Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,2,Mod(49,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("176.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.m (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: | \(1.40536707557\) |
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: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.97 |
Dual form | 176.2.m.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | + | 0.224514i | −0.178411 | + | 0.129623i | −0.673407 | − | 0.739272i | \(-0.735170\pi\) |
0.494996 | + | 0.868895i | \(0.335170\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.190983 | + | 0.587785i | 0.0854102 | + | 0.262866i | 0.984636 | − | 0.174619i | \(-0.0558694\pi\) |
−0.899226 | + | 0.437485i | \(0.855869\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30902 | + | 1.67760i | 0.872726 | + | 0.634073i | 0.931317 | − | 0.364209i | \(-0.118661\pi\) |
−0.0585908 | + | 0.998282i | \(0.518661\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.881966 | + | 2.71441i | −0.293989 | + | 0.904804i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | − | 0.726543i | 0.975711 | − | 0.219061i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42705 | − | 4.39201i | 0.395793 | − | 1.21812i | −0.532550 | − | 0.846399i | \(-0.678766\pi\) |
0.928342 | − | 0.371726i | \(-0.121234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.190983 | − | 0.138757i | −0.0493116 | − | 0.0358270i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.42705 | + | 4.39201i | 0.346111 | + | 1.06522i | 0.960987 | + | 0.276595i | \(0.0892061\pi\) |
−0.614876 | + | 0.788624i | \(0.710794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.30902 | + | 1.67760i | −0.529725 | + | 0.384868i | −0.820255 | − | 0.571998i | \(-0.806168\pi\) |
0.290530 | + | 0.956866i | \(0.406168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.09017 | −0.237895 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.73607 | − | 2.71441i | 0.747214 | − | 0.542882i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.690983 | − | 2.12663i | −0.132980 | − | 0.409270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16312 | − | 3.75123i | −0.958767 | − | 0.696585i | −0.00590304 | − | 0.999983i | \(-0.501879\pi\) |
−0.952864 | + | 0.303397i | \(0.901879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.80902 | − | 5.56758i | 0.324909 | − | 0.999967i | −0.646573 | − | 0.762852i | \(-0.723798\pi\) |
0.971482 | − | 0.237115i | \(-0.0762017\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.836881 | + | 0.951057i | −0.145682 | + | 0.165558i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.545085 | + | 1.67760i | −0.0921362 | + | 0.283566i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.92705 | − | 2.85317i | −0.645603 | − | 0.469058i | 0.216167 | − | 0.976356i | \(-0.430644\pi\) |
−0.861771 | + | 0.507298i | \(0.830644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.545085 | + | 1.67760i | 0.0872835 | + | 0.268631i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.16312 | + | 3.75123i | −0.806344 | + | 0.585843i | −0.912768 | − | 0.408478i | \(-0.866060\pi\) |
0.106425 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.76393 | −0.262951 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.92705 | − | 2.12663i | 0.426954 | − | 0.310200i | −0.353476 | − | 0.935444i | \(-0.615000\pi\) |
0.780430 | + | 0.625243i | \(0.215000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.354102 | + | 1.08981i | 0.0505860 | + | 0.155688i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.42705 | − | 1.03681i | −0.199827 | − | 0.145183i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.19098 | − | 6.74315i | 0.300955 | − | 0.926243i | −0.680201 | − | 0.733025i | \(-0.738108\pi\) |
0.981156 | − | 0.193218i | \(-0.0618924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.04508 | + | 1.76336i | 0.140919 | + | 0.237771i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.336881 | − | 1.03681i | 0.0446210 | − | 0.137329i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.16312 | − | 5.93085i | −1.06275 | − | 0.772131i | −0.0881528 | − | 0.996107i | \(-0.528096\pi\) |
−0.974595 | + | 0.223976i | \(0.928096\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.42705 | + | 4.39201i | 0.182715 | + | 0.562339i | 0.999902 | − | 0.0140341i | \(-0.00446734\pi\) |
−0.817186 | + | 0.576374i | \(0.804467\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.59017 | + | 4.78804i | −0.830283 | + | 0.603236i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.85410 | 0.354008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.94427 | 0.604039 | 0.302019 | − | 0.953302i | \(-0.402339\pi\) | ||||
0.302019 | + | 0.953302i | \(0.402339\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | − | 1.45309i | 0.240772 | − | 0.174931i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.66312 | + | 8.19624i | 0.316054 | + | 0.972714i | 0.975318 | + | 0.220803i | \(0.0708678\pi\) |
−0.659264 | + | 0.751911i | \(0.729132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.78115 | + | 7.10642i | 1.14480 | + | 0.831744i | 0.987780 | − | 0.155852i | \(-0.0498123\pi\) |
0.157017 | + | 0.987596i | \(0.449812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.545085 | + | 1.67760i | −0.0629410 | + | 0.193712i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.69098 | + | 3.75123i | 0.990429 | + | 0.427492i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.28115 | − | 13.1760i | 0.481667 | − | 1.48242i | −0.355083 | − | 0.934835i | \(-0.615547\pi\) |
0.836750 | − | 0.547585i | \(-0.184453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.23607 | − | 4.53077i | −0.692896 | − | 0.503419i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.95492 | + | 15.2497i | 0.543873 | + | 1.67387i | 0.723655 | + | 0.690161i | \(0.242460\pi\) |
−0.179783 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30902 | + | 1.67760i | −0.250448 | + | 0.181961i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.43769 | 0.261348 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.47214 | −0.898045 | −0.449022 | − | 0.893521i | \(-0.648228\pi\) | ||||
−0.449022 | + | 0.893521i | \(0.648228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6631 | − | 7.74721i | 1.11780 | − | 0.812128i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.690983 | + | 2.12663i | 0.0716516 | + | 0.220521i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.42705 | − | 1.03681i | −0.146412 | − | 0.106375i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.71885 | − | 5.29007i | 0.174522 | − | 0.537125i | −0.825089 | − | 0.565003i | \(-0.808875\pi\) |
0.999611 | + | 0.0278780i | \(0.00887501\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.881966 | + | 9.42481i | −0.0886409 | + | 0.947229i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.10081 | + | 6.46564i | −0.209039 | + | 0.643355i | 0.790485 | + | 0.612482i | \(0.209829\pi\) |
−0.999523 | + | 0.0308731i | \(0.990171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.927051 | − | 0.673542i | −0.0913450 | − | 0.0663661i | 0.541175 | − | 0.840910i | \(-0.317980\pi\) |
−0.632520 | + | 0.774544i | \(0.717980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.208204 | − | 0.640786i | −0.0203186 | − | 0.0625343i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92705 | − | 5.03280i | 0.669663 | − | 0.486539i | −0.200249 | − | 0.979745i | \(-0.564175\pi\) |
0.869912 | + | 0.493206i | \(0.164175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52786 | −0.337908 | −0.168954 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168954 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.85410 | 0.175984 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.07295 | − | 1.50609i | 0.195007 | − | 0.141681i | −0.485997 | − | 0.873960i | \(-0.661544\pi\) |
0.681004 | + | 0.732280i | \(0.261544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.23607 | − | 3.80423i | −0.115264 | − | 0.354746i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.6631 | + | 7.74721i | 0.985806 | + | 0.716230i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.07295 | + | 12.5352i | −0.373367 | + | 1.14910i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | − | 4.70228i | 0.904025 | − | 0.427480i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.753289 | − | 2.31838i | 0.0679218 | − | 0.209042i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.80902 | + | 3.49396i | 0.430132 | + | 0.312509i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.42705 | + | 4.39201i | 0.126630 | + | 0.389728i | 0.994195 | − | 0.107597i | \(-0.0343156\pi\) |
−0.867564 | + | 0.497325i | \(0.834316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4721 | −1.61392 | −0.806959 | − | 0.590607i | \(-0.798888\pi\) | ||||
−0.806959 | + | 0.590607i | \(0.798888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.14590 | −0.706339 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.11803 | − | 0.812299i | 0.0962250 | − | 0.0699116i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.33688 | − | 10.2699i | −0.285089 | − | 0.877414i | −0.986372 | − | 0.164531i | \(-0.947389\pi\) |
0.701283 | − | 0.712883i | \(-0.252611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92705 | − | 5.03280i | −0.587545 | − | 0.426876i | 0.253891 | − | 0.967233i | \(-0.418289\pi\) |
−0.841436 | + | 0.540356i | \(0.818289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.427051 | + | 1.31433i | −0.0359642 | + | 0.110686i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.42705 | − | 15.2497i | 0.119336 | − | 1.27524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.21885 | − | 3.75123i | 0.101220 | − | 0.311522i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.354102 | − | 0.257270i | −0.0292058 | − | 0.0212193i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.42705 | + | 4.39201i | 0.116909 | + | 0.359808i | 0.992340 | − | 0.123534i | \(-0.0394229\pi\) |
−0.875432 | + | 0.483342i | \(0.839423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5451 | + | 8.38800i | −0.939526 | + | 0.682605i | −0.948306 | − | 0.317356i | \(-0.897205\pi\) |
0.00878076 | + | 0.999961i | \(0.497205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.1803 | −1.06557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.61803 | 0.290607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.07295 | − | 1.50609i | 0.165439 | − | 0.120199i | −0.501985 | − | 0.864876i | \(-0.667397\pi\) |
0.667424 | + | 0.744678i | \(0.267397\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.836881 | + | 2.57565i | 0.0663690 | + | 0.204263i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.9443 | − | 10.8576i | −1.17777 | − | 0.855703i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33688 | − | 4.11450i | 0.104713 | − | 0.322272i | −0.884950 | − | 0.465686i | \(-0.845808\pi\) |
0.989663 | + | 0.143413i | \(0.0458078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.718847 | − | 0.310271i | −0.0559622 | − | 0.0241545i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.10081 | − | 6.46564i | 0.162566 | − | 0.500326i | −0.836283 | − | 0.548298i | \(-0.815276\pi\) |
0.998849 | + | 0.0479722i | \(0.0152759\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.73607 | − | 4.89404i | −0.518159 | − | 0.376465i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.51722 | − | 7.74721i | −0.192497 | − | 0.592444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3992 | + | 10.4616i | −1.09475 | + | 0.795382i | −0.980195 | − | 0.198035i | \(-0.936544\pi\) |
−0.114555 | + | 0.993417i | \(0.536544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.1803 | 0.996340 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.85410 | 0.289692 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.309017 | + | 0.224514i | −0.0230970 | + | 0.0167810i | −0.599274 | − | 0.800544i | \(-0.704544\pi\) |
0.576177 | + | 0.817325i | \(0.304544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.190983 | + | 0.587785i | 0.0141957 | + | 0.0436897i | 0.957903 | − | 0.287091i | \(-0.0926881\pi\) |
−0.943708 | + | 0.330780i | \(0.892688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.42705 | − | 1.03681i | −0.105491 | − | 0.0766434i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.927051 | − | 2.85317i | 0.0681581 | − | 0.209769i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.80902 | + | 13.1760i | 0.571052 | + | 0.963527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.97214 | − | 6.06961i | 0.143452 | − | 0.441499i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.45492 | − | 1.78360i | −0.177631 | − | 0.129057i | 0.495417 | − | 0.868655i | \(-0.335015\pi\) |
−0.673048 | + | 0.739599i | \(0.735015\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.753289 | − | 2.31838i | −0.0542229 | − | 0.166881i | 0.920278 | − | 0.391266i | \(-0.127963\pi\) |
−0.974501 | + | 0.224385i | \(0.927963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.881966 | + | 0.640786i | −0.0631589 | + | 0.0458876i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9443 | 1.06474 | 0.532368 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532368 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9443 | −1.20115 | −0.600574 | − | 0.799569i | \(-0.705061\pi\) | ||||
−0.600574 | + | 0.799569i | \(0.705061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52786 | + | 1.11006i | −0.107767 | + | 0.0782975i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.62868 | − | 17.3233i | −0.395056 | − | 1.21586i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.19098 | − | 2.31838i | −0.222868 | − | 0.161923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.70820 | − | 17.5680i | 0.396748 | − | 1.22106i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.25329 | + | 7.10642i | −0.432549 | + | 0.491562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.13525 | + | 21.9601i | −0.491211 | + | 1.51179i | 0.331568 | + | 0.943431i | \(0.392422\pi\) |
−0.822779 | + | 0.568361i | \(0.807578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.66312 | − | 1.93487i | −0.182474 | − | 0.132575i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5172 | − | 9.82084i | 0.917609 | − | 0.666682i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.61803 | −0.312058 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.3262 | 1.43456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.2533 | + | 11.0822i | −1.02144 | + | 0.742117i | −0.966577 | − | 0.256378i | \(-0.917471\pi\) |
−0.0548591 | + | 0.998494i | \(0.517471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.07295 | + | 12.5352i | 0.271530 | + | 0.835683i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2533 | + | 12.5352i | 1.14514 | + | 0.831994i | 0.987827 | − | 0.155555i | \(-0.0497166\pi\) |
0.157314 | + | 0.987549i | \(0.449717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.33688 | + | 16.4252i | −0.352671 | + | 1.08541i | 0.604677 | + | 0.796471i | \(0.293302\pi\) |
−0.957348 | + | 0.288939i | \(0.906698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.52786 | + | 0.792055i | −0.232116 | + | 0.0521134i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.42705 | − | 4.39201i | 0.0934892 | − | 0.287730i | −0.893368 | − | 0.449326i | \(-0.851664\pi\) |
0.986857 | + | 0.161596i | \(0.0516641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.80902 | + | 1.31433i | 0.118007 | + | 0.0857373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.63525 | + | 5.03280i | 0.106221 | + | 0.326915i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.92705 | − | 5.03280i | 0.448074 | − | 0.325545i | −0.340761 | − | 0.940150i | \(-0.610685\pi\) |
0.788835 | + | 0.614605i | \(0.210685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.52786 | 0.227250 | 0.113625 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113625 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.572949 | + | 0.416272i | −0.0366044 | + | 0.0265946i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07295 | + | 12.5352i | 0.259156 | + | 0.797599i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.95492 | − | 3.59996i | −0.314005 | − | 0.228138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.371323 | + | 1.14281i | −0.0234377 | + | 0.0721338i | −0.962091 | − | 0.272728i | \(-0.912074\pi\) |
0.938654 | + | 0.344862i | \(0.112074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.9443 | + | 4.70228i | −1.31676 | + | 0.295630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.336881 | − | 1.03681i | 0.0210963 | − | 0.0649278i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0172 | + | 9.45756i | 0.811992 | + | 0.589947i | 0.914407 | − | 0.404795i | \(-0.132657\pi\) |
−0.102416 | + | 0.994742i | \(0.532657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.28115 | − | 13.1760i | −0.266018 | − | 0.818719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.7361 | − | 10.7064i | 0.912140 | − | 0.662708i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.8885 | 1.84301 | 0.921503 | − | 0.388371i | \(-0.126962\pi\) | ||||
0.921503 | + | 0.388371i | \(0.126962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.38197 | 0.269182 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.61803 | − | 1.90211i | 0.160221 | − | 0.116407i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.98936 | − | 12.2780i | −0.243235 | − | 0.748602i | −0.995922 | − | 0.0902222i | \(-0.971242\pi\) |
0.752686 | − | 0.658379i | \(-0.228758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5451 | + | 8.38800i | 0.701314 | + | 0.509534i | 0.880360 | − | 0.474306i | \(-0.157301\pi\) |
−0.179046 | + | 0.983841i | \(0.557301\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.55573 | + | 4.78804i | −0.0941569 | + | 0.289785i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.1180 | − | 11.4984i | 0.610140 | − | 0.693382i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.753289 | + | 2.31838i | −0.0452607 | + | 0.139298i | −0.971133 | − | 0.238538i | \(-0.923332\pi\) |
0.925872 | + | 0.377836i | \(0.123332\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.5172 | + | 9.82084i | 0.809255 | + | 0.587958i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.60739 | + | 11.1024i | 0.215199 | + | 0.662314i | 0.999139 | + | 0.0414782i | \(0.0132067\pi\) |
−0.783941 | + | 0.620836i | \(0.786793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.92705 | − | 5.03280i | 0.411770 | − | 0.299169i | −0.362548 | − | 0.931965i | \(-0.618093\pi\) |
0.774318 | + | 0.632796i | \(0.218093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.673762 | 0.0399102 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.2148 | −1.07518 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 2.54290i | −0.205882 | + | 0.149582i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.656541 | + | 2.02063i | 0.0384871 | + | 0.118451i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.16312 | − | 3.75123i | −0.301633 | − | 0.219149i | 0.426665 | − | 0.904410i | \(-0.359688\pi\) |
−0.728298 | + | 0.685261i | \(0.759688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.92705 | − | 5.93085i | 0.112197 | − | 0.345308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.78115 | − | 6.37988i | −0.219405 | − | 0.370198i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.23607 | + | 28.4257i | −0.534136 | + | 1.64390i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.802439 | − | 2.46965i | −0.0460989 | − | 0.141878i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.30902 | + | 1.67760i | −0.132214 | + | 0.0960590i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4721 | −1.05426 | −0.527130 | − | 0.849785i | \(-0.676732\pi\) | ||||
−0.527130 | + | 0.849785i | \(0.676732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.437694 | 0.0248995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.30902 | + | 4.58377i | −0.357752 | + | 0.259922i | −0.752114 | − | 0.659033i | \(-0.770966\pi\) |
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.42705 | + | 29.0135i | 0.532848 | + | 1.63994i | 0.748253 | + | 0.663414i | \(0.230893\pi\) |
−0.215404 | + | 0.976525i | \(0.569107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.07295 | − | 2.95917i | −0.229485 | − | 0.166730i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.71885 | − | 5.29007i | 0.0965401 | − | 0.297120i | −0.891112 | − | 0.453784i | \(-0.850074\pi\) |
0.987652 | + | 0.156664i | \(0.0500739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.4336 | − | 8.38800i | −1.08807 | − | 0.469638i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.01064 | + | 3.11044i | −0.0564086 | + | 0.173608i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.6631 | − | 7.74721i | −0.593312 | − | 0.431066i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.59017 | − | 20.2825i | −0.365557 | − | 1.12507i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.09017 | − | 0.792055i | 0.0602865 | − | 0.0438007i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.3262 | 0.569304 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.2082 | − | 8.14324i | 0.614206 | − | 0.446247i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.944272 | + | 2.90617i | 0.0515911 | + | 0.158781i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.07295 | + | 2.95917i | 0.221868 | + | 0.161196i | 0.693167 | − | 0.720777i | \(-0.256215\pi\) |
−0.471299 | + | 0.881973i | \(0.656215\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.302439 | + | 0.930812i | −0.0164262 | + | 0.0505548i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.80902 | − | 19.3314i | 0.0979638 | − | 1.04685i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.16312 | − | 15.8904i | 0.278782 | − | 0.858003i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.23607 | + | 0.898056i | 0.0665477 | + | 0.0483497i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.10081 | − | 6.46564i | −0.112778 | − | 0.347094i | 0.878699 | − | 0.477375i | \(-0.158412\pi\) |
−0.991477 | + | 0.130282i | \(0.958412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.545085 | − | 0.396027i | 0.0291777 | − | 0.0211989i | −0.573101 | − | 0.819485i | \(-0.694260\pi\) |
0.602279 | + | 0.798286i | \(0.294260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3262 | −0.551174 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.94427 | 0.156708 | 0.0783539 | − | 0.996926i | \(-0.475034\pi\) | ||||
0.0783539 | + | 0.996926i | \(0.475034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.30902 | + | 3.13068i | −0.228699 | + | 0.166159i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.55573 | − | 4.78804i | −0.0823379 | − | 0.253410i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.92705 | − | 5.03280i | −0.365596 | − | 0.265621i | 0.389787 | − | 0.920905i | \(-0.372549\pi\) |
−0.755382 | + | 0.655284i | \(0.772549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.35410 | + | 10.3229i | −0.176532 | + | 0.543309i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.01722 | + | 3.68571i | −0.105877 | + | 0.193450i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.30902 | + | 7.10642i | −0.120859 | + | 0.371967i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.7254 | + | 15.7844i | 1.13406 | + | 0.823941i | 0.986280 | − | 0.165079i | \(-0.0527880\pi\) |
0.147778 | + | 0.989021i | \(0.452788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.62868 | − | 17.3233i | −0.293017 | − | 0.901814i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3713 | − | 11.8945i | 0.849957 | − | 0.617530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.4164 | −1.73024 | −0.865118 | − | 0.501568i | \(-0.832757\pi\) | ||||
−0.865118 | + | 0.501568i | \(0.832757\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.27051 | −0.117249 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.8435 | + | 17.3233i | −1.22800 | + | 0.892195i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.04508 | − | 9.37181i | −0.156416 | − | 0.481397i | 0.841886 | − | 0.539655i | \(-0.181445\pi\) |
−0.998302 | + | 0.0582579i | \(0.981445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.42705 | − | 1.03681i | −0.0731100 | − | 0.0531176i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.60739 | + | 29.5685i | −0.490915 | + | 1.51088i | 0.332313 | + | 0.943169i | \(0.392171\pi\) |
−0.823228 | + | 0.567711i | \(0.807829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.545085 | + | 5.82485i | −0.0277801 | + | 0.296862i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.78115 | + | 1.29408i | 0.0903080 | + | 0.0656126i | 0.632023 | − | 0.774950i | \(-0.282225\pi\) |
−0.541715 | + | 0.840562i | \(0.682225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.23607 | − | 28.4257i | −0.467088 | − | 1.43755i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.70820 | − | 4.14725i | 0.287941 | − | 0.209201i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.56231 | 0.430816 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8328 | −1.04557 | −0.522785 | − | 0.852465i | \(-0.675107\pi\) | ||||
−0.522785 | + | 0.852465i | \(0.675107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.51722 | − | 1.82887i | 0.126019 | − | 0.0915579i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0451 | − | 33.9933i | −0.551565 | − | 1.69754i | −0.704846 | − | 0.709361i | \(-0.748984\pi\) |
0.153281 | − | 0.988183i | \(-0.451016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8713 | − | 15.8904i | −1.08949 | − | 0.791560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.47214 | − | 4.53077i | 0.0731510 | − | 0.225136i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.7812 | − | 6.37988i | −0.732675 | − | 0.316239i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.28115 | + | 13.1760i | −0.211689 | + | 0.651513i | 0.787683 | + | 0.616081i | \(0.211281\pi\) |
−0.999372 | + | 0.0354318i | \(0.988719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.33688 | + | 2.42439i | 0.164596 | + | 0.119586i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.89919 | − | 27.3889i | −0.437900 | − | 1.34772i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.01722 | + | 5.82485i | −0.393550 | + | 0.285931i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.27051 | 0.160158 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.4164 | 1.53479 | 0.767396 | − | 0.641173i | \(-0.221552\pi\) | ||||
0.767396 | + | 0.641173i | \(0.221552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.6353 | + | 14.2658i | −0.956964 | + | 0.695275i | −0.952444 | − | 0.304715i | \(-0.901439\pi\) |
−0.00452016 | + | 0.999990i | \(0.501439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.19098 | + | 9.82084i | 0.155151 | + | 0.477505i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2533 | + | 12.5352i | 0.836907 | + | 0.608049i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.07295 | + | 12.5352i | −0.197104 | + | 0.606623i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.98278 | + | 5.03280i | 0.144010 | + | 0.242986i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.98936 | − | 30.7441i | 0.481170 | − | 1.48089i | −0.356281 | − | 0.934379i | \(-0.615956\pi\) |
0.837452 | − | 0.546511i | \(-0.184044\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.4894 | + | 21.4253i | 1.41717 | + | 1.02963i | 0.992231 | + | 0.124410i | \(0.0397038\pi\) |
0.424937 | + | 0.905223i | \(0.360296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.465558 | + | 1.43284i | 0.0223218 | + | 0.0686995i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.9443 | − | 10.8576i | 0.714881 | − | 0.519392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.4164 | −0.544875 | −0.272438 | − | 0.962173i | \(-0.587830\pi\) | ||||
−0.272438 | + | 0.962173i | \(0.587830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.27051 | −0.155739 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.4894 | + | 17.7926i | −1.16352 | + | 0.845350i | −0.990220 | − | 0.139518i | \(-0.955445\pi\) |
−0.173305 | + | 0.984868i | \(0.555445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.61803 | − | 4.97980i | −0.0767022 | − | 0.236065i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.42705 | − | 1.03681i | −0.0674972 | − | 0.0490396i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.71885 | − | 5.29007i | 0.0811174 | − | 0.249654i | −0.902270 | − | 0.431171i | \(-0.858101\pi\) |
0.983388 | + | 0.181517i | \(0.0581007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9828 | + | 15.8904i | −0.658423 | + | 0.748252i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.68441 | − | 5.18407i | 0.0791403 | − | 0.243569i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.59017 | + | 4.78804i | 0.308952 | + | 0.224467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.28115 | − | 13.1760i | −0.200264 | − | 0.616349i | −0.999875 | − | 0.0158303i | \(-0.994961\pi\) |
0.799611 | − | 0.600519i | \(-0.205039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.35410 | − | 6.06961i | 0.389936 | − | 0.283305i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.7771 | 1.75945 | 0.879727 | − | 0.475479i | \(-0.157725\pi\) | ||||
0.879727 | + | 0.475479i | \(0.157725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.11803 | + | 0.812299i | −0.0518476 | + | 0.0376695i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.75329 | − | 26.9399i | −0.405054 | − | 1.24663i | −0.920850 | − | 0.389916i | \(-0.872504\pi\) |
0.515796 | − | 0.856711i | \(-0.327496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4164 | + | 8.29451i | 0.527161 | + | 0.383005i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.302439 | + | 0.930812i | −0.0139357 | + | 0.0428896i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.07295 | + | 12.5352i | −0.186880 | + | 0.575157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.3713 | + | 11.8945i | 0.749591 | + | 0.544610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.60739 | + | 11.1024i | 0.164826 | + | 0.507282i | 0.999023 | − | 0.0441838i | \(-0.0140687\pi\) |
−0.834198 | + | 0.551466i | \(0.814069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.1353 | + | 13.1760i | −0.826896 | + | 0.600775i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.05573 | 0.321047 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.43769 | 0.156098 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.92705 | − | 6.48588i | 0.404523 | − | 0.293903i | −0.366858 | − | 0.930277i | \(-0.619566\pi\) |
0.771381 | + | 0.636374i | \(0.219566\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.510643 | + | 1.57160i | 0.0230921 | + | 0.0710701i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.92705 | − | 5.03280i | −0.312613 | − | 0.227127i | 0.420404 | − | 0.907337i | \(-0.361888\pi\) |
−0.733017 | + | 0.680210i | \(0.761888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.10739 | − | 28.0297i | 0.410176 | − | 1.26239i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.70820 | + | 1.28157i | −0.256565 | + | 0.0576024i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.60081 | + | 23.3929i | −0.340943 | + | 1.04931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.30902 | + | 6.03685i | 0.371963 | + | 0.270247i | 0.758024 | − | 0.652226i | \(-0.226165\pi\) |
−0.386062 | + | 0.922473i | \(0.626165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.802439 | + | 2.46965i | 0.0358503 | + | 0.110336i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.21885 | − | 0.885544i | 0.0543457 | − | 0.0394845i | −0.560281 | − | 0.828303i | \(-0.689307\pi\) |
0.614626 | + | 0.788818i | \(0.289307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.20163 | −0.186970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.18034 | 0.141244 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.6353 | + | 18.6251i | −1.13626 | + | 0.825543i | −0.986594 | − | 0.163193i | \(-0.947821\pi\) |
−0.149669 | + | 0.988736i | \(0.547821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.6631 | + | 32.8177i | 0.471709 | + | 1.45177i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.16312 | + | 3.75123i | 0.227957 | + | 0.165621i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.218847 | − | 0.673542i | 0.00964355 | − | 0.0296798i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.92705 | − | 9.00854i | 0.348631 | − | 0.396195i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.10081 | − | 6.46564i | 0.0922155 | − | 0.283810i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.8713 | − | 13.7108i | −0.826768 | − | 0.600682i | 0.0918753 | − | 0.995771i | \(-0.470714\pi\) |
−0.918643 | + | 0.395089i | \(0.870714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.48278 | + | 26.1073i | 0.370926 | + | 1.14159i | 0.946186 | + | 0.323622i | \(0.104901\pi\) |
−0.575260 | + | 0.817970i | \(0.695099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.07295 | + | 2.95917i | −0.177758 | + | 0.129149i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.0344 | 1.17764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.2984 | − | 16.9273i | 1.01106 | − | 0.734580i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.10739 | + | 28.0297i | 0.394485 | + | 1.21410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.28115 | + | 3.11044i | 0.185090 | + | 0.134476i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0450850 | − | 0.138757i | 0.00194556 | − | 0.00598782i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.93769 | + | 3.26944i | 0.0834624 | + | 0.140825i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.80902 | + | 24.0337i | −0.335736 | + | 1.03329i | 0.630623 | + | 0.776090i | \(0.282800\pi\) |
−0.966358 | + | 0.257199i | \(0.917200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.190983 | − | 0.138757i | −0.00819587 | − | 0.00595464i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.673762 | − | 2.07363i | −0.0288608 | − | 0.0888244i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3435 | − | 13.3273i | 0.784310 | − | 0.569834i | −0.121960 | − | 0.992535i | \(-0.538918\pi\) |
0.906269 | + | 0.422701i | \(0.138918\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.1803 | −0.562523 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.2148 | 0.775976 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.9894 | − | 23.2416i | 1.36033 | − | 0.988335i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.354102 | + | 1.08981i | 0.0150308 | + | 0.0462600i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.69098 | − | 6.31437i | −0.368249 | − | 0.267548i | 0.388236 | − | 0.921560i | \(-0.373085\pi\) |
−0.756484 | + | 0.654012i | \(0.773085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.37132 | − | 2.31838i | −0.226777 | − | 0.0978823i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.95492 | + | 15.2497i | −0.208825 | + | 0.642697i | 0.790710 | + | 0.612191i | \(0.209712\pi\) |
−0.999535 | + | 0.0305054i | \(0.990288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.28115 | + | 0.930812i | 0.0538985 | + | 0.0391596i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.79837 | − | 20.9232i | −0.285505 | − | 0.878694i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2533 | − | 20.5272i | 1.18444 | − | 0.860546i | 0.191774 | − | 0.981439i | \(-0.438576\pi\) |
0.992665 | + | 0.120893i | \(0.0385759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.4721 | −0.773035 | −0.386517 | − | 0.922282i | \(-0.626322\pi\) | ||||
−0.386517 | + | 0.922282i | \(0.626322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.15905 | 0.0484202 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.1803 | + | 17.5680i | −1.00839 | + | 0.732638i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.69756 | − | 23.6907i | −0.320454 | − | 0.986255i | −0.973451 | − | 0.228895i | \(-0.926489\pi\) |
0.652998 | − | 0.757360i | \(-0.273511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.753289 | + | 0.547296i | 0.0313056 | + | 0.0227449i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.1418 | + | 43.5241i | −0.586702 | + | 1.80568i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19098 | − | 23.4131i | 0.0907412 | − | 0.969673i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.51722 | + | 7.74721i | −0.104074 | + | 0.320308i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.927051 | − | 0.673542i | −0.0382635 | − | 0.0278001i | 0.568489 | − | 0.822691i | \(-0.307528\pi\) |
−0.606753 | + | 0.794891i | \(0.707528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.16312 | + | 15.8904i | 0.212743 | + | 0.654754i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.61803 | + | 3.35520i | −0.189961 | + | 0.138014i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5836 | 0.434616 | 0.217308 | − | 0.976103i | \(-0.430272\pi\) | ||||
0.217308 | + | 0.976103i | \(0.430272\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.14590 | −0.333949 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.23607 | − | 3.80423i | 0.214298 | − | 0.155697i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.302439 | + | 0.930812i | 0.0123573 | + | 0.0380320i | 0.957045 | − | 0.289939i | \(-0.0936351\pi\) |
−0.944688 | + | 0.327971i | \(0.893635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8713 | − | 7.89848i | −0.443451 | − | 0.322186i | 0.343554 | − | 0.939133i | \(-0.388369\pi\) |
−0.787004 | + | 0.616947i | \(0.788369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.36068 | + | 13.4208i | −0.177581 | + | 0.546537i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.66312 | + | 4.94704i | 0.189583 | + | 0.201126i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.8435 | + | 39.5281i | −0.521300 | + | 1.60440i | 0.250219 | + | 0.968189i | \(0.419497\pi\) |
−0.771519 | + | 0.636207i | \(0.780503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.62868 | + | 4.08947i | 0.228086 | + | 0.165714i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.16312 | − | 15.8904i | −0.208877 | − | 0.642859i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7254 | − | 17.9641i | 0.998651 | − | 0.725562i | 0.0368521 | − | 0.999321i | \(-0.488267\pi\) |
0.961798 | + | 0.273759i | \(0.0882670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.50658 | 0.0607511 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4721 | −0.663143 | −0.331572 | − | 0.943430i | \(-0.607579\pi\) | ||||
−0.331572 | + | 0.943430i | \(0.607579\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.39919 | − | 3.92274i | 0.217012 | − | 0.157668i | −0.473969 | − | 0.880542i | \(-0.657179\pi\) |
0.690980 | + | 0.722873i | \(0.257179\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.47214 | + | 13.7638i | 0.179461 | + | 0.552323i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.5623 | − | 14.2128i | −0.783747 | − | 0.569426i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.00000 | − | 18.4661i | 0.240000 | − | 0.738644i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.336881 | − | 3.59996i | 0.0134537 | − | 0.143768i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.92705 | − | 21.3193i | 0.276200 | − | 0.850055i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.8713 | − | 10.0781i | −0.552209 | − | 0.401203i | 0.276390 | − | 0.961045i | \(-0.410862\pi\) |
−0.828599 | + | 0.559842i | \(0.810862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.72542 | − | 8.38800i | −0.108326 | − | 0.333393i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.30902 | + | 1.67760i | −0.0916305 | + | 0.0665735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.29180 | 0.209669 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.5967 | −0.973032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8713 | + | 9.35156i | −0.508387 | + | 0.369365i | −0.812211 | − | 0.583363i | \(-0.801736\pi\) |
0.303825 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.57295 | − | 20.2295i | −0.259212 | − | 0.797772i | −0.992971 | − | 0.118362i | \(-0.962236\pi\) |
0.733759 | − | 0.679410i | \(-0.237764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0451 | − | 33.9933i | 0.434227 | − | 1.33641i | −0.459649 | − | 0.888100i | \(-0.652025\pi\) |
0.893877 | − | 0.448313i | \(-0.147975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.7254 | − | 13.2618i | −1.20608 | − | 0.520571i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.97214 | + | 6.06961i | −0.0772941 | + | 0.237887i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.8713 | − | 13.7108i | −0.738492 | − | 0.536546i | 0.153747 | − | 0.988110i | \(-0.450866\pi\) |
−0.892238 | + | 0.451565i | \(0.850866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.52786 | − | 10.8576i | −0.137845 | − | 0.424243i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.9164 | + | 20.2825i | −1.08912 | + | 0.791294i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.36068 | 0.169868 | 0.0849340 | − | 0.996387i | \(-0.472932\pi\) | ||||
0.0849340 | + | 0.996387i | \(0.472932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.3607 | 0.558566 | 0.279283 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279283 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.59017 | + | 4.78804i | −0.255941 | + | 0.185952i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.55573 | − | 4.78804i | −0.0603285 | − | 0.185672i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.4164 | + | 24.2784i | 1.29389 | + | 0.940065i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.22542 | − | 6.84915i | 0.0860399 | − | 0.264804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.80902 | + | 13.1760i | 0.301464 | + | 0.508655i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.31559 | − | 28.6705i | 0.359090 | − | 1.10516i | −0.594510 | − | 0.804088i | \(-0.702654\pi\) |
0.953600 | − | 0.301077i | \(-0.0973460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.35410 | − | 6.06961i | −0.321550 | − | 0.233619i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6631 | + | 32.8177i | 0.409817 | + | 1.26129i | 0.916805 | + | 0.399334i | \(0.130759\pi\) |
−0.506989 | + | 0.861953i | \(0.669241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.8435 | − | 9.33132i | 0.492887 | − | 0.358103i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.14590 | −0.312151 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.9443 | −0.648355 | −0.324177 | − | 0.945996i | \(-0.605087\pi\) | ||||
−0.324177 | + | 0.945996i | \(0.605087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.39919 | − | 3.92274i | 0.206292 | − | 0.149880i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.03851 | − | 6.27388i | −0.0777739 | − | 0.239363i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.4894 | − | 19.2456i | −1.00916 | − | 0.733201i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.98936 | − | 12.2780i | 0.151762 | − | 0.467076i | −0.846056 | − | 0.533094i | \(-0.821029\pi\) |
0.997818 | + | 0.0660174i | \(0.0210293\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.8475 | + | 20.2825i | −0.677971 | + | 0.770467i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.63525 | − | 5.03280i | 0.0620288 | − | 0.190905i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.8435 | − | 17.3233i | −0.903135 | − | 0.656166i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.545085 | + | 1.67760i | 0.0206170 | + | 0.0634526i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.63525 | + | 1.18808i | −0.0617627 | + | 0.0448732i | −0.618238 | − | 0.785991i | \(-0.712153\pi\) |
0.556476 | + | 0.830864i | \(0.312153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8541 | 0.522517 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.854102 | −0.0321673 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.6976 | + | 11.4049i | −0.590368 | + | 0.428927i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.37132 | + | 7.29818i | 0.0890569 | + | 0.274089i | 0.985659 | − | 0.168747i | \(-0.0539722\pi\) |
−0.896602 | + | 0.442836i | \(0.853972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.9894 | + | 23.2416i | 1.19969 | + | 0.871629i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.7082 | + | 36.0341i | −0.438476 | + | 1.34949i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.23607 | − | 2.07363i | 0.345409 | − | 0.0775492i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.01064 | + | 3.11044i | −0.0377432 | + | 0.116161i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.63525 | − | 3.36771i | −0.172866 | − | 0.125594i | 0.497988 | − | 0.867184i | \(-0.334072\pi\) |
−0.670854 | + | 0.741589i | \(0.734072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.01064 | − | 3.11044i | −0.0376383 | − | 0.115839i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.09017 | + | 0.792055i | −0.0405439 | + | 0.0294568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.4721 | −1.09457 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7254 | − | 11.4252i | 0.582423 | − | 0.423155i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8713 | − | 7.89848i | −0.401541 | − | 0.291737i | 0.368627 | − | 0.929577i | \(-0.379828\pi\) |
−0.770169 | + | 0.637840i | \(0.779828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0835921 | − | 0.257270i | 0.00308334 | − | 0.00948955i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | − | 3.59222i | 0.589368 | − | 0.132321i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3369 | − | 34.8913i | 0.417034 | − | 1.28350i | −0.493385 | − | 0.869811i | \(-0.664241\pi\) |
0.910419 | − | 0.413687i | \(-0.135759\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.07295 | − | 2.95917i | −0.149624 | − | 0.108708i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6631 | + | 32.8177i | 0.391192 | + | 1.20396i | 0.931888 | + | 0.362747i | \(0.118161\pi\) |
−0.540696 | + | 0.841218i | \(0.681839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.30902 | + | 1.67760i | −0.0845958 | + | 0.0614625i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.7639 | −1.67441 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.4377 | 0.892934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6353 | − | 10.6331i | 0.534048 | − | 0.388009i | −0.287822 | − | 0.957684i | \(-0.592931\pi\) |
0.821870 | + | 0.569675i | \(0.192931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.141833 | − | 0.436516i | −0.00516867 | − | 0.0159075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.13525 | − | 5.18407i | −0.259679 | − | 0.188667i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.86475 | + | 14.9721i | −0.176812 | + | 0.544172i | −0.999712 | − | 0.0240152i | \(-0.992355\pi\) |
0.822899 | + | 0.568187i | \(0.192355\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.41641 | − | 6.15537i | 0.196603 | − | 0.223426i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1910 | − | 43.6754i | 0.514423 | − | 1.58323i | −0.269907 | − | 0.962886i | \(-0.586993\pi\) |
0.784330 | − | 0.620344i | \(-0.213007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.14590 | − | 5.91834i | −0.294901 | − | 0.214258i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.51722 | − | 7.74721i | −0.0910103 | − | 0.280101i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.6976 | + | 27.3889i | −1.36118 | + | 0.988955i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.5836 | 0.381654 | 0.190827 | − | 0.981624i | \(-0.438883\pi\) | ||||
0.190827 | + | 0.981624i | \(0.438883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.14590 | −0.221339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2533 | − | 7.44945i | 0.368785 | − | 0.267938i | −0.387922 | − | 0.921692i | \(-0.626807\pi\) |
0.756707 | + | 0.653754i | \(0.226807\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.35410 | − | 25.7113i | −0.300088 | − | 0.923577i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.28115 | + | 3.11044i | 0.153586 | + | 0.111586i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.62868 | − | 17.3233i | 0.201668 | − | 0.620671i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5729 | + | 24.5887i | 0.521461 | + | 0.879853i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.40983 | + | 13.5721i | −0.157594 | + | 0.485026i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.28115 | + | 0.930812i | 0.0457263 | + | 0.0332221i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.98936 | − | 30.7441i | −0.356082 | − | 1.09591i | −0.955379 | − | 0.295382i | \(-0.904553\pi\) |
0.599297 | − | 0.800527i | \(-0.295447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.23607 | + | 6.71040i | −0.328813 | + | 0.238896i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.31308 | 0.260023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3262 | 0.757317 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.35410 | + | 0.983813i | −0.0480250 | + | 0.0348922i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.33688 | − | 10.2699i | −0.118198 | − | 0.363777i | 0.874402 | − | 0.485202i | \(-0.161254\pi\) |
−0.992601 | + | 0.121424i | \(0.961254\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5172 | + | 9.82084i | 0.478205 | + | 0.347436i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.47214 | − | 22.9969i | 0.264015 | − | 0.812554i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.8156 | + | 15.8904i | 1.29919 | + | 0.560762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.52786 | − | 10.8576i | 0.124341 | − | 0.382682i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.98936 | + | 2.89844i | 0.140432 | + | 0.102030i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.1910 | + | 43.6754i | 0.498928 | + | 1.53554i | 0.810744 | + | 0.585401i | \(0.199063\pi\) |
−0.311815 | + | 0.950143i | \(0.600937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9615 | + | 16.6825i | −0.806287 | + | 0.585802i | −0.912752 | − | 0.408515i | \(-0.866047\pi\) |
0.106465 | + | 0.994316i | \(0.466047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.45085 | −0.191170 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.67376 | 0.0936578 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.6246 | + | 35.7769i | 0.406197 | + | 1.25015i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.4894 | + | 11.2537i | 0.540582 | + | 0.392756i | 0.824301 | − | 0.566151i | \(-0.191568\pi\) |
−0.283719 | + | 0.958907i | \(0.591568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.461493 | − | 1.42033i | 0.0160866 | − | 0.0495096i | −0.942691 | − | 0.333667i | \(-0.891714\pi\) |
0.958778 | + | 0.284158i | \(0.0917139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.545085 | + | 5.82485i | −0.0189774 | + | 0.202795i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.95492 | + | 15.2497i | −0.172299 | + | 0.530283i | −0.999500 | − | 0.0316241i | \(-0.989932\pi\) |
0.827201 | + | 0.561907i | \(0.189932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.7254 | + | 28.1357i | 1.34499 | + | 0.977192i | 0.999245 | + | 0.0388637i | \(0.0123738\pi\) |
0.345745 | + | 0.938328i | \(0.387626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.287731 | − | 0.885544i | −0.00998127 | − | 0.0307192i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.28115 | + | 3.11044i | −0.148333 | + | 0.107770i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.20163 | 0.145403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.0902 | −0.452462 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.309017 | + | 0.224514i | −0.0106685 | + | 0.00775108i | −0.593107 | − | 0.805124i | \(-0.702099\pi\) |
0.582438 | + | 0.812875i | \(0.302099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.62461 | + | 11.1554i | 0.124987 | + | 0.384669i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.60739 | − | 2.62092i | −0.124245 | − | 0.0902694i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.59017 | − | 4.89404i | 0.0547035 | − | 0.168360i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.8500 | + | 5.82485i | 1.06002 | + | 0.200144i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.01064 | + | 3.11044i | −0.0346852 | + | 0.106750i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.4164 | + | 18.4661i | 0.871263 | + | 0.633010i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.10081 | − | 6.46564i | −0.0719305 | − | 0.221379i | 0.908628 | − | 0.417607i | \(-0.137131\pi\) |
−0.980558 | + | 0.196227i | \(0.937131\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.07295 | − | 2.95917i | 0.139292 | − | 0.101202i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9443 | −0.510487 | −0.255243 | − | 0.966877i | \(-0.582156\pi\) | ||||
−0.255243 | + | 0.966877i | \(0.582156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.9443 | 1.66996 | 0.834979 | − | 0.550283i | \(-0.185480\pi\) | ||||
0.834979 | + | 0.550283i | \(0.185480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.62868 | − | 4.08947i | 0.191825 | − | 0.139369i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.10081 | − | 24.9317i | −0.275755 | − | 0.848686i | −0.989019 | − | 0.147791i | \(-0.952784\pi\) |
0.713264 | − | 0.700896i | \(-0.247216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.89919 | − | 6.46564i | −0.302581 | − | 0.219838i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.510643 | − | 1.57160i | 0.0173423 | − | 0.0533743i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.28115 | − | 45.7490i | 0.145228 | − | 1.55193i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.05573 | − | 21.7153i | 0.239074 | − | 0.735795i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.8435 | + | 9.33132i | 0.434685 | + | 0.315817i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.24265 | + | 16.1352i | 0.177234 | + | 0.545469i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.0517 | + | 25.4665i | −1.18361 | + | 0.859943i | −0.992574 | − | 0.121640i | \(-0.961185\pi\) |
−0.191036 | + | 0.981583i | \(0.561185\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.43769 | 0.0822214 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8885 | −0.670062 | −0.335031 | − | 0.942207i | \(-0.608747\pi\) | ||||
−0.335031 | + | 0.942207i | \(0.608747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0517 | − | 30.5523i | 1.41515 | − | 1.02817i | 0.422603 | − | 0.906315i | \(-0.361117\pi\) |
0.992548 | − | 0.121853i | \(-0.0388835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.736068 | + | 2.26538i | 0.0247427 | + | 0.0761501i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.8713 | − | 15.8904i | −0.734367 | − | 0.533549i | 0.156575 | − | 0.987666i | \(-0.449955\pi\) |
−0.890942 | + | 0.454117i | \(0.849955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.07295 | + | 12.5352i | −0.136602 | + | 0.420419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4721 | − | 10.1311i | −0.786346 | − | 0.339405i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.19098 | + | 9.82084i | −0.106782 | + | 0.328642i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.190983 | − | 0.138757i | −0.00638386 | − | 0.00463814i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.52786 | − | 10.8576i | −0.117792 | − | 0.362526i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.2254 | + | 21.9601i | −1.00807 | + | 0.732409i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.7426 | 1.09082 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.309017 | + | 0.224514i | −0.0102721 | + | 0.00746310i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8992 | + | 42.7773i | 0.461515 | + | 1.42040i | 0.863313 | + | 0.504669i | \(0.168385\pi\) |
−0.401798 | + | 0.915728i | \(0.631615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.6976 | − | 11.4049i | −0.520655 | − | 0.378278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.71885 | + | 17.6008i | −0.189474 | + | 0.583141i | −0.999997 | − | 0.00256645i | \(-0.999183\pi\) |
0.810523 | + | 0.585707i | \(0.199183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.1140 | + | 45.7490i | 0.897341 | + | 1.51407i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.336881 | − | 1.03681i | 0.0111369 | − | 0.0342760i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.6525 | − | 30.9888i | −1.40851 | − | 1.02334i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8435 | + | 39.5281i | 0.423667 | + | 1.30391i | 0.904265 | + | 0.426971i | \(0.140419\pi\) |
−0.480599 | + | 0.876941i | \(0.659581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.70820 | − | 4.14725i | 0.188092 | − | 0.136657i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.7984 | 1.30998 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.4164 | −0.737047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.64590 | − | 1.92236i | 0.0869027 | − | 0.0631385i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.60739 | + | 29.5685i | 0.315208 | + | 0.970111i | 0.975669 | + | 0.219250i | \(0.0703612\pi\) |
−0.660460 | + | 0.750861i | \(0.729639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.64590 | − | 1.92236i | −0.0867158 | − | 0.0630027i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.920473 | − | 2.83293i | 0.0301349 | − | 0.0927458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.25329 | + | 7.10642i | −0.204504 | + | 0.232405i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.28115 | + | 13.1760i | −0.139859 | + | 0.430442i | −0.996314 | − | 0.0857795i | \(-0.972662\pi\) |
0.856455 | + | 0.516222i | \(0.172662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.42705 | − | 6.84915i | −0.307640 | − | 0.223514i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.13525 | + | 21.9601i | 0.232603 | + | 0.715877i | 0.997430 | + | 0.0716425i | \(0.0228241\pi\) |
−0.764828 | + | 0.644235i | \(0.777176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.4164 | − | 24.2784i | 1.08819 | − | 0.790615i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.94427 | 0.128307 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.7771 | −1.55255 | −0.776273 | − | 0.630396i | \(-0.782892\pi\) | ||||
−0.776273 | + | 0.630396i | \(0.782892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.1697 | − | 32.8177i | 1.46627 | − | 1.06531i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.656541 | + | 2.02063i | 0.0212898 | + | 0.0655233i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.4894 | + | 27.2376i | 1.21440 | + | 0.882313i | 0.995623 | − | 0.0934622i | \(-0.0297934\pi\) |
0.218777 | + | 0.975775i | \(0.429793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.579527 | − | 1.78360i | 0.0187530 | − | 0.0577159i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.88854 | − | 1.77109i | 0.255000 | − | 0.0572512i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.52380 | − | 29.3112i | 0.307540 | − | 0.946509i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64590 | − | 1.92236i | −0.0853515 | − | 0.0620115i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.55166 | + | 23.2416i | 0.243349 | + | 0.748951i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.21885 | − | 0.885544i | 0.0392361 | − | 0.0285067i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0000 | −1.41494 | −0.707472 | − | 0.706741i | \(-0.750165\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.03444 | 0.161730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.6353 | − | 10.6331i | 0.469668 | − | 0.341234i | −0.327644 | − | 0.944801i | \(-0.606255\pi\) |
0.797312 | + | 0.603568i | \(0.206255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.55166 | − | 23.2416i | −0.242095 | − | 0.745092i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.59017 | + | 4.78804i | 0.211054 | + | 0.153340i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9549 | − | 33.7158i | 0.350479 | − | 1.07866i | −0.608106 | − | 0.793856i | \(-0.708070\pi\) |
0.958585 | − | 0.284807i | \(-0.0919295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.4164 | + | 6.15537i | −0.876232 | + | 0.196726i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.11146 | − | 9.57608i | 0.0993412 | − | 0.305741i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.63525 | − | 3.36771i | −0.147842 | − | 0.107413i | 0.511406 | − | 0.859339i | \(-0.329125\pi\) |
−0.659247 | + | 0.751926i | \(0.729125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.85410 | + | 8.78402i | 0.0909393 | + | 0.279882i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.19098 | + | 2.31838i | −0.101570 | + | 0.0737950i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.70820 | + | 2.69417i | −0.117676 | + | 0.0854968i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.23607 | − | 9.95959i | −0.102590 | − | 0.315740i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.2533 | + | 20.5272i | 0.894791 | + | 0.650103i | 0.937123 | − | 0.349000i | \(-0.113479\pi\) |
−0.0423320 | + | 0.999104i | \(0.513479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.35410 | + | 10.3229i | −0.106119 | + | 0.326601i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))