Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [44,2,Mod(5,44)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(44, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("44.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 44 = 2^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 44.e (of order \(5\), degree \(4\), 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: | \(0.351341768894\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 44.37 |
Dual form | 44.2.e.a.25.1 |
$q$-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 \(\left(\mathbb{Z}/44\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.809017 | + | 2.48990i | −0.467086 | + | 1.43754i | 0.389254 | + | 0.921131i | \(0.372733\pi\) |
−0.856340 | + | 0.516413i | \(0.827267\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.30902 | − | 0.951057i | 0.585410 | − | 0.425325i | −0.255260 | − | 0.966872i | \(-0.582161\pi\) |
0.840670 | + | 0.541547i | \(0.182161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19098 | − | 3.66547i | −0.450149 | − | 1.38542i | −0.876737 | − | 0.480971i | \(-0.840284\pi\) |
0.426587 | − | 0.904446i | \(-0.359716\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.11803 | − | 2.26538i | −1.03934 | − | 0.755128i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23607 | + | 3.07768i | 0.372689 | + | 0.927957i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.92705 | − | 1.40008i | −0.534468 | − | 0.388314i | 0.287559 | − | 0.957763i | \(-0.407156\pi\) |
−0.822026 | + | 0.569449i | \(0.807156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30902 | + | 4.02874i | 0.337987 | + | 1.04022i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.92705 | + | 1.40008i | −0.467379 | + | 0.339570i | −0.796419 | − | 0.604746i | \(-0.793275\pi\) |
0.329040 | + | 0.944316i | \(0.393275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.19098 | − | 3.66547i | 0.273230 | − | 0.840916i | −0.716452 | − | 0.697636i | \(-0.754235\pi\) |
0.989682 | − | 0.143280i | \(-0.0457649\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.0902 | 2.20186 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.736068 | + | 2.26538i | −0.147214 | + | 0.453077i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.80902 | − | 1.31433i | 0.348145 | − | 0.252942i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.66312 | + | 8.19624i | 0.494529 | + | 1.52200i | 0.817690 | + | 0.575659i | \(0.195254\pi\) |
−0.323161 | + | 0.946344i | \(0.604746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.690983 | − | 0.502029i | −0.124104 | − | 0.0901670i | 0.524002 | − | 0.851717i | \(-0.324439\pi\) |
−0.648106 | + | 0.761550i | \(0.724439\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.66312 | + | 0.587785i | −1.50806 | + | 0.102320i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.04508 | − | 3.66547i | −0.852775 | − | 0.619577i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.572949 | − | 1.76336i | −0.0941922 | − | 0.289894i | 0.892850 | − | 0.450354i | \(-0.148702\pi\) |
−0.987042 | + | 0.160460i | \(0.948702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.04508 | − | 3.66547i | 0.807860 | − | 0.586945i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66312 | − | 8.19624i | 0.415909 | − | 1.28004i | −0.495526 | − | 0.868593i | \(-0.665025\pi\) |
0.911435 | − | 0.411444i | \(-0.134975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.23607 | −0.929618 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.427051 | − | 1.31433i | 0.0622918 | − | 0.191714i | −0.915068 | − | 0.403301i | \(-0.867863\pi\) |
0.977359 | + | 0.211586i | \(0.0678629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35410 | + | 4.61653i | −0.907729 | + | 0.659504i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.92705 | − | 5.93085i | −0.269841 | − | 0.830486i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.30902 | + | 2.40414i | 0.454528 | + | 0.330234i | 0.791381 | − | 0.611323i | \(-0.209362\pi\) |
−0.336853 | + | 0.941557i | \(0.609362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.54508 | + | 2.85317i | 0.612859 | + | 0.384721i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.16312 | + | 5.93085i | 1.08123 | + | 0.785561i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.336881 | + | 1.03681i | 0.0438582 | + | 0.134982i | 0.970588 | − | 0.240747i | \(-0.0773924\pi\) |
−0.926730 | + | 0.375729i | \(0.877392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92705 | + | 1.40008i | −0.246734 | + | 0.179262i | −0.704278 | − | 0.709924i | \(-0.748729\pi\) |
0.457544 | + | 0.889187i | \(0.348729\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.59017 | + | 14.1271i | −0.578307 | + | 1.77985i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.85410 | −0.478043 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9443 | 1.58139 | 0.790697 | − | 0.612207i | \(-0.209718\pi\) | ||||
0.790697 | + | 0.612207i | \(0.209718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | − | 6.15537i | 0.240772 | − | 0.741019i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.16312 | − | 3.75123i | 0.612749 | − | 0.445189i | −0.237632 | − | 0.971355i | \(-0.576371\pi\) |
0.850381 | + | 0.526167i | \(0.176371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.281153 | − | 0.865300i | −0.0329065 | − | 0.101276i | 0.933254 | − | 0.359217i | \(-0.116956\pi\) |
−0.966161 | + | 0.257941i | \(0.916956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.04508 | − | 3.66547i | −0.582556 | − | 0.423252i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.80902 | − | 8.19624i | 1.11784 | − | 0.934048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.78115 | + | 4.20025i | 0.650431 | + | 0.472565i | 0.863418 | − | 0.504490i | \(-0.168319\pi\) |
−0.212987 | + | 0.977055i | \(0.568319\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.76393 | − | 5.42882i | −0.195992 | − | 0.603203i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.5451 | + | 7.66145i | −1.15747 | + | 0.840954i | −0.989456 | − | 0.144830i | \(-0.953736\pi\) |
−0.168017 | + | 0.985784i | \(0.553736\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19098 | + | 3.66547i | −0.129180 | + | 0.397576i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.5623 | −2.41893 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.472136 | 0.0500463 | 0.0250232 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250232 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.83688 | + | 8.73102i | −0.297386 | + | 0.915260i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.80902 | − | 1.31433i | 0.187586 | − | 0.136289i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.92705 | − | 5.93085i | −0.197711 | − | 0.608493i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7812 | + | 8.55951i | 1.19619 | + | 0.869086i | 0.993905 | − | 0.110239i | \(-0.0351617\pi\) |
0.202290 | + | 0.979326i | \(0.435162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.11803 | − | 12.3965i | 0.313374 | − | 1.24589i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.3992 | − | 10.4616i | −1.43277 | − | 1.04097i | −0.989492 | − | 0.144587i | \(-0.953815\pi\) |
−0.443281 | − | 0.896383i | \(-0.646185\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.42705 | − | 7.46969i | −0.239144 | − | 0.736011i | −0.996545 | − | 0.0830599i | \(-0.973531\pi\) |
0.757400 | − | 0.652951i | \(-0.226469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.2082 | − | 9.59632i | 1.28899 | − | 0.936505i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.57295 | + | 10.9964i | −0.345410 | + | 1.06306i | 0.615954 | + | 0.787782i | \(0.288771\pi\) |
−0.961364 | + | 0.275281i | \(0.911229\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4721 | −1.19461 | −0.597307 | − | 0.802013i | \(-0.703763\pi\) | ||||
−0.597307 | + | 0.802013i | \(0.703763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.85410 | 0.460731 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.42705 | − | 16.7027i | 0.510534 | − | 1.57126i | −0.280730 | − | 0.959787i | \(-0.590576\pi\) |
0.791264 | − | 0.611475i | \(-0.209424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.23607 | + | 2.35114i | −0.301765 | + | 0.219245i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.83688 | + | 8.73102i | 0.262270 | + | 0.807183i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.42705 | + | 5.39607i | 0.680837 | + | 0.494657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.94427 | + | 7.60845i | −0.722207 | + | 0.691677i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.2533 | + | 13.2618i | 1.64584 | + | 1.19578i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.69098 | + | 11.3597i | 0.330132 | + | 1.01604i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.92705 | − | 1.40008i | 0.170998 | − | 0.124237i | −0.498995 | − | 0.866605i | \(-0.666297\pi\) |
0.669993 | + | 0.742368i | \(0.266297\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.52786 | 0.832453 | 0.416227 | − | 0.909261i | \(-0.363352\pi\) | ||||
0.416227 | + | 0.909261i | \(0.363352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.8541 | −1.28801 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.11803 | − | 3.44095i | 0.0962250 | − | 0.296150i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1631 | + | 8.11048i | −0.953730 | + | 0.692925i | −0.951686 | − | 0.307073i | \(-0.900650\pi\) |
−0.00204358 | + | 0.999998i | \(0.500650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.57295 | + | 10.9964i | 0.303054 | + | 0.932703i | 0.980396 | + | 0.197035i | \(0.0631314\pi\) |
−0.677343 | + | 0.735668i | \(0.736869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.92705 | + | 2.12663i | 0.246502 | + | 0.179094i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.92705 | − | 7.66145i | 0.161148 | − | 0.640683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2812 | + | 8.19624i | 0.936849 | + | 0.680660i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.35410 | − | 19.5559i | −0.524077 | − | 1.61294i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.92705 | + | 1.40008i | −0.157870 | + | 0.114699i | −0.663916 | − | 0.747807i | \(-0.731107\pi\) |
0.506046 | + | 0.862507i | \(0.331107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.95492 | − | 18.3273i | 0.484604 | − | 1.49146i | −0.347949 | − | 0.937513i | \(-0.613122\pi\) |
0.832553 | − | 0.553945i | \(-0.186878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.18034 | 0.742186 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.38197 | −0.111002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.42705 | − | 16.7027i | 0.433126 | − | 1.33302i | −0.461869 | − | 0.886948i | \(-0.652821\pi\) |
0.894995 | − | 0.446076i | \(-0.147179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.66312 | + | 6.29412i | −0.687030 | + | 0.499157i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.94427 | + | 9.06154i | 0.232041 | + | 0.714149i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.16312 | − | 6.65740i | −0.717711 | − | 0.521447i | 0.167941 | − | 0.985797i | \(-0.446288\pi\) |
−0.885652 | + | 0.464350i | \(0.846288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.7812 | + | 9.00854i | −0.839312 | + | 0.701314i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.3992 | − | 10.4616i | −1.11424 | − | 0.809545i | −0.130916 | − | 0.991393i | \(-0.541792\pi\) |
−0.983326 | + | 0.181849i | \(0.941792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.26393 | − | 6.96767i | −0.174149 | − | 0.535974i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0172 | + | 8.73102i | −0.918980 | + | 0.667678i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.10081 | + | 6.46564i | −0.159722 | + | 0.491573i | −0.998609 | − | 0.0527326i | \(-0.983207\pi\) |
0.838887 | + | 0.544306i | \(0.183207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.18034 | 0.693968 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.85410 | −0.214527 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.809017 | + | 2.48990i | −0.0604688 | + | 0.186104i | −0.976728 | − | 0.214482i | \(-0.931194\pi\) |
0.916259 | + | 0.400586i | \(0.131194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.30902 | − | 0.951057i | 0.0972985 | − | 0.0706915i | −0.538072 | − | 0.842899i | \(-0.680847\pi\) |
0.635371 | + | 0.772207i | \(0.280847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.92705 | − | 5.93085i | −0.142452 | − | 0.438421i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42705 | − | 1.76336i | −0.178440 | − | 0.129644i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.69098 | − | 4.20025i | −0.489293 | − | 0.307153i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.97214 | − | 5.06555i | −0.507148 | − | 0.368465i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.04508 | + | 24.7602i | 0.582122 | + | 1.79159i | 0.610533 | + | 0.791991i | \(0.290955\pi\) |
−0.0284112 | + | 0.999596i | \(0.509045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2533 | − | 13.2618i | 1.31390 | − | 0.954605i | 0.313914 | − | 0.949451i | \(-0.398360\pi\) |
0.999987 | − | 0.00515308i | \(-0.00164028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.11803 | − | 9.59632i | 0.223287 | − | 0.687207i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.944272 | −0.0669377 | −0.0334688 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334688 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4721 | + | 32.2299i | −0.738648 | + | 2.27332i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.8713 | − | 19.5232i | 1.88600 | − | 1.37026i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.30902 | − | 13.2618i | −0.300955 | − | 0.926244i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.70820 | + | 5.60034i | 0.535757 | + | 0.389250i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.7533 | − | 0.865300i | 0.882163 | − | 0.0598540i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.63525 | − | 7.00042i | −0.663318 | − | 0.481929i | 0.204464 | − | 0.978874i | \(-0.434455\pi\) |
−0.867782 | + | 0.496945i | \(0.834455\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.16312 | + | 15.8904i | 0.353771 | + | 1.08880i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.01722 | + | 3.13068i | −0.0690535 | + | 0.212525i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.38197 | 0.160958 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.67376 | 0.381659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.75329 | + | 11.5514i | −0.251339 | + | 0.773541i | 0.743190 | + | 0.669080i | \(0.233312\pi\) |
−0.994529 | + | 0.104461i | \(0.966688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.42705 | − | 5.39607i | 0.495137 | − | 0.359738i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.75329 | + | 5.39607i | 0.116370 | + | 0.358150i | 0.992230 | − | 0.124415i | \(-0.0397054\pi\) |
−0.875860 | + | 0.482565i | \(0.839705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1631 | − | 9.56357i | −0.869843 | − | 0.631978i | 0.0607015 | − | 0.998156i | \(-0.480666\pi\) |
−0.930545 | + | 0.366178i | \(0.880666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.4721 | + | 31.0543i | 0.820606 | + | 2.04323i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.92705 | − | 1.40008i | −0.126245 | − | 0.0917226i | 0.522871 | − | 0.852412i | \(-0.324861\pi\) |
−0.649116 | + | 0.760689i | \(0.724861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.690983 | − | 2.12663i | −0.0450748 | − | 0.138726i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1353 | + | 10.9964i | −0.983140 | + | 0.714293i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.57295 | + | 10.9964i | −0.231115 | + | 0.711298i | 0.766498 | + | 0.642246i | \(0.221997\pi\) |
−0.997613 | + | 0.0690519i | \(0.978003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4721 | 0.803401 | 0.401700 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401700 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.92705 | + | 12.0862i | −0.250890 | + | 0.772160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.42705 | + | 5.39607i | −0.472572 | + | 0.343344i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5451 | − | 32.4544i | −0.668268 | − | 2.05672i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.8713 | − | 15.1639i | −1.31739 | − | 0.957137i | −0.999961 | − | 0.00885387i | \(-0.997182\pi\) |
−0.317425 | − | 0.948283i | \(-0.602818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.05573 | − | 7.60845i | −0.192112 | − | 0.478339i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.16312 | − | 5.93085i | −0.511194 | − | 0.371404i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.51722 | − | 4.66953i | −0.0946416 | − | 0.291277i | 0.892518 | − | 0.451011i | \(-0.148936\pi\) |
−0.987160 | + | 0.159734i | \(0.948936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.78115 | + | 4.20025i | −0.359223 | + | 0.260991i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2639 | − | 31.5891i | 0.635321 | − | 1.95532i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.88854 | 0.363103 | 0.181552 | − | 0.983381i | \(-0.441888\pi\) | ||||
0.181552 | + | 0.983381i | \(0.441888\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.61803 | 0.406543 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.381966 | + | 1.17557i | −0.0233759 | + | 0.0719437i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4894 | − | 14.1598i | 1.18829 | − | 0.863341i | 0.195205 | − | 0.980762i | \(-0.437463\pi\) |
0.993082 | + | 0.117421i | \(0.0374628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.95492 | − | 18.3273i | −0.361735 | − | 1.11331i | −0.952000 | − | 0.306097i | \(-0.900977\pi\) |
0.590265 | − | 0.807210i | \(-0.299023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.4443 | − | 14.1271i | −1.17682 | − | 0.855010i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.88197 | + | 0.534785i | −0.475300 | + | 0.0322487i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2533 | + | 13.2618i | 1.09673 | + | 0.796824i | 0.980524 | − | 0.196401i | \(-0.0629254\pi\) |
0.116210 | + | 0.993225i | \(0.462925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.01722 | + | 3.13068i | 0.0608994 | + | 0.187429i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1074 | + | 16.0620i | −1.31882 | + | 0.958176i | −0.318870 | + | 0.947798i | \(0.603303\pi\) |
−0.999946 | + | 0.0103778i | \(0.996697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.57295 | + | 10.9964i | −0.212390 | + | 0.653669i | 0.786939 | + | 0.617031i | \(0.211665\pi\) |
−0.999329 | + | 0.0366375i | \(0.988335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.3262 | 0.967083 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.2148 | −1.96061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 10.7719i | −0.205882 | + | 0.633641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.8435 | + | 22.4091i | −1.80808 | + | 1.31364i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.66312 | + | 8.19624i | 0.155581 | + | 0.478829i | 0.998219 | − | 0.0596508i | \(-0.0189987\pi\) |
−0.842638 | + | 0.538480i | \(0.818999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.42705 | + | 1.03681i | 0.0830861 | + | 0.0603656i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.28115 | + | 3.94298i | 0.364469 | + | 0.228795i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.76393 | + | 3.46120i | 0.275505 | + | 0.200166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.6976 | − | 27.3889i | 2.16567 | − | 1.57345i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.19098 | + | 3.66547i | −0.0681955 | + | 0.209884i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.52786 | 0.543784 | 0.271892 | − | 0.962328i | \(-0.412351\pi\) | ||||
0.271892 | + | 0.962328i | \(0.412351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.5623 | 1.16975 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.19098 | − | 15.9762i | 0.294354 | − | 0.905927i | −0.689084 | − | 0.724681i | \(-0.741987\pi\) |
0.983438 | − | 0.181246i | \(-0.0580130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.07295 | − | 4.41226i | 0.343263 | − | 0.249395i | −0.402774 | − | 0.915299i | \(-0.631954\pi\) |
0.746037 | + | 0.665904i | \(0.231954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.42705 | + | 22.8581i | 0.418467 | + | 1.28791i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7812 | + | 8.55951i | 0.661695 | + | 0.480750i | 0.867235 | − | 0.497899i | \(-0.165895\pi\) |
−0.205540 | + | 0.978649i | \(0.565895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9336 | + | 18.3273i | −1.22805 | + | 1.02613i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.4894 | − | 17.7926i | −1.36686 | − | 0.993084i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.83688 | + | 8.73102i | 0.157848 | + | 0.485807i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.59017 | − | 3.33495i | 0.254617 | − | 0.184990i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0902 | − | 31.0543i | 0.557988 | − | 1.71731i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.32624 | −0.293645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.20820 | + | 6.79615i | −0.121009 | + | 0.372427i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.9443 | − | 12.3107i | 0.925764 | − | 0.672607i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.42705 | + | 22.8581i | 0.404577 | + | 1.24516i | 0.921248 | + | 0.388976i | \(0.127171\pi\) |
−0.516670 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 37.1976 | + | 27.0256i | 2.02029 | + | 1.46783i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.690983 | − | 2.74717i | 0.0374188 | − | 0.148768i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.66312 | + | 1.93487i | 0.143795 | + | 0.104473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.23607 | − | 9.95959i | −0.174224 | − | 0.536206i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.3992 | − | 10.4616i | 0.772989 | − | 0.561609i | −0.129878 | − | 0.991530i | \(-0.541458\pi\) |
0.902867 | + | 0.429921i | \(0.141458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.04508 | + | 15.5272i | −0.270057 | + | 0.831151i | 0.720428 | + | 0.693530i | \(0.243945\pi\) |
−0.990485 | + | 0.137621i | \(0.956055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.32624 | −0.284294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.9443 | −0.795403 | −0.397702 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397702 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.19098 | − | 9.82084i | 0.169360 | − | 0.521236i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.4443 | + | 14.1271i | −1.02910 | + | 0.747685i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.57295 | + | 10.9964i | 0.188573 | + | 0.580368i | 0.999992 | − | 0.00409736i | \(-0.00130423\pi\) |
−0.811419 | + | 0.584465i | \(0.801304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.35410 | + | 2.43690i | 0.176532 | + | 0.128258i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.5172 | − | 25.9358i | −0.656984 | − | 1.36128i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.19098 | − | 0.865300i | −0.0623389 | − | 0.0452919i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.22542 | + | 19.1599i | 0.324965 | + | 1.00014i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) |
−0.646492 | + | 0.762921i | \(0.723765\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.8713 | + | 19.5232i | −1.39887 | + | 1.01634i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.87132 | − | 14.9924i | 0.252906 | − | 0.778366i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.58359 | −0.340885 | −0.170443 | − | 0.985368i | \(-0.554520\pi\) | ||||
−0.170443 | + | 0.985368i | \(0.554520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.2705 | −1.61480 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.34346 | − | 19.5232i | 0.326705 | − | 1.00549i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.54508 | + | 1.84911i | −0.130732 | + | 0.0949825i | −0.651230 | − | 0.758881i | \(-0.725747\pi\) |
0.520497 | + | 0.853863i | \(0.325747\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.92705 | + | 5.93085i | 0.0987258 | + | 0.303847i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.1074 | − | 11.7027i | −0.823049 | − | 0.597980i | 0.0945351 | − | 0.995522i | \(-0.469864\pi\) |
−0.917584 | + | 0.397541i | \(0.869864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.04508 | − | 20.0579i | 0.257121 | − | 1.02225i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.28115 | − | 25.4868i | −0.419871 | − | 1.29223i | −0.907821 | − | 0.419359i | \(-0.862255\pi\) |
0.487950 | − | 0.872872i | \(-0.337745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.76393 | − | 3.46120i | 0.240922 | − | 0.175040i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.70820 | + | 23.7234i | −0.388827 | + | 1.19669i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.5623 | 0.581763 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.8328 | 1.64783 | 0.823916 | − | 0.566712i | \(-0.191785\pi\) | ||||
0.823916 | + | 0.566712i | \(0.191785\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0172 | − | 36.9852i | 0.601614 | − | 1.85158i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.45492 | + | 3.96323i | −0.272405 | + | 0.197914i | −0.715598 | − | 0.698512i | \(-0.753846\pi\) |
0.443193 | + | 0.896426i | \(0.353846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.628677 | + | 1.93487i | 0.0313166 | + | 0.0963827i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.47214 | − | 5.42882i | −0.371293 | − | 0.269760i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.71885 | − | 3.94298i | 0.233905 | − | 0.195446i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.78115 | + | 4.20025i | 0.285860 | + | 0.207689i | 0.721469 | − | 0.692447i | \(-0.243467\pi\) |
−0.435610 | + | 0.900136i | \(0.643467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1631 | − | 34.3565i | −0.550636 | − | 1.69468i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.39919 | − | 2.46965i | 0.167263 | − | 0.121524i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.51722 | + | 20.0579i | −0.319918 | + | 0.984606i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.2705 | −1.48235 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.58359 | −0.223923 | −0.111962 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111962 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.86475 | + | 8.81678i | −0.139619 | + | 0.429704i | −0.996280 | − | 0.0861767i | \(-0.972535\pi\) |
0.856661 | + | 0.515880i | \(0.172535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.30902 | + | 3.13068i | −0.209512 | + | 0.152219i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.75329 | − | 5.39607i | −0.0850470 | − | 0.261748i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.42705 | + | 5.39607i | 0.359420 | + | 0.261134i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.5172 | + | 10.9964i | 0.845739 | + | 0.530912i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4894 | + | 9.80059i | 0.649759 | + | 0.472078i | 0.863189 | − | 0.504881i | \(-0.168463\pi\) |
−0.213430 | + | 0.976958i | \(0.568463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.01064 | + | 18.4989i | 0.288853 | + | 0.888998i | 0.985217 | + | 0.171310i | \(0.0547999\pi\) |
−0.696364 | + | 0.717689i | \(0.745200\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −29.5344 | + | 21.4580i | −1.41607 | + | 1.02883i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.94427 | + | 9.06154i | −0.140844 | + | 0.433472i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4164 | −0.735785 | −0.367893 | − | 0.929868i | \(-0.619921\pi\) | ||||
−0.367893 | + | 0.929868i | \(0.619921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.2705 | 1.44145 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.01064 | − | 3.11044i | 0.0480171 | − | 0.147781i | −0.924173 | − | 0.381974i | \(-0.875245\pi\) |
0.972190 | + | 0.234192i | \(0.0752445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.618034 | − | 0.449028i | 0.0292976 | − | 0.0212860i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.92705 | − | 5.93085i | −0.0911464 | − | 0.280520i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.7812 | + | 8.55951i | 0.555987 | + | 0.403948i | 0.829988 | − | 0.557781i | \(-0.188347\pi\) |
−0.274001 | + | 0.961729i | \(0.588347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.5172 | − | 1.93487i | 1.34282 | − | 0.0911094i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.8156 | + | 29.6543i | 1.91768 | + | 1.39328i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.59017 | + | 14.1271i | 0.215190 | + | 0.662288i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.78115 | − | 4.20025i | 0.270431 | − | 0.196480i | −0.444302 | − | 0.895877i | \(-0.646548\pi\) |
0.714733 | + | 0.699398i | \(0.246548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.64590 | + | 5.06555i | −0.0768239 | + | 0.236440i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.7771 | −1.57316 | −0.786578 | − | 0.617491i | \(-0.788149\pi\) | ||||
−0.786578 | + | 0.617491i | \(0.788149\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0000 | −0.557687 | −0.278844 | − | 0.960337i | \(-0.589951\pi\) | ||||
−0.278844 | + | 0.960337i | \(0.589951\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.11803 | − | 3.44095i | 0.0518476 | − | 0.159570i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.2533 | + | 7.44945i | −0.474466 | + | 0.344719i | −0.799179 | − | 0.601093i | \(-0.794732\pi\) |
0.324713 | + | 0.945812i | \(0.394732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4164 | − | 47.4468i | −0.711864 | − | 2.19089i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.1976 | + | 27.0256i | 1.71397 | + | 1.24527i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.42705 | + | 5.39607i | 0.340776 | + | 0.247589i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.87132 | − | 14.9924i | −0.223043 | − | 0.686454i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1074 | − | 16.0620i | 1.01011 | − | 0.733890i | 0.0458798 | − | 0.998947i | \(-0.485391\pi\) |
0.964233 | + | 0.265057i | \(0.0853909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36475 | + | 4.20025i | −0.0622270 | + | 0.191515i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.9443 | −1.13500 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.5623 | 1.06991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.57295 | + | 17.1518i | −0.252534 | + | 0.777221i | 0.741771 | + | 0.670653i | \(0.233986\pi\) |
−0.994305 | + | 0.106568i | \(0.966014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.9894 | − | 17.4293i | 1.08484 | − | 0.788180i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.57295 | + | 10.9964i | 0.161245 | + | 0.496261i | 0.998740 | − | 0.0501840i | \(-0.0159808\pi\) |
−0.837495 | + | 0.546445i | \(0.815981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.6074 | − | 12.0660i | −0.747959 | − | 0.543424i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.70820 | − | 19.1926i | −0.346458 | − | 0.862645i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.8992 | − | 14.4576i | −0.892601 | − | 0.648512i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.19098 | − | 22.1316i | −0.321913 | − | 0.990745i | −0.972815 | − | 0.231584i | \(-0.925609\pi\) |
0.650902 | − | 0.759161i | \(-0.274391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.6976 | − | 27.3889i | 1.68420 | − | 1.22364i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.2812 | + | 34.7198i | −0.503002 | + | 1.54808i | 0.301102 | + | 0.953592i | \(0.402645\pi\) |
−0.804104 | + | 0.594488i | \(0.797355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.7984 | −1.28151 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.1803 | 0.851829 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.86475 | + | 27.2829i | −0.392923 | + | 1.20929i | 0.537644 | + | 0.843172i | \(0.319314\pi\) |
−0.930567 | + | 0.366121i | \(0.880686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.83688 | + | 2.06111i | −0.125496 | + | 0.0911783i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.66312 | − | 8.19624i | −0.117580 | − | 0.361873i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.2812 | − | 7.46969i | −0.453042 | − | 0.329154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.57295 | − | 0.310271i | 0.201118 | − | 0.0136457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3992 | − | 10.4616i | −0.632054 | − | 0.459214i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.37132 | + | 7.29818i | 0.103890 | + | 0.319739i | 0.989468 | − | 0.144750i | \(-0.0462379\pi\) |
−0.885579 | + | 0.464489i | \(0.846238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.0172 | + | 16.7230i | −1.00647 | + | 0.731245i | −0.963466 | − | 0.267830i | \(-0.913694\pi\) |
−0.0430065 | + | 0.999075i | \(0.513694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.42705 | + | 22.8581i | −0.324143 | + | 0.997610i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.03444 | 0.0886217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.29837 | − | 3.99598i | 0.0563446 | − | 0.173411i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6074 | + | 12.0660i | −0.719346 | + | 0.522635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.78115 | + | 17.7926i | 0.249941 | + | 0.769239i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.54508 | − | 4.02874i | −0.239288 | − | 0.173853i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.0623 | − | 13.8496i | −0.950291 | − | 0.596543i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.69098 | − | 4.86128i | −0.287668 | − | 0.209003i | 0.434587 | − | 0.900630i | \(-0.356894\pi\) |
−0.722255 | + | 0.691627i | \(0.756894\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.30902 | + | 4.02874i | 0.0561753 | + | 0.172890i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.3262 | + | 11.8617i | −0.699339 | + | 0.508100i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8435 | − | 36.4504i | 0.506390 | − | 1.55851i | −0.292032 | − | 0.956409i | \(-0.594331\pi\) |
0.798422 | − | 0.602099i | \(-0.205669\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.18034 | 0.391807 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.2148 | 1.41500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.51064 | − | 26.1931i | 0.361909 | − | 1.11384i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.35410 | − | 4.61653i | 0.269717 | − | 0.195961i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.80902 | − | 30.1891i | −0.415621 | − | 1.27915i | −0.911694 | − | 0.410870i | \(-0.865225\pi\) |
0.496073 | − | 0.868281i | \(-0.334775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8713 | − | 13.2618i | 0.670088 | − | 0.559913i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5451 | + | 7.66145i | 0.444422 | + | 0.322892i | 0.787390 | − | 0.616456i | \(-0.211432\pi\) |
−0.342967 | + | 0.939347i | \(0.611432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.78115 | − | 27.0256i | −0.369426 | − | 1.13698i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.7984 | + | 12.9313i | −0.747461 | + | 0.543063i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.24671 | − | 28.4585i | 0.387642 | − | 1.19304i | −0.546903 | − | 0.837196i | \(-0.684193\pi\) |
0.934545 | − | 0.355844i | \(-0.115807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.52786 | 0.398729 | 0.199364 | − | 0.979925i | \(-0.436112\pi\) | ||||
0.199364 | + | 0.979925i | \(0.436112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −68.1591 | −2.84739 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.81966 | − | 5.60034i | 0.0758851 | − | 0.233550i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1976 | − | 21.2133i | 1.21551 | − | 0.883120i | 0.219791 | − | 0.975547i | \(-0.429462\pi\) |
0.995719 | + | 0.0924270i | \(0.0294625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.2533 | + | 56.1778i | 0.758581 | + | 2.33467i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.6418 | + | 29.5280i | 1.68611 | + | 1.22503i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.30902 | + | 13.1558i | −0.137045 | + | 0.544857i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0172 | + | 8.73102i | 0.496851 | + | 0.360983i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.42705 | − | 7.46969i | −0.100175 | − | 0.308307i | 0.888393 | − | 0.459084i | \(-0.151822\pi\) |
−0.988568 | + | 0.150777i | \(0.951822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.66312 | + | 1.93487i | −0.109732 | + | 0.0797249i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.38197 | − | 7.33094i | 0.0979810 | − | 0.301554i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4164 | 1.53651 | 0.768254 | − | 0.640145i | \(-0.221126\pi\) | ||||
0.768254 | + | 0.640145i | \(0.221126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.8541 | 0.608959 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.763932 | − | 2.35114i | 0.0312657 | − | 0.0962258i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1976 | + | 27.0256i | −1.51985 | + | 1.10424i | −0.558290 | + | 0.829646i | \(0.688542\pi\) |
−0.961561 | + | 0.274591i | \(0.911458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3713 | + | 31.9196i | 0.423055 | + | 1.30203i | 0.904844 | + | 0.425743i | \(0.139987\pi\) |
−0.481789 | + | 0.876287i | \(0.660013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −40.3607 | − | 29.3238i | −1.64361 | − | 1.19416i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.16312 | + | 17.5150i | −0.128599 | + | 0.712088i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.3435 | − | 12.6008i | −0.703949 | − | 0.511449i | 0.177267 | − | 0.984163i | \(-0.443274\pi\) |
−0.881216 | + | 0.472714i | \(0.843274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.8713 | + | 82.7014i | 1.08888 | + | 3.35123i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.66312 | + | 1.93487i | −0.107738 | + | 0.0782764i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.22542 | + | 9.92684i | −0.130274 | + | 0.400941i | −0.994825 | − | 0.101603i | \(-0.967603\pi\) |
0.864551 | + | 0.502545i | \(0.167603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.5066 | 1.47209 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.52786 | −0.303060 | −0.151530 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151530 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.89919 | − | 21.2335i | 0.277302 | − | 0.853447i | −0.711299 | − | 0.702889i | \(-0.751893\pi\) |
0.988601 | − | 0.150558i | \(-0.0481070\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.47214 | + | 3.24920i | −0.179461 | + | 0.130386i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.562306 | − | 1.73060i | −0.0225283 | − | 0.0693350i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.00000 | + | 4.35926i | 0.240000 | + | 0.174370i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.16312 | + | 32.4544i | −0.326004 | + | 1.29611i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.57295 | + | 2.59590i | 0.142463 | + | 0.103505i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.37132 | − | 22.6866i | −0.293448 | − | 0.903139i | −0.983738 | − | 0.179607i | \(-0.942517\pi\) |
0.690291 | − | 0.723532i | \(-0.257483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.2254 | − | 18.3273i | 1.00262 | − | 0.728447i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.19098 | − | 3.66547i | 0.0472627 | − | 0.145460i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.7082 | 0.741246 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.5967 | −0.973032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.37132 | − | 25.7643i | 0.330647 | − | 1.01763i | −0.638179 | − | 0.769888i | \(-0.720312\pi\) |
0.968827 | − | 0.247740i | \(-0.0796879\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.92705 | − | 7.21242i | 0.391485 | − | 0.284430i | −0.374579 | − | 0.927195i | \(-0.622213\pi\) |
0.766064 | + | 0.642765i | \(0.222213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.45492 | − | 3.96323i | −0.214455 | − | 0.155811i | 0.475372 | − | 0.879785i | \(-0.342313\pi\) |
−0.689827 | + | 0.723974i | \(0.742313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.77458 | + | 2.31838i | −0.108912 | + | 0.0910046i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.97214 | − | 5.06555i | −0.273260 | − | 0.198535i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.37132 | + | 7.29818i | 0.0927970 | + | 0.285600i | 0.986673 | − | 0.162714i | \(-0.0520247\pi\) |
−0.893876 | + | 0.448314i | \(0.852025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.4721 | − | 9.06154i | 0.487327 | − | 0.354064i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.08359 | + | 3.33495i | −0.0422750 | + | 0.130109i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.3607 | 1.57223 | 0.786114 | − | 0.618081i | \(-0.212090\pi\) | ||||
0.786114 | + | 0.618081i | \(0.212090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3607 | −1.18089 | −0.590447 | − | 0.807077i | \(-0.701048\pi\) | ||||
−0.590447 | + | 0.807077i | \(0.701048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.59017 | + | 14.1271i | −0.178267 | + | 0.548651i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.4443 | + | 14.1271i | −0.754017 | + | 0.547825i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.58359 | − | 20.2622i | −0.254918 | − | 0.784556i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.7254 | − | 18.6906i | −0.994602 | − | 0.722621i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.69098 | − | 4.20025i | −0.258303 | − | 0.162149i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.8156 | − | 21.6623i | −1.14931 | − | 0.835020i | −0.160918 | − | 0.986968i | \(-0.551446\pi\) |
−0.988389 | + | 0.151948i | \(0.951446\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.64590 | + | 5.06555i | 0.0633506 | + | 0.194973i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.83688 | − | 2.06111i | 0.109030 | − | 0.0792151i | −0.531934 | − | 0.846786i | \(-0.678535\pi\) |
0.640964 | + | 0.767571i | \(0.278535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3435 | − | 53.3777i | 0.665581 | − | 2.04845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8541 | −0.569210 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.944272 | −0.0361316 | −0.0180658 | − | 0.999837i | \(-0.505751\pi\) | ||||
−0.0180658 | + | 0.999837i | \(0.505751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.89919 | + | 21.2335i | −0.263604 | + | 0.811291i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.4615 | − | 25.0377i | 1.31479 | − | 0.955249i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.01064 | − | 9.26581i | −0.114696 | − | 0.352999i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.4894 | + | 14.1598i | 0.741410 | + | 0.538666i | 0.893152 | − | 0.449754i | \(-0.148488\pi\) |
−0.151742 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −49.1525 | + | 3.33495i | −1.86715 | + | 0.126684i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.1353 | + | 10.9964i | 0.574113 | + | 0.417117i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.34346 | + | 19.5232i | 0.240276 | + | 0.739492i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.04508 | − | 3.66547i | 0.190823 | − | 0.138641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1353 | − | 46.5815i | 0.571651 | − | 1.75936i | −0.0756600 | − | 0.997134i | \(-0.524106\pi\) |
0.647311 | − | 0.762226i | \(-0.275894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.14590 | −0.269513 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.85410 | 0.220478 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.1976 | + | 65.2394i | −0.797216 | + | 2.45358i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8713 | + | 13.7108i | −0.708727 | + | 0.514921i | −0.882763 | − | 0.469819i | \(-0.844319\pi\) |
0.174035 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.51064 | − | 26.1931i | −0.319174 | − | 0.982317i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.70820 | + | 1.24108i | 0.0639727 | + | 0.0464789i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.76393 | − | 11.8617i | −0.178161 | − | 0.443603i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.4894 | − | 17.7926i | −0.914572 | − | 0.664475i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.1353 | − | 37.3485i | −0.452569 | − | 1.39286i | −0.873966 | − | 0.485987i | \(-0.838460\pi\) |
0.421397 | − | 0.906876i | \(-0.361540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.4894 | + | 17.7926i | −0.912031 | + | 0.662630i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0902 | + | 31.0543i | −0.375257 | + | 1.15492i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.5279 | −0.762386 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2254 | + | 37.6260i | −0.452794 | + | 1.39356i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3713 | + | 31.9196i | 0.383074 | + | 1.17898i | 0.937868 | + | 0.346992i | \(0.112797\pi\) |
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.9164 | − | 19.5559i | −0.992827 | − | 0.721331i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | + | 39.8384i | 0.589368 | + | 1.46747i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.1631 | − | 13.9228i | −0.704927 | − | 0.512159i | 0.176606 | − | 0.984282i | \(-0.443488\pi\) |
−0.881533 | + | 0.472122i | \(0.843488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.42705 | − | 22.8581i | −0.272840 | − | 0.839714i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.83688 | + | 2.06111i | −0.104075 | + | 0.0756150i | −0.638606 | − | 0.769534i | \(-0.720488\pi\) |
0.534531 | + | 0.845149i | \(0.320488\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.19098 | + | 3.66547i | −0.0436342 | + | 0.134292i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.2361 | 1.83804 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.5623 | 1.62827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13525 | − | 6.57164i | 0.0779166 | − | 0.239803i | −0.904510 | − | 0.426453i | \(-0.859763\pi\) |
0.982426 | + | 0.186650i | \(0.0597631\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.6418 | − | 39.6996i | 1.99126 | − | 1.44673i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.63525 | − | 29.6543i | −0.350663 | − | 1.07923i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.6353 | − | 15.7189i | −0.786347 | − | 0.571314i | 0.120530 | − | 0.992710i | \(-0.461540\pi\) |
−0.906877 | + | 0.421395i | \(0.861540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.4164 | − | 1.45309i | 0.777366 | − | 0.0527436i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.3090 | + | 11.1227i | 0.554951 | + | 0.403196i | 0.829608 | − | 0.558347i | \(-0.188564\pi\) |
−0.274656 | + | 0.961542i | \(0.588564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8541 | + | 45.7162i | 0.537755 | + | 1.65504i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.0172 | − | 8.73102i | 0.434484 | − | 0.315671i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.802439 | − | 2.46965i | 0.0289744 | − | 0.0891740i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4164 | 1.34927 | 0.674635 | − | 0.738151i | \(-0.264301\pi\) | ||||
0.674635 | + | 0.738151i | \(0.264301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8541 | 0.462929 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.75329 | + | 26.9399i | −0.314834 | + | 0.968959i | 0.660989 | + | 0.750396i | \(0.270137\pi\) |
−0.975823 | + | 0.218563i | \(0.929863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64590 | − | 1.19581i | 0.0591224 | − | 0.0429549i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.78115 | − | 17.7926i | −0.207398 | − | 0.638305i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.8713 | − | 19.5232i | −0.962765 | − | 0.699490i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9271 | + | 11.2537i | 0.641480 | + | 0.402688i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.5902 | + | 11.3269i | 0.557147 | + | 0.404791i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.78115 | − | 27.0256i | −0.313413 | − | 0.964585i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4894 | + | 9.80059i | −0.480844 | + | 0.349353i | −0.801652 | − | 0.597791i | \(-0.796045\pi\) |
0.320809 | + | 0.947144i | \(0.396045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.76393 | + | 14.6619i | −0.169600 | + | 0.521977i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −67.6869 | −2.40667 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.67376 | 0.201481 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.35410 | + | 16.4782i | −0.189890 | + | 0.584423i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.1631 | + | 8.11048i | −0.395418 | + | 0.287288i | −0.767672 | − | 0.640843i | \(-0.778585\pi\) |
0.372254 | + | 0.928131i | \(0.378585\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.01722 | + | 3.13068i | 0.0359867 | + | 0.110756i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.47214 | − | 1.06957i | −0.0520154 | − | 0.0377914i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.31559 | − | 1.93487i | 0.0817156 | − | 0.0682801i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.4721 | + | 9.06154i | 0.439585 | + | 0.319377i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.4894 | + | 59.9821i | 0.686058 | + | 2.11147i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.3090 | − | 11.1227i | 0.538236 | − | 0.391052i | −0.285193 | − | 0.958470i | \(-0.592058\pi\) |
0.823430 | + | 0.567418i | \(0.192058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.46149 | + | 29.1195i | −0.332238 | + | 1.02252i | 0.635829 | + | 0.771830i | \(0.280658\pi\) |
−0.968067 | + | 0.250693i | \(0.919342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 50.4508 | 1.76939 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.3262 | −0.641940 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.6246 | − | 20.7970i | 1.00022 | − | 0.726706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.98936 | − | 24.5887i | −0.278830 | − | 0.858152i | −0.988180 | − | 0.153295i | \(-0.951011\pi\) |
0.709350 | − | 0.704857i | \(-0.248989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.9615 | + | 23.2214i | 1.11411 | + | 0.809447i | 0.983306 | − | 0.181962i | \(-0.0582448\pi\) |
0.130802 | + | 0.991409i | \(0.458245\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.04508 | − | 20.0579i | 0.175647 | − | 0.698328i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.5451 | + | 7.66145i | 0.366689 | + | 0.266415i | 0.755836 | − | 0.654760i | \(-0.227231\pi\) |
−0.389148 | + | 0.921175i | \(0.627231\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7746 | + | 33.1607i | 0.374216 | + | 1.15172i | 0.944006 | + | 0.329929i | \(0.107025\pi\) |
−0.569789 | + | 0.821791i | \(0.692975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.7877 | + | 34.7198i | −1.65774 | + | 1.20442i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.78115 | − | 17.7926i | 0.200305 | − | 0.616476i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.7984 | −0.996609 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.90983 | −0.0660134 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.809017 | + | 2.48990i | −0.0279304 | + | 0.0859608i | −0.964050 | − | 0.265721i | \(-0.914390\pi\) |
0.936120 | + | 0.351682i | \(0.114390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −36.6246 | + | 26.6093i | −1.26292 | + | 0.917563i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.1074 | − | 68.0396i | −0.761419 | − | 2.34341i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.59017 | − | 6.96767i | −0.329912 | − | 0.239695i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.3500 | + | 20.0579i | 1.28336 | + | 0.689199i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.4894 | − | 17.7926i | −0.840473 | − | 0.610639i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.41641 | + | 4.35926i | 0.0485538 | + | 0.149433i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.3992 | + | 10.4616i | −0.493019 | + | 0.358199i | −0.806344 | − | 0.591447i | \(-0.798557\pi\) |
0.313325 | + | 0.949646i | \(0.398557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.42705 | + | 22.8581i | −0.254000 | + | 0.781731i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.94427 | 0.100574 | 0.0502872 | − | 0.998735i | \(-0.483986\pi\) | ||||
0.0502872 | + | 0.998735i | \(0.483986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0557 | −1.05961 | −0.529804 | − | 0.848120i | \(-0.677734\pi\) | ||||
−0.529804 | + | 0.848120i | \(0.677734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.8713 | − | 82.7014i | 0.915772 | − | 2.81846i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.3992 | − | 14.8209i | 0.694396 | − | 0.504509i | −0.183706 | − | 0.982981i | \(-0.558809\pi\) |
0.878102 | + | 0.478473i | \(0.158809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39919 | + | 10.4616i | 0.115576 | + | 0.355706i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.9894 | − | 17.4293i | −0.814721 | − | 0.591930i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.78115 | + | 22.9844i | −0.196112 | + | 0.779691i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.9443 | − | 18.1231i | −0.845204 | − | 0.614077i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.3435 | − | 53.3777i | −0.586987 | − | 1.80656i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 37.2426 | − | 27.0584i | 1.25903 | − | 0.914740i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.55166 | − | 26.3193i | 0.288769 | − | 0.888740i | −0.696474 | − | 0.717582i | \(-0.745249\pi\) |
0.985244 | − | 0.171158i | \(-0.0547510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.5623 | −0.761008 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8885 | 0.535299 | 0.267649 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267649 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.55166 | − | 4.77553i | 0.0522176 | − | 0.160709i | −0.921547 | − | 0.388267i | \(-0.873074\pi\) |
0.973765 | + | 0.227557i | \(0.0730739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.73607 | + | 2.71441i | −0.125587 | + | 0.0912440i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.628677 | + | 1.93487i | 0.0211089 | + | 0.0649665i | 0.961056 | − | 0.276353i | \(-0.0891260\pi\) |
−0.939947 | + | 0.341320i | \(0.889126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.42705 | − | 5.39607i | −0.249095 | − | 0.180978i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.5279 | − | 12.1392i | 0.486702 | − | 0.406679i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.30902 | − | 3.13068i | −0.144196 | − | 0.104764i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.30902 | + | 4.02874i | 0.0437556 | + | 0.134666i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.4721 | + | 9.06154i | −0.416432 | + | 0.302556i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.27458 | − | 7.00042i | 0.0758613 | − | 0.233477i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.74265 | −0.324575 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.809017 | − | 2.48990i | 0.0268926 | − | 0.0827670i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.60081 | + | 1.16306i | −0.0531541 | + | 0.0386187i | −0.614045 | − | 0.789271i | \(-0.710459\pi\) |
0.560891 | + | 0.827890i | \(0.310459\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.1976 | + | 65.2394i | 0.703079 | + | 2.16385i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7812 | + | 11.4657i | 0.522853 | + | 0.379875i | 0.817678 | − | 0.575676i | \(-0.195261\pi\) |
−0.294825 | + | 0.955551i | \(0.595261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.6140 | − | 22.9844i | −1.21175 | − | 0.760671i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.16312 | − | 5.93085i | −0.269864 | − | 0.196068i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.3475 | − | 34.9241i | −0.374728 | − | 1.15330i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3435 | − | 12.6008i | 0.572108 | − | 0.415661i | −0.263762 | − | 0.964588i | \(-0.584963\pi\) |
0.835870 | + | 0.548927i | \(0.184963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.70820 | + | 23.7234i | −0.253994 | + | 0.781713i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.2016 | −0.500368 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.41641 | 0.145211 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.35410 | + | 28.7890i | −0.307229 | + | 0.945554i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.1074 | + | 11.7027i | −0.528466 | + | 0.383953i | −0.819784 | − | 0.572673i | \(-0.805906\pi\) |
0.291317 | + | 0.956626i | \(0.405906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.35410 | + | 28.7890i | 0.306568 | + | 0.943520i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.5795 | + | 25.8500i | 1.16482 | + | 0.846292i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7533 | + | 0.865300i | −0.417077 | + | 0.0282983i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.78115 | + | 4.20025i | 0.188862 | + | 0.137216i | 0.678198 | − | 0.734879i | \(-0.262761\pi\) |
−0.489336 | + | 0.872095i | \(0.662761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.07295 | + | 18.6906i | 0.198183 | + | 0.609945i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.63525 | + | 7.00042i | −0.314100 | + | 0.228207i | −0.733654 | − | 0.679523i | \(-0.762187\pi\) |
0.419554 | + | 0.907731i | \(0.362187\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.58359 | + | 20.2622i | −0.214391 | + | 0.659828i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.9443 | −0.453607 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.7771 | −0.772652 | −0.386326 | − | 0.922362i | \(-0.626256\pi\) | ||||
−0.386326 | + | 0.922362i | \(0.626256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.669697 | + | 2.06111i | −0.0217393 | + | 0.0669066i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.8435 | + | 22.4091i | −1.00017 | + | 0.726664i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0106 | + | 43.1203i | 0.453849 | + | 1.39680i | 0.872481 | + | 0.488648i | \(0.162510\pi\) |
−0.418632 | + | 0.908156i | \(0.637490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.0795 | + | 24.7602i | 1.10279 | + | 0.801222i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.8885 | − | 69.4396i | −0.901509 | − | 2.24466i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.0238 | + | 31.2586i | 1.38931 | + | 1.00939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.35410 | − | 28.7890i | −0.301745 | − | 0.928676i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.0517 | − | 26.1931i | 1.16175 | − | 0.844060i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.2812 | − | 34.7198i | 0.363153 | − | 1.11767i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0000 | 1.41494 | 0.707472 | − | 0.706741i | \(-0.249835\pi\) | ||||
0.707472 | + | 0.706741i | \(0.249835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0344 | −0.772098 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.13525 | − | 6.57164i | 0.0685236 | − | 0.210894i | −0.910931 | − | 0.412559i | \(-0.864635\pi\) |
0.979455 | + | 0.201665i | \(0.0646352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.0517 | − | 26.1931i | 1.15576 | − | 0.839711i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.59017 | + | 14.1271i | 0.147003 | + | 0.452429i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.5451 | + | 12.0207i | 0.529324 | + | 0.384577i | 0.820105 | − | 0.572213i | \(-0.193915\pi\) |
−0.290781 | + | 0.956790i | \(0.593915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.583592 | + | 1.45309i | 0.0186517 | + | 0.0464408i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.8885 | + | 28.2542i | 1.24162 | + | 0.902087i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.1353 | − | 37.3485i | −0.387055 | − | 1.19123i | −0.934979 | − | 0.354703i | \(-0.884582\pi\) |
0.547924 | − | 0.836528i | \(-0.315418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.85410 | + | 2.80017i | −0.122802 | + | 0.0892208i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.30902 | − | 13.2618i | 0.137158 | − | 0.422127i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.70820 | − | 29.8788i | 0.308081 | − | 0.948174i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.23607 | + | 0.898056i | −0.0391860 | + | 0.0284703i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.24671 | + | 28.4585i | 0.292846 | + | 0.901288i | 0.983936 | + | 0.178520i | \(0.0571308\pi\) |
−0.691090 | + | 0.722769i | \(0.742869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.35410 | − | 2.43690i | −0.106119 | − | 0.0771000i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))