Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(513,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.513");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.b (of order \(2\), degree \(1\), 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: | \(60.4179558459\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 36x^{8} + 405x^{6} + 1380x^{4} + 420x^{2} + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 513.8 | ||
Root | \(0.446984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.513 |
Dual form | 1024.4.b.j.513.3 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.62644i | 0.890358i | 0.895441 | + | 0.445179i | \(0.146860\pi\) | ||||
−0.895441 | + | 0.445179i | \(0.853140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.8826i | 1.59947i | 0.600356 | + | 0.799733i | \(0.295026\pi\) | ||||
−0.600356 | + | 0.799733i | \(0.704974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.8754 | −0.749200 | −0.374600 | − | 0.927187i | \(-0.622220\pi\) | ||||
−0.374600 | + | 0.927187i | \(0.622220\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.59607 | 0.207262 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.18771i | 0.0599653i | 0.999550 | + | 0.0299827i | \(0.00954521\pi\) | ||||
−0.999550 | + | 0.0299827i | \(0.990455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.3685i | 0.989255i | 0.869105 | + | 0.494627i | \(0.164695\pi\) | ||||
−0.869105 | + | 0.494627i | \(0.835305\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −82.7326 | −1.42410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.6531 | −0.266119 | −0.133060 | − | 0.991108i | \(-0.542480\pi\) | ||||
−0.133060 | + | 0.991108i | \(0.542480\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 122.194i | − 1.47543i | −0.675111 | − | 0.737716i | \(-0.735904\pi\) | ||||
0.675111 | − | 0.737716i | \(-0.264096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 64.1936i | − 0.667057i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −134.006 | −1.21488 | −0.607438 | − | 0.794367i | \(-0.707803\pi\) | ||||
−0.607438 | + | 0.794367i | \(0.707803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −194.786 | −1.55829 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 150.804i | 1.07490i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 84.5628i | 0.541480i | 0.962653 | + | 0.270740i | \(0.0872683\pi\) | ||||
−0.962653 | + | 0.270740i | \(0.912732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.5391 | −0.182729 | −0.0913645 | − | 0.995818i | \(-0.529123\pi\) | ||||
−0.0913645 | + | 0.995818i | \(0.529123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.1213 | −0.0533906 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 248.128i | − 1.19832i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 126.129i | − 0.560418i | −0.959939 | − | 0.280209i | \(-0.909596\pi\) | ||||
0.959939 | − | 0.280209i | \(-0.0904038\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −214.521 | −0.880791 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −210.504 | −0.801834 | −0.400917 | − | 0.916114i | \(-0.631308\pi\) | ||||
−0.400917 | + | 0.916114i | \(0.631308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 168.860i | 0.598857i | 0.954119 | + | 0.299429i | \(0.0967961\pi\) | ||||
−0.954119 | + | 0.299429i | \(0.903204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 100.072i | 0.331508i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 182.902 | 0.567638 | 0.283819 | − | 0.958878i | \(-0.408398\pi\) | ||||
0.283819 | + | 0.958878i | \(0.408398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −150.474 | −0.438699 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 86.2972i | − 0.236942i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 37.0020i | − 0.0958984i | −0.998850 | − | 0.0479492i | \(-0.984731\pi\) | ||||
0.998850 | − | 0.0479492i | \(-0.0152686\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.1219 | −0.0959125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 565.323 | 1.31366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 624.494i | − 1.37800i | −0.724760 | − | 0.689001i | \(-0.758050\pi\) | ||||
0.724760 | − | 0.689001i | \(-0.241950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 246.759i | 0.517938i | 0.965886 | + | 0.258969i | \(0.0833828\pi\) | ||||
−0.965886 | + | 0.258969i | \(0.916617\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −77.6476 | −0.155281 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −829.188 | −1.58228 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 129.763i | − 0.236613i | −0.992977 | − | 0.118306i | \(-0.962253\pi\) | ||||
0.992977 | − | 0.118306i | \(-0.0377465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 619.970i | − 1.08168i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −348.360 | −0.582291 | −0.291146 | − | 0.956679i | \(-0.594036\pi\) | ||||
−0.291146 | + | 0.956679i | \(0.594036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −299.436 | −0.480087 | −0.240043 | − | 0.970762i | \(-0.577162\pi\) | ||||
−0.240043 | + | 0.970762i | \(0.577162\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 901.168i | − 1.38744i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 30.3553i | − 0.0449260i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 943.487 | 1.34368 | 0.671839 | − | 0.740697i | \(-0.265505\pi\) | ||||
0.671839 | + | 0.740697i | \(0.265505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −546.590 | −0.749781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 443.034i | 0.585895i | 0.956129 | + | 0.292947i | \(0.0946361\pi\) | ||||
−0.956129 | + | 0.292947i | \(0.905364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 333.565i | − 0.425649i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −391.224 | −0.482111 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1412.35 | −1.68212 | −0.841060 | − | 0.540942i | \(-0.818068\pi\) | ||||
−0.841060 | + | 0.540942i | \(0.818068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 643.381i | − 0.741150i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 145.914i | − 0.162694i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2185.14 | 2.35990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1515.29 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2426i | 0.0124285i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 810.631i | 0.798621i | 0.916816 | + | 0.399311i | \(0.130751\pi\) | ||||
−0.916816 | + | 0.399311i | \(0.869249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1021.00 | 0.976717 | 0.488359 | − | 0.872643i | \(-0.337596\pi\) | ||||
0.488359 | + | 0.872643i | \(0.337596\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1147.95 | 1.06693 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1754.75i | − 1.58540i | −0.609612 | − | 0.792700i | \(-0.708675\pi\) | ||||
0.609612 | − | 0.792700i | \(-0.291325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 153.624i | − 0.134996i | −0.997719 | − | 0.0674980i | \(-0.978498\pi\) | ||||
0.997719 | − | 0.0674980i | \(-0.0215016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 583.528 | 0.498973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1722.22 | 1.43374 | 0.716870 | − | 0.697207i | \(-0.245574\pi\) | ||||
0.716870 | + | 0.697207i | \(0.245574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2396.37i | − 1.94315i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 259.481i | 0.205035i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 258.818 | 0.199377 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1326.21 | 0.996404 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 973.883i | − 0.713919i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1247.96i | − 0.892969i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 699.127 | 0.488484 | 0.244242 | − | 0.969714i | \(-0.421461\pi\) | ||||
0.244242 | + | 0.969714i | \(0.421461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −781.219 | −0.533198 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 279.972i | − 0.186727i | −0.995632 | − | 0.0933636i | \(-0.970238\pi\) | ||||
0.995632 | − | 0.0933636i | \(-0.0297619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1695.49i | 1.10539i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2696.76 | −1.71926 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −271.386 | −0.169242 | −0.0846209 | − | 0.996413i | \(-0.526968\pi\) | ||||
−0.0846209 | + | 0.996413i | \(0.526968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 650.449i | 0.396909i | 0.980110 | + | 0.198455i | \(0.0635922\pi\) | ||||
−0.980110 | + | 0.198455i | \(0.936408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 846.185i | 0.505402i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −101.441 | −0.0593210 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1512.20 | −0.866079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 696.158i | − 0.390600i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 856.692i | 0.471026i | 0.971871 | + | 0.235513i | \(0.0756771\pi\) | ||||
−0.971871 | + | 0.235513i | \(0.924323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3534.47 | −1.90484 | −0.952421 | − | 0.304785i | \(-0.901415\pi\) | ||||
−0.952421 | + | 0.304785i | \(0.901415\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −104.384 | −0.0551564 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 564.001i | − 0.292269i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1744.48i | 0.886784i | 0.896328 | + | 0.443392i | \(0.146225\pi\) | ||||
−0.896328 | + | 0.443392i | \(0.853775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 171.187 | 0.0853839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1859.38 | 0.910186 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3633.63i | − 1.74606i | −0.487666 | − | 0.873030i | \(-0.662152\pi\) | ||||
0.487666 | − | 0.873030i | \(-0.337848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 180.995i | − 0.0853965i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3048.39 | −1.41252 | −0.706262 | − | 0.707950i | \(-0.749620\pi\) | ||||
−0.706262 | + | 0.707950i | \(0.749620\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 46.9618 | 0.0213754 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 683.806i | − 0.305801i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2152.51i | − 0.945965i | −0.881072 | − | 0.472983i | \(-0.843177\pi\) | ||||
0.881072 | − | 0.472983i | \(-0.156823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2702.74 | 1.16747 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2889.18 | 1.22692 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 427.457i | 0.178489i | 0.996010 | + | 0.0892447i | \(0.0284453\pi\) | ||||
−0.996010 | + | 0.0892447i | \(0.971555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2399.83i | 0.985515i | 0.870167 | + | 0.492758i | \(0.164011\pi\) | ||||
−0.870167 | + | 0.492758i | \(0.835989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1141.62 | −0.461151 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2255.51 | 0.896370 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 40.8074i | − 0.0159579i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2092.46i | − 0.805312i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4035.31 | −1.52872 | −0.764358 | − | 0.644792i | \(-0.776944\pi\) | ||||
−0.764358 | + | 0.644792i | \(0.776944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −886.172 | −0.330508 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 3836.19i | − 1.40880i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4624.65i | − 1.67255i | −0.548308 | − | 0.836276i | \(-0.684728\pi\) | ||||
0.548308 | − | 0.836276i | \(-0.315272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −222.513 | −0.0792639 | −0.0396319 | − | 0.999214i | \(-0.512619\pi\) | ||||
−0.0396319 | + | 0.999214i | \(0.512619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 600.340 | 0.210670 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1173.34i | − 0.405677i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3764.35i | − 1.28251i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −749.907 | −0.251798 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 267.325 | 0.0884748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4988.58i | − 1.62762i | −0.581131 | − | 0.813810i | \(-0.697390\pi\) | ||||
0.581131 | − | 0.813810i | \(-0.302610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1611.66i | − 0.518448i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3019.65 | −0.957852 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 437.618 | 0.136901 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1385.32i | − 0.427449i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 864.914i | − 0.263260i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5841.90 | 1.75427 | 0.877136 | − | 0.480242i | \(-0.159451\pi\) | ||||
0.877136 | + | 0.480242i | \(0.159451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1090.04 | −0.322975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1597.41i | 0.467065i | 0.972349 | + | 0.233533i | \(0.0750286\pi\) | ||||
−0.972349 | + | 0.233533i | \(0.924971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4108.86i | 1.18568i | 0.805320 | + | 0.592840i | \(0.201994\pi\) | ||||
−0.805320 | + | 0.592840i | \(0.798006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 140.437 | 0.0400003 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −734.054 | −0.206393 | −0.103196 | − | 0.994661i | \(-0.532907\pi\) | ||||
−0.103196 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3270.76i | 0.907918i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4364.98i | 1.19635i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 511.807 | 0.138519 | 0.0692595 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692595 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5920.31 | −1.58241 | −0.791204 | − | 0.611552i | \(-0.790545\pi\) | ||||
−0.791204 | + | 0.611552i | \(0.790545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1542.93i | 0.407322i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2690.86i | − 0.701685i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5665.95 | 1.45958 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2049.67 | −0.521656 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 437.462i | 0.110009i | 0.998486 | + | 0.0550046i | \(0.0175174\pi\) | ||||
−0.998486 | + | 0.0550046i | \(0.982483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 293.166i | − 0.0728505i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1543.22 | 0.378980 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 323.723 | 0.0785730 | 0.0392865 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392865 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1750.09i | 0.419865i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 473.219i | 0.112228i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2689.15 | −0.630495 | −0.315248 | − | 0.949009i | \(-0.602088\pi\) | ||||
−0.315248 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 661.691 | 0.153386 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6534.14i | − 1.49769i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6652.15i | 1.50776i | 0.657009 | + | 0.753882i | \(0.271821\pi\) | ||||
−0.657009 | + | 0.753882i | \(0.728179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2018.97 | 0.452561 | 0.226280 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226280 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2976.56 | 0.659889 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 426.136i | − 0.0934435i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4356.63i | − 0.944999i | −0.881331 | − | 0.472499i | \(-0.843352\pi\) | ||||
0.881331 | − | 0.472499i | \(-0.156648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −176.495 | −0.0378728 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3893.51 | −0.826575 | −0.413287 | − | 0.910601i | \(-0.635619\pi\) | ||||
−0.413287 | + | 0.910601i | \(0.635619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2865.74i | − 0.601945i | −0.953633 | − | 0.300972i | \(-0.902689\pi\) | ||||
0.953633 | − | 0.300972i | \(-0.0973112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10109.4i | 2.10116i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2920.82 | 0.600734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4565.06 | −0.929180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7010.39i | 1.41222i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1416.60i | 0.282452i | 0.989977 | + | 0.141226i | \(0.0451044\pi\) | ||||
−0.989977 | + | 0.141226i | \(0.954896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11167.6 | 2.20407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −329.914 | −0.0644565 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 6213.65i | − 1.20182i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2342.99i | − 0.448664i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3750.33 | −0.711059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4412.69 | −0.828425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4195.32i | 0.779934i | 0.920829 | + | 0.389967i | \(0.127514\pi\) | ||||
−0.920829 | + | 0.389967i | \(0.872486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4723.58i | 0.869628i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2911.18 | −0.530797 | −0.265399 | − | 0.964139i | \(-0.585504\pi\) | ||||
−0.265399 | + | 0.964139i | \(0.585504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8287.74 | −1.49665 | −0.748324 | − | 0.663333i | \(-0.769141\pi\) | ||||
−0.748324 | + | 0.663333i | \(0.769141\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1388.54i | − 0.248366i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8120.67i | − 1.43881i | −0.694592 | − | 0.719404i | \(-0.744415\pi\) | ||||
0.694592 | − | 0.719404i | \(-0.255585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −184.999 | −0.0324700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8118.23 | 1.41157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2279.29i | 0.392641i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9031.96i | − 1.54155i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 710.734 | 0.120195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2537.84 | −0.425275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6362.92i | 1.05661i | 0.849055 | + | 0.528305i | \(0.177172\pi\) | ||||
−0.849055 | + | 0.528305i | \(0.822828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 705.827i | − 0.116153i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2320.50 | 0.378454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5860.06 | 0.947234 | 0.473617 | − | 0.880731i | \(-0.342948\pi\) | ||||
0.473617 | + | 0.880731i | \(0.342948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7967.73i | 1.27654i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 68.9984i | − 0.0109574i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6847.14 | 1.07787 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11086.7 | 1.73010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2869.60i | 0.443942i | 0.975053 | + | 0.221971i | \(0.0712491\pi\) | ||||
−0.975053 | + | 0.221971i | \(0.928751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2748.19i | 0.421511i | 0.977539 | + | 0.210755i | \(0.0675923\pi\) | ||||
−0.977539 | + | 0.210755i | \(0.932408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6992.54 | −1.06335 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7548.63 | −1.13817 | −0.569084 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569084 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6229.57i | − 0.931355i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1197.41i | 0.177517i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5554.15 | −0.816537 | −0.408269 | − | 0.912862i | \(-0.633867\pi\) | ||||
−0.408269 | + | 0.912862i | \(0.633867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8072.37 | −1.17690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6135.65i | 0.887157i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5354.69i | − 0.767883i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3610.98 | 0.513601 | 0.256800 | − | 0.966464i | \(-0.417332\pi\) | ||||
0.256800 | + | 0.966464i | \(0.417332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1177.99 | −0.166190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 513.417i | 0.0718471i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1718.96i | 0.238618i | 0.992857 | + | 0.119309i | \(0.0380679\pi\) | ||||
−0.992857 | + | 0.119309i | \(0.961932\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5773.62 | 0.795062 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3921.05 | −0.535661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10391.4i | 1.40836i | 0.710021 | + | 0.704180i | \(0.248685\pi\) | ||||
−0.710021 | + | 0.704180i | \(0.751315\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3234.47i | 0.434926i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7668.98 | −1.02315 | −0.511575 | − | 0.859238i | \(-0.670938\pi\) | ||||
−0.511575 | + | 0.859238i | \(0.670938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 542.831 | 0.0718577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 944.951i | 0.124120i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 284.150i | 0.0370359i | 0.999829 | + | 0.0185180i | \(0.00589479\pi\) | ||||
−0.999829 | + | 0.0185180i | \(0.994105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2499.62 | 0.323302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1295.27 | 0.166254 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16872.0i | 2.14917i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9209.66i | 1.16428i | 0.813088 | + | 0.582141i | \(0.197785\pi\) | ||||
−0.813088 | + | 0.582141i | \(0.802215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7844.07 | −0.984197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5565.10 | −0.693036 | −0.346518 | − | 0.938043i | \(-0.612636\pi\) | ||||
−0.346518 | + | 0.938043i | \(0.612636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1462.42i | − 0.180765i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 9774.44i | − 1.19925i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 275.933 | 0.0336057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12077.6 | 1.46014 | 0.730072 | − | 0.683370i | \(-0.239486\pi\) | ||||
0.730072 | + | 0.683370i | \(0.239486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1255.55i | − 0.150686i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8665.08i | 1.03240i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7922.58 | −0.937119 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3009.26 | −0.353391 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2054.89i | 0.239590i | 0.992799 | + | 0.119795i | \(0.0382237\pi\) | ||||
−0.992799 | + | 0.119795i | \(0.961776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6819.69i | 0.789480i | 0.918793 | + | 0.394740i | \(0.129165\pi\) | ||||
−0.918793 | + | 0.394740i | \(0.870835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1023.53 | 0.117650 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3633.36 | 0.414692 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3423.87i | − 0.388040i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 469.309i | − 0.0528169i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12519.2 | −1.39914 | −0.699571 | − | 0.714563i | \(-0.746626\pi\) | ||||
−0.699571 | + | 0.714563i | \(0.746626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2921.40 | 0.324235 | 0.162117 | − | 0.986771i | \(-0.448168\pi\) | ||||
0.162117 | + | 0.986771i | \(0.448168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 6996.10i | − 0.771120i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16374.7i | 1.79247i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1140.50 | 0.123993 | 0.0619967 | − | 0.998076i | \(-0.480253\pi\) | ||||
0.0619967 | + | 0.998076i | \(0.480253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −842.062 | −0.0909256 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2606.46i | 0.279541i | 0.990184 | + | 0.139771i | \(0.0446365\pi\) | ||||
−0.990184 | + | 0.139771i | \(0.955363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 25256.4i | − 2.69049i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3963.43 | −0.419382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1752.13 | 0.184161 | 0.0920805 | − | 0.995752i | \(-0.470648\pi\) | ||||
0.0920805 | + | 0.995752i | \(0.470648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 460.521i | − 0.0480822i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 16352.0i | − 1.69599i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11505.3 | 1.18544 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12875.6 | 1.31794 | 0.658968 | − | 0.752171i | \(-0.270993\pi\) | ||||
0.658968 | + | 0.752171i | \(0.270993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2812.95i | − 0.286051i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 19346.0i | − 1.95452i | −0.212050 | − | 0.977259i | \(-0.568014\pi\) | ||||
0.212050 | − | 0.977259i | \(-0.431986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15002.4 | −1.50588 | −0.752938 | − | 0.658091i | \(-0.771364\pi\) | ||||
−0.752938 | + | 0.658091i | \(0.771364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2609.32 | 0.260224 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13674.6i | 1.35500i | 0.735522 | + | 0.677501i | \(0.236937\pi\) | ||||
−0.735522 | + | 0.677501i | \(0.763063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1800.51i | 0.177270i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8070.75 | −0.789555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −369.416 | −0.0359107 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23801.7i | 2.29915i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 207.066i | − 0.0198761i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3072.68 | −0.293099 | −0.146550 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146550 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5848.41 | 0.554396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8602.32i | 0.810392i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27097.3i | 2.53695i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8689.64 | −0.808553 | −0.404276 | − | 0.914637i | \(-0.632477\pi\) | ||||
−0.404276 | + | 0.914637i | \(0.632477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16810.8 | 1.55462 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15831.2i | 1.45509i | 0.686057 | + | 0.727547i | \(0.259340\pi\) | ||||
−0.686057 | + | 0.727547i | \(0.740660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1577.35i | − 0.144098i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −218.929 | −0.0198790 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4833.62 | 0.436253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 2309.01i | − 0.207146i | −0.994622 | − | 0.103573i | \(-0.966973\pi\) | ||||
0.994622 | − | 0.103573i | \(-0.0330275\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 14103.2i | − 1.25765i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6901.81 | −0.611802 | −0.305901 | − | 0.952063i | \(-0.598958\pi\) | ||||
−0.305901 | + | 0.952063i | \(0.598958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14496.2 | −1.27737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 217.266i | 0.0190318i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 131.481i | − 0.0114495i | −0.999984 | − | 0.00572475i | \(-0.998178\pi\) | ||||
0.999984 | − | 0.00572475i | \(-0.00182226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4154.79 | 0.359681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18427.3 | 1.58594 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18258.1i | 1.56223i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 400.136i | 0.0340386i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9958.43 | 0.842248 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11931.3 | −1.00330 | −0.501649 | − | 0.865071i | \(-0.667273\pi\) | ||||
−0.501649 | + | 0.865071i | \(0.667273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 13721.4i | − 1.14721i | −0.819131 | − | 0.573607i | \(-0.805544\pi\) | ||||
0.819131 | − | 0.573607i | \(-0.194456\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12504.0i | 1.03947i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 588.301 | 0.0486277 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5790.59 | 0.475926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 3494.71i | − 0.285607i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9760.75i | − 0.793218i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31379.4 | 2.53579 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1977.60 | −0.158920 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 329.193i | − 0.0263067i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12101.0i | 0.961665i | 0.876812 | + | 0.480833i | \(0.159666\pi\) | ||||
−0.876812 | + | 0.480833i | \(0.840334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11102.7 | −0.877462 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2747.20 | 0.215921 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 63.9157i | 0.00499605i | 0.999997 | + | 0.00249803i | \(0.000795147\pi\) | ||||
−0.999997 | + | 0.00249803i | \(0.999205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1380.88i | 0.107349i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10333.1 | 0.798917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13091.2 | −1.00668 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10435.0i | 0.798090i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6052.26i | 0.460400i | 0.973143 | + | 0.230200i | \(0.0739380\pi\) | ||||
−0.973143 | + | 0.230200i | \(0.926062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7829.77 | −0.592422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 188.793 | 0.0142083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20638.9i | 1.54498i | 0.635026 | + | 0.772491i | \(0.280989\pi\) | ||||
−0.635026 | + | 0.772491i | \(0.719011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30797.7i | 2.29322i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7584.14 | 0.561736 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21728.1 | 1.60086 | 0.800431 | − | 0.599425i | \(-0.204604\pi\) | ||||
0.800431 | + | 0.599425i | \(0.204604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 22737.8i | − 1.66646i | −0.552929 | − | 0.833229i | \(-0.686490\pi\) | ||||
0.552929 | − | 0.833229i | \(-0.313510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 18669.1i | − 1.36110i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26102.5 | 1.89313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26648.2 | −1.92267 | −0.961335 | − | 0.275383i | \(-0.911195\pi\) | ||||
−0.961335 | + | 0.275383i | \(0.911195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4099.82i | − 0.294270i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6147.26i | − 0.438952i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 80.9495 | 0.00575058 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4640.20 | −0.327946 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1898.75i | 0.133509i | 0.997769 | + | 0.0667544i | \(0.0212644\pi\) | ||||
−0.997769 | + | 0.0667544i | \(0.978736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3853.89i | 0.269604i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21395.7 | 1.48917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4474.79 | −0.309878 | −0.154939 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154939 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4628.34i | 0.318896i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1029.44i | − 0.0705733i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12603.8 | 0.859725 | 0.429863 | − | 0.902894i | \(-0.358562\pi\) | ||||
0.429863 | + | 0.902894i | \(0.358562\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7220.64 | −0.490077 | −0.245038 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245038 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 726.163i | − 0.0490408i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23716.1i | 1.59371i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13695.6 | −0.915796 | −0.457898 | − | 0.889005i | \(-0.651397\pi\) | ||||
−0.457898 | + | 0.889005i | \(0.651397\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5428.39 | 0.361198 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8480.89i | 0.561539i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3335.20i | 0.219751i | 0.993945 | + | 0.109876i | \(0.0350452\pi\) | ||||
−0.993945 | + | 0.109876i | \(0.964955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17415.5 | 1.14189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4186.39 | 0.273157 | 0.136579 | − | 0.990629i | \(-0.456389\pi\) | ||||
0.136579 | + | 0.990629i | \(0.456389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 6788.94i | − 0.440825i | −0.975407 | − | 0.220412i | \(-0.929260\pi\) | ||||
0.975407 | − | 0.220412i | \(-0.0707403\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 20208.6i | − 1.30587i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19596.9 | 1.26024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2031.54 | −0.130018 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1236.76i | 0.0787743i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2352.69i | 0.149138i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16106.3 | −1.01614 | −0.508069 | − | 0.861316i | \(-0.669640\pi\) | ||||
−0.508069 | + | 0.861316i | \(0.669640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23079.3 | 1.44917 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12502.2i | 0.781314i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6977.25i | − 0.433985i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1949.45 | −0.120687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6682.21 | −0.411749 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7047.69i | 0.432245i | 0.976366 | + | 0.216123i | \(0.0693411\pi\) | ||||
−0.976366 | + | 0.216123i | \(0.930659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 13970.2i | − 0.852832i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5078.45 | −0.308585 | −0.154292 | − | 0.988025i | \(-0.549310\pi\) | ||||
−0.154292 | + | 0.988025i | \(0.549310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1366.21 | 0.0826324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2024.61i | 0.121891i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8753.86i | 0.524602i | 0.964986 | + | 0.262301i | \(0.0844813\pi\) | ||||
−0.964986 | + | 0.262301i | \(0.915519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5006.62 | 0.298664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1675.67 | −0.0995037 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8133.42i | 0.480778i | 0.970677 | + | 0.240389i | \(0.0772750\pi\) | ||||
−0.970677 | + | 0.240389i | \(0.922725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8917.15i | − 0.524716i | −0.964971 | − | 0.262358i | \(-0.915500\pi\) | ||||
0.964971 | − | 0.262358i | \(-0.0845001\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4001.47 | 0.234396 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30319.7 | −1.76804 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11331.9i | − 0.657831i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27027.2i | 1.56193i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −539.837 | −0.0310584 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14664.4 | 0.839925 | 0.419963 | − | 0.907541i | \(-0.362043\pi\) | ||||
0.419963 | + | 0.907541i | \(0.362043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 29374.5i | − 1.67500i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8195.60i | − 0.465262i | −0.972565 | − | 0.232631i | \(-0.925267\pi\) | ||||
0.972565 | − | 0.232631i | \(-0.0747334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21025.2 | −1.18833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7390.32 | −0.415855 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 18574.4i | − 1.04060i | −0.853983 | − | 0.520300i | \(-0.825820\pi\) | ||||
0.853983 | − | 0.520300i | \(-0.174180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4853.09i | − 0.270696i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19009.4 | −1.05568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1715.73 | 0.0948679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20257.2i | 1.11523i | 0.830101 | + | 0.557613i | \(0.188282\pi\) | ||||
−0.830101 | + | 0.557613i | \(0.811718\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 169.870i | − 0.00931146i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11631.7 | −0.634843 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3926.54 | 0.213383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 3396.06i | − 0.183763i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 22609.3i | − 1.21818i | −0.793102 | − | 0.609089i | \(-0.791535\pi\) | ||||
0.793102 | − | 0.609089i | \(-0.208465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15412.2 | −0.826859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15132.0 | −0.808373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 11247.8i | − 0.598327i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 27690.9i | − 1.46679i | −0.679802 | − | 0.733395i | \(-0.737934\pi\) | ||||
0.679802 | − | 0.733395i | \(-0.262066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5279.82 | 0.278493 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4226.43 | 0.221993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1814.02i | − 0.0948819i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2367.84i | 0.123331i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2111.24 | 0.109507 | 0.0547537 | − | 0.998500i | \(-0.482563\pi\) | ||||
0.0547537 | + | 0.998500i | \(0.482563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14166.7 | −0.731757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 27389.9i | − 1.40891i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 16471.7i | − 0.843784i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14763.6 | −0.753164 | −0.376582 | − | 0.926383i | \(-0.622901\pi\) | ||||
−0.376582 | + | 0.926383i | \(0.622901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21896.2 | −1.11244 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3149.75i | − 0.159368i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4836.29i | − 0.243700i | −0.992549 | − | 0.121850i | \(-0.961117\pi\) | ||||
0.992549 | − | 0.121850i | \(-0.0388827\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12449.1 | 0.624751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 283.883 | 0.0141886 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16015.7i | 0.797224i | 0.917120 | + | 0.398612i | \(0.130508\pi\) | ||||
−0.917120 | + | 0.398612i | \(0.869492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26213.2i | 1.29955i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20313.3 | −1.00299 | −0.501495 | − | 0.865160i | \(-0.667217\pi\) | ||||
−0.501495 | + | 0.865160i | \(0.667217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15319.9 | −0.753391 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2479.25i | 0.121434i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24347.8i | 1.18778i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28755.3 | −1.39720 | −0.698598 | − | 0.715514i | \(-0.746192\pi\) | ||||
−0.698598 | + | 0.715514i | \(0.746192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2023.89 | −0.0979477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 63205.4i | − 3.04673i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 32535.4i | − 1.56211i | −0.624460 | − | 0.781057i | \(-0.714681\pi\) | ||||
0.624460 | − | 0.781057i | \(-0.285319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1356.31 | 0.0648631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9298.53 | 0.442932 | 0.221466 | − | 0.975168i | \(-0.428916\pi\) | ||||
0.221466 | + | 0.975168i | \(0.428916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2131.60i | 0.101139i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1866.65i | − 0.0882208i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28956.8 | 1.36319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20402.0 | −0.956717 | −0.478358 | − | 0.878165i | \(-0.658768\pi\) | ||||
−0.478358 | + | 0.878165i | \(0.658768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1497.68i | 0.0699582i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10376.1i | − 0.482798i | −0.970426 | − | 0.241399i | \(-0.922394\pi\) | ||||
0.970426 | − | 0.241399i | \(-0.0776063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6143.40 | 0.284745 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8096.67 | −0.373831 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25722.3i | 1.18305i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 762.109i | − 0.0349173i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12752.4 | −0.582034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31195.9 | −1.41838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 16869.6i | − 0.764088i | −0.924144 | − | 0.382044i | \(-0.875220\pi\) | ||||
0.924144 | − | 0.382044i | \(-0.124780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 12441.2i | − 0.561367i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23896.4 | −1.07416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11441.8 | −0.512373 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3061.27i | 0.136569i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9300.12i | 0.413334i | 0.978411 | + | 0.206667i | \(0.0662617\pi\) | ||||
−0.978411 | + | 0.206667i | \(0.933738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3411.68 | −0.151060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7903.61 | −0.348639 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 655.079i | − 0.0287886i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33250.6i | 1.45581i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30775.8 | −1.34245 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29320.9 | 1.27425 | 0.637126 | − | 0.770760i | \(-0.280123\pi\) | ||||
0.637126 | + | 0.770760i | \(0.280123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20488.9i | − 0.887132i | −0.896242 | − | 0.443566i | \(-0.853713\pi\) | ||||
0.896242 | − | 0.443566i | \(-0.146287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9340.66i | 0.402941i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64978.7 | 2.79276 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20633.6 | 0.883574 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 3600.40i | − 0.153612i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28650.9i | 1.21793i | 0.793196 | + | 0.608966i | \(0.208415\pi\) | ||||
−0.793196 | + | 0.608966i | \(0.791585\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24605.9 | −1.04217 | −0.521086 | − | 0.853504i | \(-0.674473\pi\) | ||||
−0.521086 | + | 0.853504i | \(0.674473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1971.49 | 0.0831982 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34076.6i | 1.43284i | 0.697668 | + | 0.716421i | \(0.254221\pi\) | ||||
−0.697668 | + | 0.716421i | \(0.745779\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1293.46i | 0.0541904i | 0.999633 | + | 0.0270952i | \(0.00862572\pi\) | ||||
−0.999633 | + | 0.0270952i | \(0.991374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20155.7 | 0.841388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2806.80 | 0.116746 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 54513.1i | − 2.25929i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4756.22i | − 0.196415i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28847.5 | −1.18704 | −0.593521 | − | 0.804819i | \(-0.702263\pi\) | ||||
−0.593521 | + | 0.804819i | \(0.702263\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17238.1 | 0.706800 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 18013.1i | − 0.735948i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 839.798i | 0.0341893i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18401.7 | −0.746506 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13258.2 | 0.535947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16902.0i | 0.680839i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 58.7693i | 0.00235900i | 0.999999 | + | 0.00117950i | \(0.000375446\pi\) | ||||
−0.999999 | + | 0.00117950i | \(0.999625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12228.2 | 0.489118 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20953.6 | 0.835194 | 0.417597 | − | 0.908632i | \(-0.362872\pi\) | ||||
0.417597 | + | 0.908632i | \(0.362872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 41459.5i | − 1.64677i | −0.567481 | − | 0.823387i | \(-0.692082\pi\) | ||||
0.567481 | − | 0.823387i | \(-0.307918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13513.0i | 0.534868i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3389.59 | −0.133700 | −0.0668499 | − | 0.997763i | \(-0.521295\pi\) | ||||
−0.0668499 | + | 0.997763i | \(0.521295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38492.3 | 1.51304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 21120.0i | − 0.827304i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2064.07i | 0.0805741i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6016.91 | 0.234070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8479.66 | 0.328743 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17315.9i | 0.669012i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19675.3i | − 0.757568i | −0.925485 | − | 0.378784i | \(-0.876342\pi\) | ||||
0.925485 | − | 0.378784i | \(-0.123658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6553.79 | −0.251484 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1497.48 | 0.0572660 | 0.0286330 | − | 0.999590i | \(-0.490885\pi\) | ||||
0.0286330 | + | 0.999590i | \(0.490885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5860.23i | − 0.223344i | −0.993745 | − | 0.111672i | \(-0.964379\pi\) | ||||
0.993745 | − | 0.111672i | \(-0.0356206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 51666.0i | 1.96241i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18058.0 | −0.683573 | −0.341787 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341787 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9700.66 | −0.365973 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1195.78i | − 0.0449609i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 22349.5i | − 0.837512i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7644.03 | −0.285488 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28747.1 | 1.07005 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2667.04i | − 0.0989441i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 690.200i | 0.0255204i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10839.7 | 0.399472 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42915.2 | −1.57630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30297.4i | − 1.10916i | −0.832130 | − | 0.554580i | \(-0.812879\pi\) | ||||
0.832130 | − | 0.554580i | \(-0.187121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4536.35i | 0.165524i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31977.7 | 1.16297 | 0.581487 | − | 0.813556i | \(-0.302471\pi\) | ||||
0.581487 | + | 0.813556i | \(0.302471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −969.228 | −0.0351334 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 20415.0i | − 0.737595i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3884.72i | 0.139896i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40696.7 | −1.46078 | −0.730391 | − | 0.683029i | \(-0.760662\pi\) | ||||
−0.730391 | + | 0.683029i | \(0.760662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19409.4 | −0.694421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 16152.9i | − 0.576034i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24568.2i | 0.873295i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5713.57 | 0.202436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11467.5 | −0.404989 | −0.202495 | − | 0.979283i | \(-0.564905\pi\) | ||||
−0.202495 | + | 0.979283i | \(0.564905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18387.0i | 0.647271i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 13468.4i | − 0.472600i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 729.742 | 0.0255242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14100.2 | −0.491603 | −0.245802 | − | 0.969320i | \(-0.579051\pi\) | ||||
−0.245802 | + | 0.969320i | \(0.579051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 38342.7i | − 1.33255i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 29781.6i | − 1.03172i | −0.856672 | − | 0.515862i | \(-0.827472\pi\) | ||||
0.856672 | − | 0.515862i | \(-0.172528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28208.8 | 0.974129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37418.5 | 1.28807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35353.8i | 1.21314i | 0.795030 | + | 0.606571i | \(0.207455\pi\) | ||||
−0.795030 | + | 0.606571i | \(0.792545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 13884.4i | − 0.474928i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37569.8 | 1.28106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6456.01 | −0.219445 | −0.109722 | − | 0.993962i | \(-0.534996\pi\) | ||||
−0.109722 | + | 0.993962i | \(0.534996\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 72161.7i | − 2.44513i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 855.885i | − 0.0289100i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3765.59 | 0.126796 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28796.3 | −0.966610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 9819.69i | − 0.328593i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 15847.0i | − 0.528636i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15099.9 | −0.502153 | −0.251076 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251076 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10545.0 | −0.349591 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 8800.82i | − 0.290867i | −0.989368 | − | 0.145433i | \(-0.953542\pi\) | ||||
0.989368 | − | 0.145433i | \(-0.0464577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9025.23i | − 0.297364i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41785.8 | 1.37253 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34900.0 | 1.14284 | 0.571418 | − | 0.820659i | \(-0.306393\pi\) | ||||
0.571418 | + | 0.820659i | \(0.306393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3089.81i | − 0.100869i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 859.693i | − 0.0279795i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21221.5 | 0.688567 | 0.344283 | − | 0.938866i | \(-0.388122\pi\) | ||||
0.344283 | + | 0.938866i | \(0.388122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 82700.7 | 2.67519 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 11741.1i | − 0.378647i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 22628.2i | − 0.727538i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23985.3 | 0.768838 | 0.384419 | − | 0.923159i | \(-0.374402\pi\) | ||||
0.384419 | + | 0.923159i | \(0.374402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29437.7 | −0.940761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3979.10i | − 0.126780i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 15222.3i | − 0.483547i | −0.970333 | − | 0.241773i | \(-0.922271\pi\) | ||||
0.970333 | − | 0.241773i | \(-0.0777290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19020.7 | 0.602391 |
(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 | 1024.4.b.j.513.8 | 10 | ||
4.3 | odd | 2 | 1024.4.b.k.513.3 | 10 | |||
8.3 | odd | 2 | 1024.4.b.k.513.8 | 10 | |||
8.5 | even | 2 | inner | 1024.4.b.j.513.3 | 10 | ||
16.3 | odd | 4 | 1024.4.a.m.1.8 | 10 | |||
16.5 | even | 4 | 1024.4.a.n.1.8 | 10 | |||
16.11 | odd | 4 | 1024.4.a.m.1.3 | 10 | |||
16.13 | even | 4 | 1024.4.a.n.1.3 | 10 | |||
32.3 | odd | 8 | 64.4.e.a.49.4 | 10 | |||
32.5 | even | 8 | 16.4.e.a.13.5 | yes | 10 | ||
32.11 | odd | 8 | 128.4.e.a.33.2 | 10 | |||
32.13 | even | 8 | 128.4.e.b.97.4 | 10 | |||
32.19 | odd | 8 | 128.4.e.a.97.2 | 10 | |||
32.21 | even | 8 | 128.4.e.b.33.4 | 10 | |||
32.27 | odd | 8 | 64.4.e.a.17.4 | 10 | |||
32.29 | even | 8 | 16.4.e.a.5.5 | ✓ | 10 | ||
96.5 | odd | 8 | 144.4.k.a.109.1 | 10 | |||
96.29 | odd | 8 | 144.4.k.a.37.1 | 10 | |||
96.35 | even | 8 | 576.4.k.a.433.5 | 10 | |||
96.59 | even | 8 | 576.4.k.a.145.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.5 | ✓ | 10 | 32.29 | even | 8 | ||
16.4.e.a.13.5 | yes | 10 | 32.5 | even | 8 | ||
64.4.e.a.17.4 | 10 | 32.27 | odd | 8 | |||
64.4.e.a.49.4 | 10 | 32.3 | odd | 8 | |||
128.4.e.a.33.2 | 10 | 32.11 | odd | 8 | |||
128.4.e.a.97.2 | 10 | 32.19 | odd | 8 | |||
128.4.e.b.33.4 | 10 | 32.21 | even | 8 | |||
128.4.e.b.97.4 | 10 | 32.13 | even | 8 | |||
144.4.k.a.37.1 | 10 | 96.29 | odd | 8 | |||
144.4.k.a.109.1 | 10 | 96.5 | odd | 8 | |||
576.4.k.a.145.5 | 10 | 96.59 | even | 8 | |||
576.4.k.a.433.5 | 10 | 96.35 | even | 8 | |||
1024.4.a.m.1.3 | 10 | 16.11 | odd | 4 | |||
1024.4.a.m.1.8 | 10 | 16.3 | odd | 4 | |||
1024.4.a.n.1.3 | 10 | 16.13 | even | 4 | |||
1024.4.a.n.1.8 | 10 | 16.5 | even | 4 | |||
1024.4.b.j.513.3 | 10 | 8.5 | even | 2 | inner | ||
1024.4.b.j.513.8 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.b.k.513.3 | 10 | 4.3 | odd | 2 | |||
1024.4.b.k.513.8 | 10 | 8.3 | odd | 2 |