Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.473713\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.473713 | 0.334966 | 0.167483 | − | 0.985875i | \(-0.446436\pi\) | ||||
0.167483 | + | 0.985875i | \(0.446436\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.77560 | −0.887798 | ||||||||
\(5\) | 3.75881 | 1.68099 | 0.840496 | − | 0.541818i | \(-0.182264\pi\) | ||||
0.840496 | + | 0.541818i | \(0.182264\pi\) | |||||||
\(6\) | 0.473713 | 0.193393 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.78855 | −0.632348 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.78060 | 0.563075 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.77560 | −0.512570 | ||||||||
\(13\) | 2.70774 | 0.750993 | 0.375496 | − | 0.926824i | \(-0.377472\pi\) | ||||
0.375496 | + | 0.926824i | \(0.377472\pi\) | |||||||
\(14\) | −0.473713 | −0.126605 | ||||||||
\(15\) | 3.75881 | 0.970521 | ||||||||
\(16\) | 2.70393 | 0.675983 | ||||||||
\(17\) | 2.48283 | 0.602174 | 0.301087 | − | 0.953597i | \(-0.402651\pi\) | ||||
0.301087 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(18\) | 0.473713 | 0.111655 | ||||||||
\(19\) | −1.74466 | −0.400253 | −0.200126 | − | 0.979770i | \(-0.564135\pi\) | ||||
−0.200126 | + | 0.979770i | \(0.564135\pi\) | |||||||
\(20\) | −6.67413 | −1.49238 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.79843 | 0.792028 | 0.396014 | − | 0.918244i | \(-0.370393\pi\) | ||||
0.396014 | + | 0.918244i | \(0.370393\pi\) | |||||||
\(24\) | −1.78855 | −0.365086 | ||||||||
\(25\) | 9.12868 | 1.82574 | ||||||||
\(26\) | 1.28269 | 0.251557 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.77560 | 0.335556 | ||||||||
\(29\) | −5.80060 | −1.07714 | −0.538572 | − | 0.842580i | \(-0.681036\pi\) | ||||
−0.538572 | + | 0.842580i | \(0.681036\pi\) | |||||||
\(30\) | 1.78060 | 0.325091 | ||||||||
\(31\) | 2.24763 | 0.403686 | 0.201843 | − | 0.979418i | \(-0.435307\pi\) | ||||
0.201843 | + | 0.979418i | \(0.435307\pi\) | |||||||
\(32\) | 4.85799 | 0.858779 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.17615 | 0.201707 | ||||||||
\(35\) | −3.75881 | −0.635355 | ||||||||
\(36\) | −1.77560 | −0.295933 | ||||||||
\(37\) | −7.65311 | −1.25816 | −0.629082 | − | 0.777339i | \(-0.716569\pi\) | ||||
−0.629082 | + | 0.777339i | \(0.716569\pi\) | |||||||
\(38\) | −0.826469 | −0.134071 | ||||||||
\(39\) | 2.70774 | 0.433586 | ||||||||
\(40\) | −6.72282 | −1.06297 | ||||||||
\(41\) | −4.18500 | −0.653587 | −0.326793 | − | 0.945096i | \(-0.605968\pi\) | ||||
−0.326793 | + | 0.945096i | \(0.605968\pi\) | |||||||
\(42\) | −0.473713 | −0.0730955 | ||||||||
\(43\) | 7.75162 | 1.18211 | 0.591056 | − | 0.806631i | \(-0.298711\pi\) | ||||
0.591056 | + | 0.806631i | \(0.298711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.75881 | 0.560331 | ||||||||
\(46\) | 1.79937 | 0.265302 | ||||||||
\(47\) | 12.4071 | 1.80976 | 0.904878 | − | 0.425670i | \(-0.139962\pi\) | ||||
0.904878 | + | 0.425670i | \(0.139962\pi\) | |||||||
\(48\) | 2.70393 | 0.390279 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.32437 | 0.611559 | ||||||||
\(51\) | 2.48283 | 0.347665 | ||||||||
\(52\) | −4.80786 | −0.666730 | ||||||||
\(53\) | 8.83956 | 1.21421 | 0.607103 | − | 0.794623i | \(-0.292331\pi\) | ||||
0.607103 | + | 0.794623i | \(0.292331\pi\) | |||||||
\(54\) | 0.473713 | 0.0644642 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.78855 | 0.239005 | ||||||||
\(57\) | −1.74466 | −0.231086 | ||||||||
\(58\) | −2.74782 | −0.360806 | ||||||||
\(59\) | 4.54166 | 0.591274 | 0.295637 | − | 0.955300i | \(-0.404468\pi\) | ||||
0.295637 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(60\) | −6.67413 | −0.861627 | ||||||||
\(61\) | −11.4825 | −1.47019 | −0.735093 | − | 0.677967i | \(-0.762861\pi\) | ||||
−0.735093 | + | 0.677967i | \(0.762861\pi\) | |||||||
\(62\) | 1.06473 | 0.135221 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −3.10658 | −0.388322 | ||||||||
\(65\) | 10.1779 | 1.26241 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2041 | −1.49096 | −0.745481 | − | 0.666527i | \(-0.767780\pi\) | ||||
−0.745481 | + | 0.666527i | \(0.767780\pi\) | |||||||
\(68\) | −4.40849 | −0.534609 | ||||||||
\(69\) | 3.79843 | 0.457278 | ||||||||
\(70\) | −1.78060 | −0.212822 | ||||||||
\(71\) | 7.75988 | 0.920928 | 0.460464 | − | 0.887678i | \(-0.347683\pi\) | ||||
0.460464 | + | 0.887678i | \(0.347683\pi\) | |||||||
\(72\) | −1.78855 | −0.210783 | ||||||||
\(73\) | 15.6796 | 1.83516 | 0.917580 | − | 0.397552i | \(-0.130140\pi\) | ||||
0.917580 | + | 0.397552i | \(0.130140\pi\) | |||||||
\(74\) | −3.62538 | −0.421441 | ||||||||
\(75\) | 9.12868 | 1.05409 | ||||||||
\(76\) | 3.09781 | 0.355344 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.28269 | 0.145236 | ||||||||
\(79\) | −7.05380 | −0.793615 | −0.396807 | − | 0.917902i | \(-0.629882\pi\) | ||||
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(80\) | 10.1636 | 1.13632 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.98249 | −0.218929 | ||||||||
\(83\) | 11.9004 | 1.30624 | 0.653122 | − | 0.757253i | \(-0.273459\pi\) | ||||
0.653122 | + | 0.757253i | \(0.273459\pi\) | |||||||
\(84\) | 1.77560 | 0.193733 | ||||||||
\(85\) | 9.33248 | 1.01225 | ||||||||
\(86\) | 3.67204 | 0.395967 | ||||||||
\(87\) | −5.80060 | −0.621889 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.69179 | −0.179329 | −0.0896647 | − | 0.995972i | \(-0.528580\pi\) | ||||
−0.0896647 | + | 0.995972i | \(0.528580\pi\) | |||||||
\(90\) | 1.78060 | 0.187692 | ||||||||
\(91\) | −2.70774 | −0.283848 | ||||||||
\(92\) | −6.74448 | −0.703161 | ||||||||
\(93\) | 2.24763 | 0.233068 | ||||||||
\(94\) | 5.87739 | 0.606206 | ||||||||
\(95\) | −6.55786 | −0.672822 | ||||||||
\(96\) | 4.85799 | 0.495816 | ||||||||
\(97\) | 6.99638 | 0.710375 | 0.355188 | − | 0.934795i | \(-0.384417\pi\) | ||||
0.355188 | + | 0.934795i | \(0.384417\pi\) | |||||||
\(98\) | 0.473713 | 0.0478522 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.2088 | −1.62088 | ||||||||
\(101\) | 2.71683 | 0.270335 | 0.135167 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135167 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(102\) | 1.17615 | 0.116456 | ||||||||
\(103\) | −0.255788 | −0.0252036 | −0.0126018 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0126018 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(104\) | −4.84293 | −0.474888 | ||||||||
\(105\) | −3.75881 | −0.366823 | ||||||||
\(106\) | 4.18741 | 0.406717 | ||||||||
\(107\) | 11.8608 | 1.14662 | 0.573311 | − | 0.819338i | \(-0.305659\pi\) | ||||
0.573311 | + | 0.819338i | \(0.305659\pi\) | |||||||
\(108\) | −1.77560 | −0.170857 | ||||||||
\(109\) | −15.8720 | −1.52026 | −0.760129 | − | 0.649772i | \(-0.774864\pi\) | ||||
−0.760129 | + | 0.649772i | \(0.774864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.65311 | −0.726401 | ||||||||
\(112\) | −2.70393 | −0.255498 | ||||||||
\(113\) | −5.11650 | −0.481320 | −0.240660 | − | 0.970609i | \(-0.577364\pi\) | ||||
−0.240660 | + | 0.970609i | \(0.577364\pi\) | |||||||
\(114\) | −0.826469 | −0.0774059 | ||||||||
\(115\) | 14.2776 | 1.33139 | ||||||||
\(116\) | 10.2995 | 0.956286 | ||||||||
\(117\) | 2.70774 | 0.250331 | ||||||||
\(118\) | 2.15144 | 0.198056 | ||||||||
\(119\) | −2.48283 | −0.227600 | ||||||||
\(120\) | −6.72282 | −0.613707 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.43942 | −0.492462 | ||||||||
\(123\) | −4.18500 | −0.377348 | ||||||||
\(124\) | −3.99088 | −0.358392 | ||||||||
\(125\) | 15.5189 | 1.38805 | ||||||||
\(126\) | −0.473713 | −0.0422017 | ||||||||
\(127\) | 0.203338 | 0.0180433 | 0.00902166 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902166 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(128\) | −11.1876 | −0.988853 | ||||||||
\(129\) | 7.75162 | 0.682492 | ||||||||
\(130\) | 4.82140 | 0.422865 | ||||||||
\(131\) | −10.2788 | −0.898067 | −0.449034 | − | 0.893515i | \(-0.648232\pi\) | ||||
−0.449034 | + | 0.893515i | \(0.648232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.74466 | 0.151281 | ||||||||
\(134\) | −5.78122 | −0.499421 | ||||||||
\(135\) | 3.75881 | 0.323507 | ||||||||
\(136\) | −4.44065 | −0.380783 | ||||||||
\(137\) | −17.1096 | −1.46177 | −0.730887 | − | 0.682499i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682499i | \(0.760893\pi\) | |||||||
\(138\) | 1.79937 | 0.153172 | ||||||||
\(139\) | 19.5009 | 1.65405 | 0.827023 | − | 0.562168i | \(-0.190032\pi\) | ||||
0.827023 | + | 0.562168i | \(0.190032\pi\) | |||||||
\(140\) | 6.67413 | 0.564067 | ||||||||
\(141\) | 12.4071 | 1.04486 | ||||||||
\(142\) | 3.67596 | 0.308479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.70393 | 0.225328 | ||||||||
\(145\) | −21.8034 | −1.81067 | ||||||||
\(146\) | 7.42763 | 0.614715 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 13.5888 | 1.11699 | ||||||||
\(149\) | −9.89037 | −0.810251 | −0.405125 | − | 0.914261i | \(-0.632772\pi\) | ||||
−0.405125 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(150\) | 4.32437 | 0.353084 | ||||||||
\(151\) | −15.5014 | −1.26148 | −0.630741 | − | 0.775993i | \(-0.717249\pi\) | ||||
−0.630741 | + | 0.775993i | \(0.717249\pi\) | |||||||
\(152\) | 3.12041 | 0.253099 | ||||||||
\(153\) | 2.48283 | 0.200725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.44843 | 0.678594 | ||||||||
\(156\) | −4.80786 | −0.384937 | ||||||||
\(157\) | 16.9536 | 1.35305 | 0.676523 | − | 0.736422i | \(-0.263486\pi\) | ||||
0.676523 | + | 0.736422i | \(0.263486\pi\) | |||||||
\(158\) | −3.34148 | −0.265834 | ||||||||
\(159\) | 8.83956 | 0.701022 | ||||||||
\(160\) | 18.2603 | 1.44360 | ||||||||
\(161\) | −3.79843 | −0.299359 | ||||||||
\(162\) | 0.473713 | 0.0372184 | ||||||||
\(163\) | 19.9739 | 1.56447 | 0.782237 | − | 0.622981i | \(-0.214079\pi\) | ||||
0.782237 | + | 0.622981i | \(0.214079\pi\) | |||||||
\(164\) | 7.43086 | 0.580253 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.63739 | 0.437547 | ||||||||
\(167\) | 17.4516 | 1.35044 | 0.675222 | − | 0.737615i | \(-0.264048\pi\) | ||||
0.675222 | + | 0.737615i | \(0.264048\pi\) | |||||||
\(168\) | 1.78855 | 0.137990 | ||||||||
\(169\) | −5.66813 | −0.436010 | ||||||||
\(170\) | 4.42092 | 0.339069 | ||||||||
\(171\) | −1.74466 | −0.133418 | ||||||||
\(172\) | −13.7637 | −1.04948 | ||||||||
\(173\) | −9.35944 | −0.711585 | −0.355793 | − | 0.934565i | \(-0.615789\pi\) | ||||
−0.355793 | + | 0.934565i | \(0.615789\pi\) | |||||||
\(174\) | −2.74782 | −0.208312 | ||||||||
\(175\) | −9.12868 | −0.690063 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.54166 | 0.341372 | ||||||||
\(178\) | −0.801423 | −0.0600692 | ||||||||
\(179\) | 5.49347 | 0.410602 | 0.205301 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205301 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(180\) | −6.67413 | −0.497461 | ||||||||
\(181\) | −11.1844 | −0.831332 | −0.415666 | − | 0.909517i | \(-0.636451\pi\) | ||||
−0.415666 | + | 0.909517i | \(0.636451\pi\) | |||||||
\(182\) | −1.28269 | −0.0950795 | ||||||||
\(183\) | −11.4825 | −0.848812 | ||||||||
\(184\) | −6.79369 | −0.500837 | ||||||||
\(185\) | −28.7666 | −2.11496 | ||||||||
\(186\) | 1.06473 | 0.0780699 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −22.0299 | −1.60670 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −3.10654 | −0.225372 | ||||||||
\(191\) | −5.75822 | −0.416650 | −0.208325 | − | 0.978060i | \(-0.566801\pi\) | ||||
−0.208325 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(192\) | −3.10658 | −0.224198 | ||||||||
\(193\) | −14.8846 | −1.07142 | −0.535708 | − | 0.844404i | \(-0.679955\pi\) | ||||
−0.535708 | + | 0.844404i | \(0.679955\pi\) | |||||||
\(194\) | 3.31428 | 0.237951 | ||||||||
\(195\) | 10.1779 | 0.728854 | ||||||||
\(196\) | −1.77560 | −0.126828 | ||||||||
\(197\) | 12.5476 | 0.893978 | 0.446989 | − | 0.894540i | \(-0.352496\pi\) | ||||
0.446989 | + | 0.894540i | \(0.352496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.834418 | 0.0591503 | 0.0295752 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295752 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(200\) | −16.3271 | −1.15450 | ||||||||
\(201\) | −12.2041 | −0.860808 | ||||||||
\(202\) | 1.28700 | 0.0905528 | ||||||||
\(203\) | 5.80060 | 0.407122 | ||||||||
\(204\) | −4.40849 | −0.308656 | ||||||||
\(205\) | −15.7306 | −1.09867 | ||||||||
\(206\) | −0.121170 | −0.00844233 | ||||||||
\(207\) | 3.79843 | 0.264009 | ||||||||
\(208\) | 7.32155 | 0.507658 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.78060 | −0.122873 | ||||||||
\(211\) | −26.8703 | −1.84983 | −0.924914 | − | 0.380176i | \(-0.875863\pi\) | ||||
−0.924914 | + | 0.380176i | \(0.875863\pi\) | |||||||
\(212\) | −15.6955 | −1.07797 | ||||||||
\(213\) | 7.75988 | 0.531698 | ||||||||
\(214\) | 5.61859 | 0.384079 | ||||||||
\(215\) | 29.1369 | 1.98712 | ||||||||
\(216\) | −1.78855 | −0.121695 | ||||||||
\(217\) | −2.24763 | −0.152579 | ||||||||
\(218\) | −7.51876 | −0.509234 | ||||||||
\(219\) | 15.6796 | 1.05953 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.72285 | 0.452228 | ||||||||
\(222\) | −3.62538 | −0.243319 | ||||||||
\(223\) | 4.01918 | 0.269144 | 0.134572 | − | 0.990904i | \(-0.457034\pi\) | ||||
0.134572 | + | 0.990904i | \(0.457034\pi\) | |||||||
\(224\) | −4.85799 | −0.324588 | ||||||||
\(225\) | 9.12868 | 0.608578 | ||||||||
\(226\) | −2.42375 | −0.161226 | ||||||||
\(227\) | −11.7020 | −0.776690 | −0.388345 | − | 0.921514i | \(-0.626953\pi\) | ||||
−0.388345 | + | 0.921514i | \(0.626953\pi\) | |||||||
\(228\) | 3.09781 | 0.205158 | ||||||||
\(229\) | −6.54504 | −0.432508 | −0.216254 | − | 0.976337i | \(-0.569384\pi\) | ||||
−0.216254 | + | 0.976337i | \(0.569384\pi\) | |||||||
\(230\) | 6.76349 | 0.445971 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.3746 | 0.681129 | ||||||||
\(233\) | 0.172567 | 0.0113052 | 0.00565262 | − | 0.999984i | \(-0.498201\pi\) | ||||
0.00565262 | + | 0.999984i | \(0.498201\pi\) | |||||||
\(234\) | 1.28269 | 0.0838522 | ||||||||
\(235\) | 46.6358 | 3.04219 | ||||||||
\(236\) | −8.06415 | −0.524932 | ||||||||
\(237\) | −7.05380 | −0.458194 | ||||||||
\(238\) | −1.17615 | −0.0762383 | ||||||||
\(239\) | −10.4504 | −0.675982 | −0.337991 | − | 0.941149i | \(-0.609747\pi\) | ||||
−0.337991 | + | 0.941149i | \(0.609747\pi\) | |||||||
\(240\) | 10.1636 | 0.656056 | ||||||||
\(241\) | −3.41821 | −0.220186 | −0.110093 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110093 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 20.3883 | 1.30523 | ||||||||
\(245\) | 3.75881 | 0.240142 | ||||||||
\(246\) | −1.98249 | −0.126399 | ||||||||
\(247\) | −4.72409 | −0.300587 | ||||||||
\(248\) | −4.02000 | −0.255270 | ||||||||
\(249\) | 11.9004 | 0.754160 | ||||||||
\(250\) | 7.35151 | 0.464951 | ||||||||
\(251\) | 12.6751 | 0.800047 | 0.400024 | − | 0.916505i | \(-0.369002\pi\) | ||||
0.400024 | + | 0.916505i | \(0.369002\pi\) | |||||||
\(252\) | 1.77560 | 0.111852 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.0963238 | 0.00604389 | ||||||||
\(255\) | 9.33248 | 0.584422 | ||||||||
\(256\) | 0.913441 | 0.0570901 | ||||||||
\(257\) | −18.1852 | −1.13436 | −0.567182 | − | 0.823593i | \(-0.691966\pi\) | ||||
−0.567182 | + | 0.823593i | \(0.691966\pi\) | |||||||
\(258\) | 3.67204 | 0.228611 | ||||||||
\(259\) | 7.65311 | 0.475541 | ||||||||
\(260\) | −18.0718 | −1.12077 | ||||||||
\(261\) | −5.80060 | −0.359048 | ||||||||
\(262\) | −4.86922 | −0.300822 | ||||||||
\(263\) | 15.7837 | 0.973264 | 0.486632 | − | 0.873607i | \(-0.338225\pi\) | ||||
0.486632 | + | 0.873607i | \(0.338225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.2262 | 2.04107 | ||||||||
\(266\) | 0.826469 | 0.0506741 | ||||||||
\(267\) | −1.69179 | −0.103536 | ||||||||
\(268\) | 21.6695 | 1.32367 | ||||||||
\(269\) | 22.9896 | 1.40170 | 0.700851 | − | 0.713308i | \(-0.252804\pi\) | ||||
0.700851 | + | 0.713308i | \(0.252804\pi\) | |||||||
\(270\) | 1.78060 | 0.108364 | ||||||||
\(271\) | 9.34021 | 0.567377 | 0.283689 | − | 0.958916i | \(-0.408442\pi\) | ||||
0.283689 | + | 0.958916i | \(0.408442\pi\) | |||||||
\(272\) | 6.71339 | 0.407059 | ||||||||
\(273\) | −2.70774 | −0.163880 | ||||||||
\(274\) | −8.10505 | −0.489644 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.74448 | −0.405970 | ||||||||
\(277\) | 19.4367 | 1.16784 | 0.583918 | − | 0.811813i | \(-0.301519\pi\) | ||||
0.583918 | + | 0.811813i | \(0.301519\pi\) | |||||||
\(278\) | 9.23784 | 0.554049 | ||||||||
\(279\) | 2.24763 | 0.134562 | ||||||||
\(280\) | 6.72282 | 0.401765 | ||||||||
\(281\) | −4.44358 | −0.265082 | −0.132541 | − | 0.991178i | \(-0.542314\pi\) | ||||
−0.132541 | + | 0.991178i | \(0.542314\pi\) | |||||||
\(282\) | 5.87739 | 0.349993 | ||||||||
\(283\) | 13.8486 | 0.823216 | 0.411608 | − | 0.911361i | \(-0.364967\pi\) | ||||
0.411608 | + | 0.911361i | \(0.364967\pi\) | |||||||
\(284\) | −13.7784 | −0.817598 | ||||||||
\(285\) | −6.55786 | −0.388454 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.18500 | 0.247033 | ||||||||
\(288\) | 4.85799 | 0.286260 | ||||||||
\(289\) | −10.8356 | −0.637387 | ||||||||
\(290\) | −10.3285 | −0.606512 | ||||||||
\(291\) | 6.99638 | 0.410135 | ||||||||
\(292\) | −27.8406 | −1.62925 | ||||||||
\(293\) | −19.2359 | −1.12377 | −0.561887 | − | 0.827214i | \(-0.689924\pi\) | ||||
−0.561887 | + | 0.827214i | \(0.689924\pi\) | |||||||
\(294\) | 0.473713 | 0.0276275 | ||||||||
\(295\) | 17.0713 | 0.993927 | ||||||||
\(296\) | 13.6880 | 0.795596 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.68520 | −0.271406 | ||||||||
\(299\) | 10.2852 | 0.594807 | ||||||||
\(300\) | −16.2088 | −0.935818 | ||||||||
\(301\) | −7.75162 | −0.446796 | ||||||||
\(302\) | −7.34319 | −0.422553 | ||||||||
\(303\) | 2.71683 | 0.156078 | ||||||||
\(304\) | −4.71745 | −0.270564 | ||||||||
\(305\) | −43.1606 | −2.47137 | ||||||||
\(306\) | 1.17615 | 0.0672358 | ||||||||
\(307\) | 2.24474 | 0.128114 | 0.0640571 | − | 0.997946i | \(-0.479596\pi\) | ||||
0.0640571 | + | 0.997946i | \(0.479596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.255788 | −0.0145513 | ||||||||
\(310\) | 4.00213 | 0.227306 | ||||||||
\(311\) | 12.6291 | 0.716129 | 0.358065 | − | 0.933697i | \(-0.383437\pi\) | ||||
0.358065 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(312\) | −4.84293 | −0.274177 | ||||||||
\(313\) | 1.06646 | 0.0602797 | 0.0301398 | − | 0.999546i | \(-0.490405\pi\) | ||||
0.0301398 | + | 0.999546i | \(0.490405\pi\) | |||||||
\(314\) | 8.03115 | 0.453224 | ||||||||
\(315\) | −3.75881 | −0.211785 | ||||||||
\(316\) | 12.5247 | 0.704569 | ||||||||
\(317\) | −25.1710 | −1.41374 | −0.706872 | − | 0.707342i | \(-0.749894\pi\) | ||||
−0.706872 | + | 0.707342i | \(0.749894\pi\) | |||||||
\(318\) | 4.18741 | 0.234818 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.6770 | −0.652766 | ||||||||
\(321\) | 11.8608 | 0.662003 | ||||||||
\(322\) | −1.79937 | −0.100275 | ||||||||
\(323\) | −4.33169 | −0.241022 | ||||||||
\(324\) | −1.77560 | −0.0986442 | ||||||||
\(325\) | 24.7181 | 1.37111 | ||||||||
\(326\) | 9.46188 | 0.524045 | ||||||||
\(327\) | −15.8720 | −0.877722 | ||||||||
\(328\) | 7.48507 | 0.413294 | ||||||||
\(329\) | −12.4071 | −0.684024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.53640 | −0.469203 | −0.234601 | − | 0.972092i | \(-0.575378\pi\) | ||||
−0.234601 | + | 0.972092i | \(0.575378\pi\) | |||||||
\(332\) | −21.1304 | −1.15968 | ||||||||
\(333\) | −7.65311 | −0.419388 | ||||||||
\(334\) | 8.26704 | 0.452352 | ||||||||
\(335\) | −45.8728 | −2.50630 | ||||||||
\(336\) | −2.70393 | −0.147512 | ||||||||
\(337\) | −17.2565 | −0.940020 | −0.470010 | − | 0.882661i | \(-0.655750\pi\) | ||||
−0.470010 | + | 0.882661i | \(0.655750\pi\) | |||||||
\(338\) | −2.68507 | −0.146048 | ||||||||
\(339\) | −5.11650 | −0.277890 | ||||||||
\(340\) | −16.5707 | −0.898673 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.826469 | −0.0446903 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −13.8642 | −0.747505 | ||||||||
\(345\) | 14.2776 | 0.768680 | ||||||||
\(346\) | −4.43369 | −0.238357 | ||||||||
\(347\) | 4.15698 | 0.223159 | 0.111579 | − | 0.993756i | \(-0.464409\pi\) | ||||
0.111579 | + | 0.993756i | \(0.464409\pi\) | |||||||
\(348\) | 10.2995 | 0.552112 | ||||||||
\(349\) | 7.70785 | 0.412592 | 0.206296 | − | 0.978490i | \(-0.433859\pi\) | ||||
0.206296 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(350\) | −4.32437 | −0.231147 | ||||||||
\(351\) | 2.70774 | 0.144529 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.84242 | −0.257736 | −0.128868 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128868 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(354\) | 2.15144 | 0.114348 | ||||||||
\(355\) | 29.1679 | 1.54807 | ||||||||
\(356\) | 3.00393 | 0.159208 | ||||||||
\(357\) | −2.48283 | −0.131405 | ||||||||
\(358\) | 2.60233 | 0.137537 | ||||||||
\(359\) | 4.41834 | 0.233191 | 0.116596 | − | 0.993179i | \(-0.462802\pi\) | ||||
0.116596 | + | 0.993179i | \(0.462802\pi\) | |||||||
\(360\) | −6.72282 | −0.354324 | ||||||||
\(361\) | −15.9562 | −0.839798 | ||||||||
\(362\) | −5.29821 | −0.278468 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.80786 | 0.252000 | ||||||||
\(365\) | 58.9367 | 3.08489 | ||||||||
\(366\) | −5.43942 | −0.284323 | ||||||||
\(367\) | −29.5315 | −1.54153 | −0.770766 | − | 0.637118i | \(-0.780126\pi\) | ||||
−0.770766 | + | 0.637118i | \(0.780126\pi\) | |||||||
\(368\) | 10.2707 | 0.535398 | ||||||||
\(369\) | −4.18500 | −0.217862 | ||||||||
\(370\) | −13.6271 | −0.708440 | ||||||||
\(371\) | −8.83956 | −0.458927 | ||||||||
\(372\) | −3.99088 | −0.206918 | ||||||||
\(373\) | 7.64965 | 0.396084 | 0.198042 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198042 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.5189 | 0.801394 | ||||||||
\(376\) | −22.1906 | −1.14440 | ||||||||
\(377\) | −15.7065 | −0.808927 | ||||||||
\(378\) | −0.473713 | −0.0243652 | ||||||||
\(379\) | −11.2094 | −0.575788 | −0.287894 | − | 0.957662i | \(-0.592955\pi\) | ||||
−0.287894 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(380\) | 11.6441 | 0.597330 | ||||||||
\(381\) | 0.203338 | 0.0104173 | ||||||||
\(382\) | −2.72774 | −0.139563 | ||||||||
\(383\) | −24.7447 | −1.26440 | −0.632199 | − | 0.774806i | \(-0.717847\pi\) | ||||
−0.632199 | + | 0.774806i | \(0.717847\pi\) | |||||||
\(384\) | −11.1876 | −0.570915 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.05102 | −0.358887 | ||||||||
\(387\) | 7.75162 | 0.394037 | ||||||||
\(388\) | −12.4228 | −0.630670 | ||||||||
\(389\) | −29.0347 | −1.47212 | −0.736060 | − | 0.676917i | \(-0.763316\pi\) | ||||
−0.736060 | + | 0.676917i | \(0.763316\pi\) | |||||||
\(390\) | 4.82140 | 0.244141 | ||||||||
\(391\) | 9.43085 | 0.476939 | ||||||||
\(392\) | −1.78855 | −0.0903354 | ||||||||
\(393\) | −10.2788 | −0.518499 | ||||||||
\(394\) | 5.94395 | 0.299452 | ||||||||
\(395\) | −26.5139 | −1.33406 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.27461 | −0.415291 | −0.207645 | − | 0.978204i | \(-0.566580\pi\) | ||||
−0.207645 | + | 0.978204i | \(0.566580\pi\) | |||||||
\(398\) | 0.395275 | 0.0198133 | ||||||||
\(399\) | 1.74466 | 0.0873423 | ||||||||
\(400\) | 24.6833 | 1.23417 | ||||||||
\(401\) | −26.7390 | −1.33528 | −0.667642 | − | 0.744483i | \(-0.732696\pi\) | ||||
−0.667642 | + | 0.744483i | \(0.732696\pi\) | |||||||
\(402\) | −5.78122 | −0.288341 | ||||||||
\(403\) | 6.08601 | 0.303166 | ||||||||
\(404\) | −4.82399 | −0.240003 | ||||||||
\(405\) | 3.75881 | 0.186777 | ||||||||
\(406\) | 2.74782 | 0.136372 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.44065 | −0.219845 | ||||||||
\(409\) | 34.6829 | 1.71496 | 0.857479 | − | 0.514519i | \(-0.172030\pi\) | ||||
0.857479 | + | 0.514519i | \(0.172030\pi\) | |||||||
\(410\) | −7.45180 | −0.368018 | ||||||||
\(411\) | −17.1096 | −0.843955 | ||||||||
\(412\) | 0.454177 | 0.0223757 | ||||||||
\(413\) | −4.54166 | −0.223480 | ||||||||
\(414\) | 1.79937 | 0.0884341 | ||||||||
\(415\) | 44.7315 | 2.19578 | ||||||||
\(416\) | 13.1542 | 0.644936 | ||||||||
\(417\) | 19.5009 | 0.954964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.34546 | −0.212290 | −0.106145 | − | 0.994351i | \(-0.533851\pi\) | ||||
−0.106145 | + | 0.994351i | \(0.533851\pi\) | |||||||
\(420\) | 6.67413 | 0.325664 | ||||||||
\(421\) | −4.73841 | −0.230936 | −0.115468 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115468 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(422\) | −12.7288 | −0.619629 | ||||||||
\(423\) | 12.4071 | 0.603252 | ||||||||
\(424\) | −15.8100 | −0.767800 | ||||||||
\(425\) | 22.6649 | 1.09941 | ||||||||
\(426\) | 3.67596 | 0.178101 | ||||||||
\(427\) | 11.4825 | 0.555678 | ||||||||
\(428\) | −21.0599 | −1.01797 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.8025 | 0.665617 | ||||||||
\(431\) | −29.8622 | −1.43841 | −0.719206 | − | 0.694797i | \(-0.755494\pi\) | ||||
−0.719206 | + | 0.694797i | \(0.755494\pi\) | |||||||
\(432\) | 2.70393 | 0.130093 | ||||||||
\(433\) | −21.7239 | −1.04399 | −0.521993 | − | 0.852950i | \(-0.674811\pi\) | ||||
−0.521993 | + | 0.852950i | \(0.674811\pi\) | |||||||
\(434\) | −1.06473 | −0.0511088 | ||||||||
\(435\) | −21.8034 | −1.04539 | ||||||||
\(436\) | 28.1822 | 1.34968 | ||||||||
\(437\) | −6.62698 | −0.317012 | ||||||||
\(438\) | 7.42763 | 0.354906 | ||||||||
\(439\) | −40.3447 | −1.92555 | −0.962773 | − | 0.270313i | \(-0.912873\pi\) | ||||
−0.962773 | + | 0.270313i | \(0.912873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 3.18470 | 0.151481 | ||||||||
\(443\) | −13.8789 | −0.659408 | −0.329704 | − | 0.944084i | \(-0.606949\pi\) | ||||
−0.329704 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(444\) | 13.5888 | 0.644897 | ||||||||
\(445\) | −6.35912 | −0.301451 | ||||||||
\(446\) | 1.90394 | 0.0901540 | ||||||||
\(447\) | −9.89037 | −0.467799 | ||||||||
\(448\) | 3.10658 | 0.146772 | ||||||||
\(449\) | −14.3023 | −0.674966 | −0.337483 | − | 0.941332i | \(-0.609575\pi\) | ||||
−0.337483 | + | 0.941332i | \(0.609575\pi\) | |||||||
\(450\) | 4.32437 | 0.203853 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.08484 | 0.427315 | ||||||||
\(453\) | −15.5014 | −0.728317 | ||||||||
\(454\) | −5.54340 | −0.260164 | ||||||||
\(455\) | −10.1779 | −0.477147 | ||||||||
\(456\) | 3.12041 | 0.146127 | ||||||||
\(457\) | −14.1278 | −0.660869 | −0.330435 | − | 0.943829i | \(-0.607195\pi\) | ||||
−0.330435 | + | 0.943829i | \(0.607195\pi\) | |||||||
\(458\) | −3.10047 | −0.144875 | ||||||||
\(459\) | 2.48283 | 0.115888 | ||||||||
\(460\) | −25.3513 | −1.18201 | ||||||||
\(461\) | −0.966736 | −0.0450254 | −0.0225127 | − | 0.999747i | \(-0.507167\pi\) | ||||
−0.0225127 | + | 0.999747i | \(0.507167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8119 | 1.47842 | 0.739212 | − | 0.673473i | \(-0.235198\pi\) | ||||
0.739212 | + | 0.673473i | \(0.235198\pi\) | |||||||
\(464\) | −15.6844 | −0.728131 | ||||||||
\(465\) | 8.44843 | 0.391786 | ||||||||
\(466\) | 0.0817473 | 0.00378687 | ||||||||
\(467\) | −29.6133 | −1.37034 | −0.685169 | − | 0.728384i | \(-0.740272\pi\) | ||||
−0.685169 | + | 0.728384i | \(0.740272\pi\) | |||||||
\(468\) | −4.80786 | −0.222243 | ||||||||
\(469\) | 12.2041 | 0.563531 | ||||||||
\(470\) | 22.0920 | 1.01903 | ||||||||
\(471\) | 16.9536 | 0.781181 | ||||||||
\(472\) | −8.12298 | −0.373891 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.34148 | −0.153479 | ||||||||
\(475\) | −15.9264 | −0.730756 | ||||||||
\(476\) | 4.40849 | 0.202063 | ||||||||
\(477\) | 8.83956 | 0.404735 | ||||||||
\(478\) | −4.95051 | −0.226431 | ||||||||
\(479\) | −26.5853 | −1.21471 | −0.607356 | − | 0.794430i | \(-0.707770\pi\) | ||||
−0.607356 | + | 0.794430i | \(0.707770\pi\) | |||||||
\(480\) | 18.2603 | 0.833463 | ||||||||
\(481\) | −20.7226 | −0.944871 | ||||||||
\(482\) | −1.61925 | −0.0737548 | ||||||||
\(483\) | −3.79843 | −0.172835 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.2981 | 1.19414 | ||||||||
\(486\) | 0.473713 | 0.0214881 | ||||||||
\(487\) | 14.1343 | 0.640486 | 0.320243 | − | 0.947335i | \(-0.396235\pi\) | ||||
0.320243 | + | 0.947335i | \(0.396235\pi\) | |||||||
\(488\) | 20.5370 | 0.929668 | ||||||||
\(489\) | 19.9739 | 0.903249 | ||||||||
\(490\) | 1.78060 | 0.0804392 | ||||||||
\(491\) | 15.4186 | 0.695831 | 0.347916 | − | 0.937526i | \(-0.386890\pi\) | ||||
0.347916 | + | 0.937526i | \(0.386890\pi\) | |||||||
\(492\) | 7.43086 | 0.335009 | ||||||||
\(493\) | −14.4019 | −0.648627 | ||||||||
\(494\) | −2.23786 | −0.100686 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.07744 | 0.272885 | ||||||||
\(497\) | −7.75988 | −0.348078 | ||||||||
\(498\) | 5.63739 | 0.252618 | ||||||||
\(499\) | 30.7024 | 1.37443 | 0.687214 | − | 0.726455i | \(-0.258833\pi\) | ||||
0.687214 | + | 0.726455i | \(0.258833\pi\) | |||||||
\(500\) | −27.5553 | −1.23231 | ||||||||
\(501\) | 17.4516 | 0.779679 | ||||||||
\(502\) | 6.00438 | 0.267988 | ||||||||
\(503\) | −18.1890 | −0.811005 | −0.405503 | − | 0.914094i | \(-0.632904\pi\) | ||||
−0.405503 | + | 0.914094i | \(0.632904\pi\) | |||||||
\(504\) | 1.78855 | 0.0796683 | ||||||||
\(505\) | 10.2121 | 0.454431 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.66813 | −0.251731 | ||||||||
\(508\) | −0.361046 | −0.0160188 | ||||||||
\(509\) | −32.1744 | −1.42611 | −0.713054 | − | 0.701110i | \(-0.752688\pi\) | ||||
−0.713054 | + | 0.701110i | \(0.752688\pi\) | |||||||
\(510\) | 4.42092 | 0.195761 | ||||||||
\(511\) | −15.6796 | −0.693625 | ||||||||
\(512\) | 22.8079 | 1.00798 | ||||||||
\(513\) | −1.74466 | −0.0770287 | ||||||||
\(514\) | −8.61458 | −0.379973 | ||||||||
\(515\) | −0.961461 | −0.0423670 | ||||||||
\(516\) | −13.7637 | −0.605915 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.62538 | 0.159290 | ||||||||
\(519\) | −9.35944 | −0.410834 | ||||||||
\(520\) | −18.2037 | −0.798284 | ||||||||
\(521\) | −27.8238 | −1.21898 | −0.609490 | − | 0.792793i | \(-0.708626\pi\) | ||||
−0.609490 | + | 0.792793i | \(0.708626\pi\) | |||||||
\(522\) | −2.74782 | −0.120269 | ||||||||
\(523\) | −19.1282 | −0.836419 | −0.418209 | − | 0.908351i | \(-0.637342\pi\) | ||||
−0.418209 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(524\) | 18.2511 | 0.797302 | ||||||||
\(525\) | −9.12868 | −0.398408 | ||||||||
\(526\) | 7.47694 | 0.326010 | ||||||||
\(527\) | 5.58048 | 0.243089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.57190 | −0.372691 | ||||||||
\(530\) | 15.7397 | 0.683689 | ||||||||
\(531\) | 4.54166 | 0.197091 | ||||||||
\(532\) | −3.09781 | −0.134307 | ||||||||
\(533\) | −11.3319 | −0.490839 | ||||||||
\(534\) | −0.801423 | −0.0346810 | ||||||||
\(535\) | 44.5824 | 1.92746 | ||||||||
\(536\) | 21.8275 | 0.942806 | ||||||||
\(537\) | 5.49347 | 0.237061 | ||||||||
\(538\) | 10.8905 | 0.469522 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.67413 | −0.287209 | ||||||||
\(541\) | 42.6820 | 1.83504 | 0.917521 | − | 0.397688i | \(-0.130187\pi\) | ||||
0.917521 | + | 0.397688i | \(0.130187\pi\) | |||||||
\(542\) | 4.42458 | 0.190052 | ||||||||
\(543\) | −11.1844 | −0.479970 | ||||||||
\(544\) | 12.0615 | 0.517134 | ||||||||
\(545\) | −59.6597 | −2.55554 | ||||||||
\(546\) | −1.28269 | −0.0548942 | ||||||||
\(547\) | −25.1162 | −1.07389 | −0.536946 | − | 0.843617i | \(-0.680422\pi\) | ||||
−0.536946 | + | 0.843617i | \(0.680422\pi\) | |||||||
\(548\) | 30.3798 | 1.29776 | ||||||||
\(549\) | −11.4825 | −0.490062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1201 | 0.431130 | ||||||||
\(552\) | −6.79369 | −0.289158 | ||||||||
\(553\) | 7.05380 | 0.299958 | ||||||||
\(554\) | 9.20740 | 0.391185 | ||||||||
\(555\) | −28.7666 | −1.22107 | ||||||||
\(556\) | −34.6258 | −1.46846 | ||||||||
\(557\) | −4.25720 | −0.180383 | −0.0901917 | − | 0.995924i | \(-0.528748\pi\) | ||||
−0.0901917 | + | 0.995924i | \(0.528748\pi\) | |||||||
\(558\) | 1.06473 | 0.0450737 | ||||||||
\(559\) | 20.9894 | 0.887757 | ||||||||
\(560\) | −10.1636 | −0.429490 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.10498 | −0.0887933 | ||||||||
\(563\) | −7.43714 | −0.313438 | −0.156719 | − | 0.987643i | \(-0.550092\pi\) | ||||
−0.156719 | + | 0.987643i | \(0.550092\pi\) | |||||||
\(564\) | −22.0299 | −0.927628 | ||||||||
\(565\) | −19.2320 | −0.809096 | ||||||||
\(566\) | 6.56028 | 0.275749 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −13.8789 | −0.582347 | ||||||||
\(569\) | 43.6293 | 1.82904 | 0.914518 | − | 0.404546i | \(-0.132570\pi\) | ||||
0.914518 | + | 0.404546i | \(0.132570\pi\) | |||||||
\(570\) | −3.10654 | −0.130119 | ||||||||
\(571\) | −34.1074 | −1.42735 | −0.713676 | − | 0.700476i | \(-0.752971\pi\) | ||||
−0.713676 | + | 0.700476i | \(0.752971\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.75822 | −0.240553 | ||||||||
\(574\) | 1.98249 | 0.0827474 | ||||||||
\(575\) | 34.6747 | 1.44603 | ||||||||
\(576\) | −3.10658 | −0.129441 | ||||||||
\(577\) | 28.0804 | 1.16900 | 0.584501 | − | 0.811393i | \(-0.301290\pi\) | ||||
0.584501 | + | 0.811393i | \(0.301290\pi\) | |||||||
\(578\) | −5.13295 | −0.213503 | ||||||||
\(579\) | −14.8846 | −0.618582 | ||||||||
\(580\) | 38.7140 | 1.60751 | ||||||||
\(581\) | −11.9004 | −0.493713 | ||||||||
\(582\) | 3.31428 | 0.137381 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −28.0437 | −1.16046 | ||||||||
\(585\) | 10.1779 | 0.420804 | ||||||||
\(586\) | −9.11230 | −0.376426 | ||||||||
\(587\) | −6.72735 | −0.277668 | −0.138834 | − | 0.990316i | \(-0.544335\pi\) | ||||
−0.138834 | + | 0.990316i | \(0.544335\pi\) | |||||||
\(588\) | −1.77560 | −0.0732243 | ||||||||
\(589\) | −3.92136 | −0.161577 | ||||||||
\(590\) | 8.08687 | 0.332931 | ||||||||
\(591\) | 12.5476 | 0.516138 | ||||||||
\(592\) | −20.6935 | −0.850497 | ||||||||
\(593\) | 20.8442 | 0.855969 | 0.427984 | − | 0.903786i | \(-0.359224\pi\) | ||||
0.427984 | + | 0.903786i | \(0.359224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.33248 | −0.382594 | ||||||||
\(596\) | 17.5613 | 0.719339 | ||||||||
\(597\) | 0.834418 | 0.0341504 | ||||||||
\(598\) | 4.87222 | 0.199240 | ||||||||
\(599\) | 0.180675 | 0.00738218 | 0.00369109 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369109 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(600\) | −16.3271 | −0.666550 | ||||||||
\(601\) | 27.6043 | 1.12600 | 0.563001 | − | 0.826456i | \(-0.309647\pi\) | ||||
0.563001 | + | 0.826456i | \(0.309647\pi\) | |||||||
\(602\) | −3.67204 | −0.149661 | ||||||||
\(603\) | −12.2041 | −0.496988 | ||||||||
\(604\) | 27.5241 | 1.11994 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.28700 | 0.0522807 | ||||||||
\(607\) | 23.3280 | 0.946854 | 0.473427 | − | 0.880833i | \(-0.343017\pi\) | ||||
0.473427 | + | 0.880833i | \(0.343017\pi\) | |||||||
\(608\) | −8.47554 | −0.343729 | ||||||||
\(609\) | 5.80060 | 0.235052 | ||||||||
\(610\) | −20.4457 | −0.827824 | ||||||||
\(611\) | 33.5951 | 1.35911 | ||||||||
\(612\) | −4.40849 | −0.178203 | ||||||||
\(613\) | −19.5003 | −0.787608 | −0.393804 | − | 0.919194i | \(-0.628841\pi\) | ||||
−0.393804 | + | 0.919194i | \(0.628841\pi\) | |||||||
\(614\) | 1.06336 | 0.0429139 | ||||||||
\(615\) | −15.7306 | −0.634320 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2566 | −0.936276 | −0.468138 | − | 0.883655i | \(-0.655075\pi\) | ||||
−0.468138 | + | 0.883655i | \(0.655075\pi\) | |||||||
\(618\) | −0.121170 | −0.00487418 | ||||||||
\(619\) | −28.5491 | −1.14749 | −0.573743 | − | 0.819035i | \(-0.694509\pi\) | ||||
−0.573743 | + | 0.819035i | \(0.694509\pi\) | |||||||
\(620\) | −15.0010 | −0.602454 | ||||||||
\(621\) | 3.79843 | 0.152426 | ||||||||
\(622\) | 5.98256 | 0.239879 | ||||||||
\(623\) | 1.69179 | 0.0677801 | ||||||||
\(624\) | 7.32155 | 0.293097 | ||||||||
\(625\) | 12.6893 | 0.507574 | ||||||||
\(626\) | 0.505194 | 0.0201916 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.1028 | −1.20123 | ||||||||
\(629\) | −19.0013 | −0.757633 | ||||||||
\(630\) | −1.78060 | −0.0709407 | ||||||||
\(631\) | 5.30112 | 0.211034 | 0.105517 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105517 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(632\) | 12.6161 | 0.501840 | ||||||||
\(633\) | −26.8703 | −1.06800 | ||||||||
\(634\) | −11.9238 | −0.473556 | ||||||||
\(635\) | 0.764309 | 0.0303307 | ||||||||
\(636\) | −15.6955 | −0.622366 | ||||||||
\(637\) | 2.70774 | 0.107285 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.75988 | 0.306976 | ||||||||
\(640\) | −42.0521 | −1.66225 | ||||||||
\(641\) | −29.8881 | −1.18051 | −0.590255 | − | 0.807217i | \(-0.700973\pi\) | ||||
−0.590255 | + | 0.807217i | \(0.700973\pi\) | |||||||
\(642\) | 5.61859 | 0.221748 | ||||||||
\(643\) | 38.4403 | 1.51594 | 0.757969 | − | 0.652291i | \(-0.226192\pi\) | ||||
0.757969 | + | 0.652291i | \(0.226192\pi\) | |||||||
\(644\) | 6.74448 | 0.265770 | ||||||||
\(645\) | 29.1369 | 1.14726 | ||||||||
\(646\) | −2.05198 | −0.0807340 | ||||||||
\(647\) | −32.3602 | −1.27221 | −0.636105 | − | 0.771603i | \(-0.719455\pi\) | ||||
−0.636105 | + | 0.771603i | \(0.719455\pi\) | |||||||
\(648\) | −1.78855 | −0.0702608 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.7093 | 0.459276 | ||||||||
\(651\) | −2.24763 | −0.0880916 | ||||||||
\(652\) | −35.4655 | −1.38894 | ||||||||
\(653\) | 23.9046 | 0.935459 | 0.467729 | − | 0.883872i | \(-0.345072\pi\) | ||||
0.467729 | + | 0.883872i | \(0.345072\pi\) | |||||||
\(654\) | −7.51876 | −0.294007 | ||||||||
\(655\) | −38.6363 | −1.50964 | ||||||||
\(656\) | −11.3160 | −0.441814 | ||||||||
\(657\) | 15.6796 | 0.611720 | ||||||||
\(658\) | −5.87739 | −0.229124 | ||||||||
\(659\) | 34.5124 | 1.34441 | 0.672205 | − | 0.740365i | \(-0.265347\pi\) | ||||
0.672205 | + | 0.740365i | \(0.265347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.56237 | −0.0996647 | −0.0498324 | − | 0.998758i | \(-0.515869\pi\) | ||||
−0.0498324 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(662\) | −4.04380 | −0.157167 | ||||||||
\(663\) | 6.72285 | 0.261094 | ||||||||
\(664\) | −21.2845 | −0.826000 | ||||||||
\(665\) | 6.55786 | 0.254303 | ||||||||
\(666\) | −3.62538 | −0.140480 | ||||||||
\(667\) | −22.0332 | −0.853128 | ||||||||
\(668\) | −30.9869 | −1.19892 | ||||||||
\(669\) | 4.01918 | 0.155390 | ||||||||
\(670\) | −21.7305 | −0.839523 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.85799 | −0.187401 | ||||||||
\(673\) | 36.6670 | 1.41341 | 0.706704 | − | 0.707509i | \(-0.250181\pi\) | ||||
0.706704 | + | 0.707509i | \(0.250181\pi\) | |||||||
\(674\) | −8.17462 | −0.314874 | ||||||||
\(675\) | 9.12868 | 0.351363 | ||||||||
\(676\) | 10.0643 | 0.387089 | ||||||||
\(677\) | 31.9812 | 1.22914 | 0.614568 | − | 0.788864i | \(-0.289330\pi\) | ||||
0.614568 | + | 0.788864i | \(0.289330\pi\) | |||||||
\(678\) | −2.42375 | −0.0930837 | ||||||||
\(679\) | −6.99638 | −0.268497 | ||||||||
\(680\) | −16.6916 | −0.640093 | ||||||||
\(681\) | −11.7020 | −0.448422 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.96871 | 0.266650 | 0.133325 | − | 0.991072i | \(-0.457435\pi\) | ||||
0.133325 | + | 0.991072i | \(0.457435\pi\) | |||||||
\(684\) | 3.09781 | 0.118448 | ||||||||
\(685\) | −64.3119 | −2.45723 | ||||||||
\(686\) | −0.473713 | −0.0180864 | ||||||||
\(687\) | −6.54504 | −0.249709 | ||||||||
\(688\) | 20.9599 | 0.799087 | ||||||||
\(689\) | 23.9352 | 0.911860 | ||||||||
\(690\) | 6.76349 | 0.257482 | ||||||||
\(691\) | −5.07203 | −0.192949 | −0.0964746 | − | 0.995335i | \(-0.530757\pi\) | ||||
−0.0964746 | + | 0.995335i | \(0.530757\pi\) | |||||||
\(692\) | 16.6186 | 0.631744 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.96922 | 0.0747505 | ||||||||
\(695\) | 73.3003 | 2.78044 | ||||||||
\(696\) | 10.3746 | 0.393250 | ||||||||
\(697\) | −10.3906 | −0.393573 | ||||||||
\(698\) | 3.65131 | 0.138204 | ||||||||
\(699\) | 0.172567 | 0.00652709 | ||||||||
\(700\) | 16.2088 | 0.612637 | ||||||||
\(701\) | 0.418223 | 0.0157961 | 0.00789803 | − | 0.999969i | \(-0.497486\pi\) | ||||
0.00789803 | + | 0.999969i | \(0.497486\pi\) | |||||||
\(702\) | 1.28269 | 0.0484121 | ||||||||
\(703\) | 13.3521 | 0.503583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.6358 | 1.75641 | ||||||||
\(706\) | −2.29392 | −0.0863328 | ||||||||
\(707\) | −2.71683 | −0.102177 | ||||||||
\(708\) | −8.06415 | −0.303069 | ||||||||
\(709\) | −3.60664 | −0.135450 | −0.0677251 | − | 0.997704i | \(-0.521574\pi\) | ||||
−0.0677251 | + | 0.997704i | \(0.521574\pi\) | |||||||
\(710\) | 13.8172 | 0.518551 | ||||||||
\(711\) | −7.05380 | −0.264538 | ||||||||
\(712\) | 3.02585 | 0.113398 | ||||||||
\(713\) | 8.53748 | 0.319731 | ||||||||
\(714\) | −1.17615 | −0.0440162 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.75419 | −0.364531 | ||||||||
\(717\) | −10.4504 | −0.390279 | ||||||||
\(718\) | 2.09303 | 0.0781110 | ||||||||
\(719\) | −17.9697 | −0.670155 | −0.335078 | − | 0.942190i | \(-0.608763\pi\) | ||||
−0.335078 | + | 0.942190i | \(0.608763\pi\) | |||||||
\(720\) | 10.1636 | 0.378774 | ||||||||
\(721\) | 0.255788 | 0.00952606 | ||||||||
\(722\) | −7.55864 | −0.281303 | ||||||||
\(723\) | −3.41821 | −0.127124 | ||||||||
\(724\) | 19.8590 | 0.738055 | ||||||||
\(725\) | −52.9518 | −1.96658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0774 | 0.373752 | 0.186876 | − | 0.982384i | \(-0.440164\pi\) | ||||
0.186876 | + | 0.982384i | \(0.440164\pi\) | |||||||
\(728\) | 4.84293 | 0.179491 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 27.9191 | 1.03333 | ||||||||
\(731\) | 19.2459 | 0.711836 | ||||||||
\(732\) | 20.3883 | 0.753574 | ||||||||
\(733\) | −12.2275 | −0.451631 | −0.225816 | − | 0.974170i | \(-0.572505\pi\) | ||||
−0.225816 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(734\) | −13.9895 | −0.516360 | ||||||||
\(735\) | 3.75881 | 0.138646 | ||||||||
\(736\) | 18.4527 | 0.680177 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.98249 | −0.0729764 | ||||||||
\(739\) | 3.49821 | 0.128684 | 0.0643419 | − | 0.997928i | \(-0.479505\pi\) | ||||
0.0643419 | + | 0.997928i | \(0.479505\pi\) | |||||||
\(740\) | 51.0779 | 1.87766 | ||||||||
\(741\) | −4.72409 | −0.173544 | ||||||||
\(742\) | −4.18741 | −0.153725 | ||||||||
\(743\) | 2.73642 | 0.100389 | 0.0501947 | − | 0.998739i | \(-0.484016\pi\) | ||||
0.0501947 | + | 0.998739i | \(0.484016\pi\) | |||||||
\(744\) | −4.02000 | −0.147380 | ||||||||
\(745\) | −37.1761 | −1.36203 | ||||||||
\(746\) | 3.62374 | 0.132674 | ||||||||
\(747\) | 11.9004 | 0.435414 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.8608 | −0.433382 | ||||||||
\(750\) | 7.35151 | 0.268439 | ||||||||
\(751\) | −10.0480 | −0.366655 | −0.183327 | − | 0.983052i | \(-0.558687\pi\) | ||||
−0.183327 | + | 0.983052i | \(0.558687\pi\) | |||||||
\(752\) | 33.5479 | 1.22337 | ||||||||
\(753\) | 12.6751 | 0.461908 | ||||||||
\(754\) | −7.44038 | −0.270963 | ||||||||
\(755\) | −58.2667 | −2.12054 | ||||||||
\(756\) | 1.77560 | 0.0645778 | ||||||||
\(757\) | 15.1490 | 0.550600 | 0.275300 | − | 0.961358i | \(-0.411223\pi\) | ||||
0.275300 | + | 0.961358i | \(0.411223\pi\) | |||||||
\(758\) | −5.31004 | −0.192869 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.7290 | 0.425457 | ||||||||
\(761\) | 35.4413 | 1.28475 | 0.642373 | − | 0.766392i | \(-0.277950\pi\) | ||||
0.642373 | + | 0.766392i | \(0.277950\pi\) | |||||||
\(762\) | 0.0963238 | 0.00348944 | ||||||||
\(763\) | 15.8720 | 0.574604 | ||||||||
\(764\) | 10.2243 | 0.369901 | ||||||||
\(765\) | 9.33248 | 0.337416 | ||||||||
\(766\) | −11.7219 | −0.423530 | ||||||||
\(767\) | 12.2976 | 0.444042 | ||||||||
\(768\) | 0.913441 | 0.0329610 | ||||||||
\(769\) | 38.7592 | 1.39769 | 0.698845 | − | 0.715273i | \(-0.253698\pi\) | ||||
0.698845 | + | 0.715273i | \(0.253698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1852 | −0.654925 | ||||||||
\(772\) | 26.4290 | 0.951200 | ||||||||
\(773\) | 26.5419 | 0.954646 | 0.477323 | − | 0.878728i | \(-0.341607\pi\) | ||||
0.477323 | + | 0.878728i | \(0.341607\pi\) | |||||||
\(774\) | 3.67204 | 0.131989 | ||||||||
\(775\) | 20.5179 | 0.737025 | ||||||||
\(776\) | −12.5134 | −0.449204 | ||||||||
\(777\) | 7.65311 | 0.274554 | ||||||||
\(778\) | −13.7541 | −0.493109 | ||||||||
\(779\) | 7.30140 | 0.261600 | ||||||||
\(780\) | −18.0718 | −0.647075 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.46752 | 0.159758 | ||||||||
\(783\) | −5.80060 | −0.207296 | ||||||||
\(784\) | 2.70393 | 0.0965690 | ||||||||
\(785\) | 63.7255 | 2.27446 | ||||||||
\(786\) | −4.86922 | −0.173679 | ||||||||
\(787\) | 19.6802 | 0.701524 | 0.350762 | − | 0.936465i | \(-0.385923\pi\) | ||||
0.350762 | + | 0.936465i | \(0.385923\pi\) | |||||||
\(788\) | −22.2794 | −0.793672 | ||||||||
\(789\) | 15.7837 | 0.561914 | ||||||||
\(790\) | −12.5600 | −0.446864 | ||||||||
\(791\) | 5.11650 | 0.181922 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0917 | −1.10410 | ||||||||
\(794\) | −3.91979 | −0.139108 | ||||||||
\(795\) | 33.2262 | 1.17841 | ||||||||
\(796\) | −1.48159 | −0.0525135 | ||||||||
\(797\) | −25.2797 | −0.895451 | −0.447726 | − | 0.894171i | \(-0.647766\pi\) | ||||
−0.447726 | + | 0.894171i | \(0.647766\pi\) | |||||||
\(798\) | 0.826469 | 0.0292567 | ||||||||
\(799\) | 30.8046 | 1.08979 | ||||||||
\(800\) | 44.3470 | 1.56790 | ||||||||
\(801\) | −1.69179 | −0.0597764 | ||||||||
\(802\) | −12.6666 | −0.447274 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.6695 | 0.764223 | ||||||||
\(805\) | −14.2776 | −0.503219 | ||||||||
\(806\) | 2.88302 | 0.101550 | ||||||||
\(807\) | 22.9896 | 0.809273 | ||||||||
\(808\) | −4.85918 | −0.170945 | ||||||||
\(809\) | −35.7891 | −1.25828 | −0.629138 | − | 0.777293i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(810\) | 1.78060 | 0.0625639 | ||||||||
\(811\) | 20.9415 | 0.735355 | 0.367677 | − | 0.929953i | \(-0.380153\pi\) | ||||
0.367677 | + | 0.929953i | \(0.380153\pi\) | |||||||
\(812\) | −10.2995 | −0.361442 | ||||||||
\(813\) | 9.34021 | 0.327575 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 75.0780 | 2.62987 | ||||||||
\(816\) | 6.71339 | 0.235016 | ||||||||
\(817\) | −13.5240 | −0.473143 | ||||||||
\(818\) | 16.4297 | 0.574452 | ||||||||
\(819\) | −2.70774 | −0.0946162 | ||||||||
\(820\) | 27.9312 | 0.975401 | ||||||||
\(821\) | −8.06663 | −0.281527 | −0.140764 | − | 0.990043i | \(-0.544956\pi\) | ||||
−0.140764 | + | 0.990043i | \(0.544956\pi\) | |||||||
\(822\) | −8.10505 | −0.282696 | ||||||||
\(823\) | −20.1359 | −0.701895 | −0.350948 | − | 0.936395i | \(-0.614140\pi\) | ||||
−0.350948 | + | 0.936395i | \(0.614140\pi\) | |||||||
\(824\) | 0.457490 | 0.0159374 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.15144 | −0.0748583 | ||||||||
\(827\) | −21.4181 | −0.744780 | −0.372390 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372390 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(828\) | −6.74448 | −0.234387 | ||||||||
\(829\) | −27.3960 | −0.951504 | −0.475752 | − | 0.879580i | \(-0.657824\pi\) | ||||
−0.475752 | + | 0.879580i | \(0.657824\pi\) | |||||||
\(830\) | 21.1899 | 0.735512 | ||||||||
\(831\) | 19.4367 | 0.674251 | ||||||||
\(832\) | −8.41181 | −0.291627 | ||||||||
\(833\) | 2.48283 | 0.0860248 | ||||||||
\(834\) | 9.23784 | 0.319880 | ||||||||
\(835\) | 65.5972 | 2.27008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.24763 | 0.0776895 | ||||||||
\(838\) | −2.05850 | −0.0711097 | ||||||||
\(839\) | −20.3757 | −0.703446 | −0.351723 | − | 0.936104i | \(-0.614404\pi\) | ||||
−0.351723 | + | 0.936104i | \(0.614404\pi\) | |||||||
\(840\) | 6.72282 | 0.231959 | ||||||||
\(841\) | 4.64691 | 0.160238 | ||||||||
\(842\) | −2.24465 | −0.0773556 | ||||||||
\(843\) | −4.44358 | −0.153045 | ||||||||
\(844\) | 47.7108 | 1.64227 | ||||||||
\(845\) | −21.3055 | −0.732930 | ||||||||
\(846\) | 5.87739 | 0.202069 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.9016 | 0.820783 | ||||||||
\(849\) | 13.8486 | 0.475284 | ||||||||
\(850\) | 10.7367 | 0.368264 | ||||||||
\(851\) | −29.0698 | −0.996501 | ||||||||
\(852\) | −13.7784 | −0.472041 | ||||||||
\(853\) | −8.28686 | −0.283737 | −0.141868 | − | 0.989886i | \(-0.545311\pi\) | ||||
−0.141868 | + | 0.989886i | \(0.545311\pi\) | |||||||
\(854\) | 5.43942 | 0.186133 | ||||||||
\(855\) | −6.55786 | −0.224274 | ||||||||
\(856\) | −21.2135 | −0.725064 | ||||||||
\(857\) | −31.0459 | −1.06051 | −0.530254 | − | 0.847839i | \(-0.677903\pi\) | ||||
−0.530254 | + | 0.847839i | \(0.677903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.63124 | −0.0556573 | −0.0278287 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278287 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(860\) | −51.7354 | −1.76416 | ||||||||
\(861\) | 4.18500 | 0.142624 | ||||||||
\(862\) | −14.1461 | −0.481819 | ||||||||
\(863\) | 5.32862 | 0.181388 | 0.0906942 | − | 0.995879i | \(-0.471091\pi\) | ||||
0.0906942 | + | 0.995879i | \(0.471091\pi\) | |||||||
\(864\) | 4.85799 | 0.165272 | ||||||||
\(865\) | −35.1804 | −1.19617 | ||||||||
\(866\) | −10.2909 | −0.349699 | ||||||||
\(867\) | −10.8356 | −0.367996 | ||||||||
\(868\) | 3.99088 | 0.135459 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.3285 | −0.350170 | ||||||||
\(871\) | −33.0454 | −1.11970 | ||||||||
\(872\) | 28.3878 | 0.961332 | ||||||||
\(873\) | 6.99638 | 0.236792 | ||||||||
\(874\) | −3.13929 | −0.106188 | ||||||||
\(875\) | −15.5189 | −0.524635 | ||||||||
\(876\) | −27.8406 | −0.940648 | ||||||||
\(877\) | −16.1267 | −0.544561 | −0.272281 | − | 0.962218i | \(-0.587778\pi\) | ||||
−0.272281 | + | 0.962218i | \(0.587778\pi\) | |||||||
\(878\) | −19.1118 | −0.644992 | ||||||||
\(879\) | −19.2359 | −0.648811 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.1173 | −1.18313 | −0.591565 | − | 0.806257i | \(-0.701490\pi\) | ||||
−0.591565 | + | 0.806257i | \(0.701490\pi\) | |||||||
\(882\) | 0.473713 | 0.0159507 | ||||||||
\(883\) | 0.480232 | 0.0161611 | 0.00808054 | − | 0.999967i | \(-0.497428\pi\) | ||||
0.00808054 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(884\) | −11.9371 | −0.401487 | ||||||||
\(885\) | 17.0713 | 0.573844 | ||||||||
\(886\) | −6.57463 | −0.220879 | ||||||||
\(887\) | 36.7238 | 1.23306 | 0.616532 | − | 0.787330i | \(-0.288537\pi\) | ||||
0.616532 | + | 0.787330i | \(0.288537\pi\) | |||||||
\(888\) | 13.6880 | 0.459338 | ||||||||
\(889\) | −0.203338 | −0.00681973 | ||||||||
\(890\) | −3.01240 | −0.100976 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.13644 | −0.238946 | ||||||||
\(893\) | −21.6461 | −0.724360 | ||||||||
\(894\) | −4.68520 | −0.156696 | ||||||||
\(895\) | 20.6489 | 0.690218 | ||||||||
\(896\) | 11.1876 | 0.373751 | ||||||||
\(897\) | 10.2852 | 0.343412 | ||||||||
\(898\) | −6.77517 | −0.226090 | ||||||||
\(899\) | −13.0376 | −0.434828 | ||||||||
\(900\) | −16.2088 | −0.540295 | ||||||||
\(901\) | 21.9471 | 0.731163 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.75162 | −0.257958 | ||||||||
\(904\) | 9.15112 | 0.304362 | ||||||||
\(905\) | −42.0402 | −1.39746 | ||||||||
\(906\) | −7.34319 | −0.243961 | ||||||||
\(907\) | 12.1917 | 0.404818 | 0.202409 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202409 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(908\) | 20.7781 | 0.689544 | ||||||||
\(909\) | 2.71683 | 0.0901116 | ||||||||
\(910\) | −4.82140 | −0.159828 | ||||||||
\(911\) | −8.11848 | −0.268977 | −0.134489 | − | 0.990915i | \(-0.542939\pi\) | ||||
−0.134489 | + | 0.990915i | \(0.542939\pi\) | |||||||
\(912\) | −4.71745 | −0.156210 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.69251 | −0.221369 | ||||||||
\(915\) | −43.1606 | −1.42685 | ||||||||
\(916\) | 11.6213 | 0.383980 | ||||||||
\(917\) | 10.2788 | 0.339438 | ||||||||
\(918\) | 1.17615 | 0.0388186 | ||||||||
\(919\) | −49.6539 | −1.63793 | −0.818965 | − | 0.573843i | \(-0.805452\pi\) | ||||
−0.818965 | + | 0.573843i | \(0.805452\pi\) | |||||||
\(920\) | −25.5362 | −0.841903 | ||||||||
\(921\) | 2.24474 | 0.0739668 | ||||||||
\(922\) | −0.457955 | −0.0150820 | ||||||||
\(923\) | 21.0118 | 0.691610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69.8627 | −2.29707 | ||||||||
\(926\) | 15.0697 | 0.495221 | ||||||||
\(927\) | −0.255788 | −0.00840119 | ||||||||
\(928\) | −28.1792 | −0.925028 | ||||||||
\(929\) | −0.373776 | −0.0122632 | −0.00613160 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613160 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(930\) | 4.00213 | 0.131235 | ||||||||
\(931\) | −1.74466 | −0.0571790 | ||||||||
\(932\) | −0.306409 | −0.0100368 | ||||||||
\(933\) | 12.6291 | 0.413458 | ||||||||
\(934\) | −14.0282 | −0.459016 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.84293 | −0.158296 | ||||||||
\(937\) | −46.0667 | −1.50493 | −0.752467 | − | 0.658630i | \(-0.771136\pi\) | ||||
−0.752467 | + | 0.658630i | \(0.771136\pi\) | |||||||
\(938\) | 5.78122 | 0.188763 | ||||||||
\(939\) | 1.06646 | 0.0348025 | ||||||||
\(940\) | −82.8064 | −2.70085 | ||||||||
\(941\) | −19.3374 | −0.630380 | −0.315190 | − | 0.949029i | \(-0.602068\pi\) | ||||
−0.315190 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(942\) | 8.03115 | 0.261669 | ||||||||
\(943\) | −15.8964 | −0.517659 | ||||||||
\(944\) | 12.2803 | 0.399691 | ||||||||
\(945\) | −3.75881 | −0.122274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.06969 | −0.262230 | −0.131115 | − | 0.991367i | \(-0.541856\pi\) | ||||
−0.131115 | + | 0.991367i | \(0.541856\pi\) | |||||||
\(948\) | 12.5247 | 0.406783 | ||||||||
\(949\) | 42.4563 | 1.37819 | ||||||||
\(950\) | −7.54457 | −0.244778 | ||||||||
\(951\) | −25.1710 | −0.816225 | ||||||||
\(952\) | 4.44065 | 0.143922 | ||||||||
\(953\) | 34.6358 | 1.12196 | 0.560982 | − | 0.827828i | \(-0.310424\pi\) | ||||
0.560982 | + | 0.827828i | \(0.310424\pi\) | |||||||
\(954\) | 4.18741 | 0.135572 | ||||||||
\(955\) | −21.6441 | −0.700385 | ||||||||
\(956\) | 18.5557 | 0.600136 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.5938 | −0.406887 | ||||||||
\(959\) | 17.1096 | 0.552498 | ||||||||
\(960\) | −11.6770 | −0.376875 | ||||||||
\(961\) | −25.9482 | −0.837037 | ||||||||
\(962\) | −9.81659 | −0.316499 | ||||||||
\(963\) | 11.8608 | 0.382207 | ||||||||
\(964\) | 6.06935 | 0.195481 | ||||||||
\(965\) | −55.9483 | −1.80104 | ||||||||
\(966\) | −1.79937 | −0.0578937 | ||||||||
\(967\) | 8.15074 | 0.262110 | 0.131055 | − | 0.991375i | \(-0.458164\pi\) | ||||
0.131055 | + | 0.991375i | \(0.458164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.33169 | −0.139154 | ||||||||
\(970\) | 12.4578 | 0.399994 | ||||||||
\(971\) | 33.4330 | 1.07292 | 0.536458 | − | 0.843927i | \(-0.319762\pi\) | ||||
0.536458 | + | 0.843927i | \(0.319762\pi\) | |||||||
\(972\) | −1.77560 | −0.0569523 | ||||||||
\(973\) | −19.5009 | −0.625171 | ||||||||
\(974\) | 6.69560 | 0.214541 | ||||||||
\(975\) | 24.7181 | 0.791613 | ||||||||
\(976\) | −31.0480 | −0.993821 | ||||||||
\(977\) | −5.48798 | −0.175576 | −0.0877880 | − | 0.996139i | \(-0.527980\pi\) | ||||
−0.0877880 | + | 0.996139i | \(0.527980\pi\) | |||||||
\(978\) | 9.46188 | 0.302557 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.67413 | −0.213197 | ||||||||
\(981\) | −15.8720 | −0.506753 | ||||||||
\(982\) | 7.30398 | 0.233080 | ||||||||
\(983\) | 14.5404 | 0.463767 | 0.231884 | − | 0.972744i | \(-0.425511\pi\) | ||||
0.231884 | + | 0.972744i | \(0.425511\pi\) | |||||||
\(984\) | 7.48507 | 0.238615 | ||||||||
\(985\) | 47.1640 | 1.50277 | ||||||||
\(986\) | −6.82235 | −0.217268 | ||||||||
\(987\) | −12.4071 | −0.394921 | ||||||||
\(988\) | 8.38808 | 0.266860 | ||||||||
\(989\) | 29.4440 | 0.936266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.68326 | −0.307599 | −0.153799 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153799 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(992\) | 10.9190 | 0.346677 | ||||||||
\(993\) | −8.53640 | −0.270894 | ||||||||
\(994\) | −3.67596 | −0.116594 | ||||||||
\(995\) | 3.13642 | 0.0994312 | ||||||||
\(996\) | −21.1304 | −0.669542 | ||||||||
\(997\) | −25.2216 | −0.798775 | −0.399388 | − | 0.916782i | \(-0.630777\pi\) | ||||
−0.399388 | + | 0.916782i | \(0.630777\pi\) | |||||||
\(998\) | 14.5441 | 0.460387 | ||||||||
\(999\) | −7.65311 | −0.242134 |
(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 | 2541.2.a.bq.1.6 | 10 | ||
3.2 | odd | 2 | 7623.2.a.cx.1.5 | 10 | |||
11.5 | even | 5 | 231.2.j.g.190.3 | yes | 20 | ||
11.9 | even | 5 | 231.2.j.g.169.3 | ✓ | 20 | ||
11.10 | odd | 2 | 2541.2.a.br.1.5 | 10 | |||
33.5 | odd | 10 | 693.2.m.j.190.3 | 20 | |||
33.20 | odd | 10 | 693.2.m.j.631.3 | 20 | |||
33.32 | even | 2 | 7623.2.a.cy.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.169.3 | ✓ | 20 | 11.9 | even | 5 | ||
231.2.j.g.190.3 | yes | 20 | 11.5 | even | 5 | ||
693.2.m.j.190.3 | 20 | 33.5 | odd | 10 | |||
693.2.m.j.631.3 | 20 | 33.20 | odd | 10 | |||
2541.2.a.bq.1.6 | 10 | 1.1 | even | 1 | trivial | ||
2541.2.a.br.1.5 | 10 | 11.10 | odd | 2 | |||
7623.2.a.cx.1.5 | 10 | 3.2 | odd | 2 | |||
7623.2.a.cy.1.6 | 10 | 33.32 | even | 2 |