Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.65306824704.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + x^{4} - 40x^{3} + 36x^{2} - 12x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.4 | ||
Root | \(-0.136233 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.g.485.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.192662i | − 0.0963311i | −0.998839 | − | 0.0481656i | \(-0.984662\pi\) | ||||
0.998839 | − | 0.0481656i | \(-0.0153375\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.96288 | 0.990720 | ||||||||
\(5\) | − 7.62670i | − 1.52534i | −0.646787 | − | 0.762670i | \(-0.723888\pi\) | ||||
0.646787 | − | 0.762670i | \(-0.276112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.45638 | 0.350912 | 0.175456 | − | 0.984487i | \(-0.443860\pi\) | ||||
0.175456 | + | 0.984487i | \(0.443860\pi\) | |||||||
\(8\) | − 1.53415i | − 0.191768i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.46938 | −0.146938 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.4775 | −1.57519 | −0.787597 | − | 0.616191i | \(-0.788675\pi\) | ||||
−0.787597 | + | 0.616191i | \(0.788675\pi\) | |||||||
\(14\) | − 0.473253i | − 0.0338038i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5560 | 0.972247 | ||||||||
\(17\) | − 14.2972i | − 0.841015i | −0.907289 | − | 0.420507i | \(-0.861852\pi\) | ||||
0.907289 | − | 0.420507i | \(-0.138148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2249 | 1.32762 | 0.663812 | − | 0.747899i | \(-0.268937\pi\) | ||||
0.663812 | + | 0.747899i | \(0.268937\pi\) | |||||||
\(20\) | − 30.2237i | − 1.51119i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.64508i | 0.332395i | 0.986093 | + | 0.166197i | \(0.0531489\pi\) | ||||
−0.986093 | + | 0.166197i | \(0.946851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33.1666 | −1.32666 | ||||||||
\(26\) | 3.94524i | 0.151740i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.73436 | 0.347656 | ||||||||
\(29\) | − 43.4065i | − 1.49678i | −0.663261 | − | 0.748388i | \(-0.730828\pi\) | ||||
0.663261 | − | 0.748388i | \(-0.269172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.4706 | −1.07970 | −0.539848 | − | 0.841762i | \(-0.681518\pi\) | ||||
−0.539848 | + | 0.841762i | \(0.681518\pi\) | |||||||
\(32\) | − 9.13363i | − 0.285426i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.75454 | −0.0810159 | ||||||||
\(35\) | − 18.7341i | − 0.535261i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.5717 | 0.664100 | 0.332050 | − | 0.943262i | \(-0.392260\pi\) | ||||
0.332050 | + | 0.943262i | \(0.392260\pi\) | |||||||
\(38\) | − 4.85988i | − 0.127892i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.7005 | −0.292512 | ||||||||
\(41\) | − 21.8024i | − 0.531766i | −0.964005 | − | 0.265883i | \(-0.914336\pi\) | ||||
0.964005 | − | 0.265883i | \(-0.0856635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.2744 | 0.401731 | 0.200866 | − | 0.979619i | \(-0.435625\pi\) | ||||
0.200866 | + | 0.979619i | \(0.435625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.47292 | 0.0320200 | ||||||||
\(47\) | − 76.8928i | − 1.63602i | −0.575207 | − | 0.818008i | \(-0.695078\pi\) | ||||
0.575207 | − | 0.818008i | \(-0.304922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.9662 | −0.876861 | ||||||||
\(50\) | 6.38995i | 0.127799i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −81.1500 | −1.56058 | ||||||||
\(53\) | 3.42175i | 0.0645613i | 0.999479 | + | 0.0322806i | \(0.0102770\pi\) | ||||
−0.999479 | + | 0.0322806i | \(0.989723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 3.76845i | − 0.0672938i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.36280 | −0.144186 | ||||||||
\(59\) | 68.7090i | 1.16456i | 0.812989 | + | 0.582279i | \(0.197839\pi\) | ||||
−0.812989 | + | 0.582279i | \(0.802161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31.6154 | −0.518285 | −0.259143 | − | 0.965839i | \(-0.583440\pi\) | ||||
−0.259143 | + | 0.965839i | \(0.583440\pi\) | |||||||
\(62\) | 6.44852i | 0.104008i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 60.4641 | 0.944752 | ||||||||
\(65\) | 156.176i | 2.40271i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30.0905 | 0.449112 | 0.224556 | − | 0.974461i | \(-0.427907\pi\) | ||||
0.224556 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(68\) | − 56.6583i | − 0.833210i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.60936 | −0.0515622 | ||||||||
\(71\) | 102.248i | 1.44011i | 0.693915 | + | 0.720057i | \(0.255884\pi\) | ||||
−0.693915 | + | 0.720057i | \(0.744116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −131.058 | −1.79531 | −0.897655 | − | 0.440698i | \(-0.854731\pi\) | ||||
−0.897655 | + | 0.440698i | \(0.854731\pi\) | |||||||
\(74\) | − 4.73404i | − 0.0639735i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 99.9632 | 1.31531 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6412 | 0.134698 | 0.0673491 | − | 0.997729i | \(-0.478546\pi\) | ||||
0.0673491 | + | 0.997729i | \(0.478546\pi\) | |||||||
\(80\) | − 118.641i | − 1.48301i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.20050 | −0.0512256 | ||||||||
\(83\) | 126.454i | 1.52355i | 0.647843 | + | 0.761774i | \(0.275671\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −109.041 | −1.28283 | ||||||||
\(86\) | − 3.32813i | − 0.0386992i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 114.555i | − 1.28713i | −0.765390 | − | 0.643566i | \(-0.777454\pi\) | ||||
0.765390 | − | 0.643566i | \(-0.222546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −50.3007 | −0.552755 | ||||||||
\(92\) | 30.2965i | 0.329310i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.8143 | −0.157599 | ||||||||
\(95\) | − 192.383i | − 2.02508i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −109.469 | −1.12854 | −0.564272 | − | 0.825589i | \(-0.690843\pi\) | ||||
−0.564272 | + | 0.825589i | \(0.690843\pi\) | |||||||
\(98\) | 8.27796i | 0.0844690i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −131.435 | −1.31435 | ||||||||
\(101\) | − 25.4237i | − 0.251720i | −0.992048 | − | 0.125860i | \(-0.959831\pi\) | ||||
0.992048 | − | 0.125860i | \(-0.0401690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.9485 | 0.572316 | 0.286158 | − | 0.958182i | \(-0.407622\pi\) | ||||
0.286158 | + | 0.958182i | \(0.407622\pi\) | |||||||
\(104\) | 31.4155i | 0.302072i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.659241 | 0.00621926 | ||||||||
\(107\) | − 193.507i | − 1.80848i | −0.427028 | − | 0.904238i | \(-0.640439\pi\) | ||||
0.427028 | − | 0.904238i | \(-0.359561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 85.6390 | 0.785679 | 0.392839 | − | 0.919607i | \(-0.371493\pi\) | ||||
0.392839 | + | 0.919607i | \(0.371493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 38.2114 | 0.341173 | ||||||||
\(113\) | − 60.6031i | − 0.536310i | −0.963376 | − | 0.268155i | \(-0.913586\pi\) | ||||
0.963376 | − | 0.268155i | \(-0.0864140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 58.3068 | 0.507015 | ||||||||
\(116\) | − 172.015i | − 1.48289i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.2376 | 0.112183 | ||||||||
\(119\) | − 35.1195i | − 0.295122i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.09110i | 0.0499270i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −132.640 | −1.06968 | ||||||||
\(125\) | 62.2844i | 0.498275i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 154.958 | 1.22014 | 0.610069 | − | 0.792348i | \(-0.291142\pi\) | ||||
0.610069 | + | 0.792348i | \(0.291142\pi\) | |||||||
\(128\) | − 48.1837i | − 0.376435i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.0892 | 0.231455 | ||||||||
\(131\) | 208.528i | 1.59182i | 0.605415 | + | 0.795910i | \(0.293007\pi\) | ||||
−0.605415 | + | 0.795910i | \(0.706993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.9620 | 0.465880 | ||||||||
\(134\) | − 5.79731i | − 0.0432635i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21.9341 | −0.161280 | ||||||||
\(137\) | − 197.914i | − 1.44463i | −0.691565 | − | 0.722315i | \(-0.743078\pi\) | ||||
0.691565 | − | 0.722315i | \(-0.256922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9225 | −0.136133 | −0.0680665 | − | 0.997681i | \(-0.521683\pi\) | ||||
−0.0680665 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(140\) | − 74.2411i | − 0.530294i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.6994 | 0.138728 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −331.049 | −2.28309 | ||||||||
\(146\) | 25.2499i | 0.172944i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 97.3747 | 0.657937 | ||||||||
\(149\) | 40.7220i | 0.273302i | 0.990619 | + | 0.136651i | \(0.0436339\pi\) | ||||
−0.990619 | + | 0.136651i | \(0.956366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 177.672 | 1.17663 | 0.588316 | − | 0.808631i | \(-0.299791\pi\) | ||||
0.588316 | + | 0.808631i | \(0.299791\pi\) | |||||||
\(152\) | − 38.6986i | − 0.254596i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 255.270i | 1.64690i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −115.968 | −0.738649 | −0.369324 | − | 0.929301i | \(-0.620411\pi\) | ||||
−0.369324 | + | 0.929301i | \(0.620411\pi\) | |||||||
\(158\) | − 2.05015i | − 0.0129756i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −69.6595 | −0.435372 | ||||||||
\(161\) | 18.7793i | 0.116641i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2020 | 0.0625892 | 0.0312946 | − | 0.999510i | \(-0.490037\pi\) | ||||
0.0312946 | + | 0.999510i | \(0.490037\pi\) | |||||||
\(164\) | − 86.4004i | − 0.526832i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.3630 | 0.146765 | ||||||||
\(167\) | − 47.0263i | − 0.281595i | −0.990038 | − | 0.140797i | \(-0.955033\pi\) | ||||
0.990038 | − | 0.140797i | \(-0.0449666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 250.329 | 1.48124 | ||||||||
\(170\) | 21.0081i | 0.123577i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 68.4565 | 0.398003 | ||||||||
\(173\) | 166.304i | 0.961292i | 0.876915 | + | 0.480646i | \(0.159598\pi\) | ||||
−0.876915 | + | 0.480646i | \(0.840402\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −81.4700 | −0.465543 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.0704 | −0.123991 | ||||||||
\(179\) | − 156.259i | − 0.872957i | −0.899715 | − | 0.436479i | \(-0.856225\pi\) | ||||
0.899715 | − | 0.436479i | \(-0.143775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 86.0399 | 0.475359 | 0.237679 | − | 0.971344i | \(-0.423613\pi\) | ||||
0.237679 | + | 0.971344i | \(0.423613\pi\) | |||||||
\(182\) | 9.69104i | 0.0532475i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.7287 | 0.0637428 | ||||||||
\(185\) | − 187.401i | − 1.01298i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 304.717i | − 1.62083i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −37.0649 | −0.195078 | ||||||||
\(191\) | − 14.8142i | − 0.0775615i | −0.999248 | − | 0.0387807i | \(-0.987653\pi\) | ||||
0.999248 | − | 0.0387807i | \(-0.0123474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −80.0888 | −0.414968 | −0.207484 | − | 0.978238i | \(-0.566527\pi\) | ||||
−0.207484 | + | 0.978238i | \(0.566527\pi\) | |||||||
\(194\) | 21.0905i | 0.108714i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −170.270 | −0.868724 | ||||||||
\(197\) | − 245.361i | − 1.24549i | −0.782426 | − | 0.622743i | \(-0.786018\pi\) | ||||
0.782426 | − | 0.622743i | \(-0.213982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 67.4910 | 0.339151 | 0.169575 | − | 0.985517i | \(-0.445760\pi\) | ||||
0.169575 | + | 0.985517i | \(0.445760\pi\) | |||||||
\(200\) | 50.8824i | 0.254412i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.89819 | −0.0242485 | ||||||||
\(203\) | − 106.623i | − 0.525237i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −166.281 | −0.811125 | ||||||||
\(206\) | − 11.3572i | − 0.0551318i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −318.547 | −1.53148 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 351.934 | 1.66793 | 0.833967 | − | 0.551814i | \(-0.186064\pi\) | ||||
0.833967 | + | 0.551814i | \(0.186064\pi\) | |||||||
\(212\) | 13.5600i | 0.0639622i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −37.2815 | −0.174213 | ||||||||
\(215\) | − 131.747i | − 0.612777i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −82.2166 | −0.378878 | ||||||||
\(218\) | − 16.4994i | − 0.0756853i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 292.772i | 1.32476i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 274.780 | 1.23220 | 0.616098 | − | 0.787669i | \(-0.288712\pi\) | ||||
0.616098 | + | 0.787669i | \(0.288712\pi\) | |||||||
\(224\) | − 22.4357i | − 0.100159i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.6759 | −0.0516634 | ||||||||
\(227\) | − 205.054i | − 0.903323i | −0.892189 | − | 0.451662i | \(-0.850831\pi\) | ||||
0.892189 | − | 0.451662i | \(-0.149169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −60.3823 | −0.263678 | −0.131839 | − | 0.991271i | \(-0.542088\pi\) | ||||
−0.131839 | + | 0.991271i | \(0.542088\pi\) | |||||||
\(230\) | − 11.2335i | − 0.0488413i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −66.5920 | −0.287034 | ||||||||
\(233\) | − 60.9371i | − 0.261533i | −0.991413 | − | 0.130766i | \(-0.958256\pi\) | ||||
0.991413 | − | 0.130766i | \(-0.0417438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −586.438 | −2.49548 | ||||||||
\(236\) | 272.285i | 1.15375i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.76621 | −0.0284295 | ||||||||
\(239\) | 371.303i | 1.55357i | 0.629767 | + | 0.776784i | \(0.283150\pi\) | ||||
−0.629767 | + | 0.776784i | \(0.716850\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 323.523 | 1.34242 | 0.671211 | − | 0.741267i | \(-0.265775\pi\) | ||||
0.671211 | + | 0.741267i | \(0.265775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −125.288 | −0.513476 | ||||||||
\(245\) | 327.690i | 1.33751i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −516.543 | −2.09127 | ||||||||
\(248\) | 51.3488i | 0.207051i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.9999 | 0.0479994 | ||||||||
\(251\) | 160.951i | 0.641241i | 0.947208 | + | 0.320620i | \(0.103891\pi\) | ||||
−0.947208 | + | 0.320620i | \(0.896109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 29.8545i | − 0.117537i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 232.573 | 0.908489 | ||||||||
\(257\) | − 22.6233i | − 0.0880284i | −0.999031 | − | 0.0440142i | \(-0.985985\pi\) | ||||
0.999031 | − | 0.0440142i | \(-0.0140147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 60.3575 | 0.233041 | ||||||||
\(260\) | 618.907i | 2.38041i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 40.1755 | 0.153342 | ||||||||
\(263\) | − 39.0014i | − 0.148294i | −0.997247 | − | 0.0741472i | \(-0.976377\pi\) | ||||
0.997247 | − | 0.0741472i | \(-0.0236235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.0967 | 0.0984780 | ||||||||
\(266\) | − 11.9377i | − 0.0448787i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 119.245 | 0.444945 | ||||||||
\(269\) | 79.9847i | 0.297341i | 0.988887 | + | 0.148670i | \(0.0474993\pi\) | ||||
−0.988887 | + | 0.148670i | \(0.952501\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 203.564 | 0.751158 | 0.375579 | − | 0.926790i | \(-0.377444\pi\) | ||||
0.375579 | + | 0.926790i | \(0.377444\pi\) | |||||||
\(272\) | − 222.407i | − 0.817674i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −38.1306 | −0.139163 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 443.367 | 1.60060 | 0.800302 | − | 0.599598i | \(-0.204673\pi\) | ||||
0.800302 | + | 0.599598i | \(0.204673\pi\) | |||||||
\(278\) | 3.64565i | 0.0131139i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −28.7409 | −0.102646 | ||||||||
\(281\) | 258.628i | 0.920385i | 0.887819 | + | 0.460192i | \(0.152220\pi\) | ||||
−0.887819 | + | 0.460192i | \(0.847780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −189.227 | −0.668648 | −0.334324 | − | 0.942458i | \(-0.608508\pi\) | ||||
−0.334324 | + | 0.942458i | \(0.608508\pi\) | |||||||
\(284\) | 405.197i | 1.42675i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 53.5551i | − 0.186603i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 84.5887 | 0.292694 | ||||||||
\(290\) | 63.7806i | 0.219933i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −519.366 | −1.77865 | ||||||||
\(293\) | 349.594i | 1.19315i | 0.802556 | + | 0.596576i | \(0.203473\pi\) | ||||
−0.802556 | + | 0.596576i | \(0.796527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 524.023 | 1.77635 | ||||||||
\(296\) | − 37.6966i | − 0.127353i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.84560 | 0.0263275 | ||||||||
\(299\) | − 156.552i | − 0.523586i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.4327 | 0.140972 | ||||||||
\(302\) | − 34.2306i | − 0.113346i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 392.397 | 1.29078 | ||||||||
\(305\) | 241.121i | 0.790562i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −105.879 | −0.344883 | −0.172442 | − | 0.985020i | \(-0.555166\pi\) | ||||
−0.172442 | + | 0.985020i | \(0.555166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 49.1809 | 0.158648 | ||||||||
\(311\) | 423.614i | 1.36210i | 0.732236 | + | 0.681051i | \(0.238477\pi\) | ||||
−0.732236 | + | 0.681051i | \(0.761523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 213.445 | 0.681934 | 0.340967 | − | 0.940075i | \(-0.389245\pi\) | ||||
0.340967 | + | 0.940075i | \(0.389245\pi\) | |||||||
\(314\) | 22.3426i | 0.0711548i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 42.1696 | 0.133448 | ||||||||
\(317\) | 211.598i | 0.667503i | 0.942661 | + | 0.333751i | \(0.108315\pi\) | ||||
−0.942661 | + | 0.333751i | \(0.891685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 461.142i | − 1.44107i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.61805 | 0.0112362 | ||||||||
\(323\) | − 360.646i | − 1.11655i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 679.170 | 2.08975 | ||||||||
\(326\) | − 1.96555i | − 0.00602929i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −33.4481 | −0.101976 | ||||||||
\(329\) | − 188.878i | − 0.574098i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 47.5307 | 0.143597 | 0.0717987 | − | 0.997419i | \(-0.477126\pi\) | ||||
0.0717987 | + | 0.997419i | \(0.477126\pi\) | |||||||
\(332\) | 501.124i | 1.50941i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.06020 | −0.0271263 | ||||||||
\(335\) | − 229.492i | − 0.685049i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −121.159 | −0.359524 | −0.179762 | − | 0.983710i | \(-0.557533\pi\) | ||||
−0.179762 | + | 0.983710i | \(0.557533\pi\) | |||||||
\(338\) | − 48.2289i | − 0.142689i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −432.116 | −1.27093 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −225.904 | −0.658613 | ||||||||
\(344\) | − 26.5015i | − 0.0770393i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.0404 | 0.0926023 | ||||||||
\(347\) | 192.577i | 0.554978i | 0.960729 | + | 0.277489i | \(0.0895023\pi\) | ||||
−0.960729 | + | 0.277489i | \(0.910498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 261.888 | 0.750396 | 0.375198 | − | 0.926945i | \(-0.377575\pi\) | ||||
0.375198 | + | 0.926945i | \(0.377575\pi\) | |||||||
\(350\) | 15.6962i | 0.0448462i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 424.807i | 1.20342i | 0.798715 | + | 0.601709i | \(0.205513\pi\) | ||||
−0.798715 | + | 0.601709i | \(0.794487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 779.816 | 2.19667 | ||||||||
\(356\) | − 453.967i | − 1.27519i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.1053 | −0.0840930 | ||||||||
\(359\) | − 176.407i | − 0.491384i | −0.969348 | − | 0.245692i | \(-0.920985\pi\) | ||||
0.969348 | − | 0.245692i | \(-0.0790153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 275.294 | 0.762588 | ||||||||
\(362\) | − 16.5766i | − 0.0457918i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −199.336 | −0.547625 | ||||||||
\(365\) | 999.538i | 2.73846i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.0741 | −0.0546979 | −0.0273489 | − | 0.999626i | \(-0.508707\pi\) | ||||
−0.0273489 | + | 0.999626i | \(0.508707\pi\) | |||||||
\(368\) | 118.926i | 0.323170i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −36.1051 | −0.0975813 | ||||||||
\(371\) | 8.40513i | 0.0226553i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 78.8064 | 0.211277 | 0.105639 | − | 0.994405i | \(-0.466311\pi\) | ||||
0.105639 | + | 0.994405i | \(0.466311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −117.965 | −0.313736 | ||||||||
\(377\) | 888.858i | 2.35771i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 601.156 | 1.58616 | 0.793082 | − | 0.609116i | \(-0.208475\pi\) | ||||
0.793082 | + | 0.609116i | \(0.208475\pi\) | |||||||
\(380\) | − 762.390i | − 2.00629i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.85414 | −0.00747158 | ||||||||
\(383\) | − 154.201i | − 0.402614i | −0.979528 | − | 0.201307i | \(-0.935481\pi\) | ||||
0.979528 | − | 0.201307i | \(-0.0645188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.4301i | 0.0399743i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −433.812 | −1.11807 | ||||||||
\(389\) | − 182.994i | − 0.470422i | −0.971944 | − | 0.235211i | \(-0.924422\pi\) | ||||
0.971944 | − | 0.235211i | \(-0.0755781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 109.304 | 0.279549 | ||||||||
\(392\) | 65.9164i | 0.168154i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −47.2718 | −0.119979 | ||||||||
\(395\) | − 81.1569i | − 0.205461i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 111.625 | 0.281171 | 0.140586 | − | 0.990069i | \(-0.455102\pi\) | ||||
0.140586 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(398\) | − 13.0030i | − 0.0326708i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −515.938 | −1.28985 | ||||||||
\(401\) | − 225.641i | − 0.562695i | −0.959606 | − | 0.281348i | \(-0.909219\pi\) | ||||
0.959606 | − | 0.281348i | \(-0.0907814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 685.395 | 1.70073 | ||||||||
\(404\) | − 100.751i | − 0.249384i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.5422 | −0.0505967 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 305.427 | 0.746764 | 0.373382 | − | 0.927678i | \(-0.378198\pi\) | ||||
0.373382 | + | 0.927678i | \(0.378198\pi\) | |||||||
\(410\) | 32.0360i | 0.0781365i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 233.606 | 0.567005 | ||||||||
\(413\) | 168.776i | 0.408658i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 964.431 | 2.32393 | ||||||||
\(416\) | 187.034i | 0.449601i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 163.669i | 0.390618i | 0.980742 | + | 0.195309i | \(0.0625709\pi\) | ||||
−0.980742 | + | 0.195309i | \(0.937429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −330.809 | −0.785770 | −0.392885 | − | 0.919588i | \(-0.628523\pi\) | ||||
−0.392885 | + | 0.919588i | \(0.628523\pi\) | |||||||
\(422\) | − 67.8044i | − 0.160674i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.24946 | 0.0123808 | ||||||||
\(425\) | 474.191i | 1.11574i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −77.6596 | −0.181873 | ||||||||
\(428\) | − 766.845i | − 1.79169i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.3827 | −0.0590295 | ||||||||
\(431\) | − 339.558i | − 0.787837i | −0.919145 | − | 0.393919i | \(-0.871119\pi\) | ||||
0.919145 | − | 0.393919i | \(-0.128881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 604.853 | 1.39689 | 0.698444 | − | 0.715665i | \(-0.253876\pi\) | ||||
0.698444 | + | 0.715665i | \(0.253876\pi\) | |||||||
\(434\) | 15.8400i | 0.0364978i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 339.377 | 0.778388 | ||||||||
\(437\) | 192.846i | 0.441296i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −319.471 | −0.727724 | −0.363862 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363862 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 56.4061 | 0.127616 | ||||||||
\(443\) | 129.981i | 0.293411i | 0.989180 | + | 0.146705i | \(0.0468669\pi\) | ||||
−0.989180 | + | 0.146705i | \(0.953133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −873.675 | −1.96332 | ||||||||
\(446\) | − 52.9397i | − 0.118699i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 148.523 | 0.331525 | ||||||||
\(449\) | 92.5002i | 0.206014i | 0.994681 | + | 0.103007i | \(0.0328464\pi\) | ||||
−0.994681 | + | 0.103007i | \(0.967154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 240.163i | − 0.531333i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −39.5062 | −0.0870181 | ||||||||
\(455\) | 383.628i | 0.843139i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −136.208 | −0.298049 | −0.149024 | − | 0.988834i | \(-0.547613\pi\) | ||||
−0.149024 | + | 0.988834i | \(0.547613\pi\) | |||||||
\(458\) | 11.6334i | 0.0254004i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 231.063 | 0.502310 | ||||||||
\(461\) | − 326.820i | − 0.708937i | −0.935068 | − | 0.354468i | \(-0.884662\pi\) | ||||
0.935068 | − | 0.354468i | \(-0.115338\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 547.369 | 1.18222 | 0.591112 | − | 0.806590i | \(-0.298689\pi\) | ||||
0.591112 | + | 0.806590i | \(0.298689\pi\) | |||||||
\(464\) | − 675.230i | − 1.45524i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.7403 | −0.0251937 | ||||||||
\(467\) | − 603.588i | − 1.29248i | −0.763135 | − | 0.646239i | \(-0.776341\pi\) | ||||
0.763135 | − | 0.646239i | \(-0.223659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 73.9139 | 0.157599 | ||||||||
\(470\) | 112.985i | 0.240393i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 105.410 | 0.223325 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −836.624 | −1.76131 | ||||||||
\(476\) | − 139.175i | − 0.292384i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 71.5360 | 0.149657 | ||||||||
\(479\) | 457.810i | 0.955762i | 0.878425 | + | 0.477881i | \(0.158595\pi\) | ||||
−0.878425 | + | 0.477881i | \(0.841405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −503.167 | −1.04609 | ||||||||
\(482\) | − 62.3308i | − 0.129317i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 834.886i | 1.72141i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 665.399 | 1.36632 | 0.683161 | − | 0.730268i | \(-0.260605\pi\) | ||||
0.683161 | + | 0.730268i | \(0.260605\pi\) | |||||||
\(488\) | 48.5027i | 0.0993907i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 63.1335 | 0.128844 | ||||||||
\(491\) | − 52.3694i | − 0.106659i | −0.998577 | − | 0.0533293i | \(-0.983017\pi\) | ||||
0.998577 | − | 0.0533293i | \(-0.0169833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −620.594 | −1.25881 | ||||||||
\(494\) | 99.5183i | 0.201454i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −520.667 | −1.04973 | ||||||||
\(497\) | 251.161i | 0.505354i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −489.865 | −0.981694 | −0.490847 | − | 0.871246i | \(-0.663313\pi\) | ||||
−0.490847 | + | 0.871246i | \(0.663313\pi\) | |||||||
\(500\) | 246.826i | 0.493651i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.0093 | 0.0617714 | ||||||||
\(503\) | 759.327i | 1.50960i | 0.655957 | + | 0.754798i | \(0.272265\pi\) | ||||
−0.655957 | + | 0.754798i | \(0.727735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −193.899 | −0.383959 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 614.079 | 1.20882 | ||||||||
\(509\) | − 362.954i | − 0.713073i | −0.934281 | − | 0.356536i | \(-0.883958\pi\) | ||||
0.934281 | − | 0.356536i | \(-0.116042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −321.928 | −0.629996 | ||||||||
\(512\) | − 237.543i | − 0.463951i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.35865 | −0.00847987 | ||||||||
\(515\) | − 449.583i | − 0.872976i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 11.6286i | − 0.0224491i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 239.597 | 0.460763 | ||||||||
\(521\) | 184.301i | 0.353746i | 0.984234 | + | 0.176873i | \(0.0565981\pi\) | ||||
−0.984234 | + | 0.176873i | \(0.943402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −461.562 | −0.882528 | −0.441264 | − | 0.897377i | \(-0.645470\pi\) | ||||
−0.441264 | + | 0.897377i | \(0.645470\pi\) | |||||||
\(524\) | 826.373i | 1.57705i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.51410 | −0.0142854 | ||||||||
\(527\) | 478.537i | 0.908040i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 470.553 | 0.889514 | ||||||||
\(530\) | − 5.02784i | − 0.00948649i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 245.548 | 0.461556 | ||||||||
\(533\) | 446.459i | 0.837635i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1475.82 | −2.75854 | ||||||||
\(536\) | − 46.1633i | − 0.0861255i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.4100 | 0.0286432 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 200.369 | 0.370367 | 0.185184 | − | 0.982704i | \(-0.440712\pi\) | ||||
0.185184 | + | 0.982704i | \(0.440712\pi\) | |||||||
\(542\) | − 39.2190i | − 0.0723598i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −130.586 | −0.240047 | ||||||||
\(545\) | − 653.143i | − 1.19843i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −394.746 | −0.721657 | −0.360828 | − | 0.932632i | \(-0.617506\pi\) | ||||
−0.360828 | + | 0.932632i | \(0.617506\pi\) | |||||||
\(548\) | − 784.311i | − 1.43122i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1094.92i | − 1.98716i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1388 | 0.0472672 | ||||||||
\(554\) | − 85.4201i | − 0.154188i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −74.9876 | −0.134870 | ||||||||
\(557\) | − 1055.65i | − 1.89524i | −0.319397 | − | 0.947621i | \(-0.603480\pi\) | ||||
0.319397 | − | 0.947621i | \(-0.396520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −353.738 | −0.632804 | ||||||||
\(560\) | − 291.427i | − 0.520406i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 49.8279 | 0.0886617 | ||||||||
\(563\) | − 610.342i | − 1.08409i | −0.840350 | − | 0.542044i | \(-0.817650\pi\) | ||||
0.840350 | − | 0.542044i | \(-0.182350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −462.202 | −0.818056 | ||||||||
\(566\) | 36.4570i | 0.0644116i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 156.864 | 0.276168 | ||||||||
\(569\) | 125.347i | 0.220294i | 0.993915 | + | 0.110147i | \(0.0351321\pi\) | ||||
−0.993915 | + | 0.110147i | \(0.964868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −465.273 | −0.814838 | −0.407419 | − | 0.913241i | \(-0.633571\pi\) | ||||
−0.407419 | + | 0.913241i | \(0.633571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.3180 | −0.0179757 | ||||||||
\(575\) | − 253.561i | − 0.440976i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.9960 | 0.0831820 | 0.0415910 | − | 0.999135i | \(-0.486757\pi\) | ||||
0.0415910 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(578\) | − 16.2970i | − 0.0281956i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1311.91 | −2.26191 | ||||||||
\(581\) | 310.621i | 0.534631i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 201.062i | 0.344284i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 67.3535 | 0.114938 | ||||||||
\(587\) | − 811.870i | − 1.38308i | −0.722337 | − | 0.691542i | \(-0.756932\pi\) | ||||
0.722337 | − | 0.691542i | \(-0.243068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −844.291 | −1.43343 | ||||||||
\(590\) | − 100.959i | − 0.171118i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 382.236 | 0.645669 | ||||||||
\(593\) | 746.682i | 1.25916i | 0.776936 | + | 0.629580i | \(0.216773\pi\) | ||||
−0.776936 | + | 0.629580i | \(0.783227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −267.846 | −0.450162 | ||||||||
\(596\) | 161.377i | 0.270766i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.1617 | −0.0504376 | ||||||||
\(599\) | 699.995i | 1.16861i | 0.811536 | + | 0.584303i | \(0.198632\pi\) | ||||
−0.811536 | + | 0.584303i | \(0.801368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −387.630 | −0.644976 | −0.322488 | − | 0.946574i | \(-0.604519\pi\) | ||||
−0.322488 | + | 0.946574i | \(0.604519\pi\) | |||||||
\(602\) | − 8.17517i | − 0.0135800i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 704.091 | 1.16571 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 635.808 | 1.04746 | 0.523730 | − | 0.851884i | \(-0.324540\pi\) | ||||
0.523730 | + | 0.851884i | \(0.324540\pi\) | |||||||
\(608\) | − 230.395i | − 0.378939i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 46.4550 | 0.0761557 | ||||||||
\(611\) | 1574.57i | 2.57704i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 996.122 | 1.62499 | 0.812497 | − | 0.582965i | \(-0.198107\pi\) | ||||
0.812497 | + | 0.582965i | \(0.198107\pi\) | |||||||
\(614\) | 20.3989i | 0.0332230i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.79534i | 0.00453054i | 0.999997 | + | 0.00226527i | \(0.000721059\pi\) | ||||
−0.999997 | + | 0.00226527i | \(0.999279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −889.865 | −1.43759 | −0.718793 | − | 0.695224i | \(-0.755305\pi\) | ||||
−0.718793 | + | 0.695224i | \(0.755305\pi\) | |||||||
\(620\) | 1011.61i | 1.63162i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 81.6143 | 0.131213 | ||||||||
\(623\) | − 281.391i | − 0.451670i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −354.141 | −0.566625 | ||||||||
\(626\) | − 41.1229i | − 0.0656915i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −459.567 | −0.731794 | ||||||||
\(629\) | − 351.308i | − 0.558518i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 973.037 | 1.54205 | 0.771027 | − | 0.636802i | \(-0.219743\pi\) | ||||
0.771027 | + | 0.636802i | \(0.219743\pi\) | |||||||
\(632\) | − 16.3251i | − 0.0258308i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 40.7670 | 0.0643013 | ||||||||
\(635\) | − 1181.82i | − 1.86113i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 879.841 | 1.38123 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −367.483 | −0.574192 | ||||||||
\(641\) | − 909.627i | − 1.41907i | −0.704668 | − | 0.709537i | \(-0.748904\pi\) | ||||
0.704668 | − | 0.709537i | \(-0.251096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −816.993 | −1.27059 | −0.635297 | − | 0.772268i | \(-0.719123\pi\) | ||||
−0.635297 | + | 0.772268i | \(0.719123\pi\) | |||||||
\(644\) | 74.4200i | 0.115559i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −69.4829 | −0.107559 | ||||||||
\(647\) | 975.225i | 1.50730i | 0.657274 | + | 0.753651i | \(0.271709\pi\) | ||||
−0.657274 | + | 0.753651i | \(0.728291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 130.850i | − 0.201308i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 40.4295 | 0.0620084 | ||||||||
\(653\) | 1212.65i | 1.85705i | 0.371272 | + | 0.928524i | \(0.378922\pi\) | ||||
−0.371272 | + | 0.928524i | \(0.621078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1590.38 | 2.42807 | ||||||||
\(656\) | − 339.157i | − 0.517008i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.3897 | −0.0553035 | ||||||||
\(659\) | 541.200i | 0.821245i | 0.911805 | + | 0.410622i | \(0.134689\pi\) | ||||
−0.911805 | + | 0.410622i | \(0.865311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.0390 | 0.0726763 | 0.0363381 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363381 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(662\) | − 9.15737i | − 0.0138329i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 194.000 | 0.292168 | ||||||||
\(665\) | − 472.566i | − 0.710625i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 331.846 | 0.497521 | ||||||||
\(668\) | − 186.360i | − 0.278982i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −44.2143 | −0.0659916 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −662.951 | −0.985068 | −0.492534 | − | 0.870293i | \(-0.663929\pi\) | ||||
−0.492534 | + | 0.870293i | \(0.663929\pi\) | |||||||
\(674\) | 23.3429i | 0.0346333i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 992.023 | 1.46749 | ||||||||
\(677\) | − 797.622i | − 1.17817i | −0.808070 | − | 0.589086i | \(-0.799488\pi\) | ||||
0.808070 | − | 0.589086i | \(-0.200512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −268.897 | −0.396020 | ||||||||
\(680\) | 167.285i | 0.246007i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 816.752i | 1.19583i | 0.801559 | + | 0.597915i | \(0.204004\pi\) | ||||
−0.801559 | + | 0.597915i | \(0.795996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1509.43 | −2.20355 | ||||||||
\(686\) | 43.5232i | 0.0634449i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 268.720 | 0.390582 | ||||||||
\(689\) | − 70.0689i | − 0.101697i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 697.023 | 1.00872 | 0.504358 | − | 0.863495i | \(-0.331729\pi\) | ||||
0.504358 | + | 0.863495i | \(0.331729\pi\) | |||||||
\(692\) | 659.041i | 0.952372i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.1024 | 0.0534617 | ||||||||
\(695\) | 144.316i | 0.207649i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −311.715 | −0.447223 | ||||||||
\(698\) | − 50.4560i | − 0.0722865i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −322.856 | −0.461223 | ||||||||
\(701\) | − 1184.54i | − 1.68979i | −0.534934 | − | 0.844894i | \(-0.679664\pi\) | ||||
0.534934 | − | 0.844894i | \(-0.320336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 619.818 | 0.881675 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 81.8442 | 0.115927 | ||||||||
\(707\) | − 62.4505i | − 0.0883317i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1189.88 | 1.67825 | 0.839126 | − | 0.543937i | \(-0.183067\pi\) | ||||
0.839126 | + | 0.543937i | \(0.183067\pi\) | |||||||
\(710\) | − 150.241i | − 0.211607i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −175.744 | −0.246831 | ||||||||
\(713\) | − 255.885i | − 0.358885i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 619.237i | − 0.864857i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.9870 | −0.0473356 | ||||||||
\(719\) | − 219.672i | − 0.305524i | −0.988263 | − | 0.152762i | \(-0.951183\pi\) | ||||
0.988263 | − | 0.152762i | \(-0.0488168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 144.800 | 0.200832 | ||||||||
\(722\) | − 53.0388i | − 0.0734610i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 340.966 | 0.470947 | ||||||||
\(725\) | 1439.65i | 1.98572i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −391.450 | −0.538445 | −0.269223 | − | 0.963078i | \(-0.586767\pi\) | ||||
−0.269223 | + | 0.963078i | \(0.586767\pi\) | |||||||
\(728\) | 77.1686i | 0.106001i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 192.573 | 0.263799 | ||||||||
\(731\) | − 246.977i | − 0.337862i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 161.674 | 0.220564 | 0.110282 | − | 0.993900i | \(-0.464825\pi\) | ||||
0.110282 | + | 0.993900i | \(0.464825\pi\) | |||||||
\(734\) | 3.86753i | 0.00526911i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 69.8273 | 0.0948741 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −908.158 | −1.22890 | −0.614451 | − | 0.788955i | \(-0.710622\pi\) | ||||
−0.614451 | + | 0.788955i | \(0.710622\pi\) | |||||||
\(740\) | − 742.648i | − 1.00358i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.61935 | 0.00218241 | ||||||||
\(743\) | − 424.124i | − 0.570826i | −0.958405 | − | 0.285413i | \(-0.907869\pi\) | ||||
0.958405 | − | 0.285413i | \(-0.0921307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 310.575 | 0.416879 | ||||||||
\(746\) | − 15.1830i | − 0.0203526i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 475.328i | − 0.634616i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8598 | −0.0544072 | −0.0272036 | − | 0.999630i | \(-0.508660\pi\) | ||||
−0.0272036 | + | 0.999630i | \(0.508660\pi\) | |||||||
\(752\) | − 1196.14i | − 1.59061i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 171.249 | 0.227121 | ||||||||
\(755\) | − 1355.05i | − 1.79477i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −786.700 | −1.03923 | −0.519617 | − | 0.854400i | \(-0.673925\pi\) | ||||
−0.519617 | + | 0.854400i | \(0.673925\pi\) | |||||||
\(758\) | − 115.820i | − 0.152797i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −295.143 | −0.388346 | ||||||||
\(761\) | 591.917i | 0.777815i | 0.921277 | + | 0.388908i | \(0.127147\pi\) | ||||
−0.921277 | + | 0.388908i | \(0.872853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 210.362 | 0.275704 | ||||||||
\(764\) | − 58.7071i | − 0.0768417i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.7087 | −0.0387842 | ||||||||
\(767\) | − 1406.99i | − 1.83441i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 662.841 | 0.861952 | 0.430976 | − | 0.902363i | \(-0.358169\pi\) | ||||
0.430976 | + | 0.902363i | \(0.358169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −317.382 | −0.411117 | ||||||||
\(773\) | − 194.400i | − 0.251487i | −0.992063 | − | 0.125744i | \(-0.959868\pi\) | ||||
0.992063 | − | 0.125744i | \(-0.0401317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1110.11 | 1.43239 | ||||||||
\(776\) | 167.941i | 0.216419i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.2561 | −0.0453163 | ||||||||
\(779\) | − 549.963i | − 0.705986i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 21.0587i | − 0.0269293i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −668.380 | −0.852525 | ||||||||
\(785\) | 884.452i | 1.12669i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −590.745 | −0.750629 | −0.375315 | − | 0.926898i | \(-0.622465\pi\) | ||||
−0.375315 | + | 0.926898i | \(0.622465\pi\) | |||||||
\(788\) | − 972.336i | − 1.23393i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.6359 | −0.0197922 | ||||||||
\(791\) | − 148.864i | − 0.188198i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 647.405 | 0.816400 | ||||||||
\(794\) | − 21.5059i | − 0.0270855i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 267.459 | 0.336003 | ||||||||
\(797\) | 44.3027i | 0.0555868i | 0.999614 | + | 0.0277934i | \(0.00884805\pi\) | ||||
−0.999614 | + | 0.0277934i | \(0.991152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1099.36 | −1.37591 | ||||||||
\(800\) | 302.932i | 0.378665i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −43.4725 | −0.0542051 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 143.224 | 0.177918 | ||||||||
\(806\) | − 132.050i | − 0.163833i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −39.0037 | −0.0482720 | ||||||||
\(809\) | 642.524i | 0.794220i | 0.917771 | + | 0.397110i | \(0.129987\pi\) | ||||
−0.917771 | + | 0.397110i | \(0.870013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −771.414 | −0.951189 | −0.475594 | − | 0.879665i | \(-0.657767\pi\) | ||||
−0.475594 | + | 0.879665i | \(0.657767\pi\) | |||||||
\(812\) | − 422.535i | − 0.520363i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 77.8080i | − 0.0954699i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 435.745 | 0.533348 | ||||||||
\(818\) | − 58.8442i | − 0.0719366i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −658.950 | −0.803598 | ||||||||
\(821\) | − 313.109i | − 0.381375i | −0.981651 | − | 0.190687i | \(-0.938928\pi\) | ||||
0.981651 | − | 0.190687i | \(-0.0610717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −606.931 | −0.737462 | −0.368731 | − | 0.929536i | \(-0.620208\pi\) | ||||
−0.368731 | + | 0.929536i | \(0.620208\pi\) | |||||||
\(824\) | − 90.4356i | − 0.109752i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32.5167 | 0.0393665 | ||||||||
\(827\) | − 297.721i | − 0.360002i | −0.983666 | − | 0.180001i | \(-0.942390\pi\) | ||||
0.983666 | − | 0.180001i | \(-0.0576101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1378.56 | 1.66292 | 0.831458 | − | 0.555588i | \(-0.187507\pi\) | ||||
0.831458 | + | 0.555588i | \(0.187507\pi\) | |||||||
\(830\) | − 185.809i | − 0.223867i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1238.15 | −1.48817 | ||||||||
\(833\) | 614.298i | 0.737453i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −358.656 | −0.429528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.5328 | 0.0376286 | ||||||||
\(839\) | − 567.982i | − 0.676975i | −0.940971 | − | 0.338488i | \(-0.890085\pi\) | ||||
0.940971 | − | 0.338488i | \(-0.109915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1043.13 | −1.24034 | ||||||||
\(842\) | 63.7344i | 0.0756941i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1394.67 | 1.65246 | ||||||||
\(845\) | − 1909.18i | − 2.25939i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 53.2285i | 0.0627695i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 91.3588 | 0.107481 | ||||||||
\(851\) | 187.853i | 0.220743i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.4201 | −0.0368348 | −0.0184174 | − | 0.999830i | \(-0.505863\pi\) | ||||
−0.0184174 | + | 0.999830i | \(0.505863\pi\) | |||||||
\(854\) | 14.9621i | 0.0175200i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −296.868 | −0.346808 | ||||||||
\(857\) | 478.358i | 0.558178i | 0.960265 | + | 0.279089i | \(0.0900324\pi\) | ||||
−0.960265 | + | 0.279089i | \(0.909968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −630.421 | −0.733902 | −0.366951 | − | 0.930240i | \(-0.619598\pi\) | ||||
−0.366951 | + | 0.930240i | \(0.619598\pi\) | |||||||
\(860\) | − 522.098i | − 0.607090i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −65.4200 | −0.0758932 | ||||||||
\(863\) | 164.632i | 0.190768i | 0.995441 | + | 0.0953838i | \(0.0304078\pi\) | ||||
−0.995441 | + | 0.0953838i | \(0.969592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1268.35 | 1.46630 | ||||||||
\(866\) | − 116.532i | − 0.134564i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −325.815 | −0.375363 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −616.179 | −0.707439 | ||||||||
\(872\) | − 131.383i | − 0.150668i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.1542 | 0.0425105 | ||||||||
\(875\) | 152.994i | 0.174851i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1455.14 | −1.65922 | −0.829612 | − | 0.558341i | \(-0.811438\pi\) | ||||
−0.829612 | + | 0.558341i | \(0.811438\pi\) | |||||||
\(878\) | 61.5500i | 0.0701025i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 377.222i | − 0.428174i | −0.976815 | − | 0.214087i | \(-0.931322\pi\) | ||||
0.976815 | − | 0.214087i | \(-0.0686777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1561.28 | −1.76816 | −0.884078 | − | 0.467339i | \(-0.845213\pi\) | ||||
−0.884078 | + | 0.467339i | \(0.845213\pi\) | |||||||
\(884\) | 1160.22i | 1.31247i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.0424 | 0.0282646 | ||||||||
\(887\) | 813.843i | 0.917524i | 0.888559 | + | 0.458762i | \(0.151707\pi\) | ||||
−0.888559 | + | 0.458762i | \(0.848293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 380.636 | 0.428161 | ||||||||
\(890\) | 168.324i | 0.189128i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1088.92 | 1.22076 | ||||||||
\(893\) | − 1939.61i | − 2.17202i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1191.74 | −1.33156 | ||||||||
\(896\) | − 118.358i | − 0.132096i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.8213 | 0.0198455 | ||||||||
\(899\) | 1452.84i | 1.61606i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.9216 | 0.0542970 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −92.9740 | −0.102847 | ||||||||
\(905\) | − 656.201i | − 0.725084i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −486.113 | −0.535957 | −0.267979 | − | 0.963425i | \(-0.586356\pi\) | ||||
−0.267979 | + | 0.963425i | \(0.586356\pi\) | |||||||
\(908\) | − 812.606i | − 0.894941i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 73.9107 | 0.0812205 | ||||||||
\(911\) | 868.058i | 0.952863i | 0.879212 | + | 0.476432i | \(0.158070\pi\) | ||||
−0.879212 | + | 0.476432i | \(0.841930\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.2422i | 0.0287114i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −239.288 | −0.261231 | ||||||||
\(917\) | 512.226i | 0.558589i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 828.692 | 0.901732 | 0.450866 | − | 0.892592i | \(-0.351115\pi\) | ||||
0.450866 | + | 0.892592i | \(0.351115\pi\) | |||||||
\(920\) | − 89.4511i | − 0.0972295i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −62.9658 | −0.0682926 | ||||||||
\(923\) | − 2093.79i | − 2.26846i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −814.960 | −0.881038 | ||||||||
\(926\) | − 105.457i | − 0.113885i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −396.459 | −0.427219 | ||||||||
\(929\) | 1250.65i | 1.34623i | 0.739539 | + | 0.673114i | \(0.235044\pi\) | ||||
−0.739539 | + | 0.673114i | \(0.764956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1083.82 | −1.16414 | ||||||||
\(932\) | − 241.487i | − 0.259106i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −116.289 | −0.124506 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 628.988 | 0.671278 | 0.335639 | − | 0.941991i | \(-0.391048\pi\) | ||||
0.335639 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(938\) | − 14.2404i | − 0.0151817i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2323.99 | −2.47233 | ||||||||
\(941\) | − 633.442i | − 0.673159i | −0.941655 | − | 0.336579i | \(-0.890730\pi\) | ||||
0.941655 | − | 0.336579i | \(-0.109270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 166.681 | 0.176756 | ||||||||
\(944\) | 1068.83i | 1.13224i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 929.570i | 0.981594i | 0.871274 | + | 0.490797i | \(0.163294\pi\) | ||||
−0.871274 | + | 0.490797i | \(0.836706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2683.74 | 2.82796 | ||||||||
\(950\) | 161.186i | 0.169669i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −53.8785 | −0.0565951 | ||||||||
\(953\) | 1189.77i | 1.24845i | 0.781244 | + | 0.624225i | \(0.214585\pi\) | ||||
−0.781244 | + | 0.624225i | \(0.785415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −112.984 | −0.118308 | ||||||||
\(956\) | 1471.43i | 1.53915i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 88.2027 | 0.0920696 | ||||||||
\(959\) | − 486.153i | − 0.506938i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 159.280 | 0.165744 | ||||||||
\(962\) | 96.9413i | 0.100771i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1282.09 | 1.32996 | ||||||||
\(965\) | 610.813i | 0.632967i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 920.308 | 0.951714 | 0.475857 | − | 0.879523i | \(-0.342138\pi\) | ||||
0.475857 | + | 0.879523i | \(0.342138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 160.851 | 0.165826 | ||||||||
\(971\) | − 295.006i | − 0.303816i | −0.988395 | − | 0.151908i | \(-0.951458\pi\) | ||||
0.988395 | − | 0.151908i | \(-0.0485418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.4809 | −0.0477708 | ||||||||
\(974\) | − 128.197i | − 0.131619i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −491.808 | −0.503902 | ||||||||
\(977\) | − 1373.57i | − 1.40591i | −0.711235 | − | 0.702955i | \(-0.751864\pi\) | ||||
0.711235 | − | 0.702955i | \(-0.248136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1298.60i | 1.32510i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.0896 | −0.0102745 | ||||||||
\(983\) | − 944.469i | − 0.960803i | −0.877049 | − | 0.480401i | \(-0.840491\pi\) | ||||
0.877049 | − | 0.480401i | \(-0.159509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1871.30 | −1.89979 | ||||||||
\(986\) | 119.565i | 0.121263i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2047.00 | −2.07186 | ||||||||
\(989\) | 132.064i | 0.133533i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 357.852 | 0.361102 | 0.180551 | − | 0.983566i | \(-0.442212\pi\) | ||||
0.180551 | + | 0.983566i | \(0.442212\pi\) | |||||||
\(992\) | 305.708i | 0.308173i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 48.3892 | 0.0486813 | ||||||||
\(995\) | − 514.734i | − 0.517320i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 197.472 | 0.198066 | 0.0990330 | − | 0.995084i | \(-0.468425\pi\) | ||||
0.0990330 | + | 0.995084i | \(0.468425\pi\) | |||||||
\(998\) | 94.3786i | 0.0945677i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.b.g.485.4 | 8 | ||
3.2 | odd | 2 | inner | 1089.3.b.g.485.5 | 8 | ||
11.10 | odd | 2 | 99.3.b.a.89.5 | yes | 8 | ||
33.32 | even | 2 | 99.3.b.a.89.4 | ✓ | 8 | ||
44.43 | even | 2 | 1584.3.i.b.881.1 | 8 | |||
132.131 | odd | 2 | 1584.3.i.b.881.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.b.a.89.4 | ✓ | 8 | 33.32 | even | 2 | ||
99.3.b.a.89.5 | yes | 8 | 11.10 | odd | 2 | ||
1089.3.b.g.485.4 | 8 | 1.1 | even | 1 | trivial | ||
1089.3.b.g.485.5 | 8 | 3.2 | odd | 2 | inner | ||
1584.3.i.b.881.1 | 8 | 44.43 | even | 2 | |||
1584.3.i.b.881.8 | 8 | 132.131 | odd | 2 |