Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,2,Mod(71,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.e (of order \(2\), degree \(1\), 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: | \(0.670743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.7 | ||
Root | \(1.37027 + 0.349801i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.71 |
Dual form | 84.2.e.a.71.8 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.349801 | − | 1.37027i | 0.247347 | − | 0.968927i | ||||
\(3\) | −1.72007 | − | 0.203364i | −0.993083 | − | 0.117412i | ||||
\(4\) | −1.75528 | − | 0.958643i | −0.877639 | − | 0.479321i | ||||
\(5\) | − | 2.27740i | − | 1.01848i | −0.860624 | − | 0.509242i | \(-0.829926\pi\) | ||
0.860624 | − | 0.509242i | \(-0.170074\pi\) | |||||||
\(6\) | −0.880346 | + | 2.28582i | −0.359400 | + | 0.933184i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −1.92760 | + | 2.06987i | −0.681509 | + | 0.731810i | ||||
\(9\) | 2.91729 | + | 0.699602i | 0.972429 | + | 0.233201i | ||||
\(10\) | −3.12065 | − | 0.796636i | −0.986836 | − | 0.251918i | ||||
\(11\) | 4.31834 | 1.30203 | 0.651014 | − | 0.759066i | \(-0.274344\pi\) | ||||
0.651014 | + | 0.759066i | \(0.274344\pi\) | |||||||
\(12\) | 2.82425 | + | 2.00589i | 0.815291 | + | 0.579052i | ||||
\(13\) | −0.406728 | −0.112806 | −0.0564031 | − | 0.998408i | \(-0.517963\pi\) | ||||
−0.0564031 | + | 0.998408i | \(0.517963\pi\) | |||||||
\(14\) | −1.37027 | − | 0.349801i | −0.366220 | − | 0.0934882i | ||||
\(15\) | −0.463141 | + | 3.91729i | −0.119583 | + | 1.01144i | ||||
\(16\) | 2.16201 | + | 3.36537i | 0.540502 | + | 0.841343i | ||||
\(17\) | 4.31834i | 1.04735i | 0.851918 | + | 0.523675i | \(0.175439\pi\) | ||||
−0.851918 | + | 0.523675i | \(0.824561\pi\) | |||||||
\(18\) | 1.97911 | − | 3.75275i | 0.466481 | − | 0.884531i | ||||
\(19\) | − | 5.42784i | − | 1.24523i | −0.782527 | − | 0.622616i | \(-0.786070\pi\) | ||
0.782527 | − | 0.622616i | \(-0.213930\pi\) | |||||||
\(20\) | −2.18321 | + | 3.99747i | −0.488181 | + | 0.893861i | ||||
\(21\) | −0.203364 | + | 1.72007i | −0.0443777 | + | 0.375350i | ||||
\(22\) | 1.51056 | − | 5.91729i | 0.322052 | − | 1.26157i | ||||
\(23\) | 1.16274 | 0.242449 | 0.121224 | − | 0.992625i | \(-0.461318\pi\) | ||||
0.121224 | + | 0.992625i | \(0.461318\pi\) | |||||||
\(24\) | 3.73654 | − | 3.16832i | 0.762718 | − | 0.646731i | ||||
\(25\) | −0.186543 | −0.0373086 | ||||||||
\(26\) | −0.142274 | + | 0.557328i | −0.0279022 | + | 0.109301i | ||||
\(27\) | −4.87566 | − | 1.79664i | −0.938322 | − | 0.345763i | ||||
\(28\) | −0.958643 | + | 1.75528i | −0.181166 | + | 0.331717i | ||||
\(29\) | − | 3.72469i | − | 0.691657i | −0.938298 | − | 0.345829i | \(-0.887598\pi\) | ||
0.938298 | − | 0.345829i | \(-0.112402\pi\) | |||||||
\(30\) | 5.20573 | + | 2.00490i | 0.950432 | + | 0.366043i | ||||
\(31\) | 5.83457i | 1.04792i | 0.851743 | + | 0.523960i | \(0.175546\pi\) | ||||
−0.851743 | + | 0.523960i | \(0.824454\pi\) | |||||||
\(32\) | 5.36774 | − | 1.78532i | 0.948891 | − | 0.315604i | ||||
\(33\) | −7.42784 | − | 0.878195i | −1.29302 | − | 0.152874i | ||||
\(34\) | 5.91729 | + | 1.51056i | 1.01481 | + | 0.259058i | ||||
\(35\) | −2.27740 | −0.384951 | ||||||||
\(36\) | −4.44998 | − | 4.02463i | −0.741664 | − | 0.670772i | ||||
\(37\) | −7.83457 | −1.28800 | −0.643998 | − | 0.765027i | \(-0.722725\pi\) | ||||
−0.643998 | + | 0.765027i | \(0.722725\pi\) | |||||||
\(38\) | −7.43761 | − | 1.89866i | −1.20654 | − | 0.308004i | ||||
\(39\) | 0.699602 | + | 0.0827140i | 0.112026 | + | 0.0132448i | ||||
\(40\) | 4.71392 | + | 4.38991i | 0.745336 | + | 0.694105i | ||||
\(41\) | 2.56195i | 0.400109i | 0.979785 | + | 0.200054i | \(0.0641119\pi\) | ||||
−0.979785 | + | 0.200054i | \(0.935888\pi\) | |||||||
\(42\) | 2.28582 | + | 0.880346i | 0.352710 | + | 0.135840i | ||||
\(43\) | 11.0211i | 1.68070i | 0.542041 | + | 0.840352i | \(0.317652\pi\) | ||||
−0.542041 | + | 0.840352i | \(0.682348\pi\) | |||||||
\(44\) | −7.57988 | − | 4.13974i | −1.14271 | − | 0.624090i | ||||
\(45\) | 1.59327 | − | 6.64382i | 0.237511 | − | 0.990403i | ||||
\(46\) | 0.406728 | − | 1.59327i | 0.0599688 | − | 0.234915i | ||||
\(47\) | 2.32549 | 0.339207 | 0.169603 | − | 0.985512i | \(-0.445751\pi\) | ||||
0.169603 | + | 0.985512i | \(0.445751\pi\) | |||||||
\(48\) | −3.03441 | − | 6.22835i | −0.437979 | − | 0.898985i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.0652529 | + | 0.255614i | −0.00922816 | + | 0.0361493i | ||||
\(51\) | 0.878195 | − | 7.42784i | 0.122972 | − | 1.04011i | ||||
\(52\) | 0.713922 | + | 0.389907i | 0.0990031 | + | 0.0540704i | ||||
\(53\) | − | 5.48108i | − | 0.752884i | −0.926440 | − | 0.376442i | \(-0.877147\pi\) | ||
0.926440 | − | 0.376442i | \(-0.122853\pi\) | |||||||
\(54\) | −4.16739 | + | 6.05251i | −0.567110 | + | 0.823642i | ||||
\(55\) | − | 9.83457i | − | 1.32609i | ||||||
\(56\) | 2.06987 | + | 1.92760i | 0.276598 | + | 0.257586i | ||||
\(57\) | −1.10383 | + | 9.33627i | −0.146206 | + | 1.23662i | ||||
\(58\) | −5.10383 | − | 1.30290i | −0.670166 | − | 0.171079i | ||||
\(59\) | 3.91306 | 0.509437 | 0.254719 | − | 0.967015i | \(-0.418017\pi\) | ||||
0.254719 | + | 0.967015i | \(0.418017\pi\) | |||||||
\(60\) | 4.56822 | − | 6.43194i | 0.589755 | − | 0.830360i | ||||
\(61\) | 10.4490 | 1.33785 | 0.668926 | − | 0.743329i | \(-0.266754\pi\) | ||||
0.668926 | + | 0.743329i | \(0.266754\pi\) | |||||||
\(62\) | 7.99494 | + | 2.04094i | 1.01536 | + | 0.259199i | ||||
\(63\) | 0.699602 | − | 2.91729i | 0.0881415 | − | 0.367543i | ||||
\(64\) | −0.568736 | − | 7.97976i | −0.0710920 | − | 0.997470i | ||||
\(65\) | 0.926283i | 0.114891i | ||||||||
\(66\) | −3.80163 | + | 9.87096i | −0.467948 | + | 1.21503i | ||||
\(67\) | 7.83457i | 0.957145i | 0.878048 | + | 0.478573i | \(0.158846\pi\) | ||||
−0.878048 | + | 0.478573i | \(0.841154\pi\) | |||||||
\(68\) | 4.13974 | − | 7.57988i | 0.502018 | − | 0.919196i | ||||
\(69\) | −2.00000 | − | 0.236460i | −0.240772 | − | 0.0284665i | ||||
\(70\) | −0.796636 | + | 3.12065i | −0.0952162 | + | 0.372989i | ||||
\(71\) | −4.88743 | −0.580031 | −0.290016 | − | 0.957022i | \(-0.593661\pi\) | ||||
−0.290016 | + | 0.957022i | \(0.593661\pi\) | |||||||
\(72\) | −7.07144 | + | 4.68986i | −0.833377 | + | 0.552705i | ||||
\(73\) | 2.81346 | 0.329290 | 0.164645 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164645 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(74\) | −2.74054 | + | 10.7355i | −0.318581 | + | 1.24797i | ||||
\(75\) | 0.320867 | + | 0.0379362i | 0.0370506 | + | 0.00438050i | ||||
\(76\) | −5.20336 | + | 9.52738i | −0.596867 | + | 1.09287i | ||||
\(77\) | − | 4.31834i | − | 0.492120i | ||||||
\(78\) | 0.358062 | − | 0.929710i | 0.0405425 | − | 0.105269i | ||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | 7.66429 | − | 4.92375i | 0.856894 | − | 0.550492i | ||||
\(81\) | 8.02112 | + | 4.08188i | 0.891235 | + | 0.453542i | ||||
\(82\) | 3.51056 | + | 0.896171i | 0.387676 | + | 0.0989655i | ||||
\(83\) | 0.641735 | 0.0704395 | 0.0352198 | − | 0.999380i | \(-0.488787\pi\) | ||||
0.0352198 | + | 0.999380i | \(0.488787\pi\) | |||||||
\(84\) | 2.00589 | − | 2.82425i | 0.218861 | − | 0.308151i | ||||
\(85\) | 9.83457 | 1.06671 | ||||||||
\(86\) | 15.1019 | + | 3.85520i | 1.62848 | + | 0.415716i | ||||
\(87\) | −0.757468 | + | 6.40673i | −0.0812091 | + | 0.686873i | ||||
\(88\) | −8.32401 | + | 8.93840i | −0.887343 | + | 0.952837i | ||||
\(89\) | 13.9970i | 1.48368i | 0.670576 | + | 0.741841i | \(0.266047\pi\) | ||||
−0.670576 | + | 0.741841i | \(0.733953\pi\) | |||||||
\(90\) | −8.54650 | − | 4.50723i | −0.900880 | − | 0.475103i | ||||
\(91\) | 0.406728i | 0.0426367i | ||||||||
\(92\) | −2.04094 | − | 1.11466i | −0.212782 | − | 0.116211i | ||||
\(93\) | 1.18654 | − | 10.0359i | 0.123039 | − | 1.04067i | ||||
\(94\) | 0.813457 | − | 3.18654i | 0.0839017 | − | 0.328667i | ||||
\(95\) | −12.3614 | −1.26825 | ||||||||
\(96\) | −9.59596 | + | 1.97928i | −0.979384 | + | 0.202009i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −0.349801 | + | 1.37027i | −0.0353352 | + | 0.138418i | ||||
\(99\) | 12.5978 | + | 3.02112i | 1.26613 | + | 0.303633i | ||||
\(100\) | 0.327435 | + | 0.178828i | 0.0327435 | + | 0.0178828i | ||||
\(101\) | 8.68476i | 0.864166i | 0.901834 | + | 0.432083i | \(0.142221\pi\) | ||||
−0.901834 | + | 0.432083i | \(0.857779\pi\) | |||||||
\(102\) | −9.87096 | − | 3.80163i | −0.977370 | − | 0.376417i | ||||
\(103\) | − | 10.6480i | − | 1.04918i | −0.851355 | − | 0.524591i | \(-0.824218\pi\) | ||
0.851355 | − | 0.524591i | \(-0.175782\pi\) | |||||||
\(104\) | 0.784009 | − | 0.841876i | 0.0768784 | − | 0.0825527i | ||||
\(105\) | 3.91729 | + | 0.463141i | 0.382288 | + | 0.0451980i | ||||
\(106\) | −7.51056 | − | 1.91729i | −0.729490 | − | 0.186223i | ||||
\(107\) | −8.40021 | −0.812079 | −0.406040 | − | 0.913855i | \(-0.633090\pi\) | ||||
−0.406040 | + | 0.913855i | \(0.633090\pi\) | |||||||
\(108\) | 6.83582 | + | 7.82762i | 0.657777 | + | 0.753213i | ||||
\(109\) | −10.4826 | −1.00405 | −0.502026 | − | 0.864853i | \(-0.667412\pi\) | ||||
−0.502026 | + | 0.864853i | \(0.667412\pi\) | |||||||
\(110\) | −13.4760 | − | 3.44014i | −1.28489 | − | 0.328005i | ||||
\(111\) | 13.4760 | + | 1.59327i | 1.27909 | + | 0.151227i | ||||
\(112\) | 3.36537 | − | 2.16201i | 0.317998 | − | 0.204290i | ||||
\(113\) | − | 9.56296i | − | 0.899607i | −0.893128 | − | 0.449804i | \(-0.851494\pi\) | ||
0.893128 | − | 0.449804i | \(-0.148506\pi\) | |||||||
\(114\) | 12.4071 | + | 4.77838i | 1.16203 | + | 0.447536i | ||||
\(115\) | − | 2.64803i | − | 0.246930i | ||||||
\(116\) | −3.57065 | + | 6.53787i | −0.331526 | + | 0.607026i | ||||
\(117\) | −1.18654 | − | 0.284548i | −0.109696 | − | 0.0263065i | ||||
\(118\) | 1.36879 | − | 5.36195i | 0.126008 | − | 0.493608i | ||||
\(119\) | 4.31834 | 0.395861 | ||||||||
\(120\) | −7.21553 | − | 8.50959i | −0.658685 | − | 0.776816i | ||||
\(121\) | 7.64803 | 0.695275 | ||||||||
\(122\) | 3.65505 | − | 14.3179i | 0.330913 | − | 1.29628i | ||||
\(123\) | 0.521008 | − | 4.40673i | 0.0469777 | − | 0.397341i | ||||
\(124\) | 5.59327 | − | 10.2413i | 0.502291 | − | 0.919696i | ||||
\(125\) | − | 10.9622i | − | 0.980485i | ||||||
\(126\) | −3.75275 | − | 1.97911i | −0.334321 | − | 0.176313i | ||||
\(127\) | − | 6.20766i | − | 0.550841i | −0.961324 | − | 0.275420i | \(-0.911183\pi\) | ||
0.961324 | − | 0.275420i | \(-0.0888170\pi\) | |||||||
\(128\) | −11.1334 | − | 2.01200i | −0.984060 | − | 0.177838i | ||||
\(129\) | 2.24130 | − | 18.9571i | 0.197335 | − | 1.66908i | ||||
\(130\) | 1.26926 | + | 0.324014i | 0.111321 | + | 0.0284179i | ||||
\(131\) | −14.4023 | −1.25833 | −0.629167 | − | 0.777270i | \(-0.716604\pi\) | ||||
−0.629167 | + | 0.777270i | \(0.716604\pi\) | |||||||
\(132\) | 12.1961 | + | 8.66213i | 1.06153 | + | 0.753941i | ||||
\(133\) | −5.42784 | −0.470654 | ||||||||
\(134\) | 10.7355 | + | 2.74054i | 0.927404 | + | 0.236747i | ||||
\(135\) | −4.09166 | + | 11.1038i | −0.352154 | + | 0.955665i | ||||
\(136\) | −8.93840 | − | 8.32401i | −0.766462 | − | 0.713778i | ||||
\(137\) | − | 2.32549i | − | 0.198680i | −0.995054 | − | 0.0993398i | \(-0.968327\pi\) | ||
0.995054 | − | 0.0993398i | \(-0.0316731\pi\) | |||||||
\(138\) | −1.02362 | + | 2.65783i | −0.0871360 | + | 0.226249i | ||||
\(139\) | 9.22019i | 0.782046i | 0.920381 | + | 0.391023i | \(0.127879\pi\) | ||||
−0.920381 | + | 0.391023i | \(0.872121\pi\) | |||||||
\(140\) | 3.99747 | + | 2.18321i | 0.337848 | + | 0.184515i | ||||
\(141\) | −4.00000 | − | 0.472921i | −0.336861 | − | 0.0398271i | ||||
\(142\) | −1.70963 | + | 6.69710i | −0.143469 | + | 0.562008i | ||||
\(143\) | −1.75639 | −0.146877 | ||||||||
\(144\) | 3.95277 | + | 11.3303i | 0.329398 | + | 0.944191i | ||||
\(145\) | −8.48260 | −0.704442 | ||||||||
\(146\) | 0.984149 | − | 3.85520i | 0.0814488 | − | 0.319058i | ||||
\(147\) | 1.72007 | + | 0.203364i | 0.141869 | + | 0.0167732i | ||||
\(148\) | 13.7519 | + | 7.51056i | 1.13040 | + | 0.617364i | ||||
\(149\) | 17.3891i | 1.42457i | 0.701891 | + | 0.712284i | \(0.252339\pi\) | ||||
−0.701891 | + | 0.712284i | \(0.747661\pi\) | |||||||
\(150\) | 0.164223 | − | 0.426405i | 0.0134087 | − | 0.0348158i | ||||
\(151\) | − | 4.16543i | − | 0.338978i | −0.985532 | − | 0.169489i | \(-0.945788\pi\) | ||
0.985532 | − | 0.169489i | \(-0.0542117\pi\) | |||||||
\(152\) | 11.2349 | + | 10.4627i | 0.911274 | + | 0.848637i | ||||
\(153\) | −3.02112 | + | 12.5978i | −0.244243 | + | 1.01847i | ||||
\(154\) | −5.91729 | − | 1.51056i | −0.476828 | − | 0.121724i | ||||
\(155\) | 13.2876 | 1.06729 | ||||||||
\(156\) | −1.14870 | − | 0.815854i | −0.0919698 | − | 0.0653206i | ||||
\(157\) | −19.2624 | −1.53731 | −0.768654 | − | 0.639665i | \(-0.779073\pi\) | ||||
−0.768654 | + | 0.639665i | \(0.779073\pi\) | |||||||
\(158\) | −5.48108 | − | 1.39920i | −0.436051 | − | 0.111315i | ||||
\(159\) | −1.11466 | + | 9.42784i | −0.0883979 | + | 0.747677i | ||||
\(160\) | −4.06589 | − | 12.2245i | −0.321437 | − | 0.966430i | ||||
\(161\) | − | 1.16274i | − | 0.0916370i | ||||||
\(162\) | 8.39906 | − | 9.56325i | 0.659893 | − | 0.751360i | ||||
\(163\) | 8.64803i | 0.677366i | 0.940901 | + | 0.338683i | \(0.109981\pi\) | ||||
−0.940901 | + | 0.338683i | \(0.890019\pi\) | |||||||
\(164\) | 2.45599 | − | 4.49693i | 0.191781 | − | 0.351151i | ||||
\(165\) | −2.00000 | + | 16.9162i | −0.155700 | + | 1.31692i | ||||
\(166\) | 0.224479 | − | 0.879350i | 0.0174230 | − | 0.0682508i | ||||
\(167\) | −1.75639 | −0.135914 | −0.0679568 | − | 0.997688i | \(-0.521648\pi\) | ||||
−0.0679568 | + | 0.997688i | \(0.521648\pi\) | |||||||
\(168\) | −3.16832 | − | 3.73654i | −0.244441 | − | 0.288280i | ||||
\(169\) | −12.8346 | −0.987275 | ||||||||
\(170\) | 3.44014 | − | 13.4760i | 0.263847 | − | 1.03356i | ||||
\(171\) | 3.79733 | − | 15.8346i | 0.290389 | − | 1.21090i | ||||
\(172\) | 10.5653 | − | 19.3451i | 0.805598 | − | 1.47505i | ||||
\(173\) | − | 7.87421i | − | 0.598665i | −0.954149 | − | 0.299333i | \(-0.903236\pi\) | ||
0.954149 | − | 0.299333i | \(-0.0967640\pi\) | |||||||
\(174\) | 8.51398 | + | 3.27902i | 0.645443 | + | 0.248581i | ||||
\(175\) | 0.186543i | 0.0141013i | ||||||||
\(176\) | 9.33627 | + | 14.5328i | 0.703748 | + | 1.09545i | ||||
\(177\) | −6.73074 | − | 0.795777i | −0.505914 | − | 0.0598142i | ||||
\(178\) | 19.1797 | + | 4.89617i | 1.43758 | + | 0.366984i | ||||
\(179\) | −9.34605 | −0.698557 | −0.349278 | − | 0.937019i | \(-0.613573\pi\) | ||||
−0.349278 | + | 0.937019i | \(0.613573\pi\) | |||||||
\(180\) | −9.16569 | + | 10.1344i | −0.683170 | + | 0.755372i | ||||
\(181\) | 16.8893 | 1.25537 | 0.627687 | − | 0.778466i | \(-0.284002\pi\) | ||||
0.627687 | + | 0.778466i | \(0.284002\pi\) | |||||||
\(182\) | 0.557328 | + | 0.142274i | 0.0413119 | + | 0.0105460i | ||||
\(183\) | −17.9729 | − | 2.12494i | −1.32860 | − | 0.157080i | ||||
\(184\) | −2.24130 | + | 2.40673i | −0.165231 | + | 0.177426i | ||||
\(185\) | 17.8424i | 1.31180i | ||||||||
\(186\) | −13.3368 | − | 5.13644i | −0.977902 | − | 0.376622i | ||||
\(187\) | 18.6480i | 1.36368i | ||||||||
\(188\) | −4.08188 | − | 2.22931i | −0.297701 | − | 0.162589i | ||||
\(189\) | −1.79664 | + | 4.87566i | −0.130686 | + | 0.354652i | ||||
\(190\) | −4.32401 | + | 16.9384i | −0.313697 | + | 1.22884i | ||||
\(191\) | 20.3082 | 1.46945 | 0.734725 | − | 0.678365i | \(-0.237311\pi\) | ||||
0.734725 | + | 0.678365i | \(0.237311\pi\) | |||||||
\(192\) | −0.644532 | + | 13.8414i | −0.0465151 | + | 0.998918i | ||||
\(193\) | 6.85569 | 0.493483 | 0.246742 | − | 0.969081i | \(-0.420640\pi\) | ||||
0.246742 | + | 0.969081i | \(0.420640\pi\) | |||||||
\(194\) | −0.699602 | + | 2.74054i | −0.0502285 | + | 0.196759i | ||||
\(195\) | 0.188373 | − | 1.59327i | 0.0134897 | − | 0.114097i | ||||
\(196\) | 1.75528 | + | 0.958643i | 0.125377 | + | 0.0684745i | ||||
\(197\) | 1.96830i | 0.140235i | 0.997539 | + | 0.0701177i | \(0.0223375\pi\) | ||||
−0.997539 | + | 0.0701177i | \(0.977662\pi\) | |||||||
\(198\) | 8.54647 | − | 16.2056i | 0.607371 | − | 1.15168i | ||||
\(199\) | − | 6.37309i | − | 0.451776i | −0.974153 | − | 0.225888i | \(-0.927472\pi\) | ||
0.974153 | − | 0.225888i | \(-0.0725284\pi\) | |||||||
\(200\) | 0.359580 | − | 0.386120i | 0.0254262 | − | 0.0273028i | ||||
\(201\) | 1.59327 | − | 13.4760i | 0.112381 | − | 0.950525i | ||||
\(202\) | 11.9005 | + | 3.03794i | 0.837314 | + | 0.213748i | ||||
\(203\) | −3.72469 | −0.261422 | ||||||||
\(204\) | −8.66213 | + | 12.1961i | −0.606470 | + | 0.853895i | ||||
\(205\) | 5.83457 | 0.407504 | ||||||||
\(206\) | −14.5907 | − | 3.72469i | −1.01658 | − | 0.259511i | ||||
\(207\) | 3.39205 | + | 0.813457i | 0.235764 | + | 0.0565392i | ||||
\(208\) | −0.879350 | − | 1.36879i | −0.0609719 | − | 0.0949087i | ||||
\(209\) | − | 23.4393i | − | 1.62133i | ||||||
\(210\) | 2.00490 | − | 5.20573i | 0.138351 | − | 0.359230i | ||||
\(211\) | − | 25.1306i | − | 1.73006i | −0.501717 | − | 0.865032i | \(-0.667298\pi\) | ||
0.501717 | − | 0.865032i | \(-0.332702\pi\) | |||||||
\(212\) | −5.25440 | + | 9.62082i | −0.360874 | + | 0.660761i | ||||
\(213\) | 8.40673 | + | 0.993929i | 0.576020 | + | 0.0681029i | ||||
\(214\) | −2.93840 | + | 11.5106i | −0.200865 | + | 0.786846i | ||||
\(215\) | 25.0995 | 1.71177 | ||||||||
\(216\) | 13.1171 | − | 6.62881i | 0.892507 | − | 0.451033i | ||||
\(217\) | 5.83457 | 0.396077 | ||||||||
\(218\) | −3.66682 | + | 14.3640i | −0.248349 | + | 0.972852i | ||||
\(219\) | −4.83934 | − | 0.572156i | −0.327013 | − | 0.0386627i | ||||
\(220\) | −9.42784 | + | 17.2624i | −0.635625 | + | 1.16383i | ||||
\(221\) | − | 1.75639i | − | 0.118148i | ||||||
\(222\) | 6.89713 | − | 17.9085i | 0.462905 | − | 1.20194i | ||||
\(223\) | 9.22877i | 0.618004i | 0.951061 | + | 0.309002i | \(0.0999950\pi\) | ||||
−0.951061 | + | 0.309002i | \(0.900005\pi\) | |||||||
\(224\) | −1.78532 | − | 5.36774i | −0.119287 | − | 0.358647i | ||||
\(225\) | −0.544200 | − | 0.130506i | −0.0362800 | − | 0.00870039i | ||||
\(226\) | −13.1038 | − | 3.34513i | −0.871654 | − | 0.222515i | ||||
\(227\) | 19.5262 | 1.29600 | 0.647999 | − | 0.761641i | \(-0.275606\pi\) | ||||
0.647999 | + | 0.761641i | \(0.275606\pi\) | |||||||
\(228\) | 10.8877 | − | 15.3296i | 0.721054 | − | 1.01523i | ||||
\(229\) | 2.03364 | 0.134387 | 0.0671934 | − | 0.997740i | \(-0.478596\pi\) | ||||
0.0671934 | + | 0.997740i | \(0.478596\pi\) | |||||||
\(230\) | −3.62851 | − | 0.926283i | −0.239257 | − | 0.0610773i | ||||
\(231\) | −0.878195 | + | 7.42784i | −0.0577810 | + | 0.488716i | ||||
\(232\) | 7.70963 | + | 7.17970i | 0.506162 | + | 0.471370i | ||||
\(233\) | − | 3.27133i | − | 0.214312i | −0.994242 | − | 0.107156i | \(-0.965826\pi\) | ||
0.994242 | − | 0.107156i | \(-0.0341744\pi\) | |||||||
\(234\) | −0.804961 | + | 1.52635i | −0.0526220 | + | 0.0997806i | ||||
\(235\) | − | 5.29606i | − | 0.345477i | ||||||
\(236\) | −6.86851 | − | 3.75123i | −0.447102 | − | 0.244184i | ||||
\(237\) | −0.813457 | + | 6.88028i | −0.0528397 | + | 0.446922i | ||||
\(238\) | 1.51056 | − | 5.91729i | 0.0979149 | − | 0.383561i | ||||
\(239\) | −24.5058 | −1.58515 | −0.792575 | − | 0.609775i | \(-0.791260\pi\) | ||||
−0.792575 | + | 0.609775i | \(0.791260\pi\) | |||||||
\(240\) | −14.1844 | + | 6.91056i | −0.915601 | + | 0.446075i | ||||
\(241\) | 18.4153 | 1.18623 | 0.593117 | − | 0.805116i | \(-0.297897\pi\) | ||||
0.593117 | + | 0.805116i | \(0.297897\pi\) | |||||||
\(242\) | 2.67529 | − | 10.4799i | 0.171974 | − | 0.673671i | ||||
\(243\) | −12.9668 | − | 8.65232i | −0.831819 | − | 0.555047i | ||||
\(244\) | −18.3408 | − | 10.0168i | −1.17415 | − | 0.641261i | ||||
\(245\) | 2.27740i | 0.145498i | ||||||||
\(246\) | −5.85616 | − | 2.25540i | −0.373375 | − | 0.143799i | ||||
\(247\) | 2.20766i | 0.140470i | ||||||||
\(248\) | −12.0768 | − | 11.2467i | −0.766878 | − | 0.714167i | ||||
\(249\) | −1.10383 | − | 0.130506i | −0.0699523 | − | 0.00827047i | ||||
\(250\) | −15.0211 | − | 3.83457i | −0.950019 | − | 0.242520i | ||||
\(251\) | −15.4443 | −0.974837 | −0.487418 | − | 0.873169i | \(-0.662061\pi\) | ||||
−0.487418 | + | 0.873169i | \(0.662061\pi\) | |||||||
\(252\) | −4.02463 | + | 4.44998i | −0.253528 | + | 0.280323i | ||||
\(253\) | 5.02112 | 0.315675 | ||||||||
\(254\) | −8.50617 | − | 2.17144i | −0.533724 | − | 0.136249i | ||||
\(255\) | −16.9162 | − | 2.00000i | −1.05933 | − | 0.125245i | ||||
\(256\) | −6.65145 | + | 14.5519i | −0.415716 | + | 0.909495i | ||||
\(257\) | − | 8.96931i | − | 0.559490i | −0.960074 | − | 0.279745i | \(-0.909750\pi\) | ||
0.960074 | − | 0.279745i | \(-0.0902499\pi\) | |||||||
\(258\) | −25.1923 | − | 9.70239i | −1.56841 | − | 0.604045i | ||||
\(259\) | 7.83457i | 0.486817i | ||||||||
\(260\) | 0.887974 | − | 1.62588i | 0.0550698 | − | 0.100833i | ||||
\(261\) | 2.60580 | − | 10.8660i | 0.161295 | − | 0.672587i | ||||
\(262\) | −5.03794 | + | 19.7350i | −0.311245 | + | 1.21923i | ||||
\(263\) | 19.3624 | 1.19393 | 0.596967 | − | 0.802265i | \(-0.296372\pi\) | ||||
0.596967 | + | 0.802265i | \(0.296372\pi\) | |||||||
\(264\) | 16.1356 | − | 13.6819i | 0.993080 | − | 0.842061i | ||||
\(265\) | −12.4826 | −0.766800 | ||||||||
\(266\) | −1.89866 | + | 7.43761i | −0.116415 | + | 0.456029i | ||||
\(267\) | 2.84649 | − | 24.0759i | 0.174203 | − | 1.47342i | ||||
\(268\) | 7.51056 | − | 13.7519i | 0.458780 | − | 0.840028i | ||||
\(269\) | 0.0480876i | 0.00293195i | 0.999999 | + | 0.00146598i | \(0.000466635\pi\) | ||||
−0.999999 | + | 0.00146598i | \(0.999533\pi\) | |||||||
\(270\) | 13.7840 | + | 9.49080i | 0.838866 | + | 0.577592i | ||||
\(271\) | 19.8768i | 1.20743i | 0.797200 | + | 0.603715i | \(0.206313\pi\) | ||||
−0.797200 | + | 0.603715i | \(0.793687\pi\) | |||||||
\(272\) | −14.5328 | + | 9.33627i | −0.881181 | + | 0.566095i | ||||
\(273\) | 0.0827140 | − | 0.699602i | 0.00500608 | − | 0.0423418i | ||||
\(274\) | −3.18654 | − | 0.813457i | −0.192506 | − | 0.0491427i | ||||
\(275\) | −0.805556 | −0.0485769 | ||||||||
\(276\) | 3.28388 | + | 2.33234i | 0.197666 | + | 0.140390i | ||||
\(277\) | 10.2749 | 0.617361 | 0.308681 | − | 0.951166i | \(-0.400113\pi\) | ||||
0.308681 | + | 0.951166i | \(0.400113\pi\) | |||||||
\(278\) | 12.6341 | + | 3.22523i | 0.757745 | + | 0.193436i | ||||
\(279\) | −4.08188 | + | 17.0211i | −0.244376 | + | 1.01903i | ||||
\(280\) | 4.38991 | − | 4.71392i | 0.262347 | − | 0.281711i | ||||
\(281\) | − | 6.78411i | − | 0.404706i | −0.979313 | − | 0.202353i | \(-0.935141\pi\) | ||
0.979313 | − | 0.202353i | \(-0.0648588\pi\) | |||||||
\(282\) | −2.04723 | + | 5.31565i | −0.121911 | + | 0.316542i | ||||
\(283\) | 5.42784i | 0.322652i | 0.986901 | + | 0.161326i | \(0.0515770\pi\) | ||||
−0.986901 | + | 0.161326i | \(0.948423\pi\) | |||||||
\(284\) | 8.57881 | + | 4.68530i | 0.509058 | + | 0.278022i | ||||
\(285\) | 21.2624 | + | 2.51386i | 1.25948 | + | 0.148908i | ||||
\(286\) | −0.614387 | + | 2.40673i | −0.0363294 | + | 0.142313i | ||||
\(287\) | 2.56195 | 0.151227 | ||||||||
\(288\) | 16.9082 | − | 1.45302i | 0.996328 | − | 0.0856201i | ||||
\(289\) | −1.64803 | −0.0969429 | ||||||||
\(290\) | −2.96722 | + | 11.6235i | −0.174241 | + | 0.682553i | ||||
\(291\) | 3.44014 | + | 0.406728i | 0.201665 | + | 0.0238428i | ||||
\(292\) | −4.93840 | − | 2.69710i | −0.288998 | − | 0.157836i | ||||
\(293\) | 28.1874i | 1.64673i | 0.567515 | + | 0.823363i | \(0.307905\pi\) | ||||
−0.567515 | + | 0.823363i | \(0.692095\pi\) | |||||||
\(294\) | 0.880346 | − | 2.28582i | 0.0513428 | − | 0.133312i | ||||
\(295\) | − | 8.91160i | − | 0.518853i | ||||||
\(296\) | 15.1019 | − | 16.2166i | 0.877780 | − | 0.942568i | ||||
\(297\) | −21.0548 | − | 7.75848i | −1.22172 | − | 0.450193i | ||||
\(298\) | 23.8277 | + | 6.08271i | 1.38030 | + | 0.352362i | ||||
\(299\) | −0.472921 | −0.0273497 | ||||||||
\(300\) | −0.526844 | − | 0.374186i | −0.0304174 | − | 0.0216036i | ||||
\(301\) | 11.0211 | 0.635247 | ||||||||
\(302\) | −5.70776 | − | 1.45707i | −0.328445 | − | 0.0838450i | ||||
\(303\) | 1.76617 | − | 14.9384i | 0.101464 | − | 0.858189i | ||||
\(304\) | 18.2667 | − | 11.7350i | 1.04767 | − | 0.673051i | ||||
\(305\) | − | 23.7964i | − | 1.36258i | ||||||
\(306\) | 16.2056 | + | 8.54647i | 0.926414 | + | 0.488569i | ||||
\(307\) | 2.24130i | 0.127918i | 0.997953 | + | 0.0639589i | \(0.0203727\pi\) | ||||
−0.997953 | + | 0.0639589i | \(0.979627\pi\) | |||||||
\(308\) | −4.13974 | + | 7.57988i | −0.235884 | + | 0.431904i | ||||
\(309\) | −2.16543 | + | 18.3154i | −0.123187 | + | 1.04192i | ||||
\(310\) | 4.64803 | − | 18.2077i | 0.263990 | − | 1.03413i | ||||
\(311\) | −26.4791 | −1.50149 | −0.750746 | − | 0.660591i | \(-0.770306\pi\) | ||||
−0.750746 | + | 0.660591i | \(0.770306\pi\) | |||||||
\(312\) | −1.51976 | + | 1.28865i | −0.0860393 | + | 0.0729552i | ||||
\(313\) | 0.440371 | 0.0248912 | 0.0124456 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124456 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(314\) | −6.73801 | + | 26.3947i | −0.380248 | + | 1.48954i | ||||
\(315\) | −6.64382 | − | 1.59327i | −0.374337 | − | 0.0897707i | ||||
\(316\) | −3.83457 | + | 7.02112i | −0.215712 | + | 0.394969i | ||||
\(317\) | 11.7923i | 0.662320i | 0.943575 | + | 0.331160i | \(0.107440\pi\) | ||||
−0.943575 | + | 0.331160i | \(0.892560\pi\) | |||||||
\(318\) | 12.5288 | + | 4.82525i | 0.702579 | + | 0.270586i | ||||
\(319\) | − | 16.0845i | − | 0.900557i | ||||||
\(320\) | −18.1731 | + | 1.29524i | −1.01591 | + | 0.0724060i | ||||
\(321\) | 14.4490 | + | 1.70830i | 0.806462 | + | 0.0953482i | ||||
\(322\) | −1.59327 | − | 0.406728i | −0.0887896 | − | 0.0226661i | ||||
\(323\) | 23.4393 | 1.30419 | ||||||||
\(324\) | −10.1662 | − | 14.8542i | −0.564791 | − | 0.825234i | ||||
\(325\) | 0.0758724 | 0.00420864 | ||||||||
\(326\) | 11.8501 | + | 3.02509i | 0.656318 | + | 0.167544i | ||||
\(327\) | 18.0308 | + | 2.13179i | 0.997106 | + | 0.117888i | ||||
\(328\) | −5.30290 | − | 4.93840i | −0.292804 | − | 0.272678i | ||||
\(329\) | − | 2.32549i | − | 0.128208i | ||||||
\(330\) | 22.4801 | + | 8.65783i | 1.23749 | + | 0.476598i | ||||
\(331\) | 1.30974i | 0.0719899i | 0.999352 | + | 0.0359949i | \(0.0114600\pi\) | ||||
−0.999352 | + | 0.0359949i | \(0.988540\pi\) | |||||||
\(332\) | −1.12642 | − | 0.615195i | −0.0618205 | − | 0.0337632i | ||||
\(333\) | −22.8557 | − | 5.48108i | −1.25248 | − | 0.300361i | ||||
\(334\) | −0.614387 | + | 2.40673i | −0.0336177 | + | 0.131690i | ||||
\(335\) | 17.8424 | 0.974837 | ||||||||
\(336\) | −6.22835 | + | 3.03441i | −0.339784 | + | 0.165541i | ||||
\(337\) | −15.4615 | −0.842241 | −0.421120 | − | 0.907005i | \(-0.638363\pi\) | ||||
−0.421120 | + | 0.907005i | \(0.638363\pi\) | |||||||
\(338\) | −4.48954 | + | 17.5868i | −0.244199 | + | 0.956597i | ||||
\(339\) | −1.94476 | + | 16.4490i | −0.105625 | + | 0.893385i | ||||
\(340\) | −17.2624 | − | 9.42784i | −0.936186 | − | 0.511297i | ||||
\(341\) | 25.1956i | 1.36442i | ||||||||
\(342\) | −20.3693 | − | 10.7423i | −1.10145 | − | 0.580878i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −22.8123 | − | 21.2443i | −1.22996 | − | 1.14541i | ||||
\(345\) | −0.538514 | + | 4.55480i | −0.0289926 | + | 0.245222i | ||||
\(346\) | −10.7898 | − | 2.75441i | −0.580063 | − | 0.148078i | ||||
\(347\) | 27.6614 | 1.48494 | 0.742471 | − | 0.669878i | \(-0.233654\pi\) | ||||
0.742471 | + | 0.669878i | \(0.233654\pi\) | |||||||
\(348\) | 7.47133 | − | 10.5195i | 0.400506 | − | 0.563902i | ||||
\(349\) | −18.9316 | −1.01338 | −0.506692 | − | 0.862127i | \(-0.669132\pi\) | ||||
−0.506692 | + | 0.862127i | \(0.669132\pi\) | |||||||
\(350\) | 0.255614 | + | 0.0652529i | 0.0136632 | + | 0.00348792i | ||||
\(351\) | 1.98307 | + | 0.730743i | 0.105849 | + | 0.0390042i | ||||
\(352\) | 23.1797 | − | 7.70963i | 1.23548 | − | 0.410925i | ||||
\(353\) | 1.99285i | 0.106069i | 0.998593 | + | 0.0530344i | \(0.0168893\pi\) | ||||
−0.998593 | + | 0.0530344i | \(0.983111\pi\) | |||||||
\(354\) | −3.44485 | + | 8.94457i | −0.183092 | + | 0.475399i | ||||
\(355\) | 11.1306i | 0.590752i | ||||||||
\(356\) | 13.4182 | − | 24.5687i | 0.711161 | − | 1.30214i | ||||
\(357\) | −7.42784 | − | 0.878195i | −0.393123 | − | 0.0464790i | ||||
\(358\) | −3.26926 | + | 12.8066i | −0.172786 | + | 0.676851i | ||||
\(359\) | −2.35004 | −0.124030 | −0.0620151 | − | 0.998075i | \(-0.519753\pi\) | ||||
−0.0620151 | + | 0.998075i | \(0.519753\pi\) | |||||||
\(360\) | 10.6807 | + | 16.1045i | 0.562921 | + | 0.848781i | ||||
\(361\) | −10.4615 | −0.550605 | ||||||||
\(362\) | 5.90790 | − | 23.1429i | 0.310512 | − | 1.21637i | ||||
\(363\) | −13.1551 | − | 1.55534i | −0.690466 | − | 0.0816339i | ||||
\(364\) | 0.389907 | − | 0.713922i | 0.0204367 | − | 0.0374197i | ||||
\(365\) | − | 6.40736i | − | 0.335377i | ||||||
\(366\) | −9.19870 | + | 23.8845i | −0.480824 | + | 1.24846i | ||||
\(367\) | − | 34.1940i | − | 1.78491i | −0.451135 | − | 0.892455i | \(-0.648981\pi\) | ||
0.451135 | − | 0.892455i | \(-0.351019\pi\) | |||||||
\(368\) | 2.51386 | + | 3.91306i | 0.131044 | + | 0.203982i | ||||
\(369\) | −1.79234 | + | 7.47393i | −0.0933056 | + | 0.389077i | ||||
\(370\) | 24.4490 | + | 6.24130i | 1.27104 | + | 0.324470i | ||||
\(371\) | −5.48108 | −0.284563 | ||||||||
\(372\) | −11.7035 | + | 16.4783i | −0.606800 | + | 0.854359i | ||||
\(373\) | −17.6691 | −0.914874 | −0.457437 | − | 0.889242i | \(-0.651232\pi\) | ||||
−0.457437 | + | 0.889242i | \(0.651232\pi\) | |||||||
\(374\) | 25.5528 | + | 6.52310i | 1.32131 | + | 0.337301i | ||||
\(375\) | −2.22931 | + | 18.8557i | −0.115121 | + | 0.973703i | ||||
\(376\) | −4.48260 | + | 4.81346i | −0.231172 | + | 0.248235i | ||||
\(377\) | 1.51494i | 0.0780232i | ||||||||
\(378\) | 6.05251 | + | 4.16739i | 0.311308 | + | 0.214347i | ||||
\(379\) | 5.39420i | 0.277082i | 0.990357 | + | 0.138541i | \(0.0442412\pi\) | ||||
−0.990357 | + | 0.138541i | \(0.955759\pi\) | |||||||
\(380\) | 21.6976 | + | 11.8501i | 1.11307 | + | 0.607899i | ||||
\(381\) | −1.26242 | + | 10.6776i | −0.0646755 | + | 0.547031i | ||||
\(382\) | 7.10383 | − | 27.8277i | 0.363464 | − | 1.42379i | ||||
\(383\) | 1.85257 | 0.0946617 | 0.0473308 | − | 0.998879i | \(-0.484928\pi\) | ||||
0.0473308 | + | 0.998879i | \(0.484928\pi\) | |||||||
\(384\) | 18.7410 | + | 5.72492i | 0.956373 | + | 0.292149i | ||||
\(385\) | −9.83457 | −0.501216 | ||||||||
\(386\) | 2.39812 | − | 9.39414i | 0.122061 | − | 0.478149i | ||||
\(387\) | −7.71039 | + | 32.1517i | −0.391941 | + | 1.63437i | ||||
\(388\) | 3.51056 | + | 1.91729i | 0.178222 | + | 0.0973354i | ||||
\(389\) | − | 5.38490i | − | 0.273025i | −0.990638 | − | 0.136513i | \(-0.956411\pi\) | ||
0.990638 | − | 0.136513i | \(-0.0435895\pi\) | |||||||
\(390\) | −2.11732 | − | 0.815449i | −0.107215 | − | 0.0412919i | ||||
\(391\) | 5.02112i | 0.253929i | ||||||||
\(392\) | 1.92760 | − | 2.06987i | 0.0973584 | − | 0.104544i | ||||
\(393\) | 24.7730 | + | 2.92891i | 1.24963 | + | 0.147744i | ||||
\(394\) | 2.69710 | + | 0.688513i | 0.135878 | + | 0.0346868i | ||||
\(395\) | −9.10959 | −0.458353 | ||||||||
\(396\) | −19.2165 | − | 17.3797i | −0.965666 | − | 0.873363i | ||||
\(397\) | −21.6355 | −1.08585 | −0.542927 | − | 0.839780i | \(-0.682684\pi\) | ||||
−0.542927 | + | 0.839780i | \(0.682684\pi\) | |||||||
\(398\) | −8.73285 | − | 2.22931i | −0.437738 | − | 0.111745i | ||||
\(399\) | 9.33627 | + | 1.10383i | 0.467398 | + | 0.0552606i | ||||
\(400\) | −0.403308 | − | 0.627787i | −0.0201654 | − | 0.0313893i | ||||
\(401\) | − | 38.2714i | − | 1.91118i | −0.294697 | − | 0.955591i | \(-0.595219\pi\) | ||
0.294697 | − | 0.955591i | \(-0.404781\pi\) | |||||||
\(402\) | −17.9085 | − | 6.89713i | −0.893192 | − | 0.343998i | ||||
\(403\) | − | 2.37309i | − | 0.118212i | ||||||
\(404\) | 8.32558 | − | 15.2442i | 0.414213 | − | 0.758426i | ||||
\(405\) | 9.29606 | − | 18.2673i | 0.461925 | − | 0.907708i | ||||
\(406\) | −1.30290 | + | 5.10383i | −0.0646618 | + | 0.253299i | ||||
\(407\) | −33.8323 | −1.67701 | ||||||||
\(408\) | 13.6819 | + | 16.1356i | 0.677354 | + | 0.798833i | ||||
\(409\) | 4.77123 | 0.235922 | 0.117961 | − | 0.993018i | \(-0.462364\pi\) | ||||
0.117961 | + | 0.993018i | \(0.462364\pi\) | |||||||
\(410\) | 2.04094 | − | 7.99494i | 0.100795 | − | 0.394842i | ||||
\(411\) | −0.472921 | + | 4.00000i | −0.0233275 | + | 0.197305i | ||||
\(412\) | −10.2077 | + | 18.6903i | −0.502895 | + | 0.920803i | ||||
\(413\) | − | 3.91306i | − | 0.192549i | ||||||
\(414\) | 2.30120 | − | 4.36348i | 0.113098 | − | 0.214453i | ||||
\(415\) | − | 1.46149i | − | 0.0717415i | ||||||
\(416\) | −2.18321 | + | 0.726142i | −0.107041 | + | 0.0356020i | ||||
\(417\) | 1.87506 | − | 15.8594i | 0.0918219 | − | 0.776637i | ||||
\(418\) | −32.1181 | − | 8.19907i | −1.57095 | − | 0.401030i | ||||
\(419\) | −8.33257 | −0.407072 | −0.203536 | − | 0.979067i | \(-0.565243\pi\) | ||||
−0.203536 | + | 0.979067i | \(0.565243\pi\) | |||||||
\(420\) | −6.43194 | − | 4.56822i | −0.313847 | − | 0.222906i | ||||
\(421\) | −20.7325 | −1.01044 | −0.505220 | − | 0.862991i | \(-0.668589\pi\) | ||||
−0.505220 | + | 0.862991i | \(0.668589\pi\) | |||||||
\(422\) | −34.4357 | − | 8.79071i | −1.67631 | − | 0.427925i | ||||
\(423\) | 6.78411 | + | 1.62691i | 0.329855 | + | 0.0791033i | ||||
\(424\) | 11.3451 | + | 10.5653i | 0.550968 | + | 0.513097i | ||||
\(425\) | − | 0.805556i | − | 0.0390752i | ||||||
\(426\) | 4.30263 | − | 11.1718i | 0.208463 | − | 0.541276i | ||||
\(427\) | − | 10.4490i | − | 0.505661i | ||||||
\(428\) | 14.7447 | + | 8.05280i | 0.712713 | + | 0.389247i | ||||
\(429\) | 3.02112 | + | 0.357187i | 0.145861 | + | 0.0172451i | ||||
\(430\) | 8.77981 | − | 34.3930i | 0.423400 | − | 1.65858i | ||||
\(431\) | −34.9951 | −1.68565 | −0.842826 | − | 0.538186i | \(-0.819110\pi\) | ||||
−0.842826 | + | 0.538186i | \(0.819110\pi\) | |||||||
\(432\) | −4.49487 | − | 20.2928i | −0.216260 | − | 0.976336i | ||||
\(433\) | 17.3383 | 0.833225 | 0.416612 | − | 0.909084i | \(-0.363217\pi\) | ||||
0.416612 | + | 0.909084i | \(0.363217\pi\) | |||||||
\(434\) | 2.04094 | − | 7.99494i | 0.0979682 | − | 0.383769i | ||||
\(435\) | 14.5907 | + | 1.72506i | 0.699569 | + | 0.0827102i | ||||
\(436\) | 18.3999 | + | 10.0491i | 0.881195 | + | 0.481263i | ||||
\(437\) | − | 6.31119i | − | 0.301905i | ||||||
\(438\) | −2.47682 | + | 6.43107i | −0.118347 | + | 0.307288i | ||||
\(439\) | − | 33.2961i | − | 1.58913i | −0.607176 | − | 0.794567i | \(-0.707698\pi\) | ||
0.607176 | − | 0.794567i | \(-0.292302\pi\) | |||||||
\(440\) | 20.3563 | + | 18.9571i | 0.970449 | + | 0.903744i | ||||
\(441\) | −2.91729 | − | 0.699602i | −0.138918 | − | 0.0333144i | ||||
\(442\) | −2.40673 | − | 0.614387i | −0.114476 | − | 0.0292234i | ||||
\(443\) | −8.87313 | −0.421575 | −0.210788 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210788 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(444\) | −22.1268 | − | 15.7153i | −1.05009 | − | 0.745816i | ||||
\(445\) | 31.8768 | 1.51111 | ||||||||
\(446\) | 12.6459 | + | 3.22823i | 0.598801 | + | 0.152861i | ||||
\(447\) | 3.53632 | − | 29.9104i | 0.167262 | − | 1.41472i | ||||
\(448\) | −7.97976 | + | 0.568736i | −0.377008 | + | 0.0268702i | ||||
\(449\) | 26.3829i | 1.24509i | 0.782585 | + | 0.622544i | \(0.213901\pi\) | ||||
−0.782585 | + | 0.622544i | \(0.786099\pi\) | |||||||
\(450\) | −0.369190 | + | 0.700049i | −0.0174038 | + | 0.0330006i | ||||
\(451\) | 11.0633i | 0.520953i | ||||||||
\(452\) | −9.16746 | + | 16.7857i | −0.431201 | + | 0.789531i | ||||
\(453\) | −0.847099 | + | 7.16483i | −0.0398002 | + | 0.336633i | ||||
\(454\) | 6.83028 | − | 26.7562i | 0.320561 | − | 1.25573i | ||||
\(455\) | 0.926283 | 0.0434248 | ||||||||
\(456\) | −17.1971 | − | 20.2814i | −0.805330 | − | 0.949762i | ||||
\(457\) | 30.2499 | 1.41503 | 0.707515 | − | 0.706698i | \(-0.249816\pi\) | ||||
0.707515 | + | 0.706698i | \(0.249816\pi\) | |||||||
\(458\) | 0.711370 | − | 2.78664i | 0.0332401 | − | 0.130211i | ||||
\(459\) | 7.75848 | − | 21.0548i | 0.362135 | − | 0.982752i | ||||
\(460\) | −2.53851 | + | 4.64803i | −0.118359 | + | 0.216715i | ||||
\(461\) | 1.56302i | 0.0727973i | 0.999337 | + | 0.0363987i | \(0.0115886\pi\) | ||||
−0.999337 | + | 0.0363987i | \(0.988411\pi\) | |||||||
\(462\) | 9.87096 | + | 3.80163i | 0.459238 | + | 0.176868i | ||||
\(463\) | 33.2961i | 1.54740i | 0.633553 | + | 0.773700i | \(0.281596\pi\) | ||||
−0.633553 | + | 0.773700i | \(0.718404\pi\) | |||||||
\(464\) | 12.5350 | − | 8.05280i | 0.581921 | − | 0.373842i | ||||
\(465\) | −22.8557 | − | 2.70223i | −1.05991 | − | 0.125313i | ||||
\(466\) | −4.48260 | − | 1.14431i | −0.207652 | − | 0.0530093i | ||||
\(467\) | −17.2969 | −0.800404 | −0.400202 | − | 0.916427i | \(-0.631060\pi\) | ||||
−0.400202 | + | 0.916427i | \(0.631060\pi\) | |||||||
\(468\) | 1.80993 | + | 1.63693i | 0.0836642 | + | 0.0756672i | ||||
\(469\) | 7.83457 | 0.361767 | ||||||||
\(470\) | −7.25703 | − | 1.85257i | −0.334742 | − | 0.0854525i | ||||
\(471\) | 33.1327 | + | 3.91729i | 1.52667 | + | 0.180499i | ||||
\(472\) | −7.54281 | + | 8.09954i | −0.347186 | + | 0.372811i | ||||
\(473\) | 47.5929i | 2.18832i | ||||||||
\(474\) | 9.14330 | + | 3.52138i | 0.419965 | + | 0.161743i | ||||
\(475\) | 1.01253i | 0.0464579i | ||||||||
\(476\) | −7.57988 | − | 4.13974i | −0.347423 | − | 0.189745i | ||||
\(477\) | 3.83457 | − | 15.9899i | 0.175573 | − | 0.732126i | ||||
\(478\) | −8.57216 | + | 33.5796i | −0.392081 | + | 1.53589i | ||||
\(479\) | 16.6081 | 0.758842 | 0.379421 | − | 0.925224i | \(-0.376123\pi\) | ||||
0.379421 | + | 0.925224i | \(0.376123\pi\) | |||||||
\(480\) | 4.50760 | + | 21.8538i | 0.205743 | + | 0.997486i | ||||
\(481\) | 3.18654 | 0.145294 | ||||||||
\(482\) | 6.44169 | − | 25.2340i | 0.293411 | − | 1.14938i | ||||
\(483\) | −0.236460 | + | 2.00000i | −0.0107593 | + | 0.0910032i | ||||
\(484\) | −13.4244 | − | 7.33173i | −0.610201 | − | 0.333260i | ||||
\(485\) | 4.55480i | 0.206823i | ||||||||
\(486\) | −16.3918 | + | 14.7414i | −0.743547 | + | 0.668683i | ||||
\(487\) | 24.2499i | 1.09887i | 0.835537 | + | 0.549434i | \(0.185156\pi\) | ||||
−0.835537 | + | 0.549434i | \(0.814844\pi\) | |||||||
\(488\) | −20.1414 | + | 21.6280i | −0.911758 | + | 0.979054i | ||||
\(489\) | 1.75870 | − | 14.8752i | 0.0795311 | − | 0.672681i | ||||
\(490\) | 3.12065 | + | 0.796636i | 0.140977 | + | 0.0359883i | ||||
\(491\) | 20.3082 | 0.916497 | 0.458248 | − | 0.888824i | \(-0.348477\pi\) | ||||
0.458248 | + | 0.888824i | \(0.348477\pi\) | |||||||
\(492\) | −5.13899 | + | 7.23558i | −0.231684 | + | 0.326205i | ||||
\(493\) | 16.0845 | 0.724408 | ||||||||
\(494\) | 3.02509 | + | 0.772241i | 0.136105 | + | 0.0347447i | ||||
\(495\) | 6.88028 | − | 28.6903i | 0.309246 | − | 1.28953i | ||||
\(496\) | −19.6355 | + | 12.6144i | −0.881660 | + | 0.566403i | ||||
\(497\) | 4.88743i | 0.219231i | ||||||||
\(498\) | −0.564949 | + | 1.46689i | −0.0253160 | + | 0.0657330i | ||||
\(499\) | − | 10.5385i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(500\) | −10.5088 | + | 19.2416i | −0.469968 | + | 0.860512i | ||||
\(501\) | 3.02112 | + | 0.357187i | 0.134973 | + | 0.0159579i | ||||
\(502\) | −5.40243 | + | 21.1629i | −0.241122 | + | 0.944546i | ||||
\(503\) | 27.6664 | 1.23358 | 0.616792 | − | 0.787126i | \(-0.288432\pi\) | ||||
0.616792 | + | 0.787126i | \(0.288432\pi\) | |||||||
\(504\) | 4.68986 | + | 7.07144i | 0.208903 | + | 0.314987i | ||||
\(505\) | 19.7787 | 0.880139 | ||||||||
\(506\) | 1.75639 | − | 6.88028i | 0.0780811 | − | 0.305866i | ||||
\(507\) | 22.0764 | + | 2.61009i | 0.980446 | + | 0.115918i | ||||
\(508\) | −5.95093 | + | 10.8962i | −0.264030 | + | 0.483439i | ||||
\(509\) | − | 28.1874i | − | 1.24939i | −0.780871 | − | 0.624693i | \(-0.785224\pi\) | ||
0.780871 | − | 0.624693i | \(-0.214776\pi\) | |||||||
\(510\) | −8.65783 | + | 22.4801i | −0.383375 | + | 0.995436i | ||||
\(511\) | − | 2.81346i | − | 0.124460i | ||||||
\(512\) | 17.6134 | + | 14.2046i | 0.778408 | + | 0.627758i | ||||
\(513\) | −9.75186 | + | 26.4643i | −0.430555 | + | 1.16843i | ||||
\(514\) | −12.2904 | − | 3.13747i | −0.542105 | − | 0.138388i | ||||
\(515\) | −24.2498 | −1.06857 | ||||||||
\(516\) | −22.1072 | + | 31.1264i | −0.973215 | + | 1.37026i | ||||
\(517\) | 10.0422 | 0.441657 | ||||||||
\(518\) | 10.7355 | + | 2.74054i | 0.471690 | + | 0.120412i | ||||
\(519\) | −1.60133 | + | 13.5442i | −0.0702907 | + | 0.594524i | ||||
\(520\) | −1.91729 | − | 1.78550i | −0.0840786 | − | 0.0782994i | ||||
\(521\) | − | 24.0133i | − | 1.05204i | −0.850471 | − | 0.526022i | \(-0.823683\pi\) | ||
0.850471 | − | 0.526022i | \(-0.176317\pi\) | |||||||
\(522\) | −13.9778 | − | 7.37158i | −0.611793 | − | 0.322645i | ||||
\(523\) | − | 2.77981i | − | 0.121553i | −0.998151 | − | 0.0607764i | \(-0.980642\pi\) | ||
0.998151 | − | 0.0607764i | \(-0.0193577\pi\) | |||||||
\(524\) | 25.2801 | + | 13.8067i | 1.10436 | + | 0.603147i | ||||
\(525\) | 0.0379362 | − | 0.320867i | 0.00165567 | − | 0.0140038i | ||||
\(526\) | 6.77297 | − | 26.5317i | 0.295316 | − | 1.15684i | ||||
\(527\) | −25.1956 | −1.09754 | ||||||||
\(528\) | −13.1036 | − | 26.8961i | −0.570261 | − | 1.17050i | ||||
\(529\) | −21.6480 | −0.941219 | ||||||||
\(530\) | −4.36642 | + | 17.1045i | −0.189665 | + | 0.742973i | ||||
\(531\) | 11.4155 | + | 2.73758i | 0.495391 | + | 0.118801i | ||||
\(532\) | 9.52738 | + | 5.20336i | 0.413064 | + | 0.225594i | ||||
\(533\) | − | 1.04202i | − | 0.0451347i | ||||||
\(534\) | −31.9947 | − | 12.3222i | −1.38455 | − | 0.533235i | ||||
\(535\) | 19.1306i | 0.827089i | ||||||||
\(536\) | −16.2166 | − | 15.1019i | −0.700449 | − | 0.652303i | ||||
\(537\) | 16.0759 | + | 1.90065i | 0.693725 | + | 0.0820192i | ||||
\(538\) | 0.0658929 | + | 0.0168211i | 0.00284085 | + | 0.000725208i | ||||
\(539\) | −4.31834 | −0.186004 | ||||||||
\(540\) | 17.8266 | − | 15.5679i | 0.767135 | − | 0.669935i | ||||
\(541\) | 8.31717 | 0.357583 | 0.178792 | − | 0.983887i | \(-0.442781\pi\) | ||||
0.178792 | + | 0.983887i | \(0.442781\pi\) | |||||||
\(542\) | 27.2366 | + | 6.95292i | 1.16991 | + | 0.298654i | ||||
\(543\) | −29.0508 | − | 3.43469i | −1.24669 | − | 0.147396i | ||||
\(544\) | 7.70963 | + | 23.1797i | 0.330548 | + | 0.993822i | ||||
\(545\) | 23.8731i | 1.02261i | ||||||||
\(546\) | −0.929710 | − | 0.358062i | −0.0397879 | − | 0.0153236i | ||||
\(547\) | 15.4364i | 0.660014i | 0.943978 | + | 0.330007i | \(0.107051\pi\) | ||||
−0.943978 | + | 0.330007i | \(0.892949\pi\) | |||||||
\(548\) | −2.22931 | + | 4.08188i | −0.0952314 | + | 0.174369i | ||||
\(549\) | 30.4826 | + | 7.31011i | 1.30097 | + | 0.311988i | ||||
\(550\) | −0.281784 | + | 1.10383i | −0.0120153 | + | 0.0470674i | ||||
\(551\) | −20.2170 | −0.861274 | ||||||||
\(552\) | 4.34464 | − | 3.68394i | 0.184920 | − | 0.156799i | ||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 3.59418 | − | 14.0794i | 0.152702 | − | 0.598178i | ||||
\(555\) | 3.62851 | − | 30.6903i | 0.154022 | − | 1.30273i | ||||
\(556\) | 8.83887 | − | 16.1840i | 0.374851 | − | 0.686354i | ||||
\(557\) | 13.4525i | 0.570000i | 0.958528 | + | 0.285000i | \(0.0919936\pi\) | ||||
−0.958528 | + | 0.285000i | \(0.908006\pi\) | |||||||
\(558\) | 21.8957 | + | 11.5473i | 0.926918 | + | 0.488835i | ||||
\(559\) | − | 4.48260i | − | 0.189594i | ||||||
\(560\) | −4.92375 | − | 7.66429i | −0.208066 | − | 0.323875i | ||||
\(561\) | 3.79234 | − | 32.0759i | 0.160113 | − | 1.35425i | ||||
\(562\) | −9.29606 | − | 2.37309i | −0.392131 | − | 0.100103i | ||||
\(563\) | 34.0011 | 1.43298 | 0.716488 | − | 0.697599i | \(-0.245748\pi\) | ||||
0.716488 | + | 0.697599i | \(0.245748\pi\) | |||||||
\(564\) | 6.56775 | + | 4.66468i | 0.276552 | + | 0.196418i | ||||
\(565\) | −21.7787 | −0.916235 | ||||||||
\(566\) | 7.43761 | + | 1.89866i | 0.312626 | + | 0.0798068i | ||||
\(567\) | 4.08188 | − | 8.02112i | 0.171423 | − | 0.336855i | ||||
\(568\) | 9.42100 | − | 10.1164i | 0.395296 | − | 0.424473i | ||||
\(569\) | 26.5948i | 1.11491i | 0.830206 | + | 0.557457i | \(0.188223\pi\) | ||||
−0.830206 | + | 0.557457i | \(0.811777\pi\) | |||||||
\(570\) | 10.8823 | − | 28.2559i | 0.455808 | − | 1.18351i | ||||
\(571\) | − | 8.23271i | − | 0.344528i | −0.985051 | − | 0.172264i | \(-0.944892\pi\) | ||
0.985051 | − | 0.172264i | \(-0.0551083\pi\) | |||||||
\(572\) | 3.08295 | + | 1.68375i | 0.128905 | + | 0.0704012i | ||||
\(573\) | −34.9316 | − | 4.12996i | −1.45929 | − | 0.172532i | ||||
\(574\) | 0.896171 | − | 3.51056i | 0.0374054 | − | 0.146528i | ||||
\(575\) | −0.216902 | −0.00904543 | ||||||||
\(576\) | 3.92349 | − | 23.6771i | 0.163479 | − | 0.986547i | ||||
\(577\) | 1.58468 | 0.0659712 | 0.0329856 | − | 0.999456i | \(-0.489498\pi\) | ||||
0.0329856 | + | 0.999456i | \(0.489498\pi\) | |||||||
\(578\) | −0.576482 | + | 2.25824i | −0.0239785 | + | 0.0939306i | ||||
\(579\) | −11.7923 | − | 1.39420i | −0.490070 | − | 0.0579410i | ||||
\(580\) | 14.8893 | + | 8.13179i | 0.618246 | + | 0.337654i | ||||
\(581\) | − | 0.641735i | − | 0.0266236i | ||||||
\(582\) | 1.76069 | − | 4.57165i | 0.0729830 | − | 0.189501i | ||||
\(583\) | − | 23.6691i | − | 0.980276i | ||||||
\(584\) | −5.42321 | + | 5.82349i | −0.224414 | + | 0.240978i | ||||
\(585\) | −0.648029 | + | 2.70223i | −0.0267927 | + | 0.111724i | ||||
\(586\) | 38.6244 | + | 9.85998i | 1.59556 | + | 0.407312i | ||||
\(587\) | −30.8651 | −1.27394 | −0.636969 | − | 0.770889i | \(-0.719812\pi\) | ||||
−0.636969 | + | 0.770889i | \(0.719812\pi\) | |||||||
\(588\) | −2.82425 | − | 2.00589i | −0.116470 | − | 0.0827217i | ||||
\(589\) | 31.6691 | 1.30490 | ||||||||
\(590\) | −12.2113 | − | 3.11729i | −0.502731 | − | 0.128337i | ||||
\(591\) | 0.400282 | − | 3.38561i | 0.0164654 | − | 0.139266i | ||||
\(592\) | −16.9384 | − | 26.3662i | −0.696164 | − | 1.08365i | ||||
\(593\) | − | 6.45147i | − | 0.264930i | −0.991188 | − | 0.132465i | \(-0.957711\pi\) | ||
0.991188 | − | 0.132465i | \(-0.0422892\pi\) | |||||||
\(594\) | −17.9962 | + | 26.1368i | −0.738392 | + | 1.07240i | ||||
\(595\) | − | 9.83457i | − | 0.403178i | ||||||
\(596\) | 16.6699 | − | 30.5227i | 0.682826 | − | 1.25026i | ||||
\(597\) | −1.29606 | + | 10.9622i | −0.0530441 | + | 0.448651i | ||||
\(598\) | −0.165428 | + | 0.648029i | −0.00676485 | + | 0.0264999i | ||||
\(599\) | 12.8097 | 0.523391 | 0.261696 | − | 0.965150i | \(-0.415718\pi\) | ||||
0.261696 | + | 0.965150i | \(0.415718\pi\) | |||||||
\(600\) | −0.697026 | + | 0.591029i | −0.0284560 | + | 0.0241286i | ||||
\(601\) | −37.2710 | −1.52032 | −0.760158 | − | 0.649738i | \(-0.774878\pi\) | ||||
−0.760158 | + | 0.649738i | \(0.774878\pi\) | |||||||
\(602\) | 3.85520 | − | 15.1019i | 0.157126 | − | 0.615508i | ||||
\(603\) | −5.48108 | + | 22.8557i | −0.223207 | + | 0.930756i | ||||
\(604\) | −3.99316 | + | 7.31149i | −0.162479 | + | 0.297500i | ||||
\(605\) | − | 17.4176i | − | 0.708126i | ||||||
\(606\) | −19.8518 | − | 7.64559i | −0.806426 | − | 0.310581i | ||||
\(607\) | 20.8135i | 0.844792i | 0.906411 | + | 0.422396i | \(0.138811\pi\) | ||||
−0.906411 | + | 0.422396i | \(0.861189\pi\) | |||||||
\(608\) | −9.69046 | − | 29.1352i | −0.393000 | − | 1.18159i | ||||
\(609\) | 6.40673 | + | 0.757468i | 0.259614 | + | 0.0306942i | ||||
\(610\) | −32.6075 | − | 8.32401i | −1.32024 | − | 0.337029i | ||||
\(611\) | −0.945841 | −0.0382646 | ||||||||
\(612\) | 17.3797 | − | 19.2165i | 0.702533 | − | 0.776782i | ||||
\(613\) | 19.2288 | 0.776643 | 0.388321 | − | 0.921524i | \(-0.373055\pi\) | ||||
0.388321 | + | 0.921524i | \(0.373055\pi\) | |||||||
\(614\) | 3.07119 | + | 0.784009i | 0.123943 | + | 0.0316400i | ||||
\(615\) | −10.0359 | − | 1.18654i | −0.404686 | − | 0.0478460i | ||||
\(616\) | 8.93840 | + | 8.32401i | 0.360138 | + | 0.335384i | ||||
\(617\) | − | 29.3933i | − | 1.18333i | −0.806185 | − | 0.591664i | \(-0.798471\pi\) | ||
0.806185 | − | 0.591664i | \(-0.201529\pi\) | |||||||
\(618\) | 24.3395 | + | 9.37395i | 0.979079 | + | 0.377076i | ||||
\(619\) | 19.9241i | 0.800818i | 0.916336 | + | 0.400409i | \(0.131132\pi\) | ||||
−0.916336 | + | 0.400409i | \(0.868868\pi\) | |||||||
\(620\) | −23.3235 | − | 12.7381i | −0.936695 | − | 0.511575i | ||||
\(621\) | −5.66914 | − | 2.08903i | −0.227495 | − | 0.0838297i | ||||
\(622\) | −9.26242 | + | 36.2835i | −0.371389 | + | 1.45484i | ||||
\(623\) | 13.9970 | 0.560779 | ||||||||
\(624\) | 1.23418 | + | 2.53325i | 0.0494068 | + | 0.101411i | ||||
\(625\) | −25.8979 | −1.03592 | ||||||||
\(626\) | 0.154042 | − | 0.603426i | 0.00615676 | − | 0.0241178i | ||||
\(627\) | −4.76671 | + | 40.3172i | −0.190364 | + | 1.61011i | ||||
\(628\) | 33.8109 | + | 18.4658i | 1.34920 | + | 0.736865i | ||||
\(629\) | − | 33.8323i | − | 1.34898i | ||||||
\(630\) | −4.50723 | + | 8.54650i | −0.179572 | + | 0.340501i | ||||
\(631\) | 17.6269i | 0.701716i | 0.936429 | + | 0.350858i | \(0.114110\pi\) | ||||
−0.936429 | + | 0.350858i | \(0.885890\pi\) | |||||||
\(632\) | 8.27949 | + | 7.71039i | 0.329340 | + | 0.306703i | ||||
\(633\) | −5.11067 | + | 43.2265i | −0.203131 | + | 1.71810i | ||||
\(634\) | 16.1586 | + | 4.12494i | 0.641739 | + | 0.163822i | ||||
\(635\) | −14.1373 | −0.561022 | ||||||||
\(636\) | 10.9945 | − | 15.4799i | 0.435959 | − | 0.613819i | ||||
\(637\) | 0.406728 | 0.0161152 | ||||||||
\(638\) | −22.0401 | − | 5.62636i | −0.872574 | − | 0.222750i | ||||
\(639\) | −14.2580 | − | 3.41926i | −0.564039 | − | 0.135264i | ||||
\(640\) | −4.58214 | + | 25.3551i | −0.181125 | + | 1.00225i | ||||
\(641\) | 21.9439i | 0.866731i | 0.901218 | + | 0.433365i | \(0.142674\pi\) | ||||
−0.901218 | + | 0.433365i | \(0.857326\pi\) | |||||||
\(642\) | 7.39509 | − | 19.2014i | 0.291861 | − | 0.757819i | ||||
\(643\) | − | 49.5796i | − | 1.95523i | −0.210406 | − | 0.977614i | \(-0.567479\pi\) | ||
0.210406 | − | 0.977614i | \(-0.432521\pi\) | |||||||
\(644\) | −1.11466 | + | 2.04094i | −0.0439236 | + | 0.0804242i | ||||
\(645\) | −43.1729 | − | 5.10433i | −1.69993 | − | 0.200983i | ||||
\(646\) | 8.19907 | − | 32.1181i | 0.322588 | − | 1.26367i | ||||
\(647\) | −23.9122 | −0.940085 | −0.470042 | − | 0.882644i | \(-0.655761\pi\) | ||||
−0.470042 | + | 0.882644i | \(0.655761\pi\) | |||||||
\(648\) | −23.9104 | + | 8.73446i | −0.939291 | + | 0.343122i | ||||
\(649\) | 16.8979 | 0.663301 | ||||||||
\(650\) | 0.0265402 | − | 0.103966i | 0.00104099 | − | 0.00407787i | ||||
\(651\) | −10.0359 | − | 1.18654i | −0.393337 | − | 0.0465043i | ||||
\(652\) | 8.29037 | − | 15.1797i | 0.324676 | − | 0.594483i | ||||
\(653\) | − | 46.6666i | − | 1.82621i | −0.407730 | − | 0.913103i | \(-0.633680\pi\) | ||
0.407730 | − | 0.913103i | \(-0.366320\pi\) | |||||||
\(654\) | 9.22832 | − | 23.9614i | 0.360856 | − | 0.936964i | ||||
\(655\) | 32.7998i | 1.28159i | ||||||||
\(656\) | −8.62190 | + | 5.53895i | −0.336629 | + | 0.216260i | ||||
\(657\) | 8.20766 | + | 1.96830i | 0.320211 | + | 0.0767907i | ||||
\(658\) | −3.18654 | − | 0.813457i | −0.124224 | − | 0.0317118i | ||||
\(659\) | 30.4598 | 1.18655 | 0.593273 | − | 0.805001i | \(-0.297835\pi\) | ||||
0.593273 | + | 0.805001i | \(0.297835\pi\) | |||||||
\(660\) | 19.7271 | − | 27.7753i | 0.767877 | − | 1.08115i | ||||
\(661\) | −49.3046 | −1.91773 | −0.958864 | − | 0.283865i | \(-0.908383\pi\) | ||||
−0.958864 | + | 0.283865i | \(0.908383\pi\) | |||||||
\(662\) | 1.79470 | + | 0.458148i | 0.0697529 | + | 0.0178064i | ||||
\(663\) | −0.357187 | + | 3.02112i | −0.0138720 | + | 0.117330i | ||||
\(664\) | −1.23701 | + | 1.32831i | −0.0480052 | + | 0.0515484i | ||||
\(665\) | 12.3614i | 0.479353i | ||||||||
\(666\) | −15.5055 | + | 29.4012i | −0.600826 | + | 1.13927i | ||||
\(667\) | − | 4.33086i | − | 0.167691i | ||||||
\(668\) | 3.08295 | + | 1.68375i | 0.119283 | + | 0.0651463i | ||||
\(669\) | 1.87680 | − | 15.8741i | 0.0725614 | − | 0.613730i | ||||
\(670\) | 6.24130 | − | 24.4490i | 0.241122 | − | 0.944546i | ||||
\(671\) | 45.1221 | 1.74192 | ||||||||
\(672\) | 1.97928 | + | 9.59596i | 0.0763523 | + | 0.370172i | ||||
\(673\) | −19.4364 | −0.749219 | −0.374610 | − | 0.927183i | \(-0.622223\pi\) | ||||
−0.374610 | + | 0.927183i | \(0.622223\pi\) | |||||||
\(674\) | −5.40844 | + | 21.1864i | −0.208325 | + | 0.816070i | ||||
\(675\) | 0.909522 | + | 0.335150i | 0.0350075 | + | 0.0128999i | ||||
\(676\) | 22.5283 | + | 12.3038i | 0.866471 | + | 0.473222i | ||||
\(677\) | − | 9.96823i | − | 0.383110i | −0.981482 | − | 0.191555i | \(-0.938647\pi\) | ||
0.981482 | − | 0.191555i | \(-0.0613531\pi\) | |||||||
\(678\) | 21.8592 | + | 8.41871i | 0.839499 | + | 0.323319i | ||||
\(679\) | 2.00000i | 0.0767530i | ||||||||
\(680\) | −18.9571 | + | 20.3563i | −0.726971 | + | 0.780628i | ||||
\(681\) | −33.5864 | − | 3.97093i | −1.28703 | − | 0.152166i | ||||
\(682\) | 34.5248 | + | 8.81346i | 1.32202 | + | 0.337485i | ||||
\(683\) | 29.6102 | 1.13300 | 0.566501 | − | 0.824061i | \(-0.308297\pi\) | ||||
0.566501 | + | 0.824061i | \(0.308297\pi\) | |||||||
\(684\) | −21.8451 | + | 24.1538i | −0.835267 | + | 0.923544i | ||||
\(685\) | −5.29606 | −0.202352 | ||||||||
\(686\) | 1.37027 | + | 0.349801i | 0.0523171 | + | 0.0133555i | ||||
\(687\) | −3.49801 | − | 0.413570i | −0.133457 | − | 0.0157787i | ||||
\(688\) | −37.0901 | + | 23.8277i | −1.41405 | + | 0.908424i | ||||
\(689\) | 2.22931i | 0.0849300i | ||||||||
\(690\) | 6.05293 | + | 2.33118i | 0.230431 | + | 0.0887466i | ||||
\(691\) | − | 44.1603i | − | 1.67994i | −0.542634 | − | 0.839969i | \(-0.682573\pi\) | ||
0.542634 | − | 0.839969i | \(-0.317427\pi\) | |||||||
\(692\) | −7.54856 | + | 13.8214i | −0.286953 | + | 0.525412i | ||||
\(693\) | 3.02112 | − | 12.5978i | 0.114763 | − | 0.478552i | ||||
\(694\) | 9.67599 | − | 37.9036i | 0.367295 | − | 1.43880i | ||||
\(695\) | 20.9980 | 0.796501 | ||||||||
\(696\) | −11.8010 | − | 13.9175i | −0.447316 | − | 0.527540i | ||||
\(697\) | −11.0633 | −0.419054 | ||||||||
\(698\) | −6.62227 | + | 25.9413i | −0.250657 | + | 0.981894i | ||||
\(699\) | −0.665271 | + | 5.62691i | −0.0251629 | + | 0.212829i | ||||
\(700\) | 0.178828 | − | 0.327435i | 0.00675907 | − | 0.0123759i | ||||
\(701\) | 38.2714i | 1.44549i | 0.691115 | + | 0.722745i | \(0.257120\pi\) | ||||
−0.691115 | + | 0.722745i | \(0.742880\pi\) | |||||||
\(702\) | 1.69499 | − | 2.46173i | 0.0639735 | − | 0.0929119i | ||||
\(703\) | 42.5248i | 1.60385i | ||||||||
\(704\) | −2.45599 | − | 34.4593i | −0.0925637 | − | 1.29873i | ||||
\(705\) | −1.07703 | + | 9.10959i | −0.0405632 | + | 0.343087i | ||||
\(706\) | 2.73074 | + | 0.697101i | 0.102773 | + | 0.0262357i | ||||
\(707\) | 8.68476 | 0.326624 | ||||||||
\(708\) | 11.0515 | + | 7.84919i | 0.415339 | + | 0.294991i | ||||
\(709\) | 6.89792 | 0.259057 | 0.129528 | − | 0.991576i | \(-0.458654\pi\) | ||||
0.129528 | + | 0.991576i | \(0.458654\pi\) | |||||||
\(710\) | 15.2520 | + | 3.89350i | 0.572396 | + | 0.146121i | ||||
\(711\) | 2.79841 | − | 11.6691i | 0.104948 | − | 0.437627i | ||||
\(712\) | −28.9720 | − | 26.9806i | −1.08577 | − | 1.01114i | ||||
\(713\) | 6.78411i | 0.254067i | ||||||||
\(714\) | −3.80163 | + | 9.87096i | −0.142272 | + | 0.369411i | ||||
\(715\) | 4.00000i | 0.149592i | ||||||||
\(716\) | 16.4049 | + | 8.95953i | 0.613081 | + | 0.334833i | ||||
\(717\) | 42.1517 | + | 4.98361i | 1.57419 | + | 0.186116i | ||||
\(718\) | −0.822045 | + | 3.22019i | −0.0306784 | + | 0.120176i | ||||
\(719\) | 28.2355 | 1.05301 | 0.526503 | − | 0.850173i | \(-0.323503\pi\) | ||||
0.526503 | + | 0.850173i | \(0.323503\pi\) | |||||||
\(720\) | 25.8036 | − | 9.00204i | 0.961643 | − | 0.335486i | ||||
\(721\) | −10.6480 | −0.396553 | ||||||||
\(722\) | −3.65944 | + | 14.3351i | −0.136190 | + | 0.533496i | ||||
\(723\) | −31.6756 | − | 3.74502i | −1.17803 | − | 0.139279i | ||||
\(724\) | −29.6455 | − | 16.1908i | −1.10177 | − | 0.601728i | ||||
\(725\) | 0.694815i | 0.0258048i | ||||||||
\(726\) | −6.73291 | + | 17.4820i | −0.249882 | + | 0.648820i | ||||
\(727\) | − | 27.3942i | − | 1.01599i | −0.861359 | − | 0.507997i | \(-0.830386\pi\) | ||
0.861359 | − | 0.507997i | \(-0.169614\pi\) | |||||||
\(728\) | −0.841876 | − | 0.784009i | −0.0312020 | − | 0.0290573i | ||||
\(729\) | 20.5442 | + | 17.5196i | 0.760896 | + | 0.648874i | ||||
\(730\) | −8.77981 | − | 2.24130i | −0.324956 | − | 0.0829543i | ||||
\(731\) | −47.5929 | −1.76029 | ||||||||
\(732\) | 29.5105 | + | 20.9595i | 1.09074 | + | 0.774686i | ||||
\(733\) | −29.7028 | −1.09710 | −0.548549 | − | 0.836119i | \(-0.684819\pi\) | ||||
−0.548549 | + | 0.836119i | \(0.684819\pi\) | |||||||
\(734\) | −46.8550 | − | 11.9611i | −1.72945 | − | 0.441492i | ||||
\(735\) | 0.463141 | − | 3.91729i | 0.0170832 | − | 0.144491i | ||||
\(736\) | 6.24130 | − | 2.07587i | 0.230057 | − | 0.0765177i | ||||
\(737\) | 33.8323i | 1.24623i | ||||||||
\(738\) | 9.61434 | + | 5.07038i | 0.353909 | + | 0.186643i | ||||
\(739\) | − | 27.4364i | − | 1.00927i | −0.863334 | − | 0.504633i | \(-0.831628\pi\) | ||
0.863334 | − | 0.504633i | \(-0.168372\pi\) | |||||||
\(740\) | 17.1045 | − | 31.3185i | 0.628775 | − | 1.15129i | ||||
\(741\) | 0.448959 | − | 3.79733i | 0.0164929 | − | 0.139498i | ||||
\(742\) | −1.91729 | + | 7.51056i | −0.0703858 | + | 0.275721i | ||||
\(743\) | −2.30093 | −0.0844131 | −0.0422065 | − | 0.999109i | \(-0.513439\pi\) | ||||
−0.0422065 | + | 0.999109i | \(0.513439\pi\) | |||||||
\(744\) | 18.4858 | + | 21.8011i | 0.677722 | + | 0.799268i | ||||
\(745\) | 39.6019 | 1.45090 | ||||||||
\(746\) | −6.18068 | + | 24.2115i | −0.226291 | + | 0.886446i | ||||
\(747\) | 1.87212 | + | 0.448959i | 0.0684974 | + | 0.0164265i | ||||
\(748\) | 17.8768 | − | 32.7325i | 0.653641 | − | 1.19682i | ||||
\(749\) | 8.40021i | 0.306937i | ||||||||
\(750\) | 25.0576 | + | 9.65049i | 0.914973 | + | 0.352386i | ||||
\(751\) | 19.4193i | 0.708619i | 0.935128 | + | 0.354309i | \(0.115284\pi\) | ||||
−0.935128 | + | 0.354309i | \(0.884716\pi\) | |||||||
\(752\) | 5.02772 | + | 7.82612i | 0.183342 | + | 0.285389i | ||||
\(753\) | 26.5653 | + | 3.14082i | 0.968094 | + | 0.114458i | ||||
\(754\) | 2.07587 | + | 0.529926i | 0.0755988 | + | 0.0192988i | ||||
\(755\) | −9.48634 | −0.345243 | ||||||||
\(756\) | 7.82762 | − | 6.83582i | 0.284688 | − | 0.248616i | ||||
\(757\) | 13.9327 | 0.506393 | 0.253197 | − | 0.967415i | \(-0.418518\pi\) | ||||
0.253197 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(758\) | 7.39151 | + | 1.88690i | 0.268472 | + | 0.0685352i | ||||
\(759\) | −8.63667 | − | 1.02112i | −0.313491 | − | 0.0370641i | ||||
\(760\) | 23.8277 | − | 25.5864i | 0.864323 | − | 0.928117i | ||||
\(761\) | 12.3859i | 0.448989i | 0.974475 | + | 0.224495i | \(0.0720731\pi\) | ||||
−0.974475 | + | 0.224495i | \(0.927927\pi\) | |||||||
\(762\) | 14.1896 | + | 5.46489i | 0.514035 | + | 0.197972i | ||||
\(763\) | 10.4826i | 0.379496i | ||||||||
\(764\) | −35.6466 | − | 19.4683i | −1.28965 | − | 0.704339i | ||||
\(765\) | 28.6903 | + | 6.88028i | 1.03730 | + | 0.248757i | ||||
\(766\) | 0.648029 | − | 2.53851i | 0.0234142 | − | 0.0917203i | ||||
\(767\) | −1.59155 | −0.0574677 | ||||||||
\(768\) | 14.4003 | − | 23.6777i | 0.519626 | − | 0.854394i | ||||
\(769\) | 45.0074 | 1.62301 | 0.811505 | − | 0.584346i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584346i | \(0.198649\pi\) | |||||||
\(770\) | −3.44014 | + | 13.4760i | −0.123974 | + | 0.485642i | ||||
\(771\) | −1.82404 | + | 15.4278i | −0.0656911 | + | 0.555620i | ||||
\(772\) | −12.0336 | − | 6.57216i | −0.433100 | − | 0.236537i | ||||
\(773\) | − | 51.4814i | − | 1.85166i | −0.377944 | − | 0.925828i | \(-0.623369\pi\) | ||
0.377944 | − | 0.925828i | \(-0.376631\pi\) | |||||||
\(774\) | 41.3595 | + | 21.8120i | 1.48664 | + | 0.784017i | ||||
\(775\) | − | 1.08840i | − | 0.0390965i | ||||||
\(776\) | 3.85520 | − | 4.13974i | 0.138393 | − | 0.148608i | ||||
\(777\) | 1.59327 | − | 13.4760i | 0.0571583 | − | 0.483449i | ||||
\(778\) | −7.37877 | − | 1.88364i | −0.264542 | − | 0.0675319i | ||||
\(779\) | 13.9058 | 0.498229 | ||||||||
\(780\) | −1.85803 | + | 2.61605i | −0.0665280 | + | 0.0936697i | ||||
\(781\) | −21.1056 | −0.755217 | ||||||||
\(782\) | 6.88028 | + | 1.75639i | 0.246038 | + | 0.0628084i | ||||
\(783\) | −6.69191 | + | 18.1603i | −0.239149 | + | 0.648997i | ||||
\(784\) | −2.16201 | − | 3.36537i | −0.0772145 | − | 0.120192i | ||||
\(785\) | 43.8682i | 1.56572i | ||||||||
\(786\) | 12.6790 | − | 32.9211i | 0.452245 | − | 1.17426i | ||||
\(787\) | − | 41.2202i | − | 1.46934i | −0.678424 | − | 0.734670i | \(-0.737337\pi\) | ||
0.678424 | − | 0.734670i | \(-0.262663\pi\) | |||||||
\(788\) | 1.88690 | − | 3.45491i | 0.0672179 | − | 0.123076i | ||||
\(789\) | −33.3046 | − | 3.93761i | −1.18568 | − | 0.140183i | ||||
\(790\) | −3.18654 | + | 12.4826i | −0.113372 | + | 0.444111i | ||||
\(791\) | −9.56296 | −0.340020 | ||||||||
\(792\) | −30.5369 | + | 20.2524i | −1.08508 | + | 0.719637i | ||||
\(793\) | −4.24989 | −0.150918 | ||||||||
\(794\) | −7.56812 | + | 29.6465i | −0.268582 | + | 1.05211i | ||||
\(795\) | 21.4710 | + | 2.53851i | 0.761496 | + | 0.0900318i | ||||
\(796\) | −6.10951 | + | 11.1865i | −0.216546 | + | 0.396497i | ||||
\(797\) | 37.0164i | 1.31119i | 0.755113 | + | 0.655595i | \(0.227582\pi\) | ||||
−0.755113 | + | 0.655595i | \(0.772418\pi\) | |||||||
\(798\) | 4.77838 | − | 12.4071i | 0.169153 | − | 0.439206i | ||||
\(799\) | 10.0422i | 0.355269i | ||||||||
\(800\) | −1.00131 | + | 0.333040i | −0.0354018 | + | 0.0117747i | ||||
\(801\) | −9.79234 | + | 40.8333i | −0.345995 | + | 1.44277i | ||||
\(802\) | −52.4421 | − | 13.3874i | −1.85180 | − | 0.472724i | ||||
\(803\) | 12.1495 | 0.428745 | ||||||||
\(804\) | −15.7153 | + | 22.1268i | −0.554237 | + | 0.780352i | ||||
\(805\) | −2.64803 | −0.0933308 | ||||||||
\(806\) | −3.25177 | − | 0.830108i | −0.114539 | − | 0.0292393i | ||||
\(807\) | 0.00977929 | − | 0.0827140i | 0.000344247 | − | 0.00291167i | ||||
\(808\) | −17.9763 | − | 16.7407i | −0.632405 | − | 0.588937i | ||||
\(809\) | − | 52.3125i | − | 1.83921i | −0.392844 | − | 0.919605i | \(-0.628509\pi\) | ||
0.392844 | − | 0.919605i | \(-0.371491\pi\) | |||||||
\(810\) | −21.7793 | − | 19.1280i | −0.765248 | − | 0.672090i | ||||
\(811\) | 25.3719i | 0.890929i | 0.895300 | + | 0.445464i | \(0.146961\pi\) | ||||
−0.895300 | + | 0.445464i | \(0.853039\pi\) | |||||||
\(812\) | 6.53787 | + | 3.57065i | 0.229434 | + | 0.125305i | ||||
\(813\) | 4.04223 | − | 34.1895i | 0.141767 | − | 1.19908i | ||||
\(814\) | −11.8346 | + | 46.3594i | −0.414802 | + | 1.62490i | ||||
\(815\) | 19.6950 | 0.689886 | ||||||||
\(816\) | 26.8961 | − | 13.1036i | 0.941552 | − | 0.458718i | ||||
\(817\) | 59.8209 | 2.09287 | ||||||||
\(818\) | 1.66898 | − | 6.53787i | 0.0583545 | − | 0.228591i | ||||
\(819\) | −0.284548 | + | 1.18654i | −0.00994291 | + | 0.0414612i | ||||
\(820\) | −10.2413 | − | 5.59327i | −0.357642 | − | 0.195326i | ||||
\(821\) | − | 29.0656i | − | 1.01440i | −0.861829 | − | 0.507198i | \(-0.830681\pi\) | ||
0.861829 | − | 0.507198i | \(-0.169319\pi\) | |||||||
\(822\) | 5.31565 | + | 2.04723i | 0.185405 | + | 0.0714054i | ||||
\(823\) | − | 28.6343i | − | 0.998131i | −0.866564 | − | 0.499065i | \(-0.833677\pi\) | ||
0.866564 | − | 0.499065i | \(-0.166323\pi\) | |||||||
\(824\) | 22.0401 | + | 20.5251i | 0.767802 | + | 0.715026i | ||||
\(825\) | 1.38561 | + | 0.163821i | 0.0482409 | + | 0.00570352i | ||||
\(826\) | −5.36195 | − | 1.36879i | −0.186566 | − | 0.0476264i | ||||
\(827\) | 4.88743 | 0.169953 | 0.0849763 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849763 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(828\) | −5.17419 | − | 4.67961i | −0.179815 | − | 0.162628i | ||||
\(829\) | −38.9316 | −1.35215 | −0.676074 | − | 0.736833i | \(-0.736320\pi\) | ||||
−0.676074 | + | 0.736833i | \(0.736320\pi\) | |||||||
\(830\) | −2.00263 | − | 0.511229i | −0.0695123 | − | 0.0177450i | ||||
\(831\) | −17.6736 | − | 2.08956i | −0.613091 | − | 0.0724859i | ||||
\(832\) | 0.231321 | + | 3.24559i | 0.00801961 | + | 0.112521i | ||||
\(833\) | − | 4.31834i | − | 0.149621i | ||||||
\(834\) | −21.0757 | − | 8.11695i | −0.729793 | − | 0.281067i | ||||
\(835\) | 4.00000i | 0.138426i | ||||||||
\(836\) | −22.4699 | + | 41.1424i | −0.777137 | + | 1.42294i | ||||
\(837\) | 10.4826 | − | 28.4474i | 0.362332 | − | 0.983286i | ||||
\(838\) | −2.91474 | + | 11.4179i | −0.100688 | + | 0.394424i | ||||
\(839\) | −49.3493 | −1.70373 | −0.851863 | − | 0.523765i | \(-0.824527\pi\) | ||||
−0.851863 | + | 0.523765i | \(0.824527\pi\) | |||||||
\(840\) | −8.50959 | + | 7.21553i | −0.293609 | + | 0.248959i | ||||
\(841\) | 15.1267 | 0.521610 | ||||||||
\(842\) | −7.25224 | + | 28.4091i | −0.249929 | + | 0.979042i | ||||
\(843\) | −1.37964 | + | 11.6691i | −0.0475175 | + | 0.401907i | ||||
\(844\) | −24.0913 | + | 44.1113i | −0.829257 | + | 1.51837i | ||||
\(845\) | 29.2294i | 1.00552i | ||||||||
\(846\) | 4.60240 | − | 8.72696i | 0.158234 | − | 0.300039i | ||||
\(847\) | − | 7.64803i | − | 0.262789i | ||||||
\(848\) | 18.4459 | − | 11.8501i | 0.633434 | − | 0.406935i | ||||
\(849\) | 1.10383 | − | 9.33627i | 0.0378833 | − | 0.320420i | ||||
\(850\) | −1.10383 | − | 0.281784i | −0.0378610 | − | 0.00966512i | ||||
\(851\) | −9.10959 | −0.312273 | ||||||||
\(852\) | −13.8033 | − | 9.80367i | −0.472894 | − | 0.335868i | ||||
\(853\) | 36.4912 | 1.24943 | 0.624717 | − | 0.780851i | \(-0.285214\pi\) | ||||
0.624717 | + | 0.780851i | \(0.285214\pi\) | |||||||
\(854\) | −14.3179 | − | 3.65505i | −0.489948 | − | 0.125073i | ||||
\(855\) | −36.0616 | − | 8.64803i | −1.23328 | − | 0.295756i | ||||
\(856\) | 16.1922 | − | 17.3874i | 0.553439 | − | 0.594288i | ||||
\(857\) | − | 36.4434i | − | 1.24488i | −0.782667 | − | 0.622441i | \(-0.786141\pi\) | ||
0.782667 | − | 0.622441i | \(-0.213859\pi\) | |||||||
\(858\) | 1.54623 | − | 4.01480i | 0.0527875 | − | 0.137063i | ||||
\(859\) | − | 11.8682i | − | 0.404938i | −0.979289 | − | 0.202469i | \(-0.935103\pi\) | ||
0.979289 | − | 0.202469i | \(-0.0648966\pi\) | |||||||
\(860\) | −44.0566 | − | 24.0614i | −1.50232 | − | 0.820488i | ||||
\(861\) | −4.40673 | − | 0.521008i | −0.150181 | − | 0.0177559i | ||||
\(862\) | −12.2413 | + | 47.9527i | −0.416940 | + | 1.63327i | ||||
\(863\) | 16.3225 | 0.555625 | 0.277812 | − | 0.960635i | \(-0.410391\pi\) | ||||
0.277812 | + | 0.960635i | \(0.410391\pi\) | |||||||
\(864\) | −29.3789 | − | 0.939234i | −0.999489 | − | 0.0319534i | ||||
\(865\) | −17.9327 | −0.609731 | ||||||||
\(866\) | 6.06495 | − | 23.7581i | 0.206095 | − | 0.807334i | ||||
\(867\) | 2.83473 | + | 0.335150i | 0.0962723 | + | 0.0113823i | ||||
\(868\) | −10.2413 | − | 5.59327i | −0.347612 | − | 0.189848i | ||||
\(869\) | − | 17.2733i | − | 0.585958i | ||||||
\(870\) | 7.46762 | − | 19.3897i | 0.253176 | − | 0.657373i | ||||
\(871\) | − | 3.18654i | − | 0.107972i | ||||||
\(872\) | 20.2062 | − | 21.6976i | 0.684269 | − | 0.734775i | ||||
\(873\) | −5.83457 | − | 1.39920i | −0.197470 | − | 0.0473559i | ||||
\(874\) | −8.64803 | − | 2.20766i | −0.292524 | − | 0.0746752i | ||||
\(875\) | −10.9622 | −0.370589 | ||||||||
\(876\) | 7.94591 | + | 5.64350i | 0.268467 | + | 0.190676i | ||||
\(877\) | 6.81346 | 0.230074 | 0.115037 | − | 0.993361i | \(-0.463301\pi\) | ||||
0.115037 | + | 0.993361i | \(0.463301\pi\) | |||||||
\(878\) | −45.6246 | − | 11.6470i | −1.53976 | − | 0.393067i | ||||
\(879\) | 5.73231 | − | 48.4843i | 0.193346 | − | 1.63534i | ||||
\(880\) | 33.0970 | − | 21.2624i | 1.11570 | − | 0.716756i | ||||
\(881\) | − | 10.1075i | − | 0.340530i | −0.985398 | − | 0.170265i | \(-0.945538\pi\) | ||
0.985398 | − | 0.170265i | \(-0.0544624\pi\) | |||||||
\(882\) | −1.97911 | + | 3.75275i | −0.0666402 | + | 0.126362i | ||||
\(883\) | − | 29.4615i | − | 0.991458i | −0.868477 | − | 0.495729i | \(-0.834901\pi\) | ||
0.868477 | − | 0.495729i | \(-0.165099\pi\) | |||||||
\(884\) | −1.68375 | + | 3.08295i | −0.0566307 | + | 0.103691i | ||||
\(885\) | −1.81230 | + | 15.3286i | −0.0609198 | + | 0.515265i | ||||
\(886\) | −3.10383 | + | 12.1586i | −0.104275 | + | 0.408476i | ||||
\(887\) | 44.4668 | 1.49305 | 0.746525 | − | 0.665357i | \(-0.231721\pi\) | ||||
0.746525 | + | 0.665357i | \(0.231721\pi\) | |||||||
\(888\) | −29.2742 | + | 24.8224i | −0.982378 | + | 0.832986i | ||||
\(889\) | −6.20766 | −0.208198 | ||||||||
\(890\) | 11.1505 | − | 43.6798i | 0.373767 | − | 1.46415i | ||||
\(891\) | 34.6379 | + | 17.6269i | 1.16041 | + | 0.590524i | ||||
\(892\) | 8.84710 | − | 16.1991i | 0.296223 | − | 0.542385i | ||||
\(893\) | − | 12.6224i | − | 0.422392i | ||||||
\(894\) | −39.7484 | − | 15.3084i | −1.32938 | − | 0.511990i | ||||
\(895\) | 21.2847i | 0.711469i | ||||||||
\(896\) | −2.01200 | + | 11.1334i | −0.0672164 | + | 0.371940i | ||||
\(897\) | 0.813457 | + | 0.0961751i | 0.0271605 | + | 0.00321119i | ||||
\(898\) | 36.1517 | + | 9.22877i | 1.20640 | + | 0.307968i | ||||
\(899\) | 21.7320 | 0.724802 | ||||||||
\(900\) | 0.830114 | + | 0.750767i | 0.0276705 | + | 0.0250256i | ||||
\(901\) | 23.6691 | 0.788534 | ||||||||
\(902\) | 15.1598 | + | 3.86997i | 0.504765 | + | 0.128856i | ||||
\(903\) | −18.9571 | − | 2.24130i | −0.630853 | − | 0.0745858i | ||||
\(904\) | 19.7941 | + | 18.4335i | 0.658342 | + | 0.613090i | ||||
\(905\) | − | 38.4637i | − | 1.27858i | ||||||
\(906\) | 9.52144 | + | 3.66702i | 0.316328 | + | 0.121829i | ||||
\(907\) | 55.9190i | 1.85676i | 0.371631 | + | 0.928380i | \(0.378799\pi\) | ||||
−0.371631 | + | 0.928380i | \(0.621201\pi\) | |||||||
\(908\) | −34.2739 | − | 18.7186i | −1.13742 | − | 0.621200i | ||||
\(909\) | −6.07587 | + | 25.3359i | −0.201524 | + | 0.840340i | ||||
\(910\) | 0.324014 | − | 1.26926i | 0.0107410 | − | 0.0420755i | ||||
\(911\) | −7.71538 | −0.255622 | −0.127811 | − | 0.991799i | \(-0.540795\pi\) | ||||
−0.127811 | + | 0.991799i | \(0.540795\pi\) | |||||||
\(912\) | −33.8065 | + | 16.4703i | −1.11945 | + | 0.545386i | ||||
\(913\) | 2.77123 | 0.0917142 | ||||||||
\(914\) | 10.5814 | − | 41.4505i | 0.350003 | − | 1.37106i | ||||
\(915\) | −4.83934 | + | 40.9316i | −0.159984 | + | 1.35316i | ||||
\(916\) | −3.56961 | − | 1.94954i | −0.117943 | − | 0.0644145i | ||||
\(917\) | 14.4023i | 0.475606i | ||||||||
\(918\) | −26.1368 | − | 17.9962i | −0.862642 | − | 0.593962i | ||||
\(919\) | 10.0422i | 0.331263i | 0.986188 | + | 0.165631i | \(0.0529662\pi\) | ||||
−0.986188 | + | 0.165631i | \(0.947034\pi\) | |||||||
\(920\) | 5.48108 | + | 5.10433i | 0.180706 | + | 0.168285i | ||||
\(921\) | 0.455800 | − | 3.85520i | 0.0150191 | − | 0.127033i | ||||
\(922\) | 2.14177 | + | 0.546747i | 0.0705353 | + | 0.0180062i | ||||
\(923\) | 1.98786 | 0.0654311 | ||||||||
\(924\) | 8.66213 | − | 12.1961i | 0.284963 | − | 0.401221i | ||||
\(925\) | 1.46149 | 0.0480534 | ||||||||
\(926\) | 45.6246 | + | 11.6470i | 1.49932 | + | 0.382744i | ||||
\(927\) | 7.44938 | − | 31.0633i | 0.244670 | − | 1.02025i | ||||
\(928\) | −6.64978 | − | 19.9932i | −0.218290 | − | 0.656308i | ||||
\(929\) | 3.13104i | 0.102726i | 0.998680 | + | 0.0513631i | \(0.0163566\pi\) | ||||
−0.998680 | + | 0.0513631i | \(0.983643\pi\) | |||||||
\(930\) | −11.6977 | + | 30.3732i | −0.383583 | + | 0.995977i | ||||
\(931\) | 5.42784i | 0.177890i | ||||||||
\(932\) | −3.13603 | + | 5.74209i | −0.102724 | + | 0.188088i | ||||
\(933\) | 45.5459 | + | 5.38490i | 1.49111 | + | 0.176294i | ||||
\(934\) | −6.05046 | + | 23.7014i | −0.197977 | + | 0.775533i | ||||
\(935\) | 42.4690 | 1.38888 | ||||||||
\(936\) | 2.87616 | − | 1.90750i | 0.0940101 | − | 0.0623485i | ||||
\(937\) | −47.0325 | −1.53648 | −0.768242 | − | 0.640159i | \(-0.778868\pi\) | ||||
−0.768242 | + | 0.640159i | \(0.778868\pi\) | |||||||
\(938\) | 2.74054 | − | 10.7355i | 0.0894818 | − | 0.350526i | ||||
\(939\) | −0.757468 | − | 0.0895556i | −0.0247190 | − | 0.00292254i | ||||
\(940\) | −5.07703 | + | 9.29606i | −0.165594 | + | 0.303204i | ||||
\(941\) | 22.2530i | 0.725426i | 0.931901 | + | 0.362713i | \(0.118150\pi\) | ||||
−0.931901 | + | 0.362713i | \(0.881850\pi\) | |||||||
\(942\) | 16.9576 | − | 44.0305i | 0.552508 | − | 1.43459i | ||||
\(943\) | 2.97888i | 0.0970058i | ||||||||
\(944\) | 8.46007 | + | 13.1689i | 0.275352 | + | 0.428611i | ||||
\(945\) | 11.1038 | + | 4.09166i | 0.361208 | + | 0.133102i | ||||
\(946\) | 65.2151 | + | 16.6480i | 2.12033 | + | 0.541274i | ||||
\(947\) | −33.9335 | −1.10269 | −0.551345 | − | 0.834277i | \(-0.685885\pi\) | ||||
−0.551345 | + | 0.834277i | \(0.685885\pi\) | |||||||
\(948\) | 8.02358 | − | 11.2970i | 0.260594 | − | 0.366909i | ||||
\(949\) | −1.14431 | −0.0371460 | ||||||||
\(950\) | 1.38744 | + | 0.354183i | 0.0450143 | + | 0.0114912i | ||||
\(951\) | 2.39812 | − | 20.2835i | 0.0777645 | − | 0.657739i | ||||
\(952\) | −8.32401 | + | 8.93840i | −0.269783 | + | 0.289695i | ||||
\(953\) | 20.2641i | 0.656419i | 0.944605 | + | 0.328209i | \(0.106445\pi\) | ||||
−0.944605 | + | 0.328209i | \(0.893555\pi\) | |||||||
\(954\) | −20.5691 | − | 10.8477i | −0.665949 | − | 0.351206i | ||||
\(955\) | − | 46.2499i | − | 1.49661i | ||||||
\(956\) | 43.0145 | + | 23.4923i | 1.39119 | + | 0.759796i | ||||
\(957\) | −3.27100 | + | 27.6664i | −0.105737 | + | 0.894328i | ||||
\(958\) | 5.80952 | − | 22.7575i | 0.187697 | − | 0.735263i | ||||
\(959\) | −2.32549 | −0.0750939 | ||||||||
\(960\) | 31.5224 | + | 1.46786i | 1.01738 | + | 0.0473748i | ||||
\(961\) | −3.04223 | −0.0981365 | ||||||||
\(962\) | 1.11466 | − | 4.36642i | 0.0359379 | − | 0.140779i | ||||
\(963\) | −24.5058 | − | 5.87680i | −0.789689 | − | 0.189377i | ||||
\(964\) | −32.3240 | − | 17.6537i | −1.04109 | − | 0.568588i | ||||
\(965\) | − | 15.6131i | − | 0.502604i | ||||||
\(966\) | 2.65783 | + | 1.02362i | 0.0855141 | + | 0.0329343i | ||||
\(967\) | − | 43.5882i | − | 1.40170i | −0.713308 | − | 0.700851i | \(-0.752804\pi\) | ||
0.713308 | − | 0.700851i | \(-0.247196\pi\) | |||||||
\(968\) | −14.7423 | + | 15.8304i | −0.473836 | + | 0.508810i | ||||
\(969\) | −40.3172 | − | 4.76671i | −1.29517 | − | 0.153129i | ||||
\(970\) | 6.24130 | + | 1.59327i | 0.200396 | + | 0.0511569i | ||||
\(971\) | 3.67161 | 0.117828 | 0.0589138 | − | 0.998263i | \(-0.481236\pi\) | ||||
0.0589138 | + | 0.998263i | \(0.481236\pi\) | |||||||
\(972\) | 14.4658 | + | 27.6177i | 0.463991 | + | 0.885840i | ||||
\(973\) | 9.22019 | 0.295586 | ||||||||
\(974\) | 33.2289 | + | 8.48263i | 1.06472 | + | 0.271801i | ||||
\(975\) | −0.130506 | − | 0.0154297i | −0.00417953 | − | 0.000494147i | ||||
\(976\) | 22.5907 | + | 35.1646i | 0.723111 | + | 1.12559i | ||||
\(977\) | 34.0738i | 1.09012i | 0.838398 | + | 0.545058i | \(0.183492\pi\) | ||||
−0.838398 | + | 0.545058i | \(0.816508\pi\) | |||||||
\(978\) | −19.7679 | − | 7.61326i | −0.632107 | − | 0.243445i | ||||
\(979\) | 60.4439i | 1.93179i | ||||||||
\(980\) | 2.18321 | − | 3.99747i | 0.0697401 | − | 0.127694i | ||||
\(981\) | −30.5807 | − | 7.33364i | −0.976368 | − | 0.234145i | ||||
\(982\) | 7.10383 | − | 27.8277i | 0.226692 | − | 0.888019i | ||||
\(983\) | −54.2808 | −1.73129 | −0.865645 | − | 0.500659i | \(-0.833091\pi\) | ||||
−0.865645 | + | 0.500659i | \(0.833091\pi\) | |||||||
\(984\) | 8.11707 | + | 9.57282i | 0.258763 | + | 0.305170i | ||||
\(985\) | 4.48260 | 0.142828 | ||||||||
\(986\) | 5.62636 | − | 22.0401i | 0.179180 | − | 0.701898i | ||||
\(987\) | −0.472921 | + | 4.00000i | −0.0150532 | + | 0.127321i | ||||
\(988\) | 2.11636 | − | 3.87506i | 0.0673303 | − | 0.123282i | ||||
\(989\) | 12.8147i | 0.407485i | ||||||||
\(990\) | −36.9067 | − | 19.4637i | −1.17297 | − | 0.618598i | ||||
\(991\) | 10.5077i | 0.333787i | 0.985975 | + | 0.166893i | \(0.0533736\pi\) | ||||
−0.985975 | + | 0.166893i | \(0.946626\pi\) | |||||||
\(992\) | 10.4166 | + | 31.3185i | 0.330727 | + | 0.994362i | ||||
\(993\) | 0.266354 | − | 2.25285i | 0.00845250 | − | 0.0714919i | ||||
\(994\) | 6.69710 | + | 1.70963i | 0.212419 | + | 0.0542261i | ||||
\(995\) | −14.5141 | −0.460127 | ||||||||
\(996\) | 1.81242 | + | 1.28725i | 0.0574287 | + | 0.0407881i | ||||
\(997\) | 21.4564 | 0.679531 | 0.339765 | − | 0.940510i | \(-0.389652\pi\) | ||||
0.339765 | + | 0.940510i | \(0.389652\pi\) | |||||||
\(998\) | −14.4406 | − | 3.68638i | −0.457109 | − | 0.116690i | ||||
\(999\) | 38.1987 | + | 14.0759i | 1.20855 | + | 0.445341i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 84.2.e.a.71.7 | yes | 12 | |
3.2 | odd | 2 | inner | 84.2.e.a.71.6 | yes | 12 | |
4.3 | odd | 2 | inner | 84.2.e.a.71.5 | ✓ | 12 | |
7.2 | even | 3 | 588.2.n.f.263.2 | 24 | |||
7.3 | odd | 6 | 588.2.n.g.275.9 | 24 | |||
7.4 | even | 3 | 588.2.n.f.275.9 | 24 | |||
7.5 | odd | 6 | 588.2.n.g.263.2 | 24 | |||
7.6 | odd | 2 | 588.2.e.c.491.7 | 12 | |||
8.3 | odd | 2 | 1344.2.h.h.575.1 | 12 | |||
8.5 | even | 2 | 1344.2.h.h.575.12 | 12 | |||
12.11 | even | 2 | inner | 84.2.e.a.71.8 | yes | 12 | |
21.2 | odd | 6 | 588.2.n.f.263.11 | 24 | |||
21.5 | even | 6 | 588.2.n.g.263.11 | 24 | |||
21.11 | odd | 6 | 588.2.n.f.275.4 | 24 | |||
21.17 | even | 6 | 588.2.n.g.275.4 | 24 | |||
21.20 | even | 2 | 588.2.e.c.491.6 | 12 | |||
24.5 | odd | 2 | 1344.2.h.h.575.2 | 12 | |||
24.11 | even | 2 | 1344.2.h.h.575.11 | 12 | |||
28.3 | even | 6 | 588.2.n.g.275.11 | 24 | |||
28.11 | odd | 6 | 588.2.n.f.275.11 | 24 | |||
28.19 | even | 6 | 588.2.n.g.263.4 | 24 | |||
28.23 | odd | 6 | 588.2.n.f.263.4 | 24 | |||
28.27 | even | 2 | 588.2.e.c.491.5 | 12 | |||
84.11 | even | 6 | 588.2.n.f.275.2 | 24 | |||
84.23 | even | 6 | 588.2.n.f.263.9 | 24 | |||
84.47 | odd | 6 | 588.2.n.g.263.9 | 24 | |||
84.59 | odd | 6 | 588.2.n.g.275.2 | 24 | |||
84.83 | odd | 2 | 588.2.e.c.491.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.e.a.71.5 | ✓ | 12 | 4.3 | odd | 2 | inner | |
84.2.e.a.71.6 | yes | 12 | 3.2 | odd | 2 | inner | |
84.2.e.a.71.7 | yes | 12 | 1.1 | even | 1 | trivial | |
84.2.e.a.71.8 | yes | 12 | 12.11 | even | 2 | inner | |
588.2.e.c.491.5 | 12 | 28.27 | even | 2 | |||
588.2.e.c.491.6 | 12 | 21.20 | even | 2 | |||
588.2.e.c.491.7 | 12 | 7.6 | odd | 2 | |||
588.2.e.c.491.8 | 12 | 84.83 | odd | 2 | |||
588.2.n.f.263.2 | 24 | 7.2 | even | 3 | |||
588.2.n.f.263.4 | 24 | 28.23 | odd | 6 | |||
588.2.n.f.263.9 | 24 | 84.23 | even | 6 | |||
588.2.n.f.263.11 | 24 | 21.2 | odd | 6 | |||
588.2.n.f.275.2 | 24 | 84.11 | even | 6 | |||
588.2.n.f.275.4 | 24 | 21.11 | odd | 6 | |||
588.2.n.f.275.9 | 24 | 7.4 | even | 3 | |||
588.2.n.f.275.11 | 24 | 28.11 | odd | 6 | |||
588.2.n.g.263.2 | 24 | 7.5 | odd | 6 | |||
588.2.n.g.263.4 | 24 | 28.19 | even | 6 | |||
588.2.n.g.263.9 | 24 | 84.47 | odd | 6 | |||
588.2.n.g.263.11 | 24 | 21.5 | even | 6 | |||
588.2.n.g.275.2 | 24 | 84.59 | odd | 6 | |||
588.2.n.g.275.4 | 24 | 21.17 | even | 6 | |||
588.2.n.g.275.9 | 24 | 7.3 | odd | 6 | |||
588.2.n.g.275.11 | 24 | 28.3 | even | 6 | |||
1344.2.h.h.575.1 | 12 | 8.3 | odd | 2 | |||
1344.2.h.h.575.2 | 12 | 24.5 | odd | 2 | |||
1344.2.h.h.575.11 | 12 | 24.11 | even | 2 | |||
1344.2.h.h.575.12 | 12 | 8.5 | even | 2 |