Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.182130\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.182130 | 0.128785 | 0.0643927 | − | 0.997925i | \(-0.479489\pi\) | ||||
0.0643927 | + | 0.997925i | \(0.479489\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.96683 | −0.983414 | ||||||||
\(5\) | 1.12886 | 0.504841 | 0.252420 | − | 0.967618i | \(-0.418773\pi\) | ||||
0.252420 | + | 0.967618i | \(0.418773\pi\) | |||||||
\(6\) | 0.182130 | 0.0743543 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.722479 | −0.255435 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.205599 | 0.0650161 | ||||||||
\(11\) | 4.01616 | 1.21092 | 0.605459 | − | 0.795877i | \(-0.292990\pi\) | ||||
0.605459 | + | 0.795877i | \(0.292990\pi\) | |||||||
\(12\) | −1.96683 | −0.567775 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.182130 | −0.0486763 | ||||||||
\(15\) | 1.12886 | 0.291470 | ||||||||
\(16\) | 3.80207 | 0.950518 | ||||||||
\(17\) | 3.02631 | 0.733988 | 0.366994 | − | 0.930223i | \(-0.380387\pi\) | ||||
0.366994 | + | 0.930223i | \(0.380387\pi\) | |||||||
\(18\) | 0.182130 | 0.0429285 | ||||||||
\(19\) | 5.30303 | 1.21660 | 0.608300 | − | 0.793708i | \(-0.291852\pi\) | ||||
0.608300 | + | 0.793708i | \(0.291852\pi\) | |||||||
\(20\) | −2.22027 | −0.496468 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.731463 | 0.155948 | ||||||||
\(23\) | −2.17379 | −0.453267 | −0.226634 | − | 0.973980i | \(-0.572772\pi\) | ||||
−0.226634 | + | 0.973980i | \(0.572772\pi\) | |||||||
\(24\) | −0.722479 | −0.147475 | ||||||||
\(25\) | −3.72568 | −0.745136 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.96683 | 0.371696 | ||||||||
\(29\) | 3.53344 | 0.656143 | 0.328072 | − | 0.944653i | \(-0.393601\pi\) | ||||
0.328072 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(30\) | 0.205599 | 0.0375371 | ||||||||
\(31\) | −4.85911 | −0.872721 | −0.436361 | − | 0.899772i | \(-0.643733\pi\) | ||||
−0.436361 | + | 0.899772i | \(0.643733\pi\) | |||||||
\(32\) | 2.13743 | 0.377848 | ||||||||
\(33\) | 4.01616 | 0.699123 | ||||||||
\(34\) | 0.551182 | 0.0945269 | ||||||||
\(35\) | −1.12886 | −0.190812 | ||||||||
\(36\) | −1.96683 | −0.327805 | ||||||||
\(37\) | −6.38019 | −1.04890 | −0.524448 | − | 0.851442i | \(-0.675728\pi\) | ||||
−0.524448 | + | 0.851442i | \(0.675728\pi\) | |||||||
\(38\) | 0.965841 | 0.156680 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.815576 | −0.128954 | ||||||||
\(41\) | 4.76127 | 0.743586 | 0.371793 | − | 0.928316i | \(-0.378743\pi\) | ||||
0.371793 | + | 0.928316i | \(0.378743\pi\) | |||||||
\(42\) | −0.182130 | −0.0281033 | ||||||||
\(43\) | −2.34151 | −0.357077 | −0.178538 | − | 0.983933i | \(-0.557137\pi\) | ||||
−0.178538 | + | 0.983933i | \(0.557137\pi\) | |||||||
\(44\) | −7.89910 | −1.19083 | ||||||||
\(45\) | 1.12886 | 0.168280 | ||||||||
\(46\) | −0.395913 | −0.0583742 | ||||||||
\(47\) | −9.81123 | −1.43111 | −0.715557 | − | 0.698554i | \(-0.753827\pi\) | ||||
−0.715557 | + | 0.698554i | \(0.753827\pi\) | |||||||
\(48\) | 3.80207 | 0.548782 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.678558 | −0.0959626 | ||||||||
\(51\) | 3.02631 | 0.423768 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.98129 | 0.409512 | 0.204756 | − | 0.978813i | \(-0.434360\pi\) | ||||
0.204756 | + | 0.978813i | \(0.434360\pi\) | |||||||
\(54\) | 0.182130 | 0.0247848 | ||||||||
\(55\) | 4.53367 | 0.611321 | ||||||||
\(56\) | 0.722479 | 0.0965453 | ||||||||
\(57\) | 5.30303 | 0.702404 | ||||||||
\(58\) | 0.643546 | 0.0845017 | ||||||||
\(59\) | 11.4726 | 1.49361 | 0.746803 | − | 0.665046i | \(-0.231588\pi\) | ||||
0.746803 | + | 0.665046i | \(0.231588\pi\) | |||||||
\(60\) | −2.22027 | −0.286636 | ||||||||
\(61\) | 4.70310 | 0.602170 | 0.301085 | − | 0.953597i | \(-0.402651\pi\) | ||||
0.301085 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(62\) | −0.884989 | −0.112394 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −7.21485 | −0.901857 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.731463 | 0.0900369 | ||||||||
\(67\) | −1.77088 | −0.216347 | −0.108174 | − | 0.994132i | \(-0.534500\pi\) | ||||
−0.108174 | + | 0.994132i | \(0.534500\pi\) | |||||||
\(68\) | −5.95223 | −0.721814 | ||||||||
\(69\) | −2.17379 | −0.261694 | ||||||||
\(70\) | −0.205599 | −0.0245738 | ||||||||
\(71\) | 3.24776 | 0.385438 | 0.192719 | − | 0.981254i | \(-0.438269\pi\) | ||||
0.192719 | + | 0.981254i | \(0.438269\pi\) | |||||||
\(72\) | −0.722479 | −0.0851449 | ||||||||
\(73\) | −7.80784 | −0.913838 | −0.456919 | − | 0.889508i | \(-0.651047\pi\) | ||||
−0.456919 | + | 0.889508i | \(0.651047\pi\) | |||||||
\(74\) | −1.16202 | −0.135083 | ||||||||
\(75\) | −3.72568 | −0.430204 | ||||||||
\(76\) | −10.4302 | −1.19642 | ||||||||
\(77\) | −4.01616 | −0.457684 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.4983 | 1.96871 | 0.984354 | − | 0.176200i | \(-0.0563805\pi\) | ||||
0.984354 | + | 0.176200i | \(0.0563805\pi\) | |||||||
\(80\) | 4.29200 | 0.479860 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.867171 | 0.0957630 | ||||||||
\(83\) | −0.705610 | −0.0774508 | −0.0387254 | − | 0.999250i | \(-0.512330\pi\) | ||||
−0.0387254 | + | 0.999250i | \(0.512330\pi\) | |||||||
\(84\) | 1.96683 | 0.214599 | ||||||||
\(85\) | 3.41627 | 0.370547 | ||||||||
\(86\) | −0.426459 | −0.0459863 | ||||||||
\(87\) | 3.53344 | 0.378825 | ||||||||
\(88\) | −2.90159 | −0.309310 | ||||||||
\(89\) | 13.0567 | 1.38401 | 0.692004 | − | 0.721894i | \(-0.256728\pi\) | ||||
0.692004 | + | 0.721894i | \(0.256728\pi\) | |||||||
\(90\) | 0.205599 | 0.0216720 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.27548 | 0.445750 | ||||||||
\(93\) | −4.85911 | −0.503866 | ||||||||
\(94\) | −1.78692 | −0.184307 | ||||||||
\(95\) | 5.98637 | 0.614189 | ||||||||
\(96\) | 2.13743 | 0.218150 | ||||||||
\(97\) | 1.76727 | 0.179439 | 0.0897195 | − | 0.995967i | \(-0.471403\pi\) | ||||
0.0897195 | + | 0.995967i | \(0.471403\pi\) | |||||||
\(98\) | 0.182130 | 0.0183979 | ||||||||
\(99\) | 4.01616 | 0.403639 | ||||||||
\(100\) | 7.32777 | 0.732777 | ||||||||
\(101\) | 15.3230 | 1.52469 | 0.762347 | − | 0.647169i | \(-0.224047\pi\) | ||||
0.762347 | + | 0.647169i | \(0.224047\pi\) | |||||||
\(102\) | 0.551182 | 0.0545751 | ||||||||
\(103\) | 8.19962 | 0.807933 | 0.403966 | − | 0.914774i | \(-0.367631\pi\) | ||||
0.403966 | + | 0.914774i | \(0.367631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.12886 | −0.110165 | ||||||||
\(106\) | 0.542982 | 0.0527391 | ||||||||
\(107\) | 16.8953 | 1.63333 | 0.816664 | − | 0.577114i | \(-0.195821\pi\) | ||||
0.816664 | + | 0.577114i | \(0.195821\pi\) | |||||||
\(108\) | −1.96683 | −0.189258 | ||||||||
\(109\) | 5.62135 | 0.538427 | 0.269214 | − | 0.963080i | \(-0.413236\pi\) | ||||
0.269214 | + | 0.963080i | \(0.413236\pi\) | |||||||
\(110\) | 0.825718 | 0.0787291 | ||||||||
\(111\) | −6.38019 | −0.605581 | ||||||||
\(112\) | −3.80207 | −0.359262 | ||||||||
\(113\) | −2.71753 | −0.255644 | −0.127822 | − | 0.991797i | \(-0.540799\pi\) | ||||
−0.127822 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(114\) | 0.965841 | 0.0904593 | ||||||||
\(115\) | −2.45391 | −0.228828 | ||||||||
\(116\) | −6.94967 | −0.645261 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.08950 | 0.192354 | ||||||||
\(119\) | −3.02631 | −0.277421 | ||||||||
\(120\) | −0.815576 | −0.0744516 | ||||||||
\(121\) | 5.12953 | 0.466321 | ||||||||
\(122\) | 0.856575 | 0.0775507 | ||||||||
\(123\) | 4.76127 | 0.429310 | ||||||||
\(124\) | 9.55703 | 0.858247 | ||||||||
\(125\) | −9.85006 | −0.881016 | ||||||||
\(126\) | −0.182130 | −0.0162254 | ||||||||
\(127\) | 11.6456 | 1.03338 | 0.516691 | − | 0.856172i | \(-0.327164\pi\) | ||||
0.516691 | + | 0.856172i | \(0.327164\pi\) | |||||||
\(128\) | −5.58890 | −0.493994 | ||||||||
\(129\) | −2.34151 | −0.206158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7907 | 1.29227 | 0.646133 | − | 0.763225i | \(-0.276385\pi\) | ||||
0.646133 | + | 0.763225i | \(0.276385\pi\) | |||||||
\(132\) | −7.89910 | −0.687528 | ||||||||
\(133\) | −5.30303 | −0.459831 | ||||||||
\(134\) | −0.322530 | −0.0278623 | ||||||||
\(135\) | 1.12886 | 0.0971567 | ||||||||
\(136\) | −2.18644 | −0.187486 | ||||||||
\(137\) | 15.4499 | 1.31998 | 0.659989 | − | 0.751276i | \(-0.270561\pi\) | ||||
0.659989 | + | 0.751276i | \(0.270561\pi\) | |||||||
\(138\) | −0.395913 | −0.0337024 | ||||||||
\(139\) | −11.4715 | −0.973001 | −0.486501 | − | 0.873680i | \(-0.661727\pi\) | ||||
−0.486501 | + | 0.873680i | \(0.661727\pi\) | |||||||
\(140\) | 2.22027 | 0.187647 | ||||||||
\(141\) | −9.81123 | −0.826254 | ||||||||
\(142\) | 0.591514 | 0.0496388 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.80207 | 0.316839 | ||||||||
\(145\) | 3.98875 | 0.331248 | ||||||||
\(146\) | −1.42204 | −0.117689 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 12.5487 | 1.03150 | ||||||||
\(149\) | −2.99238 | −0.245146 | −0.122573 | − | 0.992460i | \(-0.539114\pi\) | ||||
−0.122573 | + | 0.992460i | \(0.539114\pi\) | |||||||
\(150\) | −0.678558 | −0.0554040 | ||||||||
\(151\) | 0.860674 | 0.0700407 | 0.0350203 | − | 0.999387i | \(-0.488850\pi\) | ||||
0.0350203 | + | 0.999387i | \(0.488850\pi\) | |||||||
\(152\) | −3.83133 | −0.310762 | ||||||||
\(153\) | 3.02631 | 0.244663 | ||||||||
\(154\) | −0.731463 | −0.0589430 | ||||||||
\(155\) | −5.48525 | −0.440585 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.62432 | −0.369061 | −0.184530 | − | 0.982827i | \(-0.559076\pi\) | ||||
−0.184530 | + | 0.982827i | \(0.559076\pi\) | |||||||
\(158\) | 3.18696 | 0.253541 | ||||||||
\(159\) | 2.98129 | 0.236432 | ||||||||
\(160\) | 2.41285 | 0.190753 | ||||||||
\(161\) | 2.17379 | 0.171319 | ||||||||
\(162\) | 0.182130 | 0.0143095 | ||||||||
\(163\) | −23.0446 | −1.80499 | −0.902496 | − | 0.430698i | \(-0.858267\pi\) | ||||
−0.902496 | + | 0.430698i | \(0.858267\pi\) | |||||||
\(164\) | −9.36461 | −0.731253 | ||||||||
\(165\) | 4.53367 | 0.352946 | ||||||||
\(166\) | −0.128513 | −0.00997453 | ||||||||
\(167\) | 3.47296 | 0.268745 | 0.134373 | − | 0.990931i | \(-0.457098\pi\) | ||||
0.134373 | + | 0.990931i | \(0.457098\pi\) | |||||||
\(168\) | 0.722479 | 0.0557404 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.622206 | 0.0477210 | ||||||||
\(171\) | 5.30303 | 0.405533 | ||||||||
\(172\) | 4.60535 | 0.351154 | ||||||||
\(173\) | 19.7442 | 1.50112 | 0.750560 | − | 0.660802i | \(-0.229784\pi\) | ||||
0.750560 | + | 0.660802i | \(0.229784\pi\) | |||||||
\(174\) | 0.643546 | 0.0487871 | ||||||||
\(175\) | 3.72568 | 0.281635 | ||||||||
\(176\) | 15.2697 | 1.15100 | ||||||||
\(177\) | 11.4726 | 0.862333 | ||||||||
\(178\) | 2.37802 | 0.178240 | ||||||||
\(179\) | 19.0553 | 1.42426 | 0.712129 | − | 0.702049i | \(-0.247731\pi\) | ||||
0.712129 | + | 0.702049i | \(0.247731\pi\) | |||||||
\(180\) | −2.22027 | −0.165489 | ||||||||
\(181\) | −3.45717 | −0.256969 | −0.128485 | − | 0.991712i | \(-0.541011\pi\) | ||||
−0.128485 | + | 0.991712i | \(0.541011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.70310 | 0.347663 | ||||||||
\(184\) | 1.57052 | 0.115780 | ||||||||
\(185\) | −7.20233 | −0.529526 | ||||||||
\(186\) | −0.884989 | −0.0648906 | ||||||||
\(187\) | 12.1541 | 0.888798 | ||||||||
\(188\) | 19.2970 | 1.40738 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.09030 | 0.0790986 | ||||||||
\(191\) | −21.0189 | −1.52087 | −0.760437 | − | 0.649411i | \(-0.775015\pi\) | ||||
−0.760437 | + | 0.649411i | \(0.775015\pi\) | |||||||
\(192\) | −7.21485 | −0.520687 | ||||||||
\(193\) | −18.9411 | −1.36341 | −0.681704 | − | 0.731628i | \(-0.738761\pi\) | ||||
−0.681704 | + | 0.731628i | \(0.738761\pi\) | |||||||
\(194\) | 0.321873 | 0.0231091 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.96683 | −0.140488 | ||||||||
\(197\) | −8.43497 | −0.600966 | −0.300483 | − | 0.953787i | \(-0.597148\pi\) | ||||
−0.300483 | + | 0.953787i | \(0.597148\pi\) | |||||||
\(198\) | 0.731463 | 0.0519828 | ||||||||
\(199\) | 20.3783 | 1.44458 | 0.722291 | − | 0.691590i | \(-0.243089\pi\) | ||||
0.722291 | + | 0.691590i | \(0.243089\pi\) | |||||||
\(200\) | 2.69172 | 0.190334 | ||||||||
\(201\) | −1.77088 | −0.124908 | ||||||||
\(202\) | 2.79077 | 0.196358 | ||||||||
\(203\) | −3.53344 | −0.247999 | ||||||||
\(204\) | −5.95223 | −0.416740 | ||||||||
\(205\) | 5.37481 | 0.375393 | ||||||||
\(206\) | 1.49340 | 0.104050 | ||||||||
\(207\) | −2.17379 | −0.151089 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.2978 | 1.47320 | ||||||||
\(210\) | −0.205599 | −0.0141877 | ||||||||
\(211\) | 24.7518 | 1.70398 | 0.851992 | − | 0.523555i | \(-0.175394\pi\) | ||||
0.851992 | + | 0.523555i | \(0.175394\pi\) | |||||||
\(212\) | −5.86369 | −0.402720 | ||||||||
\(213\) | 3.24776 | 0.222533 | ||||||||
\(214\) | 3.07714 | 0.210349 | ||||||||
\(215\) | −2.64323 | −0.180267 | ||||||||
\(216\) | −0.722479 | −0.0491584 | ||||||||
\(217\) | 4.85911 | 0.329858 | ||||||||
\(218\) | 1.02382 | 0.0693416 | ||||||||
\(219\) | −7.80784 | −0.527605 | ||||||||
\(220\) | −8.91696 | −0.601181 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.16202 | −0.0779899 | ||||||||
\(223\) | −24.1397 | −1.61652 | −0.808258 | − | 0.588829i | \(-0.799589\pi\) | ||||
−0.808258 | + | 0.588829i | \(0.799589\pi\) | |||||||
\(224\) | −2.13743 | −0.142813 | ||||||||
\(225\) | −3.72568 | −0.248379 | ||||||||
\(226\) | −0.494944 | −0.0329232 | ||||||||
\(227\) | −20.6751 | −1.37226 | −0.686128 | − | 0.727480i | \(-0.740691\pi\) | ||||
−0.686128 | + | 0.727480i | \(0.740691\pi\) | |||||||
\(228\) | −10.4302 | −0.690754 | ||||||||
\(229\) | −7.17578 | −0.474189 | −0.237094 | − | 0.971487i | \(-0.576195\pi\) | ||||
−0.237094 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(230\) | −0.446930 | −0.0294697 | ||||||||
\(231\) | −4.01616 | −0.264244 | ||||||||
\(232\) | −2.55284 | −0.167602 | ||||||||
\(233\) | −15.9753 | −1.04658 | −0.523288 | − | 0.852156i | \(-0.675295\pi\) | ||||
−0.523288 | + | 0.852156i | \(0.675295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0755 | −0.722485 | ||||||||
\(236\) | −22.5646 | −1.46883 | ||||||||
\(237\) | 17.4983 | 1.13663 | ||||||||
\(238\) | −0.551182 | −0.0357278 | ||||||||
\(239\) | −16.2796 | −1.05304 | −0.526519 | − | 0.850164i | \(-0.676503\pi\) | ||||
−0.526519 | + | 0.850164i | \(0.676503\pi\) | |||||||
\(240\) | 4.29200 | 0.277048 | ||||||||
\(241\) | 23.2533 | 1.49788 | 0.748939 | − | 0.662639i | \(-0.230563\pi\) | ||||
0.748939 | + | 0.662639i | \(0.230563\pi\) | |||||||
\(242\) | 0.934241 | 0.0600553 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.25018 | −0.592182 | ||||||||
\(245\) | 1.12886 | 0.0721201 | ||||||||
\(246\) | 0.867171 | 0.0552888 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.51060 | 0.222923 | ||||||||
\(249\) | −0.705610 | −0.0447162 | ||||||||
\(250\) | −1.79399 | −0.113462 | ||||||||
\(251\) | 3.48547 | 0.220001 | 0.110000 | − | 0.993932i | \(-0.464915\pi\) | ||||
0.110000 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(252\) | 1.96683 | 0.123899 | ||||||||
\(253\) | −8.73030 | −0.548869 | ||||||||
\(254\) | 2.12102 | 0.133084 | ||||||||
\(255\) | 3.41627 | 0.213935 | ||||||||
\(256\) | 13.4118 | 0.838238 | ||||||||
\(257\) | −12.3642 | −0.771260 | −0.385630 | − | 0.922654i | \(-0.626016\pi\) | ||||
−0.385630 | + | 0.922654i | \(0.626016\pi\) | |||||||
\(258\) | −0.426459 | −0.0265502 | ||||||||
\(259\) | 6.38019 | 0.396446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.53344 | 0.218714 | ||||||||
\(262\) | 2.69382 | 0.166425 | ||||||||
\(263\) | −24.7086 | −1.52360 | −0.761800 | − | 0.647813i | \(-0.775684\pi\) | ||||
−0.761800 | + | 0.647813i | \(0.775684\pi\) | |||||||
\(264\) | −2.90159 | −0.178580 | ||||||||
\(265\) | 3.36545 | 0.206738 | ||||||||
\(266\) | −0.965841 | −0.0592195 | ||||||||
\(267\) | 13.0567 | 0.799057 | ||||||||
\(268\) | 3.48301 | 0.212759 | ||||||||
\(269\) | −12.5615 | −0.765887 | −0.382944 | − | 0.923772i | \(-0.625090\pi\) | ||||
−0.382944 | + | 0.923772i | \(0.625090\pi\) | |||||||
\(270\) | 0.205599 | 0.0125124 | ||||||||
\(271\) | 3.82063 | 0.232087 | 0.116044 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116044 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(272\) | 11.5062 | 0.697669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.81390 | 0.169994 | ||||||||
\(275\) | −14.9629 | −0.902298 | ||||||||
\(276\) | 4.27548 | 0.257354 | ||||||||
\(277\) | 20.1591 | 1.21124 | 0.605620 | − | 0.795754i | \(-0.292925\pi\) | ||||
0.605620 | + | 0.795754i | \(0.292925\pi\) | |||||||
\(278\) | −2.08931 | −0.125308 | ||||||||
\(279\) | −4.85911 | −0.290907 | ||||||||
\(280\) | 0.815576 | 0.0487400 | ||||||||
\(281\) | 7.17004 | 0.427729 | 0.213864 | − | 0.976863i | \(-0.431395\pi\) | ||||
0.213864 | + | 0.976863i | \(0.431395\pi\) | |||||||
\(282\) | −1.78692 | −0.106409 | ||||||||
\(283\) | −9.74389 | −0.579214 | −0.289607 | − | 0.957146i | \(-0.593525\pi\) | ||||
−0.289607 | + | 0.957146i | \(0.593525\pi\) | |||||||
\(284\) | −6.38778 | −0.379045 | ||||||||
\(285\) | 5.98637 | 0.354602 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.76127 | −0.281049 | ||||||||
\(288\) | 2.13743 | 0.125949 | ||||||||
\(289\) | −7.84145 | −0.461262 | ||||||||
\(290\) | 0.726472 | 0.0426599 | ||||||||
\(291\) | 1.76727 | 0.103599 | ||||||||
\(292\) | 15.3567 | 0.898681 | ||||||||
\(293\) | 0.348391 | 0.0203532 | 0.0101766 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101766 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(294\) | 0.182130 | 0.0106220 | ||||||||
\(295\) | 12.9509 | 0.754033 | ||||||||
\(296\) | 4.60955 | 0.267925 | ||||||||
\(297\) | 4.01616 | 0.233041 | ||||||||
\(298\) | −0.545003 | −0.0315712 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.32777 | 0.423069 | ||||||||
\(301\) | 2.34151 | 0.134962 | ||||||||
\(302\) | 0.156755 | 0.00902021 | ||||||||
\(303\) | 15.3230 | 0.880282 | ||||||||
\(304\) | 20.1625 | 1.15640 | ||||||||
\(305\) | 5.30913 | 0.304000 | ||||||||
\(306\) | 0.551182 | 0.0315090 | ||||||||
\(307\) | 5.97146 | 0.340809 | 0.170405 | − | 0.985374i | \(-0.445493\pi\) | ||||
0.170405 | + | 0.985374i | \(0.445493\pi\) | |||||||
\(308\) | 7.89910 | 0.450093 | ||||||||
\(309\) | 8.19962 | 0.466460 | ||||||||
\(310\) | −0.999028 | −0.0567410 | ||||||||
\(311\) | −6.16012 | −0.349308 | −0.174654 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174654 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.5210 | 1.27296 | 0.636482 | − | 0.771291i | \(-0.280389\pi\) | ||||
0.636482 | + | 0.771291i | \(0.280389\pi\) | |||||||
\(314\) | −0.842228 | −0.0475296 | ||||||||
\(315\) | −1.12886 | −0.0636040 | ||||||||
\(316\) | −34.4161 | −1.93606 | ||||||||
\(317\) | −30.4700 | −1.71136 | −0.855682 | − | 0.517501i | \(-0.826862\pi\) | ||||
−0.855682 | + | 0.517501i | \(0.826862\pi\) | |||||||
\(318\) | 0.542982 | 0.0304489 | ||||||||
\(319\) | 14.1909 | 0.794535 | ||||||||
\(320\) | −8.14455 | −0.455294 | ||||||||
\(321\) | 16.8953 | 0.943002 | ||||||||
\(322\) | 0.395913 | 0.0220634 | ||||||||
\(323\) | 16.0486 | 0.892969 | ||||||||
\(324\) | −1.96683 | −0.109268 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.19711 | −0.232457 | ||||||||
\(327\) | 5.62135 | 0.310861 | ||||||||
\(328\) | −3.43992 | −0.189938 | ||||||||
\(329\) | 9.81123 | 0.540910 | ||||||||
\(330\) | 0.825718 | 0.0454543 | ||||||||
\(331\) | −1.62675 | −0.0894142 | −0.0447071 | − | 0.999000i | \(-0.514235\pi\) | ||||
−0.0447071 | + | 0.999000i | \(0.514235\pi\) | |||||||
\(332\) | 1.38781 | 0.0761662 | ||||||||
\(333\) | −6.38019 | −0.349632 | ||||||||
\(334\) | 0.632530 | 0.0346105 | ||||||||
\(335\) | −1.99907 | −0.109221 | ||||||||
\(336\) | −3.80207 | −0.207420 | ||||||||
\(337\) | 3.76808 | 0.205261 | 0.102630 | − | 0.994720i | \(-0.467274\pi\) | ||||
0.102630 | + | 0.994720i | \(0.467274\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.71753 | −0.147596 | ||||||||
\(340\) | −6.71923 | −0.364401 | ||||||||
\(341\) | −19.5149 | −1.05679 | ||||||||
\(342\) | 0.965841 | 0.0522267 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.69169 | 0.0912098 | ||||||||
\(345\) | −2.45391 | −0.132114 | ||||||||
\(346\) | 3.59600 | 0.193322 | ||||||||
\(347\) | 11.2926 | 0.606216 | 0.303108 | − | 0.952956i | \(-0.401976\pi\) | ||||
0.303108 | + | 0.952956i | \(0.401976\pi\) | |||||||
\(348\) | −6.94967 | −0.372542 | ||||||||
\(349\) | 2.74933 | 0.147168 | 0.0735840 | − | 0.997289i | \(-0.476556\pi\) | ||||
0.0735840 | + | 0.997289i | \(0.476556\pi\) | |||||||
\(350\) | 0.678558 | 0.0362704 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.58425 | 0.457542 | ||||||||
\(353\) | 21.6903 | 1.15446 | 0.577229 | − | 0.816582i | \(-0.304134\pi\) | ||||
0.577229 | + | 0.816582i | \(0.304134\pi\) | |||||||
\(354\) | 2.08950 | 0.111056 | ||||||||
\(355\) | 3.66626 | 0.194585 | ||||||||
\(356\) | −25.6803 | −1.36105 | ||||||||
\(357\) | −3.02631 | −0.160169 | ||||||||
\(358\) | 3.47054 | 0.183424 | ||||||||
\(359\) | −25.2837 | −1.33442 | −0.667212 | − | 0.744868i | \(-0.732512\pi\) | ||||
−0.667212 | + | 0.744868i | \(0.732512\pi\) | |||||||
\(360\) | −0.815576 | −0.0429846 | ||||||||
\(361\) | 9.12216 | 0.480114 | ||||||||
\(362\) | −0.629654 | −0.0330939 | ||||||||
\(363\) | 5.12953 | 0.269230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.81394 | −0.461343 | ||||||||
\(366\) | 0.856575 | 0.0447739 | ||||||||
\(367\) | 38.1307 | 1.99041 | 0.995203 | − | 0.0978339i | \(-0.0311914\pi\) | ||||
0.995203 | + | 0.0978339i | \(0.0311914\pi\) | |||||||
\(368\) | −8.26492 | −0.430839 | ||||||||
\(369\) | 4.76127 | 0.247862 | ||||||||
\(370\) | −1.31176 | −0.0681952 | ||||||||
\(371\) | −2.98129 | −0.154781 | ||||||||
\(372\) | 9.55703 | 0.495509 | ||||||||
\(373\) | −26.6379 | −1.37926 | −0.689630 | − | 0.724162i | \(-0.742227\pi\) | ||||
−0.689630 | + | 0.724162i | \(0.742227\pi\) | |||||||
\(374\) | 2.21363 | 0.114464 | ||||||||
\(375\) | −9.85006 | −0.508655 | ||||||||
\(376\) | 7.08840 | 0.365556 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.182130 | −0.00936776 | ||||||||
\(379\) | 6.72882 | 0.345636 | 0.172818 | − | 0.984954i | \(-0.444713\pi\) | ||||
0.172818 | + | 0.984954i | \(0.444713\pi\) | |||||||
\(380\) | −11.7742 | −0.604002 | ||||||||
\(381\) | 11.6456 | 0.596623 | ||||||||
\(382\) | −3.82817 | −0.195866 | ||||||||
\(383\) | 1.17016 | 0.0597924 | 0.0298962 | − | 0.999553i | \(-0.490482\pi\) | ||||
0.0298962 | + | 0.999553i | \(0.490482\pi\) | |||||||
\(384\) | −5.58890 | −0.285207 | ||||||||
\(385\) | −4.53367 | −0.231057 | ||||||||
\(386\) | −3.44974 | −0.175587 | ||||||||
\(387\) | −2.34151 | −0.119026 | ||||||||
\(388\) | −3.47592 | −0.176463 | ||||||||
\(389\) | −21.3343 | −1.08169 | −0.540847 | − | 0.841121i | \(-0.681896\pi\) | ||||
−0.540847 | + | 0.841121i | \(0.681896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.57857 | −0.332693 | ||||||||
\(392\) | −0.722479 | −0.0364907 | ||||||||
\(393\) | 14.7907 | 0.746090 | ||||||||
\(394\) | −1.53626 | −0.0773957 | ||||||||
\(395\) | 19.7531 | 0.993885 | ||||||||
\(396\) | −7.89910 | −0.396944 | ||||||||
\(397\) | −26.3909 | −1.32452 | −0.662262 | − | 0.749273i | \(-0.730403\pi\) | ||||
−0.662262 | + | 0.749273i | \(0.730403\pi\) | |||||||
\(398\) | 3.71151 | 0.186041 | ||||||||
\(399\) | −5.30303 | −0.265484 | ||||||||
\(400\) | −14.1653 | −0.708265 | ||||||||
\(401\) | 11.6178 | 0.580165 | 0.290082 | − | 0.957002i | \(-0.406317\pi\) | ||||
0.290082 | + | 0.957002i | \(0.406317\pi\) | |||||||
\(402\) | −0.322530 | −0.0160863 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −30.1377 | −1.49941 | ||||||||
\(405\) | 1.12886 | 0.0560934 | ||||||||
\(406\) | −0.643546 | −0.0319386 | ||||||||
\(407\) | −25.6239 | −1.27013 | ||||||||
\(408\) | −2.18644 | −0.108245 | ||||||||
\(409\) | 10.8356 | 0.535785 | 0.267893 | − | 0.963449i | \(-0.413673\pi\) | ||||
0.267893 | + | 0.963449i | \(0.413673\pi\) | |||||||
\(410\) | 0.978913 | 0.0483451 | ||||||||
\(411\) | 15.4499 | 0.762089 | ||||||||
\(412\) | −16.1273 | −0.794533 | ||||||||
\(413\) | −11.4726 | −0.564530 | ||||||||
\(414\) | −0.395913 | −0.0194581 | ||||||||
\(415\) | −0.796534 | −0.0391003 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4715 | −0.561763 | ||||||||
\(418\) | 3.87897 | 0.189727 | ||||||||
\(419\) | −37.6639 | −1.84000 | −0.920001 | − | 0.391917i | \(-0.871812\pi\) | ||||
−0.920001 | + | 0.391917i | \(0.871812\pi\) | |||||||
\(420\) | 2.22027 | 0.108338 | ||||||||
\(421\) | −2.59040 | −0.126249 | −0.0631243 | − | 0.998006i | \(-0.520106\pi\) | ||||
−0.0631243 | + | 0.998006i | \(0.520106\pi\) | |||||||
\(422\) | 4.50805 | 0.219448 | ||||||||
\(423\) | −9.81123 | −0.477038 | ||||||||
\(424\) | −2.15392 | −0.104603 | ||||||||
\(425\) | −11.2751 | −0.546920 | ||||||||
\(426\) | 0.591514 | 0.0286590 | ||||||||
\(427\) | −4.70310 | −0.227599 | ||||||||
\(428\) | −33.2301 | −1.60624 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.481412 | −0.0232157 | ||||||||
\(431\) | 39.9546 | 1.92455 | 0.962273 | − | 0.272086i | \(-0.0877134\pi\) | ||||
0.962273 | + | 0.272086i | \(0.0877134\pi\) | |||||||
\(432\) | 3.80207 | 0.182927 | ||||||||
\(433\) | 6.08994 | 0.292664 | 0.146332 | − | 0.989236i | \(-0.453253\pi\) | ||||
0.146332 | + | 0.989236i | \(0.453253\pi\) | |||||||
\(434\) | 0.884989 | 0.0424808 | ||||||||
\(435\) | 3.98875 | 0.191246 | ||||||||
\(436\) | −11.0562 | −0.529497 | ||||||||
\(437\) | −11.5277 | −0.551445 | ||||||||
\(438\) | −1.42204 | −0.0679478 | ||||||||
\(439\) | −20.6796 | −0.986984 | −0.493492 | − | 0.869750i | \(-0.664280\pi\) | ||||
−0.493492 | + | 0.869750i | \(0.664280\pi\) | |||||||
\(440\) | −3.27548 | −0.156153 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.26524 | −0.440205 | −0.220102 | − | 0.975477i | \(-0.570639\pi\) | ||||
−0.220102 | + | 0.975477i | \(0.570639\pi\) | |||||||
\(444\) | 12.5487 | 0.595537 | ||||||||
\(445\) | 14.7392 | 0.698704 | ||||||||
\(446\) | −4.39657 | −0.208184 | ||||||||
\(447\) | −2.99238 | −0.141535 | ||||||||
\(448\) | 7.21485 | 0.340870 | ||||||||
\(449\) | 36.2207 | 1.70936 | 0.854681 | − | 0.519154i | \(-0.173753\pi\) | ||||
0.854681 | + | 0.519154i | \(0.173753\pi\) | |||||||
\(450\) | −0.678558 | −0.0319875 | ||||||||
\(451\) | 19.1220 | 0.900421 | ||||||||
\(452\) | 5.34492 | 0.251404 | ||||||||
\(453\) | 0.860674 | 0.0404380 | ||||||||
\(454\) | −3.76556 | −0.176727 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.83133 | −0.179418 | ||||||||
\(457\) | 16.7049 | 0.781422 | 0.390711 | − | 0.920513i | \(-0.372229\pi\) | ||||
0.390711 | + | 0.920513i | \(0.372229\pi\) | |||||||
\(458\) | −1.30693 | −0.0610686 | ||||||||
\(459\) | 3.02631 | 0.141256 | ||||||||
\(460\) | 4.82641 | 0.225033 | ||||||||
\(461\) | 24.5420 | 1.14303 | 0.571517 | − | 0.820590i | \(-0.306355\pi\) | ||||
0.571517 | + | 0.820590i | \(0.306355\pi\) | |||||||
\(462\) | −0.731463 | −0.0340307 | ||||||||
\(463\) | 18.5726 | 0.863143 | 0.431572 | − | 0.902079i | \(-0.357959\pi\) | ||||
0.431572 | + | 0.902079i | \(0.357959\pi\) | |||||||
\(464\) | 13.4344 | 0.623676 | ||||||||
\(465\) | −5.48525 | −0.254372 | ||||||||
\(466\) | −2.90958 | −0.134784 | ||||||||
\(467\) | 11.8882 | 0.550119 | 0.275059 | − | 0.961427i | \(-0.411302\pi\) | ||||
0.275059 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.77088 | 0.0817715 | ||||||||
\(470\) | −2.01718 | −0.0930455 | ||||||||
\(471\) | −4.62432 | −0.213077 | ||||||||
\(472\) | −8.28871 | −0.381519 | ||||||||
\(473\) | −9.40387 | −0.432390 | ||||||||
\(474\) | 3.18696 | 0.146382 | ||||||||
\(475\) | −19.7574 | −0.906531 | ||||||||
\(476\) | 5.95223 | 0.272820 | ||||||||
\(477\) | 2.98129 | 0.136504 | ||||||||
\(478\) | −2.96500 | −0.135616 | ||||||||
\(479\) | 11.8285 | 0.540460 | 0.270230 | − | 0.962796i | \(-0.412900\pi\) | ||||
0.270230 | + | 0.962796i | \(0.412900\pi\) | |||||||
\(480\) | 2.41285 | 0.110131 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.23513 | 0.192905 | ||||||||
\(483\) | 2.17379 | 0.0989110 | ||||||||
\(484\) | −10.0889 | −0.458586 | ||||||||
\(485\) | 1.99500 | 0.0905882 | ||||||||
\(486\) | 0.182130 | 0.00826158 | ||||||||
\(487\) | −30.3027 | −1.37315 | −0.686573 | − | 0.727061i | \(-0.740886\pi\) | ||||
−0.686573 | + | 0.727061i | \(0.740886\pi\) | |||||||
\(488\) | −3.39789 | −0.153815 | ||||||||
\(489\) | −23.0446 | −1.04211 | ||||||||
\(490\) | 0.205599 | 0.00928802 | ||||||||
\(491\) | −5.28571 | −0.238541 | −0.119270 | − | 0.992862i | \(-0.538056\pi\) | ||||
−0.119270 | + | 0.992862i | \(0.538056\pi\) | |||||||
\(492\) | −9.36461 | −0.422189 | ||||||||
\(493\) | 10.6933 | 0.481601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.53367 | 0.203774 | ||||||||
\(496\) | −18.4747 | −0.829538 | ||||||||
\(497\) | −3.24776 | −0.145682 | ||||||||
\(498\) | −0.128513 | −0.00575880 | ||||||||
\(499\) | −34.7232 | −1.55442 | −0.777211 | − | 0.629240i | \(-0.783366\pi\) | ||||
−0.777211 | + | 0.629240i | \(0.783366\pi\) | |||||||
\(500\) | 19.3734 | 0.866404 | ||||||||
\(501\) | 3.47296 | 0.155160 | ||||||||
\(502\) | 0.634809 | 0.0283329 | ||||||||
\(503\) | −25.8848 | −1.15414 | −0.577072 | − | 0.816693i | \(-0.695805\pi\) | ||||
−0.577072 | + | 0.816693i | \(0.695805\pi\) | |||||||
\(504\) | 0.722479 | 0.0321818 | ||||||||
\(505\) | 17.2975 | 0.769728 | ||||||||
\(506\) | −1.59005 | −0.0706863 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.9049 | −1.01624 | ||||||||
\(509\) | −21.4431 | −0.950449 | −0.475224 | − | 0.879865i | \(-0.657633\pi\) | ||||
−0.475224 | + | 0.879865i | \(0.657633\pi\) | |||||||
\(510\) | 0.622206 | 0.0275518 | ||||||||
\(511\) | 7.80784 | 0.345398 | ||||||||
\(512\) | 13.6205 | 0.601946 | ||||||||
\(513\) | 5.30303 | 0.234135 | ||||||||
\(514\) | −2.25190 | −0.0993270 | ||||||||
\(515\) | 9.25622 | 0.407878 | ||||||||
\(516\) | 4.60535 | 0.202739 | ||||||||
\(517\) | −39.4034 | −1.73296 | ||||||||
\(518\) | 1.16202 | 0.0510564 | ||||||||
\(519\) | 19.7442 | 0.866672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.1058 | −1.09990 | −0.549951 | − | 0.835197i | \(-0.685354\pi\) | ||||
−0.549951 | + | 0.835197i | \(0.685354\pi\) | |||||||
\(522\) | 0.643546 | 0.0281672 | ||||||||
\(523\) | 11.4300 | 0.499797 | 0.249898 | − | 0.968272i | \(-0.419603\pi\) | ||||
0.249898 | + | 0.968272i | \(0.419603\pi\) | |||||||
\(524\) | −29.0907 | −1.27083 | ||||||||
\(525\) | 3.72568 | 0.162602 | ||||||||
\(526\) | −4.50018 | −0.196217 | ||||||||
\(527\) | −14.7052 | −0.640567 | ||||||||
\(528\) | 15.2697 | 0.664529 | ||||||||
\(529\) | −18.2746 | −0.794549 | ||||||||
\(530\) | 0.612950 | 0.0266249 | ||||||||
\(531\) | 11.4726 | 0.497868 | ||||||||
\(532\) | 10.4302 | 0.452205 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.37802 | 0.102907 | ||||||||
\(535\) | 19.0724 | 0.824571 | ||||||||
\(536\) | 1.27942 | 0.0552626 | ||||||||
\(537\) | 19.0553 | 0.822295 | ||||||||
\(538\) | −2.28782 | −0.0986351 | ||||||||
\(539\) | 4.01616 | 0.172988 | ||||||||
\(540\) | −2.22027 | −0.0955453 | ||||||||
\(541\) | 1.47534 | 0.0634297 | 0.0317148 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317148 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(542\) | 0.695852 | 0.0298894 | ||||||||
\(543\) | −3.45717 | −0.148361 | ||||||||
\(544\) | 6.46852 | 0.277335 | ||||||||
\(545\) | 6.34571 | 0.271820 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19462 | 0.393134 | 0.196567 | − | 0.980490i | \(-0.437021\pi\) | ||||
0.196567 | + | 0.980490i | \(0.437021\pi\) | |||||||
\(548\) | −30.3874 | −1.29808 | ||||||||
\(549\) | 4.70310 | 0.200723 | ||||||||
\(550\) | −2.72520 | −0.116203 | ||||||||
\(551\) | 18.7380 | 0.798264 | ||||||||
\(552\) | 1.57052 | 0.0668457 | ||||||||
\(553\) | −17.4983 | −0.744102 | ||||||||
\(554\) | 3.67157 | 0.155990 | ||||||||
\(555\) | −7.20233 | −0.305722 | ||||||||
\(556\) | 22.5625 | 0.956863 | ||||||||
\(557\) | 7.14740 | 0.302845 | 0.151423 | − | 0.988469i | \(-0.451615\pi\) | ||||
0.151423 | + | 0.988469i | \(0.451615\pi\) | |||||||
\(558\) | −0.884989 | −0.0374646 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.29200 | −0.181370 | ||||||||
\(561\) | 12.1541 | 0.513148 | ||||||||
\(562\) | 1.30588 | 0.0550852 | ||||||||
\(563\) | −39.3042 | −1.65648 | −0.828238 | − | 0.560376i | \(-0.810657\pi\) | ||||
−0.828238 | + | 0.560376i | \(0.810657\pi\) | |||||||
\(564\) | 19.2970 | 0.812550 | ||||||||
\(565\) | −3.06771 | −0.129059 | ||||||||
\(566\) | −1.77465 | −0.0745943 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −2.34644 | −0.0984542 | ||||||||
\(569\) | 29.9610 | 1.25603 | 0.628015 | − | 0.778201i | \(-0.283868\pi\) | ||||
0.628015 | + | 0.778201i | \(0.283868\pi\) | |||||||
\(570\) | 1.09030 | 0.0456676 | ||||||||
\(571\) | 39.1397 | 1.63795 | 0.818973 | − | 0.573833i | \(-0.194544\pi\) | ||||
0.818973 | + | 0.573833i | \(0.194544\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.0189 | −0.878078 | ||||||||
\(574\) | −0.867171 | −0.0361950 | ||||||||
\(575\) | 8.09886 | 0.337746 | ||||||||
\(576\) | −7.21485 | −0.300619 | ||||||||
\(577\) | −23.2869 | −0.969445 | −0.484723 | − | 0.874668i | \(-0.661079\pi\) | ||||
−0.484723 | + | 0.874668i | \(0.661079\pi\) | |||||||
\(578\) | −1.42816 | −0.0594038 | ||||||||
\(579\) | −18.9411 | −0.787164 | ||||||||
\(580\) | −7.84520 | −0.325754 | ||||||||
\(581\) | 0.705610 | 0.0292736 | ||||||||
\(582\) | 0.321873 | 0.0133421 | ||||||||
\(583\) | 11.9733 | 0.495885 | ||||||||
\(584\) | 5.64099 | 0.233426 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0634524 | 0.00262120 | ||||||||
\(587\) | 14.6189 | 0.603387 | 0.301694 | − | 0.953405i | \(-0.402448\pi\) | ||||
0.301694 | + | 0.953405i | \(0.402448\pi\) | |||||||
\(588\) | −1.96683 | −0.0811106 | ||||||||
\(589\) | −25.7680 | −1.06175 | ||||||||
\(590\) | 2.35875 | 0.0971084 | ||||||||
\(591\) | −8.43497 | −0.346968 | ||||||||
\(592\) | −24.2579 | −0.996995 | ||||||||
\(593\) | −28.8553 | −1.18495 | −0.592473 | − | 0.805590i | \(-0.701848\pi\) | ||||
−0.592473 | + | 0.805590i | \(0.701848\pi\) | |||||||
\(594\) | 0.731463 | 0.0300123 | ||||||||
\(595\) | −3.41627 | −0.140054 | ||||||||
\(596\) | 5.88550 | 0.241080 | ||||||||
\(597\) | 20.3783 | 0.834029 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.1056 | 0.739773 | 0.369887 | − | 0.929077i | \(-0.379397\pi\) | ||||
0.369887 | + | 0.929077i | \(0.379397\pi\) | |||||||
\(600\) | 2.69172 | 0.109889 | ||||||||
\(601\) | 0.149746 | 0.00610829 | 0.00305414 | − | 0.999995i | \(-0.499028\pi\) | ||||
0.00305414 | + | 0.999995i | \(0.499028\pi\) | |||||||
\(602\) | 0.426459 | 0.0173812 | ||||||||
\(603\) | −1.77088 | −0.0721157 | ||||||||
\(604\) | −1.69280 | −0.0688790 | ||||||||
\(605\) | 5.79051 | 0.235418 | ||||||||
\(606\) | 2.79077 | 0.113367 | ||||||||
\(607\) | 14.2380 | 0.577904 | 0.288952 | − | 0.957344i | \(-0.406693\pi\) | ||||
0.288952 | + | 0.957344i | \(0.406693\pi\) | |||||||
\(608\) | 11.3349 | 0.459689 | ||||||||
\(609\) | −3.53344 | −0.143182 | ||||||||
\(610\) | 0.966952 | 0.0391507 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.95223 | −0.240605 | ||||||||
\(613\) | 1.87784 | 0.0758451 | 0.0379226 | − | 0.999281i | \(-0.487926\pi\) | ||||
0.0379226 | + | 0.999281i | \(0.487926\pi\) | |||||||
\(614\) | 1.08758 | 0.0438912 | ||||||||
\(615\) | 5.37481 | 0.216733 | ||||||||
\(616\) | 2.90159 | 0.116908 | ||||||||
\(617\) | −38.8688 | −1.56480 | −0.782400 | − | 0.622776i | \(-0.786005\pi\) | ||||
−0.782400 | + | 0.622776i | \(0.786005\pi\) | |||||||
\(618\) | 1.49340 | 0.0600733 | ||||||||
\(619\) | 41.6563 | 1.67431 | 0.837153 | − | 0.546969i | \(-0.184218\pi\) | ||||
0.837153 | + | 0.546969i | \(0.184218\pi\) | |||||||
\(620\) | 10.7885 | 0.433278 | ||||||||
\(621\) | −2.17379 | −0.0872313 | ||||||||
\(622\) | −1.12194 | −0.0449858 | ||||||||
\(623\) | −13.0567 | −0.523106 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.50907 | 0.300363 | ||||||||
\(626\) | 4.10176 | 0.163939 | ||||||||
\(627\) | 21.2978 | 0.850553 | ||||||||
\(628\) | 9.09525 | 0.362940 | ||||||||
\(629\) | −19.3084 | −0.769877 | ||||||||
\(630\) | −0.205599 | −0.00819126 | ||||||||
\(631\) | 28.6876 | 1.14203 | 0.571017 | − | 0.820938i | \(-0.306549\pi\) | ||||
0.571017 | + | 0.820938i | \(0.306549\pi\) | |||||||
\(632\) | −12.6421 | −0.502877 | ||||||||
\(633\) | 24.7518 | 0.983796 | ||||||||
\(634\) | −5.54950 | −0.220399 | ||||||||
\(635\) | 13.1463 | 0.521693 | ||||||||
\(636\) | −5.86369 | −0.232510 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.58458 | 0.102325 | ||||||||
\(639\) | 3.24776 | 0.128479 | ||||||||
\(640\) | −6.30908 | −0.249388 | ||||||||
\(641\) | −18.5217 | −0.731564 | −0.365782 | − | 0.930701i | \(-0.619198\pi\) | ||||
−0.365782 | + | 0.930701i | \(0.619198\pi\) | |||||||
\(642\) | 3.07714 | 0.121445 | ||||||||
\(643\) | −31.6909 | −1.24977 | −0.624884 | − | 0.780718i | \(-0.714854\pi\) | ||||
−0.624884 | + | 0.780718i | \(0.714854\pi\) | |||||||
\(644\) | −4.27548 | −0.168477 | ||||||||
\(645\) | −2.64323 | −0.104077 | ||||||||
\(646\) | 2.92293 | 0.115001 | ||||||||
\(647\) | 22.6938 | 0.892184 | 0.446092 | − | 0.894987i | \(-0.352815\pi\) | ||||
0.446092 | + | 0.894987i | \(0.352815\pi\) | |||||||
\(648\) | −0.722479 | −0.0283816 | ||||||||
\(649\) | 46.0758 | 1.80863 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85911 | 0.190443 | ||||||||
\(652\) | 45.3248 | 1.77505 | ||||||||
\(653\) | −45.9806 | −1.79936 | −0.899680 | − | 0.436550i | \(-0.856200\pi\) | ||||
−0.899680 | + | 0.436550i | \(0.856200\pi\) | |||||||
\(654\) | 1.02382 | 0.0400344 | ||||||||
\(655\) | 16.6966 | 0.652389 | ||||||||
\(656\) | 18.1027 | 0.706792 | ||||||||
\(657\) | −7.80784 | −0.304613 | ||||||||
\(658\) | 1.78692 | 0.0696613 | ||||||||
\(659\) | 26.6785 | 1.03925 | 0.519623 | − | 0.854396i | \(-0.326072\pi\) | ||||
0.519623 | + | 0.854396i | \(0.326072\pi\) | |||||||
\(660\) | −8.91696 | −0.347092 | ||||||||
\(661\) | 8.73868 | 0.339895 | 0.169948 | − | 0.985453i | \(-0.445640\pi\) | ||||
0.169948 | + | 0.985453i | \(0.445640\pi\) | |||||||
\(662\) | −0.296280 | −0.0115152 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.509788 | 0.0197836 | ||||||||
\(665\) | −5.98637 | −0.232142 | ||||||||
\(666\) | −1.16202 | −0.0450275 | ||||||||
\(667\) | −7.68097 | −0.297408 | ||||||||
\(668\) | −6.83071 | −0.264288 | ||||||||
\(669\) | −24.1397 | −0.933296 | ||||||||
\(670\) | −0.364091 | −0.0140660 | ||||||||
\(671\) | 18.8884 | 0.729178 | ||||||||
\(672\) | −2.13743 | −0.0824531 | ||||||||
\(673\) | 45.5288 | 1.75501 | 0.877503 | − | 0.479570i | \(-0.159207\pi\) | ||||
0.877503 | + | 0.479570i | \(0.159207\pi\) | |||||||
\(674\) | 0.686281 | 0.0264346 | ||||||||
\(675\) | −3.72568 | −0.143401 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.826184 | 0.0317528 | 0.0158764 | − | 0.999874i | \(-0.494946\pi\) | ||||
0.0158764 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(678\) | −0.494944 | −0.0190082 | ||||||||
\(679\) | −1.76727 | −0.0678216 | ||||||||
\(680\) | −2.46819 | −0.0946506 | ||||||||
\(681\) | −20.6751 | −0.792273 | ||||||||
\(682\) | −3.55426 | −0.136100 | ||||||||
\(683\) | −24.3274 | −0.930860 | −0.465430 | − | 0.885085i | \(-0.654100\pi\) | ||||
−0.465430 | + | 0.885085i | \(0.654100\pi\) | |||||||
\(684\) | −10.4302 | −0.398807 | ||||||||
\(685\) | 17.4408 | 0.666378 | ||||||||
\(686\) | −0.182130 | −0.00695376 | ||||||||
\(687\) | −7.17578 | −0.273773 | ||||||||
\(688\) | −8.90259 | −0.339408 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.446930 | −0.0170143 | ||||||||
\(691\) | −24.8245 | −0.944367 | −0.472184 | − | 0.881500i | \(-0.656534\pi\) | ||||
−0.472184 | + | 0.881500i | \(0.656534\pi\) | |||||||
\(692\) | −38.8334 | −1.47622 | ||||||||
\(693\) | −4.01616 | −0.152561 | ||||||||
\(694\) | 2.05671 | 0.0780718 | ||||||||
\(695\) | −12.9497 | −0.491211 | ||||||||
\(696\) | −2.55284 | −0.0967650 | ||||||||
\(697\) | 14.4091 | 0.545783 | ||||||||
\(698\) | 0.500735 | 0.0189531 | ||||||||
\(699\) | −15.9753 | −0.604241 | ||||||||
\(700\) | −7.32777 | −0.276964 | ||||||||
\(701\) | −51.0338 | −1.92752 | −0.963760 | − | 0.266770i | \(-0.914044\pi\) | ||||
−0.963760 | + | 0.266770i | \(0.914044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.8344 | −1.27609 | ||||||||
\(704\) | −28.9760 | −1.09207 | ||||||||
\(705\) | −11.0755 | −0.417127 | ||||||||
\(706\) | 3.95045 | 0.148677 | ||||||||
\(707\) | −15.3230 | −0.576280 | ||||||||
\(708\) | −22.5646 | −0.848031 | ||||||||
\(709\) | −12.6412 | −0.474752 | −0.237376 | − | 0.971418i | \(-0.576287\pi\) | ||||
−0.237376 | + | 0.971418i | \(0.576287\pi\) | |||||||
\(710\) | 0.667736 | 0.0250597 | ||||||||
\(711\) | 17.4983 | 0.656236 | ||||||||
\(712\) | −9.43319 | −0.353524 | ||||||||
\(713\) | 10.5627 | 0.395576 | ||||||||
\(714\) | −0.551182 | −0.0206275 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37.4784 | −1.40064 | ||||||||
\(717\) | −16.2796 | −0.607971 | ||||||||
\(718\) | −4.60493 | −0.171854 | ||||||||
\(719\) | −7.25090 | −0.270413 | −0.135206 | − | 0.990817i | \(-0.543170\pi\) | ||||
−0.135206 | + | 0.990817i | \(0.543170\pi\) | |||||||
\(720\) | 4.29200 | 0.159953 | ||||||||
\(721\) | −8.19962 | −0.305370 | ||||||||
\(722\) | 1.66142 | 0.0618316 | ||||||||
\(723\) | 23.2533 | 0.864801 | ||||||||
\(724\) | 6.79966 | 0.252707 | ||||||||
\(725\) | −13.1645 | −0.488916 | ||||||||
\(726\) | 0.934241 | 0.0346729 | ||||||||
\(727\) | 18.1643 | 0.673677 | 0.336838 | − | 0.941563i | \(-0.390642\pi\) | ||||
0.336838 | + | 0.941563i | \(0.390642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.60528 | −0.0594142 | ||||||||
\(731\) | −7.08613 | −0.262090 | ||||||||
\(732\) | −9.25018 | −0.341897 | ||||||||
\(733\) | −13.6504 | −0.504189 | −0.252094 | − | 0.967703i | \(-0.581119\pi\) | ||||
−0.252094 | + | 0.967703i | \(0.581119\pi\) | |||||||
\(734\) | 6.94474 | 0.256335 | ||||||||
\(735\) | 1.12886 | 0.0416386 | ||||||||
\(736\) | −4.64633 | −0.171266 | ||||||||
\(737\) | −7.11212 | −0.261978 | ||||||||
\(738\) | 0.867171 | 0.0319210 | ||||||||
\(739\) | 24.7742 | 0.911333 | 0.455667 | − | 0.890150i | \(-0.349401\pi\) | ||||
0.455667 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(740\) | 14.1658 | 0.520743 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.542982 | −0.0199335 | ||||||||
\(743\) | 29.4286 | 1.07963 | 0.539815 | − | 0.841783i | \(-0.318494\pi\) | ||||
0.539815 | + | 0.841783i | \(0.318494\pi\) | |||||||
\(744\) | 3.51060 | 0.128705 | ||||||||
\(745\) | −3.37798 | −0.123760 | ||||||||
\(746\) | −4.85157 | −0.177629 | ||||||||
\(747\) | −0.705610 | −0.0258169 | ||||||||
\(748\) | −23.9051 | −0.874057 | ||||||||
\(749\) | −16.8953 | −0.617340 | ||||||||
\(750\) | −1.79399 | −0.0655073 | ||||||||
\(751\) | −23.6648 | −0.863543 | −0.431771 | − | 0.901983i | \(-0.642111\pi\) | ||||
−0.431771 | + | 0.901983i | \(0.642111\pi\) | |||||||
\(752\) | −37.3030 | −1.36030 | ||||||||
\(753\) | 3.48547 | 0.127018 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.971579 | 0.0353594 | ||||||||
\(756\) | 1.96683 | 0.0715329 | ||||||||
\(757\) | 18.5355 | 0.673683 | 0.336841 | − | 0.941561i | \(-0.390641\pi\) | ||||
0.336841 | + | 0.941561i | \(0.390641\pi\) | |||||||
\(758\) | 1.22552 | 0.0445129 | ||||||||
\(759\) | −8.73030 | −0.316890 | ||||||||
\(760\) | −4.32503 | −0.156885 | ||||||||
\(761\) | −9.30977 | −0.337479 | −0.168739 | − | 0.985661i | \(-0.553970\pi\) | ||||
−0.168739 | + | 0.985661i | \(0.553970\pi\) | |||||||
\(762\) | 2.12102 | 0.0768363 | ||||||||
\(763\) | −5.62135 | −0.203506 | ||||||||
\(764\) | 41.3406 | 1.49565 | ||||||||
\(765\) | 3.41627 | 0.123516 | ||||||||
\(766\) | 0.213121 | 0.00770039 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 13.4118 | 0.483957 | ||||||||
\(769\) | 10.5730 | 0.381272 | 0.190636 | − | 0.981661i | \(-0.438945\pi\) | ||||
0.190636 | + | 0.981661i | \(0.438945\pi\) | |||||||
\(770\) | −0.825718 | −0.0297568 | ||||||||
\(771\) | −12.3642 | −0.445287 | ||||||||
\(772\) | 37.2539 | 1.34080 | ||||||||
\(773\) | −35.7370 | −1.28537 | −0.642686 | − | 0.766130i | \(-0.722180\pi\) | ||||
−0.642686 | + | 0.766130i | \(0.722180\pi\) | |||||||
\(774\) | −0.426459 | −0.0153288 | ||||||||
\(775\) | 18.1035 | 0.650296 | ||||||||
\(776\) | −1.27681 | −0.0458350 | ||||||||
\(777\) | 6.38019 | 0.228888 | ||||||||
\(778\) | −3.88562 | −0.139306 | ||||||||
\(779\) | 25.2492 | 0.904646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0435 | 0.466733 | ||||||||
\(782\) | −1.19816 | −0.0428459 | ||||||||
\(783\) | 3.53344 | 0.126275 | ||||||||
\(784\) | 3.80207 | 0.135788 | ||||||||
\(785\) | −5.22020 | −0.186317 | ||||||||
\(786\) | 2.69382 | 0.0960855 | ||||||||
\(787\) | 15.8102 | 0.563574 | 0.281787 | − | 0.959477i | \(-0.409073\pi\) | ||||
0.281787 | + | 0.959477i | \(0.409073\pi\) | |||||||
\(788\) | 16.5901 | 0.590999 | ||||||||
\(789\) | −24.7086 | −0.879650 | ||||||||
\(790\) | 3.59763 | 0.127998 | ||||||||
\(791\) | 2.71753 | 0.0966243 | ||||||||
\(792\) | −2.90159 | −0.103103 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.80658 | −0.170579 | ||||||||
\(795\) | 3.36545 | 0.119360 | ||||||||
\(796\) | −40.0807 | −1.42062 | ||||||||
\(797\) | 42.4880 | 1.50500 | 0.752502 | − | 0.658590i | \(-0.228847\pi\) | ||||
0.752502 | + | 0.658590i | \(0.228847\pi\) | |||||||
\(798\) | −0.965841 | −0.0341904 | ||||||||
\(799\) | −29.6918 | −1.05042 | ||||||||
\(800\) | −7.96337 | −0.281548 | ||||||||
\(801\) | 13.0567 | 0.461336 | ||||||||
\(802\) | 2.11595 | 0.0747167 | ||||||||
\(803\) | −31.3575 | −1.10658 | ||||||||
\(804\) | 3.48301 | 0.122836 | ||||||||
\(805\) | 2.45391 | 0.0864888 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.5615 | −0.442185 | ||||||||
\(808\) | −11.0705 | −0.389460 | ||||||||
\(809\) | −18.9303 | −0.665553 | −0.332776 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332776 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(810\) | 0.205599 | 0.00722401 | ||||||||
\(811\) | 18.5956 | 0.652978 | 0.326489 | − | 0.945201i | \(-0.394134\pi\) | ||||
0.326489 | + | 0.945201i | \(0.394134\pi\) | |||||||
\(812\) | 6.94967 | 0.243886 | ||||||||
\(813\) | 3.82063 | 0.133996 | ||||||||
\(814\) | −4.66687 | −0.163574 | ||||||||
\(815\) | −26.0141 | −0.911234 | ||||||||
\(816\) | 11.5062 | 0.402799 | ||||||||
\(817\) | −12.4171 | −0.434419 | ||||||||
\(818\) | 1.97349 | 0.0690013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.5713 | −0.369167 | ||||||||
\(821\) | −46.8163 | −1.63390 | −0.816951 | − | 0.576707i | \(-0.804337\pi\) | ||||
−0.816951 | + | 0.576707i | \(0.804337\pi\) | |||||||
\(822\) | 2.81390 | 0.0981459 | ||||||||
\(823\) | −36.5999 | −1.27579 | −0.637896 | − | 0.770123i | \(-0.720195\pi\) | ||||
−0.637896 | + | 0.770123i | \(0.720195\pi\) | |||||||
\(824\) | −5.92405 | −0.206374 | ||||||||
\(825\) | −14.9629 | −0.520942 | ||||||||
\(826\) | −2.08950 | −0.0727032 | ||||||||
\(827\) | 37.5007 | 1.30403 | 0.652013 | − | 0.758208i | \(-0.273925\pi\) | ||||
0.652013 | + | 0.758208i | \(0.273925\pi\) | |||||||
\(828\) | 4.27548 | 0.148583 | ||||||||
\(829\) | 3.74445 | 0.130050 | 0.0650250 | − | 0.997884i | \(-0.479287\pi\) | ||||
0.0650250 | + | 0.997884i | \(0.479287\pi\) | |||||||
\(830\) | −0.145073 | −0.00503555 | ||||||||
\(831\) | 20.1591 | 0.699310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.02631 | 0.104855 | ||||||||
\(834\) | −2.08931 | −0.0723468 | ||||||||
\(835\) | 3.92048 | 0.135674 | ||||||||
\(836\) | −41.8892 | −1.44877 | ||||||||
\(837\) | −4.85911 | −0.167955 | ||||||||
\(838\) | −6.85972 | −0.236965 | ||||||||
\(839\) | −24.0282 | −0.829547 | −0.414773 | − | 0.909925i | \(-0.636139\pi\) | ||||
−0.414773 | + | 0.909925i | \(0.636139\pi\) | |||||||
\(840\) | 0.815576 | 0.0281400 | ||||||||
\(841\) | −16.5148 | −0.569476 | ||||||||
\(842\) | −0.471790 | −0.0162590 | ||||||||
\(843\) | 7.17004 | 0.246949 | ||||||||
\(844\) | −48.6825 | −1.67572 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.78692 | −0.0614355 | ||||||||
\(847\) | −5.12953 | −0.176253 | ||||||||
\(848\) | 11.3351 | 0.389248 | ||||||||
\(849\) | −9.74389 | −0.334409 | ||||||||
\(850\) | −2.05353 | −0.0704353 | ||||||||
\(851\) | 13.8692 | 0.475431 | ||||||||
\(852\) | −6.38778 | −0.218842 | ||||||||
\(853\) | −42.2325 | −1.44601 | −0.723006 | − | 0.690841i | \(-0.757240\pi\) | ||||
−0.723006 | + | 0.690841i | \(0.757240\pi\) | |||||||
\(854\) | −0.856575 | −0.0293114 | ||||||||
\(855\) | 5.98637 | 0.204730 | ||||||||
\(856\) | −12.2065 | −0.417209 | ||||||||
\(857\) | 16.7604 | 0.572524 | 0.286262 | − | 0.958151i | \(-0.407587\pi\) | ||||
0.286262 | + | 0.958151i | \(0.407587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9949 | −1.29637 | −0.648185 | − | 0.761483i | \(-0.724472\pi\) | ||||
−0.648185 | + | 0.761483i | \(0.724472\pi\) | |||||||
\(860\) | 5.19879 | 0.177277 | ||||||||
\(861\) | −4.76127 | −0.162264 | ||||||||
\(862\) | 7.27693 | 0.247853 | ||||||||
\(863\) | 31.3316 | 1.06654 | 0.533269 | − | 0.845945i | \(-0.320963\pi\) | ||||
0.533269 | + | 0.845945i | \(0.320963\pi\) | |||||||
\(864\) | 2.13743 | 0.0727168 | ||||||||
\(865\) | 22.2884 | 0.757827 | ||||||||
\(866\) | 1.10916 | 0.0376908 | ||||||||
\(867\) | −7.84145 | −0.266310 | ||||||||
\(868\) | −9.55703 | −0.324387 | ||||||||
\(869\) | 70.2758 | 2.38394 | ||||||||
\(870\) | 0.726472 | 0.0246297 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.06130 | −0.137533 | ||||||||
\(873\) | 1.76727 | 0.0598130 | ||||||||
\(874\) | −2.09954 | −0.0710180 | ||||||||
\(875\) | 9.85006 | 0.332993 | ||||||||
\(876\) | 15.3567 | 0.518854 | ||||||||
\(877\) | 21.5909 | 0.729075 | 0.364537 | − | 0.931189i | \(-0.381227\pi\) | ||||
0.364537 | + | 0.931189i | \(0.381227\pi\) | |||||||
\(878\) | −3.76638 | −0.127109 | ||||||||
\(879\) | 0.348391 | 0.0117509 | ||||||||
\(880\) | 17.2374 | 0.581071 | ||||||||
\(881\) | −8.51629 | −0.286921 | −0.143461 | − | 0.989656i | \(-0.545823\pi\) | ||||
−0.143461 | + | 0.989656i | \(0.545823\pi\) | |||||||
\(882\) | 0.182130 | 0.00613264 | ||||||||
\(883\) | 7.62183 | 0.256495 | 0.128248 | − | 0.991742i | \(-0.459065\pi\) | ||||
0.128248 | + | 0.991742i | \(0.459065\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.9509 | 0.435341 | ||||||||
\(886\) | −1.68748 | −0.0566919 | ||||||||
\(887\) | −5.49147 | −0.184385 | −0.0921927 | − | 0.995741i | \(-0.529388\pi\) | ||||
−0.0921927 | + | 0.995741i | \(0.529388\pi\) | |||||||
\(888\) | 4.60955 | 0.154686 | ||||||||
\(889\) | −11.6456 | −0.390581 | ||||||||
\(890\) | 2.68445 | 0.0899828 | ||||||||
\(891\) | 4.01616 | 0.134546 | ||||||||
\(892\) | 47.4787 | 1.58970 | ||||||||
\(893\) | −52.0293 | −1.74109 | ||||||||
\(894\) | −0.545003 | −0.0182276 | ||||||||
\(895\) | 21.5107 | 0.719023 | ||||||||
\(896\) | 5.58890 | 0.186712 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.59688 | 0.220141 | ||||||||
\(899\) | −17.1694 | −0.572630 | ||||||||
\(900\) | 7.32777 | 0.244259 | ||||||||
\(901\) | 9.02230 | 0.300576 | ||||||||
\(902\) | 3.48270 | 0.115961 | ||||||||
\(903\) | 2.34151 | 0.0779205 | ||||||||
\(904\) | 1.96336 | 0.0653003 | ||||||||
\(905\) | −3.90265 | −0.129729 | ||||||||
\(906\) | 0.156755 | 0.00520782 | ||||||||
\(907\) | 52.3003 | 1.73660 | 0.868301 | − | 0.496038i | \(-0.165212\pi\) | ||||
0.868301 | + | 0.496038i | \(0.165212\pi\) | |||||||
\(908\) | 40.6644 | 1.34950 | ||||||||
\(909\) | 15.3230 | 0.508231 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.1804 | −1.76195 | −0.880973 | − | 0.473167i | \(-0.843111\pi\) | ||||
−0.880973 | + | 0.473167i | \(0.843111\pi\) | |||||||
\(912\) | 20.1625 | 0.667648 | ||||||||
\(913\) | −2.83384 | −0.0937865 | ||||||||
\(914\) | 3.04246 | 0.100636 | ||||||||
\(915\) | 5.30913 | 0.175514 | ||||||||
\(916\) | 14.1135 | 0.466324 | ||||||||
\(917\) | −14.7907 | −0.488431 | ||||||||
\(918\) | 0.551182 | 0.0181917 | ||||||||
\(919\) | 9.23684 | 0.304695 | 0.152348 | − | 0.988327i | \(-0.451317\pi\) | ||||
0.152348 | + | 0.988327i | \(0.451317\pi\) | |||||||
\(920\) | 1.77289 | 0.0584506 | ||||||||
\(921\) | 5.97146 | 0.196766 | ||||||||
\(922\) | 4.46983 | 0.147206 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.89910 | 0.259861 | ||||||||
\(925\) | 23.7705 | 0.781570 | ||||||||
\(926\) | 3.38263 | 0.111160 | ||||||||
\(927\) | 8.19962 | 0.269311 | ||||||||
\(928\) | 7.55248 | 0.247922 | ||||||||
\(929\) | −25.2833 | −0.829517 | −0.414759 | − | 0.909931i | \(-0.636134\pi\) | ||||
−0.414759 | + | 0.909931i | \(0.636134\pi\) | |||||||
\(930\) | −0.999028 | −0.0327594 | ||||||||
\(931\) | 5.30303 | 0.173800 | ||||||||
\(932\) | 31.4206 | 1.02922 | ||||||||
\(933\) | −6.16012 | −0.201673 | ||||||||
\(934\) | 2.16519 | 0.0708473 | ||||||||
\(935\) | 13.7203 | 0.448702 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.6293 | −1.39264 | −0.696320 | − | 0.717732i | \(-0.745180\pi\) | ||||
−0.696320 | + | 0.717732i | \(0.745180\pi\) | |||||||
\(938\) | 0.322530 | 0.0105310 | ||||||||
\(939\) | 22.5210 | 0.734947 | ||||||||
\(940\) | 21.7836 | 0.710502 | ||||||||
\(941\) | −4.78825 | −0.156093 | −0.0780463 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780463 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(942\) | −0.842228 | −0.0274413 | ||||||||
\(943\) | −10.3500 | −0.337043 | ||||||||
\(944\) | 43.6196 | 1.41970 | ||||||||
\(945\) | −1.12886 | −0.0367218 | ||||||||
\(946\) | −1.71273 | −0.0556856 | ||||||||
\(947\) | 9.40557 | 0.305640 | 0.152820 | − | 0.988254i | \(-0.451165\pi\) | ||||
0.152820 | + | 0.988254i | \(0.451165\pi\) | |||||||
\(948\) | −34.4161 | −1.11778 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.59841 | −0.116748 | ||||||||
\(951\) | −30.4700 | −0.988057 | ||||||||
\(952\) | 2.18644 | 0.0708630 | ||||||||
\(953\) | −11.7968 | −0.382135 | −0.191068 | − | 0.981577i | \(-0.561195\pi\) | ||||
−0.191068 | + | 0.981577i | \(0.561195\pi\) | |||||||
\(954\) | 0.542982 | 0.0175797 | ||||||||
\(955\) | −23.7274 | −0.767800 | ||||||||
\(956\) | 32.0191 | 1.03557 | ||||||||
\(957\) | 14.1909 | 0.458725 | ||||||||
\(958\) | 2.15433 | 0.0696033 | ||||||||
\(959\) | −15.4499 | −0.498904 | ||||||||
\(960\) | −8.14455 | −0.262864 | ||||||||
\(961\) | −7.38907 | −0.238357 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.8953 | 0.544443 | ||||||||
\(964\) | −45.7353 | −1.47304 | ||||||||
\(965\) | −21.3818 | −0.688304 | ||||||||
\(966\) | 0.395913 | 0.0127383 | ||||||||
\(967\) | 30.0746 | 0.967135 | 0.483568 | − | 0.875307i | \(-0.339341\pi\) | ||||
0.483568 | + | 0.875307i | \(0.339341\pi\) | |||||||
\(968\) | −3.70597 | −0.119115 | ||||||||
\(969\) | 16.0486 | 0.515556 | ||||||||
\(970\) | 0.363349 | 0.0116664 | ||||||||
\(971\) | −19.2259 | −0.616987 | −0.308494 | − | 0.951226i | \(-0.599825\pi\) | ||||
−0.308494 | + | 0.951226i | \(0.599825\pi\) | |||||||
\(972\) | −1.96683 | −0.0630861 | ||||||||
\(973\) | 11.4715 | 0.367760 | ||||||||
\(974\) | −5.51903 | −0.176841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.8815 | 0.572373 | ||||||||
\(977\) | 19.0860 | 0.610615 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(978\) | −4.19711 | −0.134209 | ||||||||
\(979\) | 52.4378 | 1.67592 | ||||||||
\(980\) | −2.22027 | −0.0709240 | ||||||||
\(981\) | 5.62135 | 0.179476 | ||||||||
\(982\) | −0.962686 | −0.0307206 | ||||||||
\(983\) | −42.0109 | −1.33994 | −0.669970 | − | 0.742389i | \(-0.733693\pi\) | ||||
−0.669970 | + | 0.742389i | \(0.733693\pi\) | |||||||
\(984\) | −3.43992 | −0.109661 | ||||||||
\(985\) | −9.52188 | −0.303392 | ||||||||
\(986\) | 1.94757 | 0.0620232 | ||||||||
\(987\) | 9.81123 | 0.312295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.08996 | 0.161851 | ||||||||
\(990\) | 0.825718 | 0.0262430 | ||||||||
\(991\) | −20.0564 | −0.637112 | −0.318556 | − | 0.947904i | \(-0.603198\pi\) | ||||
−0.318556 | + | 0.947904i | \(0.603198\pi\) | |||||||
\(992\) | −10.3860 | −0.329756 | ||||||||
\(993\) | −1.62675 | −0.0516233 | ||||||||
\(994\) | −0.591514 | −0.0187617 | ||||||||
\(995\) | 23.0043 | 0.729284 | ||||||||
\(996\) | 1.38781 | 0.0439746 | ||||||||
\(997\) | 31.9271 | 1.01114 | 0.505570 | − | 0.862785i | \(-0.331282\pi\) | ||||
0.505570 | + | 0.862785i | \(0.331282\pi\) | |||||||
\(998\) | −6.32413 | −0.200187 | ||||||||
\(999\) | −6.38019 | −0.201860 |
(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 | 3549.2.a.bh.1.8 | yes | 15 | |
13.12 | even | 2 | 3549.2.a.bg.1.8 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.8 | ✓ | 15 | 13.12 | even | 2 | ||
3549.2.a.bh.1.8 | yes | 15 | 1.1 | even | 1 | trivial |