Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.30799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.307988 | −0.217781 | −0.108890 | − | 0.994054i | \(-0.534730\pi\) | ||||
−0.108890 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(3\) | −1.64392 | −0.949117 | −0.474558 | − | 0.880224i | \(-0.657392\pi\) | ||||
−0.474558 | + | 0.880224i | \(0.657392\pi\) | |||||||
\(4\) | −1.90514 | −0.952572 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.506308 | 0.206699 | ||||||||
\(7\) | 0.0891959 | 0.0337129 | 0.0168564 | − | 0.999858i | \(-0.494634\pi\) | ||||
0.0168564 | + | 0.999858i | \(0.494634\pi\) | |||||||
\(8\) | 1.20274 | 0.425232 | ||||||||
\(9\) | −0.297533 | −0.0991778 | ||||||||
\(10\) | −0.307988 | −0.0973945 | ||||||||
\(11\) | −3.36682 | −1.01513 | −0.507567 | − | 0.861612i | \(-0.669455\pi\) | ||||
−0.507567 | + | 0.861612i | \(0.669455\pi\) | |||||||
\(12\) | 3.13190 | 0.904101 | ||||||||
\(13\) | 0.212870 | 0.0590395 | 0.0295198 | − | 0.999564i | \(-0.490602\pi\) | ||||
0.0295198 | + | 0.999564i | \(0.490602\pi\) | |||||||
\(14\) | −0.0274713 | −0.00734201 | ||||||||
\(15\) | −1.64392 | −0.424458 | ||||||||
\(16\) | 3.43986 | 0.859964 | ||||||||
\(17\) | −2.51423 | −0.609791 | −0.304896 | − | 0.952386i | \(-0.598622\pi\) | ||||
−0.304896 | + | 0.952386i | \(0.598622\pi\) | |||||||
\(18\) | 0.0916368 | 0.0215990 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.90514 | −0.426003 | ||||||||
\(21\) | −0.146631 | −0.0319975 | ||||||||
\(22\) | 1.03694 | 0.221077 | ||||||||
\(23\) | −5.96699 | −1.24420 | −0.622101 | − | 0.782937i | \(-0.713721\pi\) | ||||
−0.622101 | + | 0.782937i | \(0.713721\pi\) | |||||||
\(24\) | −1.97720 | −0.403595 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.0655615 | −0.0128577 | ||||||||
\(27\) | 5.42087 | 1.04325 | ||||||||
\(28\) | −0.169931 | −0.0321139 | ||||||||
\(29\) | −4.80823 | −0.892866 | −0.446433 | − | 0.894817i | \(-0.647306\pi\) | ||||
−0.446433 | + | 0.894817i | \(0.647306\pi\) | |||||||
\(30\) | 0.506308 | 0.0924387 | ||||||||
\(31\) | 8.06815 | 1.44908 | 0.724541 | − | 0.689232i | \(-0.242052\pi\) | ||||
0.724541 | + | 0.689232i | \(0.242052\pi\) | |||||||
\(32\) | −3.46491 | −0.612516 | ||||||||
\(33\) | 5.53478 | 0.963481 | ||||||||
\(34\) | 0.774354 | 0.132801 | ||||||||
\(35\) | 0.0891959 | 0.0150769 | ||||||||
\(36\) | 0.566844 | 0.0944739 | ||||||||
\(37\) | 1.84372 | 0.303106 | 0.151553 | − | 0.988449i | \(-0.451573\pi\) | ||||
0.151553 | + | 0.988449i | \(0.451573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.349941 | −0.0560354 | ||||||||
\(40\) | 1.20274 | 0.190170 | ||||||||
\(41\) | −3.01234 | −0.470448 | −0.235224 | − | 0.971941i | \(-0.575582\pi\) | ||||
−0.235224 | + | 0.971941i | \(0.575582\pi\) | |||||||
\(42\) | 0.0451606 | 0.00696842 | ||||||||
\(43\) | −2.44787 | −0.373297 | −0.186648 | − | 0.982427i | \(-0.559763\pi\) | ||||
−0.186648 | + | 0.982427i | \(0.559763\pi\) | |||||||
\(44\) | 6.41428 | 0.966989 | ||||||||
\(45\) | −0.297533 | −0.0443537 | ||||||||
\(46\) | 1.83776 | 0.270963 | ||||||||
\(47\) | −7.61831 | −1.11125 | −0.555623 | − | 0.831435i | \(-0.687520\pi\) | ||||
−0.555623 | + | 0.831435i | \(0.687520\pi\) | |||||||
\(48\) | −5.65484 | −0.816206 | ||||||||
\(49\) | −6.99204 | −0.998863 | ||||||||
\(50\) | −0.307988 | −0.0435561 | ||||||||
\(51\) | 4.13319 | 0.578763 | ||||||||
\(52\) | −0.405548 | −0.0562394 | ||||||||
\(53\) | −8.39967 | −1.15378 | −0.576891 | − | 0.816821i | \(-0.695734\pi\) | ||||
−0.576891 | + | 0.816821i | \(0.695734\pi\) | |||||||
\(54\) | −1.66957 | −0.227199 | ||||||||
\(55\) | −3.36682 | −0.453982 | ||||||||
\(56\) | 0.107279 | 0.0143358 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.48088 | 0.194449 | ||||||||
\(59\) | 10.4354 | 1.35858 | 0.679289 | − | 0.733871i | \(-0.262288\pi\) | ||||
0.679289 | + | 0.733871i | \(0.262288\pi\) | |||||||
\(60\) | 3.13190 | 0.404326 | ||||||||
\(61\) | −0.988579 | −0.126575 | −0.0632873 | − | 0.997995i | \(-0.520158\pi\) | ||||
−0.0632873 | + | 0.997995i | \(0.520158\pi\) | |||||||
\(62\) | −2.48490 | −0.315582 | ||||||||
\(63\) | −0.0265388 | −0.00334357 | ||||||||
\(64\) | −5.81256 | −0.726570 | ||||||||
\(65\) | 0.212870 | 0.0264033 | ||||||||
\(66\) | −1.70465 | −0.209828 | ||||||||
\(67\) | 9.97964 | 1.21921 | 0.609604 | − | 0.792706i | \(-0.291329\pi\) | ||||
0.609604 | + | 0.792706i | \(0.291329\pi\) | |||||||
\(68\) | 4.78997 | 0.580870 | ||||||||
\(69\) | 9.80923 | 1.18089 | ||||||||
\(70\) | −0.0274713 | −0.00328345 | ||||||||
\(71\) | 6.17719 | 0.733097 | 0.366549 | − | 0.930399i | \(-0.380539\pi\) | ||||
0.366549 | + | 0.930399i | \(0.380539\pi\) | |||||||
\(72\) | −0.357855 | −0.0421736 | ||||||||
\(73\) | 15.7450 | 1.84281 | 0.921407 | − | 0.388600i | \(-0.127041\pi\) | ||||
0.921407 | + | 0.388600i | \(0.127041\pi\) | |||||||
\(74\) | −0.567844 | −0.0660106 | ||||||||
\(75\) | −1.64392 | −0.189823 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.300307 | −0.0342231 | ||||||||
\(78\) | 0.107778 | 0.0122034 | ||||||||
\(79\) | −1.02849 | −0.115715 | −0.0578573 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578573 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(80\) | 3.43986 | 0.384588 | ||||||||
\(81\) | −8.01887 | −0.890986 | ||||||||
\(82\) | 0.927765 | 0.102455 | ||||||||
\(83\) | 17.9388 | 1.96904 | 0.984518 | − | 0.175284i | \(-0.0560842\pi\) | ||||
0.984518 | + | 0.175284i | \(0.0560842\pi\) | |||||||
\(84\) | 0.279353 | 0.0304799 | ||||||||
\(85\) | −2.51423 | −0.272707 | ||||||||
\(86\) | 0.753916 | 0.0812968 | ||||||||
\(87\) | 7.90434 | 0.847434 | ||||||||
\(88\) | −4.04941 | −0.431668 | ||||||||
\(89\) | 0.656354 | 0.0695734 | 0.0347867 | − | 0.999395i | \(-0.488925\pi\) | ||||
0.0347867 | + | 0.999395i | \(0.488925\pi\) | |||||||
\(90\) | 0.0916368 | 0.00965937 | ||||||||
\(91\) | 0.0189871 | 0.00199039 | ||||||||
\(92\) | 11.3680 | 1.18519 | ||||||||
\(93\) | −13.2634 | −1.37535 | ||||||||
\(94\) | 2.34635 | 0.242008 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.69603 | 0.581349 | ||||||||
\(97\) | 16.8130 | 1.70711 | 0.853553 | − | 0.521006i | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521006i | \(0.174443\pi\) | |||||||
\(98\) | 2.15347 | 0.217533 | ||||||||
\(99\) | 1.00174 | 0.100679 | ||||||||
\(100\) | −1.90514 | −0.190514 | ||||||||
\(101\) | 3.67973 | 0.366146 | 0.183073 | − | 0.983099i | \(-0.441395\pi\) | ||||
0.183073 | + | 0.983099i | \(0.441395\pi\) | |||||||
\(102\) | −1.27298 | −0.126043 | ||||||||
\(103\) | −3.53420 | −0.348235 | −0.174118 | − | 0.984725i | \(-0.555707\pi\) | ||||
−0.174118 | + | 0.984725i | \(0.555707\pi\) | |||||||
\(104\) | 0.256027 | 0.0251055 | ||||||||
\(105\) | −0.146631 | −0.0143097 | ||||||||
\(106\) | 2.58700 | 0.251272 | ||||||||
\(107\) | −1.88660 | −0.182385 | −0.0911923 | − | 0.995833i | \(-0.529068\pi\) | ||||
−0.0911923 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(108\) | −10.3275 | −0.993768 | ||||||||
\(109\) | −13.1599 | −1.26049 | −0.630244 | − | 0.776397i | \(-0.717045\pi\) | ||||
−0.630244 | + | 0.776397i | \(0.717045\pi\) | |||||||
\(110\) | 1.03694 | 0.0988685 | ||||||||
\(111\) | −3.03093 | −0.287683 | ||||||||
\(112\) | 0.306821 | 0.0289919 | ||||||||
\(113\) | 12.3456 | 1.16138 | 0.580689 | − | 0.814125i | \(-0.302783\pi\) | ||||
0.580689 | + | 0.814125i | \(0.302783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.96699 | −0.556424 | ||||||||
\(116\) | 9.16037 | 0.850519 | ||||||||
\(117\) | −0.0633359 | −0.00585541 | ||||||||
\(118\) | −3.21399 | −0.295872 | ||||||||
\(119\) | −0.224259 | −0.0205578 | ||||||||
\(120\) | −1.97720 | −0.180493 | ||||||||
\(121\) | 0.335489 | 0.0304990 | ||||||||
\(122\) | 0.304471 | 0.0275655 | ||||||||
\(123\) | 4.95204 | 0.446510 | ||||||||
\(124\) | −15.3710 | −1.38035 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.00817363 | 0.000728164 0 | ||||||||
\(127\) | 21.2121 | 1.88227 | 0.941134 | − | 0.338035i | \(-0.109762\pi\) | ||||
0.941134 | + | 0.338035i | \(0.109762\pi\) | |||||||
\(128\) | 8.72003 | 0.770749 | ||||||||
\(129\) | 4.02410 | 0.354302 | ||||||||
\(130\) | −0.0655615 | −0.00575012 | ||||||||
\(131\) | 6.95074 | 0.607289 | 0.303645 | − | 0.952785i | \(-0.401796\pi\) | ||||
0.303645 | + | 0.952785i | \(0.401796\pi\) | |||||||
\(132\) | −10.5445 | −0.917785 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.07361 | −0.265520 | ||||||||
\(135\) | 5.42087 | 0.466555 | ||||||||
\(136\) | −3.02396 | −0.259303 | ||||||||
\(137\) | 21.0068 | 1.79474 | 0.897368 | − | 0.441283i | \(-0.145477\pi\) | ||||
0.897368 | + | 0.441283i | \(0.145477\pi\) | |||||||
\(138\) | −3.02113 | −0.257176 | ||||||||
\(139\) | 15.7214 | 1.33347 | 0.666736 | − | 0.745294i | \(-0.267691\pi\) | ||||
0.666736 | + | 0.745294i | \(0.267691\pi\) | |||||||
\(140\) | −0.169931 | −0.0143618 | ||||||||
\(141\) | 12.5239 | 1.05470 | ||||||||
\(142\) | −1.90250 | −0.159654 | ||||||||
\(143\) | −0.716695 | −0.0599331 | ||||||||
\(144\) | −1.02347 | −0.0852894 | ||||||||
\(145\) | −4.80823 | −0.399302 | ||||||||
\(146\) | −4.84928 | −0.401329 | ||||||||
\(147\) | 11.4943 | 0.948038 | ||||||||
\(148\) | −3.51255 | −0.288730 | ||||||||
\(149\) | −19.5194 | −1.59909 | −0.799546 | − | 0.600605i | \(-0.794927\pi\) | ||||
−0.799546 | + | 0.600605i | \(0.794927\pi\) | |||||||
\(150\) | 0.506308 | 0.0413398 | ||||||||
\(151\) | 11.2284 | 0.913758 | 0.456879 | − | 0.889529i | \(-0.348967\pi\) | ||||
0.456879 | + | 0.889529i | \(0.348967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.748068 | 0.0604777 | ||||||||
\(154\) | 0.0924909 | 0.00745313 | ||||||||
\(155\) | 8.06815 | 0.648049 | ||||||||
\(156\) | 0.666687 | 0.0533777 | ||||||||
\(157\) | 4.61281 | 0.368143 | 0.184071 | − | 0.982913i | \(-0.441072\pi\) | ||||
0.184071 | + | 0.982913i | \(0.441072\pi\) | |||||||
\(158\) | 0.316764 | 0.0252004 | ||||||||
\(159\) | 13.8084 | 1.09507 | ||||||||
\(160\) | −3.46491 | −0.273925 | ||||||||
\(161\) | −0.532231 | −0.0419456 | ||||||||
\(162\) | 2.46972 | 0.194039 | ||||||||
\(163\) | −0.574735 | −0.0450167 | −0.0225084 | − | 0.999747i | \(-0.507165\pi\) | ||||
−0.0225084 | + | 0.999747i | \(0.507165\pi\) | |||||||
\(164\) | 5.73894 | 0.448136 | ||||||||
\(165\) | 5.53478 | 0.430882 | ||||||||
\(166\) | −5.52493 | −0.428818 | ||||||||
\(167\) | 4.12202 | 0.318971 | 0.159486 | − | 0.987200i | \(-0.449016\pi\) | ||||
0.159486 | + | 0.987200i | \(0.449016\pi\) | |||||||
\(168\) | −0.176358 | −0.0136063 | ||||||||
\(169\) | −12.9547 | −0.996514 | ||||||||
\(170\) | 0.774354 | 0.0593903 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.66355 | 0.355592 | ||||||||
\(173\) | −6.43458 | −0.489212 | −0.244606 | − | 0.969623i | \(-0.578659\pi\) | ||||
−0.244606 | + | 0.969623i | \(0.578659\pi\) | |||||||
\(174\) | −2.43444 | −0.184555 | ||||||||
\(175\) | 0.0891959 | 0.00674258 | ||||||||
\(176\) | −11.5814 | −0.872980 | ||||||||
\(177\) | −17.1550 | −1.28945 | ||||||||
\(178\) | −0.202149 | −0.0151517 | ||||||||
\(179\) | 3.83032 | 0.286291 | 0.143146 | − | 0.989702i | \(-0.454278\pi\) | ||||
0.143146 | + | 0.989702i | \(0.454278\pi\) | |||||||
\(180\) | 0.566844 | 0.0422500 | ||||||||
\(181\) | 16.6878 | 1.24039 | 0.620195 | − | 0.784447i | \(-0.287053\pi\) | ||||
0.620195 | + | 0.784447i | \(0.287053\pi\) | |||||||
\(182\) | −0.00584781 | −0.000433469 0 | ||||||||
\(183\) | 1.62514 | 0.120134 | ||||||||
\(184\) | −7.17672 | −0.529075 | ||||||||
\(185\) | 1.84372 | 0.135553 | ||||||||
\(186\) | 4.08496 | 0.299524 | ||||||||
\(187\) | 8.46497 | 0.619020 | ||||||||
\(188\) | 14.5140 | 1.05854 | ||||||||
\(189\) | 0.483520 | 0.0351709 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.92694 | 0.573573 | 0.286787 | − | 0.957994i | \(-0.407413\pi\) | ||||
0.286787 | + | 0.957994i | \(0.407413\pi\) | |||||||
\(192\) | 9.55538 | 0.689600 | ||||||||
\(193\) | −21.2669 | −1.53082 | −0.765412 | − | 0.643540i | \(-0.777465\pi\) | ||||
−0.765412 | + | 0.643540i | \(0.777465\pi\) | |||||||
\(194\) | −5.17822 | −0.371775 | ||||||||
\(195\) | −0.349941 | −0.0250598 | ||||||||
\(196\) | 13.3208 | 0.951489 | ||||||||
\(197\) | 2.88742 | 0.205720 | 0.102860 | − | 0.994696i | \(-0.467201\pi\) | ||||
0.102860 | + | 0.994696i | \(0.467201\pi\) | |||||||
\(198\) | −0.308525 | −0.0219259 | ||||||||
\(199\) | 11.6149 | 0.823355 | 0.411678 | − | 0.911330i | \(-0.364943\pi\) | ||||
0.411678 | + | 0.911330i | \(0.364943\pi\) | |||||||
\(200\) | 1.20274 | 0.0850464 | ||||||||
\(201\) | −16.4057 | −1.15717 | ||||||||
\(202\) | −1.13331 | −0.0797396 | ||||||||
\(203\) | −0.428874 | −0.0301011 | ||||||||
\(204\) | −7.87432 | −0.551313 | ||||||||
\(205\) | −3.01234 | −0.210391 | ||||||||
\(206\) | 1.08849 | 0.0758389 | ||||||||
\(207\) | 1.77538 | 0.123397 | ||||||||
\(208\) | 0.732242 | 0.0507719 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.0451606 | 0.00311637 | ||||||||
\(211\) | −23.7001 | −1.63158 | −0.815790 | − | 0.578349i | \(-0.803697\pi\) | ||||
−0.815790 | + | 0.578349i | \(0.803697\pi\) | |||||||
\(212\) | 16.0026 | 1.09906 | ||||||||
\(213\) | −10.1548 | −0.695795 | ||||||||
\(214\) | 0.581051 | 0.0397198 | ||||||||
\(215\) | −2.44787 | −0.166943 | ||||||||
\(216\) | 6.51989 | 0.443623 | ||||||||
\(217\) | 0.719646 | 0.0488527 | ||||||||
\(218\) | 4.05309 | 0.274510 | ||||||||
\(219\) | −25.8835 | −1.74904 | ||||||||
\(220\) | 6.41428 | 0.432451 | ||||||||
\(221\) | −0.535205 | −0.0360018 | ||||||||
\(222\) | 0.933490 | 0.0626517 | ||||||||
\(223\) | −8.81587 | −0.590354 | −0.295177 | − | 0.955443i | \(-0.595379\pi\) | ||||
−0.295177 | + | 0.955443i | \(0.595379\pi\) | |||||||
\(224\) | −0.309056 | −0.0206497 | ||||||||
\(225\) | −0.297533 | −0.0198356 | ||||||||
\(226\) | −3.80231 | −0.252926 | ||||||||
\(227\) | −1.04512 | −0.0693671 | −0.0346835 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346835 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.4837 | −0.891031 | −0.445515 | − | 0.895274i | \(-0.646980\pi\) | ||||
−0.445515 | + | 0.895274i | \(0.646980\pi\) | |||||||
\(230\) | 1.83776 | 0.121178 | ||||||||
\(231\) | 0.493680 | 0.0324817 | ||||||||
\(232\) | −5.78304 | −0.379675 | ||||||||
\(233\) | 11.2178 | 0.734905 | 0.367452 | − | 0.930042i | \(-0.380230\pi\) | ||||
0.367452 | + | 0.930042i | \(0.380230\pi\) | |||||||
\(234\) | 0.0195067 | 0.00127519 | ||||||||
\(235\) | −7.61831 | −0.496964 | ||||||||
\(236\) | −19.8810 | −1.29414 | ||||||||
\(237\) | 1.69076 | 0.109827 | ||||||||
\(238\) | 0.0690692 | 0.00447709 | ||||||||
\(239\) | −20.3290 | −1.31497 | −0.657487 | − | 0.753466i | \(-0.728380\pi\) | ||||
−0.657487 | + | 0.753466i | \(0.728380\pi\) | |||||||
\(240\) | −5.65484 | −0.365019 | ||||||||
\(241\) | −3.84452 | −0.247647 | −0.123824 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123824 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(242\) | −0.103327 | −0.00664209 | ||||||||
\(243\) | −3.08025 | −0.197598 | ||||||||
\(244\) | 1.88339 | 0.120571 | ||||||||
\(245\) | −6.99204 | −0.446705 | ||||||||
\(246\) | −1.52517 | −0.0972413 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.70387 | 0.616197 | ||||||||
\(249\) | −29.4899 | −1.86884 | ||||||||
\(250\) | −0.307988 | −0.0194789 | ||||||||
\(251\) | −7.93776 | −0.501027 | −0.250513 | − | 0.968113i | \(-0.580599\pi\) | ||||
−0.250513 | + | 0.968113i | \(0.580599\pi\) | |||||||
\(252\) | 0.0505601 | 0.00318499 | ||||||||
\(253\) | 20.0898 | 1.26303 | ||||||||
\(254\) | −6.53307 | −0.409921 | ||||||||
\(255\) | 4.13319 | 0.258831 | ||||||||
\(256\) | 8.93946 | 0.558716 | ||||||||
\(257\) | 24.2278 | 1.51129 | 0.755643 | − | 0.654984i | \(-0.227325\pi\) | ||||
0.755643 | + | 0.654984i | \(0.227325\pi\) | |||||||
\(258\) | −1.23938 | −0.0771602 | ||||||||
\(259\) | 0.164452 | 0.0102186 | ||||||||
\(260\) | −0.405548 | −0.0251510 | ||||||||
\(261\) | 1.43061 | 0.0885525 | ||||||||
\(262\) | −2.14075 | −0.132256 | ||||||||
\(263\) | −12.3772 | −0.763212 | −0.381606 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381606 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(264\) | 6.65689 | 0.409703 | ||||||||
\(265\) | −8.39967 | −0.515987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.07899 | −0.0660333 | ||||||||
\(268\) | −19.0127 | −1.16138 | ||||||||
\(269\) | −24.3788 | −1.48640 | −0.743202 | − | 0.669067i | \(-0.766694\pi\) | ||||
−0.743202 | + | 0.669067i | \(0.766694\pi\) | |||||||
\(270\) | −1.66957 | −0.101607 | ||||||||
\(271\) | 17.4183 | 1.05809 | 0.529043 | − | 0.848595i | \(-0.322551\pi\) | ||||
0.529043 | + | 0.848595i | \(0.322551\pi\) | |||||||
\(272\) | −8.64860 | −0.524398 | ||||||||
\(273\) | −0.0312133 | −0.00188911 | ||||||||
\(274\) | −6.46986 | −0.390859 | ||||||||
\(275\) | −3.36682 | −0.203027 | ||||||||
\(276\) | −18.6880 | −1.12489 | ||||||||
\(277\) | 20.7839 | 1.24879 | 0.624393 | − | 0.781110i | \(-0.285346\pi\) | ||||
0.624393 | + | 0.781110i | \(0.285346\pi\) | |||||||
\(278\) | −4.84201 | −0.290404 | ||||||||
\(279\) | −2.40054 | −0.143717 | ||||||||
\(280\) | 0.107279 | 0.00641117 | ||||||||
\(281\) | −6.00987 | −0.358519 | −0.179259 | − | 0.983802i | \(-0.557370\pi\) | ||||
−0.179259 | + | 0.983802i | \(0.557370\pi\) | |||||||
\(282\) | −3.85721 | −0.229694 | ||||||||
\(283\) | 11.5738 | 0.687993 | 0.343997 | − | 0.938971i | \(-0.388219\pi\) | ||||
0.343997 | + | 0.938971i | \(0.388219\pi\) | |||||||
\(284\) | −11.7684 | −0.698327 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.220734 | 0.0130523 | ||||||||
\(287\) | −0.268688 | −0.0158602 | ||||||||
\(288\) | 1.03093 | 0.0607480 | ||||||||
\(289\) | −10.6786 | −0.628155 | ||||||||
\(290\) | 1.48088 | 0.0869602 | ||||||||
\(291\) | −27.6393 | −1.62024 | ||||||||
\(292\) | −29.9965 | −1.75541 | ||||||||
\(293\) | 17.4693 | 1.02057 | 0.510284 | − | 0.860006i | \(-0.329540\pi\) | ||||
0.510284 | + | 0.860006i | \(0.329540\pi\) | |||||||
\(294\) | −3.54012 | −0.206464 | ||||||||
\(295\) | 10.4354 | 0.607574 | ||||||||
\(296\) | 2.21751 | 0.128890 | ||||||||
\(297\) | −18.2511 | −1.05904 | ||||||||
\(298\) | 6.01175 | 0.348251 | ||||||||
\(299\) | −1.27019 | −0.0734571 | ||||||||
\(300\) | 3.13190 | 0.180820 | ||||||||
\(301\) | −0.218340 | −0.0125849 | ||||||||
\(302\) | −3.45823 | −0.198999 | ||||||||
\(303\) | −6.04917 | −0.347516 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.988579 | −0.0566059 | ||||||||
\(306\) | −0.230396 | −0.0131709 | ||||||||
\(307\) | 29.6533 | 1.69240 | 0.846201 | − | 0.532863i | \(-0.178884\pi\) | ||||
0.846201 | + | 0.532863i | \(0.178884\pi\) | |||||||
\(308\) | 0.572127 | 0.0326000 | ||||||||
\(309\) | 5.80994 | 0.330516 | ||||||||
\(310\) | −2.48490 | −0.141133 | ||||||||
\(311\) | −11.6224 | −0.659045 | −0.329522 | − | 0.944148i | \(-0.606888\pi\) | ||||
−0.329522 | + | 0.944148i | \(0.606888\pi\) | |||||||
\(312\) | −0.420887 | −0.0238280 | ||||||||
\(313\) | −0.474863 | −0.0268409 | −0.0134204 | − | 0.999910i | \(-0.504272\pi\) | ||||
−0.0134204 | + | 0.999910i | \(0.504272\pi\) | |||||||
\(314\) | −1.42069 | −0.0801743 | ||||||||
\(315\) | −0.0265388 | −0.00149529 | ||||||||
\(316\) | 1.95943 | 0.110226 | ||||||||
\(317\) | −20.2283 | −1.13613 | −0.568066 | − | 0.822983i | \(-0.692308\pi\) | ||||
−0.568066 | + | 0.822983i | \(0.692308\pi\) | |||||||
\(318\) | −4.25281 | −0.238486 | ||||||||
\(319\) | 16.1885 | 0.906379 | ||||||||
\(320\) | −5.81256 | −0.324932 | ||||||||
\(321\) | 3.10142 | 0.173104 | ||||||||
\(322\) | 0.163921 | 0.00913495 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.2771 | 0.848728 | ||||||||
\(325\) | 0.212870 | 0.0118079 | ||||||||
\(326\) | 0.177012 | 0.00980377 | ||||||||
\(327\) | 21.6338 | 1.19635 | ||||||||
\(328\) | −3.62306 | −0.200050 | ||||||||
\(329\) | −0.679522 | −0.0374633 | ||||||||
\(330\) | −1.70465 | −0.0938377 | ||||||||
\(331\) | −6.01306 | −0.330508 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(332\) | −34.1759 | −1.87565 | ||||||||
\(333\) | −0.548568 | −0.0300614 | ||||||||
\(334\) | −1.26953 | −0.0694658 | ||||||||
\(335\) | 9.97964 | 0.545246 | ||||||||
\(336\) | −0.504389 | −0.0275167 | ||||||||
\(337\) | −8.86733 | −0.483034 | −0.241517 | − | 0.970397i | \(-0.577645\pi\) | ||||
−0.241517 | + | 0.970397i | \(0.577645\pi\) | |||||||
\(338\) | 3.98989 | 0.217022 | ||||||||
\(339\) | −20.2952 | −1.10228 | ||||||||
\(340\) | 4.78997 | 0.259773 | ||||||||
\(341\) | −27.1640 | −1.47101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.24803 | −0.0673874 | ||||||||
\(344\) | −2.94415 | −0.158738 | ||||||||
\(345\) | 9.80923 | 0.528111 | ||||||||
\(346\) | 1.98177 | 0.106541 | ||||||||
\(347\) | 19.9712 | 1.07211 | 0.536055 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536055 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(348\) | −15.0589 | −0.807241 | ||||||||
\(349\) | −0.810214 | −0.0433698 | −0.0216849 | − | 0.999765i | \(-0.506903\pi\) | ||||
−0.0216849 | + | 0.999765i | \(0.506903\pi\) | |||||||
\(350\) | −0.0274713 | −0.00146840 | ||||||||
\(351\) | 1.15394 | 0.0615928 | ||||||||
\(352\) | 11.6657 | 0.621786 | ||||||||
\(353\) | −20.9503 | −1.11507 | −0.557536 | − | 0.830153i | \(-0.688253\pi\) | ||||
−0.557536 | + | 0.830153i | \(0.688253\pi\) | |||||||
\(354\) | 5.28354 | 0.280817 | ||||||||
\(355\) | 6.17719 | 0.327851 | ||||||||
\(356\) | −1.25045 | −0.0662736 | ||||||||
\(357\) | 0.368664 | 0.0195118 | ||||||||
\(358\) | −1.17969 | −0.0623487 | ||||||||
\(359\) | 25.7019 | 1.35649 | 0.678246 | − | 0.734835i | \(-0.262740\pi\) | ||||
0.678246 | + | 0.734835i | \(0.262740\pi\) | |||||||
\(360\) | −0.357855 | −0.0188606 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.13963 | −0.270133 | ||||||||
\(363\) | −0.551516 | −0.0289471 | ||||||||
\(364\) | −0.0361732 | −0.00189599 | ||||||||
\(365\) | 15.7450 | 0.824131 | ||||||||
\(366\) | −0.500525 | −0.0261629 | ||||||||
\(367\) | −24.2860 | −1.26772 | −0.633858 | − | 0.773449i | \(-0.718530\pi\) | ||||
−0.633858 | + | 0.773449i | \(0.718530\pi\) | |||||||
\(368\) | −20.5256 | −1.06997 | ||||||||
\(369\) | 0.896271 | 0.0466580 | ||||||||
\(370\) | −0.567844 | −0.0295208 | ||||||||
\(371\) | −0.749216 | −0.0388973 | ||||||||
\(372\) | 25.2686 | 1.31012 | ||||||||
\(373\) | 10.8809 | 0.563390 | 0.281695 | − | 0.959504i | \(-0.409103\pi\) | ||||
0.281695 | + | 0.959504i | \(0.409103\pi\) | |||||||
\(374\) | −2.60711 | −0.134811 | ||||||||
\(375\) | −1.64392 | −0.0848916 | ||||||||
\(376\) | −9.16284 | −0.472537 | ||||||||
\(377\) | −1.02353 | −0.0527144 | ||||||||
\(378\) | −0.148918 | −0.00765954 | ||||||||
\(379\) | 19.3318 | 0.993008 | 0.496504 | − | 0.868034i | \(-0.334617\pi\) | ||||
0.496504 | + | 0.868034i | \(0.334617\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.8709 | −1.78649 | ||||||||
\(382\) | −2.44140 | −0.124913 | ||||||||
\(383\) | −1.04305 | −0.0532973 | −0.0266487 | − | 0.999645i | \(-0.508484\pi\) | ||||
−0.0266487 | + | 0.999645i | \(0.508484\pi\) | |||||||
\(384\) | −14.3350 | −0.731530 | ||||||||
\(385\) | −0.300307 | −0.0153050 | ||||||||
\(386\) | 6.54995 | 0.333384 | ||||||||
\(387\) | 0.728323 | 0.0370228 | ||||||||
\(388\) | −32.0313 | −1.62614 | ||||||||
\(389\) | 26.6031 | 1.34883 | 0.674416 | − | 0.738352i | \(-0.264395\pi\) | ||||
0.674416 | + | 0.738352i | \(0.264395\pi\) | |||||||
\(390\) | 0.107778 | 0.00545753 | ||||||||
\(391\) | 15.0024 | 0.758703 | ||||||||
\(392\) | −8.40960 | −0.424749 | ||||||||
\(393\) | −11.4264 | −0.576388 | ||||||||
\(394\) | −0.889293 | −0.0448019 | ||||||||
\(395\) | −1.02849 | −0.0517491 | ||||||||
\(396\) | −1.90846 | −0.0959038 | ||||||||
\(397\) | −3.69756 | −0.185575 | −0.0927877 | − | 0.995686i | \(-0.529578\pi\) | ||||
−0.0927877 | + | 0.995686i | \(0.529578\pi\) | |||||||
\(398\) | −3.57724 | −0.179311 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.43986 | 0.171993 | ||||||||
\(401\) | −20.2351 | −1.01049 | −0.505245 | − | 0.862976i | \(-0.668598\pi\) | ||||
−0.505245 | + | 0.862976i | \(0.668598\pi\) | |||||||
\(402\) | 5.05277 | 0.252009 | ||||||||
\(403\) | 1.71747 | 0.0855531 | ||||||||
\(404\) | −7.01040 | −0.348781 | ||||||||
\(405\) | −8.01887 | −0.398461 | ||||||||
\(406\) | 0.132088 | 0.00655543 | ||||||||
\(407\) | −6.20748 | −0.307693 | ||||||||
\(408\) | 4.97115 | 0.246109 | ||||||||
\(409\) | 12.4768 | 0.616939 | 0.308470 | − | 0.951234i | \(-0.400183\pi\) | ||||
0.308470 | + | 0.951234i | \(0.400183\pi\) | |||||||
\(410\) | 0.927765 | 0.0458191 | ||||||||
\(411\) | −34.5335 | −1.70341 | ||||||||
\(412\) | 6.73316 | 0.331719 | ||||||||
\(413\) | 0.930798 | 0.0458016 | ||||||||
\(414\) | −0.546795 | −0.0268735 | ||||||||
\(415\) | 17.9388 | 0.880580 | ||||||||
\(416\) | −0.737576 | −0.0361626 | ||||||||
\(417\) | −25.8447 | −1.26562 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.9962 | 1.41656 | 0.708279 | − | 0.705933i | \(-0.249472\pi\) | ||||
0.708279 | + | 0.705933i | \(0.249472\pi\) | |||||||
\(420\) | 0.279353 | 0.0136310 | ||||||||
\(421\) | 14.5960 | 0.711368 | 0.355684 | − | 0.934606i | \(-0.384248\pi\) | ||||
0.355684 | + | 0.934606i | \(0.384248\pi\) | |||||||
\(422\) | 7.29934 | 0.355326 | ||||||||
\(423\) | 2.26670 | 0.110211 | ||||||||
\(424\) | −10.1026 | −0.490626 | ||||||||
\(425\) | −2.51423 | −0.121958 | ||||||||
\(426\) | 3.12756 | 0.151531 | ||||||||
\(427\) | −0.0881772 | −0.00426720 | ||||||||
\(428\) | 3.59424 | 0.173734 | ||||||||
\(429\) | 1.17819 | 0.0568835 | ||||||||
\(430\) | 0.753916 | 0.0363570 | ||||||||
\(431\) | 13.5081 | 0.650663 | 0.325332 | − | 0.945600i | \(-0.394524\pi\) | ||||
0.325332 | + | 0.945600i | \(0.394524\pi\) | |||||||
\(432\) | 18.6470 | 0.897156 | ||||||||
\(433\) | 38.0206 | 1.82715 | 0.913576 | − | 0.406668i | \(-0.133310\pi\) | ||||
0.913576 | + | 0.406668i | \(0.133310\pi\) | |||||||
\(434\) | −0.221642 | −0.0106392 | ||||||||
\(435\) | 7.90434 | 0.378984 | ||||||||
\(436\) | 25.0714 | 1.20070 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 7.97181 | 0.380908 | ||||||||
\(439\) | −23.7870 | −1.13529 | −0.567645 | − | 0.823273i | \(-0.692146\pi\) | ||||
−0.567645 | + | 0.823273i | \(0.692146\pi\) | |||||||
\(440\) | −4.04941 | −0.193048 | ||||||||
\(441\) | 2.08037 | 0.0990651 | ||||||||
\(442\) | 0.164837 | 0.00784049 | ||||||||
\(443\) | −19.2991 | −0.916929 | −0.458465 | − | 0.888713i | \(-0.651600\pi\) | ||||
−0.458465 | + | 0.888713i | \(0.651600\pi\) | |||||||
\(444\) | 5.77435 | 0.274038 | ||||||||
\(445\) | 0.656354 | 0.0311142 | ||||||||
\(446\) | 2.71518 | 0.128568 | ||||||||
\(447\) | 32.0883 | 1.51772 | ||||||||
\(448\) | −0.518457 | −0.0244948 | ||||||||
\(449\) | −26.4136 | −1.24654 | −0.623268 | − | 0.782008i | \(-0.714195\pi\) | ||||
−0.623268 | + | 0.782008i | \(0.714195\pi\) | |||||||
\(450\) | 0.0916368 | 0.00431980 | ||||||||
\(451\) | 10.1420 | 0.477569 | ||||||||
\(452\) | −23.5202 | −1.10630 | ||||||||
\(453\) | −18.4586 | −0.867263 | ||||||||
\(454\) | 0.321885 | 0.0151068 | ||||||||
\(455\) | 0.0189871 | 0.000890130 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.4641 | −1.79927 | −0.899637 | − | 0.436638i | \(-0.856169\pi\) | ||||
−0.899637 | + | 0.436638i | \(0.856169\pi\) | |||||||
\(458\) | 4.15283 | 0.194049 | ||||||||
\(459\) | −13.6293 | −0.636163 | ||||||||
\(460\) | 11.3680 | 0.530034 | ||||||||
\(461\) | 33.9836 | 1.58277 | 0.791387 | − | 0.611315i | \(-0.209359\pi\) | ||||
0.791387 | + | 0.611315i | \(0.209359\pi\) | |||||||
\(462\) | −0.152048 | −0.00707389 | ||||||||
\(463\) | −5.39446 | −0.250702 | −0.125351 | − | 0.992112i | \(-0.540006\pi\) | ||||
−0.125351 | + | 0.992112i | \(0.540006\pi\) | |||||||
\(464\) | −16.5396 | −0.767833 | ||||||||
\(465\) | −13.2634 | −0.615074 | ||||||||
\(466\) | −3.45496 | −0.160048 | ||||||||
\(467\) | 22.4289 | 1.03788 | 0.518942 | − | 0.854809i | \(-0.326326\pi\) | ||||
0.518942 | + | 0.854809i | \(0.326326\pi\) | |||||||
\(468\) | 0.120664 | 0.00557770 | ||||||||
\(469\) | 0.890143 | 0.0411030 | ||||||||
\(470\) | 2.34635 | 0.108229 | ||||||||
\(471\) | −7.58309 | −0.349410 | ||||||||
\(472\) | 12.5511 | 0.577711 | ||||||||
\(473\) | 8.24155 | 0.378947 | ||||||||
\(474\) | −0.520734 | −0.0239181 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.427246 | 0.0195828 | ||||||||
\(477\) | 2.49918 | 0.114430 | ||||||||
\(478\) | 6.26109 | 0.286376 | ||||||||
\(479\) | −28.7406 | −1.31319 | −0.656597 | − | 0.754242i | \(-0.728005\pi\) | ||||
−0.656597 | + | 0.754242i | \(0.728005\pi\) | |||||||
\(480\) | 5.69603 | 0.259987 | ||||||||
\(481\) | 0.392473 | 0.0178952 | ||||||||
\(482\) | 1.18407 | 0.0539328 | ||||||||
\(483\) | 0.874943 | 0.0398113 | ||||||||
\(484\) | −0.639154 | −0.0290525 | ||||||||
\(485\) | 16.8130 | 0.763441 | ||||||||
\(486\) | 0.948682 | 0.0430331 | ||||||||
\(487\) | −34.4441 | −1.56081 | −0.780406 | − | 0.625273i | \(-0.784988\pi\) | ||||
−0.780406 | + | 0.625273i | \(0.784988\pi\) | |||||||
\(488\) | −1.18900 | −0.0538236 | ||||||||
\(489\) | 0.944817 | 0.0427261 | ||||||||
\(490\) | 2.15347 | 0.0972838 | ||||||||
\(491\) | −19.3862 | −0.874887 | −0.437444 | − | 0.899246i | \(-0.644116\pi\) | ||||
−0.437444 | + | 0.899246i | \(0.644116\pi\) | |||||||
\(492\) | −9.43434 | −0.425333 | ||||||||
\(493\) | 12.0890 | 0.544462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00174 | 0.0450249 | ||||||||
\(496\) | 27.7533 | 1.24616 | ||||||||
\(497\) | 0.550980 | 0.0247148 | ||||||||
\(498\) | 9.08254 | 0.406998 | ||||||||
\(499\) | 11.2685 | 0.504445 | 0.252223 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252223 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(500\) | −1.90514 | −0.0852006 | ||||||||
\(501\) | −6.77626 | −0.302741 | ||||||||
\(502\) | 2.44474 | 0.109114 | ||||||||
\(503\) | 10.5918 | 0.472266 | 0.236133 | − | 0.971721i | \(-0.424120\pi\) | ||||
0.236133 | + | 0.971721i | \(0.424120\pi\) | |||||||
\(504\) | −0.0319192 | −0.00142179 | ||||||||
\(505\) | 3.67973 | 0.163746 | ||||||||
\(506\) | −6.18742 | −0.275064 | ||||||||
\(507\) | 21.2964 | 0.945808 | ||||||||
\(508\) | −40.4120 | −1.79299 | ||||||||
\(509\) | −2.17937 | −0.0965988 | −0.0482994 | − | 0.998833i | \(-0.515380\pi\) | ||||
−0.0482994 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(510\) | −1.27298 | −0.0563683 | ||||||||
\(511\) | 1.40439 | 0.0621266 | ||||||||
\(512\) | −20.1933 | −0.892426 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.46186 | −0.329129 | ||||||||
\(515\) | −3.53420 | −0.155735 | ||||||||
\(516\) | −7.66649 | −0.337498 | ||||||||
\(517\) | 25.6495 | 1.12806 | ||||||||
\(518\) | −0.0506494 | −0.00222541 | ||||||||
\(519\) | 10.5779 | 0.464319 | ||||||||
\(520\) | 0.256027 | 0.0112275 | ||||||||
\(521\) | −11.4473 | −0.501517 | −0.250759 | − | 0.968050i | \(-0.580680\pi\) | ||||
−0.250759 | + | 0.968050i | \(0.580680\pi\) | |||||||
\(522\) | −0.440611 | −0.0192850 | ||||||||
\(523\) | −9.75228 | −0.426437 | −0.213219 | − | 0.977004i | \(-0.568395\pi\) | ||||
−0.213219 | + | 0.977004i | \(0.568395\pi\) | |||||||
\(524\) | −13.2422 | −0.578486 | ||||||||
\(525\) | −0.146631 | −0.00639949 | ||||||||
\(526\) | 3.81204 | 0.166213 | ||||||||
\(527\) | −20.2852 | −0.883637 | ||||||||
\(528\) | 19.0388 | 0.828560 | ||||||||
\(529\) | 12.6049 | 0.548040 | ||||||||
\(530\) | 2.58700 | 0.112372 | ||||||||
\(531\) | −3.10489 | −0.134741 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.641237 | −0.0277750 | ||||||||
\(534\) | 0.332317 | 0.0143808 | ||||||||
\(535\) | −1.88660 | −0.0815649 | ||||||||
\(536\) | 12.0029 | 0.518446 | ||||||||
\(537\) | −6.29673 | −0.271724 | ||||||||
\(538\) | 7.50840 | 0.323710 | ||||||||
\(539\) | 23.5410 | 1.01398 | ||||||||
\(540\) | −10.3275 | −0.444427 | ||||||||
\(541\) | 22.8160 | 0.980938 | 0.490469 | − | 0.871459i | \(-0.336825\pi\) | ||||
0.490469 | + | 0.871459i | \(0.336825\pi\) | |||||||
\(542\) | −5.36463 | −0.230430 | ||||||||
\(543\) | −27.4333 | −1.17728 | ||||||||
\(544\) | 8.71160 | 0.373507 | ||||||||
\(545\) | −13.1599 | −0.563707 | ||||||||
\(546\) | 0.00961333 | 0.000411412 0 | ||||||||
\(547\) | 30.9172 | 1.32192 | 0.660962 | − | 0.750419i | \(-0.270148\pi\) | ||||
0.660962 | + | 0.750419i | \(0.270148\pi\) | |||||||
\(548\) | −40.0210 | −1.70961 | ||||||||
\(549\) | 0.294135 | 0.0125534 | ||||||||
\(550\) | 1.03694 | 0.0442153 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 11.7979 | 0.502154 | ||||||||
\(553\) | −0.0917374 | −0.00390107 | ||||||||
\(554\) | −6.40121 | −0.271961 | ||||||||
\(555\) | −3.03093 | −0.128656 | ||||||||
\(556\) | −29.9515 | −1.27023 | ||||||||
\(557\) | −9.82887 | −0.416463 | −0.208231 | − | 0.978080i | \(-0.566771\pi\) | ||||
−0.208231 | + | 0.978080i | \(0.566771\pi\) | |||||||
\(558\) | 0.739339 | 0.0312987 | ||||||||
\(559\) | −0.521078 | −0.0220393 | ||||||||
\(560\) | 0.306821 | 0.0129656 | ||||||||
\(561\) | −13.9157 | −0.587522 | ||||||||
\(562\) | 1.85097 | 0.0780785 | ||||||||
\(563\) | 33.4193 | 1.40846 | 0.704228 | − | 0.709974i | \(-0.251293\pi\) | ||||
0.704228 | + | 0.709974i | \(0.251293\pi\) | |||||||
\(564\) | −23.8598 | −1.00468 | ||||||||
\(565\) | 12.3456 | 0.519384 | ||||||||
\(566\) | −3.56461 | −0.149832 | ||||||||
\(567\) | −0.715251 | −0.0300377 | ||||||||
\(568\) | 7.42954 | 0.311736 | ||||||||
\(569\) | 37.6326 | 1.57764 | 0.788820 | − | 0.614624i | \(-0.210692\pi\) | ||||
0.788820 | + | 0.614624i | \(0.210692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.75232 | −0.115181 | −0.0575904 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575904 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(572\) | 1.36541 | 0.0570905 | ||||||||
\(573\) | −13.0312 | −0.544388 | ||||||||
\(574\) | 0.0827528 | 0.00345404 | ||||||||
\(575\) | −5.96699 | −0.248840 | ||||||||
\(576\) | 1.72943 | 0.0720596 | ||||||||
\(577\) | 0.0370999 | 0.00154449 | 0.000772245 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772245 | 1.00000i | \(0.499754\pi\) | ||||||||
\(578\) | 3.28889 | 0.136800 | ||||||||
\(579\) | 34.9610 | 1.45293 | ||||||||
\(580\) | 9.16037 | 0.380363 | ||||||||
\(581\) | 1.60006 | 0.0663819 | ||||||||
\(582\) | 8.51257 | 0.352857 | ||||||||
\(583\) | 28.2802 | 1.17125 | ||||||||
\(584\) | 18.9371 | 0.783624 | ||||||||
\(585\) | −0.0633359 | −0.00261862 | ||||||||
\(586\) | −5.38035 | −0.222260 | ||||||||
\(587\) | −3.60678 | −0.148868 | −0.0744340 | − | 0.997226i | \(-0.523715\pi\) | ||||
−0.0744340 | + | 0.997226i | \(0.523715\pi\) | |||||||
\(588\) | −21.8984 | −0.903074 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.21399 | −0.132318 | ||||||||
\(591\) | −4.74669 | −0.195253 | ||||||||
\(592\) | 6.34214 | 0.260660 | ||||||||
\(593\) | 17.8435 | 0.732744 | 0.366372 | − | 0.930469i | \(-0.380600\pi\) | ||||
0.366372 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(594\) | 5.62113 | 0.230638 | ||||||||
\(595\) | −0.224259 | −0.00919373 | ||||||||
\(596\) | 37.1873 | 1.52325 | ||||||||
\(597\) | −19.0939 | −0.781460 | ||||||||
\(598\) | 0.391204 | 0.0159975 | ||||||||
\(599\) | −21.9448 | −0.896642 | −0.448321 | − | 0.893873i | \(-0.647978\pi\) | ||||
−0.448321 | + | 0.893873i | \(0.647978\pi\) | |||||||
\(600\) | −1.97720 | −0.0807190 | ||||||||
\(601\) | 10.2808 | 0.419362 | 0.209681 | − | 0.977770i | \(-0.432757\pi\) | ||||
0.209681 | + | 0.977770i | \(0.432757\pi\) | |||||||
\(602\) | 0.0672462 | 0.00274075 | ||||||||
\(603\) | −2.96928 | −0.120918 | ||||||||
\(604\) | −21.3918 | −0.870420 | ||||||||
\(605\) | 0.335489 | 0.0136396 | ||||||||
\(606\) | 1.86307 | 0.0756822 | ||||||||
\(607\) | 32.2616 | 1.30946 | 0.654729 | − | 0.755864i | \(-0.272783\pi\) | ||||
0.654729 | + | 0.755864i | \(0.272783\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.705034 | 0.0285694 | ||||||||
\(610\) | 0.304471 | 0.0123277 | ||||||||
\(611\) | −1.62171 | −0.0656074 | ||||||||
\(612\) | −1.42518 | −0.0576094 | ||||||||
\(613\) | −16.3957 | −0.662215 | −0.331108 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331108 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(614\) | −9.13287 | −0.368573 | ||||||||
\(615\) | 4.95204 | 0.199685 | ||||||||
\(616\) | −0.361190 | −0.0145528 | ||||||||
\(617\) | −12.7768 | −0.514377 | −0.257188 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257188 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(618\) | −1.78939 | −0.0719799 | ||||||||
\(619\) | 4.28207 | 0.172111 | 0.0860555 | − | 0.996290i | \(-0.472574\pi\) | ||||
0.0860555 | + | 0.996290i | \(0.472574\pi\) | |||||||
\(620\) | −15.3710 | −0.617313 | ||||||||
\(621\) | −32.3463 | −1.29801 | ||||||||
\(622\) | 3.57956 | 0.143527 | ||||||||
\(623\) | 0.0585441 | 0.00234552 | ||||||||
\(624\) | −1.20375 | −0.0481884 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.146252 | 0.00584542 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.78807 | −0.350682 | ||||||||
\(629\) | −4.63554 | −0.184831 | ||||||||
\(630\) | 0.00817363 | 0.000325645 0 | ||||||||
\(631\) | −22.7879 | −0.907170 | −0.453585 | − | 0.891213i | \(-0.649855\pi\) | ||||
−0.453585 | + | 0.891213i | \(0.649855\pi\) | |||||||
\(632\) | −1.23701 | −0.0492055 | ||||||||
\(633\) | 38.9610 | 1.54856 | ||||||||
\(634\) | 6.23007 | 0.247428 | ||||||||
\(635\) | 21.2121 | 0.841776 | ||||||||
\(636\) | −26.3069 | −1.04314 | ||||||||
\(637\) | −1.48840 | −0.0589724 | ||||||||
\(638\) | −4.98585 | −0.197392 | ||||||||
\(639\) | −1.83792 | −0.0727069 | ||||||||
\(640\) | 8.72003 | 0.344689 | ||||||||
\(641\) | −31.3626 | −1.23875 | −0.619373 | − | 0.785097i | \(-0.712613\pi\) | ||||
−0.619373 | + | 0.785097i | \(0.712613\pi\) | |||||||
\(642\) | −0.955200 | −0.0376987 | ||||||||
\(643\) | −11.1490 | −0.439674 | −0.219837 | − | 0.975537i | \(-0.570553\pi\) | ||||
−0.219837 | + | 0.975537i | \(0.570553\pi\) | |||||||
\(644\) | 1.01398 | 0.0399562 | ||||||||
\(645\) | 4.02410 | 0.158449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.5536 | −0.690102 | −0.345051 | − | 0.938584i | \(-0.612138\pi\) | ||||
−0.345051 | + | 0.938584i | \(0.612138\pi\) | |||||||
\(648\) | −9.64461 | −0.378876 | ||||||||
\(649\) | −35.1342 | −1.37914 | ||||||||
\(650\) | −0.0655615 | −0.00257153 | ||||||||
\(651\) | −1.18304 | −0.0463669 | ||||||||
\(652\) | 1.09495 | 0.0428816 | ||||||||
\(653\) | −2.09533 | −0.0819966 | −0.0409983 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409983 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(654\) | −6.66294 | −0.260542 | ||||||||
\(655\) | 6.95074 | 0.271588 | ||||||||
\(656\) | −10.3620 | −0.404569 | ||||||||
\(657\) | −4.68466 | −0.182766 | ||||||||
\(658\) | 0.209285 | 0.00815878 | ||||||||
\(659\) | −13.0001 | −0.506411 | −0.253205 | − | 0.967413i | \(-0.581485\pi\) | ||||
−0.253205 | + | 0.967413i | \(0.581485\pi\) | |||||||
\(660\) | −10.5445 | −0.410446 | ||||||||
\(661\) | 38.0961 | 1.48177 | 0.740884 | − | 0.671633i | \(-0.234407\pi\) | ||||
0.740884 | + | 0.671633i | \(0.234407\pi\) | |||||||
\(662\) | 1.85195 | 0.0719782 | ||||||||
\(663\) | 0.879833 | 0.0341699 | ||||||||
\(664\) | 21.5756 | 0.837298 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.168953 | 0.00654678 | ||||||||
\(667\) | 28.6906 | 1.11091 | ||||||||
\(668\) | −7.85304 | −0.303843 | ||||||||
\(669\) | 14.4926 | 0.560315 | ||||||||
\(670\) | −3.07361 | −0.118744 | ||||||||
\(671\) | 3.32837 | 0.128490 | ||||||||
\(672\) | 0.508063 | 0.0195989 | ||||||||
\(673\) | 33.9497 | 1.30867 | 0.654333 | − | 0.756207i | \(-0.272950\pi\) | ||||
0.654333 | + | 0.756207i | \(0.272950\pi\) | |||||||
\(674\) | 2.73103 | 0.105196 | ||||||||
\(675\) | 5.42087 | 0.208650 | ||||||||
\(676\) | 24.6805 | 0.949251 | ||||||||
\(677\) | −16.5562 | −0.636307 | −0.318153 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318153 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(678\) | 6.25068 | 0.240056 | ||||||||
\(679\) | 1.49965 | 0.0575515 | ||||||||
\(680\) | −3.02396 | −0.115964 | ||||||||
\(681\) | 1.71809 | 0.0658374 | ||||||||
\(682\) | 8.36620 | 0.320358 | ||||||||
\(683\) | 5.33328 | 0.204072 | 0.102036 | − | 0.994781i | \(-0.467464\pi\) | ||||
0.102036 | + | 0.994781i | \(0.467464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0068 | 0.802630 | ||||||||
\(686\) | 0.384380 | 0.0146757 | ||||||||
\(687\) | 22.1662 | 0.845692 | ||||||||
\(688\) | −8.42033 | −0.321022 | ||||||||
\(689\) | −1.78804 | −0.0681188 | ||||||||
\(690\) | −3.02113 | −0.115012 | ||||||||
\(691\) | −14.1302 | −0.537538 | −0.268769 | − | 0.963205i | \(-0.586617\pi\) | ||||
−0.268769 | + | 0.963205i | \(0.586617\pi\) | |||||||
\(692\) | 12.2588 | 0.466009 | ||||||||
\(693\) | 0.0893513 | 0.00339417 | ||||||||
\(694\) | −6.15089 | −0.233485 | ||||||||
\(695\) | 15.7214 | 0.596347 | ||||||||
\(696\) | 9.50685 | 0.360356 | ||||||||
\(697\) | 7.57372 | 0.286875 | ||||||||
\(698\) | 0.249536 | 0.00944510 | ||||||||
\(699\) | −18.4412 | −0.697510 | ||||||||
\(700\) | −0.169931 | −0.00642279 | ||||||||
\(701\) | −38.1622 | −1.44137 | −0.720683 | − | 0.693265i | \(-0.756172\pi\) | ||||
−0.720683 | + | 0.693265i | \(0.756172\pi\) | |||||||
\(702\) | −0.355400 | −0.0134137 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 19.5699 | 0.737567 | ||||||||
\(705\) | 12.5239 | 0.471677 | ||||||||
\(706\) | 6.45245 | 0.242841 | ||||||||
\(707\) | 0.328216 | 0.0123438 | ||||||||
\(708\) | 32.6827 | 1.22829 | ||||||||
\(709\) | 33.1675 | 1.24563 | 0.622816 | − | 0.782368i | \(-0.285988\pi\) | ||||
0.622816 | + | 0.782368i | \(0.285988\pi\) | |||||||
\(710\) | −1.90250 | −0.0713996 | ||||||||
\(711\) | 0.306011 | 0.0114763 | ||||||||
\(712\) | 0.789422 | 0.0295849 | ||||||||
\(713\) | −48.1425 | −1.80295 | ||||||||
\(714\) | −0.113544 | −0.00424928 | ||||||||
\(715\) | −0.716695 | −0.0268029 | ||||||||
\(716\) | −7.29730 | −0.272713 | ||||||||
\(717\) | 33.4192 | 1.24806 | ||||||||
\(718\) | −7.91587 | −0.295418 | ||||||||
\(719\) | 42.3410 | 1.57905 | 0.789527 | − | 0.613716i | \(-0.210326\pi\) | ||||
0.789527 | + | 0.613716i | \(0.210326\pi\) | |||||||
\(720\) | −1.02347 | −0.0381426 | ||||||||
\(721\) | −0.315236 | −0.0117400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.32007 | 0.235046 | ||||||||
\(724\) | −31.7926 | −1.18156 | ||||||||
\(725\) | −4.80823 | −0.178573 | ||||||||
\(726\) | 0.169861 | 0.00630412 | ||||||||
\(727\) | −4.20162 | −0.155829 | −0.0779147 | − | 0.996960i | \(-0.524826\pi\) | ||||
−0.0779147 | + | 0.996960i | \(0.524826\pi\) | |||||||
\(728\) | 0.0228365 | 0.000846379 0 | ||||||||
\(729\) | 29.1203 | 1.07853 | ||||||||
\(730\) | −4.84928 | −0.179480 | ||||||||
\(731\) | 6.15452 | 0.227633 | ||||||||
\(732\) | −3.09613 | −0.114436 | ||||||||
\(733\) | 16.9357 | 0.625536 | 0.312768 | − | 0.949830i | \(-0.398744\pi\) | ||||
0.312768 | + | 0.949830i | \(0.398744\pi\) | |||||||
\(734\) | 7.47979 | 0.276084 | ||||||||
\(735\) | 11.4943 | 0.423975 | ||||||||
\(736\) | 20.6751 | 0.762094 | ||||||||
\(737\) | −33.5997 | −1.23766 | ||||||||
\(738\) | −0.276041 | −0.0101612 | ||||||||
\(739\) | 20.8465 | 0.766852 | 0.383426 | − | 0.923572i | \(-0.374744\pi\) | ||||
0.383426 | + | 0.923572i | \(0.374744\pi\) | |||||||
\(740\) | −3.51255 | −0.129124 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.230750 | 0.00847109 | ||||||||
\(743\) | 45.3499 | 1.66373 | 0.831863 | − | 0.554981i | \(-0.187274\pi\) | ||||
0.831863 | + | 0.554981i | \(0.187274\pi\) | |||||||
\(744\) | −15.9524 | −0.584842 | ||||||||
\(745\) | −19.5194 | −0.715136 | ||||||||
\(746\) | −3.35118 | −0.122695 | ||||||||
\(747\) | −5.33738 | −0.195285 | ||||||||
\(748\) | −16.1270 | −0.589661 | ||||||||
\(749\) | −0.168277 | −0.00614871 | ||||||||
\(750\) | 0.506308 | 0.0184877 | ||||||||
\(751\) | −8.67683 | −0.316622 | −0.158311 | − | 0.987389i | \(-0.550605\pi\) | ||||
−0.158311 | + | 0.987389i | \(0.550605\pi\) | |||||||
\(752\) | −26.2059 | −0.955631 | ||||||||
\(753\) | 13.0490 | 0.475533 | ||||||||
\(754\) | 0.315235 | 0.0114802 | ||||||||
\(755\) | 11.2284 | 0.408645 | ||||||||
\(756\) | −0.921174 | −0.0335028 | ||||||||
\(757\) | 10.0763 | 0.366229 | 0.183114 | − | 0.983092i | \(-0.441382\pi\) | ||||
0.183114 | + | 0.983092i | \(0.441382\pi\) | |||||||
\(758\) | −5.95397 | −0.216258 | ||||||||
\(759\) | −33.0259 | −1.19877 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.52014 | 0.163855 | 0.0819275 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819275 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(762\) | 10.7398 | 0.389063 | ||||||||
\(763\) | −1.17381 | −0.0424947 | ||||||||
\(764\) | −15.1020 | −0.546370 | ||||||||
\(765\) | 0.748068 | 0.0270465 | ||||||||
\(766\) | 0.321247 | 0.0116071 | ||||||||
\(767\) | 2.22139 | 0.0802097 | ||||||||
\(768\) | −14.6957 | −0.530287 | ||||||||
\(769\) | −39.5765 | −1.42717 | −0.713583 | − | 0.700571i | \(-0.752929\pi\) | ||||
−0.713583 | + | 0.700571i | \(0.752929\pi\) | |||||||
\(770\) | 0.0924909 | 0.00333314 | ||||||||
\(771\) | −39.8284 | −1.43439 | ||||||||
\(772\) | 40.5165 | 1.45822 | ||||||||
\(773\) | −23.4986 | −0.845187 | −0.422593 | − | 0.906319i | \(-0.638880\pi\) | ||||
−0.422593 | + | 0.906319i | \(0.638880\pi\) | |||||||
\(774\) | −0.224315 | −0.00806284 | ||||||||
\(775\) | 8.06815 | 0.289816 | ||||||||
\(776\) | 20.2217 | 0.725917 | ||||||||
\(777\) | −0.270346 | −0.00969861 | ||||||||
\(778\) | −8.19345 | −0.293749 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.666687 | 0.0238712 | ||||||||
\(781\) | −20.7975 | −0.744192 | ||||||||
\(782\) | −4.62056 | −0.165231 | ||||||||
\(783\) | −26.0648 | −0.931480 | ||||||||
\(784\) | −24.0516 | −0.858987 | ||||||||
\(785\) | 4.61281 | 0.164638 | ||||||||
\(786\) | 3.51921 | 0.125526 | ||||||||
\(787\) | 7.52483 | 0.268231 | 0.134116 | − | 0.990966i | \(-0.457181\pi\) | ||||
0.134116 | + | 0.990966i | \(0.457181\pi\) | |||||||
\(788\) | −5.50096 | −0.195963 | ||||||||
\(789\) | 20.3471 | 0.724377 | ||||||||
\(790\) | 0.316764 | 0.0112700 | ||||||||
\(791\) | 1.10118 | 0.0391534 | ||||||||
\(792\) | 1.20483 | 0.0428119 | ||||||||
\(793\) | −0.210439 | −0.00747290 | ||||||||
\(794\) | 1.13881 | 0.0404147 | ||||||||
\(795\) | 13.8084 | 0.489732 | ||||||||
\(796\) | −22.1280 | −0.784305 | ||||||||
\(797\) | −18.7858 | −0.665426 | −0.332713 | − | 0.943028i | \(-0.607964\pi\) | ||||
−0.332713 | + | 0.943028i | \(0.607964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.1542 | 0.677627 | ||||||||
\(800\) | −3.46491 | −0.122503 | ||||||||
\(801\) | −0.195287 | −0.00690014 | ||||||||
\(802\) | 6.23216 | 0.220065 | ||||||||
\(803\) | −53.0106 | −1.87070 | ||||||||
\(804\) | 31.2552 | 1.10229 | ||||||||
\(805\) | −0.532231 | −0.0187587 | ||||||||
\(806\) | −0.528960 | −0.0186318 | ||||||||
\(807\) | 40.0768 | 1.41077 | ||||||||
\(808\) | 4.42575 | 0.155697 | ||||||||
\(809\) | −19.4930 | −0.685338 | −0.342669 | − | 0.939456i | \(-0.611331\pi\) | ||||
−0.342669 | + | 0.939456i | \(0.611331\pi\) | |||||||
\(810\) | 2.46972 | 0.0867771 | ||||||||
\(811\) | 15.2060 | 0.533954 | 0.266977 | − | 0.963703i | \(-0.413975\pi\) | ||||
0.266977 | + | 0.963703i | \(0.413975\pi\) | |||||||
\(812\) | 0.817067 | 0.0286734 | ||||||||
\(813\) | −28.6342 | −1.00425 | ||||||||
\(814\) | 1.91183 | 0.0670096 | ||||||||
\(815\) | −0.574735 | −0.0201321 | ||||||||
\(816\) | 14.2176 | 0.497715 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.84272 | −0.134357 | ||||||||
\(819\) | −0.00564930 | −0.000197403 0 | ||||||||
\(820\) | 5.73894 | 0.200412 | ||||||||
\(821\) | −26.7664 | −0.934154 | −0.467077 | − | 0.884217i | \(-0.654693\pi\) | ||||
−0.467077 | + | 0.884217i | \(0.654693\pi\) | |||||||
\(822\) | 10.6359 | 0.370970 | ||||||||
\(823\) | 27.6484 | 0.963763 | 0.481881 | − | 0.876236i | \(-0.339954\pi\) | ||||
0.481881 | + | 0.876236i | \(0.339954\pi\) | |||||||
\(824\) | −4.25072 | −0.148081 | ||||||||
\(825\) | 5.53478 | 0.192696 | ||||||||
\(826\) | −0.286675 | −0.00997469 | ||||||||
\(827\) | 12.8221 | 0.445869 | 0.222935 | − | 0.974833i | \(-0.428436\pi\) | ||||
0.222935 | + | 0.974833i | \(0.428436\pi\) | |||||||
\(828\) | −3.38235 | −0.117545 | ||||||||
\(829\) | 45.4531 | 1.57865 | 0.789326 | − | 0.613974i | \(-0.210430\pi\) | ||||
0.789326 | + | 0.613974i | \(0.210430\pi\) | |||||||
\(830\) | −5.52493 | −0.191773 | ||||||||
\(831\) | −34.1671 | −1.18524 | ||||||||
\(832\) | −1.23732 | −0.0428963 | ||||||||
\(833\) | 17.5796 | 0.609098 | ||||||||
\(834\) | 7.95986 | 0.275628 | ||||||||
\(835\) | 4.12202 | 0.142648 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43.7364 | 1.51175 | ||||||||
\(838\) | −8.93049 | −0.308499 | ||||||||
\(839\) | 23.3132 | 0.804859 | 0.402430 | − | 0.915451i | \(-0.368166\pi\) | ||||
0.402430 | + | 0.915451i | \(0.368166\pi\) | |||||||
\(840\) | −0.176358 | −0.00608494 | ||||||||
\(841\) | −5.88093 | −0.202791 | ||||||||
\(842\) | −4.49541 | −0.154922 | ||||||||
\(843\) | 9.87974 | 0.340276 | ||||||||
\(844\) | 45.1520 | 1.55420 | ||||||||
\(845\) | −12.9547 | −0.445655 | ||||||||
\(846\) | −0.698118 | −0.0240018 | ||||||||
\(847\) | 0.0299242 | 0.00102821 | ||||||||
\(848\) | −28.8937 | −0.992212 | ||||||||
\(849\) | −19.0264 | −0.652986 | ||||||||
\(850\) | 0.774354 | 0.0265601 | ||||||||
\(851\) | −11.0015 | −0.377125 | ||||||||
\(852\) | 19.3463 | 0.662794 | ||||||||
\(853\) | −45.7832 | −1.56759 | −0.783793 | − | 0.621022i | \(-0.786718\pi\) | ||||
−0.783793 | + | 0.621022i | \(0.786718\pi\) | |||||||
\(854\) | 0.0271576 | 0.000929312 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.26909 | −0.0775558 | ||||||||
\(857\) | 6.44896 | 0.220292 | 0.110146 | − | 0.993915i | \(-0.464868\pi\) | ||||
0.110146 | + | 0.993915i | \(0.464868\pi\) | |||||||
\(858\) | −0.362868 | −0.0123881 | ||||||||
\(859\) | −14.5369 | −0.495993 | −0.247997 | − | 0.968761i | \(-0.579772\pi\) | ||||
−0.247997 | + | 0.968761i | \(0.579772\pi\) | |||||||
\(860\) | 4.66355 | 0.159026 | ||||||||
\(861\) | 0.441702 | 0.0150531 | ||||||||
\(862\) | −4.16034 | −0.141702 | ||||||||
\(863\) | −4.57136 | −0.155611 | −0.0778054 | − | 0.996969i | \(-0.524791\pi\) | ||||
−0.0778054 | + | 0.996969i | \(0.524791\pi\) | |||||||
\(864\) | −18.7829 | −0.639006 | ||||||||
\(865\) | −6.43458 | −0.218782 | ||||||||
\(866\) | −11.7099 | −0.397918 | ||||||||
\(867\) | 17.5548 | 0.596192 | ||||||||
\(868\) | −1.37103 | −0.0465357 | ||||||||
\(869\) | 3.46275 | 0.117466 | ||||||||
\(870\) | −2.43444 | −0.0825353 | ||||||||
\(871\) | 2.12437 | 0.0719814 | ||||||||
\(872\) | −15.8279 | −0.536000 | ||||||||
\(873\) | −5.00244 | −0.169307 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0891959 | 0.00301537 | ||||||||
\(876\) | 49.3118 | 1.66609 | ||||||||
\(877\) | 32.9569 | 1.11288 | 0.556438 | − | 0.830889i | \(-0.312168\pi\) | ||||
0.556438 | + | 0.830889i | \(0.312168\pi\) | |||||||
\(878\) | 7.32611 | 0.247244 | ||||||||
\(879\) | −28.7181 | −0.968639 | ||||||||
\(880\) | −11.5814 | −0.390408 | ||||||||
\(881\) | −16.2413 | −0.547184 | −0.273592 | − | 0.961846i | \(-0.588212\pi\) | ||||
−0.273592 | + | 0.961846i | \(0.588212\pi\) | |||||||
\(882\) | −0.640729 | −0.0215745 | ||||||||
\(883\) | −28.5141 | −0.959575 | −0.479787 | − | 0.877385i | \(-0.659286\pi\) | ||||
−0.479787 | + | 0.877385i | \(0.659286\pi\) | |||||||
\(884\) | 1.01964 | 0.0342943 | ||||||||
\(885\) | −17.1550 | −0.576659 | ||||||||
\(886\) | 5.94391 | 0.199689 | ||||||||
\(887\) | 38.6352 | 1.29724 | 0.648622 | − | 0.761111i | \(-0.275346\pi\) | ||||
0.648622 | + | 0.761111i | \(0.275346\pi\) | |||||||
\(888\) | −3.64541 | −0.122332 | ||||||||
\(889\) | 1.89203 | 0.0634567 | ||||||||
\(890\) | −0.202149 | −0.00677606 | ||||||||
\(891\) | 26.9981 | 0.904471 | ||||||||
\(892\) | 16.7955 | 0.562355 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −9.88282 | −0.330531 | ||||||||
\(895\) | 3.83032 | 0.128033 | ||||||||
\(896\) | 0.777791 | 0.0259842 | ||||||||
\(897\) | 2.08809 | 0.0697193 | ||||||||
\(898\) | 8.13508 | 0.271471 | ||||||||
\(899\) | −38.7935 | −1.29384 | ||||||||
\(900\) | 0.566844 | 0.0188948 | ||||||||
\(901\) | 21.1187 | 0.703566 | ||||||||
\(902\) | −3.12362 | −0.104005 | ||||||||
\(903\) | 0.358933 | 0.0119446 | ||||||||
\(904\) | 14.8486 | 0.493855 | ||||||||
\(905\) | 16.6878 | 0.554720 | ||||||||
\(906\) | 5.68505 | 0.188873 | ||||||||
\(907\) | 28.6565 | 0.951522 | 0.475761 | − | 0.879575i | \(-0.342173\pi\) | ||||
0.475761 | + | 0.879575i | \(0.342173\pi\) | |||||||
\(908\) | 1.99110 | 0.0660771 | ||||||||
\(909\) | −1.09484 | −0.0363136 | ||||||||
\(910\) | −0.00584781 | −0.000193853 0 | ||||||||
\(911\) | −47.5952 | −1.57690 | −0.788450 | − | 0.615099i | \(-0.789116\pi\) | ||||
−0.788450 | + | 0.615099i | \(0.789116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.3966 | −1.99884 | ||||||||
\(914\) | 11.8465 | 0.391847 | ||||||||
\(915\) | 1.62514 | 0.0537256 | ||||||||
\(916\) | 25.6885 | 0.848770 | ||||||||
\(917\) | 0.619978 | 0.0204735 | ||||||||
\(918\) | 4.19768 | 0.138544 | ||||||||
\(919\) | −27.2196 | −0.897891 | −0.448945 | − | 0.893559i | \(-0.648200\pi\) | ||||
−0.448945 | + | 0.893559i | \(0.648200\pi\) | |||||||
\(920\) | −7.17672 | −0.236610 | ||||||||
\(921\) | −48.7476 | −1.60629 | ||||||||
\(922\) | −10.4666 | −0.344698 | ||||||||
\(923\) | 1.31494 | 0.0432817 | ||||||||
\(924\) | −0.940530 | −0.0309412 | ||||||||
\(925\) | 1.84372 | 0.0606212 | ||||||||
\(926\) | 1.66143 | 0.0545980 | ||||||||
\(927\) | 1.05154 | 0.0345372 | ||||||||
\(928\) | 16.6601 | 0.546894 | ||||||||
\(929\) | −32.2399 | −1.05776 | −0.528879 | − | 0.848697i | \(-0.677387\pi\) | ||||
−0.528879 | + | 0.848697i | \(0.677387\pi\) | |||||||
\(930\) | 4.08496 | 0.133951 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.3716 | −0.700049 | ||||||||
\(933\) | 19.1062 | 0.625510 | ||||||||
\(934\) | −6.90783 | −0.226031 | ||||||||
\(935\) | 8.46497 | 0.276834 | ||||||||
\(936\) | −0.0761765 | −0.00248991 | ||||||||
\(937\) | 18.1725 | 0.593668 | 0.296834 | − | 0.954929i | \(-0.404069\pi\) | ||||
0.296834 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(938\) | −0.274154 | −0.00895144 | ||||||||
\(939\) | 0.780637 | 0.0254751 | ||||||||
\(940\) | 14.5140 | 0.473394 | ||||||||
\(941\) | 23.5571 | 0.767939 | 0.383970 | − | 0.923346i | \(-0.374557\pi\) | ||||
0.383970 | + | 0.923346i | \(0.374557\pi\) | |||||||
\(942\) | 2.33550 | 0.0760948 | ||||||||
\(943\) | 17.9746 | 0.585333 | ||||||||
\(944\) | 35.8964 | 1.16833 | ||||||||
\(945\) | 0.483520 | 0.0157289 | ||||||||
\(946\) | −2.53830 | −0.0825273 | ||||||||
\(947\) | −8.43157 | −0.273989 | −0.136995 | − | 0.990572i | \(-0.543744\pi\) | ||||
−0.136995 | + | 0.990572i | \(0.543744\pi\) | |||||||
\(948\) | −3.22114 | −0.104618 | ||||||||
\(949\) | 3.35164 | 0.108799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.2536 | 1.07832 | ||||||||
\(952\) | −0.269725 | −0.00874184 | ||||||||
\(953\) | 50.0741 | 1.62206 | 0.811029 | − | 0.585005i | \(-0.198908\pi\) | ||||
0.811029 | + | 0.585005i | \(0.198908\pi\) | |||||||
\(954\) | −0.769719 | −0.0249206 | ||||||||
\(955\) | 7.92694 | 0.256510 | ||||||||
\(956\) | 38.7296 | 1.25261 | ||||||||
\(957\) | −26.6125 | −0.860260 | ||||||||
\(958\) | 8.85178 | 0.285988 | ||||||||
\(959\) | 1.87372 | 0.0605057 | ||||||||
\(960\) | 9.55538 | 0.308398 | ||||||||
\(961\) | 34.0950 | 1.09984 | ||||||||
\(962\) | −0.120877 | −0.00389723 | ||||||||
\(963\) | 0.561327 | 0.0180885 | ||||||||
\(964\) | 7.32436 | 0.235902 | ||||||||
\(965\) | −21.2669 | −0.684605 | ||||||||
\(966\) | −0.269472 | −0.00867013 | ||||||||
\(967\) | −6.00845 | −0.193219 | −0.0966094 | − | 0.995322i | \(-0.530800\pi\) | ||||
−0.0966094 | + | 0.995322i | \(0.530800\pi\) | |||||||
\(968\) | 0.403505 | 0.0129692 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.17822 | −0.166263 | ||||||||
\(971\) | 35.9725 | 1.15441 | 0.577206 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577206 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(972\) | 5.86832 | 0.188227 | ||||||||
\(973\) | 1.40228 | 0.0449552 | ||||||||
\(974\) | 10.6084 | 0.339915 | ||||||||
\(975\) | −0.349941 | −0.0112071 | ||||||||
\(976\) | −3.40057 | −0.108850 | ||||||||
\(977\) | 33.6347 | 1.07607 | 0.538035 | − | 0.842922i | \(-0.319167\pi\) | ||||
0.538035 | + | 0.842922i | \(0.319167\pi\) | |||||||
\(978\) | −0.290993 | −0.00930492 | ||||||||
\(979\) | −2.20983 | −0.0706264 | ||||||||
\(980\) | 13.3208 | 0.425519 | ||||||||
\(981\) | 3.91550 | 0.125012 | ||||||||
\(982\) | 5.97072 | 0.190533 | ||||||||
\(983\) | 45.0395 | 1.43654 | 0.718268 | − | 0.695766i | \(-0.244935\pi\) | ||||
0.718268 | + | 0.695766i | \(0.244935\pi\) | |||||||
\(984\) | 5.95601 | 0.189871 | ||||||||
\(985\) | 2.88742 | 0.0920010 | ||||||||
\(986\) | −3.72327 | −0.118573 | ||||||||
\(987\) | 1.11708 | 0.0355570 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.6064 | 0.464457 | ||||||||
\(990\) | −0.308525 | −0.00980556 | ||||||||
\(991\) | −6.12993 | −0.194724 | −0.0973619 | − | 0.995249i | \(-0.531040\pi\) | ||||
−0.0973619 | + | 0.995249i | \(0.531040\pi\) | |||||||
\(992\) | −27.9554 | −0.887586 | ||||||||
\(993\) | 9.88498 | 0.313690 | ||||||||
\(994\) | −0.169695 | −0.00538241 | ||||||||
\(995\) | 11.6149 | 0.368216 | ||||||||
\(996\) | 56.1824 | 1.78021 | ||||||||
\(997\) | −44.9173 | −1.42255 | −0.711273 | − | 0.702916i | \(-0.751881\pi\) | ||||
−0.711273 | + | 0.702916i | \(0.751881\pi\) | |||||||
\(998\) | −3.47055 | −0.109858 | ||||||||
\(999\) | 9.99458 | 0.316214 |
(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 | 1805.2.a.v.1.3 | 9 | ||
5.4 | even | 2 | 9025.2.a.cc.1.7 | 9 | |||
19.9 | even | 9 | 95.2.k.a.81.3 | yes | 18 | ||
19.17 | even | 9 | 95.2.k.a.61.3 | ✓ | 18 | ||
19.18 | odd | 2 | 1805.2.a.s.1.7 | 9 | |||
57.17 | odd | 18 | 855.2.bs.c.631.1 | 18 | |||
57.47 | odd | 18 | 855.2.bs.c.271.1 | 18 | |||
95.9 | even | 18 | 475.2.l.c.176.1 | 18 | |||
95.17 | odd | 36 | 475.2.u.b.99.3 | 36 | |||
95.28 | odd | 36 | 475.2.u.b.24.3 | 36 | |||
95.47 | odd | 36 | 475.2.u.b.24.4 | 36 | |||
95.74 | even | 18 | 475.2.l.c.251.1 | 18 | |||
95.93 | odd | 36 | 475.2.u.b.99.4 | 36 | |||
95.94 | odd | 2 | 9025.2.a.cf.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.61.3 | ✓ | 18 | 19.17 | even | 9 | ||
95.2.k.a.81.3 | yes | 18 | 19.9 | even | 9 | ||
475.2.l.c.176.1 | 18 | 95.9 | even | 18 | |||
475.2.l.c.251.1 | 18 | 95.74 | even | 18 | |||
475.2.u.b.24.3 | 36 | 95.28 | odd | 36 | |||
475.2.u.b.24.4 | 36 | 95.47 | odd | 36 | |||
475.2.u.b.99.3 | 36 | 95.17 | odd | 36 | |||
475.2.u.b.99.4 | 36 | 95.93 | odd | 36 | |||
855.2.bs.c.271.1 | 18 | 57.47 | odd | 18 | |||
855.2.bs.c.631.1 | 18 | 57.17 | odd | 18 | |||
1805.2.a.s.1.7 | 9 | 19.18 | odd | 2 | |||
1805.2.a.v.1.3 | 9 | 1.1 | even | 1 | trivial | ||
9025.2.a.cc.1.7 | 9 | 5.4 | even | 2 | |||
9025.2.a.cf.1.3 | 9 | 95.94 | odd | 2 |