Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
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 | 1.7 | ||
Root | \(0.171582\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.171582 | 0.121327 | 0.0606633 | − | 0.998158i | \(-0.480678\pi\) | ||||
0.0606633 | + | 0.998158i | \(0.480678\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97056 | −0.985280 | ||||||||
\(5\) | −0.133072 | −0.0595116 | −0.0297558 | − | 0.999557i | \(-0.509473\pi\) | ||||
−0.0297558 | + | 0.999557i | \(0.509473\pi\) | |||||||
\(6\) | −0.171582 | −0.0700479 | ||||||||
\(7\) | 0.615329 | 0.232572 | 0.116286 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116286 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(8\) | −0.681275 | −0.240867 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0228327 | −0.00722034 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.97056 | 0.568852 | ||||||||
\(13\) | −4.70459 | −1.30482 | −0.652409 | − | 0.757867i | \(-0.726241\pi\) | ||||
−0.652409 | + | 0.757867i | \(0.726241\pi\) | |||||||
\(14\) | 0.105579 | 0.0282172 | ||||||||
\(15\) | 0.133072 | 0.0343590 | ||||||||
\(16\) | 3.82423 | 0.956056 | ||||||||
\(17\) | 2.34281 | 0.568215 | 0.284108 | − | 0.958792i | \(-0.408303\pi\) | ||||
0.284108 | + | 0.958792i | \(0.408303\pi\) | |||||||
\(18\) | 0.171582 | 0.0404422 | ||||||||
\(19\) | −7.85906 | −1.80299 | −0.901496 | − | 0.432788i | \(-0.857530\pi\) | ||||
−0.901496 | + | 0.432788i | \(0.857530\pi\) | |||||||
\(20\) | 0.262226 | 0.0586356 | ||||||||
\(21\) | −0.615329 | −0.134276 | ||||||||
\(22\) | 0.171582 | 0.0365813 | ||||||||
\(23\) | 1.86581 | 0.389048 | 0.194524 | − | 0.980898i | \(-0.437684\pi\) | ||||
0.194524 | + | 0.980898i | \(0.437684\pi\) | |||||||
\(24\) | 0.681275 | 0.139065 | ||||||||
\(25\) | −4.98229 | −0.996458 | ||||||||
\(26\) | −0.807221 | −0.158309 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.21254 | −0.229149 | ||||||||
\(29\) | 4.53951 | 0.842965 | 0.421482 | − | 0.906837i | \(-0.361510\pi\) | ||||
0.421482 | + | 0.906837i | \(0.361510\pi\) | |||||||
\(30\) | 0.0228327 | 0.00416867 | ||||||||
\(31\) | 3.06900 | 0.551208 | 0.275604 | − | 0.961271i | \(-0.411122\pi\) | ||||
0.275604 | + | 0.961271i | \(0.411122\pi\) | |||||||
\(32\) | 2.01872 | 0.356862 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.401984 | 0.0689396 | ||||||||
\(35\) | −0.0818830 | −0.0138408 | ||||||||
\(36\) | −1.97056 | −0.328427 | ||||||||
\(37\) | 9.24562 | 1.51997 | 0.759986 | − | 0.649940i | \(-0.225206\pi\) | ||||
0.759986 | + | 0.649940i | \(0.225206\pi\) | |||||||
\(38\) | −1.34847 | −0.218751 | ||||||||
\(39\) | 4.70459 | 0.753337 | ||||||||
\(40\) | 0.0906587 | 0.0143344 | ||||||||
\(41\) | 1.52969 | 0.238897 | 0.119449 | − | 0.992840i | \(-0.461887\pi\) | ||||
0.119449 | + | 0.992840i | \(0.461887\pi\) | |||||||
\(42\) | −0.105579 | −0.0162912 | ||||||||
\(43\) | 1.17504 | 0.179193 | 0.0895963 | − | 0.995978i | \(-0.471442\pi\) | ||||
0.0895963 | + | 0.995978i | \(0.471442\pi\) | |||||||
\(44\) | −1.97056 | −0.297073 | ||||||||
\(45\) | −0.133072 | −0.0198372 | ||||||||
\(46\) | 0.320139 | 0.0472019 | ||||||||
\(47\) | −7.78342 | −1.13533 | −0.567664 | − | 0.823260i | \(-0.692153\pi\) | ||||
−0.567664 | + | 0.823260i | \(0.692153\pi\) | |||||||
\(48\) | −3.82423 | −0.551979 | ||||||||
\(49\) | −6.62137 | −0.945910 | ||||||||
\(50\) | −0.854870 | −0.120897 | ||||||||
\(51\) | −2.34281 | −0.328059 | ||||||||
\(52\) | 9.27067 | 1.28561 | ||||||||
\(53\) | −11.1113 | −1.52626 | −0.763130 | − | 0.646246i | \(-0.776338\pi\) | ||||
−0.763130 | + | 0.646246i | \(0.776338\pi\) | |||||||
\(54\) | −0.171582 | −0.0233493 | ||||||||
\(55\) | −0.133072 | −0.0179434 | ||||||||
\(56\) | −0.419208 | −0.0560191 | ||||||||
\(57\) | 7.85906 | 1.04096 | ||||||||
\(58\) | 0.778896 | 0.102274 | ||||||||
\(59\) | 11.0751 | 1.44185 | 0.720925 | − | 0.693013i | \(-0.243717\pi\) | ||||
0.720925 | + | 0.693013i | \(0.243717\pi\) | |||||||
\(60\) | −0.262226 | −0.0338533 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 0.526584 | 0.0668762 | ||||||||
\(63\) | 0.615329 | 0.0775242 | ||||||||
\(64\) | −7.30207 | −0.912759 | ||||||||
\(65\) | 0.626049 | 0.0776518 | ||||||||
\(66\) | −0.171582 | −0.0211202 | ||||||||
\(67\) | 11.2239 | 1.37121 | 0.685607 | − | 0.727972i | \(-0.259537\pi\) | ||||
0.685607 | + | 0.727972i | \(0.259537\pi\) | |||||||
\(68\) | −4.61665 | −0.559851 | ||||||||
\(69\) | −1.86581 | −0.224617 | ||||||||
\(70\) | −0.0140496 | −0.00167925 | ||||||||
\(71\) | −6.59487 | −0.782668 | −0.391334 | − | 0.920249i | \(-0.627986\pi\) | ||||
−0.391334 | + | 0.920249i | \(0.627986\pi\) | |||||||
\(72\) | −0.681275 | −0.0802891 | ||||||||
\(73\) | 4.36946 | 0.511406 | 0.255703 | − | 0.966755i | \(-0.417693\pi\) | ||||
0.255703 | + | 0.966755i | \(0.417693\pi\) | |||||||
\(74\) | 1.58638 | 0.184413 | ||||||||
\(75\) | 4.98229 | 0.575306 | ||||||||
\(76\) | 15.4867 | 1.77645 | ||||||||
\(77\) | 0.615329 | 0.0701232 | ||||||||
\(78\) | 0.807221 | 0.0913998 | ||||||||
\(79\) | 11.7882 | 1.32628 | 0.663141 | − | 0.748495i | \(-0.269223\pi\) | ||||
0.663141 | + | 0.748495i | \(0.269223\pi\) | |||||||
\(80\) | −0.508897 | −0.0568964 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.262467 | 0.0289846 | ||||||||
\(83\) | 10.8873 | 1.19503 | 0.597517 | − | 0.801856i | \(-0.296154\pi\) | ||||
0.597517 | + | 0.801856i | \(0.296154\pi\) | |||||||
\(84\) | 1.21254 | 0.132299 | ||||||||
\(85\) | −0.311763 | −0.0338154 | ||||||||
\(86\) | 0.201616 | 0.0217408 | ||||||||
\(87\) | −4.53951 | −0.486686 | ||||||||
\(88\) | −0.681275 | −0.0726242 | ||||||||
\(89\) | 15.1533 | 1.60625 | 0.803123 | − | 0.595813i | \(-0.203170\pi\) | ||||
0.803123 | + | 0.595813i | \(0.203170\pi\) | |||||||
\(90\) | −0.0228327 | −0.00240678 | ||||||||
\(91\) | −2.89487 | −0.303465 | ||||||||
\(92\) | −3.67669 | −0.383321 | ||||||||
\(93\) | −3.06900 | −0.318240 | ||||||||
\(94\) | −1.33549 | −0.137745 | ||||||||
\(95\) | 1.04582 | 0.107299 | ||||||||
\(96\) | −2.01872 | −0.206035 | ||||||||
\(97\) | 15.1739 | 1.54068 | 0.770340 | − | 0.637633i | \(-0.220086\pi\) | ||||
0.770340 | + | 0.637633i | \(0.220086\pi\) | |||||||
\(98\) | −1.13611 | −0.114764 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 9.81790 | 0.981790 | ||||||||
\(101\) | 14.9729 | 1.48986 | 0.744931 | − | 0.667141i | \(-0.232482\pi\) | ||||
0.744931 | + | 0.667141i | \(0.232482\pi\) | |||||||
\(102\) | −0.401984 | −0.0398023 | ||||||||
\(103\) | 2.65906 | 0.262005 | 0.131003 | − | 0.991382i | \(-0.458180\pi\) | ||||
0.131003 | + | 0.991382i | \(0.458180\pi\) | |||||||
\(104\) | 3.20512 | 0.314288 | ||||||||
\(105\) | 0.0818830 | 0.00799097 | ||||||||
\(106\) | −1.90650 | −0.185176 | ||||||||
\(107\) | 9.97635 | 0.964450 | 0.482225 | − | 0.876047i | \(-0.339829\pi\) | ||||
0.482225 | + | 0.876047i | \(0.339829\pi\) | |||||||
\(108\) | 1.97056 | 0.189617 | ||||||||
\(109\) | −8.83359 | −0.846104 | −0.423052 | − | 0.906105i | \(-0.639041\pi\) | ||||
−0.423052 | + | 0.906105i | \(0.639041\pi\) | |||||||
\(110\) | −0.0228327 | −0.00217701 | ||||||||
\(111\) | −9.24562 | −0.877556 | ||||||||
\(112\) | 2.35316 | 0.222352 | ||||||||
\(113\) | −4.24584 | −0.399415 | −0.199707 | − | 0.979856i | \(-0.563999\pi\) | ||||
−0.199707 | + | 0.979856i | \(0.563999\pi\) | |||||||
\(114\) | 1.34847 | 0.126296 | ||||||||
\(115\) | −0.248287 | −0.0231529 | ||||||||
\(116\) | −8.94537 | −0.830556 | ||||||||
\(117\) | −4.70459 | −0.434939 | ||||||||
\(118\) | 1.90028 | 0.174935 | ||||||||
\(119\) | 1.44160 | 0.132151 | ||||||||
\(120\) | −0.0906587 | −0.00827597 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.171582 | −0.0155343 | ||||||||
\(123\) | −1.52969 | −0.137927 | ||||||||
\(124\) | −6.04764 | −0.543094 | ||||||||
\(125\) | 1.32836 | 0.118812 | ||||||||
\(126\) | 0.105579 | 0.00940574 | ||||||||
\(127\) | 19.3085 | 1.71335 | 0.856675 | − | 0.515856i | \(-0.172526\pi\) | ||||
0.856675 | + | 0.515856i | \(0.172526\pi\) | |||||||
\(128\) | −5.29034 | −0.467604 | ||||||||
\(129\) | −1.17504 | −0.103457 | ||||||||
\(130\) | 0.107419 | 0.00942123 | ||||||||
\(131\) | 16.1882 | 1.41437 | 0.707187 | − | 0.707027i | \(-0.249964\pi\) | ||||
0.707187 | + | 0.707027i | \(0.249964\pi\) | |||||||
\(132\) | 1.97056 | 0.171515 | ||||||||
\(133\) | −4.83590 | −0.419326 | ||||||||
\(134\) | 1.92581 | 0.166365 | ||||||||
\(135\) | 0.133072 | 0.0114530 | ||||||||
\(136\) | −1.59610 | −0.136864 | ||||||||
\(137\) | −16.9876 | −1.45135 | −0.725674 | − | 0.688038i | \(-0.758472\pi\) | ||||
−0.725674 | + | 0.688038i | \(0.758472\pi\) | |||||||
\(138\) | −0.320139 | −0.0272520 | ||||||||
\(139\) | 0.981625 | 0.0832604 | 0.0416302 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416302 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(140\) | 0.161355 | 0.0136370 | ||||||||
\(141\) | 7.78342 | 0.655482 | ||||||||
\(142\) | −1.13156 | −0.0949584 | ||||||||
\(143\) | −4.70459 | −0.393417 | ||||||||
\(144\) | 3.82423 | 0.318685 | ||||||||
\(145\) | −0.604081 | −0.0501662 | ||||||||
\(146\) | 0.749719 | 0.0620472 | ||||||||
\(147\) | 6.62137 | 0.546121 | ||||||||
\(148\) | −18.2191 | −1.49760 | ||||||||
\(149\) | 19.9181 | 1.63175 | 0.815876 | − | 0.578227i | \(-0.196255\pi\) | ||||
0.815876 | + | 0.578227i | \(0.196255\pi\) | |||||||
\(150\) | 0.854870 | 0.0697999 | ||||||||
\(151\) | −9.27179 | −0.754528 | −0.377264 | − | 0.926106i | \(-0.623135\pi\) | ||||
−0.377264 | + | 0.926106i | \(0.623135\pi\) | |||||||
\(152\) | 5.35418 | 0.434282 | ||||||||
\(153\) | 2.34281 | 0.189405 | ||||||||
\(154\) | 0.105579 | 0.00850781 | ||||||||
\(155\) | −0.408397 | −0.0328033 | ||||||||
\(156\) | −9.27067 | −0.742248 | ||||||||
\(157\) | 9.62702 | 0.768320 | 0.384160 | − | 0.923267i | \(-0.374491\pi\) | ||||
0.384160 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(158\) | 2.02265 | 0.160913 | ||||||||
\(159\) | 11.1113 | 0.881186 | ||||||||
\(160\) | −0.268635 | −0.0212374 | ||||||||
\(161\) | 1.14809 | 0.0904818 | ||||||||
\(162\) | 0.171582 | 0.0134807 | ||||||||
\(163\) | 17.0593 | 1.33619 | 0.668093 | − | 0.744077i | \(-0.267111\pi\) | ||||
0.668093 | + | 0.744077i | \(0.267111\pi\) | |||||||
\(164\) | −3.01434 | −0.235381 | ||||||||
\(165\) | 0.133072 | 0.0103596 | ||||||||
\(166\) | 1.86806 | 0.144989 | ||||||||
\(167\) | 8.92176 | 0.690387 | 0.345193 | − | 0.938532i | \(-0.387813\pi\) | ||||
0.345193 | + | 0.938532i | \(0.387813\pi\) | |||||||
\(168\) | 0.419208 | 0.0323426 | ||||||||
\(169\) | 9.13314 | 0.702549 | ||||||||
\(170\) | −0.0534928 | −0.00410271 | ||||||||
\(171\) | −7.85906 | −0.600997 | ||||||||
\(172\) | −2.31549 | −0.176555 | ||||||||
\(173\) | 3.85738 | 0.293271 | 0.146636 | − | 0.989191i | \(-0.453156\pi\) | ||||
0.146636 | + | 0.989191i | \(0.453156\pi\) | |||||||
\(174\) | −0.778896 | −0.0590480 | ||||||||
\(175\) | −3.06575 | −0.231749 | ||||||||
\(176\) | 3.82423 | 0.288262 | ||||||||
\(177\) | −11.0751 | −0.832453 | ||||||||
\(178\) | 2.60003 | 0.194880 | ||||||||
\(179\) | −10.4383 | −0.780194 | −0.390097 | − | 0.920774i | \(-0.627558\pi\) | ||||
−0.390097 | + | 0.920774i | \(0.627558\pi\) | |||||||
\(180\) | 0.262226 | 0.0195452 | ||||||||
\(181\) | 13.9705 | 1.03842 | 0.519208 | − | 0.854648i | \(-0.326227\pi\) | ||||
0.519208 | + | 0.854648i | \(0.326227\pi\) | |||||||
\(182\) | −0.496706 | −0.0368183 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −1.27113 | −0.0937089 | ||||||||
\(185\) | −1.23033 | −0.0904559 | ||||||||
\(186\) | −0.526584 | −0.0386110 | ||||||||
\(187\) | 2.34281 | 0.171323 | ||||||||
\(188\) | 15.3377 | 1.11862 | ||||||||
\(189\) | −0.615329 | −0.0447586 | ||||||||
\(190\) | 0.179444 | 0.0130182 | ||||||||
\(191\) | −24.4448 | −1.76876 | −0.884382 | − | 0.466763i | \(-0.845420\pi\) | ||||
−0.884382 | + | 0.466763i | \(0.845420\pi\) | |||||||
\(192\) | 7.30207 | 0.526982 | ||||||||
\(193\) | −6.16239 | −0.443578 | −0.221789 | − | 0.975095i | \(-0.571190\pi\) | ||||
−0.221789 | + | 0.975095i | \(0.571190\pi\) | |||||||
\(194\) | 2.60357 | 0.186926 | ||||||||
\(195\) | −0.626049 | −0.0448323 | ||||||||
\(196\) | 13.0478 | 0.931986 | ||||||||
\(197\) | −16.1438 | −1.15020 | −0.575100 | − | 0.818083i | \(-0.695037\pi\) | ||||
−0.575100 | + | 0.818083i | \(0.695037\pi\) | |||||||
\(198\) | 0.171582 | 0.0121938 | ||||||||
\(199\) | −11.7030 | −0.829600 | −0.414800 | − | 0.909913i | \(-0.636149\pi\) | ||||
−0.414800 | + | 0.909913i | \(0.636149\pi\) | |||||||
\(200\) | 3.39431 | 0.240014 | ||||||||
\(201\) | −11.2239 | −0.791670 | ||||||||
\(202\) | 2.56908 | 0.180760 | ||||||||
\(203\) | 2.79329 | 0.196050 | ||||||||
\(204\) | 4.61665 | 0.323230 | ||||||||
\(205\) | −0.203559 | −0.0142172 | ||||||||
\(206\) | 0.456247 | 0.0317882 | ||||||||
\(207\) | 1.86581 | 0.129683 | ||||||||
\(208\) | −17.9914 | −1.24748 | ||||||||
\(209\) | −7.85906 | −0.543622 | ||||||||
\(210\) | 0.0140496 | 0.000969517 0 | ||||||||
\(211\) | −13.0881 | −0.901019 | −0.450509 | − | 0.892772i | \(-0.648758\pi\) | ||||
−0.450509 | + | 0.892772i | \(0.648758\pi\) | |||||||
\(212\) | 21.8955 | 1.50379 | ||||||||
\(213\) | 6.59487 | 0.451873 | ||||||||
\(214\) | 1.71176 | 0.117013 | ||||||||
\(215\) | −0.156365 | −0.0106640 | ||||||||
\(216\) | 0.681275 | 0.0463549 | ||||||||
\(217\) | 1.88844 | 0.128196 | ||||||||
\(218\) | −1.51568 | −0.102655 | ||||||||
\(219\) | −4.36946 | −0.295261 | ||||||||
\(220\) | 0.262226 | 0.0176793 | ||||||||
\(221\) | −11.0220 | −0.741417 | ||||||||
\(222\) | −1.58638 | −0.106471 | ||||||||
\(223\) | 2.06775 | 0.138467 | 0.0692334 | − | 0.997600i | \(-0.477945\pi\) | ||||
0.0692334 | + | 0.997600i | \(0.477945\pi\) | |||||||
\(224\) | 1.24218 | 0.0829963 | ||||||||
\(225\) | −4.98229 | −0.332153 | ||||||||
\(226\) | −0.728508 | −0.0484596 | ||||||||
\(227\) | −6.15200 | −0.408322 | −0.204161 | − | 0.978937i | \(-0.565447\pi\) | ||||
−0.204161 | + | 0.978937i | \(0.565447\pi\) | |||||||
\(228\) | −15.4867 | −1.02563 | ||||||||
\(229\) | 19.5963 | 1.29496 | 0.647479 | − | 0.762083i | \(-0.275823\pi\) | ||||
0.647479 | + | 0.762083i | \(0.275823\pi\) | |||||||
\(230\) | −0.0426015 | −0.00280906 | ||||||||
\(231\) | −0.615329 | −0.0404857 | ||||||||
\(232\) | −3.09265 | −0.203043 | ||||||||
\(233\) | −20.5752 | −1.34792 | −0.673962 | − | 0.738766i | \(-0.735409\pi\) | ||||
−0.673962 | + | 0.738766i | \(0.735409\pi\) | |||||||
\(234\) | −0.807221 | −0.0527697 | ||||||||
\(235\) | 1.03575 | 0.0675652 | ||||||||
\(236\) | −21.8241 | −1.42063 | ||||||||
\(237\) | −11.7882 | −0.765729 | ||||||||
\(238\) | 0.247352 | 0.0160335 | ||||||||
\(239\) | −23.1378 | −1.49666 | −0.748330 | − | 0.663327i | \(-0.769144\pi\) | ||||
−0.748330 | + | 0.663327i | \(0.769144\pi\) | |||||||
\(240\) | 0.508897 | 0.0328492 | ||||||||
\(241\) | 0.0983366 | 0.00633442 | 0.00316721 | − | 0.999995i | \(-0.498992\pi\) | ||||
0.00316721 | + | 0.999995i | \(0.498992\pi\) | |||||||
\(242\) | 0.171582 | 0.0110297 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.97056 | 0.126152 | ||||||||
\(245\) | 0.881119 | 0.0562926 | ||||||||
\(246\) | −0.262467 | −0.0167343 | ||||||||
\(247\) | 36.9736 | 2.35257 | ||||||||
\(248\) | −2.09083 | −0.132768 | ||||||||
\(249\) | −10.8873 | −0.689953 | ||||||||
\(250\) | 0.227923 | 0.0144151 | ||||||||
\(251\) | −3.43655 | −0.216913 | −0.108457 | − | 0.994101i | \(-0.534591\pi\) | ||||
−0.108457 | + | 0.994101i | \(0.534591\pi\) | |||||||
\(252\) | −1.21254 | −0.0763830 | ||||||||
\(253\) | 1.86581 | 0.117302 | ||||||||
\(254\) | 3.31298 | 0.207875 | ||||||||
\(255\) | 0.311763 | 0.0195233 | ||||||||
\(256\) | 13.6964 | 0.856027 | ||||||||
\(257\) | −12.4152 | −0.774439 | −0.387220 | − | 0.921988i | \(-0.626564\pi\) | ||||
−0.387220 | + | 0.921988i | \(0.626564\pi\) | |||||||
\(258\) | −0.201616 | −0.0125521 | ||||||||
\(259\) | 5.68910 | 0.353503 | ||||||||
\(260\) | −1.23367 | −0.0765087 | ||||||||
\(261\) | 4.53951 | 0.280988 | ||||||||
\(262\) | 2.77761 | 0.171601 | ||||||||
\(263\) | 4.10959 | 0.253408 | 0.126704 | − | 0.991941i | \(-0.459560\pi\) | ||||
0.126704 | + | 0.991941i | \(0.459560\pi\) | |||||||
\(264\) | 0.681275 | 0.0419296 | ||||||||
\(265\) | 1.47861 | 0.0908301 | ||||||||
\(266\) | −0.829753 | −0.0508754 | ||||||||
\(267\) | −15.1533 | −0.927367 | ||||||||
\(268\) | −22.1173 | −1.35103 | ||||||||
\(269\) | 17.7222 | 1.08054 | 0.540270 | − | 0.841492i | \(-0.318322\pi\) | ||||
0.540270 | + | 0.841492i | \(0.318322\pi\) | |||||||
\(270\) | 0.0228327 | 0.00138956 | ||||||||
\(271\) | 6.97502 | 0.423702 | 0.211851 | − | 0.977302i | \(-0.432051\pi\) | ||||
0.211851 | + | 0.977302i | \(0.432051\pi\) | |||||||
\(272\) | 8.95944 | 0.543246 | ||||||||
\(273\) | 2.89487 | 0.175205 | ||||||||
\(274\) | −2.91476 | −0.176087 | ||||||||
\(275\) | −4.98229 | −0.300444 | ||||||||
\(276\) | 3.67669 | 0.221311 | ||||||||
\(277\) | −2.67748 | −0.160874 | −0.0804371 | − | 0.996760i | \(-0.525632\pi\) | ||||
−0.0804371 | + | 0.996760i | \(0.525632\pi\) | |||||||
\(278\) | 0.168429 | 0.0101017 | ||||||||
\(279\) | 3.06900 | 0.183736 | ||||||||
\(280\) | 0.0557849 | 0.00333379 | ||||||||
\(281\) | −16.1747 | −0.964905 | −0.482452 | − | 0.875922i | \(-0.660254\pi\) | ||||
−0.482452 | + | 0.875922i | \(0.660254\pi\) | |||||||
\(282\) | 1.33549 | 0.0795274 | ||||||||
\(283\) | 14.1430 | 0.840715 | 0.420357 | − | 0.907359i | \(-0.361905\pi\) | ||||
0.420357 | + | 0.907359i | \(0.361905\pi\) | |||||||
\(284\) | 12.9956 | 0.771147 | ||||||||
\(285\) | −1.04582 | −0.0619490 | ||||||||
\(286\) | −0.807221 | −0.0477320 | ||||||||
\(287\) | 0.941262 | 0.0555609 | ||||||||
\(288\) | 2.01872 | 0.118954 | ||||||||
\(289\) | −11.5112 | −0.677131 | ||||||||
\(290\) | −0.103649 | −0.00608649 | ||||||||
\(291\) | −15.1739 | −0.889512 | ||||||||
\(292\) | −8.61028 | −0.503878 | ||||||||
\(293\) | −8.25000 | −0.481970 | −0.240985 | − | 0.970529i | \(-0.577471\pi\) | ||||
−0.240985 | + | 0.970529i | \(0.577471\pi\) | |||||||
\(294\) | 1.13611 | 0.0662591 | ||||||||
\(295\) | −1.47378 | −0.0858068 | ||||||||
\(296\) | −6.29882 | −0.366111 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 3.41758 | 0.197975 | ||||||||
\(299\) | −8.77786 | −0.507637 | ||||||||
\(300\) | −9.81790 | −0.566837 | ||||||||
\(301\) | 0.723038 | 0.0416752 | ||||||||
\(302\) | −1.59087 | −0.0915443 | ||||||||
\(303\) | −14.9729 | −0.860173 | ||||||||
\(304\) | −30.0548 | −1.72376 | ||||||||
\(305\) | 0.133072 | 0.00761968 | ||||||||
\(306\) | 0.401984 | 0.0229799 | ||||||||
\(307\) | −5.17139 | −0.295147 | −0.147573 | − | 0.989051i | \(-0.547146\pi\) | ||||
−0.147573 | + | 0.989051i | \(0.547146\pi\) | |||||||
\(308\) | −1.21254 | −0.0690910 | ||||||||
\(309\) | −2.65906 | −0.151269 | ||||||||
\(310\) | −0.0700735 | −0.00397991 | ||||||||
\(311\) | 5.56505 | 0.315565 | 0.157783 | − | 0.987474i | \(-0.449565\pi\) | ||||
0.157783 | + | 0.987474i | \(0.449565\pi\) | |||||||
\(312\) | −3.20512 | −0.181454 | ||||||||
\(313\) | −26.1339 | −1.47718 | −0.738589 | − | 0.674156i | \(-0.764507\pi\) | ||||
−0.738589 | + | 0.674156i | \(0.764507\pi\) | |||||||
\(314\) | 1.65182 | 0.0932176 | ||||||||
\(315\) | −0.0818830 | −0.00461359 | ||||||||
\(316\) | −23.2294 | −1.30676 | ||||||||
\(317\) | −9.26111 | −0.520156 | −0.260078 | − | 0.965588i | \(-0.583748\pi\) | ||||
−0.260078 | + | 0.965588i | \(0.583748\pi\) | |||||||
\(318\) | 1.90650 | 0.106911 | ||||||||
\(319\) | 4.53951 | 0.254163 | ||||||||
\(320\) | 0.971702 | 0.0543198 | ||||||||
\(321\) | −9.97635 | −0.556825 | ||||||||
\(322\) | 0.196991 | 0.0109779 | ||||||||
\(323\) | −18.4123 | −1.02449 | ||||||||
\(324\) | −1.97056 | −0.109476 | ||||||||
\(325\) | 23.4396 | 1.30020 | ||||||||
\(326\) | 2.92706 | 0.162115 | ||||||||
\(327\) | 8.83359 | 0.488499 | ||||||||
\(328\) | −1.04214 | −0.0575425 | ||||||||
\(329\) | −4.78936 | −0.264046 | ||||||||
\(330\) | 0.0228327 | 0.00125690 | ||||||||
\(331\) | −2.06884 | −0.113714 | −0.0568569 | − | 0.998382i | \(-0.518108\pi\) | ||||
−0.0568569 | + | 0.998382i | \(0.518108\pi\) | |||||||
\(332\) | −21.4540 | −1.17744 | ||||||||
\(333\) | 9.24562 | 0.506657 | ||||||||
\(334\) | 1.53081 | 0.0837622 | ||||||||
\(335\) | −1.49358 | −0.0816031 | ||||||||
\(336\) | −2.35316 | −0.128375 | ||||||||
\(337\) | −0.238290 | −0.0129805 | −0.00649024 | − | 0.999979i | \(-0.502066\pi\) | ||||
−0.00649024 | + | 0.999979i | \(0.502066\pi\) | |||||||
\(338\) | 1.56708 | 0.0852379 | ||||||||
\(339\) | 4.24584 | 0.230602 | ||||||||
\(340\) | 0.614347 | 0.0333176 | ||||||||
\(341\) | 3.06900 | 0.166195 | ||||||||
\(342\) | −1.34847 | −0.0729169 | ||||||||
\(343\) | −8.38162 | −0.452565 | ||||||||
\(344\) | −0.800529 | −0.0431616 | ||||||||
\(345\) | 0.248287 | 0.0133673 | ||||||||
\(346\) | 0.661856 | 0.0355816 | ||||||||
\(347\) | 27.9023 | 1.49787 | 0.748937 | − | 0.662641i | \(-0.230564\pi\) | ||||
0.748937 | + | 0.662641i | \(0.230564\pi\) | |||||||
\(348\) | 8.94537 | 0.479522 | ||||||||
\(349\) | 30.6969 | 1.64317 | 0.821585 | − | 0.570086i | \(-0.193090\pi\) | ||||
0.821585 | + | 0.570086i | \(0.193090\pi\) | |||||||
\(350\) | −0.526026 | −0.0281173 | ||||||||
\(351\) | 4.70459 | 0.251112 | ||||||||
\(352\) | 2.01872 | 0.107598 | ||||||||
\(353\) | 32.2120 | 1.71447 | 0.857236 | − | 0.514924i | \(-0.172180\pi\) | ||||
0.857236 | + | 0.514924i | \(0.172180\pi\) | |||||||
\(354\) | −1.90028 | −0.100999 | ||||||||
\(355\) | 0.877593 | 0.0465778 | ||||||||
\(356\) | −29.8605 | −1.58260 | ||||||||
\(357\) | −1.44160 | −0.0762976 | ||||||||
\(358\) | −1.79102 | −0.0946582 | ||||||||
\(359\) | −25.4721 | −1.34437 | −0.672184 | − | 0.740384i | \(-0.734644\pi\) | ||||
−0.672184 | + | 0.740384i | \(0.734644\pi\) | |||||||
\(360\) | 0.0906587 | 0.00477813 | ||||||||
\(361\) | 42.7648 | 2.25078 | ||||||||
\(362\) | 2.39708 | 0.125987 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 5.70451 | 0.298998 | ||||||||
\(365\) | −0.581452 | −0.0304346 | ||||||||
\(366\) | 0.171582 | 0.00896872 | ||||||||
\(367\) | 35.8891 | 1.87340 | 0.936698 | − | 0.350138i | \(-0.113865\pi\) | ||||
0.936698 | + | 0.350138i | \(0.113865\pi\) | |||||||
\(368\) | 7.13527 | 0.371952 | ||||||||
\(369\) | 1.52969 | 0.0796324 | ||||||||
\(370\) | −0.211103 | −0.0109747 | ||||||||
\(371\) | −6.83713 | −0.354966 | ||||||||
\(372\) | 6.04764 | 0.313556 | ||||||||
\(373\) | 26.2640 | 1.35990 | 0.679950 | − | 0.733259i | \(-0.262002\pi\) | ||||
0.679950 | + | 0.733259i | \(0.262002\pi\) | |||||||
\(374\) | 0.401984 | 0.0207861 | ||||||||
\(375\) | −1.32836 | −0.0685964 | ||||||||
\(376\) | 5.30265 | 0.273463 | ||||||||
\(377\) | −21.3565 | −1.09992 | ||||||||
\(378\) | −0.105579 | −0.00543041 | ||||||||
\(379\) | −22.5811 | −1.15991 | −0.579957 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579957 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(380\) | −2.06085 | −0.105719 | ||||||||
\(381\) | −19.3085 | −0.989203 | ||||||||
\(382\) | −4.19428 | −0.214598 | ||||||||
\(383\) | 1.52359 | 0.0778520 | 0.0389260 | − | 0.999242i | \(-0.487606\pi\) | ||||
0.0389260 | + | 0.999242i | \(0.487606\pi\) | |||||||
\(384\) | 5.29034 | 0.269971 | ||||||||
\(385\) | −0.0818830 | −0.00417315 | ||||||||
\(386\) | −1.05735 | −0.0538179 | ||||||||
\(387\) | 1.17504 | 0.0597308 | ||||||||
\(388\) | −29.9012 | −1.51800 | ||||||||
\(389\) | −21.4415 | −1.08713 | −0.543563 | − | 0.839369i | \(-0.682925\pi\) | ||||
−0.543563 | + | 0.839369i | \(0.682925\pi\) | |||||||
\(390\) | −0.107419 | −0.00543935 | ||||||||
\(391\) | 4.37124 | 0.221063 | ||||||||
\(392\) | 4.51098 | 0.227839 | ||||||||
\(393\) | −16.1882 | −0.816589 | ||||||||
\(394\) | −2.76999 | −0.139550 | ||||||||
\(395\) | −1.56869 | −0.0789291 | ||||||||
\(396\) | −1.97056 | −0.0990244 | ||||||||
\(397\) | −7.89768 | −0.396373 | −0.198187 | − | 0.980164i | \(-0.563505\pi\) | ||||
−0.198187 | + | 0.980164i | \(0.563505\pi\) | |||||||
\(398\) | −2.00801 | −0.100653 | ||||||||
\(399\) | 4.83590 | 0.242098 | ||||||||
\(400\) | −19.0534 | −0.952670 | ||||||||
\(401\) | 11.0900 | 0.553807 | 0.276903 | − | 0.960898i | \(-0.410692\pi\) | ||||
0.276903 | + | 0.960898i | \(0.410692\pi\) | |||||||
\(402\) | −1.92581 | −0.0960507 | ||||||||
\(403\) | −14.4384 | −0.719226 | ||||||||
\(404\) | −29.5051 | −1.46793 | ||||||||
\(405\) | −0.133072 | −0.00661240 | ||||||||
\(406\) | 0.479277 | 0.0237861 | ||||||||
\(407\) | 9.24562 | 0.458289 | ||||||||
\(408\) | 1.59610 | 0.0790187 | ||||||||
\(409\) | 1.82984 | 0.0904797 | 0.0452399 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452399 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(410\) | −0.0349270 | −0.00172492 | ||||||||
\(411\) | 16.9876 | 0.837937 | ||||||||
\(412\) | −5.23985 | −0.258149 | ||||||||
\(413\) | 6.81481 | 0.335335 | ||||||||
\(414\) | 0.320139 | 0.0157340 | ||||||||
\(415\) | −1.44879 | −0.0711183 | ||||||||
\(416\) | −9.49723 | −0.465640 | ||||||||
\(417\) | −0.981625 | −0.0480704 | ||||||||
\(418\) | −1.34847 | −0.0659558 | ||||||||
\(419\) | 29.0901 | 1.42115 | 0.710573 | − | 0.703623i | \(-0.248436\pi\) | ||||
0.710573 | + | 0.703623i | \(0.248436\pi\) | |||||||
\(420\) | −0.161355 | −0.00787334 | ||||||||
\(421\) | −0.0560143 | −0.00272997 | −0.00136499 | − | 0.999999i | \(-0.500434\pi\) | ||||
−0.00136499 | + | 0.999999i | \(0.500434\pi\) | |||||||
\(422\) | −2.24567 | −0.109318 | ||||||||
\(423\) | −7.78342 | −0.378443 | ||||||||
\(424\) | 7.56988 | 0.367626 | ||||||||
\(425\) | −11.6726 | −0.566203 | ||||||||
\(426\) | 1.13156 | 0.0548243 | ||||||||
\(427\) | −0.615329 | −0.0297779 | ||||||||
\(428\) | −19.6590 | −0.950253 | ||||||||
\(429\) | 4.70459 | 0.227140 | ||||||||
\(430\) | −0.0268294 | −0.00129383 | ||||||||
\(431\) | −2.07838 | −0.100112 | −0.0500561 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500561 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(432\) | −3.82423 | −0.183993 | ||||||||
\(433\) | −5.73899 | −0.275798 | −0.137899 | − | 0.990446i | \(-0.544035\pi\) | ||||
−0.137899 | + | 0.990446i | \(0.544035\pi\) | |||||||
\(434\) | 0.324022 | 0.0155536 | ||||||||
\(435\) | 0.604081 | 0.0289635 | ||||||||
\(436\) | 17.4071 | 0.833650 | ||||||||
\(437\) | −14.6635 | −0.701450 | ||||||||
\(438\) | −0.749719 | −0.0358230 | ||||||||
\(439\) | 32.6721 | 1.55935 | 0.779677 | − | 0.626182i | \(-0.215383\pi\) | ||||
0.779677 | + | 0.626182i | \(0.215383\pi\) | |||||||
\(440\) | 0.0906587 | 0.00432198 | ||||||||
\(441\) | −6.62137 | −0.315303 | ||||||||
\(442\) | −1.89117 | −0.0899537 | ||||||||
\(443\) | −25.8218 | −1.22683 | −0.613415 | − | 0.789761i | \(-0.710205\pi\) | ||||
−0.613415 | + | 0.789761i | \(0.710205\pi\) | |||||||
\(444\) | 18.2191 | 0.864638 | ||||||||
\(445\) | −2.01648 | −0.0955903 | ||||||||
\(446\) | 0.354788 | 0.0167997 | ||||||||
\(447\) | −19.9181 | −0.942093 | ||||||||
\(448\) | −4.49318 | −0.212283 | ||||||||
\(449\) | −18.6591 | −0.880579 | −0.440290 | − | 0.897856i | \(-0.645124\pi\) | ||||
−0.440290 | + | 0.897856i | \(0.645124\pi\) | |||||||
\(450\) | −0.854870 | −0.0402990 | ||||||||
\(451\) | 1.52969 | 0.0720303 | ||||||||
\(452\) | 8.36667 | 0.393535 | ||||||||
\(453\) | 9.27179 | 0.435627 | ||||||||
\(454\) | −1.05557 | −0.0495404 | ||||||||
\(455\) | 0.385226 | 0.0180597 | ||||||||
\(456\) | −5.35418 | −0.250733 | ||||||||
\(457\) | −4.37660 | −0.204729 | −0.102364 | − | 0.994747i | \(-0.532641\pi\) | ||||
−0.102364 | + | 0.994747i | \(0.532641\pi\) | |||||||
\(458\) | 3.36236 | 0.157113 | ||||||||
\(459\) | −2.34281 | −0.109353 | ||||||||
\(460\) | 0.489264 | 0.0228120 | ||||||||
\(461\) | −36.4443 | −1.69738 | −0.848689 | − | 0.528891i | \(-0.822608\pi\) | ||||
−0.848689 | + | 0.528891i | \(0.822608\pi\) | |||||||
\(462\) | −0.105579 | −0.00491199 | ||||||||
\(463\) | 14.5793 | 0.677557 | 0.338779 | − | 0.940866i | \(-0.389986\pi\) | ||||
0.338779 | + | 0.940866i | \(0.389986\pi\) | |||||||
\(464\) | 17.3601 | 0.805922 | ||||||||
\(465\) | 0.408397 | 0.0189390 | ||||||||
\(466\) | −3.53032 | −0.163539 | ||||||||
\(467\) | 26.5701 | 1.22952 | 0.614760 | − | 0.788714i | \(-0.289253\pi\) | ||||
0.614760 | + | 0.788714i | \(0.289253\pi\) | |||||||
\(468\) | 9.27067 | 0.428537 | ||||||||
\(469\) | 6.90637 | 0.318906 | ||||||||
\(470\) | 0.177717 | 0.00819745 | ||||||||
\(471\) | −9.62702 | −0.443590 | ||||||||
\(472\) | −7.54517 | −0.347295 | ||||||||
\(473\) | 1.17504 | 0.0540286 | ||||||||
\(474\) | −2.02265 | −0.0929033 | ||||||||
\(475\) | 39.1561 | 1.79661 | ||||||||
\(476\) | −2.84076 | −0.130206 | ||||||||
\(477\) | −11.1113 | −0.508753 | ||||||||
\(478\) | −3.97002 | −0.181585 | ||||||||
\(479\) | 4.66442 | 0.213123 | 0.106561 | − | 0.994306i | \(-0.466016\pi\) | ||||
0.106561 | + | 0.994306i | \(0.466016\pi\) | |||||||
\(480\) | 0.268635 | 0.0122614 | ||||||||
\(481\) | −43.4968 | −1.98329 | ||||||||
\(482\) | 0.0168728 | 0.000768533 0 | ||||||||
\(483\) | −1.14809 | −0.0522397 | ||||||||
\(484\) | −1.97056 | −0.0895709 | ||||||||
\(485\) | −2.01923 | −0.0916884 | ||||||||
\(486\) | −0.171582 | −0.00778310 | ||||||||
\(487\) | 16.2253 | 0.735240 | 0.367620 | − | 0.929976i | \(-0.380173\pi\) | ||||
0.367620 | + | 0.929976i | \(0.380173\pi\) | |||||||
\(488\) | 0.681275 | 0.0308399 | ||||||||
\(489\) | −17.0593 | −0.771448 | ||||||||
\(490\) | 0.151184 | 0.00682979 | ||||||||
\(491\) | 37.8484 | 1.70808 | 0.854038 | − | 0.520210i | \(-0.174146\pi\) | ||||
0.854038 | + | 0.520210i | \(0.174146\pi\) | |||||||
\(492\) | 3.01434 | 0.135897 | ||||||||
\(493\) | 10.6352 | 0.478986 | ||||||||
\(494\) | 6.34400 | 0.285430 | ||||||||
\(495\) | −0.133072 | −0.00598114 | ||||||||
\(496\) | 11.7365 | 0.526986 | ||||||||
\(497\) | −4.05802 | −0.182027 | ||||||||
\(498\) | −1.86806 | −0.0837096 | ||||||||
\(499\) | −12.9470 | −0.579586 | −0.289793 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289793 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(500\) | −2.61762 | −0.117063 | ||||||||
\(501\) | −8.92176 | −0.398595 | ||||||||
\(502\) | −0.589650 | −0.0263174 | ||||||||
\(503\) | −22.8525 | −1.01894 | −0.509471 | − | 0.860488i | \(-0.670159\pi\) | ||||
−0.509471 | + | 0.860488i | \(0.670159\pi\) | |||||||
\(504\) | −0.419208 | −0.0186730 | ||||||||
\(505\) | −1.99248 | −0.0886641 | ||||||||
\(506\) | 0.320139 | 0.0142319 | ||||||||
\(507\) | −9.13314 | −0.405617 | ||||||||
\(508\) | −38.0485 | −1.68813 | ||||||||
\(509\) | 1.26053 | 0.0558720 | 0.0279360 | − | 0.999610i | \(-0.491107\pi\) | ||||
0.0279360 | + | 0.999610i | \(0.491107\pi\) | |||||||
\(510\) | 0.0534928 | 0.00236870 | ||||||||
\(511\) | 2.68865 | 0.118939 | ||||||||
\(512\) | 12.9307 | 0.571463 | ||||||||
\(513\) | 7.85906 | 0.346986 | ||||||||
\(514\) | −2.13022 | −0.0939601 | ||||||||
\(515\) | −0.353847 | −0.0155924 | ||||||||
\(516\) | 2.31549 | 0.101934 | ||||||||
\(517\) | −7.78342 | −0.342314 | ||||||||
\(518\) | 0.976146 | 0.0428894 | ||||||||
\(519\) | −3.85738 | −0.169320 | ||||||||
\(520\) | −0.426512 | −0.0187038 | ||||||||
\(521\) | 33.2078 | 1.45486 | 0.727430 | − | 0.686182i | \(-0.240715\pi\) | ||||
0.727430 | + | 0.686182i | \(0.240715\pi\) | |||||||
\(522\) | 0.778896 | 0.0340914 | ||||||||
\(523\) | 22.8888 | 1.00086 | 0.500428 | − | 0.865778i | \(-0.333176\pi\) | ||||
0.500428 | + | 0.865778i | \(0.333176\pi\) | |||||||
\(524\) | −31.8999 | −1.39355 | ||||||||
\(525\) | 3.06575 | 0.133800 | ||||||||
\(526\) | 0.705131 | 0.0307452 | ||||||||
\(527\) | 7.19008 | 0.313205 | ||||||||
\(528\) | −3.82423 | −0.166428 | ||||||||
\(529\) | −19.5188 | −0.848642 | ||||||||
\(530\) | 0.253702 | 0.0110201 | ||||||||
\(531\) | 11.0751 | 0.480617 | ||||||||
\(532\) | 9.52944 | 0.413154 | ||||||||
\(533\) | −7.19656 | −0.311717 | ||||||||
\(534\) | −2.60003 | −0.112514 | ||||||||
\(535\) | −1.32757 | −0.0573959 | ||||||||
\(536\) | −7.64654 | −0.330280 | ||||||||
\(537\) | 10.4383 | 0.450445 | ||||||||
\(538\) | 3.04080 | 0.131098 | ||||||||
\(539\) | −6.62137 | −0.285203 | ||||||||
\(540\) | −0.262226 | −0.0112844 | ||||||||
\(541\) | −7.47250 | −0.321268 | −0.160634 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160634 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(542\) | 1.19679 | 0.0514064 | ||||||||
\(543\) | −13.9705 | −0.599530 | ||||||||
\(544\) | 4.72948 | 0.202775 | ||||||||
\(545\) | 1.17550 | 0.0503530 | ||||||||
\(546\) | 0.496706 | 0.0212571 | ||||||||
\(547\) | 42.4596 | 1.81544 | 0.907721 | − | 0.419574i | \(-0.137820\pi\) | ||||
0.907721 | + | 0.419574i | \(0.137820\pi\) | |||||||
\(548\) | 33.4751 | 1.42998 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −0.854870 | −0.0364518 | ||||||||
\(551\) | −35.6762 | −1.51986 | ||||||||
\(552\) | 1.27113 | 0.0541029 | ||||||||
\(553\) | 7.25365 | 0.308457 | ||||||||
\(554\) | −0.459407 | −0.0195183 | ||||||||
\(555\) | 1.23033 | 0.0522247 | ||||||||
\(556\) | −1.93435 | −0.0820348 | ||||||||
\(557\) | 33.5690 | 1.42236 | 0.711182 | − | 0.703008i | \(-0.248160\pi\) | ||||
0.711182 | + | 0.703008i | \(0.248160\pi\) | |||||||
\(558\) | 0.526584 | 0.0222921 | ||||||||
\(559\) | −5.52810 | −0.233814 | ||||||||
\(560\) | −0.313139 | −0.0132325 | ||||||||
\(561\) | −2.34281 | −0.0989136 | ||||||||
\(562\) | −2.77529 | −0.117069 | ||||||||
\(563\) | −6.90978 | −0.291212 | −0.145606 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145606 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(564\) | −15.3377 | −0.645833 | ||||||||
\(565\) | 0.565002 | 0.0237698 | ||||||||
\(566\) | 2.42668 | 0.102001 | ||||||||
\(567\) | 0.615329 | 0.0258414 | ||||||||
\(568\) | 4.49293 | 0.188519 | ||||||||
\(569\) | −43.2342 | −1.81247 | −0.906236 | − | 0.422772i | \(-0.861057\pi\) | ||||
−0.906236 | + | 0.422772i | \(0.861057\pi\) | |||||||
\(570\) | −0.179444 | −0.00751607 | ||||||||
\(571\) | 36.9917 | 1.54805 | 0.774027 | − | 0.633153i | \(-0.218240\pi\) | ||||
0.774027 | + | 0.633153i | \(0.218240\pi\) | |||||||
\(572\) | 9.27067 | 0.387626 | ||||||||
\(573\) | 24.4448 | 1.02120 | ||||||||
\(574\) | 0.161503 | 0.00674102 | ||||||||
\(575\) | −9.29600 | −0.387670 | ||||||||
\(576\) | −7.30207 | −0.304253 | ||||||||
\(577\) | −43.0272 | −1.79125 | −0.895623 | − | 0.444815i | \(-0.853270\pi\) | ||||
−0.895623 | + | 0.444815i | \(0.853270\pi\) | |||||||
\(578\) | −1.97512 | −0.0821540 | ||||||||
\(579\) | 6.16239 | 0.256100 | ||||||||
\(580\) | 1.19038 | 0.0494277 | ||||||||
\(581\) | 6.69925 | 0.277932 | ||||||||
\(582\) | −2.60357 | −0.107922 | ||||||||
\(583\) | −11.1113 | −0.460184 | ||||||||
\(584\) | −2.97680 | −0.123181 | ||||||||
\(585\) | 0.626049 | 0.0258839 | ||||||||
\(586\) | −1.41555 | −0.0584758 | ||||||||
\(587\) | 2.31390 | 0.0955048 | 0.0477524 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477524 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(588\) | −13.0478 | −0.538082 | ||||||||
\(589\) | −24.1194 | −0.993823 | ||||||||
\(590\) | −0.252874 | −0.0104107 | ||||||||
\(591\) | 16.1438 | 0.664069 | ||||||||
\(592\) | 35.3573 | 1.45318 | ||||||||
\(593\) | 10.2698 | 0.421731 | 0.210865 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210865 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(594\) | −0.171582 | −0.00704008 | ||||||||
\(595\) | −0.191837 | −0.00786453 | ||||||||
\(596\) | −39.2498 | −1.60773 | ||||||||
\(597\) | 11.7030 | 0.478970 | ||||||||
\(598\) | −1.50612 | −0.0615898 | ||||||||
\(599\) | 21.7905 | 0.890335 | 0.445167 | − | 0.895447i | \(-0.353144\pi\) | ||||
0.445167 | + | 0.895447i | \(0.353144\pi\) | |||||||
\(600\) | −3.39431 | −0.138572 | ||||||||
\(601\) | −20.7713 | −0.847279 | −0.423640 | − | 0.905831i | \(-0.639248\pi\) | ||||
−0.423640 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(602\) | 0.124060 | 0.00505632 | ||||||||
\(603\) | 11.2239 | 0.457071 | ||||||||
\(604\) | 18.2706 | 0.743421 | ||||||||
\(605\) | −0.133072 | −0.00541015 | ||||||||
\(606\) | −2.56908 | −0.104362 | ||||||||
\(607\) | 1.14578 | 0.0465057 | 0.0232528 | − | 0.999730i | \(-0.492598\pi\) | ||||
0.0232528 | + | 0.999730i | \(0.492598\pi\) | |||||||
\(608\) | −15.8652 | −0.643420 | ||||||||
\(609\) | −2.79329 | −0.113190 | ||||||||
\(610\) | 0.0228327 | 0.000924470 0 | ||||||||
\(611\) | 36.6178 | 1.48140 | ||||||||
\(612\) | −4.61665 | −0.186617 | ||||||||
\(613\) | 13.2402 | 0.534766 | 0.267383 | − | 0.963590i | \(-0.413841\pi\) | ||||
0.267383 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(614\) | −0.887316 | −0.0358092 | ||||||||
\(615\) | 0.203559 | 0.00820828 | ||||||||
\(616\) | −0.419208 | −0.0168904 | ||||||||
\(617\) | −19.1708 | −0.771787 | −0.385894 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385894 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(618\) | −0.456247 | −0.0183529 | ||||||||
\(619\) | 3.63574 | 0.146133 | 0.0730663 | − | 0.997327i | \(-0.476722\pi\) | ||||
0.0730663 | + | 0.997327i | \(0.476722\pi\) | |||||||
\(620\) | 0.804771 | 0.0323204 | ||||||||
\(621\) | −1.86581 | −0.0748723 | ||||||||
\(622\) | 0.954861 | 0.0382864 | ||||||||
\(623\) | 9.32426 | 0.373569 | ||||||||
\(624\) | 17.9914 | 0.720232 | ||||||||
\(625\) | 24.7347 | 0.989388 | ||||||||
\(626\) | −4.48411 | −0.179221 | ||||||||
\(627\) | 7.85906 | 0.313860 | ||||||||
\(628\) | −18.9706 | −0.757010 | ||||||||
\(629\) | 21.6608 | 0.863671 | ||||||||
\(630\) | −0.0140496 | −0.000559751 0 | ||||||||
\(631\) | 34.0488 | 1.35546 | 0.677732 | − | 0.735309i | \(-0.262963\pi\) | ||||
0.677732 | + | 0.735309i | \(0.262963\pi\) | |||||||
\(632\) | −8.03105 | −0.319458 | ||||||||
\(633\) | 13.0881 | 0.520203 | ||||||||
\(634\) | −1.58904 | −0.0631087 | ||||||||
\(635\) | −2.56942 | −0.101964 | ||||||||
\(636\) | −21.8955 | −0.868215 | ||||||||
\(637\) | 31.1508 | 1.23424 | ||||||||
\(638\) | 0.778896 | 0.0308368 | ||||||||
\(639\) | −6.59487 | −0.260889 | ||||||||
\(640\) | 0.703996 | 0.0278279 | ||||||||
\(641\) | 1.72492 | 0.0681302 | 0.0340651 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340651 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(642\) | −1.71176 | −0.0675577 | ||||||||
\(643\) | −37.6517 | −1.48484 | −0.742420 | − | 0.669935i | \(-0.766322\pi\) | ||||
−0.742420 | + | 0.669935i | \(0.766322\pi\) | |||||||
\(644\) | −2.26237 | −0.0891499 | ||||||||
\(645\) | 0.156365 | 0.00615688 | ||||||||
\(646\) | −3.15921 | −0.124298 | ||||||||
\(647\) | 46.6191 | 1.83279 | 0.916393 | − | 0.400279i | \(-0.131087\pi\) | ||||
0.916393 | + | 0.400279i | \(0.131087\pi\) | |||||||
\(648\) | −0.681275 | −0.0267630 | ||||||||
\(649\) | 11.0751 | 0.434734 | ||||||||
\(650\) | 4.02181 | 0.157748 | ||||||||
\(651\) | −1.88844 | −0.0740139 | ||||||||
\(652\) | −33.6164 | −1.31652 | ||||||||
\(653\) | −32.6575 | −1.27799 | −0.638993 | − | 0.769212i | \(-0.720649\pi\) | ||||
−0.638993 | + | 0.769212i | \(0.720649\pi\) | |||||||
\(654\) | 1.51568 | 0.0592679 | ||||||||
\(655\) | −2.15420 | −0.0841716 | ||||||||
\(656\) | 5.84988 | 0.228399 | ||||||||
\(657\) | 4.36946 | 0.170469 | ||||||||
\(658\) | −0.821767 | −0.0320358 | ||||||||
\(659\) | 36.3322 | 1.41530 | 0.707651 | − | 0.706562i | \(-0.249755\pi\) | ||||
0.707651 | + | 0.706562i | \(0.249755\pi\) | |||||||
\(660\) | −0.262226 | −0.0102071 | ||||||||
\(661\) | 20.6126 | 0.801736 | 0.400868 | − | 0.916136i | \(-0.368709\pi\) | ||||
0.400868 | + | 0.916136i | \(0.368709\pi\) | |||||||
\(662\) | −0.354975 | −0.0137965 | ||||||||
\(663\) | 11.0220 | 0.428058 | ||||||||
\(664\) | −7.41723 | −0.287844 | ||||||||
\(665\) | 0.643523 | 0.0249548 | ||||||||
\(666\) | 1.58638 | 0.0614710 | ||||||||
\(667\) | 8.46985 | 0.327954 | ||||||||
\(668\) | −17.5809 | −0.680224 | ||||||||
\(669\) | −2.06775 | −0.0799438 | ||||||||
\(670\) | −0.256271 | −0.00990063 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −1.24218 | −0.0479180 | ||||||||
\(673\) | −5.41924 | −0.208896 | −0.104448 | − | 0.994530i | \(-0.533308\pi\) | ||||
−0.104448 | + | 0.994530i | \(0.533308\pi\) | |||||||
\(674\) | −0.0408862 | −0.00157488 | ||||||||
\(675\) | 4.98229 | 0.191769 | ||||||||
\(676\) | −17.9974 | −0.692208 | ||||||||
\(677\) | −15.1357 | −0.581713 | −0.290857 | − | 0.956767i | \(-0.593940\pi\) | ||||
−0.290857 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(678\) | 0.728508 | 0.0279782 | ||||||||
\(679\) | 9.33697 | 0.358320 | ||||||||
\(680\) | 0.212396 | 0.00814502 | ||||||||
\(681\) | 6.15200 | 0.235745 | ||||||||
\(682\) | 0.526584 | 0.0201639 | ||||||||
\(683\) | 5.25700 | 0.201154 | 0.100577 | − | 0.994929i | \(-0.467931\pi\) | ||||
0.100577 | + | 0.994929i | \(0.467931\pi\) | |||||||
\(684\) | 15.4867 | 0.592150 | ||||||||
\(685\) | 2.26057 | 0.0863721 | ||||||||
\(686\) | −1.43813 | −0.0549082 | ||||||||
\(687\) | −19.5963 | −0.747644 | ||||||||
\(688\) | 4.49363 | 0.171318 | ||||||||
\(689\) | 52.2742 | 1.99149 | ||||||||
\(690\) | 0.0426015 | 0.00162181 | ||||||||
\(691\) | −37.8441 | −1.43966 | −0.719828 | − | 0.694152i | \(-0.755780\pi\) | ||||
−0.719828 | + | 0.694152i | \(0.755780\pi\) | |||||||
\(692\) | −7.60120 | −0.288954 | ||||||||
\(693\) | 0.615329 | 0.0233744 | ||||||||
\(694\) | 4.78753 | 0.181732 | ||||||||
\(695\) | −0.130627 | −0.00495496 | ||||||||
\(696\) | 3.09265 | 0.117227 | ||||||||
\(697\) | 3.58377 | 0.135745 | ||||||||
\(698\) | 5.26703 | 0.199360 | ||||||||
\(699\) | 20.5752 | 0.778224 | ||||||||
\(700\) | 6.04124 | 0.228337 | ||||||||
\(701\) | −26.2157 | −0.990154 | −0.495077 | − | 0.868849i | \(-0.664860\pi\) | ||||
−0.495077 | + | 0.868849i | \(0.664860\pi\) | |||||||
\(702\) | 0.807221 | 0.0304666 | ||||||||
\(703\) | −72.6619 | −2.74049 | ||||||||
\(704\) | −7.30207 | −0.275207 | ||||||||
\(705\) | −1.03575 | −0.0390088 | ||||||||
\(706\) | 5.52699 | 0.208011 | ||||||||
\(707\) | 9.21328 | 0.346501 | ||||||||
\(708\) | 21.8241 | 0.820199 | ||||||||
\(709\) | −22.3870 | −0.840762 | −0.420381 | − | 0.907348i | \(-0.638104\pi\) | ||||
−0.420381 | + | 0.907348i | \(0.638104\pi\) | |||||||
\(710\) | 0.150579 | 0.00565113 | ||||||||
\(711\) | 11.7882 | 0.442094 | ||||||||
\(712\) | −10.3236 | −0.386892 | ||||||||
\(713\) | 5.72616 | 0.214446 | ||||||||
\(714\) | −0.247352 | −0.00925692 | ||||||||
\(715\) | 0.626049 | 0.0234129 | ||||||||
\(716\) | 20.5693 | 0.768709 | ||||||||
\(717\) | 23.1378 | 0.864097 | ||||||||
\(718\) | −4.37055 | −0.163108 | ||||||||
\(719\) | −21.7396 | −0.810751 | −0.405376 | − | 0.914150i | \(-0.632859\pi\) | ||||
−0.405376 | + | 0.914150i | \(0.632859\pi\) | |||||||
\(720\) | −0.508897 | −0.0189655 | ||||||||
\(721\) | 1.63620 | 0.0609352 | ||||||||
\(722\) | 7.33765 | 0.273079 | ||||||||
\(723\) | −0.0983366 | −0.00365718 | ||||||||
\(724\) | −27.5296 | −1.02313 | ||||||||
\(725\) | −22.6171 | −0.839979 | ||||||||
\(726\) | −0.171582 | −0.00636799 | ||||||||
\(727\) | −24.4460 | −0.906653 | −0.453327 | − | 0.891344i | \(-0.649763\pi\) | ||||
−0.453327 | + | 0.891344i | \(0.649763\pi\) | |||||||
\(728\) | 1.97220 | 0.0730947 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0997666 | −0.00369253 | ||||||||
\(731\) | 2.75291 | 0.101820 | ||||||||
\(732\) | −1.97056 | −0.0728340 | ||||||||
\(733\) | 13.6034 | 0.502452 | 0.251226 | − | 0.967928i | \(-0.419166\pi\) | ||||
0.251226 | + | 0.967928i | \(0.419166\pi\) | |||||||
\(734\) | 6.15792 | 0.227293 | ||||||||
\(735\) | −0.881119 | −0.0325006 | ||||||||
\(736\) | 3.76654 | 0.138837 | ||||||||
\(737\) | 11.2239 | 0.413436 | ||||||||
\(738\) | 0.262467 | 0.00966153 | ||||||||
\(739\) | 1.68561 | 0.0620061 | 0.0310031 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310031 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(740\) | 2.42445 | 0.0891244 | ||||||||
\(741\) | −36.9736 | −1.35826 | ||||||||
\(742\) | −1.17313 | −0.0430668 | ||||||||
\(743\) | 45.8835 | 1.68330 | 0.841652 | − | 0.540020i | \(-0.181583\pi\) | ||||
0.841652 | + | 0.540020i | \(0.181583\pi\) | |||||||
\(744\) | 2.09083 | 0.0766536 | ||||||||
\(745\) | −2.65054 | −0.0971082 | ||||||||
\(746\) | 4.50643 | 0.164992 | ||||||||
\(747\) | 10.8873 | 0.398344 | ||||||||
\(748\) | −4.61665 | −0.168801 | ||||||||
\(749\) | 6.13873 | 0.224304 | ||||||||
\(750\) | −0.227923 | −0.00832257 | ||||||||
\(751\) | −47.2695 | −1.72489 | −0.862445 | − | 0.506151i | \(-0.831068\pi\) | ||||
−0.862445 | + | 0.506151i | \(0.831068\pi\) | |||||||
\(752\) | −29.7655 | −1.08544 | ||||||||
\(753\) | 3.43655 | 0.125235 | ||||||||
\(754\) | −3.66438 | −0.133449 | ||||||||
\(755\) | 1.23382 | 0.0449032 | ||||||||
\(756\) | 1.21254 | 0.0440997 | ||||||||
\(757\) | −33.4045 | −1.21411 | −0.607054 | − | 0.794661i | \(-0.707649\pi\) | ||||
−0.607054 | + | 0.794661i | \(0.707649\pi\) | |||||||
\(758\) | −3.87451 | −0.140728 | ||||||||
\(759\) | −1.86581 | −0.0677245 | ||||||||
\(760\) | −0.712492 | −0.0258448 | ||||||||
\(761\) | 19.2821 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(762\) | −3.31298 | −0.120017 | ||||||||
\(763\) | −5.43556 | −0.196781 | ||||||||
\(764\) | 48.1700 | 1.74273 | ||||||||
\(765\) | −0.311763 | −0.0112718 | ||||||||
\(766\) | 0.261421 | 0.00944551 | ||||||||
\(767\) | −52.1036 | −1.88135 | ||||||||
\(768\) | −13.6964 | −0.494227 | ||||||||
\(769\) | −27.7997 | −1.00248 | −0.501242 | − | 0.865307i | \(-0.667123\pi\) | ||||
−0.501242 | + | 0.865307i | \(0.667123\pi\) | |||||||
\(770\) | −0.0140496 | −0.000506314 0 | ||||||||
\(771\) | 12.4152 | 0.447123 | ||||||||
\(772\) | 12.1434 | 0.437049 | ||||||||
\(773\) | 15.4428 | 0.555438 | 0.277719 | − | 0.960662i | \(-0.410422\pi\) | ||||
0.277719 | + | 0.960662i | \(0.410422\pi\) | |||||||
\(774\) | 0.201616 | 0.00724694 | ||||||||
\(775\) | −15.2906 | −0.549256 | ||||||||
\(776\) | −10.3376 | −0.371100 | ||||||||
\(777\) | −5.68910 | −0.204095 | ||||||||
\(778\) | −3.67896 | −0.131897 | ||||||||
\(779\) | −12.0219 | −0.430730 | ||||||||
\(780\) | 1.23367 | 0.0441723 | ||||||||
\(781\) | −6.59487 | −0.235983 | ||||||||
\(782\) | 0.750024 | 0.0268208 | ||||||||
\(783\) | −4.53951 | −0.162229 | ||||||||
\(784\) | −25.3216 | −0.904343 | ||||||||
\(785\) | −1.28109 | −0.0457239 | ||||||||
\(786\) | −2.77761 | −0.0990740 | ||||||||
\(787\) | −39.8594 | −1.42083 | −0.710417 | − | 0.703781i | \(-0.751494\pi\) | ||||
−0.710417 | + | 0.703781i | \(0.751494\pi\) | |||||||
\(788\) | 31.8124 | 1.13327 | ||||||||
\(789\) | −4.10959 | −0.146305 | ||||||||
\(790\) | −0.269158 | −0.00957620 | ||||||||
\(791\) | −2.61259 | −0.0928929 | ||||||||
\(792\) | −0.681275 | −0.0242081 | ||||||||
\(793\) | 4.70459 | 0.167065 | ||||||||
\(794\) | −1.35510 | −0.0480906 | ||||||||
\(795\) | −1.47861 | −0.0524408 | ||||||||
\(796\) | 23.0614 | 0.817388 | ||||||||
\(797\) | −17.9931 | −0.637348 | −0.318674 | − | 0.947864i | \(-0.603238\pi\) | ||||
−0.318674 | + | 0.947864i | \(0.603238\pi\) | |||||||
\(798\) | 0.829753 | 0.0293729 | ||||||||
\(799\) | −18.2351 | −0.645111 | ||||||||
\(800\) | −10.0578 | −0.355598 | ||||||||
\(801\) | 15.1533 | 0.535415 | ||||||||
\(802\) | 1.90284 | 0.0671915 | ||||||||
\(803\) | 4.36946 | 0.154195 | ||||||||
\(804\) | 22.1173 | 0.780017 | ||||||||
\(805\) | −0.152778 | −0.00538472 | ||||||||
\(806\) | −2.47736 | −0.0872612 | ||||||||
\(807\) | −17.7222 | −0.623850 | ||||||||
\(808\) | −10.2007 | −0.358859 | ||||||||
\(809\) | −36.0517 | −1.26751 | −0.633755 | − | 0.773534i | \(-0.718487\pi\) | ||||
−0.633755 | + | 0.773534i | \(0.718487\pi\) | |||||||
\(810\) | −0.0228327 | −0.000802260 0 | ||||||||
\(811\) | 17.6858 | 0.621032 | 0.310516 | − | 0.950568i | \(-0.399498\pi\) | ||||
0.310516 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(812\) | −5.50434 | −0.193165 | ||||||||
\(813\) | −6.97502 | −0.244625 | ||||||||
\(814\) | 1.58638 | 0.0556026 | ||||||||
\(815\) | −2.27011 | −0.0795186 | ||||||||
\(816\) | −8.95944 | −0.313643 | ||||||||
\(817\) | −9.23474 | −0.323082 | ||||||||
\(818\) | 0.313967 | 0.0109776 | ||||||||
\(819\) | −2.89487 | −0.101155 | ||||||||
\(820\) | 0.401125 | 0.0140079 | ||||||||
\(821\) | −14.5517 | −0.507858 | −0.253929 | − | 0.967223i | \(-0.581723\pi\) | ||||
−0.253929 | + | 0.967223i | \(0.581723\pi\) | |||||||
\(822\) | 2.91476 | 0.101664 | ||||||||
\(823\) | 48.1384 | 1.67800 | 0.838999 | − | 0.544133i | \(-0.183141\pi\) | ||||
0.838999 | + | 0.544133i | \(0.183141\pi\) | |||||||
\(824\) | −1.81156 | −0.0631085 | ||||||||
\(825\) | 4.98229 | 0.173461 | ||||||||
\(826\) | 1.16930 | 0.0406850 | ||||||||
\(827\) | 27.5769 | 0.958943 | 0.479472 | − | 0.877557i | \(-0.340828\pi\) | ||||
0.479472 | + | 0.877557i | \(0.340828\pi\) | |||||||
\(828\) | −3.67669 | −0.127774 | ||||||||
\(829\) | −10.6222 | −0.368926 | −0.184463 | − | 0.982839i | \(-0.559055\pi\) | ||||
−0.184463 | + | 0.982839i | \(0.559055\pi\) | |||||||
\(830\) | −0.248586 | −0.00862855 | ||||||||
\(831\) | 2.67748 | 0.0928808 | ||||||||
\(832\) | 34.3532 | 1.19098 | ||||||||
\(833\) | −15.5126 | −0.537481 | ||||||||
\(834\) | −0.168429 | −0.00583222 | ||||||||
\(835\) | −1.18724 | −0.0410860 | ||||||||
\(836\) | 15.4867 | 0.535620 | ||||||||
\(837\) | −3.06900 | −0.106080 | ||||||||
\(838\) | 4.99134 | 0.172423 | ||||||||
\(839\) | −48.1933 | −1.66382 | −0.831909 | − | 0.554912i | \(-0.812752\pi\) | ||||
−0.831909 | + | 0.554912i | \(0.812752\pi\) | |||||||
\(840\) | −0.0557849 | −0.00192476 | ||||||||
\(841\) | −8.39289 | −0.289410 | ||||||||
\(842\) | −0.00961104 | −0.000331218 0 | ||||||||
\(843\) | 16.1747 | 0.557088 | ||||||||
\(844\) | 25.7908 | 0.887756 | ||||||||
\(845\) | −1.21536 | −0.0418098 | ||||||||
\(846\) | −1.33549 | −0.0459152 | ||||||||
\(847\) | 0.615329 | 0.0211430 | ||||||||
\(848\) | −42.4922 | −1.45919 | ||||||||
\(849\) | −14.1430 | −0.485387 | ||||||||
\(850\) | −2.00280 | −0.0686955 | ||||||||
\(851\) | 17.2506 | 0.591342 | ||||||||
\(852\) | −12.9956 | −0.445222 | ||||||||
\(853\) | 46.5258 | 1.59301 | 0.796507 | − | 0.604629i | \(-0.206679\pi\) | ||||
0.796507 | + | 0.604629i | \(0.206679\pi\) | |||||||
\(854\) | −0.105579 | −0.00361285 | ||||||||
\(855\) | 1.04582 | 0.0357663 | ||||||||
\(856\) | −6.79664 | −0.232304 | ||||||||
\(857\) | −10.3918 | −0.354979 | −0.177489 | − | 0.984123i | \(-0.556798\pi\) | ||||
−0.177489 | + | 0.984123i | \(0.556798\pi\) | |||||||
\(858\) | 0.807221 | 0.0275581 | ||||||||
\(859\) | 57.1315 | 1.94930 | 0.974651 | − | 0.223732i | \(-0.0718241\pi\) | ||||
0.974651 | + | 0.223732i | \(0.0718241\pi\) | |||||||
\(860\) | 0.308127 | 0.0105071 | ||||||||
\(861\) | −0.941262 | −0.0320781 | ||||||||
\(862\) | −0.356613 | −0.0121463 | ||||||||
\(863\) | 21.5752 | 0.734429 | 0.367214 | − | 0.930136i | \(-0.380312\pi\) | ||||
0.367214 | + | 0.930136i | \(0.380312\pi\) | |||||||
\(864\) | −2.01872 | −0.0686782 | ||||||||
\(865\) | −0.513309 | −0.0174530 | ||||||||
\(866\) | −0.984706 | −0.0334617 | ||||||||
\(867\) | 11.5112 | 0.390942 | ||||||||
\(868\) | −3.72129 | −0.126309 | ||||||||
\(869\) | 11.7882 | 0.399889 | ||||||||
\(870\) | 0.103649 | 0.00351404 | ||||||||
\(871\) | −52.8036 | −1.78918 | ||||||||
\(872\) | 6.01811 | 0.203799 | ||||||||
\(873\) | 15.1739 | 0.513560 | ||||||||
\(874\) | −2.51599 | −0.0851045 | ||||||||
\(875\) | 0.817380 | 0.0276325 | ||||||||
\(876\) | 8.61028 | 0.290914 | ||||||||
\(877\) | −19.6961 | −0.665092 | −0.332546 | − | 0.943087i | \(-0.607908\pi\) | ||||
−0.332546 | + | 0.943087i | \(0.607908\pi\) | |||||||
\(878\) | 5.60594 | 0.189191 | ||||||||
\(879\) | 8.25000 | 0.278266 | ||||||||
\(880\) | −0.508897 | −0.0171549 | ||||||||
\(881\) | −13.2882 | −0.447691 | −0.223845 | − | 0.974625i | \(-0.571861\pi\) | ||||
−0.223845 | + | 0.974625i | \(0.571861\pi\) | |||||||
\(882\) | −1.13611 | −0.0382547 | ||||||||
\(883\) | 12.8872 | 0.433688 | 0.216844 | − | 0.976206i | \(-0.430424\pi\) | ||||
0.216844 | + | 0.976206i | \(0.430424\pi\) | |||||||
\(884\) | 21.7194 | 0.730504 | ||||||||
\(885\) | 1.47378 | 0.0495406 | ||||||||
\(886\) | −4.43055 | −0.148847 | ||||||||
\(887\) | 1.36425 | 0.0458071 | 0.0229036 | − | 0.999738i | \(-0.492709\pi\) | ||||
0.0229036 | + | 0.999738i | \(0.492709\pi\) | |||||||
\(888\) | 6.29882 | 0.211374 | ||||||||
\(889\) | 11.8811 | 0.398478 | ||||||||
\(890\) | −0.345991 | −0.0115976 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −4.07463 | −0.136429 | ||||||||
\(893\) | 61.1703 | 2.04699 | ||||||||
\(894\) | −3.41758 | −0.114301 | ||||||||
\(895\) | 1.38904 | 0.0464306 | ||||||||
\(896\) | −3.25530 | −0.108752 | ||||||||
\(897\) | 8.77786 | 0.293084 | ||||||||
\(898\) | −3.20157 | −0.106838 | ||||||||
\(899\) | 13.9317 | 0.464649 | ||||||||
\(900\) | 9.81790 | 0.327263 | ||||||||
\(901\) | −26.0318 | −0.867244 | ||||||||
\(902\) | 0.262467 | 0.00873919 | ||||||||
\(903\) | −0.723038 | −0.0240612 | ||||||||
\(904\) | 2.89258 | 0.0962059 | ||||||||
\(905\) | −1.85908 | −0.0617978 | ||||||||
\(906\) | 1.59087 | 0.0528531 | ||||||||
\(907\) | 52.3304 | 1.73760 | 0.868802 | − | 0.495160i | \(-0.164890\pi\) | ||||
0.868802 | + | 0.495160i | \(0.164890\pi\) | |||||||
\(908\) | 12.1229 | 0.402312 | ||||||||
\(909\) | 14.9729 | 0.496621 | ||||||||
\(910\) | 0.0660977 | 0.00219112 | ||||||||
\(911\) | 4.50180 | 0.149151 | 0.0745756 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745756 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(912\) | 30.0548 | 0.995214 | ||||||||
\(913\) | 10.8873 | 0.360316 | ||||||||
\(914\) | −0.750944 | −0.0248390 | ||||||||
\(915\) | −0.133072 | −0.00439922 | ||||||||
\(916\) | −38.6156 | −1.27590 | ||||||||
\(917\) | 9.96110 | 0.328944 | ||||||||
\(918\) | −0.401984 | −0.0132674 | ||||||||
\(919\) | 25.3477 | 0.836143 | 0.418072 | − | 0.908414i | \(-0.362706\pi\) | ||||
0.418072 | + | 0.908414i | \(0.362706\pi\) | |||||||
\(920\) | 0.169152 | 0.00557677 | ||||||||
\(921\) | 5.17139 | 0.170403 | ||||||||
\(922\) | −6.25317 | −0.205937 | ||||||||
\(923\) | 31.0262 | 1.02124 | ||||||||
\(924\) | 1.21254 | 0.0398897 | ||||||||
\(925\) | −46.0644 | −1.51459 | ||||||||
\(926\) | 2.50154 | 0.0822057 | ||||||||
\(927\) | 2.65906 | 0.0873351 | ||||||||
\(928\) | 9.16398 | 0.300822 | ||||||||
\(929\) | 20.9203 | 0.686372 | 0.343186 | − | 0.939267i | \(-0.388494\pi\) | ||||
0.343186 | + | 0.939267i | \(0.388494\pi\) | |||||||
\(930\) | 0.0700735 | 0.00229780 | ||||||||
\(931\) | 52.0377 | 1.70547 | ||||||||
\(932\) | 40.5446 | 1.32808 | ||||||||
\(933\) | −5.56505 | −0.182192 | ||||||||
\(934\) | 4.55895 | 0.149173 | ||||||||
\(935\) | −0.311763 | −0.0101957 | ||||||||
\(936\) | 3.20512 | 0.104763 | ||||||||
\(937\) | 33.7225 | 1.10167 | 0.550833 | − | 0.834615i | \(-0.314310\pi\) | ||||
0.550833 | + | 0.834615i | \(0.314310\pi\) | |||||||
\(938\) | 1.18501 | 0.0386918 | ||||||||
\(939\) | 26.1339 | 0.852849 | ||||||||
\(940\) | −2.04102 | −0.0665706 | ||||||||
\(941\) | −45.8406 | −1.49436 | −0.747180 | − | 0.664621i | \(-0.768593\pi\) | ||||
−0.747180 | + | 0.664621i | \(0.768593\pi\) | |||||||
\(942\) | −1.65182 | −0.0538192 | ||||||||
\(943\) | 2.85411 | 0.0929425 | ||||||||
\(944\) | 42.3535 | 1.37849 | ||||||||
\(945\) | 0.0818830 | 0.00266366 | ||||||||
\(946\) | 0.201616 | 0.00655510 | ||||||||
\(947\) | −31.2864 | −1.01667 | −0.508336 | − | 0.861159i | \(-0.669739\pi\) | ||||
−0.508336 | + | 0.861159i | \(0.669739\pi\) | |||||||
\(948\) | 23.2294 | 0.754457 | ||||||||
\(949\) | −20.5565 | −0.667292 | ||||||||
\(950\) | 6.71847 | 0.217976 | ||||||||
\(951\) | 9.26111 | 0.300312 | ||||||||
\(952\) | −0.982127 | −0.0318309 | ||||||||
\(953\) | 58.6406 | 1.89955 | 0.949777 | − | 0.312926i | \(-0.101309\pi\) | ||||
0.949777 | + | 0.312926i | \(0.101309\pi\) | |||||||
\(954\) | −1.90650 | −0.0617253 | ||||||||
\(955\) | 3.25292 | 0.105262 | ||||||||
\(956\) | 45.5944 | 1.47463 | ||||||||
\(957\) | −4.53951 | −0.146741 | ||||||||
\(958\) | 0.800329 | 0.0258574 | ||||||||
\(959\) | −10.4530 | −0.337544 | ||||||||
\(960\) | −0.971702 | −0.0313615 | ||||||||
\(961\) | −21.5813 | −0.696170 | ||||||||
\(962\) | −7.46326 | −0.240625 | ||||||||
\(963\) | 9.97635 | 0.321483 | ||||||||
\(964\) | −0.193778 | −0.00624117 | ||||||||
\(965\) | 0.820041 | 0.0263981 | ||||||||
\(966\) | −0.196991 | −0.00633807 | ||||||||
\(967\) | −35.3660 | −1.13729 | −0.568647 | − | 0.822582i | \(-0.692533\pi\) | ||||
−0.568647 | + | 0.822582i | \(0.692533\pi\) | |||||||
\(968\) | −0.681275 | −0.0218970 | ||||||||
\(969\) | 18.4123 | 0.591488 | ||||||||
\(970\) | −0.346462 | −0.0111242 | ||||||||
\(971\) | 21.4189 | 0.687366 | 0.343683 | − | 0.939086i | \(-0.388325\pi\) | ||||
0.343683 | + | 0.939086i | \(0.388325\pi\) | |||||||
\(972\) | 1.97056 | 0.0632057 | ||||||||
\(973\) | 0.604022 | 0.0193641 | ||||||||
\(974\) | 2.78397 | 0.0892042 | ||||||||
\(975\) | −23.4396 | −0.750669 | ||||||||
\(976\) | −3.82423 | −0.122410 | ||||||||
\(977\) | −50.4860 | −1.61519 | −0.807595 | − | 0.589737i | \(-0.799231\pi\) | ||||
−0.807595 | + | 0.589737i | \(0.799231\pi\) | |||||||
\(978\) | −2.92706 | −0.0935971 | ||||||||
\(979\) | 15.1533 | 0.484301 | ||||||||
\(980\) | −1.73630 | −0.0554640 | ||||||||
\(981\) | −8.83359 | −0.282035 | ||||||||
\(982\) | 6.49410 | 0.207235 | ||||||||
\(983\) | −4.20465 | −0.134107 | −0.0670537 | − | 0.997749i | \(-0.521360\pi\) | ||||
−0.0670537 | + | 0.997749i | \(0.521360\pi\) | |||||||
\(984\) | 1.04214 | 0.0332222 | ||||||||
\(985\) | 2.14829 | 0.0684503 | ||||||||
\(986\) | 1.82481 | 0.0581137 | ||||||||
\(987\) | 4.78936 | 0.152447 | ||||||||
\(988\) | −72.8587 | −2.31794 | ||||||||
\(989\) | 2.19241 | 0.0697145 | ||||||||
\(990\) | −0.0228327 | −0.000725671 0 | ||||||||
\(991\) | 14.4063 | 0.457631 | 0.228816 | − | 0.973470i | \(-0.426515\pi\) | ||||
0.228816 | + | 0.973470i | \(0.426515\pi\) | |||||||
\(992\) | 6.19544 | 0.196705 | ||||||||
\(993\) | 2.06884 | 0.0656527 | ||||||||
\(994\) | −0.696282 | −0.0220847 | ||||||||
\(995\) | 1.55734 | 0.0493708 | ||||||||
\(996\) | 21.4540 | 0.679797 | ||||||||
\(997\) | 25.4235 | 0.805169 | 0.402585 | − | 0.915383i | \(-0.368112\pi\) | ||||
0.402585 | + | 0.915383i | \(0.368112\pi\) | |||||||
\(998\) | −2.22147 | −0.0703193 | ||||||||
\(999\) | −9.24562 | −0.292519 |
(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 | 2013.2.a.e.1.7 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.7 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.7 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.7 | 13 | 3.2 | odd | 2 |