Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [484,2,Mod(9,484)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(484, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("484.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 484 = 2^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 484.e (of order \(5\), 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: | \(3.86475945783\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 484.81 |
Dual form | 484.2.e.a.245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/484\mathbb{Z}\right)^\times\).
\(n\) | \(243\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | −0.821362 | − | 0.570408i | \(-0.806785\pi\) |
0.999773 | + | 0.0213149i | \(0.00678525\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42705 | − | 1.76336i | 1.08541 | − | 0.788597i | 0.106792 | − | 0.994281i | \(-0.465942\pi\) |
0.978618 | + | 0.205685i | \(0.0659421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | + | 1.90211i | 0.233595 | + | 0.718931i | 0.997305 | + | 0.0733714i | \(0.0233759\pi\) |
−0.763710 | + | 0.645560i | \(0.776624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.61803 | + | 1.17557i | 0.539345 | + | 0.391857i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607 | + | 2.35114i | 0.897524 | + | 0.652089i | 0.937829 | − | 0.347098i | \(-0.112833\pi\) |
−0.0403050 | + | 0.999187i | \(0.512833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.927051 | − | 2.85317i | −0.239364 | − | 0.736685i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.85410 | + | 3.52671i | −1.17729 | + | 0.855353i | −0.991864 | − | 0.127304i | \(-0.959367\pi\) |
−0.185429 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47214 | − | 7.60845i | 0.567147 | − | 1.74550i | −0.0943381 | − | 0.995540i | \(-0.530073\pi\) |
0.661485 | − | 0.749958i | \(-0.269927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23607 | − | 3.80423i | 0.247214 | − | 0.760845i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.04508 | − | 2.93893i | 0.778477 | − | 0.565597i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04508 | − | 2.93893i | −0.726519 | − | 0.527847i | 0.161942 | − | 0.986800i | \(-0.448224\pi\) |
−0.888460 | + | 0.458954i | \(0.848224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.85410 | + | 3.52671i | 0.820493 | + | 0.596123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.309017 | − | 0.951057i | −0.0508021 | − | 0.156353i | 0.922437 | − | 0.386148i | \(-0.126194\pi\) |
−0.973239 | + | 0.229795i | \(0.926194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.23607 | − | 2.35114i | 0.518186 | − | 0.376484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42705 | − | 1.76336i | 0.346722 | − | 0.251908i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85410 | + | 5.70634i | 0.259626 | + | 0.799047i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85410 | + | 3.52671i | 0.666762 | + | 0.484431i | 0.868940 | − | 0.494918i | \(-0.164802\pi\) |
−0.202178 | + | 0.979349i | \(0.564802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.47214 | − | 4.70228i | −0.857255 | − | 0.622832i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.927051 | + | 2.85317i | 0.120692 | + | 0.371451i | 0.993092 | − | 0.117342i | \(-0.0374373\pi\) |
−0.872400 | + | 0.488793i | \(0.837437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.23607 | − | 2.35114i | 0.414336 | − | 0.301033i | −0.361019 | − | 0.932559i | \(-0.617571\pi\) |
0.775355 | + | 0.631526i | \(0.217571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23607 | + | 3.80423i | −0.155730 | + | 0.479287i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | −0.0610847 | − | 0.998133i | \(-0.519456\pi\) | ||||
−0.0610847 | + | 0.998133i | \(0.519456\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.927051 | + | 2.85317i | −0.111604 | + | 0.343481i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1353 | + | 8.81678i | −1.44019 | + | 1.04636i | −0.452187 | + | 0.891923i | \(0.649356\pi\) |
−0.988003 | + | 0.154436i | \(0.950644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.23607 | − | 3.80423i | −0.144671 | − | 0.445251i | 0.852298 | − | 0.523057i | \(-0.175209\pi\) |
−0.996969 | + | 0.0778060i | \(0.975209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.23607 | − | 2.35114i | −0.373669 | − | 0.271486i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.61803 | − | 1.17557i | −0.182043 | − | 0.132262i | 0.493032 | − | 0.870011i | \(-0.335889\pi\) |
−0.675075 | + | 0.737749i | \(0.735889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.85410 | + | 3.52671i | −0.532807 | + | 0.387107i | −0.821407 | − | 0.570343i | \(-0.806810\pi\) |
0.288600 | + | 0.957450i | \(0.406810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.56231 | + | 17.1190i | −0.603317 | + | 1.85682i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47214 | + | 7.60845i | −0.259150 | + | 0.797582i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.04508 | + | 2.93893i | −0.419456 | + | 0.304752i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.41641 | − | 22.8254i | −0.760907 | − | 2.34183i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.66312 | + | 4.11450i | 0.575003 | + | 0.417764i | 0.836919 | − | 0.547327i | \(-0.184354\pi\) |
−0.261916 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.5623 | − | 10.5801i | −1.44900 | − | 1.05276i | −0.986063 | − | 0.166374i | \(-0.946794\pi\) |
−0.462941 | − | 0.886389i | \(-0.653206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.47214 | + | 7.60845i | 0.243587 | + | 0.749683i | 0.995866 | + | 0.0908382i | \(0.0289546\pi\) |
−0.752279 | + | 0.658845i | \(0.771045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.85410 | − | 3.52671i | 0.473712 | − | 0.344172i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.85410 | − | 5.70634i | 0.179243 | − | 0.551653i | −0.820559 | − | 0.571562i | \(-0.806338\pi\) |
0.999802 | + | 0.0199092i | \(0.00633772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.63525 | + | 14.2658i | −0.436048 | + | 1.34202i | 0.455961 | + | 0.890000i | \(0.349296\pi\) |
−0.892009 | + | 0.452018i | \(0.850704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.28115 | + | 5.29007i | −0.678971 | + | 0.493301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.47214 | + | 7.60845i | 0.228549 | + | 0.703402i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.70820 | − | 7.05342i | −0.889950 | − | 0.646586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.927051 | + | 2.85317i | 0.0829180 | + | 0.255195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9443 | − | 9.40456i | 1.14862 | − | 0.834520i | 0.160322 | − | 0.987065i | \(-0.448747\pi\) |
0.988297 | + | 0.152545i | \(0.0487468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.09017 | + | 9.51057i | −0.272074 | + | 0.837359i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000 | 1.38738 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.63525 | − | 14.2658i | 0.398939 | − | 1.22781i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.28115 | + | 5.29007i | −0.622071 | + | 0.451961i | −0.853644 | − | 0.520856i | \(-0.825613\pi\) |
0.231573 | + | 0.972817i | \(0.425613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.32624 | + | 13.3148i | 0.366947 | + | 1.12935i | 0.948753 | + | 0.316018i | \(0.102346\pi\) |
−0.581806 | + | 0.813327i | \(0.697654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.927051 | − | 2.85317i | −0.0764619 | − | 0.235325i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.85410 | + | 3.52671i | −0.397664 | + | 0.288919i | −0.768589 | − | 0.639743i | \(-0.779041\pi\) |
0.370925 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.09017 | + | 9.51057i | −0.251474 | + | 0.773959i | 0.743029 | + | 0.669259i | \(0.233388\pi\) |
−0.994504 | + | 0.104700i | \(0.966612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.0000 | −1.20483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.54508 | − | 4.75528i | 0.123311 | − | 0.379513i | −0.870278 | − | 0.492560i | \(-0.836061\pi\) |
0.993590 | + | 0.113047i | \(0.0360612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.85410 | − | 3.52671i | 0.384955 | − | 0.279686i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.85410 | − | 5.70634i | −0.146124 | − | 0.449723i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.23607 | + | 2.35114i | 0.253468 | + | 0.184156i | 0.707263 | − | 0.706951i | \(-0.249930\pi\) |
−0.453794 | + | 0.891107i | \(0.649930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.70820 | + | 7.05342i | 0.751243 | + | 0.545810i | 0.896212 | − | 0.443626i | \(-0.146308\pi\) |
−0.144969 | + | 0.989436i | \(0.546308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.927051 | + | 2.85317i | 0.0713116 | + | 0.219475i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9443 | − | 9.40456i | 0.989873 | − | 0.719185i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.56231 | − | 17.1190i | 0.422894 | − | 1.30153i | −0.482102 | − | 0.876115i | \(-0.660127\pi\) |
0.904996 | − | 0.425420i | \(-0.139873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | 0.225494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.78115 | + | 8.55951i | −0.207873 | + | 0.639768i | 0.791710 | + | 0.610897i | \(0.209191\pi\) |
−0.999583 | + | 0.0288706i | \(0.990809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5172 | − | 7.64121i | 0.781739 | − | 0.567967i | −0.123762 | − | 0.992312i | \(-0.539496\pi\) |
0.905500 | + | 0.424345i | \(0.139496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.23607 | − | 3.80423i | −0.0913728 | − | 0.281216i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42705 | − | 1.76336i | −0.178440 | − | 0.129644i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.09017 | + | 5.87785i | 0.588473 | + | 0.427551i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.48936 | − | 19.9722i | −0.469553 | − | 1.44514i | −0.853164 | − | 0.521642i | \(-0.825320\pi\) |
0.383611 | − | 0.923495i | \(-0.374680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.1803 | + | 11.7557i | −1.16469 | + | 0.846194i | −0.990363 | − | 0.138494i | \(-0.955774\pi\) |
−0.174323 | + | 0.984689i | \(0.555774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.70820 | − | 11.4127i | 0.265550 | − | 0.817279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.309017 | + | 0.951057i | −0.0217964 | + | 0.0670824i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.85410 | − | 3.52671i | −0.337383 | − | 0.245123i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1803 | − | 11.7557i | −1.11390 | − | 0.809296i | −0.130627 | − | 0.991432i | \(-0.541699\pi\) |
−0.983273 | + | 0.182135i | \(0.941699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.63525 | + | 14.2658i | 0.317602 | + | 0.977480i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.2705 | + | 17.6336i | −1.65524 | + | 1.20260i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09017 | − | 9.51057i | 0.209774 | − | 0.645619i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.25329 | − | 16.1680i | 0.351786 | − | 1.08269i | −0.606063 | − | 0.795416i | \(-0.707252\pi\) |
0.957850 | − | 0.287270i | \(-0.0927478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.47214 | − | 4.70228i | 0.431476 | − | 0.313485i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.85410 | + | 5.70634i | 0.123061 | + | 0.378743i | 0.993543 | − | 0.113458i | \(-0.0361926\pi\) |
−0.870482 | + | 0.492201i | \(0.836193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5172 | + | 7.64121i | 0.694998 | + | 0.504945i | 0.878299 | − | 0.478111i | \(-0.158679\pi\) |
−0.183302 | + | 0.983057i | \(0.558679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4164 | + | 14.1068i | 1.27201 | + | 0.924170i | 0.999281 | − | 0.0379203i | \(-0.0120733\pi\) |
0.272730 | + | 0.962090i | \(0.412073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.61803 | + | 1.17557i | −0.105103 | + | 0.0763615i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.85410 | − | 5.70634i | 0.119932 | − | 0.369112i | −0.873012 | − | 0.487699i | \(-0.837836\pi\) |
0.992944 | + | 0.118587i | \(0.0378363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.78115 | − | 8.55951i | 0.177681 | − | 0.546847i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.8885 | − | 18.8091i | 1.64725 | − | 1.19680i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.85410 | + | 5.70634i | 0.117499 | + | 0.361625i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.28115 | + | 5.29007i | 0.459582 | + | 0.333906i | 0.793367 | − | 0.608743i | \(-0.208326\pi\) |
−0.333785 | + | 0.942649i | \(0.608326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.5623 | + | 10.5801i | 0.911927 | + | 0.662554i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.56231 | − | 17.1190i | −0.346967 | − | 1.06785i | −0.960522 | − | 0.278203i | \(-0.910261\pi\) |
0.613555 | − | 0.789652i | \(-0.289739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.61803 | − | 1.17557i | 0.100540 | − | 0.0730464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0000 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.78115 | + | 8.55951i | −0.170204 | + | 0.523833i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.85410 | − | 3.52671i | 0.295960 | − | 0.215027i | −0.429889 | − | 0.902882i | \(-0.641447\pi\) |
0.725849 | + | 0.687854i | \(0.241447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.18034 | + | 19.0211i | 0.375429 | + | 1.15545i | 0.943189 | + | 0.332257i | \(0.107810\pi\) |
−0.567760 | + | 0.823194i | \(0.692190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.47214 | + | 4.70228i | 0.391711 | + | 0.284595i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.09017 | + | 5.87785i | 0.486091 | + | 0.353166i | 0.803679 | − | 0.595063i | \(-0.202873\pi\) |
−0.317588 | + | 0.948229i | \(0.602873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.09017 | − | 9.51057i | −0.185004 | − | 0.569383i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5623 | − | 10.5801i | 0.868714 | − | 0.631158i | −0.0615273 | − | 0.998105i | \(-0.519597\pi\) |
0.930242 | + | 0.366947i | \(0.119597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23607 | + | 3.80423i | −0.0734766 | + | 0.226138i | −0.981050 | − | 0.193756i | \(-0.937933\pi\) |
0.907573 | + | 0.419894i | \(0.137933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | −1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.87132 | − | 18.0701i | 0.345372 | − | 1.06295i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.66312 | − | 4.11450i | 0.331978 | − | 0.241196i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.28115 | + | 5.29007i | 0.423925 | + | 0.308000i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.70820 | − | 7.05342i | −0.561440 | − | 0.407910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.18034 | − | 19.0211i | −0.356229 | − | 1.09636i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5623 | + | 10.5801i | −0.836583 | + | 0.607813i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.70820 | − | 11.4127i | 0.212331 | − | 0.653488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.70820 | − | 11.4127i | 0.210273 | − | 0.647154i | −0.789183 | − | 0.614159i | \(-0.789495\pi\) |
0.999456 | − | 0.0329949i | \(-0.0105045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.809017 | − | 0.587785i | 0.0457283 | − | 0.0332236i | −0.564686 | − | 0.825306i | \(-0.691003\pi\) |
0.610415 | + | 0.792082i | \(0.291003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.70820 | + | 11.4127i | 0.208934 | + | 0.643032i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.6976 | − | 19.3969i | −1.49948 | − | 1.08944i | −0.970586 | − | 0.240754i | \(-0.922605\pi\) |
−0.528898 | − | 0.848685i | \(-0.677395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.85410 | − | 3.52671i | −0.270930 | − | 0.196842i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.8328 | + | 45.6507i | 0.825320 | + | 2.54007i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.9443 | − | 9.40456i | 0.718019 | − | 0.521671i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.618034 | − | 1.90211i | 0.0341774 | − | 0.105187i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | −0.384755 | −0.192377 | − | 0.981321i | \(-0.561620\pi\) | ||||
−0.192377 | + | 0.981321i | \(0.561620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.618034 | − | 1.90211i | 0.0338681 | − | 0.104235i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.42705 | + | 1.76336i | −0.132604 | + | 0.0963424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.618034 | + | 1.90211i | 0.0336665 | + | 0.103615i | 0.966478 | − | 0.256751i | \(-0.0826520\pi\) |
−0.932811 | + | 0.360366i | \(0.882652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1353 | + | 8.81678i | 0.659097 | + | 0.478862i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1803 | + | 11.7557i | 0.873656 | + | 0.634748i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.78115 | + | 8.55951i | 0.149732 | + | 0.460828i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.70820 | + | 7.05342i | −0.521164 | + | 0.378648i | −0.817042 | − | 0.576578i | \(-0.804388\pi\) |
0.295878 | + | 0.955226i | \(0.404388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.32624 | − | 13.3148i | 0.231578 | − | 0.712724i | −0.765979 | − | 0.642866i | \(-0.777745\pi\) |
0.997557 | − | 0.0698585i | \(-0.0222548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9058 | + | 42.7975i | −0.738041 | + | 2.27146i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.70820 | + | 7.05342i | −0.513813 | + | 0.373307i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1246 | − | 34.2380i | −0.587135 | − | 1.80701i | −0.590524 | − | 0.807020i | \(-0.701079\pi\) |
0.00338942 | − | 0.999994i | \(-0.498921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.4058 | − | 26.4503i | −1.91609 | − | 1.39212i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.70820 | − | 7.05342i | −0.508151 | − | 0.369193i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.87132 | − | 18.0701i | −0.306481 | − | 0.943250i | −0.979121 | − | 0.203280i | \(-0.934840\pi\) |
0.672640 | − | 0.739970i | \(-0.265160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.70820 | + | 11.4127i | −0.192520 | + | 0.592517i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.00000 | 0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.4615 | + | 17.0458i | −1.20514 | + | 0.875583i | −0.994780 | − | 0.102042i | \(-0.967462\pi\) |
−0.210356 | + | 0.977625i | \(0.567462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.94427 | − | 15.2169i | −0.253303 | − | 0.779586i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8435 | + | 15.8702i | 1.11615 | + | 0.810929i | 0.983621 | − | 0.180250i | \(-0.0576906\pi\) |
0.132528 | + | 0.991179i | \(0.457691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.1803 | − | 11.7557i | −0.822493 | − | 0.597576i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.34346 | − | 25.6785i | −0.423030 | − | 1.30195i | −0.904868 | − | 0.425692i | \(-0.860031\pi\) |
0.481838 | − | 0.876260i | \(-0.339969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5623 | − | 10.5801i | 0.736447 | − | 0.535060i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.85410 | + | 5.70634i | −0.0935271 | + | 0.287847i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.94427 | − | 15.2169i | 0.247523 | − | 0.761798i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.5623 | + | 10.5801i | −0.727207 | + | 0.528347i | −0.888679 | − | 0.458531i | \(-0.848376\pi\) |
0.161472 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.18034 | − | 19.0211i | −0.307865 | − | 0.947510i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.42705 | + | 1.76336i | 0.120601 | + | 0.0876219i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.61803 | − | 1.17557i | −0.0800066 | − | 0.0581282i | 0.547063 | − | 0.837091i | \(-0.315746\pi\) |
−0.627070 | + | 0.778963i | \(0.715746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.78115 | + | 8.55951i | 0.137184 | + | 0.422209i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.85410 | + | 3.52671i | −0.238855 | + | 0.173538i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.56231 | + | 17.1190i | −0.273043 | + | 0.840340i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0000 | 0.685583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09017 | + | 9.51057i | −0.150606 | + | 0.463517i | −0.997689 | − | 0.0679432i | \(-0.978356\pi\) |
0.847084 | + | 0.531460i | \(0.178356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.41641 | + | 22.8254i | 0.359749 | + | 1.10719i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.47214 | + | 4.70228i | 0.313209 | + | 0.227559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5623 | − | 10.5801i | −0.701442 | − | 0.509627i | 0.178960 | − | 0.983856i | \(-0.442727\pi\) |
−0.880401 | + | 0.474229i | \(0.842727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.96149 | + | 27.5806i | 0.430662 | + | 1.32544i | 0.897467 | + | 0.441081i | \(0.145405\pi\) |
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.41641 | + | 22.8254i | −0.354775 | + | 1.09188i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | 0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.48936 | + | 19.9722i | −0.308319 | + | 0.948907i | 0.670099 | + | 0.742271i | \(0.266252\pi\) |
−0.978418 | + | 0.206636i | \(0.933748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.8435 | + | 15.8702i | −1.03548 | + | 0.752320i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.85410 | + | 5.70634i | 0.0876960 | + | 0.269901i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.42705 | − | 1.76336i | −0.114540 | − | 0.0832179i | 0.529041 | − | 0.848596i | \(-0.322552\pi\) |
−0.643580 | + | 0.765378i | \(0.722552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.09017 | + | 5.87785i | 0.380109 | + | 0.276166i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.41641 | + | 22.8254i | 0.347687 | + | 1.07007i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6525 | − | 16.4580i | 1.05964 | − | 0.769872i | 0.0856167 | − | 0.996328i | \(-0.472714\pi\) |
0.974021 | + | 0.226456i | \(0.0727139\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.27051 | + | 28.5317i | −0.432710 | + | 1.33175i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0000 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.63525 | + | 14.2658i | −0.214955 | + | 0.661563i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.42705 | + | 1.76336i | −0.112311 | + | 0.0815984i | −0.642523 | − | 0.766267i | \(-0.722112\pi\) |
0.530212 | + | 0.847865i | \(0.322112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.618034 | − | 1.90211i | −0.0285382 | − | 0.0878314i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.04508 | − | 2.93893i | −0.186388 | − | 0.135419i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.8885 | − | 18.8091i | −1.18785 | − | 0.863022i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.70820 | + | 11.4127i | 0.169787 | + | 0.522551i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.70820 | − | 7.05342i | 0.443579 | − | 0.322279i | −0.343476 | − | 0.939161i | \(-0.611605\pi\) |
0.787055 | + | 0.616882i | \(0.211605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23607 | − | 3.80423i | 0.0563598 | − | 0.173458i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | −0.273009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.96149 | − | 27.5806i | 0.406084 | − | 1.24980i | −0.513903 | − | 0.857848i | \(-0.671801\pi\) |
0.919987 | − | 0.391950i | \(-0.128199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.23607 | − | 2.35114i | 0.146340 | − | 0.106322i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.41641 | + | 22.8254i | 0.334698 | + | 1.03009i | 0.966871 | + | 0.255267i | \(0.0821632\pi\) |
−0.632173 | + | 0.774827i | \(0.717837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.2705 | − | 17.6336i | −1.08868 | − | 0.790973i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.23607 | − | 3.80423i | −0.0553340 | − | 0.170301i | 0.919570 | − | 0.392926i | \(-0.128537\pi\) |
−0.974904 | + | 0.222626i | \(0.928537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.70820 | − | 7.05342i | 0.433731 | − | 0.315124i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.27051 | + | 28.5317i | −0.413352 | + | 1.27217i | 0.500365 | + | 0.865814i | \(0.333199\pi\) |
−0.913717 | + | 0.406351i | \(0.866801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −54.0000 | −2.40297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | 0.133235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.48936 | + | 19.9722i | −0.287636 | + | 0.885252i | 0.697961 | + | 0.716136i | \(0.254091\pi\) |
−0.985596 | + | 0.169115i | \(0.945909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.47214 | − | 4.70228i | 0.286310 | − | 0.208017i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3607 | − | 38.0423i | −0.545737 | − | 1.67961i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.4164 | + | 14.1068i | 0.855589 | + | 0.621622i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.5623 | − | 10.5801i | −0.639214 | − | 0.464416i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.34346 | − | 25.6785i | −0.365534 | − | 1.12500i | −0.949646 | − | 0.313324i | \(-0.898557\pi\) |
0.584113 | − | 0.811673i | \(-0.301443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.47214 | + | 4.70228i | −0.283007 | + | 0.205616i | −0.720228 | − | 0.693738i | \(-0.755963\pi\) |
0.437221 | + | 0.899354i | \(0.355963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.47214 | − | 7.60845i | 0.107893 | − | 0.332060i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0000 | 1.30682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.85410 | + | 5.70634i | −0.0804612 | + | 0.247634i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.56231 | − | 17.1190i | −0.240479 | − | 0.740120i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.28115 | + | 5.29007i | 0.314205 | + | 0.228283i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9443 | + | 9.40456i | 0.556518 | + | 0.404334i | 0.830183 | − | 0.557491i | \(-0.188236\pi\) |
−0.273665 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.01722 | − | 12.3637i | −0.172395 | − | 0.530579i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.85410 | − | 3.52671i | 0.207927 | − | 0.151068i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47214 | − | 7.60845i | 0.105701 | − | 0.325314i | −0.884193 | − | 0.467121i | \(-0.845291\pi\) |
0.989894 | + | 0.141807i | \(0.0452913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.23607 | − | 3.80423i | 0.0525630 | − | 0.161772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.42705 | + | 1.76336i | −0.103023 | + | 0.0748503i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.56231 | − | 17.1190i | −0.235682 | − | 0.725356i | −0.997030 | − | 0.0770122i | \(-0.975462\pi\) |
0.761348 | − | 0.648344i | \(-0.224538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.3607 | − | 23.5114i | −1.36871 | − | 0.994427i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1246 | + | 21.1603i | 1.22746 | + | 0.891799i | 0.996697 | − | 0.0812119i | \(-0.0258790\pi\) |
0.230759 | + | 0.973011i | \(0.425879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.9058 | + | 42.7975i | 0.585020 | + | 1.80051i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.61803 | + | 1.17557i | −0.0679510 | + | 0.0493693i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.0000 | −0.877288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.70820 | + | 11.4127i | −0.154643 | + | 0.475942i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7533 | + | 9.99235i | −0.572557 | + | 0.415987i | −0.836033 | − | 0.548679i | \(-0.815131\pi\) |
0.263476 | + | 0.964666i | \(0.415131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.18034 | + | 19.0211i | 0.256846 | + | 0.790491i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.70820 | − | 7.05342i | −0.402764 | − | 0.292625i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.4164 | + | 14.1068i | 0.802770 | + | 0.583246i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.70820 | − | 11.4127i | −0.153054 | − | 0.471052i | 0.844905 | − | 0.534917i | \(-0.179657\pi\) |
−0.997959 | + | 0.0638654i | \(0.979657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.3607 | + | 23.5114i | −1.33340 | + | 0.968771i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.85410 | − | 5.70634i | 0.0762676 | − | 0.234727i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.47214 | − | 7.60845i | 0.101178 | − | 0.311393i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.03444 | + | 24.7275i | 0.327732 | + | 1.00865i | 0.970192 | + | 0.242336i | \(0.0779136\pi\) |
−0.642461 | + | 0.766319i | \(0.722086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.61803 | − | 1.17557i | −0.0658914 | − | 0.0478729i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3262 | − | 8.22899i | −0.459718 | − | 0.334005i | 0.333703 | − | 0.942678i | \(-0.391702\pi\) |
−0.793421 | + | 0.608674i | \(0.791702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.88854 | − | 30.4338i | 0.399395 | − | 1.22921i | −0.526091 | − | 0.850428i | \(-0.676343\pi\) |
0.925486 | − | 0.378782i | \(-0.123657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.25329 | − | 16.1680i | 0.211148 | − | 0.649845i | −0.788257 | − | 0.615346i | \(-0.789016\pi\) |
0.999405 | − | 0.0344993i | \(-0.0109837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.1353 | + | 8.81678i | −0.486971 | + | 0.353805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.56231 | − | 17.1190i | −0.222849 | − | 0.685859i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4615 | + | 17.0458i | 0.938460 | + | 0.681831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.85410 | + | 3.52671i | 0.193546 | + | 0.140619i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2877 | − | 40.8954i | −0.528976 | − | 1.62802i | −0.756316 | − | 0.654206i | \(-0.773003\pi\) |
0.227340 | − | 0.973815i | \(-0.426997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.1803 | + | 11.7557i | −0.643111 | + | 0.467247i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.8328 | − | 45.6507i | 0.588622 | − | 1.81159i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | 0.475457 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.0000 | −1.18678 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0517 | − | 37.0912i | 0.476012 | − | 1.46501i | −0.368576 | − | 0.929598i | \(-0.620155\pi\) |
0.844588 | − | 0.535417i | \(-0.179845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5172 | − | 7.64121i | 0.414759 | − | 0.301340i | −0.360767 | − | 0.932656i | \(-0.617485\pi\) |
0.775526 | + | 0.631316i | \(0.217485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.27051 | + | 28.5317i | 0.365026 | + | 1.12343i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.42705 | − | 1.76336i | −0.0954172 | − | 0.0693247i | 0.539054 | − | 0.842271i | \(-0.318782\pi\) |
−0.634471 | + | 0.772947i | \(0.718782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.09017 | − | 5.87785i | −0.317079 | − | 0.230371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.927051 | + | 2.85317i | 0.0362783 | + | 0.111653i | 0.967556 | − | 0.252658i | \(-0.0813046\pi\) |
−0.931277 | + | 0.364311i | \(0.881305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5623 | + | 10.5801i | −0.568996 | + | 0.413400i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.47214 | − | 7.60845i | 0.0964472 | − | 0.296834i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.0000 | −1.63609 | −0.818044 | − | 0.575156i | \(-0.804941\pi\) | ||||
−0.818044 | + | 0.575156i | \(0.804941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | 0.661223 | 0.330612 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330612 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.41641 | + | 22.8254i | −0.288029 | + | 0.886463i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38.8328 | − | 28.2137i | 1.50587 | − | 1.09408i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.7533 | − | 9.99235i | −0.531733 | − | 0.386327i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.5066 | + | 19.9847i | 1.06030 | + | 0.770354i | 0.974144 | − | 0.225928i | \(-0.0725414\pi\) |
0.0861567 | + | 0.996282i | \(0.472541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.18034 | − | 19.0211i | −0.237881 | − | 0.732124i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.9787 | − | 24.6870i | 1.30591 | − | 0.948798i | 0.305913 | − | 0.952059i | \(-0.401038\pi\) |
0.999995 | + | 0.00326161i | \(0.00103820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.32624 | + | 13.3148i | −0.166026 | + | 0.510975i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.34346 | + | 25.6785i | −0.318787 | + | 0.981126i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.5172 | − | 7.64121i | 0.401257 | − | 0.291530i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.41641 | + | 22.8254i | 0.282543 | + | 0.869577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.809017 | + | 0.587785i | 0.0307765 | + | 0.0223604i | 0.603067 | − | 0.797690i | \(-0.293945\pi\) |
−0.572291 | + | 0.820051i | \(0.693945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.9787 | + | 24.6870i | 1.28889 | + | 0.936431i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.4164 | − | 14.1068i | 0.734396 | − | 0.533570i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.56231 | − | 17.1190i | 0.210085 | − | 0.646576i | −0.789381 | − | 0.613904i | \(-0.789598\pi\) |
0.999466 | − | 0.0326724i | \(-0.0104018\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.1246 | − | 34.2380i | 0.418384 | − | 1.28765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.9336 | − | 21.7481i | 1.12418 | − | 0.816765i | 0.139343 | − | 0.990244i | \(-0.455501\pi\) |
0.984838 | + | 0.173479i | \(0.0555008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.23607 | − | 3.80423i | −0.0463562 | − | 0.142670i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.1353 | + | 8.81678i | 0.454469 | + | 0.330191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.85410 | − | 3.52671i | −0.181280 | − | 0.131707i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.9058 | + | 42.7975i | 0.518598 | + | 1.59608i | 0.776639 | + | 0.629945i | \(0.216923\pi\) |
−0.258042 | + | 0.966134i | \(0.583077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9443 | + | 9.40456i | −0.482070 | + | 0.350244i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.47214 | − | 7.60845i | 0.0919397 | − | 0.282961i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.01722 | − | 12.3637i | 0.148786 | − | 0.457916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.5410 | − | 35.2671i | 1.79535 | − | 1.30440i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.23607 | − | 3.80423i | −0.0456552 | − | 0.140512i | 0.925630 | − | 0.378429i | \(-0.123536\pi\) |
−0.971286 | + | 0.237917i | \(0.923536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.28115 | − | 5.29007i | −0.268569 | − | 0.195127i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5066 | + | 19.9847i | 1.01185 | + | 0.735149i | 0.964595 | − | 0.263734i | \(-0.0849541\pi\) |
0.0472504 | + | 0.998883i | \(0.484954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.88854 | − | 30.4338i | −0.363265 | − | 1.11801i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.70820 | + | 7.05342i | −0.356159 | + | 0.258765i | −0.751448 | − | 0.659792i | \(-0.770644\pi\) |
0.395289 | + | 0.918557i | \(0.370644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56231 | + | 17.1190i | −0.203787 | + | 0.627192i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8156 | − | 33.2870i | 0.394667 | − | 1.21466i | −0.534554 | − | 0.845134i | \(-0.679520\pi\) |
0.929221 | − | 0.369525i | \(-0.120480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.28115 | − | 5.29007i | 0.265340 | − | 0.192781i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.27051 | + | 28.5317i | 0.337388 | + | 1.03837i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7984 | + | 12.9313i | 0.646893 | + | 0.469995i | 0.862211 | − | 0.506549i | \(-0.169079\pi\) |
−0.215318 | + | 0.976544i | \(0.569079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.1246 | − | 21.1603i | −1.05577 | − | 0.767059i | −0.0824659 | − | 0.996594i | \(-0.526280\pi\) |
−0.973300 | + | 0.229535i | \(0.926280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.23607 | + | 3.80423i | 0.0447487 | + | 0.137722i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −29.1246 | + | 21.1603i | −1.05300 | + | 0.765051i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.70820 | + | 11.4127i | −0.133895 | + | 0.412088i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0000 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.9787 | − | 39.9444i | 0.466812 | − | 1.43670i | −0.389878 | − | 0.920867i | \(-0.627483\pi\) |
0.856689 | − | 0.515833i | \(-0.172517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.1803 | + | 11.7557i | −0.581215 | + | 0.422277i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.618034 | − | 1.90211i | −0.0221718 | − | 0.0682379i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.63525 | − | 14.2658i | −0.165439 | − | 0.509170i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8885 | + | 18.8091i | −0.922827 | + | 0.670473i | −0.944226 | − | 0.329298i | \(-0.893188\pi\) |
0.0213991 | + | 0.999771i | \(0.493188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.56231 | − | 17.1190i | 0.198023 | − | 0.609453i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.56231 | − | 17.1190i | 0.197275 | − | 0.607149i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.28115 | + | 5.29007i | −0.257912 | + | 0.187384i | −0.709226 | − | 0.704981i | \(-0.750955\pi\) |
0.451314 | + | 0.892365i | \(0.350955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.5623 | − | 10.5801i | −0.514534 | − | 0.373831i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.5623 | − | 10.5801i | −0.513254 | − | 0.372901i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.85410 | − | 5.70634i | −0.0652675 | − | 0.200873i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.4164 | − | 14.1068i | 0.682645 | − | 0.495970i | −0.191589 | − | 0.981475i | \(-0.561364\pi\) |
0.874234 | + | 0.485505i | \(0.161364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.7426 | − | 36.1401i | 0.412340 | − | 1.26905i | −0.502268 | − | 0.864712i | \(-0.667501\pi\) |
0.914609 | − | 0.404340i | \(-0.132499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.7214 | + | 76.0845i | −0.864891 | + | 2.66186i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9443 | + | 9.40456i | −0.452309 | + | 0.328622i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.27051 | + | 28.5317i | 0.323543 | + | 0.995763i | 0.972094 | + | 0.234592i | \(0.0753753\pi\) |
−0.648551 | + | 0.761171i | \(0.724625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.7877 | + | 25.2748i | 1.21262 | + | 0.881023i | 0.995466 | − | 0.0951136i | \(-0.0303214\pi\) |
0.217158 | + | 0.976137i | \(0.430321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1246 | + | 21.1603i | 1.01276 | + | 0.735815i | 0.964787 | − | 0.263034i | \(-0.0847231\pi\) |
0.0479754 | + | 0.998849i | \(0.484723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.87132 | − | 18.0701i | −0.203919 | − | 0.627600i | −0.999756 | − | 0.0220881i | \(-0.992969\pi\) |
0.795837 | − | 0.605512i | \(-0.207031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.09017 | − | 5.87785i | 0.280645 | − | 0.203900i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.56231 | + | 17.1190i | −0.192722 | + | 0.593139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.0000 | 1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0000 | −0.864126 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0517 | + | 37.0912i | −0.416070 | + | 1.28053i | 0.495221 | + | 0.868767i | \(0.335087\pi\) |
−0.911291 | + | 0.411764i | \(0.864913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.56231 | − | 17.1190i | −0.191576 | − | 0.589610i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.28115 | + | 5.29007i | 0.250479 | + | 0.181984i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.23607 | + | 2.35114i | 0.111062 | + | 0.0806910i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.927051 | + | 2.85317i | 0.0317789 | + | 0.0978054i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.7426 | + | 22.3358i | −1.05261 | + | 0.764765i | −0.972707 | − | 0.232038i | \(-0.925461\pi\) |
−0.0799015 | + | 0.996803i | \(0.525461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.8328 | − | 45.6507i | 0.507272 | − | 1.56122i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | 0.819824 | 0.409912 | − | 0.912125i | \(-0.365559\pi\) | ||||
0.409912 | + | 0.912125i | \(0.365559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0000 | −0.852989 | −0.426494 | − | 0.904490i | \(-0.640252\pi\) | ||||
−0.426494 | + | 0.904490i | \(0.640252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.8328 | + | 28.2137i | −1.32188 | + | 0.960405i | −0.321978 | + | 0.946747i | \(0.604348\pi\) |
−0.999907 | + | 0.0136580i | \(0.995652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.6869 | − | 51.3571i | −0.567372 | − | 1.74619i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.3713 | − | 11.1679i | −0.522037 | − | 0.379282i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.23607 | − | 2.35114i | −0.109650 | − | 0.0796654i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.32624 | + | 13.3148i | 0.146421 | + | 0.450637i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.85410 | + | 3.52671i | −0.164099 | + | 0.119225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0689 | + | 49.4549i | −0.542608 | + | 1.66997i | 0.184003 | + | 0.982926i | \(0.441094\pi\) |
−0.726611 | + | 0.687049i | \(0.758906\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0000 | −0.909653 | −0.454827 | − | 0.890580i | \(-0.650299\pi\) | ||||
−0.454827 | + | 0.890580i | \(0.650299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.23607 | + | 3.80423i | −0.0415970 | + | 0.128022i | −0.969698 | − | 0.244305i | \(-0.921440\pi\) |
0.928101 | + | 0.372327i | \(0.121440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.28115 | − | 5.29007i | 0.244753 | − | 0.177824i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.27051 | + | 28.5317i | 0.311273 | + | 0.958001i | 0.977261 | + | 0.212038i | \(0.0680101\pi\) |
−0.665988 | + | 0.745962i | \(0.731990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.8885 | + | 18.8091i | 0.868274 | + | 0.630838i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.34346 | + | 25.6785i | 0.278891 | + | 0.858338i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.70820 | + | 7.05342i | −0.324147 | + | 0.235507i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0000 | −0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.0517 | − | 37.0912i | 0.400611 | − | 1.23295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.23607 | − | 2.35114i | 0.107452 | − | 0.0780684i | −0.532762 | − | 0.846265i | \(-0.678846\pi\) |
0.640214 | + | 0.768197i | \(0.278846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1246 | − | 34.2380i | −0.368980 | − | 1.13560i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.70820 | − | 7.05342i | −0.321647 | − | 0.233690i | 0.415231 | − | 0.909716i | \(-0.363701\pi\) |
−0.736878 | + | 0.676026i | \(0.763701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.70820 | − | 7.05342i | −0.320943 | − | 0.233179i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.70820 | − | 11.4127i | −0.122456 | − | 0.376880i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5066 | − | 19.9847i | 0.907358 | − | 0.659234i | −0.0329871 | − | 0.999456i | \(-0.510502\pi\) |
0.940345 | + | 0.340221i | \(0.110502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.94427 | + | 15.2169i | −0.162919 | + | 0.501414i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.94427 | + | 15.2169i | −0.162391 | + | 0.499789i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5623 | + | 10.5801i | −0.477774 | + | 0.347123i | −0.800463 | − | 0.599382i | \(-0.795413\pi\) |
0.322689 | + | 0.946505i | \(0.395413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.41641 | − | 22.8254i | −0.243063 | − | 0.748071i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.70820 | − | 7.05342i | −0.317832 | − | 0.230919i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.8885 | − | 18.8091i | −0.845742 | − | 0.614467i | 0.0782268 | − | 0.996936i | \(-0.475074\pi\) |
−0.923969 | + | 0.382468i | \(0.875074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.309017 | − | 0.951057i | −0.0100844 | − | 0.0310366i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2705 | − | 17.6336i | 0.791196 | − | 0.574838i | −0.117122 | − | 0.993118i | \(-0.537367\pi\) |
0.908318 | + | 0.418280i | \(0.137367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.0000 | 0.975900 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | 0.877382 | 0.438691 | − | 0.898638i | \(-0.355442\pi\) | ||||
0.438691 | + | 0.898638i | \(0.355442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.94427 | − | 15.2169i | 0.160498 | − | 0.493962i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.6976 | + | 19.3969i | −0.865728 | + | 0.628988i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.9787 | + | 39.9444i | 0.420422 | + | 1.29393i | 0.907311 | + | 0.420461i | \(0.138132\pi\) |
−0.486889 | + | 0.873464i | \(0.661868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.9681 | − | 37.0305i | −1.64929 | − | 1.19828i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.5623 | − | 10.5801i | −0.470241 | − | 0.341650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.85410 | − | 5.70634i | −0.0598097 | − | 0.184075i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.70820 | − | 7.05342i | 0.312842 | − | 0.227293i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.5410 | + | 57.0634i | −0.596857 | + | 1.83694i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.0000 | 1.54198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.63525 | + | 14.2658i | −0.148752 | + | 0.457813i | −0.997474 | − | 0.0710264i | \(-0.977373\pi\) |
0.848722 | + | 0.528839i | \(0.177373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.6525 | + | 16.4580i | −0.726205 | + | 0.527619i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.94427 | − | 15.2169i | −0.158343 | − | 0.487331i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4058 | − | 26.4503i | −1.16472 | − | 0.846221i | −0.174356 | − | 0.984683i | \(-0.555784\pi\) |
−0.990368 | + | 0.138461i | \(0.955784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.23607 | + | 2.35114i | 0.103320 | + | 0.0750662i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9058 | + | 42.7975i | 0.443525 | + | 1.36503i | 0.884093 | + | 0.467311i | \(0.154777\pi\) |
−0.440568 | + | 0.897719i | \(0.645223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.5623 | − | 10.5801i | 0.463994 | − | 0.337111i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0000 | 0.953945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.16312 | + | 6.65740i | −0.0686445 | + | 0.211266i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.4164 | − | 14.1068i | 0.615542 | − | 0.447217i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.09017 | − | 9.51057i | −0.0978667 | − | 0.301203i | 0.890124 | − | 0.455719i | \(-0.150618\pi\) |
−0.987990 | + | 0.154517i | \(0.950618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.04508 | − | 2.93893i | −0.127981 | − | 0.0929835i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))