Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 41x^{6} + 460x^{4} + 969x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.6 | ||
Root | \(-4.73066i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.6.c.d.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 5.49000i | 0.352184i | 0.984374 | + | 0.176092i | \(0.0563456\pi\) | ||||
−0.984374 | + | 0.176092i | \(0.943654\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −53.0051 | + | 17.7613i | −0.948183 | + | 0.317724i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 188.968i | − | 1.45761i | −0.684720 | − | 0.728807i | \(-0.740075\pi\) | ||
0.684720 | − | 0.728807i | \(-0.259925\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 212.860 | 0.875967 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 501.871 | 1.25058 | 0.625288 | − | 0.780394i | \(-0.284982\pi\) | ||||
0.625288 | + | 0.780394i | \(0.284982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1061.48i | 1.74203i | 0.491259 | + | 0.871013i | \(0.336537\pi\) | ||||
−0.491259 | + | 0.871013i | \(0.663463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −97.5095 | − | 290.998i | −0.111897 | − | 0.333935i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 29.5861i | 0.0248294i | 0.999923 | + | 0.0124147i | \(0.00395182\pi\) | ||||
−0.999923 | + | 0.0124147i | \(0.996048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1578.33 | 1.00303 | 0.501515 | − | 0.865149i | \(-0.332776\pi\) | ||||
0.501515 | + | 0.865149i | \(0.332776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1037.43 | 0.513347 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1295.86i | 0.510786i | 0.966837 | + | 0.255393i | \(0.0822048\pi\) | ||||
−0.966837 | + | 0.255393i | \(0.917795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2494.07 | − | 1882.88i | 0.798103 | − | 0.602521i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2502.67i | 0.660685i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3586.63 | 0.791938 | 0.395969 | − | 0.918264i | \(-0.370409\pi\) | ||||
0.395969 | + | 0.918264i | \(0.370409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3526.32 | 0.659048 | 0.329524 | − | 0.944147i | \(-0.393112\pi\) | ||||
0.329524 | + | 0.944147i | \(0.393112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2755.27i | 0.440432i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3356.31 | + | 10016.2i | 0.463118 | + | 1.38208i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8413.79i | − | 1.01039i | −0.863006 | − | 0.505193i | \(-0.831421\pi\) | ||
0.863006 | − | 0.505193i | \(-0.168579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5827.54 | −0.613513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7015.12 | 0.651742 | 0.325871 | − | 0.945414i | \(-0.394343\pi\) | ||||
0.325871 | + | 0.945414i | \(0.394343\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 22694.2i | − | 1.87173i | −0.352358 | − | 0.935865i | \(-0.614620\pi\) | ||
0.352358 | − | 0.935865i | \(-0.385380\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11282.7 | + | 3780.67i | −0.830577 | + | 0.278316i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3501.99i | − | 0.231244i | −0.993293 | − | 0.115622i | \(-0.963114\pi\) | ||
0.993293 | − | 0.115622i | \(-0.0368861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18901.8 | −1.12464 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −162.428 | −0.00874449 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27309.1i | 1.33542i | 0.744422 | + | 0.667710i | \(0.232725\pi\) | ||||
−0.744422 | + | 0.667710i | \(0.767275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −26601.7 | + | 8913.88i | −1.18578 | + | 0.397338i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8665.04i | 0.353251i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7925.39 | 0.296409 | 0.148204 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7020.54 | −0.241572 | −0.120786 | − | 0.992679i | \(-0.538541\pi\) | ||||
−0.120786 | + | 0.992679i | \(0.538541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 40223.6i | − | 1.27682i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18853.3 | − | 56264.0i | −0.553483 | − | 1.65176i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17631.2i | 0.479837i | 0.970793 | + | 0.239919i | \(0.0771208\pi\) | ||||
−0.970793 | + | 0.239919i | \(0.922879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7114.27 | −0.179890 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13432.9 | −0.316246 | −0.158123 | − | 0.987419i | \(-0.550544\pi\) | ||||
−0.158123 | + | 0.987419i | \(0.550544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39946.8i | 0.877353i | 0.898645 | + | 0.438677i | \(0.144553\pi\) | ||||
−0.898645 | + | 0.438677i | \(0.855447\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10337.0 | + | 13692.5i | 0.212198 | + | 0.281079i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 94837.3i | − | 1.82286i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −93321.2 | −1.68234 | −0.841168 | − | 0.540774i | \(-0.818131\pi\) | ||||
−0.841168 | + | 0.540774i | \(0.818131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37985.3 | 0.643284 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58448.5i | 0.931275i | 0.884975 | + | 0.465638i | \(0.154175\pi\) | ||||
−0.884975 | + | 0.465638i | \(0.845825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −525.488 | − | 1568.21i | −0.00788888 | − | 0.0235428i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19690.6i | 0.278908i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13989.4 | 0.187208 | 0.0936038 | − | 0.995610i | \(-0.470161\pi\) | ||||
0.0936038 | + | 0.995610i | \(0.470161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 200586. | 2.53920 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19359.5i | 0.232106i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −83659.6 | + | 28033.2i | −0.951057 | + | 0.318687i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110640.i | 1.19394i | 0.802264 | + | 0.596969i | \(0.203629\pi\) | ||||
−0.802264 | + | 0.596969i | \(0.796371\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 106828. | 1.09546 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 198468. | 1.93592 | 0.967960 | − | 0.251103i | \(-0.0807934\pi\) | ||||
0.967960 | + | 0.251103i | \(0.0807934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 134780.i | − | 1.25179i | −0.779906 | − | 0.625897i | \(-0.784733\pi\) | ||
0.779906 | − | 0.625897i | \(-0.215267\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −54989.1 | + | 18426.1i | −0.486747 | + | 0.163103i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 39785.5i | 0.335943i | 0.985792 | + | 0.167971i | \(0.0537216\pi\) | ||||
−0.985792 | + | 0.167971i | \(0.946278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −92692.6 | −0.747272 | −0.373636 | − | 0.927575i | \(-0.621889\pi\) | ||||
−0.373636 | + | 0.927575i | \(0.621889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 46191.7 | 0.355841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 66923.1i | − | 0.493037i | −0.969138 | − | 0.246519i | \(-0.920713\pi\) | ||
0.969138 | − | 0.246519i | \(-0.0792866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23016.2 | − | 68687.2i | −0.162289 | − | 0.484318i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 225947.i | 1.52596i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5590.81 | 0.0361916 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90823.1 | 0.563940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38513.0i | 0.229533i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −98756.1 | + | 144100.i | −0.565313 | + | 0.824877i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 58998.9i | − | 0.324589i | −0.986742 | − | 0.162295i | \(-0.948110\pi\) | ||
0.986742 | − | 0.162295i | \(-0.0518895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 124591. | 0.659193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 209380. | 1.06600 | 0.533001 | − | 0.846115i | \(-0.321064\pi\) | ||||
0.533001 | + | 0.846115i | \(0.321064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 298254.i | − | 1.46203i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −44450.7 | − | 132654.i | −0.209915 | − | 0.626450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 326432.i | − | 1.48591i | −0.669344 | − | 0.742953i | \(-0.733425\pi\) | ||
0.669344 | − | 0.742953i | \(-0.266575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −233648. | −1.02571 | −0.512856 | − | 0.858475i | \(-0.671412\pi\) | ||||
−0.512856 | + | 0.858475i | \(0.671412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19225.9 | 0.0814403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 532727.i | 2.17854i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −190109. | + | 63703.2i | −0.750902 | + | 0.251618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 103771.i | − | 0.396078i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −145336. | −0.536299 | −0.268149 | − | 0.963377i | \(-0.586412\pi\) | ||||
−0.268149 | + | 0.963377i | \(0.586412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −287343. | −1.02555 | −0.512777 | − | 0.858522i | \(-0.671383\pi\) | ||||
−0.512777 | + | 0.858522i | \(0.671383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6297.69i | 0.0217497i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −186913. | + | 62632.0i | −0.624899 | + | 0.209395i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 42626.2i | 0.138015i | 0.997616 | + | 0.0690077i | \(0.0219833\pi\) | ||||
−0.997616 | + | 0.0690077i | \(0.978017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −149927. | −0.470313 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 244876. | 0.744528 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 221599.i | 0.653279i | 0.945149 | + | 0.326639i | \(0.105916\pi\) | ||||
−0.945149 | + | 0.326639i | \(0.894084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48937.2 | − | 146043.i | −0.139936 | − | 0.417611i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 334835.i | − | 0.929051i | −0.885560 | − | 0.464525i | \(-0.846225\pi\) | ||
0.885560 | − | 0.464525i | \(-0.153775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −755454. | −2.03466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 335964. | 0.878622 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 268475.i | − | 0.682006i | −0.940062 | − | 0.341003i | \(-0.889233\pi\) | ||
0.940062 | − | 0.341003i | \(-0.110767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −355803. | − | 471299.i | −0.878242 | − | 1.16333i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 43510.4i | 0.104390i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −268052. | −0.625297 | −0.312649 | − | 0.949869i | \(-0.601216\pi\) | ||||
−0.312649 | + | 0.949869i | \(0.601216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −90565.5 | −0.205479 | −0.102739 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102739 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 38542.8i | − | 0.0850776i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 149440. | + | 445973.i | 0.321024 | + | 0.958031i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14848.4i | 0.0310510i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 472924. | 0.963023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 706725. | 1.40174 | 0.700870 | − | 0.713290i | \(-0.252796\pi\) | ||||
0.700870 | + | 0.713290i | \(0.252796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 236999.i | 0.457988i | 0.973428 | + | 0.228994i | \(0.0735435\pi\) | ||||
−0.973428 | + | 0.228994i | \(0.926456\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 308889. | − | 103505.i | 0.581723 | − | 0.194928i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 607901.i | 1.11601i | 0.829838 | + | 0.558004i | \(0.188433\pi\) | ||||
−0.829838 | + | 0.558004i | \(0.811567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 621060. | 1.11173 | 0.555867 | − | 0.831272i | \(-0.312387\pi\) | ||||
0.555867 | + | 0.831272i | \(0.312387\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96795.1 | −0.168991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 677756.i | − | 1.15434i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −371837. | + | 124598.i | −0.617971 | + | 0.207074i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 275837.i | 0.447431i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 792118. | 1.25437 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.06177e6 | −1.64181 | −0.820906 | − | 0.571063i | \(-0.806531\pi\) | ||||
−0.820906 | + | 0.571063i | \(0.806531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 73746.8i | − | 0.111377i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 403078. | + | 1.20291e6i | 0.594693 | + | 1.77474i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 666360.i | − | 0.960638i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −219308. | −0.308989 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31405.2 | −0.0432534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 240721.i | − | 0.324154i | −0.986778 | − | 0.162077i | \(-0.948181\pi\) | ||
0.986778 | − | 0.162077i | \(-0.0518193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 530888. | − | 400789.i | 0.699112 | − | 0.527788i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 202494.i | − | 0.260824i | −0.991460 | − | 0.130412i | \(-0.958370\pi\) | ||
0.991460 | − | 0.130412i | \(-0.0416299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 284279. | 0.358225 | 0.179112 | − | 0.983829i | \(-0.442677\pi\) | ||||
0.179112 | + | 0.983829i | \(0.442677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 520657. | 0.641980 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 345405.i | 0.416811i | 0.978042 | + | 0.208406i | \(0.0668274\pi\) | ||||
−0.978042 | + | 0.208406i | \(0.933173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 62199.9 | + | 185623.i | 0.0734717 | + | 0.219262i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 512333.i | − | 0.592491i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.59920e6 | 1.81095 | 0.905476 | − | 0.424398i | \(-0.139514\pi\) | ||||
0.905476 | + | 0.424398i | \(0.139514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −42246.4 | −0.0468541 | −0.0234270 | − | 0.999726i | \(-0.507458\pi\) | ||||
−0.0234270 | + | 0.999726i | \(0.507458\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 816688.i | 0.887239i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00189e6 | − | 335720.i | 1.06636 | − | 0.357324i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.67537e6i | 1.74731i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −320882. | −0.327980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −802841. | −0.804351 | −0.402175 | − | 0.915563i | \(-0.631746\pi\) | ||||
−0.402175 | + | 0.915563i | \(0.631746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 650354.i | 0.638776i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8609.49 | − | 2884.93i | 0.00829138 | − | 0.00277833i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 941153.i | 0.888848i | 0.895817 | + | 0.444424i | \(0.146592\pi\) | ||||
−0.895817 | + | 0.444424i | \(0.853408\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58993e6 | −1.47275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 763449. | 0.693711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.53130e6i | − | 1.36512i | −0.730830 | − | 0.682560i | \(-0.760867\pi\) | ||
0.730830 | − | 0.682560i | \(-0.239133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −485045. | − | 1.44752e6i | −0.424294 | − | 1.26622i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 76801.7i | 0.0659315i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.25712e6 | −1.05924 | −0.529621 | − | 0.848234i | \(-0.677666\pi\) | ||||
−0.529621 | + | 0.848234i | \(0.677666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −843976. | −0.698083 | −0.349041 | − | 0.937107i | \(-0.613493\pi\) | ||||
−0.349041 | + | 0.937107i | \(0.613493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.10122e6i | 0.894265i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.25170e6 | − | 944961.i | 0.998089 | − | 0.753498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.52070e6i | − | 1.19082i | −0.803423 | − | 0.595408i | \(-0.796990\pi\) | ||
0.803423 | − | 0.595408i | \(-0.203010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 750612. | 0.577305 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.97975e6 | −1.49570 | −0.747848 | − | 0.663870i | \(-0.768913\pi\) | ||||
−0.747848 | + | 0.663870i | \(0.768913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.02901e6i | − | 1.50597i | −0.658036 | − | 0.752986i | \(-0.728613\pi\) | ||
0.658036 | − | 0.752986i | \(-0.271387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −153902. | − | 459291.i | −0.112236 | − | 0.334947i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.32563e6i | − | 0.949987i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41898e6 | 0.999384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −607412. | −0.420485 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.23140e6i | 1.51848i | 0.650813 | + | 0.759238i | \(0.274428\pi\) | ||||
−0.650813 | + | 0.759238i | \(0.725572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −420086. | + | 140765.i | −0.281050 | + | 0.0941761i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.25602e6i | 0.826236i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.37553e6 | −0.889802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.28847e6 | −2.72826 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.08959e6i | 0.681799i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 372124. | − | 124694.i | 0.229054 | − | 0.0767531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 334318.i | − | 0.202448i | −0.994864 | − | 0.101224i | \(-0.967724\pi\) | ||
0.994864 | − | 0.101224i | \(-0.0322759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 739943. | 0.440861 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.39090e6 | −1.40172 | −0.700858 | − | 0.713300i | \(-0.747200\pi\) | ||||
−0.700858 | + | 0.713300i | \(0.747200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.88563e6i | − | 1.08791i | −0.839113 | − | 0.543957i | \(-0.816925\pi\) | ||
0.839113 | − | 0.543957i | \(-0.183075\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 714424. | + | 2.13206e6i | 0.405676 | + | 1.21066i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 179636.i | − | 0.100403i | −0.998739 | − | 0.0502014i | \(-0.984014\pi\) | ||
0.998739 | − | 0.0502014i | \(-0.0159863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80002e6 | 0.990378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −218422. | −0.118313 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46696.7i | 0.0249046i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.99864e6 | + | 2.64742e6i | 1.04961 | + | 1.39032i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 508882.i | − | 0.263177i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −661763. | −0.337064 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −168620. | −0.0845937 | −0.0422968 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422968 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.79096e6i | − | 0.885064i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −313152. | − | 934541.i | −0.152456 | − | 0.454974i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.74240e6i | − | 0.835744i | −0.908506 | − | 0.417872i | \(-0.862776\pi\) | ||
0.908506 | − | 0.417872i | \(-0.137224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 367407. | 0.173640 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.76976e6 | 0.824190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 395842.i | 0.181672i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 377092. | − | 126359.i | 0.170569 | − | 0.0571554i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.89447e6i | 1.29046i | 0.763987 | + | 0.645232i | \(0.223239\pi\) | ||||
−0.763987 | + | 0.645232i | \(0.776761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −63803.8 | −0.0280403 | −0.0140202 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140202 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65654e6 | −1.15093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.79206e6i | − | 1.19258i | −0.802769 | − | 0.596290i | \(-0.796641\pi\) | ||
0.802769 | − | 0.596290i | \(-0.203359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 712014. | − | 238586.i | 0.299859 | − | 0.100479i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30693.6i | 0.0127461i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.48391e6 | 0.607674 | 0.303837 | − | 0.952724i | \(-0.401732\pi\) | ||||
0.303837 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15032.0 | 0.00607083 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 498619.i | 0.198610i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −709507. | − | 2.11738e6i | −0.278756 | − | 0.831892i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.08188e6i | 0.419289i | 0.977778 | + | 0.209644i | \(0.0672306\pi\) | ||||
−0.977778 | + | 0.209644i | \(0.932769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.49324e6 | 0.570904 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.16053e6 | 1.94652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 127750.i | − | 0.0475434i | −0.999717 | − | 0.0237717i | \(-0.992433\pi\) | ||
0.999717 | − | 0.0237717i | \(-0.00756748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −791109. | − | 542171.i | −0.290508 | − | 0.199094i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.80714e6i | 1.37958i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.61295e6 | −0.576798 | −0.288399 | − | 0.957510i | \(-0.593123\pi\) | ||||
−0.288399 | + | 0.957510i | \(0.593123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 323904. | 0.114315 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.96656e6i | 1.38171i | 0.722993 | + | 0.690855i | \(0.242766\pi\) | ||||
−0.722993 | + | 0.690855i | \(0.757234\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.68443e6 | + | 5.02686e6i | 0.579165 | + | 1.72840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.83068e6i | − | 1.63957i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.54852e6 | 1.18898 | 0.594488 | − | 0.804104i | \(-0.297355\pi\) | ||||
0.594488 | + | 0.804104i | \(0.297355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38339.5 | −0.0126825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.14950e6i | 0.375428i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.94650e6 | − | 1.65751e6i | 1.59516 | − | 0.534518i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 580854.i | 0.184965i | 0.995714 | + | 0.0924827i | \(0.0294803\pi\) | ||||
−0.995714 | + | 0.0924827i | \(0.970520\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.63741e6 | 0.514903 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.10413e6 | 0.653449 | 0.326725 | − | 0.945120i | \(-0.394055\pi\) | ||||
0.326725 | + | 0.945120i | \(0.394055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.74313e6i | 1.14808i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.01341e6 | + | 674668.i | −0.609952 | + | 0.204387i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.22263e6i | − | 1.26356i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.23687e6 | −0.956790 | −0.478395 | − | 0.878145i | \(-0.658781\pi\) | ||||
−0.478395 | + | 0.878145i | \(0.658781\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79211e6 | 0.523312 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.49764e6i | − | 0.432049i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.03812e6 | − | 3.09807e6i | −0.295888 | − | 0.883020i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.28273e6i | − | 0.361239i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.03059e6 | −0.565049 | −0.282525 | − | 0.959260i | \(-0.591172\pi\) | ||||
−0.282525 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.15883e6 | 0.593625 | 0.296813 | − | 0.954936i | \(-0.404076\pi\) | ||||
0.296813 | + | 0.954936i | \(0.404076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 745434.i | − | 0.202562i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 55707.0 | + | 73789.9i | 0.0149602 | + | 0.0198164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32665e6i | 0.352118i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.92467e6 | −0.767245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.49812e6 | −1.42568 | −0.712838 | − | 0.701328i | \(-0.752591\pi\) | ||||
−0.712838 | + | 0.701328i | \(0.752591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.87201e6i | 0.992470i | 0.868188 | + | 0.496235i | \(0.165284\pi\) | ||||
−0.868188 | + | 0.496235i | \(0.834716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −349730. | − | 1.04370e6i | −0.0886156 | − | 0.264455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.04530e6i | 0.512334i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.15465e6 | 0.781250 | 0.390625 | − | 0.920550i | \(-0.372259\pi\) | ||||
0.390625 | + | 0.920550i | \(0.372259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.02343e6 | −0.985144 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.07021e6i | 0.985389i | 0.870202 | + | 0.492694i | \(0.163988\pi\) | ||||
−0.870202 | + | 0.492694i | \(0.836012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −741508. | + | 248470.i | −0.177507 | + | 0.0594803i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 797893.i | − | 0.188876i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −957718. | −0.224193 | −0.112096 | − | 0.993697i | \(-0.535757\pi\) | ||||
−0.112096 | + | 0.993697i | \(0.535757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52068e6 | 0.815052 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.57751e6i | − | 0.361183i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.06321e7 | + | 3.56267e6i | −2.40763 | + | 0.806765i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.38167e6i | − | 1.65335i | −0.562682 | − | 0.826673i | \(-0.690231\pi\) | ||
0.562682 | − | 0.826673i | \(-0.309769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −74044.2 | −0.0164044 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.96862e6 | −0.650582 | −0.325291 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325291 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.84593e6i | − | 1.48416i | −0.670313 | − | 0.742079i | \(-0.733840\pi\) | ||
0.670313 | − | 0.742079i | \(-0.266160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −343850. | − | 1.02615e6i | −0.0737456 | − | 0.220079i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.20816e6i | 0.892895i | 0.894810 | + | 0.446447i | \(0.147311\pi\) | ||||
−0.894810 | + | 0.446447i | \(0.852689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.33172e6 | 0.699417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −234018. | −0.0486068 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.13895e7i | − | 2.34074i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.93647e6 | − | 2.97181e6i | 0.800522 | − | 0.604347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.81301e6i | 1.16978i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.73077e6 | −1.14123 | −0.570617 | − | 0.821217i | \(-0.693296\pi\) | ||||
−0.570617 | + | 0.821217i | \(0.693296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.93110e6 | 1.76012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.34437e6i | 0.262211i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.96511e6 | − | 5.86447e6i | −0.379343 | − | 1.13207i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.63249e6i | 1.26723i | 0.773650 | + | 0.633613i | \(0.218429\pi\) | ||||
−0.773650 | + | 0.633613i | \(0.781571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.21658e6 | −0.230074 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26463e6 | 0.611125 | 0.305563 | − | 0.952172i | \(-0.401156\pi\) | ||||
0.305563 | + | 0.952172i | \(0.401156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 106114.i | 0.0196633i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.66243e6 | + | 1.89741e6i | −1.03870 | + | 0.348055i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.53839e6i | 0.460965i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.51527e6 | −1.53090 | −0.765450 | − | 0.643495i | \(-0.777484\pi\) | ||||
−0.765450 | + | 0.643495i | \(0.777484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.83824e6 | 0.327196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.24174e6i | − | 0.571292i | −0.958335 | − | 0.285646i | \(-0.907792\pi\) | ||
0.958335 | − | 0.285646i | \(-0.0922082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.05198e7 | + | 3.52505e6i | −1.83561 | + | 0.615088i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.14744e6i | − | 0.716573i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.04569e7 | −1.78900 | −0.894499 | − | 0.447070i | \(-0.852467\pi\) | ||||
−0.894499 | + | 0.447070i | \(0.852467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.54865e6 | 1.27884 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.95004e6i | 0.662687i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.39387e6 | + | 7.14403e6i | 0.397725 | + | 1.18693i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.75755e6i | − | 0.289188i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.47393e6 | 0.240191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −328142. | −0.0529625 | −0.0264812 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264812 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.42102e6i | − | 1.50606i | −0.657984 | − | 0.753032i | \(-0.728590\pi\) | ||
0.657984 | − | 0.753032i | \(-0.271410\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.58743e6 | − | 1.95336e6i | 0.409704 | − | 0.309303i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 104330.i | 0.0163637i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.75709e6 | 0.739098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.68700e6 | 0.259644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.44643e6i | 1.13535i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −706642. | − | 2.10883e6i | −0.106737 | − | 0.318535i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.47160e6i | − | 0.220219i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.48624e6 | −1.40644 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.08041e6 | 0.893182 | 0.446591 | − | 0.894738i | \(-0.352638\pi\) | ||||
0.446591 | + | 0.894738i | \(0.352638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 497205.i | − | 0.0723662i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.91318e6 | − | 1.64634e6i | 0.708551 | − | 0.237426i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.32182e6i | 0.617587i | 0.951129 | + | 0.308794i | \(0.0999253\pi\) | ||||
−0.951129 | + | 0.308794i | \(0.900075\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.49439e6 | −0.211609 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.66089e6 | 0.794338 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.76347e7i | 2.45220i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.44839e6 | + | 820424.i | −0.337403 | + | 0.113059i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.41019e6i | − | 1.01203i | −0.862526 | − | 0.506013i | \(-0.831119\pi\) | ||
0.862526 | − | 0.506013i | \(-0.168881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.40895e7 | 3.26061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −81517.7 | −0.0109356 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.08039e7i | − | 1.43652i | −0.695775 | − | 0.718260i | \(-0.744939\pi\) | ||
0.695775 | − | 0.718260i | \(-0.255061\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.18864e6 | + | 3.54726e6i | 0.156650 | + | 0.467490i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 7.17799e6i | − | 0.937660i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.77404e6 | −0.229712 | −0.114856 | − | 0.993382i | \(-0.536641\pi\) | ||||
−0.114856 | + | 0.993382i | \(0.536641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 70981.0 | 0.00911070 | 0.00455535 | − | 0.999990i | \(-0.498550\pi\) | ||||
0.00455535 | + | 0.999990i | \(0.498550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.87992e6i | 0.493669i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.43995e6 | + | 3.23197e6i | 0.307759 | + | 0.407660i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.04410e6i | 0.505688i | 0.967507 | + | 0.252844i | \(0.0813659\pi\) | ||||
−0.967507 | + | 0.252844i | \(0.918634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.30113e6 | −0.161296 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10449e7 | 1.35744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.37056e7i | 1.67004i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.01312e6 | − | 1.19763e7i | −0.484833 | − | 1.44689i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.86862e6i | − | 0.343620i | −0.985130 | − | 0.171810i | \(-0.945038\pi\) | ||
0.985130 | − | 0.171810i | \(-0.0549615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.56570e6 | 0.661046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.33737e6 | −0.393040 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.23131e6i | − | 0.377347i | −0.982040 | − | 0.188674i | \(-0.939581\pi\) | ||
0.982040 | − | 0.188674i | \(-0.0604188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −296341. | + | 99300.1i | −0.0343163 | + | 0.0114989i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.40962e6i | 0.391534i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.80078e6 | 0.432819 | 0.216409 | − | 0.976303i | \(-0.430565\pi\) | ||||
0.216409 | + | 0.976303i | \(0.430565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.45289e6 | 0.615801 | 0.307900 | − | 0.951419i | \(-0.400374\pi\) | ||||
0.307900 | + | 0.951419i | \(0.400374\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.75297e6i | 0.420321i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.81408e6 | + | 1.61314e6i | −0.534719 | + | 0.179177i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50483e7i | 1.65774i | 0.559441 | + | 0.828870i | \(0.311016\pi\) | ||||
−0.559441 | + | 0.828870i | \(0.688984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.72088e6 | 0.406539 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.71731e6 | 0.402833 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.30782e6i | − | 0.248056i | −0.992279 | − | 0.124028i | \(-0.960419\pi\) | ||
0.992279 | − | 0.124028i | \(-0.0395813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −684041. | − | 2.04138e6i | −0.0729280 | − | 0.217639i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 381761.i | − | 0.0403718i | −0.999796 | − | 0.0201859i | \(-0.993574\pi\) | ||
0.999796 | − | 0.0201859i | \(-0.00642581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.07208e7 | −1.12460 | −0.562302 | − | 0.826932i | \(-0.690084\pi\) | ||||
−0.562302 | + | 0.826932i | \(0.690084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.24311e6 | −0.337468 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.64354e6i | − | 0.272876i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.67517e6 | − | 9.39207e6i | 0.273937 | − | 0.961748i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.34873e6i | 0.441767i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 248931. | 0.0250872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.56189e6 | 0.456112 | 0.228056 | − | 0.973648i | \(-0.426763\pi\) | ||||
0.228056 | + | 0.973648i | \(0.426763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.82910e6i | − | 0.578219i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.04790e6 | + | 3.12724e6i | 0.103130 | + | 0.307770i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.00639e7i | − | 1.95915i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.85933e6 | −0.277021 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.70983e6 | −0.260494 | −0.130247 | − | 0.991482i | \(-0.541577\pi\) | ||||
−0.130247 | + | 0.991482i | \(0.541577\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.10481e6i | − | 0.582297i | −0.956678 | − | 0.291149i | \(-0.905963\pi\) | ||
0.956678 | − | 0.291149i | \(-0.0940374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.60395e6 | + | 2.21290e6i | −0.625036 | + | 0.209441i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.22081e7i | − | 1.14654i | −0.819367 | − | 0.573269i | \(-0.805675\pi\) | ||
0.819367 | − | 0.573269i | \(-0.194325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.97752e6 | 0.370681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.65832e6 | 0.338321 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.26514e6i | 0.574973i | 0.957785 | + | 0.287487i | \(0.0928197\pi\) | ||||
−0.957785 | + | 0.287487i | \(0.907180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10982e7 | + | 3.71887e6i | −1.01076 | + | 0.338694i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.50307e6i | 0.768532i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.85107e7 | −1.66039 | −0.830194 | − | 0.557474i | \(-0.811771\pi\) | ||||
−0.830194 | + | 0.557474i | \(0.811771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.46041e6 | −0.753161 | −0.376581 | − | 0.926384i | \(-0.622900\pi\) | ||||
−0.376581 | + | 0.926384i | \(0.622900\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 172414.i | − | 0.0152331i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.29737e6 | + | 1.58089e7i | 0.464522 | + | 1.38627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.64777e6i | 0.404511i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.32156e6 | 0.114162 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.52340e6 | −0.302104 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 7.25182e6i | − | 0.617177i | −0.951196 | − | 0.308588i | \(-0.900143\pi\) | ||
0.951196 | − | 0.308588i | \(-0.0998566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.71222e6 | + | 6.24184e6i | 0.398076 | + | 0.527294i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.74893e6i | 0.398221i | 0.979977 | + | 0.199110i | \(0.0638052\pi\) | ||||
−0.979977 | + | 0.199110i | \(0.936195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.09073e7 | 1.74030 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11169e6 | 0.0918578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.37712e7i | 1.12959i | 0.825233 | + | 0.564793i | \(0.191044\pi\) | ||||
−0.825233 | + | 0.564793i | \(0.808956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.79786e6 | + | 1.73025e7i | 0.472108 | + | 1.40891i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.56069e6i | 0.126161i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.89882e7 | −2.32634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.64305e7 | −1.30905 | −0.654526 | − | 0.756040i | \(-0.727132\pi\) | ||||
−0.654526 | + | 0.756040i | \(0.727132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2.01871e7i | − | 1.59676i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.23845e7 | − | 4.14990e6i | 0.972563 | − | 0.325893i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 207550.i | 0.0161823i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.89628e6 | −0.146794 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.05170e7 | −0.808342 | −0.404171 | − | 0.914683i | \(-0.632440\pi\) | ||||
−0.404171 | + | 0.914683i | \(0.632440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.32797e7i | − | 1.01345i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.01907e6 | + | 341478.i | −0.0772204 | + | 0.0258755i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 3.75041e7i | − | 2.82182i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.32691e6 | 0.0991349 | 0.0495674 | − | 0.998771i | \(-0.484216\pi\) | ||||
0.0495674 | + | 0.998771i | \(0.484216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.98643e7 | −1.47367 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.56962e6i | 0.336633i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.46193e6 | − | 2.82372e7i | −0.692173 | − | 2.06565i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.77958e6i | 0.637787i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.65753e6 | 0.335995 | 0.167998 | − | 0.985787i | \(-0.446270\pi\) | ||||
0.167998 | + | 0.985787i | \(0.446270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.54691e7 | −1.82463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 231933.i | − | 0.0165012i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.94531e6 | − | 6.75318e6i | 0.632048 | − | 0.477159i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.47884e6i | 0.103773i | 0.998653 | + | 0.0518867i | \(0.0165235\pi\) | ||||
−0.998653 | + | 0.0518867i | \(0.983477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.74681e6 | 0.330814 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 671432. | 0.0464739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.41118e7i | − | 0.970115i | −0.874482 | − | 0.485057i | \(-0.838799\pi\) | ||
0.874482 | − | 0.485057i | \(-0.161201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.84310e6 | + | 5.50037e6i | 0.125844 | + | 0.375555i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.84856e6i | 0.600073i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.94045e6 | −0.400137 | −0.200068 | − | 0.979782i | \(-0.564116\pi\) | ||||
−0.200068 | + | 0.979782i | \(0.564116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.19780e6 | −0.615373 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.46589e7i | 0.974156i | 0.873359 | + | 0.487078i | \(0.161937\pi\) | ||||
−0.873359 | + | 0.487078i | \(0.838063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.70353e6 | − | 2.58135e6i | 0.508510 | − | 0.170395i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.24413e7i | 0.815766i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.51817e6 | 0.489674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.08263e6 | 0.393543 | 0.196771 | − | 0.980449i | \(-0.436954\pi\) | ||||
0.196771 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.40760e6i | − | 0.283279i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.52306e7 | − | 5.10359e6i | 0.972413 | − | 0.325843i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.11757e6i | 0.514856i | 0.966297 | + | 0.257428i | \(0.0828751\pi\) | ||||
−0.966297 | + | 0.257428i | \(0.917125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.57044e6 | −0.224966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63567e7 | 1.02384 | 0.511921 | − | 0.859033i | \(-0.328934\pi\) | ||||
0.511921 | + | 0.859033i | \(0.328934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.75159e7i | 1.08923i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −111855. | − | 333810.i | −0.00691039 | − | 0.0206227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.41267e6i | 0.516352i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.09586e7 | 1.27805 | 0.639024 | − | 0.769187i | \(-0.279339\pi\) | ||||
0.639024 | + | 0.769187i | \(0.279339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.16693e6 | −0.313038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.95651e6i | 0.539126i | 0.962983 | + | 0.269563i | \(0.0868793\pi\) | ||||
−0.962983 | + | 0.269563i | \(0.913121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.79489e6 | − | 6.63963e6i | 0.525989 | − | 0.397090i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 8.72873e6i | − | 0.518679i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.10722e7 | 0.653717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.74160e6 | −0.395490 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.97614e6i | 0.523221i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −757097. | − | 2.25940e6i | −0.0438508 | − | 0.130864i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42009e7i | 1.39282i | 0.717643 | + | 0.696411i | \(0.245221\pi\) | ||||
−0.717643 | + | 0.696411i | \(0.754779\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.40683e6 | 0.480773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.26463e7 | −0.718657 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.45219e6i | − | 0.420824i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.94688e6 | − | 2.66290e6i | 0.445943 | − | 0.149430i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.91659e6i | 0.552989i | 0.961016 | + | 0.276494i | \(0.0891728\pi\) | ||||
−0.961016 | + | 0.276494i | \(0.910827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 103610. | 0.00574164 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.97778e6 | 0.163988 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00481e7i | 1.09720i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.29797e7 | + | 4.34931e6i | −0.705949 | + | 0.236554i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.90158e6i | − | 0.373048i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.15657e6 | 0.491883 | 0.245941 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245941 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.49145e7 | −0.796264 | −0.398132 | − | 0.917328i | \(-0.630341\pi\) | ||||
−0.398132 | + | 0.917328i | \(0.630341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.63343e6i | − | 0.245853i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.93588e6 | − | 1.17459e7i | −0.207562 | − | 0.619428i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.58189e7i | − | 1.87740i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.26967e7 | 2.22426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.39549e6 | 0.486476 | 0.243238 | − | 0.969967i | \(-0.421790\pi\) | ||||
0.243238 | + | 0.969967i | \(0.421790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.59508e7i | 0.820884i | 0.911887 | + | 0.410442i | \(0.134626\pi\) | ||||
−0.911887 | + | 0.410442i | \(0.865374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.18783e6 | + | 6.87184e6i | 0.265370 | + | 0.351510i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.68518e7i | − | 0.856805i | −0.903588 | − | 0.428403i | \(-0.859077\pi\) | ||
0.903588 | − | 0.428403i | \(-0.140923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.92620e6 | 0.198420 | 0.0992101 | − | 0.995067i | \(-0.468368\pi\) | ||||
0.0992101 | + | 0.995067i | \(0.468368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.34865e6 | 0.419386 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 559229.i | − | 0.0279240i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.94710e6 | + | 1.77479e7i | 0.295182 | + | 0.880910i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.82521e6i | 0.435423i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.23626e7 | −0.606322 | −0.303161 | − | 0.952939i | \(-0.598042\pi\) | ||||
−0.303161 | + | 0.952939i | \(0.598042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.64726e6 | −0.372834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.08688e7i | − | 0.526760i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00429e7 | − | 1.34179e7i | 1.92923 | − | 0.646459i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.71626e7i | − | 0.822006i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.11392e7 | 0.530379 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09031e7 | 0.516091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.17612e6i | 0.149460i | 0.997204 | + | 0.0747299i | \(0.0238095\pi\) | ||||
−0.997204 | + | 0.0747299i | \(0.976191\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.78078e7 | + | 5.96715e6i | −0.833094 | + | 0.279159i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.97233e7i | 0.917334i | 0.888608 | + | 0.458667i | \(0.151673\pi\) | ||||
−0.888608 | + | 0.458667i | \(0.848327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.18456e6 | 0.193494 | 0.0967470 | − | 0.995309i | \(-0.469156\pi\) | ||||
0.0967470 | + | 0.995309i | \(0.469156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.27771e6 | 0.334570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.89684e7i | − | 1.32403i | −0.749490 | − | 0.662015i | \(-0.769701\pi\) | ||
0.749490 | − | 0.662015i | \(-0.230299\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.76846e6 | + | 1.42305e7i | 0.216689 | + | 0.646667i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.79021e6i | 0.351966i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.68352e7 | −2.10389 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.87152e7 | −0.835889 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.35508e7i | 1.04585i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.72302e7 | + | 1.86617e7i | 1.20235 | + | 0.824007i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.78801e7i | 1.22404i | 0.790843 | + | 0.612019i | \(0.209642\pi\) | ||||
−0.790843 | + | 0.612019i | \(0.790358\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.22504e7 | −0.534783 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.21471e7 | −1.82948 | −0.914741 | − | 0.404040i | \(-0.867606\pi\) | ||||
−0.914741 | + | 0.404040i | \(0.867606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.38615e7i | − | 1.89314i | −0.322505 | − | 0.946568i | \(-0.604525\pi\) | ||
0.322505 | − | 0.946568i | \(-0.395475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −772801. | − | 2.30627e6i | −0.0331673 | − | 0.0989811i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.32386e7i | 0.991747i | 0.868395 | + | 0.495874i | \(0.165152\pi\) | ||||
−0.868395 | + | 0.495874i | \(0.834848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.11489e7 | −0.473126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.90637e7 | 0.804476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.52731e6i | − | 0.231945i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.42081e7 | − | 4.76095e6i | 0.592896 | − | 0.198672i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.55168e6i | − | 0.313374i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.26476e7 | 0.521925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −807970. | −0.0331576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.35437e7i | − | 0.960848i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.80043e6 | − | 1.60856e6i | 0.194831 | − | 0.0652854i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.74916e6i | 0.312778i | 0.987696 | + | 0.156389i | \(0.0499853\pi\) | ||||
−0.987696 | + | 0.156389i | \(0.950015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.22459e7 | 1.69580 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.54221e7 | −0.615668 | −0.307834 | − | 0.951440i | \(-0.599604\pi\) | ||||
−0.307834 | + | 0.951440i | \(0.599604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.93336e7i | 1.16463i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 684570. | + | 2.04296e6i | 0.0270312 | + | 0.0806691i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.95661e7i | − | 1.55382i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.40744e7 | −0.940302 | −0.470151 | − | 0.882586i | \(-0.655801\pi\) | ||||
−0.470151 | + | 0.882586i | \(0.655801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.83540e6 | 0.0712989 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.42588e7i | − | 0.550909i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58421e7 | − | 2.09846e7i | −0.608779 | − | 0.806392i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.86893e7i | − | 1.09653i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.51619e7 | 0.576387 | 0.288193 | − | 0.957572i | \(-0.406945\pi\) | ||||
0.288193 | + | 0.957572i | \(0.406945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.98333e7 | −1.12804 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.31260e7i | − | 0.493662i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −263727. | − | 787040.i | −0.00986564 | − | 0.0294420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90390e6i | 0.182470i | 0.995829 | + | 0.0912352i | \(0.0290815\pi\) | ||||
−0.995829 | + | 0.0912352i | \(0.970918\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.03521e7 | 0.383146 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.62296e7 | −0.597495 | −0.298748 | − | 0.954332i | \(-0.596569\pi\) | ||||
−0.298748 | + | 0.954332i | \(0.596569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.09062e6i | 0.332900i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.50673e7 | + | 8.39974e6i | −0.913122 | + | 0.305975i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.16817e7i | 1.51033i | 0.655537 | + | 0.755163i | \(0.272442\pi\) | ||||
−0.655537 | + | 0.755163i | \(0.727558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.24028e7 | −1.52837 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 986202. | 0.0353602 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.61135e7i | − | 0.574723i | −0.957822 | − | 0.287362i | \(-0.907222\pi\) | ||
0.957822 | − | 0.287362i | \(-0.0927781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.74600e7 | + | 1.25524e7i | −1.32911 | + | 0.445366i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.88212e6i | 0.348795i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.16851e7 | −2.16588 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.61942e7 | −0.565655 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.46873e6i | 0.294274i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.20942e6 | − | 1.25622e7i | −0.145514 | − | 0.434256i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.51707e7i | − | 0.521722i | −0.965376 | − | 0.260861i | \(-0.915994\pi\) | ||
0.965376 | − | 0.260861i | \(-0.0840064\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −256365. | −0.00877099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82884e7 | 0.962854 | 0.481427 | − | 0.876486i | \(-0.340119\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.41519e7i | 1.49509i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.45343e7 | + | 1.09726e7i | −0.489647 | + | 0.369655i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.88218e7i | − | 0.966017i | −0.875616 | − | 0.483009i | \(-0.839544\pi\) | ||
0.875616 | − | 0.483009i | \(-0.160456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.02086e6 | 0.234117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.97305e7 | −0.654586 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.26448e6i | 0.0747453i | 0.999301 | + | 0.0373727i | \(0.0118989\pi\) | ||||
−0.999301 | + | 0.0373727i | \(0.988101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.07971e7 | − | 3.22218e7i | −0.354582 | − | 1.05818i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.63308e6i | − | 0.118709i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.94085e7 | 0.956053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −995592. | −0.0322031 | −0.0161015 | − | 0.999870i | \(-0.505125\pi\) | ||||
−0.0161015 | + | 0.999870i | \(0.505125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 925721.i | − | 0.0297925i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.29193e7 | + | 1.10308e7i | −1.05413 | + | 0.353224i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.57133e7i | − | 1.77509i | −0.460718 | − | 0.887547i | \(-0.652408\pi\) | ||
0.460718 | − | 0.887547i | \(-0.347592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.10569e7 | 0.667546 |
(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 | 80.6.c.d.49.6 | 8 | ||
3.2 | odd | 2 | 720.6.f.n.289.7 | 8 | |||
4.3 | odd | 2 | 40.6.c.a.9.3 | ✓ | 8 | ||
5.2 | odd | 4 | 400.6.a.z.1.3 | 4 | |||
5.3 | odd | 4 | 400.6.a.ba.1.2 | 4 | |||
5.4 | even | 2 | inner | 80.6.c.d.49.3 | 8 | ||
8.3 | odd | 2 | 320.6.c.j.129.6 | 8 | |||
8.5 | even | 2 | 320.6.c.i.129.3 | 8 | |||
12.11 | even | 2 | 360.6.f.b.289.7 | 8 | |||
15.14 | odd | 2 | 720.6.f.n.289.8 | 8 | |||
20.3 | even | 4 | 200.6.a.j.1.3 | 4 | |||
20.7 | even | 4 | 200.6.a.k.1.2 | 4 | |||
20.19 | odd | 2 | 40.6.c.a.9.6 | yes | 8 | ||
40.19 | odd | 2 | 320.6.c.j.129.3 | 8 | |||
40.29 | even | 2 | 320.6.c.i.129.6 | 8 | |||
60.59 | even | 2 | 360.6.f.b.289.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.3 | ✓ | 8 | 4.3 | odd | 2 | ||
40.6.c.a.9.6 | yes | 8 | 20.19 | odd | 2 | ||
80.6.c.d.49.3 | 8 | 5.4 | even | 2 | inner | ||
80.6.c.d.49.6 | 8 | 1.1 | even | 1 | trivial | ||
200.6.a.j.1.3 | 4 | 20.3 | even | 4 | |||
200.6.a.k.1.2 | 4 | 20.7 | even | 4 | |||
320.6.c.i.129.3 | 8 | 8.5 | even | 2 | |||
320.6.c.i.129.6 | 8 | 40.29 | even | 2 | |||
320.6.c.j.129.3 | 8 | 40.19 | odd | 2 | |||
320.6.c.j.129.6 | 8 | 8.3 | odd | 2 | |||
360.6.f.b.289.7 | 8 | 12.11 | even | 2 | |||
360.6.f.b.289.8 | 8 | 60.59 | even | 2 | |||
400.6.a.z.1.3 | 4 | 5.2 | odd | 4 | |||
400.6.a.ba.1.2 | 4 | 5.3 | odd | 4 | |||
720.6.f.n.289.7 | 8 | 3.2 | odd | 2 | |||
720.6.f.n.289.8 | 8 | 15.14 | odd | 2 |