Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), 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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.l.217.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.00000 | − | 13.8564i | 0.715542 | − | 1.23935i | −0.247208 | − | 0.968962i | \(-0.579513\pi\) |
0.962750 | − | 0.270392i | \(-0.0871534\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | + | 10.3923i | 0.323970 | + | 0.561132i | 0.981303 | − | 0.192468i | \(-0.0616491\pi\) |
−0.657334 | + | 0.753600i | \(0.728316\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.0000 | + | 55.4256i | 0.877124 | + | 1.51922i | 0.854483 | + | 0.519480i | \(0.173874\pi\) |
0.0226410 | + | 0.999744i | \(0.492793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −29.0000 | + | 50.2295i | −0.618704 | + | 1.07163i | 0.371018 | + | 0.928626i | \(0.379009\pi\) |
−0.989722 | + | 0.143001i | \(0.954325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −32.0000 | −0.456538 | −0.228269 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228269 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −136.000 | −1.64213 | −0.821067 | − | 0.570832i | \(-0.806621\pi\) | ||||
−0.821067 | + | 0.570832i | \(0.806621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −64.0000 | + | 110.851i | −0.580214 | + | 1.00496i | 0.415240 | + | 0.909712i | \(0.363698\pi\) |
−0.995454 | + | 0.0952481i | \(0.969636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −65.5000 | − | 113.449i | −0.524000 | − | 0.907595i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −72.0000 | − | 124.708i | −0.461037 | − | 0.798539i | 0.537976 | − | 0.842960i | \(-0.319189\pi\) |
−0.999013 | + | 0.0444210i | \(0.985856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | + | 17.3205i | −0.0579372 | + | 0.100350i | −0.893539 | − | 0.448985i | \(-0.851786\pi\) |
0.835602 | + | 0.549335i | \(0.185119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 192.000 | 0.927255 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.0000 | −0.0799779 | −0.0399889 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399889 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −144.000 | + | 249.415i | −0.548513 | + | 0.950052i | 0.449864 | + | 0.893097i | \(0.351472\pi\) |
−0.998377 | + | 0.0569549i | \(0.981861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 100.000 | + | 173.205i | 0.354648 | + | 0.614268i | 0.987058 | − | 0.160366i | \(-0.0512674\pi\) |
−0.632410 | + | 0.774634i | \(0.717934\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 192.000 | + | 332.554i | 0.595874 | + | 1.03208i | 0.993423 | + | 0.114503i | \(0.0365276\pi\) |
−0.397549 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 99.5000 | − | 172.339i | 0.290087 | − | 0.502446i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −496.000 | −1.28549 | −0.642744 | − | 0.766081i | \(-0.722204\pi\) | ||||
−0.642744 | + | 0.766081i | \(0.722204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1024.00 | 2.51048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −64.0000 | + | 110.851i | −0.141222 | + | 0.244603i | −0.927957 | − | 0.372687i | \(-0.878436\pi\) |
0.786735 | + | 0.617291i | \(0.211770\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 229.000 | + | 396.640i | 0.480663 | + | 0.832533i | 0.999754 | − | 0.0221863i | \(-0.00706269\pi\) |
−0.519091 | + | 0.854719i | \(0.673729\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 464.000 | + | 803.672i | 0.885417 | + | 1.53359i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 248.000 | − | 429.549i | 0.452209 | − | 0.783249i | −0.546314 | − | 0.837581i | \(-0.683969\pi\) |
0.998523 | + | 0.0543312i | \(0.0173027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −512.000 | −0.855820 | −0.427910 | − | 0.903821i | \(-0.640750\pi\) | ||||
−0.427910 | + | 0.903821i | \(0.640750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −602.000 | −0.965189 | −0.482594 | − | 0.875844i | \(-0.660305\pi\) | ||||
−0.482594 | + | 0.875844i | \(0.660305\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −384.000 | + | 665.108i | −0.568323 | + | 0.984364i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −554.000 | − | 959.556i | −0.788986 | − | 1.36656i | −0.926589 | − | 0.376076i | \(-0.877273\pi\) |
0.137603 | − | 0.990487i | \(-0.456060\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 352.000 | + | 609.682i | 0.465506 | + | 0.806280i | 0.999224 | − | 0.0393820i | \(-0.0125389\pi\) |
−0.533718 | + | 0.845663i | \(0.679206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −256.000 | + | 443.405i | −0.326672 | + | 0.565812i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 960.000 | 1.14337 | 0.571684 | − | 0.820474i | \(-0.306290\pi\) | ||||
0.571684 | + | 0.820474i | \(0.306290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −696.000 | −0.801765 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1088.00 | + | 1884.47i | −1.17502 | + | 2.03519i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −103.000 | − | 178.401i | −0.107815 | − | 0.186741i | 0.807070 | − | 0.590456i | \(-0.201052\pi\) |
−0.914885 | + | 0.403715i | \(0.867719\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 216.000 | + | 374.123i | 0.212800 | + | 0.368580i | 0.952590 | − | 0.304258i | \(-0.0984084\pi\) |
−0.739790 | + | 0.672838i | \(0.765075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 34.0000 | − | 58.8897i | 0.0325254 | − | 0.0563357i | −0.849304 | − | 0.527903i | \(-0.822978\pi\) |
0.881830 | + | 0.471568i | \(0.156312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 384.000 | 0.346941 | 0.173470 | − | 0.984839i | \(-0.444502\pi\) | ||||
0.173470 | + | 0.984839i | \(0.444502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −518.000 | −0.455187 | −0.227594 | − | 0.973756i | \(-0.573086\pi\) | ||||
−0.227594 | + | 0.973756i | \(0.573086\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −480.000 | + | 831.384i | −0.399598 | + | 0.692124i | −0.993676 | − | 0.112283i | \(-0.964184\pi\) |
0.594078 | + | 0.804407i | \(0.297517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1024.00 | + | 1773.62i | 0.830335 | + | 1.43818i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −192.000 | − | 332.554i | −0.147904 | − | 0.256178i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1382.50 | + | 2394.56i | −1.03869 | + | 1.79907i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −96.0000 | −0.0686920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 796.000 | 0.556170 | 0.278085 | − | 0.960556i | \(-0.410300\pi\) | ||||
0.278085 | + | 0.960556i | \(0.410300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 256.000 | − | 443.405i | 0.170739 | − | 0.295729i | −0.767939 | − | 0.640523i | \(-0.778718\pi\) |
0.938678 | + | 0.344794i | \(0.112051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −816.000 | − | 1413.35i | −0.532001 | − | 0.921453i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 912.000 | + | 1579.63i | 0.568740 | + | 0.985087i | 0.996691 | + | 0.0812849i | \(0.0259024\pi\) |
−0.427951 | + | 0.903802i | \(0.640764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1080.00 | − | 1870.61i | 0.659024 | − | 1.14146i | −0.321844 | − | 0.946793i | \(-0.604303\pi\) |
0.980869 | − | 0.194671i | \(-0.0623640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3712.00 | −2.17072 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2304.00 | −1.31956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −344.000 | + | 595.825i | −0.189138 | + | 0.327597i | −0.944963 | − | 0.327177i | \(-0.893903\pi\) |
0.755825 | + | 0.654774i | \(0.227236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 422.000 | + | 730.925i | 0.227430 | + | 0.393920i | 0.957046 | − | 0.289937i | \(-0.0936345\pi\) |
−0.729616 | + | 0.683857i | \(0.760301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 160.000 | + | 277.128i | 0.0829130 | + | 0.143609i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −59.0000 | + | 102.191i | −0.0299918 | + | 0.0519473i | −0.880632 | − | 0.473801i | \(-0.842881\pi\) |
0.850640 | + | 0.525749i | \(0.176215\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1536.00 | −0.751887 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3576.00 | 1.71837 | 0.859184 | − | 0.511667i | \(-0.170972\pi\) | ||||
0.859184 | + | 0.511667i | \(0.170972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 192.000 | − | 332.554i | 0.0889665 | − | 0.154095i | −0.818108 | − | 0.575065i | \(-0.804977\pi\) |
0.907075 | + | 0.420970i | \(0.138310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −583.500 | − | 1010.65i | −0.265589 | − | 0.460014i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1224.00 | + | 2120.03i | 0.537913 | + | 0.931693i | 0.999016 | + | 0.0443465i | \(0.0141206\pi\) |
−0.461103 | + | 0.887347i | \(0.652546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 786.000 | − | 1361.39i | 0.339520 | − | 0.588066i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4224.00 | 1.76378 | 0.881890 | − | 0.471455i | \(-0.156271\pi\) | ||||
0.881890 | + | 0.471455i | \(0.156271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −510.000 | −0.209436 | −0.104718 | − | 0.994502i | \(-0.533394\pi\) | ||||
−0.104718 | + | 0.994502i | \(0.533394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −144.000 | + | 249.415i | −0.0572275 | + | 0.0991210i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1024.00 | − | 1773.62i | −0.400440 | − | 0.693583i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192.000 | − | 332.554i | −0.0727363 | − | 0.125983i | 0.827363 | − | 0.561667i | \(-0.189840\pi\) |
−0.900100 | + | 0.435684i | \(0.856506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1727.00 | − | 2991.25i | 0.644105 | − | 1.11562i | −0.340403 | − | 0.940280i | \(-0.610563\pi\) |
0.984508 | − | 0.175342i | \(-0.0561032\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3216.00 | 1.16310 | 0.581550 | − | 0.813511i | \(-0.302447\pi\) | ||||
0.581550 | + | 0.813511i | \(0.302447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1708.00 | 0.608427 | 0.304213 | − | 0.952604i | \(-0.401606\pi\) | ||||
0.304213 | + | 0.952604i | \(0.401606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 864.000 | − | 1496.49i | 0.298724 | − | 0.517405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2304.00 | + | 3990.65i | 0.784968 | + | 1.35960i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4352.00 | − | 7537.89i | −1.44035 | − | 2.49477i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1160.00 | + | 2009.18i | −0.378472 | + | 0.655534i | −0.990840 | − | 0.135039i | \(-0.956884\pi\) |
0.612368 | + | 0.790573i | \(0.290217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3200.00 | 1.01506 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −240.000 | −0.0750795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 928.000 | − | 1607.34i | 0.282462 | − | 0.489238i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 58.0000 | + | 100.459i | 0.0174169 | + | 0.0301669i | 0.874602 | − | 0.484841i | \(-0.161122\pi\) |
−0.857186 | + | 0.515008i | \(0.827789\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 672.000 | + | 1163.94i | 0.196485 | + | 0.340323i | 0.947386 | − | 0.320092i | \(-0.103714\pi\) |
−0.750901 | + | 0.660415i | \(0.770380\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2297.00 | + | 3978.52i | −0.662839 | + | 1.14807i | 0.317028 | + | 0.948416i | \(0.397315\pi\) |
−0.979866 | + | 0.199654i | \(0.936018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5056.00 | −1.42159 | −0.710793 | − | 0.703401i | \(-0.751664\pi\) | ||||
−0.710793 | + | 0.703401i | \(0.751664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6144.00 | 1.70549 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1856.00 | + | 3214.69i | −0.502321 | + | 0.870045i | 0.497676 | + | 0.867363i | \(0.334187\pi\) |
−0.999996 | + | 0.00268185i | \(0.999146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 489.000 | + | 846.973i | 0.130702 | + | 0.226383i | 0.923948 | − | 0.382519i | \(-0.124943\pi\) |
−0.793245 | + | 0.608902i | \(0.791610\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1592.00 | − | 2757.42i | −0.415139 | − | 0.719043i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3944.00 | − | 6831.21i | 1.01599 | − | 1.75975i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1856.00 | −0.466732 | −0.233366 | − | 0.972389i | \(-0.574974\pi\) | ||||
−0.233366 | + | 0.972389i | \(0.574974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8192.00 | −2.03568 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3904.00 | − | 6761.93i | 0.947567 | − | 1.64123i | 0.197040 | − | 0.980395i | \(-0.436867\pi\) |
0.750527 | − | 0.660840i | \(-0.229800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −108.000 | − | 187.061i | −0.0259104 | − | 0.0448781i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 512.000 | + | 886.810i | 0.120043 | + | 0.207920i | 0.919784 | − | 0.392424i | \(-0.128363\pi\) |
−0.799741 | + | 0.600345i | \(0.795030\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3968.00 | + | 6872.78i | −0.919820 | + | 1.59317i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1328.00 | −0.301002 | −0.150501 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150501 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5812.00 | −1.30278 | −0.651391 | − | 0.758742i | \(-0.725814\pi\) | ||||
−0.651391 | + | 0.758742i | \(0.725814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4192.00 | − | 7260.76i | 0.919226 | − | 1.59215i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4193.00 | − | 7262.49i | −0.909505 | − | 1.57531i | −0.814753 | − | 0.579808i | \(-0.803127\pi\) |
−0.0947524 | − | 0.995501i | \(-0.530206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −320.000 | − | 554.256i | −0.0679345 | − | 0.117666i | 0.830057 | − | 0.557678i | \(-0.188308\pi\) |
−0.897992 | + | 0.440012i | \(0.854974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2416.00 | + | 4184.63i | −0.507478 | + | 0.878978i | 0.492484 | + | 0.870321i | \(0.336089\pi\) |
−0.999963 | + | 0.00865656i | \(0.997244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3456.00 | −0.710806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3889.00 | −0.791573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3192.00 | − | 5528.71i | 0.636446 | − | 1.10236i | −0.349761 | − | 0.936839i | \(-0.613737\pi\) |
0.986207 | − | 0.165518i | \(-0.0529295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1024.00 | + | 1773.62i | 0.202100 | + | 0.350048i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3712.00 | − | 6429.37i | −0.717962 | − | 1.24355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1200.00 | + | 2078.46i | −0.229790 | + | 0.398008i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7328.00 | 1.37574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3312.00 | −0.615719 | −0.307860 | − | 0.951432i | \(-0.599613\pi\) | ||||
−0.307860 | + | 0.951432i | \(0.599613\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4992.00 | − | 8646.40i | 0.910194 | − | 1.57650i | 0.0964048 | − | 0.995342i | \(-0.469266\pi\) |
0.813789 | − | 0.581160i | \(-0.197401\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1293.00 | − | 2239.54i | −0.233497 | − | 0.404429i | 0.725338 | − | 0.688393i | \(-0.241684\pi\) |
−0.958835 | + | 0.283964i | \(0.908350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1416.00 | − | 2452.58i | −0.250885 | − | 0.434545i | 0.712885 | − | 0.701281i | \(-0.247388\pi\) |
−0.963770 | + | 0.266736i | \(0.914055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4608.00 | − | 7981.29i | 0.808773 | − | 1.40084i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4352.00 | 0.749696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7598.00 | 1.29680 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2304.00 | + | 3990.65i | −0.386090 | + | 0.668728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2960.00 | + | 5126.87i | 0.491530 | + | 0.851354i | 0.999952 | − | 0.00975326i | \(-0.00310461\pi\) |
−0.508423 | + | 0.861108i | \(0.669771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3968.00 | − | 6872.78i | −0.647149 | − | 1.12090i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2337.00 | − | 4047.80i | 0.377758 | − | 0.654296i | −0.612978 | − | 0.790100i | \(-0.710028\pi\) |
0.990736 | + | 0.135804i | \(0.0433617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1280.00 | −0.203272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6504.00 | 1.02386 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4512.00 | + | 7815.01i | −0.698031 | + | 1.20903i | 0.271117 | + | 0.962546i | \(0.412607\pi\) |
−0.969148 | + | 0.246479i | \(0.920726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2181.00 | + | 3777.60i | 0.334516 | + | 0.579400i | 0.983392 | − | 0.181495i | \(-0.0580937\pi\) |
−0.648875 | + | 0.760895i | \(0.724760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4384.00 | + | 7593.31i | 0.661011 | + | 1.14490i | 0.980350 | + | 0.197264i | \(0.0632056\pi\) |
−0.319340 | + | 0.947640i | \(0.603461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4096.00 | + | 7094.48i | −0.612375 | + | 1.06066i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6144.00 | 0.903253 | 0.451627 | − | 0.892207i | \(-0.350844\pi\) | ||||
0.451627 | + | 0.892207i | \(0.350844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11637.0 | 1.69660 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4816.00 | + | 8341.56i | −0.690633 | + | 1.19621i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2282.00 | − | 3952.54i | −0.324576 | − | 0.562182i | 0.656850 | − | 0.754021i | \(-0.271888\pi\) |
−0.981426 | + | 0.191839i | \(0.938555\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2976.00 | − | 5154.58i | −0.416459 | − | 0.721328i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4385.00 | − | 7595.04i | 0.608704 | − | 1.05431i | −0.382750 | − | 0.923852i | \(-0.625023\pi\) |
0.991454 | − | 0.130455i | \(-0.0416437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8352.00 | 1.14098 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1096.00 | −0.148543 | −0.0742714 | − | 0.997238i | \(-0.523663\pi\) | ||||
−0.0742714 | + | 0.997238i | \(0.523663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5184.00 | − | 8978.95i | 0.691619 | − | 1.19792i | −0.279688 | − | 0.960091i | \(-0.590231\pi\) |
0.971307 | − | 0.237828i | \(-0.0764355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6144.00 | + | 10641.7i | 0.813317 | + | 1.40871i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1624.00 | − | 2812.85i | −0.211671 | − | 0.366625i | 0.740567 | − | 0.671983i | \(-0.234557\pi\) |
−0.952238 | + | 0.305358i | \(0.901224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2048.00 | − | 3547.24i | 0.264890 | − | 0.458802i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17728.0 | −2.25821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6106.00 | −0.771918 | −0.385959 | − | 0.922516i | \(-0.626129\pi\) | ||||
−0.385959 | + | 0.922516i | \(0.626129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3504.00 | − | 6069.11i | 0.436363 | − | 0.755802i | −0.561043 | − | 0.827787i | \(-0.689600\pi\) |
0.997406 | + | 0.0719843i | \(0.0229332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −580.000 | − | 1004.59i | −0.0716920 | − | 0.124174i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −576.000 | − | 997.661i | −0.0701505 | − | 0.121504i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −795.000 | + | 1376.98i | −0.0961130 | + | 0.166473i | −0.910073 | − | 0.414449i | \(-0.863974\pi\) |
0.813960 | + | 0.580922i | \(0.197308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1536.00 | −0.183006 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11264.0 | 1.33236 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −96.0000 | + | 166.277i | −0.0111931 | + | 0.0193870i | −0.871568 | − | 0.490275i | \(-0.836896\pi\) |
0.860375 | + | 0.509662i | \(0.170230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4537.00 | − | 7858.31i | −0.525225 | − | 0.909717i | −0.999568 | − | 0.0293768i | \(-0.990648\pi\) |
0.474343 | − | 0.880340i | \(-0.342686\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2096.00 | + | 3630.38i | 0.239226 | + | 0.414351i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2748.00 | + | 4759.68i | −0.311440 | + | 0.539431i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5248.00 | 0.586513 | 0.293257 | − | 0.956034i | \(-0.405261\pi\) | ||||
0.293257 | + | 0.956034i | \(0.405261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8222.00 | −0.912527 | −0.456263 | − | 0.889845i | \(-0.650813\pi\) | ||||
−0.456263 | + | 0.889845i | \(0.650813\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8704.00 | − | 15075.8i | 0.952789 | − | 1.65028i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8118.00 | − | 14060.8i | −0.882576 | − | 1.52867i | −0.848467 | − | 0.529249i | \(-0.822474\pi\) |
−0.0341097 | − | 0.999418i | \(-0.510860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7264.00 | + | 12581.6i | 0.779059 | + | 1.34937i | 0.932485 | + | 0.361209i | \(0.117636\pi\) |
−0.153426 | + | 0.988160i | \(0.549031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7680.00 | − | 13302.2i | 0.818128 | − | 1.41704i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6304.00 | −0.662593 | −0.331296 | − | 0.943527i | \(-0.607486\pi\) | ||||
−0.331296 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18432.0 | −1.92445 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5568.00 | + | 9644.06i | −0.573696 | + | 0.993671i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −979.000 | − | 1695.68i | −0.100209 | − | 0.173568i | 0.811561 | − | 0.584267i | \(-0.198618\pi\) |
−0.911771 | + | 0.410699i | \(0.865285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2024.00 | + | 3505.67i | 0.204484 | + | 0.354177i | 0.949968 | − | 0.312347i | \(-0.101115\pi\) |
−0.745484 | + | 0.666523i | \(0.767782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8494.00 | + | 14712.0i | −0.852591 | + | 1.47673i | 0.0262709 | + | 0.999655i | \(0.491637\pi\) |
−0.878862 | + | 0.477076i | \(0.841697\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6720.00 | −0.665877 | −0.332938 | − | 0.942949i | \(-0.608040\pi\) | ||||
−0.332938 | + | 0.942949i | \(0.608040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5952.00 | 0.586008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6400.00 | + | 11085.1i | −0.622140 | + | 1.07758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8908.00 | + | 15429.1i | 0.860478 | + | 1.49039i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4864.00 | + | 8424.70i | 0.463970 | + | 0.803620i | 0.999154 | − | 0.0411152i | \(-0.0130911\pi\) |
−0.535184 | + | 0.844736i | \(0.679758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 522.000 | − | 904.131i | 0.0494826 | − | 0.0857065i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3296.00 | −0.308585 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8444.00 | −0.785696 | −0.392848 | − | 0.919603i | \(-0.628510\pi\) | ||||
−0.392848 | + | 0.919603i | \(0.628510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7680.00 | + | 13302.2i | −0.705893 | + | 1.22264i | 0.260475 | + | 0.965481i | \(0.416121\pi\) |
−0.966368 | + | 0.257162i | \(0.917213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2304.00 | + | 3990.65i | 0.210481 | + | 0.364563i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3072.00 | − | 5320.86i | −0.277260 | − | 0.480228i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3312.00 | + | 5736.55i | −0.297125 | + | 0.514636i | −0.975477 | − | 0.220101i | \(-0.929361\pi\) |
0.678352 | + | 0.734737i | \(0.262695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6912.00 | 0.612705 | 0.306353 | − | 0.951918i | \(-0.400891\pi\) | ||||
0.306353 | + | 0.951918i | \(0.400891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6912.00 | 0.609069 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9960.00 | + | 17251.2i | −0.867327 | + | 1.50225i | −0.00260828 | + | 0.999997i | \(0.500830\pi\) |
−0.864718 | + | 0.502257i | \(0.832503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3612.00 | − | 6256.17i | −0.312692 | − | 0.541598i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −544.000 | − | 942.236i | −0.0465466 | − | 0.0806211i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12288.0 | + | 21283.4i | −1.04531 | + | 1.81053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3680.00 | −0.309451 | −0.154725 | − | 0.987958i | \(-0.549449\pi\) | ||||
−0.154725 | + | 0.987958i | \(0.549449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11720.0 | −0.979885 | −0.489942 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489942 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 320.000 | − | 554.256i | 0.0264505 | − | 0.0458136i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2108.50 | − | 3652.03i | −0.173297 | − | 0.300159i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8352.00 | − | 14466.1i | −0.678734 | − | 1.17560i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3072.00 | − | 5320.86i | 0.248251 | − | 0.429983i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12736.0 | 1.01777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11754.0 | 0.934092 | 0.467046 | − | 0.884233i | \(-0.345318\pi\) | ||||
0.467046 | + | 0.884233i | \(0.345318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4144.00 | + | 7177.62i | −0.325705 | + | 0.564138i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9452.00 | + | 16371.3i | 0.738827 | + | 1.27969i | 0.953024 | + | 0.302895i | \(0.0979532\pi\) |
−0.214197 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9792.00 | + | 16960.2i | 0.757084 | + | 1.31131i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6648.00 | − | 11514.7i | 0.511215 | − | 0.885450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3088.00 | −0.234906 | −0.117453 | − | 0.993078i | \(-0.537473\pi\) | ||||
−0.117453 | + | 0.993078i | \(0.537473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11600.0 | −0.877688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10720.0 | + | 18567.6i | −0.802476 | + | 1.38993i | 0.115505 | + | 0.993307i | \(0.463151\pi\) |
−0.917982 | + | 0.396623i | \(0.870182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7680.00 | + | 13302.2i | 0.571858 | + | 0.990488i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11312.0 | + | 19593.0i | 0.833434 | + | 1.44355i | 0.895299 | + | 0.445465i | \(0.146962\pi\) |
−0.0618659 | + | 0.998084i | \(0.519705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3000.00 | − | 5196.15i | 0.219871 | − | 0.380827i | −0.734898 | − | 0.678178i | \(-0.762770\pi\) |
0.954768 | + | 0.297351i | \(0.0961032\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16768.0 | 1.21613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19922.0 | 1.43737 | 0.718686 | − | 0.695335i | \(-0.244744\pi\) | ||||
0.718686 | + | 0.695335i | \(0.244744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4224.00 | + | 7316.18i | −0.301620 | + | 0.522421i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15872.0 | − | 27491.1i | −1.12753 | − | 1.95294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1792.00 | − | 3103.84i | −0.126003 | − | 0.218244i | 0.796122 | − | 0.605137i | \(-0.206882\pi\) |
−0.922125 | + | 0.386893i | \(0.873548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1360.00 | − | 2355.59i | 0.0951406 | − | 0.164788i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1984.00 | −0.137391 | −0.0686957 | − | 0.997638i | \(-0.521884\pi\) | ||||
−0.0686957 | + | 0.997638i | \(0.521884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6144.00 | −0.423327 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7488.00 | − | 12969.6i | 0.510770 | − | 0.884680i | −0.489152 | − | 0.872199i | \(-0.662694\pi\) |
0.999922 | − | 0.0124814i | \(-0.00397306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12869.0 | − | 22289.8i | −0.873440 | − | 1.51284i | −0.858415 | − | 0.512955i | \(-0.828551\pi\) |
−0.0150248 | − | 0.999887i | \(-0.504783\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22120.0 | + | 38313.0i | 1.48646 | + | 2.57462i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4274.00 | − | 7402.79i | 0.285793 | − | 0.495008i | −0.687008 | − | 0.726650i | \(-0.741076\pi\) |
0.972801 | + | 0.231642i | \(0.0744097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22272.0 | −1.47468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8558.00 | 0.563873 | 0.281937 | − | 0.959433i | \(-0.409023\pi\) | ||||
0.281937 | + | 0.959433i | \(0.409023\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5184.00 | + | 8978.95i | −0.338250 | + | 0.585865i | −0.984104 | − | 0.177596i | \(-0.943168\pi\) |
0.645854 | + | 0.763461i | \(0.276501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6544.00 | + | 11334.5i | 0.424920 | + | 0.735983i | 0.996413 | − | 0.0846238i | \(-0.0269688\pi\) |
−0.571493 | + | 0.820607i | \(0.693636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5760.00 | + | 9976.61i | 0.370417 | + | 0.641580i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7419.50 | − | 12851.0i | 0.474848 | − | 0.822461i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 576.000 | 0.0365129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4412.00 | −0.278350 | −0.139175 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139175 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6368.00 | − | 11029.7i | 0.397963 | − | 0.689292i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5771.00 | + | 9995.67i | 0.358957 | + | 0.621731i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15088.0 | − | 26133.2i | −0.929704 | − | 1.61029i | −0.783816 | − | 0.620993i | \(-0.786729\pi\) |
−0.145888 | − | 0.989301i | \(-0.546604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10644.0 | + | 18435.9i | −0.652812 | + | 1.13070i | 0.329625 | + | 0.944112i | \(0.393078\pi\) |
−0.982437 | + | 0.186592i | \(0.940256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17024.0 | −1.03444 | −0.517220 | − | 0.855853i | \(-0.673033\pi\) | ||||
−0.517220 | + | 0.855853i | \(0.673033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8192.00 | −0.495476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1128.00 | − | 1953.75i | 0.0675989 | − | 0.117085i | −0.830245 | − | 0.557399i | \(-0.811800\pi\) |
0.897844 | + | 0.440314i | \(0.145133\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4096.00 | − | 7094.48i | −0.244342 | − | 0.423213i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11904.0 | + | 20618.3i | 0.703663 | + | 1.21878i | 0.967172 | + | 0.254123i | \(0.0817869\pi\) |
−0.263509 | + | 0.964657i | \(0.584880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13121.0 | − | 22726.2i | 0.772084 | − | 1.33729i | −0.164334 | − | 0.986405i | \(-0.552548\pi\) |
0.936419 | − | 0.350885i | \(-0.114119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26112.0 | −1.52268 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18432.0 | 1.07000 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14656.0 | + | 25384.9i | −0.843202 | + | 1.46047i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12295.0 | + | 21295.6i | 0.704216 | + | 1.21974i | 0.966974 | + | 0.254876i | \(0.0820347\pi\) |
−0.262758 | + | 0.964862i | \(0.584632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1432.00 | − | 2480.30i | −0.0812943 | − | 0.140806i | 0.822512 | − | 0.568748i | \(-0.192572\pi\) |
−0.903806 | + | 0.427942i | \(0.859239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1236.00 | − | 2140.81i | 0.0698576 | − | 0.120997i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7616.00 | 0.426674 | 0.213337 | − | 0.976979i | \(-0.431567\pi\) | ||||
0.213337 | + | 0.976979i | \(0.431567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29184.0 | 1.62783 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14384.0 | − | 24913.8i | 0.795336 | − | 1.37756i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1084.00 | − | 1877.54i | −0.0596777 | − | 0.103365i | 0.834643 | − | 0.550791i | \(-0.185674\pi\) |
−0.894321 | + | 0.447426i | \(0.852341\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17280.0 | − | 29929.8i | −0.943119 | − | 1.63353i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4608.00 | − | 7981.29i | 0.250417 | − | 0.433734i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18000.0 | 0.969830 | 0.484915 | − | 0.874561i | \(-0.338851\pi\) | ||||
0.484915 | + | 0.874561i | \(0.338851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2448.00 | 0.131334 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2592.00 | + | 4489.48i | −0.137881 | + | 0.238818i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1753.00 | − | 3036.29i | −0.0928566 | − | 0.160832i | 0.815855 | − | 0.578256i | \(-0.196266\pi\) |
−0.908712 | + | 0.417424i | \(0.862933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1280.00 | − | 2217.03i | −0.0672319 | − | 0.116449i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29696.0 | + | 51435.0i | −1.55324 | + | 2.69029i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15616.0 | −0.809984 | −0.404992 | − | 0.914320i | \(-0.632726\pi\) | ||||
−0.404992 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 816.000 | 0.0421490 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9432.00 | + | 16336.7i | −0.483166 | + | 0.836869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7518.00 | + | 13021.6i | 0.383531 | + | 0.664296i | 0.991564 | − | 0.129616i | \(-0.0413745\pi\) |
−0.608033 | + | 0.793912i | \(0.708041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3200.00 | − | 5542.56i | −0.161910 | − | 0.280437i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9563.00 | − | 16563.6i | 0.481879 | − | 0.834639i | −0.517904 | − | 0.855438i | \(-0.673288\pi\) |
0.999784 | + | 0.0207992i | \(0.00662106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31744.0 | 1.58657 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17392.0 | −0.865731 | −0.432865 | − | 0.901459i | \(-0.642497\pi\) | ||||
−0.432865 | + | 0.901459i | \(0.642497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16192.0 | + | 28045.4i | −0.799498 | + | 1.38477i | 0.120446 | + | 0.992720i | \(0.461568\pi\) |
−0.919944 | + | 0.392051i | \(0.871766\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5504.00 | + | 9533.21i | 0.270672 | + | 0.468818i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2304.00 | + | 3990.65i | 0.112398 | + | 0.194680i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13854.0 | − | 23995.8i | 0.673155 | − | 1.16594i | −0.303849 | − | 0.952720i | \(-0.598272\pi\) |
0.977004 | − | 0.213219i | \(-0.0683948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13504.0 | 0.650942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37246.0 | −1.78828 | −0.894141 | − | 0.447786i | \(-0.852213\pi\) | ||||
−0.894141 | + | 0.447786i | \(0.852213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2096.00 | + | 3630.38i | −0.0998422 | + | 0.172932i | −0.911619 | − | 0.411036i | \(-0.865167\pi\) |
0.811777 | + | 0.583968i | \(0.198500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3108.00 | − | 5383.21i | −0.147467 | − | 0.255420i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3712.00 | − | 6429.37i | −0.174749 | − | 0.302674i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13441.0 | + | 23280.5i | −0.630292 | + | 1.09170i | 0.357199 | + | 0.934028i | \(0.383732\pi\) |
−0.987492 | + | 0.157670i | \(0.949602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17232.0 | 0.801801 | 0.400900 | − | 0.916122i | \(-0.368697\pi\) | ||||
0.400900 | + | 0.916122i | \(0.368697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2620.00 | 0.121436 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19584.0 | − | 33920.5i | 0.900731 | − | 1.56011i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16384.0 | − | 28377.9i | −0.750660 | − | 1.30018i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 944.000 | + | 1635.06i | 0.0429208 | + | 0.0743410i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15908.0 | + | 27553.5i | −0.720532 | + | 1.24800i | 0.240254 | + | 0.970710i | \(0.422769\pi\) |
−0.960787 | + | 0.277289i | \(0.910564\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11520.0 | −0.517831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26564.0 | −1.18955 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4136.00 | − | 7163.76i | 0.183820 | − | 0.318386i | −0.759358 | − | 0.650673i | \(-0.774487\pi\) |
0.943178 | + | 0.332287i | \(0.107820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6144.00 | − | 10641.7i | −0.272039 | − | 0.471185i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19264.0 | − | 33366.2i | −0.846590 | − | 1.46634i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12288.0 | + | 21283.4i | −0.538006 | + | 0.931854i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9184.00 | 0.399125 | 0.199563 | − | 0.979885i | \(-0.436048\pi\) | ||||
0.199563 | + | 0.979885i | \(0.436048\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19832.0 | −0.858688 | −0.429344 | − | 0.903141i | \(-0.641255\pi\) | ||||
−0.429344 | + | 0.903141i | \(0.641255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28608.0 | − | 49550.5i | 1.22956 | − | 2.12967i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13600.0 | − | 23555.9i | −0.582379 | − | 1.00871i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7608.00 | + | 13177.4i | 0.323412 | + | 0.560166i | 0.981190 | − | 0.193046i | \(-0.0618368\pi\) |
−0.657778 | + | 0.753212i | \(0.728503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19886.0 | − | 34443.6i | 0.842263 | − | 1.45884i | −0.0457142 | − | 0.998955i | \(-0.514556\pi\) |
0.887977 | − | 0.459888i | \(-0.152110\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18304.0 | 0.769640 | 0.384820 | − | 0.922992i | \(-0.374263\pi\) | ||||
0.384820 | + | 0.922992i | \(0.374263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4906.00 | 0.205540 | 0.102770 | − | 0.994705i | \(-0.467229\pi\) | ||||
0.102770 | + | 0.994705i | \(0.467229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3184.00 | + | 5514.85i | −0.132436 | + | 0.229386i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3072.00 | − | 5320.86i | −0.127318 | − | 0.220522i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7680.00 | + | 13302.2i | 0.316023 | + | 0.547367i | 0.979654 | − | 0.200692i | \(-0.0643191\pi\) |
−0.663632 | + | 0.748060i | \(0.730986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1826.50 | − | 3163.59i | 0.0748903 | − | 0.129714i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18672.0 | −0.760161 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33180.0 | −1.34602 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1152.00 | − | 1995.32i | 0.0464043 | − | 0.0803746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12401.0 | + | 21479.2i | 0.497775 | + | 0.862172i | 0.999997 | − | 0.00256720i | \(-0.000817166\pi\) |
−0.502222 | + | 0.864739i | \(0.667484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7536.00 | + | 13052.7i | 0.300379 | + | 0.520272i | 0.976222 | − | 0.216774i | \(-0.0695535\pi\) |
−0.675843 | + | 0.737046i | \(0.736220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −900.000 | + | 1558.85i | −0.0357481 | + | 0.0619175i | −0.883346 | − | 0.468722i | \(-0.844715\pi\) |
0.847598 | + | 0.530639i | \(0.178048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7552.00 | −0.297883 | −0.148942 | − | 0.988846i | \(-0.547587\pi\) | ||||
−0.148942 | + | 0.988846i | \(0.547587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39168.0 | 1.53960 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35456.0 | − | 61411.6i | 1.38408 | − | 2.39729i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14384.0 | + | 24913.8i | 0.559567 | + | 0.969199i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −576.000 | − | 997.661i | −0.0222541 | − | 0.0385453i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10419.0 | + | 18046.2i | −0.401168 | + | 0.694844i | −0.993867 | − | 0.110580i | \(-0.964729\pi\) |
0.592699 | + | 0.805424i | \(0.298062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47744.0 | −1.82581 | −0.912904 | − | 0.408175i | \(-0.866165\pi\) | ||||
−0.912904 | + | 0.408175i | \(0.866165\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28280.0 | 1.07780 | 0.538900 | − | 0.842370i | \(-0.318840\pi\) | ||||
0.538900 | + | 0.842370i | \(0.318840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3712.00 | − | 6429.37i | 0.140515 | − | 0.243379i | −0.787176 | − | 0.616729i | \(-0.788458\pi\) |
0.927691 | + | 0.373350i | \(0.121791\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4776.00 | + | 8272.27i | 0.180182 | + | 0.312085i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26112.0 | − | 45227.3i | −0.978505 | − | 1.69482i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33792.0 | − | 58529.5i | 1.26206 | − | 2.18595i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2880.00 | 0.106845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15872.0 | 0.586873 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4080.00 | + | 7066.77i | −0.149861 | + | 0.259566i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2956.00 | + | 5119.94i | 0.108217 | + | 0.187436i | 0.915048 | − | 0.403345i | \(-0.132153\pi\) |
−0.806831 | + | 0.590782i | \(0.798819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13120.0 | − | 22724.5i | −0.477151 | − | 0.826451i | 0.522506 | − | 0.852636i | \(-0.324997\pi\) |
−0.999657 | + | 0.0261852i | \(0.991664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22528.0 | + | 39019.6i | −0.816613 | + | 1.41442i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6144.00 | 0.221257 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35620.0 | 1.27856 | 0.639279 | − | 0.768975i | \(-0.279233\pi\) | ||||
0.639279 | + | 0.768975i | \(0.279233\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14848.0 | − | 25717.5i | 0.529499 | − | 0.917120i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1179.00 | + | 2042.09i | 0.0419084 | + | 0.0725875i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1616.00 | − | 2798.99i | −0.0570713 | − | 0.0988504i | 0.836078 | − | 0.548610i | \(-0.184843\pi\) |
−0.893150 | + | 0.449760i | \(0.851510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13532.0 | + | 23438.1i | −0.476362 | + | 0.825084i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32768.0 | −1.14613 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11478.0 | −0.400181 | −0.200091 | − | 0.979777i | \(-0.564124\pi\) | ||||
−0.200091 | + | 0.979777i | \(0.564124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19992.0 | + | 34627.2i | −0.692583 | + | 1.19959i | 0.278406 | + | 0.960464i | \(0.410194\pi\) |
−0.970989 | + | 0.239125i | \(0.923139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18432.0 | − | 31925.2i | −0.636510 | − | 1.10247i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12096.0 | + | 20950.9i | 0.415066 | + | 0.718915i | 0.995435 | − | 0.0954383i | \(-0.0304253\pi\) |
−0.580370 | + | 0.814353i | \(0.697092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17458.0 | − | 30238.1i | 0.597166 | − | 1.03432i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39456.0 | 1.34114 | 0.670569 | − | 0.741847i | \(-0.266050\pi\) | ||||
0.670569 | + | 0.741847i | \(0.266050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6144.00 | −0.208183 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10944.0 | + | 18955.6i | −0.368509 | + | 0.638276i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14695.5 | + | 25453.4i | 0.493287 | + | 0.854397i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27632.0 | − | 47860.0i | −0.921767 | − | 1.59655i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20834.0 | − | 36085.5i | 0.692840 | − | 1.20003i | −0.278063 | − | 0.960563i | \(-0.589693\pi\) |
0.970903 | − | 0.239471i | \(-0.0769741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51648.0 | 1.70697 | 0.853483 | − | 0.521121i | \(-0.174486\pi\) | ||||
0.853483 | + | 0.521121i | \(0.174486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25920.0 | 0.854015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27888.0 | − | 48303.4i | 0.913220 | − | 1.58174i | 0.103734 | − | 0.994605i | \(-0.466921\pi\) |
0.809486 | − | 0.587139i | \(-0.199746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30720.0 | + | 53208.6i | 1.00288 | + | 1.73703i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18048.0 | − | 31260.1i | −0.585597 | − | 1.01428i | −0.994801 | − | 0.101841i | \(-0.967527\pi\) |
0.409204 | − | 0.912443i | \(-0.365807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25728.0 | − | 44562.2i | 0.832246 | − | 1.44149i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25600.0 | −0.823087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42532.0 | 1.36334 | 0.681672 | − | 0.731658i | \(-0.261253\pi\) | ||||
0.681672 | + | 0.731658i | \(0.261253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13664.0 | − | 23666.7i | 0.435355 | − | 0.754056i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14903.0 | − | 25812.8i | −0.473403 | − | 0.819958i | 0.526134 | − | 0.850402i | \(-0.323641\pi\) |
−0.999536 | + | 0.0304440i | \(0.990308\pi\) | |||||||
\(998\) | 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 | 648.4.i.l.433.1 | 2 | ||
3.2 | odd | 2 | 648.4.i.a.433.1 | 2 | |||
9.2 | odd | 6 | 648.4.i.a.217.1 | 2 | |||
9.4 | even | 3 | 72.4.a.a.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 72.4.a.d.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 648.4.i.l.217.1 | 2 | ||
36.23 | even | 6 | 144.4.a.f.1.1 | 1 | |||
36.31 | odd | 6 | 144.4.a.a.1.1 | 1 | |||
45.4 | even | 6 | 1800.4.a.z.1.1 | 1 | |||
45.13 | odd | 12 | 1800.4.f.b.649.2 | 2 | |||
45.14 | odd | 6 | 1800.4.a.ba.1.1 | 1 | |||
45.22 | odd | 12 | 1800.4.f.b.649.1 | 2 | |||
45.23 | even | 12 | 1800.4.f.x.649.2 | 2 | |||
45.32 | even | 12 | 1800.4.f.x.649.1 | 2 | |||
72.5 | odd | 6 | 576.4.a.c.1.1 | 1 | |||
72.13 | even | 6 | 576.4.a.w.1.1 | 1 | |||
72.59 | even | 6 | 576.4.a.d.1.1 | 1 | |||
72.67 | odd | 6 | 576.4.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.4.a.a.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
72.4.a.d.1.1 | yes | 1 | 9.5 | odd | 6 | ||
144.4.a.a.1.1 | 1 | 36.31 | odd | 6 | |||
144.4.a.f.1.1 | 1 | 36.23 | even | 6 | |||
576.4.a.c.1.1 | 1 | 72.5 | odd | 6 | |||
576.4.a.d.1.1 | 1 | 72.59 | even | 6 | |||
576.4.a.w.1.1 | 1 | 72.13 | even | 6 | |||
576.4.a.x.1.1 | 1 | 72.67 | odd | 6 | |||
648.4.i.a.217.1 | 2 | 9.2 | odd | 6 | |||
648.4.i.a.433.1 | 2 | 3.2 | odd | 2 | |||
648.4.i.l.217.1 | 2 | 9.7 | even | 3 | inner | ||
648.4.i.l.433.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.z.1.1 | 1 | 45.4 | even | 6 | |||
1800.4.a.ba.1.1 | 1 | 45.14 | odd | 6 | |||
1800.4.f.b.649.1 | 2 | 45.22 | odd | 12 | |||
1800.4.f.b.649.2 | 2 | 45.13 | odd | 12 | |||
1800.4.f.x.649.1 | 2 | 45.32 | even | 12 | |||
1800.4.f.x.649.2 | 2 | 45.23 | even | 12 |