Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 19x^{6} + 42x^{5} + 78x^{4} - 156x^{3} - 127x^{2} + 136x + 94 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.72517\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.26449 | 1.45992 | 0.729961 | − | 0.683489i | \(-0.239538\pi\) | ||||
0.729961 | + | 0.683489i | \(0.239538\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.26449 | −1.03232 | ||||||||
\(11\) | −3.52160 | −1.06180 | −0.530901 | − | 0.847434i | \(-0.678146\pi\) | ||||
−0.530901 | + | 0.847434i | \(0.678146\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.86293 | 0.516683 | 0.258342 | − | 0.966054i | \(-0.416824\pi\) | ||||
0.258342 | + | 0.966054i | \(0.416824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.26449 | −0.842886 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 8.13828 | 1.97382 | 0.986911 | − | 0.161264i | \(-0.0515571\pi\) | ||||
0.986911 | + | 0.161264i | \(0.0515571\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.86456 | −1.57484 | −0.787419 | − | 0.616418i | \(-0.788583\pi\) | ||||
−0.787419 | + | 0.616418i | \(0.788583\pi\) | |||||||
\(20\) | 3.26449 | 0.729961 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.52160 | 0.750808 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.65686 | 1.13137 | ||||||||
\(26\) | −1.86293 | −0.365350 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.17278 | −1.70334 | −0.851671 | − | 0.524076i | \(-0.824411\pi\) | ||||
−0.851671 | + | 0.524076i | \(0.824411\pi\) | |||||||
\(30\) | 3.26449 | 0.596011 | ||||||||
\(31\) | −2.47100 | −0.443805 | −0.221902 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221902 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.52160 | 0.613032 | ||||||||
\(34\) | −8.13828 | −1.39570 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.84322 | −0.796221 | −0.398110 | − | 0.917338i | \(-0.630334\pi\) | ||||
−0.398110 | + | 0.917338i | \(0.630334\pi\) | |||||||
\(38\) | 6.86456 | 1.11358 | ||||||||
\(39\) | −1.86293 | −0.298307 | ||||||||
\(40\) | −3.26449 | −0.516160 | ||||||||
\(41\) | −1.54379 | −0.241100 | −0.120550 | − | 0.992707i | \(-0.538466\pi\) | ||||
−0.120550 | + | 0.992707i | \(0.538466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.60008 | 0.549007 | 0.274503 | − | 0.961586i | \(-0.411487\pi\) | ||||
0.274503 | + | 0.961586i | \(0.411487\pi\) | |||||||
\(44\) | −3.52160 | −0.530901 | ||||||||
\(45\) | 3.26449 | 0.486641 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 1.88641 | 0.275161 | 0.137580 | − | 0.990491i | \(-0.456067\pi\) | ||||
0.137580 | + | 0.990491i | \(0.456067\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.65686 | −0.800001 | ||||||||
\(51\) | −8.13828 | −1.13959 | ||||||||
\(52\) | 1.86293 | 0.258342 | ||||||||
\(53\) | 1.87216 | 0.257161 | 0.128580 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128580 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −11.4962 | −1.55015 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.86456 | 0.909234 | ||||||||
\(58\) | 9.17278 | 1.20445 | ||||||||
\(59\) | 5.17414 | 0.673616 | 0.336808 | − | 0.941573i | \(-0.390653\pi\) | ||||
0.336808 | + | 0.941573i | \(0.390653\pi\) | |||||||
\(60\) | −3.26449 | −0.421443 | ||||||||
\(61\) | −5.43605 | −0.696015 | −0.348007 | − | 0.937492i | \(-0.613142\pi\) | ||||
−0.348007 | + | 0.937492i | \(0.613142\pi\) | |||||||
\(62\) | 2.47100 | 0.313817 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.08150 | 0.754317 | ||||||||
\(66\) | −3.52160 | −0.433479 | ||||||||
\(67\) | −13.6143 | −1.66326 | −0.831628 | − | 0.555333i | \(-0.812591\pi\) | ||||
−0.831628 | + | 0.555333i | \(0.812591\pi\) | |||||||
\(68\) | 8.13828 | 0.986911 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.33512 | −0.989197 | −0.494598 | − | 0.869122i | \(-0.664685\pi\) | ||||
−0.494598 | + | 0.869122i | \(0.664685\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 16.2661 | 1.90381 | 0.951903 | − | 0.306398i | \(-0.0991239\pi\) | ||||
0.951903 | + | 0.306398i | \(0.0991239\pi\) | |||||||
\(74\) | 4.84322 | 0.563013 | ||||||||
\(75\) | −5.65686 | −0.653198 | ||||||||
\(76\) | −6.86456 | −0.787419 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.86293 | 0.210935 | ||||||||
\(79\) | −7.99198 | −0.899168 | −0.449584 | − | 0.893238i | \(-0.648428\pi\) | ||||
−0.449584 | + | 0.893238i | \(0.648428\pi\) | |||||||
\(80\) | 3.26449 | 0.364981 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.54379 | 0.170484 | ||||||||
\(83\) | −13.2103 | −1.45002 | −0.725008 | − | 0.688740i | \(-0.758164\pi\) | ||||
−0.725008 | + | 0.688740i | \(0.758164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.5673 | 2.88163 | ||||||||
\(86\) | −3.60008 | −0.388206 | ||||||||
\(87\) | 9.17278 | 0.983425 | ||||||||
\(88\) | 3.52160 | 0.375404 | ||||||||
\(89\) | −14.4840 | −1.53530 | −0.767650 | − | 0.640869i | \(-0.778574\pi\) | ||||
−0.767650 | + | 0.640869i | \(0.778574\pi\) | |||||||
\(90\) | −3.26449 | −0.344107 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 2.47100 | 0.256231 | ||||||||
\(94\) | −1.88641 | −0.194568 | ||||||||
\(95\) | −22.4093 | −2.29914 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.0068 | −1.62524 | −0.812621 | − | 0.582793i | \(-0.801960\pi\) | ||||
−0.812621 | + | 0.582793i | \(0.801960\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.52160 | −0.353934 | ||||||||
\(100\) | 5.65686 | 0.565686 | ||||||||
\(101\) | −1.42084 | −0.141378 | −0.0706892 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706892 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(102\) | 8.13828 | 0.805810 | ||||||||
\(103\) | 6.60440 | 0.650751 | 0.325375 | − | 0.945585i | \(-0.394509\pi\) | ||||
0.325375 | + | 0.945585i | \(0.394509\pi\) | |||||||
\(104\) | −1.86293 | −0.182675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.87216 | −0.181840 | ||||||||
\(107\) | 0.965389 | 0.0933277 | 0.0466638 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466638 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.67346 | −0.447636 | −0.223818 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223818 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(110\) | 11.4962 | 1.09612 | ||||||||
\(111\) | 4.84322 | 0.459698 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.88771 | 0.930157 | 0.465079 | − | 0.885269i | \(-0.346026\pi\) | ||||
0.465079 | + | 0.885269i | \(0.346026\pi\) | |||||||
\(114\) | −6.86456 | −0.642925 | ||||||||
\(115\) | −3.26449 | −0.304415 | ||||||||
\(116\) | −9.17278 | −0.851671 | ||||||||
\(117\) | 1.86293 | 0.172228 | ||||||||
\(118\) | −5.17414 | −0.476318 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.26449 | 0.298005 | ||||||||
\(121\) | 1.40166 | 0.127424 | ||||||||
\(122\) | 5.43605 | 0.492157 | ||||||||
\(123\) | 1.54379 | 0.139199 | ||||||||
\(124\) | −2.47100 | −0.221902 | ||||||||
\(125\) | 2.14432 | 0.191794 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9378 | 1.68046 | 0.840230 | − | 0.542231i | \(-0.182420\pi\) | ||||
0.840230 | + | 0.542231i | \(0.182420\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.60008 | −0.316969 | ||||||||
\(130\) | −6.08150 | −0.533383 | ||||||||
\(131\) | −15.8296 | −1.38304 | −0.691521 | − | 0.722356i | \(-0.743059\pi\) | ||||
−0.691521 | + | 0.722356i | \(0.743059\pi\) | |||||||
\(132\) | 3.52160 | 0.306516 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6143 | 1.17610 | ||||||||
\(135\) | −3.26449 | −0.280962 | ||||||||
\(136\) | −8.13828 | −0.697852 | ||||||||
\(137\) | 15.5908 | 1.33201 | 0.666005 | − | 0.745948i | \(-0.268003\pi\) | ||||
0.666005 | + | 0.745948i | \(0.268003\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 16.4445 | 1.39480 | 0.697402 | − | 0.716680i | \(-0.254339\pi\) | ||||
0.697402 | + | 0.716680i | \(0.254339\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.88641 | −0.158864 | ||||||||
\(142\) | 8.33512 | 0.699468 | ||||||||
\(143\) | −6.56049 | −0.548616 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −29.9444 | −2.48675 | ||||||||
\(146\) | −16.2661 | −1.34619 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.84322 | −0.398110 | ||||||||
\(149\) | −11.6445 | −0.953956 | −0.476978 | − | 0.878915i | \(-0.658268\pi\) | ||||
−0.476978 | + | 0.878915i | \(0.658268\pi\) | |||||||
\(150\) | 5.65686 | 0.461881 | ||||||||
\(151\) | −18.2149 | −1.48230 | −0.741152 | − | 0.671337i | \(-0.765720\pi\) | ||||
−0.741152 | + | 0.671337i | \(0.765720\pi\) | |||||||
\(152\) | 6.86456 | 0.556790 | ||||||||
\(153\) | 8.13828 | 0.657941 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.06654 | −0.647920 | ||||||||
\(156\) | −1.86293 | −0.149154 | ||||||||
\(157\) | −12.1317 | −0.968218 | −0.484109 | − | 0.875008i | \(-0.660856\pi\) | ||||
−0.484109 | + | 0.875008i | \(0.660856\pi\) | |||||||
\(158\) | 7.99198 | 0.635807 | ||||||||
\(159\) | −1.87216 | −0.148472 | ||||||||
\(160\) | −3.26449 | −0.258080 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.53819 | −0.433785 | −0.216892 | − | 0.976196i | \(-0.569592\pi\) | ||||
−0.216892 | + | 0.976196i | \(0.569592\pi\) | |||||||
\(164\) | −1.54379 | −0.120550 | ||||||||
\(165\) | 11.4962 | 0.894979 | ||||||||
\(166\) | 13.2103 | 1.02532 | ||||||||
\(167\) | −5.26791 | −0.407643 | −0.203822 | − | 0.979008i | \(-0.565336\pi\) | ||||
−0.203822 | + | 0.979008i | \(0.565336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.52950 | −0.733038 | ||||||||
\(170\) | −26.5673 | −2.03762 | ||||||||
\(171\) | −6.86456 | −0.524946 | ||||||||
\(172\) | 3.60008 | 0.274503 | ||||||||
\(173\) | −18.3100 | −1.39208 | −0.696041 | − | 0.718002i | \(-0.745057\pi\) | ||||
−0.696041 | + | 0.718002i | \(0.745057\pi\) | |||||||
\(174\) | −9.17278 | −0.695387 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.52160 | −0.265451 | ||||||||
\(177\) | −5.17414 | −0.388912 | ||||||||
\(178\) | 14.4840 | 1.08562 | ||||||||
\(179\) | −3.77091 | −0.281851 | −0.140925 | − | 0.990020i | \(-0.545008\pi\) | ||||
−0.140925 | + | 0.990020i | \(0.545008\pi\) | |||||||
\(180\) | 3.26449 | 0.243320 | ||||||||
\(181\) | 17.0151 | 1.26472 | 0.632362 | − | 0.774673i | \(-0.282086\pi\) | ||||
0.632362 | + | 0.774673i | \(0.282086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.43605 | 0.401844 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −15.8106 | −1.16242 | ||||||||
\(186\) | −2.47100 | −0.181183 | ||||||||
\(187\) | −28.6598 | −2.09581 | ||||||||
\(188\) | 1.88641 | 0.137580 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 22.4093 | 1.62574 | ||||||||
\(191\) | −3.33717 | −0.241469 | −0.120735 | − | 0.992685i | \(-0.538525\pi\) | ||||
−0.120735 | + | 0.992685i | \(0.538525\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.3679 | 0.746296 | 0.373148 | − | 0.927772i | \(-0.378278\pi\) | ||||
0.373148 | + | 0.927772i | \(0.378278\pi\) | |||||||
\(194\) | 16.0068 | 1.14922 | ||||||||
\(195\) | −6.08150 | −0.435505 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3204 | 1.59027 | 0.795133 | − | 0.606436i | \(-0.207401\pi\) | ||||
0.795133 | + | 0.606436i | \(0.207401\pi\) | |||||||
\(198\) | 3.52160 | 0.250269 | ||||||||
\(199\) | 8.22716 | 0.583208 | 0.291604 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291604 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(200\) | −5.65686 | −0.400001 | ||||||||
\(201\) | 13.6143 | 0.960281 | ||||||||
\(202\) | 1.42084 | 0.0999697 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.13828 | −0.569793 | ||||||||
\(205\) | −5.03969 | −0.351988 | ||||||||
\(206\) | −6.60440 | −0.460150 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 1.86293 | 0.129171 | ||||||||
\(209\) | 24.1742 | 1.67217 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.22292 | 0.359561 | 0.179780 | − | 0.983707i | \(-0.442461\pi\) | ||||
0.179780 | + | 0.983707i | \(0.442461\pi\) | |||||||
\(212\) | 1.87216 | 0.128580 | ||||||||
\(213\) | 8.33512 | 0.571113 | ||||||||
\(214\) | −0.965389 | −0.0659926 | ||||||||
\(215\) | 11.7524 | 0.801507 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.67346 | 0.316526 | ||||||||
\(219\) | −16.2661 | −1.09916 | ||||||||
\(220\) | −11.4962 | −0.775074 | ||||||||
\(221\) | 15.1610 | 1.01984 | ||||||||
\(222\) | −4.84322 | −0.325056 | ||||||||
\(223\) | 3.71741 | 0.248936 | 0.124468 | − | 0.992224i | \(-0.460278\pi\) | ||||
0.124468 | + | 0.992224i | \(0.460278\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.65686 | 0.377124 | ||||||||
\(226\) | −9.88771 | −0.657721 | ||||||||
\(227\) | −6.94798 | −0.461154 | −0.230577 | − | 0.973054i | \(-0.574061\pi\) | ||||
−0.230577 | + | 0.973054i | \(0.574061\pi\) | |||||||
\(228\) | 6.86456 | 0.454617 | ||||||||
\(229\) | −18.7523 | −1.23919 | −0.619595 | − | 0.784922i | \(-0.712703\pi\) | ||||
−0.619595 | + | 0.784922i | \(0.712703\pi\) | |||||||
\(230\) | 3.26449 | 0.215254 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.17278 | 0.602223 | ||||||||
\(233\) | −3.59491 | −0.235511 | −0.117755 | − | 0.993043i | \(-0.537570\pi\) | ||||
−0.117755 | + | 0.993043i | \(0.537570\pi\) | |||||||
\(234\) | −1.86293 | −0.121783 | ||||||||
\(235\) | 6.15815 | 0.401713 | ||||||||
\(236\) | 5.17414 | 0.336808 | ||||||||
\(237\) | 7.99198 | 0.519135 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4835 | 1.19560 | 0.597798 | − | 0.801647i | \(-0.296043\pi\) | ||||
0.597798 | + | 0.801647i | \(0.296043\pi\) | |||||||
\(240\) | −3.26449 | −0.210722 | ||||||||
\(241\) | −5.79561 | −0.373328 | −0.186664 | − | 0.982424i | \(-0.559768\pi\) | ||||
−0.186664 | + | 0.982424i | \(0.559768\pi\) | |||||||
\(242\) | −1.40166 | −0.0901023 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.43605 | −0.348007 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.54379 | −0.0984287 | ||||||||
\(247\) | −12.7882 | −0.813693 | ||||||||
\(248\) | 2.47100 | 0.156909 | ||||||||
\(249\) | 13.2103 | 0.837167 | ||||||||
\(250\) | −2.14432 | −0.135619 | ||||||||
\(251\) | −11.4361 | −0.721840 | −0.360920 | − | 0.932597i | \(-0.617537\pi\) | ||||
−0.360920 | + | 0.932597i | \(0.617537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.52160 | 0.221401 | ||||||||
\(254\) | −18.9378 | −1.18826 | ||||||||
\(255\) | −26.5673 | −1.66371 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.59132 | −0.473533 | −0.236767 | − | 0.971567i | \(-0.576088\pi\) | ||||
−0.236767 | + | 0.971567i | \(0.576088\pi\) | |||||||
\(258\) | 3.60008 | 0.224131 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.08150 | 0.377159 | ||||||||
\(261\) | −9.17278 | −0.567781 | ||||||||
\(262\) | 15.8296 | 0.977959 | ||||||||
\(263\) | 14.7902 | 0.912004 | 0.456002 | − | 0.889979i | \(-0.349281\pi\) | ||||
0.456002 | + | 0.889979i | \(0.349281\pi\) | |||||||
\(264\) | −3.52160 | −0.216739 | ||||||||
\(265\) | 6.11164 | 0.375435 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4840 | 0.886406 | ||||||||
\(268\) | −13.6143 | −0.831628 | ||||||||
\(269\) | 14.7414 | 0.898800 | 0.449400 | − | 0.893331i | \(-0.351638\pi\) | ||||
0.449400 | + | 0.893331i | \(0.351638\pi\) | |||||||
\(270\) | 3.26449 | 0.198670 | ||||||||
\(271\) | 22.3652 | 1.35859 | 0.679296 | − | 0.733865i | \(-0.262285\pi\) | ||||
0.679296 | + | 0.733865i | \(0.262285\pi\) | |||||||
\(272\) | 8.13828 | 0.493456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.5908 | −0.941873 | ||||||||
\(275\) | −19.9212 | −1.20129 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −1.40187 | −0.0842303 | −0.0421152 | − | 0.999113i | \(-0.513410\pi\) | ||||
−0.0421152 | + | 0.999113i | \(0.513410\pi\) | |||||||
\(278\) | −16.4445 | −0.986276 | ||||||||
\(279\) | −2.47100 | −0.147935 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.8403 | −1.54150 | −0.770752 | − | 0.637135i | \(-0.780119\pi\) | ||||
−0.770752 | + | 0.637135i | \(0.780119\pi\) | |||||||
\(282\) | 1.88641 | 0.112334 | ||||||||
\(283\) | −15.0410 | −0.894097 | −0.447049 | − | 0.894510i | \(-0.647525\pi\) | ||||
−0.447049 | + | 0.894510i | \(0.647525\pi\) | |||||||
\(284\) | −8.33512 | −0.494598 | ||||||||
\(285\) | 22.4093 | 1.32741 | ||||||||
\(286\) | 6.56049 | 0.387930 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 49.2316 | 2.89598 | ||||||||
\(290\) | 29.9444 | 1.75840 | ||||||||
\(291\) | 16.0068 | 0.938334 | ||||||||
\(292\) | 16.2661 | 0.951903 | ||||||||
\(293\) | −10.7035 | −0.625307 | −0.312654 | − | 0.949867i | \(-0.601218\pi\) | ||||
−0.312654 | + | 0.949867i | \(0.601218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.8909 | 0.983427 | ||||||||
\(296\) | 4.84322 | 0.281507 | ||||||||
\(297\) | 3.52160 | 0.204344 | ||||||||
\(298\) | 11.6445 | 0.674549 | ||||||||
\(299\) | −1.86293 | −0.107736 | ||||||||
\(300\) | −5.65686 | −0.326599 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.2149 | 1.04815 | ||||||||
\(303\) | 1.42084 | 0.0816249 | ||||||||
\(304\) | −6.86456 | −0.393710 | ||||||||
\(305\) | −17.7459 | −1.01613 | ||||||||
\(306\) | −8.13828 | −0.465234 | ||||||||
\(307\) | −15.2043 | −0.867755 | −0.433878 | − | 0.900972i | \(-0.642855\pi\) | ||||
−0.433878 | + | 0.900972i | \(0.642855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.60440 | −0.375711 | ||||||||
\(310\) | 8.06654 | 0.458149 | ||||||||
\(311\) | 22.6959 | 1.28696 | 0.643482 | − | 0.765461i | \(-0.277489\pi\) | ||||
0.643482 | + | 0.765461i | \(0.277489\pi\) | |||||||
\(312\) | 1.86293 | 0.105468 | ||||||||
\(313\) | 9.63818 | 0.544782 | 0.272391 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272391 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(314\) | 12.1317 | 0.684633 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.99198 | −0.449584 | ||||||||
\(317\) | 0.432571 | 0.0242956 | 0.0121478 | − | 0.999926i | \(-0.496133\pi\) | ||||
0.0121478 | + | 0.999926i | \(0.496133\pi\) | |||||||
\(318\) | 1.87216 | 0.104985 | ||||||||
\(319\) | 32.3029 | 1.80861 | ||||||||
\(320\) | 3.26449 | 0.182490 | ||||||||
\(321\) | −0.965389 | −0.0538828 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −55.8657 | −3.10845 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 10.5383 | 0.584561 | ||||||||
\(326\) | 5.53819 | 0.306732 | ||||||||
\(327\) | 4.67346 | 0.258443 | ||||||||
\(328\) | 1.54379 | 0.0852418 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11.4962 | −0.632846 | ||||||||
\(331\) | 16.0925 | 0.884525 | 0.442262 | − | 0.896886i | \(-0.354176\pi\) | ||||
0.442262 | + | 0.896886i | \(0.354176\pi\) | |||||||
\(332\) | −13.2103 | −0.725008 | ||||||||
\(333\) | −4.84322 | −0.265407 | ||||||||
\(334\) | 5.26791 | 0.288247 | ||||||||
\(335\) | −44.4438 | −2.42822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.138091 | 0.00752232 | 0.00376116 | − | 0.999993i | \(-0.498803\pi\) | ||||
0.00376116 | + | 0.999993i | \(0.498803\pi\) | |||||||
\(338\) | 9.52950 | 0.518336 | ||||||||
\(339\) | −9.88771 | −0.537027 | ||||||||
\(340\) | 26.5673 | 1.44081 | ||||||||
\(341\) | 8.70187 | 0.471233 | ||||||||
\(342\) | 6.86456 | 0.371193 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.60008 | −0.194103 | ||||||||
\(345\) | 3.26449 | 0.175754 | ||||||||
\(346\) | 18.3100 | 0.984350 | ||||||||
\(347\) | −1.83026 | −0.0982534 | −0.0491267 | − | 0.998793i | \(-0.515644\pi\) | ||||
−0.0491267 | + | 0.998793i | \(0.515644\pi\) | |||||||
\(348\) | 9.17278 | 0.491713 | ||||||||
\(349\) | 8.91678 | 0.477304 | 0.238652 | − | 0.971105i | \(-0.423294\pi\) | ||||
0.238652 | + | 0.971105i | \(0.423294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.86293 | −0.0994358 | ||||||||
\(352\) | 3.52160 | 0.187702 | ||||||||
\(353\) | −9.41654 | −0.501192 | −0.250596 | − | 0.968092i | \(-0.580627\pi\) | ||||
−0.250596 | + | 0.968092i | \(0.580627\pi\) | |||||||
\(354\) | 5.17414 | 0.275003 | ||||||||
\(355\) | −27.2099 | −1.44415 | ||||||||
\(356\) | −14.4840 | −0.767650 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.77091 | 0.199299 | ||||||||
\(359\) | 6.35300 | 0.335298 | 0.167649 | − | 0.985847i | \(-0.446382\pi\) | ||||
0.167649 | + | 0.985847i | \(0.446382\pi\) | |||||||
\(360\) | −3.26449 | −0.172053 | ||||||||
\(361\) | 28.1222 | 1.48012 | ||||||||
\(362\) | −17.0151 | −0.894295 | ||||||||
\(363\) | −1.40166 | −0.0735682 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 53.1006 | 2.77941 | ||||||||
\(366\) | −5.43605 | −0.284147 | ||||||||
\(367\) | 1.88989 | 0.0986514 | 0.0493257 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493257 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −1.54379 | −0.0803667 | ||||||||
\(370\) | 15.8106 | 0.821955 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.47100 | 0.128115 | ||||||||
\(373\) | 24.5803 | 1.27272 | 0.636360 | − | 0.771392i | \(-0.280439\pi\) | ||||
0.636360 | + | 0.771392i | \(0.280439\pi\) | |||||||
\(374\) | 28.6598 | 1.48196 | ||||||||
\(375\) | −2.14432 | −0.110732 | ||||||||
\(376\) | −1.88641 | −0.0972840 | ||||||||
\(377\) | −17.0882 | −0.880089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.4906 | 1.20663 | 0.603315 | − | 0.797503i | \(-0.293846\pi\) | ||||
0.603315 | + | 0.797503i | \(0.293846\pi\) | |||||||
\(380\) | −22.4093 | −1.14957 | ||||||||
\(381\) | −18.9378 | −0.970213 | ||||||||
\(382\) | 3.33717 | 0.170745 | ||||||||
\(383\) | −30.5288 | −1.55995 | −0.779975 | − | 0.625811i | \(-0.784768\pi\) | ||||
−0.779975 | + | 0.625811i | \(0.784768\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.3679 | −0.527711 | ||||||||
\(387\) | 3.60008 | 0.183002 | ||||||||
\(388\) | −16.0068 | −0.812621 | ||||||||
\(389\) | 27.5805 | 1.39839 | 0.699193 | − | 0.714933i | \(-0.253543\pi\) | ||||
0.699193 | + | 0.714933i | \(0.253543\pi\) | |||||||
\(390\) | 6.08150 | 0.307949 | ||||||||
\(391\) | −8.13828 | −0.411570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.8296 | 0.798500 | ||||||||
\(394\) | −22.3204 | −1.12449 | ||||||||
\(395\) | −26.0897 | −1.31271 | ||||||||
\(396\) | −3.52160 | −0.176967 | ||||||||
\(397\) | −14.5938 | −0.732444 | −0.366222 | − | 0.930528i | \(-0.619349\pi\) | ||||
−0.366222 | + | 0.930528i | \(0.619349\pi\) | |||||||
\(398\) | −8.22716 | −0.412391 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.65686 | 0.282843 | ||||||||
\(401\) | 6.68159 | 0.333663 | 0.166831 | − | 0.985985i | \(-0.446646\pi\) | ||||
0.166831 | + | 0.985985i | \(0.446646\pi\) | |||||||
\(402\) | −13.6143 | −0.679022 | ||||||||
\(403\) | −4.60330 | −0.229307 | ||||||||
\(404\) | −1.42084 | −0.0706892 | ||||||||
\(405\) | 3.26449 | 0.162214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.0559 | 0.845429 | ||||||||
\(408\) | 8.13828 | 0.402905 | ||||||||
\(409\) | 34.9189 | 1.72663 | 0.863315 | − | 0.504666i | \(-0.168384\pi\) | ||||
0.863315 | + | 0.504666i | \(0.168384\pi\) | |||||||
\(410\) | 5.03969 | 0.248893 | ||||||||
\(411\) | −15.5908 | −0.769036 | ||||||||
\(412\) | 6.60440 | 0.325375 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −43.1248 | −2.11691 | ||||||||
\(416\) | −1.86293 | −0.0913376 | ||||||||
\(417\) | −16.4445 | −0.805291 | ||||||||
\(418\) | −24.1742 | −1.18240 | ||||||||
\(419\) | −32.1728 | −1.57174 | −0.785871 | − | 0.618390i | \(-0.787785\pi\) | ||||
−0.785871 | + | 0.618390i | \(0.787785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.98710 | −0.340530 | −0.170265 | − | 0.985398i | \(-0.554462\pi\) | ||||
−0.170265 | + | 0.985398i | \(0.554462\pi\) | |||||||
\(422\) | −5.22292 | −0.254248 | ||||||||
\(423\) | 1.88641 | 0.0917203 | ||||||||
\(424\) | −1.87216 | −0.0909201 | ||||||||
\(425\) | 46.0371 | 2.23313 | ||||||||
\(426\) | −8.33512 | −0.403838 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.965389 | 0.0466638 | ||||||||
\(429\) | 6.56049 | 0.316743 | ||||||||
\(430\) | −11.7524 | −0.566751 | ||||||||
\(431\) | −39.3097 | −1.89348 | −0.946741 | − | 0.321995i | \(-0.895646\pi\) | ||||
−0.946741 | + | 0.321995i | \(0.895646\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 29.8712 | 1.43552 | 0.717759 | − | 0.696291i | \(-0.245168\pi\) | ||||
0.717759 | + | 0.696291i | \(0.245168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.9444 | 1.43572 | ||||||||
\(436\) | −4.67346 | −0.223818 | ||||||||
\(437\) | 6.86456 | 0.328377 | ||||||||
\(438\) | 16.2661 | 0.777226 | ||||||||
\(439\) | −32.7457 | −1.56287 | −0.781434 | − | 0.623988i | \(-0.785511\pi\) | ||||
−0.781434 | + | 0.623988i | \(0.785511\pi\) | |||||||
\(440\) | 11.4962 | 0.548060 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.1610 | −0.721137 | ||||||||
\(443\) | −24.5277 | −1.16535 | −0.582673 | − | 0.812706i | \(-0.697993\pi\) | ||||
−0.582673 | + | 0.812706i | \(0.697993\pi\) | |||||||
\(444\) | 4.84322 | 0.229849 | ||||||||
\(445\) | −47.2828 | −2.24142 | ||||||||
\(446\) | −3.71741 | −0.176025 | ||||||||
\(447\) | 11.6445 | 0.550767 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.9912 | −0.849057 | −0.424529 | − | 0.905415i | \(-0.639560\pi\) | ||||
−0.424529 | + | 0.905415i | \(0.639560\pi\) | |||||||
\(450\) | −5.65686 | −0.266667 | ||||||||
\(451\) | 5.43663 | 0.256001 | ||||||||
\(452\) | 9.88771 | 0.465079 | ||||||||
\(453\) | 18.2149 | 0.855809 | ||||||||
\(454\) | 6.94798 | 0.326085 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.86456 | −0.321463 | ||||||||
\(457\) | 37.3345 | 1.74643 | 0.873217 | − | 0.487332i | \(-0.162030\pi\) | ||||
0.873217 | + | 0.487332i | \(0.162030\pi\) | |||||||
\(458\) | 18.7523 | 0.876240 | ||||||||
\(459\) | −8.13828 | −0.379862 | ||||||||
\(460\) | −3.26449 | −0.152207 | ||||||||
\(461\) | −8.87335 | −0.413273 | −0.206636 | − | 0.978418i | \(-0.566252\pi\) | ||||
−0.206636 | + | 0.978418i | \(0.566252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6281 | −0.772774 | −0.386387 | − | 0.922337i | \(-0.626277\pi\) | ||||
−0.386387 | + | 0.922337i | \(0.626277\pi\) | |||||||
\(464\) | −9.17278 | −0.425836 | ||||||||
\(465\) | 8.06654 | 0.374077 | ||||||||
\(466\) | 3.59491 | 0.166531 | ||||||||
\(467\) | 25.6060 | 1.18490 | 0.592452 | − | 0.805606i | \(-0.298160\pi\) | ||||
0.592452 | + | 0.805606i | \(0.298160\pi\) | |||||||
\(468\) | 1.86293 | 0.0861139 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.15815 | −0.284054 | ||||||||
\(471\) | 12.1317 | 0.559001 | ||||||||
\(472\) | −5.17414 | −0.238159 | ||||||||
\(473\) | −12.6780 | −0.582936 | ||||||||
\(474\) | −7.99198 | −0.367084 | ||||||||
\(475\) | −38.8319 | −1.78173 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.87216 | 0.0857203 | ||||||||
\(478\) | −18.4835 | −0.845414 | ||||||||
\(479\) | −4.73824 | −0.216496 | −0.108248 | − | 0.994124i | \(-0.534524\pi\) | ||||
−0.108248 | + | 0.994124i | \(0.534524\pi\) | |||||||
\(480\) | 3.26449 | 0.149003 | ||||||||
\(481\) | −9.02258 | −0.411394 | ||||||||
\(482\) | 5.79561 | 0.263983 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.40166 | 0.0637120 | ||||||||
\(485\) | −52.2539 | −2.37273 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 22.6113 | 1.02461 | 0.512307 | − | 0.858802i | \(-0.328791\pi\) | ||||
0.512307 | + | 0.858802i | \(0.328791\pi\) | |||||||
\(488\) | 5.43605 | 0.246078 | ||||||||
\(489\) | 5.53819 | 0.250446 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.6247 | −0.524614 | −0.262307 | − | 0.964984i | \(-0.584483\pi\) | ||||
−0.262307 | + | 0.964984i | \(0.584483\pi\) | |||||||
\(492\) | 1.54379 | 0.0695996 | ||||||||
\(493\) | −74.6506 | −3.36210 | ||||||||
\(494\) | 12.7882 | 0.575368 | ||||||||
\(495\) | −11.4962 | −0.516716 | ||||||||
\(496\) | −2.47100 | −0.110951 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.2103 | −0.591967 | ||||||||
\(499\) | −12.1423 | −0.543562 | −0.271781 | − | 0.962359i | \(-0.587613\pi\) | ||||
−0.271781 | + | 0.962359i | \(0.587613\pi\) | |||||||
\(500\) | 2.14432 | 0.0958970 | ||||||||
\(501\) | 5.26791 | 0.235353 | ||||||||
\(502\) | 11.4361 | 0.510418 | ||||||||
\(503\) | 12.4765 | 0.556300 | 0.278150 | − | 0.960538i | \(-0.410279\pi\) | ||||
0.278150 | + | 0.960538i | \(0.410279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.63830 | −0.206402 | ||||||||
\(506\) | −3.52160 | −0.156554 | ||||||||
\(507\) | 9.52950 | 0.423220 | ||||||||
\(508\) | 18.9378 | 0.840230 | ||||||||
\(509\) | −34.0894 | −1.51098 | −0.755492 | − | 0.655157i | \(-0.772602\pi\) | ||||
−0.755492 | + | 0.655157i | \(0.772602\pi\) | |||||||
\(510\) | 26.5673 | 1.17642 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.86456 | 0.303078 | ||||||||
\(514\) | 7.59132 | 0.334839 | ||||||||
\(515\) | 21.5600 | 0.950045 | ||||||||
\(516\) | −3.60008 | −0.158485 | ||||||||
\(517\) | −6.64317 | −0.292166 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3100 | 0.803719 | ||||||||
\(520\) | −6.08150 | −0.266691 | ||||||||
\(521\) | −44.2138 | −1.93704 | −0.968520 | − | 0.248936i | \(-0.919919\pi\) | ||||
−0.968520 | + | 0.248936i | \(0.919919\pi\) | |||||||
\(522\) | 9.17278 | 0.401482 | ||||||||
\(523\) | −21.5177 | −0.940904 | −0.470452 | − | 0.882426i | \(-0.655909\pi\) | ||||
−0.470452 | + | 0.882426i | \(0.655909\pi\) | |||||||
\(524\) | −15.8296 | −0.691521 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.7902 | −0.644884 | ||||||||
\(527\) | −20.1097 | −0.875992 | ||||||||
\(528\) | 3.52160 | 0.153258 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.11164 | −0.265473 | ||||||||
\(531\) | 5.17414 | 0.224539 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.87598 | −0.124572 | ||||||||
\(534\) | −14.4840 | −0.626784 | ||||||||
\(535\) | 3.15150 | 0.136251 | ||||||||
\(536\) | 13.6143 | 0.588050 | ||||||||
\(537\) | 3.77091 | 0.162727 | ||||||||
\(538\) | −14.7414 | −0.635548 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.26449 | −0.140481 | ||||||||
\(541\) | −30.2223 | −1.29936 | −0.649679 | − | 0.760209i | \(-0.725097\pi\) | ||||
−0.649679 | + | 0.760209i | \(0.725097\pi\) | |||||||
\(542\) | −22.3652 | −0.960669 | ||||||||
\(543\) | −17.0151 | −0.730189 | ||||||||
\(544\) | −8.13828 | −0.348926 | ||||||||
\(545\) | −15.2564 | −0.653514 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.8306 | −1.10444 | −0.552219 | − | 0.833699i | \(-0.686219\pi\) | ||||
−0.552219 | + | 0.833699i | \(0.686219\pi\) | |||||||
\(548\) | 15.5908 | 0.666005 | ||||||||
\(549\) | −5.43605 | −0.232005 | ||||||||
\(550\) | 19.9212 | 0.849443 | ||||||||
\(551\) | 62.9671 | 2.68249 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.40187 | 0.0595598 | ||||||||
\(555\) | 15.8106 | 0.671124 | ||||||||
\(556\) | 16.4445 | 0.697402 | ||||||||
\(557\) | −38.9155 | −1.64890 | −0.824452 | − | 0.565931i | \(-0.808517\pi\) | ||||
−0.824452 | + | 0.565931i | \(0.808517\pi\) | |||||||
\(558\) | 2.47100 | 0.104606 | ||||||||
\(559\) | 6.70669 | 0.283663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.6598 | 1.21002 | ||||||||
\(562\) | 25.8403 | 1.09001 | ||||||||
\(563\) | −7.52616 | −0.317190 | −0.158595 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158595 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(564\) | −1.88641 | −0.0794321 | ||||||||
\(565\) | 32.2783 | 1.35796 | ||||||||
\(566\) | 15.0410 | 0.632222 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.33512 | 0.349734 | ||||||||
\(569\) | −41.5969 | −1.74383 | −0.871917 | − | 0.489653i | \(-0.837123\pi\) | ||||
−0.871917 | + | 0.489653i | \(0.837123\pi\) | |||||||
\(570\) | −22.4093 | −0.938621 | ||||||||
\(571\) | 2.87509 | 0.120319 | 0.0601595 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601595 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(572\) | −6.56049 | −0.274308 | ||||||||
\(573\) | 3.33717 | 0.139412 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.65686 | −0.235908 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.28662 | 0.386607 | 0.193303 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193303 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(578\) | −49.2316 | −2.04776 | ||||||||
\(579\) | −10.3679 | −0.430874 | ||||||||
\(580\) | −29.9444 | −1.24337 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.0068 | −0.663502 | ||||||||
\(583\) | −6.59300 | −0.273054 | ||||||||
\(584\) | −16.2661 | −0.673097 | ||||||||
\(585\) | 6.08150 | 0.251439 | ||||||||
\(586\) | 10.7035 | 0.442159 | ||||||||
\(587\) | 11.2199 | 0.463095 | 0.231547 | − | 0.972824i | \(-0.425621\pi\) | ||||
0.231547 | + | 0.972824i | \(0.425621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9623 | 0.698921 | ||||||||
\(590\) | −16.8909 | −0.695388 | ||||||||
\(591\) | −22.3204 | −0.918140 | ||||||||
\(592\) | −4.84322 | −0.199055 | ||||||||
\(593\) | −38.9350 | −1.59887 | −0.799434 | − | 0.600754i | \(-0.794867\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(594\) | −3.52160 | −0.144493 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.6445 | −0.476978 | ||||||||
\(597\) | −8.22716 | −0.336715 | ||||||||
\(598\) | 1.86293 | 0.0761808 | ||||||||
\(599\) | 8.65877 | 0.353788 | 0.176894 | − | 0.984230i | \(-0.443395\pi\) | ||||
0.176894 | + | 0.984230i | \(0.443395\pi\) | |||||||
\(600\) | 5.65686 | 0.230941 | ||||||||
\(601\) | −32.5669 | −1.32843 | −0.664216 | − | 0.747541i | \(-0.731234\pi\) | ||||
−0.664216 | + | 0.747541i | \(0.731234\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.6143 | −0.554419 | ||||||||
\(604\) | −18.2149 | −0.741152 | ||||||||
\(605\) | 4.57571 | 0.186029 | ||||||||
\(606\) | −1.42084 | −0.0577175 | ||||||||
\(607\) | 30.0087 | 1.21802 | 0.609008 | − | 0.793164i | \(-0.291568\pi\) | ||||
0.609008 | + | 0.793164i | \(0.291568\pi\) | |||||||
\(608\) | 6.86456 | 0.278395 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.7459 | 0.718510 | ||||||||
\(611\) | 3.51424 | 0.142171 | ||||||||
\(612\) | 8.13828 | 0.328970 | ||||||||
\(613\) | 13.1291 | 0.530280 | 0.265140 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265140 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(614\) | 15.2043 | 0.613595 | ||||||||
\(615\) | 5.03969 | 0.203220 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.21361 | 0.129375 | 0.0646875 | − | 0.997906i | \(-0.479395\pi\) | ||||
0.0646875 | + | 0.997906i | \(0.479395\pi\) | |||||||
\(618\) | 6.60440 | 0.265668 | ||||||||
\(619\) | −32.8446 | −1.32014 | −0.660069 | − | 0.751205i | \(-0.729473\pi\) | ||||
−0.660069 | + | 0.751205i | \(0.729473\pi\) | |||||||
\(620\) | −8.06654 | −0.323960 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −22.6959 | −0.910021 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.86293 | −0.0745768 | ||||||||
\(625\) | −21.2842 | −0.851368 | ||||||||
\(626\) | −9.63818 | −0.385219 | ||||||||
\(627\) | −24.1742 | −0.965426 | ||||||||
\(628\) | −12.1317 | −0.484109 | ||||||||
\(629\) | −39.4155 | −1.57160 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.90402 | 0.235035 | 0.117518 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117518 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(632\) | 7.99198 | 0.317904 | ||||||||
\(633\) | −5.22292 | −0.207592 | ||||||||
\(634\) | −0.432571 | −0.0171796 | ||||||||
\(635\) | 61.8222 | 2.45334 | ||||||||
\(636\) | −1.87216 | −0.0742359 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.3029 | −1.27888 | ||||||||
\(639\) | −8.33512 | −0.329732 | ||||||||
\(640\) | −3.26449 | −0.129040 | ||||||||
\(641\) | −25.1157 | −0.992009 | −0.496005 | − | 0.868320i | \(-0.665200\pi\) | ||||
−0.496005 | + | 0.868320i | \(0.665200\pi\) | |||||||
\(642\) | 0.965389 | 0.0381009 | ||||||||
\(643\) | 8.16448 | 0.321976 | 0.160988 | − | 0.986956i | \(-0.448532\pi\) | ||||
0.160988 | + | 0.986956i | \(0.448532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.7524 | −0.462750 | ||||||||
\(646\) | 55.8657 | 2.19801 | ||||||||
\(647\) | −4.07837 | −0.160337 | −0.0801686 | − | 0.996781i | \(-0.525546\pi\) | ||||
−0.0801686 | + | 0.996781i | \(0.525546\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −18.2213 | −0.715247 | ||||||||
\(650\) | −10.5383 | −0.413347 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.53819 | −0.216892 | ||||||||
\(653\) | 38.0394 | 1.48860 | 0.744298 | − | 0.667848i | \(-0.232784\pi\) | ||||
0.744298 | + | 0.667848i | \(0.232784\pi\) | |||||||
\(654\) | −4.67346 | −0.182747 | ||||||||
\(655\) | −51.6756 | −2.01913 | ||||||||
\(656\) | −1.54379 | −0.0602751 | ||||||||
\(657\) | 16.2661 | 0.634602 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.73327 | −0.379154 | −0.189577 | − | 0.981866i | \(-0.560712\pi\) | ||||
−0.189577 | + | 0.981866i | \(0.560712\pi\) | |||||||
\(660\) | 11.4962 | 0.447489 | ||||||||
\(661\) | 36.5750 | 1.42260 | 0.711301 | − | 0.702888i | \(-0.248106\pi\) | ||||
0.711301 | + | 0.702888i | \(0.248106\pi\) | |||||||
\(662\) | −16.0925 | −0.625453 | ||||||||
\(663\) | −15.1610 | −0.588806 | ||||||||
\(664\) | 13.2103 | 0.512658 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.84322 | 0.187671 | ||||||||
\(667\) | 9.17278 | 0.355171 | ||||||||
\(668\) | −5.26791 | −0.203822 | ||||||||
\(669\) | −3.71741 | −0.143724 | ||||||||
\(670\) | 44.4438 | 1.71701 | ||||||||
\(671\) | 19.1436 | 0.739030 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.1935 | −1.12533 | −0.562663 | − | 0.826687i | \(-0.690223\pi\) | ||||
−0.562663 | + | 0.826687i | \(0.690223\pi\) | |||||||
\(674\) | −0.138091 | −0.00531908 | ||||||||
\(675\) | −5.65686 | −0.217733 | ||||||||
\(676\) | −9.52950 | −0.366519 | ||||||||
\(677\) | −6.31369 | −0.242655 | −0.121327 | − | 0.992613i | \(-0.538715\pi\) | ||||
−0.121327 | + | 0.992613i | \(0.538715\pi\) | |||||||
\(678\) | 9.88771 | 0.379735 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −26.5673 | −1.01881 | ||||||||
\(681\) | 6.94798 | 0.266247 | ||||||||
\(682\) | −8.70187 | −0.333212 | ||||||||
\(683\) | −27.3125 | −1.04508 | −0.522542 | − | 0.852614i | \(-0.675016\pi\) | ||||
−0.522542 | + | 0.852614i | \(0.675016\pi\) | |||||||
\(684\) | −6.86456 | −0.262473 | ||||||||
\(685\) | 50.8958 | 1.94463 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.7523 | 0.715447 | ||||||||
\(688\) | 3.60008 | 0.137252 | ||||||||
\(689\) | 3.48770 | 0.132871 | ||||||||
\(690\) | −3.26449 | −0.124277 | ||||||||
\(691\) | −24.4925 | −0.931737 | −0.465868 | − | 0.884854i | \(-0.654258\pi\) | ||||
−0.465868 | + | 0.884854i | \(0.654258\pi\) | |||||||
\(692\) | −18.3100 | −0.696041 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.83026 | 0.0694756 | ||||||||
\(695\) | 53.6828 | 2.03631 | ||||||||
\(696\) | −9.17278 | −0.347693 | ||||||||
\(697\) | −12.5638 | −0.475889 | ||||||||
\(698\) | −8.91678 | −0.337505 | ||||||||
\(699\) | 3.59491 | 0.135972 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.6574 | −1.30899 | −0.654496 | − | 0.756066i | \(-0.727119\pi\) | ||||
−0.654496 | + | 0.756066i | \(0.727119\pi\) | |||||||
\(702\) | 1.86293 | 0.0703117 | ||||||||
\(703\) | 33.2466 | 1.25392 | ||||||||
\(704\) | −3.52160 | −0.132725 | ||||||||
\(705\) | −6.15815 | −0.231929 | ||||||||
\(706\) | 9.41654 | 0.354396 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.17414 | −0.194456 | ||||||||
\(709\) | −14.6297 | −0.549428 | −0.274714 | − | 0.961526i | \(-0.588583\pi\) | ||||
−0.274714 | + | 0.961526i | \(0.588583\pi\) | |||||||
\(710\) | 27.2099 | 1.02117 | ||||||||
\(711\) | −7.99198 | −0.299723 | ||||||||
\(712\) | 14.4840 | 0.542811 | ||||||||
\(713\) | 2.47100 | 0.0925397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.4166 | −0.800936 | ||||||||
\(716\) | −3.77091 | −0.140925 | ||||||||
\(717\) | −18.4835 | −0.690278 | ||||||||
\(718\) | −6.35300 | −0.237092 | ||||||||
\(719\) | 47.1823 | 1.75960 | 0.879802 | − | 0.475340i | \(-0.157675\pi\) | ||||
0.879802 | + | 0.475340i | \(0.157675\pi\) | |||||||
\(720\) | 3.26449 | 0.121660 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −28.1222 | −1.04660 | ||||||||
\(723\) | 5.79561 | 0.215541 | ||||||||
\(724\) | 17.0151 | 0.632362 | ||||||||
\(725\) | −51.8892 | −1.92712 | ||||||||
\(726\) | 1.40166 | 0.0520206 | ||||||||
\(727\) | −41.9531 | −1.55596 | −0.777978 | − | 0.628292i | \(-0.783754\pi\) | ||||
−0.777978 | + | 0.628292i | \(0.783754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −53.1006 | −1.96534 | ||||||||
\(731\) | 29.2984 | 1.08364 | ||||||||
\(732\) | 5.43605 | 0.200922 | ||||||||
\(733\) | −12.0469 | −0.444961 | −0.222480 | − | 0.974937i | \(-0.571415\pi\) | ||||
−0.222480 | + | 0.974937i | \(0.571415\pi\) | |||||||
\(734\) | −1.88989 | −0.0697571 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 47.9442 | 1.76605 | ||||||||
\(738\) | 1.54379 | 0.0568279 | ||||||||
\(739\) | 37.7894 | 1.39011 | 0.695053 | − | 0.718959i | \(-0.255381\pi\) | ||||
0.695053 | + | 0.718959i | \(0.255381\pi\) | |||||||
\(740\) | −15.8106 | −0.581210 | ||||||||
\(741\) | 12.7882 | 0.469786 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.05540 | 0.0387190 | 0.0193595 | − | 0.999813i | \(-0.493837\pi\) | ||||
0.0193595 | + | 0.999813i | \(0.493837\pi\) | |||||||
\(744\) | −2.47100 | −0.0905913 | ||||||||
\(745\) | −38.0134 | −1.39270 | ||||||||
\(746\) | −24.5803 | −0.899949 | ||||||||
\(747\) | −13.2103 | −0.483339 | ||||||||
\(748\) | −28.6598 | −1.04790 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.14432 | 0.0782996 | ||||||||
\(751\) | 14.7129 | 0.536880 | 0.268440 | − | 0.963296i | \(-0.413492\pi\) | ||||
0.268440 | + | 0.963296i | \(0.413492\pi\) | |||||||
\(752\) | 1.88641 | 0.0687902 | ||||||||
\(753\) | 11.4361 | 0.416755 | ||||||||
\(754\) | 17.0882 | 0.622317 | ||||||||
\(755\) | −59.4621 | −2.16405 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7115 | −0.607389 | −0.303694 | − | 0.952770i | \(-0.598220\pi\) | ||||
−0.303694 | + | 0.952770i | \(0.598220\pi\) | |||||||
\(758\) | −23.4906 | −0.853217 | ||||||||
\(759\) | −3.52160 | −0.127826 | ||||||||
\(760\) | 22.4093 | 0.812869 | ||||||||
\(761\) | 18.0482 | 0.654245 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(762\) | 18.9378 | 0.686045 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.33717 | −0.120735 | ||||||||
\(765\) | 26.5673 | 0.960542 | ||||||||
\(766\) | 30.5288 | 1.10305 | ||||||||
\(767\) | 9.63906 | 0.348046 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −30.1276 | −1.08643 | −0.543215 | − | 0.839594i | \(-0.682793\pi\) | ||||
−0.543215 | + | 0.839594i | \(0.682793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.59132 | 0.273395 | ||||||||
\(772\) | 10.3679 | 0.373148 | ||||||||
\(773\) | −38.8904 | −1.39879 | −0.699395 | − | 0.714735i | \(-0.746547\pi\) | ||||
−0.699395 | + | 0.714735i | \(0.746547\pi\) | |||||||
\(774\) | −3.60008 | −0.129402 | ||||||||
\(775\) | −13.9781 | −0.502109 | ||||||||
\(776\) | 16.0068 | 0.574610 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −27.5805 | −0.988809 | ||||||||
\(779\) | 10.5975 | 0.379694 | ||||||||
\(780\) | −6.08150 | −0.217753 | ||||||||
\(781\) | 29.3530 | 1.05033 | ||||||||
\(782\) | 8.13828 | 0.291024 | ||||||||
\(783\) | 9.17278 | 0.327808 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.6039 | −1.41352 | ||||||||
\(786\) | −15.8296 | −0.564625 | ||||||||
\(787\) | 41.8653 | 1.49234 | 0.746168 | − | 0.665758i | \(-0.231892\pi\) | ||||
0.746168 | + | 0.665758i | \(0.231892\pi\) | |||||||
\(788\) | 22.3204 | 0.795133 | ||||||||
\(789\) | −14.7902 | −0.526546 | ||||||||
\(790\) | 26.0897 | 0.928229 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.52160 | 0.125135 | ||||||||
\(793\) | −10.1270 | −0.359619 | ||||||||
\(794\) | 14.5938 | 0.517916 | ||||||||
\(795\) | −6.11164 | −0.216757 | ||||||||
\(796\) | 8.22716 | 0.291604 | ||||||||
\(797\) | −49.9218 | −1.76832 | −0.884160 | − | 0.467185i | \(-0.845268\pi\) | ||||
−0.884160 | + | 0.467185i | \(0.845268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3521 | 0.543119 | ||||||||
\(800\) | −5.65686 | −0.200000 | ||||||||
\(801\) | −14.4840 | −0.511767 | ||||||||
\(802\) | −6.68159 | −0.235935 | ||||||||
\(803\) | −57.2828 | −2.02147 | ||||||||
\(804\) | 13.6143 | 0.480141 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.60330 | 0.162144 | ||||||||
\(807\) | −14.7414 | −0.518922 | ||||||||
\(808\) | 1.42084 | 0.0499848 | ||||||||
\(809\) | 12.3792 | 0.435230 | 0.217615 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217615 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(810\) | −3.26449 | −0.114702 | ||||||||
\(811\) | 27.8928 | 0.979448 | 0.489724 | − | 0.871878i | \(-0.337098\pi\) | ||||
0.489724 | + | 0.871878i | \(0.337098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.3652 | −0.784383 | ||||||||
\(814\) | −17.0559 | −0.597809 | ||||||||
\(815\) | −18.0793 | −0.633292 | ||||||||
\(816\) | −8.13828 | −0.284897 | ||||||||
\(817\) | −24.7130 | −0.864597 | ||||||||
\(818\) | −34.9189 | −1.22091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.03969 | −0.175994 | ||||||||
\(821\) | −7.26843 | −0.253670 | −0.126835 | − | 0.991924i | \(-0.540482\pi\) | ||||
−0.126835 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(822\) | 15.5908 | 0.543790 | ||||||||
\(823\) | 0.328444 | 0.0114488 | 0.00572442 | − | 0.999984i | \(-0.498178\pi\) | ||||
0.00572442 | + | 0.999984i | \(0.498178\pi\) | |||||||
\(824\) | −6.60440 | −0.230075 | ||||||||
\(825\) | 19.9212 | 0.693567 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.7779 | 1.59185 | 0.795927 | − | 0.605392i | \(-0.206984\pi\) | ||||
0.795927 | + | 0.605392i | \(0.206984\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 14.0218 | 0.486999 | 0.243499 | − | 0.969901i | \(-0.421705\pi\) | ||||
0.243499 | + | 0.969901i | \(0.421705\pi\) | |||||||
\(830\) | 43.1248 | 1.49688 | ||||||||
\(831\) | 1.40187 | 0.0486304 | ||||||||
\(832\) | 1.86293 | 0.0645854 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.4445 | 0.569427 | ||||||||
\(835\) | −17.1970 | −0.595127 | ||||||||
\(836\) | 24.1742 | 0.836084 | ||||||||
\(837\) | 2.47100 | 0.0854103 | ||||||||
\(838\) | 32.1728 | 1.11139 | ||||||||
\(839\) | −29.2636 | −1.01029 | −0.505146 | − | 0.863034i | \(-0.668561\pi\) | ||||
−0.505146 | + | 0.863034i | \(0.668561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.1399 | 1.90138 | ||||||||
\(842\) | 6.98710 | 0.240791 | ||||||||
\(843\) | 25.8403 | 0.889988 | ||||||||
\(844\) | 5.22292 | 0.179780 | ||||||||
\(845\) | −31.1089 | −1.07018 | ||||||||
\(846\) | −1.88641 | −0.0648560 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.87216 | 0.0642902 | ||||||||
\(849\) | 15.0410 | 0.516207 | ||||||||
\(850\) | −46.0371 | −1.57906 | ||||||||
\(851\) | 4.84322 | 0.166024 | ||||||||
\(852\) | 8.33512 | 0.285557 | ||||||||
\(853\) | 10.1911 | 0.348936 | 0.174468 | − | 0.984663i | \(-0.444179\pi\) | ||||
0.174468 | + | 0.984663i | \(0.444179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.4093 | −0.766381 | ||||||||
\(856\) | −0.965389 | −0.0329963 | ||||||||
\(857\) | −32.8461 | −1.12200 | −0.561001 | − | 0.827815i | \(-0.689584\pi\) | ||||
−0.561001 | + | 0.827815i | \(0.689584\pi\) | |||||||
\(858\) | −6.56049 | −0.223971 | ||||||||
\(859\) | −38.2994 | −1.30676 | −0.653380 | − | 0.757031i | \(-0.726649\pi\) | ||||
−0.653380 | + | 0.757031i | \(0.726649\pi\) | |||||||
\(860\) | 11.7524 | 0.400753 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.3097 | 1.33889 | ||||||||
\(863\) | −15.2798 | −0.520131 | −0.260066 | − | 0.965591i | \(-0.583744\pi\) | ||||
−0.260066 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −59.7726 | −2.03233 | ||||||||
\(866\) | −29.8712 | −1.01506 | ||||||||
\(867\) | −49.2316 | −1.67199 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.1445 | 0.954738 | ||||||||
\(870\) | −29.9444 | −1.01521 | ||||||||
\(871\) | −25.3625 | −0.859377 | ||||||||
\(872\) | 4.67346 | 0.158263 | ||||||||
\(873\) | −16.0068 | −0.541747 | ||||||||
\(874\) | −6.86456 | −0.232197 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.2661 | −0.549582 | ||||||||
\(877\) | 4.36608 | 0.147432 | 0.0737160 | − | 0.997279i | \(-0.476514\pi\) | ||||
0.0737160 | + | 0.997279i | \(0.476514\pi\) | |||||||
\(878\) | 32.7457 | 1.10511 | ||||||||
\(879\) | 10.7035 | 0.361021 | ||||||||
\(880\) | −11.4962 | −0.387537 | ||||||||
\(881\) | 5.58075 | 0.188020 | 0.0940101 | − | 0.995571i | \(-0.470031\pi\) | ||||
0.0940101 | + | 0.995571i | \(0.470031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.6306 | −0.929844 | −0.464922 | − | 0.885352i | \(-0.653918\pi\) | ||||
−0.464922 | + | 0.885352i | \(0.653918\pi\) | |||||||
\(884\) | 15.1610 | 0.509921 | ||||||||
\(885\) | −16.8909 | −0.567782 | ||||||||
\(886\) | 24.5277 | 0.824025 | ||||||||
\(887\) | 34.5221 | 1.15914 | 0.579570 | − | 0.814922i | \(-0.303220\pi\) | ||||
0.579570 | + | 0.814922i | \(0.303220\pi\) | |||||||
\(888\) | −4.84322 | −0.162528 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 47.2828 | 1.58492 | ||||||||
\(891\) | −3.52160 | −0.117978 | ||||||||
\(892\) | 3.71741 | 0.124468 | ||||||||
\(893\) | −12.9494 | −0.433334 | ||||||||
\(894\) | −11.6445 | −0.389451 | ||||||||
\(895\) | −12.3101 | −0.411480 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.86293 | 0.0622014 | ||||||||
\(898\) | 17.9912 | 0.600374 | ||||||||
\(899\) | 22.6659 | 0.755952 | ||||||||
\(900\) | 5.65686 | 0.188562 | ||||||||
\(901\) | 15.2362 | 0.507590 | ||||||||
\(902\) | −5.43663 | −0.181020 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.88771 | −0.328860 | ||||||||
\(905\) | 55.5456 | 1.84640 | ||||||||
\(906\) | −18.2149 | −0.605148 | ||||||||
\(907\) | 44.1694 | 1.46662 | 0.733310 | − | 0.679894i | \(-0.237974\pi\) | ||||
0.733310 | + | 0.679894i | \(0.237974\pi\) | |||||||
\(908\) | −6.94798 | −0.230577 | ||||||||
\(909\) | −1.42084 | −0.0471262 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.84456 | −0.226770 | −0.113385 | − | 0.993551i | \(-0.536169\pi\) | ||||
−0.113385 | + | 0.993551i | \(0.536169\pi\) | |||||||
\(912\) | 6.86456 | 0.227308 | ||||||||
\(913\) | 46.5213 | 1.53963 | ||||||||
\(914\) | −37.3345 | −1.23491 | ||||||||
\(915\) | 17.7459 | 0.586661 | ||||||||
\(916\) | −18.7523 | −0.619595 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.13828 | 0.268603 | ||||||||
\(919\) | 9.23681 | 0.304694 | 0.152347 | − | 0.988327i | \(-0.451317\pi\) | ||||
0.152347 | + | 0.988327i | \(0.451317\pi\) | |||||||
\(920\) | 3.26449 | 0.107627 | ||||||||
\(921\) | 15.2043 | 0.500999 | ||||||||
\(922\) | 8.87335 | 0.292228 | ||||||||
\(923\) | −15.5277 | −0.511102 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.3974 | −0.900823 | ||||||||
\(926\) | 16.6281 | 0.546434 | ||||||||
\(927\) | 6.60440 | 0.216917 | ||||||||
\(928\) | 9.17278 | 0.301111 | ||||||||
\(929\) | −13.1079 | −0.430056 | −0.215028 | − | 0.976608i | \(-0.568984\pi\) | ||||
−0.215028 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(930\) | −8.06654 | −0.264512 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.59491 | −0.117755 | ||||||||
\(933\) | −22.6959 | −0.743029 | ||||||||
\(934\) | −25.6060 | −0.837854 | ||||||||
\(935\) | −93.5594 | −3.05972 | ||||||||
\(936\) | −1.86293 | −0.0608917 | ||||||||
\(937\) | −43.6679 | −1.42657 | −0.713285 | − | 0.700874i | \(-0.752793\pi\) | ||||
−0.713285 | + | 0.700874i | \(0.752793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.63818 | −0.314530 | ||||||||
\(940\) | 6.15815 | 0.200857 | ||||||||
\(941\) | 14.9034 | 0.485838 | 0.242919 | − | 0.970047i | \(-0.421895\pi\) | ||||
0.242919 | + | 0.970047i | \(0.421895\pi\) | |||||||
\(942\) | −12.1317 | −0.395273 | ||||||||
\(943\) | 1.54379 | 0.0502729 | ||||||||
\(944\) | 5.17414 | 0.168404 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.6780 | 0.412198 | ||||||||
\(947\) | 46.8338 | 1.52190 | 0.760948 | − | 0.648813i | \(-0.224734\pi\) | ||||
0.760948 | + | 0.648813i | \(0.224734\pi\) | |||||||
\(948\) | 7.99198 | 0.259567 | ||||||||
\(949\) | 30.3026 | 0.983665 | ||||||||
\(950\) | 38.8319 | 1.25987 | ||||||||
\(951\) | −0.432571 | −0.0140271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1448 | 1.39760 | 0.698798 | − | 0.715319i | \(-0.253719\pi\) | ||||
0.698798 | + | 0.715319i | \(0.253719\pi\) | |||||||
\(954\) | −1.87216 | −0.0606134 | ||||||||
\(955\) | −10.8942 | −0.352527 | ||||||||
\(956\) | 18.4835 | 0.597798 | ||||||||
\(957\) | −32.3029 | −1.04420 | ||||||||
\(958\) | 4.73824 | 0.153086 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.26449 | −0.105361 | ||||||||
\(961\) | −24.8942 | −0.803037 | ||||||||
\(962\) | 9.02258 | 0.290899 | ||||||||
\(963\) | 0.965389 | 0.0311092 | ||||||||
\(964\) | −5.79561 | −0.186664 | ||||||||
\(965\) | 33.8458 | 1.08953 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.9474 | 1.02736 | 0.513679 | − | 0.857983i | \(-0.328282\pi\) | ||||
0.513679 | + | 0.857983i | \(0.328282\pi\) | |||||||
\(968\) | −1.40166 | −0.0450512 | ||||||||
\(969\) | 55.8657 | 1.79467 | ||||||||
\(970\) | 52.2539 | 1.67777 | ||||||||
\(971\) | 40.1186 | 1.28747 | 0.643734 | − | 0.765250i | \(-0.277384\pi\) | ||||
0.643734 | + | 0.765250i | \(0.277384\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.6113 | −0.724512 | ||||||||
\(975\) | −10.5383 | −0.337497 | ||||||||
\(976\) | −5.43605 | −0.174004 | ||||||||
\(977\) | 17.5748 | 0.562267 | 0.281134 | − | 0.959669i | \(-0.409290\pi\) | ||||
0.281134 | + | 0.959669i | \(0.409290\pi\) | |||||||
\(978\) | −5.53819 | −0.177092 | ||||||||
\(979\) | 51.0068 | 1.63019 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.67346 | −0.149212 | ||||||||
\(982\) | 11.6247 | 0.370958 | ||||||||
\(983\) | −55.1421 | −1.75876 | −0.879379 | − | 0.476122i | \(-0.842042\pi\) | ||||
−0.879379 | + | 0.476122i | \(0.842042\pi\) | |||||||
\(984\) | −1.54379 | −0.0492144 | ||||||||
\(985\) | 72.8647 | 2.32166 | ||||||||
\(986\) | 74.6506 | 2.37736 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.7882 | −0.406846 | ||||||||
\(989\) | −3.60008 | −0.114476 | ||||||||
\(990\) | 11.4962 | 0.365374 | ||||||||
\(991\) | −0.518377 | −0.0164668 | −0.00823339 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823339 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(992\) | 2.47100 | 0.0784543 | ||||||||
\(993\) | −16.0925 | −0.510681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.8575 | 0.851439 | ||||||||
\(996\) | 13.2103 | 0.418584 | ||||||||
\(997\) | 19.1245 | 0.605678 | 0.302839 | − | 0.953042i | \(-0.402066\pi\) | ||||
0.302839 | + | 0.953042i | \(0.402066\pi\) | |||||||
\(998\) | 12.1423 | 0.384357 | ||||||||
\(999\) | 4.84322 | 0.153233 |
(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 | 6762.2.a.cu.1.7 | ✓ | 8 | |
7.6 | odd | 2 | 6762.2.a.cv.1.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cu.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6762.2.a.cv.1.2 | yes | 8 | 7.6 | odd | 2 |