Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(47,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("80.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (of order \(4\), degree \(2\), 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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + \cdots + 57\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{65}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.5 | ||
Root | \(-1.99079 - 10.4027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.47 |
Dual form | 80.6.n.d.63.5 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.839817 | − | 0.839817i | −0.0538743 | − | 0.0538743i | 0.679656 | − | 0.733531i | \(-0.262129\pi\) |
−0.733531 | + | 0.679656i | \(0.762129\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.71634 | + | 55.7780i | 0.0664799 | + | 0.997788i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 99.3589 | − | 99.3589i | 0.766411 | − | 0.766411i | −0.211062 | − | 0.977473i | \(-0.567692\pi\) |
0.977473 | + | 0.211062i | \(0.0676921\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 241.589i | − | 0.994195i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 637.781i | 1.58924i | 0.607107 | + | 0.794620i | \(0.292330\pi\) | ||||
−0.607107 | + | 0.794620i | \(0.707670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −640.389 | + | 640.389i | −1.05096 | + | 1.05096i | −0.0523281 | + | 0.998630i | \(0.516664\pi\) |
−0.998630 | + | 0.0523281i | \(0.983336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 43.7223 | − | 49.9644i | 0.0501736 | − | 0.0573367i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 648.760 | + | 648.760i | 0.544455 | + | 0.544455i | 0.924832 | − | 0.380377i | \(-0.124206\pi\) |
−0.380377 | + | 0.924832i | \(0.624206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2506.12 | 1.59264 | 0.796321 | − | 0.604874i | \(-0.206776\pi\) | ||||
0.796321 | + | 0.604874i | \(0.206776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −166.887 | −0.0825797 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2801.60 | + | 2801.60i | 1.10430 | + | 1.10430i | 0.993886 | + | 0.110413i | \(0.0352174\pi\) |
0.110413 | + | 0.993886i | \(0.464783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3097.38 | + | 414.580i | −0.991161 | + | 0.132666i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −406.966 | + | 406.966i | −0.107436 | + | 0.107436i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4955.21i | 1.09413i | 0.837091 | + | 0.547063i | \(0.184254\pi\) | ||||
−0.837091 | + | 0.547063i | \(0.815746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1961.18i | 0.366533i | 0.983063 | + | 0.183267i | \(0.0586672\pi\) | ||||
−0.983063 | + | 0.183267i | \(0.941333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 535.619 | − | 535.619i | 0.0856192 | − | 0.0856192i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5911.30 | + | 5172.79i | 0.815666 | + | 0.713765i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1897.88 | − | 1897.88i | −0.227911 | − | 0.227911i | 0.583909 | − | 0.811819i | \(-0.301523\pi\) |
−0.811819 | + | 0.583909i | \(0.801523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1075.62 | 0.113239 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5828.95 | −0.541540 | −0.270770 | − | 0.962644i | \(-0.587278\pi\) | ||||
−0.270770 | + | 0.962644i | \(0.587278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10692.1 | − | 10692.1i | −0.881844 | − | 0.881844i | 0.111878 | − | 0.993722i | \(-0.464314\pi\) |
−0.993722 | + | 0.111878i | \(0.964314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13475.4 | − | 897.828i | 0.991996 | − | 0.0660940i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8309.52 | − | 8309.52i | 0.548695 | − | 0.548695i | −0.377368 | − | 0.926063i | \(-0.623171\pi\) |
0.926063 | + | 0.377368i | \(0.123171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2937.38i | − | 0.174771i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1089.68i | − | 0.0586642i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7437.17 | − | 7437.17i | 0.363679 | − | 0.363679i | −0.501487 | − | 0.865165i | \(-0.667213\pi\) |
0.865165 | + | 0.501487i | \(0.167213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35574.2 | + | 2370.21i | −1.58572 | + | 0.105653i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2104.68 | − | 2104.68i | −0.0858025 | − | 0.0858025i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16738.4 | −0.626014 | −0.313007 | − | 0.949751i | \(-0.601336\pi\) | ||||
−0.313007 | + | 0.949751i | \(0.601336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23742.5 | 0.816961 | 0.408481 | − | 0.912767i | \(-0.366059\pi\) | ||||
0.408481 | + | 0.912767i | \(0.366059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24004.1 | − | 24004.1i | −0.761962 | − | 0.761962i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −38099.5 | − | 33339.7i | −1.11850 | − | 0.978765i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4154.05 | − | 4154.05i | 0.113054 | − | 0.113054i | −0.648317 | − | 0.761371i | \(-0.724527\pi\) |
0.761371 | + | 0.648317i | \(0.224527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4705.66i | − | 0.118987i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12276.0i | − | 0.289008i | −0.989504 | − | 0.144504i | \(-0.953841\pi\) | ||
0.989504 | − | 0.144504i | \(-0.0461587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 36092.8 | − | 36092.8i | 0.792709 | − | 0.792709i | −0.189225 | − | 0.981934i | \(-0.560598\pi\) |
0.981934 | + | 0.189225i | \(0.0605976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2949.40 | + | 2253.06i | 0.0605454 | + | 0.0462508i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 63369.2 | + | 63369.2i | 1.21801 | + | 1.21801i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 64330.4 | 1.15971 | 0.579854 | − | 0.814721i | \(-0.303110\pi\) | ||||
0.579854 | + | 0.814721i | \(0.303110\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58022.7 | −0.982619 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −62856.9 | − | 62856.9i | −1.00152 | − | 1.00152i | −0.999999 | − | 0.00151672i | \(-0.999517\pi\) |
−0.00151672 | − | 0.999999i | \(-0.500483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33775.5 | + | 38597.6i | −0.507055 | + | 0.579446i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4161.47 | − | 4161.47i | 0.0589453 | − | 0.0589453i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 24423.5i | 0.326838i | 0.986557 | + | 0.163419i | \(0.0522523\pi\) | ||||
−0.986557 | + | 0.163419i | \(0.947748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 127257.i | 1.61093i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1647.03 | − | 1647.03i | 0.0197467 | − | 0.0197467i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9313.60 | + | 139787.i | 0.105879 | + | 1.58912i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −89666.0 | − | 89666.0i | −0.967605 | − | 0.967605i | 0.0318862 | − | 0.999492i | \(-0.489849\pi\) |
−0.999492 | + | 0.0318862i | \(0.989849\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 154081. | 1.58002 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 31536.0 | 0.307612 | 0.153806 | − | 0.988101i | \(-0.450847\pi\) | ||||
0.153806 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4384.20 | + | 4384.20i | 0.0407190 | + | 0.0407190i | 0.727173 | − | 0.686454i | \(-0.240834\pi\) |
−0.686454 | + | 0.727173i | \(0.740834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −620.207 | − | 9308.61i | −0.00548989 | − | 0.0823970i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 150691. | − | 150691.i | 1.27241 | − | 1.27241i | 0.327589 | − | 0.944820i | \(-0.393764\pi\) |
0.944820 | − | 0.327589i | \(-0.106236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 201206.i | 1.62209i | 0.584984 | + | 0.811045i | \(0.301101\pi\) | ||||
−0.584984 | + | 0.811045i | \(0.698899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3187.75i | 0.0245571i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −25930.0 | + | 25930.0i | −0.191032 | + | 0.191032i | −0.796142 | − | 0.605110i | \(-0.793129\pi\) |
0.605110 | + | 0.796142i | \(0.293129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −145856. | + | 166679.i | −1.02844 | + | 1.17527i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 154711. | + | 154711.i | 1.04486 | + | 1.04486i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 128920. | 0.834552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −245713. | −1.52569 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4895.25 | + | 4895.25i | 0.0291751 | + | 0.0291751i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −34635.4 | − | 171225.i | −0.198264 | − | 0.980149i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 46278.8 | − | 46278.8i | 0.254609 | − | 0.254609i | −0.568248 | − | 0.822857i | \(-0.692379\pi\) |
0.822857 | + | 0.568248i | \(0.192379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17958.8i | 0.0950175i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 83739.0i | 0.426333i | 0.977016 | + | 0.213167i | \(0.0683777\pi\) | ||||
−0.977016 | + | 0.213167i | \(0.931622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 249006. | − | 249006.i | 1.22062 | − | 1.22062i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24212.2 | − | 21187.4i | −0.114341 | − | 0.100056i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 29275.6 | + | 29275.6i | 0.133261 | + | 0.133261i | 0.770591 | − | 0.637330i | \(-0.219961\pi\) |
−0.637330 | + | 0.770591i | \(0.719961\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −56681.4 | −0.248830 | −0.124415 | − | 0.992230i | \(-0.539705\pi\) | ||||
−0.124415 | + | 0.992230i | \(0.539705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13957.0 | −0.0591211 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −408428. | − | 408428.i | −1.67023 | − | 1.67023i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −276392. | + | 18415.3i | −1.09171 | + | 0.0727374i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2466.86 | + | 2466.86i | −0.00941568 | + | 0.00941568i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 30050.0i | 0.110886i | 0.998462 | + | 0.0554432i | \(0.0176572\pi\) | ||||
−0.998462 | + | 0.0554432i | \(0.982343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255984.i | 0.913631i | 0.889561 | + | 0.456816i | \(0.151010\pi\) | ||||
−0.889561 | + | 0.456816i | \(0.848990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 156734. | − | 156734.i | 0.541294 | − | 0.541294i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −109391. | + | 7288.42i | −0.365723 | + | 0.0243671i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 30035.3 | + | 30035.3i | 0.0972486 | + | 0.0972486i | 0.754057 | − | 0.656809i | \(-0.228094\pi\) |
−0.656809 | + | 0.754057i | \(0.728094\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12491.7 | −0.0391859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 556728. | 1.69269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −397588. | − | 397588.i | −1.17210 | − | 1.17210i | −0.981708 | − | 0.190391i | \(-0.939024\pi\) |
−0.190391 | − | 0.981708i | \(-0.560976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31866.3 | + | 27885.2i | 0.0911218 | + | 0.0797379i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 162249. | − | 162249.i | 0.450185 | − | 0.450185i | −0.445231 | − | 0.895416i | \(-0.646878\pi\) |
0.895416 | + | 0.445231i | \(0.146878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 448903.i | − | 1.20903i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 605453.i | − | 1.58340i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −158564. | + | 158564.i | −0.402800 | + | 0.402800i | −0.879219 | − | 0.476419i | \(-0.841935\pi\) |
0.476419 | + | 0.879219i | \(0.341935\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −266560. | + | 348944.i | −0.657960 | + | 0.861313i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14057.2 | + | 14057.2i | 0.0337261 | + | 0.0337261i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 509602. | 1.18877 | 0.594386 | − | 0.804180i | \(-0.297395\pi\) | ||||
0.594386 | + | 0.804180i | \(0.297395\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −356971. | −0.809910 | −0.404955 | − | 0.914337i | \(-0.632713\pi\) | ||||
−0.404955 | + | 0.914337i | \(0.632713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19939.3 | − | 19939.3i | −0.0440132 | − | 0.0440132i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 98807.0 | − | 112913.i | 0.212255 | − | 0.242558i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −413767. | + | 413767.i | −0.865270 | + | 0.865270i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 80871.5i | 0.164680i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 296067.i | 0.587227i | 0.955924 | + | 0.293614i | \(0.0948579\pi\) | ||||
−0.955924 | + | 0.293614i | \(0.905142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10953.8 | − | 10953.8i | 0.0211676 | − | 0.0211676i | −0.696444 | − | 0.717611i | \(-0.745235\pi\) |
0.717611 | + | 0.696444i | \(0.245235\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3997.37 | + | 59995.9i | 0.00752813 | + | 0.112989i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −153834. | − | 153834.i | −0.282415 | − | 0.282415i | 0.551656 | − | 0.834071i | \(-0.313996\pi\) |
−0.834071 | + | 0.551656i | \(0.813996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −415211. | −0.743252 | −0.371626 | − | 0.928383i | \(-0.621200\pi\) | ||||
−0.371626 | + | 0.928383i | \(0.621200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6977.28 | −0.0121814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 492345. | + | 492345.i | 0.838550 | + | 0.838550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21662.4 | − | 325127.i | −0.0360016 | − | 0.540342i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 676837. | − | 676837.i | 1.09789 | − | 1.09789i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.59836e6i | 2.53109i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 673870.i | 1.04200i | 0.853555 | + | 0.521002i | \(0.174442\pi\) | ||||
−0.853555 | + | 0.521002i | \(0.825558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10309.6 | + | 10309.6i | −0.0155701 | + | 0.0155701i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 556649. | − | 636120.i | 0.821269 | − | 0.938518i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 194861. | + | 194861.i | 0.280915 | + | 0.280915i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −60622.7 | −0.0854132 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −830917. | −1.14440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 916244. | + | 916244.i | 1.23381 | + | 1.23381i | 0.962488 | + | 0.271323i | \(0.0874611\pi\) |
0.271323 | + | 0.962488i | \(0.412539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 100158. | + | 748294.i | 0.131896 | + | 0.985407i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 317650. | − | 317650.i | 0.409152 | − | 0.409152i | −0.472291 | − | 0.881443i | \(-0.656573\pi\) |
0.881443 | + | 0.472291i | \(0.156573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.15003e6i | − | 1.44917i | −0.689183 | − | 0.724587i | \(-0.742030\pi\) | ||
0.689183 | − | 0.724587i | \(-0.257970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 106437.i | − | 0.131239i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 290928. | − | 290928.i | 0.351071 | − | 0.351071i | −0.509437 | − | 0.860508i | \(-0.670146\pi\) |
0.860508 | + | 0.509437i | \(0.170146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 494370. | + | 432608.i | 0.583959 | + | 0.511004i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −54025.7 | − | 54025.7i | −0.0624784 | − | 0.0624784i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 152082. | 0.172220 | 0.0861101 | − | 0.996286i | \(-0.472556\pi\) | ||||
0.0861101 | + | 0.996286i | \(0.472556\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 43181.5 | 0.0478912 | 0.0239456 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239456 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 147621. | + | 147621.i | 0.160374 | + | 0.160374i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 163841. | − | 10916.3i | 0.174385 | − | 0.0116188i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.60489e6 | + | 1.60489e6i | −1.67380 | + | 1.67380i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 105577.i | 0.107912i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 547660.i | − | 0.548689i | −0.961631 | − | 0.274345i | \(-0.911539\pi\) | ||
0.961631 | − | 0.274345i | \(-0.0884609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.78681e6 | + | 1.78681e6i | −1.75500 | + | 1.75500i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 60780.2 | − | 4049.62i | 0.0585344 | − | 0.00389999i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −226438. | − | 226438.i | −0.213853 | − | 0.213853i | 0.592049 | − | 0.805902i | \(-0.298319\pi\) |
−0.805902 | + | 0.592049i | \(0.798319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −377143. | −0.349347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.19713e6 | 1.08778 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21617.3 | − | 21617.3i | −0.0192714 | − | 0.0192714i | 0.697405 | − | 0.716677i | \(-0.254338\pi\) |
−0.716677 | + | 0.697405i | \(0.754338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 442470. | + | 387191.i | 0.387051 | + | 0.338697i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20511.3 | − | 20511.3i | 0.0176082 | − | 0.0176082i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.78124e6i | − | 1.50087i | −0.660947 | − | 0.750433i | \(-0.729845\pi\) | ||
0.660947 | − | 0.750433i | \(-0.270155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.45155e6i | − | 1.20063i | −0.799765 | − | 0.600314i | \(-0.795042\pi\) | ||
0.799765 | − | 0.600314i | \(-0.204958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 106872. | − | 106872.i | 0.0867878 | − | 0.0867878i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −264411. | − | 1.97545e6i | −0.210838 | − | 1.57519i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −831788. | − | 831788.i | −0.651348 | − | 0.651348i | 0.301969 | − | 0.953318i | \(-0.402356\pi\) |
−0.953318 | + | 0.301969i | \(0.902356\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 473801. | 0.364406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.43146e6 | 1.83696 | 0.918482 | − | 0.395463i | \(-0.129416\pi\) | ||||
0.918482 | + | 0.395463i | \(0.129416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 141203. | + | 141203.i | 0.104804 | + | 0.104804i | 0.757565 | − | 0.652760i | \(-0.226389\pi\) |
−0.652760 | + | 0.757565i | \(0.726389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 109573. | − | 125217.i | 0.0799085 | − | 0.0913168i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −579158. | + | 579158.i | −0.415042 | + | 0.415042i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 578078.i | − | 0.407138i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 150606.i | 0.104258i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 540576. | − | 540576.i | 0.367864 | − | 0.367864i | −0.498834 | − | 0.866698i | \(-0.666238\pi\) |
0.866698 | + | 0.498834i | \(0.166238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −62205.6 | − | 933636.i | −0.0416174 | − | 0.624629i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −259555. | − | 259555.i | −0.170741 | − | 0.170741i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.58823e6 | −2.32114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.12471e6 | −1.35171 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26484.5 | − | 26484.5i | −0.0165724 | − | 0.0165724i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 88235.1 | + | 1.32431e6i | 0.0543115 | + | 0.815154i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −779170. | + | 779170.i | −0.471831 | + | 0.471831i | −0.902507 | − | 0.430676i | \(-0.858275\pi\) |
0.430676 | + | 0.902507i | \(0.358275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 7363.86i | − | 0.00438742i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.56490e6i | − | 0.917459i | −0.888576 | − | 0.458730i | \(-0.848305\pi\) | ||
0.888576 | − | 0.458730i | \(-0.151695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 684828. | − | 684828.i | 0.395112 | − | 0.395112i | −0.481393 | − | 0.876505i | \(-0.659869\pi\) |
0.876505 | + | 0.481393i | \(0.159869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.24969e6 | − | 1.42811e6i | 0.709621 | − | 0.810932i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.90957e6 | + | 1.90957e6i | 1.06730 | + | 1.06730i | 0.997565 | + | 0.0697372i | \(0.0222161\pi\) |
0.0697372 | + | 0.997565i | \(0.477784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16034e6 | −1.73883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −253105. | −0.137100 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.62587e6 | + | 1.62587e6i | 0.867122 | + | 0.867122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.71803e6 | − | 2.24902e6i | 0.902242 | − | 1.18109i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 168976. | − | 168976.i | 0.0873890 | − | 0.0873890i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.65125e6i | − | 0.841052i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 740425.i | 0.371459i | 0.982601 | + | 0.185730i | \(0.0594649\pi\) | ||||
−0.982601 | + | 0.185730i | \(0.940535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −458508. | + | 458508.i | −0.226588 | + | 0.226588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 247142. | + | 216267.i | 0.120319 | + | 0.105288i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.17170e6 | − | 2.17170e6i | −1.04166 | − | 1.04166i | −0.999094 | − | 0.0425641i | \(-0.986447\pi\) |
−0.0425641 | − | 0.999094i | \(-0.513553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43553.0 | 0.0205835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.25080e6 | −0.582510 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.37807e6 | + | 1.37807e6i | 0.632464 | + | 0.632464i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 262473. | − | 17487.8i | 0.118723 | − | 0.00791022i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 706412. | − | 706412.i | 0.314945 | − | 0.314945i | −0.531877 | − | 0.846822i | \(-0.678513\pi\) |
0.846822 | + | 0.531877i | \(0.178513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.03307e6i | 1.33297i | 0.745520 | + | 0.666483i | \(0.232201\pi\) | ||||
−0.745520 | + | 0.666483i | \(0.767799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 521234.i | − | 0.225821i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.72516e6 | + | 2.72516e6i | −1.16401 | + | 1.16401i | −0.180418 | + | 0.983590i | \(0.557745\pi\) |
−0.983590 | + | 0.180418i | \(0.942255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 684730. | − | 45621.7i | 0.288369 | − | 0.0192132i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −108269. | − | 108269.i | −0.0449609 | − | 0.0449609i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.47478e6 | 1.01345 | 0.506723 | − | 0.862109i | \(-0.330857\pi\) | ||||
0.506723 | + | 0.862109i | \(0.330857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.80455e6 | 1.53651 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 206354. | + | 206354.i | 0.0821953 | + | 0.0821953i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.14732e6 | + | 1.87905e6i | 0.843654 | + | 0.738256i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −405936. | + | 405936.i | −0.157323 | + | 0.157323i | −0.781379 | − | 0.624056i | \(-0.785484\pi\) |
0.624056 | + | 0.781379i | \(0.285484\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.40821e6i | 0.538397i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.47790e6i | − | 0.557455i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −378559. | + | 378559.i | −0.140884 | + | 0.140884i | −0.774031 | − | 0.633147i | \(-0.781763\pi\) |
0.633147 | + | 0.774031i | \(0.281763\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −114710. | + | 172885.i | −0.0421235 | + | 0.0634862i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.17326e6 | − | 3.17326e6i | −1.14988 | − | 1.14988i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.91279e6 | 1.39923 | 0.699614 | − | 0.714521i | \(-0.253355\pi\) | ||||
0.699614 | + | 0.714521i | \(0.253355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −77731.5 | −0.0274337 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.53247e6 | + | 2.53247e6i | 0.882161 | + | 0.882161i | 0.993754 | − | 0.111593i | \(-0.0355952\pi\) |
−0.111593 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.29911e6 | + | 3.77011e6i | −1.13434 | + | 1.29629i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.58310e6 | + | 2.58310e6i | −0.876725 | + | 0.876725i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.01392e6i | − | 1.00985i | −0.863163 | − | 0.504925i | \(-0.831520\pi\) | ||
0.863163 | − | 0.504925i | \(-0.168480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.63513e6i | 1.20248i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 70325.4 | − | 70325.4i | 0.0229684 | − | 0.0229684i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 239074. | + | 3.58822e6i | 0.0770972 | + | 1.15714i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.43650e6 | + | 3.43650e6i | 1.09431 | + | 1.09431i | 0.995063 | + | 0.0992459i | \(0.0316430\pi\) |
0.0992459 | + | 0.995063i | \(0.468357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −418238. | −0.131520 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.30306e6 | −1.33634 | −0.668169 | − | 0.744009i | \(-0.732922\pi\) | ||||
−0.668169 | + | 0.744009i | \(0.732922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.25592e6 | − | 1.25592e6i | −0.385211 | − | 0.385211i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −215632. | − | 3.23639e6i | −0.0653244 | − | 0.980445i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.21043e6 | − | 1.21043e6i | 0.362205 | − | 0.362205i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 452926.i | − | 0.133881i | −0.997757 | − | 0.0669405i | \(-0.978676\pi\) | ||
0.997757 | − | 0.0669405i | \(-0.0213238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 49172.2i | − | 0.0143587i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.66311e6 | + | 1.66311e6i | −0.479784 | + | 0.479784i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.27244e6 | − | 3.73963e6i | 0.932719 | − | 1.06588i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47602.0 | + | 47602.0i | 0.0134056 | + | 0.0134056i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −448753. | −0.124874 | −0.0624370 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624370 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.61031e6 | 0.992748 | 0.496374 | − | 0.868109i | \(-0.334664\pi\) | ||||
0.496374 | + | 0.868109i | \(0.334664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00749e6 | − | 2.00749e6i | −0.545510 | − | 0.545510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.27842e6 | − | 1.74049e6i | −0.611873 | − | 0.467412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.35903e6 | − | 2.35903e6i | 0.626128 | − | 0.626128i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 686009.i | 0.179964i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.33480e6i | 0.864722i | 0.901701 | + | 0.432361i | \(0.142319\pi\) | ||||
−0.901701 | + | 0.432361i | \(0.857681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.26797e6 | − | 4.26797e6i | 1.09396 | − | 1.09396i | 0.0988602 | − | 0.995101i | \(-0.468480\pi\) |
0.995101 | − | 0.0988602i | \(-0.0315197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 247584. | + | 216653.i | 0.0627336 | + | 0.0548962i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.02115e6 | + | 7.02115e6i | 1.75875 | + | 1.75875i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −985119. | −0.243965 | −0.121982 | − | 0.992532i | \(-0.538925\pi\) | ||||
−0.121982 | + | 0.992532i | \(0.538925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −709641. | −0.173757 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −941343. | − | 941343.i | −0.227897 | − | 0.227897i | 0.583917 | − | 0.811814i | \(-0.301519\pi\) |
−0.811814 | + | 0.583917i | \(0.801519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.36229e6 | + | 90766.0i | −0.326115 | + | 0.0217282i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25236.5 | − | 25236.5i | 0.00597393 | − | 0.00597393i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.05024e6i | 0.479941i | 0.970780 | + | 0.239971i | \(0.0771378\pi\) | ||||
−0.970780 | + | 0.239971i | \(0.922862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.71759e6i | − | 0.860638i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 214980. | − | 214980.i | 0.0492213 | − | 0.0492213i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.09813e6 | + | 472929.i | −1.60737 | + | 0.107095i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.54554e6 | − | 5.54554e6i | −1.24209 | − | 1.24209i | −0.959132 | − | 0.282958i | \(-0.908684\pi\) |
−0.282958 | − | 0.959132i | \(-0.591316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −528047. | −0.116988 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.71258e6 | −0.813624 | −0.406812 | − | 0.913512i | \(-0.633360\pi\) | ||||
−0.406812 | + | 0.913512i | \(0.633360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.14889e6 | − | 4.14889e6i | −0.899455 | − | 0.899455i | 0.0959328 | − | 0.995388i | \(-0.469417\pi\) |
−0.995388 | + | 0.0959328i | \(0.969417\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 97989.3 | + | 85747.4i | 0.0210158 | + | 0.0183903i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −599788. | + | 599788.i | −0.127264 | + | 0.127264i | −0.767870 | − | 0.640606i | \(-0.778683\pi\) |
0.640606 | + | 0.767870i | \(0.278683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 825483.i | − | 0.173291i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 50448.4i | − | 0.0104784i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.81922e6 | − | 6.81922e6i | 1.40146 | − | 1.40146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.76241e6 | + | 1.03899e6i | −1.57857 | + | 0.211289i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.79674e6 | − | 1.79674e6i | −0.361568 | − | 0.361568i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 130460. | 0.0259799 | 0.0129900 | − | 0.999916i | \(-0.495865\pi\) | ||||
0.0129900 | + | 0.999916i | \(0.495865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.43077e6 | 0.479049 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −467550. | − | 467550.i | −0.0911927 | − | 0.0911927i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.66816e6 | − | 5.33462e6i | 0.901138 | − | 1.02979i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.53566e6 | − | 5.53566e6i | 1.05766 | − | 1.05766i | 0.0594298 | − | 0.998232i | \(-0.481072\pi\) |
0.998232 | − | 0.0594298i | \(-0.0189283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 667803.i | 0.126292i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.06198e6i | 0.385993i | 0.981199 | + | 0.192997i | \(0.0618206\pi\) | ||||
−0.981199 | + | 0.192997i | \(0.938179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.21474e6 | + | 3.21474e6i | −0.595702 | + | 0.595702i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 572618. | + | 8.59434e6i | 0.105039 | + | 1.57652i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.21973e6 | − | 1.21973e6i | −0.221499 | − | 0.221499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.96927e6 | 0.713608 | 0.356804 | − | 0.934179i | \(-0.383866\pi\) | ||||
0.356804 | + | 0.934179i | \(0.383866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −272519. | −0.0485068 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.68593e6 | − | 7.68593e6i | −1.35449 | − | 1.35449i | −0.880564 | − | 0.473928i | \(-0.842836\pi\) |
−0.473928 | − | 0.880564i | \(-0.657164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 117199. | + | 1.75902e6i | 0.0204500 | + | 0.306932i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −376996. | + | 376996.i | −0.0651354 | + | 0.0651354i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 149834.i | − | 0.0256340i | −0.999918 | − | 0.0128170i | \(-0.995920\pi\) | ||
0.999918 | − | 0.0128170i | \(-0.00407988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.17229e6i | − | 1.21508i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01991e6 | + | 1.01991e6i | −0.171107 | + | 0.171107i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −228249. | + | 260835.i | −0.0379220 | + | 0.0433360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.29965e6 | + | 5.29965e6i | 0.872009 | + | 0.872009i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 266330. | 0.0434011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.13714e6 | 0.183536 | 0.0917678 | − | 0.995780i | \(-0.470748\pi\) | ||||
0.0917678 | + | 0.995780i | \(0.470748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.86949e6 | − | 4.86949e6i | −0.778447 | − | 0.778447i | 0.201119 | − | 0.979567i | \(-0.435542\pi\) |
−0.979567 | + | 0.201119i | \(0.935542\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 516911. | − | 69187.9i | 0.0818498 | − | 0.0109555i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.27234e6 | + | 1.27234e6i | −0.199561 | + | 0.199561i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.26159e6i | 1.43895i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.04382e6i | 0.622380i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.73280e6 | − | 3.73280e6i | 0.569136 | − | 0.569136i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.96524e6 | + | 7.84521e6i | 1.35418 | + | 1.18500i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −427972. | − | 427972.i | −0.0640442 | − | 0.0640442i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.87341e6 | 0.277754 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.42771e6 | −0.944198 | −0.472099 | − | 0.881546i | \(-0.656503\pi\) | ||||
−0.472099 | + | 0.881546i | \(0.656503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 299790. | + | 299790.i | 0.0436333 | + | 0.0436333i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.12229e7 | + | 747751.i | −1.61850 | + | 0.107836i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.88980e6 | − | 6.88980e6i | 0.984551 | − | 0.984551i | −0.0153314 | − | 0.999882i | \(-0.504880\pi\) |
0.999882 | + | 0.0153314i | \(0.00488033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5.73593e6i | − | 0.812219i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.24184e7i | 1.74255i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.39179e6 | − | 6.39179e6i | 0.888812 | − | 0.888812i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −177806. | + | 11846.8i | −0.0245027 | + | 0.00163255i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −626234. | − | 626234.i | −0.0855261 | − | 0.0855261i | 0.663049 | − | 0.748576i | \(-0.269262\pi\) |
−0.748576 | + | 0.663049i | \(0.769262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.36942e7 | 1.85356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 694977. | 0.0932316 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.78102e6 | + | 3.78102e6i | 0.502733 | + | 0.502733i | 0.912286 | − | 0.409553i | \(-0.134315\pi\) |
−0.409553 | + | 0.912286i | \(0.634315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.54269e6 | − | 1.34996e6i | −0.203309 | − | 0.177910i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.76507e6 | + | 5.76507e6i | −0.753090 | + | 0.753090i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.86991e6i | 0.760065i | 0.924973 | + | 0.380032i | \(0.124087\pi\) | ||||
−0.924973 | + | 0.380032i | \(0.875913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.63228e6i | 0.466218i | 0.972451 | + | 0.233109i | \(0.0748899\pi\) | ||||
−0.972451 | + | 0.233109i | \(0.925110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 248642. | − | 248642.i | 0.0316365 | − | 0.0316365i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.83910e6 | − | 7.51613e6i | −1.24104 | − | 0.948035i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.85335e6 | + | 7.85335e6i | 0.982009 | + | 0.982009i | 0.999841 | − | 0.0178322i | \(-0.00567647\pi\) |
−0.0178322 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18398.4 | −0.00228078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.24908e7 | −1.53514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.74328e6 | + | 4.74328e6i | 0.577973 | + | 0.577973i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.05452e6 | + | 9.20444e6i | −0.973084 | + | 1.11201i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.62105e6 | − | 4.62105e6i | 0.553535 | − | 0.553535i | −0.373924 | − | 0.927459i | \(-0.621988\pi\) |
0.927459 | + | 0.373924i | \(0.121988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.91496e6i | 0.583757i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 258386.i | 0.0304298i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.65088e6 | + | 6.65088e6i | −0.776681 | + | 0.776681i | −0.979265 | − | 0.202584i | \(-0.935066\pi\) |
0.202584 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 479111. | + | 7.19091e6i | 0.0554809 | + | 0.832706i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 348701. | + | 348701.i | 0.0400422 | + | 0.0400422i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.31406e6 | 0.491269 | 0.245634 | − | 0.969363i | \(-0.421004\pi\) | ||||
0.245634 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43695e7 | 1.62277 | 0.811384 | − | 0.584513i | \(-0.198714\pi\) | ||||
0.811384 | + | 0.584513i | \(0.198714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00357e6 | − | 1.00357e6i | −0.112397 | − | 0.112397i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −913154. | − | 1.37054e7i | −0.101427 | − | 1.52231i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 997962. | − | 997962.i | 0.109937 | − | 0.109937i | −0.649999 | − | 0.759935i | \(-0.725231\pi\) |
0.759935 | + | 0.649999i | \(0.225231\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 826959.i | − | 0.0903526i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.06426e7i | 1.15331i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.18198e6 | + | 6.18198e6i | −0.664472 | + | 0.664472i | −0.956431 | − | 0.291959i | \(-0.905693\pi\) |
0.291959 | + | 0.956431i | \(0.405693\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −254855. | + | 291240.i | −0.0271710 | + | 0.0310501i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −274155. | − | 274155.i | −0.0289924 | − | 0.0289924i | 0.692462 | − | 0.721454i | \(-0.256526\pi\) |
−0.721454 | + | 0.692462i | \(0.756526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04395e7 | 1.09510 | 0.547549 | − | 0.836774i | \(-0.315561\pi\) | ||||
0.547549 | + | 0.836774i | \(0.315561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.28031e6 | −0.237283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42669e6 | + | 2.42669e6i | 0.250492 | + | 0.250492i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.42187e6 | − | 2.56822e6i | 0.964800 | − | 0.262986i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.34233e6 | − | 1.34233e6i | 0.136361 | − | 0.136361i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.46254e6i | − | 0.248174i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.95332e7i | − | 1.95299i | −0.215544 | − | 0.976494i | \(-0.569152\pi\) | ||
0.215544 | − | 0.976494i | \(-0.430848\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 565927. | − | 565927.i | 0.0561373 | − | 0.0561373i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.75333e6 | + | 2.40935e6i | 0.270972 | + | 0.237119i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.88107e6 | + | 1.88107e6i | 0.183677 | + | 0.183677i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.96574e6 | −0.287330 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.16310e7 | 1.11808 | 0.559038 | − | 0.829142i | \(-0.311171\pi\) | ||||
0.559038 | + | 0.829142i | \(0.311171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.86995e6 | − | 8.86995e6i | −0.846045 | − | 0.846045i | 0.143592 | − | 0.989637i | \(-0.454135\pi\) |
−0.989637 | + | 0.143592i | \(0.954135\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00171e6 | + | 66741.1i | −0.0948073 | + | 0.00631675i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.82351e6 | − | 7.82351e6i | 0.734752 | − | 0.734752i | −0.236805 | − | 0.971557i | \(-0.576100\pi\) |
0.971557 | + | 0.236805i | \(0.0761003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.06754e7i | − | 0.994887i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 327295.i | − | 0.0302682i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.80259e6 | + | 5.80259e6i | −0.532524 | + | 0.532524i | −0.921323 | − | 0.388799i | \(-0.872890\pi\) |
0.388799 | + | 0.921323i | \(0.372890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.67079e6 | + | 311202.i | −0.425390 | + | 0.0283426i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.71964e6 | − | 8.71964e6i | −0.788107 | − | 0.788107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.87531e7 | −1.68213 | −0.841065 | − | 0.540934i | \(-0.818071\pi\) | ||||
−0.841065 | + | 0.540934i | \(0.818071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.79645e7 | −1.59923 | −0.799615 | − | 0.600513i | \(-0.794963\pi\) | ||||
−0.799615 | + | 0.600513i | \(0.794963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 697819. | + | 697819.i | 0.0616536 | + | 0.0616536i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.48144e7 | + | 1.29637e7i | 1.29907 | + | 1.13677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.38825e7 | + | 1.38825e7i | −1.20824 | + | 1.20824i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.53895e6i | − | 0.132941i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.51425e7i | 1.29835i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.23479e7 | − | 1.23479e7i | 1.05089 | − | 1.05089i | 0.0522545 | − | 0.998634i | \(-0.483359\pi\) |
0.998634 | − | 0.0522545i | \(-0.0166407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09181e6 | − | 1.42925e6i | 0.0922332 | − | 0.120739i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.66444e6 | − | 5.66444e6i | −0.474991 | − | 0.474991i | 0.428535 | − | 0.903525i | \(-0.359030\pi\) |
−0.903525 | + | 0.428535i | \(0.859030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.78182e7 | −1.48317 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −533536. | −0.0440855 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.21820e6 | − | 2.21820e6i | −0.181948 | − | 0.181948i | 0.610256 | − | 0.792204i | \(-0.291067\pi\) |
−0.792204 | + | 0.610256i | \(0.791067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52413e6 | + | 1.74173e6i | −0.124107 | + | 0.141826i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −965815. | + | 965815.i | −0.0780732 | + | 0.0780732i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.52536e6i | 0.764422i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.63246e7i | − | 1.30061i | −0.759674 | − | 0.650304i | \(-0.774642\pi\) | ||
0.759674 | − | 0.650304i | \(-0.225358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.53093e7 | − | 1.53093e7i | 1.21094 | − | 1.21094i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −210647. | − | 3.16157e6i | −0.0165422 | − | 0.248280i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.78159e6 | − | 3.78159e6i | −0.294844 | − | 0.294844i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −488652. | −0.0378274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.64161e7 | 1.26175 | 0.630876 | − | 0.775884i | \(-0.282696\pi\) | ||||
0.630876 | + | 0.775884i | \(0.282696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.75633e6 | − | 4.75633e6i | −0.362981 | − | 0.362981i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51868.8 | − | 778491.i | −0.00393037 | − | 0.0589903i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.13338e6 | − | 3.13338e6i | 0.235757 | − | 0.235757i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.37201e6i | − | 0.177215i | −0.996067 | − | 0.0886077i | \(-0.971758\pi\) | ||
0.996067 | − | 0.0886077i | \(-0.0282417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.55415e7i | − | 1.15298i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.49445e6 | + | 5.49445e6i | −0.404762 | + | 0.404762i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.12634e7 | − | 2.42991e7i | 1.55549 | − | 1.77757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −127721. | − | 127721.i | −0.00927824 | − | 0.00927824i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.62894e6 | −0.622494 | −0.311247 | − | 0.950329i | \(-0.600747\pi\) | ||||
−0.311247 | + | 0.950329i | \(0.600747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 871219. | 0.0624150 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36264.6 | − | 36264.6i | −0.00258010 | − | 0.00258010i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.05433e6 | − | 1.53482e7i | −0.145153 | − | 1.08446i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.16170e7 | + | 1.16170e7i | −0.815187 | + | 0.815187i | −0.985406 | − | 0.170219i | \(-0.945552\pi\) |
0.170219 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.38516e7i | 0.965339i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.38732e7i | − | 0.960249i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.58933e6 | + | 7.58933e6i | −0.521727 | + | 0.521727i | −0.918093 | − | 0.396366i | \(-0.870271\pi\) |
0.396366 | + | 0.918093i | \(0.370271\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −146765. | − | 128429.i | −0.0100208 | − | 0.00876890i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.64937e6 | + | 2.64937e6i | 0.179669 | + | 0.179669i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.89099e6 | −0.127373 | −0.0636867 | − | 0.997970i | \(-0.520286\pi\) | ||||
−0.0636867 | + | 0.997970i | \(0.520286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.69563e6 | 0.180350 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.86435e7 | + | 1.86435e7i | 1.23895 | + | 1.23895i | 0.960430 | + | 0.278523i | \(0.0898447\pi\) |
0.278523 | + | 0.960430i | \(0.410155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.67613e6 | + | 111676.i | −0.110641 | + | 0.00737172i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.51856e7 | + | 1.51856e7i | −0.995702 | + | 0.995702i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.99449e7i | − | 1.95038i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.60302e6i | 0.297813i | 0.988851 | + | 0.148906i | \(0.0475753\pi\) | ||||
−0.988851 | + | 0.148906i | \(0.952425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −459934. | + | 459934.i | −0.0295602 | + | 0.0295602i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.42783e7 | + | 951325.i | −0.911610 | + | 0.0607381i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.60445e6 | + | 6.60445e6i | 0.418887 | + | 0.418887i | 0.884820 | − | 0.465933i | \(-0.154281\pi\) |
−0.465933 | + | 0.884820i | \(0.654281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00118e6 | 0.189098 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.76470e6 | −0.486030 | −0.243015 | − | 0.970023i | \(-0.578136\pi\) | ||||
−0.243015 | + | 0.970023i | \(0.578136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.99916e7 | + | 1.99916e7i | 1.24319 | + | 1.24319i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.32476e6 | + | 8.15981e6i | 0.576082 | + | 0.504112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.07191e7 | − | 1.07191e7i | 0.657915 | − | 0.657915i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.03998e7i | − | 0.634172i | −0.948397 | − | 0.317086i | \(-0.897296\pi\) | ||
0.948397 | − | 0.317086i | \(-0.102704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 380332.i | 0.0230424i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.28295e7 | + | 2.28295e7i | −1.37419 | + | 1.37419i | −0.520068 | + | 0.854125i | \(0.674093\pi\) |
−0.854125 | + | 0.520068i | \(0.825907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −813067. | − | 6.07452e6i | −0.0486264 | − | 0.363294i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 316731. | + | 316731.i | 0.0188208 | + | 0.0188208i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.46081e7 | −0.862480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.82938e6 | 0.459303 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.01661e6 | − | 2.01661e6i | −0.117548 | − | 0.117548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.56369e6 | + | 1.78693e6i | −0.0905683 | + | 0.103498i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.72096e6 | + | 5.72096e6i | −0.329255 | + | 0.329255i | −0.852303 | − | 0.523048i | \(-0.824795\pi\) |
0.523048 | + | 0.852303i | \(0.324795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36309.2i | 0.00207646i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.15276e6i | 0.292818i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.52044e7 | + | 1.52044e7i | −0.858592 | + | 0.858592i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −46423.5 | − | 696764.i | −0.00260507 | − | 0.0390992i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.79102e6 | + | 4.79102e6i | 0.267167 | + | 0.267167i | 0.827957 | − | 0.560791i | \(-0.189503\pi\) |
−0.560791 | + | 0.827957i | \(0.689503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.07818e7 | 0.597479 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.90046e6 | 0.324941 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.30193e7 | + | 2.30193e7i | 1.25980 | + | 1.25980i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.06899e6 | + | 3.10532e7i | 0.112530 | + | 1.68895i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.49592e6 | + | 1.49592e6i | −0.0808580 | + | 0.0808580i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.42552e7i | − | 0.765778i | −0.923794 | − | 0.382889i | \(-0.874929\pi\) | ||
0.923794 | − | 0.382889i | \(-0.125071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.56090e7i | 1.36723i | 0.729843 | + | 0.683614i | \(0.239593\pi\) | ||||
−0.729843 | + | 0.683614i | \(0.760407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.21904e6 | + | 1.21904e6i | −0.0646830 | + | 0.0646830i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.06991e7 | − | 2.36543e7i | 1.09159 | − | 1.24743i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.67957e7 | − | 2.67957e7i | −1.40446 | − | 1.40446i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.07439e7 | 1.60158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.31917e6 | 0.120081 | 0.0600406 | − | 0.998196i | \(-0.480877\pi\) | ||||
0.0600406 | + | 0.998196i | \(0.480877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.90869e6 | + | 4.90869e6i | 0.252619 | + | 0.252619i | 0.822044 | − | 0.569425i | \(-0.192834\pi\) |
−0.569425 | + | 0.822044i | \(0.692834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.43696e6 | + | 1.88107e6i | −0.0735037 | + | 0.0962211i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.02142e7 | − | 2.02142e7i | 1.02776 | − | 1.02776i | 0.0281570 | − | 0.999604i | \(-0.491036\pi\) |
0.999604 | − | 0.0281570i | \(-0.00896383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.54977e6i | 0.229934i | 0.993369 | + | 0.114967i | \(0.0366762\pi\) | ||||
−0.993369 | + | 0.114967i | \(0.963324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.39710e6i | 0.0701818i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.90566e6 | − | 1.90566e6i | 0.0951551 | − | 0.0951551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.65290e6 | + | 8.44696e6i | 0.479117 | + | 0.419261i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −798135. | − | 798135.i | −0.0393788 | − | 0.0393788i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.98332e7 | −0.972719 | −0.486360 | − | 0.873759i | \(-0.661675\pi\) | ||||
−0.486360 | + | 0.873759i | \(0.661675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.04300e6 | −0.197112 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.04198e6 | − | 2.04198e6i | −0.0989651 | − | 0.0989651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.50389e7 | − | 1.66827e6i | 1.20635 | − | 0.0803759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.44138e7 | + | 2.44138e7i | −1.16930 | + | 1.16930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 237170.i | − | 0.0112925i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.06342e7i | − | 0.503363i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −693392. | + | 693392.i | −0.0326292 | + | 0.0326292i | −0.723233 | − | 0.690604i | \(-0.757345\pi\) |
0.690604 | + | 0.723233i | \(0.257345\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.37710e7 | − | 2.25007e6i | 1.57989 | − | 0.105264i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.01743e7 | + | 2.01743e7i | 0.938308 | + | 0.938308i | 0.998205 | − | 0.0598966i | \(-0.0190771\pi\) |
−0.0598966 | + | 0.998205i | \(0.519077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.16047e7 | −0.999001 | −0.499501 | − | 0.866314i | \(-0.666483\pi\) | ||||
−0.499501 | + | 0.866314i | \(0.666483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 972774. | 0.0447202 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.05264e6 | + | 7.05264e6i | 0.322348 | + | 0.322348i | 0.849667 | − | 0.527319i | \(-0.176803\pi\) |
−0.527319 | + | 0.849667i | \(0.676803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.43367e6 | − | 8.25511e6i | −0.428687 | − | 0.375131i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −485480. | + | 485480.i | −0.0219343 | + | 0.0219343i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.10287e7i | 1.84305i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.32041e6i | 0.237629i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.16623e7 | + | 2.16623e7i | −0.961988 | + | 0.961988i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.04541e7 | − | 1.35714e7i | −0.903149 | − | 0.599244i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.77065e7 | − | 1.77065e7i | −0.777381 | − | 0.777381i | 0.202004 | − | 0.979385i | \(-0.435255\pi\) |
−0.979385 | + | 0.202004i | \(0.935255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −907969. | −0.0396368 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.88929e7 | −1.25416 | −0.627078 | − | 0.778957i | \(-0.715749\pi\) | ||||
−0.627078 | + | 0.778957i | \(0.715749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.58238e6 | + | 4.58238e6i | 0.197783 | + | 0.197783i | 0.799049 | − | 0.601266i | \(-0.205337\pi\) |
−0.601266 | + | 0.799049i | \(0.705337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −731842. | + | 836325.i | −0.0314094 | + | 0.0358936i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.54412e6 | + | 9.54412e6i | −0.407312 | + | 0.407312i | −0.880800 | − | 0.473488i | \(-0.842995\pi\) |
0.473488 | + | 0.880800i | \(0.342995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.19643e6i | − | 0.390270i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.70057e7i | − | 1.56162i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.08247e7 | − | 2.08247e7i | 0.873875 | − | 0.873875i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.89385e6 | + | 2.84246e7i | 0.0790294 | + | 1.18614i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.01345e6 | + | 3.01345e6i | 0.125050 | + | 0.125050i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.71808e6 | −0.401034 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64987e6 | 0.396013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.78437e6 | + | 1.78437e6i | 0.0728224 | + | 0.0728224i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.32663e6 | − | 1.99111e7i | −0.0538427 | − | 0.808118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.57152e7 | + | 1.57152e7i | −0.634312 | + | 0.634312i | −0.949147 | − | 0.314835i | \(-0.898051\pi\) |
0.314835 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 7.61877e6i | − | 0.305826i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.37011e7i | − | 1.34539i | −0.739920 | − | 0.672694i | \(-0.765137\pi\) | ||
0.739920 | − | 0.672694i | \(-0.234863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00889e7 | − | 4.00889e7i | 1.59165 | − | 1.59165i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.03808e6 | − | 1.18628e6i | 0.0409899 | − | 0.0468418i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.32021e6 | + | 8.32021e6i | 0.326747 | + | 0.326747i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.69860e7 | −0.663440 | −0.331720 | − | 0.943378i | \(-0.607629\pi\) | ||||
−0.331720 | + | 0.943378i | \(0.607629\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.30872e6 | 0.0508391 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.86139e6 | + | 7.86139e6i | 0.303735 | + | 0.303735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.66528e6 | + | 5.09163e6i | 0.256132 | + | 0.195660i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.05918e6 | − | 1.05918e6i | 0.0404827 | − | 0.0404827i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.74089e7i | − | 1.04196i | −0.853568 | − | 0.520982i | \(-0.825566\pi\) | ||
0.853568 | − | 0.520982i | \(-0.174434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.36144e6i | − | 0.278348i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.31423e6 | + | 1.31423e6i | −0.0494275 | + | 0.0494275i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.46168e7 | − | 2.15414e7i | −0.920878 | − | 0.805832i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.46447e7 | − | 3.46447e7i | −1.28910 | − | 1.28910i | −0.935333 | − | 0.353769i | \(-0.884900\pi\) |
−0.353769 | − | 0.935333i | \(-0.615100\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.15026e6 | −0.0425728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.97677e7 | 0.727750 | 0.363875 | − | 0.931448i | \(-0.381454\pi\) | ||||
0.363875 | + | 0.931448i | \(0.381454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63304e7 | − | 1.63304e7i | −0.598022 | − | 0.598022i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.51085e6 | + | 300546.i | −0.164316 | + | 0.0109479i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45673e7 | − | 1.45673e7i | 0.527842 | − | 0.527842i | −0.392086 | − | 0.919928i | \(-0.628247\pi\) |
0.919928 | + | 0.392086i | \(0.128247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.62269e7i | 1.66621i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.20738e6i | − | 0.115000i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.23751e7 | + | 2.23751e7i | −0.798055 | + | 0.798055i | −0.982789 | − | 0.184734i | \(-0.940858\pi\) |
0.184734 | + | 0.982789i | \(0.440858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.65140e7 | + | 1.10028e6i | −0.585928 | + | 0.0390388i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.65411e6 | + | 2.65411e6i | 0.0936782 | + | 0.0936782i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.81757e6 | 0.204266 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.47829e7 | 0.865653 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.64053e7 | − | 3.64053e7i | −1.26502 | − | 1.26502i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 651690. | + | 570273.i | 0.0225280 | + | 0.0197136i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.87842e7 | − | 2.87842e7i | 0.989894 | − | 0.989894i | −0.0100555 | − | 0.999949i | \(-0.503201\pi\) |
0.999949 | + | 0.0100555i | \(0.00320081\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2.73087e6i | − | 0.0934311i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.09828e7i | 1.73530i | 0.497173 | + | 0.867651i | \(0.334371\pi\) | ||||
−0.497173 | + | 0.867651i | \(0.665629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.63180e6 | + | 5.63180e6i | −0.190706 | + | 0.190706i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.33160e6 | + | 445930.i | −0.112238 | + | 0.0150230i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.93752e7 | + | 3.93752e7i | 1.31973 | + | 1.31973i | 0.913984 | + | 0.405749i | \(0.132989\pi\) |
0.405749 | + | 0.913984i | \(0.367011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.55768e7 | −0.519424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.86093e7 | 1.61267 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.47236e7 | − | 2.47236e7i | −0.816070 | − | 0.816070i | 0.169466 | − | 0.985536i | \(-0.445796\pi\) |
−0.985536 | + | 0.169466i | \(0.945796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.00888e6 | − | 9.15228e6i | 0.263015 | − | 0.300565i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.38675e6 | + | 1.38675e6i | −0.0453111 | + | 0.0453111i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.99100e7i | − | 1.94764i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85549e7i | 0.923627i | 0.886977 | + | 0.461814i | \(0.152801\pi\) | ||||
−0.886977 | + | 0.461814i | \(0.847199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 621822. | − | 621822.i | 0.0200121 | − | 0.0200121i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.54306e6 | − | 2.31596e7i | −0.0494113 | − | 0.741608i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.29416e7 | − | 1.29416e7i | −0.412335 | − | 0.412335i | 0.470216 | − | 0.882551i | \(-0.344176\pi\) |
−0.882551 | + | 0.470216i | \(0.844176\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.54475e6 | 0.0489716 |
(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.n.d.47.5 | ✓ | 20 | |
4.3 | odd | 2 | inner | 80.6.n.d.47.6 | yes | 20 | |
5.2 | odd | 4 | 400.6.n.g.143.5 | 20 | |||
5.3 | odd | 4 | inner | 80.6.n.d.63.6 | yes | 20 | |
5.4 | even | 2 | 400.6.n.g.207.6 | 20 | |||
20.3 | even | 4 | inner | 80.6.n.d.63.5 | yes | 20 | |
20.7 | even | 4 | 400.6.n.g.143.6 | 20 | |||
20.19 | odd | 2 | 400.6.n.g.207.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.n.d.47.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
80.6.n.d.47.6 | yes | 20 | 4.3 | odd | 2 | inner | |
80.6.n.d.63.5 | yes | 20 | 20.3 | even | 4 | inner | |
80.6.n.d.63.6 | yes | 20 | 5.3 | odd | 4 | inner | |
400.6.n.g.143.5 | 20 | 5.2 | odd | 4 | |||
400.6.n.g.143.6 | 20 | 20.7 | even | 4 | |||
400.6.n.g.207.5 | 20 | 20.19 | odd | 2 | |||
400.6.n.g.207.6 | 20 | 5.4 | even | 2 |