Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.10 | ||
Character | \(\chi\) | \(=\) | 128.49 |
Dual form | 128.4.g.a.81.10 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 6.06585 | − | 2.51256i | 1.16737 | − | 0.483542i | 0.287050 | − | 0.957916i | \(-0.407325\pi\) |
0.880324 | + | 0.474373i | \(0.157325\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.91165 | + | 7.02935i | −0.260426 | + | 0.628724i | −0.998965 | − | 0.0454866i | \(-0.985516\pi\) |
0.738539 | + | 0.674211i | \(0.235516\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.3899 | + | 13.3899i | 0.722989 | + | 0.722989i | 0.969213 | − | 0.246224i | \(-0.0791898\pi\) |
−0.246224 | + | 0.969213i | \(0.579190\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.3897 | − | 11.3897i | 0.421842 | − | 0.421842i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49.6279 | + | 20.5565i | 1.36031 | + | 0.563457i | 0.939143 | − | 0.343527i | \(-0.111622\pi\) |
0.421164 | + | 0.906985i | \(0.361622\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.74801 | + | 21.1196i | 0.186635 | + | 0.450578i | 0.989308 | − | 0.145842i | \(-0.0465892\pi\) |
−0.802672 | + | 0.596420i | \(0.796589\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 49.9547i | 0.859884i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 77.7412i | − | 1.10912i | −0.832144 | − | 0.554559i | \(-0.812887\pi\) | ||
0.832144 | − | 0.554559i | \(-0.187113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −53.3229 | − | 128.733i | −0.643848 | − | 1.55439i | −0.821447 | − | 0.570284i | \(-0.806833\pi\) |
0.177599 | − | 0.984103i | \(-0.443167\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 114.864 | + | 47.5784i | 1.19359 | + | 0.494403i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.5116 | − | 35.5116i | 0.321943 | − | 0.321943i | −0.527569 | − | 0.849512i | \(-0.676897\pi\) |
0.849512 | + | 0.527569i | \(0.176897\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 47.4543 | + | 47.4543i | 0.379634 | + | 0.379634i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.3680 | + | 66.0722i | −0.195073 | + | 0.470948i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −245.435 | + | 101.662i | −1.57159 | + | 0.650973i | −0.987053 | − | 0.160395i | \(-0.948723\pi\) |
−0.584535 | + | 0.811368i | \(0.698723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 202.613 | 1.17389 | 0.586943 | − | 0.809629i | \(-0.300331\pi\) | ||||
0.586943 | + | 0.809629i | \(0.300331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 352.685 | 1.86044 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −133.110 | + | 55.1358i | −0.642846 | + | 0.266276i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.3055 | − | 87.6493i | 0.161313 | − | 0.389445i | −0.822469 | − | 0.568809i | \(-0.807404\pi\) |
0.983783 | + | 0.179365i | \(0.0574042\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 106.128 | + | 106.128i | 0.435747 | + | 0.435747i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −36.8088 | + | 36.8088i | −0.140209 | + | 0.140209i | −0.773728 | − | 0.633518i | \(-0.781610\pi\) |
0.633518 | + | 0.773728i | \(0.281610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −185.642 | − | 76.8954i | −0.658375 | − | 0.272708i | 0.0283797 | − | 0.999597i | \(-0.490965\pi\) |
−0.686754 | + | 0.726889i | \(0.740965\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 46.8995 | + | 113.225i | 0.155364 | + | 0.375081i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 82.9731i | 0.257508i | 0.991677 | + | 0.128754i | \(0.0410977\pi\) | ||||
−0.991677 | + | 0.128754i | \(0.958902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.5815i | 0.0454271i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −195.329 | − | 471.567i | −0.536305 | − | 1.29476i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −534.758 | − | 221.504i | −1.38594 | − | 0.574074i | −0.439876 | − | 0.898059i | \(-0.644978\pi\) |
−0.946062 | + | 0.323984i | \(0.894978\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −288.998 | + | 288.998i | −0.708519 | + | 0.708519i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −646.898 | − | 646.898i | −1.50322 | − | 1.50322i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −75.7461 | + | 182.867i | −0.167141 | + | 0.403513i | −0.985151 | − | 0.171690i | \(-0.945077\pi\) |
0.818010 | + | 0.575204i | \(0.195077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −472.240 | + | 195.608i | −0.991216 | + | 0.410575i | −0.818569 | − | 0.574409i | \(-0.805232\pi\) |
−0.172647 | + | 0.984984i | \(0.555232\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 305.016 | 0.609975 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −173.928 | −0.331894 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.750 | − | 42.5604i | 0.187357 | − | 0.0776057i | −0.287033 | − | 0.957921i | \(-0.592669\pi\) |
0.474389 | + | 0.880315i | \(0.342669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 126.183 | − | 304.633i | 0.220155 | − | 0.531500i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −520.392 | − | 520.392i | −0.869847 | − | 0.869847i | 0.122608 | − | 0.992455i | \(-0.460874\pi\) |
−0.992455 | + | 0.122608i | \(0.960874\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 244.389 | − | 244.389i | 0.391829 | − | 0.391829i | −0.483510 | − | 0.875339i | \(-0.660638\pi\) |
0.875339 | + | 0.483510i | \(0.160638\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 407.082 | + | 168.619i | 0.626744 | + | 0.259606i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 389.264 | + | 939.766i | 0.576113 | + | 1.39086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 774.758i | − | 1.10338i | −0.834049 | − | 0.551690i | \(-0.813983\pi\) | ||
0.834049 | − | 0.551690i | \(-0.186017\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 904.451i | 1.24067i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23.9166 | + | 57.7397i | 0.0316287 | + | 0.0763585i | 0.938905 | − | 0.344177i | \(-0.111842\pi\) |
−0.907276 | + | 0.420536i | \(0.861842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 546.470 | + | 226.355i | 0.697330 | + | 0.288843i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1233.34 | + | 1233.34i | −1.51986 | + | 1.51986i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −351.137 | − | 351.137i | −0.418207 | − | 0.418207i | 0.466378 | − | 0.884585i | \(-0.345559\pi\) |
−0.884585 | + | 0.466378i | \(0.845559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −165.654 | + | 399.925i | −0.190827 | + | 0.460698i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1229.02 | − | 509.078i | 1.37036 | − | 0.567623i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1060.17 | 1.14496 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1302.03 | 1.36290 | 0.681452 | − | 0.731863i | \(-0.261349\pi\) | ||||
0.681452 | + | 0.731863i | \(0.261349\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 799.382 | − | 331.115i | 0.811525 | − | 0.336145i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 255.210 | − | 616.132i | 0.251429 | − | 0.607004i | −0.746891 | − | 0.664947i | \(-0.768454\pi\) |
0.998320 | + | 0.0579428i | \(0.0184541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −119.916 | − | 119.916i | −0.114715 | − | 0.114715i | 0.647419 | − | 0.762134i | \(-0.275848\pi\) |
−0.762134 | + | 0.647419i | \(0.775848\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −668.891 | + | 668.891i | −0.621687 | + | 0.621687i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 659.373 | + | 273.121i | 0.595738 | + | 0.246763i | 0.660117 | − | 0.751163i | \(-0.270507\pi\) |
−0.0643789 | + | 0.997926i | \(0.520507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −471.995 | − | 1139.50i | −0.414761 | − | 1.00132i | −0.983842 | − | 0.179040i | \(-0.942701\pi\) |
0.569081 | − | 0.822281i | \(-0.307299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 622.887i | − | 0.532629i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 832.434i | 0.692998i | 0.938050 | + | 0.346499i | \(0.112630\pi\) | ||||
−0.938050 | + | 0.346499i | \(0.887370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 146.226 | + | 353.021i | 0.118571 | + | 0.286255i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 340.184 | + | 140.909i | 0.268803 | + | 0.111342i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1040.95 | − | 1040.95i | 0.801880 | − | 0.801880i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1099.20 | + | 1099.20i | 0.825843 | + | 0.825843i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −130.793 | + | 315.761i | −0.0958795 | + | 0.231473i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1350.41 | + | 559.359i | −0.966276 | + | 0.400245i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −187.556 | −0.131046 | −0.0655232 | − | 0.997851i | \(-0.520872\pi\) | ||||
−0.0655232 | + | 0.997851i | \(0.520872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1319.28 | −0.900435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1001.26 | + | 414.737i | −0.667793 | + | 0.276609i | −0.690714 | − | 0.723128i | \(-0.742703\pi\) |
0.0229207 | + | 0.999737i | \(0.492703\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1009.74 | − | 2437.72i | 0.658310 | − | 1.58930i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −384.759 | − | 384.759i | −0.245294 | − | 0.245294i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1273.38 | + | 1273.38i | −0.794101 | + | 0.794101i | −0.982158 | − | 0.188057i | \(-0.939781\pi\) |
0.188057 | + | 0.982158i | \(0.439781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2129.20 | + | 881.945i | 1.29926 | + | 0.538170i | 0.921731 | − | 0.387830i | \(-0.126775\pi\) |
0.377525 | + | 0.925999i | \(0.376775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 208.475 | + | 503.302i | 0.124516 | + | 0.300608i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1227.95i | 0.718085i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2021.25i | − | 1.15763i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 39.1494 | + | 94.5150i | 0.0219659 | + | 0.0530304i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 139.146 | + | 57.6361i | 0.0765051 | + | 0.0316895i | 0.420608 | − | 0.907243i | \(-0.361817\pi\) |
−0.344103 | + | 0.938932i | \(0.611817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2027.42 | − | 2027.42i | 1.09264 | − | 1.09264i | 0.0973988 | − | 0.995245i | \(-0.468948\pi\) |
0.995245 | − | 0.0973988i | \(-0.0310522\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −885.452 | − | 885.452i | −0.467873 | − | 0.467873i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −589.940 | + | 1424.24i | −0.305710 | + | 0.738050i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 816.713 | − | 338.294i | 0.415164 | − | 0.171967i | −0.165317 | − | 0.986241i | \(-0.552865\pi\) |
0.580481 | + | 0.814274i | \(0.302865\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3800.31 | −1.89550 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 950.997 | 0.465522 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 953.491 | − | 394.949i | 0.458179 | − | 0.189784i | −0.141642 | − | 0.989918i | \(-0.545238\pi\) |
0.599821 | + | 0.800134i | \(0.295238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1026.90 | + | 2479.15i | −0.484508 | + | 1.16971i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 896.156 | + | 896.156i | 0.415249 | + | 0.415249i | 0.883563 | − | 0.468313i | \(-0.155138\pi\) |
−0.468313 | + | 0.883563i | \(0.655138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1184.01 | − | 1184.01i | 0.538919 | − | 0.538919i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2073.57 | − | 858.900i | −0.927308 | − | 0.384104i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −268.247 | − | 647.606i | −0.117887 | − | 0.284604i | 0.853911 | − | 0.520419i | \(-0.174224\pi\) |
−0.971798 | + | 0.235815i | \(0.924224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1270.82i | 0.548943i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1299.56i | 0.551870i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −842.440 | − | 2033.83i | −0.351770 | − | 0.849249i | −0.996402 | − | 0.0847553i | \(-0.972989\pi\) |
0.644631 | − | 0.764494i | \(-0.277011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1394.35 | + | 577.557i | 0.572602 | + | 0.237180i | 0.650146 | − | 0.759809i | \(-0.274708\pi\) |
−0.0775438 | + | 0.996989i | \(0.524708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2373.06 | + | 2373.06i | −0.958589 | + | 0.958589i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 510.408 | + | 510.408i | 0.202843 | + | 0.202843i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1598.09 | − | 3858.13i | 0.624941 | − | 1.50874i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1251.16 | + | 518.247i | −0.481526 | + | 0.199455i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −779.721 | −0.295386 | −0.147693 | − | 0.989033i | \(-0.547185\pi\) | ||||
−0.147693 | + | 0.989033i | \(0.547185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4175.15 | −1.55717 | −0.778585 | − | 0.627539i | \(-0.784062\pi\) | ||||
−0.778585 | + | 0.627539i | \(0.784062\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1055.02 | + | 437.004i | −0.387444 | + | 0.160485i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1793.41 | + | 4329.67i | −0.648604 | + | 1.56587i | 0.166174 | + | 0.986096i | \(0.446859\pi\) |
−0.814778 | + | 0.579773i | \(0.803141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1333.84 | − | 1333.84i | −0.475144 | − | 0.475144i | 0.428431 | − | 0.903575i | \(-0.359067\pi\) |
−0.903575 | + | 0.428431i | \(0.859067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 516.330 | − | 516.330i | 0.181190 | − | 0.181190i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4647.61 | − | 1925.10i | −1.60689 | − | 0.665595i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −151.568 | − | 365.917i | −0.0516388 | − | 0.124667i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 808.935i | − | 0.271618i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7484.88i | − | 2.47722i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1172.83 | + | 2831.46i | 0.382658 | + | 0.923818i | 0.991450 | + | 0.130488i | \(0.0416544\pi\) |
−0.608792 | + | 0.793330i | \(0.708346\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4464.13 | − | 1849.11i | −1.43604 | − | 0.594829i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1081.05 | − | 1081.05i | 0.342916 | − | 0.342916i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2712.98 | + | 2712.98i | 0.848707 | + | 0.848707i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 868.385 | − | 2096.47i | 0.267945 | − | 0.646877i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1641.86 | − | 680.080i | 0.499744 | − | 0.207001i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2462.13 | 0.739356 | 0.369678 | − | 0.929160i | \(-0.379468\pi\) | ||||
0.369678 | + | 0.929160i | \(0.379468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1080.98 | 0.320291 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2912.19 | + | 1206.27i | −0.851494 | + | 0.352700i | −0.765375 | − | 0.643585i | \(-0.777446\pi\) |
−0.0861187 | + | 0.996285i | \(0.527446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −578.212 | + | 1395.93i | −0.166853 | + | 0.402819i | −0.985085 | − | 0.172070i | \(-0.944955\pi\) |
0.818232 | + | 0.574889i | \(0.194955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4722.43 | + | 4722.43i | 1.34508 | + | 1.34508i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3037.56 | − | 3037.56i | 0.854065 | − | 0.854065i | −0.136566 | − | 0.990631i | \(-0.543607\pi\) |
0.990631 | + | 0.136566i | \(0.0436067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −583.247 | − | 241.589i | −0.161901 | − | 0.0670618i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1946.62 | − | 4699.57i | −0.533531 | − | 1.28806i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 68.1814i | 0.0184531i | 0.999957 | + | 0.00922654i | \(0.00293694\pi\) | ||||
−0.999957 | + | 0.00922654i | \(0.997063\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6115.20i | 1.63450i | 0.576282 | + | 0.817251i | \(0.304503\pi\) | ||||
−0.576282 | + | 0.817251i | \(0.695497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1533.55 | + | 3702.32i | 0.404845 | + | 0.977382i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −109.528 | − | 45.3679i | −0.0285611 | − | 0.0118304i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2252.31 | − | 2252.31i | 0.580207 | − | 0.580207i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 290.149 | + | 290.149i | 0.0738451 | + | 0.0738451i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −183.755 | + | 443.623i | −0.0462092 | + | 0.111559i | −0.945299 | − | 0.326206i | \(-0.894230\pi\) |
0.899090 | + | 0.437765i | \(0.144230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2492.36 | − | 1032.37i | 0.619341 | − | 0.256540i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3883.54 | 0.953712 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.1354 | −0.00634350 | −0.00317175 | − | 0.999995i | \(-0.501010\pi\) | ||||
−0.00317175 | + | 0.999995i | \(0.501010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1659.75 | − | 687.490i | 0.398192 | − | 0.164937i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1637.53 | + | 3953.34i | −0.388354 | + | 0.937570i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2404.98 | + | 2404.98i | 0.563869 | + | 0.563869i | 0.930404 | − | 0.366535i | \(-0.119456\pi\) |
−0.366535 | + | 0.930404i | \(0.619456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3114.06 | − | 3114.06i | 0.721869 | − | 0.721869i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3012.20 | − | 1247.69i | −0.690425 | − | 0.285983i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3217.65 | + | 7768.09i | 0.729306 | + | 1.76070i | 0.644896 | + | 0.764270i | \(0.276901\pi\) |
0.0844104 | + | 0.996431i | \(0.473099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4099.60i | 0.918941i | 0.888193 | + | 0.459471i | \(0.151961\pi\) | ||||
−0.888193 | + | 0.459471i | \(0.848039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2842.10i | 0.630080i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1379.56 | + | 3330.55i | 0.302511 | + | 0.730327i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −62.6281 | − | 25.9414i | −0.0135847 | − | 0.00562696i | 0.375881 | − | 0.926668i | \(-0.377340\pi\) |
−0.389465 | + | 0.921041i | \(0.627340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2307.71 | − | 2307.71i | 0.495194 | − | 0.495194i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 371.515 | + | 371.515i | 0.0788709 | + | 0.0788709i | 0.745442 | − | 0.666571i | \(-0.232239\pi\) |
−0.666571 | + | 0.745442i | \(0.732239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1150.78 | − | 2778.24i | 0.241721 | − | 0.583566i | −0.755733 | − | 0.654880i | \(-0.772719\pi\) |
0.997454 | + | 0.0713139i | \(0.0227192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6430.82 | − | 2663.73i | 1.33659 | − | 0.553634i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −985.737 | −0.202739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1130.69 | −0.230143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7897.95 | − | 3271.44i | 1.59102 | − | 0.659021i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1547.04 | − | 3734.89i | 0.308461 | − | 0.744691i | −0.691294 | − | 0.722573i | \(-0.742959\pi\) |
0.999755 | − | 0.0221175i | \(-0.00704081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1064.89 | − | 1064.89i | −0.210171 | − | 0.210171i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2716.43 | + | 2716.43i | −0.530718 | + | 0.530718i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1060.64 | + | 439.333i | 0.205146 | + | 0.0849743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1456.11 | − | 3515.36i | −0.278833 | − | 0.673163i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4378.60i | − | 0.830178i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3889.09i | − | 0.730126i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2115.16 | − | 5106.46i | −0.393221 | − | 0.949319i | −0.989234 | − | 0.146344i | \(-0.953249\pi\) |
0.596013 | − | 0.802975i | \(-0.296751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1028.69 | − | 426.097i | −0.189386 | − | 0.0784461i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3571.19 | + | 3571.19i | −0.651137 | + | 0.651137i | −0.953267 | − | 0.302130i | \(-0.902302\pi\) |
0.302130 | + | 0.953267i | \(0.402302\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −304.665 | − | 304.665i | −0.0550182 | − | 0.0550182i | 0.679062 | − | 0.734081i | \(-0.262387\pi\) |
−0.734081 | + | 0.679062i | \(0.762387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −888.101 | + | 2144.07i | −0.158853 | + | 0.383506i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6782.93 | + | 2809.58i | −1.20179 | + | 0.497798i | −0.891577 | − | 0.452869i | \(-0.850400\pi\) |
−0.310213 | + | 0.950667i | \(0.600400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14270.2 | −2.50464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4685.89 | 0.814770 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10007.8 | + | 4145.39i | −1.72400 | + | 0.714104i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −587.083 | + | 1417.34i | −0.100202 | + | 0.241908i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5726.10 | − | 5726.10i | −0.968362 | − | 0.968362i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1111.01 | + | 1111.01i | −0.186175 | + | 0.186175i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3670.23 | + | 1520.26i | 0.609468 | + | 0.252450i | 0.666001 | − | 0.745951i | \(-0.268005\pi\) |
−0.0565331 | + | 0.998401i | \(0.518005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −584.792 | − | 1411.81i | −0.0962354 | − | 0.232333i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 846.186i | 0.138006i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5082.79i | − | 0.821593i | −0.911727 | − | 0.410797i | \(-0.865251\pi\) | ||
0.911727 | − | 0.410797i | \(-0.134749\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2091.54 | + | 5049.42i | 0.335094 | + | 0.808988i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10055.3 | + | 4165.03i | 1.59684 | + | 0.661434i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4384.12 | − | 4384.12i | 0.690146 | − | 0.690146i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1773.97 | + | 1773.97i | 0.276833 | + | 0.276833i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1154.04 | − | 2786.09i | 0.178536 | − | 0.431023i | −0.809124 | − | 0.587638i | \(-0.800058\pi\) |
0.987660 | + | 0.156615i | \(0.0500580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2241.53 | + | 928.474i | −0.343801 | + | 0.142407i | −0.547901 | − | 0.836543i | \(-0.684573\pi\) |
0.204100 | + | 0.978950i | \(0.434573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1634.83 | −0.248606 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8284.27 | −1.24908 | −0.624542 | − | 0.780991i | \(-0.714715\pi\) | ||||
−0.624542 | + | 0.780991i | \(0.714715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5173.22 | − | 2142.82i | 0.773425 | − | 0.320363i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3698.80 | − | 8929.70i | 0.548351 | − | 1.32384i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1889.18 | − | 1889.18i | −0.277736 | − | 0.277736i | 0.554469 | − | 0.832205i | \(-0.312922\pi\) |
−0.832205 | + | 0.554469i | \(0.812922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8878.78 | + | 8878.78i | −1.29447 | + | 1.29447i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9429.36 | + | 3905.77i | 1.36340 | + | 0.564738i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1006.32 | + | 2429.47i | 0.144310 | + | 0.348395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7429.67i | 1.05675i | 0.849012 | + | 0.528373i | \(0.177198\pi\) | ||||
−0.849012 | + | 0.528373i | \(0.822802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 838.486i | 0.118292i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4194.46 | − | 10126.3i | −0.586969 | − | 1.41707i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1661.51 | + | 688.219i | 0.230642 | + | 0.0955351i | 0.495012 | − | 0.868886i | \(-0.335164\pi\) |
−0.264369 | + | 0.964421i | \(0.585164\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6785.98 | + | 6785.98i | −0.934471 | + | 0.934471i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4294.13 | − | 4294.13i | −0.586628 | − | 0.586628i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3773.37 | + | 9109.72i | −0.511412 | + | 1.23466i | 0.431651 | + | 0.902041i | \(0.357931\pi\) |
−0.943062 | + | 0.332616i | \(0.892069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1137.69 | + | 471.245i | −0.152980 | + | 0.0633664i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13137.5 | 1.75273 | 0.876366 | − | 0.481646i | \(-0.159961\pi\) | ||||
0.876366 | + | 0.481646i | \(0.159961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7739.35 | −1.02450 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2990.23 | + | 1238.59i | −0.392770 | + | 0.162691i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1767.36 | − | 4266.78i | 0.230357 | − | 0.556130i | −0.765863 | − | 0.643004i | \(-0.777688\pi\) |
0.996219 | + | 0.0868742i | \(0.0276878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2760.71 | − | 2760.71i | −0.357072 | − | 0.357072i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5031.47 | + | 5031.47i | −0.645812 | + | 0.645812i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5446.04 | + | 2255.83i | 0.693722 | + | 0.287349i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5649.54 | − | 13639.2i | −0.714212 | − | 1.72426i | −0.689197 | − | 0.724574i | \(-0.742037\pi\) |
−0.0250151 | − | 0.999687i | \(-0.507963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 17323.9i | − | 2.17363i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5422.25i | 0.675247i | 0.941281 | + | 0.337624i | \(0.109623\pi\) | ||||
−0.941281 | + | 0.337624i | \(0.890377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1772.46 | + | 4279.11i | 0.219089 | + | 0.528927i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6357.70 | − | 2633.45i | −0.780042 | − | 0.323104i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3603.53 | − | 3603.53i | 0.438871 | − | 0.438871i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2622.89 | − | 2622.89i | −0.317099 | − | 0.317099i | 0.530553 | − | 0.847652i | \(-0.321984\pi\) |
−0.847652 | + | 0.530553i | \(0.821984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4524.68 | + | 10923.5i | −0.543031 | + | 1.31099i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3462.82 | + | 1434.35i | −0.412577 | + | 0.170895i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −475.509 | −0.0562454 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15131.4 | 1.77695 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1293.33 | − | 535.717i | 0.150796 | − | 0.0624617i | −0.306009 | − | 0.952029i | \(-0.598994\pi\) |
0.456805 | + | 0.889567i | \(0.348994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −871.790 | + | 2104.69i | −0.100923 | + | 0.243649i | −0.966274 | − | 0.257517i | \(-0.917096\pi\) |
0.865351 | + | 0.501166i | \(0.167096\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 945.041 | + | 945.041i | 0.108628 | + | 0.108628i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3689.15 | − | 3689.15i | 0.421059 | − | 0.421059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8942.46 | − | 3704.09i | −1.01348 | − | 0.419797i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3085.29 | + | 7448.55i | 0.347224 | + | 0.838274i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5681.29i | − | 0.634938i | −0.948269 | − | 0.317469i | \(-0.897167\pi\) | ||
0.948269 | − | 0.317469i | \(-0.102833\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9616.41i | 1.06729i | 0.845710 | + | 0.533643i | \(0.179178\pi\) | ||||
−0.845710 | + | 0.533643i | \(0.820822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5078.51 | − | 12260.6i | −0.559761 | − | 1.35138i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6465.09 | − | 2677.93i | −0.707705 | − | 0.293141i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10175.7 | + | 10175.7i | −1.10629 | + | 1.10629i | −0.112657 | + | 0.993634i | \(0.535936\pi\) |
−0.993634 | + | 0.112657i | \(0.964064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 177.469 | + | 177.469i | 0.0191630 | + | 0.0191630i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −925.474 | + | 2234.29i | −0.0992564 | + | 0.239626i | −0.965706 | − | 0.259639i | \(-0.916397\pi\) |
0.866449 | + | 0.499265i | \(0.166397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3490.65 | − | 1445.88i | 0.371849 | − | 0.154025i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 988.852 | 0.104633 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8501.56 | 0.893571 | 0.446785 | − | 0.894641i | \(-0.352569\pi\) | ||||
0.446785 | + | 0.894641i | \(0.352569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2583.41 | + | 1070.08i | −0.269729 | + | 0.111726i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7204.03 | − | 17392.1i | 0.747185 | − | 1.80386i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2328.89 | − | 2328.89i | −0.239956 | − | 0.239956i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7829.53 | − | 7829.53i | 0.801422 | − | 0.801422i | −0.181895 | − | 0.983318i | \(-0.558223\pi\) |
0.983318 | + | 0.181895i | \(0.0582232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5136.53 | + | 2127.62i | 0.522337 | + | 0.216359i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4138.96 | + | 9992.34i | 0.418158 | + | 1.00952i | 0.982881 | + | 0.184241i | \(0.0589828\pi\) |
−0.564723 | + | 0.825280i | \(0.691017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13379.7i | 1.34300i | 0.741004 | + | 0.671501i | \(0.234350\pi\) | ||||
−0.741004 | + | 0.671501i | \(0.765650\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10121.5i | 1.00940i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2256.68 | − | 5448.12i | −0.223612 | − | 0.539848i | 0.771763 | − | 0.635910i | \(-0.219375\pi\) |
−0.995375 | + | 0.0960626i | \(0.969375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1945.70 | + | 805.934i | 0.191565 | + | 0.0793488i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4104.08 | − | 4104.08i | 0.401499 | − | 0.401499i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7632.31 | − | 7632.31i | −0.741932 | − | 0.741932i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3578.53 | − | 8639.33i | 0.345672 | − | 0.834525i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8613.63 | + | 3567.88i | −0.826816 | + | 0.342478i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15500.6 | 1.47858 | 0.739289 | − | 0.673389i | \(-0.235162\pi\) | ||||
0.739289 | + | 0.673389i | \(0.235162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2168.71 | 0.205582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5768.61 | − | 2389.44i | 0.543438 | − | 0.225100i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3791.07 | + | 9152.46i | −0.354936 | + | 0.856891i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3384.07 | + | 3384.07i | 0.314880 | + | 0.314880i | 0.846797 | − | 0.531917i | \(-0.178528\pi\) |
−0.531917 | + | 0.846797i | \(0.678528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4791.40 | − | 4791.40i | 0.443098 | − | 0.443098i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5913.07 | + | 2449.27i | 0.543489 | + | 0.225121i | 0.637500 | − | 0.770451i | \(-0.279969\pi\) |
−0.0940105 | + | 0.995571i | \(0.529969\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7903.35 | + | 19080.4i | 0.722006 | + | 1.74308i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6583.23i | 0.597766i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13936.0i | − | 1.25778i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5163.06 | + | 12464.7i | 0.463187 | + | 1.11823i | 0.967081 | + | 0.254467i | \(0.0819001\pi\) |
−0.503894 | + | 0.863765i | \(0.668100\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7687.60 | + | 3184.31i | 0.685542 | + | 0.283961i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6921.39 | + | 6921.39i | −0.613537 | + | 0.613537i | −0.943866 | − | 0.330329i | \(-0.892840\pi\) |
0.330329 | + | 0.943866i | \(0.392840\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3587.93 | + | 3587.93i | 0.316160 | + | 0.316160i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4207.12 | − | 10156.9i | 0.368530 | − | 0.889710i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14532.1 | − | 6019.39i | 1.26547 | − | 0.524174i | 0.353885 | − | 0.935289i | \(-0.384860\pi\) |
0.911584 | + | 0.411115i | \(0.134860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6544.71 | 0.566577 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9965.00 | 0.857633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1192.09 | − | 493.779i | 0.101999 | − | 0.0422495i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1705.64 | + | 4117.78i | −0.145095 | + | 0.350290i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3254.29 | − | 3254.29i | −0.275236 | − | 0.275236i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6505.72 | + | 6505.72i | −0.547065 | + | 0.547065i | −0.925591 | − | 0.378526i | \(-0.876431\pi\) |
0.378526 | + | 0.925591i | \(0.376431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18929.1 | − | 7840.67i | −1.58262 | − | 0.655543i | −0.593794 | − | 0.804617i | \(-0.702370\pi\) |
−0.988826 | + | 0.149075i | \(0.952370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3193.01 | + | 7708.61i | 0.265437 | + | 0.640822i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15751.4i | − | 1.30198i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9644.85i | 0.792706i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1220.08 | + | 2945.54i | 0.0997119 | + | 0.240726i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1099.39 | − | 455.382i | −0.0893431 | − | 0.0370071i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3839.73 | + | 3839.73i | −0.310292 | + | 0.310292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10220.2 | − | 10220.2i | −0.821295 | − | 0.821295i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −320.301 | + | 773.276i | −0.0255962 | + | 0.0617947i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14495.4 | + | 6004.19i | −1.15195 | + | 0.477154i | −0.875188 | − | 0.483783i | \(-0.839262\pi\) |
−0.276765 | + | 0.960938i | \(0.589262\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9909.05 | 0.783127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9384.21 | 0.737569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17281.4 | − | 7158.21i | 1.35082 | − | 0.559530i | 0.414303 | − | 0.910139i | \(-0.364025\pi\) |
0.936522 | + | 0.350609i | \(0.114025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3150.76 | + | 7606.62i | −0.244939 | + | 0.591334i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26174.6 | + | 26174.6i | 2.02373 | + | 2.02373i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10374.0 | − | 10374.0i | 0.797732 | − | 0.797732i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4378.49 | + | 1813.63i | 0.334877 | + | 0.138711i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3341.04 | − | 8065.99i | −0.254155 | − | 0.613585i | 0.744376 | − | 0.667761i | \(-0.232747\pi\) |
−0.998531 | + | 0.0541753i | \(0.982747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4593.35i | − | 0.347546i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 27418.1i | − | 2.06345i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4945.85 | − | 11940.3i | −0.370236 | − | 0.893828i | −0.993710 | − | 0.111984i | \(-0.964279\pi\) |
0.623474 | − | 0.781844i | \(-0.285721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5851.47 | − | 2423.76i | −0.435705 | − | 0.180475i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12110.6 | + | 12110.6i | −0.896994 | + | 0.896994i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8205.09 | − | 8205.09i | −0.604526 | − | 0.604526i | 0.336984 | − | 0.941510i | \(-0.390593\pi\) |
−0.941510 | + | 0.336984i | \(0.890593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4078.90 | + | 9847.33i | −0.298943 | + | 0.721712i | 0.701020 | + | 0.713141i | \(0.252728\pi\) |
−0.999963 | + | 0.00857103i | \(0.997272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4729.67 | + | 1959.09i | −0.344825 | + | 0.142831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3370.35 | 0.244441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4675.49 | −0.337337 | −0.168668 | − | 0.985673i | \(-0.553947\pi\) | ||||
−0.168668 | + | 0.985673i | \(0.553947\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25325.8 | + | 10490.3i | −1.81780 | + | 0.752958i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −452.890 | + | 1093.37i | −0.0323391 | + | 0.0780736i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21985.6 | − | 21985.6i | −1.56183 | − | 1.56183i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1980.99 | + | 1980.99i | −0.140007 | + | 0.140007i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3400.03 | − | 1408.34i | −0.239070 | − | 0.0990260i | 0.259932 | − | 0.965627i | \(-0.416300\pi\) |
−0.499002 | + | 0.866601i | \(0.666300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10803.9 | − | 26083.0i | −0.755804 | − | 1.82467i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30769.2i | 2.14158i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15975.1i | 1.10627i | 0.833090 | + | 0.553137i | \(0.186569\pi\) | ||||
−0.833090 | + | 0.553137i | \(0.813431\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4286.32 | + | 10348.1i | 0.295331 | + | 0.712993i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11442.3 | − | 4739.54i | −0.784422 | − | 0.324918i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14655.9 | − | 14655.9i | 0.999707 | − | 0.999707i | −0.000292806 | − | 1.00000i | \(-0.500093\pi\) |
1.00000 | 0.000292806i | \(9.32030e-5\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12665.9 | + | 12665.9i | 0.859656 | + | 0.859656i | 0.991297 | − | 0.131641i | \(-0.0420247\pi\) |
−0.131641 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 685.542 | − | 1655.05i | 0.0462976 | − | 0.111772i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10927.1 | + | 4526.16i | −0.734299 | + | 0.304156i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18257.0 | −1.22080 | −0.610402 | − | 0.792092i | \(-0.708992\pi\) | ||||
−0.610402 | + | 0.792092i | \(0.708992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33028.7 | −2.19768 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1752.35 | + | 725.849i | −0.116027 | + | 0.0480601i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2056.78 | + | 4965.49i | −0.135518 | + | 0.327169i | −0.977041 | − | 0.213053i | \(-0.931659\pi\) |
0.841523 | + | 0.540221i | \(0.181659\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1838.77 | − | 1838.77i | −0.120564 | − | 0.120564i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2198.69 | − | 2198.69i | 0.143462 | − | 0.143462i | −0.631728 | − | 0.775190i | \(-0.717654\pi\) |
0.775190 | + | 0.631728i | \(0.217654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14373.8 | − | 5953.83i | −0.933331 | − | 0.386598i | −0.136390 | − | 0.990655i | \(-0.543550\pi\) |
−0.796941 | + | 0.604057i | \(0.793550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1374.45 | + | 3318.21i | 0.0888159 | + | 0.214421i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 9403.41i | − | 0.604719i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 2732.38i | − | 0.174872i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18806.2 | − | 45402.2i | −1.19784 | − | 2.89185i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6813.96 | − | 2822.43i | −0.431940 | − | 0.178915i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21029.2 | − | 21029.2i | 1.32672 | − | 1.32672i | 0.418502 | − | 0.908216i | \(-0.362555\pi\) |
0.908216 | − | 0.418502i | \(-0.137445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14228.4 | + | 14228.4i | 0.893410 | + | 0.893410i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 546.098 | − | 1318.40i | 0.0341279 | − | 0.0823921i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −329.074 | + | 136.307i | −0.0204684 | + | 0.00847830i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11854.3 | −0.733876 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22576.4 | 1.39113 | 0.695564 | − | 0.718464i | \(-0.255155\pi\) | ||||
0.695564 | + | 0.718464i | \(0.255155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15365.6 | + | 6364.66i | −0.942398 | + | 0.390354i | −0.800368 | − | 0.599509i | \(-0.795363\pi\) |
−0.142029 | + | 0.989862i | \(0.545363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3841.29 | − | 9273.69i | 0.234497 | − | 0.566126i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2866.06 | + | 2866.06i | 0.174152 | + | 0.174152i | 0.788801 | − | 0.614649i | \(-0.210702\pi\) |
−0.614649 | + | 0.788801i | \(0.710702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7518.24 | + | 7518.24i | −0.454725 | + | 0.454725i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23273.1 | + | 9640.03i | 1.40114 | + | 0.580373i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1656.18 | − | 3998.36i | −0.0992514 | − | 0.239614i | 0.866453 | − | 0.499259i | \(-0.166394\pi\) |
−0.965704 | + | 0.259645i | \(0.916394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8245.81i | − | 0.491894i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5567.05i | − | 0.330580i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7707.07 | + | 18606.5i | 0.455576 | + | 1.09986i | 0.970170 | + | 0.242424i | \(0.0779426\pi\) |
−0.514594 | + | 0.857434i | \(0.672057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25591.1 | + | 10600.2i | 1.50587 | + | 0.623751i | 0.974700 | − | 0.223515i | \(-0.0717533\pi\) |
0.531168 | + | 0.847267i | \(0.321753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8250.53 | − | 8250.53i | 0.483294 | − | 0.483294i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14195.6 | + | 14195.6i | 0.827791 | + | 0.827791i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5105.58 | + | 12326.0i | −0.296385 | + | 0.715537i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14934.9 | − | 6186.24i | 0.863105 | − | 0.357510i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27457.3 | −1.57970 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32715.5 | −1.87383 | −0.936917 | − | 0.349553i | \(-0.886333\pi\) | ||||
−0.936917 | + | 0.349553i | \(0.886333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4434.14 | + | 1836.68i | −0.252844 | + | 0.104732i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −249.757 | + | 602.967i | −0.0141786 | + | 0.0342303i | −0.930810 | − | 0.365503i | \(-0.880897\pi\) |
0.916632 | + | 0.399733i | \(0.130897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17434.2 | + | 17434.2i | 0.985365 | + | 0.985365i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14634.1 | + | 14634.1i | −0.823466 | + | 0.823466i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1024.16 | + | 424.220i | 0.0573767 | + | 0.0237662i | 0.411187 | − | 0.911551i | \(-0.365114\pi\) |
−0.353811 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5243.38 | − | 12658.6i | −0.292466 | − | 0.706075i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9920.29i | 0.550921i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13231.6i | − | 0.731615i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6429.36 | + | 15521.9i | 0.353957 | + | 0.854528i | 0.996124 | + | 0.0879632i | \(0.0280358\pi\) |
−0.642166 | + | 0.766565i | \(0.721964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15137.3 | + | 6270.08i | 0.829753 | + | 0.343695i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12399.0 | + | 12399.0i | −0.676721 | + | 0.676721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2861.56 | + | 2861.56i | 0.155508 | + | 0.155508i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10793.3 | − | 26057.4i | 0.584037 | − | 1.40999i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20337.8 | − | 8424.21i | 1.09579 | − | 0.453892i | 0.239769 | − | 0.970830i | \(-0.422928\pi\) |
0.856023 | + | 0.516938i | \(0.172928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13219.3 | −0.709209 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4144.90 | −0.221427 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11667.2 | − | 4832.72i | 0.620638 | − | 0.257077i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11697.5 | + | 28240.4i | −0.619620 | + | 1.49589i | 0.232527 | + | 0.972590i | \(0.425301\pi\) |
−0.852146 | + | 0.523304i | \(0.824699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8824.29 | − | 8824.29i | −0.465452 | − | 0.465452i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7195.13 | − | 7195.13i | 0.377924 | − | 0.377924i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8631.68 | − | 3575.36i | −0.451478 | − | 0.187008i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 171.310 | + | 413.578i | 0.00892284 | + | 0.0215416i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2930.75i | 0.152015i | 0.997107 | + | 0.0760074i | \(0.0242173\pi\) | ||||
−0.997107 | + | 0.0760074i | \(0.975783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3211.34i | − | 0.165876i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15364.8 | + | 37093.9i | 0.790350 | + | 1.90807i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16471.2 | − | 6822.61i | −0.843760 | − | 0.349497i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11618.1 | − | 11618.1i | 0.592696 | − | 0.592696i | −0.345663 | − | 0.938359i | \(-0.612346\pi\) |
0.938359 | + | 0.345663i | \(0.112346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1336.91 | + | 1336.91i | 0.0679218 | + | 0.0679218i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5977.94 | + | 14432.0i | −0.302465 | + | 0.730215i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8786.76 | − | 3639.59i | 0.442764 | − | 0.183399i | −0.150152 | − | 0.988663i | \(-0.547976\pi\) |
0.592917 | + | 0.805264i | \(0.297976\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −778.369 | −0.0390620 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5974.15 | 0.298590 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30367.3 | − | 12578.6i | 1.51161 | − | 0.626130i | 0.535721 | − | 0.844395i | \(-0.320040\pi\) |
0.975890 | + | 0.218265i | \(0.0700397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8003.13 | − | 19321.3i | 0.396764 | − | 0.957874i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28118.1 | − | 28118.1i | −1.38836 | − | 1.38836i | −0.828765 | − | 0.559596i | \(-0.810956\pi\) |
−0.559596 | − | 0.828765i | \(-0.689044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −810.288 | + | 810.288i | −0.0398479 | + | 0.0398479i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 930.043 | + | 385.236i | 0.0455535 | + | 0.0188689i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5171.89 | + | 12486.1i | 0.252305 | + | 0.609119i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2199.78i | − | 0.106886i | −0.998571 | − | 0.0534428i | \(-0.982981\pi\) | ||
0.998571 | − | 0.0534428i | \(-0.0170195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3152.65i | 0.152575i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8348.32 | + | 20154.6i | 0.402419 | + | 0.971525i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1609.12 | + | 666.518i | 0.0772581 | + | 0.0320013i | 0.420978 | − | 0.907071i | \(-0.361687\pi\) |
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12524.4 | − | 12524.4i | 0.598955 | − | 0.598955i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13159.3 | − | 13159.3i | −0.626837 | − | 0.626837i | 0.320434 | − | 0.947271i | \(-0.396171\pi\) |
−0.947271 | + | 0.320434i | \(0.896171\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8937.81 | − | 21577.8i | 0.424077 | − | 1.02381i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8802.28 | − | 3646.02i | 0.416009 | − | 0.172317i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4524.70 | −0.213008 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13781.4 | −0.646253 | −0.323127 | − | 0.946356i | \(-0.604734\pi\) | ||||
−0.323127 | + | 0.946356i | \(0.604734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −158.533 | + | 65.6667i | −0.00740524 | + | 0.00306735i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −904.546 | + | 2183.77i | −0.0420883 | + | 0.101610i | −0.943526 | − | 0.331299i | \(-0.892513\pi\) |
0.901437 | + | 0.432909i | \(0.142513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9614.87 | + | 9614.87i | 0.445647 | + | 0.445647i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8340.43 | − | 8340.43i | 0.385085 | − | 0.385085i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6701.26 | + | 2775.75i | 0.308213 | + | 0.127666i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15128.5 | − | 36523.4i | −0.693137 | − | 1.67338i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 18998.7i | − | 0.867124i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6725.96i | 0.305809i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7363.51 | + | 17777.1i | 0.333521 | + | 0.805190i | 0.998307 | + | 0.0581569i | \(0.0185224\pi\) |
−0.664787 | + | 0.747033i | \(0.731478\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20630.9 | + | 8545.61i | 0.930901 | + | 0.385592i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11146.2 | + | 11146.2i | −0.501030 | + | 0.501030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8262.32 | − | 8262.32i | −0.369992 | − | 0.369992i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11065.2 | − | 26713.7i | 0.493637 | − | 1.19175i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2646.36 | + | 1096.16i | −0.117615 | + | 0.0487177i | −0.440715 | − | 0.897647i | \(-0.645275\pi\) |
0.323100 | + | 0.946365i | \(0.395275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6450.42 | 0.285607 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7998.71 | −0.352835 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17152.3 | − | 7104.71i | 0.753787 | − | 0.312229i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2768.97 | + | 6684.89i | −0.121234 | + | 0.292685i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39035.6 | + | 39035.6i | 1.70275 | + | 1.70275i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25414.2 | + | 25414.2i | −1.10447 | + | 1.10447i | −0.110607 | + | 0.993864i | \(0.535280\pi\) |
−0.993864 | + | 0.110607i | \(0.964720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3623.77 | − | 1501.01i | −0.156902 | − | 0.0649910i | 0.302850 | − | 0.953038i | \(-0.402062\pi\) |
−0.459752 | + | 0.888047i | \(0.652062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10300.5 | + | 24867.6i | 0.444347 | + | 1.07275i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7852.38i | 0.337493i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27998.5i | 1.19895i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2668.28 | + | 6441.80i | 0.113843 | + | 0.274841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12700.5 | − | 5260.71i | −0.539890 | − | 0.223630i | 0.0960388 | − | 0.995378i | \(-0.469383\pi\) |
−0.635929 | + | 0.771748i | \(0.719383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12604.5 | + | 12604.5i | −0.533857 | + | 0.533857i | −0.921718 | − | 0.387861i | \(-0.873214\pi\) |
0.387861 | + | 0.921718i | \(0.373214\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16736.4 | + | 16736.4i | 0.706287 | + | 0.706287i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 759.345 | − | 1833.22i | 0.0319287 | − | 0.0770826i | −0.907111 | − | 0.420892i | \(-0.861717\pi\) |
0.939040 | + | 0.343809i | \(0.111717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33918.6 | − | 14049.5i | 1.42104 | − | 0.588614i | 0.465918 | − | 0.884828i | \(-0.345724\pi\) |
0.955122 | + | 0.296214i | \(0.0957241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −445.072 | −0.0185793 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1211.32 | 0.0503840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8908.70 | + | 3690.10i | −0.369219 | + | 0.152936i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5545.12 | + | 13387.1i | −0.228993 | + | 0.552839i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23682.3 | − | 23682.3i | −0.974498 | − | 0.974498i | 0.0251848 | − | 0.999683i | \(-0.491983\pi\) |
−0.999683 | + | 0.0251848i | \(0.991983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32657.3 | − | 32657.3i | 1.33902 | − | 1.33902i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3187.01 | + | 1320.10i | 0.130209 | + | 0.0539344i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4875.38 | + | 11770.2i | 0.198483 | + | 0.479180i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29436.4i | 1.19415i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 19743.8i | − | 0.798122i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1823.30 | − | 4401.83i | −0.0734452 | − | 0.177312i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22116.2 | − | 9160.83i | −0.887742 | − | 0.367715i | −0.108248 | − | 0.994124i | \(-0.534524\pi\) |
−0.779495 | + | 0.626409i | \(0.784524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12075.0 | − | 12075.0i | 0.482991 | − | 0.482991i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28853.3 | + | 28853.3i | 1.15007 | + | 1.15007i | 0.986538 | + | 0.163530i | \(0.0522880\pi\) |
0.163530 | + | 0.986538i | \(0.447712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4841.92 | + | 11689.4i | −0.192321 | + | 0.464305i | −0.990397 | − | 0.138252i | \(-0.955851\pi\) |
0.798076 | + | 0.602557i | \(0.205851\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5979.33 | + | 2476.72i | −0.236673 | + | 0.0980330i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17390.7 | 0.685965 | 0.342982 | − | 0.939342i | \(-0.388563\pi\) | ||||
0.342982 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5333.29 | 0.209639 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6858.61 | + | 2840.93i | −0.268663 | + | 0.111284i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15926.3 | − | 38449.6i | 0.621708 | − | 1.50094i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1797.71 | + | 1797.71i | 0.0699348 | + | 0.0699348i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14829.8 | − | 14829.8i | 0.574930 | − | 0.574930i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25571.7 | − | 10592.2i | −0.987980 | − | 0.409235i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 596.594 | + | 1440.31i | 0.0229710 | + | 0.0554569i | 0.934949 | − | 0.354783i | \(-0.115445\pi\) |
−0.911978 | + | 0.410239i | \(0.865445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 26542.3i | − | 1.01849i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33644.4i | 1.28662i | 0.765607 | + | 0.643308i | \(0.222439\pi\) | ||||
−0.765607 | + | 0.643308i | \(0.777561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4327.10 | − | 10446.6i | −0.164913 | − | 0.398136i | 0.819721 | − | 0.572763i | \(-0.194128\pi\) |
−0.984635 | + | 0.174626i | \(0.944128\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9135.08 | − | 3783.87i | −0.346974 | − | 0.143721i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13569.1 | + | 13569.1i | −0.513647 | + | 0.513647i | −0.915642 | − | 0.401995i | \(-0.868317\pi\) |
0.401995 | + | 0.915642i | \(0.368317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2511.36 | − | 2511.36i | −0.0947451 | − | 0.0947451i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18592.4 | + | 44886.0i | −0.699067 | + | 1.68770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10681.4 | − | 4424.37i | 0.400267 | − | 0.165796i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16749.4 | 0.625554 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7537.56 | 0.280571 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49728.3 | + | 20598.2i | −1.84486 | + | 0.764168i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17220.0 | + | 41572.8i | −0.636716 | + | 1.53717i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17665.1 | − | 17665.1i | −0.651005 | − | 0.651005i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8119.71 | + | 8119.71i | −0.298241 | + | 0.298241i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23791.9 | − | 9854.94i | −0.871001 | − | 0.360780i | −0.0980007 | − | 0.995186i | \(-0.531245\pi\) |
−0.773000 | + | 0.634406i | \(0.781245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4110.80 | − | 9924.36i | −0.149996 | − | 0.362123i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42220.1i | − | 1.53547i | −0.640767 | − | 0.767736i | \(-0.721383\pi\) | ||
0.640767 | − | 0.767736i | \(-0.278617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3357.14i | 0.121692i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9771.56 | − | 23590.6i | −0.353047 | − | 0.852330i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18960.2 | − | 7853.57i | −0.682792 | − | 0.282822i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29324.7 | − | 29324.7i | 1.05259 | − | 1.05259i | 0.0540546 | − | 0.998538i | \(-0.482786\pi\) |
0.998538 | − | 0.0540546i | \(-0.0172145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25660.6 | − | 25660.6i | −0.918072 | − | 0.918072i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6438.05 | − | 15542.8i | 0.229589 | − | 0.554278i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5882.18 | − | 2436.48i | 0.209086 | − | 0.0866065i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2731.63 | −0.0967836 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12957.9 | −0.457625 | −0.228812 | − | 0.973471i | \(-0.573484\pi\) | ||||
−0.228812 | + | 0.973471i | \(0.573484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2005.85 | − | 830.850i | 0.0706112 | − | 0.0292481i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12689.5 | + | 30635.1i | −0.445268 | + | 1.07497i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22467.1 | + | 22467.1i | 0.785831 | + | 0.785831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30016.0 | − | 30016.0i | 1.04651 | − | 1.04651i | 0.0476462 | − | 0.998864i | \(-0.484828\pi\) |
0.998864 | − | 0.0476462i | \(-0.0151720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2613.54 | − | 1082.56i | −0.0908304 | − | 0.0376232i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15045.0 | − | 36321.8i | −0.521203 | − | 1.25830i | −0.937156 | − | 0.348910i | \(-0.886552\pi\) |
0.415953 | − | 0.909386i | \(-0.363448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2614.28i | 0.0902786i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 10303.8i | − | 0.354690i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12223.9 | − | 29511.1i | −0.419454 | − | 1.01265i | −0.982506 | − | 0.186230i | \(-0.940373\pi\) |
0.563052 | − | 0.826421i | \(-0.309627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7299.30 | + | 3023.47i | 0.249679 | + | 0.103420i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34085.0 | + | 34085.0i | −1.16223 | + | 1.16223i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26512.6 | − | 26512.6i | −0.901183 | − | 0.901183i | 0.0943555 | − | 0.995539i | \(-0.469921\pi\) |
−0.995539 | + | 0.0943555i | \(0.969921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2270.28 | − | 5480.93i | 0.0769261 | − | 0.185716i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −86561.1 | + | 35854.8i | −2.92385 | + | 1.21110i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34100.9 | −1.14825 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11261.2 | 0.378007 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10620.9 | − | 4399.31i | 0.355402 | − | 0.147213i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12156.6 | − | 29348.6i | 0.405528 | − | 0.979031i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2114.28 | − | 2114.28i | −0.0703109 | − | 0.0703109i | 0.671077 | − | 0.741388i | \(-0.265832\pi\) |
−0.741388 | + | 0.671077i | \(0.765832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50290.6 | + | 50290.6i | −1.66725 | + | 1.66725i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9687.75 | + | 4012.80i | 0.320180 | + | 0.132623i | 0.536984 | − | 0.843592i | \(-0.319563\pi\) |
−0.216805 | + | 0.976215i | \(0.569563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16700.7 | + | 40319.1i | 0.550257 | + | 1.32844i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10072.5i | 0.330849i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29819.0i | − | 0.976453i | −0.872717 | − | 0.488226i | \(-0.837644\pi\) | ||
0.872717 | − | 0.488226i | \(-0.162356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10208.0 | − | 24644.3i | −0.333248 | − | 0.804532i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18354.5 | − | 7602.67i | −0.597363 | − | 0.247436i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30424.5 | + | 30424.5i | −0.987174 | + | 0.987174i | −0.999919 | − | 0.0127444i | \(-0.995943\pi\) |
0.0127444 | + | 0.999919i | \(0.495943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25213.0 | − | 25213.0i | −0.815587 | − | 0.815587i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3947.73 | + | 9530.66i | −0.127313 | + | 0.307360i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9323.11 | + | 3861.76i | −0.299755 | + | 0.124163i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23803.1 | 0.762999 | 0.381499 | − | 0.924369i | \(-0.375408\pi\) | ||||
0.381499 | + | 0.924369i | \(0.375408\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26082.8 | 0.833547 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13259.7 | − | 5492.36i | 0.422474 | − | 0.174995i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2498.66 | − | 6032.29i | 0.0793714 | − | 0.191619i | −0.879213 | − | 0.476430i | \(-0.841931\pi\) |
0.958584 | + | 0.284810i | \(0.0919306\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4797.57 | + | 4797.57i | 0.151940 | + | 0.151940i |
(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 | 128.4.g.a.49.10 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.21.5 | ✓ | 44 | ||
8.3 | odd | 2 | 256.4.g.b.97.10 | 44 | |||
8.5 | even | 2 | 256.4.g.a.97.2 | 44 | |||
32.3 | odd | 8 | 32.4.g.a.29.5 | yes | 44 | ||
32.13 | even | 8 | 256.4.g.a.161.2 | 44 | |||
32.19 | odd | 8 | 256.4.g.b.161.10 | 44 | |||
32.29 | even | 8 | inner | 128.4.g.a.81.10 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.5 | ✓ | 44 | 4.3 | odd | 2 | ||
32.4.g.a.29.5 | yes | 44 | 32.3 | odd | 8 | ||
128.4.g.a.49.10 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.81.10 | 44 | 32.29 | even | 8 | inner | ||
256.4.g.a.97.2 | 44 | 8.5 | even | 2 | |||
256.4.g.a.161.2 | 44 | 32.13 | even | 8 | |||
256.4.g.b.97.10 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.161.10 | 44 | 32.19 | odd | 8 |