Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,5,Mod(17,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (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: | \(4.96175822802\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.17 |
Dual form | 48.5.e.b.17.1 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000 | + | 8.48528i | 0.333333 | + | 0.942809i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.9706i | 0.678823i | 0.940638 | + | 0.339411i | \(0.110228\pi\) | ||||
−0.940638 | + | 0.339411i | \(0.889772\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.0000 | −0.530612 | −0.265306 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265306 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −63.0000 | + | 50.9117i | −0.777778 | + | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 118.794i | 0.981768i | 0.871225 | + | 0.490884i | \(0.163326\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0000 | 0.295858 | 0.147929 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147929 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −144.000 | + | 50.9117i | −0.640000 | + | 0.226274i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 203.647i | 0.704660i | 0.935876 | + | 0.352330i | \(0.114611\pi\) | ||||
−0.935876 | + | 0.352330i | \(0.885389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 358.000 | 0.991690 | 0.495845 | − | 0.868411i | \(-0.334858\pi\) | ||||
0.495845 | + | 0.868411i | \(0.334858\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −78.0000 | − | 220.617i | −0.176871 | − | 0.500266i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 373.352i | − | 0.705770i | −0.935667 | − | 0.352885i | \(-0.885201\pi\) | ||
0.935667 | − | 0.352885i | \(-0.114799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 337.000 | 0.539200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −621.000 | − | 381.838i | −0.851852 | − | 0.523783i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1442.50i | − | 1.71522i | −0.514303 | − | 0.857609i | \(-0.671949\pi\) | ||
0.514303 | − | 0.857609i | \(-0.328051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 742.000 | 0.772112 | 0.386056 | − | 0.922475i | \(-0.373837\pi\) | ||||
0.386056 | + | 0.922475i | \(0.373837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1008.00 | + | 356.382i | −0.925620 | + | 0.327256i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 441.235i | − | 0.360192i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1874.00 | 1.36888 | 0.684441 | − | 0.729068i | \(-0.260046\pi\) | ||||
0.684441 | + | 0.729068i | \(0.260046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 150.000 | + | 424.264i | 0.0986193 | + | 0.278938i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2409.82i | 1.43356i | 0.697298 | + | 0.716782i | \(0.254386\pi\) | ||||
−0.697298 | + | 0.716782i | \(0.745614\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 262.000 | 0.141698 | 0.0708491 | − | 0.997487i | \(-0.477429\pi\) | ||||
0.0708491 | + | 0.997487i | \(0.477429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −864.000 | − | 1069.15i | −0.426667 | − | 0.527973i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1697.06i | 0.768246i | 0.923282 | + | 0.384123i | \(0.125496\pi\) | ||||
−0.923282 | + | 0.384123i | \(0.874504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1725.00 | −0.718451 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1728.00 | + | 610.940i | −0.664360 | + | 0.234887i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 458.205i | − | 0.163120i | −0.996668 | − | 0.0815602i | \(-0.974010\pi\) | ||
0.996668 | − | 0.0815602i | \(-0.0259903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2016.00 | −0.666446 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1074.00 | + | 3037.73i | 0.330563 | + | 0.934974i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1815.85i | 0.521646i | 0.965387 | + | 0.260823i | \(0.0839939\pi\) | ||||
−0.965387 | + | 0.260823i | \(0.916006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1486.00 | −0.399355 | −0.199678 | − | 0.979862i | \(-0.563989\pi\) | ||||
−0.199678 | + | 0.979862i | \(0.563989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1638.00 | − | 1323.70i | 0.412698 | − | 0.333511i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 848.528i | 0.200835i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4486.00 | 0.999332 | 0.499666 | − | 0.866218i | \(-0.333456\pi\) | ||||
0.499666 | + | 0.866218i | \(0.333456\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3168.00 | − | 1120.06i | 0.665406 | − | 0.235257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3563.82i | − | 0.706967i | −0.935441 | − | 0.353483i | \(-0.884997\pi\) | ||
0.935441 | − | 0.353483i | \(-0.115003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 290.000 | 0.0544192 | 0.0272096 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272096 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1011.00 | + | 2859.54i | 0.179733 | + | 0.508363i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3088.64i | − | 0.520938i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9818.00 | −1.57315 | −0.786573 | − | 0.617498i | \(-0.788146\pi\) | ||||
−0.786573 | + | 0.617498i | \(0.788146\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1377.00 | − | 6414.87i | 0.209877 | − | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7110.67i | − | 1.03218i | −0.856535 | − | 0.516088i | \(-0.827388\pi\) | ||
0.856535 | − | 0.516088i | \(-0.172612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3456.00 | −0.478339 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12240.0 | − | 4327.49i | 1.61712 | − | 0.571739i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7840.40i | − | 0.989825i | −0.868943 | − | 0.494912i | \(-0.835200\pi\) | ||
0.868943 | − | 0.494912i | \(-0.164800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1300.00 | −0.156986 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2226.00 | + | 6296.08i | 0.257371 | + | 0.727955i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6075.46i | 0.673181i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −478.000 | −0.0508024 | −0.0254012 | − | 0.999677i | \(-0.508086\pi\) | ||||
−0.0254012 | + | 0.999677i | \(0.508086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6048.00 | − | 7484.02i | −0.617080 | − | 0.763597i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13729.2i | 1.34587i | 0.739703 | + | 0.672933i | \(0.234966\pi\) | ||||
−0.739703 | + | 0.672933i | \(0.765034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2138.00 | −0.201527 | −0.100764 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100764 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3744.00 | − | 1323.70i | 0.339592 | − | 0.120064i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10844.2i | 0.947174i | 0.880747 | + | 0.473587i | \(0.157041\pi\) | ||||
−0.880747 | + | 0.473587i | \(0.842959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4750.00 | −0.399798 | −0.199899 | − | 0.979817i | \(-0.564061\pi\) | ||||
−0.199899 | + | 0.979817i | \(0.564061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5622.00 | + | 15901.4i | 0.456294 | + | 1.29059i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3190.47i | − | 0.249860i | −0.992166 | − | 0.124930i | \(-0.960129\pi\) | ||
0.992166 | − | 0.124930i | \(-0.0398707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6336.00 | 0.479093 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3150.00 | + | 2545.58i | −0.230112 | + | 0.185958i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5294.82i | − | 0.373901i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 529.000 | 0.0361314 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20448.0 | + | 7229.46i | −1.35158 | + | 0.477854i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16325.7i | 1.04484i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8282.00 | −0.513485 | −0.256743 | − | 0.966480i | \(-0.582649\pi\) | ||||
−0.256743 | + | 0.966480i | \(0.582649\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 786.000 | + | 2223.14i | 0.0472327 | + | 0.133594i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5413.61i | − | 0.315460i | −0.987482 | − | 0.157730i | \(-0.949582\pi\) | ||
0.987482 | − | 0.157730i | \(-0.0504176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9308.00 | −0.526203 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6480.00 | − | 10538.7i | 0.355556 | − | 0.578256i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18090.6i | − | 0.963856i | −0.876211 | − | 0.481928i | \(-0.839937\pi\) | ||
0.876211 | − | 0.481928i | \(-0.160063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23206.0 | 1.20108 | 0.600538 | − | 0.799596i | \(-0.294953\pi\) | ||||
0.600538 | + | 0.799596i | \(0.294953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14400.0 | + | 5091.17i | −0.724310 | + | 0.256082i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5939.70i | 0.290464i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24480.0 | 1.16433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5175.00 | − | 14637.1i | −0.239484 | − | 0.677362i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11183.6i | − | 0.503743i | −0.967761 | − | 0.251872i | \(-0.918954\pi\) | ||
0.967761 | − | 0.251872i | \(-0.0810460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14426.0 | −0.632692 | −0.316346 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316346 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10368.0 | − | 12829.7i | −0.442907 | − | 0.548069i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12592.2i | 0.524127i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 49010.0 | 1.98832 | 0.994158 | − | 0.107935i | \(-0.0344238\pi\) | ||||
0.994158 | + | 0.107935i | \(0.0344238\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3888.00 | − | 1374.62i | 0.153791 | − | 0.0543735i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9707.16i | 0.374490i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 42982.0 | 1.61775 | 0.808875 | − | 0.587981i | \(-0.200077\pi\) | ||||
0.808875 | + | 0.587981i | \(0.200077\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6048.00 | − | 17106.3i | −0.222149 | − | 0.628332i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 44157.4i | − | 1.58333i | −0.610957 | − | 0.791663i | \(-0.709215\pi\) | ||
0.610957 | − | 0.791663i | \(-0.290785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26061.0 | −0.912468 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22554.0 | + | 18226.4i | −0.771314 | + | 0.623316i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22418.1i | − | 0.749043i | −0.927218 | − | 0.374522i | \(-0.877807\pi\) | ||
0.927218 | − | 0.374522i | \(-0.122193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8762.00 | −0.286106 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15408.0 | + | 5447.55i | −0.491813 | + | 0.173882i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 30597.9i | − | 0.954962i | −0.878642 | − | 0.477481i | \(-0.841550\pi\) | ||
0.878642 | − | 0.477481i | \(-0.158450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13102.0 | −0.399927 | −0.199963 | − | 0.979803i | \(-0.564082\pi\) | ||||
−0.199963 | + | 0.979803i | \(0.564082\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4458.00 | − | 12609.1i | −0.133118 | − | 0.376516i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31802.8i | 0.929228i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24192.0 | −0.691813 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16146.0 | + | 9927.78i | 0.452003 | + | 0.277926i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 70326.0i | 1.92774i | 0.266367 | + | 0.963872i | \(0.414177\pi\) | ||||
−0.266367 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18050.0 | 0.484577 | 0.242288 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242288 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7200.00 | + | 2545.58i | −0.189349 | + | 0.0669450i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26321.3i | − | 0.678228i | −0.940745 | − | 0.339114i | \(-0.889873\pi\) | ||
0.940745 | − | 0.339114i | \(-0.110127\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 37222.0 | 0.939926 | 0.469963 | − | 0.882686i | \(-0.344267\pi\) | ||||
0.469963 | + | 0.882686i | \(0.344267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13458.0 | + | 38065.0i | 0.333111 | + | 0.942179i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 37504.9i | 0.910115i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −40896.0 | −0.973135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19008.0 | + | 23521.2i | 0.443604 | + | 0.548932i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42528.2i | 0.973609i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15098.0 | −0.339121 | −0.169560 | − | 0.985520i | \(-0.554235\pi\) | ||||
−0.169560 | + | 0.985520i | \(0.554235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30240.0 | − | 10691.5i | 0.666534 | − | 0.235656i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4446.29i | 0.0961879i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19292.0 | −0.409692 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 870.000 | + | 2460.73i | 0.0181397 | + | 0.0513069i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10182.3i | 0.208479i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −58778.0 | −1.18197 | −0.590983 | − | 0.806684i | \(-0.701260\pi\) | ||||
−0.590983 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21231.0 | + | 17157.2i | −0.419378 | + | 0.338908i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 68001.0i | − | 1.31967i | −0.751412 | − | 0.659833i | \(-0.770627\pi\) | ||
0.751412 | − | 0.659833i | \(-0.229373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28562.0 | 0.544650 | 0.272325 | − | 0.962205i | \(-0.412207\pi\) | ||||
0.272325 | + | 0.962205i | \(0.412207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26208.0 | − | 9265.93i | 0.491145 | − | 0.173646i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22503.0i | 0.414503i | 0.978288 | + | 0.207252i | \(0.0664519\pi\) | ||||
−0.978288 | + | 0.207252i | \(0.933548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28800.0 | −0.521503 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29454.0 | − | 83308.5i | −0.524382 | − | 1.48318i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1289.76i | − | 0.0225795i | −0.999936 | − | 0.0112897i | \(-0.996406\pi\) | ||
0.999936 | − | 0.0112897i | \(-0.00359371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −61246.0 | −1.05449 | −0.527246 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527246 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 58563.0 | − | 7560.39i | 0.991770 | − | 0.128036i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 29274.2i | − | 0.487700i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17900.0 | 0.293399 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 60336.0 | − | 21332.0i | 0.973146 | − | 0.344059i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 45260.5i | 0.718409i | 0.933259 | + | 0.359205i | \(0.116952\pi\) | ||||
−0.933259 | + | 0.359205i | \(0.883048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44352.0 | 0.692903 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10368.0 | − | 29325.1i | −0.159446 | − | 0.450982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 85260.1i | − | 1.29086i | −0.763819 | − | 0.645431i | \(-0.776678\pi\) | ||
0.763819 | − | 0.645431i | \(-0.223322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48724.0 | −0.726346 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73440.0 | + | 90877.4i | 1.07808 | + | 1.33406i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 84751.0i | − | 1.22527i | −0.790364 | − | 0.612637i | \(-0.790109\pi\) | ||
0.790364 | − | 0.612637i | \(-0.209891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7776.00 | 0.110730 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66528.0 | − | 23521.2i | 0.933216 | − | 0.329942i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 42918.6i | − | 0.593117i | −0.955015 | − | 0.296559i | \(-0.904161\pi\) | ||
0.955015 | − | 0.296559i | \(-0.0958390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27430.0 | 0.373497 | 0.186749 | − | 0.982408i | \(-0.440205\pi\) | ||||
0.186749 | + | 0.982408i | \(0.440205\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3900.00 | − | 11030.9i | −0.0523286 | − | 0.148008i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 40033.6i | 0.529369i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −93934.0 | −1.22423 | −0.612115 | − | 0.790768i | \(-0.709681\pi\) | ||||
−0.612115 | + | 0.790768i | \(0.709681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −46746.0 | + | 37776.5i | −0.600532 | + | 0.485303i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24471.6i | 0.309919i | 0.987921 | + | 0.154960i | \(0.0495248\pi\) | ||||
−0.987921 | + | 0.154960i | \(0.950475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 65830.0 | 0.821961 | 0.410980 | − | 0.911644i | \(-0.365187\pi\) | ||||
0.410980 | + | 0.911644i | \(0.365187\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −51552.0 | + | 18226.4i | −0.634681 | + | 0.224394i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 62655.3i | − | 0.760666i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42049.0 | 0.503454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1434.00 | − | 4055.96i | −0.0169341 | − | 0.0478970i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 90028.8i | 1.04869i | 0.851506 | + | 0.524344i | \(0.175689\pi\) | ||||
−0.851506 | + | 0.524344i | \(0.824311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30816.0 | −0.354105 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 45360.0 | − | 73771.0i | 0.514233 | − | 0.836321i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 18667.6i | − | 0.208808i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6812.00 | −0.0751868 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −116496. | + | 41187.6i | −1.26890 | + | 0.448622i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 25218.3i | − | 0.271091i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −67322.0 | −0.714299 | −0.357150 | − | 0.934047i | \(-0.616251\pi\) | ||||
−0.357150 | + | 0.934047i | \(0.616251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6414.00 | − | 18141.5i | −0.0671757 | − | 0.190001i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 131997.i | 1.36472i | 0.731017 | + | 0.682360i | \(0.239046\pi\) | ||||
−0.731017 | + | 0.682360i | \(0.760954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22078.0 | −0.225357 | −0.112679 | − | 0.993631i | \(-0.535943\pi\) | ||||
−0.112679 | + | 0.993631i | \(0.535943\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22464.0 | + | 27797.8i | 0.226395 | + | 0.280149i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 117894.i | 1.17321i | 0.809874 | + | 0.586604i | \(0.199535\pi\) | ||||
−0.809874 | + | 0.586604i | \(0.800465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 171360. | 1.68395 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −92016.0 | + | 32532.6i | −0.893004 | + | 0.315725i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 72905.5i | 0.698804i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16850.0 | 0.159527 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14250.0 | − | 40305.1i | −0.133266 | − | 0.376933i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 44123.5i | − | 0.407641i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −167642. | −1.53012 | −0.765062 | − | 0.643956i | \(-0.777292\pi\) | ||||
−0.765062 | + | 0.643956i | \(0.777292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −118062. | + | 95408.5i | −1.06469 | + | 0.860396i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 76129.9i | 0.678369i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 162914. | 1.43449 | 0.717247 | − | 0.696819i | \(-0.245402\pi\) | ||||
0.717247 | + | 0.696819i | \(0.245402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27072.0 | − | 9571.40i | 0.235571 | − | 0.0832868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 88145.1i | 0.758035i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 107276. | 0.911831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19008.0 | + | 53762.7i | 0.159698 | + | 0.451693i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 132184.i | − | 1.09779i | −0.835892 | − | 0.548895i | \(-0.815049\pi\) | ||
0.835892 | − | 0.548895i | \(-0.184951\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 53234.0 | 0.437057 | 0.218529 | − | 0.975831i | \(-0.429874\pi\) | ||||
0.218529 | + | 0.975831i | \(0.429874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31050.0 | − | 19091.9i | −0.252027 | − | 0.154965i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 144861.i | − | 1.16252i | −0.813717 | − | 0.581261i | \(-0.802560\pi\) | ||
0.813717 | − | 0.581261i | \(-0.197440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 60480.0 | 0.479905 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44928.0 | − | 15884.4i | 0.352517 | − | 0.124634i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12931.6i | − | 0.100337i | −0.998741 | − | 0.0501686i | \(-0.984024\pi\) | ||
0.998741 | − | 0.0501686i | \(-0.0159759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2157.00 | −0.0165514 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1587.00 | + | 4488.71i | 0.0120438 | + | 0.0340650i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4921.46i | 0.0369410i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 44326.0 | 0.329099 | 0.164549 | − | 0.986369i | \(-0.447383\pi\) | ||||
0.164549 | + | 0.986369i | \(0.447383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −122688. | − | 151819.i | −0.901051 | − | 1.11499i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11913.3i | 0.0865537i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −60718.0 | −0.436415 | −0.218208 | − | 0.975902i | \(-0.570021\pi\) | ||||
−0.218208 | + | 0.975902i | \(0.570021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −138528. | + | 48977.0i | −0.985088 | + | 0.348281i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 72124.9i | − | 0.507461i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30458.0 | −0.212043 | −0.106021 | − | 0.994364i | \(-0.533811\pi\) | ||||
−0.106021 | + | 0.994364i | \(0.533811\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24846.0 | − | 70275.1i | −0.171162 | − | 0.484118i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 235687.i | − | 1.60671i | −0.595498 | − | 0.803357i | \(-0.703045\pi\) | ||
0.595498 | − | 0.803357i | \(-0.296955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52416.0 | 0.353625 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16506.0 | + | 13338.9i | −0.110210 | + | 0.0890629i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 150410.i | − | 0.993980i | −0.867756 | − | 0.496990i | \(-0.834439\pi\) | ||
0.867756 | − | 0.496990i | \(-0.165561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 76032.0 | 0.497328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45936.0 | − | 16240.8i | 0.297419 | − | 0.105153i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 166617.i | − | 1.06789i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 172658. | 1.09548 | 0.547742 | − | 0.836648i | \(-0.315488\pi\) | ||||
0.547742 | + | 0.836648i | \(0.315488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27924.0 | − | 78981.0i | −0.175401 | − | 0.496109i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 167466.i | 1.04145i | 0.853726 | + | 0.520723i | \(0.174338\pi\) | ||||
−0.853726 | + | 0.520723i | \(0.825662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37100.0 | 0.228436 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 108864. | + | 23368.5i | 0.663704 | + | 0.142469i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 222620.i | 1.34393i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −150430. | −0.899265 | −0.449633 | − | 0.893214i | \(-0.648445\pi\) | ||||
−0.449633 | + | 0.893214i | \(0.648445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 153504. | − | 54271.9i | 0.908732 | − | 0.321285i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 47212.1i | − | 0.276792i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 120672. | 0.700665 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 69618.0 | + | 196909.i | 0.400359 | + | 1.13239i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 178276.i | 1.01546i | 0.861515 | + | 0.507732i | \(0.169516\pi\) | ||||
−0.861515 | + | 0.507732i | \(0.830484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −216046. | −1.21894 | −0.609470 | − | 0.792809i | \(-0.708618\pi\) | ||||
−0.609470 | + | 0.792809i | \(0.708618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −86400.0 | − | 106915.i | −0.482873 | − | 0.597525i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 68629.0i | 0.379953i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38636.0 | 0.211903 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −50400.0 | + | 17819.1i | −0.273852 | + | 0.0968213i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5498.46i | 0.0295997i | 0.999890 | + | 0.0147998i | \(0.00471110\pi\) | ||||
−0.999890 | + | 0.0147998i | \(0.995289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 108002. | 0.576044 | 0.288022 | − | 0.957624i | \(-0.407002\pi\) | ||||
0.288022 | + | 0.957624i | \(0.407002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 73440.0 | + | 207720.i | 0.388109 | + | 1.09774i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 133660.i | − | 0.699905i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −357722. | −1.85617 | −0.928083 | − | 0.372374i | \(-0.878544\pi\) | ||||
−0.928083 | + | 0.372374i | \(0.878544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 108675. | − | 87822.7i | 0.558795 | − | 0.451575i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 86261.4i | 0.439551i | 0.975551 | + | 0.219775i | \(0.0705324\pi\) | ||||
−0.975551 | + | 0.219775i | \(0.929468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 133056. | 0.671915 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 94896.0 | − | 33550.8i | 0.474934 | − | 0.167914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 301397.i | 1.49502i | 0.664251 | + | 0.747509i | \(0.268750\pi\) | ||||
−0.664251 | + | 0.747509i | \(0.731250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −286272. | −1.40743 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −43278.0 | − | 122409.i | −0.210897 | − | 0.596507i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 22061.7i | − | 0.106566i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −399070. | −1.91081 | −0.955403 | − | 0.295305i | \(-0.904579\pi\) | ||||
−0.955403 | + | 0.295305i | \(0.904579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 77760.0 | − | 126465.i | 0.369089 | − | 0.600266i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38268.6i | 0.180070i | 0.995939 | + | 0.0900349i | \(0.0286979\pi\) | ||||
−0.995939 | + | 0.0900349i | \(0.971302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −144410. | −0.673652 | −0.336826 | − | 0.941567i | \(-0.609353\pi\) | ||||
−0.336826 | + | 0.941567i | \(0.609353\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −106848. | + | 37776.5i | −0.494152 | + | 0.174709i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 148204.i | 0.679557i | 0.940505 | + | 0.339779i | \(0.110352\pi\) | ||||
−0.940505 | + | 0.339779i | \(0.889648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −116636. | −0.530258 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 147030. | + | 415864.i | 0.662772 | + | 1.87460i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31124.0i | 0.139115i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 120646. | 0.534719 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23328.0 | + | 28866.9i | 0.102528 | + | 0.126871i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 305606.i | − | 1.33196i | −0.745970 | − | 0.665979i | \(-0.768014\pi\) | ||
0.745970 | − | 0.665979i | \(-0.231986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 93700.0 | 0.404995 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −82368.0 | + | 29121.5i | −0.353073 | + | 0.124830i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8111.93i | − | 0.0344858i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 196774. | 0.829678 | 0.414839 | − | 0.909895i | \(-0.363838\pi\) | ||||
0.414839 | + | 0.909895i | \(0.363838\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 128946. | + | 364714.i | 0.539250 | + | 1.52523i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 166193.i | − | 0.689365i | −0.938719 | − | 0.344682i | \(-0.887987\pi\) | ||
0.938719 | − | 0.344682i | \(-0.112013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 293760. | 1.20865 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 127008. | − | 102638.i | 0.518347 | − | 0.418888i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 92659.3i | 0.375125i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −189050. | −0.759234 | −0.379617 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379617 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 374688. | − | 132472.i | 1.49277 | − | 0.527776i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 344061.i | 1.35988i | 0.733269 | + | 0.679939i | \(0.237994\pi\) | ||||
−0.733269 | + | 0.679939i | \(0.762006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −232992. | −0.913605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −78183.0 | − | 221135.i | −0.304156 | − | 0.860283i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 353208.i | − | 1.36331i | −0.731673 | − | 0.681656i | \(-0.761260\pi\) | ||
0.731673 | − | 0.681656i | \(-0.238740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7540.00 | −0.0288755 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −222318. | − | 136698.i | −0.844773 | − | 0.519430i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 36283.1i | − | 0.136801i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −201600. | −0.754240 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 190224. | − | 67254.3i | 0.706205 | − | 0.249681i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 276043.i | − | 1.01695i | −0.861075 | − | 0.508477i | \(-0.830209\pi\) | ||
0.861075 | − | 0.508477i | \(-0.169791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 146950. | 0.537237 | 0.268619 | − | 0.963247i | \(-0.413433\pi\) | ||||
0.268619 | + | 0.963247i | \(0.413433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −26286.0 | − | 74348.0i | −0.0953687 | − | 0.269743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 151106.i | 0.544077i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 140449. | 0.501889 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −92448.0 | − | 114399.i | −0.327875 | − | 0.405725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 120491.i | 0.424131i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −184032. | −0.642963 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 259632. | − | 91793.8i | 0.900346 | − | 0.318321i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 204920.i | − | 0.705352i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −244942. | −0.836891 | −0.418445 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418445 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39306.0 | − | 111174.i | −0.133309 | − | 0.377055i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 80610.2i | − | 0.271392i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 283366. | 0.947050 | 0.473525 | − | 0.880780i | \(-0.342981\pi\) | ||||
0.473525 | + | 0.880780i | \(0.342981\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 93618.0 | − | 75654.8i | 0.310609 | − | 0.251010i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 516414.i | − | 1.70096i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 255268. | 0.834730 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −269856. | + | 95408.5i | −0.876085 | + | 0.309743i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 47093.3i | 0.151792i | 0.997116 | + | 0.0758960i | \(0.0241817\pi\) | ||||
−0.997116 | + | 0.0758960i | \(0.975818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13100.0 | 0.0419225 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72576.0 | − | 205276.i | −0.230604 | − | 0.652247i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 84.8528i | 0.000267701i | 1.00000 | 0.000133850i | \(4.26059e-5\pi\) | |||||
−1.00000 | 0.000133850i | \(0.999957\pi\) | ||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54144.0 | 0.169611 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35802.0 | + | 166787.i | −0.111363 | + | 0.518794i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 239115.i | 0.738555i | 0.929319 | + | 0.369277i | \(0.120395\pi\) | ||||
−0.929319 | + | 0.369277i | \(0.879605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 140710. | 0.431571 | 0.215786 | − | 0.976441i | \(-0.430769\pi\) | ||||
0.215786 | + | 0.976441i | \(0.430769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −596736. | + | 210978.i | −1.81749 | + | 0.642581i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 125820.i | − | 0.380551i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36002.0 | 0.108137 | 0.0540686 | − | 0.998537i | \(-0.482781\pi\) | ||||
0.0540686 | + | 0.998537i | \(0.482781\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54150.0 | + | 153159.i | 0.161526 | + | 0.456863i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 184877.i | 0.547686i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 54432.0 | 0.160146 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −43200.0 | − | 53457.3i | −0.126233 | − | 0.156205i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 316179.i | 0.917606i | 0.888538 | + | 0.458803i | \(0.151722\pi\) | ||||
−0.888538 | + | 0.458803i | \(0.848278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 265636. | 0.765696 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 223344. | − | 78964.0i | 0.639439 | − | 0.226076i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 262093.i | − | 0.745327i | −0.927967 | − | 0.372663i | \(-0.878445\pi\) | ||
0.927967 | − | 0.372663i | \(-0.121555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 89856.0 | 0.253813 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 111666. | + | 315839.i | 0.313309 | + | 0.886171i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 606494.i | 1.69034i | 0.534501 | + | 0.845168i | \(0.320499\pi\) | ||||
−0.534501 | + | 0.845168i | \(0.679501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 306530. | 0.848641 | 0.424321 | − | 0.905512i | \(-0.360513\pi\) | ||||
0.424321 | + | 0.905512i | \(0.360513\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −282618. | + | 228390.i | −0.777258 | + | 0.628119i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8977.43i | 0.0245268i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −563162. | −1.52847 | −0.764233 | − | 0.644940i | \(-0.776882\pi\) | ||||
−0.764233 | + | 0.644940i | \(0.776882\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −318240. | + | 112515.i | −0.858065 | + | 0.303372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 84852.8i | 0.227292i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 111314. | 0.296230 | 0.148115 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148115 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −122688. | − | 347014.i | −0.324378 | − | 0.917481i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 121340.i | 0.318737i | 0.987219 | + | 0.159368i | \(0.0509457\pi\) | ||||
−0.987219 | + | 0.159368i | \(0.949054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 581158. | 1.51675 | 0.758373 | − | 0.651821i | \(-0.225995\pi\) | ||||
0.758373 | + | 0.651821i | \(0.225995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −142560. | + | 231852.i | −0.369670 | + | 0.601212i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 203850.i | 0.525213i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −66431.0 | −0.170063 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −360864. | + | 127585.i | −0.917928 | + | 0.324536i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 381634.i | 0.964597i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −232346. | −0.583548 | −0.291774 | − | 0.956487i | \(-0.594245\pi\) | ||||
−0.291774 | + | 0.956487i | \(0.594245\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45294.0 | − | 128111.i | −0.113040 | − | 0.319726i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 140550.i | − | 0.348565i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −86250.0 | −0.212559 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 181440. | + | 224521.i | 0.444356 | + | 0.549863i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 653570.i | − | 1.59066i | −0.606179 | − | 0.795328i | \(-0.707299\pi\) | ||
0.606179 | − | 0.795328i | \(-0.292701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 424678. | 1.02716 | 0.513580 | − | 0.858042i | \(-0.328319\pi\) | ||||
0.513580 | + | 0.858042i | \(0.328319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37728.0 | + | 13338.9i | −0.0906869 | + | 0.0320626i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 427964.i | − | 1.02235i | −0.859478 | − | 0.511173i | \(-0.829211\pi\) | ||
0.859478 | − | 0.511173i | \(-0.170789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −215712. | −0.512136 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −57876.0 | − | 163698.i | −0.136564 | − | 0.386262i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 720621.i | 1.68998i | 0.534785 | + | 0.844988i | \(0.320393\pi\) | ||||
−0.534785 | + | 0.844988i | \(0.679607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 91872.0 | 0.214141 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18270.0 | + | 14764.4i | −0.0423261 | + | 0.0342046i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40135.4i | 0.0924180i | 0.998932 | + | 0.0462090i | \(0.0147140\pi\) | ||||
−0.998932 | + | 0.0462090i | \(0.985286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −358510. | −0.820537 | −0.410269 | − | 0.911965i | \(-0.634565\pi\) | ||||
−0.410269 | + | 0.911965i | \(0.634565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −86400.0 | + | 30547.0i | −0.196556 | + | 0.0694931i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 157962.i | − | 0.357198i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −538560. | −1.21055 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −176334. | − | 498748.i | −0.393989 | − | 1.11437i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 176528.i | − | 0.392074i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 582434. | 1.28593 | 0.642964 | − | 0.765896i | \(-0.277705\pi\) | ||||
0.642964 | + | 0.765896i | \(0.277705\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −209277. | − | 128679.i | −0.459319 | − | 0.282424i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37352.2i | 0.0814965i | 0.999169 | + | 0.0407482i | \(0.0129742\pi\) | ||||
−0.999169 | + | 0.0407482i | \(0.987026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12428.0 | 0.0269564 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 577008. | − | 204003.i | 1.24419 | − | 0.439889i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 161848.i | − | 0.346950i | −0.984838 | − | 0.173475i | \(-0.944500\pi\) | ||
0.984838 | − | 0.173475i | \(-0.0554995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 307008. | 0.654287 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 85686.0 | + | 242357.i | 0.181550 | + | 0.513501i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 22910.3i | − | 0.0482605i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 630118. | 1.31967 | 0.659836 | − | 0.751410i | \(-0.270626\pi\) | ||||
0.659836 | + | 0.751410i | \(0.270626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 157248. | + | 194584.i | 0.327430 | + | 0.405174i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 393819.i | 0.815318i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −490752. | −1.01017 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −190944. | + | 67508.9i | −0.390797 | + | 0.138168i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 457747.i | − | 0.931514i | −0.884913 | − | 0.465757i | \(-0.845782\pi\) | ||
0.884913 | − | 0.465757i | \(-0.154218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 670892. | 1.35751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −86400.0 | − | 244376.i | −0.173834 | − | 0.491678i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 356959.i | − | 0.714133i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 274130. | 0.545336 | 0.272668 | − | 0.962108i | \(-0.412094\pi\) | ||||
0.272668 | + | 0.962108i | \(0.412094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 618534. | − | 499851.i | 1.22356 | − | 0.988784i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 277027.i | − | 0.544934i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −100800. | −0.197173 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10944.0 | − | 3869.29i | 0.0212881 | − | 0.00752650i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 304045.i | 0.588138i | 0.955784 | + | 0.294069i | \(0.0950096\pi\) | ||||
−0.955784 | + | 0.294069i | \(0.904990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55588.0 | 0.106933 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −183738. | − | 519690.i | −0.351498 | − | 0.994185i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 486122.i | − | 0.924845i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −364058. | −0.688814 | −0.344407 | − | 0.938821i | \(-0.611920\pi\) | ||||
−0.344407 | + | 0.938821i | \(0.611920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 239841. | + | 474242.i | 0.451303 | + | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53355.4i | 0.0998491i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −301198. | −0.560588 | −0.280294 | − | 0.959914i | \(-0.590432\pi\) | ||||
−0.280294 | + | 0.959914i | \(0.590432\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 248400. | − | 87822.7i | 0.459808 | − | 0.162567i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 532910.i | 0.981112i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −872570. | −1.59776 | −0.798880 | − | 0.601491i | \(-0.794574\pi\) | ||||
−0.798880 | + | 0.601491i | \(0.794574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53700.0 | + | 151887.i | 0.0977998 | + | 0.276620i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 874222.i | − | 1.58359i | −0.610784 | − | 0.791797i | \(-0.709146\pi\) | ||
0.610784 | − | 0.791797i | \(-0.290854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 189792. | 0.341952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 362016. | + | 447972.i | 0.648764 | + | 0.802804i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 281949.i | − | 0.502582i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −916250. | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −384048. | + | 135781.i | −0.677323 | + | 0.239470i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 244817.i | − | 0.429485i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −691630. | −1.20693 | −0.603465 | − | 0.797390i | \(-0.706214\pi\) | ||||
−0.603465 | + | 0.797390i | \(0.706214\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 133056. | + | 376339.i | 0.230968 | + | 0.653275i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 90249.5i | − | 0.155839i | −0.996960 | − | 0.0779193i | \(-0.975172\pi\) | ||
0.996960 | − | 0.0779193i | \(-0.0248277\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 123500. | 0.212138 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 217728. | − | 175951.i | 0.372042 | − | 0.300655i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 90792.5i | 0.154333i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −515326. | −0.871424 | −0.435712 | − | 0.900086i | \(-0.643503\pi\) | ||||
−0.435712 | + | 0.900086i | \(0.643503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 723456. | − | 255780.i | 1.21704 | − | 0.430287i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 100449.i | − | 0.168107i | −0.996461 | − | 0.0840535i | \(-0.973213\pi\) | ||
0.996461 | − | 0.0840535i | \(-0.0267867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 250054. | 0.416323 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −146172. | − | 413437.i | −0.242115 | − | 0.684805i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 862716.i | 1.42165i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 423360. | 0.694077 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −550800. | + | 895791.i | −0.898401 | + | 1.46111i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 831727.i | 1.34971i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 107878. | 0.174174 | 0.0870870 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870870 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 719136. | − | 254253.i | 1.15520 | − | 0.408425i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 82952.1i | 0.132579i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −74300.0 | −0.118152 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23328.0 | + | 65981.5i | 0.0369099 | + | 0.104397i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 489482.i | 0.770584i | 0.922795 | + | 0.385292i | \(0.125899\pi\) | ||||
−0.922795 | + | 0.385292i | \(0.874101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −345600. | −0.541353 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 399168. | + | 493945.i | 0.622144 | + | 0.769864i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34450.2i | 0.0534270i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −164736. | −0.254212 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 364176. | − | 128756.i | 0.559196 | − | 0.197706i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.04074e6i | 1.59017i | 0.606497 | + | 0.795086i | \(0.292574\pi\) | ||||
−0.606497 | + | 0.795086i | \(0.707426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −611066. | −0.929066 | −0.464533 | − | 0.885556i | \(-0.653778\pi\) | ||||
−0.464533 | + | 0.885556i | \(0.653778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 82290.0 | + | 232751.i | 0.124499 | + | 0.352136i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 729429.i | 1.09817i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 93796.0 | 0.140521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 81900.0 | − | 66185.2i | 0.122100 | − | 0.0986718i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 345300.i | − | 0.512283i | −0.966639 | − | 0.256142i | \(-0.917549\pi\) | ||
0.966639 | − | 0.256142i | \(-0.0824514\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 178150. | 0.263018 | 0.131509 | − | 0.991315i | \(-0.458018\pi\) | ||||
0.131509 | + | 0.991315i | \(0.458018\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −339696. | + | 120101.i | −0.499094 | + | 0.176456i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.13844e6i | 1.66455i | 0.554361 | + | 0.832277i | \(0.312963\pi\) | ||||
−0.554361 | + | 0.832277i | \(0.687037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 100082. | 0.145629 | 0.0728143 | − | 0.997346i | \(-0.476802\pi\) | ||||
0.0728143 | + | 0.997346i | \(0.476802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −281802. | − | 797056.i | −0.408077 | − | 1.15422i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 351291.i | − | 0.506263i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 749376. | 1.07480 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −460782. | − | 283324.i | −0.657725 | − | 0.404419i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.13964e6i | − | 1.61899i | −0.587127 | − | 0.809495i | \(-0.699741\pi\) | ||
0.587127 | − | 0.809495i | \(-0.300259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37352e6 | −1.94197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −207648. | + | 73414.7i | −0.292195 | + | 0.103306i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 442270.i | − | 0.619404i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13754.0 | −0.0191718 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 197490. | + | 558586.i | 0.273987 | + | 0.774952i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 699662.i | − | 0.966116i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 172754. | 0.237427 | 0.118713 | − | 0.992929i | \(-0.462123\pi\) | ||||
0.118713 | + | 0.992929i | \(0.462123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −309312. | − | 382754.i | −0.423121 | − | 0.523585i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 299802.i | 0.408200i | 0.978950 | + | 0.204100i | \(0.0654267\pi\) | ||||
−0.978950 | + | 0.204100i | \(0.934573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8186.00 | −0.0110939 | −0.00554696 | − | 0.999985i | \(-0.501766\pi\) | ||||
−0.00554696 | + | 0.999985i | \(0.501766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 531648. | − | 187966.i | 0.717163 | − | 0.253555i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 387336.i | 0.520076i | 0.965598 | + | 0.260038i | \(0.0837350\pi\) | ||||
−0.965598 | + | 0.260038i | \(0.916265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 380448. | 0.508467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 126147. | + | 356798.i | 0.167818 | + | 0.474661i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.16632e6i | − | 1.54446i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 224300. | 0.295660 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30114.0 | − | 24335.8i | 0.0395130 | − | 0.0319313i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 424468.i | − | 0.554407i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 245426. | 0.319096 | 0.159548 | − | 0.987190i | \(-0.448996\pi\) | ||||
0.159548 | + | 0.987190i | \(0.448996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −763920. | + | 270087.i | −0.988713 | + | 0.349563i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 607071.i | − | 0.782146i | −0.920360 | − | 0.391073i | \(-0.872104\pi\) | ||
0.920360 | − | 0.391073i | \(-0.127896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −759962. | −0.974699 | −0.487349 | − | 0.873207i | \(-0.662036\pi\) | ||||
−0.487349 | + | 0.873207i | \(0.662036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92448.0 | − | 261482.i | −0.118035 | − | 0.333854i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5736.05i | 0.00729064i | 0.999993 | + | 0.00364532i | \(0.00116034\pi\) | ||||
−0.999993 | + | 0.00364532i | \(0.998840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 215332. | 0.272461 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 762048. | + | 163579.i | 0.959902 | + | 0.206050i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 607546.i | 0.761862i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 519264. | 0.648249 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 158400. | − | 56002.9i | 0.196866 | − | 0.0696026i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.07033e6i | − | 1.32434i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 93312.0 | 0.114944 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20436.0 | − | 57801.7i | −0.0250623 | − | 0.0708868i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 222348.i | − | 0.271479i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 138502. | 0.168361 | 0.0841805 | − | 0.996451i | \(-0.473173\pi\) | ||||
0.0841805 | + | 0.996451i | \(0.473173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −698976. | − | 864939.i | −0.845930 | − | 1.04679i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 266845.i | 0.321531i | 0.986993 | + | 0.160765i | \(0.0513962\pi\) | ||||
−0.986993 | + | 0.160765i | \(0.948604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 844704. | 1.01336 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 213984. | − | 75654.8i | 0.255587 | − | 0.0903637i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 140754.i | 0.167387i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.44266e6 | 1.70818 | 0.854090 | − | 0.520125i | \(-0.174115\pi\) | ||||
0.854090 | + | 0.520125i | \(0.174115\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −201966. | − | 571246.i | −0.238100 | − | 0.673448i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 178191.i | − | 0.209162i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 631538. | 0.738101 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 134694. | − | 108849.i | 0.156743 | − | 0.126668i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 511696.i | 0.592899i | 0.955048 | + | 0.296450i | \(0.0958027\pi\) | ||||
−0.955048 | + | 0.296450i | \(0.904197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −617550. | −0.712480 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.12003e6 | + | 395991.i | −1.28667 | + | 0.454907i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 410552.i | − | 0.469618i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 868610. | 0.989340 | 0.494670 | − | 0.869081i | \(-0.335289\pi\) | ||||
0.494670 | + | 0.869081i | \(0.335289\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −66234.0 | − | 187338.i | −0.0751190 | − | 0.212469i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 101942.i | 0.115126i | 0.998342 | + | 0.0575632i | \(0.0183331\pi\) | ||||
−0.998342 | + | 0.0575632i | \(0.981667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 899712. | 1.01177 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −168480. | + | 274007.i | −0.188662 | + | 0.306830i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 233159.i | − | 0.259987i | −0.991515 | − | 0.129993i | \(-0.958504\pi\) | ||
0.991515 | − | 0.129993i | \(-0.0414956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14500.0 | 0.0161004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00037e6 | + | 353683.i | −1.10611 | + | 0.391069i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 927916.i | − | 1.02170i | −0.859670 | − | 0.510850i | \(-0.829331\pi\) | ||
0.859670 | − | 0.510850i | \(-0.170669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.19347e6 | −1.30860 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 514080. | + | 1.45404e6i | 0.561315 | + | 1.58764i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 470356.i | 0.511434i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −372957. | −0.403842 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −552096. | − | 683184.i | −0.595336 | − | 0.736691i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 306319.i | 0.328942i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −150746. | −0.161210 | −0.0806052 | − | 0.996746i | \(-0.525685\pi\) | ||||
−0.0806052 | + | 0.996746i | \(0.525685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −618624. | + | 218717.i | −0.658839 | + | 0.232935i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 508150.i | 0.538956i | 0.963007 | + | 0.269478i | \(0.0868511\pi\) | ||||
−0.963007 | + | 0.269478i | \(0.913149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −603356. | −0.637306 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 50550.0 | + | 142977.i | 0.0531755 | + | 0.150403i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 214576.i | − | 0.224798i | −0.993663 | − | 0.112399i | \(-0.964147\pi\) | ||
0.993663 | − | 0.112399i | \(-0.0358534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 931392. | 0.971778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 299250. | − | 241831.i | 0.310954 | − | 0.251289i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.34831e6i | 1.39535i | 0.716414 | + | 0.697675i | \(0.245782\pi\) | ||||
−0.716414 | + | 0.697675i | \(0.754218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 446688. | 0.460396 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 374400. | − | 132370.i | 0.384328 | − | 0.135880i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 97818.3i | − | 0.100006i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 879910. | 0.895965 | 0.447982 | − | 0.894042i | \(-0.352143\pi\) | ||||
0.447982 | + | 0.894042i | \(0.352143\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −502926. | − | 1.42249e6i | −0.510042 | − | 1.44262i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 631678.i | 0.638043i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 935378. | 0.941016 | 0.470508 | − | 0.882396i | \(-0.344071\pi\) | ||||
0.470508 | + | 0.882396i | \(0.344071\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.16375e6 | − | 715564.i | −1.16609 | − | 0.716997i |
(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 | 48.5.e.b.17.2 | 2 | ||
3.2 | odd | 2 | inner | 48.5.e.b.17.1 | 2 | ||
4.3 | odd | 2 | 6.5.b.a.5.2 | yes | 2 | ||
8.3 | odd | 2 | 192.5.e.d.65.2 | 2 | |||
8.5 | even | 2 | 192.5.e.c.65.1 | 2 | |||
12.11 | even | 2 | 6.5.b.a.5.1 | ✓ | 2 | ||
20.3 | even | 4 | 150.5.b.a.149.3 | 4 | |||
20.7 | even | 4 | 150.5.b.a.149.2 | 4 | |||
20.19 | odd | 2 | 150.5.d.a.101.1 | 2 | |||
24.5 | odd | 2 | 192.5.e.c.65.2 | 2 | |||
24.11 | even | 2 | 192.5.e.d.65.1 | 2 | |||
28.27 | even | 2 | 294.5.b.a.197.2 | 2 | |||
36.7 | odd | 6 | 162.5.d.a.53.2 | 4 | |||
36.11 | even | 6 | 162.5.d.a.53.1 | 4 | |||
36.23 | even | 6 | 162.5.d.a.107.2 | 4 | |||
36.31 | odd | 6 | 162.5.d.a.107.1 | 4 | |||
60.23 | odd | 4 | 150.5.b.a.149.1 | 4 | |||
60.47 | odd | 4 | 150.5.b.a.149.4 | 4 | |||
60.59 | even | 2 | 150.5.d.a.101.2 | 2 | |||
84.83 | odd | 2 | 294.5.b.a.197.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.5.b.a.5.1 | ✓ | 2 | 12.11 | even | 2 | ||
6.5.b.a.5.2 | yes | 2 | 4.3 | odd | 2 | ||
48.5.e.b.17.1 | 2 | 3.2 | odd | 2 | inner | ||
48.5.e.b.17.2 | 2 | 1.1 | even | 1 | trivial | ||
150.5.b.a.149.1 | 4 | 60.23 | odd | 4 | |||
150.5.b.a.149.2 | 4 | 20.7 | even | 4 | |||
150.5.b.a.149.3 | 4 | 20.3 | even | 4 | |||
150.5.b.a.149.4 | 4 | 60.47 | odd | 4 | |||
150.5.d.a.101.1 | 2 | 20.19 | odd | 2 | |||
150.5.d.a.101.2 | 2 | 60.59 | even | 2 | |||
162.5.d.a.53.1 | 4 | 36.11 | even | 6 | |||
162.5.d.a.53.2 | 4 | 36.7 | odd | 6 | |||
162.5.d.a.107.1 | 4 | 36.31 | odd | 6 | |||
162.5.d.a.107.2 | 4 | 36.23 | even | 6 | |||
192.5.e.c.65.1 | 2 | 8.5 | even | 2 | |||
192.5.e.c.65.2 | 2 | 24.5 | odd | 2 | |||
192.5.e.d.65.1 | 2 | 24.11 | even | 2 | |||
192.5.e.d.65.2 | 2 | 8.3 | odd | 2 | |||
294.5.b.a.197.1 | 2 | 84.83 | odd | 2 | |||
294.5.b.a.197.2 | 2 | 28.27 | even | 2 |