Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} - 6927 x^{3} - 3639 x^{2} + 5508 x + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.76721\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.76721 | −0.790320 | −0.395160 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395160 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.53166 | 0.956879 | 0.478440 | − | 0.878120i | \(-0.341203\pi\) | ||||
0.478440 | + | 0.878120i | \(0.341203\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.76721 | −0.558841 | ||||||||
\(11\) | −0.172733 | −0.0520811 | −0.0260405 | − | 0.999661i | \(-0.508290\pi\) | ||||
−0.0260405 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.33396 | 0.369973 | 0.184987 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184987 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(14\) | 2.53166 | 0.676616 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.35073 | 1.54028 | 0.770139 | − | 0.637876i | \(-0.220187\pi\) | ||||
0.770139 | + | 0.637876i | \(0.220187\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.244981 | 0.0562025 | 0.0281012 | − | 0.999605i | \(-0.491054\pi\) | ||||
0.0281012 | + | 0.999605i | \(0.491054\pi\) | |||||||
\(20\) | −1.76721 | −0.395160 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.172733 | −0.0368269 | ||||||||
\(23\) | 0.777947 | 0.162213 | 0.0811065 | − | 0.996705i | \(-0.474155\pi\) | ||||
0.0811065 | + | 0.996705i | \(0.474155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.87697 | −0.375394 | ||||||||
\(26\) | 1.33396 | 0.261611 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.53166 | 0.478440 | ||||||||
\(29\) | −0.922435 | −0.171292 | −0.0856460 | − | 0.996326i | \(-0.527295\pi\) | ||||
−0.0856460 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.24473 | −0.403166 | −0.201583 | − | 0.979471i | \(-0.564609\pi\) | ||||
−0.201583 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.35073 | 1.08914 | ||||||||
\(35\) | −4.47398 | −0.756241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.59906 | 0.756081 | 0.378040 | − | 0.925789i | \(-0.376598\pi\) | ||||
0.378040 | + | 0.925789i | \(0.376598\pi\) | |||||||
\(38\) | 0.244981 | 0.0397411 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.76721 | −0.279420 | ||||||||
\(41\) | 7.99362 | 1.24839 | 0.624197 | − | 0.781267i | \(-0.285426\pi\) | ||||
0.624197 | + | 0.781267i | \(0.285426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.41776 | −1.43620 | −0.718098 | − | 0.695943i | \(-0.754987\pi\) | ||||
−0.718098 | + | 0.695943i | \(0.754987\pi\) | |||||||
\(44\) | −0.172733 | −0.0260405 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.777947 | 0.114702 | ||||||||
\(47\) | 10.3563 | 1.51062 | 0.755308 | − | 0.655370i | \(-0.227487\pi\) | ||||
0.755308 | + | 0.655370i | \(0.227487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.590673 | −0.0843818 | ||||||||
\(50\) | −1.87697 | −0.265444 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.33396 | 0.184987 | ||||||||
\(53\) | −1.53474 | −0.210813 | −0.105406 | − | 0.994429i | \(-0.533614\pi\) | ||||
−0.105406 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.305256 | 0.0411607 | ||||||||
\(56\) | 2.53166 | 0.338308 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.922435 | −0.121122 | ||||||||
\(59\) | 7.87122 | 1.02475 | 0.512373 | − | 0.858763i | \(-0.328767\pi\) | ||||
0.512373 | + | 0.858763i | \(0.328767\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.82082 | 0.233133 | 0.116566 | − | 0.993183i | \(-0.462811\pi\) | ||||
0.116566 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(62\) | −2.24473 | −0.285081 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.35738 | −0.292397 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3809 | 1.26822 | 0.634111 | − | 0.773242i | \(-0.281366\pi\) | ||||
0.634111 | + | 0.773242i | \(0.281366\pi\) | |||||||
\(68\) | 6.35073 | 0.770139 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.47398 | −0.534743 | ||||||||
\(71\) | −10.1375 | −1.20310 | −0.601549 | − | 0.798836i | \(-0.705450\pi\) | ||||
−0.601549 | + | 0.798836i | \(0.705450\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6495 | −1.71459 | −0.857296 | − | 0.514824i | \(-0.827857\pi\) | ||||
−0.857296 | + | 0.514824i | \(0.827857\pi\) | |||||||
\(74\) | 4.59906 | 0.534630 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.244981 | 0.0281012 | ||||||||
\(77\) | −0.437303 | −0.0498353 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04066 | −0.229592 | −0.114796 | − | 0.993389i | \(-0.536621\pi\) | ||||
−0.114796 | + | 0.993389i | \(0.536621\pi\) | |||||||
\(80\) | −1.76721 | −0.197580 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.99362 | 0.882747 | ||||||||
\(83\) | 13.6488 | 1.49815 | 0.749075 | − | 0.662485i | \(-0.230498\pi\) | ||||
0.749075 | + | 0.662485i | \(0.230498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2231 | −1.21731 | ||||||||
\(86\) | −9.41776 | −1.01554 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.172733 | −0.0184134 | ||||||||
\(89\) | −0.542300 | −0.0574837 | −0.0287419 | − | 0.999587i | \(-0.509150\pi\) | ||||
−0.0287419 | + | 0.999587i | \(0.509150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.37713 | 0.354020 | ||||||||
\(92\) | 0.777947 | 0.0811065 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3563 | 1.06817 | ||||||||
\(95\) | −0.432933 | −0.0444179 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9739 | 1.41883 | 0.709416 | − | 0.704790i | \(-0.248959\pi\) | ||||
0.709416 | + | 0.704790i | \(0.248959\pi\) | |||||||
\(98\) | −0.590673 | −0.0596669 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.87697 | −0.187697 | ||||||||
\(101\) | 15.5965 | 1.55191 | 0.775956 | − | 0.630787i | \(-0.217268\pi\) | ||||
0.775956 | + | 0.630787i | \(0.217268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.33732 | −0.920034 | −0.460017 | − | 0.887910i | \(-0.652157\pi\) | ||||
−0.460017 | + | 0.887910i | \(0.652157\pi\) | |||||||
\(104\) | 1.33396 | 0.130805 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.53474 | −0.149067 | ||||||||
\(107\) | 14.2996 | 1.38239 | 0.691196 | − | 0.722667i | \(-0.257084\pi\) | ||||
0.691196 | + | 0.722667i | \(0.257084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.28655 | −0.889490 | −0.444745 | − | 0.895657i | \(-0.646706\pi\) | ||||
−0.444745 | + | 0.895657i | \(0.646706\pi\) | |||||||
\(110\) | 0.305256 | 0.0291050 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.53166 | 0.239220 | ||||||||
\(113\) | −16.1535 | −1.51959 | −0.759796 | − | 0.650161i | \(-0.774701\pi\) | ||||
−0.759796 | + | 0.650161i | \(0.774701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.37479 | −0.128200 | ||||||||
\(116\) | −0.922435 | −0.0856460 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.87122 | 0.724605 | ||||||||
\(119\) | 16.0779 | 1.47386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9702 | −0.997288 | ||||||||
\(122\) | 1.82082 | 0.164850 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.24473 | −0.201583 | ||||||||
\(125\) | 12.1530 | 1.08700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5280 | 1.02294 | 0.511472 | − | 0.859300i | \(-0.329101\pi\) | ||||
0.511472 | + | 0.859300i | \(0.329101\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.35738 | −0.206756 | ||||||||
\(131\) | −13.2407 | −1.15685 | −0.578424 | − | 0.815736i | \(-0.696332\pi\) | ||||
−0.578424 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.620210 | 0.0537790 | ||||||||
\(134\) | 10.3809 | 0.896769 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.35073 | 0.544571 | ||||||||
\(137\) | 10.2575 | 0.876353 | 0.438177 | − | 0.898889i | \(-0.355624\pi\) | ||||
0.438177 | + | 0.898889i | \(0.355624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2051 | −0.950403 | −0.475201 | − | 0.879877i | \(-0.657625\pi\) | ||||
−0.475201 | + | 0.879877i | \(0.657625\pi\) | |||||||
\(140\) | −4.47398 | −0.378121 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.1375 | −0.850719 | ||||||||
\(143\) | −0.230419 | −0.0192686 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.63014 | 0.135375 | ||||||||
\(146\) | −14.6495 | −1.21240 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.59906 | 0.378040 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0529 | −1.71326 | −0.856632 | − | 0.515928i | \(-0.827447\pi\) | ||||
−0.856632 | + | 0.515928i | \(0.827447\pi\) | |||||||
\(152\) | 0.244981 | 0.0198706 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.437303 | −0.0352389 | ||||||||
\(155\) | 3.96691 | 0.318630 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.29923 | 0.103690 | 0.0518448 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518448 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(158\) | −2.04066 | −0.162346 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.76721 | −0.139710 | ||||||||
\(161\) | 1.96950 | 0.155218 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8886 | 1.40114 | 0.700572 | − | 0.713582i | \(-0.252928\pi\) | ||||
0.700572 | + | 0.713582i | \(0.252928\pi\) | |||||||
\(164\) | 7.99362 | 0.624197 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6488 | 1.05935 | ||||||||
\(167\) | 23.5919 | 1.82560 | 0.912798 | − | 0.408412i | \(-0.133917\pi\) | ||||
0.912798 | + | 0.408412i | \(0.133917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2206 | −0.863120 | ||||||||
\(170\) | −11.2231 | −0.860771 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.41776 | −0.718098 | ||||||||
\(173\) | −5.42628 | −0.412552 | −0.206276 | − | 0.978494i | \(-0.566135\pi\) | ||||
−0.206276 | + | 0.978494i | \(0.566135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.75186 | −0.359207 | ||||||||
\(176\) | −0.172733 | −0.0130203 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.542300 | −0.0406471 | ||||||||
\(179\) | 9.10535 | 0.680566 | 0.340283 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340283 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.26853 | −0.317278 | −0.158639 | − | 0.987337i | \(-0.550711\pi\) | ||||
−0.158639 | + | 0.987337i | \(0.550711\pi\) | |||||||
\(182\) | 3.37713 | 0.250330 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.777947 | 0.0573510 | ||||||||
\(185\) | −8.12750 | −0.597546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.09698 | −0.0802194 | ||||||||
\(188\) | 10.3563 | 0.755308 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.432933 | −0.0314082 | ||||||||
\(191\) | −19.1244 | −1.38379 | −0.691895 | − | 0.721998i | \(-0.743224\pi\) | ||||
−0.691895 | + | 0.721998i | \(0.743224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6585 | 1.34307 | 0.671535 | − | 0.740973i | \(-0.265635\pi\) | ||||
0.671535 | + | 0.740973i | \(0.265635\pi\) | |||||||
\(194\) | 13.9739 | 1.00327 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.590673 | −0.0421909 | ||||||||
\(197\) | 6.74520 | 0.480575 | 0.240288 | − | 0.970702i | \(-0.422758\pi\) | ||||
0.240288 | + | 0.970702i | \(0.422758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9797 | 1.20366 | 0.601828 | − | 0.798625i | \(-0.294439\pi\) | ||||
0.601828 | + | 0.798625i | \(0.294439\pi\) | |||||||
\(200\) | −1.87697 | −0.132722 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.5965 | 1.09737 | ||||||||
\(203\) | −2.33530 | −0.163906 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.1264 | −0.986630 | ||||||||
\(206\) | −9.33732 | −0.650562 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.33396 | 0.0924933 | ||||||||
\(209\) | −0.0423164 | −0.00292709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.62775 | −0.112059 | −0.0560296 | − | 0.998429i | \(-0.517844\pi\) | ||||
−0.0560296 | + | 0.998429i | \(0.517844\pi\) | |||||||
\(212\) | −1.53474 | −0.105406 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.2996 | 0.977499 | ||||||||
\(215\) | 16.6432 | 1.13505 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.68291 | −0.385781 | ||||||||
\(218\) | −9.28655 | −0.628965 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.305256 | 0.0205804 | ||||||||
\(221\) | 8.47161 | 0.569862 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.2695 | 1.89306 | 0.946531 | − | 0.322612i | \(-0.104561\pi\) | ||||
0.946531 | + | 0.322612i | \(0.104561\pi\) | |||||||
\(224\) | 2.53166 | 0.169154 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.1535 | −1.07451 | ||||||||
\(227\) | −17.1689 | −1.13954 | −0.569769 | − | 0.821805i | \(-0.692967\pi\) | ||||
−0.569769 | + | 0.821805i | \(0.692967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0079 | 0.793502 | 0.396751 | − | 0.917926i | \(-0.370138\pi\) | ||||
0.396751 | + | 0.917926i | \(0.370138\pi\) | |||||||
\(230\) | −1.37479 | −0.0906513 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.922435 | −0.0605608 | ||||||||
\(233\) | 20.2171 | 1.32447 | 0.662233 | − | 0.749298i | \(-0.269609\pi\) | ||||
0.662233 | + | 0.749298i | \(0.269609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3017 | −1.19387 | ||||||||
\(236\) | 7.87122 | 0.512373 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.0779 | 1.04218 | ||||||||
\(239\) | 5.11495 | 0.330859 | 0.165429 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165429 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.0965 | 1.87427 | 0.937136 | − | 0.348963i | \(-0.113466\pi\) | ||||
0.937136 | + | 0.348963i | \(0.113466\pi\) | |||||||
\(242\) | −10.9702 | −0.705189 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.82082 | 0.116566 | ||||||||
\(245\) | 1.04384 | 0.0666886 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.326794 | 0.0207934 | ||||||||
\(248\) | −2.24473 | −0.142541 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1530 | 0.768626 | ||||||||
\(251\) | 21.0454 | 1.32837 | 0.664186 | − | 0.747567i | \(-0.268778\pi\) | ||||
0.664186 | + | 0.747567i | \(0.268778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.134377 | −0.00844823 | ||||||||
\(254\) | 11.5280 | 0.723330 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.4128 | −1.89710 | −0.948549 | − | 0.316631i | \(-0.897448\pi\) | ||||
−0.948549 | + | 0.316631i | \(0.897448\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6433 | 0.723478 | ||||||||
\(260\) | −2.35738 | −0.146199 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.2407 | −0.818015 | ||||||||
\(263\) | 2.41012 | 0.148614 | 0.0743070 | − | 0.997235i | \(-0.476326\pi\) | ||||
0.0743070 | + | 0.997235i | \(0.476326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.71221 | 0.166610 | ||||||||
\(266\) | 0.620210 | 0.0380275 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.3809 | 0.634111 | ||||||||
\(269\) | 5.99638 | 0.365606 | 0.182803 | − | 0.983150i | \(-0.441483\pi\) | ||||
0.182803 | + | 0.983150i | \(0.441483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.7372 | 1.32044 | 0.660220 | − | 0.751072i | \(-0.270463\pi\) | ||||
0.660220 | + | 0.751072i | \(0.270463\pi\) | |||||||
\(272\) | 6.35073 | 0.385070 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2575 | 0.619675 | ||||||||
\(275\) | 0.324215 | 0.0195509 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50975 | 0.391133 | 0.195567 | − | 0.980690i | \(-0.437345\pi\) | ||||
0.195567 | + | 0.980690i | \(0.437345\pi\) | |||||||
\(278\) | −11.2051 | −0.672036 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.47398 | −0.267372 | ||||||||
\(281\) | −6.28645 | −0.375018 | −0.187509 | − | 0.982263i | \(-0.560041\pi\) | ||||
−0.187509 | + | 0.982263i | \(0.560041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.2940 | −1.44413 | −0.722064 | − | 0.691826i | \(-0.756806\pi\) | ||||
−0.722064 | + | 0.691826i | \(0.756806\pi\) | |||||||
\(284\) | −10.1375 | −0.601549 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.230419 | −0.0136250 | ||||||||
\(287\) | 20.2372 | 1.19456 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.3318 | 1.37246 | ||||||||
\(290\) | 1.63014 | 0.0957249 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.6495 | −0.857296 | ||||||||
\(293\) | −10.7390 | −0.627376 | −0.313688 | − | 0.949526i | \(-0.601565\pi\) | ||||
−0.313688 | + | 0.949526i | \(0.601565\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.9101 | −0.809877 | ||||||||
\(296\) | 4.59906 | 0.267315 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 1.03775 | 0.0600145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.8426 | −1.37427 | ||||||||
\(302\) | −21.0529 | −1.21146 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.244981 | 0.0140506 | ||||||||
\(305\) | −3.21778 | −0.184250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8387 | 0.732741 | 0.366370 | − | 0.930469i | \(-0.380600\pi\) | ||||
0.366370 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(308\) | −0.437303 | −0.0249177 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.96691 | 0.225305 | ||||||||
\(311\) | −10.6858 | −0.605938 | −0.302969 | − | 0.953000i | \(-0.597978\pi\) | ||||
−0.302969 | + | 0.953000i | \(0.597978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2652 | 0.862842 | 0.431421 | − | 0.902151i | \(-0.358012\pi\) | ||||
0.431421 | + | 0.902151i | \(0.358012\pi\) | |||||||
\(314\) | 1.29923 | 0.0733197 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.04066 | −0.114796 | ||||||||
\(317\) | 33.7500 | 1.89559 | 0.947794 | − | 0.318882i | \(-0.103307\pi\) | ||||
0.947794 | + | 0.318882i | \(0.103307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.159335 | 0.00892107 | ||||||||
\(320\) | −1.76721 | −0.0987900 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.96950 | 0.109756 | ||||||||
\(323\) | 1.55581 | 0.0865675 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50380 | −0.138886 | ||||||||
\(326\) | 17.8886 | 0.990758 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.99362 | 0.441374 | ||||||||
\(329\) | 26.2186 | 1.44548 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.851427 | −0.0467987 | −0.0233993 | − | 0.999726i | \(-0.507449\pi\) | ||||
−0.0233993 | + | 0.999726i | \(0.507449\pi\) | |||||||
\(332\) | 13.6488 | 0.749075 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.5919 | 1.29089 | ||||||||
\(335\) | −18.3451 | −1.00230 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5751 | 0.793957 | 0.396979 | − | 0.917828i | \(-0.370059\pi\) | ||||
0.396979 | + | 0.917828i | \(0.370059\pi\) | |||||||
\(338\) | −11.2206 | −0.610318 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.2231 | −0.608657 | ||||||||
\(341\) | 0.387740 | 0.0209973 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2170 | −1.03762 | ||||||||
\(344\) | −9.41776 | −0.507772 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.42628 | −0.291719 | ||||||||
\(347\) | 13.5016 | 0.724806 | 0.362403 | − | 0.932021i | \(-0.381956\pi\) | ||||
0.362403 | + | 0.932021i | \(0.381956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9484 | 0.693110 | 0.346555 | − | 0.938030i | \(-0.387351\pi\) | ||||
0.346555 | + | 0.938030i | \(0.387351\pi\) | |||||||
\(350\) | −4.75186 | −0.253998 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.172733 | −0.00920672 | ||||||||
\(353\) | −22.5635 | −1.20093 | −0.600466 | − | 0.799650i | \(-0.705018\pi\) | ||||
−0.600466 | + | 0.799650i | \(0.705018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.9151 | 0.950833 | ||||||||
\(356\) | −0.542300 | −0.0287419 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.10535 | 0.481233 | ||||||||
\(359\) | 8.30844 | 0.438503 | 0.219251 | − | 0.975668i | \(-0.429639\pi\) | ||||
0.219251 | + | 0.975668i | \(0.429639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9400 | −0.996841 | ||||||||
\(362\) | −4.26853 | −0.224349 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.37713 | 0.177010 | ||||||||
\(365\) | 25.8887 | 1.35508 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2813 | 0.849876 | 0.424938 | − | 0.905223i | \(-0.360296\pi\) | ||||
0.424938 | + | 0.905223i | \(0.360296\pi\) | |||||||
\(368\) | 0.777947 | 0.0405533 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.12750 | −0.422529 | ||||||||
\(371\) | −3.88545 | −0.201722 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5063 | −0.958220 | −0.479110 | − | 0.877755i | \(-0.659040\pi\) | ||||
−0.479110 | + | 0.877755i | \(0.659040\pi\) | |||||||
\(374\) | −1.09698 | −0.0567237 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3563 | 0.534083 | ||||||||
\(377\) | −1.23049 | −0.0633734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.2996 | −1.29955 | −0.649777 | − | 0.760125i | \(-0.725138\pi\) | ||||
−0.649777 | + | 0.760125i | \(0.725138\pi\) | |||||||
\(380\) | −0.432933 | −0.0222090 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.1244 | −0.978488 | ||||||||
\(383\) | −37.6264 | −1.92262 | −0.961310 | − | 0.275470i | \(-0.911166\pi\) | ||||
−0.961310 | + | 0.275470i | \(0.911166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.772806 | 0.0393859 | ||||||||
\(386\) | 18.6585 | 0.949694 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.9739 | 0.709416 | ||||||||
\(389\) | 26.1522 | 1.32597 | 0.662985 | − | 0.748633i | \(-0.269289\pi\) | ||||
0.662985 | + | 0.748633i | \(0.269289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.94053 | 0.249853 | ||||||||
\(392\) | −0.590673 | −0.0298335 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.74520 | 0.339818 | ||||||||
\(395\) | 3.60627 | 0.181451 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.99278 | −0.451335 | −0.225667 | − | 0.974204i | \(-0.572456\pi\) | ||||
−0.225667 | + | 0.974204i | \(0.572456\pi\) | |||||||
\(398\) | 16.9797 | 0.851114 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.87697 | −0.0938485 | ||||||||
\(401\) | 26.9760 | 1.34712 | 0.673558 | − | 0.739135i | \(-0.264765\pi\) | ||||
0.673558 | + | 0.739135i | \(0.264765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.99438 | −0.149161 | ||||||||
\(404\) | 15.5965 | 0.775956 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.33530 | −0.115899 | ||||||||
\(407\) | −0.794411 | −0.0393775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.843424 | −0.0417047 | −0.0208523 | − | 0.999783i | \(-0.506638\pi\) | ||||
−0.0208523 | + | 0.999783i | \(0.506638\pi\) | |||||||
\(410\) | −14.1264 | −0.697653 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.33732 | −0.460017 | ||||||||
\(413\) | 19.9273 | 0.980558 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.1203 | −1.18402 | ||||||||
\(416\) | 1.33396 | 0.0654027 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0423164 | −0.00206976 | ||||||||
\(419\) | −32.4722 | −1.58637 | −0.793185 | − | 0.608980i | \(-0.791579\pi\) | ||||
−0.793185 | + | 0.608980i | \(0.791579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.3692 | 1.52884 | 0.764420 | − | 0.644719i | \(-0.223026\pi\) | ||||
0.764420 | + | 0.644719i | \(0.223026\pi\) | |||||||
\(422\) | −1.62775 | −0.0792379 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.53474 | −0.0745336 | ||||||||
\(425\) | −11.9201 | −0.578211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.60972 | 0.223080 | ||||||||
\(428\) | 14.2996 | 0.691196 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.6432 | 0.802604 | ||||||||
\(431\) | 32.0091 | 1.54182 | 0.770911 | − | 0.636942i | \(-0.219801\pi\) | ||||
0.770911 | + | 0.636942i | \(0.219801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.5149 | −0.937825 | −0.468912 | − | 0.883245i | \(-0.655354\pi\) | ||||
−0.468912 | + | 0.883245i | \(0.655354\pi\) | |||||||
\(434\) | −5.68291 | −0.272788 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.28655 | −0.444745 | ||||||||
\(437\) | 0.190582 | 0.00911678 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.2094 | −1.82363 | −0.911817 | − | 0.410597i | \(-0.865320\pi\) | ||||
−0.911817 | + | 0.410597i | \(0.865320\pi\) | |||||||
\(440\) | 0.305256 | 0.0145525 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.47161 | 0.402953 | ||||||||
\(443\) | 13.6766 | 0.649796 | 0.324898 | − | 0.945749i | \(-0.394670\pi\) | ||||
0.324898 | + | 0.945749i | \(0.394670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.958359 | 0.0454306 | ||||||||
\(446\) | 28.2695 | 1.33860 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.53166 | 0.119610 | ||||||||
\(449\) | −34.9553 | −1.64964 | −0.824821 | − | 0.565395i | \(-0.808724\pi\) | ||||
−0.824821 | + | 0.565395i | \(0.808724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.38076 | −0.0650177 | ||||||||
\(452\) | −16.1535 | −0.759796 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.1689 | −0.805775 | ||||||||
\(455\) | −5.96810 | −0.279789 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5492 | 0.914471 | 0.457235 | − | 0.889346i | \(-0.348840\pi\) | ||||
0.457235 | + | 0.889346i | \(0.348840\pi\) | |||||||
\(458\) | 12.0079 | 0.561091 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.37479 | −0.0641001 | ||||||||
\(461\) | 23.0442 | 1.07328 | 0.536638 | − | 0.843812i | \(-0.319694\pi\) | ||||
0.536638 | + | 0.843812i | \(0.319694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.30744 | −0.107236 | −0.0536180 | − | 0.998562i | \(-0.517075\pi\) | ||||
−0.0536180 | + | 0.998562i | \(0.517075\pi\) | |||||||
\(464\) | −0.922435 | −0.0428230 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.2171 | 0.936539 | ||||||||
\(467\) | 12.1472 | 0.562106 | 0.281053 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281053 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2808 | 1.21354 | ||||||||
\(470\) | −18.3017 | −0.844193 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.87122 | 0.362302 | ||||||||
\(473\) | 1.62676 | 0.0747986 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.459822 | −0.0210981 | ||||||||
\(476\) | 16.0779 | 0.736930 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.11495 | 0.233952 | ||||||||
\(479\) | −17.3346 | −0.792037 | −0.396018 | − | 0.918243i | \(-0.629608\pi\) | ||||
−0.396018 | + | 0.918243i | \(0.629608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.13495 | 0.279730 | ||||||||
\(482\) | 29.0965 | 1.32531 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9702 | −0.498644 | ||||||||
\(485\) | −24.6948 | −1.12133 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.5694 | −1.56649 | −0.783244 | − | 0.621714i | \(-0.786436\pi\) | ||||
−0.783244 | + | 0.621714i | \(0.786436\pi\) | |||||||
\(488\) | 1.82082 | 0.0824249 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.04384 | 0.0471560 | ||||||||
\(491\) | −37.6299 | −1.69821 | −0.849106 | − | 0.528223i | \(-0.822859\pi\) | ||||
−0.849106 | + | 0.528223i | \(0.822859\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.85814 | −0.263837 | ||||||||
\(494\) | 0.326794 | 0.0147032 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.24473 | −0.100791 | ||||||||
\(497\) | −25.6647 | −1.15122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.7585 | 1.60077 | 0.800386 | − | 0.599485i | \(-0.204628\pi\) | ||||
0.800386 | + | 0.599485i | \(0.204628\pi\) | |||||||
\(500\) | 12.1530 | 0.543501 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.0454 | 0.939301 | ||||||||
\(503\) | −23.8571 | −1.06374 | −0.531868 | − | 0.846827i | \(-0.678510\pi\) | ||||
−0.531868 | + | 0.846827i | \(0.678510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.5623 | −1.22651 | ||||||||
\(506\) | −0.134377 | −0.00597380 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.5280 | 0.511472 | ||||||||
\(509\) | −31.3319 | −1.38876 | −0.694381 | − | 0.719608i | \(-0.744322\pi\) | ||||
−0.694381 | + | 0.719608i | \(0.744322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.0876 | −1.64066 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.4128 | −1.34145 | ||||||||
\(515\) | 16.5010 | 0.727121 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.78887 | −0.0786745 | ||||||||
\(518\) | 11.6433 | 0.511576 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.35738 | −0.103378 | ||||||||
\(521\) | −16.5473 | −0.724953 | −0.362476 | − | 0.931993i | \(-0.618069\pi\) | ||||
−0.362476 | + | 0.931993i | \(0.618069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.5828 | 1.81829 | 0.909145 | − | 0.416479i | \(-0.136736\pi\) | ||||
0.909145 | + | 0.416479i | \(0.136736\pi\) | |||||||
\(524\) | −13.2407 | −0.578424 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.41012 | 0.105086 | ||||||||
\(527\) | −14.2557 | −0.620987 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3948 | −0.973687 | ||||||||
\(530\) | 2.71221 | 0.117811 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.620210 | 0.0268895 | ||||||||
\(533\) | 10.6631 | 0.461872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.2704 | −1.09253 | ||||||||
\(536\) | 10.3809 | 0.448385 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.99638 | 0.258522 | ||||||||
\(539\) | 0.102029 | 0.00439470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.87819 | 0.424697 | 0.212348 | − | 0.977194i | \(-0.431889\pi\) | ||||
0.212348 | + | 0.977194i | \(0.431889\pi\) | |||||||
\(542\) | 21.7372 | 0.933692 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.35073 | 0.272285 | ||||||||
\(545\) | 16.4113 | 0.702982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4891 | 1.13259 | 0.566296 | − | 0.824202i | \(-0.308376\pi\) | ||||
0.566296 | + | 0.824202i | \(0.308376\pi\) | |||||||
\(548\) | 10.2575 | 0.438177 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.324215 | 0.0138246 | ||||||||
\(551\) | −0.225979 | −0.00962703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.16626 | −0.219692 | ||||||||
\(554\) | 6.50975 | 0.276573 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2051 | −0.475201 | ||||||||
\(557\) | −6.61527 | −0.280298 | −0.140149 | − | 0.990130i | \(-0.544758\pi\) | ||||
−0.140149 | + | 0.990130i | \(0.544758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.5629 | −0.531354 | ||||||||
\(560\) | −4.47398 | −0.189060 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.28645 | −0.265178 | ||||||||
\(563\) | −4.89783 | −0.206419 | −0.103209 | − | 0.994660i | \(-0.532911\pi\) | ||||
−0.103209 | + | 0.994660i | \(0.532911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.5466 | 1.20096 | ||||||||
\(566\) | −24.2940 | −1.02115 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1375 | −0.425360 | ||||||||
\(569\) | −25.9447 | −1.08766 | −0.543829 | − | 0.839196i | \(-0.683026\pi\) | ||||
−0.543829 | + | 0.839196i | \(0.683026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.66808 | 0.279050 | 0.139525 | − | 0.990219i | \(-0.455442\pi\) | ||||
0.139525 | + | 0.990219i | \(0.455442\pi\) | |||||||
\(572\) | −0.230419 | −0.00963431 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.2372 | 0.844683 | ||||||||
\(575\) | −1.46018 | −0.0608938 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.48415 | 0.0617861 | 0.0308931 | − | 0.999523i | \(-0.490165\pi\) | ||||
0.0308931 | + | 0.999523i | \(0.490165\pi\) | |||||||
\(578\) | 23.3318 | 0.970475 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.63014 | 0.0676877 | ||||||||
\(581\) | 34.5542 | 1.43355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.265101 | 0.0109794 | ||||||||
\(584\) | −14.6495 | −0.606200 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7390 | −0.443622 | ||||||||
\(587\) | 3.09748 | 0.127847 | 0.0639233 | − | 0.997955i | \(-0.479639\pi\) | ||||
0.0639233 | + | 0.997955i | \(0.479639\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.549916 | −0.0226589 | ||||||||
\(590\) | −13.9101 | −0.572670 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.59906 | 0.189020 | ||||||||
\(593\) | 30.2541 | 1.24239 | 0.621194 | − | 0.783657i | \(-0.286648\pi\) | ||||
0.621194 | + | 0.783657i | \(0.286648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.4131 | −1.16482 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.03775 | 0.0424367 | ||||||||
\(599\) | −23.2842 | −0.951368 | −0.475684 | − | 0.879616i | \(-0.657799\pi\) | ||||
−0.475684 | + | 0.879616i | \(0.657799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.07413 | −0.0846057 | −0.0423029 | − | 0.999105i | \(-0.513469\pi\) | ||||
−0.0423029 | + | 0.999105i | \(0.513469\pi\) | |||||||
\(602\) | −23.8426 | −0.971752 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.0529 | −0.856632 | ||||||||
\(605\) | 19.3866 | 0.788177 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3319 | −0.581715 | −0.290858 | − | 0.956766i | \(-0.593941\pi\) | ||||
−0.290858 | + | 0.956766i | \(0.593941\pi\) | |||||||
\(608\) | 0.244981 | 0.00993529 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.21778 | −0.130284 | ||||||||
\(611\) | 13.8148 | 0.558887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.8495 | −0.922882 | −0.461441 | − | 0.887171i | \(-0.652667\pi\) | ||||
−0.461441 | + | 0.887171i | \(0.652667\pi\) | |||||||
\(614\) | 12.8387 | 0.518126 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.437303 | −0.0176194 | ||||||||
\(617\) | −13.4688 | −0.542234 | −0.271117 | − | 0.962546i | \(-0.587393\pi\) | ||||
−0.271117 | + | 0.962546i | \(0.587393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0564 | 0.564976 | 0.282488 | − | 0.959271i | \(-0.408840\pi\) | ||||
0.282488 | + | 0.959271i | \(0.408840\pi\) | |||||||
\(620\) | 3.96691 | 0.159315 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.6858 | −0.428463 | ||||||||
\(623\) | −1.37292 | −0.0550050 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0921 | −0.483685 | ||||||||
\(626\) | 15.2652 | 0.610122 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.29923 | 0.0518448 | ||||||||
\(629\) | 29.2074 | 1.16458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.52689 | −0.259831 | −0.129916 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129916 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(632\) | −2.04066 | −0.0811730 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.7500 | 1.34038 | ||||||||
\(635\) | −20.3724 | −0.808453 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.787932 | −0.0312190 | ||||||||
\(638\) | 0.159335 | 0.00630815 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.76721 | −0.0698551 | ||||||||
\(641\) | 38.1961 | 1.50866 | 0.754328 | − | 0.656498i | \(-0.227963\pi\) | ||||
0.754328 | + | 0.656498i | \(0.227963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0076 | −0.394661 | −0.197330 | − | 0.980337i | \(-0.563227\pi\) | ||||
−0.197330 | + | 0.980337i | \(0.563227\pi\) | |||||||
\(644\) | 1.96950 | 0.0776092 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.55581 | 0.0612124 | ||||||||
\(647\) | 7.87727 | 0.309688 | 0.154844 | − | 0.987939i | \(-0.450513\pi\) | ||||
0.154844 | + | 0.987939i | \(0.450513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.35962 | −0.0533699 | ||||||||
\(650\) | −2.50380 | −0.0982070 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.8886 | 0.700572 | ||||||||
\(653\) | 48.3734 | 1.89300 | 0.946498 | − | 0.322709i | \(-0.104594\pi\) | ||||
0.946498 | + | 0.322709i | \(0.104594\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.3992 | 0.914281 | ||||||||
\(656\) | 7.99362 | 0.312098 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.2186 | 1.02211 | ||||||||
\(659\) | 26.3964 | 1.02826 | 0.514129 | − | 0.857713i | \(-0.328115\pi\) | ||||
0.514129 | + | 0.857713i | \(0.328115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.1213 | −1.44385 | −0.721925 | − | 0.691971i | \(-0.756743\pi\) | ||||
−0.721925 | + | 0.691971i | \(0.756743\pi\) | |||||||
\(662\) | −0.851427 | −0.0330917 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6488 | 0.529676 | ||||||||
\(665\) | −1.09604 | −0.0425026 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.717605 | −0.0277858 | ||||||||
\(668\) | 23.5919 | 0.912798 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.3451 | −0.708735 | ||||||||
\(671\) | −0.314517 | −0.0121418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.8295 | −0.841467 | −0.420733 | − | 0.907184i | \(-0.638227\pi\) | ||||
−0.420733 | + | 0.907184i | \(0.638227\pi\) | |||||||
\(674\) | 14.5751 | 0.561413 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.2206 | −0.431560 | ||||||||
\(677\) | 16.2095 | 0.622982 | 0.311491 | − | 0.950249i | \(-0.399172\pi\) | ||||
0.311491 | + | 0.950249i | \(0.399172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.3772 | 1.35765 | ||||||||
\(680\) | −11.2231 | −0.430385 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.387740 | 0.0148473 | ||||||||
\(683\) | 28.1909 | 1.07869 | 0.539347 | − | 0.842084i | \(-0.318671\pi\) | ||||
0.539347 | + | 0.842084i | \(0.318671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.1271 | −0.692600 | ||||||||
\(686\) | −19.2170 | −0.733710 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.41776 | −0.359049 | ||||||||
\(689\) | −2.04728 | −0.0779951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1916 | −0.615957 | −0.307979 | − | 0.951393i | \(-0.599653\pi\) | ||||
−0.307979 | + | 0.951393i | \(0.599653\pi\) | |||||||
\(692\) | −5.42628 | −0.206276 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.5016 | 0.512515 | ||||||||
\(695\) | 19.8017 | 0.751123 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.7653 | 1.92287 | ||||||||
\(698\) | 12.9484 | 0.490103 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.75186 | −0.179603 | ||||||||
\(701\) | 11.9775 | 0.452382 | 0.226191 | − | 0.974083i | \(-0.427373\pi\) | ||||
0.226191 | + | 0.974083i | \(0.427373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12668 | 0.0424936 | ||||||||
\(704\) | −0.172733 | −0.00651014 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.5635 | −0.849187 | ||||||||
\(707\) | 39.4852 | 1.48499 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.4090 | −1.59270 | −0.796351 | − | 0.604835i | \(-0.793239\pi\) | ||||
−0.796351 | + | 0.604835i | \(0.793239\pi\) | |||||||
\(710\) | 17.9151 | 0.672341 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.542300 | −0.0203236 | ||||||||
\(713\) | −1.74628 | −0.0653987 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.407199 | 0.0152284 | ||||||||
\(716\) | 9.10535 | 0.340283 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.30844 | 0.310068 | ||||||||
\(719\) | −36.5998 | −1.36494 | −0.682472 | − | 0.730912i | \(-0.739095\pi\) | ||||
−0.682472 | + | 0.730912i | \(0.739095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.6390 | −0.880361 | ||||||||
\(722\) | −18.9400 | −0.704873 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.26853 | −0.158639 | ||||||||
\(725\) | 1.73138 | 0.0643020 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.46378 | 0.165552 | 0.0827762 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827762 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(728\) | 3.37713 | 0.125165 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.8887 | 0.958184 | ||||||||
\(731\) | −59.8097 | −2.21214 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.4559 | −1.23572 | −0.617862 | − | 0.786287i | \(-0.712001\pi\) | ||||
−0.617862 | + | 0.786287i | \(0.712001\pi\) | |||||||
\(734\) | 16.2813 | 0.600953 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.777947 | 0.0286755 | ||||||||
\(737\) | −1.79312 | −0.0660504 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5841 | −0.389344 | −0.194672 | − | 0.980868i | \(-0.562364\pi\) | ||||
−0.194672 | + | 0.980868i | \(0.562364\pi\) | |||||||
\(740\) | −8.12750 | −0.298773 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.88545 | −0.142639 | ||||||||
\(743\) | −8.83031 | −0.323953 | −0.161976 | − | 0.986795i | \(-0.551787\pi\) | ||||
−0.161976 | + | 0.986795i | \(0.551787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.76721 | −0.0647456 | ||||||||
\(746\) | −18.5063 | −0.677564 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.09698 | −0.0401097 | ||||||||
\(749\) | 36.2017 | 1.32278 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7397 | 0.428389 | 0.214194 | − | 0.976791i | \(-0.431287\pi\) | ||||
0.214194 | + | 0.976791i | \(0.431287\pi\) | |||||||
\(752\) | 10.3563 | 0.377654 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.23049 | −0.0448118 | ||||||||
\(755\) | 37.2050 | 1.35403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.7776 | −1.37305 | −0.686525 | − | 0.727107i | \(-0.740865\pi\) | ||||
−0.686525 | + | 0.727107i | \(0.740865\pi\) | |||||||
\(758\) | −25.2996 | −0.918924 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.432933 | −0.0157041 | ||||||||
\(761\) | −9.75982 | −0.353793 | −0.176897 | − | 0.984229i | \(-0.556606\pi\) | ||||
−0.176897 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.5104 | −0.851135 | ||||||||
\(764\) | −19.1244 | −0.691895 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.6264 | −1.35950 | ||||||||
\(767\) | 10.4999 | 0.379129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.0317 | −1.94843 | −0.974217 | − | 0.225614i | \(-0.927561\pi\) | ||||
−0.974217 | + | 0.225614i | \(0.927561\pi\) | |||||||
\(770\) | 0.772806 | 0.0278500 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.6585 | 0.671535 | ||||||||
\(773\) | 42.5648 | 1.53095 | 0.765475 | − | 0.643465i | \(-0.222504\pi\) | ||||
0.765475 | + | 0.643465i | \(0.222504\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.21329 | 0.151346 | ||||||||
\(776\) | 13.9739 | 0.501633 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.1522 | 0.937603 | ||||||||
\(779\) | 1.95828 | 0.0701628 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.75108 | 0.0626587 | ||||||||
\(782\) | 4.94053 | 0.176673 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.590673 | −0.0210954 | ||||||||
\(785\) | −2.29601 | −0.0819481 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5826 | 1.26838 | 0.634191 | − | 0.773177i | \(-0.281333\pi\) | ||||
0.634191 | + | 0.773177i | \(0.281333\pi\) | |||||||
\(788\) | 6.74520 | 0.240288 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.60627 | 0.128305 | ||||||||
\(791\) | −40.8952 | −1.45407 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.42890 | 0.0862529 | ||||||||
\(794\) | −8.99278 | −0.319142 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.9797 | 0.601828 | ||||||||
\(797\) | −48.5637 | −1.72021 | −0.860107 | − | 0.510114i | \(-0.829603\pi\) | ||||
−0.860107 | + | 0.510114i | \(0.829603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.7698 | 2.32677 | ||||||||
\(800\) | −1.87697 | −0.0663609 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.9760 | 0.952554 | ||||||||
\(803\) | 2.53045 | 0.0892978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.48052 | −0.122672 | ||||||||
\(806\) | −2.99438 | −0.105472 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.5965 | 0.548684 | ||||||||
\(809\) | −37.5919 | −1.32166 | −0.660831 | − | 0.750535i | \(-0.729796\pi\) | ||||
−0.660831 | + | 0.750535i | \(0.729796\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.1414 | −0.391228 | −0.195614 | − | 0.980681i | \(-0.562670\pi\) | ||||
−0.195614 | + | 0.980681i | \(0.562670\pi\) | |||||||
\(812\) | −2.33530 | −0.0819529 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.794411 | −0.0278441 | ||||||||
\(815\) | −31.6129 | −1.10735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.30717 | −0.0807177 | ||||||||
\(818\) | −0.843424 | −0.0294896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.1264 | −0.493315 | ||||||||
\(821\) | 1.38903 | 0.0484775 | 0.0242387 | − | 0.999706i | \(-0.492284\pi\) | ||||
0.0242387 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.3396 | −0.848426 | −0.424213 | − | 0.905563i | \(-0.639449\pi\) | ||||
−0.424213 | + | 0.905563i | \(0.639449\pi\) | |||||||
\(824\) | −9.33732 | −0.325281 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.9273 | 0.693359 | ||||||||
\(827\) | 41.5712 | 1.44557 | 0.722786 | − | 0.691072i | \(-0.242861\pi\) | ||||
0.722786 | + | 0.691072i | \(0.242861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.7876 | −1.20822 | −0.604112 | − | 0.796900i | \(-0.706472\pi\) | ||||
−0.604112 | + | 0.796900i | \(0.706472\pi\) | |||||||
\(830\) | −24.1203 | −0.837228 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.33396 | 0.0462467 | ||||||||
\(833\) | −3.75120 | −0.129971 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.6918 | −1.44280 | ||||||||
\(836\) | −0.0423164 | −0.00146354 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.4722 | −1.12173 | ||||||||
\(839\) | 22.5319 | 0.777887 | 0.388944 | − | 0.921262i | \(-0.372840\pi\) | ||||
0.388944 | + | 0.921262i | \(0.372840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1491 | −0.970659 | ||||||||
\(842\) | 31.3692 | 1.08105 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.62775 | −0.0560296 | ||||||||
\(845\) | 19.8291 | 0.682141 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.7728 | −0.954284 | ||||||||
\(848\) | −1.53474 | −0.0527032 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.9201 | −0.408857 | ||||||||
\(851\) | 3.57782 | 0.122646 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.8670 | 1.05687 | 0.528433 | − | 0.848975i | \(-0.322780\pi\) | ||||
0.528433 | + | 0.848975i | \(0.322780\pi\) | |||||||
\(854\) | 4.60972 | 0.157741 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.2996 | 0.488750 | ||||||||
\(857\) | −3.26408 | −0.111499 | −0.0557495 | − | 0.998445i | \(-0.517755\pi\) | ||||
−0.0557495 | + | 0.998445i | \(0.517755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8097 | 0.812376 | 0.406188 | − | 0.913790i | \(-0.366858\pi\) | ||||
0.406188 | + | 0.913790i | \(0.366858\pi\) | |||||||
\(860\) | 16.6432 | 0.567527 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.0091 | 1.09023 | ||||||||
\(863\) | 24.1010 | 0.820408 | 0.410204 | − | 0.911994i | \(-0.365457\pi\) | ||||
0.410204 | + | 0.911994i | \(0.365457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.58937 | 0.326048 | ||||||||
\(866\) | −19.5149 | −0.663142 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.68291 | −0.192890 | ||||||||
\(869\) | 0.352490 | 0.0119574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8476 | 0.469209 | ||||||||
\(872\) | −9.28655 | −0.314482 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.190582 | 0.00644653 | ||||||||
\(875\) | 30.7674 | 1.04013 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.84472 | 0.332433 | 0.166216 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166216 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(878\) | −38.2094 | −1.28950 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.305256 | 0.0102902 | ||||||||
\(881\) | 16.5879 | 0.558862 | 0.279431 | − | 0.960166i | \(-0.409854\pi\) | ||||
0.279431 | + | 0.960166i | \(0.409854\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.2685 | −1.59071 | −0.795355 | − | 0.606143i | \(-0.792716\pi\) | ||||
−0.795355 | + | 0.606143i | \(0.792716\pi\) | |||||||
\(884\) | 8.47161 | 0.284931 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.6766 | 0.459475 | ||||||||
\(887\) | 0.359158 | 0.0120593 | 0.00602967 | − | 0.999982i | \(-0.498081\pi\) | ||||
0.00602967 | + | 0.999982i | \(0.498081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.1850 | 0.978833 | ||||||||
\(890\) | 0.958359 | 0.0321243 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.2695 | 0.946531 | ||||||||
\(893\) | 2.53708 | 0.0849003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.0911 | −0.537865 | ||||||||
\(896\) | 2.53166 | 0.0845770 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.9553 | −1.16647 | ||||||||
\(899\) | 2.07062 | 0.0690590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.74672 | −0.324710 | ||||||||
\(902\) | −1.38076 | −0.0459744 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1535 | −0.537257 | ||||||||
\(905\) | 7.54340 | 0.250751 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7279 | 0.522236 | 0.261118 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261118 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(908\) | −17.1689 | −0.569769 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.96810 | −0.197841 | ||||||||
\(911\) | −8.06624 | −0.267246 | −0.133623 | − | 0.991032i | \(-0.542661\pi\) | ||||
−0.133623 | + | 0.991032i | \(0.542661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.35760 | −0.0780253 | ||||||||
\(914\) | 19.5492 | 0.646628 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.0079 | 0.396751 | ||||||||
\(917\) | −33.5211 | −1.10696 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.4648 | −0.444163 | −0.222081 | − | 0.975028i | \(-0.571285\pi\) | ||||
−0.222081 | + | 0.975028i | \(0.571285\pi\) | |||||||
\(920\) | −1.37479 | −0.0453256 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.0442 | 0.758921 | ||||||||
\(923\) | −13.5230 | −0.445114 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.63230 | −0.283828 | ||||||||
\(926\) | −2.30744 | −0.0758273 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.922435 | −0.0302804 | ||||||||
\(929\) | −19.3356 | −0.634380 | −0.317190 | − | 0.948362i | \(-0.602739\pi\) | ||||
−0.317190 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.144703 | −0.00474246 | ||||||||
\(932\) | 20.2171 | 0.662233 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.1472 | 0.397469 | ||||||||
\(935\) | 1.93860 | 0.0633990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.1949 | −1.37845 | −0.689224 | − | 0.724548i | \(-0.742049\pi\) | ||||
−0.689224 | + | 0.724548i | \(0.742049\pi\) | |||||||
\(938\) | 26.2808 | 0.858100 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.3017 | −0.596935 | ||||||||
\(941\) | 18.3595 | 0.598502 | 0.299251 | − | 0.954174i | \(-0.403263\pi\) | ||||
0.299251 | + | 0.954174i | \(0.403263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.21861 | 0.202506 | ||||||||
\(944\) | 7.87122 | 0.256186 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.62676 | 0.0528906 | ||||||||
\(947\) | −15.5641 | −0.505766 | −0.252883 | − | 0.967497i | \(-0.581379\pi\) | ||||
−0.252883 | + | 0.967497i | \(0.581379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5418 | −0.634353 | ||||||||
\(950\) | −0.459822 | −0.0149186 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.0779 | 0.521089 | ||||||||
\(953\) | −8.81570 | −0.285569 | −0.142784 | − | 0.989754i | \(-0.545606\pi\) | ||||
−0.142784 | + | 0.989754i | \(0.545606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.7968 | 1.09364 | ||||||||
\(956\) | 5.11495 | 0.165429 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.3346 | −0.560055 | ||||||||
\(959\) | 25.9684 | 0.838564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9612 | −0.837458 | ||||||||
\(962\) | 6.13495 | 0.197799 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.0965 | 0.937136 | ||||||||
\(965\) | −32.9735 | −1.06146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.39034 | −0.237657 | −0.118829 | − | 0.992915i | \(-0.537914\pi\) | ||||
−0.118829 | + | 0.992915i | \(0.537914\pi\) | |||||||
\(968\) | −10.9702 | −0.352594 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.6948 | −0.792901 | ||||||||
\(971\) | −43.6961 | −1.40228 | −0.701138 | − | 0.713026i | \(-0.747324\pi\) | ||||
−0.701138 | + | 0.713026i | \(0.747324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.3675 | −0.909421 | ||||||||
\(974\) | −34.5694 | −1.10767 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.82082 | 0.0582832 | ||||||||
\(977\) | 46.3239 | 1.48203 | 0.741016 | − | 0.671488i | \(-0.234344\pi\) | ||||
0.741016 | + | 0.671488i | \(0.234344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0936734 | 0.00299382 | ||||||||
\(980\) | 1.04384 | 0.0333443 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.6299 | −1.20082 | ||||||||
\(983\) | −53.7041 | −1.71289 | −0.856447 | − | 0.516235i | \(-0.827333\pi\) | ||||
−0.856447 | + | 0.516235i | \(0.827333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9202 | −0.379808 | ||||||||
\(986\) | −5.85814 | −0.186561 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.326794 | 0.0103967 | ||||||||
\(989\) | −7.32652 | −0.232970 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.7809 | −1.04132 | −0.520659 | − | 0.853765i | \(-0.674314\pi\) | ||||
−0.520659 | + | 0.853765i | \(0.674314\pi\) | |||||||
\(992\) | −2.24473 | −0.0712703 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.6647 | −0.814036 | ||||||||
\(995\) | −30.0066 | −0.951274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9203 | 0.662554 | 0.331277 | − | 0.943534i | \(-0.392521\pi\) | ||||
0.331277 | + | 0.943534i | \(0.392521\pi\) | |||||||
\(998\) | 35.7585 | 1.13192 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.o.1.4 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.j.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.9 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.o.1.4 | yes | 12 | 1.1 | even | 1 | trivial |