Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(43,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.r (of order \(18\), degree \(6\), 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.909039 - 1.08335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.67 |
Dual form | 216.3.r.a.187.2 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{4}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.347296 | − | 1.96962i | −0.173648 | − | 0.984808i | ||||
\(3\) | 1.05203 | + | 2.80949i | 0.350678 | + | 0.936496i | ||||
\(4\) | −3.75877 | + | 1.36808i | −0.939693 | + | 0.342020i | ||||
\(5\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(6\) | 5.16824 | − | 3.04783i | 0.861374 | − | 0.507971i | ||||
\(7\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(8\) | 4.00000 | + | 6.92820i | 0.500000 | + | 0.866025i | ||||
\(9\) | −6.78645 | + | 5.91135i | −0.754050 | + | 0.656817i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.63152 | + | 4.72540i | −0.511956 | + | 0.429582i | −0.861817 | − | 0.507220i | \(-0.830673\pi\) |
0.349861 | + | 0.936802i | \(0.386229\pi\) | |||||||
\(12\) | −7.79796 | − | 9.12096i | −0.649830 | − | 0.760080i | ||||
\(13\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2567 | − | 10.2846i | 0.766044 | − | 0.642788i | ||||
\(17\) | −16.8864 | + | 29.2481i | −0.993317 | + | 1.72048i | −0.396704 | + | 0.917947i | \(0.629846\pi\) |
−0.596613 | + | 0.802529i | \(0.703487\pi\) | |||||||
\(18\) | 14.0000 | + | 11.3137i | 0.777778 | + | 0.628539i | ||||
\(19\) | 7.56852 | + | 13.1091i | 0.398343 | + | 0.689951i | 0.993522 | − | 0.113643i | \(-0.0362520\pi\) |
−0.595178 | + | 0.803594i | \(0.702919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.2630 | + | 9.45081i | 0.511956 | + | 0.429582i | ||||
\(23\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(24\) | −15.2566 | + | 18.5267i | −0.635691 | + | 0.771944i | ||||
\(25\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −23.7474 | − | 12.8475i | −0.879535 | − | 0.475834i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(32\) | −24.5134 | − | 20.5692i | −0.766044 | − | 0.642788i | ||||
\(33\) | −19.2005 | − | 10.8504i | −0.581834 | − | 0.328800i | ||||
\(34\) | 63.4721 | + | 23.1019i | 1.86683 | + | 0.679469i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 17.4215 | − | 31.5038i | 0.483931 | − | 0.875106i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 23.1913 | − | 19.4598i | 0.610297 | − | 0.512100i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.45792 | − | 8.26827i | 0.0355590 | − | 0.201665i | −0.961853 | − | 0.273568i | \(-0.911796\pi\) |
0.997412 | + | 0.0719030i | \(0.0229072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 65.8758 | − | 55.2764i | 1.53200 | − | 1.28550i | 0.758918 | − | 0.651186i | \(-0.225728\pi\) |
0.773078 | − | 0.634311i | \(-0.218716\pi\) | |||||||
\(44\) | 14.7028 | − | 25.4661i | 0.334156 | − | 0.578774i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(48\) | 41.7889 | + | 23.6153i | 0.870603 | + | 0.491986i | ||||
\(49\) | 37.5362 | + | 31.4966i | 0.766044 | + | 0.642788i | ||||
\(50\) | 46.9846 | − | 17.1010i | 0.939693 | − | 0.342020i | ||||
\(51\) | −99.9372 | − | 16.6722i | −1.95955 | − | 0.326905i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −17.0573 | + | 51.2352i | −0.315875 | + | 0.948801i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −28.8674 | + | 35.0548i | −0.506446 | + | 0.614997i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −89.9014 | − | 75.4363i | −1.52375 | − | 1.27858i | −0.828838 | − | 0.559489i | \(-0.810997\pi\) |
−0.694915 | − | 0.719092i | \(-0.744558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32.0000 | + | 55.4256i | −0.500000 | + | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.7028 | + | 41.5859i | −0.222770 | + | 0.630090i | ||||
\(67\) | −3.06159 | + | 17.3632i | −0.0456954 | + | 0.259152i | −0.999094 | − | 0.0425626i | \(-0.986448\pi\) |
0.953398 | + | 0.301714i | \(0.0975589\pi\) | |||||||
\(68\) | 23.4583 | − | 133.039i | 0.344975 | − | 1.95645i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | −68.1009 | − | 23.3725i | −0.945845 | − | 0.324618i | ||||
\(73\) | −4.38372 | − | 7.59283i | −0.0600510 | − | 0.104011i | 0.834437 | − | 0.551103i | \(-0.185793\pi\) |
−0.894488 | + | 0.447092i | \(0.852460\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −64.6031 | + | 38.0978i | −0.861374 | + | 0.507971i | ||||
\(76\) | −46.3826 | − | 38.9196i | −0.610297 | − | 0.512100i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.1118 | − | 80.2342i | 0.137183 | − | 0.990546i | ||||
\(82\) | −16.7917 | −0.204776 | ||||||||
\(83\) | −6.06192 | − | 34.3788i | −0.0730351 | − | 0.414203i | −0.999303 | − | 0.0373364i | \(-0.988113\pi\) |
0.926268 | − | 0.376866i | \(-0.122998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −131.752 | − | 110.553i | −1.53200 | − | 1.28550i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −55.2646 | − | 20.1147i | −0.628007 | − | 0.228576i | ||||
\(89\) | 80.5908 | + | 139.587i | 0.905515 | + | 1.56840i | 0.820225 | + | 0.572041i | \(0.193848\pi\) |
0.0852901 | + | 0.996356i | \(0.472818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 32.0000 | − | 90.5097i | 0.333333 | − | 0.942809i | ||||
\(97\) | 112.129 | − | 94.0873i | 1.15597 | − | 0.969972i | 0.156126 | − | 0.987737i | \(-0.450100\pi\) |
0.999842 | + | 0.0177651i | \(0.00565510\pi\) | |||||||
\(98\) | 49.0000 | − | 84.8705i | 0.500000 | − | 0.866025i | ||||
\(99\) | 10.2845 | − | 65.3586i | 0.103884 | − | 0.660188i | ||||
\(100\) | −50.0000 | − | 86.6025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(102\) | 1.87010 | + | 202.628i | 0.0183343 | + | 1.98655i | ||||
\(103\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −147.899 | −1.38223 | −0.691115 | − | 0.722745i | \(-0.742880\pi\) | ||||
−0.691115 | + | 0.722745i | \(0.742880\pi\) | |||||||
\(108\) | 106.838 | + | 15.8024i | 0.989237 | + | 0.146319i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 97.5659 | + | 81.8675i | 0.863415 | + | 0.724491i | 0.962701 | − | 0.270568i | \(-0.0872114\pi\) |
−0.0992858 | + | 0.995059i | \(0.531656\pi\) | |||||||
\(114\) | 79.0701 | + | 44.6833i | 0.693598 | + | 0.391959i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −117.358 | + | 203.270i | −0.994559 | + | 1.72263i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.6269 | + | 65.9394i | −0.0960900 | + | 0.544953i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.7634 | − | 4.60249i | 0.201328 | − | 0.0374186i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 120.281 | + | 43.7786i | 0.939693 | + | 0.342020i | ||||
\(129\) | 224.602 | + | 126.925i | 1.74110 | + | 0.983913i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 236.290 | − | 86.0024i | 1.80374 | − | 0.656507i | 0.805808 | − | 0.592177i | \(-0.201731\pi\) |
0.997929 | − | 0.0643300i | \(-0.0204910\pi\) | |||||||
\(132\) | 87.0145 | + | 14.5163i | 0.659201 | + | 0.109972i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 35.2620 | 0.263150 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −270.182 | −1.98663 | ||||||||
\(137\) | 30.7727 | + | 174.520i | 0.224618 | + | 1.27387i | 0.863414 | + | 0.504496i | \(0.168322\pi\) |
−0.638796 | + | 0.769376i | \(0.720567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 241.899 | − | 88.0441i | 1.74028 | − | 0.633411i | 0.741007 | − | 0.671497i | \(-0.234348\pi\) |
0.999274 | + | 0.0380864i | \(0.0121262\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −22.3837 | + | 142.250i | −0.155442 | + | 0.987845i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.4325 | + | 11.2712i | −0.0920034 | + | 0.0772000i | ||||
\(147\) | −49.0000 | + | 138.593i | −0.333333 | + | 0.942809i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(150\) | 97.4745 | + | 114.012i | 0.649830 | + | 0.760080i | ||||
\(151\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(152\) | −60.5482 | + | 104.873i | −0.398343 | + | 0.689951i | ||||
\(153\) | −58.2971 | − | 298.312i | −0.381027 | − | 1.94975i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −161.890 | + | 5.97900i | −0.999319 | + | 0.0369074i | ||||
\(163\) | 205.091 | 1.25823 | 0.629113 | − | 0.777314i | \(-0.283418\pi\) | ||||
0.629113 | + | 0.777314i | \(0.283418\pi\) | |||||||
\(164\) | 5.83168 | + | 33.0731i | 0.0355590 | + | 0.201665i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −65.6078 | + | 23.8793i | −0.395228 | + | 0.143851i | ||||
\(167\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −158.808 | − | 57.8014i | −0.939693 | − | 0.342020i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −128.856 | − | 44.2238i | −0.753542 | − | 0.258619i | ||||
\(172\) | −171.990 | + | 297.895i | −0.999939 | + | 1.73195i | ||||
\(173\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.4250 | + | 115.836i | −0.116051 | + | 0.658158i | ||||
\(177\) | 117.358 | − | 331.938i | 0.663039 | − | 1.87536i | ||||
\(178\) | 246.945 | − | 207.211i | 1.38733 | − | 1.16411i | ||||
\(179\) | −162.818 | + | 282.009i | −0.909597 | + | 1.57547i | −0.0949721 | + | 0.995480i | \(0.530276\pi\) |
−0.814625 | + | 0.579988i | \(0.803057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −43.1130 | − | 244.506i | −0.230551 | − | 1.30752i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(192\) | −189.383 | − | 31.5940i | −0.986368 | − | 0.164552i | ||||
\(193\) | −296.058 | + | 107.756i | −1.53398 | + | 0.558323i | −0.964592 | − | 0.263745i | \(-0.915042\pi\) |
−0.569388 | + | 0.822069i | \(0.692820\pi\) | |||||||
\(194\) | −224.258 | − | 188.175i | −1.15597 | − | 0.969972i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −184.180 | − | 67.0359i | −0.939693 | − | 0.342020i | ||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | −132.303 | + | 2.44231i | −0.668197 | + | 0.0123349i | ||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | −153.209 | + | 128.558i | −0.766044 | + | 0.642788i | ||||
\(201\) | −52.0025 | + | 9.66512i | −0.258719 | + | 0.0480852i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 398.450 | − | 74.0554i | 1.95319 | − | 0.363016i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −104.568 | − | 38.0596i | −0.500325 | − | 0.182103i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 322.992 | + | 271.022i | 1.53077 | + | 1.28447i | 0.792086 | + | 0.610410i | \(0.208995\pi\) |
0.738680 | + | 0.674056i | \(0.235449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 51.3646 | + | 291.303i | 0.240022 | + | 1.36123i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.97959 | − | 215.917i | −0.0276833 | − | 0.999617i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.7201 | − | 20.3039i | 0.0763477 | − | 0.0927120i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −175.000 | − | 141.421i | −0.777778 | − | 0.628539i | ||||
\(226\) | 127.363 | − | 220.600i | 0.563554 | − | 0.976105i | ||||
\(227\) | 123.341 | − | 103.496i | 0.543354 | − | 0.455928i | −0.329329 | − | 0.944215i | \(-0.606822\pi\) |
0.872683 | + | 0.488287i | \(0.162378\pi\) | |||||||
\(228\) | 60.5482 | − | 171.256i | 0.265562 | − | 0.751123i | ||||
\(229\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −220.774 | + | 382.392i | −0.947528 | + | 1.64117i | −0.196919 | + | 0.980420i | \(0.563093\pi\) |
−0.750609 | + | 0.660746i | \(0.770240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 441.122 | + | 160.555i | 1.86916 | + | 0.680319i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −57.8616 | − | 328.149i | −0.240090 | − | 1.36162i | −0.831626 | − | 0.555337i | \(-0.812589\pi\) |
0.591536 | − | 0.806279i | \(-0.298522\pi\) | |||||||
\(242\) | 133.913 | 0.553360 | ||||||||
\(243\) | 237.107 | − | 53.1905i | 0.975749 | − | 0.218891i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.6654 | − | 47.1760i | −0.0718105 | − | 0.191772i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 90.2096 | − | 53.1986i | 0.362288 | − | 0.213649i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −51.4601 | − | 89.1314i | −0.205020 | − | 0.355105i | 0.745119 | − | 0.666932i | \(-0.232393\pi\) |
−0.950139 | + | 0.311826i | \(0.899059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 44.4539 | − | 252.111i | 0.173648 | − | 0.984808i | ||||
\(257\) | −83.1439 | + | 471.533i | −0.323517 | + | 1.83476i | 0.196379 | + | 0.980528i | \(0.437082\pi\) |
−0.519896 | + | 0.854229i | \(0.674029\pi\) | |||||||
\(258\) | 171.990 | − | 486.460i | 0.666626 | − | 1.88550i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −251.454 | − | 435.531i | −0.959748 | − | 1.66233i | ||||
\(263\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(264\) | −1.62828 | − | 176.427i | −0.00616772 | − | 0.668283i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −307.385 | + | 373.270i | −1.15125 | + | 1.39801i | ||||
\(268\) | −12.2464 | − | 69.4527i | −0.0456954 | − | 0.259152i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 93.8333 | + | 532.155i | 0.344975 | + | 1.95645i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 333.051 | − | 121.221i | 1.21551 | − | 0.442411i | ||||
\(275\) | −140.788 | − | 118.135i | −0.511956 | − | 0.429582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(278\) | −257.424 | − | 445.871i | −0.925985 | − | 1.60385i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 428.915 | − | 359.902i | 1.52639 | − | 1.28079i | 0.707785 | − | 0.706428i | \(-0.249695\pi\) |
0.818601 | − | 0.574362i | \(-0.194750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −77.0996 | + | 437.254i | −0.272437 | + | 1.54507i | 0.474551 | + | 0.880228i | \(0.342610\pi\) |
−0.746988 | + | 0.664838i | \(0.768501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 287.951 | − | 5.31557i | 0.999830 | − | 0.0184568i | ||||
\(289\) | −425.800 | − | 737.508i | −1.47336 | − | 2.55193i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 382.301 | + | 216.042i | 1.31375 | + | 0.742412i | ||||
\(292\) | 26.8650 | + | 22.5424i | 0.0920034 | + | 0.0772000i | ||||
\(293\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(294\) | 289.992 | + | 48.3783i | 0.986368 | + | 0.164552i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 194.444 | − | 39.8653i | 0.654693 | − | 0.134227i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 190.707 | − | 231.583i | 0.635691 | − | 0.771944i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 227.587 | + | 82.8348i | 0.748640 | + | 0.272483i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −567.314 | + | 218.426i | −1.85397 | + | 0.713809i | ||||
\(307\) | −114.876 | + | 198.971i | −0.374189 | + | 0.648115i | −0.990205 | − | 0.139619i | \(-0.955412\pi\) |
0.616016 | + | 0.787734i | \(0.288746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −475.797 | + | 399.241i | −1.52012 | + | 1.27553i | −0.679862 | + | 0.733340i | \(0.737960\pi\) |
−0.840256 | + | 0.542191i | \(0.817595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −155.594 | − | 415.519i | −0.484717 | − | 1.29445i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −511.220 | −1.58272 | ||||||||
\(324\) | 68.0000 | + | 316.784i | 0.209877 | + | 0.977728i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −71.2273 | − | 403.950i | −0.218489 | − | 1.23911i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 63.1160 | − | 22.9723i | 0.192427 | − | 0.0700376i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −532.036 | − | 193.645i | −1.60736 | − | 0.585031i | −0.626444 | − | 0.779467i | \(-0.715490\pi\) |
−0.980915 | + | 0.194436i | \(0.937712\pi\) | |||||||
\(332\) | 69.8184 | + | 120.929i | 0.210296 | + | 0.364244i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −95.6733 | + | 542.590i | −0.283897 | + | 1.61006i | 0.425302 | + | 0.905052i | \(0.360168\pi\) |
−0.709199 | + | 0.705009i | \(0.750943\pi\) | |||||||
\(338\) | −58.6931 | + | 332.865i | −0.173648 | + | 0.984808i | ||||
\(339\) | −127.363 | + | 360.238i | −0.375703 | + | 1.06265i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −42.3528 | + | 269.155i | −0.123839 | + | 0.787003i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 646.469 | + | 235.296i | 1.87927 | + | 0.683999i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 340.401 | − | 123.896i | 0.980983 | − | 0.357048i | 0.198761 | − | 0.980048i | \(-0.436308\pi\) |
0.782222 | + | 0.623000i | \(0.214086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 235.246 | 0.668311 | ||||||||
\(353\) | −110.236 | − | 625.178i | −0.312282 | − | 1.77104i | −0.587070 | − | 0.809536i | \(-0.699719\pi\) |
0.274788 | − | 0.961505i | \(-0.411392\pi\) | |||||||
\(354\) | −694.549 | − | 115.869i | −1.96200 | − | 0.327314i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −493.889 | − | 414.422i | −1.38733 | − | 1.16411i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 611.995 | + | 222.748i | 1.70948 | + | 0.622201i | ||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 65.9350 | − | 114.203i | 0.182645 | − | 0.316351i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −197.488 | + | 36.7048i | −0.544043 | + | 0.101115i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.9826 | + | 64.7305i | 0.105644 | + | 0.175421i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(374\) | −466.610 | + | 169.832i | −1.24762 | + | 0.454097i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 732.767 | 1.93342 | 0.966712 | − | 0.255869i | \(-0.0823614\pi\) | ||||
0.966712 | + | 0.255869i | \(0.0823614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(384\) | 3.54386 | + | 383.984i | 0.00922881 | + | 0.999957i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 315.059 | + | 545.698i | 0.816214 | + | 1.41372i | ||||
\(387\) | −120.305 | + | 764.546i | −0.310865 | + | 1.97557i | ||||
\(388\) | −292.748 | + | 507.054i | −0.754504 | + | 1.30684i | ||||
\(389\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −68.0701 | + | 386.045i | −0.173648 | + | 0.984808i | ||||
\(393\) | 490.207 | + | 573.375i | 1.24735 | + | 1.45897i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 50.7588 | + | 259.738i | 0.128179 | + | 0.655904i | ||||
\(397\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 306.418 | + | 257.115i | 0.766044 | + | 0.642788i | ||||
\(401\) | 694.911 | − | 252.927i | 1.73294 | − | 0.630740i | 0.734111 | − | 0.679029i | \(-0.237599\pi\) |
0.998833 | + | 0.0482891i | \(0.0153769\pi\) | |||||||
\(402\) | 37.0969 | + | 99.0683i | 0.0922807 | + | 0.246439i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −284.241 | − | 759.074i | −0.696669 | − | 1.86048i | ||||
\(409\) | −636.512 | + | 231.671i | −1.55626 | + | 0.566434i | −0.969877 | − | 0.243596i | \(-0.921673\pi\) |
−0.586388 | + | 0.810030i | \(0.699451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −457.939 | + | 270.057i | −1.11421 | + | 0.657072i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 501.845 | + | 586.988i | 1.20346 | + | 1.40764i | ||||
\(418\) | −38.6467 | + | 219.176i | −0.0924563 | + | 0.524346i | ||||
\(419\) | 144.159 | − | 817.568i | 0.344056 | − | 1.95124i | 0.0378083 | − | 0.999285i | \(-0.487962\pi\) |
0.306247 | − | 0.951952i | \(-0.400927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(422\) | 421.636 | − | 730.294i | 0.999137 | − | 1.73056i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −793.401 | − | 288.774i | −1.86683 | − | 0.679469i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 555.917 | − | 202.337i | 1.29887 | − | 0.472750i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −423.197 | + | 86.7648i | −0.979623 | + | 0.200844i | ||||
\(433\) | 735.453 | 1.69851 | 0.849253 | − | 0.527987i | \(-0.177053\pi\) | ||||
0.849253 | + | 0.527987i | \(0.177053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −45.7978 | − | 25.8808i | −0.104561 | − | 0.0590885i | ||||
\(439\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −440.925 | + | 8.13946i | −0.999830 | + | 0.0184568i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 573.726 | − | 481.413i | 1.29509 | − | 1.08671i | 0.304122 | − | 0.952633i | \(-0.401637\pi\) |
0.990971 | − | 0.134079i | \(-0.0428076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 447.517 | − | 775.122i | 0.996697 | − | 1.72633i | 0.428015 | − | 0.903772i | \(-0.359213\pi\) |
0.568681 | − | 0.822558i | \(-0.307454\pi\) | |||||||
\(450\) | −217.769 | + | 393.798i | −0.483931 | + | 0.875106i | ||||
\(451\) | 30.8606 | + | 53.4522i | 0.0684271 | + | 0.118519i | ||||
\(452\) | −478.729 | − | 174.243i | −1.05914 | − | 0.385494i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −246.683 | − | 206.991i | −0.543354 | − | 0.455928i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −358.337 | − | 59.7800i | −0.785826 | − | 0.131097i | ||||
\(457\) | 66.8410 | + | 379.074i | 0.146260 | + | 0.829483i | 0.966347 | + | 0.257244i | \(0.0828143\pi\) |
−0.820086 | + | 0.572240i | \(0.806075\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 776.774 | − | 477.619i | 1.69232 | − | 1.04056i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 829.839 | + | 302.037i | 1.78077 | + | 0.648147i | ||||
\(467\) | −286.960 | − | 497.029i | −0.614476 | − | 1.06430i | −0.990476 | − | 0.137684i | \(-0.956034\pi\) |
0.376001 | − | 0.926619i | \(-0.377299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 163.032 | − | 924.600i | 0.345407 | − | 1.95890i | ||||
\(473\) | −109.778 | + | 622.580i | −0.232088 | + | 1.31624i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −289.891 | + | 243.248i | −0.610297 | + | 0.512100i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −626.233 | + | 227.930i | −1.29924 | + | 0.472884i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.5076 | − | 263.757i | −0.0960900 | − | 0.544953i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −187.111 | − | 448.537i | −0.385003 | − | 0.922916i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 215.762 | + | 576.200i | 0.441232 | + | 1.17832i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 552.118 | + | 463.282i | 1.12448 | + | 0.943548i | 0.998822 | − | 0.0485262i | \(-0.0154524\pi\) |
0.125655 | + | 0.992074i | \(0.459897\pi\) | |||||||
\(492\) | −86.7834 | + | 51.1780i | −0.176389 | + | 0.104020i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −136.110 | − | 159.203i | −0.273314 | − | 0.319684i | ||||
\(499\) | 77.3915 | − | 438.909i | 0.155093 | − | 0.879578i | −0.803607 | − | 0.595160i | \(-0.797089\pi\) |
0.958700 | − | 0.284418i | \(-0.0918002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −157.683 | + | 132.312i | −0.314109 | + | 0.263569i | ||||
\(503\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.67901 | − | 506.978i | −0.00922881 | − | 0.999957i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | −11.3142 | − | 408.544i | −0.0220549 | − | 0.796381i | ||||
\(514\) | 957.614 | 1.86306 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1017.87 | − | 169.808i | −1.97262 | − | 0.329084i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 221.047 | + | 382.865i | 0.424274 | + | 0.734865i | 0.996352 | − | 0.0853344i | \(-0.0271959\pi\) |
−0.572078 | + | 0.820199i | \(0.693863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −319.363 | + | 553.153i | −0.610636 | + | 1.05765i | 0.380497 | + | 0.924782i | \(0.375753\pi\) |
−0.991133 | + | 0.132871i | \(0.957580\pi\) | |||||||
\(524\) | −770.500 | + | 646.526i | −1.47042 | + | 1.23383i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −346.927 | + | 64.4794i | −0.657059 | + | 0.122120i | ||||
\(529\) | 405.238 | − | 340.035i | 0.766044 | − | 0.642788i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1056.04 | − | 19.4945i | 1.98878 | − | 0.0367128i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 841.951 | + | 475.795i | 1.57669 | + | 0.891002i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −132.542 | + | 48.2413i | −0.247280 | + | 0.0900025i | ||||
\(537\) | −963.590 | − | 160.752i | −1.79440 | − | 0.299352i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −360.220 | −0.668311 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1015.55 | − | 369.631i | 1.86683 | − | 0.679469i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −527.977 | − | 192.168i | −0.965223 | − | 0.351313i | −0.189145 | − | 0.981949i | \(-0.560572\pi\) |
−0.776078 | + | 0.630637i | \(0.782794\pi\) | |||||||
\(548\) | −354.425 | − | 613.883i | −0.646761 | − | 1.12022i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −183.786 | + | 318.326i | −0.334156 | + | 0.578774i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −788.792 | + | 661.875i | −1.41869 | + | 1.19042i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 641.581 | − | 378.354i | 1.14364 | − | 0.674428i | ||||
\(562\) | −857.829 | − | 719.804i | −1.52639 | − | 1.28079i | ||||
\(563\) | 154.962 | − | 56.4016i | 0.275244 | − | 0.100180i | −0.200710 | − | 0.979651i | \(-0.564325\pi\) |
0.475954 | + | 0.879470i | \(0.342103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 887.998 | 1.56890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8053 | − | 129.335i | −0.0400796 | − | 0.227303i | 0.958188 | − | 0.286139i | \(-0.0923720\pi\) |
−0.998268 | + | 0.0588367i | \(0.981261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 971.136 | − | 353.465i | 1.70076 | − | 0.619027i | 0.704851 | − | 0.709355i | \(-0.251014\pi\) |
0.995912 | + | 0.0903277i | \(0.0287914\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −110.474 | − | 565.307i | −0.191795 | − | 0.981435i | ||||
\(577\) | 198.285 | − | 343.440i | 0.343648 | − | 0.595216i | −0.641459 | − | 0.767157i | \(-0.721671\pi\) |
0.985107 | + | 0.171941i | \(0.0550039\pi\) | |||||||
\(578\) | −1304.73 | + | 1094.80i | −2.25731 | + | 1.89411i | ||||
\(579\) | −614.204 | − | 718.409i | −1.06080 | − | 1.24078i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 292.748 | − | 828.016i | 0.503003 | − | 1.42271i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 35.0698 | − | 60.7426i | 0.0600510 | − | 0.104011i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −912.157 | − | 331.998i | −1.55393 | − | 0.565585i | −0.584595 | − | 0.811325i | \(-0.698747\pi\) |
−0.969336 | + | 0.245741i | \(0.920969\pi\) | |||||||
\(588\) | −5.42654 | − | 587.975i | −0.00922881 | − | 0.999957i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1136.45 | 1.91645 | 0.958223 | − | 0.286021i | \(-0.0923326\pi\) | ||||
0.958223 | + | 0.286021i | \(0.0923326\pi\) | |||||||
\(594\) | −146.049 | − | 369.135i | −0.245874 | − | 0.621439i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(600\) | −522.362 | − | 295.192i | −0.870603 | − | 0.491986i | ||||
\(601\) | 556.188 | + | 202.436i | 0.925437 | + | 0.336831i | 0.760399 | − | 0.649456i | \(-0.225003\pi\) |
0.165038 | + | 0.986287i | \(0.447225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −81.8624 | − | 135.932i | −0.135759 | − | 0.225427i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(608\) | 84.1126 | − | 477.026i | 0.138343 | − | 0.784583i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 627.240 | + | 1041.53i | 1.02490 | + | 1.70185i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 431.793 | + | 157.160i | 0.703246 | + | 0.255960i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −676.726 | + | 246.308i | −1.09680 | + | 0.399203i | −0.826136 | − | 0.563471i | \(-0.809466\pi\) |
−0.270665 | + | 0.962674i | \(0.587243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −197.884 | − | 1122.25i | −0.319683 | − | 1.81301i | −0.544670 | − | 0.838651i | \(-0.683345\pi\) |
0.224987 | − | 0.974362i | \(-0.427766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −587.308 | + | 213.763i | −0.939693 | + | 0.342020i | ||||
\(626\) | 951.594 | + | 798.482i | 1.52012 | + | 1.27553i | ||||
\(627\) | −3.08091 | − | 333.822i | −0.00491374 | − | 0.532412i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −421.636 | + | 1192.57i | −0.666091 | + | 1.88399i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1064.51 | − | 387.449i | −1.66070 | − | 0.604445i | −0.670227 | − | 0.742156i | \(-0.733803\pi\) |
−0.990472 | + | 0.137711i | \(0.956025\pi\) | |||||||
\(642\) | −764.376 | + | 450.769i | −1.19062 | + | 0.702133i | ||||
\(643\) | −762.735 | − | 640.011i | −1.18621 | − | 0.995351i | −0.999917 | − | 0.0128574i | \(-0.995907\pi\) |
−0.186296 | − | 0.982494i | \(-0.559648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 177.545 | + | 1006.91i | 0.274837 | + | 1.55868i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 600.326 | − | 243.952i | 0.926429 | − | 0.376469i | ||||
\(649\) | 862.748 | 1.32935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −770.889 | + | 280.581i | −1.18235 | + | 0.430339i | ||||
\(653\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −67.1666 | − | 116.336i | −0.102388 | − | 0.177341i | ||||
\(657\) | 74.6338 | + | 25.6146i | 0.113598 | + | 0.0389873i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −193.460 | + | 162.332i | −0.293566 | + | 0.246331i | −0.777660 | − | 0.628685i | \(-0.783594\pi\) |
0.484094 | + | 0.875016i | \(0.339149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(662\) | −196.632 | + | 1115.16i | −0.297028 | + | 1.68453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 213.936 | − | 179.514i | 0.322193 | − | 0.270352i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 184.746 | + | 1047.74i | 0.274511 | + | 1.55683i | 0.740512 | + | 0.672043i | \(0.234583\pi\) |
−0.466001 | + | 0.884784i | \(0.654306\pi\) | |||||||
\(674\) | 1101.92 | 1.63490 | ||||||||
\(675\) | 213.216 | − | 640.440i | 0.315875 | − | 0.948801i | ||||
\(676\) | 676.000 | 1.00000 | ||||||||
\(677\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(678\) | 753.763 | + | 125.747i | 1.11174 | + | 0.185468i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 420.529 | + | 237.645i | 0.617517 | + | 0.348965i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 410.463 | + | 710.943i | 0.600971 | + | 1.04091i | 0.992674 | + | 0.120821i | \(0.0385527\pi\) |
−0.391703 | + | 0.920092i | \(0.628114\pi\) | |||||||
\(684\) | 544.841 | − | 10.0577i | 0.796551 | − | 0.0147043i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 238.925 | − | 1355.01i | 0.347275 | − | 1.96950i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1057.98 | + | 887.747i | −1.53108 | + | 1.28473i | −0.742201 | + | 0.670178i | \(0.766218\pi\) |
−0.788878 | + | 0.614550i | \(0.789338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −362.247 | − | 627.430i | −0.521970 | − | 0.904079i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 217.212 | + | 182.263i | 0.311639 | + | 0.261496i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1306.59 | − | 217.973i | −1.86922 | − | 0.311836i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −81.6999 | − | 463.343i | −0.116051 | − | 0.658158i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1193.07 | + | 434.244i | −1.68991 | + | 0.615076i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.9969 | + | 1408.24i | 0.0183572 | + | 1.98903i | ||||
\(709\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −644.727 | + | 1116.70i | −0.905515 | + | 1.56840i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 226.184 | − | 1282.75i | 0.315900 | − | 1.79156i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −247.834 | − | 90.2043i | −0.343261 | − | 0.124937i | ||||
\(723\) | 861.059 | − | 507.785i | 1.19095 | − | 0.702331i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 140.881 | + | 376.228i | 0.194051 | + | 0.518220i | ||||
\(727\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 398.883 | + | 610.191i | 0.547164 | + | 0.837025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 504.323 | + | 2860.16i | 0.689909 | + | 3.91267i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.8065 | − | 112.248i | −0.0879329 | − | 0.152304i | ||||
\(738\) | 113.956 | − | 99.2614i | 0.154412 | − | 0.134500i | ||||
\(739\) | −397.972 | + | 689.308i | −0.538528 | + | 0.932758i | 0.460456 | + | 0.887683i | \(0.347686\pi\) |
−0.998984 | + | 0.0450751i | \(0.985647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 244.364 | + | 197.476i | 0.327128 | + | 0.264359i | ||||
\(748\) | 496.556 | + | 860.060i | 0.663845 | + | 1.14981i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 196.276 | − | 238.346i | 0.260659 | − | 0.316528i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −254.487 | − | 1443.27i | −0.335735 | − | 1.90405i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1067.87 | + | 896.046i | 1.40324 | + | 1.17746i | 0.959639 | + | 0.281234i | \(0.0907438\pi\) |
0.443601 | + | 0.896224i | \(0.353701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 755.069 | − | 140.336i | 0.983163 | − | 0.182729i | ||||
\(769\) | 259.951 | − | 1474.26i | 0.338038 | − | 1.91711i | −0.0568609 | − | 0.998382i | \(-0.518109\pi\) |
0.394899 | − | 0.918725i | \(-0.370780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1412.24 | + | 262.476i | −1.83169 | + | 0.340436i | ||||
\(772\) | 965.396 | − | 810.063i | 1.25051 | − | 1.04930i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 1547.64 | − | 28.5694i | 1.99954 | − | 0.0369114i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1100.37 | + | 400.502i | 1.41800 | + | 0.516111i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 119.424 | − | 43.4666i | 0.153304 | − | 0.0557980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 959.082 | − | 1164.65i | 1.22021 | − | 1.48174i | ||||
\(787\) | −600.718 | + | 218.643i | −0.763301 | + | 0.277819i | −0.694191 | − | 0.719790i | \(-0.744238\pi\) |
−0.0691092 | + | 0.997609i | \(0.522016\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 493.956 | − | 190.181i | 0.623681 | − | 0.240128i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 400.000 | − | 692.820i | 0.500000 | − | 0.866025i | ||||
\(801\) | −1372.08 | − | 470.902i | −1.71295 | − | 0.587893i | ||||
\(802\) | −739.509 | − | 1280.87i | −0.922081 | − | 1.59709i | ||||
\(803\) | 60.5662 | + | 22.0443i | 0.0754249 | + | 0.0274524i | ||||
\(804\) | 182.243 | − | 107.473i | 0.226670 | − | 0.133672i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 59.5434 | 0.0736013 | 0.0368006 | − | 0.999323i | \(-0.488283\pi\) | ||||
0.0368006 | + | 0.999323i | \(0.488283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −384.141 | −0.473663 | −0.236832 | − | 0.971551i | \(-0.576109\pi\) | ||||
−0.236832 | + | 0.971551i | \(0.576109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1396.37 | + | 823.469i | −1.71124 | + | 1.00915i | ||||
\(817\) | 1223.20 | + | 445.210i | 1.49719 | + | 0.544933i | ||||
\(818\) | 677.362 | + | 1173.23i | 0.828071 | + | 1.43426i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(822\) | 690.948 | + | 808.174i | 0.840570 | + | 0.983181i | ||||
\(823\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 183.786 | − | 519.824i | 0.222770 | − | 0.630090i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −631.000 | + | 1092.92i | −0.762999 | + | 1.32155i | 0.178299 | + | 0.983976i | \(0.442940\pi\) |
−0.941298 | + | 0.337576i | \(0.890393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1555.07 | + | 565.998i | −1.86683 | + | 0.679469i | ||||
\(834\) | 981.851 | − | 1192.30i | 1.17728 | − | 1.42962i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 445.115 | 0.532434 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1660.36 | −1.98134 | ||||||||
\(839\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −790.281 | + | 287.639i | −0.939693 | + | 0.342020i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1462.37 | + | 826.401i | 1.73472 | + | 0.980310i | ||||
\(844\) | −1584.83 | − | 576.832i | −1.87776 | − | 0.683450i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1309.57 | + | 243.395i | −1.54249 | + | 0.286684i | ||||
\(850\) | −293.229 | + | 1662.98i | −0.344975 | + | 1.95645i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −591.594 | − | 1024.67i | −0.691115 | − | 1.19705i | ||||
\(857\) | −1129.51 | − | 411.108i | −1.31798 | − | 0.479706i | −0.415171 | − | 0.909743i | \(-0.636278\pi\) |
−0.902811 | + | 0.430037i | \(0.858500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1313.81 | − | 1102.42i | −1.52947 | − | 1.28337i | −0.802334 | − | 0.596875i | \(-0.796409\pi\) |
−0.727131 | − | 0.686499i | \(-0.759147\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 317.868 | + | 803.403i | 0.367903 | + | 0.929864i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −255.420 | − | 1448.56i | −0.294942 | − | 1.67270i | ||||
\(867\) | 1624.06 | − | 1972.16i | 1.87320 | − | 2.27470i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −204.774 | + | 1301.35i | −0.234564 | + | 1.49067i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −35.0698 | + | 99.1923i | −0.0400340 | + | 0.113233i | ||||
\(877\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 81.4082 | − | 141.003i | 0.0924043 | − | 0.160049i | −0.816118 | − | 0.577885i | \(-0.803878\pi\) |
0.908522 | + | 0.417836i | \(0.137211\pi\) | |||||||
\(882\) | 169.163 | + | 865.626i | 0.191795 | + | 0.981435i | ||||
\(883\) | 211.479 | + | 366.292i | 0.239500 | + | 0.414826i | 0.960571 | − | 0.278035i | \(-0.0896831\pi\) |
−0.721071 | + | 0.692861i | \(0.756350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1147.45 | − | 962.827i | −1.29509 | − | 1.08671i | ||||
\(887\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 316.562 | + | 504.348i | 0.355289 | + | 0.566047i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1682.11 | − | 612.239i | −1.87318 | − | 0.681781i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 851.261 | + | 292.156i | 0.945845 | + | 0.324618i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 94.5625 | − | 79.3473i | 0.104836 | − | 0.0879682i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −176.931 | + | 1003.43i | −0.195720 | + | 1.10999i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1078.19 | − | 904.713i | 1.18875 | − | 0.997478i | 0.188868 | − | 0.982002i | \(-0.439518\pi\) |
0.999880 | − | 0.0154761i | \(-0.00492638\pi\) | |||||||
\(908\) | −322.022 | + | 557.758i | −0.354649 | + | 0.614271i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(912\) | 6.70545 | + | 726.547i | 0.00735247 | + | 0.796653i | ||||
\(913\) | 196.592 | + | 164.960i | 0.215325 | + | 0.180679i | ||||
\(914\) | 723.416 | − | 263.302i | 0.791484 | − | 0.288077i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1210.50 | − | 1364.07i | −1.31862 | − | 1.48592i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −679.861 | − | 113.419i | −0.738177 | − | 0.123147i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 810.475 | − | 680.069i | 0.872417 | − | 0.732044i | −0.0921889 | − | 0.995742i | \(-0.529386\pi\) |
0.964606 | + | 0.263697i | \(0.0849419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −128.797 | + | 730.447i | −0.138343 | + | 0.784583i | ||||
\(932\) | 306.696 | − | 1739.36i | 0.329073 | − | 1.86627i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −879.297 | + | 737.818i | −0.941431 | + | 0.789955i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −929.044 | − | 1609.15i | −0.991509 | − | 1.71734i | −0.608371 | − | 0.793653i | \(-0.708177\pi\) |
−0.383138 | − | 0.923691i | \(-0.625157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1622.22 | − | 916.731i | −1.72760 | − | 0.976284i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1877.73 | −1.98912 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1264.37 | 1.33654 | ||||||||
\(947\) | 245.730 | + | 1393.61i | 0.259483 | + | 1.47160i | 0.784298 | + | 0.620384i | \(0.213023\pi\) |
−0.524815 | + | 0.851216i | \(0.675866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 579.782 | + | 486.495i | 0.610297 | + | 0.512100i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −391.758 | − | 678.544i | −0.411078 | − | 0.712008i | 0.583930 | − | 0.811804i | \(-0.301514\pi\) |
−0.995008 | + | 0.0997959i | \(0.968181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 736.169 | − | 617.719i | 0.766044 | − | 0.642788i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1003.71 | − | 874.280i | 1.04227 | − | 0.907872i | ||||
\(964\) | 666.423 | + | 1154.28i | 0.691310 | + | 1.19738i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(968\) | −503.349 | + | 183.204i | −0.519989 | + | 0.189260i | ||||
\(969\) | −537.821 | − | 1436.27i | −0.555026 | − | 1.48222i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 974.000 | 1.00309 | 0.501545 | − | 0.865132i | \(-0.332765\pi\) | ||||
0.501545 | + | 0.865132i | \(0.332765\pi\) | |||||||
\(972\) | −818.462 | + | 524.312i | −0.842039 | + | 0.539416i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −941.688 | − | 790.170i | −0.963857 | − | 0.808772i | 0.0177191 | − | 0.999843i | \(-0.494360\pi\) |
−0.981576 | + | 0.191071i | \(0.938804\pi\) | |||||||
\(978\) | 1059.96 | − | 625.081i | 1.08380 | − | 0.639142i | ||||
\(979\) | −1113.46 | − | 405.265i | −1.13734 | − | 0.413958i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 720.739 | − | 1248.36i | 0.733950 | − | 1.27124i | ||||
\(983\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(984\) | 130.941 | + | 153.156i | 0.133070 | + | 0.155646i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.6755 | − | 1698.47i | −0.0157860 | − | 1.71044i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −266.297 | + | 323.375i | −0.267367 | + | 0.324674i | ||||
\(997\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(998\) | −891.360 | −0.893147 | ||||||||
\(999\) | 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 | 216.3.r.a.67.2 | ✓ | 12 | |
8.3 | odd | 2 | CM | 216.3.r.a.67.2 | ✓ | 12 | |
27.25 | even | 9 | inner | 216.3.r.a.187.2 | yes | 12 | |
216.187 | odd | 18 | inner | 216.3.r.a.187.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.3.r.a.67.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
216.3.r.a.67.2 | ✓ | 12 | 8.3 | odd | 2 | CM | |
216.3.r.a.187.2 | yes | 12 | 27.25 | even | 9 | inner | |
216.3.r.a.187.2 | yes | 12 | 216.187 | odd | 18 | inner |