Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,4,Mod(125,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.x (of order \(6\), degree \(2\), 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: | \(44.6054439643\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.15 | ||
Character | \(\chi\) | \(=\) | 756.125 |
Dual form | 756.4.x.a.629.15 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.34269 | − | 4.05766i | 0.209537 | − | 0.362929i | −0.742032 | − | 0.670365i | \(-0.766138\pi\) |
0.951569 | + | 0.307436i | \(0.0994710\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.4121 | − | 1.99859i | 0.994160 | − | 0.107914i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.1150 | + | 9.30397i | −0.441713 | + | 0.255023i | −0.704324 | − | 0.709879i | \(-0.748750\pi\) |
0.262611 | + | 0.964902i | \(0.415416\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.1430 | − | 25.4860i | −0.941775 | − | 0.543734i | −0.0512589 | − | 0.998685i | \(-0.516323\pi\) |
−0.890516 | + | 0.454951i | \(0.849657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −112.833 | −1.60976 | −0.804880 | − | 0.593438i | \(-0.797770\pi\) | ||||
−0.804880 | + | 0.593438i | \(0.797770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 111.459i | 1.34581i | 0.739729 | + | 0.672905i | \(0.234954\pi\) | ||||
−0.739729 | + | 0.672905i | \(0.765046\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 124.503 | + | 71.8819i | 1.12873 | + | 0.651671i | 0.943614 | − | 0.331047i | \(-0.107402\pi\) |
0.185112 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 51.5236 | + | 89.2414i | 0.412189 | + | 0.713932i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −206.907 | + | 119.458i | −1.32489 | + | 0.764924i | −0.984504 | − | 0.175363i | \(-0.943890\pi\) |
−0.340383 | + | 0.940287i | \(0.610557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 179.999 | + | 103.923i | 1.04287 | + | 0.602099i | 0.920644 | − | 0.390404i | \(-0.127665\pi\) |
0.122222 | + | 0.992503i | \(0.460998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.0243 | − | 79.3922i | 0.169148 | − | 0.383421i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −227.815 | −1.01223 | −0.506115 | − | 0.862466i | \(-0.668919\pi\) | ||||
−0.506115 | + | 0.862466i | \(0.668919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 133.141 | − | 230.607i | 0.507149 | − | 0.878407i | −0.492817 | − | 0.870133i | \(-0.664033\pi\) |
0.999966 | − | 0.00827417i | \(-0.00263378\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −170.287 | − | 294.946i | −0.603920 | − | 1.04602i | −0.992221 | − | 0.124488i | \(-0.960271\pi\) |
0.388301 | − | 0.921533i | \(-0.373062\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −111.979 | − | 193.952i | −0.347527 | − | 0.601934i | 0.638283 | − | 0.769802i | \(-0.279645\pi\) |
−0.985809 | + | 0.167868i | \(0.946312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.011 | − | 73.5964i | 0.976709 | − | 0.214567i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 547.974i | 1.42019i | 0.704107 | + | 0.710094i | \(0.251348\pi\) | ||||
−0.704107 | + | 0.710094i | \(0.748652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 87.1854i | 0.213747i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43.9483 | + | 76.1207i | −0.0969760 | + | 0.167967i | −0.910432 | − | 0.413660i | \(-0.864250\pi\) |
0.813456 | + | 0.581627i | \(0.197584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 312.398 | − | 180.363i | 0.655712 | − | 0.378575i | −0.134929 | − | 0.990855i | \(-0.543081\pi\) |
0.790641 | + | 0.612280i | \(0.209747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −206.827 | + | 119.412i | −0.394673 | + | 0.227865i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −372.426 | + | 645.060i | −0.679090 | + | 1.17622i | 0.296165 | + | 0.955137i | \(0.404292\pi\) |
−0.975255 | + | 0.221082i | \(0.929041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 135.948i | 0.227240i | 0.993524 | + | 0.113620i | \(0.0362447\pi\) | ||||
−0.993524 | + | 0.113620i | \(0.963755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 467.289i | 0.749206i | 0.927185 | + | 0.374603i | \(0.122221\pi\) | ||||
−0.927185 | + | 0.374603i | \(0.877779\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −278.115 | + | 203.513i | −0.411613 | + | 0.301201i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 192.171 | + | 332.850i | 0.273683 | + | 0.474032i | 0.969802 | − | 0.243894i | \(-0.0784249\pi\) |
−0.696119 | + | 0.717926i | \(0.745092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 597.216 | + | 1034.41i | 0.789795 | + | 1.36796i | 0.926092 | + | 0.377297i | \(0.123146\pi\) |
−0.136297 | + | 0.990668i | \(0.543520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −264.332 | + | 457.836i | −0.337304 | + | 0.584228i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1385.63 | 1.65030 | 0.825150 | − | 0.564914i | \(-0.191091\pi\) | ||||
0.825150 | + | 0.564914i | \(0.191091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −863.702 | − | 381.027i | −0.994952 | − | 0.438929i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 452.262 | + | 261.114i | 0.488433 | + | 0.281997i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1070.10 | + | 617.821i | −1.12012 | + | 0.646704i | −0.941432 | − | 0.337202i | \(-0.890520\pi\) |
−0.178691 | + | 0.983905i | \(0.557186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −94.1707 | − | 163.108i | −0.0927756 | − | 0.160692i | 0.815902 | − | 0.578190i | \(-0.196241\pi\) |
−0.908678 | + | 0.417498i | \(0.862907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −687.152 | − | 396.727i | −0.657350 | − | 0.379521i | 0.133916 | − | 0.990993i | \(-0.457245\pi\) |
−0.791267 | + | 0.611471i | \(0.790578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1399.55i | 1.26448i | 0.774773 | + | 0.632240i | \(0.217864\pi\) | ||||
−0.774773 | + | 0.632240i | \(0.782136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2137.48 | −1.87829 | −0.939145 | − | 0.343521i | \(-0.888380\pi\) | ||||
−0.939145 | + | 0.343521i | \(0.888380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1500.15 | + | 866.110i | 1.24887 | + | 0.721034i | 0.970884 | − | 0.239552i | \(-0.0770006\pi\) |
0.277984 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 583.346 | − | 336.795i | 0.473020 | − | 0.273098i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2077.48 | + | 225.506i | −1.60036 | + | 0.173715i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −492.372 | + | 852.814i | −0.369926 | + | 0.640731i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1068.49 | 0.764549 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −770.489 | −0.538345 | −0.269173 | − | 0.963092i | \(-0.586750\pi\) | ||||
−0.269173 | + | 0.963092i | \(0.586750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −489.800 | + | 848.359i | −0.326672 | + | 0.565813i | −0.981849 | − | 0.189662i | \(-0.939261\pi\) |
0.655177 | + | 0.755475i | \(0.272594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 222.760 | + | 2052.19i | 0.145231 | + | 1.33795i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 182.458 | − | 105.342i | 0.113784 | − | 0.0656932i | −0.442028 | − | 0.897001i | \(-0.645741\pi\) |
0.555812 | + | 0.831308i | \(0.312407\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 730.515 | + | 421.763i | 0.445766 | + | 0.257363i | 0.706040 | − | 0.708172i | \(-0.250480\pi\) |
−0.260274 | + | 0.965535i | \(0.583813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 948.484 | 0.554659 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1119.41i | 0.641119i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1137.32 | − | 656.632i | −0.625321 | − | 0.361029i | 0.153617 | − | 0.988131i | \(-0.450908\pi\) |
−0.778938 | + | 0.627101i | \(0.784241\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1738.76 | − | 3011.62i | −0.937074 | − | 1.62306i | −0.770893 | − | 0.636965i | \(-0.780190\pi\) |
−0.166182 | − | 0.986095i | \(-0.553144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 843.366 | − | 486.918i | 0.437038 | − | 0.252324i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −499.729 | − | 288.519i | −0.254030 | − | 0.146664i | 0.367578 | − | 0.929993i | \(-0.380187\pi\) |
−0.621608 | + | 0.783328i | \(0.713520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2436.03 | + | 1074.67i | 1.19246 | + | 0.526060i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1595.73 | 0.766794 | 0.383397 | − | 0.923584i | \(-0.374754\pi\) | ||||
0.383397 | + | 0.923584i | \(0.374754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.918 | − | 320.287i | 0.0856850 | − | 0.148411i | −0.819998 | − | 0.572366i | \(-0.806025\pi\) |
0.905683 | + | 0.423956i | \(0.139359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 200.572 | + | 347.402i | 0.0912938 | + | 0.158125i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −973.579 | − | 1686.29i | −0.427860 | − | 0.741076i | 0.568822 | − | 0.822460i | \(-0.307399\pi\) |
−0.996683 | + | 0.0813844i | \(0.974066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1127.01 | + | 1540.15i | 0.486824 | + | 0.665282i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 851.921i | − | 0.355730i | −0.984055 | − | 0.177865i | \(-0.943081\pi\) | ||
0.984055 | − | 0.177865i | \(-0.0569190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 639.259i | − | 0.262518i | −0.991348 | − | 0.131259i | \(-0.958098\pi\) | ||
0.991348 | − | 0.131259i | \(-0.0419020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −533.700 | + | 924.395i | −0.212099 | + | 0.367367i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1818.29 | − | 1049.79i | 0.711051 | − | 0.410526i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3120.13 | + | 1801.41i | −1.18201 | + | 0.682435i | −0.956479 | − | 0.291800i | \(-0.905746\pi\) |
−0.225533 | + | 0.974235i | \(0.572412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1745.01 | + | 3022.44i | −0.650821 | + | 1.12725i | 0.332103 | + | 0.943243i | \(0.392242\pi\) |
−0.982924 | + | 0.184012i | \(0.941092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1909.86i | 0.690719i | 0.938470 | + | 0.345360i | \(0.112243\pi\) | ||||
−0.938470 | + | 0.345360i | \(0.887757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 713.005i | 0.253988i | 0.991903 | + | 0.126994i | \(0.0405329\pi\) | ||||
−0.991903 | + | 0.126994i | \(0.959467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3570.85 | + | 2612.99i | −1.23460 | + | 0.903430i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −623.816 | − | 1080.48i | −0.212533 | − | 0.368117i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1037.01 | − | 1796.15i | −0.343213 | − | 0.594462i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 788.596 | − | 1365.89i | 0.257295 | − | 0.445648i | −0.708221 | − | 0.705990i | \(-0.750502\pi\) |
0.965516 | + | 0.260343i | \(0.0838355\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1595.72 | −0.506174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3521.86 | + | 1553.69i | 1.10175 | + | 0.486043i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4980.77 | + | 2875.65i | 1.51603 | + | 0.875281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −412.569 | + | 238.197i | −0.123891 | + | 0.0715284i | −0.560665 | − | 0.828043i | \(-0.689454\pi\) |
0.436774 | + | 0.899571i | \(0.356121\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1386.85 | − | 2402.10i | −0.405501 | − | 0.702348i | 0.588879 | − | 0.808221i | \(-0.299569\pi\) |
−0.994380 | + | 0.105873i | \(0.966236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1698.53 | + | 980.646i | 0.490139 | + | 0.282982i | 0.724632 | − | 0.689136i | \(-0.242010\pi\) |
−0.234493 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4734.94i | − | 1.33132i | −0.746257 | − | 0.665658i | \(-0.768151\pi\) | ||
0.746257 | − | 0.665658i | \(-0.231849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1049.33 | −0.291279 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1055.48 | + | 609.379i | 0.285661 | + | 0.164927i | 0.635984 | − | 0.771703i | \(-0.280595\pi\) |
−0.350322 | + | 0.936629i | \(0.613928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1784.77 | − | 1030.43i | 0.477041 | − | 0.275420i | −0.242142 | − | 0.970241i | \(-0.577850\pi\) |
0.719182 | + | 0.694821i | \(0.244517\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 486.199 | − | 1531.78i | 0.126784 | − | 0.399435i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2840.64 | − | 4920.13i | 0.731763 | − | 1.26745i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2966.29 | −0.745937 | −0.372969 | − | 0.927844i | \(-0.621660\pi\) | ||||
−0.372969 | + | 0.927844i | \(0.621660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2675.15 | −0.664764 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1133.09 | − | 1962.58i | 0.275021 | − | 0.476351i | −0.695119 | − | 0.718895i | \(-0.744648\pi\) |
0.970141 | + | 0.242543i | \(0.0779817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4194.54 | + | 455.307i | −1.00632 | + | 0.109233i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1580.16 | − | 912.308i | 0.370483 | − | 0.213898i | −0.303186 | − | 0.952931i | \(-0.598050\pi\) |
0.673669 | + | 0.739033i | \(0.264717\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2223.49 | + | 1283.73i | 0.515427 | + | 0.297582i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5616.89 | 1.27312 | 0.636558 | − | 0.771229i | \(-0.280358\pi\) | ||||
0.636558 | + | 0.771229i | \(0.280358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5603.22i | − | 1.25598i | −0.778220 | − | 0.627992i | \(-0.783877\pi\) | ||
0.778220 | − | 0.627992i | \(-0.216123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1660.60 | − | 958.748i | −0.364138 | − | 0.210235i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2329.35 | + | 4034.55i | 0.505260 | + | 0.875137i | 0.999981 | + | 0.00608483i | \(0.00193687\pi\) |
−0.494721 | + | 0.869052i | \(0.664730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1939.85 | + | 1119.97i | −0.411820 | + | 0.237765i | −0.691572 | − | 0.722308i | \(-0.743081\pi\) |
0.279751 | + | 0.960073i | \(0.409748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2759.51 | − | 1593.21i | −0.579633 | − | 0.334651i | 0.181355 | − | 0.983418i | \(-0.441952\pi\) |
−0.760987 | + | 0.648767i | \(0.775285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1990.51 | − | 4512.05i | 0.409395 | − | 0.928006i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7818.18 | 1.59132 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4563.57 | + | 7904.34i | −0.909921 | + | 1.57603i | −0.0957489 | + | 0.995406i | \(0.530525\pi\) |
−0.814172 | + | 0.580624i | \(0.802809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 205.915 | + | 356.655i | 0.0406401 | + | 0.0703907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3663.97 | − | 6346.18i | −0.708671 | − | 1.22745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3724.82 | − | 5090.25i | −0.713274 | − | 0.974741i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1690.14i | − | 0.317302i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4744.58i | 0.882044i | 0.897496 | + | 0.441022i | \(0.145384\pi\) | ||||
−0.897496 | + | 0.441022i | \(0.854616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1089.62 | + | 1887.29i | −0.198672 | + | 0.344110i | −0.948098 | − | 0.317978i | \(-0.896996\pi\) |
0.749426 | + | 0.662088i | \(0.230329\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1752.85 | − | 1012.01i | 0.316540 | − | 0.182754i | −0.333309 | − | 0.942818i | \(-0.608165\pi\) |
0.649849 | + | 0.760063i | \(0.274832\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −189.948 | + | 109.666i | −0.0336547 | + | 0.0194305i | −0.516733 | − | 0.856147i | \(-0.672852\pi\) |
0.483078 | + | 0.875577i | \(0.339519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2222.87 | − | 3850.12i | 0.390146 | − | 0.675753i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12576.2i | − | 2.16643i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5252.52i | − | 0.896484i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2449.39 | − | 3347.27i | −0.410454 | − | 0.560916i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1884.36 | + | 3263.81i | 0.312912 | + | 0.541980i | 0.978991 | − | 0.203901i | \(-0.0653621\pi\) |
−0.666079 | + | 0.745881i | \(0.732029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1744.96 | + | 3022.36i | 0.284589 | + | 0.492922i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3056.60 | − | 5294.18i | 0.494076 | − | 0.855764i | −0.505901 | − | 0.862592i | \(-0.668840\pi\) |
0.999977 | + | 0.00682736i | \(0.00217323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3867.57 | −0.614196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6021.17 | − | 2024.61i | 0.947851 | − | 0.318714i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1143.36 | − | 660.117i | −0.176883 | − | 0.102124i | 0.408944 | − | 0.912559i | \(-0.365897\pi\) |
−0.585828 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2309.07 | − | 1333.14i | 0.354159 | − | 0.204474i | −0.312357 | − | 0.949965i | \(-0.601118\pi\) |
0.666515 | + | 0.745491i | \(0.267785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4725.05 | − | 8184.03i | −0.712434 | − | 1.23397i | −0.963941 | − | 0.266116i | \(-0.914260\pi\) |
0.251508 | − | 0.967855i | \(-0.419074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 551.632 | + | 318.485i | 0.0824720 | + | 0.0476152i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6846.88i | − | 1.00659i | −0.864116 | − | 0.503293i | \(-0.832122\pi\) | ||
0.864116 | − | 0.503293i | \(-0.167878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5564.07 | −0.811206 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1896.10 | + | 1094.71i | 0.271908 | + | 0.156986i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5440.63 | + | 3141.15i | −0.773838 | + | 0.446775i | −0.834242 | − | 0.551399i | \(-0.814094\pi\) |
0.0604042 | + | 0.998174i | \(0.480761\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1095.17 | + | 10089.4i | 0.153258 | + | 1.41189i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5253.75 | + | 9099.76i | −0.729300 | + | 1.26318i | 0.227880 | + | 0.973689i | \(0.426821\pi\) |
−0.957179 | + | 0.289495i | \(0.906513\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12178.0 | 1.66366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5904.89 | 0.800301 | 0.400150 | − | 0.916450i | \(-0.368958\pi\) | ||||
0.400150 | + | 0.916450i | \(0.368958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1175.26 | + | 2035.61i | −0.156797 | + | 0.271580i | −0.933712 | − | 0.358026i | \(-0.883450\pi\) |
0.776915 | + | 0.629605i | \(0.216783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 174.248 | + | 1605.27i | 0.0230662 | + | 0.212499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11034.6 | − | 6370.81i | 1.43824 | − | 0.830368i | 0.440511 | − | 0.897747i | \(-0.354797\pi\) |
0.997727 | + | 0.0673794i | \(0.0214638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14048.0 | − | 8110.62i | −1.81698 | − | 1.04903i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1800.79 | 0.229386 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13326.3i | − | 1.68470i | −0.538930 | − | 0.842350i | \(-0.681171\pi\) | ||
0.538930 | − | 0.842350i | \(-0.318829\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8090.75 | + | 4671.20i | 1.00756 | + | 0.581717i | 0.910477 | − | 0.413559i | \(-0.135715\pi\) |
0.0970856 | + | 0.995276i | \(0.469048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5297.15 | − | 9174.92i | −0.654763 | − | 1.13408i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3671.22 | − | 2119.58i | 0.447115 | − | 0.258142i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −268.033 | − | 154.749i | −0.0324044 | − | 0.0187087i | 0.483710 | − | 0.875228i | \(-0.339289\pi\) |
−0.516115 | + | 0.856519i | \(0.672622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −657.047 | + | 1489.38i | −0.0782837 | + | 0.177452i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5596.38 | 0.661965 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3008.72 | + | 5211.26i | −0.350801 | + | 0.607605i | −0.986390 | − | 0.164422i | \(-0.947424\pi\) |
0.635589 | + | 0.772028i | \(0.280757\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1920.18 | + | 3325.85i | 0.222289 | + | 0.385017i | 0.955503 | − | 0.294982i | \(-0.0953137\pi\) |
−0.733213 | + | 0.679999i | \(0.761980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5813.53 | − | 10069.3i | −0.663524 | − | 1.14926i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5391.43 | − | 3945.21i | 0.611029 | − | 0.447125i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4510.80i | − | 0.504125i | −0.967711 | − | 0.252062i | \(-0.918891\pi\) | ||
0.967711 | − | 0.252062i | \(-0.0811088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7012.84i | 0.778328i | 0.921169 | + | 0.389164i | \(0.127236\pi\) | ||||
−0.921169 | + | 0.389164i | \(0.872764\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8011.88 | + | 13877.0i | −0.877025 | + | 1.51905i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3220.45 | − | 1859.33i | 0.350122 | − | 0.202143i | −0.314617 | − | 0.949219i | \(-0.601876\pi\) |
0.664739 | + | 0.747075i | \(0.268543\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5177.61 | + | 2989.29i | −0.555295 | + | 0.320599i | −0.751255 | − | 0.660012i | \(-0.770551\pi\) |
0.195960 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3246.11 | − | 5622.43i | 0.345799 | − | 0.598941i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1188.91i | − | 0.124963i | −0.998046 | − | 0.0624813i | \(-0.980099\pi\) | ||
0.998046 | − | 0.0624813i | \(-0.0199014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4954.95i | 0.517338i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3569.47 | + | 2611.98i | −0.367779 | + | 0.269125i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2039.30 | + | 3532.17i | 0.208741 | + | 0.361549i | 0.951318 | − | 0.308211i | \(-0.0997302\pi\) |
−0.742577 | + | 0.669760i | \(0.766397\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3283.79 | − | 5687.69i | −0.331760 | − | 0.574625i | 0.651097 | − | 0.758995i | \(-0.274309\pi\) |
−0.982857 | + | 0.184369i | \(0.940976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4120.60 | + | 7137.09i | −0.413608 | + | 0.716390i | −0.995281 | − | 0.0970322i | \(-0.969065\pi\) |
0.581673 | + | 0.813423i | \(0.302398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11330.9 | 1.12276 | 0.561382 | − | 0.827557i | \(-0.310270\pi\) | ||||
0.561382 | + | 0.827557i | \(0.310270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5567.93 | + | 12621.2i | −0.548194 | + | 1.24263i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5488.35 | + | 3168.70i | 0.533519 | + | 0.308027i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9946.74 | + | 5742.76i | −0.960817 | + | 0.554728i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4151.12 | − | 7189.94i | −0.395969 | − | 0.685839i | 0.597255 | − | 0.802051i | \(-0.296258\pi\) |
−0.993224 | + | 0.116212i | \(0.962925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10056.4 | + | 5806.08i | 0.953292 | + | 0.550384i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5789.46i | 0.542033i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −76.4693 | −0.00711530 | −0.00355765 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355765 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6951.74 | − | 4013.59i | −0.638957 | − | 0.368902i | 0.145256 | − | 0.989394i | \(-0.453599\pi\) |
−0.784213 | + | 0.620492i | \(0.786933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23345.9 | − | 13478.7i | 2.13275 | − | 1.23134i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 271.704 | + | 2503.09i | 0.0245223 | + | 0.225913i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8035.68 | − | 13918.2i | 0.720895 | − | 1.24863i | −0.239747 | − | 0.970836i | \(-0.577064\pi\) |
0.960641 | − | 0.277791i | \(-0.0896023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7450.97 | 0.660481 | 0.330241 | − | 0.943897i | \(-0.392870\pi\) | ||||
0.330241 | + | 0.943897i | \(0.392870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −882.452 | −0.0777596 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6060.49 | − | 10497.1i | 0.527753 | − | 0.914095i | −0.471724 | − | 0.881746i | \(-0.656368\pi\) |
0.999477 | − | 0.0323486i | \(-0.0102987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 933.918 | + | 8603.77i | 0.0808495 | + | 0.744830i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3219.57 | + | 1858.82i | −0.275478 | + | 0.159047i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3609.06 | + | 2083.69i | 0.307014 | + | 0.177255i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10433.7 | −0.877371 | −0.438685 | − | 0.898641i | \(-0.644556\pi\) | ||||
−0.438685 | + | 0.898641i | \(0.644556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 22346.3i | − | 1.86833i | −0.356846 | − | 0.934163i | \(-0.616148\pi\) | ||
0.356846 | − | 0.934163i | \(-0.383852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20309.8 | − | 11725.9i | −1.67876 | − | 0.969234i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4250.53 | + | 7362.13i | 0.349349 | + | 0.605090i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11754.5 | + | 6786.45i | −0.955240 | + | 0.551508i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5678.89 | + | 3278.71i | 0.458916 | + | 0.264955i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4713.95 | + | 4302.94i | −0.376706 | + | 0.343860i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13690.0 | −1.08794 | −0.543972 | − | 0.839103i | \(-0.683080\pi\) | ||||
−0.543972 | + | 0.839103i | \(0.683080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5007.46 | + | 8673.18i | −0.393571 | + | 0.681685i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8042.35 | − | 13929.8i | −0.628640 | − | 1.08884i | −0.987825 | − | 0.155570i | \(-0.950279\pi\) |
0.359185 | − | 0.933266i | \(-0.383055\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13314.6 | − | 23061.6i | −1.02944 | − | 1.78305i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4203.50 | + | 5744.40i | 0.323239 | + | 0.441730i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9207.28i | 0.700404i | 0.936674 | + | 0.350202i | \(0.113887\pi\) | ||||
−0.936674 | + | 0.350202i | \(0.886113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17359.8i | 1.31349i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10095.6 | − | 17486.0i | 0.755732 | − | 1.30897i | −0.189278 | − | 0.981924i | \(-0.560615\pi\) |
0.945010 | − | 0.327042i | \(-0.106052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7028.77 | − | 4058.06i | 0.523367 | − | 0.302166i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3118.35 | − | 1800.38i | 0.229750 | − | 0.132646i | −0.380707 | − | 0.924696i | \(-0.624319\pi\) |
0.610457 | + | 0.792050i | \(0.290986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1111.32 | + | 1924.86i | −0.0814489 | + | 0.141074i | −0.903873 | − | 0.427802i | \(-0.859288\pi\) |
0.822424 | + | 0.568876i | \(0.192621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14814.5i | 1.07444i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8818.52i | 0.636256i | 0.948048 | + | 0.318128i | \(0.103054\pi\) | ||||
−0.948048 | + | 0.318128i | \(0.896946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13063.4 | + | 17852.0i | 0.932805 | + | 1.27475i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5098.33 | − | 8830.57i | −0.362181 | − | 0.627316i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9540.65 | + | 16524.9i | 0.670843 | + | 1.16193i | 0.977665 | + | 0.210167i | \(0.0674008\pi\) |
−0.306823 | + | 0.951767i | \(0.599266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11583.1 | + | 20062.5i | −0.810311 | + | 1.40350i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7386.65 | −0.511523 | −0.255762 | − | 0.966740i | \(-0.582326\pi\) | ||||
−0.255762 | + | 0.966740i | \(0.582326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3951.88 | + | 8958.02i | −0.272288 | + | 0.617215i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5442.40 | − | 3142.17i | −0.371236 | − | 0.214333i | 0.302762 | − | 0.953066i | \(-0.402091\pi\) |
−0.673998 | + | 0.738733i | \(0.735425\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23587.5 | + | 13618.2i | −1.60092 | + | 0.924291i | −0.609615 | + | 0.792697i | \(0.708676\pi\) |
−0.991304 | + | 0.131594i | \(0.957991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2306.95 | + | 3995.76i | 0.155026 | + | 0.268514i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2294.69 | + | 1324.84i | 0.153441 | + | 0.0885891i | 0.574755 | − | 0.818326i | \(-0.305098\pi\) |
−0.421314 | + | 0.906915i | \(0.638431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11415.5i | 0.755848i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19866.5 | 1.30897 | 0.654486 | − | 0.756074i | \(-0.272885\pi\) | ||||
0.654486 | + | 0.756074i | \(0.272885\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21498.0 | + | 12411.9i | 1.40272 | + | 0.809858i | 0.994671 | − | 0.103104i | \(-0.0328775\pi\) |
0.408044 | + | 0.912962i | \(0.366211\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6535.31 | + | 3773.16i | −0.424356 | + | 0.245002i | −0.696939 | − | 0.717130i | \(-0.745455\pi\) |
0.272583 | + | 0.962132i | \(0.412122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25512.4 | − | 2769.31i | 1.64066 | − | 0.178090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3937.30 | + | 6819.61i | −0.251987 | + | 0.436455i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25704.9 | 1.62944 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10950.1 | −0.690837 | −0.345418 | − | 0.938449i | \(-0.612263\pi\) | ||||
−0.345418 | + | 0.938449i | \(0.612263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1805.02 | + | 3126.39i | −0.112803 | + | 0.195381i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16664.1 | − | 5289.33i | −1.03651 | − | 0.328996i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27715.4 | + | 16001.5i | −1.70779 | + | 0.985994i | −0.770504 | + | 0.637435i | \(0.779996\pi\) |
−0.937287 | + | 0.348559i | \(0.886671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4359.15 | + | 2516.76i | 0.267353 | + | 0.154356i | 0.627684 | − | 0.778468i | \(-0.284003\pi\) |
−0.360331 | + | 0.932824i | \(0.617336\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5406.97 | −0.328547 | −0.164274 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164274 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1635.58i | − | 0.0989245i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22480.8 | + | 12979.3i | 1.34723 | + | 0.777826i | 0.987857 | − | 0.155367i | \(-0.0496561\pi\) |
0.359377 | + | 0.933193i | \(0.382989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2294.90 | + | 3974.89i | 0.136900 | + | 0.237117i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22849.6 | + | 13192.2i | −1.35067 | + | 0.779811i | −0.988344 | − | 0.152240i | \(-0.951351\pi\) |
−0.362328 | + | 0.932051i | \(0.618018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4642.84 | − | 2680.54i | −0.273200 | − | 0.157732i | 0.357141 | − | 0.934051i | \(-0.383752\pi\) |
−0.630341 | + | 0.776318i | \(0.717085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8848.96 | + | 3903.77i | 0.516012 | + | 0.227642i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34347.5 | −1.99391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3356.18 | + | 5813.08i | −0.193091 | + | 0.334443i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3378.73 | + | 5852.13i | 0.193522 | + | 0.335190i | 0.946415 | − | 0.322953i | \(-0.104676\pi\) |
−0.752893 | + | 0.658143i | \(0.771342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2962.04 | − | 5130.41i | −0.168154 | − | 0.291252i | 0.769617 | − | 0.638506i | \(-0.220447\pi\) |
−0.937771 | + | 0.347254i | \(0.887114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18468.0 | + | 13514.1i | −1.04379 | + | 0.763804i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8838.52i | 0.495163i | 0.968867 | + | 0.247582i | \(0.0796358\pi\) | ||||
−0.968867 | + | 0.247582i | \(0.920364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 987.135i | − | 0.0550606i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13965.7 | − | 24189.2i | 0.772205 | − | 1.33750i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25392.1 | − | 14660.1i | 1.39792 | − | 0.807087i | 0.403741 | − | 0.914873i | \(-0.367710\pi\) |
0.994174 | + | 0.107787i | \(0.0343763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3422.75 | − | 1976.12i | 0.186809 | − | 0.107854i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15022.6 | + | 26019.9i | −0.816387 | + | 1.41402i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15890.7i | − | 0.856184i | −0.903735 | − | 0.428092i | \(-0.859186\pi\) | ||
0.903735 | − | 0.428092i | \(-0.140814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 25391.9i | − | 1.36227i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2059.87 | − | 2814.96i | −0.109575 | − | 0.149742i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1060.77 | + | 1837.31i | 0.0561890 | + | 0.0973222i | 0.892752 | − | 0.450549i | \(-0.148772\pi\) |
−0.836563 | + | 0.547871i | \(0.815438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14940.3 | + | 25877.4i | 0.784740 | + | 1.35921i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2222.01 | − | 3848.63i | 0.116222 | − | 0.201302i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23897.3 | −1.23953 | −0.619764 | − | 0.784789i | \(-0.712772\pi\) | ||||
−0.619764 | + | 0.784789i | \(0.712772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13444.8 | − | 5931.25i | −0.694467 | − | 0.306368i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21321.2 | − | 12309.8i | −1.09221 | − | 0.630586i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10755.1 | − | 6209.44i | 0.548670 | − | 0.316775i | −0.199915 | − | 0.979813i | \(-0.564067\pi\) |
0.748586 | + | 0.663038i | \(0.230733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19213.9 | + | 33279.5i | 0.972166 | + | 1.68384i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −199.317 | − | 115.076i | −0.0100436 | − | 0.00579865i | 0.494970 | − | 0.868910i | \(-0.335179\pi\) |
−0.505013 | + | 0.863112i | \(0.668512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 13860.2i | − | 0.692734i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6421.89 | 0.319666 | 0.159833 | − | 0.987144i | \(-0.448904\pi\) | ||||
0.159833 | + | 0.987144i | \(0.448904\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 693.090 | + | 400.156i | 0.0342221 | + | 0.0197581i | 0.517013 | − | 0.855977i | \(-0.327044\pi\) |
−0.482791 | + | 0.875735i | \(0.660377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5328.78 | + | 3076.58i | −0.262056 | + | 0.151298i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2797.12 | + | 25768.6i | 0.136455 | + | 1.25710i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −971.585 | + | 1682.83i | −0.0472086 | + | 0.0817676i | −0.888664 | − | 0.458559i | \(-0.848366\pi\) |
0.841456 | + | 0.540326i | \(0.181699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16293.5 | −0.785406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16016.6 | 0.768999 | 0.384500 | − | 0.923125i | \(-0.374374\pi\) | ||||
0.384500 | + | 0.923125i | \(0.374374\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20615.4 | − | 35706.8i | 0.982005 | − | 1.70088i | 0.327450 | − | 0.944869i | \(-0.393811\pi\) |
0.654555 | − | 0.756014i | \(-0.272856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39355.5 | + | 4271.94i | −1.86732 | + | 0.202693i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3880.03 | − | 2240.13i | 0.182659 | − | 0.105458i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4147.70 | + | 2394.68i | 0.194499 | + | 0.112294i | 0.594087 | − | 0.804401i | \(-0.297513\pi\) |
−0.399588 | + | 0.916695i | \(0.630847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12950.9 | 0.602601 | 0.301301 | − | 0.953529i | \(-0.402579\pi\) | ||||
0.301301 | + | 0.953529i | \(0.402579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21417.9i | 0.992713i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25703.1 | + | 14839.7i | 1.18217 | + | 0.682526i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1264.86 | − | 2190.80i | −0.0579515 | − | 0.100375i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2341.42 | + | 1351.82i | −0.106457 | + | 0.0614632i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2678.82 | − | 1546.62i | −0.121334 | − | 0.0700521i | 0.438105 | − | 0.898924i | \(-0.355650\pi\) |
−0.559439 | + | 0.828872i | \(0.688983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29351.9 | + | 12948.7i | 1.31938 | + | 0.582053i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18386.9 | −0.823377 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5377.34 | + | 9313.83i | −0.238990 | + | 0.413943i | −0.960425 | − | 0.278539i | \(-0.910150\pi\) |
0.721434 | + | 0.692483i | \(0.243483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12634.8 | + | 21884.1i | 0.559434 | + | 0.968968i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4347.64 | − | 7530.34i | −0.191065 | − | 0.330934i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10067.5 | − | 7366.97i | 0.440786 | − | 0.322548i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29409.3i | 1.27809i | 0.769169 | + | 0.639045i | \(0.220670\pi\) | ||||
−0.769169 | + | 0.639045i | \(0.779330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8850.91i | 0.383228i | 0.981470 | + | 0.191614i | \(0.0613721\pi\) | ||||
−0.981470 | + | 0.191614i | \(0.938628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3738.31 | − | 6474.95i | 0.160672 | − | 0.278291i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32874.4 | − | 18980.0i | 1.40775 | − | 0.812763i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23750.3 | − | 13712.2i | 1.00961 | − | 0.582899i | 0.0985331 | − | 0.995134i | \(-0.468585\pi\) |
0.911078 | + | 0.412235i | \(0.135252\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12157.4 | − | 21057.2i | 0.514921 | − | 0.891869i | −0.484929 | − | 0.874554i | \(-0.661155\pi\) |
0.999850 | − | 0.0173159i | \(-0.00551209\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14415.0i | − | 0.606119i | −0.952972 | − | 0.303059i | \(-0.901992\pi\) | ||
0.952972 | − | 0.303059i | \(-0.0980081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8609.61i | 0.360704i | 0.983602 | + | 0.180352i | \(0.0577238\pi\) | ||||
−0.983602 | + | 0.180352i | \(0.942276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37800.2 | + | 8304.07i | −1.57227 | + | 0.345401i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −866.413 | − | 1500.67i | −0.0359083 | − | 0.0621950i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3728.54 | + | 6458.02i | 0.153425 | + | 0.265740i | 0.932484 | − | 0.361210i | \(-0.117636\pi\) |
−0.779059 | + | 0.626950i | \(0.784303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16345.9 | − | 28311.9i | 0.670216 | − | 1.16085i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1879.52 | 0.0765177 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7361.18 | + | 16686.1i | −0.298623 | + | 0.676910i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28363.6 | − | 16375.8i | −1.14253 | − | 0.659640i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29109.8 | + | 16806.6i | −1.16847 | + | 0.674615i | −0.953318 | − | 0.301967i | \(-0.902357\pi\) |
−0.215148 | + | 0.976581i | \(0.569024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20047.3 | − | 34723.0i | −0.799071 | − | 1.38403i | −0.920222 | − | 0.391397i | \(-0.871992\pi\) |
0.121151 | − | 0.992634i | \(-0.461341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15246.8 | − | 8802.77i | −0.605606 | − | 0.349647i | 0.165638 | − | 0.986187i | \(-0.447032\pi\) |
−0.771244 | + | 0.636540i | \(0.780365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36465.5i | 1.43835i | 0.694827 | + | 0.719177i | \(0.255481\pi\) | ||||
−0.694827 | + | 0.719177i | \(0.744519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9123.19 | −0.358610 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6193.65 | − | 3575.91i | −0.241778 | − | 0.139591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32880.0 | − | 18983.3i | 1.27910 | − | 0.738489i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19673.1 | − | 2135.47i | 0.760084 | − | 0.0825052i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16637.8 | + | 28817.5i | −0.640614 | + | 1.10958i | 0.344682 | + | 0.938719i | \(0.387987\pi\) |
−0.985296 | + | 0.170856i | \(0.945347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11874.3 | −0.454091 | −0.227045 | − | 0.973884i | \(-0.572907\pi\) | ||||
−0.227045 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17571.9 | −0.669697 | −0.334848 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334848 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14706.9 | − | 25473.1i | 0.556719 | − | 0.964266i | −0.441048 | − | 0.897483i | \(-0.645393\pi\) |
0.997768 | − | 0.0667825i | \(-0.0212734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14186.3 | + | 1539.89i | −0.535202 | + | 0.0580948i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21617.7 | − | 12481.0i | 0.810089 | − | 0.467705i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3456.81 | − | 1995.79i | −0.129104 | − | 0.0745385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49657.5 | −1.84224 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 61829.3i | − | 2.28616i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2593.90 | − | 1497.59i | −0.0952753 | − | 0.0550072i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6950.77 | + | 12039.1i | 0.254462 | + | 0.440740i | 0.964749 | − | 0.263171i | \(-0.0847684\pi\) |
−0.710288 | + | 0.703912i | \(0.751435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40292.9 | − | 23263.1i | 1.46538 | − | 0.846038i | 0.466129 | − | 0.884717i | \(-0.345648\pi\) |
0.999252 | + | 0.0386789i | \(0.0123149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19248.2 | − | 11113.0i | −0.697725 | − | 0.402832i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7322.74 | + | 16599.0i | −0.263706 | + | 0.597761i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48733.4 | 1.74926 | 0.874628 | − | 0.484794i | \(-0.161106\pi\) | ||||
0.874628 | + | 0.484794i | \(0.161106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3464.77 | − | 6001.16i | 0.123558 | − | 0.214009i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11737.8 | − | 20330.5i | −0.417229 | − | 0.722662i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24705.0 | − | 42790.3i | −0.872491 | − | 1.51120i | −0.859412 | − | 0.511284i | \(-0.829170\pi\) |
−0.0130789 | − | 0.999914i | \(-0.504163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8202.97 | + | 37340.0i | 0.288766 | + | 1.31447i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9837.35i | − | 0.344081i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37596.2i | 1.31080i | 0.755284 | + | 0.655398i | \(0.227499\pi\) | ||||
−0.755284 | + | 0.655398i | \(0.772501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4437.16 | + | 7685.39i | −0.153717 | + | 0.266245i | −0.932591 | − | 0.360935i | \(-0.882458\pi\) |
0.778874 | + | 0.627180i | \(0.215791\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33152.9 | − | 19140.8i | 1.14486 | − | 0.660987i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40026.5 | + | 23109.3i | −1.37348 | + | 0.792979i | −0.991364 | − | 0.131136i | \(-0.958138\pi\) |
−0.382115 | + | 0.924115i | \(0.624804\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11909.3 | − | 20627.5i | 0.407369 | − | 0.705583i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23772.8i | 0.808054i | 0.914747 | + | 0.404027i | \(0.132390\pi\) | ||||
−0.914747 | + | 0.404027i | \(0.867610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16880.6i | 0.571981i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3148.89 | − | 2304.22i | 0.106030 | − | 0.0775884i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6704.33 | + | 11612.2i | 0.225046 | + | 0.389790i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8176.04 | + | 14161.3i | 0.272742 | + | 0.472403i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15698.7 | − | 27190.9i | 0.522064 | − | 0.904242i | −0.477606 | − | 0.878574i | \(-0.658495\pi\) |
0.999671 | − | 0.0256679i | \(-0.00817125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42214.9 | −1.39520 | −0.697600 | − | 0.716487i | \(-0.745749\pi\) | ||||
−0.697600 | + | 0.716487i | \(0.745749\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14293.2 | + | 6305.55i | 0.470936 | + | 0.207756i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39073.6 | − | 22559.2i | −1.27950 | − | 0.738722i | −0.302747 | − | 0.953071i | \(-0.597904\pi\) |
−0.976757 | + | 0.214349i | \(0.931237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22329.4 | + | 12891.9i | −0.728959 | + | 0.420865i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17928.1 | + | 31052.5i | 0.581708 | + | 1.00755i | 0.995277 | + | 0.0970751i | \(0.0309487\pi\) |
−0.413569 | + | 0.910473i | \(0.635718\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7749.56 | + | 4474.21i | 0.250682 | + | 0.144731i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 48962.3i | − | 1.57423i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41167.8 | 1.31961 | 0.659807 | − | 0.751435i | \(-0.270638\pi\) | ||||
0.659807 | + | 0.751435i | \(0.270638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2893.14 | + | 1670.35i | 0.0921795 | + | 0.0532199i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30797.6 | + | 17781.0i | −0.978304 | + | 0.564824i | −0.901758 | − | 0.432242i | \(-0.857723\pi\) |
−0.0765462 | + | 0.997066i | \(0.524389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.4.x.a.125.15 | 48 | ||
3.2 | odd | 2 | 252.4.x.a.41.24 | yes | 48 | ||
7.6 | odd | 2 | inner | 756.4.x.a.125.10 | 48 | ||
9.2 | odd | 6 | inner | 756.4.x.a.629.10 | 48 | ||
9.4 | even | 3 | 2268.4.f.a.1133.20 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.29 | 48 | |||
9.7 | even | 3 | 252.4.x.a.209.1 | yes | 48 | ||
21.20 | even | 2 | 252.4.x.a.41.1 | ✓ | 48 | ||
63.13 | odd | 6 | 2268.4.f.a.1133.30 | 48 | |||
63.20 | even | 6 | inner | 756.4.x.a.629.15 | 48 | ||
63.34 | odd | 6 | 252.4.x.a.209.24 | yes | 48 | ||
63.41 | even | 6 | 2268.4.f.a.1133.19 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.1 | ✓ | 48 | 21.20 | even | 2 | ||
252.4.x.a.41.24 | yes | 48 | 3.2 | odd | 2 | ||
252.4.x.a.209.1 | yes | 48 | 9.7 | even | 3 | ||
252.4.x.a.209.24 | yes | 48 | 63.34 | odd | 6 | ||
756.4.x.a.125.10 | 48 | 7.6 | odd | 2 | inner | ||
756.4.x.a.125.15 | 48 | 1.1 | even | 1 | trivial | ||
756.4.x.a.629.10 | 48 | 9.2 | odd | 6 | inner | ||
756.4.x.a.629.15 | 48 | 63.20 | even | 6 | inner | ||
2268.4.f.a.1133.19 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.20 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.29 | 48 | 9.5 | odd | 6 | |||
2268.4.f.a.1133.30 | 48 | 63.13 | odd | 6 |