Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.13298000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 3x^{3} + 26x^{2} + 13x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.770059\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 3.25498 | 1.87927 | 0.939633 | − | 0.342184i | \(-0.111167\pi\) | ||||
0.939633 | + | 0.342184i | \(0.111167\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.25498 | −1.32884 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.59492 | 2.53164 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.25498 | 0.939633 | ||||||||
\(13\) | −3.57888 | −0.992603 | −0.496302 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496302 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 3.25498 | 0.840433 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.01604 | −0.731497 | −0.365749 | − | 0.930714i | \(-0.619187\pi\) | ||||
−0.365749 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(18\) | −7.59492 | −1.79014 | ||||||||
\(19\) | −2.86689 | −0.657710 | −0.328855 | − | 0.944380i | \(-0.606663\pi\) | ||||
−0.328855 | + | 0.944380i | \(0.606663\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.25498 | −0.710296 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.00193 | −1.87703 | −0.938516 | − | 0.345235i | \(-0.887799\pi\) | ||||
−0.938516 | + | 0.345235i | \(0.887799\pi\) | |||||||
\(24\) | −3.25498 | −0.664421 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.57888 | 0.701876 | ||||||||
\(27\) | 14.9564 | 2.87836 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.56460 | −0.290539 | −0.145269 | − | 0.989392i | \(-0.546405\pi\) | ||||
−0.145269 | + | 0.989392i | \(0.546405\pi\) | |||||||
\(30\) | −3.25498 | −0.594276 | ||||||||
\(31\) | −0.473234 | −0.0849954 | −0.0424977 | − | 0.999097i | \(-0.513532\pi\) | ||||
−0.0424977 | + | 0.999097i | \(0.513532\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.01604 | 0.517247 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 7.59492 | 1.26582 | ||||||||
\(37\) | −10.8935 | −1.79088 | −0.895442 | − | 0.445178i | \(-0.853140\pi\) | ||||
−0.895442 | + | 0.445178i | \(0.853140\pi\) | |||||||
\(38\) | 2.86689 | 0.465071 | ||||||||
\(39\) | −11.6492 | −1.86537 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.84241 | −0.600084 | −0.300042 | − | 0.953926i | \(-0.597001\pi\) | ||||
−0.300042 | + | 0.953926i | \(0.597001\pi\) | |||||||
\(42\) | 3.25498 | 0.502255 | ||||||||
\(43\) | −2.25195 | −0.343420 | −0.171710 | − | 0.985148i | \(-0.554929\pi\) | ||||
−0.171710 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.59492 | 1.13218 | ||||||||
\(46\) | 9.00193 | 1.32726 | ||||||||
\(47\) | −9.61359 | −1.40229 | −0.701143 | − | 0.713021i | \(-0.747326\pi\) | ||||
−0.701143 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(48\) | 3.25498 | 0.469817 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −9.81716 | −1.37468 | ||||||||
\(52\) | −3.57888 | −0.496302 | ||||||||
\(53\) | −5.62157 | −0.772182 | −0.386091 | − | 0.922461i | \(-0.626175\pi\) | ||||
−0.386091 | + | 0.922461i | \(0.626175\pi\) | |||||||
\(54\) | −14.9564 | −2.03531 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −9.33169 | −1.23601 | ||||||||
\(58\) | 1.56460 | 0.205442 | ||||||||
\(59\) | −2.73647 | −0.356258 | −0.178129 | − | 0.984007i | \(-0.557004\pi\) | ||||
−0.178129 | + | 0.984007i | \(0.557004\pi\) | |||||||
\(60\) | 3.25498 | 0.420217 | ||||||||
\(61\) | 11.8983 | 1.52343 | 0.761713 | − | 0.647915i | \(-0.224359\pi\) | ||||
0.761713 | + | 0.647915i | \(0.224359\pi\) | |||||||
\(62\) | 0.473234 | 0.0601008 | ||||||||
\(63\) | −7.59492 | −0.956870 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.57888 | −0.443906 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.752899 | 0.0919813 | 0.0459907 | − | 0.998942i | \(-0.485356\pi\) | ||||
0.0459907 | + | 0.998942i | \(0.485356\pi\) | |||||||
\(68\) | −3.01604 | −0.365749 | ||||||||
\(69\) | −29.3011 | −3.52744 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −1.90401 | −0.225965 | −0.112982 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112982 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(72\) | −7.59492 | −0.895070 | ||||||||
\(73\) | −1.66740 | −0.195155 | −0.0975774 | − | 0.995228i | \(-0.531109\pi\) | ||||
−0.0975774 | + | 0.995228i | \(0.531109\pi\) | |||||||
\(74\) | 10.8935 | 1.26635 | ||||||||
\(75\) | 3.25498 | 0.375853 | ||||||||
\(76\) | −2.86689 | −0.328855 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.6492 | 1.31901 | ||||||||
\(79\) | 14.5396 | 1.63583 | 0.817915 | − | 0.575339i | \(-0.195130\pi\) | ||||
0.817915 | + | 0.575339i | \(0.195130\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 25.8981 | 2.87756 | ||||||||
\(82\) | 3.84241 | 0.424323 | ||||||||
\(83\) | 5.31576 | 0.583481 | 0.291740 | − | 0.956498i | \(-0.405766\pi\) | ||||
0.291740 | + | 0.956498i | \(0.405766\pi\) | |||||||
\(84\) | −3.25498 | −0.355148 | ||||||||
\(85\) | −3.01604 | −0.327136 | ||||||||
\(86\) | 2.25195 | 0.242834 | ||||||||
\(87\) | −5.09274 | −0.545999 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1627 | −1.18324 | −0.591621 | − | 0.806216i | \(-0.701512\pi\) | ||||
−0.591621 | + | 0.806216i | \(0.701512\pi\) | |||||||
\(90\) | −7.59492 | −0.800575 | ||||||||
\(91\) | 3.57888 | 0.375169 | ||||||||
\(92\) | −9.00193 | −0.938516 | ||||||||
\(93\) | −1.54037 | −0.159729 | ||||||||
\(94\) | 9.61359 | 0.991566 | ||||||||
\(95\) | −2.86689 | −0.294137 | ||||||||
\(96\) | −3.25498 | −0.332210 | ||||||||
\(97\) | −1.05562 | −0.107182 | −0.0535910 | − | 0.998563i | \(-0.517067\pi\) | ||||
−0.0535910 | + | 0.998563i | \(0.517067\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.63558 | −0.560761 | −0.280381 | − | 0.959889i | \(-0.590461\pi\) | ||||
−0.280381 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(102\) | 9.81716 | 0.972044 | ||||||||
\(103\) | −7.68278 | −0.757007 | −0.378504 | − | 0.925600i | \(-0.623561\pi\) | ||||
−0.378504 | + | 0.925600i | \(0.623561\pi\) | |||||||
\(104\) | 3.57888 | 0.350938 | ||||||||
\(105\) | −3.25498 | −0.317654 | ||||||||
\(106\) | 5.62157 | 0.546015 | ||||||||
\(107\) | −17.5406 | −1.69571 | −0.847856 | − | 0.530227i | \(-0.822107\pi\) | ||||
−0.847856 | + | 0.530227i | \(0.822107\pi\) | |||||||
\(108\) | 14.9564 | 1.43918 | ||||||||
\(109\) | −10.2643 | −0.983138 | −0.491569 | − | 0.870839i | \(-0.663576\pi\) | ||||
−0.491569 | + | 0.870839i | \(0.663576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.4582 | −3.36555 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.7388 | 1.01023 | 0.505113 | − | 0.863053i | \(-0.331451\pi\) | ||||
0.505113 | + | 0.863053i | \(0.331451\pi\) | |||||||
\(114\) | 9.33169 | 0.873992 | ||||||||
\(115\) | −9.00193 | −0.839434 | ||||||||
\(116\) | −1.56460 | −0.145269 | ||||||||
\(117\) | −27.1813 | −2.51291 | ||||||||
\(118\) | 2.73647 | 0.251913 | ||||||||
\(119\) | 3.01604 | 0.276480 | ||||||||
\(120\) | −3.25498 | −0.297138 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.8983 | −1.07722 | ||||||||
\(123\) | −12.5070 | −1.12772 | ||||||||
\(124\) | −0.473234 | −0.0424977 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.59492 | 0.676609 | ||||||||
\(127\) | −0.276538 | −0.0245388 | −0.0122694 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122694 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.33008 | −0.645377 | ||||||||
\(130\) | 3.57888 | 0.313889 | ||||||||
\(131\) | 16.8708 | 1.47400 | 0.737002 | − | 0.675890i | \(-0.236241\pi\) | ||||
0.737002 | + | 0.675890i | \(0.236241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.86689 | 0.248591 | ||||||||
\(134\) | −0.752899 | −0.0650406 | ||||||||
\(135\) | 14.9564 | 1.28724 | ||||||||
\(136\) | 3.01604 | 0.258623 | ||||||||
\(137\) | 13.4886 | 1.15241 | 0.576205 | − | 0.817305i | \(-0.304533\pi\) | ||||
0.576205 | + | 0.817305i | \(0.304533\pi\) | |||||||
\(138\) | 29.3011 | 2.49428 | ||||||||
\(139\) | 1.47583 | 0.125178 | 0.0625890 | − | 0.998039i | \(-0.480064\pi\) | ||||
0.0625890 | + | 0.998039i | \(0.480064\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −31.2921 | −2.63527 | ||||||||
\(142\) | 1.90401 | 0.159781 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.59492 | 0.632910 | ||||||||
\(145\) | −1.56460 | −0.129933 | ||||||||
\(146\) | 1.66740 | 0.137995 | ||||||||
\(147\) | 3.25498 | 0.268467 | ||||||||
\(148\) | −10.8935 | −0.895442 | ||||||||
\(149\) | 16.4457 | 1.34729 | 0.673644 | − | 0.739056i | \(-0.264728\pi\) | ||||
0.673644 | + | 0.739056i | \(0.264728\pi\) | |||||||
\(150\) | −3.25498 | −0.265768 | ||||||||
\(151\) | −7.87495 | −0.640854 | −0.320427 | − | 0.947273i | \(-0.603826\pi\) | ||||
−0.320427 | + | 0.947273i | \(0.603826\pi\) | |||||||
\(152\) | 2.86689 | 0.232536 | ||||||||
\(153\) | −22.9066 | −1.85189 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.473234 | −0.0380111 | ||||||||
\(156\) | −11.6492 | −0.932683 | ||||||||
\(157\) | −11.7854 | −0.940575 | −0.470288 | − | 0.882513i | \(-0.655850\pi\) | ||||
−0.470288 | + | 0.882513i | \(0.655850\pi\) | |||||||
\(158\) | −14.5396 | −1.15671 | ||||||||
\(159\) | −18.2981 | −1.45113 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 9.00193 | 0.709452 | ||||||||
\(162\) | −25.8981 | −2.03475 | ||||||||
\(163\) | −8.20930 | −0.643002 | −0.321501 | − | 0.946909i | \(-0.604187\pi\) | ||||
−0.321501 | + | 0.946909i | \(0.604187\pi\) | |||||||
\(164\) | −3.84241 | −0.300042 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.31576 | −0.412583 | ||||||||
\(167\) | −20.1999 | −1.56312 | −0.781558 | − | 0.623832i | \(-0.785575\pi\) | ||||
−0.781558 | + | 0.623832i | \(0.785575\pi\) | |||||||
\(168\) | 3.25498 | 0.251127 | ||||||||
\(169\) | −0.191604 | −0.0147388 | ||||||||
\(170\) | 3.01604 | 0.231320 | ||||||||
\(171\) | −21.7738 | −1.66509 | ||||||||
\(172\) | −2.25195 | −0.171710 | ||||||||
\(173\) | 24.7276 | 1.88000 | 0.940001 | − | 0.341172i | \(-0.110824\pi\) | ||||
0.940001 | + | 0.341172i | \(0.110824\pi\) | |||||||
\(174\) | 5.09274 | 0.386080 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.90717 | −0.669504 | ||||||||
\(178\) | 11.1627 | 0.836678 | ||||||||
\(179\) | 25.5970 | 1.91321 | 0.956606 | − | 0.291384i | \(-0.0941157\pi\) | ||||
0.956606 | + | 0.291384i | \(0.0941157\pi\) | |||||||
\(180\) | 7.59492 | 0.566092 | ||||||||
\(181\) | −2.24943 | −0.167199 | −0.0835995 | − | 0.996499i | \(-0.526642\pi\) | ||||
−0.0835995 | + | 0.996499i | \(0.526642\pi\) | |||||||
\(182\) | −3.57888 | −0.265284 | ||||||||
\(183\) | 38.7289 | 2.86292 | ||||||||
\(184\) | 9.00193 | 0.663631 | ||||||||
\(185\) | −10.8935 | −0.800908 | ||||||||
\(186\) | 1.54037 | 0.112945 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.61359 | −0.701143 | ||||||||
\(189\) | −14.9564 | −1.08792 | ||||||||
\(190\) | 2.86689 | 0.207986 | ||||||||
\(191\) | 26.0718 | 1.88649 | 0.943244 | − | 0.332099i | \(-0.107757\pi\) | ||||
0.943244 | + | 0.332099i | \(0.107757\pi\) | |||||||
\(192\) | 3.25498 | 0.234908 | ||||||||
\(193\) | 23.7468 | 1.70934 | 0.854668 | − | 0.519175i | \(-0.173761\pi\) | ||||
0.854668 | + | 0.519175i | \(0.173761\pi\) | |||||||
\(194\) | 1.05562 | 0.0757891 | ||||||||
\(195\) | −11.6492 | −0.834217 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −8.36713 | −0.596133 | −0.298067 | − | 0.954545i | \(-0.596342\pi\) | ||||
−0.298067 | + | 0.954545i | \(0.596342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.83066 | 0.484213 | 0.242106 | − | 0.970250i | \(-0.422162\pi\) | ||||
0.242106 | + | 0.970250i | \(0.422162\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 2.45068 | 0.172857 | ||||||||
\(202\) | 5.63558 | 0.396518 | ||||||||
\(203\) | 1.56460 | 0.109813 | ||||||||
\(204\) | −9.81716 | −0.687339 | ||||||||
\(205\) | −3.84241 | −0.268366 | ||||||||
\(206\) | 7.68278 | 0.535285 | ||||||||
\(207\) | −68.3690 | −4.75197 | ||||||||
\(208\) | −3.57888 | −0.248151 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.25498 | 0.224615 | ||||||||
\(211\) | −2.84244 | −0.195682 | −0.0978409 | − | 0.995202i | \(-0.531194\pi\) | ||||
−0.0978409 | + | 0.995202i | \(0.531194\pi\) | |||||||
\(212\) | −5.62157 | −0.386091 | ||||||||
\(213\) | −6.19753 | −0.424648 | ||||||||
\(214\) | 17.5406 | 1.19905 | ||||||||
\(215\) | −2.25195 | −0.153582 | ||||||||
\(216\) | −14.9564 | −1.01765 | ||||||||
\(217\) | 0.473234 | 0.0321252 | ||||||||
\(218\) | 10.2643 | 0.695183 | ||||||||
\(219\) | −5.42737 | −0.366748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7941 | 0.726087 | ||||||||
\(222\) | 35.4582 | 2.37980 | ||||||||
\(223\) | 20.0124 | 1.34013 | 0.670064 | − | 0.742303i | \(-0.266267\pi\) | ||||
0.670064 | + | 0.742303i | \(0.266267\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 7.59492 | 0.506328 | ||||||||
\(226\) | −10.7388 | −0.714337 | ||||||||
\(227\) | 12.3334 | 0.818599 | 0.409300 | − | 0.912400i | \(-0.365773\pi\) | ||||
0.409300 | + | 0.912400i | \(0.365773\pi\) | |||||||
\(228\) | −9.33169 | −0.618006 | ||||||||
\(229\) | 5.54315 | 0.366302 | 0.183151 | − | 0.983085i | \(-0.441370\pi\) | ||||
0.183151 | + | 0.983085i | \(0.441370\pi\) | |||||||
\(230\) | 9.00193 | 0.593570 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.56460 | 0.102721 | ||||||||
\(233\) | −12.9621 | −0.849173 | −0.424586 | − | 0.905387i | \(-0.639581\pi\) | ||||
−0.424586 | + | 0.905387i | \(0.639581\pi\) | |||||||
\(234\) | 27.1813 | 1.77690 | ||||||||
\(235\) | −9.61359 | −0.627121 | ||||||||
\(236\) | −2.73647 | −0.178129 | ||||||||
\(237\) | 47.3261 | 3.07416 | ||||||||
\(238\) | −3.01604 | −0.195501 | ||||||||
\(239\) | 21.3109 | 1.37849 | 0.689244 | − | 0.724529i | \(-0.257943\pi\) | ||||
0.689244 | + | 0.724529i | \(0.257943\pi\) | |||||||
\(240\) | 3.25498 | 0.210108 | ||||||||
\(241\) | −7.67156 | −0.494169 | −0.247084 | − | 0.968994i | \(-0.579472\pi\) | ||||
−0.247084 | + | 0.968994i | \(0.579472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 39.4286 | 2.52935 | ||||||||
\(244\) | 11.8983 | 0.761713 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 12.5070 | 0.797416 | ||||||||
\(247\) | 10.2603 | 0.652845 | ||||||||
\(248\) | 0.473234 | 0.0300504 | ||||||||
\(249\) | 17.3027 | 1.09652 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 27.1182 | 1.71169 | 0.855843 | − | 0.517235i | \(-0.173039\pi\) | ||||
0.855843 | + | 0.517235i | \(0.173039\pi\) | |||||||
\(252\) | −7.59492 | −0.478435 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.276538 | 0.0173515 | ||||||||
\(255\) | −9.81716 | −0.614775 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.73716 | 0.420252 | 0.210126 | − | 0.977674i | \(-0.432613\pi\) | ||||
0.210126 | + | 0.977674i | \(0.432613\pi\) | |||||||
\(258\) | 7.33008 | 0.456351 | ||||||||
\(259\) | 10.8935 | 0.676891 | ||||||||
\(260\) | −3.57888 | −0.221953 | ||||||||
\(261\) | −11.8830 | −0.735539 | ||||||||
\(262\) | −16.8708 | −1.04228 | ||||||||
\(263\) | −32.1781 | −1.98419 | −0.992094 | − | 0.125496i | \(-0.959948\pi\) | ||||
−0.992094 | + | 0.125496i | \(0.959948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.62157 | −0.345330 | ||||||||
\(266\) | −2.86689 | −0.175780 | ||||||||
\(267\) | −36.3343 | −2.22363 | ||||||||
\(268\) | 0.752899 | 0.0459907 | ||||||||
\(269\) | −30.0523 | −1.83232 | −0.916160 | − | 0.400812i | \(-0.868728\pi\) | ||||
−0.916160 | + | 0.400812i | \(0.868728\pi\) | |||||||
\(270\) | −14.9564 | −0.910218 | ||||||||
\(271\) | 8.92828 | 0.542354 | 0.271177 | − | 0.962529i | \(-0.412587\pi\) | ||||
0.271177 | + | 0.962529i | \(0.412587\pi\) | |||||||
\(272\) | −3.01604 | −0.182874 | ||||||||
\(273\) | 11.6492 | 0.705042 | ||||||||
\(274\) | −13.4886 | −0.814877 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −29.3011 | −1.76372 | ||||||||
\(277\) | −1.68071 | −0.100984 | −0.0504919 | − | 0.998724i | \(-0.516079\pi\) | ||||
−0.0504919 | + | 0.998724i | \(0.516079\pi\) | |||||||
\(278\) | −1.47583 | −0.0885142 | ||||||||
\(279\) | −3.59418 | −0.215178 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −7.90100 | −0.471334 | −0.235667 | − | 0.971834i | \(-0.575728\pi\) | ||||
−0.235667 | + | 0.971834i | \(0.575728\pi\) | |||||||
\(282\) | 31.2921 | 1.86342 | ||||||||
\(283\) | −27.0439 | −1.60759 | −0.803795 | − | 0.594906i | \(-0.797189\pi\) | ||||
−0.803795 | + | 0.594906i | \(0.797189\pi\) | |||||||
\(284\) | −1.90401 | −0.112982 | ||||||||
\(285\) | −9.33169 | −0.552761 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.84241 | 0.226810 | ||||||||
\(288\) | −7.59492 | −0.447535 | ||||||||
\(289\) | −7.90350 | −0.464912 | ||||||||
\(290\) | 1.56460 | 0.0918764 | ||||||||
\(291\) | −3.43603 | −0.201423 | ||||||||
\(292\) | −1.66740 | −0.0975774 | ||||||||
\(293\) | −10.2007 | −0.595934 | −0.297967 | − | 0.954576i | \(-0.596308\pi\) | ||||
−0.297967 | + | 0.954576i | \(0.596308\pi\) | |||||||
\(294\) | −3.25498 | −0.189835 | ||||||||
\(295\) | −2.73647 | −0.159323 | ||||||||
\(296\) | 10.8935 | 0.633173 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.4457 | −0.952676 | ||||||||
\(299\) | 32.2168 | 1.86315 | ||||||||
\(300\) | 3.25498 | 0.187927 | ||||||||
\(301\) | 2.25195 | 0.129800 | ||||||||
\(302\) | 7.87495 | 0.453152 | ||||||||
\(303\) | −18.3437 | −1.05382 | ||||||||
\(304\) | −2.86689 | −0.164427 | ||||||||
\(305\) | 11.8983 | 0.681296 | ||||||||
\(306\) | 22.9066 | 1.30948 | ||||||||
\(307\) | −15.3552 | −0.876370 | −0.438185 | − | 0.898885i | \(-0.644379\pi\) | ||||
−0.438185 | + | 0.898885i | \(0.644379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.0073 | −1.42262 | ||||||||
\(310\) | 0.473234 | 0.0268779 | ||||||||
\(311\) | −26.3580 | −1.49463 | −0.747313 | − | 0.664473i | \(-0.768656\pi\) | ||||
−0.747313 | + | 0.664473i | \(0.768656\pi\) | |||||||
\(312\) | 11.6492 | 0.659506 | ||||||||
\(313\) | 8.60472 | 0.486368 | 0.243184 | − | 0.969980i | \(-0.421808\pi\) | ||||
0.243184 | + | 0.969980i | \(0.421808\pi\) | |||||||
\(314\) | 11.7854 | 0.665087 | ||||||||
\(315\) | −7.59492 | −0.427925 | ||||||||
\(316\) | 14.5396 | 0.817915 | ||||||||
\(317\) | 2.87738 | 0.161610 | 0.0808049 | − | 0.996730i | \(-0.474251\pi\) | ||||
0.0808049 | + | 0.996730i | \(0.474251\pi\) | |||||||
\(318\) | 18.2981 | 1.02611 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −57.0943 | −3.18669 | ||||||||
\(322\) | −9.00193 | −0.501658 | ||||||||
\(323\) | 8.64666 | 0.481113 | ||||||||
\(324\) | 25.8981 | 1.43878 | ||||||||
\(325\) | −3.57888 | −0.198521 | ||||||||
\(326\) | 8.20930 | 0.454671 | ||||||||
\(327\) | −33.4100 | −1.84758 | ||||||||
\(328\) | 3.84241 | 0.212162 | ||||||||
\(329\) | 9.61359 | 0.530014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4901 | −1.07128 | −0.535638 | − | 0.844448i | \(-0.679929\pi\) | ||||
−0.535638 | + | 0.844448i | \(0.679929\pi\) | |||||||
\(332\) | 5.31576 | 0.291740 | ||||||||
\(333\) | −82.7355 | −4.53388 | ||||||||
\(334\) | 20.1999 | 1.10529 | ||||||||
\(335\) | 0.752899 | 0.0411353 | ||||||||
\(336\) | −3.25498 | −0.177574 | ||||||||
\(337\) | 28.1366 | 1.53270 | 0.766349 | − | 0.642424i | \(-0.222071\pi\) | ||||
0.766349 | + | 0.642424i | \(0.222071\pi\) | |||||||
\(338\) | 0.191604 | 0.0104219 | ||||||||
\(339\) | 34.9548 | 1.89848 | ||||||||
\(340\) | −3.01604 | −0.163568 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 21.7738 | 1.17739 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.25195 | 0.121417 | ||||||||
\(345\) | −29.3011 | −1.57752 | ||||||||
\(346\) | −24.7276 | −1.32936 | ||||||||
\(347\) | 0.231696 | 0.0124381 | 0.00621904 | − | 0.999981i | \(-0.498020\pi\) | ||||
0.00621904 | + | 0.999981i | \(0.498020\pi\) | |||||||
\(348\) | −5.09274 | −0.273000 | ||||||||
\(349\) | 23.7081 | 1.26906 | 0.634532 | − | 0.772897i | \(-0.281193\pi\) | ||||
0.634532 | + | 0.772897i | \(0.281193\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −53.5272 | −2.85707 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.1884 | 1.07452 | 0.537259 | − | 0.843417i | \(-0.319460\pi\) | ||||
0.537259 | + | 0.843417i | \(0.319460\pi\) | |||||||
\(354\) | 8.90717 | 0.473411 | ||||||||
\(355\) | −1.90401 | −0.101055 | ||||||||
\(356\) | −11.1627 | −0.591621 | ||||||||
\(357\) | 9.81716 | 0.519579 | ||||||||
\(358\) | −25.5970 | −1.35285 | ||||||||
\(359\) | −25.7430 | −1.35866 | −0.679332 | − | 0.733831i | \(-0.737731\pi\) | ||||
−0.679332 | + | 0.733831i | \(0.737731\pi\) | |||||||
\(360\) | −7.59492 | −0.400288 | ||||||||
\(361\) | −10.7809 | −0.567418 | ||||||||
\(362\) | 2.24943 | 0.118228 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.57888 | 0.187584 | ||||||||
\(365\) | −1.66740 | −0.0872759 | ||||||||
\(366\) | −38.7289 | −2.02439 | ||||||||
\(367\) | −18.8546 | −0.984200 | −0.492100 | − | 0.870539i | \(-0.663771\pi\) | ||||
−0.492100 | + | 0.870539i | \(0.663771\pi\) | |||||||
\(368\) | −9.00193 | −0.469258 | ||||||||
\(369\) | −29.1828 | −1.51920 | ||||||||
\(370\) | 10.8935 | 0.566327 | ||||||||
\(371\) | 5.62157 | 0.291857 | ||||||||
\(372\) | −1.54037 | −0.0798645 | ||||||||
\(373\) | −8.46477 | −0.438289 | −0.219145 | − | 0.975692i | \(-0.570327\pi\) | ||||
−0.219145 | + | 0.975692i | \(0.570327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.25498 | 0.168087 | ||||||||
\(376\) | 9.61359 | 0.495783 | ||||||||
\(377\) | 5.59951 | 0.288390 | ||||||||
\(378\) | 14.9564 | 0.769274 | ||||||||
\(379\) | 16.2403 | 0.834206 | 0.417103 | − | 0.908859i | \(-0.363045\pi\) | ||||
0.417103 | + | 0.908859i | \(0.363045\pi\) | |||||||
\(380\) | −2.86689 | −0.147068 | ||||||||
\(381\) | −0.900126 | −0.0461149 | ||||||||
\(382\) | −26.0718 | −1.33395 | ||||||||
\(383\) | 34.3382 | 1.75460 | 0.877301 | − | 0.479940i | \(-0.159342\pi\) | ||||
0.877301 | + | 0.479940i | \(0.159342\pi\) | |||||||
\(384\) | −3.25498 | −0.166105 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.7468 | −1.20868 | ||||||||
\(387\) | −17.1034 | −0.869416 | ||||||||
\(388\) | −1.05562 | −0.0535910 | ||||||||
\(389\) | −1.78492 | −0.0904991 | −0.0452496 | − | 0.998976i | \(-0.514408\pi\) | ||||
−0.0452496 | + | 0.998976i | \(0.514408\pi\) | |||||||
\(390\) | 11.6492 | 0.589880 | ||||||||
\(391\) | 27.1502 | 1.37304 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 54.9140 | 2.77005 | ||||||||
\(394\) | 8.36713 | 0.421530 | ||||||||
\(395\) | 14.5396 | 0.731565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.25072 | 0.0627718 | 0.0313859 | − | 0.999507i | \(-0.490008\pi\) | ||||
0.0313859 | + | 0.999507i | \(0.490008\pi\) | |||||||
\(398\) | −6.83066 | −0.342390 | ||||||||
\(399\) | 9.33169 | 0.467169 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −19.4278 | −0.970176 | −0.485088 | − | 0.874465i | \(-0.661212\pi\) | ||||
−0.485088 | + | 0.874465i | \(0.661212\pi\) | |||||||
\(402\) | −2.45068 | −0.122229 | ||||||||
\(403\) | 1.69365 | 0.0843667 | ||||||||
\(404\) | −5.63558 | −0.280381 | ||||||||
\(405\) | 25.8981 | 1.28689 | ||||||||
\(406\) | −1.56460 | −0.0776497 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.81716 | 0.486022 | ||||||||
\(409\) | 6.77531 | 0.335017 | 0.167509 | − | 0.985871i | \(-0.446428\pi\) | ||||
0.167509 | + | 0.985871i | \(0.446428\pi\) | |||||||
\(410\) | 3.84241 | 0.189763 | ||||||||
\(411\) | 43.9052 | 2.16569 | ||||||||
\(412\) | −7.68278 | −0.378504 | ||||||||
\(413\) | 2.73647 | 0.134653 | ||||||||
\(414\) | 68.3690 | 3.36015 | ||||||||
\(415\) | 5.31576 | 0.260940 | ||||||||
\(416\) | 3.57888 | 0.175469 | ||||||||
\(417\) | 4.80379 | 0.235243 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3741 | 1.28846 | 0.644228 | − | 0.764833i | \(-0.277179\pi\) | ||||
0.644228 | + | 0.764833i | \(0.277179\pi\) | |||||||
\(420\) | −3.25498 | −0.158827 | ||||||||
\(421\) | 19.1809 | 0.934822 | 0.467411 | − | 0.884040i | \(-0.345187\pi\) | ||||
0.467411 | + | 0.884040i | \(0.345187\pi\) | |||||||
\(422\) | 2.84244 | 0.138368 | ||||||||
\(423\) | −73.0144 | −3.55008 | ||||||||
\(424\) | 5.62157 | 0.273007 | ||||||||
\(425\) | −3.01604 | −0.146299 | ||||||||
\(426\) | 6.19753 | 0.300272 | ||||||||
\(427\) | −11.8983 | −0.575801 | ||||||||
\(428\) | −17.5406 | −0.847856 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.25195 | 0.108599 | ||||||||
\(431\) | −27.4826 | −1.32379 | −0.661894 | − | 0.749597i | \(-0.730247\pi\) | ||||
−0.661894 | + | 0.749597i | \(0.730247\pi\) | |||||||
\(432\) | 14.9564 | 0.719590 | ||||||||
\(433\) | 6.92935 | 0.333003 | 0.166502 | − | 0.986041i | \(-0.446753\pi\) | ||||
0.166502 | + | 0.986041i | \(0.446753\pi\) | |||||||
\(434\) | −0.473234 | −0.0227160 | ||||||||
\(435\) | −5.09274 | −0.244178 | ||||||||
\(436\) | −10.2643 | −0.491569 | ||||||||
\(437\) | 25.8076 | 1.23454 | ||||||||
\(438\) | 5.42737 | 0.259330 | ||||||||
\(439\) | 9.07635 | 0.433191 | 0.216595 | − | 0.976261i | \(-0.430505\pi\) | ||||
0.216595 | + | 0.976261i | \(0.430505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.59492 | 0.361663 | ||||||||
\(442\) | −10.7941 | −0.513421 | ||||||||
\(443\) | −23.5991 | −1.12122 | −0.560612 | − | 0.828078i | \(-0.689434\pi\) | ||||
−0.560612 | + | 0.828078i | \(0.689434\pi\) | |||||||
\(444\) | −35.4582 | −1.68277 | ||||||||
\(445\) | −11.1627 | −0.529162 | ||||||||
\(446\) | −20.0124 | −0.947614 | ||||||||
\(447\) | 53.5306 | 2.53191 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −30.0205 | −1.41675 | −0.708377 | − | 0.705834i | \(-0.750572\pi\) | ||||
−0.708377 | + | 0.705834i | \(0.750572\pi\) | |||||||
\(450\) | −7.59492 | −0.358028 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.7388 | 0.505113 | ||||||||
\(453\) | −25.6328 | −1.20434 | ||||||||
\(454\) | −12.3334 | −0.578837 | ||||||||
\(455\) | 3.57888 | 0.167781 | ||||||||
\(456\) | 9.33169 | 0.436996 | ||||||||
\(457\) | 2.10098 | 0.0982798 | 0.0491399 | − | 0.998792i | \(-0.484352\pi\) | ||||
0.0491399 | + | 0.998792i | \(0.484352\pi\) | |||||||
\(458\) | −5.54315 | −0.259014 | ||||||||
\(459\) | −45.1091 | −2.10551 | ||||||||
\(460\) | −9.00193 | −0.419717 | ||||||||
\(461\) | −33.6599 | −1.56770 | −0.783848 | − | 0.620953i | \(-0.786746\pi\) | ||||
−0.783848 | + | 0.620953i | \(0.786746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2506 | 1.45234 | 0.726168 | − | 0.687517i | \(-0.241299\pi\) | ||||
0.726168 | + | 0.687517i | \(0.241299\pi\) | |||||||
\(464\) | −1.56460 | −0.0726346 | ||||||||
\(465\) | −1.54037 | −0.0714330 | ||||||||
\(466\) | 12.9621 | 0.600456 | ||||||||
\(467\) | 26.9260 | 1.24599 | 0.622994 | − | 0.782227i | \(-0.285916\pi\) | ||||
0.622994 | + | 0.782227i | \(0.285916\pi\) | |||||||
\(468\) | −27.1813 | −1.25646 | ||||||||
\(469\) | −0.752899 | −0.0347657 | ||||||||
\(470\) | 9.61359 | 0.443442 | ||||||||
\(471\) | −38.3612 | −1.76759 | ||||||||
\(472\) | 2.73647 | 0.125956 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −47.3261 | −2.17376 | ||||||||
\(475\) | −2.86689 | −0.131542 | ||||||||
\(476\) | 3.01604 | 0.138240 | ||||||||
\(477\) | −42.6954 | −1.95489 | ||||||||
\(478\) | −21.3109 | −0.974738 | ||||||||
\(479\) | −35.8357 | −1.63738 | −0.818688 | − | 0.574238i | \(-0.805298\pi\) | ||||
−0.818688 | + | 0.574238i | \(0.805298\pi\) | |||||||
\(480\) | −3.25498 | −0.148569 | ||||||||
\(481\) | 38.9866 | 1.77764 | ||||||||
\(482\) | 7.67156 | 0.349430 | ||||||||
\(483\) | 29.3011 | 1.33325 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.05562 | −0.0479332 | ||||||||
\(486\) | −39.4286 | −1.78852 | ||||||||
\(487\) | −10.3029 | −0.466870 | −0.233435 | − | 0.972372i | \(-0.574997\pi\) | ||||
−0.233435 | + | 0.972372i | \(0.574997\pi\) | |||||||
\(488\) | −11.8983 | −0.538612 | ||||||||
\(489\) | −26.7211 | −1.20837 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −20.0929 | −0.906778 | −0.453389 | − | 0.891313i | \(-0.649785\pi\) | ||||
−0.453389 | + | 0.891313i | \(0.649785\pi\) | |||||||
\(492\) | −12.5070 | −0.563859 | ||||||||
\(493\) | 4.71889 | 0.212528 | ||||||||
\(494\) | −10.2603 | −0.461631 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.473234 | −0.0212489 | ||||||||
\(497\) | 1.90401 | 0.0854067 | ||||||||
\(498\) | −17.3027 | −0.775353 | ||||||||
\(499\) | 26.1662 | 1.17136 | 0.585680 | − | 0.810542i | \(-0.300827\pi\) | ||||
0.585680 | + | 0.810542i | \(0.300827\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −65.7504 | −2.93751 | ||||||||
\(502\) | −27.1182 | −1.21034 | ||||||||
\(503\) | 1.78113 | 0.0794167 | 0.0397084 | − | 0.999211i | \(-0.487357\pi\) | ||||
0.0397084 | + | 0.999211i | \(0.487357\pi\) | |||||||
\(504\) | 7.59492 | 0.338305 | ||||||||
\(505\) | −5.63558 | −0.250780 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.623670 | −0.0276981 | ||||||||
\(508\) | −0.276538 | −0.0122694 | ||||||||
\(509\) | −7.96822 | −0.353185 | −0.176592 | − | 0.984284i | \(-0.556507\pi\) | ||||
−0.176592 | + | 0.984284i | \(0.556507\pi\) | |||||||
\(510\) | 9.81716 | 0.434711 | ||||||||
\(511\) | 1.66740 | 0.0737616 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −42.8784 | −1.89313 | ||||||||
\(514\) | −6.73716 | −0.297163 | ||||||||
\(515\) | −7.68278 | −0.338544 | ||||||||
\(516\) | −7.33008 | −0.322689 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.8935 | −0.478634 | ||||||||
\(519\) | 80.4878 | 3.53302 | ||||||||
\(520\) | 3.57888 | 0.156944 | ||||||||
\(521\) | −38.1254 | −1.67030 | −0.835152 | − | 0.550019i | \(-0.814621\pi\) | ||||
−0.835152 | + | 0.550019i | \(0.814621\pi\) | |||||||
\(522\) | 11.8830 | 0.520105 | ||||||||
\(523\) | 7.78040 | 0.340213 | 0.170107 | − | 0.985426i | \(-0.445589\pi\) | ||||
0.170107 | + | 0.985426i | \(0.445589\pi\) | |||||||
\(524\) | 16.8708 | 0.737002 | ||||||||
\(525\) | −3.25498 | −0.142059 | ||||||||
\(526\) | 32.1781 | 1.40303 | ||||||||
\(527\) | 1.42729 | 0.0621739 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 58.0348 | 2.52325 | ||||||||
\(530\) | 5.62157 | 0.244185 | ||||||||
\(531\) | −20.7833 | −0.901918 | ||||||||
\(532\) | 2.86689 | 0.124296 | ||||||||
\(533\) | 13.7515 | 0.595645 | ||||||||
\(534\) | 36.3343 | 1.57234 | ||||||||
\(535\) | −17.5406 | −0.758345 | ||||||||
\(536\) | −0.752899 | −0.0325203 | ||||||||
\(537\) | 83.3180 | 3.59544 | ||||||||
\(538\) | 30.0523 | 1.29565 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.9564 | 0.643621 | ||||||||
\(541\) | 9.67143 | 0.415807 | 0.207904 | − | 0.978149i | \(-0.433336\pi\) | ||||
0.207904 | + | 0.978149i | \(0.433336\pi\) | |||||||
\(542\) | −8.92828 | −0.383502 | ||||||||
\(543\) | −7.32187 | −0.314211 | ||||||||
\(544\) | 3.01604 | 0.129312 | ||||||||
\(545\) | −10.2643 | −0.439672 | ||||||||
\(546\) | −11.6492 | −0.498540 | ||||||||
\(547\) | 38.6572 | 1.65286 | 0.826432 | − | 0.563036i | \(-0.190367\pi\) | ||||
0.826432 | + | 0.563036i | \(0.190367\pi\) | |||||||
\(548\) | 13.4886 | 0.576205 | ||||||||
\(549\) | 90.3669 | 3.85677 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.48553 | 0.191090 | ||||||||
\(552\) | 29.3011 | 1.24714 | ||||||||
\(553\) | −14.5396 | −0.618286 | ||||||||
\(554\) | 1.68071 | 0.0714064 | ||||||||
\(555\) | −35.4582 | −1.50512 | ||||||||
\(556\) | 1.47583 | 0.0625890 | ||||||||
\(557\) | −1.28946 | −0.0546360 | −0.0273180 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273180 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(558\) | 3.59418 | 0.152154 | ||||||||
\(559\) | 8.05948 | 0.340880 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.90100 | 0.333284 | ||||||||
\(563\) | 22.8803 | 0.964289 | 0.482144 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482144 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(564\) | −31.2921 | −1.31763 | ||||||||
\(565\) | 10.7388 | 0.451786 | ||||||||
\(566\) | 27.0439 | 1.13674 | ||||||||
\(567\) | −25.8981 | −1.08762 | ||||||||
\(568\) | 1.90401 | 0.0798906 | ||||||||
\(569\) | 3.30473 | 0.138541 | 0.0692707 | − | 0.997598i | \(-0.477933\pi\) | ||||
0.0692707 | + | 0.997598i | \(0.477933\pi\) | |||||||
\(570\) | 9.33169 | 0.390861 | ||||||||
\(571\) | 1.86937 | 0.0782307 | 0.0391153 | − | 0.999235i | \(-0.487546\pi\) | ||||
0.0391153 | + | 0.999235i | \(0.487546\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 84.8633 | 3.54521 | ||||||||
\(574\) | −3.84241 | −0.160379 | ||||||||
\(575\) | −9.00193 | −0.375406 | ||||||||
\(576\) | 7.59492 | 0.316455 | ||||||||
\(577\) | −15.3442 | −0.638787 | −0.319394 | − | 0.947622i | \(-0.603479\pi\) | ||||
−0.319394 | + | 0.947622i | \(0.603479\pi\) | |||||||
\(578\) | 7.90350 | 0.328742 | ||||||||
\(579\) | 77.2956 | 3.21230 | ||||||||
\(580\) | −1.56460 | −0.0649664 | ||||||||
\(581\) | −5.31576 | −0.220535 | ||||||||
\(582\) | 3.43603 | 0.142428 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.66740 | 0.0689976 | ||||||||
\(585\) | −27.1813 | −1.12381 | ||||||||
\(586\) | 10.2007 | 0.421389 | ||||||||
\(587\) | 9.24503 | 0.381583 | 0.190792 | − | 0.981631i | \(-0.438895\pi\) | ||||
0.190792 | + | 0.981631i | \(0.438895\pi\) | |||||||
\(588\) | 3.25498 | 0.134233 | ||||||||
\(589\) | 1.35671 | 0.0559023 | ||||||||
\(590\) | 2.73647 | 0.112659 | ||||||||
\(591\) | −27.2349 | −1.12029 | ||||||||
\(592\) | −10.8935 | −0.447721 | ||||||||
\(593\) | −15.5998 | −0.640606 | −0.320303 | − | 0.947315i | \(-0.603785\pi\) | ||||
−0.320303 | + | 0.947315i | \(0.603785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.01604 | 0.123646 | ||||||||
\(596\) | 16.4457 | 0.673644 | ||||||||
\(597\) | 22.2337 | 0.909965 | ||||||||
\(598\) | −32.2168 | −1.31744 | ||||||||
\(599\) | −23.2701 | −0.950791 | −0.475396 | − | 0.879772i | \(-0.657695\pi\) | ||||
−0.475396 | + | 0.879772i | \(0.657695\pi\) | |||||||
\(600\) | −3.25498 | −0.132884 | ||||||||
\(601\) | −8.23116 | −0.335756 | −0.167878 | − | 0.985808i | \(-0.553691\pi\) | ||||
−0.167878 | + | 0.985808i | \(0.553691\pi\) | |||||||
\(602\) | −2.25195 | −0.0917828 | ||||||||
\(603\) | 5.71821 | 0.232864 | ||||||||
\(604\) | −7.87495 | −0.320427 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.3437 | 0.745163 | ||||||||
\(607\) | 37.1360 | 1.50730 | 0.753652 | − | 0.657274i | \(-0.228291\pi\) | ||||
0.753652 | + | 0.657274i | \(0.228291\pi\) | |||||||
\(608\) | 2.86689 | 0.116268 | ||||||||
\(609\) | 5.09274 | 0.206368 | ||||||||
\(610\) | −11.8983 | −0.481749 | ||||||||
\(611\) | 34.4059 | 1.39191 | ||||||||
\(612\) | −22.9066 | −0.925944 | ||||||||
\(613\) | 17.5909 | 0.710490 | 0.355245 | − | 0.934773i | \(-0.384397\pi\) | ||||
0.355245 | + | 0.934773i | \(0.384397\pi\) | |||||||
\(614\) | 15.3552 | 0.619687 | ||||||||
\(615\) | −12.5070 | −0.504330 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.16685 | 0.208010 | 0.104005 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104005 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(618\) | 25.0073 | 1.00594 | ||||||||
\(619\) | −17.4862 | −0.702828 | −0.351414 | − | 0.936220i | \(-0.614299\pi\) | ||||
−0.351414 | + | 0.936220i | \(0.614299\pi\) | |||||||
\(620\) | −0.473234 | −0.0190056 | ||||||||
\(621\) | −134.636 | −5.40278 | ||||||||
\(622\) | 26.3580 | 1.05686 | ||||||||
\(623\) | 11.1627 | 0.447223 | ||||||||
\(624\) | −11.6492 | −0.466341 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.60472 | −0.343914 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.7854 | −0.470288 | ||||||||
\(629\) | 32.8553 | 1.31003 | ||||||||
\(630\) | 7.59492 | 0.302589 | ||||||||
\(631\) | −18.6264 | −0.741505 | −0.370752 | − | 0.928732i | \(-0.620900\pi\) | ||||
−0.370752 | + | 0.928732i | \(0.620900\pi\) | |||||||
\(632\) | −14.5396 | −0.578353 | ||||||||
\(633\) | −9.25210 | −0.367738 | ||||||||
\(634\) | −2.87738 | −0.114275 | ||||||||
\(635\) | −0.276538 | −0.0109741 | ||||||||
\(636\) | −18.2981 | −0.725567 | ||||||||
\(637\) | −3.57888 | −0.141800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.4608 | −0.572062 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −14.4218 | −0.569625 | −0.284813 | − | 0.958583i | \(-0.591931\pi\) | ||||
−0.284813 | + | 0.958583i | \(0.591931\pi\) | |||||||
\(642\) | 57.0943 | 2.25333 | ||||||||
\(643\) | 23.0331 | 0.908338 | 0.454169 | − | 0.890915i | \(-0.349936\pi\) | ||||
0.454169 | + | 0.890915i | \(0.349936\pi\) | |||||||
\(644\) | 9.00193 | 0.354726 | ||||||||
\(645\) | −7.33008 | −0.288621 | ||||||||
\(646\) | −8.64666 | −0.340198 | ||||||||
\(647\) | 12.8918 | 0.506830 | 0.253415 | − | 0.967358i | \(-0.418446\pi\) | ||||
0.253415 | + | 0.967358i | \(0.418446\pi\) | |||||||
\(648\) | −25.8981 | −1.01737 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.57888 | 0.140375 | ||||||||
\(651\) | 1.54037 | 0.0603719 | ||||||||
\(652\) | −8.20930 | −0.321501 | ||||||||
\(653\) | −23.8203 | −0.932161 | −0.466081 | − | 0.884742i | \(-0.654334\pi\) | ||||
−0.466081 | + | 0.884742i | \(0.654334\pi\) | |||||||
\(654\) | 33.4100 | 1.30643 | ||||||||
\(655\) | 16.8708 | 0.659195 | ||||||||
\(656\) | −3.84241 | −0.150021 | ||||||||
\(657\) | −12.6638 | −0.494062 | ||||||||
\(658\) | −9.61359 | −0.374777 | ||||||||
\(659\) | −19.4714 | −0.758498 | −0.379249 | − | 0.925295i | \(-0.623818\pi\) | ||||
−0.379249 | + | 0.925295i | \(0.623818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.6251 | −1.11339 | −0.556694 | − | 0.830718i | \(-0.687930\pi\) | ||||
−0.556694 | + | 0.830718i | \(0.687930\pi\) | |||||||
\(662\) | 19.4901 | 0.757506 | ||||||||
\(663\) | 35.1345 | 1.36451 | ||||||||
\(664\) | −5.31576 | −0.206292 | ||||||||
\(665\) | 2.86689 | 0.111173 | ||||||||
\(666\) | 82.7355 | 3.20593 | ||||||||
\(667\) | 14.0844 | 0.545350 | ||||||||
\(668\) | −20.1999 | −0.781558 | ||||||||
\(669\) | 65.1400 | 2.51846 | ||||||||
\(670\) | −0.752899 | −0.0290870 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.25498 | 0.125564 | ||||||||
\(673\) | 5.76294 | 0.222145 | 0.111073 | − | 0.993812i | \(-0.464571\pi\) | ||||
0.111073 | + | 0.993812i | \(0.464571\pi\) | |||||||
\(674\) | −28.1366 | −1.08378 | ||||||||
\(675\) | 14.9564 | 0.575672 | ||||||||
\(676\) | −0.191604 | −0.00736940 | ||||||||
\(677\) | −20.1902 | −0.775973 | −0.387987 | − | 0.921665i | \(-0.626829\pi\) | ||||
−0.387987 | + | 0.921665i | \(0.626829\pi\) | |||||||
\(678\) | −34.9548 | −1.34243 | ||||||||
\(679\) | 1.05562 | 0.0405110 | ||||||||
\(680\) | 3.01604 | 0.115660 | ||||||||
\(681\) | 40.1452 | 1.53837 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.0998 | −0.730833 | −0.365417 | − | 0.930844i | \(-0.619073\pi\) | ||||
−0.365417 | + | 0.930844i | \(0.619073\pi\) | |||||||
\(684\) | −21.7738 | −0.832543 | ||||||||
\(685\) | 13.4886 | 0.515374 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 18.0429 | 0.688378 | ||||||||
\(688\) | −2.25195 | −0.0858549 | ||||||||
\(689\) | 20.1189 | 0.766470 | ||||||||
\(690\) | 29.3011 | 1.11548 | ||||||||
\(691\) | −1.77501 | −0.0675246 | −0.0337623 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337623 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(692\) | 24.7276 | 0.940001 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.231696 | −0.00879505 | ||||||||
\(695\) | 1.47583 | 0.0559813 | ||||||||
\(696\) | 5.09274 | 0.193040 | ||||||||
\(697\) | 11.5889 | 0.438960 | ||||||||
\(698\) | −23.7081 | −0.897364 | ||||||||
\(699\) | −42.1913 | −1.59582 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −8.50630 | −0.321279 | −0.160639 | − | 0.987013i | \(-0.551356\pi\) | ||||
−0.160639 | + | 0.987013i | \(0.551356\pi\) | |||||||
\(702\) | 53.5272 | 2.02025 | ||||||||
\(703\) | 31.2305 | 1.17788 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.2921 | −1.17853 | ||||||||
\(706\) | −20.1884 | −0.759799 | ||||||||
\(707\) | 5.63558 | 0.211948 | ||||||||
\(708\) | −8.90717 | −0.334752 | ||||||||
\(709\) | 22.1030 | 0.830096 | 0.415048 | − | 0.909799i | \(-0.363765\pi\) | ||||
0.415048 | + | 0.909799i | \(0.363765\pi\) | |||||||
\(710\) | 1.90401 | 0.0714564 | ||||||||
\(711\) | 110.427 | 4.14133 | ||||||||
\(712\) | 11.1627 | 0.418339 | ||||||||
\(713\) | 4.26002 | 0.159539 | ||||||||
\(714\) | −9.81716 | −0.367398 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.5970 | 0.956606 | ||||||||
\(717\) | 69.3667 | 2.59055 | ||||||||
\(718\) | 25.7430 | 0.960721 | ||||||||
\(719\) | 20.1432 | 0.751216 | 0.375608 | − | 0.926779i | \(-0.377434\pi\) | ||||
0.375608 | + | 0.926779i | \(0.377434\pi\) | |||||||
\(720\) | 7.59492 | 0.283046 | ||||||||
\(721\) | 7.68278 | 0.286122 | ||||||||
\(722\) | 10.7809 | 0.401225 | ||||||||
\(723\) | −24.9708 | −0.928674 | ||||||||
\(724\) | −2.24943 | −0.0835995 | ||||||||
\(725\) | −1.56460 | −0.0581077 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.7541 | −1.54857 | −0.774287 | − | 0.632835i | \(-0.781891\pi\) | ||||
−0.774287 | + | 0.632835i | \(0.781891\pi\) | |||||||
\(728\) | −3.57888 | −0.132642 | ||||||||
\(729\) | 50.6454 | 1.87575 | ||||||||
\(730\) | 1.66740 | 0.0617134 | ||||||||
\(731\) | 6.79199 | 0.251211 | ||||||||
\(732\) | 38.7289 | 1.43146 | ||||||||
\(733\) | −48.0596 | −1.77512 | −0.887560 | − | 0.460692i | \(-0.847601\pi\) | ||||
−0.887560 | + | 0.460692i | \(0.847601\pi\) | |||||||
\(734\) | 18.8546 | 0.695934 | ||||||||
\(735\) | 3.25498 | 0.120062 | ||||||||
\(736\) | 9.00193 | 0.331816 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 29.1828 | 1.07423 | ||||||||
\(739\) | −39.9689 | −1.47028 | −0.735140 | − | 0.677916i | \(-0.762883\pi\) | ||||
−0.735140 | + | 0.677916i | \(0.762883\pi\) | |||||||
\(740\) | −10.8935 | −0.400454 | ||||||||
\(741\) | 33.3970 | 1.22687 | ||||||||
\(742\) | −5.62157 | −0.206374 | ||||||||
\(743\) | −17.4381 | −0.639742 | −0.319871 | − | 0.947461i | \(-0.603640\pi\) | ||||
−0.319871 | + | 0.947461i | \(0.603640\pi\) | |||||||
\(744\) | 1.54037 | 0.0564727 | ||||||||
\(745\) | 16.4457 | 0.602525 | ||||||||
\(746\) | 8.46477 | 0.309917 | ||||||||
\(747\) | 40.3728 | 1.47716 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5406 | 0.640919 | ||||||||
\(750\) | −3.25498 | −0.118855 | ||||||||
\(751\) | 28.4323 | 1.03751 | 0.518754 | − | 0.854923i | \(-0.326396\pi\) | ||||
0.518754 | + | 0.854923i | \(0.326396\pi\) | |||||||
\(752\) | −9.61359 | −0.350571 | ||||||||
\(753\) | 88.2693 | 3.21671 | ||||||||
\(754\) | −5.59951 | −0.203922 | ||||||||
\(755\) | −7.87495 | −0.286599 | ||||||||
\(756\) | −14.9564 | −0.543959 | ||||||||
\(757\) | 19.9596 | 0.725445 | 0.362722 | − | 0.931897i | \(-0.381847\pi\) | ||||
0.362722 | + | 0.931897i | \(0.381847\pi\) | |||||||
\(758\) | −16.2403 | −0.589873 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.86689 | 0.103993 | ||||||||
\(761\) | −21.9752 | −0.796600 | −0.398300 | − | 0.917255i | \(-0.630400\pi\) | ||||
−0.398300 | + | 0.917255i | \(0.630400\pi\) | |||||||
\(762\) | 0.900126 | 0.0326081 | ||||||||
\(763\) | 10.2643 | 0.371591 | ||||||||
\(764\) | 26.0718 | 0.943244 | ||||||||
\(765\) | −22.9066 | −0.828190 | ||||||||
\(766\) | −34.3382 | −1.24069 | ||||||||
\(767\) | 9.79351 | 0.353623 | ||||||||
\(768\) | 3.25498 | 0.117454 | ||||||||
\(769\) | −23.8878 | −0.861417 | −0.430708 | − | 0.902491i | \(-0.641736\pi\) | ||||
−0.430708 | + | 0.902491i | \(0.641736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.9293 | 0.789766 | ||||||||
\(772\) | 23.7468 | 0.854668 | ||||||||
\(773\) | 3.82132 | 0.137443 | 0.0687216 | − | 0.997636i | \(-0.478108\pi\) | ||||
0.0687216 | + | 0.997636i | \(0.478108\pi\) | |||||||
\(774\) | 17.1034 | 0.614770 | ||||||||
\(775\) | −0.473234 | −0.0169991 | ||||||||
\(776\) | 1.05562 | 0.0378946 | ||||||||
\(777\) | 35.4582 | 1.27206 | ||||||||
\(778\) | 1.78492 | 0.0639925 | ||||||||
\(779\) | 11.0158 | 0.394681 | ||||||||
\(780\) | −11.6492 | −0.417108 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −27.1502 | −0.970889 | ||||||||
\(783\) | −23.4008 | −0.836275 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.7854 | −0.420638 | ||||||||
\(786\) | −54.9140 | −1.95872 | ||||||||
\(787\) | 31.8195 | 1.13424 | 0.567122 | − | 0.823634i | \(-0.308057\pi\) | ||||
0.567122 | + | 0.823634i | \(0.308057\pi\) | |||||||
\(788\) | −8.36713 | −0.298067 | ||||||||
\(789\) | −104.739 | −3.72882 | ||||||||
\(790\) | −14.5396 | −0.517295 | ||||||||
\(791\) | −10.7388 | −0.381829 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.5827 | −1.51216 | ||||||||
\(794\) | −1.25072 | −0.0443864 | ||||||||
\(795\) | −18.2981 | −0.648967 | ||||||||
\(796\) | 6.83066 | 0.242106 | ||||||||
\(797\) | −37.3003 | −1.32124 | −0.660622 | − | 0.750719i | \(-0.729707\pi\) | ||||
−0.660622 | + | 0.750719i | \(0.729707\pi\) | |||||||
\(798\) | −9.33169 | −0.330338 | ||||||||
\(799\) | 28.9950 | 1.02577 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −84.7797 | −2.99554 | ||||||||
\(802\) | 19.4278 | 0.686018 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.45068 | 0.0864287 | ||||||||
\(805\) | 9.00193 | 0.317276 | ||||||||
\(806\) | −1.69365 | −0.0596563 | ||||||||
\(807\) | −97.8197 | −3.44342 | ||||||||
\(808\) | 5.63558 | 0.198259 | ||||||||
\(809\) | 34.4351 | 1.21067 | 0.605337 | − | 0.795969i | \(-0.293038\pi\) | ||||
0.605337 | + | 0.795969i | \(0.293038\pi\) | |||||||
\(810\) | −25.8981 | −0.909966 | ||||||||
\(811\) | 29.0879 | 1.02142 | 0.510708 | − | 0.859754i | \(-0.329383\pi\) | ||||
0.510708 | + | 0.859754i | \(0.329383\pi\) | |||||||
\(812\) | 1.56460 | 0.0549066 | ||||||||
\(813\) | 29.0614 | 1.01923 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.20930 | −0.287559 | ||||||||
\(816\) | −9.81716 | −0.343669 | ||||||||
\(817\) | 6.45611 | 0.225871 | ||||||||
\(818\) | −6.77531 | −0.236893 | ||||||||
\(819\) | 27.1813 | 0.949793 | ||||||||
\(820\) | −3.84241 | −0.134183 | ||||||||
\(821\) | −7.44892 | −0.259969 | −0.129985 | − | 0.991516i | \(-0.541493\pi\) | ||||
−0.129985 | + | 0.991516i | \(0.541493\pi\) | |||||||
\(822\) | −43.9052 | −1.53137 | ||||||||
\(823\) | 43.3944 | 1.51263 | 0.756317 | − | 0.654206i | \(-0.226997\pi\) | ||||
0.756317 | + | 0.654206i | \(0.226997\pi\) | |||||||
\(824\) | 7.68278 | 0.267642 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.73647 | −0.0952140 | ||||||||
\(827\) | −7.19740 | −0.250278 | −0.125139 | − | 0.992139i | \(-0.539938\pi\) | ||||
−0.125139 | + | 0.992139i | \(0.539938\pi\) | |||||||
\(828\) | −68.3690 | −2.37599 | ||||||||
\(829\) | −9.22493 | −0.320395 | −0.160198 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160198 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(830\) | −5.31576 | −0.184513 | ||||||||
\(831\) | −5.47067 | −0.189776 | ||||||||
\(832\) | −3.57888 | −0.124075 | ||||||||
\(833\) | −3.01604 | −0.104500 | ||||||||
\(834\) | −4.80379 | −0.166342 | ||||||||
\(835\) | −20.1999 | −0.699047 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.07788 | −0.244647 | ||||||||
\(838\) | −26.3741 | −0.911077 | ||||||||
\(839\) | −3.04238 | −0.105034 | −0.0525172 | − | 0.998620i | \(-0.516724\pi\) | ||||
−0.0525172 | + | 0.998620i | \(0.516724\pi\) | |||||||
\(840\) | 3.25498 | 0.112308 | ||||||||
\(841\) | −26.5520 | −0.915587 | ||||||||
\(842\) | −19.1809 | −0.661019 | ||||||||
\(843\) | −25.7176 | −0.885762 | ||||||||
\(844\) | −2.84244 | −0.0978409 | ||||||||
\(845\) | −0.191604 | −0.00659139 | ||||||||
\(846\) | 73.0144 | 2.51029 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.62157 | −0.193045 | ||||||||
\(849\) | −88.0273 | −3.02109 | ||||||||
\(850\) | 3.01604 | 0.103449 | ||||||||
\(851\) | 98.0628 | 3.36155 | ||||||||
\(852\) | −6.19753 | −0.212324 | ||||||||
\(853\) | −29.9859 | −1.02670 | −0.513349 | − | 0.858180i | \(-0.671595\pi\) | ||||
−0.513349 | + | 0.858180i | \(0.671595\pi\) | |||||||
\(854\) | 11.8983 | 0.407153 | ||||||||
\(855\) | −21.7738 | −0.744649 | ||||||||
\(856\) | 17.5406 | 0.599525 | ||||||||
\(857\) | 7.77150 | 0.265469 | 0.132735 | − | 0.991152i | \(-0.457624\pi\) | ||||
0.132735 | + | 0.991152i | \(0.457624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.9695 | −1.73906 | −0.869529 | − | 0.493883i | \(-0.835577\pi\) | ||||
−0.869529 | + | 0.493883i | \(0.835577\pi\) | |||||||
\(860\) | −2.25195 | −0.0767910 | ||||||||
\(861\) | 12.5070 | 0.426237 | ||||||||
\(862\) | 27.4826 | 0.936060 | ||||||||
\(863\) | −25.2461 | −0.859386 | −0.429693 | − | 0.902975i | \(-0.641378\pi\) | ||||
−0.429693 | + | 0.902975i | \(0.641378\pi\) | |||||||
\(864\) | −14.9564 | −0.508827 | ||||||||
\(865\) | 24.7276 | 0.840762 | ||||||||
\(866\) | −6.92935 | −0.235469 | ||||||||
\(867\) | −25.7258 | −0.873693 | ||||||||
\(868\) | 0.473234 | 0.0160626 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.09274 | 0.172660 | ||||||||
\(871\) | −2.69454 | −0.0913009 | ||||||||
\(872\) | 10.2643 | 0.347592 | ||||||||
\(873\) | −8.01735 | −0.271346 | ||||||||
\(874\) | −25.8076 | −0.872954 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −5.42737 | −0.183374 | ||||||||
\(877\) | 1.25141 | 0.0422572 | 0.0211286 | − | 0.999777i | \(-0.493274\pi\) | ||||
0.0211286 | + | 0.999777i | \(0.493274\pi\) | |||||||
\(878\) | −9.07635 | −0.306312 | ||||||||
\(879\) | −33.2033 | −1.11992 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.6655 | −0.561476 | −0.280738 | − | 0.959784i | \(-0.590579\pi\) | ||||
−0.280738 | + | 0.959784i | \(0.590579\pi\) | |||||||
\(882\) | −7.59492 | −0.255734 | ||||||||
\(883\) | −1.23966 | −0.0417180 | −0.0208590 | − | 0.999782i | \(-0.506640\pi\) | ||||
−0.0208590 | + | 0.999782i | \(0.506640\pi\) | |||||||
\(884\) | 10.7941 | 0.363043 | ||||||||
\(885\) | −8.90717 | −0.299411 | ||||||||
\(886\) | 23.5991 | 0.792826 | ||||||||
\(887\) | 40.2814 | 1.35252 | 0.676259 | − | 0.736664i | \(-0.263600\pi\) | ||||
0.676259 | + | 0.736664i | \(0.263600\pi\) | |||||||
\(888\) | 35.4582 | 1.18990 | ||||||||
\(889\) | 0.276538 | 0.00927478 | ||||||||
\(890\) | 11.1627 | 0.374174 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0124 | 0.670064 | ||||||||
\(893\) | 27.5611 | 0.922297 | ||||||||
\(894\) | −53.5306 | −1.79033 | ||||||||
\(895\) | 25.5970 | 0.855615 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 104.865 | 3.50135 | ||||||||
\(898\) | 30.0205 | 1.00180 | ||||||||
\(899\) | 0.740422 | 0.0246944 | ||||||||
\(900\) | 7.59492 | 0.253164 | ||||||||
\(901\) | 16.9549 | 0.564849 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.33008 | 0.243930 | ||||||||
\(904\) | −10.7388 | −0.357169 | ||||||||
\(905\) | −2.24943 | −0.0747737 | ||||||||
\(906\) | 25.6328 | 0.851594 | ||||||||
\(907\) | −8.61141 | −0.285937 | −0.142969 | − | 0.989727i | \(-0.545665\pi\) | ||||
−0.142969 | + | 0.989727i | \(0.545665\pi\) | |||||||
\(908\) | 12.3334 | 0.409300 | ||||||||
\(909\) | −42.8018 | −1.41965 | ||||||||
\(910\) | −3.57888 | −0.118639 | ||||||||
\(911\) | 5.14473 | 0.170453 | 0.0852263 | − | 0.996362i | \(-0.472839\pi\) | ||||
0.0852263 | + | 0.996362i | \(0.472839\pi\) | |||||||
\(912\) | −9.33169 | −0.309003 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.10098 | −0.0694943 | ||||||||
\(915\) | 38.7289 | 1.28034 | ||||||||
\(916\) | 5.54315 | 0.183151 | ||||||||
\(917\) | −16.8708 | −0.557121 | ||||||||
\(918\) | 45.1091 | 1.48882 | ||||||||
\(919\) | −21.7516 | −0.717521 | −0.358760 | − | 0.933430i | \(-0.616800\pi\) | ||||
−0.358760 | + | 0.933430i | \(0.616800\pi\) | |||||||
\(920\) | 9.00193 | 0.296785 | ||||||||
\(921\) | −49.9811 | −1.64693 | ||||||||
\(922\) | 33.6599 | 1.10853 | ||||||||
\(923\) | 6.81424 | 0.224293 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8935 | −0.358177 | ||||||||
\(926\) | −31.2506 | −1.02696 | ||||||||
\(927\) | −58.3501 | −1.91647 | ||||||||
\(928\) | 1.56460 | 0.0513604 | ||||||||
\(929\) | −46.1193 | −1.51312 | −0.756562 | − | 0.653922i | \(-0.773122\pi\) | ||||
−0.756562 | + | 0.653922i | \(0.773122\pi\) | |||||||
\(930\) | 1.54037 | 0.0505107 | ||||||||
\(931\) | −2.86689 | −0.0939586 | ||||||||
\(932\) | −12.9621 | −0.424586 | ||||||||
\(933\) | −85.7949 | −2.80880 | ||||||||
\(934\) | −26.9260 | −0.881047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 27.1813 | 0.888450 | ||||||||
\(937\) | −11.2889 | −0.368793 | −0.184397 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184397 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(938\) | 0.752899 | 0.0245830 | ||||||||
\(939\) | 28.0082 | 0.914014 | ||||||||
\(940\) | −9.61359 | −0.313561 | ||||||||
\(941\) | 12.7563 | 0.415845 | 0.207922 | − | 0.978145i | \(-0.433330\pi\) | ||||
0.207922 | + | 0.978145i | \(0.433330\pi\) | |||||||
\(942\) | 38.3612 | 1.24988 | ||||||||
\(943\) | 34.5891 | 1.12638 | ||||||||
\(944\) | −2.73647 | −0.0890645 | ||||||||
\(945\) | −14.9564 | −0.486532 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.3261 | −1.53789 | −0.768945 | − | 0.639315i | \(-0.779218\pi\) | ||||
−0.768945 | + | 0.639315i | \(0.779218\pi\) | |||||||
\(948\) | 47.3261 | 1.53708 | ||||||||
\(949\) | 5.96744 | 0.193711 | ||||||||
\(950\) | 2.86689 | 0.0930142 | ||||||||
\(951\) | 9.36583 | 0.303708 | ||||||||
\(952\) | −3.01604 | −0.0977504 | ||||||||
\(953\) | 5.17931 | 0.167774 | 0.0838872 | − | 0.996475i | \(-0.473266\pi\) | ||||
0.0838872 | + | 0.996475i | \(0.473266\pi\) | |||||||
\(954\) | 42.6954 | 1.38231 | ||||||||
\(955\) | 26.0718 | 0.843663 | ||||||||
\(956\) | 21.3109 | 0.689244 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.8357 | 1.15780 | ||||||||
\(959\) | −13.4886 | −0.435570 | ||||||||
\(960\) | 3.25498 | 0.105054 | ||||||||
\(961\) | −30.7760 | −0.992776 | ||||||||
\(962\) | −38.9866 | −1.25698 | ||||||||
\(963\) | −133.219 | −4.29293 | ||||||||
\(964\) | −7.67156 | −0.247084 | ||||||||
\(965\) | 23.7468 | 0.764438 | ||||||||
\(966\) | −29.3011 | −0.942749 | ||||||||
\(967\) | −39.6832 | −1.27612 | −0.638062 | − | 0.769985i | \(-0.720264\pi\) | ||||
−0.638062 | + | 0.769985i | \(0.720264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.1447 | 0.904139 | ||||||||
\(970\) | 1.05562 | 0.0338939 | ||||||||
\(971\) | 1.43366 | 0.0460085 | 0.0230042 | − | 0.999735i | \(-0.492677\pi\) | ||||
0.0230042 | + | 0.999735i | \(0.492677\pi\) | |||||||
\(972\) | 39.4286 | 1.26467 | ||||||||
\(973\) | −1.47583 | −0.0473128 | ||||||||
\(974\) | 10.3029 | 0.330127 | ||||||||
\(975\) | −11.6492 | −0.373073 | ||||||||
\(976\) | 11.8983 | 0.380856 | ||||||||
\(977\) | −33.2754 | −1.06458 | −0.532288 | − | 0.846564i | \(-0.678667\pi\) | ||||
−0.532288 | + | 0.846564i | \(0.678667\pi\) | |||||||
\(978\) | 26.7211 | 0.854448 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −77.9562 | −2.48895 | ||||||||
\(982\) | 20.0929 | 0.641189 | ||||||||
\(983\) | 41.4050 | 1.32062 | 0.660308 | − | 0.750995i | \(-0.270426\pi\) | ||||
0.660308 | + | 0.750995i | \(0.270426\pi\) | |||||||
\(984\) | 12.5070 | 0.398708 | ||||||||
\(985\) | −8.36713 | −0.266599 | ||||||||
\(986\) | −4.71889 | −0.150280 | ||||||||
\(987\) | 31.2921 | 0.996038 | ||||||||
\(988\) | 10.2603 | 0.326423 | ||||||||
\(989\) | 20.2719 | 0.644610 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2508 | −1.18331 | −0.591655 | − | 0.806191i | \(-0.701525\pi\) | ||||
−0.591655 | + | 0.806191i | \(0.701525\pi\) | |||||||
\(992\) | 0.473234 | 0.0150252 | ||||||||
\(993\) | −63.4401 | −2.01321 | ||||||||
\(994\) | −1.90401 | −0.0603916 | ||||||||
\(995\) | 6.83066 | 0.216547 | ||||||||
\(996\) | 17.3027 | 0.548258 | ||||||||
\(997\) | −20.0494 | −0.634972 | −0.317486 | − | 0.948263i | \(-0.602839\pi\) | ||||
−0.317486 | + | 0.948263i | \(0.602839\pi\) | |||||||
\(998\) | −26.1662 | −0.828277 | ||||||||
\(999\) | −162.928 | −5.15481 |
(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 | 8470.2.a.cy.1.6 | 6 | ||
11.2 | odd | 10 | 770.2.n.i.631.3 | yes | 12 | ||
11.6 | odd | 10 | 770.2.n.i.421.3 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.de.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.i.421.3 | ✓ | 12 | 11.6 | odd | 10 | ||
770.2.n.i.631.3 | yes | 12 | 11.2 | odd | 10 | ||
8470.2.a.cy.1.6 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.de.1.6 | 6 | 11.10 | odd | 2 |