Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
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([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (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: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 47.6 | ||
Character | \(\chi\) | \(=\) | 128.47 |
Dual form | 128.3.h.a.79.6 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.31872 | − | 3.18367i | 0.439573 | − | 1.06122i | −0.536524 | − | 0.843885i | \(-0.680263\pi\) |
0.976097 | − | 0.217337i | \(-0.0697372\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.659338 | − | 1.59178i | −0.131868 | − | 0.318356i | 0.844130 | − | 0.536139i | \(-0.180118\pi\) |
−0.975997 | + | 0.217782i | \(0.930118\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.54718 | − | 9.54718i | −1.36388 | − | 1.36388i | −0.868907 | − | 0.494975i | \(-0.835177\pi\) |
−0.494975 | − | 0.868907i | \(-0.664823\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.03276 | − | 2.03276i | −0.225863 | − | 0.225863i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.96481 | + | 9.57189i | 0.360437 | + | 0.870172i | 0.995236 | + | 0.0974947i | \(0.0310829\pi\) |
−0.634799 | + | 0.772677i | \(0.718917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.91784 | − | 4.63007i | 0.147526 | − | 0.356159i | −0.832792 | − | 0.553587i | \(-0.813259\pi\) |
0.980317 | + | 0.197428i | \(0.0632587\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.93719 | −0.395813 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.3143i | − | 0.900842i | −0.892816 | − | 0.450421i | \(-0.851274\pi\) | ||
0.892816 | − | 0.450421i | \(-0.148726\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.827335 | − | 0.342693i | −0.0435439 | − | 0.0180365i | 0.360805 | − | 0.932641i | \(-0.382502\pi\) |
−0.404349 | + | 0.914605i | \(0.632502\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −42.9851 | + | 17.8050i | −2.04691 | + | 0.847857i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.9230 | − | 12.9230i | 0.561871 | − | 0.561871i | −0.367968 | − | 0.929839i | \(-0.619946\pi\) |
0.929839 | + | 0.367968i | \(0.119946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.5786 | − | 15.5786i | 0.623145 | − | 0.623145i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.5007 | − | 8.07746i | 0.722249 | − | 0.299165i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.7905 | + | 9.85436i | 0.820363 | + | 0.339805i | 0.753080 | − | 0.657929i | \(-0.228567\pi\) |
0.0672825 | + | 0.997734i | \(0.478567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.1562i | 0.811491i | 0.913986 | + | 0.405746i | \(0.132988\pi\) | ||||
−0.913986 | + | 0.405746i | \(0.867012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 35.7022 | 1.08188 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.90221 | + | 21.4918i | −0.254349 | + | 0.614053i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.6161 | + | 32.8721i | 0.368001 | + | 0.888434i | 0.994078 | + | 0.108672i | \(0.0346599\pi\) |
−0.626076 | + | 0.779762i | \(0.715340\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.2115 | − | 12.2115i | −0.313116 | − | 0.313116i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.9116 | − | 32.9116i | −0.802721 | − | 0.802721i | 0.180799 | − | 0.983520i | \(-0.442132\pi\) |
−0.983520 | + | 0.180799i | \(0.942132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.9473 | + | 43.3286i | 0.417379 | + | 1.00764i | 0.983104 | + | 0.183048i | \(0.0585964\pi\) |
−0.565725 | + | 0.824594i | \(0.691404\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.89544 | + | 4.57600i | −0.0421209 | + | 0.101689i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −20.1127 | −0.427930 | −0.213965 | − | 0.976841i | \(-0.568638\pi\) | ||||
−0.213965 | + | 0.976841i | \(0.568638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 133.297i | 2.72035i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −48.7557 | − | 20.1953i | −0.955994 | − | 0.395986i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.0503 | − | 14.5183i | 0.661327 | − | 0.273931i | −0.0266698 | − | 0.999644i | \(-0.508490\pi\) |
0.687997 | + | 0.725714i | \(0.258490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.6222 | − | 12.6222i | 0.229495 | − | 0.229495i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18204 | + | 2.18204i | −0.0382815 | + | 0.0382815i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 60.6706 | − | 25.1306i | 1.02832 | − | 0.425942i | 0.196212 | − | 0.980562i | \(-0.437136\pi\) |
0.832104 | + | 0.554619i | \(0.187136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.9825 | − | 11.5907i | −0.458730 | − | 0.190012i | 0.141338 | − | 0.989961i | \(-0.454860\pi\) |
−0.600067 | + | 0.799949i | \(0.704860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 38.8143i | 0.616100i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.63457 | −0.132839 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.13412 | + | 2.73801i | −0.0169272 | + | 0.0408659i | −0.932117 | − | 0.362157i | \(-0.882040\pi\) |
0.915190 | + | 0.403023i | \(0.132040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.1008 | − | 58.1845i | −0.349287 | − | 0.843253i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.6144 | + | 45.6144i | 0.642456 | + | 0.642456i | 0.951159 | − | 0.308702i | \(-0.0998947\pi\) |
−0.308702 | + | 0.951159i | \(0.599895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −29.1727 | − | 29.1727i | −0.399626 | − | 0.399626i | 0.478475 | − | 0.878101i | \(-0.341190\pi\) |
−0.878101 | + | 0.478475i | \(0.841190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −29.0534 | − | 70.1410i | −0.387378 | − | 0.935213i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53.5318 | − | 129.237i | 0.695219 | − | 1.67841i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.27983 | −0.0415169 | −0.0207584 | − | 0.999785i | \(-0.506608\pi\) | ||||
−0.0207584 | + | 0.999785i | \(0.506608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 98.6086i | − | 1.21739i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −56.7834 | − | 23.5205i | −0.684138 | − | 0.283379i | 0.0134176 | − | 0.999910i | \(-0.495729\pi\) |
−0.697555 | + | 0.716531i | \(0.745729\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.3770 | + | 10.0973i | −0.286789 | + | 0.118792i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 62.7460 | − | 62.7460i | 0.721218 | − | 0.721218i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −44.5059 | + | 44.5059i | −0.500066 | + | 0.500066i | −0.911458 | − | 0.411392i | \(-0.865043\pi\) |
0.411392 | + | 0.911458i | \(0.365043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −62.5140 | + | 25.8942i | −0.686967 | + | 0.284551i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 80.0891 | + | 33.1740i | 0.861173 | + | 0.356709i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.54289i | 0.0162409i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −106.417 | −1.09708 | −0.548542 | − | 0.836123i | \(-0.684817\pi\) | ||||
−0.548542 | + | 0.836123i | \(0.684817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.3979 | − | 27.5169i | 0.115130 | − | 0.277949i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.62243 | + | 8.74531i | 0.0358656 | + | 0.0865872i | 0.940797 | − | 0.338969i | \(-0.110078\pi\) |
−0.904932 | + | 0.425557i | \(0.860078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26.0911 | − | 26.0911i | −0.253312 | − | 0.253312i | 0.569015 | − | 0.822327i | \(-0.307325\pi\) |
−0.822327 | + | 0.569015i | \(0.807325\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 56.6834 | + | 56.6834i | 0.539842 | + | 0.539842i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −32.1753 | − | 77.6781i | −0.300704 | − | 0.725963i | −0.999939 | − | 0.0110713i | \(-0.996476\pi\) |
0.699235 | − | 0.714892i | \(-0.253524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −36.0541 | + | 87.0422i | −0.330771 | + | 0.798553i | 0.667760 | + | 0.744377i | \(0.267253\pi\) |
−0.998531 | + | 0.0541760i | \(0.982747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 122.609 | 1.10459 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.32445i | − | 0.0559686i | −0.999608 | − | 0.0279843i | \(-0.991091\pi\) | ||
0.999608 | − | 0.0279843i | \(-0.00890884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29.0913 | − | 12.0500i | −0.252968 | − | 0.104783i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3104 | + | 5.51333i | −0.113764 | + | 0.0471225i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −146.208 | + | 146.208i | −1.22864 | + | 1.22864i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.65850 | − | 9.65850i | 0.0798223 | − | 0.0798223i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −148.181 | + | 61.3784i | −1.20472 | + | 0.499011i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −74.8639 | − | 31.0096i | −0.598911 | − | 0.248077i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 34.6015i | − | 0.272453i | −0.990678 | − | 0.136226i | \(-0.956503\pi\) | ||
0.990678 | − | 0.136226i | \(-0.0434975\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 161.611 | 1.25280 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 68.0051 | − | 164.179i | 0.519123 | − | 1.25327i | −0.419320 | − | 0.907838i | \(-0.637732\pi\) |
0.938443 | − | 0.345434i | \(-0.112268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.62696 | + | 11.1705i | 0.0347892 | + | 0.0839885i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −25.7151 | − | 25.7151i | −0.190482 | − | 0.190482i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 71.5748 | + | 71.5748i | 0.522444 | + | 0.522444i | 0.918309 | − | 0.395865i | \(-0.129555\pi\) |
−0.395865 | + | 0.918309i | \(0.629555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 75.1916 | + | 181.529i | 0.540947 | + | 1.30596i | 0.924056 | + | 0.382258i | \(0.124853\pi\) |
−0.383109 | + | 0.923703i | \(0.625147\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −26.5230 | + | 64.0322i | −0.188107 | + | 0.454129i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 51.9224 | 0.363094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 44.3667i | − | 0.305977i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 424.374 | + | 175.781i | 2.88690 | + | 1.19579i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 211.685 | − | 87.6826i | 1.42070 | − | 0.588474i | 0.465665 | − | 0.884961i | \(-0.345815\pi\) |
0.955037 | + | 0.296487i | \(0.0958152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5820 | + | 10.5820i | −0.0700794 | + | 0.0700794i | −0.741278 | − | 0.671198i | \(-0.765780\pi\) |
0.671198 | + | 0.741278i | \(0.265780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −31.1304 | + | 31.1304i | −0.203467 | + | 0.203467i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 40.0432 | − | 16.5864i | 0.258343 | − | 0.107009i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26.9641 | + | 11.1689i | 0.171746 | + | 0.0711394i | 0.466900 | − | 0.884310i | \(-0.345371\pi\) |
−0.295154 | + | 0.955450i | \(0.595371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 130.734i | − | 0.822228i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −246.757 | −1.53265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −111.743 | + | 269.771i | −0.685540 | + | 1.65504i | 0.0680396 | + | 0.997683i | \(0.478326\pi\) |
−0.753579 | + | 0.657357i | \(0.771674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.5398 | − | 56.8301i | −0.142665 | − | 0.344425i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3664 | + | 10.3664i | 0.0620741 | + | 0.0620741i | 0.737462 | − | 0.675388i | \(-0.236024\pi\) |
−0.675388 | + | 0.737462i | \(0.736024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 101.742 | + | 101.742i | 0.602021 | + | 0.602021i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.985162 | + | 2.37839i | 0.00576118 | + | 0.0139087i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −88.6518 | + | 214.024i | −0.512438 | + | 1.23714i | 0.430022 | + | 0.902818i | \(0.358506\pi\) |
−0.942461 | + | 0.334317i | \(0.891494\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −297.464 | −1.69979 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 226.295i | − | 1.27850i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.58312 | − | 1.06996i | −0.0144308 | − | 0.00597744i | 0.375456 | − | 0.926840i | \(-0.377486\pi\) |
−0.389887 | + | 0.920863i | \(0.627486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −184.394 | + | 76.3786i | −1.01875 | + | 0.421981i | −0.828640 | − | 0.559781i | \(-0.810885\pi\) |
−0.190112 | + | 0.981762i | \(0.560885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −73.8021 | + | 73.8021i | −0.403290 | + | 0.403290i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 43.3476 | − | 43.3476i | 0.234311 | − | 0.234311i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 146.587 | − | 60.7183i | 0.783887 | − | 0.324697i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −263.294 | − | 109.060i | −1.39309 | − | 0.577036i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 185.771i | − | 0.972625i | −0.873785 | − | 0.486313i | \(-0.838342\pi\) | ||
0.873785 | − | 0.486313i | \(-0.161658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 208.055 | 1.07800 | 0.539002 | − | 0.842305i | \(-0.318802\pi\) | ||||
0.539002 | + | 0.842305i | \(0.318802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.3866 | + | 27.4896i | −0.0583926 | + | 0.140972i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 123.852 | + | 299.006i | 0.628691 | + | 1.51780i | 0.841250 | + | 0.540647i | \(0.181820\pi\) |
−0.212558 | + | 0.977148i | \(0.568180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 253.762 | + | 253.762i | 1.27519 | + | 1.27519i | 0.943329 | + | 0.331858i | \(0.107676\pi\) |
0.331858 | + | 0.943329i | \(0.392324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.22134 | + | 7.22134i | 0.0359270 | + | 0.0359270i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −133.051 | − | 321.214i | −0.655424 | − | 1.58233i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.6882 | + | 74.0879i | −0.149699 | + | 0.361404i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −52.5389 | −0.253811 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.27787i | − | 0.0443917i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −102.533 | − | 42.4705i | −0.485938 | − | 0.201282i | 0.126244 | − | 0.991999i | \(-0.459708\pi\) |
−0.612182 | + | 0.790717i | \(0.709708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 205.374 | − | 85.0685i | 0.964195 | − | 0.399383i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 57.1364 | − | 57.1364i | 0.265751 | − | 0.265751i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 240.171 | − | 240.171i | 1.10678 | − | 1.10678i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −131.347 | + | 54.4056i | −0.599757 | + | 0.248428i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −70.9063 | − | 29.3704i | −0.320843 | − | 0.132898i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 187.153i | − | 0.839252i | −0.907697 | − | 0.419626i | \(-0.862161\pi\) | ||
0.907697 | − | 0.419626i | \(-0.137839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −63.3353 | −0.281490 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.72348 | − | 6.57507i | 0.0119977 | − | 0.0289650i | −0.917767 | − | 0.397119i | \(-0.870010\pi\) |
0.929765 | + | 0.368154i | \(0.120010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −124.655 | − | 300.944i | −0.544345 | − | 1.31416i | −0.921631 | − | 0.388068i | \(-0.873143\pi\) |
0.377286 | − | 0.926097i | \(-0.376857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −340.855 | − | 340.855i | −1.47556 | − | 1.47556i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −208.047 | − | 208.047i | −0.892904 | − | 0.892904i | 0.101891 | − | 0.994796i | \(-0.467511\pi\) |
−0.994796 | + | 0.101891i | \(0.967511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.2611 | + | 32.0151i | 0.0564301 | + | 0.136234i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.32518 | + | 10.4419i | −0.0182497 | + | 0.0440587i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 277.832 | 1.16248 | 0.581239 | − | 0.813733i | \(-0.302568\pi\) | ||||
0.581239 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 63.2696i | 0.262529i | 0.991347 | + | 0.131265i | \(0.0419038\pi\) | ||||
−0.991347 | + | 0.131265i | \(0.958096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −138.431 | − | 57.3398i | −0.569673 | − | 0.235966i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 212.180 | − | 87.8879i | 0.866041 | − | 0.358726i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.17339 | + | 3.17339i | −0.0128477 | + | 0.0128477i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −149.763 | + | 149.763i | −0.601457 | + | 0.601457i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −161.948 | + | 67.0812i | −0.645212 | + | 0.267256i | −0.681201 | − | 0.732097i | \(-0.738542\pi\) |
0.0359886 | + | 0.999352i | \(0.488542\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 174.935 | + | 72.4605i | 0.691443 | + | 0.286405i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 90.9239i | 0.356564i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −82.9690 | −0.322836 | −0.161418 | − | 0.986886i | \(-0.551607\pi\) | ||||
−0.161418 | + | 0.986886i | \(0.551607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 183.840 | − | 443.830i | 0.709809 | − | 1.71363i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.3289 | − | 68.3921i | −0.108540 | − | 0.262039i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 148.394 | + | 148.394i | 0.564235 | + | 0.564235i | 0.930508 | − | 0.366272i | \(-0.119366\pi\) |
−0.366272 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −46.2200 | − | 46.2200i | −0.174415 | − | 0.174415i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 83.0012 | + | 200.383i | 0.310866 | + | 0.750497i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 78.7117 | − | 190.027i | 0.292609 | − | 0.706420i | −0.707391 | − | 0.706822i | \(-0.750128\pi\) |
1.00000 | 0.000402393i | \(0.000128086\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.7996 | 0.109962 | 0.0549809 | − | 0.998487i | \(-0.482490\pi\) | ||||
0.0549809 | + | 0.998487i | \(0.482490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 233.171i | 0.854106i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 210.883 | + | 87.3507i | 0.766848 | + | 0.317639i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −368.831 | + | 152.775i | −1.33152 | + | 0.551534i | −0.931089 | − | 0.364793i | \(-0.881140\pi\) |
−0.400431 | + | 0.916327i | \(0.631140\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 51.1367 | − | 51.1367i | 0.183286 | − | 0.183286i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −280.258 | + | 280.258i | −0.997358 | + | 0.997358i | −0.999997 | − | 0.00263807i | \(-0.999160\pi\) |
0.00263807 | + | 0.999997i | \(0.499160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 176.650 | − | 73.1708i | 0.624204 | − | 0.258554i | −0.0480840 | − | 0.998843i | \(-0.515312\pi\) |
0.672288 | + | 0.740289i | \(0.265312\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.91204 | + | 2.03463i | 0.0172352 | + | 0.00713907i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 628.425i | 2.18963i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 54.4719 | 0.188484 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −140.334 | + | 338.797i | −0.482249 | + | 1.16425i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.3590 | + | 27.4231i | 0.0387679 | + | 0.0935940i | 0.942078 | − | 0.335395i | \(-0.108870\pi\) |
−0.903310 | + | 0.428989i | \(0.858870\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −80.0049 | − | 80.0049i | −0.271203 | − | 0.271203i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 154.633 | + | 154.633i | 0.520651 | + | 0.520651i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.0503 | − | 84.6188i | −0.117225 | − | 0.283006i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 242.320 | − | 585.012i | 0.805049 | − | 1.94356i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.6191 | 0.107654 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 52.1843i | 0.171096i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −463.833 | − | 192.126i | −1.51086 | − | 0.625817i | −0.535122 | − | 0.844775i | \(-0.679734\pi\) |
−0.975734 | + | 0.218957i | \(0.929734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −117.472 | + | 48.6586i | −0.380169 | + | 0.157471i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −230.516 | + | 230.516i | −0.741210 | + | 0.741210i | −0.972811 | − | 0.231601i | \(-0.925604\pi\) |
0.231601 | + | 0.972811i | \(0.425604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.89884 | − | 2.89884i | 0.00926146 | − | 0.00926146i | −0.702461 | − | 0.711722i | \(-0.747915\pi\) |
0.711722 | + | 0.702461i | \(0.247915\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 61.7839 | − | 25.5917i | 0.196139 | − | 0.0812436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 510.087 | + | 211.285i | 1.60911 | + | 0.666514i | 0.992666 | − | 0.120887i | \(-0.0385738\pi\) |
0.616441 | + | 0.787401i | \(0.288574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 266.791i | 0.836335i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −289.731 | −0.902590 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.24811 | + | 12.6701i | −0.0162480 | + | 0.0392262i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.2528 | − | 102.007i | −0.130009 | − | 0.313869i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 229.568 | + | 229.568i | 0.702044 | + | 0.702044i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 192.020 | + | 192.020i | 0.583647 | + | 0.583647i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95.3030 | + | 230.082i | 0.287924 | + | 0.695111i | 0.999975 | − | 0.00701670i | \(-0.00223350\pi\) |
−0.712051 | + | 0.702128i | \(0.752234\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 39.1429 | − | 94.4994i | 0.117546 | − | 0.283782i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.10609 | 0.0152421 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 203.997i | 0.605334i | 0.953096 | + | 0.302667i | \(0.0978769\pi\) | ||||
−0.953096 | + | 0.302667i | \(0.902123\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.1349 | − | 8.34017i | −0.0593951 | − | 0.0246023i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −240.793 | + | 99.7396i | −0.706137 | + | 0.292491i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 804.800 | − | 804.800i | 2.34636 | − | 2.34636i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −76.7264 | + | 76.7264i | −0.222395 | + | 0.222395i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 120.709 | − | 49.9993i | 0.347865 | − | 0.144090i | −0.201908 | − | 0.979404i | \(-0.564714\pi\) |
0.549773 | + | 0.835314i | \(0.314714\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 279.116 | + | 115.614i | 0.799759 | + | 0.331271i | 0.744860 | − | 0.667221i | \(-0.232516\pi\) |
0.0548993 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 105.781i | − | 0.301370i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 608.156 | 1.72282 | 0.861410 | − | 0.507910i | \(-0.169582\pi\) | ||||
0.861410 | + | 0.507910i | \(0.169582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.5329 | − | 102.683i | 0.119811 | − | 0.289249i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 272.671 | + | 658.287i | 0.763785 | + | 1.84394i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −196.029 | − | 196.029i | −0.546041 | − | 0.546041i | 0.379252 | − | 0.925293i | \(-0.376181\pi\) |
−0.925293 | + | 0.379252i | \(0.876181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −254.699 | − | 254.699i | −0.705536 | − | 0.705536i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.0126 | − | 43.4863i | −0.0496215 | − | 0.119797i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.2019 | + | 65.6713i | −0.0745259 | + | 0.179921i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0375 | 0.0900203 | 0.0450102 | − | 0.998987i | \(-0.485668\pi\) | ||||
0.0450102 | + | 0.998987i | \(0.485668\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 133.803i | 0.362609i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −473.241 | − | 196.023i | −1.27558 | − | 0.528363i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 115.583 | − | 47.8760i | 0.309874 | − | 0.128354i | −0.222327 | − | 0.974972i | \(-0.571365\pi\) |
0.532201 | + | 0.846618i | \(0.321365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −197.449 | + | 197.449i | −0.526530 | + | 0.526530i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 91.2527 | − | 91.2527i | 0.242050 | − | 0.242050i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −164.874 | + | 68.2930i | −0.435024 | + | 0.180193i | −0.589438 | − | 0.807813i | \(-0.700651\pi\) |
0.154415 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −110.160 | − | 45.6297i | −0.289133 | − | 0.119763i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 307.309i | 0.802373i | 0.915996 | + | 0.401186i | \(0.131402\pi\) | ||||
−0.915996 | + | 0.401186i | \(0.868598\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −241.013 | −0.626008 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 51.5942 | − | 124.559i | 0.133318 | − | 0.321859i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −204.874 | − | 494.611i | −0.526669 | − | 1.27149i | −0.933693 | − | 0.358075i | \(-0.883433\pi\) |
0.407024 | − | 0.913418i | \(-0.366567\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −197.907 | − | 197.907i | −0.506157 | − | 0.506157i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −433.011 | − | 433.011i | −1.10181 | − | 1.10181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.16252 | + | 5.22078i | 0.00547473 | + | 0.0132172i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −224.796 | + | 542.706i | −0.566237 | + | 1.36702i | 0.338467 | + | 0.940978i | \(0.390092\pi\) |
−0.904705 | + | 0.426040i | \(0.859908\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 41.6647 | 0.104423 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 125.790i | − | 0.313691i | −0.987623 | − | 0.156846i | \(-0.949868\pi\) | ||
0.987623 | − | 0.156846i | \(-0.0501325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 116.475 | + | 48.2456i | 0.289020 | + | 0.119716i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −156.963 | + | 65.0164i | −0.387564 | + | 0.160534i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −260.663 | + | 260.663i | −0.640449 | + | 0.640449i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 492.952 | − | 492.952i | 1.20526 | − | 1.20526i | 0.232717 | − | 0.972544i | \(-0.425238\pi\) |
0.972544 | − | 0.232717i | \(-0.0747617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 322.257 | − | 133.483i | 0.784081 | − | 0.324777i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −819.159 | − | 339.307i | −1.98344 | − | 0.821567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 105.895i | 0.255168i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 677.084 | 1.62370 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −203.456 | + | 491.187i | −0.485576 | + | 1.17228i | 0.471349 | + | 0.881947i | \(0.343767\pi\) |
−0.956925 | + | 0.290336i | \(0.906233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.995616 | − | 2.40363i | −0.00236488 | − | 0.00570934i | 0.922693 | − | 0.385536i | \(-0.125984\pi\) |
−0.925058 | + | 0.379827i | \(0.875984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.8844 | + | 40.8844i | 0.0966535 | + | 0.0966535i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −238.576 | − | 238.576i | −0.561355 | − | 0.561355i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 156.495 | + | 377.813i | 0.366499 | + | 0.884807i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 68.4710 | − | 165.304i | 0.159606 | − | 0.385323i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −404.244 | −0.937920 | −0.468960 | − | 0.883219i | \(-0.655371\pi\) | ||||
−0.468960 | + | 0.883219i | \(0.655371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 446.431i | 1.03102i | 0.856884 | + | 0.515509i | \(0.172397\pi\) | ||||
−0.856884 | + | 0.515509i | \(0.827603\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −141.249 | − | 58.5072i | −0.324710 | − | 0.134499i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.1203 | + | 6.26304i | −0.0346003 | + | 0.0143319i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 203.077 | − | 203.077i | 0.462590 | − | 0.462590i | −0.436914 | − | 0.899503i | \(-0.643928\pi\) |
0.899503 | + | 0.436914i | \(0.143928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 270.962 | − | 270.962i | 0.614426 | − | 0.614426i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 440.203 | − | 182.338i | 0.993685 | − | 0.411598i | 0.174207 | − | 0.984709i | \(-0.444264\pi\) |
0.819478 | + | 0.573111i | \(0.194264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 100.188 | + | 41.4993i | 0.225142 | + | 0.0932568i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 789.562i | − | 1.76636i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −636.256 | −1.41705 | −0.708526 | − | 0.705685i | \(-0.750639\pi\) | ||||
−0.708526 | + | 0.705685i | \(0.750639\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 184.538 | − | 445.514i | 0.409175 | − | 0.987836i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.7349 | + | 47.6442i | 0.0435648 | + | 0.105175i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 82.4357 | + | 82.4357i | 0.181177 | + | 0.181177i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −359.285 | − | 359.285i | −0.786181 | − | 0.786181i | 0.194685 | − | 0.980866i | \(-0.437632\pi\) |
−0.980866 | + | 0.194685i | \(0.937632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −123.701 | − | 298.640i | −0.269501 | − | 0.650632i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 68.2156 | − | 164.687i | 0.147973 | − | 0.357239i | −0.832462 | − | 0.554083i | \(-0.813069\pi\) |
0.980435 | + | 0.196844i | \(0.0630692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −662.155 | −1.43014 | −0.715070 | − | 0.699053i | \(-0.753605\pi\) | ||||
−0.715070 | + | 0.699053i | \(0.753605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 149.357i | − | 0.321198i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 854.762 | + | 354.054i | 1.83033 | + | 0.758146i | 0.967607 | + | 0.252461i | \(0.0812399\pi\) |
0.862718 | + | 0.505685i | \(0.168760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.9680 | − | 15.3126i | 0.0788229 | − | 0.0326495i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.1160 | − | 71.1160i | 0.150989 | − | 0.150989i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −343.579 | + | 343.579i | −0.726383 | + | 0.726383i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.2274 | + | 7.55005i | −0.0383735 | + | 0.0158948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −100.761 | − | 41.7367i | −0.211240 | − | 0.0874984i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 926.802i | − | 1.93487i | −0.253122 | − | 0.967434i | \(-0.581458\pi\) | ||
0.253122 | − | 0.967434i | \(-0.418542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 178.313 | 0.370714 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −325.403 | + | 785.592i | −0.673712 | + | 1.62648i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 70.1649 | + | 169.393i | 0.144670 | + | 0.349264i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −586.001 | − | 586.001i | −1.20329 | − | 1.20329i | −0.973161 | − | 0.230127i | \(-0.926086\pi\) |
−0.230127 | − | 0.973161i | \(-0.573914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 711.505 | + | 711.505i | 1.45502 | + | 1.45502i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1543 | + | 41.4142i | 0.0349375 | + | 0.0843466i | 0.940385 | − | 0.340111i | \(-0.110465\pi\) |
−0.905448 | + | 0.424458i | \(0.860465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 150.913 | − | 364.335i | 0.306111 | − | 0.739017i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −51.3160 | −0.103669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 870.977i | − | 1.75247i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 143.291 | + | 59.3531i | 0.287156 | + | 0.118944i | 0.521612 | − | 0.853183i | \(-0.325331\pi\) |
−0.234456 | + | 0.972127i | \(0.575331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.6734 | − | 19.3328i | 0.0931605 | − | 0.0385884i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −74.0929 | + | 74.0929i | −0.147302 | + | 0.147302i | −0.776912 | − | 0.629610i | \(-0.783215\pi\) |
0.629610 | + | 0.776912i | \(0.283215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5322 | − | 11.5322i | 0.0228361 | − | 0.0228361i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 458.080 | − | 189.743i | 0.903511 | − | 0.374246i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 467.540 | + | 193.661i | 0.918546 | + | 0.380474i | 0.791322 | − | 0.611400i | \(-0.209393\pi\) |
0.127224 | + | 0.991874i | \(0.459393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 557.034i | 1.09009i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.9017 | −0.0368455 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.3285 | + | 58.7343i | −0.0472399 | + | 0.114047i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −79.7431 | − | 192.517i | −0.154242 | − | 0.372373i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 564.476 | + | 564.476i | 1.08762 | + | 1.08762i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 694.307 | + | 694.307i | 1.33264 | + | 1.33264i | 0.902998 | + | 0.429644i | \(0.141361\pi\) |
0.429644 | + | 0.902998i | \(0.358639\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −67.4311 | − | 162.793i | −0.128931 | − | 0.311268i | 0.846211 | − | 0.532848i | \(-0.178878\pi\) |
−0.975142 | + | 0.221581i | \(0.928878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −392.271 | + | 947.026i | −0.747183 | + | 1.80386i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 385.250 | 0.731025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 194.991i | 0.368602i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −174.414 | − | 72.2445i | −0.328463 | − | 0.136054i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −215.502 | + | 89.2638i | −0.404319 | + | 0.167474i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −102.432 | + | 102.432i | −0.191462 | + | 0.191462i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.81281 | + | 6.81281i | −0.0126868 | + | 0.0126868i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1275.91 | + | 528.498i | −2.36717 | + | 0.980515i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 125.547 | + | 52.0035i | 0.232066 | + | 0.0961247i | 0.495686 | − | 0.868502i | \(-0.334917\pi\) |
−0.263620 | + | 0.964626i | \(0.584917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 687.772i | 1.26661i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 162.324 | 0.297842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 278.945 | − | 673.432i | 0.509954 | − | 1.23114i | −0.433956 | − | 0.900934i | \(-0.642883\pi\) |
0.943910 | − | 0.330204i | \(-0.107117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.3206 | + | 80.4431i | 0.0606933 | + | 0.146527i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.3057 | − | 16.3057i | −0.0295929 | − | 0.0295929i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.3132 | + | 31.3132i | 0.0566241 | + | 0.0566241i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −80.8410 | − | 195.168i | −0.145660 | − | 0.351653i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −228.207 | + | 550.942i | −0.409708 | + | 0.989123i | 0.575506 | + | 0.817797i | \(0.304805\pi\) |
−0.985214 | + | 0.171326i | \(0.945195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 235.035 | 0.420455 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 546.754i | − | 0.974607i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 236.899 | + | 98.1268i | 0.420780 | + | 0.174293i | 0.583019 | − | 0.812459i | \(-0.301871\pi\) |
−0.162239 | + | 0.986752i | \(0.551871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0671 | + | 4.16995i | −0.0178180 | + | 0.00738044i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −941.434 | + | 941.434i | −1.66038 | + | 1.66038i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −289.568 | + | 289.568i | −0.508907 | + | 0.508907i | −0.914191 | − | 0.405284i | \(-0.867173\pi\) |
0.405284 | + | 0.914191i | \(0.367173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −801.877 | + | 332.148i | −1.40434 | + | 0.581695i | −0.950874 | − | 0.309579i | \(-0.899812\pi\) |
−0.453464 | + | 0.891275i | \(0.649812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −591.435 | − | 244.980i | −1.03217 | − | 0.427540i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 402.646i | − | 0.700254i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −107.872 | −0.186953 | −0.0934767 | − | 0.995621i | \(-0.529798\pi\) | ||||
−0.0934767 | + | 0.995621i | \(0.529798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 274.365 | − | 662.377i | 0.473861 | − | 1.14400i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 317.567 | + | 766.676i | 0.546588 | + | 1.31958i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 277.936 | + | 277.936i | 0.476734 | + | 0.476734i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.5520 | + | 17.5520i | 0.0300035 | + | 0.0300035i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 292.393 | + | 705.899i | 0.498114 | + | 1.20255i | 0.950498 | + | 0.310730i | \(0.100574\pi\) |
−0.452384 | + | 0.891823i | \(0.649426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.62087 | − | 20.8126i | 0.0146365 | − | 0.0353355i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1115.26 | 1.88707 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 247.178i | 0.416826i | 0.978041 | + | 0.208413i | \(0.0668298\pi\) | ||||
−0.978041 | + | 0.208413i | \(0.933170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 329.133 | + | 136.331i | 0.553164 | + | 0.229128i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1142.54 | − | 473.254i | 1.91380 | − | 0.792720i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 633.115 | − | 633.115i | 1.05695 | − | 1.05695i | 0.0586768 | − | 0.998277i | \(-0.481312\pi\) |
0.998277 | − | 0.0586768i | \(-0.0186881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −147.019 | + | 147.019i | −0.244624 | + | 0.244624i | −0.818760 | − | 0.574136i | \(-0.805338\pi\) |
0.574136 | + | 0.818760i | \(0.305338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.87114 | − | 3.26033i | 0.0130533 | − | 0.00540685i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.7424 | − | 9.00601i | −0.0359379 | − | 0.0148860i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 52.6594i | 0.0867536i | 0.999059 | + | 0.0433768i | \(0.0138116\pi\) | ||||
−0.999059 | + | 0.0433768i | \(0.986188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1198.09 | −1.96731 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.5729 | + | 93.1233i | −0.0631308 | + | 0.152411i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −336.988 | − | 813.562i | −0.549737 | − | 1.32718i | −0.917675 | − | 0.397331i | \(-0.869936\pi\) |
0.367939 | − | 0.929850i | \(-0.380064\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 195.402 | + | 195.402i | 0.317727 | + | 0.317727i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −150.269 | − | 150.269i | −0.243547 | − | 0.243547i | 0.574769 | − | 0.818316i | \(-0.305092\pi\) |
−0.818316 | + | 0.574769i | \(0.805092\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.34083 | − | 10.4797i | −0.00701265 | − | 0.0169300i | 0.920334 | − | 0.391132i | \(-0.127917\pi\) |
−0.927347 | + | 0.374202i | \(0.877917\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 147.623 | − | 356.394i | 0.237718 | − | 0.573903i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 849.811 | 1.36406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 411.175i | − | 0.657880i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.5377 | − | 12.2349i | −0.0471095 | − | 0.0195134i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 503.413 | − | 208.520i | 0.800338 | − | 0.331511i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −356.485 | + | 356.485i | −0.564952 | + | 0.564952i | −0.930710 | − | 0.365758i | \(-0.880810\pi\) |
0.365758 | + | 0.930710i | \(0.380810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −270.424 | + | 270.424i | −0.427210 | + | 0.427210i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −55.0781 | + | 22.8141i | −0.0867371 | + | 0.0359277i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 617.175 | + | 255.642i | 0.968878 | + | 0.401322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 185.447i | − | 0.290214i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 741.748 | 1.15717 | 0.578587 | − | 0.815621i | \(-0.303604\pi\) | ||||
0.578587 | + | 0.815621i | \(0.303604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −181.837 | + | 438.994i | −0.282795 | + | 0.682729i | −0.999899 | − | 0.0142385i | \(-0.995468\pi\) |
0.717103 | + | 0.696967i | \(0.245468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −106.556 | − | 257.250i | −0.165204 | − | 0.398837i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −520.304 | − | 520.304i | −0.804180 | − | 0.804180i | 0.179566 | − | 0.983746i | \(-0.442531\pi\) |
−0.983746 | + | 0.179566i | \(0.942531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 481.095 | + | 481.095i | 0.741286 | + | 0.741286i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −447.907 | − | 1081.34i | −0.688029 | − | 1.66105i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 161.753 | − | 390.507i | 0.247708 | − | 0.598019i | −0.750301 | − | 0.661096i | \(-0.770091\pi\) |
0.998009 | + | 0.0630771i | \(0.0200914\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −306.175 | −0.467443 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 118.603i | 0.180521i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −70.1853 | − | 29.0717i | −0.106503 | − | 0.0441149i | 0.328796 | − | 0.944401i | \(-0.393357\pi\) |
−0.435299 | + | 0.900286i | \(0.643357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −81.1193 | + | 33.6007i | −0.122722 | + | 0.0508331i | −0.443199 | − | 0.896423i | \(-0.646157\pi\) |
0.320477 | + | 0.947256i | \(0.396157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −187.011 | + | 187.011i | −0.282068 | + | 0.282068i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.7302 | − | 14.7302i | 0.0221507 | − | 0.0221507i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 434.794 | − | 180.097i | 0.651865 | − | 0.270011i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −595.833 | − | 246.802i | −0.890633 | − | 0.368912i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 313.801i | − | 0.467661i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −851.239 | −1.26484 | −0.632421 | − | 0.774625i | \(-0.717939\pi\) | ||||
−0.632421 | + | 0.774625i | \(0.717939\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 177.959 | − | 429.630i | 0.263642 | − | 0.636489i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −380.410 | − | 918.390i | −0.561905 | − | 1.35656i | −0.908241 | − | 0.418448i | \(-0.862574\pi\) |
0.346335 | − | 0.938111i | \(-0.387426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1015.98 | + | 1015.98i | 1.49629 | + | 1.49629i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.3413 | − | 17.3413i | −0.0254645 | − | 0.0254645i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −425.467 | − | 1027.17i | −0.622939 | − | 1.50391i | −0.848236 | − | 0.529618i | \(-0.822335\pi\) |
0.225297 | − | 0.974290i | \(-0.427665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 66.7395 | − | 161.123i | 0.0974299 | − | 0.235217i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1122.49 | −1.63390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 190.129i | − | 0.275950i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −260.940 | − | 108.085i | −0.377627 | − | 0.156418i | 0.185793 | − | 0.982589i | \(-0.440515\pi\) |
−0.563420 | + | 0.826171i | \(0.690515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −371.526 | + | 153.891i | −0.536113 | + | 0.222065i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 239.377 | − | 239.377i | 0.344428 | − | 0.344428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −504.018 | + | 504.018i | −0.723124 | + | 0.723124i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −936.707 | + | 387.997i | −1.34007 | + | 0.555074i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −727.192 | − | 301.213i | −1.03736 | − | 0.429690i | −0.201999 | − | 0.979386i | \(-0.564744\pi\) |
−0.835365 | + | 0.549695i | \(0.814744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.8623i | − | 0.0453234i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 119.413 | 0.169380 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.9091 | − | 118.077i | 0.0691783 | − | 0.167011i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 259.577 | + | 626.675i | 0.366118 | + | 0.883886i | 0.994379 | + | 0.105883i | \(0.0337670\pi\) |
−0.628261 | + | 0.778003i | \(0.716233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.66713 | + | 6.66713i | 0.00937711 | + | 0.00937711i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 325.095 | + | 325.095i | 0.455953 | + | 0.455953i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.2344 | − | 82.6491i | −0.0478803 | − | 0.115593i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 366.383 | − | 884.526i | 0.510994 | − | 1.23365i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1034.71 | −1.43910 | −0.719549 | − | 0.694442i | \(-0.755651\pi\) | ||||
−0.719549 | + | 0.694442i | \(0.755651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 498.193i | 0.690975i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 201.429 | + | 83.4348i | 0.278602 | + | 0.115401i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 524.141 | − | 217.106i | 0.722953 | − | 0.299457i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −227.066 | + | 227.066i | −0.312332 | + | 0.312332i | −0.845813 | − | 0.533480i | \(-0.820884\pi\) |
0.533480 | + | 0.845813i | \(0.320884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 262.439 | − | 262.439i | 0.359999 | − | 0.359999i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 663.548 | − | 274.850i | 0.907726 | − | 0.375992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 973.386 | + | 403.190i | 1.32795 | + | 0.550054i | 0.930070 | − | 0.367384i | \(-0.119746\pi\) |
0.397879 | + | 0.917438i | \(0.369746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 791.410i | − | 1.07675i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.7045 | −0.0416615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −387.131 | + | 934.616i | −0.523857 | + | 1.26470i | 0.411632 | + | 0.911350i | \(0.364959\pi\) |
−0.935490 | + | 0.353354i | \(0.885041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.91821 | + | 14.2878i | 0.00798679 | + | 0.0192818i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −528.819 | − | 528.819i | −0.711735 | − | 0.711735i | 0.255163 | − | 0.966898i | \(-0.417871\pi\) |
−0.966898 | + | 0.255163i | \(0.917871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −279.143 | − | 279.143i | −0.374689 | − | 0.374689i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67.6158 | + | 163.239i | 0.0905164 | + | 0.218526i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −434.423 | + | 1048.79i | −0.580004 | + | 1.40025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 176.760 | 0.235366 | 0.117683 | − | 0.993051i | \(-0.462453\pi\) | ||||
0.117683 | + | 0.993051i | \(0.462453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 604.051i | 0.802192i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.8213 | + | 9.86711i | 0.0315514 | + | 0.0130690i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −59.8575 | + | 24.7938i | −0.0790720 | + | 0.0327527i | −0.421869 | − | 0.906657i | \(-0.638626\pi\) |
0.342797 | + | 0.939410i | \(0.388626\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 461.381 | − | 461.381i | 0.607879 | − | 0.607879i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 713.497 | − | 713.497i | 0.937579 | − | 0.937579i | −0.0605844 | − | 0.998163i | \(-0.519296\pi\) |
0.998163 | + | 0.0605844i | \(0.0192964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1175.22 | − | 486.793i | 1.54026 | − | 0.637999i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 70.0782 | + | 29.0273i | 0.0916055 | + | 0.0379442i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 329.106i | − | 0.429082i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −147.511 | −0.191821 | −0.0959107 | − | 0.995390i | \(-0.530576\pi\) | ||||
−0.0959107 | + | 0.995390i | \(0.530576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −109.413 | + | 264.146i | −0.141910 | + | 0.342601i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 104.027 | + | 251.144i | 0.134576 | + | 0.324896i | 0.976774 | − | 0.214273i | \(-0.0687384\pi\) |
−0.842198 | + | 0.539169i | \(0.818738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 391.899 | + | 391.899i | 0.505677 | + | 0.505677i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1170.57 | − | 1170.57i | −1.50653 | − | 1.50653i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.9503 | + | 38.5075i | 0.0204754 | + | 0.0494319i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −255.764 | + | 617.468i | −0.327482 | + | 0.790612i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 543.531 | 0.694164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 50.2850i | − | 0.0640573i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −999.730 | − | 414.102i | −1.27031 | − | 0.526178i | −0.357248 | − | 0.934010i | \(-0.616285\pi\) |
−0.913057 | + | 0.407832i | \(0.866285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 668.127 | − | 276.747i | 0.846802 | − | 0.350757i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.3806 | + | 60.3806i | −0.0763345 | + | 0.0763345i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −107.332 | + | 107.332i | −0.135349 | + | 0.135349i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −208.100 | + | 86.1980i | −0.261762 | + | 0.108425i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1138.14 | − | 471.431i | −1.42802 | − | 0.591507i | −0.471162 | − | 0.882047i | \(-0.656165\pi\) |
−0.956863 | + | 0.290540i | \(0.906165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 308.012i | 0.385497i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 180.940 | 0.225893 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 163.574 | − | 394.902i | 0.203703 | − | 0.491784i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 162.696 | + | 392.783i | 0.202107 | + | 0.487929i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −501.184 | − | 501.184i | −0.621046 | − | 0.621046i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −169.569 | − | 169.569i | −0.209603 | − | 0.209603i | 0.594496 | − | 0.804099i | \(-0.297352\pi\) |
−0.804099 | + | 0.594496i | \(0.797352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 437.562 | + | 1056.37i | 0.539534 | + | 1.30255i | 0.925048 | + | 0.379849i | \(0.124024\pi\) |
−0.385514 | + | 0.922702i | \(0.625976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.2973 | − | 94.8722i | 0.0483362 | − | 0.116694i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 503.094 | 0.617293 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 41.9977i | − | 0.0514048i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 179.713 | + | 74.4396i | 0.219430 | + | 0.0908908i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −930.724 | + | 385.518i | −1.13365 | + | 0.469572i | −0.869019 | − | 0.494779i | \(-0.835249\pi\) |
−0.264627 | + | 0.964351i | \(0.585249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 320.389 | − | 320.389i | 0.389294 | − | 0.389294i | −0.485142 | − | 0.874435i | \(-0.661232\pi\) |
0.874435 | + | 0.485142i | \(0.161232\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 556.191 | − | 556.191i | 0.674171 | − | 0.674171i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.6406 | + | 6.06433i | −0.0177032 | + | 0.00733293i | −0.391517 | − | 0.920171i | \(-0.628050\pi\) |
0.373814 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −753.878 | − | 312.267i | −0.909383 | − | 0.376679i | −0.121562 | − | 0.992584i | \(-0.538790\pi\) |
−0.787820 | + | 0.615905i | \(0.788790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1375.70i | 1.65548i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2041.35 | 2.45061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.66607 | − | 23.3360i | 0.0115761 | − | 0.0279473i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 203.199 | + | 490.565i | 0.242770 | + | 0.586099i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 233.705 | + | 233.705i | 0.278552 | + | 0.278552i | 0.832531 | − | 0.553979i | \(-0.186891\pi\) |
−0.553979 | + | 0.832531i | \(0.686891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −125.796 | − | 125.796i | −0.149579 | − | 0.149579i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 522.667 | + | 1261.83i | 0.620008 | + | 1.49683i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 94.8684 | − | 229.033i | 0.112270 | − | 0.271044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −184.423 | −0.217736 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 658.886i | − | 0.776073i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 600.767 | + | 248.846i | 0.705954 | + | 0.292416i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −979.574 | + | 405.753i | −1.14839 | + | 0.475677i | −0.873992 | − | 0.485940i | \(-0.838477\pi\) |
−0.274395 | + | 0.961617i | \(0.588477\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.13633 | − | 3.13633i | 0.00366822 | − | 0.00366822i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 716.322 | − | 716.322i | 0.835848 | − | 0.835848i | −0.152461 | − | 0.988309i | \(-0.548720\pi\) |
0.988309 | + | 0.152461i | \(0.0487198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −398.325 | + | 164.992i | −0.463708 | + | 0.192074i | −0.602291 | − | 0.798277i | \(-0.705745\pi\) |
0.138583 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2000.70 | + | 828.716i | 2.32369 | + | 0.962504i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1279.79i | 1.48295i | 0.670980 | + | 0.741475i | \(0.265874\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 399.132 | 0.461424 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 71.8331 | − | 173.421i | 0.0828525 | − | 0.200024i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.0039 | − | 31.3942i | −0.0149642 | − | 0.0361268i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5021 | + | 10.5021i | 0.0120576 | + | 0.0120576i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 216.321 | + | 216.321i | 0.247790 | + | 0.247790i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 418.684 | + | 1010.79i | 0.478496 | + | 1.15519i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −351.648 | + | 848.954i | −0.400967 | + | 0.968021i | 0.586464 | + | 0.809975i | \(0.300519\pi\) |
−0.987432 | + | 0.158046i | \(0.949481\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 102.285 | 0.116365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1327.06i | 1.50632i | 0.657839 | + | 0.753158i | \(0.271471\pi\) | ||||
−0.657839 | + | 0.753158i | \(0.728529\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −412.717 | − | 170.953i | −0.467403 | − | 0.193605i | 0.136536 | − | 0.990635i | \(-0.456403\pi\) |
−0.603939 | + | 0.797030i | \(0.706403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −360.213 | + | 149.205i | −0.407020 | + | 0.168593i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 411.723 | − | 411.723i | 0.464174 | − | 0.464174i | −0.435847 | − | 0.900021i | \(-0.643551\pi\) |
0.900021 | + | 0.435847i | \(0.143551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −330.347 | + | 330.347i | −0.371594 | + | 0.371594i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 943.871 | − | 390.964i | 1.05934 | − | 0.438793i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6400 | + | 6.89250i | 0.0186338 | + | 0.00771836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.81723i | 0.00538238i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −315.620 | −0.351861 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −247.898 | + | 598.480i | −0.275749 | + | 0.665717i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −222.338 | − | 536.772i | −0.246768 | − | 0.595751i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1542.93 | − | 1542.93i | −1.70867 | − | 1.70867i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 243.156 | + | 243.156i | 0.268681 | + | 0.268681i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −307.189 | − | 741.619i | −0.338687 | − | 0.817662i | −0.997842 | − | 0.0656553i | \(-0.979086\pi\) |
0.659156 | − | 0.752006i | \(-0.270914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.4136 | − | 25.1407i | 0.0114561 | − | 0.0276575i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −708.126 | −0.777307 | −0.388653 | − | 0.921384i | \(-0.627060\pi\) | ||||
−0.388653 | + | 0.921384i | \(0.627060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 636.779i | − | 0.697458i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 166.137 | + | 68.8164i | 0.181571 | + | 0.0752091i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2216.70 | + | 918.187i | −2.41734 | + | 1.00129i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −628.260 | + | 628.260i | −0.683635 | + | 0.683635i | −0.960817 | − | 0.277183i | \(-0.910599\pi\) |
0.277183 | + | 0.960817i | \(0.410599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1223.33 | + | 1223.33i | −1.32826 | + | 1.32826i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 298.679 | − | 123.717i | 0.323596 | − | 0.134038i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 724.221 | + | 299.982i | 0.782941 | + | 0.324305i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 106.074i | 0.114427i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −972.033 | −1.04632 | −0.523161 | − | 0.852234i | \(-0.675247\pi\) | ||||
−0.523161 | + | 0.852234i | \(0.675247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.6801 | − | 110.281i | 0.0490656 | − | 0.118455i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 429.901 | + | 1037.87i | 0.460773 | + | 1.11241i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −193.301 | − | 193.301i | −0.206739 | − | 0.206739i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 396.897 | + | 396.897i | 0.423583 | + | 0.423583i | 0.886435 | − | 0.462853i | \(-0.153174\pi\) |
−0.462853 | + | 0.886435i | \(0.653174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.40618 | − | 13.0517i | −0.00575738 | − | 0.0138996i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 486.386 | − | 1174.24i | 0.516882 | − | 1.24786i | −0.422928 | − | 0.906163i | \(-0.638998\pi\) |
0.939809 | − | 0.341699i | \(-0.111002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −850.634 | −0.902051 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 491.014i | 0.519591i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 319.348 | + | 132.278i | 0.337221 | + | 0.139681i | 0.544867 | − | 0.838523i | \(-0.316580\pi\) |
−0.207646 | + | 0.978204i | \(0.566580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −191.020 | + | 79.1232i | −0.201286 | + | 0.0833753i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1345.32 | − | 1345.32i | 1.41464 | − | 1.41464i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 234.445 | − | 234.445i | 0.246007 | − | 0.246007i | −0.573322 | − | 0.819330i | \(-0.694346\pi\) |
0.819330 | + | 0.573322i | \(0.194346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −295.708 | + | 122.486i | −0.309642 | + | 0.128258i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 849.374 | + | 351.822i | 0.887538 | + | 0.367630i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1366.67i | − | 1.42510i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 328.164 | 0.341482 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −92.4964 | + | 223.306i | −0.0960502 | + | 0.231886i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −137.178 | − | 331.178i | −0.142154 | − | 0.343189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −431.918 | − | 431.918i | −0.446658 | − | 0.446658i | 0.447584 | − | 0.894242i | \(-0.352285\pi\) |
−0.894242 | + | 0.447584i | \(0.852285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.4165 | + | 33.4165i | 0.0344855 | + | 0.0344855i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 391.385 | + | 944.887i | 0.403074 | + | 0.973107i | 0.986915 | + | 0.161239i | \(0.0515490\pi\) |
−0.583841 | + | 0.811868i | \(0.698451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1015.22 | − | 2450.95i | 1.04339 | − | 2.51897i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −380.477 | −0.390233 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1157.98i | − | 1.18524i | −0.805481 | − | 0.592621i | \(-0.798093\pi\) | ||
0.805481 | − | 0.592621i | \(-0.201907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −602.463 | − | 249.548i | −0.615386 | − | 0.254901i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 250.226 | − | 103.647i | 0.255072 | − | 0.105654i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −396.529 | + | 396.529i | −0.403386 | + | 0.403386i | −0.879425 | − | 0.476038i | \(-0.842072\pi\) |
0.476038 | + | 0.879425i | \(0.342072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 394.291 | − | 394.291i | 0.400296 | − | 0.400296i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 864.547 | − | 358.107i | 0.875934 | − | 0.362824i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 791.870 | + | 328.003i | 0.800678 | + | 0.331652i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 134.269i | 0.135489i | 0.997703 | + | 0.0677444i | \(0.0215802\pi\) | ||||
−0.997703 | + | 0.0677444i | \(0.978420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 858.182 | 0.864232 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 236.619 | − | 571.249i | 0.237808 | − | 0.574120i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 470.645 | + | 1136.24i | 0.472061 | + | 1.13966i | 0.963251 | + | 0.268603i | \(0.0865620\pi\) |
−0.491190 | + | 0.871052i | \(0.663438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 531.046 | + | 531.046i | 0.531577 | + | 0.531577i |
(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 | 128.3.h.a.47.6 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.3.4 | ✓ | 28 | ||
8.3 | odd | 2 | 256.3.h.b.95.6 | 28 | |||
8.5 | even | 2 | 256.3.h.a.95.2 | 28 | |||
12.11 | even | 2 | 288.3.u.a.163.4 | 28 | |||
32.5 | even | 8 | 256.3.h.b.159.6 | 28 | |||
32.11 | odd | 8 | inner | 128.3.h.a.79.6 | 28 | ||
32.21 | even | 8 | 32.3.h.a.11.4 | yes | 28 | ||
32.27 | odd | 8 | 256.3.h.a.159.2 | 28 | |||
96.53 | odd | 8 | 288.3.u.a.235.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.4 | ✓ | 28 | 4.3 | odd | 2 | ||
32.3.h.a.11.4 | yes | 28 | 32.21 | even | 8 | ||
128.3.h.a.47.6 | 28 | 1.1 | even | 1 | trivial | ||
128.3.h.a.79.6 | 28 | 32.11 | odd | 8 | inner | ||
256.3.h.a.95.2 | 28 | 8.5 | even | 2 | |||
256.3.h.a.159.2 | 28 | 32.27 | odd | 8 | |||
256.3.h.b.95.6 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.159.6 | 28 | 32.5 | even | 8 | |||
288.3.u.a.163.4 | 28 | 12.11 | even | 2 | |||
288.3.u.a.235.4 | 28 | 96.53 | odd | 8 |