Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6825,2,Mod(1,6825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6825.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: | \(54.4978993795\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 5x^{2} + 5 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1365) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.80423 | 0.845506 | 0.422753 | − | 0.906245i | \(-0.361064\pi\) | ||||
0.422753 | + | 0.906245i | \(0.361064\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −2.01062 | −0.487647 | −0.243824 | − | 0.969820i | \(-0.578402\pi\) | ||||
−0.243824 | + | 0.969820i | \(0.578402\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | −2.34458 | −0.537883 | −0.268941 | − | 0.963157i | \(-0.586674\pi\) | ||||
−0.268941 | + | 0.963157i | \(0.586674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −4.53733 | −0.967363 | ||||||||
\(23\) | −0.939503 | −0.195900 | −0.0979499 | − | 0.995191i | \(-0.531228\pi\) | ||||
−0.0979499 | + | 0.995191i | \(0.531228\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.618034 | 0.116797 | ||||||||
\(29\) | −5.69572 | −1.05767 | −0.528834 | − | 0.848725i | \(-0.677371\pi\) | ||||
−0.528834 | + | 0.848725i | \(0.677371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.895549 | 0.160845 | 0.0804226 | − | 0.996761i | \(-0.474373\pi\) | ||||
0.0804226 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 2.80423 | 0.488153 | ||||||||
\(34\) | 3.25325 | 0.557928 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −5.52015 | −0.907507 | −0.453753 | − | 0.891127i | \(-0.649915\pi\) | ||||
−0.453753 | + | 0.891127i | \(0.649915\pi\) | |||||||
\(38\) | 3.79360 | 0.615404 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.07768 | 0.480653 | 0.240327 | − | 0.970692i | \(-0.422745\pi\) | ||||
0.240327 | + | 0.970692i | \(0.422745\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | 5.12454 | 0.781485 | 0.390743 | − | 0.920500i | \(-0.372218\pi\) | ||||
0.390743 | + | 0.920500i | \(0.372218\pi\) | |||||||
\(44\) | 1.73311 | 0.261276 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.52015 | 0.224133 | ||||||||
\(47\) | −5.96261 | −0.869736 | −0.434868 | − | 0.900494i | \(-0.643205\pi\) | ||||
−0.434868 | + | 0.900494i | \(0.643205\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.01062 | −0.281543 | ||||||||
\(52\) | 0.618034 | 0.0857059 | ||||||||
\(53\) | −1.30313 | −0.178999 | −0.0894993 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0894993 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −2.34458 | −0.310547 | ||||||||
\(58\) | 9.21586 | 1.21010 | ||||||||
\(59\) | −2.47027 | −0.321602 | −0.160801 | − | 0.986987i | \(-0.551408\pi\) | ||||
−0.160801 | + | 0.986987i | \(0.551408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15838 | −0.532427 | −0.266213 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266213 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(62\) | −1.44903 | −0.184027 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.53733 | −0.558507 | ||||||||
\(67\) | −15.4797 | −1.89115 | −0.945576 | − | 0.325402i | \(-0.894500\pi\) | ||||
−0.945576 | + | 0.325402i | \(0.894500\pi\) | |||||||
\(68\) | −1.24263 | −0.150691 | ||||||||
\(69\) | −0.939503 | −0.113103 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3416 | −1.46467 | −0.732337 | − | 0.680943i | \(-0.761570\pi\) | ||||
−0.732337 | + | 0.680943i | \(0.761570\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −2.77455 | −0.324737 | −0.162368 | − | 0.986730i | \(-0.551913\pi\) | ||||
−0.162368 | + | 0.986730i | \(0.551913\pi\) | |||||||
\(74\) | 8.93179 | 1.03830 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.44903 | −0.166215 | ||||||||
\(77\) | 2.80423 | 0.319571 | ||||||||
\(78\) | −1.61803 | −0.183206 | ||||||||
\(79\) | −6.16495 | −0.693611 | −0.346805 | − | 0.937937i | \(-0.612734\pi\) | ||||
−0.346805 | + | 0.937937i | \(0.612734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.97980 | −0.549927 | ||||||||
\(83\) | −15.5861 | −1.71079 | −0.855396 | − | 0.517975i | \(-0.826686\pi\) | ||||
−0.855396 | + | 0.517975i | \(0.826686\pi\) | |||||||
\(84\) | 0.618034 | 0.0674330 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.29168 | −0.894115 | ||||||||
\(87\) | −5.69572 | −0.610645 | ||||||||
\(88\) | 6.27044 | 0.668431 | ||||||||
\(89\) | −0.821412 | −0.0870695 | −0.0435348 | − | 0.999052i | \(-0.513862\pi\) | ||||
−0.0435348 | + | 0.999052i | \(0.513862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −0.580644 | −0.0605364 | ||||||||
\(93\) | 0.895549 | 0.0928641 | ||||||||
\(94\) | 9.64771 | 0.995085 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | −1.98281 | −0.201324 | −0.100662 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100662 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(98\) | −1.61803 | −0.163446 | ||||||||
\(99\) | 2.80423 | 0.281835 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.71883 | 0.768052 | 0.384026 | − | 0.923322i | \(-0.374537\pi\) | ||||
0.384026 | + | 0.923322i | \(0.374537\pi\) | |||||||
\(102\) | 3.25325 | 0.322120 | ||||||||
\(103\) | −19.3309 | −1.90473 | −0.952367 | − | 0.304954i | \(-0.901359\pi\) | ||||
−0.952367 | + | 0.304954i | \(0.901359\pi\) | |||||||
\(104\) | 2.23607 | 0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.10851 | 0.204796 | ||||||||
\(107\) | 7.81736 | 0.755732 | 0.377866 | − | 0.925860i | \(-0.376658\pi\) | ||||
0.377866 | + | 0.925860i | \(0.376658\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | 1.33686 | 0.128048 | 0.0640240 | − | 0.997948i | \(-0.479607\pi\) | ||||
0.0640240 | + | 0.997948i | \(0.479607\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.52015 | −0.523949 | ||||||||
\(112\) | −4.85410 | −0.458670 | ||||||||
\(113\) | −6.79766 | −0.639470 | −0.319735 | − | 0.947507i | \(-0.603594\pi\) | ||||
−0.319735 | + | 0.947507i | \(0.603594\pi\) | |||||||
\(114\) | 3.79360 | 0.355304 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.52015 | −0.326837 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 3.99698 | 0.367952 | ||||||||
\(119\) | −2.01062 | −0.184313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.13632 | −0.285120 | ||||||||
\(122\) | 6.72841 | 0.609161 | ||||||||
\(123\) | 3.07768 | 0.277505 | ||||||||
\(124\) | 0.553479 | 0.0497039 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.61803 | −0.144146 | ||||||||
\(127\) | −10.4912 | −0.930942 | −0.465471 | − | 0.885063i | \(-0.654115\pi\) | ||||
−0.465471 | + | 0.885063i | \(0.654115\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 5.12454 | 0.451191 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.09319 | −0.182883 | −0.0914413 | − | 0.995810i | \(-0.529147\pi\) | ||||
−0.0914413 | + | 0.995810i | \(0.529147\pi\) | |||||||
\(132\) | 1.73311 | 0.150848 | ||||||||
\(133\) | −2.34458 | −0.203301 | ||||||||
\(134\) | 25.0467 | 2.16371 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.49589 | −0.385519 | ||||||||
\(137\) | 12.2704 | 1.04833 | 0.524167 | − | 0.851615i | \(-0.324377\pi\) | ||||
0.524167 | + | 0.851615i | \(0.324377\pi\) | |||||||
\(138\) | 1.52015 | 0.129404 | ||||||||
\(139\) | 13.4538 | 1.14114 | 0.570568 | − | 0.821250i | \(-0.306723\pi\) | ||||
0.570568 | + | 0.821250i | \(0.306723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.96261 | −0.502142 | ||||||||
\(142\) | 19.9691 | 1.67577 | ||||||||
\(143\) | 2.80423 | 0.234501 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.48932 | 0.371539 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −3.41164 | −0.280435 | ||||||||
\(149\) | 12.6216 | 1.03400 | 0.517000 | − | 0.855985i | \(-0.327049\pi\) | ||||
0.517000 | + | 0.855985i | \(0.327049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.222429 | 0.0181010 | 0.00905051 | − | 0.999959i | \(-0.497119\pi\) | ||||
0.00905051 | + | 0.999959i | \(0.497119\pi\) | |||||||
\(152\) | −5.24263 | −0.425234 | ||||||||
\(153\) | −2.01062 | −0.162549 | ||||||||
\(154\) | −4.53733 | −0.365629 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.618034 | 0.0494823 | ||||||||
\(157\) | −19.5013 | −1.55637 | −0.778187 | − | 0.628033i | \(-0.783860\pi\) | ||||
−0.778187 | + | 0.628033i | \(0.783860\pi\) | |||||||
\(158\) | 9.97510 | 0.793576 | ||||||||
\(159\) | −1.30313 | −0.103345 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.939503 | −0.0740432 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | 1.14712 | 0.0898494 | 0.0449247 | − | 0.998990i | \(-0.485695\pi\) | ||||
0.0449247 | + | 0.998990i | \(0.485695\pi\) | |||||||
\(164\) | 1.90211 | 0.148530 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.2188 | 1.95736 | ||||||||
\(167\) | 17.8232 | 1.37920 | 0.689599 | − | 0.724191i | \(-0.257787\pi\) | ||||
0.689599 | + | 0.724191i | \(0.257787\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.34458 | −0.179294 | ||||||||
\(172\) | 3.16714 | 0.241492 | ||||||||
\(173\) | −2.11443 | −0.160757 | −0.0803786 | − | 0.996764i | \(-0.525613\pi\) | ||||
−0.0803786 | + | 0.996764i | \(0.525613\pi\) | |||||||
\(174\) | 9.21586 | 0.698653 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.6120 | −1.02604 | ||||||||
\(177\) | −2.47027 | −0.185677 | ||||||||
\(178\) | 1.32907 | 0.0996182 | ||||||||
\(179\) | 18.6737 | 1.39574 | 0.697870 | − | 0.716225i | \(-0.254131\pi\) | ||||
0.697870 | + | 0.716225i | \(0.254131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.07872 | 0.451828 | 0.225914 | − | 0.974147i | \(-0.427463\pi\) | ||||
0.225914 | + | 0.974147i | \(0.427463\pi\) | |||||||
\(182\) | −1.61803 | −0.119937 | ||||||||
\(183\) | −4.15838 | −0.307397 | ||||||||
\(184\) | −2.10079 | −0.154872 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.44903 | −0.106248 | ||||||||
\(187\) | −5.63824 | −0.412309 | ||||||||
\(188\) | −3.68510 | −0.268763 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.9329 | 1.00815 | 0.504076 | − | 0.863659i | \(-0.331833\pi\) | ||||
0.504076 | + | 0.863659i | \(0.331833\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | −3.14339 | −0.226266 | −0.113133 | − | 0.993580i | \(-0.536089\pi\) | ||||
−0.113133 | + | 0.993580i | \(0.536089\pi\) | |||||||
\(194\) | 3.20826 | 0.230340 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 5.11141 | 0.364173 | 0.182087 | − | 0.983283i | \(-0.441715\pi\) | ||||
0.182087 | + | 0.983283i | \(0.441715\pi\) | |||||||
\(198\) | −4.53733 | −0.322454 | ||||||||
\(199\) | 16.5135 | 1.17061 | 0.585304 | − | 0.810814i | \(-0.300975\pi\) | ||||
0.585304 | + | 0.810814i | \(0.300975\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.4797 | −1.09186 | ||||||||
\(202\) | −12.4893 | −0.878746 | ||||||||
\(203\) | −5.69572 | −0.399761 | ||||||||
\(204\) | −1.24263 | −0.0870017 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 31.2781 | 2.17925 | ||||||||
\(207\) | −0.939503 | −0.0652999 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | −6.57472 | −0.454783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.47078 | −0.170096 | −0.0850478 | − | 0.996377i | \(-0.527104\pi\) | ||||
−0.0850478 | + | 0.996377i | \(0.527104\pi\) | |||||||
\(212\) | −0.805379 | −0.0553136 | ||||||||
\(213\) | −12.3416 | −0.845630 | ||||||||
\(214\) | −12.6487 | −0.864650 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 0.895549 | 0.0607938 | ||||||||
\(218\) | −2.16308 | −0.146503 | ||||||||
\(219\) | −2.77455 | −0.187487 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.01062 | −0.135249 | ||||||||
\(222\) | 8.93179 | 0.599462 | ||||||||
\(223\) | −9.10445 | −0.609679 | −0.304840 | − | 0.952404i | \(-0.598603\pi\) | ||||
−0.304840 | + | 0.952404i | \(0.598603\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.9988 | 0.731632 | ||||||||
\(227\) | 7.00779 | 0.465123 | 0.232562 | − | 0.972582i | \(-0.425289\pi\) | ||||
0.232562 | + | 0.972582i | \(0.425289\pi\) | |||||||
\(228\) | −1.44903 | −0.0959642 | ||||||||
\(229\) | −20.2385 | −1.33740 | −0.668698 | − | 0.743534i | \(-0.733148\pi\) | ||||
−0.668698 | + | 0.743534i | \(0.733148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.80423 | 0.184505 | ||||||||
\(232\) | −12.7360 | −0.836160 | ||||||||
\(233\) | −14.6750 | −0.961391 | −0.480696 | − | 0.876887i | \(-0.659616\pi\) | ||||
−0.480696 | + | 0.876887i | \(0.659616\pi\) | |||||||
\(234\) | −1.61803 | −0.105774 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.52671 | −0.0993805 | ||||||||
\(237\) | −6.16495 | −0.400456 | ||||||||
\(238\) | 3.25325 | 0.210877 | ||||||||
\(239\) | 23.9963 | 1.55219 | 0.776097 | − | 0.630613i | \(-0.217197\pi\) | ||||
0.776097 | + | 0.630613i | \(0.217197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.2300 | 1.62521 | 0.812605 | − | 0.582815i | \(-0.198049\pi\) | ||||
0.812605 | + | 0.582815i | \(0.198049\pi\) | |||||||
\(242\) | 5.07467 | 0.326212 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.57002 | −0.164529 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.97980 | −0.317500 | ||||||||
\(247\) | −2.34458 | −0.149182 | ||||||||
\(248\) | 2.00251 | 0.127159 | ||||||||
\(249\) | −15.5861 | −0.987726 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8992 | 0.751069 | 0.375534 | − | 0.926808i | \(-0.377459\pi\) | ||||
0.375534 | + | 0.926808i | \(0.377459\pi\) | |||||||
\(252\) | 0.618034 | 0.0389325 | ||||||||
\(253\) | −2.63458 | −0.165634 | ||||||||
\(254\) | 16.9751 | 1.06511 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 5.49151 | 0.342551 | 0.171276 | − | 0.985223i | \(-0.445211\pi\) | ||||
0.171276 | + | 0.985223i | \(0.445211\pi\) | |||||||
\(258\) | −8.29168 | −0.516218 | ||||||||
\(259\) | −5.52015 | −0.343005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.69572 | −0.352556 | ||||||||
\(262\) | 3.38685 | 0.209240 | ||||||||
\(263\) | −2.38614 | −0.147135 | −0.0735677 | − | 0.997290i | \(-0.523439\pi\) | ||||
−0.0735677 | + | 0.997290i | \(0.523439\pi\) | |||||||
\(264\) | 6.27044 | 0.385919 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.79360 | 0.232601 | ||||||||
\(267\) | −0.821412 | −0.0502696 | ||||||||
\(268\) | −9.56701 | −0.584398 | ||||||||
\(269\) | −18.6149 | −1.13497 | −0.567485 | − | 0.823383i | \(-0.692084\pi\) | ||||
−0.567485 | + | 0.823383i | \(0.692084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.89400 | −0.175798 | −0.0878990 | − | 0.996129i | \(-0.528015\pi\) | ||||
−0.0878990 | + | 0.996129i | \(0.528015\pi\) | |||||||
\(272\) | 9.75976 | 0.591773 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | −19.8540 | −1.19942 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.580644 | −0.0349507 | ||||||||
\(277\) | −14.3261 | −0.860769 | −0.430385 | − | 0.902646i | \(-0.641622\pi\) | ||||
−0.430385 | + | 0.902646i | \(0.641622\pi\) | |||||||
\(278\) | −21.7687 | −1.30560 | ||||||||
\(279\) | 0.895549 | 0.0536151 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.57543 | 0.332603 | 0.166301 | − | 0.986075i | \(-0.446818\pi\) | ||||
0.166301 | + | 0.986075i | \(0.446818\pi\) | |||||||
\(282\) | 9.64771 | 0.574513 | ||||||||
\(283\) | 18.6838 | 1.11064 | 0.555319 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555319 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(284\) | −7.62750 | −0.452609 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.53733 | −0.268298 | ||||||||
\(287\) | 3.07768 | 0.181670 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | −12.9574 | −0.762200 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.98281 | −0.116235 | ||||||||
\(292\) | −1.71477 | −0.100349 | ||||||||
\(293\) | −31.0585 | −1.81446 | −0.907229 | − | 0.420637i | \(-0.861807\pi\) | ||||
−0.907229 | + | 0.420637i | \(0.861807\pi\) | |||||||
\(294\) | −1.61803 | −0.0943657 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.3434 | −0.717447 | ||||||||
\(297\) | 2.80423 | 0.162718 | ||||||||
\(298\) | −20.4221 | −1.18302 | ||||||||
\(299\) | −0.939503 | −0.0543328 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.12454 | 0.295374 | ||||||||
\(302\) | −0.359898 | −0.0207098 | ||||||||
\(303\) | 7.71883 | 0.443435 | ||||||||
\(304\) | 11.3808 | 0.652734 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.25325 | 0.185976 | ||||||||
\(307\) | −1.72892 | −0.0986745 | −0.0493373 | − | 0.998782i | \(-0.515711\pi\) | ||||
−0.0493373 | + | 0.998782i | \(0.515711\pi\) | |||||||
\(308\) | 1.73311 | 0.0987529 | ||||||||
\(309\) | −19.3309 | −1.09970 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7385 | 1.00586 | 0.502930 | − | 0.864327i | \(-0.332256\pi\) | ||||
0.502930 | + | 0.864327i | \(0.332256\pi\) | |||||||
\(312\) | 2.23607 | 0.126592 | ||||||||
\(313\) | −24.8522 | −1.40473 | −0.702365 | − | 0.711817i | \(-0.747872\pi\) | ||||
−0.702365 | + | 0.711817i | \(0.747872\pi\) | |||||||
\(314\) | 31.5538 | 1.78068 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.81015 | −0.214338 | ||||||||
\(317\) | 2.60626 | 0.146382 | 0.0731911 | − | 0.997318i | \(-0.476682\pi\) | ||||
0.0731911 | + | 0.997318i | \(0.476682\pi\) | |||||||
\(318\) | 2.10851 | 0.118239 | ||||||||
\(319\) | −15.9721 | −0.894265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.81736 | 0.436322 | ||||||||
\(322\) | 1.52015 | 0.0847145 | ||||||||
\(323\) | 4.71406 | 0.262297 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.85608 | −0.102799 | ||||||||
\(327\) | 1.33686 | 0.0739285 | ||||||||
\(328\) | 6.88191 | 0.379990 | ||||||||
\(329\) | −5.96261 | −0.328729 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7543 | −1.69041 | −0.845205 | − | 0.534443i | \(-0.820522\pi\) | ||||
−0.845205 | + | 0.534443i | \(0.820522\pi\) | |||||||
\(332\) | −9.63271 | −0.528664 | ||||||||
\(333\) | −5.52015 | −0.302502 | ||||||||
\(334\) | −28.8385 | −1.57797 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.85410 | −0.264813 | ||||||||
\(337\) | 14.3356 | 0.780912 | 0.390456 | − | 0.920622i | \(-0.372317\pi\) | ||||
0.390456 | + | 0.920622i | \(0.372317\pi\) | |||||||
\(338\) | −1.61803 | −0.0880094 | ||||||||
\(339\) | −6.79766 | −0.369198 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.51132 | 0.135996 | ||||||||
\(342\) | 3.79360 | 0.205135 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.4588 | 0.617818 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.42122 | 0.183926 | ||||||||
\(347\) | −28.2949 | −1.51895 | −0.759475 | − | 0.650537i | \(-0.774544\pi\) | ||||
−0.759475 | + | 0.650537i | \(0.774544\pi\) | |||||||
\(348\) | −3.52015 | −0.188700 | ||||||||
\(349\) | −7.82174 | −0.418688 | −0.209344 | − | 0.977842i | \(-0.567133\pi\) | ||||
−0.209344 | + | 0.977842i | \(0.567133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 9.48380 | 0.505488 | ||||||||
\(353\) | 12.6656 | 0.674122 | 0.337061 | − | 0.941483i | \(-0.390567\pi\) | ||||
0.337061 | + | 0.941483i | \(0.390567\pi\) | |||||||
\(354\) | 3.99698 | 0.212437 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.507661 | −0.0269060 | ||||||||
\(357\) | −2.01062 | −0.106413 | ||||||||
\(358\) | −30.2147 | −1.59690 | ||||||||
\(359\) | 4.35926 | 0.230073 | 0.115036 | − | 0.993361i | \(-0.463302\pi\) | ||||
0.115036 | + | 0.993361i | \(0.463302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5030 | −0.710682 | ||||||||
\(362\) | −9.83558 | −0.516947 | ||||||||
\(363\) | −3.13632 | −0.164614 | ||||||||
\(364\) | 0.618034 | 0.0323938 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.72841 | 0.351699 | ||||||||
\(367\) | −23.7244 | −1.23840 | −0.619201 | − | 0.785233i | \(-0.712543\pi\) | ||||
−0.619201 | + | 0.785233i | \(0.712543\pi\) | |||||||
\(368\) | 4.56044 | 0.237729 | ||||||||
\(369\) | 3.07768 | 0.160218 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.30313 | −0.0676551 | ||||||||
\(372\) | 0.553479 | 0.0286966 | ||||||||
\(373\) | −12.2595 | −0.634773 | −0.317387 | − | 0.948296i | \(-0.602805\pi\) | ||||
−0.317387 | + | 0.948296i | \(0.602805\pi\) | |||||||
\(374\) | 9.12286 | 0.471732 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.3328 | −0.687587 | ||||||||
\(377\) | −5.69572 | −0.293344 | ||||||||
\(378\) | −1.61803 | −0.0832227 | ||||||||
\(379\) | −9.44164 | −0.484984 | −0.242492 | − | 0.970153i | \(-0.577965\pi\) | ||||
−0.242492 | + | 0.970153i | \(0.577965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4912 | −0.537480 | ||||||||
\(382\) | −22.5440 | −1.15345 | ||||||||
\(383\) | 1.81922 | 0.0929578 | 0.0464789 | − | 0.998919i | \(-0.485200\pi\) | ||||
0.0464789 | + | 0.998919i | \(0.485200\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.08611 | 0.258876 | ||||||||
\(387\) | 5.12454 | 0.260495 | ||||||||
\(388\) | −1.22545 | −0.0622126 | ||||||||
\(389\) | −11.2846 | −0.572152 | −0.286076 | − | 0.958207i | \(-0.592351\pi\) | ||||
−0.286076 | + | 0.958207i | \(0.592351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.88898 | 0.0955300 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −2.09319 | −0.105587 | ||||||||
\(394\) | −8.27044 | −0.416659 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.73311 | 0.0870919 | ||||||||
\(397\) | 21.6658 | 1.08738 | 0.543688 | − | 0.839287i | \(-0.317027\pi\) | ||||
0.543688 | + | 0.839287i | \(0.317027\pi\) | |||||||
\(398\) | −26.7194 | −1.33932 | ||||||||
\(399\) | −2.34458 | −0.117376 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1128 | 0.754696 | 0.377348 | − | 0.926072i | \(-0.376836\pi\) | ||||
0.377348 | + | 0.926072i | \(0.376836\pi\) | |||||||
\(402\) | 25.0467 | 1.24922 | ||||||||
\(403\) | 0.895549 | 0.0446105 | ||||||||
\(404\) | 4.77050 | 0.237341 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.21586 | 0.457376 | ||||||||
\(407\) | −15.4797 | −0.767302 | ||||||||
\(408\) | −4.49589 | −0.222580 | ||||||||
\(409\) | 0.0919651 | 0.00454738 | 0.00227369 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227369 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.2704 | 0.605256 | ||||||||
\(412\) | −11.9472 | −0.588595 | ||||||||
\(413\) | −2.47027 | −0.121554 | ||||||||
\(414\) | 1.52015 | 0.0747112 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | 13.4538 | 0.658835 | ||||||||
\(418\) | 10.6381 | 0.520328 | ||||||||
\(419\) | 15.8705 | 0.775323 | 0.387661 | − | 0.921802i | \(-0.373283\pi\) | ||||
0.387661 | + | 0.921802i | \(0.373283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6257 | −0.664076 | −0.332038 | − | 0.943266i | \(-0.607736\pi\) | ||||
−0.332038 | + | 0.943266i | \(0.607736\pi\) | |||||||
\(422\) | 3.99781 | 0.194610 | ||||||||
\(423\) | −5.96261 | −0.289912 | ||||||||
\(424\) | −2.91389 | −0.141511 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 19.9691 | 0.967504 | ||||||||
\(427\) | −4.15838 | −0.201238 | ||||||||
\(428\) | 4.83139 | 0.233534 | ||||||||
\(429\) | 2.80423 | 0.135389 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.4756 | −1.22712 | −0.613559 | − | 0.789649i | \(-0.710263\pi\) | ||||
−0.613559 | + | 0.789649i | \(0.710263\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | −20.3956 | −0.980151 | −0.490076 | − | 0.871680i | \(-0.663031\pi\) | ||||
−0.490076 | + | 0.871680i | \(0.663031\pi\) | |||||||
\(434\) | −1.44903 | −0.0695556 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.826225 | 0.0395690 | ||||||||
\(437\) | 2.20274 | 0.105371 | ||||||||
\(438\) | 4.48932 | 0.214508 | ||||||||
\(439\) | 22.8539 | 1.09076 | 0.545379 | − | 0.838190i | \(-0.316386\pi\) | ||||
0.545379 | + | 0.838190i | \(0.316386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 3.25325 | 0.154742 | ||||||||
\(443\) | 15.9067 | 0.755750 | 0.377875 | − | 0.925857i | \(-0.376655\pi\) | ||||
0.377875 | + | 0.925857i | \(0.376655\pi\) | |||||||
\(444\) | −3.41164 | −0.161909 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.7313 | 0.697548 | ||||||||
\(447\) | 12.6216 | 0.596980 | ||||||||
\(448\) | 4.23607 | 0.200135 | ||||||||
\(449\) | −23.3073 | −1.09994 | −0.549969 | − | 0.835185i | \(-0.685360\pi\) | ||||
−0.549969 | + | 0.835185i | \(0.685360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.63052 | 0.406395 | ||||||||
\(452\) | −4.20119 | −0.197607 | ||||||||
\(453\) | 0.222429 | 0.0104506 | ||||||||
\(454\) | −11.3388 | −0.532158 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.24263 | −0.245509 | ||||||||
\(457\) | 18.1531 | 0.849164 | 0.424582 | − | 0.905389i | \(-0.360421\pi\) | ||||
0.424582 | + | 0.905389i | \(0.360421\pi\) | |||||||
\(458\) | 32.7465 | 1.53014 | ||||||||
\(459\) | −2.01062 | −0.0938478 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.5416 | 1.42246 | 0.711232 | − | 0.702957i | \(-0.248138\pi\) | ||||
0.711232 | + | 0.702957i | \(0.248138\pi\) | |||||||
\(462\) | −4.53733 | −0.211096 | ||||||||
\(463\) | −18.8199 | −0.874636 | −0.437318 | − | 0.899307i | \(-0.644072\pi\) | ||||
−0.437318 | + | 0.899307i | \(0.644072\pi\) | |||||||
\(464\) | 27.6476 | 1.28351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.7447 | 1.09995 | ||||||||
\(467\) | −14.3948 | −0.666114 | −0.333057 | − | 0.942907i | \(-0.608080\pi\) | ||||
−0.333057 | + | 0.942907i | \(0.608080\pi\) | |||||||
\(468\) | 0.618034 | 0.0285686 | ||||||||
\(469\) | −15.4797 | −0.714788 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.5013 | −0.898572 | ||||||||
\(472\) | −5.52369 | −0.254249 | ||||||||
\(473\) | 14.3704 | 0.660751 | ||||||||
\(474\) | 9.97510 | 0.458171 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.24263 | −0.0569560 | ||||||||
\(477\) | −1.30313 | −0.0596662 | ||||||||
\(478\) | −38.8269 | −1.77590 | ||||||||
\(479\) | −25.3568 | −1.15858 | −0.579292 | − | 0.815120i | \(-0.696671\pi\) | ||||
−0.579292 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52015 | −0.251697 | ||||||||
\(482\) | −40.8231 | −1.85944 | ||||||||
\(483\) | −0.939503 | −0.0427488 | ||||||||
\(484\) | −1.93835 | −0.0881068 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | −6.55671 | −0.297113 | −0.148556 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148556 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(488\) | −9.29843 | −0.420920 | ||||||||
\(489\) | 1.14712 | 0.0518746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.7728 | −1.65954 | −0.829768 | − | 0.558109i | \(-0.811527\pi\) | ||||
−0.829768 | + | 0.558109i | \(0.811527\pi\) | |||||||
\(492\) | 1.90211 | 0.0857539 | ||||||||
\(493\) | 11.4519 | 0.515769 | ||||||||
\(494\) | 3.79360 | 0.170682 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.34708 | −0.195190 | ||||||||
\(497\) | −12.3416 | −0.553595 | ||||||||
\(498\) | 25.2188 | 1.13008 | ||||||||
\(499\) | 33.8073 | 1.51342 | 0.756712 | − | 0.653748i | \(-0.226804\pi\) | ||||
0.756712 | + | 0.653748i | \(0.226804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.8232 | 0.796280 | ||||||||
\(502\) | −19.2533 | −0.859315 | ||||||||
\(503\) | 2.57397 | 0.114768 | 0.0573838 | − | 0.998352i | \(-0.481724\pi\) | ||||
0.0573838 | + | 0.998352i | \(0.481724\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.26284 | 0.189506 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −6.48391 | −0.287677 | ||||||||
\(509\) | 14.2906 | 0.633422 | 0.316711 | − | 0.948522i | \(-0.397422\pi\) | ||||
0.316711 | + | 0.948522i | \(0.397422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77455 | −0.122739 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | −2.34458 | −0.103516 | ||||||||
\(514\) | −8.88546 | −0.391921 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.16714 | 0.139426 | ||||||||
\(517\) | −16.7205 | −0.735367 | ||||||||
\(518\) | 8.93179 | 0.392440 | ||||||||
\(519\) | −2.11443 | −0.0928132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9346 | 0.698108 | 0.349054 | − | 0.937103i | \(-0.386503\pi\) | ||||
0.349054 | + | 0.937103i | \(0.386503\pi\) | |||||||
\(522\) | 9.21586 | 0.403367 | ||||||||
\(523\) | −42.2459 | −1.84729 | −0.923643 | − | 0.383254i | \(-0.874803\pi\) | ||||
−0.923643 | + | 0.383254i | \(0.874803\pi\) | |||||||
\(524\) | −1.29366 | −0.0565138 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.86085 | 0.168341 | ||||||||
\(527\) | −1.80061 | −0.0784358 | ||||||||
\(528\) | −13.6120 | −0.592386 | ||||||||
\(529\) | −22.1173 | −0.961623 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.47027 | −0.107201 | ||||||||
\(532\) | −1.44903 | −0.0628233 | ||||||||
\(533\) | 3.07768 | 0.133309 | ||||||||
\(534\) | 1.32907 | 0.0575146 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.6138 | −1.49509 | ||||||||
\(537\) | 18.6737 | 0.805830 | ||||||||
\(538\) | 30.1195 | 1.29855 | ||||||||
\(539\) | 2.80423 | 0.120787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0729 | −1.37892 | −0.689460 | − | 0.724324i | \(-0.742152\pi\) | ||||
−0.689460 | + | 0.724324i | \(0.742152\pi\) | |||||||
\(542\) | 4.68259 | 0.201134 | ||||||||
\(543\) | 6.07872 | 0.260863 | ||||||||
\(544\) | −6.79985 | −0.291541 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.61803 | −0.0692455 | ||||||||
\(547\) | 19.6201 | 0.838895 | 0.419448 | − | 0.907779i | \(-0.362224\pi\) | ||||
0.419448 | + | 0.907779i | \(0.362224\pi\) | |||||||
\(548\) | 7.58355 | 0.323953 | ||||||||
\(549\) | −4.15838 | −0.177476 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3540 | 0.568901 | ||||||||
\(552\) | −2.10079 | −0.0894156 | ||||||||
\(553\) | −6.16495 | −0.262160 | ||||||||
\(554\) | 23.1800 | 0.984826 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.31490 | 0.352630 | ||||||||
\(557\) | 0.768499 | 0.0325624 | 0.0162812 | − | 0.999867i | \(-0.494817\pi\) | ||||
0.0162812 | + | 0.999867i | \(0.494817\pi\) | |||||||
\(558\) | −1.44903 | −0.0613422 | ||||||||
\(559\) | 5.12454 | 0.216745 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.63824 | −0.238047 | ||||||||
\(562\) | −9.02124 | −0.380538 | ||||||||
\(563\) | 35.0266 | 1.47620 | 0.738098 | − | 0.674694i | \(-0.235724\pi\) | ||||
0.738098 | + | 0.674694i | \(0.235724\pi\) | |||||||
\(564\) | −3.68510 | −0.155171 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −30.2311 | −1.27071 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −27.5966 | −1.15793 | ||||||||
\(569\) | 26.3124 | 1.10307 | 0.551537 | − | 0.834150i | \(-0.314042\pi\) | ||||
0.551537 | + | 0.834150i | \(0.314042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.3772 | −1.68973 | −0.844866 | − | 0.534978i | \(-0.820320\pi\) | ||||
−0.844866 | + | 0.534978i | \(0.820320\pi\) | |||||||
\(572\) | 1.73311 | 0.0724648 | ||||||||
\(573\) | 13.9329 | 0.582057 | ||||||||
\(574\) | −4.97980 | −0.207853 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 33.7497 | 1.40502 | 0.702509 | − | 0.711675i | \(-0.252063\pi\) | ||||
0.702509 | + | 0.711675i | \(0.252063\pi\) | |||||||
\(578\) | 20.9655 | 0.872050 | ||||||||
\(579\) | −3.14339 | −0.130635 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.5861 | −0.646619 | ||||||||
\(582\) | 3.20826 | 0.132987 | ||||||||
\(583\) | −3.65427 | −0.151344 | ||||||||
\(584\) | −6.20409 | −0.256727 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 50.2537 | 2.07596 | ||||||||
\(587\) | 35.8502 | 1.47970 | 0.739848 | − | 0.672774i | \(-0.234897\pi\) | ||||
0.739848 | + | 0.672774i | \(0.234897\pi\) | |||||||
\(588\) | 0.618034 | 0.0254873 | ||||||||
\(589\) | −2.09968 | −0.0865159 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.11141 | 0.210255 | ||||||||
\(592\) | 26.7954 | 1.10128 | ||||||||
\(593\) | −28.7642 | −1.18120 | −0.590602 | − | 0.806963i | \(-0.701110\pi\) | ||||
−0.590602 | + | 0.806963i | \(0.701110\pi\) | |||||||
\(594\) | −4.53733 | −0.186169 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.80057 | 0.319524 | ||||||||
\(597\) | 16.5135 | 0.675851 | ||||||||
\(598\) | 1.52015 | 0.0621634 | ||||||||
\(599\) | −16.1612 | −0.660327 | −0.330163 | − | 0.943924i | \(-0.607104\pi\) | ||||
−0.330163 | + | 0.943924i | \(0.607104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.3491 | −1.64587 | −0.822936 | − | 0.568134i | \(-0.807666\pi\) | ||||
−0.822936 | + | 0.568134i | \(0.807666\pi\) | |||||||
\(602\) | −8.29168 | −0.337944 | ||||||||
\(603\) | −15.4797 | −0.630384 | ||||||||
\(604\) | 0.137469 | 0.00559352 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.4893 | −0.507344 | ||||||||
\(607\) | −34.9319 | −1.41784 | −0.708920 | − | 0.705289i | \(-0.750817\pi\) | ||||
−0.708920 | + | 0.705289i | \(0.750817\pi\) | |||||||
\(608\) | −7.92928 | −0.321575 | ||||||||
\(609\) | −5.69572 | −0.230802 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.96261 | −0.241221 | ||||||||
\(612\) | −1.24263 | −0.0502304 | ||||||||
\(613\) | 36.1928 | 1.46181 | 0.730907 | − | 0.682477i | \(-0.239097\pi\) | ||||
0.730907 | + | 0.682477i | \(0.239097\pi\) | |||||||
\(614\) | 2.79745 | 0.112896 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.27044 | 0.252643 | ||||||||
\(617\) | 27.8387 | 1.12074 | 0.560371 | − | 0.828242i | \(-0.310658\pi\) | ||||
0.560371 | + | 0.828242i | \(0.310658\pi\) | |||||||
\(618\) | 31.2781 | 1.25819 | ||||||||
\(619\) | 14.9807 | 0.602126 | 0.301063 | − | 0.953604i | \(-0.402659\pi\) | ||||
0.301063 | + | 0.953604i | \(0.402659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.939503 | −0.0377009 | ||||||||
\(622\) | −28.7015 | −1.15083 | ||||||||
\(623\) | −0.821412 | −0.0329092 | ||||||||
\(624\) | −4.85410 | −0.194320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 40.2117 | 1.60718 | ||||||||
\(627\) | −6.57472 | −0.262569 | ||||||||
\(628\) | −12.0525 | −0.480946 | ||||||||
\(629\) | 11.0989 | 0.442543 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7583 | 0.428281 | 0.214140 | − | 0.976803i | \(-0.431305\pi\) | ||||
0.214140 | + | 0.976803i | \(0.431305\pi\) | |||||||
\(632\) | −13.7852 | −0.548348 | ||||||||
\(633\) | −2.47078 | −0.0982047 | ||||||||
\(634\) | −4.21702 | −0.167479 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.805379 | −0.0319353 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 25.8434 | 1.02315 | ||||||||
\(639\) | −12.3416 | −0.488225 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9112 | −0.509961 | −0.254981 | − | 0.966946i | \(-0.582069\pi\) | ||||
−0.254981 | + | 0.966946i | \(0.582069\pi\) | |||||||
\(642\) | −12.6487 | −0.499206 | ||||||||
\(643\) | 20.8057 | 0.820495 | 0.410248 | − | 0.911974i | \(-0.365442\pi\) | ||||
0.410248 | + | 0.911974i | \(0.365442\pi\) | |||||||
\(644\) | −0.580644 | −0.0228806 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.62750 | −0.300100 | ||||||||
\(647\) | 25.7610 | 1.01277 | 0.506384 | − | 0.862308i | \(-0.330982\pi\) | ||||
0.506384 | + | 0.862308i | \(0.330982\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −6.92720 | −0.271916 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.895549 | 0.0350993 | ||||||||
\(652\) | 0.708959 | 0.0277650 | ||||||||
\(653\) | 33.0209 | 1.29221 | 0.646103 | − | 0.763250i | \(-0.276398\pi\) | ||||
0.646103 | + | 0.763250i | \(0.276398\pi\) | |||||||
\(654\) | −2.16308 | −0.0845833 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.9394 | −0.583285 | ||||||||
\(657\) | −2.77455 | −0.108246 | ||||||||
\(658\) | 9.64771 | 0.376107 | ||||||||
\(659\) | −36.4979 | −1.42176 | −0.710879 | − | 0.703315i | \(-0.751702\pi\) | ||||
−0.710879 | + | 0.703315i | \(0.751702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1393 | 1.36676 | 0.683380 | − | 0.730063i | \(-0.260509\pi\) | ||||
0.683380 | + | 0.730063i | \(0.260509\pi\) | |||||||
\(662\) | 49.7615 | 1.93404 | ||||||||
\(663\) | −2.01062 | −0.0780861 | ||||||||
\(664\) | −34.8515 | −1.35250 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.93179 | 0.346100 | ||||||||
\(667\) | 5.35114 | 0.207197 | ||||||||
\(668\) | 11.0153 | 0.426196 | ||||||||
\(669\) | −9.10445 | −0.351998 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6611 | −0.450170 | ||||||||
\(672\) | 3.38197 | 0.130462 | ||||||||
\(673\) | 10.0652 | 0.387985 | 0.193992 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193992 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(674\) | −23.1955 | −0.893459 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.618034 | 0.0237705 | ||||||||
\(677\) | −34.4229 | −1.32298 | −0.661489 | − | 0.749955i | \(-0.730075\pi\) | ||||
−0.661489 | + | 0.749955i | \(0.730075\pi\) | |||||||
\(678\) | 10.9988 | 0.422408 | ||||||||
\(679\) | −1.98281 | −0.0760934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.00779 | 0.268539 | ||||||||
\(682\) | −4.06340 | −0.155596 | ||||||||
\(683\) | 7.19340 | 0.275248 | 0.137624 | − | 0.990485i | \(-0.456053\pi\) | ||||
0.137624 | + | 0.990485i | \(0.456053\pi\) | |||||||
\(684\) | −1.44903 | −0.0554050 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | −20.2385 | −0.772146 | ||||||||
\(688\) | −24.8750 | −0.948352 | ||||||||
\(689\) | −1.30313 | −0.0496453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.19402 | 0.0834645 | 0.0417323 | − | 0.999129i | \(-0.486712\pi\) | ||||
0.0417323 | + | 0.999129i | \(0.486712\pi\) | |||||||
\(692\) | −1.30679 | −0.0496767 | ||||||||
\(693\) | 2.80423 | 0.106524 | ||||||||
\(694\) | 45.7821 | 1.73787 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.7360 | −0.482757 | ||||||||
\(697\) | −6.18806 | −0.234389 | ||||||||
\(698\) | 12.6558 | 0.479031 | ||||||||
\(699\) | −14.6750 | −0.555060 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.08651 | 0.343193 | 0.171596 | − | 0.985167i | \(-0.445108\pi\) | ||||
0.171596 | + | 0.985167i | \(0.445108\pi\) | |||||||
\(702\) | −1.61803 | −0.0610688 | ||||||||
\(703\) | 12.9424 | 0.488132 | ||||||||
\(704\) | 11.8789 | 0.447703 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.4934 | −0.771278 | ||||||||
\(707\) | 7.71883 | 0.290296 | ||||||||
\(708\) | −1.52671 | −0.0573773 | ||||||||
\(709\) | −17.0828 | −0.641557 | −0.320778 | − | 0.947154i | \(-0.603944\pi\) | ||||
−0.320778 | + | 0.947154i | \(0.603944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.16495 | −0.231204 | ||||||||
\(712\) | −1.83673 | −0.0688345 | ||||||||
\(713\) | −0.841370 | −0.0315096 | ||||||||
\(714\) | 3.25325 | 0.121750 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.5410 | 0.431307 | ||||||||
\(717\) | 23.9963 | 0.896160 | ||||||||
\(718\) | −7.05342 | −0.263231 | ||||||||
\(719\) | −46.0179 | −1.71618 | −0.858088 | − | 0.513502i | \(-0.828348\pi\) | ||||
−0.858088 | + | 0.513502i | \(0.828348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.3309 | −0.719922 | ||||||||
\(722\) | 21.8482 | 0.813108 | ||||||||
\(723\) | 25.2300 | 0.938315 | ||||||||
\(724\) | 3.75686 | 0.139623 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.07467 | 0.188339 | ||||||||
\(727\) | −41.4822 | −1.53849 | −0.769245 | − | 0.638954i | \(-0.779368\pi\) | ||||
−0.769245 | + | 0.638954i | \(0.779368\pi\) | |||||||
\(728\) | 2.23607 | 0.0828742 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.3035 | −0.381089 | ||||||||
\(732\) | −2.57002 | −0.0949908 | ||||||||
\(733\) | −8.95740 | −0.330849 | −0.165425 | − | 0.986222i | \(-0.552899\pi\) | ||||
−0.165425 | + | 0.986222i | \(0.552899\pi\) | |||||||
\(734\) | 38.3868 | 1.41688 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.17737 | −0.117119 | ||||||||
\(737\) | −43.4087 | −1.59898 | ||||||||
\(738\) | −4.97980 | −0.183309 | ||||||||
\(739\) | 41.1448 | 1.51354 | 0.756769 | − | 0.653683i | \(-0.226777\pi\) | ||||
0.756769 | + | 0.653683i | \(0.226777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.34458 | −0.0861302 | ||||||||
\(742\) | 2.10851 | 0.0774058 | ||||||||
\(743\) | −51.2608 | −1.88058 | −0.940288 | − | 0.340379i | \(-0.889445\pi\) | ||||
−0.940288 | + | 0.340379i | \(0.889445\pi\) | |||||||
\(744\) | 2.00251 | 0.0734155 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.8363 | 0.726258 | ||||||||
\(747\) | −15.5861 | −0.570264 | ||||||||
\(748\) | −3.48462 | −0.127410 | ||||||||
\(749\) | 7.81736 | 0.285640 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.69851 | −0.353904 | −0.176952 | − | 0.984220i | \(-0.556624\pi\) | ||||
−0.176952 | + | 0.984220i | \(0.556624\pi\) | |||||||
\(752\) | 28.9431 | 1.05545 | ||||||||
\(753\) | 11.8992 | 0.433630 | ||||||||
\(754\) | 9.21586 | 0.335622 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.618034 | 0.0224777 | ||||||||
\(757\) | −42.0784 | −1.52936 | −0.764682 | − | 0.644408i | \(-0.777104\pi\) | ||||
−0.764682 | + | 0.644408i | \(0.777104\pi\) | |||||||
\(758\) | 15.2769 | 0.554882 | ||||||||
\(759\) | −2.63458 | −0.0956291 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1288 | −0.729668 | −0.364834 | − | 0.931072i | \(-0.618874\pi\) | ||||
−0.364834 | + | 0.931072i | \(0.618874\pi\) | |||||||
\(762\) | 16.9751 | 0.614943 | ||||||||
\(763\) | 1.33686 | 0.0483976 | ||||||||
\(764\) | 8.61103 | 0.311536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.94356 | −0.106355 | ||||||||
\(767\) | −2.47027 | −0.0891963 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | 23.5408 | 0.848902 | 0.424451 | − | 0.905451i | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.49151 | 0.197772 | ||||||||
\(772\) | −1.94272 | −0.0699201 | ||||||||
\(773\) | 9.93937 | 0.357494 | 0.178747 | − | 0.983895i | \(-0.442796\pi\) | ||||
0.178747 | + | 0.983895i | \(0.442796\pi\) | |||||||
\(774\) | −8.29168 | −0.298038 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.43371 | −0.159161 | ||||||||
\(777\) | −5.52015 | −0.198034 | ||||||||
\(778\) | 18.2589 | 0.654613 | ||||||||
\(779\) | −7.21586 | −0.258535 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.6085 | −1.23839 | ||||||||
\(782\) | −3.05644 | −0.109298 | ||||||||
\(783\) | −5.69572 | −0.203548 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.38685 | 0.120805 | ||||||||
\(787\) | 37.9659 | 1.35334 | 0.676670 | − | 0.736287i | \(-0.263423\pi\) | ||||
0.676670 | + | 0.736287i | \(0.263423\pi\) | |||||||
\(788\) | 3.15903 | 0.112536 | ||||||||
\(789\) | −2.38614 | −0.0849487 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.79766 | −0.241697 | ||||||||
\(792\) | 6.27044 | 0.222810 | ||||||||
\(793\) | −4.15838 | −0.147669 | ||||||||
\(794\) | −35.0560 | −1.24409 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2059 | 0.361738 | ||||||||
\(797\) | 42.9372 | 1.52091 | 0.760456 | − | 0.649389i | \(-0.224975\pi\) | ||||
0.760456 | + | 0.649389i | \(0.224975\pi\) | |||||||
\(798\) | 3.79360 | 0.134292 | ||||||||
\(799\) | 11.9886 | 0.424125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.821412 | −0.0290232 | ||||||||
\(802\) | −24.4530 | −0.863464 | ||||||||
\(803\) | −7.78048 | −0.274567 | ||||||||
\(804\) | −9.56701 | −0.337402 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.44903 | −0.0510398 | ||||||||
\(807\) | −18.6149 | −0.655276 | ||||||||
\(808\) | 17.2598 | 0.607198 | ||||||||
\(809\) | 47.5910 | 1.67321 | 0.836605 | − | 0.547807i | \(-0.184537\pi\) | ||||
0.836605 | + | 0.547807i | \(0.184537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0579 | −1.40662 | −0.703312 | − | 0.710882i | \(-0.748296\pi\) | ||||
−0.703312 | + | 0.710882i | \(0.748296\pi\) | |||||||
\(812\) | −3.52015 | −0.123533 | ||||||||
\(813\) | −2.89400 | −0.101497 | ||||||||
\(814\) | 25.0467 | 0.877888 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.75976 | 0.341660 | ||||||||
\(817\) | −12.0149 | −0.420347 | ||||||||
\(818\) | −0.148803 | −0.00520276 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.41652 | −0.0843372 | −0.0421686 | − | 0.999111i | \(-0.513427\pi\) | ||||
−0.0421686 | + | 0.999111i | \(0.513427\pi\) | |||||||
\(822\) | −19.8540 | −0.692487 | ||||||||
\(823\) | 57.1896 | 1.99350 | 0.996752 | − | 0.0805350i | \(-0.0256629\pi\) | ||||
0.996752 | + | 0.0805350i | \(0.0256629\pi\) | |||||||
\(824\) | −43.2253 | −1.50582 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.99698 | 0.139073 | ||||||||
\(827\) | −5.71058 | −0.198576 | −0.0992881 | − | 0.995059i | \(-0.531657\pi\) | ||||
−0.0992881 | + | 0.995059i | \(0.531657\pi\) | |||||||
\(828\) | −0.580644 | −0.0201788 | ||||||||
\(829\) | −32.2179 | −1.11898 | −0.559488 | − | 0.828839i | \(-0.689002\pi\) | ||||
−0.559488 | + | 0.828839i | \(0.689002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.3261 | −0.496965 | ||||||||
\(832\) | 4.23607 | 0.146859 | ||||||||
\(833\) | −2.01062 | −0.0696639 | ||||||||
\(834\) | −21.7687 | −0.753788 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.06340 | −0.140536 | ||||||||
\(837\) | 0.895549 | 0.0309547 | ||||||||
\(838\) | −25.6789 | −0.887065 | ||||||||
\(839\) | 39.2649 | 1.35557 | 0.677787 | − | 0.735258i | \(-0.262939\pi\) | ||||
0.677787 | + | 0.735258i | \(0.262939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.44120 | 0.118662 | ||||||||
\(842\) | 22.0469 | 0.759785 | ||||||||
\(843\) | 5.57543 | 0.192028 | ||||||||
\(844\) | −1.52703 | −0.0525624 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.64771 | 0.331695 | ||||||||
\(847\) | −3.13632 | −0.107765 | ||||||||
\(848\) | 6.32553 | 0.217219 | ||||||||
\(849\) | 18.6838 | 0.641227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.18619 | 0.177780 | ||||||||
\(852\) | −7.62750 | −0.261314 | ||||||||
\(853\) | −13.4267 | −0.459722 | −0.229861 | − | 0.973224i | \(-0.573827\pi\) | ||||
−0.229861 | + | 0.973224i | \(0.573827\pi\) | |||||||
\(854\) | 6.72841 | 0.230241 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.4801 | 0.597459 | ||||||||
\(857\) | −48.4140 | −1.65379 | −0.826895 | − | 0.562356i | \(-0.809895\pi\) | ||||
−0.826895 | + | 0.562356i | \(0.809895\pi\) | |||||||
\(858\) | −4.53733 | −0.154902 | ||||||||
\(859\) | −16.8574 | −0.575168 | −0.287584 | − | 0.957755i | \(-0.592852\pi\) | ||||
−0.287584 | + | 0.957755i | \(0.592852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.07768 | 0.104887 | ||||||||
\(862\) | 41.2205 | 1.40397 | ||||||||
\(863\) | −47.6860 | −1.62325 | −0.811625 | − | 0.584178i | \(-0.801417\pi\) | ||||
−0.811625 | + | 0.584178i | \(0.801417\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.0008 | 1.12141 | ||||||||
\(867\) | −12.9574 | −0.440056 | ||||||||
\(868\) | 0.553479 | 0.0187863 | ||||||||
\(869\) | −17.2879 | −0.586452 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.4797 | −0.524511 | ||||||||
\(872\) | 2.98931 | 0.101231 | ||||||||
\(873\) | −1.98281 | −0.0671081 | ||||||||
\(874\) | −3.56410 | −0.120558 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.71477 | −0.0579367 | ||||||||
\(877\) | 5.74990 | 0.194160 | 0.0970801 | − | 0.995277i | \(-0.469050\pi\) | ||||
0.0970801 | + | 0.995277i | \(0.469050\pi\) | |||||||
\(878\) | −36.9784 | −1.24796 | ||||||||
\(879\) | −31.0585 | −1.04758 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.9157 | −0.569905 | −0.284952 | − | 0.958542i | \(-0.591978\pi\) | ||||
−0.284952 | + | 0.958542i | \(0.591978\pi\) | |||||||
\(882\) | −1.61803 | −0.0544820 | ||||||||
\(883\) | −8.09873 | −0.272544 | −0.136272 | − | 0.990671i | \(-0.543512\pi\) | ||||
−0.136272 | + | 0.990671i | \(0.543512\pi\) | |||||||
\(884\) | −1.24263 | −0.0417943 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.7376 | −0.864671 | ||||||||
\(887\) | −44.5786 | −1.49680 | −0.748401 | − | 0.663247i | \(-0.769178\pi\) | ||||
−0.748401 | + | 0.663247i | \(0.769178\pi\) | |||||||
\(888\) | −12.3434 | −0.414218 | ||||||||
\(889\) | −10.4912 | −0.351863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.80423 | 0.0939451 | ||||||||
\(892\) | −5.62686 | −0.188401 | ||||||||
\(893\) | 13.9798 | 0.467816 | ||||||||
\(894\) | −20.4221 | −0.683019 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | −0.939503 | −0.0313691 | ||||||||
\(898\) | 37.7119 | 1.25846 | ||||||||
\(899\) | −5.10079 | −0.170121 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.62010 | 0.0872882 | ||||||||
\(902\) | −13.9645 | −0.464966 | ||||||||
\(903\) | 5.12454 | 0.170534 | ||||||||
\(904\) | −15.2000 | −0.505546 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.359898 | −0.0119568 | ||||||||
\(907\) | −24.1868 | −0.803110 | −0.401555 | − | 0.915835i | \(-0.631530\pi\) | ||||
−0.401555 | + | 0.915835i | \(0.631530\pi\) | |||||||
\(908\) | 4.33105 | 0.143731 | ||||||||
\(909\) | 7.71883 | 0.256017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.27522 | 0.307302 | 0.153651 | − | 0.988125i | \(-0.450897\pi\) | ||||
0.153651 | + | 0.988125i | \(0.450897\pi\) | |||||||
\(912\) | 11.3808 | 0.376856 | ||||||||
\(913\) | −43.7068 | −1.44648 | ||||||||
\(914\) | −29.3723 | −0.971548 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5081 | −0.413278 | ||||||||
\(917\) | −2.09319 | −0.0691231 | ||||||||
\(918\) | 3.25325 | 0.107373 | ||||||||
\(919\) | −2.91209 | −0.0960611 | −0.0480305 | − | 0.998846i | \(-0.515294\pi\) | ||||
−0.0480305 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.72892 | −0.0569698 | ||||||||
\(922\) | −49.4173 | −1.62747 | ||||||||
\(923\) | −12.3416 | −0.406227 | ||||||||
\(924\) | 1.73311 | 0.0570150 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.4513 | 1.00069 | ||||||||
\(927\) | −19.3309 | −0.634911 | ||||||||
\(928\) | −19.2627 | −0.632330 | ||||||||
\(929\) | 35.9359 | 1.17902 | 0.589510 | − | 0.807761i | \(-0.299321\pi\) | ||||
0.589510 | + | 0.807761i | \(0.299321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.34458 | −0.0768404 | ||||||||
\(932\) | −9.06965 | −0.297086 | ||||||||
\(933\) | 17.7385 | 0.580733 | ||||||||
\(934\) | 23.2914 | 0.762116 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.23607 | 0.0730882 | ||||||||
\(937\) | 25.0249 | 0.817527 | 0.408763 | − | 0.912640i | \(-0.365960\pi\) | ||||
0.408763 | + | 0.912640i | \(0.365960\pi\) | |||||||
\(938\) | 25.0467 | 0.817805 | ||||||||
\(939\) | −24.8522 | −0.811021 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7170 | 0.414562 | 0.207281 | − | 0.978281i | \(-0.433538\pi\) | ||||
0.207281 | + | 0.978281i | \(0.433538\pi\) | |||||||
\(942\) | 31.5538 | 1.02808 | ||||||||
\(943\) | −2.89149 | −0.0941599 | ||||||||
\(944\) | 11.9909 | 0.390272 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.2518 | −0.755980 | ||||||||
\(947\) | −42.4461 | −1.37931 | −0.689656 | − | 0.724137i | \(-0.742238\pi\) | ||||
−0.689656 | + | 0.724137i | \(0.742238\pi\) | |||||||
\(948\) | −3.81015 | −0.123748 | ||||||||
\(949\) | −2.77455 | −0.0900658 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.60626 | 0.0845138 | ||||||||
\(952\) | −4.49589 | −0.145713 | ||||||||
\(953\) | −44.1291 | −1.42948 | −0.714741 | − | 0.699389i | \(-0.753456\pi\) | ||||
−0.714741 | + | 0.699389i | \(0.753456\pi\) | |||||||
\(954\) | 2.10851 | 0.0682655 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.8306 | 0.479654 | ||||||||
\(957\) | −15.9721 | −0.516304 | ||||||||
\(958\) | 41.0282 | 1.32556 | ||||||||
\(959\) | 12.2704 | 0.396233 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1980 | −0.974129 | ||||||||
\(962\) | 8.93179 | 0.287972 | ||||||||
\(963\) | 7.81736 | 0.251911 | ||||||||
\(964\) | 15.5930 | 0.502217 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.52015 | 0.0489099 | ||||||||
\(967\) | −5.88712 | −0.189317 | −0.0946585 | − | 0.995510i | \(-0.530176\pi\) | ||||
−0.0946585 | + | 0.995510i | \(0.530176\pi\) | |||||||
\(968\) | −7.01302 | −0.225407 | ||||||||
\(969\) | 4.71406 | 0.151437 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.7978 | 1.43763 | 0.718814 | − | 0.695202i | \(-0.244685\pi\) | ||||
0.718814 | + | 0.695202i | \(0.244685\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | 13.4538 | 0.431309 | ||||||||
\(974\) | 10.6090 | 0.339934 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.1852 | 0.646113 | ||||||||
\(977\) | 7.32375 | 0.234308 | 0.117154 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117154 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(978\) | −1.85608 | −0.0593509 | ||||||||
\(979\) | −2.30343 | −0.0736178 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.33686 | 0.0426826 | ||||||||
\(982\) | 59.4997 | 1.89871 | ||||||||
\(983\) | −15.2176 | −0.485367 | −0.242683 | − | 0.970106i | \(-0.578028\pi\) | ||||
−0.242683 | + | 0.970106i | \(0.578028\pi\) | |||||||
\(984\) | 6.88191 | 0.219387 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.5296 | −0.590103 | ||||||||
\(987\) | −5.96261 | −0.189792 | ||||||||
\(988\) | −1.44903 | −0.0460997 | ||||||||
\(989\) | −4.81452 | −0.153093 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.65833 | 0.0526785 | 0.0263393 | − | 0.999653i | \(-0.491615\pi\) | ||||
0.0263393 | + | 0.999653i | \(0.491615\pi\) | |||||||
\(992\) | 3.02871 | 0.0961618 | ||||||||
\(993\) | −30.7543 | −0.975958 | ||||||||
\(994\) | 19.9691 | 0.633380 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.63271 | −0.305224 | ||||||||
\(997\) | −2.49409 | −0.0789887 | −0.0394943 | − | 0.999220i | \(-0.512575\pi\) | ||||
−0.0394943 | + | 0.999220i | \(0.512575\pi\) | |||||||
\(998\) | −54.7014 | −1.73154 | ||||||||
\(999\) | −5.52015 | −0.174650 |
(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 | 6825.2.a.be.1.2 | 4 | ||
5.2 | odd | 4 | 1365.2.f.c.274.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1365.2.f.c.274.8 | yes | 8 | ||
5.4 | even | 2 | 6825.2.a.bm.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1365.2.f.c.274.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1365.2.f.c.274.8 | yes | 8 | 5.3 | odd | 4 | ||
6825.2.a.be.1.2 | 4 | 1.1 | even | 1 | trivial | ||
6825.2.a.bm.1.4 | 4 | 5.4 | even | 2 |