Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.437199552.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} + 49x^{2} - 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.23396\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23396 | −0.872539 | −0.436269 | − | 0.899816i | \(-0.643701\pi\) | ||||
−0.436269 | + | 0.899816i | \(0.643701\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.477352 | −0.238676 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.23396 | 0.503760 | ||||||||
\(7\) | −3.79281 | −1.43355 | −0.716773 | − | 0.697307i | \(-0.754382\pi\) | ||||
−0.716773 | + | 0.697307i | \(0.754382\pi\) | |||||||
\(8\) | 3.05694 | 1.08079 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.23396 | −0.390211 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.477352 | 0.137800 | ||||||||
\(13\) | −2.46791 | −0.684476 | −0.342238 | − | 0.939613i | \(-0.611185\pi\) | ||||
−0.342238 | + | 0.939613i | \(0.611185\pi\) | |||||||
\(14\) | 4.68016 | 1.25082 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −2.81743 | −0.704358 | ||||||||
\(17\) | 6.52105 | 1.58159 | 0.790793 | − | 0.612084i | \(-0.209668\pi\) | ||||
0.790793 | + | 0.612084i | \(0.209668\pi\) | |||||||
\(18\) | −1.23396 | −0.290846 | ||||||||
\(19\) | −8.25310 | −1.89339 | −0.946695 | − | 0.322131i | \(-0.895601\pi\) | ||||
−0.946695 | + | 0.322131i | \(0.895601\pi\) | |||||||
\(20\) | −0.477352 | −0.106739 | ||||||||
\(21\) | 3.79281 | 0.827658 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.34008 | −0.487940 | −0.243970 | − | 0.969783i | \(-0.578450\pi\) | ||||
−0.243970 | + | 0.969783i | \(0.578450\pi\) | |||||||
\(24\) | −3.05694 | −0.623996 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.04530 | 0.597232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.81050 | 0.342153 | ||||||||
\(29\) | −2.46791 | −0.458280 | −0.229140 | − | 0.973394i | \(-0.573591\pi\) | ||||
−0.229140 | + | 0.973394i | \(0.573591\pi\) | |||||||
\(30\) | 1.23396 | 0.225289 | ||||||||
\(31\) | 5.27455 | 0.947337 | 0.473669 | − | 0.880703i | \(-0.342929\pi\) | ||||
0.473669 | + | 0.880703i | \(0.342929\pi\) | |||||||
\(32\) | −2.63730 | −0.466214 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.04668 | −1.37999 | ||||||||
\(35\) | −3.79281 | −0.641101 | ||||||||
\(36\) | −0.477352 | −0.0795587 | ||||||||
\(37\) | 3.34008 | 0.549105 | 0.274553 | − | 0.961572i | \(-0.411470\pi\) | ||||
0.274553 | + | 0.961572i | \(0.411470\pi\) | |||||||
\(38\) | 10.1840 | 1.65206 | ||||||||
\(39\) | 2.46791 | 0.395182 | ||||||||
\(40\) | 3.05694 | 0.483345 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | −4.68016 | −0.722164 | ||||||||
\(43\) | −12.0459 | −1.83698 | −0.918491 | − | 0.395441i | \(-0.870592\pi\) | ||||
−0.918491 | + | 0.395441i | \(0.870592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 2.88755 | 0.425746 | ||||||||
\(47\) | −9.56933 | −1.39583 | −0.697915 | − | 0.716180i | \(-0.745889\pi\) | ||||
−0.697915 | + | 0.716180i | \(0.745889\pi\) | |||||||
\(48\) | 2.81743 | 0.406661 | ||||||||
\(49\) | 7.38537 | 1.05505 | ||||||||
\(50\) | −1.23396 | −0.174508 | ||||||||
\(51\) | −6.52105 | −0.913129 | ||||||||
\(52\) | 1.17806 | 0.163368 | ||||||||
\(53\) | −6.61463 | −0.908589 | −0.454294 | − | 0.890852i | \(-0.650109\pi\) | ||||
−0.454294 | + | 0.890852i | \(0.650109\pi\) | |||||||
\(54\) | 1.23396 | 0.167920 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.5944 | −1.54937 | ||||||||
\(57\) | 8.25310 | 1.09315 | ||||||||
\(58\) | 3.04530 | 0.399867 | ||||||||
\(59\) | 10.1840 | 1.32584 | 0.662919 | − | 0.748691i | \(-0.269317\pi\) | ||||
0.662919 | + | 0.748691i | \(0.269317\pi\) | |||||||
\(60\) | 0.477352 | 0.0616259 | ||||||||
\(61\) | 6.66788 | 0.853734 | 0.426867 | − | 0.904314i | \(-0.359617\pi\) | ||||
0.426867 | + | 0.904314i | \(0.359617\pi\) | |||||||
\(62\) | −6.50856 | −0.826588 | ||||||||
\(63\) | −3.79281 | −0.477849 | ||||||||
\(64\) | 8.88918 | 1.11115 | ||||||||
\(65\) | −2.46791 | −0.306107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34008 | 0.408055 | 0.204028 | − | 0.978965i | \(-0.434597\pi\) | ||||
0.204028 | + | 0.978965i | \(0.434597\pi\) | |||||||
\(68\) | −3.11284 | −0.377487 | ||||||||
\(69\) | 2.34008 | 0.281712 | ||||||||
\(70\) | 4.68016 | 0.559386 | ||||||||
\(71\) | 7.22925 | 0.857955 | 0.428977 | − | 0.903315i | \(-0.358874\pi\) | ||||
0.428977 | + | 0.903315i | \(0.358874\pi\) | |||||||
\(72\) | 3.05694 | 0.360264 | ||||||||
\(73\) | −9.72482 | −1.13820 | −0.569102 | − | 0.822267i | \(-0.692709\pi\) | ||||
−0.569102 | + | 0.822267i | \(0.692709\pi\) | |||||||
\(74\) | −4.12151 | −0.479116 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 3.93963 | 0.451907 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.04530 | −0.344812 | ||||||||
\(79\) | 9.65644 | 1.08643 | 0.543217 | − | 0.839592i | \(-0.317206\pi\) | ||||
0.543217 | + | 0.839592i | \(0.317206\pi\) | |||||||
\(80\) | −2.81743 | −0.314998 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.27455 | −0.472045 | ||||||||
\(83\) | −11.0497 | −1.21286 | −0.606432 | − | 0.795136i | \(-0.707400\pi\) | ||||
−0.606432 | + | 0.795136i | \(0.707400\pi\) | |||||||
\(84\) | −1.81050 | −0.197542 | ||||||||
\(85\) | 6.52105 | 0.707307 | ||||||||
\(86\) | 14.8641 | 1.60284 | ||||||||
\(87\) | 2.46791 | 0.264588 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2745 | 1.08910 | 0.544550 | − | 0.838728i | \(-0.316700\pi\) | ||||
0.544550 | + | 0.838728i | \(0.316700\pi\) | |||||||
\(90\) | −1.23396 | −0.130070 | ||||||||
\(91\) | 9.36031 | 0.981227 | ||||||||
\(92\) | 1.11704 | 0.116460 | ||||||||
\(93\) | −5.27455 | −0.546945 | ||||||||
\(94\) | 11.8081 | 1.21792 | ||||||||
\(95\) | −8.25310 | −0.846750 | ||||||||
\(96\) | 2.63730 | 0.269169 | ||||||||
\(97\) | 13.2495 | 1.34528 | 0.672641 | − | 0.739969i | \(-0.265160\pi\) | ||||
0.672641 | + | 0.739969i | \(0.265160\pi\) | |||||||
\(98\) | −9.11323 | −0.920575 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.477352 | −0.0477352 | ||||||||
\(101\) | −1.99238 | −0.198249 | −0.0991246 | − | 0.995075i | \(-0.531604\pi\) | ||||
−0.0991246 | + | 0.995075i | \(0.531604\pi\) | |||||||
\(102\) | 8.04668 | 0.796740 | ||||||||
\(103\) | −1.61463 | −0.159094 | −0.0795470 | − | 0.996831i | \(-0.525347\pi\) | ||||
−0.0795470 | + | 0.996831i | \(0.525347\pi\) | |||||||
\(104\) | −7.54427 | −0.739776 | ||||||||
\(105\) | 3.79281 | 0.370140 | ||||||||
\(106\) | 8.16216 | 0.792779 | ||||||||
\(107\) | −0.589032 | −0.0569439 | −0.0284719 | − | 0.999595i | \(-0.509064\pi\) | ||||
−0.0284719 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(108\) | 0.477352 | 0.0459333 | ||||||||
\(109\) | −4.78899 | −0.458703 | −0.229351 | − | 0.973344i | \(-0.573660\pi\) | ||||
−0.229351 | + | 0.973344i | \(0.573660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.34008 | −0.317026 | ||||||||
\(112\) | 10.6860 | 1.00973 | ||||||||
\(113\) | 18.5240 | 1.74259 | 0.871297 | − | 0.490755i | \(-0.163279\pi\) | ||||
0.871297 | + | 0.490755i | \(0.163279\pi\) | |||||||
\(114\) | −10.1840 | −0.953815 | ||||||||
\(115\) | −2.34008 | −0.218213 | ||||||||
\(116\) | 1.17806 | 0.109380 | ||||||||
\(117\) | −2.46791 | −0.228159 | ||||||||
\(118\) | −12.5666 | −1.15685 | ||||||||
\(119\) | −24.7331 | −2.26728 | ||||||||
\(120\) | −3.05694 | −0.279060 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.22787 | −0.744916 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | −2.51782 | −0.226107 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.68016 | 0.416941 | ||||||||
\(127\) | 12.1927 | 1.08193 | 0.540965 | − | 0.841045i | \(-0.318059\pi\) | ||||
0.540965 | + | 0.841045i | \(0.318059\pi\) | |||||||
\(128\) | −5.69425 | −0.503305 | ||||||||
\(129\) | 12.0459 | 1.06058 | ||||||||
\(130\) | 3.04530 | 0.267090 | ||||||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.3024 | 2.71426 | ||||||||
\(134\) | −4.12151 | −0.356044 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 19.9345 | 1.70937 | ||||||||
\(137\) | 7.93447 | 0.677888 | 0.338944 | − | 0.940807i | \(-0.389930\pi\) | ||||
0.338944 | + | 0.940807i | \(0.389930\pi\) | |||||||
\(138\) | −2.88755 | −0.245805 | ||||||||
\(139\) | 6.18226 | 0.524373 | 0.262186 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262186 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(140\) | 1.81050 | 0.153016 | ||||||||
\(141\) | 9.56933 | 0.805883 | ||||||||
\(142\) | −8.92058 | −0.748599 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.81743 | −0.234786 | ||||||||
\(145\) | −2.46791 | −0.204949 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | −7.38537 | −0.609135 | ||||||||
\(148\) | −1.59439 | −0.131058 | ||||||||
\(149\) | −1.81050 | −0.148322 | −0.0741612 | − | 0.997246i | \(-0.523628\pi\) | ||||
−0.0741612 | + | 0.997246i | \(0.523628\pi\) | |||||||
\(150\) | 1.23396 | 0.100752 | ||||||||
\(151\) | 20.0387 | 1.63072 | 0.815362 | − | 0.578952i | \(-0.196538\pi\) | ||||
0.815362 | + | 0.578952i | \(0.196538\pi\) | |||||||
\(152\) | −25.2293 | −2.04636 | ||||||||
\(153\) | 6.52105 | 0.527195 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.27455 | 0.423662 | ||||||||
\(156\) | −1.17806 | −0.0943206 | ||||||||
\(157\) | −14.5693 | −1.16276 | −0.581380 | − | 0.813632i | \(-0.697487\pi\) | ||||
−0.581380 | + | 0.813632i | \(0.697487\pi\) | |||||||
\(158\) | −11.9156 | −0.947956 | ||||||||
\(159\) | 6.61463 | 0.524574 | ||||||||
\(160\) | −2.63730 | −0.208497 | ||||||||
\(161\) | 8.87546 | 0.699484 | ||||||||
\(162\) | −1.23396 | −0.0969487 | ||||||||
\(163\) | −5.88918 | −0.461276 | −0.230638 | − | 0.973040i | \(-0.574081\pi\) | ||||
−0.230638 | + | 0.973040i | \(0.574081\pi\) | |||||||
\(164\) | −1.65360 | −0.129124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6349 | 1.05827 | ||||||||
\(167\) | 22.8454 | 1.76783 | 0.883914 | − | 0.467650i | \(-0.154899\pi\) | ||||
0.883914 | + | 0.467650i | \(0.154899\pi\) | |||||||
\(168\) | 11.5944 | 0.894527 | ||||||||
\(169\) | −6.90941 | −0.531493 | ||||||||
\(170\) | −8.04668 | −0.617152 | ||||||||
\(171\) | −8.25310 | −0.631130 | ||||||||
\(172\) | 5.75014 | 0.438444 | ||||||||
\(173\) | 12.5214 | 0.951987 | 0.475994 | − | 0.879449i | \(-0.342089\pi\) | ||||
0.475994 | + | 0.879449i | \(0.342089\pi\) | |||||||
\(174\) | −3.04530 | −0.230863 | ||||||||
\(175\) | −3.79281 | −0.286709 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1840 | −0.765473 | ||||||||
\(178\) | −12.6783 | −0.950282 | ||||||||
\(179\) | −3.04530 | −0.227616 | −0.113808 | − | 0.993503i | \(-0.536305\pi\) | ||||
−0.113808 | + | 0.993503i | \(0.536305\pi\) | |||||||
\(180\) | −0.477352 | −0.0355797 | ||||||||
\(181\) | 4.38537 | 0.325962 | 0.162981 | − | 0.986629i | \(-0.447889\pi\) | ||||
0.162981 | + | 0.986629i | \(0.447889\pi\) | |||||||
\(182\) | −11.5502 | −0.856159 | ||||||||
\(183\) | −6.66788 | −0.492904 | ||||||||
\(184\) | −7.15349 | −0.527362 | ||||||||
\(185\) | 3.34008 | 0.245567 | ||||||||
\(186\) | 6.50856 | 0.477231 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.56794 | 0.333151 | ||||||||
\(189\) | 3.79281 | 0.275886 | ||||||||
\(190\) | 10.1840 | 0.738822 | ||||||||
\(191\) | 23.4132 | 1.69412 | 0.847060 | − | 0.531497i | \(-0.178370\pi\) | ||||
0.847060 | + | 0.531497i | \(0.178370\pi\) | |||||||
\(192\) | −8.88918 | −0.641521 | ||||||||
\(193\) | 23.2424 | 1.67303 | 0.836514 | − | 0.547946i | \(-0.184590\pi\) | ||||
0.836514 | + | 0.547946i | \(0.184590\pi\) | |||||||
\(194\) | −16.3493 | −1.17381 | ||||||||
\(195\) | 2.46791 | 0.176731 | ||||||||
\(196\) | −3.52543 | −0.251816 | ||||||||
\(197\) | −1.99238 | −0.141951 | −0.0709756 | − | 0.997478i | \(-0.522611\pi\) | ||||
−0.0709756 | + | 0.997478i | \(0.522611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.72545 | 0.618531 | 0.309265 | − | 0.950976i | \(-0.399917\pi\) | ||||
0.309265 | + | 0.950976i | \(0.399917\pi\) | |||||||
\(200\) | 3.05694 | 0.216159 | ||||||||
\(201\) | −3.34008 | −0.235591 | ||||||||
\(202\) | 2.45851 | 0.172980 | ||||||||
\(203\) | 9.36031 | 0.656965 | ||||||||
\(204\) | 3.11284 | 0.217942 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | 1.99238 | 0.138816 | ||||||||
\(207\) | −2.34008 | −0.162647 | ||||||||
\(208\) | 6.95317 | 0.482116 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.68016 | −0.322961 | ||||||||
\(211\) | 16.0640 | 1.10589 | 0.552945 | − | 0.833218i | \(-0.313504\pi\) | ||||
0.552945 | + | 0.833218i | \(0.313504\pi\) | |||||||
\(212\) | 3.15751 | 0.216859 | ||||||||
\(213\) | −7.22925 | −0.495340 | ||||||||
\(214\) | 0.726839 | 0.0496857 | ||||||||
\(215\) | −12.0459 | −0.821524 | ||||||||
\(216\) | −3.05694 | −0.207999 | ||||||||
\(217\) | −20.0053 | −1.35805 | ||||||||
\(218\) | 5.90941 | 0.400236 | ||||||||
\(219\) | 9.72482 | 0.657142 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0934 | −1.08256 | ||||||||
\(222\) | 4.12151 | 0.276618 | ||||||||
\(223\) | −11.0655 | −0.741003 | −0.370501 | − | 0.928832i | \(-0.620814\pi\) | ||||
−0.370501 | + | 0.928832i | \(0.620814\pi\) | |||||||
\(224\) | 10.0028 | 0.668339 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −22.8578 | −1.52048 | ||||||||
\(227\) | 15.3965 | 1.02190 | 0.510951 | − | 0.859610i | \(-0.329293\pi\) | ||||
0.510951 | + | 0.859610i | \(0.329293\pi\) | |||||||
\(228\) | −3.93963 | −0.260909 | ||||||||
\(229\) | 4.70522 | 0.310930 | 0.155465 | − | 0.987841i | \(-0.450312\pi\) | ||||
0.155465 | + | 0.987841i | \(0.450312\pi\) | |||||||
\(230\) | 2.88755 | 0.190400 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.54427 | −0.495306 | ||||||||
\(233\) | 14.9210 | 0.977505 | 0.488753 | − | 0.872422i | \(-0.337452\pi\) | ||||
0.488753 | + | 0.872422i | \(0.337452\pi\) | |||||||
\(234\) | 3.04530 | 0.199077 | ||||||||
\(235\) | −9.56933 | −0.624234 | ||||||||
\(236\) | −4.86134 | −0.316446 | ||||||||
\(237\) | −9.65644 | −0.627253 | ||||||||
\(238\) | 30.5195 | 1.97829 | ||||||||
\(239\) | −11.3885 | −0.736660 | −0.368330 | − | 0.929695i | \(-0.620070\pi\) | ||||
−0.368330 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(240\) | 2.81743 | 0.181864 | ||||||||
\(241\) | 12.1143 | 0.780349 | 0.390175 | − | 0.920741i | \(-0.372415\pi\) | ||||
0.390175 | + | 0.920741i | \(0.372415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.18293 | −0.203766 | ||||||||
\(245\) | 7.38537 | 0.471834 | ||||||||
\(246\) | 4.27455 | 0.272535 | ||||||||
\(247\) | 20.3679 | 1.29598 | ||||||||
\(248\) | 16.1240 | 1.02388 | ||||||||
\(249\) | 11.0497 | 0.700247 | ||||||||
\(250\) | −1.23396 | −0.0780422 | ||||||||
\(251\) | −17.4132 | −1.09911 | −0.549556 | − | 0.835457i | \(-0.685203\pi\) | ||||
−0.549556 | + | 0.835457i | \(0.685203\pi\) | |||||||
\(252\) | 1.81050 | 0.114051 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −15.0453 | −0.944026 | ||||||||
\(255\) | −6.52105 | −0.408364 | ||||||||
\(256\) | −10.7519 | −0.671994 | ||||||||
\(257\) | −18.4334 | −1.14985 | −0.574923 | − | 0.818207i | \(-0.694968\pi\) | ||||
−0.574923 | + | 0.818207i | \(0.694968\pi\) | |||||||
\(258\) | −14.8641 | −0.925399 | ||||||||
\(259\) | −12.6683 | −0.787168 | ||||||||
\(260\) | 1.17806 | 0.0730604 | ||||||||
\(261\) | −2.46791 | −0.152760 | ||||||||
\(262\) | −4.27455 | −0.264083 | ||||||||
\(263\) | −2.06075 | −0.127072 | −0.0635358 | − | 0.997980i | \(-0.520238\pi\) | ||||
−0.0635358 | + | 0.997980i | \(0.520238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.61463 | −0.406333 | ||||||||
\(266\) | −38.6258 | −2.36830 | ||||||||
\(267\) | −10.2745 | −0.628792 | ||||||||
\(268\) | −1.59439 | −0.0973931 | ||||||||
\(269\) | 3.45090 | 0.210405 | 0.105203 | − | 0.994451i | \(-0.466451\pi\) | ||||
0.105203 | + | 0.994451i | \(0.466451\pi\) | |||||||
\(270\) | 1.23396 | 0.0750962 | ||||||||
\(271\) | 21.2167 | 1.28882 | 0.644412 | − | 0.764678i | \(-0.277102\pi\) | ||||
0.644412 | + | 0.764678i | \(0.277102\pi\) | |||||||
\(272\) | −18.3726 | −1.11400 | ||||||||
\(273\) | −9.36031 | −0.566512 | ||||||||
\(274\) | −9.79079 | −0.591483 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.11704 | −0.0672380 | ||||||||
\(277\) | 4.13159 | 0.248243 | 0.124122 | − | 0.992267i | \(-0.460389\pi\) | ||||
0.124122 | + | 0.992267i | \(0.460389\pi\) | |||||||
\(278\) | −7.62864 | −0.457536 | ||||||||
\(279\) | 5.27455 | 0.315779 | ||||||||
\(280\) | −11.5944 | −0.692898 | ||||||||
\(281\) | −23.0956 | −1.37777 | −0.688884 | − | 0.724871i | \(-0.741899\pi\) | ||||
−0.688884 | + | 0.724871i | \(0.741899\pi\) | |||||||
\(282\) | −11.8081 | −0.703164 | ||||||||
\(283\) | 24.7593 | 1.47179 | 0.735893 | − | 0.677097i | \(-0.236762\pi\) | ||||
0.735893 | + | 0.677097i | \(0.236762\pi\) | |||||||
\(284\) | −3.45090 | −0.204773 | ||||||||
\(285\) | 8.25310 | 0.488871 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.1387 | −0.775551 | ||||||||
\(288\) | −2.63730 | −0.155405 | ||||||||
\(289\) | 25.5240 | 1.50141 | ||||||||
\(290\) | 3.04530 | 0.178826 | ||||||||
\(291\) | −13.2495 | −0.776699 | ||||||||
\(292\) | 4.64217 | 0.271662 | ||||||||
\(293\) | −7.33536 | −0.428536 | −0.214268 | − | 0.976775i | \(-0.568737\pi\) | ||||
−0.214268 | + | 0.976775i | \(0.568737\pi\) | |||||||
\(294\) | 9.11323 | 0.531494 | ||||||||
\(295\) | 10.1840 | 0.592933 | ||||||||
\(296\) | 10.2104 | 0.593469 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.23408 | 0.129417 | ||||||||
\(299\) | 5.77511 | 0.333983 | ||||||||
\(300\) | 0.477352 | 0.0275600 | ||||||||
\(301\) | 45.6878 | 2.63340 | ||||||||
\(302\) | −24.7268 | −1.42287 | ||||||||
\(303\) | 1.99238 | 0.114459 | ||||||||
\(304\) | 23.2525 | 1.33362 | ||||||||
\(305\) | 6.66788 | 0.381801 | ||||||||
\(306\) | −8.04668 | −0.459998 | ||||||||
\(307\) | −22.7669 | −1.29938 | −0.649688 | − | 0.760201i | \(-0.725101\pi\) | ||||
−0.649688 | + | 0.760201i | \(0.725101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.61463 | 0.0918529 | ||||||||
\(310\) | −6.50856 | −0.369661 | ||||||||
\(311\) | −25.5443 | −1.44848 | −0.724241 | − | 0.689547i | \(-0.757810\pi\) | ||||
−0.724241 | + | 0.689547i | \(0.757810\pi\) | |||||||
\(312\) | 7.54427 | 0.427110 | ||||||||
\(313\) | −34.7735 | −1.96552 | −0.982758 | − | 0.184897i | \(-0.940805\pi\) | ||||
−0.982758 | + | 0.184897i | \(0.940805\pi\) | |||||||
\(314\) | 17.9779 | 1.01455 | ||||||||
\(315\) | −3.79281 | −0.213700 | ||||||||
\(316\) | −4.60953 | −0.259306 | ||||||||
\(317\) | −5.38537 | −0.302473 | −0.151236 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151236 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(318\) | −8.16216 | −0.457711 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.88918 | 0.496920 | ||||||||
\(321\) | 0.589032 | 0.0328766 | ||||||||
\(322\) | −10.9519 | −0.610327 | ||||||||
\(323\) | −53.8188 | −2.99456 | ||||||||
\(324\) | −0.477352 | −0.0265196 | ||||||||
\(325\) | −2.46791 | −0.136895 | ||||||||
\(326\) | 7.26699 | 0.402481 | ||||||||
\(327\) | 4.78899 | 0.264832 | ||||||||
\(328\) | 10.5896 | 0.584711 | ||||||||
\(329\) | 36.2946 | 2.00099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8641 | 1.09183 | 0.545915 | − | 0.837840i | \(-0.316182\pi\) | ||||
0.545915 | + | 0.837840i | \(0.316182\pi\) | |||||||
\(332\) | 5.27461 | 0.289482 | ||||||||
\(333\) | 3.34008 | 0.183035 | ||||||||
\(334\) | −28.1902 | −1.54250 | ||||||||
\(335\) | 3.34008 | 0.182488 | ||||||||
\(336\) | −10.6860 | −0.582967 | ||||||||
\(337\) | −10.9029 | −0.593918 | −0.296959 | − | 0.954890i | \(-0.595972\pi\) | ||||
−0.296959 | + | 0.954890i | \(0.595972\pi\) | |||||||
\(338\) | 8.52591 | 0.463748 | ||||||||
\(339\) | −18.5240 | −1.00609 | ||||||||
\(340\) | −3.11284 | −0.168817 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 10.1840 | 0.550685 | ||||||||
\(343\) | −1.46164 | −0.0789214 | ||||||||
\(344\) | −36.8236 | −1.98540 | ||||||||
\(345\) | 2.34008 | 0.125986 | ||||||||
\(346\) | −15.4509 | −0.830646 | ||||||||
\(347\) | 5.00420 | 0.268640 | 0.134320 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(348\) | −1.17806 | −0.0631508 | ||||||||
\(349\) | −26.7749 | −1.43323 | −0.716614 | − | 0.697470i | \(-0.754309\pi\) | ||||
−0.716614 | + | 0.697470i | \(0.754309\pi\) | |||||||
\(350\) | 4.68016 | 0.250165 | ||||||||
\(351\) | 2.46791 | 0.131727 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.2042 | 0.915687 | 0.457843 | − | 0.889033i | \(-0.348622\pi\) | ||||
0.457843 | + | 0.889033i | \(0.348622\pi\) | |||||||
\(354\) | 12.5666 | 0.667905 | ||||||||
\(355\) | 7.22925 | 0.383689 | ||||||||
\(356\) | −4.90458 | −0.259942 | ||||||||
\(357\) | 24.7331 | 1.30901 | ||||||||
\(358\) | 3.75776 | 0.198604 | ||||||||
\(359\) | −0.657408 | −0.0346966 | −0.0173483 | − | 0.999850i | \(-0.505522\pi\) | ||||
−0.0173483 | + | 0.999850i | \(0.505522\pi\) | |||||||
\(360\) | 3.05694 | 0.161115 | ||||||||
\(361\) | 49.1136 | 2.58493 | ||||||||
\(362\) | −5.41136 | −0.284415 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.46817 | −0.234196 | ||||||||
\(365\) | −9.72482 | −0.509020 | ||||||||
\(366\) | 8.22787 | 0.430077 | ||||||||
\(367\) | −33.5038 | −1.74888 | −0.874442 | − | 0.485130i | \(-0.838772\pi\) | ||||
−0.874442 | + | 0.485130i | \(0.838772\pi\) | |||||||
\(368\) | 6.59301 | 0.343684 | ||||||||
\(369\) | 3.46410 | 0.180334 | ||||||||
\(370\) | −4.12151 | −0.214267 | ||||||||
\(371\) | 25.0880 | 1.30250 | ||||||||
\(372\) | 2.51782 | 0.130543 | ||||||||
\(373\) | 7.73244 | 0.400371 | 0.200185 | − | 0.979758i | \(-0.435846\pi\) | ||||
0.200185 | + | 0.979758i | \(0.435846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −29.2529 | −1.50860 | ||||||||
\(377\) | 6.09059 | 0.313681 | ||||||||
\(378\) | −4.68016 | −0.240721 | ||||||||
\(379\) | −0.340078 | −0.0174686 | −0.00873431 | − | 0.999962i | \(-0.502780\pi\) | ||||
−0.00873431 | + | 0.999962i | \(0.502780\pi\) | |||||||
\(380\) | 3.93963 | 0.202099 | ||||||||
\(381\) | −12.1927 | −0.624653 | ||||||||
\(382\) | −28.8909 | −1.47819 | ||||||||
\(383\) | 31.0481 | 1.58648 | 0.793241 | − | 0.608908i | \(-0.208392\pi\) | ||||
0.793241 | + | 0.608908i | \(0.208392\pi\) | |||||||
\(384\) | 5.69425 | 0.290583 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.6802 | −1.45978 | ||||||||
\(387\) | −12.0459 | −0.612328 | ||||||||
\(388\) | −6.32467 | −0.321087 | ||||||||
\(389\) | −24.3150 | −1.23282 | −0.616410 | − | 0.787425i | \(-0.711414\pi\) | ||||
−0.616410 | + | 0.787425i | \(0.711414\pi\) | |||||||
\(390\) | −3.04530 | −0.154205 | ||||||||
\(391\) | −15.2598 | −0.771719 | ||||||||
\(392\) | 22.5767 | 1.14029 | ||||||||
\(393\) | −3.46410 | −0.174741 | ||||||||
\(394\) | 2.45851 | 0.123858 | ||||||||
\(395\) | 9.65644 | 0.485868 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2948 | 0.516680 | 0.258340 | − | 0.966054i | \(-0.416824\pi\) | ||||
0.258340 | + | 0.966054i | \(0.416824\pi\) | |||||||
\(398\) | −10.7668 | −0.539692 | ||||||||
\(399\) | −31.3024 | −1.56708 | ||||||||
\(400\) | −2.81743 | −0.140872 | ||||||||
\(401\) | −19.2293 | −0.960263 | −0.480132 | − | 0.877196i | \(-0.659411\pi\) | ||||
−0.480132 | + | 0.877196i | \(0.659411\pi\) | |||||||
\(402\) | 4.12151 | 0.205562 | ||||||||
\(403\) | −13.0171 | −0.648429 | ||||||||
\(404\) | 0.951067 | 0.0473173 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −11.5502 | −0.573227 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −19.9345 | −0.986903 | ||||||||
\(409\) | −6.53112 | −0.322943 | −0.161472 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161472 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(410\) | −4.27455 | −0.211105 | ||||||||
\(411\) | −7.93447 | −0.391379 | ||||||||
\(412\) | 0.770746 | 0.0379719 | ||||||||
\(413\) | −38.6258 | −1.90065 | ||||||||
\(414\) | 2.88755 | 0.141915 | ||||||||
\(415\) | −11.0497 | −0.542409 | ||||||||
\(416\) | 6.50863 | 0.319112 | ||||||||
\(417\) | −6.18226 | −0.302747 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.6878 | 1.35264 | 0.676318 | − | 0.736610i | \(-0.263575\pi\) | ||||
0.676318 | + | 0.736610i | \(0.263575\pi\) | |||||||
\(420\) | −1.81050 | −0.0883436 | ||||||||
\(421\) | −11.1637 | −0.544087 | −0.272043 | − | 0.962285i | \(-0.587699\pi\) | ||||
−0.272043 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(422\) | −19.8223 | −0.964932 | ||||||||
\(423\) | −9.56933 | −0.465277 | ||||||||
\(424\) | −20.2205 | −0.981996 | ||||||||
\(425\) | 6.52105 | 0.316317 | ||||||||
\(426\) | 8.92058 | 0.432204 | ||||||||
\(427\) | −25.2900 | −1.22387 | ||||||||
\(428\) | 0.281176 | 0.0135911 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.8641 | 0.716811 | ||||||||
\(431\) | −13.3607 | −0.643563 | −0.321782 | − | 0.946814i | \(-0.604282\pi\) | ||||
−0.321782 | + | 0.946814i | \(0.604282\pi\) | |||||||
\(432\) | 2.81743 | 0.135554 | ||||||||
\(433\) | 19.2495 | 0.925071 | 0.462536 | − | 0.886601i | \(-0.346940\pi\) | ||||
0.462536 | + | 0.886601i | \(0.346940\pi\) | |||||||
\(434\) | 24.6857 | 1.18495 | ||||||||
\(435\) | 2.46791 | 0.118327 | ||||||||
\(436\) | 2.28604 | 0.109481 | ||||||||
\(437\) | 19.3129 | 0.923861 | ||||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | −21.6572 | −1.03364 | −0.516821 | − | 0.856093i | \(-0.672885\pi\) | ||||
−0.516821 | + | 0.856093i | \(0.672885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.38537 | 0.351684 | ||||||||
\(442\) | 19.8585 | 0.944573 | ||||||||
\(443\) | 1.13866 | 0.0540995 | 0.0270498 | − | 0.999634i | \(-0.491389\pi\) | ||||
0.0270498 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(444\) | 1.59439 | 0.0756666 | ||||||||
\(445\) | 10.2745 | 0.487060 | ||||||||
\(446\) | 13.6544 | 0.646553 | ||||||||
\(447\) | 1.81050 | 0.0856339 | ||||||||
\(448\) | −33.7149 | −1.59288 | ||||||||
\(449\) | −0.0905906 | −0.00427524 | −0.00213762 | − | 0.999998i | \(-0.500680\pi\) | ||||
−0.00213762 | + | 0.999998i | \(0.500680\pi\) | |||||||
\(450\) | −1.23396 | −0.0581692 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.84249 | −0.415916 | ||||||||
\(453\) | −20.0387 | −0.941499 | ||||||||
\(454\) | −18.9986 | −0.891649 | ||||||||
\(455\) | 9.36031 | 0.438818 | ||||||||
\(456\) | 25.2293 | 1.18147 | ||||||||
\(457\) | −4.12151 | −0.192796 | −0.0963980 | − | 0.995343i | \(-0.530732\pi\) | ||||
−0.0963980 | + | 0.995343i | \(0.530732\pi\) | |||||||
\(458\) | −5.80603 | −0.271298 | ||||||||
\(459\) | −6.52105 | −0.304376 | ||||||||
\(460\) | 1.11704 | 0.0520823 | ||||||||
\(461\) | 6.74633 | 0.314208 | 0.157104 | − | 0.987582i | \(-0.449784\pi\) | ||||
0.157104 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4990 | −0.952668 | −0.476334 | − | 0.879264i | \(-0.658035\pi\) | ||||
−0.476334 | + | 0.879264i | \(0.658035\pi\) | |||||||
\(464\) | 6.95317 | 0.322793 | ||||||||
\(465\) | −5.27455 | −0.244601 | ||||||||
\(466\) | −18.4118 | −0.852911 | ||||||||
\(467\) | −4.79859 | −0.222052 | −0.111026 | − | 0.993817i | \(-0.535414\pi\) | ||||
−0.111026 | + | 0.993817i | \(0.535414\pi\) | |||||||
\(468\) | 1.17806 | 0.0544560 | ||||||||
\(469\) | −12.6683 | −0.584966 | ||||||||
\(470\) | 11.8081 | 0.544669 | ||||||||
\(471\) | 14.5693 | 0.671319 | ||||||||
\(472\) | 31.1318 | 1.43296 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 11.9156 | 0.547303 | ||||||||
\(475\) | −8.25310 | −0.378678 | ||||||||
\(476\) | 11.8064 | 0.541145 | ||||||||
\(477\) | −6.61463 | −0.302863 | ||||||||
\(478\) | 14.0529 | 0.642765 | ||||||||
\(479\) | 9.39612 | 0.429319 | 0.214660 | − | 0.976689i | \(-0.431136\pi\) | ||||
0.214660 | + | 0.976689i | \(0.431136\pi\) | |||||||
\(480\) | 2.63730 | 0.120376 | ||||||||
\(481\) | −8.24302 | −0.375849 | ||||||||
\(482\) | −14.9485 | −0.680885 | ||||||||
\(483\) | −8.87546 | −0.403847 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.2495 | 0.601628 | ||||||||
\(486\) | 1.23396 | 0.0559734 | ||||||||
\(487\) | −24.0934 | −1.09177 | −0.545887 | − | 0.837859i | \(-0.683807\pi\) | ||||
−0.545887 | + | 0.837859i | \(0.683807\pi\) | |||||||
\(488\) | 20.3833 | 0.922710 | ||||||||
\(489\) | 5.88918 | 0.266318 | ||||||||
\(490\) | −9.11323 | −0.411694 | ||||||||
\(491\) | 6.63454 | 0.299413 | 0.149706 | − | 0.988730i | \(-0.452167\pi\) | ||||
0.149706 | + | 0.988730i | \(0.452167\pi\) | |||||||
\(492\) | 1.65360 | 0.0745499 | ||||||||
\(493\) | −16.0934 | −0.724809 | ||||||||
\(494\) | −25.1331 | −1.13079 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.8607 | −0.667264 | ||||||||
\(497\) | −27.4192 | −1.22992 | ||||||||
\(498\) | −13.6349 | −0.610993 | ||||||||
\(499\) | 22.1637 | 0.992185 | 0.496092 | − | 0.868270i | \(-0.334768\pi\) | ||||
0.496092 | + | 0.868270i | \(0.334768\pi\) | |||||||
\(500\) | −0.477352 | −0.0213478 | ||||||||
\(501\) | −22.8454 | −1.02066 | ||||||||
\(502\) | 21.4871 | 0.959018 | ||||||||
\(503\) | −37.8597 | −1.68808 | −0.844040 | − | 0.536281i | \(-0.819829\pi\) | ||||
−0.844040 | + | 0.536281i | \(0.819829\pi\) | |||||||
\(504\) | −11.5944 | −0.516455 | ||||||||
\(505\) | −1.99238 | −0.0886597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.90941 | 0.306858 | ||||||||
\(508\) | −5.82023 | −0.258231 | ||||||||
\(509\) | −0.405606 | −0.0179782 | −0.00898909 | − | 0.999960i | \(-0.502861\pi\) | ||||
−0.00898909 | + | 0.999960i | \(0.502861\pi\) | |||||||
\(510\) | 8.04668 | 0.356313 | ||||||||
\(511\) | 36.8843 | 1.63167 | ||||||||
\(512\) | 24.6559 | 1.08965 | ||||||||
\(513\) | 8.25310 | 0.364383 | ||||||||
\(514\) | 22.7461 | 1.00329 | ||||||||
\(515\) | −1.61463 | −0.0711490 | ||||||||
\(516\) | −5.75014 | −0.253136 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15.6321 | 0.686834 | ||||||||
\(519\) | −12.5214 | −0.549630 | ||||||||
\(520\) | −7.54427 | −0.330838 | ||||||||
\(521\) | 22.9952 | 1.00744 | 0.503718 | − | 0.863868i | \(-0.331965\pi\) | ||||
0.503718 | + | 0.863868i | \(0.331965\pi\) | |||||||
\(522\) | 3.04530 | 0.133289 | ||||||||
\(523\) | 1.14302 | 0.0499807 | 0.0249904 | − | 0.999688i | \(-0.492044\pi\) | ||||
0.0249904 | + | 0.999688i | \(0.492044\pi\) | |||||||
\(524\) | −1.65360 | −0.0722377 | ||||||||
\(525\) | 3.79281 | 0.165532 | ||||||||
\(526\) | 2.54288 | 0.110875 | ||||||||
\(527\) | 34.3956 | 1.49829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5240 | −0.761915 | ||||||||
\(530\) | 8.16216 | 0.354542 | ||||||||
\(531\) | 10.1840 | 0.441946 | ||||||||
\(532\) | −14.9423 | −0.647830 | ||||||||
\(533\) | −8.54910 | −0.370303 | ||||||||
\(534\) | 12.6783 | 0.548646 | ||||||||
\(535\) | −0.589032 | −0.0254661 | ||||||||
\(536\) | 10.2104 | 0.441023 | ||||||||
\(537\) | 3.04530 | 0.131414 | ||||||||
\(538\) | −4.25826 | −0.183587 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.477352 | 0.0205420 | ||||||||
\(541\) | −8.92058 | −0.383526 | −0.191763 | − | 0.981441i | \(-0.561420\pi\) | ||||
−0.191763 | + | 0.981441i | \(0.561420\pi\) | |||||||
\(542\) | −26.1805 | −1.12455 | ||||||||
\(543\) | −4.38537 | −0.188194 | ||||||||
\(544\) | −17.1980 | −0.737357 | ||||||||
\(545\) | −4.78899 | −0.205138 | ||||||||
\(546\) | 11.5502 | 0.494303 | ||||||||
\(547\) | −8.73871 | −0.373640 | −0.186820 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186820 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(548\) | −3.78754 | −0.161796 | ||||||||
\(549\) | 6.66788 | 0.284578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.3679 | 0.867702 | ||||||||
\(552\) | 7.15349 | 0.304473 | ||||||||
\(553\) | −36.6250 | −1.55745 | ||||||||
\(554\) | −5.09820 | −0.216602 | ||||||||
\(555\) | −3.34008 | −0.141778 | ||||||||
\(556\) | −2.95112 | −0.125155 | ||||||||
\(557\) | −16.6197 | −0.704199 | −0.352099 | − | 0.935963i | \(-0.614532\pi\) | ||||
−0.352099 | + | 0.935963i | \(0.614532\pi\) | |||||||
\(558\) | −6.50856 | −0.275529 | ||||||||
\(559\) | 29.7282 | 1.25737 | ||||||||
\(560\) | 10.6860 | 0.451564 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.4990 | 1.20216 | ||||||||
\(563\) | 41.7060 | 1.75770 | 0.878849 | − | 0.477101i | \(-0.158312\pi\) | ||||
0.878849 | + | 0.477101i | \(0.158312\pi\) | |||||||
\(564\) | −4.56794 | −0.192345 | ||||||||
\(565\) | 18.5240 | 0.779312 | ||||||||
\(566\) | −30.5519 | −1.28419 | ||||||||
\(567\) | −3.79281 | −0.159283 | ||||||||
\(568\) | 22.0994 | 0.927271 | ||||||||
\(569\) | 7.76749 | 0.325630 | 0.162815 | − | 0.986657i | \(-0.447943\pi\) | ||||
0.162815 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(570\) | −10.1840 | −0.426559 | ||||||||
\(571\) | 26.9568 | 1.12811 | 0.564053 | − | 0.825738i | \(-0.309241\pi\) | ||||
0.564053 | + | 0.825738i | \(0.309241\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.4132 | −0.978101 | ||||||||
\(574\) | 16.2125 | 0.676698 | ||||||||
\(575\) | −2.34008 | −0.0975880 | ||||||||
\(576\) | 8.88918 | 0.370382 | ||||||||
\(577\) | 26.9345 | 1.12130 | 0.560648 | − | 0.828054i | \(-0.310552\pi\) | ||||
0.560648 | + | 0.828054i | \(0.310552\pi\) | |||||||
\(578\) | −31.4955 | −1.31004 | ||||||||
\(579\) | −23.2424 | −0.965923 | ||||||||
\(580\) | 1.17806 | 0.0489164 | ||||||||
\(581\) | 41.9094 | 1.73870 | ||||||||
\(582\) | 16.3493 | 0.677700 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −29.7282 | −1.23016 | ||||||||
\(585\) | −2.46791 | −0.102036 | ||||||||
\(586\) | 9.05151 | 0.373915 | ||||||||
\(587\) | −13.4383 | −0.554657 | −0.277328 | − | 0.960775i | \(-0.589449\pi\) | ||||
−0.277328 | + | 0.960775i | \(0.589449\pi\) | |||||||
\(588\) | 3.52543 | 0.145386 | ||||||||
\(589\) | −43.5314 | −1.79368 | ||||||||
\(590\) | −12.5666 | −0.517357 | ||||||||
\(591\) | 1.99238 | 0.0819555 | ||||||||
\(592\) | −9.41044 | −0.386767 | ||||||||
\(593\) | 23.4344 | 0.962335 | 0.481168 | − | 0.876629i | \(-0.340213\pi\) | ||||
0.481168 | + | 0.876629i | \(0.340213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.7331 | −1.01396 | ||||||||
\(596\) | 0.864249 | 0.0354010 | ||||||||
\(597\) | −8.72545 | −0.357109 | ||||||||
\(598\) | −7.12623 | −0.291413 | ||||||||
\(599\) | −40.0028 | −1.63447 | −0.817235 | − | 0.576305i | \(-0.804494\pi\) | ||||
−0.817235 | + | 0.576305i | \(0.804494\pi\) | |||||||
\(600\) | −3.05694 | −0.124799 | ||||||||
\(601\) | −15.3181 | −0.624836 | −0.312418 | − | 0.949945i | \(-0.601139\pi\) | ||||
−0.312418 | + | 0.949945i | \(0.601139\pi\) | |||||||
\(602\) | −56.3767 | −2.29774 | ||||||||
\(603\) | 3.34008 | 0.136018 | ||||||||
\(604\) | −9.56551 | −0.389215 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.45851 | −0.0998701 | ||||||||
\(607\) | 34.0086 | 1.38037 | 0.690183 | − | 0.723635i | \(-0.257530\pi\) | ||||
0.690183 | + | 0.723635i | \(0.257530\pi\) | |||||||
\(608\) | 21.7659 | 0.882724 | ||||||||
\(609\) | −9.36031 | −0.379299 | ||||||||
\(610\) | −8.22787 | −0.333137 | ||||||||
\(611\) | 23.6163 | 0.955412 | ||||||||
\(612\) | −3.11284 | −0.125829 | ||||||||
\(613\) | 40.0874 | 1.61912 | 0.809558 | − | 0.587040i | \(-0.199707\pi\) | ||||
0.809558 | + | 0.587040i | \(0.199707\pi\) | |||||||
\(614\) | 28.0934 | 1.13376 | ||||||||
\(615\) | −3.46410 | −0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.36031 | 0.135281 | 0.0676405 | − | 0.997710i | \(-0.478453\pi\) | ||||
0.0676405 | + | 0.997710i | \(0.478453\pi\) | |||||||
\(618\) | −1.99238 | −0.0801452 | ||||||||
\(619\) | 28.5491 | 1.14749 | 0.573743 | − | 0.819036i | \(-0.305491\pi\) | ||||
0.573743 | + | 0.819036i | \(0.305491\pi\) | |||||||
\(620\) | −2.51782 | −0.101118 | ||||||||
\(621\) | 2.34008 | 0.0939041 | ||||||||
\(622\) | 31.5205 | 1.26386 | ||||||||
\(623\) | −38.9694 | −1.56127 | ||||||||
\(624\) | −6.95317 | −0.278350 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 42.9090 | 1.71499 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.95470 | 0.277523 | ||||||||
\(629\) | 21.7808 | 0.868457 | ||||||||
\(630\) | 4.68016 | 0.186462 | ||||||||
\(631\) | −18.7986 | −0.748360 | −0.374180 | − | 0.927356i | \(-0.622076\pi\) | ||||
−0.374180 | + | 0.927356i | \(0.622076\pi\) | |||||||
\(632\) | 29.5192 | 1.17421 | ||||||||
\(633\) | −16.0640 | −0.638486 | ||||||||
\(634\) | 6.64531 | 0.263919 | ||||||||
\(635\) | 12.1927 | 0.483854 | ||||||||
\(636\) | −3.15751 | −0.125203 | ||||||||
\(637\) | −18.2265 | −0.722158 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.22925 | 0.285985 | ||||||||
\(640\) | −5.69425 | −0.225085 | ||||||||
\(641\) | 45.1010 | 1.78138 | 0.890691 | − | 0.454610i | \(-0.150221\pi\) | ||||
0.890691 | + | 0.454610i | \(0.150221\pi\) | |||||||
\(642\) | −0.726839 | −0.0286861 | ||||||||
\(643\) | 30.8439 | 1.21636 | 0.608182 | − | 0.793798i | \(-0.291899\pi\) | ||||
0.608182 | + | 0.793798i | \(0.291899\pi\) | |||||||
\(644\) | −4.23672 | −0.166950 | ||||||||
\(645\) | 12.0459 | 0.474307 | ||||||||
\(646\) | 66.4101 | 2.61287 | ||||||||
\(647\) | 31.3477 | 1.23240 | 0.616202 | − | 0.787588i | \(-0.288670\pi\) | ||||
0.616202 | + | 0.787588i | \(0.288670\pi\) | |||||||
\(648\) | 3.05694 | 0.120088 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.04530 | 0.119446 | ||||||||
\(651\) | 20.0053 | 0.784071 | ||||||||
\(652\) | 2.81121 | 0.110096 | ||||||||
\(653\) | 32.4585 | 1.27020 | 0.635100 | − | 0.772430i | \(-0.280959\pi\) | ||||
0.635100 | + | 0.772430i | \(0.280959\pi\) | |||||||
\(654\) | −5.90941 | −0.231076 | ||||||||
\(655\) | 3.46410 | 0.135354 | ||||||||
\(656\) | −9.75986 | −0.381059 | ||||||||
\(657\) | −9.72482 | −0.379401 | ||||||||
\(658\) | −44.7860 | −1.74594 | ||||||||
\(659\) | −21.7808 | −0.848459 | −0.424230 | − | 0.905555i | \(-0.639455\pi\) | ||||
−0.424230 | + | 0.905555i | \(0.639455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.83627 | 0.149214 | 0.0746069 | − | 0.997213i | \(-0.476230\pi\) | ||||
0.0746069 | + | 0.997213i | \(0.476230\pi\) | |||||||
\(662\) | −24.5114 | −0.952664 | ||||||||
\(663\) | 16.0934 | 0.625015 | ||||||||
\(664\) | −33.7784 | −1.31085 | ||||||||
\(665\) | 31.3024 | 1.21385 | ||||||||
\(666\) | −4.12151 | −0.159705 | ||||||||
\(667\) | 5.77511 | 0.223613 | ||||||||
\(668\) | −10.9053 | −0.421938 | ||||||||
\(669\) | 11.0655 | 0.427818 | ||||||||
\(670\) | −4.12151 | −0.159228 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −10.0028 | −0.385866 | ||||||||
\(673\) | −24.8711 | −0.958709 | −0.479355 | − | 0.877621i | \(-0.659129\pi\) | ||||
−0.479355 | + | 0.877621i | \(0.659129\pi\) | |||||||
\(674\) | 13.4537 | 0.518216 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 3.29822 | 0.126855 | ||||||||
\(677\) | 14.2202 | 0.546525 | 0.273262 | − | 0.961940i | \(-0.411897\pi\) | ||||
0.273262 | + | 0.961940i | \(0.411897\pi\) | |||||||
\(678\) | 22.8578 | 0.877850 | ||||||||
\(679\) | −50.2527 | −1.92852 | ||||||||
\(680\) | 19.9345 | 0.764452 | ||||||||
\(681\) | −15.3965 | −0.589995 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.68776 | −0.370692 | −0.185346 | − | 0.982673i | \(-0.559341\pi\) | ||||
−0.185346 | + | 0.982673i | \(0.559341\pi\) | |||||||
\(684\) | 3.93963 | 0.150636 | ||||||||
\(685\) | 7.93447 | 0.303161 | ||||||||
\(686\) | 1.80361 | 0.0688620 | ||||||||
\(687\) | −4.70522 | −0.179515 | ||||||||
\(688\) | 33.9385 | 1.29389 | ||||||||
\(689\) | 16.3243 | 0.621907 | ||||||||
\(690\) | −2.88755 | −0.109927 | ||||||||
\(691\) | −0.594394 | −0.0226118 | −0.0113059 | − | 0.999936i | \(-0.503599\pi\) | ||||
−0.0113059 | + | 0.999936i | \(0.503599\pi\) | |||||||
\(692\) | −5.97714 | −0.227217 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.17496 | −0.234398 | ||||||||
\(695\) | 6.18226 | 0.234507 | ||||||||
\(696\) | 7.54427 | 0.285965 | ||||||||
\(697\) | 22.5896 | 0.855641 | ||||||||
\(698\) | 33.0391 | 1.25055 | ||||||||
\(699\) | −14.9210 | −0.564363 | ||||||||
\(700\) | 1.81050 | 0.0684306 | ||||||||
\(701\) | −18.1598 | −0.685886 | −0.342943 | − | 0.939356i | \(-0.611424\pi\) | ||||
−0.342943 | + | 0.939356i | \(0.611424\pi\) | |||||||
\(702\) | −3.04530 | −0.114937 | ||||||||
\(703\) | −27.5660 | −1.03967 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.56933 | 0.360402 | ||||||||
\(706\) | −21.2292 | −0.798972 | ||||||||
\(707\) | 7.55671 | 0.284199 | ||||||||
\(708\) | 4.86134 | 0.182700 | ||||||||
\(709\) | −1.80341 | −0.0677287 | −0.0338643 | − | 0.999426i | \(-0.510781\pi\) | ||||
−0.0338643 | + | 0.999426i | \(0.510781\pi\) | |||||||
\(710\) | −8.92058 | −0.334783 | ||||||||
\(711\) | 9.65644 | 0.362145 | ||||||||
\(712\) | 31.4087 | 1.17709 | ||||||||
\(713\) | −12.3429 | −0.462244 | ||||||||
\(714\) | −30.5195 | −1.14216 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.45368 | 0.0543265 | ||||||||
\(717\) | 11.3885 | 0.425311 | ||||||||
\(718\) | 0.811212 | 0.0302742 | ||||||||
\(719\) | −37.0481 | −1.38166 | −0.690830 | − | 0.723017i | \(-0.742755\pi\) | ||||
−0.690830 | + | 0.723017i | \(0.742755\pi\) | |||||||
\(720\) | −2.81743 | −0.104999 | ||||||||
\(721\) | 6.12397 | 0.228068 | ||||||||
\(722\) | −60.6040 | −2.25545 | ||||||||
\(723\) | −12.1143 | −0.450535 | ||||||||
\(724\) | −2.09337 | −0.0777994 | ||||||||
\(725\) | −2.46791 | −0.0916560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.3198 | 0.864885 | 0.432443 | − | 0.901661i | \(-0.357652\pi\) | ||||
0.432443 | + | 0.901661i | \(0.357652\pi\) | |||||||
\(728\) | 28.6139 | 1.06050 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | −78.5519 | −2.90535 | ||||||||
\(732\) | 3.18293 | 0.117644 | ||||||||
\(733\) | 15.9855 | 0.590439 | 0.295220 | − | 0.955429i | \(-0.404607\pi\) | ||||
0.295220 | + | 0.955429i | \(0.404607\pi\) | |||||||
\(734\) | 41.3422 | 1.52597 | ||||||||
\(735\) | −7.38537 | −0.272414 | ||||||||
\(736\) | 6.17149 | 0.227484 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.27455 | −0.157348 | ||||||||
\(739\) | 32.9339 | 1.21149 | 0.605747 | − | 0.795657i | \(-0.292874\pi\) | ||||
0.605747 | + | 0.795657i | \(0.292874\pi\) | |||||||
\(740\) | −1.59439 | −0.0586111 | ||||||||
\(741\) | −20.3679 | −0.748234 | ||||||||
\(742\) | −30.9575 | −1.13648 | ||||||||
\(743\) | −23.2758 | −0.853905 | −0.426953 | − | 0.904274i | \(-0.640413\pi\) | ||||
−0.426953 | + | 0.904274i | \(0.640413\pi\) | |||||||
\(744\) | −16.1240 | −0.591135 | ||||||||
\(745\) | −1.81050 | −0.0663318 | ||||||||
\(746\) | −9.54149 | −0.349339 | ||||||||
\(747\) | −11.0497 | −0.404288 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.23408 | 0.0816316 | ||||||||
\(750\) | 1.23396 | 0.0450577 | ||||||||
\(751\) | −9.18396 | −0.335127 | −0.167564 | − | 0.985861i | \(-0.553590\pi\) | ||||
−0.167564 | + | 0.985861i | \(0.553590\pi\) | |||||||
\(752\) | 26.9609 | 0.983164 | ||||||||
\(753\) | 17.4132 | 0.634573 | ||||||||
\(754\) | −7.51552 | −0.273699 | ||||||||
\(755\) | 20.0387 | 0.729282 | ||||||||
\(756\) | −1.81050 | −0.0658474 | ||||||||
\(757\) | −47.2523 | −1.71741 | −0.858706 | − | 0.512468i | \(-0.828731\pi\) | ||||
−0.858706 | + | 0.512468i | \(0.828731\pi\) | |||||||
\(758\) | 0.419641 | 0.0152420 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −25.2293 | −0.915161 | ||||||||
\(761\) | −49.9941 | −1.81229 | −0.906143 | − | 0.422972i | \(-0.860987\pi\) | ||||
−0.906143 | + | 0.422972i | \(0.860987\pi\) | |||||||
\(762\) | 15.0453 | 0.545034 | ||||||||
\(763\) | 18.1637 | 0.657571 | ||||||||
\(764\) | −11.1764 | −0.404346 | ||||||||
\(765\) | 6.52105 | 0.235769 | ||||||||
\(766\) | −38.3120 | −1.38427 | ||||||||
\(767\) | −25.1331 | −0.907504 | ||||||||
\(768\) | 10.7519 | 0.387976 | ||||||||
\(769\) | 4.53874 | 0.163671 | 0.0818357 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818357 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4334 | 0.663864 | ||||||||
\(772\) | −11.0948 | −0.399312 | ||||||||
\(773\) | −31.3352 | −1.12705 | −0.563525 | − | 0.826099i | \(-0.690555\pi\) | ||||
−0.563525 | + | 0.826099i | \(0.690555\pi\) | |||||||
\(774\) | 14.8641 | 0.534280 | ||||||||
\(775\) | 5.27455 | 0.189467 | ||||||||
\(776\) | 40.5029 | 1.45397 | ||||||||
\(777\) | 12.6683 | 0.454471 | ||||||||
\(778\) | 30.0037 | 1.07568 | ||||||||
\(779\) | −28.5896 | −1.02433 | ||||||||
\(780\) | −1.17806 | −0.0421814 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 18.8299 | 0.673355 | ||||||||
\(783\) | 2.46791 | 0.0881960 | ||||||||
\(784\) | −20.8078 | −0.743135 | ||||||||
\(785\) | −14.5693 | −0.520002 | ||||||||
\(786\) | 4.27455 | 0.152468 | ||||||||
\(787\) | 5.59323 | 0.199377 | 0.0996886 | − | 0.995019i | \(-0.468215\pi\) | ||||
0.0996886 | + | 0.995019i | \(0.468215\pi\) | |||||||
\(788\) | 0.951067 | 0.0338803 | ||||||||
\(789\) | 2.06075 | 0.0733648 | ||||||||
\(790\) | −11.9156 | −0.423939 | ||||||||
\(791\) | −70.2581 | −2.49809 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.4557 | −0.584360 | ||||||||
\(794\) | −12.7033 | −0.450824 | ||||||||
\(795\) | 6.61463 | 0.234597 | ||||||||
\(796\) | −4.16511 | −0.147629 | ||||||||
\(797\) | −32.4585 | −1.14974 | −0.574870 | − | 0.818245i | \(-0.694947\pi\) | ||||
−0.574870 | + | 0.818245i | \(0.694947\pi\) | |||||||
\(798\) | 38.6258 | 1.36734 | ||||||||
\(799\) | −62.4020 | −2.20763 | ||||||||
\(800\) | −2.63730 | −0.0932427 | ||||||||
\(801\) | 10.2745 | 0.363033 | ||||||||
\(802\) | 23.7281 | 0.837867 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.59439 | 0.0562299 | ||||||||
\(805\) | 8.87546 | 0.312819 | ||||||||
\(806\) | 16.0626 | 0.565780 | ||||||||
\(807\) | −3.45090 | −0.121477 | ||||||||
\(808\) | −6.09059 | −0.214266 | ||||||||
\(809\) | 41.9128 | 1.47358 | 0.736788 | − | 0.676124i | \(-0.236342\pi\) | ||||
0.736788 | + | 0.676124i | \(0.236342\pi\) | |||||||
\(810\) | −1.23396 | −0.0433568 | ||||||||
\(811\) | 28.4285 | 0.998260 | 0.499130 | − | 0.866527i | \(-0.333653\pi\) | ||||
0.499130 | + | 0.866527i | \(0.333653\pi\) | |||||||
\(812\) | −4.46817 | −0.156802 | ||||||||
\(813\) | −21.2167 | −0.744103 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.88918 | −0.206289 | ||||||||
\(816\) | 18.3726 | 0.643169 | ||||||||
\(817\) | 99.4160 | 3.47813 | ||||||||
\(818\) | 8.05912 | 0.281781 | ||||||||
\(819\) | 9.36031 | 0.327076 | ||||||||
\(820\) | −1.65360 | −0.0577461 | ||||||||
\(821\) | 53.6401 | 1.87205 | 0.936026 | − | 0.351931i | \(-0.114475\pi\) | ||||
0.936026 | + | 0.351931i | \(0.114475\pi\) | |||||||
\(822\) | 9.79079 | 0.341493 | ||||||||
\(823\) | −11.1561 | −0.388878 | −0.194439 | − | 0.980915i | \(-0.562289\pi\) | ||||
−0.194439 | + | 0.980915i | \(0.562289\pi\) | |||||||
\(824\) | −4.93582 | −0.171948 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 47.6625 | 1.65839 | ||||||||
\(827\) | 27.8496 | 0.968424 | 0.484212 | − | 0.874951i | \(-0.339106\pi\) | ||||
0.484212 | + | 0.874951i | \(0.339106\pi\) | |||||||
\(828\) | 1.11704 | 0.0388199 | ||||||||
\(829\) | 39.4084 | 1.36871 | 0.684355 | − | 0.729149i | \(-0.260084\pi\) | ||||
0.684355 | + | 0.729149i | \(0.260084\pi\) | |||||||
\(830\) | 13.6349 | 0.473273 | ||||||||
\(831\) | −4.13159 | −0.143323 | ||||||||
\(832\) | −21.9377 | −0.760553 | ||||||||
\(833\) | 48.1604 | 1.66866 | ||||||||
\(834\) | 7.62864 | 0.264158 | ||||||||
\(835\) | 22.8454 | 0.790596 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.27455 | −0.182315 | ||||||||
\(838\) | −34.1655 | −1.18023 | ||||||||
\(839\) | 35.8188 | 1.23660 | 0.618301 | − | 0.785941i | \(-0.287821\pi\) | ||||
0.618301 | + | 0.785941i | \(0.287821\pi\) | |||||||
\(840\) | 11.5944 | 0.400045 | ||||||||
\(841\) | −22.9094 | −0.789980 | ||||||||
\(842\) | 13.7755 | 0.474737 | ||||||||
\(843\) | 23.0956 | 0.795455 | ||||||||
\(844\) | −7.66818 | −0.263950 | ||||||||
\(845\) | −6.90941 | −0.237691 | ||||||||
\(846\) | 11.8081 | 0.405972 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 18.6362 | 0.639971 | ||||||||
\(849\) | −24.7593 | −0.849737 | ||||||||
\(850\) | −8.04668 | −0.275999 | ||||||||
\(851\) | −7.81604 | −0.267930 | ||||||||
\(852\) | 3.45090 | 0.118226 | ||||||||
\(853\) | 27.4091 | 0.938469 | 0.469234 | − | 0.883074i | \(-0.344530\pi\) | ||||
0.469234 | + | 0.883074i | \(0.344530\pi\) | |||||||
\(854\) | 31.2067 | 1.06787 | ||||||||
\(855\) | −8.25310 | −0.282250 | ||||||||
\(856\) | −1.80064 | −0.0615445 | ||||||||
\(857\) | −9.82824 | −0.335726 | −0.167863 | − | 0.985810i | \(-0.553687\pi\) | ||||
−0.167863 | + | 0.985810i | \(0.553687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.9825 | −1.15947 | −0.579735 | − | 0.814805i | \(-0.696844\pi\) | ||||
−0.579735 | + | 0.814805i | \(0.696844\pi\) | |||||||
\(860\) | 5.75014 | 0.196078 | ||||||||
\(861\) | 13.1387 | 0.447764 | ||||||||
\(862\) | 16.4865 | 0.561534 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 2.63730 | 0.0897229 | ||||||||
\(865\) | 12.5214 | 0.425742 | ||||||||
\(866\) | −23.7530 | −0.807161 | ||||||||
\(867\) | −25.5240 | −0.866842 | ||||||||
\(868\) | 9.54960 | 0.324134 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.04530 | −0.103245 | ||||||||
\(871\) | −8.24302 | −0.279304 | ||||||||
\(872\) | −14.6397 | −0.495762 | ||||||||
\(873\) | 13.2495 | 0.448427 | ||||||||
\(874\) | −23.8313 | −0.806104 | ||||||||
\(875\) | −3.79281 | −0.128220 | ||||||||
\(876\) | −4.64217 | −0.156844 | ||||||||
\(877\) | 42.8941 | 1.44843 | 0.724216 | − | 0.689574i | \(-0.242202\pi\) | ||||
0.724216 | + | 0.689574i | \(0.242202\pi\) | |||||||
\(878\) | 26.7241 | 0.901893 | ||||||||
\(879\) | 7.33536 | 0.247416 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.7282 | −0.597279 | −0.298640 | − | 0.954366i | \(-0.596533\pi\) | ||||
−0.298640 | + | 0.954366i | \(0.596533\pi\) | |||||||
\(882\) | −9.11323 | −0.306858 | ||||||||
\(883\) | −0.201414 | −0.00677813 | −0.00338907 | − | 0.999994i | \(-0.501079\pi\) | ||||
−0.00338907 | + | 0.999994i | \(0.501079\pi\) | |||||||
\(884\) | 7.68221 | 0.258381 | ||||||||
\(885\) | −10.1840 | −0.342330 | ||||||||
\(886\) | −1.40506 | −0.0472039 | ||||||||
\(887\) | 43.0409 | 1.44517 | 0.722587 | − | 0.691280i | \(-0.242953\pi\) | ||||
0.722587 | + | 0.691280i | \(0.242953\pi\) | |||||||
\(888\) | −10.2104 | −0.342640 | ||||||||
\(889\) | −46.2447 | −1.55100 | ||||||||
\(890\) | −12.6783 | −0.424979 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.28216 | 0.176860 | ||||||||
\(893\) | 78.9766 | 2.64285 | ||||||||
\(894\) | −2.23408 | −0.0747189 | ||||||||
\(895\) | −3.04530 | −0.101793 | ||||||||
\(896\) | 21.5972 | 0.721511 | ||||||||
\(897\) | −5.77511 | −0.192825 | ||||||||
\(898\) | 0.111785 | 0.00373031 | ||||||||
\(899\) | −13.0171 | −0.434145 | ||||||||
\(900\) | −0.477352 | −0.0159117 | ||||||||
\(901\) | −43.1343 | −1.43701 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.6878 | −1.52039 | ||||||||
\(904\) | 56.6269 | 1.88338 | ||||||||
\(905\) | 4.38537 | 0.145775 | ||||||||
\(906\) | 24.7268 | 0.821494 | ||||||||
\(907\) | −0.204192 | −0.00678008 | −0.00339004 | − | 0.999994i | \(-0.501079\pi\) | ||||
−0.00339004 | + | 0.999994i | \(0.501079\pi\) | |||||||
\(908\) | −7.34956 | −0.243904 | ||||||||
\(909\) | −1.99238 | −0.0660830 | ||||||||
\(910\) | −11.5502 | −0.382886 | ||||||||
\(911\) | −32.9547 | −1.09184 | −0.545919 | − | 0.837838i | \(-0.683819\pi\) | ||||
−0.545919 | + | 0.837838i | \(0.683819\pi\) | |||||||
\(912\) | −23.2525 | −0.769968 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.08576 | 0.168222 | ||||||||
\(915\) | −6.66788 | −0.220433 | ||||||||
\(916\) | −2.24605 | −0.0742115 | ||||||||
\(917\) | −13.1387 | −0.433877 | ||||||||
\(918\) | 8.04668 | 0.265580 | ||||||||
\(919\) | 50.8435 | 1.67717 | 0.838586 | − | 0.544770i | \(-0.183383\pi\) | ||||
0.838586 | + | 0.544770i | \(0.183383\pi\) | |||||||
\(920\) | −7.15349 | −0.235843 | ||||||||
\(921\) | 22.7669 | 0.750195 | ||||||||
\(922\) | −8.32467 | −0.274159 | ||||||||
\(923\) | −17.8412 | −0.587249 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.34008 | 0.109821 | ||||||||
\(926\) | 25.2948 | 0.831240 | ||||||||
\(927\) | −1.61463 | −0.0530313 | ||||||||
\(928\) | 6.50863 | 0.213656 | ||||||||
\(929\) | 48.5394 | 1.59253 | 0.796264 | − | 0.604950i | \(-0.206807\pi\) | ||||
0.796264 | + | 0.604950i | \(0.206807\pi\) | |||||||
\(930\) | 6.50856 | 0.213424 | ||||||||
\(931\) | −60.9522 | −1.99763 | ||||||||
\(932\) | −7.12256 | −0.233307 | ||||||||
\(933\) | 25.5443 | 0.836282 | ||||||||
\(934\) | 5.92124 | 0.193749 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.54427 | −0.246592 | ||||||||
\(937\) | −10.3573 | −0.338357 | −0.169178 | − | 0.985585i | \(-0.554111\pi\) | ||||
−0.169178 | + | 0.985585i | \(0.554111\pi\) | |||||||
\(938\) | 15.6321 | 0.510406 | ||||||||
\(939\) | 34.7735 | 1.13479 | ||||||||
\(940\) | 4.56794 | 0.148990 | ||||||||
\(941\) | −48.9528 | −1.59582 | −0.797908 | − | 0.602779i | \(-0.794060\pi\) | ||||
−0.797908 | + | 0.602779i | \(0.794060\pi\) | |||||||
\(942\) | −17.9779 | −0.585752 | ||||||||
\(943\) | −8.10627 | −0.263976 | ||||||||
\(944\) | −28.6926 | −0.933864 | ||||||||
\(945\) | 3.79281 | 0.123380 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.5213 | −0.666851 | −0.333426 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333426 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(948\) | 4.60953 | 0.149710 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 10.1840 | 0.330411 | ||||||||
\(951\) | 5.38537 | 0.174633 | ||||||||
\(952\) | −75.6076 | −2.45046 | ||||||||
\(953\) | −11.2066 | −0.363018 | −0.181509 | − | 0.983389i | \(-0.558098\pi\) | ||||
−0.181509 | + | 0.983389i | \(0.558098\pi\) | |||||||
\(954\) | 8.16216 | 0.264260 | ||||||||
\(955\) | 23.4132 | 0.757634 | ||||||||
\(956\) | 5.43632 | 0.175823 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.5944 | −0.374598 | ||||||||
\(959\) | −30.0939 | −0.971783 | ||||||||
\(960\) | −8.88918 | −0.286897 | ||||||||
\(961\) | −3.17913 | −0.102553 | ||||||||
\(962\) | 10.1715 | 0.327943 | ||||||||
\(963\) | −0.589032 | −0.0189813 | ||||||||
\(964\) | −5.78278 | −0.186251 | ||||||||
\(965\) | 23.2424 | 0.748201 | ||||||||
\(966\) | 10.9519 | 0.352372 | ||||||||
\(967\) | −5.76022 | −0.185236 | −0.0926181 | − | 0.995702i | \(-0.529524\pi\) | ||||
−0.0926181 | + | 0.995702i | \(0.529524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.8188 | 1.72891 | ||||||||
\(970\) | −16.3493 | −0.524944 | ||||||||
\(971\) | 14.9547 | 0.479919 | 0.239960 | − | 0.970783i | \(-0.422866\pi\) | ||||
0.239960 | + | 0.970783i | \(0.422866\pi\) | |||||||
\(972\) | 0.477352 | 0.0153111 | ||||||||
\(973\) | −23.4481 | −0.751712 | ||||||||
\(974\) | 29.7302 | 0.952616 | ||||||||
\(975\) | 2.46791 | 0.0790364 | ||||||||
\(976\) | −18.7863 | −0.601334 | ||||||||
\(977\) | 14.7457 | 0.471756 | 0.235878 | − | 0.971783i | \(-0.424203\pi\) | ||||
0.235878 | + | 0.971783i | \(0.424203\pi\) | |||||||
\(978\) | −7.26699 | −0.232373 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.52543 | −0.112616 | ||||||||
\(981\) | −4.78899 | −0.152901 | ||||||||
\(982\) | −8.18674 | −0.261249 | ||||||||
\(983\) | 34.8892 | 1.11279 | 0.556396 | − | 0.830917i | \(-0.312184\pi\) | ||||
0.556396 | + | 0.830917i | \(0.312184\pi\) | |||||||
\(984\) | −10.5896 | −0.337583 | ||||||||
\(985\) | −1.99238 | −0.0634825 | ||||||||
\(986\) | 19.8585 | 0.632424 | ||||||||
\(987\) | −36.2946 | −1.15527 | ||||||||
\(988\) | −9.72267 | −0.309319 | ||||||||
\(989\) | 28.1883 | 0.896337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5289 | −0.493291 | −0.246645 | − | 0.969106i | \(-0.579328\pi\) | ||||
−0.246645 | + | 0.969106i | \(0.579328\pi\) | |||||||
\(992\) | −13.9106 | −0.441662 | ||||||||
\(993\) | −19.8641 | −0.630369 | ||||||||
\(994\) | 33.8340 | 1.07315 | ||||||||
\(995\) | 8.72545 | 0.276615 | ||||||||
\(996\) | −5.27461 | −0.167132 | ||||||||
\(997\) | 3.63590 | 0.115150 | 0.0575750 | − | 0.998341i | \(-0.481663\pi\) | ||||
0.0575750 | + | 0.998341i | \(0.481663\pi\) | |||||||
\(998\) | −27.3491 | −0.865720 | ||||||||
\(999\) | −3.34008 | −0.105675 |
(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 | 1815.2.a.y.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 5445.2.a.bz.1.4 | 6 | |||
5.4 | even | 2 | 9075.2.a.dq.1.4 | 6 | |||
11.10 | odd | 2 | inner | 1815.2.a.y.1.4 | yes | 6 | |
33.32 | even | 2 | 5445.2.a.bz.1.3 | 6 | |||
55.54 | odd | 2 | 9075.2.a.dq.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.y.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1815.2.a.y.1.4 | yes | 6 | 11.10 | odd | 2 | inner | |
5445.2.a.bz.1.3 | 6 | 33.32 | even | 2 | |||
5445.2.a.bz.1.4 | 6 | 3.2 | odd | 2 | |||
9075.2.a.dq.1.3 | 6 | 55.54 | odd | 2 | |||
9075.2.a.dq.1.4 | 6 | 5.4 | even | 2 |