||||||||
\(827\) | −16.1459 | −0.561448 | −0.280724 | − | 0.959789i | \(-0.590575\pi\) | ||||
−0.280724 | + | 0.959789i | \(0.590575\pi\) | |||||||
\(828\) | 0.618034 | 0.0214782 | ||||||||
\(829\) | −23.0689 | −0.801215 | −0.400608 | − | 0.916250i | \(-0.631201\pi\) | ||||
−0.400608 | + | 0.916250i | \(0.631201\pi\) | |||||||
\(830\) | 42.1246 | 1.46217 | ||||||||
\(831\) | −21.2148 | −0.735933 | ||||||||
\(832\) | −29.0344 | −1.00659 | ||||||||
\(833\) | 3.47214 | 0.120302 | ||||||||
\(834\) | −32.1246 | −1.11238 | ||||||||
\(835\) | −30.0344 | −1.03938 | ||||||||
\(836\) | 5.20163 | 0.179902 | ||||||||
\(837\) | 5.00000 | 0.172825 | ||||||||
\(838\) | 31.6525 | 1.09342 | ||||||||
\(839\) | −36.2705 | −1.25220 | −0.626099 | − | 0.779744i | \(-0.715349\pi\) | ||||
−0.626099 | + | 0.779744i | \(0.715349\pi\) | |||||||
\(840\) | −5.85410 | −0.201986 | ||||||||
\(841\) | 85.6656 | 2.95399 | ||||||||
\(842\) | 17.2705 | 0.595181 | ||||||||
\(843\) | 21.5967 | 0.743832 | ||||||||
\(844\) | 9.27051 | 0.319104 | ||||||||
\(845\) | −88.9574 | −3.06023 | ||||||||
\(846\) | 1.23607 | 0.0424969 | ||||||||
\(847\) | −6.00000 | −0.206162 | ||||||||
\(848\) | 6.70820 | 0.230361 | ||||||||
\(849\) | −14.3262 | −0.491675 | ||||||||
\(850\) | 10.4164 | 0.357280 | ||||||||
\(851\) | −9.47214 | −0.324701 | ||||||||
\(852\) | −7.18034 | −0.245994 | ||||||||
\(853\) | −11.3475 | −0.388532 | −0.194266 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194266 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(854\) | 3.38197 | 0.115728 | ||||||||
\(855\) | 9.85410 | 0.337003 | ||||||||
\(856\) | 1.90983 | 0.0652766 | ||||||||
\(857\) | −49.9574 | −1.70651 | −0.853257 | − | 0.521491i | \(-0.825376\pi\) | ||||
−0.853257 | + | 0.521491i | \(0.825376\pi\) | |||||||
\(858\) | −24.7984 | −0.846603 | ||||||||
\(859\) | −25.4164 | −0.867197 | −0.433598 | − | 0.901106i | \(-0.642756\pi\) | ||||
−0.433598 | + | 0.901106i | \(0.642756\pi\) | |||||||
\(860\) | −11.8541 | −0.404222 | ||||||||
\(861\) | 4.70820 | 0.160455 | ||||||||
\(862\) | 32.2148 | 1.09724 | ||||||||
\(863\) | −17.5967 | −0.599000 | −0.299500 | − | 0.954096i | \(-0.596820\pi\) | ||||
−0.299500 | + | 0.954096i | \(0.596820\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 29.5623 | 1.00515 | ||||||||
\(866\) | 37.4164 | 1.27146 | ||||||||
\(867\) | 4.94427 | 0.167916 | ||||||||
\(868\) | −3.09017 | −0.104887 | ||||||||
\(869\) | 26.7082 | 0.906014 | ||||||||
\(870\) | 45.3607 | 1.53787 | ||||||||
\(871\) | 1.00000 | 0.0338837 | ||||||||
\(872\) | 31.3820 | 1.06273 | ||||||||
\(873\) | 5.18034 | 0.175328 | ||||||||
\(874\) | −6.09017 | −0.206003 | ||||||||
\(875\) | 8.23607 | 0.278430 | ||||||||
\(876\) | −3.38197 | −0.114266 | ||||||||
\(877\) | −17.5279 | −0.591874 | −0.295937 | − | 0.955207i | \(-0.595632\pi\) | ||||
−0.295937 | + | 0.955207i | \(0.595632\pi\) | |||||||
\(878\) | −29.0344 | −0.979865 | ||||||||
\(879\) | 9.52786 | 0.321367 | ||||||||
\(880\) | −28.4164 | −0.957917 | ||||||||
\(881\) | 26.5410 | 0.894190 | 0.447095 | − | 0.894487i | \(-0.352459\pi\) | ||||
0.447095 | + | 0.894487i | \(0.352459\pi\) | |||||||
\(882\) | 1.61803 | 0.0544820 | ||||||||
\(883\) | −34.7426 | −1.16918 | −0.584592 | − | 0.811328i | \(-0.698745\pi\) | ||||
−0.584592 | + | 0.811328i | \(0.698745\pi\) | |||||||
\(884\) | −14.7082 | −0.494690 | ||||||||
\(885\) | 4.85410 | 0.163169 | ||||||||
\(886\) | −6.47214 | −0.217436 | ||||||||
\(887\) | 6.67376 | 0.224083 | 0.112041 | − | 0.993704i | \(-0.464261\pi\) | ||||
0.112041 | + | 0.993704i | \(0.464261\pi\) | |||||||
\(888\) | −21.1803 | −0.710766 | ||||||||
\(889\) | −2.67376 | −0.0896751 | ||||||||
\(890\) | 2.85410 | 0.0956697 | ||||||||
\(891\) | −2.23607 | −0.0749111 | ||||||||
\(892\) | 11.3262 | 0.379230 | ||||||||
\(893\) | −2.87539 | −0.0962212 | ||||||||
\(894\) | 23.7082 | 0.792921 | ||||||||
\(895\) | −52.4508 | −1.75324 | ||||||||
\(896\) | 13.6180 | 0.454947 | ||||||||
\(897\) | 6.85410 | 0.228852 | ||||||||
\(898\) | 20.8885 | 0.697060 | ||||||||
\(899\) | −53.5410 | −1.78569 | ||||||||
\(900\) | 1.14590 | 0.0381966 | ||||||||
\(901\) | −4.79837 | −0.159857 | ||||||||
\(902\) | 17.0344 | 0.567185 | ||||||||
\(903\) | −7.32624 | −0.243802 | ||||||||
\(904\) | 15.8541 | 0.527300 | ||||||||
\(905\) | 39.7426 | 1.32109 | ||||||||
\(906\) | 2.76393 | 0.0918255 | ||||||||
\(907\) | −16.3262 | −0.542104 | −0.271052 | − | 0.962565i | \(-0.587372\pi\) | ||||
−0.271052 | + | 0.962565i | \(0.587372\pi\) | |||||||
\(908\) | 9.43769 | 0.313201 | ||||||||
\(909\) | −4.90983 | −0.162849 | ||||||||
\(910\) | 29.0344 | 0.962482 | ||||||||
\(911\) | −18.2918 | −0.606034 | −0.303017 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303017 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(912\) | −18.2705 | −0.604997 | ||||||||
\(913\) | 22.2361 | 0.735906 | ||||||||
\(914\) | −53.0689 | −1.75536 | ||||||||
\(915\) | 5.47214 | 0.180903 | ||||||||
\(916\) | −3.50658 | −0.115861 | ||||||||
\(917\) | −12.4164 | −0.410026 | ||||||||
\(918\) | −5.61803 | −0.185423 | ||||||||
\(919\) | 36.4853 | 1.20354 | 0.601769 | − | 0.798670i | \(-0.294463\pi\) | ||||
0.601769 | + | 0.798670i | \(0.294463\pi\) | |||||||
\(920\) | 5.85410 | 0.193004 | ||||||||
\(921\) | −25.9443 | −0.854893 | ||||||||
\(922\) | 9.94427 | 0.327497 | ||||||||
\(923\) | −79.6312 | −2.62109 | ||||||||
\(924\) | 1.38197 | 0.0454633 | ||||||||
\(925\) | −17.5623 | −0.577445 | ||||||||
\(926\) | 23.6180 | 0.776137 | ||||||||
\(927\) | −6.47214 | −0.212573 | ||||||||
\(928\) | −36.2148 | −1.18881 | ||||||||
\(929\) | 33.7426 | 1.10706 | 0.553530 | − | 0.832829i | \(-0.313280\pi\) | ||||
0.553530 | + | 0.832829i | \(0.313280\pi\) | |||||||
\(930\) | −21.1803 | −0.694531 | ||||||||
\(931\) | −3.76393 | −0.123358 | ||||||||
\(932\) | 4.38197 | 0.143536 | ||||||||
\(933\) | −7.61803 | −0.249403 | ||||||||
\(934\) | 30.5623 | 1.00003 | ||||||||
\(935\) | 20.3262 | 0.664739 | ||||||||
\(936\) | 15.3262 | 0.500954 | ||||||||
\(937\) | −33.3607 | −1.08985 | −0.544923 | − | 0.838486i | \(-0.683441\pi\) | ||||
−0.544923 | + | 0.838486i | \(0.683441\pi\) | |||||||
\(938\) | −0.236068 | −0.00770789 | ||||||||
\(939\) | 1.52786 | 0.0498600 | ||||||||
\(940\) | −1.23607 | −0.0403161 | ||||||||
\(941\) | −34.8328 | −1.13552 | −0.567759 | − | 0.823195i | \(-0.692189\pi\) | ||||
−0.567759 | + | 0.823195i | \(0.692189\pi\) | |||||||
\(942\) | 22.9443 | 0.747565 | ||||||||
\(943\) | −4.70820 | −0.153320 | ||||||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 2.61803 | 0.0851647 | ||||||||
\(946\) | −26.5066 | −0.861803 | ||||||||
\(947\) | −46.7214 | −1.51824 | −0.759120 | − | 0.650951i | \(-0.774370\pi\) | ||||
−0.759120 | + | 0.650951i | \(0.774370\pi\) | |||||||
\(948\) | 7.38197 | 0.239755 | ||||||||
\(949\) | −37.5066 | −1.21752 | ||||||||
\(950\) | −11.2918 | −0.366354 | ||||||||
\(951\) | 22.1459 | 0.718130 | ||||||||
\(952\) | −7.76393 | −0.251630 | ||||||||
\(953\) | 48.9230 | 1.58477 | 0.792385 | − | 0.610021i | \(-0.208839\pi\) | ||||
0.792385 | + | 0.610021i | \(0.208839\pi\) | |||||||
\(954\) | −2.23607 | −0.0723954 | ||||||||
\(955\) | −56.8328 | −1.83907 | ||||||||
\(956\) | −4.09017 | −0.132286 | ||||||||
\(957\) | 23.9443 | 0.774008 | ||||||||
\(958\) | −9.14590 | −0.295491 | ||||||||
\(959\) | −19.9443 | −0.644034 | ||||||||
\(960\) | 11.0902 | 0.357934 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 105.048 | 3.38687 | ||||||||
\(963\) | −0.854102 | −0.0275231 | ||||||||
\(964\) | 17.7426 | 0.571452 | ||||||||
\(965\) | 47.5967 | 1.53219 | ||||||||
\(966\) | −1.61803 | −0.0520594 | ||||||||
\(967\) | −16.4721 | −0.529708 | −0.264854 | − | 0.964288i | \(-0.585324\pi\) | ||||
−0.264854 | + | 0.964288i | \(0.585324\pi\) | |||||||
\(968\) | 13.4164 | 0.431220 | ||||||||
\(969\) | 13.0689 | 0.419833 | ||||||||
\(970\) | −21.9443 | −0.704588 | ||||||||
\(971\) | −14.0902 | −0.452175 | −0.226088 | − | 0.974107i | \(-0.572594\pi\) | ||||
−0.226088 | + | 0.974107i | \(0.572594\pi\) | |||||||
\(972\) | −0.618034 | −0.0198234 | ||||||||
\(973\) | 19.8541 | 0.636493 | ||||||||
\(974\) | 28.7426 | 0.920974 | ||||||||
\(975\) | 12.7082 | 0.406988 | ||||||||
\(976\) | −10.1459 | −0.324762 | ||||||||
\(977\) | 53.9787 | 1.72693 | 0.863466 | − | 0.504407i | \(-0.168289\pi\) | ||||
0.863466 | + | 0.504407i | \(0.168289\pi\) | |||||||
\(978\) | 36.4164 | 1.16447 | ||||||||
\(979\) | 1.50658 | 0.0481504 | ||||||||
\(980\) | −1.61803 | −0.0516862 | ||||||||
\(981\) | −14.0344 | −0.448085 | ||||||||
\(982\) | 45.4508 | 1.45039 | ||||||||
\(983\) | −59.3607 | −1.89331 | −0.946656 | − | 0.322246i | \(-0.895562\pi\) | ||||
−0.946656 | + | 0.322246i | \(0.895562\pi\) | |||||||
\(984\) | −10.5279 | −0.335616 | ||||||||
\(985\) | 66.3050 | 2.11265 | ||||||||
\(986\) | 60.1591 | 1.91585 | ||||||||
\(987\) | −0.763932 | −0.0243162 | ||||||||
\(988\) | 15.9443 | 0.507255 | ||||||||
\(989\) | 7.32624 | 0.232961 | ||||||||
\(990\) | 9.47214 | 0.301044 | ||||||||
\(991\) | 2.67376 | 0.0849349 | 0.0424674 | − | 0.999098i | \(-0.486478\pi\) | ||||
0.0424674 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(992\) | 16.9098 | 0.536888 | ||||||||
\(993\) | −10.9443 | −0.347306 | ||||||||
\(994\) | 18.7984 | 0.596248 | ||||||||
\(995\) | 25.0344 | 0.793645 | ||||||||
\(996\) | 6.14590 | 0.194740 | ||||||||
\(997\) | −25.5410 | −0.808892 | −0.404446 | − | 0.914562i | \(-0.632536\pi\) | ||||
−0.404446 | + | 0.914562i | \(0.632536\pi\) | |||||||
\(998\) | 20.7082 | 0.655507 | ||||||||
\(999\) | 9.47214 | 0.299685 |
(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 | 483.2.a.g.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1449.2.a.f.1.1 | 2 | |||
4.3 | odd | 2 | 7728.2.a.bg.1.1 | 2 | |||
7.6 | odd | 2 | 3381.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.g.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1449.2.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
3381.2.a.u.1.2 | 2 | 7.6 | odd | 2 | |||
7728.2.a.bg.1.1 | 2 | 4.3 | odd | 2 |