Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(143,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.q (of order \(12\), degree \(4\), 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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.2 | ||
Root | \(0.500000 + 2.00333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.557 |
Dual form | 1350.2.q.h.143.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | − | 0.258819i | −0.683013 | − | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00635 | − | 3.75574i | 0.380364 | − | 1.41954i | −0.464984 | − | 0.885319i | \(-0.653940\pi\) |
0.845347 | − | 0.534217i | \(-0.179394\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44125 | − | 1.98681i | 1.03758 | − | 0.599044i | 0.118430 | − | 0.992962i | \(-0.462214\pi\) |
0.919145 | + | 0.393918i | \(0.128881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.256253 | + | 0.956351i | 0.0710719 | + | 0.265244i | 0.992314 | − | 0.123746i | \(-0.0394908\pi\) |
−0.921242 | + | 0.388990i | \(0.872824\pi\) | |||||||
\(14\) | −1.94411 | + | 3.36730i | −0.519586 | + | 0.899950i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 0.120239 | − | 0.120239i | 0.0291622 | − | 0.0291622i | −0.692375 | − | 0.721538i | \(-0.743436\pi\) |
0.721538 | + | 0.692375i | \(0.243436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.88492i | − | 0.432431i | −0.976346 | − | 0.216216i | \(-0.930629\pi\) | ||
0.976346 | − | 0.216216i | \(-0.0693714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.83821 | + | 1.02845i | −0.818310 | + | 0.219265i | ||||
\(23\) | 5.08911 | − | 1.36362i | 1.06115 | − | 0.284335i | 0.314299 | − | 0.949324i | \(-0.398230\pi\) |
0.746853 | + | 0.664989i | \(0.231564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.990087i | − | 0.194172i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.74939 | − | 2.74939i | 0.519586 | − | 0.519586i | ||||
\(29\) | −2.15618 | − | 3.73461i | −0.400392 | − | 0.693499i | 0.593381 | − | 0.804922i | \(-0.297793\pi\) |
−0.993773 | + | 0.111422i | \(0.964459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.70172 | + | 8.14362i | −0.844454 | + | 1.46264i | 0.0416413 | + | 0.999133i | \(0.486741\pi\) |
−0.886095 | + | 0.463504i | \(0.846592\pi\) | |||||||
\(32\) | −0.258819 | − | 0.965926i | −0.0457532 | − | 0.170753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.147262 | + | 0.0850217i | −0.0252552 | + | 0.0145811i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.26863 | − | 3.26863i | −0.537360 | − | 0.537360i | 0.385393 | − | 0.922753i | \(-0.374066\pi\) |
−0.922753 | + | 0.385393i | \(0.874066\pi\) | |||||||
\(38\) | −0.487854 | + | 1.82070i | −0.0791404 | + | 0.295356i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.15775 | − | 4.13253i | −1.11785 | − | 0.645393i | −0.177001 | − | 0.984211i | \(-0.556640\pi\) |
−0.940852 | + | 0.338818i | \(0.889973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.99285 | + | 0.533983i | 0.303907 | + | 0.0814316i | 0.407550 | − | 0.913183i | \(-0.366383\pi\) |
−0.103643 | + | 0.994615i | \(0.533050\pi\) | |||||||
\(44\) | 3.97361 | 0.599044 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.26863 | −0.776818 | ||||||||
\(47\) | 3.34787 | + | 0.897060i | 0.488338 | + | 0.130850i | 0.494582 | − | 0.869131i | \(-0.335321\pi\) |
−0.00624459 | + | 0.999981i | \(0.501988\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.03067 | − | 4.05916i | −1.00438 | − | 0.579880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.256253 | + | 0.956351i | −0.0355359 | + | 0.132622i | ||||
\(53\) | 3.66571 | + | 3.66571i | 0.503524 | + | 0.503524i | 0.912531 | − | 0.409007i | \(-0.134125\pi\) |
−0.409007 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.36730 | + | 1.94411i | −0.449975 | + | 0.259793i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.11612 | + | 4.16541i | 0.146554 | + | 0.546946i | ||||
\(59\) | 2.72877 | − | 4.72637i | 0.355255 | − | 0.615320i | −0.631906 | − | 0.775045i | \(-0.717727\pi\) |
0.987162 | + | 0.159724i | \(0.0510606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.35623 | − | 7.54520i | −0.557758 | − | 0.966064i | −0.997683 | − | 0.0680302i | \(-0.978329\pi\) |
0.439926 | − | 0.898034i | \(-0.355005\pi\) | |||||||
\(62\) | 6.64923 | − | 6.64923i | 0.844454 | − | 0.844454i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.86563 | + | 2.10759i | −0.960940 | + | 0.257483i | −0.704998 | − | 0.709209i | \(-0.749052\pi\) |
−0.255942 | + | 0.966692i | \(0.582385\pi\) | |||||||
\(68\) | 0.164249 | − | 0.0440105i | 0.0199182 | − | 0.00533705i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.94911i | 0.824708i | 0.911024 | + | 0.412354i | \(0.135293\pi\) | ||||
−0.911024 | + | 0.412354i | \(0.864707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.27728 | − | 8.27728i | 0.968783 | − | 0.968783i | −0.0307446 | − | 0.999527i | \(-0.509788\pi\) |
0.999527 | + | 0.0307446i | \(0.00978785\pi\) | |||||||
\(74\) | 2.31127 | + | 4.00324i | 0.268680 | + | 0.465368i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.942462 | − | 1.63239i | 0.108108 | − | 0.187248i | ||||
\(77\) | −3.99883 | − | 14.9238i | −0.455709 | − | 1.70073i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7529 | − | 6.78553i | 1.32230 | − | 0.763431i | 0.338206 | − | 0.941072i | \(-0.390180\pi\) |
0.984095 | + | 0.177641i | \(0.0568465\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.84428 | + | 5.84428i | 0.645393 | + | 0.645393i | ||||
\(83\) | 1.81110 | − | 6.75913i | 0.198795 | − | 0.741911i | −0.792457 | − | 0.609927i | \(-0.791199\pi\) |
0.991252 | − | 0.131984i | \(-0.0421347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.78674 | − | 1.03157i | −0.192669 | − | 0.111238i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.83821 | − | 1.02845i | −0.409155 | − | 0.109633i | ||||
\(89\) | 4.87832 | 0.517100 | 0.258550 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258550 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.84968 | 0.403557 | ||||||||
\(92\) | 5.08911 | + | 1.36362i | 0.530576 | + | 0.142168i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00162 | − | 1.73299i | −0.309594 | − | 0.178744i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.387234 | − | 1.44518i | 0.0393177 | − | 0.146736i | −0.943477 | − | 0.331439i | \(-0.892466\pi\) |
0.982794 | + | 0.184704i | \(0.0591325\pi\) | |||||||
\(98\) | 5.74052 | + | 5.74052i | 0.579880 | + | 0.579880i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.91944 | − | 5.14964i | 0.887517 | − | 0.512408i | 0.0143875 | − | 0.999896i | \(-0.495420\pi\) |
0.873130 | + | 0.487488i | \(0.162087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.67823 | − | 6.26326i | −0.165361 | − | 0.617137i | −0.997994 | − | 0.0633111i | \(-0.979834\pi\) |
0.832632 | − | 0.553826i | \(-0.186833\pi\) | |||||||
\(104\) | 0.495044 | − | 0.857441i | 0.0485430 | − | 0.0840790i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.59205 | − | 4.48956i | −0.251762 | − | 0.436065i | ||||
\(107\) | −3.70057 | + | 3.70057i | −0.357747 | + | 0.357747i | −0.862982 | − | 0.505235i | \(-0.831406\pi\) |
0.505235 | + | 0.862982i | \(0.331406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.30160i | 0.699367i | 0.936868 | + | 0.349683i | \(0.113711\pi\) | ||||
−0.936868 | + | 0.349683i | \(0.886289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.75574 | − | 1.00635i | 0.354884 | − | 0.0950909i | ||||
\(113\) | −4.07557 | + | 1.09205i | −0.383397 | + | 0.102731i | −0.445369 | − | 0.895347i | \(-0.646928\pi\) |
0.0619722 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.31235i | − | 0.400392i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.85906 | + | 3.85906i | −0.355255 | + | 0.355255i | ||||
\(119\) | −0.330584 | − | 0.572588i | −0.0303046 | − | 0.0524891i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.39479 | − | 4.14790i | 0.217708 | − | 0.377081i | ||||
\(122\) | 2.25495 | + | 8.41558i | 0.204153 | + | 0.761911i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.14362 | + | 4.70172i | −0.731318 | + | 0.422227i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7871 | − | 13.7871i | −1.22341 | − | 1.22341i | −0.966411 | − | 0.257000i | \(-0.917266\pi\) |
−0.257000 | − | 0.966411i | \(-0.582734\pi\) | |||||||
\(128\) | 0.258819 | − | 0.965926i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.88249 | + | 2.24156i | 0.339215 | + | 0.195846i | 0.659925 | − | 0.751332i | \(-0.270588\pi\) |
−0.320710 | + | 0.947178i | \(0.603921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.07929 | − | 1.89689i | −0.613852 | − | 0.164481i | ||||
\(134\) | 8.14310 | 0.703457 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.170043 | −0.0145811 | ||||||||
\(137\) | −12.0729 | − | 3.23492i | −1.03146 | − | 0.276378i | −0.296888 | − | 0.954912i | \(-0.595949\pi\) |
−0.734569 | + | 0.678534i | \(0.762616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.60435 | − | 2.08097i | −0.305717 | − | 0.176506i | 0.339291 | − | 0.940681i | \(-0.389813\pi\) |
−0.645008 | + | 0.764176i | \(0.723146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.79856 | − | 6.71233i | 0.150932 | − | 0.563286i | ||||
\(143\) | 2.78191 | + | 2.78191i | 0.232635 | + | 0.232635i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.1376 | + | 5.85292i | −0.838990 | + | 0.484391i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.19640 | − | 4.46504i | −0.0983437 | − | 0.367024i | ||||
\(149\) | 0.518244 | − | 0.897625i | 0.0424562 | − | 0.0735363i | −0.844016 | − | 0.536317i | \(-0.819815\pi\) |
0.886473 | + | 0.462781i | \(0.153148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.03451 | − | 3.52388i | −0.165566 | − | 0.286769i | 0.771290 | − | 0.636484i | \(-0.219612\pi\) |
−0.936856 | + | 0.349715i | \(0.886278\pi\) | |||||||
\(152\) | −1.33284 | + | 1.33284i | −0.108108 | + | 0.108108i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.4503i | 1.24502i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.81460 | − | 2.36186i | 0.703481 | − | 0.188497i | 0.110692 | − | 0.993855i | \(-0.464693\pi\) |
0.592789 | + | 0.805357i | \(0.298027\pi\) | |||||||
\(158\) | −13.1086 | + | 3.51245i | −1.04287 | + | 0.279435i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.4857i | − | 1.61450i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.03848 | + | 5.03848i | −0.394644 | + | 0.394644i | −0.876339 | − | 0.481695i | \(-0.840021\pi\) |
0.481695 | + | 0.876339i | \(0.340021\pi\) | |||||||
\(164\) | −4.13253 | − | 7.15775i | −0.322696 | − | 0.558926i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.49878 | + | 6.06007i | −0.271558 | + | 0.470353i | ||||
\(167\) | −2.80384 | − | 10.4641i | −0.216968 | − | 0.809734i | −0.985465 | − | 0.169881i | \(-0.945662\pi\) |
0.768497 | − | 0.639853i | \(-0.221005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4094 | − | 6.00986i | 0.800722 | − | 0.462297i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.45887 | + | 1.45887i | 0.111238 | + | 0.111238i | ||||
\(173\) | 0.975709 | − | 3.64139i | 0.0741818 | − | 0.276850i | −0.918865 | − | 0.394573i | \(-0.870893\pi\) |
0.993047 | + | 0.117722i | \(0.0375593\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.44125 | + | 1.98681i | 0.259394 | + | 0.149761i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.71209 | − | 1.26260i | −0.353186 | − | 0.0946359i | ||||
\(179\) | −12.8952 | −0.963836 | −0.481918 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481918 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.3197 | 1.80767 | 0.903835 | − | 0.427881i | \(-0.140740\pi\) | ||||
0.903835 | + | 0.427881i | \(0.140740\pi\) | |||||||
\(182\) | −3.71851 | − | 0.996372i | −0.275634 | − | 0.0738560i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.56277 | − | 2.63432i | −0.336372 | − | 0.194204i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.174880 | − | 0.652663i | 0.0127885 | − | 0.0477274i | ||||
\(188\) | 2.45081 | + | 2.45081i | 0.178744 | + | 0.178744i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8036 | + | 6.81478i | −0.854075 | + | 0.493100i | −0.862024 | − | 0.506868i | \(-0.830803\pi\) |
0.00794868 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.19397 | + | 15.6521i | 0.301889 | + | 1.12666i | 0.935591 | + | 0.353086i | \(0.114868\pi\) |
−0.633702 | + | 0.773577i | \(0.718466\pi\) | |||||||
\(194\) | −0.748079 | + | 1.29571i | −0.0537090 | + | 0.0930267i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.05916 | − | 7.03067i | −0.289940 | − | 0.502191i | ||||
\(197\) | −1.16085 | + | 1.16085i | −0.0827072 | + | 0.0827072i | −0.747250 | − | 0.664543i | \(-0.768626\pi\) |
0.664543 | + | 0.747250i | \(0.268626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.1733i | − | 1.21738i | −0.793407 | − | 0.608691i | \(-0.791695\pi\) | ||
0.793407 | − | 0.608691i | \(-0.208305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.94834 | + | 2.66565i | −0.699963 | + | 0.187554i | ||||
\(203\) | −16.1961 | + | 4.33973i | −1.13674 | + | 0.304589i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.48420i | 0.451776i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.700097 | + | 0.700097i | −0.0485430 | + | 0.0485430i | ||||
\(209\) | −3.74498 | − | 6.48649i | −0.259046 | − | 0.448680i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.10894 | + | 15.7771i | −0.627085 | + | 1.08614i | 0.361048 | + | 0.932547i | \(0.382419\pi\) |
−0.988134 | + | 0.153597i | \(0.950914\pi\) | |||||||
\(212\) | 1.34174 | + | 5.00745i | 0.0921513 | + | 0.343913i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.53225 | − | 2.61670i | 0.309818 | − | 0.178874i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.8537 | + | 25.8537i | 1.75507 | + | 1.75507i | ||||
\(218\) | 1.88979 | − | 7.05281i | 0.127993 | − | 0.477676i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.145802 | + | 0.0841789i | 0.00980771 | + | 0.00566249i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.53570 | + | 1.21534i | 0.303733 | + | 0.0813849i | 0.407466 | − | 0.913220i | \(-0.366412\pi\) |
−0.103734 | + | 0.994605i | \(0.533079\pi\) | |||||||
\(224\) | −3.88823 | −0.259793 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.21934 | 0.280666 | ||||||||
\(227\) | 24.1784 | + | 6.47859i | 1.60478 | + | 0.429999i | 0.946481 | − | 0.322759i | \(-0.104610\pi\) |
0.658297 | + | 0.752758i | \(0.271277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7350 | + | 11.3940i | 1.30412 | + | 0.752935i | 0.981108 | − | 0.193459i | \(-0.0619706\pi\) |
0.323014 | + | 0.946394i | \(0.395304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.11612 | + | 4.16541i | −0.0732768 | + | 0.273473i | ||||
\(233\) | −20.6491 | − | 20.6491i | −1.35277 | − | 1.35277i | −0.882553 | − | 0.470214i | \(-0.844177\pi\) |
−0.470214 | − | 0.882553i | \(-0.655823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.72637 | − | 2.72877i | 0.307660 | − | 0.177628i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.171123 | + | 0.638639i | 0.0110922 | + | 0.0413968i | ||||
\(239\) | −4.56277 | + | 7.90295i | −0.295141 | + | 0.511199i | −0.975018 | − | 0.222127i | \(-0.928700\pi\) |
0.679877 | + | 0.733327i | \(0.262033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.869654 | + | 1.50629i | 0.0560194 | + | 0.0970284i | 0.892675 | − | 0.450701i | \(-0.148826\pi\) |
−0.836656 | + | 0.547729i | \(0.815492\pi\) | |||||||
\(242\) | −3.38674 | + | 3.38674i | −0.217708 | + | 0.217708i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.71245i | − | 0.557758i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.80265 | − | 0.483018i | 0.114700 | − | 0.0307337i | ||||
\(248\) | 9.08302 | − | 2.43379i | 0.576773 | − | 0.154546i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.16751i | 0.389290i | 0.980874 | + | 0.194645i | \(0.0623555\pi\) | ||||
−0.980874 | + | 0.194645i | \(0.937645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.8036 | − | 14.8036i | 0.930696 | − | 0.930696i | ||||
\(254\) | 9.74898 | + | 16.8857i | 0.611706 | + | 1.05951i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.51956 | + | 28.0634i | 0.469057 | + | 1.75055i | 0.643075 | + | 0.765803i | \(0.277658\pi\) |
−0.174018 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.5655 | + | 8.98676i | −0.967194 | + | 0.558410i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.17004 | − | 3.17004i | −0.195846 | − | 0.195846i | ||||
\(263\) | −4.82975 | + | 18.0249i | −0.297815 | + | 1.11146i | 0.641141 | + | 0.767424i | \(0.278462\pi\) |
−0.938956 | + | 0.344038i | \(0.888205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.34711 | + | 3.66451i | 0.389167 | + | 0.224685i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.86563 | − | 2.10759i | −0.480470 | − | 0.128742i | ||||
\(269\) | −15.5553 | −0.948425 | −0.474212 | − | 0.880411i | \(-0.657267\pi\) | ||||
−0.474212 | + | 0.880411i | \(0.657267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.87184 | −0.113706 | −0.0568532 | − | 0.998383i | \(-0.518107\pi\) | ||||
−0.0568532 | + | 0.998383i | \(0.518107\pi\) | |||||||
\(272\) | 0.164249 | + | 0.0440105i | 0.00995908 | + | 0.00266853i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.8243 | + | 6.24939i | 0.653918 | + | 0.377540i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.06921 | − | 3.99035i | 0.0642426 | − | 0.239757i | −0.926337 | − | 0.376696i | \(-0.877060\pi\) |
0.990579 | + | 0.136940i | \(0.0437267\pi\) | |||||||
\(278\) | 2.94294 | + | 2.94294i | 0.176506 | + | 0.176506i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.248640 | + | 0.143552i | −0.0148326 | + | 0.00856361i | −0.507398 | − | 0.861712i | \(-0.669393\pi\) |
0.492565 | + | 0.870275i | \(0.336059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.68527 | + | 17.4857i | 0.278510 | + | 1.03941i | 0.953452 | + | 0.301544i | \(0.0975019\pi\) |
−0.674942 | + | 0.737871i | \(0.735831\pi\) | |||||||
\(284\) | −3.47456 | + | 6.01811i | −0.206177 | + | 0.357109i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.96711 | − | 3.40713i | −0.116318 | − | 0.201468i | ||||
\(287\) | −22.7239 | + | 22.7239i | −1.34135 | + | 1.34135i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9711i | 0.998299i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.3070 | − | 3.02970i | 0.661691 | − | 0.177300i | ||||
\(293\) | 20.6663 | − | 5.53752i | 1.20734 | − | 0.323505i | 0.401621 | − | 0.915806i | \(-0.368447\pi\) |
0.805717 | + | 0.592300i | \(0.201780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.62255i | 0.268680i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.732907 | + | 0.732907i | −0.0424562 | + | 0.0424562i | ||||
\(299\) | 2.60820 | + | 4.51754i | 0.150836 | + | 0.261256i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.01100 | − | 6.94725i | 0.231190 | − | 0.400433i | ||||
\(302\) | 1.05314 | + | 3.93037i | 0.0606014 | + | 0.226168i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.63239 | − | 0.942462i | 0.0936241 | − | 0.0540539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2953 | + | 20.2953i | 1.15831 | + | 1.15831i | 0.984838 | + | 0.173476i | \(0.0555001\pi\) |
0.173476 | + | 0.984838i | \(0.444500\pi\) | |||||||
\(308\) | 3.99883 | − | 14.9238i | 0.227855 | − | 0.850365i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9868 | + | 6.92056i | 0.679707 | + | 0.392429i | 0.799745 | − | 0.600340i | \(-0.204968\pi\) |
−0.120038 | + | 0.992769i | \(0.538302\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9081 | − | 4.79847i | −1.01223 | − | 0.271226i | −0.285668 | − | 0.958329i | \(-0.592215\pi\) |
−0.726560 | + | 0.687103i | \(0.758882\pi\) | |||||||
\(314\) | −9.12554 | −0.514984 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5711 | 0.763431 | ||||||||
\(317\) | 0.811966 | + | 0.217566i | 0.0456046 | + | 0.0122197i | 0.281549 | − | 0.959547i | \(-0.409152\pi\) |
−0.235945 | + | 0.971766i | \(0.575818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8399 | − | 8.56781i | −0.830874 | − | 0.479705i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.30208 | + | 19.7876i | −0.295473 | + | 1.10272i | ||||
\(323\) | −0.226641 | − | 0.226641i | −0.0126107 | − | 0.0126107i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.17086 | − | 3.56275i | 0.341772 | − | 0.197322i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.13915 | + | 7.98343i | 0.118115 | + | 0.440811i | ||||
\(329\) | 6.73825 | − | 11.6710i | 0.371492 | − | 0.643443i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.08211 | + | 3.60631i | 0.114443 | + | 0.198221i | 0.917557 | − | 0.397604i | \(-0.130158\pi\) |
−0.803114 | + | 0.595825i | \(0.796825\pi\) | |||||||
\(332\) | 4.94803 | − | 4.94803i | 0.271558 | − | 0.271558i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.8332i | 0.592766i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.13777 | + | 0.840764i | −0.170925 | + | 0.0457993i | −0.343267 | − | 0.939238i | \(-0.611533\pi\) |
0.172341 | + | 0.985037i | \(0.444867\pi\) | |||||||
\(338\) | −11.6102 | + | 3.11093i | −0.631510 | + | 0.169213i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.3656i | 2.02346i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.07470 | + | 3.07470i | −0.166018 | + | 0.166018i | ||||
\(344\) | −1.03157 | − | 1.78674i | −0.0556188 | − | 0.0963346i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.88492 | + | 3.26478i | −0.101334 | + | 0.175516i | ||||
\(347\) | 1.21470 | + | 4.53334i | 0.0652087 | + | 0.243362i | 0.990835 | − | 0.135076i | \(-0.0431279\pi\) |
−0.925627 | + | 0.378438i | \(0.876461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.42818 | − | 4.86601i | 0.451150 | − | 0.260472i | −0.257166 | − | 0.966367i | \(-0.582789\pi\) |
0.708316 | + | 0.705896i | \(0.249455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.80977 | − | 2.80977i | −0.149761 | − | 0.149761i | ||||
\(353\) | −1.32049 | + | 4.92815i | −0.0702827 | + | 0.262299i | −0.992122 | − | 0.125273i | \(-0.960019\pi\) |
0.921840 | + | 0.387572i | \(0.126686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.22474 | + | 2.43916i | 0.223911 | + | 0.129275i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.4559 | + | 3.33754i | 0.658312 | + | 0.176394i | ||||
\(359\) | −1.27697 | −0.0673957 | −0.0336978 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336978 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4471 | 0.813003 | ||||||||
\(362\) | −23.4910 | − | 6.29441i | −1.23466 | − | 0.330827i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.33392 | + | 1.92484i | 0.174745 | + | 0.100889i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.61063 | − | 9.74300i | 0.136274 | − | 0.508581i | −0.863716 | − | 0.503979i | \(-0.831869\pi\) |
0.999989 | − | 0.00460117i | \(-0.00146460\pi\) | |||||||
\(368\) | 3.72549 | + | 3.72549i | 0.194204 | + | 0.194204i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.4564 | − | 10.0785i | 0.906293 | − | 0.523249i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.39374 | + | 12.6656i | 0.175721 | + | 0.655801i | 0.996428 | + | 0.0844507i | \(0.0269135\pi\) |
−0.820706 | + | 0.571350i | \(0.806420\pi\) | |||||||
\(374\) | −0.337843 | + | 0.585162i | −0.0174695 | + | 0.0302580i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.73299 | − | 3.00162i | −0.0893720 | − | 0.154797i | ||||
\(377\) | 3.01907 | − | 3.01907i | 0.155490 | − | 0.155490i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.587648i | 0.0301854i | 0.999886 | + | 0.0150927i | \(0.00480434\pi\) | ||||
−0.999886 | + | 0.0150927i | \(0.995196\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.1652 | − | 3.52759i | 0.673588 | − | 0.180487i | ||||
\(383\) | 14.0071 | − | 3.75319i | 0.715729 | − | 0.191779i | 0.117464 | − | 0.993077i | \(-0.462524\pi\) |
0.598265 | + | 0.801298i | \(0.295857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.2043i | − | 0.824775i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.05794 | − | 1.05794i | 0.0537090 | − | 0.0537090i | ||||
\(389\) | 10.3789 | + | 17.9767i | 0.526230 | + | 0.911456i | 0.999533 | + | 0.0305570i | \(0.00972810\pi\) |
−0.473303 | + | 0.880899i | \(0.656939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.447948 | − | 0.775869i | 0.0226537 | − | 0.0392374i | ||||
\(392\) | 2.10118 | + | 7.84169i | 0.106125 | + | 0.396065i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.42175 | − | 0.820845i | 0.0716265 | − | 0.0413536i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.7430 | − | 15.7430i | −0.790118 | − | 0.790118i | 0.191395 | − | 0.981513i | \(-0.438699\pi\) |
−0.981513 | + | 0.191395i | \(0.938699\pi\) | |||||||
\(398\) | −4.44477 | + | 16.5881i | −0.222796 | + | 0.831487i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.11737 | − | 2.37716i | −0.205612 | − | 0.118710i | 0.393659 | − | 0.919257i | \(-0.371209\pi\) |
−0.599270 | + | 0.800547i | \(0.704543\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.99298 | − | 2.40966i | −0.447972 | − | 0.120034i | ||||
\(404\) | 10.2993 | 0.512408 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.7674 | 0.832153 | ||||||||
\(407\) | −17.7423 | − | 4.75404i | −0.879454 | − | 0.235649i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.8797 | − | 14.9417i | −1.27967 | − | 0.738817i | −0.302882 | − | 0.953028i | \(-0.597949\pi\) |
−0.976787 | + | 0.214211i | \(0.931282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.67823 | − | 6.26326i | 0.0826807 | − | 0.308568i | ||||
\(413\) | −15.0049 | − | 15.0049i | −0.738343 | − | 0.738343i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.857441 | − | 0.495044i | 0.0420395 | − | 0.0242715i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.93854 | + | 7.23474i | 0.0948172 | + | 0.353863i | ||||
\(419\) | −8.81638 | + | 15.2704i | −0.430708 | + | 0.746009i | −0.996934 | − | 0.0782412i | \(-0.975070\pi\) |
0.566226 | + | 0.824250i | \(0.308403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9462 | + | 24.1555i | 0.679696 | + | 1.17727i | 0.975072 | + | 0.221887i | \(0.0712215\pi\) |
−0.295377 | + | 0.955381i | \(0.595445\pi\) | |||||||
\(422\) | 12.8820 | − | 12.8820i | 0.627085 | − | 0.627085i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 5.18410i | − | 0.251762i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.7217 | + | 8.76775i | −1.58351 | + | 0.424301i | ||||
\(428\) | −5.05507 | + | 1.35450i | −0.244346 | + | 0.0654723i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.2910i | 0.929215i | 0.885517 | + | 0.464608i | \(0.153805\pi\) | ||||
−0.885517 | + | 0.464608i | \(0.846195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7154 | + | 16.7154i | −0.803292 | + | 0.803292i | −0.983609 | − | 0.180316i | \(-0.942288\pi\) |
0.180316 | + | 0.983609i | \(0.442288\pi\) | |||||||
\(434\) | −18.2814 | − | 31.6642i | −0.877533 | − | 1.51993i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.65080 | + | 6.32337i | −0.174842 | + | 0.302835i | ||||
\(437\) | −2.57033 | − | 9.59259i | −0.122955 | − | 0.458876i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.1811 | + | 18.0024i | −1.48819 | + | 0.859209i | −0.999909 | − | 0.0134750i | \(-0.995711\pi\) |
−0.488285 | + | 0.872684i | \(0.662377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.119047 | − | 0.119047i | −0.00566249 | − | 0.00566249i | ||||
\(443\) | −6.94511 | + | 25.9195i | −0.329972 | + | 1.23147i | 0.579246 | + | 0.815153i | \(0.303347\pi\) |
−0.909218 | + | 0.416320i | \(0.863320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.06659 | − | 2.34785i | −0.192559 | − | 0.111174i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.75574 | + | 1.00635i | 0.177442 | + | 0.0475455i | ||||
\(449\) | 41.3392 | 1.95092 | 0.975459 | − | 0.220182i | \(-0.0706652\pi\) | ||||
0.975459 | + | 0.220182i | \(0.0706652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.8421 | −1.54647 | ||||||||
\(452\) | −4.07557 | − | 1.09205i | −0.191699 | − | 0.0513655i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.6778 | − | 12.5157i | −1.01739 | − | 0.587390i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.58827 | + | 20.8557i | −0.261408 | + | 0.975589i | 0.703004 | + | 0.711186i | \(0.251842\pi\) |
−0.964412 | + | 0.264403i | \(0.914825\pi\) | |||||||
\(458\) | −16.1135 | − | 16.1135i | −0.752935 | − | 0.752935i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8706 | − | 6.27615i | 0.506295 | − | 0.292309i | −0.225015 | − | 0.974355i | \(-0.572243\pi\) |
0.731309 | + | 0.682046i | \(0.238910\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.72110 | − | 21.3514i | −0.265882 | − | 0.992286i | −0.961708 | − | 0.274076i | \(-0.911628\pi\) |
0.695826 | − | 0.718210i | \(-0.255038\pi\) | |||||||
\(464\) | 2.15618 | − | 3.73461i | 0.100098 | − | 0.173375i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.6011 | + | 25.2899i | 0.676383 | + | 1.17153i | ||||
\(467\) | 3.48137 | − | 3.48137i | 0.161099 | − | 0.161099i | −0.621955 | − | 0.783053i | \(-0.713661\pi\) |
0.783053 | + | 0.621955i | \(0.213661\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.6622i | 1.46203i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.27158 | + | 1.41251i | −0.242644 | + | 0.0650163i | ||||
\(473\) | 7.91881 | − | 2.12184i | 0.364107 | − | 0.0975622i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.661168i | − | 0.0303046i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.45273 | − | 6.45273i | 0.295141 | − | 0.295141i | ||||
\(479\) | 1.35673 | + | 2.34993i | 0.0619906 | + | 0.107371i | 0.895355 | − | 0.445353i | \(-0.146922\pi\) |
−0.833364 | + | 0.552724i | \(0.813588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.28836 | − | 3.96356i | 0.104340 | − | 0.180723i | ||||
\(482\) | −0.450166 | − | 1.68004i | −0.0205045 | − | 0.0765239i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.14790 | − | 2.39479i | 0.188541 | − | 0.108854i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.20799 | + | 8.20799i | 0.371940 | + | 0.371940i | 0.868183 | − | 0.496244i | \(-0.165288\pi\) |
−0.496244 | + | 0.868183i | \(0.665288\pi\) | |||||||
\(488\) | −2.25495 | + | 8.41558i | −0.102077 | + | 0.380955i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.28058 | − | 2.47139i | −0.193180 | − | 0.111532i | 0.400290 | − | 0.916388i | \(-0.368909\pi\) |
−0.593470 | + | 0.804856i | \(0.702243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.708301 | − | 0.189789i | −0.0319003 | − | 0.00854766i | ||||
\(494\) | −1.86624 | −0.0839661 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.40344 | −0.422227 | ||||||||
\(497\) | 26.0991 | + | 6.99322i | 1.17070 | + | 0.313689i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.1148 | + | 16.2321i | 1.25859 | + | 0.726649i | 0.972801 | − | 0.231643i | \(-0.0744102\pi\) |
0.285791 | + | 0.958292i | \(0.407744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.59627 | − | 5.95736i | 0.0712450 | − | 0.265890i | ||||
\(503\) | 19.6817 | + | 19.6817i | 0.877565 | + | 0.877565i | 0.993282 | − | 0.115717i | \(-0.0369166\pi\) |
−0.115717 | + | 0.993282i | \(0.536917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.1307 | + | 10.4677i | −0.806007 | + | 0.465348i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.04645 | − | 18.8336i | −0.223900 | − | 0.835606i | ||||
\(509\) | 5.25069 | − | 9.09446i | 0.232733 | − | 0.403105i | −0.725879 | − | 0.687823i | \(-0.758567\pi\) |
0.958611 | + | 0.284718i | \(0.0918999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.7575 | − | 39.4171i | −1.00673 | − | 1.74371i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 29.0534i | − | 1.28149i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3031 | − | 3.56457i | 0.585072 | − | 0.156770i | ||||
\(518\) | 17.3611 | − | 4.65189i | 0.762802 | − | 0.204392i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.2545i | − | 1.23785i | −0.785450 | − | 0.618925i | \(-0.787568\pi\) | ||
0.785450 | − | 0.618925i | \(-0.212432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6590 | + | 13.6590i | −0.597266 | + | 0.597266i | −0.939584 | − | 0.342318i | \(-0.888788\pi\) |
0.342318 | + | 0.939584i | \(0.388788\pi\) | |||||||
\(524\) | 2.24156 | + | 3.88249i | 0.0979230 | + | 0.169608i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.33036 | − | 16.1607i | 0.406823 | − | 0.704638i | ||||
\(527\) | 0.413850 | + | 1.54451i | 0.0180276 | + | 0.0672798i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.12099 | − | 2.37925i | 0.179173 | − | 0.103446i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.18240 | − | 5.18240i | −0.224685 | − | 0.224685i | ||||
\(533\) | 2.11795 | − | 7.90429i | 0.0917385 | − | 0.342373i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.05213 | + | 4.07155i | 0.304606 | + | 0.175864i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0253 | + | 4.02601i | 0.647786 | + | 0.173574i | ||||
\(539\) | −32.2590 | −1.38949 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7216 | −1.14885 | −0.574427 | − | 0.818556i | \(-0.694775\pi\) | ||||
−0.574427 | + | 0.818556i | \(0.694775\pi\) | |||||||
\(542\) | 1.80806 | + | 0.484468i | 0.0776628 | + | 0.0208097i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.147262 | − | 0.0850217i | −0.00631380 | − | 0.00364528i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.0627654 | + | 0.234244i | −0.00268365 | + | 0.0100155i | −0.967255 | − | 0.253808i | \(-0.918317\pi\) |
0.964571 | + | 0.263823i | \(0.0849836\pi\) | |||||||
\(548\) | −8.83798 | − | 8.83798i | −0.377540 | − | 0.377540i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.03946 | + | 4.06423i | −0.299891 | + | 0.173142i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6572 | − | 50.9693i | −0.580763 | − | 2.16744i | ||||
\(554\) | −2.06556 | + | 3.57765i | −0.0877571 | + | 0.152000i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.08097 | − | 3.60435i | −0.0882528 | − | 0.152858i | ||||
\(557\) | 31.4838 | − | 31.4838i | 1.33401 | − | 1.33401i | 0.432266 | − | 0.901746i | \(-0.357714\pi\) |
0.901746 | − | 0.432266i | \(-0.142286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.04270i | 0.0863969i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.277322 | − | 0.0743081i | 0.0116981 | − | 0.00313450i | ||||
\(563\) | 31.1771 | − | 8.35388i | 1.31396 | − | 0.352074i | 0.467247 | − | 0.884127i | \(-0.345246\pi\) |
0.846711 | + | 0.532053i | \(0.178579\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 18.1025i | − | 0.760904i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.91376 | − | 4.91376i | 0.206177 | − | 0.206177i | ||||
\(569\) | 16.1545 | + | 27.9804i | 0.677232 | + | 1.17300i | 0.975811 | + | 0.218615i | \(0.0701538\pi\) |
−0.298580 | + | 0.954385i | \(0.596513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9565 | − | 22.4413i | 0.542213 | − | 0.939141i | −0.456563 | − | 0.889691i | \(-0.650920\pi\) |
0.998777 | − | 0.0494501i | \(-0.0157469\pi\) | |||||||
\(572\) | 1.01825 | + | 3.80016i | 0.0425752 | + | 0.158893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.8310 | − | 16.0682i | 1.16164 | − | 0.670674i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.10724 | − | 6.10724i | −0.254248 | − | 0.254248i | 0.568462 | − | 0.822710i | \(-0.307539\pi\) |
−0.822710 | + | 0.568462i | \(0.807539\pi\) | |||||||
\(578\) | 4.39244 | − | 16.3928i | 0.182701 | − | 0.681851i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.5629 | − | 13.6041i | −0.977556 | − | 0.564392i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.8977 | + | 5.33157i | 0.824077 | + | 0.220811i | ||||
\(584\) | −11.7058 | −0.484391 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.3953 | −0.883833 | ||||||||
\(587\) | 1.83025 | + | 0.490414i | 0.0755424 | + | 0.0202415i | 0.296392 | − | 0.955066i | \(-0.404216\pi\) |
−0.220850 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.3501 | + | 8.86238i | 0.632490 | + | 0.365168i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.19640 | − | 4.46504i | 0.0491719 | − | 0.183512i | ||||
\(593\) | −11.0077 | − | 11.0077i | −0.452033 | − | 0.452033i | 0.443996 | − | 0.896029i | \(-0.353561\pi\) |
−0.896029 | + | 0.443996i | \(0.853561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.897625 | − | 0.518244i | 0.0367681 | − | 0.0212281i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.35011 | − | 5.03866i | −0.0552099 | − | 0.206046i | ||||
\(599\) | 12.9428 | − | 22.4176i | 0.528828 | − | 0.915957i | −0.470607 | − | 0.882343i | \(-0.655965\pi\) |
0.999435 | − | 0.0336142i | \(-0.0107018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.79604 | − | 16.9672i | −0.399589 | − | 0.692108i | 0.594086 | − | 0.804401i | \(-0.297514\pi\) |
−0.993675 | + | 0.112293i | \(0.964180\pi\) | |||||||
\(602\) | −5.67241 | + | 5.67241i | −0.231190 | + | 0.231190i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.06902i | − | 0.165566i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.7731 | − | 7.70972i | 1.16786 | − | 0.312928i | 0.377761 | − | 0.925903i | \(-0.376694\pi\) |
0.790102 | + | 0.612975i | \(0.210027\pi\) | |||||||
\(608\) | −1.82070 | + | 0.487854i | −0.0738390 | + | 0.0197851i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.43162i | 0.138828i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5028 | − | 12.5028i | 0.504982 | − | 0.504982i | −0.408000 | − | 0.912982i | \(-0.633774\pi\) |
0.912982 | + | 0.408000i | \(0.133774\pi\) | |||||||
\(614\) | −14.3510 | − | 24.8566i | −0.579157 | − | 1.00313i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.72515 | + | 13.3804i | −0.311255 | + | 0.539110i | ||||
\(617\) | −1.91482 | − | 7.14621i | −0.0770878 | − | 0.287695i | 0.916611 | − | 0.399781i | \(-0.130914\pi\) |
−0.993699 | + | 0.112085i | \(0.964247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4624 | − | 9.50460i | 0.661682 | − | 0.382022i | −0.131236 | − | 0.991351i | \(-0.541895\pi\) |
0.792917 | + | 0.609329i | \(0.208561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.78715 | − | 9.78715i | −0.392429 | − | 0.392429i | ||||
\(623\) | 4.90928 | − | 18.3217i | 0.196686 | − | 0.734043i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.0560 | + | 9.26994i | 0.641727 | + | 0.370501i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.81460 | + | 2.36186i | 0.351741 | + | 0.0942486i | ||||
\(629\) | −0.786034 | −0.0313412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.22853 | −0.0887165 | −0.0443583 | − | 0.999016i | \(-0.514124\pi\) | ||||
−0.0443583 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(632\) | −13.1086 | − | 3.51245i | −0.521433 | − | 0.139718i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.727989 | − | 0.420305i | −0.0289121 | − | 0.0166924i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.08035 | − | 7.76396i | 0.0824263 | − | 0.307619i | ||||
\(638\) | 12.1167 | + | 12.1167i | 0.479705 | + | 0.479705i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.8297 | + | 21.8410i | −1.49418 | + | 0.862666i | −0.999978 | − | 0.00667968i | \(-0.997874\pi\) |
−0.494204 | + | 0.869346i | \(0.664540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.89483 | + | 29.4639i | 0.311342 | + | 1.16194i | 0.927347 | + | 0.374202i | \(0.122083\pi\) |
−0.616006 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(644\) | 10.2428 | − | 17.7411i | 0.403624 | − | 0.699097i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.160260 | + | 0.277578i | 0.00630533 | + | 0.0109211i | ||||
\(647\) | −4.02651 | + | 4.02651i | −0.158298 | + | 0.158298i | −0.781812 | − | 0.623514i | \(-0.785704\pi\) |
0.623514 | + | 0.781812i | \(0.285704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.6861i | − | 0.851255i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.88270 | + | 1.84421i | −0.269547 | + | 0.0722249i | ||||
\(653\) | −31.5015 | + | 8.44081i | −1.23275 | + | 0.330314i | −0.815650 | − | 0.578546i | \(-0.803620\pi\) |
−0.417100 | + | 0.908861i | \(0.636954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.26506i | − | 0.322696i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.52933 | + | 9.52933i | −0.371492 | + | 0.371492i | ||||
\(659\) | −7.75612 | − | 13.4340i | −0.302136 | − | 0.523314i | 0.674484 | − | 0.738290i | \(-0.264366\pi\) |
−0.976619 | + | 0.214975i | \(0.931033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.1307 | − | 19.2789i | 0.432933 | − | 0.749862i | −0.564191 | − | 0.825644i | \(-0.690812\pi\) |
0.997124 | + | 0.0757821i | \(0.0241453\pi\) | |||||||
\(662\) | −1.07778 | − | 4.02232i | −0.0418890 | − | 0.156332i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.06007 | + | 3.49878i | −0.235176 | + | 0.135779i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.0656 | − | 16.0656i | −0.622063 | − | 0.622063i | ||||
\(668\) | 2.80384 | − | 10.4641i | 0.108484 | − | 0.404867i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.9817 | − | 17.3099i | −1.15743 | − | 0.668243i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.32657 | + | 2.49905i | 0.359513 | + | 0.0963312i | 0.434054 | − | 0.900887i | \(-0.357083\pi\) |
−0.0745413 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(674\) | 3.24846 | 0.125126 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0197 | 0.462297 | ||||||||
\(677\) | 7.30994 | + | 1.95869i | 0.280944 | + | 0.0752787i | 0.396539 | − | 0.918018i | \(-0.370211\pi\) |
−0.115596 | + | 0.993296i | \(0.536878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.03802 | − | 2.90870i | −0.193342 | − | 0.111626i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.67093 | − | 36.0924i | 0.370319 | − | 1.38205i | ||||
\(683\) | 7.48288 | + | 7.48288i | 0.286325 | + | 0.286325i | 0.835625 | − | 0.549300i | \(-0.185106\pi\) |
−0.549300 | + | 0.835625i | \(0.685106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.76572 | − | 2.17414i | 0.143776 | − | 0.0830090i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.533983 | + | 1.99285i | 0.0203579 | + | 0.0759767i | ||||
\(689\) | −2.56635 | + | 4.44506i | −0.0977703 | + | 0.169343i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3061 | + | 36.9033i | 0.810523 | + | 1.40387i | 0.912498 | + | 0.409080i | \(0.134150\pi\) |
−0.101975 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(692\) | 2.66569 | − | 2.66569i | 0.101334 | − | 0.101334i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4.69326i | − | 0.178154i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.35753 | + | 0.363749i | −0.0514201 | + | 0.0137780i | ||||
\(698\) | −9.40041 | + | 2.51883i | −0.355811 | + | 0.0953392i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.3602i | − | 1.37331i | −0.726985 | − | 0.686653i | \(-0.759079\pi\) | ||
0.726985 | − | 0.686653i | \(-0.240921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.16113 | + | 6.16113i | −0.232371 | + | 0.232371i | ||||
\(704\) | 1.98681 | + | 3.44125i | 0.0748805 | + | 0.129697i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.55100 | − | 4.41846i | 0.0960080 | − | 0.166291i | ||||
\(707\) | −10.3647 | − | 38.6814i | −0.389803 | − | 1.45476i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.356646 | + | 0.205910i | −0.0133941 | + | 0.00773310i | −0.506682 | − | 0.862133i | \(-0.669128\pi\) |
0.493288 | + | 0.869866i | \(0.335795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.44949 | − | 3.44949i | −0.129275 | − | 0.129275i | ||||
\(713\) | −12.8227 | + | 47.8551i | −0.480215 | + | 1.79219i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.1676 | − | 6.44762i | −0.417353 | − | 0.240959i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.23345 | + | 0.330503i | 0.0460321 | + | 0.0123343i | ||||
\(719\) | 34.4664 | 1.28538 | 0.642690 | − | 0.766126i | \(-0.277818\pi\) | ||||
0.642690 | + | 0.766126i | \(0.277818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.2120 | −0.938946 | ||||||||
\(722\) | −14.9207 | − | 3.99799i | −0.555291 | − | 0.148790i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.0615 | + | 12.1599i | 0.782744 | + | 0.451918i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.69508 | + | 13.7902i | −0.137043 | + | 0.511451i | 0.862938 | + | 0.505310i | \(0.168622\pi\) |
−0.999981 | + | 0.00614188i | \(0.998045\pi\) | |||||||
\(728\) | −2.72214 | − | 2.72214i | −0.100889 | − | 0.100889i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.303823 | − | 0.175413i | 0.0112373 | − | 0.00648787i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.94942 | − | 29.6676i | −0.293618 | − | 1.09580i | −0.942308 | − | 0.334746i | \(-0.891349\pi\) |
0.648690 | − | 0.761053i | \(-0.275317\pi\) | |||||||
\(734\) | −5.04335 | + | 8.73534i | −0.186153 | + | 0.322427i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.63432 | − | 4.56277i | −0.0971022 | − | 0.168186i | ||||
\(737\) | −22.8802 | + | 22.8802i | −0.842803 | + | 0.842803i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.6312i | − | 0.722144i | −0.932538 | − | 0.361072i | \(-0.882411\pi\) | ||
0.932538 | − | 0.361072i | \(-0.117589\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4701 | + | 5.21700i | −0.714771 | + | 0.191522i | ||||
\(743\) | −34.7672 | + | 9.31585i | −1.27549 | + | 0.341765i | −0.832130 | − | 0.554580i | \(-0.812879\pi\) |
−0.443356 | + | 0.896346i | \(0.646212\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 13.1124i | − | 0.480080i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.477782 | − | 0.477782i | 0.0174695 | − | 0.0174695i | ||||
\(749\) | 10.1743 | + | 17.6224i | 0.371761 | + | 0.643910i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4567 | + | 42.3603i | −0.892438 | + | 1.54575i | −0.0554938 | + | 0.998459i | \(0.517673\pi\) |
−0.836944 | + | 0.547289i | \(0.815660\pi\) | |||||||
\(752\) | 0.897060 | + | 3.34787i | 0.0327124 | + | 0.122084i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.69759 | + | 2.13480i | −0.134658 | + | 0.0777449i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9129 | − | 22.9129i | −0.832783 | − | 0.832783i | 0.155114 | − | 0.987897i | \(-0.450426\pi\) |
−0.987897 | + | 0.155114i | \(0.950426\pi\) | |||||||
\(758\) | 0.152094 | − | 0.567624i | 0.00552432 | − | 0.0206170i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.19124 | + | 5.30657i | 0.333182 | + | 0.192363i | 0.657253 | − | 0.753670i | \(-0.271718\pi\) |
−0.324071 | + | 0.946033i | \(0.605052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4229 | + | 7.34795i | 0.992777 | + | 0.266014i | ||||
\(764\) | −13.6296 | −0.493100 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.5012 | −0.523950 | ||||||||
\(767\) | 5.21932 | + | 1.39851i | 0.188459 | + | 0.0504974i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.31814 | − | 1.91573i | −0.119655 | − | 0.0690830i | 0.438978 | − | 0.898498i | \(-0.355341\pi\) |
−0.558633 | + | 0.829415i | \(0.688674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.19397 | + | 15.6521i | −0.150944 | + | 0.563332i | ||||
\(773\) | 19.8976 | + | 19.8976i | 0.715668 | + | 0.715668i | 0.967715 | − | 0.252047i | \(-0.0811037\pi\) |
−0.252047 | + | 0.967715i | \(0.581104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.29571 | + | 0.748079i | −0.0465133 | + | 0.0268545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.37250 | − | 20.0504i | −0.192613 | − | 0.718843i | ||||
\(779\) | −7.78950 | + | 13.4918i | −0.279088 | + | 0.483395i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8065 | + | 23.9136i | 0.494036 | + | 0.855696i | ||||
\(782\) | −0.633495 | + | 0.633495i | −0.0226537 | + | 0.0226537i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 8.11832i | − | 0.289940i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.98473 | + | 1.87155i | −0.248979 | + | 0.0667137i | −0.381150 | − | 0.924513i | \(-0.624472\pi\) |
0.132171 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(788\) | −1.58575 | + | 0.424901i | −0.0564901 | + | 0.0151365i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4058i | 0.583321i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.09956 | − | 6.09956i | 0.216602 | − | 0.216602i | ||||
\(794\) | 11.1320 | + | 19.2811i | 0.395059 | + | 0.684262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.58664 | − | 14.8725i | 0.304345 | − | 0.527142i | ||||
\(797\) | −8.96012 | − | 33.4396i | −0.317384 | − | 1.18449i | −0.921750 | − | 0.387786i | \(-0.873240\pi\) |
0.604366 | − | 0.796707i | \(-0.293427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.510406 | − | 0.294683i | 0.0180569 | − | 0.0104251i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.36182 | + | 3.36182i | 0.118710 | + | 0.118710i | ||||
\(803\) | 12.0388 | − | 44.9295i | 0.424841 | − | 1.58553i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.06289 | + | 4.65511i | 0.284003 | + | 0.163969i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.94834 | − | 2.66565i | −0.349981 | − | 0.0937772i | ||||
\(809\) | −52.6028 | −1.84942 | −0.924709 | − | 0.380675i | \(-0.875692\pi\) | ||||
−0.924709 | + | 0.380675i | \(0.875692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8979 | −0.488021 | −0.244011 | − | 0.969773i | \(-0.578463\pi\) | ||||
−0.244011 | + | 0.969773i | \(0.578463\pi\) | |||||||
\(812\) | −16.1961 | − | 4.33973i | −0.568371 | − | 0.152295i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.9073 | + | 9.18410i | 0.557551 | + | 0.321902i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.00652 | − | 3.75637i | 0.0352136 | − | 0.131419i | ||||
\(818\) | 21.1307 | + | 21.1307i | 0.738817 | + | 0.738817i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.9657 | − | 13.8366i | 0.836408 | − | 0.482900i | −0.0196338 | − | 0.999807i | \(-0.506250\pi\) |
0.856042 | + | 0.516907i | \(0.172917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.80049 | + | 29.1118i | 0.271908 | + | 1.01477i | 0.957885 | + | 0.287151i | \(0.0927083\pi\) |
−0.685977 | + | 0.727623i | \(0.740625\pi\) | |||||||
\(824\) | −3.24210 | + | 5.61548i | −0.112944 | + | 0.195625i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.6101 | + | 18.3772i | 0.369172 | + | 0.639424i | ||||
\(827\) | 4.09863 | − | 4.09863i | 0.142523 | − | 0.142523i | −0.632245 | − | 0.774768i | \(-0.717866\pi\) |
0.774768 | + | 0.632245i | \(0.217866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.6756i | − | 1.30853i | −0.756266 | − | 0.654264i | \(-0.772979\pi\) | ||
0.756266 | − | 0.654264i | \(-0.227021\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.956351 | + | 0.256253i | −0.0331555 | + | 0.00888399i | ||||
\(833\) | −1.33343 | + | 0.357291i | −0.0462006 | + | 0.0123794i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 7.48995i | − | 0.259046i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.4682 | − | 12.4682i | 0.430708 | − | 0.430708i | ||||
\(839\) | −16.5639 | − | 28.6895i | −0.571849 | − | 0.990471i | −0.996376 | − | 0.0850559i | \(-0.972893\pi\) |
0.424527 | − | 0.905415i | \(-0.360440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.20180 | − | 9.00978i | 0.179372 | − | 0.310682i | ||||
\(842\) | −7.21908 | − | 26.9420i | −0.248786 | − | 0.928482i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.7771 | + | 9.10894i | −0.543072 | + | 0.313543i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1684 | − | 13.1684i | −0.452472 | − | 0.452472i | ||||
\(848\) | −1.34174 | + | 5.00745i | −0.0460757 | + | 0.171957i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0916 | − | 12.1773i | −0.723011 | − | 0.417431i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.57386 | + | 0.689663i | 0.0881273 | + | 0.0236136i | 0.302613 | − | 0.953113i | \(-0.402141\pi\) |
−0.214486 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(854\) | 33.8760 | 1.15921 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.23339 | 0.178874 | ||||||||
\(857\) | 15.1284 | + | 4.05364i | 0.516776 | + | 0.138470i | 0.507775 | − | 0.861490i | \(-0.330468\pi\) |
0.00900123 | + | 0.999959i | \(0.497135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.691191 | + | 0.399059i | 0.0235831 | + | 0.0136157i | 0.511745 | − | 0.859137i | \(-0.328999\pi\) |
−0.488162 | + | 0.872753i | \(0.662333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.99288 | − | 18.6337i | 0.170058 | − | 0.634666i | ||||
\(863\) | 30.2854 | + | 30.2854i | 1.03093 | + | 1.03093i | 0.999506 | + | 0.0314193i | \(0.0100027\pi\) |
0.0314193 | + | 0.999506i | \(0.489997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.4721 | − | 11.8196i | 0.695671 | − | 0.401646i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.46313 | + | 35.3169i | 0.321199 | + | 1.19873i | ||||
\(869\) | 26.9630 | − | 46.7013i | 0.914658 | − | 1.58423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.03119 | − | 6.98222i | −0.136592 | − | 0.236584i | ||||
\(872\) | 5.16301 | − | 5.16301i | 0.174842 | − | 0.174842i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.93098i | 0.335920i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7435 | − | 4.48641i | 0.565388 | − | 0.151495i | 0.0352074 | − | 0.999380i | \(-0.488791\pi\) |
0.530180 | + | 0.847885i | \(0.322124\pi\) | |||||||
\(878\) | 34.7780 | − | 9.31875i | 1.17370 | − | 0.314492i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.1033i | − | 0.508843i | −0.967093 | − | 0.254421i | \(-0.918115\pi\) | ||
0.967093 | − | 0.254421i | \(-0.0818850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4678 | − | 16.4678i | 0.554185 | − | 0.554185i | −0.373461 | − | 0.927646i | \(-0.621829\pi\) |
0.927646 | + | 0.373461i | \(0.121829\pi\) | |||||||
\(884\) | 0.0841789 | + | 0.145802i | 0.00283124 | + | 0.00490386i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.4169 | − | 23.2388i | 0.450750 | − | 0.780723i | ||||
\(887\) | 7.07714 | + | 26.4123i | 0.237627 | + | 0.886837i | 0.976947 | + | 0.213482i | \(0.0684806\pi\) |
−0.739320 | + | 0.673355i | \(0.764853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.6556 | + | 37.9063i | −2.20202 | + | 1.27134i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.32036 | + | 3.32036i | 0.111174 | + | 0.111174i | ||||
\(893\) | 1.69089 | − | 6.31049i | 0.0565835 | − | 0.211173i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.36730 | − | 1.94411i | −0.112494 | − | 0.0649483i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.9306 | − | 10.6994i | −1.33250 | − | 0.357043i | ||||
\(899\) | 40.5510 | 1.35245 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.881522 | 0.0293678 | ||||||||
\(902\) | 31.7230 | + | 8.50016i | 1.05626 | + | 0.283025i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.65405 | + | 2.10967i | 0.121532 | + | 0.0701666i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.62626 | + | 24.7295i | −0.220021 | + | 0.821130i | 0.764317 | + | 0.644841i | \(0.223076\pi\) |
−0.984338 | + | 0.176290i | \(0.943590\pi\) | |||||||
\(908\) | 17.6998 | + | 17.6998i | 0.587390 | + | 0.587390i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.55075 | + | 2.05003i | −0.117642 | + | 0.0679204i | −0.557666 | − | 0.830065i | \(-0.688303\pi\) |
0.440025 | + | 0.897986i | \(0.354970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.19662 | − | 26.8582i | −0.238173 | − | 0.888875i | ||||
\(914\) | 10.7957 | − | 18.6987i | 0.357090 | − | 0.618499i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.3940 | + | 19.7350i | 0.376468 | + | 0.652061i | ||||
\(917\) | 12.3259 | − | 12.3259i | 0.407035 | − | 0.407035i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8740i | 0.952464i | 0.879320 | + | 0.476232i | \(0.157998\pi\) | ||||
−0.879320 | + | 0.476232i | \(0.842002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.1246 | + | 3.24877i | −0.399302 | + | 0.106993i | ||||
\(923\) | −6.64579 | + | 1.78073i | −0.218749 | + | 0.0586135i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.1046i | 0.726404i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.04930 | + | 3.04930i | −0.100098 | + | 0.100098i | ||||
\(929\) | 25.1077 | + | 43.4879i | 0.823758 | + | 1.42679i | 0.902865 | + | 0.429925i | \(0.141460\pi\) |
−0.0791067 | + | 0.996866i | \(0.525207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.65121 | + | 13.2523i | −0.250758 | + | 0.434326i | ||||
\(932\) | −7.55809 | − | 28.2072i | −0.247573 | − | 0.923956i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.26380 | + | 2.46170i | −0.139516 | + | 0.0805494i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.857094 | + | 0.857094i | 0.0280000 | + | 0.0280000i | 0.720968 | − | 0.692968i | \(-0.243697\pi\) |
−0.692968 | + | 0.720968i | \(0.743697\pi\) | |||||||
\(938\) | 8.19479 | − | 30.5834i | 0.267569 | − | 0.998582i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.4478 | + | 25.0846i | 1.41636 | + | 0.817735i | 0.995977 | − | 0.0896119i | \(-0.0285627\pi\) |
0.420382 | + | 0.907347i | \(0.361896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.0618 | − | 11.2704i | −1.36972 | − | 0.367015i | ||||
\(944\) | 5.45754 | 0.177628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.19815 | −0.266545 | ||||||||
\(947\) | 2.54334 | + | 0.681485i | 0.0826473 | + | 0.0221453i | 0.299906 | − | 0.953969i | \(-0.403045\pi\) |
−0.217258 | + | 0.976114i | \(0.569711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0371 | + | 5.79490i | 0.325817 | + | 0.188111i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.171123 | + | 0.638639i | −0.00554612 | + | 0.0206984i | ||||
\(953\) | −28.1499 | − | 28.1499i | −0.911864 | − | 0.911864i | 0.0845545 | − | 0.996419i | \(-0.473053\pi\) |
−0.996419 | + | 0.0845545i | \(0.973053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.90295 | + | 4.56277i | −0.255600 | + | 0.147571i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.702296 | − | 2.62100i | −0.0226901 | − | 0.0846808i | ||||
\(959\) | −24.2991 | + | 42.0872i | −0.784658 | + | 1.35907i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7123 | − | 49.7312i | −0.926204 | − | 1.60423i | ||||
\(962\) | −3.23623 | + | 3.23623i | −0.104340 | + | 0.104340i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.73931i | 0.0560194i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.28319 | + | 0.343829i | −0.0412646 | + | 0.0110568i | −0.279392 | − | 0.960177i | \(-0.590133\pi\) |
0.238128 | + | 0.971234i | \(0.423466\pi\) | |||||||
\(968\) | −4.62638 | + | 1.23963i | −0.148697 | + | 0.0398433i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.7906i | 1.24485i | 0.782679 | + | 0.622425i | \(0.213853\pi\) | ||||
−0.782679 | + | 0.622425i | \(0.786147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4428 | + | 11.4428i | −0.366840 | + | 0.366840i | ||||
\(974\) | −5.80393 | − | 10.0527i | −0.185970 | − | 0.322109i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.35623 | − | 7.54520i | 0.139439 | − | 0.241516i | ||||
\(977\) | 11.0953 | + | 41.4084i | 0.354972 | + | 1.32477i | 0.880520 | + | 0.474009i | \(0.157193\pi\) |
−0.525548 | + | 0.850764i | \(0.676140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.7875 | − | 9.69226i | 0.536530 | − | 0.309766i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.49508 | + | 3.49508i | 0.111532 | + | 0.111532i | ||||
\(983\) | 8.34182 | − | 31.1321i | 0.266063 | − | 0.992960i | −0.695534 | − | 0.718493i | \(-0.744832\pi\) |
0.961597 | − | 0.274466i | \(-0.0885012\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.635046 | + | 0.366644i | 0.0202240 | + | 0.0116763i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.80265 | + | 0.483018i | 0.0573499 | + | 0.0153669i | ||||
\(989\) | 10.8700 | 0.345645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1017 | 0.638551 | 0.319275 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319275 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(992\) | 9.08302 | + | 2.43379i | 0.288386 | + | 0.0772729i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.3998 | − | 13.5099i | −0.742196 | − | 0.428507i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.763421 | + | 2.84912i | −0.0241778 | + | 0.0902327i | −0.976960 | − | 0.213420i | \(-0.931540\pi\) |
0.952783 | + | 0.303653i | \(0.0982063\pi\) | |||||||
\(998\) | −22.9557 | − | 22.9557i | −0.726649 | − | 0.726649i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.2.q.h.557.2 | 16 | ||
3.2 | odd | 2 | 450.2.p.h.257.4 | 16 | |||
5.2 | odd | 4 | 270.2.m.b.233.3 | 16 | |||
5.3 | odd | 4 | inner | 1350.2.q.h.1043.1 | 16 | ||
5.4 | even | 2 | 270.2.m.b.17.4 | 16 | |||
9.2 | odd | 6 | inner | 1350.2.q.h.1007.1 | 16 | ||
9.7 | even | 3 | 450.2.p.h.407.4 | 16 | |||
15.2 | even | 4 | 90.2.l.b.23.1 | ✓ | 16 | ||
15.8 | even | 4 | 450.2.p.h.293.4 | 16 | |||
15.14 | odd | 2 | 90.2.l.b.77.1 | yes | 16 | ||
45.2 | even | 12 | 270.2.m.b.143.4 | 16 | |||
45.4 | even | 6 | 810.2.f.c.647.1 | 16 | |||
45.7 | odd | 12 | 90.2.l.b.83.1 | yes | 16 | ||
45.14 | odd | 6 | 810.2.f.c.647.8 | 16 | |||
45.22 | odd | 12 | 810.2.f.c.323.8 | 16 | |||
45.29 | odd | 6 | 270.2.m.b.197.3 | 16 | |||
45.32 | even | 12 | 810.2.f.c.323.1 | 16 | |||
45.34 | even | 6 | 90.2.l.b.47.1 | yes | 16 | ||
45.38 | even | 12 | inner | 1350.2.q.h.143.2 | 16 | ||
45.43 | odd | 12 | 450.2.p.h.443.4 | 16 | |||
60.47 | odd | 4 | 720.2.cu.b.113.3 | 16 | |||
60.59 | even | 2 | 720.2.cu.b.257.4 | 16 | |||
180.7 | even | 12 | 720.2.cu.b.353.4 | 16 | |||
180.79 | odd | 6 | 720.2.cu.b.497.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.b.23.1 | ✓ | 16 | 15.2 | even | 4 | ||
90.2.l.b.47.1 | yes | 16 | 45.34 | even | 6 | ||
90.2.l.b.77.1 | yes | 16 | 15.14 | odd | 2 | ||
90.2.l.b.83.1 | yes | 16 | 45.7 | odd | 12 | ||
270.2.m.b.17.4 | 16 | 5.4 | even | 2 | |||
270.2.m.b.143.4 | 16 | 45.2 | even | 12 | |||
270.2.m.b.197.3 | 16 | 45.29 | odd | 6 | |||
270.2.m.b.233.3 | 16 | 5.2 | odd | 4 | |||
450.2.p.h.257.4 | 16 | 3.2 | odd | 2 | |||
450.2.p.h.293.4 | 16 | 15.8 | even | 4 | |||
450.2.p.h.407.4 | 16 | 9.7 | even | 3 | |||
450.2.p.h.443.4 | 16 | 45.43 | odd | 12 | |||
720.2.cu.b.113.3 | 16 | 60.47 | odd | 4 | |||
720.2.cu.b.257.4 | 16 | 60.59 | even | 2 | |||
720.2.cu.b.353.4 | 16 | 180.7 | even | 12 | |||
720.2.cu.b.497.3 | 16 | 180.79 | odd | 6 | |||
810.2.f.c.323.1 | 16 | 45.32 | even | 12 | |||
810.2.f.c.323.8 | 16 | 45.22 | odd | 12 | |||
810.2.f.c.647.1 | 16 | 45.4 | even | 6 | |||
810.2.f.c.647.8 | 16 | 45.14 | odd | 6 | |||
1350.2.q.h.143.2 | 16 | 45.38 | even | 12 | inner | ||
1350.2.q.h.557.2 | 16 | 1.1 | even | 1 | trivial | ||
1350.2.q.h.1007.1 | 16 | 9.2 | odd | 6 | inner | ||
1350.2.q.h.1043.1 | 16 | 5.3 | odd | 4 | inner |